LMFDB - Embedded newform 600.2.w.k.557.28

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			557.28
Character	$\chi$	$=$	600.557
Dual form			600.2.w.k.293.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.21574 - 0.722477i) q^{2} +(-0.889875 + 1.48597i) q^{3} +(0.956054 - 1.75669i) q^{4} +(-0.00827553 + 2.44948i) q^{6} +(-2.09015 - 2.09015i) q^{7} +(-0.106854 - 2.82641i) q^{8} +(-1.41624 - 2.64467i) q^{9} +O(q^{10})$	\(q+(1.21574 - 0.722477i) q^{2} +(-0.889875 + 1.48597i) q^{3} +(0.956054 - 1.75669i) q^{4} +(-0.00827553 + 2.44948i) q^{6} +(-2.09015 - 2.09015i) q^{7} +(-0.106854 - 2.82641i) q^{8} +(-1.41624 - 2.64467i) q^{9} +2.65514 q^{11} +(1.75963 + 2.98391i) 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} +(-3.63250 - 2.19203i) q^{18} +3.15804 q^{19} +(4.96588 - 1.24594i) q^{21} +(3.22796 - 1.91827i) q^{22} +(1.60962 + 1.60962i) q^{23} +(4.29506 + 2.35637i) q^{24} +(-8.17226 - 2.07979i) q^{26} +(5.19019 + 0.248921i) q^{27} +(-5.67003 + 1.67345i) q^{28} +4.35078i q^{29} +1.56789 q^{31} +(-5.06728 - 2.51449i) q^{32} +(-2.36274 + 3.94546i) q^{33} +(1.89884 - 7.46125i) q^{34} +(-5.99986 - 0.0405414i) q^{36} +(-4.94127 + 4.94127i) q^{37} +(3.83936 - 2.28161i) q^{38} +(10.0175 - 2.51338i) q^{39} -10.6056i q^{41} +(5.13706 - 5.10247i) 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} +(6.92410 - 0.238347i) q^{48} +1.73743i q^{49} +(2.29471 + 9.14594i) q^{51} +(-11.4380 + 3.37579i) q^{52} +(-4.64119 + 4.64119i) q^{53} +(6.48976 - 3.44717i) q^{54} +(-5.68427 + 6.13095i) q^{56} +(-2.81027 + 4.69277i) q^{57} +(3.14334 + 5.28942i) q^{58} +9.93175i q^{59} -11.9159i q^{61} +(1.90615 - 1.13277i) q^{62} +(-2.56758 + 8.48790i) q^{63} +(-7.97716 + 0.604028i) q^{64} +(-0.0219726 + 6.50369i) q^{66} +(8.80906 - 8.80906i) q^{67} +(-3.08208 - 10.4428i) q^{68} +(-3.82422 + 0.959493i) q^{69} +2.89837i q^{71} +(-7.32357 + 4.28548i) 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} +(10.3628 - 10.2930i) q^{78} +9.02676i q^{79} +(-4.98851 + 7.49098i) q^{81} +(-7.66227 - 12.8936i) q^{82} +(-9.78801 + 9.78801i) q^{83} +(2.55892 - 9.91469i) q^{84} +(-0.426003 - 0.108415i) q^{86} +(-6.46515 - 3.87165i) q^{87} +(-0.283713 - 7.50450i) q^{88} +2.83249 q^{89} +17.6257i q^{91} +(4.36649 - 1.28872i) q^{92} +(-1.39523 + 2.32985i) q^{93} +(-0.903936 + 3.55190i) q^{94} +(8.24572 - 5.29227i) 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
$3$	−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
$6$	−0.00827553	+	2.44948i	−0.00337847	+	0.999994i
$7$	−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	$-0.368914\pi$
$11$	2.65514			0.800553			0.400277	+	0.916394i	$0.368914\pi$
$12$	1.75963	+	2.98391i	0.507961	+	0.861380i
$13$	−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	−0.0642808	−	0.997932i	$-0.520475\pi$
$17$	3.84954	−	3.84954i	0.933651	−	0.933651i	0.997932	+	0.0642808i	$0.0204753\pi$
$18$	−3.63250	−	2.19203i	−0.856187	−	0.516665i
$19$	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	0.854719	−	0.519090i	$-0.173729\pi$
$23$	1.60962	+	1.60962i	0.335629	+	0.335629i	−0.519090	+	0.854719i	$0.673729\pi$
$24$	4.29506	+	2.35637i	0.876725	+	0.480992i
$25$		0			0
$26$	−8.17226	−	2.07979i	−1.60271	−	0.407880i
$27$	5.19019	+	0.248921i	0.998852	+	0.0479048i
$28$	−5.67003	+	1.67345i	−1.07154	+	0.316252i
$29$			4.35078i			0.807919i	0.914777	+	0.403959i	$0.132366\pi$
$29$			4.35078i			0.807919i	−0.914777	+	0.403959i	$0.867634\pi$
$30$		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
$33$	−2.36274	+	3.94546i	−0.411300	+	0.686817i
$34$	1.89884	−	7.46125i	0.325649	−	1.27959i
$35$		0			0
$36$	−5.99986	−	0.0405414i	−0.999977	−	0.00675690i
$37$	−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	$-0.689391\pi$
$41$		−	10.6056i		−	1.65631i	0.560500	−	0.828154i	$-0.310609\pi$
$42$	5.13706	−	5.10247i	0.792666	−	0.787328i
$43$	−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	−0.828014	−	0.560708i	$-0.810529\pi$
$47$	−1.83256	+	1.83256i	−0.267306	+	0.267306i	0.560708	+	0.828014i	$0.310529\pi$
$48$	6.92410	−	0.238347i	0.999408	−	0.0344024i
$49$			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	−0.949942	−	0.312426i	$-0.898858\pi$
$53$	−4.64119	+	4.64119i	−0.637516	+	0.637516i	0.312426	+	0.949942i	$0.398858\pi$
$54$	6.48976	−	3.44717i	0.883145	−	0.469100i
$55$		0			0
$56$	−5.68427	+	6.13095i	−0.759592	+	0.819283i
$57$	−2.81027	+	4.69277i	−0.372229	+	0.621573i
$58$	3.14334	+	5.28942i	0.412740	+	0.694535i
$59$			9.93175i			1.29300i	0.762912	+	0.646502i	$0.223769\pi$
$59$			9.93175i			1.29300i	−0.762912	+	0.646502i	$0.776231\pi$
