LMFDB - Embedded newform 26.5.d.a.21.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,5,Mod(5,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("26.5");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	26.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.68761904018$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 234x^{4} + 13689x^{2} + 60516 $ x^6 + 234x^4 + 13689x^2 + 60516
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.2
Root			$2.19267i$ of defining polynomial
Character	$\chi$	$=$	26.21
Dual form			26.5.d.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 2.00000i) q^{2} -2.19267 q^{3} +8.00000i q^{4} +(-28.1144 - 28.1144i) q^{5} +(4.38533 + 4.38533i) q^{6} +(-49.0778 + 49.0778i) q^{7} +(16.0000 - 16.0000i) q^{8} -76.1922 q^{9} +O(q^{10})$	\(q+(-2.00000 - 2.00000i) q^{2} -2.19267 q^{3} +8.00000i q^{4} +(-28.1144 - 28.1144i) q^{5} +(4.38533 + 4.38533i) q^{6} +(-49.0778 + 49.0778i) q^{7} +(16.0000 - 16.0000i) q^{8} -76.1922 q^{9} +112.458i q^{10} +(125.843 - 125.843i) q^{11} -17.5413i q^{12} +(76.8118 - 150.536i) q^{13} +196.311 q^{14} +(61.6456 + 61.6456i) q^{15} -64.0000 q^{16} +293.870i q^{17} +(152.384 + 152.384i) q^{18} +(-165.724 - 165.724i) q^{19} +(224.916 - 224.916i) q^{20} +(107.611 - 107.611i) q^{21} -503.372 q^{22} -297.165i q^{23} +(-35.0826 + 35.0826i) q^{24} +955.844i q^{25} +(-454.695 + 147.448i) q^{26} +344.670 q^{27} +(-392.622 - 392.622i) q^{28} -1060.76 q^{29} -246.582i q^{30} +(-511.960 - 511.960i) q^{31} +(128.000 + 128.000i) q^{32} +(-275.932 + 275.932i) q^{33} +(587.740 - 587.740i) q^{34} +2759.59 q^{35} -609.538i q^{36} +(-292.878 + 292.878i) q^{37} +662.895i q^{38} +(-168.422 + 330.074i) q^{39} -899.662 q^{40} +(-804.161 - 804.161i) q^{41} -430.445 q^{42} +1005.69i q^{43} +(1006.74 + 1006.74i) q^{44} +(2142.10 + 2142.10i) q^{45} +(-594.330 + 594.330i) q^{46} +(1325.64 - 1325.64i) q^{47} +140.331 q^{48} -2416.26i q^{49} +(1911.69 - 1911.69i) q^{50} -644.359i q^{51} +(1204.28 + 614.494i) q^{52} +574.799 q^{53} +(-689.340 - 689.340i) q^{54} -7076.02 q^{55} +1570.49i q^{56} +(363.377 + 363.377i) q^{57} +(2121.52 + 2121.52i) q^{58} +(2237.69 - 2237.69i) q^{59} +(-493.165 + 493.165i) q^{60} -6068.83 q^{61} +2047.84i q^{62} +(3739.34 - 3739.34i) q^{63} -512.000i q^{64} +(-6391.74 + 2072.70i) q^{65} +1103.73 q^{66} +(3155.98 + 3155.98i) q^{67} -2350.96 q^{68} +651.583i q^{69} +(-5519.18 - 5519.18i) q^{70} +(-1607.78 - 1607.78i) q^{71} +(-1219.08 + 1219.08i) q^{72} +(22.6121 - 22.6121i) q^{73} +1171.51 q^{74} -2095.85i q^{75} +(1325.79 - 1325.79i) q^{76} +12352.2i q^{77} +(996.993 - 323.303i) q^{78} +6576.52 q^{79} +(1799.32 + 1799.32i) q^{80} +5415.82 q^{81} +3216.64i q^{82} +(-5691.45 - 5691.45i) q^{83} +(860.889 + 860.889i) q^{84} +(8261.99 - 8261.99i) q^{85} +(2011.39 - 2011.39i) q^{86} +2325.89 q^{87} -4026.98i q^{88} +(4243.56 - 4243.56i) q^{89} -8568.41i q^{90} +(3618.20 + 11157.7i) q^{91} +2377.32 q^{92} +(1122.56 + 1122.56i) q^{93} -5302.58 q^{94} +9318.47i q^{95} +(-280.661 - 280.661i) q^{96} +(3532.64 + 3532.64i) q^{97} +(-4832.51 + 4832.51i) q^{98} +(-9588.27 + 9588.27i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 12 q^{2} + 18 q^{5} - 42 q^{7} + 96 q^{8} - 18 q^{9}+O(q^{10}) $ 6 * q - 12 * q^2 + 18 * q^5 - 42 * q^7 + 96 * q^8 - 18 * q^9	$ 6 q - 12 q^{2} + 18 q^{5} - 42 q^{7} + 96 q^{8} - 18 q^{9} - 18 q^{11} + 90 q^{13} + 168 q^{14} - 432 q^{15} - 384 q^{16} + 36 q^{18} - 366 q^{19} - 144 q^{20} + 1908 q^{21} + 72 q^{22} + 12 q^{26} + 1476 q^{27} - 336 q^{28} - 6228 q^{29} + 402 q^{31} + 768 q^{32} + 792 q^{33} + 1944 q^{34} + 3024 q^{35} + 5298 q^{37} - 6120 q^{39} + 576 q^{40} - 2430 q^{41} - 7632 q^{42} - 144 q^{44} + 5382 q^{45} - 1872 q^{46} + 4014 q^{47} + 7908 q^{50} - 768 q^{52} + 6516 q^{53} - 2952 q^{54} - 28764 q^{55} - 5940 q^{57} + 12456 q^{58} + 7434 q^{59} + 3456 q^{60} + 7164 q^{61} + 12942 q^{63} - 14598 q^{65} - 3168 q^{66} + 5790 q^{67} - 7776 q^{68} - 6048 q^{70} + 15246 q^{71} - 288 q^{72} - 4254 q^{73} - 21192 q^{74} + 2928 q^{76} + 12600 q^{78} + 23364 q^{79} - 1152 q^{80} - 19602 q^{81} - 38034 q^{83} + 15264 q^{84} + 30672 q^{85} + 11160 q^{86} - 9288 q^{87} + 4122 q^{89} - 11922 q^{91} + 7488 q^{92} + 10404 q^{93} - 16056 q^{94} - 1362 q^{97} - 17076 q^{98} - 24642 q^{99}+O(q^{100}) $ 6 * q - 12 * q^2 + 18 * q^5 - 42 * q^7 + 96 * q^8 - 18 * q^9 - 18 * q^11 + 90 * q^13 + 168 * q^14 - 432 * q^15 - 384 * q^16 + 36 * q^18 - 366 * q^19 - 144 * q^20 + 1908 * q^21 + 72 * q^22 + 12 * q^26 + 1476 * q^27 - 336 * q^28 - 6228 * q^29 + 402 * q^31 + 768 * q^32 + 792 * q^33 + 1944 * q^34 + 3024 * q^35 + 5298 * q^37 - 6120 * q^39 + 576 * q^40 - 2430 * q^41 - 7632 * q^42 - 144 * q^44 + 5382 * q^45 - 1872 * q^46 + 4014 * q^47 + 7908 * q^50 - 768 * q^52 + 6516 * q^53 - 2952 * q^54 - 28764 * q^55 - 5940 * q^57 + 12456 * q^58 + 7434 * q^59 + 3456 * q^60 + 7164 * q^61 + 12942 * q^63 - 14598 * q^65 - 3168 * q^66 + 5790 * q^67 - 7776 * q^68 - 6048 * q^70 + 15246 * q^71 - 288 * q^72 - 4254 * q^73 - 21192 * q^74 + 2928 * q^76 + 12600 * q^78 + 23364 * q^79 - 1152 * q^80 - 19602 * q^81 - 38034 * q^83 + 15264 * q^84 + 30672 * q^85 + 11160 * q^86 - 9288 * q^87 + 4122 * q^89 - 11922 * q^91 + 7488 * q^92 + 10404 * q^93 - 16056 * q^94 - 1362 * q^97 - 17076 * q^98 - 24642 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$3$	−2.19267			−0.243629			−0.121815	−	0.992553i	$-0.538871\pi$
$3$	−2.19267			−0.243629			−0.121815	+	0.992553i	$0.538871\pi$
$4$			8.00000i			0.500000i
$5$	−28.1144	−	28.1144i	−1.12458	−	1.12458i	−0.991044	−	0.133534i	$-0.957368\pi$
$5$	−28.1144	−	28.1144i	−1.12458	−	1.12458i	−0.133534	−	0.991044i	$-0.542632\pi$
$6$	4.38533	+	4.38533i	0.121815	+	0.121815i
$7$	−49.0778	+	49.0778i	−1.00159	+	1.00159i	−0.00158846	+	0.999999i	$0.500506\pi$
$7$	−49.0778	+	49.0778i	−1.00159	+	1.00159i	−0.999999	+	0.00158846i	$0.999494\pi$
$8$	16.0000	−	16.0000i	0.250000	−	0.250000i
$9$	−76.1922			−0.940645
$10$			112.458i			1.12458i
$11$	125.843	−	125.843i	1.04003	−	1.04003i	0.0408609	−	0.999165i	$-0.486990\pi$
$11$	125.843	−	125.843i	1.04003	−	1.04003i	0.999165	−	0.0408609i	$-0.0130100\pi$
$12$		−	17.5413i		−	0.121815i
$13$	76.8118	−	150.536i	0.454507	−	0.890743i
$13$	76.8118	−	150.536i	0.454507	−	0.890743i
$14$	196.311			1.00159
$15$	61.6456	+	61.6456i	0.273980	+	0.273980i
$16$	−64.0000			−0.250000
$17$			293.870i			1.01685i	0.861106	+	0.508426i	$0.169772\pi$
$17$			293.870i			1.01685i	−0.861106	+	0.508426i	$0.830228\pi$
$18$	152.384	+	152.384i	0.470322	+	0.470322i
$19$	−165.724	−	165.724i	−0.459069	−	0.459069i	0.439281	−	0.898350i	$-0.355233\pi$
$19$	−165.724	−	165.724i	−0.459069	−	0.459069i	−0.898350	+	0.439281i	$0.855233\pi$
$20$	224.916	−	224.916i	0.562289	−	0.562289i
$21$	107.611	−	107.611i	0.244016	−	0.244016i
$22$	−503.372			−1.04003
$23$		−	297.165i		−	0.561748i	−0.959745	−	0.280874i	$-0.909376\pi$
$23$		−	297.165i		−	0.561748i	0.959745	−	0.280874i	$-0.0906244\pi$
$24$	−35.0826	+	35.0826i	−0.0609074	+	0.0609074i
$25$			955.844i			1.52935i
$26$	−454.695	+	147.448i	−0.672625	+	0.218118i
$27$	344.670			0.472798
$28$	−392.622	−	392.622i	−0.500794	−	0.500794i
$29$	−1060.76			−1.26131			−0.630655	−	0.776064i	$-0.717213\pi$
$29$	−1060.76			−1.26131			−0.630655	+	0.776064i	$0.717213\pi$
$30$		−	246.582i		−	0.273980i
$31$	−511.960	−	511.960i	−0.532736	−	0.532736i	0.388649	−	0.921386i	$-0.372942\pi$
$31$	−511.960	−	511.960i	−0.532736	−	0.532736i	−0.921386	+	0.388649i	$0.872942\pi$
$32$	128.000	+	128.000i	0.125000	+	0.125000i
$33$	−275.932	+	275.932i	−0.253381	+	0.253381i
$34$	587.740	−	587.740i	0.508426	−	0.508426i
$35$	2759.59			2.25273
$36$		−	609.538i		−	0.470322i
$37$	−292.878	+	292.878i	−0.213936	+	0.213936i	−0.805937	−	0.592001i	$-0.798338\pi$
$37$	−292.878	+	292.878i	−0.213936	+	0.213936i	0.592001	+	0.805937i	$0.298338\pi$
$38$			662.895i			0.459069i
$39$	−168.422	+	330.074i	−0.110731	+	0.217011i
$40$	−899.662			−0.562289
$41$	−804.161	−	804.161i	−0.478383	−	0.478383i	0.426232	−	0.904614i	$-0.359841\pi$
$41$	−804.161	−	804.161i	−0.478383	−	0.478383i	−0.904614	+	0.426232i	$0.859841\pi$
$42$	−430.445			−0.244016
$43$			1005.69i			0.543913i	0.962310	+	0.271956i	$0.0876707\pi$
$43$			1005.69i			0.543913i	−0.962310	+	0.271956i	$0.912329\pi$
$44$	1006.74	+	1006.74i	0.520013	+	0.520013i
$45$	2142.10	+	2142.10i	1.05783	+	1.05783i
$46$	−594.330	+	594.330i	−0.280874	+	0.280874i
$47$	1325.64	−	1325.64i	0.600111	−	0.600111i	−0.340231	−	0.940342i	$-0.610505\pi$
