LMFDB - Embedded newform 100.4.i.a.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,4,Mod(9,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("100.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	100.i (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.90019100057$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.4
Character	$\chi$	$=$	100.29
Dual form			100.4.i.a.69.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.991787 + 1.36508i) q^{3} +(-6.73237 - 8.92610i) q^{5} +19.2807i q^{7} +(7.46366 + 22.9708i) q^{9} +O(q^{10})$	\(q+(-0.991787 + 1.36508i) q^{3} +(-6.73237 - 8.92610i) q^{5} +19.2807i q^{7} +(7.46366 + 22.9708i) q^{9} +(-10.1176 + 31.1388i) q^{11} +(-57.7488 + 18.7637i) q^{13} +(18.8619 - 0.337414i) q^{15} +(-26.1165 - 35.9463i) q^{17} +(-66.8705 + 48.5843i) q^{19} +(-26.3197 - 19.1224i) q^{21} +(71.5207 + 23.2385i) q^{23} +(-34.3505 + 120.188i) q^{25} +(-82.0874 - 26.6718i) q^{27} +(148.327 + 107.766i) q^{29} +(218.552 - 158.787i) q^{31} +(-32.4723 - 44.6944i) q^{33} +(172.101 - 129.805i) q^{35} +(-297.997 + 96.8251i) q^{37} +(31.6606 - 97.4412i) q^{39} +(-79.4032 - 244.378i) q^{41} -22.7927i q^{43} +(154.791 - 221.269i) q^{45} +(256.967 - 353.685i) q^{47} -28.7456 q^{49} +74.9716 q^{51} +(-315.966 + 434.890i) q^{53} +(346.063 - 119.327i) q^{55} -139.469i q^{57} +(186.776 + 574.836i) q^{59} +(156.878 - 482.821i) q^{61} +(-442.893 + 143.905i) q^{63} +(556.273 + 389.147i) q^{65} +(-231.844 - 319.106i) q^{67} +(-102.656 + 74.5837i) q^{69} +(-38.5514 - 28.0092i) q^{71} +(-576.192 - 187.216i) q^{73} +(-129.997 - 166.092i) q^{75} +(-600.378 - 195.075i) q^{77} +(858.995 + 624.096i) q^{79} +(-409.761 + 297.709i) q^{81} +(278.970 + 383.969i) q^{83} +(-145.034 + 475.123i) q^{85} +(-294.218 + 95.5971i) q^{87} +(-230.458 + 709.278i) q^{89} +(-361.778 - 1113.44i) q^{91} +455.824i q^{93} +(883.865 + 269.806i) q^{95} +(-601.664 + 828.120i) q^{97} -790.797 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{5} + 122 q^{9}+O(q^{10}) $ 32 * q + 6 * q^5 + 122 * q^9	$ 32 q + 6 q^{5} + 122 q^{9} + 20 q^{11} + 68 q^{15} - 160 q^{17} + 2 q^{19} - 108 q^{21} + 290 q^{23} + 654 q^{25} + 600 q^{27} + 62 q^{29} - 378 q^{31} - 1280 q^{33} - 278 q^{35} + 680 q^{37} + 592 q^{39} - 528 q^{41} - 1044 q^{45} - 1810 q^{47} - 2796 q^{49} + 1664 q^{51} - 510 q^{53} - 1350 q^{55} + 144 q^{59} - 1346 q^{61} + 1660 q^{63} + 1142 q^{65} + 1890 q^{67} + 956 q^{69} + 786 q^{71} + 3720 q^{73} - 78 q^{75} + 2160 q^{77} + 896 q^{79} + 348 q^{81} + 570 q^{83} + 224 q^{85} + 3240 q^{87} - 2512 q^{89} - 2212 q^{91} + 1536 q^{95} - 2250 q^{97} - 2540 q^{99}+O(q^{100}) $ 32 * q + 6 * q^5 + 122 * q^9 + 20 * q^11 + 68 * q^15 - 160 * q^17 + 2 * q^19 - 108 * q^21 + 290 * q^23 + 654 * q^25 + 600 * q^27 + 62 * q^29 - 378 * q^31 - 1280 * q^33 - 278 * q^35 + 680 * q^37 + 592 * q^39 - 528 * q^41 - 1044 * q^45 - 1810 * q^47 - 2796 * q^49 + 1664 * q^51 - 510 * q^53 - 1350 * q^55 + 144 * q^59 - 1346 * q^61 + 1660 * q^63 + 1142 * q^65 + 1890 * q^67 + 956 * q^69 + 786 * q^71 + 3720 * q^73 - 78 * q^75 + 2160 * q^77 + 896 * q^79 + 348 * q^81 + 570 * q^83 + 224 * q^85 + 3240 * q^87 - 2512 * q^89 - 2212 * q^91 + 1536 * q^95 - 2250 * q^97 - 2540 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

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
$3$	−0.991787	+	1.36508i	−0.190869	+	0.262709i	−0.893717	−	0.448631i	$-0.851912\pi$
$3$	−0.991787	+	1.36508i	−0.190869	+	0.262709i	0.702847	+	0.711341i	$0.251912\pi$
$4$		0			0
$5$	−6.73237	−	8.92610i	−0.602161	−	0.798375i
$5$	−6.73237	−	8.92610i	−0.602161	−	0.798375i
$6$		0			0
$7$			19.2807i			1.04106i	0.853843	+	0.520530i	$0.174266\pi$
$7$			19.2807i			1.04106i	−0.853843	+	0.520530i	$0.825734\pi$
$8$		0			0
$9$	7.46366	+	22.9708i	0.276432	+	0.850770i
$10$		0			0
$11$	−10.1176	+	31.1388i	−0.277325	+	0.853518i	0.711270	+	0.702919i	$0.248120\pi$
$11$	−10.1176	+	31.1388i	−0.277325	+	0.853518i	−0.988595	+	0.150599i	$0.951880\pi$
$12$		0			0
$13$	−57.7488	+	18.7637i	−1.23205	+	0.400317i	−0.851456	−	0.524426i	$-0.824280\pi$
$13$	−57.7488	+	18.7637i	−1.23205	+	0.400317i	−0.380593	+	0.924743i	$0.624280\pi$
$14$		0			0
$15$	18.8619	−	0.337414i	0.324675	−	0.00580800i
$16$		0			0
$17$	−26.1165	−	35.9463i	−0.372600	−	0.512839i	0.581005	−	0.813900i	$-0.302659\pi$
$17$	−26.1165	−	35.9463i	−0.372600	−	0.512839i	−0.953605	+	0.301060i	$0.902659\pi$
$18$		0			0
$19$	−66.8705	+	48.5843i	−0.807429	+	0.586631i	−0.913084	−	0.407772i	$-0.866306\pi$
$19$	−66.8705	+	48.5843i	−0.807429	+	0.586631i	0.105655	+	0.994403i	$0.466306\pi$
$20$		0			0
$21$	−26.3197	−	19.1224i	−0.273496	−	0.198707i
$22$		0			0
$23$	71.5207	+	23.2385i	0.648395	+	0.210676i	0.614706	−	0.788756i	$-0.289274\pi$
$23$	71.5207	+	23.2385i	0.648395	+	0.210676i	0.0336889	+	0.999432i	$0.489274\pi$
$24$		0			0
$25$	−34.3505	+	120.188i	−0.274804	+	0.961500i
$26$		0			0
$27$	−82.0874	−	26.6718i	−0.585101	−	0.190111i
$28$		0			0
$29$	148.327	+	107.766i	0.949781	+	0.690056i	0.950755	−	0.309943i	$-0.100310\pi$
$29$	148.327	+	107.766i	0.949781	+	0.690056i	−0.000974143		1.00000i	$0.500310\pi$
$30$		0			0
$31$	218.552	−	158.787i	1.26623	−	0.919970i	0.267184	−	0.963646i	$-0.413907\pi$
$31$	218.552	−	158.787i	1.26623	−	0.919970i	0.999046	+	0.0436758i	$0.0139069\pi$
$32$		0			0
$33$	−32.4723	−	44.6944i	−0.171294	−	0.235766i
$34$		0			0
$35$	172.101	−	129.805i	0.831156	−	0.626886i
$36$		0			0
$37$	−297.997	+	96.8251i	−1.32406	+	0.430215i	−0.883889	−	0.467697i	$-0.845084\pi$
$37$	−297.997	+	96.8251i	−1.32406	+	0.430215i	−0.440176	+	0.897912i	$0.645084\pi$
$38$		0			0
$39$	31.6606	−	97.4412i	0.129994	−	0.400079i
$40$		0			0
$41$	−79.4032	−	244.378i	−0.302456	−	0.930863i	−0.980614	−	0.195948i	$-0.937222\pi$
$41$	−79.4032	−	244.378i	−0.302456	−	0.930863i	0.678159	−	0.734916i	$-0.262778\pi$
$42$		0			0
$43$		−	22.7927i		−	0.0808339i	−0.999183	−	0.0404169i	$-0.987131\pi$
$43$		−	22.7927i		−	0.0808339i	0.999183	−	0.0404169i	$-0.0128686\pi$
$44$		0			0
$45$	154.791	−	221.269i	0.512777	−	0.732997i
$46$		0			0
$47$	256.967	−	353.685i	0.797499	−	1.09766i	−0.195634	−	0.980677i	$-0.562676\pi$
$47$	256.967	−	353.685i	0.797499	−	1.09766i	0.993133	−	0.116987i	$-0.0373235\pi$
$48$		0			0
$49$	−28.7456			−0.0838064
$50$		0			0
$51$	74.9716			0.205846
$52$		0			0
$53$	−315.966	+	434.890i	−0.818892	+	1.12711i	0.170998	+	0.985271i	$0.445301\pi$
$53$	−315.966	+	434.890i	−0.818892	+	1.12711i	−0.989890	+	0.141837i	$0.954699\pi$
$54$		0			0
$55$	346.063	−	119.327i	0.848421	−	0.292546i
$56$		0			0
$57$		−	139.469i		−	0.324089i
$58$		0			0
$59$	186.776	+	574.836i	0.412138	+	1.26843i	0.914786	+	0.403938i	$0.132359\pi$
$59$	186.776	+	574.836i	0.412138	+	1.26843i	−0.502649	+	0.864491i	$0.667641\pi$
$60$		0			0
$61$	156.878	−	482.821i	0.329282	−	1.01343i	−0.640189	−	0.768218i	$-0.721144\pi$
$61$	156.878	−	482.821i	0.329282	−	1.01343i	0.969471	−	0.245208i	$-0.0788561\pi$
$62$		0			0
