LMFDB - Embedded newform 1380.2.t.a.1057.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(1057,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1380.1057");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.t (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:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.14
Character	$\chi$	$=$	1380.1057
Dual form			1380.2.t.a.1333.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(0.951596 - 2.02348i) q^{5} +(-3.48236 + 3.48236i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(0.951596 - 2.02348i) q^{5} +(-3.48236 + 3.48236i) q^{7} -1.00000i q^{9} +2.73277i q^{11} +(-0.367971 + 0.367971i) q^{13} +(-0.757935 - 2.10370i) q^{15} +(-5.02066 + 5.02066i) q^{17} +5.91117 q^{19} +4.92480i q^{21} +(-3.87629 + 2.82390i) q^{23} +(-3.18893 - 3.85107i) q^{25} +(-0.707107 - 0.707107i) q^{27} +2.00084i q^{29} +2.49808 q^{31} +(1.93236 + 1.93236i) q^{33} +(3.73268 + 10.3603i) q^{35} +(-6.38531 + 6.38531i) q^{37} +0.520390i q^{39} -6.05805 q^{41} +(2.07971 + 2.07971i) q^{43} +(-2.02348 - 0.951596i) q^{45} +(4.01416 + 4.01416i) q^{47} -17.2536i q^{49} +7.10029i q^{51} +(0.794878 + 0.794878i) q^{53} +(5.52971 + 2.60050i) q^{55} +(4.17983 - 4.17983i) q^{57} +5.00908i q^{59} +9.72089i q^{61} +(3.48236 + 3.48236i) q^{63} +(0.394422 + 1.09474i) q^{65} +(-2.09702 + 2.09702i) q^{67} +(-0.744154 + 4.73775i) q^{69} +9.35585 q^{71} +(8.18100 - 8.18100i) q^{73} +(-4.97803 - 0.468202i) q^{75} +(-9.51650 - 9.51650i) q^{77} +2.90814 q^{79} -1.00000 q^{81} +(-7.48074 - 7.48074i) q^{83} +(5.38156 + 14.9368i) q^{85} +(1.41481 + 1.41481i) q^{87} -11.7859 q^{89} -2.56282i q^{91} +(1.76641 - 1.76641i) q^{93} +(5.62505 - 11.9611i) q^{95} +(-0.793720 + 0.793720i) q^{97} +2.73277 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{13} - 16 q^{23} - 8 q^{25} + 8 q^{31} + 8 q^{35} - 24 q^{41} + 8 q^{47} - 32 q^{55} - 24 q^{71} + 8 q^{73} + 32 q^{75} + 40 q^{77} - 48 q^{81} + 24 q^{85} - 40 q^{87}+O(q^{100}) $ 48 * q - 8 * q^13 - 16 * q^23 - 8 * q^25 + 8 * q^31 + 8 * q^35 - 24 * q^41 + 8 * q^47 - 32 * q^55 - 24 * q^71 + 8 * q^73 + 32 * q^75 + 40 * q^77 - 48 * q^81 + 24 * q^85 - 40 * q^87

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$-1$

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			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	0.951596	−	2.02348i	0.425567	−	0.904927i
$5$	0.951596	−	2.02348i	0.425567	−	0.904927i
$6$		0			0
$7$	−3.48236	+	3.48236i	−1.31621	+	1.31621i	−0.399454	+	0.916753i	$0.630800\pi$
$7$	−3.48236	+	3.48236i	−1.31621	+	1.31621i	−0.916753	+	0.399454i	$0.869200\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$			2.73277i			0.823963i	0.911192	+	0.411981i	$0.135163\pi$
$11$			2.73277i			0.823963i	−0.911192	+	0.411981i	$0.864837\pi$
$12$		0			0
$13$	−0.367971	+	0.367971i	−0.102057	+	0.102057i	−0.756292	−	0.654235i	$-0.772991\pi$
$13$	−0.367971	+	0.367971i	−0.102057	+	0.102057i	0.654235	+	0.756292i	$0.272991\pi$
$14$		0			0
$15$	−0.757935	−	2.10370i	−0.195698	−	0.543172i
$16$		0			0
$17$	−5.02066	+	5.02066i	−1.21769	+	1.21769i	−0.249251	+	0.968439i	$0.580184\pi$
$17$	−5.02066	+	5.02066i	−1.21769	+	1.21769i	−0.968439	+	0.249251i	$0.919816\pi$
$18$		0			0
$19$	5.91117			1.35612			0.678058	−	0.735008i	$-0.262822\pi$
$19$	5.91117			1.35612			0.678058	+	0.735008i	$0.262822\pi$
$20$		0			0
$21$			4.92480i			1.07468i
$22$		0			0
$23$	−3.87629	+	2.82390i	−0.808262	+	0.588823i
$23$	−3.87629	+	2.82390i	−0.808262	+	0.588823i
$24$		0			0
$25$	−3.18893	−	3.85107i	−0.637786	−	0.770214i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			2.00084i			0.371547i	0.982593	+	0.185773i	$0.0594790\pi$
$29$			2.00084i			0.371547i	−0.982593	+	0.185773i	$0.940521\pi$
$30$		0			0
$31$	2.49808			0.448669			0.224334	−	0.974512i	$-0.427979\pi$
$31$	2.49808			0.448669			0.224334	+	0.974512i	$0.427979\pi$
$32$		0			0
$33$	1.93236	+	1.93236i	0.336381	+	0.336381i
$34$		0			0
$35$	3.73268	+	10.3603i	0.630938	+	1.75121i
$36$		0			0
$37$	−6.38531	+	6.38531i	−1.04974	+	1.04974i	−0.0510416	+	0.998697i	$0.516254\pi$
$37$	−6.38531	+	6.38531i	−1.04974	+	1.04974i	−0.998697	+	0.0510416i	$0.983746\pi$
$38$		0			0
$39$			0.520390i			0.0833291i
$40$		0			0
$41$	−6.05805			−0.946109			−0.473054	−	0.881033i	$-0.656849\pi$
$41$	−6.05805			−0.946109			−0.473054	+	0.881033i	$0.656849\pi$
$42$		0			0
$43$	2.07971	+	2.07971i	0.317153	+	0.317153i	0.847673	−	0.530520i	$-0.178003\pi$
$43$	2.07971	+	2.07971i	0.317153	+	0.317153i	−0.530520	+	0.847673i	$0.678003\pi$
$44$		0			0
$45$	−2.02348	−	0.951596i	−0.301642	−	0.141856i
$46$		0			0
$47$	4.01416	+	4.01416i	0.585526	+	0.585526i	0.936416	−	0.350891i	$-0.114121\pi$
$47$	4.01416	+	4.01416i	0.585526	+	0.585526i	−0.350891	+	0.936416i	$0.614121\pi$
$48$		0			0
$49$		−	17.2536i		−	2.46480i
$50$		0			0
$51$			7.10029i			0.994240i
$52$		0			0
$53$	0.794878	+	0.794878i	0.109185	+	0.109185i	0.759589	−	0.650404i	$-0.225400\pi$
$53$	0.794878	+	0.794878i	0.109185	+	0.109185i	−0.650404	+	0.759589i	$0.725400\pi$
$54$		0			0
$55$	5.52971	+	2.60050i	0.745626	+	0.350651i
$56$		0			0
$57$	4.17983	−	4.17983i	0.553632	−	0.553632i
$58$		0			0
$59$			5.00908i			0.652127i	0.945348	+	0.326063i	$0.105722\pi$
$59$			5.00908i			0.652127i	−0.945348	+	0.326063i	$0.894278\pi$
$60$		0			0
$61$			9.72089i			1.24463i	0.782766	+	0.622316i	$0.213808\pi$
$61$			9.72089i			1.24463i	−0.782766	+	0.622316i	$0.786192\pi$
$62$		0			0
$63$	3.48236	+	3.48236i	0.438736	+	0.438736i
$64$		0			0
$65$	0.394422	+	1.09474i	0.0489220	+	0.135786i
$66$		0			0
$67$	−2.09702	+	2.09702i	−0.256191	+	0.256191i	−0.823503	−	0.567312i	$-0.807983\pi$
$67$	−2.09702	+	2.09702i	−0.256191	+	0.256191i	0.567312	+	0.823503i	$0.307983\pi$
$68$		0			0
$69$	−0.744154	+	4.73775i	−0.0895856	+	0.570358i
$70$		0			0
$71$	9.35585			1.11034			0.555168	−	0.831738i	$-0.312654\pi$
$71$	9.35585			1.11034			0.555168	+	0.831738i	$0.312654\pi$
$72$		0			0
$73$	8.18100	−	8.18100i	0.957513	−	0.957513i	−0.0416204	−	0.999133i	$-0.513252\pi$
$73$	8.18100	−	8.18100i	0.957513	−	0.957513i	0.999133	+	0.0416204i	$0.0132520\pi$
$74$		0			0
$75$	−4.97803	−	0.468202i	−0.574813	−	0.0540634i
$76$		0			0
$77$	−9.51650	−	9.51650i	−1.08451	−	1.08451i
