LMFDB - Embedded newform 7.17.d.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,17,Mod(3,7)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 17, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7.3");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	7.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.3627180700$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 470221 x^{18} - 17792382 x^{17} + 149610140535 x^{16} - 5885709493452 x^{15} + \cdots + 26\!\cdots\!25 $ x^20 - 2x^19 + 470221x^18 - 17792382x^17 + 149610140535x^16 - 5885709493452x^15 + 25413927970368382x^14 - 921982218074544860x^13 + 3092605513604061172669x^12 - 78217760507911051825254x^11 + 217775891572550635786539387x^10 - 772894989756975230685011586x^9 + 10848813785145958185022965942709x^8 + 50328102663961537370536178622316x^7 + 292280160701254761307491650568975646x^6 + 6884264619587692201297746565224842172x^5 + 5465648386210730671112398026225318665199x^4 + 69498817213798305204024309903431721187110x^3 + 44558299163904360256389313185385225104835245x^2 - 34923314543744821707168835219945993579648950*x + 261490399505792227817024003348104130194641159225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{38}\cdot 3^{16}\cdot 7^{22} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.5
Root			$-58.5903 - 101.481i$ of defining polynomial
Character	$\chi$	$=$	7.5
Dual form			7.17.d.a.3.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-54.0903 + 93.6871i) q^{2} +(8486.99 - 4899.97i) q^{3} +(26916.5 + 46620.7i) q^{4} +(214019. + 123564. i) q^{5} +1.06016e6i q^{6} +(516705. - 5.74160e6i) q^{7} -1.29134e7 q^{8} +(2.64960e7 - 4.58924e7i) q^{9} +O(q^{10})$	\(q+(-54.0903 + 93.6871i) q^{2} +(8486.99 - 4899.97i) q^{3} +(26916.5 + 46620.7i) q^{4} +(214019. + 123564. i) q^{5} +1.06016e6i q^{6} +(516705. - 5.74160e6i) q^{7} -1.29134e7 q^{8} +(2.64960e7 - 4.58924e7i) q^{9} +(-2.31527e7 + 1.33672e7i) q^{10} +(2.02067e8 + 3.49990e8i) q^{11} +(4.56880e8 + 2.63780e8i) q^{12} -7.03308e8i q^{13} +(5.09965e8 + 3.58973e8i) q^{14} +2.42184e9 q^{15} +(-1.06551e9 + 1.84551e9i) q^{16} +(5.78012e9 - 3.33715e9i) q^{17} +(2.86635e9 + 4.96466e9i) q^{18} +(1.30680e10 + 7.54481e9i) q^{19} +1.33036e10i q^{20} +(-2.37484e10 - 5.12607e10i) q^{21} -4.37195e10 q^{22} +(-1.85797e9 + 3.21809e9i) q^{23} +(-1.09596e11 + 6.32752e10i) q^{24} +(-4.57577e10 - 7.92547e10i) q^{25} +(6.58909e10 + 3.80421e10i) q^{26} -9.74625e10i q^{27} +(2.81585e11 - 1.30454e11i) q^{28} -6.34367e11 q^{29} +(-1.30998e11 + 2.26895e11i) q^{30} +(7.23984e10 - 4.17992e10i) q^{31} +(-5.38414e11 - 9.32560e11i) q^{32} +(3.42988e12 + 1.98024e12i) q^{33} +7.22030e11i q^{34} +(8.20041e11 - 1.16497e12i) q^{35} +2.85271e12 q^{36} +(-2.10893e12 + 3.65278e12i) q^{37} +(-1.41370e12 + 8.16202e11i) q^{38} +(-3.44619e12 - 5.96897e12i) q^{39} +(-2.76372e12 - 1.59563e12i) q^{40} -8.05237e12i q^{41} +(6.08703e12 + 5.47791e11i) q^{42} -1.17455e13 q^{43} +(-1.08779e13 + 1.88410e13i) q^{44} +(1.13413e13 - 6.54791e12i) q^{45} +(-2.00996e11 - 3.48135e11i) q^{46} +(-4.21915e12 - 2.43593e12i) q^{47} +2.08838e13i q^{48} +(-3.26990e13 - 5.93343e12i) q^{49} +9.90020e12 q^{50} +(3.27039e13 - 5.66448e13i) q^{51} +(3.27887e13 - 1.89306e13i) q^{52} +(1.17107e11 + 2.02836e11i) q^{53} +(9.13098e12 + 5.27178e12i) q^{54} +9.98730e13i q^{55} +(-6.67242e12 + 7.41436e13i) q^{56} +1.47877e14 q^{57} +(3.43131e13 - 5.94321e13i) q^{58} +(-7.78589e12 + 4.49519e12i) q^{59} +(6.51874e13 + 1.12908e14i) q^{60} +(-2.29740e14 - 1.32640e14i) q^{61} +9.04373e12i q^{62} +(-2.49805e14 - 1.75842e14i) q^{63} -2.31665e13 q^{64} +(8.69037e13 - 1.50522e14i) q^{65} +(-3.71047e14 + 2.14224e14i) q^{66} +(-1.76219e14 - 3.05220e14i) q^{67} +(3.11161e14 + 1.79649e14i) q^{68} +3.64159e13i q^{69} +(6.47862e13 + 1.39841e14i) q^{70} +2.43651e13 q^{71} +(-3.42153e14 + 5.92627e14i) q^{72} +(8.48653e14 - 4.89970e14i) q^{73} +(-2.28146e14 - 3.95160e14i) q^{74} +(-7.76691e14 - 4.48423e14i) q^{75} +8.12319e14i q^{76} +(2.11391e15 - 9.79346e14i) q^{77} +7.45621e14 q^{78} +(-1.08198e15 + 1.87405e15i) q^{79} +(-4.56079e14 + 2.63317e14i) q^{80} +(6.63002e14 + 1.14835e15i) q^{81} +(7.54404e14 + 4.35555e14i) q^{82} -3.59077e14i q^{83} +(1.75059e15 - 2.48692e15i) q^{84} +1.64941e15 q^{85} +(6.35319e14 - 1.10040e15i) q^{86} +(-5.38387e15 + 3.10838e15i) q^{87} +(-2.60937e15 - 4.51957e15i) q^{88} +(-1.33707e15 - 7.71957e14i) q^{89} +1.41671e15i q^{90} +(-4.03811e15 - 3.63403e14i) q^{91} -2.00040e14 q^{92} +(4.09630e14 - 7.09499e14i) q^{93} +(4.56430e14 - 2.63520e14i) q^{94} +(1.86454e15 + 3.22947e15i) q^{95} +(-9.13903e15 - 5.27642e15i) q^{96} +1.09832e16i q^{97} +(2.32458e15 - 2.74253e15i) q^{98} +2.14159e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 92 q^{2} + 6558 q^{3} - 285924 q^{4} + 241890 q^{5} - 1847944 q^{7} + 23873872 q^{8} + 146092512 q^{9}+O(q^{10}) $ 20 * q + 92 * q^2 + 6558 * q^3 - 285924 * q^4 + 241890 * q^5 - 1847944 * q^7 + 23873872 * q^8 + 146092512 * q^9	\( 20 q + 92 q^{2} + 6558 q^{3} - 285924 q^{4} + 241890 q^{5} - 1847944 q^{7} + 23873872 q^{8} + 146092512 q^{9} - 567579804 q^{10} + 487037030 q^{11} - 2240722092 q^{12} + 598121216 q^{14} - 2098975212 q^{15} - 13522996616 q^{16} + 16479299850 q^{17} - 21631627512 q^{18} - 29753076894 q^{19} + 30310552398 q^{21} + 143879888720 q^{22} - 199076938822 q^{23} + 613456300512 q^{24} + 212723266388 q^{25} - 1359419612544 q^{26} + 2531834927748 q^{28} + 438309600272 q^{29} - 2296351012392 q^{30} + 1037434908306 q^{31} - 3523947158064 q^{32} + 411779151054 q^{33} - 7248579242478 q^{35} - 2493315404256 q^{36} + 5318067734218 q^{37} - 9079217417208 q^{38} + 13250117821332 q^{39} + 15010293809208 q^{40} + 16256122433712 q^{42} - 621187489400 q^{43} + 25172272315980 q^{44} - 85040191344096 q^{45} - 15614039192704 q^{46} + 106960600327866 q^{47} - 52978127838580 q^{49} + 35872835226128 q^{50} + 4235281588962 q^{51} + 126484190926632 q^{52} + 29048763888218 q^{53} - 635343594055560 q^{54} + 230352840277168 q^{56} + 366396034764636 q^{57} - 279762037805080 q^{58} - 99092116656282 q^{59} - 173605217618196 q^{60} - 904353032308434 q^{61} + 11\!\cdots\!92 q^{63}+ \cdots + 14\!\cdots\!92 q^{99}+O(q^{100}) \) 20 * q + 92 * q^2 + 6558 * q^3 - 285924 * q^4 + 241890 * q^5 - 1847944 * q^7 + 23873872 * q^8 + 146092512 * q^9 - 567579804 * q^10 + 487037030 * q^11 - 2240722092 * q^12 + 598121216 * q^14 - 2098975212 * q^15 - 13522996616 * q^16 + 16479299850 * q^17 - 21631627512 * q^18 - 29753076894 * q^19 + 30310552398 * q^21 + 143879888720 * q^22 - 199076938822 * q^23 + 613456300512 * q^24 + 212723266388 * q^25 - 1359419612544 * q^26 + 2531834927748 * q^28 + 438309600272 * q^29 - 2296351012392 * q^30 + 1037434908306 * q^31 - 3523947158064 * q^32 + 411779151054 * q^33 - 7248579242478 * q^35 - 2493315404256 * q^36 + 5318067734218 * q^37 - 9079217417208 * q^38 + 13250117821332 * q^39 + 15010293809208 * q^40 + 16256122433712 * q^42 - 621187489400 * q^43 + 25172272315980 * q^44 - 85040191344096 * q^45 - 15614039192704 * q^46 + 106960600327866 * q^47 - 52978127838580 * q^49 + 35872835226128 * q^50 + 4235281588962 * q^51 + 126484190926632 * q^52 + 29048763888218 * q^53 - 635343594055560 * q^54 + 230352840277168 * q^56 + 366396034764636 * q^57 - 279762037805080 * q^58 - 99092116656282 * q^59 - 173605217618196 * q^60 - 904353032308434 * q^61 + 1188663557133192 * q^63 + 2502182430870944 * q^64 - 500211967540404 * q^65 - 951679982792988 * q^66 - 33326890567694 * q^67 - 964537664673492 * q^68 - 569178593140080 * q^70 + 3111156268483352 * q^71 + 936737429904432 * q^72 - 1146801010325370 * q^73 - 2161044304782140 * q^74 - 4935640048894356 * q^75 + 1321278185203718 * q^77 + 13747974994685232 * q^78 + 126874036566250 * q^79 - 18764997660746184 * q^80 - 2081051947014102 * q^81 - 11916006908925168 * q^82 + 17065299612720828 * q^84 + 27928718307758508 * q^85 - 7493915124549152 * q^86 - 4167264363403248 * q^87 - 10398917942882000 * q^88 - 34000447101257730 * q^89 + 6895892767523928 * q^91 + 113018032389709752 * q^92 - 15597881218045122 * q^93 - 7183919979926376 * q^94 - 19569222088313322 * q^95 - 137281944028491360 * q^96 + 65453414234371436 * q^98 + 142672614742345392 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−54.0903	+	93.6871i	−0.211290	+	0.365965i	−0.952119	−	0.305729i	$-0.901100\pi$
$2$	−54.0903	+	93.6871i	−0.211290	+	0.365965i	0.740828	+	0.671694i	$0.234433\pi$
$3$	8486.99	−	4899.97i	1.29355	−	0.746832i	0.314269	−	0.949334i	$-0.398240\pi$
$3$	8486.99	−	4899.97i	1.29355	−	0.746832i	0.979282	+	0.202502i	$0.0649072\pi$
$4$	26916.5	+	46620.7i	0.410713	+	0.711376i
$5$	214019.	+	123564.i	0.547890	+	0.316324i	0.748270	−	0.663394i	$-0.230885\pi$
$5$	214019.	+	123564.i	0.547890	+	0.316324i	−0.200381	+	0.979718i	$0.564218\pi$
$6$			1.06016e6i			0.631193i
$7$	516705.	−	5.74160e6i	0.0896310	−	0.995975i
$7$	516705.	−	5.74160e6i	0.0896310	−	0.995975i
$8$	−1.29134e7			−0.769699
$9$	2.64960e7	−	4.58924e7i	0.615517	−	1.06611i
$10$	−2.31527e7	+	1.33672e7i	−0.231527	+	0.133672i
$11$	2.02067e8	+	3.49990e8i	0.942658	+	1.63273i	0.760375	+	0.649485i	$0.225015\pi$
$11$	2.02067e8	+	3.49990e8i	0.942658	+	1.63273i	0.182283	+	0.983246i	$0.441651\pi$
$12$	4.56880e8	+	2.63780e8i	1.06256	+	0.613467i
$13$		−	7.03308e8i		−	0.862182i	−0.902309	−	0.431091i	$-0.858129\pi$
$13$		−	7.03308e8i		−	0.862182i	0.902309	−	0.431091i	$-0.141871\pi$
$14$	5.09965e8	+	3.58973e8i	0.345554	+	0.243242i
$15$	2.42184e9			0.944965
$16$	−1.06551e9	+	1.84551e9i	−0.248083	+	0.429692i
$17$	5.78012e9	−	3.33715e9i	0.828601	−	0.478393i	−0.0247726	−	0.999693i	$-0.507886\pi$
$17$	5.78012e9	−	3.33715e9i	0.828601	−	0.478393i	0.853373	+	0.521300i	$0.174553\pi$
$18$	2.86635e9	+	4.96466e9i	0.260105	+	0.450516i
$19$	1.30680e10	+	7.54481e9i	0.769449	+	0.444242i	0.832678	−	0.553757i	$-0.186806\pi$
$19$	1.30680e10	+	7.54481e9i	0.769449	+	0.444242i	−0.0632287	+	0.997999i	$0.520140\pi$
$20$			1.33036e10i			0.519674i
$21$	−2.37484e10	−	5.12607e10i	−0.627884	−	1.35528i
$22$	−4.37195e10			−0.796697
$23$	−1.85797e9	+	3.21809e9i	−0.0237255	+	0.0410938i	−0.877644	−	0.479312i	$-0.840886\pi$
$23$	−1.85797e9	+	3.21809e9i	−0.0237255	+	0.0410938i	0.853919	+	0.520406i	$0.174219\pi$
$24$	−1.09596e11	+	6.32752e10i	−0.995645	+	0.574836i
$25$	−4.57577e10	−	7.92547e10i	−0.299878	−	0.519404i
$26$	6.58909e10	+	3.80421e10i	0.315529	+	0.182171i
