LMFDB - Embedded newform 7.17.d.a.5.7

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			5.7
Root			$90.3350 + 156.465i$ of defining polynomial
Character	$\chi$	$=$	7.5
Dual form			7.17.d.a.3.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(94.8350 - 164.259i) q^{2} +(-9421.11 + 5439.28i) q^{3} +(14780.6 + 25600.8i) q^{4} +(-477118. - 275464. i) q^{5} +2.06334e6i q^{6} +(5.57858e6 - 1.45338e6i) q^{7} +1.80371e7 q^{8} +(3.76482e7 - 6.52085e7i) q^{9} +O(q^{10})$	\(q+(94.8350 - 164.259i) q^{2} +(-9421.11 + 5439.28i) q^{3} +(14780.6 + 25600.8i) q^{4} +(-477118. - 275464. i) q^{5} +2.06334e6i q^{6} +(5.57858e6 - 1.45338e6i) q^{7} +1.80371e7 q^{8} +(3.76482e7 - 6.52085e7i) q^{9} +(-9.04950e7 + 5.22473e7i) q^{10} +(7.76109e7 + 1.34426e8i) q^{11} +(-2.78500e8 - 1.60792e8i) q^{12} -1.23204e9i q^{13} +(2.90314e8 - 1.05416e9i) q^{14} +5.99331e9 q^{15} +(7.41885e8 - 1.28498e9i) q^{16} +(-1.42412e9 + 8.22217e8i) q^{17} +(-7.14073e9 - 1.23681e10i) q^{18} +(1.62597e10 + 9.38754e9i) q^{19} -1.62861e10i q^{20} +(-4.46511e10 + 4.40360e10i) q^{21} +2.94409e10 q^{22} +(3.57099e10 - 6.18513e10i) q^{23} +(-1.69930e11 + 9.81088e10i) q^{24} +(7.54670e10 + 1.30713e11i) q^{25} +(-2.02375e11 - 1.16841e11i) q^{26} +3.50829e11i q^{27} +(1.19663e11 + 1.21334e11i) q^{28} -1.65746e11 q^{29} +(5.68375e11 - 9.84455e11i) q^{30} +(7.81270e11 - 4.51066e11i) q^{31} +(4.50327e11 + 7.79988e11i) q^{32} +(-1.46236e12 - 8.44294e11i) q^{33} +3.11900e11i q^{34} +(-3.06200e12 - 8.43265e11i) q^{35} +2.22586e12 q^{36} +(1.77083e12 - 3.06716e12i) q^{37} +(3.08398e12 - 1.78054e12i) q^{38} +(6.70144e12 + 1.16072e13i) q^{39} +(-8.60582e12 - 4.96857e12i) q^{40} -7.99933e12i q^{41} +(2.99882e12 + 1.15105e13i) q^{42} -8.81832e11 q^{43} +(-2.29428e12 + 3.97380e12i) q^{44} +(-3.59252e13 + 2.07414e13i) q^{45} +(-6.77309e12 - 1.17313e13i) q^{46} +(-3.12713e12 - 1.80545e12i) q^{47} +1.61413e13i q^{48} +(2.90083e13 - 1.62156e13i) q^{49} +2.86277e13 q^{50} +(8.94454e12 - 1.54924e13i) q^{51} +(3.15414e13 - 1.82104e13i) q^{52} +(-1.65300e13 - 2.86307e13i) q^{53} +(5.76268e13 + 3.32709e13i) q^{54} -8.55160e13i q^{55} +(1.00622e14 - 2.62148e13i) q^{56} -2.04246e14 q^{57} +(-1.57185e13 + 2.72253e13i) q^{58} +(-1.25737e14 + 7.25944e13i) q^{59} +(8.85849e13 + 1.53434e14i) q^{60} +(3.49743e13 + 2.01924e13i) q^{61} -1.71108e14i q^{62} +(1.15250e14 - 4.18488e14i) q^{63} +2.68067e14 q^{64} +(-3.39384e14 + 5.87831e14i) q^{65} +(-2.77366e14 + 1.60137e14i) q^{66} +(-6.43741e12 - 1.11499e13i) q^{67} +(-4.20989e13 - 2.43058e13i) q^{68} +7.76944e14i q^{69} +(-4.28898e14 + 4.22990e14i) q^{70} +3.62792e13 q^{71} +(6.79064e14 - 1.17617e15i) q^{72} +(7.23323e14 - 4.17611e14i) q^{73} +(-3.35873e14 - 5.81749e14i) q^{74} +(-1.42197e15 - 8.20972e14i) q^{75} +5.55016e14i q^{76} +(6.28331e14 + 6.37108e14i) q^{77} +2.54212e15 q^{78} +(4.69406e14 - 8.13035e14i) q^{79} +(-7.07933e14 + 4.08725e14i) q^{80} +(-2.87628e14 - 4.98186e14i) q^{81} +(-1.31396e15 - 7.58617e14i) q^{82} +7.02863e14i q^{83} +(-1.78733e15 - 4.92225e14i) q^{84} +9.05965e14 q^{85} +(-8.36286e13 + 1.44849e14i) q^{86} +(1.56151e15 - 9.01538e14i) q^{87} +(1.39988e15 + 2.42466e15i) q^{88} +(7.22314e14 + 4.17028e14i) q^{89} +7.86806e15i q^{90} +(-1.79063e15 - 6.87307e15i) q^{91} +2.11126e15 q^{92} +(-4.90695e15 + 8.49909e15i) q^{93} +(-5.93122e14 + 3.42439e14i) q^{94} +(-5.17186e15 - 8.95793e15i) q^{95} +(-8.48515e15 - 4.89890e15i) q^{96} +1.18389e16i q^{97} +(8.74349e13 - 6.30268e15i) q^{98} +1.16876e16 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 $

$2$	94.8350	−	164.259i	0.370449	−	0.641637i	−0.619185	−	0.785245i	$-0.712537\pi$
$2$	94.8350	−	164.259i	0.370449	−	0.641637i	0.989635	+	0.143608i	$0.0458704\pi$
$3$	−9421.11	+	5439.28i	−1.43593	+	0.829032i	−0.997563	−	0.0697663i	$-0.977775\pi$
$3$	−9421.11	+	5439.28i	−1.43593	+	0.829032i	−0.438362	+	0.898798i	$0.644441\pi$
$4$	14780.6	+	25600.8i	0.225535	+	0.390638i
$5$	−477118.	−	275464.i	−1.22142	−	0.705188i	−0.256201	−	0.966624i	$-0.582471\pi$
$5$	−477118.	−	275464.i	−1.22142	−	0.705188i	−0.965221	+	0.261435i	$0.915804\pi$
$6$			2.06334e6i			1.22846i
$7$	5.57858e6	−	1.45338e6i	0.967698	−	0.252113i
$7$	5.57858e6	−	1.45338e6i	0.967698	−	0.252113i
$8$	1.80371e7			1.07510
$9$	3.76482e7	−	6.52085e7i	0.874588	−	1.51483i
$10$	−9.04950e7	+	5.22473e7i	−0.904950	+	0.522473i
$11$	7.76109e7	+	1.34426e8i	0.362060	+	0.627107i	0.988300	−	0.152524i	$-0.0487401\pi$
$11$	7.76109e7	+	1.34426e8i	0.362060	+	0.627107i	−0.626239	+	0.779631i	$0.715407\pi$
$12$	−2.78500e8	−	1.60792e8i	−0.647702	−	0.373951i
$13$		−	1.23204e9i		−	1.51036i	−0.655519	−	0.755179i	$-0.727550\pi$
$13$		−	1.23204e9i		−	1.51036i	0.655519	−	0.755179i	$-0.272450\pi$
$14$	2.90314e8	−	1.05416e9i	0.196718	−	0.714306i
$15$	5.99331e9			2.33849
$16$	7.41885e8	−	1.28498e9i	0.172733	−	0.299183i
$17$	−1.42412e9	+	8.22217e8i	−0.204153	+	0.117868i	−0.598591	−	0.801055i	$-0.704273\pi$
$17$	−1.42412e9	+	8.22217e8i	−0.204153	+	0.117868i	0.394438	+	0.918923i	$0.370939\pi$
$18$	−7.14073e9	−	1.23681e10i	−0.647981	−	1.12234i
$19$	1.62597e10	+	9.38754e9i	0.957379	+	0.552743i	0.895365	−	0.445332i	$-0.146915\pi$
$19$	1.62597e10	+	9.38754e9i	0.957379	+	0.552743i	0.0620134	+	0.998075i	$0.480248\pi$
$20$		−	1.62861e10i		−	0.636178i
$21$	−4.46511e10	+	4.40360e10i	−1.18053	+	1.16427i
$22$	2.94409e10			0.536500
$23$	3.57099e10	−	6.18513e10i	0.456001	−	0.789817i	−0.542744	−	0.839898i	$-0.682615\pi$
$23$	3.57099e10	−	6.18513e10i	0.456001	−	0.789817i	0.998745	+	0.0500813i	$0.0159481\pi$
$24$	−1.69930e11	+	9.81088e10i	−1.54376	+	0.891288i
$25$	7.54670e10	+	1.30713e11i	0.494581	+	0.856639i
$26$	−2.02375e11	−	1.16841e11i	−0.969101	−	0.559511i
$27$			3.50829e11i			1.24218i
$28$	1.19663e11	+	1.21334e11i	0.316734	+	0.321159i
$29$	−1.65746e11			−0.331329			−0.165664	−	0.986182i	$-0.552977\pi$
$29$	−1.65746e11			−0.331329			−0.165664	+	0.986182i	$0.552977\pi$
$30$	5.68375e11	−	9.84455e11i	0.866293	−	1.50046i
$31$	7.81270e11	−	4.51066e11i	0.916025	−	0.528868i	0.0336605	−	0.999433i	$-0.489283\pi$
$31$	7.81270e11	−	4.51066e11i	0.916025	−	0.528868i	0.882365	+	0.470566i	$0.155950\pi$
$32$	4.50327e11	+	7.79988e11i	0.409570	+	0.709395i
$33$	−1.46236e12	−	8.44294e11i	−1.03978	−	0.600319i
$34$			3.11900e11i			0.174656i
$35$	−3.06200e12	−	8.43265e11i	−1.35975	−	0.374472i
$36$	2.22586e12			0.789000
$37$	1.77083e12	−	3.06716e12i	0.504153	−	0.873219i	−0.495835	−	0.868417i	$-0.665138\pi$
$37$	1.77083e12	−	3.06716e12i	0.504153	−	0.873219i	0.999988	−	0.00480224i	$-0.00152861\pi$
$38$	3.08398e12	−	1.78054e12i	0.709320	−	0.409526i
$39$	6.70144e12	+	1.16072e13i	1.25213	+	2.16876i
$40$	−8.60582e12	−	4.96857e12i	−1.31314	−	0.758144i
$41$		−	7.99933e12i		−	1.00180i	−0.865504	−	0.500902i	$-0.833002\pi$
$41$		−	7.99933e12i		−	1.00180i	0.865504	−	0.500902i	$-0.166998\pi$
$42$	2.99882e12	+	1.15105e13i	0.309710	+	1.18878i
$43$	−8.81832e11			−0.0754464			−0.0377232	−	0.999288i	$-0.512011\pi$
$43$	−8.81832e11			−0.0754464			−0.0377232	+	0.999288i	$0.512011\pi$
$44$	−2.29428e12	+	3.97380e12i	−0.163314	+	0.282869i
$45$	−3.59252e13	+	2.07414e13i	−2.13648	+	1.23350i
$46$	−6.77309e12	−	1.17313e13i	−0.337850	−	0.585174i
$47$	−3.12713e12	−	1.80545e12i	−0.131330	−	0.0758232i	0.432896	−	0.901444i	$-0.357492\pi$
$47$	−3.12713e12	−	1.80545e12i	−0.131330	−	0.0758232i	−0.564225	+	0.825621i	$0.690825\pi$
$48$			1.61413e13i			0.572806i
$49$	2.90083e13	−	1.62156e13i	0.872878	−	0.487939i
$50$	2.86277e13			0.732868
$51$	8.94454e12	−	1.54924e13i	0.195432	−	0.338499i
$52$	3.15414e13	−	1.82104e13i	0.590002	−	0.340638i
$53$	−1.65300e13	−	2.86307e13i	−0.265500	−	0.459860i	0.702194	−	0.711985i	$-0.252204\pi$
$53$	−1.65300e13	−	2.86307e13i	−0.265500	−	0.459860i	−0.967695	+	0.252126i	$0.918870\pi$
$54$	5.76268e13	+	3.32709e13i	0.797030	+	0.460166i
$55$		−	8.55160e13i		−	1.02128i
$56$	1.00622e14	−	2.62148e13i	1.04037	−	0.271046i
$57$	−2.04246e14			−1.83297
$58$	−1.57185e13	+	2.72253e13i	−0.122740	+	0.212593i
$59$	−1.25737e14	+	7.25944e13i	−0.856343	+	0.494410i	−0.862786	−	0.505569i	$-0.831283\pi$
$59$	−1.25737e14	+	7.25944e13i	−0.856343	+	0.494410i	0.00644272	+	0.999979i	$0.497949\pi$
$60$	8.85849e13	+	1.53434e14i	0.527412	+	0.913504i
$61$	3.49743e13	+	2.01924e13i	0.182436	+	0.105329i	0.588437	−	0.808543i	$-0.299744\pi$
$61$	3.49743e13	+	2.01924e13i	0.182436	+	0.105329i	−0.406001	+	0.913873i	$0.633077\pi$
$62$		−	1.71108e14i		−	0.783674i
$63$	1.15250e14	−	4.18488e14i	0.464428	−	1.68639i
$64$	2.68067e14			0.952366
$65$	−3.39384e14	+	5.87831e14i	−1.06509	+	1.84478i
$66$	−2.77366e14	+	1.60137e14i	−0.770374	+	0.444776i
$67$	−6.43741e12	−	1.11499e13i	−0.0158530	−	0.0274583i	0.857990	−	0.513666i	$-0.171713\pi$
$67$	−6.43741e12	−	1.11499e13i	−0.0158530	−	0.0274583i	−0.873843	+	0.486208i	$0.838380\pi$
$68$	−4.20989e13	−	2.43058e13i	−0.0920872	−	0.0531666i
$69$			7.76944e14i			1.51216i
$70$	−4.28898e14	+	4.22990e14i	−0.743995	+	0.733746i
$71$	3.62792e13			0.0561812			0.0280906	−	0.999605i	$-0.491057\pi$
$71$	3.62792e13			0.0561812			0.0280906	+	0.999605i	$0.491057\pi$
$72$	6.79064e14	−	1.17617e15i	0.940266	−	1.62859i
$73$	7.23323e14	−	4.17611e14i	0.896911	−	0.517832i	0.0207144	−	0.999785i	$-0.493406\pi$
$73$	7.23323e14	−	4.17611e14i	0.896911	−	0.517832i	0.876197	+	0.481953i	$0.160073\pi$
$74$	−3.35873e14	−	5.81749e14i	−0.373526	−	0.646966i
