LMFDB - Embedded newform 480.4.bh.a.367.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [480,4,Mod(367,480)] 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("480.367"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(480, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 480 = 2^{5} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	480.bh (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$28.3209168028$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			367.12
Character	$\chi$	$=$	480.367
Dual form			480.4.bh.a.463.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.12132 + 2.12132i) q^{3} +(11.0300 - 1.82735i) q^{5} +(-11.6097 + 11.6097i) q^{7} -9.00000i q^{9} +20.2769 q^{11} +(8.16329 + 8.16329i) q^{13} +(-19.5217 + 27.2746i) q^{15} +(-3.34192 - 3.34192i) q^{17} +109.155i q^{19} -49.2559i q^{21} +(-84.1466 - 84.1466i) q^{23} +(118.322 - 40.3114i) q^{25} +(19.0919 + 19.0919i) q^{27} +179.844 q^{29} +233.332i q^{31} +(-43.0138 + 43.0138i) q^{33} +(-106.840 + 149.270i) q^{35} +(-1.33380 + 1.33380i) q^{37} -34.6339 q^{39} -417.266 q^{41} +(-126.668 + 126.668i) q^{43} +(-16.4462 - 99.2699i) q^{45} +(330.363 - 330.363i) q^{47} +73.4285i q^{49} +14.1786 q^{51} +(232.918 + 232.918i) q^{53} +(223.654 - 37.0531i) q^{55} +(-231.552 - 231.552i) q^{57} +661.807i q^{59} +648.727i q^{61} +(104.488 + 104.488i) q^{63} +(104.958 + 75.1238i) q^{65} +(-500.969 - 500.969i) q^{67} +357.004 q^{69} +289.500i q^{71} +(-618.051 + 618.051i) q^{73} +(-165.484 + 336.511i) q^{75} +(-235.409 + 235.409i) q^{77} +24.6078 q^{79} -81.0000 q^{81} +(-501.575 + 501.575i) q^{83} +(-42.9682 - 30.7545i) q^{85} +(-381.507 + 381.507i) q^{87} +1256.38i q^{89} -189.547 q^{91} +(-494.973 - 494.973i) q^{93} +(199.464 + 1203.98i) q^{95} +(874.108 + 874.108i) q^{97} -182.492i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 104 q^{17} - 88 q^{25} - 912 q^{35} - 864 q^{43} + 1488 q^{51} - 1048 q^{65} - 3696 q^{67} + 1480 q^{73} - 5832 q^{81} + 5360 q^{83} - 3392 q^{91} - 328 q^{97}+O(q^{100}) $ 72 * q - 104 * q^17 - 88 * q^25 - 912 * q^35 - 864 * q^43 + 1488 * q^51 - 1048 * q^65 - 3696 * q^67 + 1480 * q^73 - 5832 * q^81 + 5360 * q^83 - 3392 * q^91 - 328 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/480\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$421$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.12132	+	2.12132i	−0.408248	+	0.408248i
$3$	−2.12132	+	2.12132i	−0.408248	+	0.408248i
$4$		0			0
$5$	11.0300	−	1.82735i	0.986553	−	0.163444i
$5$	11.0300	−	1.82735i	0.986553	−	0.163444i
$6$		0			0
$7$	−11.6097	+	11.6097i	−0.626866	+	0.626866i	−0.947278	−	0.320412i	$-0.896179\pi$
$7$	−11.6097	+	11.6097i	−0.626866	+	0.626866i	0.320412	+	0.947278i	$0.396179\pi$
$8$		0			0
$9$		−	9.00000i		−	0.333333i
$10$		0			0
$11$	20.2769			0.555793			0.277896	−	0.960611i	$-0.410363\pi$
$11$	20.2769			0.555793			0.277896	+	0.960611i	$0.410363\pi$
$12$		0			0
$13$	8.16329	+	8.16329i	0.174161	+	0.174161i	0.788805	−	0.614644i	$-0.210700\pi$
$13$	8.16329	+	8.16329i	0.174161	+	0.174161i	−0.614644	+	0.788805i	$0.710700\pi$
$14$		0			0
$15$	−19.5217	+	27.2746i	−0.336033	+	0.469484i
$16$		0			0
$17$	−3.34192	−	3.34192i	−0.0476785	−	0.0476785i	0.682866	−	0.730544i	$-0.260733\pi$
$17$	−3.34192	−	3.34192i	−0.0476785	−	0.0476785i	−0.730544	+	0.682866i	$0.760733\pi$
$18$		0			0
$19$			109.155i			1.31799i	0.752148	+	0.658995i	$0.229018\pi$
$19$			109.155i			1.31799i	−0.752148	+	0.658995i	$0.770982\pi$
$20$		0			0
$21$		−	49.2559i		−	0.511834i
$22$		0			0
$23$	−84.1466	−	84.1466i	−0.762860	−	0.762860i	0.213979	−	0.976838i	$-0.431358\pi$
$23$	−84.1466	−	84.1466i	−0.762860	−	0.762860i	−0.976838	+	0.213979i	$0.931358\pi$
$24$		0			0
$25$	118.322	−	40.3114i	0.946572	−	0.322491i
$26$		0			0
$27$	19.0919	+	19.0919i	0.136083	+	0.136083i
$28$		0			0
$29$	179.844			1.15159			0.575797	−	0.817593i	$-0.304692\pi$
$29$	179.844			1.15159			0.575797	+	0.817593i	$0.304692\pi$
$30$		0			0
$31$			233.332i			1.35186i	0.736965	+	0.675931i	$0.236258\pi$
$31$			233.332i			1.35186i	−0.736965	+	0.675931i	$0.763742\pi$
$32$		0			0
$33$	−43.0138	+	43.0138i	−0.226901	+	0.226901i
$34$		0			0
$35$	−106.840	+	149.270i	−0.515979	+	0.720894i
$36$		0			0
$37$	−1.33380	+	1.33380i	−0.00592635	+	0.00592635i	−0.710064	−	0.704137i	$-0.751334\pi$
$37$	−1.33380	+	1.33380i	−0.00592635	+	0.00592635i	0.704137	+	0.710064i	$0.251334\pi$
$38$		0			0
$39$	−34.6339			−0.142202
$40$		0			0
$41$	−417.266			−1.58941			−0.794707	−	0.606993i	$-0.792376\pi$
$41$	−417.266			−1.58941			−0.794707	+	0.606993i	$0.792376\pi$
$42$		0			0
$43$	−126.668	+	126.668i	−0.449226	+	0.449226i	−0.895097	−	0.445871i	$-0.852894\pi$
$43$	−126.668	+	126.668i	−0.449226	+	0.449226i	0.445871	+	0.895097i	$0.352894\pi$
$44$		0			0
$45$	−16.4462	−	99.2699i	−0.0544812	−	0.328851i
$46$		0			0
$47$	330.363	−	330.363i	1.02528	−	1.02528i	0.0256124	−	0.999672i	$-0.491846\pi$
$47$	330.363	−	330.363i	1.02528	−	1.02528i	0.999672	−	0.0256124i	$-0.00815357\pi$
$48$		0			0
$49$			73.4285i			0.214077i
$50$		0			0
$51$	14.1786			0.0389293
$52$		0			0
$53$	232.918	+	232.918i	0.603656	+	0.603656i	0.941281	−	0.337625i	$-0.109623\pi$
$53$	232.918	+	232.918i	0.603656	+	0.603656i	−0.337625	+	0.941281i	$0.609623\pi$
$54$		0			0
$55$	223.654	−	37.0531i	0.548319	−	0.0908407i
$56$		0			0
$57$	−231.552	−	231.552i	−0.538067	−	0.538067i
$58$		0			0
$59$			661.807i			1.46034i	0.683267	+	0.730169i	$0.260559\pi$
$59$			661.807i			1.46034i	−0.683267	+	0.730169i	$0.739441\pi$
$60$		0			0
$61$			648.727i			1.36166i	0.732443	+	0.680828i	$0.238380\pi$
$61$			648.727i			1.36166i	−0.732443	+	0.680828i	$0.761620\pi$
$62$		0			0
$63$	104.488	+	104.488i	0.208955	+	0.208955i
$64$		0			0
$65$	104.958	+	75.1238i	0.200284	+	0.143353i
$66$		0			0
$67$	−500.969	−	500.969i	−0.913479	−	0.913479i	0.0830648	−	0.996544i	$-0.473529\pi$
$67$	−500.969	−	500.969i	−0.913479	−	0.913479i	−0.996544	+	0.0830648i	$0.973529\pi$
$68$		0			0
$69$	357.004			0.622872
$70$		0			0
$71$			289.500i			0.483905i	0.970288	+	0.241953i	$0.0777879\pi$
$71$			289.500i			0.483905i	−0.970288	+	0.241953i	$0.922212\pi$
$72$		0			0
$73$	−618.051	+	618.051i	−0.990924	+	0.990924i	−0.999959	−	0.00903536i	$-0.997124\pi$
