LMFDB - Embedded newform 460.2.o.b.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$64$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	460.19
Dual form			460.2.o.b.339.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40029 + 0.197940i) q^{2} +(1.48939 - 0.437323i) q^{3} +(1.92164 - 0.554348i) q^{4} +(-2.20194 + 0.389205i) q^{5} +(-1.99901 + 0.907190i) q^{6} +(-0.230848 + 0.0331909i) q^{7} +(-2.58113 + 1.15662i) q^{8} +(-0.496740 + 0.319236i) q^{9} +O(q^{10})$	\(q+(-1.40029 + 0.197940i) q^{2} +(1.48939 - 0.437323i) q^{3} +(1.92164 - 0.554348i) q^{4} +(-2.20194 + 0.389205i) q^{5} +(-1.99901 + 0.907190i) q^{6} +(-0.230848 + 0.0331909i) q^{7} +(-2.58113 + 1.15662i) q^{8} +(-0.496740 + 0.319236i) q^{9} +(3.00632 - 0.980851i) q^{10} +(-1.45664 + 3.18959i) q^{11} +(2.61963 - 1.66602i) q^{12} +(-5.20665 - 0.748603i) q^{13} +(0.316685 - 0.0921710i) q^{14} +(-3.10932 + 1.54263i) q^{15} +(3.38540 - 2.13051i) q^{16} +(1.75347 + 2.02361i) q^{17} +(0.632392 - 0.545348i) q^{18} +(-3.68072 + 4.24778i) q^{19} +(-4.01557 + 1.96855i) q^{20} +(-0.329306 + 0.150389i) q^{21} +(1.40837 - 4.75468i) q^{22} +(-4.70643 - 0.921685i) q^{23} +(-3.33849 + 2.85144i) q^{24} +(4.69704 - 1.71401i) q^{25} +(7.43901 + 0.0176601i) q^{26} +(-3.64978 + 4.21207i) q^{27} +(-0.425207 + 0.191751i) q^{28} +(5.67191 + 6.54573i) q^{29} +(4.04862 - 2.77560i) q^{30} +(2.80982 - 9.56937i) q^{31} +(-4.31883 + 3.65345i) q^{32} +(-0.774613 + 5.38755i) q^{33} +(-2.85592 - 2.48657i) q^{34} +(0.495394 - 0.162931i) q^{35} +(-0.777588 + 0.888822i) q^{36} +(5.96038 - 3.83050i) q^{37} +(4.31328 - 6.67670i) q^{38} +(-8.08210 + 1.16203i) q^{39} +(5.23332 - 3.55139i) q^{40} +(-2.33881 - 1.50306i) q^{41} +(0.431357 - 0.275772i) q^{42} +(2.30644 + 7.85501i) q^{43} +(-1.03099 + 6.93672i) q^{44} +(0.969542 - 0.896270i) q^{45} +(6.77282 + 0.359039i) q^{46} -7.76422 q^{47} +(4.11044 - 4.65367i) q^{48} +(-6.66426 + 1.95680i) q^{49} +(-6.23796 + 3.32984i) q^{50} +(3.49656 + 2.24711i) q^{51} +(-10.4203 + 1.44775i) q^{52} +(1.12277 + 7.80907i) q^{53} +(4.27702 - 6.62057i) q^{54} +(1.96602 - 7.59020i) q^{55} +(0.557459 - 0.352673i) q^{56} +(-3.62436 + 7.93625i) q^{57} +(-9.23799 - 8.04324i) q^{58} +(-5.45147 - 0.783803i) q^{59} +(-5.11985 + 4.68803i) q^{60} +(3.29243 - 11.2130i) q^{61} +(-2.04041 + 13.9561i) q^{62} +(0.104076 - 0.0901821i) q^{63} +(5.32447 - 5.97076i) q^{64} +(11.7561 - 0.378077i) q^{65} +(0.0182737 - 7.69747i) q^{66} +(-8.08383 + 3.69176i) q^{67} +(4.49132 + 2.91662i) q^{68} +(-7.41277 + 0.685487i) q^{69} +(-0.661446 + 0.326210i) q^{70} +(-5.85329 + 2.67311i) q^{71} +(0.912918 - 1.39853i) q^{72} +(-0.213603 - 0.185088i) q^{73} +(-7.58806 + 6.54362i) q^{74} +(6.24613 - 4.60694i) q^{75} +(-4.71827 + 10.2031i) q^{76} +(0.230396 - 0.784656i) q^{77} +(11.0873 - 3.22695i) q^{78} +(-0.786842 + 5.47261i) q^{79} +(-6.62522 + 6.00886i) q^{80} +(-2.85802 + 6.25819i) q^{81} +(3.57254 + 1.64179i) q^{82} +(3.35494 + 5.22039i) q^{83} +(-0.549440 + 0.471544i) q^{84} +(-4.64862 - 3.77340i) q^{85} +(-4.78451 - 10.5428i) q^{86} +(11.3103 + 7.26867i) q^{87} +(0.0706332 - 9.91751i) q^{88} +(-3.13900 - 10.6904i) q^{89} +(-1.18023 + 1.44695i) q^{90} +1.22679 q^{91} +(-9.55500 + 0.837851i) q^{92} -15.4813i q^{93} +(10.8722 - 1.53685i) q^{94} +(6.45145 - 10.7859i) q^{95} +(-4.83468 + 7.33012i) q^{96} +(5.91382 + 3.80058i) q^{97} +(8.94459 - 4.05922i) q^{98} +(-0.294660 - 2.04941i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−1.40029	+	0.197940i	−0.990157	+	0.139965i
$2$	−1.40029	+	0.197940i	−0.990157	+	0.139965i
$3$	1.48939	−	0.437323i	0.859898	−	0.252489i	0.178085	−	0.984015i	$-0.443010\pi$
$3$	1.48939	−	0.437323i	0.859898	−	0.252489i	0.681813	+	0.731526i	$0.261192\pi$
$4$	1.92164	−	0.554348i	0.960820	−	0.277174i
$5$	−2.20194	+	0.389205i	−0.984735	+	0.174058i
$5$	−2.20194	+	0.389205i	−0.984735	+	0.174058i
$6$	−1.99901	+	0.907190i	−0.816094	+	0.370359i
$7$	−0.230848	+	0.0331909i	−0.0872523	+	0.0125450i	−0.185803	−	0.982587i	$-0.559489\pi$
$7$	−0.230848	+	0.0331909i	−0.0872523	+	0.0125450i	0.0985504	+	0.995132i	$0.468579\pi$
$8$	−2.58113	+	1.15662i	−0.912567	+	0.408926i
$9$	−0.496740	+	0.319236i	−0.165580	+	0.106412i
$10$	3.00632	−	0.980851i	0.950680	−	0.310172i
$11$	−1.45664	+	3.18959i	−0.439192	+	0.961697i	0.552554	+	0.833477i	$0.313653\pi$
$11$	−1.45664	+	3.18959i	−0.439192	+	0.961697i	−0.991746	+	0.128219i	$0.959074\pi$
$12$	2.61963	−	1.66602i	0.756223	−	0.480937i
$13$	−5.20665	−	0.748603i	−1.44407	−	0.207625i	−0.624686	−	0.780876i	$-0.714773\pi$
$13$	−5.20665	−	0.748603i	−1.44407	−	0.207625i	−0.819380	+	0.573251i	$0.805682\pi$
$14$	0.316685	−	0.0921710i	0.0846375	−	0.0246337i
$15$	−3.10932	+	1.54263i	−0.802824	+	0.398306i
$16$	3.38540	−	2.13051i	0.846349	−	0.532628i
$17$	1.75347	+	2.02361i	0.425279	+	0.490798i	0.927438	−	0.373978i	$-0.122006\pi$
$17$	1.75347	+	2.02361i	0.425279	+	0.490798i	−0.502159	+	0.864775i	$0.667461\pi$
$18$	0.632392	−	0.545348i	0.149056	−	0.128540i
$19$	−3.68072	+	4.24778i	−0.844415	+	0.974507i	−0.999911	−	0.0133292i	$-0.995757\pi$
$19$	−3.68072	+	4.24778i	−0.844415	+	0.974507i	0.155496	+	0.987837i	$0.450302\pi$
$20$	−4.01557	+	1.96855i	−0.897909	+	0.440181i
$21$	−0.329306	+	0.150389i	−0.0718606	+	0.0328176i
$22$	1.40837	−	4.75468i	0.300266	−	1.01370i
$23$	−4.70643	−	0.921685i	−0.981359	−	0.192185i
$23$	−4.70643	−	0.921685i	−0.981359	−	0.192185i
$24$	−3.33849	+	2.85144i	−0.681465	+	0.582048i
$25$	4.69704	−	1.71401i	0.939408	−	0.342802i
$26$	7.43901	+	0.0176601i	1.45891	+	0.00346343i
$27$	−3.64978	+	4.21207i	−0.702400	+	0.810613i
$28$	−0.425207	+	0.191751i	−0.0803566	+	0.0362375i
$29$	5.67191	+	6.54573i	1.05325	+	1.21551i	0.975834	+	0.218513i	$0.0701205\pi$
$29$	5.67191	+	6.54573i	1.05325	+	1.21551i	0.0774128	+	0.996999i	$0.475334\pi$
$30$	4.04862	−	2.77560i	0.739173	−	0.506753i
$31$	2.80982	−	9.56937i	0.504659	−	1.71871i	−0.174445	−	0.984667i	$-0.555813\pi$
$31$	2.80982	−	9.56937i	0.504659	−	1.71871i	0.679104	−	0.734042i	$-0.262369\pi$
$32$	−4.31883	+	3.65345i	−0.763469	+	0.645844i
$33$	−0.774613	+	5.38755i	−0.134843	+	0.937852i
$34$	−2.85592	−	2.48657i	−0.489787	−	0.426443i
$35$	0.495394	−	0.162931i	0.0837369	−	0.0275404i
$36$	−0.777588	+	0.888822i	−0.129598	+	0.148137i
$37$	5.96038	−	3.83050i	0.979880	−	0.629731i	0.0504489	−	0.998727i	$-0.483935\pi$
$37$	5.96038	−	3.83050i	0.979880	−	0.629731i	0.929431	+	0.368996i	$0.120298\pi$
$38$	4.31328	−	6.67670i	0.699707	−	1.08310i
$39$	−8.08210	+	1.16203i	−1.29417	+	0.186074i
$40$	5.23332	−	3.55139i	0.827461	−	0.561523i
$41$	−2.33881	−	1.50306i	−0.365261	−	0.234739i	0.345116	−	0.938560i	$-0.387839\pi$
$41$	−2.33881	−	1.50306i	−0.365261	−	0.234739i	−0.710378	+	0.703821i	$0.751476\pi$
$42$	0.431357	−	0.275772i	0.0665599	−	0.0425525i
$43$	2.30644	+	7.85501i	0.351729	+	1.19788i	0.925463	+	0.378837i	$0.123676\pi$
$43$	2.30644	+	7.85501i	0.351729	+	1.19788i	−0.573735	+	0.819041i	$0.694506\pi$
$44$	−1.03099	+	6.93672i	−0.155427	+	1.04575i
$45$	0.969542	−	0.896270i	0.144531	−	0.133608i
$46$	6.77282	+	0.359039i	0.998598	+	0.0529374i
$47$	−7.76422			−1.13253			−0.566264	−	0.824224i	$-0.691612\pi$
$47$	−7.76422			−1.13253			−0.566264	+	0.824224i	$0.691612\pi$
$48$	4.11044	−	4.65367i	0.593291	−	0.671699i
$49$	−6.66426	+	1.95680i	−0.952037	+	0.279543i
$50$	−6.23796	+	3.32984i	−0.882181	+	0.470911i
$51$	3.49656	+	2.24711i	0.489617	+	0.314658i
$52$	−10.4203	+	1.44775i	−1.44503	+	0.200767i
$53$	1.12277	+	7.80907i	0.154225	+	1.07266i	0.909036	+	0.416717i	$0.136819\pi$
$53$	1.12277	+	7.80907i	0.154225	+	1.07266i	−0.754811	+	0.655942i	$0.772272\pi$
$54$	4.27702	−	6.62057i	0.582029	−	0.900945i
$55$	1.96602	−	7.59020i	0.265097	−	1.02346i
$56$	0.557459	−	0.352673i	0.0744936	−	0.0471279i
$57$	−3.62436	+	7.93625i	−0.480059	+	1.05118i
$58$	−9.23799	−	8.04324i	−1.21301	−	1.05613i
$59$	−5.45147	−	0.783803i	−0.709721	−	0.102042i	−0.222006	−	0.975045i	$-0.571260\pi$
$59$	−5.45147	−	0.783803i	−0.709721	−	0.102042i	−0.487715	+	0.873003i	$0.662169\pi$
$60$	−5.11985	+	4.68803i	−0.660969	+	0.605222i
$61$	3.29243	−	11.2130i	0.421552	−	1.43567i	−0.425884	−	0.904778i	$-0.640037\pi$
$61$	3.29243	−	11.2130i	0.421552	−	1.43567i	0.847436	−	0.530897i	$-0.178145\pi$
$62$	−2.04041	+	13.9561i	−0.259132	+	1.77243i
$63$	0.104076	−	0.0901821i	0.0131123	−	0.0113619i
$64$	5.32447	−	5.97076i	0.665559	−	0.746345i
$65$	11.7561	−	0.378077i	1.45816	−	0.0468947i
$66$	0.0182737	−	7.69747i	0.00224934	−	0.947493i
$67$	−8.08383	+	3.69176i	−0.987597	+	0.451021i	−0.842675	−	0.538422i	$-0.819020\pi$
$67$	−8.08383	+	3.69176i	−0.987597	+	0.451021i	−0.144922	+	0.989443i	$0.546293\pi$
$68$	4.49132	+	2.91662i	0.544652	+	0.353692i
$69$	−7.41277	+	0.685487i	−0.892393	+	0.0825229i
$70$	−0.661446	+	0.326210i	−0.0790579	+	0.0389895i
$71$	−5.85329	+	2.67311i	−0.694657	+	0.317239i	−0.731268	−	0.682090i	$-0.761071\pi$
$71$	−5.85329	+	2.67311i	−0.694657	+	0.317239i	0.0366107	+	0.999330i	$0.488344\pi$
$72$	0.912918	−	1.39853i	0.107588	−	0.164818i
$73$	−0.213603	−	0.185088i	−0.0250004	−	0.0216629i	0.642271	−	0.766478i	$-0.277992\pi$
$73$	−0.213603	−	0.185088i	−0.0250004	−	0.0216629i	−0.667271	+	0.744815i	$0.732538\pi$
$74$	−7.58806	+	6.54362i	−0.882094	+	0.760680i
$75$	6.24613	−	4.60694i	0.721241	−	0.531964i
$76$	−4.71827	+	10.2031i	−0.541223	+	1.17038i
$77$	0.230396	−	0.784656i	0.0262560	−	0.0894199i
