LMFDB - Embedded newform 308.4.w.a.13.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,4,Mod(13,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("308.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	308.w (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.1725882818$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.18
Character	$\chi$	$=$	308.13
Dual form			308.4.w.a.237.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.54235 + 3.49924i) q^{3} +(-2.06273 + 0.670222i) q^{5} +(17.6363 + 5.65332i) q^{7} +(2.56231 - 7.88597i) q^{9} +(7.01068 - 35.8029i) q^{11} +(26.3234 - 81.0150i) q^{13} +(-7.58944 - 5.51405i) q^{15} +(20.9350 + 64.4312i) q^{17} +(-13.6956 + 9.95044i) q^{19} +(25.0553 + 76.0864i) q^{21} +124.597 q^{23} +(-97.3215 + 70.7082i) q^{25} +(145.176 - 47.1707i) q^{27} +(2.95126 - 4.06207i) q^{29} +(130.639 + 42.4472i) q^{31} +(143.107 - 66.4914i) q^{33} +(-40.1680 + 0.158975i) q^{35} +(-209.449 - 152.173i) q^{37} +(350.414 - 113.856i) q^{39} +(210.999 - 153.300i) q^{41} +483.453i q^{43} +17.9839i q^{45} +(-9.51981 - 13.1029i) q^{47} +(279.080 + 199.408i) q^{49} +(-172.236 + 237.063i) q^{51} +(-91.4270 + 281.383i) q^{53} +(9.53477 + 78.5505i) q^{55} +(-69.6379 - 22.6267i) q^{57} +(324.522 - 446.666i) q^{59} +(58.1075 + 178.836i) q^{61} +(89.7716 - 124.594i) q^{63} +184.755i q^{65} -229.918 q^{67} +(316.769 + 435.995i) q^{69} +(-330.773 - 1018.02i) q^{71} +(3.14162 + 2.28252i) q^{73} +(-494.850 - 160.786i) q^{75} +(326.048 - 591.799i) q^{77} +(812.063 + 263.855i) q^{79} +(353.029 + 256.490i) q^{81} +(78.3604 + 241.169i) q^{83} +(-86.3663 - 118.873i) q^{85} +21.7173 q^{87} +221.079i q^{89} +(922.251 - 1279.99i) q^{91} +(183.597 + 565.052i) q^{93} +(21.5813 - 29.7042i) q^{95} +(382.486 + 124.277i) q^{97} +(-264.377 - 147.024i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 10 q^{7} + 168 q^{9} + 60 q^{11} - 192 q^{15} - 112 q^{23} + 548 q^{25} - 700 q^{29} - 940 q^{35} + 288 q^{37} + 460 q^{39} + 90 q^{49} - 1420 q^{51} - 2240 q^{53} + 560 q^{57} + 320 q^{63} + 4272 q^{67}+ \cdots - 10212 q^{99}+O(q^{100}) $ 96 * q - 10 * q^7 + 168 * q^9 + 60 * q^11 - 192 * q^15 - 112 * q^23 + 548 * q^25 - 700 * q^29 - 940 * q^35 + 288 * q^37 + 460 * q^39 + 90 * q^49 - 1420 * q^51 - 2240 * q^53 + 560 * q^57 + 320 * q^63 + 4272 * q^67 + 296 * q^71 + 430 * q^77 + 2100 * q^79 - 6088 * q^81 + 5900 * q^85 - 636 * q^91 - 2628 * q^93 + 780 * q^95 - 10212 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$	$1$

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
$3$	2.54235	+	3.49924i	0.489275	+	0.673429i	0.980254	−	0.197742i	$-0.0633609\pi$
$3$	2.54235	+	3.49924i	0.489275	+	0.673429i	−0.490979	+	0.871171i	$0.663361\pi$
$4$		0			0
$5$	−2.06273	+	0.670222i	−0.184496	+	0.0599465i	−0.399808	−	0.916599i	$-0.630923\pi$
$5$	−2.06273	+	0.670222i	−0.184496	+	0.0599465i	0.215312	+	0.976545i	$0.430923\pi$
$6$		0			0
$7$	17.6363	+	5.65332i	0.952272	+	0.305251i
$7$	17.6363	+	5.65332i	0.952272	+	0.305251i
$8$		0			0
$9$	2.56231	−	7.88597i	0.0949002	−	0.292073i
$10$		0			0
$11$	7.01068	−	35.8029i	0.192164	−	0.981363i
$11$	7.01068	−	35.8029i	0.192164	−	0.981363i
$12$		0			0
$13$	26.3234	−	81.0150i	0.561599	−	1.72842i	−0.116248	−	0.993220i	$-0.537087\pi$
$13$	26.3234	−	81.0150i	0.561599	−	1.72842i	0.677847	−	0.735203i	$-0.262913\pi$
$14$		0			0
$15$	−7.58944	−	5.51405i	−0.130639	−	0.0949148i
$16$		0			0
$17$	20.9350	+	64.4312i	0.298675	+	0.919227i	0.981962	+	0.189077i	$0.0605496\pi$
$17$	20.9350	+	64.4312i	0.298675	+	0.919227i	−0.683287	+	0.730149i	$0.739450\pi$
$18$		0			0
$19$	−13.6956	+	9.95044i	−0.165368	+	0.120147i	−0.667391	−	0.744707i	$-0.732589\pi$
$19$	−13.6956	+	9.95044i	−0.165368	+	0.120147i	0.502023	+	0.864854i	$0.332589\pi$
$20$		0			0
$21$	25.0553	+	76.0864i	0.260358	+	0.790639i
$22$		0			0
$23$	124.597			1.12958			0.564789	−	0.825235i	$-0.308957\pi$
$23$	124.597			1.12958			0.564789	+	0.825235i	$0.308957\pi$
$24$		0			0
$25$	−97.3215	+	70.7082i	−0.778572	+	0.565665i
$26$		0			0
$27$	145.176	−	47.1707i	1.03479	−	0.336222i
$28$		0			0
$29$	2.95126	−	4.06207i	0.0188978	−	0.0260106i	−0.799464	−	0.600715i	$-0.794883\pi$
$29$	2.95126	−	4.06207i	0.0188978	−	0.0260106i	0.818361	+	0.574704i	$0.194883\pi$
$30$		0			0
$31$	130.639	+	42.4472i	0.756885	+	0.245927i	0.661941	−	0.749556i	$-0.269733\pi$
$31$	130.639	+	42.4472i	0.756885	+	0.245927i	0.0949439	+	0.995483i	$0.469733\pi$
$32$		0			0
$33$	143.107	−	66.4914i	0.754899	−	0.350748i
$34$		0			0
$35$	−40.1680	+	0.158975i	−0.193989	+	0.000767761i
$36$		0			0
$37$	−209.449	−	152.173i	−0.930625	−	0.676139i	0.0155205	−	0.999880i	$-0.495059\pi$
$37$	−209.449	−	152.173i	−0.930625	−	0.676139i	−0.946146	+	0.323741i	$0.895059\pi$
$38$		0			0
$39$	350.414	−	113.856i	1.43875	−	0.467477i
$40$		0			0
$41$	210.999	−	153.300i	0.803721	−	0.583938i	−0.108282	−	0.994120i	$-0.534535\pi$
$41$	210.999	−	153.300i	0.803721	−	0.583938i	0.912003	+	0.410183i	$0.134535\pi$
$42$		0			0
$43$			483.453i			1.71456i	0.514854	+	0.857278i	$0.327846\pi$
$43$			483.453i			1.71456i	−0.514854	+	0.857278i	$0.672154\pi$
$44$		0			0
$45$			17.9839i			0.0595753i
$46$		0			0
$47$	−9.51981	−	13.1029i	−0.0295448	−	0.0406650i	0.793989	−	0.607932i	$-0.208001\pi$
$47$	−9.51981	−	13.1029i	−0.0295448	−	0.0406650i	−0.823534	+	0.567267i	$0.808001\pi$
$48$		0			0
$49$	279.080	+	199.408i	0.813644	+	0.581363i
$50$		0			0
$51$	−172.236	+	237.063i	−0.472900	+	0.650891i
$52$		0			0
$53$	−91.4270	+	281.383i	−0.236952	+	0.729264i	0.759904	+	0.650035i	$0.225246\pi$
$53$	−91.4270	+	281.383i	−0.236952	+	0.729264i	−0.996856	+	0.0792287i	$0.974754\pi$
$54$		0			0
$55$	9.53477	+	78.5505i	0.0233758	+	0.192577i
$56$		0			0
$57$	−69.6379	−	22.6267i	−0.161821	−	0.0525787i
$58$		0			0
$59$	324.522	−	446.666i	0.716087	−	0.985610i	−0.283557	−	0.958955i	$-0.591515\pi$
$59$	324.522	−	446.666i	0.716087	−	0.985610i	0.999645	−	0.0266545i	$-0.00848541\pi$
$60$		0			0
$61$	58.1075	+	178.836i	0.121966	+	0.375371i	0.993336	−	0.115254i	$-0.0367683\pi$
$61$	58.1075	+	178.836i	0.121966	+	0.375371i	−0.871370	+	0.490626i	$0.836768\pi$
$62$		0			0
$63$	89.7716	−	124.594i	0.179526	−	0.249165i
$64$		0			0
$65$			184.755i			0.352554i
$66$		0			0
$67$	−229.918			−0.419238			−0.209619	−	0.977783i	$-0.567222\pi$
$67$	−229.918			−0.419238			−0.209619	+	0.977783i	$0.567222\pi$
$68$		0			0
$69$	316.769	+	435.995i	0.552674	+	0.760691i
$70$		0			0
$71$	−330.773	−	1018.02i	−0.552896	−	1.70164i	−0.701437	−	0.712732i	$-0.747458\pi$
$71$	−330.773	−	1018.02i	−0.552896	−	1.70164i	0.148541	−	0.988906i	$-0.452542\pi$
$72$		0			0
$73$	3.14162	+	2.28252i	0.00503697	+	0.00365958i	0.590301	−	0.807183i	$-0.299009\pi$
