LMFDB - Embedded newform 30.5.f.a.7.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [30,5,Mod(7,30)] 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("30.7"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	30.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.10109889252$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.1
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	30.7
Dual form			30.5.f.a.13.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 - 2.00000i) q^{2} +(-3.67423 + 3.67423i) q^{3} +8.00000i q^{4} +(24.6742 + 4.02270i) q^{5} +14.6969 q^{6} +(44.4393 + 44.4393i) q^{7} +(16.0000 - 16.0000i) q^{8} -27.0000i q^{9} +(-41.3031 - 57.3939i) q^{10} +167.439 q^{11} +(-29.3939 - 29.3939i) q^{12} +(-223.621 + 223.621i) q^{13} -177.757i q^{14} +(-105.439 + 75.8786i) q^{15} -64.0000 q^{16} +(-71.0148 - 71.0148i) q^{17} +(-54.0000 + 54.0000i) q^{18} -272.211i q^{19} +(-32.1816 + 197.394i) q^{20} -326.561 q^{21} +(-334.879 - 334.879i) q^{22} +(87.6821 - 87.6821i) q^{23} +117.576i q^{24} +(592.636 + 198.514i) q^{25} +894.484 q^{26} +(99.2043 + 99.2043i) q^{27} +(-355.514 + 355.514i) q^{28} -839.832i q^{29} +(362.636 + 59.1214i) q^{30} +403.787 q^{31} +(128.000 + 128.000i) q^{32} +(-615.211 + 615.211i) q^{33} +284.059i q^{34} +(917.739 + 1275.27i) q^{35} +216.000 q^{36} +(-207.589 - 207.589i) q^{37} +(-544.422 + 544.422i) q^{38} -1643.27i q^{39} +(459.151 - 330.424i) q^{40} -1386.39 q^{41} +(653.121 + 653.121i) q^{42} +(568.393 - 568.393i) q^{43} +1339.51i q^{44} +(108.613 - 666.204i) q^{45} -350.729 q^{46} +(-2642.77 - 2642.77i) q^{47} +(235.151 - 235.151i) q^{48} +1548.70i q^{49} +(-788.243 - 1582.30i) q^{50} +521.850 q^{51} +(-1788.97 - 1788.97i) q^{52} +(-1378.64 + 1378.64i) q^{53} -396.817i q^{54} +(4131.44 + 673.559i) q^{55} +1422.06 q^{56} +(1000.17 + 1000.17i) q^{57} +(-1679.66 + 1679.66i) q^{58} -327.503i q^{59} +(-607.029 - 843.514i) q^{60} -4205.66 q^{61} +(-807.573 - 807.573i) q^{62} +(1199.86 - 1199.86i) q^{63} -512.000i q^{64} +(-6417.24 + 4618.11i) q^{65} +2460.84 q^{66} +(2832.99 + 2832.99i) q^{67} +(568.118 - 568.118i) q^{68} +644.330i q^{69} +(715.064 - 4386.02i) q^{70} +5339.03 q^{71} +(-432.000 - 432.000i) q^{72} +(6865.24 - 6865.24i) q^{73} +830.357i q^{74} +(-2906.87 + 1448.09i) q^{75} +2177.69 q^{76} +(7440.88 + 7440.88i) q^{77} +(-3286.54 + 3286.54i) q^{78} +4666.69i q^{79} +(-1579.15 - 257.453i) q^{80} -729.000 q^{81} +(2772.78 + 2772.78i) q^{82} +(4111.98 - 4111.98i) q^{83} -2612.49i q^{84} +(-1466.56 - 2037.91i) q^{85} -2273.57 q^{86} +(3085.74 + 3085.74i) q^{87} +(2679.03 - 2679.03i) q^{88} -9911.62i q^{89} +(-1549.63 + 1115.18i) q^{90} -19875.1 q^{91} +(701.457 + 701.457i) q^{92} +(-1483.61 + 1483.61i) q^{93} +10571.1i q^{94} +(1095.03 - 6716.60i) q^{95} -940.604 q^{96} +(-10688.9 - 10688.9i) q^{97} +(3097.40 - 3097.40i) q^{98} -4520.86i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} + 84 q^{5} - 28 q^{7} + 64 q^{8} - 224 q^{10} + 464 q^{11} - 336 q^{13} - 216 q^{15} - 256 q^{16} + 392 q^{17} - 216 q^{18} + 224 q^{20} - 1512 q^{21} - 928 q^{22} + 968 q^{23} + 1136 q^{25}+ \cdots + 23912 q^{98}+O(q^{100}) $ 4 * q - 8 * q^2 + 84 * q^5 - 28 * q^7 + 64 * q^8 - 224 * q^10 + 464 * q^11 - 336 * q^13 - 216 * q^15 - 256 * q^16 + 392 * q^17 - 216 * q^18 + 224 * q^20 - 1512 * q^21 - 928 * q^22 + 968 * q^23 + 1136 * q^25 + 1344 * q^26 + 224 * q^28 + 216 * q^30 - 560 * q^31 + 512 * q^32 - 756 * q^33 - 2296 * q^35 + 864 * q^36 + 2256 * q^37 + 1232 * q^38 + 896 * q^40 + 392 * q^41 + 3024 * q^42 + 216 * q^43 - 756 * q^45 - 3872 * q^46 - 9072 * q^47 - 3976 * q^50 + 4968 * q^51 - 2688 * q^52 - 4280 * q^53 + 10500 * q^55 - 896 * q^56 + 6264 * q^57 - 2192 * q^58 + 864 * q^60 - 4536 * q^61 + 1120 * q^62 - 756 * q^63 - 12912 * q^65 + 3024 * q^66 - 2248 * q^67 - 3136 * q^68 + 9856 * q^70 + 18064 * q^71 - 1728 * q^72 + 20524 * q^73 - 10584 * q^75 - 4928 * q^76 + 7336 * q^77 - 8208 * q^78 - 5376 * q^80 - 2916 * q^81 - 784 * q^82 - 336 * q^83 + 15944 * q^85 - 864 * q^86 + 8316 * q^87 + 7424 * q^88 - 3024 * q^90 - 52752 * q^91 + 7744 * q^92 - 7992 * q^93 + 23104 * q^95 - 40404 * q^97 + 23912 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$3$	−3.67423	+	3.67423i	−0.408248	+	0.408248i
$3$	−3.67423	+	3.67423i	−0.408248	+	0.408248i
$4$			8.00000i			0.500000i
$5$	24.6742	+	4.02270i	0.986969	+	0.160908i
$5$	24.6742	+	4.02270i	0.986969	+	0.160908i
$6$	14.6969			0.408248
$7$	44.4393	+	44.4393i	0.906924	+	0.906924i	0.996023	−	0.0890986i	$-0.0283986\pi$
$7$	44.4393	+	44.4393i	0.906924	+	0.906924i	−0.0890986	+	0.996023i	$0.528399\pi$
$8$	16.0000	−	16.0000i	0.250000	−	0.250000i
$9$		−	27.0000i		−	0.333333i
$10$	−41.3031	−	57.3939i	−0.413031	−	0.573939i
$11$	167.439			1.38380			0.691898	−	0.721995i	$-0.256775\pi$
$11$	167.439			1.38380			0.691898	+	0.721995i	$0.256775\pi$
$12$	−29.3939	−	29.3939i	−0.204124	−	0.204124i
$13$	−223.621	+	223.621i	−1.32320	+	1.32320i	−0.412031	+	0.911170i	$0.635180\pi$
$13$	−223.621	+	223.621i	−1.32320	+	1.32320i	−0.911170	+	0.412031i	$0.864820\pi$
$14$		−	177.757i		−	0.906924i
$15$	−105.439	+	75.8786i	−0.468619	+	0.337238i
$16$	−64.0000			−0.250000
$17$	−71.0148	−	71.0148i	−0.245726	−	0.245726i	0.573488	−	0.819214i	$-0.305590\pi$
$17$	−71.0148	−	71.0148i	−0.245726	−	0.245726i	−0.819214	+	0.573488i	$0.805590\pi$
$18$	−54.0000	+	54.0000i	−0.166667	+	0.166667i
$19$		−	272.211i		−	0.754048i	−0.926204	−	0.377024i	$-0.876947\pi$
$19$		−	272.211i		−	0.754048i	0.926204	−	0.377024i	$-0.123053\pi$
$20$	−32.1816	+	197.394i	−0.0804541	+	0.493485i
$21$	−326.561			−0.740500
$22$	−334.879	−	334.879i	−0.691898	−	0.691898i
$23$	87.6821	−	87.6821i	0.165751	−	0.165751i	−0.619358	−	0.785109i	$-0.712607\pi$
$23$	87.6821	−	87.6821i	0.165751	−	0.165751i	0.785109	+	0.619358i	$0.212607\pi$
$24$			117.576i			0.204124i
$25$	592.636	+	198.514i	0.948217	+	0.317623i
$26$	894.484			1.32320
$27$	99.2043	+	99.2043i	0.136083	+	0.136083i
$28$	−355.514	+	355.514i	−0.453462	+	0.453462i
$29$		−	839.832i		−	0.998611i	−0.866426	−	0.499306i	$-0.833588\pi$
$29$		−	839.832i		−	0.998611i	0.866426	−	0.499306i	$-0.166412\pi$
$30$	362.636	+	59.1214i	0.402929	+	0.0656905i
$31$	403.787			0.420173			0.210087	−	0.977683i	$-0.432625\pi$
$31$	403.787			0.420173			0.210087	+	0.977683i	$0.432625\pi$
$32$	128.000	+	128.000i	0.125000	+	0.125000i
$33$	−615.211	+	615.211i	−0.564932	+	0.564932i
$34$			284.059i			0.245726i
$35$	917.739	+	1275.27i	0.749175	+	1.04104i
$36$	216.000			0.166667
$37$	−207.589	−	207.589i	−0.151636	−	0.151636i	0.627212	−	0.778848i	$-0.284196\pi$
$37$	−207.589	−	207.589i	−0.151636	−	0.151636i	−0.778848	+	0.627212i	$0.784196\pi$
$38$	−544.422	+	544.422i	−0.377024	+	0.377024i
$39$		−	1643.27i		−	1.08039i
$40$	459.151	−	330.424i	0.286969	−	0.206515i
$41$	−1386.39			−0.824742			−0.412371	−	0.911016i	$-0.635299\pi$
$41$	−1386.39			−0.824742			−0.412371	+	0.911016i	$0.635299\pi$
$42$	653.121	+	653.121i	0.370250	+	0.370250i
$43$	568.393	−	568.393i	0.307406	−	0.307406i	−0.536497	−	0.843902i	$-0.680253\pi$
$43$	568.393	−	568.393i	0.307406	−	0.307406i	0.843902	+	0.536497i	$0.180253\pi$
$44$			1339.51i			0.691898i
$45$	108.613	−	666.204i	0.0536361	−	0.328990i
$46$	−350.729			−0.165751
$47$	−2642.77	−	2642.77i	−1.19637	−	1.19637i	−0.975247	−	0.221119i	$-0.929029\pi$
$47$	−2642.77	−	2642.77i	−1.19637	−	1.19637i	−0.221119	−	0.975247i	$-0.570971\pi$
$48$	235.151	−	235.151i	0.102062	−	0.102062i
$49$			1548.70i			0.645023i
$50$	−788.243	−	1582.30i	−0.315297	−	0.632920i
$51$	521.850			0.200634
$52$	−1788.97	−	1788.97i	−0.661600	−	0.661600i
$53$	−1378.64	+	1378.64i	−0.490792	+	0.490792i	−0.908556	−	0.417763i	$-0.862814\pi$
$53$	−1378.64	+	1378.64i	−0.490792	+	0.490792i	0.417763	+	0.908556i	$0.362814\pi$
$54$		−	396.817i		−	0.136083i
$55$	4131.44	+	673.559i	1.36576	+	0.222664i
$56$	1422.06			0.453462
$57$	1000.17	+	1000.17i	0.307839	+	0.307839i
$58$	−1679.66	+	1679.66i	−0.499306	+	0.499306i
$59$		−	327.503i		−	0.0940829i	−0.998893	−	0.0470415i	$-0.985021\pi$
$59$		−	327.503i		−	0.0940829i	0.998893	−	0.0470415i	$-0.0149793\pi$
$60$	−607.029	−	843.514i	−0.168619	−	0.234310i
$61$	−4205.66			−1.13025			−0.565125	−	0.825005i	$-0.691172\pi$
$61$	−4205.66			−1.13025			−0.565125	+	0.825005i	$0.691172\pi$
$62$	−807.573	−	807.573i	−0.210087	−	0.210087i
$63$	1199.86	−	1199.86i	0.302308	−	0.302308i
$64$		−	512.000i		−	0.125000i
$65$	−6417.24	+	4618.11i	−1.51887	+	1.09304i