$60$		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
$63$	−2.56758	+	8.48790i	−0.323485	+	1.06937i
$64$	−7.97716	+	0.604028i	−0.997146	+	0.0755035i
$65$		0			0
$66$	−0.0219726	+	6.50369i	−0.00270465	+	0.800549i
$67$	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	$0.0550185\pi$
$71$			2.89837i			0.343973i	−0.985099	+	0.171986i	$0.944982\pi$
$72$	−7.32357	+	4.28548i	−0.863091	+	0.505048i
$73$	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
$78$	10.3628	−	10.2930i	1.17336	−	1.16546i
$79$			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	$0.524653\pi$
$83$	−9.78801	+	9.78801i	−1.07437	+	1.07437i	−0.997002	+	0.0773719i	$0.975347\pi$
$84$	2.55892	−	9.91469i	0.279201	−	1.08178i
$85$		0			0
$86$	−0.426003	−	0.108415i	−0.0459371	−	0.0116907i
$87$	−6.46515	−	3.87165i	−0.693136	−	0.415084i
$88$	−0.283713	−	7.50450i	−0.0302439	−	0.799982i
$89$	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
$92$	4.36649	−	1.28872i	0.455238	−	0.134358i
$93$	−1.39523	+	2.32985i	−0.144679	+	0.241594i
$94$	−0.903936	+	3.55190i	−0.0932339	+	0.366351i
$95$		0			0
$96$	8.24572	−	5.29227i	0.841575	−	0.540140i
$97$	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	$-0.321690\pi$
$101$	10.6797			1.06267			0.531337	+	0.847160i	$0.321690\pi$
$102$	9.39750	+	9.46122i	0.930491	+	0.936800i
$103$	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	0.854760	−	0.519023i	$-0.173704\pi$
$107$	3.47289	+	3.47289i	0.335737	+	0.335737i	−0.519023	+	0.854760i	$0.673704\pi$
$108$	5.39937	−	8.87957i	0.519555	−	0.854437i
$109$	−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	0.933627	−	0.358248i	$-0.116626\pi$
$113$	6.11636	+	6.11636i	0.575379	+	0.575379i	−0.358248	+	0.933627i	$0.616626\pi$
$114$	−0.0261345	+	7.73555i	−0.00244772	+	0.724501i
$115$		0			0
$116$	7.64297	+	4.15958i	0.709632	+	0.386207i
$117$	−5.17949	+	17.1223i	−0.478844	+	1.58296i
$118$	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
$123$	15.7596	+	9.43762i	1.42099	+	0.850962i
$124$	1.49899	−	2.75430i	0.134613	−	0.247344i
$125$		0			0
$126$	3.01079	+	12.1741i	0.268223	+	1.08456i
$127$	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	$-0.592455\pi$
$131$	−6.55577			−0.572780			−0.286390	+	0.958113i	$0.592455\pi$
$132$	4.67205	+	7.92268i	0.406650	+	0.689581i
$133$	−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	$0.281521\pi$
$138$	−3.95604	+	3.92940i	−0.336761	+	0.334493i
$139$	−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
$144$	−5.80741	+	10.5011i	−0.483951	+	0.875095i
$145$		0			0
$146$	1.13342	−	4.45361i	0.0938022	−	0.368583i
$147$	−2.58178	−	1.54610i	−0.212942	−	0.127520i
$148$	3.95616	+	13.4044i	0.325194	+	1.10183i
$149$		−	3.60278i		−	0.295151i	−0.989051	−	0.147576i	$-0.952853\pi$
$149$		−	3.60278i		−	0.295151i	0.989051	−	0.147576i	$-0.0471470\pi$
$150$		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
$153$	−15.6326	−	4.72886i	−1.26382	−	0.382306i
$154$	−10.7564	−	2.73743i	−0.866774	−	0.220588i
$155$		0			0
$156$	5.16202	−	20.0005i	0.413292	−	1.60132i
$157$	−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
$162$	−0.652676	+	12.7112i	−0.0512791	+	0.998684i
$163$	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	$-0.460747\pi$
$167$	14.4143	−	14.4143i	1.11541	−	1.11541i	0.992406	−	0.123005i	$-0.0392532\pi$
$168$	−4.05215	−	13.9025i	−0.312630	−	1.07260i
$169$			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	$-0.324738\pi$
$173$	18.0907	−	18.0907i	1.37541	−	1.37541i	0.852209	−	0.523202i	$-0.175262\pi$
$174$	−10.6571	−	0.0360050i	−0.807914	−	0.00272953i
$175$		0			0
$176$	−5.76675	−	8.91855i	−0.434685	−	0.672261i
$177$	−14.7583	−	8.83802i	−1.10930	−	0.664307i
$178$	3.44357	−	2.04641i	0.258107	−	0.153385i
$179$		−	5.81962i		−	0.434979i	−0.976063	−	0.217489i	$-0.930213\pi$
$179$		−	5.81962i		−	0.434979i	0.976063	−	0.217489i	$-0.0697868\pi$
$180$		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
$183$	17.7067	+	10.6037i	1.30892	+	0.783846i
$184$	4.37745	−	4.72144i	0.322710	−	0.348069i
$185$		0			0
$186$	−0.0129752	+	3.84052i	−0.000951384	+	0.281601i
$187$	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	$0.137898\pi$
$191$			11.6034i			0.839591i	−0.907619	+	0.419796i	$0.862102\pi$
$192$	6.20111	−	12.3914i	0.447527	−	0.894271i
$193$	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	0.633318	−	0.773892i	$-0.281693\pi$
$197$	−1.97306	−	1.97306i	−0.140574	−	0.140574i	−0.773892	+	0.633318i	$0.781693\pi$
$198$	−9.64477	−	5.82012i	−0.685424	−	0.413618i
$199$		−	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
