LMFDB - Embedded newform 100.4.i.a.69.3

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			69.3
Character	$\chi$	$=$	100.69
Dual form			100.4.i.a.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72442 - 2.37346i) q^{3} +(6.46300 + 9.12303i) q^{5} +7.35306i q^{7} +(5.68377 - 17.4928i) q^{9} +O(q^{10})$	\(q+(-1.72442 - 2.37346i) q^{3} +(6.46300 + 9.12303i) q^{5} +7.35306i q^{7} +(5.68377 - 17.4928i) q^{9} +(14.2454 + 43.8427i) q^{11} +(51.4644 + 16.7218i) q^{13} +(10.5082 - 31.0716i) q^{15} +(63.8784 - 87.9210i) q^{17} +(112.665 + 81.8557i) q^{19} +(17.4522 - 12.6798i) q^{21} +(-97.8452 + 31.7918i) q^{23} +(-41.4593 + 117.924i) q^{25} +(-126.654 + 41.1525i) q^{27} +(72.5388 - 52.7025i) q^{29} +(-88.2855 - 64.1432i) q^{31} +(79.4939 - 109.414i) q^{33} +(-67.0822 + 47.5228i) q^{35} +(-199.854 - 64.9367i) q^{37} +(-49.0576 - 150.984i) q^{39} +(-134.913 + 415.220i) q^{41} -289.719i q^{43} +(196.322 - 61.2030i) q^{45} +(-148.801 - 204.807i) q^{47} +288.933 q^{49} -318.830 q^{51} +(-197.489 - 271.820i) q^{53} +(-307.910 + 413.316i) q^{55} -408.559i q^{57} +(-80.7360 + 248.480i) q^{59} +(-117.100 - 360.398i) q^{61} +(128.626 + 41.7931i) q^{63} +(180.061 + 577.584i) q^{65} +(-190.387 + 262.045i) q^{67} +(244.183 + 177.409i) q^{69} +(-572.964 + 416.283i) q^{71} +(875.989 - 284.626i) q^{73} +(351.382 - 104.949i) q^{75} +(-322.378 + 104.747i) q^{77} +(550.542 - 399.992i) q^{79} +(-85.6893 - 62.2569i) q^{81} +(542.864 - 747.188i) q^{83} +(1214.95 + 14.5308i) q^{85} +(-250.175 - 81.2867i) q^{87} +(196.275 + 604.072i) q^{89} +(-122.956 + 378.420i) q^{91} +320.152i q^{93} +(-18.6202 + 1556.88i) q^{95} +(-308.018 - 423.951i) q^{97} +847.901 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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
$3$	−1.72442	−	2.37346i	−0.331865	−	0.456772i	0.610179	−	0.792264i	$-0.291098\pi$
$3$	−1.72442	−	2.37346i	−0.331865	−	0.456772i	−0.942043	+	0.335491i	$0.891098\pi$
$4$		0			0
$5$	6.46300	+	9.12303i	0.578068	+	0.815989i
$5$	6.46300	+	9.12303i	0.578068	+	0.815989i
$6$		0			0
$7$			7.35306i			0.397028i	0.980098	+	0.198514i	$0.0636115\pi$
$7$			7.35306i			0.397028i	−0.980098	+	0.198514i	$0.936389\pi$
$8$		0			0
$9$	5.68377	−	17.4928i	0.210510	−	0.647883i
$10$		0			0
$11$	14.2454	+	43.8427i	0.390467	+	1.20173i	0.932436	+	0.361335i	$0.117679\pi$
$11$	14.2454	+	43.8427i	0.390467	+	1.20173i	−0.541969	+	0.840398i	$0.682321\pi$
$12$		0			0
$13$	51.4644	+	16.7218i	1.09797	+	0.356753i	0.801322	−	0.598233i	$-0.204130\pi$
$13$	51.4644	+	16.7218i	1.09797	+	0.356753i	0.296650	+	0.954986i	$0.404130\pi$
$14$		0			0
$15$	10.5082	−	31.0716i	0.180881	−	0.534843i
$16$		0			0
$17$	63.8784	−	87.9210i	0.911340	−	1.25435i	−0.0553669	−	0.998466i	$-0.517633\pi$
$17$	63.8784	−	87.9210i	0.911340	−	1.25435i	0.966707	−	0.255886i	$-0.0823671\pi$
$18$		0			0
$19$	112.665	+	81.8557i	1.36037	+	0.988368i	0.998421	+	0.0561709i	$0.0178892\pi$
$19$	112.665	+	81.8557i	1.36037	+	0.988368i	0.361951	+	0.932197i	$0.382111\pi$
$20$		0			0
$21$	17.4522	−	12.6798i	0.181351	−	0.131759i
$22$		0			0
$23$	−97.8452	+	31.7918i	−0.887049	+	0.288220i	−0.716881	−	0.697195i	$-0.754431\pi$
$23$	−97.8452	+	31.7918i	−0.887049	+	0.288220i	−0.170168	+	0.985415i	$0.554431\pi$
$24$		0			0
$25$	−41.4593	+	117.924i	−0.331675	+	0.943394i
$26$		0			0
$27$	−126.654	+	41.1525i	−0.902764	+	0.293326i
$28$		0			0
$29$	72.5388	−	52.7025i	0.464487	−	0.337469i	−0.330802	−	0.943700i	$-0.607319\pi$
$29$	72.5388	−	52.7025i	0.464487	−	0.337469i	0.795289	+	0.606231i	$0.207319\pi$
$30$		0			0
$31$	−88.2855	−	64.1432i	−0.511502	−	0.371628i	0.301891	−	0.953342i	$-0.402382\pi$
$31$	−88.2855	−	64.1432i	−0.511502	−	0.371628i	−0.813393	+	0.581715i	$0.802382\pi$
$32$		0			0
$33$	79.4939	−	109.414i	0.419337	−	0.577167i
$34$		0			0
$35$	−67.0822	+	47.5228i	−0.323970	+	0.229509i
$36$		0			0
$37$	−199.854	−	64.9367i	−0.887997	−	0.288528i	−0.170723	−	0.985319i	$-0.554610\pi$
$37$	−199.854	−	64.9367i	−0.887997	−	0.288528i	−0.717274	+	0.696791i	$0.754610\pi$
$38$		0			0
$39$	−49.0576	−	150.984i	−0.201423	−	0.619917i
$40$		0			0
$41$	−134.913	+	415.220i	−0.513900	+	1.58162i	0.271375	+	0.962474i	$0.412522\pi$
$41$	−134.913	+	415.220i	−0.513900	+	1.58162i	−0.785275	+	0.619148i	$0.787478\pi$
$42$		0			0
$43$		−	289.719i		−	1.02748i	−0.857946	−	0.513741i	$-0.828259\pi$
$43$		−	289.719i		−	1.02748i	0.857946	−	0.513741i	$-0.171741\pi$
$44$		0			0
$45$	196.322	−	61.2030i	0.650354	−	0.202747i
$46$		0			0
$47$	−148.801	−	204.807i	−0.461805	−	0.635620i	0.513077	−	0.858343i	$-0.328506\pi$
$47$	−148.801	−	204.807i	−0.461805	−	0.635620i	−0.974882	+	0.222723i	$0.928506\pi$
$48$		0			0
$49$	288.933			0.842369
$50$		0			0
$51$	−318.830			−0.875395
$52$		0			0
$53$	−197.489	−	271.820i	−0.511833	−	0.704478i	0.472394	−	0.881387i	$-0.343390\pi$
$53$	−197.489	−	271.820i	−0.511833	−	0.704478i	−0.984227	+	0.176910i	$0.943390\pi$
$54$		0			0
$55$	−307.910	+	413.316i	−0.754884	+	1.01330i
$56$		0			0
$57$		−	408.559i		−	0.949385i
$58$		0			0
$59$	−80.7360	+	248.480i	−0.178151	+	0.548294i	−0.999763	−	0.0217535i	$-0.993075\pi$
$59$	−80.7360	+	248.480i	−0.178151	+	0.548294i	0.821612	+	0.570047i	$0.193075\pi$
$60$		0			0
$61$	−117.100	−	360.398i	−0.245790	−	0.756463i	−0.995506	−	0.0947029i	$-0.969810\pi$
$61$	−117.100	−	360.398i	−0.245790	−	0.756463i	0.749716	−	0.661760i	$-0.230190\pi$
$62$		0			0
$63$	128.626	+	41.7931i	0.257228	+	0.0835783i
$64$		0			0
$65$	180.061	+	577.584i	0.343597	+	1.10216i
$66$		0			0
$67$	−190.387	+	262.045i	−0.347156	+	0.477819i	−0.946514	−	0.322662i	$-0.895422\pi$
$67$	−190.387	+	262.045i	−0.347156	+	0.477819i	0.599358	+	0.800481i	$0.295422\pi$
$68$		0			0
$69$	244.183	+	177.409i	0.426031	+	0.309530i
$70$		0			0
$71$	−572.964	+	416.283i	−0.957723	+	0.695826i	−0.952621	−	0.304161i	$-0.901624\pi$
$71$	−572.964	+	416.283i	−0.957723	+	0.695826i	−0.00510208	+	0.999987i	$0.501624\pi$
$72$		0			0
$73$	875.989	−	284.626i	1.40448	−	0.456342i	0.493840	−	0.869553i	$-0.335593\pi$
$73$	875.989	−	284.626i	1.40448	−	0.456342i	0.910635	+	0.413211i	$0.135593\pi$
$74$		0			0
$75$	351.382	−	104.949i	0.540987	−	0.161579i
$76$		0			0
$77$	−322.378	+	104.747i	−0.477122	+	0.155026i
$78$		0			0
$79$	550.542	−	399.992i	0.784060	−	0.569653i	−0.122135	−	0.992514i	$-0.538974\pi$
$79$	550.542	−	399.992i	0.784060	−	0.569653i	0.906195	+	0.422860i	$0.138974\pi$
$80$		0			0
$81$	−85.6893	−	62.2569i	−0.117544	−	0.0854004i
$82$		0			0
$83$	542.864	−	747.188i	0.717916	−	0.988127i	−0.281674	−	0.959510i	$-0.590890\pi$
$83$	542.864	−	747.188i	0.717916	−	0.988127i	0.999590	−	0.0286166i	$-0.00911018\pi$