$66$	2460.84			0.564932
$67$	2832.99	+	2832.99i	0.631097	+	0.631097i	0.948343	−	0.317246i	$-0.102758\pi$
$67$	2832.99	+	2832.99i	0.631097	+	0.631097i	−0.317246	+	0.948343i	$0.602758\pi$
$68$	568.118	−	568.118i	0.122863	−	0.122863i
$69$			644.330i			0.135335i
$70$	715.064	−	4386.02i	0.145931	−	0.895106i
$71$	5339.03			1.05912			0.529560	−	0.848272i	$-0.322357\pi$
$71$	5339.03			1.05912			0.529560	+	0.848272i	$0.322357\pi$
$72$	−432.000	−	432.000i	−0.0833333	−	0.0833333i
$73$	6865.24	−	6865.24i	1.28828	−	1.28828i	0.352447	−	0.935832i	$-0.385350\pi$
$73$	6865.24	−	6865.24i	1.28828	−	1.28828i	0.935832	−	0.352447i	$-0.114650\pi$
$74$			830.357i			0.151636i
$75$	−2906.87	+	1448.09i	−0.516777	+	0.257439i
$76$	2177.69			0.377024
$77$	7440.88	+	7440.88i	1.25500	+	1.25500i
$78$	−3286.54	+	3286.54i	−0.540194	+	0.540194i
$79$			4666.69i			0.747748i	0.927480	+	0.373874i	$0.121971\pi$
$79$			4666.69i			0.747748i	−0.927480	+	0.373874i	$0.878029\pi$
$80$	−1579.15	−	257.453i	−0.246742	−	0.0402270i
$81$	−729.000			−0.111111
$82$	2772.78	+	2772.78i	0.412371	+	0.412371i
$83$	4111.98	−	4111.98i	0.596890	−	0.596890i	−0.342594	−	0.939484i	$-0.611305\pi$
$83$	4111.98	−	4111.98i	0.596890	−	0.596890i	0.939484	+	0.342594i	$0.111305\pi$
$84$		−	2612.49i		−	0.370250i
$85$	−1466.56	−	2037.91i	−0.202985	−	0.282063i
$86$	−2273.57			−0.307406
$87$	3085.74	+	3085.74i	0.407681	+	0.407681i
$88$	2679.03	−	2679.03i	0.345949	−	0.345949i
$89$		−	9911.62i		−	1.25131i	−0.780100	−	0.625654i	$-0.784832\pi$
$89$		−	9911.62i		−	1.25131i	0.780100	−	0.625654i	$-0.215168\pi$
$90$	−1549.63	+	1115.18i	−0.191313	+	0.137677i
$91$	−19875.1			−2.40009
$92$	701.457	+	701.457i	0.0828754	+	0.0828754i
$93$	−1483.61	+	1483.61i	−0.171535	+	0.171535i
$94$			10571.1i			1.19637i
$95$	1095.03	−	6716.60i	0.121332	−	0.744222i
$96$	−940.604			−0.102062
$97$	−10688.9	−	10688.9i	−1.13603	−	1.13603i	−0.989156	−	0.146871i	$-0.953080\pi$
$97$	−10688.9	−	10688.9i	−1.13603	−	1.13603i	−0.146871	−	0.989156i	$-0.546920\pi$
$98$	3097.40	−	3097.40i	0.322511	−	0.322511i
$99$		−	4520.86i		−	0.461265i
$100$	−1588.11	+	4741.09i	−0.158811	+	0.474109i
$101$	−1763.09			−0.172835			−0.0864177	−	0.996259i	$-0.527542\pi$
$101$	−1763.09			−0.172835			−0.0864177	+	0.996259i	$0.527542\pi$
$102$	−1043.70	−	1043.70i	−0.100317	−	0.100317i
$103$	−2414.27	+	2414.27i	−0.227568	+	0.227568i	−0.811676	−	0.584108i	$-0.801444\pi$
$103$	−2414.27	+	2414.27i	−0.227568	+	0.227568i	0.584108	+	0.811676i	$0.301444\pi$
$104$			7155.87i			0.661600i
$105$	−8057.64	−	1313.66i	−0.730851	−	0.119153i
$106$	5514.54			0.490792
$107$	4279.03	+	4279.03i	0.373747	+	0.373747i	0.868840	−	0.495093i	$-0.164866\pi$
$107$	4279.03	+	4279.03i	0.373747	+	0.373747i	−0.495093	+	0.868840i	$0.664866\pi$
$108$	−793.635	+	793.635i	−0.0680414	+	0.0680414i
$109$			11819.5i			0.994827i	0.867514	+	0.497413i	$0.165717\pi$
$109$			11819.5i			0.994827i	−0.867514	+	0.497413i	$0.834283\pi$
$110$	−6915.76	−	9609.99i	−0.571550	−	0.794214i
$111$	1525.46			0.123810
$112$	−2844.11	−	2844.11i	−0.226731	−	0.226731i
$113$	1620.60	−	1620.60i	0.126917	−	0.126917i	−0.640795	−	0.767712i	$-0.721395\pi$
$113$	1620.60	−	1620.60i	0.126917	−	0.126917i	0.767712	+	0.640795i	$0.221395\pi$
$114$		−	4000.67i		−	0.307839i
$115$	2516.21	−	1810.77i	0.190262	−	0.136920i
$116$	6718.66			0.499306
$117$	6037.76	+	6037.76i	0.441067	+	0.441067i
$118$	−655.005	+	655.005i	−0.0470415	+	0.0470415i
$119$		−	6311.69i		−	0.445710i
$120$	−472.971	+	2901.09i	−0.0328452	+	0.201464i
$121$	13394.9			0.914891
$122$	8411.32	+	8411.32i	0.565125	+	0.565125i
$123$	5093.93	−	5093.93i	0.336699	−	0.336699i
$124$			3230.29i			0.210087i
$125$	13824.3	+	7282.19i	0.884753	+	0.466060i
$126$	−4799.44			−0.302308
$127$	−11572.5	−	11572.5i	−0.717494	−	0.717494i	0.250597	−	0.968091i	$-0.419373\pi$
$127$	−11572.5	−	11572.5i	−0.717494	−	0.717494i	−0.968091	+	0.250597i	$0.919373\pi$
$128$	−1024.00	+	1024.00i	−0.0625000	+	0.0625000i
$129$			4176.82i			0.250996i
$130$	22070.7	+	3598.24i	1.30596	+	0.212914i
$131$	65.6230			0.00382396			0.00191198	−	0.999998i	$-0.499391\pi$
$131$	65.6230			0.00382396			0.00191198	+	0.999998i	$0.499391\pi$
$132$	−4921.69	−	4921.69i	−0.282466	−	0.282466i
$133$	12096.9	−	12096.9i	0.683864	−	0.683864i
$134$		−	11332.0i		−	0.631097i
$135$	2048.72	+	2846.86i	0.112413	+	0.156206i
$136$	−2272.47			−0.122863
$137$	579.439	+	579.439i	0.0308721	+	0.0308721i	0.722374	−	0.691502i	$-0.243051\pi$
$137$	579.439	+	579.439i	0.0308721	+	0.0308721i	−0.691502	+	0.722374i	$0.743051\pi$
$138$	1288.66	−	1288.66i	0.0676675	−	0.0676675i
$139$			36158.2i			1.87145i	0.352734	+	0.935724i	$0.385252\pi$
$139$			36158.2i			1.87145i	−0.352734	+	0.935724i	$0.614748\pi$
$140$	−10202.2	+	7341.91i	−0.520519	+	0.374587i
$141$	19420.3			0.976829
$142$	−10678.1	−	10678.1i	−0.529560	−	0.529560i
$143$	−37442.9	+	37442.9i	−1.83104	+	1.83104i
$144$			1728.00i			0.0833333i
$145$	3378.40	−	20722.2i	0.160685	−	0.985599i
$146$	−27461.0			−1.28828
$147$	−5690.29	−	5690.29i	−0.263330	−	0.263330i
$148$	1660.71	−	1660.71i	0.0758178	−	0.0758178i
$149$		−	2143.94i		−	0.0965695i	−0.998834	−	0.0482847i	$-0.984625\pi$
$149$		−	2143.94i		−	0.0965695i	0.998834	−	0.0482847i	$-0.0153755\pi$
$150$	8709.93	+	2917.55i	0.387108	+	0.129669i
$151$	−8940.59			−0.392114			−0.196057	−	0.980593i	$-0.562814\pi$
$151$	−8940.59			−0.392114			−0.196057	+	0.980593i	$0.562814\pi$
$152$	−4355.38	−	4355.38i	−0.188512	−	0.188512i
$153$	−1917.40	+	1917.40i	−0.0819086	+	0.0819086i
$154$		−	29763.5i		−	1.25500i
$155$	9963.13	+	1624.31i	0.414698	+	0.0676093i
$156$	13146.2			0.540194
$157$	18032.9	+	18032.9i	0.731586	+	0.731586i	0.970934	−	0.239348i	$-0.0769337\pi$
$157$	18032.9	+	18032.9i	0.731586	+	0.731586i	−0.239348	+	0.970934i	$0.576934\pi$
$158$	9333.39	−	9333.39i	0.373874	−	0.373874i
$159$		−	10130.9i		−	0.400730i
$160$	2643.40	+	3673.21i	0.103258	+	0.143485i
$161$	7793.06			0.300647
$162$	1458.00	+	1458.00i	0.0555556	+	0.0555556i
$163$	−6859.00	+	6859.00i	−0.258158	+	0.258158i	−0.824305	−	0.566147i	$-0.808434\pi$
$163$	−6859.00	+	6859.00i	−0.258158	+	0.258158i	0.566147	+	0.824305i	$0.308434\pi$
$164$		−	11091.1i		−	0.412371i
$165$	−17654.7	+	12705.1i	−0.648473	+	0.466669i
$166$	−16447.9			−0.596890
$167$	−37439.2	−	37439.2i	−1.34244	−	1.34244i	−0.893627	−	0.448811i	$-0.851848\pi$
$167$	−37439.2	−	37439.2i	−1.34244	−	1.34244i	−0.448811	−	0.893627i	$-0.648152\pi$
$168$	−5224.97	+	5224.97i	−0.185125	+	0.185125i
$169$		−	71451.6i		−	2.50172i
$170$	−1142.69	+	7008.94i	−0.0395393	+	0.242524i
$171$	−7349.70			−0.251349
$172$	4547.14	+	4547.14i	0.153703	+	0.153703i
$173$	−32638.2	+	32638.2i	−1.09052	+	1.09052i	−0.0950500	+	0.995472i	$0.530301\pi$
$173$	−32638.2	+	32638.2i	−1.09052	+	1.09052i	−0.995472	+	0.0950500i	$0.969699\pi$
$174$		−	12343.0i		−	0.407681i
$175$	17514.5	+	35158.1i	0.571901	+	1.14802i
$176$	−10716.1			−0.345949
$177$	1203.32	+	1203.32i	0.0384092	+	0.0384092i
$178$	−19823.2	+	19823.2i	−0.625654	+	0.625654i
$179$		−	6396.19i		−	0.199625i	−0.995006	−	0.0998126i	$-0.968176\pi$
$179$		−	6396.19i		−	0.199625i	0.995006	−	0.0998126i	$-0.0318243\pi$
$180$	5329.63	+	868.904i	0.164495	+	0.0268180i
$181$	49025.9			1.49647			0.748236	−	0.663432i	$-0.230901\pi$
$181$	49025.9			1.49647			0.748236	+	0.663432i	$0.230901\pi$
$182$	39750.2	+	39750.2i	1.20004	+	1.20004i
$183$	15452.6	−	15452.6i	0.461423	−	0.461423i
$184$		−	2805.83i		−	0.0828754i
$185$	−4287.04	−	5957.18i	−0.125260	−	0.174059i
$186$	5934.43			0.171535
$187$	−11890.7	−	11890.7i	−0.340034	−	0.340034i
$188$	21142.2	−	21142.2i	0.598183	−	0.598183i
$189$			8817.14i			0.246833i
$190$	−15623.3	+	11243.2i	−0.432777	+	0.311445i
$191$	39949.0			1.09506			0.547531	−	0.836785i	$-0.315568\pi$
$191$	39949.0			1.09506			0.547531	+	0.836785i	$0.315568\pi$
$192$	1881.21	+	1881.21i	0.0510310	+	0.0510310i
$193$	−23749.1	+	23749.1i	−0.637577	+	0.637577i	−0.949957	−	0.312380i	$-0.898874\pi$
$193$	−23749.1	+	23749.1i	−0.637577	+	0.637577i	0.312380	+	0.949957i	$0.398874\pi$
$194$			42755.5i			1.13603i
$195$	6610.39	−	40546.5i	0.173843	−	1.06631i
$196$	−12389.6			−0.322511
$197$	−2725.09	−	2725.09i	−0.0702181	−	0.0702181i	0.671126	−	0.741344i	$-0.265811\pi$
$197$	−2725.09	−	2725.09i	−0.0702181	−	0.0702181i	−0.741344	+	0.671126i	$0.765811\pi$
$198$	−9041.72	+	9041.72i	−0.230633	+	0.230633i
$199$			63212.5i			1.59624i	0.602502	+	0.798118i	$0.294171\pi$
$199$			63212.5i			1.59624i	−0.602502	+	0.798118i	$0.705829\pi$