$204$	18.2604	+	4.71291i	1.27849	+	0.329970i
$205$		0			0
$206$	5.09877	−	20.0350i	0.355248	−	1.39590i
$207$	1.97729	−	6.53652i	0.137431	−	0.454319i
$208$	−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
$213$	−4.30690	−	2.57918i	−0.295104	−	0.176723i
$214$	6.73123	+	1.71305i	0.460137	+	0.117102i
$215$		0			0
$216$	0.148957	−	14.6962i	0.0101353	−	0.999949i
$217$	−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
$222$	−12.0626	−	12.1444i	−0.809590	−	0.815079i
$223$	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	0.495235	−	0.868759i	$-0.335082\pi$
$227$	−5.62771	−	5.62771i	−0.373524	−	0.373524i	−0.868759	+	0.495235i	$0.835082\pi$
$228$	5.55699	+	9.42331i	0.368020	+	0.624074i
$229$	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	0.999921	−	0.0125551i	$-0.00399652\pi$
$233$	15.0715	+	15.0715i	0.987366	+	0.987366i	−0.0125551	+	0.999921i	$0.503997\pi$
$234$	6.07357	+	24.5584i	0.397041	+	1.60543i
$235$		0			0
$236$	17.4470	+	9.49529i	1.13570	+	0.618091i
$237$	−13.4135	−	8.03269i	−0.871303	−	0.521780i
$238$	−19.5640	+	11.6263i	−1.26814	+	0.753618i
$239$	−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	$0.494342\pi$
$242$	−4.80249	+	2.85397i	−0.308716	+	0.183460i
$243$	−6.69226	−	14.0788i	−0.429308	−	0.903158i
$244$	−20.9326	−	11.3923i	−1.34007	−	0.729314i
$245$		0			0
$246$	25.9780	+	0.0877665i	1.65630	+	0.00559579i
$247$	−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	$-0.563681\pi$
$251$	−6.29691			−0.397457			−0.198729	+	0.980055i	$0.563681\pi$
$252$	12.4559	+	12.6253i	0.784645	+	0.795321i
$253$	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	$0.409939\pi$
$258$	0.540192	−	0.536554i	0.0336309	−	0.0334044i
$259$	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	$-0.878343\pi$
$263$	−21.0955	−	21.0955i	−1.30081	−	1.30081i	−0.372959	−	0.927848i	$-0.621657\pi$
$264$	11.4040	+	6.25648i	0.701865	+	0.385059i
$265$		0			0
$266$	−12.7937	−	3.25593i	−0.784435	−	0.199634i
$267$	−2.52056	+	4.20900i	−0.154256	+	0.257587i
$268$	−7.05286	−	23.8967i	−0.430822	−	1.45973i
$269$		−	20.6115i		−	1.25671i	−0.777929	−	0.628353i	$-0.783729\pi$
$269$		−	20.6115i		−	1.25671i	0.777929	−	0.628353i	$-0.216271\pi$
$270$		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
$273$	−26.1913	−	15.6847i	−1.58517	−	0.949280i
$274$	−0.807234	+	3.17192i	−0.0487668	+	0.191623i
$275$		0			0
$276$	−1.97062	+	7.63529i	−0.118618	+	0.459590i
$277$	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	$0.0847127\pi$
$281$			8.81745i			0.526005i	−0.964795	+	0.263002i	$0.915287\pi$
$282$	−4.47364	−	4.50397i	−0.266402	−	0.268208i
$283$	−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
$288$	0.526525	+	16.9624i	0.0310258	+	0.999519i
$289$		−	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	−0.878151	−	0.478383i	$-0.841223\pi$
$293$	−6.84294	+	6.84294i	−0.399769	+	0.399769i	0.478383	+	0.878151i	$0.341223\pi$
$294$	−4.25579	−	0.0143782i	−0.248203	−	0.000838551i
$295$		0			0
$296$	14.4940	+	13.4380i	0.842448	+	0.781070i
$297$	13.7806	+	0.660918i	0.799634	+	0.0383503i
$298$	−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
$303$	−9.50365	+	15.8698i	−0.545970	+	0.911698i
$304$	−6.85902	−	10.6078i	−0.393392	−	0.608400i
$305$		0			0
$306$	−22.4217	+	5.54515i	−1.28177	+	0.316995i
$307$	−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	$0.348787\pi$
$311$			31.3649i			1.77854i	−0.457382	+	0.889270i	$0.651213\pi$
$312$	−8.17425	−	28.0449i	−0.462776	−	1.58773i
$313$	−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	0.968972	−	0.247172i	$-0.0795013\pi$
$317$	12.8513	+	12.8513i	0.721799	+	0.721799i	−0.247172	+	0.968972i	$0.579501\pi$
$318$	−11.3301	−	11.4069i	−0.635358	−	0.639666i
$319$			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
$324$	8.39005	+	15.9250i	0.466114	+	0.884725i
$325$		0			0
$326$	18.4251	+	4.68908i	1.02047	+	0.259704i
$327$	2.38446	−	3.98173i	0.131861	−	0.220190i
$328$	−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
$333$	20.0660	+	6.06996i	1.09961	+	0.332632i
$334$	7.11005	−	27.9380i	0.389045	−	1.52870i
$335$		0			0
$336$	−14.9706	−	13.9742i	−0.816712	−	0.762356i
$337$	−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
$342$	−11.4716	−	6.92251i	−0.620312	−	0.374327i
$343$	−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	0.653994	−	0.756500i	$-0.273092\pi$
$347$	−1.90948	−	1.90948i	−0.102506	−	0.102506i	−0.756500	+	0.653994i	$0.773092\pi$
$348$	−12.9823	+	7.65575i	−0.695925	+	0.410391i
$349$	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	0.698360	−	0.715747i	$-0.253914\pi$
