LMFDB - Embedded newform 525.2.bc.d.418.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(82,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("525.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bc (of order $12$, degree $4$, 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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			418.2
Character	$\chi$	$=$	525.418
Dual form			525.2.bc.d.157.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.538972 - 2.01147i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-2.02348 + 1.16825i) q^{4} -2.08243i q^{6} +(-1.74285 - 1.99060i) q^{7} +(0.495509 + 0.495509i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.538972 - 2.01147i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-2.02348 + 1.16825i) q^{4} -2.08243i q^{6} +(-1.74285 - 1.99060i) q^{7} +(0.495509 + 0.495509i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.971690 - 1.68302i) q^{11} +(-2.25689 + 0.604733i) q^{12} +(1.84334 - 1.84334i) q^{13} +(-3.06469 + 4.57856i) q^{14} +(-1.60687 + 2.78318i) q^{16} +(1.62536 - 6.06591i) q^{17} +(0.538972 - 2.01147i) q^{18} +(-1.50783 + 2.61164i) q^{19} +(-1.16825 - 2.37385i) q^{21} +(-2.86163 + 2.86163i) q^{22} +(-5.35754 + 1.43555i) q^{23} +(0.350378 + 0.606872i) q^{24} +(-4.70133 - 2.71431i) q^{26} +(0.707107 + 0.707107i) q^{27} +(5.85213 + 1.99184i) q^{28} -5.27036i q^{29} +(-5.10687 + 2.94845i) q^{31} +(7.81811 + 2.09486i) q^{32} +(-0.502984 - 1.87716i) q^{33} -13.0774 q^{34} -2.33651 q^{36} +(0.241537 + 0.901429i) q^{37} +(6.06591 + 1.62536i) q^{38} +(2.25762 - 1.30344i) q^{39} -10.2942i q^{41} +(-4.14528 + 3.62935i) q^{42} +(-6.54989 - 6.54989i) q^{43} +(3.93238 + 2.27036i) q^{44} +(5.77513 + 10.0028i) q^{46} +(3.75432 - 1.00597i) q^{47} +(-2.27246 + 2.27246i) q^{48} +(-0.924978 + 6.93862i) q^{49} +(3.13994 - 5.43854i) q^{51} +(-1.57646 + 5.88343i) q^{52} +(-0.301706 + 1.12598i) q^{53} +(1.04121 - 1.80344i) q^{54} +(0.122765 - 1.84996i) q^{56} +(-2.13239 + 2.13239i) q^{57} +(-10.6012 + 2.84058i) q^{58} +(3.06469 + 5.30820i) q^{59} +(6.50476 + 3.75553i) q^{61} +(8.68319 + 8.68319i) q^{62} +(-0.514049 - 2.59533i) q^{63} -10.4275i q^{64} +(-3.50476 + 2.02348i) q^{66} +(14.3996 + 3.85836i) q^{67} +(3.79766 + 14.1730i) q^{68} -5.54653 q^{69} +15.1571 q^{71} +(0.181369 + 0.676878i) q^{72} +(-6.05671 - 1.62289i) q^{73} +(1.68302 - 0.971690i) q^{74} -7.04611i q^{76} +(-1.65671 + 4.86749i) q^{77} +(-3.83862 - 3.83862i) q^{78} +(14.2349 + 8.21851i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-20.7066 + 5.54831i) q^{82} +(-0.197912 + 0.197912i) q^{83} +(5.13720 + 3.43862i) q^{84} +(-9.64471 + 16.7051i) q^{86} +(1.36407 - 5.09078i) q^{87} +(0.352469 - 1.31543i) q^{88} +(6.08035 - 10.5315i) q^{89} +(-6.88200 - 0.456695i) q^{91} +(9.16376 - 9.16376i) q^{92} +(-5.69598 + 1.52623i) q^{93} +(-4.04695 - 7.00953i) q^{94} +(7.00953 + 4.04695i) q^{96} +(-10.9957 - 10.9957i) q^{97} +(14.4554 - 1.87915i) q^{98} -1.94338i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 24 q^{11} + 48 q^{16} - 24 q^{21} - 144 q^{26} - 36 q^{31} - 48 q^{36} + 48 q^{46} + 24 q^{51} + 168 q^{56} + 144 q^{61} - 72 q^{66} + 96 q^{71} + 12 q^{81} - 168 q^{86} + 12 q^{91} + 144 q^{96}+O(q^{100}) $ 24 * q + 24 * q^11 + 48 * q^16 - 24 * q^21 - 144 * q^26 - 36 * q^31 - 48 * q^36 + 48 * q^46 + 24 * q^51 + 168 * q^56 + 144 * q^61 - 72 * q^66 + 96 * q^71 + 12 * q^81 - 168 * q^86 + 12 * q^91 + 144 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.538972	−	2.01147i	−0.381111	−	1.42233i	−0.844207	−	0.536017i	$-0.819928\pi$
$2$	−0.538972	−	2.01147i	−0.381111	−	1.42233i	0.463096	−	0.886308i	$-0.346738\pi$
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	−2.02348	+	1.16825i	−1.01174	+	0.584127i
$5$		0			0
$5$		0			0
$6$		−	2.08243i		−	0.850148i
$7$	−1.74285	−	1.99060i	−0.658734	−	0.752376i
$7$	−1.74285	−	1.99060i	−0.658734	−	0.752376i
$8$	0.495509	+	0.495509i	0.175189	+	0.175189i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	−0.971690	−	1.68302i	−0.292976	−	0.507449i	0.681536	−	0.731784i	$-0.261312\pi$
$11$	−0.971690	−	1.68302i	−0.292976	−	0.507449i	−0.974512	+	0.224336i	$0.927979\pi$
$12$	−2.25689	+	0.604733i	−0.651509	+	0.174571i
$13$	1.84334	−	1.84334i	0.511250	−	0.511250i	−0.403660	−	0.914909i	$-0.632262\pi$
$13$	1.84334	−	1.84334i	0.511250	−	0.511250i	0.914909	+	0.403660i	$0.132262\pi$
$14$	−3.06469	+	4.57856i	−0.819073	+	1.22367i
$15$		0			0
$16$	−1.60687	+	2.78318i	−0.401718	+	0.695796i
$17$	1.62536	−	6.06591i	0.394207	−	1.47120i	−0.428921	−	0.903342i	$-0.641106\pi$
$17$	1.62536	−	6.06591i	0.394207	−	1.47120i	0.823127	−	0.567857i	$-0.192227\pi$
$18$	0.538972	−	2.01147i	0.127037	−	0.474108i
$19$	−1.50783	+	2.61164i	−0.345920	+	0.599150i	−0.985520	−	0.169557i	$-0.945766\pi$
$19$	−1.50783	+	2.61164i	−0.345920	+	0.599150i	0.639601	+	0.768707i	$0.279100\pi$
$20$		0			0
$21$	−1.16825	−	2.37385i	−0.254934	−	0.518017i
$22$	−2.86163	+	2.86163i	−0.610101	+	0.610101i
$23$	−5.35754	+	1.43555i	−1.11712	+	0.299332i	−0.769719	−	0.638383i	$-0.779604\pi$
$23$	−5.35754	+	1.43555i	−1.11712	+	0.299332i	−0.347405	+	0.937715i	$0.612937\pi$
$24$	0.350378	+	0.606872i	0.0715206	+	0.123877i
$25$		0			0
$26$	−4.70133	−	2.71431i	−0.922006	−	0.532320i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	5.85213	+	1.99184i	1.10595	+	0.376423i
$29$		−	5.27036i		−	0.978682i	−0.872093	−	0.489341i	$-0.837237\pi$
$29$		−	5.27036i		−	0.978682i	0.872093	−	0.489341i	$-0.162763\pi$
$30$		0			0
$31$	−5.10687	+	2.94845i	−0.917221	+	0.529558i	−0.882748	−	0.469848i	$-0.844309\pi$
$31$	−5.10687	+	2.94845i	−0.917221	+	0.529558i	−0.0344738	+	0.999406i	$0.510976\pi$
$32$	7.81811	+	2.09486i	1.38206	+	0.370322i
$33$	−0.502984	−	1.87716i	−0.0875583	−	0.326772i
$34$	−13.0774			−2.24276
$35$		0			0
$36$	−2.33651			−0.389418
$37$	0.241537	+	0.901429i	0.0397085	+	0.148194i	0.982934	−	0.183959i	$-0.0588915\pi$
$37$	0.241537	+	0.901429i	0.0397085	+	0.148194i	−0.943225	+	0.332153i	$0.892225\pi$
$38$	6.06591	+	1.62536i	0.984020	+	0.263667i
$39$	2.25762	−	1.30344i	0.361508	−	0.208717i
$40$		0			0
$41$		−	10.2942i		−	1.60769i	−0.594839	−	0.803845i	$-0.702784\pi$
$41$		−	10.2942i		−	1.60769i	0.594839	−	0.803845i	$-0.297216\pi$
$42$	−4.14528	+	3.62935i	−0.639631	+	0.560021i
$43$	−6.54989	−	6.54989i	−0.998849	−	0.998849i	0.00115057	−	0.999999i	$-0.499634\pi$
$43$	−6.54989	−	6.54989i	−0.998849	−	0.998849i	−0.999999	+	0.00115057i	$0.999634\pi$
$44$	3.93238	+	2.27036i	0.592829	+	0.342270i
$45$		0			0
$46$	5.77513	+	10.0028i	0.851496	+	1.47483i
$47$	3.75432	−	1.00597i	0.547624	−	0.146736i	0.0256097	−	0.999672i	$-0.491847\pi$
$47$	3.75432	−	1.00597i	0.547624	−	0.146736i	0.522015	+	0.852937i	$0.325181\pi$
$48$	−2.27246	+	2.27246i	−0.328001	+	0.328001i
$49$	−0.924978	+	6.93862i	−0.132140	+	0.991231i
$50$		0			0
$51$	3.13994	−	5.43854i	0.439680	−	0.761548i
$52$	−1.57646	+	5.88343i	−0.218616	+	0.815886i
$53$	−0.301706	+	1.12598i	−0.0414424	+	0.154665i	−0.983546	−	0.180656i	$-0.942178\pi$
$53$	−0.301706	+	1.12598i	−0.0414424	+	0.154665i	0.942104	+	0.335321i	$0.108845\pi$
$54$	1.04121	−	1.80344i	0.141691	−	0.245417i
$55$		0			0
$56$	0.122765	−	1.84996i	0.0164051	−	0.247211i
$57$	−2.13239	+	2.13239i	−0.282442	+	0.282442i
$58$	−10.6012	+	2.84058i	−1.39200	+	0.372986i
$59$	3.06469	+	5.30820i	0.398989	+	0.691069i	0.993601	−	0.112944i	$-0.0360279\pi$
$59$	3.06469	+	5.30820i	0.398989	+	0.691069i	−0.594613	+	0.804012i	$0.702695\pi$
$60$		0			0
$61$	6.50476	+	3.75553i	0.832850	+	0.480846i	0.854827	−	0.518913i	$-0.173663\pi$
$61$	6.50476	+	3.75553i	0.832850	+	0.480846i	−0.0219778	+	0.999758i	$0.506996\pi$
$62$	8.68319	+	8.68319i	1.10277	+	1.10277i
$63$	−0.514049	−	2.59533i	−0.0647640	−	0.326981i
$64$		−	10.4275i		−	1.30344i
$65$		0			0
$66$	−3.50476	+	2.02348i	−0.431407	+	0.249073i
$67$	14.3996	+	3.85836i	1.75919	+	0.471373i	0.986548	−	0.163471i	$-0.0522690\pi$
$67$	14.3996	+	3.85836i	1.75919	+	0.471373i	0.772640	+	0.634844i	$0.218936\pi$
$68$	3.79766	+	14.1730i	0.460533	+	1.71873i
$69$	−5.54653			−0.667724
$70$		0			0
$71$	15.1571			1.79882			0.899410	−	0.437106i	$-0.143997\pi$
$71$	15.1571			1.79882			0.899410	+	0.437106i	$0.143997\pi$
