LMFDB - Embedded newform 600.2.w.k.557.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("600.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			557.27
Character	$\chi$	$=$	600.557
Dual form			600.2.w.k.293.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.21574	−	0.722477i	0.859659	−	0.510868i
$2$	1.21574	−	0.722477i	0.859659	−	0.510868i
$3$	−1.48597	+	0.889875i	−0.857928	+	0.513770i
$3$	−1.48597	+	0.889875i	−0.857928	+	0.513770i
$4$	0.956054	−	1.75669i	0.478027	−	0.878345i
$5$		0			0
$5$		0			0
$6$	−1.16365	+	2.15544i	−0.475057	+	0.879955i
$7$	2.09015	+	2.09015i	0.790001	+	0.790001i	0.981494	−	0.191493i	$-0.0613328\pi$
$7$	2.09015	+	2.09015i	0.790001	+	0.790001i	−0.191493	+	0.981494i	$0.561333\pi$
$8$	−0.106854	−	2.82641i	−0.0377787	−	0.999286i
$9$	1.41624	−	2.64467i	0.472081	−	0.881555i
$10$		0			0
$11$	−2.65514			−0.800553			−0.400277	−	0.916394i	$-0.631086\pi$
$11$	−2.65514			−0.800553			−0.400277	+	0.916394i	$0.631086\pi$
$12$	0.142564	+	3.46117i	0.0411546	+	0.999153i
$13$	4.21638	+	4.21638i	1.16941	+	1.16941i	0.982347	+	0.187065i	$0.0598976\pi$
$13$	4.21638	+	4.21638i	1.16941	+	1.16941i	0.187065	+	0.982347i	$0.440102\pi$
$14$	4.05116	+	1.03099i	1.08272	+	0.275545i
$15$		0			0
$16$	−2.17192	−	3.35898i	−0.542981	−	0.839745i
$17$	3.84954	−	3.84954i	0.933651	−	0.933651i	−0.0642808	−	0.997932i	$-0.520475\pi$
$17$	3.84954	−	3.84954i	0.933651	−	0.933651i	0.997932	+	0.0642808i	$0.0204753\pi$
$18$	−0.188924	−	4.23843i	−0.0445299	−	0.999008i
$19$	3.15804			0.724505			0.362252	−	0.932080i	$-0.382008\pi$
$19$	3.15804			0.724505			0.362252	+	0.932080i	$0.382008\pi$
$20$		0			0
$21$	−4.96588	−	1.24594i	−1.08364	−	0.271885i
$22$	−3.22796	+	1.91827i	−0.688203	+	0.408977i
$23$	1.60962	+	1.60962i	0.335629	+	0.335629i	0.854719	−	0.519090i	$-0.173729\pi$
$23$	1.60962	+	1.60962i	0.335629	+	0.335629i	−0.519090	+	0.854719i	$0.673729\pi$
$24$	2.67393	+	4.10488i	0.545814	+	0.837906i
$25$		0			0
$26$	8.17226	+	2.07979i	1.60271	+	0.407880i
$27$	0.248921	+	5.19019i	0.0479048	+	0.998852i
$28$	5.67003	−	1.67345i	1.07154	−	0.316252i
$29$		−	4.35078i		−	0.807919i	−0.914777	−	0.403959i	$-0.867634\pi$
$29$		−	4.35078i		−	0.807919i	0.914777	−	0.403959i	$-0.132366\pi$
$30$		0			0
$31$	1.56789			0.281602			0.140801	−	0.990038i	$-0.455032\pi$
$31$	1.56789			0.281602			0.140801	+	0.990038i	$0.455032\pi$
$32$	−5.06728	−	2.51449i	−0.895777	−	0.444503i
$33$	3.94546	−	2.36274i	0.686817	−	0.411300i
$34$	1.89884	−	7.46125i	0.325649	−	1.27959i
$35$		0			0
$36$	−3.29185	−	5.01634i	−0.548642	−	0.836057i
$37$	4.94127	−	4.94127i	0.812339	−	0.812339i	−0.172645	−	0.984984i	$-0.555231\pi$
$37$	4.94127	−	4.94127i	0.812339	−	0.812339i	0.984984	+	0.172645i	$0.0552313\pi$
$38$	3.83936	−	2.28161i	0.622827	−	0.370127i
$39$	−10.0175	−	2.51338i	−1.60408	−	0.402463i
$40$		0			0
$41$			10.6056i			1.65631i	0.560500	+	0.828154i	$0.310609\pi$
$41$			10.6056i			1.65631i	−0.560500	+	0.828154i	$0.689391\pi$
$42$	−6.93738	+	2.07300i	−1.07046	+	0.319870i
$43$	0.219791	+	0.219791i	0.0335178	+	0.0335178i	0.723667	−	0.690149i	$-0.242455\pi$
$43$	0.219791	+	0.219791i	0.0335178	+	0.0335178i	−0.690149	+	0.723667i	$0.742455\pi$
$44$	−2.53845	+	4.66425i	−0.382686	+	0.703162i
$45$		0			0
$46$	3.11979	+	0.793968i	0.459989	+	0.117064i
$47$	−1.83256	+	1.83256i	−0.267306	+	0.267306i	−0.828014	−	0.560708i	$-0.810529\pi$
$47$	−1.83256	+	1.83256i	−0.267306	+	0.267306i	0.560708	+	0.828014i	$0.310529\pi$
$48$	6.21650	+	3.05862i	0.897274	+	0.441474i
$49$			1.73743i			0.248204i
$50$		0			0
$51$	−2.29471	+	9.14594i	−0.321324	+	1.28069i
$52$	11.4380	−	3.37579i	1.58616	−	0.468137i
$53$	−4.64119	+	4.64119i	−0.637516	+	0.637516i	−0.949942	−	0.312426i	$-0.898858\pi$
$53$	−4.64119	+	4.64119i	−0.637516	+	0.637516i	0.312426	+	0.949942i	$0.398858\pi$
$54$	4.05241	+	6.13009i	0.551464	+	0.834199i
$55$		0			0
$56$	5.68427	−	6.13095i	0.759592	−	0.819283i
$57$	−4.69277	+	2.81027i	−0.621573	+	0.372229i
$58$	−3.14334	−	5.28942i	−0.412740	−	0.694535i
$59$		−	9.93175i		−	1.29300i	−0.762912	−	0.646502i	$-0.776231\pi$
$59$		−	9.93175i		−	1.29300i	0.762912	−	0.646502i	$-0.223769\pi$
$60$		0			0
$61$		−	11.9159i		−	1.52568i	−0.646590	−	0.762838i	$-0.723805\pi$
$61$		−	11.9159i		−	1.52568i	0.646590	−	0.762838i	$-0.276195\pi$
$62$	1.90615	−	1.13277i	0.242082	−	0.143862i
$63$	8.48790	−	2.56758i	1.06937	−	0.323485i
$64$	−7.97716	+	0.604028i	−0.997146	+	0.0755035i
$65$		0			0
$66$	3.08964	−	5.72299i	0.380308	−	0.704451i
$67$	−8.80906	+	8.80906i	−1.07620	+	1.07620i	−0.0793517	+	0.996847i	$0.525285\pi$
$67$	−8.80906	+	8.80906i	−1.07620	+	1.07620i	−0.996847	+	0.0793517i	$0.974715\pi$
$68$	−3.08208	−	10.4428i	−0.373758	−	1.26638i
$69$	−3.82422	−	0.959493i	−0.460381	−	0.115509i
$70$		0			0
$71$		−	2.89837i		−	0.343973i	−0.985099	−	0.171986i	$-0.944982\pi$
$71$		−	2.89837i		−	0.343973i	0.985099	−	0.171986i	$-0.0550185\pi$
$72$	−7.62624	−	3.72029i	−0.898760	−	0.438440i
$73$	−2.29779	+	2.29779i	−0.268936	+	0.268936i	−0.828671	−	0.559736i	$-0.810903\pi$
$73$	−2.29779	+	2.29779i	−0.268936	+	0.268936i	0.559736	+	0.828671i	$0.310903\pi$
$74$	2.43735	−	9.57725i	0.283336	−	1.11333i
$75$		0			0
$76$	3.01926	−	5.54770i	0.346333	−	0.636365i
$77$	−5.54962	−	5.54962i	−0.632438	−	0.632438i
$78$	−13.9945	+	4.18178i	−1.58457	+	0.473493i
$79$			9.02676i			1.01559i	0.861478	+	0.507795i	$0.169539\pi$
$79$			9.02676i			1.01559i	−0.861478	+	0.507795i	$0.830461\pi$
$80$		0			0
$81$	−4.98851	−	7.49098i	−0.554279	−	0.832331i
$82$	7.66227	+	12.8936i	0.846156	+	1.42386i
$83$	−9.78801	+	9.78801i	−1.07437	+	1.07437i	−0.0773719	+	0.997002i	$0.524653\pi$
$83$	−9.78801	+	9.78801i	−1.07437	+	1.07437i	−0.997002	+	0.0773719i	$0.975347\pi$
$84$	−6.93637	+	7.53233i	−0.756820	+	0.821844i
$85$		0			0
$86$	0.426003	+	0.108415i	0.0459371	+	0.0116907i
$87$	3.87165	+	6.46515i	0.415084	+	0.693136i
$88$	0.283713	+	7.50450i	0.0302439	+	0.799982i
$89$	−2.83249			−0.300243			−0.150121	−	0.988668i	$-0.547966\pi$
$89$	−2.83249			−0.300243			−0.150121	+	0.988668i	$0.547966\pi$
$90$		0			0
$91$			17.6257i			1.84768i
$92$	4.36649	−	1.28872i	0.455238	−	0.134358i
$93$	−2.32985	+	1.39523i	−0.241594	+	0.144679i
$94$	−0.903936	+	3.55190i	−0.0932339	+	0.366351i
$95$		0			0
$96$	9.76744	−	0.772783i	0.996885	−	0.0788719i
$97$	−9.26375	−	9.26375i	−0.940592	−	0.940592i	0.0577400	−	0.998332i	$-0.481611\pi$
$97$	−9.26375	−	9.26375i	−0.940592	−	0.940592i	−0.998332	+	0.0577400i	$0.981611\pi$
$98$	1.25525	+	2.11227i	0.126800	+	0.213371i
$99$	−3.76032	+	7.02194i	−0.377926	+	0.705732i
$100$		0			0
$101$	−10.6797			−1.06267			−0.531337	−	0.847160i	$-0.678310\pi$
$101$	−10.6797			−1.06267			−0.531337	+	0.847160i	$0.678310\pi$
$102$	3.81795	+	12.7770i	0.378034	+	1.26511i
$103$	−10.3368	+	10.3368i	−1.01851	+	1.01851i	−0.0186893	+	0.999825i	$0.505949\pi$
$103$	−10.3368	+	10.3368i	−1.01851	+	1.01851i	−0.999825	+	0.0186893i	$0.994051\pi$
$104$	11.4667	−	12.3677i	1.12440	−	1.21276i
$105$		0			0
$106$	−2.28933	+	8.99563i	−0.222359	+	0.873733i
$107$	3.47289	+	3.47289i	0.335737	+	0.335737i	0.854760	−	0.519023i	$-0.173704\pi$
$107$	3.47289	+	3.47289i	0.335737	+	0.335737i	−0.519023	+	0.854760i	$0.673704\pi$