$353$	−0.326679	−	0.326679i	−0.0173874	−	0.0173874i	−0.715747	+	0.698360i	$0.753914\pi$
$354$	−24.3276	−	0.0821905i	−1.29300	−	0.00436838i
$355$		0			0
$356$	2.70801	−	4.97580i	0.143524	−	0.263717i
$357$	14.3201	−	23.9126i	0.757898	−	1.26559i
$358$	−4.20454	−	7.07515i	−0.222217	−	0.373934i
$359$	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
$362$	−2.58898	−	4.35658i	−0.136074	−	0.228977i
$363$	3.51524	−	5.86998i	0.184502	−	0.308094i
$364$	30.9629	+	16.8511i	1.62290	+	0.883239i
$365$		0			0
$366$	29.1877	+	0.0986104i	1.52567	+	0.00515445i
$367$	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
$372$	2.75891	+	4.67845i	0.143043	+	0.242566i
$373$	−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
$378$	−20.7696	−	6.35947i	−1.06828	−	0.327096i
$379$	−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	0.655799	−	0.754935i	$-0.272332\pi$
$383$	−1.94014	−	1.94014i	−0.0991364	−	0.0991364i	−0.754935	+	0.655799i	$0.772332\pi$
$384$	−1.41354	−	19.5449i	−0.0721342	−	0.997395i
$385$		0			0
$386$	4.84915	−	19.0541i	0.246815	−	0.969829i
$387$	−0.269996	+	0.892551i	−0.0137247	+	0.0453709i
$388$	25.1302	−	7.41690i	1.27579	−	0.376536i
$389$			15.7785i			0.800003i	0.916515	+	0.400001i	$0.130990\pi$
$389$			15.7785i			0.800003i	−0.916515	+	0.400001i	$0.869010\pi$
$390$		0			0
$391$	12.3926			0.626721
$392$	4.91069	−	0.185652i	0.248027	−	0.00937684i
$393$	5.83382	−	9.74171i	0.294277	−	0.491404i
$394$	−3.82422	−	0.973239i	−0.192661	−	0.0490310i
$395$		0			0
$396$	−15.9304	−	0.107643i	−0.800535	−	0.00540926i
$397$	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	$-0.677944\pi$
$401$		−	33.9532i		−	1.69554i	0.530362	−	0.847771i	$-0.322056\pi$
$402$	21.5047	+	21.6505i	1.07256	+	1.07983i
$403$	−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
$408$	25.6049	−	7.46307i	1.26763	−	0.369477i
$409$		−	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
$414$	−2.31861	−	9.37526i	−0.113953	−	0.460769i
$415$		0			0
$416$	10.7635	+	31.9676i	0.527726	+	1.56734i
$417$	0.918113	−	1.53313i	0.0449602	−	0.0750776i
$418$	10.1940	−	6.05799i	0.498606	−	0.296306i
$419$			0.494053i			0.0241361i	0.999927	+	0.0120680i	$0.00384147\pi$
$419$			0.494053i			0.0241361i	−0.999927	+	0.0120680i	$0.996159\pi$
$420$		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
$423$	7.44186	+	2.25116i	0.361835	+	0.109455i
$424$	13.6138	+	12.6220i	0.661145	+	0.612976i
$425$		0			0
$426$	−7.09948	−	0.0239855i	−0.343971	−	0.00116210i
$427$	−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	$0.0633316\pi$
$431$			8.20673i			0.395304i	−0.980272	+	0.197652i	$0.936668\pi$
$432$	−10.4366	−	17.9744i	−0.502129	−	0.864793i
$433$	−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
$438$	5.60936	+	5.64739i	0.268025	+	0.269843i
$439$		−	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	$0.510509\pi$
$443$	−21.7308	+	21.7308i	−1.03246	+	1.03246i	−0.999455	+	0.0330087i	$0.989491\pi$
$444$	−23.4391	−	6.04949i	−1.11237	−	0.287096i
$445$		0			0
$446$	1.30170	−	5.11487i	0.0616374	−	0.242196i
$447$	5.35364	+	3.20603i	0.253219	+	0.151640i
$448$	17.9360	+	15.4109i	0.847394	+	0.728099i
$449$	−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
$452$	16.5921	−	4.89698i	0.780428	−	0.230335i
$453$	−12.1899	+	20.3556i	−0.572732	+	0.956388i
$454$	−10.9077	−	2.77595i	−0.511925	−	0.130282i
$455$		0			0
$456$	13.5640	+	7.44151i	0.635192	+	0.348481i
$457$	−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	$-0.502182\pi$
$461$	−0.294401			−0.0137116			−0.00685580	+	0.999976i	$0.502182\pi$
$462$	13.6396	−	13.5477i	0.634571	−	0.630298i
$463$	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	0.992751	−	0.120190i	$-0.0383504\pi$
$467$	18.8562	+	18.8562i	0.872561	+	0.872561i	−0.120190	+	0.992751i	$0.538350\pi$
$468$	25.1268	+	25.4686i	1.16148	+	1.17729i
$469$	−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
$474$	−22.1108	−	0.0747012i	−1.01558	−	0.00343114i
$475$		0			0
$476$	−15.3850	+	28.2690i	−0.705172	+	1.29571i
$477$	18.8474	+	5.70133i	0.862964	+	0.261046i
$478$	−3.52366	+	2.09400i	−0.161169	+	0.0957774i
$479$	−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
$482$	0.670968	−	0.398735i	0.0305617	−	0.0181619i
$483$	9.99866	+	5.98769i	0.454955	+	0.272449i
$484$	−3.77666	+	6.93938i	−0.171666	+	0.315426i
$485$		0			0
$486$	−18.3077	−	12.2812i	−0.830454	−	0.557088i
$487$	−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	$-0.365452\pi$
$491$	18.1797			0.820439			0.410219	+	0.911987i	$0.365452\pi$
$492$	31.6460	−	18.6618i	1.42671	−	0.841341i
$493$	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
