LMFDB - Embedded newform 650.2.ba.b.73.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(73,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([11, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("650.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.ba (of order $20$, degree $8$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			73.7
Character	$\chi$	$=$	650.73
Dual form			650.2.ba.b.187.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-1.17085 + 0.596579i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.522021 + 2.17428i) q^{5} +(-0.596579 + 1.17085i) q^{6} -4.83730i q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.748366 + 1.03004i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(-1.17085 + 0.596579i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.522021 + 2.17428i) q^{5} +(-0.596579 + 1.17085i) q^{6} -4.83730i q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.748366 + 1.03004i) q^{9} +(0.855686 + 2.06587i) q^{10} +(0.456552 - 2.88256i) q^{11} +(0.205567 + 1.29790i) q^{12} +(3.48480 - 0.925289i) q^{13} +(-2.84329 - 3.91346i) q^{14} +(-0.685921 - 2.85719i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.29869 + 2.54882i) q^{17} +1.27320i q^{18} +(-2.26663 - 1.15491i) q^{19} +(1.90655 + 1.16836i) q^{20} +(2.88583 + 5.66377i) q^{21} +(-1.32497 - 2.60039i) q^{22} +(1.03048 - 6.50623i) q^{23} +(0.929194 + 0.929194i) q^{24} +(-4.45499 - 2.27004i) q^{25} +(2.27539 - 2.79689i) q^{26} +(0.878429 - 5.54618i) q^{27} +(-4.60054 - 1.49481i) q^{28} +(0.720727 + 0.234178i) q^{29} +(-2.23434 - 1.90834i) q^{30} +(4.94712 - 9.70927i) q^{31} -1.00000 q^{32} +(1.18512 + 3.64742i) q^{33} +(0.447498 + 2.82539i) q^{34} +(10.5176 + 2.52517i) q^{35} +(0.748366 + 1.03004i) q^{36} +(6.49376 - 8.93789i) q^{37} +(-2.51258 + 0.397954i) q^{38} +(-3.52818 + 3.16234i) q^{39} +(2.22918 - 0.175418i) q^{40} +(0.144600 + 0.912967i) q^{41} +(5.66377 + 2.88583i) q^{42} +(-6.45832 + 6.45832i) q^{43} +(-2.60039 - 1.32497i) q^{44} +(-1.84893 - 2.16486i) q^{45} +(-2.99058 - 5.86935i) q^{46} +(3.64698 + 1.18498i) q^{47} +(1.29790 + 0.205567i) q^{48} -16.3995 q^{49} +(-4.93846 + 0.782075i) q^{50} -3.75906i q^{51} +(0.196861 - 3.60017i) q^{52} +(3.39591 - 1.73030i) q^{53} +(-2.54930 - 5.00328i) q^{54} +(6.02916 + 2.49743i) q^{55} +(-4.60054 + 1.49481i) q^{56} +3.34289 q^{57} +(0.720727 - 0.234178i) q^{58} +(1.80757 + 11.4126i) q^{59} +(-2.92931 - 0.230571i) q^{60} +(1.03419 - 0.751384i) q^{61} +(-1.70466 - 10.7628i) q^{62} +(4.98260 + 3.62007i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.192697 + 8.05995i) q^{65} +(3.10268 + 2.25423i) q^{66} +(2.70947 + 8.33890i) q^{67} +(2.02275 + 2.02275i) q^{68} +(2.67493 + 8.23260i) q^{69} +(9.99321 - 4.13921i) q^{70} +(-14.0423 + 7.15492i) q^{71} +(1.21088 + 0.393439i) q^{72} +(3.93517 - 2.85907i) q^{73} -11.0478i q^{74} +(6.57040 + 0.000129410i) q^{75} +(-1.79881 + 1.79881i) q^{76} +(-13.9438 - 2.20848i) q^{77} +(-0.995584 + 4.63220i) q^{78} +(-13.3091 - 4.32437i) q^{79} +(1.70033 - 1.45219i) q^{80} +(1.09991 + 3.38518i) q^{81} +(0.653612 + 0.653612i) q^{82} +(5.00777 - 1.62712i) q^{83} +(6.27833 - 0.994390i) q^{84} +(-4.86391 - 4.15425i) q^{85} +(-1.42878 + 9.02099i) q^{86} +(-0.983571 + 0.155782i) q^{87} +(-2.88256 + 0.456552i) q^{88} +(-3.87349 - 0.613500i) q^{89} +(-2.76828 - 0.664635i) q^{90} +(-4.47590 - 16.8570i) q^{91} +(-5.86935 - 2.99058i) q^{92} +14.3195i q^{93} +(3.64698 - 1.18498i) q^{94} +(3.69432 - 4.32541i) q^{95} +(1.17085 - 0.596579i) q^{96} +(-0.738455 + 2.27273i) q^{97} +(-13.2674 + 9.63936i) q^{98} +(2.62747 + 2.62747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 36 q^{2} - 36 q^{4} + 36 q^{8} - 20 q^{9}+O(q^{10}) $ 144 * q + 36 * q^2 - 36 * q^4 + 36 * q^8 - 20 * q^9	$ 144 q + 36 q^{2} - 36 q^{4} + 36 q^{8} - 20 q^{9} + 6 q^{13} + 8 q^{15} - 36 q^{16} - 6 q^{17} - 20 q^{19} - 6 q^{21} + 12 q^{23} + 2 q^{25} + 14 q^{26} - 24 q^{27} + 20 q^{29} + 12 q^{30} - 6 q^{31} - 144 q^{32} - 54 q^{33} + 6 q^{34} + 40 q^{35} + 20 q^{36} - 60 q^{37} + 20 q^{39} + 52 q^{41} + 6 q^{42} - 12 q^{43} - 6 q^{45} + 28 q^{46} + 50 q^{47} - 160 q^{49} - 22 q^{50} + 6 q^{52} + 20 q^{53} - 6 q^{54} - 32 q^{55} - 28 q^{57} + 20 q^{58} - 16 q^{59} - 12 q^{60} + 12 q^{61} + 6 q^{62} - 70 q^{63} - 36 q^{64} + 44 q^{65} - 16 q^{66} - 8 q^{67} - 6 q^{68} + 26 q^{69} + 10 q^{70} + 72 q^{71} - 52 q^{73} + 32 q^{75} - 56 q^{77} - 50 q^{78} - 20 q^{79} + 124 q^{81} - 22 q^{82} + 70 q^{83} - 6 q^{84} - 18 q^{85} - 8 q^{86} + 8 q^{87} + 28 q^{89} - 14 q^{90} - 26 q^{91} + 12 q^{92} + 50 q^{94} - 46 q^{95} + 28 q^{97} - 20 q^{98} + 40 q^{99}+O(q^{100}) $ 144 * q + 36 * q^2 - 36 * q^4 + 36 * q^8 - 20 * q^9 + 6 * q^13 + 8 * q^15 - 36 * q^16 - 6 * q^17 - 20 * q^19 - 6 * q^21 + 12 * q^23 + 2 * q^25 + 14 * q^26 - 24 * q^27 + 20 * q^29 + 12 * q^30 - 6 * q^31 - 144 * q^32 - 54 * q^33 + 6 * q^34 + 40 * q^35 + 20 * q^36 - 60 * q^37 + 20 * q^39 + 52 * q^41 + 6 * q^42 - 12 * q^43 - 6 * q^45 + 28 * q^46 + 50 * q^47 - 160 * q^49 - 22 * q^50 + 6 * q^52 + 20 * q^53 - 6 * q^54 - 32 * q^55 - 28 * q^57 + 20 * q^58 - 16 * q^59 - 12 * q^60 + 12 * q^61 + 6 * q^62 - 70 * q^63 - 36 * q^64 + 44 * q^65 - 16 * q^66 - 8 * q^67 - 6 * q^68 + 26 * q^69 + 10 * q^70 + 72 * q^71 - 52 * q^73 + 32 * q^75 - 56 * q^77 - 50 * q^78 - 20 * q^79 + 124 * q^81 - 22 * q^82 + 70 * q^83 - 6 * q^84 - 18 * q^85 - 8 * q^86 + 8 * q^87 + 28 * q^89 - 14 * q^90 - 26 * q^91 + 12 * q^92 + 50 * q^94 - 46 * q^95 + 28 * q^97 - 20 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	−1.17085	+	0.596579i	−0.675992	+	0.344435i	−0.758054	−	0.652192i	$-0.773850\pi$
$3$	−1.17085	+	0.596579i	−0.675992	+	0.344435i	0.0820615	+	0.996627i	$0.473850\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.522021	+	2.17428i	−0.233455	+	0.972368i
$5$	−0.522021	+	2.17428i	−0.233455	+	0.972368i
$6$	−0.596579	+	1.17085i	−0.243553	+	0.477999i
$7$		−	4.83730i		−	1.82833i	−0.405346	−	0.914163i	$-0.632849\pi$
$7$		−	4.83730i		−	1.82833i	0.405346	−	0.914163i	$-0.367151\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.748366	+	1.03004i	−0.249455	+	0.343346i
$10$	0.855686	+	2.06587i	0.270592	+	0.653284i
$11$	0.456552	−	2.88256i	0.137656	−	0.869124i	−0.818124	−	0.575041i	$-0.804986\pi$
$11$	0.456552	−	2.88256i	0.137656	−	0.869124i	0.955780	−	0.294082i	$-0.0950140\pi$
$12$	0.205567	+	1.29790i	0.0593422	+	0.374672i
$13$	3.48480	−	0.925289i	0.966510	−	0.256629i
$13$	3.48480	−	0.925289i	0.966510	−	0.256629i
$14$	−2.84329	−	3.91346i	−0.759902	−	1.04592i
$15$	−0.685921	−	2.85719i	−0.177104	−	0.737723i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.29869	+	2.54882i	−0.314978	+	0.618180i	−0.993166	−	0.116709i	$-0.962766\pi$
$17$	−1.29869	+	2.54882i	−0.314978	+	0.618180i	0.678188	+	0.734889i	$0.262766\pi$
$18$			1.27320i			0.300095i
$19$	−2.26663	−	1.15491i	−0.520001	−	0.264954i	0.174231	−	0.984705i	$-0.444256\pi$
$19$	−2.26663	−	1.15491i	−0.520001	−	0.264954i	−0.694232	+	0.719751i	$0.744256\pi$
$20$	1.90655	+	1.16836i	0.426318	+	0.261253i
$21$	2.88583	+	5.66377i	0.629740	+	1.23594i
$22$	−1.32497	−	2.60039i	−0.282484	−	0.554406i
$23$	1.03048	−	6.50623i	0.214871	−	1.35664i	−0.610484	−	0.792028i	$-0.709025\pi$
$23$	1.03048	−	6.50623i	0.214871	−	1.35664i	0.825355	−	0.564614i	$-0.190975\pi$
$24$	0.929194	+	0.929194i	0.189671	+	0.189671i
$25$	−4.45499	−	2.27004i	−0.890998	−	0.454008i
$26$	2.27539	−	2.79689i	0.446241	−	0.548515i
$27$	0.878429	−	5.54618i	0.169054	−	1.06736i
$28$	−4.60054	−	1.49481i	−0.869421	−	0.282492i
$29$	0.720727	+	0.234178i	0.133836	+	0.0434858i	0.375169	−	0.926956i	$-0.377585\pi$
$29$	0.720727	+	0.234178i	0.133836	+	0.0434858i	−0.241333	+	0.970442i	$0.577585\pi$
$30$	−2.23434	−	1.90834i	−0.407932	−	0.348414i
$31$	4.94712	−	9.70927i	0.888529	−	1.74384i	0.260823	−	0.965387i	$-0.416006\pi$
$31$	4.94712	−	9.70927i	0.888529	−	1.74384i	0.627707	−	0.778450i	$-0.283994\pi$
$32$	−1.00000			−0.176777
$33$	1.18512	+	3.64742i	0.206303	+	0.634935i
$34$	0.447498	+	2.82539i	0.0767452	+	0.484550i
$35$	10.5176	+	2.52517i	1.77781	+	0.426832i
$36$	0.748366	+	1.03004i	0.124728	+	0.171673i
$37$	6.49376	−	8.93789i	1.06757	−	1.46938i	0.195053	−	0.980793i	$-0.437512\pi$
$37$	6.49376	−	8.93789i	1.06757	−	1.46938i	0.872515	−	0.488588i	$-0.162488\pi$
$38$	−2.51258	+	0.397954i	−0.407595	+	0.0645566i
$39$	−3.52818	+	3.16234i	−0.564961	+	0.506379i
$40$	2.22918	−	0.175418i	0.352464	−	0.0277360i
$41$	0.144600	+	0.912967i	0.0225827	+	0.142582i	0.996403	−	0.0847357i	$-0.0270046\pi$
$41$	0.144600	+	0.912967i	0.0225827	+	0.142582i	−0.973821	+	0.227317i	$0.927005\pi$
$42$	5.66377	+	2.88583i	0.873938	+	0.445294i
$43$	−6.45832	+	6.45832i	−0.984884	+	0.984884i	−0.999887	−	0.0150033i	$-0.995224\pi$
$43$	−6.45832	+	6.45832i	−0.984884	+	0.984884i	0.0150033	+	0.999887i	$0.495224\pi$
$44$	−2.60039	−	1.32497i	−0.392024	−	0.199746i
$45$	−1.84893	−	2.16486i	−0.275622	−	0.322718i
$46$	−2.99058	−	5.86935i	−0.440938	−	0.865389i
$47$	3.64698	+	1.18498i	0.531967	+	0.172847i	0.562669	−	0.826682i	$-0.309774\pi$
$47$	3.64698	+	1.18498i	0.531967	+	0.172847i	−0.0307023	+	0.999529i	$0.509774\pi$
$48$	1.29790	+	0.205567i	0.187336	+	0.0296711i
$49$	−16.3995			−2.34278
$50$	−4.93846	+	0.782075i	−0.698403	+	0.110602i
$51$		−	3.75906i		−	0.526374i
$52$	0.196861	−	3.60017i	0.0272997	−	0.499254i
$53$	3.39591	−	1.73030i	0.466464	−	0.237675i	−0.204929	−	0.978777i	$-0.565696\pi$
$53$	3.39591	−	1.73030i	0.466464	−	0.237675i	0.671393	+	0.741102i	$0.265696\pi$
$54$	−2.54930	−	5.00328i	−0.346916	−	0.680861i
$55$	6.02916	+	2.49743i	0.812971	+	0.336753i
$56$	−4.60054	+	1.49481i	−0.614774	+	0.199752i
$57$	3.34289			0.442776