$72$	0.181369	+	0.676878i	0.0213745	+	0.0797708i
$73$	−6.05671	−	1.62289i	−0.708884	−	0.189945i	−0.113677	−	0.993518i	$-0.536263\pi$
$73$	−6.05671	−	1.62289i	−0.708884	−	0.189945i	−0.595206	+	0.803573i	$0.702930\pi$
$74$	1.68302	−	0.971690i	0.195647	−	0.112957i
$75$		0			0
$76$		−	7.04611i		−	0.808244i
$77$	−1.65671	+	4.86749i	−0.188799	+	0.554702i
$78$	−3.83862	−	3.83862i	−0.434638	−	0.434638i
$79$	14.2349	+	8.21851i	1.60155	+	0.924654i	0.991178	+	0.132538i	$0.0423127\pi$
$79$	14.2349	+	8.21851i	1.60155	+	0.924654i	0.610370	+	0.792116i	$0.291021\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−20.7066	+	5.54831i	−2.28666	+	0.612708i
$83$	−0.197912	+	0.197912i	−0.0217237	+	0.0217237i	−0.717885	−	0.696162i	$-0.754890\pi$
$83$	−0.197912	+	0.197912i	−0.0217237	+	0.0217237i	0.696162	+	0.717885i	$0.254890\pi$
$84$	5.13720	+	3.43862i	0.560514	+	0.375184i
$85$		0			0
$86$	−9.64471	+	16.7051i	−1.04002	+	1.80136i
$87$	1.36407	−	5.09078i	0.146244	−	0.545789i
$88$	0.352469	−	1.31543i	0.0375733	−	0.140225i
$89$	6.08035	−	10.5315i	0.644515	−	1.11633i	−0.339898	−	0.940462i	$-0.610392\pi$
$89$	6.08035	−	10.5315i	0.644515	−	1.11633i	0.984413	−	0.175871i	$-0.0562742\pi$
$90$		0			0
$91$	−6.88200	−	0.456695i	−0.721429	−	0.0478746i
$92$	9.16376	−	9.16376i	0.955388	−	0.955388i
$93$	−5.69598	+	1.52623i	−0.590645	+	0.158263i
$94$	−4.04695	−	7.00953i	−0.417411	−	0.722977i
$95$		0			0
$96$	7.00953	+	4.04695i	0.715407	+	0.413040i
$97$	−10.9957	−	10.9957i	−1.11644	−	1.11644i	−0.992259	−	0.124184i	$-0.960369\pi$
$97$	−10.9957	−	10.9957i	−1.11644	−	1.11644i	−0.124184	−	0.992259i	$-0.539631\pi$
$98$	14.4554	−	1.87915i	1.46021	−	0.189823i
$99$		−	1.94338i		−	0.195317i
$100$		0			0
$101$	−0.289146	+	0.166939i	−0.0287711	+	0.0166110i	−0.514317	−	0.857600i	$-0.671954\pi$
$101$	−0.289146	+	0.166939i	−0.0287711	+	0.0166110i	0.485545	+	0.874211i	$0.338621\pi$
$102$	−12.6318	−	3.38469i	−1.25074	−	0.335134i
$103$	1.96634	+	7.33847i	0.193749	+	0.723081i	0.992587	+	0.121535i	$0.0387817\pi$
$103$	1.96634	+	7.33847i	0.193749	+	0.723081i	−0.798838	+	0.601546i	$0.794552\pi$
$104$	1.82678			0.179131
$105$		0			0
$106$	2.42749			0.235779
$107$	−0.538972	−	2.01147i	−0.0521044	−	0.194456i	0.934968	−	0.354733i	$-0.115428\pi$
$107$	−0.538972	−	2.01147i	−0.0521044	−	0.194456i	−0.987072	+	0.160276i	$0.948761\pi$
$108$	−2.25689	−	0.604733i	−0.217170	−	0.0581905i
$109$	13.1837	−	7.61164i	1.26277	−	0.729062i	0.289163	−	0.957280i	$-0.406623\pi$
$109$	13.1837	−	7.61164i	1.26277	−	0.729062i	0.973610	+	0.228217i	$0.0732897\pi$
$110$		0			0
$111$			0.933228i			0.0885781i
$112$	8.34074	−	1.65202i	0.788126	−	0.156101i
$113$	4.26478	+	4.26478i	0.401197	+	0.401197i	0.878655	−	0.477458i	$-0.158442\pi$
$113$	4.26478	+	4.26478i	0.401197	+	0.401197i	−0.477458	+	0.878655i	$0.658442\pi$
$114$	5.43854	+	3.13994i	0.509366	+	0.294083i
$115$		0			0
$116$	6.15713	+	10.6645i	0.571675	+	0.990170i
$117$	2.51805	−	0.674708i	0.232793	−	0.0623768i
$118$	9.02551	−	9.02551i	0.830865	−	0.830865i
$119$	−14.9075	+	7.33651i	−1.36657	+	0.672537i
$120$		0			0
$121$	3.61164	−	6.25554i	0.328330	−	0.568685i
$122$	4.04825	−	15.1083i	0.366511	−	1.36784i
$123$	2.66434	−	9.94347i	0.240236	−	0.896573i
$124$	6.88909	−	11.9323i	0.618658	−	1.07155i
$125$		0			0
$126$	−4.94338	+	2.43281i	−0.440391	+	0.216732i
$127$	2.20174	−	2.20174i	0.195372	−	0.195372i	−0.602640	−	0.798013i	$-0.705885\pi$
$127$	2.20174	−	2.20174i	0.195372	−	0.195372i	0.798013	+	0.602640i	$0.205885\pi$
$128$	−5.33837	+	1.43041i	−0.471850	+	0.126432i
$129$	−4.63147	−	8.02194i	−0.407778	−	0.706293i
$130$		0			0
$131$	−10.6164	−	6.12938i	−0.927559	−	0.535526i	−0.0415203	−	0.999138i	$-0.513220\pi$
$131$	−10.6164	−	6.12938i	−0.927559	−	0.535526i	−0.886039	+	0.463611i	$0.846553\pi$
$132$	3.21078	+	3.21078i	0.279462	+	0.279462i
$133$	7.82663	−	1.55019i	0.678655	−	0.134419i
$134$		−	31.0439i		−	2.68178i
$135$		0			0
$136$	3.81109	−	2.20033i	0.326798	−	0.188677i
$137$	−11.1833	−	2.99657i	−0.955457	−	0.256014i	−0.252781	−	0.967524i	$-0.581345\pi$
$137$	−11.1833	−	2.99657i	−0.955457	−	0.256014i	−0.702676	+	0.711510i	$0.748012\pi$
$138$	2.98943	+	11.1567i	0.254477	+	0.949720i
$139$	4.88211			0.414095			0.207048	−	0.978331i	$-0.433614\pi$
$139$	4.88211			0.414095			0.207048	+	0.978331i	$0.433614\pi$
$140$		0			0
$141$	3.88676			0.327324
$142$	−8.16927	−	30.4881i	−0.685550	−	2.55851i
$143$	−4.89352	−	1.31121i	−0.409217	−	0.109649i
$144$	−2.78318	+	1.60687i	−0.231932	+	0.133906i
$145$		0			0
$146$			13.0576i			1.08065i
$147$	−2.68931	+	6.46279i	−0.221810	+	0.533042i
$148$	−1.54184	−	1.54184i	−0.126739	−	0.126739i
$149$	−2.31490	−	1.33651i	−0.189644	−	0.109491i	0.402172	−	0.915564i	$-0.368255\pi$
$149$	−2.31490	−	1.33651i	−0.189644	−	0.109491i	−0.591816	+	0.806073i	$0.701589\pi$
$150$		0			0
$151$	−7.38200	−	12.7860i	−0.600739	−	1.04051i	−0.992709	−	0.120532i	$-0.961540\pi$
$151$	−7.38200	−	12.7860i	−0.600739	−	1.04051i	0.391971	−	0.919978i	$-0.371793\pi$
$152$	−2.04123	+	0.546946i	−0.165566	+	0.0443632i
$153$	4.44055	−	4.44055i	0.358997	−	0.358997i
$154$	10.6837	+	0.708981i	0.860919	+	0.0571313i
$155$		0			0
$156$	−3.04549	+	5.27494i	−0.243834	+	0.422333i
$157$	−5.83890	+	21.7911i	−0.465995	+	1.73912i	0.187574	+	0.982250i	$0.439937\pi$
$157$	−5.83890	+	21.7911i	−0.465995	+	1.73912i	−0.653569	+	0.756867i	$0.726729\pi$
$158$	8.85909	−	33.0626i	0.704792	−	2.63032i
$159$	−0.582850	+	1.00953i	−0.0462230	+	0.0800607i
$160$		0			0
$161$	12.1950	+	8.16278i	0.961098	+	0.643317i
$162$	1.47250	−	1.47250i	0.115690	−	0.115690i
$163$	14.9977	−	4.01861i	1.17471	−	0.314762i	0.381883	−	0.924211i	$-0.375276\pi$
$163$	14.9977	−	4.01861i	1.17471	−	0.314762i	0.792825	+	0.609449i	$0.208609\pi$
$164$	12.0263	+	20.8301i	0.939095	+	1.62656i
$165$		0			0
$166$	0.504763	+	0.291425i	0.0391772	+	0.0226190i
$167$	−4.44055	−	4.44055i	−0.343620	−	0.343620i	0.514106	−	0.857727i	$-0.328124\pi$
$167$	−4.44055	−	4.44055i	−0.343620	−	0.343620i	−0.857727	+	0.514106i	$0.828124\pi$
$168$	0.597385	−	1.75515i	0.0460893	−	0.135412i
$169$			6.20422i			0.477248i
$170$		0			0
$171$	−2.61164	+	1.50783i	−0.199717	+	0.115307i
$172$	20.9055	+	5.60161i	1.59403	+	0.427119i
$173$	5.28702	+	19.7314i	0.401965	+	1.50015i	0.809585	+	0.587002i	$0.199692\pi$
$173$	5.28702	+	19.7314i	0.401965	+	1.50015i	−0.407621	+	0.913151i	$0.633641\pi$
$174$	−10.9752			−0.832024
$175$		0			0
$176$	6.24553			0.470774
$177$	1.58640	+	5.92053i	0.119241	+	0.445014i
$178$	−24.4609	−	6.55428i	−1.83342	−	0.491264i
$179$	7.29842	−	4.21374i	0.545509	−	0.314950i	−0.201799	−	0.979427i	$-0.564679\pi$
$179$	7.29842	−	4.21374i	0.545509	−	0.314950i	0.747309	+	0.664477i	$0.231346\pi$
$180$		0			0
$181$		−	12.0461i		−	0.895382i	−0.894188	−	0.447691i	$-0.852247\pi$
$181$		−	12.0461i		−	0.895382i	0.894188	−	0.447691i	$-0.147753\pi$
$182$	2.79058	+	14.0891i	0.206851	+	1.04435i
$183$	5.31112	+	5.31112i	0.392609	+	0.392609i
$184$	−3.36603	−	1.94338i	−0.248147	−	0.143268i
$185$		0			0
$186$	6.13994	+	10.6347i	0.450203	+	0.779774i
$187$	−11.7884	+	3.15868i	−0.862051	+	0.230986i
$188$	−6.42156	+	6.42156i	−0.468340	+	0.468340i
$189$	0.175189	−	2.63994i	0.0127431	−	0.192028i
$190$		0			0
$191$	−3.27989	+	5.68094i	−0.237324	+	0.411058i	−0.959946	−	0.280186i	$-0.909604\pi$
$191$	−3.27989	+	5.68094i	−0.237324	+	0.411058i	0.722621	+	0.691244i	$0.242937\pi$
$192$	2.69883	−	10.0722i	0.194771	−	0.726897i
$193$	−1.01778	+	3.79839i	−0.0732611	+	0.273414i	−0.992833	−	0.119507i	$-0.961869\pi$
$193$	−1.01778	+	3.79839i	−0.0732611	+	0.273414i	0.919572	+	0.392921i	$0.128535\pi$
$194$	−16.1911	+	28.0439i	−1.16246	+	2.01343i
$195$		0			0
$196$	−6.23440	−	15.1207i	−0.445314	−	1.08005i
$197$	8.32546	−	8.32546i	0.593164	−	0.593164i	−0.345320	−	0.938485i	$-0.612230\pi$
$197$	8.32546	−	8.32546i	0.593164	−	0.593164i	0.938485	+	0.345320i	$0.112230\pi$
$198$	−3.90906	+	1.04743i	−0.277804	+	0.0744375i
$199$	6.77118	+	11.7280i	0.479996	+	0.831378i	0.999737	−	0.0229461i	$-0.00730460\pi$
$199$	6.77118	+	11.7280i	0.479996	+	0.831378i	−0.519740	+	0.854324i	$0.673971\pi$
$200$		0			0
$201$	12.9103	+	7.45377i	0.910623	+	0.525748i
$202$	0.491634	+	0.491634i	0.0345913	+	0.0345913i