$47$	1325.64	−	1325.64i	0.600111	−	0.600111i	0.940342	+	0.340231i	$0.110505\pi$
$48$	140.331			0.0609074
$49$		−	2416.26i		−	1.00635i
$50$	1911.69	−	1911.69i	0.764675	−	0.764675i
$51$		−	644.359i		−	0.247735i
$52$	1204.28	+	614.494i	0.445371	+	0.227254i
$53$	574.799			0.204628			0.102314	−	0.994752i	$-0.467375\pi$
$53$	574.799			0.204628			0.102314	+	0.994752i	$0.467375\pi$
$54$	−689.340	−	689.340i	−0.236399	−	0.236399i
$55$	−7076.02			−2.33918
$56$			1570.49i			0.500794i
$57$	363.377	+	363.377i	0.111843	+	0.111843i
$58$	2121.52	+	2121.52i	0.630655	+	0.630655i
$59$	2237.69	−	2237.69i	0.642829	−	0.642829i	−0.308421	−	0.951250i	$-0.599800\pi$
$59$	2237.69	−	2237.69i	0.642829	−	0.642829i	0.951250	+	0.308421i	$0.0998004\pi$
$60$	−493.165	+	493.165i	−0.136990	+	0.136990i
$61$	−6068.83			−1.63097			−0.815484	−	0.578779i	$-0.803529\pi$
$61$	−6068.83			−1.63097			−0.815484	+	0.578779i	$0.803529\pi$
$62$			2047.84i			0.532736i
$63$	3739.34	−	3739.34i	0.942138	−	0.942138i
$64$		−	512.000i		−	0.125000i
$65$	−6391.74	+	2072.70i	−1.51284	+	0.490581i
$66$	1103.73			0.253381
$67$	3155.98	+	3155.98i	0.703046	+	0.703046i	0.965063	−	0.262017i	$-0.0843876\pi$
$67$	3155.98	+	3155.98i	0.703046	+	0.703046i	−0.262017	+	0.965063i	$0.584388\pi$
$68$	−2350.96			−0.508426
$69$			651.583i			0.136858i
$70$	−5519.18	−	5519.18i	−1.12636	−	1.12636i
$71$	−1607.78	−	1607.78i	−0.318940	−	0.318940i	0.529420	−	0.848360i	$-0.322410\pi$
$71$	−1607.78	−	1607.78i	−0.318940	−	0.318940i	−0.848360	+	0.529420i	$0.822410\pi$
$72$	−1219.08	+	1219.08i	−0.235161	+	0.235161i
$73$	22.6121	−	22.6121i	0.00424321	−	0.00424321i	−0.704982	−	0.709225i	$-0.749045\pi$
$73$	22.6121	−	22.6121i	0.00424321	−	0.00424321i	0.709225	+	0.704982i	$0.249045\pi$
$74$	1171.51			0.213936
$75$		−	2095.85i		−	0.372595i
$76$	1325.79	−	1325.79i	0.229534	−	0.229534i
$77$			12352.2i			2.08335i
$78$	996.993	−	323.303i	0.163871	−	0.0531399i
$79$	6576.52			1.05376			0.526880	−	0.849940i	$-0.323362\pi$
$79$	6576.52			1.05376			0.526880	+	0.849940i	$0.323362\pi$
$80$	1799.32	+	1799.32i	0.281144	+	0.281144i
$81$	5415.82			0.825457
$82$			3216.64i			0.478383i
$83$	−5691.45	−	5691.45i	−0.826165	−	0.826165i	0.160819	−	0.986984i	$-0.448586\pi$
$83$	−5691.45	−	5691.45i	−0.826165	−	0.826165i	−0.986984	+	0.160819i	$0.948586\pi$
$84$	860.889	+	860.889i	0.122008	+	0.122008i
$85$	8261.99	−	8261.99i	1.14353	−	1.14353i
$86$	2011.39	−	2011.39i	0.271956	−	0.271956i
$87$	2325.89			0.307292
$88$		−	4026.98i		−	0.520013i
$89$	4243.56	−	4243.56i	0.535735	−	0.535735i	−0.386538	−	0.922273i	$-0.626329\pi$
$89$	4243.56	−	4243.56i	0.535735	−	0.535735i	0.922273	+	0.386538i	$0.126329\pi$
$90$		−	8568.41i		−	1.05783i
$91$	3618.20	+	11157.7i	0.436928	+	1.34739i
$92$	2377.32			0.280874
$93$	1122.56	+	1122.56i	0.129790	+	0.129790i
$94$	−5302.58			−0.600111
$95$			9318.47i			1.03252i
$96$	−280.661	−	280.661i	−0.0304537	−	0.0304537i
$97$	3532.64	+	3532.64i	0.375453	+	0.375453i	0.869459	−	0.494006i	$-0.164468\pi$
$97$	3532.64	+	3532.64i	0.375453	+	0.375453i	−0.494006	+	0.869459i	$0.664468\pi$
$98$	−4832.51	+	4832.51i	−0.503177	+	0.503177i
$99$	−9588.27	+	9588.27i	−0.978295	+	0.978295i
$100$	−7646.75			−0.764675
$101$		−	18045.3i		−	1.76897i	−0.466567	−	0.884486i	$-0.654509\pi$
$101$		−	18045.3i		−	1.76897i	0.466567	−	0.884486i	$-0.345491\pi$
$102$	−1288.72	+	1288.72i	−0.123867	+	0.123867i
$103$		−	2128.08i		−	0.200592i	−0.994958	−	0.100296i	$-0.968021\pi$
$103$		−	2128.08i		−	0.200592i	0.994958	−	0.100296i	$-0.0319790\pi$
$104$	−1179.58	−	3637.56i	−0.109059	−	0.336313i
$105$	−6050.85			−0.548830
$106$	−1149.60	−	1149.60i	−0.102314	−	0.102314i
$107$	−8838.57			−0.771995			−0.385997	−	0.922500i	$-0.626143\pi$
$107$	−8838.57			−0.771995			−0.385997	+	0.922500i	$0.626143\pi$
$108$			2757.36i			0.236399i
$109$	−2517.64	−	2517.64i	−0.211905	−	0.211905i	0.593171	−	0.805076i	$-0.297876\pi$
$109$	−2517.64	−	2517.64i	−0.211905	−	0.211905i	−0.805076	+	0.593171i	$0.797876\pi$
$110$	14152.0	+	14152.0i	1.16959	+	1.16959i
$111$	642.183	−	642.183i	0.0521210	−	0.0521210i
$112$	3140.98	−	3140.98i	0.250397	−	0.250397i
$113$	1933.19			0.151397			0.0756984	−	0.997131i	$-0.475881\pi$
$113$	1933.19			0.151397			0.0756984	+	0.997131i	$0.475881\pi$
$114$		−	1453.51i		−	0.111843i
$115$	−8354.62	+	8354.62i	−0.631730	+	0.631730i
$116$		−	8486.09i		−	0.630655i
$117$	−5852.46	+	11469.6i	−0.427530	+	0.837873i
$118$	−8950.76			−0.642829
$119$	−14422.5	−	14422.5i	−1.01847	−	1.01847i
$120$	1972.66			0.136990
$121$		−	17032.0i		−	1.16331i
$122$	12137.7	+	12137.7i	0.815484	+	0.815484i
$123$	1763.26	+	1763.26i	0.116548	+	0.116548i
$124$	4095.68	−	4095.68i	0.266368	−	0.266368i
$125$	9301.50	−	9301.50i	0.595296	−	0.595296i
$126$	−14957.4			−0.942138
$127$			7762.26i			0.481261i	0.970617	+	0.240630i	$0.0773542\pi$
$127$			7762.26i			0.481261i	−0.970617	+	0.240630i	$0.922646\pi$
$128$	−1024.00	+	1024.00i	−0.0625000	+	0.0625000i
$129$		−	2205.15i		−	0.132513i
$130$	16928.9	+	8638.08i	1.00171	+	0.511129i
$131$	10467.8			0.609974			0.304987	−	0.952357i	$-0.401348\pi$
$131$	10467.8			0.609974			0.304987	+	0.952357i	$0.401348\pi$
$132$	−2207.45	−	2207.45i	−0.126690	−	0.126690i
$133$	16266.7			0.919595
$134$		−	12623.9i		−	0.703046i
$135$	−9690.20	−	9690.20i	−0.531698	−	0.531698i
$136$	4701.92	+	4701.92i	0.254213	+	0.254213i
$137$	−10192.9	+	10192.9i	−0.543072	+	0.543072i	−0.924428	−	0.381356i	$-0.875457\pi$
$137$	−10192.9	+	10192.9i	−0.543072	+	0.543072i	0.381356	+	0.924428i	$0.375457\pi$
$138$	1303.17	−	1303.17i	0.0684292	−	0.0684292i
$139$	29697.1			1.53704			0.768519	−	0.639827i	$-0.220994\pi$
$139$	29697.1			1.53704			0.768519	+	0.639827i	$0.220994\pi$
$140$			22076.7i			1.12636i
$141$	−2906.69	+	2906.69i	−0.146205	+	0.146205i
$142$			6431.11i			0.318940i
$143$	−9277.63	−	28610.1i	−0.453696	−	1.39910i
$144$	4876.30			0.235161
$145$	29822.7	+	29822.7i	1.41844	+	1.41844i
$146$	−90.4483			−0.00424321
$147$			5298.04i			0.245177i
$148$	−2343.02	−	2343.02i	−0.106968	−	0.106968i
$149$	−22208.2	−	22208.2i	−1.00033	−	1.00033i	−1.00000		0.000326486i	$-0.999896\pi$
$149$	−22208.2	−	22208.2i	−1.00033	−	1.00033i	−0.000326486	−	1.00000i	$-0.500104\pi$
$150$	−4191.69	+	4191.69i	−0.186297	+	0.186297i
$151$	−27423.8	+	27423.8i	−1.20274	+	1.20274i	−0.229417	+	0.973328i	$0.573682\pi$
$151$	−27423.8	+	27423.8i	−1.20274	+	1.20274i	−0.973328	+	0.229417i	$0.926318\pi$
$152$	−5303.16			−0.229534
$153$		−	22390.6i		−	0.956496i
$154$	24704.4	−	24704.4i	1.04168	−	1.04168i
$155$			28786.9i			1.19821i
$156$	−2640.59	−	1347.38i	−0.108506	−	0.0553657i
$157$	3402.51			0.138038			0.0690192	−	0.997615i	$-0.478013\pi$
$157$	3402.51			0.138038			0.0690192	+	0.997615i	$0.478013\pi$
$158$	−13153.0	−	13153.0i	−0.526880	−	0.526880i
$159$	−1260.34			−0.0498533
$160$		−	7197.30i		−	0.281144i
$161$	14584.2	+	14584.2i	0.562640	+	0.562640i
$162$	−10831.6	−	10831.6i	−0.412729	−	0.412729i
$163$	19832.3	−	19832.3i	0.746445	−	0.746445i	−0.227365	−	0.973810i	$-0.573011\pi$
$163$	19832.3	−	19832.3i	0.746445	−	0.746445i	0.973810	+	0.227365i	$0.0730110\pi$
$164$	6433.29	−	6433.29i	0.239191	−	0.239191i
$165$	15515.3			0.569893
$166$			22765.8i			0.826165i
$167$	−6728.75	+	6728.75i	−0.241269	+	0.241269i	−0.817375	−	0.576106i	$-0.804572\pi$
$167$	−6728.75	+	6728.75i	−0.241269	+	0.241269i	0.576106	+	0.817375i	$0.304572\pi$
$168$		−	3443.56i		−	0.122008i
$169$	−16760.9	−	23125.8i	−0.586846	−	0.809699i
$170$	−33048.0			−1.14353
$171$	12626.9	+	12626.9i	0.431821	+	0.431821i
$172$	−8045.56			−0.271956
$173$			32296.9i			1.07912i	0.841948	+	0.539558i	$0.181409\pi$
$173$			32296.9i			1.07912i	−0.841948	+	0.539558i	$0.818591\pi$
$174$	−4651.79	−	4651.79i	−0.153646	−	0.153646i
$175$	−46910.7	−	46910.7i	−1.53178	−	1.53178i
$176$	−8053.96	+	8053.96i	−0.260006	+	0.260006i
$177$	−4906.50	+	4906.50i	−0.156612	+	0.156612i
$178$	−16974.2			−0.535735
$179$			41174.2i			1.28505i	0.766266	+	0.642524i	$0.222113\pi$
$179$			41174.2i			1.28505i	−0.766266	+	0.642524i	$0.777887\pi$
$180$	−17136.8	+	17136.8i	−0.528914	+	0.528914i
$181$		−	31653.5i		−	0.966196i	−0.875566	−	0.483098i	$-0.839511\pi$
$181$		−	31653.5i		−	0.966196i	0.875566	−	0.483098i	$-0.160489\pi$
$182$	15079.0	−	29551.8i	0.455229	−	0.892157i
$183$	13306.9			0.397352
$184$	−4754.64	−	4754.64i	−0.140437	−	0.140437i
$185$	16468.2			0.481175
$186$		−	4490.23i		−	0.129790i
$187$	36981.5	+	36981.5i	1.05755	+	1.05755i
$188$	10605.2	+	10605.2i	0.300055	+	0.300055i
$189$	−16915.6	+	16915.6i	−0.473549	+	0.473549i
$190$	18636.9	−	18636.9i	0.516258	−	0.516258i
