LMFDB - Embedded newform 961.2.d.o.628.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-6,9,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			628.1
Root			$-1.14660i$ of defining polynomial
Character	$\chi$	$=$	961.628
Dual form			961.2.d.o.531.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.831304 + 2.55849i) q^{2} +(0.438546 + 1.34971i) q^{3} +(-4.23677 - 3.07819i) q^{4} +0.608384 q^{5} -3.81777 q^{6} +(1.39707 + 1.01503i) q^{7} +(7.04481 - 5.11835i) q^{8} +(0.797669 - 0.579540i) q^{9} +(-0.505752 + 1.55654i) q^{10} +(1.08197 + 0.786100i) q^{11} +(2.29664 - 7.06832i) q^{12} +(1.13430 + 3.49101i) q^{13} +(-3.75835 + 2.73060i) q^{14} +(0.266804 + 0.821139i) q^{15} +(4.00227 + 12.3177i) q^{16} +(2.23517 - 1.62394i) q^{17} +(0.819643 + 2.52260i) q^{18} +(-0.793456 + 2.44201i) q^{19} +(-2.57758 - 1.87272i) q^{20} +(-0.757316 + 2.33078i) q^{21} +(-2.91068 + 2.11473i) q^{22} +(0.436271 - 0.316969i) q^{23} +(9.99774 + 7.26378i) q^{24} -4.62987 q^{25} -9.87466 q^{26} +(4.57641 + 3.32495i) q^{27} +(-2.79461 - 8.60093i) q^{28} +(-2.51258 + 7.73291i) q^{29} -2.32267 q^{30} -17.4262 q^{32} +(-0.586508 + 1.80509i) q^{33} +(2.29674 + 7.06865i) q^{34} +(0.849957 + 0.617530i) q^{35} -5.16348 q^{36} +7.74498 q^{37} +(-5.58825 - 4.06010i) q^{38} +(-4.21439 + 3.06194i) q^{39} +(4.28595 - 3.11392i) q^{40} +(-0.0321538 + 0.0989592i) q^{41} +(-5.33371 - 3.87517i) q^{42} +(-0.928504 + 2.85764i) q^{43} +(-2.16431 - 6.66105i) q^{44} +(0.485289 - 0.352583i) q^{45} +(0.448289 + 1.37969i) q^{46} +(-2.07813 - 6.39584i) q^{47} +(-14.8701 + 10.8038i) q^{48} +(-1.24160 - 3.82124i) q^{49} +(3.84883 - 11.8455i) q^{50} +(3.17207 + 2.30464i) q^{51} +(5.94025 - 18.2822i) q^{52} +(-2.26423 + 1.64506i) q^{53} +(-12.3112 + 8.94464i) q^{54} +(0.658255 + 0.478250i) q^{55} +15.0374 q^{56} -3.64396 q^{57} +(-17.6959 - 12.8568i) q^{58} +(0.144074 + 0.443414i) q^{59} +(1.39724 - 4.30025i) q^{60} -5.11468 q^{61} +1.70266 q^{63} +(6.48190 - 19.9492i) q^{64} +(0.690088 + 2.12387i) q^{65} +(-4.13073 - 3.00115i) q^{66} +8.29847 q^{67} -14.4687 q^{68} +(0.619140 + 0.449832i) q^{69} +(-2.28652 + 1.66125i) q^{70} +(-3.84988 + 2.79710i) q^{71} +(2.65313 - 8.16550i) q^{72} +(-6.07264 - 4.41203i) q^{73} +(-6.43843 + 19.8154i) q^{74} +(-2.03041 - 6.24896i) q^{75} +(10.8787 - 7.90381i) q^{76} +(0.713679 + 2.19648i) q^{77} +(-4.33049 - 13.3279i) q^{78} +(7.84662 - 5.70090i) q^{79} +(2.43492 + 7.49391i) q^{80} +(-1.56670 + 4.82180i) q^{81} +(-0.226457 - 0.164530i) q^{82} +(-5.15582 + 15.8680i) q^{83} +(10.3832 - 7.54381i) q^{84} +(1.35984 - 0.987981i) q^{85} +(-6.53938 - 4.75114i) q^{86} -11.5390 q^{87} +11.6458 q^{88} +(12.3911 + 9.00268i) q^{89} +(0.498657 + 1.53471i) q^{90} +(-1.95880 + 6.02855i) q^{91} -2.82407 q^{92} +18.0912 q^{94} +(-0.482726 + 1.48568i) q^{95} +(-7.64218 - 23.5202i) q^{96} +(1.03488 + 0.751881i) q^{97} +10.8087 q^{98} +1.31863 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 9 q^{3} - 14 q^{4} + 6 q^{5} - 22 q^{6} + 11 q^{7} + 17 q^{8} + 5 q^{9} + 19 q^{10} + 14 q^{11} + 5 q^{12} - q^{13} + 27 q^{14} + 14 q^{15} - 2 q^{16} - 3 q^{17} - 9 q^{18} + 13 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) $ 16 * q - 6 * q^2 + 9 * q^3 - 14 * q^4 + 6 * q^5 - 22 * q^6 + 11 * q^7 + 17 * q^8 + 5 * q^9 + 19 * q^10 + 14 * q^11 + 5 * q^12 - q^13 + 27 * q^14 + 14 * q^15 - 2 * q^16 - 3 * q^17 - 9 * q^18 + 13 * q^19 - 29 * q^20 - 3 * q^21 + 12 * q^22 + q^23 + 25 * q^24 + 26 * q^25 - 18 * q^26 + 9 * q^27 - 15 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 + 49 * q^34 - 9 * q^35 - 2 * q^36 + 16 * q^37 - 31 * q^38 - 3 * q^39 + 2 * q^40 + 16 * q^41 - 18 * q^42 + 14 * q^43 - 33 * q^44 + 5 * q^45 + 34 * q^46 + 14 * q^47 - 38 * q^48 + 41 * q^49 - 6 * q^50 + 9 * q^51 + 17 * q^52 + 3 * q^53 - 46 * q^54 - q^55 + 60 * q^56 + 34 * q^57 - 15 * q^58 + 7 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 - 6 * q^65 - 30 * q^66 - 26 * q^67 - 60 * q^68 - q^69 + 12 * q^70 - 17 * q^71 + q^72 + 11 * q^73 - 56 * q^74 + 4 * q^75 + 24 * q^76 + 18 * q^77 - 15 * q^78 - 6 * q^79 - 42 * q^80 - q^81 - 13 * q^82 - 28 * q^83 - 31 * q^84 + 37 * q^85 + 7 * q^86 - 30 * q^87 + 34 * q^88 + q^89 + 16 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 - 22 * q^95 - 16 * q^96 + 3 * q^97 + 20 * q^98 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.831304	+	2.55849i	−0.587821	+	1.80913i	−0.000184800		1.00000i	$0.500059\pi$
$2$	−0.831304	+	2.55849i	−0.587821	+	1.80913i	−0.587636	+	0.809126i	$0.699941\pi$
$3$	0.438546	+	1.34971i	0.253195	+	0.779253i	0.994180	+	0.107732i	$0.0343587\pi$
$3$	0.438546	+	1.34971i	0.253195	+	0.779253i	−0.740985	+	0.671521i	$0.765641\pi$
$4$	−4.23677	−	3.07819i	−2.11839	−	1.53910i
$5$	0.608384			0.272077			0.136039	−	0.990704i	$-0.456563\pi$
$5$	0.608384			0.272077			0.136039	+	0.990704i	$0.456563\pi$
$6$	−3.81777			−1.55860
$7$	1.39707	+	1.01503i	0.528045	+	0.383647i	0.819626	−	0.572899i	$-0.194181\pi$
$7$	1.39707	+	1.01503i	0.528045	+	0.383647i	−0.291581	+	0.956546i	$0.594181\pi$
$8$	7.04481	−	5.11835i	2.49072	−	1.80961i
$9$	0.797669	−	0.579540i	0.265890	−	0.193180i
$10$	−0.505752	+	1.55654i	−0.159933	+	0.492222i
$11$	1.08197	+	0.786100i	0.326227	+	0.237018i	0.738828	−	0.673894i	$-0.235380\pi$
$11$	1.08197	+	0.786100i	0.326227	+	0.237018i	−0.412601	+	0.910912i	$0.635380\pi$
$12$	2.29664	−	7.06832i	0.662982	−	2.04045i
$13$	1.13430	+	3.49101i	0.314598	+	0.968232i	0.975920	+	0.218130i	$0.0699956\pi$
$13$	1.13430	+	3.49101i	0.314598	+	0.968232i	−0.661322	+	0.750102i	$0.730004\pi$
$14$	−3.75835	+	2.73060i	−1.00446	+	0.729783i
$15$	0.266804	+	0.821139i	0.0688885	+	0.212017i
$16$	4.00227	+	12.3177i	1.00057	+	3.07943i
$17$	2.23517	−	1.62394i	0.542108	−	0.393864i	−0.282759	−	0.959191i	$-0.591250\pi$
$17$	2.23517	−	1.62394i	0.542108	−	0.393864i	0.824867	+	0.565326i	$0.191250\pi$
$18$	0.819643	+	2.52260i	0.193192	+	0.594583i
$19$	−0.793456	+	2.44201i	−0.182031	+	0.560235i	−0.999885	−	0.0151921i	$-0.995164\pi$
$19$	−0.793456	+	2.44201i	−0.182031	+	0.560235i	0.817853	+	0.575427i	$0.195164\pi$
$20$	−2.57758	−	1.87272i	−0.576365	−	0.418754i
$21$	−0.757316	+	2.33078i	−0.165260	+	0.508617i
$22$	−2.91068	+	2.11473i	−0.620558	+	0.450862i
$23$	0.436271	−	0.316969i	0.0909688	−	0.0660927i	−0.541371	−	0.840784i	$-0.682095\pi$
$23$	0.436271	−	0.316969i	0.0909688	−	0.0660927i	0.632340	+	0.774691i	$0.282095\pi$
$24$	9.99774	+	7.26378i	2.04078	+	1.48271i
$25$	−4.62987			−0.925974
$26$	−9.87466			−1.93658
$27$	4.57641	+	3.32495i	0.880730	+	0.639888i
$28$	−2.79461	−	8.60093i	−0.528132	−	1.62542i
$29$	−2.51258	+	7.73291i	−0.466574	+	1.43597i	0.390419	+	0.920637i	$0.372330\pi$
$29$	−2.51258	+	7.73291i	−0.466574	+	1.43597i	−0.856993	+	0.515329i	$0.827670\pi$
$30$	−2.32267			−0.424060
$31$		0			0
$31$		0			0
$32$	−17.4262			−3.08054
$33$	−0.586508	+	1.80509i	−0.102098	+	0.314225i
$34$	2.29674	+	7.06865i	0.393888	+	1.21226i
$35$	0.849957	+	0.617530i	0.143669	+	0.104382i
$36$	−5.16348			−0.860580
$37$	7.74498			1.27327			0.636633	−	0.771167i	$-0.280327\pi$
$37$	7.74498			1.27327			0.636633	+	0.771167i	$0.280327\pi$
$38$	−5.58825	−	4.06010i	−0.906533	−	0.658635i
$39$	−4.21439	+	3.06194i	−0.674843	+	0.490302i
$40$	4.28595	−	3.11392i	0.677668	−	0.492354i
$41$	−0.0321538	+	0.0989592i	−0.00502158	+	0.0154548i	−0.953536	−	0.301279i	$-0.902586\pi$
$41$	−0.0321538	+	0.0989592i	−0.00502158	+	0.0154548i	0.948514	+	0.316734i	$0.102586\pi$
$42$	−5.33371	−	3.87517i	−0.823010	−	0.597952i
$43$	−0.928504	+	2.85764i	−0.141596	+	0.435786i	−0.996558	−	0.0829044i	$-0.973580\pi$
$43$	−0.928504	+	2.85764i	−0.141596	+	0.435786i	0.854962	+	0.518691i	$0.173580\pi$
$44$	−2.16431	−	6.66105i	−0.326281	−	1.00419i
$45$	0.485289	−	0.352583i	0.0723426	−	0.0525600i
$46$	0.448289	+	1.37969i	0.0660967	+	0.203425i
$47$	−2.07813	−	6.39584i	−0.303127	−	0.932929i	−0.980370	−	0.197169i	$-0.936825\pi$
$47$	−2.07813	−	6.39584i	−0.303127	−	0.932929i	0.677243	−	0.735760i	$-0.263175\pi$
$48$	−14.8701	+	10.8038i	−2.14632	+	1.55939i
$49$	−1.24160	−	3.82124i	−0.177371	−	0.545891i
$50$	3.84883	−	11.8455i	0.544306	−	1.67520i
$51$	3.17207	+	2.30464i	0.444179	+	0.322715i
$52$	5.94025	−	18.2822i	0.823764	−	2.53528i
$53$	−2.26423	+	1.64506i	−0.311016	+	0.225967i	−0.732332	−	0.680947i	$-0.761568\pi$
$53$	−2.26423	+	1.64506i	−0.311016	+	0.225967i	0.421316	+	0.906914i	$0.361568\pi$
$54$	−12.3112	+	8.94464i	−1.67535	+	1.21721i
$55$	0.658255	+	0.478250i	0.0887591	+	0.0644872i
$56$	15.0374			2.00946
$57$	−3.64396			−0.482654
$58$	−17.6959	−	12.8568i	−2.32358	−	1.68818i
$59$	0.144074	+	0.443414i	0.0187568	+	0.0577275i	0.959997	−	0.280011i	$-0.0903381\pi$
$59$	0.144074	+	0.443414i	0.0187568	+	0.0577275i	−0.941240	+	0.337738i	$0.890338\pi$
$60$	1.39724	−	4.30025i	0.180382	−	0.555160i
$61$	−5.11468			−0.654867			−0.327434	−	0.944874i	$-0.606184\pi$
$61$	−5.11468			−0.654867			−0.327434	+	0.944874i	$0.606184\pi$
$62$		0			0
$63$	1.70266			0.214514
$64$	6.48190	−	19.9492i	0.810238	−	2.49365i
$65$	0.690088	+	2.12387i	0.0855949	+	0.263434i
$66$	−4.13073	−	3.00115i	−0.508457	−	0.369416i
$67$	8.29847			1.01382			0.506910	−	0.861999i	$-0.330788\pi$
$67$	8.29847			1.01382			0.506910	+	0.861999i	$0.330788\pi$
