LMFDB - Embedded newform 833.2.bc.d.80.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(31,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([8, 27]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("833.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.bc (of order $48$, degree $16$, not 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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$9$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			80.2
Character	$\chi$	$=$	833.80
Dual form			833.2.bc.d.656.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08860 + 1.41869i) q^{2} +(0.543906 - 0.0356495i) q^{3} +(-0.309994 - 1.15691i) q^{4} +(2.53857 - 0.861728i) q^{5} +(-0.541520 + 0.810442i) q^{6} +(-1.32544 - 0.549014i) q^{8} +(-2.67977 + 0.352799i) q^{9} +O(q^{10})$	\(q+(-1.08860 + 1.41869i) q^{2} +(0.543906 - 0.0356495i) q^{3} +(-0.309994 - 1.15691i) q^{4} +(2.53857 - 0.861728i) q^{5} +(-0.541520 + 0.810442i) q^{6} +(-1.32544 - 0.549014i) q^{8} +(-2.67977 + 0.352799i) q^{9} +(-1.54096 + 4.53951i) q^{10} +(-2.21771 - 4.49707i) q^{11} +(-0.209851 - 0.618201i) q^{12} +(4.70535 - 4.70535i) q^{13} +(1.35002 - 0.559198i) q^{15} +(4.29627 - 2.48045i) q^{16} +(-4.12294 + 0.0371267i) q^{17} +(2.41668 - 4.18582i) q^{18} +(-4.21946 - 3.23771i) q^{19} +(-1.78388 - 2.66977i) q^{20} +(8.79414 + 1.74926i) q^{22} +(-0.267530 + 4.08172i) q^{23} +(-0.740486 - 0.251361i) q^{24} +(1.73498 - 1.33130i) q^{25} +(1.55319 + 11.7977i) q^{26} +(-3.04877 + 0.606437i) q^{27} +(1.90098 - 9.55688i) q^{29} +(-0.676305 + 2.52400i) q^{30} +(0.0502494 + 0.766657i) q^{31} +(-0.783404 + 5.95055i) q^{32} +(-1.36654 - 2.36692i) q^{33} +(4.43555 - 5.88958i) q^{34} +(1.23887 + 2.99090i) q^{36} +(-5.32156 - 2.62430i) q^{37} +(9.18660 - 2.46154i) q^{38} +(2.39153 - 2.72701i) q^{39} +(-3.83781 - 0.251544i) q^{40} +(-0.0510695 - 0.256744i) q^{41} +(0.397620 - 0.959941i) q^{43} +(-4.51524 + 3.95976i) q^{44} +(-6.49877 + 3.20484i) q^{45} +(-5.49946 - 4.82290i) q^{46} +(-8.29355 - 2.22225i) q^{47} +(2.24834 - 1.50229i) q^{48} +3.91066i q^{50} +(-2.24117 + 0.167174i) q^{51} +(-6.90231 - 3.98505i) q^{52} +(1.81423 + 0.238848i) q^{53} +(2.45854 - 4.98542i) q^{54} +(-9.50506 - 9.50506i) q^{55} +(-2.41041 - 1.61059i) q^{57} +(11.4888 + 13.1005i) q^{58} +(3.63474 + 4.73689i) q^{59} +(-1.06544 - 1.38851i) q^{60} +(0.999567 + 1.13979i) q^{61} +(-1.14235 - 0.763294i) q^{62} +(-0.573383 - 0.573383i) q^{64} +(7.89012 - 15.9996i) q^{65} +(4.84555 + 0.637929i) q^{66} +(10.7106 + 6.18377i) q^{67} +(1.32104 + 4.75837i) q^{68} +2.22961i q^{69} +(-3.95416 + 2.64209i) q^{71} +(3.74556 + 1.00362i) q^{72} +(0.852445 + 0.747574i) q^{73} +(9.51611 - 4.69283i) q^{74} +(0.896209 - 0.785954i) q^{75} +(-2.43774 + 5.88522i) q^{76} +(1.26537 + 6.36145i) q^{78} +(12.0747 + 0.791417i) q^{79} +(8.76890 - 9.99901i) q^{80} +(6.19577 - 1.66015i) q^{81} +(0.419833 + 0.207039i) q^{82} +(5.11069 + 12.3383i) q^{83} +(-10.4344 + 3.64710i) q^{85} +(0.929008 + 1.60909i) q^{86} +(0.693258 - 5.26582i) q^{87} +(0.470480 + 7.17814i) q^{88} +(0.507083 - 1.89246i) q^{89} +(2.52788 - 12.7085i) q^{90} +(4.80513 - 0.955800i) q^{92} +(0.0546619 + 0.415198i) q^{93} +(12.1810 - 9.34683i) q^{94} +(-13.5014 - 4.58311i) q^{95} +(-0.213964 + 3.26447i) q^{96} +(9.84825 + 1.95894i) q^{97} +(7.52952 + 11.2687i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{3} + 8 q^{5} - 16 q^{6} - 24 q^{9}+O(q^{10}) $ 144 * q + 8 * q^3 + 8 * q^5 - 16 * q^6 - 24 * q^9	$ 144 q + 8 q^{3} + 8 q^{5} - 16 q^{6} - 24 q^{9} - 8 q^{11} + 64 q^{13} + 40 q^{18} + 24 q^{19} + 48 q^{22} - 8 q^{23} - 24 q^{24} - 8 q^{25} - 16 q^{27} + 80 q^{31} + 40 q^{32} - 80 q^{33} + 240 q^{36} - 48 q^{37} - 56 q^{38} + 16 q^{39} - 32 q^{40} - 48 q^{41} + 48 q^{43} - 32 q^{44} - 48 q^{45} - 40 q^{47} + 40 q^{51} + 24 q^{53} + 200 q^{54} - 96 q^{57} - 32 q^{58} + 8 q^{59} + 80 q^{60} - 256 q^{62} + 24 q^{65} - 8 q^{66} - 40 q^{68} - 48 q^{73} + 32 q^{74} + 128 q^{75} - 144 q^{76} - 96 q^{78} + 32 q^{79} + 256 q^{80} - 16 q^{81} - 152 q^{82} - 64 q^{85} + 80 q^{86} - 64 q^{87} - 56 q^{88} - 64 q^{89} + 752 q^{90} - 432 q^{92} + 32 q^{93} - 128 q^{94} - 32 q^{95} + 32 q^{96} + 16 q^{97} + 80 q^{99}+O(q^{100}) $ 144 * q + 8 * q^3 + 8 * q^5 - 16 * q^6 - 24 * q^9 - 8 * q^11 + 64 * q^13 + 40 * q^18 + 24 * q^19 + 48 * q^22 - 8 * q^23 - 24 * q^24 - 8 * q^25 - 16 * q^27 + 80 * q^31 + 40 * q^32 - 80 * q^33 + 240 * q^36 - 48 * q^37 - 56 * q^38 + 16 * q^39 - 32 * q^40 - 48 * q^41 + 48 * q^43 - 32 * q^44 - 48 * q^45 - 40 * q^47 + 40 * q^51 + 24 * q^53 + 200 * q^54 - 96 * q^57 - 32 * q^58 + 8 * q^59 + 80 * q^60 - 256 * q^62 + 24 * q^65 - 8 * q^66 - 40 * q^68 - 48 * q^73 + 32 * q^74 + 128 * q^75 - 144 * q^76 - 96 * q^78 + 32 * q^79 + 256 * q^80 - 16 * q^81 - 152 * q^82 - 64 * q^85 + 80 * q^86 - 64 * q^87 - 56 * q^88 - 64 * q^89 + 752 * q^90 - 432 * q^92 + 32 * q^93 - 128 * q^94 - 32 * q^95 + 32 * q^96 + 16 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{16}\right)$

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 $

$2$	−1.08860	+	1.41869i	−0.769755	+	1.00316i	0.229797	+	0.973239i	$0.426194\pi$
$2$	−1.08860	+	1.41869i	−0.769755	+	1.00316i	−0.999552	+	0.0299259i	$0.990473\pi$
$3$	0.543906	−	0.0356495i	0.314024	−	0.0205822i	0.0924238	−	0.995720i	$-0.470539\pi$
$3$	0.543906	−	0.0356495i	0.314024	−	0.0205822i	0.221601	+	0.975138i	$0.428872\pi$
$4$	−0.309994	−	1.15691i	−0.154997	−	0.578457i
$5$	2.53857	−	0.861728i	1.13528	−	0.385376i	0.310358	−	0.950620i	$-0.399551\pi$
$5$	2.53857	−	0.861728i	1.13528	−	0.385376i	0.824924	+	0.565243i	$0.191218\pi$
$6$	−0.541520	+	0.810442i	−0.221075	+	0.330861i
$7$		0			0
$7$		0			0
$8$	−1.32544	−	0.549014i	−0.468613	−	0.194106i
$9$	−2.67977	+	0.352799i	−0.893257	+	0.117600i
$10$	−1.54096	+	4.53951i	−0.487293	+	1.43552i
$11$	−2.21771	−	4.49707i	−0.668665	−	1.35592i	−0.921488	−	0.388406i	$-0.873026\pi$
$11$	−2.21771	−	4.49707i	−0.668665	−	1.35592i	0.252824	−	0.967512i	$-0.418641\pi$
$12$	−0.209851	−	0.618201i	−0.0605788	−	0.178459i
$13$	4.70535	−	4.70535i	1.30503	−	1.30503i	0.380072	−	0.924957i	$-0.375899\pi$
$13$	4.70535	−	4.70535i	1.30503	−	1.30503i	0.924957	−	0.380072i	$-0.124101\pi$
$14$		0			0
$15$	1.35002	−	0.559198i	0.348574	−	0.144384i
$16$	4.29627	−	2.48045i	1.07407	−	0.620113i
$17$	−4.12294	+	0.0371267i	−0.999959	+	0.00900454i
$17$	−4.12294	+	0.0371267i	−0.999959	+	0.00900454i
$18$	2.41668	−	4.18582i	0.569618	−	0.986607i
$19$	−4.21946	−	3.23771i	−0.968011	−	0.742781i	−0.00165754	−	0.999999i	$-0.500528\pi$
$19$	−4.21946	−	3.23771i	−0.968011	−	0.742781i	−0.966354	+	0.257218i	$0.917194\pi$
$20$	−1.78388	−	2.66977i	−0.398889	−	0.596979i
$21$		0			0
$22$	8.79414	+	1.74926i	1.87492	+	0.372944i
$23$	−0.267530	+	4.08172i	−0.0557839	+	0.851098i	0.874677	+	0.484706i	$0.161074\pi$
$23$	−0.267530	+	4.08172i	−0.0557839	+	0.851098i	−0.930461	+	0.366391i	$0.880593\pi$
$24$	−0.740486	−	0.251361i	−0.151151	−	0.0513089i
$25$	1.73498	−	1.33130i	0.346997	−	0.266260i
$26$	1.55319	+	11.7977i	0.304606	+	2.31371i
$27$	−3.04877	+	0.606437i	−0.586735	+	0.116709i
$28$		0			0
$29$	1.90098	−	9.55688i	0.353004	−	1.77467i	−0.241323	−	0.970445i	$-0.577581\pi$
$29$	1.90098	−	9.55688i	0.353004	−	1.77467i	0.594327	−	0.804224i	$-0.297419\pi$
$30$	−0.676305	+	2.52400i	−0.123476	+	0.460818i
$31$	0.0502494	+	0.766657i	0.00902505	+	0.137696i	0.999994	+	0.00360059i	$0.00114611\pi$
$31$	0.0502494	+	0.766657i	0.00902505	+	0.137696i	−0.990968	+	0.134095i	$0.957187\pi$
$32$	−0.783404	+	5.95055i	−0.138488	+	1.05192i
$33$	−1.36654	−	2.36692i	−0.237885	−	0.412029i
$34$	4.43555	−	5.88958i	0.760691	−	1.01006i
$35$		0			0
$36$	1.23887	+	2.99090i	0.206478	+	0.498483i
$37$	−5.32156	−	2.62430i	−0.874859	−	0.431433i	−0.0513132	−	0.998683i	$-0.516341\pi$
$37$	−5.32156	−	2.62430i	−0.874859	−	0.431433i	−0.823546	+	0.567250i	$0.808007\pi$
$38$	9.18660	−	2.46154i	1.49026	−	0.399315i
$39$	2.39153	−	2.72701i	0.382950	−	0.436671i
$40$	−3.83781	−	0.251544i	−0.606812	−	0.0397725i
$41$	−0.0510695	−	0.256744i	−0.00797571	−	0.0400966i	0.976593	−	0.215098i	$-0.0690070\pi$
$41$	−0.0510695	−	0.256744i	−0.00797571	−	0.0400966i	−0.984568	+	0.175001i	$0.944007\pi$
$42$		0			0
$43$	0.397620	−	0.959941i	0.0606365	−	0.146390i	−0.890657	−	0.454675i	$-0.849755\pi$
$43$	0.397620	−	0.959941i	0.0606365	−	0.146390i	0.951294	+	0.308286i	$0.0997553\pi$
$44$	−4.51524	+	3.95976i	−0.680699	+	0.596957i
$45$	−6.49877	+	3.20484i	−0.968779	+	0.477749i
$46$	−5.49946	−	4.82290i	−0.810851	−	0.711098i
$47$	−8.29355	−	2.22225i	−1.20974	−	0.324148i	−0.403079	−	0.915165i	$-0.632060\pi$
$47$	−8.29355	−	2.22225i	−1.20974	−	0.324148i	−0.806659	+	0.591017i	$0.798727\pi$
$48$	2.24834	−	1.50229i	0.324520	−	0.216837i
$49$		0			0
$50$			3.91066i			0.553050i
$51$	−2.24117	+	0.167174i	−0.313826	+	0.0234091i
$52$	−6.90231	−	3.98505i	−0.957178	−	0.552627i
$53$	1.81423	+	0.238848i	0.249203	+	0.0328083i	0.254093	−	0.967180i	$-0.418223\pi$
$53$	1.81423	+	0.238848i	0.249203	+	0.0328083i	−0.00488954	+	0.999988i	$0.501556\pi$
$54$	2.45854	−	4.98542i	0.334564	−	0.678429i
$55$	−9.50506	−	9.50506i	−1.28166	−	1.28166i
$56$		0			0