$58$	0.720727	−	0.234178i	0.0946360	−	0.0307491i
$59$	1.80757	+	11.4126i	0.235326	+	1.48579i	0.768536	+	0.639806i	$0.220985\pi$
$59$	1.80757	+	11.4126i	0.235326	+	1.48579i	−0.533210	+	0.845983i	$0.679015\pi$
$60$	−2.92931	−	0.230571i	−0.378172	−	0.0297666i
$61$	1.03419	−	0.751384i	0.132415	−	0.0962049i	−0.519606	−	0.854406i	$-0.673921\pi$
$61$	1.03419	−	0.751384i	0.132415	−	0.0962049i	0.652021	+	0.758201i	$0.273921\pi$
$62$	−1.70466	−	10.7628i	−0.216492	−	1.36688i
$63$	4.98260	+	3.62007i	0.627748	+	0.456086i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.192697	+	8.05995i	0.0239011	+	0.999714i
$66$	3.10268	+	2.25423i	0.381914	+	0.277477i
$67$	2.70947	+	8.33890i	0.331015	+	1.01876i	0.968652	+	0.248422i	$0.0799120\pi$
$67$	2.70947	+	8.33890i	0.331015	+	1.01876i	−0.637637	+	0.770337i	$0.720088\pi$
$68$	2.02275	+	2.02275i	0.245295	+	0.245295i
$69$	2.67493	+	8.23260i	0.322024	+	0.991089i
$70$	9.99321	−	4.13921i	1.19442	−	0.494730i
$71$	−14.0423	+	7.15492i	−1.66652	+	0.849133i	−0.672478	+	0.740117i	$0.734770\pi$
$71$	−14.0423	+	7.15492i	−1.66652	+	0.849133i	−0.994040	+	0.109016i	$0.965230\pi$
$72$	1.21088	+	0.393439i	0.142704	+	0.0463672i
$73$	3.93517	−	2.85907i	0.460577	−	0.334629i	−0.333181	−	0.942863i	$-0.608122\pi$
$73$	3.93517	−	2.85907i	0.460577	−	0.334629i	0.793757	+	0.608234i	$0.208122\pi$
$74$		−	11.0478i		−	1.28429i
$75$	6.57040		0.000129410i	0.758684		1.49430e-5i
$76$	−1.79881	+	1.79881i	−0.206338	+	0.206338i
$77$	−13.9438	−	2.20848i	−1.58904	−	0.251680i
$78$	−0.995584	+	4.63220i	−0.112728	+	0.524493i
$79$	−13.3091	−	4.32437i	−1.49739	−	0.486530i	−0.558132	−	0.829752i	$-0.688482\pi$
$79$	−13.3091	−	4.32437i	−1.49739	−	0.486530i	−0.939254	+	0.343222i	$0.888482\pi$
$80$	1.70033	−	1.45219i	0.190103	−	0.162360i
$81$	1.09991	+	3.38518i	0.122212	+	0.376131i
$82$	0.653612	+	0.653612i	0.0721794	+	0.0721794i
$83$	5.00777	−	1.62712i	0.549674	−	0.178600i	−0.0209957	−	0.999780i	$-0.506684\pi$
$83$	5.00777	−	1.62712i	0.549674	−	0.178600i	0.570670	+	0.821180i	$0.306684\pi$
$84$	6.27833	−	0.994390i	0.685022	−	0.108497i
$85$	−4.86391	−	4.15425i	−0.527565	−	0.450592i
$86$	−1.42878	+	9.02099i	−0.154070	+	0.972759i
$87$	−0.983571	+	0.155782i	−0.105450	+	0.0167016i
$88$	−2.88256	+	0.456552i	−0.307282	+	0.0486686i
$89$	−3.87349	−	0.613500i	−0.410589	−	0.0650309i	−0.0522764	−	0.998633i	$-0.516648\pi$
$89$	−3.87349	−	0.613500i	−0.410589	−	0.0650309i	−0.358312	+	0.933602i	$0.616648\pi$
$90$	−2.76828	−	0.664635i	−0.291803	−	0.0700587i
$91$	−4.47590	−	16.8570i	−0.469202	−	1.76710i
$92$	−5.86935	−	2.99058i	−0.611922	−	0.311790i
$93$			14.3195i			1.48486i
$94$	3.64698	−	1.18498i	0.376158	−	0.122221i
$95$	3.69432	−	4.32541i	0.379029	−	0.443778i
$96$	1.17085	−	0.596579i	0.119500	−	0.0608881i
$97$	−0.738455	+	2.27273i	−0.0749787	+	0.230761i	−0.981521	−	0.191354i	$-0.938712\pi$
$97$	−0.738455	+	2.27273i	−0.0749787	+	0.230761i	0.906542	+	0.422115i	$0.138712\pi$
$98$	−13.2674	+	9.63936i	−1.34021	+	0.973722i
$99$	2.62747	+	2.62747i	0.264071	+	0.264071i
$100$	−3.53560	+	3.53546i	−0.353560	+	0.353546i
$101$			0.839441i			0.0835275i	0.999128	+	0.0417638i	$0.0132977\pi$
$101$			0.839441i			0.0835275i	−0.999128	+	0.0417638i	$0.986702\pi$
$102$	−2.20952	−	3.04115i	−0.218775	−	0.301118i
$103$	4.18564	+	8.21478i	0.412424	+	0.809427i	1.00000		0.000258054i	$8.21411e-5\pi$
$103$	4.18564	+	8.21478i	0.412424	+	0.809427i	−0.587576	+	0.809169i	$0.699918\pi$
$104$	−1.95686	−	3.02831i	−0.191886	−	0.296951i
$105$	−13.8211	+	3.31800i	−1.34880	+	0.323804i
$106$	1.73030	−	3.39591i	0.168062	−	0.329840i
$107$	−2.60029	+	2.60029i	−0.251379	+	0.251379i	−0.821536	−	0.570157i	$-0.806883\pi$
$107$	−2.60029	+	2.60029i	−0.251379	+	0.251379i	0.570157	+	0.821536i	$0.306883\pi$
$108$	−5.00328	−	2.54930i	−0.481441	−	0.245307i
$109$	9.89233	−	1.56679i	0.947513	−	0.150071i	0.336493	−	0.941686i	$-0.390759\pi$
$109$	9.89233	−	1.56679i	0.947513	−	0.150071i	0.611020	+	0.791615i	$0.290759\pi$
$110$	6.34564	−	1.52339i	0.605033	−	0.145249i
$111$	−2.27108	+	14.3390i	−0.215561	+	1.36100i
$112$	−2.84329	+	3.91346i	−0.268666	+	0.369787i
$113$	2.67826	+	16.9099i	0.251949	+	1.59075i	0.711560	+	0.702625i	$0.247989\pi$
$113$	2.67826	+	16.9099i	0.251949	+	1.59075i	−0.459611	+	0.888121i	$0.652011\pi$
$114$	2.70445	−	1.96490i	0.253295	−	0.184030i
$115$	13.6084	+	5.63695i	1.26899	+	0.525648i
$116$	0.445434	−	0.613087i	0.0413575	−	0.0569237i
$117$	−1.65482	+	4.28193i	−0.152989	+	0.395864i
$118$	8.17049	+	8.17049i	0.752155	+	0.752155i
$119$	12.3294	+	6.28214i	1.13023	+	0.575883i
$120$	−2.50539	+	1.53527i	−0.228710	+	0.140150i
$121$	2.36092	+	0.767111i	0.214629	+	0.0697373i
$122$	0.395026	−	1.21576i	0.0357640	−	0.110070i
$123$	−0.713963	−	0.982685i	−0.0643758	−	0.0886057i
$124$	−7.70532	−	7.70532i	−0.691958	−	0.691958i
$125$	7.26130	−	8.50138i	0.649471	−	0.760387i
$126$	6.15883			0.548672
$127$	6.91308	+	1.09492i	0.613437	+	0.0971589i	0.455419	−	0.890277i	$-0.349490\pi$
$127$	6.91308	+	1.09492i	0.613437	+	0.0971589i	0.158018	+	0.987436i	$0.449490\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	3.70884	−	11.4146i	0.326545	−	1.00500i
$130$	4.89342	+	6.40738i	0.429181	+	0.561964i
$131$	−1.47136	−	4.52838i	−0.128553	−	0.395646i	0.865978	−	0.500081i	$-0.166697\pi$
$131$	−1.47136	−	4.52838i	−0.128553	−	0.395646i	−0.994532	+	0.104435i	$0.966697\pi$
$132$	3.83513			0.333805
$133$	−5.58663	+	10.9644i	−0.484422	+	0.950732i
$134$	7.09350	+	5.15373i	0.612785	+	0.445214i
$135$	11.6004	+	4.80518i	0.998403	+	0.413564i
$136$	2.82539	+	0.447498i	0.242275	+	0.0383726i
$137$	−0.620942	+	0.854653i	−0.0530506	+	0.0730179i	−0.834718	−	0.550677i	$-0.814369\pi$
$137$	−0.620942	+	0.854653i	−0.0530506	+	0.0730179i	0.781667	+	0.623695i	$0.214369\pi$
$138$	7.00307	+	5.08803i	0.596141	+	0.433122i
$139$	−1.46783	−	2.02029i	−0.124500	−	0.171359i	0.742217	−	0.670159i	$-0.233774\pi$
$139$	−1.46783	−	2.02029i	−0.124500	−	0.171359i	−0.866717	+	0.498800i	$0.833774\pi$
$140$	5.65171	−	9.22255i	0.477657	−	0.779448i
$141$	−4.97702	+	0.788282i	−0.419140	+	0.0663853i
$142$	−7.15492	+	14.0423i	−0.600428	+	1.17841i
$143$	−1.07620	−	10.4676i	−0.0899967	−	0.875343i
$144$	1.21088	−	0.393439i	0.100907	−	0.0327866i
$145$	−0.885404	+	1.44482i	−0.0735288	+	0.119985i
$146$	1.50310	−	4.62607i	0.124398	−	0.382856i
$147$	19.2014	−	9.78358i	1.58370	−	0.806936i
$148$	−6.49376	−	8.93789i	−0.533784	−	0.734690i
$149$	2.71435	−	2.71435i	0.222368	−	0.222368i	−0.587127	−	0.809495i	$-0.699741\pi$
$149$	2.71435	−	2.71435i	0.222368	−	0.222368i	0.809495	+	0.587127i	$0.199741\pi$
$150$	5.31564	−	3.86188i	0.434020	−	0.315321i
$151$	−11.0347	+	11.0347i	−0.897988	+	0.897988i	−0.995258	−	0.0972698i	$-0.968989\pi$
$151$	−11.0347	+	11.0347i	−0.897988	+	0.897988i	0.0972698	+	0.995258i	$0.468989\pi$
$152$	−0.397954	+	2.51258i	−0.0322783	+	0.203797i
$153$	−1.65348	−	3.24515i	−0.133676	−	0.262355i
$154$	−12.5789	+	6.40926i	−1.01363	+	0.516473i
$155$	18.5282	+	15.8249i	1.48822	+	1.27108i
$156$	1.91729	+	4.33272i	0.153506	+	0.346895i
$157$	13.5553	−	13.5553i	1.08183	−	1.08183i	0.0854892	−	0.996339i	$-0.472755\pi$
$157$	13.5553	−	13.5553i	1.08183	−	1.08183i	0.996339	−	0.0854892i	$-0.0272453\pi$
$158$	−13.3091	+	4.32437i	−1.05881	+	0.344029i
$159$	−2.94385	+	4.05186i	−0.233462	+	0.321333i
$160$	0.522021	−	2.17428i	0.0412694	−	0.171892i
$161$	−31.4726	−	4.98476i	−2.48038	−	0.392854i
$162$	2.87960	+	2.09215i	0.226243	+	0.164375i
$163$	−14.7043	−	10.6833i	−1.15173	−	0.836782i	−0.163021	−	0.986623i	$-0.552124\pi$
$163$	−14.7043	−	10.6833i	−1.15173	−	0.836782i	−0.988710	+	0.149841i	$0.952124\pi$
$164$	0.912967	+	0.144600i	0.0712908	+	0.0112913i
$165$	−8.54917	+	0.672750i	−0.665552	+	0.0523735i
$166$	3.09497	−	4.25986i	0.240216	−	0.330630i
$167$	13.4701	−	4.37671i	1.04235	−	0.338680i	0.262687	−	0.964881i	$-0.415391\pi$
$167$	13.4701	−	4.37671i	1.04235	−	0.338680i	0.779661	+	0.626201i	$0.215391\pi$
$168$	4.49479	−	4.49479i	0.346781	−	0.346781i
$169$	11.2877	−	6.44890i	0.868283	−	0.496069i
$170$	−6.37679	−	0.501927i	−0.489077	−	0.0384961i
$171$	2.88587	−	1.47042i	0.220688	−	0.112446i
$172$	4.14649	+	8.13795i	0.316167	+	0.620513i
$173$	−1.23757	+	7.81372i	−0.0940909	+	0.594066i	0.894920	+	0.446226i	$0.147232\pi$
$173$	−1.23757	+	7.81372i	−0.0940909	+	0.594066i	−0.989011	+	0.147840i	$0.952768\pi$
$174$	−0.704159	+	0.704159i	−0.0533822	+	0.0533822i
$175$	−10.9809	+	21.5501i	−0.830075	+	1.62903i
$176$	−2.06368	+	2.06368i	−0.155556	+	0.155556i
$177$	−8.92490	−	12.2841i	−0.670837	−	0.923328i
$178$	−3.49432	+	1.78045i	−0.261911	+	0.133450i
$179$	4.91130	−	15.1154i	0.367088	−	1.12978i	−0.581575	−	0.813493i	$-0.697563\pi$
$179$	4.91130	−	15.1154i	0.367088	−	1.12978i	0.948663	−	0.316288i	$-0.102437\pi$
$180$	−2.63025	+	1.08946i	−0.196047	+	0.0812032i
$181$	−15.6361	+	5.08049i	−1.16223	+	0.377630i	−0.825736	−	0.564057i	$-0.809240\pi$
$181$	−15.6361	+	5.08049i	−1.16223	+	0.377630i	−0.336490	+	0.941687i	$0.609240\pi$
$182$	−13.5294	−	11.0068i	−1.00286	−	0.815875i
$183$	−0.762626	+	1.49674i	−0.0563749	+	0.110642i
$184$	−6.50623	+	1.03048i	−0.479645	+	0.0759684i
$185$	16.0436	+	18.7850i	1.17955	+	1.38110i
$186$	8.41678	+	11.5847i	0.617148	+	0.849432i
$187$	6.75420	+	4.90721i	0.493916	+	0.358851i
$188$	2.25396	−	3.10231i	0.164387	−	0.226259i
$189$	−26.8285	−	4.24922i	−1.95149	−	0.309086i
$190$	0.446358	−	5.67080i	0.0323822	−	0.411403i
$191$	−0.468620	−	0.340473i	−0.0339082	−	0.0246357i	0.570702	−	0.821157i	$-0.306671\pi$
$191$	−0.468620	−	0.340473i	−0.0339082	−	0.0246357i	−0.604610	+	0.796521i	$0.706671\pi$
$192$	0.596579	−	1.17085i	0.0430544	−	0.0844990i
$193$	−5.27431			−0.379653			−0.189826	−	0.981818i	$-0.560793\pi$
