LMFDB - Embedded newform 600.2.w.k.557.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(293,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("600.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			557.21
Character	$\chi$	$=$	600.557
Dual form			600.2.w.k.293.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.722477 - 1.21574i) q^{2} +(0.889875 - 1.48597i) q^{3} +(-0.956054 - 1.75669i) q^{4} +(-1.16365 - 2.15544i) q^{6} +(-2.09015 - 2.09015i) q^{7} +(-2.82641 - 0.106854i) q^{8} +(-1.41624 - 2.64467i) q^{9} +O(q^{10})$	\(q+(0.722477 - 1.21574i) q^{2} +(0.889875 - 1.48597i) q^{3} +(-0.956054 - 1.75669i) q^{4} +(-1.16365 - 2.15544i) q^{6} +(-2.09015 - 2.09015i) q^{7} +(-2.82641 - 0.106854i) q^{8} +(-1.41624 - 2.64467i) q^{9} -2.65514 q^{11} +(-3.46117 - 0.142564i) q^{12} +(4.21638 + 4.21638i) q^{13} +(-4.05116 + 1.03099i) q^{14} +(-2.17192 + 3.35898i) q^{16} +(3.84954 - 3.84954i) q^{17} +(-4.23843 - 0.188924i) q^{18} -3.15804 q^{19} +(-4.96588 + 1.24594i) q^{21} +(-1.91827 + 3.22796i) q^{22} +(1.60962 + 1.60962i) q^{23} +(-2.67393 + 4.10488i) q^{24} +(8.17226 - 2.07979i) q^{26} +(-5.19019 - 0.248921i) q^{27} +(-1.67345 + 5.67003i) q^{28} -4.35078i q^{29} +1.56789 q^{31} +(2.51449 + 5.06728i) q^{32} +(-2.36274 + 3.94546i) q^{33} +(-1.89884 - 7.46125i) q^{34} +(-3.29185 + 5.01634i) q^{36} +(4.94127 - 4.94127i) q^{37} +(-2.28161 + 3.83936i) q^{38} +(10.0175 - 2.51338i) q^{39} -10.6056i q^{41} +(-2.07300 + 6.93738i) q^{42} +(0.219791 + 0.219791i) q^{43} +(2.53845 + 4.66425i) q^{44} +(3.11979 - 0.793968i) q^{46} +(-1.83256 + 1.83256i) q^{47} +(3.05862 + 6.21650i) q^{48} +1.73743i q^{49} +(-2.29471 - 9.14594i) q^{51} +(3.37579 - 11.4380i) q^{52} +(4.64119 - 4.64119i) q^{53} +(-4.05241 + 6.13009i) q^{54} +(5.68427 + 6.13095i) q^{56} +(-2.81027 + 4.69277i) q^{57} +(-5.28942 - 3.14334i) q^{58} -9.93175i q^{59} +11.9159i q^{61} +(1.13277 - 1.90615i) q^{62} +(-2.56758 + 8.48790i) q^{63} +(7.97716 + 0.604028i) q^{64} +(3.08964 + 5.72299i) q^{66} +(-8.80906 + 8.80906i) q^{67} +(-10.4428 - 3.08208i) q^{68} +(3.82422 - 0.959493i) q^{69} +2.89837i q^{71} +(3.72029 + 7.62624i) q^{72} +(2.29779 - 2.29779i) q^{73} +(-2.43735 - 9.57725i) q^{74} +(3.01926 + 5.54770i) q^{76} +(5.54962 + 5.54962i) q^{77} +(4.18178 - 13.9945i) q^{78} +9.02676i q^{79} +(-4.98851 + 7.49098i) q^{81} +(-12.8936 - 7.66227i) q^{82} +(9.78801 - 9.78801i) q^{83} +(6.93637 + 7.53233i) q^{84} +(0.426003 - 0.108415i) q^{86} +(-6.46515 - 3.87165i) q^{87} +(7.50450 + 0.283713i) q^{88} +2.83249 q^{89} -17.6257i q^{91} +(1.28872 - 4.36649i) q^{92} +(1.39523 - 2.32985i) q^{93} +(0.903936 + 3.55190i) q^{94} +(9.76744 + 0.772783i) q^{96} +(9.26375 + 9.26375i) q^{97} +(2.11227 + 1.25525i) q^{98} +(3.76032 + 7.02194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 12 q^{6}+O(q^{10}) $ 64 * q + 12 * q^6	$ 64 q + 12 q^{6} - 40 q^{16} + 32 q^{31} - 84 q^{36} - 128 q^{46} - 180 q^{66} + 168 q^{76} + 48 q^{81} + 228 q^{96}+O(q^{100}) $ 64 * q + 12 * q^6 - 40 * q^16 + 32 * q^31 - 84 * q^36 - 128 * q^46 - 180 * q^66 + 168 * q^76 + 48 * q^81 + 228 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.722477	−	1.21574i	0.510868	−	0.859659i
$2$	0.722477	−	1.21574i	0.510868	−	0.859659i
$3$	0.889875	−	1.48597i	0.513770	−	0.857928i
$3$	0.889875	−	1.48597i	0.513770	−	0.857928i
$4$	−0.956054	−	1.75669i	−0.478027	−	0.878345i
$5$		0			0
$5$		0			0
$6$	−1.16365	−	2.15544i	−0.475057	−	0.879955i
$7$	−2.09015	−	2.09015i	−0.790001	−	0.790001i	0.191493	−	0.981494i	$-0.438667\pi$
$7$	−2.09015	−	2.09015i	−0.790001	−	0.790001i	−0.981494	+	0.191493i	$0.938667\pi$
$8$	−2.82641	−	0.106854i	−0.999286	−	0.0377787i
$9$	−1.41624	−	2.64467i	−0.472081	−	0.881555i
$10$		0			0
$11$	−2.65514			−0.800553			−0.400277	−	0.916394i	$-0.631086\pi$
$11$	−2.65514			−0.800553			−0.400277	+	0.916394i	$0.631086\pi$
$12$	−3.46117	−	0.142564i	−0.999153	−	0.0411546i
$13$	4.21638	+	4.21638i	1.16941	+	1.16941i	0.982347	+	0.187065i	$0.0598976\pi$
$13$	4.21638	+	4.21638i	1.16941	+	1.16941i	0.187065	+	0.982347i	$0.440102\pi$
$14$	−4.05116	+	1.03099i	−1.08272	+	0.275545i
$15$		0			0
$16$	−2.17192	+	3.35898i	−0.542981	+	0.839745i
$17$	3.84954	−	3.84954i	0.933651	−	0.933651i	−0.0642808	−	0.997932i	$-0.520475\pi$
$17$	3.84954	−	3.84954i	0.933651	−	0.933651i	0.997932	+	0.0642808i	$0.0204753\pi$
$18$	−4.23843	−	0.188924i	−0.999008	−	0.0445299i
$19$	−3.15804			−0.724505			−0.362252	−	0.932080i	$-0.617992\pi$
$19$	−3.15804			−0.724505			−0.362252	+	0.932080i	$0.617992\pi$
$20$		0			0
$21$	−4.96588	+	1.24594i	−1.08364	+	0.271885i
$22$	−1.91827	+	3.22796i	−0.408977	+	0.688203i
$23$	1.60962	+	1.60962i	0.335629	+	0.335629i	0.854719	−	0.519090i	$-0.173729\pi$
$23$	1.60962	+	1.60962i	0.335629	+	0.335629i	−0.519090	+	0.854719i	$0.673729\pi$
$24$	−2.67393	+	4.10488i	−0.545814	+	0.837906i
$25$		0			0
$26$	8.17226	−	2.07979i	1.60271	−	0.407880i
$27$	−5.19019	−	0.248921i	−0.998852	−	0.0479048i
$28$	−1.67345	+	5.67003i	−0.316252	+	1.07154i
$29$		−	4.35078i		−	0.807919i	−0.914777	−	0.403959i	$-0.867634\pi$
$29$		−	4.35078i		−	0.807919i	0.914777	−	0.403959i	$-0.132366\pi$
$30$		0			0
$31$	1.56789			0.281602			0.140801	−	0.990038i	$-0.455032\pi$
$31$	1.56789			0.281602			0.140801	+	0.990038i	$0.455032\pi$
$32$	2.51449	+	5.06728i	0.444503	+	0.895777i
$33$	−2.36274	+	3.94546i	−0.411300	+	0.686817i
$34$	−1.89884	−	7.46125i	−0.325649	−	1.27959i
$35$		0			0
$36$	−3.29185	+	5.01634i	−0.548642	+	0.836057i
$37$	4.94127	−	4.94127i	0.812339	−	0.812339i	−0.172645	−	0.984984i	$-0.555231\pi$
$37$	4.94127	−	4.94127i	0.812339	−	0.812339i	0.984984	+	0.172645i	$0.0552313\pi$
$38$	−2.28161	+	3.83936i	−0.370127	+	0.622827i
$39$	10.0175	−	2.51338i	1.60408	−	0.402463i
$40$		0			0
$41$		−	10.6056i		−	1.65631i	−0.560500	−	0.828154i	$-0.689391\pi$
$41$		−	10.6056i		−	1.65631i	0.560500	−	0.828154i	$-0.310609\pi$
$42$	−2.07300	+	6.93738i	−0.319870	+	1.07046i
$43$	0.219791	+	0.219791i	0.0335178	+	0.0335178i	0.723667	−	0.690149i	$-0.242455\pi$
$43$	0.219791	+	0.219791i	0.0335178	+	0.0335178i	−0.690149	+	0.723667i	$0.742455\pi$
$44$	2.53845	+	4.66425i	0.382686	+	0.703162i
$45$		0			0
$46$	3.11979	−	0.793968i	0.459989	−	0.117064i
$47$	−1.83256	+	1.83256i	−0.267306	+	0.267306i	−0.828014	−	0.560708i	$-0.810529\pi$
$47$	−1.83256	+	1.83256i	−0.267306	+	0.267306i	0.560708	+	0.828014i	$0.310529\pi$
$48$	3.05862	+	6.21650i	0.441474	+	0.897274i
$49$			1.73743i			0.248204i
$50$		0			0
$51$	−2.29471	−	9.14594i	−0.321324	−	1.28069i
$52$	3.37579	−	11.4380i	0.468137	−	1.58616i
$53$	4.64119	−	4.64119i	0.637516	−	0.637516i	−0.312426	−	0.949942i	$-0.601142\pi$
$53$	4.64119	−	4.64119i	0.637516	−	0.637516i	0.949942	+	0.312426i	$0.101142\pi$
$54$	−4.05241	+	6.13009i	−0.551464	+	0.834199i
$55$		0			0
$56$	5.68427	+	6.13095i	0.759592	+	0.819283i
$57$	−2.81027	+	4.69277i	−0.372229	+	0.621573i
$58$	−5.28942	−	3.14334i	−0.694535	−	0.412740i
$59$		−	9.93175i		−	1.29300i	−0.762912	−	0.646502i	$-0.776231\pi$
$59$		−	9.93175i		−	1.29300i	0.762912	−	0.646502i	$-0.223769\pi$
$60$		0			0
$61$			11.9159i			1.52568i	0.646590	+	0.762838i	$0.276195\pi$
$61$			11.9159i			1.52568i	−0.646590	+	0.762838i	$0.723805\pi$
$62$	1.13277	−	1.90615i	0.143862	−	0.242082i
$63$	−2.56758	+	8.48790i	−0.323485	+	1.06937i
$64$	7.97716	+	0.604028i	0.997146	+	0.0755035i
$65$		0			0
$66$	3.08964	+	5.72299i	0.380308	+	0.704451i
$67$	−8.80906	+	8.80906i	−1.07620	+	1.07620i	−0.0793517	+	0.996847i	$0.525285\pi$
$67$	−8.80906	+	8.80906i	−1.07620	+	1.07620i	−0.996847	+	0.0793517i	$0.974715\pi$
$68$	−10.4428	−	3.08208i	−1.26638	−	0.373758i
$69$	3.82422	−	0.959493i	0.460381	−	0.115509i
$70$		0			0
$71$			2.89837i			0.343973i	0.985099	+	0.171986i	$0.0550185\pi$
$71$			2.89837i			0.343973i	−0.985099	+	0.171986i	$0.944982\pi$
$72$	3.72029	+	7.62624i	0.438440	+	0.898760i
$73$	2.29779	−	2.29779i	0.268936	−	0.268936i	−0.559736	−	0.828671i	$-0.689097\pi$
$73$	2.29779	−	2.29779i	0.268936	−	0.268936i	0.828671	+	0.559736i	$0.189097\pi$
$74$	−2.43735	−	9.57725i	−0.283336	−	1.11333i
$75$		0			0