$108$	9.35553	+	4.52482i	0.900237	+	0.435401i
$109$	−2.67954			−0.256654			−0.128327	−	0.991732i	$-0.540961\pi$
$109$	−2.67954			−0.256654			−0.128327	+	0.991732i	$0.540961\pi$
$110$		0			0
$111$	−2.94549	+	11.7397i	−0.279573	+	1.11428i
$112$	2.48113	−	11.5604i	0.234445	−	1.09236i
$113$	6.11636	+	6.11636i	0.575379	+	0.575379i	0.933627	−	0.358248i	$-0.116626\pi$
$113$	6.11636	+	6.11636i	0.575379	+	0.575379i	−0.358248	+	0.933627i	$0.616626\pi$
$114$	−3.67485	+	6.80698i	−0.344181	+	0.637532i
$115$		0			0
$116$	−7.64297	−	4.15958i	−0.709632	−	0.386207i
$117$	17.1223	−	5.17949i	1.58296	−	0.478844i
$118$	−7.17546	−	12.0744i	−0.660555	−	1.11154i
$119$	16.0922			1.47517
$120$		0			0
$121$	−3.95026			−0.359114
$122$	−8.60897	−	14.4867i	−0.779420	−	1.31156i
$123$	−9.43762	−	15.7596i	−0.850962	−	1.42099i
$124$	1.49899	−	2.75430i	0.134613	−	0.247344i
$125$		0			0
$126$	8.46407	−	9.25383i	0.754039	−	0.824396i
$127$	−11.2254	−	11.2254i	−0.996089	−	0.996089i	0.00390306	−	0.999992i	$-0.498758\pi$
$127$	−11.2254	−	11.2254i	−0.996089	−	0.996089i	−0.999992	+	0.00390306i	$0.998758\pi$
$128$	−9.26177	+	6.49766i	−0.818633	+	0.574317i
$129$	−0.522191	−	0.131017i	−0.0459763	−	0.0115354i
$130$		0			0
$131$	6.55577			0.572780			0.286390	−	0.958113i	$-0.407545\pi$
$131$	6.55577			0.572780			0.286390	+	0.958113i	$0.407545\pi$
$132$	−0.378525	−	9.18987i	−0.0329464	−	0.799875i
$133$	6.60078	+	6.60078i	0.572360	+	0.572360i
$134$	−4.34520	+	17.0739i	−0.375368	+	1.47496i
$135$		0			0
$136$	−11.2917	−	10.4690i	−0.968257	−	0.897712i
$137$	−1.63651	+	1.63651i	−0.139817	+	0.139817i	−0.773551	−	0.633734i	$-0.781521\pi$
$137$	−1.63651	+	1.63651i	−0.139817	+	0.139817i	0.633734	+	0.773551i	$0.281521\pi$
$138$	−5.34247	+	1.59641i	−0.454781	+	0.135896i
$139$	−1.03173			−0.0875104			−0.0437552	−	0.999042i	$-0.513932\pi$
$139$	−1.03173			−0.0875104			−0.0437552	+	0.999042i	$0.513932\pi$
$140$		0			0
$141$	1.09239	−	4.35389i	0.0919956	−	0.366663i
$142$	−2.09400	−	3.52366i	−0.175725	−	0.295699i
$143$	−11.1951	−	11.1951i	−0.936177	−	0.936177i
$144$	−11.9594	+	0.986872i	−0.996613	+	0.0822394i
$145$		0			0
$146$	−1.13342	+	4.45361i	−0.0938022	+	0.368583i
$147$	−1.54610	−	2.58178i	−0.127520	−	0.212942i
$148$	−3.95616	−	13.4044i	−0.325194	−	1.10183i
$149$			3.60278i			0.295151i	0.989051	+	0.147576i	$0.0471470\pi$
$149$			3.60278i			0.295151i	−0.989051	+	0.147576i	$0.952853\pi$
$150$		0			0
$151$	13.6985			1.11476			0.557382	−	0.830256i	$-0.311806\pi$
$151$	13.6985			1.11476			0.557382	+	0.830256i	$0.311806\pi$
$152$	−0.337451	−	8.92592i	−0.0273709	−	0.723988i
$153$	−4.72886	−	15.6326i	−0.382306	−	1.26382i
$154$	−10.7564	−	2.73743i	−0.866774	−	0.220588i
$155$		0			0
$156$	−13.9925	+	15.1947i	−1.12030	+	1.21655i
$157$	7.26828	−	7.26828i	0.580072	−	0.580072i	−0.354851	−	0.934923i	$-0.615468\pi$
$157$	7.26828	−	7.26828i	0.580072	−	0.580072i	0.934923	+	0.354851i	$0.115468\pi$
$158$	6.52163	+	10.9742i	0.518833	+	0.873061i
$159$	2.76661	−	11.0268i	0.219406	−	0.874479i
$160$		0			0
$161$			6.72868i			0.530295i
$162$	−11.4768	−	5.50301i	−0.901702	−	0.432357i
$163$	−9.50622	−	9.50622i	−0.744585	−	0.744585i	0.228872	−	0.973457i	$-0.426496\pi$
$163$	−9.50622	−	9.50622i	−0.744585	−	0.744585i	−0.973457	+	0.228872i	$0.926496\pi$
$164$	18.6307	+	10.1395i	1.45481	+	0.791760i
$165$		0			0
$166$	−4.82808	+	18.9713i	−0.374732	+	1.47246i
$167$	14.4143	−	14.4143i	1.11541	−	1.11541i	0.123005	−	0.992406i	$-0.460747\pi$
$167$	14.4143	−	14.4143i	1.11541	−	1.11541i	0.992406	−	0.123005i	$-0.0392532\pi$
$168$	−2.99090	+	14.1687i	−0.230753	+	1.09314i
$169$			22.5557i			1.73505i
$170$		0			0
$171$	4.47256	−	8.35197i	0.342025	−	0.638691i
$172$	0.596237	−	0.175973i	0.0454626	−	0.0134178i
$173$	18.0907	−	18.0907i	1.37541	−	1.37541i	0.523202	−	0.852209i	$-0.324738\pi$
$173$	18.0907	−	18.0907i	1.37541	−	1.37541i	0.852209	−	0.523202i	$-0.175262\pi$
$174$	9.37784	+	5.06277i	0.710932	+	0.383807i
$175$		0			0
$176$	5.76675	+	8.91855i	0.434685	+	0.672261i
$177$	8.83802	+	14.7583i	0.664307	+	1.10930i
$178$	−3.44357	+	2.04641i	−0.258107	+	0.153385i
$179$			5.81962i			0.434979i	0.976063	+	0.217489i	$0.0697868\pi$
$179$			5.81962i			0.434979i	−0.976063	+	0.217489i	$0.930213\pi$
$180$		0			0
$181$		−	3.58348i		−	0.266358i	−0.991092	−	0.133179i	$-0.957481\pi$
$181$		−	3.58348i		−	0.266358i	0.991092	−	0.133179i	$-0.0425185\pi$
$182$	12.7342	+	21.4283i	0.943919	+	1.58837i
$183$	10.6037	+	17.7067i	0.783846	+	1.30892i
$184$	4.37745	−	4.72144i	0.322710	−	0.348069i
$185$		0			0
$186$	−1.82447	+	3.37950i	−0.133777	+	0.247797i
$187$	−10.2211	+	10.2211i	−0.747437	+	0.747437i
$188$	1.46721	+	4.97126i	0.107008	+	0.362567i
$189$	−10.3280	+	11.3685i	−0.751250	+	0.826939i
$190$		0			0
$191$		−	11.6034i		−	0.839591i	−0.907619	−	0.419796i	$-0.862102\pi$
$191$		−	11.6034i		−	0.839591i	0.907619	−	0.419796i	$-0.137898\pi$
$192$	11.3164	−	7.99625i	0.816688	−	0.577080i
$193$	−9.83073	+	9.83073i	−0.707632	+	0.707632i	−0.966037	−	0.258405i	$-0.916803\pi$
$193$	−9.83073	+	9.83073i	−0.707632	+	0.707632i	0.258405	+	0.966037i	$0.416803\pi$
$194$	−17.9552	−	4.56948i	−1.28911	−	0.328069i
$195$		0			0
$196$	3.05213	+	1.66108i	0.218009	+	0.118648i
$197$	−1.97306	−	1.97306i	−0.140574	−	0.140574i	0.633318	−	0.773892i	$-0.281693\pi$
$197$	−1.97306	−	1.97306i	−0.140574	−	0.140574i	−0.773892	+	0.633318i	$0.781693\pi$
$198$	0.501620	+	11.2536i	0.0356486	+	0.799759i
$199$		−	4.09303i		−	0.290147i	−0.989421	−	0.145074i	$-0.953658\pi$
$199$		−	4.09303i		−	0.290147i	0.989421	−	0.145074i	$-0.0463419\pi$
$200$		0			0
$201$	5.25108	−	20.9290i	0.370383	−	1.47622i
$202$	−12.9838	+	7.71587i	−0.913538	+	0.542887i
$203$	9.09376	−	9.09376i	0.638257	−	0.638257i
$204$	13.8727	+	12.7751i	0.971284	+	0.894436i
$205$		0			0
$206$	−5.09877	+	20.0350i	−0.355248	+	1.39590i
$207$	6.53652	−	1.97729i	0.454319	−	0.137431i
$208$	5.00509	−	23.3204i	0.347040	−	1.61698i
$209$	−8.38503			−0.580005
$210$		0			0
$211$		−	5.39432i		−	0.371361i	−0.982610	−	0.185680i	$-0.940551\pi$
$211$		−	5.39432i		−	0.371361i	0.982610	−	0.185680i	$-0.0594489\pi$
$212$	3.71590	+	12.5903i	0.255209	+	0.864709i
$213$	2.57918	+	4.30690i	0.176723	+	0.295104i
$214$	6.73123	+	1.71305i	0.460137	+	0.117102i
$215$		0			0
$216$	14.6430	−	1.25815i	0.996329	−	0.0856059i
$217$	3.27713	+	3.27713i	0.222466	+	0.222466i
$218$	−3.25763	+	1.93591i	−0.220635	+	0.131116i
$219$	1.36971	−	5.45920i	0.0925564	−	0.368898i
$220$		0			0
$221$	32.4622			2.18365
$222$	4.90072	+	16.4005i	0.328915	+	1.10073i
$223$	−2.63896	+	2.63896i	−0.176718	+	0.176718i	−0.789923	−	0.613206i	$-0.789880\pi$
$223$	−2.63896	+	2.63896i	−0.176718	+	0.176718i	0.613206	+	0.789923i	$0.289880\pi$
$224$	−5.33572	−	15.8470i	−0.356507	−	1.05882i
$225$		0			0
$226$	11.8548	+	3.01698i	0.788572	+	0.200687i
$227$	−5.62771	−	5.62771i	−0.373524	−	0.373524i	0.495235	−	0.868759i	$-0.335082\pi$
$227$	−5.62771	−	5.62771i	−0.373524	−	0.373524i	−0.868759	+	0.495235i	$0.835082\pi$
$228$	0.450222	+	10.9305i	0.0298167	+	0.723891i
$229$	11.2319			0.742225			0.371113	−	0.928588i	$-0.378976\pi$
$229$	11.2319			0.742225			0.371113	+	0.928588i	$0.378976\pi$