$84$		0			0
$85$	1214.95	+	14.5308i	1.55035	+	0.0185422i
$86$		0			0
$87$	−250.175	−	81.2867i	−0.308293	−	0.100171i
$88$		0			0
$89$	196.275	+	604.072i	0.233765	+	0.719455i	0.997283	+	0.0736681i	$0.0234706\pi$
$89$	196.275	+	604.072i	0.233765	+	0.719455i	−0.763518	+	0.645787i	$0.776529\pi$
$90$		0			0
$91$	−122.956	+	378.420i	−0.141641	+	0.435926i
$92$		0			0
$93$			320.152i			0.356970i
$94$		0			0
$95$	−18.6202	+	1556.88i	−0.0201094	+	1.68139i
$96$		0			0
$97$	−308.018	−	423.951i	−0.322418	−	0.443770i	0.616786	−	0.787131i	$-0.288435\pi$
$97$	−308.018	−	423.951i	−0.322418	−	0.443770i	−0.939203	+	0.343361i	$0.888435\pi$
$98$		0			0
$99$	847.901			0.860780
$100$		0			0
$101$	502.816			0.495367			0.247684	−	0.968841i	$-0.420331\pi$
$101$	502.816			0.495367			0.247684	+	0.968841i	$0.420331\pi$
$102$		0			0
$103$	−762.832	−	1049.95i	−0.729748	−	1.00441i	−0.999143	−	0.0413824i	$-0.986824\pi$
$103$	−762.832	−	1049.95i	−0.729748	−	1.00441i	0.269395	−	0.963030i	$-0.413176\pi$
$104$		0			0
$105$	228.471	+	77.2676i	0.212348	+	0.0718147i
$106$		0			0
$107$			524.903i			0.474246i	0.971480	+	0.237123i	$0.0762045\pi$
$107$			524.903i			0.474246i	−0.971480	+	0.237123i	$0.923796\pi$
$108$		0			0
$109$	251.321	−	773.487i	0.220846	−	0.679694i	−0.777841	−	0.628461i	$-0.783685\pi$
$109$	251.321	−	773.487i	0.220846	−	0.679694i	0.998687	−	0.0512327i	$-0.0163150\pi$
$110$		0			0
$111$	190.508	+	586.325i	0.162903	+	0.501365i
$112$		0			0
$113$	−517.239	−	168.061i	−0.430600	−	0.139910i	0.0856948	−	0.996321i	$-0.472689\pi$
$113$	−517.239	−	168.061i	−0.430600	−	0.139910i	−0.516294	+	0.856411i	$0.672689\pi$
$114$		0			0
$115$	−922.411	−	687.174i	−0.747959	−	0.557211i
$116$		0			0
$117$	585.023	−	805.215i	0.462268	−	0.636258i
$118$		0			0
$119$	646.488	+	469.701i	0.498013	+	0.361827i
$120$		0			0
$121$	−642.450	+	466.767i	−0.482682	+	0.350689i
$122$		0			0
$123$	1218.15	−	395.803i	0.892986	−	0.290149i
$124$		0			0
$125$	−1343.78	+	383.909i	−0.961529	+	0.274703i
$126$		0			0
$127$	336.721	−	109.407i	0.235269	−	0.0764436i	−0.189009	−	0.981975i	$-0.560528\pi$
$127$	336.721	−	109.407i	0.235269	−	0.0764436i	0.424279	+	0.905532i	$0.360528\pi$
$128$		0			0
$129$	−687.636	+	499.596i	−0.469325	+	0.340985i
$130$		0			0
$131$	−1506.07	−	1094.23i	−1.00448	−	0.729794i	−0.0414324	−	0.999141i	$-0.513192\pi$
$131$	−1506.07	−	1094.23i	−1.00448	−	0.729794i	−0.963043	+	0.269347i	$0.913192\pi$
$132$		0			0
$133$	−601.890	+	828.430i	−0.392410	+	0.540105i
$134$		0			0
$135$	−1194.00	−	889.503i	−0.761210	−	0.567083i
$136$		0			0
$137$	−1089.37	−	353.958i	−0.679352	−	0.220735i	−0.0510405	−	0.998697i	$-0.516254\pi$
$137$	−1089.37	−	353.958i	−0.679352	−	0.220735i	−0.628312	+	0.777962i	$0.716254\pi$
$138$		0			0
$139$	−400.123	−	1231.45i	−0.244158	−	0.751442i	−0.995774	−	0.0918403i	$-0.970725\pi$
$139$	−400.123	−	1231.45i	−0.244158	−	0.751442i	0.751616	−	0.659601i	$-0.229275\pi$
$140$		0			0
$141$	−229.506	+	706.346i	−0.137077	+	0.421880i
$142$		0			0
$143$			2494.54i			1.45877i
$144$		0			0
$145$	949.625	+	321.157i	0.543876	+	0.183936i
$146$		0			0
$147$	−498.241	−	685.770i	−0.279552	−	0.384771i
$148$		0			0
$149$	−2469.47			−1.35776			−0.678882	−	0.734247i	$-0.737535\pi$
$149$	−2469.47			−1.35776			−0.678882	+	0.734247i	$0.737535\pi$
$150$		0			0
$151$	1532.59			0.825965			0.412983	−	0.910739i	$-0.364487\pi$
$151$	1532.59			0.825965			0.412983	+	0.910739i	$0.364487\pi$
$152$		0			0
$153$	−1174.92	−	1617.14i	−0.620827	−	0.854496i
$154$		0			0
$155$	14.5910	−	1219.99i	0.00756116	−	0.632206i
$156$		0			0
$157$		−	1300.55i		−	0.661118i	−0.943785	−	0.330559i	$-0.892763\pi$
$157$		−	1300.55i		−	0.661118i	0.943785	−	0.330559i	$-0.107237\pi$
$158$		0			0
$159$	−304.600	+	937.462i	−0.151927	+	0.467582i
$160$		0			0
$161$	−233.767	−	719.461i	−0.114431	−	0.352183i
$162$		0			0
$163$	1006.51	+	327.035i	0.483657	+	0.157150i	0.540689	−	0.841223i	$-0.318164\pi$
$163$	1006.51	+	327.035i	0.483657	+	0.157150i	−0.0570320	+	0.998372i	$0.518164\pi$
$164$		0			0
$165$	1511.96	+	18.0830i	0.713367	+	0.00853186i
$166$		0			0
$167$	−1451.40	+	1997.68i	−0.672530	+	0.925659i	−0.999814	−	0.0192675i	$-0.993867\pi$
$167$	−1451.40	+	1997.68i	−0.672530	+	0.925659i	0.327284	+	0.944926i	$0.393867\pi$
$168$		0			0
$169$	591.551	+	429.787i	0.269254	+	0.195625i
$170$		0			0
$171$	2072.25	−	1505.58i	0.926719	−	0.673301i
$172$		0			0
$173$	−2843.66	+	923.961i	−1.24971	+	0.406055i	−0.857816	−	0.513957i	$-0.828179\pi$
$173$	−2843.66	+	923.961i	−1.24971	+	0.406055i	−0.391891	+	0.920012i	$0.628179\pi$
$174$		0			0
$175$	−867.104	−	304.853i	−0.374554	−	0.131684i
$176$		0			0
$177$	728.980	−	236.860i	0.309568	−	0.100585i
$178$		0			0
$179$	3587.87	−	2606.74i	1.49816	−	1.08847i	0.527048	−	0.849836i	$-0.323299\pi$
$179$	3587.87	−	2606.74i	1.49816	−	1.08847i	0.971108	−	0.238638i	$-0.0767011\pi$
$180$		0			0
$181$	1027.44	+	746.482i	0.421930	+	0.306550i	0.778414	−	0.627751i	$-0.216025\pi$
$181$	1027.44	+	746.482i	0.421930	+	0.306550i	−0.356484	+	0.934301i	$0.616025\pi$
$182$		0			0
$183$	−653.460	+	899.410i	−0.263962	+	0.363313i
$184$		0			0
$185$	−699.240	−	2242.96i	−0.277887	−	0.891384i
$186$		0			0
$187$	4764.67	+	1548.13i	1.86325	+	0.605405i
$188$		0			0
$189$	−302.597	−	931.297i	−0.116459	−	0.358423i
$190$		0			0
$191$	−448.348	+	1379.87i	−0.169850	+	0.522745i	−0.999361	−	0.0357459i	$-0.988619\pi$
$191$	−448.348	+	1379.87i	−0.169850	+	0.522745i	0.829511	+	0.558491i	$0.188619\pi$
$192$		0			0
$193$			1503.47i			0.560737i	0.959892	+	0.280368i	$0.0904566\pi$
$193$			1503.47i			0.560737i	−0.959892	+	0.280368i	$0.909543\pi$
$194$		0			0
$195$	1060.37	−	1423.36i	0.389409	−	0.522714i
$196$		0			0
$197$	1757.10	+	2418.44i	0.635472	+	0.874652i	0.998364	−	0.0571789i	$-0.0182105\pi$
$197$	1757.10	+	2418.44i	0.635472	+	0.874652i	−0.362892	+	0.931831i	$0.618211\pi$
$198$		0			0
$199$	−3714.90			−1.32333			−0.661664	−	0.749800i	$-0.730150\pi$
$199$	−3714.90			−1.32333			−0.661664	+	0.749800i	$0.730150\pi$
$200$		0			0
$201$	950.260			0.333464
$202$		0			0
$203$	387.525	+	533.382i	0.133985	+	0.184414i
$204$		0			0
$205$	−4660.01	+	1452.75i	−1.58765	+	0.494948i
$206$		0			0
$207$			1892.29i			0.635377i
$208$		0			0
$209$	−1983.83	+	6105.59i	−0.656575	+	2.02073i
$210$		0			0
$211$	−165.339	−	508.862i	−0.0539451	−	0.166026i	0.920454	−	0.390851i	$-0.127819\pi$
$211$	−165.339	−	508.862i	−0.0539451	−	0.166026i	−0.974399	+	0.224825i	$0.927819\pi$
$212$		0			0
$213$	1976.06	+	642.061i	0.635669	+	0.206541i
$214$		0			0
$215$	2643.11	−	1872.45i	0.838413	−	0.593954i
