LMFDB - Embedded newform 2380.2.cb.b.781.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2380,2,Mod(781,2380)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2380.781"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2380, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2380 = 2^{2} \cdot 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2380.cb (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [92] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$19.0043956811$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			781.17
Character	$\chi$	$=$	2380.781
Dual form			2380.2.cb.b.1801.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.04428 - 0.602915i) q^{3} +(-0.866025 + 0.500000i) q^{5} +(-2.63869 - 0.193203i) q^{7} +(-0.772986 - 1.33885i) q^{9} +(-4.44707 - 2.56752i) q^{11} +4.07119 q^{13} +1.20583 q^{15} +(-1.20468 - 3.94319i) q^{17} +(-1.73962 - 3.01311i) q^{19} +(2.63904 + 1.79266i) q^{21} +(4.53516 - 2.61837i) q^{23} +(0.500000 - 0.866025i) q^{25} +5.48167i q^{27} -3.81818i q^{29} +(0.00579115 + 0.00334352i) q^{31} +(3.09599 + 5.36241i) q^{33} +(2.38177 - 1.15202i) q^{35} +(2.34387 - 1.35324i) q^{37} +(-4.25146 - 2.45458i) q^{39} +12.1509i q^{41} -6.54181 q^{43} +(1.33885 + 0.772986i) q^{45} +(-2.89492 - 5.01416i) q^{47} +(6.92534 + 1.01961i) q^{49} +(-1.11939 + 4.84411i) q^{51} +(-6.88257 + 11.9210i) q^{53} +5.13503 q^{55} +4.19538i q^{57} +(-3.14237 + 5.44274i) q^{59} +(1.41701 - 0.818110i) q^{61} +(1.78100 + 3.68215i) q^{63} +(-3.52576 + 2.03560i) q^{65} +(2.53109 - 4.38398i) q^{67} -6.31463 q^{69} +6.01442i q^{71} +(-7.77495 - 4.48887i) q^{73} +(-1.04428 + 0.602915i) q^{75} +(11.2384 + 7.63406i) q^{77} +(-5.09285 + 2.94036i) q^{79} +(0.986026 - 1.70785i) q^{81} -6.46133 q^{83} +(3.01488 + 2.81257i) q^{85} +(-2.30204 + 3.98725i) q^{87} +(6.01404 + 10.4166i) q^{89} +(-10.7426 - 0.786568i) q^{91} +(-0.00403172 - 0.00698315i) q^{93} +(3.01311 + 1.73962i) q^{95} -8.99376i q^{97} +7.93862i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 56 q^{9} - 24 q^{13} + 12 q^{15} + 4 q^{17} - 24 q^{21} + 46 q^{25} - 24 q^{33} + 14 q^{35} - 64 q^{43} + 16 q^{47} + 38 q^{49} - 22 q^{51} - 8 q^{53} + 18 q^{59} + 16 q^{67} - 36 q^{69} - 12 q^{77}+ \cdots + 44 q^{93}+O(q^{100}) $ 92 * q + 56 * q^9 - 24 * q^13 + 12 * q^15 + 4 * q^17 - 24 * q^21 + 46 * q^25 - 24 * q^33 + 14 * q^35 - 64 * q^43 + 16 * q^47 + 38 * q^49 - 22 * q^51 - 8 * q^53 + 18 * q^59 + 16 * q^67 - 36 * q^69 - 12 * q^77 - 86 * q^81 + 8 * q^83 - 20 * q^85 + 20 * q^87 + 2 * q^89 + 44 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2380\mathbb{Z}\right)^\times$.

$n$	$477$	$1191$	$1261$	$1361$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.04428	−	0.602915i	−0.602915	−	0.348093i	0.167272	−	0.985911i	$-0.446504\pi$
$3$	−1.04428	−	0.602915i	−0.602915	−	0.348093i	−0.770188	+	0.637817i	$0.779837\pi$
$4$		0			0
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$		0			0
$7$	−2.63869	−	0.193203i	−0.997330	−	0.0730240i
$7$	−2.63869	−	0.193203i	−0.997330	−	0.0730240i
$8$		0			0
$9$	−0.772986	−	1.33885i	−0.257662	−	0.446284i
$10$		0			0
$11$	−4.44707	−	2.56752i	−1.34084	−	0.774136i	−0.353911	−	0.935279i	$-0.615148\pi$
$11$	−4.44707	−	2.56752i	−1.34084	−	0.774136i	−0.986931	+	0.161144i	$0.948482\pi$
$12$		0			0
$13$	4.07119			1.12915			0.564573	−	0.825383i	$-0.309041\pi$
$13$	4.07119			1.12915			0.564573	+	0.825383i	$0.309041\pi$
$14$		0			0
$15$	1.20583			0.311344
$16$		0			0
$17$	−1.20468	−	3.94319i	−0.292177	−	0.956364i
$17$	−1.20468	−	3.94319i	−0.292177	−	0.956364i
$18$		0			0
$19$	−1.73962	−	3.01311i	−0.399097	−	0.691256i	0.594518	−	0.804082i	$-0.297343\pi$
$19$	−1.73962	−	3.01311i	−0.399097	−	0.691256i	−0.993615	+	0.112827i	$0.964010\pi$
$20$		0			0
$21$	2.63904	+	1.79266i	0.575886	+	0.391191i
$22$		0			0
$23$	4.53516	−	2.61837i	0.945645	−	0.545969i	0.0539199	−	0.998545i	$-0.482828\pi$
$23$	4.53516	−	2.61837i	0.945645	−	0.545969i	0.891725	+	0.452577i	$0.149495\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		0			0
$27$			5.48167i			1.05495i
$28$		0			0
$29$		−	3.81818i		−	0.709019i	−0.935052	−	0.354509i	$-0.884648\pi$
$29$		−	3.81818i		−	0.709019i	0.935052	−	0.354509i	$-0.115352\pi$
$30$		0			0
$31$	0.00579115	+	0.00334352i	0.00104012	+	0.000600515i	0.500520	−	0.865725i	$-0.333142\pi$
$31$	0.00579115	+	0.00334352i	0.00104012	+	0.000600515i	−0.499480	+	0.866326i	$0.666476\pi$
$32$		0			0
$33$	3.09599	+	5.36241i	0.538943	+	0.933476i
$34$		0			0
$35$	2.38177	−	1.15202i	0.402593	−	0.194728i
$36$		0			0
$37$	2.34387	−	1.35324i	0.385330	−	0.222471i	−0.294805	−	0.955558i	$-0.595255\pi$
$37$	2.34387	−	1.35324i	0.385330	−	0.222471i	0.680135	+	0.733087i	$0.261921\pi$
$38$		0			0
$39$	−4.25146	−	2.45458i	−0.680779	−	0.393048i
$40$		0			0
$41$			12.1509i			1.89764i	0.315810	+	0.948822i	$0.397724\pi$
$41$			12.1509i			1.89764i	−0.315810	+	0.948822i	$0.602276\pi$
$42$		0			0
$43$	−6.54181			−0.997616			−0.498808	−	0.866712i	$-0.666229\pi$
$43$	−6.54181			−0.997616			−0.498808	+	0.866712i	$0.666229\pi$
$44$		0			0
$45$	1.33885	+	0.772986i	0.199584	+	0.115230i
$46$		0			0
$47$	−2.89492	−	5.01416i	−0.422268	−	0.731390i	0.573893	−	0.818930i	$-0.305433\pi$
$47$	−2.89492	−	5.01416i	−0.422268	−	0.731390i	−0.996161	+	0.0875405i	$0.972099\pi$
$48$		0			0
$49$	6.92534	+	1.01961i	0.989335	+	0.145658i
$50$		0			0
$51$	−1.11939	+	4.84411i	−0.156746	+	0.678312i
$52$		0			0
$53$	−6.88257	+	11.9210i	−0.945393	+	1.63747i	−0.190432	+	0.981700i	$0.560989\pi$
$53$	−6.88257	+	11.9210i	−0.945393	+	1.63747i	−0.754961	+	0.655769i	$0.772344\pi$
$54$		0			0
$55$	5.13503			0.692408
$56$		0			0
$57$			4.19538i			0.555692i
$58$		0			0
$59$	−3.14237	+	5.44274i	−0.409101	+	0.708585i	−0.994789	−	0.101952i	$-0.967491\pi$
$59$	−3.14237	+	5.44274i	−0.409101	+	0.708585i	0.585688	+	0.810537i	$0.300824\pi$
$60$		0			0
$61$	1.41701	−	0.818110i	0.181429	−	0.104748i	−0.406535	−	0.913635i	$-0.633263\pi$
$61$	1.41701	−	0.818110i	0.181429	−	0.104748i	0.587964	+	0.808887i	$0.299930\pi$
$62$		0			0
$63$	1.78100	+	3.68215i	0.224385	+	0.463908i
$64$		0			0
$65$	−3.52576	+	2.03560i	−0.437316	+	0.252485i
$66$		0			0
$67$	2.53109	−	4.38398i	0.309222	−	0.535588i	−0.668971	−	0.743289i	$-0.733265\pi$
$67$	2.53109	−	4.38398i	0.309222	−	0.535588i	0.978192	+	0.207701i	$0.0665981\pi$
$68$		0			0
$69$	−6.31463			−0.760192
$70$		0			0
$71$			6.01442i			0.713780i	0.934146	+	0.356890i	$0.116163\pi$
$71$			6.01442i			0.713780i	−0.934146	+	0.356890i	$0.883837\pi$
$72$		0			0