$57$	−2.41041	−	1.61059i	−0.319267	−	0.213327i
$58$	11.4888	+	13.1005i	1.50856	+	1.72018i
$59$	3.63474	+	4.73689i	0.473203	+	0.616691i	0.967582	−	0.252556i	$-0.0812712\pi$
$59$	3.63474	+	4.73689i	0.473203	+	0.616691i	−0.494379	+	0.869246i	$0.664604\pi$
$60$	−1.06544	−	1.38851i	−0.137548	−	0.179256i
$61$	0.999567	+	1.13979i	0.127981	+	0.145935i	0.812281	−	0.583266i	$-0.198225\pi$
$61$	0.999567	+	1.13979i	0.127981	+	0.145935i	−0.684300	+	0.729201i	$0.739892\pi$
$62$	−1.14235	−	0.763294i	−0.145079	−	0.0969384i
$63$		0			0
$64$	−0.573383	−	0.573383i	−0.0716728	−	0.0716728i
$65$	7.89012	−	15.9996i	0.978649	−	1.98450i
$66$	4.84555	+	0.637929i	0.596446	+	0.0785236i
$67$	10.7106	+	6.18377i	1.30851	+	0.755467i	0.981847	−	0.189674i	$-0.0607433\pi$
$67$	10.7106	+	6.18377i	1.30851	+	0.755467i	0.326661	+	0.945142i	$0.394077\pi$
$68$	1.32104	+	4.75837i	0.160199	+	0.577037i
$69$			2.22961i			0.268414i
$70$		0			0
$71$	−3.95416	+	2.64209i	−0.469273	+	0.313558i	−0.767627	−	0.640897i	$-0.778562\pi$
$71$	−3.95416	+	2.64209i	−0.469273	+	0.313558i	0.298354	+	0.954455i	$0.403562\pi$
$72$	3.74556	+	1.00362i	0.441419	+	0.118278i
$73$	0.852445	+	0.747574i	0.0997711	+	0.0874969i	0.707778	−	0.706435i	$-0.249698\pi$
$73$	0.852445	+	0.747574i	0.0997711	+	0.0874969i	−0.608007	+	0.793931i	$0.708031\pi$
$74$	9.51611	−	4.69283i	1.10623	−	0.545530i
$75$	0.896209	−	0.785954i	0.103485	−	0.0907542i
$76$	−2.43774	+	5.88522i	−0.279628	+	0.675081i
$77$		0			0
$78$	1.26537	+	6.36145i	0.143275	+	0.720292i
$79$	12.0747	+	0.791417i	1.35851	+	0.0890414i	0.727166	−	0.686462i	$-0.240837\pi$
$79$	12.0747	+	0.791417i	1.35851	+	0.0890414i	0.631343	+	0.775503i	$0.282504\pi$
$80$	8.76890	−	9.99901i	0.980393	−	1.11792i
$81$	6.19577	−	1.66015i	0.688418	−	0.184461i
$82$	0.419833	+	0.207039i	0.0463628	+	0.0228636i
$83$	5.11069	+	12.3383i	0.560971	+	1.35430i	0.908990	+	0.416817i	$0.136854\pi$
$83$	5.11069	+	12.3383i	0.560971	+	1.35430i	−0.348019	+	0.937488i	$0.613146\pi$
$84$		0			0
$85$	−10.4344	+	3.64710i	−1.13177	+	0.395583i
$86$	0.929008	+	1.60909i	0.100178	+	0.173513i
$87$	0.693258	−	5.26582i	0.0743250	−	0.564555i
$88$	0.470480	+	7.17814i	0.0501534	+	0.765193i
$89$	0.507083	−	1.89246i	0.0537506	−	0.200600i	−0.933829	−	0.357720i	$-0.883554\pi$
$89$	0.507083	−	1.89246i	0.0537506	−	0.200600i	0.987580	+	0.157120i	$0.0502209\pi$
$90$	2.52788	−	12.7085i	0.266462	−	1.33959i
$91$		0			0
$92$	4.80513	−	0.955800i	0.500969	−	0.0996490i
$93$	0.0546619	+	0.415198i	0.00566817	+	0.0430541i
$94$	12.1810	−	9.34683i	1.25638	−	0.964052i
$95$	−13.5014	−	4.58311i	−1.38522	−	0.470217i
$96$	−0.213964	+	3.26447i	−0.0218377	+	0.333178i
$97$	9.84825	+	1.95894i	0.999938	+	0.198900i	0.667808	−	0.744334i	$-0.267233\pi$
$97$	9.84825	+	1.95894i	0.999938	+	0.198900i	0.332130	+	0.943234i	$0.392233\pi$
$98$		0			0
$99$	7.52952	+	11.2687i	0.756745	+	1.13255i
$100$	−2.07803	−	1.59453i	−0.207803	−	0.159453i
$101$	2.60445	−	4.51103i	0.259152	−	0.448865i	−0.706863	−	0.707351i	$-0.749890\pi$
$101$	2.60445	−	4.51103i	0.259152	−	0.448865i	0.966015	+	0.258486i	$0.0832236\pi$
$102$	2.20256	−	3.36151i	0.218086	−	0.332839i
$103$	5.55189	−	3.20538i	0.547044	−	0.315836i	−0.200885	−	0.979615i	$-0.564382\pi$
$103$	5.55189	−	3.20538i	0.547044	−	0.315836i	0.747929	+	0.663779i	$0.231048\pi$
$104$	−8.81995	+	3.65334i	−0.864867	+	0.358240i
$105$		0			0
$106$	−2.31382	+	2.31382i	−0.224738	+	0.224738i
$107$	−1.74168	−	5.13082i	−0.168375	−	0.496016i	0.829688	−	0.558227i	$-0.188518\pi$
$107$	−1.74168	−	5.13082i	−0.168375	−	0.496016i	−0.998063	+	0.0622112i	$0.980185\pi$
$108$	1.64669	+	3.33917i	0.158453	+	0.321311i
$109$	−0.751286	+	2.21322i	−0.0719602	+	0.211988i	−0.976959	−	0.213425i	$-0.931538\pi$
$109$	−0.751286	+	2.21322i	−0.0719602	+	0.211988i	0.904999	+	0.425413i	$0.139871\pi$
$110$	23.8319	−	3.13753i	2.27228	−	0.299152i
$111$	−2.98798	−	1.23766i	−0.283607	−	0.117474i
$112$		0			0
$113$	10.3160	−	15.4390i	0.970451	−	1.45238i	0.0802713	−	0.996773i	$-0.474421\pi$
$113$	10.3160	−	15.4390i	0.970451	−	1.45238i	0.890180	−	0.455610i	$-0.150579\pi$
$114$	4.90890	−	1.66635i	0.459760	−	0.156068i
$115$	2.83819	+	10.5923i	0.264663	+	0.987734i
$116$	−11.6458	+	0.763304i	−1.08128	+	0.0708710i
$117$	−10.9492	+	14.2693i	−1.01226	+	1.31920i
$118$	−10.6769			−0.982893
$119$		0			0
$120$	−2.09638			−0.191372
$121$	−8.60904	+	11.2195i	−0.782640	+	1.01996i
$122$	−2.70513	+	0.177304i	−0.244911	+	0.0160523i
$123$	−0.0369298	−	0.137824i	−0.00332985	−	0.0124272i
$124$	0.871379	−	0.295793i	0.0782521	−	0.0265630i
$125$	−4.18982	+	6.27050i	−0.374748	+	0.560851i
$126$		0			0
$127$	1.38122	+	0.572121i	0.122564	+	0.0507675i	0.443122	−	0.896461i	$-0.353871\pi$
$127$	1.38122	+	0.572121i	0.122564	+	0.0507675i	−0.320559	+	0.947229i	$0.603871\pi$
$128$	−10.4635	+	1.37754i	−0.924848	+	0.121759i
$129$	0.182047	−	0.536293i	0.0160283	−	0.0472179i
$130$	14.1093	+	28.6107i	1.23746	+	2.50933i
$131$	1.15391	+	3.39931i	0.100818	+	0.296999i	0.985622	−	0.168963i	$-0.0540418\pi$
$131$	1.15391	+	3.39931i	0.100818	+	0.296999i	−0.884805	+	0.465962i	$0.845708\pi$
$132$	−2.31471	+	2.31471i	−0.201469	+	0.201469i
$133$		0			0
$134$	−20.4324	+	8.46337i	−1.76509	+	0.731124i
$135$	−7.21692	+	4.16669i	−0.621133	+	0.358611i
$136$	5.48508	+	2.21434i	0.470342	+	0.189878i
$137$	−2.44057	+	4.22720i	−0.208512	+	0.361154i	−0.951246	−	0.308433i	$-0.900195\pi$
$137$	−2.44057	+	4.22720i	−0.208512	+	0.361154i	0.742734	+	0.669587i	$0.233529\pi$
$138$	−3.16312	−	2.42715i	−0.269263	−	0.206613i
$139$	2.96540	+	4.43803i	0.251522	+	0.376429i	0.935648	−	0.352935i	$-0.114816\pi$
$139$	2.96540	+	4.43803i	0.251522	+	0.376429i	−0.684126	+	0.729364i	$0.739816\pi$
$140$		0			0
$141$	−4.59013	−	0.913034i	−0.386559	−	0.0768914i
$142$	0.556195	−	8.48590i	0.0466749	−	0.712121i
$143$	−31.5954	−	10.7252i	−2.64214	−	0.896886i
$144$	−10.6379	+	8.16276i	−0.886493	+	0.680230i
$145$	−3.40966	−	25.8989i	−0.283157	−	2.15079i
$146$	−1.98854	+	0.395546i	−0.164573	+	0.0327356i
$147$		0			0
$148$	−1.38644	+	6.97010i	−0.113965	+	0.572939i
$149$	1.94392	−	7.25482i	0.159252	−	0.594338i	−0.839451	−	0.543435i	$-0.817123\pi$
$149$	1.94392	−	7.25482i	0.159252	−	0.594338i	0.998704	−	0.0509031i	$-0.0162100\pi$
$150$	0.139413	+	2.12703i	0.0113830	+	0.173671i
$151$	0.750711	−	5.70222i	0.0610920	−	0.464040i	−0.933368	−	0.358922i	$-0.883145\pi$
$151$	0.750711	−	5.70222i	0.0610920	−	0.464040i	0.994460	−	0.105118i	$-0.0335221\pi$
$152$	3.81509	+	6.60793i	0.309444	+	0.535974i
$153$	11.0354	−	1.55406i	0.892162	−	0.125638i
$154$		0			0
$155$	0.788211	+	1.90291i	0.0633107	+	0.152845i
$156$	−3.89627	−	1.92143i	−0.311952	−	0.153837i
$157$	−6.69003	+	1.79259i	−0.533923	+	0.143064i	−0.515699	−	0.856770i	$-0.672468\pi$
$157$	−6.69003	+	1.79259i	−0.533923	+	0.143064i	−0.0182236	+	0.999834i	$0.505801\pi$
$158$	−14.2673	+	16.2687i	−1.13504	+	1.29427i
$159$	0.995285	+	0.0652344i	0.0789312	+	0.00517343i
$160$	3.13903	+	15.7809i	0.248162	+	1.24759i
$161$		0			0
$162$	−4.38946	+	10.5971i	−0.344869	+	0.832587i
$163$	9.48461	−	8.31778i	0.742892	−	0.651499i	−0.201811	−	0.979424i	$-0.564683\pi$
$163$	9.48461	−	8.31778i	0.742892	−	0.651499i	0.944704	+	0.327925i	$0.106349\pi$
$164$	−0.281199	+	0.138672i	−0.0219579	+	0.0108285i
$165$	−5.50871	−	4.83101i	−0.428853	−	0.376094i
$166$	−23.0677	−	6.18097i	−1.79040	−	0.479737i
$167$	11.1181	−	7.42888i	0.860345	−	0.574864i	−0.0452651	−	0.998975i	$-0.514413\pi$
$167$	11.1181	−	7.42888i	0.860345	−	0.574864i	0.905610	+	0.424111i	$0.139413\pi$
$168$		0			0
$169$		−	31.2806i		−	2.40620i
$170$	6.18473	−	18.7733i	0.474347	−	1.43985i
$171$	12.4495	+	7.18770i	0.952034	+	0.549657i
$172$	−1.23383	−	0.162437i	−0.0940785	−	0.0123857i
$173$	−1.56835	+	3.18030i	−0.119239	+	0.241794i	−0.948307	−	0.317355i	$-0.897205\pi$
$173$	−1.56835	+	3.18030i	−0.119239	+	0.241794i	0.829067	+	0.559149i	$0.188872\pi$
$174$	6.71588	+	6.71588i	0.509129	+	0.509129i
$175$		0			0
$176$	−20.6827	−	13.8197i	−1.55901	−	1.04170i
$177$	2.14583	+	2.44685i	0.161290	+	0.183916i
$178$	2.13280	+	2.77952i	0.159860	+	0.208334i
$179$	−5.21888	−	6.80137i	−0.390077	−	0.508358i	0.556495	−	0.830851i	$-0.312146\pi$
$179$	−5.21888	−	6.80137i	−0.390077	−	0.508358i	−0.946572	+	0.322493i	$0.895479\pi$
$180$	5.72229	+	6.52503i	0.426515	+	0.486347i
$181$	−4.23355	−	2.82877i	−0.314677	−	0.210261i	0.388194	−	0.921578i	$-0.373099\pi$
$181$	−4.23355	−	2.82877i	−0.314677	−	0.210261i	−0.702871	+	0.711317i	$0.748099\pi$
$182$		0			0
$183$	0.584303	+	0.584303i	0.0431930	+	0.0431930i
$184$	2.59552	−	5.26319i	0.191344	−	0.388008i
$185$	−15.7706	−	2.07624i	−1.15948	−	0.152648i
$186$	−0.648542	−	0.374436i	−0.0475534	−	0.0274550i
$187$	9.31045	+	18.4588i	0.680847	+	1.34984i
$188$			10.2838i			0.750023i
$189$		0			0
$190$	21.1996	−	14.1651i	1.53798	−	1.02765i
$191$	−23.8250	−	6.38390i	−1.72392	−	0.461923i	−0.745151	−	0.666896i	$-0.767623\pi$
$191$	−23.8250	−	6.38390i	−1.72392	−	0.461923i	−0.978768	+	0.204973i	$0.934289\pi$
$192$	−0.332307	−	0.291426i	−0.0239822	−	0.0210318i
$193$	18.3146	−	9.03176i	1.31831	−	0.650121i	0.359232	−	0.933248i	$-0.383039\pi$
