LMFDB - Embedded newform 525.2.q.g.299.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(299,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("525.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.q (of order $6$, degree $2$, not 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.19
Character	$\chi$	$=$	525.299
Dual form			525.2.q.g.374.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36696 - 2.36764i) q^{2} +(0.583411 - 1.63084i) q^{3} +(-2.73715 - 4.74088i) q^{4} +(-3.06374 - 3.61059i) q^{6} +(1.39384 + 2.24882i) q^{7} -9.49844 q^{8} +(-2.31926 - 1.90290i) q^{9} +O(q^{10})$	\(q+(1.36696 - 2.36764i) q^{2} +(0.583411 - 1.63084i) q^{3} +(-2.73715 - 4.74088i) q^{4} +(-3.06374 - 3.61059i) q^{6} +(1.39384 + 2.24882i) q^{7} -9.49844 q^{8} +(-2.31926 - 1.90290i) q^{9} +(1.79388 - 1.03570i) q^{11} +(-9.32849 + 1.69796i) q^{12} -2.04106 q^{13} +(7.22973 - 0.226073i) q^{14} +(-7.50967 + 13.0071i) q^{16} +(1.82114 - 1.05144i) q^{17} +(-7.67571 + 2.89000i) q^{18} +(2.41421 + 1.39384i) q^{19} +(4.48065 - 0.961143i) q^{21} -5.66303i q^{22} +(0.888591 - 1.53909i) q^{23} +(-5.54150 + 15.4904i) q^{24} +(-2.79004 + 4.83250i) q^{26} +(-4.45640 + 2.67217i) q^{27} +(6.84624 - 12.7634i) q^{28} -2.79774i q^{29} +(6.04532 - 3.49027i) q^{31} +(11.0324 + 19.1086i) q^{32} +(-0.642485 - 3.52977i) q^{33} -5.74909i q^{34} +(-2.67324 + 16.2039i) q^{36} +(-5.25381 - 3.03329i) q^{37} +(6.60024 - 3.81065i) q^{38} +(-1.19078 + 3.32864i) q^{39} +11.7165 q^{41} +(3.84922 - 11.9224i) q^{42} +4.37014i q^{43} +(-9.82025 - 5.66973i) q^{44} +(-2.42933 - 4.20773i) q^{46} +(2.55277 + 1.47384i) q^{47} +(16.8313 + 19.8356i) q^{48} +(-3.11440 + 6.26901i) q^{49} +(-0.652249 - 3.58341i) q^{51} +(5.58669 + 9.67643i) q^{52} +(3.09709 + 5.36432i) q^{53} +(0.235023 + 14.2039i) q^{54} +(-13.2393 - 21.3603i) q^{56} +(3.68161 - 3.12400i) q^{57} +(-6.62405 - 3.82440i) q^{58} +(1.44301 + 2.49936i) q^{59} +(-6.30263 - 3.63883i) q^{61} -19.0842i q^{62} +(1.04659 - 7.86795i) q^{63} +30.2845 q^{64} +(-9.23548 - 3.30387i) q^{66} +(-6.41119 + 3.70150i) q^{67} +(-9.96949 - 5.75589i) q^{68} +(-1.99158 - 2.34707i) q^{69} -3.80885i q^{71} +(22.0294 + 18.0746i) q^{72} +(-3.35598 - 5.81273i) q^{73} +(-14.3635 + 8.29276i) q^{74} -15.2606i q^{76} +(4.82949 + 2.59052i) q^{77} +(6.25328 + 7.36944i) q^{78} +(-2.95787 + 5.12317i) q^{79} +(1.75796 + 8.82664i) q^{81} +(16.0160 - 27.7405i) q^{82} +5.96419i q^{83} +(-16.8209 - 18.6114i) q^{84} +(10.3469 + 5.97380i) q^{86} +(-4.56267 - 1.63224i) q^{87} +(-17.0391 + 9.83752i) q^{88} +(6.20912 - 10.7545i) q^{89} +(-2.84492 - 4.58998i) q^{91} -9.72883 q^{92} +(-2.16515 - 11.8952i) q^{93} +(6.97906 - 4.02936i) q^{94} +(37.5995 - 6.84382i) q^{96} -9.97170 q^{97} +(10.5855 + 15.9433i) q^{98} +(-6.13132 - 1.01152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 28 q^{4} + 14 q^{9}+O(q^{10}) $ 40 * q - 28 * q^4 + 14 * q^9	$ 40 q - 28 q^{4} + 14 q^{9} - 36 q^{16} - 18 q^{21} - 36 q^{24} + 84 q^{31} - 72 q^{36} - 16 q^{46} + 8 q^{49} + 42 q^{51} + 150 q^{54} - 180 q^{61} + 240 q^{64} + 12 q^{66} - 92 q^{79} + 58 q^{81} - 150 q^{84} - 60 q^{91} - 12 q^{94} + 270 q^{96} - 188 q^{99}+O(q^{100}) $ 40 * q - 28 * q^4 + 14 * q^9 - 36 * q^16 - 18 * q^21 - 36 * q^24 + 84 * q^31 - 72 * q^36 - 16 * q^46 + 8 * q^49 + 42 * q^51 + 150 * q^54 - 180 * q^61 + 240 * q^64 + 12 * q^66 - 92 * q^79 + 58 * q^81 - 150 * q^84 - 60 * q^91 - 12 * q^94 + 270 * q^96 - 188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.36696	−	2.36764i	0.966585	−	1.67417i	0.261291	−	0.965260i	$-0.415852\pi$
$2$	1.36696	−	2.36764i	0.966585	−	1.67417i	0.705294	−	0.708915i	$-0.250815\pi$
$3$	0.583411	−	1.63084i	0.336833	−	0.941565i
$3$	0.583411	−	1.63084i	0.336833	−	0.941565i
$4$	−2.73715	−	4.74088i	−1.36857	−	2.37044i
$5$		0			0
$5$		0			0
$6$	−3.06374	−	3.61059i	−1.25077	−	1.47402i
$7$	1.39384	+	2.24882i	0.526823	+	0.849975i
$7$	1.39384	+	2.24882i	0.526823	+	0.849975i
$8$	−9.49844			−3.35821
$9$	−2.31926	−	1.90290i	−0.773088	−	0.634299i
$10$		0			0
$11$	1.79388	−	1.03570i	0.540876	−	0.312275i	−0.204558	−	0.978854i	$-0.565576\pi$
$11$	1.79388	−	1.03570i	0.540876	−	0.312275i	0.745434	+	0.666579i	$0.232242\pi$
$12$	−9.32849	+	1.69796i	−2.69290	+	0.490160i
$13$	−2.04106			−0.566088			−0.283044	−	0.959107i	$-0.591344\pi$
$13$	−2.04106			−0.566088			−0.283044	+	0.959107i	$0.591344\pi$
$14$	7.22973	−	0.226073i	1.93223	−	0.0604206i
$15$		0			0
$16$	−7.50967	+	13.0071i	−1.87742	+	3.25178i
$17$	1.82114	−	1.05144i	0.441692	−	0.255011i	−0.262623	−	0.964899i	$-0.584587\pi$
$17$	1.82114	−	1.05144i	0.441692	−	0.255011i	0.704315	+	0.709887i	$0.251254\pi$
$18$	−7.67571	+	2.89000i	−1.80918	+	0.681179i
$19$	2.41421	+	1.39384i	0.553857	+	0.319769i	0.750676	−	0.660670i	$-0.229728\pi$
$19$	2.41421	+	1.39384i	0.553857	+	0.319769i	−0.196819	+	0.980440i	$0.563061\pi$
$20$		0			0
$21$	4.48065	−	0.961143i	0.977757	−	0.209739i
$22$		−	5.66303i		−	1.20736i
$23$	0.888591	−	1.53909i	0.185284	−	0.320921i	−0.758388	−	0.651803i	$-0.774013\pi$
$23$	0.888591	−	1.53909i	0.185284	−	0.320921i	0.943672	+	0.330882i	$0.107346\pi$
$24$	−5.54150	+	15.4904i	−1.13115	+	3.16197i
$25$		0			0
$26$	−2.79004	+	4.83250i	−0.547173	+	0.947731i
$27$	−4.45640	+	2.67217i	−0.857635	+	0.514259i
$28$	6.84624	−	12.7634i	1.29382	−	2.41206i
$29$		−	2.79774i		−	0.519528i	−0.965672	−	0.259764i	$-0.916355\pi$
$29$		−	2.79774i		−	0.519528i	0.965672	−	0.259764i	$-0.0836448\pi$
$30$		0			0
$31$	6.04532	−	3.49027i	1.08577	−	0.626870i	0.153324	−	0.988176i	$-0.451002\pi$
$31$	6.04532	−	3.49027i	1.08577	−	0.626870i	0.932447	+	0.361306i	$0.117669\pi$
$32$	11.0324	+	19.1086i	1.95027	+	3.37796i
$33$	−0.642485	−	3.52977i	−0.111842	−	0.614454i
$34$		−	5.74909i		−	0.985961i
$35$		0			0
$36$	−2.67324	+	16.2039i	−0.445541	+	2.70064i
$37$	−5.25381	−	3.03329i	−0.863722	−	0.498670i	0.00153522	−	0.999999i	$-0.499511\pi$
$37$	−5.25381	−	3.03329i	−0.863722	−	0.498670i	−0.865257	+	0.501329i	$0.832845\pi$
$38$	6.60024	−	3.81065i	1.07070	−	0.618169i
$39$	−1.19078	+	3.32864i	−0.190677	+	0.533009i
$40$		0			0
$41$	11.7165			1.82981			0.914905	−	0.403670i	$-0.132266\pi$
$41$	11.7165			1.82981			0.914905	+	0.403670i	$0.132266\pi$
$42$	3.84922	−	11.9224i	0.593947	−	1.83967i
$43$			4.37014i			0.666440i	0.942849	+	0.333220i	$0.108135\pi$
$43$			4.37014i			0.666440i	−0.942849	+	0.333220i	$0.891865\pi$
$44$	−9.82025	−	5.66973i	−1.48046	−	0.854743i
$45$		0			0
$46$	−2.42933	−	4.20773i	−0.358186	−	0.620396i
$47$	2.55277	+	1.47384i	0.372360	+	0.214982i	0.674489	−	0.738285i	$-0.264364\pi$
$47$	2.55277	+	1.47384i	0.372360	+	0.214982i	−0.302129	+	0.953267i	$0.597697\pi$
$48$	16.8313	+	19.8356i	2.42939	+	2.86302i
$49$	−3.11440	+	6.26901i	−0.444915	+	0.895573i
$50$		0			0
$51$	−0.652249	−	3.58341i	−0.0913331	−	0.501778i
$52$	5.58669	+	9.67643i	0.774734	+	1.34188i
$53$	3.09709	+	5.36432i	0.425418	+	0.736846i	0.996459	−	0.0840757i	$-0.0267938\pi$
$53$	3.09709	+	5.36432i	0.425418	+	0.736846i	−0.571041	+	0.820921i	$0.693460\pi$
$54$	0.235023	+	14.2039i	0.0319825	+	1.93291i
$55$		0			0
$56$	−13.2393	−	21.3603i	−1.76918	−	2.85439i
$57$	3.68161	−	3.12400i	0.487641	−	0.413783i
$58$	−6.62405	−	3.82440i	−0.869781	−	0.502168i
$59$	1.44301	+	2.49936i	0.187864	+	0.325389i	0.944538	−	0.328403i	$-0.106510\pi$
$59$	1.44301	+	2.49936i	0.187864	+	0.325389i	−0.756674	+	0.653792i	$0.773177\pi$
$60$		0			0
$61$	−6.30263	−	3.63883i	−0.806969	−	0.465904i	0.0389331	−	0.999242i	$-0.487604\pi$
$61$	−6.30263	−	3.63883i	−0.806969	−	0.465904i	−0.845902	+	0.533338i	$0.820937\pi$
$62$		−	19.0842i		−	2.42369i
$63$	1.04659	−	7.86795i	0.131858	−	0.991269i
$64$	30.2845			3.78556
$65$		0			0
$66$	−9.23548	−	3.30387i	−1.13681	−	0.406679i
$67$	−6.41119	+	3.70150i	−0.783252	+	0.452211i	−0.837581	−	0.546312i	$-0.816031\pi$
$67$	−6.41119	+	3.70150i	−0.783252	+	0.452211i	0.0543297	+	0.998523i	$0.482698\pi$
$68$	−9.96949	−	5.75589i	−1.20898	−	0.698004i
$69$	−1.99158	−	2.34707i	−0.239759	−	0.282554i
$70$		0			0
$71$		−	3.80885i		−	0.452027i	−0.974124	−	0.226014i	$-0.927431\pi$