$76$	3.01926	+	5.54770i	0.346333	+	0.636365i
$77$	5.54962	+	5.54962i	0.632438	+	0.632438i
$78$	4.18178	−	13.9945i	0.473493	−	1.58457i
$79$			9.02676i			1.01559i	0.861478	+	0.507795i	$0.169539\pi$
$79$			9.02676i			1.01559i	−0.861478	+	0.507795i	$0.830461\pi$
$80$		0			0
$81$	−4.98851	+	7.49098i	−0.554279	+	0.832331i
$82$	−12.8936	−	7.66227i	−1.42386	−	0.846156i
$83$	9.78801	−	9.78801i	1.07437	−	1.07437i	0.0773719	−	0.997002i	$-0.475347\pi$
$83$	9.78801	−	9.78801i	1.07437	−	1.07437i	0.997002	−	0.0773719i	$-0.0246529\pi$
$84$	6.93637	+	7.53233i	0.756820	+	0.821844i
$85$		0			0
$86$	0.426003	−	0.108415i	0.0459371	−	0.0116907i
$87$	−6.46515	−	3.87165i	−0.693136	−	0.415084i
$88$	7.50450	+	0.283713i	0.799982	+	0.0302439i
$89$	2.83249			0.300243			0.150121	−	0.988668i	$-0.452034\pi$
$89$	2.83249			0.300243			0.150121	+	0.988668i	$0.452034\pi$
$90$		0			0
$91$		−	17.6257i		−	1.84768i
$92$	1.28872	−	4.36649i	0.134358	−	0.455238i
$93$	1.39523	−	2.32985i	0.144679	−	0.241594i
$94$	0.903936	+	3.55190i	0.0932339	+	0.366351i
$95$		0			0
$96$	9.76744	+	0.772783i	0.996885	+	0.0788719i
$97$	9.26375	+	9.26375i	0.940592	+	0.940592i	0.998332	−	0.0577400i	$-0.0183894\pi$
$97$	9.26375	+	9.26375i	0.940592	+	0.940592i	−0.0577400	+	0.998332i	$0.518389\pi$
$98$	2.11227	+	1.25525i	0.213371	+	0.126800i
$99$	3.76032	+	7.02194i	0.377926	+	0.705732i
$100$		0			0
$101$	−10.6797			−1.06267			−0.531337	−	0.847160i	$-0.678310\pi$
$101$	−10.6797			−1.06267			−0.531337	+	0.847160i	$0.678310\pi$
$102$	−12.7770	−	3.81795i	−1.26511	−	0.378034i
$103$	10.3368	−	10.3368i	1.01851	−	1.01851i	0.0186893	−	0.999825i	$-0.494051\pi$
$103$	10.3368	−	10.3368i	1.01851	−	1.01851i	0.999825	−	0.0186893i	$-0.00594934\pi$
$104$	−11.4667	−	12.3677i	−1.12440	−	1.21276i
$105$		0			0
$106$	−2.28933	−	8.99563i	−0.222359	−	0.873733i
$107$	−3.47289	−	3.47289i	−0.335737	−	0.335737i	0.519023	−	0.854760i	$-0.326296\pi$
$107$	−3.47289	−	3.47289i	−0.335737	−	0.335737i	−0.854760	+	0.519023i	$0.826296\pi$
$108$	4.52482	+	9.35553i	0.435401	+	0.900237i
$109$	2.67954			0.256654			0.128327	−	0.991732i	$-0.459039\pi$
$109$	2.67954			0.256654			0.128327	+	0.991732i	$0.459039\pi$
$110$		0			0
$111$	−2.94549	−	11.7397i	−0.279573	−	1.11428i
$112$	11.5604	−	2.48113i	1.09236	−	0.234445i
$113$	6.11636	+	6.11636i	0.575379	+	0.575379i	0.933627	−	0.358248i	$-0.116626\pi$
$113$	6.11636	+	6.11636i	0.575379	+	0.575379i	−0.358248	+	0.933627i	$0.616626\pi$
$114$	3.67485	+	6.80698i	0.344181	+	0.637532i
$115$		0			0
$116$	−7.64297	+	4.15958i	−0.709632	+	0.386207i
$117$	5.17949	−	17.1223i	0.478844	−	1.58296i
$118$	−12.0744	−	7.17546i	−1.11154	−	0.660555i
$119$	−16.0922			−1.47517
$120$		0			0
$121$	−3.95026			−0.359114
$122$	14.4867	+	8.60897i	1.31156	+	0.779420i
$123$	−15.7596	−	9.43762i	−1.42099	−	0.850962i
$124$	−1.49899	−	2.75430i	−0.134613	−	0.247344i
$125$		0			0
$126$	8.46407	+	9.25383i	0.754039	+	0.824396i
$127$	11.2254	+	11.2254i	0.996089	+	0.996089i	0.999992	−	0.00390306i	$-0.00124239\pi$
$127$	11.2254	+	11.2254i	0.996089	+	0.996089i	−0.00390306	+	0.999992i	$0.501242\pi$
$128$	6.49766	−	9.26177i	0.574317	−	0.818633i
$129$	0.522191	−	0.131017i	0.0459763	−	0.0115354i
$130$		0			0
$131$	6.55577			0.572780			0.286390	−	0.958113i	$-0.407545\pi$
$131$	6.55577			0.572780			0.286390	+	0.958113i	$0.407545\pi$
$132$	9.18987	+	0.378525i	0.799875	+	0.0329464i
$133$	6.60078	+	6.60078i	0.572360	+	0.572360i
$134$	4.34520	+	17.0739i	0.375368	+	1.47496i
$135$		0			0
$136$	−11.2917	+	10.4690i	−0.968257	+	0.897712i
$137$	−1.63651	+	1.63651i	−0.139817	+	0.139817i	−0.773551	−	0.633734i	$-0.781521\pi$
$137$	−1.63651	+	1.63651i	−0.139817	+	0.139817i	0.633734	+	0.773551i	$0.281521\pi$
$138$	1.59641	−	5.34247i	0.135896	−	0.454781i
$139$	1.03173			0.0875104			0.0437552	−	0.999042i	$-0.486068\pi$
$139$	1.03173			0.0875104			0.0437552	+	0.999042i	$0.486068\pi$
$140$		0			0
$141$	1.09239	+	4.35389i	0.0919956	+	0.366663i
$142$	3.52366	+	2.09400i	0.295699	+	0.175725i
$143$	−11.1951	−	11.1951i	−0.936177	−	0.936177i
$144$	11.9594	+	0.986872i	0.996613	+	0.0822394i
$145$		0			0
$146$	−1.13342	−	4.45361i	−0.0938022	−	0.368583i
$147$	2.58178	+	1.54610i	0.212942	+	0.127520i
$148$	−13.4044	−	3.95616i	−1.10183	−	0.325194i
$149$			3.60278i			0.295151i	0.989051	+	0.147576i	$0.0471470\pi$
$149$			3.60278i			0.295151i	−0.989051	+	0.147576i	$0.952853\pi$
$150$		0			0
$151$	13.6985			1.11476			0.557382	−	0.830256i	$-0.311806\pi$
$151$	13.6985			1.11476			0.557382	+	0.830256i	$0.311806\pi$
$152$	8.92592	+	0.337451i	0.723988	+	0.0273709i
$153$	−15.6326	−	4.72886i	−1.26382	−	0.382306i
$154$	10.7564	−	2.73743i	0.866774	−	0.220588i
$155$		0			0
$156$	−13.9925	−	15.1947i	−1.12030	−	1.21655i
$157$	7.26828	−	7.26828i	0.580072	−	0.580072i	−0.354851	−	0.934923i	$-0.615468\pi$
$157$	7.26828	−	7.26828i	0.580072	−	0.580072i	0.934923	+	0.354851i	$0.115468\pi$
$158$	10.9742	+	6.52163i	0.873061	+	0.518833i
$159$	−2.76661	−	11.0268i	−0.219406	−	0.874479i
$160$		0			0
$161$		−	6.72868i		−	0.530295i
$162$	5.50301	+	11.4768i	0.432357	+	0.901702i
$163$	−9.50622	−	9.50622i	−0.744585	−	0.744585i	0.228872	−	0.973457i	$-0.426496\pi$
$163$	−9.50622	−	9.50622i	−0.744585	−	0.744585i	−0.973457	+	0.228872i	$0.926496\pi$
$164$	−18.6307	+	10.1395i	−1.45481	+	0.791760i
$165$		0			0
$166$	−4.82808	−	18.9713i	−0.374732	−	1.47246i
$167$	14.4143	−	14.4143i	1.11541	−	1.11541i	0.123005	−	0.992406i	$-0.460747\pi$
$167$	14.4143	−	14.4143i	1.11541	−	1.11541i	0.992406	−	0.123005i	$-0.0392532\pi$
$168$	14.1687	−	2.99090i	1.09314	−	0.230753i
$169$			22.5557i			1.73505i
$170$		0			0
$171$	4.47256	+	8.35197i	0.342025	+	0.638691i
$172$	0.175973	−	0.596237i	0.0134178	−	0.0454626i
$173$	−18.0907	+	18.0907i	−1.37541	+	1.37541i	−0.523202	+	0.852209i	$0.675262\pi$
$173$	−18.0907	+	18.0907i	−1.37541	+	1.37541i	−0.852209	+	0.523202i	$0.824738\pi$
$174$	−9.37784	+	5.06277i	−0.710932	+	0.383807i
$175$		0			0
$176$	5.76675	−	8.91855i	0.434685	−	0.672261i
$177$	−14.7583	−	8.83802i	−1.10930	−	0.664307i
$178$	2.04641	−	3.44357i	0.153385	−	0.258107i
$179$			5.81962i			0.434979i	0.976063	+	0.217489i	$0.0697868\pi$
$179$			5.81962i			0.434979i	−0.976063	+	0.217489i	$0.930213\pi$
$180$		0			0
$181$			3.58348i			0.266358i	0.991092	+	0.133179i	$0.0425185\pi$
$181$			3.58348i			0.266358i	−0.991092	+	0.133179i	$0.957481\pi$
$182$	−21.4283	−	12.7342i	−1.58837	−	0.943919i
$183$	17.7067	+	10.6037i	1.30892	+	0.783846i
$184$	−4.37745	−	4.72144i	−0.322710	−	0.348069i
$185$		0			0
$186$	−1.82447	−	3.37950i	−0.133777	−	0.247797i
$187$	−10.2211	+	10.2211i	−0.747437	+	0.747437i
$188$	4.97126	+	1.46721i	0.362567	+	0.107008i
$189$	10.3280	+	11.3685i	0.751250	+	0.826939i
$190$		0			0
$191$			11.6034i			0.839591i	0.907619	+	0.419796i	$0.137898\pi$
$191$			11.6034i			0.839591i	−0.907619	+	0.419796i	$0.862102\pi$
$192$	7.99625	−	11.3164i	0.577080	−	0.816688i
$193$	9.83073	−	9.83073i	0.707632	−	0.707632i	−0.258405	−	0.966037i	$-0.583197\pi$
$193$	9.83073	−	9.83073i	0.707632	−	0.707632i	0.966037	+	0.258405i	$0.0831969\pi$
$194$	17.9552	−	4.56948i	1.28911	−	0.328069i
$195$		0			0
$196$	3.05213	−	1.66108i	0.218009	−	0.118648i
$197$	1.97306	+	1.97306i	0.140574	+	0.140574i	0.773892	−	0.633318i	$-0.218307\pi$
$197$	1.97306	+	1.97306i	0.140574	+	0.140574i	−0.633318	+	0.773892i	$0.718307\pi$
$198$	11.2536	+	0.501620i	0.799759	+	0.0356486i
$199$		−	4.09303i		−	0.290147i	−0.989421	−	0.145074i	$-0.953658\pi$
$199$		−	4.09303i		−	0.290147i	0.989421	−	0.145074i	$-0.0463419\pi$
$200$		0			0
$201$	5.25108	+	20.9290i	0.370383	+	1.47622i
$202$	−7.71587	+	12.9838i	−0.542887	+	0.913538i
$203$	−9.09376	+	9.09376i	−0.638257	+	0.638257i
$204$	−13.8727	+	12.7751i	−0.971284	+	0.894436i
$205$		0			0
$206$	−5.09877	−	20.0350i	−0.355248	−	1.39590i
$207$	1.97729	−	6.53652i	0.137431	−	0.454319i
$208$	−23.3204	+	5.00509i	−1.61698	+	0.347040i
$209$	8.38503			0.580005
$210$		0			0
$211$			5.39432i			0.371361i	0.982610	+	0.185680i	$0.0594489\pi$
$211$			5.39432i			0.371361i	−0.982610	+	0.185680i	$0.940551\pi$