$27$		−	9.74625e10i		−	0.345086i
$28$	2.81585e11	−	1.30454e11i	0.745325	−	0.345298i
$29$	−6.34367e11			−1.26811			−0.634055	−	0.773288i	$-0.718611\pi$
$29$	−6.34367e11			−1.26811			−0.634055	+	0.773288i	$0.718611\pi$
$30$	−1.30998e11	+	2.26895e11i	−0.199662	+	0.345824i
$31$	7.23984e10	−	4.17992e10i	0.0848858	−	0.0490089i	−0.456956	−	0.889489i	$-0.651060\pi$
$31$	7.23984e10	−	4.17992e10i	0.0848858	−	0.0490089i	0.541842	+	0.840480i	$0.317727\pi$
$32$	−5.38414e11	−	9.32560e11i	−0.489684	−	0.848158i
$33$	3.42988e12	+	1.98024e12i	2.43875	+	1.40801i
$34$			7.22030e11i			0.404319i
$35$	8.20041e11	−	1.16497e12i	0.364159	−	0.517332i
$36$	2.85271e12			1.01120
$37$	−2.10893e12	+	3.65278e12i	−0.600412	+	1.03994i	0.392347	+	0.919817i	$0.371663\pi$
$37$	−2.10893e12	+	3.65278e12i	−0.600412	+	1.03994i	−0.992759	+	0.120126i	$0.961670\pi$
$38$	−1.41370e12	+	8.16202e11i	−0.325154	+	0.187728i
$39$	−3.44619e12	−	5.96897e12i	−0.643905	−	1.11528i
$40$	−2.76372e12	−	1.59563e12i	−0.421710	−	0.243474i
$41$		−	8.05237e12i		−	1.00845i	−0.863573	−	0.504223i	$-0.831779\pi$
$41$		−	8.05237e12i		−	1.00845i	0.863573	−	0.504223i	$-0.168221\pi$
$42$	6.08703e12	+	5.47791e11i	0.628653	+	0.0565745i
$43$	−1.17455e13			−1.00490			−0.502452	−	0.864605i	$-0.667569\pi$
$43$	−1.17455e13			−1.00490			−0.502452	+	0.864605i	$0.667569\pi$
$44$	−1.08779e13	+	1.88410e13i	−0.774323	+	1.34117i
$45$	1.13413e13	−	6.54791e12i	0.674470	−	0.389406i
$46$	−2.00996e11	−	3.48135e11i	−0.0100259	−	0.0173654i
$47$	−4.21915e12	−	2.43593e12i	−0.177191	−	0.102301i	0.408781	−	0.912632i	$-0.365954\pi$
$47$	−4.21915e12	−	2.43593e12i	−0.177191	−	0.102301i	−0.585972	+	0.810331i	$0.699287\pi$
$48$			2.08838e13i			0.741106i
$49$	−3.26990e13	−	5.93343e12i	−0.983933	−	0.178541i
$50$	9.90020e12			0.253445
$51$	3.27039e13	−	5.66448e13i	0.714558	−	1.23765i
$52$	3.27887e13	−	1.89306e13i	0.613335	−	0.354109i
$53$	1.17107e11	+	2.02836e11i	0.00188095	+	0.00325790i	0.866964	−	0.498370i	$-0.166068\pi$
$53$	1.17107e11	+	2.02836e11i	0.00188095	+	0.00325790i	−0.865083	+	0.501628i	$0.832735\pi$
$54$	9.13098e12	+	5.27178e12i	0.126290	+	0.0729133i
$55$			9.98730e13i			1.19274i
$56$	−6.67242e12	+	7.41436e13i	−0.0689889	+	0.766601i
$57$	1.47877e14			1.32710
$58$	3.43131e13	−	5.94321e13i	0.267939	−	0.464084i
$59$	−7.78589e12	+	4.49519e12i	−0.0530264	+	0.0306148i	−0.526279	−	0.850312i	$-0.676413\pi$
$59$	−7.78589e12	+	4.49519e12i	−0.0530264	+	0.0306148i	0.473252	+	0.880927i	$0.343080\pi$
$60$	6.51874e13	+	1.12908e14i	0.388109	+	0.672225i
$61$	−2.29740e14	−	1.32640e14i	−1.19839	−	0.691890i	−0.238192	−	0.971218i	$-0.576555\pi$
$61$	−2.29740e14	−	1.32640e14i	−1.19839	−	0.691890i	−0.960196	+	0.279328i	$0.909888\pi$
$62$			9.04373e12i			0.0414204i
$63$	−2.49805e14	−	1.75842e14i	−1.00665	−	0.708595i
$64$	−2.31665e13			−0.0823038
$65$	8.69037e13	−	1.50522e14i	0.272729	−	0.472380i
$66$	−3.71047e14	+	2.14224e14i	−1.03057	+	0.594999i
$67$	−1.76219e14	−	3.05220e14i	−0.433964	−	0.751648i	0.563246	−	0.826289i	$-0.309552\pi$
$67$	−1.76219e14	−	3.05220e14i	−0.433964	−	0.751648i	−0.997210	+	0.0746411i	$0.976219\pi$
$68$	3.11161e14	+	1.79649e14i	0.680634	+	0.392964i
$69$			3.64159e13i			0.0708759i
$70$	6.47862e13	+	1.39841e14i	0.112382	+	0.242577i
$71$	2.43651e13			0.0377313			0.0188657	−	0.999822i	$-0.493995\pi$
$71$	2.43651e13			0.0377313			0.0188657	+	0.999822i	$0.493995\pi$
$72$	−3.42153e14	+	5.92627e14i	−0.473762	+	0.820581i
$73$	8.48653e14	−	4.89970e14i	1.05232	−	0.607557i	0.129021	−	0.991642i	$-0.458816\pi$
$73$	8.48653e14	−	4.89970e14i	1.05232	−	0.607557i	0.923298	+	0.384085i	$0.125483\pi$
$74$	−2.28146e14	−	3.95160e14i	−0.253722	−	0.439460i
$75$	−7.76691e14	−	4.48423e14i	−0.775815	−	0.447917i
$76$			8.12319e14i			0.729823i
$77$	2.11391e15	−	9.79346e14i	1.71065	−	0.792520i
$78$	7.45621e14			0.544203
$79$	−1.08198e15	+	1.87405e15i	−0.713188	+	1.23528i	0.250466	+	0.968125i	$0.419416\pi$
$79$	−1.08198e15	+	1.87405e15i	−0.713188	+	1.23528i	−0.963654	+	0.267153i	$0.913917\pi$
$80$	−4.56079e14	+	2.63317e14i	−0.271844	+	0.156949i
$81$	6.63002e14	+	1.14835e15i	0.357795	+	0.619719i
$82$	7.54404e14	+	4.35555e14i	0.369057	+	0.213075i
$83$		−	3.59077e14i		−	0.159427i	−0.996818	−	0.0797137i	$-0.974599\pi$
$83$		−	3.59077e14i		−	0.159427i	0.996818	−	0.0797137i	$-0.0254006\pi$
$84$	1.75059e15	−	2.48692e15i	0.706236	−	1.00329i
$85$	1.64941e15			0.605309
$86$	6.35319e14	−	1.10040e15i	0.212326	−	0.367760i
$87$	−5.38387e15	+	3.10838e15i	−1.64037	+	0.947065i
$88$	−2.60937e15	−	4.51957e15i	−0.725563	−	1.25671i
$89$	−1.33707e15	−	7.71957e14i	−0.339652	−	0.196098i	0.320466	−	0.947260i	$-0.396160\pi$
$89$	−1.33707e15	−	7.71957e14i	−0.339652	−	0.196098i	−0.660118	+	0.751162i	$0.729494\pi$
$90$			1.41671e15i			0.329110i
$91$	−4.03811e15	−	3.63403e14i	−0.858711	−	0.0772782i
$92$	−2.00040e14			−0.0389775
$93$	4.09630e14	−	7.09499e14i	0.0732028	−	0.126791i
$94$	4.56430e14	−	2.63520e14i	0.0748775	−	0.0432306i
$95$	1.86454e15	+	3.22947e15i	0.281049	+	0.486791i
$96$	−9.13903e15	−	5.27642e15i	−1.26686	−	0.731424i
$97$			1.09832e16i			1.40138i	0.713465	+	0.700691i	$0.247125\pi$
$97$			1.09832e16i			1.40138i	−0.713465	+	0.700691i	$0.752875\pi$
$98$	2.32458e15	−	2.74253e15i	0.273235	−	0.322361i
$99$	2.14159e16			2.32089
$100$	2.46327e15	−	4.26652e15i	0.246327	−	0.426652i
$101$	−4.70699e15	+	2.71758e15i	−0.434683	+	0.250964i	−0.701340	−	0.712827i	$-0.747414\pi$
$101$	−4.70699e15	+	2.71758e15i	−0.434683	+	0.250964i	0.266657	+	0.963792i	$0.414081\pi$
$102$	3.53792e15	+	6.12786e15i	0.301958	+	0.523007i
$103$	−1.02227e16	−	5.90210e15i	−0.806993	−	0.465918i	0.0389176	−	0.999242i	$-0.487609\pi$
$103$	−1.02227e16	−	5.90210e15i	−0.806993	−	0.465918i	−0.845911	+	0.533325i	$0.820942\pi$
$104$			9.08210e15i			0.663620i
$105$	1.25138e15	−	1.39052e16i	0.0846982	−	0.941161i
$106$	−2.53375e13			−0.00158971
$107$	6.74098e15	−	1.16757e16i	0.392331	−	0.679538i	−0.600425	−	0.799681i	$-0.705002\pi$
$107$	6.74098e15	−	1.16757e16i	0.392331	−	0.679538i	0.992757	+	0.120143i	$0.0383353\pi$
$108$	4.54377e15	−	2.62335e15i	0.245486	−	0.141731i
$109$	1.49999e15	+	2.59807e15i	0.0752797	+	0.130388i	0.901208	−	0.433387i	$-0.142682\pi$
$109$	1.49999e15	+	2.59807e15i	0.0752797	+	0.130388i	−0.825928	+	0.563775i	$0.809348\pi$
$110$	−9.35681e15	−	5.40216e15i	−0.436502	−	0.252015i
$111$			4.13348e16i			1.79363i
$112$	1.00457e16	+	7.07131e15i	0.405727	+	0.285598i
$113$	4.44806e16			1.67318			0.836591	−	0.547828i	$-0.184545\pi$
$113$	4.44806e16			1.67318			0.836591	+	0.547828i	$0.184545\pi$
$114$	−7.99872e15	+	1.38542e16i	−0.280402	+	0.485671i
$115$	−7.95282e14	+	4.59156e14i	−0.0259979	+	0.0150099i
$116$	−1.70749e16	−	2.95747e16i	−0.520829	−	0.902102i
$117$	−3.22765e16	−	1.86348e16i	−0.919177	−	0.530687i
$118$		−	9.72584e14i		−	0.0258745i
$119$	−1.61740e16	−	3.49114e16i	−0.402199	−	0.868145i
$120$	−3.12742e16			−0.727338
$121$	−5.86873e16	+	1.01649e17i	−1.27721	+	2.21219i
$122$	2.48534e16	−	1.43491e16i	0.506415	−	0.292379i
$123$	−3.94563e16	−	6.83404e16i	−0.753140	−	1.30448i
$124$	3.89742e15	+	2.25018e15i	0.0697274	+	0.0402571i
$125$		−	6.03249e16i		−	1.01208i
$126$	2.99862e16	−	1.38922e16i	0.472016	−	0.218678i
$127$	5.99703e16			0.886148			0.443074	−	0.896485i	$-0.353888\pi$
$127$	5.99703e16			0.886148			0.443074	+	0.896485i	$0.353888\pi$
$128$	3.65386e16	−	6.32867e16i	0.507074	−	0.878279i
$129$	−9.96841e16	+	5.75527e16i	−1.29990	+	0.750495i
$130$	9.40129e15	+	1.62835e16i	0.115250	+	0.199619i
$131$	1.26390e17	+	7.29711e16i	1.45727	+	0.841357i	0.998876	−	0.0473900i	$-0.0150904\pi$
$131$	1.26390e17	+	7.29711e16i	1.45727	+	0.841357i	0.458397	+	0.888747i	$0.348424\pi$
$132$			2.13205e17i			2.31316i
$133$	5.00716e16	−	7.11327e16i	0.511420	−	0.726535i
$134$	3.81269e16			0.366770
$135$	1.20429e16	−	2.08589e16i	0.109159	−	0.189069i
$136$	−7.46410e16	+	4.30940e16i	−0.637773	+	0.368218i
$137$	−8.49674e15	−	1.47168e16i	−0.0684680	−	0.118590i	0.829759	−	0.558122i	$-0.188478\pi$
$137$	−8.49674e15	−	1.47168e16i	−0.0684680	−	0.118590i	−0.898227	+	0.439532i	$0.855144\pi$
$138$	−3.41170e15	−	1.96975e15i	−0.0259381	−	0.0149754i
$139$		−	1.63663e17i		−	1.17444i	−0.809427	−	0.587220i	$-0.800222\pi$
$139$		−	1.63663e17i		−	1.17444i	0.809427	−	0.587220i	$-0.199778\pi$
$140$	7.63842e16	+	6.87406e15i	0.517582	+	0.0465789i
$141$	−4.77438e16			−0.305608
$142$	−1.31792e15	+	2.28270e15i	−0.00797226	+	0.0138084i
$143$	2.46151e17	−	1.42115e17i	1.40771	−	0.812742i
$144$	5.64634e16	+	9.77974e16i	0.305398	+	0.528966i
$145$	−1.35767e17	−	7.83851e16i	−0.694784	−	0.401134i
$146$			1.06011e17i			0.513483i
$147$	−3.06589e17	+	1.09867e17i	−1.40611	+	0.503881i
$148$	−2.27060e17			−0.986387
$149$	2.96334e16	−	5.13266e16i	0.121981	−	0.211277i	−0.798568	−	0.601905i	$-0.794409\pi$
$149$	2.96334e16	−	5.13266e16i	0.121981	−	0.211277i	0.920549	+	0.390628i	$0.127742\pi$
$150$	8.40229e16	−	4.85106e16i	0.327844	−	0.189281i
$151$	1.56855e17	+	2.71681e17i	0.580342	+	1.00518i	0.995439	+	0.0954042i	$0.0304144\pi$
$151$	1.56855e17	+	2.71681e17i	0.580342	+	1.00518i	−0.415097	+	0.909777i	$0.636252\pi$
$152$	−1.68752e17	−	9.74292e16i	−0.592244	−	0.341932i
$153$		−	3.53684e17i		−	1.17784i
$154$	−2.25901e16	+	2.51020e17i	−0.0714088	+	0.793491i
$155$	2.06595e16			0.0620108
$156$	1.85518e17	−	3.21327e17i	0.528920	−	0.916117i
$157$	−5.01724e17	+	2.89670e17i	−1.35915	+	0.784706i	−0.989509	−	0.144469i	$-0.953853\pi$
$157$	−5.01724e17	+	2.89670e17i	−1.35915	+	0.784706i	−0.369641	+	0.929175i	$0.620519\pi$
$158$	−1.17050e17	−	2.02736e17i	−0.301379	−	0.522004i
$159$	1.98778e15	+	1.14765e15i	0.00486622	+	0.00280951i
$160$		−	2.66115e17i		−	0.619596i
$161$	1.75170e16	+	1.23305e16i	0.0388018	+	0.0273133i
$162$	−1.43448e17			−0.302395
$163$	−6.47866e16	+	1.12214e17i	−0.130012	+	0.225188i	−0.923681	−	0.383162i	$-0.874835\pi$
$163$	−6.47866e16	+	1.12214e17i	−0.130012	+	0.225188i	0.793669	+	0.608350i	$0.208168\pi$
$164$	3.75407e17	−	2.16741e17i	0.717384	−	0.414182i
$165$	4.89374e17	+	8.47621e17i	0.890778	+	1.54287i
$166$	3.36409e16	+	1.94226e16i	0.0583449	+	0.0336855i
$167$		−	2.61382e17i		−	0.432060i	−0.976387	−	0.216030i	$-0.930689\pi$
$167$		−	2.61382e17i		−	0.432060i	0.976387	−	0.216030i	$-0.0693110\pi$
$168$	3.06672e17	+	6.61950e17i	0.483282	+	1.04316i
$169$	1.70774e17			0.256643
$170$	−8.92171e16	+	1.54529e17i	−0.127896	+	0.221522i
$171$	6.92498e17	−	3.99814e17i	0.947218	−	0.546876i