$71$		−	3.80885i		−	0.452027i	0.974124	−	0.226014i	$-0.0725694\pi$
$72$	22.0294	+	18.0746i	2.59619	+	2.13011i
$73$	−3.35598	−	5.81273i	−0.392788	−	0.680328i	0.600028	−	0.799979i	$-0.295156\pi$
$73$	−3.35598	−	5.81273i	−0.392788	−	0.680328i	−0.992816	+	0.119651i	$0.961823\pi$
$74$	−14.3635	+	8.29276i	−1.66972	+	0.964014i
$75$		0			0
$76$		−	15.2606i		−	1.75051i
$77$	4.82949	+	2.59052i	0.550372	+	0.295218i
$78$	6.25328	+	7.36944i	0.708044	+	0.834425i
$79$	−2.95787	+	5.12317i	−0.332786	+	0.576402i	−0.983057	−	0.183300i	$-0.941322\pi$
$79$	−2.95787	+	5.12317i	−0.332786	+	0.576402i	0.650271	+	0.759702i	$0.274655\pi$
$80$		0			0
$81$	1.75796	+	8.82664i	0.195329	+	0.980738i
$82$	16.0160	−	27.7405i	1.76867	−	3.06342i
$83$			5.96419i			0.654655i	0.944911	+	0.327327i	$0.106148\pi$
$83$			5.96419i			0.654655i	−0.944911	+	0.327327i	$0.893852\pi$
$84$	−16.8209	−	18.6114i	−1.83531	−	2.03067i
$85$		0			0
$86$	10.3469	+	5.97380i	1.11574	+	0.644171i
$87$	−4.56267	−	1.63224i	−0.489169	−	0.174994i
$88$	−17.0391	+	9.83752i	−1.81637	+	1.04868i
$89$	6.20912	−	10.7545i	0.658166	−	1.13998i	−0.322924	−	0.946425i	$-0.604666\pi$
$89$	6.20912	−	10.7545i	0.658166	−	1.13998i	0.981090	−	0.193552i	$-0.0620008\pi$
$90$		0			0
$91$	−2.84492	−	4.58998i	−0.298228	−	0.481161i
$92$	−9.72883			−1.01430
$93$	−2.16515	−	11.8952i	−0.224516	−	1.23347i
$94$	6.97906	−	4.02936i	0.719835	−	0.415597i
$95$		0			0
$96$	37.5995	−	6.84382i	3.83748	−	0.698494i
$97$	−9.97170			−1.01247			−0.506237	−	0.862395i	$-0.668964\pi$
$97$	−9.97170			−1.01247			−0.506237	+	0.862395i	$0.668964\pi$
$98$	10.5855	+	15.9433i	1.06930	+	1.61051i
$99$	−6.13132	−	1.01152i	−0.616220	−	0.101661i
$100$		0			0
$101$	8.06825	+	13.9746i	0.802821	+	1.39053i	0.917752	+	0.397153i	$0.130002\pi$
$101$	8.06825	+	13.9746i	0.802821	+	1.39053i	−0.114931	+	0.993373i	$0.536665\pi$
$102$	−9.37583	−	3.35408i	−0.928345	−	0.332104i
$103$	−0.261583	+	0.453075i	−0.0257745	+	0.0446428i	−0.878625	−	0.477513i	$-0.841539\pi$
$103$	−0.261583	+	0.453075i	−0.0257745	+	0.0446428i	0.852850	+	0.522155i	$0.174872\pi$
$104$	19.3869			1.90104
$105$		0			0
$106$	16.9344			1.64481
$107$	−1.54125	+	2.66952i	−0.148998	+	0.258073i	−0.930858	−	0.365382i	$-0.880938\pi$
$107$	−1.54125	+	2.66952i	−0.148998	+	0.258073i	0.781859	+	0.623455i	$0.214272\pi$
$108$	24.8663	+	13.8131i	2.39276	+	1.32917i
$109$	6.77743	+	11.7389i	0.649160	+	1.12438i	0.983324	+	0.181864i	$0.0582129\pi$
$109$	6.77743	+	11.7389i	0.649160	+	1.12438i	−0.334163	+	0.942515i	$0.608454\pi$
$110$		0			0
$111$	−8.01194	+	6.79846i	−0.760459	+	0.645281i
$112$	−39.7180	+	1.24198i	−3.75300	+	0.117356i
$113$	−11.0653			−1.04093			−0.520466	−	0.853883i	$-0.674242\pi$
$113$	−11.0653			−1.04093			−0.520466	+	0.853883i	$0.674242\pi$
$114$	−2.36390	−	12.9871i	−0.221399	−	1.21635i
$115$		0			0
$116$	−13.2638	+	7.65784i	−1.23151	+	0.711013i
$117$	4.73376	+	3.88393i	0.437636	+	0.359069i
$118$	7.89013			0.726345
$119$	4.90289	+	2.62989i	0.449447	+	0.241082i
$120$		0			0
$121$	−3.35465	+	5.81043i	−0.304969	+	0.528221i
$122$	−17.2309	+	9.94824i	−1.56001	+	0.900672i
$123$	6.83554	−	19.1077i	0.616340	−	1.72288i
$124$	−33.0939	−	19.1068i	−2.97192	−	1.71584i
$125$		0			0
$126$	−17.1978	−	13.2331i	−1.53210	−	1.17890i
$127$			4.98617i			0.442451i	0.975223	+	0.221226i	$0.0710057\pi$
$127$			4.98617i			0.442451i	−0.975223	+	0.221226i	$0.928994\pi$
$128$	19.3329	−	33.4855i	1.70880	−	2.95973i
$129$	7.12699	+	2.54959i	0.627497	+	0.224479i
$130$		0			0
$131$	5.85196	−	10.1359i	0.511288	−	0.885577i	−0.488626	−	0.872493i	$-0.662502\pi$
$131$	5.85196	−	10.1359i	0.511288	−	0.885577i	0.999914	−	0.0130842i	$-0.00416493\pi$
$132$	−14.9756	+	12.7075i	−1.30346	+	1.10604i
$133$	0.230519	+	7.37192i	0.0199886	+	0.639226i
$134$			20.2392i			1.74840i
$135$		0			0
$136$	−17.2980	+	9.98702i	−1.48329	+	0.856380i
$137$	−6.32808	−	10.9606i	−0.540644	−	0.936423i	−0.998867	−	0.0475860i	$-0.984847\pi$
$137$	−6.32808	−	10.9606i	−0.540644	−	0.936423i	0.458223	−	0.888837i	$-0.348486\pi$
$138$	−8.27943	+	1.50701i	−0.704791	+	0.128285i
$139$		−	18.0304i		−	1.52932i	−0.644434	−	0.764660i	$-0.722907\pi$
$139$		−	18.0304i		−	1.52932i	0.644434	−	0.764660i	$-0.277093\pi$
$140$		0			0
$141$	3.89291	−	3.30330i	0.327842	−	0.278188i
$142$	−9.01798	−	5.20654i	−0.756772	−	0.436923i
$143$	−3.66143	+	2.11392i	−0.306184	+	0.176775i
$144$	42.1681	−	15.8768i	3.51401	−	1.32307i
$145$		0			0
$146$	−18.3499			−1.51865
$147$	8.40676	+	8.73650i	0.693378	+	0.720574i
$148$			33.2103i			2.72987i
$149$	12.6249	+	7.28898i	1.03427	+	0.597136i	0.918205	−	0.396105i	$-0.129638\pi$
$149$	12.6249	+	7.28898i	1.03427	+	0.597136i	0.116065	+	0.993242i	$0.462972\pi$
$150$		0			0
$151$	3.51450	+	6.08730i	0.286006	+	0.495377i	0.972853	−	0.231425i	$-0.0743389\pi$
$151$	3.51450	+	6.08730i	0.286006	+	0.495377i	−0.686847	+	0.726802i	$0.741006\pi$
$152$	−22.9312	−	13.2393i	−1.85997	−	1.07385i
$153$	−6.22449	−	1.02689i	−0.503220	−	0.0830192i
$154$	12.7351	−	7.89337i	1.02623	−	0.636066i
$155$		0			0
$156$	19.0400	−	3.46564i	1.52442	−	0.277474i
$157$	10.9512	+	18.9680i	0.874000	+	1.51381i	0.857824	+	0.513943i	$0.171816\pi$
$157$	10.9512	+	18.9680i	0.874000	+	1.51381i	0.0161753	+	0.999869i	$0.494851\pi$
$158$	8.08656	+	14.0063i	0.643332	+	1.11428i
$159$	10.5552	−	1.92125i	0.837082	−	0.152365i
$160$		0			0
$161$	4.69969	−	0.146959i	0.370387	−	0.0115820i
$162$	23.3014	+	7.90343i	1.83073	+	0.620952i
$163$	7.01159	+	4.04815i	0.549190	+	0.317075i	0.748795	−	0.662801i	$-0.230633\pi$
$163$	7.01159	+	4.04815i	0.549190	+	0.317075i	−0.199605	+	0.979876i	$0.563966\pi$
$164$	−32.0698	−	55.5465i	−2.50423	−	4.33745i
$165$		0			0
$166$	14.1211	+	8.15279i	1.09601	+	0.632780i
$167$		−	3.58777i		−	0.277630i	−0.990318	−	0.138815i	$-0.955671\pi$
$167$		−	3.58777i		−	0.277630i	0.990318	−	0.138815i	$-0.0443293\pi$
$168$	−42.5592	+	9.12936i	−3.28351	+	0.704345i
$169$	−8.83407			−0.679544
$170$		0			0
$171$	−2.94684	−	7.82668i	−0.225350	−	0.598521i
$172$	20.7183	−	11.9617i	1.57976	−	0.912073i
$173$	11.2663	+	6.50462i	0.856563	+	0.494537i	0.862860	−	0.505443i	$-0.168671\pi$
$173$	11.2663	+	6.50462i	0.856563	+	0.494537i	−0.00629680	+	0.999980i	$0.502004\pi$
$174$	−10.1015	+	8.57156i	−0.765794	+	0.649808i
$175$		0			0
$176$			31.1110i			2.34508i
$177$	4.91792	−	0.895156i	0.369654	−	0.0672840i
$178$	−16.9752	−	29.4020i	−1.27235	−	2.20377i
$179$	3.50400	−	2.02304i	0.261902	−	0.151209i	−0.363300	−	0.931672i	$-0.618350\pi$
$179$	3.50400	−	2.02304i	0.261902	−	0.151209i	0.625202	+	0.780463i	$0.285017\pi$
$180$		0			0
$181$			9.00970i			0.669686i	0.942274	+	0.334843i	$0.108683\pi$
$181$			9.00970i			0.669686i	−0.942274	+	0.334843i	$0.891317\pi$
$182$	−14.7563	+	0.461429i	−1.09381	+	0.0342034i
$183$	−9.61136	+	8.15564i	−0.710492	+	0.602882i
$184$	−8.44023	+	14.6189i	−0.622222	+	1.07772i
$185$		0			0
$186$	−31.1232	−	11.1339i	−2.28206	−	0.816379i
$187$	2.17795	−	3.77232i	0.159267	−	0.275859i
$188$		−	16.1365i		−	1.17688i
$189$	−12.2208	−	6.29707i	−0.888929	−	0.458045i
$190$		0			0
$191$	−22.6067	−	13.0520i	−1.63576	−	0.944409i	−0.982269	−	0.187478i	$-0.939969\pi$
$191$	−22.6067	−	13.0520i	−1.63576	−	0.944409i	−0.653495	−	0.756931i	$-0.726698\pi$
$192$	17.6683	−	49.3891i	1.27510	−	3.56435i
$193$	6.50213	−	3.75401i	0.468034	−	0.270219i	−0.247383	−	0.968918i	$-0.579570\pi$
$193$	6.50213	−	3.75401i	0.468034	−	0.270219i	0.715416	+	0.698699i	$0.246237\pi$
$194$	−13.6309	+	23.6094i	−0.978642	+	1.69506i
$195$		0			0
$196$	38.2452	−	2.39419i	2.73180	−	0.171014i
$197$	20.7941			1.48152			0.740758	−	0.671772i	$-0.234466\pi$
$197$	20.7941			1.48152			0.740758	+	0.671772i	$0.234466\pi$
$198$	−10.7762	+	13.1341i	−0.765829	+	0.933396i
$199$	19.8822	−	11.4790i	1.40941	−	0.813725i	0.414081	−	0.910240i	$-0.364103\pi$
$199$	19.8822	−	11.4790i	1.40941	−	0.813725i	0.995332	+	0.0965149i	$0.0307695\pi$
$200$		0			0
$201$	2.29619	+	12.6151i	0.161961	+	0.889801i
$202$	44.1158			3.10398
$203$	6.29163	−	3.89962i	0.441586	−	0.273699i
$204$	−15.2032	+	12.9006i	−1.06444	+	0.903220i
$205$		0			0
