LMFDB - Embedded newform 600.2.w.k.293.22

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			293.22
Character	$\chi$	$=$	600.293
Dual form			600.2.w.k.557.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.722477 + 1.21574i) q^{2} +(1.48597 + 0.889875i) q^{3} +(-0.956054 + 1.75669i) q^{4} +(-0.00827553 + 2.44948i) q^{6} +(2.09015 - 2.09015i) q^{7} +(-2.82641 + 0.106854i) q^{8} +(1.41624 + 2.64467i) q^{9} +O(q^{10})$	\(q+(0.722477 + 1.21574i) q^{2} +(1.48597 + 0.889875i) q^{3} +(-0.956054 + 1.75669i) q^{4} +(-0.00827553 + 2.44948i) q^{6} +(2.09015 - 2.09015i) q^{7} +(-2.82641 + 0.106854i) q^{8} +(1.41624 + 2.64467i) q^{9} +2.65514 q^{11} +(-2.98391 + 1.75963i) 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} +(-2.19203 + 3.63250i) q^{18} -3.15804 q^{19} +(4.96588 - 1.24594i) q^{21} +(1.91827 + 3.22796i) q^{22} +(1.60962 - 1.60962i) q^{23} +(-4.29506 - 2.35637i) q^{24} +(-8.17226 - 2.07979i) q^{26} +(-0.248921 + 5.19019i) q^{27} +(1.67345 + 5.67003i) q^{28} -4.35078i q^{29} +1.56789 q^{31} +(2.51449 - 5.06728i) q^{32} +(3.94546 + 2.36274i) q^{33} +(-1.89884 + 7.46125i) q^{34} +(-5.99986 - 0.0405414i) q^{36} +(-4.94127 - 4.94127i) q^{37} +(-2.28161 - 3.83936i) q^{38} +(-10.0175 + 2.51338i) q^{39} -10.6056i q^{41} +(5.10247 + 5.13706i) 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} +(-0.238347 - 6.92410i) q^{48} -1.73743i q^{49} +(2.29471 + 9.14594i) q^{51} +(-3.37579 - 11.4380i) q^{52} +(4.64119 + 4.64119i) q^{53} +(-6.48976 + 3.44717i) q^{54} +(-5.68427 + 6.13095i) q^{56} +(-4.69277 - 2.81027i) q^{57} +(5.28942 - 3.14334i) q^{58} -9.93175i q^{59} -11.9159i q^{61} +(1.13277 + 1.90615i) q^{62} +(8.48790 + 2.56758i) q^{63} +(7.97716 - 0.604028i) q^{64} +(-0.0219726 + 6.50369i) q^{66} +(8.80906 + 8.80906i) q^{67} +(-10.4428 + 3.08208i) q^{68} +(3.82422 - 0.959493i) q^{69} +2.89837i q^{71} +(-4.28548 - 7.32357i) 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} +(-10.2930 - 10.3628i) q^{78} -9.02676i q^{79} +(-4.98851 + 7.49098i) q^{81} +(12.8936 - 7.66227i) q^{82} +(9.78801 + 9.78801i) q^{83} +(-2.55892 + 9.91469i) q^{84} +(-0.426003 - 0.108415i) q^{86} +(3.87165 - 6.46515i) q^{87} +(-7.50450 + 0.283713i) q^{88} -2.83249 q^{89} +17.6257i q^{91} +(1.28872 + 4.36649i) q^{92} +(2.32985 + 1.39523i) q^{93} +(0.903936 - 3.55190i) q^{94} +(8.24572 - 5.29227i) q^{96} +(-9.26375 + 9.26375i) q^{97} +(2.11227 - 1.25525i) q^{98} +(3.76032 + 7.02194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 12 q^{6}+O(q^{10}) $ 64 * q + 12 * q^6	$ 64 q + 12 q^{6} - 40 q^{16} + 32 q^{31} - 84 q^{36} - 128 q^{46} - 180 q^{66} + 168 q^{76} + 48 q^{81} + 228 q^{96}+O(q^{100}) $ 64 * q + 12 * q^6 - 40 * q^16 + 32 * q^31 - 84 * q^36 - 128 * q^46 - 180 * q^66 + 168 * q^76 + 48 * q^81 + 228 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.722477	+	1.21574i	0.510868	+	0.859659i
$2$	0.722477	+	1.21574i	0.510868	+	0.859659i
$3$	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
$6$	−0.00827553	+	2.44948i	−0.00337847	+	0.999994i
$7$	2.09015	−	2.09015i	0.790001	−	0.790001i	−0.191493	−	0.981494i	$-0.561333\pi$
$7$	2.09015	−	2.09015i	0.790001	−	0.790001i	0.981494	+	0.191493i	$0.0613328\pi$
$8$	−2.82641	+	0.106854i	−0.999286	+	0.0377787i
$9$	1.41624	+	2.64467i	0.472081	+	0.881555i
$10$		0			0
$11$	2.65514			0.800553			0.400277	−	0.916394i	$-0.368914\pi$
$11$	2.65514			0.800553			0.400277	+	0.916394i	$0.368914\pi$
$12$	−2.98391	+	1.75963i	−0.861380	+	0.507961i
$13$	−4.21638	+	4.21638i	−1.16941	+	1.16941i	−0.187065	+	0.982347i	$0.559898\pi$
$13$	−4.21638	+	4.21638i	−1.16941	+	1.16941i	−0.982347	+	0.187065i	$0.940102\pi$
$14$	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	$-0.0204753\pi$
$17$	3.84954	+	3.84954i	0.933651	+	0.933651i	−0.0642808	+	0.997932i	$0.520475\pi$
$18$	−2.19203	+	3.63250i	−0.516665	+	0.856187i
$19$	−3.15804			−0.724505			−0.362252	−	0.932080i	$-0.617992\pi$
$19$	−3.15804			−0.724505			−0.362252	+	0.932080i	$0.617992\pi$
$20$		0			0
$21$	4.96588	−	1.24594i	1.08364	−	0.271885i
$22$	1.91827	+	3.22796i	0.408977	+	0.688203i
$23$	1.60962	−	1.60962i	0.335629	−	0.335629i	−0.519090	−	0.854719i	$-0.673729\pi$
$23$	1.60962	−	1.60962i	0.335629	−	0.335629i	0.854719	+	0.519090i	$0.173729\pi$
$24$	−4.29506	−	2.35637i	−0.876725	−	0.480992i
$25$		0			0
$26$	−8.17226	−	2.07979i	−1.60271	−	0.407880i
$27$	−0.248921	+	5.19019i	−0.0479048	+	0.998852i
$28$	1.67345	+	5.67003i	0.316252	+	1.07154i
$29$		−	4.35078i		−	0.807919i	−0.914777	−	0.403959i	$-0.867634\pi$
$29$		−	4.35078i		−	0.807919i	0.914777	−	0.403959i	$-0.132366\pi$
$30$		0			0
$31$	1.56789			0.281602			0.140801	−	0.990038i	$-0.455032\pi$
$31$	1.56789			0.281602			0.140801	+	0.990038i	$0.455032\pi$
$32$	2.51449	−	5.06728i	0.444503	−	0.895777i
$33$	3.94546	+	2.36274i	0.686817	+	0.411300i
$34$	−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	0.172645	−	0.984984i	$-0.444769\pi$
$37$	−4.94127	−	4.94127i	−0.812339	−	0.812339i	−0.984984	+	0.172645i	$0.944769\pi$
$38$	−2.28161	−	3.83936i	−0.370127	−	0.622827i
$39$	−10.0175	+	2.51338i	−1.60408	+	0.402463i
$40$		0			0
$41$		−	10.6056i		−	1.65631i	−0.560500	−	0.828154i	$-0.689391\pi$
$41$		−	10.6056i		−	1.65631i	0.560500	−	0.828154i	$-0.310609\pi$
$42$	5.10247	+	5.13706i	0.787328	+	0.792666i
$43$	−0.219791	+	0.219791i	−0.0335178	+	0.0335178i	−0.723667	−	0.690149i	$-0.757545\pi$
$43$	−0.219791	+	0.219791i	−0.0335178	+	0.0335178i	0.690149	+	0.723667i	$0.257545\pi$
$44$	−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	$-0.310529\pi$
$47$	−1.83256	−	1.83256i	−0.267306	−	0.267306i	−0.828014	+	0.560708i	$0.810529\pi$
$48$	−0.238347	−	6.92410i	−0.0344024	−	0.999408i
$49$		−	1.73743i		−	0.248204i
$50$		0			0
$51$	2.29471	+	9.14594i	0.321324	+	1.28069i
$52$	−3.37579	−	11.4380i	−0.468137	−	1.58616i
$53$	4.64119	+	4.64119i	0.637516	+	0.637516i	0.949942	−	0.312426i	$-0.101142\pi$
$53$	4.64119	+	4.64119i	0.637516	+	0.637516i	−0.312426	+	0.949942i	$0.601142\pi$
$54$	−6.48976	+	3.44717i	−0.883145	+	0.469100i
$55$		0			0
$56$	−5.68427	+	6.13095i	−0.759592	+	0.819283i
$57$	−4.69277	−	2.81027i	−0.621573	−	0.372229i
$58$	5.28942	−	3.14334i	0.694535	−	0.412740i
$59$		−	9.93175i		−	1.29300i	−0.762912	−	0.646502i	$-0.776231\pi$
$59$		−	9.93175i		−	1.29300i	0.762912	−	0.646502i	$-0.223769\pi$
$60$		0			0
$61$		−	11.9159i		−	1.52568i	−0.646590	−	0.762838i	$-0.723805\pi$
$61$		−	11.9159i		−	1.52568i	0.646590	−	0.762838i	$-0.276195\pi$
$62$	1.13277	+	1.90615i	0.143862	+	0.242082i
$63$	8.48790	+	2.56758i	1.06937	+	0.323485i
$64$	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	0.996847	+	0.0793517i	$0.0252850\pi$