$193$	18.3146	−	9.03176i	1.31831	−	0.650121i	0.959082	+	0.283128i	$0.0913720\pi$
$194$	−13.4999	+	11.8391i	−0.969237	+	0.849998i
$195$	3.72111	−	8.98355i	0.266474	−	0.643325i
$196$		0			0
$197$	1.66733	+	8.38222i	0.118792	+	0.597208i	0.993621	+	0.112775i	$0.0359740\pi$
$197$	1.66733	+	8.38222i	0.118792	+	0.597208i	−0.874828	+	0.484433i	$0.839026\pi$
$198$	−24.1834	−	1.58507i	−1.71864	−	0.112646i
$199$	−10.7161	+	12.2193i	−0.759641	+	0.866205i	−0.994382	−	0.105853i	$-0.966243\pi$
$199$	−10.7161	+	12.2193i	−0.759641	+	0.866205i	0.234741	+	0.972058i	$0.424576\pi$
$200$	−3.03052	+	0.812025i	−0.214290	+	0.0574188i
$201$	6.04601	+	2.98156i	0.426452	+	0.210303i
$202$	3.56456	+	8.60560i	0.250801	+	0.605488i
$203$		0			0
$204$	0.888154	+	2.54101i	0.0621832	+	0.177907i
$205$	−0.350886	−	0.607753i	−0.0245070	−	0.0424473i
$206$	−1.49633	+	11.3658i	−0.104254	+	0.791891i
$207$	−0.723106	−	11.0325i	−0.0502594	−	0.766810i
$208$	8.54405	−	31.8868i	0.592424	−	2.21095i
$209$	−5.20266	+	26.1555i	−0.359875	+	1.80922i
$210$		0			0
$211$	−9.74454	+	1.93831i	−0.670842	+	0.133439i	−0.518748	−	0.854927i	$-0.673602\pi$
$211$	−9.74454	+	1.93831i	−0.670842	+	0.133439i	−0.152094	+	0.988366i	$0.548602\pi$
$212$	−0.286074	−	2.17295i	−0.0196476	−	0.149239i
$213$	−2.05650	+	1.57801i	−0.140909	+	0.108124i
$214$	9.17503	+	3.11450i	0.627192	+	0.212903i
$215$	0.182179	−	2.77951i	0.0124245	−	0.189561i
$216$	4.37389	+	0.870022i	0.297606	+	0.0591975i
$217$		0			0
$218$	−2.32202	−	3.47515i	−0.157267	−	0.235367i
$219$	0.490301	+	0.376221i	0.0331314	+	0.0254227i
$220$	−8.05002	+	13.9430i	−0.542732	+	0.940039i
$221$	−19.2252	+	19.5746i	−1.29322	+	1.31673i
$222$	5.00857	−	2.89170i	0.336153	−	0.194078i
$223$	1.88077	−	0.779040i	0.125946	−	0.0521684i	−0.318821	−	0.947815i	$-0.603287\pi$
$223$	1.88077	−	0.779040i	0.125946	−	0.0521684i	0.444766	+	0.895647i	$0.353287\pi$
$224$		0			0
$225$	−4.17968	+	4.17968i	−0.278645	+	0.278645i
$226$	10.6732	+	31.4422i	0.709969	+	2.09150i
$227$	−0.631956	−	1.28148i	−0.0419444	−	0.0850548i	0.874892	−	0.484319i	$-0.160932\pi$
$227$	−0.631956	−	1.28148i	−0.0419444	−	0.0850548i	−0.916836	+	0.399264i	$0.869266\pi$
$228$	−1.11610	+	3.28791i	−0.0739152	+	0.217747i
$229$	8.95970	−	1.17957i	0.592073	−	0.0779479i	0.171465	−	0.985190i	$-0.445150\pi$
$229$	8.95970	−	1.17957i	0.592073	−	0.0779479i	0.420608	+	0.907242i	$0.361817\pi$
$230$	−18.1168	−	7.50422i	−1.19459	−	0.494813i
$231$		0			0
$232$	−7.76650	+	11.6234i	−0.509896	+	0.763113i
$233$	1.72102	−	0.584207i	0.112748	−	0.0382727i	−0.264495	−	0.964387i	$-0.585205\pi$
$233$	1.72102	−	0.584207i	0.112748	−	0.0382727i	0.377243	+	0.926114i	$0.376872\pi$
$234$	−8.32440	−	31.0671i	−0.544183	−	2.03092i
$235$	−22.9687	+	1.50545i	−1.49831	+	0.0982046i
$236$	4.35342	−	5.67349i	0.283384	−	0.369313i
$237$	6.59571			0.428438
$238$		0			0
$239$	−4.77316			−0.308750			−0.154375	−	0.988012i	$-0.549336\pi$
$239$	−4.77316			−0.308750			−0.154375	+	0.988012i	$0.549336\pi$
$240$	4.41300	−	5.75113i	0.284858	−	0.371234i
$241$	14.4316	−	0.945895i	0.929619	−	0.0609304i	0.406935	−	0.913457i	$-0.366598\pi$
$241$	14.4316	−	0.945895i	0.929619	−	0.0609304i	0.522684	+	0.852527i	$0.324931\pi$
$242$	−6.54522	−	24.4271i	−0.420743	−	1.57023i
$243$	12.1413	−	4.12142i	0.778866	−	0.264389i
$244$	1.00878	−	1.50974i	0.0645802	−	0.0966512i
$245$		0			0
$246$	0.235731	+	0.0976429i	0.0150296	+	0.00622548i
$247$	−35.0886	+	4.61950i	−2.23263	+	0.293932i
$248$	0.354303	−	1.04374i	0.0224983	−	0.0662778i
$249$	3.21959	+	6.52869i	0.204033	+	0.413739i
$250$	−4.33487	−	12.7701i	−0.274161	−	0.807652i
$251$	−22.0951	+	22.0951i	−1.39463	+	1.39463i	−0.580038	+	0.814589i	$0.696963\pi$
$251$	−22.0951	+	22.0951i	−1.39463	+	1.39463i	−0.814589	+	0.580038i	$0.803037\pi$
$252$		0			0
$253$	18.9491	−	7.84898i	1.19132	−	0.493461i
$254$	−2.31526	+	1.33671i	−0.145272	+	0.0838730i
$255$	−5.54530	+	2.35566i	−0.347260	+	0.147517i
$256$	10.2471	−	17.7485i	0.640443	−	1.10928i
$257$	−17.7380	−	13.6109i	−1.10647	−	0.849023i	−0.116908	−	0.993143i	$-0.537298\pi$
$257$	−17.7380	−	13.6109i	−1.10647	−	0.849023i	−0.989560	+	0.144120i	$0.953965\pi$
$258$	0.562657	+	0.842075i	0.0350295	+	0.0524253i
$259$		0			0
$260$	−20.9560	−	4.16841i	−1.29964	−	0.258514i
$261$	−1.72254	+	26.2809i	−0.106623	+	1.62675i
$262$	−6.07870	−	2.06344i	−0.375543	−	0.127480i
$263$	5.58330	−	4.28422i	0.344281	−	0.264176i	−0.422118	−	0.906541i	$-0.638713\pi$
$263$	5.58330	−	4.28422i	0.344281	−	0.264176i	0.766399	+	0.642365i	$0.222047\pi$
$264$	0.511794	+	3.88746i	0.0314988	+	0.239257i
$265$	4.81136	−	0.957040i	0.295560	−	0.0587905i
$266$		0			0
$267$	0.208340	−	1.04740i	0.0127502	−	0.0640996i
$268$	3.83386	−	14.3082i	0.234190	−	0.874010i
$269$	0.274950	+	4.19493i	0.0167640	+	0.255769i	0.998012	+	0.0630208i	$0.0200734\pi$
$269$	0.274950	+	4.19493i	0.0167640	+	0.255769i	−0.981248	+	0.192748i	$0.938260\pi$
$270$	1.94509	−	14.7744i	0.118374	−	0.899142i
$271$	2.14798	+	3.72042i	0.130481	+	0.225999i	0.923862	−	0.382726i	$-0.125015\pi$
$271$	2.14798	+	3.72042i	0.130481	+	0.225999i	−0.793381	+	0.608725i	$0.791681\pi$
$272$	−17.6212	+	10.3863i	−1.06844	+	0.629759i
$273$		0			0
$274$	−3.34027	−	8.06414i	−0.201793	−	0.487172i
$275$	−9.83465	−	4.84991i	−0.593052	−	0.292461i
$276$	2.57947	−	0.691166i	0.155266	−	0.0416033i
$277$	8.23070	−	9.38532i	0.494535	−	0.563909i	−0.449701	−	0.893179i	$-0.648469\pi$
$277$	8.23070	−	9.38532i	0.494535	−	0.563909i	0.944236	+	0.329270i	$0.106803\pi$
$278$	−9.52432	−	0.624257i	−0.571231	−	0.0374404i
$279$	−0.405133	−	2.03674i	−0.0242546	−	0.121936i
$280$		0			0
$281$	−2.91965	+	7.04865i	−0.174172	+	0.420487i	−0.986725	−	0.162399i	$-0.948077\pi$
$281$	−2.91965	+	7.04865i	−0.174172	+	0.420487i	0.812554	+	0.582887i	$0.198077\pi$
$282$	6.29212	−	5.51804i	0.374691	−	0.328595i
$283$	−6.42883	+	3.17035i	−0.382154	+	0.188458i	−0.623212	−	0.782053i	$-0.714173\pi$
$283$	−6.42883	+	3.17035i	−0.382154	+	0.188458i	0.241057	+	0.970511i	$0.422506\pi$
$284$	4.28243	+	3.75559i	0.254116	+	0.222853i
$285$	−7.50689	−	2.01146i	−0.444670	−	0.119149i
$286$	49.6104	−	33.1486i	2.93352	−	1.96012i
$287$		0			0
$288$		−	16.2225i		−	0.955919i
$289$	16.9972	−	0.306142i	0.999838	−	0.0180084i
$290$	40.4543	+	23.3563i	2.37556	+	1.37153i
$291$	5.42636	+	0.714394i	0.318099	+	0.0418785i
$292$	0.600625	−	1.21795i	0.0351489	−	0.0712750i
$293$	−4.15110	−	4.15110i	−0.242510	−	0.242510i	0.575378	−	0.817888i	$-0.304855\pi$
$293$	−4.15110	−	4.15110i	−0.242510	−	0.242510i	−0.817888	+	0.575378i	$0.804855\pi$
$294$		0			0
$295$	13.3090	+	8.89276i	0.774877	+	0.517756i
$296$	5.61262	+	6.39996i	0.326227	+	0.371990i
$297$	9.48847	+	12.3656i	0.550577	+	0.717526i
$298$	8.17618	+	10.6554i	0.473634	+	0.617251i
$299$	17.9471	+	20.4648i	1.03791	+	1.18351i
$300$	−1.18710	−	0.793195i	−0.0685372	−	0.0457951i
$301$		0			0
$302$	7.27245	+	7.27245i	0.418482	+	0.418482i
$303$	1.25576	−	2.54643i	0.0721414	−	0.146288i
$304$	−26.1589	−	3.44389i	−1.50032	−	0.197521i
$305$	3.51965	+	2.03207i	0.201535	+	0.116356i
$306$	−9.80843	+	17.3476i	−0.560711	+	0.991696i
$307$			24.0844i			1.37457i	0.726387	+	0.687286i	$0.241198\pi$
$307$			24.0844i			1.37457i	−0.726387	+	0.687286i	$0.758802\pi$
$308$		0			0
$309$	2.90544	−	1.94135i	0.165284	−	0.110440i
$310$	−3.55768	−	0.953278i	−0.202063	−	0.0541426i
$311$	−2.43224	−	2.13301i	−0.137920	−	0.120952i	0.587607	−	0.809147i	$-0.300070\pi$
$311$	−2.43224	−	2.13301i	−0.137920	−	0.120952i	−0.725526	+	0.688195i	$0.758404\pi$
$312$	−4.66699	+	2.30150i	−0.264216	+	0.130297i
$313$	4.98316	−	4.37011i	0.281665	−	0.247013i	−0.506843	−	0.862039i	$-0.669187\pi$
$313$	4.98316	−	4.37011i	0.281665	−	0.247013i	0.788507	+	0.615025i	$0.210854\pi$
$314$	4.73963	−	11.4425i	0.267473	−	0.645737i
$315$		0			0
$316$	−2.82748	−	14.2147i	−0.159058	−	0.799639i
$317$	−11.3232	−	0.742161i	−0.635974	−	0.0416839i	−0.255993	−	0.966679i	$-0.582403\pi$
$317$	−11.3232	−	0.742161i	−0.635974	−	0.0416839i	−0.379980	+	0.924995i	$0.624069\pi$
$318$	−1.17601	+	1.34099i	−0.0659475	+	0.0751987i
$319$	−47.1938	+	12.6455i	−2.64235	+	0.708015i
$320$	−1.94967	−	0.961471i	−0.108990	−	0.0537479i
$321$	−1.13022	−	2.72860i	−0.0630828	−	0.152295i
$322$		0			0
$323$	17.5168	+	13.1922i	0.974660	+	0.734034i
$324$	−3.84130	−	6.65332i	−0.213405	−	0.369629i
$325$	1.89947	−	14.4279i	0.105364	−	0.800318i
$326$	1.47541	+	22.5104i	0.0817155	+	1.24674i
$327$	−0.329729	+	1.23057i	−0.0182341	+	0.0680505i
$328$	−0.0732665	+	0.368335i	−0.00404546	+	0.0203379i
$329$		0			0
$330$	12.8505	−	2.55612i	0.707395	−	0.140710i
$331$	−3.20682	−	24.3582i	−0.176263	−	1.33885i	−0.819455	−	0.573144i	$-0.805724\pi$
$331$	−3.20682	−	24.3582i	−0.176263	−	1.33885i	0.643192	−	0.765705i	$-0.277610\pi$
$332$	12.6901	−	9.73743i	0.696458	−	0.534411i
$333$	15.1864	+	5.15509i	0.832210	+	0.282497i
$334$	−1.56388	+	23.8602i	−0.0855718	+	1.30557i
$335$	32.5183	+	6.46829i	1.77666	+	0.353401i
$336$		0			0
$337$	2.83989	+	4.25020i	0.154699	+	0.231523i	0.900721	−	0.434398i	$-0.143039\pi$
$337$	2.83989	+	4.25020i	0.154699	+	0.231523i	−0.746022	+	0.665921i	$0.768039\pi$
$338$	44.3775	+	34.0520i	2.41382	+	1.85219i
$339$	5.06056	−	8.76515i	0.274852	−	0.476058i
