LMFDB - Embedded newform 100.4.i.a.9.6

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			9.6
Character	$\chi$	$=$	100.9
Dual form			100.4.i.a.89.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.55368 - 1.15466i) q^{3} +(10.9812 + 2.10091i) q^{5} -30.1378i q^{7} +(-10.5481 + 7.66362i) q^{9} +O(q^{10})$	\(q+(3.55368 - 1.15466i) q^{3} +(10.9812 + 2.10091i) q^{5} -30.1378i q^{7} +(-10.5481 + 7.66362i) q^{9} +(51.5392 + 37.4454i) q^{11} +(-23.8598 - 32.8402i) q^{13} +(41.4494 - 5.21355i) q^{15} +(42.1411 + 13.6925i) q^{17} +(35.4205 - 109.013i) q^{19} +(-34.7989 - 107.100i) q^{21} +(-14.3499 + 19.7510i) q^{23} +(116.172 + 46.1410i) q^{25} +(-87.9355 + 121.033i) q^{27} +(2.06864 + 6.36663i) q^{29} +(-97.5855 + 300.337i) q^{31} +(226.390 + 73.5587i) q^{33} +(63.3169 - 330.948i) q^{35} +(-201.761 - 277.701i) q^{37} +(-122.709 - 89.1536i) q^{39} +(-356.735 + 259.183i) q^{41} +291.568i q^{43} +(-131.931 + 61.9949i) q^{45} +(100.734 - 32.7305i) q^{47} -565.287 q^{49} +165.566 q^{51} +(-346.881 + 112.709i) q^{53} +(487.291 + 519.474i) q^{55} -428.296i q^{57} +(-269.443 + 195.762i) q^{59} +(10.8762 + 7.90204i) q^{61} +(230.965 + 317.896i) q^{63} +(-193.014 - 410.751i) q^{65} +(54.7080 + 17.7757i) q^{67} +(-28.1894 + 86.7580i) q^{69} +(-72.3999 - 222.824i) q^{71} +(262.000 - 360.613i) q^{73} +(466.116 + 29.8307i) q^{75} +(1128.52 - 1553.28i) q^{77} +(-17.4949 - 53.8438i) q^{79} +(-63.9597 + 196.848i) q^{81} +(1298.38 + 421.871i) q^{83} +(433.992 + 238.894i) q^{85} +(14.7026 + 20.2364i) q^{87} +(-426.176 - 309.635i) q^{89} +(-989.732 + 719.082i) q^{91} +1179.98i q^{93} +(617.985 - 1122.68i) q^{95} +(-1271.95 + 413.282i) q^{97} -830.606 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

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
$3$	3.55368	−	1.15466i	0.683906	−	0.222214i	0.0536012	−	0.998562i	$-0.482930\pi$
$3$	3.55368	−	1.15466i	0.683906	−	0.222214i	0.630305	+	0.776348i	$0.282930\pi$
$4$		0			0
$5$	10.9812	+	2.10091i	0.982186	+	0.187911i
$5$	10.9812	+	2.10091i	0.982186	+	0.187911i
$6$		0			0
$7$		−	30.1378i		−	1.62729i	−0.581363	−	0.813644i	$-0.697480\pi$
$7$		−	30.1378i		−	1.62729i	0.581363	−	0.813644i	$-0.302520\pi$
$8$		0			0
$9$	−10.5481	+	7.66362i	−0.390669	+	0.283838i
$10$		0			0
$11$	51.5392	+	37.4454i	1.41269	+	1.02638i	0.992924	+	0.118753i	$0.0378896\pi$
$11$	51.5392	+	37.4454i	1.41269	+	1.02638i	0.419771	+	0.907630i	$0.362110\pi$
$12$		0			0
$13$	−23.8598	−	32.8402i	−0.509040	−	0.700633i	0.474717	−	0.880138i	$-0.342550\pi$
$13$	−23.8598	−	32.8402i	−0.509040	−	0.700633i	−0.983757	+	0.179505i	$0.942550\pi$
$14$		0			0
$15$	41.4494	−	5.21355i	0.713479	−	0.0897422i
$16$		0			0
$17$	42.1411	+	13.6925i	0.601218	+	0.195348i	0.593784	−	0.804625i	$-0.297633\pi$
$17$	42.1411	+	13.6925i	0.601218	+	0.195348i	0.00743462	+	0.999972i	$0.497633\pi$
$18$		0			0
$19$	35.4205	−	109.013i	0.427685	−	1.31628i	−0.472715	−	0.881216i	$-0.656726\pi$
$19$	35.4205	−	109.013i	0.427685	−	1.31628i	0.900400	−	0.435064i	$-0.143274\pi$
$20$		0			0
$21$	−34.7989	−	107.100i	−0.361607	−	1.11291i
$22$		0			0
$23$	−14.3499	+	19.7510i	−0.130094	+	0.179059i	−0.869095	−	0.494645i	$-0.835298\pi$
$23$	−14.3499	+	19.7510i	−0.130094	+	0.179059i	0.739001	+	0.673705i	$0.235298\pi$
$24$		0			0
$25$	116.172	+	46.1410i	0.929379	+	0.369128i
$26$		0			0
$27$	−87.9355	+	121.033i	−0.626785	+	0.862696i
$28$		0			0
$29$	2.06864	+	6.36663i	0.0132461	+	0.0407674i	0.957461	−	0.288562i	$-0.0931772\pi$
$29$	2.06864	+	6.36663i	0.0132461	+	0.0407674i	−0.944215	+	0.329330i	$0.893177\pi$
$30$		0			0
$31$	−97.5855	+	300.337i	−0.565383	+	1.74007i	0.101429	+	0.994843i	$0.467659\pi$
$31$	−97.5855	+	300.337i	−0.565383	+	1.74007i	−0.666812	+	0.745226i	$0.732341\pi$
$32$		0			0
$33$	226.390	+	73.5587i	1.19423	+	0.388028i
$34$		0			0
$35$	63.3169	−	330.948i	0.305786	−	1.59830i
$36$		0			0
$37$	−201.761	−	277.701i	−0.896469	−	1.23388i	−0.971581	−	0.236709i	$-0.923931\pi$
$37$	−201.761	−	277.701i	−0.896469	−	1.23388i	0.0751118	−	0.997175i	$-0.476069\pi$
$38$		0			0
$39$	−122.709	−	89.1536i	−0.503826	−	0.366051i
$40$		0			0
$41$	−356.735	+	259.183i	−1.35885	+	0.987259i	−0.360328	+	0.932826i	$0.617335\pi$
$41$	−356.735	+	259.183i	−1.35885	+	0.987259i	−0.998517	+	0.0544332i	$0.982665\pi$
$42$		0			0
$43$			291.568i			1.03404i	0.855973	+	0.517020i	$0.172959\pi$
$43$			291.568i			1.03404i	−0.855973	+	0.517020i	$0.827041\pi$
$44$		0			0
$45$	−131.931	+	61.9949i	−0.437046	+	0.205370i
$46$		0			0
$47$	100.734	−	32.7305i	0.312629	−	0.101579i	−0.148500	−	0.988912i	$-0.547445\pi$
$47$	100.734	−	32.7305i	0.312629	−	0.101579i	0.461129	+	0.887333i	$0.347445\pi$
$48$		0			0
$49$	−565.287			−1.64807
$50$		0			0
$51$	165.566			0.454586
$52$		0			0
$53$	−346.881	+	112.709i	−0.899016	+	0.292108i	−0.721831	−	0.692070i	$-0.756699\pi$
$53$	−346.881	+	112.709i	−0.899016	+	0.292108i	−0.177185	+	0.984178i	$0.556699\pi$
$54$		0			0
$55$	487.291	+	519.474i	1.19466	+	1.27356i
$56$		0			0
$57$		−	428.296i		−	0.995249i
$58$		0			0
$59$	−269.443	+	195.762i	−0.594551	+	0.431967i	−0.843941	−	0.536436i	$-0.819770\pi$
$59$	−269.443	+	195.762i	−0.594551	+	0.431967i	0.249389	+	0.968403i	$0.419770\pi$
$60$		0			0
$61$	10.8762	+	7.90204i	0.0228288	+	0.0165861i	0.599141	−	0.800643i	$-0.295509\pi$
$61$	10.8762	+	7.90204i	0.0228288	+	0.0165861i	−0.576312	+	0.817230i	$0.695509\pi$
$62$		0			0
$63$	230.965	+	317.896i	0.461886	+	0.635731i
$64$		0			0
$65$	−193.014	−	410.751i	−0.368315	−	0.783807i
$66$		0			0
$67$	54.7080	+	17.7757i	0.0997559	+	0.0324126i	0.358470	−	0.933541i	$-0.383299\pi$
$67$	54.7080	+	17.7757i	0.0997559	+	0.0324126i	−0.258714	+	0.965954i	$0.583299\pi$
$68$		0			0
$69$	−28.1894	+	86.7580i	−0.0491826	+	0.151369i
$70$		0			0
$71$	−72.3999	−	222.824i	−0.121018	−	0.372456i	0.872136	−	0.489263i	$-0.162734\pi$
$71$	−72.3999	−	222.824i	−0.121018	−	0.372456i	−0.993155	+	0.116807i	$0.962734\pi$
$72$		0			0
$73$	262.000	−	360.613i	0.420066	−	0.578171i	−0.545571	−	0.838064i	$-0.683687\pi$
$73$	262.000	−	360.613i	0.420066	−	0.578171i	0.965637	+	0.259893i	$0.0836873\pi$
$74$		0			0
$75$	466.116	+	29.8307i	0.717633	+	0.0459274i
$76$		0			0
$77$	1128.52	−	1553.28i	1.67022	−	2.29886i
$78$		0			0
$79$	−17.4949	−	53.8438i	−0.0249156	−	0.0766822i	0.937826	−	0.347107i	$-0.112836\pi$
$79$	−17.4949	−	53.8438i	−0.0249156	−	0.0766822i	−0.962741	+	0.270425i	$0.912836\pi$
$80$		0			0
$81$	−63.9597	+	196.848i	−0.0877362	+	0.270024i
$82$		0			0
$83$	1298.38	+	421.871i	1.71706	+	0.557908i	0.991484	−	0.130231i	$-0.0415719\pi$