$68$	−14.4687			−1.75459
$69$	0.619140	+	0.449832i	0.0745357	+	0.0541534i
$70$	−2.28652	+	1.66125i	−0.273291	+	0.198558i
$71$	−3.84988	+	2.79710i	−0.456896	+	0.331955i	−0.792312	−	0.610115i	$-0.791123\pi$
$71$	−3.84988	+	2.79710i	−0.456896	+	0.331955i	0.335416	+	0.942070i	$0.391123\pi$
$72$	2.65313	−	8.16550i	0.312675	−	0.962314i
$73$	−6.07264	−	4.41203i	−0.710748	−	0.516389i	0.172667	−	0.984980i	$-0.444762\pi$
$73$	−6.07264	−	4.41203i	−0.710748	−	0.516389i	−0.883415	+	0.468591i	$0.844762\pi$
$74$	−6.43843	+	19.8154i	−0.748452	+	2.30350i
$75$	−2.03041	−	6.24896i	−0.234452	−	0.721568i
$76$	10.8787	−	7.90381i	1.24787	−	0.906629i
$77$	0.713679	+	2.19648i	0.0813313	+	0.250312i
$78$	−4.33049	−	13.3279i	−0.490332	−	1.50909i
$79$	7.84662	−	5.70090i	0.882814	−	0.641402i	−0.0511806	−	0.998689i	$-0.516298\pi$
$79$	7.84662	−	5.70090i	0.882814	−	0.641402i	0.933994	+	0.357288i	$0.116298\pi$
$80$	2.43492	+	7.49391i	0.272232	+	0.837845i
$81$	−1.56670	+	4.82180i	−0.174077	+	0.535755i
$82$	−0.226457	−	0.164530i	−0.0250079	−	0.0181693i
$83$	−5.15582	+	15.8680i	−0.565925	+	1.74174i	0.0992626	+	0.995061i	$0.468352\pi$
$83$	−5.15582	+	15.8680i	−0.565925	+	1.74174i	−0.665187	+	0.746676i	$0.731648\pi$
$84$	10.3832	−	7.54381i	1.13290	−	0.823097i
$85$	1.35984	−	0.987981i	0.147495	−	0.107162i
$86$	−6.53938	−	4.75114i	−0.705160	−	0.512328i
$87$	−11.5390			−1.23711
$88$	11.6458			1.24145
$89$	12.3911	+	9.00268i	1.31346	+	0.954282i	0.999989	+	0.00468333i	$0.00149075\pi$
$89$	12.3911	+	9.00268i	1.31346	+	0.954282i	0.313468	+	0.949599i	$0.398509\pi$
$90$	0.498657	+	1.53471i	0.0525631	+	0.161773i
$91$	−1.95880	+	6.02855i	−0.205338	+	0.631964i
$92$	−2.82407			−0.294430
$93$		0			0
$94$	18.0912			1.86597
$95$	−0.482726	+	1.48568i	−0.0495266	+	0.152427i
$96$	−7.64218	−	23.5202i	−0.779977	−	2.40052i
$97$	1.03488	+	0.751881i	0.105076	+	0.0763420i	0.639082	−	0.769138i	$-0.279314\pi$
$97$	1.03488	+	0.751881i	0.105076	+	0.0763420i	−0.534007	+	0.845480i	$0.679314\pi$
$98$	10.8087			1.09185
$99$	1.31863			0.132528
$100$	19.6157	+	14.2516i	1.96157	+	1.42516i
$101$	−6.56941	+	4.77296i	−0.653681	+	0.474927i	−0.864523	−	0.502593i	$-0.832379\pi$
$101$	−6.56941	+	4.77296i	−0.653681	+	0.474927i	0.210842	+	0.977520i	$0.432379\pi$
$102$	−8.53336	+	6.19985i	−0.844929	+	0.613877i
$103$	4.68238	−	14.4109i	0.461369	−	1.41995i	−0.402123	−	0.915585i	$-0.631728\pi$
$103$	4.68238	−	14.4109i	0.461369	−	1.41995i	0.863492	−	0.504362i	$-0.168272\pi$
$104$	25.8591	+	18.7878i	2.53570	+	1.84229i
$105$	−0.460739	+	1.41801i	−0.0449635	+	0.138383i
$106$	−2.32661	−	7.16056i	−0.225980	−	0.695495i
$107$	10.0121	−	7.27420i	0.967904	−	0.703224i	0.0129314	−	0.999916i	$-0.495884\pi$
$107$	10.0121	−	7.27420i	0.967904	−	0.703224i	0.954973	+	0.296693i	$0.0958837\pi$
$108$	−9.15433	−	28.1741i	−0.880876	−	2.71106i
$109$	2.22788	+	6.85672i	0.213392	+	0.656755i	0.999264	+	0.0383645i	$0.0122148\pi$
$109$	2.22788	+	6.85672i	0.213392	+	0.656755i	−0.785871	+	0.618390i	$0.787785\pi$
$110$	−1.77081	+	1.28657i	−0.168840	+	0.122669i
$111$	3.39653	+	10.4534i	0.322384	+	0.992196i
$112$	−6.91144	+	21.2712i	−0.653070	+	2.00994i
$113$	−13.4878	−	9.79944i	−1.26882	−	0.921854i	−0.269668	−	0.962953i	$-0.586914\pi$
$113$	−13.4878	−	9.79944i	−1.26882	−	0.921854i	−0.999155	+	0.0410999i	$0.986914\pi$
$114$	3.02923	−	9.32302i	0.283714	−	0.873181i
$115$	0.265420	−	0.192839i	0.0247506	−	0.0179823i
$116$	34.4486	−	25.0284i	3.19847	−	2.32383i
$117$	2.92798	+	2.12730i	0.270691	+	0.196669i
$118$	−1.25424			−0.115462
$119$	4.77105			0.437362
$120$	6.08246	+	4.41917i	0.555250	+	0.403413i
$121$	−2.84647	−	8.76054i	−0.258770	−	0.796413i
$122$	4.25185	−	13.0859i	0.384944	−	1.18474i
$123$	−0.147667			−0.0133147
$124$		0			0
$125$	−5.85866			−0.524014
$126$	−1.41542	+	4.35623i	−0.126096	+	0.388084i
$127$	−3.98923	−	12.2776i	−0.353987	−	1.08946i	−0.956594	−	0.291423i	$-0.905871\pi$
$127$	−3.98923	−	12.2776i	−0.353987	−	1.08946i	0.602607	−	0.798038i	$-0.294129\pi$
$128$	17.4553	+	12.6820i	1.54285	+	1.12095i
$129$	−4.26417			−0.375439
$130$	−6.00758			−0.526900
$131$	1.97221	+	1.43289i	0.172313	+	0.125192i	0.670599	−	0.741820i	$-0.266037\pi$
$131$	1.97221	+	1.43289i	0.172313	+	0.125192i	−0.498286	+	0.867013i	$0.666037\pi$
$132$	8.04130	−	5.84235i	0.699906	−	0.508511i
$133$	−3.58724	+	2.60628i	−0.311053	+	0.225993i
$134$	−6.89855	+	21.2315i	−0.595944	+	1.83413i
$135$	2.78421	+	2.02285i	0.239627	+	0.174099i
$136$	7.43441	−	22.8808i	0.637495	−	1.96201i
$137$	2.51658	+	7.74524i	0.215006	+	0.661720i	0.999153	+	0.0411454i	$0.0131007\pi$
$137$	2.51658	+	7.74524i	0.215006	+	0.661720i	−0.784147	+	0.620575i	$0.786899\pi$
$138$	−1.66558	+	1.21012i	−0.141784	+	0.103012i
$139$	−0.418212	−	1.28712i	−0.0354723	−	0.109172i	0.931753	−	0.363094i	$-0.118280\pi$
$139$	−0.418212	−	1.28712i	−0.0354723	−	0.109172i	−0.967225	+	0.253921i	$0.918280\pi$
$140$	−1.70020	−	5.23267i	−0.143693	−	0.442241i
$141$	7.72114	−	5.60974i	0.650237	−	0.472425i
$142$	−3.95593	−	12.1751i	−0.331974	−	1.02171i
$143$	−1.51700	+	4.66885i	−0.126858	+	0.390429i
$144$	10.3311	+	7.50599i	0.860926	+	0.625499i
$145$	−1.52861	+	4.70458i	−0.126944	+	0.390694i
$146$	16.3363	−	11.8690i	1.35200	−	0.982289i
$147$	4.61305	−	3.35158i	0.380478	−	0.276433i
$148$	−32.8137	−	23.8405i	−2.69727	−	1.95968i
$149$	−9.00385			−0.737624			−0.368812	−	0.929504i	$-0.620235\pi$
$149$	−9.00385			−0.737624			−0.368812	+	0.929504i	$0.620235\pi$
$150$	17.6758			1.44322
$151$	2.59566	+	1.88585i	0.211232	+	0.153469i	0.688371	−	0.725359i	$-0.258326\pi$
$151$	2.59566	+	1.88585i	0.211232	+	0.153469i	−0.477139	+	0.878828i	$0.658326\pi$
$152$	6.90931	+	21.2647i	0.560419	+	1.72479i
$153$	0.841782	−	2.59074i	0.0680541	−	0.209449i
$154$	−6.21295			−0.500654
$155$		0			0
$156$	27.2807			2.18420
$157$	−1.02803	+	3.16395i	−0.0820456	+	0.252510i	−0.983662	−	0.180027i	$-0.942382\pi$
$157$	−1.02803	+	3.16395i	−0.0820456	+	0.252510i	0.901616	+	0.432537i	$0.142382\pi$
$158$	8.06278	+	24.8147i	0.641440	+	1.97415i
$159$	−3.21332	−	2.33461i	−0.254833	−	0.185147i
$160$	−10.6018			−0.838146
$161$	0.931238			0.0733918
$162$	−11.0341	−	8.01676i	−0.866922	−	0.629856i
$163$	−1.40797	+	1.02295i	−0.110281	+	0.0801236i	−0.641559	−	0.767074i	$-0.721712\pi$
$163$	−1.40797	+	1.02295i	−0.110281	+	0.0801236i	0.531278	+	0.847198i	$0.321712\pi$
$164$	0.440844	−	0.320292i	0.0344241	−	0.0250106i
$165$	−0.356822	+	1.09818i	−0.0277785	+	0.0854936i
$166$	−36.3120	−	26.3822i	−2.81836	−	2.04766i
$167$	−4.33133	+	13.3305i	−0.335168	+	1.03154i	0.631471	+	0.775400i	$0.282452\pi$
$167$	−4.33133	+	13.3305i	−0.335168	+	1.03154i	−0.966639	+	0.256142i	$0.917548\pi$
$168$	6.59460	+	20.2961i	0.508785	+	1.56588i
$169$	−0.383297	+	0.278482i	−0.0294844	+	0.0214217i
$170$	1.39730	+	4.30045i	0.107168	+	0.329829i
$171$	0.782326	+	2.40775i	0.0598260	+	0.184125i
$172$	12.7302	−	9.24906i	0.970672	−	0.705234i
$173$	−0.00370230	−	0.0113945i	−0.000281480	−	0.000866308i	0.950916	−	0.309450i	$-0.100145\pi$
$173$	−0.00370230	−	0.0113945i	−0.000281480	−	0.000866308i	−0.951197	+	0.308584i	$0.900145\pi$
$174$	9.59244	−	29.5225i	0.727201	−	2.23810i
$175$	−6.46827	−	4.69947i	−0.488955	−	0.355247i
$176$	−5.35261	+	16.4736i	−0.403468	+	1.24175i
$177$	−0.535295	+	0.388914i	−0.0402352	+	0.0292326i
$178$	−33.3341	+	24.2186i	−2.49849	+	1.81526i
$179$	8.07238	+	5.86492i	0.603358	+	0.438365i	0.847069	−	0.531483i	$-0.178365\pi$
$179$	8.07238	+	5.86492i	0.603358	+	0.438365i	−0.243711	+	0.969848i	$0.578365\pi$
$180$	−3.14138			−0.234144
$181$	−18.6032			−1.38276			−0.691381	−	0.722490i	$-0.742997\pi$
$181$	−18.6032			−1.38276			−0.691381	+	0.722490i	$0.742997\pi$
$182$	−13.7956	−	10.0231i	−1.02260	−	0.742963i
$183$	−2.24302	−	6.90331i	−0.165809	−	0.510307i
$184$	1.45108	−	4.46598i	0.106975	−	0.329236i
$185$	4.71192			0.346427
$186$		0			0
$187$	3.69497			0.270203
$188$	−10.8831	+	33.4946i	−0.793728	+	2.44284i
$189$	3.01864	+	9.29042i	0.219574	+	0.675778i
$190$	−3.39980	−	2.47010i	−0.246647	−	0.179200i
$191$	1.19812			0.0866928			0.0433464	−	0.999060i	$-0.486198\pi$
$191$	1.19812			0.0866928			0.0433464	+	0.999060i	$0.486198\pi$
$192$	29.7682			2.14834
$193$	−10.2960	−	7.48048i	−0.741122	−	0.538457i	0.151940	−	0.988390i	$-0.451448\pi$
$193$	−10.2960	−	7.48048i	−0.741122	−	0.538457i	−0.893062	+	0.449933i	$0.851448\pi$
$194$	−2.78398	+	2.02268i	−0.199878	+	0.145220i
$195$	−2.56397	+	1.86283i	−0.183610	+	0.133400i
$196$	−6.50216	+	20.0116i	−0.464440	+	1.42940i
$197$	2.40164	+	1.74490i	0.171110	+	0.124319i	0.670044	−	0.742321i	$-0.266275\pi$
$197$	2.40164	+	1.74490i	0.171110	+	0.124319i	−0.498934	+	0.866640i	$0.666275\pi$
$198$	−1.09618	+	3.37371i	−0.0779024	+	0.239759i
$199$	−4.07410	−	12.5388i	−0.288805	−	0.888851i	−0.985232	−	0.171223i	$-0.945228\pi$
$199$	−4.07410	−	12.5388i	−0.288805	−	0.888851i	0.696427	−	0.717627i	$-0.254772\pi$
$200$	−32.6165	+	23.6973i	−2.30634	+	1.67565i
$201$	3.63926	+	11.2005i	0.256694	+	0.790021i
$202$	−6.75039	−	20.7755i	−0.474955	−	1.46176i
$203$	−11.3594	+	8.25311i	−0.797275	+	0.579255i
$204$	−6.34519	−	19.5285i	−0.444252	−	1.36727i
$205$	−0.0195618	+	0.0602052i	−0.00136626	+	0.00420491i
$206$	32.9776	+	23.9597i	2.29766	+	1.66935i
