LMFDB - Embedded newform 600.2.w.k.293.11

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			293.11
Character	$\chi$	$=$	600.293
Dual form			600.2.w.k.557.11

$q$-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	−0.981494	−	0.191493i	$-0.938667\pi$
$7$	−2.09015	+	2.09015i	−0.790001	+	0.790001i	0.191493	+	0.981494i	$0.438667\pi$
$8$	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	$-0.440102\pi$
$13$	4.21638	−	4.21638i	1.16941	−	1.16941i	0.982347	−	0.187065i	$-0.0598976\pi$
$14$	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	$-0.479525\pi$
$17$	−3.84954	−	3.84954i	−0.933651	−	0.933651i	−0.997932	+	0.0642808i	$0.979525\pi$
$18$	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	−0.854719	−	0.519090i	$-0.826271\pi$
$23$	−1.60962	+	1.60962i	−0.335629	+	0.335629i	0.519090	+	0.854719i	$0.326271\pi$
$24$	−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	0.984984	−	0.172645i	$-0.0552313\pi$
$37$	4.94127	+	4.94127i	0.812339	+	0.812339i	−0.172645	+	0.984984i	$0.555231\pi$
$38$	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	−0.690149	−	0.723667i	$-0.742455\pi$
$43$	0.219791	−	0.219791i	0.0335178	−	0.0335178i	0.723667	+	0.690149i	$0.242455\pi$
$44$	−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	$-0.189471\pi$
$47$	1.83256	+	1.83256i	0.267306	+	0.267306i	−0.560708	+	0.828014i	$0.689471\pi$
$48$	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	0.312426	−	0.949942i	$-0.398858\pi$
$53$	−4.64119	−	4.64119i	−0.637516	−	0.637516i	−0.949942	+	0.312426i	$0.898858\pi$
$54$	−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	$-0.974715\pi$
$67$	−8.80906	−	8.80906i	−1.07620	−	1.07620i	−0.0793517	−	0.996847i	$-0.525285\pi$
$68$	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	0.828671	−	0.559736i	$-0.189097\pi$
$73$	2.29779	+	2.29779i	0.268936	+	0.268936i	−0.559736	+	0.828671i	$0.689097\pi$
$74$	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	$-0.975347\pi$
$83$	−9.78801	−	9.78801i	−1.07437	−	1.07437i	−0.0773719	−	0.997002i	$-0.524653\pi$
$84$	−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	−0.0577400	−	0.998332i	$-0.518389\pi$
$97$	9.26375	−	9.26375i	0.940592	−	0.940592i	0.998332	+	0.0577400i	$0.0183894\pi$
$98$	−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	$0.00594934\pi$
$103$	10.3368	+	10.3368i	1.01851	+	1.01851i	0.0186893	+	0.999825i	$0.494051\pi$
$104$	11.4667	−	12.3677i	1.12440	−	1.21276i
$105$		0			0
$106$	−2.28933	+	8.99563i	−0.222359	+	0.873733i
$107$	3.47289	−	3.47289i	0.335737	−	0.335737i	−0.519023	−	0.854760i	$-0.673704\pi$
$107$	3.47289	−	3.47289i	0.335737	−	0.335737i	0.854760	+	0.519023i	$0.173704\pi$
$108$	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	−0.933627	−	0.358248i	$-0.883374\pi$
$113$	−6.11636	+	6.11636i	−0.575379	+	0.575379i	0.358248	+	0.933627i	$0.383374\pi$
$114$	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	−0.00390306	−	0.999992i	$-0.501242\pi$
$127$	11.2254	−	11.2254i	0.996089	−	0.996089i	0.999992	+	0.00390306i	$0.00124239\pi$
$128$	−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	0.773551	−	0.633734i	$-0.218479\pi$
$137$	1.63651	+	1.63651i	0.139817	+	0.139817i	−0.633734	+	0.773551i	$0.718479\pi$
$138$	−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	0.934923	−	0.354851i	$-0.115468\pi$
$157$	7.26828	+	7.26828i	0.580072	+	0.580072i	−0.354851	+	0.934923i	$0.615468\pi$