$73$	−7.77495	−	4.48887i	−0.909989	−	0.525382i	−0.0295613	−	0.999563i	$-0.509411\pi$
$73$	−7.77495	−	4.48887i	−0.909989	−	0.525382i	−0.880428	+	0.474181i	$0.842744\pi$
$74$		0			0
$75$	−1.04428	+	0.602915i	−0.120583	+	0.0696187i
$76$		0			0
$77$	11.2384	+	7.63406i	1.28073	+	0.869982i
$78$		0			0
$79$	−5.09285	+	2.94036i	−0.572991	+	0.330816i	−0.758343	−	0.651856i	$-0.773991\pi$
$79$	−5.09285	+	2.94036i	−0.572991	+	0.330816i	0.185352	+	0.982672i	$0.440657\pi$
$80$		0			0
$81$	0.986026	−	1.70785i	0.109558	−	0.189761i
$82$		0			0
$83$	−6.46133			−0.709223			−0.354612	−	0.935014i	$-0.615387\pi$
$83$	−6.46133			−0.709223			−0.354612	+	0.935014i	$0.615387\pi$
$84$		0			0
$85$	3.01488	+	2.81257i	0.327009	+	0.305066i
$86$		0			0
$87$	−2.30204	+	3.98725i	−0.246805	+	0.427478i
$88$		0			0
$89$	6.01404	+	10.4166i	0.637487	+	1.10416i	0.985982	+	0.166849i	$0.0533593\pi$
$89$	6.01404	+	10.4166i	0.637487	+	1.10416i	−0.348496	+	0.937310i	$0.613307\pi$
$90$		0			0
$91$	−10.7426	−	0.786568i	−1.12613	−	0.0824547i
$92$		0			0
$93$	−0.00403172	−	0.00698315i	−0.000418070	−	0.000724119i
$94$		0			0
$95$	3.01311	+	1.73962i	0.309139	+	0.178481i
$96$		0			0
$97$		−	8.99376i		−	0.913178i	−0.889678	−	0.456589i	$-0.849071\pi$
$97$		−	8.99376i		−	0.913178i	0.889678	−	0.456589i	$-0.150929\pi$
$98$		0			0
$99$			7.93862i			0.797861i
$100$		0			0
$101$	4.18044	−	7.24074i	0.415969	−	0.720480i	−0.579560	−	0.814929i	$-0.696776\pi$
$101$	4.18044	−	7.24074i	0.415969	−	0.720480i	0.995530	+	0.0944492i	$0.0301090\pi$
$102$		0			0
$103$	1.54083	+	2.66880i	0.151823	+	0.262965i	0.931898	−	0.362721i	$-0.118152\pi$
$103$	1.54083	+	2.66880i	0.151823	+	0.262965i	−0.780075	+	0.625686i	$0.784819\pi$
$104$		0			0
$105$	−3.18181	−	0.232971i	−0.310513	−	0.0227356i
$106$		0			0
$107$	−16.1458	+	9.32181i	−1.56088	+	0.901173i	−0.563709	+	0.825974i	$0.690626\pi$
$107$	−16.1458	+	9.32181i	−1.56088	+	0.901173i	−0.997169	+	0.0751993i	$0.976041\pi$
$108$		0			0
$109$	3.01624	+	1.74143i	0.288904	+	0.166799i	0.637447	−	0.770494i	$-0.279990\pi$
$109$	3.01624	+	1.74143i	0.288904	+	0.166799i	−0.348544	+	0.937293i	$0.613324\pi$
$110$		0			0
$111$	−3.26355			−0.309762
$112$		0			0
$113$		−	2.93517i		−	0.276118i	−0.990424	−	0.138059i	$-0.955914\pi$
$113$		−	2.93517i		−	0.276118i	0.990424	−	0.138059i	$-0.0440863\pi$
$114$		0			0
$115$	−2.61837	+	4.53516i	−0.244165	+	0.422905i
$116$		0			0
$117$	−3.14698	−	5.45072i	−0.290938	−	0.503919i
$118$		0			0
$119$	2.41693	+	10.6376i	0.221559	+	0.975147i
$120$		0			0
$121$	7.68429	+	13.3096i	0.698572	+	1.20996i
$122$		0			0
$123$	7.32594	−	12.6889i	0.660558	−	1.14412i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−4.31721			−0.383090			−0.191545	−	0.981484i	$-0.561350\pi$
$127$	−4.31721			−0.383090			−0.191545	+	0.981484i	$0.561350\pi$
$128$		0			0
$129$	6.83148	+	3.94416i	0.601478	+	0.347264i
$130$		0			0
$131$	16.7631	−	9.67820i	1.46460	−	0.845588i	0.465383	−	0.885109i	$-0.345917\pi$
$131$	16.7631	−	9.67820i	1.46460	−	0.845588i	0.999219	+	0.0395212i	$0.0125833\pi$
$132$		0			0
$133$	4.00818	+	8.28677i	0.347553	+	0.718554i
$134$		0			0
$135$	−2.74084	−	4.74727i	−0.235894	−	0.408580i
$136$		0			0
$137$	−2.15060	+	3.72495i	−0.183738	+	0.318244i	−0.943151	−	0.332365i	$-0.892153\pi$
$137$	−2.15060	+	3.72495i	−0.183738	+	0.318244i	0.759412	+	0.650610i	$0.225487\pi$
$138$		0			0
$139$			18.1388i			1.53851i	0.638942	+	0.769255i	$0.279372\pi$
$139$			18.1388i			1.53851i	−0.638942	+	0.769255i	$0.720628\pi$
$140$		0			0
$141$			6.98158i			0.587955i
$142$		0			0
$143$	−18.1049	−	10.4529i	−1.51401	−	0.874112i
$144$		0			0
$145$	1.90909	+	3.30664i	0.158541	+	0.274602i
$146$		0			0
$147$	−6.61726	−	5.24015i	−0.545783	−	0.432200i
$148$		0			0
$149$	2.96369	+	5.13326i	0.242795	+	0.420533i	0.961509	−	0.274772i	$-0.0886025\pi$
$149$	2.96369	+	5.13326i	0.242795	+	0.420533i	−0.718714	+	0.695305i	$0.755269\pi$
$150$		0			0
$151$	−3.95007	+	6.84173i	−0.321452	+	0.556772i	−0.980788	−	0.195077i	$-0.937504\pi$
$151$	−3.95007	+	6.84173i	−0.321452	+	0.556772i	0.659335	+	0.751849i	$0.270838\pi$
$152$		0			0
$153$	−4.34815	+	4.66091i	−0.351527	+	0.376813i
$154$		0			0
$155$	−0.00668705			−0.000537117
$156$		0			0
$157$	6.91423	−	11.9758i	0.551815	−	0.955772i	−0.446328	−	0.894869i	$-0.647269\pi$
$157$	6.91423	−	11.9758i	0.551815	−	0.955772i	0.998144	−	0.0609029i	$-0.0193980\pi$
$158$		0			0
$159$	14.3747	−	8.29921i	1.13998	−	0.658170i
$160$		0			0
$161$	−12.4727	+	6.03286i	−0.982989	+	0.475456i
$162$		0			0
$163$	16.2689	−	9.39283i	1.27428	−	0.735703i	0.298486	−	0.954414i	$-0.403519\pi$
$163$	16.2689	−	9.39283i	1.27428	−	0.735703i	0.975790	+	0.218711i	$0.0701852\pi$
$164$		0			0
$165$	−5.36241	−	3.09599i	−0.417463	−	0.241023i
$166$		0			0
$167$		−	22.7775i		−	1.76258i	−0.472576	−	0.881290i	$-0.656676\pi$
$167$		−	22.7775i		−	1.76258i	0.472576	−	0.881290i	$-0.343324\pi$
$168$		0			0
$169$	3.57460			0.274970
$170$		0			0
$171$	−2.68941	+	4.65819i	−0.205664	+	0.356221i
$172$		0			0
$173$	−11.6090	+	6.70248i	−0.882618	+	0.509580i	−0.871521	−	0.490359i	$-0.836866\pi$
$173$	−11.6090	+	6.70248i	−0.882618	+	0.509580i	−0.0110973	+	0.999938i	$0.503532\pi$
$174$		0			0
$175$	−1.48666	+	2.18857i	−0.112381	+	0.165440i
$176$		0			0
$177$	6.56302	−	3.78916i	0.493307	−	0.284811i
$178$		0			0
$179$	−8.11388	+	14.0536i	−0.606460	+	1.05042i	0.385359	+	0.922767i	$0.374078\pi$
$179$	−8.11388	+	14.0536i	−0.606460	+	1.05042i	−0.991819	+	0.127652i	$0.959256\pi$
$180$		0			0
$181$		−	7.48593i		−	0.556425i	−0.960520	−	0.278212i	$-0.910258\pi$
$181$		−	7.48593i		−	0.556425i	0.960520	−	0.278212i	$-0.0897419\pi$
$182$		0			0
$183$	−1.97300			−0.145849
$184$		0			0
$185$	−1.35324	+	2.34387i	−0.0994919	+	0.172325i
$186$		0			0
$187$	−4.76693	+	20.6287i	−0.348592	+	1.50852i
$188$		0			0
$189$	1.05908	−	14.4644i	0.0770366	−	1.05213i
$190$		0			0
$191$	−0.746997	−	1.29384i	−0.0540508	−	0.0936187i	0.837734	−	0.546078i	$-0.183880\pi$
$191$	−0.746997	−	1.29384i	−0.0540508	−	0.0936187i	−0.891785	+	0.452460i	$0.850547\pi$
$192$		0			0
$193$	11.6536	+	6.72822i	0.838845	+	0.484308i	0.856872	−	0.515530i	$-0.172405\pi$
$193$	11.6536	+	6.72822i	0.838845	+	0.484308i	−0.0180262	+	0.999838i	$0.505738\pi$
$194$		0			0
$195$	4.90917			0.351553
$196$		0			0
$197$		−	0.424278i		−	0.0302285i	−0.999886	−	0.0151143i	$-0.995189\pi$
$197$		−	0.424278i		−	0.0302285i	0.999886	−	0.0151143i	$-0.00481120\pi$
$198$		0			0
$199$	13.9066	+	8.02898i	0.985812	+	0.569159i	0.904020	−	0.427490i	$-0.140602\pi$