$78$	11.0873	−	3.22695i	1.25539	−	0.365380i
$79$	−0.786842	+	5.47261i	−0.0885266	+	0.615716i	0.896465	+	0.443114i	$0.146126\pi$
$79$	−0.786842	+	5.47261i	−0.0885266	+	0.615716i	−0.984992	+	0.172602i	$0.944783\pi$
$80$	−6.62522	+	6.00886i	−0.740722	+	0.671811i
$81$	−2.85802	+	6.25819i	−0.317558	+	0.695354i
$82$	3.57254	+	1.64179i	0.394521	+	0.181305i
$83$	3.35494	+	5.22039i	0.368253	+	0.573012i	0.975089	−	0.221815i	$-0.0711980\pi$
$83$	3.35494	+	5.22039i	0.368253	+	0.573012i	−0.606836	+	0.794827i	$0.707562\pi$
$84$	−0.549440	+	0.471544i	−0.0599489	+	0.0514497i
$85$	−4.64862	−	3.77340i	−0.504214	−	0.409283i
$86$	−4.78451	−	10.5428i	−0.515927	−	1.13686i
$87$	11.3103	+	7.26867i	1.21259	+	0.779283i
$88$	0.0706332	−	9.91751i	0.00752952	−	1.05721i
$89$	−3.13900	−	10.6904i	−0.332733	−	1.13318i	−0.940705	−	0.339226i	$-0.889835\pi$
$89$	−3.13900	−	10.6904i	−0.332733	−	1.13318i	0.607972	−	0.793958i	$-0.291983\pi$
$90$	−1.18023	+	1.44695i	−0.124408	+	0.152522i
$91$	1.22679			0.128603
$92$	−9.55500	+	0.837851i	−0.996178	+	0.0873521i
$93$		−	15.4813i		−	1.60533i
$94$	10.8722	−	1.53685i	1.12138	−	0.158514i
$95$	6.45145	−	10.7859i	0.661905	−	1.10661i
$96$	−4.83468	+	7.33012i	−0.493437	+	0.748127i
$97$	5.91382	+	3.80058i	0.600457	+	0.385890i	0.805268	−	0.592911i	$-0.202021\pi$
$97$	5.91382	+	3.80058i	0.600457	+	0.385890i	−0.204811	+	0.978802i	$0.565658\pi$
$98$	8.94459	−	4.05922i	0.903540	−	0.410043i
$99$	−0.294660	−	2.04941i	−0.0296145	−	0.205973i
$100$	8.07586	−	5.89750i	0.807586	−	0.589750i
$101$	7.10527	−	4.56628i	0.707001	−	0.454362i	−0.137092	−	0.990558i	$-0.543776\pi$
$101$	7.10527	−	4.56628i	0.707001	−	0.454362i	0.844093	+	0.536196i	$0.180139\pi$
$102$	−5.34101	−	2.45450i	−0.528838	−	0.243031i
$103$	10.4429	+	4.76909i	1.02897	+	0.469913i	0.857069	−	0.515202i	$-0.172283\pi$
$103$	10.4429	+	4.76909i	1.02897	+	0.469913i	0.171897	+	0.985115i	$0.445010\pi$
$104$	14.3049	−	4.08986i	1.40271	−	0.401044i
$105$	0.666579	−	0.459315i	0.0650515	−	0.0448246i
$106$	−3.11794	−	10.7127i	−0.302841	−	1.04051i
$107$	3.88835	−	13.2425i	0.375901	−	1.28020i	−0.526821	−	0.849976i	$-0.676616\pi$
$107$	3.88835	−	13.2425i	0.375901	−	1.28020i	0.902722	−	0.430224i	$-0.141566\pi$
$108$	−4.67861	+	10.1173i	−0.450199	+	0.973540i
$109$	5.18956	−	4.49678i	0.497070	−	0.430713i	−0.369902	−	0.929071i	$-0.620609\pi$
$109$	5.18956	−	4.49678i	0.497070	−	0.430713i	0.866972	+	0.498358i	$0.166063\pi$
$110$	−1.25059	+	11.0176i	−0.119240	+	1.05049i
$111$	7.20214	−	8.31171i	0.683597	−	0.788912i
$112$	−0.710798	+	0.604188i	−0.0671641	+	0.0570904i
$113$	−3.09602	−	6.77934i	−0.291249	−	0.637747i	0.706285	−	0.707927i	$-0.250370\pi$
$113$	−3.09602	−	6.77934i	−0.291249	−	0.637747i	−0.997534	+	0.0701808i	$0.977642\pi$
$114$	3.50427	−	11.8305i	0.328205	−	1.10803i
$115$	10.7220	+	0.197726i	0.999830	+	0.0184380i
$116$	14.5280	+	9.43433i	1.34889	+	0.875955i
$117$	2.82533	−	1.29029i	0.261202	−	0.119287i
$118$	7.78880	+	0.0184905i	0.717017	+	0.00170219i
$119$	−0.471950	−	0.408947i	−0.0432636	−	0.0374881i
$120$	6.24133	−	7.57804i	0.569753	−	0.691777i
$121$	−0.848213	−	0.978890i	−0.0771103	−	0.0889900i
$122$	−2.39087	+	16.3532i	−0.216459	+	1.48055i
$123$	−4.14072	−	1.21583i	−0.373356	−	0.109627i
$124$	0.0947059	−	19.9465i	0.00850484	−	1.79125i
$125$	−9.67548	+	5.60224i	−0.865401	+	0.501080i
$126$	−0.127886	+	0.146882i	−0.0113930	+	0.0130853i
$127$	−3.68609	+	8.07141i	−0.327087	+	0.716222i	−0.999718	−	0.0237571i	$-0.992437\pi$
$127$	−3.68609	+	8.07141i	−0.327087	+	0.716222i	0.672630	+	0.739979i	$0.265164\pi$
$128$	−6.27396	+	9.41474i	−0.554545	+	0.832153i
$129$	6.87036	+	10.6905i	0.604902	+	0.941245i
$130$	−16.3871	+	2.85641i	−1.43724	+	0.250524i
$131$	17.1296	−	2.46286i	1.49662	−	0.215181i	0.655154	−	0.755495i	$-0.272604\pi$
$131$	17.1296	−	2.46286i	1.49662	−	0.215181i	0.841463	+	0.540314i	$0.181695\pi$
$132$	1.49805	+	10.7823i	0.130388	+	0.938482i
$133$	0.708699	−	1.10276i	0.0614520	−	0.0956212i
$134$	10.5890	−	6.76966i	0.914749	−	0.584810i
$135$	6.39722	−	10.6952i	0.550585	−	0.920498i
$136$	−6.86648	−	3.19511i	−0.588795	−	0.273978i
$137$	−0.230142			−0.0196623			−0.00983117	−	0.999952i	$-0.503129\pi$
$137$	−0.230142			−0.0196623			−0.00983117	+	0.999952i	$0.503129\pi$
$138$	10.2444	−	2.42716i	0.872058	−	0.206614i
$139$			9.10387i			0.772181i	0.922461	+	0.386090i	$0.126175\pi$
$139$			9.10387i			0.772181i	−0.922461	+	0.386090i	$0.873825\pi$
$140$	0.861648	−	0.587716i	0.0728225	−	0.0496710i
$141$	−11.5639	+	3.39548i	−0.973859	+	0.285951i
$142$	7.66720	−	4.90173i	0.643417	−	0.411344i
$143$	9.97193	−	15.5166i	0.833895	−	1.29757i
$144$	−1.00153	+	2.13905i	−0.0834606	+	0.178254i
$145$	−15.0368	−	12.2057i	−1.24874	−	1.01363i
$146$	0.335743	+	0.216897i	0.0277863	+	0.0179505i
$147$	−9.06991	+	5.82887i	−0.748073	+	0.480757i
$148$	9.33027	−	10.6650i	0.766943	−	0.876655i
$149$	13.0458	+	5.95781i	1.06875	+	0.488083i	0.870551	−	0.492078i	$-0.163763\pi$
$149$	13.0458	+	5.95781i	1.06875	+	0.488083i	0.198202	+	0.980161i	$0.436490\pi$
$150$	−7.83451	+	7.68743i	−0.639685	+	0.627676i
$151$	−6.07665	−	0.873690i	−0.494510	−	0.0710999i	−0.109452	−	0.993992i	$-0.534910\pi$
$151$	−6.07665	−	0.873690i	−0.494510	−	0.0710999i	−0.385058	+	0.922892i	$0.625819\pi$
$152$	4.58737	−	15.2213i	0.372084	−	1.23461i
$153$	−1.51703	−	0.445439i	−0.122644	−	0.0360116i
$154$	−0.167307	+	1.14435i	−0.0134820	+	0.0922146i
$155$	−2.46260	+	22.1647i	−0.197801	+	1.78031i
$156$	−14.8867	+	6.71329i	−1.19189	+	0.537494i
$157$	−2.66285	+	3.07309i	−0.212518	+	0.245259i	−0.851993	−	0.523553i	$-0.824606\pi$
$157$	−2.66285	+	3.07309i	−0.212518	+	0.245259i	0.639475	+	0.768812i	$0.279152\pi$
$158$	0.0185622	−	7.81900i	0.00147673	−	0.622046i
$159$	5.08733	+	11.1397i	0.403452	+	0.883436i
$160$	8.08786	−	9.72556i	0.639401	−	0.768873i
$161$	1.11706	+	0.0565583i	0.0880367	+	0.00445742i
$162$	2.76332	−	9.32901i	0.217107	−	0.732956i
$163$	−0.289985	−	0.634979i	−0.0227134	−	0.0497354i	0.897935	−	0.440127i	$-0.145067\pi$
$163$	−0.289985	−	0.634979i	−0.0227134	−	0.0497354i	−0.920649	+	0.390392i	$0.872339\pi$
$164$	−5.32758	−	1.59183i	−0.416014	−	0.124301i
$165$	−0.391213	−	12.1645i	−0.0304559	−	0.947007i
$166$	−5.73122	−	6.64600i	−0.444829	−	0.515829i
$167$	−11.9775	−	13.8228i	−0.926850	−	1.06964i	−0.997395	−	0.0721334i	$-0.977019\pi$
$167$	−11.9775	−	13.8228i	−0.926850	−	1.06964i	0.0705449	−	0.997509i	$-0.477526\pi$
$168$	0.676040	−	0.769056i	0.0521576	−	0.0593340i
$169$	14.0754	+	4.13291i	1.08272	+	0.317916i
$170$	7.25634	+	4.36372i	0.556536	+	0.334682i
$171$	0.472320	−	3.28506i	0.0361192	−	0.251215i
$172$	8.78655	+	13.8159i	0.669968	+	1.05346i
$173$	−7.22689	−	3.30041i	−0.549450	−	0.250925i	0.121291	−	0.992617i	$-0.461297\pi$
$173$	−7.22689	−	3.30041i	−0.549450	−	0.250925i	−0.670741	+	0.741692i	$0.734024\pi$
$174$	−17.2764	−	7.93951i	−1.30972	−	0.601893i
$175$	−1.02741	+	0.551574i	−0.0776650	+	0.0416951i
$176$	1.86416	+	13.9014i	0.140517	+	1.04786i
$177$	−8.46212	+	1.21667i	−0.636052	+	0.0914505i
$178$	6.51158	+	14.3484i	0.488063	+	1.07546i
$179$	−3.89446	+	6.05990i	−0.291085	+	0.452938i	−0.955740	−	0.294213i	$-0.904942\pi$
$179$	−3.89446	+	6.05990i	−0.291085	+	0.452938i	0.664654	+	0.747151i	$0.268579\pi$
$180$	1.36627	−	2.25977i	0.101835	−	0.168433i
$181$	2.88561	+	9.82749i	0.214486	+	0.730471i	0.994503	+	0.104713i	$0.0333923\pi$
$181$	2.88561	+	9.82749i	0.214486	+	0.730471i	−0.780017	+	0.625759i	$0.784790\pi$
$182$	−1.71787	+	0.242831i	−0.127337	+	0.0179998i
$183$		−	18.1403i		−	1.34097i
$184$	13.2140	−	3.06455i	0.974145	−	0.225922i
$185$	−11.6335	+	10.7543i	−0.855313	+	0.790674i
$186$	3.06436	+	21.6783i	0.224690	+	1.58953i
$187$	−9.00865	+	2.64518i	−0.658778	+	0.193435i
$188$	−14.9200	+	4.30408i	−1.08816	+	0.313907i
$189$	0.702741	−	1.09349i	0.0511169	−	0.0795394i
$190$	−6.89897	+	16.3804i	−0.500504	+	1.18836i
$191$	1.24205	+	8.63863i	0.0898714	+	0.625070i	0.984121	+	0.177500i	$0.0568011\pi$
$191$	1.24205	+	8.63863i	0.0898714	+	0.625070i	−0.894249	+	0.447569i	$0.852290\pi$
$192$	5.31904	−	11.2213i	0.383869	−	0.809827i
$193$	4.34608	+	6.76263i	0.312838	+	0.486785i	0.961694	−	0.274126i	$-0.0883887\pi$
$193$	4.34608	+	6.76263i	0.312838	+	0.486785i	−0.648856	+	0.760911i	$0.724752\pi$
$194$	−9.03336	−	4.15135i	−0.648558	−	0.298049i
$195$	17.3440	−	5.70431i	1.24203	−	0.408494i
$196$	−11.7216	+	7.45459i	−0.837254	+	0.532471i
$197$	−8.34579	−	1.19994i	−0.594613	−	0.0854924i	−0.161563	−	0.986862i	$-0.551654\pi$
$197$	−8.34579	−	1.19994i	−0.594613	−	0.0854924i	−0.433050	+	0.901370i	$0.642563\pi$
$198$	0.818270	+	2.81144i	0.0581519	+	0.199801i
$199$	−21.4053	−	6.28517i	−1.51738	−	0.445544i	−0.586222	−	0.810150i	$-0.699385\pi$
$199$	−21.4053	−	6.28517i	−1.51738	−	0.445544i	−0.931162	+	0.364606i	$0.881204\pi$
$200$	−10.1412	+	9.85676i	−0.717093	+	0.696978i
$201$	−10.4255	+	9.03371i	−0.735355	+	0.637189i
$202$	−9.04561	+	7.80055i	−0.636447	+	0.548845i
$203$	−1.52661	−	1.32281i	−0.107147	−	0.0928432i
$204$	7.96482	+	2.37982i	0.557649	+	0.166620i
$205$	5.73492	+	2.39937i	0.400544	+	0.167580i
$206$	−15.5671	−	4.61107i	−1.08461	−	0.321268i
$207$	2.63211	−	1.04462i	0.182944	−	0.0726062i
$208$	−19.2215	+	8.55851i	−1.33277	+	0.593426i
$209$	−8.18719	−	17.9275i	−0.566320	−	1.24007i
$210$	−0.842489	+	0.775118i	−0.0581373	+	0.0534882i
$211$	−3.74238	−	3.24279i	−0.257636	−	0.223243i	0.516460	−	0.856312i	$-0.327250\pi$