$75$	−1.42197e15	−	8.20972e14i	−1.42036	−	0.820046i
$76$			5.55016e14i			0.498651i
$77$	6.28331e14	+	6.37108e14i	0.508467	+	0.515570i
$78$	2.54212e15			1.85541
$79$	4.69406e14	−	8.13035e14i	0.309408	−	0.535911i	−0.668825	−	0.743420i	$-0.733202\pi$
$79$	4.69406e14	−	8.13035e14i	0.309408	−	0.535911i	0.978233	+	0.207509i	$0.0665356\pi$
$80$	−7.07933e14	+	4.08725e14i	−0.421961	+	0.243619i
$81$	−2.87628e14	−	4.98186e14i	−0.155221	−	0.268851i
$82$	−1.31396e15	−	7.58617e14i	−0.642795	−	0.371118i
$83$			7.02863e14i			0.312066i	0.987752	+	0.156033i	$0.0498706\pi$
$83$			7.02863e14i			0.312066i	−0.987752	+	0.156033i	$0.950129\pi$
$84$	−1.78733e15	−	4.92225e14i	−0.721058	−	0.198577i
$85$	9.05965e14			0.332476
$86$	−8.36286e13	+	1.44849e14i	−0.0279490	+	0.0484092i
$87$	1.56151e15	−	9.01538e14i	0.475763	−	0.274682i
$88$	1.39988e15	+	2.42466e15i	0.389249	+	0.674200i
$89$	7.22314e14	+	4.17028e14i	0.183487	+	0.105936i	0.588930	−	0.808184i	$-0.299549\pi$
$89$	7.22314e14	+	4.17028e14i	0.183487	+	0.105936i	−0.405443	+	0.914120i	$0.632883\pi$
$90$			7.86806e15i			1.82779i
$91$	−1.79063e15	−	6.87307e15i	−0.380781	−	1.46157i
$92$	2.11126e15			0.411376
$93$	−4.90695e15	+	8.49909e15i	−0.876896	+	1.51883i
$94$	−5.93122e14	+	3.42439e14i	−0.0973019	+	0.0561773i
$95$	−5.17186e15	−	8.95793e15i	−0.779575	−	1.35026i
$96$	−8.48515e15	−	4.89890e15i	−1.17622	−	0.679093i
$97$			1.18389e16i			1.51056i	0.655405	+	0.755278i	$0.272498\pi$
$97$			1.18389e16i			1.51056i	−0.655405	+	0.755278i	$0.727502\pi$
$98$	8.74349e13	−	6.30268e15i	0.0102772	−	0.740827i
$99$	1.16876e16			1.26662
$100$	−2.23090e15	+	3.86404e15i	−0.223090	+	0.386404i
$101$	−6.21120e15	+	3.58604e15i	−0.573594	+	0.331165i	−0.758584	−	0.651576i	$-0.774108\pi$
$101$	−6.21120e15	+	3.58604e15i	−0.573594	+	0.331165i	0.184989	+	0.982741i	$0.440775\pi$
$102$	−1.69651e15	−	2.93844e15i	−0.144796	−	0.250793i
$103$	1.95881e16	+	1.13092e16i	1.54630	+	0.892759i	0.998419	+	0.0562060i	$0.0179003\pi$
$103$	1.95881e16	+	1.13092e16i	1.54630	+	0.892759i	0.547885	+	0.836553i	$0.315433\pi$
$104$		−	2.22225e16i		−	1.62378i
$105$	3.34342e16	−	8.71057e15i	2.26296	−	0.589566i
$106$	−6.27047e15			−0.393417
$107$	9.64704e15	−	1.67092e16i	0.561467	−	0.972489i	−0.435902	−	0.899994i	$-0.643571\pi$
$107$	9.64704e15	−	1.67092e16i	0.561467	−	0.972489i	0.997369	−	0.0724946i	$-0.0230960\pi$
$108$	−8.98151e15	+	5.18548e15i	−0.485243	+	0.280155i
$109$	−9.46110e15	−	1.63871e16i	−0.474821	−	0.822413i	0.524764	−	0.851248i	$-0.324154\pi$
$109$	−9.46110e15	−	1.63871e16i	−0.474821	−	0.822413i	−0.999584	+	0.0288346i	$0.990820\pi$
$110$	−1.40468e16	−	8.10991e15i	−0.655293	−	0.378333i
$111$			3.85281e16i			1.67184i
$112$	2.27110e15	−	8.24662e15i	0.0917257	−	0.333067i
$113$	2.03077e16			0.763895			0.381948	−	0.924184i	$-0.375253\pi$
$113$	2.03077e16			0.763895			0.381948	+	0.924184i	$0.375253\pi$
$114$	−1.93697e16	+	3.35492e16i	−0.679021	+	1.17610i
$115$	−3.40756e16	+	1.96736e16i	−1.11394	+	0.643133i
$116$	−2.44983e15	−	4.24323e15i	−0.0747261	−	0.129429i
$117$	−8.03398e16	−	4.63842e16i	−2.28794	−	1.32094i
$118$			2.75380e16i			0.732615i
$119$	−6.74959e15	+	6.65660e15i	−0.167842	+	0.165530i
$120$	1.08102e17			2.51410
$121$	1.09280e16	−	1.89278e16i	0.237825	−	0.411924i
$122$	6.63357e15	−	3.82989e15i	0.135166	−	0.0780383i
$123$	4.35106e16	+	7.53626e16i	0.830528	+	1.43852i
$124$	2.30953e16	+	1.33341e16i	0.413191	+	0.238556i
$125$			9.11150e14i			0.0152866i
$126$	−5.78107e16	−	5.86183e16i	−0.910006	−	0.922718i
$127$	−7.50413e16			−1.10885			−0.554423	−	0.832235i	$-0.687061\pi$
$127$	−7.50413e16			−1.10885			−0.554423	+	0.832235i	$0.687061\pi$
$128$	−4.09044e15	+	7.08486e15i	−0.0567663	+	0.0983221i
$129$	8.30784e15	−	4.79653e15i	0.108335	−	0.0625475i
$130$	6.43710e16	+	1.11494e17i	0.789121	+	1.36680i
$131$	−1.48956e17	−	8.59997e16i	−1.71746	−	0.991578i	−0.923488	−	0.383627i	$-0.874675\pi$
$131$	−1.48956e17	−	8.59997e16i	−1.71746	−	0.991578i	−0.793975	−	0.607950i	$-0.791992\pi$
$132$		−	4.99168e16i		−	0.541571i
$133$	1.04350e17	+	2.87376e16i	1.06581	+	0.293520i
$134$	−2.44197e15			−0.0234910
$135$	9.66408e16	−	1.67387e17i	0.875972	−	1.51723i
$136$	−2.56870e16	+	1.48304e16i	−0.219484	+	0.126719i
$137$	−8.68130e16	−	1.50364e17i	−0.699552	−	1.21166i	−0.968622	−	0.248539i	$-0.920050\pi$
$137$	−8.68130e16	−	1.50364e17i	−0.699552	−	1.21166i	0.269070	−	0.963121i	$-0.413284\pi$
$138$	1.27620e17	+	7.36815e16i	0.970256	+	0.560178i
$139$			1.96268e17i			1.40841i	0.709995	+	0.704207i	$0.248697\pi$
$139$			1.96268e17i			1.40841i	−0.709995	+	0.704207i	$0.751303\pi$
$140$	−2.36700e16	−	9.08536e16i	−0.160389	−	0.615628i
$141$	3.92813e16			0.251439
$142$	3.44054e15	−	5.95919e15i	0.0208123	−	0.0360480i
$143$	1.65619e17	−	9.56201e16i	0.947156	−	0.546841i
$144$	−5.58612e16	−	9.67544e16i	−0.302141	−	0.523324i
$145$	7.90803e16	+	4.56570e16i	0.404692	+	0.233649i
$146$		−	1.58416e17i		−	0.767322i
$147$	−1.85089e17	+	3.10553e17i	−0.848870	+	1.42429i
$148$	1.04696e17			0.454816
$149$	−1.88377e17	+	3.26279e17i	−0.775423	+	1.34307i	0.159133	+	0.987257i	$0.449130\pi$
$149$	−1.88377e17	+	3.26279e17i	−0.775423	+	1.34307i	−0.934556	+	0.355815i	$0.884203\pi$
$150$	−2.69704e17	+	1.55714e17i	−1.05234	+	0.607571i
$151$	−1.65040e17	−	2.85857e17i	−0.610623	−	1.05763i	−0.991136	−	0.132854i	$-0.957586\pi$
$151$	−1.65040e17	−	2.85857e17i	−0.610623	−	1.05763i	0.380513	−	0.924776i	$-0.375747\pi$
$152$	2.93278e17	+	1.69324e17i	1.02927	+	0.594251i
$153$			1.23820e17i			0.412343i
$154$	1.64239e17	−	4.27889e16i	0.519170	−	0.135259i
$155$	−4.97010e17			−1.49180
$156$	−1.98103e17	+	3.43125e17i	−0.564800	+	0.978262i
$157$	1.95849e17	−	1.13073e17i	0.530547	−	0.306312i	−0.210692	−	0.977553i	$-0.567572\pi$
$157$	1.95849e17	−	1.13073e17i	0.530547	−	0.306312i	0.741239	+	0.671241i	$0.234238\pi$
$158$	−8.90323e16	−	1.54208e17i	−0.229240	−	0.397056i
$159$	3.11461e17	+	1.79822e17i	0.762477	+	0.440216i
$160$		−	4.96195e17i		−	1.15529i
$161$	1.09317e17	−	3.96943e17i	0.242148	−	0.879268i
$162$	−1.09109e17			−0.230006
$163$	4.63063e16	−	8.02049e16i	0.0929265	−	0.160953i	−0.815815	−	0.578313i	$-0.803711\pi$
$163$	4.63063e16	−	8.02049e16i	0.0929265	−	0.160953i	0.908741	+	0.417360i	$0.137045\pi$
$164$	2.04789e17	−	1.18235e17i	0.391342	−	0.225942i
$165$	4.65146e17	+	8.05656e17i	0.846676	+	1.46649i
$166$	1.15452e17	+	6.66561e16i	0.200233	+	0.115605i
$167$		−	8.99300e17i		−	1.48653i	−0.668999	−	0.743263i	$-0.733277\pi$
$167$		−	8.99300e17i		−	1.48653i	0.668999	−	0.743263i	$-0.266723\pi$
$168$	−8.05376e17	+	7.94281e17i	−1.26918	+	1.25170i
$169$	−8.52518e17			−1.28118
$170$	8.59172e16	−	1.48813e17i	0.123165	−	0.213329i
$171$	1.22430e18	−	7.06847e17i	1.67462	−	0.966845i
$172$	−1.30340e16	−	2.25756e16i	−0.0170158	−	0.0294722i
$173$	2.51938e17	+	1.45457e17i	0.313997	+	0.181286i	0.648714	−	0.761033i	$-0.275307\pi$
$173$	2.51938e17	+	1.45457e17i	0.313997	+	0.181286i	−0.334717	+	0.942319i	$0.608641\pi$
$174$		−	3.41990e17i		−	0.407023i
$175$	6.10975e17	+	6.19509e17i	0.694575	+	0.704277i
$176$	2.30313e17			0.250160
$177$	7.89723e17	−	1.36784e18i	0.819764	−	1.41987i
$178$	1.37001e17	−	7.90977e16i	0.135945	−	0.0784881i
$179$	1.34138e16	+	2.32334e16i	0.0127271	+	0.0220439i	0.872319	−	0.488938i	$-0.162615\pi$
$179$	1.34138e16	+	2.32334e16i	0.0127271	+	0.0220439i	−0.859592	+	0.510981i	$0.829282\pi$
$180$	−1.06200e18	−	6.13143e17i	−0.963702	−	0.556393i
$181$			1.92618e18i			1.67212i	0.548637	+	0.836061i	$0.315147\pi$
$181$			1.92618e18i			1.67212i	−0.548637	+	0.836061i	$0.684853\pi$
$182$	−1.29878e18	−	3.57680e17i	−1.07886	−	0.297114i
$183$	−4.39328e17			−0.349285
$184$	6.44103e17	−	1.11562e18i	0.490244	−	0.849128i
$185$	−1.68979e18	+	9.75599e17i	−1.23157	+	0.711046i
$186$	9.30702e17	+	1.61202e18i	0.649691	+	1.12530i
$187$	−2.21055e17	−	1.27626e17i	−0.147831	−	0.0853505i
$188$		−	1.06743e17i		−	0.0684030i
$189$	5.09889e17	+	1.95713e18i	0.313171	+	1.20206i
$190$	−1.96189e18			−1.15517
$191$	−7.76776e17	+	1.34542e18i	−0.438560	+	0.759608i	−0.997579	−	0.0695469i	$-0.977845\pi$
$191$	−7.76776e17	+	1.34542e18i	−0.438560	+	0.759608i	0.559019	+	0.829155i	$0.311178\pi$
$192$	−2.52549e18	+	1.45809e18i	−1.36753	+	0.789542i
$193$	5.93687e16	+	1.02830e17i	0.0308389	+	0.0534146i	0.881033	−	0.473055i	$-0.156849\pi$
$193$	5.93687e16	+	1.02830e17i	0.0308389	+	0.0534146i	−0.850194	+	0.526469i	$0.823515\pi$
$194$	1.94464e18	+	1.12274e18i	0.969228	+	0.559584i
$195$		−	7.38402e18i		−	3.53196i
$196$	8.43895e17	+	5.02958e17i	0.387472	+	0.230932i
$197$	2.88739e18			1.27285			0.636423	−	0.771340i	$-0.280413\pi$
$197$	2.88739e18			1.27285			0.636423	+	0.771340i	$0.280413\pi$
$198$	1.10840e18	−	1.91980e18i	0.469217	−	0.812707i
$199$	1.08004e18	−	6.23561e17i	0.439152	−	0.253545i	−0.264086	−	0.964499i	$-0.585070\pi$
$199$	1.08004e18	−	6.23561e17i	0.439152	−	0.253545i	0.703238	+	0.710955i	$0.251737\pi$
$200$	1.36121e18	+	2.35768e18i	0.531721	+	0.920968i
$201$	1.21295e17	+	7.00297e16i	0.0455276	+	0.0262854i
$202$			1.36033e18i			0.490719i
$203$	−9.24628e17	+	2.40892e17i	−0.320626	+	0.0835323i
$204$	5.28824e17			0.176307
$205$	−2.20353e18	+	3.81662e18i	−0.706460	+	1.22363i
$206$	3.71528e18	−	2.14502e18i	1.14565	−	0.661444i
$207$	−2.68882e18	−	4.65718e18i	−0.797626	−	1.38153i
$208$	−1.58316e18	−	9.14035e17i	−0.451873	−	0.260889i