$340$	7.45397	+	10.9411i	0.404248	+	0.593363i
$341$	3.33627	−	1.92620i	0.180669	−	0.104310i
$342$	−23.7496	+	9.83739i	−1.28423	+	0.531945i
$343$		0			0
$344$	−1.05404	+	1.05404i	−0.0568302	+	0.0568302i
$345$	1.92132	+	5.66002i	0.103440	+	0.304725i
$346$	−2.80455	−	5.68707i	−0.150774	−	0.305739i
$347$	6.75895	−	19.9112i	0.362839	−	1.06889i	−0.600274	−	0.799794i	$-0.704942\pi$
$347$	6.75895	−	19.9112i	0.362839	−	1.06889i	0.963113	−	0.269096i	$-0.0867249\pi$
$348$	−6.30700	+	0.830332i	−0.338091	+	0.0445105i
$349$	−26.1712	−	10.8405i	−1.40091	−	0.580276i	−0.450923	−	0.892563i	$-0.648905\pi$
$349$	−26.1712	−	10.8405i	−1.40091	−	0.580276i	−0.949988	+	0.312287i	$0.898905\pi$
$350$		0			0
$351$	−11.4920	+	17.1990i	−0.613398	+	0.918015i
$352$	28.4974	−	9.67356i	1.51892	−	0.515603i
$353$	−1.48164	−	5.52956i	−0.0788598	−	0.294309i	0.915221	−	0.402952i	$-0.132016\pi$
$353$	−1.48164	−	5.52956i	−0.0788598	−	0.294309i	−0.994081	+	0.108644i	$0.965349\pi$
$354$	−5.80726	+	0.380628i	−0.308652	+	0.0202301i
$355$	−7.76115	+	10.1145i	−0.411919	+	0.536823i
$356$	−2.34660			−0.124370
$357$		0			0
$358$	15.3303			0.810231
$359$	−13.4900	+	17.5806i	−0.711977	+	0.927866i	−0.999553	−	0.0298914i	$-0.990484\pi$
$359$	−13.4900	+	17.5806i	−0.711977	+	0.927866i	0.287576	+	0.957758i	$0.407151\pi$
$360$	10.3732	−	0.679896i	0.546716	−	0.0358337i
$361$	2.40355	+	8.97018i	0.126503	+	0.472115i
$362$	8.62178	−	2.92670i	0.453151	−	0.153824i
$363$	−4.28254	+	6.40927i	−0.224775	+	0.336400i
$364$		0			0
$365$	2.80819	+	1.16319i	0.146988	+	0.0608843i
$366$	−1.46502	+	0.192873i	−0.0765776	+	0.0100816i
$367$	8.89760	−	26.2115i	0.464451	−	1.36823i	−0.422499	−	0.906363i	$-0.638847\pi$
$367$	8.89760	−	26.2115i	0.464451	−	1.36823i	0.886950	−	0.461865i	$-0.152820\pi$
$368$	8.97514	+	18.1998i	0.467861	+	0.948729i
$369$	0.227433	+	0.669997i	0.0118397	+	0.0348786i
$370$	20.1134	−	20.1134i	1.04564	−	1.04564i
$371$		0			0
$372$	0.463403	−	0.191948i	0.0240264	−	0.00995204i
$373$	22.6098	−	13.0538i	1.17069	−	0.675899i	0.216849	−	0.976205i	$-0.430422\pi$
$373$	22.6098	−	13.0538i	1.17069	−	0.675899i	0.953843	+	0.300306i	$0.0970889\pi$
$374$	−36.3227	−	6.88561i	−1.87820	−	0.356046i
$375$	−2.05533	+	3.55993i	−0.106137	+	0.183834i
$376$	9.77254	+	7.49873i	0.503980	+	0.386718i
$377$	−36.0237	−	53.9132i	−1.85531	−	2.77667i
$378$		0			0
$379$	6.55946	+	1.30476i	0.336937	+	0.0670209i	0.360659	−	0.932698i	$-0.382552\pi$
$379$	6.55946	+	1.30476i	0.336937	+	0.0670209i	−0.0237224	+	0.999719i	$0.507552\pi$
$380$	−1.11691	+	17.0407i	−0.0572961	+	0.874169i
$381$	0.771651	+	0.261940i	0.0395329	+	0.0134196i
$382$	34.9927	−	26.8508i	1.79038	−	1.37381i
$383$	−1.90614	−	14.4786i	−0.0973992	−	0.739820i	−0.968553	−	0.248809i	$-0.919961\pi$
$383$	−1.90614	−	14.4786i	−0.0973992	−	0.739820i	0.871153	−	0.491011i	$-0.163373\pi$
$384$	−5.64203	+	1.12227i	−0.287919	+	0.0572706i
$385$		0			0
$386$	−7.12399	+	35.8147i	−0.362601	+	1.82292i
$387$	−0.726866	+	2.71270i	−0.0369487	+	0.137894i
$388$	−0.786576	−	12.0008i	−0.0399323	−	0.609250i
$389$	1.64849	−	12.5215i	0.0835817	−	0.634866i	−0.897464	−	0.441088i	$-0.854593\pi$
$389$	1.64849	−	12.5215i	0.0835817	−	0.634866i	0.981045	−	0.193778i	$-0.0620741\pi$
$390$	8.69407	+	15.0586i	0.440241	+	0.762520i
$391$	0.951470	−	16.8386i	0.0481179	−	0.851566i
$392$		0			0
$393$	0.748802	+	1.80777i	0.0377721	+	0.0911898i
$394$	−13.7068	−	6.75945i	−0.690539	−	0.340536i
$395$	31.3344	−	8.39603i	1.57661	−	0.422450i
$396$	10.7028	−	12.2042i	0.537837	−	0.613286i
$397$	3.82001	+	0.250377i	0.191721	+	0.0125660i	0.160961	−	0.986961i	$-0.448541\pi$
$397$	3.82001	+	0.250377i	0.191721	+	0.0125660i	0.0307598	+	0.999527i	$0.490207\pi$
$398$	−5.66993	−	28.5047i	−0.284208	−	1.42881i
$399$		0			0
$400$	4.15174	−	10.0232i	0.207587	−	0.501159i
$401$	8.93141	−	7.83264i	0.446014	−	0.391143i	−0.406667	−	0.913577i	$-0.633309\pi$
$401$	8.93141	−	7.83264i	0.446014	−	0.391143i	0.852680	+	0.522433i	$0.174976\pi$
$402$	−10.8116	+	5.33168i	−0.539233	+	0.265920i
$403$	3.84383	+	3.37095i	0.191475	+	0.167919i
$404$	−6.02623	−	1.61472i	−0.299816	−	0.0803356i
$405$	14.2978	−	9.55347i	0.710462	−	0.474716i
$406$		0			0
$407$			29.7514i			1.47472i
$408$	3.06231	+	1.00885i	0.151607	+	0.0499457i
$409$	−2.12696	−	1.22800i	−0.105171	−	0.0607207i	0.446492	−	0.894788i	$-0.352673\pi$
$409$	−2.12696	−	1.22800i	−0.105171	−	0.0607207i	−0.551663	+	0.834067i	$0.686007\pi$
$410$	1.24419	+	0.163800i	0.0614460	+	0.00808952i
$411$	−1.17675	+	2.38620i	−0.0580446	+	0.117703i
$412$	−5.42940	−	5.42940i	−0.267487	−	0.267487i
$413$		0			0
$414$	16.4388	+	10.9841i	0.807924	+	0.539837i
$415$	23.6061	+	26.9176i	1.15878	+	1.32133i
$416$	24.3132	+	31.6856i	1.19205	+	1.55351i
$417$	1.77111	+	2.30816i	0.0867318	+	0.113031i
$418$	−31.4429	−	35.8538i	−1.53792	−	1.75367i
$419$	−28.3283	−	18.9283i	−1.38393	−	0.924710i	−0.999999	−	0.00134678i	$-0.999571\pi$
$419$	−28.3283	−	18.9283i	−1.38393	−	0.924710i	−0.383927	−	0.923363i	$-0.625429\pi$
$420$		0			0
$421$	−0.501993	−	0.501993i	−0.0244656	−	0.0244656i	0.694768	−	0.719234i	$-0.255507\pi$
$421$	−0.501993	−	0.501993i	−0.0244656	−	0.0244656i	−0.719234	+	0.694768i	$0.755507\pi$
$422$	7.85803	−	15.9345i	0.382523	−	0.775680i
$423$	23.0088	+	3.02917i	1.11873	+	0.147283i
$424$	−2.27352	−	1.31262i	−0.110412	−	0.0637462i
$425$	−7.10381	+	5.55329i	−0.344585	+	0.269374i
$426$		−	4.63536i		−	0.224584i
$427$		0			0
$428$	−5.39601	+	3.60550i	−0.260826	+	0.174278i
$429$	−17.5673	−	4.70714i	−0.848156	−	0.227263i
$430$	3.74495	+	3.28423i	0.180597	+	0.158380i
$431$	10.0870	−	4.97433i	0.485871	−	0.239605i	−0.182819	−	0.983147i	$-0.558522\pi$
$431$	10.0870	−	4.97433i	0.485871	−	0.239605i	0.668690	+	0.743541i	$0.266855\pi$
$432$	−11.5941	+	10.1677i	−0.557821	+	0.489196i
$433$	−2.47687	+	5.97968i	−0.119031	+	0.287365i	−0.972154	−	0.234345i	$-0.924706\pi$
$433$	−2.47687	+	5.97968i	−0.119031	+	0.287365i	0.853123	+	0.521710i	$0.174706\pi$
$434$		0			0
$435$	−2.77782	−	13.9650i	−0.133186	−	0.669572i
$436$	2.79340	+	0.183089i	0.133779	+	0.00876836i
$437$	14.3443	−	16.3565i	0.686179	−	0.782437i
$438$	−1.06748	+	0.286031i	−0.0510062	+	0.0136671i
$439$	−19.3112	−	9.52324i	−0.921675	−	0.454520i	−0.0814006	−	0.996681i	$-0.525939\pi$
$439$	−19.3112	−	9.52324i	−0.921675	−	0.454520i	−0.840274	+	0.542162i	$0.817606\pi$
$440$	7.37995	+	17.8168i	0.351825	+	0.849382i
$441$		0			0
$442$	−6.84172	−	48.5834i	−0.325427	−	2.31088i
$443$	16.1621	+	27.9936i	0.767886	+	1.33002i	0.938707	+	0.344715i	$0.112024\pi$
$443$	16.1621	+	27.9936i	0.767886	+	1.33002i	−0.170822	+	0.985302i	$0.554642\pi$
$444$	−0.505612	+	3.84051i	−0.0239953	+	0.182262i
$445$	−0.343520	−	5.24110i	−0.0162844	−	0.248452i
$446$	−0.942186	+	3.51629i	−0.0446138	+	0.166501i
$447$	0.798681	−	4.01524i	0.0377763	−	0.189914i
$448$		0			0
$449$	−21.1303	+	4.20309i	−0.997203	+	0.198356i	−0.666601	−	0.745415i	$-0.732252\pi$
$449$	−21.1303	+	4.20309i	−0.997203	+	0.198356i	−0.330601	+	0.943770i	$0.607252\pi$
$450$	−1.37967	−	10.4797i	−0.0650385	−	0.494016i
$451$	−1.04134	+	0.799046i	−0.0490346	+	0.0376256i
$452$	−21.0595	−	7.14875i	−0.990557	−	0.336249i
$453$	0.205035	−	3.12823i	0.00963340	−	0.146977i
$454$	2.50597	+	0.498468i	0.117611	+	0.0233943i
$455$		0			0
$456$	2.31062	+	3.45809i	0.108205	+	0.161940i
$457$	−3.35760	−	2.57638i	−0.157062	−	0.120518i	0.527241	−	0.849716i	$-0.323227\pi$
$457$	−3.35760	−	2.57638i	−0.157062	−	0.120518i	−0.684303	+	0.729198i	$0.739893\pi$
$458$	−8.08007	+	13.9951i	−0.377557	+	0.653948i
$459$	12.5474	−	2.61349i	0.585661	−	0.121987i
$460$	11.3745	−	6.56708i	0.530339	−	0.306192i
$461$	33.5138	−	13.8819i	1.56089	−	0.646544i	0.575650	−	0.817696i	$-0.304749\pi$
$461$	33.5138	−	13.8819i	1.56089	−	0.646544i	0.985245	+	0.171152i	$0.0547490\pi$
$462$		0			0
$463$	9.81782	−	9.81782i	0.456273	−	0.456273i	−0.441157	−	0.897430i	$-0.645432\pi$
$463$	9.81782	−	9.81782i	0.456273	−	0.456273i	0.897430	+	0.441157i	$0.145432\pi$
$464$	−15.5383	−	45.7742i	−0.721346	−	2.12502i
$465$	0.496551	+	1.00691i	0.0230270	+	0.0466941i
$466$	−1.04469	+	3.07756i	−0.0483943	+	0.142565i
$467$	35.1543	−	4.62815i	1.62675	−	0.214165i	0.738739	−	0.673991i	$-0.235422\pi$
$467$	35.1543	−	4.62815i	1.62675	−	0.214165i	0.888009	+	0.459826i	$0.152088\pi$
$468$	19.9025	+	8.24390i	0.919995	+	0.381074i
$469$		0			0
$470$	22.8679	−	34.2243i	1.05482	−	1.57865i
$471$	−3.57484	+	1.21350i	−0.164720	+	0.0559150i
$472$	−2.21701	−	8.27398i	−0.102046	−	0.380841i
$473$	−5.19873	+	0.340743i	−0.239038	+	0.0156674i
$474$	−7.18008	+	9.35726i	−0.329792	+	0.429793i
$475$	−11.6311			−0.533670
$476$		0			0
$477$	−4.94598			−0.226461
$478$	5.19605	−	6.77162i	0.237662	−	0.309727i
$479$	11.5459	−	0.756757i	0.527545	−	0.0345771i	0.200696	−	0.979654i	$-0.435680\pi$
$479$	11.5459	−	0.756757i	0.527545	−	0.0345771i	0.326849	+	0.945077i	$0.394013\pi$
$480$	2.26992	+	8.47145i	0.103607	+	0.386667i
$481$	−37.3881	+	12.6915i	−1.70475	+	0.578684i
$482$	−14.3682	+	21.5036i	−0.654456	+	0.979462i
$483$		0			0
$484$	15.6488	+	6.48193i	0.711307	+	0.294633i
$485$	26.6885	−	3.51361i	1.21186	−	0.159545i
$486$	−7.37000	+	21.7113i	−0.334310	+	0.984846i