$63$	−442.893	+	143.905i	−0.885703	+	0.287782i
$64$		0			0
$65$	556.273	+	389.147i	1.06150	+	0.742581i
$66$		0			0
$67$	−231.844	−	319.106i	−0.422750	−	0.581865i	0.543520	−	0.839396i	$-0.317091\pi$
$67$	−231.844	−	319.106i	−0.422750	−	0.581865i	−0.966270	+	0.257531i	$0.917091\pi$
$68$		0			0
$69$	−102.656	+	74.5837i	−0.179106	+	0.130128i
$70$		0			0
$71$	−38.5514	−	28.0092i	−0.0644396	−	0.0468181i	0.555099	−	0.831784i	$-0.312680\pi$
$71$	−38.5514	−	28.0092i	−0.0644396	−	0.0468181i	−0.619539	+	0.784966i	$0.712680\pi$
$72$		0			0
$73$	−576.192	−	187.216i	−0.923811	−	0.300165i	−0.191782	−	0.981438i	$-0.561427\pi$
$73$	−576.192	−	187.216i	−0.923811	−	0.300165i	−0.732029	+	0.681273i	$0.761427\pi$
$74$		0			0
$75$	−129.997	−	166.092i	−0.200143	−	0.255715i
$76$		0			0
$77$	−600.378	−	195.075i	−0.888563	−	0.288712i
$78$		0			0
$79$	858.995	+	624.096i	1.22335	+	0.888814i	0.996374	−	0.0850870i	$-0.0271168\pi$
$79$	858.995	+	624.096i	1.22335	+	0.888814i	0.226974	+	0.973901i	$0.427117\pi$
$80$		0			0
$81$	−409.761	+	297.709i	−0.562086	+	0.408380i
$82$		0			0
$83$	278.970	+	383.969i	0.368927	+	0.507784i	0.952609	−	0.304198i	$-0.0983885\pi$
$83$	278.970	+	383.969i	0.368927	+	0.507784i	−0.583682	+	0.811982i	$0.698389\pi$
$84$		0			0
$85$	−145.034	+	475.123i	−0.185073	+	0.606286i
$86$		0			0
$87$	−294.218	+	95.5971i	−0.362568	+	0.117806i
$88$		0			0
$89$	−230.458	+	709.278i	−0.274478	+	0.844756i	0.714879	+	0.699248i	$0.246482\pi$
$89$	−230.458	+	709.278i	−0.274478	+	0.844756i	−0.989357	+	0.145508i	$0.953518\pi$
$90$		0			0
$91$	−361.778	−	1113.44i	−0.416754	−	1.28264i
$92$		0			0
$93$			455.824i			0.508245i
$94$		0			0
$95$	883.865	+	269.806i	0.954554	+	0.291384i
$96$		0			0
$97$	−601.664	+	828.120i	−0.629791	+	0.866833i	−0.998020	−	0.0629023i	$-0.979964\pi$
$97$	−601.664	+	828.120i	−0.629791	+	0.866833i	0.368229	+	0.929735i	$0.379964\pi$
$98$		0			0
$99$	−790.797			−0.802809
$100$		0			0
$101$	689.131			0.678922			0.339461	−	0.940620i	$-0.389755\pi$
$101$	689.131			0.678922			0.339461	+	0.940620i	$0.389755\pi$
$102$		0			0
$103$	−954.265	+	1313.43i	−0.912879	+	1.25647i	0.0532953	+	0.998579i	$0.483028\pi$
$103$	−954.265	+	1313.43i	−0.912879	+	1.25647i	−0.966174	+	0.257891i	$0.916972\pi$
$104$		0			0
$105$	6.50559	+	363.671i	0.00604648	+	0.338006i
$106$		0			0
$107$		−	192.974i		−	0.174351i	−0.996193	−	0.0871754i	$-0.972216\pi$
$107$		−	192.974i		−	0.174351i	0.996193	−	0.0871754i	$-0.0277841\pi$
$108$		0			0
$109$	−238.932	−	735.356i	−0.209959	−	0.646186i	−0.999473	−	0.0324546i	$-0.989668\pi$
$109$	−238.932	−	735.356i	−0.209959	−	0.646186i	0.789514	−	0.613732i	$-0.210332\pi$
$110$		0			0
$111$	163.376	−	502.819i	0.139702	−	0.429959i
$112$		0			0
$113$	567.098	−	184.261i	0.472107	−	0.153397i	−0.0632937	−	0.997995i	$-0.520160\pi$
$113$	567.098	−	184.261i	0.472107	−	0.153397i	0.535401	+	0.844598i	$0.320160\pi$
$114$		0			0
$115$	−274.074	−	794.851i	−0.222240	−	0.644524i
$116$		0			0
$117$	−862.035	−	1186.49i	−0.681156	−	0.937530i
$118$		0			0
$119$	693.071	−	503.545i	0.533897	−	0.387899i
$120$		0			0
$121$	209.544	+	152.242i	0.157433	+	0.114382i
$122$		0			0
$123$	412.346	+	133.979i	0.302276	+	0.0982155i
$124$		0			0
$125$	1304.07	−	502.531i	0.933114	−	0.359582i
$126$		0			0
$127$	826.369	+	268.504i	0.577389	+	0.187605i	0.583131	−	0.812378i	$-0.301828\pi$
$127$	826.369	+	268.504i	0.577389	+	0.187605i	−0.00574145	+	0.999984i	$0.501828\pi$
$128$		0			0
$129$	31.1138	+	22.6055i	0.0212358	+	0.0154287i
$130$		0			0
$131$	746.378	−	542.275i	0.497796	−	0.361670i	−0.310378	−	0.950613i	$-0.600456\pi$
$131$	746.378	−	542.275i	0.497796	−	0.361670i	0.808175	+	0.588943i	$0.200456\pi$
$132$		0			0
$133$	−936.739	−	1289.31i	−0.610719	−	0.840582i
$134$		0			0
$135$	314.567	+	912.285i	0.200545	+	0.581607i
$136$		0			0
$137$	966.377	−	313.995i	0.602651	−	0.195813i	0.00822836	−	0.999966i	$-0.497381\pi$
$137$	966.377	−	313.995i	0.602651	−	0.195813i	0.594422	+	0.804153i	$0.297381\pi$
$138$		0			0
$139$	−685.596	+	2110.05i	−0.418356	+	1.28757i	0.490859	+	0.871239i	$0.336683\pi$
$139$	−685.596	+	2110.05i	−0.418356	+	1.28757i	−0.909215	+	0.416328i	$0.863317\pi$
$140$		0			0
$141$	227.950	+	701.559i	0.136148	+	0.419021i
$142$		0			0
$143$		−	1988.07i		−	1.16259i
$144$		0			0
$145$	−36.6629	−	2049.50i	−0.0209978	−	1.17381i
$146$		0			0
$147$	28.5095	−	39.2400i	0.0159961	−	0.0220167i
$148$		0			0
$149$	2196.91			1.20790			0.603952	−	0.797020i	$-0.293592\pi$
$149$	2196.91			1.20790			0.603952	+	0.797020i	$0.293592\pi$
$150$		0			0
$151$	416.323			0.224370			0.112185	−	0.993687i	$-0.464215\pi$
$151$	416.323			0.224370			0.112185	+	0.993687i	$0.464215\pi$
$152$		0			0
$153$	630.791	−	868.209i	0.333310	−	0.458762i
$154$		0			0
$155$	−2888.73	−	881.803i	−1.49695	−	0.456956i
$156$		0			0
$157$		−	834.384i		−	0.424147i	−0.977254	−	0.212074i	$-0.931978\pi$
$157$		−	834.384i		−	0.424147i	0.977254	−	0.212074i	$-0.0680216\pi$
$158$		0			0
$159$	−280.288	−	862.636i	−0.139800	−	0.430261i
$160$		0			0
$161$	−448.054	+	1378.97i	−0.219327	+	0.675019i
$162$		0			0
$163$	−298.523	+	96.9959i	−0.143448	+	0.0466092i	−0.379861	−	0.925043i	$-0.624028\pi$
$163$	−298.523	+	96.9959i	−0.143448	+	0.0466092i	0.236413	+	0.971653i	$0.424028\pi$
$164$		0			0
$165$	−180.330	+	590.750i	−0.0850831	+	0.278726i
$166$		0			0
$167$	1456.22	+	2004.32i	0.674765	+	0.928734i	0.999856	−	0.0169483i	$-0.00539508\pi$
$167$	1456.22	+	2004.32i	0.674765	+	0.928734i	−0.325091	+	0.945683i	$0.605395\pi$
$168$		0			0
$169$	1205.44	−	875.802i	0.548675	−	0.398635i
$170$		0			0
$171$	−1615.12	−	1173.45i	−0.722288	−	0.524773i
$172$		0			0
$173$	3678.17	+	1195.11i	1.61645	+	0.525216i	0.971100	−	0.238671i	$-0.0767119\pi$
$173$	3678.17	+	1195.11i	1.61645	+	0.525216i	0.645349	+	0.763888i	$0.276712\pi$
$174$		0			0
$175$	−2317.30	−	662.302i	−1.00098	−	0.286087i
$176$		0			0
$177$	−969.938	−	315.152i	−0.411893	−	0.133832i
$178$		0			0
$179$	−1784.60	−	1296.59i	−0.745181	−	0.541405i	0.149149	−	0.988815i	$-0.452347\pi$
$179$	−1784.60	−	1296.59i	−0.745181	−	0.541405i	−0.894329	+	0.447409i	$0.852347\pi$
$180$		0			0
$181$	−2056.80	+	1494.35i	−0.844644	+	0.613670i	−0.923664	−	0.383203i	$-0.874821\pi$
$181$	−2056.80	+	1494.35i	−0.844644	+	0.613670i	0.0790201	+	0.996873i	$0.474821\pi$
$182$		0			0
$183$	503.499	+	693.007i	0.203386	+	0.279937i
$184$		0			0
$185$	2870.49	+	2008.09i	1.14077	+	0.798041i
$186$		0			0
$187$	1383.56	−	449.547i	0.541049	−	0.175797i
$188$		0			0
$189$	514.251	−	1582.70i	0.197917	−	0.609125i
$190$		0			0
$191$	788.513	+	2426.79i	0.298716	+	0.919354i	0.981948	+	0.189152i	$0.0605740\pi$
$191$	788.513	+	2426.79i	0.298716	+	0.919354i	−0.683231	+	0.730202i	$0.739426\pi$
$192$		0			0
$193$		−	3107.44i		−	1.15895i	−0.814988	−	0.579477i	$-0.803257\pi$
$193$		−	3107.44i		−	1.15895i	0.814988	−	0.579477i	$-0.196743\pi$
$194$		0			0
$195$	−1082.92	+	373.405i	−0.397690	+	0.137129i
$196$		0			0