$207$	0.164303	−	0.505673i	0.0114199	−	0.0351467i
$208$	−38.4616	+	27.9440i	−2.66683	+	1.93757i
$209$	−2.77816	+	2.01845i	−0.192169	+	0.139619i
$210$	−3.24494	−	2.35759i	−0.223922	−	0.162689i
$211$	18.3323			1.26205			0.631023	−	0.775764i	$-0.282635\pi$
$211$	18.3323			1.26205			0.631023	+	0.775764i	$0.282635\pi$
$212$	14.6569			1.00664
$213$	−5.46361	−	3.96954i	−0.374360	−	0.271989i
$214$	10.2879	+	31.6629i	0.703266	+	2.16443i
$215$	−0.564887	+	1.73854i	−0.0385250	+	0.118568i
$216$	49.2582			3.35160
$217$		0			0
$218$	−19.3949			−1.31359
$219$	3.29181	−	10.1311i	0.222440	−	0.684599i
$220$	−1.31673	−	4.05247i	−0.0887738	−	0.273218i
$221$	8.20455	+	5.96096i	0.551898	+	0.400977i
$222$	−29.5686			−1.98451
$223$	9.39601			0.629203			0.314602	−	0.949224i	$-0.398129\pi$
$223$	9.39601			0.629203			0.314602	+	0.949224i	$0.398129\pi$
$224$	−24.3457	−	17.6882i	−1.62666	−	1.18184i
$225$	−3.69310	+	2.68320i	−0.246207	+	0.178880i
$226$	36.2842	−	26.3620i	2.41359	−	1.75358i
$227$	2.61411	−	8.04539i	0.173504	−	0.533991i	−0.826058	−	0.563585i	$-0.809422\pi$
$227$	2.61411	−	8.04539i	0.173504	−	0.533991i	0.999562	+	0.0295943i	$0.00942154\pi$
$228$	15.4386	+	11.2168i	1.02245	+	0.742851i
$229$	7.05901	−	21.7254i	0.466473	−	1.43565i	−0.390649	−	0.920540i	$-0.627749\pi$
$229$	7.05901	−	21.7254i	0.466473	−	1.43565i	0.857121	−	0.515115i	$-0.172251\pi$
$230$	0.272732	+	0.839383i	0.0179834	+	0.0553473i
$231$	−2.65162	+	1.92651i	−0.174464	+	0.126755i
$232$	21.8792	+	67.3372i	1.43644	+	4.42090i
$233$	5.02260	+	15.4580i	0.329042	+	1.01269i	0.969583	+	0.244762i	$0.0787099\pi$
$233$	5.02260	+	15.4580i	0.329042	+	1.01269i	−0.640542	+	0.767923i	$0.721290\pi$
$234$	−7.87671	+	5.72276i	−0.514917	+	0.374109i
$235$	−1.26430	−	3.89112i	−0.0824740	−	0.253829i
$236$	0.754505	−	2.32213i	0.0491141	−	0.151158i
$237$	11.1356	+	8.09052i	0.723338	+	0.525536i
$238$	−3.96620	+	12.2067i	−0.257090	+	0.791243i
$239$	−14.7832	+	10.7406i	−0.956243	+	0.694751i	−0.952275	−	0.305241i	$-0.901263\pi$
$239$	−14.7832	+	10.7406i	−0.956243	+	0.694751i	−0.00396806	+	0.999992i	$0.501263\pi$
$240$	−9.04675	+	6.57285i	−0.583965	+	0.424275i
$241$	14.7011	+	10.6810i	0.946981	+	0.688022i	0.950091	−	0.311974i	$-0.100990\pi$
$241$	14.7011	+	10.6810i	0.946981	+	0.688022i	−0.00311025	+	0.999995i	$0.500990\pi$
$242$	24.7800			1.59292
$243$	9.77517			0.627078
$244$	21.6697	+	15.7440i	1.38726	+	1.00790i
$245$	−0.755367	−	2.32478i	−0.0482586	−	0.148525i
$246$	0.122756	−	0.377804i	0.00782663	−	0.0240879i
$247$	−9.42508			−0.599704
$248$		0			0
$249$	−23.6782			−1.50054
$250$	4.87032	−	14.9893i	0.308026	−	0.948007i
$251$	−7.08583	−	21.8079i	−0.447253	−	1.37650i	−0.879994	−	0.474986i	$-0.842453\pi$
$251$	−7.08583	−	21.8079i	−0.447253	−	1.37650i	0.432740	−	0.901519i	$-0.357547\pi$
$252$	−7.21376	−	5.24111i	−0.454424	−	0.330159i
$253$	0.721203			0.0453417
$254$	34.7284			2.17905
$255$	1.92984	+	1.40211i	0.120851	+	0.0878034i
$256$	−13.0179	+	9.45807i	−0.813620	+	0.591129i
$257$	−0.0859120	+	0.0624187i	−0.00535904	+	0.00389357i	−0.590462	−	0.807066i	$-0.701054\pi$
$257$	−0.0859120	+	0.0624187i	−0.00535904	+	0.00389357i	0.585103	+	0.810959i	$0.301054\pi$
$258$	3.54482	−	10.9098i	0.220691	−	0.679216i
$259$	10.8203	+	7.86142i	0.672341	+	0.488485i
$260$	3.61395	−	11.1226i	0.224128	−	0.689794i
$261$	2.47733	+	7.62444i	0.153343	+	0.471941i
$262$	−5.30555	+	3.85471i	−0.327778	+	0.238145i
$263$	−2.25499	−	6.94015i	−0.139049	−	0.427948i	0.857149	−	0.515068i	$-0.172234\pi$
$263$	−2.25499	−	6.94015i	−0.139049	−	0.427948i	−0.996198	+	0.0871204i	$0.972234\pi$
$264$	5.10723	+	15.7184i	0.314328	+	0.967403i
$265$	−1.37752	+	1.00083i	−0.0846205	+	0.0614804i
$266$	−3.68606	−	11.3445i	−0.226007	−	0.695577i
$267$	−6.71689	+	20.6725i	−0.411067	+	1.26513i
$268$	−35.1587	−	25.5443i	−2.14766	−	1.56037i
$269$	5.01206	−	15.4255i	0.305591	−	0.940511i	−0.673866	−	0.738854i	$-0.735367\pi$
$269$	5.01206	−	15.4255i	0.305591	−	0.940511i	0.979456	−	0.201657i	$-0.0646327\pi$
$270$	−7.48996	+	5.44178i	−0.455825	+	0.331176i
$271$	4.16291	−	3.02453i	0.252879	−	0.183727i	−0.454123	−	0.890939i	$-0.650047\pi$
$271$	4.16291	−	3.02453i	0.252879	−	0.183727i	0.707002	+	0.707212i	$0.250047\pi$
$272$	28.9491	+	21.0327i	1.75530	+	1.27530i
$273$	−8.99579			−0.544450
$274$	−21.9082			−1.32352
$275$	−5.00939	−	3.63954i	−0.302078	−	0.219472i
$276$	−1.23849	−	3.81167i	−0.0745481	−	0.229435i
$277$	−5.22944	+	16.0946i	−0.314207	+	0.967029i	0.661873	+	0.749616i	$0.269762\pi$
$277$	−5.22944	+	16.0946i	−0.314207	+	0.967029i	−0.976080	+	0.217413i	$0.930238\pi$
$278$	3.64076			0.218358
$279$		0			0
$280$	9.14853			0.546729
$281$	0.589193	−	1.81335i	0.0351483	−	0.108175i	−0.931943	−	0.362605i	$-0.881888\pi$
$281$	0.589193	−	1.81335i	0.0351483	−	0.108175i	0.967091	+	0.254429i	$0.0818876\pi$
$282$	7.93384	+	24.4178i	0.472453	+	1.45406i
$283$	12.3859	+	8.99888i	0.736265	+	0.534928i	0.891539	−	0.452944i	$-0.149626\pi$
$283$	12.3859	+	8.99888i	0.736265	+	0.534928i	−0.155274	+	0.987871i	$0.549626\pi$
$284$	24.9211			1.47879
$285$	−2.21692			−0.131319
$286$	−10.6841	−	7.76247i	−0.631765	−	0.459004i
$287$	−0.145368	+	0.105616i	−0.00858081	+	0.00623433i
$288$	−13.9003	+	10.0992i	−0.819084	+	0.595100i
$289$	−2.89451	+	8.90838i	−0.170265	+	0.524023i
$290$	−10.7659	−	7.82187i	−0.632194	−	0.459316i
$291$	−0.560978	+	1.72651i	−0.0328851	+	0.101210i
$292$	12.1473	+	37.3855i	0.710866	+	2.18782i
$293$	−21.6765	+	15.7489i	−1.26636	+	0.920062i	−0.999051	−	0.0435500i	$-0.986133\pi$
$293$	−21.6765	+	15.7489i	−1.26636	+	0.920062i	−0.267305	+	0.963612i	$0.586133\pi$
$294$	4.74013	+	14.5886i	0.276450	+	0.850826i
$295$	0.0876522	+	0.269766i	0.00510331	+	0.0157064i
$296$	54.5619	−	39.6415i	3.17135	−	2.30412i
$297$	2.33780	+	7.19502i	0.135653	+	0.417498i
$298$	7.48493	−	23.0363i	0.433591	−	1.33445i
$299$	1.60140	+	1.16349i	0.0926116	+	0.0672863i
$300$	−10.6331	+	32.7254i	−0.613904	+	1.88940i
$301$	−4.19779	+	3.04988i	−0.241957	+	0.175792i
$302$	−6.98272	+	5.07324i	−0.401810	+	0.291932i
$303$	−9.32307	−	6.77361i	−0.535597	−	0.389134i
$304$	−33.2556			−1.90734
$305$	−3.11169			−0.178175
$306$	5.92860	+	4.30738i	0.338916	+	0.246237i
$307$	2.76609	+	8.51316i	0.157869	+	0.485871i	0.998440	−	0.0558298i	$-0.0177804\pi$
$307$	2.76609	+	8.51316i	0.157869	+	0.485871i	−0.840571	+	0.541701i	$0.817780\pi$
$308$	3.73749	−	11.5028i	0.212963	−	0.655434i
$309$	21.5039			1.22331
$310$		0			0
$311$	20.6556			1.17127			0.585637	−	0.810574i	$-0.300844\pi$
$311$	20.6556			1.17127			0.585637	+	0.810574i	$0.300844\pi$
$312$	−14.0175	+	43.1415i	−0.793586	+	2.44241i
$313$	0.139466	+	0.429232i	0.00788307	+	0.0242616i	0.954921	−	0.296861i	$-0.0959398\pi$
$313$	0.139466	+	0.429232i	0.00788307	+	0.0242616i	−0.947038	+	0.321123i	$0.895940\pi$
$314$	−7.24032	−	5.26040i	−0.408595	−	0.296862i
$315$	1.03587			0.0583646
$316$	−50.7928			−2.85732
$317$	4.51500	+	3.28034i	0.253588	+	0.184242i	0.707315	−	0.706898i	$-0.249906\pi$
$317$	4.51500	+	3.28034i	0.253588	+	0.184242i	−0.453728	+	0.891140i	$0.649906\pi$
$318$	8.64432	−	6.28047i	0.484750	−	0.352191i
$319$	−8.79738	+	6.39167i	−0.492559	+	0.357865i
$320$	3.94348	−	12.1368i	0.220447	−	0.678467i
$321$	14.2088	+	10.3233i	0.793057	+	0.576190i
$322$	−0.774142	+	2.38256i	−0.0431412	+	0.132775i
$323$	2.19218	+	6.74682i	0.121976	+	0.375403i
$324$	21.4802	−	15.6063i	1.19334	−	0.867014i
$325$	−5.25165	−	16.1629i	−0.291309	−	0.896557i
$326$	−1.44676	−	4.45266i	−0.0801284	−	0.246610i
$327$	−8.27752	+	6.01397i	−0.457748	+	0.332573i
$328$	0.279991	+	0.861723i	0.0154599	+	0.0475807i
$329$	3.58868	−	11.0448i	0.197851	−	0.608922i
$330$	−2.51307	−	1.82585i	−0.138340	−	0.100510i
$331$	7.47990	−	23.0208i	0.411132	−	1.26534i	−0.504533	−	0.863393i	$-0.668335\pi$
$331$	7.47990	−	23.0208i	0.411132	−	1.26534i	0.915665	−	0.401943i	$-0.131665\pi$
$332$	70.6888	−	51.3584i	3.87955	−	2.81866i
$333$	6.17793	−	4.48853i	0.338548	−	0.245970i
$334$	−30.5052	−	22.1633i	−1.66917	−	1.21272i
$335$	5.04865			0.275837
$336$	−31.7409			−1.73161
$337$	−8.92830	−	6.48679i	−0.486355	−	0.353358i	0.317426	−	0.948283i	$-0.397182\pi$
$337$	−8.92830	−	6.48679i	−0.486355	−	0.353358i	−0.803781	+	0.594925i	$0.797182\pi$
$338$	−0.393857	−	1.21217i	−0.0214230	−	0.0659331i
$339$	7.31135	−	22.5020i	0.397098	−	1.22214i
$340$	−8.80253			−0.477384
$341$		0			0
$342$	−6.81056			−0.368273
$343$	5.87953	−	18.0953i	0.317465	−	0.977056i
$344$	8.08529	+	24.8840i	0.435930	+	1.34165i
$345$	0.376675	+	0.273670i	0.0202795	+	0.0147339i
$346$	0.0322304			0.00173272
$347$	−18.5674			−0.996749			−0.498375	−	0.866962i	$-0.666070\pi$
$347$	−18.5674			−0.996749			−0.498375	+	0.866962i	$0.666070\pi$
$348$	48.8883	+	35.5194i	2.62069	+	1.90404i
$349$	26.0298	−	18.9118i	1.39334	−	1.01232i	0.397855	−	0.917448i	$-0.369755\pi$
$349$	26.0298	−	18.9118i	1.39334	−	1.01232i	0.995489	−	0.0948756i	$-0.0302453\pi$
$350$	17.4007	−	12.6423i	0.930104	−	0.675760i
$351$	−6.41644	+	19.7478i	−0.342484	+	1.05406i
$352$	−18.8547	−	13.6987i	−1.00496	−	0.730144i
$353$	9.95448	−	30.6367i	0.529824	−	1.63063i	−0.224752	−	0.974416i	$-0.572157\pi$
$353$	9.95448	−	30.6367i	0.529824	−	1.63063i	0.754575	−	0.656213i	$-0.227843\pi$