$203$	−10.4912	+	9.18543i	−0.736337	+	0.644691i
$204$			14.6730i			1.02732i
$205$		0			0
$206$	13.7013	−	7.91046i	0.954617	−	0.551148i
$207$	−5.35754	−	1.43555i	−0.372375	−	0.0997775i
$208$	2.16834	+	8.09235i	0.150347	+	0.561104i
$209$	5.86057			0.405384
$210$		0			0
$211$	−4.22327			−0.290742			−0.145371	−	0.989377i	$-0.546438\pi$
$211$	−4.22327			−0.290742			−0.145371	+	0.989377i	$0.546438\pi$
$212$	−0.704938	−	2.63086i	−0.0484153	−	0.180688i
$213$	14.6407	+	3.92295i	1.00316	+	0.268796i
$214$	−3.75553	+	2.16825i	−0.256723	+	0.148219i
$215$		0			0
$216$			0.700756i			0.0476804i
$217$	14.7697	+	5.02704i	1.00263	+	0.341258i
$218$	−22.4163	−	22.4163i	−1.51822	−	1.51822i
$219$	−5.43029	−	3.13518i	−0.366945	−	0.211856i
$220$		0			0
$221$	−8.18543	−	14.1776i	−0.550612	−	0.953688i
$222$	1.87716	−	0.502984i	0.125987	−	0.0337581i
$223$	8.56535	−	8.56535i	0.573578	−	0.573578i	−0.359548	−	0.933127i	$-0.617069\pi$
$223$	8.56535	−	8.56535i	0.573578	−	0.573578i	0.933127	+	0.359548i	$0.117069\pi$
$224$	−9.45574	−	19.2137i	−0.631788	−	1.28377i
$225$		0			0
$226$	6.27989	−	10.8771i	0.417732	−	0.723533i
$227$	−3.63729	+	13.5746i	−0.241415	+	0.900975i	0.733736	+	0.679435i	$0.237775\pi$
$227$	−3.63729	+	13.5746i	−0.241415	+	0.900975i	−0.975151	+	0.221540i	$0.928892\pi$
$228$	1.82367	−	6.80602i	0.120775	−	0.450740i
$229$	1.89732	−	3.28626i	0.125378	−	0.217162i	−0.796502	−	0.604635i	$-0.793319\pi$
$229$	1.89732	−	3.28626i	0.125378	−	0.217162i	0.921881	+	0.387474i	$0.126652\pi$
$230$		0			0
$231$	−2.86006	+	4.27284i	−0.188178	+	0.281132i
$232$	2.61151	−	2.61151i	0.171454	−	0.171454i
$233$	−21.4301	+	5.74219i	−1.40394	+	0.376183i	−0.879756	−	0.475425i	$-0.842294\pi$
$233$	−21.4301	+	5.74219i	−1.40394	+	0.376183i	−0.524179	+	0.851608i	$0.675628\pi$
$234$	−2.71431	−	4.70133i	−0.177440	−	0.307335i
$235$		0			0
$236$	−12.4027	−	7.16068i	−0.807344	−	0.466120i
$237$	11.6227	+	11.6227i	0.754977	+	0.754977i
$238$	22.7919	+	26.0319i	1.47738	+	1.68740i
$239$			20.3333i			1.31525i	0.753345	+	0.657626i	$0.228439\pi$
$239$			20.3333i			1.31525i	−0.753345	+	0.657626i	$0.771561\pi$
$240$		0			0
$241$	−8.93225	+	5.15704i	−0.575377	+	0.332194i	−0.759294	−	0.650748i	$-0.774456\pi$
$241$	−8.93225	+	5.15704i	−0.575377	+	0.332194i	0.183917	+	0.982942i	$0.441122\pi$
$242$	−14.5294	−	3.89314i	−0.933985	−	0.250261i
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	−17.5496			−1.12350
$245$		0			0
$246$	−21.4370			−1.36677
$247$	2.03469	+	7.59356i	0.129464	+	0.483167i
$248$	−3.99149	−	1.06952i	−0.253460	−	0.0679143i
$249$	−0.242392	+	0.139945i	−0.0153609	+	0.00886865i
$250$		0			0
$251$			7.26208i			0.458378i	0.973382	+	0.229189i	$0.0736075\pi$
$251$			7.26208i			0.458378i	−0.973382	+	0.229189i	$0.926393\pi$
$252$	4.07217	+	4.65105i	0.256523	+	0.292989i
$253$	7.62192	+	7.62192i	0.479186	+	0.479186i
$254$	−5.61540	−	3.24205i	−0.352342	−	0.203425i
$255$		0			0
$256$	−4.67302	−	8.09390i	−0.292064	−	0.505869i
$257$	−5.19706	+	1.39255i	−0.324184	+	0.0868648i	−0.417241	−	0.908796i	$-0.637003\pi$
$257$	−5.19706	+	1.39255i	−0.324184	+	0.0868648i	0.0930569	+	0.995661i	$0.470336\pi$
$258$	−13.6397	+	13.6397i	−0.849169	+	0.849169i
$259$	1.37342	−	2.05186i	0.0853403	−	0.127496i
$260$		0			0
$261$	2.63518	−	4.56427i	0.163114	−	0.282521i
$262$	−6.60713	+	24.6581i	−0.408190	+	1.52339i
$263$	0.232132	−	0.866329i	0.0143139	−	0.0534201i	−0.958400	−	0.285430i	$-0.907864\pi$
$263$	0.232132	−	0.866329i	0.0143139	−	0.0534201i	0.972713	+	0.232010i	$0.0745302\pi$
$264$	0.680917	−	1.17938i	0.0419076	−	0.0725860i
$265$		0			0
$266$	−7.33651	−	14.9075i	−0.449830	−	0.914040i
$267$	8.59891	−	8.59891i	0.526245	−	0.526245i
$268$	−33.6447	+	9.01508i	−2.05518	+	0.550684i
$269$	−12.2786	−	21.2672i	−0.748639	−	1.29668i	−0.948475	−	0.316852i	$-0.897374\pi$
$269$	−12.2786	−	21.2672i	−0.748639	−	1.29668i	0.199836	−	0.979829i	$-0.435959\pi$
$270$		0			0
$271$	7.31585	+	4.22381i	0.444406	+	0.256578i	0.705465	−	0.708745i	$-0.250738\pi$
$271$	7.31585	+	4.22381i	0.444406	+	0.256578i	−0.261059	+	0.965323i	$0.584072\pi$
$272$	14.2708	+	14.2708i	0.865294	+	0.865294i
$273$	−6.52930	−	2.22233i	−0.395171	−	0.134501i
$274$			24.1100i			1.45654i
$275$		0			0
$276$	11.2233	−	6.47976i	0.675562	−	0.390036i
$277$	14.5135	+	3.88887i	0.872030	+	0.233660i	0.666965	−	0.745089i	$-0.267593\pi$
$277$	14.5135	+	3.88887i	0.872030	+	0.233660i	0.205064	+	0.978748i	$0.434260\pi$
$278$	−2.63132	−	9.82023i	−0.157816	−	0.588978i
$279$	−5.89691			−0.353039
$280$		0			0
$281$	4.54073			0.270877			0.135439	−	0.990786i	$-0.456756\pi$
$281$	4.54073			0.270877			0.135439	+	0.990786i	$0.456756\pi$
$282$	−2.09486	−	7.81811i	−0.124747	−	0.465562i
$283$	−14.3064	−	3.83339i	−0.850428	−	0.227872i	−0.192822	−	0.981234i	$-0.561764\pi$
$283$	−14.3064	−	3.83339i	−0.850428	−	0.227872i	−0.657606	+	0.753362i	$0.728431\pi$
$284$	−30.6701	+	17.7074i	−1.81993	+	1.05074i
$285$		0			0
$286$			10.5499i			0.623828i
$287$	−20.4917	+	17.9413i	−1.20959	+	1.05904i
$288$	5.72325	+	5.72325i	0.337246	+	0.337246i
$289$	−19.4310	−	11.2185i	−1.14300	−	0.659912i
$290$		0			0
$291$	−7.77513	−	13.4669i	−0.455786	−	0.789444i
$292$	14.1515	−	3.79190i	0.828157	−	0.221904i
$293$	3.21078	−	3.21078i	0.187576	−	0.187576i	−0.607072	−	0.794647i	$-0.707656\pi$
$293$	3.21078	−	3.21078i	0.187576	−	0.187576i	0.794647	+	0.607072i	$0.207656\pi$
$294$	14.4492	+	1.92620i	0.842693	+	0.112338i
$295$		0			0
$296$	−0.326982	+	0.566350i	−0.0190055	+	0.0329184i
$297$	0.502984	−	1.87716i	0.0291861	−	0.108924i
$298$	−1.44068	+	5.37670i	−0.0834565	+	0.311464i
$299$	−7.22955	+	12.5219i	−0.418096	+	0.724163i
$300$		0			0
$301$	−1.62276	+	24.4537i	−0.0935346	+	1.40949i
$302$	−21.7400	+	21.7400i	−1.25100	+	1.25100i
$303$	−0.322501	+	0.0864139i	−0.0185272	+	0.00496435i
$304$	−4.84577	−	8.39313i	−0.277924	−	0.481379i
$305$		0			0
$306$	−11.3254	−	6.53871i	−0.647429	−	0.373793i
$307$	−13.5394	−	13.5394i	−0.772734	−	0.772734i	0.205849	−	0.978584i	$-0.434004\pi$
$307$	−13.5394	−	13.5394i	−0.772734	−	0.772734i	−0.978584	+	0.205849i	$0.934004\pi$
$308$	−2.33415	−	11.7847i	−0.133001	−	0.671496i
$309$			7.59735i			0.432198i
$310$		0			0
$311$	−22.5315	+	13.0086i	−1.27764	+	0.737647i	−0.976414	−	0.215905i	$-0.930730\pi$
$311$	−22.5315	+	13.0086i	−1.27764	+	0.737647i	−0.301228	+	0.953552i	$0.597397\pi$
$312$	1.76453	+	0.472805i	0.0998971	+	0.0267673i
$313$	−0.935993	−	3.49317i	−0.0529054	−	0.197446i	0.934415	−	0.356187i	$-0.115923\pi$
$313$	−0.935993	−	3.49317i	−0.0529054	−	0.197446i	−0.987320	+	0.158741i	$0.949257\pi$
$314$	46.9791			2.65119
$315$		0			0
$316$	−38.4052			−2.16046
$317$	−2.46273	−	9.19103i	−0.138321	−	0.516220i	−0.999962	−	0.00870220i	$-0.997230\pi$
$317$	−2.46273	−	9.19103i	−0.138321	−	0.516220i	0.861642	−	0.507517i	$-0.169437\pi$
$318$	2.34477	+	0.628280i	0.131488	+	0.0352322i
$319$	−8.87011	+	5.12116i	−0.496631	+	0.286730i
$320$		0			0
$321$		−	2.08243i		−	0.116230i
$322$	9.84645	−	28.9293i	0.548721	−	1.61217i
$323$	13.3912	+	13.3912i	0.745105	+	0.745105i
$324$	−2.02348	−	1.16825i	−0.112415	−	0.0649030i
$325$		0			0
$326$	−16.1667	−	28.0015i	−0.895388	−	1.55086i
$327$	14.7046	−	3.94007i	0.813163	−	0.217886i
$328$	5.10089	−	5.10089i	0.281649	−	0.281649i
$329$	−8.54569	−	5.72011i	−0.471139	−	0.315360i
$330$		0			0
$331$	2.82698	−	4.89648i	0.155385	−	0.269135i	−0.777814	−	0.628494i	$-0.783672\pi$
$331$	2.82698	−	4.89648i	0.155385	−	0.269135i	0.933199	+	0.359360i	$0.117005\pi$
$332$	0.169259	−	0.631681i	0.00928927	−	0.0346680i
$333$	−0.241537	+	0.901429i	−0.0132362	+	0.0493980i
$334$	−6.53871	+	11.3254i	−0.357782	+	0.619697i
$335$		0			0
$336$	8.48411	+	0.563012i	0.462846	+	0.0307148i
$337$	7.10071	−	7.10071i	0.386801	−	0.386801i	−0.486744	−	0.873545i	$-0.661816\pi$
$337$	7.10071	−	7.10071i	0.386801	−	0.386801i	0.873545	+	0.486744i	$0.161816\pi$
$338$	12.4796	−	3.34390i	0.678801	−	0.181884i
$339$	3.01566	+	5.22327i	0.163788	+	0.283689i
$340$		0			0
$341$	9.92460	+	5.72997i	0.537447	+	0.310295i
$342$	4.44055	+	4.44055i	0.240118	+	0.240118i
$343$	15.4241	−	10.2517i	0.832824	−	0.553539i
$344$		−	6.49106i		−	0.349974i
$345$		0			0
$346$	36.8397	−	21.2694i	1.98051	−	1.14345i
$347$	−6.50268	−	1.74239i	−0.349082	−	0.0935363i	0.0800175	−	0.996793i	$-0.474502\pi$
