LMFDB - Embedded newform 600.2.w.k.557.6

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			557.6
Character	$\chi$	$=$	600.557
Dual form			600.2.w.k.293.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$2$	−1.21574	+	0.722477i	−0.859659	+	0.510868i
$2$	−1.21574	+	0.722477i	−0.859659	+	0.510868i
$3$	1.48597	−	0.889875i	0.857928	−	0.513770i
$3$	1.48597	−	0.889875i	0.857928	−	0.513770i
$4$	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	$0.938667\pi$
$8$	0.106854	+	2.82641i	0.0377787	+	0.999286i
$9$	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	$0.631086\pi$
$12$	−0.142564	−	3.46117i	−0.0411546	−	0.999153i
$13$	−4.21638	−	4.21638i	−1.16941	−	1.16941i	−0.982347	−	0.187065i	$-0.940102\pi$
$13$	−4.21638	−	4.21638i	−1.16941	−	1.16941i	−0.187065	−	0.982347i	$-0.559898\pi$
$14$	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	−0.997932	−	0.0642808i	$-0.979525\pi$
$17$	−3.84954	+	3.84954i	−0.933651	+	0.933651i	0.0642808	+	0.997932i	$0.479525\pi$
$18$	0.188924	+	4.23843i	0.0445299	+	0.999008i
$19$	3.15804			0.724505			0.362252	−	0.932080i	$-0.382008\pi$
$19$	3.15804			0.724505			0.362252	+	0.932080i	$0.382008\pi$
$20$		0			0
$21$	−4.96588	−	1.24594i	−1.08364	−	0.271885i
$22$	3.22796	−	1.91827i	0.688203	−	0.408977i
$23$	−1.60962	−	1.60962i	−0.335629	−	0.335629i	0.519090	−	0.854719i	$-0.326271\pi$
$23$	−1.60962	−	1.60962i	−0.335629	−	0.335629i	−0.854719	+	0.519090i	$0.826271\pi$
$24$	2.67393	+	4.10488i	0.545814	+	0.837906i
$25$		0			0
$26$	8.17226	+	2.07979i	1.60271	+	0.407880i
$27$	−0.248921	−	5.19019i	−0.0479048	−	0.998852i
$28$	−5.67003	+	1.67345i	−1.07154	+	0.316252i
$29$		−	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	$0.455032\pi$
$32$	5.06728	+	2.51449i	0.895777	+	0.444503i
$33$	−3.94546	+	2.36274i	−0.686817	+	0.411300i
$34$	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	−0.984984	−	0.172645i	$-0.944769\pi$
$37$	−4.94127	+	4.94127i	−0.812339	+	0.812339i	0.172645	+	0.984984i	$0.444769\pi$
$38$	−3.83936	+	2.28161i	−0.622827	+	0.370127i
$39$	−10.0175	−	2.51338i	−1.60408	−	0.402463i
$40$		0			0
$41$			10.6056i			1.65631i	0.560500	+	0.828154i	$0.310609\pi$
$41$			10.6056i			1.65631i	−0.560500	+	0.828154i	$0.689391\pi$
$42$	6.93738	−	2.07300i	1.07046	−	0.319870i
$43$	−0.219791	−	0.219791i	−0.0335178	−	0.0335178i	0.690149	−	0.723667i	$-0.257545\pi$
$43$	−0.219791	−	0.219791i	−0.0335178	−	0.0335178i	−0.723667	+	0.690149i	$0.757545\pi$
$44$	−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	−0.560708	−	0.828014i	$-0.689471\pi$
$47$	1.83256	−	1.83256i	0.267306	−	0.267306i	0.828014	+	0.560708i	$0.189471\pi$
$48$	−6.21650	−	3.05862i	−0.897274	−	0.441474i
$49$			1.73743i			0.248204i
$50$		0			0
$51$	−2.29471	+	9.14594i	−0.321324	+	1.28069i
$52$	−11.4380	+	3.37579i	−1.58616	+	0.468137i
$53$	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
$57$	4.69277	−	2.81027i	0.621573	−	0.372229i
$58$	3.14334	+	5.28942i	0.412740	+	0.694535i
$59$		−	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	$-0.723805\pi$
$61$		−	11.9159i		−	1.52568i	0.646590	−	0.762838i	$-0.276195\pi$
$62$	−1.90615	+	1.13277i	−0.242082	+	0.143862i
$63$	−8.48790	+	2.56758i	−1.06937	+	0.323485i
$64$	−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	$-0.474715\pi$
$67$	8.80906	−	8.80906i	1.07620	−	1.07620i	0.996847	−	0.0793517i	$-0.0252850\pi$
$68$	3.08208	+	10.4428i	0.373758	+	1.26638i
$69$	−3.82422	−	0.959493i	−0.460381	−	0.115509i
$70$		0			0
$71$		−	2.89837i		−	0.343973i	−0.985099	−	0.171986i	$-0.944982\pi$
$71$		−	2.89837i		−	0.343973i	0.985099	−	0.171986i	$-0.0550185\pi$
$72$	7.62624	+	3.72029i	0.898760	+	0.438440i
$73$	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
$78$	13.9945	−	4.18178i	1.58457	−	0.473493i
$79$			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
$82$	−7.66227	−	12.8936i	−0.846156	−	1.42386i
$83$	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
$87$	−3.87165	−	6.46515i	−0.415084	−	0.693136i
$88$	−0.283713	−	7.50450i	−0.0302439	−	0.799982i
$89$	−2.83249			−0.300243			−0.150121	−	0.988668i	$-0.547966\pi$
$89$	−2.83249			−0.300243			−0.150121	+	0.988668i	$0.547966\pi$
$90$		0			0
$91$			17.6257i			1.84768i
$92$	−4.36649	+	1.28872i	−0.455238	+	0.134358i
$93$	2.32985	−	1.39523i	0.241594	−	0.144679i
$94$	−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	$0.518389\pi$
$98$	−1.25525	−	2.11227i	−0.126800	−	0.213371i
$99$	−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	$0.678310\pi$
$102$	−3.81795	−	12.7770i	−0.378034	−	1.26511i
$103$	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	$0.826296\pi$
$108$	−9.35553	−	4.52482i	−0.900237	−	0.435401i
$109$	−2.67954			−0.256654			−0.128327	−	0.991732i	$-0.540961\pi$
$109$	−2.67954			−0.256654			−0.128327	+	0.991732i	$0.540961\pi$
$110$		0			0
$111$	−2.94549	+	11.7397i	−0.279573	+	1.11428i
$112$	−2.48113	+	11.5604i	−0.234445	+	1.09236i
$113$	−6.11636	−	6.11636i	−0.575379	−	0.575379i	0.358248	−	0.933627i	$-0.383374\pi$