$200$	12658.4	−	6305.94i	0.316460	−	0.157649i
$201$	−20818.2			−0.515288
$202$	3526.19	+	3526.19i	0.0864177	+	0.0864177i
$203$	37321.5	−	37321.5i	0.905665	−	0.905665i
$204$			4174.80i			0.100317i
$205$	−34208.1	−	5577.04i	−0.813995	−	0.132708i
$206$	9657.07			0.227568
$207$	−2367.42	−	2367.42i	−0.0552502	−	0.0552502i
$208$	14311.7	−	14311.7i	0.330800	−	0.330800i
$209$		−	45578.9i		−	1.04345i
$210$	13488.0	+	18742.6i	0.305849	+	0.425002i
$211$	15470.2			0.347480			0.173740	−	0.984792i	$-0.444415\pi$
$211$	15470.2			0.347480			0.173740	+	0.984792i	$0.444415\pi$
$212$	−11029.1	−	11029.1i	−0.245396	−	0.245396i
$213$	−19616.8	+	19616.8i	−0.432384	+	0.432384i
$214$		−	17116.1i		−	0.373747i
$215$	16311.1	−	11738.2i	0.352864	−	0.253936i
$216$	3174.54			0.0680414
$217$	17944.0	+	17944.0i	0.381065	+	0.381065i
$218$	23639.1	−	23639.1i	0.497413	−	0.497413i
$219$			50449.0i			1.05188i
$220$	−5388.47	+	33051.5i	−0.111332	+	0.682882i
$221$	31760.8			0.650289
$222$	−3050.93	−	3050.93i	−0.0619050	−	0.0619050i
$223$	28817.8	−	28817.8i	0.579496	−	0.579496i	−0.355268	−	0.934764i	$-0.615611\pi$
$223$	28817.8	−	28817.8i	0.579496	−	0.579496i	0.934764	+	0.355268i	$0.115611\pi$
$224$			11376.5i			0.226731i
$225$	5359.89	−	16001.2i	0.105874	−	0.316072i
$226$	−6482.41			−0.126917
$227$	884.237	+	884.237i	0.0171600	+	0.0171600i	0.715635	−	0.698475i	$-0.246138\pi$
$227$	884.237	+	884.237i	0.0171600	+	0.0171600i	−0.698475	+	0.715635i	$0.746138\pi$
$228$	−8001.34	+	8001.34i	−0.153919	+	0.153919i
$229$		−	12076.4i		−	0.230285i	−0.993349	−	0.115143i	$-0.963268\pi$
$229$		−	12076.4i		−	0.230285i	0.993349	−	0.115143i	$-0.0367325\pi$
$230$	−8653.96	−	1410.88i	−0.163591	−	0.0266706i
$231$	−54679.1			−1.02470
$232$	−13437.3	−	13437.3i	−0.249653	−	0.249653i
$233$	−24695.8	+	24695.8i	−0.454894	+	0.454894i	−0.896975	−	0.442081i	$-0.854240\pi$
$233$	−24695.8	+	24695.8i	−0.454894	+	0.454894i	0.442081	+	0.896975i	$0.354240\pi$
$234$		−	24151.1i		−	0.441067i
$235$	−54577.3	−	75839.5i	−0.988271	−	1.37328i
$236$	2620.02			0.0470415
$237$	−17146.5	−	17146.5i	−0.305267	−	0.305267i
$238$	−12623.4	+	12623.4i	−0.222855	+	0.222855i
$239$			48187.8i			0.843608i	0.906687	+	0.421804i	$0.138603\pi$
$239$			48187.8i			0.843608i	−0.906687	+	0.421804i	$0.861397\pi$
$240$	6748.11	−	4856.23i	0.117155	−	0.0843095i
$241$	−55184.2			−0.950125			−0.475062	−	0.879952i	$-0.657574\pi$
$241$	−55184.2			−0.950125			−0.475062	+	0.879952i	$0.657574\pi$
$242$	−26789.8	−	26789.8i	−0.457445	−	0.457445i
$243$	2678.52	−	2678.52i	0.0453609	−	0.0453609i
$244$		−	33645.3i		−	0.565125i
$245$	−6229.96	+	38213.0i	−0.103789	+	0.636618i
$246$	−20375.7			−0.336699
$247$	60872.1	+	60872.1i	0.997756	+	0.997756i
$248$	6460.59	−	6460.59i	0.105043	−	0.105043i
$249$			30216.7i			0.487359i
$250$	−13084.2	−	42212.9i	−0.209347	−	0.675407i
$251$	−69667.8			−1.10582			−0.552910	−	0.833241i	$-0.686483\pi$
$251$	−69667.8			−1.10582			−0.552910	+	0.833241i	$0.686483\pi$
$252$	9598.89	+	9598.89i	0.151154	+	0.151154i
$253$	14681.4	−	14681.4i	0.229365	−	0.229365i
$254$			46289.8i			0.717494i
$255$	12876.2	+	2099.25i	0.198020	+	0.0322837i
$256$	4096.00			0.0625000
$257$	−11614.4	−	11614.4i	−0.175846	−	0.175846i	0.613696	−	0.789542i	$-0.289682\pi$
$257$	−11614.4	−	11614.4i	−0.175846	−	0.175846i	−0.789542	+	0.613696i	$0.789682\pi$
$258$	8353.63	−	8353.63i	0.125498	−	0.125498i
$259$		−	18450.2i		−	0.275044i
$260$	−36944.9	−	51337.9i	−0.546522	−	0.759436i
$261$	−22675.5			−0.332870
$262$	−131.246	−	131.246i	−0.00191198	−	0.00191198i
$263$	86811.6	−	86811.6i	1.25507	−	1.25507i	0.301646	−	0.953420i	$-0.402464\pi$
$263$	86811.6	−	86811.6i	1.25507	−	1.25507i	0.953420	−	0.301646i	$-0.0975360\pi$
$264$			19686.8i			0.282466i
$265$	−39562.6	+	28470.9i	−0.563370	+	0.405425i
$266$	−48387.5			−0.683864
$267$	36417.6	+	36417.6i	0.510845	+	0.510845i
$268$	−22663.9	+	22663.9i	−0.315548	+	0.315548i
$269$			93439.3i			1.29129i	0.763636	+	0.645647i	$0.223412\pi$
$269$			93439.3i			1.29129i	−0.763636	+	0.645647i	$0.776588\pi$
$270$	1596.28	−	9791.16i	0.0218968	−	0.134310i
$271$	−10856.5			−0.147826			−0.0739131	−	0.997265i	$-0.523549\pi$
$271$	−10856.5			−0.147826			−0.0739131	+	0.997265i	$0.523549\pi$
$272$	4544.95	+	4544.95i	0.0614315	+	0.0614315i
$273$	73025.8	−	73025.8i	0.979831	−	0.979831i
$274$		−	2317.76i		−	0.0308721i
$275$	99230.5	+	33239.1i	1.31214	+	0.439525i
$276$	−5154.64			−0.0676675
$277$	65214.7	+	65214.7i	0.849935	+	0.849935i	0.990125	−	0.140189i	$-0.0447711\pi$
$277$	65214.7	+	65214.7i	0.849935	+	0.849935i	−0.140189	+	0.990125i	$0.544771\pi$
$278$	72316.5	−	72316.5i	0.935724	−	0.935724i
$279$		−	10902.2i		−	0.140058i
$280$	35088.2	+	5720.51i	0.447553	+	0.0729657i
$281$	−8669.34			−0.109793			−0.0548963	−	0.998492i	$-0.517483\pi$
$281$	−8669.34			−0.109793			−0.0548963	+	0.998492i	$0.517483\pi$
$282$	−38840.7	−	38840.7i	−0.488414	−	0.488414i
$283$	−23747.0	+	23747.0i	−0.296508	+	0.296508i	−0.839645	−	0.543136i	$-0.817237\pi$
$283$	−23747.0	+	23747.0i	−0.296508	+	0.296508i	0.543136	+	0.839645i	$0.317237\pi$
$284$			42712.2i			0.529560i
$285$	20655.0	+	28701.8i	0.254294	+	0.353361i
$286$	149772.			1.83104
$287$	−61610.2	−	61610.2i	−0.747978	−	0.747978i
$288$	3456.00	−	3456.00i	0.0416667	−	0.0416667i
$289$		−	73434.8i		−	0.879238i
$290$	−48201.2	+	34687.6i	−0.573142	+	0.412457i
$291$	78546.9			0.927562
$292$	54921.9	+	54921.9i	0.644139	+	0.644139i
$293$	−55077.2	+	55077.2i	−0.641559	+	0.641559i	−0.950939	−	0.309380i	$-0.899879\pi$
$293$	−55077.2	+	55077.2i	−0.641559	+	0.641559i	0.309380	+	0.950939i	$0.399879\pi$
$294$			22761.1i			0.263330i
$295$	1317.45	−	8080.88i	0.0151387	−	0.0928569i
$296$	−6642.86			−0.0758178
$297$	16610.7	+	16610.7i	0.188311	+	0.188311i
$298$	−4287.88	+	4287.88i	−0.0482847	+	0.0482847i
$299$			39215.1i			0.438643i
$300$	−11584.8	−	23255.0i	−0.128720	−	0.258389i
$301$	50517.9			0.557587
$302$	17881.2	+	17881.2i	0.196057	+	0.196057i
$303$	6478.02	−	6478.02i	0.0705597	−	0.0705597i
$304$			17421.5i			0.188512i
$305$	−103771.	−	16918.1i	−1.11552	−	0.181866i
$306$	7669.60			0.0819086
$307$	11961.1	+	11961.1i	0.126910	+	0.126910i	0.767709	−	0.640799i	$-0.221397\pi$
$307$	11961.1	+	11961.1i	0.126910	+	0.126910i	−0.640799	+	0.767709i	$0.721397\pi$
$308$	−59527.1	+	59527.1i	−0.627499	+	0.627499i
$309$		−	17741.2i		−	0.185808i
$310$	−16677.6	−	23174.9i	−0.173545	−	0.241154i
$311$	−65284.5			−0.674977			−0.337489	−	0.941330i	$-0.609577\pi$
$311$	−65284.5			−0.674977			−0.337489	+	0.941330i	$0.609577\pi$
$312$	−26292.3	−	26292.3i	−0.270097	−	0.270097i
$313$	−6418.45	+	6418.45i	−0.0655151	+	0.0655151i	−0.739105	−	0.673590i	$-0.764751\pi$
$313$	−6418.45	+	6418.45i	−0.0655151	+	0.0655151i	0.673590	+	0.739105i	$0.264751\pi$
$314$		−	72131.4i		−	0.731586i
$315$	34432.3	−	24779.0i	0.347013	−	0.249725i
$316$	−37333.5			−0.373874
$317$	22100.1	+	22100.1i	0.219926	+	0.219926i	0.808467	−	0.588541i	$-0.200298\pi$
$317$	22100.1	+	22100.1i	0.219926	+	0.219926i	−0.588541	+	0.808467i	$0.700298\pi$
$318$	−20261.7	+	20261.7i	−0.200365	+	0.200365i
$319$		−	140621.i		−	1.38187i
$320$	2059.62	−	12633.2i	0.0201135	−	0.123371i
$321$	−31444.3			−0.305163
$322$	−15586.1	−	15586.1i	−0.150323	−	0.150323i
$323$	−19331.0	+	19331.0i	−0.185289	+	0.185289i
$324$		−	5832.00i		−	0.0555556i
$325$	−176918.	+	88133.8i	−1.67496	+	0.834403i
$326$	27436.0			0.258158
$327$	−43427.7	−	43427.7i	−0.406136	−	0.406136i
$328$	−22182.3	+	22182.3i	−0.206185	+	0.206185i
$329$		−	234886.i		−	2.17003i
$330$	60719.5	+	9899.25i	0.557571	+	0.0909022i
$331$	−49108.7			−0.448231			−0.224116	−	0.974563i	$-0.571949\pi$
$331$	−49108.7			−0.448231			−0.224116	+	0.974563i	$0.571949\pi$
$332$	32895.8	+	32895.8i	0.298445	+	0.298445i
$333$	−5604.91	+	5604.91i	−0.0505452	+	0.0505452i
$334$			149757.i			1.34244i
$335$	58505.6	+	81298.2i	0.521324	+	0.724422i
$336$	20899.9			0.185125
$337$	−142816.	−	142816.i	−1.25753	−	1.25753i	−0.952269	−	0.305260i	$-0.901257\pi$
$337$	−142816.	−	142816.i	−1.25753	−	1.25753i	−0.305260	−	0.952269i	$-0.598743\pi$
$338$	−142903.	+	142903.i	−1.25086	+	1.25086i
$339$			11909.0i			0.103627i
$340$	16303.3	−	11732.5i	0.141032	−	0.101492i
$341$	67609.8			0.581434
$342$	14699.4	+	14699.4i	0.125675	+	0.125675i
$343$	37875.6	−	37875.6i	0.321937	−	0.321937i
$344$		−	18188.6i		−	0.153703i
$345$	−2591.95	+	15898.3i	−0.0217765	+	0.133571i
$346$	130553.			1.09052