$209$			2.91430e18i			0.800505i
$210$	1.73994e18	−	6.31793e18i	0.460023	−	1.67040i
$211$	−3.23874e18			−0.824358			−0.412179	−	0.911103i	$-0.635232\pi$
$211$	−3.23874e18			−0.824358			−0.412179	+	0.911103i	$0.635232\pi$
$212$	4.88647e17	−	8.46361e17i	0.119759	−	0.207429i
$213$	−3.41791e17	+	1.97333e17i	−0.0806721	+	0.0465760i
$214$	−1.82975e18	−	3.16923e18i	−0.415990	−	0.720515i
$215$	4.20738e17	+	2.42913e17i	0.0921518	+	0.0532039i
$216$			6.32794e18i			1.33546i
$217$	3.70281e18	−	3.65180e18i	0.753101	−	0.742726i
$218$	−3.58897e18			−0.703588
$219$	−4.54300e18	+	7.86871e18i	−0.858599	+	1.48714i
$220$	2.18928e18	−	1.26398e18i	0.398951	−	0.230335i
$221$	1.01301e18	+	1.75458e18i	0.178023	+	0.308344i
$222$	6.32859e18	+	3.65381e18i	1.07271	+	0.619331i
$223$		−	1.72984e18i		−	0.282858i	−0.989948	−	0.141429i	$-0.954830\pi$
$223$		−	1.72984e18i		−	0.282858i	0.989948	−	0.141429i	$-0.0451697\pi$
$224$	3.64581e18	+	3.69673e18i	0.575188	+	0.583222i
$225$	1.13648e19			1.73022
$226$	1.92588e18	−	3.33573e18i	0.282984	−	0.490143i
$227$	−4.12145e18	+	2.37952e18i	−0.584579	+	0.337507i	−0.762951	−	0.646456i	$-0.776250\pi$
$227$	−4.12145e18	+	2.37952e18i	−0.584579	+	0.337507i	0.178372	+	0.983963i	$0.442917\pi$
$228$	−3.01889e18	−	5.22886e18i	−0.413397	−	0.716025i
$229$	−9.67912e18	−	5.58824e18i	−1.27983	−	0.738910i	−0.303013	−	0.952987i	$-0.597992\pi$
$229$	−9.67912e18	−	5.58824e18i	−1.27983	−	0.738910i	−0.976817	+	0.214077i	$0.931326\pi$
$230$			7.46298e18i			0.952992i
$231$	−9.38499e18	−	2.58460e18i	−1.15754	−	0.318784i
$232$	−2.98958e18			−0.356210
$233$	−1.62252e18	+	2.81029e18i	−0.186786	+	0.323522i	−0.944177	−	0.329439i	$-0.893140\pi$
$233$	−1.62252e18	+	2.81029e18i	−0.186786	+	0.323522i	0.757391	+	0.652961i	$0.226474\pi$
$234$	−1.52381e19	+	8.79769e18i	−1.69513	+	0.978683i
$235$	9.94672e17	+	1.72282e18i	0.106939	+	0.185224i
$236$	−3.71696e18	−	2.14599e18i	−0.386270	−	0.223013i
$237$			1.02129e19i			1.02604i
$238$	4.53310e17	+	1.73996e18i	0.0440331	+	0.169014i
$239$	1.85914e19			1.74634			0.873170	−	0.487416i	$-0.162061\pi$
$239$	1.85914e19			1.74634			0.873170	+	0.487416i	$0.162061\pi$
$240$	4.44634e18	−	7.70129e18i	0.403936	−	0.699638i
$241$	1.22196e19	−	7.05498e18i	1.07379	−	0.619954i	0.144577	−	0.989494i	$-0.453818\pi$
$241$	1.22196e19	−	7.05498e18i	1.07379	−	0.619954i	0.929215	+	0.369540i	$0.120485\pi$
$242$	−2.07271e18	−	3.59004e18i	−0.176204	−	0.305194i
$243$	−7.65921e18	−	4.42205e18i	−0.629990	−	0.363725i
$244$			1.19383e18i			0.0950217i
$245$	−1.83072e19	−	2.53969e17i	−1.41024	−	0.0195638i
$246$	1.65053e19			1.23067
$247$	1.15659e19	−	2.00327e19i	0.834839	−	1.44598i
$248$	1.40918e19	−	8.13593e18i	0.984814	−	0.568583i
$249$	−3.82307e18	−	6.62175e18i	−0.258713	−	0.448103i
$250$	1.49665e17	+	8.64090e16i	0.00980843	+	0.00566290i
$251$			4.58198e18i			0.290846i	0.989370	+	0.145423i	$0.0464544\pi$
$251$			4.58198e18i			0.290846i	−0.989370	+	0.145423i	$0.953546\pi$
$252$	1.24171e19	−	3.23502e18i	0.763513	−	0.198917i
$253$	1.10859e19			0.660399
$254$	−7.11655e18	+	1.23262e19i	−0.410771	+	0.711476i
$255$	−8.53520e18	+	4.92780e18i	−0.477411	+	0.275633i
$256$	9.55986e18	+	1.65582e19i	0.518241	+	0.897620i
$257$	−7.32684e18	−	4.23015e18i	−0.384992	−	0.222275i	0.294996	−	0.955498i	$-0.404682\pi$
$257$	−7.32684e18	−	4.23015e18i	−0.384992	−	0.222275i	−0.679988	+	0.733223i	$0.738015\pi$
$258$		−	1.81952e18i		−	0.0926826i
$259$	5.42095e18	−	1.96841e19i	0.267718	−	0.972116i
$260$	−2.00653e19			−0.960855
$261$	−6.24003e18	+	1.08080e19i	−0.289776	+	0.501907i
$262$	−2.82525e19	+	1.63116e19i	−1.27247	+	0.734658i
$263$	1.29063e19	+	2.23544e19i	0.563840	+	0.976599i	0.997157	+	0.0753574i	$0.0240098\pi$
$263$	1.29063e19	+	2.23544e19i	0.563840	+	0.976599i	−0.433317	+	0.901242i	$0.642657\pi$
$264$	−2.63768e19	−	1.52286e19i	−1.11787	−	0.645400i
$265$			1.82136e19i			0.748910i
$266$	1.46164e19	−	1.44151e19i	0.583161	−	0.575127i
$267$	−9.07333e18			−0.351299
$268$	1.90298e17	−	3.29606e17i	0.00715082	−	0.0123856i
$269$	2.82618e19	−	1.63170e19i	1.03082	−	0.595143i	0.113600	−	0.993527i	$-0.463762\pi$
$269$	2.82618e19	−	1.63170e19i	1.03082	−	0.595143i	0.917219	+	0.398383i	$0.130429\pi$
$270$	−1.83299e19	−	3.17483e19i	−0.649007	−	1.12411i
$271$	−2.42657e18	−	1.40098e18i	−0.0834140	−	0.0481591i	0.457713	−	0.889100i	$-0.348669\pi$
$271$	−2.42657e18	−	1.40098e18i	−0.0834140	−	0.0481591i	−0.541127	+	0.840941i	$0.682002\pi$
$272$			2.43996e18i			0.0814389i
$273$	5.42543e19	+	5.50121e19i	1.75846	+	1.78302i
$274$	−3.29316e19			−1.03659
$275$	−1.17141e19	+	2.02895e19i	−0.358136	+	0.620310i
$276$	−1.98904e19	+	1.14837e19i	−0.590705	+	0.341044i
$277$	1.96519e19	+	3.40381e19i	0.566979	+	0.982036i	0.996863	+	0.0791516i	$0.0252211\pi$
$277$	1.96519e19	+	3.40381e19i	0.566979	+	0.982036i	−0.429884	+	0.902884i	$0.641446\pi$
$278$	3.22387e19	+	1.86130e19i	0.903690	+	0.521746i
$279$		−	6.79273e19i		−	1.85017i
$280$	−5.52296e19	−	1.52101e19i	−1.46187	−	0.402593i
$281$	−5.68762e19			−1.46312			−0.731561	−	0.681776i	$-0.761208\pi$
$281$	−5.68762e19			−1.46312			−0.731561	+	0.681776i	$0.761208\pi$
$282$	3.72524e18	−	6.45231e18i	0.0931455	−	0.161333i
$283$	−8.56680e18	+	4.94604e18i	−0.208222	+	0.120217i	−0.600485	−	0.799636i	$-0.705026\pi$
$283$	−8.56680e18	+	4.94604e18i	−0.208222	+	0.120217i	0.392263	+	0.919853i	$0.371692\pi$
$284$	5.36230e17	+	9.28778e17i	0.0126708	+	0.0219465i
$285$	9.74494e19	+	5.62624e19i	2.23882	+	1.29259i
$286$		−	3.62725e19i		−	0.810307i
$287$	−1.16261e19	−	4.46250e19i	−0.252568	−	0.969444i
$288$	6.78159e19			1.43282
$289$	−2.29785e19	+	3.98000e19i	−0.472214	+	0.817899i
$290$	1.49992e19	−	8.65977e18i	0.299836	−	0.173110i
$291$	−6.43950e19	−	1.11535e20i	−1.25230	−	2.16905i
$292$	2.13824e19	+	1.23451e19i	0.404569	+	0.233578i
$293$		−	1.33762e19i		−	0.246259i	−0.992391	−	0.123129i	$-0.960707\pi$
$293$		−	1.33762e19i		−	0.246259i	0.992391	−	0.123129i	$-0.0392930\pi$
$294$	3.34583e19	+	5.98538e19i	0.599412	+	1.07229i
$295$	7.99887e19			1.39461
$296$	3.19406e19	−	5.53227e19i	0.542013	−	0.938793i
$297$	−4.71605e19	+	2.72281e19i	−0.778981	+	0.449745i
$298$	3.57295e19	+	6.18854e19i	0.574510	+	0.995080i
$299$	−7.62036e19	−	4.39962e19i	−1.19291	−	0.688724i
$300$		−	4.85380e19i		−	0.739796i
$301$	−4.91938e18	+	1.28164e18i	−0.0730093	+	0.0190210i
$302$	−6.26062e19			−0.904819
$303$	3.90109e19	−	6.75689e19i	0.549092	−	0.951056i
$304$	2.41256e19	−	1.39289e19i	0.330743	−	0.190954i
$305$	−1.11246e19	−	1.92683e19i	−0.148554	−	0.257303i
$306$	2.03385e19	+	1.17425e19i	0.264575	+	0.152752i
$307$			4.91475e19i			0.622866i	0.950268	+	0.311433i	$0.100809\pi$
$307$			4.91475e19i			0.622866i	−0.950268	+	0.311433i	$0.899191\pi$
$308$	−7.02336e18	+	2.55027e19i	−0.0867240	+	0.314905i
$309$	−2.46056e20			−2.96050
$310$	−4.71340e19	+	8.16385e19i	−0.552638	+	0.957197i
$311$	9.89206e19	−	5.71119e19i	1.13033	−	0.652594i	0.186309	−	0.982491i	$-0.440347\pi$
$311$	9.89206e19	−	5.71119e19i	1.13033	−	0.652594i	0.944017	+	0.329897i	$0.107014\pi$
$312$	1.20874e20	+	2.09361e20i	1.34616	+	2.33162i
$313$	3.98772e19	+	2.30231e19i	0.432882	+	0.249925i	0.700574	−	0.713580i	$-0.252928\pi$
$313$	3.98772e19	+	2.30231e19i	0.432882	+	0.249925i	−0.267692	+	0.963505i	$0.586261\pi$
$314$		−	4.28933e19i		−	0.453892i
$315$	−1.70267e20	+	1.67921e20i	−1.75649	+	1.73229i
$316$	2.77525e19			0.279129
$317$	8.83019e19	−	1.52943e20i	0.865957	−	1.49988i	−0.000137489	−	1.00000i	$-0.500044\pi$
$317$	8.83019e19	−	1.52943e20i	0.865957	−	1.49988i	0.866094	−	0.499881i	$-0.166623\pi$
$318$	5.90748e19	−	3.41069e19i	0.564918	−	0.326156i
$319$	−1.28637e19	−	2.22806e19i	−0.119961	−	0.207778i
$320$	−1.27900e20	−	7.38429e19i	−1.16324	−	0.671597i
$321$			2.09892e20i			1.86190i
$322$	−5.48344e19	−	5.56004e19i	−0.474467	−	0.481095i
$323$	−3.08744e19			−0.260602
$324$	8.50264e18	−	1.47270e19i	0.0700154	−	0.121270i
$325$	1.61044e20	−	9.29788e19i	1.29383	−	0.746994i
$326$	−8.78292e18	−	1.52125e19i	−0.0688491	−	0.119250i
$327$	1.78268e20	+	1.02923e20i	1.36361	+	0.787283i
$328$		−	1.44285e20i		−	1.07703i
$329$	−2.00689e19	−	5.52693e18i	−0.146203	−	0.0402640i
$330$	1.76448e20			1.25460
$331$	−9.87953e19	+	1.71118e20i	−0.685665	+	1.18761i	0.287562	+	0.957762i	$0.407155\pi$
$331$	−9.87953e19	+	1.71118e20i	−0.685665	+	1.18761i	−0.973227	+	0.229845i	$0.926178\pi$
$332$	−1.79939e19	+	1.03888e19i	−0.121905	+	0.0703817i
$333$	−1.33337e20	−	2.30946e20i	−0.881853	−	1.52741i
$334$	−1.47718e20	−	8.52851e19i	−0.953811	−	0.550683i
$335$			7.09310e18i			0.0447175i
$336$	2.34595e19	+	9.00455e19i	0.144412	+	0.554303i
$337$	−1.02733e20			−0.617551			−0.308775	−	0.951135i	$-0.599919\pi$
$337$	−1.02733e20			−0.617551			−0.308775	+	0.951135i	$0.599919\pi$
$338$	−8.08485e19	+	1.40034e20i	−0.474612	+	0.822052i
$339$	−1.91321e20	+	1.10459e20i	−1.09690	+	0.633294i
$340$	1.33908e19	+	2.31935e19i	0.0749849	+	0.129878i
$341$	1.21270e20	+	7.00153e19i	0.663313	+	0.382964i
$342$		−	2.68136e20i		−	1.43267i
$343$	1.38258e20	−	1.32620e20i	0.721666	−	0.692242i
$344$	−1.59057e19			−0.0811120
$345$	2.14020e20	−	3.70694e20i	1.06636	−	1.84698i
$346$	4.77851e19	−	2.75888e19i	0.232640	−	0.134315i
$347$	9.53314e19	+	1.65119e20i	0.453524	+	0.785526i	0.998602	−	0.0528589i	$-0.0168334\pi$
$347$	9.53314e19	+	1.65119e20i	0.453524	+	0.785526i	−0.545078	+	0.838385i	$0.683500\pi$
