LMFDB - Embedded newform 93.4.c.b.92.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [93,4,Mod(92,93)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("93.92"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(93, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	93.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.48717763053$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			92.10
Character	$\chi$	$=$	93.92
Dual form			93.4.c.b.92.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.97231i q^{2} +(4.89717 - 1.73716i) q^{3} -0.834616 q^{4} +8.81124i q^{5} +(-5.16337 - 14.5559i) q^{6} +20.5950 q^{7} -21.2977i q^{8} +(20.9646 - 17.0143i) q^{9} +26.1897 q^{10} -14.3060 q^{11} +(-4.08726 + 1.44986i) q^{12} +20.9481i q^{13} -61.2148i q^{14} +(15.3065 + 43.1501i) q^{15} -69.9803 q^{16} -72.5833 q^{17} +(-50.5718 - 62.3132i) q^{18} +9.18310 q^{19} -7.35400i q^{20} +(100.857 - 35.7768i) q^{21} +42.5220i q^{22} -124.620 q^{23} +(-36.9975 - 104.299i) q^{24} +47.3621 q^{25} +62.2643 q^{26} +(73.1105 - 119.741i) q^{27} -17.1890 q^{28} -4.57622 q^{29} +(128.256 - 45.4957i) q^{30} +(-34.3496 + 169.148i) q^{31} +37.6213i q^{32} +(-70.0591 + 24.8518i) q^{33} +215.740i q^{34} +181.468i q^{35} +(-17.4974 + 14.2004i) q^{36} -164.987i q^{37} -27.2950i q^{38} +(36.3902 + 102.587i) q^{39} +187.659 q^{40} +301.602i q^{41} +(-106.340 - 299.779i) q^{42} +114.689i q^{43} +11.9401 q^{44} +(149.917 + 184.724i) q^{45} +370.408i q^{46} +313.591i q^{47} +(-342.706 + 121.567i) q^{48} +81.1555 q^{49} -140.775i q^{50} +(-355.453 + 126.089i) q^{51} -17.4836i q^{52} +704.030 q^{53} +(-355.906 - 217.307i) q^{54} -126.054i q^{55} -438.628i q^{56} +(44.9712 - 15.9525i) q^{57} +13.6019i q^{58} -81.5758i q^{59} +(-12.7751 - 36.0138i) q^{60} +210.196i q^{61} +(502.761 + 102.098i) q^{62} +(431.766 - 350.410i) q^{63} -448.021 q^{64} -184.579 q^{65} +(73.8674 + 208.237i) q^{66} -789.501 q^{67} +60.5792 q^{68} +(-610.284 + 216.484i) q^{69} +539.378 q^{70} -650.622i q^{71} +(-362.366 - 446.498i) q^{72} -960.640i q^{73} -490.391 q^{74} +(231.940 - 82.2754i) q^{75} -7.66437 q^{76} -294.633 q^{77} +(304.919 - 108.163i) q^{78} +1140.44i q^{79} -616.613i q^{80} +(150.026 - 713.395i) q^{81} +896.453 q^{82} -1079.90 q^{83} +(-84.1772 + 29.8599i) q^{84} -639.549i q^{85} +340.891 q^{86} +(-22.4105 + 7.94962i) q^{87} +304.686i q^{88} +545.699 q^{89} +(549.056 - 445.600i) q^{90} +431.427i q^{91} +104.010 q^{92} +(125.621 + 888.018i) q^{93} +932.090 q^{94} +80.9145i q^{95} +(65.3542 + 184.238i) q^{96} -487.900 q^{97} -241.219i q^{98} +(-299.920 + 243.408i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 144 q^{4} - 64 q^{7} + 20 q^{9} - 8 q^{10} + 248 q^{16} + 88 q^{18} + 308 q^{19} - 840 q^{25} - 420 q^{28} + 328 q^{31} - 180 q^{33} + 540 q^{36} + 1152 q^{39} + 44 q^{40} - 1568 q^{45} - 84 q^{49}+ \cdots - 988 q^{97}+O(q^{100}) $ 28 * q - 144 * q^4 - 64 * q^7 + 20 * q^9 - 8 * q^10 + 248 * q^16 + 88 * q^18 + 308 * q^19 - 840 * q^25 - 420 * q^28 + 328 * q^31 - 180 * q^33 + 540 * q^36 + 1152 * q^39 + 44 * q^40 - 1568 * q^45 - 84 * q^49 + 1620 * q^51 - 200 * q^63 + 148 * q^64 + 2052 * q^66 - 748 * q^67 - 288 * q^69 - 2068 * q^70 - 628 * q^72 + 4560 * q^76 - 3312 * q^78 + 164 * q^81 - 5396 * q^82 + 5688 * q^87 - 1312 * q^90 - 1368 * q^93 - 932 * q^94 - 988 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	2.97231i		−	1.05087i	−0.850834	−	0.525435i	$-0.823903\pi$
$2$		−	2.97231i		−	1.05087i	0.850834	−	0.525435i	$-0.176097\pi$
$3$	4.89717	−	1.73716i	0.942461	−	0.334316i
$3$	4.89717	−	1.73716i	0.942461	−	0.334316i
$4$	−0.834616			−0.104327
$5$			8.81124i			0.788101i	0.919089	+	0.394051i	$0.128926\pi$
$5$			8.81124i			0.788101i	−0.919089	+	0.394051i	$0.871074\pi$
$6$	−5.16337	−	14.5559i	−0.351323	−	0.990404i
$7$	20.5950			1.11203			0.556014	−	0.831173i	$-0.312330\pi$
$7$	20.5950			1.11203			0.556014	+	0.831173i	$0.312330\pi$
$8$		−	21.2977i		−	0.941236i
$9$	20.9646	−	17.0143i	0.776465	−	0.630160i
$10$	26.1897			0.828191
$11$	−14.3060			−0.392130			−0.196065	−	0.980591i	$-0.562816\pi$
$11$	−14.3060			−0.392130			−0.196065	+	0.980591i	$0.562816\pi$
$12$	−4.08726	+	1.44986i	−0.0983242	+	0.0348782i
$13$			20.9481i			0.446920i	0.974713	+	0.223460i	$0.0717352\pi$
$13$			20.9481i			0.446920i	−0.974713	+	0.223460i	$0.928265\pi$
$14$		−	61.2148i		−	1.16860i
$15$	15.3065	+	43.1501i	0.263475	+	0.742754i
$16$	−69.9803			−1.09344
$17$	−72.5833			−1.03553			−0.517766	−	0.855522i	$-0.673236\pi$
$17$	−72.5833			−1.03553			−0.517766	+	0.855522i	$0.673236\pi$
$18$	−50.5718	−	62.3132i	−0.662216	−	0.815964i
$19$	9.18310			0.110881			0.0554407	−	0.998462i	$-0.482344\pi$
$19$	9.18310			0.110881			0.0554407	+	0.998462i	$0.482344\pi$
$20$		−	7.35400i		−	0.0822202i
$21$	100.857	−	35.7768i	1.04804	−	0.371769i
$22$			42.5220i			0.412078i
$23$	−124.620			−1.12978			−0.564892	−	0.825165i	$-0.691082\pi$
$23$	−124.620			−1.12978			−0.564892	+	0.825165i	$0.691082\pi$
$24$	−36.9975	−	104.299i	−0.314670	−	0.887078i
$25$	47.3621			0.378897
$26$	62.2643			0.469655
$27$	73.1105	−	119.741i	0.521116	−	0.853486i
$28$	−17.1890			−0.116015
$29$	−4.57622			−0.0293029			−0.0146514	−	0.999893i	$-0.504664\pi$
$29$	−4.57622			−0.0293029			−0.0146514	+	0.999893i	$0.504664\pi$
$30$	128.256	−	45.4957i	0.780538	−	0.276878i
$31$	−34.3496	+	169.148i	−0.199012	+	0.979997i
$31$	−34.3496	+	169.148i	−0.199012	+	0.979997i
$32$			37.6213i			0.207830i
$33$	−70.0591	+	24.8518i	−0.369568	+	0.131096i
$34$			215.740i			1.08821i
$35$			181.468i			0.876390i
$36$	−17.4974	+	14.2004i	−0.0810063	+	0.0657427i
$37$		−	164.987i		−	0.733071i	−0.930404	−	0.366536i	$-0.880544\pi$
$37$		−	164.987i		−	0.733071i	0.930404	−	0.366536i	$-0.119456\pi$
$38$		−	27.2950i		−	0.116522i
$39$	36.3902	+	102.587i	0.149413	+	0.421205i
$40$	187.659			0.741789
$41$			301.602i			1.14884i	0.818562	+	0.574418i	$0.194771\pi$
$41$			301.602i			1.14884i	−0.818562	+	0.574418i	$0.805229\pi$
$42$	−106.340	−	299.779i	−0.390680	−	1.10136i
$43$			114.689i			0.406742i	0.979102	+	0.203371i	$0.0651898\pi$
$43$			114.689i			0.406742i	−0.979102	+	0.203371i	$0.934810\pi$
$44$	11.9401			0.0409098
$45$	149.917	+	184.724i	0.496630	+	0.611933i
$46$			370.408i			1.18726i
$47$			313.591i			0.973234i	0.873615	+	0.486617i	$0.161769\pi$
$47$			313.591i			0.973234i	−0.873615	+	0.486617i	$0.838231\pi$
$48$	−342.706	+	121.567i	−1.03053	+	0.365556i
$49$	81.1555			0.236605
$50$		−	140.775i		−	0.398171i
$51$	−355.453	+	126.089i	−0.975949	+	0.346195i
$52$		−	17.4836i		−	0.0466259i
$53$	704.030			1.82464			0.912321	−	0.409476i	$-0.134289\pi$
$53$	704.030			1.82464			0.912321	+	0.409476i	$0.134289\pi$
$54$	−355.906	−	217.307i	−0.896902	−	0.547625i
$55$		−	126.054i		−	0.309038i
$56$		−	438.628i		−	1.04668i
$57$	44.9712	−	15.9525i	0.104501	−	0.0370695i
$58$			13.6019i			0.0307935i
$59$		−	81.5758i		−	0.180005i	−0.995942	−	0.0900023i	$-0.971313\pi$
$59$		−	81.5758i		−	0.180005i	0.995942	−	0.0900023i	$-0.0286874\pi$
$60$	−12.7751	−	36.0138i	−0.0274875	−	0.0774894i
$61$			210.196i			0.441194i	0.975365	+	0.220597i	$0.0708005\pi$
$61$			210.196i			0.441194i	−0.975365	+	0.220597i	$0.929199\pi$
$62$	502.761	+	102.098i	1.02985	+	0.209136i
$63$	431.766	−	350.410i	0.863451	−	0.700755i
$64$	−448.021			−0.875040
$65$	−184.579			−0.352218
$66$	73.8674	+	208.237i	0.137764	+	0.388367i
$67$	−789.501			−1.43960			−0.719798	−	0.694184i	$-0.755765\pi$