$197$	−980.816	+	1349.98i	−0.354722	+	0.488233i	−0.948669	−	0.316272i	$-0.897569\pi$
$197$	−980.816	+	1349.98i	−0.354722	+	0.488233i	0.593947	+	0.804504i	$0.297569\pi$
$198$		0			0
$199$	−4910.67			−1.74929			−0.874644	−	0.484767i	$-0.838905\pi$
$199$	−4910.67			−1.74929			−0.874644	+	0.484767i	$0.838905\pi$
$200$		0			0
$201$	665.544			0.233552
$202$		0			0
$203$	−2077.80	+	2859.85i	−0.718390	+	0.988779i
$204$		0			0
$205$	−1646.77	+	2354.00i	−0.561050	+	0.802003i
$206$		0			0
$207$			1816.33i			0.609873i
$208$		0			0
$209$	−836.286	−	2573.82i	−0.276780	−	0.851842i
$210$		0			0
$211$	−832.877	+	2563.33i	−0.271742	+	0.836337i	0.718321	+	0.695712i	$0.244911\pi$
$211$	−832.877	+	2563.33i	−0.271742	+	0.836337i	−0.990063	+	0.140625i	$0.955089\pi$
$212$		0			0
$213$	76.4696	−	24.8465i	0.0245991	−	0.00799274i
$214$		0			0
$215$	−203.450	+	153.449i	−0.0645357	+	0.0486750i
$216$		0			0
$217$	3061.53	+	4213.84i	0.957744	+	1.31822i
$218$		0			0
$219$	827.025	−	600.869i	0.255183	−	0.185402i
$220$		0			0
$221$	2182.69	+	1585.82i	0.664359	+	0.482685i
$222$		0			0
$223$	5873.35	+	1908.37i	1.76372	+	0.573066i	0.997575	−	0.0696065i	$-0.0221744\pi$
$223$	5873.35	+	1908.37i	1.76372	+	0.573066i	0.766141	+	0.642672i	$0.222174\pi$
$224$		0			0
$225$	−3017.18	+	107.981i	−0.893980	+	0.0319945i
$226$		0			0
$227$	1905.02	+	618.979i	0.557007	+	0.180983i	0.573974	−	0.818873i	$-0.305401\pi$
$227$	1905.02	+	618.979i	0.557007	+	0.180983i	−0.0169668	+	0.999856i	$0.505401\pi$
$228$		0			0
$229$	−592.410	−	430.411i	−0.170950	−	0.124202i	0.499020	−	0.866590i	$-0.333693\pi$
$229$	−592.410	−	430.411i	−0.170950	−	0.124202i	−0.669970	+	0.742388i	$0.733693\pi$
$230$		0			0
$231$	861.739	−	626.090i	0.245447	−	0.178328i
$232$		0			0
$233$	−3237.49	−	4456.03i	−0.910280	−	1.25289i	−0.967071	−	0.254507i	$-0.918087\pi$
$233$	−3237.49	−	4456.03i	−0.910280	−	1.25289i	0.0567904	−	0.998386i	$-0.481913\pi$
$234$		0			0
$235$	−4887.02	+	87.4223i	−1.35657	+	0.0242672i
$236$		0			0
$237$	−1703.88	+	553.624i	−0.466999	+	0.151737i
$238$		0			0
$239$	−718.451	+	2211.17i	−0.194447	+	0.598445i	0.805536	+	0.592547i	$0.201878\pi$
$239$	−718.451	+	2211.17i	−0.194447	+	0.598445i	−0.999983	+	0.00589834i	$0.998122\pi$
$240$		0			0
$241$	−540.267	−	1662.77i	−0.144405	−	0.444433i	0.852529	−	0.522680i	$-0.175068\pi$
$241$	−540.267	−	1662.77i	−0.144405	−	0.444433i	−0.996934	+	0.0782468i	$0.975068\pi$
$242$		0			0
$243$		−	3185.04i		−	0.840824i
$244$		0			0
$245$	193.526	+	256.586i	0.0504649	+	0.0669089i
$246$		0			0
$247$	2950.07	−	4060.42i	0.759953	−	1.04599i
$248$		0			0
$249$	−800.826			−0.203817
$250$		0			0
$251$	−5678.16			−1.42790			−0.713948	−	0.700198i	$-0.753095\pi$
$251$	−5678.16			−1.42790			−0.713948	+	0.700198i	$0.753095\pi$
$252$		0			0
$253$	−1447.24	+	1991.95i	−0.359632	+	0.494991i
$254$		0			0
$255$	−504.736	−	669.204i	−0.123952	−	0.164342i
$256$		0			0
$257$			892.188i			0.216549i	0.994121	+	0.108275i	$0.0345326\pi$
$257$			892.188i			0.216549i	−0.994121	+	0.108275i	$0.965467\pi$
$258$		0			0
$259$	−1866.86	−	5745.59i	−0.447879	−	1.37843i
$260$		0			0
$261$	−1368.41	+	4211.52i	−0.324529	+	0.998799i
$262$		0			0
$263$	3981.72	−	1293.74i	0.933550	−	0.303329i	0.197536	−	0.980296i	$-0.436706\pi$
$263$	3981.72	−	1293.74i	0.933550	−	0.303329i	0.736013	+	0.676967i	$0.236706\pi$
$264$		0			0
$265$	6009.07	−	107.494i	1.39296	−	0.0249182i
$266$		0			0
$267$	−739.654	−	1018.05i	−0.169536	−	0.233346i
$268$		0			0
$269$	5480.31	−	3981.68i	1.24216	−	0.902480i	0.244417	−	0.969670i	$-0.421403\pi$
$269$	5480.31	−	3981.68i	1.24216	−	0.902480i	0.997740	+	0.0671899i	$0.0214033\pi$
$270$		0			0
$271$	3530.87	+	2565.33i	0.791458	+	0.575028i	0.908396	−	0.418111i	$-0.137308\pi$
$271$	3530.87	+	2565.33i	0.791458	+	0.575028i	−0.116938	+	0.993139i	$0.537308\pi$
$272$		0			0
$273$	1878.74	+	610.438i	0.416506	+	0.135331i
$274$		0			0
$275$	−3394.95	−	2285.64i	−0.744448	−	0.501198i
$276$		0			0
$277$	3474.96	+	1129.08i	0.753754	+	0.244910i	0.660596	−	0.750742i	$-0.270304\pi$
$277$	3474.96	+	1129.08i	0.753754	+	0.244910i	0.0931583	+	0.995651i	$0.470304\pi$
$278$		0			0
$279$	5278.67	+	3835.18i	1.13271	+	0.822961i
$280$		0			0
$281$	−5247.59	+	3812.59i	−1.11404	+	0.809396i	−0.983295	−	0.182020i	$-0.941736\pi$
$281$	−5247.59	+	3812.59i	−1.11404	+	0.809396i	−0.130743	+	0.991416i	$0.541736\pi$
$282$		0			0
$283$	2104.14	+	2896.10i	0.441972	+	0.608322i	0.970649	−	0.240501i	$-0.0773117\pi$
$283$	2104.14	+	2896.10i	0.441972	+	0.608322i	−0.528677	+	0.848823i	$0.677312\pi$
$284$		0			0
$285$	−1244.91	+	938.954i	−0.258744	+	0.195154i
$286$		0			0
$287$	4711.78	−	1530.95i	0.969085	−	0.314875i
$288$		0			0
$289$	908.135	−	2794.95i	0.184843	−	0.568889i
$290$		0			0
$291$	−533.725	−	1642.64i	−0.107517	−	0.330904i
$292$		0			0
$293$		−	8577.82i		−	1.71031i	−0.518371	−	0.855156i	$-0.673461\pi$
$293$		−	8577.82i		−	1.71031i	0.518371	−	0.855156i	$-0.326539\pi$
$294$		0			0
$295$	3873.60	−	5537.19i	0.764508	−	1.09284i
$296$		0			0
$297$	1661.06	−	2286.25i	0.324526	−	0.446672i
$298$		0			0
$299$	−4566.28			−0.883192
$300$		0			0
$301$	439.460			0.0841529
$302$		0			0
$303$	−683.472	+	940.718i	−0.129586	+	0.178359i
$304$		0			0
$305$	−5365.87	+	1850.22i	−1.00737	+	0.347355i
$306$		0			0
$307$			2898.31i			0.538812i	0.963027	+	0.269406i	$0.0868274\pi$
$307$			2898.31i			0.538812i	−0.963027	+	0.269406i	$0.913173\pi$
$308$		0			0
$309$	−846.510	−	2605.29i	−0.155846	−	0.479644i
$310$		0			0
$311$	3054.97	−	9402.24i	0.557015	−	1.71431i	−0.133548	−	0.991042i	$-0.542637\pi$
$311$	3054.97	−	9402.24i	0.557015	−	1.71431i	0.690563	−	0.723272i	$-0.257363\pi$
$312$		0			0
$313$	−2315.67	+	752.406i	−0.418177	+	0.135874i	−0.510545	−	0.859851i	$-0.670556\pi$
$313$	−2315.67	+	752.406i	−0.418177	+	0.135874i	0.0923683	+	0.995725i	$0.470556\pi$
$314$		0			0
$315$	4266.23	+	2984.49i	0.763094	+	0.533831i
$316$		0			0
$317$	−3542.09	−	4875.27i	−0.627582	−	0.863793i	0.370295	−	0.928914i	$-0.379257\pi$
$317$	−3542.09	−	4875.27i	−0.627582	−	0.863793i	−0.997877	+	0.0651213i	$0.979257\pi$
$318$		0			0
$319$	−4856.41	+	3528.39i	−0.852373	+	0.619285i
$320$		0			0
$321$	263.425	+	191.389i	0.0458036	+	0.0332782i
$322$		0			0
$323$	3492.85	+	1134.90i	0.601695	+	0.195503i
$324$		0			0
$325$	−271.466	−	7585.23i	−0.0463331	−	1.29462i
$326$		0			0
$327$	1240.79	+	403.156i	0.209834	+	0.0681792i
$328$		0			0
$329$	6819.29	+	4954.50i	1.14273	+	0.830245i
$330$		0			0
$331$	8199.30	−	5957.14i	1.36155	−	0.989227i	0.363209	−	0.931707i	$-0.381681\pi$
$331$	8199.30	−	5957.14i	1.36155	−	0.989227i	0.998344	−	0.0575193i	$-0.0183191\pi$
$332$		0			0
$333$	−4448.30	−	6122.56i	−0.732028	−	1.00755i
$334$		0			0
$335$	−1287.51	+	4217.80i	−0.209983	+	0.687890i
$336$		0			0
$337$	−8498.46	+	2761.32i	−1.37371	+	0.446346i	−0.900597	−	0.434656i	$-0.856870\pi$
$337$	−8498.46	+	2761.32i	−1.37371	+	0.446346i	−0.473114	+	0.881001i	$0.656870\pi$
$338$		0			0