$193$	−5.27431			−0.379653			−0.189826	+	0.981818i	$0.560793\pi$
$194$	0.738455	+	2.27273i	0.0530180	+	0.163173i
$195$	−5.03402	−	9.32206i	−0.360494	−	0.667567i
$196$	−5.06771	+	15.5968i	−0.361979	+	1.11406i
$197$	6.19196	−	19.0569i	0.441159	−	1.35775i	−0.445484	−	0.895290i	$-0.646968\pi$
$197$	6.19196	−	19.0569i	0.441159	−	1.35775i	0.886642	−	0.462456i	$-0.153032\pi$
$198$	3.67006	+	0.581280i	0.260820	+	0.0413098i
$199$	21.1927			1.50231			0.751155	−	0.660126i	$-0.229497\pi$
$199$	21.1927			1.50231			0.751155	+	0.660126i	$0.229497\pi$
$200$	−0.782270	+	4.93843i	−0.0553148	+	0.349199i
$201$	−8.14722	−	8.14722i	−0.574660	−	0.574660i
$202$	0.493411	+	0.679122i	0.0347163	+	0.0477829i
$203$	1.13279	−	3.48637i	0.0795063	−	0.244695i
$204$	−3.57508	−	1.16161i	−0.250306	−	0.0813293i
$205$	−2.06053	−	0.162188i	−0.143914	−	0.0113277i
$206$	8.21478	+	4.18564i	0.572351	+	0.291627i
$207$	5.93047	+	5.93047i	0.412196	+	0.412196i
$208$	−3.36313	−	1.29974i	−0.233191	−	0.0901208i
$209$	−4.36392	+	6.00642i	−0.301859	+	0.415473i
$210$	−9.23121	+	10.8081i	−0.637014	+	0.745833i
$211$	−3.80215	+	2.76243i	−0.261751	+	0.190173i	−0.710919	−	0.703274i	$-0.751721\pi$
$211$	−3.80215	+	2.76243i	−0.261751	+	0.190173i	0.449168	+	0.893447i	$0.351721\pi$
$212$	−0.596221	−	3.76439i	−0.0409487	−	0.258540i
$213$	12.1730	−	16.7547i	0.834082	−	1.14802i
$214$	−0.575266	+	3.63209i	−0.0393244	+	0.248285i
$215$	−10.6708	−	17.4136i	−0.727743	−	1.18760i
$216$	−5.54618	+	0.878429i	−0.377370	+	0.0597695i
$217$	−46.9666	−	23.9307i	−3.18830	−	1.62452i
$218$	7.08212	−	7.08212i	0.479662	−	0.479662i
$219$	−2.90184	+	5.69519i	−0.196088	+	0.384845i
$220$	4.23831	−	4.96232i	0.285747	−	0.334560i
$221$	−2.16728	+	10.0838i	−0.145787	+	0.678309i
$222$	6.59092	+	12.9354i	0.442353	+	0.868168i
$223$	2.11004	+	2.90422i	0.141299	+	0.194481i	0.873801	−	0.486283i	$-0.161648\pi$
$223$	2.11004	+	2.90422i	0.141299	+	0.194481i	−0.732502	+	0.680764i	$0.761648\pi$
$224$			4.83730i			0.323206i
$225$	5.67219	−	2.88998i	0.378146	−	0.192665i
$226$	12.1061	+	12.1061i	0.805287	+	0.805287i
$227$	18.0905	−	13.1435i	1.20071	−	0.872364i	0.206353	−	0.978478i	$-0.433841\pi$
$227$	18.0905	−	13.1435i	1.20071	−	0.872364i	0.994354	+	0.106113i	$0.0338406\pi$
$228$	1.03301	−	3.17928i	0.0684127	−	0.210553i
$229$	−3.29323	+	1.67799i	−0.217623	+	0.110884i	−0.559404	−	0.828895i	$-0.688970\pi$
$229$	−3.29323	+	1.67799i	−0.217623	+	0.110884i	0.341781	+	0.939780i	$0.388970\pi$
$230$	14.3228	−	3.43844i	0.944415	−	0.226724i
$231$	17.6437	−	5.73277i	1.16087	−	0.377189i
$232$		−	0.757817i		−	0.0497531i
$233$	11.5693	+	5.89487i	0.757932	+	0.386186i	0.789846	−	0.613305i	$-0.210160\pi$
$233$	11.5693	+	5.89487i	0.757932	+	0.386186i	−0.0319139	+	0.999491i	$0.510160\pi$
$234$	1.17807	+	4.43683i	0.0770131	+	0.290045i
$235$	−4.48027	+	7.31098i	−0.292261	+	0.476916i
$236$	11.4126	+	1.80757i	0.742895	+	0.117663i
$237$	18.1628	−	2.87670i	1.17980	−	0.186862i
$238$	13.6672	−	2.16468i	0.885916	−	0.140315i
$239$	−2.61207	+	16.4920i	−0.168961	+	1.06678i	0.746799	+	0.665050i	$0.231590\pi$
$239$	−2.61207	+	16.4920i	−0.168961	+	1.06678i	−0.915760	+	0.401726i	$0.868410\pi$
$240$	−1.12449	+	2.71469i	−0.0725857	+	0.175232i
$241$	−13.0734	+	2.07062i	−0.842130	+	0.133380i	−0.562572	−	0.826748i	$-0.690188\pi$
$241$	−13.0734	+	2.07062i	−0.842130	+	0.133380i	−0.279558	+	0.960129i	$0.590188\pi$
$242$	2.36092	−	0.767111i	0.151766	−	0.0493117i
$243$	8.60453	+	8.60453i	0.551981	+	0.551981i
$244$	−0.395026	−	1.21576i	−0.0252889	−	0.0778314i
$245$	8.56086	−	35.6570i	0.546933	−	2.27804i
$246$	−1.15522	−	0.375352i	−0.0736539	−	0.0239316i
$247$	−8.96739	−	1.92733i	−0.570581	−	0.122633i
$248$	−10.7628	−	1.70466i	−0.683439	−	0.108246i
$249$	−4.89266	+	4.89266i	−0.310059	+	0.310059i
$250$	0.877529	−	11.1458i	0.0554998	−	0.704925i
$251$			4.08378i			0.257766i	0.991660	+	0.128883i	$0.0411391\pi$
$251$			4.08378i			0.257766i	−0.991660	+	0.128883i	$0.958861\pi$
$252$	4.98260	−	3.62007i	0.313874	−	0.228043i
$253$	−18.2841	−	5.94086i	−1.14951	−	0.373499i
$254$	6.23638	−	3.17760i	0.391305	−	0.199380i
$255$	8.17326	+	1.96231i	0.511829	+	0.122885i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	13.1231	+	13.1231i	0.818596	+	0.818596i	0.985905	−	0.167308i	$-0.0535075\pi$
$257$	13.1231	+	13.1231i	0.818596	+	0.818596i	−0.167308	+	0.985905i	$0.553508\pi$
$258$	−3.70884	−	11.4146i	−0.230902	−	0.710644i
$259$	−43.2353	−	31.4123i	−2.68651	−	1.95186i
$260$	7.72502	+	2.30740i	0.479085	+	0.143099i
$261$	−0.780579	+	0.567124i	−0.0483167	+	0.0351041i
$262$	−3.85207	−	2.79869i	−0.237982	−	0.172904i
$263$	−4.75700	−	30.0345i	−0.293329	−	1.85201i	−0.490241	−	0.871587i	$-0.663091\pi$
$263$	−4.75700	−	30.0345i	−0.293329	−	1.85201i	0.196912	−	0.980421i	$-0.436909\pi$
$264$	3.10268	−	2.25423i	0.190957	−	0.138738i
$265$	1.98943	+	8.28691i	0.122209	+	0.509061i
$266$	1.92502	+	12.1541i	0.118031	+	0.745216i
$267$	4.90128	−	1.59252i	0.299954	−	0.0974609i
$268$	8.76804			0.535593
$269$	8.85237	−	2.87631i	0.539739	−	0.175372i	−0.0264458	−	0.999650i	$-0.508419\pi$
$269$	8.85237	−	2.87631i	0.539739	−	0.175372i	0.566185	+	0.824279i	$0.308419\pi$
$270$	12.2093	−	2.93107i	0.743036	−	0.178379i
$271$	−2.53310	−	4.97150i	−0.153875	−	0.301997i	0.801181	−	0.598422i	$-0.204205\pi$
$271$	−2.53310	−	4.97150i	−0.153875	−	0.301997i	−0.955056	+	0.296425i	$0.904205\pi$
$272$	2.54882	−	1.29869i	0.154545	−	0.0787446i
$273$	15.2972	+	17.0669i	0.925827	+	1.03293i
$274$			1.05641i			0.0638200i
$275$	−8.57746	+	11.8054i	−0.517240	+	0.711890i
$276$	8.65627			0.521046
$277$	−4.11992	−	0.652531i	−0.247542	−	0.0392068i	0.0314303	−	0.999506i	$-0.489994\pi$
$277$	−4.11992	−	0.652531i	−0.247542	−	0.0392068i	−0.278972	+	0.960299i	$0.589994\pi$
$278$	−2.37500	−	0.771684i	−0.142443	−	0.0462825i
$279$	6.29865	+	12.3618i	0.377091	+	0.740082i
$280$	−0.848549	−	10.7832i	−0.0507105	−	0.644419i
$281$	13.2363	+	6.74422i	0.789610	+	0.402326i	0.801795	−	0.597599i	$-0.203879\pi$
$281$	13.2363	+	6.74422i	0.789610	+	0.402326i	−0.0121848	+	0.999926i	$0.503879\pi$
$282$	−3.56315	+	3.56315i	−0.212182	+	0.212182i
$283$	5.65640	+	2.88208i	0.336238	+	0.171322i	0.613955	−	0.789341i	$-0.289578\pi$
$283$	5.65640	+	2.88208i	0.336238	+	0.171322i	−0.277717	+	0.960663i	$0.589578\pi$
$284$	2.46542	+	15.5660i	0.146296	+	0.923675i
$285$	−1.74506	+	7.26837i	−0.103368	+	0.430541i
$286$	−7.02336	−	7.83588i	−0.415300	−	0.463345i
$287$	4.41629	−	0.699472i	0.260686	−	0.0412885i
$288$	0.748366	−	1.03004i	0.0440979	−	0.0606955i
$289$	5.18246	+	7.13304i	0.304851	+	0.419591i
$290$	0.132935	+	1.68931i	0.00780619	+	0.0991996i
$291$	−0.491242	−	3.10158i	−0.0287971	−	0.181818i
$292$	−1.50310	−	4.62607i	−0.0879623	−	0.270720i
$293$	9.08208			0.530581			0.265290	−	0.964169i	$-0.414532\pi$
$293$	9.08208			0.530581			0.265290	+	0.964169i	$0.414532\pi$
$294$	9.78358	−	19.2014i	0.570590	−	1.11985i
$295$	−25.7577	−	2.02743i	−1.49967	−	0.118042i
$296$	−10.5071	−	3.41397i	−0.610714	−	0.198433i
$297$	−15.5861	−	5.06425i	−0.904400	−	0.293857i
$298$	0.600500	−	3.79141i	0.0347860	−	0.219630i
$299$	−2.42910	−	23.6264i	−0.140479	−	1.36635i
$300$	2.03049	−	6.24878i	0.117230	−	0.360773i
$301$	31.2408	+	31.2408i	1.80069	+	1.80069i
$302$	−2.44122	+	15.4132i	−0.140476	+	0.886932i
$303$	−0.500793	−	0.982862i	−0.0287698	−	0.0564640i
$304$	1.15491	+	2.26663i	0.0662385	+	0.130000i
$305$	1.09385	+	2.64086i	0.0626336	+	0.151215i
$306$	−3.24515	−	1.65348i	−0.185513	−	0.0945234i
$307$			9.15188i			0.522325i	0.965295	+	0.261163i	$0.0841059\pi$
$307$			9.15188i			0.522325i	−0.965295	+	0.261163i	$0.915894\pi$
$308$	−6.40926	+	12.5789i	−0.365201	+	0.716748i
$309$	−9.80154	−	7.12124i	−0.557590	−	0.405113i
$310$	24.2912	+	1.91200i	1.37965	+	0.108594i
$311$	−3.44558	−	4.74244i	−0.195381	−	0.268919i	0.700075	−	0.714070i	$-0.253150\pi$
$311$	−3.44558	−	4.74244i	−0.195381	−	0.268919i	−0.895456	+	0.445151i	$0.853150\pi$
$312$	4.09783	+	2.37828i	0.231994	+	0.134644i
$313$	−0.853268	−	5.38732i	−0.0482296	−	0.304510i	0.951768	−	0.306819i	$-0.0992648\pi$
$313$	−0.853268	−	5.38732i	−0.0482296	−	0.304510i	−0.999997	+	0.00230984i	$0.999265\pi$
$314$	2.99886	−	18.9340i	0.169235	−	1.06851i
$315$	−10.4721	+	8.94381i	−0.590034	+	0.503926i
$316$	−8.22545	+	11.3214i	−0.462718	+	0.636876i
$317$	−1.90003	−	5.84769i	−0.106716	−	0.328439i	0.883413	−	0.468595i	$-0.155240\pi$
$317$	−1.90003	−	5.84769i	−0.106716	−	0.328439i	−0.990129	+	0.140156i	$0.955240\pi$
$318$			5.00837i			0.280856i
$319$	1.00408	−	1.97062i	0.0562178	−	0.110334i
$320$	−0.855686	−	2.06587i	−0.0478343	−	0.115485i
$321$	1.49328	−	4.59584i	0.0833466	−	0.256515i
$322$	−28.3918	+	14.4663i	−1.58221	+	0.806178i
$323$	5.88730	−	4.27737i	0.327578	−	0.237999i
$324$	3.55939			0.197744
$325$	−17.6252	−	3.78849i	−0.977670	−	0.210148i
$326$	−18.1755			−1.00665
$327$	−10.6477	+	7.73604i	−0.588822	+	0.427804i
$328$	0.823600	−	0.419645i	0.0454757	−	0.0231710i
$329$	5.73209	−	17.6415i	0.316020	−	0.972610i
$330$	−6.52099	+	5.56934i	−0.358969	+	0.306582i
$331$	10.5499	−	20.7054i	0.579878	−	1.13807i	−0.395692	−	0.918383i	$-0.629495\pi$
$331$	10.5499	−	20.7054i	0.579878	−	1.13807i	0.975570	−	0.219690i	$-0.0705047\pi$
$332$		−	5.26548i		−	0.288981i
$333$	4.34665	+	13.3776i	0.238195	+	0.733089i
$334$	8.32499	−	11.4584i	0.455523	−	0.626974i
$335$	−19.5455	+	1.53807i	−1.06789	+	0.0840338i
$336$	0.994390	−	6.27833i	0.0542484	−	0.342511i
$337$	3.85760	+	24.3559i	0.210137	+	1.32675i	0.836820	+	0.547478i	$0.184412\pi$
$337$	3.85760	+	24.3559i	0.210137	+	1.32675i	−0.626683	+	0.779274i	$0.715588\pi$
$338$	5.34136	−	11.8520i	0.290532	−	0.644664i
$339$	−13.2239	−	18.2012i	−0.718225	−	0.988552i
$340$	−5.45396	+	3.34211i	−0.295782	+	0.181252i