$216$		0			0
$217$	471.649	−	649.169i	0.147547	−	0.203080i
$218$		0			0
$219$	−2186.12	−	1588.31i	−0.674540	−	0.490082i
$220$		0			0
$221$	4757.66	−	3456.64i	1.44812	−	1.05212i
$222$		0			0
$223$	5851.04	−	1901.12i	1.75702	−	0.570889i	0.760133	−	0.649768i	$-0.225134\pi$
$223$	5851.04	−	1901.12i	1.75702	−	0.570889i	0.996884	+	0.0788787i	$0.0251340\pi$
$224$		0			0
$225$	1827.19	+	1395.50i	0.541388	+	0.413480i
$226$		0			0
$227$	2485.61	−	807.623i	0.726765	−	0.236140i	0.0778112	−	0.996968i	$-0.475207\pi$
$227$	2485.61	−	807.623i	0.726765	−	0.236140i	0.648954	+	0.760828i	$0.275207\pi$
$228$		0			0
$229$	−1656.52	+	1203.53i	−0.478017	+	0.347299i	−0.800557	−	0.599256i	$-0.795463\pi$
$229$	−1656.52	+	1203.53i	−0.478017	+	0.347299i	0.322541	+	0.946556i	$0.395463\pi$
$230$		0			0
$231$	804.527	+	584.523i	0.229152	+	0.166488i
$232$		0			0
$233$	−2832.81	+	3899.03i	−0.796495	+	1.09628i	0.196773	+	0.980449i	$0.436954\pi$
$233$	−2832.81	+	3899.03i	−0.796495	+	1.09628i	−0.993269	+	0.115833i	$0.963046\pi$
$234$		0			0
$235$	906.759	−	2681.18i	0.251704	−	0.744259i
$236$		0			0
$237$	−1898.73	−	616.934i	−0.520404	−	0.169089i
$238$		0			0
$239$	−934.406	−	2875.81i	−0.252894	−	0.778328i	−0.994237	−	0.107202i	$-0.965811\pi$
$239$	−934.406	−	2875.81i	−0.252894	−	0.778328i	0.741343	−	0.671126i	$-0.234189\pi$
$240$		0			0
$241$	2194.00	−	6752.45i	0.586424	−	1.80483i	−0.00705249	−	0.999975i	$-0.502245\pi$
$241$	2194.00	−	6752.45i	0.586424	−	1.80483i	0.593476	−	0.804852i	$-0.297755\pi$
$242$		0			0
$243$			3906.39i			1.03125i
$244$		0			0
$245$	1867.37	+	2635.94i	0.486947	+	0.687363i
$246$		0			0
$247$	4429.44	+	6096.61i	1.14105	+	1.57052i
$248$		0			0
$249$	−2709.54			−0.689600
$250$		0			0
$251$	−587.003			−0.147615			−0.0738074	−	0.997273i	$-0.523515\pi$
$251$	−587.003			−0.147615			−0.0738074	+	0.997273i	$0.523515\pi$
$252$		0			0
$253$	−2787.68	−	3836.91i	−0.692727	−	0.953456i
$254$		0			0
$255$	−2060.60	−	2908.70i	−0.506038	−	0.714312i
$256$		0			0
$257$			2317.47i			0.562490i	0.959636	+	0.281245i	$0.0907474\pi$
$257$			2317.47i			0.562490i	−0.959636	+	0.281245i	$0.909253\pi$
$258$		0			0
$259$	477.483	−	1469.54i	0.114553	−	0.352559i
$260$		0			0
$261$	−509.623	−	1568.46i	−0.120862	−	0.371974i
$262$		0			0
$263$	−3609.34	−	1172.74i	−0.846240	−	0.274960i	−0.146370	−	0.989230i	$-0.546759\pi$
$263$	−3609.34	−	1172.74i	−0.846240	−	0.274960i	−0.699870	+	0.714270i	$0.746759\pi$
$264$		0			0
$265$	1203.45	−	3558.46i	0.278971	−	0.824886i
$266$		0			0
$267$	1095.28	−	1507.52i	0.251049	−	0.345539i
$268$		0			0
$269$	2773.49	+	2015.06i	0.628635	+	0.456730i	0.855927	−	0.517097i	$-0.172987\pi$
$269$	2773.49	+	2015.06i	0.628635	+	0.456730i	−0.227292	+	0.973827i	$0.572987\pi$
$270$		0			0
$271$	−6587.86	+	4786.36i	−1.47669	+	1.07288i	−0.498091	+	0.867125i	$0.665965\pi$
$271$	−6587.86	+	4786.36i	−1.47669	+	1.07288i	−0.978603	+	0.205756i	$0.934035\pi$
$272$		0			0
$273$	1110.19	−	360.724i	0.246124	−	0.0799707i
$274$		0			0
$275$	−5760.72	−	137.816i	−1.26322	−	0.0302204i
$276$		0			0
$277$	−3815.93	+	1239.87i	−0.827715	+	0.268941i	−0.692083	−	0.721818i	$-0.743307\pi$
$277$	−3815.93	+	1239.87i	−0.827715	+	0.268941i	−0.135632	+	0.990759i	$0.543307\pi$
$278$		0			0
$279$	−1623.84	+	1179.79i	−0.348448	+	0.253162i
$280$		0			0
$281$	2111.97	+	1534.44i	0.448362	+	0.325754i	0.788949	−	0.614459i	$-0.210626\pi$
$281$	2111.97	+	1534.44i	0.448362	+	0.325754i	−0.340586	+	0.940213i	$0.610626\pi$
$282$		0			0
$283$	−2753.63	+	3790.04i	−0.578396	+	0.796094i	−0.993518	−	0.113672i	$-0.963739\pi$
$283$	−2753.63	+	3790.04i	−0.578396	+	0.796094i	0.415122	+	0.909766i	$0.363739\pi$
$284$		0			0
$285$	3727.29	−	2640.51i	0.774687	−	0.548809i
$286$		0			0
$287$	−3053.14	−	992.024i	−0.627948	−	0.204033i
$288$		0			0
$289$	−2131.46	−	6559.97i	−0.433841	−	1.33523i
$290$		0			0
$291$	−475.078	+	1462.14i	−0.0957029	+	0.294543i
$292$		0			0
$293$			4287.21i			0.854817i	0.904059	+	0.427408i	$0.140573\pi$
$293$			4287.21i			0.854817i	−0.904059	+	0.427408i	$0.859427\pi$
$294$		0			0
$295$	−2788.69	+	869.368i	−0.550385	+	0.171582i
$296$		0			0
$297$	−3608.47	−	4966.64i	−0.704999	−	0.970348i
$298$		0			0
$299$	−5567.15			−1.07678
$300$		0			0
$301$	2130.32			0.407939
$302$		0			0
$303$	−867.066	−	1193.41i	−0.164395	−	0.226270i
$304$		0			0
$305$	2531.10	−	3397.56i	0.475182	−	0.637848i
$306$		0			0
$307$			1347.35i			0.250480i	0.992126	+	0.125240i	$0.0399701\pi$
$307$			1347.35i			0.250480i	−0.992126	+	0.125240i	$0.960030\pi$
$308$		0			0
$309$	−1176.57	+	3621.10i	−0.216610	+	0.666658i
$310$		0			0
$311$	−907.704	−	2793.62i	−0.165502	−	0.509363i	0.833571	−	0.552413i	$-0.186293\pi$
$311$	−907.704	−	2793.62i	−0.165502	−	0.509363i	−0.999073	+	0.0430495i	$0.986293\pi$
$312$		0			0
$313$	−7316.71	−	2377.34i	−1.32129	−	0.429314i	−0.438354	−	0.898802i	$-0.644438\pi$
$313$	−7316.71	−	2377.34i	−1.32129	−	0.429314i	−0.882939	+	0.469488i	$0.844438\pi$
$314$		0			0
$315$	450.029	+	1443.57i	0.0804961	+	0.258209i
$316$		0			0
$317$	3908.08	−	5379.02i	0.692429	−	0.953046i	−0.307570	−	0.951525i	$-0.599516\pi$
$317$	3908.08	−	5379.02i	0.692429	−	0.953046i	0.999999	−	0.00152100i	$-0.000484149\pi$
$318$		0			0
$319$	3343.96	+	2429.53i	0.586915	+	0.426419i
$320$		0			0
$321$	1245.84	−	905.154i	0.216623	−	0.157386i
$322$		0			0
$323$	14393.7	−	4676.79i	2.47952	−	0.805646i
$324$		0			0
$325$	−4105.58	+	5375.62i	−0.700728	+	0.917495i
$326$		0			0
$327$	−2269.22	+	737.316i	−0.383757	+	0.124690i
$328$		0			0
$329$	1505.96	−	1094.14i	0.252359	−	0.183349i
$330$		0			0
$331$	959.283	+	696.960i	0.159296	+	0.115735i	0.664578	−	0.747219i	$-0.268611\pi$
$331$	959.283	+	696.960i	0.159296	+	0.115735i	−0.505282	+	0.862954i	$0.668611\pi$
$332$		0			0
$333$	−2271.85	+	3126.94i	−0.373864	+	0.514580i
$334$		0			0
$335$	−3621.11	−	43.3084i	−0.590575	−	0.00706326i
$336$		0			0
$337$	10241.6	+	3327.68i	1.65547	+	0.537895i	0.979915	−	0.199415i	$-0.0639043\pi$
$337$	10241.6	+	3327.68i	1.65547	+	0.537895i	0.675555	+	0.737310i	$0.263904\pi$
$338$		0			0
$339$	493.051	+	1517.45i	0.0789936	+	0.243117i
$340$		0			0
$341$	1554.55	−	4784.42i	0.246873	−	0.759797i
$342$		0			0
$343$			4646.64i			0.731472i
$344$		0			0
$345$	−40.3563	+	3374.28i	−0.00629771	+	0.526566i
$346$		0			0
$347$	−2313.42	−	3184.15i	−0.357899	−	0.492606i	0.591663	−	0.806186i	$-0.298472\pi$
$347$	−2313.42	−	3184.15i	−0.357899	−	0.492606i	−0.949562	+	0.313580i	$0.898472\pi$
$348$		0			0
$349$	5193.88			0.796625			0.398313	−	0.917250i	$-0.369596\pi$
$349$	5193.88			0.796625			0.398313	+	0.917250i	$0.369596\pi$