$206$	0.715145	+	1.23867i	0.0498265	+	0.0863021i
$207$	−4.98960	+	1.87864i	−0.346801	+	0.130575i
$208$	15.3277	−	26.5483i	1.06278	−	1.84080i
$209$	5.77441			0.399424
$210$		0			0
$211$	−18.9736			−1.30620			−0.653098	−	0.757273i	$-0.726531\pi$
$211$	−18.9736			−1.30620			−0.653098	+	0.757273i	$0.726531\pi$
$212$	16.9544	−	29.3659i	1.16443	−	2.01686i
$213$	−6.21161	−	2.22212i	−0.425613	−	0.152257i
$214$	4.21365	+	7.29826i	0.288039	+	0.498899i
$215$		0			0
$216$	42.3289	−	25.3814i	2.88011	−	1.72699i
$217$	16.2752	+	8.72996i	1.10483	+	0.592628i
$218$	37.0579			2.50988
$219$	−11.4375	+	2.08185i	−0.772877	+	0.140678i
$220$		0			0
$221$	−3.71707	+	2.14605i	−0.250037	+	0.144359i
$222$	5.14433	+	28.2626i	0.345265	+	1.89686i
$223$	6.06277			0.405993			0.202997	−	0.979179i	$-0.434932\pi$
$223$	6.06277			0.405993			0.202997	+	0.979179i	$0.434932\pi$
$224$	−27.5945	+	51.4443i	−1.84374	+	3.43726i
$225$		0			0
$226$	−15.1257	+	26.1985i	−1.00615	+	1.74270i
$227$	−18.8837	+	10.9025i	−1.25336	+	0.723626i	−0.971775	−	0.235911i	$-0.924193\pi$
$227$	−18.8837	+	10.9025i	−1.25336	+	0.723626i	−0.281582	+	0.959537i	$0.590859\pi$
$228$	−24.8876	−	8.90322i	−1.64822	−	0.589630i
$229$	7.94782	+	4.58868i	0.525207	+	0.303228i	0.739062	−	0.673637i	$-0.235269\pi$
$229$	7.94782	+	4.58868i	0.525207	+	0.303228i	−0.213856	+	0.976865i	$0.568602\pi$
$230$		0			0
$231$	7.04230	−	6.36478i	0.463350	−	0.418772i
$232$			26.5742i			1.74468i
$233$	−9.09122	+	15.7465i	−0.595586	+	1.03158i	0.397878	+	0.917438i	$0.369747\pi$
$233$	−9.09122	+	15.7465i	−0.595586	+	1.03158i	−0.993464	+	0.114146i	$0.963587\pi$
$234$	15.6666	−	5.89866i	1.02416	−	0.385608i
$235$		0			0
$236$	7.89946	−	13.6823i	0.514211	−	0.890640i
$237$	6.62941	+	7.81271i	0.430627	+	0.507490i
$238$	12.9287	−	8.01333i	0.838042	−	0.519427i
$239$		−	13.1450i		−	0.850278i	−0.905128	−	0.425139i	$-0.860225\pi$
$239$		−	13.1450i		−	0.850278i	0.905128	−	0.425139i	$-0.139775\pi$
$240$		0			0
$241$	0.0154860	−	0.00894087i	0.000997544	−	0.000575932i	−0.499501	−	0.866313i	$-0.666483\pi$
$241$	0.0154860	−	0.00894087i	0.000997544	−	0.000575932i	0.500499	+	0.865737i	$0.333150\pi$
$242$	9.17135	+	15.8852i	0.589556	+	1.02114i
$243$	15.4204	+	2.28261i	0.989221	+	0.146430i
$244$			39.8400i			2.55050i
$245$		0			0
$246$	−35.8963	−	42.3035i	−2.28866	−	2.69717i
$247$	−4.92754	−	2.84492i	−0.313532	−	0.181018i
$248$	−57.4211	+	33.1521i	−3.64624	+	2.10516i
$249$	9.72662	+	3.47957i	0.616400	+	0.220509i
$250$		0			0
$251$	−5.38577			−0.339947			−0.169973	−	0.985449i	$-0.554368\pi$
$251$	−5.38577			−0.339947			−0.169973	+	0.985449i	$0.554368\pi$
$252$	−40.1657	+	16.5740i	−2.53020	+	1.04406i
$253$		−	3.68125i		−	0.231438i
$254$	11.8055	+	6.81589i	0.740741	+	0.427667i
$255$		0			0
$256$	−22.5700	−	39.0923i	−1.41062	−	2.44327i
$257$	−18.7790	−	10.8420i	−1.17140	−	0.676308i	−0.217391	−	0.976085i	$-0.569755\pi$
$257$	−18.7790	−	10.8420i	−1.17140	−	0.676308i	−0.954009	+	0.299777i	$0.903088\pi$
$258$	15.7788	−	13.3890i	0.982346	−	0.833561i
$259$	−0.501658	−	16.0428i	−0.0311715	−	0.996852i
$260$		0			0
$261$	−5.32382	+	6.48871i	−0.329536	+	0.401641i
$262$	−15.9988	−	27.7107i	−0.988408	−	1.71197i
$263$	0.716573	+	1.24114i	0.0441858	+	0.0765320i	0.887272	−	0.461246i	$-0.152597\pi$
$263$	0.716573	+	1.24114i	0.0441858	+	0.0765320i	−0.843087	+	0.537778i	$0.819264\pi$
$264$	6.10261	+	33.5273i	0.375590	+	2.06346i
$265$		0			0
$266$	17.7692	+	9.53132i	1.08950	+	0.584403i
$267$	−13.9164	−	16.4004i	−0.851670	−	1.00369i
$268$	35.0968	+	20.2631i	2.14388	+	1.23777i
$269$	9.99414	+	17.3104i	0.609354	+	1.05543i	0.991347	+	0.131266i	$0.0419044\pi$
$269$	9.99414	+	17.3104i	0.609354	+	1.05543i	−0.381993	+	0.924165i	$0.624762\pi$
$270$		0			0
$271$	−13.6061	−	7.85550i	−0.826513	−	0.477187i	0.0261443	−	0.999658i	$-0.491677\pi$
$271$	−13.6061	−	7.85550i	−0.826513	−	0.477187i	−0.852657	+	0.522471i	$0.825010\pi$
$272$			31.5838i			1.91505i
$273$	−9.14527	+	1.96175i	−0.553497	+	0.118731i
$274$	−34.6009			−2.09032
$275$		0			0
$276$	−5.67591	+	15.8661i	−0.341649	+	0.955029i
$277$	−1.89637	+	1.09487i	−0.113942	+	0.0657844i	−0.555888	−	0.831257i	$-0.687622\pi$
$277$	−1.89637	+	1.09487i	−0.113942	+	0.0657844i	0.441946	+	0.897042i	$0.354288\pi$
$278$	−42.6896	−	24.6468i	−2.56035	−	1.47822i
$279$	−20.6623	−	3.40878i	−1.23702	−	0.204078i
$280$		0			0
$281$		−	0.0597482i		−	0.00356428i	−0.999998	−	0.00178214i	$-0.999433\pi$
$281$		−	0.0597482i		−	0.00356428i	0.999998	−	0.00178214i	$-0.000567273\pi$
$282$	−2.49957	−	13.7325i	−0.148847	−	0.817757i
$283$	7.97086	+	13.8059i	0.473818	+	0.820677i	0.999551	−	0.0299727i	$-0.00954205\pi$
$283$	7.97086	+	13.8059i	0.473818	+	0.820677i	−0.525733	+	0.850650i	$0.676209\pi$
$284$	−18.0573	+	10.4254i	−1.07150	+	0.618633i
$285$		0			0
$286$			11.5586i			0.683474i
$287$	16.3310	+	26.3483i	0.963986	+	1.55529i
$288$	10.7748	−	65.3114i	0.634911	−	3.84851i
$289$	−6.28895	+	10.8928i	−0.369939	+	0.640752i
$290$		0			0
$291$	−5.81760	+	16.2622i	−0.341034	+	0.953309i
$292$	−18.3716	+	31.8206i	−1.07512	+	1.86216i
$293$			19.3670i			1.13143i	0.824601	+	0.565715i	$0.191400\pi$
$293$			19.3670i			1.13143i	−0.824601	+	0.565715i	$0.808600\pi$
$294$	32.1766	−	7.96176i	1.87658	−	0.464339i
$295$		0			0
$296$	49.9030	+	28.8115i	2.90055	+	1.67464i
$297$	−5.22670	+	9.40905i	−0.303284	+	0.545968i
$298$	34.5154	−	19.9275i	1.99942	−	1.15437i
$299$	−1.81367	+	3.14137i	−0.104887	+	0.181670i
$300$		0			0
$301$	−9.82767	+	6.09129i	−0.566458	+	0.351096i
$302$	19.2167			1.10580
$303$	27.4974	−	5.00506i	1.57969	−	0.287533i
$304$	−36.2598	+	20.9346i	−2.07964	+	1.20068i
$305$		0			0
$306$	−10.9399	+	13.3336i	−0.625394	+	0.762234i
$307$	−17.7639			−1.01384			−0.506921	−	0.861993i	$-0.669216\pi$
$307$	−17.7639			−1.01384			−0.506921	+	0.861993i	$0.669216\pi$
$308$	−0.937683	−	29.9867i	−0.0534294	−	1.70865i
$309$	0.586281	+	0.690928i	0.0333523	+	0.0393055i
$310$		0			0
$311$	3.58777	+	6.21419i	0.203444	+	0.352375i	0.949636	−	0.313356i	$-0.101453\pi$
$311$	3.58777	+	6.21419i	0.203444	+	0.352375i	−0.746192	+	0.665731i	$0.768120\pi$
$312$	11.3105	−	31.6169i	0.640333	−	1.78995i
$313$	−6.79679	+	11.7724i	−0.384177	+	0.665414i	−0.991655	−	0.128922i	$-0.958848\pi$
$313$	−6.79679	+	11.7724i	−0.384177	+	0.665414i	0.607477	+	0.794337i	$0.292182\pi$
$314$	59.8792			3.37918
$315$		0			0
$316$	32.3845			1.82177
$317$	1.61021	−	2.78896i	0.0904383	−	0.156644i	−0.817257	−	0.576273i	$-0.804507\pi$
$317$	1.61021	−	2.78896i	0.0904383	−	0.156644i	0.907696	+	0.419629i	$0.137840\pi$
$318$	9.87970	−	27.6172i	0.554026	−	1.54870i
$319$	−2.89762	−	5.01883i	−0.162236	−	0.281000i
$320$		0			0
$321$	3.45438	+	4.07096i	0.192805	+	0.227219i
$322$	6.07633	−	11.3281i	0.338621	−	0.631288i
$323$	5.86216			0.326179
$324$	37.0343	−	32.4941i	2.05746	−	1.80523i
$325$		0			0
$326$	19.1691	−	11.0673i	1.06168	−	0.612961i
$327$	23.0982	−	4.20431i	1.27733	−	0.232499i
$328$	−111.288			−6.14488
$329$	0.243750	+	7.79503i	0.0134384	+	0.429754i
$330$		0			0
$331$	1.59353	−	2.76008i	0.0875885	−	0.151708i	−0.818903	−	0.573932i	$-0.805417\pi$
$331$	1.59353	−	2.76008i	0.0875885	−	0.151708i	0.906491	+	0.422224i	$0.138751\pi$
$332$	28.2755	−	16.3249i	1.55182	−	0.895944i
$333$	6.41293	+	17.0325i	0.351426	+	0.933373i
$334$	−8.49454	−	4.90433i	−0.464801	−	0.268353i
$335$		0			0
$336$	−21.1465	+	65.4982i	−1.15363	+	3.57322i
$337$		−	33.9495i		−	1.84935i	−0.380763	−	0.924673i	$-0.624339\pi$
$337$		−	33.9495i		−	1.84935i	0.380763	−	0.924673i	$-0.375661\pi$
$338$	−12.0758	+	20.9159i	−0.656837	+	1.13768i
$339$	−6.45559	+	18.0456i	−0.350620	+	0.980104i
$340$		0			0
$341$	7.22973	−	12.5223i	0.391512	−	0.678118i
$342$	−22.5590	−	3.72168i	−1.21985	−	0.201246i
$343$	−18.4389	+	1.73427i	−0.995606	+	0.0936419i
$344$		−	41.5095i		−	2.23804i
$345$		0			0
$346$	30.8012	−	17.7831i	1.65588	−	0.956024i
$347$	−13.9854	−	24.2234i	−0.750773	−	1.30038i	−0.947448	−	0.319909i	$-0.896348\pi$
$347$	−13.9854	−	24.2234i	−0.750773	−	1.30038i	0.196675	−	0.980469i	$-0.436986\pi$
$348$	4.75047	+	26.0987i	0.254652	+	1.39904i