$199$	13.9066	+	8.02898i	0.985812	+	0.569159i	0.0817924	+	0.996649i	$0.473936\pi$
$200$		0			0
$201$	−5.28633	+	3.05206i	−0.372869	+	0.215276i
$202$		0			0
$203$	−0.737686	+	10.0750i	−0.0517754	+	0.707126i
$204$		0			0
$205$	−6.07543	−	10.5230i	−0.424326	−	0.734955i
$206$		0			0
$207$	−7.01123	−	4.04793i	−0.487314	−	0.281351i
$208$		0			0
$209$			17.8660i			1.23582i
$210$		0			0
$211$			5.29980i			0.364853i	0.983219	+	0.182427i	$0.0583952\pi$
$211$			5.29980i			0.364853i	−0.983219	+	0.182427i	$0.941605\pi$
$212$		0			0
$213$	3.62618	−	6.28073i	0.248462	−	0.430349i
$214$		0			0
$215$	5.66537	−	3.27090i	0.386375	−	0.223074i
$216$		0			0
$217$	−0.0146351	−	0.00994138i	−0.000993493	−	0.000674865i
$218$		0			0
$219$	5.41282	+	9.37527i	0.365764	+	0.633522i
$220$		0			0
$221$	−4.90447	−	16.0535i	−0.329910	−	1.07987i
$222$		0			0
$223$	18.0585			1.20929			0.604643	−	0.796496i	$-0.293316\pi$
$223$	18.0585			1.20929			0.604643	+	0.796496i	$0.293316\pi$
$224$		0			0
$225$	−1.54597			−0.103065
$226$		0			0
$227$	0.571118	+	0.329735i	0.0379064	+	0.0218853i	0.518833	−	0.854875i	$-0.326366\pi$
$227$	0.571118	+	0.329735i	0.0379064	+	0.0218853i	−0.480927	+	0.876761i	$0.659700\pi$
$228$		0			0
$229$	9.45623	+	16.3787i	0.624885	+	1.08233i	0.988563	+	0.150808i	$0.0481875\pi$
$229$	9.45623	+	16.3787i	0.624885	+	1.08233i	−0.363678	+	0.931525i	$0.618479\pi$
$230$		0			0
$231$	−7.13332	−	14.7479i	−0.469338	−	0.970340i
$232$		0			0
$233$	−16.6315	+	9.60220i	−1.08957	+	0.629061i	−0.933461	−	0.358679i	$-0.883227\pi$
$233$	−16.6315	+	9.60220i	−1.08957	+	0.629061i	−0.156105	+	0.987740i	$0.549894\pi$
$234$		0			0
$235$	5.01416	+	2.89492i	0.327088	+	0.188844i
$236$		0			0
$237$	7.09115			0.460620
$238$		0			0
$239$	23.3550			1.51071			0.755355	−	0.655316i	$-0.227464\pi$
$239$	23.3550			1.51071			0.755355	+	0.655316i	$0.227464\pi$
$240$		0			0
$241$	4.95035	+	2.85809i	0.318880	+	0.184106i	0.650893	−	0.759169i	$-0.274394\pi$
$241$	4.95035	+	2.85809i	0.318880	+	0.184106i	−0.332013	+	0.943275i	$0.607728\pi$
$242$		0			0
$243$	12.1824	−	7.03353i	0.781503	−	0.451201i
$244$		0			0
$245$	−6.50733	+	2.57967i	−0.415738	+	0.164809i
$246$		0			0
$247$	−7.08234	−	12.2670i	−0.450638	−	0.780528i
$248$		0			0
$249$	6.74744	+	3.89564i	0.427602	+	0.246876i
$250$		0			0
$251$	−16.3377			−1.03122			−0.515612	−	0.856822i	$-0.672435\pi$
$251$	−16.3377			−1.03122			−0.515612	+	0.856822i	$0.672435\pi$
$252$		0			0
$253$	−26.8909			−1.69061
$254$		0			0
$255$	−1.45264	−	4.75482i	−0.0909676	−	0.297758i
$256$		0			0
$257$	1.04134	+	1.80365i	0.0649569	+	0.112509i	0.896675	−	0.442690i	$-0.145976\pi$
$257$	1.04134	+	1.80365i	0.0649569	+	0.112509i	−0.831718	+	0.555198i	$0.812642\pi$
$258$		0			0
$259$	−6.44620	+	3.11792i	−0.400547	+	0.193738i
$260$		0			0
$261$	−5.11198	+	2.95140i	−0.316424	+	0.182687i
$262$		0			0
$263$	−14.0545	+	24.3431i	−0.866638	+	1.50106i	−0.00122743	+	0.999999i	$0.500391\pi$
$263$	−14.0545	+	24.3431i	−0.866638	+	1.50106i	−0.865411	+	0.501063i	$0.832943\pi$
$264$		0			0
$265$		−	13.7651i		−	0.845586i
$266$		0			0
$267$		−	14.5038i		−	0.887620i
$268$		0			0
$269$	14.8622	+	8.58070i	0.906165	+	0.523175i	0.879195	−	0.476462i	$-0.158081\pi$
$269$	14.8622	+	8.58070i	0.906165	+	0.523175i	0.0269697	+	0.999636i	$0.491414\pi$
$270$		0			0
$271$	5.73299	+	9.92983i	0.348254	+	0.603194i	0.985939	−	0.167103i	$-0.0534412\pi$
$271$	5.73299	+	9.92983i	0.348254	+	0.603194i	−0.637685	+	0.770297i	$0.720108\pi$
$272$		0			0
$273$	10.7441	+	7.29828i	0.650260	+	0.441712i
$274$		0			0
$275$	−4.44707	+	2.56752i	−0.268168	+	0.154827i
$276$		0			0
$277$	3.29124	+	1.90020i	0.197752	+	0.114172i	0.595606	−	0.803276i	$-0.296912\pi$
$277$	3.29124	+	1.90020i	0.197752	+	0.114172i	−0.397855	+	0.917448i	$0.630245\pi$
$278$		0			0
$279$		−	0.0103380i		−	0.000618919i
$280$		0			0
$281$	10.3438			0.617062			0.308531	−	0.951214i	$-0.400163\pi$
$281$	10.3438			0.617062			0.308531	+	0.951214i	$0.400163\pi$
$282$		0			0
$283$	13.3493	+	7.70723i	0.793535	+	0.458147i	0.841205	−	0.540716i	$-0.181846\pi$
$283$	13.3493	+	7.70723i	0.793535	+	0.458147i	−0.0476708	+	0.998863i	$0.515180\pi$
$284$		0			0
$285$	−2.09769	−	3.63331i	−0.124256	−	0.215218i
$286$		0			0
$287$	2.34759	−	32.0623i	0.138574	−	1.89258i
$288$		0			0
$289$	−14.0975	+	9.50054i	−0.829265	+	0.558855i
$290$		0			0
$291$	−5.42248	+	9.39201i	−0.317871	+	0.550569i
$292$		0			0
$293$	15.4879			0.904814			0.452407	−	0.891812i	$-0.350566\pi$
$293$	15.4879			0.904814			0.452407	+	0.891812i	$0.350566\pi$
$294$		0			0
$295$		−	6.28474i		−	0.365911i
$296$		0			0
$297$	14.0743	−	24.3774i	0.816673	−	1.41452i
$298$		0			0
$299$	18.4635	−	10.6599i	1.06777	−	0.616478i
$300$		0			0
$301$	17.2618	+	1.26390i	0.994953	+	0.0728500i
$302$		0			0
$303$	−8.73110	+	5.04090i	−0.501589	+	0.289592i
$304$		0			0
$305$	−0.818110	+	1.41701i	−0.0468448	+	0.0811376i
$306$		0			0
$307$	−25.3694			−1.44791			−0.723953	−	0.689849i	$-0.757677\pi$
$307$	−25.3694			−1.44791			−0.723953	+	0.689849i	$0.757677\pi$
$308$		0			0
$309$		−	3.71597i		−	0.211394i
$310$		0			0
$311$	−9.57589	−	5.52864i	−0.542999	−	0.313501i	0.203294	−	0.979118i	$-0.434835\pi$
$311$	−9.57589	−	5.52864i	−0.542999	−	0.313501i	−0.746294	+	0.665617i	$0.768168\pi$
$312$		0			0
$313$	17.4477	−	10.0735i	0.986204	−	0.569385i	0.0820669	−	0.996627i	$-0.473848\pi$
$313$	17.4477	−	10.0735i	0.986204	−	0.569385i	0.904138	+	0.427241i	$0.140515\pi$
$314$		0			0
$315$	−3.38347	−	2.29834i	−0.190637	−	0.129497i
$316$		0			0
$317$	−16.4187	+	9.47932i	−0.922164	+	0.532412i	−0.884325	−	0.466872i	$-0.845381\pi$
$317$	−16.4187	+	9.47932i	−0.922164	+	0.532412i	−0.0378394	+	0.999284i	$0.512048\pi$
$318$		0			0
$319$	−9.80325	+	16.9797i	−0.548876	+	0.950682i
$320$		0			0
$321$	22.4810			1.25477
$322$		0			0
$323$	−9.78560	+	10.4895i	−0.544485	+	0.583651i
$324$		0			0
$325$	2.03560	−	3.52576i	0.112915	−	0.195574i
$326$		0			0
$327$	−2.09987	−	3.63708i	−0.116123	−	0.201131i
$328$		0			0
$329$	6.67005	+	13.7901i	0.367732	+	0.760273i
$330$		0			0
$331$	−11.0401	−	19.1220i	−0.606819	−	1.05104i	−0.991761	−	0.128101i	$-0.959112\pi$
$331$	−11.0401	−	19.1220i	−0.606819	−	1.05104i	0.384942	−	0.922941i	$-0.374221\pi$
$332$		0			0
$333$	−3.62356	−	2.09207i	−0.198570	−	0.114644i
$334$		0			0
$335$			5.06218i			0.276576i
$336$		0			0
$337$			28.4706i			1.55089i	0.631413	+	0.775447i	$0.282475\pi$
$337$			28.4706i			1.55089i	−0.631413	+	0.775447i	$0.717525\pi$
$338$		0			0
$339$	−1.76966	+	3.06514i	−0.0961148	+	0.166476i
