LMFDB - Embedded newform 7.17.d.a.5.10

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			5.10
Root			$230.136 + 398.607i$ of defining polynomial
Character	$\chi$	$=$	7.5
Dual form			7.17.d.a.3.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(234.636 - 406.401i) q^{2} +(-4044.92 + 2335.34i) q^{3} +(-77340.0 - 133957. i) q^{4} +(59013.4 + 34071.4i) q^{5} +2.19181e6i q^{6} +(-5.75487e6 - 338210. i) q^{7} -4.18327e7 q^{8} +(-1.06158e7 + 1.83871e7i) q^{9} +O(q^{10})$	\(q+(234.636 - 406.401i) q^{2} +(-4044.92 + 2335.34i) q^{3} +(-77340.0 - 133957. i) q^{4} +(59013.4 + 34071.4i) q^{5} +2.19181e6i q^{6} +(-5.75487e6 - 338210. i) q^{7} -4.18327e7 q^{8} +(-1.06158e7 + 1.83871e7i) q^{9} +(2.76933e7 - 1.59887e7i) q^{10} +(1.14580e8 + 1.98458e8i) q^{11} +(6.25668e8 + 3.61230e8i) q^{12} -1.08556e9i q^{13} +(-1.48775e9 + 2.25943e9i) q^{14} -3.18273e8 q^{15} +(-4.74691e9 + 8.22188e9i) q^{16} +(-6.78285e8 + 3.91608e8i) q^{17} +(4.98168e9 + 8.62853e9i) q^{18} +(-2.45630e10 - 1.41815e10i) q^{19} -1.05403e10i q^{20} +(2.40678e10 - 1.20715e10i) q^{21} +1.07538e11 q^{22} +(-4.24275e10 + 7.34866e10i) q^{23} +(1.69210e11 - 9.76935e10i) q^{24} +(-7.39722e10 - 1.28124e11i) q^{25} +(-4.41175e11 - 2.54712e11i) q^{26} -3.00223e11i q^{27} +(3.99776e11 + 7.97061e11i) q^{28} -5.71793e11 q^{29} +(-7.46781e10 + 1.29346e11i) q^{30} +(7.61056e11 - 4.39396e11i) q^{31} +(8.56814e11 + 1.48405e12i) q^{32} +(-9.26932e11 - 5.35164e11i) q^{33} +3.67541e11i q^{34} +(-3.28091e11 - 2.16035e11i) q^{35} +3.28410e12 q^{36} +(9.66695e11 - 1.67437e12i) q^{37} +(-1.15267e13 + 6.65496e12i) q^{38} +(2.53516e12 + 4.39102e12i) q^{39} +(-2.46869e12 - 1.42530e12i) q^{40} -4.03517e12i q^{41} +(7.41293e11 - 1.26136e13i) q^{42} -3.48769e12 q^{43} +(1.77232e13 - 3.06975e13i) q^{44} +(-1.25295e12 + 7.23389e11i) q^{45} +(1.99100e13 + 3.44852e13i) q^{46} +(2.40341e13 + 1.38761e13i) q^{47} -4.43425e13i q^{48} +(3.30042e13 + 3.89271e12i) q^{49} -6.94261e13 q^{50} +(1.82907e12 - 3.16805e12i) q^{51} +(-1.45419e14 + 8.39575e13i) q^{52} +(2.76544e13 + 4.78988e13i) q^{53} +(-1.22011e14 - 7.04430e13i) q^{54} +1.56156e13i q^{55} +(2.40742e14 + 1.41482e13i) q^{56} +1.32474e14 q^{57} +(-1.34163e14 + 2.32377e14i) q^{58} +(1.32596e14 - 7.65541e13i) q^{59} +(2.46152e13 + 4.26348e13i) q^{60} +(-1.82367e14 - 1.05290e14i) q^{61} -4.12392e14i q^{62} +(6.73111e13 - 1.02225e14i) q^{63} +1.81971e14 q^{64} +(3.69867e13 - 6.40628e13i) q^{65} +(-4.34983e14 + 2.51137e14i) q^{66} +(1.30928e14 + 2.26774e14i) q^{67} +(1.04917e14 + 6.05739e13i) q^{68} -3.96330e14i q^{69} +(-1.64779e14 + 8.26470e13i) q^{70} -6.97886e14 q^{71} +(4.44087e14 - 7.69181e14i) q^{72} +(3.30055e14 - 1.90557e14i) q^{73} +(-4.53643e14 - 7.85732e14i) q^{74} +(5.98423e14 + 3.45500e14i) q^{75} +4.38718e15i q^{76} +(-5.92271e14 - 1.18085e15i) q^{77} +2.37936e15 q^{78} +(1.62858e14 - 2.82079e14i) q^{79} +(-5.60262e14 + 3.23467e14i) q^{80} +(2.44146e14 + 4.22874e14i) q^{81} +(-1.63990e15 - 9.46795e14i) q^{82} +2.91937e15i q^{83} +(-3.47847e15 - 2.29044e15i) q^{84} -5.33705e13 q^{85} +(-8.18337e14 + 1.41740e15i) q^{86} +(2.31286e15 - 1.33533e15i) q^{87} +(-4.79318e15 - 8.30204e15i) q^{88} +(1.17758e15 + 6.79874e14i) q^{89} +6.78932e14i q^{90} +(-3.67149e14 + 6.24728e15i) q^{91} +1.31254e16 q^{92} +(-2.05227e15 + 3.55464e15i) q^{93} +(1.12785e16 - 6.51165e15i) q^{94} +(-9.66364e14 - 1.67379e15i) q^{95} +(-6.93149e15 - 4.00190e15i) q^{96} -6.22903e15i q^{97} +(9.32596e15 - 1.24996e16i) q^{98} -4.86541e15 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 $

$2$	234.636	−	406.401i	0.916546	−	1.58750i	0.111925	−	0.993717i	$-0.464298\pi$
$2$	234.636	−	406.401i	0.916546	−	1.58750i	0.804621	−	0.593788i	$-0.202368\pi$
$3$	−4044.92	+	2335.34i	−0.616510	+	0.355942i	−0.775509	−	0.631337i	$-0.782507\pi$
$3$	−4044.92	+	2335.34i	−0.616510	+	0.355942i	0.158999	+	0.987279i	$0.449173\pi$
$4$	−77340.0	−	133957.i	−1.18011	−	2.04402i
$5$	59013.4	+	34071.4i	0.151074	+	0.0872228i	0.573632	−	0.819113i	$-0.305534\pi$
$5$	59013.4	+	34071.4i	0.151074	+	0.0872228i	−0.422557	+	0.906336i	$0.638867\pi$
$6$			2.19181e6i			1.30495i
$7$	−5.75487e6	−	338210.i	−0.998278	−	0.0586681i
$7$	−5.75487e6	−	338210.i	−0.998278	−	0.0586681i
$8$	−4.18327e7			−2.49343
$9$	−1.06158e7	+	1.83871e7i	−0.246611	+	0.427142i
$10$	2.76933e7	−	1.59887e7i	0.276933	−	0.159887i
$11$	1.14580e8	+	1.98458e8i	0.534523	+	0.925821i	0.999186	+	0.0403334i	$0.0128420\pi$
$11$	1.14580e8	+	1.98458e8i	0.534523	+	0.925821i	−0.464663	+	0.885487i	$0.653825\pi$
$12$	6.25668e8	+	3.61230e8i	1.45510	+	0.840104i
$13$		−	1.08556e9i		−	1.33079i	−0.746492	−	0.665394i	$-0.768264\pi$
$13$		−	1.08556e9i		−	1.33079i	0.746492	−	0.665394i	$-0.231736\pi$
$14$	−1.48775e9	+	2.25943e9i	−1.00810	+	1.53100i
$15$	−3.18273e8			−0.124185
$16$	−4.74691e9	+	8.22188e9i	−1.10523	+	1.91431i
$17$	−6.78285e8	+	3.91608e8i	−0.0972346	+	0.0561384i	−0.547829	−	0.836590i	$-0.684545\pi$
$17$	−6.78285e8	+	3.91608e8i	−0.0972346	+	0.0561384i	0.450594	+	0.892729i	$0.351212\pi$
$18$	4.98168e9	+	8.62853e9i	0.452060	+	0.782991i
$19$	−2.45630e10	−	1.41815e10i	−1.44628	−	0.835011i	−0.448024	−	0.894021i	$-0.647872\pi$
$19$	−2.45630e10	−	1.41815e10i	−1.44628	−	0.835011i	−0.998257	+	0.0590104i	$0.981205\pi$
$20$		−	1.05403e10i		−	0.411731i
$21$	2.40678e10	−	1.20715e10i	0.636330	−	0.319159i
$22$	1.07538e11			1.95966
$23$	−4.24275e10	+	7.34866e10i	−0.541782	+	0.938394i	0.457020	+	0.889457i	$0.348917\pi$
$23$	−4.24275e10	+	7.34866e10i	−0.541782	+	0.938394i	−0.998802	+	0.0489375i	$0.984416\pi$
$24$	1.69210e11	−	9.76935e10i	1.53722	−	0.887515i
$25$	−7.39722e10	−	1.28124e11i	−0.484784	−	0.839671i
$26$	−4.41175e11	−	2.54712e11i	−2.11263	−	1.21973i
$27$		−	3.00223e11i		−	1.06300i
$28$	3.99776e11	+	7.97061e11i	1.05816	+	2.10973i
$29$	−5.71793e11			−1.14302			−0.571512	−	0.820594i	$-0.693643\pi$
$29$	−5.71793e11			−1.14302			−0.571512	+	0.820594i	$0.693643\pi$
$30$	−7.46781e10	+	1.29346e11i	−0.113821	+	0.197144i
$31$	7.61056e11	−	4.39396e11i	0.892325	−	0.515184i	0.0176228	−	0.999845i	$-0.494390\pi$
$31$	7.61056e11	−	4.39396e11i	0.892325	−	0.515184i	0.874702	+	0.484661i	$0.161057\pi$
$32$	8.56814e11	+	1.48405e12i	0.779268	+	1.34973i
$33$	−9.26932e11	−	5.35164e11i	−0.659077	−	0.380518i
$34$			3.67541e11i			0.205814i
$35$	−3.28091e11	−	2.16035e11i	−0.145697	−	0.0959358i
$36$	3.28410e12			1.16411
$37$	9.66695e11	−	1.67437e12i	0.275217	−	0.476691i	−0.694973	−	0.719036i	$-0.744584\pi$
$37$	9.66695e11	−	1.67437e12i	0.275217	−	0.476691i	0.970190	+	0.242346i	$0.0779168\pi$
$38$	−1.15267e13	+	6.65496e12i	−2.65117	+	1.53065i
$39$	2.53516e12	+	4.39102e12i	0.473683	+	0.820443i
$40$	−2.46869e12	−	1.42530e12i	−0.376692	−	0.217483i
$41$		−	4.03517e12i		−	0.505348i	−0.967551	−	0.252674i	$-0.918690\pi$
$41$		−	4.03517e12i		−	0.505348i	0.967551	−	0.252674i	$-0.0813101\pi$
$42$	7.41293e11	−	1.26136e13i	0.0765589	−	1.30270i
$43$	−3.48769e12			−0.298394			−0.149197	−	0.988807i	$-0.547669\pi$
$43$	−3.48769e12			−0.298394			−0.149197	+	0.988807i	$0.547669\pi$
$44$	1.77232e13	−	3.06975e13i	1.26160	−	2.18515i
$45$	−1.25295e12	+	7.23389e11i	−0.0745130	+	0.0430201i
$46$	1.99100e13	+	3.44852e13i	0.993137	+	1.72016i
$47$	2.40341e13	+	1.38761e13i	1.00936	+	0.582752i	0.911003	−	0.412400i	$-0.135309\pi$
$47$	2.40341e13	+	1.38761e13i	1.00936	+	0.582752i	0.0983527	+	0.995152i	$0.468643\pi$
$48$		−	4.43425e13i		−	1.57358i
$49$	3.30042e13	+	3.89271e12i	0.993116	+	0.117134i
$50$	−6.94261e13			−1.77731
$51$	1.82907e12	−	3.16805e12i	0.0399641	−	0.0692198i
$52$	−1.45419e14	+	8.39575e13i	−2.72015	+	1.57048i
$53$	2.76544e13	+	4.78988e13i	0.444178	+	0.769339i	0.997995	−	0.0632995i	$-0.0201623\pi$
$53$	2.76544e13	+	4.78988e13i	0.444178	+	0.769339i	−0.553816	+	0.832639i	$0.686829\pi$
$54$	−1.22011e14	−	7.04430e13i	−1.68752	−	0.974289i
$55$			1.56156e13i			0.186490i
$56$	2.40742e14	+	1.41482e13i	2.48913	+	0.146285i
$57$	1.32474e14			1.18886
$58$	−1.34163e14	+	2.32377e14i	−1.04763	+	1.81455i
$59$	1.32596e14	−	7.65541e13i	0.903053	−	0.521378i	0.0248635	−	0.999691i	$-0.492085\pi$
$59$	1.32596e14	−	7.65541e13i	0.903053	−	0.521378i	0.878189	+	0.478313i	$0.158752\pi$
$60$	2.46152e13	+	4.26348e13i	0.146552	+	0.253836i
$61$	−1.82367e14	−	1.05290e14i	−0.951280	−	0.549222i	−0.0578014	−	0.998328i	$-0.518409\pi$
$61$	−1.82367e14	−	1.05290e14i	−0.951280	−	0.549222i	−0.893478	+	0.449107i	$0.851742\pi$
$62$		−	4.12392e14i		−	1.88876i
$63$	6.73111e13	−	1.02225e14i	0.271245	−	0.411938i
$64$	1.81971e14			0.646490
$65$	3.69867e13	−	6.40628e13i	0.116075	−	0.201048i
$66$	−4.34983e14	+	2.51137e14i	−1.20815	+	0.697525i
$67$	1.30928e14	+	2.26774e14i	0.322429	+	0.558464i	0.980989	−	0.194065i	$-0.0621672\pi$
$67$	1.30928e14	+	2.26774e14i	0.322429	+	0.558464i	−0.658559	+	0.752529i	$0.728834\pi$
$68$	1.04917e14	+	6.05739e13i	0.229496	+	0.132500i
$69$		−	3.96330e14i		−	0.771372i
$70$	−1.64779e14	+	8.26470e13i	−0.285836	+	0.143365i
$71$	−6.97886e14			−1.08073			−0.540366	−	0.841430i	$-0.681714\pi$
$71$	−6.97886e14			−1.08073			−0.540366	+	0.841430i	$0.681714\pi$
$72$	4.44087e14	−	7.69181e14i	0.614905	−	1.06505i
$73$	3.30055e14	−	1.90557e14i	0.409264	−	0.236289i	−0.281209	−	0.959646i	$-0.590736\pi$
$73$	3.30055e14	−	1.90557e14i	0.409264	−	0.236289i	0.690473	+	0.723358i	$0.257402\pi$
$74$	−4.53643e14	−	7.85732e14i	−0.504499	−	0.873818i