$73$	−618.051	+	618.051i	−0.990924	+	0.990924i	0.00903536	+	0.999959i	$0.497124\pi$
$74$		0			0
$75$	−165.484	+	336.511i	−0.254780	+	0.518093i
$76$		0			0
$77$	−235.409	+	235.409i	−0.348408	+	0.348408i
$78$		0			0
$79$	24.6078			0.0350454			0.0175227	−	0.999846i	$-0.494422\pi$
$79$	24.6078			0.0350454			0.0175227	+	0.999846i	$0.494422\pi$
$80$		0			0
$81$	−81.0000			−0.111111
$82$		0			0
$83$	−501.575	+	501.575i	−0.663314	+	0.663314i	−0.956160	−	0.292846i	$-0.905398\pi$
$83$	−501.575	+	501.575i	−0.663314	+	0.663314i	0.292846	+	0.956160i	$0.405398\pi$
$84$		0			0
$85$	−42.9682	−	30.7545i	−0.0548301	−	0.0392446i
$86$		0			0
$87$	−381.507	+	381.507i	−0.470136	+	0.470136i
$88$		0			0
$89$			1256.38i			1.49636i	0.663496	+	0.748180i	$0.269072\pi$
$89$			1256.38i			1.49636i	−0.663496	+	0.748180i	$0.730928\pi$
$90$		0			0
$91$	−189.547			−0.218351
$92$		0			0
$93$	−494.973	−	494.973i	−0.551895	−	0.551895i
$94$		0			0
$95$	199.464	+	1203.98i	0.215417	+	1.30027i
$96$		0			0
$97$	874.108	+	874.108i	0.914972	+	0.914972i	0.996658	−	0.0816865i	$-0.0260306\pi$
$97$	874.108	+	874.108i	0.914972	+	0.914972i	−0.0816865	+	0.996658i	$0.526031\pi$
$98$		0			0
$99$		−	182.492i		−	0.185264i
$100$		0			0
$101$			185.971i			0.183216i	0.995795	+	0.0916080i	$0.0292007\pi$
$101$			185.971i			0.183216i	−0.995795	+	0.0916080i	$0.970799\pi$
$102$		0			0
$103$	−10.2636	−	10.2636i	−0.00981852	−	0.00981852i	0.702180	−	0.711999i	$-0.252210\pi$
$103$	−10.2636	−	10.2636i	−0.00981852	−	0.00981852i	−0.711999	+	0.702180i	$0.752210\pi$
$104$		0			0
$105$	−90.0080	−	543.292i	−0.0836560	−	0.504951i
$106$		0			0
$107$	173.917	+	173.917i	0.157132	+	0.157132i	0.781295	−	0.624162i	$-0.214560\pi$
$107$	173.917	+	173.917i	0.157132	+	0.157132i	−0.624162	+	0.781295i	$0.714560\pi$
$108$		0			0
$109$	−178.177			−0.156571			−0.0782856	−	0.996931i	$-0.524945\pi$
$109$	−178.177			−0.156571			−0.0782856	+	0.996931i	$0.524945\pi$
$110$		0			0
$111$		−	5.65883i		−	0.00483885i
$112$		0			0
$113$	−918.474	+	918.474i	−0.764626	+	0.764626i	−0.977155	−	0.212528i	$-0.931830\pi$
$113$	−918.474	+	918.474i	−0.764626	+	0.764626i	0.212528	+	0.977155i	$0.431830\pi$
$114$		0			0
$115$	−1081.90	−	774.371i	−0.877286	−	0.627917i
$116$		0			0
$117$	73.4696	−	73.4696i	0.0580536	−	0.0580536i
$118$		0			0
$119$	77.5975			0.0597761
$120$		0			0
$121$	−919.847			−0.691095
$122$		0			0
$123$	885.155	−	885.155i	0.648876	−	0.648876i
$124$		0			0
$125$	1231.42	−	660.850i	0.881134	−	0.472866i
$126$		0			0
$127$	1487.16	−	1487.16i	1.03909	−	1.03909i	0.0398852	−	0.999204i	$-0.487301\pi$
$127$	1487.16	−	1487.16i	1.03909	−	1.03909i	0.999204	−	0.0398852i	$-0.0126992\pi$
$128$		0			0
$129$		−	537.408i		−	0.366792i
$130$		0			0
$131$	1824.29			1.21671			0.608354	−	0.793666i	$-0.291830\pi$
$131$	1824.29			1.21671			0.608354	+	0.793666i	$0.291830\pi$
$132$		0			0
$133$	−1267.26	−	1267.26i	−0.826203	−	0.826203i
$134$		0			0
$135$	245.471	+	175.696i	0.156495	+	0.112011i
$136$		0			0
$137$	−62.9299	−	62.9299i	−0.0392443	−	0.0392443i	0.687212	−	0.726457i	$-0.258834\pi$
$137$	−62.9299	−	62.9299i	−0.0392443	−	0.0392443i	−0.726457	+	0.687212i	$0.758834\pi$
$138$		0			0
$139$		−	2360.98i		−	1.44069i	−0.693618	−	0.720343i	$-0.743984\pi$
$139$		−	2360.98i		−	1.44069i	0.693618	−	0.720343i	$-0.256016\pi$
$140$		0			0
$141$			1401.61i			0.837141i
$142$		0			0
$143$	165.526	+	165.526i	0.0967972	+	0.0967972i
$144$		0			0
$145$	1983.68	−	328.639i	1.13611	−	0.188221i
$146$		0			0
$147$	−155.765	−	155.765i	−0.0873967	−	0.0873967i
$148$		0			0
$149$	1824.91			1.00337			0.501687	−	0.865049i	$-0.332713\pi$
$149$	1824.91			1.00337			0.501687	+	0.865049i	$0.332713\pi$
$150$		0			0
$151$		−	1963.31i		−	1.05809i	−0.848593	−	0.529047i	$-0.822550\pi$
$151$		−	1963.31i		−	1.05809i	0.848593	−	0.529047i	$-0.177450\pi$
$152$		0			0
$153$	−30.0773	+	30.0773i	−0.0158928	+	0.0158928i
$154$		0			0
$155$	426.381	+	2573.65i	0.220953	+	1.33368i
$156$		0			0
$157$	−79.7910	+	79.7910i	−0.0405606	+	0.0405606i	−0.727096	−	0.686536i	$-0.759131\pi$
$157$	−79.7910	+	79.7910i	−0.0405606	+	0.0405606i	0.686536	+	0.727096i	$0.259131\pi$
$158$		0			0
$159$	−988.188			−0.492883
$160$		0			0
$161$	1953.84			0.956422
$162$		0			0
$163$	−991.369	+	991.369i	−0.476381	+	0.476381i	−0.903972	−	0.427591i	$-0.859362\pi$
$163$	−991.369	+	991.369i	−0.476381	+	0.476381i	0.427591	+	0.903972i	$0.359362\pi$
$164$		0			0
$165$	−395.841	+	553.044i	−0.186765	+	0.260936i
$166$		0			0
$167$	1793.86	−	1793.86i	0.831215	−	0.831215i	−0.156468	−	0.987683i	$-0.550011\pi$
$167$	1793.86	−	1793.86i	0.831215	−	0.831215i	0.987683	+	0.156468i	$0.0500107\pi$
$168$		0			0
$169$		−	2063.72i		−	0.939336i
$170$		0			0
$171$	982.392			0.439330
$172$		0			0
$173$	−2329.23	−	2329.23i	−1.02363	−	1.02363i	−0.999714	−	0.0239156i	$-0.992387\pi$
$173$	−2329.23	−	2329.23i	−1.02363	−	1.02363i	−0.0239156	−	0.999714i	$-0.507613\pi$
$174$		0			0
$175$	−905.676	+	1841.69i	−0.391215	+	0.795533i
$176$		0			0
$177$	−1403.90	−	1403.90i	−0.596180	−	0.596180i
$178$		0			0
$179$		−	1670.80i		−	0.697663i	−0.937185	−	0.348832i	$-0.886578\pi$
$179$		−	1670.80i		−	0.697663i	0.937185	−	0.348832i	$-0.113422\pi$
$180$		0			0
$181$			2655.30i			1.09043i	0.838297	+	0.545213i	$0.183551\pi$
$181$			2655.30i			1.09043i	−0.838297	+	0.545213i	$0.816449\pi$
$182$		0			0
$183$	−1376.16	−	1376.16i	−0.555894	−	0.555894i
$184$		0			0
$185$	−12.2745	+	17.1491i	−0.00487804	+	0.00681528i
$186$		0			0
$187$	−67.7638	−	67.7638i	−0.0264993	−	0.0264993i
$188$		0			0
$189$	−443.303			−0.170611
$190$		0			0
$191$			1427.48i			0.540778i	0.962751	+	0.270389i	$0.0871523\pi$
$191$			1427.48i			0.540778i	−0.962751	+	0.270389i	$0.912848\pi$
$192$		0			0
$193$	3096.39	−	3096.39i	1.15483	−	1.15483i	0.169263	−	0.985571i	$-0.445861\pi$
$193$	3096.39	−	3096.39i	1.15483	−	1.15483i	0.985571	−	0.169263i	$-0.0541388\pi$
$194$		0			0
$195$	−382.012	+	63.2884i	−0.140289	+	0.0232419i
$196$		0			0
$197$	1472.44	−	1472.44i	0.532522	−	0.532522i	−0.388800	−	0.921322i	$-0.627110\pi$
$197$	1472.44	−	1472.44i	0.532522	−	0.532522i	0.921322	+	0.388800i	$0.127110\pi$
$198$		0			0
$199$	−4404.69			−1.56904			−0.784522	−	0.620100i	$-0.787092\pi$
$199$	−4404.69			−1.56904			−0.784522	+	0.620100i	$0.787092\pi$
$200$		0			0
$201$	2125.43			0.745853
$202$		0			0