$67$	8.80906	+	8.80906i	1.07620	+	1.07620i	0.0793517	+	0.996847i	$0.474715\pi$
$68$	−10.4428	+	3.08208i	−1.26638	+	0.373758i
$69$	3.82422	−	0.959493i	0.460381	−	0.115509i
$70$		0			0
$71$			2.89837i			0.343973i	0.985099	+	0.171986i	$0.0550185\pi$
$71$			2.89837i			0.343973i	−0.985099	+	0.171986i	$0.944982\pi$
$72$	−4.28548	−	7.32357i	−0.505048	−	0.863091i
$73$	−2.29779	−	2.29779i	−0.268936	−	0.268936i	0.559736	−	0.828671i	$-0.310903\pi$
$73$	−2.29779	−	2.29779i	−0.268936	−	0.268936i	−0.828671	+	0.559736i	$0.810903\pi$
$74$	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
$78$	−10.2930	−	10.3628i	−1.16546	−	1.17336i
$79$		−	9.02676i		−	1.01559i	−0.861478	−	0.507795i	$-0.830461\pi$
$79$		−	9.02676i		−	1.01559i	0.861478	−	0.507795i	$-0.169539\pi$
$80$		0			0
$81$	−4.98851	+	7.49098i	−0.554279	+	0.832331i
$82$	12.8936	−	7.66227i	1.42386	−	0.846156i
$83$	9.78801	+	9.78801i	1.07437	+	1.07437i	0.997002	+	0.0773719i	$0.0246529\pi$
$83$	9.78801	+	9.78801i	1.07437	+	1.07437i	0.0773719	+	0.997002i	$0.475347\pi$
$84$	−2.55892	+	9.91469i	−0.279201	+	1.08178i
$85$		0			0
$86$	−0.426003	−	0.108415i	−0.0459371	−	0.0116907i
$87$	3.87165	−	6.46515i	0.415084	−	0.693136i
$88$	−7.50450	+	0.283713i	−0.799982	+	0.0302439i
$89$	−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
$92$	1.28872	+	4.36649i	0.134358	+	0.455238i
$93$	2.32985	+	1.39523i	0.241594	+	0.144679i
$94$	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	$-0.981611\pi$
$97$	−9.26375	+	9.26375i	−0.940592	+	0.940592i	0.0577400	+	0.998332i	$0.481611\pi$
$98$	2.11227	−	1.25525i	0.213371	−	0.126800i
$99$	3.76032	+	7.02194i	0.377926	+	0.705732i
$100$		0			0
$101$	10.6797			1.06267			0.531337	−	0.847160i	$-0.321690\pi$
$101$	10.6797			1.06267			0.531337	+	0.847160i	$0.321690\pi$
$102$	−9.46122	+	9.39750i	−0.936800	+	0.930491i
$103$	−10.3368	−	10.3368i	−1.01851	−	1.01851i	−0.999825	−	0.0186893i	$-0.994051\pi$
$103$	−10.3368	−	10.3368i	−1.01851	−	1.01851i	−0.0186893	−	0.999825i	$-0.505949\pi$
$104$	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	$-0.826296\pi$
$107$	−3.47289	+	3.47289i	−0.335737	+	0.335737i	0.519023	+	0.854760i	$0.326296\pi$
$108$	−8.87957	−	5.39937i	−0.854437	−	0.519555i
$109$	2.67954			0.256654			0.128327	−	0.991732i	$-0.459039\pi$
$109$	2.67954			0.256654			0.128327	+	0.991732i	$0.459039\pi$
$110$		0			0
$111$	−2.94549	−	11.7397i	−0.279573	−	1.11428i
$112$	−11.5604	−	2.48113i	−1.09236	−	0.234445i
$113$	6.11636	−	6.11636i	0.575379	−	0.575379i	−0.358248	−	0.933627i	$-0.616626\pi$
$113$	6.11636	−	6.11636i	0.575379	−	0.575379i	0.933627	+	0.358248i	$0.116626\pi$
$114$	0.0261345	−	7.73555i	0.00244772	−	0.724501i
$115$		0			0
$116$	7.64297	+	4.15958i	0.709632	+	0.386207i
$117$	−17.1223	−	5.17949i	−1.58296	−	0.478844i
$118$	12.0744	−	7.17546i	1.11154	−	0.660555i
$119$	16.0922			1.47517
$120$		0			0
$121$	−3.95026			−0.359114
$122$	14.4867	−	8.60897i	1.31156	−	0.779420i
$123$	9.43762	−	15.7596i	0.850962	−	1.42099i
$124$	−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	$-0.998758\pi$
$127$	−11.2254	+	11.2254i	−0.996089	+	0.996089i	0.00390306	+	0.999992i	$0.498758\pi$
$128$	6.49766	+	9.26177i	0.574317	+	0.818633i
$129$	−0.522191	+	0.131017i	−0.0459763	+	0.0115354i
$130$		0			0
$131$	−6.55577			−0.572780			−0.286390	−	0.958113i	$-0.592455\pi$
$131$	−6.55577			−0.572780			−0.286390	+	0.958113i	$0.592455\pi$
$132$	−7.92268	+	4.67205i	−0.689581	+	0.406650i
$133$	−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	$-0.281521\pi$
$137$	−1.63651	−	1.63651i	−0.139817	−	0.139817i	−0.773551	+	0.633734i	$0.781521\pi$
$138$	3.92940	+	3.95604i	0.334493	+	0.336761i
$139$	1.03173			0.0875104			0.0437552	−	0.999042i	$-0.486068\pi$
$139$	1.03173			0.0875104			0.0437552	+	0.999042i	$0.486068\pi$
$140$		0			0
$141$	−1.09239	−	4.35389i	−0.0919956	−	0.366663i
$142$	−3.52366	+	2.09400i	−0.295699	+	0.175725i
$143$	−11.1951	+	11.1951i	−0.936177	+	0.936177i
$144$	5.80741	−	10.5011i	0.483951	−	0.875095i
$145$		0			0
$146$	1.13342	−	4.45361i	0.0938022	−	0.368583i
$147$	1.54610	−	2.58178i	0.127520	−	0.212942i
$148$	13.4044	−	3.95616i	1.10183	−	0.325194i
$149$			3.60278i			0.295151i	0.989051	+	0.147576i	$0.0471470\pi$
$149$			3.60278i			0.295151i	−0.989051	+	0.147576i	$0.952853\pi$
$150$		0			0
$151$	13.6985			1.11476			0.557382	−	0.830256i	$-0.311806\pi$
$151$	13.6985			1.11476			0.557382	+	0.830256i	$0.311806\pi$
$152$	8.92592	−	0.337451i	0.723988	−	0.0273709i
$153$	−4.72886	+	15.6326i	−0.382306	+	1.26382i
$154$	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	0.354851	−	0.934923i	$-0.384532\pi$
$157$	−7.26828	−	7.26828i	−0.580072	−	0.580072i	−0.934923	+	0.354851i	$0.884532\pi$
$158$	10.9742	−	6.52163i	0.873061	−	0.518833i
$159$	2.76661	+	11.0268i	0.219406	+	0.874479i
$160$		0			0
$161$		−	6.72868i		−	0.530295i
$162$	−12.7112	−	0.652676i	−0.998684	−	0.0512791i
$163$	9.50622	−	9.50622i	0.744585	−	0.744585i	−0.228872	−	0.973457i	$-0.573504\pi$
$163$	9.50622	−	9.50622i	0.744585	−	0.744585i	0.973457	+	0.228872i	$0.0735036\pi$
$164$	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	0.992406	+	0.123005i	$0.0392532\pi$
$167$	14.4143	+	14.4143i	1.11541	+	1.11541i	0.123005	+	0.992406i	$0.460747\pi$
$168$	−13.9025	+	4.05215i	−1.07260	+	0.312630i
$169$		−	22.5557i		−	1.73505i
$170$		0			0
$171$	−4.47256	−	8.35197i	−0.342025	−	0.638691i
$172$	−0.175973	−	0.596237i	−0.0134178	−	0.0454626i
$173$	−18.0907	−	18.0907i	−1.37541	−	1.37541i	−0.852209	−	0.523202i	$-0.824738\pi$
$173$	−18.0907	−	18.0907i	−1.37541	−	1.37541i	−0.523202	−	0.852209i	$-0.675262\pi$
$174$	10.6571	+	0.0360050i	0.807914	+	0.00272953i
$175$		0			0
$176$	−5.76675	−	8.91855i	−0.434685	−	0.672261i
$177$	8.83802	−	14.7583i	0.664307	−	1.10930i
$178$	−2.04641	−	3.44357i	−0.153385	−	0.258107i
$179$			5.81962i			0.434979i	0.976063	+	0.217489i	$0.0697868\pi$
$179$			5.81962i			0.434979i	−0.976063	+	0.217489i	$0.930213\pi$
$180$		0			0
$181$		−	3.58348i		−	0.266358i	−0.991092	−	0.133179i	$-0.957481\pi$
$181$		−	3.58348i		−	0.266358i	0.991092	−	0.133179i	$-0.0425185\pi$
$182$	−21.4283	+	12.7342i	−1.58837	+	0.943919i
$183$	10.6037	−	17.7067i	0.783846	−	1.30892i
$184$	−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
$188$	4.97126	−	1.46721i	0.362567	−	0.107008i
$189$	10.3280	+	11.3685i	0.751250	+	0.826939i
$190$		0			0
$191$			11.6034i			0.839591i	0.907619	+	0.419796i	$0.137898\pi$
$191$			11.6034i			0.839591i	−0.907619	+	0.419796i	$0.862102\pi$
$192$	12.3914	+	6.20111i	0.894271	+	0.447527i
$193$	−9.83073	−	9.83073i	−0.707632	−	0.707632i	0.258405	−	0.966037i	$-0.416803\pi$
$193$	−9.83073	−	9.83073i	−0.707632	−	0.707632i	−0.966037	+	0.258405i	$0.916803\pi$