$212$	−12.5903	−	3.71590i	−0.864709	−	0.255209i
$213$	4.30690	+	2.57918i	0.295104	+	0.176723i
$214$	−6.73123	+	1.71305i	−0.460137	+	0.117102i
$215$		0			0
$216$	14.6430	+	1.25815i	0.996329	+	0.0856059i
$217$	−3.27713	−	3.27713i	−0.222466	−	0.222466i
$218$	1.93591	−	3.25763i	0.131116	−	0.220635i
$219$	−1.36971	−	5.45920i	−0.0925564	−	0.368898i
$220$		0			0
$221$	32.4622			2.18365
$222$	−16.4005	−	4.90072i	−1.10073	−	0.328915i
$223$	2.63896	−	2.63896i	0.176718	−	0.176718i	−0.613206	−	0.789923i	$-0.710120\pi$
$223$	2.63896	−	2.63896i	0.176718	−	0.176718i	0.789923	+	0.613206i	$0.210120\pi$
$224$	5.33572	−	15.8470i	0.356507	−	1.05882i
$225$		0			0
$226$	11.8548	−	3.01698i	0.788572	−	0.200687i
$227$	5.62771	+	5.62771i	0.373524	+	0.373524i	0.868759	−	0.495235i	$-0.164918\pi$
$227$	5.62771	+	5.62771i	0.373524	+	0.373524i	−0.495235	+	0.868759i	$0.664918\pi$
$228$	10.9305	+	0.450222i	0.723891	+	0.0298167i
$229$	−11.2319			−0.742225			−0.371113	−	0.928588i	$-0.621024\pi$
$229$	−11.2319			−0.742225			−0.371113	+	0.928588i	$0.621024\pi$
$230$		0			0
$231$	13.1851	−	3.30813i	0.867514	−	0.217659i
$232$	−0.464899	+	12.2971i	−0.0305221	+	0.807342i
$233$	15.0715	+	15.0715i	0.987366	+	0.987366i	0.999921	−	0.0125551i	$-0.00399652\pi$
$233$	15.0715	+	15.0715i	0.987366	+	0.987366i	−0.0125551	+	0.999921i	$0.503997\pi$
$234$	−17.0743	−	18.6674i	−1.11618	−	1.22033i
$235$		0			0
$236$	−17.4470	+	9.49529i	−1.13570	+	0.618091i
$237$	13.4135	+	8.03269i	0.871303	+	0.521780i
$238$	−11.6263	+	19.5640i	−0.753618	+	1.26814i
$239$	−2.89837			−0.187480			−0.0937398	−	0.995597i	$-0.529882\pi$
$239$	−2.89837			−0.187480			−0.0937398	+	0.995597i	$0.529882\pi$
$240$		0			0
$241$	0.551900			0.0355510			0.0177755	−	0.999842i	$-0.494342\pi$
$241$	0.551900			0.0355510			0.0177755	+	0.999842i	$0.494342\pi$
$242$	−2.85397	+	4.80249i	−0.183460	+	0.308716i
$243$	6.69226	+	14.0788i	0.429308	+	0.903158i
$244$	20.9326	−	11.3923i	1.34007	−	0.729314i
$245$		0			0
$246$	−22.8596	+	12.3411i	−1.45748	+	0.786841i
$247$	−13.3155	−	13.3155i	−0.847245	−	0.847245i
$248$	−4.43151	−	0.167536i	−0.281401	−	0.0106386i
$249$	−5.83463	−	23.2549i	−0.369755	−	1.47372i
$250$		0			0
$251$	6.29691			0.397457			0.198729	−	0.980055i	$-0.436319\pi$
$251$	6.29691			0.397457			0.198729	+	0.980055i	$0.436319\pi$
$252$	17.3654	−	3.60444i	1.09391	−	0.227058i
$253$	−4.27376	−	4.27376i	−0.268689	−	0.268689i
$254$	21.7572	−	5.53707i	1.36517	−	0.347426i
$255$		0			0
$256$	−6.56551	−	14.5909i	−0.410344	−	0.911931i
$257$	−10.9183	+	10.9183i	−0.681066	+	0.681066i	−0.960240	−	0.279174i	$-0.909939\pi$
$257$	−10.9183	+	10.9183i	−0.681066	+	0.681066i	0.279174	+	0.960240i	$0.409939\pi$
$258$	0.217988	−	0.729506i	0.0135713	−	0.0454171i
$259$	−20.6559			−1.28350
$260$		0			0
$261$	−11.5063	+	6.16176i	−0.712225	+	0.381403i
$262$	4.73639	−	7.97012i	0.292615	−	0.492396i
$263$	−21.0955	−	21.0955i	−1.30081	−	1.30081i	−0.927848	−	0.372959i	$-0.878343\pi$
$263$	−21.0955	−	21.0955i	−1.30081	−	1.30081i	−0.372959	−	0.927848i	$-0.621657\pi$
$264$	7.09966	−	10.8990i	0.436954	−	0.670788i
$265$		0			0
$266$	12.7937	−	3.25593i	0.784435	−	0.199634i
$267$	2.52056	−	4.20900i	0.154256	−	0.257587i
$268$	23.8967	+	7.05286i	1.45973	+	0.430822i
$269$			20.6115i			1.25671i	0.777929	+	0.628353i	$0.216271\pi$
$269$			20.6115i			1.25671i	−0.777929	+	0.628353i	$0.783729\pi$
$270$		0			0
$271$	−24.2931			−1.47570			−0.737851	−	0.674964i	$-0.764159\pi$
$271$	−24.2931			−1.47570			−0.737851	+	0.674964i	$0.764159\pi$
$272$	4.56963	+	21.2914i	0.277075	+	1.29098i
$273$	−26.1913	−	15.6847i	−1.58517	−	0.949280i
$274$	0.807234	+	3.17192i	0.0487668	+	0.191623i
$275$		0			0
$276$	−5.34169	−	5.80063i	−0.321532	−	0.349157i
$277$	−12.6491	+	12.6491i	−0.760013	+	0.760013i	−0.976324	−	0.216312i	$-0.930597\pi$
$277$	−12.6491	+	12.6491i	−0.760013	+	0.760013i	0.216312	+	0.976324i	$0.430597\pi$
$278$	0.745403	−	1.25432i	0.0447063	−	0.0752291i
$279$	−2.22052	−	4.14656i	−0.132939	−	0.248248i
$280$		0			0
$281$			8.81745i			0.526005i	0.964795	+	0.263002i	$0.0847127\pi$
$281$			8.81745i			0.526005i	−0.964795	+	0.263002i	$0.915287\pi$
$282$	6.08242	+	1.81752i	0.362203	+	0.108232i
$283$	13.4928	+	13.4928i	0.802061	+	0.802061i	0.983417	−	0.181357i	$-0.0580488\pi$
$283$	13.4928	+	13.4928i	0.802061	+	0.802061i	−0.181357	+	0.983417i	$0.558049\pi$
$284$	5.09153	−	2.77099i	0.302127	−	0.164428i
$285$		0			0
$286$	−21.6985	+	5.52212i	−1.28306	+	0.326530i
$287$	−22.1672	+	22.1672i	−1.30849	+	1.30849i
$288$	9.84014	−	13.8265i	0.579836	−	0.814733i
$289$		−	12.6379i		−	0.743409i
$290$		0			0
$291$	22.0093	−	5.52212i	1.29021	−	0.323712i
$292$	−6.23331	−	1.83969i	−0.364777	−	0.107660i
$293$	6.84294	−	6.84294i	0.399769	−	0.399769i	−0.478383	−	0.878151i	$-0.658777\pi$
$293$	6.84294	−	6.84294i	0.399769	−	0.399769i	0.878151	+	0.478383i	$0.158777\pi$
$294$	3.74493	−	2.02176i	0.218409	−	0.117911i
$295$		0			0
$296$	−14.4940	+	13.4380i	−0.842448	+	0.781070i
$297$	13.7806	+	0.660918i	0.799634	+	0.0383503i
$298$	4.38005	+	2.60293i	0.253730	+	0.150784i
$299$			13.5735i			0.784977i
$300$		0			0
$301$		−	0.918791i		−	0.0529583i
$302$	9.89682	−	16.6538i	0.569498	−	0.958317i
$303$	−9.50365	+	15.8698i	−0.545970	+	0.911698i
$304$	6.85902	−	10.6078i	0.393392	−	0.608400i
$305$		0			0
$306$	−17.0433	+	15.5887i	−0.974300	+	0.891150i
$307$	5.31757	−	5.31757i	0.303490	−	0.303490i	−0.538888	−	0.842378i	$-0.681155\pi$
$307$	5.31757	−	5.31757i	0.303490	−	0.303490i	0.842378	+	0.538888i	$0.181155\pi$
$308$	4.44323	−	15.0547i	0.253177	−	0.857822i
$309$	−6.16176	−	24.5587i	−0.350530	−	1.39709i
$310$		0			0
$311$			31.3649i			1.77854i	0.457382	+	0.889270i	$0.348787\pi$
$311$			31.3649i			1.77854i	−0.457382	+	0.889270i	$0.651213\pi$
$312$	−28.5821	+	6.03343i	−1.61814	+	0.341576i
$313$	−5.42321	+	5.42321i	−0.306538	+	0.306538i	−0.843565	−	0.537027i	$-0.819547\pi$
$313$	−5.42321	+	5.42321i	−0.306538	+	0.306538i	0.537027	+	0.843565i	$0.319547\pi$
$314$	−3.58518	−	14.0875i	−0.202324	−	0.795005i
$315$		0			0
$316$	15.8572	−	8.63007i	0.892039	−	0.485479i
$317$	−12.8513	−	12.8513i	−0.721799	−	0.721799i	0.247172	−	0.968972i	$-0.420499\pi$
$317$	−12.8513	−	12.8513i	−0.721799	−	0.721799i	−0.968972	+	0.247172i	$0.920499\pi$
$318$	−15.4045	−	4.60310i	−0.863841	−	0.258129i
$319$			11.5519i			0.646782i
$320$		0			0
$321$	−8.25108	+	2.07019i	−0.460530	+	0.115547i
$322$	−8.18034	−	4.86132i	−0.455872	−	0.270911i
$323$	−12.1570	+	12.1570i	−0.676435	+	0.676435i
$324$	17.9286	+	1.60149i	0.996034	+	0.0889715i
$325$		0			0
$326$	−18.4251	+	4.68908i	−1.02047	+	0.259704i
$327$	2.38446	−	3.98173i	0.131861	−	0.220190i
$328$	−1.13325	+	29.9756i	−0.0625732	+	1.65513i
$329$	7.66064			0.422345
$330$		0			0
$331$			10.6434i			0.585016i	0.956263	+	0.292508i	$0.0944899\pi$
$331$			10.6434i			0.585016i	−0.956263	+	0.292508i	$0.905510\pi$
$332$	−26.5524	−	7.83664i	−1.45725	−	0.430092i
$333$	−20.0660	−	6.06996i	−1.09961	−	0.332632i
$334$	−7.11005	−	27.9380i	−0.389045	−	1.52870i
$335$		0			0
$336$	6.60042	−	19.3864i	0.360083	−	1.05761i
$337$	−0.581584	−	0.581584i	−0.0316809	−	0.0316809i	0.691089	−	0.722770i	$-0.257131\pi$
$337$	−0.581584	−	0.581584i	−0.0316809	−	0.0316809i	−0.722770	+	0.691089i	$0.757131\pi$
$338$	27.4219	+	16.2960i	1.49155	+	0.886383i
$339$	14.5316	−	3.64596i	0.789246	−	0.198021i
$340$		0			0
$341$	−4.16297			−0.225438
$342$	13.3852	+	0.596632i	0.723786	+	0.0322621i
$343$	−10.9995	+	10.9995i	−0.593920	+	0.593920i
$344$	−0.597734	−	0.644705i	−0.0322276	−	0.0347602i
$345$		0			0
$346$	8.92350	+	35.0637i	0.479730	+	1.88504i
$347$	1.90948	+	1.90948i	0.102506	+	0.102506i	0.756500	−	0.653994i	$-0.226908\pi$
$347$	1.90948	+	1.90948i	0.102506	+	0.102506i	−0.653994	+	0.756500i	$0.726908\pi$
$348$	−0.620262	+	15.0588i	−0.0332495	+	0.807234i
$349$	−16.3562			−0.875528			−0.437764	−	0.899090i	$-0.644229\pi$
$349$	−16.3562			−0.875528			−0.437764	+	0.899090i	$0.644229\pi$
$350$		0			0
$351$	−20.8342	−	22.9333i	−1.11205	−	1.22409i
$352$	−6.67631	−	13.4543i	−0.355848	−	0.717118i