$348$	4.61602e19	+	2.66506e19i	0.214602	+	0.123901i
$349$			1.74724e19i			0.0793871i	0.999212	+	0.0396936i	$0.0126382\pi$
$349$			1.74724e19i			0.0793871i	−0.999212	+	0.0396936i	$0.987362\pi$
$350$	1.59702e20	−	4.16070e19i	0.709195	−	0.184766i
$351$	4.32237e20			1.87614
$352$	−6.99005e19	+	1.21071e20i	−0.296578	+	0.513688i
$353$	−2.29731e19	+	1.32635e19i	−0.0952844	+	0.0550125i	−0.546885	−	0.837208i	$-0.684187\pi$
$353$	−2.29731e19	+	1.32635e19i	−0.0952844	+	0.0550125i	0.451601	+	0.892220i	$0.350853\pi$
$354$	−1.49787e20	−	2.59438e20i	−0.607362	−	1.05198i
$355$	−1.73095e19	−	9.99363e18i	−0.0686210	−	0.0396183i
$356$			2.46558e19i			0.0955694i
$357$	2.73815e19	−	9.94255e19i	0.103779	−	0.376836i
$358$	5.08840e18			0.0188589
$359$	−1.92488e20	+	3.33400e20i	−0.697668	+	1.20840i	0.271605	+	0.962409i	$0.412446\pi$
$359$	−1.92488e20	+	3.33400e20i	−0.697668	+	1.20840i	−0.969273	+	0.245988i	$0.920888\pi$
$360$	−6.47987e20	+	3.74115e20i	−2.29692	+	1.32613i
$361$	3.20312e19	+	5.54797e19i	0.111049	+	0.192343i
$362$	3.16392e20	+	1.82669e20i	1.07289	+	0.619436i
$363$			2.37761e20i			0.788657i
$364$	1.49489e20	−	1.47430e20i	0.485064	−	0.478382i
$365$	−4.60147e20			−1.46068
$366$	−4.16637e19	+	7.21637e19i	−0.129393	+	0.224114i
$367$	1.24470e20	−	7.18626e19i	0.378212	−	0.218361i	−0.298828	−	0.954307i	$-0.596596\pi$
$367$	1.24470e20	−	7.18626e19i	0.378212	−	0.218361i	0.677040	+	0.735946i	$0.263262\pi$
$368$	−5.29852e19	−	9.17731e19i	−0.157533	−	0.272856i
$369$	−5.21625e20	−	3.01160e20i	−1.51756	−	0.876166i
$370$			3.70084e20i			1.05363i
$371$	−1.33825e20	−	1.35695e20i	−0.372861	−	0.378069i
$372$	−2.90112e20			−0.791082
$373$	1.07382e19	−	1.85992e19i	0.0286591	−	0.0496390i	−0.851340	−	0.524614i	$-0.824210\pi$
$373$	1.07382e19	−	1.85992e19i	0.0286591	−	0.0496390i	0.879999	+	0.474975i	$0.157543\pi$
$374$	−4.19274e19	+	2.42068e19i	−0.109528	+	0.0632361i
$375$	−4.95600e18	−	8.58405e18i	−0.0126731	−	0.0219504i
$376$	−5.64043e19	−	3.25650e19i	−0.141192	−	0.0815171i
$377$			2.04206e20i			0.500424i
$378$	3.69832e20	+	1.01851e20i	0.887298	+	0.244359i
$379$	3.59150e20			0.843650			0.421825	−	0.906677i	$-0.361390\pi$
$379$	3.59150e20			0.843650			0.421825	+	0.906677i	$0.361390\pi$
$380$	1.52887e20	−	2.64808e20i	0.351643	−	0.609063i
$381$	7.06973e20	−	4.08171e20i	1.59222	−	0.919268i
$382$	1.47331e20	+	2.55185e20i	0.324928	+	0.562793i
$383$	3.01492e20	+	1.74067e20i	0.651158	+	0.375946i	0.788900	−	0.614522i	$-0.210651\pi$
$383$	3.01492e20	+	1.74067e20i	0.651158	+	0.375946i	−0.137742	+	0.990468i	$0.543984\pi$
$384$		−	8.89963e19i		−	0.188244i
$385$	−1.24288e20	−	4.77058e20i	−0.257479	−	0.988293i
$386$	2.25209e19			0.0456970
$387$	−3.31994e19	+	5.75030e19i	−0.0659845	+	0.114289i
$388$	−3.03085e20	+	1.74986e20i	−0.590080	+	0.340683i
$389$	2.97907e20	+	5.15990e20i	0.568177	+	0.984111i	0.996746	+	0.0806023i	$0.0256844\pi$
$389$	2.97907e20	+	5.15990e20i	0.568177	+	0.984111i	−0.428570	+	0.903509i	$0.640982\pi$
$390$	−1.21289e21	−	7.00264e20i	−2.26624	−	1.30841i
$391$			1.17445e20i			0.214991i
$392$	5.23225e20	−	2.92483e20i	0.938427	−	0.524581i
$393$	1.87111e21			3.28820
$394$	2.73826e20	−	4.74281e20i	0.471525	−	0.816706i
$395$	−4.47924e20	+	2.58609e20i	−0.755836	+	0.436382i
$396$	1.72751e20	+	2.99213e20i	0.285666	+	0.494787i
$397$	−9.59039e20	−	5.53701e20i	−1.55422	−	0.897328i	−0.997791	−	0.0664321i	$-0.978838\pi$
$397$	−9.59039e20	−	5.53701e20i	−1.55422	−	0.897328i	−0.556427	−	0.830896i	$-0.687828\pi$
$398$		−	2.36542e20i		−	0.375702i
$399$	−1.13940e21	+	2.96848e20i	−1.77376	+	0.462115i
$400$	2.23951e20			0.341723
$401$	−1.55699e20	+	2.69678e20i	−0.232879	+	0.403358i	−0.958654	−	0.284574i	$-0.908148\pi$
$401$	−1.55699e20	+	2.69678e20i	−0.232879	+	0.403358i	0.725775	+	0.687932i	$0.241481\pi$
$402$	2.30060e19	−	1.32825e19i	0.0337313	−	0.0194748i
$403$	−5.55734e20	−	9.62559e20i	−0.798779	−	1.38353i
$404$	−1.83611e20	−	1.06008e20i	−0.258731	−	0.149378i
$405$			3.16924e20i			0.437840i
$406$	−4.81183e19	+	1.74723e20i	−0.0651782	+	0.236670i
$407$	5.49742e20			0.730136
$408$	1.61334e20	−	2.79438e20i	0.210108	−	0.363918i
$409$	−3.23046e20	+	1.86511e20i	−0.412552	+	0.238187i	−0.691886	−	0.722007i	$-0.743220\pi$
$409$	−3.23046e20	+	1.86511e20i	−0.412552	+	0.238187i	0.279334	+	0.960194i	$0.409886\pi$
$410$	4.17943e20	+	7.23899e20i	0.523416	+	0.906582i
$411$	1.63575e21	+	9.44400e20i	2.00901	+	1.15990i
$412$			6.68629e20i			0.805393i
$413$	−5.95928e20	+	5.87719e20i	−0.704034	+	0.694335i
$414$	−1.01998e21			−1.18192
$415$	1.93614e20	−	3.35349e20i	0.220065	−	0.381164i
$416$	9.60981e20	−	5.54822e20i	1.07144	−	0.618596i
$417$	−1.06755e21	−	1.84906e21i	−1.16762	−	2.02238i
$418$	4.78700e20	+	2.76378e20i	0.513634	+	0.296547i
$419$			3.90704e19i			0.0411278i	0.999789	+	0.0205639i	$0.00654616\pi$
$419$			3.90704e19i			0.0411278i	−0.999789	+	0.0205639i	$0.993454\pi$
$420$	7.17176e20	+	7.27194e20i	0.740681	+	0.751028i
$421$	−1.59544e21			−1.61667			−0.808337	−	0.588720i	$-0.799632\pi$
$421$	−1.59544e21			−1.61667			−0.808337	+	0.588720i	$0.799632\pi$
$422$	−3.07146e20	+	5.31992e20i	−0.305383	+	0.528939i
$423$	−2.35461e20	+	1.35944e20i	−0.229719	+	0.132628i
$424$	−2.98153e20	−	5.16415e20i	−0.285438	−	0.494393i
$425$	−2.14949e20	−	1.24101e20i	−0.201940	−	0.116590i
$426$			7.48562e19i			0.0690162i
$427$	2.24454e20	+	6.18140e19i	0.203098	+	0.0559325i
$428$	5.70358e20			0.506521
$429$	−1.04021e21	+	1.80169e21i	−0.906697	+	1.57044i
$430$	7.98014e19	−	4.60733e19i	0.0682752	−	0.0394187i
$431$	9.83127e19	+	1.70283e20i	0.0825641	+	0.143005i	0.904351	−	0.426790i	$-0.140356\pi$
$431$	9.83127e19	+	1.70283e20i	0.0825641	+	0.143005i	−0.821787	+	0.569795i	$0.807022\pi$
$432$	4.50809e20	+	2.60275e20i	0.371640	+	0.214567i
$433$			1.41564e21i			1.14564i	0.819681	+	0.572820i	$0.194151\pi$
$433$			1.41564e21i			1.14564i	−0.819681	+	0.572820i	$0.805849\pi$
$434$	−2.48685e20	−	9.54538e20i	−0.197575	−	0.758360i
$435$	−9.93366e20			−0.774810
$436$	2.79682e20	−	4.84424e20i	0.214177	−	0.370966i
$437$	1.16126e21	−	6.70456e20i	0.873131	−	0.504102i
$438$	8.61672e20	+	1.49246e21i	0.636134	+	1.10182i
$439$	8.64306e20	+	4.99007e20i	0.626544	+	0.361735i	0.779412	−	0.626511i	$-0.215518\pi$
$439$	8.64306e20	+	4.99007e20i	0.626544	+	0.361735i	−0.152869	+	0.988247i	$0.548851\pi$
$440$		−	1.54246e21i		−	1.09798i
$441$	3.47104e19	−	2.50208e21i	0.0242634	−	1.74901i
$442$	3.84275e20			0.263793
$443$	1.95978e20	−	3.39443e20i	0.132123	−	0.228843i	−0.792372	−	0.610038i	$-0.791154\pi$
$443$	1.95978e20	−	3.39443e20i	0.132123	−	0.228843i	0.924495	+	0.381195i	$0.124487\pi$
$444$	−9.86351e20	+	5.69470e20i	−0.653082	+	0.377057i
$445$	−2.29753e20	−	3.97943e20i	−0.149410	−	0.258786i
$446$	−2.84143e20	−	1.64050e20i	−0.181492	−	0.104784i
$447$		−	4.09855e21i		−	2.57140i
$448$	1.49544e21	−	3.89604e20i	0.921602	−	0.240104i
$449$	−1.23486e21			−0.747560			−0.373780	−	0.927517i	$-0.621939\pi$
$449$	−1.23486e21			−0.747560			−0.373780	+	0.927517i	$0.621939\pi$
$450$	1.07778e21	−	1.86677e21i	0.640958	−	1.11017i
$451$	1.07532e21	−	6.20835e20i	0.628238	−	0.362714i
$452$	3.00161e20	+	5.19895e20i	0.172285	+	0.298406i
$453$	3.10971e21	+	1.79539e21i	1.75362	+	1.01245i
$454$			9.02648e20i			0.500117i
$455$	−1.03894e21	+	3.77252e21i	−0.565587	+	2.05371i
$456$	−3.68400e21			−1.97061
$457$	−1.07751e21	+	1.86630e21i	−0.566359	+	0.980963i	0.430562	+	0.902561i	$0.358315\pi$
$457$	−1.07751e21	+	1.86630e21i	−0.566359	+	0.980963i	−0.996922	+	0.0784024i	$0.975018\pi$
$458$	−1.83584e21	+	1.05992e21i	−0.948224	+	0.547457i
$459$	−2.88458e20	−	4.99623e20i	−0.146413	−	0.253595i
$460$	−1.00732e21	−	5.81576e20i	−0.502464	−	0.290098i
$461$		−	1.19390e21i		−	0.585275i	−0.956223	−	0.292638i	$-0.905467\pi$
$461$		−	1.19390e21i		−	0.585275i	0.956223	−	0.292638i	$-0.0945330\pi$
$462$	−1.31457e21	+	1.29646e21i	−0.633355	+	0.624630i
$463$	3.20358e21			1.51701			0.758504	−	0.651669i	$-0.225931\pi$
$463$	3.20358e21			1.51701			0.758504	+	0.651669i	$0.225931\pi$
$464$	−1.22964e20	+	2.12980e20i	−0.0572315	+	0.0991279i
$465$	4.68239e21	−	2.70338e21i	2.14212	−	1.23675i
$466$	3.07744e20	+	5.33028e20i	0.138389	+	0.239697i
$467$	−6.71360e20	−	3.87610e20i	−0.296770	−	0.171340i	0.344221	−	0.938889i	$-0.388143\pi$
$467$	−6.71360e20	−	3.87610e20i	−0.296770	−	0.171340i	−0.640991	+	0.767548i	$0.721476\pi$
$468$		−	2.74235e21i		−	1.19167i
$469$	−5.21167e19	−	5.28447e19i	−0.0222635	−	0.0225745i
$470$	3.77319e20			0.158462
$471$	−1.23008e21	+	2.13055e21i	−0.507884	+	0.879682i
$472$	−2.26794e21	+	1.30939e21i	−0.920651	+	0.531538i
$473$	−6.84398e19	−	1.18541e20i	−0.0273161	−	0.0473129i
$474$	1.67757e21	+	9.68543e20i	0.658344	+	0.380095i
$475$			2.83380e21i			1.09350i
$476$	−2.70178e20	−	7.44062e19i	−0.102517	−	0.0282328i
$477$	−2.48929e21			−0.928813
$478$	1.76311e21	−	3.05380e21i	0.646930	−	1.12052i
$479$	−3.09676e21	+	1.78791e21i	−1.11744	+	0.645153i	−0.940745	−	0.339113i	$-0.889873\pi$
$479$	−3.09676e21	+	1.78791e21i	−1.11744	+	0.645153i	−0.176692	+	0.984266i	$0.556540\pi$
$480$	2.69894e21	+	4.67471e21i	0.957776	+	1.65892i
$481$	−3.77888e21	−	2.18174e21i	−1.31887	−	0.761451i
$482$		−	2.67624e21i		−	0.918646i
$483$	1.12920e21	+	4.33425e21i	0.381235	+	1.46331i
$484$	6.46090e20			0.214551
$485$	3.26119e21	−	5.64854e21i	1.06523	−	1.84503i
$486$	−1.45272e21	+	8.38730e20i	−0.466759	+	0.269483i