$158$	−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	−0.973457	−	0.228872i	$-0.926496\pi$
$163$	−9.50622	+	9.50622i	−0.744585	+	0.744585i	0.228872	+	0.973457i	$0.426496\pi$
$164$	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	$-0.960747\pi$
$167$	−14.4143	−	14.4143i	−1.11541	−	1.11541i	−0.123005	−	0.992406i	$-0.539253\pi$
$168$	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	$0.175262\pi$
$173$	18.0907	+	18.0907i	1.37541	+	1.37541i	0.523202	+	0.852209i	$0.324738\pi$
$174$	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	0.966037	−	0.258405i	$-0.0831969\pi$
$193$	9.83073	+	9.83073i	0.707632	+	0.707632i	−0.258405	+	0.966037i	$0.583197\pi$
$194$	−17.9552	−	4.56948i	−1.28911	−	0.328069i
$195$		0			0
$196$	3.05213	+	1.66108i	0.218009	+	0.118648i
$197$	−1.97306	+	1.97306i	−0.140574	+	0.140574i	−0.773892	−	0.633318i	$-0.781693\pi$
$197$	−1.97306	+	1.97306i	−0.140574	+	0.140574i	0.633318	+	0.773892i	$0.281693\pi$
$198$	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	0.789923	−	0.613206i	$-0.210120\pi$
$223$	2.63896	+	2.63896i	0.176718	+	0.176718i	−0.613206	+	0.789923i	$0.710120\pi$
$224$	−5.33572	−	15.8470i	−0.356507	−	1.05882i
$225$		0			0
$226$	11.8548	+	3.01698i	0.788572	+	0.200687i
$227$	−5.62771	+	5.62771i	−0.373524	+	0.373524i	−0.868759	−	0.495235i	$-0.835082\pi$
$227$	−5.62771	+	5.62771i	−0.373524	+	0.373524i	0.495235	+	0.868759i	$0.335082\pi$
$228$	−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	−0.999921	−	0.0125551i	$-0.996003\pi$
$233$	−15.0715	+	15.0715i	−0.987366	+	0.987366i	0.0125551	+	0.999921i	$0.496003\pi$
$234$	−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	0.960240	−	0.279174i	$-0.0900607\pi$
$257$	10.9183	+	10.9183i	0.681066	+	0.681066i	−0.279174	+	0.960240i	$0.590061\pi$
$258$	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	$-0.378343\pi$
$263$	21.0955	−	21.0955i	1.30081	−	1.30081i	0.927848	−	0.372959i	$-0.121657\pi$
$264$	−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	0.216312	−	0.976324i	$-0.430597\pi$
$277$	−12.6491	−	12.6491i	−0.760013	−	0.760013i	−0.976324	+	0.216312i	$0.930597\pi$
$278$	−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	−0.181357	−	0.983417i	$-0.558049\pi$
$283$	13.4928	−	13.4928i	0.802061	−	0.802061i	0.983417	+	0.181357i	$0.0580488\pi$
$284$	−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	0.478383	−	0.878151i	$-0.341223\pi$
$293$	−6.84294	−	6.84294i	−0.399769	−	0.399769i	−0.878151	+	0.478383i	$0.841223\pi$
$294$	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	0.842378	−	0.538888i	$-0.181155\pi$
$307$	5.31757	+	5.31757i	0.303490	+	0.303490i	−0.538888	+	0.842378i	$0.681155\pi$
$308$	−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	0.537027	−	0.843565i	$-0.319547\pi$
$313$	−5.42321	−	5.42321i	−0.306538	−	0.306538i	−0.843565	+	0.537027i	$0.819547\pi$
$314$	3.58518	−	14.0875i	0.202324	−	0.795005i
$315$		0			0
$316$	15.8572	+	8.63007i	0.892039	+	0.485479i
$317$	12.8513	−	12.8513i	0.721799	−	0.721799i	−0.247172	−	0.968972i	$-0.579501\pi$
$317$	12.8513	−	12.8513i	0.721799	−	0.721799i	0.968972	+	0.247172i	$0.0795013\pi$
$318$	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	−0.722770	−	0.691089i	$-0.757131\pi$
$337$	−0.581584	+	0.581584i	−0.0316809	+	0.0316809i	0.691089	+	0.722770i	$0.257131\pi$
$338$	−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	−0.756500	−	0.653994i	$-0.773092\pi$