$353$	−0.326679	−	0.326679i	−0.0173874	−	0.0173874i	0.698360	−	0.715747i	$-0.253914\pi$
$353$	−0.326679	−	0.326679i	−0.0173874	−	0.0173874i	−0.715747	+	0.698360i	$0.753914\pi$
$354$	−21.4073	+	11.5571i	−1.13779	+	0.614250i
$355$		0			0
$356$	−2.70801	−	4.97580i	−0.143524	−	0.263717i
$357$	−14.3201	+	23.9126i	−0.757898	+	1.26559i
$358$	7.07515	+	4.20454i	0.373934	+	0.222217i
$359$	16.0922			0.849315			0.424657	−	0.905354i	$-0.360395\pi$
$359$	16.0922			0.849315			0.424657	+	0.905354i	$0.360395\pi$
$360$		0			0
$361$	−9.02676			−0.475093
$362$	4.35658	+	2.58898i	0.228977	+	0.136074i
$363$	−3.51524	+	5.86998i	−0.184502	+	0.308094i
$364$	−30.9629	+	16.8511i	−1.62290	+	0.883239i
$365$		0			0
$366$	25.6840	−	13.8659i	1.34253	−	0.724783i
$367$	17.3259	+	17.3259i	0.904406	+	0.904406i	0.995814	−	0.0914078i	$-0.0291367\pi$
$367$	17.3259	+	17.3259i	0.904406	+	0.904406i	−0.0914078	+	0.995814i	$0.529137\pi$
$368$	−8.90265	+	1.91071i	−0.464083	+	0.0996028i
$369$	−28.0481	+	15.0200i	−1.46013	+	0.781912i
$370$		0			0
$371$	−19.4015			−1.00728
$372$	−5.42674	−	0.223525i	−0.281364	−	0.0115892i
$373$	4.04391	+	4.04391i	0.209386	+	0.209386i	0.804006	−	0.594621i	$-0.202698\pi$
$373$	4.04391	+	4.04391i	0.209386	+	0.209386i	−0.594621	+	0.804006i	$0.702698\pi$
$374$	5.04168	+	19.8106i	0.260699	+	1.02438i
$375$		0			0
$376$	5.37538	−	4.98374i	0.277214	−	0.257017i
$377$	18.3445	−	18.3445i	0.944791	−	0.944791i
$378$	21.2829	−	4.34264i	1.09468	−	0.223361i
$379$	9.37395			0.481507			0.240754	−	0.970586i	$-0.422605\pi$
$379$	9.37395			0.481507			0.240754	+	0.970586i	$0.422605\pi$
$380$		0			0
$381$	26.6698	−	6.69143i	1.36633	−	0.342812i
$382$	14.1067	+	8.38318i	0.721762	+	0.428921i
$383$	−1.94014	−	1.94014i	−0.0991364	−	0.0991364i	0.655799	−	0.754935i	$-0.272332\pi$
$383$	−1.94014	−	1.94014i	−0.0991364	−	0.0991364i	−0.754935	+	0.655799i	$0.772332\pi$
$384$	−7.98065	−	17.8972i	−0.407261	−	0.913312i
$385$		0			0
$386$	−4.84915	−	19.0541i	−0.246815	−	0.969829i
$387$	0.269996	−	0.892551i	0.0137247	−	0.0453709i
$388$	7.41690	−	25.1302i	0.376536	−	1.27579i
$389$		−	15.7785i		−	0.800003i	−0.916515	−	0.400001i	$-0.869010\pi$
$389$		−	15.7785i		−	0.800003i	0.916515	−	0.400001i	$-0.130990\pi$
$390$		0			0
$391$	12.3926			0.626721
$392$	0.185652	−	4.91069i	0.00937684	−	0.248027i
$393$	5.83382	−	9.74171i	0.294277	−	0.491404i
$394$	3.82422	−	0.973239i	0.192661	−	0.0490310i
$395$		0			0
$396$	8.74032	−	13.3191i	0.439217	−	0.669308i
$397$	−16.1961	+	16.1961i	−0.812858	+	0.812858i	−0.985061	−	0.172204i	$-0.944911\pi$
$397$	−16.1961	+	16.1961i	−0.812858	+	0.812858i	0.172204	+	0.985061i	$0.444911\pi$
$398$	−4.97607	−	2.95712i	−0.249428	−	0.148227i
$399$	15.6825	−	3.93472i	0.785105	−	0.196982i
$400$		0			0
$401$		−	33.9532i		−	1.69554i	−0.530362	−	0.847771i	$-0.677944\pi$
$401$		−	33.9532i		−	1.69554i	0.530362	−	0.847771i	$-0.322056\pi$
$402$	29.2381	+	8.73678i	1.45826	+	0.435751i
$403$	6.61083	+	6.61083i	0.329309	+	0.329309i
$404$	10.2104	+	18.7610i	0.507987	+	0.933395i
$405$		0			0
$406$	4.48563	+	17.6257i	0.222618	+	0.874749i
$407$	−13.1197	+	13.1197i	−0.650321	+	0.650321i
$408$	5.50850	+	26.0953i	0.272712	+	1.29191i
$409$		−	11.9177i		−	0.589294i	−0.955606	−	0.294647i	$-0.904798\pi$
$409$		−	11.9177i		−	0.589294i	0.955606	−	0.294647i	$-0.0952021\pi$
$410$		0			0
$411$	0.975525	+	3.88811i	0.0481191	+	0.191786i
$412$	−28.0411	−	8.27602i	−1.38148	−	0.407730i
$413$	−20.7588	+	20.7588i	−1.02148	+	1.02148i
$414$	−6.51817	−	7.12636i	−0.320350	−	0.350241i
$415$		0			0
$416$	−10.7635	+	31.9676i	−0.527726	+	1.56734i
$417$	0.918113	−	1.53313i	0.0449602	−	0.0750776i
$418$	6.05799	−	10.1940i	0.296306	−	0.498606i
$419$		−	0.494053i		−	0.0241361i	−0.999927	−	0.0120680i	$-0.996159\pi$
$419$		−	0.494053i		−	0.0241361i	0.999927	−	0.0120680i	$-0.00384147\pi$
$420$		0			0
$421$		−	28.0844i		−	1.36875i	−0.729129	−	0.684376i	$-0.760075\pi$
$421$		−	28.0844i		−	1.36875i	0.729129	−	0.684376i	$-0.239925\pi$
$422$	6.55810	+	3.89727i	0.319243	+	0.189716i
$423$	7.44186	+	2.25116i	0.361835	+	0.109455i
$424$	−13.6138	+	12.6220i	−0.661145	+	0.612976i
$425$		0			0
$426$	6.24726	−	3.37267i	0.302681	−	0.163407i
$427$	24.9060	−	24.9060i	1.20529	−	1.20529i
$428$	−2.78053	+	9.42108i	−0.134402	+	0.455385i
$429$	−26.5978	+	6.67337i	−1.28415	+	0.322193i
$430$		0			0
$431$			8.20673i			0.395304i	0.980272	+	0.197652i	$0.0633316\pi$
$431$			8.20673i			0.395304i	−0.980272	+	0.197652i	$0.936668\pi$
$432$	12.1088	−	16.8931i	0.582585	−	0.812770i
$433$	−8.09993	+	8.09993i	−0.389258	+	0.389258i	−0.874423	−	0.485165i	$-0.838760\pi$
$433$	−8.09993	+	8.09993i	−0.389258	+	0.389258i	0.485165	+	0.874423i	$0.338760\pi$
$434$	−6.35179	+	1.61649i	−0.304896	+	0.0775941i
$435$		0			0
$436$	−2.56179	−	4.70713i	−0.122687	−	0.225431i
$437$	−5.08325	−	5.08325i	−0.243165	−	0.243165i
$438$	−7.62655	−	2.27893i	−0.364411	−	0.108892i
$439$		−	5.21928i		−	0.249103i	−0.992213	−	0.124551i	$-0.960251\pi$
$439$		−	5.21928i		−	0.249103i	0.992213	−	0.124551i	$-0.0397491\pi$
$440$		0			0
$441$	4.59492	−	2.46062i	0.218806	−	0.117173i
$442$	23.4532	−	39.4657i	1.11556	−	1.87719i
$443$	21.7308	−	21.7308i	1.03246	−	1.03246i	0.0330087	−	0.999455i	$-0.489491\pi$
$443$	21.7308	−	21.7308i	1.03246	−	1.03246i	0.999455	−	0.0330087i	$-0.0105089\pi$
$444$	−17.8070	+	16.3981i	−0.845082	+	0.778219i
$445$		0			0
$446$	−1.30170	−	5.11487i	−0.0616374	−	0.242196i
$447$	5.35364	+	3.20603i	0.253219	+	0.151640i
$448$	−15.4109	−	17.9360i	−0.728099	−	0.847394i
$449$	−0.611967			−0.0288805			−0.0144403	−	0.999896i	$-0.504597\pi$
$449$	−0.611967			−0.0288805			−0.0144403	+	0.999896i	$0.504597\pi$
$450$		0			0
$451$			28.1592i			1.32596i
$452$	4.89698	−	16.5921i	0.230335	−	0.780428i
$453$	12.1899	−	20.3556i	0.572732	−	0.956388i
$454$	10.9077	−	2.77595i	0.511925	−	0.130282i
$455$		0			0
$456$	8.44440	−	12.9634i	0.395445	−	0.607067i
$457$	−3.44344	−	3.44344i	−0.161077	−	0.161077i	0.621967	−	0.783044i	$-0.286334\pi$
$457$	−3.44344	−	3.44344i	−0.161077	−	0.161077i	−0.783044	+	0.621967i	$0.786334\pi$
$458$	−8.11480	+	13.6551i	−0.379180	+	0.638061i
$459$	−20.9381	+	19.0216i	−0.977305	+	0.887853i
$460$		0			0
$461$	0.294401			0.0137116			0.00685580	−	0.999976i	$-0.497818\pi$
$461$	0.294401			0.0137116			0.00685580	+	0.999976i	$0.497818\pi$
$462$	5.50409	−	18.4197i	0.256073	−	0.856961i
$463$	9.79796	−	9.79796i	0.455350	−	0.455350i	−0.441776	−	0.897126i	$-0.645651\pi$
$463$	9.79796	−	9.79796i	0.455350	−	0.455350i	0.897126	+	0.441776i	$0.145651\pi$
$464$	14.6142	+	9.44955i	0.678446	+	0.438684i
$465$		0			0
$466$	29.2118	−	7.43423i	1.35321	−	0.344384i
$467$	−18.8562	−	18.8562i	−0.872561	−	0.872561i	0.120190	−	0.992751i	$-0.461650\pi$
$467$	−18.8562	−	18.8562i	−0.872561	−	0.872561i	−0.992751	+	0.120190i	$0.961650\pi$
$468$	−35.0305	+	7.27110i	−1.61929	+	0.336107i
$469$	36.8245			1.70040
$470$		0			0
$471$	−4.33262	−	17.2684i	−0.199637	−	0.795684i
$472$	−1.06125	+	28.0712i	−0.0488480	+	1.29208i
$473$	−0.583575	−	0.583575i	−0.0268328	−	0.0268328i
$474$	19.4567	−	10.5040i	0.893674	−	0.482463i
$475$		0			0
$476$	15.3850	+	28.2690i	0.705172	+	1.29571i
$477$	−18.8474	−	5.70133i	−0.862964	−	0.261046i
$478$	−2.09400	+	3.52366i	−0.0957774	+	0.161169i
$479$	−18.9906			−0.867702			−0.433851	−	0.900985i	$-0.642846\pi$
$479$	−18.9906			−0.867702			−0.433851	+	0.900985i	$0.642846\pi$
$480$		0			0
$481$	41.6685			1.89992
$482$	0.398735	−	0.670968i	0.0181619	−	0.0305617i
$483$	−9.99866	−	5.98769i	−0.454955	−	0.272449i
$484$	3.77666	+	6.93938i	0.171666	+	0.315426i
$485$		0			0
$486$	21.9512	+	2.03559i	0.995728	+	0.0923361i
$487$	−12.0580	−	12.0580i	−0.546399	−	0.546399i	0.378998	−	0.925397i	$-0.376269\pi$
$487$	−12.0580	−	12.0580i	−0.546399	−	0.546399i	−0.925397	+	0.378998i	$0.876269\pi$
$488$	1.27327	−	33.6792i	0.0576381	−	1.52459i
$489$	−22.5854	+	5.66666i	−1.02135	+	0.256255i
$490$		0			0
$491$	−18.1797			−0.820439			−0.410219	−	0.911987i	$-0.634548\pi$
$491$	−18.1797			−0.820439			−0.410219	+	0.911987i	$0.634548\pi$
$492$	−1.51197	+	36.7076i	−0.0681647	+	1.65491i
$493$	−16.7485	−	16.7485i	−0.754314	−	0.754314i