$83$	1298.38	+	421.871i	1.71706	+	0.557908i	0.725579	+	0.688139i	$0.241572\pi$
$84$		0			0
$85$	433.992	+	238.894i	0.553800	+	0.304844i
$86$		0			0
$87$	14.7026	+	20.2364i	0.0181182	+	0.0249376i
$88$		0			0
$89$	−426.176	−	309.635i	−0.507579	−	0.368778i	0.304325	−	0.952568i	$-0.401569\pi$
$89$	−426.176	−	309.635i	−0.507579	−	0.368778i	−0.811904	+	0.583790i	$0.801569\pi$
$90$		0			0
$91$	−989.732	+	719.082i	−1.14013	+	0.828355i
$92$		0			0
$93$			1179.98i			1.31568i
$94$		0			0
$95$	617.985	−	1122.68i	0.667410	−	1.21246i
$96$		0			0
$97$	−1271.95	+	413.282i	−1.33141	+	0.432602i	−0.886399	−	0.462921i	$-0.846801\pi$
$97$	−1271.95	+	413.282i	−1.33141	+	0.432602i	−0.445014	+	0.895524i	$0.646801\pi$
$98$		0			0
$99$	−830.606			−0.843222
$100$		0			0
$101$	285.966			0.281729			0.140865	−	0.990029i	$-0.455012\pi$
$101$	285.966			0.281729			0.140865	+	0.990029i	$0.455012\pi$
$102$		0			0
$103$	1203.95	−	391.185i	1.15173	−	0.374220i	0.329936	−	0.944003i	$-0.392973\pi$
$103$	1203.95	−	391.185i	1.15173	−	0.374220i	0.821795	+	0.569784i	$0.192973\pi$
$104$		0			0
$105$	−157.125	−	1249.19i	−0.146036	−	1.16104i
$106$		0			0
$107$		−	308.993i		−	0.279173i	−0.990210	−	0.139586i	$-0.955423\pi$
$107$		−	308.993i		−	0.279173i	0.990210	−	0.139586i	$-0.0445773\pi$
$108$		0			0
$109$	549.773	−	399.434i	0.483108	−	0.350998i	−0.319420	−	0.947613i	$-0.603488\pi$
$109$	549.773	−	399.434i	0.483108	−	0.350998i	0.802528	+	0.596615i	$0.203488\pi$
$110$		0			0
$111$	−1037.64	−	753.893i	−0.887287	−	0.644652i
$112$		0			0
$113$	283.657	+	390.420i	0.236143	+	0.325023i	0.910598	−	0.413293i	$-0.135621\pi$
$113$	283.657	+	390.420i	0.236143	+	0.325023i	−0.674455	+	0.738316i	$0.735621\pi$
$114$		0			0
$115$	−199.074	+	186.741i	−0.161424	+	0.151423i
$116$		0			0
$117$	503.350	+	163.548i	0.397732	+	0.129231i
$118$		0			0
$119$	412.661	−	1270.04i	0.317887	−	0.978356i
$120$		0			0
$121$	842.826	+	2593.95i	0.633228	+	1.94887i
$122$		0			0
$123$	−968.453	+	1332.96i	−0.709939	+	0.977147i
$124$		0			0
$125$	1178.77	+	750.750i	0.843459	+	0.537193i
$126$		0			0
$127$	59.3638	−	81.7072i	0.0414778	−	0.0570893i	−0.787774	−	0.615964i	$-0.788767\pi$
$127$	59.3638	−	81.7072i	0.0414778	−	0.0570893i	0.829252	+	0.558875i	$0.188767\pi$
$128$		0			0
$129$	336.662	+	1036.14i	0.229779	+	0.707186i
$130$		0			0
$131$	400.011	−	1231.11i	0.266788	−	0.821088i	−0.724489	−	0.689287i	$-0.757924\pi$
$131$	400.011	−	1231.11i	0.266788	−	0.821088i	0.991276	−	0.131801i	$-0.0420759\pi$
$132$		0			0
$133$	−3285.41	−	1067.50i	−2.14197	−	0.695967i
$134$		0			0
$135$	−1219.91	+	1144.34i	−0.777730	+	0.729547i
$136$		0			0
$137$	332.304	+	457.377i	0.207231	+	0.285229i	0.899963	−	0.435966i	$-0.143593\pi$
$137$	332.304	+	457.377i	0.207231	+	0.285229i	−0.692732	+	0.721195i	$0.743593\pi$
$138$		0			0
$139$	367.233	+	266.810i	0.224088	+	0.162810i	0.694165	−	0.719816i	$-0.255774\pi$
$139$	367.233	+	266.810i	0.224088	+	0.162810i	−0.470077	+	0.882626i	$0.655774\pi$
$140$		0			0
$141$	320.184	−	232.627i	0.191236	−	0.138941i
$142$		0			0
$143$		−	2586.00i		−	1.51225i
$144$		0			0
$145$	9.34039	+	74.2591i	0.00534950	+	0.0425302i
$146$		0			0
$147$	−2008.85	+	652.715i	−1.12712	+	0.366224i
$148$		0			0
$149$	−1802.47			−0.991032			−0.495516	−	0.868599i	$-0.665021\pi$
$149$	−1802.47			−0.991032			−0.495516	+	0.868599i	$0.665021\pi$
$150$		0			0
$151$	−916.230			−0.493787			−0.246893	−	0.969043i	$-0.579410\pi$
$151$	−916.230			−0.493787			−0.246893	+	0.969043i	$0.579410\pi$
$152$		0			0
$153$	−549.441	+	178.524i	−0.290324	+	0.0943321i
$154$		0			0
$155$	−1702.59	+	3093.04i	−0.882290	+	1.60283i
$156$		0			0
$157$		−	324.017i		−	0.164709i	−0.996603	−	0.0823546i	$-0.973756\pi$
$157$		−	324.017i		−	0.164709i	0.996603	−	0.0823546i	$-0.0262440\pi$
$158$		0			0
$159$	−1102.57	+	801.060i	−0.549931	+	0.399549i
$160$		0			0
$161$	595.251	+	432.475i	0.291381	+	0.211701i
$162$		0			0
$163$	36.8853	+	50.7683i	0.0177244	+	0.0243956i	0.817787	−	0.575521i	$-0.195201\pi$
$163$	36.8853	+	50.7683i	0.0177244	+	0.0243956i	−0.800063	+	0.599916i	$0.795201\pi$
$164$		0			0
$165$	2331.49	+	1283.39i	1.10004	+	0.605525i
$166$		0			0
$167$	−664.290	−	215.841i	−0.307810	−	0.100014i	0.151039	−	0.988528i	$-0.451738\pi$
$167$	−664.290	−	215.841i	−0.307810	−	0.100014i	−0.458849	+	0.888514i	$0.651738\pi$
$168$		0			0
$169$	169.722	−	522.349i	0.0772515	−	0.237756i
$170$		0			0
$171$	461.817	+	1421.33i	0.206526	+	0.635623i
$172$		0			0
$173$	566.246	−	779.371i	0.248849	−	0.342511i	−0.666259	−	0.745721i	$-0.732105\pi$
$173$	566.246	−	779.371i	0.248849	−	0.342511i	0.915108	+	0.403209i	$0.132105\pi$
$174$		0			0
$175$	1390.59	−	3501.18i	0.600678	−	1.51237i
$176$		0			0
$177$	−731.476	+	1006.79i	−0.310628	+	0.427543i
$178$		0			0
$179$	−213.050	−	655.701i	−0.0889616	−	0.273796i	0.896671	−	0.442697i	$-0.145978\pi$
$179$	−213.050	−	655.701i	−0.0889616	−	0.273796i	−0.985633	+	0.168901i	$0.945978\pi$
$180$		0			0
$181$	361.641	−	1113.02i	0.148511	−	0.457071i	−0.848935	−	0.528498i	$-0.822755\pi$
$181$	361.641	−	1113.02i	0.148511	−	0.457071i	0.997446	+	0.0714273i	$0.0227554\pi$
$182$		0			0
$183$	47.7748	+	15.5230i	0.0192984	+	0.00627044i
$184$		0			0
$185$	−1632.15	−	3473.36i	−0.648638	−	1.38036i
$186$		0			0
$187$	1659.20	+	2283.69i	0.648837	+	0.893047i
$188$		0			0
$189$	3647.66	+	2650.18i	1.40385	+	1.01996i
$190$		0			0
$191$	3568.05	−	2592.34i	1.35170	−	0.982070i	0.352778	−	0.935707i	$-0.385237\pi$
$191$	3568.05	−	2592.34i	1.35170	−	0.982070i	0.998925	−	0.0463629i	$-0.0147631\pi$
$192$		0			0
$193$		−	373.506i		−	0.139303i	−0.997571	−	0.0696517i	$-0.977811\pi$
$193$		−	373.506i		−	0.139303i	0.997571	−	0.0696517i	$-0.0221888\pi$
$194$		0			0
$195$	−1160.19	−	1236.81i	−0.426066	−	0.454205i
$196$		0			0
$197$	−1065.46	+	346.190i	−0.385335	+	0.125203i	−0.495277	−	0.868735i	$-0.664934\pi$
$197$	−1065.46	+	346.190i	−0.385335	+	0.125203i	0.109942	+	0.993938i	$0.464934\pi$
$198$		0			0
$199$	1988.77			0.708443			0.354221	−	0.935162i	$-0.384746\pi$
$199$	1988.77			0.708443			0.354221	+	0.935162i	$0.384746\pi$
$200$		0			0
$201$	214.939			0.0754262
$202$		0			0
$203$	191.876	−	62.3444i	0.0663403	−	0.0215553i
$204$		0			0
$205$	−4461.89	+	2096.67i	−1.52016	+	0.714329i
$206$		0			0
$207$		−	318.307i		−	0.106879i
$208$		0			0
$209$	5907.58	−	4292.11i	1.95519	−	1.42053i
$210$		0			0
$211$	−2909.60	−	2113.95i	−0.949314	−	0.689717i	0.00133070	−	0.999999i	$-0.499576\pi$
$211$	−2909.60	−	2113.95i	−0.949314	−	0.689717i	−0.950644	+	0.310282i	$0.899576\pi$
$212$		0			0
$213$	−514.572	−	708.248i	−0.165530	−	0.227833i
$214$		0			0
$215$	−612.559	+	3201.76i	−0.194308	+	1.01562i
