LMFDB - Embedded newform 525.2.bc.d.82.5

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			82.5
Character	$\chi$	$=$	525.82
Dual form			525.2.bc.d.493.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.01147 - 0.538972i) q^{2} +(0.258819 - 0.965926i) q^{3} +(2.02348 - 1.16825i) q^{4} -2.08243i q^{6} +(1.99060 - 1.74285i) q^{7} +(0.495509 - 0.495509i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(2.01147 - 0.538972i) q^{2} +(0.258819 - 0.965926i) q^{3} +(2.02348 - 1.16825i) q^{4} -2.08243i q^{6} +(1.99060 - 1.74285i) q^{7} +(0.495509 - 0.495509i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.971690 - 1.68302i) q^{11} +(-0.604733 - 2.25689i) q^{12} +(-1.84334 - 1.84334i) q^{13} +(3.06469 - 4.57856i) q^{14} +(-1.60687 + 2.78318i) q^{16} +(6.06591 + 1.62536i) q^{17} +(-2.01147 - 0.538972i) q^{18} +(1.50783 - 2.61164i) q^{19} +(-1.16825 - 2.37385i) q^{21} +(-2.86163 - 2.86163i) q^{22} +(1.43555 + 5.35754i) q^{23} +(-0.350378 - 0.606872i) q^{24} +(-4.70133 - 2.71431i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.99184 - 5.85213i) q^{28} +5.27036i q^{29} +(-5.10687 + 2.94845i) q^{31} +(-2.09486 + 7.81811i) q^{32} +(-1.87716 + 0.502984i) q^{33} +13.0774 q^{34} -2.33651 q^{36} +(-0.901429 + 0.241537i) q^{37} +(1.62536 - 6.06591i) q^{38} +(-2.25762 + 1.30344i) q^{39} -10.2942i q^{41} +(-3.62935 - 4.14528i) q^{42} +(-6.54989 + 6.54989i) q^{43} +(-3.93238 - 2.27036i) q^{44} +(5.77513 + 10.0028i) q^{46} +(1.00597 + 3.75432i) q^{47} +(2.27246 + 2.27246i) q^{48} +(0.924978 - 6.93862i) q^{49} +(3.13994 - 5.43854i) q^{51} +(-5.88343 - 1.57646i) q^{52} +(1.12598 + 0.301706i) q^{53} +(-1.04121 + 1.80344i) q^{54} +(0.122765 - 1.84996i) q^{56} +(-2.13239 - 2.13239i) q^{57} +(2.84058 + 10.6012i) q^{58} +(-3.06469 - 5.30820i) q^{59} +(6.50476 + 3.75553i) q^{61} +(-8.68319 + 8.68319i) q^{62} +(-2.59533 + 0.514049i) q^{63} +10.4275i q^{64} +(-3.50476 + 2.02348i) q^{66} +(-3.85836 + 14.3996i) q^{67} +(14.1730 - 3.79766i) q^{68} +5.54653 q^{69} +15.1571 q^{71} +(-0.676878 + 0.181369i) q^{72} +(-1.62289 + 6.05671i) q^{73} +(-1.68302 + 0.971690i) q^{74} -7.04611i q^{76} +(-4.86749 - 1.65671i) q^{77} +(-3.83862 + 3.83862i) q^{78} +(-14.2349 - 8.21851i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-5.54831 - 20.7066i) q^{82} +(0.197912 + 0.197912i) q^{83} +(-5.13720 - 3.43862i) q^{84} +(-9.64471 + 16.7051i) q^{86} +(5.09078 + 1.36407i) q^{87} +(-1.31543 - 0.352469i) q^{88} +(-6.08035 + 10.5315i) q^{89} +(-6.88200 - 0.456695i) q^{91} +(9.16376 + 9.16376i) q^{92} +(1.52623 + 5.69598i) q^{93} +(4.04695 + 7.00953i) q^{94} +(7.00953 + 4.04695i) q^{96} +(10.9957 - 10.9957i) q^{97} +(-1.87915 - 14.4554i) 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.01147	−	0.538972i	1.42233	−	0.381111i	0.536017	−	0.844207i	$-0.319928\pi$
$2$	2.01147	−	0.538972i	1.42233	−	0.381111i	0.886308	+	0.463096i	$0.153262\pi$
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$	2.02348	−	1.16825i	1.01174	−	0.584127i
$5$		0			0
$5$		0			0
$6$		−	2.08243i		−	0.850148i
$7$	1.99060	−	1.74285i	0.752376	−	0.658734i
$7$	1.99060	−	1.74285i	0.752376	−	0.658734i
$8$	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	$0.927979\pi$
$12$	−0.604733	−	2.25689i	−0.174571	−	0.651509i
$13$	−1.84334	−	1.84334i	−0.511250	−	0.511250i	0.403660	−	0.914909i	$-0.367738\pi$
$13$	−1.84334	−	1.84334i	−0.511250	−	0.511250i	−0.914909	+	0.403660i	$0.867738\pi$
$14$	3.06469	−	4.57856i	0.819073	−	1.22367i
$15$		0			0
$16$	−1.60687	+	2.78318i	−0.401718	+	0.695796i
$17$	6.06591	+	1.62536i	1.47120	+	0.394207i	0.903342	−	0.428921i	$-0.141106\pi$
$17$	6.06591	+	1.62536i	1.47120	+	0.394207i	0.567857	+	0.823127i	$0.307773\pi$
$18$	−2.01147	−	0.538972i	−0.474108	−	0.127037i
$19$	1.50783	−	2.61164i	0.345920	−	0.599150i	−0.639601	−	0.768707i	$-0.720900\pi$
$19$	1.50783	−	2.61164i	0.345920	−	0.599150i	0.985520	+	0.169557i	$0.0542337\pi$
$20$		0			0
$21$	−1.16825	−	2.37385i	−0.254934	−	0.518017i
$22$	−2.86163	−	2.86163i	−0.610101	−	0.610101i
$23$	1.43555	+	5.35754i	0.299332	+	1.11712i	0.937715	+	0.347405i	$0.112937\pi$
$23$	1.43555	+	5.35754i	0.299332	+	1.11712i	−0.638383	+	0.769719i	$0.720396\pi$
$24$	−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
$28$	1.99184	−	5.85213i	0.376423	−	1.10595i
$29$			5.27036i			0.978682i	0.872093	+	0.489341i	$0.162763\pi$
$29$			5.27036i			0.978682i	−0.872093	+	0.489341i	$0.837237\pi$
$30$		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	$0.510976\pi$
$32$	−2.09486	+	7.81811i	−0.370322	+	1.38206i
$33$	−1.87716	+	0.502984i	−0.326772	+	0.0875583i
$34$	13.0774			2.24276
$35$		0			0
$36$	−2.33651			−0.389418
$37$	−0.901429	+	0.241537i	−0.148194	+	0.0397085i	−0.332153	−	0.943225i	$-0.607775\pi$
$37$	−0.901429	+	0.241537i	−0.148194	+	0.0397085i	0.183959	+	0.982934i	$0.441109\pi$
$38$	1.62536	−	6.06591i	0.263667	−	0.984020i
$39$	−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	$-0.297216\pi$
$42$	−3.62935	−	4.14528i	−0.560021	−	0.639631i
$43$	−6.54989	+	6.54989i	−0.998849	+	0.998849i	−0.999999	−	0.00115057i	$-0.999634\pi$
$43$	−6.54989	+	6.54989i	−0.998849	+	0.998849i	0.00115057	+	0.999999i	$0.499634\pi$
$44$	−3.93238	−	2.27036i	−0.592829	−	0.342270i
$45$		0			0
$46$	5.77513	+	10.0028i	0.851496	+	1.47483i
$47$	1.00597	+	3.75432i	0.146736	+	0.547624i	0.999672	+	0.0256097i	$0.00815272\pi$
$47$	1.00597	+	3.75432i	0.146736	+	0.547624i	−0.852937	+	0.522015i	$0.825181\pi$
$48$	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
$52$	−5.88343	−	1.57646i	−0.815886	−	0.218616i
$53$	1.12598	+	0.301706i	0.154665	+	0.0414424i	0.335321	−	0.942104i	$-0.391155\pi$
$53$	1.12598	+	0.301706i	0.154665	+	0.0414424i	−0.180656	+	0.983546i	$0.557822\pi$
$54$	−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
$58$	2.84058	+	10.6012i	0.372986	+	1.39200i
$59$	−3.06469	−	5.30820i	−0.398989	−	0.691069i	0.594613	−	0.804012i	$-0.297305\pi$
$59$	−3.06469	−	5.30820i	−0.398989	−	0.691069i	−0.993601	+	0.112944i	$0.963972\pi$
$60$		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
$63$	−2.59533	+	0.514049i	−0.326981	+	0.0647640i
$64$			10.4275i			1.30344i
$65$		0			0
$66$	−3.50476	+	2.02348i	−0.431407	+	0.249073i
$67$	−3.85836	+	14.3996i	−0.471373	+	1.75919i	0.163471	+	0.986548i	$0.447731\pi$