$347$	−1.90948	+	1.90948i	−0.102506	+	0.102506i	0.653994	+	0.756500i	$0.273092\pi$
$348$	−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	−0.698360	−	0.715747i	$-0.746086\pi$
$353$	0.326679	−	0.326679i	0.0173874	−	0.0173874i	0.715747	+	0.698360i	$0.246086\pi$
$354$	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	−0.0914078	−	0.995814i	$-0.529137\pi$
$367$	17.3259	−	17.3259i	0.904406	−	0.904406i	0.995814	+	0.0914078i	$0.0291367\pi$
$368$	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	−0.594621	−	0.804006i	$-0.702698\pi$
$373$	4.04391	−	4.04391i	0.209386	−	0.209386i	0.804006	+	0.594621i	$0.202698\pi$
$374$	−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	−0.655799	−	0.754935i	$-0.727668\pi$
$383$	1.94014	−	1.94014i	0.0991364	−	0.0991364i	0.754935	+	0.655799i	$0.227668\pi$
$384$	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	0.172204	−	0.985061i	$-0.444911\pi$
$397$	−16.1961	−	16.1961i	−0.812858	−	0.812858i	−0.985061	+	0.172204i	$0.944911\pi$
$398$	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	0.485165	−	0.874423i	$-0.338760\pi$
$433$	−8.09993	−	8.09993i	−0.389258	−	0.389258i	−0.874423	+	0.485165i	$0.838760\pi$
$434$	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	$-0.989491\pi$
$443$	−21.7308	−	21.7308i	−1.03246	−	1.03246i	−0.0330087	−	0.999455i	$-0.510509\pi$
$444$	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	−0.783044	−	0.621967i	$-0.786334\pi$
$457$	−3.44344	+	3.44344i	−0.161077	+	0.161077i	0.621967	+	0.783044i	$0.286334\pi$
$458$	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	0.897126	−	0.441776i	$-0.145651\pi$
$463$	9.79796	+	9.79796i	0.455350	+	0.455350i	−0.441776	+	0.897126i	$0.645651\pi$
$464$	−14.6142	+	9.44955i	−0.678446	+	0.438684i
$465$		0			0
$466$	29.2118	+	7.43423i	1.35321	+	0.344384i
$467$	18.8562	−	18.8562i	0.872561	−	0.872561i	−0.120190	−	0.992751i	$-0.538350\pi$
$467$	18.8562	−	18.8562i	0.872561	−	0.872561i	0.992751	+	0.120190i	$0.0383504\pi$
$468$	−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	−0.925397	−	0.378998i	$-0.876269\pi$
$487$	−12.0580	+	12.0580i	−0.546399	+	0.546399i	0.378998	+	0.925397i	$0.376269\pi$
$488$	−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	−0.976020	−	0.217680i	$-0.930151\pi$
$503$	−17.0078	+	17.0078i	−0.758340	+	0.758340i	0.217680	+	0.976020i	$0.430151\pi$
$504$	−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	−0.744343	−	0.667798i	$-0.767237\pi$
$523$	−1.75051	+	1.75051i	−0.0765445	+	0.0765445i	0.667798	+	0.744343i	$0.267237\pi$
$524$	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	$0.0121369\pi$
$547$	24.2626	+	24.2626i	1.03739	+	1.03739i	0.0381200	+	0.999273i	$0.487863\pi$
$548$	−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	−0.944240	−	0.329257i	$-0.893202\pi$
$557$	−14.5141	+	14.5141i	−0.614984	+	0.614984i	0.329257	+	0.944240i	$0.393202\pi$
$558$	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	0.788145	−	0.615489i	$-0.211042\pi$
$563$	4.09672	+	4.09672i	0.172656	+	0.172656i	−0.615489	+	0.788145i	$0.711042\pi$
$564$	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	−0.592896	−	0.805279i	$-0.702015\pi$
$577$	5.10163	−	5.10163i	0.212384	−	0.212384i	0.805279	+	0.592896i	$0.202015\pi$
$578$	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	−0.634130	−	0.773227i	$-0.718642\pi$