$347$	−6.50268	−	1.74239i	−0.349082	−	0.0935363i	−0.429100	+	0.903257i	$0.641169\pi$
$348$	3.18716	+	11.8947i	0.170850	+	0.637620i
$349$	2.76335			0.147919			0.0739593	−	0.997261i	$-0.476437\pi$
$349$	2.76335			0.147919			0.0739593	+	0.997261i	$0.476437\pi$
$350$		0			0
$351$	2.60687			0.139145
$352$	−4.07110	−	15.1936i	−0.216991	−	0.809820i
$353$	24.6250	+	6.59824i	1.31065	+	0.351189i	0.845469	−	0.534025i	$-0.179321\pi$
$353$	24.6250	+	6.59824i	1.31065	+	0.351189i	0.465185	+	0.885213i	$0.345988\pi$
$354$	11.0539	−	6.38200i	0.587511	−	0.339199i
$355$		0			0
$356$			28.4136i			1.50592i
$357$	−16.2984	+	3.22817i	−0.862603	+	0.170853i
$358$	−12.4095	−	12.4095i	−0.655861	−	0.655861i
$359$	−5.82804	−	3.36482i	−0.307592	−	0.177588i	0.338256	−	0.941054i	$-0.390163\pi$
$359$	−5.82804	−	3.36482i	−0.307592	−	0.177588i	−0.645848	+	0.763466i	$0.723496\pi$
$360$		0			0
$361$	4.95291	+	8.57869i	0.260679	+	0.451510i
$362$	−24.2304	+	6.49253i	−1.27352	+	0.341240i
$363$	5.10762	−	5.10762i	0.268081	−	0.268081i
$364$	14.4591	−	7.11581i	0.757862	−	0.372970i
$365$		0			0
$366$	7.82062	−	13.5457i	0.408790	−	0.708045i
$367$	4.76213	−	17.7725i	0.248581	−	0.927717i	−0.722969	−	0.690881i	$-0.757223\pi$
$367$	4.76213	−	17.7725i	0.248581	−	0.927717i	0.971550	−	0.236836i	$-0.0761105\pi$
$368$	4.61348	−	17.2178i	0.240494	−	0.897537i
$369$	5.14712	−	8.91507i	0.267948	−	0.464100i
$370$		0			0
$371$	2.76720	−	1.36183i	0.143666	−	0.0707029i
$372$	9.74264	−	9.74264i	0.505132	−	0.505132i
$373$	1.69219	−	0.453422i	0.0876185	−	0.0234773i	−0.214743	−	0.976670i	$-0.568892\pi$
$373$	1.69219	−	0.453422i	0.0876185	−	0.0234773i	0.302362	+	0.953193i	$0.402225\pi$
$374$	12.7072	+	22.0095i	0.657074	+	1.13809i
$375$		0			0
$376$	2.35877	+	1.36183i	0.121644	+	0.0702313i
$377$	−9.71506	−	9.71506i	−0.500351	−	0.500351i
$378$	−5.40460	+	1.07047i	−0.277982	+	0.0550590i
$379$			37.4275i			1.92252i	0.275642	+	0.961260i	$0.411110\pi$
$379$			37.4275i			1.92252i	−0.275642	+	0.961260i	$0.588890\pi$
$380$		0			0
$381$	2.69656	−	1.55686i	0.138149	−	0.0797605i
$382$	13.1948	+	3.53554i	0.675105	+	0.180894i
$383$	−4.74008	−	17.6902i	−0.242207	−	0.903927i	−0.974767	−	0.223225i	$-0.928341\pi$
$383$	−4.74008	−	17.6902i	−0.242207	−	0.903927i	0.732560	−	0.680702i	$-0.238325\pi$
$384$	−5.52669			−0.282033
$385$		0			0
$386$	8.18891			0.416805
$387$	−2.39743	−	8.94732i	−0.121868	−	0.454818i
$388$	35.0953	+	9.40375i	1.78169	+	0.477403i
$389$	−5.13062	+	2.96216i	−0.260133	+	0.150188i	−0.624395	−	0.781109i	$-0.714654\pi$
$389$	−5.13062	+	2.96216i	−0.260133	+	0.150188i	0.364262	+	0.931296i	$0.381321\pi$
$390$		0			0
$391$			34.8316i			1.76151i
$392$	−3.89648	+	2.97981i	−0.196802	+	0.150503i
$393$	−8.66825	−	8.66825i	−0.437256	−	0.437256i
$394$	−21.2336	−	12.2592i	−1.06973	−	0.617611i
$395$		0			0
$396$	2.27036	+	3.93238i	0.114090	+	0.197610i
$397$	−3.47477	+	0.931062i	−0.174394	+	0.0467286i	−0.344959	−	0.938618i	$-0.612107\pi$
$397$	−3.47477	+	0.931062i	−0.174394	+	0.0467286i	0.170565	+	0.985346i	$0.445441\pi$
$398$	19.9411	−	19.9411i	0.999558	−	0.999558i
$399$	7.96117	+	0.528310i	0.398557	+	0.0264486i
$400$		0			0
$401$	19.0439	−	32.9850i	0.951006	−	1.64719i	0.207753	−	0.978181i	$-0.433385\pi$
$401$	19.0439	−	32.9850i	0.951006	−	1.64719i	0.743253	−	0.669010i	$-0.233282\pi$
$402$	8.03475	−	29.9861i	0.400737	−	1.49557i
$403$	−3.97869	+	14.8487i	−0.198193	+	0.739665i
$404$	0.390054	−	0.675593i	0.0194059	−	0.0336120i
$405$		0			0
$406$	24.1307	+	16.1520i	1.19759	+	0.801612i
$407$	1.28242	−	1.28242i	0.0635673	−	0.0635673i
$408$	4.25072	−	1.13898i	0.210442	−	0.0563877i
$409$	−12.4439	−	21.5534i	−0.615310	−	1.06575i	−0.990330	−	0.138731i	$-0.955698\pi$
$409$	−12.4439	−	21.5534i	−0.615310	−	1.06575i	0.375020	−	0.927017i	$-0.377636\pi$
$410$		0			0
$411$	−10.0267	−	5.78892i	−0.494581	−	0.285546i
$412$	−12.5520	−	12.5520i	−0.618395	−	0.618395i
$413$	5.22522	−	15.3519i	0.257116	−	0.755420i
$414$			11.5503i			0.567664i
$415$		0			0
$416$	18.2729	−	10.5499i	0.895905	−	0.517251i
$417$	4.71576	+	1.26358i	0.230932	+	0.0618780i
$418$	−3.15868	−	11.7884i	−0.154496	−	0.576588i
$419$	36.9791			1.80655			0.903273	−	0.429065i	$-0.141157\pi$
$419$	36.9791			1.80655			0.903273	+	0.429065i	$0.141157\pi$
$420$		0			0
$421$	10.9968			0.535951			0.267975	−	0.963426i	$-0.413645\pi$
$421$	10.9968			0.535951			0.267975	+	0.963426i	$0.413645\pi$
$422$	2.27623	+	8.49499i	0.110805	+	0.413530i
$423$	3.75432	+	1.00597i	0.182541	+	0.0489118i
$424$	−0.707431	+	0.408436i	−0.0343559	+	0.0198354i
$425$		0			0
$426$		−	31.5636i		−	1.52926i
$427$	−3.86105	−	19.4937i	−0.186849	−	0.943366i
$428$	3.44051	+	3.44051i	0.166303	+	0.166303i
$429$	−4.38741	−	2.53307i	−0.211826	−	0.122298i
$430$		0			0
$431$	2.95291	+	5.11459i	0.142237	+	0.246361i	0.928339	−	0.371736i	$-0.121237\pi$
$431$	2.95291	+	5.11459i	0.142237	+	0.246361i	−0.786102	+	0.618097i	$0.787904\pi$
$432$	−3.10424	+	0.831778i	−0.149353	+	0.0400189i
$433$	3.82699	−	3.82699i	0.183913	−	0.183913i	−0.609145	−	0.793059i	$-0.708487\pi$
$433$	3.82699	−	3.82699i	0.183913	−	0.183913i	0.793059	+	0.609145i	$0.208487\pi$
$434$	2.15130	−	32.4182i	0.103266	−	1.55612i
$435$		0			0
$436$	−17.7847	+	30.8039i	−0.851730	+	1.47524i
$437$	4.32912	−	16.1565i	0.207090	−	0.772870i
$438$	−3.37955	+	12.6127i	−0.161481	+	0.602656i
$439$	−2.02348	+	3.50476i	−0.0965752	+	0.167273i	−0.910265	−	0.414026i	$-0.864122\pi$
$439$	−2.02348	+	3.50476i	−0.0965752	+	0.167273i	0.813690	+	0.581299i	$0.197456\pi$
$440$		0			0
$441$	−4.27036	+	5.54653i	−0.203351	+	0.264120i
$442$	−24.1061	+	24.1061i	−1.14661	+	1.14661i
$443$	−16.3131	+	4.37108i	−0.775059	+	0.207676i	−0.624605	−	0.780941i	$-0.714740\pi$
$443$	−16.3131	+	4.37108i	−0.775059	+	0.207676i	−0.150454	+	0.988617i	$0.548073\pi$
$444$	−1.09025	−	1.88836i	−0.0517409	−	0.0896178i
$445$		0			0
$446$	−21.8455	−	12.6125i	−1.03441	−	0.597218i
$447$	−1.89011	−	1.89011i	−0.0893991	−	0.0893991i
$448$	−20.7570	+	18.1735i	−0.980674	+	0.858617i
$449$		−	27.2328i		−	1.28520i	−0.766204	−	0.642598i	$-0.777857\pi$
$449$		−	27.2328i		−	1.28520i	0.766204	−	0.642598i	$-0.222143\pi$
$450$		0			0
$451$	−17.3254	+	10.0028i	−0.815820	+	0.471014i
$452$	−13.6120	−	3.64733i	−0.640256	−	0.171556i
$453$	−3.82120	−	14.2609i	−0.179536	−	0.670037i
$454$	29.2652			1.37349
$455$		0			0
$456$	−2.11324			−0.0989614
$457$	6.42774	+	23.9887i	0.300677	+	1.12214i	0.936603	+	0.350392i	$0.113952\pi$
$457$	6.42774	+	23.9887i	0.300677	+	1.12214i	−0.635926	+	0.771750i	$0.719382\pi$
$458$	−7.63281	−	2.04521i	−0.356658	−	0.0955662i
$459$	5.43854	−	3.13994i	0.253849	−	0.146560i
$460$		0			0
$461$			23.0576i			1.07390i	0.843614	+	0.536950i	$0.180424\pi$
$461$			23.0576i			1.07390i	−0.843614	+	0.536950i	$0.819576\pi$
$462$	10.1362	+	3.44998i	0.471578	+	0.160507i
$463$	3.66021	+	3.66021i	0.170104	+	0.170104i	0.787025	−	0.616921i	$-0.211620\pi$
$463$	3.66021	+	3.66021i	0.170104	+	0.170104i	−0.616921	+	0.787025i	$0.711620\pi$
$464$	14.6684	+	8.46880i	0.680963	+	0.393154i
$465$		0			0
$466$	23.1005	+	40.0113i	1.07011	+	1.85349i
$467$	2.43575	−	0.652657i	0.112713	−	0.0302014i	−0.202022	−	0.979381i	$-0.564751\pi$
$467$	2.43575	−	0.652657i	0.112713	−	0.0302014i	0.314735	+	0.949180i	$0.398084\pi$
$468$	−4.30697	+	4.30697i	−0.199090	+	0.199090i
$469$	−17.4158	−	35.3883i	−0.804187	−	1.63408i
$470$		0			0
$471$	−11.2799	+	19.5373i	−0.519750	+	0.900233i
$472$	−1.11168	+	4.14884i	−0.0511692	+	0.190966i
$473$	−4.65911	+	17.3880i	−0.214226	+	0.799503i
$474$	17.1145	−	29.6431i	0.786093	−	1.36155i
$475$		0			0
$476$	21.5941	−	32.2610i	0.989766	−	1.47868i
$477$	−0.824275	+	0.824275i	−0.0377410	+	0.0377410i
$478$	40.8999	−	10.9591i	1.87072	−	0.501257i
$479$	−6.57783	−	11.3931i	−0.300549	−	0.520565i	0.675712	−	0.737166i	$-0.263836\pi$
$479$	−6.57783	−	11.3931i	−0.300549	−	0.520565i	−0.976260	+	0.216601i	$0.930503\pi$
$480$		0			0
$481$	2.10687	+	1.21640i	0.0960651	+	0.0554632i
$482$	15.1875	+	15.1875i	0.691770	+	0.691770i
$483$	9.66675	+	11.0409i	0.439852	+	0.502379i
$484$			16.8772i			0.767147i
$485$		0			0
$486$	1.80344	−	1.04121i	0.0818055	−	0.0472304i