$349$			19.3368i			1.03508i	0.855660	+	0.517539i	$0.173152\pi$
$349$			19.3368i			1.03508i	−0.855660	+	0.517539i	$0.826848\pi$
$350$		0			0
$351$	9.09579	−	5.45406i	0.485497	−	0.291116i
$352$	39.5816	+	22.8524i	2.10971	+	1.21804i
$353$	5.96436	−	3.44352i	0.317451	−	0.183280i	−0.332805	−	0.942996i	$-0.607995\pi$
$353$	5.96436	−	3.44352i	0.317451	−	0.183280i	0.650256	+	0.759715i	$0.274662\pi$
$354$	4.60319	−	12.8675i	0.244657	−	0.683901i
$355$		0			0
$356$	−67.9812			−3.60300
$357$	7.14932	−	6.46151i	0.378382	−	0.341979i
$358$		−	11.0616i		−	0.584625i
$359$	−18.0588	−	10.4263i	−0.953108	−	0.550277i	−0.0590629	−	0.998254i	$-0.518811\pi$
$359$	−18.0588	−	10.4263i	−0.953108	−	0.550277i	−0.894045	+	0.447977i	$0.852145\pi$
$360$		0			0
$361$	−5.61440	−	9.72443i	−0.295495	−	0.511812i
$362$	21.3317	+	12.3159i	1.12117	+	0.647309i
$363$	7.51873	+	8.86077i	0.394631	+	0.465070i
$364$	−13.9736	+	26.0509i	−0.732416	+	1.36544i
$365$		0			0
$366$	6.17129	+	33.9047i	0.322579	+	1.77222i
$367$	11.9747	+	20.7408i	0.625075	+	1.08266i	0.988526	+	0.151048i	$0.0482649\pi$
$367$	11.9747	+	20.7408i	0.625075	+	1.08266i	−0.363451	+	0.931613i	$0.618402\pi$
$368$	13.3461	+	23.1160i	0.695711	+	1.20501i
$369$	−27.1736	−	22.2953i	−1.41460	−	1.16065i
$370$		0			0
$371$	−7.74654	+	14.4418i	−0.402180	+	0.749782i
$372$	−50.4673	+	42.8236i	−2.61661	+	2.22030i
$373$	−3.44723	−	1.99026i	−0.178491	−	0.103052i	0.408093	−	0.912940i	$-0.366194\pi$
$373$	−3.44723	−	1.99026i	−0.178491	−	0.103052i	−0.586583	+	0.809889i	$0.699527\pi$
$374$	−5.95433	−	10.3132i	−0.307891	−	0.533283i
$375$		0			0
$376$	−24.2473	−	13.9992i	−1.25046	−	0.721954i
$377$			5.71037i			0.294099i
$378$	−31.6145	+	20.3265i	−1.62607	+	1.04548i
$379$	13.9203			0.715038			0.357519	−	0.933906i	$-0.383623\pi$
$379$	13.9203			0.715038			0.357519	+	0.933906i	$0.383623\pi$
$380$		0			0
$381$	8.13164	+	2.90899i	0.416596	+	0.149032i
$382$	−61.8048	+	35.6830i	−3.16221	+	1.82570i
$383$	−13.6843	−	7.90064i	−0.699236	−	0.403704i	0.107827	−	0.994170i	$-0.465611\pi$
$383$	−13.6843	−	7.90064i	−0.699236	−	0.403704i	−0.807063	+	0.590466i	$0.798944\pi$
$384$	−43.3304	−	51.0646i	−2.21120	−	2.60588i
$385$		0			0
$386$		−	20.5263i		−	1.04476i
$387$	8.31593	−	10.1355i	0.422723	−	0.515217i
$388$	27.2940	+	47.2747i	1.38564	+	2.40001i
$389$	−21.7212	+	12.5407i	−1.10131	+	0.635841i	−0.936564	−	0.350495i	$-0.886013\pi$
$389$	−21.7212	+	12.5407i	−1.10131	+	0.635841i	−0.164744	+	0.986336i	$0.552680\pi$
$390$		0			0
$391$		−	3.73720i		−	0.188998i
$392$	29.5820	−	59.5458i	1.49412	−	3.00752i
$393$	−13.1159	−	15.4570i	−0.661610	−	0.779702i
$394$	28.4246	−	49.2329i	1.43201	−	2.48032i
$395$		0			0
$396$	11.9868	+	31.8365i	0.602361	+	1.59985i
$397$	0.733605	−	1.27064i	0.0368186	−	0.0637716i	−0.847029	−	0.531547i	$-0.821611\pi$
$397$	0.733605	−	1.27064i	0.0368186	−	0.0637716i	0.883847	+	0.467775i	$0.154944\pi$
$398$		−	62.7653i		−	3.14614i
$399$	12.1569	+	3.92492i	0.608606	+	0.196492i
$400$		0			0
$401$	−18.5840	−	10.7295i	−0.928039	−	0.535804i	−0.0418482	−	0.999124i	$-0.513325\pi$
$401$	−18.5840	−	10.7295i	−0.928039	−	0.535804i	−0.886191	+	0.463320i	$0.846658\pi$
$402$	33.0068	+	11.8078i	1.64623	+	0.588918i
$403$	−12.3389	+	7.12384i	−0.614642	+	0.354864i
$404$	44.1680	−	76.5012i	2.19744	−	3.80608i
$405$		0			0
$406$	−0.632495	−	20.2269i	−0.0313902	−	1.00385i
$407$	−12.5663			−0.622889
$408$	6.19535	+	34.0368i	0.306715	+	1.68507i
$409$	6.02404	−	3.47798i	0.297870	−	0.171975i	−0.343616	−	0.939110i	$-0.611652\pi$
$409$	6.02404	−	3.47798i	0.297870	−	0.171975i	0.641485	+	0.767135i	$0.278318\pi$
$410$		0			0
$411$	−21.5668	+	3.92556i	−1.06381	+	0.193634i
$412$	2.86396			0.141097
$413$	−3.60930	+	6.72879i	−0.177602	+	0.331102i
$414$	−2.37262	+	14.3816i	−0.116608	+	0.706817i
$415$		0			0
$416$	−22.5177	−	39.0019i	−1.10402	−	1.91222i
$417$	−29.4047	−	10.5192i	−1.43995	−	0.515125i
$418$	7.89337	−	13.6717i	0.386077	−	0.668706i
$419$	−34.8831			−1.70415			−0.852076	−	0.523419i	$-0.824656\pi$
$419$	−34.8831			−1.70415			−0.852076	+	0.523419i	$0.824656\pi$
$420$		0			0
$421$	−29.6603			−1.44555			−0.722777	−	0.691082i	$-0.757134\pi$
$421$	−29.6603			−1.44555			−0.722777	+	0.691082i	$0.757134\pi$
$422$	−25.9361	+	44.9227i	−1.26255	+	2.18680i
$423$	−3.11597	−	8.27589i	−0.151504	−	0.402387i
$424$	−29.4175	−	50.9526i	−1.42864	−	2.47448i
$425$		0			0
$426$	−13.7522	+	11.6693i	−0.666297	+	0.565380i
$427$	−0.601804	−	19.2454i	−0.0291233	−	0.931353i
$428$	16.8745			0.815661
$429$	1.31135	+	7.20448i	0.0633127	+	0.347835i
$430$		0			0
$431$	7.32938	−	4.23162i	0.353044	−	0.203830i	−0.312981	−	0.949759i	$-0.601328\pi$
$431$	7.32938	−	4.23162i	0.353044	−	0.203830i	0.666025	+	0.745929i	$0.267994\pi$
$432$	−1.29115	−	78.0321i	−0.0621203	−	3.75432i
$433$	−10.6435			−0.511495			−0.255748	−	0.966744i	$-0.582322\pi$
$433$	−10.6435			−0.511495			−0.255748	+	0.966744i	$0.582322\pi$
$434$	42.9169	−	26.6004i	2.06008	−	1.27686i
$435$		0			0
$436$	37.1017	−	64.2620i	1.77685	−	3.07759i
$437$	4.29049	−	2.47711i	0.205242	−	0.118496i
$438$	−10.7056	+	29.9258i	−0.511531	+	1.42991i
$439$	−10.9548	−	6.32477i	−0.522845	−	0.301865i	0.215253	−	0.976558i	$-0.430942\pi$
$439$	−10.9548	−	6.32477i	−0.522845	−	0.301865i	−0.738098	+	0.674694i	$0.764276\pi$
$440$		0			0
$441$	19.1524	−	8.61309i	0.912019	−	0.410147i
$442$			11.7342i			0.558141i
$443$	12.8656	−	22.2838i	0.611261	−	1.05874i	−0.379767	−	0.925082i	$-0.623996\pi$
$443$	12.8656	−	22.2838i	0.611261	−	1.05874i	0.991028	−	0.133654i	$-0.0426709\pi$
$444$	54.1606	+	19.3752i	2.57035	+	0.919508i
$445$		0			0
$446$	8.28756	−	14.3545i	0.392427	−	0.679704i
$447$	19.2526	−	16.3367i	0.910618	−	0.772697i
$448$	42.2118	+	68.1044i	1.99432	+	3.21763i
$449$		−	35.6974i		−	1.68466i	−0.538960	−	0.842331i	$-0.681183\pi$
$449$		−	35.6974i		−	1.68466i	0.538960	−	0.842331i	$-0.318817\pi$
$450$		0			0
$451$	21.0180	−	12.1348i	0.989700	−	0.571404i
$452$	30.2872	+	52.4590i	1.42459	+	2.46747i
$453$	11.9778	−	2.18019i	0.562766	−	0.102434i
$454$			59.6132i			2.79778i
$455$		0			0
$456$	−34.9695	+	29.6731i	−1.63760	+	1.38957i
$457$	9.61730	+	5.55255i	0.449878	+	0.259737i	0.707779	−	0.706434i	$-0.249697\pi$
$457$	9.61730	+	5.55255i	0.449878	+	0.259737i	−0.257900	+	0.966172i	$0.583031\pi$
$458$	21.7287	−	12.5451i	1.01531	−	0.586192i
$459$	−5.30613	+	9.55204i	−0.247669	+	0.445851i
$460$		0			0
$461$	18.8795			0.879304			0.439652	−	0.898168i	$-0.355102\pi$
$461$	18.8795			0.879304			0.439652	+	0.898168i	$0.355102\pi$
$462$	−5.44298	−	25.3740i	−0.253230	−	1.18051i
$463$		−	14.6440i		−	0.680565i	−0.940323	−	0.340282i	$-0.889477\pi$
$463$		−	14.6440i		−	0.680565i	0.940323	−	0.340282i	$-0.110523\pi$
$464$	36.3906	+	21.0101i	1.68939	+	0.975371i
$465$		0			0
$466$	24.8546	+	43.0495i	1.15137	+	1.99423i
$467$	4.69754	+	2.71213i	0.217376	+	0.125502i	0.604735	−	0.796427i	$-0.293279\pi$
$467$	4.69754	+	2.71213i	0.217376	+	0.125502i	−0.387359	+	0.921929i	$0.626612\pi$
$468$	5.45626	−	33.0731i	0.252216	−	1.52880i
$469$	−17.2602	−	9.25832i	−0.797003	−	0.427509i
$470$		0			0
$471$	37.3228	−	6.79346i	1.71974	−	0.313026i
$472$	−13.7063	−	23.7401i	−0.630885	−	1.09272i
$473$	4.52615	+	7.83952i	0.208113	+	0.360462i
$474$	27.5598	−	5.01641i	1.26586	−	0.230411i
$475$		0			0
$476$	−0.951932	−	30.4424i	−0.0436317	−	1.39533i
$477$	3.02478	−	18.3347i	0.138495	−	0.839488i
$478$	−31.1226	−	17.9686i	−1.42351	−	0.821866i
$479$	−1.85555	−	3.21391i	−0.0847823	−	0.146847i	0.820516	−	0.571623i	$-0.193686\pi$
$479$	−1.85555	−	3.21391i	−0.0847823	−	0.146847i	−0.905298	+	0.424776i	$0.860353\pi$
$480$		0			0
$481$	10.7234	+	6.19113i	0.488943	+	0.282291i
$482$		−	0.0488872i		−	0.00222675i
$483$	2.50218	−	7.75016i	0.113853	−	0.352645i
$484$	36.7288			1.66949
$485$		0			0
$486$	26.4835	−	33.3898i	1.20132	−	1.51459i
$487$	−15.8697	+	9.16240i	−0.719127	+	0.415188i	−0.814431	−	0.580260i	$-0.802951\pi$
$487$	−15.8697	+	9.16240i	−0.719127	+	0.415188i	0.0953043	+	0.995448i	$0.469618\pi$
$488$	59.8652	+	34.5632i	2.70997	+	1.56460i
$489$	10.6925	−	9.07304i	0.483532	−	0.410297i
$490$		0			0