$203$	−2087.94	+	2087.94i	−0.721895	+	0.721895i
$204$		0			0
$205$	−4602.44	+	762.493i	−1.56804	+	0.259780i
$206$		0			0
$207$	−757.319	+	757.319i	−0.254287	+	0.254287i
$208$		0			0
$209$			2213.32i			0.732528i
$210$		0			0
$211$	4405.31			1.43732			0.718659	−	0.695363i	$-0.244756\pi$
$211$	4405.31			1.43732			0.718659	+	0.695363i	$0.244756\pi$
$212$		0			0
$213$	−614.121	−	614.121i	−0.197554	−	0.197554i
$214$		0			0
$215$	−1165.68	+	1628.62i	−0.369762	+	0.516608i
$216$		0			0
$217$	−2708.92	−	2708.92i	−0.847437	−	0.847437i
$218$		0			0
$219$		−	2622.17i		−	0.809086i
$220$		0			0
$221$		−	54.5621i		−	0.0166074i
$222$		0			0
$223$	−1500.96	−	1500.96i	−0.450725	−	0.450725i	0.444870	−	0.895595i	$-0.353250\pi$
$223$	−1500.96	−	1500.96i	−0.450725	−	0.450725i	−0.895595	+	0.444870i	$0.853250\pi$
$224$		0			0
$225$	−362.803	−	1064.89i	−0.107497	−	0.315524i
$226$		0			0
$227$	3811.35	+	3811.35i	1.11440	+	1.11440i	0.992549	+	0.121849i	$0.0388822\pi$
$227$	3811.35	+	3811.35i	1.11440	+	1.11440i	0.121849	+	0.992549i	$0.461118\pi$
$228$		0			0
$229$	5030.37			1.45160			0.725800	−	0.687906i	$-0.241470\pi$
$229$	5030.37			1.45160			0.725800	+	0.687906i	$0.241470\pi$
$230$		0			0
$231$		−	998.757i		−	0.284474i
$232$		0			0
$233$	789.402	−	789.402i	0.221955	−	0.221955i	−0.587367	−	0.809321i	$-0.699835\pi$
$233$	789.402	−	789.402i	0.221955	−	0.221955i	0.809321	+	0.587367i	$0.199835\pi$
$234$		0			0
$235$	3040.21	−	4247.59i	0.843921	−	1.17907i
$236$		0			0
$237$	−52.2009	+	52.2009i	−0.0143072	+	0.0143072i
$238$		0			0
$239$	1841.10			0.498289			0.249145	−	0.968466i	$-0.419851\pi$
$239$	1841.10			0.498289			0.249145	+	0.968466i	$0.419851\pi$
$240$		0			0
$241$	−3541.54			−0.946601			−0.473301	−	0.880901i	$-0.656938\pi$
$241$	−3541.54			−0.946601			−0.473301	+	0.880901i	$0.656938\pi$
$242$		0			0
$243$	171.827	−	171.827i	0.0453609	−	0.0453609i
$244$		0			0
$245$	134.180	+	809.916i	0.0349896	+	0.211199i
$246$		0			0
$247$	−891.061	+	891.061i	−0.229542	+	0.229542i
$248$		0			0
$249$		−	2128.00i		−	0.541593i
$250$		0			0
$251$	−4172.19			−1.04919			−0.524594	−	0.851352i	$-0.675783\pi$
$251$	−4172.19			−1.04919			−0.524594	+	0.851352i	$0.675783\pi$
$252$		0			0
$253$	−1706.23	−	1706.23i	−0.423992	−	0.423992i
$254$		0			0
$255$	156.389	−	25.9092i	0.0384058	−	0.00636275i
$256$		0			0
$257$	−2401.58	−	2401.58i	−0.582904	−	0.582904i	0.352796	−	0.935700i	$-0.385231\pi$
$257$	−2401.58	−	2401.58i	−0.582904	−	0.582904i	−0.935700	+	0.352796i	$0.885231\pi$
$258$		0			0
$259$		−	30.9701i		−	0.00743006i
$260$		0			0
$261$		−	1618.60i		−	0.383865i
$262$		0			0
$263$	−2870.97	−	2870.97i	−0.673124	−	0.673124i	0.285311	−	0.958435i	$-0.407903\pi$
$263$	−2870.97	−	2870.97i	−0.673124	−	0.673124i	−0.958435	+	0.285311i	$0.907903\pi$
$264$		0			0
$265$	2994.71	+	2143.46i	0.694202	+	0.496875i
$266$		0			0
$267$	−2665.18	−	2665.18i	−0.610886	−	0.610886i
$268$		0			0
$269$	6613.17			1.49893			0.749465	−	0.662045i	$-0.230311\pi$
$269$	6613.17			1.49893			0.749465	+	0.662045i	$0.230311\pi$
$270$		0			0
$271$			2953.53i			0.662045i	0.943623	+	0.331023i	$0.107394\pi$
$271$			2953.53i			0.662045i	−0.943623	+	0.331023i	$0.892606\pi$
$272$		0			0
$273$	402.090	−	402.090i	0.0891414	−	0.0891414i
$274$		0			0
$275$	2399.20	−	817.391i	0.526098	−	0.179238i
$276$		0			0
$277$	3111.60	−	3111.60i	0.674938	−	0.674938i	−0.283913	−	0.958850i	$-0.591633\pi$
$277$	3111.60	−	3111.60i	0.674938	−	0.674938i	0.958850	+	0.283913i	$0.0916325\pi$
$278$		0			0
$279$	2099.99			0.450621
$280$		0			0
$281$	6645.16			1.41074			0.705369	−	0.708841i	$-0.250781\pi$
$281$	6645.16			1.41074			0.705369	+	0.708841i	$0.250781\pi$
$282$		0			0
$283$	−934.508	+	934.508i	−0.196292	+	0.196292i	−0.798408	−	0.602116i	$-0.794324\pi$
$283$	−934.508	+	934.508i	−0.196292	+	0.196292i	0.602116	+	0.798408i	$0.294324\pi$
$284$		0			0
$285$	−2977.14	−	2130.89i	−0.618775	−	0.442888i
$286$		0			0
$287$	4844.34	−	4844.34i	0.996350	−	0.996350i
$288$		0			0
$289$		−	4890.66i		−	0.995454i
$290$		0			0
$291$	−3708.53			−0.747071
$292$		0			0
$293$	−1473.16	−	1473.16i	−0.293731	−	0.293731i	0.544821	−	0.838552i	$-0.316598\pi$
$293$	−1473.16	−	1473.16i	−0.293731	−	0.293731i	−0.838552	+	0.544821i	$0.816598\pi$
$294$		0			0
$295$	1209.36	+	7299.72i	0.238683	+	1.44070i
$296$		0			0
$297$	387.124	+	387.124i	0.0756338	+	0.0756338i
$298$		0			0
$299$		−	1373.83i		−	0.265720i
$300$		0			0
$301$		−	2941.17i		−	0.563209i
$302$		0			0
$303$	−394.504	−	394.504i	−0.0747976	−	0.0747976i
$304$		0			0
$305$	1185.45	+	7155.46i	0.222554	+	1.34335i
$306$		0			0
$307$	−1659.16	−	1659.16i	−0.308446	−	0.308446i	0.535860	−	0.844307i	$-0.319987\pi$
$307$	−1659.16	−	1659.16i	−0.308446	−	0.308446i	−0.844307	+	0.535860i	$0.819987\pi$
$308$		0			0
$309$	43.5450			0.00801679
$310$		0			0
$311$		−	1571.98i		−	0.286619i	−0.989678	−	0.143310i	$-0.954225\pi$
$311$		−	1571.98i		−	0.286619i	0.989678	−	0.143310i	$-0.0457745\pi$
$312$		0			0
$313$	184.356	−	184.356i	0.0332921	−	0.0332921i	−0.690265	−	0.723557i	$-0.742506\pi$
$313$	184.356	−	184.356i	0.0332921	−	0.0332921i	0.723557	+	0.690265i	$0.242506\pi$
$314$		0			0
$315$	1343.43	+	961.561i	0.240298	+	0.171993i
$316$		0			0
$317$	−7547.19	+	7547.19i	−1.33720	+	1.33720i	−0.438440	+	0.898760i	$0.644469\pi$
$317$	−7547.19	+	7547.19i	−1.33720	+	1.33720i	−0.898760	+	0.438440i	$0.855531\pi$
$318$		0			0
$319$	3646.68			0.640047
$320$		0			0
$321$	−737.866			−0.128298
$322$		0			0
$323$	364.786	−	364.786i	0.0628397	−	0.0628397i
$324$		0			0
$325$	1294.97	+	636.819i	0.221021	+	0.108690i
$326$		0			0
$327$	377.970	−	377.970i	0.0639199	−	0.0639199i
$328$		0			0
$329$			7670.84i			1.28543i
$330$		0			0
$331$	4761.89			0.790747			0.395373	−	0.918520i	$-0.370615\pi$
$331$	4761.89			0.790747			0.395373	+	0.918520i	$0.370615\pi$
$332$		0			0
$333$	12.0042	+	12.0042i	0.00197545	+	0.00197545i
$334$		0			0
$335$	−6441.13	−	4610.24i	−1.05050	−	0.751893i
$336$		0			0
$337$	−1593.06	−	1593.06i	−0.257505	−	0.257505i	0.566533	−	0.824039i	$-0.308284\pi$
$337$	−1593.06	−	1593.06i	−0.257505	−	0.257505i	−0.824039	+	0.566533i	$0.808284\pi$
$338$		0			0
$339$		−	3896.76i		−	0.624315i
$340$		0			0
$341$			4731.26i			0.751355i
$342$		0			0
$343$	−4834.62	−	4834.62i	−0.761064	−	0.761064i
$344$		0			0
