LMFDB - Embedded newform 1380.2.t.a.1057.11

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			1057.11
Character	$\chi$	$=$	1380.1057
Dual form			1380.2.t.a.1333.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(-0.0653842 - 2.23511i) q^{5} +(-0.522235 + 0.522235i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.0653842 - 2.23511i) q^{5} +(-0.522235 + 0.522235i) q^{7} -1.00000i q^{9} +3.66808i q^{11} +(0.950820 - 0.950820i) q^{13} +(1.62670 + 1.53423i) q^{15} +(-3.43249 + 3.43249i) q^{17} -1.65402 q^{19} -0.738552i q^{21} +(4.78449 + 0.329559i) q^{23} +(-4.99145 + 0.292282i) q^{25} +(0.707107 + 0.707107i) q^{27} -1.81387i q^{29} -1.24635 q^{31} +(-2.59372 - 2.59372i) q^{33} +(1.20140 + 1.13311i) q^{35} +(-2.81999 + 2.81999i) q^{37} +1.34466i q^{39} +12.2498 q^{41} +(7.63212 + 7.63212i) q^{43} +(-2.23511 + 0.0653842i) q^{45} +(6.98933 + 6.98933i) q^{47} +6.45454i q^{49} -4.85428i q^{51} +(-1.34571 - 1.34571i) q^{53} +(8.19856 - 0.239834i) q^{55} +(1.16957 - 1.16957i) q^{57} +1.65676i q^{59} -2.65514i q^{61} +(0.522235 + 0.522235i) q^{63} +(-2.18736 - 2.06302i) q^{65} +(-5.90434 + 5.90434i) q^{67} +(-3.61618 + 3.15012i) q^{69} +6.37272 q^{71} +(-11.2037 + 11.2037i) q^{73} +(3.32281 - 3.73616i) q^{75} +(-1.91560 - 1.91560i) q^{77} +2.17955 q^{79} -1.00000 q^{81} +(8.40827 + 8.40827i) q^{83} +(7.89644 + 7.44758i) q^{85} +(1.28260 + 1.28260i) q^{87} -8.81161 q^{89} +0.993103i q^{91} +(0.881300 - 0.881300i) q^{93} +(0.108146 + 3.69691i) q^{95} +(-0.249650 + 0.249650i) q^{97} +3.66808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.0653842	−	2.23511i	−0.0292407	−	0.999572i
$5$	−0.0653842	−	2.23511i	−0.0292407	−	0.999572i
$6$		0			0
$7$	−0.522235	+	0.522235i	−0.197386	+	0.197386i	−0.798879	−	0.601492i	$-0.794573\pi$
$7$	−0.522235	+	0.522235i	−0.197386	+	0.197386i	0.601492	+	0.798879i	$0.294573\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$			3.66808i			1.10597i	0.833192	+	0.552984i	$0.186511\pi$
$11$			3.66808i			1.10597i	−0.833192	+	0.552984i	$0.813489\pi$
$12$		0			0
$13$	0.950820	−	0.950820i	0.263710	−	0.263710i	−0.562849	−	0.826559i	$-0.690295\pi$
$13$	0.950820	−	0.950820i	0.263710	−	0.263710i	0.826559	+	0.562849i	$0.190295\pi$
$14$		0			0
$15$	1.62670	+	1.53423i	0.420011	+	0.396136i
$16$		0			0
$17$	−3.43249	+	3.43249i	−0.832502	+	0.832502i	−0.987858	−	0.155356i	$-0.950347\pi$
$17$	−3.43249	+	3.43249i	−0.832502	+	0.832502i	0.155356	+	0.987858i	$0.450347\pi$
$18$		0			0
$19$	−1.65402			−0.379457			−0.189729	−	0.981837i	$-0.560761\pi$
$19$	−1.65402			−0.379457			−0.189729	+	0.981837i	$0.560761\pi$
$20$		0			0
$21$		−	0.738552i		−	0.161165i
$22$		0			0
$23$	4.78449	+	0.329559i	0.997636	+	0.0687178i
$23$	4.78449	+	0.329559i	0.997636	+	0.0687178i
$24$		0			0
$25$	−4.99145	+	0.292282i	−0.998290	+	0.0584564i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$		−	1.81387i		−	0.336827i	−0.985716	−	0.168414i	$-0.946136\pi$
$29$		−	1.81387i		−	0.336827i	0.985716	−	0.168414i	$-0.0538644\pi$
$30$		0			0
$31$	−1.24635			−0.223850			−0.111925	−	0.993717i	$-0.535702\pi$
$31$	−1.24635			−0.223850			−0.111925	+	0.993717i	$0.535702\pi$
$32$		0			0
$33$	−2.59372	−	2.59372i	−0.451509	−	0.451509i
$34$		0			0
$35$	1.20140	+	1.13311i	0.203074	+	0.191530i
$36$		0			0
$37$	−2.81999	+	2.81999i	−0.463603	+	0.463603i	−0.899834	−	0.436231i	$-0.856313\pi$
$37$	−2.81999	+	2.81999i	−0.463603	+	0.463603i	0.436231	+	0.899834i	$0.356313\pi$
$38$		0			0
$39$			1.34466i			0.215318i
$40$		0			0
$41$	12.2498			1.91310			0.956550	−	0.291569i	$-0.0941774\pi$
$41$	12.2498			1.91310			0.956550	+	0.291569i	$0.0941774\pi$
$42$		0			0
$43$	7.63212	+	7.63212i	1.16389	+	1.16389i	0.983617	+	0.180270i	$0.0576970\pi$
$43$	7.63212	+	7.63212i	1.16389	+	1.16389i	0.180270	+	0.983617i	$0.442303\pi$
$44$		0			0
$45$	−2.23511	+	0.0653842i	−0.333191	+	0.00974689i
$46$		0			0
$47$	6.98933	+	6.98933i	1.01950	+	1.01950i	0.999806	+	0.0196927i	$0.00626877\pi$
$47$	6.98933	+	6.98933i	1.01950	+	1.01950i	0.0196927	+	0.999806i	$0.493731\pi$
$48$		0			0
$49$			6.45454i			0.922077i
$50$		0			0
$51$		−	4.85428i		−	0.679735i
$52$		0			0
$53$	−1.34571	−	1.34571i	−0.184847	−	0.184847i	0.608617	−	0.793464i	$-0.291725\pi$
$53$	−1.34571	−	1.34571i	−0.184847	−	0.184847i	−0.793464	+	0.608617i	$0.791725\pi$
$54$		0			0
$55$	8.19856	−	0.239834i	1.10549	−	0.0323392i
$56$		0			0
$57$	1.16957	−	1.16957i	0.154913	−	0.154913i
$58$		0			0
$59$			1.65676i			0.215692i	0.994168	+	0.107846i	$0.0343954\pi$
$59$			1.65676i			0.215692i	−0.994168	+	0.107846i	$0.965605\pi$
$60$		0			0
$61$		−	2.65514i		−	0.339956i	−0.985448	−	0.169978i	$-0.945630\pi$
$61$		−	2.65514i		−	0.339956i	0.985448	−	0.169978i	$-0.0543697\pi$
$62$		0			0
$63$	0.522235	+	0.522235i	0.0657955	+	0.0657955i
$64$		0			0
$65$	−2.18736	−	2.06302i	−0.271308	−	0.255886i
$66$		0			0
$67$	−5.90434	+	5.90434i	−0.721330	+	0.721330i	−0.968876	−	0.247546i	$-0.920376\pi$
$67$	−5.90434	+	5.90434i	−0.721330	+	0.721330i	0.247546	+	0.968876i	$0.420376\pi$
$68$		0			0
$69$	−3.61618	+	3.15012i	−0.435337	+	0.379229i
$70$		0			0
$71$	6.37272			0.756303			0.378151	−	0.925744i	$-0.376560\pi$
$71$	6.37272			0.756303			0.378151	+	0.925744i	$0.376560\pi$
$72$		0			0
$73$	−11.2037	+	11.2037i	−1.31129	+	1.31129i	−0.390823	+	0.920466i	$0.627809\pi$
$73$	−11.2037	+	11.2037i	−1.31129	+	1.31129i	−0.920466	+	0.390823i	$0.872191\pi$
$74$		0			0
$75$	3.32281	−	3.73616i	0.383685	−	0.431415i
$76$		0			0
$77$	−1.91560	−	1.91560i	−0.218303	−	0.218303i
$78$		0			0
$79$	2.17955			0.245219			0.122609	−	0.992455i	$-0.460874\pi$
$79$	2.17955			0.245219			0.122609	+	0.992455i	$0.460874\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	8.40827	+	8.40827i	0.922928	+	0.922928i	0.997235	−	0.0743077i	$-0.0236747\pi$
$83$	8.40827	+	8.40827i	0.922928	+	0.922928i	−0.0743077	+	0.997235i	$0.523675\pi$
$84$		0			0
$85$	7.89644	+	7.44758i	0.856489	+	0.807803i
$86$		0			0
$87$	1.28260	+	1.28260i	0.137509	+	0.137509i
$88$		0			0
$89$	−8.81161			−0.934029			−0.467015	−	0.884250i	$-0.654670\pi$
$89$	−8.81161			−0.934029			−0.467015	+	0.884250i	$0.654670\pi$