$498$	−23.8945	−	24.0565i	−1.07074	−	1.07800i
$499$	−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	0.976020	−	0.217680i	$-0.0698490\pi$
$503$	17.0078	+	17.0078i	0.758340	+	0.758340i	−0.217680	+	0.976020i	$0.569849\pi$
$504$	24.2646	+	6.35007i	1.08083	+	0.282855i
$505$		0			0
$506$	8.28347	+	2.10809i	0.368245	+	0.0937161i
$507$	−33.5172	−	20.0717i	−1.48855	−	0.891418i
$508$	30.4515	−	8.98743i	1.35107	−	0.398753i
$509$		−	26.1925i		−	1.16096i	−0.814274	−	0.580481i	$-0.802865\pi$
$509$		−	26.1925i		−	1.16096i	0.814274	−	0.580481i	$-0.197135\pi$
$510$		0			0
$511$	−9.60542			−0.424919
$512$	2.55962	+	22.4822i	0.113120	+	0.993581i
$513$	16.3908	+	0.786102i	0.723673	+	0.0347073i
$514$	−5.38562	+	21.1621i	−0.237549	+	0.933420i
$515$		0			0
$516$	0.269086	−	1.04259i	0.0118458	−	0.0458973i
$517$	−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	$-0.843282\pi$
$521$		−	21.5789i		−	0.945388i	0.881227	−	0.472694i	$-0.156718\pi$
$522$	9.53701	−	15.8042i	0.417424	−	0.691730i
$523$	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
$528$	18.3844	−	0.632844i	0.800079	−	0.0275410i
$529$		−	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
$534$	−0.0234403	+	6.93811i	−0.00101436	+	0.300241i
$535$		0			0
$536$	−25.8393	−	23.9567i	−1.11609	−	1.03477i
$537$	8.64781	+	5.17874i	0.373181	+	0.223479i
$538$	−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
$543$	5.32496	+	3.18885i	0.228516	+	0.136847i
$544$	−29.1863	+	9.82709i	−1.25135	+	0.421333i
$545$		0			0
$546$	−43.1737	−	0.145862i	−1.84766	−	0.00624232i
$547$	−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
$552$	3.12055	+	10.7063i	0.132820	+	0.455689i
$553$	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	0.329257	−	0.944240i	$-0.393202\pi$
$557$	−14.5141	−	14.5141i	−0.614984	−	0.614984i	−0.944240	+	0.329257i	$0.893202\pi$
$558$	−5.69537	−	3.43686i	−0.241104	−	0.145494i
$559$			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	−0.615489	−	0.788145i	$-0.711042\pi$
$563$	4.09672	−	4.09672i	0.172656	−	0.172656i	0.788145	+	0.615489i	$0.211042\pi$
$564$	−8.69281	−	2.24356i	−0.366033	−	0.0944710i
$565$		0			0
$566$	−26.1519	−	6.65549i	−1.09925	−	0.279751i
$567$	26.0840	−	5.23053i	1.09542	−	0.219662i
$568$	8.19196	−	0.309703i	0.343727	−	0.0129948i
$569$	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	$-0.764007\pi$
$571$		−	32.2742i		−	1.35063i	0.737528	−	0.675317i	$-0.235993\pi$
$572$	−30.3693	+	8.96317i	−1.26980	+	0.374769i
$573$	−17.2423	−	10.3256i	−0.720309	−	0.431357i
$574$	−10.9343	+	42.9648i	−0.456388	+	1.79332i
$575$		0			0
$576$	12.8951	+	20.2415i	0.537294	+	0.843395i
$577$	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
$582$	−22.7680	+	22.6147i	−0.943764	+	0.937409i
$583$	−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	0.773227	−	0.634130i	$-0.218642\pi$
$587$	3.37004	+	3.37004i	0.139097	+	0.139097i	−0.634130	+	0.773227i	$0.718642\pi$
$588$	−5.18433	+	3.05723i	−0.213798	+	0.126078i
$589$	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	0.963729	−	0.266884i	$-0.0859941\pi$
$593$	16.9693	+	16.9693i	0.696844	+	0.696844i	−0.266884	+	0.963729i	$0.585994\pi$
$594$	17.2312	−	9.15270i	0.707005	−	0.375540i
$595$		0			0
$596$	−6.32897	−	3.44445i	−0.259245	−	0.141090i
$597$	6.08214	+	3.64229i	0.248926	+	0.149069i
$598$	−9.80656	−	16.5019i	−0.401020	−	0.674813i
$599$	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	$0.498411\pi$
$602$	0.663806	+	1.11701i	0.0270547	+	0.0455260i
$603$	−35.7728	−	10.8212i	−1.45678	−	0.440675i
$604$	13.0965	−	24.0639i	0.532887	−	0.979148i
$605$		0			0
$606$	−0.0883806	+	26.1598i	−0.00359021	+	1.06267i
$607$	−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
$612$	−23.2528	+	22.9407i	−0.939938	+	0.927321i
$613$	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	−0.975280	−	0.220973i	$-0.929077\pi$
$617$	−18.7366	+	18.7366i	−0.754307	+	0.754307i	0.220973	+	0.975280i	$0.429077\pi$
$618$	25.2342	+	25.4053i	1.01507	+	1.02195i
$619$	−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
$624$	−30.1996	−	28.1897i	−1.20895	−	1.12849i
$625$		0			0
$626$	−2.67508	+	10.5114i	−0.106918	+	0.420119i
$627$	−7.46163	+	12.4599i	−0.297989	+	0.497602i
$628$	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
$633$	8.01583	+	4.80028i	0.318601	+	0.190794i
$634$	24.9086	+	6.33907i	0.989246	+	0.251757i
$635$		0			0
$636$	−22.0156	−	5.68210i	−0.872977	−	0.225310i
$637$	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	$0.219249\pi$
$641$			32.1844i			1.27121i	−0.772015	+	0.635604i	$0.780751\pi$