$67$	−789.501			−1.43960			−0.719798	+	0.694184i	$0.755765\pi$
$68$	60.5792			0.108034
$69$	−610.284	+	216.484i	−1.06478	+	0.377705i
$70$	539.378			0.920972
$71$		−	650.622i		−	1.08753i	−0.839238	−	0.543765i	$-0.816998\pi$
$71$		−	650.622i		−	1.08753i	0.839238	−	0.543765i	$-0.183002\pi$
$72$	−362.366	−	446.498i	−0.593129	−	0.730837i
$73$		−	960.640i		−	1.54020i	−0.637925	−	0.770098i	$-0.720207\pi$
$73$		−	960.640i		−	1.54020i	0.637925	−	0.770098i	$-0.279793\pi$
$74$	−490.391			−0.770362
$75$	231.940	−	82.2754i	0.357095	−	0.126671i
$76$	−7.66437			−0.0115679
$77$	−294.633			−0.436060
$78$	304.919	−	108.163i	0.442631	−	0.157013i
$79$			1140.44i			1.62417i	0.583541	+	0.812084i	$0.301667\pi$
$79$			1140.44i			1.62417i	−0.583541	+	0.812084i	$0.698333\pi$
$80$		−	616.613i		−	0.861743i
$81$	150.026	−	713.395i	0.205797	−	0.978595i
$82$	896.453			1.20728
$83$	−1079.90			−1.42813			−0.714063	−	0.700082i	$-0.753147\pi$
$83$	−1079.90			−1.42813			−0.714063	+	0.700082i	$0.753147\pi$
$84$	−84.1772	+	29.8599i	−0.109339	+	0.0387855i
$85$		−	639.549i		−	0.816104i
$86$	340.891			0.427433
$87$	−22.4105	+	7.94962i	−0.0276168	+	0.00979642i
$88$			304.686i			0.369087i
$89$	545.699			0.649932			0.324966	−	0.945726i	$-0.394647\pi$
$89$	545.699			0.649932			0.324966	+	0.945726i	$0.394647\pi$
$90$	549.056	−	445.600i	0.643062	−	0.521893i
$91$			431.427i			0.496988i
$92$	104.010			0.117867
$93$	125.621	+	888.018i	0.140068	+	0.990142i
$94$	932.090			1.02274
$95$			80.9145i			0.0873858i
$96$	65.3542	+	184.238i	0.0694811	+	0.195872i
$97$	−487.900			−0.510708			−0.255354	−	0.966848i	$-0.582192\pi$
$97$	−487.900			−0.510708			−0.255354	+	0.966848i	$0.582192\pi$
$98$		−	241.219i		−	0.248641i
$99$	−299.920	+	243.408i	−0.304476	+	0.247105i
$100$	−39.5292			−0.0395292
$101$			897.314i			0.884020i	0.897010	+	0.442010i	$0.145734\pi$
$101$			897.314i			0.884020i	−0.897010	+	0.442010i	$0.854266\pi$
$102$	374.774	+	1056.52i	0.363806	+	1.02559i
$103$	1853.14			1.77277			0.886385	−	0.462949i	$-0.153209\pi$
$103$	1853.14			1.77277			0.886385	+	0.462949i	$0.153209\pi$
$104$	446.147			0.420657
$105$	315.238	+	888.679i	0.292991	+	0.825963i
$106$		−	2092.59i		−	1.91746i
$107$		−	510.380i		−	0.461124i	−0.973058	−	0.230562i	$-0.925944\pi$
$107$		−	510.380i		−	0.461124i	0.973058	−	0.230562i	$-0.0740565\pi$
$108$	−61.0192	+	99.9376i	−0.0543665	+	0.0890417i
$109$	−1211.60			−1.06468			−0.532340	−	0.846531i	$-0.678687\pi$
$109$	−1211.60			−1.06468			−0.532340	+	0.846531i	$0.678687\pi$
$110$	−374.671			−0.324759
$111$	−286.608	−	807.968i	−0.245077	−	0.690891i
$112$	−1441.25			−1.21594
$113$		−	67.5004i		−	0.0561938i	−0.999605	−	0.0280969i	$-0.991055\pi$
$113$		−	67.5004i		−	0.0561938i	0.999605	−	0.0280969i	$-0.00894470\pi$
$114$	−47.4157	−	133.668i	−0.0389552	−	0.109817i
$115$		−	1098.05i		−	0.890384i
$116$	3.81939			0.00305708
$117$	356.418	+	439.168i	0.281631	+	0.347018i
$118$	−242.468			−0.189161
$119$	−1494.86			−1.15154
$120$	919.000	−	325.994i	0.699107	−	0.247992i
$121$	−1126.34			−0.846234
$122$	624.767			0.463637
$123$	523.929	+	1476.99i	0.384074	+	1.08273i
$124$	28.6687	−	141.174i	0.0207623	−	0.102240i
$125$			1518.72i			1.08671i
$126$	−1041.53	−	1283.34i	−0.736402	−	0.907374i
$127$		−	2487.42i		−	1.73798i	−0.494833	−	0.868988i	$-0.664771\pi$
$127$		−	2487.42i		−	1.73798i	0.494833	−	0.868988i	$-0.335229\pi$
$128$			1632.63i			1.12738i
$129$	199.233	+	561.652i	0.135980	+	0.383339i
$130$			548.625i			0.370136i
$131$		−	1191.93i		−	0.794956i	−0.917612	−	0.397478i	$-0.869885\pi$
$131$		−	1191.93i		−	0.794956i	0.917612	−	0.397478i	$-0.130115\pi$
$132$	58.4725	−	20.7418i	0.0385559	−	0.0136768i
$133$	189.126			0.123303
$134$			2346.64i			1.51283i
$135$	1055.06	+	644.194i	0.672633	+	0.410692i
$136$			1545.86i			0.974680i
$137$	1022.92			0.637912			0.318956	−	0.947770i	$-0.396668\pi$
$137$	1022.92			0.637912			0.318956	+	0.947770i	$0.396668\pi$
$138$	643.458	+	1813.95i	0.396919	+	1.11894i
$139$			1035.37i			0.631791i	0.948794	+	0.315896i	$0.102305\pi$
$139$			1035.37i			0.631791i	−0.948794	+	0.315896i	$0.897695\pi$
$140$		−	151.456i		−	0.0914312i
$141$	544.758	+	1535.71i	0.325368	+	0.917235i
$142$	−1933.85			−1.14285
$143$		−	299.685i		−	0.175251i
$144$	−1467.11	+	1190.67i	−0.849021	+	0.689044i
$145$		−	40.3222i		−	0.0230936i
$146$	−2855.32			−1.61855
$147$	397.432	−	140.980i	0.222991	−	0.0791009i
$148$			137.700i			0.0764791i
$149$		−	613.700i		−	0.337425i	−0.985665	−	0.168712i	$-0.946039\pi$
$149$		−	613.700i		−	0.337425i	0.985665	−	0.168712i	$-0.0539609\pi$
$150$	−244.548	−	689.398i	−0.133115	−	0.375261i
$151$		−	3139.09i		−	1.69176i	−0.533373	−	0.845880i	$-0.679076\pi$
$151$		−	3139.09i		−	1.69176i	0.533373	−	0.845880i	$-0.320924\pi$
$152$		−	195.579i		−	0.104366i
$153$	−1521.68	+	1234.96i	−0.804055	+	0.652551i
$154$			875.741i			0.458242i
$155$	−1490.40	−	302.663i	−0.772337	−	0.156842i
$156$	−30.3718	−	85.6204i	−0.0155878	−	0.0439431i
$157$	−666.763			−0.338939			−0.169470	−	0.985535i	$-0.554205\pi$
$157$	−666.763			−0.338939			−0.169470	+	0.985535i	$0.554205\pi$
$158$	3389.73			1.70679
$159$	3447.76	−	1223.01i	1.71965	−	0.610007i
$160$	−331.490			−0.163791
$161$	−2566.55			−1.25635
$162$	−2120.43	−	445.924i	−1.02838	−	0.216266i
$163$	1557.11			0.748235			0.374117	−	0.927381i	$-0.377946\pi$
$163$	1557.11			0.748235			0.374117	+	0.927381i	$0.377946\pi$
$164$		−	251.722i		−	0.119855i
$165$	−218.976	−	617.308i	−0.103316	−	0.291257i
$166$			3209.80i			1.50077i
$167$	1909.74			0.884909			0.442455	−	0.896791i	$-0.354108\pi$
$167$	1909.74			0.884909			0.442455	+	0.896791i	$0.354108\pi$
$168$	−761.965	−	2148.03i	−0.349922	−	0.986455i
$169$	1758.18			0.800262
$170$	−1900.94			−0.857619
$171$	192.520	−	156.244i	0.0860957	−	0.0698731i
$172$		−	95.7213i		−	0.0424342i
$173$			698.415i			0.306933i	0.988154	+	0.153467i	$0.0490438\pi$
$173$			698.415i			0.306933i	−0.988154	+	0.153467i	$0.950956\pi$
$174$	23.6287	+	66.6110i	0.0102948	+	0.0290217i
$175$	975.424			0.421344
$176$	1001.14			0.428772
$177$	−141.710	−	399.491i	−0.0601784	−	0.169647i
$178$		−	1621.99i		−	0.682994i
$179$	1176.98			0.491459			0.245730	−	0.969338i	$-0.420972\pi$
$179$	1176.98			0.491459			0.245730	+	0.969338i	$0.420972\pi$
$180$	−125.123	−	154.173i	−0.0518119	−	0.0638412i
$181$		−	4007.03i		−	1.64553i	−0.568383	−	0.822764i	$-0.692431\pi$
$181$		−	4007.03i		−	1.64553i	0.568383	−	0.822764i	$-0.307569\pi$
$182$	1282.33			0.522269
$183$	365.143	+	1029.37i	0.147498	+	0.415808i
$184$			2654.12i			1.06339i
$185$	1453.74			0.577734
$186$	2639.46	−	373.385i	1.04051	−	0.147193i
$187$	1038.38			0.406064
$188$		−	261.729i		−	0.101535i
$189$	1505.71	−	2466.07i	0.579495	−	0.949100i
$190$	240.503			0.0918311
$191$		−	5138.70i		−	1.94672i	−0.229281	−	0.973360i	$-0.573638\pi$
$191$		−	5138.70i		−	1.94672i	0.229281	−	0.973360i	$-0.426362\pi$
$192$	−2194.03	+	778.282i	−0.824691	+	0.292540i
$193$	3075.52			1.14705			0.573524	−	0.819188i	$-0.305576\pi$
$193$	3075.52			1.14705			0.573524	+	0.819188i	$0.305576\pi$
$194$			1450.19i			0.536688i
$195$	−903.914	+	320.643i	−0.331952	+	0.117752i
$196$	−67.7337			−0.0246843
$197$	2912.20			1.05323			0.526613	−	0.850105i	$-0.323462\pi$
$197$	2912.20			1.05323			0.526613	+	0.850105i	$0.323462\pi$
$198$	723.482	+	891.455i	0.259675	+	0.319964i
$199$		−	1476.08i		−	0.525812i	−0.964821	−	0.262906i	$-0.915319\pi$