$75$	5.98423e14	+	3.45500e14i	0.597748	+	0.345110i
$76$			4.38718e15i			3.94163i
$77$	−5.92271e14	−	1.18085e15i	−0.479286	−	0.955586i
$78$	2.37936e15			1.73661
$79$	1.62858e14	−	2.82079e14i	0.107348	−	0.185932i	−0.807347	−	0.590077i	$-0.799097\pi$
$79$	1.62858e14	−	2.82079e14i	0.107348	−	0.185932i	0.914695	+	0.404145i	$0.132431\pi$
$80$	−5.60262e14	+	3.23467e14i	−0.333942	+	0.192802i
$81$	2.44146e14	+	4.22874e14i	0.131756	+	0.228208i
$82$	−1.63990e15	−	9.46795e14i	−0.802243	−	0.463175i
$83$			2.91937e15i			1.29618i	0.761565	+	0.648088i	$0.224431\pi$
$83$			2.91937e15i			1.29618i	−0.761565	+	0.648088i	$0.775569\pi$
$84$	−3.47847e15	−	2.29044e15i	−1.40331	−	0.924026i
$85$	−5.33705e13			−0.0195862
$86$	−8.18337e14	+	1.41740e15i	−0.273492	+	0.473702i
$87$	2.31286e15	−	1.33533e15i	0.704685	−	0.406850i
$88$	−4.79318e15	−	8.30204e15i	−1.33279	−	2.30847i
$89$	1.17758e15	+	6.79874e14i	0.299136	+	0.172706i	0.642055	−	0.766659i	$-0.278082\pi$
$89$	1.17758e15	+	6.79874e14i	0.299136	+	0.172706i	−0.342918	+	0.939365i	$0.611415\pi$
$90$			6.78932e14i			0.157720i
$91$	−3.67149e14	+	6.24728e15i	−0.0780748	+	1.32850i
$92$	1.31254e16			2.55746
$93$	−2.05227e15	+	3.55464e15i	−0.366751	+	0.635232i
$94$	1.12785e16	−	6.51165e15i	1.85024	−	1.06824i
$95$	−9.66364e14	−	1.67379e15i	−0.145664	−	0.252297i
$96$	−6.93149e15	−	4.00190e15i	−0.960852	−	0.554748i
$97$		−	6.22903e15i		−	0.794780i	−0.917650	−	0.397390i	$-0.869916\pi$
$97$		−	6.22903e15i		−	0.794780i	0.917650	−	0.397390i	$-0.130084\pi$
$98$	9.32596e15	−	1.24996e16i	1.09619	−	1.46922i
$99$	−4.86541e15			−0.527276
$100$	−1.14420e16	+	1.98182e16i	−1.14420	+	1.98182i
$101$	−8.01498e15	+	4.62745e15i	−0.740170	+	0.427337i	−0.822131	−	0.569298i	$-0.807215\pi$
$101$	−8.01498e15	+	4.62745e15i	−0.740170	+	0.427337i	0.0819611	+	0.996636i	$0.473882\pi$
$102$	−8.58332e14	−	1.48668e15i	−0.0732578	−	0.126886i
$103$	−1.59299e16	−	9.19713e15i	−1.25752	−	0.726030i	−0.284929	−	0.958549i	$-0.591970\pi$
$103$	−1.59299e16	−	9.19713e15i	−1.25752	−	0.726030i	−0.972592	+	0.232519i	$0.925303\pi$
$104$			4.54121e16i			3.31822i
$105$	1.83162e15	+	1.07643e14i	0.123971	+	0.00728570i
$106$	2.59549e16			1.62844
$107$	6.10461e15	−	1.05735e16i	0.355294	−	0.615387i	−0.631875	−	0.775071i	$-0.717714\pi$
$107$	6.10461e15	−	1.05735e16i	0.355294	−	0.615387i	0.987168	+	0.159684i	$0.0510475\pi$
$108$	−4.02169e16	+	2.32192e16i	−2.17279	+	1.25446i
$109$	−8.56534e15	−	1.48356e16i	−0.429865	−	0.744549i	0.566996	−	0.823721i	$-0.308106\pi$
$109$	−8.56534e15	−	1.48356e16i	−0.429865	−	0.744549i	−0.996861	+	0.0791722i	$0.974772\pi$
$110$	6.34618e15	+	3.66397e15i	0.296054	+	0.170927i
$111$			9.03023e15i			0.391846i
$112$	3.00986e16	−	4.57104e16i	1.21563	−	1.84617i
$113$	−1.62827e16			−0.612492			−0.306246	−	0.951952i	$-0.599073\pi$
$113$	−1.62827e16			−0.612492			−0.306246	+	0.951952i	$0.599073\pi$
$114$	3.10831e16	−	5.38376e16i	1.08965	−	1.88732i
$115$	−5.00758e15	+	2.89113e15i	−0.163699	+	0.0945115i
$116$	4.42225e16	+	7.65956e16i	1.34890	+	2.33636i
$117$	1.99603e16	+	1.15241e16i	0.568435	+	0.328186i
$118$		−	7.18494e16i		−	1.91147i
$119$	4.03589e15	−	2.02425e15i	0.100361	−	0.0503372i
$120$	1.33142e16			0.309646
$121$	−3.28217e15	+	5.68488e15i	−0.0714295	+	0.123720i
$122$	−8.55798e16	+	4.94095e16i	−1.74378	+	1.00677i
$123$	9.42347e15	+	1.63219e16i	0.179875	+	0.311552i
$124$	−1.17720e17	−	6.79657e16i	−2.10609	−	1.21595i
$125$		−	2.04791e16i		−	0.343582i
$126$	−2.57507e16	−	5.13409e16i	−0.405345	−	0.808164i
$127$	7.10600e16			1.05001			0.525007	−	0.851098i	$-0.324063\pi$
$127$	7.10600e16			1.05001			0.525007	+	0.851098i	$0.324063\pi$
$128$	−1.34553e16	+	2.33053e16i	−0.186730	+	0.323426i
$129$	1.41074e16	−	8.14493e15i	0.183963	−	0.106211i
$130$	−1.73568e16	−	3.00629e16i	−0.212776	−	0.368539i
$131$	3.07252e15	+	1.77392e15i	0.0354262	+	0.0204533i	0.517609	−	0.855618i	$-0.326822\pi$
$131$	3.07252e15	+	1.77392e15i	0.0354262	+	0.0204533i	−0.482182	+	0.876071i	$0.660156\pi$
$132$			1.65558e17i			1.79622i
$133$	1.36561e17	+	8.99199e16i	1.39480	+	0.918423i
$134$	1.22882e17			1.18209
$135$	1.02290e16	−	1.77172e16i	0.0927178	−	0.160592i
$136$	2.83745e16	−	1.63820e16i	0.242447	−	0.139977i
$137$	1.67781e16	+	2.90605e16i	0.135200	+	0.234174i	0.925674	−	0.378322i	$-0.123499\pi$
$137$	1.67781e16	+	2.90605e16i	0.135200	+	0.234174i	−0.790474	+	0.612496i	$0.790166\pi$
$138$	−1.61069e17	−	9.29931e16i	−1.22456	−	0.706998i
$139$			4.02164e16i			0.288592i	0.989535	+	0.144296i	$0.0460918\pi$
$139$			4.02164e16i			0.288592i	−0.989535	+	0.144296i	$0.953908\pi$
$140$	−3.56484e15	+	6.06582e16i	−0.0241555	+	0.411022i
$141$	−1.29621e17			−0.829703
$142$	−1.63749e17	+	2.83622e17i	−0.990541	+	1.71567i
$143$	2.15439e17	−	1.24384e17i	1.23207	−	0.711337i
$144$	−1.00784e17	−	1.74563e17i	−0.545121	−	0.944177i
$145$	−3.37435e16	−	1.94818e16i	−0.172681	−	0.0996976i
$146$		−	1.78846e17i		−	0.866278i
$147$	−1.42590e17	+	6.13301e16i	−0.653959	+	0.281277i
$148$	−2.99057e17			−1.29915
$149$	−1.04131e15	+	1.80360e15i	−0.00428637	+	0.00742422i	−0.868161	−	0.496283i	$-0.834698\pi$
$149$	−1.04131e15	+	1.80360e15i	−0.00428637	+	0.00742422i	0.863874	+	0.503708i	$0.168031\pi$
$150$	2.80823e17	−	1.62133e17i	1.09573	−	0.632619i
$151$	−1.36337e17	−	2.36143e17i	−0.504427	−	0.873694i	−0.999987	−	0.00511970i	$-0.998370\pi$
$151$	−1.36337e17	−	2.36143e17i	−0.504427	−	0.873694i	0.495560	−	0.868574i	$-0.334963\pi$
$152$	1.02754e18	+	5.93249e17i	3.60619	+	2.08204i
$153$		−	1.66289e16i		−	0.0553773i
$154$	−6.18868e17	−	3.63704e16i	−1.95628	−	0.114970i
$155$	5.98833e16			0.179743
$156$	3.92138e17	−	6.79203e17i	1.11800	−	1.93643i
$157$	5.13417e16	−	2.96421e16i	0.139083	−	0.0802994i	−0.428844	−	0.903379i	$-0.641079\pi$
$157$	5.13417e16	−	2.96421e16i	0.139083	−	0.0802994i	0.567927	+	0.823079i	$0.307746\pi$
$158$	−7.64248e16	−	1.32372e17i	−0.196779	−	0.340830i
$159$	−2.23720e17	−	1.29165e17i	−0.547680	−	0.316203i
$160$			1.16771e17i			0.271880i
$161$	2.69019e17	−	4.08556e17i	0.595903	−	0.904992i
$162$	2.29142e17			0.483041
$163$	−2.63000e17	+	4.55530e17i	−0.527783	+	0.914146i	0.471693	+	0.881763i	$0.343643\pi$
$163$	−2.63000e17	+	4.55530e17i	−0.527783	+	0.914146i	−0.999476	+	0.0323835i	$0.989690\pi$
$164$	−5.40538e17	+	3.12080e17i	−1.03294	+	0.596369i
$165$	−3.64676e16	−	6.31637e16i	−0.0663797	−	0.114973i
$166$	1.18643e18	+	6.84988e17i	2.05769	+	1.18801i
$167$			6.14112e17i			1.01512i	0.861618	+	0.507558i	$0.169452\pi$
$167$			6.14112e17i			1.01512i	−0.861618	+	0.507558i	$0.830548\pi$
$168$	−1.00682e18	+	5.04985e17i	−1.58664	+	0.795800i
$169$	−5.13034e17			−0.770996
$170$	−1.25226e16	+	2.16899e16i	−0.0179517	+	0.0310932i
$171$	5.21511e17	−	3.01095e17i	0.713337	−	0.411845i
$172$	2.69738e17	+	4.67200e17i	0.352139	+	0.609923i
$173$	−1.33969e18	−	7.73473e17i	−1.66969	−	0.963998i	−0.967801	−	0.251715i	$-0.919005\pi$
$173$	−1.33969e18	−	7.73473e17i	−1.66969	−	0.963998i	−0.701893	−	0.712283i	$-0.747661\pi$
$174$		−	1.25326e18i		−	1.49159i
$175$	3.82368e17	+	7.62353e17i	0.434687	+	0.866666i
$176$	−2.17560e18			−2.36307
$177$	−3.57559e17	+	6.19311e17i	−0.371161	+	0.642869i
$178$	5.52603e17	−	3.19046e17i	0.548345	−	0.316587i
$179$	4.63221e17	+	8.02323e17i	0.439505	+	0.761246i	0.997651	−	0.0684971i	$-0.0218204\pi$
$179$	4.63221e17	+	8.02323e17i	0.439505	+	0.761246i	−0.558146	+	0.829743i	$0.688487\pi$
$180$	1.93806e17	+	1.11894e17i	0.175868	+	0.101537i
$181$		−	1.20879e18i		−	1.04936i	−0.851301	−	0.524678i	$-0.824186\pi$
$181$		−	1.20879e18i		−	1.04936i	0.851301	−	0.524678i	$-0.175814\pi$
$182$	2.45276e18	+	1.61505e18i	2.03743	+	1.34157i
$183$	9.83548e17			0.781964
$184$	1.77486e18	−	3.07414e18i	1.35089	−	2.33982i
$185$	1.14096e17	−	6.58733e16i	0.0831565	−	0.0480104i
$186$	9.63074e17	+	1.66809e18i	0.672289	+	1.16444i
$187$	−1.55436e17	−	8.97407e16i	−0.103948	−	0.0600146i
$188$		−	4.29270e18i		−	2.75085i
$189$	−1.01538e17	+	1.72774e18i	−0.0623642	+	1.06117i
$190$	−9.06975e17			−0.534031
$191$	−9.87280e17	+	1.71002e18i	−0.557408	+	0.965460i	0.440303	+	0.897849i	$0.354871\pi$
$191$	−9.87280e17	+	1.71002e18i	−0.557408	+	0.965460i	−0.997712	+	0.0676107i	$0.978462\pi$
$192$	−7.36057e17	+	4.24963e17i	−0.398567	+	0.230113i
$193$	−8.82964e17	−	1.52934e18i	−0.458653	−	0.794411i	0.540237	−	0.841513i	$-0.318335\pi$
$193$	−8.82964e17	−	1.52934e18i	−0.458653	−	0.794411i	−0.998890	+	0.0471021i	$0.985001\pi$
$194$	−2.53149e18	−	1.46155e18i	−1.26172	−	0.728452i
$195$			3.45505e17i			0.165264i
$196$	−2.03109e18	−	4.72219e18i	−0.932566	−	2.16818i
$197$	1.32969e18			0.586168			0.293084	−	0.956087i	$-0.405318\pi$
$197$	1.32969e18			0.586168			0.293084	+	0.956087i	$0.405318\pi$
$198$	−1.14160e18	+	1.97731e18i	−0.483273	+	0.837053i
$199$	−4.43197e17	+	2.55880e17i	−0.180207	+	0.104043i	−0.587390	−	0.809304i	$-0.699844\pi$
$199$	−4.43197e17	+	2.55880e17i	−0.180207	+	0.104043i	0.407183	+	0.913347i	$0.366511\pi$
$200$	3.09446e18	+	5.35976e18i	1.20877	+	2.09366i
$201$	−1.05919e18	−	6.11522e17i	−0.397562	−	0.229532i
$202$			4.34306e18i			1.56670i
$203$	3.29060e18	+	1.93386e17i	1.14105	+	0.0670590i
$204$	−5.65842e17			−0.188649
$205$	1.37484e17	−	2.38129e17i	0.0440779	−	0.0763451i
$206$	−7.47545e18	+	4.31595e18i	−2.30515	+	1.33088i
$207$	−9.00802e17	−	1.56023e18i	−0.267218	−	0.462836i