$341$	−25.7289	−	18.6932i	−1.39330	−	1.01229i
$342$	1.47042	−	2.88587i	0.0795114	−	0.156050i
$343$			45.4680i			2.45504i
$344$	8.13795	+	4.14649i	0.438769	+	0.223564i
$345$	−19.2964	+	1.51846i	−1.03888	+	0.0817514i
$346$	3.59157	+	7.04886i	0.193084	+	0.378949i
$347$	2.88006	+	5.65243i	0.154610	+	0.303439i	0.955299	−	0.295641i	$-0.0955333\pi$
$347$	2.88006	+	5.65243i	0.154610	+	0.303439i	−0.800689	+	0.599080i	$0.795533\pi$
$348$	−0.155782	+	0.983571i	−0.00835081	+	0.0527249i
$349$	16.3734	+	16.3734i	0.876448	+	0.876448i	0.993165	−	0.116717i	$-0.0372371\pi$
$349$	16.3734	+	16.3734i	0.876448	+	0.876448i	−0.116717	+	0.993165i	$0.537237\pi$
$350$	3.78313	+	23.8888i	0.202217	+	1.27691i
$351$	−2.07067	−	20.1402i	−0.110524	−	1.07500i
$352$	−0.456552	+	2.88256i	−0.0243343	+	0.153641i
$353$	−25.6787	−	8.34352i	−1.36674	−	0.444081i	−0.468452	−	0.883489i	$-0.655188\pi$
$353$	−25.6787	−	8.34352i	−1.36674	−	0.444081i	−0.898288	+	0.439408i	$0.855188\pi$
$354$	−14.4408	−	4.69210i	−0.767520	−	0.249382i
$355$	−8.22642	−	34.2670i	−0.436613	−	1.81870i
$356$	−1.78045	+	3.49432i	−0.0943635	+	0.185199i
$357$	−18.1837			−0.962384
$358$	−4.91130	−	15.1154i	−0.259570	−	0.798876i
$359$	1.55672	+	9.82876i	0.0821607	+	0.518742i	0.994104	+	0.108427i	$0.0345814\pi$
$359$	1.55672	+	9.82876i	0.0821607	+	0.518742i	−0.911944	+	0.410315i	$0.865419\pi$
$360$	−1.48755	+	2.42741i	−0.0784009	+	0.127936i
$361$	−7.36411	−	10.1358i	−0.387585	−	0.533464i
$362$	−9.66367	+	13.3009i	−0.507911	+	0.699080i
$363$	−3.22194	+	0.510305i	−0.169108	+	0.0267841i
$364$	−17.4151	−	0.952275i	−0.912800	−	0.0499128i
$365$	4.16217	+	10.0487i	0.217858	+	0.525971i
$366$	0.262783	+	1.65915i	0.0137359	+	0.0867250i
$367$	−10.2779	−	5.23683i	−0.536500	−	0.273360i	0.164677	−	0.986348i	$-0.447342\pi$
$367$	−10.2779	−	5.23683i	−0.536500	−	0.273360i	−0.701177	+	0.712987i	$0.747342\pi$
$368$	−4.65794	+	4.65794i	−0.242812	+	0.242812i
$369$	−1.04860	−	0.534290i	−0.0545881	−	0.0278140i
$370$	24.0211	+	5.76721i	1.24880	+	0.299823i
$371$	−8.36999	−	16.4270i	−0.434548	−	0.852849i
$372$	13.6186	+	4.42496i	0.706093	+	0.229424i
$373$	3.24236	+	0.513539i	0.167883	+	0.0265900i	0.239810	−	0.970820i	$-0.422915\pi$
$373$	3.24236	+	0.513539i	0.167883	+	0.0265900i	−0.0719270	+	0.997410i	$0.522915\pi$
$374$	8.34865			0.431698
$375$	−3.43017	+	14.2858i	−0.177133	+	0.737716i
$376$		−	3.83467i		−	0.197758i
$377$	2.72827	+	0.149185i	0.140513	+	0.00768339i
$378$	−24.2024	+	12.3317i	−1.24484	+	0.634276i
$379$	14.6545	+	28.7610i	0.752749	+	1.47735i	0.874621	+	0.484808i	$0.161111\pi$
$379$	14.6545	+	28.7610i	0.752749	+	1.47735i	−0.121871	+	0.992546i	$0.538889\pi$
$380$	−2.97210	−	4.85013i	−0.152466	−	0.248807i
$381$	−8.74741	+	2.84221i	−0.448144	+	0.145611i
$382$	−0.579246			−0.0296368
$383$	8.38456	−	2.72431i	0.428431	−	0.139206i	−0.0868609	−	0.996220i	$-0.527684\pi$
$383$	8.38456	−	2.72431i	0.428431	−	0.139206i	0.515292	+	0.857015i	$0.327684\pi$
$384$	−0.205567	−	1.29790i	−0.0104903	−	0.0662332i
$385$	12.0808	−	29.1648i	0.615695	−	1.48638i
$386$	−4.26700	+	3.10016i	−0.217185	+	0.157794i
$387$	−1.81912	−	11.4855i	−0.0924712	−	0.583840i
$388$	1.93330	+	1.40462i	0.0981484	+	0.0713090i
$389$	−5.48518	+	3.98521i	−0.278109	+	0.202058i	−0.718092	−	0.695948i	$-0.754984\pi$
$389$	−5.48518	+	3.98521i	−0.278109	+	0.202058i	0.439983	+	0.898006i	$0.354984\pi$
$390$	−9.55198	−	4.58278i	−0.483683	−	0.232058i
$391$	15.2449	+	11.0761i	0.770969	+	0.560141i
$392$	5.06771	+	15.5968i	0.255958	+	0.787758i
$393$	4.42429	+	4.42429i	0.223176	+	0.223176i
$394$	−6.19196	−	19.0569i	−0.311946	−	0.960072i
$395$	16.3500	−	26.6802i	0.822658	−	1.34243i
$396$	3.31081	−	1.68694i	0.166374	−	0.0847720i
$397$	−3.14131	−	1.02067i	−0.157658	−	0.0512261i	0.229125	−	0.973397i	$-0.426414\pi$
$397$	−3.14131	−	1.02067i	−0.157658	−	0.0512261i	−0.386783	+	0.922171i	$0.626414\pi$
$398$	17.1453	−	12.4568i	0.859414	−	0.624401i
$399$		−	16.1705i		−	0.809540i
$400$	2.26986	+	4.45508i	0.113493	+	0.222754i
$401$	−16.8314	+	16.8314i	−0.840522	+	0.840522i	−0.988927	−	0.148405i	$-0.952586\pi$
$401$	−16.8314	+	16.8314i	−0.840522	+	0.840522i	0.148405	+	0.988927i	$0.452586\pi$
$402$	−11.3800	−	1.80242i	−0.567585	−	0.0898967i
$403$	8.25585	−	38.4124i	0.411253	−	1.91346i
$404$	0.798356	+	0.259402i	0.0397197	+	0.0129057i
$405$	−7.93450	+	0.624380i	−0.394268	+	0.0310257i
$406$	−1.13279	−	3.48637i	−0.0562194	−	0.173026i
$407$	−22.7993	−	22.7993i	−1.13012	−	1.13012i
$408$	−3.57508	+	1.16161i	−0.176993	+	0.0575085i
$409$	−1.49557	+	0.236875i	−0.0739512	+	0.0117127i	−0.193300	−	0.981140i	$-0.561919\pi$
$409$	−1.49557	+	0.236875i	−0.0739512	+	0.0117127i	0.119349	+	0.992852i	$0.461919\pi$
$410$	−1.76234	+	1.07994i	−0.0870356	+	0.0533343i
$411$	0.217163	−	1.37111i	0.0107119	−	0.0676321i
$412$	9.10616	−	1.44227i	0.448628	−	0.0710557i
$413$	55.2060	−	8.74377i	2.71651	−	0.430253i
$414$	8.28370	+	1.31201i	0.407122	+	0.0644817i
$415$	0.923660	+	11.7377i	0.0453407	+	0.576180i
$416$	−3.48480	+	0.925289i	−0.170856	+	0.0453660i
$417$	2.92388	+	1.48979i	0.143183	+	0.0729554i
$418$			7.42435i			0.363137i
$419$	15.9224	−	5.17351i	0.777861	−	0.252742i	0.106934	−	0.994266i	$-0.465896\pi$
$419$	15.9224	−	5.17351i	0.777861	−	0.252742i	0.670927	+	0.741524i	$0.265896\pi$
$420$	−1.11534	+	14.1699i	−0.0544230	+	0.691423i
$421$	−8.26780	+	4.21265i	−0.402948	+	0.205312i	−0.643706	−	0.765273i	$-0.722604\pi$
$421$	−8.26780	+	4.21265i	−0.402948	+	0.205312i	0.240758	+	0.970585i	$0.422604\pi$
$422$	−1.45229	+	4.46970i	−0.0706965	+	0.217582i
$423$	−3.94985	+	2.86973i	−0.192048	+	0.139531i
$424$	−2.69501	−	2.69501i	−0.130881	−	0.130881i
$425$	11.5716	−	8.40689i	0.561303	−	0.407794i
$426$		−	20.7100i		−	1.00340i
$427$	−3.63467	−	5.00269i	−0.175894	−	0.242097i
$428$	1.66949	+	3.27656i	0.0806978	+	0.158378i
$429$	7.50482	+	11.6140i	0.362336	+	0.560727i
$430$	−18.8683	−	7.81573i	−0.909911	−	0.376908i
$431$	−4.57765	+	8.98414i	−0.220498	+	0.432751i	−0.974583	−	0.224025i	$-0.928080\pi$
$431$	−4.57765	+	8.98414i	−0.220498	+	0.432751i	0.754086	+	0.656776i	$0.228080\pi$
$432$	−3.97063	+	3.97063i	−0.191037	+	0.191037i
$433$	−14.1116	−	7.19021i	−0.678160	−	0.345540i	0.0807510	−	0.996734i	$-0.474268\pi$
$433$	−14.1116	−	7.19021i	−0.678160	−	0.345540i	−0.758911	+	0.651195i	$0.774268\pi$
$434$	−52.0629	+	8.24596i	−2.49910	+	0.395819i
$435$	0.174730	−	2.21988i	0.00837768	−	0.106435i
$436$	1.56679	−	9.89233i	0.0750357	−	0.473757i
$437$	−9.84982	+	13.5571i	−0.471181	+	0.648524i
$438$	0.999907	+	6.31317i	0.0477774	+	0.301655i
$439$	20.9399	−	15.2137i	0.999405	−	0.726110i	0.0374444	−	0.999299i	$-0.488078\pi$
$439$	20.9399	−	15.2137i	0.999405	−	0.726110i	0.961961	+	0.273189i	$0.0880783\pi$
$440$	0.512083	−	6.50582i	0.0244126	−	0.310153i
$441$	12.2728	−	16.8920i	0.584419	−	0.804383i
$442$	4.17374	+	9.43185i	0.198525	+	0.448627i
$443$	−0.453229	−	0.453229i	−0.0215335	−	0.0215335i	0.696258	−	0.717792i	$-0.254847\pi$
$443$	−0.453229	−	0.453229i	−0.0215335	−	0.0215335i	−0.717792	+	0.696258i	$0.754847\pi$
$444$	12.9354	+	6.59092i	0.613887	+	0.312791i
$445$	3.35596	−	8.10178i	0.159088	−	0.384061i
$446$	3.41411	+	1.10931i	0.161663	+	0.0525275i
$447$	−1.55878	+	4.79743i	−0.0737277	+	0.226911i
$448$	2.84329	+	3.91346i	0.134333	+	0.184893i
$449$	14.3913	+	14.3913i	0.679165	+	0.679165i	0.959811	−	0.280646i	$-0.0905488\pi$
$449$	14.3913	+	14.3913i	0.679165	+	0.679165i	−0.280646	+	0.959811i	$0.590549\pi$
$450$	2.89021	−	5.67207i	0.136246	−	0.267384i
$451$	2.69770			0.127030
$452$	16.9099	+	2.67826i	0.795373	+	0.125975i
$453$	6.33692	−	19.5030i	0.297734	−	0.916332i
$454$	6.90994	−	21.2666i	0.324300	−	0.998092i
$455$	38.9884	−	0.932133i	1.82780	−	0.0436991i
$456$	−1.03301	−	3.17928i	−0.0483751	−	0.148883i
$457$	16.4513			0.769558			0.384779	−	0.923009i	$-0.374278\pi$
$457$	16.4513			0.769558			0.384779	+	0.923009i	$0.374278\pi$
$458$	−1.67799	+	3.29323i	−0.0784072	+	0.153883i
$459$	12.9954	+	9.44172i	0.606574	+	0.440702i
$460$	9.56629	−	11.2005i	0.446031	−	0.522224i
$461$	27.6162	+	4.37397i	1.28621	+	0.203716i	0.761836	−	0.647769i	$-0.224298\pi$
$461$	27.6162	+	4.37397i	1.28621	+	0.203716i	0.524378	+	0.851486i	$0.324298\pi$
$462$	10.9044	−	15.0086i	0.507318	−	0.698263i
$463$	−5.69649	−	4.13874i	−0.264738	−	0.192344i	0.447495	−	0.894286i	$-0.352316\pi$
$463$	−5.69649	−	4.13874i	−0.264738	−	0.192344i	−0.712233	+	0.701943i	$0.752316\pi$
$464$	−0.445434	−	0.613087i	−0.0206787	−	0.0284618i
$465$	−31.1346	−	7.47507i	−1.44383	−	0.346648i
$466$	12.8247	−	2.03123i	0.594093	−	0.0940951i
$467$	10.7236	−	21.0463i	0.496230	−	0.973907i	−0.498054	−	0.867146i	$-0.665952\pi$
$467$	10.7236	−	21.0463i	0.496230	−	0.973907i	0.994285	−	0.106761i	$-0.0340480\pi$
$468$	3.56099	+	2.89702i	0.164607	+	0.133915i
$469$	40.3378	−	13.1065i	1.86262	−	0.605204i
$470$	0.672669	+	8.54815i	0.0310279	+	0.394297i
$471$	−7.78443	+	23.9580i	−0.358688	+	1.10393i
$472$	10.2954	−	5.24578i	0.473885	−	0.241457i
$473$	15.6679	+	21.5650i	0.720411	+	0.991561i
$474$	13.0031	−	13.0031i	0.597253	−	0.597253i
$475$	7.47614	+	10.2904i	0.343029	+	0.472158i
$476$	9.78467	−	9.78467i	0.448480	−	0.448480i
$477$	−0.759107	+	4.79281i	−0.0347571	+	0.219448i
$478$	7.58052	+	14.8776i	0.346725	+	0.680486i
$479$	−14.7410	+	7.51091i	−0.673533	+	0.343182i	−0.757081	−	0.653321i	$-0.773375\pi$
$479$	−14.7410	+	7.51091i	−0.673533	+	0.343182i	0.0835473	+	0.996504i	$0.473375\pi$
$480$	0.685921	+	2.85719i	0.0313079	+	0.130412i
$481$	14.3593	−	37.1554i	0.654729	−	1.69414i
$482$	−9.35951	+	9.35951i	−0.426314	+	0.426314i
$483$	39.8235	−	12.9395i	1.81203	−	0.588766i
$484$	1.45913	−	2.00832i	0.0663241	−	0.0912873i
$485$	−4.55606	−	2.79202i	−0.206880	−	0.126779i