$78$		0			0
$79$	2.90814			0.327192			0.163596	−	0.986527i	$-0.447691\pi$
$79$	2.90814			0.327192			0.163596	+	0.986527i	$0.447691\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−7.48074	−	7.48074i	−0.821118	−	0.821118i	0.165150	−	0.986268i	$-0.447189\pi$
$83$	−7.48074	−	7.48074i	−0.821118	−	0.821118i	−0.986268	+	0.165150i	$0.947189\pi$
$84$		0			0
$85$	5.38156	+	14.9368i	0.583712	+	1.62013i
$86$		0			0
$87$	1.41481	+	1.41481i	0.151683	+	0.151683i
$88$		0			0
$89$	−11.7859			−1.24930			−0.624650	−	0.780905i	$-0.714758\pi$
$89$	−11.7859			−1.24930			−0.624650	+	0.780905i	$0.714758\pi$
$90$		0			0
$91$		−	2.56282i		−	0.268656i
$92$		0			0
$93$	1.76641	−	1.76641i	0.183168	−	0.183168i
$94$		0			0
$95$	5.62505	−	11.9611i	0.577118	−	1.22719i
$96$		0			0
$97$	−0.793720	+	0.793720i	−0.0805901	+	0.0805901i	−0.746253	−	0.665663i	$-0.768149\pi$
$97$	−0.793720	+	0.793720i	−0.0805901	+	0.0805901i	0.665663	+	0.746253i	$0.268149\pi$
$98$		0			0
$99$	2.73277			0.274654
$100$		0			0
$101$	2.66129			0.264808			0.132404	−	0.991196i	$-0.457730\pi$
$101$	2.66129			0.264808			0.132404	+	0.991196i	$0.457730\pi$
$102$		0			0
$103$	3.17934	+	3.17934i	0.313269	+	0.313269i	0.846175	−	0.532906i	$-0.178900\pi$
$103$	3.17934	+	3.17934i	0.313269	+	0.313269i	−0.532906	+	0.846175i	$0.678900\pi$
$104$		0			0
$105$	9.96522	+	4.68642i	0.972506	+	0.457347i
$106$		0			0
$107$	12.5484	−	12.5484i	1.21310	−	1.21310i	0.243097	−	0.970002i	$-0.421837\pi$
$107$	12.5484	−	12.5484i	1.21310	−	1.21310i	0.970002	−	0.243097i	$-0.0781634\pi$
$108$		0			0
$109$	10.2093			0.977876			0.488938	−	0.872318i	$-0.337384\pi$
$109$	10.2093			0.977876			0.488938	+	0.872318i	$0.337384\pi$
$110$		0			0
$111$			9.03019i			0.857108i
$112$		0			0
$113$	2.74744	+	2.74744i	0.258458	+	0.258458i	0.824427	−	0.565969i	$-0.191498\pi$
$113$	2.74744	+	2.74744i	0.258458	+	0.258458i	−0.565969	+	0.824427i	$0.691498\pi$
$114$		0			0
$115$	2.02543	+	10.5308i	0.188872	+	0.982002i
$116$		0			0
$117$	0.367971	+	0.367971i	0.0340190	+	0.0340190i
$118$		0			0
$119$		−	34.9675i		−	3.20546i
$120$		0			0
$121$	3.53194			0.321086
$122$		0			0
$123$	−4.28369	+	4.28369i	−0.386247	+	0.386247i
$124$		0			0
$125$	−10.8271	+	2.78807i	−0.968408	+	0.249373i
$126$		0			0
$127$	11.1908	+	11.1908i	0.993026	+	0.993026i	0.999976	−	0.00695004i	$-0.00221228\pi$
$127$	11.1908	+	11.1908i	0.993026	+	0.993026i	−0.00695004	+	0.999976i	$0.502212\pi$
$128$		0			0
$129$	2.94116			0.258954
$130$		0			0
$131$	−14.2761			−1.24731			−0.623656	−	0.781699i	$-0.714353\pi$
$131$	−14.2761			−1.24731			−0.623656	+	0.781699i	$0.714353\pi$
$132$		0			0
$133$	−20.5848	+	20.5848i	−1.78493	+	1.78493i
$134$		0			0
$135$	−2.10370	+	0.757935i	−0.181057	+	0.0652327i
$136$		0			0
$137$	−3.74076	+	3.74076i	−0.319594	+	0.319594i	−0.848611	−	0.529017i	$-0.822561\pi$
$137$	−3.74076	+	3.74076i	−0.319594	+	0.319594i	0.529017	+	0.848611i	$0.322561\pi$
$138$		0			0
$139$		−	3.82831i		−	0.324713i	−0.986732	−	0.162356i	$-0.948091\pi$
$139$		−	3.82831i		−	0.324713i	0.986732	−	0.162356i	$-0.0519094\pi$
$140$		0			0
$141$	5.67688			0.478080
$142$		0			0
$143$	−1.00558	−	1.00558i	−0.0840911	−	0.0840911i
$144$		0			0
$145$	4.04866	+	1.90399i	0.336223	+	0.158118i
$146$		0			0
$147$	−12.2002	−	12.2002i	−1.00625	−	1.00625i
$148$		0			0
$149$	−20.3447			−1.66670			−0.833351	−	0.552744i	$-0.813581\pi$
$149$	−20.3447			−1.66670			−0.833351	+	0.552744i	$0.813581\pi$
$150$		0			0
$151$	−17.5132			−1.42521			−0.712604	−	0.701567i	$-0.752484\pi$
$151$	−17.5132			−1.42521			−0.712604	+	0.701567i	$0.752484\pi$
$152$		0			0
$153$	5.02066	+	5.02066i	0.405897	+	0.405897i
$154$		0			0
$155$	2.37716	−	5.05481i	0.190938	−	0.406012i
$156$		0			0
$157$	0.633264	−	0.633264i	0.0505400	−	0.0505400i	−0.681385	−	0.731925i	$-0.738622\pi$
$157$	0.633264	−	0.633264i	0.0505400	−	0.0505400i	0.731925	+	0.681385i	$0.238622\pi$
$158$		0			0
$159$	1.12413			0.0891491
$160$		0			0
$161$	3.66481	−	23.3324i	0.288827	−	1.83885i
$162$		0			0
$163$	−9.58716	+	9.58716i	−0.750925	+	0.750925i	−0.974652	−	0.223727i	$-0.928178\pi$
$163$	−9.58716	+	9.58716i	−0.750925	+	0.750925i	0.223727	+	0.974652i	$0.428178\pi$
$164$		0			0
$165$	5.74893	−	2.07127i	0.447553	−	0.161248i
$166$		0			0
$167$	−9.73651	−	9.73651i	−0.753434	−	0.753434i	0.221685	−	0.975118i	$-0.428844\pi$
$167$	−9.73651	−	9.73651i	−0.753434	−	0.753434i	−0.975118	+	0.221685i	$0.928844\pi$
$168$		0			0
$169$			12.7292i			0.979169i
$170$		0			0
$171$		−	5.91117i		−	0.452039i
$172$		0			0
$173$	−7.66666	+	7.66666i	−0.582885	+	0.582885i	−0.935695	−	0.352810i	$-0.885226\pi$
$173$	−7.66666	+	7.66666i	−0.582885	+	0.582885i	0.352810	+	0.935695i	$0.385226\pi$
$174$		0			0
$175$	24.5158	+	2.30580i	1.85322	+	0.174302i
$176$		0			0
$177$	3.54195	+	3.54195i	0.266230	+	0.266230i
$178$		0			0
$179$			4.25360i			0.317929i	0.987284	+	0.158964i	$0.0508155\pi$
$179$			4.25360i			0.317929i	−0.987284	+	0.158964i	$0.949185\pi$
$180$		0			0
$181$		−	14.9651i		−	1.11235i	−0.831065	−	0.556175i	$-0.812269\pi$
$181$		−	14.9651i		−	1.11235i	0.831065	−	0.556175i	$-0.187731\pi$
$182$		0			0
$183$	6.87371	+	6.87371i	0.508119	+	0.508119i
$184$		0			0
$185$	6.84430	+	18.9968i	0.503203	+	1.39667i
$186$		0			0
$187$	−13.7203	−	13.7203i	−1.00333	−	1.00333i
$188$		0			0
$189$	4.92480			0.358226
$190$		0			0
$191$			2.68877i			0.194552i	0.995257	+	0.0972762i	$0.0310130\pi$
$191$			2.68877i			0.194552i	−0.995257	+	0.0972762i	$0.968987\pi$
$192$		0			0
$193$	−2.19205	+	2.19205i	−0.157787	+	0.157787i	−0.781585	−	0.623798i	$-0.785589\pi$
$193$	−2.19205	+	2.19205i	−0.157787	+	0.157787i	0.623798	+	0.781585i	$0.285589\pi$
$194$		0			0
$195$	1.05300	+	0.495201i	0.0754068	+	0.0354621i
$196$		0			0
$197$	9.29614	+	9.29614i	0.662323	+	0.662323i	0.955927	−	0.293604i	$-0.0948548\pi$
$197$	9.29614	+	9.29614i	0.662323	+	0.662323i	−0.293604	+	0.955927i	$0.594855\pi$
$198$		0			0
$199$	−26.6926			−1.89219			−0.946096	−	0.323887i	$-0.895010\pi$
$199$	−26.6926			−1.89219			−0.946096	+	0.323887i	$0.895010\pi$
$200$		0			0
$201$			2.96563i			0.209179i
$202$		0			0
$203$	−6.96764	−	6.96764i	−0.489033	−	0.489033i
$204$		0			0
$205$	−5.76482	+	12.2583i	−0.402632	+	0.856160i
$206$		0			0