$208$	8.92538e18	+	5.15307e18i	2.54754	+	1.47082i
$209$		−	6.49963e18i		−	1.78533i
$210$	4.73509e17	−	7.19115e17i	0.125191	−	0.190127i
$211$	1.21268e18			0.308666			0.154333	−	0.988019i	$-0.450677\pi$
$211$	1.21268e18			0.308666			0.154333	+	0.988019i	$0.450677\pi$
$212$	4.27758e18	−	7.40899e18i	1.04836	−	1.81582i
$213$	2.82289e18	−	1.62980e18i	0.666282	−	0.384678i
$214$	−2.86472e18	−	4.96184e18i	−0.651286	−	1.12806i
$215$	−2.05820e17	−	1.18830e17i	−0.0450797	−	0.0260268i
$216$			1.25591e19i			2.65051i
$217$	−4.52839e18	+	2.27127e18i	−0.921013	+	0.461946i
$218$	−8.03894e18			−1.57597
$219$	−8.90031e17	+	1.54158e18i	−0.168210	+	0.291349i
$220$	2.09181e18	−	1.20771e18i	0.381189	−	0.220080i
$221$	4.25116e17	+	7.36322e17i	0.0747084	+	0.129399i
$222$	3.66990e18	+	2.11882e18i	0.622057	+	0.359145i
$223$			3.20832e18i			0.524613i	0.964985	+	0.262306i	$0.0844831\pi$
$223$			3.20832e18i			0.524613i	−0.964985	+	0.262306i	$0.915517\pi$
$224$	−4.42894e18	−	8.83027e18i	−0.698740	−	1.39312i
$225$	3.14109e18			0.478212
$226$	−3.82052e18	+	6.61733e18i	−0.561377	+	0.972333i
$227$	7.01020e18	−	4.04734e18i	0.994314	−	0.574068i	0.0877532	−	0.996142i	$-0.472031\pi$
$227$	7.01020e18	−	4.04734e18i	0.994314	−	0.574068i	0.906561	+	0.422075i	$0.138698\pi$
$228$	−1.02455e19	−	1.77458e19i	−1.40299	−	2.43006i
$229$	−1.02914e19	−	5.94176e18i	−1.36079	−	0.785654i	−0.371064	−	0.928607i	$-0.621007\pi$
$229$	−1.02914e19	−	5.94176e18i	−1.36079	−	0.785654i	−0.989729	+	0.142953i	$0.954340\pi$
$230$			2.71345e18i			0.346497i
$231$	5.15337e18	+	3.39330e18i	0.635618	+	0.418530i
$232$	2.39197e19			2.85004
$233$	−5.12226e18	+	8.87201e18i	−0.589677	+	1.02135i	0.404597	+	0.914495i	$0.367412\pi$
$233$	−5.12226e18	+	8.87201e18i	−0.589677	+	1.02135i	−0.994275	+	0.106856i	$0.965922\pi$
$234$	9.36683e18	−	5.40794e18i	1.04199	−	0.601596i
$235$	9.45554e17	+	1.63775e18i	0.101658	+	0.176078i
$236$	−2.05099e19	−	1.18414e19i	−2.13141	−	1.23057i
$237$			1.52132e18i			0.152838i
$238$	1.24306e17	−	2.11515e18i	0.0120747	−	0.205459i
$239$	1.33286e19			1.25199			0.625995	−	0.779827i	$-0.284693\pi$
$239$	1.33286e19			1.25199			0.625995	+	0.779827i	$0.284693\pi$
$240$	1.51081e18	−	2.61680e18i	0.137252	−	0.237728i
$241$	1.22319e19	−	7.06208e18i	1.07487	−	0.620578i	0.145364	−	0.989378i	$-0.453565\pi$
$241$	1.22319e19	−	7.06208e18i	1.07487	−	0.620578i	0.929509	+	0.368800i	$0.120231\pi$
$242$	1.54023e18	+	2.66775e18i	0.130937	+	0.226789i
$243$	9.21706e18	+	5.32147e18i	0.758128	+	0.437705i
$244$			3.25724e19i			2.59258i
$245$	1.81506e18	+	1.35422e18i	0.139818	+	0.104318i
$246$	8.84434e18			0.659454
$247$	−1.53949e19	+	2.66647e19i	−1.11122	+	1.92469i
$248$	−3.18371e19	+	1.83811e19i	−2.22495	+	1.28457i
$249$	−6.81770e18	−	1.18086e19i	−0.461364	−	0.799105i
$250$	−8.32274e18	−	4.80513e18i	−0.545439	−	0.314909i
$251$		−	1.87629e19i		−	1.19100i	−0.803357	−	0.595498i	$-0.796955\pi$
$251$		−	1.87629e19i		−	1.19100i	0.803357	−	0.595498i	$-0.203045\pi$
$252$	−1.88995e19	−	1.11071e18i	−1.16211	−	0.0682964i
$253$	−1.94453e19			−1.15838
$254$	1.66732e19	−	2.88789e19i	0.962387	−	1.66690i
$255$	2.15880e17	−	1.24638e17i	0.0120751	−	0.00697155i
$256$	1.22770e19	+	2.12644e19i	0.665538	+	1.15275i
$257$	−7.74735e18	−	4.47293e18i	−0.407088	−	0.235032i	0.282450	−	0.959282i	$-0.408853\pi$
$257$	−7.74735e18	−	4.47293e18i	−0.407088	−	0.235032i	−0.689538	+	0.724250i	$0.742186\pi$
$258$		−	7.64437e18i		−	0.389389i
$259$	−6.12949e18	+	9.30881e18i	−0.302710	+	0.459723i
$260$	−1.14422e19			−0.547927
$261$	6.07003e18	−	1.05136e19i	0.281882	−	0.488233i
$262$	1.44185e18	−	8.32452e17i	0.0649396	−	0.0374929i
$263$	1.67806e19	+	2.90648e19i	0.733096	+	1.26976i	0.955554	+	0.294818i	$0.0952589\pi$
$263$	1.67806e19	+	2.90648e19i	0.733096	+	1.26976i	−0.222457	+	0.974942i	$0.571408\pi$
$264$	3.87761e19	+	2.23874e19i	1.64336	+	0.948794i
$265$			3.76890e18i			0.154970i
$266$	6.85856e19	−	3.44000e19i	2.73640	−	1.37248i
$267$	−6.35094e18			−0.245894
$268$	2.02520e19	−	3.50774e19i	0.761007	−	1.31810i
$269$	−2.02779e19	+	1.17075e19i	−0.739614	+	0.427016i	−0.821929	−	0.569590i	$-0.807102\pi$
$269$	−2.02779e19	+	1.17075e19i	−0.739614	+	0.427016i	0.0823149	+	0.996606i	$0.473769\pi$
$270$	−4.80018e18	−	8.31416e18i	−0.169960	−	0.294380i
$271$	−2.81999e19	−	1.62812e19i	−0.969377	−	0.559670i	−0.0703308	−	0.997524i	$-0.522405\pi$
$271$	−2.81999e19	−	1.62812e19i	−0.969377	−	0.559670i	−0.899046	+	0.437854i	$0.855739\pi$
$272$		−	7.43571e18i		−	0.248183i
$273$	−1.31044e19	−	2.61272e19i	−0.424733	−	0.846820i
$274$	1.57470e19			0.495669
$275$	1.69514e19	−	2.93607e19i	0.518257	−	0.897647i
$276$	−5.30910e19	+	3.06521e19i	−1.57670	+	0.910307i
$277$	−2.89694e19	−	5.01765e19i	−0.835799	−	1.44765i	−0.893379	−	0.449305i	$-0.851672\pi$
$277$	−2.89694e19	−	5.01765e19i	−0.835799	−	1.44765i	0.0575801	−	0.998341i	$-0.481662\pi$
$278$	1.63440e19	+	9.43621e18i	0.458142	+	0.264508i
$279$			1.86581e19i			0.508199i
$280$	1.37249e19	+	9.03735e18i	0.363284	+	0.239209i
$281$	−1.09949e19			−0.282840			−0.141420	−	0.989950i	$-0.545167\pi$
$281$	−1.09949e19			−0.282840			−0.141420	+	0.989950i	$0.545167\pi$
$282$	−3.04138e19	+	5.26782e19i	−0.760461	+	1.31716i
$283$	−2.48402e17	+	1.43415e17i	−0.00603759	+	0.00348581i	−0.503016	−	0.864277i	$-0.667776\pi$
$283$	−2.48402e17	+	1.43415e17i	−0.00603759	+	0.00348581i	0.496978	+	0.867763i	$0.334443\pi$
$284$	5.39745e19	+	9.34866e19i	1.27539	+	2.20904i
$285$	7.81773e18	+	4.51357e18i	0.179606	+	0.103696i
$286$		−	1.16739e20i		−	2.60789i
$287$	−1.36473e18	+	2.32219e19i	−0.0296478	+	0.504478i
$288$	−3.63830e19			−0.768703
$289$	−2.40239e19	+	4.16106e19i	−0.493697	+	0.855108i
$290$	−1.58348e19	+	9.14225e18i	−0.316541	+	0.182755i
$291$	1.45469e19	+	2.51959e19i	0.282895	+	0.489989i
$292$	−5.10529e19	−	2.94754e19i	−0.965957	−	0.557695i
$293$		−	2.03018e19i		−	0.373761i	−0.982383	−	0.186880i	$-0.940162\pi$
$293$		−	2.03018e19i		−	0.373761i	0.982383	−	0.186880i	$-0.0598377\pi$
$294$	−8.53209e18	+	7.23390e19i	−0.152854	+	1.29597i
$295$	1.04332e19			0.181904
$296$	−4.04395e19	+	7.00433e19i	−0.686234	+	1.18859i
$297$	5.95816e19	−	3.43994e19i	0.984148	−	0.568198i
$298$	4.88658e17	+	8.46380e17i	0.00785732	+	0.0136093i
$299$	7.97744e19	+	4.60578e19i	1.24880	+	0.720997i
$300$		−	1.06884e20i		−	1.62908i
$301$	2.00712e19	+	1.17957e18i	0.297880	+	0.0175062i
$302$	−1.27958e20			−1.84932
$303$	2.16133e19	−	3.74353e19i	0.304215	−	0.526915i
$304$	2.33197e20	−	1.34636e20i	3.19693	−	1.84575i
$305$	−7.17474e18	−	1.24270e19i	−0.0958092	−	0.165946i
$306$	−6.75801e18	−	3.90174e18i	−0.0879118	−	0.0507559i
$307$			1.54331e20i			1.95590i	0.208832	+	0.977952i	$0.433034\pi$
$307$			1.54331e20i			1.95590i	−0.208832	+	0.977952i	$0.566966\pi$
$308$	−1.12377e20	+	1.70666e20i	−1.38762	+	2.10737i
$309$	8.59135e19			1.03370
$310$	1.40508e19	−	2.43367e19i	0.164743	−	0.285343i
$311$	2.38955e18	−	1.37961e18i	0.0273045	−	0.0157642i	−0.486286	−	0.873800i	$-0.661649\pi$
$311$	2.38955e18	−	1.37961e18i	0.0273045	−	0.0157642i	0.513590	+	0.858036i	$0.328315\pi$
$312$	−1.06053e20	−	1.83688e20i	−1.18109	−	2.04571i
$313$	1.29863e19	+	7.49767e18i	0.140972	+	0.0813901i	0.568827	−	0.822457i	$-0.307397\pi$
$313$	1.29863e19	+	7.49767e18i	0.140972	+	0.0813901i	−0.427855	+	0.903847i	$0.640731\pi$
$314$		−	2.78204e19i		−	0.294392i
$315$	7.45520e18	−	3.73925e18i	0.0769086	−	0.0385745i
$316$	−5.03818e19			−0.506731
$317$	4.91783e19	−	8.51794e19i	0.482281	−	0.835334i	−0.517513	−	0.855676i	$-0.673142\pi$
$317$	4.91783e19	−	8.51794e19i	0.482281	−	0.835334i	0.999793	+	0.0203412i	$0.00647526\pi$
$318$	−1.04985e20	+	6.06133e19i	−1.00395	+	0.579630i
$319$	−6.55159e19	−	1.13477e20i	−0.610972	−	1.05823i
$320$	1.07387e19	+	6.20000e18i	0.0976680	+	0.0563886i
$321$			5.70252e19i			0.505856i
$322$	−1.02916e20	−	2.05191e20i	−0.890507	−	1.77547i
$323$	2.22143e19			0.187505
$324$	3.77645e19	−	6.54101e19i	0.310974	−	0.538623i
$325$	−1.39086e20	+	8.03016e19i	−1.11742	+	0.645145i
$326$	1.23419e20	+	2.13767e20i	0.967475	+	1.67572i
$327$	6.92922e19	+	4.00059e19i	0.530032	+	0.306014i
$328$			1.68802e20i			1.26005i
$329$	−1.33620e20	−	8.79835e19i	−0.973428	−	0.640965i
$330$	−3.42264e19			−0.243360
$331$	8.37347e19	−	1.45033e20i	0.581141	−	1.00657i	−0.414203	−	0.910184i	$-0.635940\pi$
$331$	8.37347e19	−	1.45033e20i	0.581141	−	1.00657i	0.995344	−	0.0963815i	$-0.0307269\pi$
$332$	3.91069e20	−	2.25784e20i	2.64941	−	1.52964i
$333$	2.05244e19	+	3.55494e19i	0.135743	+	0.235114i
$334$	2.49576e20	+	1.44093e20i	1.61150	+	0.930400i
$335$			1.78436e19i			0.112493i
$336$	−1.49971e19	+	2.55185e20i	−0.0923192	+	1.57087i
$337$	−1.10220e20			−0.662552			−0.331276	−	0.943534i	$-0.607479\pi$
$337$	−1.10220e20			−0.662552			−0.331276	+	0.943534i	$0.607479\pi$
$338$	−1.20376e20	+	2.08497e20i	−0.706654	+	1.22396i
$339$	6.58624e19	−	3.80257e19i	0.377607	−	0.218011i
$340$	4.12768e18	+	7.14935e18i	0.0231140	+	0.0400346i
$341$	1.74403e20	+	1.00692e20i	0.953936	+	0.550755i
$342$		−	2.82590e20i		−	1.50990i
$343$	−1.88618e20	−	3.35644e19i	−0.984533	−	0.175197i
$344$	1.45900e20			0.744024
$345$	1.35035e19	−	2.33888e19i	0.0672812	−	0.116534i
$346$	−6.28681e20	+	3.62969e20i	−3.06070	+	1.76710i
$347$	−1.81710e20	−	3.14731e20i	−0.864457	−	1.49728i	−0.867586	−	0.497288i	$-0.834329\pi$
$347$	−1.81710e20	−	3.14731e20i	−0.864457	−	1.49728i	0.00312918	−	0.999995i	$-0.499004\pi$