$354$	−0.550041	−	1.69285i	−0.0292343	−	0.0899741i
$355$	−2.34220	+	1.70171i	−0.124311	+	0.0903174i
$356$	−24.7864	−	76.2846i	−1.31367	−	4.04307i
$357$	2.09233	+	6.43952i	0.110738	+	0.340815i
$358$	−21.7159	+	15.7776i	−1.14772	+	0.833870i
$359$	6.53950	+	20.1265i	0.345142	+	1.06224i	0.961508	+	0.274777i	$0.0886040\pi$
$359$	6.53950	+	20.1265i	0.345142	+	1.06224i	−0.616367	+	0.787459i	$0.711396\pi$
$360$	1.61412	−	4.96776i	0.0850717	−	0.261824i
$361$	10.0375	+	7.29267i	0.528289	+	0.383825i
$362$	15.4649	−	47.5960i	0.812816	−	2.50159i
$363$	10.5758	−	7.68380i	0.555088	−	0.403295i
$364$	26.8560	−	19.5120i	1.40764	−	1.02271i
$365$	−3.69449	−	2.68421i	−0.193379	−	0.140498i
$366$	19.5267			1.02068
$367$	12.9964			0.678408			0.339204	−	0.940713i	$-0.389842\pi$
$367$	12.9964			0.678408			0.339204	+	0.940713i	$0.389842\pi$
$368$	5.65042	+	4.10527i	0.294549	+	0.214002i
$369$	0.0317028	+	0.0975711i	0.00165038	+	0.00507935i
$370$	−3.91704	+	12.0554i	−0.203637	+	0.626730i
$371$	−4.83309			−0.250922
$372$		0			0
$373$	−4.42592			−0.229166			−0.114583	−	0.993414i	$-0.536553\pi$
$373$	−4.42592			−0.229166			−0.114583	+	0.993414i	$0.536553\pi$
$374$	−3.07165	+	9.45355i	−0.158831	+	0.488832i
$375$	−2.56929	−	7.90746i	−0.132678	−	0.408339i
$376$	−47.3762	−	34.4208i	−2.44324	−	1.77512i
$377$	−29.8457			−1.53713
$378$	−26.2788			−1.35164
$379$	12.0994	+	8.79076i	0.621507	+	0.451551i	0.853448	−	0.521179i	$-0.174508\pi$
$379$	12.0994	+	8.79076i	0.621507	+	0.451551i	−0.231941	+	0.972730i	$0.574508\pi$
$380$	6.61840	−	4.80855i	0.339517	−	0.246673i
$381$	14.8217	−	10.7686i	0.759338	−	0.551691i
$382$	−0.996000	+	3.06537i	−0.0509598	+	0.156838i
$383$	9.42533	+	6.84790i	0.481612	+	0.349911i	0.801949	−	0.597392i	$-0.203796\pi$
$383$	9.42533	+	6.84790i	0.481612	+	0.349911i	−0.320338	+	0.947303i	$0.603796\pi$
$384$	−9.46206	+	29.1212i	−0.482859	+	1.48609i
$385$	0.434191	+	1.33630i	0.0221284	+	0.0681043i
$386$	27.6978	−	20.1237i	1.40978	−	1.02427i
$387$	0.915480	+	2.81756i	0.0465365	+	0.143225i
$388$	−2.07009	−	6.37110i	−0.105093	−	0.323443i
$389$	−11.6514	+	8.46524i	−0.590750	+	0.429205i	−0.842584	−	0.538566i	$-0.818966\pi$
$389$	−11.6514	+	8.46524i	−0.590750	+	0.429205i	0.251834	+	0.967771i	$0.418966\pi$
$390$	−2.63460	−	8.10847i	−0.133408	−	0.410588i
$391$	0.460398	−	1.41696i	0.0232833	−	0.0716587i
$392$	−28.3053	−	20.5650i	−1.42963	−	1.03869i
$393$	−1.06908	+	3.29029i	−0.0539280	+	0.165973i
$394$	−6.46080	+	4.69404i	−0.325490	+	0.236483i
$395$	4.77376	−	3.46834i	0.240194	−	0.174511i
$396$	−5.58674	−	4.05901i	−0.280744	−	0.203973i
$397$	15.7901			0.792484			0.396242	−	0.918146i	$-0.370314\pi$
$397$	15.7901			0.792484			0.396242	+	0.918146i	$0.370314\pi$
$398$	35.4672			1.77781
$399$	−5.09088	−	3.69874i	−0.254863	−	0.185169i
$400$	−18.5300	−	57.0295i	−0.926500	−	2.85148i
$401$	9.58670	−	29.5048i	0.478737	−	1.47340i	−0.362114	−	0.932134i	$-0.617945\pi$
$401$	9.58670	−	29.5048i	0.478737	−	1.47340i	0.840851	−	0.541267i	$-0.182055\pi$
$402$	−31.6817			−1.58014
$403$		0			0
$404$	42.5252			2.11571
$405$	−0.953153	+	2.93350i	−0.0473626	+	0.145767i
$406$	−11.6724	−	35.9238i	−0.579289	−	1.78287i
$407$	8.37986	+	6.08832i	0.415374	+	0.301787i
$408$	34.1426			1.69031
$409$	6.58582			0.325648			0.162824	−	0.986655i	$-0.447940\pi$
$409$	6.58582			0.325648			0.162824	+	0.986655i	$0.447940\pi$
$410$	−0.137772	−	0.100098i	−0.00680410	−	0.00494347i
$411$	−9.35015	+	6.79328i	−0.461209	+	0.335088i
$412$	−64.1977	+	46.6424i	−3.16279	+	2.29790i
$413$	−0.248798	+	0.765722i	−0.0122425	+	0.0376787i
$414$	1.15717	+	0.840736i	0.0568720	+	0.0413199i
$415$	−3.13672	+	9.65382i	−0.153975	+	0.473888i
$416$	−19.7665	−	60.8350i	−0.969131	−	2.98268i
$417$	1.55383	−	1.12893i	0.0760916	−	0.0552838i
$418$	−2.85469	−	8.78583i	−0.139627	−	0.429729i
$419$	−4.53389	−	13.9539i	−0.221495	−	0.681692i	−0.998628	−	0.0523559i	$-0.983327\pi$
$419$	−4.53389	−	13.9539i	−0.221495	−	0.681692i	0.777133	−	0.629336i	$-0.216673\pi$
$420$	6.31695	−	4.58953i	0.308235	−	0.223946i
$421$	−8.25566	−	25.4083i	−0.402356	−	1.23832i	−0.923083	−	0.384601i	$-0.874339\pi$
$421$	−8.25566	−	25.4083i	−0.402356	−	1.23832i	0.520727	−	0.853723i	$-0.325661\pi$
$422$	−15.2397	+	46.9030i	−0.741857	+	2.28320i
$423$	−5.36431	−	3.89740i	−0.260822	−	0.189498i
$424$	−7.53108	+	23.1783i	−0.365742	+	1.12564i
$425$	−10.3485	+	7.51865i	−0.501978	+	0.364708i
$426$	14.6980	−	10.6787i	0.712118	−	0.517384i
$427$	−7.14559	−	5.19157i	−0.345799	−	0.251238i
$428$	−64.8103			−3.13272
$429$	−6.96685			−0.336363
$430$	−3.97845	−	2.89052i	−0.191858	−	0.139393i
$431$	1.23236	+	3.79282i	0.0593608	+	0.182694i	0.976340	−	0.216241i	$-0.0693798\pi$
$431$	1.23236	+	3.79282i	0.0593608	+	0.182694i	−0.916979	+	0.398935i	$0.869380\pi$
$432$	−22.6399	+	69.6783i	−1.08926	+	3.35240i
$433$	18.0766			0.868704			0.434352	−	0.900743i	$-0.356977\pi$
$433$	18.0766			0.868704			0.434352	+	0.900743i	$0.356977\pi$
$434$		0			0
$435$	−7.02016			−0.336591
$436$	11.6673	−	35.9082i	0.558762	−	1.71969i
$437$	0.427880	+	1.31688i	0.0204683	+	0.0629948i
$438$	23.1839	+	16.8441i	1.10777	+	0.804843i
$439$	22.9086			1.09337			0.546684	−	0.837339i	$-0.315890\pi$
$439$	22.9086			1.09337			0.546684	+	0.837339i	$0.315890\pi$
$440$	7.08513			0.337771
$441$	−3.20494	−	2.32853i	−0.152616	−	0.110882i
$442$	−22.0715	+	16.0359i	−1.04984	+	0.762750i
$443$	17.3868	−	12.6323i	0.826074	−	0.600178i	−0.0923721	−	0.995725i	$-0.529445\pi$
$443$	17.3868	−	12.6323i	0.826074	−	0.600178i	0.918446	+	0.395547i	$0.129445\pi$
$444$	17.7874	−	54.7440i	0.844153	−	2.59803i
$445$	7.53856	+	5.47708i	0.357362	+	0.259639i
$446$	−7.81094	+	24.0396i	−0.369859	+	1.13831i
$447$	−3.94860	−	12.1525i	−0.186762	−	0.574796i
$448$	29.3049	−	21.2912i	1.38452	−	1.00592i
$449$	5.80940	+	17.8795i	0.274163	+	0.843786i	0.989440	+	0.144945i	$0.0463005\pi$
$449$	5.80940	+	17.8795i	0.274163	+	0.843786i	−0.715277	+	0.698841i	$0.753700\pi$
$450$	−3.79484	−	11.6793i	−0.178890	−	0.550568i
$451$	−0.112581	+	0.0817951i	−0.00530125	+	0.00385158i
$452$	26.9800	+	83.0359i	1.26903	+	3.90568i
$453$	−1.40703	+	4.33041i	−0.0661082	+	0.203460i
$454$	18.4109	+	13.3763i	0.864068	+	0.627782i
$455$	−1.19170	+	3.66767i	−0.0558677	+	0.171943i
$456$	−25.6710	+	18.6511i	−1.20215	+	0.873416i
$457$	−3.32182	+	2.41344i	−0.155388	+	0.112896i	−0.662763	−	0.748830i	$-0.730616\pi$
$457$	−3.32182	+	2.41344i	−0.155388	+	0.112896i	0.507374	+	0.861726i	$0.330616\pi$
$458$	49.7160	+	36.1208i	2.32308	+	1.68781i
$459$	15.6286			0.729480
$460$	−1.71812			−0.0801078
$461$	18.5063	+	13.4456i	0.861924	+	0.626225i	0.928408	−	0.371563i	$-0.121178\pi$
$461$	18.5063	+	13.4456i	0.861924	+	0.626225i	−0.0664836	+	0.997788i	$0.521178\pi$
$462$	−2.72467	−	8.38566i	−0.126763	−	0.390136i
$463$	−5.11947	+	15.7561i	−0.237922	+	0.732249i	0.758798	+	0.651326i	$0.225787\pi$
$463$	−5.11947	+	15.7561i	−0.237922	+	0.732249i	−0.996720	+	0.0809233i	$0.974213\pi$
$464$	−105.308			−4.88880
$465$		0			0
$466$	−43.7244			−2.02549
$467$	11.7878	−	36.2792i	0.545476	−	1.67880i	−0.174379	−	0.984679i	$-0.555792\pi$
$467$	11.7878	−	36.2792i	0.545476	−	1.67880i	0.719855	−	0.694124i	$-0.244208\pi$
$468$	−5.85692	−	18.0258i	−0.270736	−	0.833241i
$469$	11.5936	+	8.42323i	0.535342	+	0.388949i
$470$	11.0064			0.507688
$471$	−4.72123			−0.217543
$472$	3.28452	+	2.38634i	0.151182	+	0.109840i
$473$	−3.25101	+	2.36200i	−0.149482	+	0.108605i
$474$	−29.9566	+	21.7648i	−1.37595	+	0.999688i
$475$	3.67360	−	11.3062i	0.168556	−	0.518763i
$476$	−20.2139	−	14.6862i	−0.926501	−	0.673142i
$477$	−0.852728	+	2.62443i	−0.0390438	+	0.120164i
$478$	−15.1904	−	46.7513i	−0.694793	−	2.13835i
$479$	27.2515	−	19.7994i	1.24515	−	0.904658i	0.247224	−	0.968958i	$-0.420482\pi$
$479$	27.2515	−	19.7994i	1.24515	−	0.904658i	0.997931	+	0.0643004i	$0.0204816\pi$
$480$	−4.64938	−	14.3093i	−0.212214	−	0.653128i
$481$	8.78511	+	27.0378i	0.400567	+	1.23282i
$482$	−39.5482	+	28.7335i	−1.80137	+	1.30877i
$483$	0.408391	+	1.25690i	0.0185824	+	0.0571908i
$484$	−14.9068	+	45.8784i	−0.677582	+	2.08538i
$485$	0.629601	+	0.457432i	0.0285887	+	0.0207709i
$486$	−8.12614	+	25.0097i	−0.368609	+	1.13446i
$487$	16.7278	−	12.1534i	0.758008	−	0.550725i	−0.140291	−	0.990110i	$-0.544804\pi$
$487$	16.7278	−	12.1534i	0.758008	−	0.550725i	0.898299	+	0.439385i	$0.144804\pi$
$488$	−36.0319	+	26.1787i	−1.63109	+	1.18506i
$489$	−1.99814	−	1.45173i	−0.0903590	−	0.0656497i
$490$	6.57587			0.297067
$491$	24.7327			1.11617			0.558087	−	0.829783i	$-0.311536\pi$
$491$	24.7327			1.11617			0.558087	+	0.829783i	$0.311536\pi$
$492$	0.625630	+	0.454547i	0.0282056	+	0.0204925i
$493$	6.94179	+	21.3646i	0.312643	+	0.962215i
$494$	7.83511	−	24.1140i	0.352518	−	1.08494i
$495$	0.802235			0.0360578
$496$		0			0
$497$	−8.21771			−0.368615
$498$	19.6838	−	60.5804i	0.882050	−	2.71467i
$499$	−7.58951	−	23.3581i	−0.339753	−	1.04565i	−0.964333	−	0.264692i	$-0.914730\pi$
$499$	−7.58951	−	23.3581i	−0.339753	−	1.04565i	0.624580	−	0.780961i	$-0.285270\pi$
$500$	24.8218	+	18.0341i	1.11006	+	0.806509i
$501$	−19.8917			−0.888695
$502$	61.6858			2.75317
$503$	−11.9242	−	8.66344i	−0.531674	−	0.386284i	0.289310	−	0.957236i	$-0.406574\pi$