$90$		0			0
$91$			0.993103i			0.104105i
$92$		0			0
$93$	0.881300	−	0.881300i	0.0913865	−	0.0913865i
$94$		0			0
$95$	0.108146	+	3.69691i	0.0110956	+	0.379295i
$96$		0			0
$97$	−0.249650	+	0.249650i	−0.0253481	+	0.0253481i	−0.719667	−	0.694319i	$-0.755706\pi$
$97$	−0.249650	+	0.249650i	−0.0253481	+	0.0253481i	0.694319	+	0.719667i	$0.255706\pi$
$98$		0			0
$99$	3.66808			0.368656
$100$		0			0
$101$	8.76357			0.872008			0.436004	−	0.899945i	$-0.356393\pi$
$101$	8.76357			0.872008			0.436004	+	0.899945i	$0.356393\pi$
$102$		0			0
$103$	−7.39435	−	7.39435i	−0.728587	−	0.728587i	0.241751	−	0.970338i	$-0.422278\pi$
$103$	−7.39435	−	7.39435i	−0.728587	−	0.728587i	−0.970338	+	0.241751i	$0.922278\pi$
$104$		0			0
$105$	−1.65075	+	0.0482896i	−0.161096	+	0.00471258i
$106$		0			0
$107$	−12.1854	+	12.1854i	−1.17801	+	1.17801i	−0.197758	+	0.980251i	$0.563366\pi$
$107$	−12.1854	+	12.1854i	−1.17801	+	1.17801i	−0.980251	+	0.197758i	$0.936634\pi$
$108$		0			0
$109$	−6.27127			−0.600679			−0.300339	−	0.953832i	$-0.597100\pi$
$109$	−6.27127			−0.600679			−0.300339	+	0.953832i	$0.597100\pi$
$110$		0			0
$111$		−	3.98806i		−	0.378530i
$112$		0			0
$113$	6.51393	+	6.51393i	0.612779	+	0.612779i	0.943669	−	0.330890i	$-0.107349\pi$
$113$	6.51393	+	6.51393i	0.612779	+	0.612779i	−0.330890	+	0.943669i	$0.607349\pi$
$114$		0			0
$115$	0.423771	−	10.7154i	0.0395168	−	0.999219i
$116$		0			0
$117$	−0.950820	−	0.950820i	−0.0879033	−	0.0879033i
$118$		0			0
$119$		−	3.58514i		−	0.328649i
$120$		0			0
$121$	−2.45480			−0.223163
$122$		0			0
$123$	−8.66193	+	8.66193i	−0.781020	+	0.781020i
$124$		0			0
$125$	0.979644	+	11.1373i	0.0876220	+	0.996154i
$126$		0			0
$127$	−9.93235	−	9.93235i	−0.881353	−	0.881353i	0.112319	−	0.993672i	$-0.464172\pi$
$127$	−9.93235	−	9.93235i	−0.881353	−	0.881353i	−0.993672	+	0.112319i	$0.964172\pi$
$128$		0			0
$129$	−10.7934			−0.950310
$130$		0			0
$131$	9.72468			0.849649			0.424824	−	0.905276i	$-0.360336\pi$
$131$	9.72468			0.849649			0.424824	+	0.905276i	$0.360336\pi$
$132$		0			0
$133$	0.863786	−	0.863786i	0.0748997	−	0.0748997i
$134$		0			0
$135$	1.53423	−	1.62670i	0.132045	−	0.140004i
$136$		0			0
$137$	−0.992658	+	0.992658i	−0.0848085	+	0.0848085i	−0.748238	−	0.663430i	$-0.769100\pi$
$137$	−0.992658	+	0.992658i	−0.0848085	+	0.0848085i	0.663430	+	0.748238i	$0.269100\pi$
$138$		0			0
$139$		−	6.95890i		−	0.590246i	−0.955459	−	0.295123i	$-0.904639\pi$
$139$		−	6.95890i		−	0.590246i	0.955459	−	0.295123i	$-0.0953606\pi$
$140$		0			0
$141$	−9.88441			−0.832417
$142$		0			0
$143$	3.48768	+	3.48768i	0.291654	+	0.291654i
$144$		0			0
$145$	−4.05420	+	0.118598i	−0.336683	+	0.00984906i
$146$		0			0
$147$	−4.56405	−	4.56405i	−0.376436	−	0.376436i
$148$		0			0
$149$	9.08810			0.744526			0.372263	−	0.928127i	$-0.378582\pi$
$149$	9.08810			0.744526			0.372263	+	0.928127i	$0.378582\pi$
$150$		0			0
$151$	8.40962			0.684365			0.342183	−	0.939633i	$-0.388834\pi$
$151$	8.40962			0.684365			0.342183	+	0.939633i	$0.388834\pi$
$152$		0			0
$153$	3.43249	+	3.43249i	0.277501	+	0.277501i
$154$		0			0
$155$	0.0814913	+	2.78572i	0.00654554	+	0.223755i
$156$		0			0
$157$	6.30557	−	6.30557i	0.503240	−	0.503240i	−0.409204	−	0.912443i	$-0.634193\pi$
$157$	6.30557	−	6.30557i	0.503240	−	0.503240i	0.912443	+	0.409204i	$0.134193\pi$
$158$		0			0
$159$	1.90312			0.150927
$160$		0			0
$161$	−2.67074	+	2.32652i	−0.210484	+	0.183356i
$162$		0			0
$163$	−2.95976	+	2.95976i	−0.231826	+	0.231826i	−0.813455	−	0.581628i	$-0.802416\pi$
$163$	−2.95976	+	2.95976i	−0.231826	+	0.231826i	0.581628	+	0.813455i	$0.302416\pi$
$164$		0			0
$165$	−5.62767	+	5.96685i	−0.438114	+	0.464519i
$166$		0			0
$167$	9.51839	+	9.51839i	0.736555	+	0.736555i	0.971910	−	0.235355i	$-0.0756251\pi$
$167$	9.51839	+	9.51839i	0.736555	+	0.736555i	−0.235355	+	0.971910i	$0.575625\pi$
$168$		0			0
$169$			11.1919i			0.860914i
$170$		0			0
$171$			1.65402i			0.126486i
$172$		0			0
$173$	−13.6077	+	13.6077i	−1.03457	+	1.03457i	−0.0351926	+	0.999381i	$0.511204\pi$
$173$	−13.6077	+	13.6077i	−1.03457	+	1.03457i	−0.999381	+	0.0351926i	$0.988796\pi$
$174$		0			0
$175$	2.45407	−	2.75935i	0.185510	−	0.208587i
$176$		0			0
$177$	−1.17151	−	1.17151i	−0.0880560	−	0.0880560i
$178$		0			0
$179$		−	24.8979i		−	1.86095i	−0.366351	−	0.930477i	$-0.619393\pi$
$179$		−	24.8979i		−	1.86095i	0.366351	−	0.930477i	$-0.380607\pi$
$180$		0			0
$181$		−	12.5916i		−	0.935927i	−0.883748	−	0.467964i	$-0.844988\pi$
$181$		−	12.5916i		−	0.935927i	0.883748	−	0.467964i	$-0.155012\pi$
$182$		0			0
$183$	1.87747	+	1.87747i	0.138786	+	0.138786i
$184$		0			0
$185$	6.48737	+	6.11860i	0.476961	+	0.449849i
$186$		0			0
$187$	−12.5907	−	12.5907i	−0.920720	−	0.920720i
$188$		0			0
$189$	−0.738552			−0.0537218
$190$		0			0
$191$			16.9364i			1.22548i	0.790286	+	0.612739i	$0.209932\pi$
$191$			16.9364i			1.22548i	−0.790286	+	0.612739i	$0.790068\pi$
$192$		0			0
$193$	2.99751	−	2.99751i	0.215765	−	0.215765i	−0.590946	−	0.806711i	$-0.701245\pi$
$193$	2.99751	−	2.99751i	0.215765	−	0.215765i	0.806711	+	0.590946i	$0.201245\pi$
$194$		0			0
$195$	3.00547	−	0.0879196i	0.215226	−	0.00629605i
$196$		0			0
$197$	−6.30825	−	6.30825i	−0.449444	−	0.449444i	0.445725	−	0.895170i	$-0.352946\pi$
$197$	−6.30825	−	6.30825i	−0.449444	−	0.449444i	−0.895170	+	0.445725i	$0.852946\pi$
$198$		0			0
$199$	1.53411			0.108750			0.0543751	−	0.998521i	$-0.482683\pi$
$199$	1.53411			0.108750			0.0543751	+	0.998521i	$0.482683\pi$
$200$		0			0
$201$		−	8.35000i		−	0.588963i
$202$		0			0
$203$	0.947267	+	0.947267i	0.0664851	+	0.0664851i
$204$		0			0
$205$	−0.800944	−	27.3797i	−0.0559403	−	1.91228i
$206$		0			0
$207$	0.329559	−	4.78449i	0.0229059	−	0.332545i
$208$		0			0
$209$		−	6.06706i		−	0.419667i
$210$		0			0
$211$	−10.4163			−0.717087			−0.358544	−	0.933513i	$-0.616727\pi$
$211$	−10.4163			−0.717087			−0.358544	+	0.933513i	$0.616727\pi$
$212$		0			0
$213$	−4.50619	+	4.50619i	−0.308759	+	0.308759i
$214$		0			0
$215$	16.5596	−	17.5577i	1.12936	−	1.19742i
$216$		0			0
$217$	0.650886	−	0.650886i	0.0441850	−	0.0441850i
$218$		0			0