$486$	12.0188	+	1.90359i	0.545185	+	0.0863488i
$487$	−19.8012	−	14.3864i	−0.897279	−	0.651912i	0.0404865	−	0.999180i	$-0.487109\pi$
$487$	−19.8012	−	14.3864i	−0.897279	−	0.651912i	−0.937766	+	0.347269i	$0.887109\pi$
$488$	−1.03419	−	0.751384i	−0.0468156	−	0.0340136i
$489$	23.5900	+	3.73630i	1.06678	+	0.168961i
$490$	−14.0328	−	33.8791i	−0.633936	−	1.53050i
$491$	−2.14394	+	2.95088i	−0.0967546	+	0.133171i	−0.854649	−	0.519205i	$-0.826228\pi$
$491$	−2.14394	+	2.95088i	−0.0967546	+	0.133171i	0.757895	+	0.652377i	$0.226228\pi$
$492$	−1.15522	+	0.375352i	−0.0520812	+	0.0169222i
$493$	−1.53288	+	1.53288i	−0.0690373	+	0.0690373i
$494$	−8.38763	+	3.71165i	−0.377377	+	0.166995i
$495$	−7.08446	+	4.34127i	−0.318423	+	0.195125i
$496$	−9.70927	+	4.94712i	−0.435959	+	0.222132i
$497$	34.6105	+	67.9269i	1.55249	+	3.04694i
$498$	−1.08241	+	6.83407i	−0.0485040	+	0.306242i
$499$	10.0777	−	10.0777i	0.451141	−	0.451141i	−0.444592	−	0.895733i	$-0.646651\pi$
$499$	10.0777	−	10.0777i	0.451141	−	0.451141i	0.895733	+	0.444592i	$0.146651\pi$
$500$	−5.84143	−	9.53298i	−0.261237	−	0.426328i
$501$	−13.1605	+	13.1605i	−0.587967	+	0.587967i
$502$	2.40038	+	3.30384i	0.107134	+	0.147458i
$503$	−20.0919	+	10.2373i	−0.895852	+	0.456459i	−0.840378	−	0.542001i	$-0.817667\pi$
$503$	−20.0919	+	10.2373i	−0.895852	+	0.456459i	−0.0554740	+	0.998460i	$0.517667\pi$
$504$	1.90318	−	5.85739i	0.0847745	−	0.260909i
$505$	−1.82518	−	0.438206i	−0.0812195	−	0.0194999i
$506$	−18.2841	+	5.94086i	−0.812827	+	0.264104i
$507$	−9.36894	+	14.2847i	−0.416089	+	0.634406i
$508$	3.17760	−	6.23638i	0.140983	−	0.276695i
$509$	−22.5868	+	3.57739i	−1.00114	+	0.158565i	−0.635426	−	0.772162i	$-0.719175\pi$
$509$	−22.5868	+	3.57739i	−1.00114	+	0.158565i	−0.365715	+	0.930727i	$0.619175\pi$
$510$	7.76572	−	3.21658i	0.343872	−	0.142432i
$511$	−13.8302	−	19.0356i	−0.611810	−	0.842085i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−8.39640	+	11.5567i	−0.370710	+	0.510239i
$514$	18.3304	+	2.90325i	0.808518	+	0.128057i
$515$	−20.0462	+	4.81247i	−0.883343	+	0.212063i
$516$	−9.70987	−	7.05464i	−0.427453	−	0.310563i
$517$	5.08080	−	9.97164i	0.223453	−	0.438552i
$518$	−53.4417			−2.34809
$519$	−3.21249	−	9.88703i	−0.141013	−	0.433992i
$520$	7.60593	−	2.67393i	0.333542	−	0.117260i
$521$	5.66105	−	17.4229i	0.248015	−	0.763312i	−0.747111	−	0.664700i	$-0.768560\pi$
$521$	5.66105	−	17.4229i	0.248015	−	0.763312i	0.995126	−	0.0986125i	$-0.0314404\pi$
$522$	−0.298155	+	0.917626i	−0.0130499	+	0.0401634i
$523$	−10.1527	−	1.60803i	−0.443947	−	0.0703143i	−0.0695408	−	0.997579i	$-0.522153\pi$
$523$	−10.1527	−	1.60803i	−0.443947	−	0.0703143i	−0.374406	+	0.927265i	$0.622153\pi$
$524$	−4.76142			−0.208004
$525$	0.000625995	−	31.7830i	2.73206e−5	−	1.38712i
$526$	−21.5023	−	21.5023i	−0.937547	−	0.937547i
$527$	18.3224	+	25.2186i	0.798137	+	1.09854i
$528$	1.18512	−	3.64742i	0.0515757	−	0.158734i
$529$	−19.3948	−	6.30174i	−0.843251	−	0.273989i
$530$	6.48040	+	5.53490i	0.281491	+	0.240421i
$531$	−13.1081	−	6.67890i	−0.568843	−	0.289840i
$532$	8.70138	+	8.70138i	0.377253	+	0.377253i
$533$	1.34866	+	3.04771i	0.0584169	+	0.132011i
$534$	3.02916	−	4.16928i	0.131085	−	0.180422i
$535$	−4.29635	−	7.01116i	−0.185747	−	0.303119i
$536$	7.09350	−	5.15373i	0.306392	−	0.222607i
$537$	3.26714	+	20.6279i	0.140988	+	0.890161i
$538$	5.47107	−	7.53028i	0.235874	−	0.324653i
$539$	−7.48721	+	47.2724i	−0.322497	+	2.03617i
$540$	8.15471	−	9.54775i	0.350923	−	0.410870i
$541$	11.1217	−	1.76150i	0.478159	−	0.0757329i	0.0872972	−	0.996182i	$-0.472177\pi$
$541$	11.1217	−	1.76150i	0.478159	−	0.0757329i	0.390862	+	0.920449i	$0.372177\pi$
$542$	−4.97150	−	2.53310i	−0.213544	−	0.108806i
$543$	15.2767	−	15.2767i	0.655586	−	0.655586i
$544$	1.29869	−	2.54882i	0.0556808	−	0.109280i
$545$	−1.75736	+	22.3266i	−0.0752771	+	0.956366i
$546$	22.4073	+	4.81594i	0.958945	+	0.206103i
$547$	−16.3088	−	32.0079i	−0.697315	−	1.36856i	−0.919319	−	0.393513i	$-0.871260\pi$
$547$	−16.3088	−	32.0079i	−0.697315	−	1.36856i	0.222004	−	0.975046i	$-0.428740\pi$
$548$	0.620942	+	0.854653i	0.0265253	+	0.0365090i
$549$			1.62757i			0.0694628i
$550$	−0.000287412		14.5924i	−1.22553e−5		0.622224i
$551$	−1.36317	−	1.36317i	−0.0580729	−	0.0580729i
$552$	7.00307	−	5.08803i	0.298070	−	0.216561i
$553$	−20.9183	+	64.3799i	−0.889536	+	2.73771i
$554$	−3.71663	+	1.89372i	−0.157905	+	0.0804565i
$555$	−29.9915	−	12.4232i	−1.27307	−	0.527336i
$556$	−2.37500	+	0.771684i	−0.100722	+	0.0327267i
$557$		−	3.19620i		−	0.135427i	−0.997705	−	0.0677136i	$-0.978430\pi$
$557$		−	3.19620i		−	0.135427i	0.997705	−	0.0677136i	$-0.0215704\pi$
$558$	12.3618	+	6.29865i	0.523317	+	0.266643i
$559$	−16.5301	+	28.4818i	−0.699151	+	1.20465i
$560$	−7.02469	−	8.22502i	−0.296847	−	0.347571i
$561$	−10.8357	−	1.71621i	−0.457484	−	0.0724584i
$562$	14.6725	−	2.32390i	0.618923	−	0.0980278i
$563$	−18.3478	+	2.90601i	−0.773269	+	0.122474i	−0.530585	−	0.847632i	$-0.678028\pi$
$563$	−18.3478	+	2.90601i	−0.773269	+	0.122474i	−0.242684	+	0.970105i	$0.578028\pi$
$564$	−0.788282	+	4.97702i	−0.0331926	+	0.209570i
$565$	−38.1649	−	3.00402i	−1.60561	−	0.126380i
$566$	6.27016	−	0.993096i	0.263555	−	0.0417430i
$567$	16.3751	−	5.32060i	0.687690	−	0.223444i
$568$	11.1441	+	11.1441i	0.467594	+	0.467594i
$569$	1.64802	+	5.07208i	0.0690885	+	0.212633i	0.979640	−	0.200764i	$-0.0643424\pi$
$569$	1.64802	+	5.07208i	0.0690885	+	0.212633i	−0.910551	+	0.413396i	$0.864342\pi$
$570$	2.86046	+	6.90596i	0.119812	+	0.289259i
$571$	29.6944	+	9.64828i	1.24267	+	0.403768i	0.855289	−	0.518152i	$-0.173380\pi$
$571$	29.6944	+	9.64828i	1.24267	+	0.403768i	0.387381	+	0.921920i	$0.373380\pi$
$572$	−10.2878	−	2.21113i	−0.430156	−	0.0924520i
$573$	0.751804	+	0.119074i	0.0314071	+	0.00497439i
$574$	3.16172	−	3.16172i	0.131968	−	0.131968i
$575$	−19.3602	+	26.6459i	−0.807376	+	1.11121i
$576$		−	1.27320i		−	0.0530498i
$577$	−0.560961	+	0.407562i	−0.0233531	+	0.0169670i	−0.599401	−	0.800449i	$-0.704594\pi$
$577$	−0.560961	+	0.407562i	−0.0233531	+	0.0169670i	0.576047	+	0.817416i	$0.304594\pi$
$578$	8.38540	+	2.72458i	0.348786	+	0.113328i
$579$	6.17544	−	3.14654i	0.256642	−	0.130766i
$580$	1.10050	+	1.28854i	0.0456956	+	0.0535038i
$581$	−7.87088	−	24.2241i	−0.326539	−	1.00498i
$582$	−2.22049	−	2.22049i	−0.0920421	−	0.0920421i
$583$	−3.43729	−	10.5789i	−0.142358	−	0.438132i
$584$	−3.93517	−	2.85907i	−0.162838	−	0.118309i
$585$	−8.44626	−	5.83331i	−0.349210	−	0.241178i
$586$	7.34756	−	5.33831i	0.303525	−	0.220524i
$587$	25.9178	+	18.8304i	1.06974	+	0.777213i	0.975866	−	0.218371i	$-0.0700742\pi$
$587$	25.9178	+	18.8304i	1.06974	+	0.777213i	0.0938764	+	0.995584i	$0.470074\pi$
$588$	−3.37119	−	21.2849i	−0.139026	−	0.877773i
$589$	−22.4266	+	16.2939i	−0.924073	+	0.671378i
$590$	−22.0301	+	13.4998i	−0.906965	+	0.555777i
$591$	4.11907	+	26.0068i	0.169436	+	1.06978i
$592$	−10.5071	+	3.41397i	−0.431840	+	0.140313i
$593$	15.2192			0.624976			0.312488	−	0.949922i	$-0.398838\pi$
$593$	15.2192			0.624976			0.312488	+	0.949922i	$0.398838\pi$
$594$	−15.5861	+	5.06425i	−0.639507	+	0.207789i
$595$	−20.0953	+	23.5282i	−0.823829	+	0.964561i
$596$	−1.74272	−	3.42028i	−0.0713846	−	0.140100i
$597$	−24.8135	+	12.6431i	−1.01555	+	0.517449i
$598$	−15.8524	−	17.6864i	−0.648254	−	0.723249i
$599$			22.9255i			0.936709i	0.883541	+	0.468355i	$0.155153\pi$
$599$			22.9255i			0.936709i	−0.883541	+	0.468355i	$0.844847\pi$
$600$	−2.03024	−	6.24886i	−0.0828842	−	0.255109i
$601$	33.1620			1.35271			0.676354	−	0.736577i	$-0.263559\pi$
$601$	33.1620			1.35271			0.676354	+	0.736577i	$0.263559\pi$
$602$	43.6372	+	6.91146i	1.77852	+	0.281690i
$603$	−10.6171	−	3.44969i	−0.432360	−	0.140482i
$604$	7.08469	+	13.9045i	0.288272	+	0.565766i
$605$	−2.90037	+	4.73286i	−0.117917	+	0.192418i
$606$	−0.982862	−	0.500793i	−0.0399261	−	0.0203433i
$607$	−4.07437	+	4.07437i	−0.165373	+	0.165373i	−0.784942	−	0.619569i	$-0.787307\pi$
$607$	−4.07437	+	4.07437i	−0.165373	+	0.165373i	0.619569	+	0.784942i	$0.287307\pi$
$608$	2.26663	+	1.15491i	0.0919241	+	0.0468377i
$609$	0.753566	+	4.75783i	0.0305360	+	0.192797i
$610$	2.43720	+	1.49355i	0.0986794	+	0.0604722i
$611$	13.8055	+	0.754896i	0.558509	+	0.0305398i
$612$	−3.59727	+	0.569752i	−0.145411	+	0.0230309i
$613$	15.8402	−	21.8022i	0.639781	−	0.880583i	−0.358823	−	0.933406i	$-0.616822\pi$
$613$	15.8402	−	21.8022i	0.639781	−	0.880583i	0.998604	+	0.0528229i	$0.0168219\pi$
$614$	5.37934	+	7.40403i	0.217093	+	0.298802i
$615$	2.50934	−	1.03937i	0.101186	−	0.0419115i
$616$	2.20848	+	13.9438i	0.0889822	+	0.561811i
$617$	4.01945	+	12.3706i	0.161817	+	0.498021i	0.998788	−	0.0492266i	$-0.0156756\pi$
$617$	4.01945	+	12.3706i	0.161817	+	0.498021i	−0.836971	+	0.547248i	$0.815676\pi$
$618$	−12.1154			−0.487352
$619$	−12.7685	+	25.0596i	−0.513210	+	1.00723i	0.478421	+	0.878130i	$0.341209\pi$
$619$	−12.7685	+	25.0596i	−0.513210	+	1.00723i	−0.991631	+	0.129101i	$0.958791\pi$
$620$	20.7759	−	12.7312i	0.834379	−	0.511297i
$621$	−35.1795	−	11.4305i	−1.41171	−	0.458691i
$622$	−5.57507	−	1.81145i	−0.223540	−	0.0726325i
$623$	−2.96768	+	18.7372i	−0.118898	+	0.750690i
$624$	4.71314	−	0.484572i	0.188676	−	0.0193984i
$625$	14.6938	+	20.2260i	0.587753	+	0.809040i
$626$	−3.85690	−	3.85690i	−0.154153	−	0.154153i
$627$	1.52620	−	9.63607i	0.0609507	−	0.384827i
$628$	−8.70302	−	17.0806i	−0.347288	−	0.681592i
$629$	14.3477	+	28.1590i	0.572081	+	1.12277i
$630$	−3.21504	+	13.3910i	−0.128090	+	0.533511i
$631$	32.2738	+	16.4443i	1.28480	+	0.654638i	0.956994	−	0.290107i	$-0.0936910\pi$
$631$	32.2738	+	16.4443i	1.28480	+	0.654638i	0.327805	+	0.944745i	$0.393691\pi$
$632$			13.9940i			0.556650i
$633$	2.80376	−	5.50268i	0.111439	−	0.218712i