$216$		0			0
$217$	9051.50	+	2941.01i	2.83159	+	0.920041i
$218$		0			0
$219$	514.680	−	1584.02i	0.158808	−	0.488759i
$220$		0			0
$221$	−555.814	−	1710.62i	−0.169177	−	0.520673i
$222$		0			0
$223$	1109.72	−	1527.39i	0.333238	−	0.458663i	−0.609213	−	0.793007i	$-0.708515\pi$
$223$	1109.72	−	1527.39i	0.333238	−	0.458663i	0.942451	+	0.334343i	$0.108515\pi$
$224$		0			0
$225$	−1579.00	+	403.602i	−0.467852	+	0.119586i
$226$		0			0
$227$	−2552.82	+	3513.65i	−0.746416	+	1.02735i	0.251808	+	0.967777i	$0.418975\pi$
$227$	−2552.82	+	3513.65i	−0.746416	+	1.02735i	−0.998224	+	0.0595762i	$0.981025\pi$
$228$		0			0
$229$	1848.68	+	5689.65i	0.533468	+	1.64185i	0.746935	+	0.664897i	$0.231524\pi$
$229$	1848.68	+	5689.65i	0.533468	+	1.64185i	−0.213467	+	0.976950i	$0.568476\pi$
$230$		0			0
$231$	2216.90	−	6822.91i	0.631433	−	1.94335i
$232$		0			0
$233$	1068.93	+	347.318i	0.300550	+	0.0976547i	0.455410	−	0.890282i	$-0.349493\pi$
$233$	1068.93	+	347.318i	0.300550	+	0.0976547i	−0.154860	+	0.987936i	$0.549493\pi$
$234$		0			0
$235$	1174.94	−	147.785i	0.326148	−	0.0410232i
$236$		0			0
$237$	−124.343	−	171.143i	−0.0340798	−	0.0469068i
$238$		0			0
$239$	−1250.90	−	908.829i	−0.338551	−	0.245972i	0.405499	−	0.914095i	$-0.367098\pi$
$239$	−1250.90	−	908.829i	−0.338551	−	0.245972i	−0.744050	+	0.668124i	$0.767098\pi$
$240$		0			0
$241$	−1569.99	+	1140.66i	−0.419634	+	0.304882i	−0.777491	−	0.628895i	$-0.783508\pi$
$241$	−1569.99	+	1140.66i	−0.419634	+	0.304882i	0.357856	+	0.933777i	$0.383508\pi$
$242$		0			0
$243$		−	3265.95i		−	0.862183i
$244$		0			0
$245$	−6207.52	−	1187.62i	−1.61871	−	0.309691i
$246$		0			0
$247$	−4425.14	+	1437.81i	−1.13994	+	0.370388i
$248$		0			0
$249$	5101.16			1.29828
$250$		0			0
$251$	5850.12			1.47114			0.735570	−	0.677448i	$-0.236914\pi$
$251$	5850.12			1.47114			0.735570	+	0.677448i	$0.236914\pi$
$252$		0			0
$253$	−1479.17	+	480.611i	−0.367567	+	0.119430i
$254$		0			0
$255$	1818.11	+	347.840i	0.446488	+	0.0854219i
$256$		0			0
$257$		−	5451.41i		−	1.32315i	−0.749879	−	0.661575i	$-0.769888\pi$
$257$		−	5451.41i		−	1.32315i	0.749879	−	0.661575i	$-0.230112\pi$
$258$		0			0
$259$	−8369.29	+	6080.64i	−2.00788	+	1.45881i
$260$		0			0
$261$	−70.6116	−	51.3024i	−0.0167462	−	0.0121668i
$262$		0			0
$263$	−2546.87	−	3505.47i	−0.597137	−	0.821888i	0.398306	−	0.917253i	$-0.369598\pi$
$263$	−2546.87	−	3505.47i	−0.597137	−	0.821888i	−0.995442	+	0.0953646i	$0.969598\pi$
$264$		0			0
$265$	−4045.96	+	508.905i	−0.937891	+	0.117969i
$266$		0			0
$267$	−1872.01	−	608.254i	−0.429084	−	0.139418i
$268$		0			0
$269$	−2020.60	+	6218.77i	−0.457986	+	1.40954i	0.409607	+	0.912262i	$0.365666\pi$
$269$	−2020.60	+	6218.77i	−0.457986	+	1.40954i	−0.867593	+	0.497274i	$0.834334\pi$
$270$		0			0
$271$	−256.539	−	789.544i	−0.0575041	−	0.176979i	0.918179	−	0.396166i	$-0.129660\pi$
$271$	−256.539	−	789.544i	−0.0575041	−	0.176979i	−0.975683	+	0.219187i	$0.929660\pi$
$272$		0			0
$273$	−2686.89	+	3698.19i	−0.595671	+	0.819871i
$274$		0			0
$275$	4259.66	+	6728.19i	0.934062	+	1.47536i
$276$		0			0
$277$	4022.06	−	5535.89i	0.872426	−	1.20079i	−0.106035	−	0.994362i	$-0.533816\pi$
$277$	4022.06	−	5535.89i	0.872426	−	1.20079i	0.978462	−	0.206429i	$-0.0661844\pi$
$278$		0			0
$279$	−1272.33	−	3915.83i	−0.273020	−	0.840268i
$280$		0			0
$281$	−890.654	+	2741.15i	−0.189082	+	0.581934i	−0.999995	−	0.00323279i	$-0.998971\pi$
$281$	−890.654	+	2741.15i	−0.189082	+	0.581934i	0.810913	+	0.585167i	$0.198971\pi$
$282$		0			0
$283$	−1872.09	−	608.281i	−0.393231	−	0.127769i	0.105726	−	0.994395i	$-0.466283\pi$
$283$	−1872.09	−	608.281i	−0.393231	−	0.127769i	−0.498957	+	0.866627i	$0.666283\pi$
$284$		0			0
$285$	899.813	−	4703.19i	0.187019	−	0.977519i
$286$		0			0
$287$	7811.21	+	10751.2i	1.60655	+	2.21123i
$288$		0			0
$289$	−2386.31	−	1733.76i	−0.485714	−	0.352892i
$290$		0			0
$291$	−4042.91	+	2937.34i	−0.814431	+	0.591719i
$292$		0			0
$293$			3067.07i			0.611535i	0.952106	+	0.305768i	$0.0989131\pi$
$293$			3067.07i			0.611535i	−0.952106	+	0.305768i	$0.901087\pi$
$294$		0			0
$295$	−3370.08	+	1583.62i	−0.665132	+	0.312549i
$296$		0			0
$297$	−9064.25	+	2945.15i	−1.77091	+	0.575404i
$298$		0			0
$299$	991.013			0.191678
$300$		0			0
$301$	8787.22			1.68268
$302$		0			0
$303$	1016.23	−	330.193i	0.192676	−	0.0626043i
$304$		0			0
$305$	102.832	+	109.624i	0.0193054	+	0.0205804i
$306$		0			0
$307$		−	1679.74i		−	0.312273i	−0.987735	−	0.156137i	$-0.950096\pi$
$307$		−	1679.74i		−	0.312273i	0.987735	−	0.156137i	$-0.0499040\pi$
$308$		0			0
$309$	3826.75	−	2780.29i	0.704518	−	0.511862i
$310$		0			0
$311$	−2549.42	−	1852.26i	−0.464836	−	0.337723i	0.330589	−	0.943775i	$-0.392753\pi$
$311$	−2549.42	−	1852.26i	−0.464836	−	0.337723i	−0.795425	+	0.606051i	$0.792753\pi$
$312$		0			0
$313$	−4090.65	−	5630.29i	−0.738713	−	1.01675i	−0.998692	−	0.0511366i	$-0.983716\pi$
$313$	−4090.65	−	5630.29i	−0.738713	−	1.01675i	0.259979	−	0.965614i	$-0.416284\pi$
$314$		0			0
$315$	1868.39	+	3976.10i	0.334197	+	0.711200i
$316$		0			0
$317$	−7620.04	−	2475.90i	−1.35011	−	0.438677i	−0.457379	−	0.889272i	$-0.651212\pi$
$317$	−7620.04	−	2475.90i	−1.35011	−	0.438677i	−0.892728	+	0.450595i	$0.851212\pi$
$318$		0			0
$319$	−131.785	+	405.592i	−0.0231302	+	0.0711875i
$320$		0			0
$321$	−356.782	−	1098.06i	−0.0620362	−	0.190928i
$322$		0			0
$323$	2985.31	−	4108.93i	0.514264	−	0.707824i
$324$		0			0
$325$	−1256.57	−	4916.04i	−0.214467	−	0.839055i
$326$		0			0
$327$	1492.51	−	2054.26i	0.252403	−	0.347403i
$328$		0			0
$329$	−986.424	−	3035.90i	−0.165299	−	0.508738i
$330$		0			0
$331$	1800.16	−	5540.31i	0.298929	−	0.920009i	−0.682944	−	0.730471i	$-0.739301\pi$
$331$	1800.16	−	5540.31i	0.298929	−	0.920009i	0.981873	−	0.189539i	$-0.0606993\pi$
$332$		0			0
$333$	4256.38	+	1382.98i	0.700445	+	0.227589i
$334$		0			0
$335$	563.412	+	310.135i	0.0918881	+	0.0505805i
$336$		0			0
$337$	5489.31	+	7555.39i	0.887306	+	1.22127i	0.974343	+	0.225066i	$0.0722599\pi$
$337$	5489.31	+	7555.39i	0.887306	+	1.22127i	−0.0870380	+	0.996205i	$0.527740\pi$
$338$		0			0
$339$	1458.83	+	1059.90i	0.233725	+	0.169811i
$340$		0			0
$341$	−16275.7	+	11825.0i	−2.58469	+	1.87789i
$342$		0			0
$343$			6699.25i			1.05459i
$344$		0			0
$345$	−491.823	+	893.481i	−0.0767504	+	0.139430i
$346$		0			0
$347$	−5032.82	+	1635.26i	−0.778605	+	0.252984i	−0.671245	−	0.741236i	$-0.734240\pi$
$347$	−5032.82	+	1635.26i	−0.778605	+	0.252984i	−0.107361	+	0.994220i	$0.534240\pi$
$348$		0			0
$349$	5464.91			0.838195			0.419097	−	0.907941i	$-0.362347\pi$