$113$	−6.11636	−	6.11636i	−0.575379	−	0.575379i	−0.933627	+	0.358248i	$0.883374\pi$
$114$	−3.67485	+	6.80698i	−0.344181	+	0.637532i
$115$		0			0
$116$	−7.64297	−	4.15958i	−0.709632	−	0.386207i
$117$	−17.1223	+	5.17949i	−1.58296	+	0.478844i
$118$	7.17546	+	12.0744i	0.660555	+	1.11154i
$119$	16.0922			1.47517
$120$		0			0
$121$	−3.95026			−0.359114
$122$	8.60897	+	14.4867i	0.779420	+	1.31156i
$123$	9.43762	+	15.7596i	0.850962	+	1.42099i
$124$	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	$0.501242\pi$
$128$	9.26177	−	6.49766i	0.818633	−	0.574317i
$129$	−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	$0.407545\pi$
$132$	0.378525	+	9.18987i	0.0329464	+	0.799875i
$133$	−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	−0.633734	−	0.773551i	$-0.718479\pi$
$137$	1.63651	−	1.63651i	0.139817	−	0.139817i	0.773551	+	0.633734i	$0.218479\pi$
$138$	5.34247	−	1.59641i	0.454781	−	0.135896i
$139$	−1.03173			−0.0875104			−0.0437552	−	0.999042i	$-0.513932\pi$
$139$	−1.03173			−0.0875104			−0.0437552	+	0.999042i	$0.513932\pi$
$140$		0			0
$141$	1.09239	−	4.35389i	0.0919956	−	0.366663i
$142$	2.09400	+	3.52366i	0.175725	+	0.295699i
$143$	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
$147$	1.54610	+	2.58178i	0.127520	+	0.212942i
$148$	3.95616	+	13.4044i	0.325194	+	1.10183i
$149$			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	$0.311806\pi$
$152$	0.337451	+	8.92592i	0.0273709	+	0.723988i
$153$	4.72886	+	15.6326i	0.382306	+	1.26382i
$154$	−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	−0.934923	−	0.354851i	$-0.884532\pi$
$157$	−7.26828	+	7.26828i	−0.580072	+	0.580072i	0.354851	+	0.934923i	$0.384532\pi$
$158$	−6.52163	−	10.9742i	−0.518833	−	0.873061i
$159$	2.76661	−	11.0268i	0.219406	−	0.874479i
$160$		0			0
$161$			6.72868i			0.530295i
$162$	11.4768	+	5.50301i	0.901702	+	0.432357i
$163$	9.50622	+	9.50622i	0.744585	+	0.744585i	0.973457	−	0.228872i	$-0.0735036\pi$
$163$	9.50622	+	9.50622i	0.744585	+	0.744585i	−0.228872	+	0.973457i	$0.573504\pi$
$164$	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	$0.539253\pi$
$167$	−14.4143	+	14.4143i	−1.11541	+	1.11541i	−0.992406	+	0.123005i	$0.960747\pi$
$168$	2.99090	−	14.1687i	0.230753	−	1.09314i
$169$			22.5557i			1.73505i
$170$		0			0
$171$	4.47256	−	8.35197i	0.342025	−	0.638691i
$172$	−0.596237	+	0.175973i	−0.0454626	+	0.0134178i
$173$	−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
$177$	−8.83802	−	14.7583i	−0.664307	−	1.10930i
$178$	3.44357	−	2.04641i	0.258107	−	0.153385i
$179$			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	$-0.957481\pi$
$181$		−	3.58348i		−	0.266358i	0.991092	−	0.133179i	$-0.0425185\pi$
$182$	−12.7342	−	21.4283i	−0.943919	−	1.58837i
$183$	−10.6037	−	17.7067i	−0.783846	−	1.30892i
$184$	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
$188$	−1.46721	−	4.97126i	−0.107008	−	0.362567i
$189$	−10.3280	+	11.3685i	−0.751250	+	0.826939i
$190$		0			0
$191$		−	11.6034i		−	0.839591i	−0.907619	−	0.419796i	$-0.862102\pi$
$191$		−	11.6034i		−	0.839591i	0.907619	−	0.419796i	$-0.137898\pi$
$192$	−11.3164	+	7.99625i	−0.816688	+	0.577080i
$193$	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	$0.718307\pi$
$198$	−0.501620	−	11.2536i	−0.0356486	−	0.799759i
$199$		−	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
$202$	12.9838	−	7.71587i	0.913538	−	0.542887i
$203$	−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
$207$	−6.53652	+	1.97729i	−0.454319	+	0.137431i
$208$	−5.00509	+	23.3204i	−0.347040	+	1.61698i
$209$	−8.38503			−0.580005
$210$		0			0
$211$		−	5.39432i		−	0.371361i	−0.982610	−	0.185680i	$-0.940551\pi$
$211$		−	5.39432i		−	0.371361i	0.982610	−	0.185680i	$-0.0594489\pi$
$212$	−3.71590	−	12.5903i	−0.255209	−	0.864709i
$213$	−2.57918	−	4.30690i	−0.176723	−	0.295104i
$214$	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
$218$	3.25763	−	1.93591i	0.220635	−	0.131116i
$219$	1.36971	−	5.45920i	0.0925564	−	0.368898i
$220$		0			0
$221$	32.4622			2.18365
$222$	−4.90072	−	16.4005i	−0.328915	−	1.10073i
$223$	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	$0.664918\pi$
$228$	−0.450222	−	10.9305i	−0.0298167	−	0.723891i
$229$	11.2319			0.742225			0.371113	−	0.928588i	$-0.378976\pi$
$229$	11.2319			0.742225			0.371113	+	0.928588i	$0.378976\pi$
$230$		0			0
$231$	13.1851	+	3.30813i	0.867514	+	0.217659i
$232$	12.2971	−	0.464899i	0.807342	−	0.0305221i
$233$	−15.0715	−	15.0715i	−0.987366	−	0.987366i	0.0125551	−	0.999921i	$-0.496003\pi$
$233$	−15.0715	−	15.0715i	−0.987366	−	0.987366i	−0.999921	+	0.0125551i	$0.996003\pi$
$234$	17.0743	−	18.6674i	1.11618	−	1.22033i
$235$		0			0
$236$	−17.4470	−	9.49529i	−1.13570	−	0.618091i
$237$	8.03269	+	13.4135i	0.521780	+	0.871303i
$238$	−19.5640	+	11.6263i	−1.26814	+	0.753618i
$239$	2.89837			0.187480			0.0937398	−	0.995597i	$-0.470118\pi$
$239$	2.89837			0.187480			0.0937398	+	0.995597i	$0.470118\pi$
$240$		0			0
$241$	0.551900			0.0355510			0.0177755	−	0.999842i	$-0.494342\pi$
$241$	0.551900			0.0355510			0.0177755	+	0.999842i	$0.494342\pi$