$219$		−	15.8444i		−	1.07066i
$220$		0			0
$221$			6.52736i			0.439078i
$222$		0			0
$223$	3.61774	−	3.61774i	0.242262	−	0.242262i	−0.575523	−	0.817785i	$-0.695202\pi$
$223$	3.61774	−	3.61774i	0.242262	−	0.242262i	0.817785	+	0.575523i	$0.195202\pi$
$224$		0			0
$225$	0.292282	+	4.99145i	0.0194855	+	0.332763i
$226$		0			0
$227$	9.17087	−	9.17087i	0.608692	−	0.608692i	−0.333912	−	0.942604i	$-0.608369\pi$
$227$	9.17087	−	9.17087i	0.608692	−	0.608692i	0.942604	+	0.333912i	$0.108369\pi$
$228$		0			0
$229$	−0.601252			−0.0397318			−0.0198659	−	0.999803i	$-0.506324\pi$
$229$	−0.601252			−0.0397318			−0.0198659	+	0.999803i	$0.506324\pi$
$230$		0			0
$231$	2.70907			0.178244
$232$		0			0
$233$	−3.45391	+	3.45391i	−0.226273	+	0.226273i	−0.811134	−	0.584861i	$-0.801149\pi$
$233$	−3.45391	+	3.45391i	−0.226273	+	0.226273i	0.584861	+	0.811134i	$0.301149\pi$
$234$		0			0
$235$	15.1649	−	16.0789i	0.989252	−	1.04887i
$236$		0			0
$237$	−1.54118	+	1.54118i	−0.100110	+	0.100110i
$238$		0			0
$239$			15.5823i			1.00794i	0.863722	+	0.503968i	$0.168127\pi$
$239$			15.5823i			1.00794i	−0.863722	+	0.503968i	$0.831873\pi$
$240$		0			0
$241$		−	17.2192i		−	1.10919i	−0.832121	−	0.554595i	$-0.812873\pi$
$241$		−	17.2192i		−	1.10919i	0.832121	−	0.554595i	$-0.187127\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	14.4266	−	0.422025i	0.921683	−	0.0269622i
$246$		0			0
$247$	−1.57267	+	1.57267i	−0.100067	+	0.100067i
$248$		0			0
$249$	−11.8911			−0.753567
$250$		0			0
$251$		−	16.2834i		−	1.02780i	−0.857851	−	0.513898i	$-0.828201\pi$
$251$		−	16.2834i		−	1.02780i	0.857851	−	0.513898i	$-0.171799\pi$
$252$		0			0
$253$	−1.20885	+	17.5499i	−0.0759996	+	1.10335i
$254$		0			0
$255$	−10.8499	+	0.317393i	−0.679444	+	0.0198759i
$256$		0			0
$257$	−12.5837	−	12.5837i	−0.784949	−	0.784949i	0.195713	−	0.980661i	$-0.437298\pi$
$257$	−12.5837	−	12.5837i	−0.784949	−	0.784949i	−0.980661	+	0.195713i	$0.937298\pi$
$258$		0			0
$259$		−	2.94539i		−	0.183018i
$260$		0			0
$261$	−1.81387			−0.112276
$262$		0			0
$263$	12.6049	+	12.6049i	0.777252	+	0.777252i	0.979363	−	0.202110i	$-0.0647800\pi$
$263$	12.6049	+	12.6049i	0.777252	+	0.777252i	−0.202110	+	0.979363i	$0.564780\pi$
$264$		0			0
$265$	−2.91982	+	3.09579i	−0.179363	+	0.190173i
$266$		0			0
$267$	6.23075	−	6.23075i	0.381316	−	0.381316i
$268$		0			0
$269$		−	22.1039i		−	1.34770i	−0.738868	−	0.673850i	$-0.764639\pi$
$269$		−	22.1039i		−	1.34770i	0.738868	−	0.673850i	$-0.235361\pi$
$270$		0			0
$271$	19.1797			1.16508			0.582542	−	0.812801i	$-0.302058\pi$
$271$	19.1797			1.16508			0.582542	+	0.812801i	$0.302058\pi$
$272$		0			0
$273$	−0.702230	−	0.702230i	−0.0425009	−	0.0425009i
$274$		0			0
$275$	−1.07211	−	18.3090i	−0.0646508	−	1.10408i
$276$		0			0
$277$	−2.17312	−	2.17312i	−0.130570	−	0.130570i	0.638802	−	0.769371i	$-0.279430\pi$
$277$	−2.17312	−	2.17312i	−0.130570	−	0.130570i	−0.769371	+	0.638802i	$0.779430\pi$
$278$		0			0
$279$			1.24635i			0.0746168i
$280$		0			0
$281$		−	23.3501i		−	1.39295i	−0.717580	−	0.696476i	$-0.754750\pi$
$281$		−	23.3501i		−	1.39295i	0.717580	−	0.696476i	$-0.245250\pi$
$282$		0			0
$283$	6.64860	+	6.64860i	0.395218	+	0.395218i	0.876543	−	0.481324i	$-0.159844\pi$
$283$	6.64860	+	6.64860i	0.395218	+	0.395218i	−0.481324	+	0.876543i	$0.659844\pi$
$284$		0			0
$285$	−2.69058	−	2.53764i	−0.159376	−	0.150317i
$286$		0			0
$287$	−6.39728	+	6.39728i	−0.377620	+	0.377620i
$288$		0			0
$289$		−	6.56403i		−	0.386119i
$290$		0			0
$291$		−	0.353059i		−	0.0206967i
$292$		0			0
$293$	−1.13824	−	1.13824i	−0.0664966	−	0.0664966i	0.673076	−	0.739573i	$-0.264973\pi$
$293$	−1.13824	−	1.13824i	−0.0664966	−	0.0664966i	−0.739573	+	0.673076i	$0.764973\pi$
$294$		0			0
$295$	3.70305	−	0.108326i	0.215600	−	0.00630699i
$296$		0			0
$297$	−2.59372	+	2.59372i	−0.150503	+	0.150503i
$298$		0			0
$299$	4.86254	−	4.23584i	0.281208	−	0.244965i
$300$		0			0
$301$	−7.97152			−0.459471
$302$		0			0
$303$	−6.19678	+	6.19678i	−0.355996	+	0.355996i
$304$		0			0
$305$	−5.93454	+	0.173604i	−0.339811	+	0.00994055i
$306$		0			0
$307$	−9.82503	−	9.82503i	−0.560744	−	0.560744i	0.368775	−	0.929519i	$-0.379777\pi$
$307$	−9.82503	−	9.82503i	−0.560744	−	0.560744i	−0.929519	+	0.368775i	$0.879777\pi$
$308$		0			0
$309$	10.4572			0.594889
$310$		0			0
$311$	−19.0921			−1.08261			−0.541306	−	0.840825i	$-0.682070\pi$
$311$	−19.0921			−1.08261			−0.541306	+	0.840825i	$0.682070\pi$
$312$		0			0
$313$	15.5236	+	15.5236i	0.877449	+	0.877449i	0.993270	−	0.115821i	$-0.0369501\pi$
$313$	15.5236	+	15.5236i	0.877449	+	0.877449i	−0.115821	+	0.993270i	$0.536950\pi$
$314$		0			0
$315$	1.13311	−	1.20140i	0.0638434	−	0.0676912i
$316$		0			0
$317$	12.0364	+	12.0364i	0.676032	+	0.676032i	0.959100	−	0.283068i	$-0.0913522\pi$
$317$	12.0364	+	12.0364i	0.676032	+	0.676032i	−0.283068	+	0.959100i	$0.591352\pi$
$318$		0			0
$319$	6.65342			0.372520
$320$		0			0
$321$		−	17.2328i		−	0.961840i
$322$		0			0
$323$	5.67740	−	5.67740i	0.315899	−	0.315899i
$324$		0			0
$325$	−4.46806	+	5.02388i	−0.247843	+	0.278674i
$326$		0			0
$327$	4.43446	−	4.43446i	0.245226	−	0.245226i
$328$		0			0
$329$	−7.30015			−0.402470
$330$		0			0
$331$	−26.0896			−1.43402			−0.717008	−	0.697065i	$-0.754489\pi$
$331$	−26.0896			−1.43402			−0.717008	+	0.697065i	$0.754489\pi$
$332$		0			0
$333$	2.81999	+	2.81999i	0.154534	+	0.154534i
$334$		0			0
$335$	13.5829	+	12.8108i	0.742114	+	0.699929i
$336$		0			0
$337$	−22.1363	+	22.1363i	−1.20584	+	1.20584i	−0.233477	+	0.972362i	$0.575010\pi$
$337$	−22.1363	+	22.1363i	−1.20584	+	1.20584i	−0.972362	+	0.233477i	$0.924990\pi$
$338$		0			0
$339$	−9.21208			−0.500332
$340$		0			0
$341$		−	4.57170i		−	0.247571i
$342$		0			0
$343$	−7.02644	−	7.02644i	−0.379392	−	0.379392i
$344$		0			0
$345$	7.27730	+	7.87660i	0.391797	+	0.424062i
$346$		0			0
$347$	−0.952983	−	0.952983i	−0.0511588	−	0.0511588i	0.681065	−	0.732223i	$-0.261517\pi$
$347$	−0.952983	−	0.952983i	−0.0511588	−	0.0511588i	−0.732223	+	0.681065i	$0.761517\pi$
$348$		0			0
$349$		−	1.65693i		−	0.0886933i	−0.999016	−	0.0443467i	$-0.985879\pi$