$339$	−310.910	+	956.881i	−0.0498121	+	0.153306i
$340$		0			0
$341$	2733.22	+	8412.00i	0.434054	+	1.33588i
$342$		0			0
$343$			6059.05i			0.953813i
$344$		0			0
$345$	1356.86	+	414.190i	0.211741	+	0.0646354i
$346$		0			0
$347$	−4282.45	+	5894.29i	−0.662519	+	0.911879i	−0.999562	−	0.0296103i	$-0.990573\pi$
$347$	−4282.45	+	5894.29i	−0.662519	+	0.911879i	0.337043	+	0.941489i	$0.390573\pi$
$348$		0			0
$349$	−10203.2			−1.56494			−0.782471	−	0.622686i	$-0.786041\pi$
$349$	−10203.2			−1.56494			−0.782471	+	0.622686i	$0.786041\pi$
$350$		0			0
$351$	5240.91			0.796978
$352$		0			0
$353$	−4237.06	+	5831.82i	−0.638856	+	0.879310i	−0.998554	−	0.0537590i	$-0.982880\pi$
$353$	−4237.06	+	5831.82i	−0.638856	+	0.879310i	0.359698	+	0.933069i	$0.382880\pi$
$354$		0			0
$355$	9.52898	+	532.682i	0.00142464	+	0.0796390i
$356$		0			0
$357$			1445.51i			0.214298i
$358$		0			0
$359$	−211.613	−	651.278i	−0.0311101	−	0.0957469i	0.934296	−	0.356499i	$-0.116030\pi$
$359$	−211.613	−	651.278i	−0.0311101	−	0.0957469i	−0.965406	+	0.260752i	$0.916030\pi$
$360$		0			0
$361$	−8.31402	+	25.5879i	−0.00121213	+	0.00373056i
$362$		0			0
$363$	−415.646	+	135.051i	−0.0600985	+	0.0195272i
$364$		0			0
$365$	2208.03	+	6403.56i	0.316640	+	0.918295i
$366$		0			0
$367$	−113.089	−	155.653i	−0.0160850	−	0.0221391i	0.800899	−	0.598800i	$-0.204355\pi$
$367$	−113.089	−	155.653i	−0.0160850	−	0.0221391i	−0.816984	+	0.576661i	$0.804355\pi$
$368$		0			0
$369$	5020.91	−	3647.91i	0.708342	−	0.514641i
$370$		0			0
$371$	−8384.99	−	6092.05i	−1.17339	−	0.852516i
$372$		0			0
$373$	8275.25	+	2688.79i	1.14873	+	0.373245i	0.820665	−	0.571410i	$-0.193603\pi$
$373$	8275.25	+	2688.79i	1.14873	+	0.373245i	0.328065	+	0.944655i	$0.393603\pi$
$374$		0			0
$375$	−607.362	+	2278.55i	−0.0836375	+	0.313771i
$376$		0			0
$377$	−10587.8	−	3440.19i	−1.44642	−	0.469970i
$378$		0			0
$379$	5368.94	+	3900.76i	0.727662	+	0.528677i	0.888823	−	0.458251i	$-0.151524\pi$
$379$	5368.94	+	3900.76i	0.727662	+	0.528677i	−0.161161	+	0.986928i	$0.551524\pi$
$380$		0			0
$381$	−1186.11	+	861.760i	−0.159492	+	0.115877i
$382$		0			0
$383$	−4445.27	−	6118.39i	−0.593062	−	0.816280i	0.401989	−	0.915644i	$-0.368319\pi$
$383$	−4445.27	−	6118.39i	−0.593062	−	0.816280i	−0.995051	+	0.0993646i	$0.968319\pi$
$384$		0			0
$385$	2300.71	+	6672.34i	0.304558	+	0.883257i
$386$		0			0
$387$	523.567	−	170.117i	0.0687711	−	0.0223451i
$388$		0			0
$389$	−4684.95	+	14418.8i	−0.610633	+	1.87934i	−0.158575	+	0.987347i	$0.550690\pi$
$389$	−4684.95	+	14418.8i	−0.610633	+	1.87934i	−0.452059	+	0.891988i	$0.649310\pi$
$390$		0			0
$391$	−1032.54	−	3177.82i	−0.133549	−	0.411021i
$392$		0			0
$393$			1556.69i			0.199808i
$394$		0			0
$395$	−212.323	−	11869.1i	−0.0270459	−	1.51190i
$396$		0			0
$397$	481.428	−	662.629i	0.0608620	−	0.0837693i	−0.777501	−	0.628882i	$-0.783513\pi$
$397$	481.428	−	662.629i	0.0608620	−	0.0837693i	0.838363	+	0.545112i	$0.183513\pi$
$398$		0			0
$399$	2689.05			0.337396
$400$		0			0
$401$	−5143.65			−0.640552			−0.320276	−	0.947324i	$-0.603776\pi$
$401$	−5143.65			−0.640552			−0.320276	+	0.947324i	$0.603776\pi$
$402$		0			0
$403$	−9641.68	+	13270.6i	−1.19178	+	1.64034i
$404$		0			0
$405$	5416.04	+	1653.28i	0.664507	+	0.202845i
$406$		0			0
$407$		−	10258.9i		−	1.24942i
$408$		0			0
$409$	1703.05	+	5241.44i	0.205893	+	0.633673i	0.999676	+	0.0254717i	$0.00810877\pi$
$409$	1703.05	+	5241.44i	0.205893	+	0.633673i	−0.793783	+	0.608202i	$0.791891\pi$
$410$		0			0
$411$	−529.812	+	1630.60i	−0.0635857	+	0.195697i
$412$		0			0
$413$	−11083.2	+	3601.17i	−1.32051	+	0.429060i
$414$		0			0
$415$	1549.22	−	5075.13i	0.183249	−	0.600310i
$416$		0			0
$417$	−2200.41	−	3028.61i	−0.258404	−	0.355663i
$418$		0			0
$419$	3808.22	−	2766.84i	0.444019	−	0.322599i	−0.343211	−	0.939258i	$-0.611515\pi$
$419$	3808.22	−	2766.84i	0.444019	−	0.322599i	0.787230	+	0.616660i	$0.211515\pi$
$420$		0			0
$421$	−4927.80	−	3580.26i	−0.570466	−	0.414468i	0.264808	−	0.964301i	$-0.414691\pi$
$421$	−4927.80	−	3580.26i	−0.570466	−	0.414468i	−0.835274	+	0.549833i	$0.814691\pi$
$422$		0			0
$423$	10042.3	+	3262.95i	1.15431	+	0.375059i
$424$		0			0
$425$	5217.42	−	1904.11i	0.595487	−	0.217324i
$426$		0			0
$427$	9309.14	+	3024.72i	1.05504	+	0.342802i
$428$		0			0
$429$	2713.87	+	1971.74i	0.305424	+	0.221904i
$430$		0			0
$431$	1905.82	−	1384.66i	0.212993	−	0.154749i	−0.476174	−	0.879351i	$-0.657977\pi$
$431$	1905.82	−	1384.66i	0.212993	−	0.154749i	0.689167	+	0.724603i	$0.257977\pi$
$432$		0			0
$433$	−2467.43	−	3396.12i	−0.273850	−	0.376922i	0.649835	−	0.760075i	$-0.274838\pi$
$433$	−2467.43	−	3396.12i	−0.273850	−	0.376922i	−0.923685	+	0.383153i	$0.874838\pi$
$434$		0			0
$435$	2834.09	+	1982.62i	0.312378	+	0.218527i
$436$		0			0
$437$	−5911.65	+	1920.81i	−0.647122	+	0.210263i
$438$		0			0
$439$	−3217.74	+	9903.19i	−0.349828	+	1.07666i	0.609120	+	0.793078i	$0.291523\pi$
$439$	−3217.74	+	9903.19i	−0.349828	+	1.07666i	−0.958948	+	0.283582i	$0.908477\pi$
$440$		0			0
$441$	−214.547	−	660.309i	−0.0231668	−	0.0713000i
$442$		0			0
$443$		−	8409.69i		−	0.901933i	−0.892541	−	0.450967i	$-0.851079\pi$
$443$		−	8409.69i		−	0.901933i	0.892541	−	0.450967i	$-0.148921\pi$
$444$		0			0
$445$	7882.61	−	2718.02i	0.839712	−	0.289543i
$446$		0			0
$447$	−2178.87	+	2998.95i	−0.230552	+	0.317328i
$448$		0			0
$449$	4201.34			0.441589			0.220794	−	0.975320i	$-0.429135\pi$
$449$	4201.34			0.441589			0.220794	+	0.975320i	$0.429135\pi$
$450$		0			0
$451$	8413.00			0.878387
$452$		0			0
$453$	−412.903	+	568.313i	−0.0428254	+	0.0589441i
$454$		0			0
$455$	−7503.04	+	10725.3i	−0.773072	+	1.10508i
$456$		0			0
$457$		−	5321.74i		−	0.544727i	−0.962194	−	0.272364i	$-0.912195\pi$
$457$		−	5321.74i		−	0.544727i	0.962194	−	0.272364i	$-0.0878054\pi$
$458$		0			0
$459$	1185.09	+	3647.32i	0.120512	+	0.370898i
$460$		0			0
$461$	2738.41	−	8427.97i	0.276661	−	0.851474i	−0.712114	−	0.702063i	$-0.752262\pi$
$461$	2738.41	−	8427.97i	0.276661	−	0.851474i	0.988775	−	0.149411i	$-0.0477377\pi$
$462$		0			0
$463$	−17895.3	+	5814.55i	−1.79626	+	0.583639i	−0.999779	−	0.0210289i	$-0.993306\pi$
$463$	−17895.3	+	5814.55i	−1.79626	+	0.583639i	−0.796478	+	0.604668i	$0.793306\pi$
$464$		0			0
$465$	4068.73	−	3068.77i	0.405769	−	0.306045i
$466$		0			0
$467$	−6828.19	−	9398.20i	−0.676598	−	0.931257i	0.323289	−	0.946300i	$-0.395211\pi$
$467$	−6828.19	−	9398.20i	−0.676598	−	0.931257i	−0.999887	+	0.0150435i	$0.995211\pi$
$468$		0			0
$469$	6152.59	−	4470.11i	0.605757	−	0.440108i
$470$		0			0
$471$	1139.00	+	827.531i	0.111427	+	0.0809567i
$472$		0			0
$473$	709.738	+	230.608i	0.0689932	+	0.0224172i
$474$		0			0
$475$	−3542.19	−	9705.89i	−0.342162	−	0.937552i
$476$		0			0
$477$	−12348.0	−	4012.12i	−1.18528	−	0.385120i
$478$		0			0
$479$	−1194.46	−	867.827i	−0.113938	−	0.0827809i	0.529357	−	0.848399i	$-0.322433\pi$
$479$	−1194.46	−	867.827i	−0.113938	−	0.0827809i	−0.643295	+	0.765618i	$0.722433\pi$