$348$	−3.57753e20	−	2.06549e20i	−1.66322	−	0.960259i
$349$			7.64114e19i			0.347180i	0.984818	+	0.173590i	$0.0555367\pi$
$349$			7.64114e19i			0.347180i	−0.984818	+	0.173590i	$0.944463\pi$
$350$	3.99539e20	+	2.34806e19i	1.77425	+	0.104271i
$351$	−3.25911e20			−1.41463
$352$	−1.96347e20	+	3.40083e20i	−0.833073	+	1.44293i
$353$	1.46846e20	−	8.47816e19i	0.609067	−	0.351645i	−0.163534	−	0.986538i	$-0.552289\pi$
$353$	1.46846e20	−	8.47816e19i	0.609067	−	0.351645i	0.772600	+	0.634893i	$0.218956\pi$
$354$	1.67792e20	+	2.90625e20i	0.680372	+	1.17844i
$355$	−4.11846e19	−	2.37780e19i	−0.163271	−	0.0942644i
$356$		−	2.10326e20i		−	0.815253i
$357$	−1.15975e19	+	1.76131e19i	−0.0439562	+	0.0667559i
$358$	4.34753e20			1.61131
$359$	−7.22252e19	+	1.25098e20i	−0.261778	+	0.453413i	−0.966714	−	0.255858i	$-0.917642\pi$
$359$	−7.22252e19	+	1.25098e20i	−0.261778	+	0.453413i	0.704936	+	0.709270i	$0.250975\pi$
$360$	5.24142e19	−	3.02613e19i	0.185793	−	0.107267i
$361$	2.58007e20	+	4.46881e20i	0.894487	+	1.54930i
$362$	−4.91255e20	−	2.83626e20i	−1.66586	−	0.961784i
$363$		−	3.06598e19i		−	0.101699i
$364$	8.65261e20	−	4.33983e20i	2.80761	−	1.40819i
$365$	2.59702e19			0.0824390
$366$	2.30776e20	−	3.99715e20i	0.716706	−	1.24137i
$367$	−1.66909e19	+	9.63647e18i	−0.0507166	+	0.0292812i	−0.525144	−	0.851013i	$-0.675989\pi$
$367$	−1.66909e19	+	9.63647e18i	−0.0507166	+	0.0292812i	0.474427	+	0.880295i	$0.342655\pi$
$368$	−4.02799e20	−	6.97668e20i	−1.19758	−	2.07427i
$369$	7.41949e19	+	4.28364e19i	0.215856	+	0.124624i
$370$		−	6.18250e19i		−	0.176015i
$371$	−1.42948e20	−	2.85005e20i	−0.398278	−	0.794073i
$372$	6.34891e20			1.73123
$373$	7.59745e18	−	1.31592e19i	0.0202767	−	0.0351202i	−0.855709	−	0.517457i	$-0.826879\pi$
$373$	7.59745e18	−	1.31592e19i	0.0202767	−	0.0351202i	0.875986	+	0.482337i	$0.160212\pi$
$374$	−7.29415e19	+	4.21128e19i	−0.190547	+	0.110012i
$375$	4.78256e19	+	8.28364e19i	0.122295	+	0.211822i
$376$	−1.00541e21	−	5.80474e20i	−2.51675	−	1.45305i
$377$			6.20718e20i			1.52112i
$378$	6.78332e20	+	4.46656e20i	1.62745	+	1.07161i
$379$	4.83778e19			0.113640			0.0568202	−	0.998384i	$-0.481904\pi$
$379$	4.83778e19			0.113640			0.0568202	+	0.998384i	$0.481904\pi$
$380$	−1.49477e20	+	2.58902e20i	−0.343800	+	0.595479i
$381$	−2.87432e20	+	1.65949e20i	−0.647344	+	0.373744i
$382$	4.63303e20	+	8.02464e20i	1.02178	+	1.76978i
$383$	3.60552e20	+	2.08165e20i	0.778714	+	0.449591i	0.835974	−	0.548768i	$-0.184903\pi$
$383$	3.60552e20	+	2.08165e20i	0.778714	+	0.449591i	−0.0572602	+	0.998359i	$0.518236\pi$
$384$		−	1.25691e20i		−	0.265860i
$385$	5.28134e18	−	8.98656e19i	0.0109410	−	0.186169i
$386$	−8.28700e20			−1.68151
$387$	3.70245e19	−	6.41284e19i	0.0735872	−	0.127457i
$388$	−8.34421e20	+	4.81753e20i	−1.62454	+	0.937931i
$389$	−1.90946e20	−	3.30729e20i	−0.364179	−	0.630776i	0.624465	−	0.781053i	$-0.285317\pi$
$389$	−1.90946e20	−	3.30729e20i	−0.364179	−	0.630776i	−0.988644	+	0.150276i	$0.951984\pi$
$390$	1.40414e20	+	8.10679e19i	0.262357	+	0.151472i
$391$		−	6.64598e19i		−	0.121659i
$392$	−1.38065e21	−	1.62843e20i	−2.47626	−	0.292065i
$393$	−1.65708e19			−0.0291208
$394$	3.11994e20	−	5.40389e20i	0.537250	−	0.930544i
$395$	1.92216e19	−	1.10976e19i	0.0324350	−	0.0187264i
$396$	3.76291e20	+	6.51755e20i	0.622246	+	1.07776i
$397$	3.76306e20	+	2.17261e20i	0.609842	+	0.352092i	0.772904	−	0.634523i	$-0.218804\pi$
$397$	3.76306e20	+	2.17261e20i	0.609842	+	0.352092i	−0.163062	+	0.986616i	$0.552137\pi$
$398$			2.40154e20i			0.381439i
$399$	−7.62370e20	−	4.48040e19i	−1.18681	−	0.0697483i
$400$	1.40456e21			2.14318
$401$	1.09863e20	−	1.90288e20i	0.164322	−	0.284614i	−0.772092	−	0.635510i	$-0.780790\pi$
$401$	1.09863e20	−	1.90288e20i	0.164322	−	0.284614i	0.936414	+	0.350896i	$0.114123\pi$
$402$	−4.97047e20	+	2.86970e20i	−0.728767	+	0.420754i
$403$	−4.76993e20	−	8.26175e20i	−0.685601	−	1.18750i
$404$	1.23976e21	+	7.15774e20i	1.74697	+	1.00861i
$405$			3.32736e19i			0.0459684i
$406$	8.50684e20	−	1.29193e21i	1.15229	−	1.74997i
$407$	4.43055e20			0.588440
$408$	−7.65151e19	+	1.32528e20i	−0.0996474	+	0.172594i
$409$	1.22894e21	−	7.09530e20i	1.56944	−	0.906117i	0.573208	−	0.819410i	$-0.305699\pi$
$409$	1.22894e21	−	7.09530e20i	1.56944	−	0.906117i	0.996234	−	0.0867074i	$-0.0276345\pi$
$410$	−6.45173e19	−	1.11747e20i	−0.0807988	−	0.139948i
$411$	−1.35732e20	−	7.83649e19i	−0.166705	−	0.0962469i
$412$			2.84522e21i			3.42719i
$413$	−7.88962e20	+	3.95714e20i	−0.932086	+	0.467499i
$414$	−8.45441e20			−0.979672
$415$	−9.94669e19	+	1.72282e20i	−0.113056	+	0.195819i
$416$	1.61103e21	−	9.30127e20i	1.79621	−	1.03704i
$417$	−9.39188e19	−	1.62672e20i	−0.102722	−	0.177920i
$418$	−2.64146e21	−	1.52505e21i	−2.83422	−	1.63634i
$419$		−	3.35732e20i		−	0.353411i	−0.984264	−	0.176706i	$-0.943456\pi$
$419$		−	3.35732e20i		−	0.353411i	0.984264	−	0.176706i	$-0.0565441\pi$
$420$	−1.27238e20	−	2.53683e20i	−0.131408	−	0.261997i
$421$	1.24976e21			1.26640			0.633198	−	0.773990i	$-0.281742\pi$
$421$	1.24976e21			1.26640			0.633198	+	0.773990i	$0.281742\pi$
$422$	2.84539e20	−	4.92836e20i	0.282906	−	0.490008i
$423$	−5.10280e20	+	2.94611e20i	−0.497836	+	0.287425i
$424$	−1.15686e21	−	2.00374e21i	−1.10753	−	1.91829i
$425$	1.00349e20	+	5.79363e19i	0.0942757	+	0.0544301i
$426$		−	1.52964e21i		−	1.41030i
$427$	1.01389e21	+	6.67608e20i	0.917419	+	0.604085i
$428$	−1.88852e21			−1.67715
$429$	−5.80955e20	+	1.00624e21i	−0.506389	+	0.877092i
$430$	−9.65857e19	+	5.57638e19i	−0.0826352	+	0.0477095i
$431$	−6.27159e20	−	1.08627e21i	−0.526696	−	0.912264i	−0.999516	−	0.0311048i	$-0.990097\pi$
$431$	−6.27159e20	−	1.08627e21i	−0.526696	−	0.912264i	0.472820	−	0.881159i	$-0.343236\pi$
$432$	2.46840e21	+	1.42513e21i	2.03491	+	1.17485i
$433$		−	1.13484e19i		−	0.00918396i	−0.999989	−	0.00459198i	$-0.998538\pi$
$433$		−	1.13484e19i		−	0.00918396i	0.999989	−	0.00459198i	$-0.00146168\pi$
$434$	−1.39475e20	+	2.37326e21i	−0.110810	+	1.88551i
$435$	1.81986e20			0.141946
$436$	−1.32489e21	+	2.29477e21i	−1.01458	+	1.75730i
$437$	2.08429e21	−	1.20337e21i	1.56714	−	0.904788i
$438$	4.17666e20	+	7.23419e20i	0.308345	+	0.534069i
$439$	−6.14518e20	−	3.54792e20i	−0.445470	−	0.257192i	0.260445	−	0.965489i	$-0.416131\pi$
$439$	−6.14518e20	−	3.54792e20i	−0.445470	−	0.257192i	−0.705915	+	0.708296i	$0.749464\pi$
$440$		−	6.53242e20i		−	0.465000i
$441$	−4.21940e20	+	5.65526e20i	−0.294946	+	0.395315i
$442$	3.98990e20			0.273895
$443$	−2.55016e19	+	4.41701e19i	−0.0171924	+	0.0297782i	−0.874494	−	0.485037i	$-0.838806\pi$
$443$	−2.55016e19	+	4.41701e19i	−0.0171924	+	0.0297782i	0.857301	+	0.514815i	$0.172139\pi$
$444$	1.20966e21	−	6.98398e20i	0.800940	−	0.462423i
$445$	4.63285e19	+	8.02434e19i	0.0301279	+	0.0521830i
$446$	1.30387e21	+	7.52787e20i	0.832825	+	0.480832i
$447$		−	9.72724e18i		−	0.00610280i
$448$	−1.04722e21	−	6.15443e19i	−0.645376	−	0.0379283i
$449$	−8.75187e20			−0.529822			−0.264911	−	0.964273i	$-0.585343\pi$
$449$	−8.75187e20			−0.529822			−0.264911	+	0.964273i	$0.585343\pi$
$450$	7.37013e20	−	1.27654e21i	0.438303	−	0.759164i
$451$	8.00811e20	−	4.62349e20i	0.467862	−	0.270120i
$452$	1.25931e21	+	2.18118e21i	0.722810	+	1.25194i
$453$	1.10295e21	+	6.36786e20i	0.621968	+	0.359094i
$454$		−	3.79861e21i		−	2.10464i
$455$	−2.34520e20	+	3.56164e20i	−0.127670	+	0.193892i
$456$	−5.54174e21			−2.96434
$457$	−1.35938e21	+	2.35451e21i	−0.714514	+	1.23757i	0.248633	+	0.968598i	$0.420019\pi$
$457$	−1.35938e21	+	2.35451e21i	−0.714514	+	1.23757i	−0.963147	+	0.268976i	$0.913315\pi$
$458$	−4.82948e21	+	2.78830e21i	−2.49446	+	1.44018i
$459$	1.17570e20	+	2.03637e20i	0.0596752	+	0.103360i
$460$	7.74572e20	+	4.47199e20i	0.386366	+	0.223069i
$461$			1.01882e21i			0.499449i	0.968317	+	0.249724i	$0.0803400\pi$
$461$			1.01882e21i			0.499449i	−0.968317	+	0.249724i	$0.919660\pi$
$462$	2.58821e21	−	1.29815e21i	1.24699	−	0.625444i
$463$	3.09018e21			1.46331			0.731653	−	0.681677i	$-0.238749\pi$
$463$	3.09018e21			1.46331			0.731653	+	0.681677i	$0.238749\pi$
$464$	2.71425e21	−	4.70122e21i	1.26330	−	2.18810i
$465$	−2.42223e20	+	1.39848e20i	−0.110813	+	0.0639781i
$466$	2.40373e21	+	4.16339e21i	1.08093	+	1.87223i
$467$	−2.66114e21	−	1.53641e21i	−1.17634	−	0.679159i	−0.221173	−	0.975235i	$-0.570989\pi$
$467$	−2.66114e21	−	1.53641e21i	−1.17634	−	0.679159i	−0.955164	+	0.296076i	$0.904322\pi$
$468$		−	3.56510e21i		−	1.54919i
$469$	−6.76777e20	−	1.34934e21i	−0.289110	−	0.576418i
$470$	8.87443e20			0.372699
$471$	−1.38449e20	+	2.39800e20i	−0.0571638	+	0.0990107i
$472$	−5.54684e21	+	3.20247e21i	−2.25169	+	1.30002i
$473$	−3.99619e20	−	6.92160e20i	−0.159499	−	0.276260i
$474$	6.18265e20	+	3.56955e20i	0.242632	+	0.140083i
$475$			4.19614e21i			1.61920i
$476$	−5.83298e20	−	3.84079e20i	−0.221327	−	0.145735i
$477$	−1.17429e21			−0.438156
$478$	3.12737e21	−	5.41676e21i	1.14751	−	1.98754i
$479$	1.32405e21	−	7.64443e20i	0.477773	−	0.275843i	−0.241715	−	0.970347i	$-0.577710\pi$
$479$	1.32405e21	−	7.64443e20i	0.477773	−	0.275843i	0.719488	+	0.694505i	$0.244376\pi$
$480$	−2.72700e20	−	4.72331e20i	−0.0967734	−	0.167616i
$481$	−1.81763e21	−	1.04941e21i	−0.634374	−	0.366256i
$482$		−	6.62807e21i		−	2.27515i
$483$	−1.34043e20	+	2.28083e21i	−0.0452549	+	0.770043i
$484$	1.01537e21			0.337180
$485$	2.12232e20	−	3.67596e20i	0.0693229	−	0.120071i