$642$	−8.53551	+	8.47803i	−0.336870	+	0.334601i
$643$	−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	−0.942840	−	0.333246i	$-0.891856\pi$
$647$	−15.5057	+	15.5057i	−0.609594	+	0.609594i	0.333246	+	0.942840i	$0.391856\pi$
$648$	21.7056	+	13.2991i	0.852677	+	0.522439i
$649$			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	−0.262736	−	0.964868i	$-0.584625\pi$
$653$	17.9422	−	17.9422i	0.702132	−	0.702132i	0.964868	+	0.262736i	$0.0846248\pi$
$654$	0.0221746	−	6.56348i	0.000867097	−	0.256652i
$655$		0			0
$656$	−35.6238	+	23.0344i	−1.39088	+	0.899343i
$657$	−9.33110	−	2.82265i	−0.364041	−	0.110122i
$658$	9.31335	−	5.53463i	0.363072	−	0.215763i
$659$			39.4445i			1.53654i	0.640127	+	0.768269i	$0.278882\pi$
$659$			39.4445i			1.53654i	−0.640127	+	0.768269i	$0.721118\pi$
$660$		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
$663$	28.8874	−	48.2381i	1.12189	−	1.87341i
$664$	28.7108	+	26.6190i	1.11420	+	1.03302i
$665$		0			0
$666$	28.7805	−	7.11775i	1.11522	−	0.275807i
$667$	−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
$672$	−28.2964	−	6.17313i	−1.09156	−	0.238134i
$673$	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	0.822693	−	0.568487i	$-0.192471\pi$
$677$	6.61424	+	6.61424i	0.254206	+	0.254206i	−0.568487	+	0.822693i	$0.692471\pi$
$678$	−15.0325	+	14.9313i	−0.577319	+	0.573431i
$679$		−	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	−0.925830	−	0.377941i	$-0.876632\pi$
$683$	−14.3187	+	14.3187i	−0.547889	+	0.547889i	0.377941	+	0.925830i	$0.376632\pi$
$684$	−18.9478	−	0.128032i	−0.724488	−	0.00489541i
$685$		0			0
$686$	−5.42568	+	21.3195i	−0.207154	+	0.813983i
$687$	−9.99500	+	16.6903i	−0.381333	+	0.636776i
$688$	−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
$693$	−6.81728	+	22.5365i	−0.258967	+	0.856091i
$694$	−3.70098	−	0.941876i	−0.140487	−	0.0357531i
$695$		0			0
$696$	−10.2520	+	18.6868i	−0.388602	+	0.708323i
$697$	−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	$-0.861719\pi$
$701$	−48.0342			−1.81423			−0.907113	+	0.420887i	$0.861719\pi$
$702$	−41.8979	−	12.8287i	−1.58133	−	0.484189i
$703$	−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
$708$	−29.6354	+	17.4762i	−1.11377	+	0.656796i
$709$	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
$714$	0.133172	−	39.4175i	0.00498382	−	1.47516i
$715$		0			0
$716$	−10.2233	−	5.56387i	−0.382062	−	0.207932i
$717$	2.57918	−	4.30690i	0.0963214	−	0.160844i
$718$	19.5640	−	11.6263i	0.730121	−	0.433888i
$719$	−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
$722$	−10.9742	+	6.52163i	−0.408418	+	0.242710i
$723$	−0.491122	+	0.820109i	−0.0182650	+	0.0305002i
$724$	−6.29506	−	3.42600i	−0.233954	−	0.127326i
$725$		0			0
$726$	0.0326905	−	9.67606i	0.00121326	−	0.359112i
$727$	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
$732$	35.5560	−	20.9676i	1.31419	−	0.774984i
$733$	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
$738$	−23.2476	+	38.5246i	−0.855757	+	1.41811i
$739$	−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	0.926020	−	0.377474i	$-0.123207\pi$
$743$	14.9523	+	14.9523i	0.548546	+	0.548546i	−0.377474	+	0.926020i	$0.623207\pi$
$744$	6.73420	+	3.69454i	0.246888	+	0.135448i
$745$		0			0
$746$	−7.83798	−	1.99472i	−0.286969	−	0.0730317i
$747$	39.7482	+	12.0238i	1.45431	+	0.439928i
$748$	−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
$753$	5.60346	−	9.35705i	0.204202	−	0.340990i
$754$	9.04869	−	35.5557i	0.329534	−	1.29486i
$755$		0			0
$756$	−29.8451	+	7.27412i	−1.08546	+	0.264557i
$757$	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	$-0.885488\pi$
$761$		−	19.4230i		−	0.704083i	0.935984	−	0.352042i	$-0.114512\pi$
$762$	−27.5891	+	27.4033i	−0.999449	+	0.992718i
$763$	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
$768$	−15.8392	−	22.7403i	−0.571548	−	0.820568i
$769$		−	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	−0.908927	−	0.416956i	$-0.863097\pi$
$773$	−13.6782	+	13.6782i	−0.491971	+	0.491971i	0.416956	+	0.908927i	$0.363097\pi$
$774$	0.316602	+	1.28018i	0.0113800	+	0.0460150i
$775$		0			0
$776$	25.1933	−	27.1730i	0.904386	−	0.975455i
$777$	−18.3812	+	30.6942i	−0.659423	+	1.10115i
$778$	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
$783$	−1.08300	+	22.5813i	−0.0387032	+	0.806991i
$784$	5.83600	−	3.77356i	0.208428	−	0.134770i
$785$		0			0
$786$	0.0542525	−	16.0582i	0.00193512	−	0.572777i
$787$	−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
$792$	−19.4451	+	11.3785i	−0.690951	+	0.404318i
$793$	−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	0.923078	−	0.384612i	$-0.125665\pi$