$487$	32.5155	+	8.71251i	1.47342	+	0.394802i	0.904102	−	0.427316i	$-0.140541\pi$
$487$	32.5155	+	8.71251i	1.47342	+	0.394802i	0.569317	+	0.822118i	$0.307208\pi$
$488$	1.36227	+	5.08407i	0.0616671	+	0.230145i
$489$	15.5267			0.702143
$490$		0			0
$491$	−20.5788			−0.928710			−0.464355	−	0.885649i	$-0.653714\pi$
$491$	−20.5788			−0.928710			−0.464355	+	0.885649i	$0.653714\pi$
$492$	6.22527	+	23.2330i	0.280657	+	1.04742i
$493$	−31.9695	−	8.56621i	−1.43984	−	0.385803i
$494$	14.1776	−	8.18543i	0.637880	−	0.368280i
$495$		0			0
$496$		−	18.9512i		−	0.850932i
$497$	−26.4165	−	30.1718i	−1.18494	−	1.35339i
$498$	0.412137	+	0.412137i	0.0184683	+	0.0184683i
$499$	−11.8247	−	6.82698i	−0.529345	−	0.305618i	0.211404	−	0.977399i	$-0.432196\pi$
$499$	−11.8247	−	6.82698i	−0.529345	−	0.305618i	−0.740750	+	0.671781i	$0.765530\pi$
$500$		0			0
$501$	−3.13994	−	5.43854i	−0.140282	−	0.242976i
$502$	14.6075	−	3.91406i	0.651963	−	0.174693i
$503$	−23.7213	+	23.7213i	−1.05768	+	1.05768i	−0.0594513	+	0.998231i	$0.518935\pi$
$503$	−23.7213	+	23.7213i	−1.05768	+	1.05768i	−0.998231	+	0.0594513i	$0.981065\pi$
$504$	1.03130	−	1.54073i	0.0459375	−	0.0686294i
$505$		0			0
$506$	11.2233	−	19.4393i	0.498935	−	0.864181i
$507$	−1.60577	+	5.99281i	−0.0713147	+	0.266150i
$508$	−1.88297	+	7.02735i	−0.0835434	+	0.311788i
$509$	−12.9430	+	22.4180i	−0.573689	+	0.993659i	0.422494	+	0.906366i	$0.361155\pi$
$509$	−12.9430	+	22.4180i	−0.573689	+	0.993659i	−0.996183	+	0.0872928i	$0.972178\pi$
$510$		0			0
$511$	7.32538	+	14.8849i	0.324056	+	0.658470i
$512$	−21.5780	+	21.5780i	−0.953620	+	0.953620i
$513$	−2.91290	+	0.780509i	−0.128608	+	0.0344603i
$514$	5.60214	+	9.70320i	0.247100	+	0.427990i
$515$		0			0
$516$	18.7433	+	10.8215i	0.825130	+	0.476389i
$517$	−5.34110	−	5.34110i	−0.234901	−	0.234901i
$518$	−4.86749	−	1.65671i	−0.213865	−	0.0727916i
$519$			20.4275i			0.896667i
$520$		0			0
$521$	−33.4370	+	19.3049i	−1.46490	+	0.845762i	−0.999232	−	0.0391964i	$-0.987520\pi$
$521$	−33.4370	+	19.3049i	−1.46490	+	0.845762i	−0.465671	+	0.884958i	$0.654187\pi$
$522$	−10.6012	−	2.84058i	−0.464001	−	0.124329i
$523$	4.23956	+	15.8222i	0.185383	+	0.691859i	0.994548	+	0.104277i	$0.0332530\pi$
$523$	4.23956	+	15.8222i	0.185383	+	0.691859i	−0.809165	+	0.587581i	$0.800080\pi$
$524$	28.6427			1.25126
$525$		0			0
$526$	−1.86771			−0.0814360
$527$	9.58457	+	35.7701i	0.417510	+	1.55817i
$528$	6.03272	+	1.61646i	0.262540	+	0.0703475i
$529$	6.72382	−	3.88200i	0.292340	−	0.168783i
$530$		0			0
$531$			6.12938i			0.265992i
$532$	−14.0260	+	12.2803i	−0.608104	+	0.532418i
$533$	−18.9757	−	18.9757i	−0.821931	−	0.821931i
$534$	−21.9310	−	12.6619i	−0.949049	−	0.547933i
$535$		0			0
$536$	5.22327	+	9.04697i	0.225611	+	0.390770i
$537$	8.14033	−	2.18119i	0.351281	−	0.0941255i
$538$	−36.1605	+	36.1605i	−1.55899	+	1.55899i
$539$	12.5766	−	5.18543i	0.541713	−	0.223352i
$540$		0			0
$541$	−1.11640	+	1.93366i	−0.0479977	+	0.0831345i	−0.889026	−	0.457856i	$-0.848617\pi$
$541$	−1.11640	+	1.93366i	−0.0479977	+	0.0831345i	0.841028	+	0.540991i	$0.181951\pi$
$542$	4.55303	−	16.9921i	0.195569	−	0.729875i
$543$	3.11777	−	11.6357i	0.133796	−	0.499334i
$544$	25.4144	−	44.0191i	1.08963	−	1.88730i
$545$		0			0
$546$	−0.951035	+	14.3313i	−0.0407005	+	0.613322i
$547$	15.2205	−	15.2205i	0.650782	−	0.650782i	−0.302400	−	0.953181i	$-0.597788\pi$
$547$	15.2205	−	15.2205i	0.650782	−	0.650782i	0.953181	+	0.302400i	$0.0977877\pi$
$548$	26.1300	−	7.00150i	1.11622	−	0.299089i
$549$	3.75553	+	6.50476i	0.160282	+	0.277617i
$550$		0			0
$551$	13.7643	+	7.94680i	0.586377	+	0.338545i
$552$	−2.74836	−	2.74836i	−0.116978	−	0.116978i
$553$	−8.44942	−	42.6595i	−0.359306	−	1.81407i
$554$		−	31.2894i		−	1.32936i
$555$		0			0
$556$	−9.87884	+	5.70355i	−0.418956	+	0.241884i
$557$	16.9900	+	4.55245i	0.719888	+	0.192894i	0.600122	−	0.799909i	$-0.295119\pi$
$557$	16.9900	+	4.55245i	0.719888	+	0.192894i	0.119767	+	0.992802i	$0.461785\pi$
$558$	3.17827	+	11.8615i	0.134547	+	0.502136i
$559$	−24.1473			−1.02132
$560$		0			0
$561$	−12.2042			−0.515262
$562$	−2.44733	−	9.13354i	−0.103234	−	0.385275i
$563$	−22.5505	−	6.04240i	−0.950392	−	0.254657i	−0.249863	−	0.968281i	$-0.580386\pi$
$563$	−22.5505	−	6.04240i	−0.950392	−	0.254657i	−0.700529	+	0.713624i	$0.747052\pi$
$564$	−7.86477	+	4.54073i	−0.331167	+	0.191199i
$565$		0			0
$566$			30.8430i			1.29643i
$567$	0.852487	−	2.50465i	0.0358011	−	0.105185i
$568$	7.51049	+	7.51049i	0.315133	+	0.315133i
$569$	12.8543	+	7.42144i	0.538881	+	0.311123i	0.744625	−	0.667483i	$-0.232628\pi$
$569$	12.8543	+	7.42144i	0.538881	+	0.311123i	−0.205745	+	0.978606i	$0.565962\pi$
$570$		0			0
$571$	−19.1714	−	33.2059i	−0.802299	−	1.38962i	−0.918100	−	0.396350i	$-0.870277\pi$
$571$	−19.1714	−	33.2059i	−0.802299	−	1.38962i	0.115801	−	0.993272i	$-0.463057\pi$
$572$	11.4338	−	3.06367i	0.478069	−	0.128098i
$573$	−4.63846	+	4.63846i	−0.193775	+	0.193775i
$574$	47.1328	+	31.5487i	1.96729	+	1.31682i
$575$		0			0
$576$	5.21374	−	9.03047i	0.217239	−	0.376270i
$577$	−2.75019	+	10.2639i	−0.114492	+	0.427290i	−0.999248	−	0.0387638i	$-0.987658\pi$
$577$	−2.75019	+	10.2639i	−0.114492	+	0.427290i	0.884756	+	0.466054i	$0.154325\pi$
$578$	−12.0929	+	45.1314i	−0.502999	+	1.87722i
$579$	−1.96619	+	3.40554i	−0.0817122	+	0.141530i
$580$		0			0
$581$	0.738893	+	0.0490336i	0.0306545	+	0.00203426i
$582$	−22.8977	+	22.8977i	−0.949142	+	0.949142i
$583$	2.18821	−	0.586329i	0.0906263	−	0.0242833i
$584$	−2.19700	−	3.80531i	−0.0909123	−	0.157465i
$585$		0			0
$586$	−8.18891	−	4.72787i	−0.338281	−	0.195306i
$587$	7.01529	+	7.01529i	0.289552	+	0.289552i	0.836903	−	0.547351i	$-0.184364\pi$
$587$	7.01529	+	7.01529i	0.289552	+	0.289552i	−0.547351	+	0.836903i	$0.684364\pi$
$588$	−2.10843	−	16.2191i	−0.0869503	−	0.668864i
$589$		−	17.7831i		−	0.732738i
$590$		0			0
$591$	10.1966	−	5.88699i	0.419431	−	0.242158i
$592$	−2.89696	−	0.776239i	−0.119064	−	0.0319032i
$593$	−4.69201	−	17.5108i	−0.192678	−	0.719084i	−0.992856	−	0.119321i	$-0.961928\pi$
$593$	−4.69201	−	17.5108i	−0.192678	−	0.719084i	0.800178	−	0.599763i	$-0.204738\pi$
$594$	−4.04695			−0.166048
$595$		0			0
$596$	6.24553			0.255827
$597$	3.50502	+	13.0809i	0.143451	+	0.535366i
$598$	29.0841	+	7.79305i	1.18934	+	0.318682i
$599$	−15.5885	+	9.00000i	−0.636927	+	0.367730i	−0.783430	−	0.621480i	$-0.786532\pi$
$599$	−15.5885	+	9.00000i	−0.636927	+	0.367730i	0.146503	+	0.989210i	$0.453198\pi$
$600$		0			0
$601$		−	9.94386i		−	0.405619i	−0.979218	−	0.202809i	$-0.934993\pi$
$601$		−	9.94386i		−	0.405619i	0.979218	−	0.202809i	$-0.0650071\pi$
$602$	50.0625	−	9.91570i	2.04039	−	0.404134i
$603$	10.5412	+	10.5412i	0.429272	+	0.429272i
$604$	29.8746	+	17.2481i	1.21558	+	0.701815i
$605$		0			0
$606$	0.347638	+	0.602127i	0.0141218	+	0.0244597i
$607$	−33.6402	+	9.01387i	−1.36542	+	0.365862i	−0.865802	−	0.500387i	$-0.833191\pi$
$607$	−33.6402	+	9.01387i	−1.36542	+	0.365862i	−0.499613	+	0.866249i	$0.666524\pi$
$608$	−17.2594	+	17.2594i	−0.699960	+	0.699960i
$609$	−12.5111	+	6.15713i	−0.506974	+	0.249499i
$610$		0			0
$611$	5.06615	−	8.77482i	0.204954	−	0.354991i
$612$	−3.79766	+	14.1730i	−0.153511	+	0.572911i
$613$	−6.12518	+	22.8595i	−0.247394	+	0.923285i	0.724772	+	0.688989i	$0.241945\pi$
$613$	−6.12518	+	22.8595i	−0.247394	+	0.923285i	−0.972165	+	0.234296i	$0.924721\pi$
$614$	−19.9368	+	34.5315i	−0.804582	+	1.39358i
$615$		0			0
$616$	−3.23280	+	1.59097i	−0.130253	+	0.0641020i
$617$	19.7860	−	19.7860i	0.796554	−	0.796554i	−0.185996	−	0.982550i	$-0.559551\pi$
$617$	19.7860	−	19.7860i	0.796554	−	0.796554i	0.982550	+	0.185996i	$0.0595512\pi$
$618$	15.2818	−	4.09476i	0.614726	−	0.164715i
$619$	−18.4587	−	31.9714i	−0.741917	−	1.28504i	−0.951621	−	0.307273i	$-0.900583\pi$
$619$	−18.4587	−	31.9714i	−0.741917	−	1.28504i	0.209704	−	0.977765i	$-0.432750\pi$
$620$		0			0
$621$	−4.80344	−	2.77327i	−0.192755	−	0.111287i
$622$	38.3102	+	38.3102i	1.53610	+	1.53610i
$623$	−31.5611	+	6.25119i	−1.26447	+	0.250449i
$624$			8.37782i			0.335381i
$625$		0			0
$626$	−6.52194	+	3.76545i	−0.260669	+	0.150497i
$627$	5.66088	+	1.51683i	0.226074	+	0.0605762i
$628$	−13.6426	−	50.9150i	−0.544401	−	2.03173i
$629$	5.86057			0.233676
$630$		0			0
$631$	17.6412			0.702286			0.351143	−	0.936322i	$-0.385793\pi$