$191$	−15395.5			−0.422013			−0.211007	−	0.977485i	$-0.567674\pi$
$191$	−15395.5			−0.422013			−0.211007	+	0.977485i	$0.567674\pi$
$192$			1122.64i			0.0304537i
$193$	−32248.9	+	32248.9i	−0.865765	+	0.865765i	−0.992000	−	0.126235i	$-0.959711\pi$
$193$	−32248.9	+	32248.9i	−0.865765	+	0.865765i	0.126235	+	0.992000i	$0.459711\pi$
$194$		−	14130.6i		−	0.375453i
$195$	14015.0	−	4544.75i	0.368572	−	0.119520i
$196$	19330.0			0.503177
$197$	−28366.7	−	28366.7i	−0.730930	−	0.730930i	0.239874	−	0.970804i	$-0.422894\pi$
$197$	−28366.7	−	28366.7i	−0.730930	−	0.730930i	−0.970804	+	0.239874i	$0.922894\pi$
$198$	38353.1			0.978295
$199$		−	41308.6i		−	1.04312i	−0.853214	−	0.521560i	$-0.825350\pi$
$199$		−	41308.6i		−	1.04312i	0.853214	−	0.521560i	$-0.174650\pi$
$200$	15293.5	+	15293.5i	0.382338	+	0.382338i
$201$	−6920.00	−	6920.00i	−0.171283	−	0.171283i
$202$	−36090.6	+	36090.6i	−0.884486	+	0.884486i
$203$	52059.8	−	52059.8i	1.26331	−	1.26331i
$204$	5154.87			0.123867
$205$			45217.1i			1.07596i
$206$	−4256.16	+	4256.16i	−0.100296	+	0.100296i
$207$			22641.6i			0.528406i
$208$	−4915.95	+	9634.28i	−0.113627	+	0.222686i
$209$	−41710.4			−0.954886
$210$	12101.7	+	12101.7i	0.274415	+	0.274415i
$211$	53697.8			1.20612			0.603062	−	0.797695i	$-0.293947\pi$
$211$	53697.8			1.20612			0.603062	+	0.797695i	$0.293947\pi$
$212$			4598.39i			0.102314i
$213$	3525.32	+	3525.32i	0.0777033	+	0.0777033i
$214$	17677.1	+	17677.1i	0.385997	+	0.385997i
$215$	28274.6	−	28274.6i	0.611672	−	0.611672i
$216$	5514.72	−	5514.72i	0.118200	−	0.118200i
$217$	50251.7			1.06716
$218$			10070.6i			0.211905i
$219$	−49.5807	+	49.5807i	−0.00103377	+	0.00103377i
$220$		−	56608.1i		−	1.16959i
$221$	44237.9	+	22572.7i	0.905753	+	0.462167i
$222$	−2568.73			−0.0521210
$223$	−39762.2	−	39762.2i	−0.799578	−	0.799578i	0.183451	−	0.983029i	$-0.441273\pi$
$223$	−39762.2	−	39762.2i	−0.799578	−	0.799578i	−0.983029	+	0.183451i	$0.941273\pi$
$224$	−12563.9			−0.250397
$225$		−	72827.9i		−	1.43858i
$226$	−3866.37	−	3866.37i	−0.0756984	−	0.0756984i
$227$	−13759.5	−	13759.5i	−0.267025	−	0.267025i	0.560876	−	0.827900i	$-0.310465\pi$
$227$	−13759.5	−	13759.5i	−0.267025	−	0.267025i	−0.827900	+	0.560876i	$0.810465\pi$
$228$	−2907.01	+	2907.01i	−0.0559213	+	0.0559213i
$229$	−26261.1	+	26261.1i	−0.500774	+	0.500774i	−0.911678	−	0.410905i	$-0.865213\pi$
$229$	−26261.1	+	26261.1i	−0.500774	+	0.500774i	0.410905	+	0.911678i	$0.365213\pi$
$230$	33418.5			0.631730
$231$		−	27084.2i		−	0.507566i
$232$	−16972.2	+	16972.2i	−0.315327	+	0.315327i
$233$			41383.8i			0.762287i	0.924516	+	0.381144i	$0.124470\pi$
$233$			41383.8i			0.762287i	−0.924516	+	0.381144i	$0.875530\pi$
$234$	34644.2	−	11234.4i	0.632701	−	0.205171i
$235$	−74539.5			−1.34974
$236$	17901.5	+	17901.5i	0.321415	+	0.321415i
$237$	−14420.1			−0.256727
$238$			57689.9i			1.01847i
$239$	1600.45	+	1600.45i	0.0280187	+	0.0280187i	0.720977	−	0.692959i	$-0.243693\pi$
$239$	1600.45	+	1600.45i	0.0280187	+	0.0280187i	−0.692959	+	0.720977i	$0.743693\pi$
$240$	−3945.32	−	3945.32i	−0.0684951	−	0.0684951i
$241$	−33028.9	+	33028.9i	−0.568669	+	0.568669i	−0.931755	−	0.363086i	$-0.881723\pi$
$241$	−33028.9	+	33028.9i	−0.568669	+	0.568669i	0.363086	+	0.931755i	$0.381723\pi$
$242$	−34064.0	+	34064.0i	−0.581654	+	0.581654i
$243$	−39793.4			−0.673904
$244$		−	48550.7i		−	0.815484i
$245$	−67931.7	+	67931.7i	−1.13172	+	1.13172i
$246$		−	7053.03i		−	0.116548i
$247$	−37676.9	+	12217.8i	−0.617562	+	0.200262i
$248$	−16382.7			−0.266368
$249$	12479.4	+	12479.4i	0.201278	+	0.201278i
$250$	−37206.0			−0.595296
$251$		−	16019.3i		−	0.254271i	−0.991885	−	0.127135i	$-0.959422\pi$
$251$		−	16019.3i		−	0.254271i	0.991885	−	0.127135i	$-0.0405783\pi$
$252$	29914.8	+	29914.8i	0.471069	+	0.471069i
$253$	−37396.1	−	37396.1i	−0.584233	−	0.584233i
$254$	15524.5	−	15524.5i	0.240630	−	0.240630i
$255$	−18115.8	+	18115.8i	−0.278597	+	0.278597i
$256$	4096.00			0.0625000
$257$		−	51851.4i		−	0.785044i	−0.919743	−	0.392522i	$-0.871603\pi$
$257$		−	51851.4i		−	0.785044i	0.919743	−	0.392522i	$-0.128397\pi$
$258$	−4410.31	+	4410.31i	−0.0662566	+	0.0662566i
$259$		−	28747.6i		−	0.428550i
$260$	−16581.6	−	51133.9i	−0.245290	−	0.756419i
$261$	80821.7			1.18644
$262$	−20935.5	−	20935.5i	−0.304987	−	0.304987i
$263$	112584.			1.62767			0.813833	−	0.581099i	$-0.197377\pi$
$263$	112584.			1.62767			0.813833	+	0.581099i	$0.197377\pi$
$264$			8829.82i			0.126690i
$265$	−16160.2	−	16160.2i	−0.230120	−	0.230120i
$266$	−32533.4	−	32533.4i	−0.459797	−	0.459797i
$267$	−9304.70	+	9304.70i	−0.130521	+	0.130521i
$268$	−25247.8	+	25247.8i	−0.351523	+	0.351523i
$269$	12549.4			0.173428			0.0867139	−	0.996233i	$-0.472363\pi$
$269$	12549.4			0.173428			0.0867139	+	0.996233i	$0.472363\pi$
$270$			38760.8i			0.531698i
$271$	71858.5	−	71858.5i	0.978452	−	0.978452i	−0.0213209	−	0.999773i	$-0.506787\pi$
$271$	71858.5	−	71858.5i	0.978452	−	0.978452i	0.999773	+	0.0213209i	$0.00678717\pi$
$272$		−	18807.7i		−	0.254213i
$273$	−7933.50	−	24465.1i	−0.106449	−	0.328263i
$274$	40771.6			0.543072
$275$	120286.	+	120286.i	1.59056	+	1.59056i
$276$	−5212.66			−0.0684292
$277$			14392.6i			0.187577i	0.995592	+	0.0937884i	$0.0298977\pi$
$277$			14392.6i			0.187577i	−0.995592	+	0.0937884i	$0.970102\pi$
$278$	−59394.2	−	59394.2i	−0.768519	−	0.768519i
$279$	39007.3	+	39007.3i	0.501116	+	0.501116i
$280$	44153.4	−	44153.4i	0.563181	−	0.563181i
$281$	−80935.8	+	80935.8i	−1.02501	+	1.02501i	−0.0253301	+	0.999679i	$0.508064\pi$
$281$	−80935.8	+	80935.8i	−1.02501	+	1.02501i	−0.999679	+	0.0253301i	$0.991936\pi$
$282$	11626.8			0.146205
$283$			103285.i			1.28963i	0.764339	+	0.644814i	$0.223065\pi$
$283$			103285.i			1.28963i	−0.764339	+	0.644814i	$0.776935\pi$
$284$	12862.2	−	12862.2i	0.159470	−	0.159470i
$285$		−	20432.3i		−	0.251552i
$286$	−38664.9	+	75775.5i	−0.472699	+	0.926396i
$287$	78932.9			0.958284
$288$	−9752.60	−	9752.60i	−0.117581	−	0.117581i
$289$	−2838.60			−0.0339866
$290$		−	119291.i		−	1.41844i
$291$	−7745.90	−	7745.90i	−0.0914715	−	0.0914715i
$292$	180.897	+	180.897i	0.00212161	+	0.00212161i
$293$	112492.	−	112492.i	1.31035	−	1.31035i	0.389193	−	0.921156i	$-0.372754\pi$
$293$	112492.	−	112492.i	1.31035	−	1.31035i	0.921156	−	0.389193i	$-0.127246\pi$
$294$	10596.1	−	10596.1i	0.122589	−	0.122589i
$295$	−125823.			−1.44582
$296$			9372.09i			0.106968i
$297$	43374.3	−	43374.3i	0.491722	−	0.491722i
$298$			88833.0i			1.00033i
$299$	−44733.9	−	22825.8i	−0.500373	−	0.255319i
$300$	16766.8			0.186297
$301$	−49357.3	−	49357.3i	−0.544776	−	0.544776i
$302$	109695.			1.20274
$303$			39567.3i			0.430974i
$304$	10606.3	+	10606.3i	0.114767	+	0.114767i
$305$	170622.	+	170622.i	1.83415	+	1.83415i
$306$	−44781.2	+	44781.2i	−0.478248	+	0.478248i
$307$	65869.5	−	65869.5i	0.698888	−	0.698888i	−0.265283	−	0.964171i	$-0.585465\pi$
$307$	65869.5	−	65869.5i	0.698888	−	0.698888i	0.964171	+	0.265283i	$0.0854653\pi$
$308$	−98817.6			−1.04168
$309$			4666.17i			0.0488701i
$310$	57573.9	−	57573.9i	0.599104	−	0.599104i
$311$		−	32921.8i		−	0.340379i	−0.985411	−	0.170190i	$-0.945562\pi$
$311$		−	32921.8i		−	0.340379i	0.985411	−	0.170190i	$-0.0544380\pi$
$312$	2586.43	+	7975.95i	0.0265700	+	0.0819357i
$313$	−67694.8			−0.690982			−0.345491	−	0.938422i	$-0.612288\pi$
$313$	−67694.8			−0.690982			−0.345491	+	0.938422i	$0.612288\pi$
$314$	−6805.02	−	6805.02i	−0.0690192	−	0.0690192i
$315$	−210259.			−2.11901
$316$			52612.1i			0.526880i
$317$	−87722.3	−	87722.3i	−0.872954	−	0.872954i	0.119839	−	0.992793i	$-0.461762\pi$
$317$	−87722.3	−	87722.3i	−0.872954	−	0.872954i	−0.992793	+	0.119839i	$0.961762\pi$
$318$	2520.68	+	2520.68i	0.0249267	+	0.0249267i
$319$	−133489.	+	133489.i	−1.31179	+	1.31179i
$320$	−14394.6	+	14394.6i	−0.140572	+	0.140572i
$321$	19380.0			0.188081
$322$		−	58336.8i		−	0.562640i
$323$	48701.3	−	48701.3i	0.466805	−	0.466805i
$324$			43326.6i			0.412729i
$325$	143889.	+	73420.1i	1.36226	+	0.695101i
$326$	−79329.2			−0.746445
$327$	5520.35	+	5520.35i	0.0516263	+	0.0516263i
$328$	−25733.2			−0.239191
$329$			130119.i			1.20213i
$330$	−31030.7	−	31030.7i	−0.284947	−	0.284947i
$331$	−46314.1	−	46314.1i	−0.422725	−	0.422725i	0.463416	−	0.886141i	$-0.346624\pi$
$331$	−46314.1	−	46314.1i	−0.422725	−	0.422725i	−0.886141	+	0.463416i	$0.846624\pi$
$332$	45531.6	−	45531.6i	0.413082	−	0.413082i
$333$	22315.0	−	22315.0i	0.201237	−	0.201237i
$334$	26915.0			0.241269
$335$		−	177457.i		−	1.58126i
$336$	−6887.11	+	6887.11i	−0.0610040	+	0.0610040i
$337$		−	174379.i		−	1.53545i	−0.640782	−	0.767723i	$-0.721390\pi$