$491$			36.7134i			1.65685i	0.560098	+	0.828426i	$0.310763\pi$
$491$			36.7134i			1.65685i	−0.560098	+	0.828426i	$0.689237\pi$
$492$	−109.297	+	19.8942i	−4.92750	+	0.896899i
$493$	−2.94166	−	5.09510i	−0.132486	−	0.229472i
$494$	−13.4715	+	7.77777i	−0.606111	+	0.349938i
$495$		0			0
$496$			104.843i			4.70759i
$497$	8.56542	−	5.30894i	0.384212	−	0.238138i
$498$	21.5343	−	18.2727i	0.964973	−	0.818820i
$499$	0.535767	−	0.927975i	0.0239842	−	0.0415419i	−0.853784	−	0.520627i	$-0.825698\pi$
$499$	0.535767	−	0.927975i	0.0239842	−	0.0415419i	0.877768	+	0.479085i	$0.159032\pi$
$500$		0			0
$501$	−5.85107	−	2.09314i	−0.261406	−	0.0935147i
$502$	−7.36212	+	12.7516i	−0.328588	+	0.569131i
$503$		−	27.1662i		−	1.21128i	−0.795739	−	0.605640i	$-0.792917\pi$
$503$		−	27.1662i		−	1.21128i	0.795739	−	0.605640i	$-0.207083\pi$
$504$	−9.94099	+	74.7333i	−0.442807	+	3.32888i
$505$		0			0
$506$	−8.71588	−	5.03212i	−0.387468	−	0.223705i
$507$	−5.15390	+	14.4069i	−0.228893	+	0.639834i
$508$	23.6388	−	13.6479i	1.04880	−	0.605527i
$509$	−11.8003	+	20.4387i	−0.523037	+	0.905927i	0.476603	+	0.879119i	$0.341868\pi$
$509$	−11.8003	+	20.4387i	−0.523037	+	0.905927i	−0.999641	+	0.0268088i	$0.991465\pi$
$510$		0			0
$511$	8.39408	−	15.6490i	0.371332	−	0.692272i
$512$	−46.0773			−2.03635
$513$	−14.4833	+	0.239645i	−0.639451	+	0.0105806i
$514$	−51.3401	+	29.6412i	−2.26452	+	1.30742i
$515$		0			0
$516$	−7.42033	−	40.7668i	−0.326662	−	1.79466i
$517$	6.10583			0.268534
$518$	−38.6694	−	20.7421i	−1.69904	−	0.911356i
$519$	17.1809	−	14.5787i	0.754157	−	0.639933i
$520$		0			0
$521$	12.5487	+	21.7350i	0.549770	+	0.952230i	0.998290	+	0.0584568i	$0.0186180\pi$
$521$	12.5487	+	21.7350i	0.549770	+	0.952230i	−0.448520	+	0.893773i	$0.648049\pi$
$522$	8.08548	+	21.4747i	0.353892	+	0.939922i
$523$	−3.05478	+	5.29103i	−0.133576	+	0.231361i	−0.925053	−	0.379839i	$-0.875979\pi$
$523$	−3.05478	+	5.29103i	−0.133576	+	0.231361i	0.791476	+	0.611200i	$0.209313\pi$
$524$	−64.0708			−2.79895
$525$		0			0
$526$	3.91810			0.170837
$527$	7.33960	−	12.7126i	0.319718	−	0.553768i
$528$	50.7370	+	18.1505i	2.20805	+	0.789900i
$529$	9.92081	+	17.1833i	0.431340	+	0.747102i
$530$		0			0
$531$	1.40932	−	8.54258i	0.0611592	−	0.370716i
$532$	34.3184	−	21.2709i	1.48789	−	0.922211i
$533$	−23.9141			−1.03583
$534$	−57.8533	+	10.5304i	−2.50356	+	0.455695i
$535$		0			0
$536$	60.8963	−	35.1585i	2.63032	−	1.51862i
$537$	−1.25497	−	6.89472i	−0.0541560	−	0.297529i
$538$	54.6463			2.35597
$539$	0.905929	+	14.4715i	0.0390211	+	0.623330i
$540$		0			0
$541$	11.2979	−	19.5686i	0.485737	−	0.841321i	−0.514129	−	0.857713i	$-0.671885\pi$
$541$	11.2979	−	19.5686i	0.485737	−	0.841321i	0.999866	+	0.0163924i	$0.00521808\pi$
$542$	−37.1980	+	21.4763i	−1.59779	+	0.922485i
$543$	14.6934	+	5.25636i	0.630552	+	0.225572i
$544$	40.1831	+	23.1997i	1.72284	+	0.994680i
$545$		0			0
$546$	−7.85648	+	24.3344i	−0.336226	+	1.04141i
$547$		−	20.6880i		−	0.884556i	−0.896878	−	0.442278i	$-0.854170\pi$
$547$		−	20.6880i		−	0.884556i	0.896878	−	0.442278i	$-0.145830\pi$
$548$	−34.6418	+	60.0013i	−1.47982	+	2.56313i
$549$	7.69314	+	20.4327i	0.328335	+	0.872044i
$550$		0			0
$551$	3.89962	−	6.75433i	0.166129	−	0.287744i
$552$	18.9169	+	22.2935i	0.805158	+	0.948874i
$553$	−15.6439	+	0.489184i	−0.665246	+	0.0208022i
$554$			5.98657i			0.254345i
$555$		0			0
$556$	−85.4801	+	49.3520i	−3.62516	+	2.09299i
$557$	2.36130	+	4.08989i	0.100051	+	0.173294i	0.911706	−	0.410844i	$-0.134766\pi$
$557$	2.36130	+	4.08989i	0.100051	+	0.173294i	−0.811654	+	0.584138i	$0.801433\pi$
$558$	−36.3153	+	44.2612i	−1.53735	+	1.87373i
$559$		−	8.91972i		−	0.377264i
$560$		0			0
$561$	−4.88140	−	5.75269i	−0.206093	−	0.242879i
$562$	−0.141462	−	0.0816733i	−0.00596723	−	0.00344518i
$563$	29.2995	−	16.9161i	1.23483	−	0.712927i	0.266794	−	0.963754i	$-0.414036\pi$
$563$	29.2995	−	16.9161i	1.23483	−	0.712927i	0.968032	+	0.250826i	$0.0807023\pi$
$564$	−26.3160	−	9.41422i	−1.10810	−	0.396410i
$565$		0			0
$566$	43.5833			1.83194
$567$	−17.3992	+	16.2563i	−0.730699	+	0.682700i
$568$			36.1781i			1.51800i
$569$	21.5858	+	12.4626i	0.904926	+	0.522459i	0.878795	−	0.477199i	$-0.158348\pi$
$569$	21.5858	+	12.4626i	0.904926	+	0.522459i	0.0261307	+	0.999659i	$0.491681\pi$
$570$		0			0
$571$	−1.10062	−	1.90633i	−0.0460596	−	0.0797776i	0.842076	−	0.539358i	$-0.181333\pi$
$571$	−1.10062	−	1.90633i	−0.0460596	−	0.0797776i	−0.888136	+	0.459581i	$0.848000\pi$
$572$	20.0437	+	11.5723i	0.838071	+	0.483860i
$573$	−34.4747	+	29.2532i	−1.44020	+	1.22207i
$574$	84.7071	−	2.64879i	3.53561	−	0.110558i
$575$		0			0
$576$	−70.2377	−	57.6283i	−2.92657	−	2.40118i
$577$	12.6702	+	21.9455i	0.527469	+	0.913602i	0.999487	+	0.0320140i	$0.0101921\pi$
$577$	12.6702	+	21.9455i	0.527469	+	0.913602i	−0.472019	+	0.881588i	$0.656475\pi$
$578$	17.1935	+	29.7800i	0.715154	+	1.23868i
$579$	−2.32876	−	12.7940i	−0.0967799	−	0.531702i
$580$		0			0
$581$	−13.4124	+	8.31314i	−0.556440	+	0.344887i
$582$	30.5507	+	36.0038i	1.26637	+	1.49240i
$583$	11.1116	+	6.41531i	0.460197	+	0.265695i
$584$	31.8766	+	55.2118i	1.31906	+	2.28468i
$585$		0			0
$586$	45.8540	+	26.4738i	1.89421	+	1.09362i
$587$		−	21.7712i		−	0.898593i	−0.893383	−	0.449297i	$-0.851675\pi$
$587$		−	21.7712i		−	0.898593i	0.893383	−	0.449297i	$-0.148325\pi$
$588$	18.4082	−	63.7685i	0.759139	−	2.62977i
$589$	19.4595			0.801816
$590$		0			0
$591$	12.1315	−	33.9118i	0.499023	−	1.39494i
$592$	78.9088	−	45.5580i	3.24313	−	1.87242i
$593$	−30.1501	−	17.4071i	−1.23811	−	0.714826i	−0.269406	−	0.963027i	$-0.586827\pi$
$593$	−30.1501	−	17.4071i	−1.23811	−	0.714826i	−0.968709	+	0.248201i	$0.920161\pi$
$594$	15.1326	+	25.2367i	0.620897	+	1.03548i
$595$		0			0
$596$		−	79.8041i		−	3.26890i
$597$	−7.12088	−	39.1216i	−0.291438	−	1.60114i
$598$	4.95842	+	8.58823i	0.202765	+	0.351199i
$599$	−5.38292	+	3.10783i	−0.219940	+	0.126982i	−0.605922	−	0.795524i	$-0.707196\pi$
$599$	−5.38292	+	3.10783i	−0.219940	+	0.126982i	0.385983	+	0.922506i	$0.373863\pi$
$600$		0			0
$601$		−	29.5235i		−	1.20429i	−0.798388	−	0.602144i	$-0.794313\pi$
$601$		−	29.5235i		−	1.20429i	0.798388	−	0.602144i	$-0.205687\pi$
$602$	0.987972	+	31.5949i	0.0402667	+	1.28771i
$603$	21.9128	+	3.61508i	0.892359	+	0.147218i
$604$	19.2394	−	33.3237i	0.782841	−	1.35592i
$605$		0			0
$606$	25.7377	−	71.9458i	1.04552	−	2.92260i
$607$	−9.31727	+	16.1380i	−0.378176	+	0.655021i	−0.990797	−	0.135356i	$-0.956782\pi$
$607$	−9.31727	+	16.1380i	−0.378176	+	0.655021i	0.612621	+	0.790377i	$0.290115\pi$
$608$			61.5096i			2.49454i
$609$	−2.68903	−	12.5357i	−0.108965	−	0.507973i
$610$		0			0
$611$	−5.21036	−	3.00820i	−0.210788	−	0.121699i
$612$	12.1690	+	32.3203i	0.491903	+	1.30647i
$613$	−4.49418	+	2.59472i	−0.181518	+	0.104800i	−0.588006	−	0.808857i	$-0.700087\pi$
$613$	−4.49418	+	2.59472i	−0.181518	+	0.104800i	0.406487	+	0.913656i	$0.366753\pi$
$614$	−24.2826	+	42.0586i	−0.979965	+	1.69735i
$615$		0			0
$616$	−45.8727	−	24.6059i	−1.84826	−	0.991401i
$617$	−8.86686			−0.356966			−0.178483	−	0.983943i	$-0.557119\pi$
$617$	−8.86686			−0.356966			−0.178483	+	0.983943i	$0.557119\pi$
$618$	2.43729	−	0.443633i	0.0980422	−	0.0178455i
$619$	−20.2601	+	11.6972i	−0.814321	+	0.470148i	−0.848454	−	0.529269i	$-0.822466\pi$
$619$	−20.2601	+	11.6972i	−0.814321	+	0.470148i	0.0341335	+	0.999417i	$0.489133\pi$
$620$		0			0
$621$	0.152776	+	9.23325i	0.00613071	+	0.370517i
$622$	19.6173			0.786582
$623$	32.8395	−	1.02689i	1.31569	−	0.0411415i
$624$	−34.3537	−	40.4856i	−1.37525	−	1.62072i
$625$		0			0
$626$	18.5819	+	32.1847i	0.742680	+	1.28636i
$627$	3.36885	−	9.41712i	0.134539	−	0.376084i
$628$	59.9501	−	103.837i	2.39227	−	4.14353i
$629$	−12.7573			−0.508666
$630$		0			0
$631$	−8.27702			−0.329503			−0.164752	−	0.986335i	$-0.552682\pi$
$631$	−8.27702			−0.329503			−0.164752	+	0.986335i	$0.552682\pi$
$632$	28.0951	−	48.6621i	1.11756	−	1.93568i
$633$	−11.0694	+	30.9429i	−0.439969	+	1.22987i
$634$	−4.40217	−	7.62479i	−0.174833	−	0.302819i
$635$		0			0
$636$	−37.9996	−	44.7822i	−1.50678	−	1.77573i
$637$	6.35669	−	12.7954i	0.251861	−	0.506973i