$487$	11.9424	+	24.2167i	0.541160	+	1.09736i	0.980037	+	0.198817i	$0.0637099\pi$
$487$	11.9424	+	24.2167i	0.541160	+	1.09736i	−0.438876	+	0.898547i	$0.644623\pi$
$488$	−0.699104	−	2.05949i	−0.0316470	−	0.0932289i
$489$	4.86221	−	4.86221i	0.219877	−	0.219877i
$490$		0			0
$491$	−5.96262	+	2.46980i	−0.269089	+	0.111460i	−0.513148	−	0.858300i	$-0.671521\pi$
$491$	−5.96262	+	2.46980i	−0.269089	+	0.111460i	0.244059	+	0.969760i	$0.421521\pi$
$492$	−0.148002	+	0.0854491i	−0.00667245	+	0.00385234i
$493$	−7.48282	+	39.4730i	−0.337009	+	1.77778i
$494$	31.6437	−	54.8086i	1.42372	−	2.46595i
$495$	28.8248	+	22.1180i	1.29558	+	0.994131i
$496$	2.11754	+	3.16913i	0.0950804	+	0.142298i
$497$		0			0
$498$	−12.7670	−	2.53952i	−0.572104	−	0.113798i
$499$	−2.12358	+	32.3996i	−0.0950647	+	1.45041i	0.637889	+	0.770128i	$0.279808\pi$
$499$	−2.12358	+	32.3996i	−0.0950647	+	1.45041i	−0.732954	+	0.680278i	$0.761859\pi$
$500$	8.55324	+	2.90343i	0.382513	+	0.129846i
$501$	5.78237	−	4.43697i	0.258337	−	0.198229i
$502$	−7.29337	−	55.3987i	−0.325519	−	2.47256i
$503$	27.8736	−	5.54441i	1.24282	−	0.247213i	0.470476	−	0.882413i	$-0.344082\pi$
$503$	27.8736	−	5.54441i	1.24282	−	0.247213i	0.772348	+	0.635200i	$0.219082\pi$
$504$		0			0
$505$	2.72428	−	13.6959i	0.121229	−	0.609459i
$506$	−9.49271	+	35.4273i	−0.422002	+	1.57493i
$507$	−1.11514	−	17.0137i	−0.0495250	−	0.755606i
$508$	0.233724	−	1.77531i	0.0103698	−	0.0787666i
$509$	18.1377	+	31.4154i	0.803939	+	1.39246i	0.917005	+	0.398876i	$0.130600\pi$
$509$	18.1377	+	31.4154i	0.803939	+	1.39246i	−0.113065	+	0.993588i	$0.536067\pi$
$510$	2.69465	−	10.4314i	0.119321	−	0.461911i
$511$		0			0
$512$	5.94712	+	14.3576i	0.262828	+	0.634523i
$513$	14.8276	+	7.31217i	0.654656	+	0.322840i
$514$	38.6192	−	10.3480i	1.70342	−	0.456430i
$515$	11.3317	−	12.9213i	0.499333	−	0.569380i
$516$	−0.676877	−	0.0443649i	−0.0297979	−	0.00195306i
$517$	8.39907	+	42.2250i	0.369391	+	1.85705i
$518$		0			0
$519$	−0.739659	+	1.78570i	−0.0324674	+	0.0783834i
$520$	−19.2419	+	16.8747i	−0.843811	+	0.740003i
$521$	−23.7780	+	11.7260i	−1.04173	+	0.513726i	−0.880923	−	0.473259i	$-0.843078\pi$
$521$	−23.7780	+	11.7260i	−1.04173	+	0.513726i	−0.160811	+	0.986985i	$0.551411\pi$
$522$	−35.4093	−	31.0531i	−1.54982	−	1.35916i
$523$	20.1594	+	5.40169i	0.881508	+	0.236199i	0.671058	−	0.741405i	$-0.265840\pi$
$523$	20.1594	+	5.40169i	0.881508	+	0.236199i	0.210450	+	0.977605i	$0.432507\pi$
$524$	3.57500	−	2.38874i	0.156174	−	0.104352i
$525$		0			0
$526$			12.5848i			0.548721i
$527$	−0.235639	−	3.15902i	−0.0102646	−	0.137609i
$528$	−11.7421	−	6.77930i	−0.511009	−	0.295031i
$529$	6.21435	+	0.818134i	0.270189	+	0.0355711i
$530$	−3.87990	+	7.86766i	−0.168532	+	0.341749i
$531$	−11.4115	−	11.4115i	−0.495215	−	0.495215i
$532$		0			0
$533$	−1.44837	−	0.967768i	−0.0627358	−	0.0419187i
$534$	1.25913	+	1.43576i	0.0544879	+	0.0621316i
$535$	−8.84275	−	11.5241i	−0.382305	−	0.498230i
$536$	−10.8013	−	14.0765i	−0.466543	−	0.608011i
$537$	−3.08104	−	3.51326i	−0.132957	−	0.151608i
$538$	−6.25061	−	4.17652i	−0.269483	−	0.180063i
$539$		0			0
$540$	7.05770	+	7.05770i	0.303715	+	0.303715i
$541$	15.4385	−	31.3062i	0.663752	−	1.34596i	−0.260982	−	0.965344i	$-0.584046\pi$
$541$	15.4385	−	31.3062i	0.663752	−	1.34596i	0.924734	−	0.380613i	$-0.124287\pi$
$542$	−7.61640	−	1.00272i	−0.327152	−	0.0430704i
$543$	−2.40350	−	1.38766i	−0.103144	−	0.0595502i
$544$	3.00900	−	24.5628i	0.129010	−	1.05312i
$545$			6.26581i			0.268398i
$546$		0			0
$547$	3.70359	−	2.47466i	0.158354	−	0.105809i	−0.473869	−	0.880596i	$-0.657143\pi$
$547$	3.70359	−	2.47466i	0.158354	−	0.105809i	0.632223	+	0.774787i	$0.282143\pi$
$548$	5.64706	+	1.51313i	0.241231	+	0.0646376i
$549$	−3.08073	−	2.70172i	−0.131482	−	0.115307i
$550$	17.5865	−	8.67270i	0.749891	−	0.369805i
$551$	−38.9635	+	34.1701i	−1.65990	+	1.45569i
$552$	1.22409	−	2.95521i	0.0521007	−	0.125782i
$553$		0			0
$554$	4.35492	+	21.8937i	0.185023	+	0.930172i
$555$	−8.65173	−	0.567064i	−0.367245	−	0.0240705i
$556$	4.21516	−	4.80647i	0.178763	−	0.203840i
$557$	8.03526	−	2.15304i	0.340465	−	0.0912273i	−0.0845355	−	0.996420i	$-0.526941\pi$
$557$	8.03526	−	2.15304i	0.340465	−	0.0912273i	0.425000	+	0.905193i	$0.360274\pi$
$558$	3.33053	+	1.64243i	0.140992	+	0.0695297i
$559$	−2.64591	−	6.38780i	−0.111910	−	0.270175i
$560$		0			0
$561$	5.72206	+	9.70795i	0.241585	+	0.409870i
$562$	−6.82152	−	11.8152i	−0.287749	−	0.498395i
$563$	4.71686	−	35.8281i	0.198792	−	1.50998i	−0.543221	−	0.839590i	$-0.682795\pi$
$563$	4.71686	−	35.8281i	0.198792	−	1.50998i	0.742013	−	0.670386i	$-0.233871\pi$
$564$	0.366612	+	5.59342i	0.0154372	+	0.235526i
$565$	12.8837	−	48.0827i	0.542022	−	2.02285i
$566$	2.50068	−	12.5718i	0.105111	−	0.528430i
$567$		0			0
$568$	6.69154	−	1.33103i	0.280771	−	0.0558488i
$569$	−1.10714	−	8.40959i	−0.0464139	−	0.352549i	−0.998856	−	0.0478277i	$-0.984770\pi$
$569$	−1.10714	−	8.40959i	−0.0464139	−	0.352549i	0.952442	−	0.304721i	$-0.0985632\pi$
$570$	11.0256	−	8.46026i	0.461813	−	0.354361i
$571$	−19.1472	−	6.49961i	−0.801287	−	0.272000i	−0.109392	−	0.993999i	$-0.534891\pi$
$571$	−19.1472	−	6.49961i	−0.801287	−	0.272000i	−0.691895	+	0.721998i	$0.743224\pi$
$572$	−2.61373	+	39.8779i	−0.109286	+	1.66738i
$573$	−13.1862	−	2.62289i	−0.550860	−	0.109573i
$574$		0			0
$575$	4.96984	+	7.43789i	0.207257	+	0.310181i
$576$	1.73882	+	1.33425i	0.0724510	+	0.0555936i
$577$	−18.0046	+	31.1850i	−0.749543	+	1.29825i	0.198499	+	0.980101i	$0.436393\pi$
$577$	−18.0046	+	31.1850i	−0.749543	+	1.29825i	−0.948042	+	0.318146i	$0.896940\pi$
$578$	−18.0688	+	24.4471i	−0.751565	+	1.01686i
$579$	9.63945	−	5.56534i	0.400602	−	0.231288i
$580$	−28.9058	+	11.9732i	−1.20025	+	0.497159i
$581$		0			0
$582$	−6.92063	+	6.92063i	−0.286869	+	0.286869i
$583$	−2.94932	−	8.68841i	−0.122148	−	0.359837i
$584$	−0.719434	−	1.45887i	−0.0297704	−	0.0603684i
$585$	−15.4991	+	45.6588i	−0.640808	+	1.88776i
$586$	10.4080	−	1.37024i	0.429951	−	0.0566041i
$587$	18.6945	+	7.74352i	0.771605	+	0.319609i	0.733522	−	0.679666i	$-0.237875\pi$
$587$	18.6945	+	7.74352i	0.771605	+	0.319609i	0.0380824	+	0.999275i	$0.487875\pi$
$588$		0			0
$589$	2.27019	−	3.39757i	0.0935414	−	0.139995i
$590$	−27.1042	+	9.20062i	−1.11586	+	0.378784i
$591$	1.20569	+	4.49970i	0.0495955	+	0.185093i
$592$	−29.3723	+	1.92516i	−1.20719	+	0.0791237i
$593$	15.1704	−	19.7704i	0.622973	−	0.811874i	−0.370148	−	0.928973i	$-0.620693\pi$
$593$	15.1704	−	19.7704i	0.622973	−	0.811874i	0.993120	+	0.117099i	$0.0373596\pi$
$594$	−27.8721			−1.14361
$595$		0			0
$596$	−8.99580			−0.368482
$597$	−5.39292	+	7.02818i	−0.220717	+	0.287644i
$598$	−48.5703	+	3.18347i	−1.98619	+	0.130182i
$599$	−2.94729	−	10.9994i	−0.120423	−	0.449425i	0.879212	−	0.476430i	$-0.158070\pi$
$599$	−2.94729	−	10.9994i	−0.120423	−	0.449425i	−0.999635	+	0.0270052i	$0.991403\pi$
$600$	−1.61937	+	0.549702i	−0.0661105	+	0.0224415i
$601$	−10.4548	+	15.6467i	−0.426460	+	0.638243i	−0.981021	−	0.193900i	$-0.937886\pi$
$601$	−10.4548	+	15.6467i	−0.426460	+	0.638243i	0.554561	+	0.832143i	$0.312886\pi$
$602$		0			0
$603$	−30.8836	−	12.7924i	−1.25768	−	0.520947i
$604$	−6.82969	+	0.899145i	−0.277896	+	0.0365857i
$605$	−12.1865	+	35.9002i	−0.495450	+	1.45955i
$606$	2.24557	+	4.55356i	0.0912200	+	0.184976i
$607$	11.7318	+	34.5608i	0.476179	+	1.40278i	0.874274	+	0.485433i	$0.161338\pi$
$607$	11.7318	+	34.5608i	0.476179	+	1.40278i	−0.398095	+	0.917344i	$0.630328\pi$
$608$	22.5717	−	22.5717i	0.915402	−	0.915402i
$609$		0			0
$610$	−6.71437	+	2.78118i	−0.271857	+	0.112607i
$611$	−49.4805	+	28.5676i	−2.00177	+	1.15572i
$612$	−5.21883	−	12.2853i	−0.210959	−	0.496603i
$613$	1.74342	−	3.01970i	0.0704162	−	0.121965i	−0.828668	−	0.559741i	$-0.810901\pi$
$613$	1.74342	−	3.01970i	0.0704162	−	0.121965i	0.899084	+	0.437777i	$0.144234\pi$
$614$	−34.1683	−	26.2183i	−1.37892	−	1.05808i
$615$	−0.212515	−	0.318052i	−0.00856944	−	0.0128251i
$616$		0			0
$617$	46.2155	+	9.19283i	1.86057	+	0.370089i	0.992078	−	0.125622i	$-0.0400928\pi$
$617$	46.2155	+	9.19283i	1.86057	+	0.370089i	0.868487	+	0.495712i	$0.165093\pi$
$618$	−0.408681	+	6.23526i	−0.0164395	+	0.250819i
$619$	−3.78417	−	1.28455i	−0.152098	−	0.0516305i	0.244352	−	0.969687i	$-0.421425\pi$
$619$	−3.78417	−	1.28455i	−0.152098	−	0.0516305i	−0.396450	+	0.918056i	$0.629758\pi$
$620$	1.95716	−	1.50178i	0.0786015	−	0.0603130i
$621$	−1.65967	−	12.6065i	−0.0666003	−	0.505880i
$622$	5.67381	−	1.12859i	0.227499	−	0.0452524i
$623$		0			0
$624$	3.51041	−	17.6480i	0.140529	−	0.706487i
$625$	−8.06272	+	30.0905i	−0.322509	+	1.20362i
$626$	0.775173	+	11.8269i	0.0309821	+	0.472696i
$627$	−1.89733	+	14.4116i	−0.0757719	+	0.575545i
$628$	4.14774	+	7.18409i	0.165513	+	0.286677i
$629$	22.0379	+	10.6223i	0.878708	+	0.423537i
$630$		0			0
$631$	−1.89828	−	4.58286i	−0.0755694	−	0.182441i	0.881580	−	0.472034i	$-0.156480\pi$
$631$	−1.89828	−	4.58286i	−0.0755694	−	0.182441i	−0.957150	+	0.289593i	$0.906480\pi$
$632$	−15.5698	−	7.67815i	−0.619332	−	0.305421i
$633$	−5.23101	+	1.40165i	−0.207914	+	0.0557104i
$634$	13.3793	−	15.2562i	0.531360	−	0.605900i
$635$	3.99934	+	0.262131i	0.158709	+	0.0104023i
