LMFDB - Embedded newform 273.2.j.c.100.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(100,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("273.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.7
Root			$-0.707433 + 1.22531i$ of defining polynomial
Character	$\chi$	$=$	273.100
Dual form			273.2.j.c.172.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707433 + 1.22531i) q^{2} +1.00000 q^{3} +(-0.000924008 + 0.00160043i) q^{4} +(-1.42962 + 2.47618i) q^{5} +(0.707433 + 1.22531i) q^{6} +(-1.85598 + 1.88556i) q^{7} +2.82712 q^{8} +1.00000 q^{9} -4.04546 q^{10} +2.30705 q^{11} +(-0.000924008 + 0.00160043i) q^{12} +(-3.12586 + 1.79694i) q^{13} +(-3.62338 - 0.940248i) q^{14} +(-1.42962 + 2.47618i) q^{15} +(2.00185 + 3.46730i) q^{16} +(3.72581 - 6.45329i) q^{17} +(0.707433 + 1.22531i) q^{18} +0.565673 q^{19} +(-0.00264197 - 0.00457603i) q^{20} +(-1.85598 + 1.88556i) q^{21} +(1.63208 + 2.82685i) q^{22} +(0.398944 + 0.690991i) q^{23} +2.82712 q^{24} +(-1.58765 - 2.74989i) q^{25} +(-4.41315 - 2.55894i) q^{26} +1.00000 q^{27} +(-0.00130276 - 0.00471264i) q^{28} +(3.00672 - 5.20778i) q^{29} -4.04546 q^{30} +(-3.80370 - 6.58820i) q^{31} +(-0.00522698 + 0.00905339i) q^{32} +2.30705 q^{33} +10.5431 q^{34} +(-2.01563 - 7.29139i) q^{35} +(-0.000924008 + 0.00160043i) q^{36} +(-1.15073 - 1.99313i) q^{37} +(0.400176 + 0.693125i) q^{38} +(-3.12586 + 1.79694i) q^{39} +(-4.04172 + 7.00046i) q^{40} +(-5.68100 + 9.83978i) q^{41} +(-3.62338 - 0.940248i) q^{42} +(-3.76945 - 6.52888i) q^{43} +(-0.00213173 + 0.00369227i) q^{44} +(-1.42962 + 2.47618i) q^{45} +(-0.564452 + 0.977660i) q^{46} +(0.134822 - 0.233518i) q^{47} +(2.00185 + 3.46730i) q^{48} +(-0.110659 - 6.99913i) q^{49} +(2.24632 - 3.89073i) q^{50} +(3.72581 - 6.45329i) q^{51} +(1.24483e-5 - 0.00666311i) q^{52} +(2.35993 + 4.08751i) q^{53} +(0.707433 + 1.22531i) q^{54} +(-3.29821 + 5.71267i) q^{55} +(-5.24708 + 5.33070i) q^{56} +0.565673 q^{57} +8.50820 q^{58} +(2.91090 - 5.04183i) q^{59} +(-0.00264197 - 0.00457603i) q^{60} -2.93403 q^{61} +(5.38172 - 9.32142i) q^{62} +(-1.85598 + 1.88556i) q^{63} +7.99259 q^{64} +(0.0192600 - 10.3091i) q^{65} +(1.63208 + 2.82685i) q^{66} +3.17468 q^{67} +(0.00688536 + 0.0119258i) q^{68} +(0.398944 + 0.690991i) q^{69} +(7.50830 - 7.62794i) q^{70} +(-3.01045 - 5.21425i) q^{71} +2.82712 q^{72} +(5.31799 + 9.21103i) q^{73} +(1.62813 - 2.82001i) q^{74} +(-1.58765 - 2.74989i) q^{75} +(-0.000522686 + 0.000905319i) q^{76} +(-4.28184 + 4.35007i) q^{77} +(-4.41315 - 2.55894i) q^{78} +(-2.01404 + 3.48841i) q^{79} -11.4476 q^{80} +1.00000 q^{81} -16.0757 q^{82} +16.2573 q^{83} +(-0.00130276 - 0.00471264i) q^{84} +(10.6530 + 18.4516i) q^{85} +(5.33327 - 9.23749i) q^{86} +(3.00672 - 5.20778i) q^{87} +6.52230 q^{88} +(0.709194 + 