$172$	−3.16148e17	−	5.47585e17i	−0.412727	−	0.714864i
$173$	1.23155e18	+	7.11038e17i	1.53492	+	0.886184i	0.999125	+	0.0418338i	$0.0133200\pi$
$173$	1.23155e18	+	7.11038e17i	1.53492	+	0.886184i	0.535791	+	0.844350i	$0.320013\pi$
$174$		−	6.72533e17i		−	0.800423i
$175$	−4.78692e17	+	2.21771e17i	−0.544192	+	0.252116i
$176$	−8.61217e17			−0.935429
$177$	−4.40525e16	+	7.63012e16i	−0.0457283	+	0.0792037i
$178$	1.44645e17	−	8.35107e16i	0.143530	−	0.0828671i
$179$	−5.45128e17	−	9.44190e17i	−0.517219	−	0.895850i	−0.999800	−	0.0199984i	$-0.993634\pi$
$179$	−5.45128e17	−	9.44190e17i	−0.517219	−	0.895850i	0.482581	−	0.875851i	$-0.339699\pi$
$180$	6.10536e17	+	3.52493e17i	0.554027	+	0.319868i
$181$			1.26461e17i			0.109781i	0.998492	+	0.0548906i	$0.0174810\pi$
$181$			1.26461e17i			0.109781i	−0.998492	+	0.0548906i	$0.982519\pi$
$182$	2.52469e17	−	3.58663e17i	0.209718	−	0.297931i
$183$	−2.59973e18			−2.06690
$184$	2.39927e16	−	4.15565e16i	0.0182615	−	0.0316298i
$185$	−9.02705e17	+	5.21177e17i	−0.657919	+	0.379850i
$186$	4.43140e16	+	7.67540e16i	0.0309341	+	0.0535794i
$187$	2.33594e18	+	1.34866e18i	1.56217	+	0.901921i
$188$		−	2.62266e17i		−	0.168066i
$189$	−5.59591e17	−	5.03594e16i	−0.343697	−	0.0309304i
$190$	−4.03413e17			−0.237532
$191$	6.20924e16	−	1.07547e17i	0.0350567	−	0.0607200i	−0.847965	−	0.530053i	$-0.822172\pi$
$191$	6.20924e16	−	1.07547e17i	0.0350567	−	0.0607200i	0.883021	+	0.469333i	$0.155505\pi$
$192$	−1.96614e17	+	1.13515e17i	−0.106464	+	0.0614672i
$193$	4.59198e15	+	7.95355e15i	0.00238529	+	0.00413145i	0.867216	−	0.497933i	$-0.165907\pi$
$193$	4.59198e15	+	7.95355e15i	0.00238529	+	0.00413145i	−0.864830	+	0.502064i	$0.832574\pi$
$194$	−1.02899e18	−	5.94087e17i	−0.512858	−	0.296098i
$195$		−	1.70330e18i		−	0.814731i
$196$	−6.03520e17	−	1.68416e18i	−0.277104	−	0.773274i
$197$	2.30413e17			0.101573			0.0507863	−	0.998710i	$-0.483827\pi$
$197$	2.30413e17			0.101573			0.0507863	+	0.998710i	$0.483827\pi$
$198$	−1.15839e18	+	2.00639e18i	−0.490380	+	0.849364i
$199$	2.28565e18	−	1.31962e18i	0.929362	−	0.536568i	0.0427525	−	0.999086i	$-0.486387\pi$
$199$	2.28565e18	−	1.31962e18i	0.929362	−	0.536568i	0.886610	+	0.462518i	$0.153054\pi$
$200$	5.90888e17	+	1.02345e18i	0.230816	+	0.399785i
$201$	−2.99113e18	−	1.72693e18i	−1.12271	−	0.648197i
$202$		−	5.87979e17i		−	0.212105i
$203$	−3.27781e17	+	3.64228e18i	−0.113662	+	1.26301i
$204$	3.52109e18			1.17391
$205$	9.94985e17	−	1.72336e18i	0.318996	−	0.552518i
$206$	1.10590e18	−	6.38493e17i	0.341019	−	0.196888i
$207$	9.84573e16	+	1.70533e17i	0.0292069	+	0.0505878i
$208$	1.29797e18	+	7.49381e17i	0.370473	+	0.213893i
$209$			6.09823e18i			1.67507i
$210$	1.23505e18	+	8.69376e17i	0.326537	+	0.229855i
$211$	4.27627e18			1.08844			0.544221	−	0.838942i	$-0.316825\pi$
$211$	4.27627e18			1.08844			0.544221	+	0.838942i	$0.316825\pi$
$212$	−6.30424e15	+	1.09193e16i	−0.00154506	+	0.00267613i
$213$	2.06787e17	−	1.19388e17i	0.0488074	−	0.0281790i
$214$	7.29244e17	+	1.26309e18i	0.165792	+	0.287159i
$215$	−2.51377e18	−	1.45133e18i	−0.550577	−	0.317876i
$216$			1.25857e18i			0.265612i
$217$	−2.02586e17	−	4.37280e17i	−0.0412032	−	0.0889369i
$218$	−3.24541e17			−0.0636234
$219$	4.80167e18	−	8.31674e18i	0.907486	−	1.57181i
$220$	−4.65615e18	+	2.68823e18i	−0.848488	+	0.489874i
$221$	−2.34705e18	−	4.06520e18i	−0.412462	−	0.714404i
$222$	−3.87254e18	−	2.23581e18i	−0.656405	−	0.378976i
$223$		−	3.64395e18i		−	0.595845i	−0.954590	−	0.297922i	$-0.903706\pi$
$223$		−	3.64395e18i		−	0.595845i	0.954590	−	0.297922i	$-0.0962936\pi$
$224$	−5.63259e18	+	2.60950e18i	−0.888636	+	0.411692i
$225$	−4.84958e18			−0.738319
$226$	−2.40597e18	+	4.16726e18i	−0.353527	+	0.612327i
$227$	−4.85790e18	+	2.80471e18i	−0.689036	+	0.397815i	−0.803251	−	0.595641i	$-0.796898\pi$
$227$	−4.85790e18	+	2.80471e18i	−0.689036	+	0.397815i	0.114215	+	0.993456i	$0.463565\pi$
$228$	3.98033e18	+	6.89414e18i	0.545056	+	0.944064i
$229$	−9.17835e18	−	5.29913e18i	−1.21362	−	0.700681i	−0.250070	−	0.968228i	$-0.580454\pi$
$229$	−9.17835e18	−	5.29913e18i	−1.21362	−	0.700681i	−0.963545	+	0.267547i	$0.913787\pi$
$230$		−	9.93436e16i		−	0.0126858i
$231$	1.31420e19	−	1.86698e19i	1.62093	−	2.30273i
$232$	8.19184e18			0.976063
$233$	−4.79291e18	+	8.30157e18i	−0.551763	+	0.955681i	0.446385	+	0.894841i	$0.352711\pi$
$233$	−4.79291e18	+	8.30157e18i	−0.551763	+	0.955681i	−0.998148	+	0.0608399i	$0.980622\pi$
$234$	3.49169e18	−	2.01593e18i	0.388426	−	0.224258i
$235$	−6.01987e17	−	1.04267e18i	−0.0647208	−	0.112100i
$236$	−4.19138e17	−	2.41989e17i	−0.0435573	−	0.0251478i
$237$			2.12067e19i			2.13053i
$238$	4.14561e18	+	3.73077e17i	0.402692	+	0.0362395i
$239$	4.65456e18			0.437216			0.218608	−	0.975813i	$-0.429848\pi$
$239$	4.65456e18			0.437216			0.218608	+	0.975813i	$0.429848\pi$
$240$	−2.58049e18	+	4.46954e18i	−0.234430	+	0.406044i
$241$	−1.22292e19	+	7.06053e18i	−1.07464	+	0.620442i	−0.929444	−	0.368962i	$-0.879713\pi$
$241$	−1.22292e19	+	7.06053e18i	−1.07464	+	0.620442i	−0.145192	+	0.989404i	$0.546380\pi$
$242$	−6.34883e18	−	1.09965e19i	−0.539723	−	0.934827i
$243$	1.48871e19	+	8.59509e18i	1.22451	+	0.706969i
$244$		−	1.42808e19i		−	1.13667i
$245$	−6.26505e18	−	5.31029e18i	−0.482610	−	0.409062i
$246$	8.53682e18			0.636525
$247$	5.30632e18	−	9.19082e18i	0.383017	−	0.663405i
$248$	−9.34910e17	+	5.39770e17i	−0.0653365	+	0.0377221i
$249$	−1.75947e18	−	3.04749e18i	−0.119066	−	0.206228i
$250$	5.65166e18	+	3.26299e18i	0.370387	+	0.213843i
$251$			2.00822e19i			1.27474i	0.770558	+	0.637370i	$0.219978\pi$
$251$			2.00822e19i			1.27474i	−0.770558	+	0.637370i	$0.780022\pi$
$252$	1.47401e18	−	1.63791e19i	0.0906351	−	1.00713i
$253$	−1.50174e18			−0.0894601
$254$	−3.24381e18	+	5.61844e18i	−0.187234	+	0.324299i
$255$	1.39985e19	−	8.08205e18i	0.782998	−	0.452064i
$256$	3.19365e18	+	5.53156e18i	0.173128	+	0.299866i
$257$	1.37410e19	+	7.93337e18i	0.722026	+	0.416862i	0.815498	−	0.578760i	$-0.196463\pi$
$257$	1.37410e19	+	7.93337e18i	0.722026	+	0.416862i	−0.0934716	+	0.995622i	$0.529796\pi$
$258$		−	1.24522e19i		−	0.634289i
$259$	1.98831e19	+	1.39961e19i	0.981942	+	0.691206i
$260$	9.35656e18			0.448053
$261$	−1.68082e19	+	2.91126e19i	−0.780543	+	1.35194i
$262$	−1.36729e19	+	7.89406e18i	−0.615815	+	0.355541i
$263$	−8.97652e18	−	1.55478e19i	−0.392159	−	0.679239i	0.600575	−	0.799568i	$-0.294938\pi$
$263$	−8.97652e18	−	1.55478e19i	−0.392159	−	0.679239i	−0.992734	+	0.120329i	$0.961605\pi$
$264$	−4.42915e19	−	2.55717e19i	−1.87710	−	1.08375i
$265$			5.78812e16i			0.00237996i
$266$	3.95584e18	+	8.53865e18i	0.157828	+	0.340672i
$267$	−1.51302e19			−0.585809
$268$	9.48638e18	−	1.64309e19i	0.356469	−	0.617423i
$269$	1.00047e19	−	5.77622e18i	0.364911	−	0.210681i	−0.306322	−	0.951928i	$-0.599098\pi$
$269$	1.00047e19	−	5.77622e18i	0.364911	−	0.210681i	0.671233	+	0.741247i	$0.265765\pi$
$270$	1.30281e18	+	2.25653e18i	0.0461285	+	0.0798969i
$271$	−3.61203e19	−	2.08541e19i	−1.24164	−	0.716863i	−0.272215	−	0.962236i	$-0.587756\pi$
$271$	−3.61203e19	−	2.08541e19i	−1.24164	−	0.716863i	−0.969429	+	0.245373i	$0.921090\pi$
$272$			1.42231e19i			0.474725i
$273$	−3.60521e19	+	1.67024e19i	−1.16850	+	0.541350i
$274$	1.83836e18			0.0578665
$275$	1.84923e19	−	3.20295e19i	0.565364	−	0.979240i
$276$	−1.69774e18	+	9.80188e17i	−0.0504194	+	0.0291096i
$277$	−2.82169e18	−	4.88731e18i	−0.0814087	−	0.141004i	0.822447	−	0.568842i	$-0.192609\pi$
$277$	−2.82169e18	−	4.88731e18i	−0.0814087	−	0.141004i	−0.903855	+	0.427838i	$0.859275\pi$
$278$	1.53331e19	+	8.85256e18i	0.429804	+	0.248148i
$279$		−	4.43004e18i		−	0.120663i
$280$	−1.05895e19	+	1.50437e19i	−0.280293	+	0.398190i
$281$	4.06940e19			1.04684			0.523420	−	0.852075i	$-0.324656\pi$
$281$	4.06940e19			1.04684			0.523420	+	0.852075i	$0.324656\pi$
$282$	2.58248e18	−	4.47298e18i	0.0645719	−	0.111842i
$283$	2.67552e19	−	1.54471e19i	0.650304	−	0.375453i	−0.138269	−	0.990395i	$-0.544154\pi$
$283$	2.67552e19	−	1.54471e19i	0.650304	−	0.375453i	0.788573	+	0.614942i	$0.210820\pi$
$284$	6.55824e17	+	1.13592e18i	0.0154967	+	0.0268411i
$285$	3.16486e19	+	1.82723e19i	0.727102	+	0.419793i
$286$			3.07483e19i			0.686898i
$287$	−4.62335e19	−	4.16070e18i	−1.00439	−	0.0903881i
$288$	−5.70632e19			−1.20564
$289$	−2.05742e18	+	3.56355e18i	−0.0422805	+	0.0732319i
$290$	1.46874e19	−	8.47975e18i	0.293602	−	0.169511i
$291$	5.38175e19	+	9.32147e19i	1.04660	+	1.81276i
$292$	4.56855e19	+	2.63765e19i	0.864402	+	0.499063i
$293$		−	6.87981e19i		−	1.26659i	−0.773911	−	0.633294i	$-0.781702\pi$
$293$		−	6.87981e19i		−	1.26659i	0.773911	−	0.633294i	$-0.218298\pi$
$294$	6.29040e18	−	3.46662e19i	0.112694	−	0.621052i
$295$	−2.22178e18			−0.0387369
$296$	2.72335e19	−	4.71698e19i	0.462136	−	0.800443i
$297$	3.41109e19	−	1.96940e19i	0.563433	−	0.325298i
$298$	3.20576e18	+	5.55254e18i	0.0515467	+	0.0892815i
$299$	2.26331e18	+	1.30672e18i	0.0354303	+	0.0204557i
$300$		−	4.82798e19i		−	0.735861i
$301$	−6.06897e18	+	6.74381e19i	−0.0900706	+	1.00086i
$302$	−3.39374e19			−0.490482
$303$	−2.66321e19	+	4.61282e19i	−0.374856	+	0.649270i
$304$	−2.78481e19	+	1.60781e19i	−0.381775	+	0.220418i
$305$	−3.27792e19	−	5.67752e19i	−0.437723	−	0.758158i
$306$	3.31357e19	+	1.91309e19i	0.431047	+	0.248865i
$307$		−	1.90269e19i		−	0.241135i	−0.992705	−	0.120568i	$-0.961529\pi$
$307$		−	1.90269e19i		−	0.241135i	0.992705	−	0.120568i	$-0.0384715\pi$
$308$	1.02557e20	+	7.21916e19i	1.26637	+	0.891417i
$309$	−1.15680e20			−1.39185
$310$	−1.11748e18	+	1.93553e18i	−0.0131023	+	0.0226938i
$311$	−5.55321e19	+	3.20615e19i	−0.634543	+	0.366354i	−0.782509	−	0.622639i	$-0.786061\pi$
$311$	−5.55321e19	+	3.20615e19i	−0.634543	+	0.366354i	0.147966	+	0.988992i	$0.452727\pi$
$312$	4.45020e19	+	7.70797e19i	0.495613	+	0.858427i
$313$	7.14912e19	+	4.12755e19i	0.776065	+	0.448061i	0.835034	−	0.550199i	$-0.185448\pi$
$313$	7.14912e19	+	4.12755e19i	0.776065	+	0.448061i	−0.0589690	+	0.998260i	$0.518781\pi$
$314$		−	6.26734e19i		−	0.663203i
$315$	−3.17353e19	−	6.85006e19i	−0.327385	−	0.706659i
$316$	−1.16493e20			−1.17166
$317$	1.14111e19	−	1.97646e19i	0.111906	−	0.193827i	−0.804633	−	0.593773i	$-0.797638\pi$
$317$	1.14111e19	−	1.97646e19i	0.111906	−	0.193827i	0.916539	+	0.399946i	$0.130971\pi$
$318$	−2.15039e17	+	1.24153e17i	−0.00205637	+	0.00118724i
$319$	−1.28185e20	−	2.22023e20i	−1.19539	−	2.07048i
$320$	−4.95808e18	−	2.86255e18i	−0.0450934	−	0.0260347i