$194$	−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	$-0.718307\pi$
$197$	1.97306	−	1.97306i	0.140574	−	0.140574i	0.773892	+	0.633318i	$0.218307\pi$
$198$	−5.82012	+	9.64477i	−0.413618	+	0.685424i
$199$			4.09303i			0.290147i	0.989421	+	0.145074i	$0.0463419\pi$
$199$			4.09303i			0.290147i	−0.989421	+	0.145074i	$0.953658\pi$
$200$		0			0
$201$	5.25108	+	20.9290i	0.370383	+	1.47622i
$202$	7.71587	+	12.9838i	0.542887	+	0.913538i
$203$	−9.09376	−	9.09376i	−0.638257	−	0.638257i
$204$	−18.2604	−	4.71291i	−1.27849	−	0.329970i
$205$		0			0
$206$	5.09877	−	20.0350i	0.355248	−	1.39590i
$207$	6.53652	+	1.97729i	0.454319	+	0.137431i
$208$	23.3204	+	5.00509i	1.61698	+	0.347040i
$209$	−8.38503			−0.580005
$210$		0			0
$211$		−	5.39432i		−	0.371361i	−0.982610	−	0.185680i	$-0.940551\pi$
$211$		−	5.39432i		−	0.371361i	0.982610	−	0.185680i	$-0.0594489\pi$
$212$	−12.5903	+	3.71590i	−0.864709	+	0.255209i
$213$	−2.57918	+	4.30690i	−0.176723	+	0.295104i
$214$	−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
$218$	1.93591	+	3.25763i	0.131116	+	0.220635i
$219$	−1.36971	−	5.45920i	−0.0925564	−	0.368898i
$220$		0			0
$221$	−32.4622			−2.18365
$222$	12.1444	−	12.0626i	0.815079	−	0.809590i
$223$	−2.63896	−	2.63896i	−0.176718	−	0.176718i	0.613206	−	0.789923i	$-0.289880\pi$
$223$	−2.63896	−	2.63896i	−0.176718	−	0.176718i	−0.789923	+	0.613206i	$0.789880\pi$
$224$	−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	$-0.664918\pi$
$227$	5.62771	−	5.62771i	0.373524	−	0.373524i	0.868759	+	0.495235i	$0.164918\pi$
$228$	9.42331	−	5.55699i	0.624074	−	0.368020i
$229$	−11.2319			−0.742225			−0.371113	−	0.928588i	$-0.621024\pi$
$229$	−11.2319			−0.742225			−0.371113	+	0.928588i	$0.621024\pi$
$230$		0			0
$231$	13.1851	−	3.30813i	0.867514	−	0.217659i
$232$	0.464899	+	12.2971i	0.0305221	+	0.807342i
$233$	15.0715	−	15.0715i	0.987366	−	0.987366i	−0.0125551	−	0.999921i	$-0.503997\pi$
$233$	15.0715	−	15.0715i	0.987366	−	0.987366i	0.999921	+	0.0125551i	$0.00399652\pi$
$234$	−6.07357	−	24.5584i	−0.397041	−	1.60543i
$235$		0			0
$236$	17.4470	+	9.49529i	1.13570	+	0.618091i
$237$	8.03269	−	13.4135i	0.521780	−	0.871303i
$238$	11.6263	+	19.5640i	0.753618	+	1.26814i
$239$	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	$0.494342\pi$
$242$	−2.85397	−	4.80249i	−0.183460	−	0.308716i
$243$	−14.0788	+	6.69226i	−0.903158	+	0.429308i
$244$	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
$248$	−4.43151	+	0.167536i	−0.281401	+	0.0106386i
$249$	5.83463	+	23.2549i	0.369755	+	1.47372i
$250$		0			0
$251$	−6.29691			−0.397457			−0.198729	−	0.980055i	$-0.563681\pi$
$251$	−6.29691			−0.397457			−0.198729	+	0.980055i	$0.563681\pi$
$252$	−12.6253	+	12.4559i	−0.795321	+	0.784645i
$253$	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	$-0.409939\pi$
$257$	−10.9183	−	10.9183i	−0.681066	−	0.681066i	−0.960240	+	0.279174i	$0.909939\pi$
$258$	−0.536554	−	0.540192i	−0.0334044	−	0.0336309i
$259$	−20.6559			−1.28350
$260$		0			0
$261$	11.5063	−	6.16176i	0.712225	−	0.381403i
$262$	−4.73639	−	7.97012i	−0.292615	−	0.492396i
$263$	−21.0955	+	21.0955i	−1.30081	+	1.30081i	−0.372959	+	0.927848i	$0.621657\pi$
$263$	−21.0955	+	21.0955i	−1.30081	+	1.30081i	−0.927848	+	0.372959i	$0.878343\pi$
$264$	−11.4040	−	6.25648i	−0.701865	−	0.385059i
$265$		0			0
$266$	−12.7937	−	3.25593i	−0.784435	−	0.199634i
$267$	−4.20900	−	2.52056i	−0.257587	−	0.154256i
$268$	−23.8967	+	7.05286i	−1.45973	+	0.430822i
$269$			20.6115i			1.25671i	0.777929	+	0.628353i	$0.216271\pi$
$269$			20.6115i			1.25671i	−0.777929	+	0.628353i	$0.783729\pi$
$270$		0			0
$271$	−24.2931			−1.47570			−0.737851	−	0.674964i	$-0.764159\pi$
$271$	−24.2931			−1.47570			−0.737851	+	0.674964i	$0.764159\pi$
$272$	4.56963	−	21.2914i	0.277075	−	1.29098i
$273$	−15.6847	+	26.1913i	−0.949280	+	1.58517i
$274$	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	0.976324	−	0.216312i	$-0.0694027\pi$
$277$	12.6491	+	12.6491i	0.760013	+	0.760013i	−0.216312	+	0.976324i	$0.569403\pi$
$278$	0.745403	+	1.25432i	0.0447063	+	0.0752291i
$279$	2.22052	+	4.14656i	0.132939	+	0.248248i
$280$		0			0
$281$			8.81745i			0.526005i	0.964795	+	0.263002i	$0.0847127\pi$
$281$			8.81745i			0.526005i	−0.964795	+	0.263002i	$0.915287\pi$
$282$	4.50397	−	4.47364i	0.268208	−	0.266402i
$283$	−13.4928	+	13.4928i	−0.802061	+	0.802061i	−0.983417	−	0.181357i	$-0.941951\pi$
$283$	−13.4928	+	13.4928i	−0.802061	+	0.802061i	0.181357	+	0.983417i	$0.441951\pi$
$284$	−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
$288$	16.9624	−	0.526525i	0.999519	−	0.0310258i
$289$			12.6379i			0.743409i
$290$		0			0
$291$	−22.0093	+	5.52212i	−1.29021	+	0.323712i
$292$	6.23331	−	1.83969i	0.364777	−	0.107660i
$293$	6.84294	+	6.84294i	0.399769	+	0.399769i	0.878151	−	0.478383i	$-0.158777\pi$
$293$	6.84294	+	6.84294i	0.399769	+	0.399769i	−0.478383	+	0.878151i	$0.658777\pi$
$294$	4.25579	+	0.0143782i	0.248203	+	0.000838551i
$295$		0			0
$296$	14.4940	+	13.4380i	0.842448	+	0.781070i
$297$	−0.660918	+	13.7806i	−0.0383503	+	0.799634i
$298$	−4.38005	+	2.60293i	−0.253730	+	0.150784i
$299$			13.5735i			0.784977i
$300$		0			0
$301$			0.918791i			0.0529583i
$302$	9.89682	+	16.6538i	0.569498	+	0.958317i
$303$	15.8698	+	9.50365i	0.911698	+	0.545970i
$304$	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	0.538888	−	0.842378i	$-0.318845\pi$
$307$	−5.31757	−	5.31757i	−0.303490	−	0.303490i	−0.842378	+	0.538888i	$0.818845\pi$
$308$	4.44323	+	15.0547i	0.253177	+	0.857822i
$309$	−6.16176	−	24.5587i	−0.350530	−	1.39709i
$310$		0			0
$311$			31.3649i			1.77854i	0.457382	+	0.889270i	$0.348787\pi$
$311$			31.3649i			1.77854i	−0.457382	+	0.889270i	$0.651213\pi$
$312$	28.0449	−	8.17425i	1.58773	−	0.462776i
$313$	5.42321	+	5.42321i	0.306538	+	0.306538i	0.843565	−	0.537027i	$-0.180453\pi$
$313$	5.42321	+	5.42321i	0.306538	+	0.306538i	−0.537027	+	0.843565i	$0.680453\pi$
$314$	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	$-0.920499\pi$
$317$	−12.8513	+	12.8513i	−0.721799	+	0.721799i	0.247172	+	0.968972i	$0.420499\pi$
$318$	−11.4069	+	11.3301i	−0.639666	+	0.635358i
$319$		−	11.5519i		−	0.646782i
$320$		0			0
$321$	−8.25108	+	2.07019i	−0.460530	+	0.115547i
$322$	8.18034	−	4.86132i	0.455872	−	0.270911i
$323$	−12.1570	−	12.1570i	−0.676435	−	0.676435i
$324$	−8.39005	−	15.9250i	−0.466114	−	0.884725i
$325$		0			0
$326$	18.4251	+	4.68908i	1.02047	+	0.259704i
$327$	3.98173	+	2.38446i	0.220190	+	0.131861i
$328$	1.13325	+	29.9756i	0.0625732	+	1.65513i
$329$	−7.66064			−0.422345
$330$		0			0
$331$		−	10.6434i		−	0.585016i	−0.956263	−	0.292508i	$-0.905510\pi$
$331$		−	10.6434i		−	0.585016i	0.956263	−	0.292508i	$-0.0944899\pi$
