LMFDB - Embedded newform 1148.2.k.b.729.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(337,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1148.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.k (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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			729.13
Character	$\chi$	$=$	1148.729
Dual form			1148.2.k.b.337.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.46058 - 1.46058i) q^{3} +2.07990i q^{5} +(-0.707107 + 0.707107i) q^{7} -1.26660i q^{9} +O(q^{10})$	\(q+(1.46058 - 1.46058i) q^{3} +2.07990i q^{5} +(-0.707107 + 0.707107i) q^{7} -1.26660i q^{9} +(3.13374 - 3.13374i) q^{11} +(-1.44357 + 1.44357i) q^{13} +(3.03787 + 3.03787i) q^{15} +(-2.75344 - 2.75344i) q^{17} +(3.62637 + 3.62637i) q^{19} +2.06558i q^{21} +8.09052 q^{23} +0.674015 q^{25} +(2.53177 + 2.53177i) q^{27} +(6.51134 - 6.51134i) q^{29} -6.43870 q^{31} -9.15418i q^{33} +(-1.47071 - 1.47071i) q^{35} +3.66193 q^{37} +4.21689i q^{39} +(5.32231 + 3.55991i) q^{41} -0.897994i q^{43} +2.63441 q^{45} +(8.63929 + 8.63929i) q^{47} -1.00000i q^{49} -8.04324 q^{51} +(-7.62335 + 7.62335i) q^{53} +(6.51787 + 6.51787i) q^{55} +10.5932 q^{57} -10.3975 q^{59} +1.15180i q^{61} +(0.895623 + 0.895623i) q^{63} +(-3.00247 - 3.00247i) q^{65} +(0.147560 + 0.147560i) q^{67} +(11.8169 - 11.8169i) q^{69} +(2.99467 - 2.99467i) q^{71} -8.52008i q^{73} +(0.984454 - 0.984454i) q^{75} +4.43178i q^{77} +(-5.31233 + 5.31233i) q^{79} +11.1955 q^{81} -13.1465 q^{83} +(5.72687 - 5.72687i) q^{85} -19.0207i q^{87} +(0.506568 - 0.506568i) q^{89} -2.04151i q^{91} +(-9.40426 + 9.40426i) q^{93} +(-7.54248 + 7.54248i) q^{95} +(-10.8950 - 10.8950i) q^{97} +(-3.96921 - 3.96921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q+O(q^{10}) $ 36 * q	$ 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) $ 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.46058	−	1.46058i	0.843268	−	0.843268i	−0.146015	−	0.989282i	$-0.546645\pi$
$3$	1.46058	−	1.46058i	0.843268	−	0.843268i	0.989282	+	0.146015i	$0.0466447\pi$
$4$		0			0
$5$			2.07990i			0.930160i	0.885269	+	0.465080i	$0.153974\pi$
$5$			2.07990i			0.930160i	−0.885269	+	0.465080i	$0.846026\pi$
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$		0			0
$9$		−	1.26660i		−	0.422201i
$10$		0			0
$11$	3.13374	−	3.13374i	0.944859	−	0.944859i	−0.0536980	−	0.998557i	$-0.517101\pi$
$11$	3.13374	−	3.13374i	0.944859	−	0.944859i	0.998557	+	0.0536980i	$0.0171008\pi$
$12$		0			0
$13$	−1.44357	+	1.44357i	−0.400373	+	0.400373i	−0.878364	−	0.477991i	$-0.841365\pi$
$13$	−1.44357	+	1.44357i	−0.400373	+	0.400373i	0.477991	+	0.878364i	$0.341365\pi$
$14$		0			0
$15$	3.03787	+	3.03787i	0.784374	+	0.784374i
$16$		0			0
$17$	−2.75344	−	2.75344i	−0.667806	−	0.667806i	0.289402	−	0.957208i	$-0.406544\pi$
$17$	−2.75344	−	2.75344i	−0.667806	−	0.667806i	−0.957208	+	0.289402i	$0.906544\pi$
$18$		0			0
$19$	3.62637	+	3.62637i	0.831946	+	0.831946i	0.987783	−	0.155837i	$-0.0498074\pi$
$19$	3.62637	+	3.62637i	0.831946	+	0.831946i	−0.155837	+	0.987783i	$0.549807\pi$
$20$		0			0
$21$			2.06558i			0.450746i
$22$		0			0
$23$	8.09052			1.68699			0.843496	−	0.537136i	$-0.180494\pi$
$23$	8.09052			1.68699			0.843496	+	0.537136i	$0.180494\pi$
$24$		0			0
$25$	0.674015			0.134803
$26$		0			0
$27$	2.53177	+	2.53177i	0.487239	+	0.487239i
$28$		0			0
$29$	6.51134	−	6.51134i	1.20913	−	1.20913i	0.237815	−	0.971310i	$-0.423569\pi$
$29$	6.51134	−	6.51134i	1.20913	−	1.20913i	0.971310	−	0.237815i	$-0.0764313\pi$
$30$		0			0
$31$	−6.43870			−1.15642			−0.578212	−	0.815886i	$-0.696250\pi$
$31$	−6.43870			−1.15642			−0.578212	+	0.815886i	$0.696250\pi$
$32$		0			0
$33$		−	9.15418i		−	1.59354i
$34$		0			0
$35$	−1.47071	−	1.47071i	−0.248596	−	0.248596i
$36$		0			0
$37$	3.66193			0.602018			0.301009	−	0.953621i	$-0.402677\pi$
$37$	3.66193			0.602018			0.301009	+	0.953621i	$0.402677\pi$
$38$		0			0
$39$			4.21689i			0.675243i
$40$		0			0
$41$	5.32231	+	3.55991i	0.831206	+	0.555965i
$41$	5.32231	+	3.55991i	0.831206	+	0.555965i
$42$		0			0
$43$		−	0.897994i		−	0.136943i	−0.997653	−	0.0684714i	$-0.978188\pi$
$43$		−	0.897994i		−	0.136943i	0.997653	−	0.0684714i	$-0.0218122\pi$
$44$		0			0
$45$	2.63441			0.392714
$46$		0			0
$47$	8.63929	+	8.63929i	1.26017	+	1.26017i	0.951010	+	0.309160i	$0.100048\pi$
$47$	8.63929	+	8.63929i	1.26017	+	1.26017i	0.309160	+	0.951010i	$0.399952\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	−8.04324			−1.12628
$52$		0			0
$53$	−7.62335	+	7.62335i	−1.04715	+	1.04715i	−0.0483150	+	0.998832i	$0.515385\pi$
$53$	−7.62335	+	7.62335i	−1.04715	+	1.04715i	−0.998832	+	0.0483150i	$0.984615\pi$
$54$		0			0
$55$	6.51787	+	6.51787i	0.878870	+	0.878870i
$56$		0			0
$57$	10.5932			1.40311
$58$		0			0
$59$	−10.3975			−1.35364			−0.676822	−	0.736146i	$-0.736643\pi$
$59$	−10.3975			−1.35364			−0.676822	+	0.736146i	$0.736643\pi$
$60$		0			0
$61$			1.15180i			0.147473i	0.997278	+	0.0737367i	$0.0234924\pi$
$61$			1.15180i			0.147473i	−0.997278	+	0.0737367i	$0.976508\pi$
$62$		0			0
$63$	0.895623	+	0.895623i	0.112838	+	0.112838i
$64$		0			0
$65$	−3.00247	−	3.00247i	−0.372411	−	0.372411i
$66$		0			0
$67$	0.147560	+	0.147560i	0.0180273	+	0.0180273i	0.716063	−	0.698036i	$-0.245942\pi$
$67$	0.147560	+	0.147560i	0.0180273	+	0.0180273i	−0.698036	+	0.716063i	$0.745942\pi$
$68$		0			0
$69$	11.8169	−	11.8169i	1.42259	−	1.42259i
$70$		0			0
$71$	2.99467	−	2.99467i	0.355402	−	0.355402i	−0.506713	−	0.862115i	$-0.669140\pi$
$71$	2.99467	−	2.99467i	0.355402	−	0.355402i	0.862115	+	0.506713i	$0.169140\pi$
$72$		0			0
$73$		−	8.52008i		−	0.997200i	−0.866832	−	0.498600i	$-0.833848\pi$
$73$		−	8.52008i		−	0.997200i	0.866832	−	0.498600i	$-0.166152\pi$
$74$		0			0
$75$	0.984454	−	0.984454i	0.113675	−	0.113675i
$76$		0			0
$77$			4.43178i			0.505049i
$78$		0			0
$79$	−5.31233	+	5.31233i	−0.597684	+	0.597684i	−0.939696	−	0.342012i	$-0.888892\pi$
$79$	−5.31233	+	5.31233i	−0.597684	+	0.597684i	0.342012	+	0.939696i	$0.388892\pi$