$634$	−4.97434	−	3.61407i	−0.197556	−	0.143533i
$635$	−5.98945	+	14.4594i	−0.237684	+	0.573804i
$636$	2.94385	+	4.05186i	0.116731	+	0.160667i
$637$	−57.1488	+	15.1742i	−2.26432	+	0.601225i
$638$	−0.345983	−	2.18445i	−0.0136976	−	0.0864832i
$639$	3.13896	−	19.8186i	0.124175	−	0.784012i
$640$	−1.90655	−	1.16836i	−0.0753630	−	0.0461835i
$641$	−2.34788	+	3.23158i	−0.0927358	+	0.127640i	−0.852864	−	0.522134i	$-0.825136\pi$
$641$	−2.34788	+	3.23158i	−0.0927358	+	0.127640i	0.760128	+	0.649773i	$0.225136\pi$
$642$	−1.49328	−	4.59584i	−0.0589350	−	0.181383i
$643$			19.9479i			0.786667i	0.919396	+	0.393333i	$0.128678\pi$
$643$			19.9479i			0.786667i	−0.919396	+	0.393333i	$0.871322\pi$
$644$	−14.4663	+	28.3918i	−0.570054	+	1.11879i
$645$	22.8825	+	14.0227i	0.900999	+	0.552145i
$646$	2.24875	−	6.92094i	0.0884758	−	0.272301i
$647$	29.1488	−	14.8520i	1.14596	−	0.583894i	0.225309	−	0.974287i	$-0.427661\pi$
$647$	29.1488	−	14.8520i	1.14596	−	0.583894i	0.920648	+	0.390393i	$0.127661\pi$
$648$	2.87960	−	2.09215i	0.113122	−	0.0821876i
$649$	33.7226			1.32373
$650$	−16.4859	+	7.29488i	−0.646630	+	0.286129i
$651$	69.2676			2.71481
$652$	−14.7043	+	10.6833i	−0.575866	+	0.418391i
$653$	9.20597	−	4.69068i	0.360258	−	0.183560i	−0.264488	−	0.964389i	$-0.585203\pi$
$653$	9.20597	−	4.69068i	0.360258	−	0.183560i	0.624745	+	0.780829i	$0.285203\pi$
$654$	−4.06708	+	12.5172i	−0.159035	+	0.489460i
$655$	10.6140	−	0.835239i	0.414725	−	0.0326355i
$656$	0.419645	−	0.823600i	0.0163844	−	0.0321562i
$657$			6.19300i			0.241612i
$658$	−5.73209	−	17.6415i	−0.223460	−	0.687739i
$659$	−25.3778	+	34.9295i	−0.988578	+	1.36066i	−0.0565009	+	0.998403i	$0.517994\pi$
$659$	−25.3778	+	34.9295i	−0.988578	+	1.36066i	−0.932078	+	0.362259i	$0.882006\pi$
$660$	−2.00202	+	8.33864i	−0.0779284	+	0.324581i
$661$	−1.59716	+	10.0841i	−0.0621225	+	0.392226i	0.936961	+	0.349433i	$0.113626\pi$
$661$	−1.59716	+	10.0841i	−0.0621225	+	0.392226i	−0.999084	+	0.0427932i	$0.986374\pi$
$662$	−3.63526	−	22.9522i	−0.141289	−	0.892061i
$663$	−3.47822	−	13.0996i	−0.135083	−	0.508746i
$664$	−3.09497	−	4.25986i	−0.120108	−	0.165315i
$665$	−20.9233	−	17.8705i	−0.811370	−	0.692990i
$666$	11.3797	+	8.26783i	0.440954	+	0.320372i
$667$	2.26631	−	4.44789i	0.0877521	−	0.172223i
$668$		−	14.1633i		−	0.547995i
$669$	−4.20314	−	2.14161i	−0.162503	−	0.0827994i
$670$	−14.9086	+	12.7329i	−0.575969	+	0.491915i
$671$	−1.69375	−	3.32416i	−0.0653863	−	0.128328i
$672$	−2.88583	−	5.66377i	−0.111323	−	0.218485i
$673$	3.27924	−	20.7043i	0.126405	−	0.798092i	−0.840285	−	0.542145i	$-0.817612\pi$
$673$	3.27924	−	20.7043i	0.126405	−	0.798092i	0.966691	−	0.255948i	$-0.0823875\pi$
$674$	17.4369	+	17.4369i	0.671645	+	0.671645i
$675$	−16.5035	+	22.7141i	−0.635218	+	0.874267i
$676$	−2.64518	−	12.7280i	−0.101738	−	0.489540i
$677$	4.85119	−	30.6292i	0.186446	−	1.17718i	−0.699931	−	0.714211i	$-0.746786\pi$
$677$	4.85119	−	30.6292i	0.186446	−	1.17718i	0.886377	−	0.462965i	$-0.153214\pi$
$678$	−21.3968	−	6.95223i	−0.821738	−	0.266999i
$679$	10.9939	+	3.57213i	0.421906	+	0.137086i
$680$	−2.44790	+	5.90958i	−0.0938726	+	0.226622i
$681$	−13.3401	+	26.1815i	−0.511195	+	1.00328i
$682$	−31.8027			−1.21779
$683$	−0.359977	−	1.10790i	−0.0137741	−	0.0423924i	0.943933	−	0.330136i	$-0.107095\pi$
$683$	−0.359977	−	1.10790i	−0.0137741	−	0.0423924i	−0.957707	+	0.287744i	$0.907095\pi$
$684$	−0.506673	−	3.19901i	−0.0193731	−	0.122317i
$685$	−1.53411	−	1.79625i	−0.0586154	−	0.0686311i
$686$	26.7254	+	36.7844i	1.02038	+	1.40443i
$687$	2.85484	−	3.92935i	0.108919	−	0.149914i
$688$	9.02099	−	1.42878i	0.343922	−	0.0544719i
$689$	10.2330	−	9.17195i	0.389848	−	0.349424i
$690$	−14.7185	+	12.5706i	−0.560325	+	0.478554i
$691$	6.05730	+	38.2443i	0.230431	+	1.45488i	0.783316	+	0.621624i	$0.213527\pi$
$691$	6.05730	+	38.2443i	0.230431	+	1.45488i	−0.552885	+	0.833258i	$0.686473\pi$
$692$	7.04886	+	3.59157i	0.267957	+	0.136531i
$693$	12.7099	−	12.7099i	0.482808	−	0.482808i
$694$	5.65243	+	2.88006i	0.214563	+	0.109326i
$695$	5.15892	−	2.13684i	0.195689	−	0.0810548i
$696$	0.452098	+	0.887292i	0.0171367	+	0.0336327i
$697$	−2.51478	−	0.817101i	−0.0952540	−	0.0309499i
$698$	22.8704	+	3.62232i	0.865658	+	0.137107i
$699$	−17.0628			−0.645373
$700$	17.1021	+	17.1028i	0.646398	+	0.646424i
$701$			20.1629i			0.761542i	0.924669	+	0.380771i	$0.124341\pi$
$701$			20.1629i			0.761542i	−0.924669	+	0.380771i	$0.875659\pi$
$702$	−13.5133	−	15.0766i	−0.510026	−	0.569030i
$703$	−25.0414	+	12.7592i	−0.944455	+	0.481224i
$704$	1.32497	+	2.60039i	0.0499365	+	0.0980060i
$705$	0.884162	−	11.2329i	0.0332995	−	0.423056i
$706$	−25.6787	+	8.34352i	−0.966431	+	0.314012i
$707$	4.06063			0.152716
$708$	−14.4408	+	4.69210i	−0.542718	+	0.176340i
$709$	−2.99745	−	18.9251i	−0.112572	−	0.710748i	−0.977827	−	0.209417i	$-0.932844\pi$
$709$	−2.99745	−	18.9251i	−0.112572	−	0.710748i	0.865255	−	0.501332i	$-0.167156\pi$
$710$	−26.7969	−	22.8872i	−1.00567	−	0.858941i
$711$	14.4143	−	10.4726i	0.540579	−	0.392753i
$712$	0.613500	+	3.87349i	0.0229919	+	0.145165i
$713$	−58.0728	−	42.1923i	−2.17484	−	1.58012i
$714$	−14.7109	+	10.6881i	−0.550543	+	0.399993i
$715$	23.3213	+	3.12433i	0.872166	+	0.116843i
$716$	−12.8580	−	9.34185i	−0.480524	−	0.349121i
$717$	−6.78041	−	20.8680i	−0.253219	−	0.779328i
$718$	7.03662	+	7.03662i	0.262604	+	0.262604i
$719$	−10.4114	−	32.0428i	−0.388278	−	1.19500i	−0.934074	−	0.357079i	$-0.883773\pi$
$719$	−10.4114	−	32.0428i	−0.388278	−	1.19500i	0.545797	−	0.837918i	$-0.316227\pi$
$720$	0.223341	+	2.83818i	0.00832344	+	0.105773i
$721$	39.7374	−	20.2472i	1.47990	−	0.754045i
$722$	−11.9154	−	3.87154i	−0.443444	−	0.144084i
$723$	14.0717	−	10.2237i	0.523333	−	0.380224i
$724$			16.4408i			0.611018i
$725$	−2.67923	−	2.67934i	−0.0995043	−	0.0995082i
$726$	−2.30665	+	2.30665i	−0.0856079	+	0.0856079i
$727$	−12.6638	−	2.00575i	−0.469675	−	0.0743892i	−0.0828892	−	0.996559i	$-0.526415\pi$
$727$	−12.6638	−	2.00575i	−0.469675	−	0.0743892i	−0.386786	+	0.922170i	$0.626415\pi$
$728$	−14.6489	+	9.46594i	−0.542923	+	0.350831i
$729$	−25.3635	−	8.24109i	−0.939387	−	0.305225i
$730$	9.27372	+	5.68307i	0.343236	+	0.210340i
$731$	−8.07374	−	24.8484i	−0.298618	−	0.919052i
$732$	1.18782	+	1.18782i	0.0439030	+	0.0439030i
$733$	−15.1198	+	4.91270i	−0.558461	+	0.181455i	−0.574628	−	0.818414i	$-0.694853\pi$
$733$	−15.1198	+	4.91270i	−0.558461	+	0.181455i	0.0161677	+	0.999869i	$0.494853\pi$
$734$	−11.3931	+	1.80449i	−0.420527	+	0.0666049i
$735$	11.2487	+	46.8564i	0.414916	+	1.72832i
$736$	−1.03048	+	6.50623i	−0.0379842	+	0.239823i
$737$	25.2744	−	4.00307i	0.930994	−	0.147455i
$738$	−1.16239	+	0.184104i	−0.0427880	+	0.00677696i
$739$	−14.9734	−	2.37155i	−0.550805	−	0.0872389i	−0.125172	−	0.992135i	$-0.539948\pi$
$739$	−14.9734	−	2.37155i	−0.550805	−	0.0872389i	−0.425633	+	0.904896i	$0.639948\pi$
$740$	22.8234	−	9.45348i	0.839004	−	0.347517i
$741$	11.6493	−	3.09314i	0.427948	−	0.113629i
$742$	−16.4270	−	8.36999i	−0.603055	−	0.307272i
$743$			5.23109i			0.191910i	0.995386	+	0.0959550i	$0.0305905\pi$
$743$			5.23109i			0.191910i	−0.995386	+	0.0959550i	$0.969409\pi$
$744$	13.6186	−	4.42496i	0.499283	−	0.162227i
$745$	4.48481	+	7.31870i	0.164311	+	0.268136i
$746$	2.92497	−	1.49035i	0.107091	−	0.0545655i
$747$	−2.07165	+	6.37587i	−0.0757976	+	0.233281i
$748$	6.75420	−	4.90721i	0.246958	−	0.179426i
$749$	12.5784	+	12.5784i	0.459604	+	0.459604i
$750$	5.62193	+	13.5737i	0.205284	+	0.495640i
$751$			28.9298i			1.05566i	0.849350	+	0.527831i	$0.176995\pi$
$751$			28.9298i			1.05566i	−0.849350	+	0.527831i	$0.823005\pi$
$752$	−2.25396	−	3.10231i	−0.0821935	−	0.113130i
$753$	−2.43630	−	4.78150i	−0.0887836	−	0.174248i
$754$	2.29491	−	1.48295i	0.0835756	−	0.0540057i
$755$	−18.2321	−	29.7528i	−0.663535	−	1.08281i
$756$	−12.3317	+	24.2024i	−0.448501	+	0.880232i
$757$	−31.6328	+	31.6328i	−1.14972	+	1.14972i	−0.163107	+	0.986608i	$0.552151\pi$
$757$	−31.6328	+	31.6328i	−1.14972	+	1.14972i	−0.986608	+	0.163107i	$0.947849\pi$
$758$	28.7610	+	14.6545i	1.04465	+	0.532274i
$759$	24.9522	−	3.95204i	0.905707	−	0.143450i
$760$	−5.25532	−	2.17688i	−0.190630	−	0.0789639i
$761$	3.01237	−	19.0193i	0.109198	−	0.689450i	−0.870978	−	0.491322i	$-0.836514\pi$
$761$	3.01237	−	19.0193i	0.109198	−	0.689450i	0.980176	−	0.198128i	$-0.0634862\pi$
$762$	−5.40620	+	7.44099i	−0.195846	+	0.269559i
$763$	−7.57903	−	47.8521i	−0.274379	−	1.73236i
$764$	−0.468620	+	0.340473i	−0.0169541	+	0.0123179i
$765$	7.91901	−	1.90110i	0.286312	−	0.0687346i
$766$	5.18194	−	7.13233i	0.187231	−	0.257702i
$767$	16.8589	+	38.0980i	0.608741	+	1.37564i
$768$	−0.929194	−	0.929194i	−0.0335294	−	0.0335294i
$769$	9.15075	+	4.66254i	0.329985	+	0.168136i	0.611131	−	0.791529i	$-0.290715\pi$
$769$	9.15075	+	4.66254i	0.329985	+	0.168136i	−0.281147	+	0.959665i	$0.590715\pi$
$770$	−7.36908	−	30.6958i	−0.265563	−	1.10620i
$771$	−23.1942	−	7.53625i	−0.835318	−	0.271411i
$772$	−1.62985	+	5.01616i	−0.0586596	+	0.180536i
$773$	26.8772	+	36.9933i	0.966706	+	1.33056i	0.943693	+	0.330822i	$0.107326\pi$
$773$	26.8772	+	36.9933i	0.966706	+	1.33056i	0.0230130	+	0.999735i	$0.492674\pi$
$774$	−8.22270	−	8.22270i	−0.295559	−	0.295559i
$775$	−44.0798	+	32.0245i	−1.58339	+	1.15035i
$776$	2.38969			0.0857849
$777$	69.3621	+	10.9859i	2.48835	+	0.394116i
$778$	−2.09515	+	6.44821i	−0.0751148	+	0.231180i
$779$	0.726638	−	2.23636i	0.0260345	−	0.0801259i
$780$	−10.4214	+	1.90696i	−0.373146	+	0.0682803i
$781$	14.2134	+	43.7444i	0.508596	+	1.56530i
$782$	18.8438			0.673851
$783$	1.93190	−	3.79157i	0.0690406	−	0.135500i
$784$	13.2674	+	9.63936i	0.473837	+	0.344263i
$785$	22.3968	+	36.5491i	0.799377	+	1.30449i
$786$	6.17985	+	0.978792i	0.220428	+	0.0349124i