$350$		0			0
$351$	−7206.33			−1.09586
$352$		0			0
$353$	−6831.98	−	9403.41i	−1.03011	−	1.41783i	−0.904863	−	0.425703i	$-0.860027\pi$
$353$	−6831.98	−	9403.41i	−1.03011	−	1.41783i	−0.125249	−	0.992125i	$-0.539973\pi$
$354$		0			0
$355$	−7500.82	−	2536.73i	−1.12142	−	0.379256i
$356$		0			0
$357$		−	2344.38i		−	0.347556i
$358$		0			0
$359$	1926.85	−	5930.23i	0.283273	−	0.871826i	−0.703637	−	0.710559i	$-0.748442\pi$
$359$	1926.85	−	5930.23i	0.283273	−	0.871826i	0.986911	−	0.161267i	$-0.0515580\pi$
$360$		0			0
$361$	3873.44	+	11921.2i	0.564723	+	1.73804i
$362$		0			0
$363$	2215.71	+	719.927i	0.320370	+	0.104095i
$364$		0			0
$365$	8258.16	+	6152.13i	1.18425	+	0.882239i
$366$		0			0
$367$	−6175.68	+	8500.10i	−0.878387	+	1.20900i	0.0984780	+	0.995139i	$0.468603\pi$
$367$	−6175.68	+	8500.10i	−0.878387	+	1.20900i	−0.976865	+	0.213857i	$0.931397\pi$
$368$		0			0
$369$	6496.57	+	4720.03i	0.916525	+	0.665894i
$370$		0			0
$371$	1998.71	−	1452.14i	0.279697	−	0.203212i
$372$		0			0
$373$	12014.6	−	3903.78i	1.66781	−	0.541904i	0.685323	−	0.728239i	$-0.259661\pi$
$373$	12014.6	−	3903.78i	1.66781	−	0.541904i	0.982486	+	0.186335i	$0.0596609\pi$
$374$		0			0
$375$	3228.43	+	2527.38i	0.444574	+	0.348036i
$376$		0			0
$377$	4614.44	−	1499.32i	0.630387	−	0.204825i
$378$		0			0
$379$	10219.7	−	7425.07i	1.38510	−	1.00633i	0.388715	−	0.921358i	$-0.372919\pi$
$379$	10219.7	−	7425.07i	1.38510	−	1.00633i	0.996383	−	0.0849750i	$-0.0270810\pi$
$380$		0			0
$381$	−840.323	−	610.531i	−0.112995	−	0.0820956i
$382$		0			0
$383$	−888.731	+	1223.23i	−0.118569	+	0.163197i	−0.864176	−	0.503190i	$-0.832160\pi$
$383$	−888.731	+	1223.23i	−0.118569	+	0.163197i	0.745607	+	0.666386i	$0.232160\pi$
$384$		0			0
$385$	−3039.14	−	2264.08i	−0.402308	−	0.299710i
$386$		0			0
$387$	−5068.00	−	1646.69i	−0.665688	−	0.216295i
$388$		0			0
$389$	1052.49	+	3239.23i	0.137181	+	0.422199i	0.995923	−	0.0902089i	$-0.0287535\pi$
$389$	1052.49	+	3239.23i	0.137181	+	0.422199i	−0.858742	+	0.512408i	$0.828753\pi$
$390$		0			0
$391$	−3455.02	+	10633.5i	−0.446874	+	1.37534i
$392$		0			0
$393$			5461.51i			0.701010i
$394$		0			0
$395$	7207.29	+	2437.46i	0.918071	+	0.310486i
$396$		0			0
$397$	−6307.50	−	8681.53i	−0.797391	−	1.09751i	−0.993148	−	0.116863i	$-0.962716\pi$
$397$	−6307.50	−	8681.53i	−0.797391	−	1.09751i	0.195757	−	0.980652i	$-0.437284\pi$
$398$		0			0
$399$	3004.16			0.376932
$400$		0			0
$401$	−226.033			−0.0281485			−0.0140742	−	0.999901i	$-0.504480\pi$
$401$	−226.033			−0.0281485			−0.0140742	+	0.999901i	$0.504480\pi$
$402$		0			0
$403$	−3470.97	−	4777.38i	−0.429035	−	0.590517i
$404$		0			0
$405$	14.1620	−	1184.11i	0.00173756	−	0.145282i
$406$		0			0
$407$		−	9687.21i		−	1.17980i
$408$		0			0
$409$	−3558.34	+	10951.5i	−0.430192	+	1.32400i	0.467741	+	0.883865i	$0.345068\pi$
$409$	−3558.34	+	10951.5i	−0.430192	+	1.32400i	−0.897934	+	0.440131i	$0.854932\pi$
$410$		0			0
$411$	1038.43	+	3195.95i	0.124627	+	0.383564i
$412$		0			0
$413$	−1827.09	−	593.657i	−0.217688	−	0.0707311i
$414$		0			0
$415$	10325.1	+	123.488i	1.22130	+	0.0146068i
$416$		0			0
$417$	−2232.82	+	3073.22i	−0.262210	+	0.360902i
$418$		0			0
$419$	5089.05	+	3697.41i	0.593356	+	0.431099i	0.843515	−	0.537106i	$-0.180483\pi$
$419$	5089.05	+	3697.41i	0.593356	+	0.431099i	−0.250158	+	0.968205i	$0.580483\pi$
$420$		0			0
$421$	−4521.94	+	3285.38i	−0.523482	+	0.380332i	−0.817914	−	0.575341i	$-0.804869\pi$
$421$	−4521.94	+	3285.38i	−0.523482	+	0.380332i	0.294432	+	0.955672i	$0.404869\pi$
$422$		0			0
$423$	−4428.40	+	1438.88i	−0.509022	+	0.165391i
$424$		0			0
$425$	7719.67	+	11178.0i	0.881080	+	1.27579i
$426$		0			0
$427$	2650.03	−	861.046i	0.300337	−	0.0975853i
$428$		0			0
$429$	5920.70	−	4301.64i	0.666326	−	0.484114i
$430$		0			0
$431$	−291.064	−	211.470i	−0.0325291	−	0.0236338i	0.571402	−	0.820670i	$-0.306400\pi$
$431$	−291.064	−	211.470i	−0.0325291	−	0.0236338i	−0.603931	+	0.797037i	$0.706400\pi$
$432$		0			0
$433$	6239.45	−	8587.87i	0.692492	−	0.953133i	−0.307507	−	0.951546i	$-0.599495\pi$
$433$	6239.45	−	8587.87i	0.692492	−	0.953133i	0.999999	−	0.00158755i	$-0.000505334\pi$
$434$		0			0
$435$	−875.297	−	2807.71i	−0.0964765	−	0.309469i
$436$		0			0
$437$	−13626.0	−	4427.37i	−1.49158	−	0.484645i
$438$		0			0
$439$	−4165.10	−	12818.8i	−0.452823	−	1.39365i	−0.873672	−	0.486515i	$-0.838268\pi$
$439$	−4165.10	−	12818.8i	−0.452823	−	1.39365i	0.420850	−	0.907130i	$-0.361732\pi$
$440$		0			0
$441$	1642.23	−	5054.25i	0.177327	−	0.545757i
$442$		0			0
$443$		−	9044.19i		−	0.969983i	−0.874519	−	0.484991i	$-0.838823\pi$
$443$		−	9044.19i		−	0.969983i	0.874519	−	0.484991i	$-0.161177\pi$
$444$		0			0
$445$	−4242.44	+	5694.74i	−0.451935	+	0.606644i
$446$		0			0
$447$	4258.40	+	5861.19i	0.450594	+	0.620189i
$448$		0			0
$449$	−648.205			−0.0681307			−0.0340653	−	0.999420i	$-0.510845\pi$
$449$	−648.205			−0.0681307			−0.0340653	+	0.999420i	$0.510845\pi$
$450$		0			0
$451$	−20126.3			−2.10135
$452$		0			0
$453$	−2642.84	−	3637.55i	−0.274109	−	0.377278i
$454$		0			0
$455$	−4247.01	+	1324.00i	−0.437588	+	0.136417i
$456$		0			0
$457$			2000.03i			0.204720i	0.994747	+	0.102360i	$0.0326394\pi$
$457$			2000.03i			0.204720i	−0.994747	+	0.102360i	$0.967361\pi$
$458$		0			0
$459$	−4472.30	+	13764.3i	−0.454791	+	1.39970i
$460$		0			0
$461$	−1649.41	−	5076.38i	−0.166640	−	0.512864i	0.832514	−	0.554004i	$-0.186901\pi$
$461$	−1649.41	−	5076.38i	−0.166640	−	0.512864i	−0.999153	+	0.0411402i	$0.986901\pi$
$462$		0			0
$463$	14207.7	+	4616.35i	1.42611	+	0.463370i	0.917536	−	0.397652i	$-0.130175\pi$
$463$	14207.7	+	4616.35i	1.42611	+	0.463370i	0.508569	+	0.861021i	$0.330175\pi$
$464$		0			0
$465$	−2920.76	+	2069.14i	−0.291283	+	0.206353i
$466$		0			0
$467$	−251.313	+	345.902i	−0.0249023	+	0.0342750i	−0.821287	−	0.570516i	$-0.806743\pi$
$467$	−251.313	+	345.902i	−0.0249023	+	0.0342750i	0.796384	+	0.604791i	$0.206743\pi$
$468$		0			0
$469$	−1926.83	−	1399.93i	−0.189708	−	0.137831i
$470$		0			0
$471$	−3086.81	+	2242.70i	−0.301981	+	0.219402i
$472$		0			0
$473$	12702.0	−	4127.15i	1.23476	−	0.401197i
$474$		0			0
$475$	−14323.8	+	9892.22i	−1.38362	+	0.955550i
$476$		0			0
$477$	−5877.38	+	1909.68i	−0.564165	+	0.183308i
$478$		0			0
$479$	9674.74	−	7029.11i	0.922860	−	0.670497i	−0.0213740	−	0.999772i	$-0.506804\pi$
$479$	9674.74	−	7029.11i	0.922860	−	0.670497i	0.944234	+	0.329274i	$0.106804\pi$
$480$		0			0
$481$	−9199.53	−	6683.85i	−0.872063	−	0.633591i
$482$		0			0
$483$	−1304.50	+	1795.49i	−0.122892	+	0.169146i
$484$		0			0
$485$	1876.99	−	5550.06i	0.175732	−	0.519619i
$486$		0			0