$67$	−3.85836	+	14.3996i	−0.471373	+	1.75919i	−0.634844	+	0.772640i	$0.718936\pi$
$68$	14.1730	−	3.79766i	1.71873	−	0.460533i
$69$	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	$0.143997\pi$
$72$	−0.676878	+	0.181369i	−0.0797708	+	0.0213745i
$73$	−1.62289	+	6.05671i	−0.189945	+	0.708884i	0.803573	+	0.595206i	$0.202930\pi$
$73$	−1.62289	+	6.05671i	−0.189945	+	0.708884i	−0.993518	+	0.113677i	$0.963737\pi$
$74$	−1.68302	+	0.971690i	−0.195647	+	0.112957i
$75$		0			0
$76$		−	7.04611i		−	0.808244i
$77$	−4.86749	−	1.65671i	−0.554702	−	0.188799i
$78$	−3.83862	+	3.83862i	−0.434638	+	0.434638i
$79$	−14.2349	−	8.21851i	−1.60155	−	0.924654i	−0.991178	−	0.132538i	$-0.957687\pi$
$79$	−14.2349	−	8.21851i	−1.60155	−	0.924654i	−0.610370	−	0.792116i	$-0.708979\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−5.54831	−	20.7066i	−0.612708	−	2.28666i
$83$	0.197912	+	0.197912i	0.0217237	+	0.0217237i	0.717885	−	0.696162i	$-0.245110\pi$
$83$	0.197912	+	0.197912i	0.0217237	+	0.0217237i	−0.696162	+	0.717885i	$0.745110\pi$
$84$	−5.13720	−	3.43862i	−0.560514	−	0.375184i
$85$		0			0
$86$	−9.64471	+	16.7051i	−1.04002	+	1.80136i
$87$	5.09078	+	1.36407i	0.545789	+	0.146244i
$88$	−1.31543	−	0.352469i	−0.140225	−	0.0375733i
$89$	−6.08035	+	10.5315i	−0.644515	+	1.11633i	0.339898	+	0.940462i	$0.389608\pi$
$89$	−6.08035	+	10.5315i	−0.644515	+	1.11633i	−0.984413	+	0.175871i	$0.943726\pi$
$90$		0			0
$91$	−6.88200	−	0.456695i	−0.721429	−	0.0478746i
$92$	9.16376	+	9.16376i	0.955388	+	0.955388i
$93$	1.52623	+	5.69598i	0.158263	+	0.590645i
$94$	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	0.124184	−	0.992259i	$-0.460369\pi$
$97$	10.9957	−	10.9957i	1.11644	−	1.11644i	0.992259	−	0.124184i	$-0.0396313\pi$
$98$	−1.87915	−	14.4554i	−0.189823	−	1.46021i
$99$			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	$0.338621\pi$
$102$	3.38469	−	12.6318i	0.335134	−	1.25074i
$103$	7.33847	−	1.96634i	0.723081	−	0.193749i	0.121535	−	0.992587i	$-0.461218\pi$
$103$	7.33847	−	1.96634i	0.723081	−	0.193749i	0.601546	+	0.798838i	$0.294552\pi$
$104$	−1.82678			−0.179131
$105$		0			0
$106$	2.42749			0.235779
$107$	2.01147	−	0.538972i	0.194456	−	0.0521044i	−0.160276	−	0.987072i	$-0.551239\pi$
$107$	2.01147	−	0.538972i	0.194456	−	0.0521044i	0.354733	+	0.934968i	$0.384572\pi$
$108$	−0.604733	+	2.25689i	−0.0581905	+	0.217170i
$109$	−13.1837	+	7.61164i	−1.26277	+	0.729062i	−0.973610	−	0.228217i	$-0.926710\pi$
$109$	−13.1837	+	7.61164i	−1.26277	+	0.729062i	−0.289163	+	0.957280i	$0.593377\pi$
$110$		0			0
$111$			0.933228i			0.0885781i
$112$	1.65202	+	8.34074i	0.156101	+	0.788126i
$113$	4.26478	−	4.26478i	0.401197	−	0.401197i	−0.477458	−	0.878655i	$-0.658442\pi$
$113$	4.26478	−	4.26478i	0.401197	−	0.401197i	0.878655	+	0.477458i	$0.158442\pi$
$114$	−5.43854	−	3.13994i	−0.509366	−	0.294083i
$115$		0			0
$116$	6.15713	+	10.6645i	0.571675	+	0.990170i
$117$	0.674708	+	2.51805i	0.0623768	+	0.232793i
$118$	−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
$122$	15.1083	+	4.04825i	1.36784	+	0.366511i
$123$	−9.94347	−	2.66434i	−0.896573	−	0.240236i
$124$	−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	0.798013	−	0.602640i	$-0.205885\pi$
$127$	2.20174	+	2.20174i	0.195372	+	0.195372i	−0.602640	+	0.798013i	$0.705885\pi$
$128$	1.43041	+	5.33837i	0.126432	+	0.471850i
$129$	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
$133$	−1.55019	−	7.82663i	−0.134419	−	0.678655i
$134$			31.0439i			2.68178i
$135$		0			0
$136$	3.81109	−	2.20033i	0.326798	−	0.188677i
$137$	2.99657	−	11.1833i	0.256014	−	0.955457i	−0.711510	−	0.702676i	$-0.751988\pi$
$137$	2.99657	−	11.1833i	0.256014	−	0.955457i	0.967524	−	0.252781i	$-0.0813451\pi$
$138$	11.1567	−	2.98943i	0.949720	−	0.254477i
$139$	−4.88211			−0.414095			−0.207048	−	0.978331i	$-0.566386\pi$
$139$	−4.88211			−0.414095			−0.207048	+	0.978331i	$0.566386\pi$
$140$		0			0
$141$	3.88676			0.327324
$142$	30.4881	−	8.16927i	2.55851	−	0.685550i
$143$	−1.31121	+	4.89352i	−0.109649	+	0.409217i
$144$	2.78318	−	1.60687i	0.231932	−	0.133906i
$145$		0			0
$146$			13.0576i			1.08065i
$147$	−6.46279	−	2.68931i	−0.533042	−	0.221810i
$148$	−1.54184	+	1.54184i	−0.126739	+	0.126739i
$149$	2.31490	+	1.33651i	0.189644	+	0.109491i	0.591816	−	0.806073i	$-0.298411\pi$
$149$	2.31490	+	1.33651i	0.189644	+	0.109491i	−0.402172	+	0.915564i	$0.631745\pi$
$150$		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	$-0.371793\pi$
$152$	−0.546946	−	2.04123i	−0.0443632	−	0.165566i
$153$	−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
$157$	−21.7911	−	5.83890i	−1.73912	−	0.465995i	−0.756867	−	0.653569i	$-0.773271\pi$
$157$	−21.7911	−	5.83890i	−1.73912	−	0.465995i	−0.982250	+	0.187574i	$0.939937\pi$
$158$	−33.0626	−	8.85909i	−2.63032	−	0.704792i
$159$	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
$163$	−4.01861	−	14.9977i	−0.314762	−	1.17471i	−0.924211	−	0.381883i	$-0.875276\pi$
$163$	−4.01861	−	14.9977i	−0.314762	−	1.17471i	0.609449	−	0.792825i	$-0.291391\pi$
$164$	−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	$-0.671876\pi$
$167$	4.44055	−	4.44055i	0.343620	−	0.343620i	0.857727	+	0.514106i	$0.171876\pi$
$168$	−1.75515	−	0.597385i	−0.135412	−	0.0460893i
$169$		−	6.20422i		−	0.477248i
$170$		0			0
$171$	−2.61164	+	1.50783i	−0.199717	+	0.115307i
$172$	−5.60161	+	20.9055i	−0.427119	+	1.59403i
$173$	19.7314	−	5.28702i	1.50015	−	0.401965i	0.587002	−	0.809585i	$-0.300308\pi$
$173$	19.7314	−	5.28702i	1.50015	−	0.401965i	0.913151	+	0.407621i	$0.133641\pi$
$174$	10.9752			0.832024
$175$		0			0
$176$	6.24553			0.470774
$177$	−5.92053	+	1.58640i	−0.445014	+	0.119241i
$178$	−6.55428	+	24.4609i	−0.491264	+	1.83342i
$179$	−7.29842	+	4.21374i	−0.545509	+	0.314950i	−0.747309	−	0.664477i	$-0.768654\pi$
$179$	−7.29842	+	4.21374i	−0.545509	+	0.314950i	0.201799	+	0.979427i	$0.435321\pi$
$180$		0			0
$181$		−	12.0461i		−	0.895382i	−0.894188	−	0.447691i	$-0.852247\pi$
$181$		−	12.0461i		−	0.895382i	0.894188	−	0.447691i	$-0.147753\pi$
$182$	−14.0891	+	2.79058i	−1.04435	+	0.206851i
$183$	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
$187$	−3.15868	−	11.7884i	−0.230986	−	0.862051i
$188$	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	$0.242937\pi$