$80$		0			0
$81$	11.1955			1.24395
$82$		0			0
$83$	−13.1465			−1.44302			−0.721510	−	0.692404i	$-0.756552\pi$
$83$	−13.1465			−1.44302			−0.721510	+	0.692404i	$0.756552\pi$
$84$		0			0
$85$	5.72687	−	5.72687i	0.621166	−	0.621166i
$86$		0			0
$87$		−	19.0207i		−	2.03923i
$88$		0			0
$89$	0.506568	−	0.506568i	0.0536961	−	0.0536961i	−0.679749	−	0.733445i	$-0.737911\pi$
$89$	0.506568	−	0.506568i	0.0536961	−	0.0536961i	0.733445	+	0.679749i	$0.237911\pi$
$90$		0			0
$91$		−	2.04151i		−	0.214008i
$92$		0			0
$93$	−9.40426	+	9.40426i	−0.975176	+	0.975176i
$94$		0			0
$95$	−7.54248	+	7.54248i	−0.773843	+	0.773843i
$96$		0			0
$97$	−10.8950	−	10.8950i	−1.10622	−	1.10622i	−0.993643	−	0.112579i	$-0.964089\pi$
$97$	−10.8950	−	10.8950i	−1.10622	−	1.10622i	−0.112579	−	0.993643i	$-0.535911\pi$
$98$		0			0
$99$	−3.96921	−	3.96921i	−0.398920	−	0.398920i
$100$		0			0
$101$	10.4719	+	10.4719i	1.04200	+	1.04200i	0.999079	+	0.0429187i	$0.0136657\pi$
$101$	10.4719	+	10.4719i	1.04200	+	1.04200i	0.0429187	+	0.999079i	$0.486334\pi$
$102$		0			0
$103$		−	13.1568i		−	1.29638i	−0.761480	−	0.648188i	$-0.775527\pi$
$103$		−	13.1568i		−	1.29638i	0.761480	−	0.648188i	$-0.224473\pi$
$104$		0			0
$105$	−4.29619			−0.419265
$106$		0			0
$107$	−5.74222			−0.555121			−0.277561	−	0.960708i	$-0.589526\pi$
$107$	−5.74222			−0.555121			−0.277561	+	0.960708i	$0.589526\pi$
$108$		0			0
$109$	−11.1358	−	11.1358i	−1.06661	−	1.06661i	−0.997617	−	0.0689967i	$-0.978020\pi$
$109$	−11.1358	−	11.1358i	−1.06661	−	1.06661i	−0.0689967	−	0.997617i	$-0.521980\pi$
$110$		0			0
$111$	5.34856	−	5.34856i	0.507662	−	0.507662i
$112$		0			0
$113$	−16.0102			−1.50611			−0.753056	−	0.657957i	$-0.771421\pi$
$113$	−16.0102			−1.50611			−0.753056	+	0.657957i	$0.771421\pi$
$114$		0			0
$115$			16.8275i			1.56917i
$116$		0			0
$117$	1.82842	+	1.82842i	0.169038	+	0.169038i
$118$		0			0
$119$	3.89395			0.356957
$120$		0			0
$121$		−	8.64070i		−	0.785518i
$122$		0			0
$123$	12.9732	−	2.57413i	1.16976	−	0.232102i
$124$		0			0
$125$			11.8014i			1.05555i
$126$		0			0
$127$	18.0589			1.60247			0.801234	−	0.598350i	$-0.204177\pi$
$127$	18.0589			1.60247			0.801234	+	0.598350i	$0.204177\pi$
$128$		0			0
$129$	−1.31159	−	1.31159i	−0.115479	−	0.115479i
$130$		0			0
$131$		−	21.0436i		−	1.83858i	−0.393577	−	0.919292i	$-0.628762\pi$
$131$		−	21.0436i		−	1.83858i	0.393577	−	0.919292i	$-0.371238\pi$
$132$		0			0
$133$	−5.12846			−0.444694
$134$		0			0
$135$	−5.26583	+	5.26583i	−0.453210	+	0.453210i
$136$		0			0
$137$	−11.6271	−	11.6271i	−0.993368	−	0.993368i	0.00660984	−	0.999978i	$-0.497896\pi$
$137$	−11.6271	−	11.6271i	−0.993368	−	0.993368i	−0.999978	+	0.00660984i	$0.997896\pi$
$138$		0			0
$139$	1.88786			0.160126			0.0800629	−	0.996790i	$-0.474488\pi$
$139$	1.88786			0.160126			0.0800629	+	0.996790i	$0.474488\pi$
$140$		0			0
$141$	25.2368			2.12532
$142$		0			0
$143$			9.04753i			0.756592i
$144$		0			0
$145$	13.5429	+	13.5429i	1.12468	+	1.12468i
$146$		0			0
$147$	−1.46058	−	1.46058i	−0.120467	−	0.120467i
$148$		0			0
$149$	−14.7204	−	14.7204i	−1.20594	−	1.20594i	−0.972331	−	0.233608i	$-0.924947\pi$
$149$	−14.7204	−	14.7204i	−1.20594	−	1.20594i	−0.233608	−	0.972331i	$-0.575053\pi$
$150$		0			0
$151$	−3.57223	+	3.57223i	−0.290704	+	0.290704i	−0.837358	−	0.546654i	$-0.815901\pi$
$151$	−3.57223	+	3.57223i	−0.290704	+	0.290704i	0.546654	+	0.837358i	$0.315901\pi$
$152$		0			0
$153$	−3.48751	+	3.48751i	−0.281948	+	0.281948i
$154$		0			0
$155$		−	13.3919i		−	1.07566i
$156$		0			0
$157$	9.44146	−	9.44146i	0.753510	−	0.753510i	−0.221622	−	0.975133i	$-0.571135\pi$
$157$	9.44146	−	9.44146i	0.753510	−	0.753510i	0.975133	+	0.221622i	$0.0711352\pi$
$158$		0			0
$159$			22.2691i			1.76605i
$160$		0			0
$161$	−5.72086	+	5.72086i	−0.450867	+	0.450867i
$162$		0			0
$163$	0.847363			0.0663706			0.0331853	−	0.999449i	$-0.489435\pi$
$163$	0.847363			0.0663706			0.0331853	+	0.999449i	$0.489435\pi$
$164$		0			0
$165$	19.0398			1.48225
$166$		0			0
$167$	−15.9122	+	15.9122i	−1.23132	+	1.23132i	−0.267863	+	0.963457i	$0.586317\pi$
$167$	−15.9122	+	15.9122i	−1.23132	+	1.23132i	−0.963457	+	0.267863i	$0.913683\pi$
$168$		0			0
$169$			8.83224i			0.679403i
$170$		0			0
$171$	4.59317	−	4.59317i	0.351248	−	0.351248i
$172$		0			0
$173$			11.3635i			0.863949i	0.901886	+	0.431975i	$0.142183\pi$
$173$			11.3635i			0.863949i	−0.901886	+	0.431975i	$0.857817\pi$
$174$		0			0
$175$	−0.476600	+	0.476600i	−0.0360276	+	0.0360276i
$176$		0			0
$177$	−15.1865	+	15.1865i	−1.14148	+	1.14148i
$178$		0			0
$179$	−2.51734	−	2.51734i	−0.188155	−	0.188155i	0.606743	−	0.794898i	$-0.292476\pi$
$179$	−2.51734	−	2.51734i	−0.188155	−	0.188155i	−0.794898	+	0.606743i	$0.792476\pi$
$180$		0			0
$181$	10.7989	+	10.7989i	0.802677	+	0.802677i	0.983513	−	0.180836i	$-0.0578804\pi$
$181$	10.7989	+	10.7989i	0.802677	+	0.802677i	−0.180836	+	0.983513i	$0.557880\pi$
$182$		0			0
$183$	1.68230	+	1.68230i	0.124359	+	0.124359i
$184$		0			0
$185$			7.61646i			0.559973i
$186$		0			0
$187$	−17.2571			−1.26197
$188$		0			0
$189$	−3.58046			−0.260440
$190$		0			0
$191$	17.5344	+	17.5344i	1.26875	+	1.26875i	0.946737	+	0.322009i	$0.104358\pi$
$191$	17.5344	+	17.5344i	1.26875	+	1.26875i	0.322009	+	0.946737i	$0.395642\pi$
$192$		0			0
$193$	5.28816	−	5.28816i	0.380650	−	0.380650i	−0.490686	−	0.871336i	$-0.663254\pi$
$193$	5.28816	−	5.28816i	0.380650	−	0.380650i	0.871336	+	0.490686i	$0.163254\pi$
$194$		0			0
$195$	−8.77072			−0.628084
$196$		0			0
$197$			7.36967i			0.525067i	0.964923	+	0.262534i	$0.0845580\pi$
$197$			7.36967i			0.525067i	−0.964923	+	0.262534i	$0.915442\pi$
$198$		0			0
$199$	−6.26753	−	6.26753i	−0.444293	−	0.444293i	0.449159	−	0.893452i	$-0.351724\pi$
$199$	−6.26753	−	6.26753i	−0.444293	−	0.444293i	−0.893452	+	0.449159i	$0.851724\pi$
$200$		0			0
$201$	0.431046			0.0304037
$202$		0			0
$203$			9.20843i			0.646305i
$204$		0			0
$205$	−7.40426	+	11.0699i	−0.517136	+	0.773154i
$206$		0			0
$207$		−	10.2475i		−	0.712249i
$208$		0			0