$487$	990.771	+	321.921i	0.0921891	+	0.0299541i	0.354748	−	0.934962i	$-0.384567\pi$
$487$	990.771	+	321.921i	0.0921891	+	0.0299541i	−0.262559	+	0.964916i	$0.584567\pi$
$488$		0			0
$489$	−959.442	−	2952.86i	−0.0887269	−	0.273073i
$490$		0			0
$491$	2674.38	−	8230.88i	0.245810	−	0.756527i	−0.749692	−	0.661787i	$-0.769798\pi$
$491$	2674.38	−	8230.88i	0.245810	−	0.756527i	0.995502	−	0.0947394i	$-0.0302018\pi$
$492$		0			0
$493$		−	9744.24i		−	0.890179i
$494$		0			0
$495$	5479.98	+	7735.42i	0.497590	+	0.702387i
$496$		0			0
$497$	−3060.95	−	4213.04i	−0.276262	−	0.380243i
$498$		0			0
$499$	−15748.2			−1.41280			−0.706398	−	0.707814i	$-0.749681\pi$
$499$	−15748.2			−1.41280			−0.706398	+	0.707814i	$0.749681\pi$
$500$		0			0
$501$	7244.23			0.646004
$502$		0			0
$503$	−8324.15	−	11457.2i	−0.737883	−	1.01561i	−0.998738	−	0.0502312i	$-0.984004\pi$
$503$	−8324.15	−	11457.2i	−0.737883	−	1.01561i	0.260854	−	0.965378i	$-0.415996\pi$
$504$		0			0
$505$	3249.70	+	4587.21i	0.286356	+	0.404214i
$506$		0			0
$507$		−	2145.16i		−	0.187909i
$508$		0			0
$509$	682.815	−	2101.49i	0.0594602	−	0.183000i	−0.916915	−	0.399083i	$-0.869328\pi$
$509$	682.815	−	2101.49i	0.0594602	−	0.183000i	0.976375	+	0.216084i	$0.0693284\pi$
$510$		0			0
$511$	2092.87	+	6441.20i	0.181180	+	0.557616i
$512$		0			0
$513$	−17638.0	−	5730.95i	−1.51801	−	0.493231i
$514$		0			0
$515$	4648.53	−	13745.1i	0.397745	−	1.17608i
$516$		0			0
$517$	6859.56	−	9441.38i	0.583527	−	0.803155i
$518$		0			0
$519$	7096.64	+	5156.01i	0.600208	+	0.436077i
$520$		0			0
$521$	−15948.8	+	11587.5i	−1.34113	+	0.974388i	−0.341729	+	0.939799i	$0.611013\pi$
$521$	−15948.8	+	11587.5i	−1.34113	+	0.974388i	−0.999402	+	0.0345899i	$0.988987\pi$
$522$		0			0
$523$	9936.10	−	3228.43i	0.830737	−	0.269923i	0.137381	−	0.990518i	$-0.456132\pi$
$523$	9936.10	−	3228.43i	0.830737	−	0.269923i	0.693356	+	0.720596i	$0.256132\pi$
$524$		0			0
$525$	771.695	+	2583.73i	0.0641514	+	0.214787i
$526$		0			0
$527$	−11279.1	+	3664.79i	−0.932304	+	0.302924i
$528$		0			0
$529$	−1280.35	+	930.232i	−0.105232	+	0.0764553i
$530$		0			0
$531$	3887.74	+	2824.61i	0.317728	+	0.230843i
$532$		0			0
$533$	−13886.4	+	19113.0i	−1.12850	+	1.55324i
$534$		0			0
$535$	−4788.71	+	3392.45i	−0.386979	+	0.274147i
$536$		0			0
$537$	−12374.0	−	4020.55i	−0.994370	−	0.323090i
$538$		0			0
$539$	4115.95	+	12667.6i	0.328917	+	1.01230i
$540$		0			0
$541$	−5006.16	+	15407.4i	−0.397840	+	1.22443i	0.528887	+	0.848692i	$0.322609\pi$
$541$	−5006.16	+	15407.4i	−0.397840	+	1.22443i	−0.926727	+	0.375734i	$0.877391\pi$
$542$		0			0
$543$		−	3725.85i		−	0.294459i
$544$		0			0
$545$	8680.84	−	2706.24i	0.682287	−	0.212702i
$546$		0			0
$547$	3575.35	+	4921.05i	0.279472	+	0.384660i	0.925559	−	0.378604i	$-0.123596\pi$
$547$	3575.35	+	4921.05i	0.279472	+	0.384660i	−0.646087	+	0.763264i	$0.723596\pi$
$548$		0			0
$549$	−6969.96			−0.541841
$550$		0			0
$551$	12486.6			0.965419
$552$		0			0
$553$	2941.16	+	4048.16i	0.226168	+	0.311294i
$554$		0			0
$555$	−4117.80	+	5527.43i	−0.314939	+	0.422750i
$556$		0			0
$557$			8490.81i			0.645902i	0.946416	+	0.322951i	$0.104675\pi$
$557$			8490.81i			0.645902i	−0.946416	+	0.322951i	$0.895325\pi$
$558$		0			0
$559$	4844.61	−	14910.2i	0.366557	−	1.12815i
$560$		0			0
$561$	−4541.85	−	13978.4i	−0.341813	−	1.05199i
$562$		0			0
$563$	−1155.57	−	375.466i	−0.0865033	−	0.0281066i	0.265446	−	0.964126i	$-0.414481\pi$
$563$	−1155.57	−	375.466i	−0.0865033	−	0.0281066i	−0.351949	+	0.936019i	$0.614481\pi$
$564$		0			0
$565$	−1809.69	−	5804.97i	−0.134751	−	0.432242i
$566$		0			0
$567$	457.779	−	630.078i	0.0339063	−	0.0466681i
$568$		0			0
$569$	15391.4	+	11182.5i	1.13399	+	0.823890i	0.986270	−	0.165139i	$-0.0528074\pi$
$569$	15391.4	+	11182.5i	1.13399	+	0.823890i	0.147717	+	0.989030i	$0.452807\pi$
$570$		0			0
$571$	10444.9	−	7588.65i	0.765507	−	0.556173i	−0.135088	−	0.990834i	$-0.543132\pi$
$571$	10444.9	−	7588.65i	0.765507	−	0.556173i	0.900594	+	0.434660i	$0.143132\pi$
$572$		0			0
$573$	4048.22	−	1315.35i	0.295143	−	0.0958976i
$574$		0			0
$575$	307.568	−	12856.4i	0.0223069	−	0.932432i
$576$		0			0
$577$	1166.08	−	378.881i	0.0841323	−	0.0273362i	−0.266648	−	0.963794i	$-0.585916\pi$
$577$	1166.08	−	378.881i	0.0841323	−	0.0273362i	0.350781	+	0.936458i	$0.385916\pi$
$578$		0			0
$579$	3568.43	−	2592.61i	0.256129	−	0.186089i
$580$		0			0
$581$	5494.11	+	3991.71i	0.392314	+	0.285033i
$582$		0			0
$583$	9104.01	−	12530.6i	0.646741	−	0.890162i
$584$		0			0
$585$	11127.0	+	133.079i	0.786402	+	0.00940535i
$586$		0			0
$587$	17069.0	+	5546.06i	1.20019	+	0.389966i	0.839832	−	0.542847i	$-0.182654\pi$
$587$	17069.0	+	5546.06i	1.20019	+	0.389966i	0.360361	+	0.932813i	$0.382654\pi$
$588$		0			0
$589$	−4696.18	−	14453.4i	−0.328528	−	1.01110i
$590$		0			0
$591$	2710.09	−	8340.80i	0.188626	−	0.580532i
$592$		0			0
$593$			26419.3i			1.82953i	0.403985	+	0.914766i	$0.367625\pi$
$593$			26419.3i			1.82953i	−0.403985	+	0.914766i	$0.632375\pi$
$594$		0			0
$595$	−106.846	+	8933.61i	−0.00736177	+	0.615533i
$596$		0			0
$597$	6406.05	+	8817.17i	0.439166	+	0.604460i
$598$		0			0
$599$	11468.2			0.782267			0.391134	−	0.920334i	$-0.372083\pi$
$599$	11468.2			0.782267			0.391134	+	0.920334i	$0.372083\pi$
$600$		0			0
$601$	110.443			0.00749598			0.00374799	−	0.999993i	$-0.498807\pi$
$601$	110.443			0.00749598			0.00374799	+	0.999993i	$0.498807\pi$
$602$		0			0
$603$	3501.80	+	4819.81i	0.236491	+	0.325502i
$604$		0			0
$605$	−8410.49	−	2844.38i	−0.565182	−	0.191141i
$606$		0			0
$607$			3837.94i			0.256634i	0.991733	+	0.128317i	$0.0409576\pi$
$607$			3837.94i			0.256634i	−0.991733	+	0.128317i	$0.959042\pi$
$608$		0			0
$609$	597.705	−	1839.55i	0.0397705	−	0.122401i
$610$		0			0
$611$	−4233.21	−	13028.5i	−0.280290	−	0.862644i
$612$		0			0
$613$	12151.2	+	3948.16i	0.800623	+	0.260138i	0.680621	−	0.732635i	$-0.261710\pi$
$613$	12151.2	+	3948.16i	0.800623	+	0.260138i	0.120002	+	0.992774i	$0.461710\pi$
$614$		0			0
$615$	11483.9	+	8555.19i	0.752965	+	0.560941i
$616$		0			0
$617$	3193.34	−	4395.26i	0.208362	−	0.286785i	−0.692027	−	0.721872i	$-0.743282\pi$
$617$	3193.34	−	4395.26i	0.208362	−	0.286785i	0.900389	+	0.435086i	$0.143282\pi$
$618$		0			0
$619$	−9646.49	−	7008.58i	−0.626373	−	0.455087i	0.228769	−	0.973481i	$-0.426530\pi$
$619$	−9646.49	−	7008.58i	−0.626373	−	0.455087i	−0.855142	+	0.518394i	$0.826530\pi$
$620$		0			0
$621$	11084.2	−	8053.14i	0.716254	−	0.520389i
$622$		0			0
$623$	−4441.78	+	1443.22i	−0.285644	+	0.0928112i
$624$		0			0
$625$	−12187.2	−	9778.12i	−0.779984	−	0.625800i
$626$		0			0
$627$	17912.3	−	5820.07i	1.14091	−	0.370703i