$242$	4.80249	−	2.85397i	0.308716	−	0.183460i
$243$	−14.0788	−	6.69226i	−0.903158	−	0.429308i
$244$	−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
$248$	0.167536	+	4.43151i	0.0106386	+	0.281401i
$249$	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	$0.436319\pi$
$252$	−3.60444	+	17.3654i	−0.227058	+	1.09391i
$253$	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	−0.279174	−	0.960240i	$-0.590061\pi$
$257$	10.9183	−	10.9183i	0.681066	−	0.681066i	0.960240	+	0.279174i	$0.0900607\pi$
$258$	0.729506	−	0.217988i	0.0454171	−	0.0135713i
$259$	20.6559			1.28350
$260$		0			0
$261$	−11.5063	−	6.16176i	−0.712225	−	0.381403i
$262$	−7.97012	+	4.73639i	−0.492396	+	0.292615i
$263$	21.0955	+	21.0955i	1.30081	+	1.30081i	0.927848	+	0.372959i	$0.121657\pi$
$263$	21.0955	+	21.0955i	1.30081	+	1.30081i	0.372959	+	0.927848i	$0.378343\pi$
$264$	−7.09966	−	10.8990i	−0.436954	−	0.670788i
$265$		0			0
$266$	12.7937	+	3.25593i	0.784435	+	0.199634i
$267$	−4.20900	+	2.52056i	−0.257587	+	0.154256i
$268$	−7.05286	−	23.8967i	−0.430822	−	1.45973i
$269$			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	$0.764159\pi$
$272$	21.2914	+	4.56963i	1.29098	+	0.277075i
$273$	15.6847	+	26.1913i	0.949280	+	1.58517i
$274$	−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	−0.216312	−	0.976324i	$-0.569403\pi$
$277$	12.6491	−	12.6491i	0.760013	−	0.760013i	0.976324	+	0.216312i	$0.0694027\pi$
$278$	1.25432	−	0.745403i	0.0752291	−	0.0447063i
$279$	2.22052	−	4.14656i	0.132939	−	0.248248i
$280$		0			0
$281$		−	8.81745i		−	0.526005i	−0.964795	−	0.263002i	$-0.915287\pi$
$281$		−	8.81745i		−	0.526005i	0.964795	−	0.263002i	$-0.0847127\pi$
$282$	1.81752	+	6.08242i	0.108232	+	0.362203i
$283$	−13.4928	−	13.4928i	−0.802061	−	0.802061i	0.181357	−	0.983417i	$-0.441951\pi$
$283$	−13.4928	−	13.4928i	−0.802061	−	0.802061i	−0.983417	+	0.181357i	$0.941951\pi$
$284$	−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
$288$	13.8265	−	9.84014i	0.814733	−	0.579836i
$289$		−	12.6379i		−	0.743409i
$290$		0			0
$291$	22.0093	+	5.52212i	1.29021	+	0.323712i
$292$	−1.83969	−	6.23331i	−0.107660	−	0.364777i
$293$	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
$297$	0.660918	+	13.7806i	0.0383503	+	0.799634i
$298$	−2.60293	−	4.38005i	−0.150784	−	0.253730i
$299$			13.5735i			0.784977i
$300$		0			0
$301$			0.918791i			0.0529583i
$302$	−16.6538	+	9.89682i	−0.958317	+	0.569498i
$303$	−15.8698	+	9.50365i	−0.911698	+	0.545970i
$304$	−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	−0.842378	−	0.538888i	$-0.818845\pi$
$307$	−5.31757	+	5.31757i	−0.303490	+	0.303490i	0.538888	+	0.842378i	$0.318845\pi$
$308$	15.0547	−	4.44323i	0.857822	−	0.253177i
$309$	6.16176	−	24.5587i	0.350530	−	1.39709i
$310$		0			0
$311$		−	31.3649i		−	1.77854i	−0.457382	−	0.889270i	$-0.651213\pi$
$311$		−	31.3649i		−	1.77854i	0.457382	−	0.889270i	$-0.348787\pi$
$312$	6.03343	−	28.5821i	0.341576	−	1.61814i
$313$	−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	$0.920499\pi$
$318$	4.60310	+	15.4045i	0.258129	+	0.863841i
$319$			11.5519i			0.646782i
$320$		0			0
$321$	−8.25108	−	2.07019i	−0.460530	−	0.115547i
$322$	−4.86132	−	8.18034i	−0.270911	−	0.455872i
$323$	−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
$327$	−3.98173	+	2.38446i	−0.220190	+	0.131861i
$328$	−29.9756	+	1.13325i	−1.65513	+	0.0625732i
$329$	−7.66064			−0.422345
$330$		0			0
$331$		−	10.6434i		−	0.585016i	−0.956263	−	0.292508i	$-0.905510\pi$
$331$		−	10.6434i		−	0.585016i	0.956263	−	0.292508i	$-0.0944899\pi$
$332$	−7.83664	−	26.5524i	−0.430092	−	1.45725i
$333$	6.06996	+	20.0660i	0.332632	+	1.09961i
$334$	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	$0.757131\pi$
$338$	−16.2960	−	27.4219i	−0.886383	−	1.49155i
$339$	−14.5316	−	3.64596i	−0.789246	−	0.198021i
$340$		0			0
$341$	−4.16297			−0.225438
$342$	0.596632	+	13.3852i	0.0322621	+	0.723786i
$343$	−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	$0.726908\pi$
$348$	−15.0588	+	0.620262i	−0.807234	+	0.0332495i
$349$	16.3562			0.875528			0.437764	−	0.899090i	$-0.355771\pi$
$349$	16.3562			0.875528			0.437764	+	0.899090i	$0.355771\pi$
$350$		0			0
$351$	−20.8342	+	22.9333i	−1.11205	+	1.22409i
$352$	−13.4543	−	6.67631i	−0.717118	−	0.355848i
$353$	0.326679	+	0.326679i	0.0173874	+	0.0173874i	0.715747	−	0.698360i	$-0.246086\pi$
$353$	0.326679	+	0.326679i	0.0173874	+	0.0173874i	−0.698360	+	0.715747i	$0.746086\pi$
$354$	21.4073	+	11.5571i	1.13779	+	0.614250i
$355$		0			0
$356$	−2.70801	+	4.97580i	−0.143524	+	0.263717i
$357$	23.9126	−	14.3201i	1.26559	−	0.757898i
$358$	−4.20454	−	7.07515i	−0.222217	−	0.373934i
$359$	−16.0922			−0.849315			−0.424657	−	0.905354i	$-0.639605\pi$
$359$	−16.0922			−0.849315			−0.424657	+	0.905354i	$0.639605\pi$
$360$		0			0
$361$	−9.02676			−0.475093
$362$	2.58898	+	4.35658i	0.136074	+	0.228977i
$363$	−5.86998	+	3.51524i	−0.308094	+	0.184502i
$364$	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	$0.529137\pi$
$368$	−1.91071	+	8.90265i	−0.0996028	+	0.464083i