$199$		−	1476.08i		−	0.525812i	0.964821	−	0.262906i	$-0.0846809\pi$
$200$		−	1008.71i		−	0.356631i
$201$	−3866.32	+	1371.49i	−1.35676	+	0.481280i
$202$	2667.09			0.928990
$203$	−94.2474			−0.0325856
$204$	296.667	−	105.236i	0.101818	−	0.0361175i
$205$	−2657.48			−0.905398
$206$		−	5508.10i		−	1.86295i
$207$	−2612.60	+	2120.32i	−0.877238	+	0.711944i
$208$		−	1465.96i		−	0.488682i
$209$	−131.374			−0.0434800
$210$	2641.43	−	936.985i	0.867980	−	0.307896i
$211$	−2951.37			−0.962940			−0.481470	−	0.876462i	$-0.659897\pi$
$211$	−2951.37			−0.962940			−0.481470	+	0.876462i	$0.659897\pi$
$212$	−587.595			−0.190359
$213$	−1130.23	−	3186.21i	−0.363579	−	1.02495i
$214$	−1517.01			−0.484581
$215$	−1010.55			−0.320554
$216$	−2550.21	−	1557.09i	−0.803331	−	0.490493i
$217$	−707.431	+	3483.61i	−0.221307	+	1.08978i
$218$			3601.25i			1.11884i
$219$	−1668.78	−	4704.42i	−0.514913	−	1.45158i
$220$			105.207i			0.0322411i
$221$		−	1520.48i		−	0.462800i
$222$	−2401.53	+	851.886i	−0.726036	+	0.257544i
$223$			2635.34i			0.791368i	0.918387	+	0.395684i	$0.129493\pi$
$223$			2635.34i			0.791368i	−0.918387	+	0.395684i	$0.870507\pi$
$224$			774.813i			0.231113i
$225$	992.926	−	805.834i	0.294200	−	0.238766i
$226$	−200.632			−0.0590524
$227$			303.631i			0.0887783i	0.999014	+	0.0443892i	$0.0141342\pi$
$227$			303.631i			0.0887783i	−0.999014	+	0.0443892i	$0.985866\pi$
$228$	−37.5337	+	13.3142i	−0.0109023	+	0.00386735i
$229$			4395.86i			1.26850i	0.773127	+	0.634251i	$0.218691\pi$
$229$			4395.86i			1.26850i	−0.773127	+	0.634251i	$0.781309\pi$
$230$	−3263.76			−0.935677
$231$	−1442.87	+	511.825i	−0.410969	+	0.145782i
$232$			97.4631i			0.0275809i
$233$		−	2353.50i		−	0.661728i	−0.943678	−	0.330864i	$-0.892660\pi$
$233$		−	2353.50i		−	0.661728i	0.943678	−	0.330864i	$-0.107340\pi$
$234$	1305.34	−	1059.38i	0.364671	−	0.295958i
$235$	−2763.13			−0.767007
$236$			68.0845i			0.0187793i
$237$	1981.12	+	5584.92i	0.542985	+	1.53071i
$238$			4443.17i			1.21012i
$239$	2368.19			0.640943			0.320472	−	0.947258i	$-0.396159\pi$
$239$	2368.19			0.640943			0.320472	+	0.947258i	$0.396159\pi$
$240$	−1071.15	−	3019.66i	−0.288095	−	0.812160i
$241$			5033.17i			1.34529i	0.739965	+	0.672645i	$0.234842\pi$
$241$			5033.17i			1.34529i	−0.739965	+	0.672645i	$0.765158\pi$
$242$			3347.82i			0.889281i
$243$	−504.576	−	3754.24i	−0.133204	−	0.991089i
$244$		−	175.433i		−	0.0460284i
$245$			715.080i			0.186469i
$246$	4390.08	−	1557.28i	1.13781	−	0.403612i
$247$			192.369i			0.0495552i
$248$	3602.47	+	731.569i	0.922408	+	0.187317i
$249$	−5288.45	+	1875.96i	−1.34595	+	0.477445i
$250$	4514.11			1.14199
$251$	6226.01			1.56567			0.782834	−	0.622231i	$-0.213774\pi$
$251$	6226.01			1.56567			0.782834	+	0.622231i	$0.213774\pi$
$252$	−360.359	+	292.458i	−0.0900813	+	0.0731077i
$253$	1782.82			0.443022
$254$	−7393.38			−1.82639
$255$	−1111.00	−	3131.98i	−0.272837	−	0.769146i
$256$	1268.50			0.309693
$257$			4278.00i			1.03834i	0.854670	+	0.519172i	$0.173760\pi$
$257$			4278.00i			1.03834i	−0.854670	+	0.519172i	$0.826240\pi$
$258$	1669.40	−	592.181i	0.402839	−	0.142898i
$259$		−	3397.90i		−	0.815195i
$260$	154.053			0.0367459
$261$	−95.9385	+	77.8613i	−0.0227527	+	0.0184655i
$262$	−3542.78			−0.835395
$263$	−5141.20			−1.20540			−0.602699	−	0.797969i	$-0.705908\pi$
$263$	−5141.20			−1.20540			−0.602699	+	0.797969i	$0.705908\pi$
$264$	529.288	+	1492.10i	0.123392	+	0.347850i
$265$			6203.38i			1.43800i
$266$		−	562.142i		−	0.129576i
$267$	2672.38	−	947.965i	0.612536	−	0.217283i
$268$	658.930			0.150189
$269$	−3194.61			−0.724085			−0.362043	−	0.932162i	$-0.617921\pi$
$269$	−3194.61			−0.724085			−0.362043	+	0.932162i	$0.617921\pi$
$270$	1914.74	−	3135.98i	0.431584	−	0.706850i
$271$		−	7237.20i		−	1.62225i	−0.584876	−	0.811123i	$-0.698857\pi$
$271$		−	7237.20i		−	1.62225i	0.584876	−	0.811123i	$-0.301143\pi$
$272$	5079.41			1.13230
$273$	749.457	+	2112.77i	0.166151	+	0.468391i
$274$		−	3040.43i		−	0.670362i
$275$	−677.564			−0.148577
$276$	509.353	−	180.681i	0.111085	−	0.0394048i
$277$		−	3547.29i		−	0.769445i	−0.923032	−	0.384722i	$-0.874297\pi$
$277$		−	3547.29i		−	0.769445i	0.923032	−	0.384722i	$-0.125703\pi$
$278$	3077.44			0.663930
$279$	2157.82	+	4130.55i	0.463029	+	0.886343i
$280$	3864.85			0.824889
$281$			8051.56i			1.70931i	0.519197	+	0.854655i	$0.326231\pi$
$281$			8051.56i			1.70931i	−0.519197	+	0.854655i	$0.673769\pi$
$282$	4564.61	−	1619.19i	0.963895	−	0.341919i
$283$	−2362.20			−0.496177			−0.248088	−	0.968737i	$-0.579802\pi$
$283$	−2362.20			−0.496177			−0.248088	+	0.968737i	$0.579802\pi$
$284$			543.020i			0.113459i
$285$	140.561	+	396.252i	0.0292145	+	0.0823577i
$286$	−890.755			−0.184166
$287$			6211.50i			1.27754i
$288$	640.101	+	788.715i	0.130966	+	0.161373i
$289$	355.341			0.0723267
$290$	−119.850			−0.0242684
$291$	−2389.33	+	847.559i	−0.481323	+	0.170738i
$292$			801.765i			0.160684i
$293$			1224.20i			0.244091i	0.992525	+	0.122045i	$0.0389453\pi$
$293$			1224.20i			0.244091i	−0.992525	+	0.122045i	$0.961055\pi$
$294$	−419.036	−	1181.29i	−0.0831247	−	0.234334i
$295$	718.784			0.141862
$296$	−3513.84			−0.689993
$297$	−1045.92	+	1713.02i	−0.204345	+	0.334678i
$298$	−1824.11			−0.354589
$299$		−	2610.55i		−	0.504923i
$300$	−193.581	+	68.6684i	−0.0372547	+	0.0132152i
$301$			2362.02i			0.452308i
$302$	−9330.36			−1.77782
$303$	1558.78	+	4394.30i	0.295542	+	0.833155i
$304$	−642.637			−0.121243
$305$	−1852.09			−0.347705
$306$	3670.67	+	4522.90i	0.685746	+	0.844957i
$307$	399.180			0.0742098			0.0371049	−	0.999311i	$-0.488186\pi$
$307$	399.180			0.0742098			0.0371049	+	0.999311i	$0.488186\pi$
$308$	245.906			0.0454928
$309$	9075.14	−	3219.20i	1.67077	−	0.592666i
$310$	−899.606	+	4429.94i	−0.164820	+	0.811625i
$311$		−	9440.04i		−	1.72121i	−0.509275	−	0.860604i	$-0.670086\pi$
$311$		−	9440.04i		−	1.72121i	0.509275	−	0.860604i	$-0.329914\pi$
$312$	2184.86	−	775.028i	0.396453	−	0.140632i
$313$		−	1973.12i		−	0.356317i	−0.984002	−	0.178158i	$-0.942986\pi$
$313$		−	1973.12i		−	0.356317i	0.984002	−	0.178158i	$-0.0570140\pi$
$314$			1981.82i			0.356181i
$315$	3087.55	+	3804.39i	0.552266	+	0.680487i
$316$		−	951.828i		−	0.169445i
$317$			3958.90i			0.701431i	0.936482	+	0.350716i	$0.114062\pi$
$317$			3958.90i			0.701431i	−0.936482	+	0.350716i	$0.885938\pi$
$318$	−3635.17	−	10247.8i	−0.641038	−	1.80713i
$319$	65.4676			0.0114905
$320$		−	3947.62i		−	0.689620i
$321$	−886.610	−	2499.42i	−0.154161	−	0.434591i
$322$			7628.57i			1.32026i
$323$	−666.540			−0.114821
$324$	−125.214	+	595.411i	−0.0214702	+	0.102094i
$325$			992.147i			0.169337i
$326$		−	4628.21i		−	0.786297i
$327$	−5933.41	+	2104.74i	−1.00342	+	0.355940i
$328$	6423.43			1.08132
$329$			6458.43i			1.08226i
$330$	−1834.83	+	650.863i	−0.306073	+	0.108572i
$331$			401.496i			0.0666714i	0.999444	+	0.0333357i	$0.0106130\pi$
$331$			401.496i			0.0666714i	−0.999444	+	0.0333357i	$0.989387\pi$
$332$	901.302			0.148992
$333$	−2807.13	−	3458.87i	−0.461952	−	0.569204i
$334$		−	5676.33i		−	0.929924i
$335$		−	6956.48i		−	1.13455i
$336$	−7058.04	+	2503.67i	−1.14597	+	0.406508i
$337$		−	1273.53i		−	0.205857i	−0.994689	−	0.102928i	$-0.967179\pi$
$337$		−	1273.53i		−	0.205857i	0.994689	−	0.102928i	$-0.0328213\pi$
$338$		−	5225.84i		−	0.840971i
$339$	−117.259	−	330.561i	−0.0187865	−	0.0529605i
$340$			533.778i			0.0851417i
$341$	491.407	−	2419.84i	0.0780386	−	0.384287i