$207$	2.82390	+	3.87629i	0.196274	+	0.269421i
$208$		0			0
$209$			16.1539i			1.11739i
$210$		0			0
$211$	22.7587			1.56677			0.783386	−	0.621536i	$-0.213491\pi$
$211$	22.7587			1.56677			0.783386	+	0.621536i	$0.213491\pi$
$212$		0			0
$213$	6.61559	−	6.61559i	0.453293	−	0.453293i
$214$		0			0
$215$	6.18730	−	2.22921i	0.421970	−	0.152031i
$216$		0			0
$217$	−8.69921	+	8.69921i	−0.590541	+	0.590541i
$218$		0			0
$219$		−	11.5697i		−	0.781806i
$220$		0			0
$221$		−	3.69492i		−	0.248547i
$222$		0			0
$223$	−12.5272	+	12.5272i	−0.838881	+	0.838881i	−0.988712	−	0.149831i	$-0.952127\pi$
$223$	−12.5272	+	12.5272i	−0.838881	+	0.838881i	0.149831	+	0.988712i	$0.452127\pi$
$224$		0			0
$225$	−3.85107	+	3.18893i	−0.256738	+	0.212595i
$226$		0			0
$227$	12.4018	−	12.4018i	0.823138	−	0.823138i	−0.163419	−	0.986557i	$-0.552252\pi$
$227$	12.4018	−	12.4018i	0.823138	−	0.823138i	0.986557	+	0.163419i	$0.0522522\pi$
$228$		0			0
$229$	15.2938			1.01065			0.505323	−	0.862930i	$-0.331373\pi$
$229$	15.2938			1.01065			0.505323	+	0.862930i	$0.331373\pi$
$230$		0			0
$231$	−13.4584			−0.885495
$232$		0			0
$233$	15.2955	−	15.2955i	1.00204	−	1.00204i	0.00204482	−	0.999998i	$-0.499349\pi$
$233$	15.2955	−	15.2955i	1.00204	−	1.00204i	0.999998	−	0.00204482i	$-0.000650886\pi$
$234$		0			0
$235$	11.9424	−	4.30271i	0.779038	−	0.280678i
$236$		0			0
$237$	2.05637	−	2.05637i	0.133575	−	0.133575i
$238$		0			0
$239$			8.28742i			0.536068i	0.963409	+	0.268034i	$0.0863740\pi$
$239$			8.28742i			0.536068i	−0.963409	+	0.268034i	$0.913626\pi$
$240$		0			0
$241$		−	9.97259i		−	0.642391i	−0.947013	−	0.321196i	$-0.895915\pi$
$241$		−	9.97259i		−	0.642391i	0.947013	−	0.321196i	$-0.104085\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−34.9123	−	16.4185i	−2.23047	−	1.04894i
$246$		0			0
$247$	−2.17514	+	2.17514i	−0.138401	+	0.138401i
$248$		0			0
$249$	−10.5794			−0.670440
$250$		0			0
$251$		−	3.73360i		−	0.235663i	−0.993034	−	0.117831i	$-0.962406\pi$
$251$		−	3.73360i		−	0.235663i	0.993034	−	0.117831i	$-0.0375943\pi$
$252$		0			0
$253$	−7.71707	−	10.5930i	−0.485168	−	0.665978i
$254$		0			0
$255$	14.3673	+	6.75661i	0.899714	+	0.423115i
$256$		0			0
$257$	−17.9838	−	17.9838i	−1.12180	−	1.12180i	−0.991471	−	0.130325i	$-0.958398\pi$
$257$	−17.9838	−	17.9838i	−1.12180	−	1.12180i	−0.130325	−	0.991471i	$-0.541602\pi$
$258$		0			0
$259$		−	44.4718i		−	2.76335i
$260$		0			0
$261$	2.00084			0.123849
$262$		0			0
$263$	−9.76385	−	9.76385i	−0.602065	−	0.602065i	0.338795	−	0.940860i	$-0.389981\pi$
$263$	−9.76385	−	9.76385i	−0.602065	−	0.602065i	−0.940860	+	0.338795i	$0.889981\pi$
$264$		0			0
$265$	2.36482	−	0.852016i	0.145270	−	0.0523389i
$266$		0			0
$267$	−8.33387	+	8.33387i	−0.510025	+	0.510025i
$268$		0			0
$269$			9.86177i			0.601283i	0.953737	+	0.300641i	$0.0972007\pi$
$269$			9.86177i			0.601283i	−0.953737	+	0.300641i	$0.902799\pi$
$270$		0			0
$271$	30.9582			1.88058			0.940289	−	0.340378i	$-0.110555\pi$
$271$	30.9582			1.88058			0.940289	+	0.340378i	$0.110555\pi$
$272$		0			0
$273$	−1.81218	−	1.81218i	−0.109678	−	0.109678i
$274$		0			0
$275$	10.5241	−	8.71463i	0.634627	−	0.525512i
$276$		0			0
$277$	−5.28631	−	5.28631i	−0.317624	−	0.317624i	0.530230	−	0.847854i	$-0.322106\pi$
$277$	−5.28631	−	5.28631i	−0.317624	−	0.317624i	−0.847854	+	0.530230i	$0.822106\pi$
$278$		0			0
$279$		−	2.49808i		−	0.149556i
$280$		0			0
$281$		−	8.12633i		−	0.484776i	−0.970179	−	0.242388i	$-0.922069\pi$
$281$		−	8.12633i		−	0.484776i	0.970179	−	0.242388i	$-0.0779307\pi$
$282$		0			0
$283$	−1.11664	−	1.11664i	−0.0663772	−	0.0663772i	0.673139	−	0.739516i	$-0.264946\pi$
$283$	−1.11664	−	1.11664i	−0.0663772	−	0.0663772i	−0.739516	+	0.673139i	$0.764946\pi$
$284$		0			0
$285$	−4.48029	−	12.4353i	−0.265389	−	0.736604i
$286$		0			0
$287$	21.0963	−	21.0963i	1.24528	−	1.24528i
$288$		0			0
$289$		−	33.4141i		−	1.96554i
$290$		0			0
$291$			1.12249i			0.0658015i
$292$		0			0
$293$	11.0252	+	11.0252i	0.644097	+	0.644097i	0.951560	−	0.307463i	$-0.0994800\pi$
$293$	11.0252	+	11.0252i	0.644097	+	0.644097i	−0.307463	+	0.951560i	$0.599480\pi$
$294$		0			0
$295$	10.1358	+	4.76662i	0.590127	+	0.277523i
$296$		0			0
$297$	1.93236	−	1.93236i	0.112127	−	0.112127i
$298$		0			0
$299$	0.387250	−	2.46548i	0.0223953	−	0.142582i
$300$		0			0
$301$	−14.4846			−0.834878
$302$		0			0
$303$	1.88182	−	1.88182i	0.108108	−	0.108108i
$304$		0			0
$305$	19.6700	+	9.25036i	1.12630	+	0.529674i
$306$		0			0
$307$	22.3268	+	22.3268i	1.27426	+	1.27426i	0.943833	+	0.330424i	$0.107192\pi$
$307$	22.3268	+	22.3268i	1.27426	+	1.27426i	0.330424	+	0.943833i	$0.392808\pi$
$308$		0			0
$309$	4.49626			0.255783
$310$		0			0
$311$	3.95458			0.224244			0.112122	−	0.993694i	$-0.464235\pi$
$311$	3.95458			0.224244			0.112122	+	0.993694i	$0.464235\pi$
$312$		0			0
$313$	−22.9975	−	22.9975i	−1.29990	−	1.29990i	−0.928457	−	0.371439i	$-0.878864\pi$
$313$	−22.9975	−	22.9975i	−1.29990	−	1.29990i	−0.371439	−	0.928457i	$-0.621136\pi$
$314$		0			0
$315$	10.3603	−	3.73268i	0.583735	−	0.210313i
$316$		0			0
$317$	−13.0622	−	13.0622i	−0.733647	−	0.733647i	0.237693	−	0.971340i	$-0.423609\pi$
$317$	−13.0622	−	13.0622i	−0.733647	−	0.733647i	−0.971340	+	0.237693i	$0.923609\pi$
$318$		0			0
$319$	−5.46785			−0.306141
$320$		0			0
$321$		−	17.7461i		−	0.990491i
$322$		0			0
$323$	−29.6780	+	29.6780i	−1.65133	+	1.65133i
$324$		0			0
$325$	2.59052	+	0.243648i	0.143696	+	0.0135152i
$326$		0			0
$327$	7.21908	−	7.21908i	0.399216	−	0.399216i
$328$		0			0
$329$	−27.9575			−1.54135
$330$		0			0
$331$	2.29715			0.126263			0.0631314	−	0.998005i	$-0.479891\pi$
$331$	2.29715			0.126263			0.0631314	+	0.998005i	$0.479891\pi$
$332$		0			0
$333$	6.38531	+	6.38531i	0.349913	+	0.349913i
$334$		0			0
$335$	2.24776	+	6.23878i	0.122808	+	0.340861i
$336$		0			0
$337$	23.8232	−	23.8232i	1.29773	−	1.29773i	0.367849	−	0.929885i	$-0.380094\pi$
$337$	23.8232	−	23.8232i	1.29773	−	1.29773i	0.929885	−	0.367849i	$-0.119906\pi$
$338$		0			0
$339$	3.88547			0.211030
$340$		0			0
$341$			6.82669i			0.369686i
$342$		0			0
$343$	35.7068	+	35.7068i	1.92798	+	1.92798i
$344$		0			0
$345$	8.87859	+	6.01420i	0.478007	+	0.323794i
$346$		0			0