$503$	−11.9242	−	8.66344i	−0.531674	−	0.386284i	−0.820984	+	0.570952i	$0.806574\pi$
$504$	11.9949	−	8.71479i	0.534295	−	0.388188i
$505$	−3.99672	+	2.90379i	−0.177852	+	0.129217i
$506$	−0.599539	+	1.84519i	−0.0266528	+	0.0820287i
$507$	−0.543962	−	0.395212i	−0.0241582	−	0.0175520i
$508$	−20.8914	+	64.2970i	−0.926905	+	2.85272i
$509$	4.79171	+	14.7474i	0.212389	+	0.653665i	0.999329	+	0.0366357i	$0.0116641\pi$
$509$	4.79171	+	14.7474i	0.212389	+	0.653665i	−0.786940	+	0.617030i	$0.788336\pi$
$510$	−5.19156	+	3.77189i	−0.229886	+	0.167022i
$511$	−4.00557	−	12.3279i	−0.177196	−	0.545353i
$512$	−0.0418393	−	0.128768i	−0.00184905	−	0.00569080i
$513$	−11.7507	+	8.53741i	−0.518808	+	0.376936i
$514$	−0.0882787	−	0.271694i	−0.00389381	−	0.0119839i
$515$	2.84869	−	8.76735i	0.125528	−	0.386336i
$516$	18.0663	+	13.1259i	0.795325	+	0.577837i
$517$	2.77928	−	8.55374i	0.122233	−	0.376193i
$518$	−29.1083	+	21.1484i	−1.27895	+	0.929209i
$519$	0.0137556	−	0.00999402i	0.000603803	−	0.000438689i
$520$	15.7323	+	11.4302i	0.689906	+	0.501246i
$521$	29.4146			1.28867			0.644337	−	0.764741i	$-0.277133\pi$
$521$	29.4146			1.28867			0.644337	+	0.764741i	$0.277133\pi$
$522$	−21.5665			−0.943939
$523$	−36.4268	−	26.4656i	−1.59283	−	1.15726i	−0.899754	−	0.436397i	$-0.856254\pi$
$523$	−36.4268	−	26.4656i	−1.59283	−	1.15726i	−0.693078	−	0.720863i	$-0.743746\pi$
$524$	−3.94507	−	12.1417i	−0.172341	−	0.530412i
$525$	3.50627	−	10.7912i	0.153026	−	0.470966i
$526$	19.6309			0.855947
$527$		0			0
$528$	−24.5819			−1.06979
$529$	−7.01753	+	21.5977i	−0.305110	+	0.939032i
$530$	−1.41547	−	4.35637i	−0.0614841	−	0.189229i
$531$	0.371899	+	0.270201i	0.0161391	+	0.0117257i
$532$	23.2209			1.00676
$533$	−0.381940			−0.0165436
$534$	−47.3065	−	34.3702i	−2.04715	−	1.48734i
$535$	6.09119	−	4.42551i	0.263345	−	0.191331i
$536$	58.4611	−	42.4745i	2.52514	−	1.83462i
$537$	−4.37581	+	13.4674i	−0.188830	+	0.581160i
$538$	35.2995	+	25.6466i	1.52187	+	1.10570i
$539$	1.66050	−	5.11050i	0.0715228	−	0.220125i
$540$	−5.56935	−	17.1407i	−0.239667	−	0.737618i
$541$	−30.5636	+	22.2058i	−1.31403	+	0.954701i	−0.314047	+	0.949408i	$0.601685\pi$
$541$	−30.5636	+	22.2058i	−1.31403	+	0.954701i	−0.999986	+	0.00529319i	$0.998315\pi$
$542$	4.27759	+	13.1651i	0.183738	+	0.565488i
$543$	−8.15834	−	25.1088i	−0.350108	−	1.07752i
$544$	−38.9504	+	28.2992i	−1.66999	+	1.21332i
$545$	1.35541	+	4.17152i	0.0580593	+	0.178688i
$546$	7.47823	−	23.0156i	0.320039	−	0.984978i
$547$	14.7312	+	10.7028i	0.629860	+	0.457620i	0.856352	−	0.516393i	$-0.172726\pi$
$547$	14.7312	+	10.7028i	0.629860	+	0.457620i	−0.226491	+	0.974013i	$0.572726\pi$
$548$	13.1792	−	40.5613i	0.562986	−	1.73269i
$549$	−4.07982	+	2.96416i	−0.174122	+	0.126507i
$550$	13.4761	−	9.79092i	0.574621	−	0.417486i
$551$	−16.8902	−	12.2715i	−0.719547	−	0.522782i
$552$	6.66412			0.283644
$553$	16.7489			0.712237
$554$	−36.8305	−	26.7590i	−1.56478	−	1.13688i
$555$	2.06639	+	6.35970i	0.0877135	+	0.269954i
$556$	−2.19015	+	6.74059i	−0.0928831	+	0.285865i
$557$	−9.19760			−0.389715			−0.194857	−	0.980832i	$-0.562424\pi$
$557$	−9.19760			−0.389715			−0.194857	+	0.980832i	$0.562424\pi$
$558$		0			0
$559$	−11.0293			−0.466488
$560$	−4.20481	+	12.9411i	−0.177686	+	0.546860i
$561$	1.62042	+	4.98713i	0.0684140	+	0.210557i
$562$	4.14964	+	3.01489i	0.175042	+	0.127175i
$563$	−36.1618			−1.52404			−0.762019	−	0.647555i	$-0.775792\pi$
$563$	−36.1618			−1.52404			−0.762019	+	0.647555i	$0.775792\pi$
$564$	−49.9805			−2.10456
$565$	−8.20574	−	5.96182i	−0.345218	−	0.250816i
$566$	−33.3200	+	24.2084i	−1.40054	+	1.01755i
$567$	−7.08308	+	5.14616i	−0.297461	+	0.216118i
$568$	−12.8051	+	39.4101i	−0.537290	+	1.65361i
$569$	−33.5740	−	24.3930i	−1.40750	−	1.02261i	−0.993681	−	0.112245i	$-0.964196\pi$
$569$	−33.5740	−	24.3930i	−1.40750	−	1.02261i	−0.413816	−	0.910361i	$-0.635804\pi$
$570$	1.84294	−	5.67198i	0.0771921	−	0.237573i
$571$	−10.0100	−	30.8077i	−0.418907	−	1.28926i	−0.908710	−	0.417429i	$-0.862931\pi$
$571$	−10.0100	−	30.8077i	−0.418907	−	1.28926i	0.489803	−	0.871833i	$-0.337069\pi$
$572$	20.7988	−	15.1112i	0.869642	−	0.631832i
$573$	0.525430	+	1.61711i	0.0219501	+	0.0675556i
$574$	−0.149373	−	0.459722i	−0.00623470	−	0.0191884i
$575$	−2.01988	+	1.46753i	−0.0842347	+	0.0612001i
$576$	−6.39098	−	19.6694i	−0.266291	−	0.819559i
$577$	12.6643	−	38.9767i	0.527222	−	1.62262i	−0.232659	−	0.972558i	$-0.574743\pi$
$577$	12.6643	−	38.9767i	0.527222	−	1.62262i	0.759880	−	0.650063i	$-0.225257\pi$
$578$	−20.3858	−	14.8111i	−0.847937	−	0.616062i
$579$	5.58118	−	17.1771i	0.231946	−	0.713856i
$580$	20.9580	−	15.2269i	0.870233	−	0.632261i
$581$	−23.3096	+	16.9354i	−0.967046	+	0.702600i
$582$	−3.95092	−	2.87051i	−0.163771	−	0.118987i
$583$	−3.74302			−0.155020
$584$	−65.3629			−2.70474
$585$	1.78133	+	1.29421i	0.0736490	+	0.0535092i
$586$	−22.2737	−	68.5513i	−0.920117	−	2.83183i
$587$	7.88963	−	24.2818i	0.325640	−	1.00222i	−0.645511	−	0.763751i	$-0.723356\pi$
$587$	7.88963	−	24.2818i	0.325640	−	1.00222i	0.971151	−	0.238466i	$-0.0766445\pi$
$588$	−29.8612			−1.23146
$589$		0			0
$590$	−0.763058			−0.0314146
$591$	−1.30187	+	4.00673i	−0.0535516	+	0.164815i
$592$	30.9975	+	95.4006i	1.27399	+	3.92094i
$593$	−36.0269	−	26.1751i	−1.47945	−	1.07488i	−0.977734	−	0.209850i	$-0.932702\pi$
$593$	−36.0269	−	26.1751i	−1.47945	−	1.07488i	−0.501716	−	0.865033i	$-0.667298\pi$
$594$	−20.3518			−0.835045
$595$	2.90263			0.118996
$596$	38.1472	+	27.7156i	1.56257	+	1.13527i
$597$	15.1370	−	10.9977i	0.619515	−	0.450104i
$598$	−4.30803	+	3.12997i	−0.176168	+	0.127994i
$599$	5.86513	−	18.0510i	0.239643	−	0.737544i	−0.756829	−	0.653613i	$-0.773252\pi$
$599$	5.86513	−	18.0510i	0.239643	−	0.737544i	0.996472	−	0.0839312i	$-0.0267476\pi$
$600$	−46.2882	−	33.6304i	−1.88971	−	1.37295i
$601$	−3.96772	+	12.2114i	−0.161847	+	0.498113i	−0.998790	−	0.0491767i	$-0.984340\pi$
$601$	−3.96772	+	12.2114i	−0.161847	+	0.498113i	0.836943	+	0.547289i	$0.184340\pi$
$602$	−4.31343	−	13.2754i	−0.175802	−	0.541064i
$603$	6.61943	−	4.80930i	0.269564	−	0.195850i
$604$	−5.19217	−	15.9799i	−0.211267	−	0.650212i
$605$	−1.73175	−	5.32977i	−0.0704056	−	0.216686i
$606$	25.0805	−	18.2221i	1.01883	−	0.740221i
$607$	−11.7857	−	36.2726i	−0.478366	−	1.47226i	−0.841363	−	0.540470i	$-0.818246\pi$
$607$	−11.7857	−	36.2726i	−0.478366	−	1.47226i	0.362997	−	0.931790i	$-0.381754\pi$
$608$	13.8269	−	42.5548i	0.560755	−	1.72583i
$609$	−16.1209	−	11.7125i	−0.653252	−	0.474615i
$610$	2.58676	−	7.96122i	0.104735	−	0.322340i
$611$	19.9707	−	14.5096i	0.807928	−	0.586994i
$612$	−11.5412	+	8.38520i	−0.466527	+	0.338952i
$613$	15.0011	+	10.8989i	0.605889	+	0.440204i	0.847964	−	0.530054i	$-0.177828\pi$
$613$	15.0011	+	10.8989i	0.605889	+	0.440204i	−0.242076	+	0.970257i	$0.577828\pi$
$614$	−24.0803			−0.971801
$615$	−0.0898380			−0.00362262
$616$	16.2701	+	11.8209i	0.655541	+	0.476278i
$617$	2.51402	+	7.73736i	0.101211	+	0.311495i	0.988822	−	0.149098i	$-0.0476370\pi$
$617$	2.51402	+	7.73736i	0.101211	+	0.311495i	−0.887612	+	0.460592i	$0.847637\pi$
$618$	−17.8763	+	55.0175i	−0.719089	+	2.21313i
$619$	−5.36063			−0.215462			−0.107731	−	0.994180i	$-0.534359\pi$
$619$	−5.36063			−0.215462			−0.107731	+	0.994180i	$0.534359\pi$
$620$		0			0
$621$	3.05046			0.122411
$622$	−17.1711	+	52.8472i	−0.688499	+	2.11898i
$623$	8.17330	+	25.1548i	0.327456	+	1.00781i
$624$	−54.5833	−	39.6571i	−2.18508	−	1.58755i
$625$	19.5850			0.783401
$626$	−1.21412			−0.0485261
$627$	−3.94266	−	2.86451i	−0.157455	−	0.114398i
$628$	14.0948	−	10.2404i	0.562442	−	0.408638i
$629$	17.3113	−	12.5774i	0.690248	−	0.501494i
$630$	−0.861121	+	2.65026i	−0.0343079	+	0.105589i
$631$	−23.4995	−	17.0734i	−0.935501	−	0.679682i	0.0118321	−	0.999930i	$-0.496234\pi$
$631$	−23.4995	−	17.0734i	−0.935501	−	0.679682i	−0.947334	+	0.320248i	$0.896234\pi$
$632$	26.0987	−	80.3236i	1.03815	−	3.19510i
$633$	8.03955	+	24.7432i	0.319543	+	0.983453i
$634$	−12.1460	+	8.82462i	−0.482381	+	0.350470i
$635$	−2.42699	−	7.46949i	−0.0963120	−	0.296418i
$636$	6.42770	+	19.7824i	0.254875	+	0.784424i
$637$	11.9316	−	8.66885i	0.472749	−	0.343472i
$638$	−9.03973	−	27.8214i	−0.357886	−	1.10146i
$639$	−1.44989	+	4.46232i	−0.0573569	+	0.176527i
$640$	10.6195	+	7.71555i	0.419774	+	0.304984i
$641$	−8.53058	+	26.2544i	−0.336938	+	1.03699i	0.628822	+	0.777549i	$0.283537\pi$
$641$	−8.53058	+	26.2544i	−0.336938	+	1.03699i	−0.965760	+	0.259438i	$0.916463\pi$
$642$	−38.2238	+	27.7713i	−1.50857	+	1.09604i
$643$	3.42136	−	2.48577i	0.134925	−	0.0980291i	−0.518275	−	0.855214i	$-0.673426\pi$
$643$	3.42136	−	2.48577i	0.134925	−	0.0980291i	0.653201	+	0.757185i	$0.273426\pi$
$644$	−3.94544	−	2.86653i	−0.155472	−	0.112957i
$645$	−2.59425			−0.102148
$646$	−19.0840			−0.750852
$647$	21.2617	+	15.4475i	0.835883	+	0.607304i	0.921217	−	0.389048i	$-0.127196\pi$
$647$	21.2617	+	15.4475i	0.835883	+	0.607304i	−0.0853349	+	0.996352i	$0.527196\pi$
$648$	13.6426	+	41.9876i	0.535931	+	1.64943i
$649$	−0.192683	+	0.593018i	−0.00756348	+	0.0232780i
$650$	45.7184			1.79322
$651$		0			0
$652$	9.11408			0.356935
$653$	−4.12592	+	12.6983i	−0.161460	+	0.496922i	−0.998758	−	0.0498246i	$-0.984134\pi$