$342$	−464.406	−	572.228i	−0.0734275	−	0.0904753i
$343$	−5392.70			−0.848916
$344$	2442.62			0.382840
$345$	−1907.49	−	5377.36i	−0.297670	−	0.839152i
$346$	2075.90			0.322547
$347$	−3855.03			−0.596394			−0.298197	−	0.954504i	$-0.596385\pi$
$347$	−3855.03			−0.596394			−0.298197	+	0.954504i	$0.596385\pi$
$348$	18.7042	−	6.63488i	0.00288118	−	0.00102203i
$349$	−7764.24			−1.19086			−0.595430	−	0.803407i	$-0.703018\pi$
$349$	−7764.24			−1.19086			−0.595430	+	0.803407i	$0.703018\pi$
$350$		−	2899.26i		−	0.442777i
$351$	2508.34	+	1531.53i	0.381440	+	0.232897i
$352$		−	538.212i		−	0.0814966i
$353$	5710.92			0.861081			0.430540	−	0.902571i	$-0.358323\pi$
$353$	5710.92			0.861081			0.430540	+	0.902571i	$0.358323\pi$
$354$	−1187.41	+	421.206i	−0.178277	+	0.0632397i
$355$	5732.78			0.857083
$356$	−455.449			−0.0678055
$357$	−7320.57	+	2596.80i	−1.08528	+	0.384978i
$358$		−	3498.33i		−	0.516460i
$359$			38.0667i			0.00559633i	0.999996	+	0.00279816i	$0.000890684\pi$
$359$			38.0667i			0.00559633i	−0.999996	+	0.00279816i	$0.999109\pi$
$360$	3934.20	−	3192.90i	0.575973	−	0.467445i
$361$	−6774.67			−0.987705
$362$	−11910.1			−1.72924
$363$	−5515.87	+	1956.62i	−0.797542	+	0.282910i
$364$		−	360.076i		−	0.0518492i
$365$	8464.42			1.21383
$366$	3059.59	−	1085.32i	0.436960	−	0.155001i
$367$		−	5616.01i		−	0.798783i	−0.916781	−	0.399391i	$-0.869221\pi$
$367$		−	5616.01i		−	0.798783i	0.916781	−	0.399391i	$-0.130779\pi$
$368$	8720.94			1.23535
$369$	5131.54	+	6322.95i	0.723950	+	0.892031i
$370$		−	4320.95i		−	0.607123i
$371$	14499.5			2.02905
$372$	−104.845	−	741.154i	−0.0146129	−	0.103299i
$373$	−1904.03			−0.264308			−0.132154	−	0.991229i	$-0.542189\pi$
$373$	−1904.03			−0.264308			−0.132154	+	0.991229i	$0.542189\pi$
$374$		−	3086.39i		−	0.426720i
$375$	2638.26	+	7437.45i	0.363305	+	1.02418i
$376$	6678.79			0.916043
$377$		−	95.8632i		−	0.0130960i
$378$	−7329.91	−	4475.45i	−0.997380	−	0.608974i
$379$	5603.29			0.759424			0.379712	−	0.925105i	$-0.376023\pi$
$379$	5603.29			0.759424			0.379712	+	0.925105i	$0.376023\pi$
$380$		−	67.5326i		−	0.00911670i
$381$	−4321.04	−	12181.3i	−0.581033	−	1.63797i
$382$	−15273.8			−2.04575
$383$	4230.36			0.564390			0.282195	−	0.959357i	$-0.408937\pi$
$383$	4230.36			0.564390			0.282195	+	0.959357i	$0.408937\pi$
$384$	2836.13	+	7995.25i	0.376903	+	1.06252i
$385$		−	2596.09i		−	0.343659i
$386$		−	9141.38i		−	1.20540i
$387$	1951.35	+	2404.41i	0.256312	+	0.315821i
$388$	407.209			0.0532807
$389$	−2788.06			−0.363394			−0.181697	−	0.983355i	$-0.558159\pi$
$389$	−2788.06			−0.363394			−0.181697	+	0.983355i	$0.558159\pi$
$390$	953.048	+	2686.71i	0.123742	+	0.348838i
$391$	9045.32			1.16993
$392$		−	1728.43i		−	0.222701i
$393$	−2070.57	−	5837.08i	−0.265767	−	0.749215i
$394$		−	8655.95i		−	1.10680i
$395$	−10048.7			−1.28001
$396$	250.318	−	203.152i	0.0317650	−	0.0257797i
$397$	11012.8			1.39223			0.696115	−	0.717931i	$-0.254911\pi$
$397$	11012.8			1.39223			0.696115	+	0.717931i	$0.254911\pi$
$398$	−4387.36			−0.552560
$399$	926.184	−	328.542i	0.116209	−	0.0412223i
$400$	−3314.42			−0.414302
$401$	−564.094			−0.0702481			−0.0351241	−	0.999383i	$-0.511183\pi$
$401$	−564.094			−0.0702481			−0.0351241	+	0.999383i	$0.511183\pi$
$402$	4076.48	+	11491.9i	0.505762	+	1.42578i
$403$	−3543.34	−	719.560i	−0.437981	−	0.0889425i
$404$		−	748.913i		−	0.0922272i
$405$	6285.90	+	1321.92i	0.771231	+	0.162189i
$406$			280.132i			0.0342432i
$407$			2360.31i			0.287459i
$408$	2685.40	+	7570.34i	0.325851	+	0.918598i
$409$			97.0623i			0.0117345i	0.999983	+	0.00586726i	$0.00186762\pi$
$409$			97.0623i			0.0117345i	−0.999983	+	0.00586726i	$0.998132\pi$
$410$			7898.86i			0.951456i
$411$	5009.41	−	1776.97i	0.601207	−	0.213264i
$412$	−1546.66			−0.184948
$413$		−	1680.06i		−	0.200170i
$414$	6302.25	+	7765.45i	0.748161	+	0.921863i
$415$		−	9515.25i		−	1.12551i
$416$	−788.096			−0.0928836
$417$	1798.60	+	5070.39i	0.211218	+	0.595438i
$418$			390.484i			0.0456918i
$419$			14853.7i			1.73186i	0.500163	+	0.865932i	$0.333274\pi$
$419$			14853.7i			1.73186i	−0.500163	+	0.865932i	$0.666726\pi$
$420$	−263.103	−	741.706i	−0.0305669	−	0.0861703i
$421$	15742.8			1.82246			0.911230	−	0.411898i	$-0.135134\pi$
$421$	15742.8			1.82246			0.911230	+	0.411898i	$0.135134\pi$
$422$			8772.37i			1.01192i
$423$	5335.54	+	6574.31i	0.613293	+	0.755683i
$424$		−	14994.2i		−	1.71742i
$425$	−3437.70			−0.392360
$426$	−9470.39	+	3359.40i	−1.07709	+	0.382074i
$427$			4328.99i			0.490620i
$428$			425.971i			0.0481077i
$429$	−520.600	−	1467.61i	−0.0585892	−	0.165167i
$430$			3003.67i			0.336860i
$431$		−	5617.52i		−	0.627810i	−0.949454	−	0.313905i	$-0.898363\pi$
$431$		−	5617.52i		−	0.627810i	0.949454	−	0.313905i	$-0.101637\pi$
$432$	−5116.30	+	8379.50i	−0.569810	+	0.933238i
$433$			5536.92i			0.614521i	0.951625	+	0.307260i	$0.0994123\pi$
$433$			5536.92i			0.614521i	−0.951625	+	0.307260i	$0.900588\pi$
$434$	10354.4	+	2102.70i	1.14522	+	0.232565i
$435$	−70.0460	−	197.465i	−0.00772057	−	0.0217648i
$436$	1011.22			0.111075
$437$	−1144.40			−0.125272
$438$	−13983.0	+	4960.14i	−1.52542	+	0.541106i
$439$	−8842.62			−0.961356			−0.480678	−	0.876897i	$-0.659609\pi$
$439$	−8842.62			−0.961356			−0.480678	+	0.876897i	$0.659609\pi$
$440$	−2684.66			−0.290878
$441$	1701.39	−	1380.81i	0.183716	−	0.149099i
$442$	−4519.35			−0.486343
$443$			3372.59i			0.361708i	0.983510	+	0.180854i	$0.0578861\pi$
$443$			3372.59i			0.361708i	−0.983510	+	0.180854i	$0.942114\pi$
$444$	239.207	+	674.343i	0.0255682	+	0.0720786i
$445$			4808.28i			0.512212i
$446$	7833.03			0.831625
$447$	−1066.09	−	3005.40i	−0.112807	−	0.318010i
$448$	−9227.00			−0.973069
$449$	−10281.5			−1.08065			−0.540325	−	0.841456i	$-0.681699\pi$
$449$	−10281.5			−1.08065			−0.540325	+	0.841456i	$0.681699\pi$
$450$	−2395.19	−	2951.28i	−0.250911	−	0.309166i
$451$		−	4314.73i		−	0.450493i
$452$			56.3369i			0.00586254i
$453$	−5453.10	−	15372.7i	−0.565583	−	1.59442i
$454$	902.484			0.0932944
$455$	−3801.41			−0.391676
$456$	−339.752	−	957.785i	−0.0348911	−	0.0983605i
$457$			3641.99i			0.372791i	0.982475	+	0.186395i	$0.0596805\pi$
$457$			3641.99i			0.372791i	−0.982475	+	0.186395i	$0.940319\pi$
$458$	13065.9			1.33303
$459$	−5306.61	+	8691.18i	−0.539632	+	0.883812i
$460$			916.454i			0.0928911i
$461$	8668.14			0.875738			0.437869	−	0.899039i	$-0.355733\pi$
$461$	8668.14			0.875738			0.437869	+	0.899039i	$0.355733\pi$
$462$	1521.30	+	4288.66i	0.153198	+	0.431875i
$463$			14408.6i			1.44628i	0.690703	+	0.723138i	$0.257301\pi$
$463$			14408.6i			1.44628i	−0.690703	+	0.723138i	$0.742699\pi$
$464$	320.246			0.0320410
$465$	−7824.54	+	1106.88i	−0.780332	+	0.110388i
$466$	−6995.32			−0.695390
$467$			13348.0i			1.32264i	0.750104	+	0.661320i	$0.230004\pi$
$467$			13348.0i			1.32264i	−0.750104	+	0.661320i	$0.769996\pi$
$468$	−297.472	−	366.537i	−0.0293817	−	0.0362034i
$469$	−16259.8			−1.60087
$470$			8212.87i			0.806024i
$471$	−3265.25	+	1158.27i	−0.319437	+	0.113313i
$472$	−1737.38			−0.169427
$473$		−	1640.75i		−	0.159496i
$474$	16600.1	−	5888.50i	1.60858	−	0.570607i
$475$	434.931			0.0420126
$476$	1247.63			0.120137
$477$	14759.7	−	11978.6i	1.41677	−	1.14982i
$478$		−	7038.99i		−	0.673548i
$479$		−	12332.9i		−	1.17642i	−0.808709	−	0.588208i	$-0.799833\pi$
$479$		−	12332.9i		−	1.17642i	0.808709	−	0.588208i	$-0.200167\pi$
$480$	−1623.37	+	575.851i	−0.154367	+	0.0547581i