$73$	3.14162	+	2.28252i	0.00503697	+	0.00365958i	−0.585264	+	0.810843i	$0.699009\pi$
$74$		0			0
$75$	−494.850	−	160.786i	−0.761871	−	0.247547i
$76$		0			0
$77$	326.048	−	591.799i	0.482554	−	0.875866i
$78$		0			0
$79$	812.063	+	263.855i	1.15651	+	0.375772i	0.823591	−	0.567184i	$-0.191967\pi$
$79$	812.063	+	263.855i	1.15651	+	0.375772i	0.332917	+	0.942956i	$0.391967\pi$
$80$		0			0
$81$	353.029	+	256.490i	0.484264	+	0.351839i
$82$		0			0
$83$	78.3604	+	241.169i	0.103629	+	0.318936i	0.989406	−	0.145174i	$-0.0463742\pi$
$83$	78.3604	+	241.169i	0.103629	+	0.318936i	−0.885778	+	0.464110i	$0.846374\pi$
$84$		0			0
$85$	−86.3663	−	118.873i	−0.110209	−	0.151689i
$86$		0			0
$87$	21.7173			0.0267625
$88$		0			0
$89$			221.079i			0.263306i	0.991296	+	0.131653i	$0.0420285\pi$
$89$			221.079i			0.263306i	−0.991296	+	0.131653i	$0.957971\pi$
$90$		0			0
$91$	922.251	−	1279.99i	1.06240	−	1.47450i
$92$		0			0
$93$	183.597	+	565.052i	0.204711	+	0.630034i
$94$		0			0
$95$	21.5813	−	29.7042i	0.0233074	−	0.0320798i
$96$		0			0
$97$	382.486	+	124.277i	0.400366	+	0.130087i	0.502277	−	0.864707i	$-0.332496\pi$
$97$	382.486	+	124.277i	0.400366	+	0.130087i	−0.101911	+	0.994794i	$0.532496\pi$
$98$		0			0
$99$	−264.377	−	147.024i	−0.268393	−	0.149257i
$100$		0			0
$101$	−172.467	+	530.798i	−0.169912	+	0.522934i	−0.999365	−	0.0356424i	$-0.988652\pi$
$101$	−172.467	+	530.798i	−0.169912	+	0.522934i	0.829453	+	0.558576i	$0.188652\pi$
$102$		0			0
$103$	−1178.98	+	1622.72i	−1.12784	+	1.55234i	−0.335745	+	0.941953i	$0.608988\pi$
$103$	−1178.98	+	1622.72i	−1.12784	+	1.55234i	−0.792099	+	0.610392i	$0.791012\pi$
$104$		0			0
$105$	−102.677	−	140.153i	−0.0954311	−	0.130262i
$106$		0			0
$107$	−1050.58	−	1446.00i	−0.949188	−	1.30645i	−0.951887	−	0.306449i	$-0.900859\pi$
$107$	−1050.58	−	1446.00i	−0.949188	−	1.30645i	0.00269901	−	0.999996i	$-0.499141\pi$
$108$		0			0
$109$		−	868.338i		−	0.763043i	−0.924360	−	0.381522i	$-0.875400\pi$
$109$		−	868.338i		−	0.763043i	0.924360	−	0.381522i	$-0.124600\pi$
$110$		0			0
$111$		−	1119.79i		−	0.957528i
$112$		0			0
$113$	354.548	−	257.595i	0.295160	−	0.214447i	−0.430343	−	0.902666i	$-0.641607\pi$
$113$	354.548	−	257.595i	0.295160	−	0.214447i	0.725503	+	0.688219i	$0.241607\pi$
$114$		0			0
$115$	−257.011	+	83.5078i	−0.208403	+	0.0677143i
$116$		0			0
$117$	−571.433	−	415.170i	−0.451530	−	0.328056i
$118$		0			0
$119$	4.96571	+	1254.68i	0.00382526	+	0.966524i
$120$		0			0
$121$	−1232.70	−	502.006i	−0.926146	−	0.377164i
$122$		0			0
$123$	1072.87	+	348.596i	0.786481	+	0.255543i
$124$		0			0
$125$	312.713	−	430.412i	0.223759	−	0.307978i
$126$		0			0
$127$	−1496.33	+	486.186i	−1.04549	+	0.339701i	−0.780897	−	0.624659i	$-0.785238\pi$
$127$	−1496.33	+	486.186i	−1.04549	+	0.339701i	−0.264594	+	0.964360i	$0.585238\pi$
$128$		0			0
$129$	−1691.72	+	1229.11i	−1.15463	+	0.838889i
$130$		0			0
$131$	−2048.23			−1.36607			−0.683034	−	0.730386i	$-0.739340\pi$
$131$	−2048.23			−1.36607			−0.683034	+	0.730386i	$0.739340\pi$
$132$		0			0
$133$	−297.793	+	98.0635i	−0.194150	+	0.0639337i
$134$		0			0
$135$	−267.845	+	194.601i	−0.170759	+	0.124064i
$136$		0			0
$137$	664.498	+	2045.11i	0.414393	+	1.27537i	0.912792	+	0.408424i	$0.133921\pi$
$137$	664.498	+	2045.11i	0.414393	+	1.27537i	−0.498399	+	0.866948i	$0.666079\pi$
$138$		0			0
$139$	−1513.84	−	1099.87i	−0.923755	−	0.671147i	0.0207010	−	0.999786i	$-0.493410\pi$
$139$	−1513.84	−	1099.87i	−0.923755	−	0.671147i	−0.944456	+	0.328639i	$0.893410\pi$
$140$		0			0
$141$	21.6475	−	66.6242i	0.0129294	−	0.0397927i
$142$		0			0
$143$	−2716.03	−	1510.42i	−1.58829	−	0.883272i
$144$		0			0
$145$	−3.36518	+	10.3570i	−0.00192733	+	0.00593171i
$146$		0			0
$147$	11.7431	+	1483.53i	0.00658879	+	0.832378i
$148$		0			0
$149$	207.675	−	67.4778i	0.114184	−	0.0371006i	−0.251368	−	0.967892i	$-0.580880\pi$
$149$	207.675	−	67.4778i	0.114184	−	0.0371006i	0.365552	+	0.930791i	$0.380880\pi$
$150$		0			0
$151$	−87.6604	−	120.654i	−0.0472430	−	0.0650245i	0.784742	−	0.619823i	$-0.212795\pi$
$151$	−87.6604	−	120.654i	−0.0472430	−	0.0650245i	−0.831985	+	0.554798i	$0.812795\pi$
$152$		0			0
$153$	561.744			0.296825
$154$		0			0
$155$	−297.922			−0.154385
$156$		0			0
$157$	1461.44	+	2011.49i	0.742899	+	1.02251i	0.998447	+	0.0557168i	$0.0177444\pi$
$157$	1461.44	+	2011.49i	0.742899	+	1.02251i	−0.255547	+	0.966797i	$0.582256\pi$
$158$		0			0
$159$	−1217.07	+	395.449i	−0.607042	+	0.197240i
$160$		0			0
$161$	2197.44	+	704.388i	1.07567	+	0.344805i
$162$		0			0
$163$	284.295	−	874.970i	0.136612	−	0.420448i	−0.859225	−	0.511597i	$-0.829054\pi$
$163$	284.295	−	874.970i	0.136612	−	0.420448i	0.995837	+	0.0911494i	$0.0290541\pi$
$164$		0			0
$165$	−250.626	+	233.067i	−0.118250	+	0.109965i
$166$		0			0
$167$	461.592	−	1420.64i	0.213887	−	0.658276i	−0.785344	−	0.619060i	$-0.787514\pi$
$167$	461.592	−	1420.64i	0.213887	−	0.658276i	0.999231	−	0.0392162i	$-0.0124861\pi$
$168$		0			0
$169$	−4093.09	−	2973.81i	−1.86304	−	1.35358i
$170$		0			0
$171$	43.3765	+	133.499i	0.0193982	+	0.0597014i
$172$		0			0
$173$	−103.246	+	75.0123i	−0.0453735	+	0.0329658i	−0.610241	−	0.792216i	$-0.708927\pi$
$173$	−103.246	+	75.0123i	−0.0453735	+	0.0329658i	0.564867	+	0.825182i	$0.308927\pi$
$174$		0			0
$175$	−2116.13	+	696.843i	−0.914082	+	0.301008i
$176$		0			0
$177$	2388.04			1.01410
$178$		0			0
$179$	2653.80	−	1928.10i	1.10813	−	0.805100i	0.125758	−	0.992061i	$-0.459864\pi$
$179$	2653.80	−	1928.10i	1.10813	−	0.805100i	0.982367	+	0.186960i	$0.0598636\pi$
$180$		0			0
$181$	−2509.53	+	815.394i	−1.03056	+	0.334850i	−0.775012	−	0.631946i	$-0.782256\pi$
$181$	−2509.53	+	815.394i	−1.03056	+	0.334850i	−0.255549	+	0.966796i	$0.582256\pi$
$182$		0			0
$183$	−478.062	+	657.996i	−0.193111	+	0.265795i
$184$		0			0
$185$	534.026	+	173.516i	0.212229	+	0.0689574i
$186$		0			0
$187$	2453.59	−	297.827i	0.959489	−	0.116466i
$188$		0			0
$189$	2827.05	−	11.1888i	1.08803	−	0.00430615i
$190$		0			0
$191$	−1185.43	−	861.265i	−0.449082	−	0.326277i	0.340151	−	0.940371i	$-0.389522\pi$
$191$	−1185.43	−	861.265i	−0.449082	−	0.326277i	−0.789233	+	0.614094i	$0.789522\pi$
$192$		0			0
$193$	−1425.60	+	463.206i	−0.531694	+	0.172758i	−0.562546	−	0.826766i	$-0.690178\pi$
$193$	−1425.60	+	463.206i	−0.531694	+	0.172758i	0.0308517	+	0.999524i	$0.490178\pi$
$194$		0			0
$195$	−646.500	+	469.710i	−0.237420	+	0.172496i
$196$		0			0
$197$			1517.28i			0.548738i	0.961624	+	0.274369i	$0.0884690\pi$
$197$			1517.28i			0.548738i	−0.961624	+	0.274369i	$0.911531\pi$
$198$		0			0
$199$			1180.14i			0.420390i	0.977660	+	0.210195i	$0.0674099\pi$
$199$			1180.14i			0.420390i	−0.977660	+	0.210195i	$0.932590\pi$
$200$		0			0
$201$	−584.531	−	804.538i	−0.205123	−	0.282327i
$202$		0			0