$332$	−26.5524	+	7.83664i	−1.45725	+	0.430092i
$333$	6.06996	−	20.0660i	0.332632	−	1.09961i
$334$	−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	$-0.742869\pi$
$337$	0.581584	−	0.581584i	0.0316809	−	0.0316809i	0.722770	+	0.691089i	$0.242869\pi$
$338$	27.4219	−	16.2960i	1.49155	−	0.886383i
$339$	14.5316	−	3.64596i	0.789246	−	0.198021i
$340$		0			0
$341$	4.16297			0.225438
$342$	6.92251	−	11.4716i	0.374327	−	0.620312i
$343$	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	$-0.726908\pi$
$347$	1.90948	−	1.90948i	0.102506	−	0.102506i	0.756500	+	0.653994i	$0.226908\pi$
$348$	7.65575	+	12.9823i	0.410391	+	0.695925i
$349$	−16.3562			−0.875528			−0.437764	−	0.899090i	$-0.644229\pi$
$349$	−16.3562			−0.875528			−0.437764	+	0.899090i	$0.644229\pi$
$350$		0			0
$351$	−20.8342	−	22.9333i	−1.11205	−	1.22409i
$352$	6.67631	−	13.4543i	0.355848	−	0.717118i
$353$	−0.326679	+	0.326679i	−0.0173874	+	0.0173874i	−0.715747	−	0.698360i	$-0.753914\pi$
$353$	−0.326679	+	0.326679i	−0.0173874	+	0.0173874i	0.698360	+	0.715747i	$0.253914\pi$
$354$	24.3276	+	0.0821905i	1.29300	+	0.00436838i
$355$		0			0
$356$	2.70801	−	4.97580i	0.143524	−	0.263717i
$357$	23.9126	+	14.3201i	1.26559	+	0.757898i
$358$	−7.07515	+	4.20454i	−0.373934	+	0.222217i
$359$	−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
$362$	4.35658	−	2.58898i	0.228977	−	0.136074i
$363$	−5.86998	−	3.51524i	−0.308094	−	0.184502i
$364$	−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	$-0.970863\pi$
$367$	−17.3259	+	17.3259i	−0.904406	+	0.904406i	0.0914078	+	0.995814i	$0.470863\pi$
$368$	−8.90265	−	1.91071i	−0.464083	−	0.0996028i
$369$	28.0481	−	15.0200i	1.46013	−	0.781912i
$370$		0			0
$371$	19.4015			1.00728
$372$	−4.67845	+	2.75891i	−0.242566	+	0.143043i
$373$	−4.04391	+	4.04391i	−0.209386	+	0.209386i	−0.804006	−	0.594621i	$-0.797302\pi$
$373$	−4.04391	+	4.04391i	−0.209386	+	0.209386i	0.594621	+	0.804006i	$0.297302\pi$
$374$	−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
$378$	−6.35947	+	20.7696i	−0.327096	+	1.06828i
$379$	9.37395			0.481507			0.240754	−	0.970586i	$-0.422605\pi$
$379$	9.37395			0.481507			0.240754	+	0.970586i	$0.422605\pi$
$380$		0			0
$381$	−26.6698	+	6.69143i	−1.36633	+	0.342812i
$382$	−14.1067	+	8.38318i	−0.721762	+	0.428921i
$383$	−1.94014	+	1.94014i	−0.0991364	+	0.0991364i	−0.754935	−	0.655799i	$-0.772332\pi$
$383$	−1.94014	+	1.94014i	−0.0991364	+	0.0991364i	0.655799	+	0.754935i	$0.272332\pi$
$384$	1.41354	+	19.5449i	0.0721342	+	0.997395i
$385$		0			0
$386$	4.84915	−	19.0541i	0.246815	−	0.969829i
$387$	−0.892551	−	0.269996i	−0.0453709	−	0.0137247i
$388$	−7.41690	−	25.1302i	−0.376536	−	1.27579i
$389$		−	15.7785i		−	0.800003i	−0.916515	−	0.400001i	$-0.869010\pi$
$389$		−	15.7785i		−	0.800003i	0.916515	−	0.400001i	$-0.130990\pi$
$390$		0			0
$391$	12.3926			0.626721
$392$	0.185652	+	4.91069i	0.00937684	+	0.248027i
$393$	−9.74171	−	5.83382i	−0.491404	−	0.294277i
$394$	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	0.985061	−	0.172204i	$-0.0550887\pi$
$397$	16.1961	+	16.1961i	0.812858	+	0.812858i	−0.172204	+	0.985061i	$0.555089\pi$
$398$	−4.97607	+	2.95712i	−0.249428	+	0.148227i
$399$	−15.6825	+	3.93472i	−0.785105	+	0.196982i
$400$		0			0
$401$		−	33.9532i		−	1.69554i	−0.530362	−	0.847771i	$-0.677944\pi$
$401$		−	33.9532i		−	1.69554i	0.530362	−	0.847771i	$-0.322056\pi$
$402$	−21.6505	+	21.5047i	−1.07983	+	1.07256i
$403$	−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
$408$	−7.46307	−	25.6049i	−0.369477	−	1.26763i
$409$			11.9177i			0.589294i	0.955606	+	0.294647i	$0.0952021\pi$
$409$			11.9177i			0.589294i	−0.955606	+	0.294647i	$0.904798\pi$
$410$		0			0
$411$	−0.975525	−	3.88811i	−0.0481191	−	0.191786i
$412$	28.0411	−	8.27602i	1.38148	−	0.407730i
$413$	−20.7588	−	20.7588i	−1.02148	−	1.02148i
$414$	2.31861	+	9.37526i	0.113953	+	0.460769i
$415$		0			0
$416$	10.7635	+	31.9676i	0.527726	+	1.56734i
$417$	1.53313	+	0.918113i	0.0750776	+	0.0449602i
$418$	−6.05799	−	10.1940i	−0.296306	−	0.498606i
$419$		−	0.494053i		−	0.0241361i	−0.999927	−	0.0120680i	$-0.996159\pi$
$419$		−	0.494053i		−	0.0241361i	0.999927	−	0.0120680i	$-0.00384147\pi$
$420$		0			0
$421$			28.0844i			1.36875i	0.729129	+	0.684376i	$0.239925\pi$
$421$			28.0844i			1.36875i	−0.729129	+	0.684376i	$0.760075\pi$
$422$	6.55810	−	3.89727i	0.319243	−	0.189716i
$423$	2.25116	−	7.44186i	0.109455	−	0.361835i
$424$	−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
$428$	−2.78053	−	9.42108i	−0.134402	−	0.455385i
$429$	−26.5978	+	6.67337i	−1.28415	+	0.322193i
$430$		0			0
$431$			8.20673i			0.395304i	0.980272	+	0.197652i	$0.0633316\pi$
$431$			8.20673i			0.395304i	−0.980272	+	0.197652i	$0.936668\pi$
$432$	17.9744	−	10.4366i	0.864793	−	0.502129i
$433$	8.09993	+	8.09993i	0.389258	+	0.389258i	0.874423	−	0.485165i	$-0.161240\pi$
$433$	8.09993	+	8.09993i	0.389258	+	0.389258i	−0.485165	+	0.874423i	$0.661240\pi$
$434$	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
$438$	5.64739	−	5.60936i	0.269843	−	0.268025i
$439$			5.21928i			0.249103i	0.992213	+	0.124551i	$0.0397491\pi$
$439$			5.21928i			0.249103i	−0.992213	+	0.124551i	$0.960251\pi$
$440$		0			0
$441$	4.59492	−	2.46062i	0.218806	−	0.117173i
$442$	−23.4532	−	39.4657i	−1.11556	−	1.87719i
$443$	21.7308	+	21.7308i	1.03246	+	1.03246i	0.999455	+	0.0330087i	$0.0105089\pi$
$443$	21.7308	+	21.7308i	1.03246	+	1.03246i	0.0330087	+	0.999455i	$0.489491\pi$
$444$	23.4391	+	6.04949i	1.11237	+	0.287096i
$445$		0			0
$446$	1.30170	−	5.11487i	0.0616374	−	0.242196i
$447$	−3.20603	+	5.35364i	−0.151640	+	0.253219i
$448$	15.4109	−	17.9360i	0.728099	−	0.847394i
$449$	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
$452$	4.89698	+	16.5921i	0.230335	+	0.780428i
$453$	20.3556	+	12.1899i	0.956388	+	0.572732i
$454$	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	$-0.713666\pi$
$457$	3.44344	−	3.44344i	0.161077	−	0.161077i	0.783044	+	0.621967i	$0.213666\pi$
$458$	−8.11480	−	13.6551i	−0.379180	−	0.638061i
$459$	−20.9381	+	19.0216i	−0.977305	+	0.887853i
$460$		0			0
$461$	−0.294401			−0.0137116			−0.00685580	−	0.999976i	$-0.502182\pi$
$461$	−0.294401			−0.0137116			−0.00685580	+	0.999976i	$0.502182\pi$
$462$	13.5477	+	13.6396i	0.630298	+	0.634571i
$463$	−9.79796	−	9.79796i	−0.455350	−	0.455350i	0.441776	−	0.897126i	$-0.354349\pi$
$463$	−9.79796	−	9.79796i	−0.455350	−	0.455350i	−0.897126	+	0.441776i	$0.854349\pi$
$464$	−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	$-0.961650\pi$
$467$	−18.8562	+	18.8562i	−0.872561	+	0.872561i	0.120190	+	0.992751i	$0.461650\pi$
$468$	25.4686	−	25.1268i	1.17729	−	1.16148i
$469$	36.8245			1.70040