$587$	3.37004	−	3.37004i	0.139097	−	0.139097i	0.773227	+	0.634130i	$0.218642\pi$
$588$	−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	−0.963729	−	0.266884i	$-0.914006\pi$
$593$	−16.9693	+	16.9693i	−0.696844	+	0.696844i	0.266884	+	0.963729i	$0.414006\pi$
$594$	−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	−0.782754	−	0.622331i	$-0.786186\pi$
$607$	−3.95241	+	3.95241i	−0.160423	+	0.160423i	0.622331	+	0.782754i	$0.286186\pi$
$608$	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	−0.990030	−	0.140858i	$-0.955014\pi$
$613$	−21.0245	+	21.0245i	−0.849172	+	0.849172i	0.140858	+	0.990030i	$0.455014\pi$
$614$	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	$-0.0709231\pi$
$617$	18.7366	+	18.7366i	0.754307	+	0.754307i	−0.220973	+	0.975280i	$0.570923\pi$
$618$	−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	−0.380164	−	0.924919i	$-0.624132\pi$
$643$	13.8136	−	13.8136i	0.544755	−	0.544755i	0.924919	+	0.380164i	$0.124132\pi$
$644$	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	$-0.108144\pi$
$647$	15.5057	+	15.5057i	0.609594	+	0.609594i	−0.333246	+	0.942840i	$0.608144\pi$
$648$	−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	0.964868	−	0.262736i	$-0.0846248\pi$
$653$	17.9422	+	17.9422i	0.702132	+	0.702132i	−0.262736	+	0.964868i	$0.584625\pi$
$654$	−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	0.751380	−	0.659870i	$-0.229389\pi$
$673$	2.37397	+	2.37397i	0.0915096	+	0.0915096i	−0.659870	+	0.751380i	$0.729389\pi$
$674$	1.12724	+	0.286875i	0.0434196	+	0.0110500i
$675$		0			0
$676$	39.6233	+	21.5644i	1.52397	+	0.829402i
$677$	6.61424	−	6.61424i	0.254206	−	0.254206i	−0.568487	−	0.822693i	$-0.692471\pi$
$677$	6.61424	−	6.61424i	0.254206	−	0.254206i	0.822693	+	0.568487i	$0.192471\pi$
$678$	−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	0.377941	−	0.925830i	$-0.376632\pi$
$683$	−14.3187	−	14.3187i	−0.547889	−	0.547889i	−0.925830	+	0.377941i	$0.876632\pi$
$684$	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	−0.596620	−	0.802524i	$-0.703490\pi$
$727$	5.55176	−	5.55176i	0.205903	−	0.205903i	0.802524	+	0.596620i	$0.203490\pi$
$728$	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	−0.869995	−	0.493061i	$-0.835878\pi$
$733$	−10.2051	+	10.2051i	−0.376934	+	0.376934i	0.493061	+	0.869995i	$0.335878\pi$
$734$	−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	−0.926020	−	0.377474i	$-0.876793\pi$
$743$	−14.9523	+	14.9523i	−0.548546	+	0.548546i	0.377474	+	0.926020i	$0.376793\pi$
$744$	−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	0.522075	−	0.852900i	$-0.325158\pi$
$757$	−9.10219	−	9.10219i	−0.330825	−	0.330825i	−0.852900	+	0.522075i	$0.825158\pi$
$758$	−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	0.416956	−	0.908927i	$-0.363097\pi$
$773$	−13.6782	−	13.6782i	−0.491971	−	0.491971i	−0.908927	+	0.416956i	$0.863097\pi$
$774$	−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	0.735894	−	0.677097i	$-0.236762\pi$
$787$	1.64945	+	1.64945i	0.0587966	+	0.0587966i	−0.677097	+	0.735894i	$0.736762\pi$
$788$	−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	−0.384612	−	0.923078i	$-0.625665\pi$
$797$	15.2015	−	15.2015i	0.538466	−	0.538466i	0.923078	+	0.384612i	$0.125665\pi$
$798$	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	$-0.990882\pi$
$823$	−29.4978	−	29.4978i	−1.02823	−	1.02823i	−0.0286405	−	0.999590i	$-0.509118\pi$