$230$		0			0
$231$	13.1851	+	3.30813i	0.867514	+	0.217659i
$232$	−12.2971	+	0.464899i	−0.807342	+	0.0305221i
$233$	15.0715	+	15.0715i	0.987366	+	0.987366i	0.999921	−	0.0125551i	$-0.00399652\pi$
$233$	15.0715	+	15.0715i	0.987366	+	0.987366i	−0.0125551	+	0.999921i	$0.503997\pi$
$234$	17.0743	−	18.6674i	1.11618	−	1.22033i
$235$		0			0
$236$	−17.4470	−	9.49529i	−1.13570	−	0.618091i
$237$	−8.03269	−	13.4135i	−0.521780	−	0.871303i
$238$	19.5640	−	11.6263i	1.26814	−	0.753618i
$239$	2.89837			0.187480			0.0937398	−	0.995597i	$-0.470118\pi$
$239$	2.89837			0.187480			0.0937398	+	0.995597i	$0.470118\pi$
$240$		0			0
$241$	0.551900			0.0355510			0.0177755	−	0.999842i	$-0.494342\pi$
$241$	0.551900			0.0355510			0.0177755	+	0.999842i	$0.494342\pi$
$242$	−4.80249	+	2.85397i	−0.308716	+	0.183460i
$243$	14.0788	+	6.69226i	0.903158	+	0.429308i
$244$	−20.9326	−	11.3923i	−1.34007	−	0.729314i
$245$		0			0
$246$	−22.8596	−	12.3411i	−1.45748	−	0.786841i
$247$	13.3155	+	13.3155i	0.847245	+	0.847245i
$248$	−0.167536	−	4.43151i	−0.0106386	−	0.281401i
$249$	5.83463	−	23.2549i	0.369755	−	1.47372i
$250$		0			0
$251$	6.29691			0.397457			0.198729	−	0.980055i	$-0.436319\pi$
$251$	6.29691			0.397457			0.198729	+	0.980055i	$0.436319\pi$
$252$	3.60444	−	17.3654i	0.227058	−	1.09391i
$253$	−4.27376	−	4.27376i	−0.268689	−	0.268689i
$254$	−21.7572	−	5.53707i	−1.36517	−	0.347426i
$255$		0			0
$256$	−6.56551	+	14.5909i	−0.410344	+	0.911931i
$257$	−10.9183	+	10.9183i	−0.681066	+	0.681066i	−0.960240	−	0.279174i	$-0.909939\pi$
$257$	−10.9183	+	10.9183i	−0.681066	+	0.681066i	0.279174	+	0.960240i	$0.409939\pi$
$258$	−0.729506	+	0.217988i	−0.0454171	+	0.0135713i
$259$	20.6559			1.28350
$260$		0			0
$261$	−11.5063	−	6.16176i	−0.712225	−	0.381403i
$262$	7.97012	−	4.73639i	0.492396	−	0.292615i
$263$	−21.0955	−	21.0955i	−1.30081	−	1.30081i	−0.927848	−	0.372959i	$-0.878343\pi$
$263$	−21.0955	−	21.0955i	−1.30081	−	1.30081i	−0.372959	−	0.927848i	$-0.621657\pi$
$264$	−7.09966	−	10.8990i	−0.436954	−	0.670788i
$265$		0			0
$266$	12.7937	+	3.25593i	0.784435	+	0.199634i
$267$	4.20900	−	2.52056i	0.257587	−	0.154256i
$268$	7.05286	+	23.8967i	0.430822	+	1.45973i
$269$			20.6115i			1.25671i	0.777929	+	0.628353i	$0.216271\pi$
$269$			20.6115i			1.25671i	−0.777929	+	0.628353i	$0.783729\pi$
$270$		0			0
$271$	−24.2931			−1.47570			−0.737851	−	0.674964i	$-0.764159\pi$
$271$	−24.2931			−1.47570			−0.737851	+	0.674964i	$0.764159\pi$
$272$	−21.2914	−	4.56963i	−1.29098	−	0.277075i
$273$	−15.6847	−	26.1913i	−0.949280	−	1.58517i
$274$	−0.807234	+	3.17192i	−0.0487668	+	0.191623i
$275$		0			0
$276$	−5.34169	+	5.80063i	−0.321532	+	0.349157i
$277$	−12.6491	+	12.6491i	−0.760013	+	0.760013i	−0.976324	−	0.216312i	$-0.930597\pi$
$277$	−12.6491	+	12.6491i	−0.760013	+	0.760013i	0.216312	+	0.976324i	$0.430597\pi$
$278$	−1.25432	+	0.745403i	−0.0752291	+	0.0447063i
$279$	2.22052	−	4.14656i	0.132939	−	0.248248i
$280$		0			0
$281$		−	8.81745i		−	0.526005i	−0.964795	−	0.263002i	$-0.915287\pi$
$281$		−	8.81745i		−	0.526005i	0.964795	−	0.263002i	$-0.0847127\pi$
$282$	−1.81752	−	6.08242i	−0.108232	−	0.362203i
$283$	13.4928	+	13.4928i	0.802061	+	0.802061i	0.983417	−	0.181357i	$-0.0580488\pi$
$283$	13.4928	+	13.4928i	0.802061	+	0.802061i	−0.181357	+	0.983417i	$0.558049\pi$
$284$	−5.09153	−	2.77099i	−0.302127	−	0.164428i
$285$		0			0
$286$	−21.6985	−	5.52212i	−1.28306	−	0.326530i
$287$	−22.1672	+	22.1672i	−1.30849	+	1.30849i
$288$	−13.8265	+	9.84014i	−0.814733	+	0.579836i
$289$		−	12.6379i		−	0.743409i
$290$		0			0
$291$	22.0093	+	5.52212i	1.29021	+	0.323712i
$292$	1.83969	+	6.23331i	0.107660	+	0.364777i
$293$	−6.84294	+	6.84294i	−0.399769	+	0.399769i	−0.878151	−	0.478383i	$-0.841223\pi$
$293$	−6.84294	+	6.84294i	−0.399769	+	0.399769i	0.478383	+	0.878151i	$0.341223\pi$
$294$	−3.74493	−	2.02176i	−0.218409	−	0.117911i
$295$		0			0
$296$	−14.4940	−	13.4380i	−0.842448	−	0.781070i
$297$	−0.660918	−	13.7806i	−0.0383503	−	0.799634i
$298$	2.60293	+	4.38005i	0.150784	+	0.253730i
$299$			13.5735i			0.784977i
$300$		0			0
$301$			0.918791i			0.0529583i
$302$	16.6538	−	9.89682i	0.958317	−	0.569498i
$303$	15.8698	−	9.50365i	0.911698	−	0.545970i
$304$	−6.85902	−	10.6078i	−0.393392	−	0.608400i
$305$		0			0
$306$	−17.0433	−	15.5887i	−0.974300	−	0.891150i
$307$	5.31757	−	5.31757i	0.303490	−	0.303490i	−0.538888	−	0.842378i	$-0.681155\pi$
$307$	5.31757	−	5.31757i	0.303490	−	0.303490i	0.842378	+	0.538888i	$0.181155\pi$
$308$	−15.0547	+	4.44323i	−0.857822	+	0.253177i
$309$	6.16176	−	24.5587i	0.350530	−	1.39709i
$310$		0			0
$311$		−	31.3649i		−	1.77854i	−0.457382	−	0.889270i	$-0.651213\pi$
$311$		−	31.3649i		−	1.77854i	0.457382	−	0.889270i	$-0.348787\pi$
$312$	−6.03343	+	28.5821i	−0.341576	+	1.61814i
$313$	5.42321	−	5.42321i	0.306538	−	0.306538i	−0.537027	−	0.843565i	$-0.680453\pi$
$313$	5.42321	−	5.42321i	0.306538	−	0.306538i	0.843565	+	0.537027i	$0.180453\pi$
$314$	3.58518	−	14.0875i	0.202324	−	0.795005i
$315$		0			0
$316$	15.8572	+	8.63007i	0.892039	+	0.485479i
$317$	12.8513	+	12.8513i	0.721799	+	0.721799i	0.968972	−	0.247172i	$-0.0795013\pi$
$317$	12.8513	+	12.8513i	0.721799	+	0.721799i	−0.247172	+	0.968972i	$0.579501\pi$
$318$	−4.60310	−	15.4045i	−0.258129	−	0.863841i
$319$			11.5519i			0.646782i
$320$		0			0
$321$	−8.25108	−	2.07019i	−0.460530	−	0.115547i
$322$	4.86132	+	8.18034i	0.270911	+	0.455872i
$323$	12.1570	−	12.1570i	0.676435	−	0.676435i
$324$	−17.9286	+	1.60149i	−0.996034	+	0.0889715i
$325$		0			0
$326$	−18.4251	−	4.68908i	−1.02047	−	0.259704i
$327$	3.98173	−	2.38446i	0.220190	−	0.131861i
$328$	29.9756	−	1.13325i	1.65513	−	0.0625732i
$329$	−7.66064			−0.422345
$330$		0			0
$331$		−	10.6434i		−	0.585016i	−0.956263	−	0.292508i	$-0.905510\pi$
$331$		−	10.6434i		−	0.585016i	0.956263	−	0.292508i	$-0.0944899\pi$
$332$	7.83664	+	26.5524i	0.430092	+	1.45725i
$333$	−6.06996	−	20.0660i	−0.332632	−	1.09961i
$334$	7.11005	−	27.9380i	0.389045	−	1.52870i
$335$		0			0
$336$	6.60042	+	19.3864i	0.360083	+	1.05761i
$337$	0.581584	+	0.581584i	0.0316809	+	0.0316809i	0.722770	−	0.691089i	$-0.242869\pi$
$337$	0.581584	+	0.581584i	0.0316809	+	0.0316809i	−0.691089	+	0.722770i	$0.742869\pi$
$338$	16.2960	+	27.4219i	0.886383	+	1.49155i
$339$	−14.5316	−	3.64596i	−0.789246	−	0.198021i
$340$		0			0
$341$	−4.16297			−0.225438
$342$	−0.596632	−	13.3852i	−0.0322621	−	0.723786i
$343$	10.9995	−	10.9995i	0.593920	−	0.593920i
$344$	0.597734	−	0.644705i	0.0322276	−	0.0347602i
$345$		0			0
$346$	8.92350	−	35.0637i	0.479730	−	1.88504i
$347$	−1.90948	−	1.90948i	−0.102506	−	0.102506i	0.653994	−	0.756500i	$-0.273092\pi$
$347$	−1.90948	−	1.90948i	−0.102506	−	0.102506i	−0.756500	+	0.653994i	$0.773092\pi$
$348$	15.0588	−	0.620262i	0.807234	−	0.0332495i
$349$	16.3562			0.875528			0.437764	−	0.899090i	$-0.355771\pi$
$349$	16.3562			0.875528			0.437764	+	0.899090i	$0.355771\pi$
$350$		0			0
$351$	−20.8342	+	22.9333i	−1.11205	+	1.22409i
$352$	13.4543	+	6.67631i	0.717118	+	0.355848i
$353$	−0.326679	−	0.326679i	−0.0173874	−	0.0173874i	0.698360	−	0.715747i	$-0.253914\pi$
$353$	−0.326679	−	0.326679i	−0.0173874	−	0.0173874i	−0.715747	+	0.698360i	$0.753914\pi$