$481$	3456.16			0.327624
$482$	14960.1			1.41372
$483$	−12568.8	+	4458.50i	−1.18406	+	0.420018i
$484$	940.059			0.0882851
$485$		−	4299.00i		−	0.402490i
$486$	−11158.8	+	1499.76i	−1.04150	+	0.139980i
$487$			8959.38i			0.833651i	0.908986	+	0.416826i	$0.136857\pi$
$487$			8959.38i			0.833651i	−0.908986	+	0.416826i	$0.863143\pi$
$488$	4476.69			0.415267
$489$	7625.43	−	2704.95i	0.705182	−	0.250147i
$490$	2125.44			0.195954
$491$	−19485.3			−1.79096			−0.895478	−	0.445105i	$-0.853166\pi$
$491$	−19485.3			−1.79096			−0.895478	+	0.445105i	$0.853166\pi$
$492$	−437.280	−	1232.72i	−0.0400693	−	0.112958i
$493$	332.157			0.0303440
$494$	571.779			0.0520760
$495$	−2144.72	−	2642.67i	−0.194744	−	0.239958i
$496$	2403.80	−	11837.0i	0.217608	−	1.07157i
$497$		−	13399.6i		−	1.20936i
$498$	5575.92	+	15718.9i	0.501733	+	1.41442i
$499$			19575.1i			1.75612i	0.478554	+	0.878058i	$0.341161\pi$
$499$			19575.1i			1.75612i	−0.478554	+	0.878058i	$0.658839\pi$
$500$		−	1267.55i		−	0.113373i
$501$	9352.31	−	3317.51i	0.833992	−	0.295839i
$502$		−	18505.6i		−	1.64531i
$503$			5482.86i			0.486021i	0.970024	+	0.243011i	$0.0781350\pi$
$503$			5482.86i			0.486021i	−0.970024	+	0.243011i	$0.921865\pi$
$504$	−7462.95	−	9195.64i	−0.659575	−	0.812711i
$505$	−7906.44			−0.696697
$506$		−	5299.08i		−	0.465559i
$507$	8610.09	−	3054.23i	0.754216	−	0.267541i
$508$			2076.04i			0.181318i
$509$	−16074.3			−1.39976			−0.699882	−	0.714258i	$-0.746764\pi$
$509$	−16074.3			−1.39976			−0.699882	+	0.714258i	$0.746764\pi$
$510$	−9309.21	+	3302.23i	−0.808272	+	0.286716i
$511$		−	19784.4i		−	1.71274i
$512$			9290.63i			0.801937i
$513$	671.382	−	1099.59i	0.0577821	−	0.0946358i
$514$	12715.5			1.09116
$515$			16328.5i			1.39712i
$516$	−166.283	−	468.764i	−0.0141864	−	0.0399926i
$517$		−	4486.25i		−	0.381635i
$518$	−10099.6			−0.856664
$519$	1213.26	+	3420.26i	0.102613	+	0.289273i
$520$			3931.11i			0.331520i
$521$		−	14626.0i		−	1.22990i	−0.788566	−	0.614950i	$-0.789176\pi$
$521$		−	14626.0i		−	1.22990i	0.788566	−	0.614950i	$-0.210824\pi$
$522$	231.428	+	285.159i	0.0194048	+	0.0239101i
$523$			7530.66i			0.629623i	0.949154	+	0.314811i	$0.101941\pi$
$523$			7530.66i			0.629623i	−0.949154	+	0.314811i	$0.898059\pi$
$524$			994.803i			0.0829354i
$525$	4776.82	−	1694.47i	0.397100	−	0.140862i
$526$			15281.2i			1.26672i
$527$	2493.21	−	12277.3i	0.206083	−	1.01482i
$528$	4902.76	−	1739.14i	0.404101	−	0.143345i
$529$	3363.09			0.276411
$530$	18438.3			1.51115
$531$	−1387.96	−	1710.20i	−0.113432	−	0.139767i
$532$	−157.848			−0.0128639
$533$	−6317.99			−0.513438
$534$	−2817.64	−	7943.14i	−0.228336	−	0.643695i
$535$	4497.08			0.363412
$536$			16814.6i			1.35500i
$537$	5763.85	−	2044.59i	0.463181	−	0.164303i
$538$			9495.37i			0.760919i
$539$	−1161.01			−0.0927800
$540$	−880.574	−	537.655i	−0.0701738	−	0.0428463i
$541$	9029.58			0.717582			0.358791	−	0.933418i	$-0.383189\pi$
$541$	9029.58			0.717582			0.358791	+	0.933418i	$0.383189\pi$
$542$	−21511.2			−1.70477
$543$	−6960.85	−	19623.1i	−0.550127	−	1.55085i
$544$		−	2730.68i		−	0.215215i
$545$		−	10675.7i		−	0.839075i
$546$	6279.81	−	2227.62i	0.492218	−	0.174603i
$547$	−163.580			−0.0127864			−0.00639322	−	0.999980i	$-0.502035\pi$
$547$	−163.580			−0.0127864			−0.00639322	+	0.999980i	$0.502035\pi$
$548$	−853.745			−0.0665514
$549$	3576.34	+	4406.67i	0.278023	+	0.342572i
$550$			2013.93i			0.156135i
$551$	−42.0239			−0.00324914
$552$	4610.62	+	12997.7i	0.355509	+	1.00221i
$553$			23487.4i			1.80612i
$554$	−10543.6			−0.808586
$555$	7119.19	−	2525.37i	0.544492	−	0.193146i
$556$		−	864.137i		−	0.0659129i
$557$	−5158.90			−0.392441			−0.196221	−	0.980560i	$-0.562867\pi$
$557$	−5158.90			−0.392441			−0.196221	+	0.980560i	$0.562867\pi$
$558$	12277.3	−	6413.69i	0.931431	−	0.486583i
$559$	−2402.52			−0.181781
$560$		−	12699.2i		−	0.958282i
$561$	5085.13	−	1803.83i	0.382699	−	0.135754i
$562$	23931.7			1.79626
$563$		−	9206.84i		−	0.689204i	−0.938749	−	0.344602i	$-0.888014\pi$
$563$		−	9206.84i		−	0.689204i	0.938749	−	0.344602i	$-0.111986\pi$
$564$	−454.664	−	1281.73i	−0.0339447	−	0.0956924i
$565$	594.762			0.0442864
$566$			7021.18i			0.521417i
$567$	3089.80	−	14692.4i	0.228852	−	1.08822i
$568$	−13856.8			−1.02362
$569$	9467.71			0.697552			0.348776	−	0.937206i	$-0.386597\pi$
$569$	9467.71			0.697552			0.348776	+	0.937206i	$0.386597\pi$
$570$	1177.78	−	417.791i	0.0865472	−	0.0307006i
$571$			2989.83i			0.219125i	0.993980	+	0.109563i	$0.0349450\pi$
$571$			2989.83i			0.219125i	−0.993980	+	0.109563i	$0.965055\pi$
$572$			250.122i			0.0182834i
$573$	−8926.74	−	25165.1i	−0.650820	−	1.83471i
$574$	18462.5			1.34252
$575$	−5902.26			−0.428071
$576$	−9392.56	+	7622.76i	−0.679439	+	0.551415i
$577$	17108.6			1.23438			0.617191	−	0.786813i	$-0.288270\pi$
$577$	17108.6			1.23438			0.617191	+	0.786813i	$0.288270\pi$
$578$		−	1056.18i		−	0.0760059i
$579$	15061.3	−	5342.65i	1.08105	−	0.383477i
$580$			33.6535i			0.00240929i
$581$	−22240.6			−1.58811
$582$	2519.21	+	7101.82i	0.179423	+	0.505807i
$583$	−10071.9			−0.715497
$584$	−20459.4			−1.44969
$585$	−3869.62	+	3140.48i	−0.273485	+	0.221954i
$586$	3638.70			0.256507
$587$	24548.3			1.72610			0.863048	−	0.505121i	$-0.168552\pi$
$587$	24548.3			1.72610			0.863048	+	0.505121i	$0.168552\pi$
$588$	−331.704	+	117.664i	−0.0232640	+	0.00825236i
$589$	−315.436	+	1553.31i	−0.0220667	+	0.108664i
$590$		−	2136.45i		−	0.149078i
$591$	14261.5	−	5058.95i	0.992624	−	0.352110i
$592$			11545.8i			0.801571i
$593$		−	10603.5i		−	0.734287i	−0.930164	−	0.367144i	$-0.880336\pi$
$593$		−	10603.5i		−	0.734287i	0.930164	−	0.367144i	$-0.119664\pi$
$594$	5091.61	+	3108.80i	0.351703	+	0.214740i
$595$		−	13171.5i		−	0.907530i
$596$			512.204i			0.0352025i
$597$	−2564.18	−	7228.62i	−0.175787	−	0.495557i
$598$	−7759.36			−0.530608
$599$			5005.13i			0.341409i	0.985322	+	0.170705i	$0.0546044\pi$
$599$			5005.13i			0.341409i	−0.985322	+	0.170705i	$0.945396\pi$
$600$	−1752.28	−	4939.80i	−0.119228	−	0.336111i
$601$		−	18720.9i		−	1.27062i	−0.772258	−	0.635310i	$-0.780873\pi$
$601$		−	18720.9i		−	1.27062i	0.772258	−	0.635310i	$-0.219127\pi$
$602$	7020.66			0.475317
$603$	−16551.5	+	13432.8i	−1.11780	+	0.907175i
$604$			2619.94i			0.176496i
$605$		−	9924.42i		−	0.666918i
$606$	13061.2	−	4633.16i	0.875537	−	0.310576i
$607$	−2711.94			−0.181341			−0.0906707	−	0.995881i	$-0.528901\pi$
$607$	−2711.94			−0.181341			−0.0906707	+	0.995881i	$0.528901\pi$
$608$			345.481i			0.0230445i
$609$	−461.546	+	163.723i	−0.0307106	+	0.0108939i
$610$			5504.97i			0.365393i
$611$	−6569.15			−0.434958
$612$	1270.02	−	1030.71i	0.0838847	−	0.0680787i
$613$			24789.5i			1.63334i	0.577104	+	0.816671i	$0.304183\pi$
$613$			24789.5i			1.63334i	−0.577104	+	0.816671i	$0.695817\pi$
$614$		−	1186.49i		−	0.0779848i
$615$	−13014.1	+	4616.47i	−0.853303	+	0.302689i
$616$			6275.02i			0.410435i
$617$			12412.2i			0.809879i	0.914343	+	0.404940i	$0.132707\pi$
$617$			12412.2i			0.809879i	−0.914343	+	0.404940i	$0.867293\pi$
$618$	−9568.44	−	26974.1i	−0.622814	−	1.75576i
$619$		−	14277.4i		−	0.927072i	−0.886078	−	0.463536i	$-0.846581\pi$
$619$		−	14277.4i		−	0.927072i	0.886078	−	0.463536i	$-0.153419\pi$
$620$	1243.92	+	252.607i	0.0805756	+	0.0163628i
$621$	−9111.02	+	14922.1i	−0.588748	+	0.964254i
$622$	−28058.7			−1.80876
$623$	11238.7			0.722743
$624$	−2546.60	−	7179.04i	−0.163374	−	0.460564i