$209$	22.7282			1.57214
$210$		0			0
$211$	−12.7875	−	12.7875i	−0.880328	−	0.880328i	0.113240	−	0.993568i	$-0.463877\pi$
$211$	−12.7875	−	12.7875i	−0.880328	−	0.880328i	−0.993568	+	0.113240i	$0.963877\pi$
$212$		0			0
$213$		−	8.74793i		−	0.599399i
$214$		0			0
$215$	1.86774			0.127379
$216$		0			0
$217$	4.55285	−	4.55285i	0.309068	−	0.309068i
$218$		0			0
$219$	−12.4443	−	12.4443i	−0.840907	−	0.840907i
$220$		0			0
$221$	7.94953			0.534743
$222$		0			0
$223$	−26.4926			−1.77408			−0.887038	−	0.461697i	$-0.847241\pi$
$223$	−26.4926			−1.77408			−0.887038	+	0.461697i	$0.847241\pi$
$224$		0			0
$225$		−	0.853709i		−	0.0569139i
$226$		0			0
$227$	−1.06921	−	1.06921i	−0.0709656	−	0.0709656i	0.670733	−	0.741699i	$-0.265980\pi$
$227$	−1.06921	−	1.06921i	−0.0709656	−	0.0709656i	−0.741699	+	0.670733i	$0.765980\pi$
$228$		0			0
$229$	6.38701	+	6.38701i	0.422065	+	0.422065i	0.885914	−	0.463849i	$-0.153532\pi$
$229$	6.38701	+	6.38701i	0.422065	+	0.422065i	−0.463849	+	0.885914i	$0.653532\pi$
$230$		0			0
$231$	6.47298	+	6.47298i	0.425891	+	0.425891i
$232$		0			0
$233$	−4.17317	+	4.17317i	−0.273393	+	0.273393i	−0.830465	−	0.557071i	$-0.811925\pi$
$233$	−4.17317	+	4.17317i	−0.273393	+	0.273393i	0.557071	+	0.830465i	$0.311925\pi$
$234$		0			0
$235$	−17.9689	+	17.9689i	−1.17216	+	1.17216i
$236$		0			0
$237$			15.5182i			1.00802i
$238$		0			0
$239$	−6.29633	+	6.29633i	−0.407276	+	0.407276i	−0.880787	−	0.473512i	$-0.842986\pi$
$239$	−6.29633	+	6.29633i	−0.407276	+	0.407276i	0.473512	+	0.880787i	$0.342986\pi$
$240$		0			0
$241$		−	14.8553i		−	0.956912i	−0.878111	−	0.478456i	$-0.841197\pi$
$241$		−	14.8553i		−	0.956912i	0.878111	−	0.478456i	$-0.158803\pi$
$242$		0			0
$243$	8.75668	−	8.75668i	0.561741	−	0.561741i
$244$		0			0
$245$	2.07990			0.132880
$246$		0			0
$247$	−10.4698			−0.666177
$248$		0			0
$249$	−19.2016	+	19.2016i	−1.21685	+	1.21685i
$250$		0			0
$251$			19.3759i			1.22299i	0.791247	+	0.611496i	$0.209432\pi$
$251$			19.3759i			1.22299i	−0.791247	+	0.611496i	$0.790568\pi$
$252$		0			0
$253$	25.3536	−	25.3536i	1.59397	−	1.59397i
$254$		0			0
$255$		−	16.7291i		−	1.04762i
$256$		0			0
$257$	−0.0866284	+	0.0866284i	−0.00540373	+	0.00540373i	−0.709803	−	0.704400i	$-0.751216\pi$
$257$	−0.0866284	+	0.0866284i	−0.00540373	+	0.00540373i	0.704400	+	0.709803i	$0.251216\pi$
$258$		0			0
$259$	−2.58938	+	2.58938i	−0.160896	+	0.160896i
$260$		0			0
$261$	−8.24728	−	8.24728i	−0.510494	−	0.510494i
$262$		0			0
$263$	−9.10876	−	9.10876i	−0.561670	−	0.561670i	0.368112	−	0.929782i	$-0.380004\pi$
$263$	−9.10876	−	9.10876i	−0.561670	−	0.561670i	−0.929782	+	0.368112i	$0.880004\pi$
$264$		0			0
$265$	−15.8558	−	15.8558i	−0.974014	−	0.974014i
$266$		0			0
$267$		−	1.47977i		−	0.0905603i
$268$		0			0
$269$	−12.8010			−0.780491			−0.390245	−	0.920711i	$-0.627610\pi$
$269$	−12.8010			−0.780491			−0.390245	+	0.920711i	$0.627610\pi$
$270$		0			0
$271$	0.850365			0.0516560			0.0258280	−	0.999666i	$-0.491778\pi$
$271$	0.850365			0.0516560			0.0258280	+	0.999666i	$0.491778\pi$
$272$		0			0
$273$	−2.98179	−	2.98179i	−0.180466	−	0.180466i
$274$		0			0
$275$	2.11219	−	2.11219i	0.127370	−	0.127370i
$276$		0			0
$277$	8.62452			0.518197			0.259099	−	0.965851i	$-0.416575\pi$
$277$	8.62452			0.518197			0.259099	+	0.965851i	$0.416575\pi$
$278$		0			0
$279$			8.15528i			0.488244i
$280$		0			0
$281$	5.20382	+	5.20382i	0.310434	+	0.310434i	0.845078	−	0.534644i	$-0.179554\pi$
$281$	5.20382	+	5.20382i	0.310434	+	0.310434i	−0.534644	+	0.845078i	$0.679554\pi$
$282$		0			0
$283$	−3.91912			−0.232967			−0.116484	−	0.993193i	$-0.537162\pi$
$283$	−3.91912			−0.232967			−0.116484	+	0.993193i	$0.537162\pi$
$284$		0			0
$285$			22.0328i			1.30511i
$286$		0			0
$287$	−6.28068	+	1.24621i	−0.370737	+	0.0735612i
$288$		0			0
$289$		−	1.83719i		−	0.108070i
$290$		0			0
$291$	−31.8262			−1.86568
$292$		0			0
$293$	6.13507	+	6.13507i	0.358414	+	0.358414i	0.863228	−	0.504814i	$-0.168439\pi$
$293$	6.13507	+	6.13507i	0.358414	+	0.358414i	−0.504814	+	0.863228i	$0.668439\pi$
$294$		0			0
$295$		−	21.6259i		−	1.25911i
$296$		0			0
$297$	15.8678			0.920745
$298$		0			0
$299$	−11.6792	+	11.6792i	−0.675426	+	0.675426i
$300$		0			0
$301$	0.634977	+	0.634977i	0.0365995	+	0.0365995i
$302$		0			0
$303$	30.5903			1.75737
$304$		0			0
$305$	−2.39564			−0.137174
$306$		0			0
$307$		−	5.36025i		−	0.305926i	−0.988232	−	0.152963i	$-0.951118\pi$
$307$		−	5.36025i		−	0.305926i	0.988232	−	0.152963i	$-0.0488815\pi$
$308$		0			0
$309$	−19.2166	−	19.2166i	−1.09319	−	1.09319i
$310$		0			0
$311$	7.92997	+	7.92997i	0.449667	+	0.449667i	0.895244	−	0.445577i	$-0.147001\pi$
$311$	7.92997	+	7.92997i	0.449667	+	0.449667i	−0.445577	+	0.895244i	$0.647001\pi$
$312$		0			0
$313$	3.30950	+	3.30950i	0.187064	+	0.187064i	0.794425	−	0.607362i	$-0.207772\pi$
$313$	3.30950	+	3.30950i	0.187064	+	0.187064i	−0.607362	+	0.794425i	$0.707772\pi$
$314$		0			0
$315$	−1.86281	+	1.86281i	−0.104957	+	0.104957i
$316$		0			0
$317$	−3.89022	+	3.89022i	−0.218497	+	0.218497i	−0.807865	−	0.589368i	$-0.799377\pi$
$317$	−3.89022	+	3.89022i	−0.218497	+	0.218497i	0.589368	+	0.807865i	$0.299377\pi$
$318$		0			0
$319$		−	40.8097i		−	2.28491i
$320$		0			0
$321$	−8.38698	+	8.38698i	−0.468116	+	0.468116i
$322$		0			0
$323$		−	19.9699i		−	1.11116i
$324$		0			0
$325$	−0.972984	+	0.972984i	−0.0539715	+	0.0539715i
$326$		0			0
$327$	−32.5294			−1.79888
$328$		0			0
$329$	−12.2178			−0.673589
$330$		0			0
$331$	0.742152	−	0.742152i	0.0407924	−	0.0407924i	−0.686416	−	0.727209i	$-0.740817\pi$
$331$	0.742152	−	0.742152i	0.0407924	−	0.0407924i	0.727209	+	0.686416i	$0.240817\pi$
$332$		0			0
$333$		−	4.63822i		−	0.254173i
$334$		0			0
$335$	−0.306909	+	0.306909i	−0.0167683	+	0.0167683i
$336$		0			0
$337$		−	6.77218i		−	0.368904i	−0.982841	−	0.184452i	$-0.940949\pi$
$337$		−	6.77218i		−	0.368904i	0.982841	−	0.184452i	$-0.0590511\pi$
$338$		0			0
$339$	−23.3842	+	23.3842i	−1.27005	+	1.27005i
$340$		0			0
$341$	−20.1772	+	20.1772i	−1.09266	+	1.09266i