$354$	21.4073	+	11.5571i	1.13779	+	0.614250i
$355$		0			0
$356$	−2.70801	+	4.97580i	−0.143524	+	0.263717i
$357$	−23.9126	+	14.3201i	−1.26559	+	0.757898i
$358$	4.20454	+	7.07515i	0.222217	+	0.373934i
$359$	−16.0922			−0.849315			−0.424657	−	0.905354i	$-0.639605\pi$
$359$	−16.0922			−0.849315			−0.424657	+	0.905354i	$0.639605\pi$
$360$		0			0
$361$	−9.02676			−0.475093
$362$	−2.58898	−	4.35658i	−0.136074	−	0.228977i
$363$	5.86998	−	3.51524i	0.308094	−	0.184502i
$364$	30.9629	+	16.8511i	1.62290	+	0.883239i
$365$		0			0
$366$	25.6840	+	13.8659i	1.34253	+	0.724783i
$367$	−17.3259	−	17.3259i	−0.904406	−	0.904406i	0.0914078	−	0.995814i	$-0.470863\pi$
$367$	−17.3259	−	17.3259i	−0.904406	−	0.904406i	−0.995814	+	0.0914078i	$0.970863\pi$
$368$	1.91071	−	8.90265i	0.0996028	−	0.464083i
$369$	28.0481	+	15.0200i	1.46013	+	0.781912i
$370$		0			0
$371$	−19.4015			−1.00728
$372$	0.223525	+	5.42674i	0.0115892	+	0.281364i
$373$	4.04391	+	4.04391i	0.209386	+	0.209386i	0.804006	−	0.594621i	$-0.202698\pi$
$373$	4.04391	+	4.04391i	0.209386	+	0.209386i	−0.594621	+	0.804006i	$0.702698\pi$
$374$	−5.04168	+	19.8106i	−0.260699	+	1.02438i
$375$		0			0
$376$	5.37538	+	4.98374i	0.277214	+	0.257017i
$377$	18.3445	−	18.3445i	0.944791	−	0.944791i
$378$	−4.34264	+	21.2829i	−0.223361	+	1.09468i
$379$	−9.37395			−0.481507			−0.240754	−	0.970586i	$-0.577395\pi$
$379$	−9.37395			−0.481507			−0.240754	+	0.970586i	$0.577395\pi$
$380$		0			0
$381$	26.6698	+	6.69143i	1.36633	+	0.342812i
$382$	−8.38318	−	14.1067i	−0.428921	−	0.721762i
$383$	−1.94014	−	1.94014i	−0.0991364	−	0.0991364i	0.655799	−	0.754935i	$-0.272332\pi$
$383$	−1.94014	−	1.94014i	−0.0991364	−	0.0991364i	−0.754935	+	0.655799i	$0.772332\pi$
$384$	7.98065	−	17.8972i	0.407261	−	0.913312i
$385$		0			0
$386$	−4.84915	+	19.0541i	−0.246815	+	0.969829i
$387$	0.892551	−	0.269996i	0.0453709	−	0.0137247i
$388$	−25.1302	+	7.41690i	−1.27579	+	0.376536i
$389$		−	15.7785i		−	0.800003i	−0.916515	−	0.400001i	$-0.869010\pi$
$389$		−	15.7785i		−	0.800003i	0.916515	−	0.400001i	$-0.130990\pi$
$390$		0			0
$391$	12.3926			0.626721
$392$	4.91069	−	0.185652i	0.248027	−	0.00937684i
$393$	−9.74171	+	5.83382i	−0.491404	+	0.294277i
$394$	−3.82422	−	0.973239i	−0.192661	−	0.0490310i
$395$		0			0
$396$	8.74032	+	13.3191i	0.439217	+	0.669308i
$397$	−16.1961	+	16.1961i	−0.812858	+	0.812858i	−0.985061	−	0.172204i	$-0.944911\pi$
$397$	−16.1961	+	16.1961i	−0.812858	+	0.812858i	0.172204	+	0.985061i	$0.444911\pi$
$398$	−2.95712	−	4.97607i	−0.148227	−	0.249428i
$399$	−15.6825	−	3.93472i	−0.785105	−	0.196982i
$400$		0			0
$401$			33.9532i			1.69554i	0.530362	+	0.847771i	$0.322056\pi$
$401$			33.9532i			1.69554i	−0.530362	+	0.847771i	$0.677944\pi$
$402$	−8.73678	−	29.2381i	−0.435751	−	1.45826i
$403$	6.61083	+	6.61083i	0.329309	+	0.329309i
$404$	−10.2104	+	18.7610i	−0.507987	+	0.933395i
$405$		0			0
$406$	4.48563	−	17.6257i	0.222618	−	0.874749i
$407$	−13.1197	+	13.1197i	−0.650321	+	0.650321i
$408$	26.0953	+	5.50850i	1.29191	+	0.272712i
$409$		−	11.9177i		−	0.589294i	−0.955606	−	0.294647i	$-0.904798\pi$
$409$		−	11.9177i		−	0.589294i	0.955606	−	0.294647i	$-0.0952021\pi$
$410$		0			0
$411$	0.975525	−	3.88811i	0.0481191	−	0.191786i
$412$	8.27602	+	28.0411i	0.407730	+	1.38148i
$413$	20.7588	−	20.7588i	1.02148	−	1.02148i
$414$	6.51817	−	7.12636i	0.320350	−	0.350241i
$415$		0			0
$416$	−10.7635	−	31.9676i	−0.527726	−	1.56734i
$417$	1.53313	−	0.918113i	0.0750776	−	0.0449602i
$418$	−10.1940	+	6.05799i	−0.498606	+	0.296306i
$419$		−	0.494053i		−	0.0241361i	−0.999927	−	0.0120680i	$-0.996159\pi$
$419$		−	0.494053i		−	0.0241361i	0.999927	−	0.0120680i	$-0.00384147\pi$
$420$		0			0
$421$			28.0844i			1.36875i	0.729129	+	0.684376i	$0.239925\pi$
$421$			28.0844i			1.36875i	−0.729129	+	0.684376i	$0.760075\pi$
$422$	−3.89727	−	6.55810i	−0.189716	−	0.319243i
$423$	2.25116	+	7.44186i	0.109455	+	0.361835i
$424$	13.6138	+	12.6220i	0.661145	+	0.612976i
$425$		0			0
$426$	6.24726	+	3.37267i	0.302681	+	0.163407i
$427$	24.9060	−	24.9060i	1.20529	−	1.20529i
$428$	9.42108	−	2.78053i	0.455385	−	0.134402i
$429$	26.5978	+	6.67337i	1.28415	+	0.322193i
$430$		0			0
$431$		−	8.20673i		−	0.395304i	−0.980272	−	0.197652i	$-0.936668\pi$
$431$		−	8.20673i		−	0.395304i	0.980272	−	0.197652i	$-0.0633316\pi$
$432$	16.8931	−	12.1088i	0.812770	−	0.582585i
$433$	8.09993	−	8.09993i	0.389258	−	0.389258i	−0.485165	−	0.874423i	$-0.661240\pi$
$433$	8.09993	−	8.09993i	0.389258	−	0.389258i	0.874423	+	0.485165i	$0.161240\pi$
$434$	6.35179	+	1.61649i	0.304896	+	0.0775941i
$435$		0			0
$436$	−2.56179	+	4.70713i	−0.122687	+	0.225431i
$437$	5.08325	+	5.08325i	0.243165	+	0.243165i
$438$	−2.27893	−	7.62655i	−0.108892	−	0.364411i
$439$		−	5.21928i		−	0.249103i	−0.992213	−	0.124551i	$-0.960251\pi$
$439$		−	5.21928i		−	0.249103i	0.992213	−	0.124551i	$-0.0397491\pi$
$440$		0			0
$441$	4.59492	+	2.46062i	0.218806	+	0.117173i
$442$	39.4657	−	23.4532i	1.87719	−	1.11556i
$443$	−21.7308	+	21.7308i	−1.03246	+	1.03246i	−0.0330087	+	0.999455i	$0.510509\pi$
$443$	−21.7308	+	21.7308i	−1.03246	+	1.03246i	−0.999455	+	0.0330087i	$0.989491\pi$
$444$	17.8070	+	16.3981i	0.845082	+	0.778219i
$445$		0			0
$446$	−1.30170	+	5.11487i	−0.0616374	+	0.242196i
$447$	−3.20603	−	5.35364i	−0.151640	−	0.253219i
$448$	−17.9360	−	15.4109i	−0.847394	−	0.728099i
$449$	0.611967			0.0288805			0.0144403	−	0.999896i	$-0.495403\pi$
$449$	0.611967			0.0288805			0.0144403	+	0.999896i	$0.495403\pi$
$450$		0			0
$451$		−	28.1592i		−	1.32596i
$452$	16.5921	−	4.89698i	0.780428	−	0.230335i
$453$	−20.3556	+	12.1899i	−0.956388	+	0.572732i
$454$	−10.9077	−	2.77595i	−0.511925	−	0.130282i
$455$		0			0
$456$	8.44440	+	12.9634i	0.395445	+	0.607067i
$457$	3.44344	+	3.44344i	0.161077	+	0.161077i	0.783044	−	0.621967i	$-0.213666\pi$
$457$	3.44344	+	3.44344i	0.161077	+	0.161077i	−0.621967	+	0.783044i	$0.713666\pi$
$458$	13.6551	−	8.11480i	0.638061	−	0.379180i
$459$	20.9381	+	19.0216i	0.977305	+	0.887853i
$460$		0			0
$461$	0.294401			0.0137116			0.00685580	−	0.999976i	$-0.497818\pi$
$461$	0.294401			0.0137116			0.00685580	+	0.999976i	$0.497818\pi$
$462$	18.4197	−	5.50409i	0.856961	−	0.256073i
$463$	−9.79796	+	9.79796i	−0.455350	+	0.455350i	−0.897126	−	0.441776i	$-0.854349\pi$
$463$	−9.79796	+	9.79796i	−0.455350	+	0.455350i	0.441776	+	0.897126i	$0.354349\pi$
$464$	−14.6142	+	9.44955i	−0.678446	+	0.438684i
$465$		0			0
$466$	29.2118	+	7.43423i	1.35321	+	0.344384i
$467$	18.8562	+	18.8562i	0.872561	+	0.872561i	0.992751	−	0.120190i	$-0.0383504\pi$
$467$	18.8562	+	18.8562i	0.872561	+	0.872561i	−0.120190	+	0.992751i	$0.538350\pi$
$468$	7.27110	−	35.0305i	0.336107	−	1.61929i
$469$	−36.8245			−1.70040
$470$		0			0
$471$	−4.33262	+	17.2684i	−0.199637	+	0.795684i
$472$	−28.0712	+	1.06125i	−1.29208	+	0.0488480i
$473$	−0.583575	−	0.583575i	−0.0268328	−	0.0268328i
$474$	−19.4567	−	10.5040i	−0.893674	−	0.482463i
$475$		0			0
$476$	15.3850	−	28.2690i	0.705172	−	1.29571i
$477$	5.70133	+	18.8474i	0.261046	+	0.862964i
$478$	3.52366	−	2.09400i	0.161169	−	0.0957774i
$479$	18.9906			0.867702			0.433851	−	0.900985i	$-0.357154\pi$
$479$	18.9906			0.867702			0.433851	+	0.900985i	$0.357154\pi$