$625$	−7461.57			−0.477540
$626$	−5864.71			−0.374443
$627$	−643.360	+	228.217i	−0.0409782	+	0.0145361i
$628$	556.491			0.0353605
$629$			11975.3i			0.759119i
$630$	11307.8	−	9177.15i	0.715103	−	0.580359i
$631$		−	7379.14i		−	0.465545i	−0.972531	−	0.232773i	$-0.925220\pi$
$631$		−	7379.14i		−	0.465545i	0.972531	−	0.232773i	$-0.0747798\pi$
$632$	24288.7			1.52872
$633$	−14453.3	+	5126.99i	−0.907534	+	0.321927i
$634$	11767.1			0.737113
$635$	21917.3			1.36970
$636$	−2877.55	+	1020.75i	−0.179406	+	0.0636402i
$637$			1700.06i			0.105744i
$638$		−	194.590i		−	0.0120751i
$639$	−11069.9	−	13640.0i	−0.685318	−	0.844429i
$640$	−14385.5			−0.888492
$641$	28893.9			1.78041			0.890204	−	0.455563i	$-0.150562\pi$
$641$	28893.9			1.78041			0.890204	+	0.455563i	$0.150562\pi$
$642$	−7429.04	+	2635.28i	−0.456699	+	0.162003i
$643$			7057.87i			0.432870i	0.976297	+	0.216435i	$0.0694429\pi$
$643$			7057.87i			0.432870i	−0.976297	+	0.216435i	$0.930557\pi$
$644$	2142.08			0.131071
$645$	−4948.85	+	1755.49i	−0.302109	+	0.107166i
$646$			1981.16i			0.120662i
$647$	−13569.4			−0.824525			−0.412262	−	0.911065i	$-0.635261\pi$
$647$	−13569.4			−0.824525			−0.412262	+	0.911065i	$0.635261\pi$
$648$	−15193.7	−	3195.22i	−0.921088	−	0.193704i
$649$			1167.03i			0.0705852i
$650$	2948.97			0.177951
$651$	2587.17	+	18288.8i	0.155759	+	1.10106i
$652$	−1299.59			−0.0780611
$653$		−	21670.4i		−	1.29867i	−0.760504	−	0.649333i	$-0.775048\pi$
$653$		−	21670.4i		−	1.29867i	0.760504	−	0.649333i	$-0.224952\pi$
$654$	6255.93	+	17635.9i	0.374046	+	1.05446i
$655$	10502.4			0.626506
$656$		−	21106.2i		−	1.25619i
$657$	−16344.6	−	20139.4i	−0.970570	−	1.19591i
$658$	19196.4			1.13732
$659$			23225.1i			1.37287i	0.727191	+	0.686435i	$0.240825\pi$
$659$			23225.1i			1.37287i	−0.727191	+	0.686435i	$0.759175\pi$
$660$	182.761	+	515.215i	0.0107787	+	0.0303859i
$661$	2397.07			0.141052			0.0705260	−	0.997510i	$-0.477532\pi$
$661$	2397.07			0.141052			0.0705260	+	0.997510i	$0.477532\pi$
$662$	1193.37			0.0700629
$663$	−2641.32	−	7446.07i	−0.154722	−	0.436171i
$664$			22999.4i			1.34420i
$665$			1666.44i			0.0971754i
$666$	−10280.8	+	8343.67i	−0.598160	+	0.485451i
$667$	570.288			0.0331059
$668$	−1593.90			−0.0923199
$669$	4577.99	+	12905.7i	0.264567	+	0.745834i
$670$	−20676.8			−1.19226
$671$		−	3007.07i		−	0.173005i
$672$	1345.97	+	3794.39i	0.0772648	+	0.217815i
$673$			14022.1i			0.803139i	0.915828	+	0.401570i	$0.131535\pi$
$673$			14022.1i			0.803139i	−0.915828	+	0.401570i	$0.868465\pi$
$674$	−3785.33			−0.216329
$675$	3462.67	−	5671.17i	0.197449	−	0.323383i
$676$	−1467.40			−0.0834890
$677$	18829.6			1.06895			0.534477	−	0.845183i	$-0.320509\pi$
$677$	18829.6			1.06895			0.534477	+	0.845183i	$0.320509\pi$
$678$	−982.529	+	348.529i	−0.0556546	+	0.0197422i
$679$	−10048.3			−0.567922
$680$	−13620.9			−0.768146
$681$	527.454	+	1486.93i	0.0296800	+	0.0836701i
$682$	−7192.51	−	1460.61i	−0.403835	−	0.0820084i
$683$			4208.36i			0.235766i	0.993027	+	0.117883i	$0.0376108\pi$
$683$			4208.36i			0.235766i	−0.993027	+	0.117883i	$0.962389\pi$
$684$	−160.680	+	130.404i	−0.00898210	+	0.00728965i
$685$			9013.18i			0.502739i
$686$			16028.8i			0.892100i
$687$	7636.31	+	21527.3i	0.424080	+	1.19551i
$688$		−	8025.98i		−	0.444749i
$689$			14748.1i			0.815469i
$690$	−15983.2	+	5669.66i	−0.881839	+	0.312812i
$691$	−30904.4			−1.70139			−0.850695	−	0.525660i	$-0.823818\pi$
$691$	−30904.4			−1.70139			−0.850695	+	0.525660i	$0.823818\pi$
$692$		−	582.908i		−	0.0320214i
$693$	−6176.86	+	5012.99i	−0.338585	+	0.274787i
$694$			11458.3i			0.626732i
$695$	−9122.89			−0.497915
$696$	169.309	+	477.294i	0.00922074	+	0.0259939i
$697$		−	21891.3i		−	1.18966i
$698$			23077.7i			1.25144i
$699$	−4088.39	−	11525.5i	−0.221226	−	0.623653i
$700$	−814.105			−0.0439575
$701$			30479.0i			1.64219i	0.570789	+	0.821097i	$0.306637\pi$
$701$			30479.0i			1.64219i	−0.570789	+	0.821097i	$0.693363\pi$
$702$	4552.17	−	7455.57i	0.244745	−	0.400844i
$703$		−	1515.09i		−	0.0812840i
$704$	6409.40			0.343130
$705$	−13531.5	+	4799.99i	−0.722874	+	0.256423i
$706$		−	16974.6i		−	0.904884i
$707$			18480.2i			0.983055i
$708$	118.273	+	333.421i	0.00627823	+	0.0176988i
$709$			20137.8i			1.06670i	0.845894	+	0.533352i	$0.179068\pi$
$709$			20137.8i			1.06670i	−0.845894	+	0.533352i	$0.820932\pi$
$710$		−	17039.6i		−	0.900683i
$711$	19403.8	+	23908.8i	1.02349	+	1.26111i
$712$		−	11622.2i		−	0.611739i
$713$	4280.64	−	21079.2i	0.224840	−	1.10718i
$714$	7718.49	+	21759.0i	0.404562	+	1.14049i
$715$	2640.59			0.138115
$716$	−982.322			−0.0512725
$717$	11597.4	−	4113.92i	0.604064	−	0.214278i
$718$	113.146			0.00588101
$719$	−19685.9			−1.02109			−0.510544	−	0.859852i	$-0.670556\pi$
$719$	−19685.9			−1.02109			−0.510544	+	0.859852i	$0.670556\pi$
$720$	−10491.3	−	12927.0i	−0.543036	−	0.669114i
$721$	38165.5			1.97137
$722$			20136.4i			1.03795i
$723$	8743.41	+	24648.3i	0.449752	+	1.26788i
$724$			3344.34i			0.171673i
$725$	−216.739			−0.0111028
$726$	5815.69	+	16394.9i	0.297301	+	0.838113i
$727$	33311.1			1.69937			0.849683	−	0.527294i	$-0.176793\pi$
$727$	33311.1			1.69937			0.849683	+	0.527294i	$0.176793\pi$
$728$	9188.42			0.467782
$729$	−8992.70	−	17508.6i	−0.456877	−	0.889530i
$730$		−	25158.9i		−	1.27558i
$731$		−	8324.51i		−	0.421194i
$732$	−304.755	−	859.125i	−0.0153880	−	0.0433800i
$733$	20598.6			1.03796			0.518982	−	0.854785i	$-0.326311\pi$
$733$	20598.6			1.03796			0.518982	+	0.854785i	$0.326311\pi$
$734$	−16692.5			−0.839416
$735$	1242.21	+	3501.87i	0.0623395	+	0.175739i
$736$		−	4688.36i		−	0.234803i
$737$	11294.6			0.564509
$738$	18793.7	−	15252.5i	0.937408	−	0.760777i
$739$		−	17265.4i		−	0.859427i	−0.902965	−	0.429713i	$-0.858615\pi$
$739$		−	17265.4i		−	0.859427i	0.902965	−	0.429713i	$-0.141385\pi$
$740$	−1213.31			−0.0602733
$741$	334.175	+	942.063i	0.0165671	+	0.0467038i
$742$		−	43097.1i		−	2.13227i
$743$	22772.4			1.12441			0.562206	−	0.826997i	$-0.309953\pi$
$743$	22772.4			1.12441			0.562206	+	0.826997i	$0.309953\pi$
$744$	18912.8	−	2675.44i	0.931957	−	0.131837i
$745$	5407.46			0.265925
$746$			5659.36i			0.277753i
$747$	−22639.6	+	18373.8i	−1.10889	+	0.899947i
$748$	−866.649			−0.0423634
$749$		−	10511.3i		−	0.512783i
$750$	22106.4	−	7841.73i	1.07628	−	0.381786i
$751$	−4265.09			−0.207237			−0.103619	−	0.994617i	$-0.533042\pi$
$751$	−4265.09			−0.207237			−0.103619	+	0.994617i	$0.533042\pi$
$752$		−	21945.2i		−	1.06418i
$753$	30489.9	−	10815.6i	1.47558	−	0.523428i
$754$	−284.935			−0.0137622
$755$	27659.3			1.33328
$756$	−1256.69	+	2058.22i	−0.0604570	+	0.0990168i
$757$			21433.9i			1.02910i	0.857461	+	0.514550i	$0.172041\pi$
$757$			21433.9i			1.02910i	−0.857461	+	0.514550i	$0.827959\pi$
$758$		−	16654.7i		−	0.798056i
$759$	8730.75	−	3097.03i	0.417531	−	0.148110i
$760$	1723.30			0.0822506
$761$	2976.92			0.141805			0.0709023	−	0.997483i	$-0.477412\pi$
$761$	2976.92			0.141805			0.0709023	+	0.997483i	$0.477412\pi$
$762$	−36206.7	+	12843.5i	−1.72130	+	0.610590i
$763$	−24952.9			−1.18395
$764$			4288.85i			0.203096i
$765$	−10881.5	−	13407.9i	−0.514276	−	0.633676i
$766$		−	12573.9i		−	0.593100i
$767$	1708.86			0.0804477
$768$	6212.07	−	2203.59i	0.291874	−	0.103535i
$769$	−25904.8			−1.21476			−0.607381	−	0.794410i	$-0.707780\pi$
$769$	−25904.8			−1.21476			−0.607381	+	0.794410i	$0.707780\pi$
$770$	−7716.37			−0.361141
$771$	7431.56	+	20950.1i	0.347135	+	0.978599i