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$		0			0
$345$	24.5779	+	24.5779i	1.32323	+	1.32323i
$346$		0			0
$347$	3.29604	+	3.29604i	0.176941	+	0.176941i	0.790021	−	0.613080i	$-0.210070\pi$
$347$	3.29604	+	3.29604i	0.176941	+	0.176941i	−0.613080	+	0.790021i	$0.710070\pi$
$348$		0			0
$349$		−	34.5405i		−	1.84891i	−0.381290	−	0.924456i	$-0.624520\pi$
$349$		−	34.5405i		−	1.84891i	0.381290	−	0.924456i	$-0.375480\pi$
$350$		0			0
$351$	−7.30955			−0.390155
$352$		0			0
$353$	25.5874			1.36188			0.680939	−	0.732340i	$-0.261572\pi$
$353$	25.5874			1.36188			0.680939	+	0.732340i	$0.261572\pi$
$354$		0			0
$355$	6.22862	+	6.22862i	0.330581	+	0.330581i
$356$		0			0
$357$	5.68743	−	5.68743i	0.301011	−	0.301011i
$358$		0			0
$359$	23.5577			1.24333			0.621663	−	0.783285i	$-0.286457\pi$
$359$	23.5577			1.24333			0.621663	+	0.783285i	$0.286457\pi$
$360$		0			0
$361$			7.30109i			0.384268i
$362$		0			0
$363$	−12.6205	−	12.6205i	−0.662402	−	0.662402i
$364$		0			0
$365$	17.7209			0.927556
$366$		0			0
$367$			27.6733i			1.44453i	0.691615	+	0.722267i	$0.256900\pi$
$367$			27.6733i			1.44453i	−0.691615	+	0.722267i	$0.743100\pi$
$368$		0			0
$369$	4.50899	−	6.74126i	0.234729	−	0.350936i
$370$		0			0
$371$		−	10.7810i		−	0.559724i
$372$		0			0
$373$	−16.5781			−0.858380			−0.429190	−	0.903214i	$-0.641201\pi$
$373$	−16.5781			−0.858380			−0.429190	+	0.903214i	$0.641201\pi$
$374$		0			0
$375$	17.2369	+	17.2369i	0.890110	+	0.890110i
$376$		0			0
$377$			18.7991i			0.968203i
$378$		0			0
$379$	−20.3072			−1.04311			−0.521555	−	0.853218i	$-0.674648\pi$
$379$	−20.3072			−1.04311			−0.521555	+	0.853218i	$0.674648\pi$
$380$		0			0
$381$	26.3765	−	26.3765i	1.35131	−	1.35131i
$382$		0			0
$383$	−21.4939	−	21.4939i	−1.09829	−	1.09829i	−0.994611	−	0.103678i	$-0.966939\pi$
$383$	−21.4939	−	21.4939i	−1.09829	−	1.09829i	−0.103678	−	0.994611i	$-0.533061\pi$
$384$		0			0
$385$	−9.21767			−0.469776
$386$		0			0
$387$	−1.13740			−0.0578174
$388$		0			0
$389$		−	18.5132i		−	0.938657i	−0.883024	−	0.469328i	$-0.844496\pi$
$389$		−	18.5132i		−	0.938657i	0.883024	−	0.469328i	$-0.155504\pi$
$390$		0			0
$391$	−22.2767	−	22.2767i	−1.12658	−	1.12658i
$392$		0			0
$393$	−30.7358	−	30.7358i	−1.55042	−	1.55042i
$394$		0			0
$395$	−11.0491	−	11.0491i	−0.555942	−	0.555942i
$396$		0			0
$397$	−18.0383	+	18.0383i	−0.905317	+	0.905317i	−0.995890	−	0.0905730i	$-0.971130\pi$
$397$	−18.0383	+	18.0383i	−0.905317	+	0.905317i	0.0905730	+	0.995890i	$0.471130\pi$
$398$		0			0
$399$	−7.49054	+	7.49054i	−0.374996	+	0.374996i
$400$		0			0
$401$			19.6451i			0.981027i	0.871433	+	0.490514i	$0.163191\pi$
$401$			19.6451i			0.981027i	−0.871433	+	0.490514i	$0.836809\pi$
$402$		0			0
$403$	9.29469	−	9.29469i	0.463001	−	0.463001i
$404$		0			0
$405$			23.2856i			1.15707i
$406$		0			0
$407$	11.4756	−	11.4756i	0.568822	−	0.568822i
$408$		0			0
$409$	11.3486			0.561153			0.280576	−	0.959832i	$-0.409474\pi$
$409$	11.3486			0.561153			0.280576	+	0.959832i	$0.409474\pi$
$410$		0			0
$411$	−33.9646			−1.67535
$412$		0			0
$413$	7.35217	−	7.35217i	0.361777	−	0.361777i
$414$		0			0
$415$		−	27.3435i		−	1.34224i
$416$		0			0
$417$	2.75737	−	2.75737i	0.135029	−	0.135029i
$418$		0			0
$419$		−	2.51864i		−	0.123044i	−0.998106	−	0.0615218i	$-0.980405\pi$
$419$		−	2.51864i		−	0.123044i	0.998106	−	0.0615218i	$-0.0195954\pi$
$420$		0			0
$421$	27.2063	−	27.2063i	1.32595	−	1.32595i	0.417084	−	0.908868i	$-0.363052\pi$
$421$	27.2063	−	27.2063i	1.32595	−	1.32595i	0.908868	−	0.417084i	$-0.136948\pi$
$422$		0			0
$423$	10.9425	−	10.9425i	0.532045	−	0.532045i
$424$		0			0
$425$	−1.85586	−	1.85586i	−0.0900222	−	0.0900222i
$426$		0			0
$427$	−0.814448	−	0.814448i	−0.0394139	−	0.0394139i
$428$		0			0
$429$	13.2147	+	13.2147i	0.638010	+	0.638010i
$430$		0			0
$431$		−	26.9611i		−	1.29867i	−0.760502	−	0.649335i	$-0.775047\pi$
$431$		−	26.9611i		−	1.29867i	0.760502	−	0.649335i	$-0.224953\pi$
$432$		0			0
$433$	−1.99421			−0.0958356			−0.0479178	−	0.998851i	$-0.515259\pi$
$433$	−1.99421			−0.0958356			−0.0479178	+	0.998851i	$0.515259\pi$
$434$		0			0
$435$	39.5612			1.89681
$436$		0			0
$437$	29.3392	+	29.3392i	1.40349	+	1.40349i
$438$		0			0
$439$	−23.0565	+	23.0565i	−1.10043	+	1.10043i	−0.106068	+	0.994359i	$0.533826\pi$
$439$	−23.0565	+	23.0565i	−1.10043	+	1.10043i	−0.994359	+	0.106068i	$0.966174\pi$
$440$		0			0
$441$	−1.26660			−0.0603144
$442$		0			0
$443$			36.8966i			1.75301i	0.481393	+	0.876505i	$0.340131\pi$
$443$			36.8966i			1.75301i	−0.481393	+	0.876505i	$0.659869\pi$
$444$		0			0
$445$	1.05361	+	1.05361i	0.0499459	+	0.0499459i
$446$		0			0
$447$	−43.0006			−2.03386
$448$		0			0
$449$		−	3.55024i		−	0.167546i	−0.996485	−	0.0837730i	$-0.973303\pi$
$449$		−	3.55024i		−	0.167546i	0.996485	−	0.0837730i	$-0.0266971\pi$
$450$		0			0
$451$	27.8346	−	5.52292i	1.31068	−	0.260064i
$452$		0			0
$453$			10.4351i			0.490283i
$454$		0			0
$455$	4.24614			0.199062
$456$		0			0
$457$	5.23465	+	5.23465i	0.244867	+	0.244867i	0.818860	−	0.573993i	$-0.194606\pi$
$457$	5.23465	+	5.23465i	0.244867	+	0.244867i	−0.573993	+	0.818860i	$0.694606\pi$
$458$		0			0
$459$		−	13.9421i		−	0.650763i
$460$		0			0
$461$	−1.11794			−0.0520675			−0.0260337	−	0.999661i	$-0.508288\pi$
$461$	−1.11794			−0.0520675			−0.0260337	+	0.999661i	$0.508288\pi$
$462$		0			0
$463$	−12.7319	+	12.7319i	−0.591702	+	0.591702i	−0.938091	−	0.346389i	$-0.887408\pi$
$463$	−12.7319	+	12.7319i	−0.591702	+	0.591702i	0.346389	+	0.938091i	$0.387408\pi$
$464$		0			0
$465$	−19.5599	−	19.5599i	−0.907069	−	0.907069i
$466$		0			0
$467$	33.8870			1.56810			0.784051	−	0.620697i	$-0.213150\pi$
$467$	33.8870			1.56810			0.784051	+	0.620697i	$0.213150\pi$
$468$		0			0
$469$	−0.208681			−0.00963599
$470$		0			0
$471$		−	27.5801i		−	1.27082i
$472$		0			0
$473$	−2.81408	−	2.81408i	−0.129392	−	0.129392i
$474$		0			0
$475$	2.44423	+	2.44423i	0.112149	+	0.112149i
$476$		0			0
$477$	9.65575	+	9.65575i	0.442107	+	0.442107i
$478$		0			0