$203$	75.0136	−	54.9555i	0.0259356	−	0.0190006i
$204$		0			0
$205$	−332.490	+	457.633i	−0.113279	+	0.155915i
$206$		0			0
$207$	319.256	−	982.570i	0.107197	−	0.329919i
$208$		0			0
$209$	260.239	+	560.102i	0.0861298	+	0.185374i
$210$		0			0
$211$	−3222.97	−	1047.21i	−1.05156	−	0.341671i	−0.268277	−	0.963342i	$-0.586454\pi$
$211$	−3222.97	−	1047.21i	−1.05156	−	0.341671i	−0.783279	+	0.621670i	$0.786454\pi$
$212$		0			0
$213$	2721.34	−	3745.61i	0.875414	−	1.20490i
$214$		0			0
$215$	−324.021	−	997.234i	−0.102782	−	0.316329i
$216$		0			0
$217$	2064.02	+	1487.16i	0.645691	+	0.465229i
$218$		0			0
$219$			16.7962i			0.00518258i
$220$		0			0
$221$	5770.97			1.75655
$222$		0			0
$223$	1921.34	+	2644.50i	0.576962	+	0.794120i	0.993358	−	0.115063i	$-0.0367070\pi$
$223$	1921.34	+	2644.50i	0.576962	+	0.794120i	−0.416396	+	0.909183i	$0.636707\pi$
$224$		0			0
$225$	308.235	+	948.650i	0.0913289	+	0.281081i
$226$		0			0
$227$	−4366.05	−	3172.12i	−1.27658	−	0.927493i	−0.277140	−	0.960829i	$-0.589387\pi$
$227$	−4366.05	−	3172.12i	−1.27658	−	0.927493i	−0.999444	+	0.0333365i	$0.989387\pi$
$228$		0			0
$229$	6294.14	+	2045.09i	1.81628	+	0.590145i	0.999921	+	0.0126016i	$0.00401132\pi$
$229$	6294.14	+	2045.09i	1.81628	+	0.590145i	0.816360	+	0.577544i	$0.195989\pi$
$230$		0			0
$231$	2899.77	−	363.637i	0.825935	−	0.103574i
$232$		0			0
$233$	−5031.98	−	1634.99i	−1.41483	−	0.459707i	−0.500877	−	0.865519i	$-0.666989\pi$
$233$	−5031.98	−	1634.99i	−1.41483	−	0.459707i	−0.913957	+	0.405811i	$0.866989\pi$
$234$		0			0
$235$	28.4187	+	20.6474i	0.00788863	+	0.00573143i
$236$		0			0
$237$	1141.25	+	3512.41i	0.312794	+	0.962682i
$238$		0			0
$239$	−3269.97	−	4500.72i	−0.885006	−	1.21811i	−0.975009	−	0.222165i	$-0.928688\pi$
$239$	−3269.97	−	4500.72i	−0.885006	−	1.21811i	0.0900026	−	0.995942i	$-0.471312\pi$
$240$		0			0
$241$	3234.87			0.864632			0.432316	−	0.901722i	$-0.357697\pi$
$241$	3234.87			0.864632			0.432316	+	0.901722i	$0.357697\pi$
$242$		0			0
$243$		−	2234.06i		−	0.589775i
$244$		0			0
$245$	−709.314	−	224.279i	−0.184965	−	0.0584842i
$246$		0			0
$247$	445.620	+	1371.48i	0.114794	+	0.353300i
$248$		0			0
$249$	−644.688	+	887.336i	−0.164078	+	0.225834i
$250$		0			0
$251$	3675.20	+	1194.15i	0.924211	+	0.300294i	0.732193	−	0.681097i	$-0.238497\pi$
$251$	3675.20	+	1194.15i	0.924211	+	0.300294i	0.192018	+	0.981391i	$0.438497\pi$
$252$		0			0
$253$	873.511	−	4460.95i	0.217064	−	1.10853i
$254$		0			0
$255$	196.392	−	604.433i	0.0482296	−	0.148436i
$256$		0			0
$257$	−2054.76	+	2828.13i	−0.498725	+	0.686435i	−0.981967	−	0.189051i	$-0.939459\pi$
$257$	−2054.76	+	2828.13i	−0.498725	+	0.686435i	0.483243	+	0.875486i	$0.339459\pi$
$258$		0			0
$259$	−2833.62	−	3867.86i	−0.679817	−	0.927942i
$260$		0			0
$261$	−24.4713	−	33.6818i	−0.00580358	−	0.00798794i
$262$		0			0
$263$			6583.01i			1.54344i	0.635961	+	0.771722i	$0.280604\pi$
$263$			6583.01i			1.54344i	−0.635961	+	0.771722i	$0.719396\pi$
$264$		0			0
$265$		−	641.694i		−	0.148751i
$266$		0			0
$267$	−773.607	+	562.058i	−0.177318	+	0.128829i
$268$		0			0
$269$	8046.67	−	2614.52i	1.82384	−	0.592603i	0.824191	−	0.566313i	$-0.191630\pi$
$269$	8046.67	−	2614.52i	1.82384	−	0.592603i	0.999654	−	0.0262906i	$-0.00836951\pi$
$270$		0			0
$271$	4160.64	+	3022.88i	0.932624	+	0.677591i	0.946634	−	0.322311i	$-0.104460\pi$
$271$	4160.64	+	3022.88i	0.932624	+	0.677591i	−0.0140099	+	0.999902i	$0.504460\pi$
$272$		0			0
$273$	6823.68	−	27.0064i	1.51278	−	0.00598719i
$274$		0			0
$275$	1849.27	+	3980.11i	0.405510	+	0.872762i
$276$		0			0
$277$	8445.79	+	2744.20i	1.83198	+	0.595246i	0.999128	+	0.0417477i	$0.0132926\pi$
$277$	8445.79	+	2744.20i	1.83198	+	0.595246i	0.832850	+	0.553498i	$0.186707\pi$
$278$		0			0
$279$	669.474	−	921.452i	0.143657	−	0.197727i
$280$		0			0
$281$	−4940.84	+	1605.38i	−1.04892	+	0.340814i	−0.782243	−	0.622973i	$-0.785925\pi$
$281$	−4940.84	+	1605.38i	−1.04892	+	0.340814i	−0.266674	+	0.963787i	$0.585925\pi$
$282$		0			0
$283$	−4603.73	+	3344.80i	−0.967008	+	0.702572i	−0.954768	−	0.297353i	$-0.903896\pi$
$283$	−4603.73	+	3344.80i	−0.967008	+	0.702572i	−0.0122400	+	0.999925i	$0.503896\pi$
$284$		0			0
$285$	158.809			0.0330072
$286$		0			0
$287$	4587.91	−	1510.80i	0.943608	−	0.310731i
$288$		0			0
$289$	261.599	−	190.063i	0.0532463	−	0.0386857i
$290$		0			0
$291$	537.536	+	1654.36i	0.108285	+	0.333267i
$292$		0			0
$293$	−3192.82	−	2319.72i	−0.636610	−	0.462524i	0.222074	−	0.975030i	$-0.428717\pi$
$293$	−3192.82	−	2319.72i	−0.636610	−	0.462524i	−0.858684	+	0.512506i	$0.828717\pi$
$294$		0			0
$295$	−370.036	+	1138.85i	−0.0730316	+	0.224768i
$296$		0			0
$297$	−671.063	−	5528.44i	−0.131108	−	1.08011i
$298$		0			0
$299$	3279.82	−	10094.2i	0.634370	−	1.95239i
$300$		0			0
$301$	−2733.11	+	8526.33i	−0.523369	+	1.63272i
$302$		0			0
$303$	−2295.86	+	745.970i	−0.435292	+	0.141435i
$304$		0			0
$305$	−239.720	−	329.946i	−0.0450044	−	0.0619432i
$306$		0			0
$307$	−3020.41			−0.561511			−0.280755	−	0.959779i	$-0.590585\pi$
$307$	−3020.41			−0.561511			−0.280755	+	0.959779i	$0.590585\pi$
$308$		0			0
$309$	−8675.66			−1.59722
$310$		0			0
$311$	3859.46	+	5312.09i	0.703698	+	0.968557i	0.999910	+	0.0134347i	$0.00427652\pi$
$311$	3859.46	+	5312.09i	0.703698	+	0.968557i	−0.296212	+	0.955122i	$0.595723\pi$
$312$		0			0
$313$	56.2863	−	18.2885i	0.0101645	−	0.00330265i	−0.303930	−	0.952694i	$-0.598299\pi$
$313$	56.2863	−	18.2885i	0.0101645	−	0.00330265i	0.314095	+	0.949392i	$0.398299\pi$
$314$		0			0
$315$	−101.669	+	317.171i	−0.0181854	+	0.0567319i
$316$		0			0
$317$	−1824.02	+	5613.75i	−0.323177	+	0.994636i	0.649080	+	0.760720i	$0.275154\pi$
$317$	−1824.02	+	5613.75i	−0.323177	+	0.994636i	−0.972257	+	0.233916i	$0.924846\pi$
$318$		0			0
$319$	−124.744	−	134.142i	−0.0218944	−	0.0235439i
$320$		0			0
$321$	2388.95	−	7352.44i	0.415384	−	1.27842i
$322$		0			0
$323$	−927.835	−	674.112i	−0.159833	−	0.116126i
$324$		0			0
$325$	3166.59	+	9745.77i	0.540464	+	1.66338i
$326$		0			0
$327$	3038.52	−	2207.62i	0.513855	−	0.373338i
$328$		0			0
$329$	−93.8197	−	284.906i	−0.0157217	−	0.0477427i
$330$		0			0
$331$	−5222.07			−0.867164			−0.433582	−	0.901114i	$-0.642750\pi$
$331$	−5222.07			−0.867164			−0.433582	+	0.901114i	$0.642750\pi$
$332$		0			0
$333$	−1736.71	+	1261.79i	−0.285798	+	0.207645i
$334$		0			0
$335$	474.259	−	154.096i	0.0773478	−	0.0251318i
$336$		0			0
$337$	−2954.43	+	4066.42i	−0.477561	+	0.657306i	−0.978034	−	0.208446i	$-0.933159\pi$
$337$	−2954.43	+	4066.42i	−0.477561	+	0.657306i	0.500473	+	0.865752i	$0.333159\pi$
$338$		0			0
$339$	1802.77	+	585.756i	0.288829	+	0.0938462i
$340$		0			0
$341$	2435.60	−	4379.67i	0.386789	−	0.695521i
$342$		0			0
$343$	3794.63	+	5094.54i	0.597349	+	0.801981i