$486$	4.32531e21	−	2.49722e21i	1.38972	−	0.802354i
$487$	−1.01109e21	−	1.75126e21i	−0.319564	−	0.553501i	0.660833	−	0.750533i	$-0.270203\pi$
$487$	−1.01109e21	−	1.75126e21i	−0.319564	−	0.553501i	−0.980397	+	0.197032i	$0.936870\pi$
$488$	7.62892e21	+	4.40456e21i	2.37194	+	1.36944i
$489$		−	2.45677e21i		−	0.751440i
$490$	9.76234e20	−	4.19893e20i	0.293755	−	0.126348i
$491$	−5.07858e21			−1.50345			−0.751727	−	0.659475i	$-0.770779\pi$
$491$	−5.07858e21			−1.50345			−0.751727	+	0.659475i	$0.770779\pi$
$492$	1.45762e21	−	2.52468e21i	0.424545	−	0.735334i
$493$	3.87839e20	−	2.23919e20i	0.111141	−	0.0641675i
$494$	7.22439e21	+	1.25130e22i	2.03697	+	3.52814i
$495$	−2.87124e20	−	1.65771e20i	−0.0796578	−	0.0459905i
$496$			8.34309e21i			2.27758i
$497$	4.01625e21	+	2.36032e20i	1.07887	+	0.0634045i
$498$	−6.39871e21			−1.69144
$499$	−4.26647e20	+	7.38974e20i	−0.110985	+	0.192232i	−0.916168	−	0.400795i	$-0.868734\pi$
$499$	−4.26647e20	+	7.38974e20i	−0.110985	+	0.192232i	0.805183	+	0.593027i	$0.202067\pi$
$500$	−2.74332e21	+	1.58385e21i	−0.702289	+	0.405467i
$501$	−1.43416e21	−	2.48403e21i	−0.361322	−	0.625829i
$502$	−7.62527e21	−	4.40245e21i	−1.89071	−	1.09160i
$503$		−	5.58144e21i		−	1.36208i	−0.732246	−	0.681040i	$-0.761528\pi$
$503$		−	5.58144e21i		−	1.36208i	0.732246	−	0.681040i	$-0.238472\pi$
$504$	−2.81581e21	+	4.27634e21i	−0.676330	+	1.02714i
$505$	−6.30655e20			−0.149094
$506$	−4.56257e21	+	7.90260e21i	−1.06171	+	1.83893i
$507$	2.07518e21	−	1.19811e21i	0.475326	−	0.274430i
$508$	−5.49578e21	−	9.51897e21i	−1.23914	−	2.14625i
$509$	−3.68350e21	−	2.12667e21i	−0.817557	−	0.472017i	0.0320163	−	0.999487i	$-0.489807\pi$
$509$	−3.68350e21	−	2.12667e21i	−0.817557	−	0.472017i	−0.849573	+	0.527471i	$0.823140\pi$
$510$		−	1.16978e20i		−	0.0255590i
$511$	−1.96387e21	+	9.85006e20i	−0.422422	+	0.211871i
$512$	9.75890e21			2.06653
$513$	−4.25760e21	+	7.37437e21i	−0.887617	+	1.53740i
$514$	−3.63561e21	+	2.09902e21i	−0.746229	+	0.430836i
$515$	−6.26718e20	−	1.08551e21i	−0.126653	−	0.219369i
$516$	−2.18214e21	−	1.25986e21i	−0.434194	−	0.250682i
$517$			6.35966e21i			1.24598i
$518$	2.34491e21	+	4.67522e21i	0.452365	+	0.901911i
$519$	7.22527e21			1.37251
$520$	−1.54725e21	+	2.67992e21i	−0.289424	+	0.501298i
$521$	7.49642e21	−	4.32806e21i	1.38087	−	0.797245i	0.388606	−	0.921404i	$-0.372957\pi$
$521$	7.49642e21	−	4.32806e21i	1.38087	−	0.797245i	0.992262	+	0.124160i	$0.0396235\pi$
$522$	−2.84849e21	−	4.93373e21i	−0.516715	−	0.894977i
$523$	5.28071e21	+	3.04882e21i	0.943364	+	0.544651i	0.891013	−	0.453978i	$-0.149995\pi$
$523$	5.28071e21	+	3.04882e21i	0.943364	+	0.544651i	0.0523505	+	0.998629i	$0.483329\pi$
$524$		−	5.48781e20i		−	0.0965492i
$525$	−3.32700e21	−	2.19070e21i	−0.576472	−	0.379585i
$526$	1.57493e22			2.68767
$527$	−3.44142e20	+	5.96072e20i	−0.0578433	+	0.100187i
$528$	8.80012e21	−	5.08075e21i	1.45686	−	0.841117i
$529$	−5.33878e20	−	9.24704e20i	−0.0870556	−	0.150785i
$530$	1.53168e21	+	8.84318e20i	0.246015	+	0.142037i
$531$			3.25073e21i			0.514309i
$532$	1.48379e21	−	2.52476e22i	0.231248	−	3.93484i
$533$	−4.38044e21			−0.672511
$534$	−1.49016e21	+	2.58103e21i	−0.225373	+	0.390358i
$535$	7.20507e20	−	4.15985e20i	0.107351	−	0.0619794i
$536$	−5.47708e21	−	9.48659e21i	−0.803954	−	1.39249i
$537$	−3.74739e21	−	2.16355e21i	−0.541919	−	0.312877i
$538$			1.09880e22i			1.56552i
$539$	3.00907e21	+	6.99596e21i	0.422398	+	0.982058i
$540$	−3.16444e21			−0.437671
$541$	6.11457e21	−	1.05907e22i	0.833274	−	1.44327i	−0.0621541	−	0.998067i	$-0.519797\pi$
$541$	6.11457e21	−	1.05907e22i	0.833274	−	1.44327i	0.895428	−	0.445206i	$-0.146870\pi$
$542$	−1.32334e22	+	7.64031e21i	−1.77696	+	1.02593i
$543$	2.82293e21	+	4.88947e21i	0.373510	+	0.646938i
$544$	−1.16233e21	−	6.71071e20i	−0.151544	−	0.0874938i
$545$		−	1.16733e21i		−	0.149976i
$546$	−1.36929e22	−	8.04721e20i	−1.73362	−	0.101884i
$547$	2.79217e21			0.348372			0.174186	−	0.984713i	$-0.444271\pi$
$547$	2.79217e21			0.348372			0.174186	+	0.984713i	$0.444271\pi$
$548$	2.59523e21	−	4.49507e21i	0.319104	−	0.552704i
$549$	3.87194e21	−	2.23547e21i	0.469191	−	0.270888i
$550$	−7.95483e21	−	1.37782e22i	−0.950013	−	1.64547i
$551$	1.40450e22	+	8.10886e21i	1.65313	+	0.954437i
$552$			1.65796e22i			1.92336i
$553$	−1.03263e21	+	1.56825e21i	−0.118071	+	0.179314i
$554$	−2.71891e22			−3.06419
$555$	−3.07673e20	+	5.32905e20i	−0.0341779	+	0.0591978i
$556$	5.38726e21	−	3.11033e21i	0.589888	−	0.340572i
$557$	1.37742e21	+	2.38576e21i	0.148671	+	0.257505i	0.930736	−	0.365691i	$-0.119167\pi$
$557$	1.37742e21	+	2.38576e21i	0.148671	+	0.257505i	−0.782066	+	0.623196i	$0.785834\pi$
$558$	7.58268e21	+	4.37786e21i	0.806769	+	0.465788i
$559$			3.78611e21i			0.397099i
$560$	3.33364e21	−	1.67203e21i	0.344678	−	0.172878i
$561$	8.38299e20			0.0854468
$562$	−2.57980e21	+	4.46834e21i	−0.259236	+	0.449010i
$563$	−1.01137e22	+	5.83917e21i	−1.00195	+	0.578474i	−0.908824	−	0.417181i	$-0.863018\pi$
$563$	−1.01137e22	+	5.83917e21i	−1.00195	+	0.578474i	−0.0931228	+	0.995655i	$0.529685\pi$
$564$	1.00249e22	+	1.73636e22i	0.979145	+	1.69593i
$565$	−9.60900e20	−	5.54776e20i	−0.0925317	−	0.0534232i
$566$			1.34601e20i			0.0127796i
$567$	−1.26201e21	−	2.51616e21i	−0.118140	−	0.235545i
$568$	2.91945e22			2.69472
$569$	7.72871e21	−	1.33865e22i	0.703411	−	1.21834i	−0.263851	−	0.964563i	$-0.584993\pi$
$569$	7.72871e21	−	1.33865e22i	0.703411	−	1.21834i	0.967262	−	0.253780i	$-0.0816739\pi$
$570$	3.66864e21	−	2.11809e21i	0.329235	−	0.190084i
$571$	−5.65562e21	−	9.79583e21i	−0.500486	−	0.866866i	−1.00000		0.000560771i	$-0.999822\pi$
$571$	−5.65562e21	−	9.79583e21i	−0.500486	−	0.866866i	0.499514	−	0.866306i	$-0.333512\pi$
$572$	−3.33241e22	−	1.92397e22i	−2.90797	−	1.67892i
$573$		−	9.22252e21i		−	0.793620i
$574$	9.11718e21	+	6.00331e21i	0.773687	+	0.509443i
$575$	1.25538e22			1.05059
$576$	−1.93176e21	+	3.34591e21i	−0.159431	+	0.276143i
$577$	−1.86591e22	+	1.07728e22i	−1.51874	+	0.876846i	−0.518986	+	0.854783i	$0.673690\pi$
$577$	−1.86591e22	+	1.07728e22i	−1.51874	+	0.876846i	−0.999757	+	0.0220635i	$0.992976\pi$
$578$	1.12737e22	+	1.95267e22i	0.904992	+	1.56749i
$579$	7.14304e21	+	4.12404e21i	0.565529	+	0.326508i
$580$			6.02688e21i			0.470618i
$581$	9.87359e20	−	1.68006e22i	0.0760442	−	1.29394i
$582$	1.36529e22			1.03715
$583$	−6.33727e21	+	1.09765e22i	−0.474847	+	0.822459i
$584$	−1.38071e22	+	7.97154e21i	−1.02047	+	0.589168i
$585$	7.85285e20	+	1.36015e21i	0.0572506	+	0.0991610i
$586$	−8.25067e21	−	4.76353e21i	−0.593347	−	0.342569i
$587$		−	1.82677e21i		−	0.129592i	−0.997899	−	0.0647962i	$-0.979360\pi$
$587$		−	1.82677e21i		−	0.129592i	0.997899	−	0.0647962i	$-0.0206397\pi$
$588$	1.92435e22	+	1.43576e22i	1.34668	+	1.00476i
$589$	−2.49251e22			−1.72074
$590$	2.44801e21	−	4.24008e21i	0.166724	−	0.288774i
$591$	−5.37851e21	+	3.10528e21i	−0.361378	+	0.208642i
$592$	9.17763e21	+	1.58961e22i	0.608355	+	1.05370i
$593$	−1.19087e22	−	6.87551e21i	−0.778804	−	0.449643i	0.0572022	−	0.998363i	$-0.481782\pi$
$593$	−1.19087e22	−	6.87551e21i	−0.778804	−	0.449643i	−0.836006	+	0.548720i	$0.815115\pi$
$594$		−	3.22854e22i		−	2.08312i
$595$	3.07141e20	+	1.80504e19i	0.0195525	+	0.00114909i
$596$	3.22140e20			0.0202336
$597$	1.19513e21	−	2.07002e21i	0.0740662	−	0.128286i
$598$	3.74359e22	−	2.16136e22i	2.28917	−	1.32165i
$599$	−4.29677e21	−	7.44223e21i	−0.259255	−	0.449044i	0.706787	−	0.707426i	$-0.250144\pi$
$599$	−4.29677e21	−	7.44223e21i	−0.259255	−	0.449044i	−0.966043	+	0.258383i	$0.916810\pi$
$600$	−2.50337e22	−	1.44532e22i	−1.49044	−	0.860507i
$601$		−	4.93102e20i		−	0.0289695i	−0.999895	−	0.0144848i	$-0.995389\pi$
$601$		−	4.93102e20i		−	0.0289695i	0.999895	−	0.0144848i	$-0.00461080\pi$
$602$	5.18881e21	−	7.88019e21i	0.300812	−	0.456841i
$603$	−5.55962e21			−0.318058
$604$	−2.10886e22	+	3.65266e22i	−1.19056	+	2.06212i
$605$	−3.87384e20	+	2.23656e20i	−0.0215823	+	0.0124606i
$606$	−1.01425e22	−	1.75673e22i	−0.557654	−	0.965884i
$607$	−1.13280e22	−	6.54023e21i	−0.614673	−	0.354882i	0.160119	−	0.987098i	$-0.448812\pi$
$607$	−1.13280e22	−	6.54023e21i	−0.614673	−	0.354882i	−0.774792	+	0.632216i	$0.782145\pi$
$608$		−	4.86035e22i		−	2.60279i
$609$	−1.37618e22	+	6.90241e21i	−0.727340	+	0.364807i
$610$	−6.73380e21			−0.351254
$611$	1.50634e22	−	2.60905e22i	0.775519	−	1.34324i
$612$	−2.22755e21	+	1.28608e21i	−0.113192	+	0.0653516i
$613$	1.81333e22	+	3.14077e22i	0.909478	+	1.57526i	0.814791	+	0.579755i	$0.196852\pi$
$613$	1.81333e22	+	3.14077e22i	0.909478	+	1.57526i	0.0946867	+	0.995507i	$0.469815\pi$
$614$	6.27205e22	+	3.62117e22i	3.10501	+	1.79268i
$615$			1.28428e21i			0.0627567i
$616$	2.47763e22	+	4.93983e22i	1.19506	+	2.38268i
$617$	1.99849e22			0.951528			0.475764	−	0.879573i	$-0.342172\pi$
$617$	1.99849e22			0.951528			0.475764	+	0.879573i	$0.342172\pi$
$618$	2.01584e22	−	3.49154e22i	0.947432	−	1.64100i
$619$	−1.48620e22	+	8.58058e21i	−0.689528	+	0.398099i	−0.803435	−	0.595392i	$-0.796997\pi$
$619$	−1.48620e22	+	8.58058e21i	−0.689528	+	0.398099i	0.113907	+	0.993491i	$0.463663\pi$
$620$	−4.63137e21	−	8.02178e21i	−0.212117	−	0.367398i
$621$	2.20623e22	+	1.27377e22i	0.997513	+	0.575914i
$622$		−	1.29482e21i		−	0.0577946i
$623$	−6.54686e21	−	4.31086e21i	−0.288489	−	0.189959i
$624$	−4.81366e22			−2.09411
$625$	−1.05895e22	+	1.83416e22i	−0.454816	+	0.787765i