$636$	−0.233062	−	1.17168i	−0.00924150	−	0.0464602i
$637$		0			0
$638$	33.4350	−	80.7193i	1.32370	−	3.19571i
$639$	9.66413	−	8.47521i	0.382307	−	0.335274i
$640$	−25.3751	+	12.5136i	−1.00304	+	0.494645i
$641$	−25.0628	−	21.9795i	−0.989921	−	0.868138i	0.00134697	−	0.999999i	$-0.499571\pi$
$641$	−25.0628	−	21.9795i	−0.989921	−	0.868138i	−0.991268	+	0.131862i	$0.957905\pi$
$642$	5.10139	+	1.36691i	0.201336	+	0.0539477i
$643$	−27.9715	+	18.6900i	−1.10309	+	0.737061i	−0.967289	−	0.253675i	$-0.918361\pi$
$643$	−27.9715	+	18.6900i	−1.10309	+	0.737061i	−0.135800	+	0.990736i	$0.543361\pi$
$644$		0			0
$645$		−	1.51829i		−	0.0597826i
$646$	−37.7844	+	10.4899i	−1.48661	+	0.412718i
$647$	−30.0850	−	17.3696i	−1.18276	−	0.682868i	−0.226110	−	0.974102i	$-0.572601\pi$
$647$	−30.0850	−	17.3696i	−1.18276	−	0.682868i	−0.956652	+	0.291234i	$0.905934\pi$
$648$	−9.12355	−	1.20114i	−0.358407	−	0.0471852i
$649$	13.2413	−	26.8508i	0.519768	−	1.05398i
$650$	18.4010	+	18.4010i	0.721747	+	0.721747i
$651$		0			0
$652$	−12.5631	−	8.39441i	−0.492010	−	0.328750i
$653$	−23.6554	−	26.9739i	−0.925709	−	1.05557i	−0.998305	−	0.0582070i	$-0.981462\pi$
$653$	−23.6554	−	26.9739i	−0.925709	−	1.05557i	0.0725958	−	0.997361i	$-0.476872\pi$
$654$	−1.38685	−	1.80738i	−0.0542300	−	0.0706740i
$655$	5.85855	+	7.63501i	0.228913	+	0.298325i
$656$	−0.856248	−	0.976364i	−0.0334309	−	0.0381206i
$657$	−2.54810	−	1.70259i	−0.0994109	−	0.0664242i
$658$		0			0
$659$	−4.30369	−	4.30369i	−0.167648	−	0.167648i	0.618297	−	0.785945i	$-0.287823\pi$
$659$	−4.30369	−	4.30369i	−0.167648	−	0.167648i	−0.785945	+	0.618297i	$0.787823\pi$
$660$	−3.88139	+	7.87068i	−0.151083	+	0.306366i
$661$	32.7821	+	4.31585i	1.27508	+	0.167867i	0.737499	−	0.675348i	$-0.236006\pi$
$661$	32.7821	+	4.31585i	1.27508	+	0.167867i	0.537577	+	0.843215i	$0.319340\pi$
$662$	38.0477	+	21.9668i	1.47877	+	0.853766i
$663$	−9.75887	+	11.3321i	−0.379003	+	0.440102i
$664$		−	19.1595i		−	0.743533i
$665$		0			0
$666$	−23.8454	+	15.9330i	−0.923990	+	0.617390i
$667$	38.5000	+	10.3160i	1.49072	+	0.399438i
$668$	−12.0411	−	10.5598i	−0.465885	−	0.408570i
$669$	0.995189	−	0.490773i	0.0384762	−	0.0189744i
$670$	−44.5759	+	39.0920i	−1.72212	+	1.51025i
$671$	2.90896	−	7.02284i	0.112299	−	0.271114i
$672$		0			0
$673$	−3.94208	−	19.8182i	−0.151956	−	0.763934i	−0.979328	−	0.202279i	$-0.935165\pi$
$673$	−3.94208	−	19.8182i	−0.151956	−	0.763934i	0.827372	−	0.561654i	$-0.189835\pi$
$674$	−9.12121	−	0.597835i	−0.351336	−	0.0230278i
$675$	−4.48221	+	5.11098i	−0.172520	+	0.196722i
$676$	−36.1890	+	9.69680i	−1.39188	+	0.372954i
$677$	−23.0645	−	11.3742i	−0.886441	−	0.437144i	−0.0587135	−	0.998275i	$-0.518700\pi$
$677$	−23.0645	−	11.3742i	−0.886441	−	0.437144i	−0.827727	+	0.561131i	$0.810367\pi$
$678$	6.92610	+	16.7211i	0.265995	+	0.642170i
$679$		0			0
$680$	15.8324	+	0.894614i	0.607145	+	0.0343069i
$681$	−0.389409	−	0.674476i	−0.0149222	−	0.0258460i
$682$	−0.899186	+	6.82999i	−0.0344316	+	0.261534i
$683$	1.71419	+	26.1535i	0.0655916	+	1.00073i	0.896135	+	0.443781i	$0.146363\pi$
$683$	1.71419	+	26.1535i	0.0655916	+	1.00073i	−0.830544	+	0.556953i	$0.811970\pi$
$684$	4.45628	−	16.6311i	0.170390	−	0.635905i
$685$	−2.55287	+	12.8341i	−0.0975401	+	0.490367i
$686$		0			0
$687$	4.83118	−	0.960982i	0.184321	−	0.0366637i
$688$	−0.672803	−	5.11044i	−0.0256504	−	0.194834i
$689$	9.66044	−	7.41272i	0.368033	−	0.282402i
$690$	−10.1213	−	3.43574i	−0.385313	−	0.130796i
$691$	−2.59734	+	39.6277i	−0.0988073	+	1.50751i	0.604490	+	0.796613i	$0.293377\pi$
$691$	−2.59734	+	39.6277i	−0.0988073	+	1.50751i	−0.703298	+	0.710896i	$0.748290\pi$
$692$	4.16551	+	0.828572i	0.158349	+	0.0314976i
$693$		0			0
$694$	20.8901	+	31.2642i	0.792975	+	1.18677i
$695$	11.3522	+	8.71088i	0.430615	+	0.330423i
$696$	−3.80988	+	6.59890i	−0.144413	+	0.250131i
$697$	0.220088	+	1.05664i	0.00833644	+	0.0400232i
$698$	43.8691	−	25.3279i	1.66047	−	0.958673i
$699$	0.915246	−	0.379107i	0.0346178	−	0.0143392i
$700$		0			0
$701$	9.39878	−	9.39878i	0.354987	−	0.354987i	−0.506974	−	0.861961i	$-0.669236\pi$
$701$	9.39878	−	9.39878i	0.354987	−	0.354987i	0.861961	+	0.506974i	$0.169236\pi$
$702$	−11.8899	−	35.0264i	−0.448754	−	1.32199i
$703$	13.9574	+	28.3028i	0.526413	+	1.06746i
$704$	−1.30695	+	3.85014i	−0.0492574	+	0.145108i
$705$	−12.4392	+	1.63765i	−0.468486	+	0.0616773i
$706$	9.45764	+	3.91748i	0.355943	+	0.147436i
$707$		0			0
$708$	2.16560	−	3.24104i	0.0813881	−	0.121806i
$709$	40.2328	−	13.6572i	1.51098	−	0.512907i	0.561697	−	0.827343i	$-0.310149\pi$
$709$	40.2328	−	13.6572i	1.51098	−	0.512907i	0.949279	+	0.314436i	$0.101815\pi$
$710$	−5.90059	−	22.0213i	−0.221445	−	0.826445i
$711$	−32.6366	+	2.13912i	−1.22397	+	0.0802232i
$712$	−1.71109	+	2.22994i	−0.0641259	+	0.0835705i
$713$	−3.14273			−0.117696
$714$		0			0
$715$	−89.4492			−3.34521
$716$	−6.25078	+	8.14617i	−0.233602	+	0.304437i
$717$	−2.59615	+	0.170161i	−0.0969550	+	0.00635476i
$718$	−10.2561	−	38.2763i	−0.382755	−	1.42846i
$719$	−19.0741	+	6.47478i	−0.711343	+	0.241468i	−0.653575	−	0.756862i	$-0.726732\pi$
$719$	−19.0741	+	6.47478i	−0.711343	+	0.241468i	−0.0577679	+	0.998330i	$0.518398\pi$
$720$	−19.9710	+	29.8887i	−0.744275	+	1.11389i
$721$		0			0
$722$	−15.3424	−	6.35503i	−0.570985	−	0.236510i
$723$	7.81570	−	1.02896i	0.290669	−	0.0382673i
$724$	−1.96026	+	5.77475i	−0.0728526	+	0.214617i
$725$	−9.42491	−	19.1118i	−0.350032	−	0.709795i
$726$	−4.43080	−	13.0527i	−0.164442	−	0.484432i
$727$	15.6585	−	15.6585i	0.580743	−	0.580743i	−0.354364	−	0.935107i	$-0.615303\pi$
$727$	15.6585	−	15.6585i	0.580743	−	0.580743i	0.935107	+	0.354364i	$0.115303\pi$
$728$		0			0
$729$	−11.3214	+	4.68947i	−0.419311	+	0.173684i
$730$	−4.70720	+	2.71770i	−0.174221	+	0.100587i
$731$	−1.60373	+	3.97254i	−0.0593159	+	0.146930i
$732$	0.494858	−	0.857119i	0.0182905	−	0.0316800i
$733$	−26.1840	−	20.0917i	−0.967127	−	0.742103i	−0.000954952	−	1.00000i	$-0.500304\pi$
$733$	−26.1840	−	20.0917i	−0.967127	−	0.742103i	−0.966173	+	0.257897i	$0.916971\pi$
$734$	27.5000	+	41.1567i	1.01505	+	1.51912i
$735$		0			0
$736$	−24.0789	−	4.78959i	−0.887560	−	0.176547i
$737$	4.05584	−	61.8801i	0.149399	−	2.27938i
$738$	−1.19810	−	0.406700i	−0.0441027	−	0.0149708i
$739$	−18.3573	+	14.0860i	−0.675282	+	0.518162i	−0.888520	−	0.458838i	$-0.848266\pi$
$739$	−18.3573	+	14.0860i	−0.675282	+	0.518162i	0.213238	+	0.977000i	$0.431599\pi$
$740$	2.48676	+	18.8888i	0.0914150	+	0.694366i
$741$	−18.9202	+	3.76346i	−0.695051	+	0.138254i
$742$		0			0
$743$	−4.30776	+	21.6566i	−0.158037	+	0.794503i	0.817715	+	0.575623i	$0.195240\pi$
$743$	−4.30776	+	21.6566i	−0.158037	+	0.794503i	−0.975752	+	0.218880i	$0.929760\pi$
$744$	0.155499	−	0.580330i	0.00570087	−	0.0212759i
$745$	−1.31690	−	20.0920i	−0.0482474	−	0.736114i
$746$	−6.09375	+	46.2866i	−0.223108	+	1.69467i
$747$	−18.0484	−	31.2608i	−0.660357	−	1.14377i
$748$	18.4691	−	16.4935i	0.675296	−	0.603062i
$749$		0			0
$750$	−2.81301	−	6.79120i	−0.102717	−	0.247980i
$751$	2.28253	+	1.12562i	0.0832908	+	0.0410745i	0.483457	−	0.875368i	$-0.339381\pi$
$751$	2.28253	+	1.12562i	0.0832908	+	0.0410745i	−0.400166	+	0.916443i	$0.631048\pi$
$752$	−41.1435	+	11.0244i	−1.50035	+	0.402017i
$753$	−11.2300	+	12.8053i	−0.409242	+	0.466652i
$754$	115.701	+	7.58347i	4.21360	+	0.276174i
$755$	−3.00803	−	15.1224i	−0.109473	−	0.550360i
$756$		0			0
$757$	−14.2277	+	34.3488i	−0.517115	+	1.24843i	0.422552	+	0.906339i	$0.361134\pi$
$757$	−14.2277	+	34.3488i	−0.517115	+	1.24843i	−0.939668	+	0.342089i	$0.888866\pi$
$758$	−8.99166	+	7.88547i	−0.326592	+	0.286413i
$759$	10.0267	−	4.94463i	0.363947	−	0.179479i
$760$	15.3791	+	13.4871i	0.557858	+	0.489229i
$761$	2.80595	+	0.751851i	0.101715	+	0.0272546i	0.309318	−	0.950959i	$-0.399899\pi$
$761$	2.80595	+	0.751851i	0.101715	+	0.0272546i	−0.207602	+	0.978213i	$0.566566\pi$
$762$	−1.21163	+	0.809585i	−0.0438927	+	0.0293282i
$763$		0			0
$764$			29.5425i			1.06881i
$765$	26.6750	−	13.4546i	0.964438	−	0.486453i
$766$	22.6156	+	13.0571i	0.817135	+	0.471773i
$767$	39.3915	+	5.18598i	1.42234	+	0.187255i
$768$	4.94073	−	10.0188i	0.178283	−	0.361523i
$769$	22.1893	+	22.1893i	0.800166	+	0.800166i	0.983121	−	0.182955i	$-0.0585663\pi$
$769$	22.1893	+	22.1893i	0.800166	+	0.800166i	−0.182955	+	0.983121i	$0.558566\pi$
$770$		0			0
$771$	−10.1330	−	6.77069i	−0.364933	−	0.243840i
$772$	−16.1264	−	18.3886i	−0.580401	−	0.661821i
$773$	−2.17164	−	2.83013i	−0.0781084	−	0.101793i	0.752665	−	0.658404i	$-0.228768\pi$
$773$	−2.17164	−	2.83013i	−0.0781084	−	0.101793i	−0.830773	+	0.556611i	$0.812101\pi$
$774$	−3.05721	−	3.98424i	−0.109889	−	0.143211i
$775$	1.10783	+	1.26324i	0.0397946	+	0.0453770i
$776$	−11.9778	−	8.00328i	−0.429976	−	0.287301i
$777$		0			0
$778$	15.9696	+	15.9696i	0.572538	+	0.572538i
$779$	−0.615775	+	1.24867i	−0.0220624	+	0.0447382i
$780$	−11.5467	−	1.52015i	−0.413438	−	0.0544302i
$781$	20.6508	+	11.9228i	0.738945	+	0.426630i
$782$	22.8530	+	19.6803i	0.817222	+	0.703767i
$783$			30.2895i			1.08246i
$784$		0			0
$785$	−15.4384	+	10.3156i	−0.551019	+	0.368179i
$786$	−3.37980	−	0.905616i	−0.120554	−	0.0323022i