$494$	−25.8084	+	6.56806i	−1.16117	+	0.295511i
$495$		0			0
$496$	−3.40534	+	5.26653i	−0.152904	+	0.236474i
$497$	6.05801	−	6.05801i	0.271739	−	0.271739i
$498$	−32.4873	−	9.70770i	−1.45579	−	0.435012i
$499$	24.8457			1.11225			0.556124	−	0.831100i	$-0.312288\pi$
$499$	24.8457			1.11225			0.556124	+	0.831100i	$0.312288\pi$
$500$		0			0
$501$	−8.59235	−	34.2462i	−0.383878	−	1.53001i
$502$	4.54937	−	7.65541i	0.203048	−	0.341678i
$503$	17.0078	+	17.0078i	0.758340	+	0.758340i	0.976020	−	0.217680i	$-0.0698490\pi$
$503$	17.0078	+	17.0078i	0.758340	+	0.758340i	−0.217680	+	0.976020i	$0.569849\pi$
$504$	8.16401	−	23.7159i	0.363654	−	1.05639i
$505$		0			0
$506$	−8.28347	+	2.10809i	−0.368245	+	0.0937161i
$507$	33.5172	+	20.0717i	1.48855	+	0.891418i
$508$	8.98743	−	30.4515i	0.398753	−	1.35107i
$509$			26.1925i			1.16096i	0.814274	+	0.580481i	$0.197135\pi$
$509$			26.1925i			1.16096i	−0.814274	+	0.580481i	$0.802865\pi$
$510$		0			0
$511$	−9.60542			−0.424919
$512$	−22.4822	−	2.55962i	−0.993581	−	0.113120i
$513$	16.3908	+	0.786102i	0.723673	+	0.0347073i
$514$	5.38562	+	21.1621i	0.237549	+	0.933420i
$515$		0			0
$516$	−0.729399	−	0.792068i	−0.0321100	−	0.0348688i
$517$	4.86569	−	4.86569i	0.213993	−	0.213993i
$518$	−14.9234	+	25.1123i	−0.655699	+	1.10337i
$519$	10.7839	+	42.9808i	0.473359	+	1.88665i
$520$		0			0
$521$		−	21.5789i		−	0.945388i	−0.881227	−	0.472694i	$-0.843282\pi$
$521$		−	21.5789i		−	0.945388i	0.881227	−	0.472694i	$-0.156718\pi$
$522$	−0.821968	+	18.4405i	−0.0359766	+	0.807118i
$523$	−1.75051	−	1.75051i	−0.0765445	−	0.0765445i	0.667798	−	0.744343i	$-0.267237\pi$
$523$	−1.75051	−	1.75051i	−0.0765445	−	0.0765445i	−0.744343	+	0.667798i	$0.767237\pi$
$524$	−6.26767	−	11.5165i	−0.273804	−	0.503099i
$525$		0			0
$526$	−40.8878	+	10.4057i	−1.78279	+	0.453709i
$527$	6.03567	−	6.03567i	0.262918	−	0.262918i
$528$	−8.12105	−	16.5056i	−0.353424	−	0.718316i
$529$		−	17.8182i		−	0.774707i
$530$		0			0
$531$	−26.2662	+	14.0658i	−1.13985	+	0.610403i
$532$	5.28482	−	17.9062i	0.229126	−	0.776333i
$533$	44.7170	−	44.7170i	1.93691	−	1.93691i
$534$	−3.29601	−	6.10526i	−0.142632	−	0.264200i
$535$		0			0
$536$	25.8393	−	23.9567i	1.11609	−	1.03477i
$537$	8.64781	+	5.17874i	0.373181	+	0.223479i
$538$	25.0583	+	14.8913i	1.08034	+	0.642011i
$539$		−	4.61311i		−	0.198701i
$540$		0			0
$541$		−	22.6515i		−	0.973864i	−0.873440	−	0.486932i	$-0.838116\pi$
$541$		−	22.6515i		−	0.973864i	0.873440	−	0.486932i	$-0.161884\pi$
$542$	−17.5512	+	29.5341i	−0.753889	+	1.26860i
$543$	5.32496	+	3.18885i	0.228516	+	0.136847i
$544$	29.1863	+	9.82709i	1.25135	+	0.421333i
$545$		0			0
$546$	−37.9912	+	20.5101i	−1.62587	+	0.877751i
$547$	24.2626	−	24.2626i	1.03739	−	1.03739i	0.0381200	−	0.999273i	$-0.487863\pi$
$547$	24.2626	−	24.2626i	1.03739	−	1.03739i	0.999273	−	0.0381200i	$-0.0121369\pi$
$548$	4.43944	+	1.31025i	0.189644	+	0.0559712i
$549$	31.5136	−	16.8758i	1.34497	−	0.720243i
$550$		0			0
$551$			13.7399i			0.585341i
$552$	−10.9113	+	2.30329i	−0.464417	+	0.0980344i
$553$	18.8673	−	18.8673i	0.802318	−	0.802318i
$554$	6.23937	+	24.5168i	0.265085	+	1.04162i
$555$		0			0
$556$	−0.986391	−	1.81243i	−0.0418323	−	0.0768643i
$557$	14.5141	+	14.5141i	0.614984	+	0.614984i	0.944240	−	0.329257i	$-0.106798\pi$
$557$	14.5141	+	14.5141i	0.614984	+	0.614984i	−0.329257	+	0.944240i	$0.606798\pi$
$558$	−6.64541	−	0.296214i	−0.281323	−	0.0125397i
$559$			1.85344i			0.0783923i
$560$		0			0
$561$	6.09277	+	24.2837i	0.257237	+	1.02526i
$562$	10.7197	+	6.37040i	0.452185	+	0.268719i
$563$	−4.09672	+	4.09672i	−0.172656	+	0.172656i	−0.788145	−	0.615489i	$-0.788958\pi$
$563$	−4.09672	+	4.09672i	−0.172656	+	0.172656i	0.615489	+	0.788145i	$0.288958\pi$
$564$	6.60405	−	6.08154i	0.278081	−	0.256079i
$565$		0			0
$566$	26.1519	−	6.65549i	1.09925	−	0.279751i
$567$	26.0840	−	5.23053i	1.09542	−	0.219662i
$568$	0.309703	−	8.19196i	0.0129948	−	0.343727i
$569$	27.6005			1.15707			0.578536	−	0.815657i	$-0.303624\pi$
$569$	27.6005			1.15707			0.578536	+	0.815657i	$0.303624\pi$
$570$		0			0
$571$			32.2742i			1.35063i	0.737528	+	0.675317i	$0.235993\pi$
$571$			32.2742i			1.35063i	−0.737528	+	0.675317i	$0.764007\pi$
$572$	−8.96317	+	30.3693i	−0.374769	+	1.26980i
$573$	17.2423	+	10.3256i	0.720309	+	0.431357i
$574$	10.9343	+	42.9648i	0.456388	+	1.79332i
$575$		0			0
$576$	−9.70015	−	21.9524i	−0.404173	−	0.914683i
$577$	5.10163	+	5.10163i	0.212384	+	0.212384i	0.805279	−	0.592896i	$-0.202015\pi$
$577$	5.10163	+	5.10163i	0.212384	+	0.212384i	−0.592896	+	0.805279i	$0.702015\pi$
$578$	−15.3645	−	9.13063i	−0.639078	−	0.379784i
$579$	−5.86010	−	23.3564i	−0.243537	−	0.970657i
$580$		0			0
$581$	−40.9168			−1.69751
$582$	9.18774	−	30.7472i	0.380844	−	1.27451i
$583$	−12.3230	+	12.3230i	−0.510365	+	0.510365i
$584$	−6.74001	+	6.24895i	−0.278904	+	0.258584i
$585$		0			0
$586$	−3.37538	−	13.2631i	−0.139436	−	0.547894i
$587$	−3.37004	−	3.37004i	−0.139097	−	0.139097i	0.634130	−	0.773227i	$-0.281358\pi$
$587$	−3.37004	−	3.37004i	−0.139097	−	0.139097i	−0.773227	+	0.634130i	$0.781358\pi$
$588$	0.247694	−	6.01354i	0.0102147	−	0.247994i
$589$	−4.95148			−0.204022
$590$		0			0
$591$	4.68769	−	1.17614i	0.192826	−	0.0483799i
$592$	5.86557	+	27.3297i	0.241074	+	1.12324i
$593$	16.9693	+	16.9693i	0.696844	+	0.696844i	0.963729	−	0.266884i	$-0.0859941\pi$
$593$	16.9693	+	16.9693i	0.696844	+	0.696844i	−0.266884	+	0.963729i	$0.585994\pi$
$594$	10.7597	−	16.2762i	0.441476	−	0.667821i
$595$		0			0
$596$	6.32897	−	3.44445i	0.259245	−	0.141090i
$597$	−6.08214	−	3.64229i	−0.248926	−	0.149069i
$598$	16.5019	+	9.80656i	0.674813	+	0.401020i
$599$	1.04438			0.0426723			0.0213361	−	0.999772i	$-0.493208\pi$
$599$	1.04438			0.0426723			0.0213361	+	0.999772i	$0.493208\pi$
$600$		0			0
$601$	0.244816			0.00998624			0.00499312	−	0.999988i	$-0.498411\pi$
$601$	0.244816			0.00998624			0.00499312	+	0.999988i	$0.498411\pi$
$602$	−1.11701	−	0.663806i	−0.0455260	−	0.0270547i
$603$	35.7728	+	10.8212i	1.45678	+	0.440675i
$604$	−13.0965	−	24.0639i	−0.532887	−	0.979148i
$605$		0			0
$606$	12.4275	+	23.0196i	0.504831	+	0.935106i
$607$	−3.95241	−	3.95241i	−0.160423	−	0.160423i	0.622331	−	0.782754i	$-0.286186\pi$
$607$	−3.95241	−	3.95241i	−0.160423	−	0.160423i	−0.782754	+	0.622331i	$0.786186\pi$
$608$	−7.94086	−	16.0027i	−0.322045	−	0.648995i
$609$	5.42079	+	21.6054i	0.219661	+	0.875496i
$610$		0			0
$611$	−15.4535			−0.625183
$612$	6.63850	+	31.9828i	0.268345	+	1.29283i
$613$	−21.0245	−	21.0245i	−0.849172	−	0.849172i	0.140858	−	0.990030i	$-0.455014\pi$
$613$	−21.0245	−	21.0245i	−0.849172	−	0.849172i	−0.990030	+	0.140858i	$0.955014\pi$
$614$	−2.62297	−	10.3066i	−0.105854	−	0.415941i
$615$		0			0
$616$	−15.0925	−	16.2785i	−0.608094	−	0.655879i
$617$	−18.7366	+	18.7366i	−0.754307	+	0.754307i	−0.975280	−	0.220973i	$-0.929077\pi$
$617$	−18.7366	+	18.7366i	−0.754307	+	0.754307i	0.220973	+	0.975280i	$0.429077\pi$
$618$	−34.3087	−	10.2520i	−1.38010	−	0.412395i
$619$	8.66233			0.348169			0.174084	−	0.984731i	$-0.444303\pi$
$619$	8.66233			0.348169			0.174084	+	0.984731i	$0.444303\pi$
$620$		0			0
$621$	−7.95356	−	8.75489i	−0.319165	−	0.351322i
$622$	38.1316	+	22.6604i	1.52894	+	0.908600i
$623$	−5.92031	−	5.92031i	−0.237192	−	0.237192i
$624$	−13.3148	+	39.1074i	−0.533018	+	1.56555i
$625$		0			0
$626$	2.67508	+	10.5114i	0.106918	+	0.420119i
$627$	7.46163	−	12.4599i	0.297989	−	0.497602i
$628$	−19.7170	−	5.81925i	−0.786794	−	0.232214i
$629$		−	38.0432i		−	1.51688i
$630$		0			0
$631$	−1.38183			−0.0550097			−0.0275049	−	0.999622i	$-0.508756\pi$
$631$	−1.38183			−0.0550097			−0.0275049	+	0.999622i	$0.508756\pi$
$632$	0.964549	−	25.5133i	0.0383677	−	1.01487i
$633$	8.01583	+	4.80028i	0.318601	+	0.190794i
$634$	−24.9086	+	6.33907i	−0.989246	+	0.251757i
$635$		0			0
$636$	−16.7256	+	15.4023i	−0.663212	+	0.610739i
$637$	−7.32566	+	7.32566i	−0.290253	+	0.290253i
$638$	14.0441	+	8.34598i	0.556012	+	0.330421i
$639$	7.66521	−	4.10479i	0.303231	−	0.162383i
$640$		0			0
$641$			32.1844i			1.27121i	0.772015	+	0.635604i	$0.219249\pi$