$347$	15.1228	+	15.1228i	0.811836	+	0.811836i	0.984909	−	0.173073i	$-0.0553698\pi$
$347$	15.1228	+	15.1228i	0.811836	+	0.811836i	−0.173073	+	0.984909i	$0.555370\pi$
$348$		0			0
$349$			3.85339i			0.206267i	0.994668	+	0.103133i	$0.0328869\pi$
$349$			3.85339i			0.206267i	−0.994668	+	0.103133i	$0.967113\pi$
$350$		0			0
$351$	0.520390			0.0277764
$352$		0			0
$353$	−17.0525	+	17.0525i	−0.907611	+	0.907611i	−0.996079	−	0.0884682i	$-0.971803\pi$
$353$	−17.0525	+	17.0525i	−0.907611	+	0.907611i	0.0884682	+	0.996079i	$0.471803\pi$
$354$		0			0
$355$	8.90299	−	18.9314i	0.472522	−	1.00477i
$356$		0			0
$357$	−24.7257	−	24.7257i	−1.30863	−	1.30863i
$358$		0			0
$359$	−6.39323			−0.337422			−0.168711	−	0.985666i	$-0.553960\pi$
$359$	−6.39323			−0.337422			−0.168711	+	0.985666i	$0.553960\pi$
$360$		0			0
$361$	15.9420			0.839050
$362$		0			0
$363$	2.49746	−	2.49746i	0.131083	−	0.131083i
$364$		0			0
$365$	−8.76906	−	24.3391i	−0.458994	−	1.27397i
$366$		0			0
$367$	1.27685	−	1.27685i	0.0666508	−	0.0666508i	−0.672996	−	0.739646i	$-0.734993\pi$
$367$	1.27685	−	1.27685i	0.0666508	−	0.0666508i	0.739646	+	0.672996i	$0.234993\pi$
$368$		0			0
$369$			6.05805i			0.315370i
$370$		0			0
$371$	−5.53610			−0.287420
$372$		0			0
$373$	−11.0669	−	11.0669i	−0.573021	−	0.573021i	0.359951	−	0.932971i	$-0.382794\pi$
$373$	−11.0669	−	11.0669i	−0.573021	−	0.573021i	−0.932971	+	0.359951i	$0.882794\pi$
$374$		0			0
$375$	−5.68447	+	9.62740i	−0.293545	+	0.497157i
$376$		0			0
$377$	−0.736252	−	0.736252i	−0.0379189	−	0.0379189i
$378$		0			0
$379$	−12.2350			−0.628467			−0.314234	−	0.949346i	$-0.601748\pi$
$379$	−12.2350			−0.628467			−0.314234	+	0.949346i	$0.601748\pi$
$380$		0			0
$381$	15.8262			0.810802
$382$		0			0
$383$	11.9126	+	11.9126i	0.608708	+	0.608708i	0.942608	−	0.333901i	$-0.108365\pi$
$383$	11.9126	+	11.9126i	0.608708	+	0.608708i	−0.333901	+	0.942608i	$0.608365\pi$
$384$		0			0
$385$	−28.3123	+	10.2006i	−1.44293	+	0.519869i
$386$		0			0
$387$	2.07971	−	2.07971i	0.105718	−	0.105718i
$388$		0			0
$389$	6.06586			0.307551			0.153776	−	0.988106i	$-0.450857\pi$
$389$	6.06586			0.307551			0.153776	+	0.988106i	$0.450857\pi$
$390$		0			0
$391$	5.28371	−	33.6394i	0.267209	−	1.70122i
$392$		0			0
$393$	−10.0947	+	10.0947i	−0.509213	+	0.509213i
$394$		0			0
$395$	2.76738	−	5.88456i	0.139242	−	0.296085i
$396$		0			0
$397$	−5.17259	−	5.17259i	−0.259605	−	0.259605i	0.565288	−	0.824893i	$-0.308765\pi$
$397$	−5.17259	−	5.17259i	−0.259605	−	0.259605i	−0.824893	+	0.565288i	$0.808765\pi$
$398$		0			0
$399$			29.1113i			1.45739i
$400$		0			0
$401$		−	30.5270i		−	1.52445i	−0.647314	−	0.762223i	$-0.724108\pi$
$401$		−	30.5270i		−	1.52445i	0.647314	−	0.762223i	$-0.275892\pi$
$402$		0			0
$403$	−0.919222	+	0.919222i	−0.0457897	+	0.0457897i
$404$		0			0
$405$	−0.951596	+	2.02348i	−0.0472852	+	0.100547i
$406$		0			0
$407$	−17.4496	−	17.4496i	−0.864945	−	0.864945i
$408$		0			0
$409$			14.7162i			0.727668i	0.931464	+	0.363834i	$0.118532\pi$
$409$			14.7162i			0.727668i	−0.931464	+	0.363834i	$0.881468\pi$
$410$		0			0
$411$			5.29023i			0.260948i
$412$		0			0
$413$	−17.4434	−	17.4434i	−0.858334	−	0.858334i
$414$		0			0
$415$	−22.2558	+	8.01847i	−1.09249	+	0.393611i
$416$		0			0
$417$	−2.70702	−	2.70702i	−0.132563	−	0.132563i
$418$		0			0
$419$	32.7417			1.59954			0.799769	−	0.600308i	$-0.204955\pi$
$419$	32.7417			1.59954			0.799769	+	0.600308i	$0.204955\pi$
$420$		0			0
$421$			17.8474i			0.869828i	0.900472	+	0.434914i	$0.143221\pi$
$421$			17.8474i			0.869828i	−0.900472	+	0.434914i	$0.856779\pi$
$422$		0			0
$423$	4.01416	−	4.01416i	0.195175	−	0.195175i
$424$		0			0
$425$	35.3455	+	3.32437i	1.71451	+	0.161256i
$426$		0			0
$427$	−33.8516	−	33.8516i	−1.63819	−	1.63819i
$428$		0			0
$429$	−1.42211			−0.0686601
$430$		0			0
$431$			12.2783i			0.591424i	0.955277	+	0.295712i	$0.0955569\pi$
$431$			12.2783i			0.591424i	−0.955277	+	0.295712i	$0.904443\pi$
$432$		0			0
$433$	23.1039	+	23.1039i	1.11030	+	1.11030i	0.993109	+	0.117192i	$0.0373892\pi$
$433$	23.1039	+	23.1039i	1.11030	+	1.11030i	0.117192	+	0.993109i	$0.462611\pi$
$434$		0			0
$435$	4.20916	−	1.51651i	0.201814	−	0.0727110i
$436$		0			0
$437$	−22.9134	+	16.6925i	−1.09610	+	0.798512i
$438$		0			0
$439$		−	16.3865i		−	0.782084i	−0.920373	−	0.391042i	$-0.872115\pi$
$439$		−	16.3865i		−	0.782084i	0.920373	−	0.391042i	$-0.127885\pi$
$440$		0			0
$441$	−17.2536			−0.821601
$442$		0			0
$443$	−17.9738	+	17.9738i	−0.853959	+	0.853959i	−0.990618	−	0.136659i	$-0.956364\pi$
$443$	−17.9738	+	17.9738i	−0.853959	+	0.853959i	0.136659	+	0.990618i	$0.456364\pi$
$444$		0			0
$445$	−11.2154	+	23.8485i	−0.531661	+	1.13053i
$446$		0			0
$447$	−14.3859	+	14.3859i	−0.680429	+	0.680429i
$448$		0			0
$449$		−	2.07546i		−	0.0979471i	−0.998800	−	0.0489736i	$-0.984405\pi$
$449$		−	2.07546i		−	0.0979471i	0.998800	−	0.0489736i	$-0.0155950\pi$
$450$		0			0
$451$		−	16.5553i		−	0.779558i
$452$		0			0
$453$	−12.3837	+	12.3837i	−0.581838	+	0.581838i
$454$		0			0
$455$	−5.18580	−	2.43876i	−0.243114	−	0.114331i
$456$		0			0
$457$	17.7693	−	17.7693i	0.831215	−	0.831215i	−0.156468	−	0.987683i	$-0.550011\pi$
$457$	17.7693	−	17.7693i	0.831215	−	0.831215i	0.987683	+	0.156468i	$0.0500108\pi$
$458$		0			0
$459$	7.10029			0.331413
$460$		0			0
$461$	8.62611			0.401758			0.200879	−	0.979616i	$-0.435620\pi$
$461$	8.62611			0.401758			0.200879	+	0.979616i	$0.435620\pi$
$462$		0			0
$463$	−8.70757	+	8.70757i	−0.404675	+	0.404675i	−0.879877	−	0.475202i	$-0.842375\pi$
$463$	−8.70757	+	8.70757i	−0.404675	+	0.404675i	0.475202	+	0.879877i	$0.342375\pi$
$464$		0			0
$465$	−1.89338	−	5.25520i	−0.0878036	−	0.243704i
$466$		0			0
$467$	2.96286	−	2.96286i	0.137105	−	0.137105i	−0.635224	−	0.772328i	$-0.719092\pi$
$467$	2.96286	−	2.96286i	0.137105	−	0.137105i	0.772328	+	0.635224i	$0.219092\pi$
$468$		0			0
$469$		−	14.6051i		−	0.674402i
$470$		0			0
$471$		−	0.895570i		−	0.0412657i
$472$		0			0
$473$	−5.68338	+	5.68338i	−0.261322	+	0.261322i
$474$		0			0
$475$	−18.8503	−	22.7643i	−0.864912	−	1.04450i
$476$		0			0
$477$	0.794878	−	0.794878i	0.0363950	−	0.0363950i
$478$		0			0
$479$	23.4955			1.07354			0.536768	−	0.843730i	$-0.319645\pi$
$479$	23.4955			1.07354			0.536768	+	0.843730i	$0.319645\pi$