$631$	17.6412			0.702286			0.351143	+	0.936322i	$0.385793\pi$
$632$	2.98116	+	11.1259i	0.118584	+	0.442563i
$633$	−4.07937	−	1.09306i	−0.162140	−	0.0434453i
$634$	−17.1602	+	9.90742i	−0.681517	+	0.393474i
$635$		0			0
$636$		−	2.72367i		−	0.108001i
$637$	11.0852	+	14.4953i	0.439210	+	0.574323i
$638$	15.0818	+	15.0818i	0.597095	+	0.597095i
$639$	13.1265	+	7.57856i	0.519275	+	0.299803i
$640$		0			0
$641$	20.3082	+	35.1748i	0.802126	+	1.38932i	0.918214	+	0.396084i	$0.129631\pi$
$641$	20.3082	+	35.1748i	0.802126	+	1.38932i	−0.116089	+	0.993239i	$0.537036\pi$
$642$	−4.18875	+	1.12237i	−0.165317	+	0.0442965i
$643$	17.6354	−	17.6354i	0.695471	−	0.695471i	−0.267959	−	0.963430i	$-0.586349\pi$
$643$	17.6354	−	17.6354i	0.695471	−	0.695471i	0.963430	+	0.267959i	$0.0863493\pi$
$644$	−34.2124	−	2.27036i	−1.34816	−	0.0894648i
$645$		0			0
$646$	19.7185	−	34.1535i	0.775814	−	1.34375i
$647$	−2.00304	+	7.47546i	−0.0787477	+	0.293891i	−0.994057	−	0.108861i	$-0.965280\pi$
$647$	−2.00304	+	7.47546i	−0.0787477	+	0.293891i	0.915309	+	0.402752i	$0.131946\pi$
$648$	−0.181369	+	0.676878i	−0.00712484	+	0.0265903i
$649$	5.95586	−	10.3159i	0.233788	−	0.404933i
$650$		0			0
$651$	12.9653	+	8.67842i	0.508151	+	0.340134i
$652$	−25.6527	+	25.6527i	−1.00464	+	1.00464i
$653$	−8.74193	+	2.34239i	−0.342098	+	0.0916649i	−0.425778	−	0.904828i	$-0.639999\pi$
$653$	−8.74193	+	2.34239i	−0.342098	+	0.0916649i	0.0836796	+	0.996493i	$0.473333\pi$
$654$	−15.8507	−	27.4542i	−0.619811	−	1.07354i
$655$		0			0
$656$	28.6508	+	16.5415i	1.11862	+	0.645838i
$657$	−4.43382	−	4.43382i	−0.172980	−	0.172980i
$658$	−6.89995	+	20.2724i	−0.268988	+	0.790300i
$659$			7.36509i			0.286903i	0.989657	+	0.143452i	$0.0458201\pi$
$659$			7.36509i			0.286903i	−0.989657	+	0.143452i	$0.954180\pi$
$660$		0			0
$661$	42.6555	−	24.6272i	1.65911	−	0.957886i	0.685980	−	0.727621i	$-0.259374\pi$
$661$	42.6555	−	24.6272i	1.65911	−	0.957886i	0.973128	−	0.230265i	$-0.0739595\pi$
$662$	−11.3728	−	3.04733i	−0.442016	−	0.118438i
$663$	−4.23709	−	15.8130i	−0.164555	−	0.614128i
$664$	−0.196134			−0.00761149
$665$		0			0
$666$	1.94338			0.0753045
$667$	7.56586	+	28.2362i	0.292951	+	1.09331i
$668$	14.1730	+	3.79766i	0.548372	+	0.146936i
$669$	10.4904	−	6.05662i	0.405581	−	0.234162i
$670$		0			0
$671$		−	14.5968i		−	0.563505i
$672$	−4.16066	−	21.0064i	−0.160501	−	0.810339i
$673$	−8.14312	−	8.14312i	−0.313894	−	0.313894i	0.532522	−	0.846416i	$-0.321244\pi$
$673$	−8.14312	−	8.14312i	−0.313894	−	0.313894i	−0.846416	+	0.532522i	$0.821244\pi$
$674$	−18.1100	−	10.4558i	−0.697570	−	0.402742i
$675$		0			0
$676$	−7.24810	−	12.5541i	−0.278773	−	0.482849i
$677$	30.8702	−	8.27166i	1.18644	−	0.317906i	0.388962	−	0.921254i	$-0.372834\pi$
$677$	30.8702	−	8.27166i	1.18644	−	0.317906i	0.797478	+	0.603348i	$0.206167\pi$
$678$	8.88111	−	8.88111i	0.341077	−	0.341077i
$679$	−2.72423	+	41.0518i	−0.104546	+	1.57542i
$680$		0			0
$681$	−7.02671	+	12.1706i	−0.269264	+	0.466379i
$682$	6.17659	−	23.0513i	0.236514	−	0.882681i
$683$	4.72869	−	17.6477i	0.180938	−	0.675270i	−0.814526	−	0.580128i	$-0.803003\pi$
$683$	4.72869	−	17.6477i	0.180938	−	0.675270i	0.995464	−	0.0951425i	$-0.0303307\pi$
$684$	3.52305	−	6.10211i	0.134707	−	0.233320i
$685$		0			0
$686$	−28.9341	−	25.4998i	−1.10471	−	0.973586i
$687$	2.68322	−	2.68322i	0.102371	−	0.102371i
$688$	28.7544	−	7.70471i	1.09625	−	0.293739i
$689$	1.51942	+	2.63171i	0.0578852	+	0.100260i
$690$		0			0
$691$	−14.7423	−	8.51148i	−0.560824	−	0.323792i	0.192652	−	0.981267i	$-0.438291\pi$
$691$	−14.7423	−	8.51148i	−0.560824	−	0.323792i	−0.753476	+	0.657475i	$0.771625\pi$
$692$	−33.7495	−	33.7495i	−1.28296	−	1.28296i
$693$	−3.86849	+	3.38701i	−0.146952	+	0.128662i
$694$			14.0191i			0.532156i
$695$		0			0
$696$	3.19844	−	1.84662i	0.121236	−	0.0699959i
$697$	−62.4439	−	16.7318i	−2.36523	−	0.633762i
$698$	−1.48937	−	5.55839i	−0.0563734	−	0.210388i
$699$	−22.1861			−0.839156
$700$		0			0
$701$	14.5973			0.551334			0.275667	−	0.961253i	$-0.411101\pi$
$701$	14.5973			0.551334			0.275667	+	0.961253i	$0.411101\pi$
$702$	−1.40503	−	5.24365i	−0.0530295	−	0.197909i
$703$	−2.71840	−	0.728393i	−0.102526	−	0.0274719i
$704$	−17.5496	+	10.1323i	−0.661427	+	0.381875i
$705$		0			0
$706$		−	53.0887i		−	1.99802i
$707$	0.836246	+	0.284626i	0.0314503	+	0.0107045i
$708$	−10.1267	−	10.1267i	−0.380586	−	0.380586i
$709$	−0.209858	−	0.121162i	−0.00788139	−	0.00455032i	0.496054	−	0.868292i	$-0.334782\pi$
$709$	−0.209858	−	0.121162i	−0.00788139	−	0.00455032i	−0.503936	+	0.863741i	$0.668115\pi$
$710$		0			0
$711$	8.21851	+	14.2349i	0.308218	+	0.533849i
$712$	8.23130	−	2.20557i	0.308481	−	0.0826573i
$713$	23.1276	−	23.1276i	0.866136	−	0.866136i
$714$	15.2778	+	31.0439i	0.571756	+	1.16179i
$715$		0			0
$716$	−9.84545	+	17.0528i	−0.367942	+	0.637294i
$717$	−5.26265	+	19.6405i	−0.196537	+	0.733487i
$718$	−3.62709	+	13.5365i	−0.135362	+	0.505177i
$719$	−3.26797	+	5.66029i	−0.121875	+	0.211093i	−0.920507	−	0.390726i	$-0.872224\pi$
$719$	−3.26797	+	5.66029i	−0.121875	+	0.211093i	0.798632	+	0.601819i	$0.205557\pi$
$720$		0			0
$721$	11.1809	−	16.7040i	0.416400	−	0.622090i
$722$	14.5863	−	14.5863i	0.542846	−	0.542846i
$723$	−9.96263	+	2.66948i	−0.370514	+	0.0992790i
$724$	14.0729	+	24.3750i	0.523017	+	0.905892i
$725$		0			0
$726$	−13.0267	−	7.52097i	−0.483466	−	0.279129i
$727$	−6.33740	−	6.33740i	−0.235041	−	0.235041i	0.579752	−	0.814793i	$-0.303149\pi$
$727$	−6.33740	−	6.33740i	−0.235041	−	0.235041i	−0.814793	+	0.579752i	$0.803149\pi$
$728$	−3.18380	−	3.63639i	−0.117999	−	0.134774i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−50.3769	+	29.0851i	−1.86326	+	1.07575i
$732$	−16.9517	−	4.54218i	−0.626551	−	0.167884i
$733$	2.97148	+	11.0897i	0.109754	+	0.409607i	0.998841	−	0.0481307i	$-0.0153264\pi$
$733$	2.97148	+	11.0897i	0.109754	+	0.409607i	−0.889087	+	0.457738i	$0.848660\pi$
$734$	−38.3155			−1.41425
$735$		0			0
$736$	−44.8931			−1.65478
$737$	−7.49825	−	27.9839i	−0.276202	−	1.03080i
$738$	−20.7066	−	5.54831i	−0.762219	−	0.204236i
$739$	28.2058	−	16.2847i	1.03757	−	0.599041i	0.118425	−	0.992963i	$-0.462215\pi$
$739$	28.2058	−	16.2847i	1.03757	−	0.599041i	0.919144	+	0.393922i	$0.128882\pi$
$740$		0			0
$741$			7.86143i			0.288797i
$742$	−4.23074	−	4.83216i	−0.155315	−	0.177394i
$743$	25.4999	+	25.4999i	0.935502	+	0.935502i	0.998042	−	0.0625403i	$-0.0199202\pi$
$743$	25.4999	+	25.4999i	0.935502	+	0.935502i	−0.0625403	+	0.998042i	$0.519920\pi$
$744$	−3.57867	−	2.06615i	−0.131200	−	0.0757486i
$745$		0			0
$746$	−1.82409	−	3.15942i	−0.0667847	−	0.115675i
$747$	−0.270353	+	0.0724408i	−0.00989169	+	0.00265047i
$748$	20.1633	−	20.1633i	0.737245	−	0.737245i
$749$	−3.06469	+	4.57856i	−0.111981	+	0.167297i
$750$		0			0
$751$	−10.8931	+	18.8675i	−0.397496	+	0.688483i	−0.993416	−	0.114560i	$-0.963454\pi$
$751$	−10.8931	+	18.8675i	−0.397496	+	0.688483i	0.595920	+	0.803044i	$0.296787\pi$
$752$	−3.23292	+	12.0654i	−0.117893	+	0.439981i
$753$	−1.87956	+	7.01463i	−0.0684951	+	0.255627i
$754$	−14.3054	+	24.7777i	−0.520972	+	0.902351i
$755$		0			0
$756$	2.72964	+	5.54653i	0.0992759	+	0.201725i
$757$	23.5319	−	23.5319i	0.855283	−	0.855283i	−0.135495	−	0.990778i	$-0.543263\pi$
$757$	23.5319	−	23.5319i	0.855283	−	0.855283i	0.990778	+	0.135495i	$0.0432626\pi$
$758$	75.2843	−	20.1724i	2.73445	−	0.732694i
$759$	5.38951	+	9.33491i	0.195627	+	0.338836i
$760$		0			0
$761$	−9.08493	−	5.24519i	−0.329328	−	0.190138i	0.326214	−	0.945296i	$-0.394227\pi$
$761$	−9.08493	−	5.24519i	−0.329328	−	0.190138i	−0.655543	+	0.755158i	$0.727560\pi$
$762$	−4.58496	−	4.58496i	−0.166095	−	0.166095i
$763$	−38.1289	−	12.9776i	−1.38036	−	0.469822i
$764$		−	15.3270i		−	0.554511i
$765$		0			0
$766$	−33.0286	+	19.0691i	−1.19337	+	0.688993i
$767$	15.4341	+	4.13554i	0.557291	+	0.149326i
$768$	−2.41893	−	9.02758i	−0.0872857	−	0.325755i
$769$	−3.95222			−0.142521			−0.0712604	−	0.997458i	$-0.522702\pi$
$769$	−3.95222			−0.142521			−0.0712604	+	0.997458i	$0.522702\pi$
$770$		0			0
$771$	−5.38040			−0.193770
$772$	−2.37804	−	8.87498i	−0.0855876	−	0.319417i
$773$	30.9612	+	8.29603i	1.11360	+	0.298388i	0.768290	−	0.640102i	$-0.221108\pi$