$369$	28.0481	+	15.0200i	1.46013	+	0.781912i
$370$		0			0
$371$	−19.4015			−1.00728
$372$	−0.223525	−	5.42674i	−0.0115892	−	0.281364i
$373$	−4.04391	−	4.04391i	−0.209386	−	0.209386i	0.594621	−	0.804006i	$-0.297302\pi$
$373$	−4.04391	−	4.04391i	−0.209386	−	0.209386i	−0.804006	+	0.594621i	$0.797302\pi$
$374$	−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
$378$	4.34264	−	21.2829i	0.223361	−	1.09468i
$379$	−9.37395			−0.481507			−0.240754	−	0.970586i	$-0.577395\pi$
$379$	−9.37395			−0.481507			−0.240754	+	0.970586i	$0.577395\pi$
$380$		0			0
$381$	26.6698	+	6.69143i	1.36633	+	0.342812i
$382$	8.38318	+	14.1067i	0.428921	+	0.721762i
$383$	1.94014	+	1.94014i	0.0991364	+	0.0991364i	0.754935	−	0.655799i	$-0.227668\pi$
$383$	1.94014	+	1.94014i	0.0991364	+	0.0991364i	−0.655799	+	0.754935i	$0.727668\pi$
$384$	7.98065	−	17.8972i	0.407261	−	0.913312i
$385$		0			0
$386$	−4.84915	+	19.0541i	−0.246815	+	0.969829i
$387$	−0.892551	+	0.269996i	−0.0453709	+	0.0137247i
$388$	25.1302	−	7.41690i	1.27579	−	0.376536i
$389$		−	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
$392$	−4.91069	+	0.185652i	−0.248027	+	0.00937684i
$393$	9.74171	−	5.83382i	0.491404	−	0.294277i
$394$	−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	−0.172204	−	0.985061i	$-0.555089\pi$
$397$	16.1961	−	16.1961i	0.812858	−	0.812858i	0.985061	+	0.172204i	$0.0550887\pi$
$398$	2.95712	+	4.97607i	0.148227	+	0.249428i
$399$	−15.6825	−	3.93472i	−0.785105	−	0.196982i
$400$		0			0
$401$			33.9532i			1.69554i	0.530362	+	0.847771i	$0.322056\pi$
$401$			33.9532i			1.69554i	−0.530362	+	0.847771i	$0.677944\pi$
$402$	8.73678	+	29.2381i	0.435751	+	1.45826i
$403$	−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
$408$	−26.0953	−	5.50850i	−1.29191	−	0.272712i
$409$		−	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
$412$	−8.27602	−	28.0411i	−0.407730	−	1.38148i
$413$	−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
$417$	−1.53313	+	0.918113i	−0.0750776	+	0.0449602i
$418$	10.1940	−	6.05799i	0.498606	−	0.296306i
$419$		−	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	$0.239925\pi$
$421$			28.0844i			1.36875i	−0.729129	+	0.684376i	$0.760075\pi$
$422$	3.89727	+	6.55810i	0.189716	+	0.319243i
$423$	−2.25116	−	7.44186i	−0.109455	−	0.361835i
$424$	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
$428$	−9.42108	+	2.78053i	−0.455385	+	0.134402i
$429$	26.5978	+	6.67337i	1.28415	+	0.322193i
$430$		0			0
$431$		−	8.20673i		−	0.395304i	−0.980272	−	0.197652i	$-0.936668\pi$
$431$		−	8.20673i		−	0.395304i	0.980272	−	0.197652i	$-0.0633316\pi$
$432$	−16.8931	+	12.1088i	−0.812770	+	0.582585i
$433$	−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
$438$	2.27893	+	7.62655i	0.108892	+	0.364411i
$439$		−	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
$442$	−39.4657	+	23.4532i	−1.87719	+	1.11556i
$443$	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
$447$	3.20603	+	5.35364i	0.151640	+	0.253219i
$448$	17.9360	+	15.4109i	0.847394	+	0.728099i
$449$	0.611967			0.0288805			0.0144403	−	0.999896i	$-0.495403\pi$
$449$	0.611967			0.0288805			0.0144403	+	0.999896i	$0.495403\pi$
$450$		0			0
$451$		−	28.1592i		−	1.32596i
$452$	−16.5921	+	4.89698i	−0.780428	+	0.230335i
$453$	20.3556	−	12.1899i	0.956388	−	0.572732i
$454$	−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	$0.786334\pi$
$458$	−13.6551	+	8.11480i	−0.638061	+	0.379180i
$459$	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	$0.497818\pi$
$462$	−18.4197	+	5.50409i	−0.856961	+	0.256073i
$463$	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	$0.961650\pi$
$468$	−7.27110	+	35.0305i	−0.336107	+	1.61929i
$469$	−36.8245			−1.70040
$470$		0			0
$471$	−4.33262	+	17.2684i	−0.199637	+	0.795684i
$472$	28.0712	−	1.06125i	1.29208	−	0.0488480i
$473$	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
$477$	−5.70133	−	18.8474i	−0.261046	−	0.862964i
$478$	−3.52366	+	2.09400i	−0.161169	+	0.0957774i
$479$	18.9906			0.867702			0.433851	−	0.900985i	$-0.357154\pi$
$479$	18.9906			0.867702			0.433851	+	0.900985i	$0.357154\pi$
$480$		0			0
$481$	41.6685			1.89992
$482$	−0.670968	+	0.398735i	−0.0305617	+	0.0181619i
$483$	5.98769	+	9.99866i	0.272449	+	0.454955i
$484$	−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	$0.876269\pi$
$488$	33.6792	−	1.27327i	1.52459	−	0.0576381i
$489$	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	$0.634548\pi$
$492$	36.7076	−	1.51197i	1.65491	−	0.0681647i
$493$	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
$498$	9.70770	+	32.4873i	0.435012	+	1.45579i
$499$	−24.8457			−1.11225			−0.556124	−	0.831100i	$-0.687712\pi$
$499$	−24.8457			−1.11225			−0.556124	+	0.831100i	$0.687712\pi$
$500$		0			0
$501$	−8.59235	+	34.2462i	−0.383878	+	1.53001i
$502$	−7.65541	+	4.54937i	−0.341678	+	0.203048i
$503$	−17.0078	−	17.0078i	−0.758340	−	0.758340i	0.217680	−	0.976020i	$-0.430151\pi$
$503$	−17.0078	−	17.0078i	−0.758340	−	0.758340i	−0.976020	+	0.217680i	$0.930151\pi$
$504$	−8.16401	−	23.7159i	−0.363654	−	1.05639i