$192$	10.0722	+	2.69883i	0.726897	+	0.194771i
$193$	3.79839	+	1.01778i	0.273414	+	0.0732611i	0.392921	−	0.919572i	$-0.371465\pi$
$193$	3.79839	+	1.01778i	0.273414	+	0.0732611i	−0.119507	+	0.992833i	$0.538131\pi$
$194$	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	0.938485	−	0.345320i	$-0.112230\pi$
$197$	8.32546	+	8.32546i	0.593164	+	0.593164i	−0.345320	+	0.938485i	$0.612230\pi$
$198$	1.04743	+	3.90906i	0.0744375	+	0.277804i
$199$	−6.77118	−	11.7280i	−0.479996	−	0.831378i	0.519740	−	0.854324i	$-0.326029\pi$
$199$	−6.77118	−	11.7280i	−0.479996	−	0.831378i	−0.999737	+	0.0229461i	$0.992695\pi$
$200$		0			0
$201$	12.9103	+	7.45377i	0.910623	+	0.525748i
$202$	−0.491634	+	0.491634i	−0.0345913	+	0.0345913i
$203$	9.18543	+	10.4912i	0.644691	+	0.736337i
$204$		−	14.6730i		−	1.02732i
$205$		0			0
$206$	13.7013	−	7.91046i	0.954617	−	0.551148i
$207$	1.43555	−	5.35754i	0.0997775	−	0.372375i
$208$	8.09235	−	2.16834i	0.561104	−	0.150347i
$209$	−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	$0.546438\pi$
$212$	2.63086	−	0.704938i	0.180688	−	0.0484153i
$213$	3.92295	−	14.6407i	0.268796	−	1.00316i
$214$	3.75553	−	2.16825i	0.256723	−	0.148219i
$215$		0			0
$216$			0.700756i			0.0476804i
$217$	−5.02704	+	14.7697i	−0.341258	+	1.00263i
$218$	−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
$222$	0.502984	+	1.87716i	0.0337581	+	0.125987i
$223$	−8.56535	−	8.56535i	−0.573578	−	0.573578i	0.359548	−	0.933127i	$-0.382931\pi$
$223$	−8.56535	−	8.56535i	−0.573578	−	0.573578i	−0.933127	+	0.359548i	$0.882931\pi$
$224$	9.45574	+	19.2137i	0.631788	+	1.28377i
$225$		0			0
$226$	6.27989	−	10.8771i	0.417732	−	0.723533i
$227$	−13.5746	−	3.63729i	−0.900975	−	0.241415i	−0.221540	−	0.975151i	$-0.571108\pi$
$227$	−13.5746	−	3.63729i	−0.900975	−	0.241415i	−0.679435	+	0.733736i	$0.737775\pi$
$228$	−6.80602	−	1.82367i	−0.450740	−	0.120775i
$229$	−1.89732	+	3.28626i	−0.125378	+	0.217162i	−0.921881	−	0.387474i	$-0.873348\pi$
$229$	−1.89732	+	3.28626i	−0.125378	+	0.217162i	0.796502	+	0.604635i	$0.206681\pi$
$230$		0			0
$231$	−2.86006	+	4.27284i	−0.188178	+	0.281132i
$232$	2.61151	+	2.61151i	0.171454	+	0.171454i
$233$	5.74219	+	21.4301i	0.376183	+	1.40394i	0.851608	+	0.524179i	$0.175628\pi$
$233$	5.74219	+	21.4301i	0.376183	+	1.40394i	−0.475425	+	0.879756i	$0.657706\pi$
$234$	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
$238$	26.0319	−	22.7919i	1.68740	−	1.47738i
$239$		−	20.3333i		−	1.31525i	−0.753345	−	0.657626i	$-0.771561\pi$
$239$		−	20.3333i		−	1.31525i	0.753345	−	0.657626i	$-0.228439\pi$
$240$		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	$0.441122\pi$
$242$	3.89314	−	14.5294i	0.250261	−	0.933985i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	17.5496			1.12350
$245$		0			0
$246$	−21.4370			−1.36677
$247$	−7.59356	+	2.03469i	−0.483167	+	0.129464i
$248$	−1.06952	+	3.99149i	−0.0679143	+	0.253460i
$249$	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	$0.926393\pi$
$252$	−4.65105	+	4.07217i	−0.292989	+	0.256523i
$253$	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
$257$	−1.39255	−	5.19706i	−0.0868648	−	0.324184i	0.908796	−	0.417241i	$-0.137003\pi$
$257$	−1.39255	−	5.19706i	−0.0868648	−	0.324184i	−0.995661	+	0.0930569i	$0.970336\pi$
$258$	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
$262$	−24.6581	−	6.60713i	−1.52339	−	0.408190i
$263$	−0.866329	−	0.232132i	−0.0534201	−	0.0143139i	0.232010	−	0.972713i	$-0.425470\pi$
$263$	−0.866329	−	0.232132i	−0.0534201	−	0.0143139i	−0.285430	+	0.958400i	$0.592136\pi$
$264$	−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
$268$	9.01508	+	33.6447i	0.550684	+	2.05518i
$269$	12.2786	+	21.2672i	0.748639	+	1.29668i	0.948475	+	0.316852i	$0.102626\pi$
$269$	12.2786	+	21.2672i	0.748639	+	1.29668i	−0.199836	+	0.979829i	$0.564041\pi$
$270$		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
$273$	−2.22233	+	6.52930i	−0.134501	+	0.395171i
$274$		−	24.1100i		−	1.45654i
$275$		0			0
$276$	11.2233	−	6.47976i	0.675562	−	0.390036i
$277$	−3.88887	+	14.5135i	−0.233660	+	0.872030i	0.745089	+	0.666965i	$0.232407\pi$
$277$	−3.88887	+	14.5135i	−0.233660	+	0.872030i	−0.978748	+	0.205064i	$0.934260\pi$
$278$	−9.82023	+	2.63132i	−0.588978	+	0.157816i
$279$	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	$0.456756\pi$
$282$	7.81811	−	2.09486i	0.465562	−	0.124747i
$283$	−3.83339	+	14.3064i	−0.227872	+	0.850428i	0.753362	+	0.657606i	$0.228431\pi$
$283$	−3.83339	+	14.3064i	−0.227872	+	0.850428i	−0.981234	+	0.192822i	$0.938236\pi$
$284$	30.6701	−	17.7074i	1.81993	−	1.05074i
$285$		0			0
$286$			10.5499i			0.623828i
$287$	−17.9413	−	20.4917i	−1.05904	−	1.20959i
$288$	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
$292$	3.79190	+	14.1515i	0.221904	+	0.828157i
$293$	−3.21078	−	3.21078i	−0.187576	−	0.187576i	0.607072	−	0.794647i	$-0.292344\pi$
$293$	−3.21078	−	3.21078i	−0.187576	−	0.187576i	−0.794647	+	0.607072i	$0.792344\pi$
$294$	−14.4492	−	1.92620i	−0.842693	−	0.112338i
$295$		0			0
$296$	−0.326982	+	0.566350i	−0.0190055	+	0.0329184i
$297$	1.87716	+	0.502984i	0.108924	+	0.0291861i
$298$	5.37670	+	1.44068i	0.311464	+	0.0834565i
$299$	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
$303$	0.0864139	+	0.322501i	0.00496435	+	0.0185272i
$304$	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	$-0.565996\pi$
$307$	13.5394	−	13.5394i	0.772734	−	0.772734i	0.978584	+	0.205849i	$0.0659957\pi$
$308$	−11.7847	+	2.33415i	−0.671496	+	0.133001i
$309$		−	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	$0.597397\pi$
$312$	−0.472805	+	1.76453i	−0.0267673	+	0.0998971i
$313$	−3.49317	+	0.935993i	−0.197446	+	0.0529054i	−0.356187	−	0.934415i	$-0.615923\pi$
$313$	−3.49317	+	0.935993i	−0.197446	+	0.0529054i	0.158741	+	0.987320i	$0.449257\pi$
$314$	−46.9791			−2.65119
$315$		0			0
$316$	−38.4052			−2.16046
$317$	9.19103	−	2.46273i	0.516220	−	0.138321i	0.00870220	−	0.999962i	$-0.497230\pi$
$317$	9.19103	−	2.46273i	0.516220	−	0.138321i	0.507517	+	0.861642i	$0.330563\pi$
$318$	0.628280	−	2.34477i	0.0352322	−	0.131488i
$319$	8.87011	−	5.12116i	0.496631	−	0.286730i
$320$		0			0
$321$		−	2.08243i		−	0.116230i
$322$	28.9293	+	9.84645i	1.61217	+	0.548721i