$340$		0			0
$341$	−0.0171691	−	0.0297378i	−0.000929759	−	0.00161039i
$342$		0			0
$343$	−18.0768	−	4.02842i	−0.976057	−	0.217514i
$344$		0			0
$345$	5.46863	−	3.15731i	0.294421	−	0.169984i
$346$		0			0
$347$	−22.6259	−	13.0631i	−1.21462	−	0.701263i	−0.250860	−	0.968023i	$-0.580713\pi$
$347$	−22.6259	−	13.0631i	−1.21462	−	0.701263i	−0.963763	+	0.266761i	$0.914047\pi$
$348$		0			0
$349$	−11.1950			−0.599252			−0.299626	−	0.954057i	$-0.596862\pi$
$349$	−11.1950			−0.599252			−0.299626	+	0.954057i	$0.596862\pi$
$350$		0			0
$351$			22.3169i			1.19119i
$352$		0			0
$353$	9.62215	−	16.6660i	0.512135	−	0.887044i	−0.487766	−	0.872975i	$-0.662188\pi$
$353$	9.62215	−	16.6660i	0.512135	−	0.887044i	0.999901	−	0.0140697i	$-0.00447868\pi$
$354$		0			0
$355$	−3.00721	−	5.20864i	−0.159606	−	0.276446i
$356$		0			0
$357$	3.88962	−	12.5658i	0.205861	−	0.665054i
$358$		0			0
$359$	−17.7299	−	30.7092i	−0.935751	−	1.62077i	−0.773290	−	0.634053i	$-0.781390\pi$
$359$	−17.7299	−	30.7092i	−0.935751	−	1.62077i	−0.162461	−	0.986715i	$-0.551943\pi$
$360$		0			0
$361$	3.44743	−	5.97112i	0.181444	−	0.314270i
$362$		0			0
$363$		−	18.5319i		−	0.972672i
$364$		0			0
$365$	8.97774			0.469916
$366$		0			0
$367$	−6.36087	−	3.67245i	−0.332035	−	0.191700i	0.324709	−	0.945814i	$-0.394734\pi$
$367$	−6.36087	−	3.67245i	−0.332035	−	0.191700i	−0.656744	+	0.754114i	$0.728067\pi$
$368$		0			0
$369$	16.2682	−	9.39244i	0.846888	−	0.488951i
$370$		0			0
$371$	20.4641	−	30.1259i	1.06244	−	1.56406i
$372$		0			0
$373$	−6.27993	−	10.8772i	−0.325163	−	0.563198i	0.656383	−	0.754428i	$-0.272086\pi$
$373$	−6.27993	−	10.8772i	−0.325163	−	0.563198i	−0.981545	+	0.191230i	$0.938752\pi$
$374$		0			0
$375$	0.602915	−	1.04428i	0.0311344	−	0.0539264i
$376$		0			0
$377$		−	15.5446i		−	0.800585i
$378$		0			0
$379$			5.32598i			0.273577i	0.990600	+	0.136788i	$0.0436781\pi$
$379$			5.32598i			0.273577i	−0.990600	+	0.136788i	$0.956322\pi$
$380$		0			0
$381$	4.50838	+	2.60291i	0.230971	+	0.133351i
$382$		0			0
$383$	−8.92740	−	15.4627i	−0.456169	−	0.790107i	0.542586	−	0.840000i	$-0.317445\pi$
$383$	−8.92740	−	15.4627i	−0.456169	−	0.790107i	−0.998755	+	0.0498931i	$0.984112\pi$
$384$		0			0
$385$	−13.5498	−	0.992106i	−0.690559	−	0.0505624i
$386$		0			0
$387$	5.05673	+	8.75851i	0.257048	+	0.445220i
$388$		0			0
$389$	−18.4070	+	31.8819i	−0.933272	+	1.61647i	−0.155585	+	0.987823i	$0.549726\pi$
$389$	−18.4070	+	31.8819i	−0.933272	+	1.61647i	−0.777687	+	0.628652i	$0.783607\pi$
$390$		0			0
$391$	−15.7881	−	14.7287i	−0.798441	−	0.744862i
$392$		0			0
$393$	−23.3405			−1.17737
$394$		0			0
$395$	2.94036	−	5.09285i	0.147946	−	0.256249i
$396$		0			0
$397$	−5.82107	+	3.36080i	−0.292151	+	0.168674i	−0.638912	−	0.769280i	$-0.720615\pi$
$397$	−5.82107	+	3.36080i	−0.292151	+	0.168674i	0.346760	+	0.937954i	$0.387282\pi$
$398$		0			0
$399$	0.810562	−	11.0703i	0.0405788	−	0.554208i
$400$		0			0
$401$	28.2672	−	16.3201i	1.41160	−	0.814986i	0.416058	−	0.909338i	$-0.363411\pi$
$401$	28.2672	−	16.3201i	1.41160	−	0.814986i	0.995539	+	0.0943528i	$0.0300782\pi$
$402$		0			0
$403$	0.0235769	+	0.0136121i	0.00117445	+	0.000678068i
$404$		0			0
$405$			1.97205i			0.0979920i
$406$		0			0
$407$	−13.8978			−0.688890
$408$		0			0
$409$	7.21463	−	12.4961i	0.356740	−	0.617893i	−0.630674	−	0.776048i	$-0.717221\pi$
$409$	7.21463	−	12.4961i	0.356740	−	0.617893i	0.987414	+	0.158155i	$0.0505547\pi$
$410$		0			0
$411$	4.49166	−	2.59326i	0.221557	−	0.127916i
$412$		0			0
$413$	9.34328	−	13.7546i	0.459753	−	0.676818i
$414$		0			0
$415$	5.59568	−	3.23067i	0.274681	−	0.158587i
$416$		0			0
$417$	10.9361	−	18.9419i	0.535545	−	0.927591i
$418$		0			0
$419$		−	24.9214i		−	1.21749i	−0.793365	−	0.608746i	$-0.791673\pi$
$419$		−	24.9214i		−	1.21749i	0.793365	−	0.608746i	$-0.208327\pi$
$420$		0			0
$421$	−28.5780			−1.39281			−0.696403	−	0.717651i	$-0.745217\pi$
$421$	−28.5780			−1.39281			−0.696403	+	0.717651i	$0.745217\pi$
$422$		0			0
$423$	−4.47547	+	7.75175i	−0.217605	+	0.376903i
$424$		0			0
$425$	−4.01724	−	0.928315i	−0.194865	−	0.0450299i
$426$		0			0
$427$	−3.89710	+	1.88497i	−0.188594	+	0.0912199i
$428$		0			0
$429$	12.6044	+	21.8314i	0.608545	+	1.05403i
$430$		0			0
$431$	11.3962	+	6.57962i	0.548938	+	0.316929i	0.748693	−	0.662916i	$-0.230682\pi$
$431$	11.3962	+	6.57962i	0.548938	+	0.316929i	−0.199756	+	0.979846i	$0.564015\pi$
$432$		0			0
$433$	−0.394201			−0.0189441			−0.00947204	−	0.999955i	$-0.503015\pi$
$433$	−0.394201			−0.0189441			−0.00947204	+	0.999955i	$0.503015\pi$
$434$		0			0
$435$		−	4.60408i		−	0.220749i
$436$		0			0
$437$	−15.7789	−	9.10996i	−0.754808	−	0.435789i
$438$		0			0
$439$	12.7311	−	7.35033i	0.607624	−	0.350812i	−0.164411	−	0.986392i	$-0.552572\pi$
$439$	12.7311	−	7.35033i	0.607624	−	0.350812i	0.772035	+	0.635580i	$0.219239\pi$
$440$		0			0
$441$	−3.98809	−	10.0602i	−0.189909	−	0.479055i
$442$		0			0
$443$	12.8615	+	22.2769i	0.611071	+	1.05841i	0.991060	+	0.133415i	$0.0425942\pi$
$443$	12.8615	+	22.2769i	0.611071	+	1.05841i	−0.379990	+	0.924991i	$0.624073\pi$
$444$		0			0
$445$	−10.4166	−	6.01404i	−0.493795	−	0.285093i
$446$		0			0
$447$		−	7.14741i		−	0.338061i
$448$		0			0
$449$			5.14935i			0.243013i	0.992591	+	0.121506i	$0.0387725\pi$
$449$			5.14935i			0.243013i	−0.992591	+	0.121506i	$0.961228\pi$
$450$		0			0
$451$	31.1975	−	54.0357i	1.46903	−	2.54444i
$452$		0			0
$453$	8.24997	−	4.76312i	0.387617	−	0.223791i
$454$		0			0
$455$	9.69665	−	4.69011i	0.454586	−	0.219876i
$456$		0			0
$457$	2.99204	+	5.18237i	0.139962	+	0.242421i	0.927482	−	0.373868i	$-0.121969\pi$
$457$	2.99204	+	5.18237i	0.139962	+	0.242421i	−0.787520	+	0.616289i	$0.788635\pi$
$458$		0			0
$459$	21.6153	−	6.60364i	1.00892	−	0.308232i
$460$		0			0
$461$	−23.4084			−1.09024			−0.545118	−	0.838359i	$-0.683515\pi$
$461$	−23.4084			−1.09024			−0.545118	+	0.838359i	$0.683515\pi$
$462$		0			0
$463$	−4.89401			−0.227444			−0.113722	−	0.993513i	$-0.536277\pi$
$463$	−4.89401			−0.227444			−0.113722	+	0.993513i	$0.536277\pi$
$464$		0			0
$465$	0.00698315	+	0.00403172i	0.000323836	+	0.000186967i
$466$		0			0
$467$	−0.537681	−	0.931290i	−0.0248809	−	0.0430950i	0.853317	−	0.521393i	$-0.174587\pi$
$467$	−0.537681	−	0.931290i	−0.0248809	−	0.0430950i	−0.878198	+	0.478298i	$0.841254\pi$
$468$		0			0
$469$	−7.52575	+	11.0789i	−0.347507	+	0.511577i
$470$		0			0
$471$	−14.4408	+	8.33739i	−0.665396	+	0.384166i
$472$		0			0
$473$	29.0919	+	16.7962i	1.33765	+	0.772290i
$474$		0			0
$475$	−3.47924			−0.159639
$476$		0			0