$787$	4.90254	−	6.74776i	0.174757	−	0.240532i	−0.712650	−	0.701520i	$-0.752505\pi$
$787$	4.90254	−	6.74776i	0.174757	−	0.240532i	0.887406	+	0.460988i	$0.152505\pi$
$788$	−16.2107	−	11.7778i	−0.577484	−	0.419567i
$789$	23.4877	+	32.3281i	0.836185	+	1.15091i
$790$	−2.45479	−	31.1950i	−0.0873376	−	1.10987i
$791$	81.7980	−	12.9555i	2.90840	−	0.460646i
$792$	1.68694	−	3.31081i	0.0599429	−	0.117644i
$793$	2.90870	−	3.57535i	0.103291	−	0.126964i
$794$	−3.14131	+	1.02067i	−0.111481	+	0.0362223i
$795$	−7.27313	−	8.51591i	−0.257951	−	0.302028i
$796$	6.54890	−	20.1555i	0.232120	−	0.714391i
$797$	−26.6159	+	13.5615i	−0.942783	+	0.480372i	−0.856642	−	0.515911i	$-0.827453\pi$
$797$	−26.6159	+	13.5615i	−0.942783	+	0.480372i	−0.0861407	+	0.996283i	$0.527453\pi$
$798$	−9.50481	−	13.0822i	−0.336467	−	0.463107i
$799$	−7.75659	+	7.75659i	−0.274408	+	0.274408i
$800$	4.45499	+	2.27004i	0.157508	+	0.0802580i
$801$	3.53071	−	3.53071i	0.124752	−	0.124752i
$802$	−3.72365	+	23.5102i	−0.131487	+	0.830173i
$803$	−6.44482	−	12.6487i	−0.227433	−	0.446362i
$804$	−10.2661	+	5.23083i	−0.362057	+	0.184477i
$805$	27.2676	−	65.8280i	0.961057	−	2.32013i
$806$	−15.8991	−	35.9290i	−0.560022	−	1.26554i
$807$	−8.64888	+	8.64888i	−0.304455	+	0.304455i
$808$	0.798356	−	0.259402i	0.0280861	−	0.00912572i
$809$	−5.48960	+	7.55578i	−0.193004	+	0.265647i	−0.894541	−	0.446986i	$-0.852497\pi$
$809$	−5.48960	+	7.55578i	−0.193004	+	0.265647i	0.701537	+	0.712633i	$0.252497\pi$
$810$	−6.05214	+	5.16892i	−0.212651	+	0.181617i
$811$	−10.9358	−	1.73207i	−0.384009	−	0.0608211i	−0.0385545	−	0.999256i	$-0.512275\pi$
$811$	−10.9358	−	1.73207i	−0.384009	−	0.0608211i	−0.345455	+	0.938435i	$0.612275\pi$
$812$	−2.96568	−	2.15470i	−0.104075	−	0.0756150i
$813$	5.93179	+	4.30970i	0.208037	+	0.151148i
$814$	−31.8461	−	5.04392i	−1.11620	−	0.176789i
$815$	30.9045	−	26.3944i	1.08254	−	0.924555i
$816$	−2.20952	+	3.04115i	−0.0773488	+	0.106461i
$817$	22.0974	−	7.17988i	0.773090	−	0.251192i
$818$	−1.07071	+	1.07071i	−0.0374365	+	0.0374365i
$819$	20.7130	+	8.00488i	0.723770	+	0.279713i
$820$	−0.790989	+	1.90956i	−0.0276225	+	0.0666848i
$821$	3.23544	−	1.64854i	0.112918	−	0.0575344i	−0.396619	−	0.917983i	$-0.629817\pi$
$821$	3.23544	−	1.64854i	0.112918	−	0.0575344i	0.509537	+	0.860449i	$0.329817\pi$
$822$	−0.630232	−	1.23690i	−0.0219819	−	0.0431419i
$823$	−0.0924570	+	0.583751i	−0.00322285	+	0.0203483i	−0.989247	−	0.146252i	$-0.953279\pi$
$823$	−0.0924570	+	0.583751i	−0.00322285	+	0.0203483i	0.986025	+	0.166600i	$0.0532790\pi$
$824$	6.51929	−	6.51929i	0.227110	−	0.227110i
$825$	3.00010	−	18.9395i	0.104450	−	0.659388i
$826$	39.5231	−	39.5231i	1.37519	−	1.37519i
$827$	−29.8217	−	41.0460i	−1.03700	−	1.42731i	−0.899559	−	0.436800i	$-0.856112\pi$
$827$	−29.8217	−	41.0460i	−1.03700	−	1.42731i	−0.137442	−	0.990510i	$-0.543888\pi$
$828$	7.47283	−	3.80760i	0.259699	−	0.132323i
$829$	12.5692	−	38.6839i	0.436545	−	1.34355i	−0.454949	−	0.890517i	$-0.650343\pi$
$829$	12.5692	−	38.6839i	0.436545	−	1.34355i	0.891495	−	0.453031i	$-0.149657\pi$
$830$	7.64650	+	8.95307i	0.265414	+	0.310766i
$831$	5.21311	−	1.69384i	0.180841	−	0.0587587i
$832$	−2.27539	+	2.79689i	−0.0788850	+	0.0969647i
$833$	21.2978	−	41.7993i	0.737925	−	1.44826i
$834$	3.24114	−	0.513347i	0.112232	−	0.0177757i
$835$	2.48450	+	31.5725i	0.0859797	+	1.09261i
$836$	4.36392	+	6.00642i	0.150929	+	0.207737i
$837$	−49.5037	−	35.9666i	−1.71110	−	1.24319i
$838$	9.84060	−	13.5444i	0.339938	−	0.467884i
$839$	28.1469	+	4.45803i	0.971738	+	0.153908i	0.622067	−	0.782964i	$-0.286293\pi$
$839$	28.1469	+	4.45803i	0.971738	+	0.153908i	0.349672	+	0.936872i	$0.386293\pi$
$840$	7.42656	+	12.1193i	0.256241	+	0.418156i
$841$	−22.9969	−	16.7082i	−0.792996	−	0.576145i
$842$	−4.21265	+	8.26780i	−0.145178	+	0.284927i
$843$	−19.5212			−0.672346
$844$	1.45229	+	4.46970i	0.0499900	+	0.153853i
$845$	8.12930	+	27.9090i	0.279656	+	0.960100i
$846$	−1.50871	+	4.64332i	−0.0518704	+	0.159641i
$847$	3.71074	−	11.4205i	0.127503	−	0.392413i
$848$	−3.76439	−	0.596221i	−0.129270	−	0.0204743i
$849$	−8.34220			−0.286303
$850$	4.42015	−	13.6029i	0.151610	−	0.466576i
$851$	−51.4602	−	51.4602i	−1.76403	−	1.76403i
$852$	−12.1730	−	16.7547i	−0.417041	−	0.574008i
$853$	4.70896	−	14.4927i	0.161232	−	0.496220i	−0.837507	−	0.546426i	$-0.815988\pi$
$853$	4.70896	−	14.4927i	0.161232	−	0.496220i	0.998739	+	0.0502061i	$0.0159878\pi$
$854$	−5.88102	−	1.91086i	−0.201244	−	0.0653882i
$855$	1.69063	+	7.04228i	0.0578182	+	0.240841i
$856$	3.27656	+	1.66949i	0.111990	+	0.0570619i
$857$	1.78468	+	1.78468i	0.0609634	+	0.0609634i	0.736931	−	0.675968i	$-0.236274\pi$
$857$	1.78468	+	1.78468i	0.0609634	+	0.0609634i	−0.675968	+	0.736931i	$0.736274\pi$
$858$	12.8980	+	4.98467i	0.440332	+	0.170174i
$859$	−3.56867	+	4.91185i	−0.121761	+	0.167590i	−0.865546	−	0.500829i	$-0.833029\pi$
$859$	−3.56867	+	4.91185i	−0.121761	+	0.167590i	0.743785	+	0.668419i	$0.233029\pi$
$860$	−19.8587	+	4.76746i	−0.677178	+	0.162569i
$861$	−4.75354	+	3.45365i	−0.162000	+	0.117700i
$862$	1.57735	+	9.95900i	0.0537248	+	0.339205i
$863$	−32.9806	+	45.3939i	−1.12267	+	1.54523i	−0.321386	+	0.946948i	$0.604149\pi$
$863$	−32.9806	+	45.3939i	−1.12267	+	1.54523i	−0.801288	+	0.598279i	$0.795851\pi$
$864$	−0.878429	+	5.54618i	−0.0298848	+	0.188685i
$865$	−16.3432	−	6.76976i	−0.555685	−	0.230179i
$866$	−15.6428	+	2.47758i	−0.531565	+	0.0841916i
$867$	−10.3233	−	5.26000i	−0.350599	−	0.178639i
$868$	−37.2729	+	37.2729i	−1.26513	+	1.26513i
$869$	−18.5415	+	36.3898i	−0.628979	+	1.23444i
$870$	−1.16345	−	1.89863i	−0.0394448	−	0.0643694i
$871$	17.1579	+	26.5524i	0.581372	+	0.899693i
$872$	−4.54700	−	8.92400i	−0.153981	−	0.302205i
$873$	−1.78836	−	2.46147i	−0.0605269	−	0.0833081i
$874$			16.7575i			0.566831i
$875$	−41.1237	−	35.1251i	−1.39024	−	1.18744i
$876$	4.51973	+	4.51973i	0.152707	+	0.152707i
$877$	−5.19160	+	3.77192i	−0.175308	+	0.127369i	−0.671979	−	0.740570i	$-0.734555\pi$
$877$	−5.19160	+	3.77192i	−0.175308	+	0.127369i	0.496671	+	0.867939i	$0.334555\pi$
$878$	7.99831	−	24.6163i	0.269930	−	0.830759i
$879$	−10.6338	+	5.41818i	−0.358669	+	0.182751i
$880$	−3.40974	−	5.56431i	−0.114942	−	0.187573i
$881$	−8.22290	+	2.67178i	−0.277036	+	0.0900146i	−0.444240	−	0.895908i	$-0.646526\pi$
$881$	−8.22290	+	2.67178i	−0.277036	+	0.0900146i	0.167204	+	0.985922i	$0.446526\pi$
$882$		−	20.8797i		−	0.703057i
$883$	−18.1640	−	9.25504i	−0.611269	−	0.311457i	0.120811	−	0.992675i	$-0.461450\pi$
$883$	−18.1640	−	9.25504i	−0.611269	−	0.311457i	−0.732080	+	0.681218i	$0.761450\pi$
$884$	8.92053	+	5.17727i	0.300030	+	0.174130i
$885$	31.3680	−	12.9927i	1.05442	−	0.436745i
$886$	−0.633071	−	0.100269i	−0.0212684	−	0.00336859i
$887$	32.8919	−	5.20956i	1.10440	−	0.174920i	0.422499	−	0.906363i	$-0.361153\pi$
$887$	32.8919	−	5.20956i	1.10440	−	0.174920i	0.681902	+	0.731444i	$0.261153\pi$
$888$	14.3390	−	2.27108i	0.481186	−	0.0762123i
$889$	5.29648	−	33.4406i	0.177638	−	1.12156i
$890$	−2.04708	−	8.52707i	−0.0686182	−	0.285828i
$891$	10.2601	−	1.62505i	0.343727	−	0.0544411i
$892$	3.41411	−	1.10931i	0.114313	−	0.0371425i
$893$	−6.89783	−	6.89783i	−0.230827	−	0.230827i
$894$	1.55878	+	4.79743i	0.0521334	+	0.160450i
$895$	30.3014	+	18.5691i	1.01286	+	0.620697i
$896$	4.60054	+	1.49481i	0.153693	+	0.0499380i
$897$	16.9391	+	26.2139i	0.565582	+	0.875256i
$898$	20.1017	+	3.18380i	0.670803	+	0.106245i
$899$	5.83922	−	5.83922i	0.194749	−	0.194749i
$900$	−0.995735	−	6.28762i	−0.0331912	−	0.209587i
$901$			10.9027i			0.363221i
$902$	2.18248	−	1.58567i	0.0726687	−	0.0527969i
$903$	−55.2160	−	17.9408i	−1.83747	−	0.597032i
$904$	15.2546	−	7.77261i	0.507361	−	0.258513i
$905$	−2.88401	−	36.6495i	−0.0958678	−	1.21827i
$906$	−6.33692	−	19.5030i	−0.210530	−	0.647945i
$907$	1.03358	+	1.03358i	0.0343196	+	0.0343196i	0.724058	−	0.689739i	$-0.242275\pi$
$907$	1.03358	+	1.03358i	0.0343196	+	0.0343196i	−0.689739	+	0.724058i	$0.742275\pi$
$908$	−6.90994	−	21.2666i	−0.229315	−	0.705758i
$909$	−0.864655	−	0.628209i	−0.0286788	−	0.0208364i
$910$	30.9944	−	23.6709i	1.02745	−	0.784683i
$911$	11.9146	−	8.65644i	0.394747	−	0.286801i	−0.372651	−	0.927972i	$-0.621551\pi$
$911$	11.9146	−	8.65644i	0.394747	−	0.286801i	0.767398	+	0.641171i	$0.221551\pi$
$912$	−2.70445	−	1.96490i	−0.0895534	−	0.0650644i
$913$	−2.40397	−	15.1781i	−0.0795597	−	0.502320i
$914$	13.3094	−	9.66982i	0.440235	−	0.319849i
$915$	−2.85622	−	2.43949i	−0.0944237	−	0.0806471i
$916$	0.578195	+	3.65058i	0.0191041	+	0.120619i
$917$	−21.9051	+	7.11741i	−0.723371	+	0.235037i
$918$	16.0632			0.530165
$919$	38.9878	−	12.6679i	1.28609	−	0.417876i	0.415369	−	0.909653i	$-0.363653\pi$
$919$	38.9878	−	12.6679i	1.28609	−	0.417876i	0.870721	+	0.491777i	$0.163653\pi$
$920$	1.15582	−	14.6843i	0.0381064	−	0.484127i
$921$	−5.45982	−	10.7155i	−0.179907	−	0.353088i
$922$	24.9129	−	12.6938i	0.820463	−	0.418047i
$923$	−42.3144	+	37.9267i	−1.39279	+	1.24837i
$924$		−	18.5516i		−	0.610304i
$925$	−49.2190	+	25.0771i	−1.61831	+	0.824530i
$926$	−7.04125			−0.231390
$927$	−11.5939	−	1.83630i	−0.380794	−	0.0603119i
$928$	−0.720727	−	0.234178i	−0.0236590	−	0.00768728i
$929$	−11.2311	−	22.0422i	−0.368479	−	0.723182i	0.630097	−	0.776516i	$-0.283015\pi$
$929$	−11.2311	−	22.0422i	−0.368479	−	0.723182i	−0.998577	+	0.0533346i	$0.983015\pi$
$930$	−29.5821	+	12.2530i	−0.970036	+	0.401791i
$931$	37.1715	+	18.9398i	1.21825	+	0.620728i
$932$	9.18148	−	9.18148i	0.300749	−	0.300749i
$933$	6.86351	+	3.49713i	0.224701	+	0.114491i
$934$	−3.69511	−	23.3300i	−0.120908	−	0.763381i
$935$	−14.1955	+	12.1239i	−0.464242	+	0.396492i
$936$	4.58372	+	0.250643i	0.149824	+	0.00819251i
$937$	20.6711	−	3.27397i	0.675294	−	0.106956i	0.190637	−	0.981661i	$-0.438945\pi$