$323$	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
$327$	3.94007	+	14.7046i	0.217886	+	0.813163i
$328$	−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	$0.117005\pi$
$332$	0.631681	+	0.169259i	0.0346680	+	0.00928927i
$333$	0.901429	+	0.241537i	0.0493980	+	0.0132362i
$334$	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	0.873545	−	0.486744i	$-0.161816\pi$
$337$	7.10071	+	7.10071i	0.386801	+	0.386801i	−0.486744	+	0.873545i	$0.661816\pi$
$338$	−3.34390	−	12.4796i	−0.181884	−	0.678801i
$339$	−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
$343$	−10.2517	−	15.4241i	−0.553539	−	0.832824i
$344$			6.49106i			0.349974i
$345$		0			0
$346$	36.8397	−	21.2694i	1.98051	−	1.14345i
$347$	1.74239	−	6.50268i	0.0935363	−	0.349082i	−0.903257	−	0.429100i	$-0.858831\pi$
$347$	1.74239	−	6.50268i	0.0935363	−	0.349082i	0.996793	+	0.0800175i	$0.0254976\pi$
$348$	11.8947	−	3.18716i	0.637620	−	0.170850i
$349$	−2.76335			−0.147919			−0.0739593	−	0.997261i	$-0.523563\pi$
$349$	−2.76335			−0.147919			−0.0739593	+	0.997261i	$0.523563\pi$
$350$		0			0
$351$	2.60687			0.139145
$352$	15.1936	−	4.07110i	0.809820	−	0.216991i
$353$	6.59824	−	24.6250i	0.351189	−	1.31065i	−0.534025	−	0.845469i	$-0.679321\pi$
$353$	6.59824	−	24.6250i	0.351189	−	1.31065i	0.885213	−	0.465185i	$-0.154012\pi$
$354$	−11.0539	+	6.38200i	−0.587511	+	0.339199i
$355$		0			0
$356$			28.4136i			1.50592i
$357$	−3.22817	−	16.2984i	−0.170853	−	0.862603i
$358$	−12.4095	+	12.4095i	−0.655861	+	0.655861i
$359$	5.82804	+	3.36482i	0.307592	+	0.177588i	0.645848	−	0.763466i	$-0.276504\pi$
$359$	5.82804	+	3.36482i	0.307592	+	0.177588i	−0.338256	+	0.941054i	$0.609837\pi$
$360$		0			0
$361$	4.95291	+	8.57869i	0.260679	+	0.451510i
$362$	−6.49253	−	24.2304i	−0.341240	−	1.27352i
$363$	−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
$367$	17.7725	+	4.76213i	0.927717	+	0.248581i	0.690881	−	0.722969i	$-0.257223\pi$
$367$	17.7725	+	4.76213i	0.927717	+	0.248581i	0.236836	+	0.971550i	$0.423890\pi$
$368$	−17.2178	−	4.61348i	−0.897537	−	0.240494i
$369$	−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
$373$	−0.453422	−	1.69219i	−0.0234773	−	0.0876185i	0.953193	−	0.302362i	$-0.0977751\pi$
$373$	−0.453422	−	1.69219i	−0.0234773	−	0.0876185i	−0.976670	+	0.214743i	$0.931108\pi$
$374$	−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
$378$	1.07047	+	5.40460i	0.0550590	+	0.277982i
$379$		−	37.4275i		−	1.92252i	−0.275642	−	0.961260i	$-0.588890\pi$
$379$		−	37.4275i		−	1.92252i	0.275642	−	0.961260i	$-0.411110\pi$
$380$		0			0
$381$	2.69656	−	1.55686i	0.138149	−	0.0797605i
$382$	−3.53554	+	13.1948i	−0.180894	+	0.675105i
$383$	−17.6902	+	4.74008i	−0.903927	+	0.242207i	−0.680702	−	0.732560i	$-0.738325\pi$
$383$	−17.6902	+	4.74008i	−0.903927	+	0.242207i	−0.223225	+	0.974767i	$0.571659\pi$
$384$	5.52669			0.282033
$385$		0			0
$386$	8.18891			0.416805
$387$	8.94732	−	2.39743i	0.454818	−	0.121868i
$388$	9.40375	−	35.0953i	0.477403	−	1.78169i
$389$	5.13062	−	2.96216i	0.260133	−	0.150188i	−0.364262	−	0.931296i	$-0.618679\pi$
$389$	5.13062	−	2.96216i	0.260133	−	0.150188i	0.624395	+	0.781109i	$0.285346\pi$
$390$		0			0
$391$			34.8316i			1.76151i
$392$	−2.97981	−	3.89648i	−0.150503	−	0.196802i
$393$	−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
$397$	−0.931062	−	3.47477i	−0.0467286	−	0.174394i	0.938618	−	0.344959i	$-0.112107\pi$
$397$	−0.931062	−	3.47477i	−0.0467286	−	0.174394i	−0.985346	+	0.170565i	$0.945441\pi$
$398$	−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	$-0.233282\pi$
$402$	29.9861	+	8.03475i	1.49557	+	0.400737i
$403$	14.8487	+	3.97869i	0.739665	+	0.198193i
$404$	−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
$408$	−1.13898	−	4.25072i	−0.0563877	−	0.210442i
$409$	12.4439	+	21.5534i	0.615310	+	1.06575i	0.990330	+	0.138731i	$0.0443024\pi$
$409$	12.4439	+	21.5534i	0.615310	+	1.06575i	−0.375020	+	0.927017i	$0.622364\pi$
$410$		0			0
$411$	−10.0267	−	5.78892i	−0.494581	−	0.285546i
$412$	12.5520	−	12.5520i	0.618395	−	0.618395i
$413$	−15.3519	−	5.22522i	−0.755420	−	0.257116i
$414$		−	11.5503i		−	0.567664i
$415$		0			0
$416$	18.2729	−	10.5499i	0.895905	−	0.517251i
$417$	−1.26358	+	4.71576i	−0.0618780	+	0.230932i
$418$	−11.7884	+	3.15868i	−0.576588	+	0.154496i
$419$	−36.9791			−1.80655			−0.903273	−	0.429065i	$-0.858843\pi$
$419$	−36.9791			−1.80655			−0.903273	+	0.429065i	$0.858843\pi$
$420$		0			0
$421$	10.9968			0.535951			0.267975	−	0.963426i	$-0.413645\pi$
$421$	10.9968			0.535951			0.267975	+	0.963426i	$0.413645\pi$
$422$	−8.49499	+	2.27623i	−0.413530	+	0.110805i
$423$	1.00597	−	3.75432i	0.0489118	−	0.182541i
$424$	0.707431	−	0.408436i	0.0343559	−	0.0198354i
$425$		0			0
$426$		−	31.5636i		−	1.52926i
$427$	19.4937	−	3.86105i	0.943366	−	0.186849i
$428$	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	$0.787904\pi$
$432$	−0.831778	−	3.10424i	−0.0400189	−	0.149353i
$433$	−3.82699	−	3.82699i	−0.183913	−	0.183913i	0.609145	−	0.793059i	$-0.291513\pi$
$433$	−3.82699	−	3.82699i	−0.183913	−	0.183913i	−0.793059	+	0.609145i	$0.791513\pi$
$434$	−2.15130	+	32.4182i	−0.103266	+	1.55612i
$435$		0			0
$436$	−17.7847	+	30.8039i	−0.851730	+	1.47524i
$437$	16.1565	+	4.32912i	0.772870	+	0.207090i
$438$	12.6127	+	3.37955i	0.602656	+	0.161481i
$439$	2.02348	−	3.50476i	0.0965752	−	0.167273i	−0.813690	−	0.581299i	$-0.802544\pi$
$439$	2.02348	−	3.50476i	0.0965752	−	0.167273i	0.910265	+	0.414026i	$0.135878\pi$
$440$		0			0
$441$	−4.27036	+	5.54653i	−0.203351	+	0.264120i
$442$	−24.1061	−	24.1061i	−1.14661	−	1.14661i
$443$	4.37108	+	16.3131i	0.207676	+	0.775059i	0.988617	+	0.150454i	$0.0480734\pi$
$443$	4.37108	+	16.3131i	0.207676	+	0.775059i	−0.780941	+	0.624605i	$0.785260\pi$
$444$	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
$448$	18.1735	+	20.7570i	0.858617	+	0.980674i
$449$			27.2328i			1.28520i	0.766204	+	0.642598i	$0.222143\pi$
$449$			27.2328i			1.28520i	−0.766204	+	0.642598i	$0.777857\pi$
$450$		0			0
$451$	−17.3254	+	10.0028i	−0.815820	+	0.471014i
$452$	3.64733	−	13.6120i	0.171556	−	0.640256i
$453$	−14.2609	+	3.82120i	−0.670037	+	0.179536i
$454$	−29.2652			−1.37349
$455$		0			0
$456$	−2.11324			−0.0989614
$457$	−23.9887	+	6.42774i	−1.12214	+	0.300677i	−0.771750	−	0.635926i	$-0.780618\pi$