$211$	−3.74238	−	3.24279i	−0.257636	−	0.223243i	−0.774096	+	0.633069i	$0.781795\pi$
$212$	6.48651	+	14.3838i	0.445495	+	0.987884i
$213$	−7.54879	+	6.54107i	−0.517235	+	0.448187i
$214$	−2.82361	+	19.3130i	−0.193018	+	1.32021i
$215$	−8.13584	−	16.3986i	−0.554860	−	1.11837i
$216$	4.54880	−	15.0933i	0.309507	−	1.02697i
$217$	−0.331025	+	2.30233i	−0.0224714	+	0.156292i
$218$	−6.37681	+	7.32403i	−0.431892	+	0.496046i
$219$	−0.399081	−	0.182254i	−0.0269674	−	0.0123156i
$220$	−0.429633	−	15.6755i	−0.0289659	−	1.05684i
$221$	−7.61482	−	11.8489i	−0.512228	−	0.797042i
$222$	−8.43988	+	13.0644i	−0.566448	+	0.876826i
$223$	1.25498	+	8.72858i	0.0840397	+	0.584509i	0.987712	+	0.156285i	$0.0499517\pi$
$223$	1.25498	+	8.72858i	0.0840397	+	0.584509i	−0.903672	+	0.428225i	$0.859139\pi$
$224$	0.875732	−	0.986736i	0.0585123	−	0.0659291i
$225$	−1.78604	+	2.35088i	−0.119069	+	0.156725i
$226$	5.67724	+	8.88023i	0.377644	+	0.590704i
$227$	0.460798	+	1.56933i	0.0305842	+	0.104160i	0.973371	−	0.229237i	$-0.0736231\pi$
$227$	0.460798	+	1.56933i	0.0305842	+	0.104160i	−0.942786	+	0.333397i	$0.891805\pi$
$228$	−2.56528	+	17.2598i	−0.169890	+	1.14306i
$229$			19.7530i			1.30531i	0.757654	+	0.652656i	$0.226345\pi$
$229$			19.7530i			1.30531i	−0.757654	+	0.652656i	$0.773655\pi$
$230$	−15.0531	+	1.84543i	−0.992569	+	0.121684i
$231$		−	1.26941i		−	0.0835213i
$232$	−22.2108	−	10.3352i	−1.45821	−	0.678536i
$233$	2.59091	+	8.82384i	0.169736	+	0.578069i	0.999792	+	0.0203885i	$0.00649030\pi$
$233$	2.59091	+	8.82384i	0.169736	+	0.578069i	−0.830056	+	0.557680i	$0.811692\pi$
$234$	−3.70089	+	2.36603i	−0.241935	+	0.154672i
$235$	17.0963	−	3.02187i	1.11524	−	0.197125i
$236$	−10.9103	+	1.51582i	−0.710197	+	0.0986716i
$237$	1.22139	+	8.49493i	0.0793376	+	0.551805i
$238$	0.741815	+	0.479228i	0.0480847	+	0.0310637i
$239$	6.32207	+	9.83733i	0.408940	+	0.636324i	0.983239	−	0.182322i	$-0.0583614\pi$
$239$	6.32207	+	9.83733i	0.408940	+	0.636324i	−0.574298	+	0.818646i	$0.694725\pi$
$240$	−7.23970	+	11.8469i	−0.467321	+	0.764713i
$241$	13.1561	+	6.00820i	0.847461	+	0.387022i	0.791321	−	0.611400i	$-0.209394\pi$
$241$	13.1561	+	6.00820i	0.847461	+	0.387022i	0.0561396	+	0.998423i	$0.482121\pi$
$242$	1.38151	+	1.20284i	0.0888067	+	0.0773213i
$243$	0.859676	−	5.97918i	0.0551483	−	0.383565i
$244$	0.110972	−	23.3725i	0.00710428	−	1.49627i
$245$	13.9127	−	6.90252i	0.888848	−	0.440986i
$246$	6.03889	+	0.882898i	0.385025	+	0.0562915i
$247$	22.3441	−	19.3613i	1.42172	−	1.23193i
$248$	3.81559	+	27.9497i	0.242290	+	1.77481i
$249$	7.27980	+	6.30798i	0.461339	+	0.399752i
$250$	12.4396	−	9.75994i	0.786749	−	0.617273i
$251$	5.33322	+	11.6781i	0.336630	+	0.737117i	0.999937	−	0.0112307i	$-0.00357493\pi$
$251$	5.33322	+	11.6781i	0.336630	+	0.737117i	−0.663307	+	0.748347i	$0.730848\pi$
$252$	0.150004	−	0.230992i	0.00944934	−	0.0145511i
$253$	9.79535	−	13.6690i	0.615829	−	0.859364i
$254$	3.56395	−	12.0320i	0.223622	−	0.754952i
$255$	−8.57379	−	3.58710i	−0.536912	−	0.224633i
$256$	6.92183	−	14.4253i	0.432615	−	0.901579i
$257$	16.2156	+	14.0509i	1.01150	+	0.876471i	0.992364	−	0.123346i	$-0.0393626\pi$
$257$	16.2156	+	14.0509i	1.01150	+	0.876471i	0.0191373	+	0.999817i	$0.493908\pi$
$258$	−11.7366	−	13.6099i	−0.730688	−	0.847315i
$259$	−1.24880	+	1.08209i	−0.0775968	+	0.0672380i
$260$	22.3813	−	7.24348i	1.38803	−	0.449221i
$261$	−4.90709	−	1.44085i	−0.303742	−	0.0891866i
$262$	−23.4989	+	6.83935i	−1.45177	+	0.422536i
$263$	−16.6009	−	2.38685i	−1.02366	−	0.147180i	−0.390017	−	0.920808i	$-0.627531\pi$
$263$	−16.6009	−	2.38685i	−1.02366	−	0.147180i	−0.633640	+	0.773628i	$0.718440\pi$
$264$	−4.23196	−	14.8019i	−0.260459	−	0.910994i
$265$	−5.51161	−	16.7581i	−0.338575	−	1.02944i
$266$	−0.774106	+	1.68446i	−0.0474635	+	0.103281i
$267$	−9.35035	−	14.5494i	−0.572232	−	0.890411i
$268$	−13.4877	+	11.5755i	−0.823892	+	0.707086i
$269$	−2.24502	−	15.6144i	−0.136881	−	0.952030i	−0.936286	−	0.351237i	$-0.885761\pi$
$269$	−2.24502	−	15.6144i	−0.136881	−	0.952030i	0.799405	−	0.600792i	$-0.205148\pi$
$270$	−6.84097	+	16.2427i	−0.416328	+	0.988499i
$271$	−5.35494	+	8.33245i	−0.325289	+	0.506160i	−0.964928	−	0.262516i	$-0.915448\pi$
$271$	−5.35494	+	8.33245i	−0.325289	+	0.506160i	0.639638	+	0.768676i	$0.279084\pi$
$272$	10.2475	+	3.11494i	0.621347	+	0.188871i
$273$	1.82717	−	0.536504i	0.110585	−	0.0324707i
$274$	0.322266	−	0.0455542i	0.0194688	−	0.00275203i
$275$	−1.37490	+	17.4783i	−0.0829095	+	1.05398i
$276$	−13.8647	+	5.42651i	−0.834555	+	0.326637i
$277$		−	6.36187i		−	0.382248i	−0.981566	−	0.191124i	$-0.938787\pi$
$277$		−	6.36187i		−	0.382248i	0.981566	−	0.191124i	$-0.0612132\pi$
$278$	−1.80202	−	12.7481i	−0.108078	−	0.764580i
$279$	1.65913	+	5.65048i	0.0993296	+	0.338286i
$280$	−1.09023	+	0.993528i	−0.0651535	+	0.0593747i
$281$	−3.78800	+	5.89424i	−0.225973	+	0.351621i	−0.935664	−	0.352892i	$-0.885198\pi$
$281$	−3.78800	+	5.89424i	−0.225973	+	0.351621i	0.709691	+	0.704513i	$0.248835\pi$
$282$	15.5208	−	7.04362i	0.924249	−	0.419442i
$283$	−7.21331	+	1.03712i	−0.428787	+	0.0616503i	−0.353330	−	0.935499i	$-0.614951\pi$
$283$	−7.21331	+	1.03712i	−0.428787	+	0.0616503i	−0.0754571	+	0.997149i	$0.524042\pi$
$284$	−9.76608	+	8.38150i	−0.579510	+	0.497351i
$285$	4.89179	−	18.8857i	0.289765	−	1.11869i
$286$	−10.8923	+	23.7017i	−0.644073	+	1.40151i
$287$	0.589798	+	0.269352i	0.0348147	+	0.0158993i
$288$	0.979029	−	3.19354i	0.0576898	−	0.188181i
$289$	1.39900	−	9.73029i	0.0822944	−	0.572370i
$290$	23.4719	+	14.1152i	1.37832	+	0.828875i
$291$	10.4700	+	3.07428i	0.613765	+	0.180218i
$292$	−0.513071	−	0.237262i	−0.0300252	−	0.0138847i
$293$	6.02299	+	6.95090i	0.351867	+	0.406076i	0.903898	−	0.427747i	$-0.140693\pi$
$293$	6.02299	+	6.95090i	0.351867	+	0.406076i	−0.552031	+	0.833823i	$0.686147\pi$
$294$	11.5468	−	9.95743i	0.673421	−	0.580729i
$295$	12.3088	−	0.395854i	0.716649	−	0.0230475i
$296$	−10.9541	+	16.7809i	−0.636693	+	0.975370i
$297$	−8.11837	−	17.7767i	−0.471075	−	1.03151i
$298$	−19.4472	−	5.76040i	−1.12655	−	0.333691i
$299$	23.8148	+	8.32214i	1.37724	+	0.481282i
$300$	9.44897	−	12.3154i	0.545536	−	0.711031i
$301$	−0.793152	−	1.73676i	−0.0457165	−	0.100105i
$302$	8.68202	+	0.0206110i	0.499594	+	0.00118603i
$303$	8.58556	−	9.90826i	0.493227	−	0.569215i
$304$	−3.41076	+	22.2222i	−0.195621	+	1.27453i
$305$	−2.88557	+	25.9717i	−0.165227	+	1.48713i
$306$	2.21245	+	0.323465i	0.126477	+	0.0184913i
$307$	23.3355	+	6.85191i	1.33182	+	0.391059i	0.868746	−	0.495258i	$-0.164926\pi$
$307$	23.3355	+	6.85191i	1.33182	+	0.391059i	0.463079	+	0.886317i	$0.346745\pi$
$308$	0.00776557	−	1.63555i	0.000442484	−	0.0931939i
$309$	17.6391	+	2.53612i	1.00345	+	0.144275i
$310$	−0.938924	−	31.5245i	−0.0533273	−	1.79047i
$311$	−25.9286	−	11.8412i	−1.47028	−	0.671453i	−0.490481	−	0.871452i	$-0.663179\pi$
$311$	−25.9286	−	11.8412i	−1.47028	−	0.671453i	−0.979796	+	0.199999i	$0.935906\pi$
$312$	19.5169	−	12.3473i	1.10493	−	0.699025i
$313$	3.28937	−	2.11395i	0.185926	−	0.119488i	−0.444367	−	0.895845i	$-0.646571\pi$
$313$	3.28937	−	2.11395i	0.185926	−	0.119488i	0.630293	+	0.776357i	$0.282935\pi$
$314$	3.12048	−	4.83031i	0.176099	−	0.272590i
$315$	−0.194069	+	0.239082i	−0.0109345	+	0.0134707i
$316$	1.52170	+	10.9526i	0.0856023	+	0.616130i
$317$	3.06786	−	4.77368i	0.172308	−	0.268116i	−0.744349	−	0.667790i	$-0.767240\pi$
$317$	3.06786	−	4.77368i	0.172308	−	0.268116i	0.916657	+	0.399674i	$0.130877\pi$
$318$	−9.32875	−	14.5919i	−0.523130	−	0.818271i
$319$	−29.1401	+	8.55630i	−1.63153	+	0.479061i
$320$	−9.40029	+	15.2195i	−0.525492	+	0.850798i
$321$		−	21.4237i		−	1.19575i
$322$	−1.57541	+	0.141913i	−0.0877940	+	0.00790848i
$323$	−15.0499			−0.837398
$324$	−2.02287	+	13.6103i	−0.112382	+	0.756128i
$325$	−25.7390	+	5.40802i	−1.42774	+	0.299983i
$326$	0.531752	+	0.831757i	0.0294510	+	0.0460668i
$327$	5.76271	−	8.96696i	0.318679	−	0.495874i
$328$	7.77526	+	1.17449i	0.429317	+	0.0648504i
$329$	1.79235	−	0.257702i	0.0988157	−	0.0142075i
$330$	2.95566	+	16.9565i	0.162704	+	0.933422i
$331$	−7.49810	−	11.6673i	−0.412133	−	0.641292i	0.571683	−	0.820475i	$-0.306291\pi$
$331$	−7.49810	−	11.6673i	−0.412133	−	0.641292i	−0.983816	+	0.179183i	$0.942654\pi$
$332$	9.34090	+	8.17190i	0.512648	+	0.448491i
$333$	−1.73793	+	3.80553i	−0.0952378	+	0.208542i
$334$	19.5082	+	16.9852i	1.06744	+	0.929387i
$335$	16.3632	−	11.2753i	0.894018	−	0.616035i
$336$	−0.794427	+	1.21072i	−0.0433396	+	0.0660501i
$337$	1.61446	+	0.474049i	0.0879453	+	0.0258231i	0.325409	−	0.945573i	$-0.394498\pi$
$337$	1.61446	+	0.474049i	0.0879453	+	0.0258231i	−0.237464	+	0.971396i	$0.576316\pi$
$338$	−20.5277	−	3.00120i	−1.11656	−	0.163244i
$339$	−7.57593	−	8.74309i	−0.411468	−	0.474860i
$340$	−11.0248	−	4.67417i	−0.597901	−	0.253492i
$341$	26.4295	+	22.9012i	1.43123	+	1.24017i
$342$	−0.0111424	+	4.69354i	−0.000602511	+	0.253797i
$343$	2.95850	−	1.35110i	0.159744	−	0.0729527i
$344$	−15.0385	−	17.6071i	−0.810820	−	0.949314i
$345$	16.0556	−	4.39448i	0.864407	−	0.236591i
$346$	10.7730	+	3.19105i	0.579162	+	0.171552i
$347$	1.93426	+	4.23545i	0.103837	+	0.227371i	0.954418	−	0.298472i	$-0.0964771\pi$
$347$	1.93426	+	4.23545i	0.103837	+	0.227371i	−0.850581	+	0.525843i	$0.823750\pi$
$348$	25.7636	+	7.69794i	1.38107	+	0.412653i
$349$	−18.9596	+	21.8805i	−1.01488	+	1.17124i	−0.0297300	+	0.999558i	$0.509465\pi$