$626$	6.09412e21	−	3.51844e21i	0.258414	−	0.149196i
$627$	1.51788e22	+	2.62905e22i	0.635474	+	1.10067i
$628$	−7.94153e21	−	4.58504e21i	−0.328267	−	0.189525i
$629$			1.51426e21i			0.0618011i
$630$	2.29621e20	−	3.90716e21i	0.00925312	−	0.157448i
$631$	−2.28246e22			−0.908174			−0.454087	−	0.890957i	$-0.650034\pi$
$631$	−2.28246e22			−0.908174			−0.454087	+	0.890957i	$0.650034\pi$
$632$	−6.81281e21	+	1.18001e22i	−0.267664	+	0.463607i
$633$	−4.90521e21	+	2.83202e21i	−0.190295	+	0.109867i
$634$	−2.30780e22	−	3.99723e22i	−0.884065	−	1.53125i
$635$	4.19349e21	+	2.42111e21i	0.158630	+	0.0915852i
$636$			3.99584e22i			1.49262i
$637$	4.22579e21	−	3.58281e22i	0.155881	−	1.32163i
$638$	−6.14895e22			−2.23994
$639$	7.40861e21	−	1.28321e22i	0.266520	−	0.461626i
$640$	−1.58809e21	+	9.16883e20i	−0.0564202	+	0.0325742i
$641$	6.35747e21	+	1.10115e22i	0.223059	+	0.386350i	0.955735	−	0.294228i	$-0.0950624\pi$
$641$	6.35747e21	+	1.10115e22i	0.223059	+	0.386350i	−0.732676	+	0.680577i	$0.761729\pi$
$642$	2.31751e22	+	1.33802e22i	0.803048	+	0.463640i
$643$			4.41545e21i			0.151108i	0.997142	+	0.0755539i	$0.0240725\pi$
$643$			4.41545e21i			0.151108i	−0.997142	+	0.0755539i	$0.975927\pi$
$644$	−7.55348e22	−	4.43913e21i	−2.55305	−	0.150041i
$645$	1.11004e21			0.0370561
$646$	5.21227e21	−	9.02792e21i	0.171857	−	0.297665i
$647$	−6.24658e21	+	3.60647e21i	−0.203427	+	0.117449i	−0.598253	−	0.801307i	$-0.704138\pi$
$647$	−6.24658e21	+	3.60647e21i	−0.203427	+	0.117449i	0.394826	+	0.918756i	$0.370805\pi$
$648$	−1.02133e22	−	1.76900e22i	−0.328523	−	0.569019i
$649$	3.03856e22	+	1.75431e22i	0.965405	+	0.557377i
$650$			7.53666e22i			2.36522i
$651$	1.30128e22	−	1.97624e22i	0.403387	−	0.612621i
$652$	8.13617e22			2.49138
$653$	−3.68282e21	+	6.37884e21i	−0.111398	+	0.192946i	−0.916334	−	0.400415i	$-0.868866\pi$
$653$	−3.68282e21	+	6.37884e21i	−0.111398	+	0.192946i	0.804936	+	0.593361i	$0.202199\pi$
$654$	3.25169e22	−	1.87736e22i	0.971598	−	0.560952i
$655$	1.20880e20	+	2.09370e20i	0.00356800	+	0.00617995i
$656$	3.31767e22	+	1.91546e22i	0.967392	+	0.558524i
$657$			8.09166e21i			0.233085i
$658$	−6.71086e22	+	3.36592e22i	−1.90973	+	0.957848i
$659$	−2.68650e20			−0.00755273			−0.00377636	−	0.999993i	$-0.501202\pi$
$659$	−2.68650e20			−0.00755273			−0.00377636	+	0.999993i	$0.501202\pi$
$660$	−5.64080e21	+	9.77016e21i	−0.156671	+	0.271363i
$661$	4.78389e21	−	2.76198e21i	0.131271	−	0.0757895i	−0.432926	−	0.901429i	$-0.642519\pi$
$661$	4.78389e21	−	2.76198e21i	0.131271	−	0.0757895i	0.564198	+	0.825640i	$0.309186\pi$
$662$	−3.92943e22	−	6.80598e22i	−1.06529	−	1.84513i
$663$	−3.43912e21	−	1.98558e21i	−0.0921168	−	0.0531837i
$664$		−	1.22125e23i		−	3.23192i
$665$	4.99521e21	+	9.95929e21i	0.130611	+	0.260409i
$666$	1.92631e22			0.497659
$667$	2.42597e22	−	4.20191e22i	0.619269	−	1.07261i
$668$	8.22644e22	−	4.74954e22i	2.07491	−	1.19795i
$669$	−7.49250e21	−	1.29774e22i	−0.186732	−	0.323429i
$670$	7.25167e21	+	4.18675e21i	0.178583	+	0.103105i
$671$		−	4.82563e22i		−	1.17429i
$672$	3.85363e22	+	2.53747e22i	0.926651	+	0.610164i
$673$	−2.04986e22			−0.487083			−0.243542	−	0.969890i	$-0.578309\pi$
$673$	−2.04986e22			−0.487083			−0.243542	+	0.969890i	$0.578309\pi$
$674$	−2.58615e22	+	4.47934e22i	−0.607260	+	1.05180i
$675$	−3.84656e22	+	2.22081e22i	−0.892571	+	0.515326i
$676$	3.96780e22	+	6.87243e22i	0.909863	+	1.57593i
$677$	−9.91229e21	−	5.72286e21i	−0.224628	−	0.129689i	0.383463	−	0.923556i	$-0.374731\pi$
$677$	−9.91229e21	−	5.72286e21i	−0.224628	−	0.129689i	−0.608092	+	0.793867i	$0.708065\pi$
$678$		−	3.56887e22i		−	0.799270i
$679$	−2.10672e21	+	3.58473e22i	−0.0466282	+	0.793411i
$680$	2.23264e21			0.0488367
$681$	−1.89038e22	+	3.27423e22i	−0.408670	+	0.707836i
$682$	8.18425e22	−	4.72518e22i	1.74865	−	1.00959i
$683$	−1.02776e22	−	1.78014e22i	−0.217034	−	0.375914i	0.736866	−	0.676039i	$-0.236305\pi$
$683$	−1.02776e22	−	1.78014e22i	−0.217034	−	0.375914i	−0.953900	+	0.300125i	$0.902972\pi$
$684$	−8.06673e22	−	4.65733e22i	−1.68364	−	0.972049i
$685$			2.28661e21i			0.0471702i
$686$	−5.78972e22	+	6.87792e22i	−1.18050	+	1.40238i
$687$	5.55040e22			1.11859
$688$	1.65557e22	−	2.86754e22i	0.329793	−	0.571218i
$689$	5.19973e22	−	3.00206e22i	1.02383	−	0.591107i
$690$	−6.33681e21	−	1.09757e22i	−0.123333	−	0.213618i
$691$	−7.11999e22	−	4.11073e22i	−1.36979	−	0.790851i	−0.378892	−	0.925441i	$-0.623695\pi$
$691$	−7.11999e22	−	4.11073e22i	−1.36979	−	0.790851i	−0.990901	+	0.134590i	$0.957028\pi$
$692$			2.39281e23i			4.55051i
$693$	2.79998e22	+	1.64553e21i	0.526368	+	0.0309343i
$694$	−1.70543e23			−3.16926
$695$	−1.37023e21	+	2.37331e21i	−0.0251718	+	0.0435989i
$696$	−9.67532e22	+	5.58605e22i	−1.75708	+	1.01445i
$697$	1.58020e21	+	2.73700e21i	0.0283695	+	0.0491374i
$698$	3.10537e22	+	1.79288e22i	0.551150	+	0.318206i
$699$		−	4.78488e22i		−	0.839563i
$700$	7.25501e22	−	1.10181e23i	1.25850	−	1.91127i
$701$	1.58970e22			0.272628			0.136314	−	0.990666i	$-0.456474\pi$
$701$	1.58970e22			0.272628			0.136314	+	0.990666i	$0.456474\pi$
$702$	−7.64704e22	+	1.32451e23i	−1.29657	+	2.24573i
$703$	−4.74899e22	+	2.74183e22i	−0.796084	+	0.459619i
$704$	2.08502e22	+	3.61135e22i	0.345564	+	0.598534i
$705$	−7.64938e21	−	4.41637e21i	−0.125347	−	0.0723690i
$706$		−	7.95712e22i		−	1.28919i
$707$	4.76902e22	−	2.39196e22i	0.763966	−	0.383177i
$708$	1.10614e23			1.75205
$709$	5.39339e22	−	9.34163e22i	0.844680	−	1.46303i	−0.0412193	−	0.999150i	$-0.513124\pi$
$709$	5.39339e22	−	9.34163e22i	0.844680	−	1.46303i	0.885899	−	0.463878i	$-0.153542\pi$
$710$	−1.93268e22	+	1.11583e22i	−0.299290	+	0.172795i
$711$	3.45774e21	+	5.98897e21i	0.0529462	+	0.0917056i
$712$	−4.92613e22	−	2.84410e22i	−0.745874	−	0.430631i
$713$			7.45699e22i			1.11647i
$714$	4.43678e21	+	8.84592e21i	0.0656875	+	0.130966i
$715$	1.69517e22			0.248179
$716$	7.16510e22	−	1.24103e23i	1.03733	−	1.79671i
$717$	−5.39131e22	+	3.11267e22i	−0.771864	+	0.445636i
$718$	3.38932e22	+	5.87048e22i	0.479863	+	0.831148i
$719$	4.62662e21	+	2.67118e21i	0.0647788	+	0.0374001i	0.532040	−	0.846719i	$-0.321426\pi$
$719$	4.62662e21	+	2.67118e21i	0.0647788	+	0.0374001i	−0.467261	+	0.884120i	$0.654759\pi$
$720$		−	1.37354e22i		−	0.190188i
$721$	8.85639e22	+	5.83159e22i	1.21276	+	0.798556i
$722$	2.42151e23			3.27935
$723$	−3.29847e22	+	5.71311e22i	−0.441779	+	0.765185i
$724$	−1.61926e23	+	9.34879e22i	−2.14490	+	1.23836i
$725$	4.22968e22	+	7.32602e22i	0.554120	+	0.959764i
$726$	−1.24602e22	−	7.19390e21i	−0.161448	−	0.0932119i
$727$		−	1.67749e22i		−	0.214974i	−0.994207	−	0.107487i	$-0.965720\pi$
$727$		−	1.67749e22i		−	0.214974i	0.994207	−	0.107487i	$-0.0342804\pi$
$728$	1.53588e22	−	2.61341e23i	0.194674	−	3.31250i
$729$	−7.07291e22			−0.886702
$730$	6.09355e21	−	1.05543e22i	0.0755592	−	0.130872i
$731$	2.36565e21	−	1.36581e21i	0.0290142	−	0.0167514i
$732$	−7.60676e22	−	1.31753e23i	−0.922807	−	1.59835i
$733$	7.51570e22	+	4.33919e22i	0.901857	+	0.520687i	0.877802	−	0.479023i	$-0.159009\pi$
$733$	7.51570e22	+	4.33919e22i	0.901857	+	0.520687i	0.0240549	+	0.999711i	$0.492342\pi$
$734$			9.04424e21i			0.107350i
$735$	−1.05043e22	−	1.23894e21i	−0.123330	−	0.0145463i
$736$	−1.45410e23			−1.68877
$737$	−3.00034e22	+	5.19675e22i	−0.344692	+	0.597024i
$738$	3.48176e22	−	2.01019e22i	0.395683	−	0.228448i
$739$	2.73175e22	+	4.73153e22i	0.307104	+	0.531919i	0.977728	−	0.209878i	$-0.0673068\pi$
$739$	2.73175e22	+	4.73153e22i	0.307104	+	0.531919i	−0.670624	+	0.741798i	$0.733973\pi$
$740$	−1.76484e22	−	1.01893e22i	−0.196268	−	0.113316i
$741$		−	1.43809e23i		−	1.58212i
$742$	−1.49367e23	−	8.77819e21i	−1.62564	−	0.0955375i
$743$	−1.59262e23			−1.71475			−0.857377	−	0.514689i	$-0.827907\pi$
$743$	−1.59262e23			−1.71475			−0.857377	+	0.514689i	$0.827907\pi$
$744$	8.58522e22	−	1.48700e23i	0.914467	−	1.58390i
$745$	−1.22903e20	+	7.09578e19i	−0.00129512	+	0.000747739i
$746$	−3.56527e21	−	6.17522e21i	−0.0371690	−	0.0643787i
$747$	−5.36786e22	−	3.09914e22i	−0.553652	−	0.319651i
$748$			2.77622e22i			0.283296i
$749$	−3.87073e22	+	5.87844e22i	−0.390785	+	0.593482i
$750$	4.48864e22			0.448358
$751$	−1.27602e22	+	2.21014e22i	−0.126107	+	0.218424i	−0.922165	−	0.386796i	$-0.873582\pi$
$751$	−1.27602e22	+	2.21014e22i	−0.126107	+	0.218424i	0.796058	+	0.605220i	$0.206915\pi$
$752$	−2.28175e23	+	1.31737e23i	−2.23113	+	1.28814i
$753$	4.38177e22	+	7.58945e22i	0.423926	+	0.734261i
$754$	2.52261e23	+	1.45643e23i	2.41479	+	1.39418i
$755$		−	1.85808e22i		−	0.175990i
$756$	2.39296e23	−	1.20022e23i	2.24265	−	1.12483i
$757$	8.48424e22			0.786767			0.393383	−	0.919375i	$-0.371304\pi$
$757$	8.48424e22			0.786767			0.393383	+	0.919375i	$0.371304\pi$
$758$	1.13512e22	−	1.96608e22i	0.104157	−	0.180405i
$759$	7.86548e22	−	4.54113e22i	0.714152	−	0.412316i
$760$	4.04257e22	+	7.00193e22i	0.363202	+	0.629085i
$761$	−1.70318e23	−	9.83333e22i	−1.51420	−	0.874225i	−0.999862	−	0.0166392i	$-0.994703\pi$
$761$	−1.70318e23	−	9.83333e22i	−1.51420	−	0.874225i	−0.514341	−	0.857586i	$-0.671963\pi$
$762$			1.55750e23i			1.37022i
$763$	4.42749e22	+	8.82738e22i	0.385444	+	0.768485i
$764$	3.05425e23			2.63122
$765$	5.66570e20	−	9.81328e20i	0.00483017	−	0.00836609i
$766$	1.69197e23	−	9.76859e22i	1.42746	−	0.824142i
$767$	−8.31044e22	−	1.43941e23i	−0.693843	−	1.20177i
$768$	−9.93191e22	−	5.73419e22i	−0.820622	−	0.473786i