$487$	9.63126e19	+	1.66818e20i	0.0304405	+	0.0527244i	0.880844	−	0.473406i	$-0.156976\pi$
$487$	9.63126e19	+	1.66818e20i	0.0304405	+	0.0527244i	−0.850404	+	0.526131i	$0.823642\pi$
$488$	6.30834e20	+	3.64212e20i	0.196136	+	0.113239i
$489$			1.00749e21i			0.308156i
$490$	−1.77788e21	+	2.98304e21i	−0.534975	+	0.897615i
$491$	−1.47368e21			−0.436267			−0.218134	−	0.975919i	$-0.569997\pi$
$491$	−1.47368e21			−0.436267			−0.218134	+	0.975919i	$0.569997\pi$
$492$	−1.28623e21	+	2.22781e21i	−0.374626	+	0.648871i
$493$	2.36042e20	−	1.36279e20i	0.0676417	−	0.0390530i
$494$	−2.19370e21	−	3.79960e21i	−0.618531	−	1.07133i
$495$	−5.57637e21	−	3.21952e21i	−1.54707	−	0.893202i
$496$		−	1.33856e21i		−	0.365413i
$497$	2.02387e20	−	5.27276e19i	0.0543664	−	0.0141640i
$498$	−1.45024e21			−0.383359
$499$	2.74088e21	−	4.74734e21i	0.712993	−	1.23494i	−0.250736	−	0.968056i	$-0.580673\pi$
$499$	2.74088e21	−	4.74734e21i	0.712993	−	1.23494i	0.963729	−	0.266884i	$-0.0859941\pi$
$500$	−2.33262e19	+	1.34674e19i	−0.00597151	+	0.00344765i
$501$	4.89154e21	+	8.47240e21i	1.23238	+	2.13454i
$502$	7.52632e20	+	4.34532e20i	0.186618	+	0.107744i
$503$			3.59430e21i			0.877144i	0.898696	+	0.438572i	$0.144516\pi$
$503$			3.59430e21i			0.877144i	−0.898696	+	0.438572i	$0.855484\pi$
$504$	2.07878e21	−	7.54832e21i	0.499304	−	1.81303i
$505$	3.95130e21			0.934134
$506$	1.05133e21	−	1.82096e21i	0.244644	−	0.423737i
$507$	8.03166e21	−	4.63708e21i	1.83968	−	1.06214i
$508$	−1.10916e21	−	1.92112e21i	−0.250083	−	0.433157i
$509$	6.06386e21	+	3.50097e21i	1.34588	+	0.777045i	0.987663	−	0.156594i	$-0.0500513\pi$
$509$	6.06386e21	+	3.50097e21i	1.34588	+	0.777045i	0.358218	+	0.933638i	$0.383385\pi$
$510$			1.86931e21i			0.408432i
$511$	3.42817e21	−	3.38094e21i	0.737387	−	0.727228i
$512$	3.09030e21			0.654395
$513$	−3.29342e21	+	5.70438e21i	−0.686608	+	1.18924i
$514$	−1.38968e21	+	8.02333e20i	−0.285240	+	0.164683i
$515$	−6.23056e21	−	1.07917e22i	−1.25913	−	2.18087i
$516$	2.45590e20	+	1.41792e20i	0.0488668	+	0.0282132i
$517$		−	5.60489e20i		−	0.109810i
$518$	−2.71920e21	−	2.75718e21i	−0.524569	−	0.531897i
$519$	−3.16472e21			−0.601168
$520$	−6.12151e21	+	1.06028e22i	−1.14507	+	1.98332i
$521$	2.45793e21	−	1.41909e21i	0.452760	−	0.261401i	−0.256235	−	0.966614i	$-0.582482\pi$
$521$	2.45793e21	−	1.41909e21i	0.452760	−	0.261401i	0.708995	+	0.705213i	$0.249149\pi$
$522$	1.18355e21	+	2.04996e21i	0.214695	+	0.371862i
$523$	1.01338e21	+	5.85077e20i	0.181034	+	0.104520i	0.587778	−	0.809022i	$-0.300003\pi$
$523$	1.01338e21	+	5.85077e20i	0.181034	+	0.104520i	−0.406744	+	0.913542i	$0.633336\pi$
$524$		−	5.08453e21i		−	0.894541i
$525$	−9.12574e21	−	2.51320e21i	−1.58123	−	0.435465i
$526$	4.89587e21			0.835496
$527$	−7.41749e20	+	1.28475e21i	−0.124673	+	0.215940i
$528$	−2.16981e21	+	1.25274e21i	−0.359211	+	0.207391i
$529$	5.15914e20	+	8.93590e20i	0.0841264	+	0.145711i
$530$	2.99175e21	+	1.72729e21i	0.480528	+	0.277433i
$531$			1.09322e22i			1.72962i
$532$	8.06650e20	+	3.09620e21i	0.125717	+	0.482543i
$533$	−9.85554e21			−1.51308
$534$	−8.60469e20	+	1.49038e21i	−0.130138	+	0.225406i
$535$	−9.20555e21	+	5.31483e21i	−1.37157	+	0.791879i
$536$	−1.16112e20	−	2.01112e20i	−0.0170435	−	0.0295202i
$537$	−2.52746e20	−	1.45923e20i	−0.0365503	−	0.0211023i
$538$		−	6.18968e21i		−	0.881882i
$539$	4.43116e21	+	2.64096e21i	0.622024	+	0.370724i
$540$	5.71365e21			0.790249
$541$	−3.23335e21	+	5.60032e21i	−0.440630	+	0.763194i	−0.997736	−	0.0672474i	$-0.978578\pi$
$541$	−3.23335e21	+	5.60032e21i	−0.440630	+	0.763194i	0.557106	+	0.830441i	$0.311912\pi$
$542$	−4.60248e20	+	2.65724e20i	−0.0618013	+	0.0356810i
$543$	−1.04770e22	−	1.81467e22i	−1.38624	−	2.40104i
$544$	−1.28264e21	−	7.40532e20i	−0.167230	−	0.0965501i
$545$			1.04248e22i			1.33935i
$546$	1.41814e22	−	3.69468e21i	1.79548	−	0.467773i
$547$	1.16063e22			1.44808			0.724042	−	0.689756i	$-0.242282\pi$
$547$	1.16063e22			1.44808			0.724042	+	0.689756i	$0.242282\pi$
$548$	2.56630e21	−	4.44497e21i	0.315547	−	0.546543i
$549$	2.63343e21	−	1.52041e21i	0.319112	−	0.184240i
$550$	2.22182e21	+	3.84830e21i	0.265343	+	0.459587i
$551$	−2.69498e21	−	1.55595e21i	−0.317207	−	0.183139i
$552$			1.40138e22i			1.62571i
$553$	1.43697e21	−	5.21781e21i	0.164303	−	0.596606i
$554$	7.45476e21			0.840147
$555$	1.06131e22	−	1.83824e22i	1.17896	−	2.04202i
$556$	−5.02461e21	+	2.90096e21i	−0.550179	+	0.317646i
$557$	2.55680e21	+	4.42850e21i	0.275965	+	0.477986i	0.970378	−	0.241591i	$-0.0776692\pi$
$557$	2.55680e21	+	4.42850e21i	0.275965	+	0.477986i	−0.694413	+	0.719577i	$0.744336\pi$
$558$	−1.11577e22	−	6.44188e21i	−1.18713	−	0.685392i
$559$			1.08646e21i			0.113951i
$560$	−3.35523e21	+	3.30901e21i	−0.346911	+	0.342132i
$561$	2.77677e21			0.283033
$562$	−5.39386e21	+	9.34244e21i	−0.542012	+	0.938793i
$563$	−9.14556e21	+	5.28019e21i	−0.906031	+	0.523097i	−0.879152	−	0.476542i	$-0.841890\pi$
$563$	−9.14556e21	+	5.28019e21i	−0.906031	+	0.523097i	−0.0268788	+	0.999639i	$0.508557\pi$
$564$	5.80603e20	+	1.00563e21i	0.0567083	+	0.0982217i
$565$	−9.68918e21	−	5.59405e21i	−0.933038	−	0.538690i
$566$			1.87623e21i			0.178137i
$567$	−2.32861e21	−	2.36114e21i	−0.217988	−	0.221033i
$568$	6.54372e20			0.0604002
$569$	−8.18392e21	+	1.41750e22i	−0.744840	+	1.29010i	0.205429	+	0.978672i	$0.434141\pi$
$569$	−8.18392e21	+	1.41750e22i	−0.744840	+	1.29010i	−0.950269	+	0.311429i	$0.899192\pi$
$570$	1.84832e22	−	1.06713e22i	1.65874	−	0.957675i
$571$	−9.69514e21	−	1.67925e22i	−0.857956	−	1.48602i	−0.873875	−	0.486150i	$-0.838401\pi$
$571$	−9.69514e21	−	1.67925e22i	−0.857956	−	1.48602i	0.0159194	−	0.999873i	$-0.494932\pi$
$572$	4.89590e21	+	2.82665e21i	0.427233	+	0.246663i
$573$		−	1.69004e22i		−	1.45432i
$574$	−8.43261e21	−	2.32232e21i	−0.715595	−	0.197073i
$575$	1.07797e22			0.902117
$576$	1.00922e22	−	1.74803e22i	0.832928	−	1.44267i
$577$	7.86013e21	−	4.53805e21i	0.639769	−	0.369371i	−0.144756	−	0.989467i	$-0.546240\pi$
$577$	7.86013e21	−	4.53805e21i	0.639769	−	0.369371i	0.784526	+	0.620096i	$0.212907\pi$
$578$	4.35834e21	+	7.54886e21i	0.349863	+	0.605980i
$579$	−1.11864e21	−	6.45846e20i	−0.0885648	−	0.0511329i
$580$			2.69936e21i			0.210784i
$581$	1.02153e21	+	3.92098e21i	0.0786760	+	0.301985i
$582$	−2.44276e22			−1.85565
$583$	2.56581e21	−	4.44411e21i	0.192254	−	0.332994i
$584$	1.30467e22	−	7.53249e21i	0.964265	−	0.556719i
$585$	2.55544e22	+	4.42615e22i	1.86302	+	3.22685i
$586$	−2.19716e21	−	1.26853e21i	−0.158009	−	0.0912263i
$587$		−	2.73886e21i		−	0.194297i	−0.995270	−	0.0971484i	$-0.969028\pi$
$587$		−	2.73886e21i		−	0.194297i	0.995270	−	0.0971484i	$-0.0309721\pi$
$588$	−1.06862e22	−	1.48245e20i	−0.747830	−	0.0103744i
$589$	1.69376e22			1.16931
$590$	7.58573e21	−	1.31389e22i	0.516632	−	0.894832i
$591$	−2.72024e22	+	1.57053e22i	−1.82771	+	1.05523i
$592$	−2.62750e21	−	4.55096e21i	−0.174168	−	0.301668i
$593$	−6.18481e20	−	3.57080e20i	−0.0404472	−	0.0233522i	0.479640	−	0.877465i	$-0.340767\pi$
$593$	−6.18481e20	−	3.57080e20i	−0.0404472	−	0.0233522i	−0.520087	+	0.854113i	$0.674101\pi$
$594$			1.03287e22i			0.666431i
$595$	5.05401e21	−	1.31671e21i	0.321736	−	0.0838216i
$596$	−1.11374e22			−0.699539
$597$	−6.78345e21	+	1.17493e22i	−0.420393	+	0.728142i
$598$	−1.44535e22	+	8.34475e21i	−0.883822	+	0.510275i
$599$	1.10581e22	+	1.91532e22i	0.667216	+	1.15565i	0.978679	+	0.205393i	$0.0658474\pi$
$599$	1.10581e22	+	1.91532e22i	0.667216	+	1.15565i	−0.311464	+	0.950258i	$0.600819\pi$
$600$	−2.56481e22	−	1.48080e22i	−1.52702	−	0.881628i
$601$		−	7.83006e21i		−	0.460012i	−0.973189	−	0.230006i	$-0.926125\pi$
$601$		−	7.83006e21i		−	0.460012i	0.973189	−	0.230006i	$-0.0738746\pi$
$602$	−2.56008e20	+	9.29596e20i	−0.0148416	+	0.0538918i
$603$	−9.69426e20			−0.0554595
$604$	4.87879e21	−	8.45031e21i	0.275433	−	0.477064i
$605$	−1.04279e22	+	6.02053e21i	−0.580968	+	0.335422i
$606$	−7.39921e21	−	1.28158e22i	−0.406822	−	0.704636i
$607$	2.17871e22	+	1.25788e22i	1.18220	+	0.682541i	0.956521	−	0.291662i	$-0.0942083\pi$
$607$	2.17871e22	+	1.25788e22i	1.18220	+	0.682541i	0.225674	+	0.974203i	$0.427542\pi$
$608$			1.69098e22i			0.905547i
$609$	7.40074e21	−	7.29878e21i	0.391144	−	0.385755i
$610$	−4.21999e21			−0.220127
$611$	−2.22439e21	+	3.85276e21i	−0.114520	+	0.198355i
$612$	−3.16989e21	+	1.83014e21i	−0.161077	+	0.0929977i
$613$	1.02827e21	+	1.78101e21i	0.0515731	+	0.0893272i	0.890659	−	0.454671i	$-0.150243\pi$
$613$	1.02827e21	+	1.78101e21i	0.0515731	+	0.0893272i	−0.839086	+	0.543998i	$0.816910\pi$
$614$	8.07292e21	+	4.66090e21i	0.399654	+	0.230740i
$615$		−	4.79424e22i		−	2.34271i
$616$	1.13333e22	+	1.14916e22i	0.546650	+	0.554287i
$617$	−2.49940e22			−1.19002			−0.595010	−	0.803718i	$-0.702852\pi$
$617$	−2.49940e22			−1.19002			−0.595010	+	0.803718i	$0.702852\pi$
$618$	−2.33347e22	+	4.04169e22i	−1.09672	+	1.89957i
$619$	1.61009e22	−	9.29584e21i	0.747006	−	0.431284i	−0.0776050	−	0.996984i	$-0.524727\pi$
$619$	1.61009e22	−	9.29584e21i	0.747006	−	0.431284i	0.824611	+	0.565700i	$0.191394\pi$
$620$	−7.34613e21	−	1.27239e22i	−0.336454	−	0.582755i
$621$	2.16992e22	+	1.25281e22i	0.981097	+	0.566436i
$622$		−	2.16648e22i		−	0.967012i
$623$	4.63559e21	+	1.27663e21i	0.204268	+	0.0562549i
$624$	1.98868e22			0.865142
$625$	1.17663e22	−	2.03799e22i	0.505361	−	0.875310i
$626$	7.56350e21	−	4.36679e21i	0.320722	−	0.185169i