$477$	21.2805			0.974368
$478$		0			0
$479$	−12.2793	−	7.08944i	−0.561055	−	0.323925i	0.192514	−	0.981294i	$-0.438336\pi$
$479$	−12.2793	−	7.08944i	−0.561055	−	0.323925i	−0.753569	+	0.657369i	$0.771669\pi$
$480$		0			0
$481$	9.54236	−	5.50928i	0.435094	−	0.251202i
$482$		0			0
$483$	16.6623	+	1.22001i	0.758163	+	0.0555123i
$484$		0			0
$485$	4.49688	+	7.78883i	0.204193	+	0.353672i
$486$		0			0
$487$	−0.0335976	−	0.0193976i	−0.00152245	−	0.000878989i	0.499239	−	0.866465i	$-0.333613\pi$
$487$	−0.0335976	−	0.0193976i	−0.00152245	−	0.000878989i	−0.500761	+	0.865586i	$0.666946\pi$
$488$		0			0
$489$	−22.6523			−1.02437
$490$		0			0
$491$	−34.9950			−1.57930			−0.789652	−	0.613555i	$-0.789739\pi$
$491$	−34.9950			−1.57930			−0.789652	+	0.613555i	$0.789739\pi$
$492$		0			0
$493$	−15.0558	+	4.59967i	−0.678080	+	0.207159i
$494$		0			0
$495$	−3.96931	−	6.87505i	−0.178407	−	0.309010i
$496$		0			0
$497$	1.16201	−	15.8702i	0.0521231	−	0.711874i
$498$		0			0
$499$	−2.72495	+	1.57325i	−0.121986	+	0.0704285i	−0.559751	−	0.828661i	$-0.689103\pi$
$499$	−2.72495	+	1.57325i	−0.121986	+	0.0704285i	0.437766	+	0.899089i	$0.355770\pi$
$500$		0			0
$501$	−13.7329	+	23.7861i	−0.613542	+	1.06269i
$502$		0			0
$503$			9.81051i			0.437429i	0.975789	+	0.218715i	$0.0701864\pi$
$503$			9.81051i			0.437429i	−0.975789	+	0.218715i	$0.929814\pi$
$504$		0			0
$505$			8.36088i			0.372054i
$506$		0			0
$507$	−3.73289	−	2.15518i	−0.165783	−	0.0957151i
$508$		0			0
$509$	7.85529	+	13.6058i	0.348180	+	0.603065i	0.985926	−	0.167182i	$-0.0534666\pi$
$509$	7.85529	+	13.6058i	0.348180	+	0.603065i	−0.637747	+	0.770246i	$0.720133\pi$
$510$		0			0
$511$	19.6484	+	13.3469i	0.869194	+	0.590431i
$512$		0			0
$513$	16.5169	−	9.53604i	0.729239	−	0.421026i
$514$		0			0
$515$	−2.66880	−	1.54083i	−0.117601	−	0.0678972i
$516$		0			0
$517$			29.7311i			1.30757i
$518$		0			0
$519$	16.1641			0.709525
$520$		0			0
$521$	−10.7931	−	6.23141i	−0.472855	−	0.273003i	0.244579	−	0.969629i	$-0.421350\pi$
$521$	−10.7931	−	6.23141i	−0.472855	−	0.273003i	−0.717434	+	0.696626i	$0.754684\pi$
$522$		0			0
$523$	−13.8437	−	23.9780i	−0.605343	−	1.04848i	−0.991997	−	0.126260i	$-0.959703\pi$
$523$	−13.8437	−	23.9780i	−0.605343	−	1.04848i	0.386655	−	0.922225i	$-0.373631\pi$
$524$		0			0
$525$	2.87201	−	1.38915i	0.125345	−	0.0606273i
$526$		0			0
$527$	0.00620769	−	0.0268635i	0.000270411	−	0.00117019i
$528$		0			0
$529$	2.21176	−	3.83088i	0.0961634	−	0.166560i
$530$		0			0
$531$	9.71603			0.421640
$532$		0			0
$533$			49.4685i			2.14272i
$534$		0			0
$535$	9.32181	−	16.1458i	0.403017	−	0.698046i
$536$		0			0
$537$	16.9463	−	9.78396i	0.731288	−	0.422209i
$538$		0			0
$539$	−28.1796	−	22.3152i	−1.21378	−	0.961184i
$540$		0			0
$541$	4.95269	−	2.85944i	0.212933	−	0.122937i	−0.389741	−	0.920925i	$-0.627435\pi$
$541$	4.95269	−	2.85944i	0.212933	−	0.122937i	0.602674	+	0.797988i	$0.294102\pi$
$542$		0			0
$543$	−4.51338	+	7.81741i	−0.193688	+	0.335477i
$544$		0			0
$545$	−3.48286			−0.149189
$546$		0			0
$547$			19.7092i			0.842704i	0.906897	+	0.421352i	$0.138444\pi$
$547$			19.7092i			0.842704i	−0.906897	+	0.421352i	$0.861556\pi$
$548$		0			0
$549$	−2.19065	−	1.26478i	−0.0934949	−	0.0539793i
$550$		0			0
$551$	−11.5046	+	6.64219i	−0.490113	+	0.282967i
$552$		0			0
$553$	14.0065	−	6.77474i	0.595619	−	0.288091i
$554$		0			0
$555$	2.82631	−	1.63177i	0.119970	−	0.0692649i
$556$		0			0
$557$	2.09640	−	3.63107i	0.0888273	−	0.153853i	−0.818188	−	0.574950i	$-0.805021\pi$
$557$	2.09640	−	3.63107i	0.0888273	−	0.153853i	0.907016	+	0.421097i	$0.138355\pi$
$558$		0			0
$559$	−26.6330			−1.12645
$560$		0			0
$561$	17.4154	−	18.6681i	0.735277	−	0.788166i
$562$		0			0
$563$	−21.2651	+	36.8322i	−0.896217	+	1.55229i	−0.0639266	+	0.997955i	$0.520362\pi$
$563$	−21.2651	+	36.8322i	−0.896217	+	1.55229i	−0.832291	+	0.554339i	$0.812971\pi$
$564$		0			0
$565$	1.46759	+	2.54193i	0.0617418	+	0.106940i
$566$		0			0
$567$	−2.93178	+	4.31597i	−0.123123	+	0.181254i
$568$		0			0
$569$	−19.9970	−	34.6358i	−0.838318	−	1.45201i	−0.891300	−	0.453414i	$-0.850206\pi$
$569$	−19.9970	−	34.6358i	−0.838318	−	1.45201i	0.0529825	−	0.998595i	$-0.483127\pi$
$570$		0			0
$571$	5.28048	+	3.04869i	0.220981	+	0.127584i	0.606405	−	0.795156i	$-0.292611\pi$
$571$	5.28048	+	3.04869i	0.220981	+	0.127584i	−0.385423	+	0.922740i	$0.625945\pi$
$572$		0			0
$573$			1.80150i			0.0752589i
$574$		0			0
$575$		−	5.23675i		−	0.218387i
$576$		0			0
$577$	16.5865	−	28.7287i	0.690506	−	1.19599i	−0.281166	−	0.959659i	$-0.590721\pi$
$577$	16.5865	−	28.7287i	0.690506	−	1.19599i	0.971672	−	0.236333i	$-0.0759456\pi$
$578$		0			0
$579$	−8.11309	−	14.0523i	−0.337168	−	0.583993i
$580$		0			0
$581$	17.0494	+	1.24835i	0.707330	+	0.0517903i
$582$		0			0
$583$	61.2145	−	35.3422i	2.53525	−	1.46373i
$584$		0			0
$585$	5.45072	+	3.14698i	0.225360	+	0.130111i
$586$		0			0
$587$	45.2579			1.86799			0.933997	−	0.357281i	$-0.116296\pi$
$587$	45.2579			1.86799			0.933997	+	0.357281i	$0.116296\pi$
$588$		0			0
$589$		−	0.0232659i		−	0.000958654i
$590$		0			0
$591$	−0.255803	+	0.443065i	−0.0105223	+	0.0182252i
$592$		0			0
$593$	3.76623	+	6.52330i	0.154661	+	0.267880i	0.932935	−	0.360044i	$-0.117238\pi$
$593$	3.76623	+	6.52330i	0.154661	+	0.267880i	−0.778275	+	0.627924i	$0.783905\pi$
$594$		0			0
$595$	−7.41192	−	8.00397i	−0.303859	−	0.328131i
$596$		0			0
$597$	−9.68158	−	16.7690i	−0.396241	−	0.686309i
$598$		0			0
$599$	−12.8794	+	22.3079i	−0.526240	+	0.911474i	0.473293	+	0.880905i	$0.343065\pi$
$599$	−12.8794	+	22.3079i	−0.526240	+	0.911474i	−0.999533	+	0.0305689i	$0.990268\pi$
$600$		0			0
$601$			12.9515i			0.528304i	0.964481	+	0.264152i	$0.0850921\pi$
$601$			12.9515i			0.528304i	−0.964481	+	0.264152i	$0.914908\pi$
$602$		0			0
$603$	−7.82599			−0.318699
$604$		0			0
$605$	−13.3096	−	7.68429i	−0.541111	−	0.312411i
$606$		0			0
$607$	12.0957	−	6.98346i	0.490950	−	0.283450i	−0.234019	−	0.972232i	$-0.575188\pi$
$607$	12.0957	−	6.98346i	0.490950	−	0.283450i	0.724968	+	0.688782i	$0.241854\pi$
$608$		0			0
$609$	6.84472	−	10.0763i	0.277362	−	0.408314i
$610$		0			0
$611$	−11.7858	−	20.4136i	−0.476802	−	0.825846i
$612$		0			0
$613$	15.9922	−	27.6992i	0.645917	−	1.11876i	−0.338172	−	0.941084i	$-0.609809\pi$
$613$	15.9922	−	27.6992i	0.645917	−	1.11876i	0.984089	−	0.177677i	$-0.0568581\pi$
$614$		0			0
$615$			14.6519i			0.590821i
$616$		0			0
$617$		−	28.8328i		−	1.16077i	−0.814344	−	0.580383i	$-0.802903\pi$
$617$		−	28.8328i		−	1.16077i	0.814344	−	0.580383i	$-0.197097\pi$