1.22836i) q^{89} -4.04546 q^{90} +(2.41331 - 9.22908i) q^{91} -0.00147451 q^{92} +(-3.80370 - 6.58820i) q^{93} +0.381509 q^{94} +(-0.808700 + 1.40071i) q^{95} +(-0.00522698 + 0.00905339i) q^{96} +(-5.23049 - 9.05948i) q^{97} +(8.49782 - 5.08701i) q^{98} +2.30705 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) $ 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9 + 8 * q^10 + 16 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 - 20 * q^16 - 14 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 - 14 * q^23 - 12 * q^24 - 32 * q^25 + 4 * q^26 + 20 * q^27 + 13 * q^28 - 9 * q^29 + 8 * q^30 - 9 * q^31 + 17 * q^32 + 16 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 + 18 * q^37 + 22 * q^38 - 5 * q^39 - 9 * q^40 - q^41 - 9 * q^42 - 11 * q^43 + 8 * q^44 - 10 * q^46 + 13 * q^47 - 20 * q^48 - 21 * q^49 + 5 * q^50 - 2 * q^52 - 6 * q^53 - 19 * q^55 - 5 * q^56 - 14 * q^57 - 15 * q^59 + 12 * q^60 + 22 * q^62 - 9 * q^63 + 72 * q^64 - 27 * q^65 - 9 * q^66 + 44 * q^67 + 39 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 - 12 * q^72 - 3 * q^74 - 32 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 - 96 * q^80 + 20 * q^81 + 26 * q^82 + 40 * q^83 + 13 * q^84 - 16 * q^85 + 4 * q^86 - 9 * q^87 + 24 * q^88 + 2 * q^89 + 8 * q^90 + 9 * q^91 + 66 * q^92 - 9 * q^93 + 88 * q^94 - 36 * q^95 + 17 * q^96 + 21 * q^97 - 79 * q^98 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.707433	+	1.22531i	0.500231	+	0.866425i	1.00000		0.000266697i	$8.48923e-5\pi$
$2$	0.707433	+	1.22531i	0.500231	+	0.866425i	−0.499769	+	0.866159i	$0.666582\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.000924008		0.00160043i	−0.000462004		0.000800215i
$5$	−1.42962	+	2.47618i	−0.639347	+	1.10738i	0.346229	+	0.938150i	$0.387462\pi$
$5$	−1.42962	+	2.47618i	−0.639347	+	1.10738i	−0.985576	+	0.169232i	$0.945871\pi$
$6$	0.707433	+	1.22531i	0.288808	+	0.500231i
$7$	−1.85598	+	1.88556i	−0.701495	+	0.712674i
$7$	−1.85598	+	1.88556i	−0.701495	+	0.712674i
$8$	2.82712			0.999537
$9$	1.00000			0.333333
$10$	−4.04546			−1.27929
$11$	2.30705			0.695601			0.347801	−	0.937569i	$-0.386929\pi$
$11$	2.30705			0.695601			0.347801	+	0.937569i	$0.386929\pi$
$12$	−0.000924008		0.00160043i	−0.000266738		0.000462004i
$13$	−3.12586	+	1.79694i	−0.866958	+	0.498381i
$13$	−3.12586	+	1.79694i	−0.866958	+	0.498381i
$14$	−3.62338	−	0.940248i	−0.968389	−	0.251292i
$15$	−1.42962	+	2.47618i	−0.369127	+	0.639347i
$16$	2.00185	+	3.46730i	0.500462	+	0.866825i
$17$	3.72581	−	6.45329i	0.903642	−	1.56515i	0.0809118	−	0.996721i	$-0.474217\pi$
$17$	3.72581	−	6.45329i	0.903642	−	1.56515i	0.822730	−	0.568432i	$-0.192450\pi$
$18$	0.707433	+	1.22531i	0.166744	+	0.288808i
$19$	0.565673			0.129774			0.0648871	−	0.997893i	$-0.479331\pi$
$19$	0.565673			0.129774			0.0648871	+	0.997893i	$0.479331\pi$