$480$		0			0
$481$	15392.2	−	11183.1i	1.45909	−	1.06009i
$482$		0			0
$483$	−1438.03	−	1979.27i	−0.135471	−	0.186460i
$484$		0			0
$485$	11442.5	−	204.691i	1.07129	−	0.0191640i
$486$		0			0
$487$	15279.3	−	4964.53i	1.42170	−	0.461939i	0.505560	−	0.862791i	$-0.331286\pi$
$487$	15279.3	−	4964.53i	1.42170	−	0.461939i	0.916143	+	0.400852i	$0.131286\pi$
$488$		0			0
$489$	163.664	−	503.706i	0.0151353	−	0.0465815i
$490$		0			0
$491$	−2308.39	−	7104.51i	−0.212172	−	0.652998i	−0.999342	−	0.0362624i	$-0.988455\pi$
$491$	−2308.39	−	7104.51i	−0.212172	−	0.652998i	0.787170	−	0.616736i	$-0.211545\pi$
$492$		0			0
$493$		−	8146.29i		−	0.744200i
$494$		0			0
$495$	5323.93	+	7058.73i	0.483420	+	0.640942i
$496$		0			0
$497$	540.038	−	743.299i	0.0487405	−	0.0670855i
$498$		0			0
$499$	−1630.62			−0.146286			−0.0731429	−	0.997321i	$-0.523303\pi$
$499$	−1630.62			−0.146286			−0.0731429	+	0.997321i	$0.523303\pi$
$500$		0			0
$501$	−4180.31			−0.372779
$502$		0			0
$503$	−7000.91	+	9635.92i	−0.620586	+	0.854164i	−0.997395	−	0.0721271i	$-0.977021\pi$
$503$	−7000.91	+	9635.92i	−0.620586	+	0.854164i	0.376809	+	0.926291i	$0.377021\pi$
$504$		0			0
$505$	−4639.49	−	6151.26i	−0.408821	−	0.542034i
$506$		0			0
$507$			2514.13i			0.220229i
$508$		0			0
$509$	−4075.26	−	12542.4i	−0.354878	−	1.09220i	−0.956080	−	0.293105i	$-0.905311\pi$
$509$	−4075.26	−	12542.4i	−0.354878	−	1.09220i	0.601202	−	0.799097i	$-0.294689\pi$
$510$		0			0
$511$	3609.66	−	11109.4i	0.312489	−	0.961743i
$512$		0			0
$513$	6785.06	−	2204.60i	0.583952	−	0.189738i
$514$		0			0
$515$	18148.3	−	324.649i	1.55283	−	0.0277781i
$516$		0			0
$517$	8413.42	+	11580.1i	0.715709	+	0.985089i
$518$		0			0
$519$	−5279.37	+	3835.69i	−0.446510	+	0.324409i
$520$		0			0
$521$	4856.93	+	3528.77i	0.408418	+	0.296733i	0.772961	−	0.634453i	$-0.218775\pi$
$521$	4856.93	+	3528.77i	0.408418	+	0.296733i	−0.364543	+	0.931187i	$0.618775\pi$
$522$		0			0
$523$	12843.3	+	4173.06i	1.07381	+	0.348901i	0.791969	−	0.610562i	$-0.209056\pi$
$523$	12843.3	+	4173.06i	1.07381	+	0.348901i	0.281837	+	0.959462i	$0.409056\pi$
$524$		0			0
$525$	3202.36	−	2506.43i	0.266214	−	0.208361i
$526$		0			0
$527$	−11415.7	−	3709.17i	−0.943593	−	0.306592i
$528$		0			0
$529$	−5268.13	−	3827.52i	−0.432985	−	0.314582i
$530$		0			0
$531$	−11810.4	+	8580.77i	−0.965214	+	0.701269i
$532$		0			0
$533$	9170.88	+	12622.6i	0.745281	+	1.02579i
$534$		0			0
$535$	−1722.51	+	1299.17i	−0.139197	+	0.104987i
$536$		0			0
$537$	3539.89	−	1150.18i	0.284464	−	0.0924281i
$538$		0			0
$539$	290.836	−	895.103i	0.0232416	−	0.0715302i
$540$		0			0
$541$	−2161.22	−	6651.56i	−0.171753	−	0.528600i	0.827718	−	0.561145i	$-0.189639\pi$
$541$	−2161.22	−	6651.56i	−0.171753	−	0.528600i	−0.999470	+	0.0325445i	$0.989639\pi$
$542$		0			0
$543$		−	4289.77i		−	0.339027i
$544$		0			0
$545$	−4955.28	+	7083.41i	−0.389470	+	0.556734i
$546$		0			0
$547$	−2719.63	+	3743.25i	−0.212583	+	0.292596i	−0.901971	−	0.431797i	$-0.857880\pi$
$547$	−2719.63	+	3743.25i	−0.212583	+	0.292596i	0.689388	+	0.724393i	$0.257880\pi$
$548$		0			0
$549$	12261.7			0.953216
$550$		0			0
$551$	−15154.4			−1.17169
$552$		0			0
$553$	−12033.0	+	16562.0i	−0.925309	+	1.27358i
$554$		0			0
$555$	−5588.12	+	1926.85i	−0.427392	+	0.147370i
$556$		0			0
$557$		−	4886.32i		−	0.371705i	−0.982578	−	0.185853i	$-0.940495\pi$
$557$		−	4886.32i		−	0.371705i	0.982578	−	0.185853i	$-0.0595047\pi$
$558$		0			0
$559$	427.676	+	1316.25i	0.0323592	+	0.0995913i
$560$		0			0
$561$	−758.533	+	2334.52i	−0.0570861	+	0.175693i
$562$		0			0
$563$	16501.7	−	5361.74i	1.23528	−	0.401368i	0.382659	−	0.923890i	$-0.375009\pi$
$563$	16501.7	−	5361.74i	1.23528	−	0.401368i	0.852626	+	0.522521i	$0.175009\pi$
$564$		0			0
$565$	−5462.65	−	3821.46i	−0.406753	−	0.284549i
$566$		0			0
$567$	−5740.04	−	7900.48i	−0.425148	−	0.585166i
$568$		0			0
$569$	6342.28	−	4607.94i	0.467280	−	0.339499i	−0.329100	−	0.944295i	$-0.606745\pi$
$569$	6342.28	−	4607.94i	0.467280	−	0.339499i	0.796380	+	0.604796i	$0.206745\pi$
$570$		0			0
$571$	12182.9	+	8851.37i	0.892885	+	0.648719i	0.936629	−	0.350324i	$-0.113929\pi$
$571$	12182.9	+	8851.37i	0.892885	+	0.648719i	−0.0437438	+	0.999043i	$0.513929\pi$
$572$		0			0
$573$	−4094.80	−	1330.48i	−0.298539	−	0.0970011i
$574$		0			0
$575$	−5249.75	+	7797.64i	−0.380747	+	0.565538i
$576$		0			0
$577$	4703.23	+	1528.17i	0.339338	+	0.110258i	0.473729	−	0.880671i	$-0.342908\pi$
$577$	4703.23	+	1528.17i	0.339338	+	0.110258i	−0.134391	+	0.990928i	$0.542908\pi$
$578$		0			0
$579$	4241.89	+	3081.92i	0.304468	+	0.221209i
$580$		0			0
$581$	−7403.20	+	5378.74i	−0.528634	+	0.384075i
$582$		0			0
$583$	−10345.1	−	14238.8i	−0.734908	−	1.01151i
$584$		0			0
$585$	−4787.19	+	15682.5i	−0.338335	+	1.10836i
$586$		0			0
$587$	−20710.9	+	6729.38i	−1.45627	+	0.473171i	−0.926928	−	0.375239i	$-0.877561\pi$
$587$	−20710.9	+	6729.38i	−1.45627	+	0.473171i	−0.529341	+	0.848409i	$0.677561\pi$
$588$		0			0
$589$	−6900.12	+	21236.4i	−0.482707	+	1.48562i
$590$		0			0
$591$	−870.063	−	2677.78i	−0.0605577	−	0.186377i
$592$		0			0
$593$		−	12196.0i		−	0.844573i	−0.906462	−	0.422286i	$-0.861228\pi$
$593$		−	12196.0i		−	0.844573i	0.906462	−	0.422286i	$-0.138772\pi$
$594$		0			0
$595$	−9160.70	−	2796.37i	−0.631180	−	0.192672i
$596$		0			0
$597$	4870.34	−	6703.45i	0.333886	−	0.459554i
$598$		0			0
$599$	−16092.8			−1.09772			−0.548859	−	0.835915i	$-0.684938\pi$
$599$	−16092.8			−1.09772			−0.548859	+	0.835915i	$0.684938\pi$
$600$		0			0
$601$	15700.0			1.06559			0.532794	−	0.846245i	$-0.321142\pi$
$601$	15700.0			1.06559			0.532794	+	0.846245i	$0.321142\pi$
$602$		0			0
$603$	5599.71	−	7707.34i	0.378172	−	0.520509i
$604$		0			0
$605$	−51.7942	−	2895.36i	−0.00348055	−	0.194567i
$606$		0			0
$607$			18627.9i			1.24561i	0.782378	+	0.622803i	$0.214006\pi$
$607$			18627.9i			1.24561i	−0.782378	+	0.622803i	$0.785994\pi$
$608$		0			0
$609$	−1843.18	−	5672.73i	−0.122643	−	0.377456i
$610$		0			0
$611$	−8203.09	+	25246.5i	−0.543145	+	1.67163i
$612$		0			0
$613$	3603.22	−	1170.76i	0.237411	−	0.0771394i	−0.187895	−	0.982189i	$-0.560167\pi$
$613$	3603.22	−	1170.76i	0.237411	−	0.0771394i	0.425306	+	0.905050i	$0.360167\pi$
$614$		0			0
$615$	−1580.15	−	4582.64i	−0.103606	−	0.300471i
$616$		0			0
$617$	16292.6	+	22424.8i	1.06307	+	1.46319i	0.876901	+	0.480672i	$0.159607\pi$
$617$	16292.6	+	22424.8i	1.06307	+	1.46319i	0.186169	+	0.982518i	$0.440393\pi$
$618$		0			0
$619$	6193.13	−	4499.57i	0.402137	−	0.292170i	−0.368274	−	0.929717i	$-0.620051\pi$
$619$	6193.13	−	4499.57i	0.402137	−	0.292170i	0.770411	+	0.637548i	$0.220051\pi$
$620$		0			0
$621$	−5251.13	−	3815.17i	−0.339325	−	0.246534i
$622$		0			0
$623$	−13675.4	−	4443.40i	−0.879442	−	0.285748i
$624$		0			0
$625$	−13265.1	−	8257.00i	−0.848966	−	0.528448i
$626$		0			0
$627$	4342.88	+	1411.09i	0.276616	+	0.0898779i
$628$		0			0
$629$	11263.2	+	8183.16i	0.713977	+	0.518735i
$630$		0			0