$479$	−11.6403	+	11.6403i	−0.531859	+	0.531859i	−0.921125	−	0.389266i	$-0.872729\pi$
$479$	−11.6403	+	11.6403i	−0.531859	+	0.531859i	0.389266	+	0.921125i	$0.372729\pi$
$480$		0			0
$481$	−5.28624	+	5.28624i	−0.241032	+	0.241032i
$482$		0			0
$483$			16.7116i			0.760404i
$484$		0			0
$485$	22.6606	−	22.6606i	1.02896	−	1.02896i
$486$		0			0
$487$			31.9191i			1.44639i	0.690643	+	0.723196i	$0.257328\pi$
$487$			31.9191i			1.44639i	−0.690643	+	0.723196i	$0.742672\pi$
$488$		0			0
$489$	1.23764	−	1.23764i	0.0559682	−	0.0559682i
$490$		0			0
$491$	27.8592			1.25727			0.628633	−	0.777702i	$-0.283615\pi$
$491$	27.8592			1.25727			0.628633	+	0.777702i	$0.283615\pi$
$492$		0			0
$493$	−35.8571			−1.61492
$494$		0			0
$495$	8.25556	−	8.25556i	0.371060	−	0.371060i
$496$		0			0
$497$			4.23511i			0.189971i
$498$		0			0
$499$	−0.964813	+	0.964813i	−0.0431910	+	0.0431910i	−0.728372	−	0.685181i	$-0.759723\pi$
$499$	−0.964813	+	0.964813i	−0.0431910	+	0.0431910i	0.685181	+	0.728372i	$0.259723\pi$
$500$		0			0
$501$			46.4820i			2.07666i
$502$		0			0
$503$	−12.8206	+	12.8206i	−0.571643	+	0.571643i	−0.932587	−	0.360944i	$-0.882454\pi$
$503$	−12.8206	+	12.8206i	−0.571643	+	0.571643i	0.360944	+	0.932587i	$0.382454\pi$
$504$		0			0
$505$	−21.7806	+	21.7806i	−0.969224	+	0.969224i
$506$		0			0
$507$	12.9002	+	12.9002i	0.572919	+	0.572919i
$508$		0			0
$509$	−20.0927	−	20.0927i	−0.890595	−	0.890595i	0.103984	−	0.994579i	$-0.466841\pi$
$509$	−20.0927	−	20.0927i	−0.890595	−	0.890595i	−0.994579	+	0.103984i	$0.966841\pi$
$510$		0			0
$511$	6.02461	+	6.02461i	0.266513	+	0.266513i
$512$		0			0
$513$			18.3623i			0.810714i
$514$		0			0
$515$	27.3648			1.20584
$516$		0			0
$517$	54.1466			2.38137
$518$		0			0
$519$	16.5973	+	16.5973i	0.728540	+	0.728540i
$520$		0			0
$521$	−2.46015	+	2.46015i	−0.107781	+	0.107781i	−0.758941	−	0.651160i	$-0.774283\pi$
$521$	−2.46015	+	2.46015i	−0.107781	+	0.107781i	0.651160	+	0.758941i	$0.274283\pi$
$522$		0			0
$523$	−6.88317			−0.300980			−0.150490	−	0.988612i	$-0.548085\pi$
$523$	−6.88317			−0.300980			−0.150490	+	0.988612i	$0.548085\pi$
$524$		0			0
$525$			1.39223i			0.0607618i
$526$		0			0
$527$	17.7285	+	17.7285i	0.772268	+	0.772268i
$528$		0			0
$529$	42.4566			1.84594
$530$		0			0
$531$			13.1696i			0.571510i
$532$		0			0
$533$	−12.8221	+	2.54414i	−0.555386	+	0.110199i
$534$		0			0
$535$		−	11.9432i		−	0.516351i
$536$		0			0
$537$	−7.35356			−0.317330
$538$		0			0
$539$	−3.13374	−	3.13374i	−0.134980	−	0.134980i
$540$		0			0
$541$		−	40.4359i		−	1.73847i	−0.494395	−	0.869237i	$-0.664610\pi$
$541$		−	40.4359i		−	1.73847i	0.494395	−	0.869237i	$-0.335390\pi$
$542$		0			0
$543$	31.5454			1.35374
$544$		0			0
$545$	23.1613	−	23.1613i	0.992121	−	0.992121i
$546$		0			0
$547$	18.2571	+	18.2571i	0.780618	+	0.780618i	0.979935	−	0.199317i	$-0.0638723\pi$
$547$	18.2571	+	18.2571i	0.780618	+	0.780618i	−0.199317	+	0.979935i	$0.563872\pi$
$548$		0			0
$549$	1.45888			0.0622634
$550$		0			0
$551$	47.2250			2.01185
$552$		0			0
$553$		−	7.51277i		−	0.319476i
$554$		0			0
$555$	11.1245	+	11.1245i	0.472207	+	0.472207i
$556$		0			0
$557$	16.9196	+	16.9196i	0.716908	+	0.716908i	0.967971	−	0.251063i	$-0.0807802\pi$
$557$	16.9196	+	16.9196i	0.716908	+	0.716908i	−0.251063	+	0.967971i	$0.580780\pi$
$558$		0			0
$559$	1.29631	+	1.29631i	0.0548282	+	0.0548282i
$560$		0			0
$561$	−25.2054	+	25.2054i	−1.06417	+	1.06417i
$562$		0			0
$563$	14.3657	−	14.3657i	0.605441	−	0.605441i	−0.336310	−	0.941751i	$-0.609179\pi$
$563$	14.3657	−	14.3657i	0.605441	−	0.605441i	0.941751	+	0.336310i	$0.109179\pi$
$564$		0			0
$565$		−	33.2996i		−	1.40092i
$566$		0			0
$567$	−7.91643	+	7.91643i	−0.332459	+	0.332459i
$568$		0			0
$569$		−	19.1050i		−	0.800922i	−0.916314	−	0.400461i	$-0.868850\pi$
$569$		−	19.1050i		−	0.800922i	0.916314	−	0.400461i	$-0.131150\pi$
$570$		0			0
$571$	17.7211	−	17.7211i	0.741606	−	0.741606i	−0.231281	−	0.972887i	$-0.574292\pi$
$571$	17.7211	−	17.7211i	0.741606	−	0.741606i	0.972887	+	0.231281i	$0.0742917\pi$
$572$		0			0
$573$	51.2209			2.13978
$574$		0			0
$575$	5.45313			0.227411
$576$		0			0
$577$	12.1528	−	12.1528i	0.505929	−	0.505929i	−0.407346	−	0.913274i	$-0.633546\pi$
$577$	12.1528	−	12.1528i	0.505929	−	0.505929i	0.913274	+	0.407346i	$0.133546\pi$
$578$		0			0
$579$		−	15.4476i		−	0.641980i
$580$		0			0
$581$	9.29601	−	9.29601i	0.385663	−	0.385663i
$582$		0			0
$583$			47.7792i			1.97881i
$584$		0			0
$585$	−3.80294	+	3.80294i	−0.157232	+	0.157232i
$586$		0			0
$587$	−24.6953	+	24.6953i	−1.01928	+	1.01928i	−0.0194733	+	0.999810i	$0.506199\pi$
$587$	−24.6953	+	24.6953i	−1.01928	+	1.01928i	−0.999810	+	0.0194733i	$0.993801\pi$
$588$		0			0
$589$	−23.3491	−	23.3491i	−0.962083	−	0.962083i
$590$		0			0
$591$	10.7640	+	10.7640i	0.442772	+	0.442772i
$592$		0			0
$593$	−22.9185	−	22.9185i	−0.941151	−	0.941151i	0.0572107	−	0.998362i	$-0.481779\pi$
$593$	−22.9185	−	22.9185i	−0.941151	−	0.941151i	−0.998362	+	0.0572107i	$0.981779\pi$
$594$		0			0
$595$			8.09902i			0.332027i
$596$		0			0
$597$	−18.3085			−0.749316
$598$		0			0
$599$	4.17456			0.170568			0.0852839	−	0.996357i	$-0.472820\pi$
$599$	4.17456			0.170568			0.0852839	+	0.996357i	$0.472820\pi$
$600$		0			0
$601$	−5.08430	−	5.08430i	−0.207393	−	0.207393i	0.595765	−	0.803158i	$-0.296849\pi$
$601$	−5.08430	−	5.08430i	−0.207393	−	0.207393i	−0.803158	+	0.595765i	$0.796849\pi$
$602$		0			0
$603$	0.186900	−	0.186900i	0.00761114	−	0.00761114i
$604$		0			0
$605$	17.9718			0.730657
$606$		0			0
$607$		−	4.41771i		−	0.179309i	−0.995973	−	0.0896547i	$-0.971424\pi$
$607$		−	4.41771i		−	0.179309i	0.995973	−	0.0896547i	$-0.0285763\pi$
$608$		0			0
$609$	13.4497	+	13.4497i	0.545008	+	0.545008i
$610$		0			0
$611$	−24.9428			−1.00908
$612$		0			0
$613$		−	17.7771i		−	0.718009i	−0.933336	−	0.359004i	$-0.883116\pi$
$613$		−	17.7771i		−	0.718009i	0.933336	−	0.359004i	$-0.116884\pi$
$614$		0			0
$615$	5.35394	+	26.9830i	0.215892	+	1.08806i
$616$		0			0
$617$		−	26.1370i		−	1.05224i	−0.850411	−	0.526119i	$-0.823647\pi$
