LMFDB - Embedded newform 3150.2.m.i.1457.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1457,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("3150.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.3
Root			$1.69230i$ of defining polynomial
Character	$\chi$	$=$	3150.1457
Dual form			3150.2.m.i.2843.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} -6.36365i q^{11} +(1.69230 - 1.69230i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-0.979056 + 0.979056i) q^{17} +(-4.49978 - 4.49978i) q^{22} +(1.38459 + 1.38459i) q^{23} -2.39327i q^{26} +(-0.707107 + 0.707107i) q^{28} -5.81975 q^{29} +2.36365 q^{31} +(-0.707107 + 0.707107i) q^{32} +1.38459i q^{34} +(-0.157074 - 0.157074i) q^{37} -8.94944i q^{41} +(-5.88438 + 5.88438i) q^{43} -6.36365 q^{44} +1.95811 q^{46} +(-3.05595 + 3.05595i) q^{47} +1.00000i q^{49} +(-1.69230 - 1.69230i) q^{52} +(-0.192517 - 0.192517i) q^{53} +1.00000i q^{56} +(-4.11519 + 4.11519i) q^{58} +10.3842 q^{59} -0.979056 q^{61} +(1.67135 - 1.67135i) q^{62} +1.00000i q^{64} +(-9.88438 - 9.88438i) q^{67} +(0.979056 + 0.979056i) q^{68} +12.3423i q^{71} +(-4.71324 + 4.71324i) q^{73} -0.222136 q^{74} +(-4.49978 + 4.49978i) q^{77} -6.68541i q^{79} +(-6.32821 - 6.32821i) q^{82} +(-11.3427 - 11.3427i) q^{83} +8.32176i q^{86} +(-4.49978 + 4.49978i) q^{88} -11.8371 q^{89} -2.39327 q^{91} +(1.38459 - 1.38459i) q^{92} +4.32176i q^{94} +(9.39866 + 9.39866i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 4 q^{13} - 8 q^{14} - 8 q^{16} + 4 q^{22} - 8 q^{23} - 24 q^{29} - 8 q^{31} + 4 q^{37} + 12 q^{43} - 24 q^{44} + 12 q^{47} - 4 q^{52} - 32 q^{53} - 12 q^{58} - 16 q^{59} - 4 q^{62} - 20 q^{67} - 36 q^{73} - 40 q^{74} + 4 q^{77} + 12 q^{82} - 56 q^{83} + 4 q^{88} - 72 q^{89} - 8 q^{92} + 4 q^{97}+O(q^{100}) $ 8 * q + 4 * q^13 - 8 * q^14 - 8 * q^16 + 4 * q^22 - 8 * q^23 - 24 * q^29 - 8 * q^31 + 4 * q^37 + 12 * q^43 - 24 * q^44 + 12 * q^47 - 4 * q^52 - 32 * q^53 - 12 * q^58 - 16 * q^59 - 4 * q^62 - 20 * q^67 - 36 * q^73 - 40 * q^74 + 4 * q^77 + 12 * q^82 - 56 * q^83 + 4 * q^88 - 72 * q^89 - 8 * q^92 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$		−	6.36365i		−	1.91871i	−0.282197	−	0.959356i	$-0.591063\pi$
$11$		−	6.36365i		−	1.91871i	0.282197	−	0.959356i	$-0.408937\pi$
$12$		0			0
$13$	1.69230	−	1.69230i	0.469359	−	0.469359i	−0.432348	−	0.901707i	$-0.642315\pi$
$13$	1.69230	−	1.69230i	0.469359	−	0.469359i	0.901707	+	0.432348i	$0.142315\pi$
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−0.979056	+	0.979056i	−0.237456	+	0.237456i	−0.815796	−	0.578340i	$-0.803701\pi$
$17$	−0.979056	+	0.979056i	−0.237456	+	0.237456i	0.578340	+	0.815796i	$0.303701\pi$
$18$		0			0
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$		0			0
$22$	−4.49978	−	4.49978i	−0.959356	−	0.959356i
$23$	1.38459	+	1.38459i	0.288708	+	0.288708i	0.836569	−	0.547861i	$-0.184558\pi$
$23$	1.38459	+	1.38459i	0.288708	+	0.288708i	−0.547861	+	0.836569i	$0.684558\pi$
$24$		0			0
$25$		0			0
$26$		−	2.39327i		−	0.469359i
$27$		0			0
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$	−5.81975			−1.08070			−0.540350	−	0.841440i	$-0.681708\pi$
$29$	−5.81975			−1.08070			−0.540350	+	0.841440i	$0.681708\pi$
$30$		0			0
$31$	2.36365			0.424524			0.212262	−	0.977213i	$-0.431917\pi$
$31$	2.36365			0.424524			0.212262	+	0.977213i	$0.431917\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			1.38459i			0.237456i
$35$		0			0
$36$		0			0
$37$	−0.157074	−	0.157074i	−0.0258227	−	0.0258227i	0.694078	−	0.719900i	$-0.255812\pi$
$37$	−0.157074	−	0.157074i	−0.0258227	−	0.0258227i	−0.719900	+	0.694078i	$0.755812\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	8.94944i		−	1.39767i	−0.715284	−	0.698834i	$-0.753703\pi$
$41$		−	8.94944i		−	1.39767i	0.715284	−	0.698834i	$-0.246297\pi$
$42$		0			0
$43$	−5.88438	+	5.88438i	−0.897359	+	0.897359i	−0.995202	−	0.0978430i	$-0.968806\pi$
$43$	−5.88438	+	5.88438i	−0.897359	+	0.897359i	0.0978430	+	0.995202i	$0.468806\pi$
$44$	−6.36365			−0.959356
$45$		0			0
$46$	1.95811			0.288708
$47$	−3.05595	+	3.05595i	−0.445756	+	0.445756i	−0.893941	−	0.448185i	$-0.852071\pi$
$47$	−3.05595	+	3.05595i	−0.445756	+	0.445756i	0.448185	+	0.893941i	$0.352071\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$		0			0
$52$	−1.69230	−	1.69230i	−0.234679	−	0.234679i
$53$	−0.192517	−	0.192517i	−0.0264442	−	0.0264442i	0.693761	−	0.720205i	$-0.255952\pi$
$53$	−0.192517	−	0.192517i	−0.0264442	−	0.0264442i	−0.720205	+	0.693761i	$0.755952\pi$
$54$		0			0
$55$		0			0
$56$			1.00000i			0.133631i
$57$		0			0
$58$	−4.11519	+	4.11519i	−0.540350	+	0.540350i
$59$	10.3842			1.35190			0.675951	−	0.736947i	$-0.263733\pi$
$59$	10.3842			1.35190			0.675951	+	0.736947i	$0.263733\pi$
$60$		0			0
$61$	−0.979056			−0.125355			−0.0626777	−	0.998034i	$-0.519964\pi$
$61$	−0.979056			−0.125355			−0.0626777	+	0.998034i	$0.519964\pi$
$62$	1.67135	−	1.67135i	0.212262	−	0.212262i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	−9.88438	−	9.88438i	−1.20757	−	1.20757i	−0.971812	−	0.235756i	$-0.924243\pi$
$67$	−9.88438	−	9.88438i	−1.20757	−	1.20757i	−0.235756	−	0.971812i	$-0.575757\pi$
$68$	0.979056	+	0.979056i	0.118728	+	0.118728i
$69$		0			0
$70$		0			0
$71$			12.3423i			1.46476i	0.680897	+	0.732379i	$0.261590\pi$
$71$			12.3423i			1.46476i	−0.680897	+	0.732379i	$0.738410\pi$
$72$		0			0
$73$	−4.71324	+	4.71324i	−0.551643	+	0.551643i	−0.926915	−	0.375272i	$-0.877549\pi$
$73$	−4.71324	+	4.71324i	−0.551643	+	0.551643i	0.375272	+	0.926915i	$0.377549\pi$
$74$	−0.222136			−0.0258227
$75$		0			0
$76$		0			0
$77$	−4.49978	+	4.49978i	−0.512798	+	0.512798i
$78$		0			0
$79$		−	6.68541i		−	0.752168i	−0.926586	−	0.376084i	$-0.877270\pi$
$79$		−	6.68541i		−	0.752168i	0.926586	−	0.376084i	$-0.122730\pi$
$80$		0			0
$81$		0			0
$82$	−6.32821	−	6.32821i	−0.698834	−	0.698834i
$83$	−11.3427	−	11.3427i	−1.24502	−	1.24502i	−0.957891	−	0.287133i	$-0.907298\pi$
$83$	−11.3427	−	11.3427i	−1.24502	−	1.24502i	−0.287133	−	0.957891i	$-0.592702\pi$
$84$		0			0
$85$		0			0
$86$			8.32176i			0.897359i
$87$		0			0