$345$	3937.75	−	652.372i	0.614496	−	0.101804i
$346$		0			0
$347$	1539.62	+	1539.62i	0.238187	+	0.238187i	0.816099	−	0.577912i	$-0.196132\pi$
$347$	1539.62	+	1539.62i	0.238187	+	0.238187i	−0.577912	+	0.816099i	$0.696132\pi$
$348$		0			0
$349$	−11598.4			−1.77894			−0.889471	−	0.456992i	$-0.848927\pi$
$349$	−11598.4			−1.77894			−0.889471	+	0.456992i	$0.848927\pi$
$350$		0			0
$351$			311.705i			0.0474005i
$352$		0			0
$353$	−6548.96	+	6548.96i	−0.987439	+	0.987439i	−0.999922	−	0.0124830i	$-0.996026\pi$
$353$	−6548.96	+	6548.96i	−0.987439	+	0.987439i	0.0124830	+	0.999922i	$0.496026\pi$
$354$		0			0
$355$	529.018	+	3193.18i	0.0790912	+	0.477398i
$356$		0			0
$357$	−164.609	+	164.609i	−0.0244035	+	0.0244035i
$358$		0			0
$359$	10655.5			1.56651			0.783256	−	0.621700i	$-0.213558\pi$
$359$	10655.5			1.56651			0.783256	+	0.621700i	$0.213558\pi$
$360$		0			0
$361$	−5055.73			−0.737095
$362$		0			0
$363$	1951.29	−	1951.29i	0.282138	−	0.282138i
$364$		0			0
$365$	−5687.70	+	7946.50i	−0.815638	+	1.13956i
$366$		0			0
$367$	2990.84	−	2990.84i	0.425397	−	0.425397i	−0.461660	−	0.887057i	$-0.652746\pi$
$367$	2990.84	−	2990.84i	0.425397	−	0.425397i	0.887057	+	0.461660i	$0.152746\pi$
$368$		0			0
$369$			3755.39i			0.529805i
$370$		0			0
$371$	−5408.23			−0.756824
$372$		0			0
$373$	2267.12	+	2267.12i	0.314710	+	0.314710i	0.846731	−	0.532021i	$-0.178567\pi$
$373$	2267.12	+	2267.12i	0.314710	+	0.314710i	−0.532021	+	0.846731i	$0.678567\pi$
$374$		0			0
$375$	−1210.37	+	4014.12i	−0.166675	+	0.552768i
$376$		0			0
$377$	1468.12	+	1468.12i	0.200562	+	0.200562i
$378$		0			0
$379$			8327.26i			1.12861i	0.825567	+	0.564304i	$0.190855\pi$
$379$			8327.26i			1.12861i	−0.825567	+	0.564304i	$0.809145\pi$
$380$		0			0
$381$			6309.50i			0.848413i
$382$		0			0
$383$	6226.87	+	6226.87i	0.830752	+	0.830752i	0.987620	−	0.156868i	$-0.0501396\pi$
$383$	6226.87	+	6226.87i	0.830752	+	0.830752i	−0.156868	+	0.987620i	$0.550140\pi$
$384$		0			0
$385$	−2166.39	+	3026.74i	−0.286777	+	0.400667i
$386$		0			0
$387$	1140.01	+	1140.01i	0.149742	+	0.149742i
$388$		0			0
$389$	13285.9			1.73167			0.865836	−	0.500328i	$-0.166787\pi$
$389$	13285.9			1.73167			0.865836	+	0.500328i	$0.166787\pi$
$390$		0			0
$391$			562.422i			0.0727440i
$392$		0			0
$393$	−3869.90	+	3869.90i	−0.496719	+	0.496719i
$394$		0			0
$395$	271.423	−	44.9671i	0.0345742	−	0.00572795i
$396$		0			0
$397$	6798.31	−	6798.31i	0.859439	−	0.859439i	−0.131833	−	0.991272i	$-0.542086\pi$
$397$	6798.31	−	6798.31i	0.859439	−	0.859439i	0.991272	+	0.131833i	$0.0420863\pi$
$398$		0			0
$399$	5376.51			0.674592
$400$		0			0
$401$	−54.8890			−0.00683547			−0.00341774	−	0.999994i	$-0.501088\pi$
$401$	−54.8890			−0.00683547			−0.00341774	+	0.999994i	$0.501088\pi$
$402$		0			0
$403$	−1904.76	+	1904.76i	−0.235441	+	0.235441i
$404$		0			0
$405$	−893.430	+	148.016i	−0.109617	+	0.0181604i
$406$		0			0
$407$	−27.0453	+	27.0453i	−0.00329382	+	0.00329382i
$408$		0			0
$409$			1347.06i			0.162856i	0.996679	+	0.0814278i	$0.0259480\pi$
$409$			1347.06i			0.162856i	−0.996679	+	0.0814278i	$0.974052\pi$
$410$		0			0
$411$	266.989			0.0320428
$412$		0			0
$413$	−7683.39	−	7683.39i	−0.915436	−	0.915436i
$414$		0			0
$415$	−4615.82	+	6448.93i	−0.545980	+	0.762808i
$416$		0			0
$417$	5008.38	+	5008.38i	0.588157	+	0.588157i
$418$		0			0
$419$		−	5499.27i		−	0.641186i	−0.947217	−	0.320593i	$-0.896118\pi$
$419$		−	5499.27i		−	0.641186i	0.947217	−	0.320593i	$-0.103882\pi$
$420$		0			0
$421$		−	5000.27i		−	0.578855i	−0.957200	−	0.289428i	$-0.906535\pi$
$421$		−	5000.27i		−	0.578855i	0.957200	−	0.289428i	$-0.0934649\pi$
$422$		0			0
$423$	−2973.27	−	2973.27i	−0.341761	−	0.341761i
$424$		0			0
$425$	−530.138	−	260.703i	−0.0605070	−	0.0297552i
$426$		0			0
$427$	−7531.55	−	7531.55i	−0.853576	−	0.853576i
$428$		0			0
$429$	−702.269			−0.0790346
$430$		0			0
$431$			11144.8i			1.24554i	0.782406	+	0.622769i	$0.213992\pi$
$431$			11144.8i			1.24554i	−0.782406	+	0.622769i	$0.786008\pi$
$432$		0			0
$433$	−7324.04	+	7324.04i	−0.812866	+	0.812866i	−0.985063	−	0.172196i	$-0.944914\pi$
$433$	−7324.04	+	7324.04i	−0.812866	+	0.812866i	0.172196	+	0.985063i	$0.444914\pi$
$434$		0			0
$435$	−3510.87	+	4905.17i	−0.386973	+	0.540655i
$436$		0			0
$437$	9184.99	−	9184.99i	1.00544	−	1.00544i
$438$		0			0
$439$	12924.4			1.40512			0.702561	−	0.711623i	$-0.252040\pi$
$439$	12924.4			1.40512			0.702561	+	0.711623i	$0.252040\pi$
$440$		0			0
$441$	660.857			0.0713591
$442$		0			0
$443$	−11973.7	+	11973.7i	−1.28417	+	1.28417i	−0.345894	+	0.938274i	$0.612424\pi$
$443$	−11973.7	+	11973.7i	−1.28417	+	1.28417i	−0.938274	+	0.345894i	$0.887576\pi$
$444$		0			0
$445$	2295.85	+	13857.9i	0.244570	+	1.47624i
$446$		0			0
$447$	−3871.23	+	3871.23i	−0.409626	+	0.409626i
$448$		0			0
$449$		−	18382.0i		−	1.93207i	−0.258411	−	0.966035i	$-0.583199\pi$
$449$		−	18382.0i		−	1.93207i	0.258411	−	0.966035i	$-0.416801\pi$
$450$		0			0
$451$	−8460.86			−0.883385
$452$		0			0
$453$	4164.81	+	4164.81i	0.431965	+	0.431965i
$454$		0			0
$455$	−2090.70	+	346.370i	−0.215415	+	0.0356881i
$456$		0			0
$457$	−1959.28	−	1959.28i	−0.200550	−	0.200550i	0.599686	−	0.800236i	$-0.295292\pi$
$457$	−1959.28	−	1959.28i	−0.200550	−	0.200550i	−0.800236	+	0.599686i	$0.795292\pi$
$458$		0			0
$459$		−	127.607i		−	0.0129764i
$460$		0			0
$461$		−	6217.07i		−	0.628108i	−0.949405	−	0.314054i	$-0.898313\pi$
$461$		−	6217.07i		−	0.628108i	0.949405	−	0.314054i	$-0.101687\pi$
$462$		0			0
$463$	−3651.33	−	3651.33i	−0.366505	−	0.366505i	0.499696	−	0.866201i	$-0.333445\pi$
$463$	−3651.33	−	3651.33i	−0.366505	−	0.366505i	−0.866201	+	0.499696i	$0.833445\pi$
$464$		0			0
$465$	−6364.04	−	4555.06i	−0.634678	−	0.454270i
$466$		0			0
$467$	−1088.44	−	1088.44i	−0.107853	−	0.107853i	0.651121	−	0.758974i	$-0.274299\pi$
$467$	−1088.44	−	1088.44i	−0.107853	−	0.107853i	−0.758974	+	0.651121i	$0.774299\pi$
$468$		0			0
$469$	11632.2			1.14526
$470$		0			0
$471$		−	338.524i		−	0.0331176i
$472$		0			0
$473$	−2568.44	+	2568.44i	−0.249676	+	0.249676i
$474$		0			0
$475$	4400.18	+	12915.3i	0.425040	+	1.24757i
$476$		0			0
$477$	2096.26	−	2096.26i	0.201219	−	0.201219i
$478$		0			0
$479$	−10095.2			−0.962967			−0.481483	−	0.876455i	$-0.659902\pi$
$479$	−10095.2			−0.962967			−0.481483	+	0.876455i	$0.659902\pi$