$480$		0			0
$481$	41.6685			1.89992
$482$	0.670968	−	0.398735i	0.0305617	−	0.0181619i
$483$	−5.98769	−	9.99866i	−0.272449	−	0.454955i
$484$	−3.77666	+	6.93938i	−0.171666	+	0.315426i
$485$		0			0
$486$	21.9512	−	2.03559i	0.995728	−	0.0923361i
$487$	12.0580	+	12.0580i	0.546399	+	0.546399i	0.925397	−	0.378998i	$-0.123731\pi$
$487$	12.0580	+	12.0580i	0.546399	+	0.546399i	−0.378998	+	0.925397i	$0.623731\pi$
$488$	−33.6792	+	1.27327i	−1.52459	+	0.0576381i
$489$	22.5854	+	5.66666i	1.02135	+	0.256255i
$490$		0			0
$491$	−18.1797			−0.820439			−0.410219	−	0.911987i	$-0.634548\pi$
$491$	−18.1797			−0.820439			−0.410219	+	0.911987i	$0.634548\pi$
$492$	−36.7076	+	1.51197i	−1.65491	+	0.0681647i
$493$	−16.7485	−	16.7485i	−0.754314	−	0.754314i
$494$	25.8084	+	6.56806i	1.16117	+	0.295511i
$495$		0			0
$496$	−3.40534	−	5.26653i	−0.152904	−	0.236474i
$497$	6.05801	−	6.05801i	0.271739	−	0.271739i
$498$	−9.70770	−	32.4873i	−0.435012	−	1.45579i
$499$	−24.8457			−1.11225			−0.556124	−	0.831100i	$-0.687712\pi$
$499$	−24.8457			−1.11225			−0.556124	+	0.831100i	$0.687712\pi$
$500$		0			0
$501$	−8.59235	+	34.2462i	−0.383878	+	1.53001i
$502$	7.65541	−	4.54937i	0.341678	−	0.203048i
$503$	17.0078	+	17.0078i	0.758340	+	0.758340i	0.976020	−	0.217680i	$-0.0698490\pi$
$503$	17.0078	+	17.0078i	0.758340	+	0.758340i	−0.217680	+	0.976020i	$0.569849\pi$
$504$	−8.16401	−	23.7159i	−0.363654	−	1.05639i
$505$		0			0
$506$	−8.28347	−	2.10809i	−0.368245	−	0.0937161i
$507$	−20.0717	−	33.5172i	−0.891418	−	1.48855i
$508$	−30.4515	+	8.98743i	−1.35107	+	0.398753i
$509$			26.1925i			1.16096i	0.814274	+	0.580481i	$0.197135\pi$
$509$			26.1925i			1.16096i	−0.814274	+	0.580481i	$0.802865\pi$
$510$		0			0
$511$	−9.60542			−0.424919
$512$	2.55962	+	22.4822i	0.113120	+	0.993581i
$513$	0.786102	+	16.3908i	0.0347073	+	0.723673i
$514$	−5.38562	+	21.1621i	−0.237549	+	0.933420i
$515$		0			0
$516$	−0.729399	+	0.792068i	−0.0321100	+	0.0348688i
$517$	4.86569	−	4.86569i	0.213993	−	0.213993i
$518$	25.1123	−	14.9234i	1.10337	−	0.655699i
$519$	−10.7839	+	42.9808i	−0.473359	+	1.88665i
$520$		0			0
$521$			21.5789i			0.945388i	0.881227	+	0.472694i	$0.156718\pi$
$521$			21.5789i			0.945388i	−0.881227	+	0.472694i	$0.843282\pi$
$522$	−18.4405	+	0.821968i	−0.807118	+	0.0359766i
$523$	−1.75051	−	1.75051i	−0.0765445	−	0.0765445i	0.667798	−	0.744343i	$-0.267237\pi$
$523$	−1.75051	−	1.75051i	−0.0765445	−	0.0765445i	−0.744343	+	0.667798i	$0.767237\pi$
$524$	6.26767	−	11.5165i	0.273804	−	0.503099i
$525$		0			0
$526$	−40.8878	−	10.4057i	−1.78279	−	0.453709i
$527$	6.03567	−	6.03567i	0.262918	−	0.262918i
$528$	−16.5056	−	8.12105i	−0.718316	−	0.353424i
$529$		−	17.8182i		−	0.774707i
$530$		0			0
$531$	−26.2662	−	14.0658i	−1.13985	−	0.610403i
$532$	17.9062	−	5.28482i	0.776333	−	0.229126i
$533$	−44.7170	+	44.7170i	−1.93691	+	1.93691i
$534$	3.29601	−	6.10526i	0.142632	−	0.264200i
$535$		0			0
$536$	25.8393	+	23.9567i	1.11609	+	1.03477i
$537$	−5.17874	−	8.64781i	−0.223479	−	0.373181i
$538$	14.8913	+	25.0583i	0.642011	+	1.08034i
$539$		−	4.61311i		−	0.198701i
$540$		0			0
$541$			22.6515i			0.973864i	0.873440	+	0.486932i	$0.161884\pi$
$541$			22.6515i			0.973864i	−0.873440	+	0.486932i	$0.838116\pi$
$542$	−29.5341	+	17.5512i	−1.26860	+	0.753889i
$543$	3.18885	+	5.32496i	0.136847	+	0.228516i
$544$	−29.1863	+	9.82709i	−1.25135	+	0.421333i
$545$		0			0
$546$	−37.9912	−	20.5101i	−1.62587	−	0.877751i
$547$	24.2626	−	24.2626i	1.03739	−	1.03739i	0.0381200	−	0.999273i	$-0.487863\pi$
$547$	24.2626	−	24.2626i	1.03739	−	1.03739i	0.999273	−	0.0381200i	$-0.0121369\pi$
$548$	1.31025	+	4.43944i	0.0559712	+	0.189644i
$549$	−31.5136	−	16.8758i	−1.34497	−	0.720243i
$550$		0			0
$551$		−	13.7399i		−	0.585341i
$552$	−2.30329	+	10.9113i	−0.0980344	+	0.464417i
$553$	−18.8673	+	18.8673i	−0.802318	+	0.802318i
$554$	−6.23937	+	24.5168i	−0.265085	+	1.04162i
$555$		0			0
$556$	−0.986391	+	1.81243i	−0.0418323	+	0.0768643i
$557$	−14.5141	−	14.5141i	−0.614984	−	0.614984i	0.329257	−	0.944240i	$-0.393202\pi$
$557$	−14.5141	−	14.5141i	−0.614984	−	0.614984i	−0.944240	+	0.329257i	$0.893202\pi$
$558$	−0.296214	−	6.64541i	−0.0125397	−	0.281323i
$559$			1.85344i			0.0783923i
$560$		0			0
$561$	6.09277	−	24.2837i	0.257237	−	1.02526i
$562$	−6.37040	−	10.7197i	−0.268719	−	0.452185i
$563$	4.09672	−	4.09672i	0.172656	−	0.172656i	−0.615489	−	0.788145i	$-0.711042\pi$
$563$	4.09672	−	4.09672i	0.172656	−	0.172656i	0.788145	+	0.615489i	$0.211042\pi$
$564$	−6.60405	−	6.08154i	−0.278081	−	0.256079i
$565$		0			0
$566$	26.1519	+	6.65549i	1.09925	+	0.279751i
$567$	5.23053	−	26.0840i	0.219662	−	1.09542i
$568$	−8.19196	+	0.309703i	−0.343727	+	0.0129948i
$569$	−27.6005			−1.15707			−0.578536	−	0.815657i	$-0.696376\pi$
$569$	−27.6005			−1.15707			−0.578536	+	0.815657i	$0.696376\pi$
$570$		0			0
$571$		−	32.2742i		−	1.35063i	−0.737528	−	0.675317i	$-0.764007\pi$
$571$		−	32.2742i		−	1.35063i	0.737528	−	0.675317i	$-0.235993\pi$
$572$	−30.3693	+	8.96317i	−1.26980	+	0.374769i
$573$	10.3256	+	17.2423i	0.431357	+	0.720309i
$574$	−10.9343	+	42.9648i	−0.456388	+	1.79332i
$575$		0			0
$576$	−9.70015	+	21.9524i	−0.404173	+	0.914683i
$577$	−5.10163	−	5.10163i	−0.212384	−	0.212384i	0.592896	−	0.805279i	$-0.297985\pi$
$577$	−5.10163	−	5.10163i	−0.212384	−	0.212384i	−0.805279	+	0.592896i	$0.797985\pi$
$578$	−9.13063	−	15.3645i	−0.379784	−	0.639078i
$579$	5.86010	−	23.3564i	0.243537	−	0.970657i
$580$		0			0
$581$	−40.9168			−1.69751
$582$	30.7472	−	9.18774i	1.27451	−	0.380844i
$583$	12.3230	−	12.3230i	0.510365	−	0.510365i
$584$	6.74001	+	6.24895i	0.278904	+	0.258584i
$585$		0			0
$586$	−3.37538	+	13.2631i	−0.139436	+	0.547894i
$587$	3.37004	+	3.37004i	0.139097	+	0.139097i	0.773227	−	0.634130i	$-0.218642\pi$
$587$	3.37004	+	3.37004i	0.139097	+	0.139097i	−0.634130	+	0.773227i	$0.718642\pi$
$588$	−6.01354	+	0.247694i	−0.247994	+	0.0102147i
$589$	4.95148			0.204022
$590$		0			0
$591$	4.68769	+	1.17614i	0.192826	+	0.0483799i
$592$	−27.3297	−	5.86557i	−1.12324	−	0.241074i
$593$	16.9693	+	16.9693i	0.696844	+	0.696844i	0.963729	−	0.266884i	$-0.0859941\pi$
$593$	16.9693	+	16.9693i	0.696844	+	0.696844i	−0.266884	+	0.963729i	$0.585994\pi$
$594$	−10.7597	−	16.2762i	−0.441476	−	0.667821i
$595$		0			0
$596$	6.32897	+	3.44445i	0.259245	+	0.141090i
$597$	3.64229	+	6.08214i	0.149069	+	0.248926i
$598$	9.80656	+	16.5019i	0.401020	+	0.674813i
$599$	−1.04438			−0.0426723			−0.0213361	−	0.999772i	$-0.506792\pi$
$599$	−1.04438			−0.0426723			−0.0213361	+	0.999772i	$0.506792\pi$
$600$		0			0
$601$	0.244816			0.00998624			0.00499312	−	0.999988i	$-0.498411\pi$
$601$	0.244816			0.00998624			0.00499312	+	0.999988i	$0.498411\pi$
$602$	0.663806	+	1.11701i	0.0270547	+	0.0455260i
$603$	10.8212	+	35.7728i	0.440675	+	1.45678i
$604$	13.0965	−	24.0639i	0.532887	−	0.979148i
$605$		0			0
$606$	12.4275	−	23.0196i	0.504831	−	0.935106i
$607$	3.95241	+	3.95241i	0.160423	+	0.160423i	0.782754	−	0.622331i	$-0.213814\pi$
$607$	3.95241	+	3.95241i	0.160423	+	0.160423i	−0.622331	+	0.782754i	$0.713814\pi$
$608$	−16.0027	−	7.94086i	−0.648995	−	0.322045i
$609$	−5.42079	+	21.6054i	−0.219661	+	0.875496i
$610$		0			0