$349$		−	1.65693i		−	0.0886933i	0.999016	−	0.0443467i	$-0.0141206\pi$
$350$		0			0
$351$	1.34466			0.0717727
$352$		0			0
$353$	23.9968	−	23.9968i	1.27722	−	1.27722i	0.335004	−	0.942217i	$-0.391262\pi$
$353$	23.9968	−	23.9968i	1.27722	−	1.27722i	0.942217	−	0.335004i	$-0.108738\pi$
$354$		0			0
$355$	−0.416675	−	14.2437i	−0.0221148	−	0.755979i
$356$		0			0
$357$	2.53508	+	2.53508i	0.134170	+	0.134170i
$358$		0			0
$359$	−24.8750			−1.31285			−0.656426	−	0.754391i	$-0.727932\pi$
$359$	−24.8750			−1.31285			−0.656426	+	0.754391i	$0.727932\pi$
$360$		0			0
$361$	−16.2642			−0.856012
$362$		0			0
$363$	1.73580	−	1.73580i	0.0911060	−	0.0911060i
$364$		0			0
$365$	25.7740	+	24.3089i	1.34907	+	1.27238i
$366$		0			0
$367$	16.6814	−	16.6814i	0.870764	−	0.870764i	−0.121792	−	0.992556i	$-0.538864\pi$
$367$	16.6814	−	16.6814i	0.870764	−	0.870764i	0.992556	+	0.121792i	$0.0388641\pi$
$368$		0			0
$369$		−	12.2498i		−	0.637700i
$370$		0			0
$371$	1.40555			0.0729726
$372$		0			0
$373$	−25.8674	−	25.8674i	−1.33936	−	1.33936i	−0.896676	−	0.442688i	$-0.854025\pi$
$373$	−25.8674	−	25.8674i	−1.33936	−	1.33936i	−0.442688	−	0.896676i	$-0.645975\pi$
$374$		0			0
$375$	−8.56800	−	7.18257i	−0.442450	−	0.370907i
$376$		0			0
$377$	−1.72466	−	1.72466i	−0.0888247	−	0.0888247i
$378$		0			0
$379$	10.1957			0.523718			0.261859	−	0.965106i	$-0.415664\pi$
$379$	10.1957			0.523718			0.261859	+	0.965106i	$0.415664\pi$
$380$		0			0
$381$	14.0465			0.719622
$382$		0			0
$383$	15.9633	+	15.9633i	0.815687	+	0.815687i	0.985480	−	0.169793i	$-0.0543099\pi$
$383$	15.9633	+	15.9633i	0.815687	+	0.815687i	−0.169793	+	0.985480i	$0.554310\pi$
$384$		0			0
$385$	−4.15633	+	4.40683i	−0.211826	+	0.224593i
$386$		0			0
$387$	7.63212	−	7.63212i	0.387962	−	0.387962i
$388$		0			0
$389$	−22.3409			−1.13273			−0.566364	−	0.824155i	$-0.691651\pi$
$389$	−22.3409			−1.13273			−0.566364	+	0.824155i	$0.691651\pi$
$390$		0			0
$391$	−17.5540	+	15.2915i	−0.887742	+	0.773326i
$392$		0			0
$393$	−6.87638	+	6.87638i	−0.346868	+	0.346868i
$394$		0			0
$395$	−0.142508	−	4.87154i	−0.00717037	−	0.245114i
$396$		0			0
$397$	−25.2679	−	25.2679i	−1.26816	−	1.26816i	−0.947039	−	0.321119i	$-0.895941\pi$
$397$	−25.2679	−	25.2679i	−1.26816	−	1.26816i	−0.321119	−	0.947039i	$-0.604059\pi$
$398$		0			0
$399$			1.22158i			0.0611554i
$400$		0			0
$401$		−	21.4878i		−	1.07305i	−0.843884	−	0.536525i	$-0.819737\pi$
$401$		−	21.4878i		−	1.07305i	0.843884	−	0.536525i	$-0.180263\pi$
$402$		0			0
$403$	−1.18505	+	1.18505i	−0.0590316	+	0.0590316i
$404$		0			0
$405$	0.0653842	+	2.23511i	0.00324896	+	0.111064i
$406$		0			0
$407$	−10.3439	−	10.3439i	−0.512730	−	0.512730i
$408$		0			0
$409$			26.0814i			1.28964i	0.764333	+	0.644821i	$0.223068\pi$
$409$			26.0814i			1.28964i	−0.764333	+	0.644821i	$0.776932\pi$
$410$		0			0
$411$		−	1.40383i		−	0.0692459i
$412$		0			0
$413$	−0.865220	−	0.865220i	−0.0425747	−	0.0425747i
$414$		0			0
$415$	18.2437	−	19.3432i	0.895546	−	0.949520i
$416$		0			0
$417$	4.92068	+	4.92068i	0.240967	+	0.240967i
$418$		0			0
$419$	0.603397			0.0294778			0.0147389	−	0.999891i	$-0.495308\pi$
$419$	0.603397			0.0294778			0.0147389	+	0.999891i	$0.495308\pi$
$420$		0			0
$421$			18.9912i			0.925572i	0.886470	+	0.462786i	$0.153150\pi$
$421$			18.9912i			0.925572i	−0.886470	+	0.462786i	$0.846850\pi$
$422$		0			0
$423$	6.98933	−	6.98933i	0.339833	−	0.339833i
$424$		0			0
$425$	16.1299	−	18.1364i	0.782413	−	0.879743i
$426$		0			0
$427$	1.38661	+	1.38661i	0.0671027	+	0.0671027i
$428$		0			0
$429$	−4.93232			−0.238135
$430$		0			0
$431$		−	14.4341i		−	0.695266i	−0.937631	−	0.347633i	$-0.886986\pi$
$431$		−	14.4341i		−	0.695266i	0.937631	−	0.347633i	$-0.113014\pi$
$432$		0			0
$433$	0.939865	+	0.939865i	0.0451670	+	0.0451670i	0.729330	−	0.684163i	$-0.239832\pi$
$433$	0.939865	+	0.939865i	0.0451670	+	0.0451670i	−0.684163	+	0.729330i	$0.739832\pi$
$434$		0			0
$435$	2.78289	−	2.95062i	0.133430	−	0.141471i
$436$		0			0
$437$	−7.91363	−	0.545096i	−0.378560	−	0.0260755i
$438$		0			0
$439$		−	6.72744i		−	0.321083i	−0.987029	−	0.160542i	$-0.948676\pi$
$439$		−	6.72744i		−	0.321083i	0.987029	−	0.160542i	$-0.0513241\pi$
$440$		0			0
$441$	6.45454			0.307359
$442$		0			0
$443$	−19.9853	+	19.9853i	−0.949528	+	0.949528i	−0.998786	−	0.0492578i	$-0.984314\pi$
$443$	−19.9853	+	19.9853i	−0.949528	+	0.949528i	0.0492578	+	0.998786i	$0.484314\pi$
$444$		0			0
$445$	0.576140	+	19.6949i	0.0273117	+	0.933630i
$446$		0			0
$447$	−6.42625	+	6.42625i	−0.303951	+	0.303951i
$448$		0			0
$449$			27.9125i			1.31727i	0.752462	+	0.658636i	$0.228866\pi$
$449$			27.9125i			1.31727i	−0.752462	+	0.658636i	$0.771134\pi$
$450$		0			0
$451$			44.9333i			2.11583i
$452$		0			0
$453$	−5.94650	+	5.94650i	−0.279391	+	0.279391i
$454$		0			0
$455$	2.21970	−	0.0649332i	0.104061	−	0.00304412i
$456$		0			0
$457$	−15.7711	+	15.7711i	−0.737741	+	0.737741i	−0.972140	−	0.234399i	$-0.924688\pi$
$457$	−15.7711	+	15.7711i	−0.737741	+	0.737741i	0.234399	+	0.972140i	$0.424688\pi$
$458$		0			0
$459$	−4.85428			−0.226578
$460$		0			0
$461$	8.80413			0.410049			0.205025	−	0.978757i	$-0.434273\pi$
$461$	8.80413			0.410049			0.205025	+	0.978757i	$0.434273\pi$
$462$		0			0
$463$	−14.6273	+	14.6273i	−0.679786	+	0.679786i	−0.959952	−	0.280166i	$-0.909611\pi$
$463$	−14.6273	+	14.6273i	−0.679786	+	0.679786i	0.280166	+	0.959952i	$0.409611\pi$
$464$		0			0
$465$	−2.02743	−	1.91218i	−0.0940197	−	0.0886753i
$466$		0			0
$467$	−1.41354	+	1.41354i	−0.0654108	+	0.0654108i	−0.739055	−	0.673645i	$-0.764728\pi$
$467$	−1.41354	+	1.41354i	−0.0654108	+	0.0654108i	0.673645	+	0.739055i	$0.264728\pi$
$468$		0			0
$469$		−	6.16691i		−	0.284761i
$470$		0			0
$471$			8.91743i			0.410893i
$472$		0			0
$473$	−27.9952	+	27.9952i	−1.28722	+	1.28722i
$474$		0			0
$475$	8.25594	−	0.483439i	0.378809	−	0.0221817i
$476$		0			0
$477$	−1.34571	+	1.34571i	−0.0616157	+	0.0616157i
$478$		0			0
$479$	−34.7740			−1.58887			−0.794433	−	0.607352i	$-0.792232\pi$
$479$	−34.7740			−1.58887			−0.794433	+	0.607352i	$0.792232\pi$
$480$		0			0
$481$			5.36260i			0.244513i
$482$		0			0
$483$	0.243396	−	3.53360i	0.0110749	−	0.160784i