$505$		0			0
$506$	−8.28347	−	2.10809i	−0.368245	−	0.0937161i
$507$	20.0717	+	33.5172i	0.891418	+	1.48855i
$508$	30.4515	−	8.98743i	1.35107	−	0.398753i
$509$			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
$512$	−2.55962	−	22.4822i	−0.113120	−	0.993581i
$513$	−0.786102	−	16.3908i	−0.0347073	−	0.723673i
$514$	−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
$518$	−25.1123	+	14.9234i	−1.10337	+	0.655699i
$519$	−10.7839	+	42.9808i	−0.473359	+	1.88665i
$520$		0			0
$521$			21.5789i			0.945388i	0.881227	+	0.472694i	$0.156718\pi$
$521$			21.5789i			0.945388i	−0.881227	+	0.472694i	$0.843282\pi$
$522$	18.4405	−	0.821968i	0.807118	−	0.0359766i
$523$	1.75051	+	1.75051i	0.0765445	+	0.0765445i	0.744343	−	0.667798i	$-0.232763\pi$
$523$	1.75051	+	1.75051i	0.0765445	+	0.0765445i	−0.667798	+	0.744343i	$0.732763\pi$
$524$	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
$528$	16.5056	+	8.12105i	0.718316	+	0.353424i
$529$		−	17.8182i		−	0.774707i
$530$		0			0
$531$	−26.2662	−	14.0658i	−1.13985	−	0.610403i
$532$	−17.9062	+	5.28482i	−0.776333	+	0.229126i
$533$	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
$537$	5.17874	+	8.64781i	0.223479	+	0.373181i
$538$	−14.8913	−	25.0583i	−0.642011	−	1.08034i
$539$		−	4.61311i		−	0.198701i
$540$		0			0
$541$			22.6515i			0.973864i	0.873440	+	0.486932i	$0.161884\pi$
$541$			22.6515i			0.973864i	−0.873440	+	0.486932i	$0.838116\pi$
$542$	29.5341	−	17.5512i	1.26860	−	0.753889i
$543$	−3.18885	−	5.32496i	−0.136847	−	0.228516i
$544$	−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	$0.512137\pi$
$547$	−24.2626	+	24.2626i	−1.03739	+	1.03739i	−0.999273	+	0.0381200i	$0.987863\pi$
$548$	−1.31025	−	4.43944i	−0.0559712	−	0.189644i
$549$	−31.5136	−	16.8758i	−1.34497	−	0.720243i
$550$		0			0
$551$		−	13.7399i		−	0.585341i
$552$	2.30329	−	10.9113i	0.0980344	−	0.464417i
$553$	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	$0.606798\pi$
$558$	0.296214	+	6.64541i	0.0125397	+	0.281323i
$559$			1.85344i			0.0783923i
$560$		0			0
$561$	6.09277	−	24.2837i	0.257237	−	1.02526i
$562$	6.37040	+	10.7197i	0.268719	+	0.452185i
$563$	−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
$567$	−5.23053	+	26.0840i	−0.219662	+	1.09542i
$568$	8.19196	−	0.309703i	0.343727	−	0.0129948i
$569$	−27.6005			−1.15707			−0.578536	−	0.815657i	$-0.696376\pi$
$569$	−27.6005			−1.15707			−0.578536	+	0.815657i	$0.696376\pi$
$570$		0			0
$571$		−	32.2742i		−	1.35063i	−0.737528	−	0.675317i	$-0.764007\pi$
$571$		−	32.2742i		−	1.35063i	0.737528	−	0.675317i	$-0.235993\pi$
$572$	30.3693	−	8.96317i	1.26980	−	0.374769i
$573$	−10.3256	−	17.2423i	−0.431357	−	0.720309i
$574$	−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	$0.702015\pi$
$578$	9.13063	+	15.3645i	0.379784	+	0.639078i
$579$	5.86010	−	23.3564i	0.243537	−	0.970657i
$580$		0			0
$581$	−40.9168			−1.69751
$582$	−30.7472	+	9.18774i	−1.27451	+	0.380844i
$583$	−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	$0.781358\pi$
$588$	6.01354	−	0.247694i	0.247994	−	0.0102147i
$589$	4.95148			0.204022
$590$		0			0
$591$	4.68769	+	1.17614i	0.192826	+	0.0483799i
$592$	27.3297	+	5.86557i	1.12324	+	0.241074i
$593$	−16.9693	−	16.9693i	−0.696844	−	0.696844i	0.266884	−	0.963729i	$-0.414006\pi$
$593$	−16.9693	−	16.9693i	−0.696844	−	0.696844i	−0.963729	+	0.266884i	$0.914006\pi$
$594$	−10.7597	−	16.2762i	−0.441476	−	0.667821i
$595$		0			0
$596$	6.32897	+	3.44445i	0.259245	+	0.141090i
$597$	−3.64229	−	6.08214i	−0.149069	−	0.248926i
$598$	−9.80656	−	16.5019i	−0.401020	−	0.674813i
$599$	−1.04438			−0.0426723			−0.0213361	−	0.999772i	$-0.506792\pi$
$599$	−1.04438			−0.0426723			−0.0213361	+	0.999772i	$0.506792\pi$
$600$		0			0
$601$	0.244816			0.00998624			0.00499312	−	0.999988i	$-0.498411\pi$
$601$	0.244816			0.00998624			0.00499312	+	0.999988i	$0.498411\pi$
$602$	−0.663806	−	1.11701i	−0.0270547	−	0.0455260i
$603$	−10.8212	−	35.7728i	−0.440675	−	1.45678i
$604$	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	$0.786186\pi$
$608$	16.0027	+	7.94086i	0.648995	+	0.322045i
$609$	−5.42079	+	21.6054i	−0.219661	+	0.875496i
$610$		0			0
$611$	−15.4535			−0.625183
$612$	31.9828	+	6.63850i	1.29283	+	0.268345i
$613$	21.0245	+	21.0245i	0.849172	+	0.849172i	0.990030	−	0.140858i	$-0.0449861\pi$
$613$	21.0245	+	21.0245i	0.849172	+	0.849172i	−0.140858	+	0.990030i	$0.544986\pi$
$614$	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	−0.220973	−	0.975280i	$-0.570923\pi$
$617$	18.7366	−	18.7366i	0.754307	−	0.754307i	0.975280	+	0.220973i	$0.0709231\pi$
$618$	10.2520	+	34.3087i	0.412395	+	1.38010i
$619$	−8.66233			−0.348169			−0.174084	−	0.984731i	$-0.555697\pi$
$619$	−8.66233			−0.348169			−0.174084	+	0.984731i	$0.555697\pi$
$620$		0			0
$621$	−7.95356	+	8.75489i	−0.319165	+	0.351322i
$622$	22.6604	+	38.1316i	0.908600	+	1.52894i
$623$	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
$627$	−12.4599	+	7.46163i	−0.497602	+	0.297989i
$628$	5.81925	+	19.7170i	0.232214	+	0.786794i