$617$		−	26.1370i		−	1.05224i	0.850411	−	0.526119i	$-0.176353\pi$
$618$		0			0
$619$	43.9659			1.76714			0.883570	−	0.468299i	$-0.155133\pi$
$619$	43.9659			1.76714			0.883570	+	0.468299i	$0.155133\pi$
$620$		0			0
$621$	20.4833	+	20.4833i	0.821968	+	0.821968i
$622$		0			0
$623$			0.716395i			0.0287018i
$624$		0			0
$625$	−21.1756			−0.847025
$626$		0			0
$627$	33.1964	−	33.1964i	1.32574	−	1.32574i
$628$		0			0
$629$	−10.0829	−	10.0829i	−0.402031	−	0.402031i
$630$		0			0
$631$	−33.3447			−1.32743			−0.663717	−	0.747984i	$-0.731022\pi$
$631$	−33.3447			−1.32743			−0.663717	+	0.747984i	$0.731022\pi$
$632$		0			0
$633$	−37.3544			−1.48470
$634$		0			0
$635$			37.5607i			1.49055i
$636$		0			0
$637$	1.44357	+	1.44357i	0.0571961	+	0.0571961i
$638$		0			0
$639$	−3.79306	−	3.79306i	−0.150051	−	0.150051i
$640$		0			0
$641$	−13.8479	−	13.8479i	−0.546960	−	0.546960i	0.378601	−	0.925560i	$-0.376405\pi$
$641$	−13.8479	−	13.8479i	−0.546960	−	0.546960i	−0.925560	+	0.378601i	$0.876405\pi$
$642$		0			0
$643$	−15.4069	+	15.4069i	−0.607588	+	0.607588i	−0.942315	−	0.334727i	$-0.891356\pi$
$643$	−15.4069	+	15.4069i	−0.607588	+	0.607588i	0.334727	+	0.942315i	$0.391356\pi$
$644$		0			0
$645$	2.72798	−	2.72798i	0.107414	−	0.107414i
$646$		0			0
$647$		−	1.18670i		−	0.0466541i	−0.999728	−	0.0233271i	$-0.992574\pi$
$647$		−	1.18670i		−	0.0466541i	0.999728	−	0.0233271i	$-0.00742591\pi$
$648$		0			0
$649$	−32.5832	+	32.5832i	−1.27900	+	1.27900i
$650$		0			0
$651$		−	13.2996i		−	0.521253i
$652$		0			0
$653$	22.2416	−	22.2416i	0.870383	−	0.870383i	−0.122131	−	0.992514i	$-0.538973\pi$
$653$	22.2416	−	22.2416i	0.870383	−	0.870383i	0.992514	+	0.122131i	$0.0389729\pi$
$654$		0			0
$655$	43.7685			1.71018
$656$		0			0
$657$	−10.7916			−0.421019
$658$		0			0
$659$	16.7069	−	16.7069i	0.650809	−	0.650809i	−0.302379	−	0.953188i	$-0.597781\pi$
$659$	16.7069	−	16.7069i	0.650809	−	0.650809i	0.953188	+	0.302379i	$0.0977807\pi$
$660$		0			0
$661$		−	31.3617i		−	1.21983i	−0.792467	−	0.609914i	$-0.791204\pi$
$661$		−	31.3617i		−	1.21983i	0.792467	−	0.609914i	$-0.208796\pi$
$662$		0			0
$663$	11.6109	−	11.6109i	0.450932	−	0.450932i
$664$		0			0
$665$		−	10.6667i		−	0.413636i
$666$		0			0
$667$	52.6802	−	52.6802i	2.03978	−	2.03978i
$668$		0			0
$669$	−38.6946	+	38.6946i	−1.49602	+	1.49602i
$670$		0			0
$671$	3.60946	+	3.60946i	0.139342	+	0.139342i
$672$		0			0
$673$	12.0018	+	12.0018i	0.462636	+	0.462636i	0.899518	−	0.436883i	$-0.143918\pi$
$673$	12.0018	+	12.0018i	0.462636	+	0.462636i	−0.436883	+	0.899518i	$0.643918\pi$
$674$		0			0
$675$	1.70645	+	1.70645i	0.0656813	+	0.0656813i
$676$		0			0
$677$			24.8177i			0.953820i	0.878952	+	0.476910i	$0.158243\pi$
$677$			24.8177i			0.953820i	−0.878952	+	0.476910i	$0.841757\pi$
$678$		0			0
$679$	15.4079			0.591301
$680$		0			0
$681$	−3.12332			−0.119686
$682$		0			0
$683$	−14.2128	−	14.2128i	−0.543836	−	0.543836i	0.380815	−	0.924651i	$-0.375643\pi$
$683$	−14.2128	−	14.2128i	−0.543836	−	0.543836i	−0.924651	+	0.380815i	$0.875643\pi$
$684$		0			0
$685$	24.1832	−	24.1832i	0.923991	−	0.923991i
$686$		0			0
$687$	18.6575			0.711828
$688$		0			0
$689$		−	22.0096i		−	0.838499i
$690$		0			0
$691$	−0.580666	−	0.580666i	−0.0220896	−	0.0220896i	0.695976	−	0.718065i	$-0.254972\pi$
$691$	−0.580666	−	0.580666i	−0.0220896	−	0.0220896i	−0.718065	+	0.695976i	$0.754972\pi$
$692$		0			0
$693$	5.61331			0.213232
$694$		0			0
$695$			3.92655i			0.148943i
$696$		0			0
$697$	−4.85266	−	24.4566i	−0.183808	−	0.926361i
$698$		0			0
$699$			12.1905i			0.461088i
$700$		0			0
$701$	26.2027			0.989661			0.494831	−	0.868989i	$-0.335230\pi$
$701$	26.2027			0.989661			0.494831	+	0.868989i	$0.335230\pi$
$702$		0			0
$703$	13.2795	+	13.2795i	0.500847	+	0.500847i
$704$		0			0
$705$			52.4900i			1.97689i
$706$		0			0
$707$	−14.8096			−0.556971
$708$		0			0
$709$	−33.7554	+	33.7554i	−1.26771	+	1.26771i	−0.320444	+	0.947268i	$0.603832\pi$
$709$	−33.7554	+	33.7554i	−1.26771	+	1.26771i	−0.947268	+	0.320444i	$0.896168\pi$
$710$		0			0
$711$	6.72862	+	6.72862i	0.252343	+	0.252343i
$712$		0			0
$713$	−52.0925			−1.95088
$714$		0			0
$715$	−18.8180			−0.703752
$716$		0			0
$717$			18.3926i			0.686885i
$718$		0			0
$719$	−10.5268	−	10.5268i	−0.392584	−	0.392584i	0.483024	−	0.875607i	$-0.339539\pi$
$719$	−10.5268	−	10.5268i	−0.392584	−	0.392584i	−0.875607	+	0.483024i	$0.839539\pi$
$720$		0			0
$721$	9.30325	+	9.30325i	0.346471	+	0.346471i
$722$		0			0
$723$	−21.6974	−	21.6974i	−0.806933	−	0.806933i
$724$		0			0
$725$	4.38874	−	4.38874i	0.162994	−	0.162994i
$726$		0			0
$727$	−10.3018	+	10.3018i	−0.382074	+	0.382074i	−0.871849	−	0.489775i	$-0.837079\pi$
$727$	−10.3018	+	10.3018i	−0.382074	+	0.382074i	0.489775	+	0.871849i	$0.337079\pi$
$728$		0			0
$729$			8.00687i			0.296551i
$730$		0			0
$731$	−2.47257	+	2.47257i	−0.0914512	+	0.0914512i
$732$		0			0
$733$		−	14.1714i		−	0.523432i	−0.965145	−	0.261716i	$-0.915712\pi$
$733$		−	14.1714i		−	0.523432i	0.965145	−	0.261716i	$-0.0842883\pi$
$734$		0			0
$735$	3.03787	−	3.03787i	0.112053	−	0.112053i
$736$		0			0
$737$	0.924829			0.0340665
$738$		0			0
$739$	1.86058			0.0684426			0.0342213	−	0.999414i	$-0.489105\pi$
$739$	1.86058			0.0684426			0.0342213	+	0.999414i	$0.489105\pi$
$740$		0			0
$741$	−15.2920	+	15.2920i	−0.561766	+	0.561766i
$742$		0			0
$743$		−	0.482928i		−	0.0177169i	−0.999961	−	0.00885845i	$-0.997180\pi$
$743$		−	0.482928i		−	0.0177169i	0.999961	−	0.00885845i	$-0.00281977\pi$
$744$		0			0
$745$	30.6169	−	30.6169i	1.12172	−	1.12172i
$746$		0			0
$747$			16.6514i			0.609245i
$748$		0			0
$749$	4.06036	−	4.06036i	0.148362	−	0.148362i
$750$		0			0
$751$	−1.25608	+	1.25608i	−0.0458350	+	0.0458350i	−0.729653	−	0.683818i	$-0.760318\pi$
$751$	−1.25608	+	1.25608i	−0.0458350	+	0.0458350i	0.683818	+	0.729653i	$0.260318\pi$
$752$		0			0
$753$	28.3000	+	28.3000i	1.03131	+	1.03131i
$754$		0			0
$755$	−7.42989	−	7.42989i	−0.270401	−	0.270401i
$756$		0			0
$757$	−18.3163	−	18.3163i	−0.665717	−	0.665717i	0.291004	−	0.956722i	$-0.406011\pi$