$787$	32.3353	+	28.3573i	1.15263	+	1.01083i	0.999745	+	0.0225862i	$0.00719002\pi$
$787$	32.3353	+	28.3573i	1.15263	+	1.01083i	0.152886	+	0.988244i	$0.451143\pi$
$788$	9.18064	−	4.52739i	0.327047	−	0.161282i
$789$	2.88406	−	2.52925i	0.102675	−	0.0900438i
$790$	−22.1992	+	53.5937i	−0.789813	+	1.90678i
$791$		0			0
$792$	−3.79322	−	19.0698i	−0.134786	−	0.677616i
$793$	10.0664	+	0.659787i	0.357469	+	0.0234297i
$794$	−4.51366	+	5.14685i	−0.160184	+	0.182655i
$795$	2.58281	−	0.692063i	0.0916029	−	0.0245449i
$796$	17.4586	+	8.60963i	0.618804	+	0.305160i
$797$	4.78470	+	11.5513i	0.169483	+	0.409168i	0.985685	−	0.168599i	$-0.0539243\pi$
$797$	4.78470	+	11.5513i	0.169483	+	0.409168i	−0.816202	+	0.577767i	$0.803924\pi$
$798$		0			0
$799$	34.2763	+	8.85429i	1.21261	+	0.313242i
$800$	6.56277	+	11.3671i	0.232029	+	0.401886i
$801$	−0.691209	+	5.25025i	−0.0244227	+	0.185509i
$802$	1.38936	+	21.1975i	0.0490599	+	0.748510i
$803$	1.47142	−	5.49141i	0.0519252	−	0.193788i
$804$	1.57518	−	7.91897i	0.0555524	−	0.279281i
$805$		0			0
$806$	−8.96672	+	1.78359i	−0.315839	+	0.0628243i
$807$	0.299094	+	2.27184i	0.0105286	+	0.0799727i
$808$	−5.92865	+	4.54922i	−0.208569	+	0.160041i
$809$	43.1172	+	14.6363i	1.51592	+	0.514586i	0.950636	−	0.310309i	$-0.100432\pi$
$809$	43.1172	+	14.6363i	1.51592	+	0.514586i	0.565286	+	0.824895i	$0.308766\pi$
$810$	−2.01113	+	30.6840i	−0.0706641	+	1.07813i
$811$	−22.1324	−	4.40241i	−0.777174	−	0.154590i	−0.209462	−	0.977817i	$-0.567171\pi$
$811$	−22.1324	−	4.40241i	−0.777174	−	0.154590i	−0.567712	+	0.823227i	$0.692171\pi$
$812$		0			0
$813$	1.30093	+	1.94698i	0.0456257	+	0.0682836i
$814$	−42.2080	−	32.3873i	−1.47939	−	1.13517i
$815$	16.9097	−	29.2884i	0.592320	−	1.02593i
$816$	−9.21400	+	6.27734i	−0.322554	+	0.219751i
$817$	−4.78575	+	2.76305i	−0.167432	+	0.0966671i
$818$	4.05755	−	1.68069i	0.141869	−	0.0587641i
$819$		0			0
$820$	−0.594345	+	0.594345i	−0.0207554	+	0.0207554i
$821$	13.5948	+	40.0489i	0.474460	+	1.39772i	0.876194	+	0.481959i	$0.160074\pi$
$821$	13.5948	+	40.0489i	0.474460	+	1.39772i	−0.401734	+	0.915757i	$0.631592\pi$
$822$	−2.10428	−	4.26705i	−0.0733951	−	0.148831i
$823$	9.16159	−	26.9892i	0.319353	−	0.940783i	−0.662156	−	0.749366i	$-0.730358\pi$
$823$	9.16159	−	26.9892i	0.319353	−	0.940783i	0.981509	−	0.191417i	$-0.0613083\pi$
$824$	−9.11848	+	1.20047i	−0.317657	+	0.0418204i
$825$	−5.52202	−	2.28730i	−0.192252	−	0.0796335i
$826$		0			0
$827$	−5.50470	+	8.23837i	−0.191417	+	0.286476i	−0.914747	−	0.404026i	$-0.867610\pi$
$827$	−5.50470	+	8.23837i	−0.191417	+	0.286476i	0.723330	+	0.690502i	$0.242610\pi$
$828$	−12.5394	+	4.25657i	−0.435776	+	0.147926i
$829$	−10.4447	−	38.9802i	−0.362760	−	1.35384i	−0.870432	−	0.492288i	$-0.836161\pi$
$829$	−10.4447	−	38.9802i	−0.362760	−	1.35384i	0.507672	−	0.861550i	$-0.330506\pi$
$830$	−63.8852	+	4.18726i	−2.21749	+	0.145342i
$831$	4.14215	−	5.39815i	0.143690	−	0.187260i
$832$	−5.39593			−0.187070
$833$		0			0
$834$	−5.20259			−0.180151
$835$	21.8224	−	28.4395i	0.755195	−	0.984190i
$836$	31.8725	−	2.08903i	1.10233	−	0.0722507i
$837$	−0.618128	−	2.30689i	−0.0213656	−	0.0797377i
$838$	57.6915	−	19.5836i	1.99292	−	0.676506i
$839$	26.4350	−	39.5628i	0.912637	−	1.36586i	−0.0179698	−	0.999839i	$-0.505720\pi$
$839$	26.4350	−	39.5628i	0.912637	−	1.36586i	0.930607	−	0.366020i	$-0.119280\pi$
$840$		0			0
$841$	−60.9278	−	25.2371i	−2.10096	−	0.870245i
$842$	1.25864	−	0.165703i	0.0433756	−	0.00571050i
$843$	−1.33673	+	3.93789i	−0.0460396	+	0.135628i
$844$	5.26320	+	10.6727i	0.181167	+	0.367370i
$845$	−26.9554	−	79.4080i	−0.927293	−	2.73172i
$846$	−29.3448	+	29.3448i	−1.00890	+	1.00890i
$847$		0			0
$848$	8.38687	−	3.47395i	0.288006	−	0.119296i
$849$	−3.38366	+	1.95356i	−0.116127	+	0.0670459i
$850$	−0.145190	−	16.1234i	−0.00497996	−	0.553028i
$851$	12.1354	−	21.0190i	0.415995	−	0.720524i
$852$	2.46313	+	1.89002i	0.0843853	+	0.0647511i
$853$	−2.30560	−	3.45057i	−0.0789422	−	0.118145i	0.789897	−	0.613239i	$-0.210134\pi$
$853$	−2.30560	−	3.45057i	−0.0789422	−	0.118145i	−0.868840	+	0.495094i	$0.835134\pi$
$854$		0			0
$855$	37.7976	+	7.51841i	1.29265	+	0.257124i
$856$	−0.508407	+	7.75680i	−0.0173770	+	0.265122i
$857$	19.7744	+	6.71252i	0.675482	+	0.229295i	0.638040	−	0.770004i	$-0.279746\pi$
$857$	19.7744	+	6.71252i	0.675482	+	0.229295i	0.0374423	+	0.999299i	$0.488079\pi$
$858$	25.8017	−	19.7983i	0.880855	−	0.675904i
$859$	1.75392	+	13.3224i	0.0598431	+	0.454553i	0.994965	+	0.100226i	$0.0319567\pi$
$859$	1.75392	+	13.3224i	0.0598431	+	0.454553i	−0.935122	+	0.354327i	$0.884710\pi$
$860$	−3.27213	+	0.650867i	−0.111579	+	0.0221944i
$861$		0			0
$862$	−3.92361	+	19.7253i	−0.133639	+	0.671846i
$863$	6.72620	−	25.1025i	0.228963	−	0.854500i	−0.751816	−	0.659374i	$-0.770822\pi$
$863$	6.72620	−	25.1025i	0.228963	−	0.854500i	0.980778	−	0.195126i	$-0.0625117\pi$
$864$	−1.22022	−	18.6169i	−0.0415126	−	0.633360i
$865$	−1.24081	+	9.42490i	−0.0421889	+	0.320456i
$866$	−5.78700	−	10.0234i	−0.196650	−	0.340608i
$867$	9.23399	−	0.772456i	0.313603	−	0.0262340i
$868$		0			0
$869$	−23.2191	−	56.0559i	−0.787654	−	1.90157i
$870$	22.8360	+	11.2614i	0.774212	+	0.381799i
$871$	79.4939	−	21.3003i	2.69355	−	0.721734i
$872$	2.21087	−	2.52102i	0.0748696	−	0.0853724i
$873$	−27.0822	−	1.77506i	−0.916593	−	0.0600766i
$874$	7.58964	+	38.1557i	0.256723	+	1.29064i
$875$		0			0
$876$	0.283265	−	0.683861i	0.00957063	−	0.0231055i
$877$	21.3731	−	18.7437i	0.721717	−	0.632929i	−0.217577	−	0.976043i	$-0.569815\pi$
$877$	21.3731	−	18.7437i	0.721717	−	0.632929i	0.939294	+	0.343114i	$0.111482\pi$
$878$	34.5327	−	17.0296i	1.16542	−	0.574723i
$879$	−2.40579	−	2.10982i	−0.0811454	−	0.0711626i
$880$	−64.4131	−	17.2595i	−2.17137	−	0.581816i
$881$	−2.44242	+	1.63198i	−0.0822873	+	0.0549826i	−0.596033	−	0.802960i	$-0.703257\pi$
$881$	−2.44242	+	1.63198i	−0.0822873	+	0.0549826i	0.513746	+	0.857942i	$0.328257\pi$
$882$		0			0
$883$		−	17.1609i		−	0.577509i	−0.957403	−	0.288755i	$-0.906759\pi$
$883$		−	17.1609i		−	0.577509i	0.957403	−	0.288755i	$-0.0932411\pi$
$884$	28.6057	+	16.1739i	0.962115	+	0.543986i
$885$	7.55584	+	4.36237i	0.253987	+	0.146639i
$886$	−57.3083	−	7.54478i	−1.92531	−	0.253472i
$887$	−3.37950	+	6.85296i	−0.113473	+	0.230100i	−0.946199	−	0.323585i	$-0.895112\pi$
$887$	−3.37950	+	6.85296i	−0.113473	+	0.230100i	0.832727	+	0.553684i	$0.186779\pi$
$888$	3.28089	+	3.28089i	0.110100	+	0.110100i
$889$		0			0
$890$	7.80944	+	5.21810i	0.261773	+	0.174911i
$891$	−21.2062	−	24.1811i	−0.710435	−	0.810096i
$892$	−1.48431	−	1.93439i	−0.0496983	−	0.0647681i
$893$	27.7993	+	36.2288i	0.930269	+	1.21235i
$894$	4.82694	+	5.50407i	0.161437	+	0.184084i
$895$	−19.1094	−	12.7685i	−0.638757	−	0.426804i
$896$		0			0
$897$	10.4911	+	10.4911i	0.350288	+	0.350288i
$898$	17.0396	−	34.5529i	0.568618	−	1.15304i
$899$	7.42238	+	0.977174i	0.247550	+	0.0325906i
$900$	6.13121	+	3.53985i	0.204374	+	0.117995i
$901$	−7.48882	−	0.917398i	−0.249489	−	0.0305630i
$902$		−	2.34717i		−	0.0781523i
$903$		0			0
$904$	−22.1495	+	14.7998i	−0.736682	+	0.492235i
$905$	−13.1848	−	3.53285i	−0.438277	−	0.117436i
$906$	4.21479	+	3.69627i	0.140027	+	0.122800i
$907$	−27.1210	+	13.3746i	−0.900539	+	0.444097i	−0.832780	−	0.553605i	$-0.813252\pi$
$907$	−27.1210	+	13.3746i	−0.900539	+	0.444097i	−0.0677599	+	0.997702i	$0.521585\pi$
$908$	−1.28666	+	1.12837i	−0.0426992	+	0.0374462i
$909$	−5.38783	+	13.0074i	−0.178703	+	0.431428i
$910$		0			0
$911$	0.758034	+	3.81090i	0.0251148	+	0.126261i	0.991309	−	0.131555i	$-0.0419971\pi$
$911$	0.758034	+	3.81090i	0.0251148	+	0.126261i	−0.966194	+	0.257816i	$0.916997\pi$
$912$	−14.3508	−	0.940599i	−0.475202	−	0.0311464i
$913$	44.1522	−	50.3459i	1.46122	−	1.66621i
$914$	7.31016	−	1.95875i	0.241799	−	0.0647898i
$915$	1.98680	+	0.979784i	0.0656817	+	0.0323906i
$916$	−4.14211	−	9.99993i	−0.136859	−	0.330407i
$917$		0			0
$918$	−9.95130	+	20.6458i	−0.328442	+	0.681415i
$919$	−1.33707	−	2.31587i	−0.0441059	−	0.0763936i	0.843130	−	0.537710i	$-0.180711\pi$
$919$	−1.33707	−	2.31587i	−0.0441059	−	0.0763936i	−0.887236	+	0.461317i	$0.847377\pi$
$920$	2.05346	−	15.5976i	0.0677007	−	0.514238i
$921$	0.858598	+	13.0997i	0.0282918	+	0.431649i
$922$	−16.7890	+	62.6575i	−0.552917	+	2.06351i
$923$	−6.17377	+	31.0377i	−0.203212	+	1.02162i
$924$		0			0
$925$	−12.7266	+	2.53147i	−0.418447	+	0.0832342i
$926$	3.24077	+	24.6161i	0.106498	+	0.808935i
$927$	−13.7469	+	10.5484i	−0.451509	+	0.346455i
$928$	55.3794	+	18.7988i	1.81792	+	0.617100i
$929$	−0.484105	+	7.38602i	−0.0158830	+	0.242327i	0.982534	+	0.186083i	$0.0595793\pi$
$929$	−0.484105	+	7.38602i	−0.0158830	+	0.242327i	−0.998417	+	0.0562445i	$0.982087\pi$
$930$	−1.96903	−	0.391664i	−0.0645670	−	0.0128432i
$931$		0			0
$932$	−1.20938	−	1.80997i	−0.0396146	−	0.0592875i
$933$	−1.39895	−	1.07345i	−0.0457996	−	0.0351432i
$934$	−31.7030	+	54.9113i	−1.03735	+	1.79675i
$935$	39.5417	+	38.8359i	1.29315	+	1.27007i
$936$	22.3466	−	12.9018i	0.730420	−	0.421708i
$937$	8.20064	−	3.39682i	0.267903	−	0.110969i	−0.244688	−	0.969602i	$-0.578686\pi$
$937$	8.20064	−	3.39682i	0.267903	−	0.110969i	0.512591	+	0.858633i	$0.328686\pi$
$938$		0			0