$629$		−	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	$0.508756\pi$
$632$	−25.5133	+	0.964549i	−1.01487	+	0.0383677i
$633$	−4.80028	−	8.01583i	−0.190794	−	0.318601i
$634$	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
$638$	−8.34598	−	14.0441i	−0.330421	−	0.556012i
$639$	−7.66521	−	4.10479i	−0.303231	−	0.162383i
$640$		0			0
$641$		−	32.1844i		−	1.27121i	−0.772015	−	0.635604i	$-0.780751\pi$
$641$		−	32.1844i		−	1.27121i	0.772015	−	0.635604i	$-0.219249\pi$
$642$	11.5268	−	3.44440i	0.454928	−	0.135940i
$643$	−13.8136	−	13.8136i	−0.544755	−	0.544755i	0.380164	−	0.924919i	$-0.375868\pi$
$643$	−13.8136	−	13.8136i	−0.544755	−	0.544755i	−0.924919	+	0.380164i	$0.875868\pi$
$644$	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	−0.333246	−	0.942840i	$-0.608144\pi$
$647$	15.5057	−	15.5057i	0.609594	−	0.609594i	0.942840	+	0.333246i	$0.108144\pi$
$648$	20.6395	−	14.9000i	0.810797	−	0.585328i
$649$			26.3701i			1.03512i
$650$		0			0
$651$	−7.78597	−	1.95350i	−0.305156	−	0.0765635i
$652$	25.7880	−	7.61103i	1.00993	−	0.298071i
$653$	−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
$657$	−2.82265	−	9.33110i	−0.110122	−	0.364041i
$658$	9.31335	−	5.53463i	0.363072	−	0.215763i
$659$		−	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	$-0.952182\pi$
$661$		−	7.69555i		−	0.299322i	0.988737	−	0.149661i	$-0.0478183\pi$
$662$	7.68964	+	12.9397i	0.298866	+	0.502915i
$663$	48.2381	−	28.8874i	1.87341	−	1.12189i
$664$	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
$668$	11.5406	+	39.1023i	0.446520	+	1.51291i
$669$	1.57308	−	6.26976i	0.0608188	−	0.242403i
$670$		0			0
$671$			31.6383i			1.22138i
$672$	−22.0306	−	18.8001i	−0.849849	−	0.725231i
$673$	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	$0.807529\pi$
$678$	20.3007	−	6.06617i	0.779645	−	0.232970i
$679$		−	38.7252i		−	1.48614i
$680$		0			0
$681$	13.3706	+	3.35468i	0.512363	+	0.128552i
$682$	5.06110	−	3.00765i	0.193799	−	0.115169i
$683$	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
$687$	16.6903	−	9.99500i	0.636776	−	0.381333i
$688$	−0.260905	+	1.21564i	−0.00994691	+	0.0463460i
$689$	−39.1380			−1.49104
$690$		0			0
$691$			36.4559i			1.38685i	0.720529	+	0.693425i	$0.243899\pi$
$691$			36.4559i			1.38685i	−0.720529	+	0.693425i	$0.756101\pi$
$692$	14.4841	+	49.0754i	0.550602	+	1.86557i
$693$	22.5365	−	6.81728i	0.856091	−	0.258967i
$694$	−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
$698$	−19.8849	+	11.8170i	−0.752655	+	0.447279i
$699$	−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	$0.138281\pi$
$702$	8.76025	−	42.9333i	0.330634	−	1.62041i
$703$	−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
$708$	−34.3755	+	1.41591i	−1.29191	+	0.0532130i
$709$	6.97929			0.262113			0.131056	−	0.991375i	$-0.458163\pi$
$709$	6.97929			0.262113			0.131056	+	0.991375i	$0.458163\pi$
$710$		0			0
$711$	23.8728	+	12.7841i	0.895299	+	0.479441i
$712$	−0.302663	−	8.00576i	−0.0113428	−	0.300029i
$713$	−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
$717$	4.30690	−	2.57918i	0.160844	−	0.0963214i
$718$	19.5640	−	11.6263i	0.730121	−	0.433888i
$719$	2.63485			0.0982634			0.0491317	−	0.998792i	$-0.484355\pi$
$719$	2.63485			0.0982634			0.0491317	+	0.998792i	$0.484355\pi$
$720$		0			0
$721$	−43.2108			−1.60926
$722$	10.9742	−	6.52163i	0.408418	−	0.242710i
$723$	0.820109	−	0.491122i	0.0305002	−	0.0182650i
$724$	−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	$0.703490\pi$
$728$	−49.8174	+	1.88338i	−1.84636	+	0.0698028i
$729$	−26.8761	+	2.58389i	−0.995410	+	0.0956996i
$730$		0			0
$731$	1.69219			0.0625879
$732$	−41.2429	+	1.69877i	−1.52438	+	0.0627885i
$733$	10.2051	+	10.2051i	0.376934	+	0.376934i	0.869995	−	0.493061i	$-0.164122\pi$
$733$	10.2051	+	10.2051i	0.376934	+	0.376934i	−0.493061	+	0.869995i	$0.664122\pi$
$734$	−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
$738$	−44.9509	+	2.00365i	−1.65467	+	0.0737553i
$739$	−33.7165			−1.24028			−0.620141	−	0.784490i	$-0.712925\pi$
$739$	−33.7165			−1.24028			−0.620141	+	0.784490i	$0.712925\pi$
$740$		0			0
$741$	−31.6356	−	7.93737i	−1.16216	−	0.291586i
$742$	23.5872	−	14.0172i	0.865914	−	0.514586i
$743$	−14.9523	−	14.9523i	−0.548546	−	0.548546i	0.377474	−	0.926020i	$-0.376793\pi$
$743$	−14.9523	−	14.9523i	−0.548546	−	0.548546i	−0.926020	+	0.377474i	$0.876793\pi$
$744$	4.19245	+	6.43602i	0.153703	+	0.235956i
$745$		0			0
$746$	7.83798	+	1.99472i	0.286969	+	0.0730317i
$747$	−12.0238	−	39.7482i	−0.439928	−	1.45431i
$748$	−8.18335	−	27.7271i	−0.299213	−	1.01380i
$749$			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	$0.319647\pi$
$752$	−10.1357	−	2.17536i	−0.369611	−	0.0793271i
$753$	9.35705	−	5.60346i	0.340990	−	0.204202i
$754$	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	−0.522075	−	0.852900i	$-0.674842\pi$
$757$	9.10219	−	9.10219i	0.330825	−	0.330825i	0.852900	+	0.522075i	$0.174842\pi$
$758$	11.3963	−	6.77246i	0.413932	−	0.245987i
$759$	10.1538	+	2.54758i	0.368560	+	0.0924715i
$760$		0			0