$88$	−4.49978	+	4.49978i	−0.479678	+	0.479678i
$89$	−11.8371			−1.25473			−0.627365	−	0.778725i	$-0.715867\pi$
$89$	−11.8371			−1.25473			−0.627365	+	0.778725i	$0.715867\pi$
$90$		0			0
$91$	−2.39327			−0.250883
$92$	1.38459	−	1.38459i	0.144354	−	0.144354i
$93$		0			0
$94$			4.32176i			0.445756i
$95$		0			0
$96$		0			0
$97$	9.39866	+	9.39866i	0.954289	+	0.954289i	0.999000	−	0.0447111i	$-0.0142367\pi$
$97$	9.39866	+	9.39866i	0.954289	+	0.954289i	−0.0447111	+	0.999000i	$0.514237\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$		0			0
$100$		0			0
$101$		−	16.0501i		−	1.59705i	−0.601964	−	0.798524i	$-0.705615\pi$
$101$		−	16.0501i		−	1.59705i	0.601964	−	0.798524i	$-0.294385\pi$
$102$		0			0
$103$	0.706797	−	0.706797i	0.0696427	−	0.0696427i	−0.671428	−	0.741070i	$-0.734319\pi$
$103$	0.706797	−	0.706797i	0.0696427	−	0.0696427i	0.741070	+	0.671428i	$0.234319\pi$
$104$	−2.39327			−0.234679
$105$		0			0
$106$	−0.272260			−0.0264442
$107$	9.51384	−	9.51384i	0.919738	−	0.919738i	−0.0772723	−	0.997010i	$-0.524621\pi$
$107$	9.51384	−	9.51384i	0.919738	−	0.919738i	0.997010	+	0.0772723i	$0.0246211\pi$
$108$		0			0
$109$			14.9577i			1.43269i	0.697749	+	0.716343i	$0.254185\pi$
$109$			14.9577i			1.43269i	−0.697749	+	0.716343i	$0.745815\pi$
$110$		0			0
$111$		0			0
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	−9.22170	−	9.22170i	−0.867504	−	0.867504i	0.124691	−	0.992196i	$-0.460206\pi$
$113$	−9.22170	−	9.22170i	−0.867504	−	0.867504i	−0.992196	+	0.124691i	$0.960206\pi$
$114$		0			0
$115$		0			0
$116$			5.81975i			0.540350i
$117$		0			0
$118$	7.34271	−	7.34271i	0.675951	−	0.675951i
$119$	1.38459			0.126926
$120$		0			0
$121$	−29.4961			−2.68146
$122$	−0.692297	+	0.692297i	−0.0626777	+	0.0626777i
$123$		0			0
$124$		−	2.36365i		−	0.212262i
$125$		0			0
$126$		0			0
$127$	5.38459	+	5.38459i	0.477806	+	0.477806i	0.904429	−	0.426624i	$-0.140297\pi$
$127$	5.38459	+	5.38459i	0.477806	+	0.477806i	−0.426624	+	0.904429i	$0.640297\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$		−	13.2718i		−	1.15956i	−0.814772	−	0.579782i	$-0.803138\pi$
$131$		−	13.2718i		−	1.15956i	0.814772	−	0.579782i	$-0.196862\pi$
$132$		0			0
$133$		0			0
$134$	−13.9786			−1.20757
$135$		0			0
$136$	1.38459			0.118728
$137$	3.56484	−	3.56484i	0.304565	−	0.304565i	−0.538232	−	0.842797i	$-0.680908\pi$
$137$	3.56484	−	3.56484i	0.304565	−	0.304565i	0.842797	+	0.538232i	$0.180908\pi$
$138$		0			0
$139$		−	1.41359i		−	0.119899i	−0.998201	−	0.0599497i	$-0.980906\pi$
$139$		−	1.41359i		−	0.119899i	0.998201	−	0.0599497i	$-0.0190940\pi$
$140$		0			0
$141$		0			0
$142$	8.72730	+	8.72730i	0.732379	+	0.732379i
$143$	−10.7692	−	10.7692i	−0.900565	−	0.900565i
$144$		0			0
$145$		0			0
$146$			6.66553i			0.551643i
$147$		0			0
$148$	−0.157074	+	0.157074i	−0.0129114	+	0.0129114i
$149$	−20.0609			−1.64345			−0.821726	−	0.569882i	$-0.806989\pi$
$149$	−20.0609			−1.64345			−0.821726	+	0.569882i	$0.806989\pi$
$150$		0			0
$151$	8.81108			0.717035			0.358518	−	0.933523i	$-0.383282\pi$
$151$	8.81108			0.717035			0.358518	+	0.933523i	$0.383282\pi$
$152$		0			0
$153$		0			0
$154$			6.36365i			0.512798i
$155$		0			0
$156$		0			0
$157$	−15.2654	−	15.2654i	−1.21831	−	1.21831i	−0.968224	−	0.250086i	$-0.919541\pi$
$157$	−15.2654	−	15.2654i	−1.21831	−	1.21831i	−0.250086	−	0.968224i	$-0.580459\pi$
$158$	−4.72730	−	4.72730i	−0.376084	−	0.376084i
$159$		0			0
$160$		0			0
$161$		−	1.95811i		−	0.154321i
$162$		0			0
$163$	−7.11519	+	7.11519i	−0.557304	+	0.557304i	−0.928539	−	0.371235i	$-0.878935\pi$
$163$	−7.11519	+	7.11519i	−0.557304	+	0.557304i	0.371235	+	0.928539i	$0.378935\pi$
$164$	−8.94944			−0.698834
$165$		0			0
$166$	−16.0410			−1.24502
$167$	16.7128	−	16.7128i	1.29328	−	1.29328i	0.360527	−	0.932749i	$-0.382597\pi$
$167$	16.7128	−	16.7128i	1.29328	−	1.29328i	0.932749	−	0.360527i	$-0.117403\pi$
$168$		0			0
$169$			7.27226i			0.559405i
$170$		0			0
$171$		0			0
$172$	5.88438	+	5.88438i	0.448679	+	0.448679i
$173$	−14.7843	−	14.7843i	−1.12403	−	1.12403i	−0.991129	−	0.132901i	$-0.957571\pi$
$173$	−14.7843	−	14.7843i	−1.12403	−	1.12403i	−0.132901	−	0.991129i	$-0.542429\pi$
$174$		0			0
$175$		0			0
$176$			6.36365i			0.479678i
$177$		0			0
$178$	−8.37010	+	8.37010i	−0.627365	+	0.627365i
$179$	12.0205			0.898455			0.449227	−	0.893417i	$-0.351699\pi$
$179$	12.0205			0.898455			0.449227	+	0.893417i	$0.351699\pi$
$180$		0			0
$181$	17.5236			1.30252			0.651259	−	0.758856i	$-0.274241\pi$
$181$	17.5236			1.30252			0.651259	+	0.758856i	$0.274241\pi$
$182$	−1.69230	+	1.69230i	−0.125441	+	0.125441i
$183$		0			0
$184$		−	1.95811i		−	0.144354i
$185$		0			0
$186$		0			0
$187$	6.23037	+	6.23037i	0.455610	+	0.455610i
$188$	3.05595	+	3.05595i	0.222878	+	0.222878i
$189$		0			0
$190$		0			0
$191$			6.30038i			0.455880i	0.973675	+	0.227940i	$0.0731989\pi$
$191$			6.30038i			0.455880i	−0.973675	+	0.227940i	$0.926801\pi$
$192$		0			0
$193$	11.6435	−	11.6435i	0.838119	−	0.838119i	−0.150492	−	0.988611i	$-0.548086\pi$
$193$	11.6435	−	11.6435i	0.838119	−	0.838119i	0.988611	+	0.150492i	$0.0480857\pi$
$194$	13.2917			0.954289
$195$		0			0
$196$	1.00000			0.0714286
$197$	1.92849	−	1.92849i	0.137399	−	0.137399i	−0.635062	−	0.772461i	$-0.719025\pi$
$197$	1.92849	−	1.92849i	0.137399	−	0.137399i	0.772461	+	0.635062i	$0.219025\pi$
$198$		0			0
$199$			5.67736i			0.402457i	0.979544	+	0.201229i	$0.0644934\pi$
$199$			5.67736i			0.402457i	−0.979544	+	0.201229i	$0.935507\pi$
$200$		0			0
$201$		0			0
$202$	−11.3492	−	11.3492i	−0.798524	−	0.798524i
$203$	4.11519	+	4.11519i	0.288829	+	0.288829i
$204$		0			0
$205$		0			0
$206$		−	0.999561i		−	0.0696427i
$207$		0			0
$208$	−1.69230	+	1.69230i	−0.117340	+	0.117340i
$209$		0			0
$210$		0			0
$211$	7.91622			0.544975			0.272488	−	0.962159i	$-0.412154\pi$
$211$	7.91622			0.544975			0.272488	+	0.962159i	$0.412154\pi$
$212$	−0.192517	+	0.192517i	−0.0132221	+	0.0132221i
$213$		0			0
$214$		−	13.4546i		−	0.919738i
$215$		0			0
$216$		0			0
$217$	−1.67135	−	1.67135i	−0.113459	−	0.113459i
$218$	10.5767	+	10.5767i	0.716343	+	0.716343i