$641$			32.1844i			1.27121i	−0.772015	+	0.635604i	$0.780751\pi$
$642$	−3.44440	+	11.5268i	−0.135940	+	0.454928i
$643$	13.8136	+	13.8136i	0.544755	+	0.544755i	0.924919	−	0.380164i	$-0.124132\pi$
$643$	13.8136	+	13.8136i	0.544755	+	0.544755i	−0.380164	+	0.924919i	$0.624132\pi$
$644$	−11.8202	+	6.43298i	−0.465782	+	0.253495i
$645$		0			0
$646$	5.99662	+	23.5630i	0.235934	+	0.927072i
$647$	−15.5057	+	15.5057i	−0.609594	+	0.609594i	−0.942840	−	0.333246i	$-0.891856\pi$
$647$	−15.5057	+	15.5057i	−0.609594	+	0.609594i	0.333246	+	0.942840i	$0.391856\pi$
$648$	14.9000	−	20.6395i	0.585328	−	0.810797i
$649$			26.3701i			1.03512i
$650$		0			0
$651$	−7.78597	+	1.95350i	−0.305156	+	0.0765635i
$652$	−7.61103	+	25.7880i	−0.298071	+	1.00993i
$653$	−17.9422	+	17.9422i	−0.702132	+	0.702132i	−0.964868	−	0.262736i	$-0.915375\pi$
$653$	−17.9422	+	17.9422i	−0.702132	+	0.702132i	0.262736	+	0.964868i	$0.415375\pi$
$654$	−3.11804	−	5.77560i	−0.121925	−	0.225844i
$655$		0			0
$656$	35.6238	+	23.0344i	1.39088	+	0.899343i
$657$	−9.33110	−	2.82265i	−0.364041	−	0.110122i
$658$	5.53463	−	9.31335i	0.215763	−	0.363072i
$659$		−	39.4445i		−	1.53654i	−0.640127	−	0.768269i	$-0.721118\pi$
$659$		−	39.4445i		−	1.53654i	0.640127	−	0.768269i	$-0.278882\pi$
$660$		0			0
$661$			7.69555i			0.299322i	0.988737	+	0.149661i	$0.0478183\pi$
$661$			7.69555i			0.299322i	−0.988737	+	0.149661i	$0.952182\pi$
$662$	12.9397	+	7.68964i	0.502915	+	0.298866i
$663$	28.8874	−	48.2381i	1.12189	−	1.87341i
$664$	−28.7108	+	26.6190i	−1.11420	+	1.03302i
$665$		0			0
$666$	−21.8767	+	20.0097i	−0.847707	+	0.775360i
$667$	7.00310	−	7.00310i	0.271161	−	0.271161i
$668$	−39.1023	−	11.5406i	−1.51291	−	0.446520i
$669$	−1.57308	−	6.26976i	−0.0608188	−	0.242403i
$670$		0			0
$671$		−	31.6383i		−	1.22138i
$672$	−18.8001	−	22.0306i	−0.725231	−	0.849849i
$673$	2.37397	−	2.37397i	0.0915096	−	0.0915096i	−0.659870	−	0.751380i	$-0.729389\pi$
$673$	2.37397	−	2.37397i	0.0915096	−	0.0915096i	0.751380	+	0.659870i	$0.229389\pi$
$674$	−1.12724	+	0.286875i	−0.0434196	+	0.0110500i
$675$		0			0
$676$	39.6233	−	21.5644i	1.52397	−	0.829402i
$677$	−6.61424	−	6.61424i	−0.254206	−	0.254206i	0.568487	−	0.822693i	$-0.307529\pi$
$677$	−6.61424	−	6.61424i	−0.254206	−	0.254206i	−0.822693	+	0.568487i	$0.807529\pi$
$678$	6.06617	−	20.3007i	0.232970	−	0.779645i
$679$		−	38.7252i		−	1.48614i
$680$		0			0
$681$	13.3706	−	3.35468i	0.512363	−	0.128552i
$682$	−3.00765	+	5.06110i	−0.115169	+	0.193799i
$683$	14.3187	−	14.3187i	0.547889	−	0.547889i	−0.377941	−	0.925830i	$-0.623368\pi$
$683$	14.3187	−	14.3187i	0.547889	−	0.547889i	0.925830	+	0.377941i	$0.123368\pi$
$684$	10.3958	−	15.8418i	0.397494	−	0.605728i
$685$		0			0
$686$	5.42568	+	21.3195i	0.207154	+	0.813983i
$687$	−9.99500	+	16.6903i	−0.381333	+	0.636776i
$688$	−1.21564	+	0.260905i	−0.0463460	+	0.00994691i
$689$	39.1380			1.49104
$690$		0			0
$691$		−	36.4559i		−	1.38685i	−0.720529	−	0.693425i	$-0.756101\pi$
$691$		−	36.4559i		−	1.38685i	0.720529	−	0.693425i	$-0.243899\pi$
$692$	49.0754	+	14.4841i	1.86557	+	0.550602i
$693$	6.81728	−	22.5365i	0.258967	−	0.856091i
$694$	3.70098	−	0.941876i	0.140487	−	0.0357531i
$695$		0			0
$696$	17.8594	+	11.6337i	0.676960	+	0.440974i
$697$	−40.8265	−	40.8265i	−1.54641	−	1.54641i
$698$	−11.8170	+	19.8849i	−0.447279	+	0.752655i
$699$	35.8076	−	8.98411i	1.35437	−	0.339810i
$700$		0			0
$701$	48.0342			1.81423			0.907113	−	0.420887i	$-0.138281\pi$
$701$	48.0342			1.81423			0.907113	+	0.420887i	$0.138281\pi$
$702$	−42.9333	+	8.76025i	−1.62041	+	0.330634i
$703$	−15.6047	+	15.6047i	−0.588544	+	0.588544i
$704$	−21.1804	−	1.60378i	−0.798268	−	0.0604446i
$705$		0			0
$706$	−0.633175	+	0.161139i	−0.0238299	+	0.00606455i
$707$	22.3222	+	22.3222i	0.839515	+	0.839515i
$708$	−1.41591	+	34.3755i	−0.0532130	+	1.29191i
$709$	−6.97929			−0.262113			−0.131056	−	0.991375i	$-0.541837\pi$
$709$	−6.97929			−0.262113			−0.131056	+	0.991375i	$0.541837\pi$
$710$		0			0
$711$	23.8728	−	12.7841i	0.895299	−	0.479441i
$712$	−8.00576	−	0.302663i	−0.300029	−	0.0113428i
$713$	2.52371	+	2.52371i	0.0945138	+	0.0945138i
$714$	18.7257	+	34.6858i	0.700790	+	1.29808i
$715$		0			0
$716$	10.2233	−	5.56387i	0.382062	−	0.207932i
$717$	−2.57918	+	4.30690i	−0.0963214	+	0.160844i
$718$	11.6263	−	19.5640i	0.433888	−	0.730121i
$719$	−2.63485			−0.0982634			−0.0491317	−	0.998792i	$-0.515645\pi$
$719$	−2.63485			−0.0982634			−0.0491317	+	0.998792i	$0.515645\pi$
$720$		0			0
$721$	−43.2108			−1.60926
$722$	−6.52163	+	10.9742i	−0.242710	+	0.408418i
$723$	0.491122	−	0.820109i	0.0182650	−	0.0305002i
$724$	6.29506	−	3.42600i	0.233954	−	0.127326i
$725$		0			0
$726$	4.59670	+	8.51455i	0.170600	+	0.316005i
$727$	5.55176	+	5.55176i	0.205903	+	0.205903i	0.802524	−	0.596620i	$-0.203490\pi$
$727$	5.55176	+	5.55176i	0.205903	+	0.205903i	−0.596620	+	0.802524i	$0.703490\pi$
$728$	−1.88338	+	49.8174i	−0.0698028	+	1.84636i
$729$	26.8761	+	2.58389i	0.995410	+	0.0956996i
$730$		0			0
$731$	1.69219			0.0625879
$732$	1.69877	−	41.2429i	0.0627885	−	1.52438i
$733$	−10.2051	−	10.2051i	−0.376934	−	0.376934i	0.493061	−	0.869995i	$-0.335878\pi$
$733$	−10.2051	−	10.2051i	−0.376934	−	0.376934i	−0.869995	+	0.493061i	$0.835878\pi$
$734$	33.5814	−	8.54626i	1.23951	−	0.315448i
$735$		0			0
$736$	−4.10903	+	12.2038i	−0.151461	+	0.449837i
$737$	23.3893	−	23.3893i	0.861554	−	0.861554i
$738$	−2.00365	+	44.9509i	−0.0737553	+	1.65467i
$739$	33.7165			1.24028			0.620141	−	0.784490i	$-0.287075\pi$
$739$	33.7165			1.24028			0.620141	+	0.784490i	$0.287075\pi$
$740$		0			0
$741$	−31.6356	+	7.93737i	−1.16216	+	0.291586i
$742$	−14.0172	+	23.5872i	−0.514586	+	0.865914i
$743$	14.9523	+	14.9523i	0.548546	+	0.548546i	0.926020	−	0.377474i	$-0.123207\pi$
$743$	14.9523	+	14.9523i	0.548546	+	0.548546i	−0.377474	+	0.926020i	$0.623207\pi$
$744$	−4.19245	+	6.43602i	−0.153703	+	0.235956i
$745$		0			0
$746$	7.83798	−	1.99472i	0.286969	−	0.0730317i
$747$	−39.7482	−	12.0238i	−1.45431	−	0.439928i
$748$	27.7271	+	8.18335i	1.01380	+	0.299213i
$749$			14.5177i			0.530466i
$750$		0			0
$751$	29.4194			1.07353			0.536764	−	0.843733i	$-0.319647\pi$
$751$	29.4194			1.07353			0.536764	+	0.843733i	$0.319647\pi$
$752$	−2.17536	−	10.1357i	−0.0793271	−	0.369611i
$753$	5.60346	−	9.35705i	0.204202	−	0.340990i
$754$	−9.04869	−	35.5557i	−0.329534	−	1.29486i
$755$		0			0
$756$	10.0969	−	29.0120i	0.367221	−	1.05516i
$757$	−9.10219	+	9.10219i	−0.330825	+	0.330825i	−0.852900	−	0.522075i	$-0.825158\pi$
$757$	−9.10219	+	9.10219i	−0.330825	+	0.330825i	0.522075	+	0.852900i	$0.325158\pi$
$758$	6.77246	−	11.3963i	0.245987	−	0.413932i
$759$	−10.1538	+	2.54758i	−0.368560	+	0.0924715i
$760$		0			0
$761$		−	19.4230i		−	0.704083i	−0.935984	−	0.352042i	$-0.885488\pi$
$761$		−	19.4230i		−	0.704083i	0.935984	−	0.352042i	$-0.114512\pi$
$762$	11.1332	−	37.2579i	0.403315	−	1.34971i
$763$	−5.60064	−	5.60064i	−0.202757	−	0.202757i
$764$	20.3836	−	11.0935i	0.737451	−	0.401347i
$765$		0			0
$766$	−3.76041	+	0.957001i	−0.135869	+	0.0345778i
$767$	41.8760	−	41.8760i	1.51206	−	1.51206i
$768$	−27.5242	−	3.22789i	−0.993193	−	0.116477i
$769$		−	1.26203i		−	0.0455101i	−0.999741	−	0.0227551i	$-0.992756\pi$
$769$		−	1.26203i		−	0.0455101i	0.999741	−	0.0227551i	$-0.00724379\pi$
$770$		0			0
$771$	6.50841	+	25.9403i	0.234395	+	0.934217i
$772$	−26.6683	−	7.87085i	−0.959812	−	0.283278i
$773$	13.6782	−	13.6782i	0.491971	−	0.491971i	−0.416956	−	0.908927i	$-0.636903\pi$
$773$	13.6782	−	13.6782i	0.491971	−	0.491971i	0.908927	+	0.416956i	$0.136903\pi$
$774$	−0.890046	−	0.973093i	−0.0319920	−	0.0349771i
$775$		0			0
$776$	−25.1933	−	27.1730i	−0.904386	−	0.975455i
$777$	−18.3812	+	30.6942i	−0.659423	+	1.10115i
$778$	−19.1826	−	11.3996i	−0.687729	−	0.408696i
$779$			33.4928i			1.20000i
$780$		0			0
$781$		−	7.69555i		−	0.275368i
$782$	8.95337	−	15.0662i	0.320172	−	0.538766i
$783$	−1.08300	+	22.5813i	−0.0387032	+	0.806991i
$784$	−5.83600	−	3.77356i	−0.208428	−	0.134770i
$785$		0			0
$786$	−7.62860	−	14.1306i	−0.272103	−	0.504021i