$761$			19.4230i			0.704083i	0.935984	+	0.352042i	$0.114512\pi$
$761$			19.4230i			0.704083i	−0.935984	+	0.352042i	$0.885488\pi$
$762$	−37.2579	+	11.1332i	−1.34971	+	0.403315i
$763$	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
$768$	3.22789	+	27.5242i	0.116477	+	0.993193i
$769$		−	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
$772$	−7.87085	−	26.6683i	−0.283278	−	0.959812i
$773$	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
$777$	30.6942	−	18.3812i	1.10115	−	0.659423i
$778$	11.3996	+	19.1826i	0.408696	+	0.687729i
$779$			33.4928i			1.20000i
$780$		0			0
$781$			7.69555i			0.275368i
$782$	−15.0662	+	8.95337i	−0.538766	+	0.320172i
$783$	−22.5813	+	1.08300i	−0.806991	+	0.0387032i
$784$	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	−0.735894	−	0.677097i	$-0.763238\pi$
$787$	−1.64945	+	1.64945i	−0.0587966	+	0.0587966i	0.677097	+	0.735894i	$0.263238\pi$
$788$	5.35240	−	1.57970i	0.190671	−	0.0562745i
$789$	50.1199	+	12.5750i	1.78431	+	0.447683i
$790$		0			0
$791$			25.5682i			0.909100i
$792$	−20.2487	−	9.87787i	−0.719506	−	0.350995i
$793$	−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	$0.874335\pi$
$798$	21.9086	−	6.54661i	0.775554	−	0.231748i
$799$			14.1090i			0.499141i
$800$		0			0
$801$	−4.01149	+	7.49098i	−0.141739	+	0.264681i
$802$	−24.5304	−	41.2783i	−0.866199	−	1.45759i
$803$	−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
$807$	18.3417	+	30.6282i	0.645657	+	1.07816i
$808$	−1.14118	−	30.1853i	−0.0401465	−	1.06192i
$809$	44.9347			1.57982			0.789910	−	0.613223i	$-0.210127\pi$
$809$	44.9347			1.57982			0.789910	+	0.613223i	$0.210127\pi$
$810$		0			0
$811$			23.8947i			0.839055i	0.907743	+	0.419528i	$0.137804\pi$
$811$			23.8947i			0.839055i	−0.907743	+	0.419528i	$0.862196\pi$
$812$	7.28080	+	24.6691i	0.255506	+	0.865714i
$813$	−36.0990	+	21.6178i	−1.26605	+	0.758171i
$814$	−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
$818$	8.61029	+	14.4889i	0.301052	+	0.506592i
$819$	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	$0.771313\pi$
$822$	1.62309	+	5.43173i	0.0566116	+	0.189454i
$823$	−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	$0.453245\pi$
$828$	−2.77577	+	13.3730i	−0.0964648	+	0.464745i
$829$	19.3767			0.672980			0.336490	−	0.941687i	$-0.390760\pi$
$829$	19.3767			0.672980			0.336490	+	0.941687i	$0.390760\pi$
$830$		0			0
$831$	7.54014	−	30.0524i	0.261565	−	1.04251i
$832$	36.1815	+	31.0879i	1.25437	+	1.07778i
$833$	−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
$837$	−0.390281	−	8.13766i	−0.0134901	−	0.281279i
$838$	0.356942	+	0.600640i	0.0123304	+	0.0207488i
$839$	38.4795			1.32846			0.664229	−	0.747529i	$-0.268760\pi$
$839$	38.4795			1.32846			0.664229	+	0.747529i	$0.268760\pi$
$840$		0			0
$841$	10.0707			0.347267
$842$	−20.2904	−	34.1434i	−0.699252	−	1.17666i
$843$	−7.84643	−	13.1025i	−0.270245	−	0.451274i
$844$	−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
$848$	−25.6699	−	5.50936i	−0.881510	−	0.189192i
$849$	−32.0568	−	8.04302i	−1.10019	−	0.276036i
$850$		0			0
$851$	15.9071			0.545289
$852$	−10.0317	+	0.413201i	−0.343681	+	0.0141560i
$853$	−20.0303	−	20.0303i	−0.685823	−	0.685823i	0.275483	−	0.961306i	$-0.411162\pi$
$853$	−20.0303	−	20.0303i	−0.685823	−	0.685823i	−0.961306	+	0.275483i	$0.911162\pi$
$854$	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	−0.156226	−	0.987721i	$-0.549933\pi$
$857$	24.3417	−	24.3417i	0.831496	−	0.831496i	0.987721	+	0.156226i	$0.0499327\pi$
$858$	−37.1574	+	11.1032i	−1.26853	+	0.379057i
$859$	43.4501			1.48250			0.741249	−	0.671230i	$-0.234234\pi$
$859$	43.4501			1.48250			0.741249	+	0.671230i	$0.234234\pi$
$860$		0			0
$861$	13.2138	−	52.6659i	0.450326	−	1.79485i
$862$	5.92917	+	9.97726i	0.201948	+	0.339827i
$863$	16.6773	+	16.6773i	0.567701	+	0.567701i	0.931484	−	0.363783i	$-0.118515\pi$
$863$	16.6773	+	16.6773i	0.567701	+	0.567701i	−0.363783	+	0.931484i	$0.618515\pi$
$864$	11.7893	−	26.9260i	0.401081	−	0.916043i
$865$		0			0
$866$	3.99541	−	15.6994i	0.135769	−	0.533488i
$867$	−11.2462	−	18.7797i	−0.381941	−	0.637791i
$868$	−8.89002	+	2.62379i	−0.301747	+	0.0890572i
$869$		−	23.9673i		−	0.813034i
$870$		0			0
$871$	−74.2847			−2.51704
$872$	−0.286321	−	7.57348i	−0.00969604	−	0.256470i
$873$	37.6193	−	11.3798i	1.27322	−	0.385148i
$874$	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	−0.710639	−	0.703557i	$-0.751594\pi$
$877$	−0.209733	+	0.209733i	−0.00708216	+	0.00708216i	0.703557	+	0.710639i	$0.251594\pi$
$878$	3.77081	+	6.34529i	0.127259	+	0.214143i
$879$	4.07907	−	16.2578i	0.137584	−	0.548362i
$880$		0			0
$881$			7.66064i			0.258093i	0.991639	+	0.129047i	$0.0411917\pi$
$881$			7.66064i			0.258093i	−0.991639	+	0.129047i	$0.958808\pi$
$882$	−7.36398	+	0.328243i	−0.247958	+	0.0110525i
$883$	7.44439	+	7.44439i	0.250524	+	0.250524i	0.821185	−	0.570662i	$-0.193313\pi$
$883$	7.44439	+	7.44439i	0.250524	+	0.250524i	−0.570662	+	0.821185i	$0.693313\pi$
$884$	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	−0.920933	−	0.389722i	$-0.872571\pi$