$480$		0			0
$481$	−21.7764			−0.00206428
$482$		0			0
$483$	−4144.71	+	4144.71i	−0.390458	+	0.390458i
$484$		0			0
$485$	11238.7	+	8044.10i	1.05221	+	0.753121i
$486$		0			0
$487$	−6893.07	+	6893.07i	−0.641386	+	0.641386i	−0.950896	−	0.309510i	$-0.899835\pi$
$487$	−6893.07	+	6893.07i	−0.641386	+	0.641386i	0.309510	+	0.950896i	$0.399835\pi$
$488$		0			0
$489$		−	4206.02i		−	0.388963i
$490$		0			0
$491$	2125.84			0.195393			0.0976965	−	0.995216i	$-0.468853\pi$
$491$	2125.84			0.195393			0.0976965	+	0.995216i	$0.468853\pi$
$492$		0			0
$493$	−601.024	−	601.024i	−0.0549062	−	0.0549062i
$494$		0			0
$495$	−333.478	−	2012.89i	−0.0302802	−	0.182773i
$496$		0			0
$497$	−3361.01	−	3361.01i	−0.303344	−	0.303344i
$498$		0			0
$499$			10274.2i			0.921714i	0.887474	+	0.460857i	$0.152458\pi$
$499$			10274.2i			0.921714i	−0.887474	+	0.460857i	$0.847542\pi$
$500$		0			0
$501$			7610.70i			0.678685i
$502$		0			0
$503$	−2206.08	−	2206.08i	−0.195555	−	0.195555i	0.602536	−	0.798092i	$-0.294157\pi$
$503$	−2206.08	−	2206.08i	−0.195555	−	0.195555i	−0.798092	+	0.602536i	$0.794157\pi$
$504$		0			0
$505$	339.835	+	2051.26i	0.0299455	+	0.180752i
$506$		0			0
$507$	4377.81	+	4377.81i	0.383482	+	0.383482i
$508$		0			0
$509$	−12262.7			−1.06785			−0.533926	−	0.845531i	$-0.679284\pi$
$509$	−12262.7			−1.06785			−0.533926	+	0.845531i	$0.679284\pi$
$510$		0			0
$511$		−	14350.8i		−	1.24235i
$512$		0			0
$513$	−2083.97	+	2083.97i	−0.179356	+	0.179356i
$514$		0			0
$515$	−131.963	−	94.4527i	−0.0112913	−	0.00808171i
$516$		0			0
$517$	6698.74	−	6698.74i	0.569845	−	0.569845i
$518$		0			0
$519$	9882.08			0.835790
$520$		0			0
$521$	−6045.47			−0.508362			−0.254181	−	0.967157i	$-0.581806\pi$
$521$	−6045.47			−0.508362			−0.254181	+	0.967157i	$0.581806\pi$
$522$		0			0
$523$	568.268	−	568.268i	0.0475117	−	0.0475117i	−0.682952	−	0.730463i	$-0.739304\pi$
$523$	568.268	−	568.268i	0.0475117	−	0.0475117i	0.730463	+	0.682952i	$0.239304\pi$
$524$		0			0
$525$	−1985.58	−	5828.03i	−0.165062	−	0.484488i
$526$		0			0
$527$	779.777	−	779.777i	0.0644547	−	0.0644547i
$528$		0			0
$529$			1994.29i			0.163910i
$530$		0			0
$531$	5956.26			0.486779
$532$		0			0
$533$	−3406.26	−	3406.26i	−0.276814	−	0.276814i
$534$		0			0
$535$	2236.11	+	1600.49i	0.180702	+	0.129337i
$536$		0			0
$537$	3544.31	+	3544.31i	0.284820	+	0.284820i
$538$		0			0
$539$			1488.90i			0.118983i
$540$		0			0
$541$			7814.28i			0.621002i	0.950573	+	0.310501i	$0.100497\pi$
$541$			7814.28i			0.621002i	−0.950573	+	0.310501i	$0.899503\pi$
$542$		0			0
$543$	−5632.75	−	5632.75i	−0.445165	−	0.445165i
$544$		0			0
$545$	−1965.29	+	325.592i	−0.154466	+	0.0255906i
$546$		0			0
$547$	−5746.15	−	5746.15i	−0.449155	−	0.449155i	0.445919	−	0.895074i	$-0.352877\pi$
$547$	−5746.15	−	5746.15i	−0.449155	−	0.449155i	−0.895074	+	0.445919i	$0.852877\pi$
$548$		0			0
$549$	5838.55			0.453885
$550$		0			0
$551$			19630.8i			1.51779i
$552$		0			0
$553$	−285.689	+	285.689i	−0.0219688	+	0.0219688i
$554$		0			0
$555$	−10.3407	−	62.4168i	−0.000790878	−	0.00477378i
$556$		0			0
$557$	−5995.83	+	5995.83i	−0.456107	+	0.456107i	−0.897375	−	0.441269i	$-0.854529\pi$
$557$	−5995.83	+	5995.83i	−0.456107	+	0.456107i	0.441269	+	0.897375i	$0.354529\pi$
$558$		0			0
$559$	−2068.06			−0.156475
$560$		0			0
$561$	287.497			0.0216366
$562$		0			0
$563$	13306.6	−	13306.6i	0.996104	−	0.996104i	−0.00388821	−	0.999992i	$-0.501238\pi$
$563$	13306.6	−	13306.6i	0.996104	−	0.996104i	0.999992	+	0.00388821i	$0.00123766\pi$
$564$		0			0
$565$	−8452.39	+	11809.1i	−0.629371	+	0.879318i
$566$		0			0
$567$	940.388	−	940.388i	0.0696518	−	0.0696518i
$568$		0			0
$569$		−	19196.7i		−	1.41435i	−0.707037	−	0.707177i	$-0.749969\pi$
$569$		−	19196.7i		−	1.41435i	0.707037	−	0.707177i	$-0.250031\pi$
$570$		0			0
$571$	12838.7			0.940952			0.470476	−	0.882413i	$-0.344082\pi$
$571$	12838.7			0.940952			0.470476	+	0.882413i	$0.344082\pi$
$572$		0			0
$573$	−3028.13	−	3028.13i	−0.220772	−	0.220772i
$574$		0			0
$575$	−13348.4	−	6564.29i	−0.968118	−	0.476086i
$576$		0			0
$577$	14847.7	+	14847.7i	1.07126	+	1.07126i	0.997258	+	0.0740040i	$0.0235778\pi$
$577$	14847.7	+	14847.7i	1.07126	+	1.07126i	0.0740040	+	0.997258i	$0.476422\pi$
$578$		0			0
$579$			13136.9i			0.942918i
$580$		0			0
$581$		−	11646.3i		−	0.831618i
$582$		0			0
$583$	4722.86	+	4722.86i	0.335508	+	0.335508i
$584$		0			0
$585$	676.114	−	944.624i	0.0477844	−	0.0667614i
$586$		0			0
$587$	−5250.15	−	5250.15i	−0.369160	−	0.369160i	0.498011	−	0.867171i	$-0.334064\pi$
$587$	−5250.15	−	5250.15i	−0.369160	−	0.369160i	−0.867171	+	0.498011i	$0.834064\pi$
$588$		0			0
$589$	−25469.3			−1.78174
$590$		0			0
$591$			6247.02i			0.434802i
$592$		0			0
$593$	9616.26	−	9616.26i	0.665923	−	0.665923i	−0.290846	−	0.956770i	$-0.593937\pi$
$593$	9616.26	−	9616.26i	0.665923	−	0.665923i	0.956770	+	0.290846i	$0.0939369\pi$
$594$		0			0
$595$	855.900	−	141.798i	0.0589722	−	0.00977001i
$596$		0			0
$597$	9343.75	−	9343.75i	0.640560	−	0.640560i
$598$		0			0
$599$	985.603			0.0672298			0.0336149	−	0.999435i	$-0.489298\pi$
$599$	985.603			0.0672298			0.0336149	+	0.999435i	$0.489298\pi$
$600$		0			0
$601$	15599.0			1.05873			0.529366	−	0.848394i	$-0.322430\pi$
$601$	15599.0			1.05873			0.529366	+	0.848394i	$0.322430\pi$
$602$		0			0
$603$	−4508.72	+	4508.72i	−0.304493	+	0.304493i
$604$		0			0
$605$	−10145.9	+	1680.89i	−0.681801	+	0.112955i
$606$		0			0
$607$	14239.3	−	14239.3i	0.952152	−	0.952152i	−0.0467546	−	0.998906i	$-0.514888\pi$
$607$	14239.3	−	14239.3i	0.952152	−	0.952152i	0.998906	+	0.0467546i	$0.0148879\pi$
$608$		0			0
$609$		−	8858.39i		−	0.589425i
$610$		0			0
$611$	5393.69			0.357129
$612$		0			0
$613$	15194.0	+	15194.0i	1.00111	+	1.00111i	0.999999	+	0.00111139i	$0.000353768\pi$
$613$	15194.0	+	15194.0i	1.00111	+	1.00111i	0.00111139	+	0.999999i	$0.499646\pi$
$614$		0			0
$615$	8145.76	−	11380.7i	0.534096	−	0.746205i
$616$		0			0
$617$	−4341.49	−	4341.49i	−0.283277	−	0.283277i	0.551138	−	0.834414i	$-0.314194\pi$
$617$	−4341.49	−	4341.49i	−0.283277	−	0.283277i	−0.834414	+	0.551138i	$0.814194\pi$
$618$		0			0
$619$		−	8410.39i		−	0.546110i	−0.961998	−	0.273055i	$-0.911966\pi$
$619$		−	8410.39i		−	0.546110i	0.961998	−	0.273055i	$-0.0880341\pi$