$618$		0			0
$619$	1.33580	+	0.771223i	0.0536903	+	0.0309981i	0.526605	−	0.850110i	$-0.323465\pi$
$619$	1.33580	+	0.771223i	0.0536903	+	0.0309981i	−0.472915	+	0.881108i	$0.656798\pi$
$620$		0			0
$621$	14.3531	+	24.8602i	0.575969	+	0.997607i
$622$		0			0
$623$	−13.8566	−	28.6481i	−0.555155	−	1.14776i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	10.7717	−	18.6571i	0.430181	−	0.745095i
$628$		0			0
$629$	−8.15968	−	7.61213i	−0.325348	−	0.303515i
$630$		0			0
$631$	0.726321			0.0289144			0.0144572	−	0.999895i	$-0.495398\pi$
$631$	0.726321			0.0289144			0.0144572	+	0.999895i	$0.495398\pi$
$632$		0			0
$633$	3.19533	−	5.53447i	0.127003	−	0.219975i
$634$		0			0
$635$	3.73881	−	2.15861i	0.148370	−	0.0856616i
$636$		0			0
$637$	28.1944	+	4.15102i	1.11710	+	0.164469i
$638$		0			0
$639$	8.05241	−	4.64906i	0.318548	−	0.183914i
$640$		0			0
$641$	−17.6221	−	10.1741i	−0.696032	−	0.401854i	0.109836	−	0.993950i	$-0.464967\pi$
$641$	−17.6221	−	10.1741i	−0.696032	−	0.401854i	−0.805868	+	0.592096i	$0.798301\pi$
$642$		0			0
$643$		−	37.1266i		−	1.46413i	−0.681236	−	0.732064i	$-0.738557\pi$
$643$		−	37.1266i		−	1.46413i	0.681236	−	0.732064i	$-0.261443\pi$
$644$		0			0
$645$	−7.88831			−0.310602
$646$		0			0
$647$	12.0312	−	20.8387i	0.472996	−	0.819253i	−0.526527	−	0.850159i	$-0.676506\pi$
$647$	12.0312	−	20.8387i	0.472996	−	0.819253i	0.999522	+	0.0309061i	$0.00983927\pi$
$648$		0			0
$649$	27.9487	−	16.1362i	1.09708	−	0.633400i
$650$		0			0
$651$	0.00928929	+	0.0192053i	0.000364076	+	0.000752715i
$652$		0			0
$653$	−35.6530	+	20.5843i	−1.39521	+	0.805526i	−0.993886	−	0.110410i	$-0.964784\pi$
$653$	−35.6530	+	20.5843i	−1.39521	+	0.805526i	−0.401325	+	0.915936i	$0.631450\pi$
$654$		0			0
$655$	−9.67820	+	16.7631i	−0.378159	+	0.654990i
$656$		0			0
$657$			13.8793i			0.541484i
$658$		0			0
$659$	−35.3771			−1.37809			−0.689047	−	0.724717i	$-0.741971\pi$
$659$	−35.3771			−1.37809			−0.689047	+	0.724717i	$0.741971\pi$
$660$		0			0
$661$	−15.1954	+	26.3193i	−0.591034	+	1.02370i	0.403059	+	0.915174i	$0.367947\pi$
$661$	−15.1954	+	26.3193i	−0.591034	+	1.02370i	−0.994093	+	0.108528i	$0.965386\pi$
$662$		0			0
$663$	−4.55726	+	19.7213i	−0.176989	+	0.765912i
$664$		0			0
$665$	−7.61457	−	5.17246i	−0.295280	−	0.200580i
$666$		0			0
$667$	−9.99743	−	17.3161i	−0.387102	−	0.670480i
$668$		0			0
$669$	−18.8581	−	10.8877i	−0.729097	−	0.420945i
$670$		0			0
$671$	−8.40204			−0.324357
$672$		0			0
$673$			14.4200i			0.555850i	0.960603	+	0.277925i	$0.0896466\pi$
$673$			14.4200i			0.555850i	−0.960603	+	0.277925i	$0.910353\pi$
$674$		0			0
$675$	4.74727	+	2.74084i	0.182722	+	0.105495i
$676$		0			0
$677$	10.8797	−	6.28138i	0.418140	−	0.241413i	−0.276141	−	0.961117i	$-0.589056\pi$
$677$	10.8797	−	6.28138i	0.418140	−	0.241413i	0.694281	+	0.719704i	$0.255722\pi$
$678$		0			0
$679$	−1.73763	+	23.7317i	−0.0666840	+	0.910740i
$680$		0			0
$681$	−0.397605	−	0.688672i	−0.0152362	−	0.0263900i
$682$		0			0
$683$	12.7368	+	7.35358i	0.487359	+	0.281377i	0.723478	−	0.690347i	$-0.242542\pi$
$683$	12.7368	+	7.35358i	0.487359	+	0.281377i	−0.236119	+	0.971724i	$0.575876\pi$
$684$		0			0
$685$		−	4.30121i		−	0.164341i
$686$		0			0
$687$		−	22.8052i		−	0.870073i
$688$		0			0
$689$	−28.0203	+	48.5325i	−1.06749	+	1.84894i
$690$		0			0
$691$	−5.65962	+	3.26758i	−0.215302	+	0.124305i	−0.603773	−	0.797156i	$-0.706337\pi$
$691$	−5.65962	+	3.26758i	−0.215302	+	0.124305i	0.388471	+	0.921461i	$0.373003\pi$
$692$		0			0
$693$	1.53377	−	20.9475i	0.0582631	−	0.795731i
$694$		0			0
$695$	−9.06938	−	15.7086i	−0.344021	−	0.595862i
$696$		0			0
$697$	47.9131	−	14.6378i	1.81484	−	0.554448i
$698$		0			0
$699$	23.1573			0.875888
$700$		0			0
$701$	−23.7522			−0.897107			−0.448554	−	0.893756i	$-0.648061\pi$
$701$	−23.7522			−0.897107			−0.448554	+	0.893756i	$0.648061\pi$
$702$		0			0
$703$	−8.15491	−	4.70824i	−0.307568	−	0.177575i
$704$		0			0
$705$	−3.49079	−	6.04622i	−0.131471	−	0.227714i
$706$		0			0
$707$	−12.4298	+	18.2984i	−0.467471	+	0.688181i
$708$		0			0
$709$	25.5170	−	14.7323i	0.958312	−	0.553282i	0.0626590	−	0.998035i	$-0.480042\pi$
$709$	25.5170	−	14.7323i	0.958312	−	0.553282i	0.895653	+	0.444753i	$0.146709\pi$
$710$		0			0
$711$	7.87341	+	4.54572i	0.295276	+	0.170478i
$712$		0			0
$713$	0.0350184			0.00131145
$714$		0			0
$715$	20.9057			0.781829
$716$		0			0
$717$	−24.3892	−	14.0811i	−0.910830	−	0.525868i
$718$		0			0
$719$	19.4819	−	11.2479i	0.726552	−	0.419475i	−0.0906077	−	0.995887i	$-0.528881\pi$
$719$	19.4819	−	11.2479i	0.726552	−	0.419475i	0.817159	+	0.576412i	$0.195548\pi$
$720$		0			0
$721$	−3.55016	−	7.33983i	−0.132215	−	0.273350i
$722$		0			0
$723$	−3.44637	−	5.96929i	−0.128172	−	0.222000i
$724$		0			0
$725$	−3.30664	−	1.90909i	−0.122806	−	0.0709019i
$726$		0			0
$727$	−39.7897			−1.47572			−0.737859	−	0.674955i	$-0.764163\pi$
$727$	−39.7897			−1.47572			−0.737859	+	0.674955i	$0.764163\pi$
$728$		0			0
$729$	−22.8786			−0.847357
$730$		0			0
$731$	7.88076	+	25.7956i	0.291480	+	0.954085i
$732$		0			0
$733$	2.70061	+	4.67759i	0.0997491	+	0.172771i	0.911581	−	0.411121i	$-0.134863\pi$
$733$	2.70061	+	4.67759i	0.0997491	+	0.172771i	−0.811832	+	0.583892i	$0.801529\pi$
$734$		0			0
$735$	8.35079	+	1.22947i	0.308024	+	0.0453498i
$736$		0			0
$737$	−22.5119	+	12.9972i	−0.829235	+	0.478759i
$738$		0			0
$739$	−10.8471	+	18.7877i	−0.399016	+	0.691116i	−0.993605	−	0.112914i	$-0.963982\pi$
$739$	−10.8471	+	18.7877i	−0.399016	+	0.691116i	0.594589	+	0.804030i	$0.297315\pi$
$740$		0			0
$741$			17.0802i			0.627457i
$742$		0			0
$743$			17.5597i			0.644201i	0.946705	+	0.322101i	$0.104389\pi$
$743$			17.5597i			0.644201i	−0.946705	+	0.322101i	$0.895611\pi$
$744$		0			0
$745$	−5.13326	−	2.96369i	−0.188068	−	0.108581i
$746$		0			0
$747$	4.99452	+	8.65077i	0.182740	+	0.316515i
$748$		0			0
$749$	44.4048	−	21.4779i	1.62252	−	0.784785i
$750$		0			0
$751$	2.84809	−	1.64435i	0.103928	−	0.0600031i	−0.447135	−	0.894467i	$-0.647556\pi$
$751$	2.84809	−	1.64435i	0.103928	−	0.0600031i	0.551063	+	0.834463i	$0.314222\pi$
$752$		0			0
$753$	17.0611	+	9.85022i	0.621741	+	0.358962i
$754$		0			0
$755$		−	7.90015i		−	0.287516i
$756$		0			0
$757$	−10.0519			−0.365342			−0.182671	−	0.983174i	$-0.558474\pi$
$757$	−10.0519			−0.365342			−0.182671	+	0.983174i	$0.558474\pi$
$758$		0			0
$759$	28.0816	+	16.2129i	1.01930	+	0.588492i
$760$		0			0
$761$	16.3621	+	28.3400i	0.593125	+	1.02732i	0.993808	+	0.111107i	$0.0354395\pi$
$761$	16.3621	+	28.3400i	0.593125	+	1.02732i	−0.400683	+	0.916217i	$0.631227\pi$