$787$	1.64945	−	1.64945i	0.0587966	−	0.0587966i	−0.677097	−	0.735894i	$-0.736762\pi$
$787$	1.64945	−	1.64945i	0.0587966	−	0.0587966i	0.735894	+	0.677097i	$0.236762\pi$
$788$	1.57970	−	5.35240i	0.0562745	−	0.190671i
$789$	−50.1199	+	12.5750i	−1.78431	+	0.447683i
$790$		0			0
$791$		−	25.5682i		−	0.909100i
$792$	−9.87787	−	20.2487i	−0.350995	−	0.719506i
$793$	−50.2420	+	50.2420i	−1.78414	+	1.78414i
$794$	7.98895	+	31.3915i	0.283517	+	1.11404i
$795$		0			0
$796$	−7.19019	+	3.91316i	−0.254850	+	0.138698i
$797$	−15.2015	−	15.2015i	−0.538466	−	0.538466i	0.384612	−	0.923078i	$-0.374335\pi$
$797$	−15.2015	−	15.2015i	−0.538466	−	0.538466i	−0.923078	+	0.384612i	$0.874335\pi$
$798$	6.54661	−	21.9086i	0.231748	−	0.775554i
$799$			14.1090i			0.499141i
$800$		0			0
$801$	−4.01149	−	7.49098i	−0.141739	−	0.264681i
$802$	−41.2783	−	24.5304i	−1.45759	−	0.866199i
$803$	−6.10093	+	6.10093i	−0.215297	+	0.215297i
$804$	31.7455	−	29.2338i	1.11958	−	1.03100i
$805$		0			0
$806$	12.8132	−	3.26089i	0.451327	−	0.114860i
$807$	30.6282	+	18.3417i	1.07816	+	0.645657i
$808$	30.1853	+	1.14118i	1.06192	+	0.0401465i
$809$	−44.9347			−1.57982			−0.789910	−	0.613223i	$-0.789873\pi$
$809$	−44.9347			−1.57982			−0.789910	+	0.613223i	$0.789873\pi$
$810$		0			0
$811$		−	23.8947i		−	0.839055i	−0.907743	−	0.419528i	$-0.862196\pi$
$811$		−	23.8947i		−	0.839055i	0.907743	−	0.419528i	$-0.137804\pi$
$812$	24.6691	+	7.28080i	0.865714	+	0.255506i
$813$	−21.6178	+	36.0990i	−0.758171	+	1.26605i
$814$	6.47149	+	25.4289i	0.226826	+	0.891282i
$815$		0			0
$816$	35.7050	+	12.1564i	1.24992	+	0.425558i
$817$	−0.694110	−	0.694110i	−0.0242838	−	0.0242838i
$818$	−14.4889	−	8.61029i	−0.506592	−	0.301052i
$819$	−46.6141	+	24.9623i	−1.62883	+	0.872253i
$820$		0			0
$821$	−43.1420			−1.50567			−0.752833	−	0.658212i	$-0.771313\pi$
$821$	−43.1420			−1.50567			−0.752833	+	0.658212i	$0.771313\pi$
$822$	5.43173	+	1.62309i	0.189454	+	0.0566116i
$823$	−29.4978	+	29.4978i	−1.02823	+	1.02823i	−0.0286405	+	0.999590i	$0.509118\pi$
$823$	−29.4978	+	29.4978i	−1.02823	+	1.02823i	−0.999590	+	0.0286405i	$0.990882\pi$
$824$	−30.3205	+	28.1115i	−1.05627	+	0.979309i
$825$		0			0
$826$	10.2396	+	40.2351i	0.356281	+	1.39996i
$827$	32.6568	+	32.6568i	1.13559	+	1.13559i	0.989232	+	0.146357i	$0.0467548\pi$
$827$	32.6568	+	32.6568i	1.13559	+	1.13559i	0.146357	+	0.989232i	$0.453245\pi$
$828$	−13.3730	+	2.77577i	−0.464745	+	0.0964648i
$829$	−19.3767			−0.672980			−0.336490	−	0.941687i	$-0.609240\pi$
$829$	−19.3767			−0.672980			−0.336490	+	0.941687i	$0.609240\pi$
$830$		0			0
$831$	7.54014	+	30.0524i	0.261565	+	1.04251i
$832$	31.0879	+	36.1815i	1.07778	+	1.25437i
$833$	6.68831	+	6.68831i	0.231736	+	0.231736i
$834$	−1.20057	−	2.22384i	−0.0415724	−	0.0770052i
$835$		0			0
$836$	−8.01654	−	14.7299i	−0.277258	−	0.509444i
$837$	−8.13766	−	0.390281i	−0.281279	−	0.0134901i
$838$	−0.600640	−	0.356942i	−0.0207488	−	0.0123304i
$839$	−38.4795			−1.32846			−0.664229	−	0.747529i	$-0.731240\pi$
$839$	−38.4795			−1.32846			−0.664229	+	0.747529i	$0.731240\pi$
$840$		0			0
$841$	10.0707			0.347267
$842$	−34.1434	−	20.2904i	−1.17666	−	0.699252i
$843$	13.1025	+	7.84643i	0.451274	+	0.270245i
$844$	9.47616	−	5.15726i	0.326183	−	0.177520i
$845$		0			0
$846$	8.11339	−	7.42096i	0.278944	−	0.255138i
$847$	8.25662	+	8.25662i	0.283701	+	0.283701i
$848$	5.50936	+	25.6699i	0.189192	+	0.881510i
$849$	32.0568	−	8.04302i	1.10019	−	0.276036i
$850$		0			0
$851$	15.9071			0.545289
$852$	0.413201	−	10.0317i	0.0141560	−	0.343681i
$853$	20.0303	+	20.0303i	0.685823	+	0.685823i	0.961306	−	0.275483i	$-0.0888378\pi$
$853$	20.0303	+	20.0303i	0.685823	+	0.685823i	−0.275483	+	0.961306i	$0.588838\pi$
$854$	−12.2852	−	48.2733i	−0.420392	−	1.65188i
$855$		0			0
$856$	9.44472	+	10.1869i	0.322814	+	0.348181i
$857$	−24.3417	+	24.3417i	−0.831496	+	0.831496i	−0.987721	−	0.156226i	$-0.950067\pi$
$857$	−24.3417	+	24.3417i	−0.831496	+	0.831496i	0.156226	+	0.987721i	$0.450067\pi$
$858$	−11.1032	+	37.1574i	−0.379057	+	1.26853i
$859$	−43.4501			−1.48250			−0.741249	−	0.671230i	$-0.765766\pi$
$859$	−43.4501			−1.48250			−0.741249	+	0.671230i	$0.765766\pi$
$860$		0			0
$861$	13.2138	+	52.6659i	0.450326	+	1.79485i
$862$	9.97726	+	5.92917i	0.339827	+	0.201948i
$863$	−16.6773	−	16.6773i	−0.567701	−	0.567701i	0.363783	−	0.931484i	$-0.381485\pi$
$863$	−16.6773	−	16.6773i	−0.567701	−	0.567701i	−0.931484	+	0.363783i	$0.881485\pi$
$864$	−11.7893	−	26.9260i	−0.401081	−	0.916043i
$865$		0			0
$866$	3.99541	+	15.6994i	0.135769	+	0.533488i
$867$	−18.7797	−	11.2462i	−0.637791	−	0.381941i
$868$	−2.62379	+	8.89002i	−0.0890572	+	0.301747i
$869$		−	23.9673i		−	0.813034i
$870$		0			0
$871$	−74.2847			−2.51704
$872$	−7.57348	−	0.286321i	−0.256470	−	0.00969604i
$873$	11.3798	−	37.6193i	0.385148	−	1.27322i
$874$	−9.85245	+	2.50738i	−0.333264	+	0.0848136i
$875$		0			0
$876$	−8.28060	+	7.62544i	−0.279776	+	0.257640i
$877$	0.209733	−	0.209733i	0.00708216	−	0.00708216i	−0.703557	−	0.710639i	$-0.748406\pi$
$877$	0.209733	−	0.209733i	0.00708216	−	0.00708216i	0.710639	+	0.703557i	$0.248406\pi$
$878$	−6.34529	−	3.77081i	−0.214143	−	0.127259i
$879$	−4.07907	−	16.2578i	−0.137584	−	0.548362i
$880$		0			0
$881$		−	7.66064i		−	0.258093i	−0.991639	−	0.129047i	$-0.958808\pi$
$881$		−	7.66064i		−	0.258093i	0.991639	−	0.129047i	$-0.0411917\pi$
$882$	0.328243	−	7.36398i	0.0110525	−	0.247958i
$883$	−7.44439	−	7.44439i	−0.250524	−	0.250524i	0.570662	−	0.821185i	$-0.306687\pi$
$883$	−7.44439	−	7.44439i	−0.250524	−	0.250524i	−0.821185	+	0.570662i	$0.806687\pi$
$884$	−31.0357	−	57.0261i	−1.04384	−	1.91800i
$885$		0			0
$886$	−10.7191	−	42.1191i	−0.360114	−	1.41502i
$887$	15.8208	−	15.8208i	0.531211	−	0.531211i	−0.389722	−	0.920933i	$-0.627429\pi$
$887$	15.8208	−	15.8208i	0.531211	−	0.531211i	0.920933	+	0.389722i	$0.127429\pi$
$888$	7.07071	+	33.4959i	0.237277	+	1.12405i
$889$		−	46.9253i		−	1.57382i
$890$		0			0
$891$	13.2452	−	19.8896i	0.443730	−	0.666325i
$892$	−7.15881	−	2.11284i	−0.239695	−	0.0707433i
$893$	5.78730	−	5.78730i	0.193665	−	0.193665i
$894$	7.76558	−	4.19236i	0.259720	−	0.140214i
$895$		0			0
$896$	−32.9395	+	5.77740i	−1.10043	+	0.193009i
$897$	20.1699	+	12.0787i	0.673454	+	0.403298i
$898$	−0.442132	+	0.743993i	−0.0147541	+	0.0248274i
$899$		−	6.82156i		−	0.227512i
$900$		0			0
$901$		−	35.7329i		−	1.19043i
$902$	34.2343	+	20.3444i	1.13988	+	0.677393i
$903$	−1.36530	−	0.817610i	−0.0454344	−	0.0272084i
$904$	−16.6338	−	17.9409i	−0.553231	−	0.596705i
$905$		0			0
$906$	−15.9402	−	29.5262i	−0.529576	−	0.980943i
$907$	−33.9035	+	33.9035i	−1.12575	+	1.12575i	−0.134886	+	0.990861i	$0.543067\pi$
$907$	−33.9035	+	33.9035i	−1.12575	+	1.12575i	−0.990861	+	0.134886i	$0.956933\pi$
$908$	4.50575	−	15.2665i	0.149529	−	0.506638i
$909$	15.1251	+	28.2444i	0.501669	+	0.936806i
$910$		0			0
$911$		−	8.75281i		−	0.289994i	−0.989432	−	0.144997i	$-0.953683\pi$
$911$		−	8.75281i		−	0.289994i	0.989432	−	0.144997i	$-0.0463172\pi$
$912$	−9.65926	−	19.6320i	−0.319850	−	0.650079i
$913$	−25.9885	+	25.9885i	−0.860094	+	0.860094i
$914$	−6.67413	+	1.69852i	−0.220761	+	0.0561822i
$915$		0			0
$916$	10.7383	+	19.7310i	0.354804	+	0.651930i
$917$	−13.7025	−	13.7025i	−0.452497	−	0.452497i
$918$	7.99808	+	39.1980i	0.263976	+	1.29373i
$919$		−	27.0428i		−	0.892058i	−0.895018	−	0.446029i	$-0.852838\pi$
$919$		−	27.0428i		−	0.892058i	0.895018	−	0.446029i	$-0.147162\pi$
$920$		0			0
$921$	−3.16980	−	12.6338i	−0.104449	−	0.416297i
$922$	0.212698	−	0.357915i	0.00700483	−	0.0117873i
$923$	−12.2206	+	12.2206i	−0.402246	+	0.402246i
$924$	−18.4170	−	19.9993i	−0.605875	−	0.657930i
$925$		0			0
$926$	−4.83298	−	18.9906i	−0.158822	−	0.624069i
$927$	−41.9768	−	12.6979i	−1.37870	−	0.417055i
$928$	22.0466	−	10.9400i	0.723716	−	0.359122i
$929$	−41.2267			−1.35261			−0.676303	−	0.736624i	$-0.736419\pi$
$929$	−41.2267			−1.35261			−0.676303	+	0.736624i	$0.736419\pi$
$930$		0			0
$931$		−	5.48688i		−	0.179825i
$932$	12.0668	−	40.8851i	0.395261	−	1.33924i
$933$	46.6075	+	27.9109i	1.52586	+	0.913761i
$934$	−36.5474	+	9.30109i	−1.19587	+	0.304341i