$620$		0			0
$621$		−	3213.03i		−	0.207624i
$622$		0			0
$623$	−14586.2	−	14586.2i	−0.938017	−	0.938017i
$624$		0			0
$625$	12375.0	−	9539.42i	0.791999	−	0.610523i
$626$		0			0
$627$	−4695.16	−	4695.16i	−0.299053	−	0.299053i
$628$		0			0
$629$	8.91489			0.000565119
$630$		0			0
$631$			1596.50i			0.100722i	0.998731	+	0.0503611i	$0.0160372\pi$
$631$			1596.50i			0.100722i	−0.998731	+	0.0503611i	$0.983963\pi$
$632$		0			0
$633$	−9345.07	+	9345.07i	−0.586782	+	0.586782i
$634$		0			0
$635$	13685.8	−	19121.0i	0.855284	−	1.19495i
$636$		0			0
$637$	−599.418	+	599.418i	−0.0372839	+	0.0372839i
$638$		0			0
$639$	2605.50			0.161302
$640$		0			0
$641$	21817.7			1.34438			0.672189	−	0.740380i	$-0.265354\pi$
$641$	21817.7			1.34438			0.672189	+	0.740380i	$0.265354\pi$
$642$		0			0
$643$	14458.2	−	14458.2i	0.886746	−	0.886746i	−0.107463	−	0.994209i	$-0.534273\pi$
$643$	14458.2	−	14458.2i	0.886746	−	0.886746i	0.994209	+	0.107463i	$0.0342728\pi$
$644$		0			0
$645$	−982.034	−	5927.60i	−0.0599497	−	0.361859i
$646$		0			0
$647$	−795.224	+	795.224i	−0.0483207	+	0.0483207i	−0.730854	−	0.682534i	$-0.760878\pi$
$647$	−795.224	+	795.224i	−0.0483207	+	0.0483207i	0.682534	+	0.730854i	$0.260878\pi$
$648$		0			0
$649$			13419.4i			0.811645i
$650$		0			0
$651$	11493.0			0.691929
$652$		0			0
$653$	−13714.9	−	13714.9i	−0.821905	−	0.821905i	0.164476	−	0.986381i	$-0.447407\pi$
$653$	−13714.9	−	13714.9i	−0.821905	−	0.821905i	−0.986381	+	0.164476i	$0.947407\pi$
$654$		0			0
$655$	20121.9	−	3333.62i	1.20035	−	0.198863i
$656$		0			0
$657$	5562.46	+	5562.46i	0.330308	+	0.330308i
$658$		0			0
$659$		−	7665.59i		−	0.453124i	−0.973997	−	0.226562i	$-0.927251\pi$
$659$		−	7665.59i		−	0.453124i	0.973997	−	0.226562i	$-0.0727486\pi$
$660$		0			0
$661$		−	11948.5i		−	0.703091i	−0.936171	−	0.351546i	$-0.885656\pi$
$661$		−	11948.5i		−	0.703091i	0.936171	−	0.351546i	$-0.114344\pi$
$662$		0			0
$663$	115.744	+	115.744i	0.00677996	+	0.00677996i
$664$		0			0
$665$	−16293.5	−	11662.1i	−0.950130	−	0.680055i
$666$		0			0
$667$	−15133.3	−	15133.3i	−0.878505	−	0.878505i
$668$		0			0
$669$	6368.03			0.368015
$670$		0			0
$671$			13154.2i			0.756798i
$672$		0			0
$673$	1225.87	−	1225.87i	0.0702135	−	0.0702135i	−0.671128	−	0.741342i	$-0.734190\pi$
$673$	1225.87	−	1225.87i	0.0702135	−	0.0702135i	0.741342	+	0.671128i	$0.234190\pi$
$674$		0			0
$675$	3028.60	+	1489.36i	0.172698	+	0.0849267i
$676$		0			0
$677$	−9743.57	+	9743.57i	−0.553140	+	0.553140i	−0.927346	−	0.374206i	$-0.877915\pi$
$677$	−9743.57	+	9743.57i	−0.553140	+	0.553140i	0.374206	+	0.927346i	$0.377915\pi$
$678$		0			0
$679$	−20296.3			−1.14713
$680$		0			0
$681$	−16170.2			−0.909902
$682$		0			0
$683$	6683.51	−	6683.51i	0.374432	−	0.374432i	−0.494656	−	0.869089i	$-0.664706\pi$
$683$	6683.51	−	6683.51i	0.374432	−	0.374432i	0.869089	+	0.494656i	$0.164706\pi$
$684$		0			0
$685$	−809.112	−	579.121i	−0.0451308	−	0.0323023i
$686$		0			0
$687$	−10671.0	+	10671.0i	−0.592613	+	0.592613i
$688$		0			0
$689$			3802.76i			0.210266i
$690$		0			0
$691$	−14879.3			−0.819151			−0.409576	−	0.912276i	$-0.634323\pi$
$691$	−14879.3			−0.819151			−0.409576	+	0.912276i	$0.634323\pi$
$692$		0			0
$693$	2118.68	+	2118.68i	0.116136	+	0.116136i
$694$		0			0
$695$	−4314.34	−	26041.5i	−0.235471	−	1.42131i
$696$		0			0
$697$	1394.47	+	1394.47i	0.0757809	+	0.0757809i
$698$		0			0
$699$			3349.15i			0.181225i
$700$		0			0
$701$		−	692.787i		−	0.0373270i	−0.999826	−	0.0186635i	$-0.994059\pi$
$701$		−	692.787i		−	0.0373270i	0.999826	−	0.0186635i	$-0.00594112\pi$
$702$		0			0
$703$	−145.590	−	145.590i	−0.00781087	−	0.00781087i
$704$		0			0
$705$	2561.24	+	15459.8i	0.136825	+	0.825884i
$706$		0			0
$707$	−2159.07	−	2159.07i	−0.114852	−	0.114852i
$708$		0			0
$709$	−12717.4			−0.673641			−0.336820	−	0.941569i	$-0.609351\pi$
$709$	−12717.4			−0.673641			−0.336820	+	0.941569i	$0.609351\pi$
$710$		0			0
$711$		−	221.470i		−	0.0116818i
$712$		0			0
$713$	19634.1	−	19634.1i	1.03128	−	1.03128i
$714$		0			0
$715$	2128.23	+	1523.28i	0.111316	+	0.0796747i
$716$		0			0
$717$	−3905.57	+	3905.57i	−0.203426	+	0.203426i
$718$		0			0
$719$	3461.03			0.179520			0.0897599	−	0.995963i	$-0.471390\pi$
$719$	3461.03			0.179520			0.0897599	+	0.995963i	$0.471390\pi$
$720$		0			0
$721$	238.316			0.0123098
$722$		0			0
$723$	7512.75	−	7512.75i	0.386448	−	0.386448i
$724$		0			0
$725$	21279.4	−	7249.78i	1.09007	−	0.371379i
$726$		0			0
$727$	−2347.87	+	2347.87i	−0.119777	+	0.119777i	−0.764454	−	0.644678i	$-0.776992\pi$
$727$	−2347.87	+	2347.87i	−0.119777	+	0.119777i	0.644678	+	0.764454i	$0.276992\pi$
$728$		0			0
$729$			729.000i			0.0370370i
$730$		0			0
$731$	846.629			0.0428368
$732$		0			0
$733$	−17552.1	−	17552.1i	−0.884448	−	0.884448i	0.109535	−	0.993983i	$-0.465064\pi$
$733$	−17552.1	−	17552.1i	−0.884448	−	0.884448i	−0.993983	+	0.109535i	$0.965064\pi$
$734$		0			0
$735$	−2002.73	−	1433.45i	−0.100506	−	0.0719370i
$736$		0			0
$737$	−10158.1	−	10158.1i	−0.507705	−	0.507705i
$738$		0			0
$739$			9756.62i			0.485660i	0.970069	+	0.242830i	$0.0780758\pi$
$739$			9756.62i			0.485660i	−0.970069	+	0.242830i	$0.921924\pi$
$740$		0			0
$741$		−	3780.45i		−	0.187420i
$742$		0			0
$743$	1568.62	+	1568.62i	0.0774523	+	0.0774523i	0.744772	−	0.667319i	$-0.232558\pi$
$743$	1568.62	+	1568.62i	0.0774523	+	0.0774523i	−0.667319	+	0.744772i	$0.732558\pi$
$744$		0			0
$745$	20128.8	−	3334.77i	0.989882	−	0.163995i
$746$		0			0
$747$	4514.18	+	4514.18i	0.221105	+	0.221105i
$748$		0			0
$749$	−4038.25			−0.197002
$750$		0			0
$751$		−	10327.1i		−	0.501787i	−0.968015	−	0.250893i	$-0.919276\pi$
$751$		−	10327.1i		−	0.501787i	0.968015	−	0.250893i	$-0.0807244\pi$
$752$		0			0
$753$	8850.56	−	8850.56i	0.428330	−	0.428330i
$754$		0			0
$755$	−3587.67	−	21655.3i	−0.172939	−	1.04386i
$756$		0			0
$757$	19451.6	−	19451.6i	0.933922	−	0.933922i	−0.0640259	−	0.997948i	$-0.520394\pi$
$757$	19451.6	−	19451.6i	0.933922	−	0.933922i	0.997948	+	0.0640259i	$0.0203940\pi$
$758$		0			0
$759$	7238.93			0.346188
$760$		0			0
$761$	−18457.1			−0.879196			−0.439598	−	0.898195i	$-0.644879\pi$
$761$	−18457.1			−0.879196			−0.439598	+	0.898195i	$0.644879\pi$
$762$		0			0
$763$	2068.59	−	2068.59i	0.0981492	−	0.0981492i
$764$		0			0
$765$	−276.790	+	386.714i	−0.0130815	+	0.0182767i