$484$		0			0
$485$	0.574319	+	0.541673i	0.0260785	+	0.0245961i
$486$		0			0
$487$	6.63247	+	6.63247i	0.300546	+	0.300546i	0.841227	−	0.540681i	$-0.181834\pi$
$487$	6.63247	+	6.63247i	0.300546	+	0.300546i	−0.540681	+	0.841227i	$0.681834\pi$
$488$		0			0
$489$		−	4.18573i		−	0.189285i
$490$		0			0
$491$	26.4076			1.19176			0.595879	−	0.803074i	$-0.296804\pi$
$491$	26.4076			1.19176			0.595879	+	0.803074i	$0.296804\pi$
$492$		0			0
$493$	6.22610	+	6.22610i	0.280409	+	0.280409i
$494$		0			0
$495$	−0.239834	−	8.19856i	−0.0107797	−	0.368498i
$496$		0			0
$497$	−3.32806	+	3.32806i	−0.149284	+	0.149284i
$498$		0			0
$499$		−	9.14478i		−	0.409377i	−0.978827	−	0.204688i	$-0.934382\pi$
$499$		−	9.14478i		−	0.409377i	0.978827	−	0.204688i	$-0.0656181\pi$
$500$		0			0
$501$	−13.4610			−0.601395
$502$		0			0
$503$	9.63870	+	9.63870i	0.429768	+	0.429768i	0.888549	−	0.458781i	$-0.151714\pi$
$503$	9.63870	+	9.63870i	0.429768	+	0.429768i	−0.458781	+	0.888549i	$0.651714\pi$
$504$		0			0
$505$	−0.572998	−	19.5876i	−0.0254981	−	0.871635i
$506$		0			0
$507$	−7.91386	−	7.91386i	−0.351467	−	0.351467i
$508$		0			0
$509$		−	44.7928i		−	1.98541i	−0.120584	−	0.992703i	$-0.538477\pi$
$509$		−	44.7928i		−	1.98541i	0.120584	−	0.992703i	$-0.461523\pi$
$510$		0			0
$511$		−	11.7019i		−	0.517661i
$512$		0			0
$513$	−1.16957	−	1.16957i	−0.0516376	−	0.0516376i
$514$		0			0
$515$	−16.0437	+	17.0107i	−0.706971	+	0.749580i
$516$		0			0
$517$	−25.6374	+	25.6374i	−1.12753	+	1.12753i
$518$		0			0
$519$		−	19.2442i		−	0.844725i
$520$		0			0
$521$			26.3599i			1.15485i	0.816445	+	0.577424i	$0.195942\pi$
$521$			26.3599i			1.15485i	−0.816445	+	0.577424i	$0.804058\pi$
$522$		0			0
$523$	−6.83803	−	6.83803i	−0.299006	−	0.299006i	0.541618	−	0.840625i	$-0.317812\pi$
$523$	−6.83803	−	6.83803i	−0.299006	−	0.299006i	−0.840625	+	0.541618i	$0.817812\pi$
$524$		0			0
$525$	0.215865	+	3.68645i	0.00942114	+	0.160890i
$526$		0			0
$527$	4.27808	−	4.27808i	0.186356	−	0.186356i
$528$		0			0
$529$	22.7828	+	3.15355i	0.990556	+	0.137111i
$530$		0			0
$531$	1.65676			0.0718974
$532$		0			0
$533$	11.6474	−	11.6474i	0.504503	−	0.504503i
$534$		0			0
$535$	28.0325	+	26.4390i	1.21195	+	1.14306i
$536$		0			0
$537$	17.6054	+	17.6054i	0.759731	+	0.759731i
$538$		0			0
$539$	−23.6758			−1.01979
$540$		0			0
$541$	32.0778			1.37913			0.689566	−	0.724223i	$-0.257801\pi$
$541$	32.0778			1.37913			0.689566	+	0.724223i	$0.257801\pi$
$542$		0			0
$543$	8.90361	+	8.90361i	0.382091	+	0.382091i
$544$		0			0
$545$	0.410042	+	14.0170i	0.0175642	+	0.600422i
$546$		0			0
$547$	−6.25958	−	6.25958i	−0.267640	−	0.267640i	0.560508	−	0.828149i	$-0.310606\pi$
$547$	−6.25958	−	6.25958i	−0.267640	−	0.267640i	−0.828149	+	0.560508i	$0.810606\pi$
$548$		0			0
$549$	−2.65514			−0.113319
$550$		0			0
$551$			3.00017i			0.127812i
$552$		0			0
$553$	−1.13824	+	1.13824i	−0.0484029	+	0.0484029i
$554$		0			0
$555$	−8.91377	+	0.260756i	−0.378368	+	0.0110685i
$556$		0			0
$557$	23.5607	−	23.5607i	0.998298	−	0.998298i	−0.00170072	−	0.999999i	$-0.500541\pi$
$557$	23.5607	−	23.5607i	0.998298	−	0.998298i	0.999999	+	0.00170072i	$0.000541357\pi$
$558$		0			0
$559$	14.5135			0.613857
$560$		0			0
$561$	17.8059			0.751765
$562$		0			0
$563$	−4.03073	−	4.03073i	−0.169875	−	0.169875i	0.617049	−	0.786924i	$-0.288328\pi$
$563$	−4.03073	−	4.03073i	−0.169875	−	0.169875i	−0.786924	+	0.617049i	$0.788328\pi$
$564$		0			0
$565$	14.1334	−	14.9853i	0.594599	−	0.630435i
$566$		0			0
$567$	0.522235	−	0.522235i	0.0219318	−	0.0219318i
$568$		0			0
$569$	0.498596			0.0209022			0.0104511	−	0.999945i	$-0.496673\pi$
$569$	0.498596			0.0209022			0.0104511	+	0.999945i	$0.496673\pi$
$570$		0			0
$571$		−	37.6586i		−	1.57596i	−0.615698	−	0.787982i	$-0.711126\pi$
$571$		−	37.6586i		−	1.57596i	0.615698	−	0.787982i	$-0.288874\pi$
$572$		0			0
$573$	−11.9759	−	11.9759i	−0.500299	−	0.500299i
$574$		0			0
$575$	−23.9779	−	0.246556i	−0.999947	−	0.0102821i
$576$		0			0
$577$	10.8786	+	10.8786i	0.452881	+	0.452881i	0.896310	−	0.443428i	$-0.146238\pi$
$577$	10.8786	+	10.8786i	0.452881	+	0.452881i	−0.443428	+	0.896310i	$0.646238\pi$
$578$		0			0
$579$			4.23912i			0.176172i
$580$		0			0
$581$	−8.78219			−0.364347
$582$		0			0
$583$	4.93616	−	4.93616i	0.204435	−	0.204435i
$584$		0			0
$585$	−2.06302	+	2.18736i	−0.0852954	+	0.0904361i
$586$		0			0
$587$	0.0498187	+	0.0498187i	0.00205624	+	0.00205624i	0.708134	−	0.706078i	$-0.249537\pi$
$587$	0.0498187	+	0.0498187i	0.00205624	+	0.00205624i	−0.706078	+	0.708134i	$0.749537\pi$
$588$		0			0
$589$	2.06148			0.0849417
$590$		0			0
$591$	8.92122			0.366970
$592$		0			0
$593$	7.47893	−	7.47893i	0.307123	−	0.307123i	−0.536670	−	0.843793i	$-0.680318\pi$
$593$	7.47893	−	7.47893i	0.307123	−	0.307123i	0.843793	+	0.536670i	$0.180318\pi$
$594$		0			0
$595$	−8.01319	+	0.234411i	−0.328509	+	0.00960992i
$596$		0			0
$597$	−1.08478	+	1.08478i	−0.0443971	+	0.0443971i
$598$		0			0
$599$			12.0539i			0.492510i	0.969205	+	0.246255i	$0.0792001\pi$
$599$			12.0539i			0.492510i	−0.969205	+	0.246255i	$0.920800\pi$
$600$		0			0
$601$	−2.90510			−0.118502			−0.0592508	−	0.998243i	$-0.518871\pi$
$601$	−2.90510			−0.118502			−0.0592508	+	0.998243i	$0.518871\pi$
$602$		0			0
$603$	5.90434	+	5.90434i	0.240443	+	0.240443i
$604$		0			0
$605$	0.160505	+	5.48674i	0.00652545	+	0.223068i
$606$		0			0
$607$	24.7142	+	24.7142i	1.00312	+	1.00312i	0.999995	+	0.00312391i	$0.000994372\pi$
$607$	24.7142	+	24.7142i	1.00312	+	1.00312i	0.00312391	+	0.999995i	$0.499006\pi$
$608$		0			0
$609$	−1.33964			−0.0542849
$610$		0			0
$611$	13.2912			0.537704
$612$		0			0
$613$	−19.8695	−	19.8695i	−0.802522	−	0.802522i	0.180967	−	0.983489i	$-0.442077\pi$
$613$	−19.8695	−	19.8695i	−0.802522	−	0.802522i	−0.983489	+	0.180967i	$0.942077\pi$
$614$		0			0
$615$	19.9267	+	18.7940i	0.803523	+	0.757848i
$616$		0			0
$617$	24.0526	−	24.0526i	0.968319	−	0.968319i	−0.0311941	−	0.999513i	$-0.509931\pi$
$617$	24.0526	−	24.0526i	0.968319	−	0.968319i	0.999513	+	0.0311941i	$0.00993099\pi$
$618$		0			0
$619$	32.8923			1.32205			0.661026	−	0.750363i	$-0.270121\pi$