$797$	15.2015	+	15.2015i	0.538466	+	0.538466i	−0.384612	+	0.923078i	$0.625665\pi$
$798$	16.2231	−	16.1138i	0.574290	−	0.570423i
$799$			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
$804$	41.7861	+	10.7847i	1.47368	+	0.380349i
$805$		0			0
$806$	−12.8132	−	3.26089i	−0.451327	−	0.114860i
$807$	30.6282	+	18.3417i	1.07816	+	0.645657i
$808$	−1.14118	−	30.1853i	−0.0401465	−	1.06192i
$809$	−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	$0.137804\pi$
$811$			23.8947i			0.839055i	−0.907743	+	0.419528i	$0.862196\pi$
$812$	−7.28080	−	24.6691i	−0.255506	−	0.865714i
$813$	21.6178	−	36.0990i	0.758171	−	1.26605i
$814$	−6.47149	+	25.4289i	−0.226826	+	0.891282i
$815$		0			0
$816$	25.7371	−	27.5721i	0.900979	−	0.965218i
$817$	−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	$-0.228687\pi$
$821$	43.1420			1.50567			0.752833	+	0.658212i	$0.228687\pi$
$822$	−3.99506	−	4.02215i	−0.139344	−	0.140288i
$823$	−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	$-0.953245\pi$
$827$	−32.6568	−	32.6568i	−1.13559	−	1.13559i	−0.146357	−	0.989232i	$-0.546755\pi$
$828$	−9.59224	−	9.72275i	−0.333353	−	0.337889i
$829$	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
$834$	0.00853813	−	2.52720i	0.000295651	−	0.0875099i
$835$		0			0
$836$	8.01654	−	14.7299i	0.277258	−	0.509444i
$837$	8.13766	+	0.390281i	0.281279	+	0.0134901i
$838$	0.356942	+	0.600640i	0.0123304	+	0.0207488i
$839$	−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
$842$	20.2904	+	34.1434i	0.699252	+	1.17666i
$843$	−13.1025	−	7.84643i	−0.451274	−	0.270245i
$844$	−9.47616	−	5.15726i	−0.326183	−	0.177520i
$845$		0			0
$846$	10.6738	−	2.63975i	0.366972	−	0.0907564i
$847$	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
$852$	−8.64845	+	5.10005i	−0.296291	+	0.174725i
$853$	−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	−0.987721	−	0.156226i	$-0.950067\pi$
$857$	−24.3417	+	24.3417i	−0.831496	+	0.831496i	0.156226	+	0.987721i	$0.450067\pi$
$858$	27.5147	−	27.3294i	0.939335	−	0.933009i
$859$	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	0.363783	−	0.931484i	$-0.381485\pi$
$863$	−16.6773	−	16.6773i	−0.567701	−	0.567701i	−0.931484	+	0.363783i	$0.881485\pi$
$864$	−25.6742	−	14.3120i	−0.873455	−	0.486905i
$865$		0			0
$866$	−3.99541	+	15.6994i	−0.135769	+	0.533488i
$867$	18.7797	+	11.2462i	0.637791	+	0.381941i
$868$	−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
$873$	11.3798	−	37.6193i	0.385148	−	1.27322i
$874$	9.85245	+	2.50738i	0.333264	+	0.0848136i
$875$		0			0
$876$	10.8996	+	2.81313i	0.368264	+	0.0950469i
$877$	−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	$-0.958808\pi$
$881$		−	7.66064i		−	0.258093i	0.991639	−	0.129047i	$-0.0411917\pi$
$882$	3.80849	−	6.31121i	0.128239	−	0.212509i
$883$	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	−0.389722	−	0.920933i	$-0.627429\pi$
$887$	15.8208	−	15.8208i	0.531211	−	0.531211i	0.920933	+	0.389722i	$0.127429\pi$
$888$	−32.8665	+	9.57959i	−1.10293	+	0.321470i
$889$		−	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
$894$	8.82493	+	0.0298149i	0.295150	+	0.000997160i
$895$		0			0
$896$	32.9395	+	5.77740i	1.10043	+	0.193009i
$897$	20.1699	+	12.0787i	0.673454	+	0.403298i
$898$	−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
$903$	−1.36530	−	0.817610i	−0.0454344	−	0.0272084i
$904$	16.6338	−	17.9409i	0.553231	−	0.596705i
$905$		0			0
$906$	−0.113362	+	33.5540i	−0.00376620	+	1.11476i
$907$	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	$-0.953683\pi$
$911$		−	8.75281i		−	0.289994i	0.989432	−	0.144997i	$-0.0463172\pi$
$912$	21.8666	−	0.752710i	0.724076	−	0.0249247i
$913$	−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
$918$	11.7126	−	38.2526i	0.386573	−	1.26253i
$919$		−	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
$924$	6.79429	−	26.3248i	0.223516	−	0.866024i
$925$		0			0
$926$	4.83298	−	18.9906i	0.158822	−	0.624069i
$927$	−41.9768	−	12.6979i	−1.37870	−	0.417055i
$928$	10.9400	−	22.0466i	0.359122	−	0.723716i
$929$	−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
$932$	40.8851	−	12.0668i	1.33924	−	0.395261i
$933$	−46.6075	−	27.9109i	−1.52586	−	0.913761i
$934$	36.5474	+	9.30109i	1.19587	+	0.304341i
$935$		0			0
$936$	48.9481	+	12.8098i	1.59992	+	0.418700i
$937$	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	$-0.837055\pi$
$941$	−53.4869			−1.74362			−0.871812	+	0.489841i	$0.837055\pi$
$942$	−17.7433	−	17.8636i	−0.578109	−	0.582029i
$943$	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	0.978784	−	0.204893i	$-0.0656846\pi$