$470$		0			0
$471$	−4.33262	−	17.2684i	−0.199637	−	0.795684i
$472$	1.06125	+	28.0712i	0.0488480	+	1.29208i
$473$	−0.583575	+	0.583575i	−0.0268328	+	0.0268328i
$474$	22.1108	+	0.0747012i	1.01558	+	0.00343114i
$475$		0			0
$476$	−15.3850	+	28.2690i	−0.705172	+	1.29571i
$477$	−5.70133	+	18.8474i	−0.261046	+	0.862964i
$478$	2.09400	+	3.52366i	0.0957774	+	0.161169i
$479$	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
$482$	0.398735	+	0.670968i	0.0181619	+	0.0305617i
$483$	5.98769	−	9.99866i	0.272449	−	0.454955i
$484$	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	$-0.623731\pi$
$487$	12.0580	−	12.0580i	0.546399	−	0.546399i	0.925397	+	0.378998i	$0.123731\pi$
$488$	1.27327	+	33.6792i	0.0576381	+	1.52459i
$489$	22.5854	−	5.66666i	1.02135	−	0.256255i
$490$		0			0
$491$	18.1797			0.820439			0.410219	−	0.911987i	$-0.365452\pi$
$491$	18.1797			0.820439			0.410219	+	0.911987i	$0.365452\pi$
$492$	18.6618	+	31.6460i	0.841341	+	1.42671i
$493$	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
$498$	−24.0565	+	23.8945i	−1.07800	+	1.07074i
$499$	24.8457			1.11225			0.556124	−	0.831100i	$-0.312288\pi$
$499$	24.8457			1.11225			0.556124	+	0.831100i	$0.312288\pi$
$500$		0			0
$501$	8.59235	+	34.2462i	0.383878	+	1.53001i
$502$	−4.54937	−	7.65541i	−0.203048	−	0.341678i
$503$	17.0078	−	17.0078i	0.758340	−	0.758340i	−0.217680	−	0.976020i	$-0.569849\pi$
$503$	17.0078	−	17.0078i	0.758340	−	0.758340i	0.976020	+	0.217680i	$0.0698490\pi$
$504$	−24.2646	−	6.35007i	−1.08083	−	0.282855i
$505$		0			0
$506$	8.28347	+	2.10809i	0.368245	+	0.0937161i
$507$	20.0717	−	33.5172i	0.891418	−	1.48855i
$508$	−8.98743	−	30.4515i	−0.398753	−	1.35107i
$509$			26.1925i			1.16096i	0.814274	+	0.580481i	$0.197135\pi$
$509$			26.1925i			1.16096i	−0.814274	+	0.580481i	$0.802865\pi$
$510$		0			0
$511$	−9.60542			−0.424919
$512$	−22.4822	+	2.55962i	−0.993581	+	0.113120i
$513$	0.786102	−	16.3908i	0.0347073	−	0.723673i
$514$	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
$518$	−14.9234	−	25.1123i	−0.655699	−	1.10337i
$519$	−10.7839	−	42.9808i	−0.473359	−	1.88665i
$520$		0			0
$521$		−	21.5789i		−	0.945388i	−0.881227	−	0.472694i	$-0.843282\pi$
$521$		−	21.5789i		−	0.945388i	0.881227	−	0.472694i	$-0.156718\pi$
$522$	15.8042	+	9.53701i	0.691730	+	0.417424i
$523$	1.75051	−	1.75051i	0.0765445	−	0.0765445i	−0.667798	−	0.744343i	$-0.732763\pi$
$523$	1.75051	−	1.75051i	0.0765445	−	0.0765445i	0.744343	+	0.667798i	$0.232763\pi$
$524$	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
$528$	−0.632844	−	18.3844i	−0.0275410	−	0.800079i
$529$			17.8182i			0.774707i
$530$		0			0
$531$	26.2662	−	14.0658i	1.13985	−	0.610403i
$532$	−5.28482	−	17.9062i	−0.229126	−	0.776333i
$533$	44.7170	+	44.7170i	1.93691	+	1.93691i
$534$	0.0234403	−	6.93811i	0.00101436	−	0.300241i
$535$		0			0
$536$	−25.8393	−	23.9567i	−1.11609	−	1.03477i
$537$	−5.17874	+	8.64781i	−0.223479	+	0.373181i
$538$	−25.0583	+	14.8913i	−1.08034	+	0.642011i
$539$		−	4.61311i		−	0.198701i
$540$		0			0
$541$			22.6515i			0.973864i	0.873440	+	0.486932i	$0.161884\pi$
$541$			22.6515i			0.973864i	−0.873440	+	0.486932i	$0.838116\pi$
$542$	−17.5512	−	29.5341i	−0.753889	−	1.26860i
$543$	3.18885	−	5.32496i	0.136847	−	0.228516i
$544$	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	−0.999273	−	0.0381200i	$-0.987863\pi$
$547$	−24.2626	−	24.2626i	−1.03739	−	1.03739i	−0.0381200	−	0.999273i	$-0.512137\pi$
$548$	4.43944	−	1.31025i	0.189644	−	0.0559712i
$549$	31.5136	−	16.8758i	1.34497	−	0.720243i
$550$		0			0
$551$			13.7399i			0.585341i
$552$	−10.7063	+	3.12055i	−0.455689	+	0.132820i
$553$	−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	$-0.606798\pi$
$557$	14.5141	−	14.5141i	0.614984	−	0.614984i	0.944240	+	0.329257i	$0.106798\pi$
$558$	−3.43686	+	5.69537i	−0.145494	+	0.241104i
$559$		−	1.85344i		−	0.0783923i
$560$		0			0
$561$	6.09277	+	24.2837i	0.257237	+	1.02526i
$562$	−10.7197	+	6.37040i	−0.452185	+	0.268719i
$563$	−4.09672	−	4.09672i	−0.172656	−	0.172656i	0.615489	−	0.788145i	$-0.288958\pi$
$563$	−4.09672	−	4.09672i	−0.172656	−	0.172656i	−0.788145	+	0.615489i	$0.788958\pi$
$564$	8.69281	+	2.24356i	0.366033	+	0.0944710i
$565$		0			0
$566$	−26.1519	−	6.65549i	−1.09925	−	0.279751i
$567$	5.23053	+	26.0840i	0.219662	+	1.09542i
$568$	−0.309703	−	8.19196i	−0.0129948	−	0.343727i
$569$	−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	$-0.235993\pi$
$572$	−8.96317	−	30.3693i	−0.374769	−	1.26980i
$573$	−10.3256	+	17.2423i	−0.431357	+	0.720309i
$574$	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	$-0.797985\pi$
$577$	−5.10163	+	5.10163i	−0.212384	+	0.212384i	0.592896	+	0.805279i	$0.297985\pi$
$578$	−15.3645	+	9.13063i	−0.639078	+	0.379784i
$579$	−5.86010	−	23.3564i	−0.243537	−	0.970657i
$580$		0			0
$581$	40.9168			1.69751
$582$	−22.6147	−	22.7680i	−0.937409	−	0.943764i
$583$	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	$-0.781358\pi$
$587$	−3.37004	+	3.37004i	−0.139097	+	0.139097i	0.634130	+	0.773227i	$0.281358\pi$
$588$	3.05723	+	5.18433i	0.126078	+	0.213798i
$589$	−4.95148			−0.204022
$590$		0			0
$591$	4.68769	−	1.17614i	0.192826	−	0.0483799i
$592$	−5.86557	+	27.3297i	−0.241074	+	1.12324i
$593$	16.9693	−	16.9693i	0.696844	−	0.696844i	−0.266884	−	0.963729i	$-0.585994\pi$
$593$	16.9693	−	16.9693i	0.696844	−	0.696844i	0.963729	+	0.266884i	$0.0859941\pi$
$594$	−17.2312	+	9.15270i	−0.707005	+	0.375540i
$595$		0			0
$596$	−6.32897	−	3.44445i	−0.259245	−	0.141090i
$597$	−3.64229	+	6.08214i	−0.149069	+	0.248926i
$598$	−16.5019	+	9.80656i	−0.674813	+	0.401020i
$599$	−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	$0.498411\pi$
$602$	−1.11701	+	0.663806i	−0.0455260	+	0.0270547i
$603$	−10.8212	+	35.7728i	−0.440675	+	1.45678i
$604$	−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	$-0.713814\pi$
$607$	3.95241	−	3.95241i	0.160423	−	0.160423i	0.782754	+	0.622331i	$0.213814\pi$
$608$	−7.94086	+	16.0027i	−0.322045	+	0.648995i
$609$	−5.42079	−	21.6054i	−0.219661	−	0.875496i
$610$		0			0
$611$	15.4535			0.625183
$612$	−22.9407	−	23.2528i	−0.927321	−	0.939938i
$613$	21.0245	−	21.0245i	0.849172	−	0.849172i	−0.140858	−	0.990030i	$-0.544986\pi$
$613$	21.0245	−	21.0245i	0.849172	−	0.849172i	0.990030	+	0.140858i	$0.0449861\pi$
$614$	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	$-0.429077\pi$
$617$	−18.7366	−	18.7366i	−0.754307	−	0.754307i	−0.975280	+	0.220973i	$0.929077\pi$
$618$	25.4053	−	25.2342i	1.02195	−	1.01507i
$619$	8.66233			0.348169			0.174084	−	0.984731i	$-0.444303\pi$
$619$	8.66233			0.348169			0.174084	+	0.984731i	$0.444303\pi$
$620$		0			0
$621$	7.95356	+	8.75489i	0.319165	+	0.351322i