$480$		0			0
$481$		−	4.69922i		−	0.214266i
$482$		0			0
$483$	−13.9071	−	19.0899i	−0.632796	−	0.868622i
$484$		0			0
$485$	0.850775	+	2.36138i	0.0386317	+	0.107225i
$486$		0			0
$487$	16.5628	+	16.5628i	0.750532	+	0.750532i	0.974578	−	0.224047i	$-0.0719269\pi$
$487$	16.5628	+	16.5628i	0.750532	+	0.750532i	−0.224047	+	0.974578i	$0.571927\pi$
$488$		0			0
$489$			13.5583i			0.613127i
$490$		0			0
$491$	2.39587			0.108124			0.0540620	−	0.998538i	$-0.482783\pi$
$491$	2.39587			0.108124			0.0540620	+	0.998538i	$0.482783\pi$
$492$		0			0
$493$	−10.0455	−	10.0455i	−0.452429	−	0.452429i
$494$		0			0
$495$	2.60050	−	5.52971i	0.116884	−	0.248542i
$496$		0			0
$497$	−32.5804	+	32.5804i	−1.46143	+	1.46143i
$498$		0			0
$499$		−	2.30108i		−	0.103010i	−0.998673	−	0.0515052i	$-0.983598\pi$
$499$		−	2.30108i		−	0.103010i	0.998673	−	0.0515052i	$-0.0164019\pi$
$500$		0			0
$501$	−13.7695			−0.615176
$502$		0			0
$503$	−5.59225	−	5.59225i	−0.249346	−	0.249346i	0.571356	−	0.820702i	$-0.306418\pi$
$503$	−5.59225	−	5.59225i	−0.249346	−	0.249346i	−0.820702	+	0.571356i	$0.806418\pi$
$504$		0			0
$505$	2.53247	−	5.38506i	0.112694	−	0.239632i
$506$		0			0
$507$	9.00090	+	9.00090i	0.399744	+	0.399744i
$508$		0			0
$509$		−	3.88491i		−	0.172195i	−0.996287	−	0.0860977i	$-0.972560\pi$
$509$		−	3.88491i		−	0.172195i	0.996287	−	0.0860977i	$-0.0274397\pi$
$510$		0			0
$511$			56.9783i			2.52057i
$512$		0			0
$513$	−4.17983	−	4.17983i	−0.184544	−	0.184544i
$514$		0			0
$515$	9.45876	−	3.40787i	0.416803	−	0.150169i
$516$		0			0
$517$	−10.9698	+	10.9698i	−0.482451	+	0.482451i
$518$		0			0
$519$			10.8423i			0.475924i
$520$		0			0
$521$			15.4956i			0.678876i	0.940628	+	0.339438i	$0.110237\pi$
$521$			15.4956i			0.678876i	−0.940628	+	0.339438i	$0.889763\pi$
$522$		0			0
$523$	20.3365	+	20.3365i	0.889254	+	0.889254i	0.994451	−	0.105197i	$-0.0335475\pi$
$523$	20.3365	+	20.3365i	0.889254	+	0.889254i	−0.105197	+	0.994451i	$0.533547\pi$
$524$		0			0
$525$	18.9657	−	15.7048i	0.827732	−	0.685415i
$526$		0			0
$527$	−12.5420	+	12.5420i	−0.546339	+	0.546339i
$528$		0			0
$529$	7.05123	−	21.8925i	0.306575	−	0.951846i
$530$		0			0
$531$	5.00908			0.217376
$532$		0			0
$533$	2.22919	−	2.22919i	0.0965569	−	0.0965569i
$534$		0			0
$535$	−13.4504	−	37.3324i	−0.581512	−	1.61402i
$536$		0			0
$537$	3.00775	+	3.00775i	0.129794	+	0.129794i
$538$		0			0
$539$	47.1503			2.03091
$540$		0			0
$541$	33.7381			1.45051			0.725257	−	0.688478i	$-0.241721\pi$
$541$	33.7381			1.45051			0.725257	+	0.688478i	$0.241721\pi$
$542$		0			0
$543$	−10.5819	−	10.5819i	−0.454115	−	0.454115i
$544$		0			0
$545$	9.71515	−	20.6584i	0.416152	−	0.884907i
$546$		0			0
$547$	31.0432	+	31.0432i	1.32731	+	1.32731i	0.907706	+	0.419606i	$0.137832\pi$
$547$	31.0432	+	31.0432i	1.32731	+	1.32731i	0.419606	+	0.907706i	$0.362168\pi$
$548$		0			0
$549$	9.72089			0.414877
$550$		0			0
$551$			11.8273i			0.503861i
$552$		0			0
$553$	−10.1272	+	10.1272i	−0.430652	+	0.430652i
$554$		0			0
$555$	18.2724	+	8.59309i	0.775620	+	0.364756i
$556$		0			0
$557$	−16.3749	+	16.3749i	−0.693827	+	0.693827i	−0.963072	−	0.269245i	$-0.913226\pi$
$557$	−16.3749	+	16.3749i	−0.693827	+	0.693827i	0.269245	+	0.963072i	$0.413226\pi$
$558$		0			0
$559$	−1.53055			−0.0647353
$560$		0			0
$561$	−19.4035			−0.819216
$562$		0			0
$563$	−23.8732	−	23.8732i	−1.00613	−	1.00613i	−0.999981	−	0.00615292i	$-0.998041\pi$
$563$	−23.8732	−	23.8732i	−1.00613	−	1.00613i	−0.00615292	−	0.999981i	$-0.501959\pi$
$564$		0			0
$565$	8.17384	−	2.94493i	0.343876	−	0.123894i
$566$		0			0
$567$	3.48236	−	3.48236i	0.146245	−	0.146245i
$568$		0			0
$569$	24.7218			1.03639			0.518195	−	0.855262i	$-0.326604\pi$
$569$	24.7218			1.03639			0.518195	+	0.855262i	$0.326604\pi$
$570$		0			0
$571$			18.4534i			0.772249i	0.922447	+	0.386124i	$0.126186\pi$
$571$			18.4534i			0.772249i	−0.922447	+	0.386124i	$0.873814\pi$
$572$		0			0
$573$	1.90125	+	1.90125i	0.0794257	+	0.0794257i
$574$		0			0
$575$	23.2362	+	5.92265i	0.969018	+	0.246991i
$576$		0			0
$577$	−27.1580	−	27.1580i	−1.13060	−	1.13060i	−0.990077	−	0.140525i	$-0.955121\pi$
$577$	−27.1580	−	27.1580i	−1.13060	−	1.13060i	−0.140525	−	0.990077i	$-0.544879\pi$
$578$		0			0
$579$			3.10002i			0.128833i
$580$		0			0
$581$	52.1012			2.16152
$582$		0			0
$583$	−2.17222	+	2.17222i	−0.0899643	+	0.0899643i
$584$		0			0
$585$	1.09474	−	0.394422i	0.0452620	−	0.0163073i
$586$		0			0
$587$	−7.91964	−	7.91964i	−0.326878	−	0.326878i	0.524520	−	0.851398i	$-0.324245\pi$
$587$	−7.91964	−	7.91964i	−0.326878	−	0.326878i	−0.851398	+	0.524520i	$0.824245\pi$
$588$		0			0
$589$	14.7666			0.608447
$590$		0			0
$591$	13.1467			0.540784
$592$		0			0
$593$	21.1679	−	21.1679i	0.869263	−	0.869263i	−0.123128	−	0.992391i	$-0.539292\pi$
$593$	21.1679	−	21.1679i	0.869263	−	0.869263i	0.992391	+	0.123128i	$0.0392925\pi$
$594$		0			0
$595$	−70.7560	−	33.2749i	−2.90071	−	1.36414i
$596$		0			0
$597$	−18.8745	+	18.8745i	−0.772484	+	0.772484i
$598$		0			0
$599$		−	11.8908i		−	0.485843i	−0.970046	−	0.242922i	$-0.921894\pi$
$599$		−	11.8908i		−	0.485843i	0.970046	−	0.242922i	$-0.0781058\pi$
$600$		0			0
$601$	32.3702			1.32041			0.660203	−	0.751087i	$-0.270470\pi$
$601$	32.3702			1.32041			0.660203	+	0.751087i	$0.270470\pi$
$602$		0			0
$603$	2.09702	+	2.09702i	0.0853971	+	0.0853971i
$604$		0			0
$605$	3.36098	−	7.14681i	0.136643	−	0.290559i
$606$		0			0
$607$	28.1596	+	28.1596i	1.14296	+	1.14296i	0.987906	+	0.155057i	$0.0495561\pi$
$607$	28.1596	+	28.1596i	1.14296	+	1.14296i	0.155057	+	0.987906i	$0.450444\pi$
$608$		0			0
$609$	−9.85373			−0.399293
$610$		0			0
$611$	−2.95419			−0.119514
$612$		0			0
$613$	−13.4800	−	13.4800i	−0.544450	−	0.544450i	0.380380	−	0.924830i	$-0.375793\pi$
$613$	−13.4800	−	13.4800i	−0.544450	−	0.544450i	−0.924830	+	0.380380i	$0.875793\pi$
$614$		0			0
$615$	4.59161	+	12.7443i	0.185152	+	0.513900i
$616$		0			0
$617$	−14.1443	+	14.1443i	−0.569430	+	0.569430i	−0.931969	−	0.362539i	$-0.881910\pi$
$617$	−14.1443	+	14.1443i	−0.569430	+	0.569430i	0.362539	+	0.931969i	$0.381910\pi$
$618$		0			0
$619$	−5.83694			−0.234607			−0.117303	−	0.993096i	$-0.537425\pi$
$619$	−5.83694			−0.234607			−0.117303	+	0.993096i	$0.537425\pi$