$947$	23.8152	+	23.8152i	0.773891	+	0.773891i	−0.204893	+	0.978784i	$0.565685\pi$
$948$	−26.9350	+	15.8838i	−0.874809	+	0.515880i
$949$	−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	$-0.989913\pi$
$953$	−31.8333	−	31.8333i	−1.03118	−	1.03118i	−0.0316832	−	0.999498i	$-0.510087\pi$
$954$	27.0327	−	6.68549i	0.875215	−	0.216451i
$955$		0			0
$956$	−2.77099	+	5.09153i	−0.0896203	+	0.164672i
$957$	−17.1658	−	10.2798i	−0.554893	−	0.332297i
$958$	−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
$963$	4.26618	−	14.1031i	0.137476	−	0.454466i
$964$	0.527646	−	0.969517i	0.0169943	−	0.0312260i
$965$		0			0
$966$	16.4817	+	0.0556834i	0.530292	+	0.00179158i
$967$	−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	$-0.511204\pi$
$971$	−2.19315			−0.0703814			−0.0351907	+	0.999381i	$0.511204\pi$
$972$	−31.1303	−	1.70391i	−0.998505	−	0.0546528i
$973$	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	$0.266297\pi$
$978$	−23.3639	+	23.2066i	−0.747096	+	0.742065i
$979$	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	$-0.893067\pi$
$983$	−39.9359	−	39.9359i	−1.27376	−	1.27376i	−0.329656	−	0.944101i	$-0.606933\pi$
$984$	24.9906	−	45.5515i	0.796671	−	1.45213i
$985$		0			0
$986$	32.4622	+	8.26144i	1.03381	+	0.263098i
$987$	−6.81701	+	11.3835i	−0.216988	+	0.362341i
$988$	−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
$993$	15.8159	+	9.47134i	0.501902	+	0.300564i
$994$	2.98820	−	11.7417i	0.0947799	−	0.372426i
$995$		0			0
$996$	−46.4298	−	11.9833i	−1.47118	−	0.379704i
$997$	−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.557.28	yes	64
3.2	odd	2	inner	600.2.w.k.557.6	yes	64
5.2	odd	4	inner	600.2.w.k.293.22	yes	64
5.3	odd	4	inner	600.2.w.k.293.11	yes	64
5.4	even	2	inner	600.2.w.k.557.5	yes	64
8.5	even	2	inner	600.2.w.k.557.21	yes	64
15.2	even	4	inner	600.2.w.k.293.12	yes	64
15.8	even	4	inner	600.2.w.k.293.21	yes	64
15.14	odd	2	inner	600.2.w.k.557.27	yes	64
24.5	odd	2	inner	600.2.w.k.557.11	yes	64
40.13	odd	4	inner	600.2.w.k.293.6	yes	64
40.29	even	2	inner	600.2.w.k.557.12	yes	64
40.37	odd	4	inner	600.2.w.k.293.27	yes	64
120.29	odd	2	inner	600.2.w.k.557.22	yes	64
120.53	even	4	inner	600.2.w.k.293.28	yes	64
120.77	even	4	inner	600.2.w.k.293.5	✓	64

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

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)

\(f(q)\)	\(=\)	\(q+(1.21574 - 0.722477i) q^{2} +(-0.889875 + 1.48597i) q^{3} +(0.956054 - 1.75669i) q^{4} +(-0.00827553 + 2.44948i) q^{6} +(-2.09015 - 2.09015i) q^{7} +(-0.106854 - 2.82641i) q^{8} +(-1.41624 - 2.64467i) q^{9} +O(q^{10})\)	\(q+(1.21574 - 0.722477i) q^{2} +(-0.889875 + 1.48597i) q^{3} +(0.956054 - 1.75669i) q^{4} +(-0.00827553 + 2.44948i) q^{6} +(-2.09015 - 2.09015i) q^{7} +(-0.106854 - 2.82641i) q^{8} +(-1.41624 - 2.64467i) q^{9} +2.65514 q^{11} +(1.75963 + 2.98391i) 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} +(-3.63250 - 2.19203i) q^{18} +3.15804 q^{19} +(4.96588 - 1.24594i) q^{21} +(3.22796 - 1.91827i) q^{22} +(1.60962 + 1.60962i) q^{23} +(4.29506 + 2.35637i) q^{24} +(-8.17226 - 2.07979i) q^{26} +(5.19019 + 0.248921i) q^{27} +(-5.67003 + 1.67345i) q^{28} +4.35078i q^{29} +1.56789 q^{31} +(-5.06728 - 2.51449i) q^{32} +(-2.36274 + 3.94546i) q^{33} +(1.89884 - 7.46125i) q^{34} +(-5.99986 - 0.0405414i) q^{36} +(-4.94127 + 4.94127i) q^{37} +(3.83936 - 2.28161i) q^{38} +(10.0175 - 2.51338i) q^{39} -10.6056i q^{41} +(5.13706 - 5.10247i) 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} +(6.92410 - 0.238347i) q^{48} +1.73743i q^{49} +(2.29471 + 9.14594i) q^{51} +(-11.4380 + 3.37579i) q^{52} +(-4.64119 + 4.64119i) q^{53} +(6.48976 - 3.44717i) q^{54} +(-5.68427 + 6.13095i) q^{56} +(-2.81027 + 4.69277i) q^{57} +(3.14334 + 5.28942i) q^{58} +9.93175i q^{59} -11.9159i q^{61} +(1.90615 - 1.13277i) q^{62} +(-2.56758 + 8.48790i) q^{63} +(-7.97716 + 0.604028i) q^{64} +(-0.0219726 + 6.50369i) q^{66} +(8.80906 - 8.80906i) q^{67} +(-3.08208 - 10.4428i) q^{68} +(-3.82422 + 0.959493i) q^{69} +2.89837i q^{71} +(-7.32357 + 4.28548i) 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} +(10.3628 - 10.2930i) q^{78} +9.02676i q^{79} +(-4.98851 + 7.49098i) q^{81} +(-7.66227 - 12.8936i) q^{82} +(-9.78801 + 9.78801i) q^{83} +(2.55892 - 9.91469i) q^{84} +(-0.426003 - 0.108415i) q^{86} +(-6.46515 - 3.87165i) q^{87} +(-0.283713 - 7.50450i) q^{88} +2.83249 q^{89} +17.6257i q^{91} +(4.36649 - 1.28872i) q^{92} +(-1.39523 + 2.32985i) q^{93} +(-0.903936 + 3.55190i) q^{94} +(8.24572 - 5.29227i) 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

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