$219$		0			0
$220$		0			0
$221$			3.31371i			0.222904i
$222$		0			0
$223$	−8.34227	+	8.34227i	−0.558640	+	0.558640i	−0.928920	−	0.370280i	$-0.879262\pi$
$223$	−8.34227	+	8.34227i	−0.558640	+	0.558640i	0.370280	+	0.928920i	$0.379262\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	−13.0414			−0.867504
$227$	3.27270	−	3.27270i	0.217217	−	0.217217i	−0.590108	−	0.807324i	$-0.700915\pi$
$227$	3.27270	−	3.27270i	0.217217	−	0.217217i	0.807324	+	0.590108i	$0.200915\pi$
$228$		0			0
$229$			23.0901i			1.52584i	0.646496	+	0.762918i	$0.276234\pi$
$229$			23.0901i			1.52584i	−0.646496	+	0.762918i	$0.723766\pi$
$230$		0			0
$231$		0			0
$232$	4.11519	+	4.11519i	0.270175	+	0.270175i
$233$	−5.23081	−	5.23081i	−0.342682	−	0.342682i	0.514693	−	0.857375i	$-0.327906\pi$
$233$	−5.23081	−	5.23081i	−0.342682	−	0.342682i	−0.857375	+	0.514693i	$0.827906\pi$
$234$		0			0
$235$		0			0
$236$		−	10.3842i		−	0.675951i
$237$		0			0
$238$	0.979056	−	0.979056i	0.0634628	−	0.0634628i
$239$	−5.27182			−0.341006			−0.170503	−	0.985357i	$-0.554539\pi$
$239$	−5.27182			−0.341006			−0.170503	+	0.985357i	$0.554539\pi$
$240$		0			0
$241$	−5.27270			−0.339644			−0.169822	−	0.985475i	$-0.554319\pi$
$241$	−5.27270			−0.339644			−0.169822	+	0.985475i	$0.554319\pi$
$242$	−20.8569	+	20.8569i	−1.34073	+	1.34073i
$243$		0			0
$244$			0.979056i			0.0626777i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−1.67135	−	1.67135i	−0.106131	−	0.106131i
$249$		0			0
$250$		0			0
$251$			20.3423i			1.28399i	0.766708	+	0.641996i	$0.221894\pi$
$251$			20.3423i			1.28399i	−0.766708	+	0.641996i	$0.778106\pi$
$252$		0			0
$253$	8.81108	−	8.81108i	0.553948	−	0.553948i
$254$	7.61497			0.477806
$255$		0			0
$256$	1.00000			0.0625000
$257$	−2.50201	+	2.50201i	−0.156071	+	0.156071i	−0.780823	−	0.624752i	$-0.785200\pi$
$257$	−2.50201	+	2.50201i	−0.156071	+	0.156071i	0.624752	+	0.780823i	$0.285200\pi$
$258$		0			0
$259$			0.222136i			0.0138028i
$260$		0			0
$261$		0			0
$262$	−9.38459	−	9.38459i	−0.579782	−	0.579782i
$263$	12.6983	+	12.6983i	0.783011	+	0.783011i	0.980338	−	0.197327i	$-0.0632260\pi$
$263$	12.6983	+	12.6983i	0.783011	+	0.783011i	−0.197327	+	0.980338i	$0.563226\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−9.88438	+	9.88438i	−0.603784	+	0.603784i
$269$	26.9196			1.64131			0.820657	−	0.571421i	$-0.193608\pi$
$269$	26.9196			1.64131			0.820657	+	0.571421i	$0.193608\pi$
$270$		0			0
$271$	23.1320			1.40517			0.702583	−	0.711601i	$-0.252030\pi$
$271$	23.1320			1.40517			0.702583	+	0.711601i	$0.252030\pi$
$272$	0.979056	−	0.979056i	0.0593640	−	0.0593640i
$273$		0			0
$274$		−	5.04145i		−	0.304565i
$275$		0			0
$276$		0			0
$277$	−12.2271	−	12.2271i	−0.734654	−	0.734654i	0.236884	−	0.971538i	$-0.423874\pi$
$277$	−12.2271	−	12.2271i	−0.734654	−	0.734654i	−0.971538	+	0.236884i	$0.923874\pi$
$278$	−0.999561	−	0.999561i	−0.0599497	−	0.0599497i
$279$		0			0
$280$		0			0
$281$		−	10.4428i		−	0.622964i	−0.950252	−	0.311482i	$-0.899175\pi$
$281$		−	10.4428i		−	0.622964i	0.950252	−	0.311482i	$-0.100825\pi$
$282$		0			0
$283$	−22.9577	+	22.9577i	−1.36469	+	1.36469i	−0.496863	+	0.867829i	$0.665515\pi$
$283$	−22.9577	+	22.9577i	−1.36469	+	1.36469i	−0.867829	+	0.496863i	$0.834485\pi$
$284$	12.3423			0.732379
$285$		0			0
$286$	−15.2299			−0.900565
$287$	−6.32821	+	6.32821i	−0.373542	+	0.373542i
$288$		0			0
$289$			15.0829i			0.887229i
$290$		0			0
$291$		0			0
$292$	4.71324	+	4.71324i	0.275822	+	0.275822i
$293$	18.6413	+	18.6413i	1.08904	+	1.08904i	0.995628	+	0.0934082i	$0.0297762\pi$
$293$	18.6413	+	18.6413i	1.08904	+	1.08904i	0.0934082	+	0.995628i	$0.470224\pi$
$294$		0			0
$295$		0			0
$296$			0.222136i			0.0129114i
$297$		0			0
$298$	−14.1852	+	14.1852i	−0.821726	+	0.821726i
$299$	4.68629			0.271015
$300$		0			0
$301$	8.32176			0.479658
$302$	6.23037	−	6.23037i	0.358518	−	0.358518i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−0.727302	−	0.727302i	−0.0415093	−	0.0415093i	0.686047	−	0.727557i	$-0.259344\pi$
$307$	−0.727302	−	0.727302i	−0.0415093	−	0.0415093i	−0.727557	+	0.686047i	$0.759344\pi$
$308$	4.49978	+	4.49978i	0.256399	+	0.256399i
$309$		0			0
$310$		0			0
$311$		−	24.2295i		−	1.37393i	−0.726691	−	0.686964i	$-0.758943\pi$
$311$		−	24.2295i		−	1.37393i	0.726691	−	0.686964i	$-0.241057\pi$
$312$		0			0
$313$	−3.44054	+	3.44054i	−0.194471	+	0.194471i	−0.797625	−	0.603154i	$-0.793910\pi$
$313$	−3.44054	+	3.44054i	−0.194471	+	0.194471i	0.603154	+	0.797625i	$0.293910\pi$
$314$	−21.5885			−1.21831
$315$		0			0
$316$	−6.68541			−0.376084
$317$	12.9198	−	12.9198i	0.725649	−	0.725649i	−0.244101	−	0.969750i	$-0.578493\pi$
$317$	12.9198	−	12.9198i	0.725649	−	0.725649i	0.969750	+	0.244101i	$0.0784927\pi$
$318$		0			0
$319$			37.0349i			2.07355i
$320$		0			0
$321$		0			0
$322$	−1.38459	−	1.38459i	−0.0771604	−	0.0771604i
$323$		0			0
$324$		0			0
$325$		0			0
$326$			10.0624i			0.557304i
$327$		0			0
$328$	−6.32821	+	6.32821i	−0.349417	+	0.349417i
$329$	4.32176			0.238267
$330$		0			0
$331$	8.76831			0.481950			0.240975	−	0.970531i	$-0.422533\pi$
$331$	8.76831			0.481950			0.240975	+	0.970531i	$0.422533\pi$
$332$	−11.3427	+	11.3427i	−0.622512	+	0.622512i
$333$		0			0
$334$		−	23.6355i		−	1.29328i
$335$		0			0
$336$		0			0
$337$	12.3427	+	12.3427i	0.672350	+	0.672350i	0.958257	−	0.285907i	$-0.0922949\pi$
$337$	12.3427	+	12.3427i	0.672350	+	0.672350i	−0.285907	+	0.958257i	$0.592295\pi$
$338$	5.14226	+	5.14226i	0.279702	+	0.279702i
$339$		0			0
$340$		0			0
$341$		−	15.0414i		−	0.814540i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	8.32176			0.448679
$345$		0			0
$346$	−20.9082			−1.12403
$347$	5.17157	−	5.17157i	0.277625	−	0.277625i	−0.554535	−	0.832160i	$-0.687104\pi$
$347$	5.17157	−	5.17157i	0.277625	−	0.277625i	0.832160	+	0.554535i	$0.187104\pi$
$348$		0			0
$349$		−	28.9363i		−	1.54892i	−0.632620	−	0.774462i	$-0.718021\pi$
$349$		−	28.9363i		−	1.54892i	0.632620	−	0.774462i	$-0.281979\pi$
$350$		0			0
$351$		0			0
$352$	4.49978	+	4.49978i	0.239839	+	0.239839i
$353$	10.3637	+	10.3637i	0.551601	+	0.551601i	0.926903	−	0.375301i	$-0.122461\pi$