$622$	−38.1316	+	22.6604i	−1.52894	+	0.908600i
$623$	−5.92031	+	5.92031i	−0.237192	+	0.237192i
$624$	30.1996	+	28.1897i	1.20895	+	1.12849i
$625$		0			0
$626$	−2.67508	+	10.5114i	−0.106918	+	0.420119i
$627$	−12.4599	−	7.46163i	−0.497602	−	0.297989i
$628$	19.7170	−	5.81925i	0.786794	−	0.232214i
$629$		−	38.0432i		−	1.51688i
$630$		0			0
$631$	−1.38183			−0.0550097			−0.0275049	−	0.999622i	$-0.508756\pi$
$631$	−1.38183			−0.0550097			−0.0275049	+	0.999622i	$0.508756\pi$
$632$	0.964549	+	25.5133i	0.0383677	+	1.01487i
$633$	4.80028	−	8.01583i	0.190794	−	0.318601i
$634$	−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
$638$	14.0441	−	8.34598i	0.556012	−	0.330421i
$639$	−7.66521	+	4.10479i	−0.303231	+	0.162383i
$640$		0			0
$641$			32.1844i			1.27121i	0.772015	+	0.635604i	$0.219249\pi$
$641$			32.1844i			1.27121i	−0.772015	+	0.635604i	$0.780751\pi$
$642$	−8.47803	−	8.53551i	−0.334601	−	0.336870i
$643$	−13.8136	+	13.8136i	−0.544755	+	0.544755i	−0.924919	−	0.380164i	$-0.875868\pi$
$643$	−13.8136	+	13.8136i	−0.544755	+	0.544755i	0.380164	+	0.924919i	$0.375868\pi$
$644$	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	$-0.391856\pi$
$647$	−15.5057	−	15.5057i	−0.609594	−	0.609594i	−0.942840	+	0.333246i	$0.891856\pi$
$648$	13.2991	−	21.7056i	0.522439	−	0.852677i
$649$		−	26.3701i		−	1.03512i
$650$		0			0
$651$	7.78597	−	1.95350i	0.305156	−	0.0765635i
$652$	7.61103	+	25.7880i	0.298071	+	1.00993i
$653$	−17.9422	−	17.9422i	−0.702132	−	0.702132i	0.262736	−	0.964868i	$-0.415375\pi$
$653$	−17.9422	−	17.9422i	−0.702132	−	0.702132i	−0.964868	+	0.262736i	$0.915375\pi$
$654$	−0.0221746	+	6.56348i	−0.000867097	+	0.256652i
$655$		0			0
$656$	−35.6238	+	23.0344i	−1.39088	+	0.899343i
$657$	2.82265	−	9.33110i	0.110122	−	0.364041i
$658$	−5.53463	−	9.31335i	−0.215763	−	0.363072i
$659$		−	39.4445i		−	1.53654i	−0.640127	−	0.768269i	$-0.721118\pi$
$659$		−	39.4445i		−	1.53654i	0.640127	−	0.768269i	$-0.278882\pi$
$660$		0			0
$661$		−	7.69555i		−	0.299322i	−0.988737	−	0.149661i	$-0.952182\pi$
$661$		−	7.69555i		−	0.299322i	0.988737	−	0.149661i	$-0.0478183\pi$
$662$	12.9397	−	7.68964i	0.502915	−	0.298866i
$663$	−48.2381	−	28.8874i	−1.87341	−	1.12189i
$664$	−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
$668$	−39.1023	+	11.5406i	−1.51291	+	0.446520i
$669$	−1.57308	−	6.26976i	−0.0608188	−	0.242403i
$670$		0			0
$671$		−	31.6383i		−	1.22138i
$672$	6.17313	−	28.2964i	0.238134	−	1.09156i
$673$	−2.37397	−	2.37397i	−0.0915096	−	0.0915096i	0.659870	−	0.751380i	$-0.270611\pi$
$673$	−2.37397	−	2.37397i	−0.0915096	−	0.0915096i	−0.751380	+	0.659870i	$0.770611\pi$
$674$	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	$-0.807529\pi$
$677$	−6.61424	+	6.61424i	−0.254206	+	0.254206i	0.568487	+	0.822693i	$0.307529\pi$
$678$	14.9313	+	15.0325i	0.573431	+	0.577319i
$679$			38.7252i			1.48614i
$680$		0			0
$681$	13.3706	−	3.35468i	0.512363	−	0.128552i
$682$	3.00765	+	5.06110i	0.115169	+	0.193799i
$683$	14.3187	+	14.3187i	0.547889	+	0.547889i	0.925830	−	0.377941i	$-0.123368\pi$
$683$	14.3187	+	14.3187i	0.547889	+	0.547889i	−0.377941	+	0.925830i	$0.623368\pi$
$684$	18.9478	+	0.128032i	0.724488	+	0.00489541i
$685$		0			0
$686$	−5.42568	+	21.3195i	−0.207154	+	0.813983i
$687$	−16.6903	−	9.99500i	−0.636776	−	0.381333i
$688$	1.21564	+	0.260905i	0.0463460	+	0.00994691i
$689$	−39.1380			−1.49104
$690$		0			0
$691$			36.4559i			1.38685i	0.720529	+	0.693425i	$0.243899\pi$
$691$			36.4559i			1.38685i	−0.720529	+	0.693425i	$0.756101\pi$
$692$	49.0754	−	14.4841i	1.86557	−	0.550602i
$693$	22.5365	+	6.81728i	0.856091	+	0.258967i
$694$	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
$698$	−11.8170	−	19.8849i	−0.447279	−	0.752655i
$699$	35.8076	−	8.98411i	1.35437	−	0.339810i
$700$		0			0
$701$	−48.0342			−1.81423			−0.907113	−	0.420887i	$-0.861719\pi$
$701$	−48.0342			−1.81423			−0.907113	+	0.420887i	$0.861719\pi$
$702$	12.8287	−	41.8979i	0.484189	−	1.58133i
$703$	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
$708$	17.4762	+	29.6354i	0.656796	+	1.11377i
$709$	−6.97929			−0.262113			−0.131056	−	0.991375i	$-0.541837\pi$
$709$	−6.97929			−0.262113			−0.131056	+	0.991375i	$0.541837\pi$
$710$		0			0
$711$	23.8728	−	12.7841i	0.895299	−	0.479441i
$712$	8.00576	−	0.302663i	0.300029	−	0.0113428i
$713$	2.52371	−	2.52371i	0.0945138	−	0.0945138i
$714$	−0.133172	+	39.4175i	−0.00498382	+	1.47516i
$715$		0			0
$716$	−10.2233	−	5.56387i	−0.382062	−	0.207932i
$717$	4.30690	+	2.57918i	0.160844	+	0.0963214i
$718$	−11.6263	−	19.5640i	−0.433888	−	0.730121i
$719$	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
$722$	−6.52163	−	10.9742i	−0.242710	−	0.408418i
$723$	0.820109	+	0.491122i	0.0305002	+	0.0182650i
$724$	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	$-0.796510\pi$
$727$	−5.55176	+	5.55176i	−0.205903	+	0.205903i	0.596620	+	0.802524i	$0.296510\pi$
$728$	−1.88338	−	49.8174i	−0.0698028	−	1.84636i
$729$	−26.8761	−	2.58389i	−0.995410	−	0.0956996i
$730$		0			0
$731$	−1.69219			−0.0625879
$732$	20.9676	+	35.5560i	0.774984	+	1.31419i
$733$	10.2051	−	10.2051i	0.376934	−	0.376934i	−0.493061	−	0.869995i	$-0.664122\pi$
$733$	10.2051	−	10.2051i	0.376934	−	0.376934i	0.869995	+	0.493061i	$0.164122\pi$
$734$	−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
$738$	38.5246	+	23.2476i	1.41811	+	0.855757i
$739$	33.7165			1.24028			0.620141	−	0.784490i	$-0.287075\pi$
$739$	33.7165			1.24028			0.620141	+	0.784490i	$0.287075\pi$
$740$		0			0
$741$	31.6356	−	7.93737i	1.16216	−	0.291586i
$742$	14.0172	+	23.5872i	0.514586	+	0.865914i
$743$	14.9523	−	14.9523i	0.548546	−	0.548546i	−0.377474	−	0.926020i	$-0.623207\pi$
$743$	14.9523	−	14.9523i	0.548546	−	0.548546i	0.926020	+	0.377474i	$0.123207\pi$
$744$	−6.73420	−	3.69454i	−0.246888	−	0.135448i
$745$		0			0
$746$	−7.83798	−	1.99472i	−0.286969	−	0.0730317i
$747$	−12.0238	+	39.7482i	−0.439928	+	1.45431i
$748$	−27.7271	+	8.18335i	−1.01380	+	0.299213i
$749$			14.5177i			0.530466i
$750$		0			0
$751$	29.4194			1.07353			0.536764	−	0.843733i	$-0.319647\pi$
$751$	29.4194			1.07353			0.536764	+	0.843733i	$0.319647\pi$
$752$	−2.17536	+	10.1357i	−0.0793271	+	0.369611i
$753$	−9.35705	−	5.60346i	−0.340990	−	0.204202i
$754$	−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	0.852900	−	0.522075i	$-0.174842\pi$
$757$	9.10219	+	9.10219i	0.330825	+	0.330825i	−0.522075	+	0.852900i	$0.674842\pi$
$758$	6.77246	+	11.3963i	0.245987	+	0.413932i
$759$	10.1538	−	2.54758i	0.368560	−	0.0924715i
$760$		0			0
$761$		−	19.4230i		−	0.704083i	−0.935984	−	0.352042i	$-0.885488\pi$
$761$		−	19.4230i		−	0.704083i	0.935984	−	0.352042i	$-0.114512\pi$
$762$	−27.4033	−	27.5891i	−0.992718	−	0.999449i