$887$	−15.8208	+	15.8208i	−0.531211	+	0.531211i	0.389722	+	0.920933i	$0.372571\pi$
$888$	−33.4959	−	7.07071i	−1.12405	−	0.237277i
$889$		−	46.9253i		−	1.57382i
$890$		0			0
$891$	13.2452	+	19.8896i	0.443730	+	0.666325i
$892$	−2.11284	−	7.15881i	−0.0707433	−	0.239695i
$893$	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
$897$	12.0787	+	20.1699i	0.403298	+	0.673454i
$898$	−0.743993	+	0.442132i	−0.0248274	+	0.0147541i
$899$		−	6.82156i		−	0.227512i
$900$		0			0
$901$			35.7329i			1.19043i
$902$	20.3444	+	34.2343i	0.677393	+	1.13988i
$903$	0.817610	+	1.36530i	0.0272084	+	0.0454344i
$904$	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	$-0.456933\pi$
$907$	33.9035	−	33.9035i	1.12575	−	1.12575i	0.990861	−	0.134886i	$-0.0430668\pi$
$908$	15.2665	−	4.50575i	0.506638	−	0.149529i
$909$	−15.1251	+	28.2444i	−0.501669	+	0.936806i
$910$		0			0
$911$			8.75281i			0.289994i	0.989432	+	0.144997i	$0.0463172\pi$
$911$			8.75281i			0.289994i	−0.989432	+	0.144997i	$0.953683\pi$
$912$	−19.6320	−	9.65926i	−0.650079	−	0.319850i
$913$	−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
$918$	−39.1980	−	7.99808i	−1.29373	−	0.263976i
$919$		−	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
$922$	−0.357915	+	0.212698i	−0.0117873	+	0.00700483i
$923$	−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
$927$	−12.6979	−	41.9768i	−0.417055	−	1.37870i
$928$	10.9400	−	22.0466i	0.359122	−	0.723716i
$929$	41.2267			1.35261			0.676303	−	0.736624i	$-0.263581\pi$
$929$	41.2267			1.35261			0.676303	+	0.736624i	$0.263581\pi$
$930$		0			0
$931$			5.48688i			0.179825i
$932$	−40.8851	+	12.0668i	−1.33924	+	0.395261i
$933$	−27.9109	−	46.6075i	−0.913761	−	1.52586i
$934$	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	$0.412392\pi$
$938$	44.7690	−	26.6048i	1.46176	−	0.868679i
$939$	−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	$0.162945\pi$
$942$	−7.20865	−	24.1241i	−0.234870	−	0.786005i
$943$	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	$0.934315\pi$
$948$	31.2431	−	1.28689i	1.01473	−	0.0417962i
$949$	−19.3767			−0.628993
$950$		0			0
$951$	−30.5327	−	7.66064i	−0.990091	−	0.248413i
$952$	1.71952	+	45.4832i	0.0557301	+	1.47412i
$953$	31.8333	+	31.8333i	1.03118	+	1.03118i	0.999498	+	0.0316832i	$0.0100868\pi$
$953$	31.8333	+	31.8333i	1.03118	+	1.03118i	0.0316832	+	0.999498i	$0.489913\pi$
$954$	20.5482	+	18.7945i	0.665272	+	0.608495i
$955$		0			0
$956$	2.77099	−	5.09153i	0.0896203	−	0.164672i
$957$	10.2798	+	17.1658i	0.332297	+	0.554893i
$958$	−23.0876	+	13.7203i	−0.745928	+	0.443282i
$959$	−6.84111			−0.220911
$960$		0			0
$961$	−28.5417			−0.920700
$962$	−50.6581	+	30.1045i	−1.63328	+	0.970609i
$963$	−14.1031	+	4.26618i	−0.454466	+	0.137476i
$964$	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	$0.914852\pi$
$968$	−0.422102	−	11.1650i	−0.0135669	−	0.358858i
$969$	−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	$0.488796\pi$
$972$	−25.2163	+	18.3340i	−0.808815	+	0.588063i
$973$	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	−0.669992	−	0.742368i	$-0.733703\pi$
$977$	2.26226	−	2.26226i	0.0723760	−	0.0723760i	0.742368	+	0.669992i	$0.233703\pi$
$978$	−31.5520	+	9.42822i	−1.00892	+	0.301481i
$979$	7.52063			0.240361
$980$		0			0
$981$	−3.79488	+	7.08649i	−0.121161	+	0.226254i
$982$	22.1018	−	13.1344i	0.705298	−	0.419136i
$983$	39.9359	+	39.9359i	1.27376	+	1.27376i	0.944101	+	0.329656i	$0.106933\pi$
$983$	39.9359	+	39.9359i	1.27376	+	1.27376i	0.329656	+	0.944101i	$0.393067\pi$
$984$	−43.5346	+	28.3585i	−1.38783	+	0.904037i
$985$		0			0
$986$	−32.4622	−	8.26144i	−1.03381	−	0.263098i
$987$	−11.3835	+	6.81701i	−0.362341	+	0.216988i
$988$	−36.1216	+	10.6609i	−1.14918	+	0.339168i
$989$			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	$0.363509\pi$
$992$	7.94496	+	3.94245i	0.252253	+	0.125173i
$993$	−9.47134	−	15.8159i	−0.300564	−	0.501902i
$994$	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	−0.994808	−	0.101774i	$-0.967548\pi$
$997$	−28.1978	+	28.1978i	−0.893034	+	0.893034i	0.101774	+	0.994808i	$0.467548\pi$
$998$	30.2060	−	17.9505i	0.956153	−	0.568212i
$999$	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.557.6	yes	64
3.2	odd	2	inner	600.2.w.k.557.28	yes	64
5.2	odd	4	inner	600.2.w.k.293.12	yes	64
5.3	odd	4	inner	600.2.w.k.293.21	yes	64
5.4	even	2	inner	600.2.w.k.557.27	yes	64
8.5	even	2	inner	600.2.w.k.557.11	yes	64
15.2	even	4	inner	600.2.w.k.293.22	yes	64
15.8	even	4	inner	600.2.w.k.293.11	yes	64
15.14	odd	2	inner	600.2.w.k.557.5	yes	64
24.5	odd	2	inner	600.2.w.k.557.21	yes	64
40.13	odd	4	inner	600.2.w.k.293.28	yes	64
40.29	even	2	inner	600.2.w.k.557.22	yes	64
40.37	odd	4	inner	600.2.w.k.293.5	✓	64
120.29	odd	2	inner	600.2.w.k.557.12	yes	64
120.53	even	4	inner	600.2.w.k.293.6	yes	64
120.77	even	4	inner	600.2.w.k.293.27	yes	64

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

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

Properties

Related objects

Downloads

Learn more