$321$		−	1.32122e20i		−	1.17202i
$322$	−2.10271e18	+	9.74155e17i	−0.0181942	+	0.00842910i
$323$	1.00713e20			0.850089
$324$	−3.56913e19	+	6.18192e19i	−0.293902	+	0.509054i
$325$	−5.57405e19	+	3.21818e19i	−0.447820	+	0.258549i
$326$	−7.00865e18	−	1.21393e19i	−0.0549406	−	0.0951600i
$327$	2.54609e19	+	1.46998e19i	0.194756	+	0.112443i
$328$			1.03984e20i			0.776200i
$329$	−1.61662e19	+	2.29660e19i	−0.117771	+	0.167309i
$330$	−1.05882e20			−0.752851
$331$	−4.35120e19	+	7.53650e19i	−0.301985	+	0.523053i	−0.976585	−	0.215130i	$-0.930983\pi$
$331$	−4.35120e19	+	7.53650e19i	−0.301985	+	0.523053i	0.674601	+	0.738183i	$0.264316\pi$
$332$	1.67404e19	−	9.66510e18i	0.113413	−	0.0654789i
$333$	1.11756e20	+	1.93568e20i	0.739127	+	1.28020i
$334$	2.44882e19	+	1.41382e19i	0.158119	+	0.0912901i
$335$		−	8.70973e19i		−	0.549094i
$336$	1.19907e20	+	1.07908e19i	0.738123	+	0.0664261i
$337$	8.76965e19			0.527161			0.263580	−	0.964637i	$-0.415097\pi$
$337$	8.76965e19			0.527161			0.263580	+	0.964637i	$0.415097\pi$
$338$	−9.23724e18	+	1.59994e19i	−0.0542261	+	0.0939224i
$339$	3.77506e20	−	2.17953e20i	2.16435	−	1.24959i
$340$	4.43963e19	+	7.68967e19i	0.248608	+	0.430602i
$341$	2.92587e19	+	1.68925e19i	0.160037	+	0.0923972i
$342$			8.65043e19i			0.462199i
$343$	−5.09631e19	+	1.84678e20i	−0.266013	+	0.963969i
$344$	1.51675e20			0.773474
$345$	−4.49970e18	+	7.79371e18i	−0.0224198	+	0.0388322i
$346$	−1.33230e20	+	7.69205e19i	−0.648625	+	0.374484i
$347$	4.75734e19	+	8.23996e19i	0.226323	+	0.392003i	0.956716	−	0.291025i	$-0.0939962\pi$
$347$	4.75734e19	+	8.23996e19i	0.226323	+	0.392003i	−0.730393	+	0.683028i	$0.760663\pi$
$348$	−2.89830e20	−	1.67333e20i	−1.34744	−	0.777944i
$349$		−	1.62304e20i		−	0.737436i	−0.929541	−	0.368718i	$-0.879797\pi$
$349$		−	1.62304e20i		−	0.737436i	0.929541	−	0.368718i	$-0.120203\pi$
$350$	5.11548e18	−	5.68430e19i	0.0227165	−	0.252425i
$351$	−6.85462e19			−0.297527
$352$	2.17591e20	−	3.76879e20i	0.923210	−	1.59905i
$353$	−2.08806e20	+	1.20554e20i	−0.866053	+	0.500016i	−0.866035	−	0.499984i	$-0.833339\pi$
$353$	−2.08806e20	+	1.20554e20i	−0.866053	+	0.500016i	−1.87094e−5		1.00000i	$0.500006\pi$
$354$	−4.76563e18	−	8.25431e18i	−0.0193239	−	0.0334699i
$355$	5.21461e18	+	3.01066e18i	0.0206726	+	0.0119353i
$356$		−	8.31134e19i		−	0.322160i
$357$	−3.08333e20	−	2.17041e20i	−1.16862	−	0.822614i
$358$	1.17945e20			0.437133
$359$	−3.94266e19	+	6.82889e19i	−0.142901	+	0.247511i	−0.928588	−	0.371113i	$-0.878976\pi$
$359$	−3.94266e19	+	6.82889e19i	−0.142901	+	0.247511i	0.785687	+	0.618624i	$0.212310\pi$
$360$	−1.46455e20	+	8.45558e19i	−0.519139	+	0.299725i
$361$	−3.03724e19	−	5.26066e19i	−0.105298	−	0.182382i
$362$	−1.18478e19	−	6.84032e18i	−0.0401762	−	0.0231957i
$363$			1.15026e21i			3.81544i
$364$	−9.17497e19	−	1.98041e20i	−0.297710	−	0.642605i
$365$	2.42171e20			0.768740
$366$	1.40620e20	−	2.43561e20i	0.436716	−	0.756415i
$367$	1.93428e20	−	1.11676e20i	0.587748	−	0.339336i	−0.176459	−	0.984308i	$-0.556464\pi$
$367$	1.93428e20	−	1.11676e20i	0.587748	−	0.339336i	0.764207	+	0.644972i	$0.223131\pi$
$368$	−3.95936e18	−	6.85781e18i	−0.0117718	−	0.0203893i
$369$	−3.69542e20	−	2.13355e20i	−1.07511	−	0.620716i
$370$		−	1.12763e20i		−	0.321034i
$371$	1.22511e18	−	5.67578e17i	0.00341338	−	0.00158137i
$372$	4.41031e19			0.120261
$373$	−9.54765e19	+	1.65370e20i	−0.254815	+	0.441353i	−0.964845	−	0.262818i	$-0.915348\pi$
$373$	−9.54765e19	+	1.65370e20i	−0.254815	+	0.441353i	0.710030	+	0.704171i	$0.248681\pi$
$374$	−2.52704e20	+	1.45899e20i	−0.660144	+	0.381134i
$375$	−2.95590e20	−	5.11976e20i	−0.755856	−	1.30918i
$376$	5.44836e19	+	3.14561e19i	0.136384	+	0.0787413i
$377$			4.46156e20i			1.09334i
$378$	3.49864e19	−	4.97025e19i	0.0839393	−	0.119246i
$379$	−3.77656e19			−0.0887122			−0.0443561	−	0.999016i	$-0.514124\pi$
$379$	−3.77656e19			−0.0887122			−0.0443561	+	0.999016i	$0.514124\pi$
$380$	−1.00373e20	+	1.73852e20i	−0.230861	+	0.399863i
$381$	5.08967e20	−	2.93852e20i	1.14628	−	0.661804i
$382$	6.71719e18	+	1.16345e19i	0.0148143	+	0.0256591i
$383$	−3.33433e19	−	1.92508e19i	−0.0720143	−	0.0415775i	0.463560	−	0.886065i	$-0.346572\pi$
$383$	−3.33433e19	−	1.92508e19i	−0.0720143	−	0.0415775i	−0.535575	+	0.844488i	$0.679905\pi$
$384$		−	7.16151e20i		−	1.51480i
$385$	5.73431e20	+	5.16049e19i	1.18794	+	0.106907i
$386$	−9.93527e17			−0.00201596
$387$	−3.11209e20	+	5.39030e20i	−0.618535	+	1.07133i
$388$	−5.12047e20	+	2.95630e20i	−0.996909	+	0.575566i
$389$	−4.09219e20	−	7.08788e20i	−0.780475	−	1.35182i	−0.931665	−	0.363317i	$-0.881644\pi$
$389$	−4.09219e20	−	7.08788e20i	−0.780475	−	1.35182i	0.151191	−	0.988505i	$-0.451689\pi$
$390$	1.59577e20	+	9.21320e19i	0.298163	+	0.172145i
$391$			2.48013e19i			0.0454004i
$392$	4.22255e20	+	7.66207e19i	0.757332	+	0.137422i
$393$	1.43022e21			2.51341
$394$	−1.24631e19	+	2.15867e19i	−0.0214613	+	0.0371721i
$395$	−4.63131e20	+	2.67389e20i	−0.781497	+	0.451197i
$396$	5.76439e20	+	9.98422e20i	0.953218	+	1.65102i
$397$	4.35361e20	+	2.51356e20i	0.705546	+	0.407347i	0.809410	−	0.587245i	$-0.199787\pi$
$397$	4.35361e20	+	2.51356e20i	0.705546	+	0.407347i	−0.103864	+	0.994592i	$0.533121\pi$
$398$			2.85515e20i			0.453486i
$399$	7.64089e19	−	8.49052e20i	0.118949	−	1.32175i
$400$	1.95021e20			0.297578
$401$	2.18215e19	−	3.77959e19i	0.0326384	−	0.0565314i	−0.849245	−	0.527999i	$-0.822942\pi$
$401$	2.18215e19	−	3.77959e19i	0.0326384	−	0.0565314i	0.881883	+	0.471468i	$0.156276\pi$
$402$	3.23583e20	−	1.86821e20i	0.474435	−	0.273915i
$403$	−2.93977e19	−	5.09184e19i	−0.0422545	−	0.0731870i
$404$	−2.53391e20	−	1.46296e20i	−0.357060	−	0.206148i
$405$			3.27693e20i			0.452717i
$406$	−3.23505e20	−	2.27721e20i	−0.438201	−	0.308457i
$407$	−1.70458e21			−2.26393
$408$	−4.22318e20	+	7.31477e20i	−0.549995	+	0.952619i
$409$	6.13813e20	−	3.54385e20i	0.783880	−	0.452573i	−0.0539236	−	0.998545i	$-0.517173\pi$
$409$	6.13813e20	−	3.54385e20i	0.783880	−	0.452573i	0.837804	+	0.545972i	$0.183839\pi$
$410$	1.07638e20	+	1.86435e20i	0.134802	+	0.233483i
$411$	−1.44223e20	−	8.32675e19i	−0.177134	−	0.102268i
$412$		−	6.35455e20i		−	0.765433i
$413$	2.17866e19	+	4.70262e19i	0.0257388	+	0.0555570i
$414$	−2.13023e19			−0.0246845
$415$	4.43691e19	−	7.68495e19i	0.0504308	−	0.0873487i
$416$	−6.55877e20	+	3.78671e20i	−0.731267	+	0.422197i
$417$	−8.01941e20	−	1.38900e21i	−0.877110	−	1.51920i
$418$	−5.71326e20	−	3.29855e20i	−0.613018	−	0.353926i
$419$			4.28033e20i			0.450572i	0.974293	+	0.225286i	$0.0723317\pi$
$419$			4.28033e20i			0.450572i	−0.974293	+	0.225286i	$0.927668\pi$
$420$	6.81955e20	−	3.15940e20i	0.704306	−	0.326295i
$421$	1.27959e20			0.129663			0.0648313	−	0.997896i	$-0.479349\pi$
$421$	1.27959e20			0.129663			0.0648313	+	0.997896i	$0.479349\pi$
$422$	−2.31304e20	+	4.00631e20i	−0.229977	+	0.398332i
$423$	−2.23581e20	+	1.29085e20i	−0.218128	+	0.125936i
$424$	−1.51226e18	−	2.61931e18i	−0.00144777	−	0.00250761i
$425$	−5.28970e20	−	3.05401e20i	−0.496958	−	0.286919i
$426$			2.58310e19i			0.0238158i
$427$	−8.80275e20	+	1.25054e21i	−0.796518	+	1.13155i
$428$	7.25774e20			0.644542
$429$	1.39272e21	−	2.41226e21i	1.21396	−	2.10265i
$430$	2.71941e20	−	1.57005e20i	0.232663	−	0.134328i
$431$	1.08047e21	+	1.87143e21i	0.907389	+	1.57164i	0.817677	+	0.575677i	$0.195261\pi$
$431$	1.08047e21	+	1.87143e21i	0.907389	+	1.57164i	0.0897123	+	0.995968i	$0.471405\pi$
$432$	1.79869e20	+	1.03847e20i	0.148281	+	0.0856100i
$433$			7.10405e19i			0.0574914i	0.999587	+	0.0287457i	$0.00915130\pi$
$433$			7.10405e19i			0.0574914i	−0.999587	+	0.0287457i	$0.990849\pi$
$434$	5.19255e19	+	4.67294e18i	0.0412537	+	0.00371255i
$435$	−1.53634e21			−1.19832
$436$	−8.07491e19	+	1.39862e20i	−0.0618367	+	0.107104i
$437$	−4.85598e19	+	2.80360e19i	−0.0365111	+	0.0210797i
$438$	5.19448e20	+	8.99710e20i	0.383486	+	0.664217i
$439$	4.46300e20	+	2.57671e20i	0.323527	+	0.186788i	0.652964	−	0.757389i	$-0.273525\pi$
$439$	4.46300e20	+	2.57671e20i	0.323527	+	0.186788i	−0.329437	+	0.944178i	$0.606859\pi$
$440$		−	1.28970e21i		−	0.918052i
$441$	−1.13869e21	+	1.34342e21i	−0.795970	+	0.939082i
$442$	5.07810e20			0.348596
$443$	1.10751e21	−	1.91826e21i	0.746649	−	1.29323i	−0.202771	−	0.979226i	$-0.564995\pi$
$443$	1.10751e21	−	1.91826e21i	0.746649	−	1.29323i	0.949420	−	0.314009i	$-0.101672\pi$
$444$	−1.92706e21	+	1.11259e21i	−1.27594	+	0.736666i
$445$	−1.90772e20	−	3.30428e20i	−0.124061	−	0.214880i
$446$	3.41391e20	+	1.97102e20i	0.218058	+	0.125896i
$447$		−	5.80811e20i		−	0.364397i
$448$	−1.19702e19	+	1.33013e20i	−0.00737698	+	0.0819726i
$449$	6.82792e20			0.413350			0.206675	−	0.978410i	$-0.433736\pi$
$449$	6.82792e20			0.413350			0.206675	+	0.978410i	$0.433736\pi$
$450$	2.62315e20	−	4.54344e20i	0.156000	−	0.270199i
$451$	2.81825e21	−	1.62712e21i	1.64652	−	0.950620i
$452$	1.19726e21	+	2.07372e21i	0.687197	+	1.19026i
$453$	2.66246e21	+	1.53717e21i	1.50140	+	0.866836i
$454$		−	6.06831e20i		−	0.336218i
$455$	−8.19331e20	−	5.76741e20i	−0.446034	−	0.313971i
$456$	−1.90960e21			−1.02146
$457$	−9.85217e20	+	1.70645e21i	−0.517848	+	0.896939i	0.481937	+	0.876206i	$0.339933\pi$
$457$	−9.85217e20	+	1.70645e21i	−0.517848	+	0.896939i	−0.999785	+	0.0207329i	$0.993400\pi$
$458$	9.92920e20	−	5.73263e20i	0.512850	−	0.296094i
$459$	−3.25247e20	−	5.63345e20i	−0.165087	−	0.285939i
$460$	−4.28124e19	−	2.47177e19i	−0.0213554	−	0.0123295i
$461$			8.51440e20i			0.417394i	0.977980	+	0.208697i	$0.0669223\pi$
$461$			8.51440e20i			0.417394i	−0.977980	+	0.208697i	$0.933078\pi$
$462$	1.03827e21	+	2.24109e21i	0.500233	+	1.07975i
$463$	−7.68410e20			−0.363869			−0.181934	−	0.983311i	$-0.558236\pi$
$463$	−7.68410e20			−0.363869			−0.181934	+	0.983311i	$0.558236\pi$
$464$	6.75924e20	−	1.17073e21i	0.314597	−	0.544897i
$465$	1.75337e20	−	1.01231e20i	0.0802141	−	0.0463116i
$466$	−5.18500e20	−	8.98069e20i	−0.233164	−	0.403852i
$467$	−1.28956e21	−	7.44530e20i	−0.570043	−	0.329115i	0.187123	−	0.982336i	$-0.440084\pi$
$467$	−1.28956e21	−	7.44530e20i	−0.570043	−	0.329115i	−0.757167	+	0.653222i	$0.773417\pi$
$468$		−	2.00634e21i		−	0.871840i
$469$	−1.84350e21	+	8.54069e20i	−0.787519	+	0.364846i
$470$	1.30247e20			0.0546995
$471$	−2.83875e21	+	4.91686e21i	−1.17209	+	2.03011i
$472$	1.00542e20	−	5.80482e19i	0.0408144	−	0.0235642i
$473$	−2.37338e21	−	4.11082e21i	−0.947281	−	1.64074i
$474$	−1.98680e21	−	1.14708e21i	−0.779699	−	0.450160i
$475$		−	1.38093e21i		−	0.532873i