$762$		0			0
$763$	−7.62248	−	5.17784i	−0.275952	−	0.187450i
$764$		0			0
$765$	1.43515	−	6.21055i	0.0518879	−	0.224543i
$766$		0			0
$767$	−12.7932	+	22.1584i	−0.461935	+	0.800095i
$768$		0			0
$769$	−24.4696			−0.882396			−0.441198	−	0.897410i	$-0.645446\pi$
$769$	−24.4696			−0.882396			−0.441198	+	0.897410i	$0.645446\pi$
$770$		0			0
$771$		−	2.51136i		−	0.0904443i
$772$		0			0
$773$	−7.11250	+	12.3192i	−0.255819	+	0.443091i	−0.965118	−	0.261817i	$-0.915678\pi$
$773$	−7.11250	+	12.3192i	−0.255819	+	0.443091i	0.709299	+	0.704908i	$0.249012\pi$
$774$		0			0
$775$	0.00579115	−	0.00334352i	0.000208024	−	0.000120103i
$776$		0			0
$777$	8.61148	+	0.630528i	0.308935	+	0.0226201i
$778$		0			0
$779$	36.6119	−	21.1379i	1.31176	−	0.757344i
$780$		0			0
$781$	15.4421	−	26.7465i	0.552562	−	0.957066i
$782$		0			0
$783$	20.9300			0.747978
$784$		0			0
$785$			13.8285i			0.493559i
$786$		0			0
$787$	−7.82186	−	4.51596i	−0.278819	−	0.160976i	0.354069	−	0.935219i	$-0.384798\pi$
$787$	−7.82186	−	4.51596i	−0.278819	−	0.160976i	−0.632889	+	0.774243i	$0.718131\pi$
$788$		0			0
$789$	29.3537	−	16.9474i	1.04502	−	0.603342i
$790$		0			0
$791$	−0.567086	+	7.74501i	−0.0201632	+	0.275381i
$792$		0			0
$793$	5.76891	−	3.33068i	0.204860	−	0.118276i
$794$		0			0
$795$	−8.29921	+	14.3747i	−0.294343	+	0.509817i
$796$		0			0
$797$	−49.2978			−1.74622			−0.873109	−	0.487526i	$-0.837899\pi$
$797$	−49.2978			−1.74622			−0.873109	+	0.487526i	$0.837899\pi$
$798$		0			0
$799$	−16.2843	+	17.4557i	−0.576098	+	0.617537i
$800$		0			0
$801$	9.29754	−	16.1038i	0.328512	−	0.569000i
$802$		0			0
$803$	23.0505	+	39.9246i	0.813434	+	1.40891i
$804$		0			0
$805$	7.78528	−	11.4610i	0.274395	−	0.403947i
$806$		0			0
$807$	−10.3469	−	17.9213i	−0.364227	−	0.630860i
$808$		0			0
$809$	46.0777	+	26.6030i	1.62001	+	0.935311i	0.986917	+	0.161232i	$0.0515468\pi$
$809$	46.0777	+	26.6030i	1.62001	+	0.935311i	0.633089	+	0.774079i	$0.281787\pi$
$810$		0			0
$811$			41.7704i			1.46676i	0.679821	+	0.733378i	$0.262057\pi$
$811$			41.7704i			1.46676i	−0.679821	+	0.733378i	$0.737943\pi$
$812$		0			0
$813$		−	13.8260i		−	0.484900i
$814$		0			0
$815$	−9.39283	+	16.2689i	−0.329016	+	0.569873i
$816$		0			0
$817$	11.3803	+	19.7112i	0.398145	+	0.689608i
$818$		0			0
$819$	7.25079	+	14.9908i	0.253363	+	0.523819i
$820$		0			0
$821$	−34.3634	+	19.8397i	−1.19929	+	0.692412i	−0.960397	−	0.278634i	$-0.910118\pi$
$821$	−34.3634	+	19.8397i	−1.19929	+	0.692412i	−0.238895	+	0.971046i	$0.576785\pi$
$822$		0			0
$823$	28.4177	+	16.4070i	0.990579	+	0.571911i	0.905447	−	0.424458i	$-0.139536\pi$
$823$	28.4177	+	16.4070i	0.990579	+	0.571911i	0.0851319	+	0.996370i	$0.472869\pi$
$824$		0			0
$825$	6.19198			0.215577
$826$		0			0
$827$			4.22679i			0.146980i	0.997296	+	0.0734899i	$0.0234137\pi$
$827$			4.22679i			0.146980i	−0.997296	+	0.0734899i	$0.976586\pi$
$828$		0			0
$829$	−22.0876	+	38.2569i	−0.767135	+	1.32872i	0.171976	+	0.985101i	$0.444985\pi$
$829$	−22.0876	+	38.2569i	−0.767135	+	1.32872i	−0.939110	+	0.343615i	$0.888348\pi$
$830$		0			0
$831$	−2.29132	−	3.96868i	−0.0794850	−	0.137672i
$832$		0			0
$833$	−4.32229	−	28.5363i	−0.149759	−	0.988723i
$834$		0			0
$835$	11.3888	+	19.7259i	0.394125	+	0.682644i
$836$		0			0
$837$	−0.0183281	+	0.0317452i	−0.000633512	+	0.00109727i
$838$		0			0
$839$			17.5893i			0.607249i	0.952792	+	0.303624i	$0.0981968\pi$
$839$			17.5893i			0.607249i	−0.952792	+	0.303624i	$0.901803\pi$
$840$		0			0
$841$	14.4215			0.497293
$842$		0			0
$843$	−10.8019	−	6.23646i	−0.372036	−	0.214795i
$844$		0			0
$845$	−3.09570	+	1.78730i	−0.106495	+	0.0614851i
$846$		0			0
$847$	−17.7050	−	36.6044i	−0.608350	−	1.25774i
$848$		0			0
$849$	−9.29362	−	16.0970i	−0.318956	−	0.552448i
$850$		0			0
$851$	7.08655	−	12.2743i	0.242924	−	0.420757i
$852$		0			0
$853$			33.8296i			1.15830i	0.815219	+	0.579152i	$0.196616\pi$
$853$			33.8296i			1.15830i	−0.815219	+	0.579152i	$0.803384\pi$
$854$		0			0
$855$		−	5.37882i		−	0.183952i
$856$		0			0
$857$	−31.6736	−	18.2868i	−1.08195	−	0.624664i	−0.150528	−	0.988606i	$-0.548097\pi$
$857$	−31.6736	−	18.2868i	−1.08195	−	0.624664i	−0.931422	+	0.363942i	$0.881431\pi$
$858$		0			0
$859$	14.9858	+	25.9561i	0.511308	+	0.885611i	0.999914	+	0.0131068i	$0.00417214\pi$
$859$	14.9858	+	25.9561i	0.511308	+	0.885611i	−0.488606	+	0.872504i	$0.662495\pi$
$860$		0			0
$861$	−21.7824	+	32.0666i	−0.742342	+	1.09283i
$862$		0			0
$863$	9.69410	+	16.7907i	0.329991	+	0.571561i	0.982510	−	0.186212i	$-0.0596210\pi$
$863$	9.69410	+	16.7907i	0.329991	+	0.571561i	−0.652519	+	0.757773i	$0.726288\pi$
$864$		0			0
$865$	6.70248	−	11.6090i	0.227891	−	0.394719i
$866$		0			0
$867$	20.4498	−	1.42162i	0.694510	−	0.0482806i
$868$		0			0
$869$	30.1977			1.02439
$870$		0			0
$871$	10.3046	−	17.8480i	0.349156	−	0.604757i
$872$		0			0
$873$	−12.0413	+	6.95206i	−0.407537	+	0.235291i
$874$		0			0
$875$	0.193203	−	2.63869i	0.00653147	−	0.0892039i
$876$		0			0
$877$	11.0936	−	6.40491i	0.374605	−	0.216279i	−0.300863	−	0.953667i	$-0.597275\pi$
$877$	11.0936	−	6.40491i	0.374605	−	0.216279i	0.675469	+	0.737389i	$0.263941\pi$
$878$		0			0
$879$	−16.1737	−	9.33790i	−0.545526	−	0.314960i
$880$		0			0
$881$			29.9050i			1.00752i	0.863842	+	0.503762i	$0.168051\pi$
$881$			29.9050i			1.00752i	−0.863842	+	0.503762i	$0.831949\pi$
$882$		0			0
$883$	4.29501			0.144538			0.0722692	−	0.997385i	$-0.476976\pi$
$883$	4.29501			0.144538			0.0722692	+	0.997385i	$0.476976\pi$
$884$		0			0
$885$	−3.78916	+	6.56302i	−0.127371	+	0.220614i
$886$		0			0
$887$	8.55747	−	4.94066i	0.287332	−	0.165891i	−0.349406	−	0.936971i	$-0.613617\pi$
$887$	8.55747	−	4.94066i	0.287332	−	0.165891i	0.636738	+	0.771080i	$0.280283\pi$
$888$		0			0
$889$	11.3918	+	0.834100i	0.382068	+	0.0279748i
$890$		0			0
$891$	−8.76985	+	5.06328i	−0.293801	+	0.169626i
$892$		0			0
$893$	−10.0722	+	17.4455i	−0.337052	+	0.583791i
$894$		0			0
$895$		−	16.2278i		−	0.542434i
$896$		0			0
$897$	−25.7081			−0.858367
$898$		0			0
$899$	0.0127662	−	0.0221117i	0.000425776	−	0.000737466i
$900$		0			0
$901$	55.2979	+	12.7784i	1.84224	+	0.425710i
$902$		0			0
$903$	−17.2641	−	11.7273i	−0.574514	−	0.390259i
$904$		0			0
$905$	3.74296	+	6.48301i	0.124420	+	0.215502i
$906$		0			0
$907$	−47.8008	−	27.5978i	−1.58720	−	0.916370i	−0.993766	−	0.111487i	$-0.964439\pi$
$907$	−47.8008	−	27.5978i	−1.58720	−	0.916370i	−0.593433	−	0.804883i	$-0.702228\pi$
$908$		0			0
$909$	−12.9257			−0.428718
$910$		0			0