$347$	−21400.3	−	21400.3i	−0.177730	−	0.177730i	0.612635	−	0.790366i	$-0.290109\pi$
$347$	−21400.3	−	21400.3i	−0.177730	−	0.177730i	−0.790366	+	0.612635i	$0.790109\pi$
$348$	−24685.9	+	24685.9i	−0.203841	+	0.203841i
$349$		−	34091.2i		−	0.279893i	−0.990159	−	0.139946i	$-0.955307\pi$
$349$		−	34091.2i		−	0.279893i	0.990159	−	0.139946i	$-0.0446930\pi$
$350$	35287.3	−	105345.i	0.288060	−	0.859961i
$351$	−44368.3			−0.360130
$352$	21432.2	+	21432.2i	0.172974	+	0.172974i
$353$	28.7539	−	28.7539i	0.000230753	−	0.000230753i	−0.706991	−	0.707222i	$-0.749948\pi$
$353$	28.7539	−	28.7539i	0.000230753	−	0.000230753i	0.707222	+	0.706991i	$0.249948\pi$
$354$		−	4813.29i		−	0.0384092i
$355$	131736.	+	21477.3i	1.04532	+	0.170421i
$356$	79292.9			0.625654
$357$	23190.6	+	23190.6i	0.181960	+	0.181960i
$358$	−12792.4	+	12792.4i	−0.0998126	+	0.0998126i
$359$			173943.i			1.34964i	0.737984	+	0.674818i	$0.235778\pi$
$359$			173943.i			1.34964i	−0.737984	+	0.674818i	$0.764222\pi$
$360$	−8921.46	−	12397.1i	−0.0688384	−	0.0956565i
$361$	56222.1			0.431412
$362$	−98051.9	−	98051.9i	−0.748236	−	0.748236i
$363$	−49216.1	+	49216.1i	−0.373503	+	0.373503i
$364$		−	159001.i		−	1.20004i
$365$	197011.	−	141778.i	1.47879	−	1.06420i
$366$	−61810.3			−0.461423
$367$	−41954.1	−	41954.1i	−0.311489	−	0.311489i	0.533997	−	0.845486i	$-0.320689\pi$
$367$	−41954.1	−	41954.1i	−0.311489	−	0.311489i	−0.845486	+	0.533997i	$0.820689\pi$
$368$	−5611.66	+	5611.66i	−0.0414377	+	0.0414377i
$369$			37432.6i			0.274914i
$370$	−3340.28	+	20488.4i	−0.0243994	+	0.149660i
$371$	−122531.			−0.890223
$372$	−11868.9	−	11868.9i	−0.0857676	−	0.0857676i
$373$	−65875.2	+	65875.2i	−0.473483	+	0.473483i	−0.903040	−	0.429557i	$-0.858670\pi$
$373$	−65875.2	+	65875.2i	−0.473483	+	0.473483i	0.429557	+	0.903040i	$0.358670\pi$
$374$			47562.7i			0.340034i
$375$	−77550.1	+	24037.1i	−0.551467	+	0.170931i
$376$	−84568.7			−0.598183
$377$	187804.	+	187804.i	1.32136	+	1.32136i
$378$	17634.3	−	17634.3i	0.123417	−	0.123417i
$379$		−	10837.0i		−	0.0754448i	−0.999288	−	0.0377224i	$-0.987990\pi$
$379$		−	10837.0i		−	0.0754448i	0.999288	−	0.0377224i	$-0.0120103\pi$
$380$	53732.8	+	8760.20i	0.372111	+	0.0606662i
$381$	85039.9			0.585831
$382$	−79898.0	−	79898.0i	−0.547531	−	0.547531i
$383$	22327.5	−	22327.5i	0.152210	−	0.152210i	−0.626894	−	0.779104i	$-0.715674\pi$
$383$	22327.5	−	22327.5i	0.152210	−	0.152210i	0.779104	+	0.626894i	$0.215674\pi$
$384$		−	7524.83i		−	0.0510310i
$385$	153666.	+	213531.i	1.03671	+	1.44058i
$386$	94996.5			0.637577
$387$	−15346.6	−	15346.6i	−0.102469	−	0.102469i
$388$	85511.0	−	85511.0i	0.568013	−	0.568013i
$389$		−	203884.i		−	1.34736i	−0.739023	−	0.673680i	$-0.764713\pi$
$389$		−	203884.i		−	1.34736i	0.739023	−	0.673680i	$-0.235287\pi$
$390$	−94313.7	+	67872.1i	−0.620077	+	0.446234i
$391$	−12453.5			−0.0814585
$392$	24779.2	+	24779.2i	0.161256	+	0.161256i
$393$	−241.114	+	241.114i	−0.00156113	+	0.00156113i
$394$			10900.4i			0.0702181i
$395$	−18772.7	+	115147.i	−0.120319	+	0.738004i
$396$	36166.9			0.230633
$397$	117299.	+	117299.i	0.744238	+	0.744238i	0.973390	−	0.229153i	$-0.0735955\pi$
$397$	117299.	+	117299.i	0.744238	+	0.744238i	−0.229153	+	0.973390i	$0.573596\pi$
$398$	126425.	−	126425.i	0.798118	−	0.798118i
$399$			88893.5i			0.558373i
$400$	−37928.7	−	12704.9i	−0.237054	−	0.0794057i
$401$	43093.1			0.267990			0.133995	−	0.990982i	$-0.457219\pi$
$401$	43093.1			0.267990			0.133995	+	0.990982i	$0.457219\pi$
$402$	41636.3	+	41636.3i	0.257644	+	0.257644i
$403$	−90295.2	+	90295.2i	−0.555974	+	0.555974i
$404$		−	14104.7i		−	0.0864177i
$405$	−17987.5	−	2932.55i	−0.109663	−	0.0178787i
$406$	−149286.			−0.905665
$407$	−34758.6	−	34758.6i	−0.209833	−	0.209833i
$408$	8349.60	−	8349.60i	0.0501586	−	0.0501586i
$409$			186090.i			1.11244i	0.831036	+	0.556219i	$0.187748\pi$
$409$			186090.i			1.11244i	−0.831036	+	0.556219i	$0.812252\pi$
$410$	57262.2	+	79570.3i	0.340644	+	0.473351i
$411$	−4257.99			−0.0252070
$412$	−19314.1	−	19314.1i	−0.113784	−	0.113784i
$413$	14554.0	−	14554.0i	0.0853261	−	0.0853261i
$414$			9469.67i			0.0552502i
$415$	118001.	−	84918.6i	0.685157	−	0.493068i
$416$	−57247.0			−0.330800
$417$	−132854.	−	132854.i	−0.764015	−	0.764015i
$418$	−91157.7	+	91157.7i	−0.521724	+	0.521724i
$419$		−	101699.i		−	0.579278i	−0.957136	−	0.289639i	$-0.906465\pi$
$419$		−	101699.i		−	0.579278i	0.957136	−	0.289639i	$-0.0935352\pi$
$420$	10509.3	−	64461.1i	0.0595763	−	0.365426i
$421$	−22533.0			−0.127132			−0.0635659	−	0.997978i	$-0.520247\pi$
$421$	−22533.0			−0.127132			−0.0635659	+	0.997978i	$0.520247\pi$
$422$	−30940.3	−	30940.3i	−0.173740	−	0.173740i
$423$	−71354.8	+	71354.8i	−0.398789	+	0.398789i
$424$			44116.3i			0.245396i
$425$	−27988.5	−	56183.4i	−0.154953	−	0.311050i
$426$	78467.4			0.432384
$427$	−186897.	−	186897.i	−1.02505	−	1.02505i
$428$	−34232.2	+	34232.2i	−0.186873	+	0.186873i
$429$		−	275148.i		−	1.49504i
$430$	−56098.6	−	9145.90i	−0.303400	−	0.0494641i
$431$	210598.			1.13370			0.566852	−	0.823820i	$-0.308161\pi$
$431$	210598.			1.13370			0.566852	+	0.823820i	$0.308161\pi$
$432$	−6349.08	−	6349.08i	−0.0340207	−	0.0340207i
$433$	123405.	−	123405.i	0.658201	−	0.658201i	−0.296754	−	0.954954i	$-0.595904\pi$
$433$	123405.	−	123405.i	0.658201	−	0.658201i	0.954954	+	0.296754i	$0.0959040\pi$
$434$		−	71776.0i		−	0.381065i
$435$	63725.3	+	88551.3i	0.336770	+	0.467968i
$436$	−94556.3			−0.497413
$437$	−23868.1	−	23868.1i	−0.124984	−	0.124984i
$438$	100898.	−	100898.i	0.525938	−	0.525938i
$439$			265180.i			1.37598i	0.725721	+	0.687989i	$0.241506\pi$
$439$			265180.i			1.37598i	−0.725721	+	0.687989i	$0.758494\pi$
$440$	76879.9	−	55326.0i	0.397107	−	0.285775i
$441$	41814.9			0.215008
$442$	−63521.6	−	63521.6i	−0.325145	−	0.325145i
$443$	−99815.9	+	99815.9i	−0.508619	+	0.508619i	−0.914102	−	0.405484i	$-0.867103\pi$
$443$	−99815.9	+	99815.9i	−0.508619	+	0.508619i	0.405484	+	0.914102i	$0.367103\pi$
$444$			12203.7i			0.0619050i
$445$	39871.5	−	244562.i	0.201346	−	1.23500i
$446$	−115271.			−0.579496
$447$	7877.34	+	7877.34i	0.0394243	+	0.0394243i
$448$	22752.9	−	22752.9i	0.113366	−	0.113366i
$449$			182934.i			0.907408i	0.891152	+	0.453704i	$0.149898\pi$
$449$			182934.i			0.907408i	−0.891152	+	0.453704i	$0.850102\pi$
$450$	−42722.1	+	21282.6i	−0.210973	+	0.105099i
$451$	−232136.			−1.14127
$452$	12964.8	+	12964.8i	0.0634585	+	0.0634585i
$453$	32849.8	−	32849.8i	0.160080	−	0.160080i
$454$		−	3536.95i		−	0.0171600i
$455$	−490403.	−	79951.7i	−2.36881	−	0.386193i
$456$	32005.4			0.153919
$457$	147497.	+	147497.i	0.706239	+	0.706239i	0.965742	−	0.259503i	$-0.0835588\pi$
$457$	147497.	+	147497.i	0.706239	+	0.706239i	−0.259503	+	0.965742i	$0.583559\pi$
$458$	−24152.8	+	24152.8i	−0.115143	+	0.115143i
$459$		−	14090.0i		−	0.0668781i
$460$	14486.2	+	20129.7i	0.0684601	+	0.0951308i
$461$	−354912.			−1.67001			−0.835006	−	0.550241i	$-0.814536\pi$
$461$	−354912.			−1.67001			−0.835006	+	0.550241i	$0.814536\pi$
$462$	109358.	+	109358.i	0.512351	+	0.512351i
$463$	182475.	−	182475.i	0.851221	−	0.851221i	−0.139063	−	0.990284i	$-0.544409\pi$
$463$	182475.	−	182475.i	0.851221	−	0.851221i	0.990284	+	0.139063i	$0.0444090\pi$
$464$			53749.3i			0.249653i
$465$	−42575.0	+	30638.8i	−0.196901	+	0.141699i
$466$	98783.0			0.454894
$467$	4348.30	+	4348.30i	0.0199382	+	0.0199382i	0.717006	−	0.697067i	$-0.245512\pi$
$467$	4348.30	+	4348.30i	0.0199382	+	0.0199382i	−0.697067	+	0.717006i	$0.745512\pi$
$468$	−48302.1	+	48302.1i	−0.220533	+	0.220533i
$469$			251792.i			1.14471i
$470$	−42524.4	+	260833.i	−0.192505	+	1.18078i
$471$	−132514.			−0.597337
$472$	−5240.04	−	5240.04i	−0.0235207	−	0.0235207i
$473$	95171.3	−	95171.3i	0.425386	−	0.425386i
$474$			68586.1i			0.305267i
$475$	54037.8	−	161322.i	0.239503	−	0.715001i
$476$	50493.5			0.222855
$477$	37223.2	+	37223.2i	0.163597	+	0.163597i
$478$	96375.5	−	96375.5i	0.421804	−	0.421804i
$479$		−	77346.0i		−	0.337106i	−0.985693	−	0.168553i	$-0.946091\pi$
$479$		−	77346.0i		−	0.337106i	0.985693	−	0.168553i	$-0.0539095\pi$
$480$	−23208.7	−	3783.77i	−0.100732	−	0.0164226i
$481$	92842.6			0.401289
$482$	110368.	+	110368.i	0.475062	+	0.475062i
$483$	−28633.5	+	28633.5i	−0.122739	+	0.122739i
$484$			107159.i			0.457445i
$485$	−220742.	−	306738.i	−0.938428	−	1.30402i
$486$	−10714.1			−0.0453609
$487$	77225.6	+	77225.6i	0.325614	+	0.325614i	0.850916	−	0.525302i	$-0.176048\pi$
$487$	77225.6	+	77225.6i	0.325614	+	0.325614i	−0.525302	+	0.850916i	$0.676048\pi$