$349$	5464.91			0.838195			0.419097	+	0.907941i	$0.362347\pi$
$350$		0			0
$351$	6072.87			0.923492
$352$		0			0
$353$	−10279.6	+	3340.05i	−1.54994	+	0.503606i	−0.954098	−	0.299494i	$-0.903182\pi$
$353$	−10279.6	+	3340.05i	−1.54994	+	0.503606i	−0.595843	+	0.803101i	$0.703182\pi$
$354$		0			0
$355$	−326.902	−	2598.98i	−0.0488737	−	0.388562i
$356$		0			0
$357$		−	4989.80i		−	0.739742i
$358$		0			0
$359$	6279.93	−	4562.63i	0.923236	−	0.670770i	−0.0210912	−	0.999778i	$-0.506714\pi$
$359$	6279.93	−	4562.63i	0.923236	−	0.670770i	0.944327	+	0.329007i	$0.106714\pi$
$360$		0			0
$361$	−5080.18	−	3690.97i	−0.740660	−	0.538121i
$362$		0			0
$363$	5990.27	+	8244.90i	0.866136	+	1.19213i
$364$		0			0
$365$	3634.69	−	3409.51i	0.521228	−	0.488936i
$366$		0			0
$367$	2365.29	+	768.529i	0.336422	+	0.109310i	0.472356	−	0.881408i	$-0.343404\pi$
$367$	2365.29	+	768.529i	0.336422	+	0.109310i	−0.135934	+	0.990718i	$0.543404\pi$
$368$		0			0
$369$	1776.58	−	5467.76i	0.250638	−	0.771383i
$370$		0			0
$371$	3396.79	+	10454.2i	0.475344	+	1.46296i
$372$		0			0
$373$	4189.29	−	5766.07i	0.581537	−	0.800418i	−0.412325	−	0.911037i	$-0.635283\pi$
$373$	4189.29	−	5766.07i	0.581537	−	0.800418i	0.993863	+	0.110619i	$0.0352833\pi$
$374$		0			0
$375$	5055.83	+	1306.85i	0.696219	+	0.179961i
$376$		0			0
$377$	159.724	−	219.841i	0.0218202	−	0.0300329i
$378$		0			0
$379$	−1849.47	−	5692.09i	−0.250662	−	0.771459i	−0.994653	−	0.103269i	$-0.967070\pi$
$379$	−1849.47	−	5692.09i	−0.250662	−	0.771459i	0.743991	−	0.668189i	$-0.232930\pi$
$380$		0			0
$381$	116.616	−	358.906i	0.0156809	−	0.0482607i
$382$		0			0
$383$	3341.93	+	1085.86i	0.445860	+	0.144869i	0.523338	−	0.852125i	$-0.324687\pi$
$383$	3341.93	+	1085.86i	0.445860	+	0.144869i	−0.0774776	+	0.996994i	$0.524687\pi$
$384$		0			0
$385$	15655.8	−	14685.9i	2.07245	−	1.94406i
$386$		0			0
$387$	−2234.47	−	3075.48i	−0.293499	−	0.403967i
$388$		0			0
$389$	−5270.26	−	3829.07i	−0.686923	−	0.499079i	0.188724	−	0.982030i	$-0.439565\pi$
$389$	−5270.26	−	3829.07i	−0.686923	−	0.499079i	−0.875647	+	0.482951i	$0.839565\pi$
$390$		0			0
$391$	−875.161	+	635.842i	−0.113194	+	0.0822402i
$392$		0			0
$393$		−	4836.84i		−	0.620831i
$394$		0			0
$395$	−78.9934	−	628.023i	−0.0100623	−	0.0799981i
$396$		0			0
$397$	5012.75	−	1628.74i	0.633709	−	0.205905i	0.0254918	−	0.999675i	$-0.491885\pi$
$397$	5012.75	−	1628.74i	0.633709	−	0.205905i	0.608218	+	0.793770i	$0.291885\pi$
$398$		0			0
$399$	−12907.9			−1.61956
$400$		0			0
$401$	7692.59			0.957979			0.478990	−	0.877821i	$-0.341003\pi$
$401$	7692.59			0.957979			0.478990	+	0.877821i	$0.341003\pi$
$402$		0			0
$403$	12191.5	−	3961.26i	1.50695	−	0.489639i
$404$		0			0
$405$	−1115.91	+	2027.24i	−0.136914	+	0.248727i
$406$		0			0
$407$		−	21867.5i		−	2.66322i
$408$		0			0
$409$	−11277.7	+	8193.73i	−1.36344	+	0.990596i	−0.365221	+	0.930921i	$0.619007\pi$
$409$	−11277.7	+	8193.73i	−1.36344	+	0.990596i	−0.998218	+	0.0596754i	$0.980993\pi$
$410$		0			0
$411$	1709.01	+	1241.67i	0.205108	+	0.149020i
$412$		0			0
$413$	5899.84	+	8120.43i	0.702935	+	0.967507i
$414$		0			0
$415$	13371.5	+	7360.43i	1.58164	+	0.870625i
$416$		0			0
$417$	1613.10	+	524.129i	0.189434	+	0.0615508i
$418$		0			0
$419$	−4225.66	+	13005.2i	−0.492689	+	1.51634i	0.327838	+	0.944734i	$0.393680\pi$
$419$	−4225.66	+	13005.2i	−0.492689	+	1.51634i	−0.820527	+	0.571608i	$0.806320\pi$
$420$		0			0
$421$	3285.35	+	10111.3i	0.380328	+	1.17053i	0.939813	+	0.341690i	$0.110999\pi$
$421$	3285.35	+	10111.3i	0.380328	+	1.17053i	−0.559484	+	0.828841i	$0.689001\pi$
$422$		0			0
$423$	−811.715	+	1117.23i	−0.0933025	+	0.128420i
$424$		0			0
$425$	4263.84	+	3535.12i	0.486651	+	0.403478i
$426$		0			0
$427$	238.150	−	327.786i	0.0269904	−	0.0371491i
$428$		0			0
$429$	−2985.95	−	9189.80i	−0.336044	−	1.03424i
$430$		0			0
$431$	215.957	−	664.647i	0.0241352	−	0.0742806i	−0.938263	−	0.345922i	$-0.887566\pi$
$431$	215.957	−	664.647i	0.0241352	−	0.0742806i	0.962399	+	0.271641i	$0.0875663\pi$
$432$		0			0
$433$	−6186.13	−	2010.00i	−0.686574	−	0.223081i	−0.0551026	−	0.998481i	$-0.517549\pi$
$433$	−6186.13	−	2010.00i	−0.686574	−	0.223081i	−0.631471	+	0.775399i	$0.717549\pi$
$434$		0			0
$435$	118.937	+	253.108i	0.0131094	+	0.0278979i
$436$		0			0
$437$	1644.83	+	2263.92i	0.180053	+	0.247821i
$438$		0			0
$439$	1131.13	+	821.817i	0.122975	+	0.0893466i	0.647573	−	0.762004i	$-0.275784\pi$
$439$	1131.13	+	821.817i	0.122975	+	0.0893466i	−0.524598	+	0.851350i	$0.675784\pi$
$440$		0			0
$441$	5962.69	−	4332.14i	0.643849	−	0.467784i
$442$		0			0
$443$			9646.64i			1.03460i	0.855806	+	0.517298i	$0.173062\pi$
$443$			9646.64i			1.03460i	−0.855806	+	0.517298i	$0.826938\pi$
$444$		0			0
$445$	−4029.39	−	4295.51i	−0.429239	−	0.457588i
$446$		0			0
$447$	−6405.39	+	2081.24i	−0.677773	+	0.220222i
$448$		0			0
$449$	167.410			0.0175959			0.00879796	−	0.999961i	$-0.497199\pi$
$449$	167.410			0.0175959			0.00879796	+	0.999961i	$0.497199\pi$
$450$		0			0
$451$	−28091.0			−2.93294
$452$		0			0
$453$	−3255.99	+	1057.93i	−0.337703	+	0.109727i
$454$		0			0
$455$	−12379.1	+	5817.02i	−1.27548	+	0.599354i
$456$		0			0
$457$		−	19055.6i		−	1.95051i	−0.221082	−	0.975255i	$-0.570959\pi$
$457$		−	19055.6i		−	1.95051i	0.221082	−	0.975255i	$-0.429041\pi$
$458$		0			0
$459$	−5362.94	+	3896.40i	−0.545360	+	0.396227i
$460$		0			0
$461$	−4183.87	−	3039.76i	−0.422695	−	0.307106i	0.356026	−	0.934476i	$-0.384131\pi$
$461$	−4183.87	−	3039.76i	−0.422695	−	0.307106i	−0.778721	+	0.627370i	$0.784131\pi$
$462$		0			0
$463$	−3254.90	−	4479.98i	−0.326713	−	0.449681i	0.613789	−	0.789470i	$-0.289644\pi$
$463$	−3254.90	−	4479.98i	−0.326713	−	0.449681i	−0.940502	+	0.339789i	$0.889644\pi$
$464$		0			0
$465$	−2479.04	+	12957.6i	−0.247231	+	1.29224i
$466$		0			0
$467$	6854.00	+	2227.00i	0.679155	+	0.220671i	0.628225	−	0.778032i	$-0.283782\pi$
$467$	6854.00	+	2227.00i	0.679155	+	0.220671i	0.0509294	+	0.998702i	$0.483782\pi$
$468$		0			0
$469$	535.720	−	1648.78i	0.0527447	−	0.162332i
$470$		0			0
$471$	−374.129	−	1151.45i	−0.0366008	−	0.112646i
$472$		0			0
$473$	−10917.9	+	15027.2i	−1.06132	+	1.46078i
$474$		0			0
$475$	9144.85	−	11030.0i	0.883357	−	1.06545i
$476$		0			0
$477$	2795.17	−	3847.23i	0.268306	−	0.369292i
$478$		0			0
$479$	905.886	+	2788.03i	0.0864113	+	0.265947i	0.984920	−	0.173008i	$-0.0553488\pi$
$479$	905.886	+	2788.03i	0.0864113	+	0.265947i	−0.898509	+	0.438955i	$0.855349\pi$
$480$		0			0
$481$	−4305.76	+	13251.8i	−0.408162	+	1.25619i
$482$		0			0
$483$	2614.69	+	849.566i	0.246320	+	0.0800343i
$484$		0			0
$485$	−14835.8	+	1866.06i	−1.38899	+	0.174708i