$824$	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	$0.546755\pi$
$827$	−32.6568	+	32.6568i	−1.13559	+	1.13559i	−0.989232	+	0.146357i	$0.953245\pi$
$828$	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	−0.275483	−	0.961306i	$-0.588838\pi$
$853$	20.0303	−	20.0303i	0.685823	−	0.685823i	0.961306	+	0.275483i	$0.0888378\pi$
$854$	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	$-0.0499327\pi$
$857$	24.3417	+	24.3417i	0.831496	+	0.831496i	−0.156226	+	0.987721i	$0.549933\pi$
$858$	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	−0.363783	−	0.931484i	$-0.618515\pi$
$863$	16.6773	−	16.6773i	0.567701	−	0.567701i	0.931484	+	0.363783i	$0.118515\pi$
$864$	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	0.710639	−	0.703557i	$-0.248406\pi$
$877$	0.209733	+	0.209733i	0.00708216	+	0.00708216i	−0.703557	+	0.710639i	$0.748406\pi$
$878$	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	−0.821185	−	0.570662i	$-0.806687\pi$
$883$	−7.44439	+	7.44439i	−0.250524	+	0.250524i	0.570662	+	0.821185i	$0.306687\pi$
$884$	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	$-0.372571\pi$
$887$	−15.8208	−	15.8208i	−0.531211	−	0.531211i	−0.920933	+	0.389722i	$0.872571\pi$
$888$	−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	$-0.956933\pi$
$907$	−33.9035	−	33.9035i	−1.12575	−	1.12575i	−0.134886	−	0.990861i	$-0.543067\pi$
$908$	−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	$-0.412392\pi$
$937$	37.7773	−	37.7773i	1.23413	−	1.23413i	0.962363	−	0.271766i	$-0.0876078\pi$
$938$	−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	−0.204893	−	0.978784i	$-0.565685\pi$
$947$	23.8152	−	23.8152i	0.773891	−	0.773891i	0.978784	+	0.204893i	$0.0656846\pi$
$948$	−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	$-0.489913\pi$
$953$	31.8333	−	31.8333i	1.03118	−	1.03118i	0.999498	−	0.0316832i	$-0.0100868\pi$
$954$	−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	−0.964435	−	0.264320i	$-0.914852\pi$
$967$	−21.7712	+	21.7712i	−0.700115	+	0.700115i	0.264320	+	0.964435i	$0.414852\pi$
$968$	−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	0.742368	−	0.669992i	$-0.233703\pi$
$977$	2.26226	+	2.26226i	0.0723760	+	0.0723760i	−0.669992	+	0.742368i	$0.733703\pi$
$978$	−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	$-0.393067\pi$
$983$	39.9359	−	39.9359i	1.27376	−	1.27376i	0.944101	−	0.329656i	$-0.106933\pi$
$984$	−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	0.994808	−	0.101774i	$-0.0324518\pi$
$997$	28.1978	+	28.1978i	0.893034	+	0.893034i	−0.101774	+	0.994808i	$0.532452\pi$
$998$	−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.293.11	yes	64
3.2	odd	2	inner	600.2.w.k.293.21	yes	64
5.2	odd	4	inner	600.2.w.k.557.28	yes	64
5.3	odd	4	inner	600.2.w.k.557.5	yes	64
5.4	even	2	inner	600.2.w.k.293.22	yes	64
8.5	even	2	inner	600.2.w.k.293.6	yes	64
15.2	even	4	inner	600.2.w.k.557.6	yes	64
15.8	even	4	inner	600.2.w.k.557.27	yes	64
15.14	odd	2	inner	600.2.w.k.293.12	yes	64
24.5	odd	2	inner	600.2.w.k.293.28	yes	64
40.13	odd	4	inner	600.2.w.k.557.12	yes	64
40.29	even	2	inner	600.2.w.k.293.27	yes	64
40.37	odd	4	inner	600.2.w.k.557.21	yes	64
120.29	odd	2	inner	600.2.w.k.293.5	✓	64
120.53	even	4	inner	600.2.w.k.557.22	yes	64
120.77	even	4	inner	600.2.w.k.557.11	yes	64

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

Properties

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