$772$	−2566.87			−0.119668
$773$	−25452.7			−1.18431			−0.592155	−	0.805824i	$-0.701723\pi$
$773$	−25452.7			−1.18431			−0.592155	+	0.805824i	$0.701723\pi$
$774$	7146.63	−	5800.03i	0.331887	−	0.269351i
$775$	−1626.87	+	8011.21i	−0.0754050	+	0.371318i
$776$			10391.2i			0.480697i
$777$	−5902.70	−	16640.1i	−0.272533	−	0.768290i
$778$			8286.97i			0.381880i
$779$			2769.64i			0.127385i
$780$	754.421	−	267.613i	0.0346316	−	0.0122847i
$781$			9307.83i			0.426454i
$782$		−	26885.5i		−	1.22944i
$783$	−334.570	+	547.960i	−0.0152702	+	0.0250096i
$784$	−5679.29			−0.258714
$785$		−	5875.00i		−	0.267118i
$786$	−17349.6	+	6154.36i	−0.787327	+	0.279286i
$787$		−	34774.5i		−	1.57506i	−0.616273	−	0.787532i	$-0.711358\pi$
$787$		−	34774.5i		−	1.57506i	0.616273	−	0.787532i	$-0.288642\pi$
$788$	−2430.57			−0.109880
$789$	−25177.3	+	8931.07i	−1.13604	+	0.402984i
$790$			29867.7i			1.34512i
$791$		−	1390.17i		−	0.0624891i
$792$	5184.03	+	6387.61i	0.232584	+	0.286583i
$793$	−4403.21			−0.197178
$794$		−	32733.3i		−	1.46305i
$795$	10776.2	+	30379.0i	0.480747	+	1.35526i
$796$			1231.96i			0.0548564i
$797$	8714.80			0.387320			0.193660	−	0.981069i	$-0.437964\pi$
$797$	8714.80			0.387320			0.193660	+	0.981069i	$0.437964\pi$
$798$	−976.529	−	2752.90i	−0.0433192	−	0.122120i
$799$		−	22761.5i		−	1.00782i
$800$			1781.82i			0.0787463i
$801$	11440.3	−	9284.69i	0.504650	−	0.409561i
$802$			1676.66i			0.0738216i
$803$			13743.0i			0.603958i
$804$	3226.89	−	1144.67i	0.141547	−	0.0502105i
$805$		−	22614.5i		−	0.990131i
$806$	−2138.75	+	10531.9i	−0.0934670	+	0.460260i
$807$	−15644.6	+	5549.54i	−0.682422	+	0.242073i
$808$	19110.7			0.832071
$809$	−44038.8			−1.91387			−0.956936	−	0.290299i	$-0.906245\pi$
$809$	−44038.8			−1.91387			−0.956936	+	0.290299i	$0.906245\pi$
$810$	3929.14	−	18683.6i	0.170440	−	0.810464i
$811$	−19919.2			−0.862461			−0.431231	−	0.902242i	$-0.641920\pi$
$811$	−19919.2			−0.862461			−0.431231	+	0.902242i	$0.641920\pi$
$812$	78.6604			0.00339956
$813$	−12572.2	−	35441.8i	−0.542343	−	1.52890i
$814$	7015.55			0.302082
$815$			13720.1i			0.589685i
$816$	24874.7	−	8823.73i	1.06714	−	0.378545i
$817$			1053.20i			0.0451002i
$818$	288.499			0.0123315
$819$	7340.44	+	9044.69i	0.313182	+	0.385894i
$820$	2217.98			0.0944575
$821$	4036.09			0.171572			0.0857860	−	0.996314i	$-0.472660\pi$
$821$	4036.09			0.171572			0.0857860	+	0.996314i	$0.472660\pi$
$822$	−5281.71	−	14889.5i	−0.224113	−	0.631790i
$823$		−	18584.9i		−	0.787154i	−0.919292	−	0.393577i	$-0.871238\pi$
$823$		−	18584.9i		−	0.787154i	0.919292	−	0.393577i	$-0.128762\pi$
$824$		−	39467.7i		−	1.66859i
$825$	−3318.15	+	1177.04i	−0.140028	+	0.0496717i
$826$	−4993.65			−0.210353
$827$	−23115.7			−0.971962			−0.485981	−	0.873970i	$-0.661537\pi$
$827$	−23115.7			−0.971962			−0.485981	+	0.873970i	$0.661537\pi$
$828$	2180.52	−	1769.65i	0.0915196	−	0.0742750i
$829$			31598.8i			1.32385i	0.749570	+	0.661925i	$0.230260\pi$
$829$			31598.8i			1.32385i	−0.749570	+	0.661925i	$0.769740\pi$
$830$	−28282.3			−1.18276
$831$	−6162.21	−	17371.7i	−0.257238	−	0.725172i
$832$		−	9385.19i		−	0.391073i
$833$	−5890.54			−0.245012
$834$	15070.7	−	5346.00i	0.625728	−	0.221963i
$835$			16827.1i			0.697398i
$836$	109.647			0.00453614
$837$	17742.6	+	16479.6i	0.732705	+	0.680546i
$838$	44149.8			1.81996
$839$			4104.00i			0.168875i	0.996429	+	0.0844373i	$0.0269093\pi$
$839$			4104.00i			0.168875i	−0.996429	+	0.0844373i	$0.973091\pi$
$840$	18926.8	−	6713.85i	0.777426	−	0.275774i
$841$	−24368.1			−0.999141
$842$		−	46792.4i		−	1.91517i
$843$	13986.8	+	39429.9i	0.571450	+	1.61096i
$844$	2463.26			0.100461
$845$			15491.7i			0.630688i
$846$	19540.9	−	15858.9i	0.794124	−	0.644491i
$847$	−23197.0			−0.941035
$848$	−49268.3			−1.99514
$849$	−11568.1	+	4103.51i	−0.467627	+	0.165880i
$850$			10217.9i			0.412319i
$851$			20560.6i			0.828212i
$852$	943.311	+	2659.26i	0.0379311	+	0.106930i
$853$	24686.6			0.990918			0.495459	−	0.868631i	$-0.335000\pi$
$853$	24686.6			0.990918			0.495459	+	0.868631i	$0.335000\pi$
$854$	12867.1			0.515577
$855$	1376.70	+	1696.34i	0.0550670	+	0.0678521i
$856$	−10869.9			−0.434026
$857$		−	34020.0i		−	1.35601i	−0.735057	−	0.678006i	$-0.762845\pi$
$857$		−	34020.0i		−	1.35601i	0.735057	−	0.678006i	$-0.237155\pi$
$858$	−4362.18	+	1547.38i	−0.173569	+	0.0615696i
$859$		−	8931.78i		−	0.354771i	−0.984141	−	0.177386i	$-0.943236\pi$
$859$		−	8931.78i		−	0.354771i	0.984141	−	0.177386i	$-0.0567640\pi$
$860$	843.423			0.0334424
$861$	10790.3	+	30418.8i	0.427101	+	1.20403i
$862$	−16697.0			−0.659747
$863$	18976.2			0.748502			0.374251	−	0.927327i	$-0.377900\pi$
$863$	18976.2			0.748502			0.374251	+	0.927327i	$0.377900\pi$
$864$	4504.81	+	2750.52i	0.177380	+	0.108304i
$865$	−6153.90			−0.241895
$866$	16457.4			0.645781
$867$	1740.17	−	617.283i	0.0681651	−	0.0241800i
$868$	590.434	−	2907.48i	0.0230883	−	0.113694i
$869$		−	16315.1i		−	0.636886i
$870$	−586.925	+	208.198i	−0.0228720	+	0.00811331i
$871$		−	16538.6i		−	0.643384i
$872$			25804.3i			1.00211i
$873$	−10228.6	+	8301.28i	−0.396547	+	0.321828i
$874$			3401.50i			0.131645i
$875$			31278.2i			1.20845i
$876$	1392.79	+	3926.38i	0.0537193	+	0.151439i
$877$	6449.07			0.248312			0.124156	−	0.992263i	$-0.460378\pi$
$877$	6449.07			0.248312			0.124156	+	0.992263i	$0.460378\pi$
$878$			26283.0i			1.01026i
$879$	2126.63	+	5995.12i	0.0816034	+	0.230046i
$880$			8821.30i			0.337916i
$881$	−2648.84			−0.101296			−0.0506479	−	0.998717i	$-0.516129\pi$
$881$	−2648.84			−0.101296			−0.0506479	+	0.998717i	$0.516129\pi$
$882$	−4104.18	−	5057.06i	−0.156684	−	0.193061i
$883$		−	34477.6i		−	1.31400i	−0.753889	−	0.657001i	$-0.771825\pi$
$883$		−	34477.6i		−	1.31400i	0.753889	−	0.657001i	$-0.228175\pi$
$884$			1269.02i			0.0482826i
$885$	3520.01	−	1248.64i	0.133699	−	0.0474267i
$886$	10024.4			0.380107
$887$		−	37405.5i		−	1.41596i	−0.706233	−	0.707979i	$-0.749607\pi$
$887$		−	37405.5i		−	1.41596i	0.706233	−	0.707979i	$-0.250393\pi$
$888$	−17207.9	+	6104.09i	−0.650291	+	0.230676i
$889$		−	51228.5i		−	1.93268i
$890$	14291.7			0.538268
$891$	−2146.28	+	10205.9i	−0.0806994	+	0.383737i
$892$		−	2199.49i		−	0.0825611i
$893$			2879.74i			0.107914i
$894$	−8932.96	+	3168.76i	−0.334187	+	0.118545i
$895$			10370.6i			0.387320i
$896$			33624.0i			1.25368i
$897$	−4534.94	−	12784.3i	−0.168804	−	0.475870i
$898$			30559.6i			1.13562i
$899$	157.191	−	774.059i	0.00583162	−	0.0287167i
$900$	−828.712	+	672.562i	−0.0306930	+	0.0249097i
$901$	−51100.9			−1.88947
$902$	−12824.7			−0.473410
$903$	4103.21	+	11567.2i	0.151214	+	0.426283i
$904$	−1437.61			−0.0528916
$905$	35306.9			1.29684
$906$	−45692.3	+	16208.3i	−1.67553	+	0.594354i
$907$	4284.28			0.156844			0.0784219	−	0.996920i	$-0.475012\pi$
$907$	4284.28			0.156844			0.0784219	+	0.996920i	$0.475012\pi$
$908$		−	253.415i		−	0.00926198i
$909$	15267.2	+	18811.8i	0.557074	+	0.686411i
$910$			11299.0i			0.411601i
$911$	−27054.7			−0.983931			−0.491966	−	0.870615i	$-0.663721\pi$
$911$	−27054.7			−0.983931			−0.491966	+	0.870615i	$0.663721\pi$
$912$	−3147.10	+	1116.36i	−0.114266	+	0.0405334i
$913$	15449.1			0.560011
$914$	10825.1			0.391754
$915$	−9069.98	+	3217.36i	−0.327699	+	0.116243i
$916$		−	3668.86i		−	0.132339i
$917$		−	24547.8i		−	0.884013i
$918$	25832.9	+	15772.9i	0.928771	+	0.567083i
$919$	17395.7			0.624408			0.312204	−	0.950015i	$-0.398933\pi$