$619$	32.8923			1.32205			0.661026	+	0.750363i	$0.270121\pi$
$620$		0			0
$621$	3.15012	+	3.61618i	0.126410	+	0.145112i
$622$		0			0
$623$	4.60174	−	4.60174i	0.184365	−	0.184365i
$624$		0			0
$625$	24.8291	−	2.91782i	0.993166	−	0.116713i
$626$		0			0
$627$	4.29006	+	4.29006i	0.171329	+	0.171329i
$628$		0			0
$629$		−	19.3592i		−	0.771901i
$630$		0			0
$631$			44.0416i			1.75327i	0.481157	+	0.876634i	$0.340217\pi$
$631$			44.0416i			1.75327i	−0.481157	+	0.876634i	$0.659783\pi$
$632$		0			0
$633$	7.36543	−	7.36543i	0.292750	−	0.292750i
$634$		0			0
$635$	−21.5505	+	22.8493i	−0.855205	+	0.906748i
$636$		0			0
$637$	6.13710	+	6.13710i	0.243161	+	0.243161i
$638$		0			0
$639$		−	6.37272i		−	0.252101i
$640$		0			0
$641$		−	6.74592i		−	0.266448i	−0.991086	−	0.133224i	$-0.957467\pi$
$641$		−	6.74592i		−	0.266448i	0.991086	−	0.133224i	$-0.0425330\pi$
$642$		0			0
$643$	12.3276	+	12.3276i	0.486153	+	0.486153i	0.907090	−	0.420937i	$-0.138299\pi$
$643$	12.3276	+	12.3276i	0.486153	+	0.486153i	−0.420937	+	0.907090i	$0.638299\pi$
$644$		0			0
$645$	0.705720	+	24.1246i	0.0277877	+	0.949903i
$646$		0			0
$647$	21.0975	+	21.0975i	0.829427	+	0.829427i	0.987437	−	0.158011i	$-0.0505081\pi$
$647$	21.0975	+	21.0975i	0.829427	+	0.829427i	−0.158011	+	0.987437i	$0.550508\pi$
$648$		0			0
$649$	−6.07714			−0.238548
$650$		0			0
$651$			0.920492i			0.0360769i
$652$		0			0
$653$	−6.97002	+	6.97002i	−0.272758	+	0.272758i	−0.830210	−	0.557451i	$-0.811779\pi$
$653$	−6.97002	+	6.97002i	−0.272758	+	0.272758i	0.557451	+	0.830210i	$0.311779\pi$
$654$		0			0
$655$	−0.635840	−	21.7357i	−0.0248443	−	0.849286i
$656$		0			0
$657$	11.2037	+	11.2037i	0.437096	+	0.437096i
$658$		0			0
$659$	43.6582			1.70068			0.850340	−	0.526233i	$-0.176396\pi$
$659$	43.6582			1.70068			0.850340	+	0.526233i	$0.176396\pi$
$660$		0			0
$661$		−	40.6310i		−	1.58036i	−0.612874	−	0.790180i	$-0.709987\pi$
$661$		−	40.6310i		−	1.58036i	0.612874	−	0.790180i	$-0.290013\pi$
$662$		0			0
$663$	−4.61554	−	4.61554i	−0.179253	−	0.179253i
$664$		0			0
$665$	−1.98714	−	1.87418i	−0.0770578	−	0.0726776i
$666$		0			0
$667$	0.597777	−	8.67846i	0.0231460	−	0.336031i
$668$		0			0
$669$			5.11626i			0.197806i
$670$		0			0
$671$	9.73927			0.375980
$672$		0			0
$673$	27.1613	−	27.1613i	1.04699	−	1.04699i	0.0481519	−	0.998840i	$-0.484667\pi$
$673$	27.1613	−	27.1613i	1.04699	−	1.04699i	0.998840	−	0.0481519i	$-0.0153331\pi$
$674$		0			0
$675$	−3.73616	−	3.32281i	−0.143805	−	0.127895i
$676$		0			0
$677$	−1.14803	+	1.14803i	−0.0441224	+	0.0441224i	−0.728824	−	0.684701i	$-0.759933\pi$
$677$	−1.14803	+	1.14803i	−0.0441224	+	0.0441224i	0.684701	+	0.728824i	$0.259933\pi$
$678$		0			0
$679$		−	0.260752i		−	0.0100067i
$680$		0			0
$681$			12.9696i			0.496995i
$682$		0			0
$683$	−21.7994	+	21.7994i	−0.834133	+	0.834133i	−0.988079	−	0.153946i	$-0.950802\pi$
$683$	−21.7994	+	21.7994i	−0.834133	+	0.834133i	0.153946	+	0.988079i	$0.450802\pi$
$684$		0			0
$685$	2.28361	+	2.15380i	0.0872521	+	0.0822924i
$686$		0			0
$687$	0.425149	−	0.425149i	0.0162205	−	0.0162205i
$688$		0			0
$689$	−2.55905			−0.0974920
$690$		0			0
$691$	−5.34906			−0.203488			−0.101744	−	0.994811i	$-0.532442\pi$
$691$	−5.34906			−0.203488			−0.101744	+	0.994811i	$0.532442\pi$
$692$		0			0
$693$	−1.91560	+	1.91560i	−0.0727676	+	0.0727676i
$694$		0			0
$695$	−15.5539	+	0.455002i	−0.589994	+	0.0172592i
$696$		0			0
$697$	−42.0474	+	42.0474i	−1.59266	+	1.59266i
$698$		0			0
$699$		−	4.88456i		−	0.184751i
$700$		0			0
$701$			17.0899i			0.645476i	0.946488	+	0.322738i	$0.104603\pi$
$701$			17.0899i			0.645476i	−0.946488	+	0.322738i	$0.895397\pi$
$702$		0			0
$703$	4.66431	−	4.66431i	0.175918	−	0.175918i
$704$		0			0
$705$	0.646284	+	22.0928i	0.0243404	+	0.832061i
$706$		0			0
$707$	−4.57664	+	4.57664i	−0.172122	+	0.172122i
$708$		0			0
$709$	3.58262			0.134548			0.0672741	−	0.997735i	$-0.478570\pi$
$709$	3.58262			0.134548			0.0672741	+	0.997735i	$0.478570\pi$
$710$		0			0
$711$		−	2.17955i		−	0.0817396i
$712$		0			0
$713$	−5.96314	−	0.410745i	−0.223321	−	0.0153825i
$714$		0			0
$715$	7.56732	−	8.02339i	0.283002	−	0.300058i
$716$		0			0
$717$	−11.0184	−	11.0184i	−0.411488	−	0.411488i
$718$		0			0
$719$			33.3021i			1.24196i	0.783828	+	0.620979i	$0.213265\pi$
$719$			33.3021i			1.24196i	−0.783828	+	0.620979i	$0.786735\pi$
$720$		0			0
$721$	7.72318			0.287626
$722$		0			0
$723$	12.1758	+	12.1758i	0.452825	+	0.452825i
$724$		0			0
$725$	0.530161	+	9.05384i	0.0196897	+	0.336251i
$726$		0			0
$727$	−18.1248	+	18.1248i	−0.672212	+	0.672212i	−0.958226	−	0.286013i	$-0.907670\pi$
$727$	−18.1248	+	18.1248i	−0.672212	+	0.672212i	0.286013	+	0.958226i	$0.407670\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−52.3944			−1.93788
$732$		0			0
$733$	7.26149	+	7.26149i	0.268209	+	0.268209i	0.828378	−	0.560169i	$-0.189264\pi$
$733$	7.26149	+	7.26149i	0.268209	+	0.268209i	−0.560169	+	0.828378i	$0.689264\pi$
$734$		0			0
$735$	−9.90274	+	10.4996i	−0.365268	+	0.387283i
$736$		0			0
$737$	−21.6576	−	21.6576i	−0.797767	−	0.797767i
$738$		0			0
$739$			13.2258i			0.486520i	0.969961	+	0.243260i	$0.0782168\pi$
$739$			13.2258i			0.486520i	−0.969961	+	0.243260i	$0.921783\pi$
$740$		0			0
$741$		−	2.22409i		−	0.0817041i
$742$		0			0
$743$	3.52716	+	3.52716i	0.129399	+	0.129399i	0.768840	−	0.639441i	$-0.220834\pi$
$743$	3.52716	+	3.52716i	0.129399	+	0.129399i	−0.639441	+	0.768840i	$0.720834\pi$
$744$		0			0
$745$	−0.594217	−	20.3129i	−0.0217704	−	0.744207i
$746$		0			0
$747$	8.40827	−	8.40827i	0.307643	−	0.307643i
$748$		0			0
$749$		−	12.7273i		−	0.465046i
$750$		0			0
$751$			53.6972i			1.95944i	0.200379	+	0.979718i	$0.435783\pi$
$751$			53.6972i			1.95944i	−0.200379	+	0.979718i	$0.564217\pi$
$752$		0			0
$753$	11.5141	+	11.5141i	0.419596	+	0.419596i
$754$		0			0
$755$	−0.549856	−	18.7964i	−0.0200113	−	0.684073i
$756$		0			0
$757$	7.87289	−	7.87289i	0.286145	−	0.286145i	−0.549409	−	0.835554i	$-0.685147\pi$
$757$	7.87289	−	7.87289i	0.286145	−	0.286145i	0.835554	+	0.549409i	$0.185147\pi$
$758$		0			0
$759$	−11.5549	−	13.2644i	−0.419415	−	0.481469i