$631$	−3163.92	+	2298.73i	−0.199610	+	0.145025i	−0.683100	−	0.730325i	$-0.739369\pi$
$631$	−3163.92	+	2298.73i	−0.199610	+	0.145025i	0.483490	+	0.875350i	$0.339369\pi$
$632$		0			0
$633$	−2673.11	−	3679.22i	−0.167846	−	0.231021i
$634$		0			0
$635$	−3166.73	−	9183.92i	−0.197902	−	0.573941i
$636$		0			0
$637$	1660.02	−	539.374i	0.103254	−	0.0335491i
$638$		0			0
$639$	355.660	−	1094.61i	0.0220183	−	0.0677653i
$640$		0			0
$641$	6800.66	+	20930.3i	0.419048	+	1.28970i	0.908579	+	0.417712i	$0.137168\pi$
$641$	6800.66	+	20930.3i	0.419048	+	1.28970i	−0.489531	+	0.871986i	$0.662832\pi$
$642$		0			0
$643$			25885.7i			1.58761i	0.608174	+	0.793804i	$0.291902\pi$
$643$			25885.7i			1.58761i	−0.608174	+	0.793804i	$0.708098\pi$
$644$		0			0
$645$	−7.69059	−	429.914i	−0.000469483	−	0.0262447i
$646$		0			0
$647$	10603.3	−	14594.2i	0.644295	−	0.886796i	−0.354541	−	0.935041i	$-0.615363\pi$
$647$	10603.3	−	14594.2i	0.644295	−	0.886796i	0.998836	+	0.0482446i	$0.0153627\pi$
$648$		0			0
$649$	−19789.4			−1.19692
$650$		0			0
$651$	−8788.61			−0.529113
$652$		0			0
$653$	8836.01	−	12161.7i	0.529525	−	0.728829i	−0.457533	−	0.889193i	$-0.651267\pi$
$653$	8836.01	−	12161.7i	0.529525	−	0.728829i	0.987058	+	0.160364i	$0.0512668\pi$
$654$		0			0
$655$	−9865.29	−	3011.45i	−0.588502	−	0.179644i
$656$		0			0
$657$		−	14632.9i		−	0.868926i
$658$		0			0
$659$	139.210	+	428.445i	0.00822893	+	0.0253260i	0.955087	−	0.296327i	$-0.0957617\pi$
$659$	139.210	+	428.445i	0.00822893	+	0.0253260i	−0.946858	+	0.321653i	$0.895762\pi$
$660$		0			0
$661$	527.128	−	1622.33i	0.0310180	−	0.0954636i	−0.934349	−	0.356359i	$-0.884018\pi$
$661$	527.128	−	1622.33i	0.0310180	−	0.0954636i	0.965367	+	0.260896i	$0.0840179\pi$
$662$		0			0
$663$	−4329.52	+	1406.75i	−0.253612	+	0.0824035i
$664$		0			0
$665$	−5202.04	+	17041.5i	−0.303348	+	0.993748i
$666$		0			0
$667$	8104.14	+	11154.4i	0.470455	+	0.647526i
$668$		0			0
$669$	−8430.18	+	6124.88i	−0.487189	+	0.353964i
$670$		0			0
$671$	13447.2	+	9769.99i	0.773659	+	0.562096i
$672$		0			0
$673$	13179.2	+	4282.18i	0.754860	+	0.245269i	0.661071	−	0.750323i	$-0.270102\pi$
$673$	13179.2	+	4282.18i	0.754860	+	0.245269i	0.0937886	+	0.995592i	$0.470102\pi$
$674$		0			0
$675$	6025.36	−	8949.69i	0.343580	−	0.510332i
$676$		0			0
$677$	21113.6	+	6860.24i	1.19862	+	0.389454i	0.839252	−	0.543743i	$-0.182994\pi$
$677$	21113.6	+	6860.24i	1.19862	+	0.389454i	0.359364	+	0.933197i	$0.382994\pi$
$678$		0			0
$679$	−15966.7	−	11600.5i	−0.902425	−	0.655650i
$680$		0			0
$681$	−2734.33	+	1986.61i	−0.153862	+	0.111787i
$682$		0			0
$683$	5007.49	+	6892.22i	0.280536	+	0.386125i	0.925911	−	0.377741i	$-0.123299\pi$
$683$	5007.49	+	6892.22i	0.280536	+	0.386125i	−0.645375	+	0.763866i	$0.723299\pi$
$684$		0			0
$685$	−9308.75	−	6512.05i	−0.519225	−	0.363230i
$686$		0			0
$687$	1175.09	−	381.810i	0.0652583	−	0.0212037i
$688$		0			0
$689$	10086.5	−	31043.1i	0.557715	−	1.71647i
$690$		0			0
$691$	−3099.30	−	9538.68i	−0.170627	−	0.525135i	0.828780	−	0.559575i	$-0.189035\pi$
$691$	−3099.30	−	9538.68i	−0.170627	−	0.525135i	−0.999407	+	0.0344394i	$0.989035\pi$
$692$		0			0
$693$		−	15247.1i		−	0.835772i
$694$		0			0
$695$	23450.2	−	8085.91i	1.27988	−	0.441318i
$696$		0			0
$697$	−6710.75	+	9236.56i	−0.364688	+	0.501951i
$698$		0			0
$699$	9293.73			0.502892
$700$		0			0
$701$	11359.4			0.612037			0.306019	−	0.952026i	$-0.401003\pi$
$701$	11359.4			0.612037			0.306019	+	0.952026i	$0.401003\pi$
$702$		0			0
$703$	15223.0	−	20952.7i	0.816710	−	1.12411i
$704$		0			0
$705$	4727.54	−	6757.86i	0.252553	−	0.361015i
$706$		0			0
$707$			13286.9i			0.706799i
$708$		0			0
$709$	−8360.88	−	25732.1i	−0.442876	−	1.36303i	−0.884796	−	0.465979i	$-0.845702\pi$
$709$	−8360.88	−	25732.1i	−0.442876	−	1.36303i	0.441920	−	0.897055i	$-0.354298\pi$
$710$		0			0
$711$	−7924.74	+	24389.8i	−0.418004	+	1.28648i
$712$		0			0
$713$	19321.0	−	6277.77i	1.01483	−	0.329739i
$714$		0			0
$715$	−17745.7	+	13384.4i	−0.928185	+	0.700069i
$716$		0			0
$717$	−2305.86	−	3173.75i	−0.120103	−	0.165308i
$718$		0			0
$719$	11187.4	−	8128.15i	0.580279	−	0.421598i	−0.258545	−	0.965999i	$-0.583243\pi$
$719$	11187.4	−	8128.15i	0.580279	−	0.421598i	0.838825	+	0.544401i	$0.183243\pi$
$720$		0			0
$721$	−25323.9	−	18398.9i	−1.30806	−	0.950362i
$722$		0			0
$723$	2805.64	+	911.608i	0.144319	+	0.0468922i
$724$		0			0
$725$	−18047.2	+	14125.3i	−0.924493	+	0.723584i
$726$		0			0
$727$	−1128.78	−	366.762i	−0.0575846	−	0.0187104i	0.280083	−	0.959976i	$-0.409638\pi$
$727$	−1128.78	−	366.762i	−0.0575846	−	0.0187104i	−0.337668	+	0.941265i	$0.609638\pi$
$728$		0			0
$729$	−6715.72	−	4879.26i	−0.341194	−	0.247892i
$730$		0			0
$731$	−819.315	+	595.267i	−0.0414548	+	0.0301187i
$732$		0			0
$733$	9185.72	+	12643.1i	0.462868	+	0.637083i	0.975100	−	0.221764i	$-0.0711814\pi$
$733$	9185.72	+	12643.1i	0.462868	+	0.637083i	−0.512232	+	0.858847i	$0.671181\pi$
$734$		0			0
$735$	−542.196	+	9.69917i	−0.0272098	+	0.000486748i
$736$		0			0
$737$	12282.3	−	3990.75i	0.613871	−	0.199459i
$738$		0			0
$739$	10445.5	−	32147.8i	0.519950	−	1.60024i	−0.254142	−	0.967167i	$-0.581793\pi$
$739$	10445.5	−	32147.8i	0.519950	−	1.60024i	0.774092	−	0.633074i	$-0.218207\pi$
$740$		0			0
$741$	2616.95	+	8054.15i	0.129738	+	0.399294i
$742$		0			0
$743$		−	24170.7i		−	1.19346i	−0.802444	−	0.596728i	$-0.796467\pi$
$743$		−	24170.7i		−	1.19346i	0.802444	−	0.596728i	$-0.203533\pi$
$744$		0			0
$745$	−14790.4	−	19609.8i	−0.727353	−	0.964361i
$746$		0			0
$747$	−6737.94	+	9273.98i	−0.330024	+	0.454240i
$748$		0			0
$749$	3720.68			0.181510
$750$		0			0
$751$	19571.2			0.950949			0.475475	−	0.879729i	$-0.342276\pi$
$751$	19571.2			0.950949			0.475475	+	0.879729i	$0.342276\pi$
$752$		0			0
$753$	5631.52	−	7751.13i	0.272542	−	0.375122i
$754$		0			0
$755$	−2802.84	−	3716.14i	−0.135107	−	0.179131i
$756$		0			0
$757$			14216.2i			0.682558i	0.939962	+	0.341279i	$0.110860\pi$
$757$			14216.2i			0.682558i	−0.939962	+	0.341279i	$0.889140\pi$
$758$		0			0
$759$	−1283.82	−	3951.18i	−0.0613960	−	0.188957i
$760$		0			0
$761$	5163.31	−	15891.0i	0.245953	−	0.756964i	−0.749526	−	0.661975i	$-0.769718\pi$
$761$	5163.31	−	15891.0i	0.245953	−	0.756964i	0.995478	−	0.0949891i	$-0.0302816\pi$
$762$		0			0
$763$	14178.2	−	4606.77i	0.672719	−	0.218580i
$764$		0			0
$765$	−11996.4	+	214.600i	−0.566970	+	0.0101423i
$766$		0			0
$767$	−21572.1	−	29691.5i	−1.01555	−	1.39778i
$768$		0			0
$769$	−20725.0	+	15057.6i	−0.971864	+	0.706101i	−0.955876	−	0.293772i	$-0.905090\pi$
$769$	−20725.0	+	15057.6i	−0.971864	+	0.706101i	−0.0159885	+	0.999872i	$0.505090\pi$
$770$		0			0
$771$	−1217.91	−	884.861i	−0.0568895	−	0.0413327i
$772$		0			0
$773$	12312.8	+	4000.66i	0.572909	+	0.186150i	0.581122	−	0.813817i	$-0.302614\pi$
$773$	12312.8	+	4000.66i	0.572909	+	0.186150i	−0.00821216	+	0.999966i	$0.502614\pi$
$774$		0			0
$775$	11576.9	+	31721.7i	0.536586	+	1.47029i
$776$		0			0
$777$	9694.70	+	3150.00i	0.447613	+	0.145438i