$349$	−18.9596	+	21.8805i	−1.01488	+	1.17124i	−0.985153	+	0.171679i	$0.945081\pi$
$350$	1.32950	−	0.975731i	0.0710647	−	0.0521550i
$351$	22.1563	−	19.1985i	1.18262	−	1.02474i
$352$	−5.36202	−	19.0970i	−0.285796	−	1.01788i
$353$	0.617765	−	2.10391i	0.0328803	−	0.111980i	−0.941418	−	0.337242i	$-0.890506\pi$
$353$	0.617765	−	2.10391i	0.0328803	−	0.111980i	0.974298	+	0.225262i	$0.0723240\pi$
$354$	11.6086	−	3.37868i	0.616991	−	0.179575i
$355$	11.8482	−	8.16414i	0.628836	−	0.433307i
$356$	−11.9582	−	18.8031i	−0.633785	−	0.996561i
$357$	−0.881758	−	0.402685i	−0.0466676	−	0.0213124i
$358$	4.25389	−	9.25650i	0.224825	−	0.489221i
$359$	−10.2504	+	6.58751i	−0.540994	+	0.347676i	−0.782428	−	0.622742i	$-0.786019\pi$
$359$	−10.2504	+	6.58751i	−0.540994	+	0.347676i	0.241434	+	0.970417i	$0.422382\pi$
$360$	−1.46587	+	3.43478i	−0.0772583	+	0.181029i
$361$	−1.79193	−	12.4632i	−0.0943123	−	0.655957i
$362$	−5.98595	−	13.1902i	−0.314615	−	0.693260i
$363$	−1.69141	−	1.08700i	−0.0887759	−	0.0570528i
$364$	2.35745	−	0.680068i	0.123564	−	0.0356453i
$365$	0.542378	+	0.324417i	0.0283893	+	0.0169808i
$366$	3.59069	+	25.4018i	0.187688	+	1.32777i
$367$			27.7397i			1.44800i	0.689800	+	0.724000i	$0.257699\pi$
$367$			27.7397i			1.44800i	−0.689800	+	0.724000i	$0.742301\pi$
$368$	−17.8968	+	6.90684i	−0.932935	+	0.360044i
$369$	1.64161			0.0854590
$370$	14.1616	−	17.3619i	0.736227	−	0.902604i
$371$	−0.518380	−	1.76544i	−0.0269130	−	0.0916571i
$372$	−8.58201	−	29.7495i	−0.444957	−	1.54244i
$373$	18.7917	+	12.0767i	0.972996	+	0.625306i	0.927565	−	0.373661i	$-0.121898\pi$
$373$	18.7917	+	12.0767i	0.972996	+	0.625306i	0.0454304	+	0.998968i	$0.485534\pi$
$374$	12.0912	−	5.48719i	0.625219	−	0.283736i
$375$	−11.9605	+	12.5752i	−0.617639	+	0.649382i
$376$	20.0405	−	8.98024i	1.03351	−	0.463121i
$377$	−24.6315	−	38.3273i	−1.26859	−	1.97396i
$378$	−0.767599	+	1.67030i	−0.0394810	+	0.0859111i
$379$	−5.95074	+	13.0303i	−0.305669	+	0.669322i	−0.998667	−	0.0516176i	$-0.983562\pi$
$379$	−5.95074	+	13.0303i	−0.305669	+	0.669322i	0.692998	+	0.720940i	$0.256290\pi$
$380$	6.41824	−	24.3029i	0.329249	−	1.24671i
$381$	−1.96020	+	13.6335i	−0.100424	+	0.698463i
$382$	−3.44916	−	11.8508i	−0.176474	−	0.606338i
$383$	0.238527	−	0.812348i	0.0121882	−	0.0415091i	−0.953174	−	0.302421i	$-0.902205\pi$
$383$	0.238527	−	0.812348i	0.0121882	−	0.0415091i	0.965363	+	0.260912i	$0.0840233\pi$
$384$	−5.22707	+	16.7659i	−0.266743	+	0.855583i
$385$	−0.201925	+	1.81743i	−0.0102910	+	0.0926250i
$386$	−7.42438	−	8.60940i	−0.377891	−	0.438207i
$387$	−3.65330	−	3.16560i	−0.185708	−	0.160917i
$388$	13.4711	+	4.02504i	0.683890	+	0.204340i
$389$	−26.6017	+	12.1486i	−1.34876	+	0.615958i	−0.953161	−	0.302465i	$-0.902191\pi$
$389$	−26.6017	+	12.1486i	−1.34876	+	0.615958i	−0.395600	+	0.918423i	$0.629463\pi$
$390$	−23.1576	+	11.4208i	−1.17263	+	0.578313i
$391$	−6.38745	−	11.1401i	−0.323027	−	0.563381i
$392$	14.9381	−	12.7588i	0.754486	−	0.644415i
$393$	24.4355	−	11.1593i	1.23261	−	0.562913i
$394$	11.9241	+	0.0283076i	0.600726	+	0.00142611i
$395$	−0.397389	−	12.3566i	−0.0199948	−	0.621726i
$396$	−1.70231	−	3.77488i	−0.0855445	−	0.189695i
$397$	−24.3061	+	21.0613i	−1.21989	+	1.05704i	−0.223277	+	0.974755i	$0.571675\pi$
$397$	−24.3061	+	21.0613i	−1.21989	+	1.05704i	−0.996609	+	0.0822821i	$0.973779\pi$
$398$	31.2178	+	4.56411i	1.56481	+	0.228778i
$399$	0.573265	−	1.95236i	0.0286992	−	0.0977403i
$400$	12.2496	−	15.8097i	0.612482	−	0.790485i
$401$	24.0759	+	3.46159i	1.20229	+	0.172864i	0.714209	−	0.699933i	$-0.246787\pi$
$401$	24.0759	+	3.46159i	1.20229	+	0.172864i	0.488084	+	0.872797i	$0.337696\pi$
$402$	12.8106	−	14.7135i	0.638933	−	0.733840i
$403$	−21.7934	+	47.7209i	−1.08561	+	2.37715i
$404$	11.1225	−	12.7135i	0.553363	−	0.632522i
$405$	3.85745	−	14.8925i	0.191678	−	0.740013i
$406$	2.39953	+	1.55015i	0.119087	+	0.0769325i
$407$	3.53562	+	24.5908i	0.175254	+	1.21892i
$408$	−11.6241	−	1.75588i	−0.575480	−	0.0869292i
$409$	−28.0844	−	18.0487i	−1.38868	−	0.892453i	−0.389097	−	0.921197i	$-0.627213\pi$
$409$	−28.0844	−	18.0487i	−1.38868	−	0.892453i	−0.999587	+	0.0287442i	$0.990849\pi$
$410$	−8.50550	−	2.22466i	−0.420056	−	0.109868i
$411$	−0.342770	+	0.100646i	−0.0169076	+	0.00496452i
$412$	22.7111	+	3.37551i	1.11890	+	0.166299i
$413$	1.28447			0.0632049
$414$	−3.47895	+	1.98378i	−0.170981	+	0.0974973i
$415$	−9.41916	−	10.1892i	−0.462368	−	0.500168i
$416$	25.2216	−	15.7891i	1.23659	−	0.774126i
$417$	3.98134	+	13.5592i	0.194967	+	0.663996i
$418$	15.0130	+	23.4831i	0.734311	+	1.14860i
$419$	10.5857	+	6.80304i	0.517147	+	0.332350i	0.773043	−	0.634354i	$-0.218734\pi$
$419$	10.5857	+	6.80304i	0.517147	+	0.332350i	−0.255895	+	0.966704i	$0.582370\pi$
$420$	1.02631	−	1.25215i	0.0500786	−	0.0610989i
$421$	−10.0781	+	1.44901i	−0.491176	+	0.0706205i	−0.383453	−	0.923560i	$-0.625265\pi$
$421$	−10.0781	+	1.44901i	−0.491176	+	0.0706205i	−0.107723	+	0.994181i	$0.534356\pi$
$422$	5.88230	+	3.80009i	0.286346	+	0.184985i
$423$	3.85680	−	2.47862i	0.187524	−	0.120514i
$424$	−11.9301	−	18.8576i	−0.579379	−	0.915806i
$425$	11.7046	+	6.49952i	0.567756	+	0.315273i
$426$	9.27578	−	10.6536i	0.449413	−	0.516169i
$427$	−0.387881	+	2.69777i	−0.0187709	+	0.130554i
$428$	0.131058	−	27.6028i	0.00633493	−	1.33423i
$429$	8.06628	−	27.4712i	0.389443	−	1.32632i
$430$	14.6385	+	21.3524i	0.705930	+	1.02970i
$431$	10.2753	+	11.8583i	0.494942	+	0.571194i	0.947180	−	0.320704i	$-0.103919\pi$
$431$	10.2753	+	11.8583i	0.494942	+	0.571194i	−0.452237	+	0.891898i	$0.649374\pi$
$432$	−3.38209	+	22.0354i	−0.162721	+	1.06018i
$433$	11.7882	−	13.6043i	0.566505	−	0.653782i	−0.398143	−	0.917323i	$-0.630345\pi$
$433$	11.7882	−	13.6043i	0.566505	−	0.653782i	0.964648	+	0.263542i	$0.0848906\pi$
$434$	0.00780912	−	3.28946i	0.000374850	−	0.157899i
$435$	−27.7335	−	11.6031i	−1.32972	−	0.556327i
$436$	7.47968	−	11.5180i	0.358212	−	0.551612i
$437$	21.2382	−	16.5994i	1.01596	−	0.794058i
$438$	0.594906	+	0.176215i	0.0284257	+	0.00841989i
$439$	−16.0111	+	7.31202i	−0.764167	+	0.348984i	−0.759075	−	0.651003i	$-0.774348\pi$
$439$	−16.0111	+	7.31202i	−0.764167	+	0.348984i	−0.00509264	+	0.999987i	$0.501621\pi$
$440$	3.70441	+	21.8652i	0.176601	+	1.04238i
$441$	2.68573	−	3.09949i	0.127892	−	0.147595i
$442$	13.0083	+	15.0846i	0.618744	+	0.717503i
$443$	16.1721	+	18.6636i	0.768358	+	0.886732i	0.996212	−	0.0869632i	$-0.0277163\pi$
$443$	16.1721	+	18.6636i	0.768358	+	0.886732i	−0.227854	+	0.973695i	$0.573171\pi$
$444$	9.23234	−	19.9646i	0.438147	−	0.947478i
$445$	11.0726	+	22.3179i	0.524893	+	1.05797i
$446$	−3.48507	−	11.9742i	−0.165023	−	0.566993i
$447$	22.0357	+	3.16826i	1.04225	+	0.149853i
$448$	−1.03097	+	1.55506i	−0.0487086	+	0.0734698i
$449$	−4.03991	+	8.84616i	−0.190655	+	0.417476i	−0.980685	−	0.195591i	$-0.937337\pi$
$449$	−4.03991	+	8.84616i	−0.190655	+	0.417476i	0.790031	+	0.613068i	$0.210065\pi$
$450$	2.03564	−	3.64545i	0.0959610	−	0.171848i
$451$	8.20096	−	5.27043i	0.386168	−	0.248175i
$452$	−9.70755	−	11.3112i	−0.456605	−	0.532033i
$453$	−9.43256	+	1.35620i	−0.443180	+	0.0637197i
$454$	−0.955885	−	2.10631i	−0.0448619	−	0.0988542i
$455$	−2.70131	+	0.477473i	−0.126640	+	0.0223843i
$456$	0.175748	−	24.6765i	0.00823014	−	1.15558i
$457$	2.27947	−	0.669314i	0.106629	−	0.0313092i	−0.227983	−	0.973665i	$-0.573213\pi$
$457$	2.27947	−	0.669314i	0.106629	−	0.0313092i	0.334612	+	0.942356i	$0.391395\pi$
$458$	−3.90990	−	27.6599i	−0.182697	−	1.29246i
$459$	−14.9234			−0.696563
$460$	20.7134	−	5.56375i	0.965767	−	0.259411i
$461$	−5.44496			−0.253597			−0.126798	−	0.991928i	$-0.540470\pi$
$461$	−5.44496			−0.253597			−0.126798	+	0.991928i	$0.540470\pi$
$462$	0.251268	+	1.77755i	0.0116900	+	0.0826992i
$463$	2.68072	−	0.787130i	0.124584	−	0.0365810i	−0.218846	−	0.975759i	$-0.570229\pi$
$463$	2.68072	−	0.787130i	0.124584	−	0.0365810i	0.343430	+	0.939178i	$0.388411\pi$
$464$	33.1474	+	10.0758i	1.53883	+	0.467759i
$465$	6.02539	+	34.0888i	0.279421	+	1.58083i
$466$	−5.37462	−	11.8431i	−0.248975	−	0.548621i
$467$	−26.0981	+	3.75235i	−1.20768	+	0.173638i	−0.716604	−	0.697480i	$-0.754305\pi$
$467$	−26.0981	+	3.75235i	−1.20768	+	0.173638i	−0.491074	+	0.871118i	$0.663395\pi$
$468$	4.71401	−	4.04568i	0.217905	−	0.187012i
$469$	1.74360	−	1.12054i	0.0805121	−	0.0517420i
$470$	−23.3417	+	7.61555i	−1.07667	+	0.351279i
$471$	−2.62207	+	5.74154i	−0.120819	+	0.264556i
$472$	14.9775	−	4.28217i	0.689396	−	0.197103i
$473$	−28.4139	−	4.08530i	−1.30647	−	0.187842i
$474$	−3.39178	−	11.6536i	−0.155790	−	0.535269i
$475$	−10.0078	+	26.2608i	−0.459188	+	1.20493i
$476$	−1.13362	−	0.524224i	−0.0519592	−	0.0240278i
$477$	−3.05066	−	3.52065i	−0.139680	−	0.161199i
$478$	−10.7999	−	12.5237i	−0.493978	−	0.572823i
$479$	17.9814	−	20.7517i	0.821593	−	0.948169i	−0.177762	−	0.984074i	$-0.556886\pi$
$479$	17.9814	−	20.7517i	0.821593	−	0.948169i	0.999355	+	0.0359044i	$0.0114312\pi$
$480$	7.79273	−	18.0221i	0.355688	−	0.822594i
$481$	−33.9011	+	15.4821i	−1.54576	+	0.705924i
$482$	−19.6117	−	5.80912i	−0.893288	−	0.264598i
$483$	1.68847	−	0.404280i	0.0768280	−	0.0183954i
$484$	−2.17261	−	1.41087i	−0.0987548	−	0.0641304i
$485$	−14.5011	−	6.06695i	−0.658459	−	0.275486i
$486$	−0.0202804	+	8.54277i	−0.000919938	+	0.387508i
$487$	−4.02505	+	4.64515i	−0.182392	+	0.210492i	−0.839582	−	0.543234i	$-0.817200\pi$
$487$	−4.02505	+	4.64515i	−0.182392	+	0.210492i	0.657189	+	0.753726i	$0.271745\pi$