$638$	−15.8437			−0.627258
$639$	−7.24785	+	8.83372i	−0.286720	+	0.349457i
$640$		0			0
$641$	−35.6157	+	20.5627i	−1.40673	+	0.812179i	−0.995072	−	0.0991572i	$-0.968385\pi$
$641$	−35.6157	+	20.5627i	−1.40673	+	0.812179i	−0.411663	+	0.911336i	$0.635052\pi$
$642$	14.3606	−	2.61389i	0.566766	−	0.103162i
$643$	3.55349			0.140136			0.0700680	−	0.997542i	$-0.477678\pi$
$643$	3.55349			0.140136			0.0700680	+	0.997542i	$0.477678\pi$
$644$	−13.5605	−	21.8784i	−0.534357	−	0.862130i
$645$		0			0
$646$	8.01333	−	13.8795i	0.315280	−	0.546081i
$647$	40.4653	−	23.3627i	1.59086	−	0.918481i	0.597695	−	0.801724i	$-0.296084\pi$
$647$	40.4653	−	23.3627i	1.59086	−	0.918481i	0.993161	−	0.116757i	$-0.0372498\pi$
$648$	−16.6979	−	83.8393i	−0.655954	−	3.29352i
$649$	5.17718	+	2.98905i	0.203222	+	0.117330i
$650$		0			0
$651$	23.7323	−	21.4491i	0.930142	−	0.840655i
$652$		−	44.3215i		−	1.73576i
$653$	0.948985	−	1.64369i	0.0371367	−	0.0643226i	−0.846860	−	0.531816i	$-0.821510\pi$
$653$	0.948985	−	1.64369i	0.0371367	−	0.0643226i	0.883996	+	0.467494i	$0.154843\pi$
$654$	21.6200	−	60.4354i	0.845408	−	2.36321i
$655$		0			0
$656$	−87.9870	+	152.398i	−3.43532	+	5.95014i
$657$	−3.27763	+	19.8673i	−0.127872	+	0.775098i
$658$	18.7890	+	10.0784i	0.732472	+	0.392896i
$659$			2.32588i			0.0906035i	0.998973	+	0.0453017i	$0.0144249\pi$
$659$			2.32588i			0.0906035i	−0.998973	+	0.0453017i	$0.985575\pi$
$660$		0			0
$661$	−8.03266	+	4.63766i	−0.312434	+	0.180384i	−0.648015	−	0.761627i	$-0.724401\pi$
$661$	−8.03266	+	4.63766i	−0.312434	+	0.180384i	0.335581	+	0.942011i	$0.391067\pi$
$662$	−4.35659	−	7.54583i	−0.169324	−	0.293277i
$663$	1.33128	+	7.31396i	0.0517026	+	0.284051i
$664$		−	56.6505i		−	2.19846i
$665$		0			0
$666$	49.0930	+	8.09915i	1.90231	+	0.313836i
$667$	−4.30597	−	2.48605i	−0.166728	−	0.0962603i
$668$	−17.0092	+	9.82025i	−0.658105	+	0.379957i
$669$	3.53709	−	9.88740i	0.136752	−	0.382269i
$670$		0			0
$671$	−15.0749			−0.581961
$672$	67.7983	+	75.0153i	2.61538	+	2.89378i
$673$		−	26.5356i		−	1.02287i	−0.859321	−	0.511436i	$-0.829114\pi$
$673$		−	26.5356i		−	1.02287i	0.859321	−	0.511436i	$-0.170886\pi$
$674$	−80.3801	−	46.4075i	−3.09613	−	1.78755i
$675$		0			0
$676$	24.1802	+	41.8813i	0.930006	+	1.61082i
$677$	−31.8130	−	18.3673i	−1.22267	−	0.705911i	−0.257187	−	0.966362i	$-0.582796\pi$
$677$	−31.8130	−	18.3673i	−1.22267	−	0.705911i	−0.965487	+	0.260450i	$0.916129\pi$
$678$	33.9010	+	39.9521i	1.30196	+	1.53435i
$679$	−13.8990	−	22.4246i	−0.533394	−	0.860577i
$680$		0			0
$681$	6.76327	+	37.1569i	0.259169	+	1.42386i
$682$	−19.7655	−	34.2348i	−0.756859	−	1.31092i
$683$	−25.5940	−	44.3300i	−0.979326	−	1.69624i	−0.664851	−	0.746976i	$-0.731505\pi$
$683$	−25.5940	−	44.3300i	−0.979326	−	1.69624i	−0.314475	−	0.949266i	$-0.601829\pi$
$684$	−29.0394	+	35.3934i	−1.11035	+	1.35330i
$685$		0			0
$686$	−21.0990	+	46.0273i	−0.805565	+	1.75733i
$687$	12.1202	−	10.2845i	0.462416	−	0.392379i
$688$	−56.8430	−	32.8183i	−2.16712	−	1.25119i
$689$	−6.32135	−	10.9489i	−0.240824	−	0.417120i
$690$		0			0
$691$	15.4415	+	8.91516i	0.587423	+	0.339149i	0.764078	−	0.645124i	$-0.223194\pi$
$691$	15.4415	+	8.91516i	0.587423	+	0.339149i	−0.176655	+	0.984273i	$0.556528\pi$
$692$		−	71.2164i		−	2.70724i
$693$	−6.27137	−	15.1981i	−0.238229	−	0.577330i
$694$	−76.4696			−2.90275
$695$		0			0
$696$	43.3382	+	15.5037i	1.64273	+	0.587666i
$697$	21.3374	−	12.3192i	0.808213	−	0.466622i
$698$	45.7827	+	26.4327i	1.73290	+	1.00049i
$699$	20.3760	+	24.0130i	0.770691	+	0.908254i
$700$		0			0
$701$		−	42.3606i		−	1.59994i	−0.600041	−	0.799970i	$-0.704849\pi$
$701$		−	42.3606i		−	1.59994i	0.600041	−	0.799970i	$-0.295151\pi$
$702$	−0.479695	−	28.9910i	−0.0181049	−	1.09420i
$703$	−8.45586	−	14.6460i	−0.318919	−	0.552384i
$704$	54.3268	−	31.3656i	2.04752	−	1.18214i
$705$		0			0
$706$		−	18.8286i		−	0.708624i
$707$	−20.1806	+	37.6225i	−0.758968	+	1.41494i
$708$	−17.7049	−	20.8651i	−0.665392	−	0.784159i
$709$	−15.3029	+	26.5055i	−0.574714	+	0.995434i	0.421359	+	0.906894i	$0.361553\pi$
$709$	−15.3029	+	26.5055i	−0.574714	+	0.995434i	−0.996073	+	0.0885399i	$0.971780\pi$
$710$		0			0
$711$	16.6089	−	6.25347i	0.622884	−	0.234523i
$712$	−58.9770	+	102.151i	−2.21026	+	3.82828i
$713$		−	12.4057i		−	0.464596i
$714$	−5.52570	−	25.7596i	−0.206794	−	0.964030i
$715$		0			0
$716$	−19.1820	−	11.0747i	−0.716863	−	0.413881i
$717$	−21.4373	−	7.66893i	−0.800592	−	0.286401i
$718$	−49.3713	+	28.5045i	−1.84252	+	1.06378i
$719$	11.4617	−	19.8522i	0.427449	−	0.740364i	−0.569196	−	0.822202i	$-0.692746\pi$
$719$	11.4617	−	19.8522i	0.427449	−	0.740364i	0.996646	+	0.0818377i	$0.0260789\pi$
$720$		0			0
$721$	−1.38349	+	0.0432616i	−0.0515238	+	0.00161115i
$722$	−30.6986			−1.14248
$723$	−0.00554638	−	0.0304714i	−0.000206272	−	0.00113324i
$724$	42.7139	−	24.6609i	1.58745	−	0.916515i
$725$		0			0
$726$	31.2569	−	5.68935i	1.16005	−	0.211152i
$727$	−32.1534			−1.19250			−0.596252	−	0.802798i	$-0.703344\pi$
$727$	−32.1534			−1.19250			−0.596252	+	0.802798i	$0.703344\pi$
$728$	27.0223	+	43.5977i	1.00151	+	1.61584i
$729$	12.7190	−	23.8165i	0.471075	−	0.882093i
$730$		0			0
$731$	4.59493	+	7.95866i	0.169950	+	0.294362i
$732$	64.9726	+	23.2431i	2.40146	+	0.859090i
$733$	−6.82836	+	11.8271i	−0.252211	+	0.436843i	−0.964134	−	0.265415i	$-0.914491\pi$
$733$	−6.82836	+	11.8271i	−0.252211	+	0.436843i	0.711923	+	0.702258i	$0.247824\pi$
$734$	65.4757			2.41675
$735$		0			0
$736$	39.2131			1.44541
$737$	−7.66729	+	13.2801i	−0.282428	+	0.489180i
$738$	−89.9325	+	33.8607i	−3.31046	+	1.24643i
$739$	−9.19147	−	15.9201i	−0.338114	−	0.585630i	0.645964	−	0.763368i	$-0.276456\pi$
$739$	−9.19147	−	15.9201i	−0.338114	−	0.585630i	−0.984078	+	0.177737i	$0.943122\pi$
$740$		0			0
$741$	−7.51438	+	6.37626i	−0.276048	+	0.234238i
$742$	23.6038	+	38.0824i	0.866524	+	1.39805i
$743$	10.0307			0.367992			0.183996	−	0.982927i	$-0.441097\pi$
$743$	10.0307			0.367992			0.183996	+	0.982927i	$0.441097\pi$
$744$	20.5655	+	112.986i	0.753970	+	4.14226i
$745$		0			0
$746$	−9.42443	+	5.44120i	−0.345053	+	0.199216i
$747$	11.3492	−	13.8325i	0.415247	−	0.506105i
$748$	−23.8455			−0.871877
$749$	−8.15155	+	0.254898i	−0.297851	+	0.00931378i
$750$		0			0
$751$	−16.6659	+	28.8661i	−0.608146	+	1.05334i	0.383400	+	0.923582i	$0.374753\pi$
$751$	−16.6659	+	28.8661i	−0.608146	+	1.05334i	−0.991546	+	0.129757i	$0.958580\pi$
$752$	−38.3409	+	22.1361i	−1.39815	+	0.807222i
$753$	−3.14212	+	8.78332i	−0.114505	+	0.320082i
$754$	13.5201	+	7.80583i	0.492373	+	0.284272i
$755$		0			0
$756$	3.59636	+	75.1732i	0.130798	+	2.73402i
$757$			7.30587i			0.265536i	0.991147	+	0.132768i	$0.0423866\pi$
$757$			7.30587i			0.265536i	−0.991147	+	0.132768i	$0.957613\pi$
$758$	19.0285	−	32.9583i	0.691145	−	1.19710i
$759$	−6.00353	−	2.14768i	−0.217914	−	0.0779560i
$760$		0			0
$761$	3.12585	−	5.41414i	0.113312	−	0.196262i	−0.803792	−	0.594911i	$-0.797187\pi$
$761$	3.12585	−	5.41414i	0.113312	−	0.196262i	0.917104	+	0.398649i	$0.130521\pi$
$762$	18.0030	−	15.2763i	0.652182	−	0.553403i
$763$	−16.9519	+	31.6034i	−0.613701	+	1.14412i
$764$			142.901i			5.16998i
$765$		0			0
$766$	−37.4118	+	21.5997i	−1.35174	+	0.780429i
$767$	−2.94527	−	5.10135i	−0.106347	−	0.184199i
$768$	−76.9208	+	14.0010i	−2.77564	+	0.505219i
$769$			12.2298i			0.441018i	0.975385	+	0.220509i	$0.0707718\pi$
$769$			12.2298i			0.441018i	−0.975385	+	0.220509i	$0.929228\pi$
$770$		0			0
$771$	−28.6375	+	24.3001i	−1.03135	+	0.875146i
$772$	−35.5946	−	20.5505i	−1.28108	−	0.739630i
$773$	35.3660	−	20.4185i	1.27203	−	0.734404i	0.296656	−	0.954984i	$-0.404128\pi$
$773$	35.3660	−	20.4185i	1.27203	−	0.734404i	0.975369	+	0.220580i	$0.0707951\pi$
$774$	−12.6297	−	33.5440i	−0.453965	−	1.20571i
$775$		0			0
$776$	94.7156			3.40009
$777$	−26.4559	−	8.54144i	−0.949101	−	0.306422i
$778$			68.5707i			2.45838i
$779$	28.2860	+	16.3310i	1.01345	+	0.585117i
$780$		0			0
$781$	−3.94482	−	6.83263i	−0.141157	−	0.244491i
$782$	−8.84834	−	5.10859i	−0.316416	−	0.182683i
$783$	7.47605	+	12.4679i	0.267172	+	0.445565i
$784$	−58.1537	−	87.5877i	−2.07692	−	3.12813i