$486$		0			0
$487$	1405.54	+	1934.56i	0.130783	+	0.180007i	0.869386	−	0.494133i	$-0.164514\pi$
$487$	1405.54	+	1934.56i	0.130783	+	0.180007i	−0.738604	+	0.674140i	$0.764514\pi$
$488$		0			0
$489$	189.699	+	137.824i	0.0175429	+	0.0127457i
$490$		0			0
$491$	8634.83	−	6273.57i	0.793655	−	0.576624i	−0.115391	−	0.993320i	$-0.536812\pi$
$491$	8634.83	−	6273.57i	0.793655	−	0.576624i	0.909046	+	0.416696i	$0.136812\pi$
$492$		0			0
$493$			296.622i			0.0270977i
$494$		0			0
$495$	−9121.03	−	1745.03i	−0.828201	−	0.158451i
$496$		0			0
$497$	−6715.43	+	2181.98i	−0.606093	+	0.196932i
$498$		0			0
$499$	2019.83			0.181203			0.0906013	−	0.995887i	$-0.471121\pi$
$499$	2019.83			0.181203			0.0906013	+	0.995887i	$0.471121\pi$
$500$		0			0
$501$	−2609.90			−0.232738
$502$		0			0
$503$	16138.1	−	5243.59i	1.43054	−	0.464811i	0.511607	−	0.859220i	$-0.329051\pi$
$503$	16138.1	−	5243.59i	1.43054	−	0.464811i	0.918935	+	0.394409i	$0.129051\pi$
$504$		0			0
$505$	3140.24	+	600.789i	0.276710	+	0.0529401i
$506$		0			0
$507$		−	2052.23i		−	0.179769i
$508$		0			0
$509$	−2744.00	+	1993.63i	−0.238950	+	0.173607i	−0.700815	−	0.713343i	$-0.747180\pi$
$509$	−2744.00	+	1993.63i	−0.238950	+	0.173607i	0.461865	+	0.886950i	$0.347180\pi$
$510$		0			0
$511$	−10868.1	−	7896.11i	−0.940851	−	0.683569i
$512$		0			0
$513$	10079.4	+	13873.2i	0.867482	+	1.19399i
$514$		0			0
$515$	14042.6	−	1766.29i	1.20153	−	0.151130i
$516$		0			0
$517$	6417.35	+	2085.12i	0.545909	+	0.177376i
$518$		0			0
$519$	1112.35	−	3423.46i	0.0940783	−	0.289543i
$520$		0			0
$521$	3077.74	+	9472.30i	0.258806	+	0.796524i	0.993056	+	0.117644i	$0.0375342\pi$
$521$	3077.74	+	9472.30i	0.258806	+	0.796524i	−0.734250	+	0.678880i	$0.762466\pi$
$522$		0			0
$523$	−5333.78	+	7341.32i	−0.445947	+	0.613793i	−0.971521	−	0.236955i	$-0.923851\pi$
$523$	−5333.78	+	7341.32i	−0.445947	+	0.613793i	0.525574	+	0.850748i	$0.323851\pi$
$524$		0			0
$525$	899.033	−	14047.7i	0.0747371	−	1.16780i
$526$		0			0
$527$	−8224.71	+	11320.3i	−0.679837	+	0.935715i
$528$		0			0
$529$	3575.63	+	11004.7i	0.293879	+	0.904467i
$530$		0			0
$531$	1341.86	−	4129.82i	0.109664	−	0.337512i
$532$		0			0
$533$	17023.3	+	5531.19i	1.38341	+	0.449498i
$534$		0			0
$535$	649.167	−	3393.10i	0.0524597	−	0.274199i
$536$		0			0
$537$	−1514.22	−	2084.15i	−0.121683	−	0.167482i
$538$		0			0
$539$	−29134.4	−	21167.4i	−2.32822	−	1.69155i
$540$		0			0
$541$	−17782.9	+	12920.0i	−1.41321	+	1.02676i	−0.420364	+	0.907355i	$0.638098\pi$
$541$	−17782.9	+	12920.0i	−1.41321	+	1.02676i	−0.992846	+	0.119402i	$0.961902\pi$
$542$		0			0
$543$		−	4372.87i		−	0.345595i
$544$		0			0
$545$	6876.33	−	3231.22i	0.540458	−	0.253964i
$546$		0			0
$547$	−9651.80	+	3136.06i	−0.754444	+	0.245134i	−0.660893	−	0.750481i	$-0.729822\pi$
$547$	−9651.80	+	3136.06i	−0.754444	+	0.245134i	−0.0935519	+	0.995614i	$0.529822\pi$
$548$		0			0
$549$	−175.281			−0.0136263
$550$		0			0
$551$	767.318			0.0593264
$552$		0			0
$553$	−1622.73	+	527.258i	−0.124784	+	0.0405448i
$554$		0			0
$555$	−9810.69	−	10458.6i	−0.750343	−	0.799899i
$556$		0			0
$557$		−	172.532i		−	0.0131246i	−0.999978	−	0.00656229i	$-0.997911\pi$
$557$		−	172.532i		−	0.0131246i	0.999978	−	0.00656229i	$-0.00208886\pi$
$558$		0			0
$559$	9575.15	−	6956.76i	0.724483	−	0.526368i
$560$		0			0
$561$	8533.13	+	6199.68i	0.642191	+	0.466579i
$562$		0			0
$563$	1614.70	+	2222.45i	0.120873	+	0.166368i	0.865166	−	0.501486i	$-0.167213\pi$
$563$	1614.70	+	2222.45i	0.120873	+	0.166368i	−0.744292	+	0.667854i	$0.767213\pi$
$564$		0			0
$565$	2294.65	+	4883.21i	0.170861	+	0.363607i
$566$		0			0
$567$	5932.55	+	1927.60i	0.439407	+	0.142772i
$568$		0			0
$569$	−2101.48	+	6467.70i	−0.154831	+	0.476520i	−0.998144	−	0.0609027i	$-0.980602\pi$
$569$	−2101.48	+	6467.70i	−0.154831	+	0.476520i	0.843313	+	0.537423i	$0.180602\pi$
$570$		0			0
$571$	4560.10	+	14034.5i	0.334210	+	1.02859i	0.967110	+	0.254360i	$0.0818647\pi$
$571$	4560.10	+	14034.5i	0.334210	+	1.02859i	−0.632899	+	0.774234i	$0.718135\pi$
$572$		0			0
$573$	9686.44	−	13332.2i	0.706207	−	0.972011i
$574$		0			0
$575$	−2578.40	+	1632.40i	−0.187003	+	0.118393i
$576$		0			0
$577$	8486.82	−	11681.1i	0.612324	−	0.842791i	−0.384442	−	0.923149i	$-0.625606\pi$
$577$	8486.82	−	11681.1i	0.612324	−	0.842791i	0.996766	+	0.0803577i	$0.0256063\pi$
$578$		0			0
$579$	−431.273	−	1327.32i	−0.0309552	−	0.0952704i
$580$		0			0
$581$	12714.3	−	39130.5i	0.907877	−	2.79416i
$582$		0			0
$583$	−22098.4	−	7180.20i	−1.56985	−	0.510075i
$584$		0			0
$585$	5183.77	+	2853.45i	0.366363	+	0.201667i
$586$		0			0
$587$	−4305.85	−	5926.49i	−0.302762	−	0.416717i	0.630345	−	0.776315i	$-0.282914\pi$
$587$	−4305.85	−	5926.49i	−0.302762	−	0.416717i	−0.933107	+	0.359599i	$0.882914\pi$
$588$		0			0
$589$	29284.1	+	21276.2i	2.04861	+	1.48840i
$590$		0			0
$591$	−3386.58	+	2460.49i	−0.235711	+	0.171254i
$592$		0			0
$593$		−	10260.6i		−	0.710545i	−0.934763	−	0.355272i	$-0.884388\pi$
$593$		−	10260.6i		−	0.710545i	0.934763	−	0.355272i	$-0.115612\pi$
$594$		0			0
$595$	7199.74	−	13079.6i	0.496068	−	0.901193i
$596$		0			0
$597$	7067.45	−	2296.35i	0.484508	−	0.157426i
$598$		0			0
$599$	16885.1			1.15177			0.575883	−	0.817532i	$-0.304658\pi$
$599$	16885.1			1.15177			0.575883	+	0.817532i	$0.304658\pi$
$600$		0			0
$601$	11440.0			0.776450			0.388225	−	0.921565i	$-0.373088\pi$
$601$	11440.0			0.776450			0.388225	+	0.921565i	$0.373088\pi$
$602$		0			0
$603$	−713.289	+	231.762i	−0.0481715	+	0.0156519i
$604$		0			0
$605$	3805.55	+	30255.3i	0.255732	+	2.03315i
$606$		0			0
$607$			27885.2i			1.86462i	0.361659	+	0.932311i	$0.382211\pi$
$607$			27885.2i			1.86462i	−0.361659	+	0.932311i	$0.617789\pi$
$608$		0			0
$609$	609.880	−	443.104i	0.0405806	−	0.0294835i
$610$		0			0
$611$	−3478.37	−	2527.18i	−0.230311	−	0.167330i
$612$		0			0
$613$	−13354.8	−	18381.3i	−0.879927	−	1.21112i	−0.976441	−	0.215784i	$-0.930769\pi$
$613$	−13354.8	−	18381.3i	−0.879927	−	1.21112i	0.0965143	−	0.995332i	$-0.469231\pi$
$614$		0			0
$615$	−13435.2	+	12602.8i	−0.880909	+	0.826335i
$616$		0			0
$617$	−12322.8	−	4003.92i	−0.804048	−	0.261251i	−0.121973	−	0.992533i	$-0.538922\pi$
$617$	−12322.8	−	4003.92i	−0.804048	−	0.261251i	−0.682075	+	0.731282i	$0.738922\pi$
$618$		0			0
$619$	3359.39	−	10339.1i	0.218134	−	0.671349i	−0.780782	−	0.624804i	$-0.785179\pi$
$619$	3359.39	−	10339.1i	0.218134	−	0.671349i	0.998916	−	0.0465449i	$-0.0148211\pi$
$620$		0			0
$621$	−1128.65	−	3473.63i	−0.0729326	−	0.224464i
$622$		0			0
$623$	−9331.71	+	12844.0i	−0.600108	+	0.825977i
$624$		0			0
$625$	11367.0	+	10720.6i	0.727489	+	0.686119i