$488$	4.47095	+	32.7502i	0.202390	+	1.48253i
$489$	−0.709592	−	0.818912i	−0.0320888	−	0.0370325i
$490$	−18.1155	+	12.4194i	−0.818377	+	0.561052i
$491$	0.413054	−	1.40673i	0.0186409	−	0.0634849i	−0.949647	−	0.313321i	$-0.898558\pi$
$491$	0.413054	−	1.40673i	0.0186409	−	0.0634849i	0.968288	+	0.249836i	$0.0803767\pi$
$492$	−8.63097	−	0.0409798i	−0.389114	−	0.00184751i
$493$	−3.30050	+	22.9555i	−0.148647	+	1.03386i
$494$	−27.4560	+	31.5343i	−1.23530	+	1.41879i
$495$	1.44646	+	4.39798i	0.0650136	+	0.197674i
$496$	−10.8753	−	38.3825i	−0.488315	−	1.72342i
$497$	1.26250	−	0.811357i	0.0566307	−	0.0363943i
$498$	−11.4425	−	7.39206i	−0.512749	−	0.331246i
$499$	7.18125	−	1.03251i	0.321477	−	0.0462214i	0.0203127	−	0.999794i	$-0.493534\pi$
$499$	7.18125	−	1.03251i	0.321477	−	0.0462214i	0.301164	+	0.953572i	$0.402625\pi$
$500$	−15.4872	+	16.1291i	−0.692608	+	0.721314i
$501$	−23.8842	−	15.3495i	−1.06707	−	0.685763i
$502$	−9.77964	−	15.2971i	−0.436486	−	0.682745i
$503$	−4.69973	−	16.0058i	−0.209551	−	0.713664i	−0.995448	−	0.0953068i	$-0.969617\pi$
$503$	−4.69973	−	16.0058i	−0.209551	−	0.713664i	0.785897	−	0.618357i	$-0.212201\pi$
$504$	−0.164327	+	0.353147i	−0.00731969	+	0.0157304i
$505$	−13.8681	+	12.8201i	−0.617124	+	0.570485i
$506$	−11.0107	+	21.0795i	−0.489486	+	0.937099i
$507$	22.7711			1.01130
$508$	−2.60897	+	17.5537i	−0.115754	+	0.778820i
$509$	−19.8677	+	5.83369i	−0.880621	+	0.258574i	−0.690627	−	0.723211i	$-0.742665\pi$
$509$	−19.8677	+	5.83369i	−0.880621	+	0.258574i	−0.189995	+	0.981785i	$0.560847\pi$
$510$	12.7159	+	3.32590i	0.563067	+	0.147273i
$511$	0.0554531	+	0.0356375i	0.00245310	+	0.00157651i
$512$	−6.83726	+	21.5697i	−0.302167	+	0.953255i
$513$	−4.45812	−	31.0069i	−0.196831	−	1.36899i
$514$	−25.4878	−	16.4657i	−1.12422	−	0.726269i
$515$	−24.8507	−	6.43683i	−1.09505	−	0.283640i
$516$	19.1286	+	16.7347i	0.842090	+	0.736704i
$517$	11.3096	−	24.7647i	0.497398	−	1.08915i
$518$	1.53450	−	1.76243i	0.0674220	−	0.0774369i
$519$	−12.2070	−	1.75510i	−0.535827	−	0.0770402i
$520$	−29.9067	+	14.5731i	−1.31149	+	0.639075i
$521$	6.55407	−	22.3211i	0.287139	−	0.977906i	−0.681992	−	0.731360i	$-0.738886\pi$
$521$	6.55407	−	22.3211i	0.287139	−	0.977906i	0.969131	−	0.246546i	$-0.0792957\pi$
$522$	7.15657	+	1.04631i	0.313235	+	0.0457956i
$523$	4.59321	−	3.98004i	0.200847	−	0.174035i	−0.548630	−	0.836065i	$-0.684850\pi$
$523$	4.59321	−	3.98004i	0.200847	−	0.174035i	0.749477	+	0.662030i	$0.230305\pi$
$524$	31.5516	−	14.2285i	1.37834	−	0.621573i
$525$	−1.28900	+	1.27082i	−0.0562564	+	0.0554630i
$526$	23.7186	+	0.0563076i	1.03418	+	0.00245513i
$527$	24.2916	−	11.0936i	1.05816	−	0.483245i
$528$	8.85587	+	19.8893i	0.385402	+	0.865572i
$529$	21.3010	+	8.67570i	0.926130	+	0.377204i
$530$	11.0350	+	22.3753i	0.479328	+	0.971919i
$531$	2.95818	−	1.35096i	0.128374	−	0.0586265i
$532$	0.750553	−	2.51197i	0.0325406	−	0.108908i
$533$	11.0522	+	9.57678i	0.478723	+	0.414816i
$534$	15.9731	+	18.5227i	0.691226	+	0.801554i
$535$	−3.40785	+	30.6725i	−0.147334	+	1.32609i
$536$	16.5955	−	18.8788i	0.716815	−	0.815441i
$537$	−3.15022	+	10.7287i	−0.135942	+	0.462976i
$538$	6.23440	+	21.4204i	0.268784	+	0.923500i
$539$	3.46601	−	24.1066i	0.149291	−	1.03834i
$540$	6.36429	−	24.0986i	0.273875	−	1.03704i
$541$	1.18229	−	2.58886i	0.0508307	−	0.111304i	−0.882513	−	0.470289i	$-0.844150\pi$
$541$	1.18229	−	2.58886i	0.0508307	−	0.111304i	0.933343	+	0.358985i	$0.116877\pi$
$542$	5.84916	−	12.7278i	0.251243	−	0.546707i
$543$	8.59558	+	13.3750i	0.368872	+	0.573975i
$544$	−14.9661	−	2.33344i	−0.641666	−	0.100045i
$545$	−9.67691	+	11.9214i	−0.414513	+	0.510657i
$546$	−2.45237	+	1.11293i	−0.104952	+	0.0476291i
$547$	7.56780	+	4.86353i	0.323576	+	0.207950i	0.692336	−	0.721575i	$-0.256581\pi$
$547$	7.56780	+	4.86353i	0.323576	+	0.207950i	−0.368761	+	0.929524i	$0.620218\pi$
$548$	−0.442249	+	0.127579i	−0.0188920	+	0.00544988i
$549$	1.94410	+	6.62100i	0.0829722	+	0.282577i
$550$	−1.53439	−	24.7469i	−0.0654267	−	1.05521i
$551$	−48.6815			−2.07390
$552$	18.3405	−	10.3431i	0.780623	−	0.440230i
$553$		−	1.28946i		−	0.0548332i
$554$	1.25927	+	8.90848i	0.0535012	+	0.378485i
$555$	−12.6237	+	21.1050i	−0.535845	+	0.895855i
$556$	5.04671	+	17.4944i	0.214028	+	0.741926i
$557$	12.7403	+	8.18767i	0.539823	+	0.346923i	0.781969	−	0.623317i	$-0.214215\pi$
$557$	12.7403	+	8.18767i	0.539823	+	0.346923i	−0.242147	+	0.970240i	$0.577852\pi$
$558$	−3.44173	−	7.58392i	−0.145700	−	0.321053i
$559$	−6.12854	−	42.6249i	−0.259210	−	1.80284i
$560$	1.32998	−	1.60703i	0.0562018	−	0.0679094i
$561$	−12.2606	+	7.87939i	−0.517641	+	0.332668i
$562$	4.13760	−	9.00346i	0.174534	−	0.379788i
$563$	7.36583	+	3.36386i	0.310433	+	0.141770i	0.564539	−	0.825406i	$-0.309054\pi$
$563$	7.36583	+	3.36386i	0.310433	+	0.141770i	−0.254106	+	0.967176i	$0.581781\pi$
$564$	−20.3394	+	12.9353i	−0.856445	+	0.544675i
$565$	9.45579	+	13.7227i	0.397808	+	0.577318i
$566$	9.89546	−	2.88007i	0.415937	−	0.121058i
$567$	0.452052	−	1.53955i	0.0189844	−	0.0646550i
$568$	12.0163	−	13.6697i	0.504194	−	0.573566i
$569$	−3.24698	+	2.81353i	−0.136121	+	0.117949i	−0.720260	−	0.693704i	$-0.755978\pi$
$569$	−3.24698	+	2.81353i	−0.136121	+	0.117949i	0.584139	+	0.811653i	$0.301432\pi$
$570$	−3.11170	+	27.4138i	−0.130335	+	1.14824i
$571$	−9.02319	+	10.4133i	−0.377609	+	0.435784i	−0.912462	−	0.409161i	$-0.865821\pi$
$571$	−9.02319	+	10.4133i	−0.377609	+	0.435784i	0.534854	+	0.844945i	$0.320367\pi$
$572$	10.5609	−	35.3453i	0.441571	−	1.47786i
$573$	5.62777	+	12.3231i	0.235103	+	0.514804i
$574$	−0.879206	−	0.260427i	−0.0366973	−	0.0108700i
$575$	−23.6861	+	3.73767i	−0.987777	+	0.155871i
$576$	−0.738798	+	4.66568i	−0.0307833	+	0.194403i
$577$	16.8422	−	7.69158i	0.701151	−	0.320205i	−0.0327480	−	0.999464i	$-0.510426\pi$
$577$	16.8422	−	7.69158i	0.701151	−	0.320205i	0.733899	+	0.679259i	$0.237699\pi$
$578$	−0.0330036	+	13.9022i	−0.00137277	+	0.578254i
$579$	9.43045	+	8.17153i	0.391916	+	0.339597i
$580$	−35.6615	−	15.1194i	−1.48077	−	0.627800i
$581$	−0.947750	−	1.09376i	−0.0393193	−	0.0453769i
$582$	−15.2697	−	2.23246i	−0.632947	−	0.0925383i
$583$	−26.5432	−	7.79378i	−1.09931	−	0.322786i
$584$	0.765414	+	0.230680i	0.0316731	+	0.00954559i
$585$	−5.71902	+	3.94076i	−0.236452	+	0.162930i
$586$	−9.80981	−	8.54111i	−0.405240	−	0.352830i
$587$	9.24528	−	20.2443i	0.381594	−	0.835573i	−0.617216	−	0.786794i	$-0.711740\pi$
$587$	9.24528	−	20.2443i	0.381594	−	0.835573i	0.998810	−	0.0487797i	$-0.0155332\pi$
$588$	−14.1979	+	16.2289i	−0.585510	+	0.669268i
$589$	30.3064	+	47.1577i	1.24875	+	1.94310i
$590$	−17.1576	+	2.99072i	−0.706368	+	0.123126i
$591$	−12.9549	+	1.86263i	−0.532892	+	0.0766183i
$592$	12.0173	−	25.6664i	0.493909	−	1.05488i
$593$	6.23335	−	9.69928i	0.255973	−	0.398302i	−0.689355	−	0.724424i	$-0.742106\pi$
$593$	6.23335	−	9.69928i	0.255973	−	0.398302i	0.945328	+	0.326122i	$0.105742\pi$
$594$	14.8868	+	23.2857i	0.610813	+	0.955424i
$595$	1.19837	+	0.716790i	0.0491283	+	0.0293855i
$596$	28.3720	+	4.21687i	1.16216	+	0.172730i
$597$	−34.6295			−1.41729
$598$	−34.9949	−	6.93955i	−1.43105	−	0.283779i
$599$		−	4.31033i		−	0.176115i	−0.996115	−	0.0880576i	$-0.971934\pi$
$599$		−	4.31033i		−	0.176115i	0.996115	−	0.0880576i	$-0.0280660\pi$
$600$	−10.7936	+	19.1155i	−0.440647	+	0.780388i
$601$	34.7400	−	10.2006i	1.41708	−	0.416091i	0.518563	−	0.855039i	$-0.326467\pi$
$601$	34.7400	−	10.2006i	1.41708	−	0.416091i	0.898512	+	0.438948i	$0.144649\pi$
$602$	1.45442	+	2.27498i	0.0592777	+	0.0927211i
$603$	2.83702	−	4.41449i	0.115532	−	0.179772i
$604$	−12.1615	+	1.68966i	−0.494842	+	0.0687512i
$605$	2.24870	+	1.82532i	0.0914226	+	0.0742100i
$606$	−10.0611	+	15.5739i	−0.408702	+	0.632646i
$607$	12.0350	−	7.73443i	0.488486	−	0.313931i	−0.273110	−	0.961983i	$-0.588052\pi$
$607$	12.0350	−	7.73443i	0.488486	−	0.313931i	0.761596	+	0.648052i	$0.224416\pi$
$608$	0.377395	−	31.7928i	0.0153054	−	1.28937i
$609$	−2.85220	−	1.30256i	−0.115577	−	0.0527823i
$610$	−1.10019	−	36.9391i	−0.0445455	−	1.49562i
$611$	40.4256	+	5.81232i	1.63544	+	0.235141i
$612$	−3.16211	−	0.0150137i	−0.127821	−	0.000606892i
$613$	32.2175	+	9.45991i	1.30125	+	0.382082i	0.857693	−	0.514163i	$-0.171897\pi$
$613$	32.2175	+	9.45991i	1.30125	+	0.382082i	0.443560	+	0.896245i	$0.353715\pi$
$614$	−34.0327	−	4.97566i	−1.37345	−	0.200801i
$615$	9.59081	+	1.06558i	0.386739	+	0.0429684i
$616$	0.312866	+	2.29178i	0.0126057	+	0.0923385i
$617$	−18.1650	+	20.9635i	−0.731295	+	0.843960i	−0.992617	−	0.121292i	$-0.961296\pi$
$617$	−18.1650	+	20.9635i	−0.731295	+	0.843960i	0.261322	+	0.965252i	$0.415842\pi$
$618$	−25.2019	−	0.0598289i	−1.01377	−	0.00240667i
$619$	17.3785	+	38.0536i	0.698501	+	1.52950i	0.841780	+	0.539821i	$0.181508\pi$
$619$	17.3785	+	38.0536i	0.698501	+	1.52950i	−0.143279	+	0.989682i	$0.545765\pi$
$620$	7.55473	+	43.9577i	0.303405	+	1.76539i
$621$	21.0596	−	16.4599i	0.845094	−	0.660512i
$622$	38.6515	+	11.4488i	1.54978	+	0.459057i
$623$	1.07946	+	2.36368i	0.0432475	+	0.0946987i
$624$	−24.8854	+	21.1529i	−0.996213	+	0.846795i
$625$	19.1244	−	16.1015i	0.764974	−	0.644061i
$626$	−4.18765	+	3.61125i	−0.167372	+	0.144335i
$627$	−20.0340	−	23.1205i	−0.800080	−	0.923342i
$628$	−3.41347	+	7.38151i	−0.136212	+	0.294554i
$629$	18.2028	+	5.34482i	0.725792	+	0.213112i
$630$	0.224429	−	0.373198i	0.00894147	−	0.0148686i
$631$	1.10580	−	7.69101i	0.0440212	−	0.306174i	−0.955901	−	0.293690i	$-0.905117\pi$