$627$	−1.58517e22	−	2.74559e22i	−0.663644	−	1.14947i
$628$	5.78955e21	+	3.34260e21i	0.239314	+	0.138168i
$629$			5.82402e21i			0.237694i
$630$	1.14353e22	+	4.38926e22i	0.460811	+	1.76875i
$631$	−4.16612e22			−1.65767			−0.828833	−	0.559496i	$-0.810995\pi$
$631$	−4.16612e22			−1.65767			−0.828833	+	0.559496i	$0.810995\pi$
$632$	8.46673e21	−	1.46648e22i	0.332644	−	0.576155i
$633$	3.05125e22	−	1.76164e22i	1.18372	−	0.683419i
$634$	−1.67482e22	−	2.90088e22i	−0.641586	−	1.11126i
$635$	3.58036e22	+	2.06712e22i	1.35437	+	0.781944i
$636$			1.06315e22i			0.397136i
$637$	−1.99784e22	−	3.57395e22i	−0.736962	−	1.31836i
$638$	−4.87971e21			−0.177758
$639$	1.36585e21	−	2.36571e21i	0.0491354	−	0.0851051i
$640$	3.90325e21	−	2.25354e21i	0.138671	−	0.0800619i
$641$	−1.27511e22	−	2.20856e22i	−0.447388	−	0.774899i	0.550827	−	0.834620i	$-0.314312\pi$
$641$	−1.27511e22	−	2.20856e22i	−0.447388	−	0.774899i	−0.998215	+	0.0597202i	$0.980979\pi$
$642$	3.44766e22	+	1.99051e22i	1.19466	+	0.689738i
$643$			2.06795e22i			0.707704i	0.935301	+	0.353852i	$0.115128\pi$
$643$			2.06795e22i			0.707704i	−0.935301	+	0.353852i	$0.884872\pi$
$644$	1.17778e22	−	3.06847e21i	0.398088	−	0.103713i
$645$	−5.28509e21			−0.176431
$646$	−2.92797e21	+	5.07140e21i	−0.0965400	+	0.167212i
$647$	−3.55211e22	+	2.05081e22i	−1.15679	+	0.667870i	−0.950531	−	0.310628i	$-0.899461\pi$
$647$	−3.55211e22	+	2.05081e22i	−1.15679	+	0.667870i	−0.206254	+	0.978499i	$0.566127\pi$
$648$	−5.18797e21	−	8.98582e21i	−0.166877	−	0.289040i
$649$	−1.95172e22	−	1.12682e22i	−0.620096	−	0.358013i
$650$		−	3.52706e22i		−	1.10689i
$651$	−1.50214e22	+	5.45446e22i	−0.465653	+	1.69084i
$652$	2.73775e21			0.0838326
$653$	−4.16293e21	+	7.21041e21i	−0.125920	+	0.218099i	−0.922092	−	0.386971i	$-0.873521\pi$
$653$	−4.16293e21	+	7.21041e21i	−0.125920	+	0.218099i	0.796172	+	0.605070i	$0.206855\pi$
$654$	3.38121e22	−	1.95214e22i	1.01030	−	0.583297i
$655$	4.73797e22	+	8.20640e22i	1.39850	+	2.42227i
$656$	−1.02790e22	−	5.93458e21i	−0.299723	−	0.173045i
$657$		−	6.28891e22i		−	1.81156i
$658$	−2.81109e21	+	2.77236e21i	−0.0799958	+	0.0788937i
$659$	2.59184e22			0.728660			0.364330	−	0.931270i	$-0.381298\pi$
$659$	2.59184e22			0.728660			0.364330	+	0.931270i	$0.381298\pi$
$660$	−1.37503e22	+	2.38162e22i	−0.381910	+	0.661487i
$661$	2.66692e22	−	1.53975e22i	0.731811	−	0.422511i	−0.0872736	−	0.996184i	$-0.527815\pi$
$661$	2.66692e22	−	1.53975e22i	0.731811	−	0.422511i	0.819084	+	0.573673i	$0.194482\pi$
$662$	1.87385e22	+	3.24560e22i	0.508008	+	0.879896i
$663$	−1.90873e22	−	1.10201e22i	−0.511254	−	0.295173i
$664$			1.26776e22i			0.335500i
$665$	−4.18710e22	−	4.24559e22i	−1.09481	−	1.11011i
$666$	−5.05800e22			−1.30673
$667$	−5.91877e21	+	1.02516e22i	−0.151086	+	0.261689i
$668$	2.30228e22	−	1.32922e22i	0.580693	−	0.335263i
$669$	9.40911e21	+	1.62971e22i	0.234498	+	0.406163i
$670$	1.16511e21	+	6.72674e20i	0.0286924	+	0.0165656i
$671$			6.26860e21i			0.152542i
$672$	−5.44551e22	−	1.49968e22i	−1.30944	−	0.360615i
$673$	−5.93484e22			−1.41023			−0.705113	−	0.709095i	$-0.749104\pi$
$673$	−5.93484e22			−1.41023			−0.705113	+	0.709095i	$0.749104\pi$
$674$	−9.74272e21	+	1.68749e22i	−0.228771	+	0.396243i
$675$	−4.58578e22	+	2.64760e22i	−1.06410	+	0.614360i
$676$	−1.26008e22	−	2.18252e22i	−0.288950	−	0.500477i
$677$	−2.22662e22	−	1.28554e22i	−0.504588	−	0.291324i	0.226018	−	0.974123i	$-0.427429\pi$
$677$	−2.22662e22	−	1.28554e22i	−0.504588	−	0.291324i	−0.730606	+	0.682799i	$0.760762\pi$
$678$			4.19017e22i			0.938413i
$679$	1.72064e22	+	6.60442e22i	0.380831	+	1.46176i
$680$	1.63410e22			0.357443
$681$	2.58858e22	−	4.48355e22i	0.559608	−	0.969270i
$682$	2.30013e22	−	1.32798e22i	0.491448	−	0.283737i
$683$	6.81171e21	+	1.17982e22i	0.143844	+	0.249145i	0.928941	−	0.370228i	$-0.120720\pi$
$683$	6.81171e21	+	1.17982e22i	0.143844	+	0.249145i	−0.785097	+	0.619372i	$0.787387\pi$
$684$	3.61917e22	+	2.08953e22i	0.755372	+	0.436114i
$685$			9.56554e22i			1.97326i
$686$	−8.67245e21	−	3.52871e22i	−0.176827	−	0.719488i
$687$	1.21584e23			2.45032
$688$	−6.54218e20	+	1.13314e21i	−0.0130321	+	0.0225723i
$689$	−3.52743e22	+	2.03656e22i	−0.694552	+	0.401000i
$690$	−4.05932e22	−	7.03095e22i	−0.790061	−	1.36843i
$691$	−6.15101e22	−	3.55129e22i	−1.18337	−	0.683222i	−0.226582	−	0.973992i	$-0.572755\pi$
$691$	−6.15101e22	−	3.55129e22i	−1.18337	−	0.683222i	−0.956793	+	0.290770i	$0.906088\pi$
$692$			8.59977e21i			0.163545i
$693$	6.52004e22	−	1.69866e22i	1.22570	−	0.319331i
$694$	3.61630e22			0.672030
$695$	5.40647e22	−	9.36428e22i	0.993197	−	1.72027i
$696$	2.81651e22	−	1.62611e22i	0.511491	−	0.295309i
$697$	6.57719e21	+	1.13920e22i	0.118080	+	0.204521i
$698$	2.87001e21	+	1.65700e21i	0.0509377	+	0.0294089i
$699$		−	3.53014e22i		−	0.619405i
$700$	−6.82935e21	+	2.47982e22i	−0.118466	+	0.430166i
$701$	−3.64446e22			−0.625013			−0.312507	−	0.949916i	$-0.601169\pi$
$701$	−3.64446e22			−0.625013			−0.312507	+	0.949916i	$0.601169\pi$
$702$	4.09912e22	−	7.09989e22i	0.695014	−	1.20380i
$703$	5.75863e22	−	3.32474e22i	0.965331	−	0.557334i
$704$	2.08049e22	+	3.60352e22i	0.344814	+	0.597235i
$705$	−1.87418e22	−	1.08206e22i	−0.307113	−	0.177312i
$706$			5.03139e21i			0.0815174i
$707$	−2.94378e22	+	2.90323e22i	−0.471575	+	0.465078i
$708$	4.66904e22			0.739541
$709$	−8.06423e21	+	1.39677e22i	−0.126297	+	0.218753i	−0.922239	−	0.386620i	$-0.873643\pi$
$709$	−8.06423e21	+	1.39677e22i	−0.126297	+	0.218753i	0.795942	+	0.605373i	$0.206976\pi$
$710$	−3.28309e21	+	1.89549e21i	−0.0508412	+	0.0293532i
$711$	−3.53446e22	−	6.12186e22i	−0.541210	−	0.937403i
$712$	1.30285e22	+	7.52198e21i	0.197266	+	0.113892i
$713$		−	6.44301e22i		−	0.964656i
$714$	−1.37348e22	−	1.39267e22i	−0.203347	−	0.206187i
$715$	−1.05360e23			−1.54250
$716$	−3.96530e20	+	6.86810e20i	−0.00574079	+	0.00994334i
$717$	−1.75151e23	+	1.01124e23i	−2.50761	+	1.44777i
$718$	3.65093e22	+	6.32359e22i	0.516901	+	0.895299i
$719$	−1.96807e22	−	1.13627e22i	−0.275556	−	0.159092i	0.355854	−	0.934542i	$-0.384190\pi$
$719$	−1.96807e22	−	1.13627e22i	−0.275556	−	0.159092i	−0.631410	+	0.775449i	$0.717523\pi$
$720$			6.15510e22i			0.852266i
$721$	1.25711e23	+	3.46203e22i	1.72143	+	0.474077i
$722$	1.21507e22			0.164553
$723$	−7.67480e22	+	1.32931e23i	−1.02792	+	1.78042i
$724$	−4.93117e22	+	2.84702e22i	−0.653194	+	0.377121i
$725$	−1.25083e22	−	2.16651e22i	−0.163869	−	0.283829i
$726$	3.90544e22	+	2.25481e22i	0.506031	+	0.292157i
$727$		−	1.37020e23i		−	1.75594i	−0.478718	−	0.877969i	$-0.658898\pi$
$727$		−	1.37020e23i		−	1.75594i	0.478718	−	0.877969i	$-0.341102\pi$
$728$	−3.22978e22	−	1.23970e23i	−0.409376	−	1.57133i
$729$	1.20974e23			1.51660
$730$	−4.36381e22	+	7.55833e22i	−0.541106	+	0.937224i
$731$	1.25584e21	−	7.25058e20i	0.0154026	−	0.00889270i
$732$	−6.49356e21	−	1.12472e22i	−0.0787760	−	0.136444i
$733$	−7.31883e22	−	4.22553e22i	−0.878234	−	0.507048i	−0.00815804	−	0.999967i	$-0.502597\pi$
$733$	−7.31883e22	−	4.22553e22i	−0.878234	−	0.507048i	−0.870076	+	0.492918i	$0.835930\pi$
$734$		−	2.72604e22i		−	0.323566i
$735$	1.73856e23	−	9.71853e22i	2.04122	−	1.14104i
$736$	6.43244e22			0.747056
$737$	9.99225e20	−	1.73071e21i	0.0114795	−	0.0198831i
$738$	−9.89365e22	+	5.71210e22i	−1.12436	+	0.649150i
$739$	1.37268e22	+	2.37754e22i	0.154316	+	0.267284i	0.932810	−	0.360369i	$-0.117349\pi$
$739$	1.37268e22	+	2.37754e22i	0.154316	+	0.267284i	−0.778493	+	0.627653i	$0.784016\pi$
$740$	−4.99523e22	−	2.88400e22i	−0.555522	−	0.320731i
$741$			2.51640e23i			2.76843i
$742$	−3.49804e22	+	9.11340e21i	−0.380709	+	0.0991857i
$743$	9.91439e21			0.106747			0.0533735	−	0.998575i	$-0.483003\pi$
$743$	9.91439e21			0.106747			0.0533735	+	0.998575i	$0.483003\pi$
$744$	−8.85072e22	+	1.53299e23i	−0.942747	+	1.63289i
$745$	1.79756e23	−	1.03782e23i	1.89424	−	1.09364i
$746$	−2.03672e21	−	3.52770e21i	−0.0212335	−	0.0367774i
$747$	4.58327e22	+	2.64615e22i	0.472727	+	0.272929i
$748$		−	7.54558e21i		−	0.0769980i
$749$	2.95320e22	−	1.07234e23i	0.298153	−	1.08263i
$750$	−1.88001e21			−0.0187789
$751$	−1.81575e22	+	3.14497e22i	−0.179447	+	0.310811i	−0.941691	−	0.336478i	$-0.890764\pi$
$751$	−1.81575e22	+	3.14497e22i	−0.179447	+	0.310811i	0.762244	+	0.647289i	$0.224098\pi$
$752$	−4.63993e21	+	2.67887e21i	−0.0453700	+	0.0261944i
$753$	−2.49227e22	−	4.31674e22i	−0.241121	−	0.417634i
$754$	3.35427e22	+	1.93659e22i	0.321091	+	0.185382i
$755$			1.81850e23i			1.72242i
$756$	−4.25676e22	+	4.19812e22i	−0.398938	+	0.393442i
$757$	−9.72288e22			−0.901629			−0.450815	−	0.892618i	$-0.648866\pi$
$757$	−9.72288e22			−0.901629			−0.450815	+	0.892618i	$0.648866\pi$
$758$	3.40600e22	−	5.89937e22i	0.312530	−	0.541317i
$759$	−1.04441e23	+	6.02993e22i	−0.948285	+	0.547492i
$760$	−9.32854e22	−	1.61575e23i	−0.838118	−	1.45166i
$761$	5.58617e22	+	3.22518e22i	0.496635	+	0.286732i	0.727323	−	0.686296i	$-0.240764\pi$
$761$	5.58617e22	+	3.22518e22i	0.496635	+	0.286732i	−0.230688	+	0.973028i	$0.574098\pi$
$762$		−	1.54836e23i		−	1.36217i
$763$	−7.65963e22	−	7.76662e22i	−0.666824	−	0.676139i
$764$	−4.59250e22			−0.395642
$765$	3.41079e22	−	5.90767e22i	0.290780	−	0.503645i
$766$	5.71841e22	−	3.30152e22i	0.482442	−	0.278538i
$767$	8.94396e22	+	1.54914e23i	0.746736	+	1.29338i
$768$	−1.80129e23	−	1.03998e23i	−1.48831	−	0.859277i
$769$		−	1.63147e23i		−	1.33404i	−0.745039	−	0.667020i	$-0.767569\pi$