$457$	−23.9887	+	6.42774i	−1.12214	+	0.300677i	−0.350392	+	0.936603i	$0.613952\pi$
$458$	−2.04521	+	7.63281i	−0.0955662	+	0.356658i
$459$	−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	$0.819576\pi$
$462$	−3.44998	+	10.1362i	−0.160507	+	0.471578i
$463$	3.66021	−	3.66021i	0.170104	−	0.170104i	−0.616921	−	0.787025i	$-0.711620\pi$
$463$	3.66021	−	3.66021i	0.170104	−	0.170104i	0.787025	+	0.616921i	$0.211620\pi$
$464$	−14.6684	−	8.46880i	−0.680963	−	0.393154i
$465$		0			0
$466$	23.1005	+	40.0113i	1.07011	+	1.85349i
$467$	0.652657	+	2.43575i	0.0302014	+	0.112713i	0.979381	−	0.202022i	$-0.0647511\pi$
$467$	0.652657	+	2.43575i	0.0302014	+	0.112713i	−0.949180	+	0.314735i	$0.898084\pi$
$468$	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
$472$	−4.14884	−	1.11168i	−0.190966	−	0.0511692i
$473$	17.3880	+	4.65911i	0.799503	+	0.214226i
$474$	−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
$478$	−10.9591	−	40.8999i	−0.501257	−	1.87072i
$479$	6.57783	+	11.3931i	0.300549	+	0.520565i	0.976260	−	0.216601i	$-0.0694969\pi$
$479$	6.57783	+	11.3931i	0.300549	+	0.520565i	−0.675712	+	0.737166i	$0.736164\pi$
$480$		0			0
$481$	2.10687	+	1.21640i	0.0960651	+	0.0554632i
$482$	−15.1875	+	15.1875i	−0.691770	+	0.691770i
$483$	11.0409	−	9.66675i	0.502379	−	0.439852i
$484$		−	16.8772i		−	0.767147i
$485$		0			0
$486$	1.80344	−	1.04121i	0.0818055	−	0.0472304i
$487$	−8.71251	+	32.5155i	−0.394802	+	1.47342i	0.427316	+	0.904102i	$0.359459\pi$
$487$	−8.71251	+	32.5155i	−0.394802	+	1.47342i	−0.822118	+	0.569317i	$0.807208\pi$
$488$	5.08407	−	1.36227i	0.230145	−	0.0616671i
$489$	−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	$0.653714\pi$
$492$	−23.2330	+	6.22527i	−1.04742	+	0.280657i
$493$	−8.56621	+	31.9695i	−0.385803	+	1.43984i
$494$	−14.1776	+	8.18543i	−0.637880	+	0.368280i
$495$		0			0
$496$		−	18.9512i		−	0.850932i
$497$	30.1718	−	26.4165i	1.35339	−	1.18494i
$498$	0.412137	−	0.412137i	0.0184683	−	0.0184683i
$499$	11.8247	+	6.82698i	0.529345	+	0.305618i	0.740750	−	0.671781i	$-0.234470\pi$
$499$	11.8247	+	6.82698i	0.529345	+	0.305618i	−0.211404	+	0.977399i	$0.567804\pi$
$500$		0			0
$501$	−3.13994	−	5.43854i	−0.140282	−	0.242976i
$502$	3.91406	+	14.6075i	0.174693	+	0.651963i
$503$	23.7213	+	23.7213i	1.05768	+	1.05768i	0.998231	+	0.0594513i	$0.0189351\pi$
$503$	23.7213	+	23.7213i	1.05768	+	1.05768i	0.0594513	+	0.998231i	$0.481065\pi$
$504$	−1.03130	+	1.54073i	−0.0459375	+	0.0686294i
$505$		0			0
$506$	11.2233	−	19.4393i	0.498935	−	0.864181i
$507$	−5.99281	−	1.60577i	−0.266150	−	0.0713147i
$508$	7.02735	+	1.88297i	0.311788	+	0.0835434i
$509$	12.9430	−	22.4180i	0.573689	−	0.993659i	−0.422494	−	0.906366i	$-0.638845\pi$
$509$	12.9430	−	22.4180i	0.573689	−	0.993659i	0.996183	−	0.0872928i	$-0.0278216\pi$
$510$		0			0
$511$	7.32538	+	14.8849i	0.324056	+	0.658470i
$512$	−21.5780	−	21.5780i	−0.953620	−	0.953620i
$513$	0.780509	+	2.91290i	0.0344603	+	0.128608i
$514$	−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
$518$	−1.65671	+	4.86749i	−0.0727916	+	0.213865i
$519$		−	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	$0.654187\pi$
$522$	2.84058	−	10.6012i	0.124329	−	0.464001i
$523$	15.8222	−	4.23956i	0.691859	−	0.185383i	0.104277	−	0.994548i	$-0.466747\pi$
$523$	15.8222	−	4.23956i	0.691859	−	0.185383i	0.587581	+	0.809165i	$0.300080\pi$
$524$	−28.6427			−1.25126
$525$		0			0
$526$	−1.86771			−0.0814360
$527$	−35.7701	+	9.58457i	−1.55817	+	0.417510i
$528$	1.61646	−	6.03272i	0.0703475	−	0.262540i
$529$	−6.72382	+	3.88200i	−0.292340	+	0.168783i
$530$		0			0
$531$			6.12938i			0.265992i
$532$	−12.2803	−	14.0260i	−0.532418	−	0.608104i
$533$	−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
$537$	2.18119	+	8.14033i	0.0941255	+	0.351281i
$538$	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	$0.181951\pi$
$542$	16.9921	+	4.55303i	0.729875	+	0.195569i
$543$	−11.6357	−	3.11777i	−0.499334	−	0.133796i
$544$	−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	0.953181	−	0.302400i	$-0.0977877\pi$
$547$	15.2205	+	15.2205i	0.650782	+	0.650782i	−0.302400	+	0.953181i	$0.597788\pi$
$548$	−7.00150	−	26.1300i	−0.299089	−	1.11622i
$549$	−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
$553$	−42.6595	+	8.44942i	−1.81407	+	0.359306i
$554$			31.2894i			1.32936i
$555$		0			0
$556$	−9.87884	+	5.70355i	−0.418956	+	0.241884i
$557$	−4.55245	+	16.9900i	−0.192894	+	0.719888i	0.799909	+	0.600122i	$0.204881\pi$
$557$	−4.55245	+	16.9900i	−0.192894	+	0.719888i	−0.992802	+	0.119767i	$0.961785\pi$
$558$	11.8615	−	3.17827i	0.502136	−	0.134547i
$559$	24.1473			1.02132
$560$		0			0
$561$	−12.2042			−0.515262
$562$	9.13354	−	2.44733i	0.385275	−	0.103234i
$563$	−6.04240	+	22.5505i	−0.254657	+	0.950392i	0.713624	+	0.700529i	$0.247052\pi$
$563$	−6.04240	+	22.5505i	−0.254657	+	0.950392i	−0.968281	+	0.249863i	$0.919614\pi$
$564$	7.86477	−	4.54073i	0.331167	−	0.191199i
$565$		0			0
$566$			30.8430i			1.29643i
$567$	2.50465	+	0.852487i	0.105185	+	0.0358011i
$568$	7.51049	−	7.51049i	0.315133	−	0.315133i
$569$	−12.8543	−	7.42144i	−0.538881	−	0.311123i	0.205745	−	0.978606i	$-0.434038\pi$
$569$	−12.8543	−	7.42144i	−0.538881	−	0.311123i	−0.744625	+	0.667483i	$0.767372\pi$
$570$		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	$-0.463057\pi$
$572$	3.06367	+	11.4338i	0.128098	+	0.478069i
$573$	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
$577$	−10.2639	−	2.75019i	−0.427290	−	0.114492i	0.0387638	−	0.999248i	$-0.487658\pi$
$577$	−10.2639	−	2.75019i	−0.427290	−	0.114492i	−0.466054	+	0.884756i	$0.654325\pi$
$578$	45.1314	+	12.0929i	1.87722	+	0.502999i
$579$	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
$583$	−0.586329	−	2.18821i	−0.0242833	−	0.0906263i
$584$	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	$-0.815636\pi$
$587$	−7.01529	+	7.01529i	−0.289552	+	0.289552i	0.547351	+	0.836903i	$0.315636\pi$
$588$	−16.2191	+	2.10843i	−0.668864	+	0.0869503i
$589$			17.7831i			0.732738i
$590$		0			0
$591$	10.1966	−	5.88699i	0.419431	−	0.242158i
$592$	0.776239	−	2.89696i	0.0319032	−	0.119064i
$593$	−17.5108	+	4.69201i	−0.719084	+	0.192678i	−0.599763	−	0.800178i	$-0.704738\pi$
$593$	−17.5108	+	4.69201i	−0.719084	+	0.192678i	−0.119321	+	0.992856i	$0.538072\pi$