$766$		0			0
$767$	−5402.52	+	5402.52i	−0.254333	+	0.254333i
$768$		0			0
$769$			20844.6i			0.977471i	0.872432	+	0.488735i	$0.162542\pi$
$769$			20844.6i			0.977471i	−0.872432	+	0.488735i	$0.837458\pi$
$770$		0			0
$771$	10189.0			0.475939
$772$		0			0
$773$	249.426	+	249.426i	0.0116057	+	0.0116057i	0.712886	−	0.701280i	$-0.247388\pi$
$773$	249.426	+	249.426i	0.0116057	+	0.0116057i	−0.701280	+	0.712886i	$0.747388\pi$
$774$		0			0
$775$	9405.96	+	27608.2i	0.435964	+	1.27964i
$776$		0			0
$777$	65.6974	+	65.6974i	0.00303331	+	0.00303331i
$778$		0			0
$779$		−	45546.5i		−	2.09483i
$780$		0			0
$781$			5870.16i			0.268951i
$782$		0			0
$783$	3433.56	+	3433.56i	0.156712	+	0.156712i
$784$		0			0
$785$	−734.288	+	1025.90i	−0.0333858	+	0.0466445i
$786$		0			0
$787$	20648.2	+	20648.2i	0.935233	+	0.935233i	0.998027	−	0.0627933i	$-0.0200009\pi$
$787$	20648.2	+	20648.2i	0.935233	+	0.935233i	−0.0627933	+	0.998027i	$0.520001\pi$
$788$		0			0
$789$	12180.5			0.549603
$790$		0			0
$791$		−	21326.5i		−	0.958637i
$792$		0			0
$793$	−5295.75	+	5295.75i	−0.237147	+	0.237147i
$794$		0			0
$795$	−10899.7	+	1805.77i	−0.486255	+	0.0805586i
$796$		0			0
$797$	−24818.1	+	24818.1i	−1.10301	+	1.10301i	−0.108969	+	0.994045i	$0.534755\pi$
$797$	−24818.1	+	24818.1i	−1.10301	+	1.10301i	−0.994045	+	0.108969i	$0.965245\pi$
$798$		0			0
$799$	−2208.09			−0.0977680
$800$		0			0
$801$	11307.4			0.498787
$802$		0			0
$803$	−12532.2	+	12532.2i	−0.550748	+	0.550748i
$804$		0			0
$805$	21550.8	−	3570.35i	0.943561	−	0.156321i
$806$		0			0
$807$	−14028.6	+	14028.6i	−0.611935	+	0.611935i
$808$		0			0
$809$			540.631i			0.0234952i	0.999931	+	0.0117476i	$0.00373946\pi$
$809$			540.631i			0.0234952i	−0.999931	+	0.0117476i	$0.996261\pi$
$810$		0			0
$811$	−39390.4			−1.70553			−0.852764	−	0.522296i	$-0.825076\pi$
$811$	−39390.4			−1.70553			−0.852764	+	0.522296i	$0.825076\pi$
$812$		0			0
$813$	−6265.39	−	6265.39i	−0.270279	−	0.270279i
$814$		0			0
$815$	−9123.21	+	12746.4i	−0.392113	+	0.547836i
$816$		0			0
$817$	−13826.4	−	13826.4i	−0.592075	−	0.592075i
$818$		0			0
$819$			1705.92i			0.0727837i
$820$		0			0
$821$			19442.6i			0.826492i	0.910619	+	0.413246i	$0.135605\pi$
$821$			19442.6i			0.826492i	−0.910619	+	0.413246i	$0.864395\pi$
$822$		0			0
$823$	−776.854	−	776.854i	−0.0329033	−	0.0329033i	0.690464	−	0.723367i	$-0.257407\pi$
$823$	−776.854	−	776.854i	−0.0329033	−	0.0329033i	−0.723367	+	0.690464i	$0.757407\pi$
$824$		0			0
$825$	−3355.51	+	6823.41i	−0.141605	+	0.287952i
$826$		0			0
$827$	8014.02	+	8014.02i	0.336971	+	0.336971i	0.855226	−	0.518255i	$-0.173418\pi$
$827$	8014.02	+	8014.02i	0.336971	+	0.336971i	−0.518255	+	0.855226i	$0.673418\pi$
$828$		0			0
$829$	−27445.3			−1.14984			−0.574918	−	0.818211i	$-0.694966\pi$
$829$	−27445.3			−1.14984			−0.574918	+	0.818211i	$0.694966\pi$
$830$		0			0
$831$			13201.4i			0.551084i
$832$		0			0
$833$	245.392	−	245.392i	0.0102069	−	0.0102069i
$834$		0			0
$835$	16508.2	−	23064.3i	0.684181	−	0.955895i
$836$		0			0
$837$	−4454.75	+	4454.75i	−0.183965	+	0.183965i
$838$		0			0
$839$	72.3148			0.00297567			0.00148783	−	0.999999i	$-0.499526\pi$
$839$	72.3148			0.00297567			0.00148783	+	0.999999i	$0.499526\pi$
$840$		0			0
$841$	7954.93			0.326169
$842$		0			0
$843$	−14096.5	+	14096.5i	−0.575931	+	0.575931i
$844$		0			0
$845$	−3771.15	−	22762.8i	−0.153528	−	0.926705i
$846$		0			0
$847$	10679.2	−	10679.2i	0.433224	−	0.433224i
$848$		0			0
$849$		−	3964.78i		−	0.160272i
$850$		0			0
$851$	224.469			0.00904195
$852$		0			0
$853$	17977.6	+	17977.6i	0.721621	+	0.721621i	0.968935	−	0.247314i	$-0.0795481\pi$
$853$	17977.6	+	17977.6i	0.721621	+	0.721621i	−0.247314	+	0.968935i	$0.579548\pi$
$854$		0			0
$855$	10835.8	−	1795.18i	0.433422	−	0.0718056i
$856$		0			0
$857$	−14281.4	−	14281.4i	−0.569245	−	0.569245i	0.362672	−	0.931917i	$-0.381865\pi$
$857$	−14281.4	−	14281.4i	−0.569245	−	0.569245i	−0.931917	+	0.362672i	$0.881865\pi$
$858$		0			0
$859$			8984.15i			0.356851i	0.983953	+	0.178426i	$0.0571004\pi$
$859$			8984.15i			0.356851i	−0.983953	+	0.178426i	$0.942900\pi$
$860$		0			0
$861$			20552.8i			0.813517i
$862$		0			0
$863$	−2433.36	−	2433.36i	−0.0959823	−	0.0959823i	0.657485	−	0.753467i	$-0.271620\pi$
$863$	−2433.36	−	2433.36i	−0.0959823	−	0.0959823i	−0.753467	+	0.657485i	$0.771620\pi$
$864$		0			0
$865$	−29947.7	−	21435.0i	−1.17717	−	0.842559i
$866$		0			0
$867$	10374.7	+	10374.7i	0.406392	+	0.406392i
$868$		0			0
$869$	498.969			0.0194780
$870$		0			0
$871$		−	8179.11i		−	0.318184i
$872$		0			0
$873$	7866.97	−	7866.97i	0.304991	−	0.304991i
$874$		0			0
$875$	−6624.19	+	21968.8i	−0.255930	+	0.848777i
$876$		0			0
$877$	7651.61	−	7651.61i	0.294614	−	0.294614i	−0.544286	−	0.838900i	$-0.683199\pi$
$877$	7651.61	−	7651.61i	0.294614	−	0.294614i	0.838900	+	0.544286i	$0.183199\pi$
$878$		0			0
$879$	6250.11			0.239830
$880$		0			0
$881$	26540.1			1.01494			0.507468	−	0.861670i	$-0.330581\pi$
$881$	26540.1			1.01494			0.507468	+	0.861670i	$0.330581\pi$
$882$		0			0
$883$	−1462.95	+	1462.95i	−0.0557556	+	0.0557556i	−0.734435	−	0.678679i	$-0.762553\pi$
$883$	−1462.95	+	1462.95i	−0.0557556	+	0.0557556i	0.678679	+	0.734435i	$0.262553\pi$
$884$		0			0
$885$	−18050.5	−	12919.6i	−0.685605	−	0.490721i
$886$		0			0
$887$	8610.15	−	8610.15i	0.325931	−	0.325931i	−0.525106	−	0.851037i	$-0.675974\pi$
$887$	8610.15	−	8610.15i	0.325931	−	0.325931i	0.851037	+	0.525106i	$0.175974\pi$
$888$		0			0
$889$			34531.1i			1.30274i
$890$		0			0
$891$	−1642.43			−0.0617547
$892$		0			0
$893$	36060.6	+	36060.6i	1.35131	+	1.35131i
$894$		0			0
$895$	−3053.15	−	18429.0i	−0.114029	−	0.688282i
$896$		0			0
$897$	2914.32	+	2914.32i	0.108480	+	0.108480i
$898$		0			0
$899$			41963.5i			1.55680i
$900$		0			0
$901$		−	1556.79i		−	0.0575628i
$902$		0			0
$903$	6239.16	+	6239.16i	0.229929	+	0.229929i
$904$		0			0
$905$	4852.18	+	29288.0i	0.178223	+	1.07576i
$906$		0			0
$907$	29587.3	+	29587.3i	1.08316	+	1.08316i	0.996213	+	0.0869517i	$0.0277126\pi$
$907$	29587.3	+	29587.3i	1.08316	+	1.08316i	0.0869517	+	0.996213i	$0.472287\pi$
$908$		0			0
$909$	1673.74			0.0610720
$910$		0			0
$911$			604.812i			0.0219959i	0.999940	+	0.0109980i	$0.00350083\pi$
$911$			604.812i			0.0219959i	−0.999940	+	0.0109980i	$0.996499\pi$