$628$		0			0
$629$	−18475.7	+	13423.4i	−1.17118	+	0.850914i
$630$		0			0
$631$	19244.6	+	13982.0i	1.21413	+	0.882117i	0.995599	−	0.0937128i	$-0.0298736\pi$
$631$	19244.6	+	13982.0i	1.21413	+	0.882117i	0.218531	+	0.975830i	$0.429874\pi$
$632$		0			0
$633$	−922.649	+	1269.92i	−0.0579336	+	0.0797388i
$634$		0			0
$635$	3174.36	+	2364.82i	0.198379	+	0.147787i
$636$		0			0
$637$	14869.7	+	4831.47i	0.924898	+	0.300518i
$638$		0			0
$639$	4025.37	+	12388.8i	0.249204	+	0.766971i
$640$		0			0
$641$	−2435.02	+	7494.22i	−0.150043	+	0.461784i	−0.997625	−	0.0688799i	$-0.978057\pi$
$641$	−2435.02	+	7494.22i	−0.150043	+	0.461784i	0.847582	+	0.530664i	$0.178057\pi$
$642$		0			0
$643$			28364.2i			1.73962i	0.493387	+	0.869810i	$0.335759\pi$
$643$			28364.2i			1.73962i	−0.493387	+	0.869810i	$0.664241\pi$
$644$		0			0
$645$	−9002.02	−	3044.43i	−0.549541	−	0.185852i
$646$		0			0
$647$	−13818.9	−	19020.1i	−0.839687	−	1.15573i	−0.986042	−	0.166498i	$-0.946754\pi$
$647$	−13818.9	−	19020.1i	−0.839687	−	1.15573i	0.146355	−	0.989232i	$-0.453246\pi$
$648$		0			0
$649$	−12044.1			−0.728465
$650$		0			0
$651$	−2354.10			−0.141727
$652$		0			0
$653$	991.739	+	1365.01i	0.0594330	+	0.0818025i	0.837699	−	0.546132i	$-0.183900\pi$
$653$	991.739	+	1365.01i	0.0594330	+	0.0818025i	−0.778266	+	0.627935i	$0.783900\pi$
$654$		0			0
$655$	248.910	−	20811.9i	0.0148484	−	1.24151i
$656$		0			0
$657$		−	16941.3i		−	1.00600i
$658$		0			0
$659$	−7630.21	+	23483.4i	−0.451033	+	1.38814i	0.424697	+	0.905335i	$0.360381\pi$
$659$	−7630.21	+	23483.4i	−0.451033	+	1.38814i	−0.875730	+	0.482801i	$0.839619\pi$
$660$		0			0
$661$	6869.22	+	21141.3i	0.404208	+	1.24403i	0.921554	+	0.388249i	$0.126920\pi$
$661$	6869.22	+	21141.3i	0.404208	+	1.24403i	−0.517346	+	0.855776i	$0.673080\pi$
$662$		0			0
$663$	−16408.4	−	5331.41i	−0.961160	−	0.312300i
$664$		0			0
$665$	−11447.8	−	136.916i	−0.667559	−	0.00798400i
$666$		0			0
$667$	−5422.06	+	7462.83i	−0.314757	+	0.433226i
$668$		0			0
$669$	−14601.9	−	10608.9i	−0.843858	−	0.613099i
$670$		0			0
$671$	14132.7	−	10268.0i	0.813094	−	0.590747i
$672$		0			0
$673$	−3341.98	+	1085.88i	−0.191417	+	0.0621953i	−0.403157	−	0.915131i	$-0.632087\pi$
$673$	−3341.98	+	1085.88i	−0.191417	+	0.0621953i	0.211740	+	0.977326i	$0.432087\pi$
$674$		0			0
$675$	398.127	−	16641.8i	0.0227021	−	0.948951i
$676$		0			0
$677$	−2670.21	+	867.604i	−0.151587	+	0.0492537i	−0.383828	−	0.923405i	$-0.625394\pi$
$677$	−2670.21	+	867.604i	−0.151587	+	0.0492537i	0.232241	+	0.972658i	$0.425394\pi$
$678$		0			0
$679$	3117.34	−	2264.88i	0.176189	−	0.128009i
$680$		0			0
$681$	−6203.09	−	4506.81i	−0.349050	−	0.253600i
$682$		0			0
$683$	−12672.3	+	17442.0i	−0.709947	+	0.977158i	0.289851	+	0.957072i	$0.406394\pi$
$683$	−12672.3	+	17442.0i	−0.709947	+	0.977158i	−0.999798	+	0.0200863i	$0.993606\pi$
$684$		0			0
$685$	−3811.43	−	12226.0i	−0.212595	−	0.681944i
$686$		0			0
$687$	5713.07	+	1856.29i	0.317274	+	0.103088i
$688$		0			0
$689$	−5618.31	−	17291.4i	−0.310654	−	0.956095i
$690$		0			0
$691$	−3790.52	+	11666.0i	−0.208680	+	0.642252i	0.790862	+	0.611995i	$0.209633\pi$
$691$	−3790.52	+	11666.0i	−0.208680	+	0.642252i	−0.999542	+	0.0302572i	$0.990367\pi$
$692$		0			0
$693$			6234.66i			0.341754i
$694$		0			0
$695$	8648.58	−	11609.2i	0.472028	−	0.633615i
$696$		0			0
$697$	27888.5	+	38385.3i	1.51557	+	2.08601i
$698$		0			0
$699$	14139.1			0.765080
$700$		0			0
$701$	11281.5			0.607840			0.303920	−	0.952698i	$-0.401705\pi$
$701$	11281.5			0.607840			0.303920	+	0.952698i	$0.401705\pi$
$702$		0			0
$703$	−17201.1	−	23675.3i	−0.922834	−	1.27017i
$704$		0			0
$705$	−7927.31	+	2471.32i	−0.423489	+	0.132022i
$706$		0			0
$707$			3697.24i			0.196674i
$708$		0			0
$709$	5015.81	−	15437.1i	0.265688	−	0.817703i	−0.725847	−	0.687857i	$-0.758552\pi$
$709$	5015.81	−	15437.1i	0.265688	−	0.817703i	0.991534	−	0.129846i	$-0.0414483\pi$
$710$		0			0
$711$	−3867.84	−	11904.0i	−0.204016	−	0.627897i
$712$		0			0
$713$	10677.5	+	3469.34i	0.560837	+	0.182227i
$714$		0			0
$715$	−22757.8	+	16122.2i	−1.19034	+	0.843269i
$716$		0			0
$717$	−5214.30	+	7176.87i	−0.271592	+	0.373815i
$718$		0			0
$719$	−25901.8	−	18818.8i	−1.34350	−	0.976109i	−0.999308	−	0.0372091i	$-0.988153\pi$
$719$	−25901.8	−	18818.8i	−1.34350	−	0.976109i	−0.344191	−	0.938900i	$-0.611847\pi$
$720$		0			0
$721$	7720.33	−	5609.15i	0.398780	−	0.289730i
$722$		0			0
$723$	−19810.0	+	6436.67i	−1.01901	+	0.331096i
$724$		0			0
$725$	3207.50	+	10739.1i	0.164308	+	0.550124i
$726$		0			0
$727$	7448.56	−	2420.19i	0.379989	−	0.123466i	−0.112793	−	0.993618i	$-0.535980\pi$
$727$	7448.56	−	2420.19i	0.379989	−	0.123466i	0.492782	+	0.870153i	$0.335980\pi$
$728$		0			0
$729$	6958.04	−	5055.31i	0.353505	−	0.256837i
$730$		0			0
$731$	−25472.4	−	18506.8i	−1.28882	−	0.936385i
$732$		0			0
$733$	8609.52	−	11850.0i	0.433833	−	0.597120i	−0.534994	−	0.844856i	$-0.679686\pi$
$733$	8609.52	−	11850.0i	0.433833	−	0.597120i	0.968828	+	0.247735i	$0.0796863\pi$
$734$		0			0
$735$	3036.17	−	8977.59i	0.152368	−	0.450535i
$736$		0			0
$737$	−14200.9	−	4614.15i	−0.709764	−	0.230616i
$738$		0			0
$739$	724.221	+	2228.92i	0.0360499	+	0.110950i	0.967462	−	0.253016i	$-0.0814224\pi$
$739$	724.221	+	2228.92i	0.0360499	+	0.110950i	−0.931412	+	0.363966i	$0.881422\pi$
$740$		0			0
$741$	6831.83	−	21026.2i	0.338696	−	1.04240i
$742$		0			0
$743$			8141.78i			0.402009i	0.979590	+	0.201005i	$0.0644206\pi$
$743$			8141.78i			0.402009i	−0.979590	+	0.201005i	$0.935579\pi$
$744$		0			0
$745$	−15960.2	−	22529.0i	−0.784880	−	1.10792i
$746$		0			0
$747$	−9984.93	−	13743.1i	−0.489062	−	0.673136i
$748$		0			0
$749$	−3859.65			−0.188289
$750$		0			0
$751$	29079.6			1.41295			0.706477	−	0.707736i	$-0.250283\pi$
$751$	29079.6			1.41295			0.706477	+	0.707736i	$0.250283\pi$
$752$		0			0
$753$	1012.24	+	1393.23i	0.0489881	+	0.0674263i
$754$		0			0
$755$	9905.15	+	13981.9i	0.477464	+	0.673978i
$756$		0			0
$757$			30961.4i			1.48654i	0.668992	+	0.743270i	$0.266726\pi$
$757$			30961.4i			1.48654i	−0.668992	+	0.743270i	$0.733274\pi$
$758$		0			0
$759$	−4299.62	+	13232.9i	−0.205621	+	0.632837i
$760$		0			0
$761$	1956.14	+	6020.38i	0.0931801	+	0.286779i	0.986775	−	0.162095i	$-0.0518252\pi$
$761$	1956.14	+	6020.38i	0.0931801	+	0.286779i	−0.893595	+	0.448874i	$0.851825\pi$
$762$		0			0
$763$	5687.50	+	1847.98i	0.269857	+	0.0876820i
$764$		0			0
$765$	7159.69	−	21170.4i	0.338378	−	1.00054i
$766$		0			0
$767$	−8310.05	+	11437.8i	−0.391211	+	0.538455i
$768$		0			0
$769$	−4443.24	−	3228.20i	−0.208358	−	0.151381i	0.478712	−	0.877972i	$-0.341104\pi$