$594$	4.04695			0.166048
$595$		0			0
$596$	6.24553			0.255827
$597$	−13.0809	+	3.50502i	−0.535366	+	0.143451i
$598$	7.79305	−	29.0841i	0.318682	−	1.18934i
$599$	15.5885	−	9.00000i	0.636927	−	0.367730i	−0.146503	−	0.989210i	$-0.546802\pi$
$599$	15.5885	−	9.00000i	0.636927	−	0.367730i	0.783430	+	0.621480i	$0.213468\pi$
$600$		0			0
$601$		−	9.94386i		−	0.405619i	−0.979218	−	0.202809i	$-0.934993\pi$
$601$		−	9.94386i		−	0.405619i	0.979218	−	0.202809i	$-0.0650071\pi$
$602$	9.91570	+	50.0625i	0.404134	+	2.04039i
$603$	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
$607$	−9.01387	−	33.6402i	−0.365862	−	1.36542i	−0.866249	−	0.499613i	$-0.833476\pi$
$607$	−9.01387	−	33.6402i	−0.365862	−	1.36542i	0.500387	−	0.865802i	$-0.333191\pi$
$608$	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
$612$	−14.1730	−	3.79766i	−0.572911	−	0.153511i
$613$	22.8595	+	6.12518i	0.923285	+	0.247394i	0.688989	−	0.724772i	$-0.258055\pi$
$613$	22.8595	+	6.12518i	0.923285	+	0.247394i	0.234296	+	0.972165i	$0.424721\pi$
$614$	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	0.982550	−	0.185996i	$-0.0595512\pi$
$617$	19.7860	+	19.7860i	0.796554	+	0.796554i	−0.185996	+	0.982550i	$0.559551\pi$
$618$	−4.09476	−	15.2818i	−0.164715	−	0.614726i
$619$	18.4587	+	31.9714i	0.741917	+	1.28504i	0.951621	+	0.307273i	$0.0994165\pi$
$619$	18.4587	+	31.9714i	0.741917	+	1.28504i	−0.209704	+	0.977765i	$0.567250\pi$
$620$		0			0
$621$	−4.80344	−	2.77327i	−0.192755	−	0.111287i
$622$	−38.3102	+	38.3102i	−1.53610	+	1.53610i
$623$	6.25119	+	31.5611i	0.250449	+	1.26447i
$624$		−	8.37782i		−	0.335381i
$625$		0			0
$626$	−6.52194	+	3.76545i	−0.260669	+	0.150497i
$627$	−1.51683	+	5.66088i	−0.0605762	+	0.226074i
$628$	−50.9150	+	13.6426i	−2.03173	+	0.544401i
$629$	−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	$0.385793\pi$
$632$	−11.1259	+	2.98116i	−0.442563	+	0.118584i
$633$	−1.09306	+	4.07937i	−0.0434453	+	0.162140i
$634$	17.1602	−	9.90742i	0.681517	−	0.393474i
$635$		0			0
$636$		−	2.72367i		−	0.108001i
$637$	−14.4953	+	11.0852i	−0.574323	+	0.439210i
$638$	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	$0.537036\pi$
$642$	−1.12237	−	4.18875i	−0.0442965	−	0.165317i
$643$	−17.6354	−	17.6354i	−0.695471	−	0.695471i	0.267959	−	0.963430i	$-0.413651\pi$
$643$	−17.6354	−	17.6354i	−0.695471	−	0.695471i	−0.963430	+	0.267959i	$0.913651\pi$
$644$	34.2124	+	2.27036i	1.34816	+	0.0894648i
$645$		0			0
$646$	19.7185	−	34.1535i	0.775814	−	1.34375i
$647$	−7.47546	−	2.00304i	−0.293891	−	0.0787477i	0.108861	−	0.994057i	$-0.465280\pi$
$647$	−7.47546	−	2.00304i	−0.293891	−	0.0787477i	−0.402752	+	0.915309i	$0.631946\pi$
$648$	0.676878	+	0.181369i	0.0265903	+	0.00712484i
$649$	−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
$653$	2.34239	+	8.74193i	0.0916649	+	0.342098i	0.996493	−	0.0836796i	$-0.0266672\pi$
$653$	2.34239	+	8.74193i	0.0916649	+	0.342098i	−0.904828	+	0.425778i	$0.860001\pi$
$654$	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
$658$	20.2724	+	6.89995i	0.790300	+	0.268988i
$659$		−	7.36509i		−	0.286903i	−0.989657	−	0.143452i	$-0.954180\pi$
$659$		−	7.36509i		−	0.286903i	0.989657	−	0.143452i	$-0.0458201\pi$
$660$		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	$-0.0739595\pi$
$662$	3.04733	−	11.3728i	0.118438	−	0.442016i
$663$	−15.8130	+	4.23709i	−0.614128	+	0.164555i
$664$	0.196134			0.00761149
$665$		0			0
$666$	1.94338			0.0753045
$667$	−28.2362	+	7.56586i	−1.09331	+	0.292951i
$668$	3.79766	−	14.1730i	0.146936	−	0.548372i
$669$	−10.4904	+	6.05662i	−0.405581	+	0.234162i
$670$		0			0
$671$		−	14.5968i		−	0.563505i
$672$	21.0064	−	4.16066i	0.810339	−	0.160501i
$673$	−8.14312	+	8.14312i	−0.313894	+	0.313894i	−0.846416	−	0.532522i	$-0.821244\pi$
$673$	−8.14312	+	8.14312i	−0.313894	+	0.313894i	0.532522	+	0.846416i	$0.321244\pi$
$674$	18.1100	+	10.4558i	0.697570	+	0.402742i
$675$		0			0
$676$	−7.24810	−	12.5541i	−0.278773	−	0.482849i
$677$	8.27166	+	30.8702i	0.317906	+	1.18644i	0.921254	+	0.388962i	$0.127166\pi$
$677$	8.27166	+	30.8702i	0.317906	+	1.18644i	−0.603348	+	0.797478i	$0.706167\pi$
$678$	−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
$682$	23.0513	+	6.17659i	0.882681	+	0.236514i
$683$	−17.6477	−	4.72869i	−0.675270	−	0.180938i	−0.0951425	−	0.995464i	$-0.530331\pi$
$683$	−17.6477	−	4.72869i	−0.675270	−	0.180938i	−0.580128	+	0.814526i	$0.696997\pi$
$684$	−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
$688$	−7.70471	−	28.7544i	−0.293739	−	1.09625i
$689$	−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
$693$	3.38701	+	3.86849i	0.128662	+	0.146952i
$694$		−	14.0191i		−	0.532156i
$695$		0			0
$696$	3.19844	−	1.84662i	0.121236	−	0.0699959i
$697$	16.7318	−	62.4439i	0.633762	−	2.36523i
$698$	−5.55839	+	1.48937i	−0.210388	+	0.0563734i
$699$	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	$0.411101\pi$
$702$	5.24365	−	1.40503i	0.197909	−	0.0530295i
$703$	−0.728393	+	2.71840i	−0.0274719	+	0.102526i
$704$	17.5496	−	10.1323i	0.661427	−	0.381875i
$705$		0			0
$706$		−	53.0887i		−	1.99802i
$707$	−0.284626	+	0.836246i	−0.0107045	+	0.0314503i
$708$	−10.1267	+	10.1267i	−0.380586	+	0.380586i
$709$	0.209858	+	0.121162i	0.00788139	+	0.00455032i	0.503936	−	0.863741i	$-0.331885\pi$
$709$	0.209858	+	0.121162i	0.00788139	+	0.00455032i	−0.496054	+	0.868292i	$0.665218\pi$
$710$		0			0
$711$	8.21851	+	14.2349i	0.308218	+	0.533849i
$712$	2.20557	+	8.23130i	0.0826573	+	0.308481i
$713$	−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
$717$	−19.6405	−	5.26265i	−0.733487	−	0.196537i
$718$	13.5365	+	3.62709i	0.505177	+	0.135362i
$719$	3.26797	−	5.66029i	0.121875	−	0.211093i	−0.798632	−	0.601819i	$-0.794443\pi$
$719$	3.26797	−	5.66029i	0.121875	−	0.211093i	0.920507	+	0.390726i	$0.127776\pi$
$720$		0			0
$721$	11.1809	−	16.7040i	0.416400	−	0.622090i
$722$	14.5863	+	14.5863i	0.542846	+	0.542846i
$723$	2.66948	+	9.96263i	0.0992790	+	0.370514i
$724$	−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	$-0.696851\pi$
$727$	6.33740	−	6.33740i	0.235041	−	0.235041i	0.814793	+	0.579752i	$0.196851\pi$
$728$	−3.63639	+	3.18380i	−0.134774	+	0.117999i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−50.3769	+	29.0851i	−1.86326	+	1.07575i