$353$	10.3637	+	10.3637i	0.551601	+	0.551601i	−0.375301	+	0.926903i	$0.622461\pi$
$354$		0			0
$355$		0			0
$356$			11.8371i			0.627365i
$357$		0			0
$358$	8.49978	−	8.49978i	0.449227	−	0.449227i
$359$	13.2308			0.698295			0.349148	−	0.937068i	$-0.386471\pi$
$359$	13.2308			0.698295			0.349148	+	0.937068i	$0.386471\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$	12.3910	−	12.3910i	0.651259	−	0.651259i
$363$		0			0
$364$			2.39327i			0.125441i
$365$		0			0
$366$		0			0
$367$	3.20943	+	3.20943i	0.167531	+	0.167531i	0.785893	−	0.618362i	$-0.212204\pi$
$367$	3.20943	+	3.20943i	0.167531	+	0.167531i	−0.618362	+	0.785893i	$0.712204\pi$
$368$	−1.38459	−	1.38459i	−0.0721770	−	0.0721770i
$369$		0			0
$370$		0			0
$371$			0.272260i			0.0141350i
$372$		0			0
$373$	2.26897	−	2.26897i	0.117483	−	0.117483i	−0.645921	−	0.763404i	$-0.723527\pi$
$373$	2.26897	−	2.26897i	0.117483	−	0.117483i	0.763404	+	0.645921i	$0.223527\pi$
$374$	8.81108			0.455610
$375$		0			0
$376$	4.32176			0.222878
$377$	−9.84875	+	9.84875i	−0.507236	+	0.507236i
$378$		0			0
$379$			2.39792i			0.123173i	0.998102	+	0.0615865i	$0.0196160\pi$
$379$			2.39792i			0.123173i	−0.998102	+	0.0615865i	$0.980384\pi$
$380$		0			0
$381$		0			0
$382$	4.45504	+	4.45504i	0.227940	+	0.227940i
$383$	−16.6838	−	16.6838i	−0.852503	−	0.852503i	0.137938	−	0.990441i	$-0.455952\pi$
$383$	−16.6838	−	16.6838i	−0.852503	−	0.852503i	−0.990441	+	0.137938i	$0.955952\pi$
$384$		0			0
$385$		0			0
$386$		−	16.4664i		−	0.838119i
$387$		0			0
$388$	9.39866	−	9.39866i	0.477144	−	0.477144i
$389$	−22.0782			−1.11941			−0.559706	−	0.828691i	$-0.689086\pi$
$389$	−22.0782			−1.11941			−0.559706	+	0.828691i	$0.689086\pi$
$390$		0			0
$391$	−2.71119			−0.137111
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$		0			0
$394$		−	2.72730i		−	0.137399i
$395$		0			0
$396$		0			0
$397$	−20.9717	−	20.9717i	−1.05254	−	1.05254i	−0.998541	−	0.0540003i	$-0.982803\pi$
$397$	−20.9717	−	20.9717i	−1.05254	−	1.05254i	−0.0540003	−	0.998541i	$-0.517197\pi$
$398$	4.01450	+	4.01450i	0.201229	+	0.201229i
$399$		0			0
$400$		0			0
$401$		−	9.29574i		−	0.464207i	−0.972691	−	0.232103i	$-0.925439\pi$
$401$		−	9.29574i		−	0.464207i	0.972691	−	0.232103i	$-0.0745608\pi$
$402$		0			0
$403$	4.00000	−	4.00000i	0.199254	−	0.199254i
$404$	−16.0501			−0.798524
$405$		0			0
$406$	5.81975			0.288829
$407$	−0.999561	+	0.999561i	−0.0495464	+	0.0495464i
$408$		0			0
$409$		−	34.2367i		−	1.69289i	−0.532472	−	0.846447i	$-0.678737\pi$
$409$		−	34.2367i		−	1.69289i	0.532472	−	0.846447i	$-0.321263\pi$
$410$		0			0
$411$		0			0
$412$	−0.706797	−	0.706797i	−0.0348214	−	0.0348214i
$413$	−7.34271	−	7.34271i	−0.361311	−	0.361311i
$414$		0			0
$415$		0			0
$416$			2.39327i			0.117340i
$417$		0			0
$418$		0			0
$419$	13.7753			0.672969			0.336484	−	0.941689i	$-0.390762\pi$
$419$	13.7753			0.672969			0.336484	+	0.941689i	$0.390762\pi$
$420$		0			0
$421$	10.6283			0.517991			0.258996	−	0.965878i	$-0.416608\pi$
$421$	10.6283			0.517991			0.258996	+	0.965878i	$0.416608\pi$
$422$	5.59762	−	5.59762i	0.272488	−	0.272488i
$423$		0			0
$424$			0.272260i			0.0132221i
$425$		0			0
$426$		0			0
$427$	0.692297	+	0.692297i	0.0335026	+	0.0335026i
$428$	−9.51384	−	9.51384i	−0.459869	−	0.459869i
$429$		0			0
$430$		0			0
$431$			18.8877i			0.909787i	0.890546	+	0.454893i	$0.150323\pi$
$431$			18.8877i			0.909787i	−0.890546	+	0.454893i	$0.849677\pi$
$432$		0			0
$433$	19.3697	−	19.3697i	0.930846	−	0.930846i	−0.0669125	−	0.997759i	$-0.521315\pi$
$433$	19.3697	−	19.3697i	0.930846	−	0.930846i	0.997759	+	0.0669125i	$0.0213149\pi$
$434$	−2.36365			−0.113459
$435$		0			0
$436$	14.9577			0.716343
$437$		0			0
$438$		0			0
$439$			4.86628i			0.232255i	0.993234	+	0.116127i	$0.0370481\pi$
$439$			4.86628i			0.232255i	−0.993234	+	0.116127i	$0.962952\pi$
$440$		0			0
$441$		0			0
$442$	2.34315	+	2.34315i	0.111452	+	0.111452i
$443$	−7.17070	−	7.17070i	−0.340690	−	0.340690i	0.515937	−	0.856627i	$-0.327444\pi$
$443$	−7.17070	−	7.17070i	−0.340690	−	0.340690i	−0.856627	+	0.515937i	$0.827444\pi$
$444$		0			0
$445$		0			0
$446$			11.7977i			0.558640i
$447$		0			0
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	−8.87093			−0.418645			−0.209323	−	0.977847i	$-0.567126\pi$
$449$	−8.87093			−0.418645			−0.209323	+	0.977847i	$0.567126\pi$
$450$		0			0
$451$	−56.9511			−2.68172
$452$	−9.22170	+	9.22170i	−0.433752	+	0.433752i
$453$		0			0
$454$		−	4.62829i		−	0.217217i
$455$		0			0
$456$		0			0
$457$	−4.27270	−	4.27270i	−0.199868	−	0.199868i	0.600075	−	0.799944i	$-0.295137\pi$
$457$	−4.27270	−	4.27270i	−0.199868	−	0.199868i	−0.799944	+	0.600075i	$0.795137\pi$
$458$	16.3271	+	16.3271i	0.762918	+	0.762918i
$459$		0			0
$460$		0			0
$461$			0.771724i			0.0359428i	0.999839	+	0.0179714i	$0.00572077\pi$
$461$			0.771724i			0.0359428i	−0.999839	+	0.0179714i	$0.994279\pi$
$462$		0			0
$463$	19.6150	−	19.6150i	0.911585	−	0.911585i	−0.0848121	−	0.996397i	$-0.527029\pi$
$463$	19.6150	−	19.6150i	0.911585	−	0.911585i	0.996397	+	0.0848121i	$0.0270290\pi$
$464$	5.81975			0.270175
$465$		0			0
$466$	−7.39748			−0.342682
$467$	8.18848	−	8.18848i	0.378918	−	0.378918i	−0.491794	−	0.870712i	$-0.663659\pi$
$467$	8.18848	−	8.18848i	0.378918	−	0.378918i	0.870712	+	0.491794i	$0.163659\pi$
$468$		0			0
$469$			13.9786i			0.645473i
$470$		0			0
$471$		0			0
$472$	−7.34271	−	7.34271i	−0.337975	−	0.337975i
$473$	37.4461	+	37.4461i	1.72177	+	1.72177i
$474$		0			0
$475$		0			0
$476$		−	1.38459i		−	0.0634628i
$477$		0			0
$478$	−3.72774	+	3.72774i	−0.170503	+	0.170503i
$479$	21.0833			0.963322			0.481661	−	0.876358i	$-0.340034\pi$
$479$	21.0833			0.963322			0.481661	+	0.876358i	$0.340034\pi$
$480$		0			0
$481$	−0.531630			−0.0242403
$482$	−3.72836	+	3.72836i	−0.169822	+	0.169822i
$483$		0			0
$484$			29.4961i			1.34073i
$485$		0			0
$486$		0			0
$487$	20.6983	+	20.6983i	0.937930	+	0.937930i	0.998183	−	0.0602535i	$-0.0191909\pi$
$487$	20.6983	+	20.6983i	0.937930	+	0.937930i	−0.0602535	+	0.998183i	$0.519191\pi$
$488$	0.692297	+	0.692297i	0.0313388	+	0.0313388i