$344$		0			0
$345$	−945.623	−	687.036i	−0.147567	−	0.107214i
$346$		0			0
$347$	6031.02	−	1959.60i	0.933032	−	0.303160i	0.197230	−	0.980357i	$-0.436805\pi$
$347$	6031.02	−	1959.60i	0.933032	−	0.303160i	0.735802	+	0.677197i	$0.236805\pi$
$348$		0			0
$349$	−8006.65	+	5817.17i	−1.22804	+	0.892224i	−0.996742	−	0.0806592i	$-0.974297\pi$
$349$	−8006.65	+	5817.17i	−1.22804	+	0.892224i	−0.231299	+	0.972883i	$0.574297\pi$
$350$		0			0
$351$		−	13003.2i		−	1.97737i
$352$		0			0
$353$		−	6820.71i		−	1.02841i	−0.857667	−	0.514206i	$-0.828087\pi$
$353$		−	6820.71i		−	1.02841i	0.857667	−	0.514206i	$-0.171913\pi$
$354$		0			0
$355$	1364.59	+	1878.20i	0.204014	+	0.280802i
$356$		0			0
$357$	−4377.80	+	3207.21i	−0.649014	+	0.475472i
$358$		0			0
$359$	6402.67	−	8812.51i	0.941281	−	1.29556i	−0.0140125	−	0.999902i	$-0.504460\pi$
$359$	6402.67	−	8812.51i	0.941281	−	1.29556i	0.955293	−	0.295660i	$-0.0955395\pi$
$360$		0			0
$361$	−2030.99	+	6250.74i	−0.296106	+	0.911320i
$362$		0			0
$363$	−1377.31	−	5589.79i	−0.199147	−	0.808231i
$364$		0			0
$365$	−8.01012	−	2.60264i	−0.00114868	−	0.000373229i
$366$		0			0
$367$	−2182.38	+	3003.78i	−0.310406	+	0.427238i	−0.935508	−	0.353306i	$-0.885058\pi$
$367$	−2182.38	+	3003.78i	−0.310406	+	0.427238i	0.625102	+	0.780543i	$0.285058\pi$
$368$		0			0
$369$	−668.274	−	2056.74i	−0.0942790	−	0.290161i
$370$		0			0
$371$	−3203.19	+	4445.70i	−0.448251	+	0.622128i
$372$		0			0
$373$		−	3889.73i		−	0.539954i	−0.962867	−	0.269977i	$-0.912984\pi$
$373$		−	3889.73i		−	0.539954i	0.962867	−	0.269977i	$-0.0870160\pi$
$374$		0			0
$375$	2301.14			0.316881
$376$		0			0
$377$	−251.401	−	346.024i	−0.0343443	−	0.0472709i
$378$		0			0
$379$	−1272.60	−	3916.67i	−0.172478	−	0.530833i	0.827031	−	0.562156i	$-0.190028\pi$
$379$	−1272.60	−	3916.67i	−0.172478	−	0.530833i	−0.999509	+	0.0313228i	$0.990028\pi$
$380$		0			0
$381$	−5505.46	−	3999.95i	−0.740297	−	0.537857i
$382$		0			0
$383$	6994.20	+	2272.55i	0.933125	+	0.303191i	0.735840	−	0.677155i	$-0.236787\pi$
$383$	6994.20	+	2272.55i	0.933125	+	0.303191i	0.197285	+	0.980346i	$0.436787\pi$
$384$		0			0
$385$	−275.913	+	1439.25i	−0.0365242	+	0.190521i
$386$		0			0
$387$	3812.50	+	1238.75i	0.500775	+	0.162712i
$388$		0			0
$389$	5962.16	+	4331.77i	0.777105	+	0.564600i	0.904109	−	0.427303i	$-0.140536\pi$
$389$	5962.16	+	4331.77i	0.777105	+	0.564600i	−0.127004	+	0.991902i	$0.540536\pi$
$390$		0			0
$391$	2608.44	+	8027.94i	0.337377	+	1.03834i
$392$		0			0
$393$	−5207.32	−	7167.26i	−0.668383	−	0.919950i
$394$		0			0
$395$	−1851.91			−0.235898
$396$		0			0
$397$		−	3795.43i		−	0.479817i	−0.970796	−	0.239908i	$-0.922883\pi$
$397$		−	3795.43i		−	0.479817i	0.970796	−	0.239908i	$-0.0771174\pi$
$398$		0			0
$399$	−1100.24	−	792.738i	−0.138047	−	0.0994650i
$400$		0			0
$401$	−2265.97	−	6973.95i	−0.282188	−	0.868485i	−0.987227	−	0.159317i	$-0.949071\pi$
$401$	−2265.97	−	6973.95i	−0.282188	−	0.868485i	0.705039	−	0.709168i	$-0.250929\pi$
$402$		0			0
$403$	6877.71	−	9466.35i	0.850132	−	1.17011i
$404$		0			0
$405$	−900.109	−	292.463i	−0.110436	−	0.0358830i
$406$		0			0
$407$	−6916.63	+	6432.04i	−0.842370	+	0.783352i
$408$		0			0
$409$	−1858.03	+	5718.43i	−0.224630	+	0.691340i	0.773699	+	0.633553i	$0.218404\pi$
$409$	−1858.03	+	5718.43i	−0.224630	+	0.691340i	−0.998329	+	0.0577864i	$0.981596\pi$
$410$		0			0
$411$	−5466.96	+	7524.63i	−0.656120	+	0.903072i
$412$		0			0
$413$	8248.52	−	6042.92i	0.982768	−	0.719983i
$414$		0			0
$415$	−323.273	−	444.947i	−0.0382382	−	0.0526304i
$416$		0			0
$417$		−	8093.52i		−	0.950459i
$418$		0			0
$419$			3195.23i			0.372547i	0.982498	+	0.186274i	$0.0596411\pi$
$419$			3195.23i			0.372547i	−0.982498	+	0.186274i	$0.940359\pi$
$420$		0			0
$421$	−7268.80	+	5281.09i	−0.841471	+	0.611365i	−0.922781	−	0.385324i	$-0.874090\pi$
$421$	−7268.80	+	5281.09i	−0.841471	+	0.611365i	0.0813099	+	0.996689i	$0.474090\pi$
$422$		0			0
$423$	−127.722	+	41.4993i	−0.0146810	+	0.00477013i
$424$		0			0
$425$	−6593.23	−	4790.26i	−0.752514	−	0.546734i
$426$		0			0
$427$	13.7829	+	3482.52i	0.00156207	+	0.394686i
$428$		0			0
$429$	−1619.75	−	13344.1i	−0.182290	−	1.50176i
$430$		0			0
$431$	−7729.78	−	2511.56i	−0.863876	−	0.280690i	−0.156629	−	0.987657i	$-0.550063\pi$
$431$	−7729.78	−	2511.56i	−0.863876	−	0.280690i	−0.707246	+	0.706967i	$0.750063\pi$
$432$		0			0
$433$	−4084.30	+	5621.55i	−0.453300	+	0.623914i	−0.973102	−	0.230373i	$-0.926005\pi$
$433$	−4084.30	+	5621.55i	−0.453300	+	0.623914i	0.519803	+	0.854286i	$0.326005\pi$
$434$		0			0
$435$	−44.7969	+	14.5554i	−0.00493758	+	0.00160432i
$436$		0			0
$437$	−1706.43	+	1239.80i	−0.186796	+	0.135715i
$438$		0			0
$439$	−7039.84			−0.765360			−0.382680	−	0.923881i	$-0.624999\pi$
$439$	−7039.84			−0.765360			−0.382680	+	0.923881i	$0.624999\pi$
$440$		0			0
$441$	2287.61	−	1689.87i	0.247015	−	0.182472i
$442$		0			0
$443$	−2277.04	+	1654.36i	−0.244210	+	0.177429i	−0.703157	−	0.711035i	$-0.748227\pi$
$443$	−2277.04	+	1654.36i	−0.244210	+	0.177429i	0.458947	+	0.888464i	$0.348227\pi$
$444$		0			0
$445$	−148.172	−	456.026i	−0.0157843	−	0.0485791i
$446$		0			0
$447$	764.103	+	555.153i	0.0808520	+	0.0587424i
$448$		0			0
$449$	−337.312	+	1038.14i	−0.0354538	+	0.109116i	−0.967217	−	0.253950i	$-0.918270\pi$
$449$	−337.312	+	1038.14i	−0.0354538	+	0.109116i	0.931763	+	0.363066i	$0.118270\pi$
$450$		0			0
$451$	−4009.34	−	8629.13i	−0.418609	−	0.900954i
$452$		0			0
$453$	199.335	−	613.489i	0.0206745	−	0.0636297i
$454$		0			0
$455$	−1044.48	+	3258.39i	−0.107617	+	0.335727i
$456$		0			0
$457$	−3357.00	+	1090.76i	−0.343619	+	0.111649i	−0.475742	−	0.879585i	$-0.657821\pi$
$457$	−3357.00	+	1090.76i	−0.343619	+	0.111649i	0.132123	+	0.991233i	$0.457821\pi$
$458$		0			0
$459$	6078.52	+	8366.37i	0.618129	+	0.850781i
$460$		0			0
$461$	−14201.4			−1.43476			−0.717380	−	0.696682i	$-0.754659\pi$
$461$	−14201.4			−1.43476			−0.717380	+	0.696682i	$0.754659\pi$
$462$		0			0
$463$	−5449.54			−0.547001			−0.273501	−	0.961872i	$-0.588182\pi$
$463$	−5449.54			−0.547001			−0.273501	+	0.961872i	$0.588182\pi$
$464$		0			0
$465$	−757.421	−	1042.50i	−0.0755366	−	0.103967i
$466$		0			0
$467$	−1002.43	+	325.708i	−0.0993293	+	0.0322740i	−0.358260	−	0.933622i	$-0.616630\pi$
$467$	−1002.43	+	325.708i	−0.0993293	+	0.0322740i	0.258931	+	0.965896i	$0.416630\pi$
$468$		0			0
$469$	−4054.91	−	1299.80i	−0.399229	−	0.127973i
$470$		0			0
$471$	−3323.22	+	10227.8i	−0.325108	+	1.00058i
$472$		0			0
$473$	17309.0	+	3389.33i	1.68260	+	0.329475i
$474$		0			0
$475$	629.299	−	1936.78i	0.0607878	−	0.187086i
$476$		0			0
$477$	1984.72	+	1441.98i	0.190511	+	0.138415i
$478$		0			0
$479$	3528.95	+	10861.0i	0.336622	+	1.03602i	0.965917	+	0.258850i	$0.0833437\pi$