$773$	30.9612	+	8.29603i	1.11360	+	0.298388i	0.345308	+	0.938490i	$0.387775\pi$
$774$	−16.7051	+	9.64471i	−0.600453	+	0.346672i
$775$		0			0
$776$		−	10.8969i		−	0.391177i
$777$	1.85768	−	1.62647i	0.0666440	−	0.0583494i
$778$	8.72357	+	8.72357i	0.312755	+	0.312755i
$779$	26.8848	+	15.5219i	0.963248	+	0.556131i
$780$		0			0
$781$	−14.7280	−	25.5097i	−0.527010	−	0.912809i
$782$	70.0628	−	18.7733i	2.50544	−	0.671330i
$783$	3.72671	−	3.72671i	0.133182	−	0.133182i
$784$	−17.8251	−	13.7239i	−0.636612	−	0.490138i
$785$		0			0
$786$	−12.7640	+	22.1079i	−0.455277	+	0.788562i
$787$	5.86328	−	21.8820i	0.209003	−	0.780011i	−0.779189	−	0.626790i	$-0.784369\pi$
$787$	5.86328	−	21.8820i	0.209003	−	0.780011i	0.988192	−	0.153221i	$-0.0489647\pi$
$788$	−7.12011	+	26.5726i	−0.253644	+	0.946610i
$789$	0.448445	−	0.776729i	0.0159651	−	0.0276523i
$790$		0			0
$791$	1.05662	−	15.9223i	0.0375690	−	0.566133i
$792$	0.962963	−	0.962963i	0.0342174	−	0.0342174i
$793$	18.9132	−	5.06777i	0.671626	−	0.179962i
$794$	3.74561	+	6.48758i	0.132927	+	0.230236i
$795$		0			0
$796$	−27.4027	−	15.8209i	−0.971261	−	0.560758i
$797$	−26.7342	−	26.7342i	−0.946974	−	0.946974i	0.0516889	−	0.998663i	$-0.483540\pi$
$797$	−26.7342	−	26.7342i	−0.946974	−	0.946974i	−0.998663	+	0.0516889i	$0.983540\pi$
$798$	−3.22817	−	16.2984i	−0.114276	−	0.576957i
$799$		−	24.4084i		−	0.863508i
$800$		0			0
$801$	10.5315	−	6.08035i	0.372111	−	0.214838i
$802$	−76.6125	−	20.5283i	−2.70528	−	0.724878i
$803$	3.15389	+	11.7705i	0.111298	+	0.415371i
$804$	−34.8316			−1.22842
$805$		0			0
$806$	32.0121			1.12758
$807$	−6.35587	−	23.7204i	−0.223737	−	0.834999i
$808$	−0.225994	−	0.0605550i	−0.00795045	−	0.00213032i
$809$	−24.6354	+	14.2233i	−0.866136	+	0.500064i	−0.866062	−	0.499936i	$-0.833357\pi$
$809$	−24.6354	+	14.2233i	−0.866136	+	0.500064i	−7.34001e−5		1.00000i	$0.500023\pi$
$810$		0			0
$811$		−	47.9872i		−	1.68506i	−0.538649	−	0.842530i	$-0.681065\pi$
$811$		−	47.9872i		−	1.68506i	0.538649	−	0.842530i	$-0.318935\pi$
$812$	10.4977	−	30.8429i	0.368399	−	1.08237i
$813$	5.97337	+	5.97337i	0.209495	+	0.209495i
$814$	−3.27074	−	1.88836i	−0.114640	−	0.0661871i
$815$		0			0
$816$	10.0910	+	17.4781i	0.353255	+	0.611856i
$817$	26.9820	−	7.22981i	0.943982	−	0.252939i
$818$	−36.6472	+	36.6472i	−1.28134	+	1.28134i
$819$	−5.73164	−	3.83651i	−0.200280	−	0.134058i
$820$		0			0
$821$	−15.1193	+	26.1874i	−0.527667	+	0.913946i	0.471813	+	0.881699i	$0.343600\pi$
$821$	−15.1193	+	26.1874i	−0.527667	+	0.913946i	−0.999480	+	0.0322472i	$0.989734\pi$
$822$	−6.24014	+	23.2885i	−0.217650	+	0.812280i
$823$	7.21166	−	26.9143i	0.251383	−	0.938173i	−0.718684	−	0.695336i	$-0.755255\pi$
$823$	7.21166	−	26.9143i	0.251383	−	0.938173i	0.970067	−	0.242837i	$-0.0780779\pi$
$824$	−2.66194	+	4.61062i	−0.0927331	+	0.160618i
$825$		0			0
$826$	−33.6962	−	2.23611i	−1.17244	−	0.0778042i
$827$	−16.9844	+	16.9844i	−0.590606	+	0.590606i	−0.937795	−	0.347189i	$-0.887136\pi$
$827$	−16.9844	+	16.9844i	−0.590606	+	0.590606i	0.347189	+	0.937795i	$0.387136\pi$
$828$	12.5179	−	3.35417i	0.435028	−	0.116565i
$829$	20.3808	+	35.3005i	0.707853	+	1.22604i	0.965652	+	0.259839i	$0.0836693\pi$
$829$	20.3808	+	35.3005i	0.707853	+	1.22604i	−0.257799	+	0.966199i	$0.582997\pi$
$830$		0			0
$831$	13.0124	+	7.51272i	0.451396	+	0.260613i
$832$	−19.2214	−	19.2214i	−0.666381	−	0.666381i
$833$	40.5856	+	16.8885i	1.40621	+	0.585154i
$834$		−	10.1667i		−	0.352042i
$835$		0			0
$836$	−11.8587	+	6.84664i	−0.410142	+	0.236796i
$837$	−5.69598	−	1.52623i	−0.196882	−	0.0527543i
$838$	−19.9307	−	74.3824i	−0.688495	−	2.56950i
$839$	−32.2842			−1.11458			−0.557288	−	0.830320i	$-0.688158\pi$
$839$	−32.2842			−1.11458			−0.557288	+	0.830320i	$0.688158\pi$
$840$		0			0
$841$	1.22327			0.0421817
$842$	−5.92697	−	22.1197i	−0.204257	−	0.762297i
$843$	4.38601	+	1.17523i	0.151062	+	0.0404770i
$844$	8.54569	−	4.93385i	0.294155	−	0.169830i
$845$		0			0
$846$		−	8.09390i		−	0.278274i
$847$	−18.7468	+	3.71311i	−0.644147	+	0.127584i
$848$	−2.64901	−	2.64901i	−0.0909673	−	0.0909673i
$849$	−12.8268	−	7.40554i	−0.440214	−	0.254158i
$850$		0			0
$851$	−2.58809	−	4.48270i	−0.0887185	−	0.153665i
$852$	−34.2080	+	9.16601i	−1.17195	+	0.314022i
$853$	−27.1233	+	27.1233i	−0.928684	+	0.928684i	−0.997621	−	0.0689370i	$-0.978039\pi$
$853$	−27.1233	+	27.1233i	−0.928684	+	0.928684i	0.0689370	+	0.997621i	$0.478039\pi$
$854$	−37.1300	+	18.2729i	−1.27056	+	0.625287i
$855$		0			0
$856$	0.729637	−	1.26377i	0.0249385	−	0.0431947i
$857$	−10.3567	+	38.6518i	−0.353779	+	1.32032i	0.528235	+	0.849098i	$0.322854\pi$
$857$	−10.3567	+	38.6518i	−0.353779	+	1.32032i	−0.882014	+	0.471223i	$0.843813\pi$
$858$	−2.73051	+	10.1904i	−0.0932181	+	0.347895i
$859$	13.0383	−	22.5830i	0.444861	−	0.770522i	−0.553181	−	0.833061i	$-0.686586\pi$
$859$	13.0383	−	22.5830i	0.444861	−	0.770522i	0.998043	+	0.0625385i	$0.0199196\pi$
$860$		0			0
$861$	−24.4370	+	12.0263i	−0.832811	+	0.409855i
$862$	8.69631	−	8.69631i	0.296197	−	0.296197i
$863$	12.0305	−	3.22356i	0.409523	−	0.109731i	−0.0481753	−	0.998839i	$-0.515341\pi$
$863$	12.0305	−	3.22356i	0.409523	−	0.109731i	0.457698	+	0.889107i	$0.348674\pi$
$864$	4.04695	+	7.00953i	0.137680	+	0.238469i
$865$		0			0
$866$	−9.76052	−	5.63524i	−0.331676	−	0.191493i
$867$	−15.8654	−	15.8654i	−0.538816	−	0.538816i
$868$	−35.7590	+	7.08265i	−1.21374	+	0.240401i
$869$		−	31.9434i		−	1.08360i
$870$		0			0
$871$	33.6555	−	19.4310i	1.14037	−	0.658395i
$872$	10.3043	+	2.76103i	0.348947	+	0.0935002i
$873$	−4.02470	−	15.0204i	−0.136216	−	0.508363i
$874$	−34.8316			−1.17820
$875$		0			0
$876$	14.6508			0.495003
$877$	6.05417	+	22.5945i	0.204435	+	0.762960i	0.989621	+	0.143701i	$0.0459004\pi$
$877$	6.05417	+	22.5945i	0.204435	+	0.762960i	−0.785187	+	0.619259i	$0.787433\pi$
$878$	8.14033	+	2.18119i	0.274723	+	0.0736117i
$879$	3.93238	−	2.27036i	0.132636	−	0.0765775i
$880$		0			0
$881$		−	30.7450i		−	1.03582i	−0.855434	−	0.517912i	$-0.826709\pi$
$881$		−	30.7450i		−	1.03582i	0.855434	−	0.517912i	$-0.173291\pi$
$882$	13.4583	+	5.60029i	0.453164	+	0.188572i
$883$	34.1799	+	34.1799i	1.15024	+	1.15024i	0.986503	+	0.163741i	$0.0523560\pi$
$883$	34.1799	+	34.1799i	1.15024	+	1.15024i	0.163741	+	0.986503i	$0.447644\pi$
$884$	33.1261	+	19.1253i	1.11415	+	0.643255i
$885$		0			0
$886$	17.5846	+	30.4574i	0.590767	+	1.02324i
$887$	0.902034	−	0.241699i	0.0302873	−	0.00811547i	−0.243644	−	0.969865i	$-0.578343\pi$
$887$	0.902034	−	0.241699i	0.0302873	−	0.00811547i	0.273931	+	0.961749i	$0.411676\pi$
$888$	−0.462423	+	0.462423i	−0.0155179	+	0.0155179i
$889$	−8.22006	−	0.545490i	−0.275692	−	0.0182951i
$890$		0			0
$891$	0.971690	−	1.68302i	0.0325529	−	0.0563832i
$892$	−7.32527	+	27.3383i	−0.245268	+	0.915354i
$893$	−3.03365	+	11.3218i	−0.101517	+	0.378868i
$894$	−2.78318	+	4.82062i	−0.0930836	+	0.161226i
$895$		0			0
$896$	12.1513	+	8.13358i	0.405948	+	0.271724i
$897$	−10.2241	+	10.2241i	−0.341374	+	0.341374i
$898$	−54.7780	+	14.6777i	−1.82797	+	0.489802i
$899$	15.5394	+	26.9151i	0.518269	+	0.897668i
$900$		0			0
$901$	6.33971	+	3.66024i	0.211207	+	0.121940i
$902$	29.4583	+	29.4583i	0.980853	+	0.980853i
$903$	−7.89654	+	23.2004i	−0.262780	+	0.772062i
$904$			4.22648i			0.140571i
$905$		0			0
$906$	−26.6259	+	15.3725i	−0.884587	+	0.510717i
$907$	−34.0215	−	9.11603i	−1.12967	−	0.302693i	−0.354877	−	0.934913i	$-0.615477\pi$
$907$	−34.0215	−	9.11603i	−1.12967	−	0.302693i	−0.774789	+	0.632220i	$0.782144\pi$
$908$	−8.49856	−	31.7171i	−0.282035	−	1.05257i
$909$	−0.333878			−0.0110740
$910$		0			0
$911$	26.7487			0.886224			0.443112	−	0.896466i	$-0.353874\pi$
$911$	26.7487			0.886224			0.443112	+	0.896466i	$0.353874\pi$
$912$	−2.50836	−	9.36132i	−0.0830600	−	0.309984i
$913$	0.525398	+	0.140780i	0.0173881	+	0.00465914i
$914$	44.7882	−	25.8585i	1.48146	−	0.855322i
$915$		0			0
$916$			8.86621i			0.292948i
$917$	6.30160	+	31.8156i	0.208097	+	1.05064i
$918$	−9.24713	−	9.24713i	−0.305201	−	0.305201i
$919$	−1.36731	−	0.789416i	−0.0451034	−	0.0260404i	0.477279	−	0.878752i	$-0.341623\pi$
$919$	−1.36731	−	0.789416i	−0.0451034	−	0.0260404i	−0.522382	+	0.852712i	$0.674957\pi$
$920$		0			0
$921$	−9.57380	−	16.5823i	−0.315467	−	0.546406i
$922$	46.3797	−	12.4274i	1.52744	−	0.409275i