$489$		0			0
$490$		0			0
$491$		−	10.2799i		−	0.463924i	−0.972725	−	0.231962i	$-0.925485\pi$
$491$		−	10.2799i		−	0.463924i	0.972725	−	0.231962i	$-0.0745146\pi$
$492$		0			0
$493$	5.69786	−	5.69786i	0.256619	−	0.256619i
$494$		0			0
$495$		0			0
$496$	−2.36365			−0.106131
$497$	8.72730	−	8.72730i	0.391473	−	0.391473i
$498$		0			0
$499$		−	5.16711i		−	0.231312i	−0.993289	−	0.115656i	$-0.963103\pi$
$499$		−	5.16711i		−	0.231312i	0.993289	−	0.115656i	$-0.0368970\pi$
$500$		0			0
$501$		0			0
$502$	14.3842	+	14.3842i	0.641996	+	0.641996i
$503$	−0.741801	−	0.741801i	−0.0330753	−	0.0330753i	0.690376	−	0.723451i	$-0.257445\pi$
$503$	−0.741801	−	0.741801i	−0.0330753	−	0.0330753i	−0.723451	+	0.690376i	$0.757445\pi$
$504$		0			0
$505$		0			0
$506$		−	12.4607i		−	0.553948i
$507$		0			0
$508$	5.38459	−	5.38459i	0.238903	−	0.238903i
$509$	1.96723			0.0871958			0.0435979	−	0.999049i	$-0.486118\pi$
$509$	1.96723			0.0871958			0.0435979	+	0.999049i	$0.486118\pi$
$510$		0			0
$511$	6.66553			0.294866
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			3.53838i			0.156071i
$515$		0			0
$516$		0			0
$517$	19.4470	+	19.4470i	0.855278	+	0.855278i
$518$	0.157074	+	0.157074i	0.00690142	+	0.00690142i
$519$		0			0
$520$		0			0
$521$			5.19146i			0.227442i	0.993513	+	0.113721i	$0.0362770\pi$
$521$			5.19146i			0.227442i	−0.993513	+	0.113721i	$0.963723\pi$
$522$		0			0
$523$	28.2295	−	28.2295i	1.23439	−	1.23439i	0.272129	−	0.962261i	$-0.412272\pi$
$523$	28.2295	−	28.2295i	1.23439	−	1.23439i	0.962261	−	0.272129i	$-0.0877277\pi$
$524$	−13.2718			−0.579782
$525$		0			0
$526$	17.9581			0.783011
$527$	−2.31415	+	2.31415i	−0.100806	+	0.100806i
$528$		0			0
$529$		−	19.1658i		−	0.833295i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−15.1451	−	15.1451i	−0.656007	−	0.656007i
$534$		0			0
$535$		0			0
$536$			13.9786i			0.603784i
$537$		0			0
$538$	19.0350	−	19.0350i	0.820657	−	0.820657i
$539$	6.36365			0.274102
$540$		0			0
$541$	−14.9167			−0.641317			−0.320659	−	0.947195i	$-0.603904\pi$
$541$	−14.9167			−0.641317			−0.320659	+	0.947195i	$0.603904\pi$
$542$	16.3568	−	16.3568i	0.702583	−	0.702583i
$543$		0			0
$544$		−	1.38459i		−	0.0593640i
$545$		0			0
$546$		0			0
$547$	14.8839	+	14.8839i	0.636391	+	0.636391i	0.949663	−	0.313272i	$-0.101425\pi$
$547$	14.8839	+	14.8839i	0.636391	+	0.636391i	−0.313272	+	0.949663i	$0.601425\pi$
$548$	−3.56484	−	3.56484i	−0.152283	−	0.152283i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−4.72730	+	4.72730i	−0.201025	+	0.201025i
$554$	−17.2917			−0.734654
$555$		0			0
$556$	−1.41359			−0.0599497
$557$	−16.1925	+	16.1925i	−0.686099	+	0.686099i	−0.961367	−	0.275268i	$-0.911233\pi$
$557$	−16.1925	+	16.1925i	−0.686099	+	0.686099i	0.275268	+	0.961367i	$0.411233\pi$
$558$		0			0
$559$			19.9162i			0.842367i
$560$		0			0
$561$		0			0
$562$	−7.38416	−	7.38416i	−0.311482	−	0.311482i
$563$	−4.69830	−	4.69830i	−0.198010	−	0.198010i	0.601136	−	0.799146i	$-0.294715\pi$
$563$	−4.69830	−	4.69830i	−0.198010	−	0.198010i	−0.799146	+	0.601136i	$0.794715\pi$
$564$		0			0
$565$		0			0
$566$			32.4671i			1.36469i
$567$		0			0
$568$	8.72730	−	8.72730i	0.366189	−	0.366189i
$569$	38.1643			1.59993			0.799965	−	0.600046i	$-0.204851\pi$
$569$	38.1643			1.59993			0.799965	+	0.600046i	$0.204851\pi$
$570$		0			0
$571$	−24.6008			−1.02951			−0.514755	−	0.857337i	$-0.672117\pi$
$571$	−24.6008			−1.02951			−0.514755	+	0.857337i	$0.672117\pi$
$572$	−10.7692	+	10.7692i	−0.450282	+	0.450282i
$573$		0			0
$574$			8.94944i			0.373542i
$575$		0			0
$576$		0			0
$577$	8.01318	+	8.01318i	0.333593	+	0.333593i	0.853949	−	0.520356i	$-0.174201\pi$
$577$	8.01318	+	8.01318i	0.333593	+	0.333593i	−0.520356	+	0.853949i	$0.674201\pi$
$578$	10.6652	+	10.6652i	0.443615	+	0.443615i
$579$		0			0
$580$		0			0
$581$			16.0410i			0.665493i
$582$		0			0
$583$	−1.22511	+	1.22511i	−0.0507388	+	0.0507388i
$584$	6.66553			0.275822
$585$		0			0
$586$	26.3628			1.08904
$587$	7.42648	−	7.42648i	0.306524	−	0.306524i	−0.537036	−	0.843559i	$-0.680456\pi$
$587$	7.42648	−	7.42648i	0.306524	−	0.306524i	0.843559	+	0.537036i	$0.180456\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.157074	+	0.157074i	0.00645568	+	0.00645568i
$593$	−13.8157	−	13.8157i	−0.567344	−	0.567344i	0.364040	−	0.931383i	$-0.381397\pi$
$593$	−13.8157	−	13.8157i	−0.567344	−	0.567344i	−0.931383	+	0.364040i	$0.881397\pi$
$594$		0			0
$595$		0			0
$596$			20.0609i			0.821726i
$597$		0			0
$598$	3.31371	−	3.31371i	0.135508	−	0.135508i
$599$	−0.643527			−0.0262938			−0.0131469	−	0.999914i	$-0.504185\pi$
$599$	−0.643527			−0.0262938			−0.0131469	+	0.999914i	$0.504185\pi$
$600$		0			0
$601$	20.0548			0.818051			0.409026	−	0.912523i	$-0.365869\pi$
$601$	20.0548			0.818051			0.409026	+	0.912523i	$0.365869\pi$
$602$	5.88438	−	5.88438i	0.239829	−	0.239829i
$603$		0			0
$604$		−	8.81108i		−	0.358518i
$605$		0			0
$606$		0			0
$607$	16.3423	+	16.3423i	0.663312	+	0.663312i	0.956159	−	0.292847i	$-0.0946027\pi$
$607$	16.3423	+	16.3423i	0.663312	+	0.663312i	−0.292847	+	0.956159i	$0.594603\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			10.3431i			0.418439i
$612$		0			0
$613$	−6.29797	+	6.29797i	−0.254373	+	0.254373i	−0.822761	−	0.568388i	$-0.807567\pi$
$613$	−6.29797	+	6.29797i	−0.254373	+	0.254373i	0.568388	+	0.822761i	$0.307567\pi$
$614$	−1.02856			−0.0415093
$615$		0			0
$616$	6.36365			0.256399
$617$	−15.3632	+	15.3632i	−0.618500	+	0.618500i	−0.945146	−	0.326647i	$-0.894081\pi$
$617$	−15.3632	+	15.3632i	−0.618500	+	0.618500i	0.326647	+	0.945146i	$0.394081\pi$
$618$		0			0
$619$		−	35.1462i		−	1.41264i	−0.707891	−	0.706322i	$-0.750353\pi$
$619$		−	35.1462i		−	1.41264i	0.707891	−	0.706322i	$-0.249647\pi$
$620$		0			0
$621$		0			0
$622$	−17.1328	−	17.1328i	−0.686964	−	0.686964i
$623$	8.37010	+	8.37010i	0.335341	+	0.335341i
$624$		0			0
$625$		0			0
$626$			4.86566i			0.194471i
$627$		0			0
$628$	−15.2654	+	15.2654i	−0.609155	+	0.609155i
$629$	0.307568			0.0122635
$630$		0			0
$631$	22.5864			0.899151			0.449575	−	0.893242i	$-0.351575\pi$