$479$	3528.95	+	10861.0i	0.336622	+	1.03602i	−0.629295	+	0.777166i	$0.716656\pi$
$480$		0			0
$481$	−17841.7	+	12962.8i	−1.69129	+	1.22880i
$482$		0			0
$483$	3121.82	+	9480.16i	0.294095	+	0.893089i
$484$		0			0
$485$	−872.259			−0.0816644
$486$		0			0
$487$	−12518.3	+	9095.08i	−1.16480	+	0.846278i	−0.990377	−	0.138393i	$-0.955806\pi$
$487$	−12518.3	+	9095.08i	−1.16480	+	0.846278i	−0.174424	+	0.984671i	$0.555806\pi$
$488$		0			0
$489$	3784.51	−	1229.66i	0.349982	−	0.113716i
$490$		0			0
$491$	4293.55	−	5909.56i	0.394634	−	0.543167i	−0.564753	−	0.825260i	$-0.691029\pi$
$491$	4293.55	−	5909.56i	0.394634	−	0.543167i	0.959387	+	0.282093i	$0.0910287\pi$
$492$		0			0
$493$	323.508	+	105.114i	0.0295539	+	0.00960265i
$494$		0			0
$495$	643.878	+	126.080i	0.0584650	+	0.0114482i
$496$		0			0
$497$	−78.4586	−	19824.0i	−0.00708118	−	1.78919i
$498$		0			0
$499$	−5745.20	−	4174.13i	−0.515412	−	0.374468i	0.299461	−	0.954109i	$-0.403193\pi$
$499$	−5745.20	−	4174.13i	−0.515412	−	0.374468i	−0.814873	+	0.579640i	$0.803193\pi$
$500$		0			0
$501$	6144.67	−	1996.52i	0.547951	−	0.178040i
$502$		0			0
$503$	−6281.72	+	4563.93i	−0.556835	+	0.404564i	−0.830299	−	0.557318i	$-0.811830\pi$
$503$	−6281.72	+	4563.93i	−0.556835	+	0.404564i	0.273464	+	0.961882i	$0.411830\pi$
$504$		0			0
$505$		−	1210.48i		−	0.106665i
$506$		0			0
$507$		−	21883.2i		−	1.91689i
$508$		0			0
$509$	−4975.79	−	6848.59i	−0.433297	−	0.596382i	0.535409	−	0.844593i	$-0.320157\pi$
$509$	−4975.79	−	6848.59i	−0.433297	−	0.596382i	−0.968706	+	0.248211i	$0.920157\pi$
$510$		0			0
$511$	42.5028	+	58.0159i	0.00367948	+	0.00502245i
$512$		0			0
$513$	−1518.91	+	2090.60i	−0.130724	+	0.179926i
$514$		0			0
$515$	1344.33	−	4137.41i	0.115026	−	0.354012i
$516$		0			0
$517$	−535.863	+	248.977i	−0.0455845	+	0.0211799i
$518$		0			0
$519$	−524.972	−	170.574i	−0.0444002	−	0.0144265i
$520$		0			0
$521$	−9444.88	+	12999.8i	−0.794218	+	1.09315i	0.199352	+	0.979928i	$0.436116\pi$
$521$	−9444.88	+	12999.8i	−0.794218	+	1.09315i	−0.993570	+	0.113220i	$0.963884\pi$
$522$		0			0
$523$	4330.75	+	13328.7i	0.362085	+	1.11438i	0.951786	+	0.306762i	$0.0992457\pi$
$523$	4330.75	+	13328.7i	0.362085	+	1.11438i	−0.589701	+	0.807622i	$0.700754\pi$
$524$		0			0
$525$	−7818.35	−	5633.23i	−0.649945	−	0.468294i
$526$		0			0
$527$			9305.84i			0.769201i
$528$		0			0
$529$	3357.46			0.275948
$530$		0			0
$531$	−2690.87	−	3703.67i	−0.219913	−	0.302684i
$532$		0			0
$533$	−6865.38	−	21129.5i	−0.557923	−	1.71711i
$534$		0			0
$535$	3136.20	+	2278.58i	0.253438	+	0.184134i
$536$		0			0
$537$	13493.8	+	4384.39i	1.08436	+	0.352329i
$538$		0			0
$539$	9095.92	−	8593.90i	0.726881	−	0.686763i
$540$		0			0
$541$	5510.19	+	1790.37i	0.437896	+	0.142281i	0.519664	−	0.854370i	$-0.326057\pi$
$541$	5510.19	+	1790.37i	0.437896	+	0.142281i	−0.0817689	+	0.996651i	$0.526057\pi$
$542$		0			0
$543$	−9233.34	−	6708.42i	−0.729725	−	0.530176i
$544$		0			0
$545$	581.979	+	1791.15i	0.0457417	+	0.140779i
$546$		0			0
$547$	−3365.57	−	4632.31i	−0.263074	−	0.362090i	0.656963	−	0.753923i	$-0.271841\pi$
$547$	−3365.57	−	4632.31i	−0.263074	−	0.362090i	−0.920036	+	0.391833i	$0.871841\pi$
$548$		0			0
$549$	1559.19			0.121210
$550$		0			0
$551$			84.9988i			0.00657182i
$552$		0			0
$553$	12830.1	+	9244.29i	0.986606	+	0.710863i
$554$		0			0
$555$	750.507	+	2309.82i	0.0574004	+	0.176660i
$556$		0			0
$557$	−9239.10	+	12716.5i	−0.702825	+	0.967355i	0.297097	+	0.954847i	$0.403982\pi$
$557$	−9239.10	+	12716.5i	−0.702825	+	0.967355i	−0.999922	+	0.0125079i	$0.996018\pi$
$558$		0			0
$559$	39166.9	+	12726.1i	2.96348	+	0.962892i
$560$		0			0
$561$	7280.05	+	7828.53i	0.547886	+	0.589164i
$562$		0			0
$563$	5391.61	−	16593.7i	0.403604	−	1.24217i	−0.518450	−	0.855108i	$-0.673491\pi$
$563$	5391.61	−	16593.7i	0.403604	−	1.24217i	0.922055	−	0.387059i	$-0.126509\pi$
$564$		0			0
$565$	−558.693	+	768.974i	−0.0416007	+	0.0572584i
$566$		0			0
$567$	4776.11	+	6519.33i	0.353753	+	0.482868i
$568$		0			0
$569$	9781.85	+	13463.6i	0.720697	+	0.991954i	0.999500	+	0.0316059i	$0.0100622\pi$
$569$	9781.85	+	13463.6i	0.720697	+	0.991954i	−0.278804	+	0.960348i	$0.589938\pi$
$570$		0			0
$571$		−	5862.19i		−	0.429641i	−0.976654	−	0.214821i	$-0.931083\pi$
$571$		−	5862.19i		−	0.429641i	0.976654	−	0.214821i	$-0.0689167\pi$
$572$		0			0
$573$		−	6337.73i		−	0.462064i
$574$		0			0
$575$	−12126.0	+	8810.04i	−0.879458	+	0.638964i
$576$		0			0
$577$	−11118.6	+	3612.65i	−0.802206	+	0.260652i	−0.681293	−	0.732011i	$-0.738582\pi$
$577$	−11118.6	+	3612.65i	−0.802206	+	0.260652i	−0.120913	+	0.992663i	$0.538582\pi$
$578$		0			0
$579$	−5245.24	−	3810.89i	−0.376485	−	0.273532i
$580$		0			0
$581$	18.5869	+	4696.33i	0.00132722	+	0.335347i
$582$		0			0
$583$	9433.38	+	5246.04i	0.670139	+	0.372674i
$584$		0			0
$585$	1456.97	+	473.398i	0.102971	+	0.0334574i
$586$		0			0
$587$	8270.16	−	11382.9i	0.581510	−	0.800379i	−0.412350	−	0.911025i	$-0.635292\pi$
$587$	8270.16	−	11382.9i	0.581510	−	0.800379i	0.993860	+	0.110646i	$0.0352920\pi$
$588$		0			0
$589$	−2211.55	+	718.575i	−0.154712	+	0.0502689i
$590$		0			0
$591$	−5309.31	+	3857.44i	−0.369536	+	0.268484i
$592$		0			0
$593$	−9343.00			−0.647000			−0.323500	−	0.946228i	$-0.604860\pi$
$593$	−9343.00			−0.647000			−0.323500	+	0.946228i	$0.604860\pi$
$594$		0			0
$595$	−851.158	−	2584.74i	−0.0586455	−	0.178091i
$596$		0			0
$597$	−4129.58	+	3000.31i	−0.283103	+	0.205686i
$598$		0			0
$599$	−943.793	−	2904.70i	−0.0643779	−	0.198135i	0.913694	−	0.406403i	$-0.133217\pi$
$599$	−943.793	−	2904.70i	−0.0643779	−	0.198135i	−0.978072	+	0.208269i	$0.933217\pi$
$600$		0			0
$601$	−14334.8	−	10414.9i	−0.972927	−	0.706873i	−0.0168104	−	0.999859i	$-0.505351\pi$
$601$	−14334.8	−	10414.9i	−0.972927	−	0.706873i	−0.956117	+	0.292986i	$0.905351\pi$
$602$		0			0
$603$	−589.120	+	1813.13i	−0.0397858	+	0.122448i
$604$		0			0
$605$	2879.19	+	209.320i	0.193480	+	0.0140662i
$606$		0			0
$607$	1287.44	−	3962.35i	0.0860886	−	0.264953i	−0.898740	−	0.438481i	$-0.855517\pi$
$607$	1287.44	−	3962.35i	0.0860886	−	0.264953i	0.984829	+	0.173528i	$0.0555166\pi$
$608$		0			0
$609$	383.013	+	122.775i	0.0254852	+	0.00816927i
$610$		0			0
$611$	−1312.12	+	426.335i	−0.0868787	+	0.0282286i
$612$		0			0
$613$	−3292.96	−	4532.38i	−0.216968	−	0.298631i	0.686634	−	0.727003i	$-0.259087\pi$
$613$	−3292.96	−	4532.38i	−0.216968	−	0.298631i	−0.903603	+	0.428372i	$0.859087\pi$
$614$		0			0
$615$	−2446.67			−0.160422
$616$		0			0
$617$	29244.2			1.90814			0.954072	−	0.299577i	$-0.0968454\pi$
$617$	29244.2			1.90814			0.954072	+	0.299577i	$0.0968454\pi$
$618$		0			0
$619$	9753.62	+	13424.7i	0.633330	+	0.871704i	0.998238	−	0.0593398i	$-0.0188996\pi$