$769$		−	1.63147e23i		−	1.33404i	0.745039	−	0.667020i	$-0.232431\pi$
$770$	−9.01480e22	−	2.48265e22i	−0.729508	−	0.200904i
$771$	9.20359e22			0.737093
$772$	−1.75502e21	+	3.03978e21i	−0.0139105	+	0.0240937i
$773$	4.25525e22	−	2.45677e22i	0.333802	−	0.192721i	−0.323726	−	0.946151i	$-0.604935\pi$
$773$	4.25525e22	−	2.45677e22i	0.333802	−	0.192721i	0.657528	+	0.753430i	$0.271602\pi$
$774$	6.29692e21	+	1.09066e22i	0.0488878	+	0.0846762i
$775$	1.17920e23	+	6.80813e22i	0.906097	+	0.523135i
$776$			2.13539e23i			1.62399i
$777$	5.59961e22	+	2.14932e23i	0.421492	+	1.61783i
$778$	1.13008e23			0.841923
$779$	7.50941e22	−	1.30067e23i	0.553740	−	0.959106i
$780$	1.89037e23	−	1.09141e23i	1.37972	−	0.796580i
$781$	2.81566e21	+	4.87687e21i	0.0203410	+	0.0352316i
$782$	1.92914e22	+	1.11379e22i	0.137946	+	0.0796434i
$783$		−	5.81485e22i		−	0.411571i
$784$	6.83994e20	−	4.93053e22i	0.00479208	−	0.345434i
$785$	−1.24591e23			−0.864029
$786$	1.77446e23	−	3.07346e23i	1.21811	−	2.10983i
$787$	−4.00427e22	+	2.31187e22i	−0.272098	+	0.157096i	−0.629841	−	0.776724i	$-0.716880\pi$
$787$	−4.00427e22	+	2.31187e22i	−0.272098	+	0.157096i	0.357743	+	0.933820i	$0.383547\pi$
$788$	4.26775e22	+	7.39197e22i	0.287071	+	0.497222i
$789$	−2.43183e23	−	1.40402e23i	−1.61926	−	0.934882i
$790$			9.81008e22i			0.646630i
$791$	1.13288e23	−	2.95149e22i	0.739220	−	0.192588i
$792$	2.10811e23			1.36173
$793$	2.48779e22	−	4.30899e22i	0.159085	−	0.275543i
$794$	−1.81901e23	+	1.05021e23i	−1.15152	+	0.664829i
$795$	−9.90691e22	−	1.71593e23i	−0.620870	−	1.07538i
$796$	3.19274e22	+	1.84333e22i	0.198088	+	0.114366i
$797$			2.85340e22i			0.175265i	0.996153	+	0.0876327i	$0.0279302\pi$
$797$			2.85340e22i			0.175265i	−0.996153	+	0.0876327i	$0.972070\pi$
$798$	−5.92954e22	+	2.15309e23i	−0.360577	+	1.30930i
$799$	5.93788e21			0.0357484
$800$	−6.79696e22	+	1.17727e23i	−0.405130	+	0.701706i
$801$	5.43876e22	−	3.14007e22i	0.320952	−	0.185302i
$802$	2.95314e22	+	5.11499e22i	0.172540	+	0.298847i
$803$	1.12275e23	+	6.48223e22i	0.649472	+	0.374973i
$804$			4.14034e21i			0.0237130i
$805$	−1.61501e23	+	1.59276e23i	−0.915814	+	0.903197i
$806$	−2.10812e23			−1.18363
$807$	−1.77505e23	+	3.07448e23i	−0.986786	+	1.70916i
$808$	−1.12032e23	+	6.46818e22i	−0.616668	+	0.356034i
$809$	−4.80028e22	−	8.31432e22i	−0.261624	−	0.453146i	0.705049	−	0.709158i	$-0.250925\pi$
$809$	−4.80028e22	−	8.31432e22i	−0.261624	−	0.453146i	−0.966674	+	0.256012i	$0.917591\pi$
$810$	5.20577e22	+	3.00555e22i	0.280934	+	0.162197i
$811$		−	2.99860e21i		−	0.0160233i	−0.999968	−	0.00801164i	$-0.997450\pi$
$811$		−	2.99860e21i		−	0.0160233i	0.999968	−	0.00801164i	$-0.00255021\pi$
$812$	−1.98336e22	−	2.01107e22i	−0.104943	−	0.106409i
$813$	3.04813e22			0.159702
$814$	5.21348e22	−	9.03001e22i	0.270478	−	0.468482i
$815$	−4.41872e22	+	2.55115e22i	−0.227005	+	0.131061i
$816$	−1.32716e22	−	2.29871e22i	−0.0675154	−	0.116940i
$817$	−1.43383e22	−	8.27824e21i	−0.0722307	−	0.0417024i
$818$			7.07511e22i			0.352945i
$819$	−5.15597e23	−	1.41994e23i	−2.54706	−	0.701452i
$820$	−1.30278e23			−0.637325
$821$	6.11418e22	−	1.05901e23i	0.296205	−	0.513043i	−0.679059	−	0.734083i	$-0.737612\pi$
$821$	6.11418e22	−	1.05901e23i	0.296205	−	0.513043i	0.975265	+	0.221041i	$0.0709454\pi$
$822$	3.10252e23	−	1.79124e23i	1.48847	−	0.859370i
$823$	1.27402e23	+	2.20667e23i	0.605309	+	1.04843i	0.992003	+	0.126218i	$0.0402838\pi$
$823$	1.27402e23	+	2.20667e23i	0.605309	+	1.04843i	−0.386693	+	0.922208i	$0.626383\pi$
$824$	3.53313e23	+	2.03985e23i	1.66242	+	0.959801i
$825$		−	2.54866e23i		−	1.18763i
$826$	4.00232e22	+	1.53623e23i	0.184702	+	0.708950i
$827$	3.93130e23			1.79677			0.898384	−	0.439210i	$-0.144742\pi$
$827$	3.93130e23			1.79677			0.898384	+	0.439210i	$0.144742\pi$
$828$	7.94850e22	−	1.37672e23i	0.359785	−	0.623165i
$829$	6.54036e22	−	3.77608e22i	0.293201	−	0.169280i	−0.346184	−	0.938167i	$-0.612523\pi$
$829$	6.54036e22	−	3.77608e22i	0.293201	−	0.169280i	0.639385	+	0.768887i	$0.279189\pi$
$830$	−3.67227e22	−	6.36056e22i	−0.163046	−	0.282404i
$831$	−3.70286e23	−	2.13784e23i	−1.62828	−	0.940087i
$832$		−	3.30271e23i		−	1.43841i
$833$	−2.79786e22	+	4.69442e22i	−0.120688	+	0.202498i
$834$	−4.04966e23			−1.73018
$835$	−2.47725e23	+	4.29072e23i	−1.04828	+	1.81568i
$836$	−7.46085e22	+	4.30752e22i	−0.312707	+	0.180542i
$837$	1.58247e23	+	2.74092e23i	0.656950	+	1.13787i
$838$	6.41767e21	+	3.70524e21i	0.0263891	+	0.0152358i
$839$			5.28663e22i			0.215320i	0.994188	+	0.107660i	$0.0343357\pi$
$839$			5.28663e22i			0.215320i	−0.994188	+	0.107660i	$0.965664\pi$
$840$	6.03055e23	−	1.57113e23i	2.43289	−	0.633839i
$841$	−2.22775e23			−0.890221
$842$	−1.51303e23	+	2.62065e23i	−0.598896	+	1.03732i
$843$	5.35837e23	−	3.09366e23i	2.10093	−	1.21297i
$844$	−4.78706e22	−	8.29143e22i	−0.185921	−	0.322025i
$845$	4.06751e23	+	2.34838e23i	1.56486	+	0.903472i
$846$			5.15688e22i			0.196528i
$847$	3.34533e22	−	1.21473e23i	0.126291	−	0.458577i
$848$	−4.90533e22			−0.183443
$849$	5.38058e22	−	9.31944e22i	0.199328	−	0.345246i
$850$	−4.07693e22	+	2.35382e22i	−0.149617	+	0.0863816i
$851$	−1.26472e23	−	2.19056e23i	−0.459789	−	0.796377i
$852$	−1.01038e22	−	5.83341e21i	−0.0363887	−	0.0210090i
$853$		−	4.61601e23i		−	1.64693i	−0.567369	−	0.823463i	$-0.692039\pi$
$853$		−	4.61601e23i		−	1.64693i	0.567369	−	0.823463i	$-0.307961\pi$
$854$	3.14396e22	−	3.10065e22i	0.111126	−	0.109595i
$855$	−7.78844e23			−2.72723
$856$	1.74005e23	−	3.01385e23i	0.603630	−	1.04552i
$857$	−2.89636e23	+	1.67222e23i	−0.995420	+	0.574706i	−0.906890	−	0.421367i	$-0.861550\pi$
$857$	−2.89636e23	+	1.67222e23i	−0.995420	+	0.574706i	−0.0885303	+	0.996073i	$0.528217\pi$
$858$	1.97296e23	+	3.41727e23i	0.671770	+	1.16354i
$859$	−5.83113e22	−	3.36660e22i	−0.196701	−	0.113566i	0.398415	−	0.917205i	$-0.369561\pi$
$859$	−5.83113e22	−	3.36660e22i	−0.196701	−	0.113566i	−0.595116	+	0.803640i	$0.702894\pi$
$860$			1.43616e22i			0.0479973i
$861$	3.52258e23	+	3.57179e23i	1.16637	+	1.18266i
$862$	3.72939e22			0.122343
$863$	2.92138e23	−	5.05998e23i	0.949514	−	1.64461i	0.203064	−	0.979166i	$-0.434910\pi$
$863$	2.92138e23	−	5.05998e23i	0.949514	−	1.64461i	0.746450	−	0.665441i	$-0.231756\pi$
$864$	−2.73643e23	+	1.57988e23i	−0.881199	+	0.508760i
$865$	−8.01362e22	−	1.38800e23i	−0.255682	−	0.442854i
$866$	2.32531e23	+	1.34252e23i	0.735086	+	0.424402i
$867$		−	4.99946e23i		−	1.56592i
$868$	1.48219e23	+	4.08190e22i	0.459987	+	0.126679i
$869$	1.45724e23			0.448098
$870$	−9.42058e22	+	1.63169e23i	−0.287028	+	0.497147i
$871$	−1.37372e22	+	7.93117e21i	−0.0414718	+	0.0239437i
$872$	−1.70651e23	−	2.95576e23i	−0.510477	−	0.884173i
$873$	7.71996e23	+	4.45712e23i	2.28824	+	1.32111i
$874$		−	2.54331e23i		−	0.746978i
$875$	1.32425e21	+	5.08293e21i	0.00385395	+	0.0147928i
$876$	−2.68594e23			−0.774575
$877$	−2.86449e23	+	4.96145e23i	−0.818561	+	1.41779i	0.0881819	+	0.996104i	$0.471894\pi$
$877$	−2.86449e23	+	4.96145e23i	−0.818561	+	1.41779i	−0.906743	+	0.421684i	$0.861439\pi$
$878$	1.63933e23	−	9.46467e22i	0.464205	−	0.268009i
$879$	7.27568e22	+	1.26019e23i	0.204156	+	0.353609i
$880$	−1.09887e23	−	6.34430e22i	−0.305551	−	0.176410i
$881$			4.89600e23i			1.34907i	0.738243	+	0.674535i	$0.235656\pi$
$881$			4.89600e23i			1.34907i	−0.738243	+	0.674535i	$0.764344\pi$
$882$	−4.07697e23	−	2.42986e23i	−1.11324	−	0.663487i
$883$	3.70398e23			1.00227			0.501133	−	0.865370i	$-0.332917\pi$
$883$	3.70398e23			1.00227			0.501133	+	0.865370i	$0.332917\pi$
$884$	−2.99458e22	+	5.18677e22i	−0.0803005	+	0.139085i
$885$	−7.53582e23	+	4.35081e23i	−2.00255	+	1.15618i
$886$	−3.71711e22	−	6.43822e22i	−0.0978894	−	0.169549i
$887$	−5.41765e23	−	3.12788e23i	−1.41391	−	0.816321i	−0.418156	−	0.908375i	$-0.637323\pi$
$887$	−5.41765e23	−	3.12788e23i	−1.41391	−	0.816321i	−0.995754	+	0.0920542i	$0.970657\pi$
$888$			6.94935e23i			1.79738i
$889$	−4.18625e23	+	1.09064e23i	−1.07303	+	0.279555i
$890$	−8.71544e22			−0.221396
$891$	4.46460e22	−	7.73292e22i	0.112399	−	0.194680i
$892$	4.42854e22	−	2.55682e22i	0.110495	−	0.0637943i
$893$	−3.38974e22	−	5.87121e22i	−0.0838214	−	0.145183i
$894$	−6.73224e23	−	3.88686e23i	−1.64991	−	0.952574i
$895$		−	1.47801e22i		−	0.0358999i
$896$	−1.25219e22	+	4.54685e22i	−0.0301443	+	0.109458i
$897$	9.57230e23			2.28390
$898$	−1.17108e23	+	2.02837e23i	−0.276933	+	0.479662i
$899$	−1.29492e23	+	7.47624e22i	−0.303505	+	0.175229i
$900$	1.67979e23	+	2.90948e23i	0.390224	+	0.675888i
$901$	4.70813e22	+	2.71824e22i	0.108405	+	0.0625878i
$902$		−	2.35508e23i		−	0.537468i
$903$	3.93748e22	−	3.88323e22i	0.0890668	−	0.0878398i
$904$	3.66293e23			0.821260
$905$	5.30593e23	−	9.19014e23i	1.17916	−	2.04237i
$906$	5.89820e23	−	3.40533e23i	1.29925	−	0.750124i
$907$	2.01595e23	+	3.49172e23i	0.440170	+	0.762397i	0.997702	−	0.0677586i	$-0.0215848\pi$
$907$	2.01595e23	+	3.49172e23i	0.440170	+	0.762397i	−0.557532	+	0.830156i	$0.688251\pi$
$908$	−1.21835e23	−	7.03417e22i	−0.263686	−	0.152239i
$909$			5.40031e23i			1.15853i
$910$	5.21142e23	+	5.28422e23i	1.10822	+	1.12370i
$911$	−4.13474e23			−0.871568			−0.435784	−	0.900051i	$-0.643529\pi$
$911$	−4.13474e23			−0.871568			−0.435784	+	0.900051i	$0.643529\pi$
$912$	−1.51527e23	+	2.62452e23i	−0.316615	+	0.548393i
$913$	−9.44831e22	+	5.45498e22i	−0.195699	+	0.112987i
$914$	2.04372e23	+	3.53982e23i	0.419615	+	0.726794i