$337$		−	174379.i		−	1.53545i	0.640782	−	0.767723i	$-0.278610\pi$
$338$	−12729.8	+	79773.4i	−0.111426	+	0.698272i
$339$	−4238.83			−0.0368847
$340$	66095.9	+	66095.9i	0.571764	+	0.571764i
$341$	−128853.			−1.10812
$342$		−	50507.5i		−	0.431821i
$343$	748.709	+	748.709i	0.00636392	+	0.00636392i
$344$	16091.1	+	16091.1i	0.135978	+	0.135978i
$345$	18318.9	−	18318.9i	0.153908	−	0.153908i
$346$	64593.7	−	64593.7i	0.539558	−	0.539558i
$347$	−55837.1			−0.463729			−0.231864	−	0.972748i	$-0.574483\pi$
$347$	−55837.1			−0.463729			−0.231864	+	0.972748i	$0.574483\pi$
$348$			18607.2i			0.153646i
$349$	−30432.8	+	30432.8i	−0.249857	+	0.249857i	−0.820912	−	0.571055i	$-0.806534\pi$
$349$	−30432.8	+	30432.8i	−0.249857	+	0.249857i	0.571055	+	0.820912i	$0.306534\pi$
$350$			187643.i			1.53178i
$351$	26474.7	−	51885.1i	0.214890	−	0.421142i
$352$	32215.8			0.260006
$353$	−159731.	−	159731.i	−1.28186	−	1.28186i	−0.939610	−	0.342246i	$-0.888812\pi$
$353$	−159731.	−	159731.i	−1.28186	−	1.28186i	−0.342246	−	0.939610i	$-0.611188\pi$
$354$	19626.0			0.156612
$355$			90403.6i			0.717347i
$356$	33948.4	+	33948.4i	0.267867	+	0.267867i
$357$	31623.7	+	31623.7i	0.248128	+	0.248128i
$358$	82348.4	−	82348.4i	0.642524	−	0.642524i
$359$	−86021.7	+	86021.7i	−0.667451	+	0.667451i	−0.957125	−	0.289674i	$-0.906453\pi$
$359$	−86021.7	+	86021.7i	−0.667451	+	0.667451i	0.289674	+	0.957125i	$0.406453\pi$
$360$	68547.3			0.528914
$361$		−	75392.2i		−	0.578512i
$362$	−63307.1	+	63307.1i	−0.483098	+	0.483098i
$363$			37345.4i			0.283416i
$364$	−89261.6	+	28945.6i	−0.673693	+	0.218464i
$365$	−1271.45			−0.00954364
$366$	−26613.8	−	26613.8i	−0.198676	−	0.198676i
$367$	−77247.7			−0.573527			−0.286763	−	0.958001i	$-0.592579\pi$
$367$	−77247.7			−0.573527			−0.286763	+	0.958001i	$0.592579\pi$
$368$			19018.6i			0.140437i
$369$	61270.8	+	61270.8i	0.449988	+	0.449988i
$370$	−32936.4	−	32936.4i	−0.240587	−	0.240587i
$371$	−28209.8	+	28209.8i	−0.204952	+	0.204952i
$372$	−8980.45	+	8980.45i	−0.0648952	+	0.0648952i
$373$	213860.			1.53713			0.768566	−	0.639771i	$-0.220971\pi$
$373$	213860.			1.53713			0.768566	+	0.639771i	$0.220971\pi$
$374$		−	147926.i		−	1.05755i
$375$	−20395.1	+	20395.1i	−0.145032	+	0.145032i
$376$		−	42420.6i		−	0.300055i
$377$	−81478.9	+	159682.i	−0.573274	+	1.12350i
$378$	67662.5			0.473549
$379$	181098.	+	181098.i	1.26077	+	1.26077i	0.950721	+	0.310047i	$0.100345\pi$
$379$	181098.	+	181098.i	1.26077	+	1.26077i	0.310047	+	0.950721i	$0.399655\pi$
$380$	−74547.7			−0.516258
$381$		−	17020.0i		−	0.117249i
$382$	30790.9	+	30790.9i	0.211007	+	0.211007i
$383$	202157.	+	202157.i	1.37813	+	1.37813i	0.847769	+	0.530366i	$0.177946\pi$
$383$	202157.	+	202157.i	1.37813	+	1.37813i	0.530366	+	0.847769i	$0.322054\pi$
$384$	2245.29	−	2245.29i	0.0152268	−	0.0152268i
$385$	347275.	−	347275.i	2.34289	−	2.34289i
$386$	128996.			0.865765
$387$		−	76626.1i		−	0.511629i
$388$	−28261.1	+	28261.1i	−0.187727	+	0.187727i
$389$			16045.1i			0.106033i	0.998594	+	0.0530167i	$0.0168836\pi$
$389$			16045.1i			0.106033i	−0.998594	+	0.0530167i	$0.983116\pi$
$390$	−37119.4	−	18940.4i	−0.244046	−	0.124526i
$391$	87327.8			0.571215
$392$	−38660.1	−	38660.1i	−0.251588	−	0.251588i
$393$	−22952.3			−0.148608
$394$			113467.i			0.730930i
$395$	−184895.	−	184895.i	−1.18504	−	1.18504i
$396$	−76706.1	−	76706.1i	−0.489147	−	0.489147i
$397$	25762.9	−	25762.9i	0.163461	−	0.163461i	−0.620637	−	0.784098i	$-0.713126\pi$
$397$	25762.9	−	25762.9i	0.163461	−	0.163461i	0.784098	+	0.620637i	$0.213126\pi$
$398$	−82617.3	+	82617.3i	−0.521560	+	0.521560i
$399$	−35667.5			−0.224040
$400$		−	61174.0i		−	0.382338i
$401$	91271.3	−	91271.3i	0.567604	−	0.567604i	−0.363853	−	0.931457i	$-0.618539\pi$
$401$	91271.3	−	91271.3i	0.567604	−	0.567604i	0.931457	+	0.363853i	$0.118539\pi$
$402$			27680.0i			0.171283i
$403$	−116393.	+	37743.6i	−0.716664	+	0.232399i
$404$	144362.			0.884486
$405$	−152263.	−	152263.i	−0.928291	−	0.928291i
$406$	−208239.			−1.26331
$407$			73713.3i			0.444997i
$408$	−10309.7	−	10309.7i	−0.0619337	−	0.0619337i
$409$	4746.04	+	4746.04i	0.0283716	+	0.0283716i	0.721150	−	0.692779i	$-0.243614\pi$
$409$	4746.04	+	4746.04i	0.0283716	+	0.0283716i	−0.692779	+	0.721150i	$0.743614\pi$
$410$	90434.2	−	90434.2i	0.537978	−	0.537978i
$411$	22349.6	−	22349.6i	0.132308	−	0.132308i
$412$	17024.7			0.100296
$413$			219642.i			1.28770i
$414$	45283.3	−	45283.3i	0.264203	−	0.264203i
$415$			320024.i			1.85817i
$416$	29100.5	−	9436.65i	0.168156	−	0.0545294i
$417$	−65115.8			−0.374468
$418$	83420.8	+	83420.8i	0.477443	+	0.477443i
$419$	82509.8			0.469978			0.234989	−	0.971998i	$-0.424495\pi$
$419$	82509.8			0.469978			0.234989	+	0.971998i	$0.424495\pi$
$420$		−	48406.8i		−	0.274415i
$421$	159452.	+	159452.i	0.899636	+	0.899636i	0.995404	−	0.0957676i	$-0.0305306\pi$
$421$	159452.	+	159452.i	0.899636	+	0.899636i	−0.0957676	+	0.995404i	$0.530531\pi$
$422$	−107396.	−	107396.i	−0.603062	−	0.603062i
$423$	−101004.	+	101004.i	−0.564491	+	0.564491i
$424$	9196.78	−	9196.78i	0.0511569	−	0.0511569i
$425$	−280894.			−1.55512
$426$		−	14101.3i		−	0.0777033i
$427$	297845.	−	297845.i	1.63356	−	1.63356i
$428$		−	70708.5i		−	0.385997i
$429$	20342.7	+	62732.4i	0.110534	+	0.340861i
$430$	−113098.			−0.611672
$431$	−191869.	−	191869.i	−1.03288	−	1.03288i	−0.999441	−	0.0334379i	$-0.989354\pi$
$431$	−191869.	−	191869.i	−1.03288	−	1.03288i	−0.0334379	−	0.999441i	$-0.510646\pi$
$432$	−22058.9			−0.118200
$433$		−	167200.i		−	0.891783i	−0.895087	−	0.445892i	$-0.852887\pi$
$433$		−	167200.i		−	0.891783i	0.895087	−	0.445892i	$-0.147113\pi$
$434$	−100503.	−	100503.i	−0.533582	−	0.533582i
$435$	−65391.2	−	65391.2i	−0.345574	−	0.345574i
$436$	20141.1	−	20141.1i	0.105952	−	0.105952i
$437$	−49247.3	+	49247.3i	−0.257881	+	0.257881i
$438$	198.323			0.00103377
$439$			223012.i			1.15717i	0.815621	+	0.578587i	$0.196396\pi$
$439$			223012.i			1.15717i	−0.815621	+	0.578587i	$0.803604\pi$
$440$	−113216.	+	113216.i	−0.584795	+	0.584795i
$441$			184100.i			0.946621i
$442$	−43330.4	−	133621.i	−0.221793	−	0.683960i
$443$	−17437.9			−0.0888559			−0.0444280	−	0.999013i	$-0.514147\pi$
$443$	−17437.9			−0.0888559			−0.0444280	+	0.999013i	$0.514147\pi$
$444$	5137.47	+	5137.47i	0.0260605	+	0.0260605i
$445$	−238610.			−1.20495
$446$			159049.i			0.799578i
$447$	48695.3	+	48695.3i	0.243709	+	0.243709i
$448$	25127.8	+	25127.8i	0.125198	+	0.125198i
$449$	−102553.	+	102553.i	−0.508694	+	0.508694i	−0.914126	−	0.405431i	$-0.867121\pi$
$449$	−102553.	+	102553.i	−0.508694	+	0.508694i	0.405431	+	0.914126i	$0.367121\pi$
$450$	−145656.	+	145656.i	−0.719288	+	0.719288i
$451$	−202396.			−0.995060
$452$			15465.5i			0.0756984i
$453$	60131.2	−	60131.2i	0.293024	−	0.293024i
$454$			55038.0i			0.267025i
$455$	211969.	−	415416.i	1.02388	−	2.00660i
$456$	11628.1			0.0559213
$457$	212786.	+	212786.i	1.01885	+	1.01885i	0.999819	+	0.0190328i	$0.00605869\pi$
$457$	212786.	+	212786.i	1.01885	+	1.01885i	0.0190328	+	0.999819i	$0.493941\pi$
$458$	105044.			0.500774
$459$			101288.i			0.480766i
$460$	−66837.0	−	66837.0i	−0.315865	−	0.315865i
$461$	163359.	+	163359.i	0.768674	+	0.768674i	0.977873	−	0.209199i	$-0.0670858\pi$
$461$	163359.	+	163359.i	0.768674	+	0.768674i	−0.209199	+	0.977873i	$0.567086\pi$
$462$	−54168.5	+	54168.5i	−0.253783	+	0.253783i
$463$	−12062.7	+	12062.7i	−0.0562705	+	0.0562705i	−0.734682	−	0.678412i	$-0.762669\pi$
$463$	−12062.7	+	12062.7i	−0.0562705	+	0.0562705i	0.678412	+	0.734682i	$0.262669\pi$
$464$	67888.7			0.315327
$465$		−	63120.1i		−	0.291919i
$466$	82767.6	−	82767.6i	0.381144	−	0.381144i
$467$		−	405742.i		−	1.86044i	−0.367001	−	0.930221i	$-0.619615\pi$
$467$		−	405742.i		−	1.86044i	0.367001	−	0.930221i	$-0.380385\pi$
$468$	−91757.1	−	46819.7i	−0.418936	−	0.213765i
$469$	−309776.			−1.40832
$470$	149079.	+	149079.i	0.674871	+	0.674871i
$471$	−7460.56			−0.0336302
$472$		−	71606.1i		−	0.321415i
$473$	126560.	+	126560.i	0.565683	+	0.565683i
$474$	28840.2	+	28840.2i	0.128364	+	0.128364i
$475$	158406.	−	158406.i	0.702077	−	0.702077i
$476$	115380.	−	115380.i	0.509233	−	0.509233i
$477$	−43795.2			−0.192482
$478$		−	6401.82i		−	0.0280187i
$479$	68415.5	−	68415.5i	0.298183	−	0.298183i	−0.542119	−	0.840302i	$-0.682378\pi$
$479$	68415.5	−	68415.5i	0.298183	−	0.298183i	0.840302	+	0.542119i	$0.182378\pi$
$480$			15781.3i			0.0684951i
$481$	21592.1	+	66585.0i	0.0933263	+	0.287797i
$482$	132115.			0.568669
$483$	−31978.2	−	31978.2i	−0.137076	−	0.137076i
$484$	136256.			0.581654
$485$		−	198636.i		−	0.844453i