$732$	4.54218	−	16.9517i	0.167884	−	0.626551i
$733$	11.0897	−	2.97148i	0.409607	−	0.109754i	−0.0481307	−	0.998841i	$-0.515326\pi$
$733$	11.0897	−	2.97148i	0.409607	−	0.109754i	0.457738	+	0.889087i	$0.348660\pi$
$734$	38.3155			1.41425
$735$		0			0
$736$	−44.8931			−1.65478
$737$	27.9839	−	7.49825i	1.03080	−	0.276202i
$738$	−5.54831	+	20.7066i	−0.204236	+	0.762219i
$739$	−28.2058	+	16.2847i	−1.03757	+	0.599041i	−0.919144	−	0.393922i	$-0.871118\pi$
$739$	−28.2058	+	16.2847i	−1.03757	+	0.599041i	−0.118425	+	0.992963i	$0.537785\pi$
$740$		0			0
$741$			7.86143i			0.288797i
$742$	4.83216	−	4.23074i	0.177394	−	0.155315i
$743$	25.4999	−	25.4999i	0.935502	−	0.935502i	−0.0625403	−	0.998042i	$-0.519920\pi$
$743$	25.4999	−	25.4999i	0.935502	−	0.935502i	0.998042	+	0.0625403i	$0.0199202\pi$
$744$	3.57867	+	2.06615i	0.131200	+	0.0757486i
$745$		0			0
$746$	−1.82409	−	3.15942i	−0.0667847	−	0.115675i
$747$	−0.0724408	−	0.270353i	−0.00265047	−	0.00989169i
$748$	−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	$0.296787\pi$
$752$	−12.0654	−	3.23292i	−0.439981	−	0.117893i
$753$	7.01463	+	1.87956i	0.255627	+	0.0684951i
$754$	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	0.990778	−	0.135495i	$-0.0432626\pi$
$757$	23.5319	+	23.5319i	0.855283	+	0.855283i	−0.135495	+	0.990778i	$0.543263\pi$
$758$	−20.1724	−	75.2843i	−0.732694	−	2.73445i
$759$	−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
$763$	−12.9776	+	38.1289i	−0.469822	+	1.38036i
$764$			15.3270i			0.554511i
$765$		0			0
$766$	−33.0286	+	19.0691i	−1.19337	+	0.688993i
$767$	−4.13554	+	15.4341i	−0.149326	+	0.557291i
$768$	−9.02758	+	2.41893i	−0.325755	+	0.0872857i
$769$	3.95222			0.142521			0.0712604	−	0.997458i	$-0.477298\pi$
$769$	3.95222			0.142521			0.0712604	+	0.997458i	$0.477298\pi$
$770$		0			0
$771$	−5.38040			−0.193770
$772$	8.87498	−	2.37804i	0.319417	−	0.0855876i
$773$	8.29603	−	30.9612i	0.298388	−	1.11360i	−0.640102	−	0.768290i	$-0.721108\pi$
$773$	8.29603	−	30.9612i	0.298388	−	1.11360i	0.938490	−	0.345308i	$-0.112225\pi$
$774$	16.7051	−	9.64471i	0.600453	−	0.346672i
$775$		0			0
$776$		−	10.8969i		−	0.391177i
$777$	1.62647	+	1.85768i	0.0583494	+	0.0666440i
$778$	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
$782$	18.7733	+	70.0628i	0.671330	+	2.50544i
$783$	−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
$787$	21.8820	+	5.86328i	0.780011	+	0.209003i	0.626790	−	0.779189i	$-0.284369\pi$
$787$	21.8820	+	5.86328i	0.780011	+	0.209003i	0.153221	+	0.988192i	$0.451035\pi$
$788$	26.5726	+	7.12011i	0.946610	+	0.253644i
$789$	−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
$793$	−5.06777	−	18.9132i	−0.179962	−	0.671626i
$794$	−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	$-0.516460\pi$
$797$	26.7342	−	26.7342i	0.946974	−	0.946974i	0.998663	+	0.0516889i	$0.0164604\pi$
$798$	−16.2984	+	3.22817i	−0.576957	+	0.114276i
$799$			24.4084i			0.863508i
$800$		0			0
$801$	10.5315	−	6.08035i	0.372111	−	0.214838i
$802$	20.5283	−	76.6125i	0.724878	−	2.70528i
$803$	11.7705	−	3.15389i	0.415371	−	0.111298i
$804$	34.8316			1.22842
$805$		0			0
$806$	32.0121			1.12758
$807$	23.7204	−	6.35587i	0.834999	−	0.223737i
$808$	−0.0605550	+	0.225994i	−0.00213032	+	0.00795045i
$809$	24.6354	−	14.2233i	0.866136	−	0.500064i	7.34001e−5	−	1.00000i	$-0.499977\pi$
$809$	24.6354	−	14.2233i	0.866136	−	0.500064i	0.866062	+	0.499936i	$0.166643\pi$
$810$		0			0
$811$		−	47.9872i		−	1.68506i	−0.538649	−	0.842530i	$-0.681065\pi$
$811$		−	47.9872i		−	1.68506i	0.538649	−	0.842530i	$-0.318935\pi$
$812$	30.8429	+	10.4977i	1.08237	+	0.368399i
$813$	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
$817$	7.22981	+	26.9820i	0.252939	+	0.943982i
$818$	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	$0.989734\pi$
$822$	−23.2885	−	6.24014i	−0.812280	−	0.217650i
$823$	−26.9143	−	7.21166i	−0.938173	−	0.251383i	−0.242837	−	0.970067i	$-0.578078\pi$
$823$	−26.9143	−	7.21166i	−0.938173	−	0.251383i	−0.695336	+	0.718684i	$0.744745\pi$
$824$	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	0.347189	−	0.937795i	$-0.387136\pi$
$827$	−16.9844	−	16.9844i	−0.590606	−	0.590606i	−0.937795	+	0.347189i	$0.887136\pi$
$828$	−3.35417	−	12.5179i	−0.116565	−	0.435028i
$829$	−20.3808	−	35.3005i	−0.707853	−	1.22604i	−0.965652	−	0.259839i	$-0.916331\pi$
$829$	−20.3808	−	35.3005i	−0.707853	−	1.22604i	0.257799	−	0.966199i	$-0.417003\pi$
$830$		0			0
$831$	13.0124	+	7.51272i	0.451396	+	0.260613i
$832$	19.2214	−	19.2214i	0.666381	−	0.666381i
$833$	16.8885	−	40.5856i	0.585154	−	1.40621i
$834$			10.1667i			0.352042i
$835$		0			0
$836$	−11.8587	+	6.84664i	−0.410142	+	0.236796i
$837$	1.52623	−	5.69598i	0.0527543	−	0.196882i
$838$	−74.3824	+	19.9307i	−2.56950	+	0.688495i
$839$	32.2842			1.11458			0.557288	−	0.830320i	$-0.311842\pi$
$839$	32.2842			1.11458			0.557288	+	0.830320i	$0.311842\pi$
$840$		0			0
$841$	1.22327			0.0421817
$842$	22.1197	−	5.92697i	0.762297	−	0.204257i
$843$	1.17523	−	4.38601i	0.0404770	−	0.151062i
$844$	−8.54569	+	4.93385i	−0.294155	+	0.169830i
$845$		0			0
$846$		−	8.09390i		−	0.278274i
$847$	−3.71311	−	18.7468i	−0.127584	−	0.644147i
$848$	−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
$852$	−9.16601	−	34.2080i	−0.314022	−	1.17195i
$853$	27.1233	+	27.1233i	0.928684	+	0.928684i	0.997621	−	0.0689370i	$-0.0219607\pi$
$853$	27.1233	+	27.1233i	0.928684	+	0.928684i	−0.0689370	+	0.997621i	$0.521961\pi$
$854$	37.1300	−	18.2729i	1.27056	−	0.625287i
$855$		0			0
$856$	0.729637	−	1.26377i	0.0249385	−	0.0431947i
$857$	−38.6518	−	10.3567i	−1.32032	−	0.353779i	−0.471223	−	0.882014i	$-0.656187\pi$
$857$	−38.6518	−	10.3567i	−1.32032	−	0.353779i	−0.849098	+	0.528235i	$0.822854\pi$
$858$	10.1904	+	2.73051i	0.347895	+	0.0932181i
$859$	−13.0383	+	22.5830i	−0.444861	+	0.770522i	−0.998043	−	0.0625385i	$-0.980080\pi$
$859$	−13.0383	+	22.5830i	−0.444861	+	0.770522i	0.553181	+	0.833061i	$0.313414\pi$
$860$		0			0
$861$	−24.4370	+	12.0263i	−0.832811	+	0.409855i
$862$	8.69631	+	8.69631i	0.296197	+	0.296197i
$863$	−3.22356	−	12.0305i	−0.109731	−	0.409523i	0.889107	−	0.457698i	$-0.151326\pi$
$863$	−3.22356	−	12.0305i	−0.109731	−	0.409523i	−0.998839	+	0.0481753i	$0.984659\pi$