$476$	1.19225e21	−	1.69374e21i	0.452389	−	0.642673i
$477$	1.24115e19			0.00463103
$478$	−2.51767e20	+	4.36073e20i	−0.0923794	+	0.160006i
$479$	3.06682e21	−	1.77063e21i	1.10663	−	0.638915i	0.168678	−	0.985671i	$-0.446050\pi$
$479$	3.06682e21	−	1.77063e21i	1.10663	−	0.638915i	0.937955	+	0.346756i	$0.112717\pi$
$480$	−1.30395e21	−	2.25851e21i	−0.462735	−	0.801480i
$481$	2.56903e21	+	1.48323e21i	0.896620	+	0.517664i
$482$		−	1.52762e21i		−	0.524373i
$483$	2.09085e20	+	1.88163e19i	0.0705906	+	0.00635268i
$484$	−6.31862e21			−2.09826
$485$	−1.35714e21	+	2.35063e21i	−0.443291	+	0.767803i
$486$	−1.61050e21	+	9.29822e20i	−0.517452	+	0.298751i
$487$	2.65586e21	+	4.60008e21i	0.839407	+	1.45390i	0.890391	+	0.455197i	$0.150431\pi$
$487$	2.65586e21	+	4.60008e21i	0.839407	+	1.45390i	−0.0509837	+	0.998699i	$0.516236\pi$
$488$	2.96672e21	+	1.71284e21i	0.922398	+	0.532547i
$489$			1.26981e21i			0.388389i
$490$	8.36384e20	−	2.99720e20i	0.251673	−	0.0901876i
$491$	3.73461e19			0.0110559			0.00552794	−	0.999985i	$-0.498240\pi$
$491$	3.73461e19			0.0110559			0.00552794	+	0.999985i	$0.498240\pi$
$492$	2.12405e21	−	3.67897e21i	0.618649	−	1.07153i
$493$	−3.66672e21	+	2.11698e21i	−1.05076	+	0.606655i
$494$	5.74041e20	+	9.94269e20i	0.161856	+	0.280342i
$495$	4.58341e21	+	2.64623e21i	1.27159	+	0.734153i
$496$			1.78150e20i			0.0486331i
$497$	1.25896e19	−	1.39895e20i	0.00338190	−	0.0375794i
$498$	3.80680e20			0.100630
$499$	1.07708e21	−	1.86556e21i	0.280185	−	0.485295i	−0.691245	−	0.722620i	$-0.742938\pi$
$499$	1.07708e21	−	1.86556e21i	0.280185	−	0.485295i	0.971430	+	0.237326i	$0.0762708\pi$
$500$	2.81239e21	−	1.62373e21i	0.719971	−	0.415676i
$501$	−1.28076e21	−	2.21835e21i	−0.322677	−	0.558892i
$502$	−1.88145e21	−	1.08625e21i	−0.466511	−	0.269340i
$503$			2.22586e20i			0.0543193i	0.999631	+	0.0271596i	$0.00864624\pi$
$503$			2.22586e20i			0.0543193i	−0.999631	+	0.0271596i	$0.991354\pi$
$504$	3.22583e21	+	2.27072e21i	0.774814	+	0.545405i
$505$	−1.34318e21			−0.317544
$506$	8.12293e19	−	1.40693e20i	0.0189020	−	0.0327393i
$507$	1.44936e21	−	8.36789e20i	0.331981	−	0.191669i
$508$	1.61419e21	+	2.79586e21i	0.363952	+	0.630384i
$509$	7.77789e20	+	4.49056e20i	0.172631	+	0.0996687i	0.583826	−	0.811879i	$-0.301555\pi$
$509$	7.77789e20	+	4.49056e20i	0.172631	+	0.0996687i	−0.411195	+	0.911548i	$0.634888\pi$
$510$			1.74864e21i			0.382067i
$511$	−2.37471e21	−	5.12580e21i	−0.510791	−	1.10254i
$512$	4.09820e21			0.867828
$513$	7.35336e20	−	1.27364e21i	0.153302	−	0.265526i
$514$	−1.48651e21	+	8.58236e20i	−0.305114	+	0.176158i
$515$	−1.45858e21	−	2.52633e21i	−0.294762	−	0.510543i
$516$	−5.36629e21	−	3.09823e21i	−1.06777	−	0.616476i
$517$		−	1.96888e21i		−	0.385741i
$518$	−2.38673e21	+	1.10574e21i	−0.460432	+	0.213312i
$519$	1.39362e22			2.64732
$520$	−1.12222e21	+	1.94375e21i	−0.209919	+	0.363591i
$521$	−2.69712e21	+	1.55718e21i	−0.496819	+	0.286839i	−0.727399	−	0.686215i	$-0.759271\pi$
$521$	−2.69712e21	+	1.55718e21i	−0.496819	+	0.286839i	0.230580	+	0.973053i	$0.425938\pi$
$522$	−1.81832e21	−	3.14942e21i	−0.329842	−	0.571303i
$523$	−2.87149e21	−	1.65786e21i	−0.512973	−	0.296165i	0.221082	−	0.975255i	$-0.429041\pi$
$523$	−2.87149e21	−	1.65786e21i	−0.512973	−	0.296165i	−0.734055	+	0.679090i	$0.762374\pi$
$524$			7.85650e21i			1.38223i
$525$	−2.97598e21	+	4.22774e21i	−0.515651	+	0.732545i
$526$	1.94217e21			0.331437
$527$	2.78981e20	−	4.83209e20i	0.0468910	−	0.0812176i
$528$	−7.30914e21	+	4.21993e21i	−1.21003	+	0.698609i
$529$	3.05940e21	+	5.29904e21i	0.498874	+	0.864075i
$530$	−5.42272e18	−	3.13081e18i	−0.000870984	−	0.000502863i
$531$			4.76418e20i			0.0753757i
$532$	4.66401e21	+	4.19729e20i	0.726886	+	0.0654148i
$533$	−5.66330e21			−0.869464
$534$	8.18400e20	−	1.41751e21i	0.123776	−	0.214386i
$535$	2.88540e21	−	1.66589e21i	0.429909	−	0.248208i
$536$	2.27558e21	+	3.94143e21i	0.334022	+	0.578543i
$537$	−9.25300e21	−	5.34222e21i	−1.33810	−	0.772552i
$538$			1.24975e21i			0.178059i
$539$	−4.53074e21	−	1.26433e22i	−0.636003	−	1.77480i
$540$	1.29661e21			0.179332
$541$	4.69416e21	−	8.13052e21i	0.639705	−	1.10800i	−0.345793	−	0.938311i	$-0.612390\pi$
$541$	4.69416e21	−	8.13052e21i	0.639705	−	1.10800i	0.985497	−	0.169690i	$-0.0542767\pi$
$542$	3.90752e21	−	2.25601e21i	0.524694	−	0.302932i
$543$	6.19655e20	+	1.07327e21i	0.0819882	+	0.142008i
$544$	−6.22419e21	−	3.59354e21i	−0.811506	−	0.468523i
$545$			7.41382e20i			0.0952511i
$546$	3.85266e20	−	4.28105e21i	0.0487775	−	0.542013i
$547$	−8.34387e21			−1.04104			−0.520522	−	0.853848i	$-0.674263\pi$
$547$	−8.34387e21			−1.04104			−0.520522	+	0.853848i	$0.674263\pi$
$548$	4.57405e20	−	7.92248e20i	0.0562414	−	0.0974130i
$549$	−1.21744e22	+	7.02887e21i	−1.47526	+	0.851739i
$550$	2.00050e21	+	3.46497e21i	0.238912	+	0.413808i
$551$	−8.28991e21	−	4.78618e21i	−0.975746	−	0.563347i
$552$		−	4.70253e20i		−	0.0545531i
$553$	1.02010e22	+	7.18065e21i	1.16638	+	0.821037i
$554$	6.10504e20			0.0688034
$555$	−5.10750e21	+	8.84645e21i	−0.567368	+	0.982710i
$556$	7.63006e21	−	4.40522e21i	0.835468	−	0.482358i
$557$	−3.18454e21	−	5.51578e21i	−0.343720	−	0.595341i	0.641400	−	0.767206i	$-0.278354\pi$
$557$	−3.18454e21	−	5.51578e21i	−0.343720	−	0.595341i	−0.985120	+	0.171866i	$0.945020\pi$
$558$	4.15038e20	+	2.39622e20i	0.0441585	+	0.0254949i
$559$			8.26072e21i			0.866410i
$560$	1.27620e21	+	2.75468e21i	0.131952	+	0.284818i
$561$	2.64335e22			2.69434
$562$	−2.20115e21	+	3.81251e21i	−0.221187	+	0.383107i
$563$	1.07014e22	−	6.17848e21i	1.06017	−	0.612089i	0.134691	−	0.990888i	$-0.456996\pi$
$563$	1.07014e22	−	6.17848e21i	1.06017	−	0.612089i	0.925479	+	0.378798i	$0.123663\pi$
$564$	−1.28510e21	−	2.22585e21i	−0.125517	−	0.217402i
$565$	9.51971e21	+	5.49621e21i	0.916719	+	0.529268i
$566$			3.34216e21i			0.317318i
$567$	6.93596e21	−	3.21333e21i	0.649295	−	0.300809i
$568$	−3.14637e20			−0.0290418
$569$	−7.28344e21	+	1.26153e22i	−0.662885	+	1.14815i	0.316969	+	0.948436i	$0.397335\pi$
$569$	−7.28344e21	+	1.26153e22i	−0.662885	+	1.14815i	−0.979854	+	0.199715i	$0.935999\pi$
$570$	−3.42376e21	+	1.97671e21i	−0.307259	+	0.177396i
$571$	−6.65129e21	−	1.15204e22i	−0.588596	−	1.01948i	−0.994417	−	0.105525i	$-0.966348\pi$
$571$	−6.65129e21	−	1.15204e22i	−0.588596	−	1.01948i	0.405821	−	0.913953i	$-0.366986\pi$
$572$	1.32510e22	+	7.65049e21i	1.15633	+	0.667607i
$573$		−	1.21700e21i		−	0.104726i
$574$	2.89059e21	−	4.10643e21i	0.245296	−	0.348473i
$575$	3.40065e20			0.0284590
$576$	−6.13818e20	+	1.06316e21i	−0.0506594	+	0.0877446i
$577$	−1.59722e21	+	9.22154e20i	−0.130004	+	0.0750580i	−0.563592	−	0.826053i	$-0.690581\pi$
$577$	−1.59722e21	+	9.22154e20i	−0.130004	+	0.0750580i	0.433587	+	0.901112i	$0.357248\pi$
$578$	−2.22573e20	−	3.85507e20i	−0.0178669	−	0.0309464i
$579$	7.79442e19	+	4.50011e19i	0.00617100	+	0.00356283i
$580$		−	8.43940e21i		−	0.659004i
$581$	−2.06168e21	−	1.85537e20i	−0.158786	−	0.0142896i
$582$	−1.16440e22			−0.884543
$583$	−4.73271e19	+	8.19730e19i	−0.00354619	+	0.00614218i
$584$	−1.09590e22	+	6.32718e21i	−0.809969	+	0.467636i
$585$	−4.60519e21	−	7.97643e21i	−0.335738	−	0.581516i
$586$	6.44549e21	+	3.72131e21i	0.463527	+	0.267618i
$587$			1.23668e22i			0.877310i	0.898656	+	0.438655i	$0.144545\pi$
$587$			1.23668e22i			0.877310i	−0.898656	+	0.438655i	$0.855455\pi$
$588$	−1.33744e22	−	1.13362e22i	−0.935955	−	0.793320i
$589$	1.26147e21			0.0870872
$590$	1.20177e20	−	2.08152e20i	0.00818472	−	0.0141763i
$591$	1.95551e21	−	1.12902e21i	0.131389	−	0.0758577i
$592$	−4.49417e21	−	7.78414e21i	−0.297904	−	0.515985i
$593$	−8.69587e21	−	5.02057e21i	−0.568690	−	0.328333i	0.187936	−	0.982181i	$-0.439820\pi$
$593$	−8.69587e21	−	5.02057e21i	−0.568690	−	0.328333i	−0.756626	+	0.653848i	$0.773154\pi$
$594$			4.26101e21i			0.274929i
$595$	8.52259e20	−	9.47025e21i	0.0542545	−	0.602873i
$596$	3.19051e21			0.200396
$597$	1.29322e22	−	2.23992e22i	0.801452	−	1.38816i
$598$	−2.44846e20	+	1.41362e20i	−0.0149721	+	0.00864417i
$599$	1.04153e22	+	1.80398e22i	0.628429	+	1.08847i	0.987867	+	0.155302i	$0.0496351\pi$
$599$	1.04153e22	+	1.80398e22i	0.628429	+	1.08847i	−0.359438	+	0.933169i	$0.617032\pi$
$600$	1.00297e22	+	5.79066e21i	0.597144	+	0.344761i
$601$		−	4.39392e21i		−	0.258141i	−0.991635	−	0.129070i	$-0.958801\pi$
$601$		−	4.39392e21i		−	0.258141i	0.991635	−	0.129070i	$-0.0411993\pi$
$602$	−5.98981e21	−	4.21633e21i	−0.347249	−	0.244435i
$603$	−1.86764e22			−1.06845
$604$	−8.44399e21	+	1.46254e22i	−0.476708	+	0.825682i
$605$	−2.51204e22	+	1.45033e22i	−1.39954	+	0.808023i
$606$	−2.88108e21	−	4.99018e21i	−0.158407	−	0.274369i
$607$	2.83342e21	+	1.63587e21i	0.153745	+	0.0887647i	0.574899	−	0.818225i	$-0.305041\pi$
$607$	2.83342e21	+	1.63587e21i	0.153745	+	0.0887647i	−0.421154	+	0.906989i	$0.638375\pi$
$608$		−	1.62489e22i		−	0.870153i
$609$	1.50652e22	+	3.25181e22i	0.796226	+	1.71865i
$610$	7.09214e21			0.369946
$611$	−1.71321e21	+	2.96736e21i	−0.0882024	+	0.152771i
$612$	1.64890e22	−	9.51994e21i	0.837883	−	0.483752i
$613$	−5.63250e21	−	9.75577e21i	−0.282499	−	0.489303i	0.689500	−	0.724285i	$-0.257830\pi$
$613$	−5.63250e21	−	9.75577e21i	−0.282499	−	0.489303i	−0.972000	+	0.234982i	$0.924497\pi$
$614$	1.78257e21	+	1.02917e21i	0.0882472	+	0.0509495i
$615$		−	1.95016e22i		−	0.952946i
$616$	−2.72978e22	+	1.26467e22i	−1.31669	+	0.610002i
$617$	−3.49209e22			−1.66266			−0.831332	−	0.555776i	$-0.812421\pi$
$617$	−3.49209e22			−1.66266			−0.831332	+	0.555776i	$0.812421\pi$
$618$	6.25719e21	−	1.08378e22i	0.294084	−	0.509369i
$619$	3.52805e22	−	2.03692e22i	1.63685	−	0.945038i	0.654946	−	0.755676i	$-0.272691\pi$
$619$	3.52805e22	−	2.03692e22i	1.63685	−	0.945038i	0.981907	−	0.189362i	$-0.0606420\pi$
$620$	5.56082e20	+	9.63163e20i	0.0254686	+	0.0441130i
$621$	3.13643e20	+	1.81082e20i	0.0141809	+	0.00818734i
$622$		−	6.93686e21i		−	0.309628i
$623$	−5.12314e21	+	7.27804e21i	−0.225752	+	0.320708i
$624$	1.46878e22			0.638968
$625$	4.71915e20	−	8.17381e20i	0.0202686	−	0.0351062i
$626$	−7.73396e21	+	4.46521e21i	−0.327950	+	0.189342i
$627$	2.98811e22	+	5.17556e22i	1.25100	+	2.16679i
$628$	−2.70093e22	−	1.55938e22i	−1.11644	−	0.644578i
$629$			2.81513e22i			1.14893i
$630$	8.13419e21	+	7.32023e20i	0.327786	+	0.0294985i
$631$	−7.06307e21			−0.281034			−0.140517	−	0.990078i	$-0.544876\pi$
$631$	−7.06307e21			−0.281034			−0.140517	+	0.990078i	$0.544876\pi$
$632$	1.39721e22	−	2.42004e22i	0.548940	−	0.950792i