$631$	22.5864			0.899151			0.449575	+	0.893242i	$0.351575\pi$
$632$	−4.72730	+	4.72730i	−0.188042	+	0.188042i
$633$		0			0
$634$		−	18.2714i		−	0.725649i
$635$		0			0
$636$		0			0
$637$	1.69230	+	1.69230i	0.0670513	+	0.0670513i
$638$	26.1876	+	26.1876i	1.03678	+	1.03678i
$639$		0			0
$640$		0			0
$641$			6.90352i			0.272673i	0.990663	+	0.136336i	$0.0435328\pi$
$641$			6.90352i			0.272673i	−0.990663	+	0.136336i	$0.956467\pi$
$642$		0			0
$643$	−30.4542	+	30.4542i	−1.20100	+	1.20100i	−0.227131	+	0.973864i	$0.572934\pi$
$643$	−30.4542	+	30.4542i	−1.20100	+	1.20100i	−0.973864	+	0.227131i	$0.927066\pi$
$644$	−1.95811			−0.0771604
$645$		0			0
$646$		0			0
$647$	−13.9726	+	13.9726i	−0.549320	+	0.549320i	−0.926244	−	0.376924i	$-0.876982\pi$
$647$	−13.9726	+	13.9726i	−0.549320	+	0.549320i	0.376924	+	0.926244i	$0.376982\pi$
$648$		0			0
$649$		−	66.0811i		−	2.59391i
$650$		0			0
$651$		0			0
$652$	7.11519	+	7.11519i	0.278652	+	0.278652i
$653$	7.99597	+	7.99597i	0.312906	+	0.312906i	0.846035	−	0.533128i	$-0.178984\pi$
$653$	7.99597	+	7.99597i	0.312906	+	0.312906i	−0.533128	+	0.846035i	$0.678984\pi$
$654$		0			0
$655$		0			0
$656$			8.94944i			0.349417i
$657$		0			0
$658$	3.05595	−	3.05595i	0.119133	−	0.119133i
$659$	27.9020			1.08691			0.543454	−	0.839439i	$-0.317116\pi$
$659$	27.9020			1.08691			0.543454	+	0.839439i	$0.317116\pi$
$660$		0			0
$661$	−0.294519			−0.0114555			−0.00572774	−	0.999984i	$-0.501823\pi$
$661$	−0.294519			−0.0114555			−0.00572774	+	0.999984i	$0.501823\pi$
$662$	6.20013	−	6.20013i	0.240975	−	0.240975i
$663$		0			0
$664$			16.0410i			0.622512i
$665$		0			0
$666$		0			0
$667$	−8.05800	−	8.05800i	−0.312007	−	0.312007i
$668$	−16.7128	−	16.7128i	−0.646638	−	0.646638i
$669$		0			0
$670$		0			0
$671$			6.23037i			0.240521i
$672$		0			0
$673$	24.6569	−	24.6569i	0.950452	−	0.950452i	−0.0483773	−	0.998829i	$-0.515405\pi$
$673$	24.6569	−	24.6569i	0.950452	−	0.950452i	0.998829	+	0.0483773i	$0.0154050\pi$
$674$	17.4552			0.672350
$675$		0			0
$676$	7.27226			0.279702
$677$	28.7195	−	28.7195i	1.10378	−	1.10378i	0.109831	−	0.993950i	$-0.464969\pi$
$677$	28.7195	−	28.7195i	1.10378	−	1.10378i	0.993950	−	0.109831i	$-0.0350311\pi$
$678$		0			0
$679$		−	13.2917i		−	0.510089i
$680$		0			0
$681$		0			0
$682$	−10.6359	−	10.6359i	−0.407270	−	0.407270i
$683$	−0.221515	−	0.221515i	−0.00847605	−	0.00847605i	0.702856	−	0.711332i	$-0.251908\pi$
$683$	−0.221515	−	0.221515i	−0.00847605	−	0.00847605i	−0.711332	+	0.702856i	$0.751908\pi$
$684$		0			0
$685$		0			0
$686$		−	1.00000i		−	0.0381802i
$687$		0			0
$688$	5.88438	−	5.88438i	0.224340	−	0.224340i
$689$	−0.651591			−0.0248236
$690$		0			0
$691$	−36.2648			−1.37958			−0.689789	−	0.724010i	$-0.742297\pi$
$691$	−36.2648			−1.37958			−0.689789	+	0.724010i	$0.742297\pi$
$692$	−14.7843	+	14.7843i	−0.562015	+	0.562015i
$693$		0			0
$694$		−	7.31371i		−	0.277625i
$695$		0			0
$696$		0			0
$697$	8.76200	+	8.76200i	0.331885	+	0.331885i
$698$	−20.4610	−	20.4610i	−0.774462	−	0.774462i
$699$		0			0
$700$		0			0
$701$			21.0497i			0.795036i	0.917594	+	0.397518i	$0.130128\pi$
$701$			21.0497i			0.795036i	−0.917594	+	0.397518i	$0.869872\pi$
$702$		0			0
$703$		0			0
$704$	6.36365			0.239839
$705$		0			0
$706$	14.6564			0.551601
$707$	−11.3492	+	11.3492i	−0.426829	+	0.426829i
$708$		0			0
$709$		−	14.3617i		−	0.539366i	−0.962949	−	0.269683i	$-0.913081\pi$
$709$		−	14.3617i		−	0.539366i	0.962949	−	0.269683i	$-0.0869190\pi$
$710$		0			0
$711$		0			0
$712$	8.37010	+	8.37010i	0.313683	+	0.313683i
$713$	3.27270	+	3.27270i	0.122564	+	0.122564i
$714$		0			0
$715$		0			0
$716$		−	12.0205i		−	0.449227i
$717$		0			0
$718$	9.35560	−	9.35560i	0.349148	−	0.349148i
$719$	−16.9706			−0.632895			−0.316448	−	0.948610i	$-0.602490\pi$
$719$	−16.9706			−0.632895			−0.316448	+	0.948610i	$0.602490\pi$
$720$		0			0
$721$	−0.999561			−0.0372256
$722$	13.4350	−	13.4350i	0.500000	−	0.500000i
$723$		0			0
$724$		−	17.5236i		−	0.651259i
$725$		0			0
$726$		0			0
$727$	2.42692	+	2.42692i	0.0900095	+	0.0900095i	0.750678	−	0.660668i	$-0.229727\pi$
$727$	2.42692	+	2.42692i	0.0900095	+	0.0900095i	−0.660668	+	0.750678i	$0.729727\pi$
$728$	1.69230	+	1.69230i	0.0627207	+	0.0627207i
$729$		0			0
$730$		0			0
$731$		−	11.5223i		−	0.426167i
$732$		0			0
$733$	14.3701	−	14.3701i	0.530772	−	0.530772i	−0.390030	−	0.920802i	$-0.627536\pi$
$733$	14.3701	−	14.3701i	0.530772	−	0.530772i	0.920802	+	0.390030i	$0.127536\pi$
$734$	4.53882			0.167531
$735$		0			0
$736$	−1.95811			−0.0721770
$737$	−62.9007	+	62.9007i	−2.31698	+	2.31698i
$738$		0			0
$739$			38.0886i			1.40111i	0.713598	+	0.700556i	$0.247065\pi$
$739$			38.0886i			1.40111i	−0.713598	+	0.700556i	$0.752935\pi$
$740$		0			0
$741$		0			0
$742$	0.192517	+	0.192517i	0.00706751	+	0.00706751i
$743$	31.4965	+	31.4965i	1.15549	+	1.15549i	0.985434	+	0.170061i	$0.0543963\pi$
$743$	31.4965	+	31.4965i	1.15549	+	1.15549i	0.170061	+	0.985434i	$0.445604\pi$
$744$		0			0
$745$		0			0
$746$		−	3.20881i		−	0.117483i
$747$		0			0
$748$	6.23037	−	6.23037i	0.227805	−	0.227805i
$749$	−13.4546			−0.491621
$750$		0			0
$751$	16.9511			0.618554			0.309277	−	0.950972i	$-0.399913\pi$
$751$	16.9511			0.618554			0.309277	+	0.950972i	$0.399913\pi$
$752$	3.05595	−	3.05595i	0.111439	−	0.111439i
$753$		0			0
$754$			13.9282i			0.507236i
$755$		0			0
$756$		0			0
$757$	2.34644	+	2.34644i	0.0852826	+	0.0852826i	0.748461	−	0.663179i	$-0.230793\pi$
$757$	2.34644	+	2.34644i	0.0852826	+	0.0852826i	−0.663179	+	0.748461i	$0.730793\pi$
$758$	1.69559	+	1.69559i	0.0615865	+	0.0615865i
$759$		0			0
$760$		0			0
$761$		−	3.07510i		−	0.111472i	−0.998446	−	0.0557361i	$-0.982249\pi$
$761$		−	3.07510i		−	0.111472i	0.998446	−	0.0557361i	$-0.0177506\pi$
$762$		0			0
$763$	10.5767	−	10.5767i	0.382901	−	0.382901i
$764$	6.30038			0.227940
$765$		0			0
$766$	−23.5945			−0.852503
$767$	17.5731	−	17.5731i	0.634527	−	0.634527i
$768$		0			0
$769$		−	17.4666i		−	0.629862i	−0.949115	−	0.314931i	$-0.898019\pi$
$769$		−	17.4666i		−	0.629862i	0.949115	−	0.314931i	$-0.101981\pi$
$770$		0			0
$771$		0			0