$626$		0			0
$627$	16037.7	−	22074.0i	1.02151	−	1.40598i
$628$		0			0
$629$	−4700.03	−	14465.2i	−0.297937	−	0.916957i
$630$		0			0
$631$	−907.088	+	2791.73i	−0.0572276	+	0.176128i	−0.975584	−	0.219625i	$-0.929517\pi$
$631$	−907.088	+	2791.73i	−0.0572276	+	0.176128i	0.918357	+	0.395754i	$0.129517\pi$
$632$		0			0
$633$	−12780.7	−	4152.69i	−0.802506	−	0.260750i
$634$		0			0
$635$	823.544	−	772.523i	0.0514667	−	0.0482782i
$636$		0			0
$637$	13487.6	+	18564.1i	0.838932	+	1.15469i
$638$		0			0
$639$	2471.32	+	1795.52i	0.152995	+	0.111157i
$640$		0			0
$641$	22933.1	−	16661.9i	1.41311	−	1.02669i	0.420250	−	0.907408i	$-0.361942\pi$
$641$	22933.1	−	16661.9i	1.41311	−	1.02669i	0.992861	−	0.119277i	$-0.0380577\pi$
$642$		0			0
$643$		−	29681.1i		−	1.82038i	−0.414187	−	0.910192i	$-0.635934\pi$
$643$		−	29681.1i		−	1.82038i	0.414187	−	0.910192i	$-0.364066\pi$
$644$		0			0
$645$	1520.10	+	12085.3i	0.0927970	+	0.737766i
$646$		0			0
$647$	−13595.0	+	4417.27i	−0.826079	+	0.268409i	−0.691393	−	0.722479i	$-0.743003\pi$
$647$	−13595.0	+	4417.27i	−0.826079	+	0.268409i	−0.134686	+	0.990888i	$0.543003\pi$
$648$		0			0
$649$	−21217.3			−1.28328
$650$		0			0
$651$	35562.0			2.14099
$652$		0			0
$653$	−11894.7	+	3864.81i	−0.712824	+	0.231611i	−0.642909	−	0.765942i	$-0.722273\pi$
$653$	−11894.7	+	3864.81i	−0.712824	+	0.231611i	−0.0699147	+	0.997553i	$0.522273\pi$
$654$		0			0
$655$	6979.05	−	12678.6i	0.416327	−	0.756328i
$656$		0			0
$657$			5811.64i			0.345104i
$658$		0			0
$659$	16698.8	−	12132.4i	0.987088	−	0.717162i	0.0278067	−	0.999613i	$-0.491148\pi$
$659$	16698.8	−	12132.4i	0.987088	−	0.717162i	0.959282	+	0.282452i	$0.0911477\pi$
$660$		0			0
$661$	−2821.86	−	2050.20i	−0.166048	−	0.120641i	0.501658	−	0.865066i	$-0.332724\pi$
$661$	−2821.86	−	2050.20i	−0.166048	−	0.120641i	−0.667706	+	0.744425i	$0.732724\pi$
$662$		0			0
$663$	−3950.37	−	5437.22i	−0.231402	−	0.318498i
$664$		0			0
$665$	−33835.0	−	18624.7i	−1.97303	−	1.08607i
$666$		0			0
$667$	−155.432	−	50.5030i	−0.00902303	−	0.00293176i
$668$		0			0
$669$	2179.96	−	6709.21i	0.125982	−	0.387733i
$670$		0			0
$671$	264.657	+	814.529i	0.0152265	+	0.0468622i
$672$		0			0
$673$	19142.3	−	26347.2i	1.09641	−	1.50908i	0.256349	−	0.966584i	$-0.417481\pi$
$673$	19142.3	−	26347.2i	1.09641	−	1.50908i	0.840060	−	0.542493i	$-0.182519\pi$
$674$		0			0
$675$	−15800.2	+	10003.2i	−0.900966	+	0.570407i
$676$		0			0
$677$	−13120.4	+	18058.7i	−0.744842	+	1.02519i	0.253484	+	0.967340i	$0.418424\pi$
$677$	−13120.4	+	18058.7i	−0.744842	+	1.02519i	−0.998325	+	0.0578473i	$0.981576\pi$
$678$		0			0
$679$	12455.4	+	38333.8i	0.703969	+	2.16659i
$680$		0			0
$681$	−5014.82	+	15434.0i	−0.282185	+	0.868477i
$682$		0			0
$683$	12059.6	+	3918.42i	0.675621	+	0.219523i	0.626677	−	0.779279i	$-0.284414\pi$
$683$	12059.6	+	3918.42i	0.675621	+	0.219523i	0.0489440	+	0.998802i	$0.484414\pi$
$684$		0			0
$685$	2688.17	+	5720.67i	0.149941	+	0.319089i
$686$		0			0
$687$	13139.2	+	18084.6i	0.729684	+	1.00432i
$688$		0			0
$689$	11977.9	+	8702.45i	0.662295	+	0.481186i
$690$		0			0
$691$	−8367.39	+	6079.26i	−0.460652	+	0.334683i	−0.793787	−	0.608196i	$-0.791893\pi$
$691$	−8367.39	+	6079.26i	−0.460652	+	0.334683i	0.333135	+	0.942879i	$0.391893\pi$
$692$		0			0
$693$			25032.6i			1.37217i
$694$		0			0
$695$	3472.10	+	3701.41i	0.189503	+	0.202018i
$696$		0			0
$697$	−18582.1	+	6037.68i	−1.00982	+	0.328111i
$698$		0			0
$699$	4199.68			0.227248
$700$		0			0
$701$	2003.53			0.107949			0.0539745	−	0.998542i	$-0.482811\pi$
$701$	2003.53			0.107949			0.0539745	+	0.998542i	$0.482811\pi$
$702$		0			0
$703$	−37419.5	+	12158.3i	−2.00754	+	0.652290i
$704$		0			0
$705$	4004.72	−	1881.84i	0.213938	−	0.100531i
$706$		0			0
$707$		−	8618.37i		−	0.458454i
$708$		0			0
$709$	−8022.56	+	5828.73i	−0.424956	+	0.308748i	−0.779629	−	0.626242i	$-0.784592\pi$
$709$	−8022.56	+	5828.73i	−0.424956	+	0.308748i	0.354673	+	0.934990i	$0.384592\pi$
$710$		0			0
$711$	597.175	+	433.873i	0.0314991	+	0.0228854i
$712$		0			0
$713$	−4531.61	−	6237.23i	−0.238023	−	0.327610i
$714$		0			0
$715$	5432.96	−	28397.3i	0.284169	−	1.48531i
$716$		0			0
$717$	−5494.67	−	1785.33i	−0.286196	−	0.0929906i
$718$		0			0
$719$	9903.20	−	30478.9i	0.513667	−	1.58091i	−0.272026	−	0.962290i	$-0.587694\pi$
$719$	9903.20	−	30478.9i	0.513667	−	1.58091i	0.785694	−	0.618616i	$-0.212306\pi$
$720$		0			0
$721$	−11789.5	−	36284.3i	−0.608964	−	1.87420i
$722$		0			0
$723$	−4262.16	+	5866.35i	−0.219241	+	0.301759i
$724$		0			0
$725$	−53.4436	+	835.076i	−0.00273772	+	0.0427778i
$726$		0			0
$727$	−450.114	+	619.529i	−0.0229626	+	0.0316053i	−0.820344	−	0.571870i	$-0.806218\pi$
$727$	−450.114	+	619.529i	−0.0229626	+	0.0316053i	0.797381	+	0.603476i	$0.206218\pi$
$728$		0			0
$729$	−5497.97	−	16921.0i	−0.279326	−	0.859676i
$730$		0			0
$731$	−3992.29	+	12287.0i	−0.201997	+	0.621684i
$732$		0			0
$733$	3988.32	+	1295.88i	0.200971	+	0.0652996i	0.407773	−	0.913083i	$-0.366305\pi$
$733$	3988.32	+	1295.88i	0.200971	+	0.0652996i	−0.206802	+	0.978383i	$0.566305\pi$
$734$		0			0
$735$	−23430.8	+	2947.15i	−1.17586	+	0.147901i
$736$		0			0
$737$	2153.98	+	2964.71i	0.107657	+	0.148177i
$738$		0			0
$739$	19682.1	+	14299.9i	0.979727	+	0.711813i	0.957648	−	0.287943i	$-0.0929714\pi$
$739$	19682.1	+	14299.9i	0.979727	+	0.711813i	0.0220794	+	0.999756i	$0.492971\pi$
$740$		0			0
$741$	−14065.3	+	10219.1i	−0.697305	+	0.506621i
$742$		0			0
$743$			14266.6i			0.704431i	0.935919	+	0.352216i	$0.114572\pi$
$743$			14266.6i			0.704431i	−0.935919	+	0.352216i	$0.885428\pi$
$744$		0			0
$745$	−19793.2	−	3786.83i	−0.973378	−	0.186226i
$746$		0			0
$747$	−16928.5	+	5500.40i	−0.829159	+	0.269410i
$748$		0			0
$749$	−9312.37			−0.454294
$750$		0			0
$751$	−14050.3			−0.682694			−0.341347	−	0.939937i	$-0.610883\pi$
$751$	−14050.3			−0.682694			−0.341347	+	0.939937i	$0.610883\pi$
$752$		0			0
$753$	20789.4	−	6754.90i	1.00612	−	0.326909i
$754$		0			0
$755$	−10061.3	−	1924.92i	−0.484990	−	0.0927881i
$756$		0			0
$757$			27918.1i			1.34042i	0.742170	+	0.670211i	$0.233797\pi$
$757$			27918.1i			1.34042i	−0.742170	+	0.670211i	$0.766203\pi$
$758$		0			0
$759$	−4701.54	+	3415.87i	−0.224842	+	0.163357i
$760$		0			0
$761$	−7335.45	−	5329.52i	−0.349422	−	0.253870i	0.399205	−	0.916862i	$-0.369286\pi$
$761$	−7335.45	−	5329.52i	−0.349422	−	0.253870i	−0.748626	+	0.662992i	$0.769286\pi$
$762$		0			0
$763$	−12038.1	−	16569.0i	−0.571175	−	0.786155i
$764$		0			0
$765$	−6408.57	+	806.076i	−0.302879	+	0.0380964i
$766$		0			0
$767$	12857.7	+	4177.73i	0.605301	+	0.196674i
$768$		0			0