$486$	79586.7	+	79586.7i	0.336952	+	0.336952i
$487$	−6839.49	−	6839.49i	−0.0288380	−	0.0288380i	0.692541	−	0.721379i	$-0.256491\pi$
$487$	−6839.49	−	6839.49i	−0.0288380	−	0.0288380i	−0.721379	+	0.692541i	$0.756491\pi$
$488$	−97101.3	+	97101.3i	−0.407742	+	0.407742i
$489$	−43485.6	+	43485.6i	−0.181856	+	0.181856i
$490$	271727.			1.13172
$491$			317438.i			1.31673i	0.752701	+	0.658363i	$0.228751\pi$
$491$			317438.i			1.31673i	−0.752701	+	0.658363i	$0.771249\pi$
$492$	−14106.1	+	14106.1i	−0.0582741	+	0.0582741i
$493$		−	311726.i		−	1.28256i
$494$	99789.3	+	50918.1i	0.408912	+	0.208650i
$495$	539138.			2.20034
$496$	32765.4	+	32765.4i	0.133184	+	0.133184i
$497$	157812.			0.638893
$498$		−	49917.8i		−	0.201278i
$499$	−169318.	−	169318.i	−0.679989	−	0.679989i	0.280008	−	0.959998i	$-0.409663\pi$
$499$	−169318.	−	169318.i	−0.679989	−	0.679989i	−0.959998	+	0.280008i	$0.909663\pi$
$500$	74412.0	+	74412.0i	0.297648	+	0.297648i
$501$	14753.9	−	14753.9i	0.0587802	−	0.0587802i
$502$	−32038.6	+	32038.6i	−0.127135	+	0.127135i
$503$	53395.1			0.211040			0.105520	−	0.994417i	$-0.466349\pi$
$503$	53395.1			0.211040			0.105520	+	0.994417i	$0.466349\pi$
$504$		−	119659.i		−	0.471069i
$505$	−507333.	+	507333.i	−1.98935	+	1.98935i
$506$			149585.i			0.584233i
$507$	36751.1	+	50707.1i	0.142973	+	0.197266i
$508$	−62098.1			−0.240630
$509$	−191977.	−	191977.i	−0.740992	−	0.740992i	0.231777	−	0.972769i	$-0.425546\pi$
$509$	−191977.	−	191977.i	−0.740992	−	0.740992i	−0.972769	+	0.231777i	$0.925546\pi$
$510$	72463.1			0.278597
$511$			2219.50i			0.00849989i
$512$	−8192.00	−	8192.00i	−0.0312500	−	0.0312500i
$513$	−57120.0	−	57120.0i	−0.217047	−	0.217047i
$514$	−103703.	+	103703.i	−0.392522	+	0.392522i
$515$	−59829.8	+	59829.8i	−0.225581	+	0.225581i
$516$	17641.2			0.0662566
$517$		−	333646.i		−	1.24826i
$518$	−57495.2	+	57495.2i	−0.214275	+	0.214275i
$519$		−	70816.2i		−	0.262905i
$520$	−69104.6	+	135431.i	−0.255565	+	0.500855i
$521$	−96837.2			−0.356752			−0.178376	−	0.983962i	$-0.557084\pi$
$521$	−96837.2			−0.356752			−0.178376	+	0.983962i	$0.557084\pi$
$522$	−161643.	−	161643.i	−0.593222	−	0.593222i
$523$	99463.6			0.363631			0.181815	−	0.983333i	$-0.441803\pi$
$523$	99463.6			0.363631			0.181815	+	0.983333i	$0.441803\pi$
$524$			83742.1i			0.304987i
$525$	102859.	+	102859.i	0.373186	+	0.373186i
$526$	−225168.	−	225168.i	−0.813833	−	0.813833i
$527$	150450.	−	150450.i	0.541714	−	0.541714i
$528$	17659.6	−	17659.6i	0.0633452	−	0.0633452i
$529$	191534.			0.684439
$530$			64640.6i			0.230120i
$531$	−170495.	+	170495.i	−0.604674	+	0.604674i
$532$			130134.i			0.459797i
$533$	−182824.	+	59285.8i	−0.643544	+	0.208687i
$534$	37218.8			0.130521
$535$	248491.	+	248491.i	0.868168	+	0.868168i
$536$	100991.			0.351523
$537$		−	90281.3i		−	0.313075i
$538$	−25098.8	−	25098.8i	−0.0867139	−	0.0867139i
$539$	−304069.	−	304069.i	−1.04663	−	1.04663i
$540$	77521.6	−	77521.6i	0.265849	−	0.265849i
$541$	−78592.6	+	78592.6i	−0.268526	+	0.268526i	−0.828506	−	0.559980i	$-0.810809\pi$
$541$	−78592.6	+	78592.6i	−0.268526	+	0.268526i	0.559980	+	0.828506i	$0.310809\pi$
$542$	−287434.			−0.978452
$543$			69405.6i			0.235394i
$544$	−37615.4	+	37615.4i	−0.127106	+	0.127106i
$545$			141564.i			0.476607i
$546$	−33063.2	+	64797.2i	−0.110907	+	0.217356i
$547$	−557039.			−1.86171			−0.930853	−	0.365394i	$-0.880934\pi$
$547$	−557039.			−1.86171			−0.930853	+	0.365394i	$0.880934\pi$
$548$	−81543.3	−	81543.3i	−0.271536	−	0.271536i
$549$	462398.			1.53416
$550$		−	481146.i		−	1.59056i
$551$	175793.	+	175793.i	0.579027	+	0.579027i
$552$	10425.3	+	10425.3i	0.0342146	+	0.0342146i
$553$	−322761.	+	322761.i	−1.05543	+	1.05543i
$554$	28785.2	−	28785.2i	0.0937884	−	0.0937884i
$555$	−36109.3			−0.117228
$556$			237577.i			0.768519i
$557$	−276263.	+	276263.i	−0.890455	+	0.890455i	−0.994566	−	0.104111i	$-0.966800\pi$
$557$	−276263.	+	276263.i	−0.890455	+	0.890455i	0.104111	+	0.994566i	$0.466800\pi$
$558$		−	156029.i		−	0.501116i
$559$	151393.	+	77249.2i	0.484487	+	0.247212i
$560$	−176614.			−0.563181
$561$	−81088.1	−	81088.1i	−0.257651	−	0.257651i
$562$	323743.			1.02501
$563$		−	147215.i		−	0.464446i	−0.972663	−	0.232223i	$-0.925400\pi$
$563$		−	147215.i		−	0.464446i	0.972663	−	0.232223i	$-0.0746000\pi$
$564$	−23253.6	−	23253.6i	−0.0731023	−	0.0731023i
$565$	−54350.5	−	54350.5i	−0.170258	−	0.170258i
$566$	206570.	−	206570.i	0.644814	−	0.644814i
$567$	−265797.	+	265797.i	−0.826767	+	0.826767i
$568$	−51448.9			−0.159470
$569$		−	537852.i		−	1.66126i	−0.556824	−	0.830631i	$-0.687980\pi$
$569$		−	537852.i		−	1.66126i	0.556824	−	0.830631i	$-0.312020\pi$
$570$	−40864.6	+	40864.6i	−0.125776	+	0.125776i
$571$		−	484104.i		−	1.48480i	−0.669959	−	0.742398i	$-0.733688\pi$
$571$		−	484104.i		−	1.48480i	0.669959	−	0.742398i	$-0.266312\pi$
$572$	228881.	−	74221.1i	0.699548	−	0.226848i
$573$	33757.1			0.102815
$574$	−157866.	−	157866.i	−0.479142	−	0.479142i
$575$	284043.			0.859110
$576$			39010.4i			0.117581i
$577$	2587.79	+	2587.79i	0.00777280	+	0.00777280i	0.710982	−	0.703210i	$-0.248250\pi$
$577$	2587.79	+	2587.79i	0.00777280	+	0.00777280i	−0.703210	+	0.710982i	$0.748250\pi$
$578$	5677.20	+	5677.20i	0.0169933	+	0.0169933i
$579$	70711.0	−	70711.0i	0.210926	−	0.210926i
$580$	−238582.	+	238582.i	−0.709220	+	0.709220i
$581$	558647.			1.65495
$582$			30983.6i			0.0914715i
$583$	72334.5	−	72334.5i	0.212818	−	0.212818i
$584$		−	723.586i		−	0.00212161i
$585$	487001.	−	157924.i	1.42304	−	0.461462i
$586$	−449969.			−1.31035
$587$	164714.	+	164714.i	0.478029	+	0.478029i	0.904501	−	0.426472i	$-0.140244\pi$
$587$	164714.	+	164714.i	0.478029	+	0.478029i	−0.426472	+	0.904501i	$0.640244\pi$
$588$	−42384.3			−0.122589
$589$			169688.i			0.489125i
$590$	251646.	+	251646.i	0.722912	+	0.722912i
$591$	62198.6	+	62198.6i	0.178076	+	0.178076i
$592$	18744.2	−	18744.2i	0.0534839	−	0.0534839i
$593$	155468.	−	155468.i	0.442110	−	0.442110i	−0.450611	−	0.892721i	$-0.648794\pi$
$593$	155468.	−	155468.i	0.442110	−	0.442110i	0.892721	+	0.450611i	$0.148794\pi$
$594$	−173497.			−0.491722
$595$			810960.i			2.29069i
$596$	177666.	−	177666.i	0.500163	−	0.500163i
$597$			90576.0i			0.254135i
$598$	43816.2	+	135119.i	0.122527	+	0.377846i
$599$	254077.			0.708127			0.354063	−	0.935221i	$-0.384800\pi$
$599$	254077.			0.708127			0.354063	+	0.935221i	$0.384800\pi$
$600$	−33533.5	−	33533.5i	−0.0931487	−	0.0931487i
$601$	233247.			0.645755			0.322877	−	0.946441i	$-0.395350\pi$
$601$	233247.			0.645755			0.322877	+	0.946441i	$0.395350\pi$
$602$			197429.i			0.544776i
$603$	−240461.	−	240461.i	−0.661317	−	0.661317i
$604$	−219390.	−	219390.i	−0.601372	−	0.601372i
$605$	−478845.	+	478845.i	−1.30823	+	1.30823i
$606$	79134.5	−	79134.5i	0.215487	−	0.215487i
$607$	−406297.			−1.10272			−0.551361	−	0.834267i	$-0.685891\pi$
$607$	−406297.			−1.10272			−0.551361	+	0.834267i	$0.685891\pi$
$608$		−	42425.3i		−	0.114767i
$609$	−114150.	+	114150.i	−0.307780	+	0.307780i
$610$		−	682487.i		−	1.83415i
$611$	−97731.5	−	301382.i	−0.261790	−	0.807299i
$612$	179125.			0.478248
$613$	414689.	+	414689.i	1.10357	+	1.10357i	0.993976	+	0.109599i	$0.0349566\pi$
$613$	414689.	+	414689.i	1.10357	+	1.10357i	0.109599	+	0.993976i	$0.465043\pi$
$614$	−263478.			−0.698888
$615$		−	99146.0i		−	0.262135i
$616$	197635.	+	197635.i	0.520838	+	0.520838i
$617$	−22163.9	−	22163.9i	−0.0582204	−	0.0582204i	0.677397	−	0.735618i	$-0.263108\pi$
$617$	−22163.9	−	22163.9i	−0.0582204	−	0.0582204i	−0.735618	+	0.677397i	$0.763108\pi$
$618$	9332.34	−	9332.34i	0.0244351	−	0.0244351i
$619$	197408.	−	197408.i	0.515209	−	0.515209i	−0.400909	−	0.916118i	$-0.631306\pi$
$619$	197408.	−	197408.i	0.515209	−	0.515209i	0.916118	+	0.400909i	$0.131306\pi$
$620$	−230295.			−0.599104
$621$		−	102424.i		−	0.265594i
$622$	−65843.7	+	65843.7i	−0.170190	+	0.170190i
$623$			416529.i			1.07317i
$624$	10779.0	−	21124.7i	0.0276829	−	0.0542528i
$625$	74389.6			0.190437
$626$	135390.	+	135390.i	0.345491	+	0.345491i
$627$	91456.9			0.232639
$628$			27220.1i			0.0690192i
$629$	−86068.1	−	86068.1i	−0.217541	−	0.217541i
$630$	420518.	+	420518.i	1.05951	+	1.05951i
$631$	462597.	−	462597.i	1.16183	−	1.16183i	0.177761	−	0.984074i	$-0.443115\pi$
$631$	462597.	−	462597.i	1.16183	−	1.16183i	0.984074	−	0.177761i	$-0.0568854\pi$
$632$	105224.	−	105224.i	0.263440	−	0.263440i
$633$	−117741.			−0.293847
$634$			350889.i			0.872954i
$635$	218232.	−	218232.i	0.541215	−	0.541215i
$636$		−	10082.7i		−	0.0249267i
$637$	−363732.	−	185597.i	−0.896403	−	0.457395i