$633$	3.62926e22	−	2.09536e22i	1.40795	−	0.812883i
$634$	1.23446e21	+	2.13815e21i	0.0472893	+	0.0819074i
$635$	1.28348e22	+	7.41018e21i	0.485511	+	0.280310i
$636$			1.23562e20i			0.00461561i
$637$	−4.17303e21	+	2.29974e22i	−0.153934	+	0.848329i
$638$	2.77342e22			1.01030
$639$	6.45578e20	−	1.11817e21i	0.0232243	−	0.0402256i
$640$	1.56399e22	−	9.02972e21i	0.555642	−	0.320800i
$641$	1.52378e21	+	2.63927e21i	0.0534637	+	0.0926018i	0.891519	−	0.452984i	$-0.149641\pi$
$641$	1.52378e21	+	2.63927e21i	0.0534637	+	0.0926018i	−0.838055	+	0.545586i	$0.816307\pi$
$642$	1.23782e22	+	7.14654e21i	0.428920	+	0.247637i
$643$		−	1.08917e22i		−	0.372741i	−0.982480	−	0.186370i	$-0.940328\pi$
$643$		−	1.08917e22i		−	0.372741i	0.982480	−	0.186370i	$-0.0596724\pi$
$644$	−1.03362e20	+	1.14855e21i	−0.00349359	+	0.0388206i
$645$	−2.84458e22			−0.949599
$646$	−5.44758e21	+	9.43549e21i	−0.179615	+	0.311103i
$647$	−2.27563e22	+	1.31384e22i	−0.741085	+	0.427866i	−0.822464	−	0.568818i	$-0.807401\pi$
$647$	−2.27563e22	+	1.31384e22i	−0.741085	+	0.427866i	0.0813786	+	0.996683i	$0.474068\pi$
$648$	−8.56161e21	−	1.48291e22i	−0.275395	−	0.476997i
$649$	−3.14655e21	−	1.81666e21i	−0.0999715	−	0.0577186i
$650$		−	6.96289e21i		−	0.218516i
$651$	−3.86200e21	−	2.71853e21i	−0.119719	−	0.0842726i
$652$	−6.97531e21			−0.213591
$653$	2.13857e22	−	3.70412e22i	0.646873	−	1.12042i	−0.336993	−	0.941507i	$-0.609410\pi$
$653$	2.13857e22	−	3.70412e22i	0.646873	−	1.12042i	0.983866	−	0.178909i	$-0.0572568\pi$
$654$	−2.75437e21	+	1.59024e21i	−0.0823002	+	0.0475160i
$655$	1.80332e22	+	3.12345e22i	0.532284	+	0.921942i
$656$	1.48608e22	+	8.57987e21i	0.433322	+	0.250178i
$657$		−	5.19289e22i		−	1.49584i
$658$	−1.27719e21	−	2.75680e21i	−0.0363452	−	0.0784509i
$659$	−3.02669e22			−0.850912			−0.425456	−	0.904979i	$-0.639886\pi$
$659$	−3.02669e22			−0.850912			−0.425456	+	0.904979i	$0.639886\pi$
$660$	−2.63445e22	+	4.56299e22i	−0.731708	+	1.26736i
$661$	−6.03560e22	+	3.48465e22i	−1.65618	+	0.956198i	−0.681732	+	0.731602i	$0.738773\pi$
$661$	−6.03560e22	+	3.48465e22i	−1.65618	+	0.956198i	−0.974452	+	0.224596i	$0.927894\pi$
$662$	−4.70716e21	−	8.15303e21i	−0.127613	−	0.221032i
$663$	−3.98387e22	−	2.30009e22i	−1.06708	−	0.616079i
$664$			4.63691e21i			0.122711i
$665$	1.95057e22	−	9.03673e21i	0.510022	−	0.236286i
$666$	−2.41798e22			−0.624681
$667$	1.17863e21	−	2.04145e21i	0.0300865	−	0.0521114i
$668$	1.21858e22	−	7.03549e21i	0.307357	−	0.177453i
$669$	−1.78552e22	−	3.09261e22i	−0.444996	−	0.770755i
$670$	8.15990e21	+	4.71112e21i	0.200949	+	0.116018i
$671$		−	1.07209e23i		−	2.60886i
$672$	−3.50173e22	+	4.97463e22i	−0.842031	+	1.19621i
$673$	6.64222e22			1.57831			0.789155	−	0.614194i	$-0.210519\pi$
$673$	6.64222e22			1.57831			0.789155	+	0.614194i	$0.210519\pi$
$674$	−4.74353e21	+	8.21604e21i	−0.111384	+	0.192923i
$675$	−7.72436e21	+	4.45966e21i	−0.179239	+	0.103484i
$676$	4.59665e21	+	7.96162e21i	0.105407	+	0.182569i
$677$	5.82536e22	+	3.36327e22i	1.32012	+	0.762171i	0.983747	−	0.179558i	$-0.0574667\pi$
$677$	5.82536e22	+	3.36327e22i	1.32012	+	0.762171i	0.336372	+	0.941729i	$0.390800\pi$
$678$			4.71567e22i			1.05610i
$679$	6.30614e22	+	5.67510e21i	1.39574	+	0.125607i
$680$	−2.12995e22			−0.465906
$681$	−2.74860e22	+	4.76071e22i	−0.594202	+	1.02919i
$682$	−3.16522e21	+	1.82744e21i	−0.0676283	+	0.0390452i
$683$	−1.52604e22	−	2.64317e22i	−0.322255	−	0.558161i	0.658698	−	0.752407i	$-0.271107\pi$
$683$	−1.52604e22	−	2.64317e22i	−0.322255	−	0.558161i	−0.980953	+	0.194246i	$0.937774\pi$
$684$	3.72792e22	+	2.15232e22i	0.778069	+	0.449218i
$685$		−	4.19957e21i		−	0.0866324i
$686$	−1.45454e22	−	1.47639e22i	−0.296574	−	0.301029i
$687$	−1.03862e23			−2.09316
$688$	1.25150e22	−	2.16765e22i	0.249300	−	0.431800i
$689$	1.42656e20	−	8.23626e19i	0.00280891	−	0.00162172i
$690$	−4.86780e20	−	8.43128e20i	−0.00947415	−	0.0164097i
$691$	9.49049e21	+	5.47934e21i	0.182585	+	0.105415i	0.588507	−	0.808492i	$-0.299716\pi$
$691$	9.49049e21	+	5.47934e21i	0.182585	+	0.105415i	−0.405922	+	0.913908i	$0.633049\pi$
$692$			7.65546e22i			1.45587i
$693$	1.10657e22	−	1.22961e23i	0.208023	−	2.31154i
$694$	−1.02930e22			−0.191279
$695$	2.02228e22	−	3.50270e22i	0.371504	−	0.643464i
$696$	6.95241e22	−	4.01398e22i	1.26259	−	0.728955i
$697$	−2.68720e22	−	4.65437e22i	−0.482434	−	0.835600i
$698$	1.52058e22	+	8.77905e21i	0.269876	+	0.155813i
$699$			9.39405e22i			1.64830i
$700$	−2.32238e22	−	1.63477e22i	−0.402856	−	0.283577i
$701$	1.13800e23			1.95164			0.975821	−	0.218573i	$-0.0701401\pi$
$701$	1.13800e23			1.95164			0.975821	+	0.218573i	$0.0701401\pi$
$702$	3.70768e21	−	6.42190e21i	0.0628645	−	0.108885i
$703$	−5.51191e22	+	3.18230e22i	−0.923973	+	0.533456i
$704$	−4.68118e21	−	8.10804e21i	−0.0775843	−	0.134380i
$705$	−1.02181e22	−	5.89943e21i	−0.167439	−	0.0966712i
$706$		−	2.60832e22i		−	0.422594i
$707$	1.31711e22	+	2.84298e22i	0.210993	+	0.455427i
$708$	−4.74296e21			−0.0751248
$709$	−1.46085e22	+	2.53026e22i	−0.228789	+	0.396274i	−0.957449	−	0.288601i	$-0.906810\pi$
$709$	−1.46085e22	+	2.53026e22i	−0.228789	+	0.396274i	0.728660	+	0.684875i	$0.240143\pi$
$710$	−5.64120e20	+	3.25695e20i	−0.00873584	+	0.00504364i
$711$	5.73364e22	+	9.93096e22i	0.877958	+	1.52067i
$712$	1.72661e22	+	9.96859e21i	0.261429	+	0.150936i
$713$			3.10646e20i			0.00465104i
$714$	3.70118e22	−	1.71470e22i	0.547967	−	0.253865i
$715$	7.02415e22			1.02836
$716$	2.93459e22	−	5.08285e22i	0.424857	−	0.735874i
$717$	3.95032e22	−	2.28072e22i	0.565561	−	0.326527i
$718$	−4.26520e21	−	7.38754e21i	−0.0603870	−	0.104593i
$719$	−8.15211e22	−	4.70662e22i	−1.14140	−	0.658989i	−0.194625	−	0.980878i	$-0.562349\pi$
$719$	−8.15211e22	−	4.70662e22i	−1.14140	−	0.658989i	−0.946778	+	0.321889i	$0.895682\pi$
$720$			2.79074e22i			0.386420i
$721$	−3.91697e22	+	5.56452e22i	−0.536374	+	0.761984i
$722$	6.57141e21			0.0889941
$723$	−6.91927e22	+	1.19845e23i	−0.926731	+	1.60515i
$724$	−5.89571e21	+	3.40389e21i	−0.0780957	+	0.0450886i
$725$	2.90272e22	+	5.02766e22i	0.380278	+	0.658661i
$726$	−1.07765e23	−	6.22181e22i	−1.39632	−	0.806164i
$727$			2.86528e22i			0.367191i	0.983002	+	0.183595i	$0.0587736\pi$
$727$			2.86528e22i			0.367191i	−0.983002	+	0.183595i	$0.941226\pi$
$728$	5.21458e22	+	4.69277e21i	0.660949	+	0.0594810i
$729$	1.11383e23			1.39636
$730$	−1.30991e22	+	2.26883e22i	−0.162427	+	0.281332i
$731$	−6.78905e22	+	3.91966e22i	−0.832664	+	0.480739i
$732$	−6.99756e22	−	1.21201e23i	−0.848903	−	1.47034i
$733$	−1.06864e23	−	6.16980e22i	−1.28233	−	0.740353i	−0.305056	−	0.952334i	$-0.598675\pi$
$733$	−1.06864e23	−	6.16980e22i	−1.28233	−	0.740353i	−0.977274	+	0.211981i	$0.932009\pi$
$734$			2.41623e22i			0.286794i
$735$	−7.91917e22	−	1.43698e22i	−0.929781	−	0.168714i
$736$	4.00142e21			0.0464720
$737$	7.12160e22	−	1.23350e23i	0.818159	−	1.41709i
$738$	3.99773e22	−	2.30809e22i	0.454321	−	0.262302i
$739$	−4.51631e22	−	7.82248e22i	−0.507724	−	0.879405i	−0.999960	−	0.00894254i	$-0.997153\pi$
$739$	−4.51631e22	−	7.82248e22i	−0.507724	−	0.879405i	0.492236	−	0.870462i	$-0.336180\pi$
$740$	−4.85953e22	−	2.80565e22i	−0.540431	−	0.312018i
$741$		−	1.04003e23i		−	1.14420i
$742$	−1.30920e19	+	1.45478e20i	−0.000142487	+	0.00158331i
$743$	−4.09482e22			−0.440884			−0.220442	−	0.975400i	$-0.570750\pi$
$743$	−4.09482e22			−0.440884			−0.220442	+	0.975400i	$0.570750\pi$
$744$	−5.28971e21	+	9.16205e21i	−0.0563441	+	0.0975909i
$745$	1.26842e22	−	7.32325e21i	0.133664	−	0.0771710i
$746$	−1.03287e22	−	1.78898e22i	−0.107680	−	0.186507i
$747$	−1.64789e22	−	9.51410e21i	−0.169967	−	0.0981303i
$748$			1.45204e23i			1.48172i
$749$	−6.35542e22	−	4.47369e22i	−0.641638	−	0.451660i
$750$	6.39542e22			0.638820
$751$	−2.25552e22	+	3.90668e22i	−0.222909	+	0.386090i	−0.955690	−	0.294375i	$-0.904889\pi$
$751$	−2.25552e22	+	3.90668e22i	−0.222909	+	0.386090i	0.732781	+	0.680464i	$0.238222\pi$
$752$	8.99108e21	−	5.19100e21i	0.0879162	−	0.0507585i
$753$	9.84022e22	+	1.70438e23i	0.952018	+	1.64894i
$754$	−4.17991e22	−	2.41327e22i	−0.400125	−	0.231012i
$755$			7.75268e22i			0.734305i
$756$	−1.27144e22	−	2.74440e22i	−0.119158	−	0.257201i
$757$	8.91608e21			0.0826812			0.0413406	−	0.999145i	$-0.486837\pi$
$757$	8.91608e21			0.0826812			0.0413406	+	0.999145i	$0.486837\pi$
$758$	2.04275e21	−	3.53815e21i	0.0187440	−	0.0324656i
$759$	−1.27452e22	+	7.35845e21i	−0.115721	+	0.0668117i
$760$	−2.40775e22	−	4.17035e22i	−0.216323	−	0.374683i
$761$	1.71759e23	+	9.91649e22i	1.52701	+	0.881618i	0.999485	+	0.0320773i	$0.0102123\pi$
$761$	1.71759e23	+	9.91649e22i	1.52701	+	0.881618i	0.527522	+	0.849541i	$0.323121\pi$
$762$			6.35782e22i			0.559331i
$763$	1.56921e22	−	7.26993e21i	0.136611	−	0.0632898i
$764$	6.68523e21			0.0575930
$765$	4.37027e22	−	7.56953e22i	0.372578	−	0.645324i
$766$	3.60710e21	−	2.08256e21i	0.0304318	−	0.0175698i
$767$	3.16150e21	+	5.47588e21i	0.0263955	+	0.0457184i
$768$	5.42089e22	+	3.12975e22i	0.447899	+	0.258595i
$769$			2.58803e22i			0.211621i	0.994386	+	0.105810i	$0.0337436\pi$
$769$			2.58803e22i			0.211621i	−0.994386	+	0.105810i	$0.966256\pi$
$770$	−3.58517e22	+	5.09317e22i	−0.290125	+	0.412157i
$771$	1.55493e23			1.24530
$772$	−2.47200e20	+	4.28163e20i	−0.00195934	+	0.00339368i
$773$	−2.02267e23	+	1.16779e23i	−1.58668	+	0.916067i	−0.592825	+	0.805331i	$0.701988\pi$
$773$	−2.02267e23	+	1.16779e23i	−1.58668	+	0.916067i	−0.993850	+	0.110736i	$0.964679\pi$
$774$	−3.36668e22	−	5.83126e22i	−0.261381	−	0.452725i
$775$	−6.62557e21	−	3.82528e21i	−0.0509108	−	0.0293934i
$776$		−	1.41831e23i		−	1.07864i
$777$	2.37328e23	+	2.13579e22i	1.78641	+	0.160765i
$778$	8.85391e22			0.659627
$779$	6.07536e22	−	1.05228e23i	0.447994	−	0.775949i
$780$	7.94091e22	−	4.58468e22i	0.579580	−	0.334621i
$781$	4.92339e21	+	8.52756e21i	0.0355677	+	0.0616051i
$782$	−2.32356e21	−	1.34151e21i	−0.0166150	−	0.00959267i
$783$			6.18271e22i			0.437607i
$784$	4.57912e22	−	5.40243e22i	0.320814	−	0.378495i
$785$	−1.43172e23			−0.992886
$786$	−7.73612e22	+	1.33994e23i	−0.531059	+	0.919822i
$787$	7.48998e22	−	4.32434e22i	0.508959	−	0.293848i	−0.223446	−	0.974716i	$-0.571731\pi$
$787$	7.48998e22	−	4.32434e22i	0.508959	−	0.293848i	0.732406	+	0.680868i	$0.238397\pi$
$788$	6.20190e21	+	1.07420e22i	0.0417172	+	0.0722563i
$789$	−1.52367e23	−	8.79693e22i	−1.01455	−	0.585754i
$790$		−	5.78526e22i		−	0.381334i
$791$	2.29834e22	−	2.55390e23i	0.149969	−	1.66645i
$792$	−2.76552e23			−1.78638