$760$		0			0
$761$	3.80782			0.138033			0.0690166	−	0.997616i	$-0.478014\pi$
$761$	3.80782			0.138033			0.0690166	+	0.997616i	$0.478014\pi$
$762$		0			0
$763$	3.27508	−	3.27508i	0.118566	−	0.118566i
$764$		0			0
$765$	7.44758	−	7.89644i	0.269268	−	0.285496i
$766$		0			0
$767$	1.57528	+	1.57528i	0.0568802	+	0.0568802i
$768$		0			0
$769$	−15.1987			−0.548079			−0.274040	−	0.961718i	$-0.588360\pi$
$769$	−15.1987			−0.548079			−0.274040	+	0.961718i	$0.588360\pi$
$770$		0			0
$771$	17.7960			0.640908
$772$		0			0
$773$	19.1373	+	19.1373i	0.688320	+	0.688320i	0.961860	−	0.273541i	$-0.0881948\pi$
$773$	19.1373	+	19.1373i	0.688320	+	0.688320i	−0.273541	+	0.961860i	$0.588195\pi$
$774$		0			0
$775$	6.22108	−	0.364284i	0.223468	−	0.0130855i
$776$		0			0
$777$	2.08271	+	2.08271i	0.0747167	+	0.0747167i
$778$		0			0
$779$	−20.2614			−0.725940
$780$		0			0
$781$			23.3756i			0.836446i
$782$		0			0
$783$	1.28260	−	1.28260i	0.0458364	−	0.0458364i
$784$		0			0
$785$	−14.5059	−	13.6814i	−0.517739	−	0.488309i
$786$		0			0
$787$	−1.79366	+	1.79366i	−0.0639372	+	0.0639372i	−0.738352	−	0.674415i	$-0.764396\pi$
$787$	−1.79366	+	1.79366i	−0.0639372	+	0.0639372i	0.674415	+	0.738352i	$0.264396\pi$
$788$		0			0
$789$	−17.8260			−0.634624
$790$		0			0
$791$	−6.80360			−0.241908
$792$		0			0
$793$	−2.52456	−	2.52456i	−0.0896498	−	0.0896498i
$794$		0			0
$795$	−0.124434	−	4.25368i	−0.00441321	−	0.150862i
$796$		0			0
$797$	−24.8574	+	24.8574i	−0.880495	+	0.880495i	−0.993585	−	0.113090i	$-0.963925\pi$
$797$	−24.8574	+	24.8574i	−0.880495	+	0.880495i	0.113090	+	0.993585i	$0.463925\pi$
$798$		0			0
$799$	−47.9817			−1.69747
$800$		0			0
$801$			8.81161i			0.311343i
$802$		0			0
$803$	−41.0959	−	41.0959i	−1.45024	−	1.45024i
$804$		0			0
$805$	5.37467	+	5.81728i	0.189432	+	0.205032i
$806$		0			0
$807$	15.6298	+	15.6298i	0.550196	+	0.550196i
$808$		0			0
$809$			4.33877i			0.152543i	0.997087	+	0.0762715i	$0.0243016\pi$
$809$			4.33877i			0.152543i	−0.997087	+	0.0762715i	$0.975698\pi$
$810$		0			0
$811$	−14.7884			−0.519291			−0.259646	−	0.965704i	$-0.583606\pi$
$811$	−14.7884			−0.519291			−0.259646	+	0.965704i	$0.583606\pi$
$812$		0			0
$813$	−13.5621	+	13.5621i	−0.475643	+	0.475643i
$814$		0			0
$815$	6.80892	+	6.42187i	0.238506	+	0.224948i
$816$		0			0
$817$	−12.6236	−	12.6236i	−0.441646	−	0.441646i
$818$		0			0
$819$	0.993103			0.0347018
$820$		0			0
$821$	16.2343			0.566580			0.283290	−	0.959034i	$-0.408574\pi$
$821$	16.2343			0.566580			0.283290	+	0.959034i	$0.408574\pi$
$822$		0			0
$823$	10.9030	−	10.9030i	0.380053	−	0.380053i	−0.491068	−	0.871121i	$-0.663393\pi$
$823$	10.9030	−	10.9030i	0.380053	−	0.380053i	0.871121	+	0.491068i	$0.163393\pi$
$824$		0			0
$825$	13.7045	+	12.1883i	0.477131	+	0.424344i
$826$		0			0
$827$	13.9317	−	13.9317i	0.484451	−	0.484451i	−0.422099	−	0.906550i	$-0.638706\pi$
$827$	13.9317	−	13.9317i	0.484451	−	0.484451i	0.906550	+	0.422099i	$0.138706\pi$
$828$		0			0
$829$			49.9668i			1.73542i	0.497072	+	0.867709i	$0.334408\pi$
$829$			49.9668i			1.73542i	−0.497072	+	0.867709i	$0.665592\pi$
$830$		0			0
$831$	3.07325			0.106610
$832$		0			0
$833$	−22.1552	−	22.1552i	−0.767631	−	0.767631i
$834$		0			0
$835$	20.6523	−	21.8970i	0.714703	−	0.757777i
$836$		0			0
$837$	−0.881300	−	0.881300i	−0.0304622	−	0.0304622i
$838$		0			0
$839$	−26.9815			−0.931505			−0.465753	−	0.884915i	$-0.654216\pi$
$839$	−26.9815			−0.931505			−0.465753	+	0.884915i	$0.654216\pi$
$840$		0			0
$841$	25.7099			0.886547
$842$		0			0
$843$	16.5110	+	16.5110i	0.568671	+	0.568671i
$844$		0			0
$845$	25.0151	−	0.731772i	0.860546	−	0.0251737i
$846$		0			0
$847$	1.28198	−	1.28198i	0.0440494	−	0.0440494i
$848$		0			0
$849$	−9.40254			−0.322694
$850$		0			0
$851$	−14.4216	+	12.5629i	−0.494365	+	0.430649i
$852$		0			0
$853$	20.5802	−	20.5802i	0.704652	−	0.704652i	−0.260754	−	0.965405i	$-0.583971\pi$
$853$	20.5802	−	20.5802i	0.704652	−	0.704652i	0.965405	+	0.260754i	$0.0839711\pi$
$854$		0			0
$855$	3.69691	−	0.108146i	0.126432	−	0.00369853i
$856$		0			0
$857$	−19.2911	−	19.2911i	−0.658971	−	0.658971i	0.296165	−	0.955137i	$-0.404292\pi$
$857$	−19.2911	−	19.2911i	−0.658971	−	0.658971i	−0.955137	+	0.296165i	$0.904292\pi$
$858$		0			0
$859$			33.1554i			1.13125i	0.824663	+	0.565625i	$0.191365\pi$
$859$			33.1554i			1.13125i	−0.824663	+	0.565625i	$0.808635\pi$
$860$		0			0
$861$		−	9.04713i		−	0.308325i
$862$		0			0
$863$	−14.1751	+	14.1751i	−0.482525	+	0.482525i	−0.905937	−	0.423412i	$-0.860832\pi$
$863$	−14.1751	+	14.1751i	−0.482525	+	0.482525i	0.423412	+	0.905937i	$0.360832\pi$
$864$		0			0
$865$	31.3044	+	29.5250i	1.06438	+	1.00388i
$866$		0			0
$867$	4.64147	+	4.64147i	0.157633	+	0.157633i
$868$		0			0
$869$			7.99477i			0.271204i
$870$		0			0
$871$			11.2279i			0.380444i
$872$		0			0
$873$	0.249650	+	0.249650i	0.00844938	+	0.00844938i
$874$		0			0
$875$	−6.32791	−	5.30471i	−0.213923	−	0.179332i
$876$		0			0
$877$	11.7670	+	11.7670i	0.397344	+	0.397344i	0.877295	−	0.479951i	$-0.159346\pi$
$877$	11.7670	+	11.7670i	0.397344	+	0.397344i	−0.479951	+	0.877295i	$0.659346\pi$
$878$		0			0
$879$	1.60971			0.0542943
$880$		0			0
$881$		−	19.2402i		−	0.648218i	−0.946020	−	0.324109i	$-0.894935\pi$
$881$		−	19.2402i		−	0.648218i	0.946020	−	0.324109i	$-0.105065\pi$
$882$		0			0
$883$	14.8098	−	14.8098i	0.498390	−	0.498390i	−0.412547	−	0.910936i	$-0.635361\pi$
$883$	14.8098	−	14.8098i	0.498390	−	0.498390i	0.910936	+	0.412547i	$0.135361\pi$
$884$		0			0
$885$	−2.54185	+	2.69505i	−0.0854435	+	0.0905931i
$886$		0			0
$887$	31.2222	+	31.2222i	1.04834	+	1.04834i	0.998771	+	0.0495677i	$0.0157844\pi$
$887$	31.2222	+	31.2222i	1.04834	+	1.04834i	0.0495677	+	0.998771i	$0.484216\pi$
$888$		0			0
$889$	10.3740			0.347934
$890$		0			0
$891$		−	3.66808i		−	0.122885i
$892$		0			0
$893$	−11.5605	−	11.5605i	−0.386856	−	0.386856i
$894$		0			0
$895$	−55.6495	+	1.62793i	−1.86016	+	0.0544156i
$896$		0			0
$897$	−0.443145	+	6.43353i	−0.0147962	+	0.214809i
$898$		0			0
$899$			2.26071i			0.0753989i
$900$		0			0
$901$	9.23826			0.307771
$902$		0			0
$903$	5.63672	−	5.63672i	0.187578	−	0.187578i