$763$	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
$768$	−22.7403	+	15.8392i	−0.820568	+	0.571548i
$769$			1.26203i			0.0455101i	0.999741	+	0.0227551i	$0.00724379\pi$
$769$			1.26203i			0.0455101i	−0.999741	+	0.0227551i	$0.992756\pi$
$770$		0			0
$771$	−6.50841	−	25.9403i	−0.234395	−	0.934217i
$772$	26.6683	−	7.87085i	0.959812	−	0.283278i
$773$	13.6782	+	13.6782i	0.491971	+	0.491971i	0.908927	−	0.416956i	$-0.136903\pi$
$773$	13.6782	+	13.6782i	0.491971	+	0.491971i	−0.416956	+	0.908927i	$0.636903\pi$
$774$	−0.316602	−	1.28018i	−0.0113800	−	0.0460150i
$775$		0			0
$776$	25.1933	−	27.1730i	0.904386	−	0.975455i
$777$	−30.6942	−	18.3812i	−1.10115	−	0.659423i
$778$	19.1826	−	11.3996i	0.687729	−	0.408696i
$779$			33.4928i			1.20000i
$780$		0			0
$781$			7.69555i			0.275368i
$782$	8.95337	+	15.0662i	0.320172	+	0.538766i
$783$	22.5813	+	1.08300i	0.806991	+	0.0387032i
$784$	−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	0.677097	−	0.735894i	$-0.263238\pi$
$787$	−1.64945	−	1.64945i	−0.0587966	−	0.0587966i	−0.735894	+	0.677097i	$0.763238\pi$
$788$	1.57970	+	5.35240i	0.0562745	+	0.190671i
$789$	−50.1199	+	12.5750i	−1.78431	+	0.447683i
$790$		0			0
$791$		−	25.5682i		−	0.909100i
$792$	−11.3785	−	19.4451i	−0.404318	−	0.690951i
$793$	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	$-0.874335\pi$
$797$	−15.2015	+	15.2015i	−0.538466	+	0.538466i	0.384612	+	0.923078i	$0.374335\pi$
$798$	−16.1138	−	16.2231i	−0.570423	−	0.574290i
$799$		−	14.1090i		−	0.499141i
$800$		0			0
$801$	−4.01149	−	7.49098i	−0.141739	−	0.264681i
$802$	41.2783	−	24.5304i	1.45759	−	0.866199i
$803$	−6.10093	−	6.10093i	−0.215297	−	0.215297i
$804$	−41.7861	−	10.7847i	−1.47368	−	0.380349i
$805$		0			0
$806$	−12.8132	−	3.26089i	−0.451327	−	0.114860i
$807$	−18.3417	+	30.6282i	−0.645657	+	1.07816i
$808$	−30.1853	+	1.14118i	−1.06192	+	0.0401465i
$809$	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	$0.862196\pi$
$812$	24.6691	−	7.28080i	0.865714	−	0.255506i
$813$	−36.0990	−	21.6178i	−1.26605	−	0.758171i
$814$	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
$818$	−14.4889	+	8.61029i	−0.506592	+	0.301052i
$819$	−46.6141	+	24.9623i	−1.62883	+	0.872253i
$820$		0			0
$821$	43.1420			1.50567			0.752833	−	0.658212i	$-0.228687\pi$
$821$	43.1420			1.50567			0.752833	+	0.658212i	$0.228687\pi$
$822$	4.02215	−	3.99506i	0.140288	−	0.139344i
$823$	29.4978	+	29.4978i	1.02823	+	1.02823i	0.999590	+	0.0286405i	$0.00911780\pi$
$823$	29.4978	+	29.4978i	1.02823	+	1.02823i	0.0286405	+	0.999590i	$0.490882\pi$
$824$	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	0.146357	−	0.989232i	$-0.453245\pi$
$827$	32.6568	−	32.6568i	1.13559	−	1.13559i	0.989232	−	0.146357i	$-0.0467548\pi$
$828$	−9.72275	+	9.59224i	−0.337889	+	0.333353i
$829$	−19.3767			−0.672980			−0.336490	−	0.941687i	$-0.609240\pi$
$829$	−19.3767			−0.672980			−0.336490	+	0.941687i	$0.609240\pi$
$830$		0			0
$831$	7.54014	+	30.0524i	0.261565	+	1.04251i
$832$	−31.0879	+	36.1815i	−1.07778	+	1.25437i
$833$	6.68831	−	6.68831i	0.231736	−	0.231736i
$834$	−0.00853813	+	2.52720i	−0.000295651	+	0.0875099i
$835$		0			0
$836$	8.01654	−	14.7299i	0.277258	−	0.509444i
$837$	−0.390281	+	8.13766i	−0.0134901	+	0.281279i
$838$	0.600640	−	0.356942i	0.0207488	−	0.0123304i
$839$	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
$842$	−34.1434	+	20.2904i	−1.17666	+	0.699252i
$843$	−7.84643	+	13.1025i	−0.270245	+	0.451274i
$844$	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
$848$	5.50936	−	25.6699i	0.189192	−	0.881510i
$849$	−32.0568	+	8.04302i	−1.10019	+	0.276036i
$850$		0			0
$851$	−15.9071			−0.545289
$852$	−5.10005	−	8.64845i	−0.174725	−	0.296291i
$853$	−20.0303	+	20.0303i	−0.685823	+	0.685823i	−0.961306	−	0.275483i	$-0.911162\pi$
$853$	−20.0303	+	20.0303i	−0.685823	+	0.685823i	0.275483	+	0.961306i	$0.411162\pi$
$854$	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	$-0.450067\pi$
$857$	−24.3417	−	24.3417i	−0.831496	−	0.831496i	−0.987721	+	0.156226i	$0.950067\pi$
$858$	−27.3294	−	27.5147i	−0.933009	−	0.939335i
$859$	−43.4501			−1.48250			−0.741249	−	0.671230i	$-0.765766\pi$
$859$	−43.4501			−1.48250			−0.741249	+	0.671230i	$0.765766\pi$
$860$		0			0
$861$	−13.2138	−	52.6659i	−0.450326	−	1.79485i
$862$	−9.97726	+	5.92917i	−0.339827	+	0.201948i
$863$	−16.6773	+	16.6773i	−0.567701	+	0.567701i	−0.931484	−	0.363783i	$-0.881485\pi$
$863$	−16.6773	+	16.6773i	−0.567701	+	0.567701i	0.363783	+	0.931484i	$0.381485\pi$
$864$	25.6742	+	14.3120i	0.873455	+	0.486905i
$865$		0			0
$866$	−3.99541	+	15.6994i	−0.135769	+	0.533488i
$867$	−11.2462	+	18.7797i	−0.381941	+	0.637791i
$868$	2.62379	+	8.89002i	0.0890572	+	0.301747i
$869$		−	23.9673i		−	0.813034i
$870$		0			0
$871$	−74.2847			−2.51704
$872$	−7.57348	+	0.286321i	−0.256470	+	0.00969604i
$873$	−37.6193	−	11.3798i	−1.27322	−	0.385148i
$874$	−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	0.703557	−	0.710639i	$-0.251594\pi$
$877$	−0.209733	−	0.209733i	−0.00708216	−	0.00708216i	−0.710639	+	0.703557i	$0.751594\pi$
$878$	−6.34529	+	3.77081i	−0.214143	+	0.127259i
$879$	4.07907	+	16.2578i	0.137584	+	0.548362i
$880$		0			0
$881$		−	7.66064i		−	0.258093i	−0.991639	−	0.129047i	$-0.958808\pi$
$881$		−	7.66064i		−	0.258093i	0.991639	−	0.129047i	$-0.0411917\pi$
$882$	6.31121	+	3.80849i	0.212509	+	0.128239i
$883$	7.44439	−	7.44439i	0.250524	−	0.250524i	−0.570662	−	0.821185i	$-0.693313\pi$
$883$	7.44439	−	7.44439i	0.250524	−	0.250524i	0.821185	+	0.570662i	$0.193313\pi$
$884$	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	$-0.127429\pi$
$887$	15.8208	+	15.8208i	0.531211	+	0.531211i	−0.389722	+	0.920933i	$0.627429\pi$
$888$	9.57959	+	32.8665i	0.321470	+	1.10293i
$889$			46.9253i			1.57382i
$890$		0			0
$891$	−13.2452	+	19.8896i	−0.443730	+	0.666325i
$892$	7.15881	−	2.11284i	0.239695	−	0.0707433i
$893$	5.78730	+	5.78730i	0.193665	+	0.193665i
$894$	−8.82493	−	0.0298149i	−0.295150	−	0.000997160i
$895$		0			0
$896$	32.9395	+	5.77740i	1.10043	+	0.193009i
$897$	−12.0787	+	20.1699i	−0.403298	+	0.673454i
$898$	0.442132	+	0.743993i	0.0147541	+	0.0248274i
$899$		−	6.82156i		−	0.227512i
$900$		0			0
$901$			35.7329i			1.19043i
$902$	34.2343	−	20.3444i	1.13988	−	0.677393i
$903$	−0.817610	+	1.36530i	−0.0272084	+	0.0454344i
$904$	−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	0.990861	+	0.134886i	$0.0430668\pi$
$907$	33.9035	+	33.9035i	1.12575	+	1.12575i	0.134886	+	0.990861i	$0.456933\pi$
$908$	4.50575	+	15.2665i	0.149529	+	0.506638i
$909$	15.1251	+	28.2444i	0.501669	+	0.936806i
$910$		0			0
$911$		−	8.75281i		−	0.289994i	−0.989432	−	0.144997i	$-0.953683\pi$