$631$	1.10580	−	7.69101i	0.0440212	−	0.306174i	0.999922	−	0.0124848i	$-0.00397413\pi$
$632$	−4.29877	−	15.0356i	−0.170996	−	0.598084i
$633$	−6.99200	−	3.19314i	−0.277907	−	0.126916i
$634$	−3.35100	+	7.29180i	−0.133085	+	0.289594i
$635$	4.97510	−	19.2074i	0.197431	−	0.762221i
$636$	15.9513	+	18.5864i	0.632510	+	0.736997i
$637$	36.1634	−	5.19951i	1.43284	−	0.206012i
$638$	39.1110	−	17.7493i	1.54842	−	0.702702i
$639$	2.05421	−	3.19642i	0.0812634	−	0.126448i
$640$	10.1506	−	23.1725i	0.401238	−	0.915974i
$641$	3.82574	+	13.0293i	0.151108	+	0.514625i	0.999901	−	0.0141000i	$-0.00448832\pi$
$641$	3.82574	+	13.0293i	0.151108	+	0.514625i	−0.848793	+	0.528725i	$0.822670\pi$
$642$	4.24060	+	29.9994i	0.167363	+	1.18398i
$643$			15.9284i			0.628155i	0.949397	+	0.314077i	$0.101695\pi$
$643$			15.9284i			0.628155i	−0.949397	+	0.314077i	$0.898305\pi$
$644$	2.17794	−	0.510555i	0.0858229	−	0.0201187i
$645$	−19.2889	−	20.8658i	−0.759499	−	0.821590i
$646$	21.0742	−	2.97897i	0.829155	−	0.117206i
$647$	−7.08329	+	2.07984i	−0.278473	+	0.0817670i	−0.417987	−	0.908453i	$-0.637264\pi$
$647$	−7.08329	+	2.07984i	−0.278473	+	0.0817670i	0.139514	+	0.990220i	$0.455446\pi$
$648$	0.138587	−	19.4588i	0.00544421	−	0.764415i
$649$	10.4408	−	16.2462i	0.409838	−	0.637720i
$650$	34.9716	−	12.6676i	1.37170	−	0.496863i
$651$	0.513838	+	3.57382i	0.0201389	+	0.140069i
$652$	−0.909247	−	1.05945i	−0.0356088	−	0.0414912i
$653$	−24.6804	−	38.4035i	−0.965820	−	1.50284i	−0.861158	−	0.508337i	$-0.830261\pi$
$653$	−24.6804	−	38.4035i	−0.965820	−	1.50284i	−0.104661	−	0.994508i	$-0.533376\pi$
$654$	−6.29457	+	13.6970i	−0.246137	+	0.535596i
$655$	−36.7596	+	12.0900i	−1.43632	+	0.472394i
$656$	−11.1201	−	0.105599i	−0.434167	−	0.00412295i
$657$	0.165192	+	0.0237510i	0.00644475	+	0.000926616i
$658$	−2.45881	+	0.715636i	−0.0958544	+	0.0278984i
$659$	−37.9999	−	11.1578i	−1.48026	−	0.434645i	−0.560844	−	0.827922i	$-0.689523\pi$
$659$	−37.9999	−	11.1578i	−1.48026	−	0.434645i	−0.919420	+	0.393277i	$0.871341\pi$
$660$	−7.49514	−	23.1590i	−0.291748	−	0.901461i
$661$	8.60910	−	7.45983i	0.334855	−	0.290154i	−0.471161	−	0.882047i	$-0.656165\pi$
$661$	8.60910	−	7.45983i	0.334855	−	0.290154i	0.806016	+	0.591894i	$0.201619\pi$
$662$	12.8090	+	14.8534i	0.497834	+	0.577295i
$663$	−16.5232	−	14.3174i	−0.641708	−	0.556043i
$664$	−14.6975	−	9.59412i	−0.570375	−	0.372324i
$665$	−1.13131	+	2.70403i	−0.0438704	+	0.104858i
$666$	1.68034	−	5.67286i	0.0651118	−	0.219819i
$667$	−20.6613	−	36.0347i	−0.800010	−	1.39527i
$668$	−30.6792	−	19.9228i	−1.18701	−	0.770835i
$669$	5.68636	+	12.4514i	0.219848	+	0.481399i
$670$	−20.6815	+	19.0276i	−0.798995	+	0.735102i
$671$	30.9689	+	26.8347i	1.19554	+	1.03594i
$672$	0.872781	−	1.85261i	0.0336683	−	0.0714660i
$673$	−2.81450	+	2.43878i	−0.108491	+	0.0940080i	−0.707417	−	0.706796i	$-0.750140\pi$
$673$	−2.81450	+	2.43878i	−0.108491	+	0.0940080i	0.598926	+	0.800804i	$0.295594\pi$
$674$	−2.35455	−	0.344241i	−0.0906940	−	0.0132597i
$675$	−9.92364	+	26.0400i	−0.381961	+	1.00228i
$676$	29.3389	+	0.139301i	1.12842	+	0.00535774i
$677$	−4.52312	+	31.4590i	−0.173838	+	1.20907i	0.696845	+	0.717222i	$0.254586\pi$
$677$	−4.52312	+	31.4590i	−0.173838	+	1.20907i	−0.870683	+	0.491845i	$0.836323\pi$
$678$	12.3391	+	10.7433i	0.473882	+	0.412594i
$679$	−1.49134	−	0.681071i	−0.0572323	−	0.0261371i
$680$	16.3631	+	4.36296i	0.627496	+	0.167312i
$681$	1.37261	+	2.13582i	0.0525986	+	0.0818450i
$682$	−41.5420	−	26.8370i	−1.59073	−	1.02764i
$683$	−4.17706	−	29.0521i	−0.159831	−	1.11165i	−0.898943	−	0.438065i	$-0.855664\pi$
$683$	−4.17706	−	29.0521i	−0.159831	−	1.11165i	0.739113	−	0.673582i	$-0.235245\pi$
$684$	−0.913435	−	6.57453i	−0.0349261	−	0.251383i
$685$	0.506757	−	0.0895723i	0.0193622	−	0.00342238i
$686$	−3.87533	+	2.47755i	−0.147961	+	0.0945931i
$687$	8.63843	+	29.4198i	0.329577	+	1.12243i
$688$	24.5434	+	21.6784i	0.935709	+	0.826483i
$689$		−	41.4996i		−	1.58101i
$690$	−21.6128	+	9.33161i	−0.822784	+	0.355248i
$691$		−	11.5079i		−	0.437783i	−0.975749	−	0.218891i	$-0.929756\pi$
$691$		−	11.5079i		−	0.437783i	0.975749	−	0.218891i	$-0.0702441\pi$
$692$	−15.7170	−	2.33599i	−0.597472	−	0.0888010i
$693$	0.136043	+	0.463321i	0.00516786	+	0.0176001i
$694$	−3.54690	−	5.54800i	−0.134639	−	0.210599i
$695$	−3.54327	−	20.0461i	−0.134404	−	0.760394i
$696$	−37.6003	−	5.67972i	−1.42524	−	0.215289i
$697$	−1.05942	−	7.36843i	−0.0401284	−	0.279099i
$698$	22.2179	−	34.3920i	0.840961	−	1.30176i
$699$	7.71774	+	12.0090i	0.291912	+	0.454224i
$700$	−1.66855	+	1.62947i	−0.0630653	+	0.0615882i
$701$	−32.4822	−	14.8341i	−1.22684	−	0.560277i	−0.306674	−	0.951815i	$-0.599216\pi$
$701$	−32.4822	−	14.8341i	−1.22684	−	0.560277i	−0.920162	+	0.391537i	$0.871943\pi$
$702$	−27.2251	+	31.2692i	−1.02755	+	1.18018i
$703$	−5.66736	+	39.4174i	−0.213749	+	1.48665i
$704$	11.2885	+	25.6801i	0.425450	+	0.967855i
$705$	24.1415	−	11.9774i	0.909221	−	0.451093i
$706$	−0.448603	+	3.06837i	−0.0168834	+	0.115480i
$707$	−1.48868	+	1.28995i	−0.0559875	+	0.0485134i
$708$	−15.5867	+	7.02896i	−0.585784	+	0.264164i
$709$	1.55142	+	1.34431i	0.0582648	+	0.0504867i	0.683506	−	0.729945i	$-0.260454\pi$
$709$	1.55142	+	1.34431i	0.0582648	+	0.0504867i	−0.625242	+	0.780431i	$0.715000\pi$
$710$	−14.9749	+	13.7774i	−0.561998	+	0.517057i
$711$	−1.35619	−	2.96965i	−0.0508613	−	0.111371i
$712$	20.4669	+	23.9628i	0.767030	+	0.898044i
$713$	−22.0442	+	42.4478i	−0.825561	+	1.58968i
$714$	1.31443	+	0.389342i	0.0491912	+	0.0145708i
$715$	−15.9184	+	38.0477i	−0.595315	+	1.42290i
$716$	−4.12446	+	13.8038i	−0.154138	+	0.515873i
$717$	13.7181	+	11.8868i	0.512312	+	0.443920i
$718$	13.0496	−	11.2534i	0.487006	−	0.419973i
$719$	35.4489	−	30.7166i	1.32202	−	1.14554i	0.343552	−	0.939133i	$-0.388370\pi$
$719$	35.4489	−	30.7166i	1.32202	−	1.14554i	0.978467	−	0.206403i	$-0.0661758\pi$
$720$	1.37277	−	5.09985i	0.0511602	−	0.190060i
$721$	−2.56900	−	0.754327i	−0.0956746	−	0.0280926i
$722$	4.97619	+	17.0974i	0.185195	+	0.636299i
$723$	22.2221	+	3.19505i	0.826449	+	0.118825i
$724$	10.9929	+	17.2853i	0.408550	+	0.642401i
$725$	37.8606	+	21.0239i	1.40611	+	0.780807i
$726$	2.58363	+	1.18732i	0.0958874	+	0.0440657i
$727$	−0.885325	−	1.37759i	−0.0328349	−	0.0510921i	0.824448	−	0.565938i	$-0.191486\pi$
$727$	−0.885325	−	1.37759i	−0.0328349	−	0.0510921i	−0.857283	+	0.514845i	$0.827849\pi$
$728$	−3.16651	+	1.41893i	−0.117359	+	0.0525890i
$729$	−4.27178	−	29.7109i	−0.158214	−	1.10040i
$730$	−0.823702	−	0.346920i	−0.0304866	−	0.0128401i
$731$	−11.8512	+	18.4409i	−0.438333	+	0.682060i
$732$	−10.0560	−	34.8591i	−0.371682	−	1.28843i
$733$	−33.0348	+	9.69990i	−1.22017	+	0.358274i	−0.827531	−	0.561420i	$-0.810255\pi$
$733$	−33.0348	+	9.69990i	−1.22017	+	0.358274i	−0.392637	+	0.919693i	$0.628437\pi$
$734$	−5.49079	−	38.8437i	−0.202669	−	1.43375i
$735$	17.7027	−	16.3649i	0.652975	−	0.603627i
$736$	23.6936	−	13.2141i	0.873359	−	0.487078i
$737$		−	31.1616i		−	1.14785i
$738$	−2.29874	+	0.324941i	−0.0846178	+	0.0119612i
$739$	8.01895	+	27.3100i	0.294982	+	1.00462i	0.964995	+	0.262267i	$0.0844702\pi$
$739$	8.01895	+	27.3100i	0.294982	+	1.00462i	−0.670013	+	0.742349i	$0.733712\pi$
$740$	−16.3938	+	27.1149i	−0.602648	+	0.996765i
$741$	24.8119	−	38.6081i	0.911488	−	1.41830i
$742$	1.07534	+	2.36953i	0.0394768	+	0.0869880i
$743$	22.6508	−	3.25669i	0.830977	−	0.119476i	0.286319	−	0.958134i	$-0.407568\pi$
$743$	22.6508	−	3.25669i	0.830977	−	0.119476i	0.544658	+	0.838658i	$0.316659\pi$
$744$	17.9059	+	39.9592i	0.656463	+	1.46498i
$745$	−31.0448	−	8.04124i	−1.13739	−	0.294608i
$746$	−28.7043	−	13.1913i	−1.05094	−	0.482966i
$747$	−3.33307	−	1.52216i	−0.121951	−	0.0556930i
$748$	−15.8450	+	10.0770i	−0.579352	+	0.368452i
$749$	−0.458086	+	3.18606i	−0.0167381	+	0.116416i
$750$	14.2591	−	19.9765i	0.520669	−	0.729437i
$751$	8.06743	+	2.36881i	0.294385	+	0.0864391i	0.425590	−	0.904916i	$-0.360067\pi$
$751$	8.06743	+	2.36881i	0.294385	+	0.0864391i	−0.131205	+	0.991355i	$0.541885\pi$
$752$	−26.2850	+	16.5418i	−0.958515	+	0.603216i
$753$	13.0503	+	15.0609i	0.475581	+	0.548850i
$754$	42.0778	+	48.7940i	1.53238	+	1.77697i
$755$	13.7204	−	0.441251i	0.499337	−	0.0160588i
$756$	0.744244	−	2.49085i	0.0270679	−	0.0905913i
$757$	−19.4394	−	42.5664i	−0.706538	−	1.54710i	−0.831859	−	0.554987i	$-0.812723\pi$
$757$	−19.4394	−	42.5664i	−0.706538	−	1.54710i	0.125320	−	0.992116i	$-0.460004\pi$
$758$	5.75357	−	19.4241i	0.208979	−	0.705517i
$759$	8.61129	−	24.6422i	0.312570	−	0.894455i
$760$	−4.17689	+	35.3017i	−0.151512	+	1.28053i
$761$	14.0719	+	30.8132i	0.510107	+	1.11698i	0.973051	+	0.230590i	$0.0740657\pi$
$761$	14.0719	+	30.8132i	0.510107	+	1.11698i	−0.462944	+	0.886387i	$0.653207\pi$
$762$	0.0462425	−	19.4788i	0.00167519	−	0.705644i
$763$	−1.04875	+	1.21032i	−0.0379672	+	0.0438164i
$764$	7.17557	+	15.9118i	0.259603	+	0.575669i
$765$	3.51376	+	0.390394i	0.127040	+	0.0141147i
$766$	−0.173211	+	1.18474i	−0.00625838	+	0.0428064i
$767$	27.7971	+	8.16198i	1.00370	+	0.294712i
$768$	4.00078	−	24.5119i	0.144366	−	0.884496i
$769$	9.72145	+	1.39773i	0.350564	+	0.0504035i	0.315348	−	0.948976i	$-0.397879\pi$
$769$	9.72145	+	1.39773i	0.350564	+	0.0504035i	0.0352165	+	0.999380i	$0.488788\pi$
$770$	−0.0769887	−	2.58491i	−0.00277448	−	0.0931536i
$771$	30.2961	+	13.8358i	1.09109	+	0.498282i
$772$	12.1004	+	10.5861i	0.435504	+	0.381002i