$904$		0			0
$905$	−28.1437	+	0.823292i	−0.935527	+	0.0273671i
$906$		0			0
$907$	13.9252	−	13.9252i	0.462379	−	0.462379i	−0.437055	−	0.899435i	$-0.643979\pi$
$907$	13.9252	−	13.9252i	0.462379	−	0.462379i	0.899435	+	0.437055i	$0.143979\pi$
$908$		0			0
$909$		−	8.76357i		−	0.290669i
$910$		0			0
$911$			32.7519i			1.08512i	0.840017	+	0.542560i	$0.182545\pi$
$911$			32.7519i			1.08512i	−0.840017	+	0.542560i	$0.817455\pi$
$912$		0			0
$913$	−30.8422	+	30.8422i	−1.02073	+	1.02073i
$914$		0			0
$915$	4.07360	−	4.31911i	0.134669	−	0.142785i
$916$		0			0
$917$	−5.07857	+	5.07857i	−0.167709	+	0.167709i
$918$		0			0
$919$	28.3403			0.934861			0.467430	−	0.884030i	$-0.345180\pi$
$919$	28.3403			0.934861			0.467430	+	0.884030i	$0.345180\pi$
$920$		0			0
$921$	13.8947			0.457846
$922$		0			0
$923$	6.05931	−	6.05931i	0.199445	−	0.199445i
$924$		0			0
$925$	13.2516	−	14.9001i	0.435710	−	0.489911i
$926$		0			0
$927$	−7.39435	+	7.39435i	−0.242862	+	0.242862i
$928$		0			0
$929$		−	28.5516i		−	0.936746i	−0.883531	−	0.468373i	$-0.844840\pi$
$929$		−	28.5516i		−	0.936746i	0.883531	−	0.468373i	$-0.155160\pi$
$930$		0			0
$931$		−	10.6759i		−	0.349889i
$932$		0			0
$933$	13.5001	−	13.5001i	0.441975	−	0.441975i
$934$		0			0
$935$	−27.3183	+	28.9648i	−0.893404	+	0.947249i
$936$		0			0
$937$	4.94866	−	4.94866i	0.161666	−	0.161666i	−0.621639	−	0.783304i	$-0.713533\pi$
$937$	4.94866	−	4.94866i	0.161666	−	0.161666i	0.783304	+	0.621639i	$0.213533\pi$
$938$		0			0
$939$	−21.9538			−0.716434
$940$		0			0
$941$		−	29.9292i		−	0.975663i	−0.872938	−	0.487832i	$-0.837788\pi$
$941$		−	29.9292i		−	0.975663i	0.872938	−	0.487832i	$-0.162212\pi$
$942$		0			0
$943$	58.6092	+	4.03704i	1.90858	+	0.131464i
$944$		0			0
$945$	0.0482896	+	1.65075i	0.00157086	+	0.0536988i
$946$		0			0
$947$	13.9943	+	13.9943i	0.454753	+	0.454753i	0.896928	−	0.442176i	$-0.145793\pi$
$947$	13.9943	+	13.9943i	0.454753	+	0.454753i	−0.442176	+	0.896928i	$0.645793\pi$
$948$		0			0
$949$			21.3053i			0.691600i
$950$		0			0
$951$	−17.0220			−0.551978
$952$		0			0
$953$	17.9768	+	17.9768i	0.582326	+	0.582326i	0.935542	−	0.353216i	$-0.114912\pi$
$953$	17.9768	+	17.9768i	0.582326	+	0.582326i	−0.353216	+	0.935542i	$0.614912\pi$
$954$		0			0
$955$	37.8548	−	1.10737i	1.22495	−	0.0358338i
$956$		0			0
$957$	−4.70468	+	4.70468i	−0.152081	+	0.152081i
$958$		0			0
$959$		−	1.03680i		−	0.0334801i
$960$		0			0
$961$	−29.4466			−0.949891
$962$		0			0
$963$	12.1854	+	12.1854i	0.392670	+	0.392670i
$964$		0			0
$965$	−6.89576	−	6.50378i	−0.221982	−	0.209364i
$966$		0			0
$967$	−1.28157	−	1.28157i	−0.0412126	−	0.0412126i	0.686200	−	0.727413i	$-0.259277\pi$
$967$	−1.28157	−	1.28157i	−0.0412126	−	0.0412126i	−0.727413	+	0.686200i	$0.759277\pi$
$968$		0			0
$969$			8.02906i			0.257931i
$970$		0			0
$971$		−	53.1840i		−	1.70676i	−0.521292	−	0.853378i	$-0.674550\pi$
$971$		−	53.1840i		−	1.70676i	0.521292	−	0.853378i	$-0.325450\pi$
$972$		0			0
$973$	3.63418	+	3.63418i	0.116507	+	0.116507i
$974$		0			0
$975$	−0.393020	−	6.71181i	−0.0125867	−	0.214950i
$976$		0			0
$977$	28.0960	−	28.0960i	0.898870	−	0.898870i	−0.0964663	−	0.995336i	$-0.530754\pi$
$977$	28.0960	−	28.0960i	0.898870	−	0.898870i	0.995336	+	0.0964663i	$0.0307540\pi$
$978$		0			0
$979$		−	32.3217i		−	1.03301i
$980$		0			0
$981$			6.27127i			0.200226i
$982$		0			0
$983$	−15.7574	−	15.7574i	−0.502583	−	0.502583i	0.409657	−	0.912240i	$-0.365648\pi$
$983$	−15.7574	−	15.7574i	−0.502583	−	0.502583i	−0.912240	+	0.409657i	$0.865648\pi$
$984$		0			0
$985$	−13.6872	+	14.5121i	−0.436110	+	0.462394i
$986$		0			0
$987$	5.16199	−	5.16199i	0.164308	−	0.164308i
$988$		0			0
$989$	34.0006	+	39.0311i	1.08116	+	1.24112i
$990$		0			0
$991$	−36.5634			−1.16147			−0.580737	−	0.814091i	$-0.697236\pi$
$991$	−36.5634			−1.16147			−0.580737	+	0.814091i	$0.697236\pi$
$992$		0			0
$993$	18.4482	−	18.4482i	0.585435	−	0.585435i
$994$		0			0
$995$	−0.100306	−	3.42891i	−0.00317993	−	0.108704i
$996$		0			0
$997$	−0.938857	−	0.938857i	−0.0297339	−	0.0297339i	0.692084	−	0.721817i	$-0.256693\pi$
$997$	−0.938857	−	0.938857i	−0.0297339	−	0.0297339i	−0.721817	+	0.692084i	$0.756693\pi$
$998$		0			0
$999$	−3.98806			−0.126177

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.t.a.1057.11	✓	48
5.3	odd	4	inner	1380.2.t.a.1333.12	yes	48
23.22	odd	2	inner	1380.2.t.a.1057.12	yes	48
115.68	even	4	inner	1380.2.t.a.1333.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.t.a.1057.11	✓	48	1.1	even	1	trivial
1380.2.t.a.1057.12	yes	48	23.22	odd	2	inner
1380.2.t.a.1333.11	yes	48	115.68	even	4	inner
1380.2.t.a.1333.12	yes	48	5.3	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.0653842 - 2.23511i) q^{5} +(-0.522235 + 0.522235i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.0653842 - 2.23511i) q^{5} +(-0.522235 + 0.522235i) q^{7} -1.00000i q^{9} +3.66808i q^{11} +(0.950820 - 0.950820i) q^{13} +(1.62670 + 1.53423i) q^{15} +(-3.43249 + 3.43249i) q^{17} -1.65402 q^{19} -0.738552i q^{21} +(4.78449 + 0.329559i) q^{23} +(-4.99145 + 0.292282i) q^{25} +(0.707107 + 0.707107i) q^{27} -1.81387i q^{29} -1.24635 q^{31} +(-2.59372 - 2.59372i) q^{33} +(1.20140 + 1.13311i) q^{35} +(-2.81999 + 2.81999i) q^{37} +1.34466i q^{39} +12.2498 q^{41} +(7.63212 + 7.63212i) q^{43} +(-2.23511 + 0.0653842i) q^{45} +(6.98933 + 6.98933i) q^{47} +6.45454i q^{49} -4.85428i q^{51} +(-1.34571 - 1.34571i) q^{53} +(8.19856 - 0.239834i) q^{55} +(1.16957 - 1.16957i) q^{57} +1.65676i q^{59} -2.65514i q^{61} +(0.522235 + 0.522235i) q^{63} +(-2.18736 - 2.06302i) q^{65} +(-5.90434 + 5.90434i) q^{67} +(-3.61618 + 3.15012i) q^{69} +6.37272 q^{71} +(-11.2037 + 11.2037i) q^{73} +(3.32281 - 3.73616i) q^{75} +(-1.91560 - 1.91560i) q^{77} +2.17955 q^{79} -1.00000 q^{81} +(8.40827 + 8.40827i) q^{83} +(7.89644 + 7.44758i) q^{85} +(1.28260 + 1.28260i) q^{87} -8.81161 q^{89} +0.993103i q^{91} +(0.881300 - 0.881300i) q^{93} +(0.108146 + 3.69691i) q^{95} +(-0.249650 + 0.249650i) q^{97} +3.66808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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