$611$	−15.4535			−0.625183
$612$	−31.9828	−	6.63850i	−1.29283	−	0.268345i
$613$	−21.0245	−	21.0245i	−0.849172	−	0.849172i	0.140858	−	0.990030i	$-0.455014\pi$
$613$	−21.0245	−	21.0245i	−0.849172	−	0.849172i	−0.990030	+	0.140858i	$0.955014\pi$
$614$	2.62297	−	10.3066i	0.105854	−	0.415941i
$615$		0			0
$616$	−15.0925	+	16.2785i	−0.608094	+	0.655879i
$617$	−18.7366	+	18.7366i	−0.754307	+	0.754307i	−0.975280	−	0.220973i	$-0.929077\pi$
$617$	−18.7366	+	18.7366i	−0.754307	+	0.754307i	0.220973	+	0.975280i	$0.429077\pi$
$618$	−10.2520	−	34.3087i	−0.412395	−	1.38010i
$619$	−8.66233			−0.348169			−0.174084	−	0.984731i	$-0.555697\pi$
$619$	−8.66233			−0.348169			−0.174084	+	0.984731i	$0.555697\pi$
$620$		0			0
$621$	−7.95356	+	8.75489i	−0.319165	+	0.351322i
$622$	−22.6604	−	38.1316i	−0.908600	−	1.52894i
$623$	−5.92031	−	5.92031i	−0.237192	−	0.237192i
$624$	13.3148	+	39.1074i	0.533018	+	1.56555i
$625$		0			0
$626$	2.67508	−	10.5114i	0.106918	−	0.420119i
$627$	12.4599	−	7.46163i	0.497602	−	0.297989i
$628$	−5.81925	−	19.7170i	−0.232214	−	0.786794i
$629$		−	38.0432i		−	1.51688i
$630$		0			0
$631$	−1.38183			−0.0550097			−0.0275049	−	0.999622i	$-0.508756\pi$
$631$	−1.38183			−0.0550097			−0.0275049	+	0.999622i	$0.508756\pi$
$632$	25.5133	−	0.964549i	1.01487	−	0.0383677i
$633$	4.80028	+	8.01583i	0.190794	+	0.318601i
$634$	24.9086	+	6.33907i	0.989246	+	0.251757i
$635$		0			0
$636$	−16.7256	−	15.4023i	−0.663212	−	0.610739i
$637$	−7.32566	+	7.32566i	−0.290253	+	0.290253i
$638$	8.34598	+	14.0441i	0.330421	+	0.556012i
$639$	−7.66521	−	4.10479i	−0.303231	−	0.162383i
$640$		0			0
$641$		−	32.1844i		−	1.27121i	−0.772015	−	0.635604i	$-0.780751\pi$
$641$		−	32.1844i		−	1.27121i	0.772015	−	0.635604i	$-0.219249\pi$
$642$	−11.5268	+	3.44440i	−0.454928	+	0.135940i
$643$	13.8136	+	13.8136i	0.544755	+	0.544755i	0.924919	−	0.380164i	$-0.124132\pi$
$643$	13.8136	+	13.8136i	0.544755	+	0.544755i	−0.380164	+	0.924919i	$0.624132\pi$
$644$	11.8202	+	6.43298i	0.465782	+	0.253495i
$645$		0			0
$646$	5.99662	−	23.5630i	0.235934	−	0.927072i
$647$	−15.5057	+	15.5057i	−0.609594	+	0.609594i	−0.942840	−	0.333246i	$-0.891856\pi$
$647$	−15.5057	+	15.5057i	−0.609594	+	0.609594i	0.333246	+	0.942840i	$0.391856\pi$
$648$	−20.6395	+	14.9000i	−0.810797	+	0.585328i
$649$			26.3701i			1.03512i
$650$		0			0
$651$	−7.78597	−	1.95350i	−0.305156	−	0.0765635i
$652$	−25.7880	+	7.61103i	−1.00993	+	0.298071i
$653$	17.9422	−	17.9422i	0.702132	−	0.702132i	−0.262736	−	0.964868i	$-0.584625\pi$
$653$	17.9422	−	17.9422i	0.702132	−	0.702132i	0.964868	+	0.262736i	$0.0846248\pi$
$654$	3.11804	−	5.77560i	0.121925	−	0.225844i
$655$		0			0
$656$	35.6238	−	23.0344i	1.39088	−	0.899343i
$657$	2.82265	+	9.33110i	0.110122	+	0.364041i
$658$	−9.31335	+	5.53463i	−0.363072	+	0.215763i
$659$		−	39.4445i		−	1.53654i	−0.640127	−	0.768269i	$-0.721118\pi$
$659$		−	39.4445i		−	1.53654i	0.640127	−	0.768269i	$-0.278882\pi$
$660$		0			0
$661$		−	7.69555i		−	0.299322i	−0.988737	−	0.149661i	$-0.952182\pi$
$661$		−	7.69555i		−	0.299322i	0.988737	−	0.149661i	$-0.0478183\pi$
$662$	−7.68964	−	12.9397i	−0.298866	−	0.502915i
$663$	−48.2381	+	28.8874i	−1.87341	+	1.12189i
$664$	28.7108	+	26.6190i	1.11420	+	1.03302i
$665$		0			0
$666$	−21.8767	−	20.0097i	−0.847707	−	0.775360i
$667$	7.00310	−	7.00310i	0.271161	−	0.271161i
$668$	−11.5406	−	39.1023i	−0.446520	−	1.51291i
$669$	1.57308	−	6.26976i	0.0608188	−	0.242403i
$670$		0			0
$671$			31.6383i			1.22138i
$672$	22.0306	+	18.8001i	0.849849	+	0.725231i
$673$	−2.37397	+	2.37397i	−0.0915096	+	0.0915096i	−0.751380	−	0.659870i	$-0.770611\pi$
$673$	−2.37397	+	2.37397i	−0.0915096	+	0.0915096i	0.659870	+	0.751380i	$0.270611\pi$
$674$	1.12724	+	0.286875i	0.0434196	+	0.0110500i
$675$		0			0
$676$	39.6233	+	21.5644i	1.52397	+	0.829402i
$677$	6.61424	+	6.61424i	0.254206	+	0.254206i	0.822693	−	0.568487i	$-0.192471\pi$
$677$	6.61424	+	6.61424i	0.254206	+	0.254206i	−0.568487	+	0.822693i	$0.692471\pi$
$678$	−20.3007	+	6.06617i	−0.779645	+	0.232970i
$679$		−	38.7252i		−	1.48614i
$680$		0			0
$681$	13.3706	+	3.35468i	0.512363	+	0.128552i
$682$	−5.06110	+	3.00765i	−0.193799	+	0.115169i
$683$	−14.3187	+	14.3187i	−0.547889	+	0.547889i	−0.925830	−	0.377941i	$-0.876632\pi$
$683$	−14.3187	+	14.3187i	−0.547889	+	0.547889i	0.377941	+	0.925830i	$0.376632\pi$
$684$	−10.3958	−	15.8418i	−0.397494	−	0.605728i
$685$		0			0
$686$	5.42568	−	21.3195i	0.207154	−	0.813983i
$687$	−16.6903	+	9.99500i	−0.636776	+	0.381333i
$688$	0.260905	−	1.21564i	0.00994691	−	0.0463460i
$689$	−39.1380			−1.49104
$690$		0			0
$691$			36.4559i			1.38685i	0.720529	+	0.693425i	$0.243899\pi$
$691$			36.4559i			1.38685i	−0.720529	+	0.693425i	$0.756101\pi$
$692$	−14.4841	−	49.0754i	−0.550602	−	1.86557i
$693$	−22.5365	+	6.81728i	−0.856091	+	0.258967i
$694$	−3.70098	−	0.941876i	−0.140487	−	0.0357531i
$695$		0			0
$696$	17.8594	−	11.6337i	0.676960	−	0.440974i
$697$	40.8265	+	40.8265i	1.54641	+	1.54641i
$698$	19.8849	−	11.8170i	0.752655	−	0.447279i
$699$	−35.8076	−	8.98411i	−1.35437	−	0.339810i
$700$		0			0
$701$	48.0342			1.81423			0.907113	−	0.420887i	$-0.138281\pi$
$701$	48.0342			1.81423			0.907113	+	0.420887i	$0.138281\pi$
$702$	−8.76025	+	42.9333i	−0.330634	+	1.62041i
$703$	15.6047	−	15.6047i	0.588544	−	0.588544i
$704$	21.1804	−	1.60378i	0.798268	−	0.0604446i
$705$		0			0
$706$	−0.633175	−	0.161139i	−0.0238299	−	0.00606455i
$707$	−22.3222	−	22.3222i	−0.839515	−	0.839515i
$708$	34.3755	−	1.41591i	1.29191	−	0.0532130i
$709$	6.97929			0.262113			0.131056	−	0.991375i	$-0.458163\pi$
$709$	6.97929			0.262113			0.131056	+	0.991375i	$0.458163\pi$
$710$		0			0
$711$	23.8728	+	12.7841i	0.895299	+	0.479441i
$712$	0.302663	+	8.00576i	0.0113428	+	0.300029i
$713$	2.52371	+	2.52371i	0.0945138	+	0.0945138i
$714$	−18.7257	+	34.6858i	−0.700790	+	1.29808i
$715$		0			0
$716$	10.2233	+	5.56387i	0.382062	+	0.207932i
$717$	−4.30690	+	2.57918i	−0.160844	+	0.0963214i
$718$	−19.5640	+	11.6263i	−0.730121	+	0.433888i
$719$	2.63485			0.0982634			0.0491317	−	0.998792i	$-0.484355\pi$
$719$	2.63485			0.0982634			0.0491317	+	0.998792i	$0.484355\pi$
$720$		0			0
$721$	−43.2108			−1.60926
$722$	−10.9742	+	6.52163i	−0.408418	+	0.242710i
$723$	−0.820109	+	0.491122i	−0.0305002	+	0.0182650i
$724$	−6.29506	−	3.42600i	−0.233954	−	0.127326i
$725$		0			0
$726$	4.59670	−	8.51455i	0.170600	−	0.316005i
$727$	−5.55176	−	5.55176i	−0.205903	−	0.205903i	0.596620	−	0.802524i	$-0.296510\pi$
$727$	−5.55176	−	5.55176i	−0.205903	−	0.205903i	−0.802524	+	0.596620i	$0.796510\pi$
$728$	49.8174	−	1.88338i	1.84636	−	0.0698028i
$729$	−26.8761	+	2.58389i	−0.995410	+	0.0956996i
$730$		0			0
$731$	1.69219			0.0625879
$732$	41.2429	−	1.69877i	1.52438	−	0.0627885i
$733$	−10.2051	−	10.2051i	−0.376934	−	0.376934i	0.493061	−	0.869995i	$-0.335878\pi$
$733$	−10.2051	−	10.2051i	−0.376934	−	0.376934i	−0.869995	+	0.493061i	$0.835878\pi$
$734$	−33.5814	−	8.54626i	−1.23951	−	0.315448i
$735$		0			0
$736$	−4.10903	−	12.2038i	−0.151461	−	0.449837i
$737$	23.3893	−	23.3893i	0.861554	−	0.861554i
$738$	44.9509	−	2.00365i	1.65467	−	0.0737553i
$739$	−33.7165			−1.24028			−0.620141	−	0.784490i	$-0.712925\pi$