$769$	−4443.24	−	3228.20i	−0.208358	−	0.151381i	−0.687070	+	0.726591i	$0.741104\pi$
$770$		0			0
$771$	5500.43	−	3996.29i	0.256930	−	0.186671i
$772$		0			0
$773$	−27283.0	+	8864.79i	−1.26947	+	0.412476i	−0.864860	−	0.502012i	$-0.832593\pi$
$773$	−27283.0	+	8864.79i	−1.26947	+	0.412476i	−0.404611	+	0.914489i	$0.632593\pi$
$774$		0			0
$775$	11224.3	−	7751.67i	0.520243	−	0.359288i
$776$		0			0
$777$	−4311.28	+	1400.82i	−0.199056	+	0.0646771i
$778$		0			0
$779$	−49188.1	+	35737.3i	−2.26232	+	1.64367i
$780$		0			0
$781$	−26413.0	−	19190.2i	−1.21016	−	0.879231i
$782$		0			0
$783$	−7018.51	+	9660.15i	−0.320334	+	0.440901i
$784$		0			0
$785$	11865.0	−	8405.48i	0.539465	−	0.382171i
$786$		0			0
$787$	8463.60	+	2749.99i	0.383348	+	0.124557i	0.494350	−	0.869263i	$-0.335406\pi$
$787$	8463.60	+	2749.99i	0.383348	+	0.124557i	−0.111002	+	0.993820i	$0.535406\pi$
$788$		0			0
$789$	3440.55	+	10588.9i	0.155243	+	0.477789i
$790$		0			0
$791$	1235.76	−	3803.29i	0.0555483	−	0.170960i
$792$		0			0
$793$		−	20505.8i		−	0.918261i
$794$		0			0
$795$	−10521.1	+	3279.94i	−0.469366	+	0.146324i
$796$		0			0
$797$	2348.18	+	3231.99i	0.104362	+	0.143643i	0.858004	−	0.513643i	$-0.171704\pi$
$797$	2348.18	+	3231.99i	0.104362	+	0.143643i	−0.753641	+	0.657286i	$0.771704\pi$
$798$		0			0
$799$	−27512.0			−1.21815
$800$		0			0
$801$	11682.5			0.515333
$802$		0			0
$803$	24957.5	+	34351.1i	1.09680	+	1.50962i
$804$		0			0
$805$	5052.83	−	6782.54i	0.221228	−	0.296960i
$806$		0			0
$807$		−	10057.6i		−	0.438715i
$808$		0			0
$809$	177.394	−	545.963i	0.00770933	−	0.0237269i	−0.947128	−	0.320856i	$-0.896029\pi$
$809$	177.394	−	545.963i	0.00770933	−	0.0237269i	0.954837	+	0.297130i	$0.0960293\pi$
$810$		0			0
$811$	−6564.79	−	20204.3i	−0.284243	−	0.874809i	−0.986625	−	0.163009i	$-0.947880\pi$
$811$	−6564.79	−	20204.3i	−0.284243	−	0.874809i	0.702382	−	0.711800i	$-0.252120\pi$
$812$		0			0
$813$	22720.5	+	7382.33i	0.980125	+	0.318462i
$814$		0			0
$815$	3521.53	+	11296.1i	0.151354	+	0.485501i
$816$		0			0
$817$	23715.1	−	32641.1i	1.01553	−	1.39776i
$818$		0			0
$819$	5920.79	+	4301.71i	0.252612	+	0.183533i
$820$		0			0
$821$	−11314.5	+	8220.46i	−0.480973	+	0.349447i	−0.801702	−	0.597724i	$-0.796072\pi$
$821$	−11314.5	+	8220.46i	−0.480973	+	0.349447i	0.320730	+	0.947171i	$0.396072\pi$
$822$		0			0
$823$	−3571.33	+	1160.40i	−0.151262	+	0.0491481i	−0.383669	−	0.923470i	$-0.625340\pi$
$823$	−3571.33	+	1160.40i	−0.151262	+	0.0491481i	0.232407	+	0.972619i	$0.425340\pi$
$824$		0			0
$825$	9606.79	+	13910.5i	0.405413	+	0.587031i
$826$		0			0
$827$	6278.37	−	2039.97i	0.263991	−	0.0857758i	−0.174031	−	0.984740i	$-0.555679\pi$
$827$	6278.37	−	2039.97i	0.263991	−	0.0857758i	0.438022	+	0.898964i	$0.355679\pi$
$828$		0			0
$829$	12072.9	−	8771.49i	0.505802	−	0.367487i	−0.305427	−	0.952216i	$-0.598799\pi$
$829$	12072.9	−	8771.49i	0.505802	−	0.367487i	0.811229	+	0.584729i	$0.198799\pi$
$830$		0			0
$831$	9523.05	+	6918.90i	0.397534	+	0.288825i
$832$		0			0
$833$	18456.5	−	25403.2i	0.767685	−	1.05663i
$834$		0			0
$835$	−27605.3	−	330.158i	−1.14410	−	0.0136834i
$836$		0			0
$837$	13821.4	+	4490.84i	0.570773	+	0.185456i
$838$		0			0
$839$	−3903.51	−	12013.8i	−0.160625	−	0.494352i	0.838063	−	0.545574i	$-0.183688\pi$
$839$	−3903.51	−	12013.8i	−0.160625	−	0.494352i	−0.998687	+	0.0512220i	$0.983688\pi$
$840$		0			0
$841$	−5052.29	+	15549.4i	−0.207155	+	0.637556i
$842$		0			0
$843$		−	7658.70i		−	0.312906i
$844$		0			0
$845$	−97.7663	+	8174.45i	−0.00398019	+	0.332793i
$846$		0			0
$847$	−3432.17	−	4723.97i	−0.139233	−	0.191638i
$848$		0			0
$849$	13743.9			0.555583
$850$		0			0
$851$	21619.3			0.870856
$852$		0			0
$853$	20859.3	+	28710.4i	0.837292	+	1.15243i	0.986522	+	0.163631i	$0.0523206\pi$
$853$	20859.3	+	28710.4i	0.837292	+	1.15243i	−0.149230	+	0.988803i	$0.547679\pi$
$854$		0			0
$855$	27128.4	+	9174.65i	1.08511	+	0.366978i
$856$		0			0
$857$			41272.0i			1.64507i	0.568714	+	0.822535i	$0.307441\pi$
$857$			41272.0i			1.64507i	−0.568714	+	0.822535i	$0.692559\pi$
$858$		0			0
$859$	7009.42	−	21572.8i	0.278415	−	0.856872i	−0.709881	−	0.704322i	$-0.751251\pi$
$859$	7009.42	−	21572.8i	0.278415	−	0.856872i	0.988296	−	0.152551i	$-0.0487487\pi$
$860$		0			0
$861$	2910.36	+	8957.16i	0.115197	+	0.354540i
$862$		0			0
$863$	−29094.9	−	9453.52i	−1.14763	−	0.372887i	−0.327379	−	0.944893i	$-0.606165\pi$
$863$	−29094.9	−	9453.52i	−1.14763	−	0.372887i	−0.820249	+	0.572006i	$0.806165\pi$
$864$		0			0
$865$	−26807.9	−	19971.2i	−1.05375	−	0.785020i
$866$		0			0
$867$	−11894.3	+	16371.1i	−0.465918	+	0.641281i
$868$		0			0
$869$	25379.4	+	18439.2i	0.990721	+	0.719801i
$870$		0			0
$871$	−14180.0	+	10302.4i	−0.551631	+	0.400784i
$872$		0			0
$873$	−9166.82	+	2978.48i	−0.355383	+	0.115471i
$874$		0			0
$875$	−2822.91	−	9880.87i	−0.109065	−	0.381754i
$876$		0			0
$877$	8629.19	−	2803.79i	0.332254	−	0.107956i	−0.138139	−	0.990413i	$-0.544112\pi$
$877$	8629.19	−	2803.79i	0.332254	−	0.107956i	0.470393	+	0.882457i	$0.344112\pi$
$878$		0			0
$879$	10175.5	−	7392.94i	0.390457	−	0.283683i
$880$		0			0
$881$	14675.6	+	10662.5i	0.561220	+	0.407750i	0.831905	−	0.554918i	$-0.187250\pi$
$881$	14675.6	+	10662.5i	0.561220	+	0.407750i	−0.270686	+	0.962668i	$0.587250\pi$
$882$		0			0
$883$	9854.18	−	13563.1i	0.375560	−	0.516914i	−0.578841	−	0.815440i	$-0.696495\pi$
$883$	9854.18	−	13563.1i	0.375560	−	0.516914i	0.954401	+	0.298526i	$0.0964950\pi$
$884$		0			0
$885$	6872.27	+	5119.68i	0.261027	+	0.194459i
$886$		0			0
$887$	15770.2	+	5124.05i	0.596969	+	0.193967i	0.591888	−	0.806020i	$-0.298383\pi$
$887$	15770.2	+	5124.05i	0.596969	+	0.193967i	0.00508085	+	0.999987i	$0.498383\pi$
$888$		0			0
$889$	804.479	+	2475.93i	0.0303502	+	0.0934085i
$890$		0			0
$891$	1508.84	−	4643.72i	0.0567317	−	0.174602i
$892$		0			0
$893$		−	35254.7i		−	1.32111i
$894$		0			0
$895$	46969.8	+	15884.9i	1.75422	+	0.593266i
$896$		0			0
$897$	9600.11	+	13213.4i	0.357345	+	0.491843i
$898$		0			0
$899$	−9784.63			−0.362999
$900$		0			0
$901$	−36513.9			−1.35012
$902$		0			0
$903$	−3673.56	−	5056.22i	−0.135380	−	0.186335i
$904$		0			0
$905$	−169.807	+	14197.9i	−0.00623709	+	0.521497i
$906$		0			0
$907$		−	33347.0i		−	1.22080i	−0.792092	−	0.610401i	$-0.791008\pi$
$907$		−	33347.0i		−	1.22080i	0.792092	−	0.610401i	$-0.208992\pi$
$908$		0			0
$909$	2857.89	−	8795.69i	0.104280	−	0.320940i
$910$		0			0
$911$	5984.80	+	18419.3i	0.217657	+	0.669878i	0.998954	+	0.0457195i	$0.0145581\pi$
$911$	5984.80	+	18419.3i	0.217657	+	0.669878i	−0.781298	+	0.624159i	$0.785442\pi$
$912$		0			0