$653$	−4.12592	+	12.6983i	−0.161460	+	0.496922i	0.837298	+	0.546746i	$0.184134\pi$
$654$	−8.50555	−	26.1774i	−0.332593	−	1.02362i
$655$	1.19986	+	0.871749i	0.0468824	+	0.0340621i
$656$	−1.34764			−0.0526166
$657$	−7.40090			−0.288737
$658$	25.2748	+	18.3632i	0.985315	+	0.715873i
$659$	12.4717	−	9.06119i	0.485827	−	0.352974i	−0.317750	−	0.948174i	$-0.602927\pi$
$659$	12.4717	−	9.06119i	0.485827	−	0.352974i	0.803577	+	0.595200i	$0.202927\pi$
$660$	4.89220	−	3.55439i	0.190429	−	0.138354i
$661$	−1.45951	+	4.49190i	−0.0567682	+	0.174715i	−0.975420	−	0.220353i	$-0.929279\pi$
$661$	−1.45951	+	4.49190i	−0.0567682	+	0.174715i	0.918652	+	0.395068i	$0.129279\pi$
$662$	52.6803	+	38.2745i	2.04748	+	1.48758i
$663$	−4.44746	+	13.6879i	−0.172725	+	0.531593i
$664$	44.8962	+	138.176i	1.74231	+	5.36228i
$665$	−2.18242	+	1.58562i	−0.0846305	+	0.0614876i
$666$	6.34812	+	19.5375i	0.245984	+	0.757062i
$667$	1.35493	+	4.17006i	0.0524632	+	0.161465i
$668$	59.3846	−	43.1454i	2.29766	−	1.66935i
$669$	4.12058	+	12.6818i	0.159311	+	0.490309i
$670$	−4.19696	+	12.9169i	−0.162143	+	0.499024i
$671$	−5.53394	−	4.02065i	−0.213636	−	0.155215i
$672$	13.1971	−	40.6166i	0.509090	−	1.56682i
$673$	25.1386	−	18.2643i	0.969022	−	0.704035i	0.0137932	−	0.999905i	$-0.495609\pi$
$673$	25.1386	−	18.2643i	0.969022	−	0.704035i	0.955228	+	0.295869i	$0.0956093\pi$
$674$	24.0185	−	17.4505i	0.925158	−	0.672167i
$675$	−21.1882	−	15.3941i	−0.815533	−	0.592519i
$676$	2.48116			0.0954294
$677$	−9.03995			−0.347434			−0.173717	−	0.984796i	$-0.555578\pi$
$677$	−9.03995			−0.347434			−0.173717	+	0.984796i	$0.555578\pi$
$678$	51.4932	+	37.4120i	1.97759	+	1.43680i
$679$	0.682613	+	2.10087i	0.0261963	+	0.0806239i
$680$	4.52297	−	13.9203i	0.173448	−	0.533818i
$681$	12.0053			0.460044
$682$		0			0
$683$	7.13535			0.273027			0.136513	−	0.990638i	$-0.456410\pi$
$683$	7.13535			0.273027			0.136513	+	0.990638i	$0.456410\pi$
$684$	4.09699	−	12.6092i	0.156652	−	0.482127i
$685$	1.53105	+	4.71208i	0.0584983	+	0.180039i
$686$	41.4091	+	30.0854i	1.58101	+	1.14867i
$687$	32.4186			1.23685
$688$	−38.9158			−1.48365
$689$	−8.31124	−	6.03847i	−0.316633	−	0.230047i
$690$	−1.01331	+	0.736216i	−0.0385762	+	0.0280273i
$691$	−29.5092	+	21.4397i	−1.12258	+	0.815605i	−0.984599	−	0.174829i	$-0.944063\pi$
$691$	−29.5092	+	21.4397i	−1.12258	+	0.815605i	−0.137985	+	0.990434i	$0.544063\pi$
$692$	−0.0193887	+	0.0596723i	−0.000737047	+	0.00226840i
$693$	1.84223	+	1.33846i	0.0699805	+	0.0508438i
$694$	15.4351	−	47.5045i	0.585910	−	1.80324i
$695$	−0.254433	−	0.783066i	−0.00965121	−	0.0297034i
$696$	−81.2903	+	59.0609i	−3.08130	+	2.23870i
$697$	0.0888351	+	0.273406i	0.00336487	+	0.0103560i
$698$	26.7469	+	82.3185i	1.01238	+	3.11580i
$699$	−18.6611	+	13.5581i	−0.705827	+	0.512813i
$700$	12.9387	+	39.8212i	0.489037	+	1.50510i
$701$	−0.498890	+	1.53542i	−0.0188428	+	0.0579922i	−0.960036	−	0.279877i	$-0.909706\pi$
$701$	−0.498890	+	1.53542i	−0.0188428	+	0.0579922i	0.941193	+	0.337869i	$0.109706\pi$
$702$	−45.1905	−	32.8328i	−1.70560	−	1.23919i
$703$	−6.14530	+	18.9133i	−0.231774	+	0.713328i
$704$	22.6953	−	16.4891i	0.855362	−	0.621457i
$705$	4.69742	−	3.41287i	0.176915	−	0.128536i
$706$	70.1086	+	50.9369i	2.63857	+	1.91704i
$707$	−14.0227			−0.527377
$708$	3.46507			0.130225
$709$	−9.29395	−	6.75245i	−0.349042	−	0.253594i	0.399425	−	0.916766i	$-0.369210\pi$
$709$	−9.29395	−	6.75245i	−0.349042	−	0.253594i	−0.748467	+	0.663172i	$0.769210\pi$
$710$	−2.40672	−	7.40714i	−0.0903228	−	0.277985i
$711$	2.95510	−	9.09487i	0.110825	−	0.341084i
$712$	133.372			4.99833
$713$		0			0
$714$	−18.2148			−0.681672
$715$	−0.922919	+	2.84045i	−0.0345152	+	0.106227i
$716$	−16.1474	−	49.6967i	−0.603458	−	1.85725i
$717$	−20.9797	−	15.2427i	−0.783503	−	0.569248i
$718$	−56.9298			−2.12460
$719$	−14.1710			−0.528489			−0.264244	−	0.964456i	$-0.585123\pi$
$719$	−14.1710			−0.528489			−0.264244	+	0.964456i	$0.585123\pi$
$720$	6.28528	+	4.56652i	0.234239	+	0.170184i
$721$	21.1692	−	15.3803i	0.788382	−	0.572793i
$722$	−27.0024	+	19.6184i	−1.00493	+	0.730122i
$723$	−7.96906	+	24.5262i	−0.296372	+	0.912141i
$724$	78.8174	+	57.2642i	2.92922	+	2.12821i
$725$	11.6329	−	35.8024i	0.432035	−	1.32967i
$726$	10.8672	+	33.4458i	0.403319	+	1.24129i
$727$	21.8012	−	15.8395i	0.808561	−	0.587454i	−0.104852	−	0.994488i	$-0.533437\pi$
$727$	21.8012	−	15.8395i	0.808561	−	0.587454i	0.913413	+	0.407034i	$0.133437\pi$
$728$	17.0569	+	52.4958i	0.632172	+	1.94562i
$729$	8.98695	+	27.6590i	0.332850	+	1.02441i
$730$	9.93876	−	7.22093i	0.367850	−	0.267259i
$731$	2.56529	+	7.89515i	0.0948807	+	0.292013i
$732$	−11.7466	+	36.1522i	−0.434165	+	1.33622i
$733$	22.9951	+	16.7069i	0.849344	+	0.617085i	0.924965	−	0.380052i	$-0.124094\pi$
$733$	22.9951	+	16.7069i	0.849344	+	0.617085i	−0.0756209	+	0.997137i	$0.524094\pi$
$734$	−10.8040	+	33.2512i	−0.398782	+	1.22733i
$735$	2.80651	−	2.03905i	0.103519	−	0.0752113i
$736$	−7.60254	+	5.52357i	−0.280233	+	0.203601i
$737$	8.97872	+	6.52342i	0.330735	+	0.240293i
$738$	−0.275989			−0.0101593
$739$	−0.697306			−0.0256508			−0.0128254	−	0.999918i	$-0.504083\pi$
$739$	−0.697306			−0.0256508			−0.0128254	+	0.999918i	$0.504083\pi$
$740$	−19.9633	−	14.5042i	−0.733866	−	0.533185i
$741$	−4.13333	−	12.7211i	−0.151842	−	0.467321i
$742$	4.01777	−	12.3654i	0.147497	−	0.453949i
$743$	−18.1815			−0.667015			−0.333508	−	0.942747i	$-0.608232\pi$
$743$	−18.1815			−0.667015			−0.333508	+	0.942747i	$0.608232\pi$
$744$		0			0
$745$	−5.47779			−0.200691
$746$	3.67929	−	11.3237i	0.134708	−	0.414589i
$747$	5.08350	+	15.6454i	0.185996	+	0.572435i
$748$	−15.6548	−	11.3738i	−0.572395	−	0.415869i
$749$	21.3712			0.780886
$750$	22.3670			0.816728
$751$	29.9870	+	21.7868i	1.09424	+	0.795013i	0.980111	−	0.198452i	$-0.0635915\pi$
$751$	29.9870	+	21.7868i	1.09424	+	0.795013i	0.114131	+	0.993466i	$0.463592\pi$
$752$	70.4650	−	51.1958i	2.56959	−	1.86692i
$753$	26.3268	−	19.1276i	0.959403	−	0.697047i
$754$	24.8108	−	76.3599i	0.903557	−	2.78086i
$755$	1.57916	+	1.14732i	0.0574713	+	0.0417554i
$756$	15.8084	−	48.6533i	0.574947	−	1.76950i
$757$	1.97833	+	6.08867i	0.0719036	+	0.221296i	0.980550	−	0.196270i	$-0.0628830\pi$
$757$	1.97833	+	6.08867i	0.0719036	+	0.221296i	−0.908646	+	0.417567i	$0.862883\pi$
$758$	−32.5494	+	23.6485i	−1.18225	+	0.858953i
$759$	0.316281	+	0.973412i	0.0114803	+	0.0353326i
$760$	4.20351	+	12.9371i	0.152477	+	0.469277i
$761$	17.2635	−	12.5426i	0.625801	−	0.454671i	−0.229142	−	0.973393i	$-0.573592\pi$
$761$	17.2635	−	12.5426i	0.625801	−	0.454671i	0.854943	+	0.518722i	$0.173592\pi$
$762$	15.2300	+	46.8731i	0.551724	+	1.69803i
$763$	−3.84728	+	11.8407i	−0.139281	+	0.428663i
$764$	−5.07615	−	3.68804i	−0.183649	−	0.133429i
$765$	0.512127	−	1.57616i	0.0185160	−	0.0569863i
$766$	−25.3556	+	18.4219i	−0.916135	+	0.665611i
$767$	−1.38454	+	1.00593i	−0.0499928	+	0.0363219i
$768$	−18.4746	−	13.4226i	−0.666643	−	0.484345i
$769$	−12.2566			−0.441983			−0.220991	−	0.975276i	$-0.570929\pi$
$769$	−12.2566			−0.441983			−0.220991	+	0.975276i	$0.570929\pi$
$770$	−3.77986			−0.136217
$771$	−0.121923	−	0.0885824i	−0.00439096	−	0.00319022i
$772$	20.5954	+	63.3862i	0.741245	+	2.28132i
$773$	−10.7240	+	33.0050i	−0.385714	+	1.18711i	0.550247	+	0.835002i	$0.314534\pi$
$773$	−10.7240	+	33.0050i	−0.385714	+	1.18711i	−0.935961	+	0.352104i	$0.885466\pi$
$774$	−7.96974			−0.286466
$775$		0			0
$776$	11.1389			0.399863
$777$	−5.86539	+	18.0518i	−0.210420	+	0.647605i
$778$	−11.9724	−	36.8472i	−0.429231	−	1.32104i
$779$	−0.216146	−	0.157040i	−0.00774425	−	0.00562652i
$780$	16.5971			0.594272
$781$	−6.36426			−0.227731
$782$	3.24255	+	2.35585i	0.115953	+	0.0842450i
$783$	−37.2102	+	27.0348i	−1.32978	+	0.966144i
$784$	42.0998	−	30.5873i	1.50356	−	1.09240i
$785$	−0.625436	+	1.92489i	−0.0223228	+	0.0687024i
$786$	−7.52944	−	5.47046i	−0.268566	−	0.195125i
$787$	−6.21686	+	19.1335i	−0.221607	+	0.682037i	0.777011	+	0.629487i	$0.216735\pi$
$787$	−6.21686	+	19.1335i	−0.221607	+	0.682037i	−0.998618	+	0.0525500i	$0.983265\pi$
$788$	−4.80409	−	14.7855i	−0.171138	−	0.526710i
$789$	8.37824	−	6.08715i	0.298273	−	0.216708i
$790$	4.90526	+	15.0968i	0.174521	+	0.537122i
$791$	−8.89666	−	27.3811i	−0.316329	−	0.973559i
$792$	9.28952	−	6.74923i	0.330089	−	0.239823i
$793$	−5.80157	−	17.8554i	−0.206020	−	0.634063i
$794$	−13.1264	+	40.3989i	−0.465838	+	1.43370i
$795$	−1.95493	−	1.42034i	−0.0693342	−	0.0503743i
$796$	−21.3358	+	65.6648i	−0.756227	+	2.32743i
$797$	−21.1978	+	15.4011i	−0.750865	+	0.545536i	−0.896095	−	0.443862i	$-0.853608\pi$
$797$	−21.1978	+	15.4011i	−0.750865	+	0.545536i	0.145230	+	0.989398i	$0.453608\pi$
$798$	13.6953	−	9.95018i	0.484807	−	0.352233i
$799$	−15.0315	−	10.9210i	−0.531775	−	0.386357i
$800$	80.6809			2.85250
$801$	15.1014			0.533583
$802$	67.5183	+	49.0549i	2.38416	+	1.73219i
$803$	−3.10214	−	9.54739i	−0.109472	−	0.336920i
$804$	19.0586	−	58.6562i	0.672144	−	2.06865i
$805$	0.566550			0.0199683
$806$		0			0
$807$	23.0179			0.810270
$808$	−21.8506	+	67.2491i	−0.768700	+	2.36582i
$809$	11.2637	+	34.6662i	0.396011	+	1.21880i	0.928171	+	0.372153i	$0.121380\pi$
$809$	11.2637	+	34.6662i	0.396011	+	1.21880i	−0.532160	+	0.846644i	$0.678620\pi$
$810$	−6.71298	−	4.87727i	−0.235870	−	0.171370i