$739$	−33.7165			−1.24028			−0.620141	+	0.784490i	$0.712925\pi$
$740$		0			0
$741$	−31.6356	−	7.93737i	−1.16216	−	0.291586i
$742$	−23.5872	+	14.0172i	−0.865914	+	0.514586i
$743$	14.9523	+	14.9523i	0.548546	+	0.548546i	0.926020	−	0.377474i	$-0.123207\pi$
$743$	14.9523	+	14.9523i	0.548546	+	0.548546i	−0.377474	+	0.926020i	$0.623207\pi$
$744$	4.19245	+	6.43602i	0.153703	+	0.235956i
$745$		0			0
$746$	7.83798	+	1.99472i	0.286969	+	0.0730317i
$747$	12.0238	+	39.7482i	0.439928	+	1.45431i
$748$	8.18335	+	27.7271i	0.299213	+	1.01380i
$749$			14.5177i			0.530466i
$750$		0			0
$751$	29.4194			1.07353			0.536764	−	0.843733i	$-0.319647\pi$
$751$	29.4194			1.07353			0.536764	+	0.843733i	$0.319647\pi$
$752$	10.1357	+	2.17536i	0.369611	+	0.0793271i
$753$	−9.35705	+	5.60346i	−0.340990	+	0.204202i
$754$	9.04869	−	35.5557i	0.329534	−	1.29486i
$755$		0			0
$756$	10.0969	+	29.0120i	0.367221	+	1.05516i
$757$	−9.10219	+	9.10219i	−0.330825	+	0.330825i	−0.852900	−	0.522075i	$-0.825158\pi$
$757$	−9.10219	+	9.10219i	−0.330825	+	0.330825i	0.522075	+	0.852900i	$0.325158\pi$
$758$	−11.3963	+	6.77246i	−0.413932	+	0.245987i
$759$	10.1538	+	2.54758i	0.368560	+	0.0924715i
$760$		0			0
$761$			19.4230i			0.704083i	0.935984	+	0.352042i	$0.114512\pi$
$761$			19.4230i			0.704083i	−0.935984	+	0.352042i	$0.885488\pi$
$762$	37.2579	−	11.1332i	1.34971	−	0.403315i
$763$	−5.60064	−	5.60064i	−0.202757	−	0.202757i
$764$	−20.3836	−	11.0935i	−0.737451	−	0.401347i
$765$		0			0
$766$	−3.76041	−	0.957001i	−0.135869	−	0.0345778i
$767$	41.8760	−	41.8760i	1.51206	−	1.51206i
$768$	−3.22789	−	27.5242i	−0.116477	−	0.993193i
$769$		−	1.26203i		−	0.0455101i	−0.999741	−	0.0227551i	$-0.992756\pi$
$769$		−	1.26203i		−	0.0455101i	0.999741	−	0.0227551i	$-0.00724379\pi$
$770$		0			0
$771$	6.50841	−	25.9403i	0.234395	−	0.934217i
$772$	7.87085	+	26.6683i	0.283278	+	0.959812i
$773$	−13.6782	+	13.6782i	−0.491971	+	0.491971i	−0.908927	−	0.416956i	$-0.863097\pi$
$773$	−13.6782	+	13.6782i	−0.491971	+	0.491971i	0.416956	+	0.908927i	$0.363097\pi$
$774$	0.890046	−	0.973093i	0.0319920	−	0.0349771i
$775$		0			0
$776$	−25.1933	+	27.1730i	−0.904386	+	0.975455i
$777$	−30.6942	+	18.3812i	−1.10115	+	0.659423i
$778$	−11.3996	−	19.1826i	−0.408696	−	0.687729i
$779$			33.4928i			1.20000i
$780$		0			0
$781$			7.69555i			0.275368i
$782$	15.0662	−	8.95337i	0.538766	−	0.320172i
$783$	22.5813	−	1.08300i	0.806991	−	0.0387032i
$784$	5.83600	−	3.77356i	0.208428	−	0.134770i
$785$		0			0
$786$	−7.62860	+	14.1306i	−0.272103	+	0.504021i
$787$	1.64945	−	1.64945i	0.0587966	−	0.0587966i	−0.677097	−	0.735894i	$-0.736762\pi$
$787$	1.64945	−	1.64945i	0.0587966	−	0.0587966i	0.735894	+	0.677097i	$0.236762\pi$
$788$	−5.35240	+	1.57970i	−0.190671	+	0.0562745i
$789$	50.1199	+	12.5750i	1.78431	+	0.447683i
$790$		0			0
$791$			25.5682i			0.909100i
$792$	20.2487	+	9.87787i	0.719506	+	0.350995i
$793$	50.2420	−	50.2420i	1.78414	−	1.78414i
$794$	−7.98895	+	31.3915i	−0.283517	+	1.11404i
$795$		0			0
$796$	−7.19019	−	3.91316i	−0.254850	−	0.138698i
$797$	15.2015	+	15.2015i	0.538466	+	0.538466i	0.923078	−	0.384612i	$-0.125665\pi$
$797$	15.2015	+	15.2015i	0.538466	+	0.538466i	−0.384612	+	0.923078i	$0.625665\pi$
$798$	−21.9086	+	6.54661i	−0.775554	+	0.231748i
$799$			14.1090i			0.499141i
$800$		0			0
$801$	−4.01149	+	7.49098i	−0.141739	+	0.264681i
$802$	24.5304	+	41.2783i	0.866199	+	1.45759i
$803$	6.10093	−	6.10093i	0.215297	−	0.215297i
$804$	−31.7455	−	29.2338i	−1.11958	−	1.03100i
$805$		0			0
$806$	12.8132	+	3.26089i	0.451327	+	0.114860i
$807$	−18.3417	−	30.6282i	−0.645657	−	1.07816i
$808$	1.14118	+	30.1853i	0.0401465	+	1.06192i
$809$	44.9347			1.57982			0.789910	−	0.613223i	$-0.210127\pi$
$809$	44.9347			1.57982			0.789910	+	0.613223i	$0.210127\pi$
$810$		0			0
$811$			23.8947i			0.839055i	0.907743	+	0.419528i	$0.137804\pi$
$811$			23.8947i			0.839055i	−0.907743	+	0.419528i	$0.862196\pi$
$812$	−7.28080	−	24.6691i	−0.255506	−	0.865714i
$813$	36.0990	−	21.6178i	1.26605	−	0.758171i
$814$	−6.47149	+	25.4289i	−0.226826	+	0.891282i
$815$		0			0
$816$	35.7050	−	12.1564i	1.24992	−	0.425558i
$817$	0.694110	+	0.694110i	0.0242838	+	0.0242838i
$818$	−8.61029	−	14.4889i	−0.301052	−	0.506592i
$819$	46.6141	+	24.9623i	1.62883	+	0.872253i
$820$		0			0
$821$	−43.1420			−1.50567			−0.752833	−	0.658212i	$-0.771313\pi$
$821$	−43.1420			−1.50567			−0.752833	+	0.658212i	$0.771313\pi$
$822$	−1.62309	−	5.43173i	−0.0566116	−	0.189454i
$823$	29.4978	−	29.4978i	1.02823	−	1.02823i	0.0286405	−	0.999590i	$-0.490882\pi$
$823$	29.4978	−	29.4978i	1.02823	−	1.02823i	0.999590	−	0.0286405i	$-0.00911780\pi$
$824$	30.3205	+	28.1115i	1.05627	+	0.979309i
$825$		0			0
$826$	10.2396	−	40.2351i	0.356281	−	1.39996i
$827$	−32.6568	−	32.6568i	−1.13559	−	1.13559i	−0.989232	−	0.146357i	$-0.953245\pi$
$827$	−32.6568	−	32.6568i	−1.13559	−	1.13559i	−0.146357	−	0.989232i	$-0.546755\pi$
$828$	2.77577	−	13.3730i	0.0964648	−	0.464745i
$829$	19.3767			0.672980			0.336490	−	0.941687i	$-0.390760\pi$
$829$	19.3767			0.672980			0.336490	+	0.941687i	$0.390760\pi$
$830$		0			0
$831$	7.54014	−	30.0524i	0.261565	−	1.04251i
$832$	−36.1815	−	31.0879i	−1.25437	−	1.07778i
$833$	6.68831	+	6.68831i	0.231736	+	0.231736i
$834$	1.20057	−	2.22384i	0.0415724	−	0.0770052i
$835$		0			0
$836$	−8.01654	+	14.7299i	−0.277258	+	0.509444i
$837$	0.390281	+	8.13766i	0.0134901	+	0.281279i
$838$	−0.356942	−	0.600640i	−0.0123304	−	0.0207488i
$839$	38.4795			1.32846			0.664229	−	0.747529i	$-0.268760\pi$
$839$	38.4795			1.32846			0.664229	+	0.747529i	$0.268760\pi$
$840$		0			0
$841$	10.0707			0.347267
$842$	20.2904	+	34.1434i	0.699252	+	1.17666i
$843$	7.84643	+	13.1025i	0.270245	+	0.451274i
$844$	−9.47616	−	5.15726i	−0.326183	−	0.177520i
$845$		0			0
$846$	8.11339	+	7.42096i	0.278944	+	0.255138i
$847$	−8.25662	−	8.25662i	−0.283701	−	0.283701i
$848$	25.6699	+	5.50936i	0.881510	+	0.189192i
$849$	−32.0568	−	8.04302i	−1.10019	−	0.276036i
$850$		0			0
$851$	15.9071			0.545289
$852$	10.0317	−	0.413201i	0.343681	−	0.0141560i
$853$	20.0303	+	20.0303i	0.685823	+	0.685823i	0.961306	−	0.275483i	$-0.0888378\pi$
$853$	20.0303	+	20.0303i	0.685823	+	0.685823i	−0.275483	+	0.961306i	$0.588838\pi$
$854$	12.2852	−	48.2733i	0.420392	−	1.65188i
$855$		0			0
$856$	9.44472	−	10.1869i	0.322814	−	0.348181i
$857$	−24.3417	+	24.3417i	−0.831496	+	0.831496i	−0.987721	−	0.156226i	$-0.950067\pi$
$857$	−24.3417	+	24.3417i	−0.831496	+	0.831496i	0.156226	+	0.987721i	$0.450067\pi$
$858$	37.1574	−	11.1032i	1.26853	−	0.379057i
$859$	43.4501			1.48250			0.741249	−	0.671230i	$-0.234234\pi$
$859$	43.4501			1.48250			0.741249	+	0.671230i	$0.234234\pi$
$860$		0			0
$861$	13.2138	−	52.6659i	0.450326	−	1.79485i
$862$	−5.92917	−	9.97726i	−0.201948	−	0.339827i
$863$	−16.6773	−	16.6773i	−0.567701	−	0.567701i	0.363783	−	0.931484i	$-0.381485\pi$
$863$	−16.6773	−	16.6773i	−0.567701	−	0.567701i	−0.931484	+	0.363783i	$0.881485\pi$
$864$	11.7893	−	26.9260i	0.401081	−	0.916043i
$865$		0			0
$866$	3.99541	−	15.6994i	0.135769	−	0.533488i
$867$	11.2462	+	18.7797i	0.381941	+	0.637791i
$868$	8.89002	−	2.62379i	0.301747	−	0.0890572i
$869$		−	23.9673i		−	0.813034i
$870$		0			0