$935$		0			0
$936$	−16.4689	+	47.8412i	−0.538304	+	1.56374i
$937$	37.7773	+	37.7773i	1.23413	+	1.23413i	0.962363	+	0.271766i	$0.0876078\pi$
$937$	37.7773	+	37.7773i	1.23413	+	1.23413i	0.271766	+	0.962363i	$0.412392\pi$
$938$	26.6048	−	44.7690i	0.868679	−	1.46176i
$939$	3.23277	+	12.8847i	0.105498	+	0.420478i
$940$		0			0
$941$	53.4869			1.74362			0.871812	−	0.489841i	$-0.162945\pi$
$941$	53.4869			1.74362			0.871812	+	0.489841i	$0.162945\pi$
$942$	−24.1241	−	7.20865i	−0.786005	−	0.234870i
$943$	17.0709	−	17.0709i	0.555905	−	0.555905i
$944$	33.3606	+	21.5710i	1.08579	+	0.702076i
$945$		0			0
$946$	−1.13110	+	0.287857i	−0.0367751	+	0.00935903i
$947$	−23.8152	−	23.8152i	−0.773891	−	0.773891i	0.204893	−	0.978784i	$-0.434315\pi$
$947$	−23.8152	−	23.8152i	−0.773891	−	0.773891i	−0.978784	+	0.204893i	$0.934315\pi$
$948$	1.28689	−	31.2431i	0.0417962	−	1.01473i
$949$	19.3767			0.628993
$950$		0			0
$951$	−30.5327	+	7.66064i	−0.990091	+	0.248413i
$952$	45.4832	+	1.71952i	1.47412	+	0.0557301i
$953$	−31.8333	−	31.8333i	−1.03118	−	1.03118i	−0.999498	−	0.0316832i	$-0.989913\pi$
$953$	−31.8333	−	31.8333i	−1.03118	−	1.03118i	−0.0316832	−	0.999498i	$-0.510087\pi$
$954$	−20.5482	+	18.7945i	−0.665272	+	0.608495i
$955$		0			0
$956$	2.77099	+	5.09153i	0.0896203	+	0.164672i
$957$	17.1658	+	10.2798i	0.554893	+	0.332297i
$958$	−13.7203	+	23.0876i	−0.443282	+	0.745928i
$959$	6.84111			0.220911
$960$		0			0
$961$	−28.5417			−0.920700
$962$	30.1045	−	50.6581i	0.970609	−	1.63328i
$963$	−4.26618	+	14.1031i	−0.137476	+	0.454466i
$964$	−0.527646	−	0.969517i	−0.0169943	−	0.0312260i
$965$		0			0
$966$	−14.5033	+	7.82981i	−0.466635	+	0.251920i
$967$	−21.7712	−	21.7712i	−0.700115	−	0.700115i	0.264320	−	0.964435i	$-0.414852\pi$
$967$	−21.7712	−	21.7712i	−0.700115	−	0.700115i	−0.964435	+	0.264320i	$0.914852\pi$
$968$	11.1650	+	0.422102i	0.358858	+	0.0135669i
$969$	7.24679	+	28.8833i	0.232801	+	0.927864i
$970$		0			0
$971$	2.19315			0.0703814			0.0351907	−	0.999381i	$-0.488796\pi$
$971$	2.19315			0.0703814			0.0351907	+	0.999381i	$0.488796\pi$
$972$	18.3340	−	25.2163i	0.588063	−	0.808815i
$973$	−2.15647	−	2.15647i	−0.0691333	−	0.0691333i
$974$	−23.3710	+	5.94777i	−0.748855	+	0.190579i
$975$		0			0
$976$	−40.0253	−	25.8804i	−1.28118	−	0.828412i
$977$	−2.26226	+	2.26226i	−0.0723760	+	0.0723760i	−0.742368	−	0.669992i	$-0.766297\pi$
$977$	−2.26226	+	2.26226i	−0.0723760	+	0.0723760i	0.669992	+	0.742368i	$0.266297\pi$
$978$	−9.42822	+	31.5520i	−0.301481	+	1.00892i
$979$	−7.52063			−0.240361
$980$		0			0
$981$	−3.79488	−	7.08649i	−0.121161	−	0.226254i
$982$	−13.1344	+	22.1018i	−0.419136	+	0.705298i
$983$	−39.9359	−	39.9359i	−1.27376	−	1.27376i	−0.944101	−	0.329656i	$-0.893067\pi$
$983$	−39.9359	−	39.9359i	−1.27376	−	1.27376i	−0.329656	−	0.944101i	$-0.606933\pi$
$984$	43.5346	+	28.3585i	1.38783	+	0.904037i
$985$		0			0
$986$	−32.4622	+	8.26144i	−1.03381	+	0.263098i
$987$	6.81701	−	11.3835i	0.216988	−	0.362341i
$988$	−10.6609	+	36.1216i	−0.339168	+	1.14918i
$989$			0.707560i			0.0224991i
$990$		0			0
$991$	26.1776			0.831560			0.415780	−	0.909465i	$-0.363509\pi$
$991$	26.1776			0.831560			0.415780	+	0.909465i	$0.363509\pi$
$992$	3.94245	+	7.94496i	0.125173	+	0.252253i
$993$	15.8159	+	9.47134i	0.501902	+	0.300564i
$994$	−2.98820	−	11.7417i	−0.0947799	−	0.372426i
$995$		0			0
$996$	−35.2734	+	32.4825i	−1.11768	+	1.02925i
$997$	28.1978	−	28.1978i	0.893034	−	0.893034i	−0.101774	−	0.994808i	$-0.532452\pi$
$997$	28.1978	−	28.1978i	0.893034	−	0.893034i	0.994808	+	0.101774i	$0.0324518\pi$
$998$	17.9505	−	30.2060i	0.568212	−	0.956153i
$999$	−26.8761	+	24.4161i	−0.850321	+	0.772492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.w.k.557.21	yes	64
3.2	odd	2	inner	600.2.w.k.557.11	yes	64
5.2	odd	4	inner	600.2.w.k.293.27	yes	64
5.3	odd	4	inner	600.2.w.k.293.6	yes	64
5.4	even	2	inner	600.2.w.k.557.12	yes	64
8.5	even	2	inner	600.2.w.k.557.28	yes	64
15.2	even	4	inner	600.2.w.k.293.5	✓	64
15.8	even	4	inner	600.2.w.k.293.28	yes	64
15.14	odd	2	inner	600.2.w.k.557.22	yes	64
24.5	odd	2	inner	600.2.w.k.557.6	yes	64
40.13	odd	4	inner	600.2.w.k.293.11	yes	64
40.29	even	2	inner	600.2.w.k.557.5	yes	64
40.37	odd	4	inner	600.2.w.k.293.22	yes	64
120.29	odd	2	inner	600.2.w.k.557.27	yes	64
120.53	even	4	inner	600.2.w.k.293.21	yes	64
120.77	even	4	inner	600.2.w.k.293.12	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.w.k.293.5	✓	64	15.2	even	4	inner
600.2.w.k.293.6	yes	64	5.3	odd	4	inner
600.2.w.k.293.11	yes	64	40.13	odd	4	inner
600.2.w.k.293.12	yes	64	120.77	even	4	inner
600.2.w.k.293.21	yes	64	120.53	even	4	inner
600.2.w.k.293.22	yes	64	40.37	odd	4	inner
600.2.w.k.293.27	yes	64	5.2	odd	4	inner
600.2.w.k.293.28	yes	64	15.8	even	4	inner
600.2.w.k.557.5	yes	64	40.29	even	2	inner
600.2.w.k.557.6	yes	64	24.5	odd	2	inner
600.2.w.k.557.11	yes	64	3.2	odd	2	inner
600.2.w.k.557.12	yes	64	5.4	even	2	inner
600.2.w.k.557.21	yes	64	1.1	even	1	trivial
600.2.w.k.557.22	yes	64	15.14	odd	2	inner
600.2.w.k.557.27	yes	64	120.29	odd	2	inner
600.2.w.k.557.28	yes	64	8.5	even	2	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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.722477 - 1.21574i) q^{2} +(0.889875 - 1.48597i) q^{3} +(-0.956054 - 1.75669i) q^{4} +(-1.16365 - 2.15544i) q^{6} +(-2.09015 - 2.09015i) q^{7} +(-2.82641 - 0.106854i) q^{8} +(-1.41624 - 2.64467i) q^{9} +O(q^{10})\)	\(q+(0.722477 - 1.21574i) q^{2} +(0.889875 - 1.48597i) q^{3} +(-0.956054 - 1.75669i) q^{4} +(-1.16365 - 2.15544i) q^{6} +(-2.09015 - 2.09015i) q^{7} +(-2.82641 - 0.106854i) q^{8} +(-1.41624 - 2.64467i) q^{9} -2.65514 q^{11} +(-3.46117 - 0.142564i) q^{12} +(4.21638 + 4.21638i) q^{13} +(-4.05116 + 1.03099i) q^{14} +(-2.17192 + 3.35898i) q^{16} +(3.84954 - 3.84954i) q^{17} +(-4.23843 - 0.188924i) q^{18} -3.15804 q^{19} +(-4.96588 + 1.24594i) q^{21} +(-1.91827 + 3.22796i) q^{22} +(1.60962 + 1.60962i) q^{23} +(-2.67393 + 4.10488i) q^{24} +(8.17226 - 2.07979i) q^{26} +(-5.19019 - 0.248921i) q^{27} +(-1.67345 + 5.67003i) q^{28} -4.35078i q^{29} +1.56789 q^{31} +(2.51449 + 5.06728i) q^{32} +(-2.36274 + 3.94546i) q^{33} +(-1.89884 - 7.46125i) q^{34} +(-3.29185 + 5.01634i) q^{36} +(4.94127 - 4.94127i) q^{37} +(-2.28161 + 3.83936i) q^{38} +(10.0175 - 2.51338i) q^{39} -10.6056i q^{41} +(-2.07300 + 6.93738i) q^{42} +(0.219791 + 0.219791i) q^{43} +(2.53845 + 4.66425i) q^{44} +(3.11979 - 0.793968i) q^{46} +(-1.83256 + 1.83256i) q^{47} +(3.05862 + 6.21650i) q^{48} +1.73743i q^{49} +(-2.29471 - 9.14594i) q^{51} +(3.37579 - 11.4380i) q^{52} +(4.64119 - 4.64119i) q^{53} +(-4.05241 + 6.13009i) q^{54} +(5.68427 + 6.13095i) q^{56} +(-2.81027 + 4.69277i) q^{57} +(-5.28942 - 3.14334i) q^{58} -9.93175i q^{59} +11.9159i q^{61} +(1.13277 - 1.90615i) q^{62} +(-2.56758 + 8.48790i) q^{63} +(7.97716 + 0.604028i) q^{64} +(3.08964 + 5.72299i) q^{66} +(-8.80906 + 8.80906i) q^{67} +(-10.4428 - 3.08208i) q^{68} +(3.82422 - 0.959493i) q^{69} +2.89837i q^{71} +(3.72029 + 7.62624i) q^{72} +(2.29779 - 2.29779i) q^{73} +(-2.43735 - 9.57725i) q^{74} +(3.01926 + 5.54770i) q^{76} +(5.54962 + 5.54962i) q^{77} +(4.18178 - 13.9945i) q^{78} +9.02676i q^{79} +(-4.98851 + 7.49098i) q^{81} +(-12.8936 - 7.66227i) q^{82} +(9.78801 - 9.78801i) q^{83} +(6.93637 + 7.53233i) q^{84} +(0.426003 - 0.108415i) q^{86} +(-6.46515 - 3.87165i) q^{87} +(7.50450 + 0.283713i) q^{88} +2.83249 q^{89} -17.6257i q^{91} +(1.28872 - 4.36649i) q^{92} +(1.39523 - 2.32985i) q^{93} +(0.903936 + 3.55190i) q^{94} +(9.76744 + 0.772783i) q^{96} +(9.26375 + 9.26375i) q^{97} +(2.11227 + 1.25525i) q^{98} +(3.76032 + 7.02194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 12 q^{6}+O(q^{10}) \) 64 * q + 12 * q^6	\( 64 q + 12 q^{6} - 40 q^{16} + 32 q^{31} - 84 q^{36} - 128 q^{46} - 180 q^{66} + 168 q^{76} + 48 q^{81} + 228 q^{96}+O(q^{100}) \) 64 * q + 12 * q^6 - 40 * q^16 + 32 * q^31 - 84 * q^36 - 128 * q^46 - 180 * q^66 + 168 * q^76 + 48 * q^81 + 228 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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