$638$	533958.			1.31179
$639$	122500.	+	122500.i	0.300010	+	0.300010i
$640$	57578.4			0.140572
$641$		−	72292.1i		−	0.175944i	−0.996123	−	0.0879721i	$-0.971961\pi$
$641$		−	72292.1i		−	0.175944i	0.996123	−	0.0879721i	$-0.0280386\pi$
$642$	−38760.0	−	38760.0i	−0.0940403	−	0.0940403i
$643$	−445366.	−	445366.i	−1.07720	−	1.07720i	−0.996760	−	0.0804383i	$-0.974368\pi$
$643$	−445366.	−	445366.i	−1.07720	−	1.07720i	−0.0804383	−	0.996760i	$-0.525632\pi$
$644$	−116674.	+	116674.i	−0.281320	+	0.281320i
$645$	−61996.6	+	61996.6i	−0.149021	+	0.149021i
$646$	−194805.			−0.466805
$647$			535918.i			1.28023i	0.768277	+	0.640117i	$0.221114\pi$
$647$			535918.i			1.28023i	−0.768277	+	0.640117i	$0.778886\pi$
$648$	86653.2	−	86653.2i	0.206364	−	0.206364i
$649$		−	563196.i		−	1.33712i
$650$	−140937.	−	434617.i	−0.333578	−	1.02868i
$651$	−110185.			−0.259993
$652$	158658.	+	158658.i	0.373222	+	0.373222i
$653$	−59790.9			−0.140220			−0.0701098	−	0.997539i	$-0.522335\pi$
$653$	−59790.9			−0.140220			−0.0701098	+	0.997539i	$0.522335\pi$
$654$		−	22081.4i		−	0.0516263i
$655$	−294295.	−	294295.i	−0.685963	−	0.685963i
$656$	51466.3	+	51466.3i	0.119596	+	0.119596i
$657$	−1722.86	+	1722.86i	−0.00399135	+	0.00399135i
$658$	260239.	−	260239.i	0.601063	−	0.601063i
$659$	254900.			0.586948			0.293474	−	0.955967i	$-0.405189\pi$
$659$	254900.			0.586948			0.293474	+	0.955967i	$0.405189\pi$
$660$			124123.i			0.284947i
$661$	90948.6	−	90948.6i	0.208158	−	0.208158i	−0.595326	−	0.803484i	$-0.702977\pi$
$661$	90948.6	−	90948.6i	0.208158	−	0.208158i	0.803484	+	0.595326i	$0.202977\pi$
$662$			185257.i			0.422725i
$663$	−96998.9	−	49494.3i	−0.220668	−	0.112597i
$664$	−182126.			−0.413082
$665$	−457330.	−	457330.i	−1.03416	−	1.03416i
$666$	−89260.1			−0.201237
$667$			315221.i			0.708538i
$668$	−53830.0	−	53830.0i	−0.120634	−	0.120634i
$669$	87185.2	+	87185.2i	0.194801	+	0.194801i
$670$	−354914.	+	354914.i	−0.790630	+	0.790630i
$671$	−763721.	+	763721.i	−1.69625	+	1.69625i
$672$	27548.5			0.0610040
$673$			2365.55i			0.00522279i	0.999997	+	0.00261140i	$0.000831234\pi$
$673$			2365.55i			0.00522279i	−0.999997	+	0.00261140i	$0.999169\pi$
$674$	−348758.	+	348758.i	−0.767723	+	0.767723i
$675$			329451.i			0.723074i
$676$	185006.	−	134087.i	0.404849	−	0.293423i
$677$	−229195.			−0.500067			−0.250034	−	0.968237i	$-0.580442\pi$
$677$	−229195.			−0.500067			−0.250034	+	0.968237i	$0.580442\pi$
$678$	8477.66	+	8477.66i	0.0184424	+	0.0184424i
$679$	−346748.			−0.752098
$680$		−	264384.i		−	0.571764i
$681$	30170.0	+	30170.0i	0.0650551	+	0.0650551i
$682$	257706.	+	257706.i	0.554060	+	0.554060i
$683$	−147044.	+	147044.i	−0.315214	+	0.315214i	−0.846926	−	0.531711i	$-0.821549\pi$
$683$	−147044.	+	147044.i	−0.315214	+	0.315214i	0.531711	+	0.846926i	$0.321549\pi$
$684$	−101015.	+	101015.i	−0.215910	+	0.215910i
$685$	573136.			1.22145
$686$		−	2994.83i		−	0.00636392i
$687$	57581.8	−	57581.8i	0.122003	−	0.122003i
$688$		−	64364.5i		−	0.135978i
$689$	44151.3	−	86527.7i	0.0930048	−	0.182271i
$690$	−73275.6			−0.153908
$691$	−238903.	−	238903.i	−0.500341	−	0.500341i	0.411203	−	0.911544i	$-0.365109\pi$
$691$	−238903.	−	238903.i	−0.500341	−	0.500341i	−0.911544	+	0.411203i	$0.865109\pi$
$692$	−258375.			−0.539558
$693$		−	941141.i		−	1.95969i
$694$	111674.	+	111674.i	0.231864	+	0.231864i
$695$	−834917.	−	834917.i	−1.72852	−	1.72852i
$696$	37214.3	−	37214.3i	0.0768230	−	0.0768230i
$697$	236319.	−	236319.i	0.486444	−	0.486444i
$698$	121731.			0.249857
$699$		−	90740.8i		−	0.185716i
$700$	375286.	−	375286.i	0.765889	−	0.765889i
$701$			927743.i			1.88796i	0.330009	+	0.943978i	$0.392948\pi$
$701$			927743.i			1.88796i	−0.330009	+	0.943978i	$0.607052\pi$
$702$	−156720.	+	50820.8i	−0.318016	+	0.103126i
$703$	97073.7			0.196422
$704$	−64431.7	−	64431.7i	−0.130003	−	0.130003i
$705$	163440.			0.328837
$706$			638923.i			1.28186i
$707$	885622.	+	885622.i	1.77178	+	1.77178i
$708$	−39252.0	−	39252.0i	−0.0783061	−	0.0783061i
$709$	655343.	−	655343.i	1.30369	−	1.30369i	0.377813	−	0.925882i	$-0.376676\pi$
$709$	655343.	−	655343.i	1.30369	−	1.30369i	0.925882	−	0.377813i	$-0.123324\pi$
$710$	180807.	−	180807.i	0.358673	−	0.358673i
$711$	−501079.			−0.991214
$712$		−	135794.i		−	0.267867i
$713$	−152136.	+	152136.i	−0.299264	+	0.299264i
$714$		−	126495.i		−	0.248128i
$715$	−543521.	+	1.06519e6i	−1.06317	+	2.08361i
$716$	−329394.			−0.642524
$717$	−3509.26	−	3509.26i	−0.00682618	−	0.00682618i
$718$	344087.			0.667451
$719$		−	215165.i		−	0.416211i	−0.978106	−	0.208106i	$-0.933270\pi$
$719$		−	215165.i		−	0.416211i	0.978106	−	0.208106i	$-0.0667298\pi$
$720$	−137095.	−	137095.i	−0.264457	−	0.264457i
$721$	104441.	+	104441.i	0.200910	+	0.200910i
$722$	−150784.	+	150784.i	−0.289256	+	0.289256i
$723$	72421.3	−	72421.3i	0.138545	−	0.138545i
$724$	253228.			0.483098
$725$		−	1.01392e6i		−	1.92898i
$726$	74690.9	−	74690.9i	0.141708	−	0.141708i
$727$			803738.i			1.52071i	0.649510	+	0.760353i	$0.274974\pi$
$727$			803738.i			1.52071i	−0.649510	+	0.760353i	$0.725026\pi$
$728$	236414.	+	120632.i	0.446078	+	0.227614i
$729$	−351428.			−0.661274
$730$	2542.90	+	2542.90i	0.00477182	+	0.00477182i
$731$	−295544.			−0.553079
$732$			106455.i			0.198676i
$733$	200160.	+	200160.i	0.372537	+	0.372537i	0.868400	−	0.495864i	$-0.165148\pi$
$733$	200160.	+	200160.i	0.372537	+	0.372537i	−0.495864	+	0.868400i	$0.665148\pi$
$734$	154495.	+	154495.i	0.286763	+	0.286763i
$735$	148951.	−	148951.i	0.275721	−	0.275721i
$736$	38037.1	−	38037.1i	0.0702185	−	0.0702185i
$737$	794315.			1.46237
$738$		−	245083.i		−	0.449988i
$739$	424211.	−	424211.i	0.776771	−	0.776771i	−0.202509	−	0.979280i	$-0.564910\pi$
$739$	424211.	−	424211.i	0.776771	−	0.776771i	0.979280	+	0.202509i	$0.0649096\pi$
$740$			131746.i			0.240587i
$741$	82612.7	−	26789.5i	0.150456	−	0.0487897i
$742$	112839.			0.204952
$743$	−130672.	−	130672.i	−0.236704	−	0.236704i	0.578780	−	0.815484i	$-0.303529\pi$
$743$	−130672.	−	130672.i	−0.236704	−	0.236704i	−0.815484	+	0.578780i	$0.803529\pi$
$744$	35921.8			0.0648952
$745$			1.24875e6i			2.24989i
$746$	−427719.	−	427719.i	−0.768566	−	0.768566i
$747$	433644.	+	433644.i	0.777127	+	0.777127i
$748$	−295852.	+	295852.i	−0.528776	+	0.528776i
$749$	433777.	−	433777.i	0.773220	−	0.773220i
$750$	81580.3			0.145032
$751$		−	742621.i		−	1.31670i	−0.752711	−	0.658351i	$-0.771254\pi$
$751$		−	742621.i		−	1.31670i	0.752711	−	0.658351i	$-0.228746\pi$
$752$	−84841.2	+	84841.2i	−0.150028	+	0.150028i
$753$			35125.0i			0.0619479i
$754$	482322.	−	156407.i	0.848388	−	0.275114i
$755$	1.54201e6			2.70516
$756$	−135325.	−	135325.i	−0.236774	−	0.236774i
$757$	−382172.			−0.666910			−0.333455	−	0.942766i	$-0.608215\pi$
$757$	−382172.			−0.666910			−0.333455	+	0.942766i	$0.608215\pi$
$758$		−	724392.i		−	1.26077i
$759$	81997.2	+	81997.2i	0.142336	+	0.142336i
$760$	149095.	+	149095.i	0.258129	+	0.258129i
$761$	335972.	−	335972.i	0.580141	−	0.580141i	−0.354801	−	0.934942i	$-0.615451\pi$
$761$	335972.	−	335972.i	0.580141	−	0.580141i	0.934942	+	0.354801i	$0.115451\pi$
$762$	−34040.1	+	34040.1i	−0.0586247	+	0.0586247i
$763$	247121.			0.424482
$764$		−	123164.i		−	0.211007i
$765$	−629500.	+	629500.i	−1.07565	+	1.07565i
$766$		−	808629.i		−	1.37813i
$767$	−164971.	−	508733.i	−0.280425	−	0.864767i
$768$	−8981.16			−0.0152268
$769$	−90354.5	−	90354.5i	−0.152791	−	0.152791i	0.626572	−	0.779363i	$-0.284457\pi$
$769$	−90354.5	−	90354.5i	−0.152791	−	0.152791i	−0.779363	+	0.626572i	$0.784457\pi$
$770$	−1.38910e6			−2.34289
$771$			113693.i			0.191260i
$772$	−257991.	−	257991.i	−0.432883	−	0.432883i
$773$	511378.	+	511378.i	0.855821	+	0.855821i	0.990843	−	0.135021i	$-0.0431103\pi$
$773$	511378.	+	511378.i	0.855821	+	0.855821i	−0.135021	+	0.990843i	$0.543110\pi$
$774$	−153252.	+	153252.i	−0.255814	+	0.255814i
$775$	489354.	−	489354.i	0.814741	−	0.814741i
$776$	113044.			0.187727
$777$			63033.9i			0.104408i
$778$	32090.1	−	32090.1i	0.0530167	−	0.0530167i
$779$			266537.i			0.439221i
$780$	36358.0	+	112120.i	0.0597600	+	0.184286i
$781$	−404656.			−0.663412
$782$	−174656.	−	174656.i	−0.285607	−	0.285607i
$783$	−365612.			−0.596345
$784$			154640.i			0.251588i
$785$	−95659.7	−	95659.7i	−0.155235	−	0.155235i
$786$	45904.6	+	45904.6i	0.0743038	+	0.0743038i
$787$	−305280.	+	305280.i	−0.492888	+	0.492888i	−0.909215	−	0.416327i	$-0.863317\pi$
$787$	−305280.	+	305280.i	−0.492888	+	0.492888i	0.416327	+	0.909215i	$0.363317\pi$
$788$	226933.	−	226933.i	0.365465	−	0.365465i
$789$	−246859.			−0.396547
$790$			739580.i			1.18504i