$488$	−67290.6	+	67290.6i	−0.282562	+	0.282562i
$489$		−	50403.1i		−	0.210785i
$490$	88885.9	−	63966.1i	0.370204	−	0.266414i
$491$	340217.			1.41121			0.705607	−	0.708603i	$-0.250674\pi$
$491$	340217.			1.41121			0.705607	+	0.708603i	$0.250674\pi$
$492$	40751.4	+	40751.4i	0.168350	+	0.168350i
$493$	−59640.5	+	59640.5i	−0.245385	+	0.245385i
$494$		−	243488.i		−	0.997756i
$495$	18186.1	−	111549.i	0.0742213	−	0.455255i
$496$	−25842.4			−0.105043
$497$	237263.	+	237263.i	0.960542	+	0.960542i
$498$	60433.5	−	60433.5i	0.243679	−	0.243679i
$499$		−	331024.i		−	1.32941i	−0.747108	−	0.664703i	$-0.768558\pi$
$499$		−	331024.i		−	1.32941i	0.747108	−	0.664703i	$-0.231442\pi$
$500$	−58257.5	+	110594.i	−0.233030	+	0.442377i
$501$	275121.			1.09610
$502$	139336.	+	139336.i	0.552910	+	0.552910i
$503$	−123301.	+	123301.i	−0.487338	+	0.487338i	−0.907465	−	0.420127i	$-0.861985\pi$
$503$	−123301.	+	123301.i	−0.487338	+	0.487338i	0.420127	+	0.907465i	$0.361985\pi$
$504$		−	38395.5i		−	0.151154i
$505$	−43503.0	−	7092.40i	−0.170583	−	0.0278106i
$506$	−58725.7			−0.229365
$507$	262530.	+	262530.i	1.02132	+	1.02132i
$508$	92579.7	−	92579.7i	0.358747	−	0.358747i
$509$			364729.i			1.40778i	0.710309	+	0.703890i	$0.248555\pi$
$509$			364729.i			1.40778i	−0.710309	+	0.703890i	$0.751445\pi$
$510$	−21554.0	−	29951.0i	−0.0828681	−	0.115152i
$511$	610173.			2.33674
$512$	−8192.00	−	8192.00i	−0.0312500	−	0.0312500i
$513$	27004.5	−	27004.5i	0.102613	−	0.102613i
$514$			46457.8i			0.175846i
$515$	−69282.1	+	49858.3i	−0.261220	+	0.187985i
$516$	−33414.5			−0.125498
$517$	−442504.	−	442504.i	−1.65553	−	1.65553i
$518$	−36900.5	+	36900.5i	−0.137522	+	0.137522i
$519$		−	239841.i		−	0.890408i
$520$	−28785.9	+	176566.i	−0.106457	+	0.652979i
$521$	−203461.			−0.749560			−0.374780	−	0.927114i	$-0.622282\pi$
$521$	−203461.			−0.749560			−0.374780	+	0.927114i	$0.622282\pi$
$522$	45350.9	+	45350.9i	0.166435	+	0.166435i
$523$	72655.5	−	72655.5i	0.265623	−	0.265623i	−0.561711	−	0.827334i	$-0.689857\pi$
$523$	72655.5	−	72655.5i	0.265623	−	0.265623i	0.827334	+	0.561711i	$0.189857\pi$
$524$			524.984i			0.00191198i
$525$	−193532.	−	64827.0i	−0.702155	−	0.235200i
$526$	−347247.			−1.25507
$527$	−28674.8	−	28674.8i	−0.103248	−	0.103248i
$528$	39373.5	−	39373.5i	0.141233	−	0.141233i
$529$			264465.i			0.945053i
$530$	136067.	+	22183.4i	0.484397	+	0.0789725i
$531$	−8842.57			−0.0313610
$532$	96775.0	+	96775.0i	0.341932	+	0.341932i
$533$	310026.	−	310026.i	1.09130	−	1.09130i
$534$		−	145670.i		−	0.510845i
$535$	88368.4	+	122795.i	0.308738	+	0.429015i
$536$	90655.8			0.315548
$537$	23501.1	+	23501.1i	0.0814966	+	0.0814966i
$538$	186879.	−	186879.i	0.645647	−	0.645647i
$539$			259313.i			0.892580i
$540$	−22774.9	+	16389.8i	−0.0781032	+	0.0562063i
$541$	−91367.2			−0.312173			−0.156087	−	0.987743i	$-0.549888\pi$
$541$	−91367.2			−0.312173			−0.156087	+	0.987743i	$0.549888\pi$
$542$	21713.0	+	21713.0i	0.0739131	+	0.0739131i
$543$	−180133.	+	180133.i	−0.610932	+	0.610932i
$544$		−	18179.8i		−	0.0614315i
$545$	−47546.5	+	291638.i	−0.160076	+	0.981863i
$546$	−292103.			−0.979831
$547$	−9895.50	−	9895.50i	−0.0330722	−	0.0330722i	0.690377	−	0.723450i	$-0.257445\pi$
$547$	−9895.50	−	9895.50i	−0.0330722	−	0.0330722i	−0.723450	+	0.690377i	$0.757445\pi$
$548$	−4635.51	+	4635.51i	−0.0154361	+	0.0154361i
$549$			113553.i			0.376750i
$550$	−131983.	−	264939.i	−0.436307	−	0.875832i
$551$	−228612.			−0.753001
$552$	10309.3	+	10309.3i	0.0338337	+	0.0338337i
$553$	−207384.	+	207384.i	−0.678150	+	0.678150i
$554$		−	260859.i		−	0.849935i
$555$	37639.6	+	6136.49i	0.122197	+	0.0199220i
$556$	−289266.			−0.935724
$557$	−306800.	−	306800.i	−0.988883	−	0.988883i	0.0110558	−	0.999939i	$-0.496481\pi$
$557$	−306800.	−	306800.i	−0.988883	−	0.988883i	−0.999939	+	0.0110558i	$0.996481\pi$
$558$	−21804.5	+	21804.5i	−0.0700289	+	0.0700289i
$559$			254209.i			0.813518i
$560$	−58735.3	−	81617.4i	−0.187294	−	0.260259i
$561$	87378.2			0.277637
$562$	17338.7	+	17338.7i	0.0548963	+	0.0548963i
$563$	331132.	−	331132.i	1.04468	−	1.04468i	0.0457279	−	0.998954i	$-0.485439\pi$
$563$	331132.	−	331132.i	1.04468	−	1.04468i	0.998954	−	0.0457279i	$-0.0145607\pi$
$564$			155363.i			0.488414i
$565$	46506.4	−	33467.9i	0.145685	−	0.104841i
$566$	94988.2			0.296508
$567$	−32396.2	−	32396.2i	−0.100769	−	0.100769i
$568$	85424.5	−	85424.5i	0.264780	−	0.264780i
$569$		−	257399.i		−	0.795028i	−0.917596	−	0.397514i	$-0.869873\pi$
$569$		−	257399.i		−	0.795028i	0.917596	−	0.397514i	$-0.130127\pi$
$570$	16093.5	−	98713.5i	0.0495338	−	0.303827i
$571$	−622495.			−1.90925			−0.954626	−	0.297807i	$-0.903745\pi$
$571$	−622495.			−1.90925			−0.954626	+	0.297807i	$0.903745\pi$
$572$	−299543.	−	299543.i	−0.915520	−	0.915520i
$573$	−146782.	+	146782.i	−0.447057	+	0.447057i
$574$			246441.i			0.747978i
$575$	69369.7	−	34557.4i	0.209814	−	0.104521i
$576$	−13824.0			−0.0416667
$577$	−23928.8	−	23928.8i	−0.0718736	−	0.0718736i	0.670256	−	0.742130i	$-0.266184\pi$
$577$	−23928.8	−	23928.8i	−0.0718736	−	0.0718736i	−0.742130	+	0.670256i	$0.766184\pi$
$578$	−146870.	+	146870.i	−0.439619	+	0.439619i
$579$		−	174520.i		−	0.520580i
$580$	165778.	+	27027.2i	0.492799	+	0.0803424i
$581$	365467.			1.08267
$582$	−157094.	−	157094.i	−0.463781	−	0.463781i
$583$	−230838.	+	230838.i	−0.679156	+	0.679156i
$584$		−	219688.i		−	0.644139i
$585$	124689.	+	173265.i	0.364348	+	0.506291i
$586$	220309.			0.641559
$587$	181136.	+	181136.i	0.525690	+	0.525690i	0.919284	−	0.393595i	$-0.128769\pi$
$587$	181136.	+	181136.i	0.525690	+	0.525690i	−0.393595	+	0.919284i	$0.628769\pi$
$588$	45522.3	−	45522.3i	0.131665	−	0.131665i
$589$		−	109915.i		−	0.316831i
$590$	−18796.6	+	13526.9i	−0.0539978	+	0.0388591i
$591$	20025.3			0.0573328
$592$	13285.7	+	13285.7i	0.0379089	+	0.0379089i
$593$	−235890.	+	235890.i	−0.670812	+	0.670812i	−0.957903	−	0.287091i	$-0.907312\pi$
$593$	−235890.	+	235890.i	−0.670812	+	0.670812i	0.287091	+	0.957903i	$0.407312\pi$
$594$		−	66442.8i		−	0.188311i
$595$	25390.1	−	155736.i	0.0717183	−	0.439902i
$596$	17151.5			0.0482847
$597$	−232258.	−	232258.i	−0.651660	−	0.651660i
$598$	78430.2	−	78430.2i	0.219322	−	0.219322i
$599$			141629.i			0.394728i	0.980330	+	0.197364i	$0.0632381\pi$
$599$			141629.i			0.394728i	−0.980330	+	0.197364i	$0.936762\pi$
$600$	−23340.4	+	69679.4i	−0.0648345	+	0.193554i
$601$	−564417.			−1.56261			−0.781306	−	0.624148i	$-0.785446\pi$
$601$	−564417.			−1.56261			−0.781306	+	0.624148i	$0.785446\pi$
$602$	−101036.	−	101036.i	−0.278794	−	0.278794i
$603$	76490.8	−	76490.8i	0.210366	−	0.210366i
$604$		−	71524.7i		−	0.196057i
$605$	330509.	+	53883.8i	0.902969	+	0.147213i
$606$	−25912.1			−0.0705597
$607$	247253.	+	247253.i	0.671064	+	0.671064i	0.957961	−	0.286898i	$-0.0926240\pi$
$607$	247253.	+	247253.i	0.671064	+	0.671064i	−0.286898	+	0.957961i	$0.592624\pi$
$608$	34843.0	−	34843.0i	0.0942560	−	0.0942560i
$609$			274256.i			0.739472i
$610$	173707.	+	241379.i	0.466828	+	0.648694i
$611$	1.18196e6			3.16606
$612$	−15339.2	−	15339.2i	−0.0409543	−	0.0409543i
$613$	−163758.	+	163758.i	−0.435794	+	0.435794i	−0.890594	−	0.454800i	$-0.849711\pi$
$613$	−163758.	+	163758.i	−0.435794	+	0.435794i	0.454800	+	0.890594i	$0.349711\pi$
$614$		−	47844.5i		−	0.126910i
$615$	146180.	−	105197.i	0.386490	−	0.278134i
$616$	238108.			0.627499
$617$	273782.	+	273782.i	0.719176	+	0.719176i	0.968437	−	0.249260i	$-0.0801875\pi$
$617$	273782.	+	273782.i	0.719176	+	0.719176i	−0.249260	+	0.968437i	$0.580188\pi$
$618$	−35482.3	+	35482.3i	−0.0929042	+	0.0929042i
$619$		−	428345.i		−	1.11792i	−0.829194	−	0.558962i	$-0.811200\pi$
$619$		−	428345.i		−	1.11792i	0.829194	−	0.558962i	$-0.188800\pi$
$620$	−12994.5	+	79705.0i	−0.0338047	+	0.207349i
$621$	17396.9			0.0451116
$622$	130569.	+	130569.i	0.337489	+	0.337489i
$623$	440465.	−	440465.i	1.13484	−	1.13484i
$624$			105169.i			0.270097i
$625$	311809.	+	235293.i	0.798231	+	0.602351i
$626$	25673.8			0.0655151
$627$	167467.	+	167467.i	0.425986	+	0.425986i
$628$	−144263.	+	144263.i	−0.365793	+	0.365793i
$629$			29483.8i			0.0745216i
$630$	−118423.	−	19306.7i	−0.298369	−	0.0486438i
$631$	108870.			0.273432			0.136716	−	0.990610i	$-0.456345\pi$
$631$	108870.			0.273432			0.136716	+	0.990610i	$0.456345\pi$
$632$	74667.1	+	74667.1i	0.186937	+	0.186937i
$633$	−56841.0	+	56841.0i	−0.141858	+	0.141858i
$634$		−	88400.5i		−	0.219926i
$635$	−238989.	−	332094.i	−0.592694	−	0.823595i
$636$	81046.9			0.200365