$773$	−11.2869	+	7.25365i	−0.405962	+	0.260896i	−0.727648	−	0.685950i	$-0.759387\pi$
$773$	−11.2869	+	7.25365i	−0.405962	+	0.260896i	0.321686	+	0.946846i	$0.395750\pi$
$774$	5.74229	+	3.70964i	0.206402	+	0.133340i
$775$	−3.20413	−	49.7637i	−0.115096	−	1.78757i
$776$	−19.6602	−	2.96977i	−0.705759	−	0.106608i
$777$	−1.38672	+	2.15778i	−0.0497485	+	0.0774101i
$778$	34.8455	−	22.2771i	1.24927	−	0.798674i
$779$	14.9932	−	4.40240i	0.537187	−	0.157732i
$780$	30.1667	−	20.5762i	1.08014	−	0.736747i
$781$		−	22.5633i		−	0.807379i
$782$	11.1494	+	14.3351i	0.398701	+	0.512623i
$783$	−48.2723			−1.72511
$784$	−18.3922	+	20.8229i	−0.656864	+	0.743673i
$785$	4.66735	−	7.80313i	0.166585	−	0.278506i
$786$	−32.0080	+	20.4631i	−1.14169	+	0.729893i
$787$	6.54541	−	10.1849i	0.233319	−	0.363051i	−0.704776	−	0.709430i	$-0.748953\pi$
$787$	6.54541	−	10.1849i	0.233319	−	0.363051i	0.938095	+	0.346379i	$0.112589\pi$
$788$	−16.7028	+	2.32061i	−0.595012	+	0.0826683i
$789$	−25.7690	+	3.70503i	−0.917401	+	0.131902i
$790$	3.00232	+	17.2242i	0.106818	+	0.612808i
$791$	0.939722	+	1.46224i	0.0334127	+	0.0519911i
$792$	3.13094	+	4.94898i	0.111253	+	0.175854i
$793$	−25.5366	+	55.9174i	−0.906831	+	1.98568i
$794$	29.8667	−	34.3031i	1.05993	−	1.21737i
$795$	−15.5376	−	22.5489i	−0.551062	−	0.799727i
$796$	−44.6175	−	0.211844i	−1.58143	−	0.00750861i
$797$	−27.0987	−	7.95689i	−0.959884	−	0.281847i	−0.235988	−	0.971756i	$-0.575832\pi$
$797$	−27.0987	−	7.95689i	−0.959884	−	0.281847i	−0.723896	+	0.689909i	$0.757651\pi$
$798$	−0.416289	+	2.84735i	−0.0147365	+	0.100795i
$799$	−13.6143	−	15.7118i	−0.481640	−	0.555842i
$800$	−14.0237	+	24.5629i	−0.495813	+	0.868429i
$801$	4.97203	+	4.30829i	0.175678	+	0.152226i
$802$	−34.3985	−	0.0816615i	−1.21465	−	0.00288357i
$803$	0.901497	−	0.411700i	0.0318131	−	0.0145286i
$804$	−15.0262	+	23.1389i	−0.529932	+	0.816045i
$805$	−2.48171	+	0.310228i	−0.0874687	+	0.0109341i
$806$	21.0713	−	71.1370i	0.742204	−	2.50570i
$807$	−10.1723	−	22.2741i	−0.358081	−	0.784087i
$808$	−13.0582	+	20.0043i	−0.459386	+	0.703747i
$809$	11.8417	−	13.6660i	0.416331	−	0.480471i	−0.508385	−	0.861130i	$-0.669757\pi$
$809$	11.8417	−	13.6660i	0.416331	−	0.480471i	0.924716	+	0.380659i	$0.124303\pi$
$810$	−2.45375	+	21.6174i	−0.0862160	+	0.759557i
$811$	−38.6233	+	33.4672i	−1.35625	+	1.17519i	−0.389034	+	0.921223i	$0.627191\pi$
$811$	−38.6233	+	33.4672i	−1.35625	+	1.17519i	−0.967212	+	0.253971i	$0.918263\pi$
$812$	−3.66688	−	1.69570i	−0.128682	−	0.0595073i
$813$	−4.33160	+	14.7521i	−0.151916	+	0.517378i
$814$	−9.81840	−	33.7345i	−0.344135	−	1.18239i
$815$	0.885666	+	1.28532i	0.0310235	+	0.0450228i
$816$	16.6247	+	0.157872i	0.581983	+	0.00552663i
$817$	−41.8557	−	19.1149i	−1.46435	−	0.668745i
$818$	42.8989	+	19.7145i	1.49993	+	0.689301i
$819$	−0.609396	+	0.391635i	−0.0212940	+	0.0136848i
$820$	12.3505	+	1.43159i	0.431299	+	0.0499934i
$821$	3.46956	+	24.1313i	0.121088	+	0.842188i	0.956327	+	0.292300i	$0.0944206\pi$
$821$	3.46956	+	24.1313i	0.121088	+	0.842188i	−0.835238	+	0.549888i	$0.814670\pi$
$822$	0.460056	−	0.208782i	0.0160463	−	0.00728212i
$823$	−21.8515	−	14.0431i	−0.761696	−	0.489512i	0.101217	−	0.994864i	$-0.467726\pi$
$823$	−21.8515	−	14.0431i	−0.761696	−	0.489512i	−0.862913	+	0.505352i	$0.831363\pi$
$824$	−32.4704	−	0.231256i	−1.13116	−	0.00805619i
$825$	5.59591	+	26.6332i	0.194825	+	0.927250i
$826$	−1.79864	+	0.254249i	−0.0625827	+	0.00884645i
$827$			17.8727i			0.621495i	0.950492	+	0.310748i	$0.100579\pi$
$827$			17.8727i			0.621495i	−0.950492	+	0.310748i	$0.899421\pi$
$828$	4.47888	−	3.46649i	0.155652	−	0.120469i
$829$	5.51645			0.191594			0.0957971	−	0.995401i	$-0.469460\pi$
$829$	5.51645			0.191594			0.0957971	+	0.995401i	$0.469460\pi$
$830$	15.2064	+	12.4034i	0.527823	+	0.430530i
$831$	−2.78219	−	9.47528i	−0.0965132	−	0.328694i
$832$	−32.1924	+	27.1018i	−1.11607	+	0.939585i
$833$	−15.6454	−	10.0547i	−0.542080	−	0.348374i
$834$	−8.25894	−	18.1988i	−0.285984	−	0.630172i
$835$	31.7537	+	25.7752i	1.09888	+	0.891989i
$836$	−25.6709	−	29.9115i	−0.887846	−	1.03451i
$837$	30.0516	+	46.7612i	1.03874	+	1.61630i
$838$	−16.1697	−	7.43091i	−0.558574	−	0.256696i
$839$	7.01034	−	15.3505i	0.242024	−	0.529959i	−0.749170	−	0.662378i	$-0.769547\pi$
$839$	7.01034	−	15.3505i	0.242024	−	0.529959i	0.991194	+	0.132419i	$0.0422746\pi$
$840$	−1.18928	+	1.95653i	−0.0410339	+	0.0675067i
$841$	−6.54892	+	45.5488i	−0.225825	+	1.57065i
$842$	13.8255	−	4.02390i	0.476457	−	0.138673i
$843$	−3.06411	+	10.4354i	−0.105533	+	0.359414i
$844$	−8.98914	−	4.15689i	−0.309419	−	0.143086i
$845$	−32.6017	−	3.62219i	−1.12153	−	0.124607i
$846$	−4.91003	+	4.23420i	−0.168810	+	0.145575i
$847$	0.228298	+	0.197822i	0.00784443	+	0.00679723i
$848$	20.4384	+	24.0447i	0.701856	+	0.825699i
$849$	−10.2899	+	4.69922i	−0.353147	+	0.161277i
$850$	−17.6764	−	6.78443i	−0.606295	−	0.232704i
$851$	−31.5826	+	12.5344i	−1.08264	+	0.429674i
$852$	−10.8800	+	16.7542i	−0.372744	+	0.573990i
$853$	13.4663	−	6.14987i	0.461079	−	0.210568i	−0.171312	−	0.985217i	$-0.554801\pi$
$853$	13.4663	−	6.14987i	0.461079	−	0.210568i	0.632391	+	0.774649i	$0.282073\pi$
$854$	0.00915040	−	3.85445i	0.000313120	−	0.131896i
$855$	0.238542	+	7.41732i	0.00815797	+	0.253667i
$856$	5.28018	+	38.6780i	0.180473	+	1.32199i
$857$	38.4477	−	33.3151i	1.31335	−	1.13802i	0.332531	−	0.943092i	$-0.392097\pi$
$857$	38.4477	−	33.3151i	1.31335	−	1.13802i	0.980817	−	0.194931i	$-0.0624482\pi$
$858$	−5.85750	+	40.0644i	−0.199972	+	1.36778i
$859$	4.41005	−	15.0192i	0.150469	−	0.512450i	−0.849414	−	0.527726i	$-0.823045\pi$
$859$	4.41005	−	15.0192i	0.150469	−	0.512450i	0.999883	+	0.0152764i	$0.00486280\pi$
$860$	−24.7247	−	27.0020i	−0.843104	−	0.920761i
$861$	0.996231	+	0.143236i	0.0339515	+	0.00488148i
$862$	−16.7356	−	14.5712i	−0.570017	−	0.496297i
$863$	18.6388	−	40.8132i	0.634472	−	1.38930i	−0.270040	−	0.962849i	$-0.587037\pi$
$863$	18.6388	−	40.8132i	0.634472	−	1.38930i	0.904511	−	0.426450i	$-0.140236\pi$
$864$	0.374222	−	31.5255i	0.0127313	−	1.07252i
$865$	17.1977	+	4.45455i	0.584738	+	0.151459i
$866$	−13.8141	+	21.3834i	−0.469422	+	0.726637i
$867$	−2.17162	−	15.1040i	−0.0737522	−	0.512958i
$868$	0.640179	+	4.60775i	0.0217291	+	0.156397i
$869$	−16.3092	−	10.4813i	−0.553252	−	0.355554i
$870$	41.1317	+	10.7582i	1.39450	+	0.364737i
$871$	44.8534	−	13.1701i	1.51980	−	0.446253i
$872$	−8.19387	+	17.6091i	−0.277480	+	0.596320i
$873$	−4.15091			−0.140487
$874$	−26.4540	+	27.4479i	−0.894819	+	0.928440i
$875$	2.04762	−	1.61440i	0.0692222	−	0.0545768i
$876$	−0.867922	−	0.128997i	−0.0293244	−	0.00435841i
$877$	2.32771	+	7.92744i	0.0786010	+	0.267691i	0.989412	−	0.145133i	$-0.0463609\pi$
$877$	2.32771	+	7.92744i	0.0786010	+	0.267691i	−0.910811	+	0.412823i	$0.864543\pi$
$878$	20.9729	−	13.4082i	0.707800	−	0.452505i
$879$	12.0104	+	7.71859i	0.405099	+	0.260341i
$880$	−9.51526	−	29.8845i	−0.320759	−	1.00740i
$881$	−34.8419	+	5.00951i	−1.17385	+	0.168775i	−0.701523	−	0.712647i	$-0.747496\pi$
$881$	−34.8419	+	5.00951i	−1.17385	+	0.168775i	−0.472330	+	0.881422i	$0.656587\pi$
$882$	−3.14729	+	4.87181i	−0.105975	+	0.164042i
$883$	4.41814	−	2.83937i	0.148682	−	0.0955524i	−0.464185	−	0.885739i	$-0.653653\pi$
$883$	4.41814	−	2.83937i	0.148682	−	0.0955524i	0.612867	+	0.790186i	$0.290016\pi$
$884$	−21.2013	−	18.5480i	−0.713078	−	0.623838i
$885$	18.1595	−	5.97253i	0.610425	−	0.200764i
$886$	−26.3399	−	22.9333i	−0.884906	−	0.770461i
$887$	−5.44042	+	37.8389i	−0.182671	+	1.27051i	0.667742	+	0.744393i	$0.267261\pi$
$887$	−5.44042	+	37.8389i	−0.182671	+	1.27051i	−0.850414	+	0.526115i	$0.823648\pi$
$888$	−8.97618	+	29.7837i	−0.301221	+	0.999476i
$889$	0.583028	−	1.98561i	0.0195541	−	0.0665953i
$890$	−19.9225	−	29.0599i	−0.667805	−	0.974091i
$891$	−15.7979	−	18.2318i	−0.529251	−	0.610788i
$892$	7.25029	+	16.0775i	0.242758	+	0.538314i
$893$	28.5779	−	32.9807i	0.956324	−	1.10366i
$894$	−31.4836	−	0.0747416i	−1.05297	−	0.00249973i
$895$	6.21681	−	14.8592i	0.207805	−	0.496690i
$896$	1.13585	−	2.38161i	0.0379460	−	0.0795640i
$897$	39.1089	+	1.98014i	1.30581	+	0.0661148i
$898$	3.90604	−	13.1869i	0.130346	−	0.440052i
$899$	78.5755	−	35.8842i	2.62064	−	1.19681i
$900$	−2.12891	+	5.50763i	−0.0709638	+	0.183588i
$901$	−13.8338	+	15.9650i	−0.460870	+	0.531872i
$902$	−10.4405	+	9.00345i	−0.347631	+	0.299782i
$903$	−1.94083	−	2.23984i	−0.0645869	−	0.0745373i
$904$	15.8323	+	13.9174i	0.526576	+	0.462887i
$905$	−10.1788	−	20.5164i	−0.338356	−	0.681988i
$906$	12.9399	−	3.76615i	0.429899	−	0.125122i
$907$	−35.6016	−	5.11874i	−1.18213	−	0.169965i	−0.476910	−	0.878952i	$-0.658243\pi$
$907$	−35.6016	−	5.11874i	−1.18213	−	0.169965i	−0.705221	+	0.708987i	$0.749152\pi$
$908$	1.75544	+	2.76025i	0.0582564	+	0.0916021i
$909$	−2.07176	+	4.53651i	−0.0687158	+	0.150467i
$910$	3.68812	−	1.20330i	0.122260	−	0.0398890i
$911$	−20.4812	+	13.1625i	−0.678574	+	0.436093i	−0.834007	−	0.551754i	$-0.813959\pi$
$911$	−20.4812	+	13.1625i	−0.678574	+	0.436093i	0.155434	+	0.987846i	$0.450323\pi$
$912$	4.63837	+	34.5891i	0.153592	+	1.14536i
$913$	−21.5378	+	3.09667i	−0.712798	+	0.102485i
$914$	−3.05945	+	1.38843i	−0.101197	+	0.0459253i
$915$	7.06030	+	39.9438i	0.233406	+	1.32050i
$916$	10.9500	+	37.9581i	0.361798	+	1.25417i
$917$	−3.87258	+	1.13709i	−0.127884	+	0.0375501i
$918$	20.8971	−	2.95393i	0.689706	−	0.0974942i
$919$	50.4275			1.66345			0.831726	−	0.555187i	$-0.187353\pi$