$772$	−11.6435	−	11.6435i	−0.419060	−	0.419060i
$773$	−38.6076	−	38.6076i	−1.38862	−	1.38862i	−0.828225	−	0.560395i	$-0.810649\pi$
$773$	−38.6076	−	38.6076i	−1.38862	−	1.38862i	−0.560395	−	0.828225i	$-0.689351\pi$
$774$		0			0
$775$		0			0
$776$		−	13.2917i		−	0.477144i
$777$		0			0
$778$	−15.6117	+	15.6117i	−0.559706	+	0.559706i
$779$		0			0
$780$		0			0
$781$	78.5419			2.81045
$782$	−1.91710	+	1.91710i	−0.0685554	+	0.0685554i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$		0			0
$786$		0			0
$787$	12.3076	+	12.3076i	0.438717	+	0.438717i	0.891580	−	0.452863i	$-0.149597\pi$
$787$	12.3076	+	12.3076i	0.438717	+	0.438717i	−0.452863	+	0.891580i	$0.649597\pi$
$788$	−1.92849	−	1.92849i	−0.0686997	−	0.0686997i
$789$		0			0
$790$		0			0
$791$			13.0414i			0.463701i
$792$		0			0
$793$	−1.65685	+	1.65685i	−0.0588366	+	0.0588366i
$794$	−29.6585			−1.05254
$795$		0			0
$796$	5.67736			0.201229
$797$	4.88543	−	4.88543i	0.173051	−	0.173051i	−0.615267	−	0.788318i	$-0.710952\pi$
$797$	4.88543	−	4.88543i	0.173051	−	0.173051i	0.788318	+	0.615267i	$0.210952\pi$
$798$		0			0
$799$		−	5.98389i		−	0.211695i
$800$		0			0
$801$		0			0
$802$	−6.57308	−	6.57308i	−0.232103	−	0.232103i
$803$	29.9934	+	29.9934i	1.05844	+	1.05844i
$804$		0			0
$805$		0			0
$806$		−	5.65685i		−	0.199254i
$807$		0			0
$808$	−11.3492	+	11.3492i	−0.399262	+	0.399262i
$809$	−6.30907			−0.221815			−0.110907	−	0.993831i	$-0.535376\pi$
$809$	−6.30907			−0.221815			−0.110907	+	0.993831i	$0.535376\pi$
$810$		0			0
$811$	41.6632			1.46299			0.731496	−	0.681846i	$-0.238823\pi$
$811$	41.6632			1.46299			0.731496	+	0.681846i	$0.238823\pi$
$812$	4.11519	−	4.11519i	0.144415	−	0.144415i
$813$		0			0
$814$			1.41359i			0.0495464i
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−24.2090	−	24.2090i	−0.846447	−	0.846447i
$819$		0			0
$820$		0			0
$821$		−	46.4552i		−	1.62130i	−0.585532	−	0.810649i	$-0.699114\pi$
$821$		−	46.4552i		−	1.62130i	0.585532	−	0.810649i	$-0.300886\pi$
$822$		0			0
$823$	27.2942	−	27.2942i	0.951417	−	0.951417i	−0.0474559	−	0.998873i	$-0.515111\pi$
$823$	27.2942	−	27.2942i	0.951417	−	0.951417i	0.998873	+	0.0474559i	$0.0151114\pi$
$824$	−0.999561			−0.0348214
$825$		0			0
$826$	−10.3842			−0.361311
$827$	−37.6528	+	37.6528i	−1.30932	+	1.30932i	−0.387409	+	0.921908i	$0.626630\pi$
$827$	−37.6528	+	37.6528i	−1.30932	+	1.30932i	−0.921908	+	0.387409i	$0.873370\pi$
$828$		0			0
$829$		−	16.9791i		−	0.589707i	−0.955542	−	0.294853i	$-0.904729\pi$
$829$		−	16.9791i		−	0.589707i	0.955542	−	0.294853i	$-0.0952708\pi$
$830$		0			0
$831$		0			0
$832$	1.69230	+	1.69230i	0.0586699	+	0.0586699i
$833$	−0.979056	−	0.979056i	−0.0339223	−	0.0339223i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	9.74063	−	9.74063i	0.336484	−	0.336484i
$839$	2.63064			0.0908197			0.0454099	−	0.998968i	$-0.485541\pi$
$839$	2.63064			0.0908197			0.0454099	+	0.998968i	$0.485541\pi$
$840$		0			0
$841$	4.86951			0.167914
$842$	7.51534	−	7.51534i	0.258996	−	0.258996i
$843$		0			0
$844$		−	7.91622i		−	0.272488i
$845$		0			0
$846$		0			0
$847$	20.8569	+	20.8569i	0.716650	+	0.716650i
$848$	0.192517	+	0.192517i	0.00661105	+	0.00661105i
$849$		0			0
$850$		0			0
$851$		−	0.434966i		−	0.0149105i
$852$		0			0
$853$	35.6700	−	35.6700i	1.22132	−	1.22132i	0.254155	−	0.967163i	$-0.418203\pi$
$853$	35.6700	−	35.6700i	1.22132	−	1.22132i	0.967163	−	0.254155i	$-0.0817975\pi$
$854$	0.979056			0.0335026
$855$		0			0
$856$	−13.4546			−0.459869
$857$	2.97818	−	2.97818i	0.101733	−	0.101733i	−0.654409	−	0.756141i	$-0.727082\pi$
$857$	2.97818	−	2.97818i	0.101733	−	0.101733i	0.756141	+	0.654409i	$0.227082\pi$
$858$		0			0
$859$		−	30.9634i		−	1.05646i	−0.849102	−	0.528228i	$-0.822856\pi$
$859$		−	30.9634i		−	1.05646i	0.849102	−	0.528228i	$-0.177144\pi$
$860$		0			0
$861$		0			0
$862$	13.3556	+	13.3556i	0.454893	+	0.454893i
$863$	0.602516	+	0.602516i	0.0205099	+	0.0205099i	0.717287	−	0.696777i	$-0.245383\pi$
$863$	0.602516	+	0.602516i	0.0205099	+	0.0205099i	−0.696777	+	0.717287i	$0.745383\pi$
$864$		0			0
$865$		0			0
$866$		−	27.3928i		−	0.930846i
$867$		0			0
$868$	−1.67135	+	1.67135i	−0.0567294	+	0.0567294i
$869$	−42.5436			−1.44319
$870$		0			0
$871$	−33.4546			−1.13357
$872$	10.5767	−	10.5767i	0.358171	−	0.358171i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−28.7369	−	28.7369i	−0.970376	−	0.970376i	0.0291975	−	0.999574i	$-0.490705\pi$
$877$	−28.7369	−	28.7369i	−0.970376	−	0.970376i	−0.999574	+	0.0291975i	$0.990705\pi$
$878$	3.44098	+	3.44098i	0.116127	+	0.116127i
$879$		0			0
$880$		0			0
$881$		−	46.7691i		−	1.57569i	−0.615873	−	0.787845i	$-0.711197\pi$
$881$		−	46.7691i		−	1.57569i	0.615873	−	0.787845i	$-0.288803\pi$
$882$		0			0
$883$	27.4285	−	27.4285i	0.923041	−	0.923041i	−0.0742022	−	0.997243i	$-0.523641\pi$
$883$	27.4285	−	27.4285i	0.923041	−	0.923041i	0.997243	+	0.0742022i	$0.0236410\pi$
$884$	3.31371			0.111452
$885$		0			0
$886$	−10.1409			−0.340690
$887$	16.1393	−	16.1393i	0.541904	−	0.541904i	−0.382183	−	0.924087i	$-0.624827\pi$
$887$	16.1393	−	16.1393i	0.541904	−	0.541904i	0.924087	+	0.382183i	$0.124827\pi$
$888$		0			0
$889$		−	7.61497i		−	0.255398i
$890$		0			0
$891$		0			0
$892$	8.34227	+	8.34227i	0.279320	+	0.279320i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		−	1.00000i		−	0.0334077i
$897$		0			0
$898$	−6.27270	+	6.27270i	−0.209323	+	0.209323i
$899$	−13.7559			−0.458784
$900$		0			0
$901$	0.376969			0.0125587
$902$	−40.2705	+	40.2705i	−1.34086	+	1.34086i
$903$		0			0
$904$			13.0414i			0.433752i
$905$		0			0
$906$		0			0
$907$	2.57067	+	2.57067i	0.0853576	+	0.0853576i	0.748496	−	0.663139i	$-0.230776\pi$
$907$	2.57067	+	2.57067i	0.0853576	+	0.0853576i	−0.663139	+	0.748496i	$0.730776\pi$
$908$	−3.27270	−	3.27270i	−0.108608	−	0.108608i
$909$		0			0
$910$		0			0
$911$			37.2138i			1.23295i	0.787375	+	0.616474i	$0.211440\pi$
$911$			37.2138i			1.23295i	−0.787375	+	0.616474i	$0.788560\pi$
$912$		0			0
$913$	−72.1810	+	72.1810i	−2.38884	+	2.38884i
$914$	−6.04251			−0.199868
$915$		0			0
$916$	23.0901			0.762918
$917$	−9.38459	+	9.38459i	−0.309907	+	0.309907i