$793$	−9.32870e22	+	1.61578e23i	−0.596535	+	1.03323i
$794$	−4.70976e22	+	2.71918e22i	−0.298150	+	0.172137i
$795$	2.83616e20	+	4.91237e20i	0.00177743	+	0.00307860i
$796$	1.23043e23	+	7.10391e22i	0.763402	+	0.440750i
$797$			4.24672e22i			0.260848i	0.991458	+	0.130424i	$0.0416338\pi$
$797$			4.24672e22i			0.260848i	−0.991458	+	0.130424i	$0.958366\pi$
$798$	7.54122e22	+	5.30840e22i	0.458584	+	0.322805i
$799$	−3.25162e22			−0.195761
$800$	−4.92732e22	+	8.53437e22i	−0.293691	+	0.508688i
$801$	−7.08539e22	+	4.09075e22i	−0.418122	+	0.241403i
$802$	2.36066e21	+	4.08878e21i	0.0137924	+	0.0238891i
$803$	3.42970e23	+	1.98014e23i	1.98395	+	1.14544i
$804$		−	1.85932e23i		−	1.06489i
$805$	2.22536e21	+	4.80344e21i	0.0126193	+	0.0272386i
$806$	6.36053e21			0.0357119
$807$	5.66066e22	−	9.80455e22i	0.314687	−	0.545054i
$808$	6.07833e22	−	3.50932e22i	0.334575	−	0.193167i
$809$	2.63447e22	+	4.56303e22i	0.143583	+	0.248694i	0.928844	−	0.370472i	$-0.120804\pi$
$809$	2.63447e22	+	4.56303e22i	0.143583	+	0.248694i	−0.785260	+	0.619166i	$0.787471\pi$
$810$	−3.07006e22	−	1.77250e22i	−0.165679	−	0.0956547i
$811$		−	1.92130e23i		−	1.02667i	−0.858190	−	0.513333i	$-0.828411\pi$
$811$		−	1.92130e23i		−	1.02667i	0.858190	−	0.513333i	$-0.171589\pi$
$812$	−1.78629e23	+	8.27561e22i	−0.945154	+	0.437876i
$813$	−4.08737e23			−2.14151
$814$	9.22014e22	−	1.59698e23i	0.478346	−	0.828520i
$815$	−2.77312e22	+	1.60106e22i	−0.142465	+	0.0822520i
$816$	6.96925e22	+	1.20711e23i	0.354540	+	0.614081i
$817$	−1.53490e23	−	8.86177e22i	−0.773223	−	0.446421i
$818$			7.66752e22i			0.382497i
$819$	−1.23671e23	+	1.75690e23i	−0.610938	+	0.867911i
$820$	1.07126e23			0.524063
$821$	−1.06790e23	+	1.84966e23i	−0.517352	+	0.896080i	0.482445	+	0.875926i	$0.339749\pi$
$821$	−1.06790e23	+	1.84966e23i	−0.517352	+	0.896080i	−0.999797	+	0.0201539i	$0.993584\pi$
$822$	1.56022e22	−	9.00793e21i	0.0748533	−	0.0432166i
$823$	−1.43788e23	−	2.49048e23i	−0.683162	−	1.18327i	−0.974011	−	0.226503i	$-0.927271\pi$
$823$	−1.43788e23	−	2.49048e23i	−0.683162	−	1.18327i	0.290848	−	0.956769i	$-0.406063\pi$
$824$	1.32010e23	+	7.62163e22i	0.621142	+	0.358616i
$825$		−	3.62446e23i		−	1.68893i
$826$	−5.58419e21	−	5.02539e20i	−0.0257703	−	0.00231915i
$827$	−4.20386e22			−0.192134			−0.0960671	−	0.995375i	$-0.530626\pi$
$827$	−4.20386e22			−0.192134			−0.0960671	+	0.995375i	$0.530626\pi$
$828$	−5.30025e21	+	9.18030e21i	−0.0239913	+	0.0415541i
$829$	1.83870e23	−	1.06158e23i	0.824281	−	0.475899i	−0.0276092	−	0.999619i	$-0.508789\pi$
$829$	1.83870e23	−	1.06158e23i	0.824281	−	0.475899i	0.851891	+	0.523720i	$0.175456\pi$
$830$	4.79987e21	+	8.31363e21i	0.0213111	+	0.0369118i
$831$	−4.78953e22	−	2.76523e22i	−0.210613	−	0.121597i
$832$			1.62932e22i			0.0709609i
$833$	−2.08805e23	+	7.48255e22i	−0.900700	+	0.322768i
$834$	1.73509e23			0.741299
$835$	3.22975e22	−	5.59409e22i	0.136671	−	0.236721i
$836$	−2.84304e23	+	1.64143e23i	−1.19161	+	0.687974i
$837$	−4.07386e21	−	7.05613e21i	−0.0169123	−	0.0292929i
$838$	−4.01012e22	−	2.31524e22i	−0.164894	−	0.0952016i
$839$			1.31044e23i			0.533732i	0.963734	+	0.266866i	$0.0859881\pi$
$839$			1.31044e23i			0.533732i	−0.963734	+	0.266866i	$0.914012\pi$
$840$	−1.61595e22	+	1.79564e23i	−0.0651921	+	0.724411i
$841$	1.52176e23			0.608103
$842$	−6.92135e21	+	1.19881e22i	−0.0273964	+	0.0474520i
$843$	3.45370e23	−	1.99399e23i	1.35414	−	0.781813i
$844$	1.15102e23	+	1.99363e23i	0.447037	+	0.774291i
$845$	3.65490e22	+	2.11016e22i	0.140612	+	0.0811824i
$846$		−	2.79289e22i		−	0.106437i
$847$	5.53306e23	+	3.89482e23i	2.08881	+	1.47035i
$848$	−4.99116e20			−0.00186653
$849$	1.51381e23	−	2.62199e23i	0.560801	−	0.971336i
$850$	5.72243e22	−	3.30385e22i	0.210005	−	0.121246i
$851$	−7.83666e21	−	1.35735e22i	−0.0284901	−	0.0493464i
$852$	1.11319e22	+	6.42703e21i	0.0400916	+	0.0231469i
$853$			5.30719e22i			0.189353i	0.995508	+	0.0946765i	$0.0301817\pi$
$853$			5.30719e22i			0.189353i	−0.995508	+	0.0946765i	$0.969818\pi$
$854$	−6.95449e22	−	1.50112e23i	−0.245812	−	0.530583i
$855$	1.97611e23			0.691961
$856$	−8.70491e22	+	1.50773e23i	−0.301977	+	0.523040i
$857$	3.84031e23	−	2.21720e23i	1.31983	−	0.762007i	0.336133	−	0.941815i	$-0.390881\pi$
$857$	3.84031e23	−	2.21720e23i	1.31983	−	0.762007i	0.983702	+	0.179808i	$0.0575477\pi$
$858$	1.50665e23	+	2.60960e23i	0.512997	+	0.888538i
$859$	−3.25805e23	−	1.88103e23i	−1.09904	−	0.634529i	−0.163069	−	0.986615i	$-0.552139\pi$
$859$	−3.25805e23	−	1.88103e23i	−1.09904	−	0.634529i	−0.935968	+	0.352086i	$0.885473\pi$
$860$		−	1.56258e23i		−	0.522222i
$861$	−4.12770e23	+	1.91231e23i	−1.36673	+	0.633187i
$862$	−2.33771e23			−0.766890
$863$	2.71848e23	−	4.70854e23i	0.883567	−	1.53038i	0.0362202	−	0.999344i	$-0.488468\pi$
$863$	2.71848e23	−	4.70854e23i	0.883567	−	1.53038i	0.847347	−	0.531040i	$-0.178198\pi$
$864$	−9.08897e22	+	5.24752e22i	−0.292688	+	0.168983i
$865$	1.75718e23	+	3.04352e23i	0.560643	+	0.971062i
$866$	−6.65558e21	−	3.84260e21i	−0.0210399	−	0.0121474i
$867$			4.03251e22i			0.126306i
$868$	1.49334e22	−	2.12147e22i	0.0463449	−	0.0658385i
$869$	−8.74533e23			−2.68917
$870$	8.31009e22	−	1.43935e23i	0.253193	−	0.438543i
$871$	−2.14664e23	+	1.23936e23i	−0.648057	+	0.374156i
$872$	−1.93700e22	−	3.35499e22i	−0.0579427	−	0.100360i
$873$	5.04047e23	+	2.91012e23i	1.49402	+	0.862574i
$874$		−	6.06591e21i		−	0.0178158i
$875$	−3.46361e23	−	3.11702e22i	−1.00801	−	0.0907141i
$876$	5.16977e23			1.49086
$877$	−1.19137e23	+	2.06352e23i	−0.340448	+	0.589673i	−0.984516	−	0.175295i	$-0.943912\pi$
$877$	−1.19137e23	+	2.06352e23i	−0.340448	+	0.589673i	0.644068	+	0.764968i	$0.277245\pi$
$878$	−4.82810e22	+	2.78750e22i	−0.136716	+	0.0789331i
$879$	−3.37108e23	−	5.83888e23i	−0.945928	−	1.63840i
$880$	−1.84317e23	−	1.06416e23i	−0.512512	−	0.295899i
$881$			6.10607e23i			1.68250i	0.540647	+	0.841249i	$0.318179\pi$
$881$			6.10607e23i			1.68250i	−0.540647	+	0.841249i	$0.681821\pi$
$882$	−6.42692e22	−	1.79347e23i	−0.175491	−	0.489716i
$883$	−2.30245e23			−0.623023			−0.311512	−	0.950242i	$-0.600835\pi$
$883$	−2.30245e23			−0.623023			−0.311512	+	0.950242i	$0.600835\pi$
$884$	1.26348e23	−	2.18842e23i	0.338807	−	0.586830i
$885$	−1.88562e22	+	1.08866e22i	−0.0501081	+	0.0289299i
$886$	1.19811e23	+	2.07518e23i	0.315519	+	0.546496i
$887$	4.73333e23	+	2.73279e23i	1.23532	+	0.713210i	0.968133	−	0.250436i	$-0.0805738\pi$
$887$	4.73333e23	+	2.73279e23i	1.23532	+	0.713210i	0.267183	+	0.963646i	$0.413907\pi$
$888$		−	5.33773e23i		−	1.38055i
$889$	3.09869e22	−	3.44325e23i	0.0794263	−	0.882581i
$890$	4.12757e22			0.104852
$891$	−2.67942e23	+	4.64088e23i	−0.674557	+	1.16837i
$892$	1.69883e23	−	9.80822e22i	0.423869	−	0.244721i
$893$	−3.67572e22	−	6.36654e22i	−0.0908931	−	0.157431i
$894$	5.44145e22	+	3.14162e22i	0.133357	+	0.0769935i
$895$		−	2.69433e23i		−	0.654436i
$896$	−3.44487e23	−	2.42490e23i	−0.829294	−	0.583755i
$897$	2.56116e22			0.0611079
$898$	−3.69324e22	+	6.39689e22i	−0.0873368	+	0.151272i
$899$	−4.59272e22	+	2.65161e22i	−0.107645	+	0.0621486i
$900$	−1.30534e23	−	2.26091e23i	−0.303237	−	0.525222i
$901$	1.35379e21	+	7.81611e20i	0.00311712	+	0.00179967i
$902$			3.52045e23i			0.803427i
$903$	2.78937e23	+	6.02084e23i	0.630963	+	1.36193i
$904$	−5.74396e23			−1.28785
$905$	−1.56261e22	+	2.70651e22i	−0.0347265	+	0.0601480i
$906$	−2.88027e23	+	1.66292e23i	−0.634464	+	0.366308i
$907$	−1.31069e23	−	2.27018e23i	−0.286181	−	0.495681i	0.686714	−	0.726928i	$-0.259053\pi$
$907$	−1.31069e23	−	2.27018e23i	−0.286181	−	0.495681i	−0.972895	+	0.231247i	$0.925719\pi$
$908$	−2.61515e23	−	1.50986e23i	−0.565992	−	0.326776i
$909$			2.88020e23i			0.617891i
$910$	9.83511e22	−	4.55647e22i	0.209145	−	0.0968940i
$911$	9.33966e23			1.96872			0.984361	−	0.176165i	$-0.0563693\pi$
$911$	9.33966e23			1.96872			0.984361	+	0.176165i	$0.0563693\pi$
$912$	−1.57564e23	+	2.72910e23i	−0.329230	+	0.570243i
$913$	1.25674e23	−	7.25577e22i	0.260302	−	0.150286i
$914$	−1.06581e23	−	1.84604e23i	−0.218832	−	0.379029i
$915$	−5.56393e23	−	3.21234e23i	−1.13243	−	0.653811i
$916$		−	5.70535e23i		−	1.15111i
$917$	4.84277e23	−	6.87974e23i	0.968588	−	1.37600i
$918$	7.03709e22			0.139525
$919$	−1.77247e23	+	3.07001e23i	−0.348381	+	0.603414i	−0.985962	−	0.166970i	$-0.946602\pi$
$919$	−1.77247e23	+	3.07001e23i	−0.348381	+	0.603414i	0.637581	+	0.770383i	$0.279935\pi$
$920$	1.02698e22	−	5.92927e21i	0.0200106	−	0.0115531i
$921$	−9.32311e22	−	1.61481e23i	−0.180088	−	0.311921i
$922$	−7.97689e22	−	4.60546e22i	−0.152752	−	0.0881913i
$923$		−	1.71362e22i		−	0.0325312i
$924$	1.22414e24	+	1.10164e23i	2.30385	+	0.207331i
$925$	3.86000e23			0.720201
$926$	4.15635e22	−	7.19901e22i	0.0768819	−	0.133163i
$927$	−5.41723e23	+	3.12764e23i	−0.993435	+	0.573560i
$928$	3.41552e23	+	5.91586e23i	0.620974	+	1.07556i
$929$	5.99198e23	+	3.45947e23i	1.08005	+	0.623568i	0.930910	−	0.365248i	$-0.119016\pi$
$929$	5.99198e23	+	3.45947e23i	1.08005	+	0.623568i	0.149141	+	0.988816i	$0.452349\pi$
$930$			2.19025e22i			0.0391408i
$931$	−3.82543e23	−	3.24245e23i	−0.677771	−	0.574482i
$932$	−5.16034e23			−0.906464
$933$	−3.14200e23	+	5.44211e23i	−0.547209	+	0.947794i
$934$	1.39506e23	−	8.05437e22i	0.240889	−	0.139077i
$935$	3.33291e23	+	5.77278e23i	0.570599	+	0.988307i
$936$	4.16799e23	+	2.40639e23i	0.707490	+	0.408469i
$937$			1.12134e24i			1.88721i	0.331069	+	0.943607i	$0.392591\pi$
$937$			1.12134e24i			1.88721i	−0.331069	+	0.943607i	$0.607409\pi$
$938$	1.97004e22	−	2.18909e23i	0.0328739	−	0.365293i
$939$	8.08994e23			1.33851
$940$	3.24067e22	−	5.61301e22i	0.0531633	−	0.0920816i
$941$	3.64703e23	−	2.10562e23i	0.593229	−	0.342501i	−0.173144	−	0.984897i	$-0.555393\pi$
$941$	3.64703e23	−	2.10562e23i	0.593229	−	0.342501i	0.766373	+	0.642395i	$0.222059\pi$
$942$	−3.07098e23	−	5.31909e23i	−0.495301	−	0.857887i
$943$	2.59133e22	+	1.49610e22i	0.0414409	+	0.0239259i
$944$		−	1.91586e22i		−	0.0303801i
$945$	−1.13541e23	−	7.99232e22i	−0.178524	−	0.125666i
$946$	5.13508e23			0.800605
$947$	5.03097e23	−	8.71389e23i	0.777771	−	1.34714i	−0.155453	−	0.987843i	$-0.549684\pi$
$947$	5.03097e23	−	8.71389e23i	0.777771	−	1.34714i	0.933224	−	0.359295i	$-0.116983\pi$
$948$	−9.88673e23	+	5.70811e23i	−1.51561	+	0.875035i
$949$	−3.44600e23	−	5.96865e23i	−0.523824	−	0.907290i
$950$	1.29376e23	+	7.46951e22i	0.195013	+	0.112591i
$951$		−	2.23656e23i		−	0.334300i
$952$	2.08861e23	+	4.50826e23i	0.309572	+	0.668210i
$953$	3.79547e23			0.557856			0.278928	−	0.960312i	$-0.410021\pi$