$620$		0			0
$621$	4.73775	+	0.744154i	0.190119	+	0.0298619i
$622$		0			0
$623$	41.0426	−	41.0426i	1.64434	−	1.64434i
$624$		0			0
$625$	−4.66145	+	24.5616i	−0.186458	+	0.982463i
$626$		0			0
$627$	11.4225	+	11.4225i	0.456172	+	0.456172i
$628$		0			0
$629$		−	64.1170i		−	2.55651i
$630$		0			0
$631$		−	8.84121i		−	0.351963i	−0.984393	−	0.175982i	$-0.943690\pi$
$631$		−	8.84121i		−	0.351963i	0.984393	−	0.175982i	$-0.0563099\pi$
$632$		0			0
$633$	16.0928	−	16.0928i	0.639632	−	0.639632i
$634$		0			0
$635$	33.2936	−	11.9953i	1.32121	−	0.476017i
$636$		0			0
$637$	6.34884	+	6.34884i	0.251550	+	0.251550i
$638$		0			0
$639$		−	9.35585i		−	0.370112i
$640$		0			0
$641$			31.0727i			1.22730i	0.789579	+	0.613649i	$0.210299\pi$
$641$			31.0727i			1.22730i	−0.789579	+	0.613649i	$0.789701\pi$
$642$		0			0
$643$	25.4613	+	25.4613i	1.00410	+	1.00410i	0.999992	+	0.00410535i	$0.00130678\pi$
$643$	25.4613	+	25.4613i	1.00410	+	1.00410i	0.00410535	+	0.999992i	$0.498693\pi$
$644$		0			0
$645$	2.79879	−	5.95137i	0.110202	−	0.234335i
$646$		0			0
$647$	−10.6871	−	10.6871i	−0.420155	−	0.420155i	0.465102	−	0.885257i	$-0.346018\pi$
$647$	−10.6871	−	10.6871i	−0.420155	−	0.420155i	−0.885257	+	0.465102i	$0.846018\pi$
$648$		0			0
$649$	−13.6887			−0.537328
$650$		0			0
$651$			12.3025i			0.482175i
$652$		0			0
$653$	0.982888	−	0.982888i	0.0384634	−	0.0384634i	−0.687614	−	0.726077i	$-0.741342\pi$
$653$	0.982888	−	0.982888i	0.0384634	−	0.0384634i	0.726077	+	0.687614i	$0.241342\pi$
$654$		0			0
$655$	−13.5851	+	28.8874i	−0.530814	+	1.12873i
$656$		0			0
$657$	−8.18100	−	8.18100i	−0.319171	−	0.319171i
$658$		0			0
$659$	−14.2495			−0.555084			−0.277542	−	0.960714i	$-0.589520\pi$
$659$	−14.2495			−0.555084			−0.277542	+	0.960714i	$0.589520\pi$
$660$		0			0
$661$			27.1286i			1.05518i	0.849499	+	0.527591i	$0.176905\pi$
$661$			27.1286i			1.05518i	−0.849499	+	0.527591i	$0.823095\pi$
$662$		0			0
$663$	−2.61270	−	2.61270i	−0.101469	−	0.101469i
$664$		0			0
$665$	22.0645	+	61.2413i	0.855625	+	2.37484i
$666$		0			0
$667$	−5.65017	−	7.75584i	−0.218775	−	0.300307i
$668$		0			0
$669$			17.7161i			0.684943i
$670$		0			0
$671$	−26.5650			−1.02553
$672$		0			0
$673$	−10.3225	+	10.3225i	−0.397902	+	0.397902i	−0.877493	−	0.479590i	$-0.840785\pi$
$673$	−10.3225	+	10.3225i	−0.397902	+	0.397902i	0.479590	+	0.877493i	$0.340785\pi$
$674$		0			0
$675$	−0.468202	+	4.97803i	−0.0180211	+	0.191604i
$676$		0			0
$677$	−27.1421	+	27.1421i	−1.04316	+	1.04316i	−0.0441292	+	0.999026i	$0.514051\pi$
$677$	−27.1421	+	27.1421i	−1.04316	+	1.04316i	−0.999026	+	0.0441292i	$0.985949\pi$
$678$		0			0
$679$		−	5.52804i		−	0.212147i
$680$		0			0
$681$		−	17.5388i		−	0.672089i
$682$		0			0
$683$	−6.74055	+	6.74055i	−0.257920	+	0.257920i	−0.824208	−	0.566288i	$-0.808379\pi$
$683$	−6.74055	+	6.74055i	−0.257920	+	0.257920i	0.566288	+	0.824208i	$0.308379\pi$
$684$		0			0
$685$	4.00965	+	11.1290i	0.153201	+	0.425218i
$686$		0			0
$687$	10.8144	−	10.8144i	0.412594	−	0.412594i
$688$		0			0
$689$	−0.584985			−0.0222861
$690$		0			0
$691$	34.7074			1.32033			0.660166	−	0.751120i	$-0.270486\pi$
$691$	34.7074			1.32033			0.660166	+	0.751120i	$0.270486\pi$
$692$		0			0
$693$	−9.51650	+	9.51650i	−0.361502	+	0.361502i
$694$		0			0
$695$	−7.74650	−	3.64300i	−0.293841	−	0.138187i
$696$		0			0
$697$	30.4154	−	30.4154i	1.15207	−	1.15207i
$698$		0			0
$699$		−	21.6311i		−	0.818164i
$700$		0			0
$701$			38.3373i			1.44798i	0.689811	+	0.723990i	$0.257694\pi$
$701$			38.3373i			1.44798i	−0.689811	+	0.723990i	$0.742306\pi$
$702$		0			0
$703$	−37.7447	+	37.7447i	−1.42357	+	1.42357i
$704$		0			0
$705$	5.40210	−	11.4871i	0.203455	−	0.432627i
$706$		0			0
$707$	−9.26756	+	9.26756i	−0.348543	+	0.348543i
$708$		0			0
$709$	16.7671			0.629700			0.314850	−	0.949141i	$-0.398046\pi$
$709$	16.7671			0.629700			0.314850	+	0.949141i	$0.398046\pi$
$710$		0			0
$711$		−	2.90814i		−	0.109064i
$712$		0			0
$713$	−9.68328	+	7.05432i	−0.362642	+	0.264186i
$714$		0			0
$715$	−2.99168	+	1.07787i	−0.111883	+	0.0403099i
$716$		0			0
$717$	5.86009	+	5.86009i	0.218849	+	0.218849i
$718$		0			0
$719$			19.0730i			0.711302i	0.934619	+	0.355651i	$0.115741\pi$
$719$			19.0730i			0.711302i	−0.934619	+	0.355651i	$0.884259\pi$
$720$		0			0
$721$	−22.1432			−0.824655
$722$		0			0
$723$	−7.05169	−	7.05169i	−0.262255	−	0.262255i
$724$		0			0
$725$	7.70537	−	6.38054i	0.286170	−	0.236967i
$726$		0			0
$727$	−33.0514	+	33.0514i	−1.22581	+	1.22581i	−0.260273	+	0.965535i	$0.583813\pi$
$727$	−33.0514	+	33.0514i	−1.22581	+	1.22581i	−0.965535	+	0.260273i	$0.916187\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−20.8831			−0.772388
$732$		0			0
$733$	9.13550	+	9.13550i	0.337427	+	0.337427i	0.855398	−	0.517971i	$-0.173312\pi$
$733$	9.13550	+	9.13550i	0.337427	+	0.337427i	−0.517971	+	0.855398i	$0.673312\pi$
$734$		0			0
$735$	−36.2964	+	13.0771i	−1.33881	+	0.482357i
$736$		0			0
$737$	−5.73067	−	5.73067i	−0.211092	−	0.211092i
$738$		0			0
$739$			28.8701i			1.06200i	0.847370	+	0.531002i	$0.178184\pi$
$739$			28.8701i			1.06200i	−0.847370	+	0.531002i	$0.821816\pi$
$740$		0			0
$741$			3.07612i			0.113004i
$742$		0			0
$743$	35.7107	+	35.7107i	1.31010	+	1.31010i	0.921341	+	0.388756i	$0.127095\pi$
$743$	35.7107	+	35.7107i	1.31010	+	1.31010i	0.388756	+	0.921341i	$0.372905\pi$
$744$		0			0
$745$	−19.3599	+	41.1671i	−0.709293	+	1.50824i
$746$		0			0
$747$	−7.48074	+	7.48074i	−0.273706	+	0.273706i
$748$		0			0
$749$			87.3960i			3.19338i
$750$		0			0
$751$			18.1412i			0.661982i	0.943634	+	0.330991i	$0.107383\pi$
$751$			18.1412i			0.661982i	−0.943634	+	0.330991i	$0.892617\pi$
$752$		0			0
$753$	−2.64006	−	2.64006i	−0.0962090	−	0.0962090i
$754$		0			0
$755$	−16.6655	+	35.4377i	−0.606521	+	1.28971i
$756$		0			0
$757$	18.5361	−	18.5361i	0.673707	−	0.673707i	−0.284861	−	0.958569i	$-0.591948\pi$
$757$	18.5361	−	18.5361i	0.673707	−	0.673707i	0.958569	+	0.284861i	$0.0919475\pi$
$758$		0			0
$759$	−12.9472	−	2.03361i	−0.469953	−	0.0738152i
$760$		0			0
$761$	−44.5294			−1.61419			−0.807094	−	0.590422i	$-0.798961\pi$
$761$	−44.5294			−1.61419			−0.807094	+	0.590422i	$0.798961\pi$
$762$		0			0
$763$	−35.5525	+	35.5525i	−1.28709	+	1.28709i
$764$		0			0