$619$	9753.62	+	13424.7i	0.633330	+	0.871704i	−0.364908	+	0.931044i	$0.618900\pi$
$620$		0			0
$621$	18088.6	−	5877.34i	1.16887	−	0.379790i
$622$		0			0
$623$	−1249.83	+	3899.01i	−0.0803745	+	0.250739i
$624$		0			0
$625$	4290.12	−	13203.6i	0.274567	−	0.845032i
$626$		0			0
$627$	−1298.31	+	2334.61i	−0.0826948	+	0.148701i
$628$		0			0
$629$	5419.91	−	16680.8i	0.343570	−	1.05740i
$630$		0			0
$631$	1430.84	+	1039.57i	0.0902707	+	0.0655855i	0.632005	−	0.774964i	$-0.282232\pi$
$631$	1430.84	+	1039.57i	0.0902707	+	0.0655855i	−0.541734	+	0.840550i	$0.682232\pi$
$632$		0			0
$633$	−4529.48	−	13940.3i	−0.284409	−	0.875320i
$634$		0			0
$635$	2760.66	−	2005.74i	0.172525	−	0.125347i
$636$		0			0
$637$	23501.3	−	17360.6i	1.46178	−	1.07983i
$638$		0			0
$639$	−8875.59			−0.549472
$640$		0			0
$641$	4421.79	−	3212.62i	0.272465	−	0.197958i	−0.443159	−	0.896443i	$-0.646142\pi$
$641$	4421.79	−	3212.62i	0.272465	−	0.197958i	0.715624	+	0.698485i	$0.246142\pi$
$642$		0			0
$643$	28711.9	−	9329.05i	1.76094	−	0.572165i	0.763644	−	0.645637i	$-0.223408\pi$
$643$	28711.9	−	9329.05i	1.76094	−	0.572165i	0.997297	+	0.0734725i	$0.0234081\pi$
$644$		0			0
$645$	2665.79	−	3669.14i	0.162737	−	0.223988i
$646$		0			0
$647$	25427.0	+	8261.74i	1.54504	+	0.502013i	0.952761	−	0.303722i	$-0.0982294\pi$
$647$	25427.0	+	8261.74i	1.54504	+	0.502013i	0.592276	+	0.805735i	$0.298229\pi$
$648$		0			0
$649$	−13716.8	−	14750.3i	−0.829635	−	0.892140i
$650$		0			0
$651$	43.5486	+	11003.4i	0.00262182	+	0.662452i
$652$		0			0
$653$	−12216.4	−	8875.70i	−0.732103	−	0.531904i	0.158125	−	0.987419i	$-0.449455\pi$
$653$	−12216.4	−	8875.70i	−0.732103	−	0.531904i	−0.890228	+	0.455515i	$0.849455\pi$
$654$		0			0
$655$	4224.96	−	1372.77i	0.252035	−	0.0818910i
$656$		0			0
$657$	26.0497	−	18.9262i	0.00154687	−	0.00112387i
$658$		0			0
$659$		−	1580.96i		−	0.0934527i	−0.998908	−	0.0467264i	$-0.985121\pi$
$659$		−	1580.96i		−	0.0934527i	0.998908	−	0.0467264i	$-0.0148789\pi$
$660$		0			0
$661$			5397.05i			0.317581i	0.987312	+	0.158790i	$0.0507594\pi$
$661$			5397.05i			0.317581i	−0.987312	+	0.158790i	$0.949241\pi$
$662$		0			0
$663$	14671.8	+	20194.0i	0.859435	+	1.18291i
$664$		0			0
$665$	548.543	−	401.866i	0.0319873	−	0.0234341i
$666$		0			0
$667$	367.719	−	506.122i	0.0213465	−	0.0293810i
$668$		0			0
$669$	−4369.02	+	13446.5i	−0.252491	+	0.777086i
$670$		0			0
$671$	6810.24	−	826.653i	0.391813	−	0.0475597i
$672$		0			0
$673$	−6014.75	−	1954.31i	−0.344505	−	0.111936i	0.131654	−	0.991296i	$-0.457971\pi$
$673$	−6014.75	−	1954.31i	−0.344505	−	0.111936i	−0.476159	+	0.879359i	$0.657971\pi$
$674$		0			0
$675$	−10793.4	+	14855.9i	−0.615466	+	0.847116i
$676$		0			0
$677$	3827.34	+	11779.3i	0.217277	+	0.668710i	0.998984	+	0.0450643i	$0.0143493\pi$
$677$	3827.34	+	11779.3i	0.217277	+	0.668710i	−0.781707	+	0.623646i	$0.785651\pi$
$678$		0			0
$679$	6043.07	+	4354.11i	0.341549	+	0.246090i
$680$		0			0
$681$		−	23342.5i		−	1.31349i
$682$		0			0
$683$	−9477.48			−0.530960			−0.265480	−	0.964116i	$-0.585530\pi$
$683$	−9477.48			−0.530960			−0.265480	+	0.964116i	$0.585530\pi$
$684$		0			0
$685$	−2741.36	−	3773.16i	−0.152908	−	0.210460i
$686$		0			0
$687$	8845.62	+	27224.0i	0.491239	+	1.51188i
$688$		0			0
$689$	20389.6	+	14813.9i	1.12740	+	0.819107i
$690$		0			0
$691$	−12997.6	−	4223.16i	−0.715557	−	0.232499i	−0.0714614	−	0.997443i	$-0.522766\pi$
$691$	−12997.6	−	4223.16i	−0.715557	−	0.232499i	−0.644096	+	0.764945i	$0.722766\pi$
$692$		0			0
$693$	−3831.47	−	4087.57i	−0.210022	−	0.224061i
$694$		0			0
$695$	3859.79	+	1254.12i	0.210662	+	0.0684483i
$696$		0			0
$697$	14294.6	+	10385.6i	0.776822	+	0.564394i
$698$		0			0
$699$	−7071.82	−	21764.8i	−0.382662	−	1.17771i
$700$		0			0
$701$	10719.0	+	14753.5i	0.577534	+	0.794908i	0.993422	−	0.114508i	$-0.0365292\pi$
$701$	10719.0	+	14753.5i	0.577534	+	0.794908i	−0.415888	+	0.909416i	$0.636529\pi$
$702$		0			0
$703$	4382.72			0.235131
$704$		0			0
$705$			151.936i			0.00811668i
$706$		0			0
$707$	−6042.45	+	8386.31i	−0.321428	+	0.446110i
$708$		0			0
$709$	1122.74	+	3455.45i	0.0594719	+	0.183036i	0.976379	−	0.216065i	$-0.0693224\pi$
$709$	1122.74	+	3455.45i	0.0594719	+	0.183036i	−0.916907	+	0.399101i	$0.869322\pi$
$710$		0			0
$711$	4161.51	−	5727.82i	0.219506	−	0.302124i
$712$		0			0
$713$	16277.2	+	5288.80i	0.854961	+	0.277794i
$714$		0			0
$715$	6614.76	+	1295.26i	0.345983	+	0.0677480i
$716$		0			0
$717$	7435.72	−	22884.8i	0.387297	−	1.19198i
$718$		0			0
$719$	5800.70	−	7983.97i	0.300875	−	0.414120i	−0.631633	−	0.775267i	$-0.717615\pi$
$719$	5800.70	−	7983.97i	0.300875	−	0.414120i	0.932509	+	0.361148i	$0.117615\pi$
$720$		0			0
$721$	−29966.6	+	21953.7i	−1.54787	+	1.13398i
$722$		0			0
$723$	8224.16	+	11319.6i	0.423042	+	0.582268i
$724$		0			0
$725$			604.005i			0.0309409i
$726$		0			0
$727$			22482.0i			1.14692i	0.819234	+	0.573460i	$0.194399\pi$
$727$			22482.0i			1.14692i	−0.819234	+	0.573460i	$0.805601\pi$
$728$		0			0
$729$	17349.3	−	12605.0i	0.881436	−	0.640401i
$730$		0			0
$731$	−31149.4	+	10121.1i	−1.57607	+	0.512095i
$732$		0			0
$733$	−3981.72	−	2892.89i	−0.200639	−	0.145773i	0.482929	−	0.875659i	$-0.339573\pi$
$733$	−3981.72	−	2892.89i	−0.200639	−	0.145773i	−0.683568	+	0.729887i	$0.739573\pi$
$734$		0			0
$735$	−1018.52	−	3052.25i	−0.0511137	−	0.153176i
$736$		0			0
$737$	−1611.88	+	8231.74i	−0.0805623	+	0.411425i
$738$		0			0
$739$	3427.38	+	1113.62i	0.170607	+	0.0554335i	0.393075	−	0.919507i	$-0.371411\pi$
$739$	3427.38	+	1113.62i	0.170607	+	0.0554335i	−0.222468	+	0.974940i	$0.571411\pi$
$740$		0			0
$741$	−3666.21	+	5046.10i	−0.181756	+	0.250166i
$742$		0			0
$743$	−1844.17	+	599.207i	−0.0910579	+	0.0295865i	−0.354192	−	0.935173i	$-0.615244\pi$
$743$	−1844.17	+	599.207i	−0.0910579	+	0.0295865i	0.263134	+	0.964759i	$0.415244\pi$
$744$		0			0
$745$	−383.153	+	278.377i	−0.0188425	+	0.0136899i
$746$		0			0
$747$	2102.63			0.102987
$748$		0			0
$749$	−10353.6	−	31441.3i	−0.505092	−	1.53383i
$750$		0			0
$751$	1159.09	−	842.129i	0.0563194	−	0.0409184i	−0.559269	−	0.828986i	$-0.688918\pi$
$751$	1159.09	−	842.129i	0.0563194	−	0.0409184i	0.615589	+	0.788068i	$0.288918\pi$
$752$		0			0
$753$	5165.04	+	15896.4i	0.249966	+	0.769317i
$754$		0			0
$755$	261.685	+	190.125i	0.0126142	+	0.00916472i
$756$		0			0
$757$	−5911.62	+	18194.1i	−0.283833	+	0.873548i	0.702913	+	0.711276i	$0.251882\pi$
$757$	−5911.62	+	18194.1i	−0.283833	+	0.873548i	−0.986746	+	0.162272i	$0.948118\pi$
$758$		0			0
$759$	17830.7	−	8284.64i	0.852718	−	0.396197i
$760$		0			0
$761$	−3767.84	+	11596.2i	−0.179480	+	0.552383i	−0.999810	−	0.0195083i	$-0.993790\pi$
$761$	−3767.84	+	11596.2i	−0.179480	+	0.552383i	0.820330	+	0.571891i	$0.193790\pi$
$762$		0			0