$778$		0			0
$779$	17182.6	+	12483.9i	0.790285	+	0.574176i
$780$		0			0
$781$	1262.22	−	917.058i	0.0578308	−	0.0420165i
$782$		0			0
$783$	−9301.47	−	12802.4i	−0.424531	−	0.584316i
$784$		0			0
$785$	−7447.79	+	5617.38i	−0.338628	+	0.255405i
$786$		0			0
$787$	37063.2	−	12042.6i	1.67873	−	0.545453i	0.694067	−	0.719911i	$-0.255817\pi$
$787$	37063.2	−	12042.6i	1.67873	−	0.545453i	0.984665	+	0.174458i	$0.0558173\pi$
$788$		0			0
$789$	−2182.96	+	6718.48i	−0.0984989	+	0.303148i
$790$		0			0
$791$	3552.69	+	10934.1i	0.159695	+	0.491492i
$792$		0			0
$793$			30826.0i			1.38041i
$794$		0			0
$795$	−5812.98	+	8309.46i	−0.259327	+	0.370700i
$796$		0			0
$797$	5281.48	−	7269.33i	0.234730	−	0.323078i	−0.675361	−	0.737488i	$-0.736012\pi$
$797$	5281.48	−	7269.33i	0.234730	−	0.323078i	0.910090	+	0.414410i	$0.136012\pi$
$798$		0			0
$799$	−19424.8			−0.860073
$800$		0			0
$801$	−18012.7			−0.794568
$802$		0			0
$803$	11659.4	−	16047.8i	0.512392	−	0.705246i
$804$		0			0
$805$	15325.3	−	5284.35i	0.670988	−	0.231365i
$806$		0			0
$807$			11430.0i			0.498582i
$808$		0			0
$809$	11753.7	+	36174.1i	0.510800	+	1.57208i	0.790797	+	0.612079i	$0.209667\pi$
$809$	11753.7	+	36174.1i	0.510800	+	1.57208i	−0.279997	+	0.960001i	$0.590333\pi$
$810$		0			0
$811$	−3917.57	+	12057.0i	−0.169623	+	0.522047i	−0.999347	−	0.0361272i	$-0.988498\pi$
$811$	−3917.57	+	12057.0i	−0.169623	+	0.522047i	0.829724	+	0.558174i	$0.188498\pi$
$812$		0			0
$813$	−7003.74	+	2275.65i	−0.302130	+	0.0981681i
$814$		0			0
$815$	2875.56	+	2011.63i	0.123591	+	0.0864594i
$816$		0			0
$817$	1107.37	+	1524.16i	0.0474197	+	0.0652676i
$818$		0			0
$819$	22876.4	−	16620.7i	0.976025	−	0.709124i
$820$		0			0
$821$	1440.60	+	1046.66i	0.0612390	+	0.0444927i	0.617984	−	0.786191i	$-0.287950\pi$
$821$	1440.60	+	1046.66i	0.0612390	+	0.0444927i	−0.556745	+	0.830684i	$0.687950\pi$
$822$		0			0
$823$	−34469.3	−	11199.7i	−1.45993	−	0.474360i	−0.531882	−	0.846819i	$-0.678515\pi$
$823$	−34469.3	−	11199.7i	−1.45993	−	0.474360i	−0.928049	+	0.372459i	$0.878515\pi$
$824$		0			0
$825$	6487.15	−	2367.50i	0.273762	−	0.0999100i
$826$		0			0
$827$	32015.9	+	10402.6i	1.34619	+	0.437405i	0.891410	−	0.453198i	$-0.149717\pi$
$827$	32015.9	+	10402.6i	1.34619	+	0.437405i	0.454783	+	0.890602i	$0.349717\pi$
$828$		0			0
$829$	−30772.1	−	22357.3i	−1.28922	−	0.936670i	−0.289427	−	0.957200i	$-0.593465\pi$
$829$	−30772.1	−	22357.3i	−1.28922	−	0.936670i	−0.999789	+	0.0205302i	$0.993465\pi$
$830$		0			0
$831$	−4987.70	+	3623.78i	−0.208209	+	0.151272i
$832$		0			0
$833$	750.736	+	1033.30i	0.0312262	+	0.0429792i
$834$		0			0
$835$	8086.91	−	26492.2i	0.335161	−	1.09796i
$836$		0			0
$837$	−22175.5	+	7205.26i	−0.915769	+	0.297551i
$838$		0			0
$839$	8440.54	−	25977.3i	0.347318	−	1.06893i	−0.613013	−	0.790073i	$-0.710043\pi$
$839$	8440.54	−	25977.3i	0.347318	−	1.06893i	0.960331	−	0.278862i	$-0.0899573\pi$
$840$		0			0
$841$	2850.81	+	8773.89i	0.116889	+	0.359748i
$842$		0			0
$843$		−	10944.6i		−	0.447157i
$844$		0			0
$845$	−15932.9	−	4863.64i	−0.648651	−	0.198005i
$846$		0			0
$847$	−2935.34	+	4040.15i	−0.119079	+	0.163898i
$848$		0			0
$849$	−6040.26			−0.244171
$850$		0			0
$851$	−23563.0			−0.949153
$852$		0			0
$853$	−21198.7	+	29177.5i	−0.850914	+	1.17118i	0.132747	+	0.991150i	$0.457620\pi$
$853$	−21198.7	+	29177.5i	−0.850914	+	1.17118i	−0.983661	+	0.180033i	$0.942380\pi$
$854$		0			0
$855$	399.218	+	22316.8i	0.0159684	+	0.892654i
$856$		0			0
$857$		−	15056.8i		−	0.600151i	−0.953915	−	0.300075i	$-0.902988\pi$
$857$		−	15056.8i		−	0.600151i	0.953915	−	0.300075i	$-0.0970119\pi$
$858$		0			0
$859$	−3395.61	−	10450.6i	−0.134874	−	0.415099i	0.860697	−	0.509118i	$-0.170028\pi$
$859$	−3395.61	−	10450.6i	−0.134874	−	0.415099i	−0.995570	+	0.0940193i	$0.970028\pi$
$860$		0			0
$861$	−2583.21	+	7950.32i	−0.102248	+	0.314688i
$862$		0			0
$863$	−7464.09	+	2425.23i	−0.294415	+	0.0956614i	−0.452501	−	0.891764i	$-0.649468\pi$
$863$	−7464.09	+	2425.23i	−0.294415	+	0.0956614i	0.158085	+	0.987425i	$0.449468\pi$
$864$		0			0
$865$	−14095.1	−	40877.6i	−0.554044	−	1.60680i
$866$		0			0
$867$	2914.65	+	4011.67i	0.114172	+	0.157144i
$868$		0			0
$869$	−28124.6	+	20433.7i	−1.09788	+	0.797659i
$870$		0			0
$871$	19376.3	+	14077.7i	0.753779	+	0.547653i
$872$		0			0
$873$	−23513.2	−	7639.90i	−0.911570	−	0.296187i
$874$		0			0
$875$	9689.15	+	25143.3i	0.374346	+	0.971427i
$876$		0			0
$877$	3663.82	+	1190.45i	0.141070	+	0.0458364i	0.378701	−	0.925519i	$-0.376371\pi$
$877$	3663.82	+	1190.45i	0.141070	+	0.0458364i	−0.237631	+	0.971355i	$0.576371\pi$
$878$		0			0
$879$	11709.4	+	8507.37i	0.449315	+	0.326446i
$880$		0			0
$881$	−27189.4	+	19754.2i	−1.03976	+	0.755433i	−0.970240	−	0.242147i	$-0.922148\pi$
$881$	−27189.4	+	19754.2i	−1.03976	+	0.755433i	−0.0695253	+	0.997580i	$0.522148\pi$
$882$		0			0
$883$	20224.7	+	27836.9i	0.770798	+	1.06091i	0.996238	+	0.0866556i	$0.0276180\pi$
$883$	20224.7	+	27836.9i	0.770798	+	1.06091i	−0.225440	+	0.974257i	$0.572382\pi$
$884$		0			0
$885$	3716.90	+	10779.5i	0.141178	+	0.409433i
$886$		0			0
$887$	−24189.7	+	7859.72i	−0.915683	+	0.297524i	−0.728695	−	0.684838i	$-0.759873\pi$
$887$	−24189.7	+	7859.72i	−0.915683	+	0.297524i	−0.186989	+	0.982362i	$0.559873\pi$
$888$		0			0
$889$	−5176.94	+	15933.0i	−0.195308	+	0.601097i
$890$		0			0
$891$	−5124.49	−	15771.6i	−0.192679	−	0.593005i
$892$		0			0
$893$			36135.6i			1.35412i
$894$		0			0
$895$	441.110	+	24658.6i	0.0164745	+	0.920946i
$896$		0			0
$897$	4528.77	−	6233.32i	0.168574	−	0.232023i
$898$		0			0
$899$	49529.1			1.83747
$900$		0			0
$901$	23884.7			0.883144
$902$		0			0
$903$	−435.850	+	599.897i	−0.0160622	+	0.0221078i
$904$		0			0
$905$	27185.8	+	8298.66i	0.998550	+	0.304814i
$906$		0			0
$907$			1232.83i			0.0451327i	0.999745	+	0.0225663i	$0.00718370\pi$
$907$			1232.83i			0.0451327i	−0.999745	+	0.0225663i	$0.992816\pi$
$908$		0			0
$909$	5143.45	+	15829.9i	0.187676	+	0.577607i
$910$		0			0
$911$	3125.56	−	9619.48i	0.113671	−	0.349844i	−0.877996	−	0.478667i	$-0.841120\pi$
$911$	3125.56	−	9619.48i	0.113671	−	0.349844i	0.991668	+	0.128823i	$0.0411201\pi$
$912$		0			0
$913$	−14778.8	+	4801.94i	−0.535715	+	0.174064i
$914$		0			0
$915$	2796.11	−	9159.86i	0.101023	−	0.330946i
$916$		0			0
$917$	10455.4	+	14390.7i	0.376521	+	0.518236i
$918$		0			0
$919$	−42291.6	+	30726.7i	−1.51803	+	1.10292i	−0.555582	+	0.831462i	$0.687505\pi$
$919$	−42291.6	+	30726.7i	−1.51803	+	1.10292i	−0.962451	+	0.271454i	$0.912495\pi$
$920$		0			0
$921$	−3956.42	−	2874.51i	−0.141551	−	0.102843i
$922$		0			0
$923$	2751.86	+	894.133i	0.0981349	+	0.0318860i
$924$		0			0
$925$	−1400.83	−	39141.5i	−0.0497935	−	1.39131i
$926$		0			0
$927$	−37292.9	−	12117.2i	−1.32132	−	0.429322i
$928$		0			0
$929$	−5552.87	−	4034.40i	−0.196107	−	0.142480i	0.485398	−	0.874293i	$-0.338675\pi$
$929$	−5552.87	−	4034.40i	−0.196107	−	0.142480i	−0.681506	+	0.731813i	$0.738675\pi$