$757$	−18.3163	−	18.3163i	−0.665717	−	0.665717i	−0.956722	+	0.291004i	$0.906011\pi$
$758$		0			0
$759$		−	74.0621i		−	2.68829i
$760$		0			0
$761$	−19.4530			−0.705172			−0.352586	−	0.935779i	$-0.614698\pi$
$761$	−19.4530			−0.705172			−0.352586	+	0.935779i	$0.614698\pi$
$762$		0			0
$763$	15.7484			0.570129
$764$		0			0
$765$	−7.25367	−	7.25367i	−0.262257	−	0.262257i
$766$		0			0
$767$	15.0095	−	15.0095i	0.541963	−	0.541963i
$768$		0			0
$769$	24.8729			0.896940			0.448470	−	0.893798i	$-0.351969\pi$
$769$	24.8729			0.896940			0.448470	+	0.893798i	$0.351969\pi$
$770$		0			0
$771$			0.253056i			0.00911358i
$772$		0			0
$773$	8.54580	+	8.54580i	0.307371	+	0.307371i	0.843889	−	0.536518i	$-0.180261\pi$
$773$	8.54580	+	8.54580i	0.307371	+	0.307371i	−0.536518	+	0.843889i	$0.680261\pi$
$774$		0			0
$775$	−4.33978			−0.155889
$776$		0			0
$777$			7.56400i			0.271357i
$778$		0			0
$779$	6.39112	+	32.2102i	0.228986	+	1.15405i
$780$		0			0
$781$		−	18.7691i		−	0.671610i
$782$		0			0
$783$	32.9704			1.17827
$784$		0			0
$785$	19.6373	+	19.6373i	0.700885	+	0.700885i
$786$		0			0
$787$		−	3.13834i		−	0.111870i	−0.998434	−	0.0559349i	$-0.982186\pi$
$787$		−	3.13834i		−	0.111870i	0.998434	−	0.0559349i	$-0.0178139\pi$
$788$		0			0
$789$	−26.6082			−0.947276
$790$		0			0
$791$	11.3209	−	11.3209i	0.402525	−	0.402525i
$792$		0			0
$793$	−1.66270	−	1.66270i	−0.0590443	−	0.0590443i
$794$		0			0
$795$	−46.3174			−1.64271
$796$		0			0
$797$	−2.93668			−0.104022			−0.0520112	−	0.998647i	$-0.516563\pi$
$797$	−2.93668			−0.104022			−0.0520112	+	0.998647i	$0.516563\pi$
$798$		0			0
$799$		−	47.5755i		−	1.68310i
$800$		0			0
$801$	−0.641620	−	0.641620i	−0.0226705	−	0.0226705i
$802$		0			0
$803$	−26.6998	−	26.6998i	−0.942214	−	0.942214i
$804$		0			0
$805$	−11.8988	−	11.8988i	−0.419379	−	0.419379i
$806$		0			0
$807$	−18.6969	+	18.6969i	−0.658163	+	0.658163i
$808$		0			0
$809$	−20.9296	+	20.9296i	−0.735844	+	0.735844i	−0.971771	−	0.235927i	$-0.924188\pi$
$809$	−20.9296	+	20.9296i	−0.735844	+	0.735844i	0.235927	+	0.971771i	$0.424188\pi$
$810$		0			0
$811$		−	3.71012i		−	0.130280i	−0.997876	−	0.0651400i	$-0.979251\pi$
$811$		−	3.71012i		−	0.130280i	0.997876	−	0.0651400i	$-0.0207494\pi$
$812$		0			0
$813$	1.24203	−	1.24203i	0.0435599	−	0.0435599i
$814$		0			0
$815$			1.76243i			0.0617353i
$816$		0			0
$817$	3.25646	−	3.25646i	0.113929	−	0.113929i
$818$		0			0
$819$	−2.58578			−0.0903545
$820$		0			0
$821$	35.1203			1.22571			0.612853	−	0.790197i	$-0.290022\pi$
$821$	35.1203			1.22571			0.612853	+	0.790197i	$0.290022\pi$
$822$		0			0
$823$	−19.0118	+	19.0118i	−0.662710	+	0.662710i	−0.956018	−	0.293308i	$-0.905244\pi$
$823$	−19.0118	+	19.0118i	−0.662710	+	0.662710i	0.293308	+	0.956018i	$0.405244\pi$
$824$		0			0
$825$		−	6.17005i		−	0.214814i
$826$		0			0
$827$	−2.30633	+	2.30633i	−0.0801988	+	0.0801988i	−0.746068	−	0.665869i	$-0.768061\pi$
$827$	−2.30633	+	2.30633i	−0.0801988	+	0.0801988i	0.665869	+	0.746068i	$0.268061\pi$
$828$		0			0
$829$		−	8.00339i		−	0.277969i	−0.990295	−	0.138985i	$-0.955616\pi$
$829$		−	8.00339i		−	0.277969i	0.990295	−	0.138985i	$-0.0443838\pi$
$830$		0			0
$831$	12.5968	−	12.5968i	0.436979	−	0.436979i
$832$		0			0
$833$	−2.75344	+	2.75344i	−0.0954009	+	0.0954009i
$834$		0			0
$835$	−33.0957	−	33.0957i	−1.14532	−	1.14532i
$836$		0			0
$837$	−16.3013	−	16.3013i	−0.563456	−	0.563456i
$838$		0			0
$839$	−7.56278	−	7.56278i	−0.261096	−	0.261096i	0.564403	−	0.825499i	$-0.309106\pi$
$839$	−7.56278	−	7.56278i	−0.261096	−	0.261096i	−0.825499	+	0.564403i	$0.809106\pi$
$840$		0			0
$841$		−	55.7951i		−	1.92397i
$842$		0			0
$843$	15.2012			0.523558
$844$		0			0
$845$	−18.3702			−0.631953
$846$		0			0
$847$	6.10990	+	6.10990i	0.209939	+	0.209939i
$848$		0			0
$849$	−5.72420	+	5.72420i	−0.196454	+	0.196454i
$850$		0			0
$851$	29.6270			1.01560
$852$		0			0
$853$		−	15.0669i		−	0.515881i	−0.966161	−	0.257941i	$-0.916956\pi$
$853$		−	15.0669i		−	0.515881i	0.966161	−	0.257941i	$-0.0830439\pi$
$854$		0			0
$855$	9.55333	+	9.55333i	0.326717	+	0.326717i
$856$		0			0
$857$	−2.38471			−0.0814603			−0.0407302	−	0.999170i	$-0.512968\pi$
$857$	−2.38471			−0.0814603			−0.0407302	+	0.999170i	$0.512968\pi$
$858$		0			0
$859$		−	1.48866i		−	0.0507925i	−0.999677	−	0.0253962i	$-0.991915\pi$
$859$		−	1.48866i		−	0.0507925i	0.999677	−	0.0253962i	$-0.00808474\pi$
$860$		0			0
$861$	−7.35327	+	10.9936i	−0.250599	+	0.374662i
$862$		0			0
$863$			33.0239i			1.12415i	0.827088	+	0.562073i	$0.189996\pi$
$863$			33.0239i			1.12415i	−0.827088	+	0.562073i	$0.810004\pi$
$864$		0			0
$865$	−23.6349			−0.803611
$866$		0			0
$867$	−2.68337	−	2.68337i	−0.0911320	−	0.0911320i
$868$		0			0
$869$			33.2950i			1.12945i
$870$		0			0
$871$	−0.426024			−0.0144353
$872$		0			0
$873$	−13.7997	+	13.7997i	−0.467048	+	0.467048i
$874$		0			0
$875$	−8.34484	−	8.34484i	−0.282107	−	0.282107i
$876$		0			0
$877$	−51.6666			−1.74466			−0.872328	−	0.488921i	$-0.837390\pi$
$877$	−51.6666			−1.74466			−0.872328	+	0.488921i	$0.837390\pi$
$878$		0			0
$879$	17.9215			0.604479
$880$		0			0
$881$			45.9939i			1.54957i	0.632222	+	0.774787i	$0.282143\pi$
$881$			45.9939i			1.54957i	−0.632222	+	0.774787i	$0.717857\pi$
$882$		0			0
$883$	13.7495	+	13.7495i	0.462709	+	0.462709i	0.899542	−	0.436834i	$-0.143900\pi$
$883$	13.7495	+	13.7495i	0.462709	+	0.462709i	−0.436834	+	0.899542i	$0.643900\pi$
$884$		0			0
$885$	−31.5863	−	31.5863i	−1.06176	−	1.06176i
$886$		0			0
$887$	1.71023	+	1.71023i	0.0574238	+	0.0574238i	0.735236	−	0.677812i	$-0.237072\pi$
$887$	1.71023	+	1.71023i	0.0574238	+	0.0574238i	−0.677812	+	0.735236i	$0.737072\pi$
$888$		0			0
$889$	−12.7696	+	12.7696i	−0.428278	+	0.428278i
$890$		0			0
$891$	35.0839	−	35.0839i	1.17536	−	1.17536i
$892$		0			0
$893$			62.6585i			2.09679i
$894$		0			0
$895$	5.23581	−	5.23581i	0.175014	−	0.175014i
$896$		0			0
$897$			34.1169i			1.13913i
$898$		0			0
$899$	−41.9246	+	41.9246i	−1.39826	+	1.39826i
$900$		0			0