$939$	2.55458	−	2.55458i	0.0833655	−	0.0833655i
$940$	8.86183	+	26.1061i	0.289041	+	0.851488i
$941$	15.8165	+	32.0727i	0.515603	+	1.04554i	0.986563	+	0.163384i	$0.0522409\pi$
$941$	15.8165	+	32.0727i	0.515603	+	1.04554i	−0.470960	+	0.882155i	$0.656092\pi$
$942$	2.17000	−	6.39260i	0.0707023	−	0.208282i
$943$	1.06162	−	0.139765i	0.0345710	−	0.00455136i
$944$	27.3655	+	11.3351i	0.890670	+	0.368928i
$945$		0			0
$946$	5.17592	−	7.74631i	0.168284	−	0.251854i
$947$	−19.3839	+	6.57995i	−0.629892	+	0.213820i	−0.618086	−	0.786111i	$-0.712092\pi$
$947$	−19.3839	+	6.57995i	−0.629892	+	0.213820i	−0.0118066	+	0.999930i	$0.503758\pi$
$948$	−2.04463	−	7.63067i	−0.0664065	−	0.247833i
$949$	7.52865	−	0.493454i	0.244390	−	0.0160182i
$950$	12.6616	−	16.5009i	0.410795	−	0.535359i
$951$	−6.18521			−0.200569
$952$		0			0
$953$	25.8889			0.838625			0.419312	−	0.907842i	$-0.362271\pi$
$953$	25.8889			0.838625			0.419312	+	0.907842i	$0.362271\pi$
$954$	5.38419	−	7.01681i	0.174320	−	0.227178i
$955$	−65.9826	+	4.32473i	−2.13515	+	0.139945i
$956$	1.47965	+	5.52213i	0.0478553	+	0.178598i
$957$	−25.2182	+	8.56043i	−0.815189	+	0.276719i
$958$	−11.4952	+	17.2038i	−0.371394	+	0.555830i
$959$		0			0
$960$	−1.09471	−	0.453445i	−0.0353317	−	0.0146349i
$961$	30.1496	−	3.96926i	0.972566	−	0.128041i
$962$	22.6952	−	66.8580i	0.731724	−	2.15559i
$963$	6.47745	+	13.1350i	0.208733	+	0.423269i
$964$	−5.56801	−	16.4028i	−0.179334	−	0.528300i
$965$	38.7099	−	38.7099i	1.24612	−	1.24612i
$966$		0			0
$967$	28.4678	−	11.7917i	0.915462	−	0.379197i	0.125317	−	0.992117i	$-0.460005\pi$
$967$	28.4678	−	11.7917i	0.915462	−	0.379197i	0.790145	+	0.612920i	$0.210005\pi$
$968$	17.5704	−	10.1443i	0.564735	−	0.326050i
$969$	9.99779	+	6.55086i	0.321175	+	0.210444i
$970$	−24.0684	+	41.6876i	−0.772788	+	1.33851i
$971$	47.3068	+	36.2998i	1.51815	+	1.16492i	0.936087	+	0.351770i	$0.114420\pi$
$971$	47.3068	+	36.2998i	1.51815	+	1.16492i	0.582061	+	0.813145i	$0.302247\pi$
$972$	−8.53186	−	12.7688i	−0.273660	−	0.409560i
$973$		0			0
$974$	−47.3564	−	9.41978i	−1.51740	−	0.301829i
$975$	0.518787	−	7.91516i	0.0166145	−	0.253488i
$976$	7.12160	+	2.41746i	0.227957	+	0.0773809i
$977$	43.0219	−	33.0118i	1.37639	−	1.05614i	0.385324	−	0.922781i	$-0.374090\pi$
$977$	43.0219	−	33.0118i	1.37639	−	1.05614i	0.991068	−	0.133361i	$-0.0425769\pi$
$978$	1.60497	+	12.1910i	0.0513213	+	0.389824i
$979$	−9.63508	+	1.91654i	−0.307939	+	0.0612528i
$980$		0			0
$981$	1.23246	−	6.19597i	0.0393493	−	0.197822i
$982$	2.98702	−	11.1477i	0.0953197	−	0.355738i
$983$	2.39569	+	36.5512i	0.0764106	+	1.16580i	0.848112	+	0.529816i	$0.177739\pi$
$983$	2.39569	+	36.5512i	0.0764106	+	1.16580i	−0.771702	+	0.635985i	$0.780594\pi$
$984$	−0.0267191	+	0.202952i	−0.000851774	+	0.00646987i
$985$	11.4558	+	19.8420i	0.365012	+	0.632220i
$986$	−47.8541	−	53.5860i	−1.52399	−	1.70653i
$987$		0			0
$988$	16.2216	+	39.1624i	0.516078	+	1.24592i
$989$	3.81184	+	1.87979i	0.121209	+	0.0597738i
$990$	−62.7572	+	16.8157i	−1.99455	+	0.534439i
$991$	−28.5187	+	32.5194i	−0.905927	+	1.03301i	0.0933739	+	0.995631i	$0.470235\pi$
$991$	−28.5187	+	32.5194i	−0.905927	+	1.03301i	−0.999301	+	0.0373808i	$0.988099\pi$
$992$	−4.60140	−	0.301591i	−0.146094	−	0.00957554i
$993$	−2.61257	−	13.1343i	−0.0829074	−	0.416803i
$994$		0			0
$995$	−16.6737	+	40.2539i	−0.528592	+	1.27613i
$996$	6.55507	−	5.74864i	0.207705	−	0.182153i
$997$	−32.8762	+	16.2128i	−1.04120	+	0.513463i	−0.880750	−	0.473581i	$-0.842961\pi$
$997$	−32.8762	+	16.2128i	−1.04120	+	0.513463i	−0.160450	+	0.987044i	$0.551295\pi$
$998$	−43.6533	−	38.2829i	−1.38182	−	1.21182i
$999$	17.8157	+	4.77369i	0.563663	+	0.151033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.bc.d.80.2		144
7.2	even	3	inner	833.2.bc.d.607.8		144
7.3	odd	6		833.2.t.d.97.2	yes	72
7.4	even	3		833.2.t.a.97.2	✓	72
7.5	odd	6		833.2.bc.a.607.8		144
7.6	odd	2		833.2.bc.a.80.2		144
17.10	odd	16		833.2.bc.a.129.8		144
119.10	even	48		833.2.t.a.146.2	yes	72
119.27	even	16	inner	833.2.bc.d.129.8		144
119.44	odd	48		833.2.bc.a.656.2		144
119.61	even	48	inner	833.2.bc.d.656.2		144
119.95	odd	48		833.2.t.d.146.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
833.2.t.a.97.2	✓	72	7.4	even	3
833.2.t.a.146.2	yes	72	119.10	even	48
833.2.t.d.97.2	yes	72	7.3	odd	6
833.2.t.d.146.2	yes	72	119.95	odd	48
833.2.bc.a.80.2		144	7.6	odd	2
833.2.bc.a.129.8		144	17.10	odd	16
833.2.bc.a.607.8		144	7.5	odd	6
833.2.bc.a.656.2		144	119.44	odd	48
833.2.bc.d.80.2		144	1.1	even	1	trivial
833.2.bc.d.129.8		144	119.27	even	16	inner
833.2.bc.d.607.8		144	7.2	even	3	inner
833.2.bc.d.656.2		144	119.61	even	48	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.bc (of order \(48\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.08860 + 1.41869i) q^{2} +(0.543906 - 0.0356495i) q^{3} +(-0.309994 - 1.15691i) q^{4} +(2.53857 - 0.861728i) q^{5} +(-0.541520 + 0.810442i) q^{6} +(-1.32544 - 0.549014i) q^{8} +(-2.67977 + 0.352799i) q^{9} +O(q^{10})\)	\(q+(-1.08860 + 1.41869i) q^{2} +(0.543906 - 0.0356495i) q^{3} +(-0.309994 - 1.15691i) q^{4} +(2.53857 - 0.861728i) q^{5} +(-0.541520 + 0.810442i) q^{6} +(-1.32544 - 0.549014i) q^{8} +(-2.67977 + 0.352799i) q^{9} +(-1.54096 + 4.53951i) q^{10} +(-2.21771 - 4.49707i) q^{11} +(-0.209851 - 0.618201i) q^{12} +(4.70535 - 4.70535i) q^{13} +(1.35002 - 0.559198i) q^{15} +(4.29627 - 2.48045i) q^{16} +(-4.12294 + 0.0371267i) q^{17} +(2.41668 - 4.18582i) q^{18} +(-4.21946 - 3.23771i) q^{19} +(-1.78388 - 2.66977i) q^{20} +(8.79414 + 1.74926i) q^{22} +(-0.267530 + 4.08172i) q^{23} +(-0.740486 - 0.251361i) q^{24} +(1.73498 - 1.33130i) q^{25} +(1.55319 + 11.7977i) q^{26} +(-3.04877 + 0.606437i) q^{27} +(1.90098 - 9.55688i) q^{29} +(-0.676305 + 2.52400i) q^{30} +(0.0502494 + 0.766657i) q^{31} +(-0.783404 + 5.95055i) q^{32} +(-1.36654 - 2.36692i) q^{33} +(4.43555 - 5.88958i) q^{34} +(1.23887 + 2.99090i) q^{36} +(-5.32156 - 2.62430i) q^{37} +(9.18660 - 2.46154i) q^{38} +(2.39153 - 2.72701i) q^{39} +(-3.83781 - 0.251544i) q^{40} +(-0.0510695 - 0.256744i) q^{41} +(0.397620 - 0.959941i) q^{43} +(-4.51524 + 3.95976i) q^{44} +(-6.49877 + 3.20484i) q^{45} +(-5.49946 - 4.82290i) q^{46} +(-8.29355 - 2.22225i) q^{47} +(2.24834 - 1.50229i) q^{48} +3.91066i q^{50} +(-2.24117 + 0.167174i) q^{51} +(-6.90231 - 3.98505i) q^{52} +(1.81423 + 0.238848i) q^{53} +(2.45854 - 4.98542i) q^{54} +(-9.50506 - 9.50506i) q^{55} +(-2.41041 - 1.61059i) q^{57} +(11.4888 + 13.1005i) q^{58} +(3.63474 + 4.73689i) q^{59} +(-1.06544 - 1.38851i) q^{60} +(0.999567 + 1.13979i) q^{61} +(-1.14235 - 0.763294i) q^{62} +(-0.573383 - 0.573383i) q^{64} +(7.89012 - 15.9996i) q^{65} +(4.84555 + 0.637929i) q^{66} +(10.7106 + 6.18377i) q^{67} +(1.32104 + 4.75837i) q^{68} +2.22961i q^{69} +(-3.95416 + 2.64209i) q^{71} +(3.74556 + 1.00362i) q^{72} +(0.852445 + 0.747574i) q^{73} +(9.51611 - 4.69283i) q^{74} +(0.896209 - 0.785954i) q^{75} +(-2.43774 + 5.88522i) q^{76} +(1.26537 + 6.36145i) q^{78} +(12.0747 + 0.791417i) q^{79} +(8.76890 - 9.99901i) q^{80} +(6.19577 - 1.66015i) q^{81} +(0.419833 + 0.207039i) q^{82} +(5.11069 + 12.3383i) q^{83} +(-10.4344 + 3.64710i) q^{85} +(0.929008 + 1.60909i) q^{86} +(0.693258 - 5.26582i) q^{87} +(0.470480 + 7.17814i) q^{88} +(0.507083 - 1.89246i) q^{89} +(2.52788 - 12.7085i) q^{90} +(4.80513 - 0.955800i) q^{92} +(0.0546619 + 0.415198i) q^{93} +(12.1810 - 9.34683i) q^{94} +(-13.5014 - 4.58311i) q^{95} +(-0.213964 + 3.26447i) q^{96} +(9.84825 + 1.95894i) q^{97} +(7.52952 + 11.2687i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{3} + 8 q^{5} - 16 q^{6} - 24 q^{9}+O(q^{10}) \) 144 * q + 8 * q^3 + 8 * q^5 - 16 * q^6 - 24 * q^9	\( 144 q + 8 q^{3} + 8 q^{5} - 16 q^{6} - 24 q^{9} - 8 q^{11} + 64 q^{13} + 40 q^{18} + 24 q^{19} + 48 q^{22} - 8 q^{23} - 24 q^{24} - 8 q^{25} - 16 q^{27} + 80 q^{31} + 40 q^{32} - 80 q^{33} + 240 q^{36} - 48 q^{37} - 56 q^{38} + 16 q^{39} - 32 q^{40} - 48 q^{41} + 48 q^{43} - 32 q^{44} - 48 q^{45} - 40 q^{47} + 40 q^{51} + 24 q^{53} + 200 q^{54} - 96 q^{57} - 32 q^{58} + 8 q^{59} + 80 q^{60} - 256 q^{62} + 24 q^{65} - 8 q^{66} - 40 q^{68} - 48 q^{73} + 32 q^{74} + 128 q^{75} - 144 q^{76} - 96 q^{78} + 32 q^{79} + 256 q^{80} - 16 q^{81} - 152 q^{82} - 64 q^{85} + 80 q^{86} - 64 q^{87} - 56 q^{88} - 64 q^{89} + 752 q^{90} - 432 q^{92} + 32 q^{93} - 128 q^{94} - 32 q^{95} + 32 q^{96} + 16 q^{97} + 80 q^{99}+O(q^{100}) \) 144 * q + 8 * q^3 + 8 * q^5 - 16 * q^6 - 24 * q^9 - 8 * q^11 + 64 * q^13 + 40 * q^18 + 24 * q^19 + 48 * q^22 - 8 * q^23 - 24 * q^24 - 8 * q^25 - 16 * q^27 + 80 * q^31 + 40 * q^32 - 80 * q^33 + 240 * q^36 - 48 * q^37 - 56 * q^38 + 16 * q^39 - 32 * q^40 - 48 * q^41 + 48 * q^43 - 32 * q^44 - 48 * q^45 - 40 * q^47 + 40 * q^51 + 24 * q^53 + 200 * q^54 - 96 * q^57 - 32 * q^58 + 8 * q^59 + 80 * q^60 - 256 * q^62 + 24 * q^65 - 8 * q^66 - 40 * q^68 - 48 * q^73 + 32 * q^74 + 128 * q^75 - 144 * q^76 - 96 * q^78 + 32 * q^79 + 256 * q^80 - 16 * q^81 - 152 * q^82 - 64 * q^85 + 80 * q^86 - 64 * q^87 - 56 * q^88 - 64 * q^89 + 752 * q^90 - 432 * q^92 + 32 * q^93 - 128 * q^94 - 32 * q^95 + 32 * q^96 + 16 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more