$637$	−346322.	−	346322.i	−0.853495	−	0.853495i
$638$	−281242.	+	281242.i	−0.690937	+	0.690937i
$639$		−	144154.i		−	0.353040i
$640$	−29385.7	+	21147.2i	−0.0717423	+	0.0516288i
$641$	−501643.			−1.22090			−0.610448	−	0.792056i	$-0.709011\pi$
$641$	−501643.			−1.22090			−0.610448	+	0.792056i	$0.709011\pi$
$642$	62888.6	+	62888.6i	0.152581	+	0.152581i
$643$	−117251.	+	117251.i	−0.283592	+	0.283592i	−0.834540	−	0.550948i	$-0.814266\pi$
$643$	−117251.	+	117251.i	−0.283592	+	0.283592i	0.550948	+	0.834540i	$0.314266\pi$
$644$			62344.5i			0.150323i
$645$	−16802.1	+	103060.i	−0.0403872	+	0.247725i
$646$	77324.1			0.185289
$647$	−362031.	−	362031.i	−0.864843	−	0.864843i	0.127053	−	0.991896i	$-0.459448\pi$
$647$	−362031.	−	362031.i	−0.864843	−	0.864843i	−0.991896	+	0.127053i	$0.959448\pi$
$648$	−11664.0	+	11664.0i	−0.0277778	+	0.0277778i
$649$		−	54836.8i		−	0.130192i
$650$	530103.	+	177568.i	1.25468	+	0.420279i
$651$	−131861.			−0.311139
$652$	−54872.0	−	54872.0i	−0.129079	−	0.129079i
$653$	−411293.	+	411293.i	−0.964552	+	0.964552i	−0.999393	−	0.0348413i	$-0.988907\pi$
$653$	−411293.	+	411293.i	−0.964552	+	0.964552i	0.0348413	+	0.999393i	$0.488907\pi$
$654$			173711.i			0.406136i
$655$	1619.20	+	263.982i	0.00377413	+	0.000615306i
$656$	88729.0			0.206185
$657$	−185361.	−	185361.i	−0.429426	−	0.429426i
$658$	−469772.	+	469772.i	−1.08501	+	1.08501i
$659$			291952.i			0.672265i	0.941815	+	0.336133i	$0.109119\pi$
$659$			291952.i			0.672265i	−0.941815	+	0.336133i	$0.890881\pi$
$660$	−101640.	−	141237.i	−0.233334	−	0.324237i
$661$	757270.			1.73320			0.866599	−	0.499006i	$-0.166301\pi$
$661$	757270.			1.73320			0.866599	+	0.499006i	$0.166301\pi$
$662$	98217.4	+	98217.4i	0.224116	+	0.224116i
$663$	−116697.	+	116697.i	−0.265480	+	0.265480i
$664$		−	131583.i		−	0.298445i
$665$	347143.	−	249819.i	0.784992	−	0.564914i
$666$	22419.6			0.0505452
$667$	−73638.3	−	73638.3i	−0.165521	−	0.165521i
$668$	299514.	−	299514.i	0.671219	−	0.671219i
$669$			211766.i			0.473156i
$670$	45585.2	−	279608.i	0.101549	−	0.622873i
$671$	−704193.			−1.56404
$672$	−41799.8	−	41799.8i	−0.0925626	−	0.0925626i
$673$	310335.	−	310335.i	0.685173	−	0.685173i	−0.275988	−	0.961161i	$-0.589005\pi$
$673$	310335.	−	310335.i	0.685173	−	0.685173i	0.961161	+	0.275988i	$0.0890050\pi$
$674$			571265.i			1.25753i
$675$	39098.6	+	78485.5i	0.0858130	+	0.172259i
$676$	571613.			1.25086
$677$	9203.97	+	9203.97i	0.0200816	+	0.0200816i	0.717076	−	0.696995i	$-0.245480\pi$
$677$	9203.97	+	9203.97i	0.0200816	+	0.0200816i	−0.696995	+	0.717076i	$0.745480\pi$
$678$	23817.9	−	23817.9i	0.0518137	−	0.0518137i
$679$		−	950012.i		−	2.06058i
$680$	−56071.5	−	9141.49i	−0.121262	−	0.0197697i
$681$	−6497.79			−0.0140111
$682$	−135220.	−	135220.i	−0.290717	−	0.290717i
$683$	−421590.	+	421590.i	−0.903750	+	0.903750i	−0.995758	−	0.0920080i	$-0.970671\pi$
$683$	−421590.	+	421590.i	−0.903750	+	0.903750i	0.0920080	+	0.995758i	$0.470671\pi$
$684$		−	58797.6i		−	0.125675i
$685$	11966.3	+	16628.1i	0.0255023	+	0.0354374i
$686$	−151502.			−0.321937
$687$	44371.4	+	44371.4i	0.0940135	+	0.0940135i
$688$	−36377.1	+	36377.1i	−0.0768514	+	0.0768514i
$689$		−	616584.i		−	1.29883i
$690$	36980.6	−	26612.8i	0.0776740	−	0.0558975i
$691$	102275.			0.214197			0.107098	−	0.994248i	$-0.465844\pi$
$691$	102275.			0.214197			0.107098	+	0.994248i	$0.465844\pi$
$692$	−261106.	−	261106.i	−0.545261	−	0.545261i
$693$	200904.	−	200904.i	0.418333	−	0.418333i
$694$			85601.3i			0.177730i
$695$	−145454.	+	892177.i	−0.301131	+	1.84706i
$696$	98743.7			0.203841
$697$	98454.3	+	98454.3i	0.202660	+	0.202660i
$698$	−68182.4	+	68182.4i	−0.139946	+	0.139946i
$699$		−	181476.i		−	0.371420i
$700$	−281265.	+	140116.i	−0.574010	+	0.285951i
$701$	−685359.			−1.39471			−0.697353	−	0.716728i	$-0.745639\pi$
$701$	−685359.			−1.39471			−0.697353	+	0.716728i	$0.745639\pi$
$702$	88736.7	+	88736.7i	0.180065	+	0.180065i
$703$	−56508.1	+	56508.1i	−0.114341	+	0.114341i
$704$		−	85728.9i		−	0.172974i
$705$	479182.	+	78122.2i	0.964100	+	0.157180i
$706$	−115.016			−0.000230753
$707$	−78350.6	−	78350.6i	−0.156749	−	0.156749i
$708$	−9626.57	+	9626.57i	−0.0192046	+	0.0192046i
$709$		−	164715.i		−	0.327673i	−0.986487	−	0.163837i	$-0.947613\pi$
$709$		−	164715.i		−	0.327673i	0.986487	−	0.163837i	$-0.0523870\pi$
$710$	−220518.	−	306428.i	−0.437449	−	0.607871i
$711$	126001.			0.249249
$712$	−158586.	−	158586.i	−0.312827	−	0.312827i
$713$	35404.9	−	35404.9i	0.0696441	−	0.0696441i
$714$		−	92762.6i		−	0.181960i
$715$	−1.07450e6	+	773254.i	−2.10181	+	1.51255i
$716$	51169.5			0.0998126
$717$	−177053.	−	177053.i	−0.344402	−	0.344402i
$718$	347885.	−	347885.i	0.674818	−	0.674818i
$719$		−	782798.i		−	1.51423i	−0.653282	−	0.757115i	$-0.726608\pi$
$719$		−	782798.i		−	1.51423i	0.653282	−	0.757115i	$-0.273392\pi$
$720$	−6951.23	+	42637.1i	−0.0134090	+	0.0822474i
$721$	−214577.			−0.412774
$722$	−112444.	−	112444.i	−0.215706	−	0.215706i
$723$	202760.	−	202760.i	0.387887	−	0.387887i
$724$			392208.i			0.748236i
$725$	166719.	−	497715.i	0.317182	−	0.946900i
$726$	196864.			0.373503
$727$	659110.	+	659110.i	1.24706	+	1.24706i	0.957010	+	0.290054i	$0.0936732\pi$
$727$	659110.	+	659110.i	1.24706	+	1.24706i	0.290054	+	0.957010i	$0.406327\pi$
$728$	−318002.	+	318002.i	−0.600021	+	0.600021i
$729$			19683.0i			0.0370370i
$730$	−677578.	−	110467.i	−1.27149	−	0.207295i
$731$	−80728.6			−0.151075
$732$	123621.	+	123621.i	0.230711	+	0.230711i
$733$	356952.	−	356952.i	0.664358	−	0.664358i	−0.292046	−	0.956404i	$-0.594336\pi$
$733$	356952.	−	356952.i	0.664358	−	0.664358i	0.956404	+	0.292046i	$0.0943361\pi$
$734$			167816.i			0.311489i
$735$	−117513.	−	163294.i	−0.217526	−	0.302270i
$736$	22446.6			0.0414377
$737$	474354.	+	474354.i	0.873309	+	0.873309i
$738$	74865.1	−	74865.1i	0.137457	−	0.137457i
$739$			231725.i			0.424311i	0.977236	+	0.212156i	$0.0680483\pi$
$739$			231725.i			0.424311i	−0.977236	+	0.212156i	$0.931952\pi$
$740$	47657.4	−	34296.3i	0.0870296	−	0.0626302i
$741$	−447317.			−0.814665
$742$	245062.	+	245062.i	0.445111	+	0.445111i
$743$	−35964.9	+	35964.9i	−0.0651480	+	0.0651480i	−0.738930	−	0.673782i	$-0.764669\pi$
$743$	−35964.9	+	35964.9i	−0.0651480	+	0.0651480i	0.673782	+	0.738930i	$0.264669\pi$
$744$			47475.4i			0.0857676i
$745$	8624.43	−	52900.1i	0.0155388	−	0.0953111i
$746$	263501.			0.473483
$747$	−111023.	−	111023.i	−0.198963	−	0.198963i
$748$	95125.3	−	95125.3i	0.170017	−	0.170017i
$749$			380314.i			0.677920i
$750$	203174.	+	107026.i	0.361199	+	0.190268i
$751$	702045.			1.24476			0.622379	−	0.782716i	$-0.286166\pi$
$751$	702045.			1.24476			0.622379	+	0.782716i	$0.286166\pi$
$752$	169137.	+	169137.i	0.299091	+	0.299091i
$753$	255976.	−	255976.i	0.451449	−	0.451449i
$754$		−	751216.i		−	1.32136i
$755$	−220602.	−	35965.3i	−0.387004	−	0.0630943i
$756$	−70537.1			−0.123417
$757$	−111880.	−	111880.i	−0.195236	−	0.195236i	0.602718	−	0.797954i	$-0.294084\pi$
$757$	−111880.	−	111880.i	−0.195236	−	0.195236i	−0.797954	+	0.602718i	$0.794084\pi$
$758$	−21673.9	+	21673.9i	−0.0377224	+	0.0377224i
$759$			107886.i			0.187276i
$760$	−89945.3	−	124986.i	−0.155722	−	0.216389i
$761$	−579015.			−0.999817			−0.499908	−	0.866078i	$-0.666633\pi$
$761$	−579015.			−0.999817			−0.499908	+	0.866078i	$0.666633\pi$
$762$	−170080.	−	170080.i	−0.292916	−	0.292916i
$763$	−525252.	+	525252.i	−0.902232	+	0.902232i
$764$			319592.i			0.547531i
$765$	−55023.5	+	39597.2i	−0.0940211	+	0.0676616i
$766$	−89310.0			−0.152210
$767$	73236.4	+	73236.4i	0.124491	+	0.124491i
$768$	−15049.7	+	15049.7i	−0.0255155	+	0.0255155i
$769$			472110.i			0.798344i	0.916876	+	0.399172i	$0.130702\pi$
$769$			472110.i			0.798344i	−0.916876	+	0.399172i	$0.869298\pi$
$770$	119730.	−	734392.i	0.201939	−	1.23864i
$771$	85348.4			0.143578
$772$	−189993.	−	189993.i	−0.318789	−	0.318789i
$773$	−20353.7	+	20353.7i	−0.0340631	+	0.0340631i	−0.723933	−	0.689870i	$-0.757668\pi$
$773$	−20353.7	+	20353.7i	−0.0340631	+	0.0340631i	0.689870	+	0.723933i	$0.257668\pi$
$774$			61386.4i			0.102469i
$775$	239298.	+	80157.4i	0.398416	+	0.133457i
$776$	−342044.			−0.568013
$777$	67790.5	+	67790.5i	0.112286	+	0.112286i
$778$	−407768.	+	407768.i	−0.673680	+	0.673680i
$779$			377391.i			0.621895i
$780$	324372.	+	52883.2i	0.533155	+	0.0869217i
$781$	893963.			1.46561
$782$	24906.9	+	24906.9i	0.0407293	+	0.0407293i
$783$	83315.0	−	83315.0i	0.135894	−	0.135894i
$784$		−	99116.8i		−	0.161256i