$901$	41.9808			1.39858
$902$		0			0
$903$	1.85487			0.0617263
$904$		0			0
$905$	−22.4607	+	22.4607i	−0.746618	+	0.746618i
$906$		0			0
$907$		−	32.5921i		−	1.08220i	−0.840957	−	0.541102i	$-0.818007\pi$
$907$		−	32.5921i		−	1.08220i	0.840957	−	0.541102i	$-0.181993\pi$
$908$		0			0
$909$	13.2638	−	13.2638i	0.439932	−	0.439932i
$910$		0			0
$911$			17.5905i			0.582799i	0.956601	+	0.291400i	$0.0941210\pi$
$911$			17.5905i			0.582799i	−0.956601	+	0.291400i	$0.905879\pi$
$912$		0			0
$913$	−41.1979	+	41.1979i	−1.36345	+	1.36345i
$914$		0			0
$915$	−3.49902	+	3.49902i	−0.115674	+	0.115674i
$916$		0			0
$917$	14.8800	+	14.8800i	0.491382	+	0.491382i
$918$		0			0
$919$	−36.7528	−	36.7528i	−1.21236	−	1.21236i	−0.970248	−	0.242115i	$-0.922159\pi$
$919$	−36.7528	−	36.7528i	−1.21236	−	1.21236i	−0.242115	−	0.970248i	$-0.577841\pi$
$920$		0			0
$921$	−7.82909	−	7.82909i	−0.257977	−	0.257977i
$922$		0			0
$923$			8.64601i			0.284587i
$924$		0			0
$925$	2.46820			0.0811538
$926$		0			0
$927$	−16.6644			−0.547331
$928$		0			0
$929$	−18.7889	−	18.7889i	−0.616444	−	0.616444i	0.328173	−	0.944618i	$-0.393567\pi$
$929$	−18.7889	−	18.7889i	−0.616444	−	0.616444i	−0.944618	+	0.328173i	$0.893567\pi$
$930$		0			0
$931$	3.62637	−	3.62637i	0.118849	−	0.118849i
$932$		0			0
$933$	23.1647			0.758380
$934$		0			0
$935$		−	35.8931i		−	1.17383i
$936$		0			0
$937$	−30.5663	−	30.5663i	−0.998556	−	0.998556i	0.00144300	−	0.999999i	$-0.499541\pi$
$937$	−30.5663	−	30.5663i	−0.998556	−	0.998556i	−0.999999	+	0.00144300i	$0.999541\pi$
$938$		0			0
$939$	9.66759			0.315490
$940$		0			0
$941$		−	10.3495i		−	0.337386i	−0.985669	−	0.168693i	$-0.946045\pi$
$941$		−	10.3495i		−	0.337386i	0.985669	−	0.168693i	$-0.0539546\pi$
$942$		0			0
$943$	43.0603	+	28.8016i	1.40224	+	0.937908i
$944$		0			0
$945$		−	7.44701i		−	0.242251i
$946$		0			0
$947$	30.7188			0.998226			0.499113	−	0.866537i	$-0.333659\pi$
$947$	30.7188			0.998226			0.499113	+	0.866537i	$0.333659\pi$
$948$		0			0
$949$	12.2993	+	12.2993i	0.399252	+	0.399252i
$950$		0			0
$951$			11.3640i			0.368502i
$952$		0			0
$953$	−12.4048			−0.401830			−0.200915	−	0.979609i	$-0.564391\pi$
$953$	−12.4048			−0.401830			−0.200915	+	0.979609i	$0.564391\pi$
$954$		0			0
$955$	−36.4698	+	36.4698i	−1.18014	+	1.18014i
$956$		0			0
$957$	−59.6060	−	59.6060i	−1.92679	−	1.92679i
$958$		0			0
$959$	16.4432			0.530978
$960$		0			0
$961$	10.4569			0.337319
$962$		0			0
$963$			7.27311i			0.234373i
$964$		0			0
$965$	10.9988	+	10.9988i	0.354065	+	0.354065i
$966$		0			0
$967$	−9.46780	−	9.46780i	−0.304464	−	0.304464i	0.538294	−	0.842757i	$-0.319069\pi$
$967$	−9.46780	−	9.46780i	−0.304464	−	0.304464i	−0.842757	+	0.538294i	$0.819069\pi$
$968$		0			0
$969$	−29.1677	−	29.1677i	−0.937003	−	0.937003i
$970$		0			0
$971$	−8.78441	+	8.78441i	−0.281905	+	0.281905i	−0.833868	−	0.551963i	$-0.813879\pi$
$971$	−8.78441	+	8.78441i	−0.281905	+	0.281905i	0.551963	+	0.833868i	$0.313879\pi$
$972$		0			0
$973$	−1.33492	+	1.33492i	−0.0427954	+	0.0427954i
$974$		0			0
$975$			2.84225i			0.0910248i
$976$		0			0
$977$	−39.8877	+	39.8877i	−1.27612	+	1.27612i	−0.333300	+	0.942821i	$0.608162\pi$
$977$	−39.8877	+	39.8877i	−1.27612	+	1.27612i	−0.942821	+	0.333300i	$0.891838\pi$
$978$		0			0
$979$		−	3.17491i		−	0.101470i
$980$		0			0
$981$	−14.1046	+	14.1046i	−0.450325	+	0.450325i
$982$		0			0
$983$	−30.2946			−0.966246			−0.483123	−	0.875552i	$-0.660498\pi$
$983$	−30.2946			−0.966246			−0.483123	+	0.875552i	$0.660498\pi$
$984$		0			0
$985$	−15.3282			−0.488396
$986$		0			0
$987$	−17.8451	+	17.8451i	−0.568016	+	0.568016i
$988$		0			0
$989$		−	7.26524i		−	0.231021i
$990$		0			0
$991$	7.82972	−	7.82972i	0.248719	−	0.248719i	−0.571726	−	0.820445i	$-0.693726\pi$
$991$	7.82972	−	7.82972i	0.248719	−	0.248719i	0.820445	+	0.571726i	$0.193726\pi$
$992$		0			0
$993$		−	2.16795i		−	0.0687978i
$994$		0			0
$995$	13.0358	−	13.0358i	0.413264	−	0.413264i
$996$		0			0
$997$	−20.4746	+	20.4746i	−0.648437	+	0.648437i	−0.952615	−	0.304178i	$-0.901618\pi$
$997$	−20.4746	+	20.4746i	−0.648437	+	0.648437i	0.304178	+	0.952615i	$0.401618\pi$
$998$		0			0
$999$	9.27117	+	9.27117i	0.293327	+	0.293327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.729.13	yes	36
41.9	even	4	inner	1148.2.k.b.337.13	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.13	✓	36	41.9	even	4	inner
1148.2.k.b.729.13	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.46058 - 1.46058i) q^{3} +2.07990i q^{5} +(-0.707107 + 0.707107i) q^{7} -1.26660i q^{9} +O(q^{10})\)	\(q+(1.46058 - 1.46058i) q^{3} +2.07990i q^{5} +(-0.707107 + 0.707107i) q^{7} -1.26660i q^{9} +(3.13374 - 3.13374i) q^{11} +(-1.44357 + 1.44357i) q^{13} +(3.03787 + 3.03787i) q^{15} +(-2.75344 - 2.75344i) q^{17} +(3.62637 + 3.62637i) q^{19} +2.06558i q^{21} +8.09052 q^{23} +0.674015 q^{25} +(2.53177 + 2.53177i) q^{27} +(6.51134 - 6.51134i) q^{29} -6.43870 q^{31} -9.15418i q^{33} +(-1.47071 - 1.47071i) q^{35} +3.66193 q^{37} +4.21689i q^{39} +(5.32231 + 3.55991i) q^{41} -0.897994i q^{43} +2.63441 q^{45} +(8.63929 + 8.63929i) q^{47} -1.00000i q^{49} -8.04324 q^{51} +(-7.62335 + 7.62335i) q^{53} +(6.51787 + 6.51787i) q^{55} +10.5932 q^{57} -10.3975 q^{59} +1.15180i q^{61} +(0.895623 + 0.895623i) q^{63} +(-3.00247 - 3.00247i) q^{65} +(0.147560 + 0.147560i) q^{67} +(11.8169 - 11.8169i) q^{69} +(2.99467 - 2.99467i) q^{71} -8.52008i q^{73} +(0.984454 - 0.984454i) q^{75} +4.43178i q^{77} +(-5.31233 + 5.31233i) q^{79} +11.1955 q^{81} -13.1465 q^{83} +(5.72687 - 5.72687i) q^{85} -19.0207i q^{87} +(0.506568 - 0.506568i) q^{89} -2.04151i q^{91} +(-9.40426 + 9.40426i) q^{93} +(-7.54248 + 7.54248i) q^{95} +(-10.8950 - 10.8950i) q^{97} +(-3.96921 - 3.96921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 36 * q	\( 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) \) 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

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Database

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