$913$	40492.0	+	13156.7i	1.46779	+	0.476913i
$914$		0			0
$915$	−12428.7	−	148.646i	−0.449048	−	0.00537060i
$916$		0			0
$917$	8045.91	−	11074.2i	0.289749	−	0.398805i
$918$		0			0
$919$	5422.63	+	3939.77i	0.194642	+	0.141416i	0.680838	−	0.732434i	$-0.261616\pi$
$919$	5422.63	+	3939.77i	0.194642	+	0.141416i	−0.486196	+	0.873850i	$0.661616\pi$
$920$		0			0
$921$	3197.88	−	2323.40i	0.114412	−	0.0831255i
$922$		0			0
$923$	−36448.2	+	11842.7i	−1.29979	+	0.422328i
$924$		0			0
$925$	15943.4	−	20875.5i	0.566721	−	0.742033i
$926$		0			0
$927$	−22702.3	+	7376.44i	−0.804361	+	0.261353i
$928$		0			0
$929$	3649.17	−	2651.28i	0.128876	−	0.0936335i	−0.521480	−	0.853263i	$-0.674620\pi$
$929$	3649.17	−	2651.28i	0.128876	−	0.0936335i	0.650356	+	0.759630i	$0.274620\pi$
$930$		0			0
$931$	32552.5	+	23650.8i	1.14594	+	0.832571i
$932$		0			0
$933$	−5065.29	+	6971.78i	−0.177739	+	0.244636i
$934$		0			0
$935$	16670.4	+	53473.8i	0.583079	+	1.87035i
$936$		0			0
$937$	−21524.2	−	6993.65i	−0.750444	−	0.243834i	−0.0912718	−	0.995826i	$-0.529093\pi$
$937$	−21524.2	−	6993.65i	−0.750444	−	0.243834i	−0.659172	+	0.751992i	$0.729093\pi$
$938$		0			0
$939$	6974.54	+	21465.4i	0.242392	+	0.746004i
$940$		0			0
$941$	4235.15	−	13034.4i	0.146718	−	0.451552i	−0.850510	−	0.525959i	$-0.823706\pi$
$941$	4235.15	−	13034.4i	0.146718	−	0.451552i	0.997228	+	0.0744071i	$0.0237064\pi$
$942$		0			0
$943$		−	44916.4i		−	1.55109i
$944$		0			0
$945$	6540.56	−	8779.57i	0.225148	−	0.302221i
$946$		0			0
$947$	−31603.5	−	43498.5i	−1.08445	−	1.49262i	−0.854522	−	0.519415i	$-0.826150\pi$
$947$	−31603.5	−	43498.5i	−1.08445	−	1.49262i	−0.229931	−	0.973207i	$-0.573850\pi$
$948$		0			0
$949$	49841.6			1.70488
$950$		0			0
$951$	−19506.1			−0.665118
$952$		0			0
$953$	4488.76	+	6178.24i	0.152576	+	0.210003i	0.878462	−	0.477812i	$-0.158570\pi$
$953$	4488.76	+	6178.24i	0.152576	+	0.210003i	−0.725886	+	0.687815i	$0.758570\pi$
$954$		0			0
$955$	−15486.3	+	4827.83i	−0.524739	+	0.163586i
$956$		0			0
$957$		−	12126.3i		−	0.409600i
$958$		0			0
$959$	2602.67	−	8010.21i	0.0876379	−	0.269722i
$960$		0			0
$961$	−5525.94	−	17007.1i	−0.185490	−	0.570880i
$962$		0			0
$963$	9182.06	+	2983.43i	0.307256	+	0.0998336i
$964$		0			0
$965$	−13716.2	+	9716.93i	−0.457555	+	0.324144i
$966$		0			0
$967$	−17475.8	+	24053.4i	−0.581162	+	0.799900i	−0.993822	−	0.110985i	$-0.964600\pi$
$967$	−17475.8	+	24053.4i	−0.581162	+	0.799900i	0.412661	+	0.910885i	$0.364600\pi$
$968$		0			0
$969$	−35920.9	−	26098.1i	−1.19086	−	0.865213i
$970$		0			0
$971$	5559.56	−	4039.25i	0.183743	−	0.133497i	−0.492111	−	0.870532i	$-0.663775\pi$
$971$	5559.56	−	4039.25i	0.183743	−	0.133497i	0.675855	+	0.737035i	$0.263775\pi$
$972$		0			0
$973$	9054.94	−	2942.13i	0.298343	−	0.0969376i
$974$		0			0
$975$	19838.6	+	474.605i	0.651633	+	0.0155893i
$976$		0			0
$977$	−20623.8	+	6701.07i	−0.675346	+	0.219433i	−0.626557	−	0.779376i	$-0.715536\pi$
$977$	−20623.8	+	6701.07i	−0.675346	+	0.219433i	−0.0487896	+	0.998809i	$0.515536\pi$
$978$		0			0
$979$	−23688.1	+	17210.4i	−0.773316	+	0.561847i
$980$		0			0
$981$	−12102.0	−	8792.65i	−0.393872	−	0.286165i
$982$		0			0
$983$	7109.04	−	9784.75i	0.230664	−	0.317482i	−0.677958	−	0.735100i	$-0.737135\pi$
$983$	7109.04	−	9784.75i	0.230664	−	0.317482i	0.908623	+	0.417618i	$0.137135\pi$
$984$		0			0
$985$	−10707.4	+	31660.4i	−0.346360	+	1.02415i
$986$		0			0
$987$	−5193.80	−	1687.57i	−0.167498	−	0.0544234i
$988$		0			0
$989$	9210.68	+	28347.6i	0.296140	+	0.911426i
$990$		0			0
$991$	−10796.5	+	33228.3i	−0.346078	+	1.06512i	0.614926	+	0.788585i	$0.289186\pi$
$991$	−10796.5	+	33228.3i	−0.346078	+	1.06512i	−0.961004	+	0.276534i	$0.910814\pi$
$992$		0			0
$993$		−	3478.67i		−	0.111171i
$994$		0			0
$995$	−24009.4	−	33891.2i	−0.764974	−	1.07982i
$996$		0			0
$997$	−2194.63	−	3020.65i	−0.0697138	−	0.0959528i	0.772736	−	0.634727i	$-0.218888\pi$
$997$	−2194.63	−	3020.65i	−0.0697138	−	0.0959528i	−0.842450	+	0.538774i	$0.818888\pi$
$998$		0			0
$999$	27984.7			0.886284

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.i.a.69.3	yes	32
5.2	odd	4		500.4.g.b.401.6		64
5.3	odd	4		500.4.g.b.401.11		64
5.4	even	2		500.4.i.a.349.6		32
25.2	odd	20		2500.4.a.g.1.21		32
25.3	odd	20		500.4.g.b.101.11		64
25.4	even	10	inner	100.4.i.a.29.3	✓	32
25.21	even	5		500.4.i.a.149.6		32
25.22	odd	20		500.4.g.b.101.6		64
25.23	odd	20		2500.4.a.g.1.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.4.i.a.29.3	✓	32	25.4	even	10	inner
100.4.i.a.69.3	yes	32	1.1	even	1	trivial
500.4.g.b.101.6		64	25.22	odd	20
500.4.g.b.101.11		64	25.3	odd	20
500.4.g.b.401.6		64	5.2	odd	4
500.4.g.b.401.11		64	5.3	odd	4
500.4.i.a.149.6		32	25.21	even	5
500.4.i.a.349.6		32	5.4	even	2
2500.4.a.g.1.12		32	25.23	odd	20
2500.4.a.g.1.21		32	25.2	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)

\(f(q)\)	\(=\)	\(q+(-1.72442 - 2.37346i) q^{3} +(6.46300 + 9.12303i) q^{5} +7.35306i q^{7} +(5.68377 - 17.4928i) q^{9} +O(q^{10})\)	\(q+(-1.72442 - 2.37346i) q^{3} +(6.46300 + 9.12303i) q^{5} +7.35306i q^{7} +(5.68377 - 17.4928i) q^{9} +(14.2454 + 43.8427i) q^{11} +(51.4644 + 16.7218i) q^{13} +(10.5082 - 31.0716i) q^{15} +(63.8784 - 87.9210i) q^{17} +(112.665 + 81.8557i) q^{19} +(17.4522 - 12.6798i) q^{21} +(-97.8452 + 31.7918i) q^{23} +(-41.4593 + 117.924i) q^{25} +(-126.654 + 41.1525i) q^{27} +(72.5388 - 52.7025i) q^{29} +(-88.2855 - 64.1432i) q^{31} +(79.4939 - 109.414i) q^{33} +(-67.0822 + 47.5228i) q^{35} +(-199.854 - 64.9367i) q^{37} +(-49.0576 - 150.984i) q^{39} +(-134.913 + 415.220i) q^{41} -289.719i q^{43} +(196.322 - 61.2030i) q^{45} +(-148.801 - 204.807i) q^{47} +288.933 q^{49} -318.830 q^{51} +(-197.489 - 271.820i) q^{53} +(-307.910 + 413.316i) q^{55} -408.559i q^{57} +(-80.7360 + 248.480i) q^{59} +(-117.100 - 360.398i) q^{61} +(128.626 + 41.7931i) q^{63} +(180.061 + 577.584i) q^{65} +(-190.387 + 262.045i) q^{67} +(244.183 + 177.409i) q^{69} +(-572.964 + 416.283i) q^{71} +(875.989 - 284.626i) q^{73} +(351.382 - 104.949i) q^{75} +(-322.378 + 104.747i) q^{77} +(550.542 - 399.992i) q^{79} +(-85.6893 - 62.2569i) q^{81} +(542.864 - 747.188i) q^{83} +(1214.95 + 14.5308i) q^{85} +(-250.175 - 81.2867i) q^{87} +(196.275 + 604.072i) q^{89} +(-122.956 + 378.420i) q^{91} +320.152i q^{93} +(-18.6202 + 1556.88i) q^{95} +(-308.018 - 423.951i) q^{97} +847.901 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{5} + 122 q^{9}+O(q^{10}) \) 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

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Representations

Groups

Database

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