$765$	14.9368	−	5.38156i	0.540043	−	0.194571i
$766$		0			0
$767$	−1.84320	−	1.84320i	−0.0665540	−	0.0665540i
$768$		0			0
$769$	−22.4202			−0.808494			−0.404247	−	0.914650i	$-0.632466\pi$
$769$	−22.4202			−0.808494			−0.404247	+	0.914650i	$0.632466\pi$
$770$		0			0
$771$	−25.4329			−0.915943
$772$		0			0
$773$	−36.2172	−	36.2172i	−1.30264	−	1.30264i	−0.926603	−	0.376040i	$-0.877285\pi$
$773$	−36.2172	−	36.2172i	−1.30264	−	1.30264i	−0.376040	−	0.926603i	$-0.622715\pi$
$774$		0			0
$775$	−7.96621	−	9.62028i	−0.286155	−	0.345571i
$776$		0			0
$777$	−31.4463	−	31.4463i	−1.12813	−	1.12813i
$778$		0			0
$779$	−35.8102			−1.28303
$780$		0			0
$781$			25.5674i			0.914875i
$782$		0			0
$783$	1.41481	−	1.41481i	0.0505611	−	0.0505611i
$784$		0			0
$785$	−0.678784	−	1.88401i	−0.0242269	−	0.0672431i
$786$		0			0
$787$	35.9021	−	35.9021i	1.27977	−	1.27977i	0.338979	−	0.940794i	$-0.389918\pi$
$787$	35.9021	−	35.9021i	1.27977	−	1.27977i	0.940794	−	0.338979i	$-0.110082\pi$
$788$		0			0
$789$	−13.8082			−0.491584
$790$		0			0
$791$	−19.1351			−0.680367
$792$		0			0
$793$	−3.57701	−	3.57701i	−0.127023	−	0.127023i
$794$		0			0
$795$	1.06971	−	2.27465i	0.0379389	−	0.0806734i
$796$		0			0
$797$	20.4445	−	20.4445i	0.724181	−	0.724181i	−0.245273	−	0.969454i	$-0.578878\pi$
$797$	20.4445	−	20.4445i	0.724181	−	0.724181i	0.969454	+	0.245273i	$0.0788776\pi$
$798$		0			0
$799$	−40.3075			−1.42598
$800$		0			0
$801$			11.7859i			0.416433i
$802$		0			0
$803$	22.3568	+	22.3568i	0.788955	+	0.788955i
$804$		0			0
$805$	−43.7253	−	29.6187i	−1.54111	−	1.04392i
$806$		0			0
$807$	6.97332	+	6.97332i	0.245473	+	0.245473i
$808$		0			0
$809$			45.7899i			1.60989i	0.593352	+	0.804943i	$0.297804\pi$
$809$			45.7899i			1.60989i	−0.593352	+	0.804943i	$0.702196\pi$
$810$		0			0
$811$	−40.9944			−1.43951			−0.719755	−	0.694228i	$-0.755746\pi$
$811$	−40.9944			−1.43951			−0.719755	+	0.694228i	$0.755746\pi$
$812$		0			0
$813$	21.8908	−	21.8908i	0.767742	−	0.767742i
$814$		0			0
$815$	10.2763	+	28.5225i	0.359964	+	0.999101i
$816$		0			0
$817$	12.2935	+	12.2935i	0.430096	+	0.430096i
$818$		0			0
$819$	−2.56282			−0.0895520
$820$		0			0
$821$	38.5043			1.34381			0.671905	−	0.740637i	$-0.265476\pi$
$821$	38.5043			1.34381			0.671905	+	0.740637i	$0.265476\pi$
$822$		0			0
$823$	14.6433	−	14.6433i	0.510433	−	0.510433i	−0.404226	−	0.914659i	$-0.632459\pi$
$823$	14.6433	−	14.6433i	0.510433	−	0.510433i	0.914659	+	0.404226i	$0.132459\pi$
$824$		0			0
$825$	1.27949	−	13.6038i	0.0445462	−	0.473625i
$826$		0			0
$827$	9.37209	−	9.37209i	0.325900	−	0.325900i	−0.525125	−	0.851025i	$-0.675982\pi$
$827$	9.37209	−	9.37209i	0.325900	−	0.325900i	0.851025	+	0.525125i	$0.175982\pi$
$828$		0			0
$829$		−	32.6312i		−	1.13333i	−0.823949	−	0.566664i	$-0.808234\pi$
$829$		−	32.6312i		−	1.13333i	0.823949	−	0.566664i	$-0.191766\pi$
$830$		0			0
$831$	−7.47597			−0.259339
$832$		0			0
$833$	86.6246	+	86.6246i	3.00137	+	3.00137i
$834$		0			0
$835$	−28.9668	+	10.4364i	−1.00244	+	0.361166i
$836$		0			0
$837$	−1.76641	−	1.76641i	−0.0610561	−	0.0610561i
$838$		0			0
$839$	24.2817			0.838298			0.419149	−	0.907918i	$-0.362329\pi$
$839$	24.2817			0.838298			0.419149	+	0.907918i	$0.362329\pi$
$840$		0			0
$841$	24.9966			0.861953
$842$		0			0
$843$	−5.74618	−	5.74618i	−0.197909	−	0.197909i
$844$		0			0
$845$	25.7572	+	12.1131i	0.886076	+	0.416702i
$846$		0			0
$847$	−12.2995	+	12.2995i	−0.422615	+	0.422615i
$848$		0			0
$849$	−1.57916			−0.0541968
$850$		0			0
$851$	6.71985	−	42.7827i	0.230354	−	1.46657i
$852$		0			0
$853$	39.7179	−	39.7179i	1.35992	−	1.35992i	0.485903	−	0.874013i	$-0.338491\pi$
$853$	39.7179	−	39.7179i	1.35992	−	1.35992i	0.874013	−	0.485903i	$-0.161509\pi$
$854$		0			0
$855$	−11.9611	−	5.62505i	−0.409062	−	0.192373i
$856$		0			0
$857$	22.7395	+	22.7395i	0.776767	+	0.776767i	0.979280	−	0.202512i	$-0.0649106\pi$
$857$	22.7395	+	22.7395i	0.776767	+	0.776767i	−0.202512	+	0.979280i	$0.564911\pi$
$858$		0			0
$859$		−	49.0394i		−	1.67320i	−0.547813	−	0.836601i	$-0.684540\pi$
$859$		−	49.0394i		−	1.67320i	0.547813	−	0.836601i	$-0.315460\pi$
$860$		0			0
$861$		−	29.8347i		−	1.01676i
$862$		0			0
$863$	−19.6158	+	19.6158i	−0.667730	+	0.667730i	−0.957190	−	0.289460i	$-0.906524\pi$
$863$	−19.6158	+	19.6158i	−0.667730	+	0.667730i	0.289460	+	0.957190i	$0.406524\pi$
$864$		0			0
$865$	8.21775	+	22.8089i	0.279412	+	0.775525i
$866$		0			0
$867$	−23.6274	−	23.6274i	−0.802427	−	0.802427i
$868$		0			0
$869$			7.94730i			0.269594i
$870$		0			0
$871$		−	1.54328i		−	0.0522922i
$872$		0			0
$873$	0.793720	+	0.793720i	0.0268634	+	0.0268634i
$874$		0			0
$875$	27.9949	−	47.4130i	0.946399	−	1.60285i
$876$		0			0
$877$	29.7427	+	29.7427i	1.00434	+	1.00434i	0.999991	+	0.00434836i	$0.00138413\pi$
$877$	29.7427	+	29.7427i	1.00434	+	1.00434i	0.00434836	+	0.999991i	$0.498616\pi$
$878$		0			0
$879$	15.5919			0.525903
$880$		0			0
$881$		−	6.36193i		−	0.214339i	−0.994241	−	0.107169i	$-0.965821\pi$
$881$		−	6.36193i		−	0.214339i	0.994241	−	0.107169i	$-0.0341787\pi$
$882$		0			0
$883$	4.69497	−	4.69497i	0.157998	−	0.157998i	−0.623681	−	0.781679i	$-0.714363\pi$
$883$	4.69497	−	4.69497i	0.157998	−	0.157998i	0.781679	+	0.623681i	$0.214363\pi$
$884$		0			0
$885$	10.5376	−	3.79656i	0.354217	−	0.127620i
$886$		0			0
$887$	31.0726	+	31.0726i	1.04331	+	1.04331i	0.999018	+	0.0442963i	$0.0141046\pi$
$887$	31.0726	+	31.0726i	1.04331	+	1.04331i	0.0442963	+	0.999018i	$0.485895\pi$
$888$		0			0
$889$	−77.9409			−2.61406
$890$		0			0
$891$		−	2.73277i		−	0.0915514i
$892$		0			0
$893$	23.7284	+	23.7284i	0.794041	+	0.794041i
$894$		0			0
$895$	8.60706	+	4.04770i	0.287702	+	0.135300i
$896$		0			0
$897$	−1.46953	−	2.01718i	−0.0490661	−	0.0673517i
$898$		0			0
$899$			4.99826i			0.166701i
$900$		0			0
$901$	−7.98163			−0.265907
$902$		0			0
$903$	−10.2422	+	10.2422i	−0.340838	+	0.340838i
$904$		0			0
$905$	−30.2816	−	14.2408i	−1.00660	−	0.473379i
$906$		0			0
$907$	−6.22151	+	6.22151i	−0.206582	+	0.206582i	−0.802813	−	0.596231i	$-0.796664\pi$
$907$	−6.22151	+	6.22151i	−0.206582	+	0.206582i	0.596231	+	0.802813i	$0.296664\pi$
$908$		0			0
$909$		−	2.66129i		−	0.0882694i
$910$		0			0
$911$		−	6.14528i		−	0.203602i	−0.994805	−	0.101801i	$-0.967539\pi$