$871$	−74.2847			−2.51704
$872$	0.286321	+	7.57348i	0.00969604	+	0.256470i
$873$	−37.6193	+	11.3798i	−1.27322	+	0.385148i
$874$	9.85245	+	2.50738i	0.333264	+	0.0848136i
$875$		0			0
$876$	−8.28060	−	7.62544i	−0.279776	−	0.257640i
$877$	0.209733	−	0.209733i	0.00708216	−	0.00708216i	−0.703557	−	0.710639i	$-0.748406\pi$
$877$	0.209733	−	0.209733i	0.00708216	−	0.00708216i	0.710639	+	0.703557i	$0.248406\pi$
$878$	−3.77081	−	6.34529i	−0.127259	−	0.214143i
$879$	4.07907	−	16.2578i	0.137584	−	0.548362i
$880$		0			0
$881$			7.66064i			0.258093i	0.991639	+	0.129047i	$0.0411917\pi$
$881$			7.66064i			0.258093i	−0.991639	+	0.129047i	$0.958808\pi$
$882$	7.36398	−	0.328243i	0.247958	−	0.0110525i
$883$	−7.44439	−	7.44439i	−0.250524	−	0.250524i	0.570662	−	0.821185i	$-0.306687\pi$
$883$	−7.44439	−	7.44439i	−0.250524	−	0.250524i	−0.821185	+	0.570662i	$0.806687\pi$
$884$	31.0357	−	57.0261i	1.04384	−	1.91800i
$885$		0			0
$886$	−10.7191	+	42.1191i	−0.360114	+	1.41502i
$887$	15.8208	−	15.8208i	0.531211	−	0.531211i	−0.389722	−	0.920933i	$-0.627429\pi$
$887$	15.8208	−	15.8208i	0.531211	−	0.531211i	0.920933	+	0.389722i	$0.127429\pi$
$888$	33.4959	+	7.07071i	1.12405	+	0.237277i
$889$		−	46.9253i		−	1.57382i
$890$		0			0
$891$	13.2452	+	19.8896i	0.443730	+	0.666325i
$892$	2.11284	+	7.15881i	0.0707433	+	0.239695i
$893$	−5.78730	+	5.78730i	−0.193665	+	0.193665i
$894$	−7.76558	−	4.19236i	−0.259720	−	0.140214i
$895$		0			0
$896$	−32.9395	−	5.77740i	−1.10043	−	0.193009i
$897$	−12.0787	−	20.1699i	−0.403298	−	0.673454i
$898$	0.743993	−	0.442132i	0.0248274	−	0.0147541i
$899$		−	6.82156i		−	0.227512i
$900$		0			0
$901$			35.7329i			1.19043i
$902$	−20.3444	−	34.2343i	−0.677393	−	1.13988i
$903$	−0.817610	−	1.36530i	−0.0272084	−	0.0454344i
$904$	16.6338	−	17.9409i	0.553231	−	0.596705i
$905$		0			0
$906$	−15.9402	+	29.5262i	−0.529576	+	0.980943i
$907$	−33.9035	+	33.9035i	−1.12575	+	1.12575i	−0.134886	+	0.990861i	$0.543067\pi$
$907$	−33.9035	+	33.9035i	−1.12575	+	1.12575i	−0.990861	+	0.134886i	$0.956933\pi$
$908$	−15.2665	+	4.50575i	−0.506638	+	0.149529i
$909$	−15.1251	+	28.2444i	−0.501669	+	0.936806i
$910$		0			0
$911$			8.75281i			0.289994i	0.989432	+	0.144997i	$0.0463172\pi$
$911$			8.75281i			0.289994i	−0.989432	+	0.144997i	$0.953683\pi$
$912$	19.6320	+	9.65926i	0.650079	+	0.319850i
$913$	25.9885	−	25.9885i	0.860094	−	0.860094i
$914$	6.67413	+	1.69852i	0.220761	+	0.0561822i
$915$		0			0
$916$	10.7383	−	19.7310i	0.354804	−	0.651930i
$917$	13.7025	+	13.7025i	0.452497	+	0.452497i
$918$	39.1980	+	7.99808i	1.29373	+	0.263976i
$919$		−	27.0428i		−	0.892058i	−0.895018	−	0.446029i	$-0.852838\pi$
$919$		−	27.0428i		−	0.892058i	0.895018	−	0.446029i	$-0.147162\pi$
$920$		0			0
$921$	−3.16980	+	12.6338i	−0.104449	+	0.416297i
$922$	0.357915	−	0.212698i	0.0117873	−	0.00700483i
$923$	12.2206	−	12.2206i	0.402246	−	0.402246i
$924$	18.4170	−	19.9993i	0.605875	−	0.657930i
$925$		0			0
$926$	−4.83298	+	18.9906i	−0.158822	+	0.624069i
$927$	12.6979	+	41.9768i	0.417055	+	1.37870i
$928$	−10.9400	+	22.0466i	−0.359122	+	0.723716i
$929$	41.2267			1.35261			0.676303	−	0.736624i	$-0.263581\pi$
$929$	41.2267			1.35261			0.676303	+	0.736624i	$0.263581\pi$
$930$		0			0
$931$			5.48688i			0.179825i
$932$	40.8851	−	12.0668i	1.33924	−	0.395261i
$933$	27.9109	+	46.6075i	0.913761	+	1.52586i
$934$	36.5474	+	9.30109i	1.19587	+	0.304341i
$935$		0			0
$936$	−16.4689	−	47.8412i	−0.538304	−	1.56374i
$937$	−37.7773	−	37.7773i	−1.23413	−	1.23413i	−0.962363	−	0.271766i	$-0.912392\pi$
$937$	−37.7773	−	37.7773i	−1.23413	−	1.23413i	−0.271766	−	0.962363i	$-0.587608\pi$
$938$	−44.7690	+	26.6048i	−1.46176	+	0.868679i
$939$	−3.23277	+	12.8847i	−0.105498	+	0.420478i
$940$		0			0
$941$	53.4869			1.74362			0.871812	−	0.489841i	$-0.162945\pi$
$941$	53.4869			1.74362			0.871812	+	0.489841i	$0.162945\pi$
$942$	7.20865	+	24.1241i	0.234870	+	0.786005i
$943$	−17.0709	+	17.0709i	−0.555905	+	0.555905i
$944$	−33.3606	+	21.5710i	−1.08579	+	0.702076i
$945$		0			0
$946$	−1.13110	−	0.287857i	−0.0367751	−	0.00935903i
$947$	23.8152	+	23.8152i	0.773891	+	0.773891i	0.978784	−	0.204893i	$-0.0656846\pi$
$947$	23.8152	+	23.8152i	0.773891	+	0.773891i	−0.204893	+	0.978784i	$0.565685\pi$
$948$	−31.2431	+	1.28689i	−1.01473	+	0.0417962i
$949$	−19.3767			−0.628993
$950$		0			0
$951$	−30.5327	−	7.66064i	−0.990091	−	0.248413i
$952$	−1.71952	−	45.4832i	−0.0557301	−	1.47412i
$953$	−31.8333	−	31.8333i	−1.03118	−	1.03118i	−0.999498	−	0.0316832i	$-0.989913\pi$
$953$	−31.8333	−	31.8333i	−1.03118	−	1.03118i	−0.0316832	−	0.999498i	$-0.510087\pi$
$954$	20.5482	+	18.7945i	0.665272	+	0.608495i
$955$		0			0
$956$	2.77099	−	5.09153i	0.0896203	−	0.164672i
$957$	−10.2798	−	17.1658i	−0.332297	−	0.554893i
$958$	23.0876	−	13.7203i	0.745928	−	0.443282i
$959$	−6.84111			−0.220911
$960$		0			0
$961$	−28.5417			−0.920700
$962$	50.6581	−	30.1045i	1.63328	−	0.970609i
$963$	14.1031	−	4.26618i	0.454466	−	0.137476i
$964$	0.527646	−	0.969517i	0.0169943	−	0.0312260i
$965$		0			0
$966$	−14.5033	−	7.82981i	−0.466635	−	0.251920i
$967$	21.7712	+	21.7712i	0.700115	+	0.700115i	0.964435	−	0.264320i	$-0.0851476\pi$
$967$	21.7712	+	21.7712i	0.700115	+	0.700115i	−0.264320	+	0.964435i	$0.585148\pi$
$968$	0.422102	+	11.1650i	0.0135669	+	0.358858i
$969$	−7.24679	+	28.8833i	−0.232801	+	0.927864i
$970$		0			0
$971$	2.19315			0.0703814			0.0351907	−	0.999381i	$-0.488796\pi$
$971$	2.19315			0.0703814			0.0351907	+	0.999381i	$0.488796\pi$
$972$	25.2163	−	18.3340i	0.808815	−	0.588063i
$973$	−2.15647	−	2.15647i	−0.0691333	−	0.0691333i
$974$	23.3710	+	5.94777i	0.748855	+	0.190579i
$975$		0			0
$976$	−40.0253	+	25.8804i	−1.28118	+	0.828412i
$977$	−2.26226	+	2.26226i	−0.0723760	+	0.0723760i	−0.742368	−	0.669992i	$-0.766297\pi$
$977$	−2.26226	+	2.26226i	−0.0723760	+	0.0723760i	0.669992	+	0.742368i	$0.266297\pi$
$978$	31.5520	−	9.42822i	1.00892	−	0.301481i
$979$	7.52063			0.240361
$980$		0			0
$981$	−3.79488	+	7.08649i	−0.121161	+	0.226254i
$982$	−22.1018	+	13.1344i	−0.705298	+	0.419136i
$983$	−39.9359	−	39.9359i	−1.27376	−	1.27376i	−0.944101	−	0.329656i	$-0.893067\pi$
$983$	−39.9359	−	39.9359i	−1.27376	−	1.27376i	−0.329656	−	0.944101i	$-0.606933\pi$
$984$	−43.5346	+	28.3585i	−1.38783	+	0.904037i
$985$		0			0
$986$	−32.4622	−	8.26144i	−1.03381	−	0.263098i
$987$	11.3835	−	6.81701i	0.362341	−	0.216988i
$988$	36.1216	−	10.6609i	1.14918	−	0.339168i
$989$			0.707560i			0.0224991i
$990$		0			0
$991$	26.1776			0.831560			0.415780	−	0.909465i	$-0.363509\pi$
$991$	26.1776			0.831560			0.415780	+	0.909465i	$0.363509\pi$
$992$	−7.94496	−	3.94245i	−0.252253	−	0.125173i
$993$	9.47134	+	15.8159i	0.300564	+	0.501902i
$994$	2.98820	−	11.7417i	0.0947799	−	0.372426i
$995$		0			0
$996$	−35.2734	−	32.4825i	−1.11768	−	1.02925i
$997$	28.1978	−	28.1978i	0.893034	−	0.893034i	−0.101774	−	0.994808i	$-0.532452\pi$
$997$	28.1978	−	28.1978i	0.893034	−	0.893034i	0.994808	+	0.101774i	$0.0324518\pi$
$998$	−30.2060	+	17.9505i	−0.956153	+	0.568212i
$999$	26.8761	+	24.4161i	0.850321	+	0.772492i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

Introduction

L-functions

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