$864$	−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
$868$	7.08265	+	35.7590i	0.240401	+	1.21374i
$869$			31.9434i			1.08360i
$870$		0			0
$871$	33.6555	−	19.4310i	1.14037	−	0.658395i
$872$	−2.76103	+	10.3043i	−0.0935002	+	0.348947i
$873$	−15.0204	+	4.02470i	−0.508363	+	0.136216i
$874$	34.8316			1.17820
$875$		0			0
$876$	14.6508			0.495003
$877$	−22.5945	+	6.05417i	−0.762960	+	0.204435i	−0.619259	−	0.785187i	$-0.712567\pi$
$877$	−22.5945	+	6.05417i	−0.762960	+	0.204435i	−0.143701	+	0.989621i	$0.545900\pi$
$878$	2.18119	−	8.14033i	0.0736117	−	0.274723i
$879$	−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	$-0.173291\pi$
$882$	−5.60029	+	13.4583i	−0.188572	+	0.453164i
$883$	34.1799	−	34.1799i	1.15024	−	1.15024i	0.163741	−	0.986503i	$-0.447644\pi$
$883$	34.1799	−	34.1799i	1.15024	−	1.15024i	0.986503	−	0.163741i	$-0.0523560\pi$
$884$	−33.1261	−	19.1253i	−1.11415	−	0.643255i
$885$		0			0
$886$	17.5846	+	30.4574i	0.590767	+	1.02324i
$887$	0.241699	+	0.902034i	0.00811547	+	0.0302873i	0.969865	−	0.243644i	$-0.0783427\pi$
$887$	0.241699	+	0.902034i	0.00811547	+	0.0302873i	−0.961749	+	0.273931i	$0.911676\pi$
$888$	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
$892$	−27.3383	−	7.32527i	−0.915354	−	0.245268i
$893$	11.3218	+	3.03365i	0.378868	+	0.101517i
$894$	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
$898$	14.6777	+	54.7780i	0.489802	+	1.82797i
$899$	−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
$903$	23.2004	+	7.89654i	0.772062	+	0.262780i
$904$		−	4.22648i		−	0.140571i
$905$		0			0
$906$	−26.6259	+	15.3725i	−0.884587	+	0.510717i
$907$	9.11603	−	34.0215i	0.302693	−	1.12967i	−0.632220	−	0.774789i	$-0.717856\pi$
$907$	9.11603	−	34.0215i	0.302693	−	1.12967i	0.934913	−	0.354877i	$-0.115477\pi$
$908$	−31.7171	+	8.49856i	−1.05257	+	0.282035i
$909$	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	$0.353874\pi$
$912$	9.36132	−	2.50836i	0.309984	−	0.0830600i
$913$	0.140780	−	0.525398i	0.00465914	−	0.0173881i
$914$	−44.7882	+	25.8585i	−1.48146	+	0.855322i
$915$		0			0
$916$			8.86621i			0.292948i
$917$	−31.8156	+	6.30160i	−1.05064	+	0.208097i
$918$	−9.24713	+	9.24713i	−0.305201	+	0.305201i
$919$	1.36731	+	0.789416i	0.0451034	+	0.0260404i	0.522382	−	0.852712i	$-0.325043\pi$
$919$	1.36731	+	0.789416i	0.0451034	+	0.0260404i	−0.477279	+	0.878752i	$0.658377\pi$
$920$		0			0
$921$	−9.57380	−	16.5823i	−0.315467	−	0.546406i
$922$	12.4274	+	46.3797i	0.409275	+	1.52744i
$923$	−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
$927$	−7.33847	−	1.96634i	−0.241027	−	0.0645830i
$928$	−41.2043	−	11.0407i	−1.35260	−	0.362427i
$929$	8.00853	−	13.8712i	0.262751	−	0.455099i	−0.704221	−	0.709981i	$-0.748703\pi$
$929$	8.00853	−	13.8712i	0.262751	−	0.455099i	0.966972	+	0.254882i	$0.0820368\pi$
$930$		0			0
$931$	−16.7264	−	12.8779i	−0.548187	−	0.422058i
$932$	36.6550	+	36.6550i	1.20068	+	1.20068i
$933$	6.73372	+	25.1306i	0.220452	+	0.822739i
$934$	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	$-0.814334\pi$
$937$	−8.68993	+	8.68993i	−0.283888	+	0.283888i	0.550770	+	0.834657i	$0.314334\pi$
$938$	54.1047	+	61.7960i	1.76658	+	2.01771i
$939$			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	$0.112354\pi$
$942$	−12.1591	+	45.3784i	−0.396165	+	1.47851i
$943$	55.1518	−	14.7779i	1.79599	−	0.481234i
$944$	19.6983			0.641124
$945$		0			0
$946$	37.4867			1.21880
$947$	−45.0931	+	12.0827i	−1.46533	+	0.392634i	−0.901327	−	0.433140i	$-0.857406\pi$
$947$	−45.0931	+	12.0827i	−1.46533	+	0.392634i	−0.564002	+	0.825773i	$0.690739\pi$
$948$	−9.94000	+	37.0966i	−0.322836	+	1.20484i
$949$	14.1561	−	8.17302i	0.459526	−	0.265307i
$950$		0			0
$951$		−	9.51525i		−	0.308553i
$952$	3.75151	−	11.0221i	0.121587	−	0.357229i
$953$	40.7298	−	40.7298i	1.31937	−	1.31937i	0.405089	−	0.914277i	$-0.367241\pi$
$953$	40.7298	−	40.7298i	1.31937	−	1.31937i	0.914277	−	0.405089i	$-0.132759\pi$
$954$	−2.10227	−	1.21374i	−0.0680634	−	0.0392964i
$955$		0			0
$956$	−23.7545	−	41.1440i	−0.768274	−	1.33069i
$957$	−2.65091	−	9.89332i	−0.0856917	−	0.319806i
$958$	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
$962$	4.89352	+	1.31121i	0.157773	+	0.0422753i
$963$	−2.01147	−	0.538972i	−0.0648188	−	0.0173681i
$964$	−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	0.498066	−	0.867139i	$-0.334044\pi$
$967$	−11.4769	−	11.4769i	−0.369073	−	0.369073i	−0.867139	+	0.498066i	$0.834044\pi$
$968$	−1.31008	−	4.88927i	−0.0421075	−	0.157147i
$969$	−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
$973$	−9.71833	+	8.50877i	−0.311556	+	0.272779i
$974$			70.0999i			2.24614i
$975$		0			0
$976$	−20.9046	+	12.0693i	−0.669141	+	0.386329i
$977$	−3.72204	+	13.8908i	−0.119079	+	0.444408i	−0.999560	−	0.0296739i	$-0.990553\pi$
$977$	−3.72204	+	13.8908i	−0.119079	+	0.444408i	0.880481	+	0.474082i	$0.157220\pi$
$978$	−31.2316	+	8.36847i	−0.998676	+	0.267594i
$979$	23.6329			0.755309
$980$		0			0
$981$	15.2233			0.486042
$982$	−41.3937	+	11.0914i	−1.32093	+	0.353941i
$983$	−5.94558	+	22.1892i	−0.189635	+	0.707726i	0.803956	+	0.594689i	$0.202725\pi$
$983$	−5.94558	+	22.1892i	−0.189635	+	0.707726i	−0.993591	+	0.113037i	$0.963942\pi$
$984$	−6.24729	+	3.60687i	−0.199156	+	0.114983i
$985$		0			0
$986$			68.9228i			2.19495i
$987$	7.73699	−	6.77403i	0.246271	−	0.215620i
$988$	−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	$0.525146\pi$
$992$	−12.3532	−	46.1027i	−0.392214	−	1.46376i
$993$	−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
$997$	−18.4257	−	4.93715i	−0.583547	−	0.156361i	−0.0450448	−	0.998985i	$-0.514343\pi$
$997$	−18.4257	−	4.93715i	−0.583547	−	0.156361i	−0.538502	+	0.842624i	$0.681010\pi$
$998$	27.4646	+	7.35911i	0.869376	+	0.232948i
$999$	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.82.5	yes	24
5.2	odd	4	inner	525.2.bc.d.418.5	yes	24
5.3	odd	4	inner	525.2.bc.d.418.2	yes	24
5.4	even	2	inner	525.2.bc.d.82.2	✓	24
7.3	odd	6	inner	525.2.bc.d.157.2	yes	24
35.3	even	12	inner	525.2.bc.d.493.5	yes	24
35.17	even	12	inner	525.2.bc.d.493.2	yes	24
35.24	odd	6	inner	525.2.bc.d.157.5	yes	24

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

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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more