$811$	−19.1064			−0.670918			−0.335459	−	0.942055i	$-0.608891\pi$
$811$	−19.1064			−0.670918			−0.335459	+	0.942055i	$0.608891\pi$
$812$	73.5320			2.58047
$813$	5.90785	+	4.29231i	0.207197	+	0.150538i
$814$	−22.5431	+	16.3785i	−0.790136	+	0.574067i
$815$	−0.856586	+	0.622346i	−0.0300049	+	0.0217998i
$816$	−15.6925	+	48.2965i	−0.549347	+	1.69072i
$817$	−6.24165	−	4.53483i	−0.218368	−	0.158654i
$818$	−5.47482	+	16.8498i	−0.191422	+	0.589138i
$819$	1.93132	+	5.94399i	0.0674857	+	0.207700i
$820$	0.268202	−	0.194860i	0.00936603	−	0.00680482i
$821$	12.1937	+	37.5285i	0.425565	+	1.30975i	0.902453	+	0.430789i	$0.141765\pi$
$821$	12.1937	+	37.5285i	0.425565	+	1.30975i	−0.476888	+	0.878964i	$0.658235\pi$
$822$	−9.60773	−	29.5696i	−0.335108	−	1.03136i
$823$	25.5552	−	18.5669i	0.890799	−	0.647203i	−0.0452874	−	0.998974i	$-0.514420\pi$
$823$	25.5552	−	18.5669i	0.890799	−	0.647203i	0.936086	+	0.351771i	$0.114420\pi$
$824$	−40.7736	−	125.488i	−1.42041	−	4.37158i
$825$	2.71546	−	8.35731i	0.0945400	−	0.290964i
$826$	−1.75226	−	1.27309i	−0.0609691	−	0.0442966i
$827$	6.12776	−	18.8593i	0.213083	−	0.655802i	−0.786201	−	0.617971i	$-0.787955\pi$
$827$	6.12776	−	18.8593i	0.213083	−	0.655802i	0.999284	−	0.0378314i	$-0.0120450\pi$
$828$	−2.25268	+	1.63666i	−0.0782859	+	0.0568780i
$829$	−7.28104	+	5.28999i	−0.252881	+	0.183729i	−0.707003	−	0.707211i	$-0.749953\pi$
$829$	−7.28104	+	5.28999i	−0.252881	+	0.183729i	0.454122	+	0.890940i	$0.349953\pi$
$830$	−22.0916	−	16.0505i	−0.766812	−	0.557122i
$831$	−24.0163			−0.833115
$832$	76.9954			2.66933
$833$	−8.98066	−	6.52483i	−0.311161	−	0.226072i
$834$	1.59664	+	4.91395i	0.0552871	+	0.170156i
$835$	−2.63511	+	8.11003i	−0.0911917	+	0.280659i
$836$	17.9836			0.621976
$837$		0			0
$838$	39.4699			1.36347
$839$	−9.84070	+	30.2866i	−0.339739	+	1.04561i	0.624602	+	0.780944i	$0.285261\pi$
$839$	−9.84070	+	30.2866i	−0.339739	+	1.04561i	−0.964340	+	0.264665i	$0.914739\pi$
$840$	4.01205	+	12.3478i	0.138429	+	0.426040i
$841$	−30.0234	−	21.8133i	−1.03529	−	0.752183i
$842$	71.8698			2.47680
$843$	2.70587			0.0931953
$844$	−77.6697	−	56.4303i	−2.67350	−	1.94241i
$845$	−0.233192	+	0.169424i	−0.00802205	+	0.00582836i
$846$	14.4308	−	10.4846i	0.496142	−	0.360468i
$847$	4.91552	−	15.1284i	0.168899	−	0.519818i
$848$	−29.3255	−	21.3062i	−1.00704	−	0.731659i
$849$	−6.71405	+	20.6637i	−0.230426	+	0.709177i
$850$	−10.6336	−	32.7269i	−0.364730	−	1.12252i
$851$	3.37891	−	2.45492i	0.115828	−	0.0841536i
$852$	10.9290	+	33.6361i	0.374422	+	1.15235i
$853$	−15.1702	−	46.6890i	−0.519417	−	1.59860i	−0.775099	−	0.631839i	$-0.782300\pi$
$853$	−15.1702	−	46.6890i	−0.519417	−	1.59860i	0.255683	−	0.966761i	$-0.417700\pi$
$854$	19.2227	−	13.9661i	0.657788	−	0.477911i
$855$	0.475954	+	1.46484i	0.0162773	+	0.0500964i
$856$	33.3013	−	102.491i	1.13821	−	3.50306i
$857$	−15.5659	−	11.3093i	−0.531720	−	0.386317i	0.289281	−	0.957244i	$-0.406584\pi$
$857$	−15.5659	−	11.3093i	−0.531720	−	0.386317i	−0.821001	+	0.570927i	$0.806584\pi$
$858$	5.79157	−	17.8246i	0.197721	−	0.608522i
$859$	−3.75558	+	2.72859i	−0.128139	+	0.0930981i	−0.650008	−	0.759927i	$-0.725235\pi$
$859$	−3.75558	+	2.72859i	−0.128139	+	0.0930981i	0.521870	+	0.853025i	$0.325235\pi$
$860$	7.74487	−	5.62698i	0.264098	−	0.191878i
$861$	−0.206301	−	0.149887i	−0.00703073	−	0.00510812i
$862$	−10.7284			−0.365410
$863$	−38.5304			−1.31159			−0.655795	−	0.754939i	$-0.727667\pi$
$863$	−38.5304			−1.31159			−0.655795	+	0.754939i	$0.727667\pi$
$864$	−79.7493	−	57.9413i	−2.71313	−	1.97120i
$865$	−0.00225242	−	0.00693223i	−7.65845e−5	−	0.000235703i
$866$	−15.0271	+	46.2487i	−0.510642	+	1.57159i
$867$	−13.2931			−0.451456
$868$		0			0
$869$	12.9713			0.440022
$870$	5.83589	−	17.9610i	0.197855	−	0.608935i
$871$	9.41293	+	28.9700i	0.318945	+	0.981612i
$872$	50.7901	+	36.9012i	1.71997	+	1.24963i
$873$	1.26123			0.0426863
$874$	−3.72492			−0.125997
$875$	−8.18498	−	5.94673i	−0.276703	−	0.201036i
$876$	−45.1323	+	32.7905i	−1.52488	+	1.10789i
$877$	7.49016	−	5.44192i	0.252925	−	0.183761i	−0.454097	−	0.890952i	$-0.650038\pi$
$877$	7.49016	−	5.44192i	0.252925	−	0.183761i	0.707022	+	0.707192i	$0.250038\pi$
$878$	−19.0440	+	58.6114i	−0.642704	+	1.97804i
$879$	−30.7626	−	22.3503i	−1.03760	−	0.753857i
$880$	−3.25644	+	10.0223i	−0.109775	+	0.337852i
$881$	−5.52494	−	17.0040i	−0.186140	−	0.572880i	0.813826	−	0.581108i	$-0.197381\pi$
$881$	−5.52494	−	17.0040i	−0.186140	−	0.572880i	−0.999966	+	0.00822862i	$0.997381\pi$
$882$	8.62180	−	6.26410i	0.290311	−	0.210923i
$883$	−14.9303	−	45.9509i	−0.502446	−	1.54637i	−0.805022	−	0.593244i	$-0.797847\pi$
$883$	−14.9303	−	45.9509i	−0.502446	−	1.54637i	0.302577	−	0.953125i	$-0.402153\pi$
$884$	−16.4118	−	50.5104i	−0.551990	−	1.69885i
$885$	−0.325665	+	0.236609i	−0.0109471	+	0.00795353i
$886$	17.8658	+	54.9853i	0.600214	+	1.84727i
$887$	7.26568	−	22.3614i	0.243957	−	0.750824i	−0.751849	−	0.659336i	$-0.770838\pi$
$887$	7.26568	−	22.3614i	0.243957	−	0.750824i	0.995806	−	0.0914882i	$-0.0291624\pi$
$888$	77.4323	+	56.2578i	2.59846	+	1.88789i
$889$	6.88893	−	21.2019i	0.231047	−	0.711090i
$890$	−20.2799	+	14.7342i	−0.679784	+	0.493892i
$891$	−5.48554	+	3.98548i	−0.183772	+	0.133518i
$892$	−39.8087	−	28.9227i	−1.33290	−	0.968405i
$893$	17.2676			0.577838
$894$	34.3746			1.14966
$895$	4.91110	+	3.56812i	0.164160	+	0.119269i
$896$	11.5137	+	35.4355i	0.384646	+	1.18382i
$897$	−0.868078	+	2.67167i	−0.0289843	+	0.0892044i
$898$	−50.5739			−1.68767
$899$		0			0
$900$	23.9062			0.796874
$901$	−2.38945	+	7.35398i	−0.0796042	+	0.244996i
$902$	−0.115683	−	0.356035i	−0.00385181	−	0.0118547i
$903$	−5.95736	−	4.32827i	−0.198249	−	0.144036i
$904$	−145.176			−4.82847
$905$	−11.3179			−0.376219
$906$	−9.90963	−	7.19976i	−0.329225	−	0.239196i
$907$	10.1792	−	7.39560i	0.337994	−	0.245567i	−0.405821	−	0.913952i	$-0.633014\pi$
$907$	10.1792	−	7.39560i	0.337994	−	0.245567i	0.743815	+	0.668386i	$0.233014\pi$
$908$	−35.8406	+	26.0397i	−1.18941	+	0.864159i
$909$	−2.47409	+	7.61448i	−0.0820605	+	0.252556i
$910$	−8.39304	−	6.09790i	−0.278227	−	0.202143i
$911$	−14.6117	+	44.9702i	−0.484108	+	1.48993i	0.349162	+	0.937062i	$0.386466\pi$
$911$	−14.6117	+	44.9702i	−0.484108	+	1.48993i	−0.833269	+	0.552867i	$0.813534\pi$
$912$	−14.5841	−	44.8853i	−0.482928	−	1.48630i
$913$	−18.0523	+	13.1157i	−0.597443	+	0.434068i
$914$	−3.41333	−	10.5051i	−0.112903	−	0.347479i
$915$	−1.36462	−	4.19986i	−0.0451129	−	0.138843i
$916$	−96.7824	+	70.3165i	−3.19778	+	2.32332i
$917$	1.30089	+	4.00372i	0.0429591	+	0.132214i
$918$	−12.9921	+	39.9856i	−0.428803	+	1.31972i
$919$	18.7141	+	13.5966i	0.617320	+	0.448510i	0.851985	−	0.523567i	$-0.175399\pi$
$919$	18.7141	+	13.5966i	0.617320	+	0.448510i	−0.234664	+	0.972077i	$0.575399\pi$
$920$	0.882816	−	2.71703i	0.0291056	−	0.0895778i
$921$	−10.2772	+	7.46682i	−0.338645	+	0.246040i
$922$	−49.7848	+	36.1708i	−1.63958	+	1.19122i
$923$	−14.1316	−	10.2672i	−0.465147	−	0.337949i
$924$	17.1645			0.564670
$925$	−35.8582			−1.17901
$926$	−36.0560	−	26.1962i	−1.18488	−	0.860862i
$927$	−4.61670	−	14.2087i	−0.151632	−	0.466677i
$928$	43.7846	−	134.755i	1.43730	−	4.42355i
$929$	1.68694			0.0553468			0.0276734	−	0.999617i	$-0.491190\pi$
$929$	1.68694			0.0553468			0.0276734	+	0.999617i	$0.491190\pi$
$930$		0			0
$931$	10.3166			0.338114
$932$	26.3030	−	80.9524i	0.861585	−	2.65169i
$933$	9.05844	+	27.8790i	0.296560	+	0.912718i
$934$	83.0208	+	60.3181i	2.71652	+	1.97367i
$935$	2.24796			0.0735162
$936$	31.5153			1.03011
$937$	−15.9592	−	11.5950i	−0.521364	−	0.378793i	0.295753	−	0.955264i	$-0.404429\pi$
$937$	−15.9592	−	11.5950i	−0.521364	−	0.378793i	−0.817118	+	0.576471i	$0.804429\pi$
$938$	−31.1885	+	22.6598i	−1.01834	+	0.739868i
$939$	−0.518174	+	0.376475i	−0.0169100	+	0.0122858i
$940$	−6.62107	+	20.3776i	−0.215956	+	0.664643i
$941$	7.13817	+	5.18618i	0.232698	+	0.169065i	0.698024	−	0.716075i	$-0.254063\pi$
$941$	7.13817	+	5.18618i	0.232698	+	0.169065i	−0.465326	+	0.885139i	$0.654063\pi$
$942$	3.92478	−	12.0792i	0.127876	−	0.393563i
$943$	0.0173393	+	0.0533648i	0.000564644	+	0.00173780i
$944$	−4.88523	+	3.54933i	−0.159001	+	0.115521i
$945$	1.83649	+	5.65214i	0.0597411	+	0.183864i
$946$	−3.34057	−	10.2812i	−0.108611	−	0.334271i
$947$	−12.5893	+	9.14663i	−0.409096	+	0.297226i	−0.773236	−	0.634119i	$-0.781363\pi$
$947$	−12.5893	+	9.14663i	−0.409096	+	0.297226i	0.364140	+	0.931344i	$0.381363\pi$
$948$	−22.2750	−	68.5553i	−0.723458	−	2.22657i
$949$	8.51426	−	26.2042i	0.276384	−	0.850624i
$950$	25.8728	+	18.7977i	0.839426	+	0.609879i
$951$	−2.44746	+	7.53250i	−0.0793642	+	0.244258i
$952$	33.6112	−	24.4199i	1.08934	−	0.791455i
$953$	−7.80840	+	5.67314i	−0.252939	+	0.183771i	−0.707028	−	0.707185i	$-0.749965\pi$
$953$	−7.80840	+	5.67314i	−0.252939	+	0.183771i	0.454089	+	0.890956i	$0.349965\pi$
$954$	−6.00570	−	4.36339i	−0.194442	−	0.141270i
$955$	0.728916			0.0235872
$956$	95.6945			3.09498
$957$	−12.4849	−	9.07083i	−0.403580	−	0.293218i
$958$	28.0023	+	86.1821i	0.904712	+	2.78442i
$959$	−4.34583	+	13.3751i	−0.140334	+	0.431904i
$960$	18.1105			0.584514
$961$		0			0
$962$	−76.4790			−2.46578
$963$	3.77063	−	11.6048i	0.121507	−	0.373960i