$918$		0			0
$919$		−	0.126540i		−	0.00417416i	−0.999998	−	0.00208708i	$-0.999336\pi$
$919$		−	0.126540i		−	0.00417416i	0.999998	−	0.00208708i	$-0.000664339\pi$
$920$		0			0
$921$		0			0
$922$	0.545691	+	0.545691i	0.0179714	+	0.0179714i
$923$	20.8868	+	20.8868i	0.687497	+	0.687497i
$924$		0			0
$925$		0			0
$926$		−	27.7398i		−	0.911585i
$927$		0			0
$928$	4.11519	−	4.11519i	0.135088	−	0.135088i
$929$	−44.7882			−1.46945			−0.734727	−	0.678363i	$-0.762690\pi$
$929$	−44.7882			−1.46945			−0.734727	+	0.678363i	$0.762690\pi$
$930$		0			0
$931$		0			0
$932$	−5.23081	+	5.23081i	−0.171341	+	0.171341i
$933$		0			0
$934$		−	11.5803i		−	0.378918i
$935$		0			0
$936$		0			0
$937$	27.9303	+	27.9303i	0.912443	+	0.912443i	0.996464	−	0.0840213i	$-0.0267764\pi$
$937$	27.9303	+	27.9303i	0.912443	+	0.912443i	−0.0840213	+	0.996464i	$0.526776\pi$
$938$	9.88438	+	9.88438i	0.322736	+	0.322736i
$939$		0			0
$940$		0			0
$941$		−	18.3233i		−	0.597321i	−0.954359	−	0.298661i	$-0.903460\pi$
$941$		−	18.3233i		−	0.597321i	0.954359	−	0.298661i	$-0.0965399\pi$
$942$		0			0
$943$	12.3913	−	12.3913i	0.403518	−	0.403518i
$944$	−10.3842			−0.337975
$945$		0			0
$946$	52.9568			1.72177
$947$	−32.1360	+	32.1360i	−1.04428	+	1.04428i	−0.0453061	+	0.998973i	$0.514426\pi$
$947$	−32.1360	+	32.1360i	−1.04428	+	1.04428i	−0.998973	+	0.0453061i	$0.985574\pi$
$948$		0			0
$949$			15.9524i			0.517837i
$950$		0			0
$951$		0			0
$952$	−0.979056	−	0.979056i	−0.0317314	−	0.0317314i
$953$	1.74001	+	1.74001i	0.0563644	+	0.0563644i	0.734727	−	0.678363i	$-0.237310\pi$
$953$	1.74001	+	1.74001i	0.0563644	+	0.0563644i	−0.678363	+	0.734727i	$0.737310\pi$
$954$		0			0
$955$		0			0
$956$			5.27182i			0.170503i
$957$		0			0
$958$	14.9082	−	14.9082i	0.481661	−	0.481661i
$959$	−5.04145			−0.162797
$960$		0			0
$961$	−25.4132			−0.819779
$962$	−0.375919	+	0.375919i	−0.0121201	+	0.0121201i
$963$		0			0
$964$			5.27270i			0.169822i
$965$		0			0
$966$		0			0
$967$	−19.7140	−	19.7140i	−0.633959	−	0.633959i	0.315100	−	0.949059i	$-0.397962\pi$
$967$	−19.7140	−	19.7140i	−0.633959	−	0.633959i	−0.949059	+	0.315100i	$0.897962\pi$
$968$	20.8569	+	20.8569i	0.670365	+	0.670365i
$969$		0			0
$970$		0			0
$971$			21.2308i			0.681329i	0.940185	+	0.340665i	$0.110652\pi$
$971$			21.2308i			0.681329i	−0.940185	+	0.340665i	$0.889348\pi$
$972$		0			0
$973$	−0.999561	+	0.999561i	−0.0320445	+	0.0320445i
$974$	29.2718			0.937930
$975$		0			0
$976$	0.979056			0.0313388
$977$	−12.3013	+	12.3013i	−0.393552	+	0.393552i	−0.875951	−	0.482399i	$-0.839765\pi$
$977$	−12.3013	+	12.3013i	−0.393552	+	0.393552i	0.482399	+	0.875951i	$0.339765\pi$
$978$		0			0
$979$			75.3272i			2.40747i
$980$		0			0
$981$		0			0
$982$	−7.26897	−	7.26897i	−0.231962	−	0.231962i
$983$	23.3087	+	23.3087i	0.743433	+	0.743433i	0.973237	−	0.229804i	$-0.0738084\pi$
$983$	23.3087	+	23.3087i	0.743433	+	0.743433i	−0.229804	+	0.973237i	$0.573808\pi$
$984$		0			0
$985$		0			0
$986$		−	8.05800i		−	0.256619i
$987$		0			0
$988$		0			0
$989$	−16.2949			−0.518149
$990$		0			0
$991$	10.5606			0.335469			0.167735	−	0.985832i	$-0.446355\pi$
$991$	10.5606			0.335469			0.167735	+	0.985832i	$0.446355\pi$
$992$	−1.67135	+	1.67135i	−0.0530655	+	0.0530655i
$993$		0			0
$994$		−	12.3423i		−	0.391473i
$995$		0			0
$996$		0			0
$997$	−28.3973	−	28.3973i	−0.899353	−	0.899353i	0.0960261	−	0.995379i	$-0.469387\pi$
$997$	−28.3973	−	28.3973i	−0.899353	−	0.899353i	−0.995379	+	0.0960261i	$0.969387\pi$
$998$	−3.65370	−	3.65370i	−0.115656	−	0.115656i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.m.i.1457.3		8
3.2	odd	2		3150.2.m.j.1457.2		8
5.2	odd	4		630.2.m.d.323.3	yes	8
5.3	odd	4		3150.2.m.j.2843.1		8
5.4	even	2		630.2.m.c.197.2	✓	8
15.2	even	4		630.2.m.c.323.2	yes	8
15.8	even	4	inner	3150.2.m.i.2843.4		8
15.14	odd	2		630.2.m.d.197.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.m.c.197.2	✓	8	5.4	even	2
630.2.m.c.323.2	yes	8	15.2	even	4
630.2.m.d.197.3	yes	8	15.14	odd	2
630.2.m.d.323.3	yes	8	5.2	odd	4
3150.2.m.i.1457.3		8	1.1	even	1	trivial
3150.2.m.i.2843.4		8	15.8	even	4	inner
3150.2.m.j.1457.2		8	3.2	odd	2
3150.2.m.j.2843.1		8	5.3	odd	4

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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} -6.36365i q^{11} +(1.69230 - 1.69230i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-0.979056 + 0.979056i) q^{17} +(-4.49978 - 4.49978i) q^{22} +(1.38459 + 1.38459i) q^{23} -2.39327i q^{26} +(-0.707107 + 0.707107i) q^{28} -5.81975 q^{29} +2.36365 q^{31} +(-0.707107 + 0.707107i) q^{32} +1.38459i q^{34} +(-0.157074 - 0.157074i) q^{37} -8.94944i q^{41} +(-5.88438 + 5.88438i) q^{43} -6.36365 q^{44} +1.95811 q^{46} +(-3.05595 + 3.05595i) q^{47} +1.00000i q^{49} +(-1.69230 - 1.69230i) q^{52} +(-0.192517 - 0.192517i) q^{53} +1.00000i q^{56} +(-4.11519 + 4.11519i) q^{58} +10.3842 q^{59} -0.979056 q^{61} +(1.67135 - 1.67135i) q^{62} +1.00000i q^{64} +(-9.88438 - 9.88438i) q^{67} +(0.979056 + 0.979056i) q^{68} +12.3423i q^{71} +(-4.71324 + 4.71324i) q^{73} -0.222136 q^{74} +(-4.49978 + 4.49978i) q^{77} -6.68541i q^{79} +(-6.32821 - 6.32821i) q^{82} +(-11.3427 - 11.3427i) q^{83} +8.32176i q^{86} +(-4.49978 + 4.49978i) q^{88} -11.8371 q^{89} -2.39327 q^{91} +(1.38459 - 1.38459i) q^{92} +4.32176i q^{94} +(9.39866 + 9.39866i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 4 q^{13} - 8 q^{14} - 8 q^{16} + 4 q^{22} - 8 q^{23} - 24 q^{29} - 8 q^{31} + 4 q^{37} + 12 q^{43} - 24 q^{44} + 12 q^{47} - 4 q^{52} - 32 q^{53} - 12 q^{58} - 16 q^{59} - 4 q^{62} - 20 q^{67} - 36 q^{73} - 40 q^{74} + 4 q^{77} + 12 q^{82} - 56 q^{83} + 4 q^{88} - 72 q^{89} - 8 q^{92} + 4 q^{97}+O(q^{100}) \) 8 * q + 4 * q^13 - 8 * q^14 - 8 * q^16 + 4 * q^22 - 8 * q^23 - 24 * q^29 - 8 * q^31 + 4 * q^37 + 12 * q^43 - 24 * q^44 + 12 * q^47 - 4 * q^52 - 32 * q^53 - 12 * q^58 - 16 * q^59 - 4 * q^62 - 20 * q^67 - 36 * q^73 - 40 * q^74 + 4 * q^77 + 12 * q^82 - 56 * q^83 + 4 * q^88 - 72 * q^89 - 8 * q^92 + 4 * q^97

Introduction

L-functions

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