$791$	−94876.5	+	94876.5i	−0.151637	+	0.151637i
$792$			306825.i			0.489147i
$793$	−466158.	+	913575.i	−0.741287	+	1.45277i
$794$	−103052.			−0.163461
$795$	35433.8	+	35433.8i	0.0560639	+	0.0560639i
$796$	330469.			0.521560
$797$			304571.i			0.479481i	0.970837	+	0.239740i	$0.0770623\pi$
$797$			304571.i			0.479481i	−0.970837	+	0.239740i	$0.922938\pi$
$798$	71334.9	+	71334.9i	0.112020	+	0.112020i
$799$	389567.	+	389567.i	0.610223	+	0.610223i
$800$	−122348.	+	122348.i	−0.191169	+	0.191169i
$801$	−323326.	+	323326.i	−0.503936	+	0.503936i
$802$	−365085.			−0.567604
$803$		−	5691.15i		−	0.00882610i
$804$	55360.0	−	55360.0i	0.0856414	−	0.0856414i
$805$		−	820053.i		−	1.26546i
$806$	308273.	+	157298.i	0.474531	+	0.242133i
$807$	−27516.7			−0.0422521
$808$	−288724.	−	288724.i	−0.442243	−	0.442243i
$809$	−685883.			−1.04798			−0.523990	−	0.851725i	$-0.675557\pi$
$809$	−685883.			−1.04798			−0.523990	+	0.851725i	$0.675557\pi$
$810$			609052.i			0.928291i
$811$	−815652.	−	815652.i	−1.24012	−	1.24012i	−0.959951	−	0.280166i	$-0.909610\pi$
$811$	−815652.	−	815652.i	−1.24012	−	1.24012i	−0.280166	−	0.959951i	$-0.590390\pi$
$812$	416478.	+	416478.i	0.631656	+	0.631656i
$813$	−157562.	+	157562.i	−0.238380	+	0.238380i
$814$	147427.	−	147427.i	0.222499	−	0.222499i
$815$	−1.11515e6			−1.67887
$816$			41239.0i			0.0619337i
$817$	166668.	−	166668.i	0.249693	−	0.249693i
$818$		−	18984.1i		−	0.0283716i
$819$	−275679.	−	850130.i	−0.410994	−	1.26741i
$820$	−361737.			−0.537978
$821$	12855.5	+	12855.5i	0.0190723	+	0.0190723i	0.716579	−	0.697506i	$-0.245707\pi$
$821$	12855.5	+	12855.5i	0.0190723	+	0.0190723i	−0.697506	+	0.716579i	$0.745707\pi$
$822$	−89398.6			−0.132308
$823$		−	94810.5i		−	0.139977i	−0.997548	−	0.0699885i	$-0.977704\pi$
$823$		−	94810.5i		−	0.139977i	0.997548	−	0.0699885i	$-0.0222963\pi$
$824$	−34049.3	−	34049.3i	−0.0501480	−	0.0501480i
$825$	−263748.	−	263748.i	−0.387508	−	0.387508i
$826$	439283.	−	439283.i	0.643850	−	0.643850i
$827$	113400.	−	113400.i	0.165807	−	0.165807i	−0.619327	−	0.785134i	$-0.712594\pi$
$827$	113400.	−	113400.i	0.165807	−	0.165807i	0.785134	+	0.619327i	$0.212594\pi$
$828$	−181133.			−0.264203
$829$		−	15161.7i		−	0.0220616i	−0.999939	−	0.0110308i	$-0.996489\pi$
$829$		−	15161.7i		−	0.0220616i	0.999939	−	0.0110308i	$-0.00351129\pi$
$830$	640048.	−	640048.i	0.929086	−	0.929086i
$831$		−	31558.1i		−	0.0456992i
$832$	−77074.2	−	39327.6i	−0.111343	−	0.0568134i
$833$	710065.			1.02331
$834$	130232.	+	130232.i	0.187234	+	0.187234i
$835$	378350.			0.542651
$836$		−	333683.i		−	0.477443i
$837$	−176457.	−	176457.i	−0.251877	−	0.251877i
$838$	−165020.	−	165020.i	−0.234989	−	0.234989i
$839$	−398624.	+	398624.i	−0.566290	+	0.566290i	−0.931087	−	0.364797i	$-0.881138\pi$
$839$	−398624.	+	398624.i	−0.566290	+	0.566290i	0.364797	+	0.931087i	$0.381138\pi$
$840$	−96813.7	+	96813.7i	−0.137208	+	0.137208i
$841$	417933.			0.590901
$842$		−	637810.i		−	0.899636i
$843$	177465.	−	177465.i	0.249722	−	0.249722i
$844$			429582.i			0.603062i
$845$	−178946.	+	1.12139e6i	−0.250615	+	1.57052i
$846$	404015.			0.564491
$847$	835892.	+	835892.i	1.16515	+	1.16515i
$848$	−36787.1			−0.0511569
$849$		−	226470.i		−	0.314192i
$850$	561788.	+	561788.i	0.777561	+	0.777561i
$851$	87033.0	+	87033.0i	0.120178	+	0.120178i
$852$	−28202.6	+	28202.6i	−0.0388516	+	0.0388516i
$853$	−160276.	+	160276.i	−0.220277	+	0.220277i	−0.808615	−	0.588338i	$-0.799782\pi$
$853$	−160276.	+	160276.i	−0.220277	+	0.220277i	0.588338	+	0.808615i	$0.299782\pi$
$854$	−1.19138e6			−1.63356
$855$		−	709995.i		−	0.971232i
$856$	−141417.	+	141417.i	−0.192999	+	0.192999i
$857$		−	65742.3i		−	0.0895124i	−0.998998	−	0.0447562i	$-0.985749\pi$
$857$		−	65742.3i		−	0.0895124i	0.998998	−	0.0447562i	$-0.0142511\pi$
$858$	84779.2	−	166150.i	0.115164	−	0.225697i
$859$	−214439.			−0.290614			−0.145307	−	0.989387i	$-0.546417\pi$
$859$	−214439.			−0.290614			−0.145307	+	0.989387i	$0.546417\pi$
$860$	226196.	+	226196.i	0.305836	+	0.305836i
$861$	−173073.			−0.233466
$862$			767474.i			1.03288i
$863$	−735390.	−	735390.i	−0.987407	−	0.987407i	0.0125152	−	0.999922i	$-0.496016\pi$
$863$	−735390.	−	735390.i	−0.987407	−	0.987407i	−0.999922	+	0.0125152i	$0.996016\pi$
$864$	44117.8	+	44117.8i	0.0590998	+	0.0590998i
$865$	908009.	−	908009.i	1.21355	−	1.21355i
$866$	−334399.	+	334399.i	−0.445892	+	0.445892i
$867$	6224.10			0.00828015
$868$			402014.i			0.533582i
$869$	827609.	−	827609.i	1.09594	−	1.09594i
$870$			261565.i			0.345574i
$871$	717502.	−	232670.i	0.945773	−	0.306694i
$872$	−80564.5			−0.105952
$873$	−269160.	−	269160.i	−0.353168	−	0.353168i
$874$	196989.			0.257881
$875$			912994.i			1.19248i
$876$	−396.646	−	396.646i	−0.000516886	−	0.000516886i
$877$	−704397.	−	704397.i	−0.915838	−	0.915838i	0.0808858	−	0.996723i	$-0.474225\pi$
$877$	−704397.	−	704397.i	−0.915838	−	0.915838i	−0.996723	+	0.0808858i	$0.974225\pi$
$878$	446023.	−	446023.i	0.578587	−	0.578587i
$879$	−246658.	+	246658.i	−0.319240	+	0.319240i
$880$	452865.			0.584795
$881$			547899.i			0.705909i	0.935641	+	0.352954i	$0.114823\pi$
$881$			547899.i			0.705909i	−0.935641	+	0.352954i	$0.885177\pi$
$882$	368200.	−	368200.i	0.473311	−	0.473311i
$883$			949898.i			1.21830i	0.793054	+	0.609152i	$0.208490\pi$
$883$			949898.i			1.21830i	−0.793054	+	0.609152i	$0.791510\pi$
$884$	−180581.	+	353903.i	−0.231083	+	0.452877i
$885$	275887.			0.352245
$886$	34875.8	+	34875.8i	0.0444280	+	0.0444280i
$887$	587902.			0.747236			0.373618	−	0.927583i	$-0.378117\pi$
$887$	587902.			0.747236			0.373618	+	0.927583i	$0.378117\pi$
$888$		−	20549.9i		−	0.0260605i
$889$	−380954.	−	380954.i	−0.482025	−	0.482025i
$890$	477221.	+	477221.i	0.602476	+	0.602476i
$891$	681544.	−	681544.i	0.858497	−	0.858497i
$892$	318098.	−	318098.i	0.399789	−	0.399789i
$893$	−439382.			−0.550984
$894$		−	194781.i		−	0.243709i
$895$	1.15759e6	−	1.15759e6i	1.44514	−	1.44514i
$896$		−	100511.i		−	0.125198i
$897$	98086.4	+	50049.2i	0.121906	+	0.0622032i
$898$	410213.			0.508694
$899$	543067.	+	543067.i	0.671945	+	0.671945i
$900$	582623.			0.719288
$901$			168916.i			0.208076i
$902$	404793.	+	404793.i	0.497530	+	0.497530i
$903$	108224.	+	108224.i	0.132724	+	0.132724i
$904$	30931.0	−	30931.0i	0.0378492	−	0.0378492i
$905$	−889922.	+	889922.i	−1.08656	+	1.08656i
$906$	−240525.			−0.293024
$907$		−	490495.i		−	0.596239i	−0.954529	−	0.298119i	$-0.903641\pi$
$907$		−	490495.i		−	0.596239i	0.954529	−	0.298119i	$-0.0963594\pi$
$908$	110076.	−	110076.i	0.133512	−	0.133512i
$909$			1.37491e6i			1.66397i
$910$	−1.25477e6	+	406895.i	−1.51524	+	0.491359i
$911$	−265333.			−0.319708			−0.159854	−	0.987141i	$-0.551102\pi$
$911$	−265333.			−0.319708			−0.159854	+	0.987141i	$0.551102\pi$
$912$	−23256.1	−	23256.1i	−0.0279607	−	0.0279607i
$913$	−1.43246e6			−1.71846
$914$		−	851145.i		−	1.01885i
$915$	−374117.	−	374117.i	−0.446853	−	0.446853i
$916$	−210089.	−	210089.i	−0.250387	−	0.250387i
$917$	−513734.	+	513734.i	−0.610942	+	0.610942i
$918$	202576.	−	202576.i	0.240383	−	0.240383i
$919$	1.16310e6			1.37717			0.688584	−	0.725156i	$-0.258232\pi$
$919$	1.16310e6			1.37717			0.688584	+	0.725156i	$0.258232\pi$
$920$			267348.i			0.315865i
$921$	−144430.	+	144430.i	−0.170270	+	0.170270i
$922$		−	653437.i		−	0.768674i
$923$	−365524.	+	118532.i	−0.429055	+	0.139133i
$924$	216674.			0.253783
$925$	−279946.	−	279946.i	−0.327183	−	0.327183i
$926$	48250.6			0.0562705
$927$			162143.i			0.188686i
$928$	−135777.	−	135777.i	−0.157664	−	0.157664i
$929$	452245.	+	452245.i	0.524013	+	0.524013i	0.918781	−	0.394768i	$-0.129175\pi$
$929$	452245.	+	452245.i	0.524013	+	0.524013i	−0.394768	+	0.918781i	$0.629175\pi$
$930$	−126240.	+	126240.i	−0.145959	+	0.145959i
$931$	−400431.	+	400431.i	−0.461986	+	0.461986i
$932$	−331070.			−0.381144
$933$			72186.6i			0.0829264i
$934$	−811484.	+	811484.i	−0.930221	+	0.930221i
$935$		−	2.07943e6i		−	2.37860i
$936$	89874.9	+	277154.i	0.102586	+	0.316351i
$937$	−748585.			−0.852633			−0.426316	−	0.904574i	$-0.640189\pi$
$937$	−748585.			−0.852633			−0.426316	+	0.904574i	$0.640189\pi$
$938$	619553.	+	619553.i	0.704162	+	0.704162i
$939$	148432.			0.168344
$940$		−	596316.i		−	0.674871i
$941$	39986.3	+	39986.3i	0.0451577	+	0.0451577i	0.729325	−	0.684167i	$-0.239834\pi$
$941$	39986.3	+	39986.3i	0.0451577	+	0.0451577i	−0.684167	+	0.729325i	$0.739834\pi$
$942$	14921.1	+	14921.1i	0.0168151	+	0.0168151i
$943$	−238968.	+	238968.i	−0.268731	+	0.268731i
$944$	−143212.	+	143212.i	−0.160707	+	0.160707i
$945$	951147.			1.06508