$953$	3.79547e23			0.557856			0.278928	+	0.960312i	$0.410021\pi$
$954$	−6.71342e20	+	1.16280e21i	−0.000978491	+	0.00169480i
$955$	2.65780e22	−	1.53448e22i	0.0384144	−	0.0221786i
$956$	1.25284e23	+	2.16999e23i	0.179570	+	0.311025i
$957$	−2.17581e24	−	1.25620e24i	−3.09261	−	1.78552i
$958$			3.83095e23i			0.539986i
$959$	−8.88882e22	+	4.11806e22i	−0.124250	+	0.0575631i
$960$	−5.61055e22			−0.0777742
$961$	−3.60217e23	+	6.23915e23i	−0.495196	+	0.857705i
$962$	−2.77919e23	+	1.60457e23i	−0.378894	+	0.218755i
$963$	−3.57218e23	−	6.18720e23i	−0.482973	−	0.836534i
$964$	−6.58334e23	−	3.80089e23i	−0.882734	−	0.509647i
$965$			2.26962e21i			0.00301810i
$966$	−1.30723e22	+	1.85708e22i	−0.0172400	+	0.0244915i
$967$	−3.42695e23			−0.448225			−0.224112	−	0.974563i	$-0.571948\pi$
$967$	−3.42695e23			−0.448225			−0.224112	+	0.974563i	$0.571948\pi$
$968$	7.57853e23	−	1.31264e24i	0.983065	−	1.70272i
$969$	8.54748e23	−	4.93489e23i	1.09963	−	0.634873i
$970$	−1.46816e23	−	2.54292e23i	−0.187326	−	0.324459i
$971$	−6.74945e22	−	3.89680e22i	−0.0854111	−	0.0493121i	0.456686	−	0.889628i	$-0.349036\pi$
$971$	−6.74945e22	−	3.89680e22i	−0.0854111	−	0.0493121i	−0.542097	+	0.840316i	$0.682370\pi$
$972$			9.25399e23i			1.16145i
$973$	−9.39684e23	−	8.45653e22i	−1.16971	−	0.105266i
$974$	−5.74624e23			−0.709434
$975$	−3.15379e23	+	5.46253e23i	−0.386186	+	0.668893i
$976$	4.89579e23	−	2.82659e23i	0.594599	−	0.343292i
$977$	6.62609e23	+	1.14767e24i	0.798180	+	1.38249i	0.920800	+	0.390034i	$0.127537\pi$
$977$	6.62609e23	+	1.14767e24i	0.798180	+	1.38249i	−0.122620	+	0.992454i	$0.539130\pi$
$978$	−1.18965e23	−	6.86843e22i	−0.142137	−	0.0820629i
$979$		−	6.23948e23i		−	0.739413i
$980$	7.89362e22	−	4.35016e23i	0.0927828	−	0.511324i
$981$	1.58975e23			0.185344
$982$	−2.02006e21	+	3.49885e21i	−0.00233600	+	0.00404607i
$983$	−4.88784e23	+	2.82199e23i	−0.560646	+	0.323689i	−0.753405	−	0.657557i	$-0.771590\pi$
$983$	−4.88784e23	+	2.82199e23i	−0.560646	+	0.323689i	0.192759	+	0.981246i	$0.438257\pi$
$984$	5.09516e23	+	8.82507e23i	0.579691	+	1.00405i
$985$	4.93128e22	+	2.84708e22i	0.0556506	+	0.0321299i
$986$		−	4.58033e23i		−	0.512721i
$987$	−2.46695e22	+	2.74126e23i	−0.0273919	+	0.304378i
$988$	5.71310e23			0.629240
$989$	2.18228e22	−	3.77982e22i	0.0238419	−	0.0412953i
$990$	−4.95836e23	+	2.86271e23i	−0.537349	+	0.310239i
$991$	3.52543e23	+	6.10622e23i	0.378985	+	0.656422i	0.990915	−	0.134490i	$-0.0429398\pi$
$991$	3.52543e23	+	6.10622e23i	0.378985	+	0.656422i	−0.611930	+	0.790912i	$0.709606\pi$
$992$	−7.79606e22	−	4.50106e22i	−0.0831346	−	0.0479978i
$993$			8.52830e23i			0.902128i
$994$	1.24254e22	+	8.74643e21i	0.0130382	+	0.00917783i
$995$	6.52231e23			0.678917
$996$	9.47173e22	−	1.64055e23i	0.0978035	−	0.169401i
$997$	2.64105e23	−	1.52481e23i	0.270530	−	0.156190i	−0.358599	−	0.933492i	$-0.616745\pi$
$997$	2.64105e23	−	1.52481e23i	0.270530	−	0.156190i	0.629128	+	0.777302i	$0.283412\pi$
$998$	1.16520e23	+	2.01818e23i	0.118401	+	0.205076i
$999$	3.56009e23	+	2.05542e23i	0.358870	+	0.207194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.17.d.a.5.5	yes	20
7.2	even	3		49.17.b.a.48.12		20
7.3	odd	6	inner	7.17.d.a.3.5	✓	20
7.5	odd	6		49.17.b.a.48.11		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.17.d.a.3.5	✓	20	7.3	odd	6	inner
7.17.d.a.5.5	yes	20	1.1	even	1	trivial
49.17.b.a.48.11		20	7.5	odd	6
49.17.b.a.48.12		20	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	7.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-54.0903 + 93.6871i) q^{2} +(8486.99 - 4899.97i) q^{3} +(26916.5 + 46620.7i) q^{4} +(214019. + 123564. i) q^{5} +1.06016e6i q^{6} +(516705. - 5.74160e6i) q^{7} -1.29134e7 q^{8} +(2.64960e7 - 4.58924e7i) q^{9} +O(q^{10})\)	\(q+(-54.0903 + 93.6871i) q^{2} +(8486.99 - 4899.97i) q^{3} +(26916.5 + 46620.7i) q^{4} +(214019. + 123564. i) q^{5} +1.06016e6i q^{6} +(516705. - 5.74160e6i) q^{7} -1.29134e7 q^{8} +(2.64960e7 - 4.58924e7i) q^{9} +(-2.31527e7 + 1.33672e7i) q^{10} +(2.02067e8 + 3.49990e8i) q^{11} +(4.56880e8 + 2.63780e8i) q^{12} -7.03308e8i q^{13} +(5.09965e8 + 3.58973e8i) q^{14} +2.42184e9 q^{15} +(-1.06551e9 + 1.84551e9i) q^{16} +(5.78012e9 - 3.33715e9i) q^{17} +(2.86635e9 + 4.96466e9i) q^{18} +(1.30680e10 + 7.54481e9i) q^{19} +1.33036e10i q^{20} +(-2.37484e10 - 5.12607e10i) q^{21} -4.37195e10 q^{22} +(-1.85797e9 + 3.21809e9i) q^{23} +(-1.09596e11 + 6.32752e10i) q^{24} +(-4.57577e10 - 7.92547e10i) q^{25} +(6.58909e10 + 3.80421e10i) q^{26} -9.74625e10i q^{27} +(2.81585e11 - 1.30454e11i) q^{28} -6.34367e11 q^{29} +(-1.30998e11 + 2.26895e11i) q^{30} +(7.23984e10 - 4.17992e10i) q^{31} +(-5.38414e11 - 9.32560e11i) q^{32} +(3.42988e12 + 1.98024e12i) q^{33} +7.22030e11i q^{34} +(8.20041e11 - 1.16497e12i) q^{35} +2.85271e12 q^{36} +(-2.10893e12 + 3.65278e12i) q^{37} +(-1.41370e12 + 8.16202e11i) q^{38} +(-3.44619e12 - 5.96897e12i) q^{39} +(-2.76372e12 - 1.59563e12i) q^{40} -8.05237e12i q^{41} +(6.08703e12 + 5.47791e11i) q^{42} -1.17455e13 q^{43} +(-1.08779e13 + 1.88410e13i) q^{44} +(1.13413e13 - 6.54791e12i) q^{45} +(-2.00996e11 - 3.48135e11i) q^{46} +(-4.21915e12 - 2.43593e12i) q^{47} +2.08838e13i q^{48} +(-3.26990e13 - 5.93343e12i) q^{49} +9.90020e12 q^{50} +(3.27039e13 - 5.66448e13i) q^{51} +(3.27887e13 - 1.89306e13i) q^{52} +(1.17107e11 + 2.02836e11i) q^{53} +(9.13098e12 + 5.27178e12i) q^{54} +9.98730e13i q^{55} +(-6.67242e12 + 7.41436e13i) q^{56} +1.47877e14 q^{57} +(3.43131e13 - 5.94321e13i) q^{58} +(-7.78589e12 + 4.49519e12i) q^{59} +(6.51874e13 + 1.12908e14i) q^{60} +(-2.29740e14 - 1.32640e14i) q^{61} +9.04373e12i q^{62} +(-2.49805e14 - 1.75842e14i) q^{63} -2.31665e13 q^{64} +(8.69037e13 - 1.50522e14i) q^{65} +(-3.71047e14 + 2.14224e14i) q^{66} +(-1.76219e14 - 3.05220e14i) q^{67} +(3.11161e14 + 1.79649e14i) q^{68} +3.64159e13i q^{69} +(6.47862e13 + 1.39841e14i) q^{70} +2.43651e13 q^{71} +(-3.42153e14 + 5.92627e14i) q^{72} +(8.48653e14 - 4.89970e14i) q^{73} +(-2.28146e14 - 3.95160e14i) q^{74} +(-7.76691e14 - 4.48423e14i) q^{75} +8.12319e14i q^{76} +(2.11391e15 - 9.79346e14i) q^{77} +7.45621e14 q^{78} +(-1.08198e15 + 1.87405e15i) q^{79} +(-4.56079e14 + 2.63317e14i) q^{80} +(6.63002e14 + 1.14835e15i) q^{81} +(7.54404e14 + 4.35555e14i) q^{82} -3.59077e14i q^{83} +(1.75059e15 - 2.48692e15i) q^{84} +1.64941e15 q^{85} +(6.35319e14 - 1.10040e15i) q^{86} +(-5.38387e15 + 3.10838e15i) q^{87} +(-2.60937e15 - 4.51957e15i) q^{88} +(-1.33707e15 - 7.71957e14i) q^{89} +1.41671e15i q^{90} +(-4.03811e15 - 3.63403e14i) q^{91} -2.00040e14 q^{92} +(4.09630e14 - 7.09499e14i) q^{93} +(4.56430e14 - 2.63520e14i) q^{94} +(1.86454e15 + 3.22947e15i) q^{95} +(-9.13903e15 - 5.27642e15i) q^{96} +1.09832e16i q^{97} +(2.32458e15 - 2.74253e15i) q^{98} +2.14159e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 92 q^{2} + 6558 q^{3} - 285924 q^{4} + 241890 q^{5} - 1847944 q^{7} + 23873872 q^{8} + 146092512 q^{9}+O(q^{10}) \) 20 * q + 92 * q^2 + 6558 * q^3 - 285924 * q^4 + 241890 * q^5 - 1847944 * q^7 + 23873872 * q^8 + 146092512 * q^9	\( 20 q + 92 q^{2} + 6558 q^{3} - 285924 q^{4} + 241890 q^{5} - 1847944 q^{7} + 23873872 q^{8} + 146092512 q^{9} - 567579804 q^{10} + 487037030 q^{11} - 2240722092 q^{12} + 598121216 q^{14} - 2098975212 q^{15} - 13522996616 q^{16} + 16479299850 q^{17} - 21631627512 q^{18} - 29753076894 q^{19} + 30310552398 q^{21} + 143879888720 q^{22} - 199076938822 q^{23} + 613456300512 q^{24} + 212723266388 q^{25} - 1359419612544 q^{26} + 2531834927748 q^{28} + 438309600272 q^{29} - 2296351012392 q^{30} + 1037434908306 q^{31} - 3523947158064 q^{32} + 411779151054 q^{33} - 7248579242478 q^{35} - 2493315404256 q^{36} + 5318067734218 q^{37} - 9079217417208 q^{38} + 13250117821332 q^{39} + 15010293809208 q^{40} + 16256122433712 q^{42} - 621187489400 q^{43} + 25172272315980 q^{44} - 85040191344096 q^{45} - 15614039192704 q^{46} + 106960600327866 q^{47} - 52978127838580 q^{49} + 35872835226128 q^{50} + 4235281588962 q^{51} + 126484190926632 q^{52} + 29048763888218 q^{53} - 635343594055560 q^{54} + 230352840277168 q^{56} + 366396034764636 q^{57} - 279762037805080 q^{58} - 99092116656282 q^{59} - 173605217618196 q^{60} - 904353032308434 q^{61} + 11\!\cdots\!92 q^{63}+ \cdots + 14\!\cdots\!92 q^{99}+O(q^{100}) \) 20 * q + 92 * q^2 + 6558 * q^3 - 285924 * q^4 + 241890 * q^5 - 1847944 * q^7 + 23873872 * q^8 + 146092512 * q^9 - 567579804 * q^10 + 487037030 * q^11 - 2240722092 * q^12 + 598121216 * q^14 - 2098975212 * q^15 - 13522996616 * q^16 + 16479299850 * q^17 - 21631627512 * q^18 - 29753076894 * q^19 + 30310552398 * q^21 + 143879888720 * q^22 - 199076938822 * q^23 + 613456300512 * q^24 + 212723266388 * q^25 - 1359419612544 * q^26 + 2531834927748 * q^28 + 438309600272 * q^29 - 2296351012392 * q^30 + 1037434908306 * q^31 - 3523947158064 * q^32 + 411779151054 * q^33 - 7248579242478 * q^35 - 2493315404256 * q^36 + 5318067734218 * q^37 - 9079217417208 * q^38 + 13250117821332 * q^39 + 15010293809208 * q^40 + 16256122433712 * q^42 - 621187489400 * q^43 + 25172272315980 * q^44 - 85040191344096 * q^45 - 15614039192704 * q^46 + 106960600327866 * q^47 - 52978127838580 * q^49 + 35872835226128 * q^50 + 4235281588962 * q^51 + 126484190926632 * q^52 + 29048763888218 * q^53 - 635343594055560 * q^54 + 230352840277168 * q^56 + 366396034764636 * q^57 - 279762037805080 * q^58 - 99092116656282 * q^59 - 173605217618196 * q^60 - 904353032308434 * q^61 + 1188663557133192 * q^63 + 2502182430870944 * q^64 - 500211967540404 * q^65 - 951679982792988 * q^66 - 33326890567694 * q^67 - 964537664673492 * q^68 - 569178593140080 * q^70 + 3111156268483352 * q^71 + 936737429904432 * q^72 - 1146801010325370 * q^73 - 2161044304782140 * q^74 - 4935640048894356 * q^75 + 1321278185203718 * q^77 + 13747974994685232 * q^78 + 126874036566250 * q^79 - 18764997660746184 * q^80 - 2081051947014102 * q^81 - 11916006908925168 * q^82 + 17065299612720828 * q^84 + 27928718307758508 * q^85 - 7493915124549152 * q^86 - 4167264363403248 * q^87 - 10398917942882000 * q^88 - 34000447101257730 * q^89 + 6895892767523928 * q^91 + 113018032389709752 * q^92 - 15597881218045122 * q^93 - 7183919979926376 * q^94 - 19569222088313322 * q^95 - 137281944028491360 * q^96 + 65453414234371436 * q^98 + 142672614742345392 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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