$769$		−	4.85736e22i		−	0.397182i	−0.980082	−	0.198591i	$-0.936364\pi$
$769$		−	4.85736e22i		−	0.397182i	0.980082	−	0.198591i	$-0.0636365\pi$
$770$	−3.52823e22	−	2.32320e22i	−0.285516	−	0.188001i
$771$	4.17832e22			0.334631
$772$	−1.36577e23	+	2.36558e23i	−1.08253	+	1.87499i
$773$	−2.01171e22	+	1.16146e22i	−0.157808	+	0.0911108i	−0.576825	−	0.816868i	$-0.695708\pi$
$773$	−2.01171e22	+	1.16146e22i	−0.157808	+	0.0911108i	0.419016	+	0.907979i	$0.362375\pi$
$774$	−1.73746e22	−	3.00936e22i	−0.134892	−	0.233640i
$775$	−1.12594e23	−	6.50062e22i	−0.865171	−	0.499506i
$776$			2.60577e23i			1.98172i
$777$	3.05411e21	−	5.19678e22i	0.0229888	−	0.391171i
$778$	−1.79211e23			−1.33515
$779$	−5.72246e22	+	9.91159e22i	−0.421971	+	0.730876i
$780$	4.62828e22	−	2.67214e22i	0.337802	−	0.195030i
$781$	−7.99636e22	−	1.38501e23i	−0.577676	−	1.00056i
$782$	−2.70093e22	−	1.55939e22i	−0.193135	−	0.111506i
$783$			1.71665e23i			1.21503i
$784$	−1.88673e23	+	2.52878e23i	−1.32185	+	1.77167i
$785$	4.03979e21			0.0280157
$786$	−3.88811e21	+	6.73440e21i	−0.0266906	+	0.0462294i
$787$	1.70081e23	−	9.81963e22i	1.15573	−	0.667264i	0.205456	−	0.978666i	$-0.434132\pi$
$787$	1.70081e23	−	9.81963e22i	1.15573	−	0.667264i	0.950278	+	0.311403i	$0.100799\pi$
$788$	−1.02839e23	−	1.78122e23i	−0.691745	−	1.19814i
$789$	−1.35752e23	−	7.83766e22i	−0.903922	−	0.521879i
$790$		−	1.04156e22i		−	0.0686543i
$791$	9.37051e22	+	5.50699e21i	0.611437	+	0.0359337i
$792$	2.03533e23			1.31472
$793$	−1.14299e23	+	1.97971e23i	−0.730897	+	1.26595i
$794$	1.76590e23	−	1.01954e23i	1.11790	−	0.645418i
$795$	−8.80164e21	−	1.52449e22i	−0.0551603	−	0.0955404i
$796$	6.85536e22	+	3.95794e22i	0.425330	+	0.245564i
$797$		−	5.92359e22i		−	0.363846i	−0.983313	−	0.181923i	$-0.941768\pi$
$797$		−	5.92359e22i		−	0.363846i	0.983313	−	0.181923i	$-0.0582322\pi$
$798$	−1.97088e23	+	2.99316e23i	−1.19850	+	1.82015i
$799$	−2.17359e22			−0.130859
$800$	1.26761e23	−	2.19556e23i	0.755554	−	1.30866i
$801$	−2.50018e22	+	1.44348e22i	−0.147540	+	0.0851825i
$802$	−5.15555e22	−	8.92967e22i	−0.301217	−	0.521724i
$803$	7.56353e22	+	4.36680e22i	0.437522	+	0.252603i
$804$			1.89180e23i			1.08350i
$805$	2.97958e22	−	1.49445e22i	0.168961	−	0.0847448i
$806$	−4.47678e23			−2.51354
$807$	5.46817e22	−	9.47115e22i	0.303986	−	0.526519i
$808$	3.35289e23	−	1.93579e23i	1.84556	−	1.06553i
$809$	1.46472e23	+	2.53697e23i	0.798302	+	1.38270i	0.920721	+	0.390221i	$0.127602\pi$
$809$	1.46472e23	+	2.53697e23i	0.798302	+	1.38270i	−0.122419	+	0.992479i	$0.539065\pi$
$810$	1.35224e22	+	7.80718e21i	0.0729751	+	0.0421322i
$811$		−	2.68724e23i		−	1.43595i	−0.696069	−	0.717975i	$-0.745069\pi$
$811$		−	2.68724e23i		−	1.43595i	0.696069	−	0.717975i	$-0.254931\pi$
$812$	−2.28589e23	−	4.55754e23i	−1.20950	−	2.41147i
$813$	1.52088e23			0.796840
$814$	1.03957e23	−	1.80058e23i	0.539333	−	0.934151i
$815$	−3.10411e22	+	1.79216e22i	−0.159469	+	0.0920693i
$816$	1.73649e22	+	3.00769e22i	0.0883386	+	0.153007i
$817$	8.56682e22	+	4.94606e22i	0.431562	+	0.249162i
$818$		−	6.65925e23i		−	3.32199i
$819$	−1.10972e23	−	7.30706e22i	−0.548202	−	0.360970i
$820$	−4.25320e22			−0.208068
$821$	8.50798e22	−	1.47363e23i	0.412175	−	0.713908i	−0.582952	−	0.812506i	$-0.698103\pi$
$821$	8.50798e22	−	1.47363e23i	0.412175	−	0.713908i	0.995127	+	0.0985985i	$0.0314360\pi$
$822$	−6.36951e22	+	3.67744e22i	−0.305585	+	0.176429i
$823$	5.75887e22	+	9.97466e22i	0.273614	+	0.473914i	0.969785	−	0.243963i	$-0.0784475\pi$
$823$	5.75887e22	+	9.97466e22i	0.273614	+	0.473914i	−0.696170	+	0.717877i	$0.745114\pi$
$824$	6.66391e23	+	3.84741e23i	3.13553	+	1.81030i
$825$			1.58349e23i			0.737877i
$826$	−2.43002e22	+	4.13484e23i	−0.112142	+	1.90818i
$827$	8.08379e21			0.0369463			0.0184731	−	0.999829i	$-0.494119\pi$
$827$	8.08379e21			0.0369463			0.0184731	+	0.999829i	$0.494119\pi$
$828$	−1.39336e23	+	2.41337e23i	−0.630697	+	1.09240i
$829$	1.52390e23	−	8.79825e22i	0.683157	−	0.394421i	−0.117886	−	0.993027i	$-0.537612\pi$
$829$	1.52390e23	−	8.79825e22i	0.683157	−	0.394421i	0.801044	+	0.598606i	$0.204278\pi$
$830$	4.66770e22	+	8.08470e22i	0.207242	+	0.358954i
$831$	2.34358e23	+	1.35307e23i	1.03056	+	0.594992i
$832$		−	1.97541e23i		−	0.860341i
$833$	−2.39107e22	+	1.02843e22i	−0.103141	+	0.0443625i
$834$	−8.81468e22			−0.376598
$835$	−2.09236e22	+	3.62408e22i	−0.0885412	+	0.153358i
$836$	−8.70670e23	+	5.02681e23i	−3.64925	+	2.10689i
$837$	−1.31917e23	−	2.28486e23i	−0.547641	−	0.948542i
$838$	−1.36442e23	−	7.87748e22i	−0.561042	−	0.323918i
$839$			3.28773e23i			1.33906i	0.742785	+	0.669530i	$0.233505\pi$
$839$			3.28773e23i			1.33906i	−0.742785	+	0.669530i	$0.766495\pi$
$840$	−7.66216e22	−	4.50300e21i	−0.309113	−	0.0181663i
$841$	7.67010e22			0.306502
$842$	2.93238e23	−	5.07904e23i	1.16071	−	2.01041i
$843$	4.44735e22	−	2.56768e22i	0.174374	−	0.100675i
$844$	−9.37890e22	−	1.62447e23i	−0.364261	−	0.630918i
$845$	−3.02758e22	−	1.74798e22i	−0.116478	−	0.0672484i
$846$			2.76505e23i			1.05376i
$847$	2.08111e22	−	3.16057e22i	0.0785649	−	0.119316i
$848$	−5.25092e23			−1.96367
$849$	6.69844e20	−	1.16020e21i	0.00248149	−	0.00429807i
$850$	4.70907e22	−	2.71878e22i	0.172816	−	0.0997754i
$851$	8.20289e22	+	1.42078e23i	0.298216	+	0.516525i
$852$	−4.36645e23	−	2.52097e23i	−1.57258	−	0.907928i
$853$		−	7.26645e22i		−	0.259257i	−0.991563	−	0.129628i	$-0.958622\pi$
$853$		−	7.26645e22i		−	0.259257i	0.991563	−	0.129628i	$-0.0413784\pi$
$854$	5.09212e23	−	2.55401e23i	1.79985	−	0.902735i
$855$	4.10348e22			0.143689
$856$	−2.55372e23	+	4.42318e23i	−0.885898	+	1.53442i
$857$	−3.80806e23	+	2.19858e23i	−1.30875	+	0.755607i	−0.981888	−	0.189464i	$-0.939325\pi$
$857$	−3.80806e23	+	2.19858e23i	−1.30875	+	0.755607i	−0.326863	+	0.945072i	$0.605991\pi$
$858$	2.72626e23	+	4.72202e23i	0.928258	+	1.60779i
$859$	1.41779e23	+	8.18564e22i	0.478264	+	0.276126i	0.719693	−	0.694293i	$-0.244283\pi$
$859$	1.41779e23	+	8.18564e22i	0.478264	+	0.276126i	−0.241429	+	0.970419i	$0.577616\pi$
$860$			3.67614e22i			0.122858i
$861$	−4.87106e22	−	9.71177e22i	−0.161287	−	0.321568i
$862$	−5.88616e23			−1.93096
$863$	−1.24058e23	+	2.14875e23i	−0.403217	+	0.698393i	−0.994112	−	0.108356i	$-0.965441\pi$
$863$	−1.24058e23	+	2.14875e23i	−0.403217	+	0.698393i	0.590895	+	0.806748i	$0.298775\pi$
$864$	4.45544e23	−	2.57235e23i	1.43477	−	0.828362i
$865$	−5.27066e22	−	9.12905e22i	−0.168165	−	0.291271i
$866$	−4.61199e21	−	2.66273e21i	−0.0145796	−	0.00841753i
$867$		−	2.24415e23i		−	0.702910i
$868$	6.54477e23	+	4.30948e23i	2.03113	+	1.33742i
$869$	7.46411e22			0.229520
$870$	4.27005e22	−	7.39594e22i	0.130100	−	0.225340i
$871$	2.46178e23	−	1.42131e23i	0.743197	−	0.429085i
$872$	3.58311e23	+	6.20614e23i	1.07184	+	1.85648i
$873$	1.14534e23	+	6.61260e22i	0.339484	+	0.196001i
$874$		−	1.12941e24i		−	3.31712i
$875$	−6.92624e21	+	1.17855e23i	−0.0201573	+	0.342991i
$876$	2.75340e23			0.794029
$877$	2.29546e23	−	3.97585e23i	0.655953	−	1.13614i	−0.325700	−	0.945473i	$-0.605600\pi$
$877$	2.29546e23	−	3.97585e23i	0.655953	−	1.13614i	0.981654	−	0.190672i	$-0.0610666\pi$
$878$	−2.88376e23	+	1.66494e23i	−0.816588	+	0.471457i
$879$	4.74115e22	+	8.21191e22i	0.133037	+	0.230427i
$880$	−1.28389e23	−	7.41256e22i	−0.357000	−	0.206114i
$881$		−	6.42654e22i		−	0.177080i	−0.996073	−	0.0885401i	$-0.971780\pi$
$881$		−	6.42654e22i		−	0.177080i	0.996073	−	0.0885401i	$-0.0282201\pi$
$882$	1.30828e23	+	3.04170e23i	0.357233	+	0.830553i
$883$	8.52135e22			0.230581			0.115290	−	0.993332i	$-0.463220\pi$
$883$	8.52135e22			0.230581			0.115290	+	0.993332i	$0.463220\pi$
$884$	6.57569e22	−	1.13894e23i	0.176329	−	0.305410i
$885$	−4.22016e22	+	2.43651e22i	−0.112146	+	0.0647473i
$886$	1.19672e22	+	2.07278e22i	0.0315154	+	0.0545862i
$887$	−1.83569e23	−	1.05983e23i	−0.479081	−	0.276598i	0.240952	−	0.970537i	$-0.422540\pi$
$887$	−1.83569e23	−	1.05983e23i	−0.479081	−	0.276598i	−0.720034	+	0.693939i	$0.755874\pi$
$888$		−	3.77759e23i		−	0.977038i
$889$	−4.08941e23	−	2.40332e22i	−1.04821	−	0.0616024i
$890$	4.34813e22			0.110454
$891$	−5.59484e22	+	9.69055e22i	−0.140853	+	0.243965i
$892$	4.29776e23	−	2.48131e23i	1.07232	−	0.619103i
$893$	−3.93566e23	−	6.81676e23i	−0.973208	−	1.68565i
$894$	−3.95316e21	−	2.28236e21i	−0.00968823	−	0.00559350i
$895$			6.31304e22i			0.153340i
$896$	8.53157e22	−	1.29568e23i	0.205383	−	0.311914i
$897$	−4.30241e23			−1.02653
$898$	−2.05350e23	+	3.55677e23i	−0.485607	+	0.841096i
$899$	−4.35167e23	+	2.51244e23i	−1.01995	+	0.588867i
$900$	−2.42932e23	−	4.20770e23i	−0.564345	−	0.977474i
$901$	−3.75152e22	−	2.16594e22i	−0.0863791	−	0.0498710i
$902$		−	4.33934e23i		−	0.990311i
$903$	−8.39411e22	+	4.21017e22i	−0.189877	+	0.0952353i
$904$	6.81152e23			1.52720
$905$	4.11852e22	−	7.13349e22i	0.0915278	−	0.158531i
$906$	5.17581e23	−	2.98826e23i	1.14013	−	0.658252i
$907$	2.71444e23	+	4.70155e23i	0.592682	+	1.02656i	0.993870	+	0.110559i	$0.0352642\pi$
$907$	2.71444e23	+	4.70155e23i	0.592682	+	1.02656i	−0.401188	+	0.915996i	$0.631402\pi$
$908$	−1.08434e24	−	6.26043e23i	−2.34681	−	1.35493i
$909$		−	1.96496e23i		−	0.421544i
$910$	8.97186e22	+	1.78878e23i	0.190788	+	0.380388i
$911$	3.00371e23			0.633156			0.316578	−	0.948566i	$-0.397466\pi$
$911$	3.00371e23			0.633156			0.316578	+	0.948566i	$0.397466\pi$
$912$	−6.28841e23	+	1.08918e24i	−1.31396	+	2.27585i
$913$	−5.79372e23	+	3.34500e23i	−1.20003	+	0.692836i