$923$	27.9397	−	27.9397i	0.919646	−	0.919646i
$924$	0.795485	−	11.9873i	0.0261695	−	0.394352i
$925$		0			0
$926$	5.38965	−	9.33515i	0.177115	−	0.306772i
$927$	−1.96634	+	7.33847i	−0.0645830	+	0.241027i
$928$	11.0407	−	41.2043i	0.362427	−	1.35260i
$929$	−8.00853	+	13.8712i	−0.262751	+	0.455099i	−0.966972	−	0.254882i	$-0.917963\pi$
$929$	−8.00853	+	13.8712i	−0.262751	+	0.455099i	0.704221	+	0.709981i	$0.251297\pi$
$930$		0			0
$931$	−16.7264	−	12.8779i	−0.548187	−	0.422058i
$932$	36.6550	−	36.6550i	1.20068	−	1.20068i
$933$	−25.1306	+	6.73372i	−0.822739	+	0.220452i
$934$	−2.62560	−	4.54768i	−0.0859123	−	0.148805i
$935$		0			0
$936$	1.58204	+	0.913390i	0.0517105	+	0.0298551i
$937$	8.68993	+	8.68993i	0.283888	+	0.283888i	0.834657	−	0.550770i	$-0.185666\pi$
$937$	8.68993	+	8.68993i	0.283888	+	0.283888i	−0.550770	+	0.834657i	$0.685666\pi$
$938$	−61.7960	+	54.1047i	−2.01771	+	1.76658i
$939$		−	3.61640i		−	0.118017i
$940$		0			0
$941$	33.9933	−	19.6261i	1.10815	−	0.639791i	0.169801	−	0.985478i	$-0.445688\pi$
$941$	33.9933	−	19.6261i	1.10815	−	0.639791i	0.938350	+	0.345687i	$0.112354\pi$
$942$	45.3784	+	12.1591i	1.47851	+	0.396165i
$943$	14.7779	+	55.1518i	0.481234	+	1.79599i
$944$	−19.6983			−0.641124
$945$		0			0
$946$	37.4867			1.21880
$947$	12.0827	+	45.0931i	0.392634	+	1.46533i	0.825773	+	0.564002i	$0.190739\pi$
$947$	12.0827	+	45.0931i	0.392634	+	1.46533i	−0.433140	+	0.901327i	$0.642594\pi$
$948$	−37.0966	−	9.94000i	−1.20484	−	0.322836i
$949$	−14.1561	+	8.17302i	−0.459526	+	0.265307i
$950$		0			0
$951$		−	9.51525i		−	0.308553i
$952$	−11.0221	−	3.75151i	−0.357229	−	0.121587i
$953$	40.7298	+	40.7298i	1.31937	+	1.31937i	0.914277	+	0.405089i	$0.132759\pi$
$953$	40.7298	+	40.7298i	1.31937	+	1.31937i	0.405089	+	0.914277i	$0.367241\pi$
$954$	2.10227	+	1.21374i	0.0680634	+	0.0392964i
$955$		0			0
$956$	−23.7545	−	41.1440i	−0.768274	−	1.33069i
$957$	−9.89332	+	2.65091i	−0.319806	+	0.0856917i
$958$	−19.3717	+	19.3717i	−0.625871	+	0.625871i
$959$	13.5259	+	27.4841i	0.436773	+	0.887508i
$960$		0			0
$961$	1.88676	−	3.26797i	0.0608633	−	0.105418i
$962$	1.31121	−	4.89352i	0.0422753	−	0.157773i
$963$	0.538972	−	2.01147i	0.0173681	−	0.0648188i
$964$	12.0495	−	20.8703i	0.388087	−	0.672187i
$965$		0			0
$966$	16.9984	−	25.3951i	0.546914	−	0.817075i
$967$	−11.4769	+	11.4769i	−0.369073	+	0.369073i	−0.867139	−	0.498066i	$-0.834044\pi$
$967$	−11.4769	+	11.4769i	−0.369073	+	0.369073i	0.498066	+	0.867139i	$0.334044\pi$
$968$	4.88927	−	1.31008i	0.157147	−	0.0421075i
$969$	9.46900	+	16.4008i	0.304188	+	0.526869i
$970$		0			0
$971$	−36.2672	−	20.9389i	−1.16387	−	0.671960i	−0.211640	−	0.977348i	$-0.567881\pi$
$971$	−36.2672	−	20.9389i	−1.16387	−	0.671960i	−0.952228	+	0.305388i	$0.901214\pi$
$972$	−1.65216	−	1.65216i	−0.0529931	−	0.0529931i
$973$	−8.50877	−	9.71833i	−0.272779	−	0.311556i
$974$		−	70.0999i		−	2.24614i
$975$		0			0
$976$	−20.9046	+	12.0693i	−0.669141	+	0.386329i
$977$	13.8908	+	3.72204i	0.444408	+	0.119079i	0.474082	−	0.880481i	$-0.342780\pi$
$977$	13.8908	+	3.72204i	0.444408	+	0.119079i	−0.0296739	+	0.999560i	$0.509447\pi$
$978$	−8.36847	−	31.2316i	−0.267594	−	0.998676i
$979$	−23.6329			−0.755309
$980$		0			0
$981$	15.2233			0.486042
$982$	11.0914	+	41.3937i	0.353941	+	1.32093i
$983$	−22.1892	−	5.94558i	−0.707726	−	0.189635i	−0.113037	−	0.993591i	$-0.536058\pi$
$983$	−22.1892	−	5.94558i	−0.707726	−	0.189635i	−0.594689	+	0.803956i	$0.702725\pi$
$984$	6.24729	−	3.60687i	0.199156	−	0.114983i
$985$		0			0
$986$			68.9228i			2.19495i
$987$	−6.77403	−	7.73699i	−0.215620	−	0.246271i
$988$	−12.9884	−	12.9884i	−0.413215	−	0.413215i
$989$	44.4940	+	25.6886i	1.41483	+	0.816850i
$990$		0			0
$991$	25.9354	+	44.9215i	0.823866	+	1.42698i	0.902783	+	0.430096i	$0.141520\pi$
$991$	25.9354	+	44.9215i	0.823866	+	1.42698i	−0.0789177	+	0.996881i	$0.525146\pi$
$992$	−46.1027	+	12.3532i	−1.46376	+	0.392214i
$993$	3.99796	−	3.99796i	0.126871	−	0.126871i
$994$	−46.4519	+	69.3978i	−1.47336	+	2.20117i
$995$		0			0
$996$	0.326982	−	0.566350i	0.0103608	−	0.0179455i
$997$	−4.93715	+	18.4257i	−0.156361	+	0.583547i	0.842624	+	0.538502i	$0.181010\pi$
$997$	−4.93715	+	18.4257i	−0.156361	+	0.583547i	−0.998985	+	0.0450448i	$0.985657\pi$
$998$	−7.35911	+	27.4646i	−0.232948	+	0.869376i
$999$	−0.466614	+	0.808199i	−0.0147630	+	0.0255703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bc.d.418.2	yes	24
5.2	odd	4	inner	525.2.bc.d.82.5	yes	24
5.3	odd	4	inner	525.2.bc.d.82.2	✓	24
5.4	even	2	inner	525.2.bc.d.418.5	yes	24
7.3	odd	6	inner	525.2.bc.d.493.5	yes	24
35.3	even	12	inner	525.2.bc.d.157.5	yes	24
35.17	even	12	inner	525.2.bc.d.157.2	yes	24
35.24	odd	6	inner	525.2.bc.d.493.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bc.d.82.2	✓	24	5.3	odd	4	inner
525.2.bc.d.82.5	yes	24	5.2	odd	4	inner
525.2.bc.d.157.2	yes	24	35.17	even	12	inner
525.2.bc.d.157.5	yes	24	35.3	even	12	inner
525.2.bc.d.418.2	yes	24	1.1	even	1	trivial
525.2.bc.d.418.5	yes	24	5.4	even	2	inner
525.2.bc.d.493.2	yes	24	35.24	odd	6	inner
525.2.bc.d.493.5	yes	24	7.3	odd	6	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.538972 - 2.01147i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-2.02348 + 1.16825i) q^{4} -2.08243i q^{6} +(-1.74285 - 1.99060i) q^{7} +(0.495509 + 0.495509i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.538972 - 2.01147i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-2.02348 + 1.16825i) q^{4} -2.08243i q^{6} +(-1.74285 - 1.99060i) q^{7} +(0.495509 + 0.495509i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.971690 - 1.68302i) q^{11} +(-2.25689 + 0.604733i) q^{12} +(1.84334 - 1.84334i) q^{13} +(-3.06469 + 4.57856i) q^{14} +(-1.60687 + 2.78318i) q^{16} +(1.62536 - 6.06591i) q^{17} +(0.538972 - 2.01147i) q^{18} +(-1.50783 + 2.61164i) q^{19} +(-1.16825 - 2.37385i) q^{21} +(-2.86163 + 2.86163i) q^{22} +(-5.35754 + 1.43555i) q^{23} +(0.350378 + 0.606872i) q^{24} +(-4.70133 - 2.71431i) q^{26} +(0.707107 + 0.707107i) q^{27} +(5.85213 + 1.99184i) q^{28} -5.27036i q^{29} +(-5.10687 + 2.94845i) q^{31} +(7.81811 + 2.09486i) q^{32} +(-0.502984 - 1.87716i) q^{33} -13.0774 q^{34} -2.33651 q^{36} +(0.241537 + 0.901429i) q^{37} +(6.06591 + 1.62536i) q^{38} +(2.25762 - 1.30344i) q^{39} -10.2942i q^{41} +(-4.14528 + 3.62935i) q^{42} +(-6.54989 - 6.54989i) q^{43} +(3.93238 + 2.27036i) q^{44} +(5.77513 + 10.0028i) q^{46} +(3.75432 - 1.00597i) q^{47} +(-2.27246 + 2.27246i) q^{48} +(-0.924978 + 6.93862i) q^{49} +(3.13994 - 5.43854i) q^{51} +(-1.57646 + 5.88343i) q^{52} +(-0.301706 + 1.12598i) q^{53} +(1.04121 - 1.80344i) q^{54} +(0.122765 - 1.84996i) q^{56} +(-2.13239 + 2.13239i) q^{57} +(-10.6012 + 2.84058i) q^{58} +(3.06469 + 5.30820i) q^{59} +(6.50476 + 3.75553i) q^{61} +(8.68319 + 8.68319i) q^{62} +(-0.514049 - 2.59533i) q^{63} -10.4275i q^{64} +(-3.50476 + 2.02348i) q^{66} +(14.3996 + 3.85836i) q^{67} +(3.79766 + 14.1730i) q^{68} -5.54653 q^{69} +15.1571 q^{71} +(0.181369 + 0.676878i) q^{72} +(-6.05671 - 1.62289i) q^{73} +(1.68302 - 0.971690i) q^{74} -7.04611i q^{76} +(-1.65671 + 4.86749i) q^{77} +(-3.83862 - 3.83862i) q^{78} +(14.2349 + 8.21851i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-20.7066 + 5.54831i) q^{82} +(-0.197912 + 0.197912i) q^{83} +(5.13720 + 3.43862i) q^{84} +(-9.64471 + 16.7051i) q^{86} +(1.36407 - 5.09078i) q^{87} +(0.352469 - 1.31543i) q^{88} +(6.08035 - 10.5315i) q^{89} +(-6.88200 - 0.456695i) q^{91} +(9.16376 - 9.16376i) q^{92} +(-5.69598 + 1.52623i) q^{93} +(-4.04695 - 7.00953i) q^{94} +(7.00953 + 4.04695i) q^{96} +(-10.9957 - 10.9957i) q^{97} +(14.4554 - 1.87915i) q^{98} -1.94338i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 24 q^{11} + 48 q^{16} - 24 q^{21} - 144 q^{26} - 36 q^{31} - 48 q^{36} + 48 q^{46} + 24 q^{51} + 168 q^{56} + 144 q^{61} - 72 q^{66} + 96 q^{71} + 12 q^{81} - 168 q^{86} + 12 q^{91} + 144 q^{96}+O(q^{100}) \) 24 * q + 24 * q^11 + 48 * q^16 - 24 * q^21 - 144 * q^26 - 36 * q^31 - 48 * q^36 + 48 * q^46 + 24 * q^51 + 168 * q^56 + 144 * q^61 - 72 * q^66 + 96 * q^71 + 12 * q^81 - 168 * q^86 + 12 * q^91 + 144 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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