$785$	372406.	+	517488.i	0.604335	+	0.839771i
$786$	964.457			0.00156113
$787$	640630.	+	640630.i	1.03433	+	1.03433i	0.999390	+	0.0349373i	$0.0111232\pi$
$787$	640630.	+	640630.i	1.03433	+	1.03433i	0.0349373	+	0.999390i	$0.488877\pi$
$788$	21800.7	−	21800.7i	0.0351090	−	0.0351090i
$789$			637933.i			1.02476i
$790$	267840.	−	192749.i	0.429161	−	0.308843i
$791$	144037.			0.230208
$792$	−72333.8	−	72333.8i	−0.115316	−	0.115316i
$793$	940474.	−	940474.i	1.49555	−	1.49555i
$794$		−	469194.i		−	0.744238i
$795$	40753.5	−	249971.i	0.0644808	−	0.395509i
$796$	−505700.			−0.798118
$797$	542782.	+	542782.i	0.854494	+	0.854494i	0.990683	−	0.136189i	$-0.0434854\pi$
$797$	542782.	+	542782.i	0.854494	+	0.854494i	−0.136189	+	0.990683i	$0.543485\pi$
$798$	177787.	−	177787.i	0.279186	−	0.279186i
$799$			375352.i			0.587956i
$800$	50447.5	+	101267.i	0.0788243	+	0.158230i
$801$	−267614.			−0.417103
$802$	−86186.2	−	86186.2i	−0.133995	−	0.133995i
$803$	1.14951e6	−	1.14951e6i	1.78271	−	1.78271i
$804$		−	166545.i		−	0.257644i
$805$	192288.	+	31349.2i	0.296729	+	0.0483765i
$806$	361181.			0.555974
$807$	−343318.	−	343318.i	−0.527168	−	0.527168i
$808$	−28209.5	+	28209.5i	−0.0432088	+	0.0432088i
$809$			1.09699e6i			1.67613i	0.545571	+	0.838065i	$0.316313\pi$
$809$			1.09699e6i			1.67613i	−0.545571	+	0.838065i	$0.683687\pi$
$810$	30109.9	+	41840.1i	0.0458923	+	0.0637710i
$811$	−711398.			−1.08161			−0.540805	−	0.841148i	$-0.681880\pi$
$811$	−711398.			−1.08161			−0.540805	+	0.841148i	$0.681880\pi$
$812$	298572.	+	298572.i	0.452832	+	0.452832i
$813$	39889.3	−	39889.3i	0.0603498	−	0.0603498i
$814$			139034.i			0.209833i
$815$	−196832.	+	141649.i	−0.296334	+	0.213254i
$816$	−33398.4			−0.0501586
$817$	−154723.	−	154723.i	−0.231798	−	0.231798i
$818$	372179.	−	372179.i	0.556219	−	0.556219i
$819$			536628.i			0.800028i
$820$	44616.3	−	273665.i	0.0663538	−	0.406997i
$821$	−566243.			−0.840071			−0.420036	−	0.907508i	$-0.637982\pi$
$821$	−566243.			−0.840071			−0.420036	+	0.907508i	$0.637982\pi$
$822$	8515.98	+	8515.98i	0.0126035	+	0.0126035i
$823$	−678523.	+	678523.i	−1.00176	+	1.00176i	−0.00176504	+	0.999998i	$0.500562\pi$
$823$	−678523.	+	678523.i	−1.00176	+	1.00176i	−0.999998	+	0.00176504i	$0.999438\pi$
$824$			77256.6i			0.113784i
$825$	−486724.	+	242468.i	−0.715114	+	0.356243i
$826$	−58215.9			−0.0853261
$827$	−822466.	−	822466.i	−1.20256	−	1.20256i	−0.973385	−	0.229174i	$-0.926397\pi$
$827$	−822466.	−	822466.i	−1.20256	−	1.20256i	−0.229174	−	0.973385i	$-0.573603\pi$
$828$	18939.3	−	18939.3i	0.0276251	−	0.0276251i
$829$		−	1.26805e6i		−	1.84514i	−0.385832	−	0.922569i	$-0.626086\pi$
$829$		−	1.26805e6i		−	1.84514i	0.385832	−	0.922569i	$-0.373914\pi$
$830$	−405839.	−	66165.0i	−0.589112	−	0.0960445i
$831$	−479228.			−0.693969
$832$	114494.	+	114494.i	0.165400	+	0.165400i
$833$	109981.	−	109981.i	0.158499	−	0.158499i
$834$			531415.i			0.764015i
$835$	−773178.	−	1.07439e6i	−1.10894	−	1.54095i
$836$	364631.			0.521724
$837$	40057.4	+	40057.4i	0.0571784	+	0.0571784i
$838$	−203397.	+	203397.i	−0.289639	+	0.289639i
$839$		−	487091.i		−	0.691968i	−0.938240	−	0.345984i	$-0.887545\pi$
$839$		−	487091.i		−	0.691968i	0.938240	−	0.345984i	$-0.112455\pi$
$840$	−149941.	+	107904.i	−0.212501	+	0.152925i
$841$	1962.99			0.00277541
$842$	45065.9	+	45065.9i	0.0635659	+	0.0635659i
$843$	31853.2	−	31853.2i	0.0448227	−	0.0448227i
$844$			123761.i			0.173740i
$845$	287429.	−	1.76301e6i	0.402547	−	2.46912i
$846$	285419.			0.398789
$847$	595260.	+	595260.i	0.829736	+	0.829736i
$848$	88232.7	−	88232.7i	0.122698	−	0.122698i
$849$		−	174504.i		−	0.242098i
$850$	−56389.8	+	168344.i	−0.0780482	+	0.233002i
$851$	−36403.7			−0.0502675
$852$	−156935.	−	156935.i	−0.216192	−	0.216192i
$853$	10645.4	−	10645.4i	0.0146307	−	0.0146307i	−0.699754	−	0.714384i	$-0.746707\pi$
$853$	10645.4	−	10645.4i	0.0146307	−	0.0146307i	0.714384	+	0.699754i	$0.246707\pi$
$854$			747586.i			1.02505i
$855$	−181348.	−	29565.7i	−0.248074	−	0.0404441i
$856$	136929.			0.186873
$857$	−692563.	−	692563.i	−0.942970	−	0.942970i	0.0554896	−	0.998459i	$-0.482328\pi$
$857$	−692563.	−	692563.i	−0.942970	−	0.942970i	−0.998459	+	0.0554896i	$0.982328\pi$
$858$	−550296.	+	550296.i	−0.747519	+	0.747519i
$859$			745974.i			1.01097i	0.862836	+	0.505484i	$0.168686\pi$
$859$			745974.i			1.01097i	−0.862836	+	0.505484i	$0.831314\pi$
$860$	93905.5	+	130489.i	0.126968	+	0.176432i
$861$	452741.			0.610722
$862$	−421196.	−	421196.i	−0.566852	−	0.566852i
$863$	259362.	−	259362.i	0.348245	−	0.348245i	−0.511211	−	0.859456i	$-0.670803\pi$
$863$	259362.	−	259362.i	0.348245	−	0.348245i	0.859456	+	0.511211i	$0.170803\pi$
$864$			25396.3i			0.0340207i
$865$	−936618.	+	674030.i	−1.25179	+	0.900838i
$866$	−493621.			−0.658201
$867$	269817.	+	269817.i	0.358947	+	0.358947i
$868$	−143552.	+	143552.i	−0.190533	+	0.190533i
$869$			781388.i			1.03473i
$870$	49652.1	−	304553.i	0.0655993	−	0.402369i
$871$	−1.26703e6			−1.67013
$872$	189113.	+	189113.i	0.248707	+	0.248707i
$873$	−288600.	+	288600.i	−0.378676	+	0.378676i
$874$			95472.3i			0.124984i
$875$	290725.	+	937956.i	0.379723	+	1.22509i
$876$	−403592.			−0.525938
$877$	−191986.	−	191986.i	−0.249615	−	0.249615i	0.571197	−	0.820813i	$-0.306479\pi$
$877$	−191986.	−	191986.i	−0.249615	−	0.249615i	−0.820813	+	0.571197i	$0.806479\pi$
$878$	530360.	−	530360.i	0.687989	−	0.687989i
$879$		−	404733.i		−	0.523830i
$880$	−264412.	−	43107.8i	−0.341441	−	0.0556660i
$881$	1.08074e6			1.39241			0.696207	−	0.717841i	$-0.254870\pi$
$881$	1.08074e6			1.39241			0.696207	+	0.717841i	$0.254870\pi$
$882$	−83629.8	−	83629.8i	−0.107504	−	0.107504i
$883$	294604.	−	294604.i	0.377848	−	0.377848i	−0.492477	−	0.870325i	$-0.663909\pi$
$883$	294604.	−	294604.i	0.377848	−	0.377848i	0.870325	+	0.492477i	$0.163909\pi$
$884$			254086.i			0.325145i
$885$	24850.4	+	34531.6i	0.0317283	+	0.0440890i
$886$	399264.			0.508619
$887$	−373328.	−	373328.i	−0.474507	−	0.474507i	0.428862	−	0.903370i	$-0.358915\pi$
$887$	−373328.	−	373328.i	−0.474507	−	0.474507i	−0.903370	+	0.428862i	$0.858915\pi$
$888$	24407.4	−	24407.4i	0.0309525	−	0.0309525i
$889$		−	1.02854e6i		−	1.30143i
$890$	−568866.	+	409380.i	−0.718175	+	0.516829i
$891$	−122063.			−0.153755
$892$	230542.	+	230542.i	0.289748	+	0.289748i
$893$	−719392.	+	719392.i	−0.902117	+	0.902117i
$894$		−	31509.3i		−	0.0394243i
$895$	25730.0	−	157821.i	0.0321213	−	0.197024i
$896$	−91011.7			−0.113366
$897$	−144086.	−	144086.i	−0.179075	−	0.179075i
$898$	365869.	−	365869.i	0.453704	−	0.453704i
$899$		−	339113.i		−	0.419590i
$900$	128009.	+	42879.1i	0.158036	+	0.0529371i
$901$	195807.			0.241201
$902$	464273.	+	464273.i	0.570637	+	0.570637i
$903$	−185615.	+	185615.i	−0.227634	+	0.227634i
$904$		−	51859.3i		−	0.0634585i
$905$	1.20968e6	+	197217.i	1.47697	+	0.240795i
$906$	−131399.			−0.160080
$907$	−342694.	−	342694.i	−0.416574	−	0.416574i	0.467447	−	0.884021i	$-0.345174\pi$
$907$	−342694.	−	342694.i	−0.416574	−	0.416574i	−0.884021	+	0.467447i	$0.845174\pi$
$908$	−7073.89	+	7073.89i	−0.00857999	+	0.00857999i
$909$			47603.5i			0.0576118i
$910$	820903.	+	1.14071e6i	0.991309	+	1.37750i
$911$	653388.			0.787290			0.393645	−	0.919263i	$-0.371214\pi$
$911$	653388.			0.787290			0.393645	+	0.919263i	$0.371214\pi$
$912$	−64010.7	−	64010.7i	−0.0769597	−	0.0769597i
$913$	688506.	−	688506.i	0.825974	−	0.825974i
$914$		−	589989.i		−	0.706239i
$915$	443442.	−	319119.i	0.529657	−	0.381163i
$916$	96611.0			0.115143
$917$	2916.24	+	2916.24i	0.00346804	+	0.00346804i
$918$	−28179.9	+	28179.9i	−0.0334391	+	0.0334391i
$919$		−	316752.i		−	0.375050i	−0.982260	−	0.187525i	$-0.939953\pi$
$919$		−	316752.i		−	0.375050i	0.982260	−	0.187525i	$-0.0600465\pi$
$920$	11287.0	−	69231.7i	0.0133353	−	0.0817955i
$921$	−87896.0			−0.103621
$922$	709825.	+	709825.i	0.835006	+	0.835006i
$923$	−1.19392e6	+	1.19392e6i	−1.40143	+	1.40143i
$924$		−	437433.i		−	0.512351i
$925$	−81815.4	−	164234.i	−0.0956206	−	0.191947i
$926$	−729901.			−0.851221
$927$	65185.2	+	65185.2i	0.0758560	+	0.0758560i
$928$	107499.	−	107499.i	0.124826	−	0.124826i
$929$		−	1.39646e6i		−	1.61807i	−0.587759	−	0.809036i	$-0.699990\pi$
$929$		−	1.39646e6i		−	1.61807i	0.587759	−	0.809036i	$-0.300010\pi$
$930$	146427.	+	23872.4i	0.169300	+	0.0276014i
$931$	421574.			0.486378
$932$	−197566.	−	197566.i	−0.227447	−	0.227447i
$933$	239870.	−	239870.i	0.275558	−	0.275558i
$934$		−	17393.2i		−	0.0199382i
$935$	−245560.	−	341226.i	−0.280889	−	0.390318i