$919$	17395.7			0.624408			0.312204	+	0.950015i	$0.398933\pi$
$920$	−23386.1			−0.838061
$921$	1954.85	−	693.439i	0.0699398	−	0.0248095i
$922$		−	25764.4i		−	0.920287i
$923$	13629.3			0.486039
$924$	1204.24	−	427.177i	0.0428752	−	0.0152090i
$925$		−	7814.11i		−	0.277758i
$926$	42826.9			1.51985
$927$	38850.3	−	31529.9i	1.37649	−	1.11713i
$928$		−	172.163i		−	0.00609003i
$929$	10683.9			0.377317			0.188659	−	0.982043i	$-0.439586\pi$
$929$	10683.9			0.377317			0.188659	+	0.982043i	$0.439586\pi$
$930$	3289.98	+	23256.9i	0.116003	+	0.820027i
$931$	745.260			0.0262351
$932$			1964.27i			0.0690362i
$933$	−16398.8	−	46229.5i	−0.575427	−	1.62217i
$934$	39674.5			1.38992
$935$			9149.42i			0.320019i
$936$	9353.29	−	7590.89i	0.326626	−	0.265081i
$937$	10610.6			0.369940			0.184970	−	0.982744i	$-0.440781\pi$
$937$	10610.6			0.369940			0.184970	+	0.982744i	$0.440781\pi$
$938$			48329.1i			1.68231i
$939$	−3427.62	−	9662.69i	−0.119122	−	0.335815i
$940$	2306.15			0.0800196
$941$	−3765.52			−0.130449			−0.0652244	−	0.997871i	$-0.520776\pi$
$941$	−3765.52			−0.130449			−0.0652244	+	0.997871i	$0.520776\pi$
$942$	3442.74	+	9705.33i	0.119077	+	0.335687i
$943$		−	37585.5i		−	1.29794i
$944$			5708.70i			0.196825i
$945$	21729.1	+	13267.2i	0.747986	+	0.456701i
$946$	−4876.80			−0.167609
$947$	−26664.5			−0.914974			−0.457487	−	0.889216i	$-0.651250\pi$
$947$	−26664.5			−0.914974			−0.457487	+	0.889216i	$0.651250\pi$
$948$	−1653.47	−	4661.26i	−0.0566481	−	0.159695i
$949$	20123.6			0.688345
$950$		−	1292.75i		−	0.0441498i
$951$	6877.23	+	19387.4i	0.234500	+	0.661072i
$952$			31837.0i			1.08387i
$953$	16304.8			0.554211			0.277105	−	0.960840i	$-0.410625\pi$
$953$	16304.8			0.554211			0.277105	+	0.960840i	$0.410625\pi$
$954$	−35604.1	−	43870.3i	−1.20831	−	1.48884i
$955$	45278.3			1.53421
$956$	−1976.53			−0.0668677
$957$	320.606	−	113.728i	0.0108294	−	0.00384147i
$958$	−36657.1			−1.23626
$959$	21067.1			0.709375
$960$	−6857.63	−	19332.1i	−0.230551	−	0.649940i
$961$	−27431.2	−	11620.3i	−0.920788	−	0.390062i
$962$		−	10272.8i		−	0.344290i
$963$	−8683.76	−	10699.9i	−0.290582	−	0.358047i
$964$		−	4200.76i		−	0.140350i
$965$			27099.1i			0.903990i
$966$	13252.0	+	37358.4i	0.441384	+	1.24429i
$967$			35496.8i			1.18045i	0.807237	+	0.590227i	$0.200962\pi$
$967$			35496.8i			1.18045i	−0.807237	+	0.590227i	$0.799038\pi$
$968$			23988.4i			0.796505i
$969$	−3264.16	+	1157.89i	−0.108215	+	0.0383866i
$970$	−12778.0			−0.422964
$971$			3340.68i			0.110409i	0.998475	+	0.0552047i	$0.0175811\pi$
$971$			3340.68i			0.110409i	−0.998475	+	0.0552047i	$0.982419\pi$
$972$	421.128	+	3133.35i	0.0138968	+	0.103397i
$973$			21323.5i			0.702569i
$974$	26630.0			0.876059
$975$	1723.52	+	4858.71i	0.0566120	+	0.159593i
$976$		−	14709.6i		−	0.482420i
$977$			36129.2i			1.18309i	0.806273	+	0.591544i	$0.201481\pi$
$977$			36129.2i			1.18309i	−0.806273	+	0.591544i	$0.798519\pi$
$978$	−8039.93	−	22665.1i	−0.262872	−	0.741054i
$979$	−7806.79			−0.254858
$980$		−	596.818i		−	0.0194537i
$981$	−25400.6	+	20614.5i	−0.826687	+	0.670919i
$982$			57916.4i			1.88206i
$983$	−26337.7			−0.854568			−0.427284	−	0.904117i	$-0.640530\pi$
$983$	−26337.7			−0.854568			−0.427284	+	0.904117i	$0.640530\pi$
$984$	31456.6	−	11158.5i	1.01911	−	0.361504i
$985$			25660.1i			0.830048i
$986$		−	987.274i		−	0.0318876i
$987$	11219.3	+	31628.0i	0.361818	+	1.01999i
$988$		−	160.554i		−	0.00516995i
$989$		−	14292.5i		−	0.459531i
$990$	−7854.82	+	6374.77i	−0.252164	+	0.204650i
$991$			8193.25i			0.262631i	0.991341	+	0.131315i	$0.0419201\pi$
$991$			8193.25i			0.262631i	−0.991341	+	0.131315i	$0.958080\pi$
$992$	−6363.58	−	1292.28i	−0.203673	−	0.0413607i
$993$	697.462	+	1966.20i	0.0222893	+	0.0628352i
$994$	−39827.7			−1.27088
$995$	13006.1			0.414393
$996$	4413.83	−	1565.70i	0.140419	−	0.0498105i
$997$	−52032.0			−1.65283			−0.826414	−	0.563063i	$-0.809623\pi$
$997$	−52032.0			−1.65283			−0.826414	+	0.563063i	$0.809623\pi$
$998$	58183.2			1.84545
$999$	−19755.6	−	12062.3i	−0.625666	−	0.382015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.4.c.b.92.10	yes	28
3.2	odd	2	inner	93.4.c.b.92.19	yes	28
31.30	odd	2	inner	93.4.c.b.92.9	✓	28
93.92	even	2	inner	93.4.c.b.92.20	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.4.c.b.92.9	✓	28	31.30	odd	2	inner
93.4.c.b.92.10	yes	28	1.1	even	1	trivial
93.4.c.b.92.19	yes	28	3.2	odd	2	inner
93.4.c.b.92.20	yes	28	93.92	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	93.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.97231i q^{2} +(4.89717 - 1.73716i) q^{3} -0.834616 q^{4} +8.81124i q^{5} +(-5.16337 - 14.5559i) q^{6} +20.5950 q^{7} -21.2977i q^{8} +(20.9646 - 17.0143i) q^{9} +26.1897 q^{10} -14.3060 q^{11} +(-4.08726 + 1.44986i) q^{12} +20.9481i q^{13} -61.2148i q^{14} +(15.3065 + 43.1501i) q^{15} -69.9803 q^{16} -72.5833 q^{17} +(-50.5718 - 62.3132i) q^{18} +9.18310 q^{19} -7.35400i q^{20} +(100.857 - 35.7768i) q^{21} +42.5220i q^{22} -124.620 q^{23} +(-36.9975 - 104.299i) q^{24} +47.3621 q^{25} +62.2643 q^{26} +(73.1105 - 119.741i) q^{27} -17.1890 q^{28} -4.57622 q^{29} +(128.256 - 45.4957i) q^{30} +(-34.3496 + 169.148i) q^{31} +37.6213i q^{32} +(-70.0591 + 24.8518i) q^{33} +215.740i q^{34} +181.468i q^{35} +(-17.4974 + 14.2004i) q^{36} -164.987i q^{37} -27.2950i q^{38} +(36.3902 + 102.587i) q^{39} +187.659 q^{40} +301.602i q^{41} +(-106.340 - 299.779i) q^{42} +114.689i q^{43} +11.9401 q^{44} +(149.917 + 184.724i) q^{45} +370.408i q^{46} +313.591i q^{47} +(-342.706 + 121.567i) q^{48} +81.1555 q^{49} -140.775i q^{50} +(-355.453 + 126.089i) q^{51} -17.4836i q^{52} +704.030 q^{53} +(-355.906 - 217.307i) q^{54} -126.054i q^{55} -438.628i q^{56} +(44.9712 - 15.9525i) q^{57} +13.6019i q^{58} -81.5758i q^{59} +(-12.7751 - 36.0138i) q^{60} +210.196i q^{61} +(502.761 + 102.098i) q^{62} +(431.766 - 350.410i) q^{63} -448.021 q^{64} -184.579 q^{65} +(73.8674 + 208.237i) q^{66} -789.501 q^{67} +60.5792 q^{68} +(-610.284 + 216.484i) q^{69} +539.378 q^{70} -650.622i q^{71} +(-362.366 - 446.498i) q^{72} -960.640i q^{73} -490.391 q^{74} +(231.940 - 82.2754i) q^{75} -7.66437 q^{76} -294.633 q^{77} +(304.919 - 108.163i) q^{78} +1140.44i q^{79} -616.613i q^{80} +(150.026 - 713.395i) q^{81} +896.453 q^{82} -1079.90 q^{83} +(-84.1772 + 29.8599i) q^{84} -639.549i q^{85} +340.891 q^{86} +(-22.4105 + 7.94962i) q^{87} +304.686i q^{88} +545.699 q^{89} +(549.056 - 445.600i) q^{90} +431.427i q^{91} +104.010 q^{92} +(125.621 + 888.018i) q^{93} +932.090 q^{94} +80.9145i q^{95} +(65.3542 + 184.238i) q^{96} -487.900 q^{97} -241.219i q^{98} +(-299.920 + 243.408i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 144 q^{4} - 64 q^{7} + 20 q^{9} - 8 q^{10} + 248 q^{16} + 88 q^{18} + 308 q^{19} - 840 q^{25} - 420 q^{28} + 328 q^{31} - 180 q^{33} + 540 q^{36} + 1152 q^{39} + 44 q^{40} - 1568 q^{45} - 84 q^{49}+ \cdots - 988 q^{97}+O(q^{100}) \) 28 * q - 144 * q^4 - 64 * q^7 + 20 * q^9 - 8 * q^10 + 248 * q^16 + 88 * q^18 + 308 * q^19 - 840 * q^25 - 420 * q^28 + 328 * q^31 - 180 * q^33 + 540 * q^36 + 1152 * q^39 + 44 * q^40 - 1568 * q^45 - 84 * q^49 + 1620 * q^51 - 200 * q^63 + 148 * q^64 + 2052 * q^66 - 748 * q^67 - 288 * q^69 - 2068 * q^70 - 628 * q^72 + 4560 * q^76 - 3312 * q^78 + 164 * q^81 - 5396 * q^82 + 5688 * q^87 - 1312 * q^90 - 1368 * q^93 - 932 * q^94 - 988 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more