$763$	4908.99	−	15314.3i	0.232919	−	0.726625i
$764$		0			0
$765$	−1158.73	+	376.493i	−0.0547632	+	0.0177936i
$766$		0			0
$767$	−27644.1	−	38048.9i	−1.30140	−	1.79122i
$768$		0			0
$769$	−8589.57			−0.402793			−0.201396	−	0.979510i	$-0.564548\pi$
$769$	−8589.57			−0.402793			−0.201396	+	0.979510i	$0.564548\pi$
$770$		0			0
$771$	−15120.2			−0.706279
$772$		0			0
$773$	−16076.8	−	22127.9i	−0.748052	−	1.02960i	−0.998115	−	0.0613752i	$-0.980451\pi$
$773$	−16076.8	−	22127.9i	−0.748052	−	1.02960i	0.250063	−	0.968230i	$-0.419549\pi$
$774$		0			0
$775$	−15715.3	+	5106.22i	−0.728402	+	0.236672i
$776$		0			0
$777$	6330.52	−	19748.9i	0.292286	−	0.911827i
$778$		0			0
$779$	−1364.36	+	4199.07i	−0.0627514	+	0.193129i
$780$		0			0
$781$	−38766.9	+	4705.68i	−1.77617	+	0.215598i
$782$		0			0
$783$	236.844	−	728.930i	0.0108098	−	0.0332692i
$784$		0			0
$785$	−4362.69	−	3169.68i	−0.198358	−	0.144116i
$786$		0			0
$787$	−10526.1	−	32396.1i	−0.476768	−	1.46734i	−0.843558	−	0.537038i	$-0.819543\pi$
$787$	−10526.1	−	32396.1i	−0.476768	−	1.46734i	0.366790	−	0.930304i	$-0.380457\pi$
$788$		0			0
$789$	−23035.5	+	16736.3i	−1.03940	+	0.755168i
$790$		0			0
$791$	7709.20	−	2538.65i	0.346533	−	0.114114i
$792$		0			0
$793$	16018.0			0.717296
$794$		0			0
$795$	2245.44	−	1631.41i	0.100173	−	0.0727800i
$796$		0			0
$797$	−5157.39	+	1675.74i	−0.229215	+	0.0744764i	−0.421372	−	0.906888i	$-0.638451\pi$
$797$	−5157.39	+	1675.74i	−0.229215	+	0.0744764i	0.192158	+	0.981364i	$0.438451\pi$
$798$		0			0
$799$	644.938	−	887.681i	0.0285560	−	0.0393040i
$800$		0			0
$801$	1743.42	+	566.471i	0.0769047	+	0.0249878i
$802$		0			0
$803$	103.746	−	96.4773i	0.00455929	−	0.00423986i
$804$		0			0
$805$	−5004.82	+	19.8078i	−0.219126	+	0.000867247i
$806$		0			0
$807$	29606.3	+	21510.2i	1.29144	+	0.938284i
$808$		0			0
$809$	−31702.9	+	10300.9i	−1.37777	+	0.447664i	−0.901935	−	0.431872i	$-0.857853\pi$
$809$	−31702.9	+	10300.9i	−1.37777	+	0.447664i	−0.475833	+	0.879536i	$0.657853\pi$
$810$		0			0
$811$	−8681.41	+	6307.42i	−0.375889	+	0.273099i	−0.759649	−	0.650334i	$-0.774629\pi$
$811$	−8681.41	+	6307.42i	−0.375889	+	0.273099i	0.383760	+	0.923433i	$0.374629\pi$
$812$		0			0
$813$			22244.3i			0.959584i
$814$		0			0
$815$			1995.37i			0.0857604i
$816$		0			0
$817$	−4810.57	−	6621.18i	−0.205998	−	0.283532i
$818$		0			0
$819$	−7730.89	−	10552.6i	−0.329840	−	0.450228i
$820$		0			0
$821$	10677.6	−	14696.4i	0.453898	−	0.624737i	−0.519331	−	0.854573i	$-0.673819\pi$
$821$	10677.6	−	14696.4i	0.453898	−	0.624737i	0.973229	+	0.229836i	$0.0738189\pi$
$822$		0			0
$823$	5159.92	−	15880.6i	0.218546	−	0.672617i	−0.780336	−	0.625360i	$-0.784952\pi$
$823$	5159.92	−	15880.6i	0.218546	−	0.672617i	0.998883	−	0.0472566i	$-0.0150479\pi$
$824$		0			0
$825$	−9225.86	+	16589.9i	−0.389337	+	0.700102i
$826$		0			0
$827$	39376.3	+	12794.1i	1.65568	+	0.537964i	0.979960	−	0.199193i	$-0.0638320\pi$
$827$	39376.3	+	12794.1i	1.65568	+	0.537964i	0.675722	+	0.737157i	$0.263832\pi$
$828$		0			0
$829$	−21780.6	+	29978.4i	−0.912511	+	1.25596i	0.0537912	+	0.998552i	$0.482869\pi$
$829$	−21780.6	+	29978.4i	−0.912511	+	1.25596i	−0.966302	+	0.257411i	$0.917131\pi$
$830$		0			0
$831$	11869.5	+	36530.5i	0.495485	+	1.52495i
$832$		0			0
$833$	−7005.53	+	22156.0i	−0.291389	+	0.921562i
$834$		0			0
$835$			3239.76i			0.134271i
$836$		0			0
$837$	20968.0			0.865900
$838$		0			0
$839$	3005.33	+	4136.48i	0.123666	+	0.170211i	0.866361	−	0.499418i	$-0.166453\pi$
$839$	3005.33	+	4136.48i	0.123666	+	0.170211i	−0.742695	+	0.669630i	$0.766453\pi$
$840$		0			0
$841$	7528.83	+	23171.3i	0.308698	+	0.950073i
$842$		0			0
$843$	−18178.9	−	13207.8i	−0.742723	−	0.539620i
$844$		0			0
$845$	10436.1	+	3390.88i	0.424866	+	0.138047i
$846$		0			0
$847$	−18902.3	−	15822.4i	−0.766814	−	0.641870i
$848$		0			0
$849$	−23408.5	−	7605.90i	−0.946265	−	0.307460i
$850$		0			0
$851$	−26096.7	−	18960.4i	−1.05121	−	0.763752i
$852$		0			0
$853$	6632.22	+	20411.9i	0.266217	+	0.819330i	0.991411	+	0.130786i	$0.0417500\pi$
$853$	6632.22	+	20411.9i	0.266217	+	0.819330i	−0.725194	+	0.688545i	$0.758250\pi$
$854$		0			0
$855$	−178.948	−	246.301i	−0.00715777	−	0.00985183i
$856$		0			0
$857$	28415.0			1.13260			0.566299	−	0.824200i	$-0.308375\pi$
$857$	28415.0			1.13260			0.566299	+	0.824200i	$0.308375\pi$
$858$		0			0
$859$		−	30321.9i		−	1.20439i	−0.798350	−	0.602194i	$-0.794293\pi$
$859$		−	30321.9i		−	1.20439i	0.798350	−	0.602194i	$-0.205707\pi$
$860$		0			0
$861$	16950.7	+	12213.2i	0.670939	+	0.483420i
$862$		0			0
$863$	−222.861	−	685.895i	−0.00879058	−	0.0270546i	0.946565	−	0.322513i	$-0.104528\pi$
$863$	−222.861	−	685.895i	−0.00879058	−	0.0270546i	−0.955356	+	0.295458i	$0.904528\pi$
$864$		0			0
$865$	162.693	−	223.928i	0.00639506	−	0.00880205i
$866$		0			0
$867$	1330.15	+	432.192i	0.0521041	+	0.0169296i
$868$		0			0
$869$	15139.9	−	27224.4i	0.591008	−	1.06274i
$870$		0			0
$871$	−6052.21	+	18626.8i	−0.235444	+	0.724621i
$872$		0			0
$873$	1960.09	−	2697.83i	0.0759897	−	0.104591i
$874$		0			0
$875$	7948.36	−	5823.02i	0.307090	−	0.224976i
$876$		0			0
$877$	−26480.8	−	36447.7i	−1.01960	−	1.40336i	−0.912482	−	0.409118i	$-0.865837\pi$
$877$	−26480.8	−	36447.7i	−1.01960	−	1.40336i	−0.107122	−	0.994246i	$-0.534163\pi$
$878$		0			0
$879$		−	17070.0i		−	0.655013i
$880$		0			0
$881$			26797.1i			1.02476i	0.858758	+	0.512382i	$0.171237\pi$
$881$			26797.1i			1.02476i	−0.858758	+	0.512382i	$0.828763\pi$
$882$		0			0
$883$	24522.7	−	17816.8i	0.934602	−	0.679028i	−0.0125130	−	0.999922i	$-0.503983\pi$
$883$	24522.7	−	17816.8i	0.934602	−	0.679028i	0.947115	+	0.320893i	$0.103983\pi$
$884$		0			0
$885$	−4925.88	+	1600.52i	−0.187098	+	0.0607918i
$886$		0			0
$887$	−31530.2	−	22908.1i	−1.19355	−	0.867167i	−0.199918	−	0.979813i	$-0.564067\pi$
$887$	−31530.2	−	22908.1i	−1.19355	−	0.867167i	−0.993635	+	0.112646i	$0.964067\pi$
$888$		0			0
$889$	−29138.2	+	115.322i	−1.09929	+	0.00435070i
$890$		0			0
$891$	11658.1	−	10841.3i	0.438339	−	0.407629i
$892$		0			0
$893$	260.759	+	84.7258i	0.00977153	+	0.00317496i
$894$		0			0
$895$	−4181.83	+	5755.79i	−0.156182	+	0.214966i
$896$		0			0
$897$	43660.6	−	14186.2i	1.62518	−	0.528052i
$898$		0			0
$899$	557.973	−	405.391i	0.0207002	−	0.0150395i
$900$		0			0
$901$	−20043.9			−0.741130
$902$		0			0
$903$	−36784.2	+	12113.1i	−1.35559	+	0.446399i
$904$		0			0
$905$	4629.98	−	3363.88i	0.170062	−	0.123557i
$906$		0			0
$907$	−6945.77	−	21376.9i	−0.254278	−	0.782588i	−0.993971	−	0.109643i	$-0.965029\pi$
$907$	−6945.77	−	21376.9i	−0.254278	−	0.782588i	0.739693	−	0.672945i	$-0.234971\pi$
$908$		0			0
$909$	3743.94	+	2720.13i	0.136610	+	0.0992531i
$910$		0			0
$911$	10984.7	−	33807.6i	0.399496	−	1.22952i	−0.525909	−	0.850541i	$-0.676275\pi$