$914$	6.37917e23	+	1.10491e24i	1.30977	+	2.26859i
$915$	5.80425e22	+	3.35108e22i	0.118135	+	0.0682051i
$916$			1.83814e24i			3.70865i
$917$	−1.70820e22	−	1.12479e22i	−0.0341653	−	0.0224965i
$918$	1.10344e23			0.218780
$919$	2.02263e23	−	3.50329e23i	0.397550	−	0.688577i	−0.595873	−	0.803079i	$-0.703194\pi$
$919$	2.02263e23	−	3.50329e23i	0.397550	−	0.688577i	0.993423	+	0.114502i	$0.0365271\pi$
$920$	2.09481e23	−	1.20944e23i	0.408170	−	0.235657i
$921$	−3.60416e23	−	6.24258e23i	−0.696188	−	1.20583i
$922$	4.14051e23	+	2.39052e23i	0.792877	+	0.457768i
$923$			7.57601e23i			1.43822i
$924$	5.59935e22	−	9.52767e23i	0.105381	−	1.79313i
$925$	−2.86034e23			−0.533684
$926$	7.25066e23	−	1.25585e24i	1.34119	−	2.32301i
$927$	3.38216e23	−	1.95269e23i	0.620236	−	0.358093i
$928$	−4.89921e23	−	8.48567e23i	−0.890721	−	1.54277i
$929$	7.48566e23	+	4.32185e23i	1.34929	+	0.779012i	0.988149	−	0.153501i	$-0.0490547\pi$
$929$	7.48566e23	+	4.32185e23i	1.34929	+	0.779012i	0.361139	+	0.932512i	$0.382388\pi$
$930$			1.31253e23i			0.234556i
$931$	−7.55477e23	−	5.63664e23i	−1.33852	−	0.998672i
$932$	1.58462e24			2.78355
$933$	−6.44370e21	+	1.11608e22i	−0.0112223	+	0.0194376i
$934$	−1.24880e24	+	7.20992e23i	−2.15634	+	1.24496i
$935$	−6.11518e21	−	1.05918e22i	−0.0104693	−	0.0181333i
$936$	−8.34996e23	−	4.82085e23i	−1.41735	−	0.818308i
$937$			8.54863e23i			1.43873i	0.694631	+	0.719366i	$0.255568\pi$
$937$			8.54863e23i			1.43873i	−0.694631	+	0.719366i	$0.744432\pi$
$938$	−7.07169e23	−	4.15598e22i	−1.18005	−	0.0693507i
$939$	−7.00383e22			−0.115881
$940$	1.46258e23	−	2.53327e23i	0.239937	−	0.415583i
$941$	1.01492e24	−	5.85966e23i	1.65088	−	0.953138i	0.674174	−	0.738573i	$-0.264500\pi$
$941$	1.01492e24	−	5.85966e23i	1.65088	−	0.953138i	0.976710	−	0.214565i	$-0.0688334\pi$
$942$	6.49700e22	+	1.12531e23i	0.104787	+	0.181496i
$943$	2.96531e23	+	1.71202e23i	0.474216	+	0.273789i
$944$			1.45358e24i			2.30496i
$945$	−6.48587e22	+	9.85004e22i	−0.101980	+	0.154876i
$946$	−3.75059e23			−0.584751
$947$	−1.05298e23	+	1.82381e23i	−0.162787	+	0.281956i	−0.935867	−	0.352353i	$-0.885382\pi$
$947$	−1.05298e23	+	1.82381e23i	−0.162787	+	0.281956i	0.773080	+	0.634308i	$0.218715\pi$
$948$	2.03791e23	−	1.17659e23i	0.312404	−	0.180367i
$949$	−2.06862e23	−	3.58296e23i	−0.314450	−	0.544644i
$950$	1.70532e24	+	9.84564e23i	2.57049	+	1.48407i
$951$			4.59392e23i			0.686656i
$952$	−1.68832e23	+	8.46800e22i	−0.250242	+	0.125512i
$953$	−2.14295e23			−0.314969			−0.157485	−	0.987521i	$-0.550339\pi$
$953$	−2.14295e23			−0.314969			−0.157485	+	0.987521i	$0.550339\pi$
$954$	−2.75531e23	+	4.77234e23i	−0.401591	+	0.695575i
$955$	−1.16526e23	+	6.72760e22i	−0.168420	+	0.0972374i
$956$	−1.03083e24	−	1.78546e24i	−1.47749	−	2.55909i
$957$	5.30013e23	+	3.06003e23i	0.753340	+	0.434941i
$958$		−	7.17463e23i		−	1.01129i
$959$	−8.67271e22	−	1.72914e23i	−0.121229	−	0.241702i
$960$	−5.79163e22			−0.0802843
$961$	2.24260e22	−	3.88429e22i	0.0308294	−	0.0533980i
$962$	−8.52963e23	+	4.92459e23i	−1.16287	+	0.671381i
$963$	1.29610e23	+	2.24492e23i	0.175238	+	0.303522i
$964$	−1.89203e24	−	1.09236e24i	−2.53694	−	1.46471i
$965$		−	1.20335e23i		−	0.160020i
$966$	8.95479e23	+	5.89639e23i	1.18097	+	0.777623i
$967$	−6.53788e23			−0.855116			−0.427558	−	0.903988i	$-0.640626\pi$
$967$	−6.53788e23			−0.855116			−0.427558	+	0.903988i	$0.640626\pi$
$968$	1.37302e23	−	2.37814e23i	0.178104	−	0.308485i
$969$	−8.98551e22	+	5.18779e22i	−0.115599	+	0.0667409i
$970$	−9.95944e22	−	1.72503e23i	−0.127075	−	0.220101i
$971$	−3.44034e22	−	1.98628e22i	−0.0435359	−	0.0251355i	0.478074	−	0.878320i	$-0.341335\pi$
$971$	−3.44034e22	−	1.98628e22i	−0.0435359	−	0.0251355i	−0.521610	+	0.853184i	$0.674668\pi$
$972$		−	1.64625e24i		−	2.06617i
$973$	1.36016e22	−	2.31440e23i	0.0169312	−	0.288095i
$974$	−9.48952e23			−1.17158
$975$	3.75062e23	−	6.49627e23i	0.459268	−	0.795476i
$976$	1.73136e24	−	9.99602e23i	2.10276	−	1.21403i
$977$	7.87164e23	+	1.36341e24i	0.948219	+	1.64236i	0.749175	+	0.662372i	$0.230450\pi$
$977$	7.87164e23	+	1.36341e24i	0.948219	+	1.64236i	0.199044	+	0.979991i	$0.436216\pi$
$978$	−9.98436e23	−	5.76447e23i	−1.19291	−	0.688730i
$979$			3.11599e23i			0.369262i
$980$	4.10304e22	−	3.47874e23i	0.0482278	−	0.408897i
$981$	3.63711e23			0.424037
$982$	−1.19162e24	+	2.06394e24i	−1.37798	+	2.38674i
$983$	1.14986e24	−	6.63874e23i	1.31892	−	0.761478i	0.335364	−	0.942089i	$-0.391141\pi$
$983$	1.14986e24	−	6.63874e23i	1.31892	−	0.761478i	0.983555	+	0.180611i	$0.0578073\pi$
$984$	−3.94210e23	−	6.82791e23i	−0.448504	−	0.776832i
$985$	7.84698e22	+	4.53045e22i	0.0885549	+	0.0511272i
$986$		−	2.10158e23i		−	0.235250i
$987$	7.45953e23	+	4.38391e22i	0.828274	+	0.0486771i
$988$	4.76256e24			5.24548
$989$	1.47974e23	−	2.56298e23i	0.161665	−	0.280011i
$990$	−1.34739e23	+	7.77918e22i	−0.146020	+	0.0843048i
$991$	−3.69882e23	−	6.40655e23i	−0.397625	−	0.688707i	0.595807	−	0.803128i	$-0.296832\pi$
$991$	−3.69882e23	−	6.40655e23i	−0.397625	−	0.688707i	−0.993432	+	0.114420i	$0.963499\pi$
$992$	1.30417e24	+	7.52961e23i	1.39072	+	0.802933i
$993$			7.82195e23i			0.827410i
$994$	1.03828e24	−	1.57683e24i	1.08949	−	1.65460i
$995$	−3.48727e22			−0.0362995
$996$	−1.05456e24	+	1.82656e24i	−1.08892	+	1.88607i
$997$	−6.99809e21	+	4.04035e21i	−0.00716834	+	0.00413864i	−0.503580	−	0.863949i	$-0.667984\pi$
$997$	−6.99809e21	+	4.04035e21i	−0.00716834	+	0.00413864i	0.496412	+	0.868087i	$0.334651\pi$
$998$	2.00213e23	+	3.46779e23i	0.203446	+	0.352378i
$999$	−5.02683e23	−	2.90224e23i	−0.506722	−	0.292556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.17.d.a.5.10	yes	20
7.2	even	3		49.17.b.a.48.1		20
7.3	odd	6	inner	7.17.d.a.3.10	✓	20
7.5	odd	6		49.17.b.a.48.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.17.d.a.3.10	✓	20	7.3	odd	6	inner
7.17.d.a.5.10	yes	20	1.1	even	1	trivial
49.17.b.a.48.1		20	7.2	even	3
49.17.b.a.48.2		20	7.5	odd	6

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)

\(f(q)\)	\(=\)	\(q+(234.636 - 406.401i) q^{2} +(-4044.92 + 2335.34i) q^{3} +(-77340.0 - 133957. i) q^{4} +(59013.4 + 34071.4i) q^{5} +2.19181e6i q^{6} +(-5.75487e6 - 338210. i) q^{7} -4.18327e7 q^{8} +(-1.06158e7 + 1.83871e7i) q^{9} +O(q^{10})\)	\(q+(234.636 - 406.401i) q^{2} +(-4044.92 + 2335.34i) q^{3} +(-77340.0 - 133957. i) q^{4} +(59013.4 + 34071.4i) q^{5} +2.19181e6i q^{6} +(-5.75487e6 - 338210. i) q^{7} -4.18327e7 q^{8} +(-1.06158e7 + 1.83871e7i) q^{9} +(2.76933e7 - 1.59887e7i) q^{10} +(1.14580e8 + 1.98458e8i) q^{11} +(6.25668e8 + 3.61230e8i) q^{12} -1.08556e9i q^{13} +(-1.48775e9 + 2.25943e9i) q^{14} -3.18273e8 q^{15} +(-4.74691e9 + 8.22188e9i) q^{16} +(-6.78285e8 + 3.91608e8i) q^{17} +(4.98168e9 + 8.62853e9i) q^{18} +(-2.45630e10 - 1.41815e10i) q^{19} -1.05403e10i q^{20} +(2.40678e10 - 1.20715e10i) q^{21} +1.07538e11 q^{22} +(-4.24275e10 + 7.34866e10i) q^{23} +(1.69210e11 - 9.76935e10i) q^{24} +(-7.39722e10 - 1.28124e11i) q^{25} +(-4.41175e11 - 2.54712e11i) q^{26} -3.00223e11i q^{27} +(3.99776e11 + 7.97061e11i) q^{28} -5.71793e11 q^{29} +(-7.46781e10 + 1.29346e11i) q^{30} +(7.61056e11 - 4.39396e11i) q^{31} +(8.56814e11 + 1.48405e12i) q^{32} +(-9.26932e11 - 5.35164e11i) q^{33} +3.67541e11i q^{34} +(-3.28091e11 - 2.16035e11i) q^{35} +3.28410e12 q^{36} +(9.66695e11 - 1.67437e12i) q^{37} +(-1.15267e13 + 6.65496e12i) q^{38} +(2.53516e12 + 4.39102e12i) q^{39} +(-2.46869e12 - 1.42530e12i) q^{40} -4.03517e12i q^{41} +(7.41293e11 - 1.26136e13i) q^{42} -3.48769e12 q^{43} +(1.77232e13 - 3.06975e13i) q^{44} +(-1.25295e12 + 7.23389e11i) q^{45} +(1.99100e13 + 3.44852e13i) q^{46} +(2.40341e13 + 1.38761e13i) q^{47} -4.43425e13i q^{48} +(3.30042e13 + 3.89271e12i) q^{49} -6.94261e13 q^{50} +(1.82907e12 - 3.16805e12i) q^{51} +(-1.45419e14 + 8.39575e13i) q^{52} +(2.76544e13 + 4.78988e13i) q^{53} +(-1.22011e14 - 7.04430e13i) q^{54} +1.56156e13i q^{55} +(2.40742e14 + 1.41482e13i) q^{56} +1.32474e14 q^{57} +(-1.34163e14 + 2.32377e14i) q^{58} +(1.32596e14 - 7.65541e13i) q^{59} +(2.46152e13 + 4.26348e13i) q^{60} +(-1.82367e14 - 1.05290e14i) q^{61} -4.12392e14i q^{62} +(6.73111e13 - 1.02225e14i) q^{63} +1.81971e14 q^{64} +(3.69867e13 - 6.40628e13i) q^{65} +(-4.34983e14 + 2.51137e14i) q^{66} +(1.30928e14 + 2.26774e14i) q^{67} +(1.04917e14 + 6.05739e13i) q^{68} -3.96330e14i q^{69} +(-1.64779e14 + 8.26470e13i) q^{70} -6.97886e14 q^{71} +(4.44087e14 - 7.69181e14i) q^{72} +(3.30055e14 - 1.90557e14i) q^{73} +(-4.53643e14 - 7.85732e14i) q^{74} +(5.98423e14 + 3.45500e14i) q^{75} +4.38718e15i q^{76} +(-5.92271e14 - 1.18085e15i) q^{77} +2.37936e15 q^{78} +(1.62858e14 - 2.82079e14i) q^{79} +(-5.60262e14 + 3.23467e14i) q^{80} +(2.44146e14 + 4.22874e14i) q^{81} +(-1.63990e15 - 9.46795e14i) q^{82} +2.91937e15i q^{83} +(-3.47847e15 - 2.29044e15i) q^{84} -5.33705e13 q^{85} +(-8.18337e14 + 1.41740e15i) q^{86} +(2.31286e15 - 1.33533e15i) q^{87} +(-4.79318e15 - 8.30204e15i) q^{88} +(1.17758e15 + 6.79874e14i) q^{89} +6.78932e14i q^{90} +(-3.67149e14 + 6.24728e15i) q^{91} +1.31254e16 q^{92} +(-2.05227e15 + 3.55464e15i) q^{93} +(1.12785e16 - 6.51165e15i) q^{94} +(-9.66364e14 - 1.67379e15i) q^{95} +(-6.93149e15 - 4.00190e15i) q^{96} -6.22903e15i q^{97} +(9.32596e15 - 1.24996e16i) q^{98} -4.86541e15 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

Properties

Related objects

Downloads

Learn more