$937$	20.6711	−	3.27397i	0.675294	−	0.106956i	0.484657	+	0.874704i	$0.338945\pi$
$938$	24.9301	−	34.3134i	0.813997	−	1.12037i
$939$	4.21302	+	5.79872i	0.137487	+	0.189234i
$940$	5.56868	+	6.52021i	0.181630	+	0.212666i
$941$	−3.30777	−	20.8845i	−0.107830	−	0.680814i	−0.981089	−	0.193557i	$-0.937998\pi$
$941$	−3.30777	−	20.8845i	−0.107830	−	0.680814i	0.873259	−	0.487257i	$-0.162002\pi$
$942$	7.78443	+	23.9580i	0.253631	+	0.780595i
$943$	6.08898			0.198284
$944$	5.24578	−	10.2954i	0.170736	−	0.335087i
$945$	23.2441	−	56.1146i	0.756130	−	1.82541i
$946$	25.3512	+	8.23711i	0.824239	+	0.267811i
$947$	39.9187	+	12.9704i	1.29718	+	0.421481i	0.874601	−	0.484843i	$-0.161123\pi$
$947$	39.9187	+	12.9704i	1.29718	+	0.421481i	0.422584	+	0.906324i	$0.361123\pi$
$948$	2.87670	−	18.1628i	0.0934310	−	0.589900i
$949$	11.0678	−	13.6044i	0.359277	−	0.441619i
$950$	12.0969	+	3.93078i	0.392475	+	0.127531i
$951$	5.71327	+	5.71327i	0.185265	+	0.185265i
$952$	2.16468	−	13.6672i	0.0701577	−	0.442958i
$953$	−3.64595	−	7.15558i	−0.118104	−	0.231792i	0.824385	−	0.566030i	$-0.191521\pi$
$953$	−3.64595	−	7.15558i	−0.118104	−	0.231792i	−0.942489	+	0.334238i	$0.891521\pi$
$954$	2.20301	+	4.32366i	0.0713252	+	0.139984i
$955$	0.984912	−	0.841178i	0.0318710	−	0.0272199i
$956$	14.8776	+	7.58052i	0.481176	+	0.245172i
$957$			2.90632i			0.0939481i
$958$	−7.51091	+	14.7410i	−0.242667	+	0.476260i
$959$	4.13421	+	3.00368i	0.133501	+	0.0969939i
$960$	2.23434	+	1.90834i	0.0721129	+	0.0615914i
$961$	−51.5746	−	70.9864i	−1.66370	−	2.28988i
$962$	−10.2224	−	38.4995i	−0.329585	−	1.24128i
$963$	−0.732427	−	4.62436i	−0.0236021	−	0.149018i
$964$	−2.07062	+	13.0734i	−0.0666902	+	0.421065i
$965$	2.75330	−	11.4678i	0.0886318	−	0.369162i
$966$	24.6123	−	33.8759i	0.791888	−	1.08994i
$967$	−2.50285	−	7.70299i	−0.0804863	−	0.247711i	0.902714	−	0.430241i	$-0.141571\pi$
$967$	−2.50285	−	7.70299i	−0.0804863	−	0.247711i	−0.983200	+	0.182530i	$0.941571\pi$
$968$		−	2.48242i		−	0.0797881i
$969$	−4.34137	+	8.52042i	−0.139465	+	0.273715i
$970$	−5.32704	+	0.419195i	−0.171041	+	0.0134595i
$971$	−0.388493	+	1.19566i	−0.0124673	+	0.0383705i	−0.957097	−	0.289769i	$-0.906422\pi$
$971$	−0.388493	+	1.19566i	−0.0124673	+	0.0383705i	0.944629	+	0.328139i	$0.106422\pi$
$972$	10.8423	−	5.52445i	0.347768	−	0.177197i
$973$	−9.77277	+	7.10033i	−0.313300	+	0.227626i
$974$	−24.4757			−0.784251
$975$	22.8966	−	6.07906i	0.733280	−	0.194686i
$976$	−1.27833			−0.0409184
$977$	−47.3006	+	34.3659i	−1.51328	+	1.09946i	−0.548585	+	0.836095i	$0.684833\pi$
$977$	−47.3006	+	34.3659i	−1.51328	+	1.09946i	−0.964696	+	0.263367i	$0.915167\pi$
$978$	21.2809	−	10.8432i	0.680488	−	0.346726i
$979$	−3.53690	+	10.8855i	−0.113040	+	0.347901i
$980$	−31.2664	−	19.1605i	−0.998768	−	0.612059i
$981$	−5.78923	+	11.3620i	−0.184836	+	0.362761i
$982$			3.64748i			0.116396i
$983$	−7.75515	−	23.8679i	−0.247351	−	0.761268i	−0.995241	−	0.0974451i	$-0.968933\pi$
$983$	−7.75515	−	23.8679i	−0.247351	−	0.761268i	0.747890	−	0.663823i	$-0.231067\pi$
$984$	−0.713963	+	0.982685i	−0.0227603	+	0.0313269i
$985$	38.2027	+	23.4111i	1.21724	+	0.745941i
$986$	−0.339121	+	2.14113i	−0.0107998	+	0.0681874i
$987$	3.81315	+	24.0753i	0.121374	+	0.766325i
$988$	−4.60408	+	7.93291i	−0.146475	+	0.252380i
$989$	35.3641	+	48.6745i	1.12451	+	1.54776i
$990$	−3.17972	+	7.67630i	−0.101058	+	0.243969i
$991$	−11.0991	−	8.06399i	−0.352576	−	0.256161i	0.397373	−	0.917657i	$-0.369922\pi$
$991$	−11.0991	−	8.06399i	−0.352576	−	0.256161i	−0.749949	+	0.661496i	$0.769922\pi$
$992$	−4.94712	+	9.70927i	−0.157071	+	0.308270i
$993$			30.5369i			0.969059i
$994$	67.9269	+	34.6105i	2.15451	+	1.09778i
$995$	−11.0630	+	46.0789i	−0.350722	+	1.46080i
$996$	3.14128	+	6.16511i	0.0995352	+	0.195349i
$997$	22.3422	+	43.8491i	0.707585	+	1.38871i	0.912148	+	0.409861i	$0.134423\pi$
$997$	22.3422	+	43.8491i	0.707585	+	1.38871i	−0.204563	+	0.978853i	$0.565577\pi$
$998$	2.22951	−	14.0766i	0.0705741	−	0.445587i
$999$	−43.8669	−	43.8669i	−1.38789	−	1.38789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.ba.b.73.7	✓	144
13.5	odd	4		650.2.bd.b.473.7	yes	144
25.12	odd	20		650.2.bd.b.437.7	yes	144
325.187	even	20	inner	650.2.ba.b.187.7	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.ba.b.73.7	✓	144	1.1	even	1	trivial
650.2.ba.b.187.7	yes	144	325.187	even	20	inner
650.2.bd.b.437.7	yes	144	25.12	odd	20
650.2.bd.b.473.7	yes	144	13.5	odd	4

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.ba (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-1.17085 + 0.596579i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.522021 + 2.17428i) q^{5} +(-0.596579 + 1.17085i) q^{6} -4.83730i q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.748366 + 1.03004i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(-1.17085 + 0.596579i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.522021 + 2.17428i) q^{5} +(-0.596579 + 1.17085i) q^{6} -4.83730i q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.748366 + 1.03004i) q^{9} +(0.855686 + 2.06587i) q^{10} +(0.456552 - 2.88256i) q^{11} +(0.205567 + 1.29790i) q^{12} +(3.48480 - 0.925289i) q^{13} +(-2.84329 - 3.91346i) q^{14} +(-0.685921 - 2.85719i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.29869 + 2.54882i) q^{17} +1.27320i q^{18} +(-2.26663 - 1.15491i) q^{19} +(1.90655 + 1.16836i) q^{20} +(2.88583 + 5.66377i) q^{21} +(-1.32497 - 2.60039i) q^{22} +(1.03048 - 6.50623i) q^{23} +(0.929194 + 0.929194i) q^{24} +(-4.45499 - 2.27004i) q^{25} +(2.27539 - 2.79689i) q^{26} +(0.878429 - 5.54618i) q^{27} +(-4.60054 - 1.49481i) q^{28} +(0.720727 + 0.234178i) q^{29} +(-2.23434 - 1.90834i) q^{30} +(4.94712 - 9.70927i) q^{31} -1.00000 q^{32} +(1.18512 + 3.64742i) q^{33} +(0.447498 + 2.82539i) q^{34} +(10.5176 + 2.52517i) q^{35} +(0.748366 + 1.03004i) q^{36} +(6.49376 - 8.93789i) q^{37} +(-2.51258 + 0.397954i) q^{38} +(-3.52818 + 3.16234i) q^{39} +(2.22918 - 0.175418i) q^{40} +(0.144600 + 0.912967i) q^{41} +(5.66377 + 2.88583i) q^{42} +(-6.45832 + 6.45832i) q^{43} +(-2.60039 - 1.32497i) q^{44} +(-1.84893 - 2.16486i) q^{45} +(-2.99058 - 5.86935i) q^{46} +(3.64698 + 1.18498i) q^{47} +(1.29790 + 0.205567i) q^{48} -16.3995 q^{49} +(-4.93846 + 0.782075i) q^{50} -3.75906i q^{51} +(0.196861 - 3.60017i) q^{52} +(3.39591 - 1.73030i) q^{53} +(-2.54930 - 5.00328i) q^{54} +(6.02916 + 2.49743i) q^{55} +(-4.60054 + 1.49481i) q^{56} +3.34289 q^{57} +(0.720727 - 0.234178i) q^{58} +(1.80757 + 11.4126i) q^{59} +(-2.92931 - 0.230571i) q^{60} +(1.03419 - 0.751384i) q^{61} +(-1.70466 - 10.7628i) q^{62} +(4.98260 + 3.62007i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.192697 + 8.05995i) q^{65} +(3.10268 + 2.25423i) q^{66} +(2.70947 + 8.33890i) q^{67} +(2.02275 + 2.02275i) q^{68} +(2.67493 + 8.23260i) q^{69} +(9.99321 - 4.13921i) q^{70} +(-14.0423 + 7.15492i) q^{71} +(1.21088 + 0.393439i) q^{72} +(3.93517 - 2.85907i) q^{73} -11.0478i q^{74} +(6.57040 + 0.000129410i) q^{75} +(-1.79881 + 1.79881i) q^{76} +(-13.9438 - 2.20848i) q^{77} +(-0.995584 + 4.63220i) q^{78} +(-13.3091 - 4.32437i) q^{79} +(1.70033 - 1.45219i) q^{80} +(1.09991 + 3.38518i) q^{81} +(0.653612 + 0.653612i) q^{82} +(5.00777 - 1.62712i) q^{83} +(6.27833 - 0.994390i) q^{84} +(-4.86391 - 4.15425i) q^{85} +(-1.42878 + 9.02099i) q^{86} +(-0.983571 + 0.155782i) q^{87} +(-2.88256 + 0.456552i) q^{88} +(-3.87349 - 0.613500i) q^{89} +(-2.76828 - 0.664635i) q^{90} +(-4.47590 - 16.8570i) q^{91} +(-5.86935 - 2.99058i) q^{92} +14.3195i q^{93} +(3.64698 - 1.18498i) q^{94} +(3.69432 - 4.32541i) q^{95} +(1.17085 - 0.596579i) q^{96} +(-0.738455 + 2.27273i) q^{97} +(-13.2674 + 9.63936i) q^{98} +(2.62747 + 2.62747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 36 q^{2} - 36 q^{4} + 36 q^{8} - 20 q^{9}+O(q^{10}) \) 144 * q + 36 * q^2 - 36 * q^4 + 36 * q^8 - 20 * q^9	\( 144 q + 36 q^{2} - 36 q^{4} + 36 q^{8} - 20 q^{9} + 6 q^{13} + 8 q^{15} - 36 q^{16} - 6 q^{17} - 20 q^{19} - 6 q^{21} + 12 q^{23} + 2 q^{25} + 14 q^{26} - 24 q^{27} + 20 q^{29} + 12 q^{30} - 6 q^{31} - 144 q^{32} - 54 q^{33} + 6 q^{34} + 40 q^{35} + 20 q^{36} - 60 q^{37} + 20 q^{39} + 52 q^{41} + 6 q^{42} - 12 q^{43} - 6 q^{45} + 28 q^{46} + 50 q^{47} - 160 q^{49} - 22 q^{50} + 6 q^{52} + 20 q^{53} - 6 q^{54} - 32 q^{55} - 28 q^{57} + 20 q^{58} - 16 q^{59} - 12 q^{60} + 12 q^{61} + 6 q^{62} - 70 q^{63} - 36 q^{64} + 44 q^{65} - 16 q^{66} - 8 q^{67} - 6 q^{68} + 26 q^{69} + 10 q^{70} + 72 q^{71} - 52 q^{73} + 32 q^{75} - 56 q^{77} - 50 q^{78} - 20 q^{79} + 124 q^{81} - 22 q^{82} + 70 q^{83} - 6 q^{84} - 18 q^{85} - 8 q^{86} + 8 q^{87} + 28 q^{89} - 14 q^{90} - 26 q^{91} + 12 q^{92} + 50 q^{94} - 46 q^{95} + 28 q^{97} - 20 q^{98} + 40 q^{99}+O(q^{100}) \) 144 * q + 36 * q^2 - 36 * q^4 + 36 * q^8 - 20 * q^9 + 6 * q^13 + 8 * q^15 - 36 * q^16 - 6 * q^17 - 20 * q^19 - 6 * q^21 + 12 * q^23 + 2 * q^25 + 14 * q^26 - 24 * q^27 + 20 * q^29 + 12 * q^30 - 6 * q^31 - 144 * q^32 - 54 * q^33 + 6 * q^34 + 40 * q^35 + 20 * q^36 - 60 * q^37 + 20 * q^39 + 52 * q^41 + 6 * q^42 - 12 * q^43 - 6 * q^45 + 28 * q^46 + 50 * q^47 - 160 * q^49 - 22 * q^50 + 6 * q^52 + 20 * q^53 - 6 * q^54 - 32 * q^55 - 28 * q^57 + 20 * q^58 - 16 * q^59 - 12 * q^60 + 12 * q^61 + 6 * q^62 - 70 * q^63 - 36 * q^64 + 44 * q^65 - 16 * q^66 - 8 * q^67 - 6 * q^68 + 26 * q^69 + 10 * q^70 + 72 * q^71 - 52 * q^73 + 32 * q^75 - 56 * q^77 - 50 * q^78 - 20 * q^79 + 124 * q^81 - 22 * q^82 + 70 * q^83 - 6 * q^84 - 18 * q^85 - 8 * q^86 + 8 * q^87 + 28 * q^89 - 14 * q^90 - 26 * q^91 + 12 * q^92 + 50 * q^94 - 46 * q^95 + 28 * q^97 - 20 * q^98 + 40 * q^99

Introduction

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