$785$		0			0
$786$	−54.5255	+	9.92468i	−1.94486	+	0.354002i
$787$	−21.9467	−	38.0128i	−0.782316	−	1.35501i	−0.930589	−	0.366065i	$-0.880705\pi$
$787$	−21.9467	−	38.0128i	−0.782316	−	1.35501i	0.148273	−	0.988946i	$-0.452629\pi$
$788$	−56.9165	−	98.5822i	−2.02757	−	3.51185i
$789$	2.44215	−	0.444518i	0.0869430	−	0.0158253i
$790$		0			0
$791$	−15.4232	−	24.8838i	−0.548387	−	0.884765i
$792$	58.2379	+	9.60785i	2.06940	+	0.341400i
$793$	12.8641	+	7.42706i	0.456816	+	0.263743i
$794$	−2.00561	−	3.47382i	−0.0711766	−	0.123281i
$795$		0			0
$796$	−108.841	−	62.8395i	−3.85777	−	2.22729i
$797$			32.7354i			1.15955i	0.814778	+	0.579773i	$0.196859\pi$
$797$			32.7354i			1.15955i	−0.814778	+	0.579773i	$0.803141\pi$
$798$	25.9108	−	23.4180i	0.917231	−	0.828986i
$799$	6.19862			0.219291
$800$		0			0
$801$	−34.8653	+	13.1272i	−1.23191	+	0.463828i
$802$	−50.8070	+	29.3334i	−1.79406	+	1.03580i
$803$	−12.0405	−	6.95157i	−0.424899	−	0.245316i
$804$	53.5217	−	45.4154i	1.88757	−	1.60168i
$805$		0			0
$806$			38.9520i			1.37203i
$807$	34.0611	−	6.19976i	1.19901	−	0.218242i
$808$	−76.6358	−	132.737i	−2.69604	−	4.66967i
$809$	27.4680	−	15.8586i	0.965722	−	0.557560i	0.0677924	−	0.997699i	$-0.478404\pi$
$809$	27.4680	−	15.8586i	0.965722	−	0.557560i	0.897929	+	0.440140i	$0.145071\pi$
$810$		0			0
$811$			25.7354i			0.903691i	0.892096	+	0.451845i	$0.149234\pi$
$811$			25.7354i			0.903691i	−0.892096	+	0.451845i	$0.850766\pi$
$812$	−35.7087	−	19.1540i	−1.25313	−	0.672175i
$813$	−20.7490	+	17.6064i	−0.727699	+	0.617483i
$814$	−17.1776	+	29.7525i	−0.602075	+	1.04282i
$815$		0			0
$816$	51.5081	+	18.4264i	1.80314	+	0.645051i
$817$	−6.09129	+	10.5504i	−0.213107	+	0.369113i
$818$		−	19.0170i		−	0.664914i
$819$	−2.13616	+	16.0590i	−0.0746434	+	0.561146i
$820$		0			0
$821$	−22.3697	−	12.9152i	−0.780708	−	0.450742i	0.0559731	−	0.998432i	$-0.482174\pi$
$821$	−22.3697	−	12.9152i	−0.780708	−	0.450742i	−0.836681	+	0.547690i	$0.815507\pi$
$822$	−20.1865	+	56.4284i	−0.704086	+	1.96817i
$823$	32.9258	−	19.0097i	1.14772	−	0.662638i	0.199392	−	0.979920i	$-0.436103\pi$
$823$	32.9258	−	19.0097i	1.14772	−	0.662638i	0.948331	+	0.317282i	$0.102770\pi$
$824$	2.48463	−	4.30350i	0.0865561	−	0.149920i
$825$		0			0
$826$	10.9976	+	17.7435i	0.382655	+	0.617375i
$827$	−2.97310			−0.103385			−0.0516924	−	0.998663i	$-0.516462\pi$
$827$	−2.97310			−0.103385			−0.0516924	+	0.998663i	$0.516462\pi$
$828$	22.5637	+	18.5130i	0.784143	+	0.643370i
$829$	5.17590	−	2.98831i	0.179767	−	0.103788i	−0.407416	−	0.913243i	$-0.633570\pi$
$829$	5.17590	−	2.98831i	0.179767	−	0.103788i	0.587183	+	0.809454i	$0.300237\pi$
$830$		0			0
$831$	0.679192	+	3.73143i	0.0235609	+	0.129442i
$832$	−61.8125			−2.14296
$833$	0.919696	+	14.6914i	0.0318656	+	0.509026i
$834$	−65.1006	+	55.2405i	−2.25425	+	1.91282i
$835$		0			0
$836$	−15.8054	−	27.3758i	−0.546642	−	0.946811i
$837$	−17.6138	+	31.7081i	−0.608821	+	1.09599i
$838$	−47.6837	+	82.5907i	−1.64721	+	2.85305i
$839$	−44.9345			−1.55131			−0.775655	−	0.631157i	$-0.782580\pi$
$839$	−44.9345			−1.55131			−0.775655	+	0.631157i	$0.782580\pi$
$840$		0			0
$841$	21.1726			0.730090
$842$	−40.5444	+	70.2249i	−1.39725	+	2.42011i
$843$	−0.0974396	−	0.0348578i	−0.00335600	−	0.00120057i
$844$	51.9336	+	89.9516i	1.78763	+	3.09626i
$845$		0			0
$846$	−23.8537	−	3.93529i	−0.820108	−	0.135298i
$847$	−17.7425	+	0.554807i	−0.609639	+	0.0190634i
$848$	−93.0325			−3.19475
$849$	27.1655	−	4.94464i	0.932318	−	0.169700i
$850$		0			0
$851$	−9.33698	+	5.39071i	−0.320068	+	0.184791i
$852$	6.46728	+	35.5308i	0.221565	+	1.21727i
$853$	44.2981			1.51674			0.758368	−	0.651826i	$-0.225997\pi$
$853$	44.2981			1.51674			0.758368	+	0.651826i	$0.225997\pi$
$854$	−46.3890	−	24.8829i	−1.58740	−	0.851474i
$855$		0			0
$856$	14.6395	−	25.3563i	0.500367	−	0.866661i
$857$	−12.7700	+	7.37279i	−0.436216	+	0.251850i	−0.701991	−	0.712185i	$-0.747705\pi$
$857$	−12.7700	+	7.37279i	−0.436216	+	0.251850i	0.265775	+	0.964035i	$0.414372\pi$
$858$	18.8502	+	6.74341i	0.643534	+	0.230216i
$859$	−1.52877	−	0.882637i	−0.0521610	−	0.0301152i	0.473693	−	0.880690i	$-0.342921\pi$
$859$	−1.52877	−	0.882637i	−0.0521610	−	0.0301152i	−0.525854	+	0.850575i	$0.676254\pi$
$860$		0			0
$861$	52.4975	−	11.2612i	1.78911	−	0.383782i
$862$		−	23.1378i		−	0.788076i
$863$	−10.8467	+	18.7870i	−0.369226	+	0.639518i	−0.989445	−	0.144911i	$-0.953710\pi$
$863$	−10.8467	+	18.7870i	−0.369226	+	0.639518i	0.620219	+	0.784429i	$0.287044\pi$
$864$	−100.226	−	55.6754i	−3.40976	−	1.89411i
$865$		0			0
$866$	−14.5492	+	25.2000i	−0.494404	+	0.856332i
$867$	14.0953	+	16.6112i	0.478702	+	0.564147i
$868$	−3.15995	−	101.054i	−0.107256	−	3.43000i
$869$			12.2538i			0.415683i
$870$		0			0
$871$	13.0856	−	7.55499i	0.443390	−	0.255991i
$872$	−64.3750	−	111.501i	−2.18001	−	3.77589i
$873$	23.1270	+	18.9751i	0.782730	+	0.642211i
$874$		−	13.5444i		−	0.458147i
$875$		0			0
$876$	41.1760	+	48.5256i	1.39121	+	1.63953i
$877$	27.2482	+	15.7318i	0.920107	+	0.531224i	0.883669	−	0.468112i	$-0.155066\pi$
$877$	27.2482	+	15.7318i	0.920107	+	0.531224i	0.0364380	+	0.999336i	$0.488399\pi$
$878$	−29.9496	+	17.2914i	−1.01075	+	0.583556i
$879$	31.5844	+	11.2989i	1.06531	+	0.381102i
$880$		0			0
$881$	19.8571			0.669004			0.334502	−	0.942395i	$-0.391432\pi$
$881$	19.8571			0.669004			0.334502	+	0.942395i	$0.391432\pi$
$882$	5.78784	−	57.1198i	0.194887	−	1.92332i
$883$			30.0998i			1.01294i	0.862258	+	0.506469i	$0.169049\pi$
$883$			30.0998i			1.01294i	−0.862258	+	0.506469i	$0.830951\pi$
$884$	20.3483	+	11.7481i	0.684388	+	0.395132i
$885$		0			0
$886$	−35.1734	−	60.9221i	−1.18167	−	2.04672i
$887$	25.5312	+	14.7405i	0.857255	+	0.494937i	0.863092	−	0.505046i	$-0.168525\pi$
$887$	25.5312	+	14.7405i	0.857255	+	0.494937i	−0.00583681	+	0.999983i	$0.501858\pi$
$888$	76.1009	−	64.5748i	2.55378	−	2.16699i
$889$	−11.2130	+	6.94994i	−0.376072	+	0.233094i
$890$		0			0
$891$	12.2953	+	14.0132i	0.411909	+	0.469461i
$892$	−16.5947	−	28.7429i	−0.555632	−	0.962383i
$893$	4.10861	+	7.11632i	0.137489	+	0.238139i
$894$	−12.3618	−	67.9148i	−0.413440	−	2.27141i
$895$		0			0
$896$	102.250	−	3.19735i	3.41593	−	0.106816i
$897$	4.06494	+	4.79051i	0.135725	+	0.159950i
$898$	−84.5185	−	48.7968i	−2.82042	−	1.62837i
$899$	−9.76487	−	16.9133i	−0.325677	−	0.564089i
$900$		0			0
$901$	11.2805	+	6.51280i	0.375808	+	0.216973i
$902$		−	66.3509i		−	2.20924i
$903$	4.20033	+	19.5811i	0.139778	+	0.651617i
$904$	105.103			3.49566
$905$		0			0
$906$	11.2112	−	31.3393i	0.372469	−	1.04118i
$907$	28.9158	−	16.6945i	0.960133	−	0.554333i	0.0639189	−	0.997955i	$-0.479640\pi$
$907$	28.9158	−	16.6945i	0.960133	−	0.554333i	0.896214	+	0.443622i	$0.146307\pi$
$908$	103.375	+	59.6837i	3.43062	+	1.98067i
$909$	7.87988	−	47.7639i	0.261359	−	1.58423i
$910$		0			0
$911$			40.1277i			1.32949i	0.747071	+	0.664744i	$0.231460\pi$
$911$			40.1277i			1.32949i	−0.747071	+	0.664744i	$0.768540\pi$
$912$	12.9866	+	71.3473i	0.430028	+	2.36255i
$913$	6.17710	+	10.6991i	0.204432	+	0.354087i
$914$	26.2929	−	15.1802i	0.869692	−	0.502117i
$915$		0			0
$916$		−	50.2396i		−	1.65996i
$917$	30.9506	−	0.967822i	1.02208	−	0.0319603i
$918$	15.3625	+	25.6202i	0.507039	+	0.845594i
$919$	9.73901	−	16.8685i	0.321260	−	0.556439i	−0.659488	−	0.751715i	$-0.729227\pi$
$919$	9.73901	−	16.8685i	0.321260	−	0.556439i	0.980748	+	0.195276i	$0.0625602\pi$
$920$		0			0
$921$	−10.3637	+	28.9701i	−0.341495	+	0.954597i
$922$	25.8074	−	44.6998i	0.849922	−	1.47211i
$923$			7.77409i			0.255887i
$924$	−49.4505	−	15.9654i	−1.62680	−	0.525222i
$925$		0			0
$926$	−34.6718	−	20.0177i	−1.13938	−	0.657824i
$927$	1.46883	−	0.553034i	0.0482428	−	0.0181640i
$928$	53.4611	−	30.8658i	1.75495	−	1.01322i
$929$	−22.2310	+	38.5053i	−0.729376	+	1.26332i	0.227771	+	0.973715i	$0.426856\pi$
$929$	−22.2310	+	38.5053i	−0.729376	+	1.26332i	−0.957147	+	0.289602i	$0.906477\pi$
$930$		0			0
$931$	−16.2568	+	10.7937i	−0.532796	+	0.353749i
$932$	99.5361			3.26041
$933$	12.2275	−	2.22563i	0.400310	−	0.0728640i
$934$	12.8427	−	7.41472i	0.420225	−	0.242617i