$911$	10984.7	−	33807.6i	0.399496	−	1.22952i	0.925405	−	0.378981i	$-0.123725\pi$
$912$		0			0
$913$	9183.91	−	1114.78i	0.332906	−	0.0404094i
$914$		0			0
$915$	545.110	−	1677.68i	0.0196948	−	0.0606145i
$916$		0			0
$917$	−36123.3	−	11579.3i	−1.30087	−	0.416993i
$918$		0			0
$919$	10415.9	−	3384.32i	0.373872	−	0.121478i	−0.116053	−	0.993243i	$-0.537024\pi$
$919$	10415.9	−	3384.32i	0.373872	−	0.121478i	0.489925	+	0.871765i	$0.337024\pi$
$920$		0			0
$921$	−7678.92	−	10569.1i	−0.274733	−	0.378138i
$922$		0			0
$923$	−91181.6			−3.25166
$924$		0			0
$925$	31143.7			1.10703
$926$		0			0
$927$	9775.83	+	13455.3i	0.346365	+	0.476731i
$928$		0			0
$929$	48445.4	−	15740.9i	1.71092	−	0.555911i	0.720432	−	0.693526i	$-0.243944\pi$
$929$	48445.4	−	15740.9i	1.71092	−	0.555911i	0.990486	+	0.137615i	$0.0439436\pi$
$930$		0			0
$931$	−5806.36	+	45.9610i	−0.204399	+	0.00161795i
$932$		0			0
$933$	−8776.20	+	27010.4i	−0.307953	+	0.947781i
$934$		0			0
$935$	−4861.49	+	2258.79i	−0.170040	+	0.0790056i
$936$		0			0
$937$	15213.2	−	46821.5i	0.530411	−	1.63244i	−0.222951	−	0.974830i	$-0.571569\pi$
$937$	15213.2	−	46821.5i	0.530411	−	1.63244i	0.753362	−	0.657606i	$-0.228431\pi$
$938$		0			0
$939$	207.095	+	150.463i	0.00719733	+	0.00522917i
$940$		0			0
$941$	−8624.13	−	26542.3i	−0.298766	−	0.919507i	−0.981930	−	0.189242i	$-0.939397\pi$
$941$	−8624.13	−	26542.3i	−0.298766	−	0.919507i	0.683165	−	0.730264i	$-0.260603\pi$
$942$		0			0
$943$	26289.9	−	19100.8i	0.907866	−	0.659603i
$944$		0			0
$945$	−5823.94	+	1917.83i	−0.200479	+	0.0660180i
$946$		0			0
$947$	14301.3			0.490739			0.245370	−	0.969430i	$-0.421091\pi$
$947$	14301.3			0.490739			0.245370	+	0.969430i	$0.421091\pi$
$948$		0			0
$949$	267.616	−	194.435i	0.00915405	−	0.00665081i
$950$		0			0
$951$	−24281.2	+	7889.42i	−0.827939	+	0.269014i
$952$		0			0
$953$	−22757.6	+	31323.2i	−0.773548	+	1.06470i	0.222417	+	0.974952i	$0.428605\pi$
$953$	−22757.6	+	31323.2i	−0.773548	+	1.06470i	−0.995965	+	0.0897459i	$0.971395\pi$
$954$		0			0
$955$	3022.46	+	982.057i	0.102413	+	0.0332760i
$956$		0			0
$957$	152.253	−	777.542i	0.00514278	−	0.0262637i
$958$		0			0
$959$	157.617	+	39824.9i	0.00530732	+	1.34099i
$960$		0			0
$961$	−8836.66	−	6420.21i	−0.296622	−	0.215508i
$962$		0			0
$963$	−14095.0	+	4579.73i	−0.471655	+	0.153250i
$964$		0			0
$965$	2630.18	−	1910.94i	0.0877394	−	0.0637464i
$966$		0			0
$967$			27481.7i			0.913911i	0.889489	+	0.456956i	$0.151060\pi$
$967$			27481.7i			0.913911i	−0.889489	+	0.456956i	$0.848940\pi$
$968$		0			0
$969$		−	4960.54i		−	0.164454i
$970$		0			0
$971$	5456.06	+	7509.62i	0.180323	+	0.248193i	0.889604	−	0.456733i	$-0.150980\pi$
$971$	5456.06	+	7509.62i	0.180323	+	0.248193i	−0.709281	+	0.704926i	$0.750980\pi$
$972$		0			0
$973$	−20480.6	−	27955.8i	−0.674798	−	0.921091i
$974$		0			0
$975$	−26052.2	+	35857.8i	−0.855732	+	1.17781i
$976$		0			0
$977$	4289.99	−	13203.2i	0.140480	−	0.432352i	−0.855922	−	0.517105i	$-0.827010\pi$
$977$	4289.99	−	13203.2i	0.140480	−	0.432352i	0.996402	+	0.0847521i	$0.0270098\pi$
$978$		0			0
$979$	7915.26	+	1549.91i	0.258399	+	0.0505979i
$980$		0			0
$981$	−6847.69	−	2224.95i	−0.222864	−	0.0724130i
$982$		0			0
$983$	−28342.4	+	39009.9i	−0.919614	+	1.26574i	0.0441612	+	0.999024i	$0.485938\pi$
$983$	−28342.4	+	39009.9i	−0.919614	+	1.26574i	−0.963775	+	0.266716i	$0.914062\pi$
$984$		0			0
$985$	−1016.91	−	3129.73i	−0.0328949	−	0.101240i
$986$		0			0
$987$	758.431	−	1052.63i	0.0244591	−	0.0339468i
$988$		0			0
$989$			60236.9i			1.93673i
$990$		0			0
$991$	5388.09			0.172713			0.0863564	−	0.996264i	$-0.472478\pi$
$991$	5388.09			0.172713			0.0863564	+	0.996264i	$0.472478\pi$
$992$		0			0
$993$	−13276.3	−	18273.3i	−0.424281	−	0.583973i
$994$		0			0
$995$	−790.953	−	2434.30i	−0.0252009	−	0.0775603i
$996$		0			0
$997$	35919.6	+	26097.1i	1.14101	+	0.828991i	0.987259	−	0.159119i	$-0.0508652\pi$
$997$	35919.6	+	26097.1i	1.14101	+	0.828991i	0.153749	+	0.988110i	$0.450865\pi$
$998$		0			0
$999$	−37585.1	−	12212.1i	−1.19033	−	0.386762i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.4.w.a.13.18	yes	96
7.6	odd	2	inner	308.4.w.a.13.7	✓	96
11.6	odd	10	inner	308.4.w.a.237.7	yes	96
77.6	even	10	inner	308.4.w.a.237.18	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.4.w.a.13.7	✓	96	7.6	odd	2	inner
308.4.w.a.13.18	yes	96	1.1	even	1	trivial
308.4.w.a.237.7	yes	96	11.6	odd	10	inner
308.4.w.a.237.18	yes	96	77.6	even	10	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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	308.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.54235 + 3.49924i) q^{3} +(-2.06273 + 0.670222i) q^{5} +(17.6363 + 5.65332i) q^{7} +(2.56231 - 7.88597i) q^{9} +(7.01068 - 35.8029i) q^{11} +(26.3234 - 81.0150i) q^{13} +(-7.58944 - 5.51405i) q^{15} +(20.9350 + 64.4312i) q^{17} +(-13.6956 + 9.95044i) q^{19} +(25.0553 + 76.0864i) q^{21} +124.597 q^{23} +(-97.3215 + 70.7082i) q^{25} +(145.176 - 47.1707i) q^{27} +(2.95126 - 4.06207i) q^{29} +(130.639 + 42.4472i) q^{31} +(143.107 - 66.4914i) q^{33} +(-40.1680 + 0.158975i) q^{35} +(-209.449 - 152.173i) q^{37} +(350.414 - 113.856i) q^{39} +(210.999 - 153.300i) q^{41} +483.453i q^{43} +17.9839i q^{45} +(-9.51981 - 13.1029i) q^{47} +(279.080 + 199.408i) q^{49} +(-172.236 + 237.063i) q^{51} +(-91.4270 + 281.383i) q^{53} +(9.53477 + 78.5505i) q^{55} +(-69.6379 - 22.6267i) q^{57} +(324.522 - 446.666i) q^{59} +(58.1075 + 178.836i) q^{61} +(89.7716 - 124.594i) q^{63} +184.755i q^{65} -229.918 q^{67} +(316.769 + 435.995i) q^{69} +(-330.773 - 1018.02i) q^{71} +(3.14162 + 2.28252i) q^{73} +(-494.850 - 160.786i) q^{75} +(326.048 - 591.799i) q^{77} +(812.063 + 263.855i) q^{79} +(353.029 + 256.490i) q^{81} +(78.3604 + 241.169i) q^{83} +(-86.3663 - 118.873i) q^{85} +21.7173 q^{87} +221.079i q^{89} +(922.251 - 1279.99i) q^{91} +(183.597 + 565.052i) q^{93} +(21.5813 - 29.7042i) q^{95} +(382.486 + 124.277i) q^{97} +(-264.377 - 147.024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 10 q^{7} + 168 q^{9} + 60 q^{11} - 192 q^{15} - 112 q^{23} + 548 q^{25} - 700 q^{29} - 940 q^{35} + 288 q^{37} + 460 q^{39} + 90 q^{49} - 1420 q^{51} - 2240 q^{53} + 560 q^{57} + 320 q^{63} + 4272 q^{67}+ \cdots - 10212 q^{99}+O(q^{100}) \) 96 * q - 10 * q^7 + 168 * q^9 + 60 * q^11 - 192 * q^15 - 112 * q^23 + 548 * q^25 - 700 * q^29 - 940 * q^35 + 288 * q^37 + 460 * q^39 + 90 * q^49 - 1420 * q^51 - 2240 * q^53 + 560 * q^57 + 320 * q^63 + 4272 * q^67 + 296 * q^71 + 430 * q^77 + 2100 * q^79 - 6088 * q^81 + 5900 * q^85 - 636 * q^91 - 2628 * q^93 + 780 * q^95 - 10212 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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