$919$	50.4275			1.66345			0.831726	+	0.555187i	$0.187353\pi$
$920$	−27.9035	+	11.8909i	−0.919952	+	0.392031i
$921$	37.7520			1.24397
$922$	7.62454	−	1.07777i	0.251101	−	0.0354946i
$923$	32.4771	−	9.53614i	1.06900	−	0.313886i
$924$	−0.703697	−	2.43936i	−0.0231499	−	0.0802489i
$925$	21.4306	−	28.2081i	0.704634	−	0.927478i
$926$	−3.59799	+	1.63283i	−0.118237	+	0.0536582i
$927$	−6.70985	+	0.964731i	−0.220380	+	0.0316859i
$928$	−48.4105	−	7.54792i	−1.58915	−	0.247773i
$929$	−12.1245	+	7.79193i	−0.397791	+	0.255645i	−0.724209	−	0.689581i	$-0.757795\pi$
$929$	−12.1245	+	7.79193i	−0.397791	+	0.255645i	0.326418	+	0.945226i	$0.394158\pi$
$930$	−15.1848	−	46.5416i	−0.497931	−	1.52616i
$931$	16.2172	−	35.5108i	0.531498	−	1.16382i
$932$	9.87027	+	15.5200i	0.323312	+	0.508373i
$933$	−43.7962	−	6.29694i	−1.43382	−	0.206153i
$934$	35.8023	−	10.4202i	1.17149	−	0.340961i
$935$	18.8069	−	9.33072i	0.615053	−	0.305147i
$936$	−5.80019	+	6.59823i	−0.189585	+	0.215670i
$937$	6.32199	+	7.29596i	0.206530	+	0.238349i	0.849559	−	0.527493i	$-0.176868\pi$
$937$	6.32199	+	7.29596i	0.206530	+	0.238349i	−0.643029	+	0.765842i	$0.722322\pi$
$938$	−2.21975	+	1.91422i	−0.0724775	+	0.0625015i
$939$	3.97467	−	4.58701i	0.129708	−	0.149691i
$940$	31.1778	−	15.2843i	1.01691	−	0.498517i
$941$	−13.3742	+	6.10780i	−0.435987	+	0.199109i	−0.621303	−	0.783570i	$-0.713396\pi$
$941$	−13.3742	+	6.10780i	−0.435987	+	0.199109i	0.185316	+	0.982679i	$0.440669\pi$
$942$	2.53519	−	8.55885i	0.0826010	−	0.278862i
$943$	9.62212	+	9.22972i	0.313339	+	0.300561i
$944$	−20.1253	+	8.96094i	−0.655023	+	0.291654i
$945$	−1.12180	+	2.68130i	−0.0364922	+	0.0872226i
$946$	40.5964	+	0.0963753i	1.31990	+	0.00313343i
$947$	7.66739	−	8.84864i	0.249157	−	0.287542i	−0.617370	−	0.786673i	$-0.711802\pi$
$947$	7.66739	−	8.84864i	0.249157	−	0.287542i	0.866527	+	0.499131i	$0.166347\pi$
$948$	7.05621	+	15.6471i	0.229175	+	0.508195i
$949$	0.973599	+	1.12359i	0.0316044	+	0.0364734i
$950$	8.81575	−	38.7537i	0.286021	−	1.25734i
$951$	2.48158	−	8.45150i	0.0804709	−	0.274059i
$952$	1.69116	+	0.509680i	0.0548108	+	0.0165188i
$953$	−0.847531	+	5.89471i	−0.0274542	+	0.190948i	−0.998933	−	0.0461771i	$-0.985296\pi$
$953$	−0.847531	+	5.89471i	−0.0274542	+	0.190948i	0.971479	+	0.237125i	$0.0762052\pi$
$954$	4.96869	+	4.32609i	0.160867	+	0.140062i
$955$	−6.09711	−	18.5383i	−0.197298	−	0.599885i
$956$	17.6020	+	15.3992i	0.569290	+	0.498045i
$957$	−39.6590	+	25.4873i	−1.28199	+	0.823887i
$958$	−21.0717	+	32.6177i	−0.680796	+	1.05383i
$959$	0.0531277	−	0.00763861i	0.00171558	−	0.000246664i
$960$	−7.34480	+	26.7788i	−0.237052	+	0.864280i
$961$	−57.5988	−	37.0165i	−1.85803	−	1.19408i
$962$	44.4070	−	28.3899i	1.43174	−	0.915327i
$963$	2.29598	+	7.81938i	0.0739868	+	0.251976i
$964$	28.6120	+	4.25253i	0.921530	+	0.136965i
$965$	−12.2018	−	13.1994i	−0.392791	−	0.424902i
$966$	−2.28433	+	0.900325i	−0.0734971	+	0.0289675i
$967$	19.0249			0.611801			0.305900	−	0.952064i	$-0.401043\pi$
$967$	19.0249			0.611801			0.305900	+	0.952064i	$0.401043\pi$
$968$	3.32155	+	1.54558i	0.106759	+	0.0496770i
$969$	−22.4151	+	6.58166i	−0.720076	+	0.211434i
$970$	21.5066	+	5.62517i	0.690536	+	0.180613i
$971$	15.1428	+	9.73166i	0.485954	+	0.312304i	0.760576	−	0.649248i	$-0.224916\pi$
$971$	15.1428	+	9.73166i	0.485954	+	0.312304i	−0.274622	+	0.961552i	$0.588553\pi$
$972$	−1.66256	−	11.9664i	−0.0533265	−	0.383822i
$973$	−0.302166	−	2.10161i	−0.00968699	−	0.0673745i
$974$	4.71679	−	7.30129i	0.151136	−	0.233949i
$975$	−35.9702	+	19.3109i	−1.15197	+	0.618443i
$976$	−12.7432	−	44.9750i	−0.407900	−	1.43961i
$977$	−3.51516	+	7.69713i	−0.112460	+	0.246253i	−0.957490	−	0.288465i	$-0.906855\pi$
$977$	−3.51516	+	7.69713i	−0.112460	+	0.246253i	0.845030	+	0.534718i	$0.179582\pi$
$978$	1.15573	+	1.00626i	0.0369562	+	0.0321767i
$979$	38.6705	+	5.55997i	1.23591	+	0.177697i
$980$	22.9088	−	20.9766i	0.731793	−	0.670073i
$981$	−1.14233	+	3.89042i	−0.0364718	+	0.124212i
$982$	−0.299948	+	2.05160i	−0.00957172	+	0.0654691i
$983$	38.2671	−	33.1586i	1.22053	−	1.05760i	0.223982	−	0.974593i	$-0.428094\pi$
$983$	38.2671	−	33.1586i	1.22053	−	1.05760i	0.996549	−	0.0830033i	$-0.0264512\pi$
$984$	12.0940	−	1.65103i	0.385542	−	0.0526329i
$985$	18.8439	−	0.606023i	0.600417	−	0.0193095i
$986$	0.0778612	−	32.7977i	0.00247961	−	1.04449i
$987$	2.55681	−	1.16766i	0.0813841	−	0.0371669i
$988$	32.2045	−	49.5919i	1.02456	−	1.57773i
$989$	−3.61525	−	39.0949i	−0.114958	−	1.24315i
$990$	−2.89600	−	5.87214i	−0.0920411	−	0.186629i
$991$	30.3295	−	13.8510i	0.963449	−	0.439992i	0.129345	−	0.991600i	$-0.458713\pi$
$991$	30.3295	−	13.8510i	0.963449	−	0.439992i	0.834104	+	0.551607i	$0.185985\pi$
$992$	22.8260	+	51.5940i	0.724727	+	1.63811i
$993$	−16.2699	−	14.0980i	−0.516311	−	0.447386i
$994$	−1.60726	+	1.38604i	−0.0509793	+	0.0439624i
$995$	49.5794	+	5.50849i	1.57177	+	0.174631i
$996$	17.4860	+	8.08613i	0.554064	+	0.256219i
$997$	5.20670	−	17.7324i	0.164898	−	0.561590i	−0.835037	−	0.550193i	$-0.814554\pi$
$997$	5.20670	−	17.7324i	0.164898	−	0.561590i	0.999935	−	0.0113968i	$-0.00362781\pi$
$998$	−9.85148	+	2.86727i	−0.311843	+	0.0907618i
$999$	−5.61972	+	39.0860i	−0.177800	+	1.23663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.b.19.5	✓	640
4.3	odd	2	inner	460.2.o.b.19.16	yes	640
5.4	even	2	inner	460.2.o.b.19.60	yes	640
20.19	odd	2	inner	460.2.o.b.19.49	yes	640
23.17	odd	22	inner	460.2.o.b.339.49	yes	640
92.63	even	22	inner	460.2.o.b.339.60	yes	640
115.109	odd	22	inner	460.2.o.b.339.16	yes	640
460.339	even	22	inner	460.2.o.b.339.5	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.b.19.5	✓	640	1.1	even	1	trivial
460.2.o.b.19.16	yes	640	4.3	odd	2	inner
460.2.o.b.19.49	yes	640	20.19	odd	2	inner
460.2.o.b.19.60	yes	640	5.4	even	2	inner
460.2.o.b.339.5	yes	640	460.339	even	22	inner
460.2.o.b.339.16	yes	640	115.109	odd	22	inner
460.2.o.b.339.49	yes	640	23.17	odd	22	inner
460.2.o.b.339.60	yes	640	92.63	even	22	inner

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40029 + 0.197940i) q^{2} +(1.48939 - 0.437323i) q^{3} +(1.92164 - 0.554348i) q^{4} +(-2.20194 + 0.389205i) q^{5} +(-1.99901 + 0.907190i) q^{6} +(-0.230848 + 0.0331909i) q^{7} +(-2.58113 + 1.15662i) q^{8} +(-0.496740 + 0.319236i) q^{9} +O(q^{10})\)	\(q+(-1.40029 + 0.197940i) q^{2} +(1.48939 - 0.437323i) q^{3} +(1.92164 - 0.554348i) q^{4} +(-2.20194 + 0.389205i) q^{5} +(-1.99901 + 0.907190i) q^{6} +(-0.230848 + 0.0331909i) q^{7} +(-2.58113 + 1.15662i) q^{8} +(-0.496740 + 0.319236i) q^{9} +(3.00632 - 0.980851i) q^{10} +(-1.45664 + 3.18959i) q^{11} +(2.61963 - 1.66602i) q^{12} +(-5.20665 - 0.748603i) q^{13} +(0.316685 - 0.0921710i) q^{14} +(-3.10932 + 1.54263i) q^{15} +(3.38540 - 2.13051i) q^{16} +(1.75347 + 2.02361i) q^{17} +(0.632392 - 0.545348i) q^{18} +(-3.68072 + 4.24778i) q^{19} +(-4.01557 + 1.96855i) q^{20} +(-0.329306 + 0.150389i) q^{21} +(1.40837 - 4.75468i) q^{22} +(-4.70643 - 0.921685i) q^{23} +(-3.33849 + 2.85144i) q^{24} +(4.69704 - 1.71401i) q^{25} +(7.43901 + 0.0176601i) q^{26} +(-3.64978 + 4.21207i) q^{27} +(-0.425207 + 0.191751i) q^{28} +(5.67191 + 6.54573i) q^{29} +(4.04862 - 2.77560i) q^{30} +(2.80982 - 9.56937i) q^{31} +(-4.31883 + 3.65345i) q^{32} +(-0.774613 + 5.38755i) q^{33} +(-2.85592 - 2.48657i) q^{34} +(0.495394 - 0.162931i) q^{35} +(-0.777588 + 0.888822i) q^{36} +(5.96038 - 3.83050i) q^{37} +(4.31328 - 6.67670i) q^{38} +(-8.08210 + 1.16203i) q^{39} +(5.23332 - 3.55139i) q^{40} +(-2.33881 - 1.50306i) q^{41} +(0.431357 - 0.275772i) q^{42} +(2.30644 + 7.85501i) q^{43} +(-1.03099 + 6.93672i) q^{44} +(0.969542 - 0.896270i) q^{45} +(6.77282 + 0.359039i) q^{46} -7.76422 q^{47} +(4.11044 - 4.65367i) q^{48} +(-6.66426 + 1.95680i) q^{49} +(-6.23796 + 3.32984i) q^{50} +(3.49656 + 2.24711i) q^{51} +(-10.4203 + 1.44775i) q^{52} +(1.12277 + 7.80907i) q^{53} +(4.27702 - 6.62057i) q^{54} +(1.96602 - 7.59020i) q^{55} +(0.557459 - 0.352673i) q^{56} +(-3.62436 + 7.93625i) q^{57} +(-9.23799 - 8.04324i) q^{58} +(-5.45147 - 0.783803i) q^{59} +(-5.11985 + 4.68803i) q^{60} +(3.29243 - 11.2130i) q^{61} +(-2.04041 + 13.9561i) q^{62} +(0.104076 - 0.0901821i) q^{63} +(5.32447 - 5.97076i) q^{64} +(11.7561 - 0.378077i) q^{65} +(0.0182737 - 7.69747i) q^{66} +(-8.08383 + 3.69176i) q^{67} +(4.49132 + 2.91662i) q^{68} +(-7.41277 + 0.685487i) q^{69} +(-0.661446 + 0.326210i) q^{70} +(-5.85329 + 2.67311i) q^{71} +(0.912918 - 1.39853i) q^{72} +(-0.213603 - 0.185088i) q^{73} +(-7.58806 + 6.54362i) q^{74} +(6.24613 - 4.60694i) q^{75} +(-4.71827 + 10.2031i) q^{76} +(0.230396 - 0.784656i) q^{77} +(11.0873 - 3.22695i) q^{78} +(-0.786842 + 5.47261i) q^{79} +(-6.62522 + 6.00886i) q^{80} +(-2.85802 + 6.25819i) q^{81} +(3.57254 + 1.64179i) q^{82} +(3.35494 + 5.22039i) q^{83} +(-0.549440 + 0.471544i) q^{84} +(-4.64862 - 3.77340i) q^{85} +(-4.78451 - 10.5428i) q^{86} +(11.3103 + 7.26867i) q^{87} +(0.0706332 - 9.91751i) q^{88} +(-3.13900 - 10.6904i) q^{89} +(-1.18023 + 1.44695i) q^{90} +1.22679 q^{91} +(-9.55500 + 0.837851i) q^{92} -15.4813i q^{93} +(10.8722 - 1.53685i) q^{94} +(6.45145 - 10.7859i) q^{95} +(-4.83468 + 7.33012i) q^{96} +(5.91382 + 3.80058i) q^{97} +(8.94459 - 4.05922i) q^{98} +(-0.294660 - 2.04941i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Introduction

L-functions

Modular forms

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