$946$		−	506239.i		−	0.565683i
$947$	−811733.	+	811733.i	−0.905135	+	0.905135i	−0.995875	−	0.0907396i	$-0.971077\pi$
$947$	−811733.	+	811733.i	−0.905135	+	0.905135i	0.0907396	+	0.995875i	$0.471077\pi$
$948$		−	115361.i		−	0.128364i
$949$	−1667.05	−	5140.79i	−0.00185104	−	0.00570818i
$950$	−633624.			−0.702077
$951$	192346.	+	192346.i	0.212677	+	0.212677i
$952$	−461520.			−0.509233
$953$		−	783349.i		−	0.862521i	−0.902227	−	0.431260i	$-0.858069\pi$
$953$		−	783349.i		−	0.862521i	0.902227	−	0.431260i	$-0.141931\pi$
$954$	87590.4	+	87590.4i	0.0962409	+	0.0962409i
$955$	432835.	+	432835.i	0.474587	+	0.474587i
$956$	−12803.6	+	12803.6i	−0.0140093	+	0.0140093i
$957$	292698.	−	292698.i	0.319592	−	0.319592i
$958$	−273662.			−0.298183
$959$		−	1.00049e6i		−	1.08787i
$960$	31562.5	−	31562.5i	0.0342475	−	0.0342475i
$961$		−	399315.i		−	0.432384i
$962$	89985.9	−	176354.i	0.0972354	−	0.190562i
$963$	673430.			0.726173
$964$	−264231.	−	264231.i	−0.284335	−	0.284335i
$965$	1.81332e6			1.94724
$966$			127913.i			0.137076i
$967$	374447.	+	374447.i	0.400440	+	0.400440i	0.878388	−	0.477948i	$-0.158619\pi$
$967$	374447.	+	374447.i	0.400440	+	0.400440i	−0.477948	+	0.878388i	$0.658619\pi$
$968$	−272512.	−	272512.i	−0.290827	−	0.290827i
$969$	−106786.	+	106786.i	−0.113727	+	0.113727i
$970$	−397273.	+	397273.i	−0.422226	+	0.422226i
$971$	93108.8			0.0987535			0.0493767	−	0.998780i	$-0.484276\pi$
$971$	93108.8			0.0987535			0.0493767	+	0.998780i	$0.484276\pi$
$972$		−	318347.i		−	0.336952i
$973$	−1.45747e6	+	1.45747e6i	−1.53948	+	1.53948i
$974$			27358.0i			0.0288380i
$975$	−315499.	−	160986.i	−0.331886	−	0.169347i
$976$	388405.			0.407742
$977$	−360353.	−	360353.i	−0.377519	−	0.377519i	0.492687	−	0.870206i	$-0.336015\pi$
$977$	−360353.	−	360353.i	−0.377519	−	0.377519i	−0.870206	+	0.492687i	$0.836015\pi$
$978$	173942.			0.181856
$979$		−	1.06804e6i		−	1.11436i
$980$	−543453.	−	543453.i	−0.565862	−	0.565862i
$981$	191825.	+	191825.i	0.199327	+	0.199327i
$982$	634875.	−	634875.i	0.658363	−	0.658363i
$983$	525101.	−	525101.i	0.543420	−	0.543420i	−0.381110	−	0.924530i	$-0.624458\pi$
$983$	525101.	−	525101.i	0.543420	−	0.543420i	0.924530	+	0.381110i	$0.124458\pi$
$984$	56424.2			0.0582741
$985$			1.59503e6i			1.64398i
$986$	−623452.	+	623452.i	−0.641282	+	0.641282i
$987$		−	285308.i		−	0.292873i
$988$	−97742.3	−	301415.i	−0.100131	−	0.308781i
$989$	298857.			0.305542
$990$	−1.07828e6	−	1.07828e6i	−1.10017	−	1.10017i
$991$	−1.55237e6			−1.58069			−0.790347	−	0.612660i	$-0.790100\pi$
$991$	−1.55237e6			−1.58069			−0.790347	+	0.612660i	$0.790100\pi$
$992$		−	131062.i		−	0.133184i
$993$	101551.	+	101551.i	0.102988	+	0.102988i
$994$	−315625.	−	315625.i	−0.319447	−	0.319447i
$995$	−1.16137e6	+	1.16137e6i	−1.17307	+	1.17307i
$996$	−99835.5	+	99835.5i	−0.100639	+	0.100639i
$997$	−1.39961e6			−1.40805			−0.704024	−	0.710176i	$-0.748615\pi$
$997$	−1.39961e6			−1.40805			−0.704024	+	0.710176i	$0.748615\pi$
$998$			677272.i			0.679989i
$999$	−100946.	+	100946.i	−0.101148	+	0.101148i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.5.d.a.21.2	yes	6
3.2	odd	2		234.5.i.b.73.3		6
4.3	odd	2		208.5.t.b.177.2		6
13.5	odd	4	inner	26.5.d.a.5.2	✓	6
13.8	odd	4		338.5.d.d.239.2		6
13.12	even	2		338.5.d.d.99.2		6
39.5	even	4		234.5.i.b.109.3		6
52.31	even	4		208.5.t.b.161.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.5.d.a.5.2	✓	6	13.5	odd	4	inner
26.5.d.a.21.2	yes	6	1.1	even	1	trivial
208.5.t.b.161.2		6	52.31	even	4
208.5.t.b.177.2		6	4.3	odd	2
234.5.i.b.73.3		6	3.2	odd	2
234.5.i.b.109.3		6	39.5	even	4
338.5.d.d.99.2		6	13.12	even	2
338.5.d.d.239.2		6	13.8	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	26.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{2} -2.19267 q^{3} +8.00000i q^{4} +(-28.1144 - 28.1144i) q^{5} +(4.38533 + 4.38533i) q^{6} +(-49.0778 + 49.0778i) q^{7} +(16.0000 - 16.0000i) q^{8} -76.1922 q^{9} +O(q^{10})\)	\(q+(-2.00000 - 2.00000i) q^{2} -2.19267 q^{3} +8.00000i q^{4} +(-28.1144 - 28.1144i) q^{5} +(4.38533 + 4.38533i) q^{6} +(-49.0778 + 49.0778i) q^{7} +(16.0000 - 16.0000i) q^{8} -76.1922 q^{9} +112.458i q^{10} +(125.843 - 125.843i) q^{11} -17.5413i q^{12} +(76.8118 - 150.536i) q^{13} +196.311 q^{14} +(61.6456 + 61.6456i) q^{15} -64.0000 q^{16} +293.870i q^{17} +(152.384 + 152.384i) q^{18} +(-165.724 - 165.724i) q^{19} +(224.916 - 224.916i) q^{20} +(107.611 - 107.611i) q^{21} -503.372 q^{22} -297.165i q^{23} +(-35.0826 + 35.0826i) q^{24} +955.844i q^{25} +(-454.695 + 147.448i) q^{26} +344.670 q^{27} +(-392.622 - 392.622i) q^{28} -1060.76 q^{29} -246.582i q^{30} +(-511.960 - 511.960i) q^{31} +(128.000 + 128.000i) q^{32} +(-275.932 + 275.932i) q^{33} +(587.740 - 587.740i) q^{34} +2759.59 q^{35} -609.538i q^{36} +(-292.878 + 292.878i) q^{37} +662.895i q^{38} +(-168.422 + 330.074i) q^{39} -899.662 q^{40} +(-804.161 - 804.161i) q^{41} -430.445 q^{42} +1005.69i q^{43} +(1006.74 + 1006.74i) q^{44} +(2142.10 + 2142.10i) q^{45} +(-594.330 + 594.330i) q^{46} +(1325.64 - 1325.64i) q^{47} +140.331 q^{48} -2416.26i q^{49} +(1911.69 - 1911.69i) q^{50} -644.359i q^{51} +(1204.28 + 614.494i) q^{52} +574.799 q^{53} +(-689.340 - 689.340i) q^{54} -7076.02 q^{55} +1570.49i q^{56} +(363.377 + 363.377i) q^{57} +(2121.52 + 2121.52i) q^{58} +(2237.69 - 2237.69i) q^{59} +(-493.165 + 493.165i) q^{60} -6068.83 q^{61} +2047.84i q^{62} +(3739.34 - 3739.34i) q^{63} -512.000i q^{64} +(-6391.74 + 2072.70i) q^{65} +1103.73 q^{66} +(3155.98 + 3155.98i) q^{67} -2350.96 q^{68} +651.583i q^{69} +(-5519.18 - 5519.18i) q^{70} +(-1607.78 - 1607.78i) q^{71} +(-1219.08 + 1219.08i) q^{72} +(22.6121 - 22.6121i) q^{73} +1171.51 q^{74} -2095.85i q^{75} +(1325.79 - 1325.79i) q^{76} +12352.2i q^{77} +(996.993 - 323.303i) q^{78} +6576.52 q^{79} +(1799.32 + 1799.32i) q^{80} +5415.82 q^{81} +3216.64i q^{82} +(-5691.45 - 5691.45i) q^{83} +(860.889 + 860.889i) q^{84} +(8261.99 - 8261.99i) q^{85} +(2011.39 - 2011.39i) q^{86} +2325.89 q^{87} -4026.98i q^{88} +(4243.56 - 4243.56i) q^{89} -8568.41i q^{90} +(3618.20 + 11157.7i) q^{91} +2377.32 q^{92} +(1122.56 + 1122.56i) q^{93} -5302.58 q^{94} +9318.47i q^{95} +(-280.661 - 280.661i) q^{96} +(3532.64 + 3532.64i) q^{97} +(-4832.51 + 4832.51i) q^{98} +(-9588.27 + 9588.27i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 12 q^{2} + 18 q^{5} - 42 q^{7} + 96 q^{8} - 18 q^{9}+O(q^{10}) \) 6 * q - 12 * q^2 + 18 * q^5 - 42 * q^7 + 96 * q^8 - 18 * q^9	\( 6 q - 12 q^{2} + 18 q^{5} - 42 q^{7} + 96 q^{8} - 18 q^{9} - 18 q^{11} + 90 q^{13} + 168 q^{14} - 432 q^{15} - 384 q^{16} + 36 q^{18} - 366 q^{19} - 144 q^{20} + 1908 q^{21} + 72 q^{22} + 12 q^{26} + 1476 q^{27} - 336 q^{28} - 6228 q^{29} + 402 q^{31} + 768 q^{32} + 792 q^{33} + 1944 q^{34} + 3024 q^{35} + 5298 q^{37} - 6120 q^{39} + 576 q^{40} - 2430 q^{41} - 7632 q^{42} - 144 q^{44} + 5382 q^{45} - 1872 q^{46} + 4014 q^{47} + 7908 q^{50} - 768 q^{52} + 6516 q^{53} - 2952 q^{54} - 28764 q^{55} - 5940 q^{57} + 12456 q^{58} + 7434 q^{59} + 3456 q^{60} + 7164 q^{61} + 12942 q^{63} - 14598 q^{65} - 3168 q^{66} + 5790 q^{67} - 7776 q^{68} - 6048 q^{70} + 15246 q^{71} - 288 q^{72} - 4254 q^{73} - 21192 q^{74} + 2928 q^{76} + 12600 q^{78} + 23364 q^{79} - 1152 q^{80} - 19602 q^{81} - 38034 q^{83} + 15264 q^{84} + 30672 q^{85} + 11160 q^{86} - 9288 q^{87} + 4122 q^{89} - 11922 q^{91} + 7488 q^{92} + 10404 q^{93} - 16056 q^{94} - 1362 q^{97} - 17076 q^{98} - 24642 q^{99}+O(q^{100}) \) 6 * q - 12 * q^2 + 18 * q^5 - 42 * q^7 + 96 * q^8 - 18 * q^9 - 18 * q^11 + 90 * q^13 + 168 * q^14 - 432 * q^15 - 384 * q^16 + 36 * q^18 - 366 * q^19 - 144 * q^20 + 1908 * q^21 + 72 * q^22 + 12 * q^26 + 1476 * q^27 - 336 * q^28 - 6228 * q^29 + 402 * q^31 + 768 * q^32 + 792 * q^33 + 1944 * q^34 + 3024 * q^35 + 5298 * q^37 - 6120 * q^39 + 576 * q^40 - 2430 * q^41 - 7632 * q^42 - 144 * q^44 + 5382 * q^45 - 1872 * q^46 + 4014 * q^47 + 7908 * q^50 - 768 * q^52 + 6516 * q^53 - 2952 * q^54 - 28764 * q^55 - 5940 * q^57 + 12456 * q^58 + 7434 * q^59 + 3456 * q^60 + 7164 * q^61 + 12942 * q^63 - 14598 * q^65 - 3168 * q^66 + 5790 * q^67 - 7776 * q^68 - 6048 * q^70 + 15246 * q^71 - 288 * q^72 - 4254 * q^73 - 21192 * q^74 + 2928 * q^76 + 12600 * q^78 + 23364 * q^79 - 1152 * q^80 - 19602 * q^81 - 38034 * q^83 + 15264 * q^84 + 30672 * q^85 + 11160 * q^86 - 9288 * q^87 + 4122 * q^89 - 11922 * q^91 + 7488 * q^92 + 10404 * q^93 - 16056 * q^94 - 1362 * q^97 - 17076 * q^98 - 24642 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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