$915$	2.09611e23	+	1.21019e23i	0.426625	+	0.246312i
$916$		−	3.30391e23i		−	0.666599i
$917$	−9.55954e23	−	2.63267e23i	−1.91197	−	0.526552i
$918$	−1.09424e23			−0.216955
$919$	2.01915e23	−	3.49727e23i	0.396866	−	0.687392i	−0.596471	−	0.802634i	$-0.703431\pi$
$919$	2.01915e23	−	3.49727e23i	0.396866	−	0.687392i	0.993337	+	0.115242i	$0.0367644\pi$
$920$	−6.14626e23	+	3.54854e23i	−1.19759	+	0.691429i
$921$	−2.67327e23	−	4.63024e23i	−0.516376	−	0.894389i
$922$	−1.96109e23	−	1.13223e23i	−0.375534	−	0.216815i
$923$		−	4.46976e22i		−	0.0848537i
$924$	−7.25483e22	−	2.78465e23i	−0.136537	−	0.524077i
$925$	5.34556e23			0.997378
$926$	3.03812e23	−	5.26217e23i	0.561974	−	0.973368i
$927$	1.47491e24	−	8.51542e23i	2.70476	−	1.56159i
$928$	−7.46398e22	−	1.29280e23i	−0.135702	−	0.235043i
$929$	3.99434e23	+	2.30613e23i	0.719978	+	0.415680i	0.814745	−	0.579820i	$-0.196877\pi$
$929$	3.99434e23	+	2.30613e23i	0.719978	+	0.415680i	−0.0947665	+	0.995500i	$0.530210\pi$
$930$		−	1.02550e24i		−	1.83262i
$931$	6.23891e23	+	8.65502e21i	1.10538	+	0.0153345i
$932$	−9.59277e22			−0.168507
$933$	−6.21295e23	+	1.07611e24i	−1.08204	+	1.87415i
$934$	−1.27337e23	+	7.35180e22i	−0.219877	+	0.126946i
$935$	7.03128e22	+	1.21785e23i	0.120376	+	0.208498i
$936$	−1.44910e24	−	8.36637e23i	−2.45975	−	1.42014i
$937$			1.16423e24i			1.95940i	0.200471	+	0.979700i	$0.435753\pi$
$937$			1.16423e24i			1.95940i	−0.200471	+	0.979700i	$0.564247\pi$
$938$	−1.36227e22	+	3.54911e21i	−0.0227322	+	0.00592239i
$939$	−5.00916e23			−0.828782
$940$	−2.94038e22	+	5.09288e22i	−0.0482370	+	0.0835489i
$941$	−4.85901e22	+	2.80535e22i	−0.0790371	+	0.0456321i	−0.538998	−	0.842307i	$-0.681197\pi$
$941$	−4.85901e22	+	2.80535e22i	−0.0790371	+	0.0456321i	0.459961	+	0.887939i	$0.347864\pi$
$942$	2.33309e23	+	4.04102e23i	0.376291	+	0.651755i
$943$	−4.94769e23	−	2.85655e23i	−0.791242	−	0.456824i
$944$			2.15427e23i			0.341605i
$945$	2.95842e23	−	1.07424e24i	0.465163	−	1.68906i
$946$	−2.59619e22			−0.0404770
$947$	1.52929e23	−	2.64881e23i	0.236423	−	0.409497i	−0.723262	−	0.690574i	$-0.757358\pi$
$947$	1.52929e23	−	2.64881e23i	0.236423	−	0.409497i	0.959685	+	0.281076i	$0.0906915\pi$
$948$	−2.61459e23	+	1.50954e23i	−0.400809	+	0.231407i
$949$	−5.14515e23	−	8.91166e23i	−0.782111	−	1.35466i
$950$	4.65477e23	+	2.68743e23i	0.701632	+	0.405088i
$951$			1.92120e24i			2.87162i
$952$	−1.21743e23	+	1.20066e23i	−0.180447	+	0.177961i
$953$	9.52302e23			1.39969			0.699844	−	0.714296i	$-0.253253\pi$
$953$	9.52302e23			1.39969			0.699844	+	0.714296i	$0.253253\pi$
$954$	−2.36072e23	+	4.08888e23i	−0.344078	+	0.595961i
$955$	7.41228e23	−	4.27948e23i	1.07133	−	0.618535i
$956$	2.74793e23	+	4.75955e23i	0.393860	+	0.682186i
$957$	2.42380e23	+	1.39938e23i	0.344510	+	0.198903i
$958$			6.78227e23i			0.955985i
$959$	−7.02831e23	−	7.12648e23i	−0.982431	−	0.996154i
$960$	1.60661e24			2.22710
$961$	4.32102e22	−	7.48422e22i	0.0594017	−	0.102887i
$962$	−7.16741e23	+	4.13810e23i	−0.977151	+	0.564158i
$963$	−7.26387e23	−	1.25814e24i	−0.982104	−	1.70105i
$964$	3.61227e23	+	2.08554e23i	0.484355	+	0.279642i
$965$		−	6.54158e22i		−	0.0869890i
$966$	8.19027e23	+	2.25558e23i	1.08014	+	0.297468i
$967$	−8.08457e23			−1.05741			−0.528707	−	0.848805i	$-0.677323\pi$
$967$	−8.08457e23			−1.05741			−0.528707	+	0.848805i	$0.677323\pi$
$968$	1.97109e23	−	3.41403e23i	0.255684	−	0.442858i
$969$	2.90871e23	−	1.67934e23i	0.374206	−	0.216048i
$970$	−6.18549e23	−	1.07136e24i	−0.789224	−	1.36698i
$971$	6.61643e23	+	3.82000e23i	0.837279	+	0.483403i	0.856338	−	0.516415i	$-0.172734\pi$
$971$	6.61643e23	+	3.82000e23i	0.837279	+	0.483403i	−0.0190594	+	0.999818i	$0.506067\pi$
$972$		−	2.61443e23i		−	0.328130i
$973$	2.85252e23	+	1.09490e24i	0.355080	+	1.36292i
$974$	3.65352e22			0.0451066
$975$	−1.01147e24	+	1.75193e24i	−1.23856	+	2.14525i
$976$	5.18937e22	−	2.99609e22i	0.0630255	−	0.0363878i
$977$	−4.66467e23	−	8.07945e23i	−0.561907	−	0.973252i	−0.997330	−	0.0730257i	$-0.976734\pi$
$977$	−4.66467e23	−	8.07945e23i	−0.561907	−	0.973252i	0.435423	−	0.900226i	$-0.356599\pi$
$978$	1.65490e23	+	9.55455e22i	0.197724	+	0.114156i
$979$			1.29464e23i			0.153422i
$980$	−2.64090e23	−	4.72433e23i	−0.310416	−	0.555305i
$981$	−1.42477e24			−1.66109
$982$	−1.39757e23	+	2.42066e23i	−0.161615	+	0.279925i
$983$	−1.30491e24	+	7.53390e23i	−1.49676	+	0.864155i	−0.999993	−	0.00372790i	$-0.998813\pi$
$983$	−1.30491e24	+	7.53390e23i	−1.49676	+	0.864155i	−0.496768	+	0.867883i	$0.665480\pi$
$984$	7.84805e23	+	1.35932e24i	0.892896	+	1.54654i
$985$	−1.37763e24	−	7.95373e23i	−1.55468	−	0.897597i
$986$		−	5.16961e22i		−	0.0578686i
$987$	2.19134e23	−	5.70908e22i	0.243317	−	0.0633912i
$988$	6.83804e23			0.753141
$989$	−3.14901e22	+	5.45425e22i	−0.0344036	+	0.0595888i
$990$	−1.05767e24	+	6.10647e23i	−1.14622	+	0.661772i
$991$	4.35009e23	+	7.53458e23i	0.467637	+	0.809971i	0.999316	−	0.0369747i	$-0.0117721\pi$
$991$	4.35009e23	+	7.53458e23i	0.467637	+	0.809971i	−0.531679	+	0.846946i	$0.678439\pi$
$992$	7.03653e23	+	4.06254e23i	0.750352	+	0.433216i
$993$		−	2.14950e24i		−	2.27375i
$994$	1.05324e22	−	3.82443e22i	0.0110518	−	0.0401306i
$995$	−6.87075e23			−0.715187
$996$	1.13015e23	−	1.95747e23i	0.116697	−	0.202126i
$997$	−9.16628e23	+	5.29216e23i	−0.938927	+	0.542090i	−0.889624	−	0.456694i	$-0.849034\pi$
$997$	−9.16628e23	+	5.29216e23i	−0.938927	+	0.542090i	−0.0493035	+	0.998784i	$0.515700\pi$
$998$	−5.19862e23	−	9.00428e23i	−0.528255	−	0.914965i
$999$	1.07605e24	+	6.21258e23i	1.08470	+	0.626250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.17.d.a.5.7	yes	20
7.2	even	3		49.17.b.a.48.7		20
7.3	odd	6	inner	7.17.d.a.3.7	✓	20
7.5	odd	6		49.17.b.a.48.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.17.d.a.3.7	✓	20	7.3	odd	6	inner
7.17.d.a.5.7	yes	20	1.1	even	1	trivial
49.17.b.a.48.7		20	7.2	even	3
49.17.b.a.48.8		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)

\(f(q)\)	\(=\)	\(q+(94.8350 - 164.259i) q^{2} +(-9421.11 + 5439.28i) q^{3} +(14780.6 + 25600.8i) q^{4} +(-477118. - 275464. i) q^{5} +2.06334e6i q^{6} +(5.57858e6 - 1.45338e6i) q^{7} +1.80371e7 q^{8} +(3.76482e7 - 6.52085e7i) q^{9} +O(q^{10})\)	\(q+(94.8350 - 164.259i) q^{2} +(-9421.11 + 5439.28i) q^{3} +(14780.6 + 25600.8i) q^{4} +(-477118. - 275464. i) q^{5} +2.06334e6i q^{6} +(5.57858e6 - 1.45338e6i) q^{7} +1.80371e7 q^{8} +(3.76482e7 - 6.52085e7i) q^{9} +(-9.04950e7 + 5.22473e7i) q^{10} +(7.76109e7 + 1.34426e8i) q^{11} +(-2.78500e8 - 1.60792e8i) q^{12} -1.23204e9i q^{13} +(2.90314e8 - 1.05416e9i) q^{14} +5.99331e9 q^{15} +(7.41885e8 - 1.28498e9i) q^{16} +(-1.42412e9 + 8.22217e8i) q^{17} +(-7.14073e9 - 1.23681e10i) q^{18} +(1.62597e10 + 9.38754e9i) q^{19} -1.62861e10i q^{20} +(-4.46511e10 + 4.40360e10i) q^{21} +2.94409e10 q^{22} +(3.57099e10 - 6.18513e10i) q^{23} +(-1.69930e11 + 9.81088e10i) q^{24} +(7.54670e10 + 1.30713e11i) q^{25} +(-2.02375e11 - 1.16841e11i) q^{26} +3.50829e11i q^{27} +(1.19663e11 + 1.21334e11i) q^{28} -1.65746e11 q^{29} +(5.68375e11 - 9.84455e11i) q^{30} +(7.81270e11 - 4.51066e11i) q^{31} +(4.50327e11 + 7.79988e11i) q^{32} +(-1.46236e12 - 8.44294e11i) q^{33} +3.11900e11i q^{34} +(-3.06200e12 - 8.43265e11i) q^{35} +2.22586e12 q^{36} +(1.77083e12 - 3.06716e12i) q^{37} +(3.08398e12 - 1.78054e12i) q^{38} +(6.70144e12 + 1.16072e13i) q^{39} +(-8.60582e12 - 4.96857e12i) q^{40} -7.99933e12i q^{41} +(2.99882e12 + 1.15105e13i) q^{42} -8.81832e11 q^{43} +(-2.29428e12 + 3.97380e12i) q^{44} +(-3.59252e13 + 2.07414e13i) q^{45} +(-6.77309e12 - 1.17313e13i) q^{46} +(-3.12713e12 - 1.80545e12i) q^{47} +1.61413e13i q^{48} +(2.90083e13 - 1.62156e13i) q^{49} +2.86277e13 q^{50} +(8.94454e12 - 1.54924e13i) q^{51} +(3.15414e13 - 1.82104e13i) q^{52} +(-1.65300e13 - 2.86307e13i) q^{53} +(5.76268e13 + 3.32709e13i) q^{54} -8.55160e13i q^{55} +(1.00622e14 - 2.62148e13i) q^{56} -2.04246e14 q^{57} +(-1.57185e13 + 2.72253e13i) q^{58} +(-1.25737e14 + 7.25944e13i) q^{59} +(8.85849e13 + 1.53434e14i) q^{60} +(3.49743e13 + 2.01924e13i) q^{61} -1.71108e14i q^{62} +(1.15250e14 - 4.18488e14i) q^{63} +2.68067e14 q^{64} +(-3.39384e14 + 5.87831e14i) q^{65} +(-2.77366e14 + 1.60137e14i) q^{66} +(-6.43741e12 - 1.11499e13i) q^{67} +(-4.20989e13 - 2.43058e13i) q^{68} +7.76944e14i q^{69} +(-4.28898e14 + 4.22990e14i) q^{70} +3.62792e13 q^{71} +(6.79064e14 - 1.17617e15i) q^{72} +(7.23323e14 - 4.17611e14i) q^{73} +(-3.35873e14 - 5.81749e14i) q^{74} +(-1.42197e15 - 8.20972e14i) q^{75} +5.55016e14i q^{76} +(6.28331e14 + 6.37108e14i) q^{77} +2.54212e15 q^{78} +(4.69406e14 - 8.13035e14i) q^{79} +(-7.07933e14 + 4.08725e14i) q^{80} +(-2.87628e14 - 4.98186e14i) q^{81} +(-1.31396e15 - 7.58617e14i) q^{82} +7.02863e14i q^{83} +(-1.78733e15 - 4.92225e14i) q^{84} +9.05965e14 q^{85} +(-8.36286e13 + 1.44849e14i) q^{86} +(1.56151e15 - 9.01538e14i) q^{87} +(1.39988e15 + 2.42466e15i) q^{88} +(7.22314e14 + 4.17028e14i) q^{89} +7.86806e15i q^{90} +(-1.79063e15 - 6.87307e15i) q^{91} +2.11126e15 q^{92} +(-4.90695e15 + 8.49909e15i) q^{93} +(-5.93122e14 + 3.42439e14i) q^{94} +(-5.17186e15 - 8.95793e15i) q^{95} +(-8.48515e15 - 4.89890e15i) q^{96} +1.18389e16i q^{97} +(8.74349e13 - 6.30268e15i) q^{98} +1.16876e16 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

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Groups

Database

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