$964$	−29.4071	−	90.5056i	−0.947138	−	2.91499i
$965$	−6.26392	−	4.55100i	−0.201643	−	0.146502i
$966$	−3.55525			−0.114388
$967$	28.3976			0.913204			0.456602	−	0.889671i	$-0.349066\pi$
$967$	28.3976			0.913204			0.456602	+	0.889671i	$0.349066\pi$
$968$	−64.8924	−	47.1471i	−2.08572	−	1.51537i
$969$	−8.14485	+	5.91758i	−0.261650	+	0.190100i
$970$	−1.69373	+	1.23056i	−0.0543823	+	0.0395110i
$971$	−6.83764	+	21.0441i	−0.219430	+	0.675337i	0.779379	+	0.626553i	$0.215535\pi$
$971$	−6.83764	+	21.0441i	−0.219430	+	0.675337i	−0.998809	+	0.0487844i	$0.984465\pi$
$972$	−41.4152	−	30.0899i	−1.32839	−	0.965134i
$973$	0.722202	−	2.22271i	0.0231527	−	0.0712568i
$974$	17.1886	+	52.9011i	0.550758	+	1.69506i
$975$	19.5121	−	14.1764i	0.624887	−	0.454007i
$976$	−20.4703	−	63.0012i	−0.655240	−	2.01662i
$977$	−6.15324	−	18.9377i	−0.196859	−	0.605871i	−0.999950	−	0.0100140i	$-0.996812\pi$
$977$	−6.15324	−	18.9377i	−0.196859	−	0.605871i	0.803090	−	0.595857i	$-0.203188\pi$
$978$	5.37531	−	3.90539i	0.171883	−	0.124881i
$979$	6.32986	+	19.4813i	0.202303	+	0.622626i
$980$	−3.95581	+	12.1747i	−0.126364	+	0.388907i
$981$	5.75086	+	4.17824i	0.183611	+	0.133401i
$982$	−20.5604	+	63.2785i	−0.656110	+	2.01930i
$983$	20.1691	−	14.6537i	0.643294	−	0.467381i	−0.217686	−	0.976019i	$-0.569851\pi$
$983$	20.1691	−	14.6537i	0.643294	−	0.467381i	0.860980	+	0.508638i	$0.169851\pi$
$984$	−1.04028	+	0.755810i	−0.0331630	+	0.0240944i
$985$	1.46112	+	1.06157i	0.0465552	+	0.0338243i
$986$	−60.4320			−1.92455
$987$	16.4811			0.524598
$988$	39.9319	+	29.0122i	1.27040	+	0.923002i
$989$	0.500706	+	1.54101i	0.0159215	+	0.0490014i
$990$	−0.666901	+	2.05251i	−0.0211955	+	0.0652330i
$991$	−42.0512			−1.33580			−0.667900	−	0.744251i	$-0.732807\pi$
$991$	−42.0512			−1.33580			−0.667900	+	0.744251i	$0.732807\pi$
$992$		0			0
$993$	34.3515			1.09011
$994$	6.83142	−	21.0249i	0.216679	−	0.666871i
$995$	−2.47861	−	7.62839i	−0.0785774	−	0.241836i
$996$	100.319	+	72.8860i	3.17873	+	2.30948i
$997$	14.4647			0.458100			0.229050	−	0.973415i	$-0.426438\pi$
$997$	14.4647			0.458100			0.229050	+	0.973415i	$0.426438\pi$
$998$	66.0707			2.09143
$999$	35.4442	+	25.7517i	1.12140	+	0.814748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.o.628.1		16
31.2	even	5		961.2.a.i.1.1		8
31.3	odd	30		961.2.g.n.816.2		16
31.4	even	5	inner	961.2.d.o.531.1		16
31.5	even	3		31.2.g.a.14.1	✓	16
31.6	odd	6		961.2.g.j.846.1		16
31.7	even	15		31.2.g.a.20.1	yes	16
31.8	even	5		961.2.d.p.388.4		16
31.9	even	15		961.2.g.t.338.2		16
31.10	even	15		961.2.c.j.521.1		16
31.11	odd	30		961.2.g.j.844.1		16
31.12	odd	30		961.2.c.i.439.1		16
31.13	odd	30		961.2.g.m.732.2		16
31.14	even	15		961.2.g.s.235.2		16
31.15	odd	10		961.2.d.q.374.4		16
31.16	even	5		961.2.d.p.374.4		16
31.17	odd	30		961.2.g.m.235.2		16
31.18	even	15		961.2.g.s.732.2		16
31.19	even	15		961.2.c.j.439.1		16
31.20	even	15		961.2.g.k.844.1		16
31.21	odd	30		961.2.c.i.521.1		16
31.22	odd	30		961.2.g.n.338.2		16
31.23	odd	10		961.2.d.q.388.4		16
31.24	odd	30		961.2.g.l.547.1		16
31.25	even	3		961.2.g.k.846.1		16
31.26	odd	6		961.2.g.l.448.1		16
31.27	odd	10		961.2.d.n.531.1		16
31.28	even	15		961.2.g.t.816.2		16
31.29	odd	10		961.2.a.j.1.1		8
31.30	odd	2		961.2.d.n.628.1		16
93.2	odd	10		8649.2.a.bf.1.8		8
93.5	odd	6		279.2.y.c.262.2		16
93.29	even	10		8649.2.a.be.1.8		8
93.38	odd	30		279.2.y.c.82.2		16
124.7	odd	30		496.2.bg.c.113.1		16
124.67	odd	6		496.2.bg.c.417.1		16
155.7	odd	60		775.2.ck.a.299.4		32
155.38	odd	60		775.2.ck.a.299.1		32
155.67	odd	12		775.2.ck.a.324.1		32
155.69	even	30		775.2.bl.a.51.2		16
155.98	odd	12		775.2.ck.a.324.4		32
155.129	even	6		775.2.bl.a.76.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.1	✓	16	31.5	even	3
31.2.g.a.20.1	yes	16	31.7	even	15
279.2.y.c.82.2		16	93.38	odd	30
279.2.y.c.262.2		16	93.5	odd	6
496.2.bg.c.113.1		16	124.7	odd	30
496.2.bg.c.417.1		16	124.67	odd	6
775.2.bl.a.51.2		16	155.69	even	30
775.2.bl.a.76.2		16	155.129	even	6
775.2.ck.a.299.1		32	155.38	odd	60
775.2.ck.a.299.4		32	155.7	odd	60
775.2.ck.a.324.1		32	155.67	odd	12
775.2.ck.a.324.4		32	155.98	odd	12
961.2.a.i.1.1		8	31.2	even	5
961.2.a.j.1.1		8	31.29	odd	10
961.2.c.i.439.1		16	31.12	odd	30
961.2.c.i.521.1		16	31.21	odd	30
961.2.c.j.439.1		16	31.19	even	15
961.2.c.j.521.1		16	31.10	even	15
961.2.d.n.531.1		16	31.27	odd	10
961.2.d.n.628.1		16	31.30	odd	2
961.2.d.o.531.1		16	31.4	even	5	inner
961.2.d.o.628.1		16	1.1	even	1	trivial
961.2.d.p.374.4		16	31.16	even	5
961.2.d.p.388.4		16	31.8	even	5
961.2.d.q.374.4		16	31.15	odd	10
961.2.d.q.388.4		16	31.23	odd	10
961.2.g.j.844.1		16	31.11	odd	30
961.2.g.j.846.1		16	31.6	odd	6
961.2.g.k.844.1		16	31.20	even	15
961.2.g.k.846.1		16	31.25	even	3
961.2.g.l.448.1		16	31.26	odd	6
961.2.g.l.547.1		16	31.24	odd	30
961.2.g.m.235.2		16	31.17	odd	30
961.2.g.m.732.2		16	31.13	odd	30
961.2.g.n.338.2		16	31.22	odd	30
961.2.g.n.816.2		16	31.3	odd	30
961.2.g.s.235.2		16	31.14	even	15
961.2.g.s.732.2		16	31.18	even	15
961.2.g.t.338.2		16	31.9	even	15
961.2.g.t.816.2		16	31.28	even	15
8649.2.a.be.1.8		8	93.29	even	10
8649.2.a.bf.1.8		8	93.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.831304 + 2.55849i) q^{2} +(0.438546 + 1.34971i) q^{3} +(-4.23677 - 3.07819i) q^{4} +0.608384 q^{5} -3.81777 q^{6} +(1.39707 + 1.01503i) q^{7} +(7.04481 - 5.11835i) q^{8} +(0.797669 - 0.579540i) q^{9} +(-0.505752 + 1.55654i) q^{10} +(1.08197 + 0.786100i) q^{11} +(2.29664 - 7.06832i) q^{12} +(1.13430 + 3.49101i) q^{13} +(-3.75835 + 2.73060i) q^{14} +(0.266804 + 0.821139i) q^{15} +(4.00227 + 12.3177i) q^{16} +(2.23517 - 1.62394i) q^{17} +(0.819643 + 2.52260i) q^{18} +(-0.793456 + 2.44201i) q^{19} +(-2.57758 - 1.87272i) q^{20} +(-0.757316 + 2.33078i) q^{21} +(-2.91068 + 2.11473i) q^{22} +(0.436271 - 0.316969i) q^{23} +(9.99774 + 7.26378i) q^{24} -4.62987 q^{25} -9.87466 q^{26} +(4.57641 + 3.32495i) q^{27} +(-2.79461 - 8.60093i) q^{28} +(-2.51258 + 7.73291i) q^{29} -2.32267 q^{30} -17.4262 q^{32} +(-0.586508 + 1.80509i) q^{33} +(2.29674 + 7.06865i) q^{34} +(0.849957 + 0.617530i) q^{35} -5.16348 q^{36} +7.74498 q^{37} +(-5.58825 - 4.06010i) q^{38} +(-4.21439 + 3.06194i) q^{39} +(4.28595 - 3.11392i) q^{40} +(-0.0321538 + 0.0989592i) q^{41} +(-5.33371 - 3.87517i) q^{42} +(-0.928504 + 2.85764i) q^{43} +(-2.16431 - 6.66105i) q^{44} +(0.485289 - 0.352583i) q^{45} +(0.448289 + 1.37969i) q^{46} +(-2.07813 - 6.39584i) q^{47} +(-14.8701 + 10.8038i) q^{48} +(-1.24160 - 3.82124i) q^{49} +(3.84883 - 11.8455i) q^{50} +(3.17207 + 2.30464i) q^{51} +(5.94025 - 18.2822i) q^{52} +(-2.26423 + 1.64506i) q^{53} +(-12.3112 + 8.94464i) q^{54} +(0.658255 + 0.478250i) q^{55} +15.0374 q^{56} -3.64396 q^{57} +(-17.6959 - 12.8568i) q^{58} +(0.144074 + 0.443414i) q^{59} +(1.39724 - 4.30025i) q^{60} -5.11468 q^{61} +1.70266 q^{63} +(6.48190 - 19.9492i) q^{64} +(0.690088 + 2.12387i) q^{65} +(-4.13073 - 3.00115i) q^{66} +8.29847 q^{67} -14.4687 q^{68} +(0.619140 + 0.449832i) q^{69} +(-2.28652 + 1.66125i) q^{70} +(-3.84988 + 2.79710i) q^{71} +(2.65313 - 8.16550i) q^{72} +(-6.07264 - 4.41203i) q^{73} +(-6.43843 + 19.8154i) q^{74} +(-2.03041 - 6.24896i) q^{75} +(10.8787 - 7.90381i) q^{76} +(0.713679 + 2.19648i) q^{77} +(-4.33049 - 13.3279i) q^{78} +(7.84662 - 5.70090i) q^{79} +(2.43492 + 7.49391i) q^{80} +(-1.56670 + 4.82180i) q^{81} +(-0.226457 - 0.164530i) q^{82} +(-5.15582 + 15.8680i) q^{83} +(10.3832 - 7.54381i) q^{84} +(1.35984 - 0.987981i) q^{85} +(-6.53938 - 4.75114i) q^{86} -11.5390 q^{87} +11.6458 q^{88} +(12.3911 + 9.00268i) q^{89} +(0.498657 + 1.53471i) q^{90} +(-1.95880 + 6.02855i) q^{91} -2.82407 q^{92} +18.0912 q^{94} +(-0.482726 + 1.48568i) q^{95} +(-7.64218 - 23.5202i) q^{96} +(1.03488 + 0.751881i) q^{97} +10.8087 q^{98} +1.31863 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 9 q^{3} - 14 q^{4} + 6 q^{5} - 22 q^{6} + 11 q^{7} + 17 q^{8} + 5 q^{9} + 19 q^{10} + 14 q^{11} + 5 q^{12} - q^{13} + 27 q^{14} + 14 q^{15} - 2 q^{16} - 3 q^{17} - 9 q^{18} + 13 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 + 9 * q^3 - 14 * q^4 + 6 * q^5 - 22 * q^6 + 11 * q^7 + 17 * q^8 + 5 * q^9 + 19 * q^10 + 14 * q^11 + 5 * q^12 - q^13 + 27 * q^14 + 14 * q^15 - 2 * q^16 - 3 * q^17 - 9 * q^18 + 13 * q^19 - 29 * q^20 - 3 * q^21 + 12 * q^22 + q^23 + 25 * q^24 + 26 * q^25 - 18 * q^26 + 9 * q^27 - 15 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 + 49 * q^34 - 9 * q^35 - 2 * q^36 + 16 * q^37 - 31 * q^38 - 3 * q^39 + 2 * q^40 + 16 * q^41 - 18 * q^42 + 14 * q^43 - 33 * q^44 + 5 * q^45 + 34 * q^46 + 14 * q^47 - 38 * q^48 + 41 * q^49 - 6 * q^50 + 9 * q^51 + 17 * q^52 + 3 * q^53 - 46 * q^54 - q^55 + 60 * q^56 + 34 * q^57 - 15 * q^58 + 7 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 - 6 * q^65 - 30 * q^66 - 26 * q^67 - 60 * q^68 - q^69 + 12 * q^70 - 17 * q^71 + q^72 + 11 * q^73 - 56 * q^74 + 4 * q^75 + 24 * q^76 + 18 * q^77 - 15 * q^78 - 6 * q^79 - 42 * q^80 - q^81 - 13 * q^82 - 28 * q^83 - 31 * q^84 + 37 * q^85 + 7 * q^86 - 30 * q^87 + 34 * q^88 + q^89 + 16 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 - 22 * q^95 - 16 * q^96 + 3 * q^97 + 20 * q^98 - 12 * q^99

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