$911$		−	8.75281i		−	0.289994i	0.989432	−	0.144997i	$-0.0463172\pi$
$912$	0.752710	+	21.8666i	0.0249247	+	0.724076i
$913$	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
$918$	−38.2526	−	11.7126i	−1.26253	−	0.386573i
$919$			27.0428i			0.892058i	0.895018	+	0.446029i	$0.147162\pi$
$919$			27.0428i			0.892058i	−0.895018	+	0.446029i	$0.852838\pi$
$920$		0			0
$921$	−3.16980	−	12.6338i	−0.104449	−	0.416297i
$922$	−0.212698	−	0.357915i	−0.00700483	−	0.0117873i
$923$	−12.2206	−	12.2206i	−0.402246	−	0.402246i
$924$	−6.79429	+	26.3248i	−0.223516	+	0.866024i
$925$		0			0
$926$	4.83298	−	18.9906i	0.158822	−	0.624069i
$927$	12.6979	−	41.9768i	0.417055	−	1.37870i
$928$	−22.0466	−	10.9400i	−0.723716	−	0.359122i
$929$	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
$932$	12.0668	+	40.8851i	0.395261	+	1.33924i
$933$	−27.9109	+	46.6075i	−0.913761	+	1.52586i
$934$	−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	−0.271766	+	0.962363i	$0.587608\pi$
$937$	−37.7773	+	37.7773i	−1.23413	+	1.23413i	−0.962363	+	0.271766i	$0.912392\pi$
$938$	26.6048	+	44.7690i	0.868679	+	1.46176i
$939$	3.23277	+	12.8847i	0.105498	+	0.420478i
$940$		0			0
$941$	−53.4869			−1.74362			−0.871812	−	0.489841i	$-0.837055\pi$
$941$	−53.4869			−1.74362			−0.871812	+	0.489841i	$0.837055\pi$
$942$	17.8636	−	17.7433i	0.582029	−	0.578109i
$943$	−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	$-0.934315\pi$
$947$	−23.8152	+	23.8152i	−0.773891	+	0.773891i	0.204893	+	0.978784i	$0.434315\pi$
$948$	15.8838	+	26.9350i	0.515880	+	0.874809i
$949$	19.3767			0.628993
$950$		0			0
$951$	−30.5327	+	7.66064i	−0.990091	+	0.248413i
$952$	−45.4832	+	1.71952i	−1.47412	+	0.0557301i
$953$	−31.8333	+	31.8333i	−1.03118	+	1.03118i	−0.0316832	+	0.999498i	$0.510087\pi$
$953$	−31.8333	+	31.8333i	−1.03118	+	1.03118i	−0.999498	+	0.0316832i	$0.989913\pi$
$954$	−27.0327	+	6.68549i	−0.875215	+	0.216451i
$955$		0			0
$956$	−2.77099	+	5.09153i	−0.0896203	+	0.164672i
$957$	10.2798	−	17.1658i	0.332297	−	0.554893i
$958$	13.7203	+	23.0876i	0.443282	+	0.745928i
$959$	−6.84111			−0.220911
$960$		0			0
$961$	−28.5417			−0.920700
$962$	30.1045	+	50.6581i	0.970609	+	1.63328i
$963$	−14.1031	−	4.26618i	−0.454466	−	0.137476i
$964$	−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	$-0.585148\pi$
$967$	21.7712	−	21.7712i	0.700115	−	0.700115i	0.964435	+	0.264320i	$0.0851476\pi$
$968$	11.1650	−	0.422102i	0.358858	−	0.0135669i
$969$	−7.24679	−	28.8833i	−0.232801	−	0.927864i
$970$		0			0
$971$	−2.19315			−0.0703814			−0.0351907	−	0.999381i	$-0.511204\pi$
$971$	−2.19315			−0.0703814			−0.0351907	+	0.999381i	$0.511204\pi$
$972$	1.70391	−	31.1303i	0.0546528	−	0.998505i
$973$	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	$-0.266297\pi$
$977$	−2.26226	−	2.26226i	−0.0723760	−	0.0723760i	−0.742368	+	0.669992i	$0.766297\pi$
$978$	23.2066	+	23.3639i	0.742065	+	0.747096i
$979$	−7.52063			−0.240361
$980$		0			0
$981$	3.79488	+	7.08649i	0.121161	+	0.226254i
$982$	13.1344	+	22.1018i	0.419136	+	0.705298i
$983$	−39.9359	+	39.9359i	−1.27376	+	1.27376i	−0.329656	+	0.944101i	$0.606933\pi$
$983$	−39.9359	+	39.9359i	−1.27376	+	1.27376i	−0.944101	+	0.329656i	$0.893067\pi$
$984$	−24.9906	+	45.5515i	−0.796671	+	1.45213i
$985$		0			0
$986$	32.4622	+	8.26144i	1.03381	+	0.263098i
$987$	−11.3835	−	6.81701i	−0.362341	−	0.216988i
$988$	10.6609	+	36.1216i	0.339168	+	1.14918i
$989$			0.707560i			0.0224991i
$990$		0			0
$991$	26.1776			0.831560			0.415780	−	0.909465i	$-0.363509\pi$
$991$	26.1776			0.831560			0.415780	+	0.909465i	$0.363509\pi$
$992$	3.94245	−	7.94496i	0.125173	−	0.252253i
$993$	9.47134	−	15.8159i	0.300564	−	0.501902i
$994$	−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	0.101774	−	0.994808i	$-0.467548\pi$
$997$	−28.1978	−	28.1978i	−0.893034	−	0.893034i	−0.994808	+	0.101774i	$0.967548\pi$
$998$	17.9505	+	30.2060i	0.568212	+	0.956153i
$999$	26.8761	−	24.4161i	0.850321	−	0.772492i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.722477 + 1.21574i) q^{2} +(1.48597 + 0.889875i) q^{3} +(-0.956054 + 1.75669i) q^{4} +(-0.00827553 + 2.44948i) q^{6} +(2.09015 - 2.09015i) q^{7} +(-2.82641 + 0.106854i) q^{8} +(1.41624 + 2.64467i) q^{9} +O(q^{10})\)	\(q+(0.722477 + 1.21574i) q^{2} +(1.48597 + 0.889875i) q^{3} +(-0.956054 + 1.75669i) q^{4} +(-0.00827553 + 2.44948i) q^{6} +(2.09015 - 2.09015i) q^{7} +(-2.82641 + 0.106854i) q^{8} +(1.41624 + 2.64467i) q^{9} +2.65514 q^{11} +(-2.98391 + 1.75963i) 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} +(-2.19203 + 3.63250i) q^{18} -3.15804 q^{19} +(4.96588 - 1.24594i) q^{21} +(1.91827 + 3.22796i) q^{22} +(1.60962 - 1.60962i) q^{23} +(-4.29506 - 2.35637i) q^{24} +(-8.17226 - 2.07979i) q^{26} +(-0.248921 + 5.19019i) q^{27} +(1.67345 + 5.67003i) q^{28} -4.35078i q^{29} +1.56789 q^{31} +(2.51449 - 5.06728i) q^{32} +(3.94546 + 2.36274i) q^{33} +(-1.89884 + 7.46125i) q^{34} +(-5.99986 - 0.0405414i) q^{36} +(-4.94127 - 4.94127i) q^{37} +(-2.28161 - 3.83936i) q^{38} +(-10.0175 + 2.51338i) q^{39} -10.6056i q^{41} +(5.10247 + 5.13706i) 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} +(-0.238347 - 6.92410i) q^{48} -1.73743i q^{49} +(2.29471 + 9.14594i) q^{51} +(-3.37579 - 11.4380i) q^{52} +(4.64119 + 4.64119i) q^{53} +(-6.48976 + 3.44717i) q^{54} +(-5.68427 + 6.13095i) q^{56} +(-4.69277 - 2.81027i) q^{57} +(5.28942 - 3.14334i) q^{58} -9.93175i q^{59} -11.9159i q^{61} +(1.13277 + 1.90615i) q^{62} +(8.48790 + 2.56758i) q^{63} +(7.97716 - 0.604028i) q^{64} +(-0.0219726 + 6.50369i) q^{66} +(8.80906 + 8.80906i) q^{67} +(-10.4428 + 3.08208i) q^{68} +(3.82422 - 0.959493i) q^{69} +2.89837i q^{71} +(-4.28548 - 7.32357i) 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} +(-10.2930 - 10.3628i) q^{78} -9.02676i q^{79} +(-4.98851 + 7.49098i) q^{81} +(12.8936 - 7.66227i) q^{82} +(9.78801 + 9.78801i) q^{83} +(-2.55892 + 9.91469i) q^{84} +(-0.426003 - 0.108415i) q^{86} +(3.87165 - 6.46515i) q^{87} +(-7.50450 + 0.283713i) q^{88} -2.83249 q^{89} +17.6257i q^{91} +(1.28872 + 4.36649i) q^{92} +(2.32985 + 1.39523i) q^{93} +(0.903936 - 3.55190i) q^{94} +(8.24572 - 5.29227i) q^{96} +(-9.26375 + 9.26375i) q^{97} +(2.11227 - 1.25525i) q^{98} +(3.76032 + 7.02194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 12 q^{6}+O(q^{10}) \) 64 * q + 12 * q^6	\( 64 q + 12 q^{6} - 40 q^{16} + 32 q^{31} - 84 q^{36} - 128 q^{46} - 180 q^{66} + 168 q^{76} + 48 q^{81} + 228 q^{96}+O(q^{100}) \) 64 * q + 12 * q^6 - 40 * q^16 + 32 * q^31 - 84 * q^36 - 128 * q^46 - 180 * q^66 + 168 * q^76 + 48 * q^81 + 228 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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