$912$		0			0
$913$	−10170.4	+	10170.4i	−0.368665	+	0.368665i
$914$		0			0
$915$	−17693.8	−	12664.3i	−0.639276	−	0.457561i
$916$		0			0
$917$	−21179.5	+	21179.5i	−0.762713	+	0.762713i
$918$		0			0
$919$	−53312.0			−1.91360			−0.956801	−	0.290742i	$-0.906098\pi$
$919$	−53312.0			−1.91360			−0.956801	+	0.290742i	$0.906098\pi$
$920$		0			0
$921$	7039.20			0.251845
$922$		0			0
$923$	−2363.27	+	2363.27i	−0.0842773	+	0.0842773i
$924$		0			0
$925$	−104.050	+	211.584i	−0.00369852	+	0.00752092i
$926$		0			0
$927$	−92.3728	+	92.3728i	−0.00327284	+	0.00327284i
$928$		0			0
$929$		−	22543.8i		−	0.796165i	−0.917350	−	0.398082i	$-0.869676\pi$
$929$		−	22543.8i		−	0.796165i	0.917350	−	0.398082i	$-0.130324\pi$
$930$		0			0
$931$	−8015.06			−0.282152
$932$		0			0
$933$	3334.67	+	3334.67i	0.117012	+	0.117012i
$934$		0			0
$935$	−871.262	−	623.605i	−0.0304741	−	0.0218118i
$936$		0			0
$937$	−33066.4	−	33066.4i	−1.15286	−	1.15286i	−0.985976	−	0.166889i	$-0.946628\pi$
$937$	−33066.4	−	33066.4i	−1.15286	−	1.15286i	−0.166889	−	0.985976i	$-0.553372\pi$
$938$		0			0
$939$			782.157i			0.0271829i
$940$		0			0
$941$		−	12513.3i		−	0.433499i	−0.976227	−	0.216750i	$-0.930454\pi$
$941$		−	12513.3i		−	0.433499i	0.976227	−	0.216750i	$-0.0695455\pi$
$942$		0			0
$943$	35111.5	+	35111.5i	1.21250	+	1.21250i
$944$		0			0
$945$	−4889.63	+	810.072i	−0.168317	+	0.0278853i
$946$		0			0
$947$	12488.0	+	12488.0i	0.428516	+	0.428516i	0.888122	−	0.459607i	$-0.152010\pi$
$947$	12488.0	+	12488.0i	0.428516	+	0.428516i	−0.459607	+	0.888122i	$0.652010\pi$
$948$		0			0
$949$	−10090.7			−0.345160
$950$		0			0
$951$		−	32020.0i		−	1.09182i
$952$		0			0
$953$	3326.78	−	3326.78i	0.113080	−	0.113080i	−0.648303	−	0.761383i	$-0.724521\pi$
$953$	3326.78	−	3326.78i	0.113080	−	0.113080i	0.761383	+	0.648303i	$0.224521\pi$
$954$		0			0
$955$	2608.51	+	15745.1i	0.0883867	+	0.533506i
$956$		0			0
$957$	−7735.79	+	7735.79i	−0.261298	+	0.261298i
$958$		0			0
$959$	1461.20			0.0492018
$960$		0			0
$961$	−24653.0			−0.827532
$962$		0			0
$963$	1565.25	−	1565.25i	0.0523774	−	0.0523774i
$964$		0			0
$965$	28495.0	−	39811.4i	0.950555	−	1.32806i
$966$		0			0
$967$	5765.62	−	5765.62i	0.191737	−	0.191737i	−0.604709	−	0.796446i	$-0.706711\pi$
$967$	5765.62	−	5765.62i	0.191737	−	0.191737i	0.796446	+	0.604709i	$0.206711\pi$
$968$		0			0
$969$			1547.65i			0.0513084i
$970$		0			0
$971$	10163.6			0.335905			0.167953	−	0.985795i	$-0.446284\pi$
$971$	10163.6			0.335905			0.167953	+	0.985795i	$0.446284\pi$
$972$		0			0
$973$	27410.3	+	27410.3i	0.903117	+	0.903117i
$974$		0			0
$975$	−4097.94	+	1396.14i	−0.134604	+	0.0458588i
$976$		0			0
$977$	24320.4	+	24320.4i	0.796397	+	0.796397i	0.982525	−	0.186128i	$-0.0595940\pi$
$977$	24320.4	+	24320.4i	0.796397	+	0.796397i	−0.186128	+	0.982525i	$0.559594\pi$
$978$		0			0
$979$			25475.5i			0.831665i
$980$		0			0
$981$			1603.59i			0.0521904i
$982$		0			0
$983$	19998.9	+	19998.9i	0.648896	+	0.648896i	0.952726	−	0.303830i	$-0.0982656\pi$
$983$	19998.9	+	19998.9i	0.648896	+	0.648896i	−0.303830	+	0.952726i	$0.598266\pi$
$984$		0			0
$985$	13550.3	−	18931.6i	0.438323	−	0.612398i
$986$		0			0
$987$	−16272.3	−	16272.3i	−0.524776	−	0.524776i
$988$		0			0
$989$	21317.4			0.685393
$990$		0			0
$991$		−	41881.5i		−	1.34249i	−0.741234	−	0.671246i	$-0.765759\pi$
$991$		−	41881.5i		−	1.34249i	0.741234	−	0.671246i	$-0.234241\pi$
$992$		0			0
$993$	−10101.5	+	10101.5i	−0.322821	+	0.322821i
$994$		0			0
$995$	−48583.7	+	8048.92i	−1.54795	+	0.256450i
$996$		0			0
$997$	23857.4	−	23857.4i	0.757845	−	0.757845i	−0.218085	−	0.975930i	$-0.569981\pi$
$997$	23857.4	−	23857.4i	0.757845	−	0.757845i	0.975930	+	0.218085i	$0.0699809\pi$
$998$		0			0
$999$	−50.9294			−0.00161295

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	480.4.bh.a.367.12		72
4.3	odd	2		120.4.v.a.67.3	yes	72
5.3	odd	4	inner	480.4.bh.a.463.11		72
8.3	odd	2	inner	480.4.bh.a.367.11		72
8.5	even	2		120.4.v.a.67.22	yes	72
20.3	even	4		120.4.v.a.43.22	yes	72
40.3	even	4	inner	480.4.bh.a.463.12		72
40.13	odd	4		120.4.v.a.43.3	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.v.a.43.3	✓	72	40.13	odd	4
120.4.v.a.43.22	yes	72	20.3	even	4
120.4.v.a.67.3	yes	72	4.3	odd	2
120.4.v.a.67.22	yes	72	8.5	even	2
480.4.bh.a.367.11		72	8.3	odd	2	inner
480.4.bh.a.367.12		72	1.1	even	1	trivial
480.4.bh.a.463.11		72	5.3	odd	4	inner
480.4.bh.a.463.12		72	40.3	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	480.bh (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.12132 + 2.12132i) q^{3} +(11.0300 - 1.82735i) q^{5} +(-11.6097 + 11.6097i) q^{7} -9.00000i q^{9} +20.2769 q^{11} +(8.16329 + 8.16329i) q^{13} +(-19.5217 + 27.2746i) q^{15} +(-3.34192 - 3.34192i) q^{17} +109.155i q^{19} -49.2559i q^{21} +(-84.1466 - 84.1466i) q^{23} +(118.322 - 40.3114i) q^{25} +(19.0919 + 19.0919i) q^{27} +179.844 q^{29} +233.332i q^{31} +(-43.0138 + 43.0138i) q^{33} +(-106.840 + 149.270i) q^{35} +(-1.33380 + 1.33380i) q^{37} -34.6339 q^{39} -417.266 q^{41} +(-126.668 + 126.668i) q^{43} +(-16.4462 - 99.2699i) q^{45} +(330.363 - 330.363i) q^{47} +73.4285i q^{49} +14.1786 q^{51} +(232.918 + 232.918i) q^{53} +(223.654 - 37.0531i) q^{55} +(-231.552 - 231.552i) q^{57} +661.807i q^{59} +648.727i q^{61} +(104.488 + 104.488i) q^{63} +(104.958 + 75.1238i) q^{65} +(-500.969 - 500.969i) q^{67} +357.004 q^{69} +289.500i q^{71} +(-618.051 + 618.051i) q^{73} +(-165.484 + 336.511i) q^{75} +(-235.409 + 235.409i) q^{77} +24.6078 q^{79} -81.0000 q^{81} +(-501.575 + 501.575i) q^{83} +(-42.9682 - 30.7545i) q^{85} +(-381.507 + 381.507i) q^{87} +1256.38i q^{89} -189.547 q^{91} +(-494.973 - 494.973i) q^{93} +(199.464 + 1203.98i) q^{95} +(874.108 + 874.108i) q^{97} -182.492i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 104 q^{17} - 88 q^{25} - 912 q^{35} - 864 q^{43} + 1488 q^{51} - 1048 q^{65} - 3696 q^{67} + 1480 q^{73} - 5832 q^{81} + 5360 q^{83} - 3392 q^{91} - 328 q^{97}+O(q^{100}) \) 72 * q - 104 * q^17 - 88 * q^25 - 912 * q^35 - 864 * q^43 + 1488 * q^51 - 1048 * q^65 - 3696 * q^67 + 1480 * q^73 - 5832 * q^81 + 5360 * q^83 - 3392 * q^91 - 328 * q^97

Introduction

L-functions

Modular forms

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Database

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