$769$	−8483.35	+	26109.1i	−0.397812	+	1.22434i	0.528938	+	0.848661i	$0.322591\pi$
$769$	−8483.35	+	26109.1i	−0.397812	+	1.22434i	−0.926750	+	0.375679i	$0.877409\pi$
$770$		0			0
$771$	−6294.53	−	19372.6i	−0.294023	−	0.904910i
$772$		0			0
$773$	13714.2	−	18875.9i	0.638117	−	0.878292i	−0.360397	−	0.932799i	$-0.617359\pi$
$773$	13714.2	−	18875.9i	0.638117	−	0.878292i	0.998513	+	0.0545070i	$0.0173587\pi$
$774$		0			0
$775$	−25194.6	+	30388.2i	−1.16776	+	1.40848i
$776$		0			0
$777$	−22720.7	+	31272.3i	−1.04903	+	1.44387i
$778$		0			0
$779$	15618.6	+	48069.2i	0.718351	+	2.21086i
$780$		0			0
$781$	4612.30	−	14195.2i	0.211320	−	0.650377i
$782$		0			0
$783$	−952.479	−	309.479i	−0.0434723	−	0.0141250i
$784$		0			0
$785$	680.731	−	3558.08i	0.0309507	−	0.161775i
$786$		0			0
$787$	−11307.6	−	15563.6i	−0.512163	−	0.704932i	0.472119	−	0.881535i	$-0.343489\pi$
$787$	−11307.6	−	15563.6i	−0.512163	−	0.704932i	−0.984282	+	0.176602i	$0.943489\pi$
$788$		0			0
$789$	−13098.4	−	9516.54i	−0.591021	−	0.429402i
$790$		0			0
$791$	11766.4	−	8548.79i	0.528907	−	0.384273i
$792$		0			0
$793$		−	545.719i		−	0.0244376i
$794$		0			0
$795$	−13790.4	+	6480.19i	−0.615215	+	0.289093i
$796$		0			0
$797$	23244.7	−	7552.65i	1.03308	−	0.335669i	0.257075	−	0.966391i	$-0.417241\pi$
$797$	23244.7	−	7552.65i	1.03308	−	0.335669i	0.776009	+	0.630722i	$0.217241\pi$
$798$		0			0
$799$	4693.20			0.207802
$800$		0			0
$801$	6868.25			0.302968
$802$		0			0
$803$	27006.6	−	8774.96i	1.18685	−	0.385631i
$804$		0			0
$805$	5627.97	+	5999.66i	0.246410	+	0.262684i
$806$		0			0
$807$			24432.6i			1.06576i
$808$		0			0
$809$	29285.1	−	21276.9i	1.27269	−	0.924667i	0.273388	−	0.961904i	$-0.411856\pi$
$809$	29285.1	−	21276.9i	1.27269	−	0.924667i	0.999306	+	0.0372374i	$0.0118558\pi$
$810$		0			0
$811$	16648.6	+	12095.9i	0.720851	+	0.523729i	0.886656	−	0.462430i	$-0.153022\pi$
$811$	16648.6	+	12095.9i	0.720851	+	0.523729i	−0.165805	+	0.986159i	$0.553022\pi$
$812$		0			0
$813$	−1823.31	−	2509.57i	−0.0786547	−	0.108259i
$814$		0			0
$815$	298.384	+	634.988i	0.0128245	+	0.0272916i
$816$		0			0
$817$	31784.7	+	10327.5i	1.36109	+	0.442243i
$818$		0			0
$819$	4928.98	−	15169.9i	0.210296	−	0.647225i
$820$		0			0
$821$	−9450.96	−	29087.1i	−0.401755	−	1.23647i	−0.923575	−	0.383418i	$-0.874747\pi$
$821$	−9450.96	−	29087.1i	−0.401755	−	1.23647i	0.521820	−	0.853056i	$-0.325253\pi$
$822$		0			0
$823$	−12310.3	+	16943.6i	−0.521396	+	0.717639i	−0.985789	−	0.167990i	$-0.946272\pi$
$823$	−12310.3	+	16943.6i	−0.521396	+	0.717639i	0.464393	+	0.885629i	$0.346272\pi$
$824$		0			0
$825$	22906.2	+	18991.4i	0.966657	+	0.801448i
$826$		0			0
$827$	21687.2	−	29849.8i	0.911895	−	1.25512i	−0.0546207	−	0.998507i	$-0.517395\pi$
$827$	21687.2	−	29849.8i	0.911895	−	1.25512i	0.966515	−	0.256608i	$-0.0826050\pi$
$828$		0			0
$829$	−4640.57	−	14282.2i	−0.194419	−	0.598361i	−0.999983	−	0.00585179i	$-0.998137\pi$
$829$	−4640.57	−	14282.2i	−0.194419	−	0.598361i	0.805564	−	0.592509i	$-0.201863\pi$
$830$		0			0
$831$	7901.03	−	24316.9i	0.329824	−	1.01509i
$832$		0			0
$833$	−23821.8	−	7740.17i	−0.990848	−	0.321946i
$834$		0			0
$835$	−6841.22	−	3765.80i	−0.283533	−	0.156073i
$836$		0			0
$837$	−27769.4	−	38221.3i	−1.14678	−	1.57840i
$838$		0			0
$839$	13445.3	+	9768.59i	0.553258	+	0.401966i	0.828985	−	0.559270i	$-0.188919\pi$
$839$	13445.3	+	9768.59i	0.553258	+	0.401966i	−0.275727	+	0.961236i	$0.588919\pi$
$840$		0			0
$841$	19694.9	−	14309.2i	0.807530	−	0.586705i
$842$		0			0
$843$			10769.6i			0.440005i
$844$		0			0
$845$	2961.15	−	5379.44i	0.120552	−	0.219004i
$846$		0			0
$847$	78176.0	−	25400.9i	3.17138	−	1.03044i
$848$		0			0
$849$	−7355.18			−0.297325
$850$		0			0
$851$	8380.12			0.337564
$852$		0			0
$853$	−42173.0	+	13702.8i	−1.69282	+	0.550031i	−0.987329	−	0.158687i	$-0.949274\pi$
$853$	−42173.0	+	13702.8i	−1.69282	+	0.550031i	−0.705492	+	0.708718i	$0.749274\pi$
$854$		0			0
$855$	2085.21	+	16578.1i	0.0834065	+	0.663108i
$856$		0			0
$857$			10079.8i			0.401774i	0.979614	+	0.200887i	$0.0643824\pi$
$857$			10079.8i			0.401774i	−0.979614	+	0.200887i	$0.935618\pi$
$858$		0			0
$859$	−28145.3	+	20448.8i	−1.11794	+	0.812228i	−0.983895	−	0.178748i	$-0.942795\pi$
$859$	−28145.3	+	20448.8i	−1.11794	+	0.812228i	−0.134040	+	0.990976i	$0.542795\pi$
$860$		0			0
$861$	40172.5	+	29187.1i	1.59010	+	1.15528i
$862$		0			0
$863$	−21223.2	−	29211.2i	−0.837133	−	1.15221i	−0.986553	−	0.163441i	$-0.947741\pi$
$863$	−21223.2	−	29211.2i	−0.837133	−	1.15221i	0.149420	−	0.988774i	$-0.452259\pi$
$864$		0			0
$865$	7855.44	−	7368.77i	0.308778	−	0.289648i
$866$		0			0
$867$	−10482.1	−	3405.84i	−0.410600	−	0.133412i
$868$		0			0
$869$	1114.53	−	3430.17i	0.0435072	−	0.133902i
$870$		0			0
$871$	−721.564	−	2220.75i	−0.0280703	−	0.0863916i
$872$		0			0
$873$	10249.4	−	14107.1i	0.397353	−	0.546910i
$874$		0			0
$875$	22626.0	−	35525.5i	0.874168	−	1.37255i
$876$		0			0
$877$	−9051.10	+	12457.8i	−0.348499	+	0.479668i	−0.946900	−	0.321529i	$-0.895803\pi$
$877$	−9051.10	+	12457.8i	−0.348499	+	0.479668i	0.598400	+	0.801197i	$0.295803\pi$
$878$		0			0
$879$	3541.42	+	10899.4i	0.135892	+	0.418233i
$880$		0			0
$881$	−8283.22	+	25493.1i	−0.316764	+	0.974899i	0.658259	+	0.752792i	$0.271293\pi$
$881$	−8283.22	+	25493.1i	−0.316764	+	0.974899i	−0.975022	+	0.222107i	$0.928707\pi$
$882$		0			0
$883$	42031.4	+	13656.8i	1.60189	+	0.520486i	0.967574	−	0.252586i	$-0.0812812\pi$
$883$	42031.4	+	13656.8i	1.60189	+	0.520486i	0.634318	+	0.773073i	$0.281281\pi$
$884$		0			0
$885$	−10147.7	+	9518.98i	−0.385435	+	0.361556i
$886$		0			0
$887$	−26239.2	−	36115.2i	−0.993267	−	1.36711i	−0.929367	−	0.369158i	$-0.879646\pi$
$887$	−26239.2	−	36115.2i	−0.993267	−	1.36711i	−0.0639004	−	0.997956i	$-0.520354\pi$
$888$		0			0
$889$	−2462.48	−	1789.09i	−0.0929008	−	0.0674964i
$890$		0			0
$891$	−10667.5	+	7750.37i	−0.401093	+	0.291411i
$892$		0			0
$893$		−	12140.6i		−	0.454951i
$894$		0			0
$895$	−961.969	−	7647.97i	−0.0359275	−	0.285635i
$896$		0			0
$897$	3521.74	−	1144.28i	0.131090	−	0.0425937i
$898$		0			0
$899$	−2114.01			−0.0784272
$900$		0			0
$901$	−16161.2			−0.597567
$902$		0			0
$903$	31227.0	−	10146.3i	1.15080	−	0.373916i
$904$		0			0
$905$	6309.59	−	11462.4i	0.231755	−	0.421021i
$906$		0			0
$907$		−	15784.5i		−	0.577856i	−0.957351	−	0.288928i	$-0.906701\pi$
$907$		−	15784.5i		−	0.577856i	0.957351	−	0.288928i	$-0.0932988\pi$
$908$		0			0
$909$	−3016.38	+	2191.53i	−0.110063	+	0.0799653i
$910$		0			0
$911$	11509.1	+	8361.85i	0.418566	+	0.304106i	0.777060	−	0.629426i	$-0.216710\pi$