$911$		−	24.1925i		−	0.801533i	−0.916180	−	0.400767i	$-0.868744\pi$
$911$		−	24.1925i		−	0.801533i	0.916180	−	0.400767i	$-0.131256\pi$
$912$		0			0
$913$	28.7340	+	16.5896i	0.950957	+	0.549035i
$914$		0			0
$915$	1.70867	−	0.986502i	0.0564869	−	0.0326127i
$916$		0			0
$917$	−46.1025	+	22.2991i	−1.52244	+	0.736380i
$918$		0			0
$919$	21.2620	+	36.8269i	0.701370	+	1.21481i	0.967986	+	0.251005i	$0.0807611\pi$
$919$	21.2620	+	36.8269i	0.701370	+	1.21481i	−0.266616	+	0.963803i	$0.585906\pi$
$920$		0			0
$921$	26.4927	+	15.2956i	0.872965	+	0.504007i
$922$		0			0
$923$			24.4858i			0.805961i
$924$		0			0
$925$		−	2.70647i		−	0.0889882i
$926$		0			0
$927$	2.38209	−	4.12589i	0.0782380	−	0.135512i
$928$		0			0
$929$	−38.8284	+	22.4176i	−1.27392	+	0.735497i	−0.975723	−	0.219007i	$-0.929718\pi$
$929$	−38.8284	+	22.4176i	−1.27392	+	0.735497i	−0.298196	+	0.954505i	$0.596385\pi$
$930$		0			0
$931$	−8.97529	−	22.6406i	−0.294153	−	0.742015i
$932$		0			0
$933$	6.66661	+	11.5469i	0.218255	+	0.378029i
$934$		0			0
$935$	−6.18605	−	20.2484i	−0.202306	−	0.662194i
$936$		0			0
$937$	−17.2285			−0.562829			−0.281415	−	0.959586i	$-0.590804\pi$
$937$	−17.2285			−0.562829			−0.281415	+	0.959586i	$0.590804\pi$
$938$		0			0
$939$	−24.2938			−0.792797
$940$		0			0
$941$	−27.4327	−	15.8383i	−0.894281	−	0.516314i	−0.0189408	−	0.999821i	$-0.506029\pi$
$941$	−27.4327	−	15.8383i	−0.894281	−	0.516314i	−0.875340	+	0.483507i	$0.839363\pi$
$942$		0			0
$943$	31.8155	+	55.1060i	1.03605	+	1.79450i
$944$		0			0
$945$	6.31502	+	13.0561i	0.205428	+	0.424715i
$946$		0			0
$947$	−10.4797	+	6.05046i	−0.340545	+	0.196614i	−0.660513	−	0.750815i	$-0.729661\pi$
$947$	−10.4797	+	6.05046i	−0.340545	+	0.196614i	0.319968	+	0.947428i	$0.396328\pi$
$948$		0			0
$949$	−31.6533	−	18.2750i	−1.02751	−	0.593233i
$950$		0			0
$951$	22.8609			0.741316
$952$		0			0
$953$	−15.9775			−0.517562			−0.258781	−	0.965936i	$-0.583321\pi$
$953$	−15.9775			−0.517562			−0.258781	+	0.965936i	$0.583321\pi$
$954$		0			0
$955$	1.29384	+	0.746997i	0.0418676	+	0.0241722i
$956$		0			0
$957$	20.4747	−	11.8211i	0.661852	−	0.382120i
$958$		0			0
$959$	6.39444	−	9.41349i	0.206487	−	0.303977i
$960$		0			0
$961$	−15.5000	−	26.8467i	−0.499999	−	0.866024i
$962$		0			0
$963$	24.9610	+	14.4113i	0.804358	+	0.464396i
$964$		0			0
$965$	−13.4564			−0.433178
$966$		0			0
$967$	17.9459			0.577101			0.288550	−	0.957465i	$-0.406827\pi$
$967$	17.9459			0.577101			0.288550	+	0.957465i	$0.406827\pi$
$968$		0			0
$969$	16.5432	−	5.05407i	0.531444	−	0.162360i
$970$		0			0
$971$	−8.64970	−	14.9817i	−0.277582	−	0.480786i	0.693201	−	0.720744i	$-0.256200\pi$
$971$	−8.64970	−	14.9817i	−0.277582	−	0.480786i	−0.970783	+	0.239958i	$0.922866\pi$
$972$		0			0
$973$	3.50447	−	47.8625i	0.112348	−	1.53440i
$974$		0			0
$975$	−4.25146	+	2.45458i	−0.136156	+	0.0786096i
$976$		0			0
$977$	10.9734	−	19.0064i	0.351069	−	0.608070i	−0.635368	−	0.772210i	$-0.719152\pi$
$977$	10.9734	−	19.0064i	0.351069	−	0.608070i	0.986437	+	0.164140i	$0.0524849\pi$
$978$		0			0
$979$		−	61.7646i		−	1.97400i
$980$		0			0
$981$		−	5.38440i		−	0.171911i
$982$		0			0
$983$	−37.4822	−	21.6404i	−1.19550	−	0.690221i	−0.235950	−	0.971765i	$-0.575820\pi$
$983$	−37.4822	−	21.6404i	−1.19550	−	0.690221i	−0.959548	+	0.281544i	$0.909153\pi$
$984$		0			0
$985$	0.212139	+	0.367435i	0.00675930	+	0.0117075i
$986$		0			0
$987$	1.34886	−	18.4222i	0.0429348	−	0.586385i
$988$		0			0
$989$	−29.6681	+	17.1289i	−0.943391	+	0.544667i
$990$		0			0
$991$	36.8006	+	21.2469i	1.16901	+	0.674929i	0.953447	−	0.301561i	$-0.0975078\pi$
$991$	36.8006	+	21.2469i	1.16901	+	0.674929i	0.215564	+	0.976490i	$0.430841\pi$
$992$		0			0
$993$			26.6250i			0.844918i
$994$		0			0
$995$	−16.0580			−0.509071
$996$		0			0
$997$	−52.6484	−	30.3966i	−1.66739	−	0.962669i	−0.969037	−	0.246917i	$-0.920583\pi$
$997$	−52.6484	−	30.3966i	−1.66739	−	0.962669i	−0.698355	−	0.715752i	$-0.746084\pi$
$998$		0			0
$999$	7.41800	+	12.8483i	0.234695	+	0.406504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2380.2.cb.b.781.17	✓	92
7.2	even	3	inner	2380.2.cb.b.1801.30	yes	92
17.16	even	2	inner	2380.2.cb.b.781.30	yes	92
119.16	even	6	inner	2380.2.cb.b.1801.17	yes	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2380.2.cb.b.781.17	✓	92	1.1	even	1	trivial
2380.2.cb.b.781.30	yes	92	17.16	even	2	inner
2380.2.cb.b.1801.17	yes	92	119.16	even	6	inner
2380.2.cb.b.1801.30	yes	92	7.2	even	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2380 = 2^{2} \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2380.cb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04428 - 0.602915i) q^{3} +(-0.866025 + 0.500000i) q^{5} +(-2.63869 - 0.193203i) q^{7} +(-0.772986 - 1.33885i) q^{9} +(-4.44707 - 2.56752i) q^{11} +4.07119 q^{13} +1.20583 q^{15} +(-1.20468 - 3.94319i) q^{17} +(-1.73962 - 3.01311i) q^{19} +(2.63904 + 1.79266i) q^{21} +(4.53516 - 2.61837i) q^{23} +(0.500000 - 0.866025i) q^{25} +5.48167i q^{27} -3.81818i q^{29} +(0.00579115 + 0.00334352i) q^{31} +(3.09599 + 5.36241i) q^{33} +(2.38177 - 1.15202i) q^{35} +(2.34387 - 1.35324i) q^{37} +(-4.25146 - 2.45458i) q^{39} +12.1509i q^{41} -6.54181 q^{43} +(1.33885 + 0.772986i) q^{45} +(-2.89492 - 5.01416i) q^{47} +(6.92534 + 1.01961i) q^{49} +(-1.11939 + 4.84411i) q^{51} +(-6.88257 + 11.9210i) q^{53} +5.13503 q^{55} +4.19538i q^{57} +(-3.14237 + 5.44274i) q^{59} +(1.41701 - 0.818110i) q^{61} +(1.78100 + 3.68215i) q^{63} +(-3.52576 + 2.03560i) q^{65} +(2.53109 - 4.38398i) q^{67} -6.31463 q^{69} +6.01442i q^{71} +(-7.77495 - 4.48887i) q^{73} +(-1.04428 + 0.602915i) q^{75} +(11.2384 + 7.63406i) q^{77} +(-5.09285 + 2.94036i) q^{79} +(0.986026 - 1.70785i) q^{81} -6.46133 q^{83} +(3.01488 + 2.81257i) q^{85} +(-2.30204 + 3.98725i) q^{87} +(6.01404 + 10.4166i) q^{89} +(-10.7426 - 0.786568i) q^{91} +(-0.00403172 - 0.00698315i) q^{93} +(3.01311 + 1.73962i) q^{95} -8.99376i q^{97} +7.93862i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 56 q^{9} - 24 q^{13} + 12 q^{15} + 4 q^{17} - 24 q^{21} + 46 q^{25} - 24 q^{33} + 14 q^{35} - 64 q^{43} + 16 q^{47} + 38 q^{49} - 22 q^{51} - 8 q^{53} + 18 q^{59} + 16 q^{67} - 36 q^{69} - 12 q^{77}+ \cdots + 44 q^{93}+O(q^{100}) \) 92 * q + 56 * q^9 - 24 * q^13 + 12 * q^15 + 4 * q^17 - 24 * q^21 + 46 * q^25 - 24 * q^33 + 14 * q^35 - 64 * q^43 + 16 * q^47 + 38 * q^49 - 22 * q^51 - 8 * q^53 + 18 * q^59 + 16 * q^67 - 36 * q^69 - 12 * q^77 - 86 * q^81 + 8 * q^83 - 20 * q^85 + 20 * q^87 + 2 * q^89 + 44 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more