$936$	193208.			0.220533
$937$	81884.2	+	81884.2i	0.0932655	+	0.0932655i	0.752200	−	0.658935i	$-0.228993\pi$
$937$	81884.2	+	81884.2i	0.0932655	+	0.0932655i	−0.658935	+	0.752200i	$0.728993\pi$
$938$	503585.	−	503585.i	0.572357	−	0.572357i
$939$		−	47165.7i		−	0.0534928i
$940$	606716.	−	436618.i	0.686641	−	0.494136i
$941$	1.67094e6			1.88705			0.943524	−	0.331305i	$-0.107489\pi$
$941$	1.67094e6			1.88705			0.943524	+	0.331305i	$0.107489\pi$
$942$	265028.	+	265028.i	0.298669	+	0.298669i
$943$	−121562.	+	121562.i	−0.136702	+	0.136702i
$944$			20960.2i			0.0235207i
$945$	−35468.7	+	217556.i	−0.0397175	+	0.243617i
$946$	−380685.			−0.425386
$947$	689602.	+	689602.i	0.768950	+	0.768950i	0.977922	−	0.208971i	$-0.0670116\pi$
$947$	689602.	+	689602.i	0.768950	+	0.768950i	−0.208971	+	0.977922i	$0.567012\pi$
$948$	137172.	−	137172.i	0.152633	−	0.152633i
$949$			3.07042e6i			3.40930i
$950$	−430720.	+	214569.i	−0.477252	+	0.237749i
$951$	−162402.			−0.179569
$952$	−100987.	−	100987.i	−0.111427	−	0.111427i
$953$	150337.	−	150337.i	0.165532	−	0.165532i	−0.619480	−	0.785012i	$-0.712657\pi$
$953$	150337.	−	150337.i	0.165532	−	0.165532i	0.785012	+	0.619480i	$0.212657\pi$
$954$		−	148893.i		−	0.163597i
$955$	985710.	+	160703.i	1.08079	+	0.176204i
$956$	−385502.			−0.421804
$957$	516674.	+	516674.i	0.564148	+	0.564148i
$958$	−154692.	+	154692.i	−0.168553	+	0.168553i
$959$			51499.7i			0.0559974i
$960$	38849.8	+	53984.9i	0.0421548	+	0.0585774i
$961$	−760477.			−0.823454
$962$	−185685.	−	185685.i	−0.200644	−	0.200644i
$963$	115534.	−	115534.i	0.124582	−	0.124582i
$964$		−	441473.i		−	0.475062i
$965$	−681527.	+	490456.i	−0.731861	+	0.526678i
$966$	114534.			0.122739
$967$	−312723.	−	312723.i	−0.334432	−	0.334432i	0.519835	−	0.854267i	$-0.325993\pi$
$967$	−312723.	−	312723.i	−0.334432	−	0.334432i	−0.854267	+	0.519835i	$0.825993\pi$
$968$	214319.	−	214319.i	0.228723	−	0.228723i
$969$		−	142053.i		−	0.151288i
$970$	−171993.	+	1.05496e6i	−0.182796	+	1.12122i
$971$	1.16534e6			1.23598			0.617992	−	0.786185i	$-0.287946\pi$
$971$	1.16534e6			1.23598			0.617992	+	0.786185i	$0.287946\pi$
$972$	21428.1	+	21428.1i	0.0226805	+	0.0226805i
$973$	−1.60685e6	+	1.60685e6i	−1.69726	+	1.69726i
$974$		−	308903.i		−	0.325614i
$975$	326213.	−	973861.i	0.343156	−	1.02444i
$976$	269162.			0.282562
$977$	−748461.	−	748461.i	−0.784115	−	0.784115i	0.196407	−	0.980522i	$-0.437073\pi$
$977$	−748461.	−	748461.i	−0.784115	−	0.784115i	−0.980522	+	0.196407i	$0.937073\pi$
$978$	−100806.	+	100806.i	−0.105393	+	0.105393i
$979$		−	1.65959e6i		−	1.73156i
$980$	−305704.	−	49839.7i	−0.318309	−	0.0518947i
$981$	319127.			0.331609
$982$	−680434.	−	680434.i	−0.705607	−	0.705607i
$983$	−542812.	+	542812.i	−0.561749	+	0.561749i	−0.929804	−	0.368055i	$-0.880024\pi$
$983$	−542812.	+	542812.i	−0.561749	+	0.561749i	0.368055	+	0.929804i	$0.380024\pi$
$984$		−	163006.i		−	0.168350i
$985$	−56277.3	−	78201.8i	−0.0580044	−	0.0806017i
$986$	238562.			0.245385
$987$	863025.	+	863025.i	0.885909	+	0.885909i
$988$	−486977.	+	486977.i	−0.498878	+	0.498878i
$989$		−	99675.8i		−	0.101905i
$990$	−259470.	+	186725.i	−0.264738	+	0.190517i
$991$	1.08269e6			1.10245			0.551224	−	0.834357i	$-0.314161\pi$
$991$	1.08269e6			1.10245			0.551224	+	0.834357i	$0.314161\pi$
$992$	51684.7	+	51684.7i	0.0525217	+	0.0525217i
$993$	180437.	−	180437.i	0.182990	−	0.182990i
$994$		−	949050.i		−	0.960542i
$995$	−254285.	+	1.55972e6i	−0.256847	+	1.57544i
$996$	−241734.			−0.243679
$997$	25593.2	+	25593.2i	0.0257475	+	0.0257475i	0.719863	−	0.694116i	$-0.244204\pi$
$997$	25593.2	+	25593.2i	0.0257475	+	0.0257475i	−0.694116	+	0.719863i	$0.744204\pi$
$998$	−662047.	+	662047.i	−0.664703	+	0.664703i
$999$		−	41187.5i		−	0.0412700i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.5.f.a.7.1	✓	4
3.2	odd	2		90.5.g.e.37.1		4
4.3	odd	2		240.5.bg.b.97.2		4
5.2	odd	4		150.5.f.e.43.2		4
5.3	odd	4	inner	30.5.f.a.13.1	yes	4
5.4	even	2		150.5.f.e.7.2		4
15.2	even	4		450.5.g.f.343.1		4
15.8	even	4		90.5.g.e.73.1		4
15.14	odd	2		450.5.g.f.307.1		4
20.3	even	4		240.5.bg.b.193.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.5.f.a.7.1	✓	4	1.1	even	1	trivial
30.5.f.a.13.1	yes	4	5.3	odd	4	inner
90.5.g.e.37.1		4	3.2	odd	2
90.5.g.e.73.1		4	15.8	even	4
150.5.f.e.7.2		4	5.4	even	2
150.5.f.e.43.2		4	5.2	odd	4
240.5.bg.b.97.2		4	4.3	odd	2
240.5.bg.b.193.2		4	20.3	even	4
450.5.g.f.307.1		4	15.14	odd	2
450.5.g.f.343.1		4	15.2	even	4

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:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	30.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{2} +(-3.67423 + 3.67423i) q^{3} +8.00000i q^{4} +(24.6742 + 4.02270i) q^{5} +14.6969 q^{6} +(44.4393 + 44.4393i) q^{7} +(16.0000 - 16.0000i) q^{8} -27.0000i q^{9} +(-41.3031 - 57.3939i) q^{10} +167.439 q^{11} +(-29.3939 - 29.3939i) q^{12} +(-223.621 + 223.621i) q^{13} -177.757i q^{14} +(-105.439 + 75.8786i) q^{15} -64.0000 q^{16} +(-71.0148 - 71.0148i) q^{17} +(-54.0000 + 54.0000i) q^{18} -272.211i q^{19} +(-32.1816 + 197.394i) q^{20} -326.561 q^{21} +(-334.879 - 334.879i) q^{22} +(87.6821 - 87.6821i) q^{23} +117.576i q^{24} +(592.636 + 198.514i) q^{25} +894.484 q^{26} +(99.2043 + 99.2043i) q^{27} +(-355.514 + 355.514i) q^{28} -839.832i q^{29} +(362.636 + 59.1214i) q^{30} +403.787 q^{31} +(128.000 + 128.000i) q^{32} +(-615.211 + 615.211i) q^{33} +284.059i q^{34} +(917.739 + 1275.27i) q^{35} +216.000 q^{36} +(-207.589 - 207.589i) q^{37} +(-544.422 + 544.422i) q^{38} -1643.27i q^{39} +(459.151 - 330.424i) q^{40} -1386.39 q^{41} +(653.121 + 653.121i) q^{42} +(568.393 - 568.393i) q^{43} +1339.51i q^{44} +(108.613 - 666.204i) q^{45} -350.729 q^{46} +(-2642.77 - 2642.77i) q^{47} +(235.151 - 235.151i) q^{48} +1548.70i q^{49} +(-788.243 - 1582.30i) q^{50} +521.850 q^{51} +(-1788.97 - 1788.97i) q^{52} +(-1378.64 + 1378.64i) q^{53} -396.817i q^{54} +(4131.44 + 673.559i) q^{55} +1422.06 q^{56} +(1000.17 + 1000.17i) q^{57} +(-1679.66 + 1679.66i) q^{58} -327.503i q^{59} +(-607.029 - 843.514i) q^{60} -4205.66 q^{61} +(-807.573 - 807.573i) q^{62} +(1199.86 - 1199.86i) q^{63} -512.000i q^{64} +(-6417.24 + 4618.11i) q^{65} +2460.84 q^{66} +(2832.99 + 2832.99i) q^{67} +(568.118 - 568.118i) q^{68} +644.330i q^{69} +(715.064 - 4386.02i) q^{70} +5339.03 q^{71} +(-432.000 - 432.000i) q^{72} +(6865.24 - 6865.24i) q^{73} +830.357i q^{74} +(-2906.87 + 1448.09i) q^{75} +2177.69 q^{76} +(7440.88 + 7440.88i) q^{77} +(-3286.54 + 3286.54i) q^{78} +4666.69i q^{79} +(-1579.15 - 257.453i) q^{80} -729.000 q^{81} +(2772.78 + 2772.78i) q^{82} +(4111.98 - 4111.98i) q^{83} -2612.49i q^{84} +(-1466.56 - 2037.91i) q^{85} -2273.57 q^{86} +(3085.74 + 3085.74i) q^{87} +(2679.03 - 2679.03i) q^{88} -9911.62i q^{89} +(-1549.63 + 1115.18i) q^{90} -19875.1 q^{91} +(701.457 + 701.457i) q^{92} +(-1483.61 + 1483.61i) q^{93} +10571.1i q^{94} +(1095.03 - 6716.60i) q^{95} -940.604 q^{96} +(-10688.9 - 10688.9i) q^{97} +(3097.40 - 3097.40i) q^{98} -4520.86i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 84 q^{5} - 28 q^{7} + 64 q^{8} - 224 q^{10} + 464 q^{11} - 336 q^{13} - 216 q^{15} - 256 q^{16} + 392 q^{17} - 216 q^{18} + 224 q^{20} - 1512 q^{21} - 928 q^{22} + 968 q^{23} + 1136 q^{25}+ \cdots + 23912 q^{98}+O(q^{100}) \) 4 * q - 8 * q^2 + 84 * q^5 - 28 * q^7 + 64 * q^8 - 224 * q^10 + 464 * q^11 - 336 * q^13 - 216 * q^15 - 256 * q^16 + 392 * q^17 - 216 * q^18 + 224 * q^20 - 1512 * q^21 - 928 * q^22 + 968 * q^23 + 1136 * q^25 + 1344 * q^26 + 224 * q^28 + 216 * q^30 - 560 * q^31 + 512 * q^32 - 756 * q^33 - 2296 * q^35 + 864 * q^36 + 2256 * q^37 + 1232 * q^38 + 896 * q^40 + 392 * q^41 + 3024 * q^42 + 216 * q^43 - 756 * q^45 - 3872 * q^46 - 9072 * q^47 - 3976 * q^50 + 4968 * q^51 - 2688 * q^52 - 4280 * q^53 + 10500 * q^55 - 896 * q^56 + 6264 * q^57 - 2192 * q^58 + 864 * q^60 - 4536 * q^61 + 1120 * q^62 - 756 * q^63 - 12912 * q^65 + 3024 * q^66 - 2248 * q^67 - 3136 * q^68 + 9856 * q^70 + 18064 * q^71 - 1728 * q^72 + 20524 * q^73 - 10584 * q^75 - 4928 * q^76 + 7336 * q^77 - 8208 * q^78 - 5376 * q^80 - 2916 * q^81 - 784 * q^82 - 336 * q^83 + 15944 * q^85 - 864 * q^86 + 8316 * q^87 + 7424 * q^88 - 3024 * q^90 - 52752 * q^91 + 7744 * q^92 - 7992 * q^93 + 23104 * q^95 - 40404 * q^97 + 23912 * q^98

Introduction

L-functions

Modular forms

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Database

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