$911$		−	6.14528i		−	0.203602i	0.994805	−	0.101801i	$-0.0324605\pi$
$912$		0			0
$913$	20.4432	−	20.4432i	0.676570	−	0.676570i
$914$		0			0
$915$	20.4498	−	7.36780i	0.676049	−	0.243572i
$916$		0			0
$917$	49.7146	−	49.7146i	1.64172	−	1.64172i
$918$		0			0
$919$	−8.86802			−0.292529			−0.146265	−	0.989246i	$-0.546725\pi$
$919$	−8.86802			−0.292529			−0.146265	+	0.989246i	$0.546725\pi$
$920$		0			0
$921$	31.5748			1.04043
$922$		0			0
$923$	−3.44269	+	3.44269i	−0.113317	+	0.113317i
$924$		0			0
$925$	44.9526	+	4.22796i	1.47803	+	0.139014i
$926$		0			0
$927$	3.17934	−	3.17934i	0.104423	−	0.104423i
$928$		0			0
$929$			38.3528i			1.25831i	0.777278	+	0.629157i	$0.216600\pi$
$929$			38.3528i			1.25831i	−0.777278	+	0.629157i	$0.783400\pi$
$930$		0			0
$931$		−	101.989i		−	3.34256i
$932$		0			0
$933$	2.79631	−	2.79631i	0.0915470	−	0.0915470i
$934$		0			0
$935$	−40.8190	+	14.7066i	−1.33493	+	0.480957i
$936$		0			0
$937$	−15.6795	+	15.6795i	−0.512226	+	0.512226i	−0.915208	−	0.402982i	$-0.867974\pi$
$937$	−15.6795	+	15.6795i	−0.512226	+	0.512226i	0.402982	+	0.915208i	$0.367974\pi$
$938$		0			0
$939$	−32.5234			−1.06136
$940$		0			0
$941$			47.2322i			1.53973i	0.638209	+	0.769863i	$0.279676\pi$
$941$			47.2322i			1.53973i	−0.638209	+	0.769863i	$0.720324\pi$
$942$		0			0
$943$	23.4828	−	17.1073i	0.764704	−	0.557091i
$944$		0			0
$945$	4.68642	−	9.96522i	0.152449	−	0.324169i
$946$		0			0
$947$	7.60447	+	7.60447i	0.247112	+	0.247112i	0.819784	−	0.572672i	$-0.194093\pi$
$947$	7.60447	+	7.60447i	0.247112	+	0.247112i	−0.572672	+	0.819784i	$0.694093\pi$
$948$		0			0
$949$			6.02074i			0.195442i
$950$		0			0
$951$	−18.4728			−0.599020
$952$		0			0
$953$	−27.6487	−	27.6487i	−0.895628	−	0.895628i	0.0994175	−	0.995046i	$-0.468302\pi$
$953$	−27.6487	−	27.6487i	−0.895628	−	0.895628i	−0.995046	+	0.0994175i	$0.968302\pi$
$954$		0			0
$955$	5.44066	+	2.55862i	0.176056	+	0.0827950i
$956$		0			0
$957$	−3.86635	+	3.86635i	−0.124981	+	0.124981i
$958$		0			0
$959$		−	26.0533i		−	0.841305i
$960$		0			0
$961$	−24.7596			−0.798696
$962$		0			0
$963$	−12.5484	−	12.5484i	−0.404366	−	0.404366i
$964$		0			0
$965$	2.34962	+	6.52151i	0.0756369	+	0.209935i
$966$		0			0
$967$	−9.16686	−	9.16686i	−0.294786	−	0.294786i	0.544181	−	0.838968i	$-0.316840\pi$
$967$	−9.16686	−	9.16686i	−0.294786	−	0.294786i	−0.838968	+	0.544181i	$0.816840\pi$
$968$		0			0
$969$			41.9710i			1.34830i
$970$		0			0
$971$		−	14.3130i		−	0.459327i	−0.973270	−	0.229663i	$-0.926237\pi$
$971$		−	14.3130i		−	0.459327i	0.973270	−	0.229663i	$-0.0737626\pi$
$972$		0			0
$973$	13.3315	+	13.3315i	0.427389	+	0.427389i
$974$		0			0
$975$	2.00406	−	1.65949i	0.0641812	−	0.0531461i
$976$		0			0
$977$	−3.39164	+	3.39164i	−0.108508	+	0.108508i	−0.759276	−	0.650768i	$-0.774447\pi$
$977$	−3.39164	+	3.39164i	−0.108508	+	0.108508i	0.650768	+	0.759276i	$0.274447\pi$
$978$		0			0
$979$		−	32.2081i		−	1.02938i
$980$		0			0
$981$		−	10.2093i		−	0.325959i
$982$		0			0
$983$	28.3572	+	28.3572i	0.904454	+	0.904454i	0.995818	−	0.0913638i	$-0.0291226\pi$
$983$	28.3572	+	28.3572i	0.904454	+	0.904454i	−0.0913638	+	0.995818i	$0.529123\pi$
$984$		0			0
$985$	27.6567	−	9.96437i	0.881216	−	0.317491i
$986$		0			0
$987$	−19.7689	+	19.7689i	−0.629252	+	0.629252i
$988$		0			0
$989$	−13.9345	−	2.18867i	−0.443090	−	0.0695958i
$990$		0			0
$991$	−5.98666			−0.190172			−0.0950862	−	0.995469i	$-0.530313\pi$
$991$	−5.98666			−0.190172			−0.0950862	+	0.995469i	$0.530313\pi$
$992$		0			0
$993$	1.62433	−	1.62433i	0.0515466	−	0.0515466i
$994$		0			0
$995$	−25.4006	+	54.0120i	−0.805254	+	1.71230i
$996$		0			0
$997$	0.598100	+	0.598100i	0.0189420	+	0.0189420i	0.716514	−	0.697572i	$-0.245736\pi$
$997$	0.598100	+	0.598100i	0.0189420	+	0.0189420i	−0.697572	+	0.716514i	$0.745736\pi$
$998$		0			0
$999$	9.03019			0.285703

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.t.a.1057.14	yes	48
5.3	odd	4	inner	1380.2.t.a.1333.13	yes	48
23.22	odd	2	inner	1380.2.t.a.1057.13	✓	48
115.68	even	4	inner	1380.2.t.a.1333.14	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.t.a.1057.13	✓	48	23.22	odd	2	inner
1380.2.t.a.1057.14	yes	48	1.1	even	1	trivial
1380.2.t.a.1333.13	yes	48	5.3	odd	4	inner
1380.2.t.a.1333.14	yes	48	115.68	even	4	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:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(0.951596 - 2.02348i) q^{5} +(-3.48236 + 3.48236i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(0.951596 - 2.02348i) q^{5} +(-3.48236 + 3.48236i) q^{7} -1.00000i q^{9} +2.73277i q^{11} +(-0.367971 + 0.367971i) q^{13} +(-0.757935 - 2.10370i) q^{15} +(-5.02066 + 5.02066i) q^{17} +5.91117 q^{19} +4.92480i q^{21} +(-3.87629 + 2.82390i) q^{23} +(-3.18893 - 3.85107i) q^{25} +(-0.707107 - 0.707107i) q^{27} +2.00084i q^{29} +2.49808 q^{31} +(1.93236 + 1.93236i) q^{33} +(3.73268 + 10.3603i) q^{35} +(-6.38531 + 6.38531i) q^{37} +0.520390i q^{39} -6.05805 q^{41} +(2.07971 + 2.07971i) q^{43} +(-2.02348 - 0.951596i) q^{45} +(4.01416 + 4.01416i) q^{47} -17.2536i q^{49} +7.10029i q^{51} +(0.794878 + 0.794878i) q^{53} +(5.52971 + 2.60050i) q^{55} +(4.17983 - 4.17983i) q^{57} +5.00908i q^{59} +9.72089i q^{61} +(3.48236 + 3.48236i) q^{63} +(0.394422 + 1.09474i) q^{65} +(-2.09702 + 2.09702i) q^{67} +(-0.744154 + 4.73775i) q^{69} +9.35585 q^{71} +(8.18100 - 8.18100i) q^{73} +(-4.97803 - 0.468202i) q^{75} +(-9.51650 - 9.51650i) q^{77} +2.90814 q^{79} -1.00000 q^{81} +(-7.48074 - 7.48074i) q^{83} +(5.38156 + 14.9368i) q^{85} +(1.41481 + 1.41481i) q^{87} -11.7859 q^{89} -2.56282i q^{91} +(1.76641 - 1.76641i) q^{93} +(5.62505 - 11.9611i) q^{95} +(-0.793720 + 0.793720i) q^{97} +2.73277 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{13} - 16 q^{23} - 8 q^{25} + 8 q^{31} + 8 q^{35} - 24 q^{41} + 8 q^{47} - 32 q^{55} - 24 q^{71} + 8 q^{73} + 32 q^{75} + 40 q^{77} - 48 q^{81} + 24 q^{85} - 40 q^{87}+O(q^{100}) \) 48 * q - 8 * q^13 - 16 * q^23 - 8 * q^25 + 8 * q^31 + 8 * q^35 - 24 * q^41 + 8 * q^47 - 32 * q^55 - 24 * q^71 + 8 * q^73 + 32 * q^75 + 40 * q^77 - 48 * q^81 + 24 * q^85 - 40 * q^87

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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