$930$		0			0
$931$	1922.23	−	1396.58i	0.0676677	−	0.0491634i
$932$		0			0
$933$	9804.90	+	13495.3i	0.344049	+	0.473543i
$934$		0			0
$935$	−13327.3	−	9323.30i	−0.466151	−	0.326101i
$936$		0			0
$937$	5412.80	−	1758.73i	0.188718	−	0.0613181i	−0.213133	−	0.977023i	$-0.568367\pi$
$937$	5412.80	−	1758.73i	0.188718	−	0.0613181i	0.401851	+	0.915705i	$0.368367\pi$
$938$		0			0
$939$	1269.56	−	3907.29i	0.0441218	−	0.135793i
$940$		0			0
$941$	−10412.4	−	32046.1i	−0.360717	−	1.11017i	−0.952620	−	0.304164i	$-0.901623\pi$
$941$	−10412.4	−	32046.1i	−0.360717	−	1.11017i	0.591902	−	0.806010i	$-0.298377\pi$
$942$		0			0
$943$		−	19323.3i		−	0.667288i
$944$		0			0
$945$	−17589.5	+	6065.08i	−0.605488	+	0.208780i
$946$		0			0
$947$	−31972.9	+	44006.9i	−1.09713	+	1.51007i	−0.257989	+	0.966148i	$0.583060\pi$
$947$	−31972.9	+	44006.9i	−1.09713	+	1.51007i	−0.839138	+	0.543918i	$0.816940\pi$
$948$		0			0
$949$	36787.3			1.25834
$950$		0			0
$951$	10168.1			0.346713
$952$		0			0
$953$	18681.7	−	25713.2i	0.635006	−	0.874011i	−0.363331	−	0.931660i	$-0.618361\pi$
$953$	18681.7	−	25713.2i	0.635006	−	0.874011i	0.998337	+	0.0576496i	$0.0183606\pi$
$954$		0			0
$955$	16353.2	−	23376.4i	0.554114	−	0.792087i
$956$		0			0
$957$		−	10128.8i		−	0.342129i
$958$		0			0
$959$	6054.04	+	18632.4i	0.203853	+	0.627396i
$960$		0			0
$961$	13345.7	−	41073.7i	0.447976	−	1.37873i
$962$		0			0
$963$	4432.77	−	1440.30i	0.148332	−	0.0481961i
$964$		0			0
$965$	−27737.3	+	20920.4i	−0.925280	+	0.697878i
$966$		0			0
$967$	−12176.6	−	16759.6i	−0.404935	−	0.557346i	0.557039	−	0.830487i	$-0.311937\pi$
$967$	−12176.6	−	16759.6i	−0.404935	−	0.557346i	−0.961974	+	0.273141i	$0.911937\pi$
$968$		0			0
$969$	−5013.39	+	3642.44i	−0.166206	+	0.120755i
$970$		0			0
$971$	−3816.53	−	2772.87i	−0.126136	−	0.0916434i	0.522928	−	0.852377i	$-0.324840\pi$
$971$	−3816.53	−	2772.87i	−0.126136	−	0.0916434i	−0.649065	+	0.760733i	$0.724840\pi$
$972$		0			0
$973$	−40683.2	−	13218.8i	−1.34043	−	0.435534i
$974$		0			0
$975$	10623.7	+	7152.36i	0.348953	+	0.234932i
$976$		0			0
$977$	−19446.8	−	6318.66i	−0.636806	−	0.206911i	−0.0272184	−	0.999630i	$-0.508665\pi$
$977$	−19446.8	−	6318.66i	−0.636806	−	0.206911i	−0.609588	+	0.792719i	$0.708665\pi$
$978$		0			0
$979$	−19754.4	−	14352.4i	−0.644895	−	0.468544i
$980$		0			0
$981$	15108.4	−	10976.9i	0.491717	−	0.357253i
$982$		0			0
$983$	−6007.91	−	8269.17i	−0.194936	−	0.268307i	0.700348	−	0.713801i	$-0.253028\pi$
$983$	−6007.91	−	8269.17i	−0.194936	−	0.268307i	−0.895285	+	0.445494i	$0.853028\pi$
$984$		0			0
$985$	18653.2	−	333.682i	0.603392	−	0.0107939i
$986$		0			0
$987$	−13526.6	+	4395.05i	−0.436226	+	0.141738i
$988$		0			0
$989$	529.668	−	1630.15i	0.0170298	−	0.0524123i
$990$		0			0
$991$	−628.180	−	1933.34i	−0.0201360	−	0.0619723i	0.940484	−	0.339839i	$-0.110373\pi$
$991$	−628.180	−	1933.34i	−0.0201360	−	0.0619723i	−0.960620	+	0.277867i	$0.910373\pi$
$992$		0			0
$993$			17100.9i			0.546506i
$994$		0			0
$995$	33060.4	+	43833.1i	1.05335	+	1.39659i
$996$		0			0
$997$	35745.5	−	49199.4i	1.13548	−	1.56285i	0.358255	−	0.933624i	$-0.383372\pi$
$997$	35745.5	−	49199.4i	1.13548	−	1.56285i	0.777222	−	0.629226i	$-0.216628\pi$
$998$		0			0
$999$	27044.3			0.856500

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.i.a.29.4	✓	32
5.2	odd	4		500.4.g.b.101.10		64
5.3	odd	4		500.4.g.b.101.7		64
5.4	even	2		500.4.i.a.149.5		32
25.6	even	5		500.4.i.a.349.5		32
25.8	odd	20		500.4.g.b.401.7		64
25.12	odd	20		2500.4.a.g.1.14		32
25.13	odd	20		2500.4.a.g.1.19		32
25.17	odd	20		500.4.g.b.401.10		64
25.19	even	10	inner	100.4.i.a.69.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.4.i.a.29.4	✓	32	1.1	even	1	trivial
100.4.i.a.69.4	yes	32	25.19	even	10	inner
500.4.g.b.101.7		64	5.3	odd	4
500.4.g.b.101.10		64	5.2	odd	4
500.4.g.b.401.7		64	25.8	odd	20
500.4.g.b.401.10		64	25.17	odd	20
500.4.i.a.149.5		32	5.4	even	2
500.4.i.a.349.5		32	25.6	even	5
2500.4.a.g.1.14		32	25.12	odd	20
2500.4.a.g.1.19		32	25.13	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.991787 + 1.36508i) q^{3} +(-6.73237 - 8.92610i) q^{5} +19.2807i q^{7} +(7.46366 + 22.9708i) q^{9} +O(q^{10})\)	\(q+(-0.991787 + 1.36508i) q^{3} +(-6.73237 - 8.92610i) q^{5} +19.2807i q^{7} +(7.46366 + 22.9708i) q^{9} +(-10.1176 + 31.1388i) q^{11} +(-57.7488 + 18.7637i) q^{13} +(18.8619 - 0.337414i) q^{15} +(-26.1165 - 35.9463i) q^{17} +(-66.8705 + 48.5843i) q^{19} +(-26.3197 - 19.1224i) q^{21} +(71.5207 + 23.2385i) q^{23} +(-34.3505 + 120.188i) q^{25} +(-82.0874 - 26.6718i) q^{27} +(148.327 + 107.766i) q^{29} +(218.552 - 158.787i) q^{31} +(-32.4723 - 44.6944i) q^{33} +(172.101 - 129.805i) q^{35} +(-297.997 + 96.8251i) q^{37} +(31.6606 - 97.4412i) q^{39} +(-79.4032 - 244.378i) q^{41} -22.7927i q^{43} +(154.791 - 221.269i) q^{45} +(256.967 - 353.685i) q^{47} -28.7456 q^{49} +74.9716 q^{51} +(-315.966 + 434.890i) q^{53} +(346.063 - 119.327i) q^{55} -139.469i q^{57} +(186.776 + 574.836i) q^{59} +(156.878 - 482.821i) q^{61} +(-442.893 + 143.905i) q^{63} +(556.273 + 389.147i) q^{65} +(-231.844 - 319.106i) q^{67} +(-102.656 + 74.5837i) q^{69} +(-38.5514 - 28.0092i) q^{71} +(-576.192 - 187.216i) q^{73} +(-129.997 - 166.092i) q^{75} +(-600.378 - 195.075i) q^{77} +(858.995 + 624.096i) q^{79} +(-409.761 + 297.709i) q^{81} +(278.970 + 383.969i) q^{83} +(-145.034 + 475.123i) q^{85} +(-294.218 + 95.5971i) q^{87} +(-230.458 + 709.278i) q^{89} +(-361.778 - 1113.44i) q^{91} +455.824i q^{93} +(883.865 + 269.806i) q^{95} +(-601.664 + 828.120i) q^{97} -790.797 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{5} + 122 q^{9}+O(q^{10}) \) 32 * q + 6 * q^5 + 122 * q^9	\( 32 q + 6 q^{5} + 122 q^{9} + 20 q^{11} + 68 q^{15} - 160 q^{17} + 2 q^{19} - 108 q^{21} + 290 q^{23} + 654 q^{25} + 600 q^{27} + 62 q^{29} - 378 q^{31} - 1280 q^{33} - 278 q^{35} + 680 q^{37} + 592 q^{39} - 528 q^{41} - 1044 q^{45} - 1810 q^{47} - 2796 q^{49} + 1664 q^{51} - 510 q^{53} - 1350 q^{55} + 144 q^{59} - 1346 q^{61} + 1660 q^{63} + 1142 q^{65} + 1890 q^{67} + 956 q^{69} + 786 q^{71} + 3720 q^{73} - 78 q^{75} + 2160 q^{77} + 896 q^{79} + 348 q^{81} + 570 q^{83} + 224 q^{85} + 3240 q^{87} - 2512 q^{89} - 2212 q^{91} + 1536 q^{95} - 2250 q^{97} - 2540 q^{99}+O(q^{100}) \) 32 * q + 6 * q^5 + 122 * q^9 + 20 * q^11 + 68 * q^15 - 160 * q^17 + 2 * q^19 - 108 * q^21 + 290 * q^23 + 654 * q^25 + 600 * q^27 + 62 * q^29 - 378 * q^31 - 1280 * q^33 - 278 * q^35 + 680 * q^37 + 592 * q^39 - 528 * q^41 - 1044 * q^45 - 1810 * q^47 - 2796 * q^49 + 1664 * q^51 - 510 * q^53 - 1350 * q^55 + 144 * q^59 - 1346 * q^61 + 1660 * q^63 + 1142 * q^65 + 1890 * q^67 + 956 * q^69 + 786 * q^71 + 3720 * q^73 - 78 * q^75 + 2160 * q^77 + 896 * q^79 + 348 * q^81 + 570 * q^83 + 224 * q^85 + 3240 * q^87 - 2512 * q^89 - 2212 * q^91 + 1536 * q^95 - 2250 * q^97 - 2540 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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