$935$		0			0
$936$	−44.9633	−	36.8913i	−1.46967	−	1.20583i
$937$	7.31878			0.239094			0.119547	−	0.992829i	$-0.461856\pi$
$937$	7.31878			0.239094			0.119547	+	0.992829i	$0.461856\pi$
$938$	−45.5144	+	28.2103i	−1.48610	+	0.921098i
$939$	15.2335	+	17.9526i	0.497127	+	0.585861i
$940$		0			0
$941$	4.22911	+	7.32504i	0.137865	+	0.238790i	0.926688	−	0.375831i	$-0.122643\pi$
$941$	4.22911	+	7.32504i	0.137865	+	0.238790i	−0.788823	+	0.614620i	$0.789309\pi$
$942$	34.9342	−	97.6533i	1.13822	−	3.18172i
$943$	10.4112	−	18.0327i	0.339035	−	0.587225i
$944$	−43.3461			−1.41079
$945$		0			0
$946$	24.7482			0.804635
$947$	−9.27668	+	16.0677i	−0.301452	+	0.522129i	−0.976465	−	0.215676i	$-0.930805\pi$
$947$	−9.27668	+	16.0677i	−0.301452	+	0.522129i	0.675013	+	0.737805i	$0.264138\pi$
$948$	18.8935	−	52.8138i	0.613631	−	1.71531i
$949$	6.84976	+	11.8641i	0.222353	+	0.385126i
$950$		0			0
$951$	−3.60893	−	4.25310i	−0.117028	−	0.137916i
$952$	−46.5698	−	24.9799i	−1.50934	−	0.809602i
$953$	−12.3994			−0.401658			−0.200829	−	0.979626i	$-0.564363\pi$
$953$	−12.3994			−0.401658			−0.200829	+	0.979626i	$0.564363\pi$
$954$	−39.2752	−	32.2244i	−1.27158	−	1.04330i
$955$		0			0
$956$	−62.3188	+	35.9798i	−2.01553	+	1.16367i
$957$	−9.87540	+	1.79751i	−0.319226	+	0.0581052i
$958$	−10.1458			−0.327797
$959$	15.8280	−	29.5080i	0.511112	−	0.952863i
$960$		0			0
$961$	8.86390	−	15.3527i	0.285932	−	0.495249i
$962$	29.3167	−	16.9260i	0.945210	−	0.545717i
$963$	8.65440	−	3.25849i	0.278884	−	0.105003i
$964$	−0.0847752	−	0.0489450i	−0.00273043	−	0.00157641i
$965$		0			0
$966$	−14.9292	−	16.5184i	−0.480340	−	0.531471i
$967$			55.9627i			1.79964i	0.436263	+	0.899819i	$0.356302\pi$
$967$			55.9627i			1.79964i	−0.436263	+	0.899819i	$0.643698\pi$
$968$	31.8640	−	55.1900i	1.02415	−	1.77388i
$969$	3.42005	−	9.56023i	0.109868	−	0.307119i
$970$		0			0
$971$	20.9297	−	36.2512i	0.671665	−	1.16336i	−0.305767	−	0.952106i	$-0.598913\pi$
$971$	20.9297	−	36.2512i	0.671665	−	1.16336i	0.977432	−	0.211251i	$-0.0677539\pi$
$972$	−31.3864	−	79.3543i	−1.00672	−	2.54529i
$973$	40.5472	−	25.1316i	1.29988	−	0.805681i
$974$			50.0985i			1.60526i
$975$		0			0
$976$	94.6614	−	54.6528i	3.03004	−	1.74939i
$977$	9.23058	+	15.9878i	0.295312	+	0.511496i	0.975058	−	0.221952i	$-0.0712429\pi$
$977$	9.23058	+	15.9878i	0.295312	+	0.511496i	−0.679745	+	0.733448i	$0.737910\pi$
$978$	−6.86548	−	37.7185i	−0.219534	−	1.20610i
$979$		−	25.7231i		−	0.822115i
$980$		0			0
$981$	6.61920	−	40.1223i	0.211335	−	1.28101i
$982$	86.9241	+	50.1857i	2.77386	+	1.60149i
$983$	−33.7581	+	19.4902i	−1.07672	+	0.621642i	−0.930008	−	0.367538i	$-0.880201\pi$
$983$	−33.7581	+	19.4902i	−1.07672	+	0.621642i	−0.146707	+	0.989180i	$0.546867\pi$
$984$	−64.9269	+	181.493i	−2.06979	+	5.78580i
$985$		0			0
$986$	−16.0845			−0.512234
$987$	12.8546	+	4.15019i	0.409167	+	0.132102i
$988$			31.1479i			0.990945i
$989$	6.72602	+	3.88327i	0.213875	+	0.123481i
$990$		0			0
$991$	2.60812	+	4.51739i	0.0828495	+	0.143500i	0.904473	−	0.426531i	$-0.140265\pi$
$991$	2.60812	+	4.51739i	0.0828495	+	0.143500i	−0.821623	+	0.570031i	$0.806931\pi$
$992$	133.388	+	77.0118i	4.23508	+	2.44513i
$993$	−3.57156	−	4.20906i	−0.113340	−	0.133570i
$994$	−0.861078	−	27.5369i	−0.0273117	−	0.873419i
$995$		0			0
$996$	−10.1270	−	55.6369i	−0.320885	−	1.76292i
$997$	16.4727	+	28.5316i	0.521696	+	0.903604i	0.999682	+	0.0252363i	$0.00803381\pi$
$997$	16.4727	+	28.5316i	0.521696	+	0.903604i	−0.477985	+	0.878368i	$0.658633\pi$
$998$	−1.46474	−	2.53701i	−0.0463656	−	0.0803075i
$999$	31.5186	−	0.521517i	0.997203	−	0.0165001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.q.g.299.19		40
3.2	odd	2	inner	525.2.q.g.299.1		40
5.2	odd	4		525.2.t.i.26.10	yes	20
5.3	odd	4		525.2.t.h.26.1	✓	20
5.4	even	2	inner	525.2.q.g.299.2		40
7.3	odd	6	inner	525.2.q.g.374.20		40
15.2	even	4		525.2.t.i.26.1	yes	20
15.8	even	4		525.2.t.h.26.10	yes	20
15.14	odd	2	inner	525.2.q.g.299.20		40
21.17	even	6	inner	525.2.q.g.374.2		40
35.3	even	12		525.2.t.h.101.10	yes	20
35.17	even	12		525.2.t.i.101.1	yes	20
35.24	odd	6	inner	525.2.q.g.374.1		40
105.17	odd	12		525.2.t.i.101.10	yes	20
105.38	odd	12		525.2.t.h.101.1	yes	20
105.59	even	6	inner	525.2.q.g.374.19		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.q.g.299.1		40	3.2	odd	2	inner
525.2.q.g.299.2		40	5.4	even	2	inner
525.2.q.g.299.19		40	1.1	even	1	trivial
525.2.q.g.299.20		40	15.14	odd	2	inner
525.2.q.g.374.1		40	35.24	odd	6	inner
525.2.q.g.374.2		40	21.17	even	6	inner
525.2.q.g.374.19		40	105.59	even	6	inner
525.2.q.g.374.20		40	7.3	odd	6	inner
525.2.t.h.26.1	✓	20	5.3	odd	4
525.2.t.h.26.10	yes	20	15.8	even	4
525.2.t.h.101.1	yes	20	105.38	odd	12
525.2.t.h.101.10	yes	20	35.3	even	12
525.2.t.i.26.1	yes	20	15.2	even	4
525.2.t.i.26.10	yes	20	5.2	odd	4
525.2.t.i.101.1	yes	20	35.17	even	12
525.2.t.i.101.10	yes	20	105.17	odd	12

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36696 - 2.36764i) q^{2} +(0.583411 - 1.63084i) q^{3} +(-2.73715 - 4.74088i) q^{4} +(-3.06374 - 3.61059i) q^{6} +(1.39384 + 2.24882i) q^{7} -9.49844 q^{8} +(-2.31926 - 1.90290i) q^{9} +O(q^{10})\)	\(q+(1.36696 - 2.36764i) q^{2} +(0.583411 - 1.63084i) q^{3} +(-2.73715 - 4.74088i) q^{4} +(-3.06374 - 3.61059i) q^{6} +(1.39384 + 2.24882i) q^{7} -9.49844 q^{8} +(-2.31926 - 1.90290i) q^{9} +(1.79388 - 1.03570i) q^{11} +(-9.32849 + 1.69796i) q^{12} -2.04106 q^{13} +(7.22973 - 0.226073i) q^{14} +(-7.50967 + 13.0071i) q^{16} +(1.82114 - 1.05144i) q^{17} +(-7.67571 + 2.89000i) q^{18} +(2.41421 + 1.39384i) q^{19} +(4.48065 - 0.961143i) q^{21} -5.66303i q^{22} +(0.888591 - 1.53909i) q^{23} +(-5.54150 + 15.4904i) q^{24} +(-2.79004 + 4.83250i) q^{26} +(-4.45640 + 2.67217i) q^{27} +(6.84624 - 12.7634i) q^{28} -2.79774i q^{29} +(6.04532 - 3.49027i) q^{31} +(11.0324 + 19.1086i) q^{32} +(-0.642485 - 3.52977i) q^{33} -5.74909i q^{34} +(-2.67324 + 16.2039i) q^{36} +(-5.25381 - 3.03329i) q^{37} +(6.60024 - 3.81065i) q^{38} +(-1.19078 + 3.32864i) q^{39} +11.7165 q^{41} +(3.84922 - 11.9224i) q^{42} +4.37014i q^{43} +(-9.82025 - 5.66973i) q^{44} +(-2.42933 - 4.20773i) q^{46} +(2.55277 + 1.47384i) q^{47} +(16.8313 + 19.8356i) q^{48} +(-3.11440 + 6.26901i) q^{49} +(-0.652249 - 3.58341i) q^{51} +(5.58669 + 9.67643i) q^{52} +(3.09709 + 5.36432i) q^{53} +(0.235023 + 14.2039i) q^{54} +(-13.2393 - 21.3603i) q^{56} +(3.68161 - 3.12400i) q^{57} +(-6.62405 - 3.82440i) q^{58} +(1.44301 + 2.49936i) q^{59} +(-6.30263 - 3.63883i) q^{61} -19.0842i q^{62} +(1.04659 - 7.86795i) q^{63} +30.2845 q^{64} +(-9.23548 - 3.30387i) q^{66} +(-6.41119 + 3.70150i) q^{67} +(-9.96949 - 5.75589i) q^{68} +(-1.99158 - 2.34707i) q^{69} -3.80885i q^{71} +(22.0294 + 18.0746i) q^{72} +(-3.35598 - 5.81273i) q^{73} +(-14.3635 + 8.29276i) q^{74} -15.2606i q^{76} +(4.82949 + 2.59052i) q^{77} +(6.25328 + 7.36944i) q^{78} +(-2.95787 + 5.12317i) q^{79} +(1.75796 + 8.82664i) q^{81} +(16.0160 - 27.7405i) q^{82} +5.96419i q^{83} +(-16.8209 - 18.6114i) q^{84} +(10.3469 + 5.97380i) q^{86} +(-4.56267 - 1.63224i) q^{87} +(-17.0391 + 9.83752i) q^{88} +(6.20912 - 10.7545i) q^{89} +(-2.84492 - 4.58998i) q^{91} -9.72883 q^{92} +(-2.16515 - 11.8952i) q^{93} +(6.97906 - 4.02936i) q^{94} +(37.5995 - 6.84382i) q^{96} -9.97170 q^{97} +(10.5855 + 15.9433i) q^{98} +(-6.13132 - 1.01152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 28 q^{4} + 14 q^{9}+O(q^{10}) \) 40 * q - 28 * q^4 + 14 * q^9	\( 40 q - 28 q^{4} + 14 q^{9} - 36 q^{16} - 18 q^{21} - 36 q^{24} + 84 q^{31} - 72 q^{36} - 16 q^{46} + 8 q^{49} + 42 q^{51} + 150 q^{54} - 180 q^{61} + 240 q^{64} + 12 q^{66} - 92 q^{79} + 58 q^{81} - 150 q^{84} - 60 q^{91} - 12 q^{94} + 270 q^{96} - 188 q^{99}+O(q^{100}) \) 40 * q - 28 * q^4 + 14 * q^9 - 36 * q^16 - 18 * q^21 - 36 * q^24 + 84 * q^31 - 72 * q^36 - 16 * q^46 + 8 * q^49 + 42 * q^51 + 150 * q^54 - 180 * q^61 + 240 * q^64 + 12 * q^66 - 92 * q^79 + 58 * q^81 - 150 * q^84 - 60 * q^91 - 12 * q^94 + 270 * q^96 - 188 * q^99

Introduction

L-functions

Modular forms

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