$911$	11509.1	+	8361.85i	0.418566	+	0.304106i	−0.358495	+	0.933532i	$0.616710\pi$
$912$		0			0
$913$	51120.5	+	70361.4i	1.85306	+	2.55052i
$914$		0			0
$915$	492.011	+	270.831i	0.0177764	+	0.00978514i
$916$		0			0
$917$	−37102.9	−	12055.5i	−1.33615	−	0.434140i
$918$		0			0
$919$	−11019.3	+	33914.1i	−0.395533	+	1.21732i	0.533013	+	0.846107i	$0.321060\pi$
$919$	−11019.3	+	33914.1i	−0.395533	+	1.21732i	−0.928546	+	0.371218i	$0.878940\pi$
$920$		0			0
$921$	−1939.53	−	5969.26i	−0.0693916	−	0.213565i
$922$		0			0
$923$	−5590.14	+	7694.17i	−0.199352	+	0.274384i
$924$		0			0
$925$	−10625.7	−	41570.6i	−0.377698	−	1.47766i
$926$		0			0
$927$	−9701.40	+	13352.8i	−0.343728	+	0.473101i
$928$		0			0
$929$	−12401.4	−	38167.7i	−0.437974	−	1.34795i	−0.890008	−	0.455944i	$-0.849302\pi$
$929$	−12401.4	−	38167.7i	−0.437974	−	1.34795i	0.452034	−	0.892001i	$-0.350698\pi$
$930$		0			0
$931$	−20022.7	+	61623.7i	−0.704854	+	2.16932i
$932$		0			0
$933$	−11198.5	−	3638.62i	−0.392951	−	0.127678i
$934$		0			0
$935$	13422.1	+	28563.4i	0.469464	+	0.999062i
$936$		0			0
$937$	−19.3066	−	26.5732i	−0.000673125	−	0.000926478i	0.808680	−	0.588248i	$-0.200182\pi$
$937$	−19.3066	−	26.5732i	−0.000673125	−	0.000926478i	−0.809353	+	0.587322i	$0.800182\pi$
$938$		0			0
$939$	−21037.9	−	15284.9i	−0.731147	−	0.531209i
$940$		0			0
$941$	29475.4	−	21415.1i	1.02112	−	0.741884i	0.0546044	−	0.998508i	$-0.482610\pi$
$941$	29475.4	−	21415.1i	1.02112	−	0.741884i	0.966511	+	0.256624i	$0.0826102\pi$
$942$		0			0
$943$		−	10765.1i		−	0.371751i
$944$		0			0
$945$	34487.8	+	36765.5i	1.18718	+	1.26559i
$946$		0			0
$947$	7330.28	−	2381.75i	0.251533	−	0.0817281i	−0.180537	−	0.983568i	$-0.557783\pi$
$947$	7330.28	−	2381.75i	0.251533	−	0.0817281i	0.432070	+	0.901840i	$0.357783\pi$
$948$		0			0
$949$	−18093.9			−0.618916
$950$		0			0
$951$	−29938.0			−1.02083
$952$		0			0
$953$	12714.5	−	4131.19i	0.432175	−	0.140422i	−0.0848477	−	0.996394i	$-0.527040\pi$
$953$	12714.5	−	4131.19i	0.432175	−	0.140422i	0.517022	+	0.855972i	$0.327040\pi$
$954$		0			0
$955$	44627.7	−	20970.8i	1.51217	−	0.710575i
$956$		0			0
$957$			1593.51i			0.0538254i
$958$		0			0
$959$	13784.3	−	10014.9i	0.464149	−	0.337224i
$960$		0			0
$961$	−56578.1	−	41106.4i	−1.89917	−	1.37982i
$962$		0			0
$963$	2368.00	+	3259.28i	0.0792397	+	0.109064i
$964$		0			0
$965$	784.704	−	4101.54i	0.0261767	−	0.136822i
$966$		0			0
$967$	28341.8	+	9208.80i	0.942513	+	0.306241i	0.739670	−	0.672970i	$-0.234982\pi$
$967$	28341.8	+	9208.80i	0.942513	+	0.306241i	0.202843	+	0.979211i	$0.434982\pi$
$968$		0			0
$969$	5864.43	−	18048.9i	0.194420	−	0.598362i
$970$		0			0
$971$	13899.8	+	42779.1i	0.459387	+	1.41385i	0.865906	+	0.500206i	$0.166743\pi$
$971$	13899.8	+	42779.1i	0.459387	+	1.41385i	−0.406519	+	0.913642i	$0.633257\pi$
$972$		0			0
$973$	8041.07	−	11067.6i	0.264938	−	0.364656i
$974$		0			0
$975$	−10141.8	−	16019.1i	−0.333126	−	0.526176i
$976$		0			0
$977$	730.797	−	1005.86i	0.0239307	−	0.0329377i	−0.796884	−	0.604132i	$-0.793520\pi$
$977$	730.797	−	1005.86i	0.0239307	−	0.0329377i	0.820815	+	0.571195i	$0.193520\pi$
$978$		0			0
$979$	−10370.3	−	31916.6i	−0.338547	−	1.04194i
$980$		0			0
$981$	−2737.94	+	8426.51i	−0.0891087	+	0.274248i
$982$		0			0
$983$	−31332.9	−	10180.7i	−1.01665	−	0.330329i	−0.247150	−	0.968977i	$-0.579494\pi$
$983$	−31332.9	−	10180.7i	−1.01665	−	0.330329i	−0.769499	+	0.638648i	$0.779494\pi$
$984$		0			0
$985$	−12427.3	+	1563.12i	−0.401998	+	0.0505637i
$986$		0			0
$987$	−7010.87	−	9649.63i	−0.226098	−	0.311197i
$988$		0			0
$989$	−5758.76	−	4183.98i	−0.185155	−	0.134523i
$990$		0			0
$991$	13151.5	−	9555.14i	0.421566	−	0.306286i	−0.356702	−	0.934218i	$-0.616099\pi$
$991$	13151.5	−	9555.14i	0.421566	−	0.306286i	0.778268	+	0.627933i	$0.216099\pi$
$992$		0			0
$993$		−	21767.1i		−	0.695626i
$994$		0			0
$995$	21839.0	+	4178.23i	0.695823	+	0.133125i
$996$		0			0
$997$	−27931.2	+	9075.40i	−0.887252	+	0.288286i	−0.716965	−	0.697109i	$-0.754469\pi$
$997$	−27931.2	+	9075.40i	−0.887252	+	0.288286i	−0.170287	+	0.985395i	$0.554469\pi$
$998$		0			0
$999$	51352.9			1.62636

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.i.a.9.6	✓	32
5.2	odd	4		500.4.g.b.201.6		64
5.3	odd	4		500.4.g.b.201.11		64
5.4	even	2		500.4.i.a.49.3		32
25.2	odd	20		500.4.g.b.301.6		64
25.8	odd	20		2500.4.a.g.1.22		32
25.11	even	5		500.4.i.a.449.3		32
25.14	even	10	inner	100.4.i.a.89.6	yes	32
25.17	odd	20		2500.4.a.g.1.11		32
25.23	odd	20		500.4.g.b.301.11		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.4.i.a.9.6	✓	32	1.1	even	1	trivial
100.4.i.a.89.6	yes	32	25.14	even	10	inner
500.4.g.b.201.6		64	5.2	odd	4
500.4.g.b.201.11		64	5.3	odd	4
500.4.g.b.301.6		64	25.2	odd	20
500.4.g.b.301.11		64	25.23	odd	20
500.4.i.a.49.3		32	5.4	even	2
500.4.i.a.449.3		32	25.11	even	5
2500.4.a.g.1.11		32	25.17	odd	20
2500.4.a.g.1.22		32	25.8	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)

\(f(q)\)	\(=\)	\(q+(3.55368 - 1.15466i) q^{3} +(10.9812 + 2.10091i) q^{5} -30.1378i q^{7} +(-10.5481 + 7.66362i) q^{9} +O(q^{10})\)	\(q+(3.55368 - 1.15466i) q^{3} +(10.9812 + 2.10091i) q^{5} -30.1378i q^{7} +(-10.5481 + 7.66362i) q^{9} +(51.5392 + 37.4454i) q^{11} +(-23.8598 - 32.8402i) q^{13} +(41.4494 - 5.21355i) q^{15} +(42.1411 + 13.6925i) q^{17} +(35.4205 - 109.013i) q^{19} +(-34.7989 - 107.100i) q^{21} +(-14.3499 + 19.7510i) q^{23} +(116.172 + 46.1410i) q^{25} +(-87.9355 + 121.033i) q^{27} +(2.06864 + 6.36663i) q^{29} +(-97.5855 + 300.337i) q^{31} +(226.390 + 73.5587i) q^{33} +(63.3169 - 330.948i) q^{35} +(-201.761 - 277.701i) q^{37} +(-122.709 - 89.1536i) q^{39} +(-356.735 + 259.183i) q^{41} +291.568i q^{43} +(-131.931 + 61.9949i) q^{45} +(100.734 - 32.7305i) q^{47} -565.287 q^{49} +165.566 q^{51} +(-346.881 + 112.709i) q^{53} +(487.291 + 519.474i) q^{55} -428.296i q^{57} +(-269.443 + 195.762i) q^{59} +(10.8762 + 7.90204i) q^{61} +(230.965 + 317.896i) q^{63} +(-193.014 - 410.751i) q^{65} +(54.7080 + 17.7757i) q^{67} +(-28.1894 + 86.7580i) q^{69} +(-72.3999 - 222.824i) q^{71} +(262.000 - 360.613i) q^{73} +(466.116 + 29.8307i) q^{75} +(1128.52 - 1553.28i) q^{77} +(-17.4949 - 53.8438i) q^{79} +(-63.9597 + 196.848i) q^{81} +(1298.38 + 421.871i) q^{83} +(433.992 + 238.894i) q^{85} +(14.7026 + 20.2364i) q^{87} +(-426.176 - 309.635i) q^{89} +(-989.732 + 719.082i) q^{91} +1179.98i q^{93} +(617.985 - 1122.68i) q^{95} +(-1271.95 + 413.282i) q^{97} -830.606 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{5} + 122 q^{9}+O(q^{10}) \) 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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