$20$	−0.00264197	−	0.00457603i	−0.000590762	−	0.00102323i
$21$	−1.85598	+	1.88556i	−0.405009	+	0.411463i
$22$	1.63208	+	2.82685i	0.347961	+	0.602686i
$23$	0.398944	+	0.690991i	0.0831855	+	0.144082i	0.904617	−	0.426226i	$-0.140157\pi$
$23$	0.398944	+	0.690991i	0.0831855	+	0.144082i	−0.821431	+	0.570308i	$0.806824\pi$
$24$	2.82712			0.577083
$25$	−1.58765	−	2.74989i	−0.317530	−	0.549979i
$26$	−4.41315	−	2.55894i	−0.865489	−	0.501849i
$27$	1.00000			0.192450
$28$	−0.00130276	−	0.00471264i	−0.000246198	−	0.000890605i
$29$	3.00672	−	5.20778i	0.558333	−	0.967061i	−0.439303	−	0.898339i	$-0.644775\pi$
$29$	3.00672	−	5.20778i	0.558333	−	0.967061i	0.997636	−	0.0687221i	$-0.0218922\pi$
$30$	−4.04546			−0.738596
$31$	−3.80370	−	6.58820i	−0.683164	−	1.18328i	−0.974010	−	0.226505i	$-0.927270\pi$
$31$	−3.80370	−	6.58820i	−0.683164	−	1.18328i	0.290846	−	0.956770i	$-0.406063\pi$
$32$	−0.00522698	+	0.00905339i	−0.000924008	+	0.00160043i
$33$	2.30705			0.401605
$34$	10.5431			1.80812
$35$	−2.01563	−	7.29139i	−0.340703	−	1.23247i
$36$	−0.000924008		0.00160043i	−0.000154001		0.000266738i
$37$	−1.15073	−	1.99313i	−0.189179	−	0.327668i	0.755798	−	0.654805i	$-0.227249\pi$
$37$	−1.15073	−	1.99313i	−0.189179	−	0.327668i	−0.944977	+	0.327137i	$0.893916\pi$
$38$	0.400176	+	0.693125i	0.0649171	+	0.112440i
$39$	−3.12586	+	1.79694i	−0.500538	+	0.287741i
$40$	−4.04172	+	7.00046i	−0.639052	+	1.10687i
$41$	−5.68100	+	9.83978i	−0.887223	+	1.53672i	−0.0440794	+	0.999028i	$0.514035\pi$
$41$	−5.68100	+	9.83978i	−0.887223	+	1.53672i	−0.843144	+	0.537688i	$0.819298\pi$
$42$	−3.62338	−	0.940248i	−0.559099	−	0.145083i
$43$	−3.76945	−	6.52888i	−0.574835	−	0.995644i	−0.996059	−	0.0886876i	$-0.971733\pi$
$43$	−3.76945	−	6.52888i	−0.574835	−	0.995644i	0.421224	−	0.906957i	$-0.361601\pi$
$44$	−0.00213173	+	0.00369227i	−0.000321371	+	0.000556630i
$45$	−1.42962	+	2.47618i	−0.213116	+	0.369127i
$46$	−0.564452	+	0.977660i	−0.0832240	+	0.144148i
$47$	0.134822	−	0.233518i	0.0196658	−	0.0340621i	−0.856025	−	0.516934i	$-0.827073\pi$
$47$	0.134822	−	0.233518i	0.0196658	−	0.0340621i	0.875691	+	0.482872i	$0.160406\pi$
$48$	2.00185	+	3.46730i	0.288942	+	0.500462i
$49$	−0.110659	−	6.99913i	−0.0158084	−	0.999875i
$50$	2.24632	−	3.89073i	0.317677	−	0.550233i
$51$	3.72581	−	6.45329i	0.521718	−	0.903642i
$52$	1.24483e−5	−	0.00666311i	1.72627e−6	−	0.000924007i
$53$	2.35993	+	4.08751i	0.324161	+	0.561463i	0.981342	−	0.192269i	$-0.0615847\pi$
$53$	2.35993	+	4.08751i	0.324161	+	0.561463i	−0.657181	+	0.753733i	$0.728251\pi$
$54$	0.707433	+	1.22531i	0.0962695	+	0.166744i
$55$	−3.29821	+	5.71267i	−0.444731	+	0.770296i
$56$	−5.24708	+	5.33070i	−0.701171	+	0.712344i
$57$	0.565673			0.0749252
$58$	8.50820			1.11718
$59$	2.91090	−	5.04183i	0.378967	−	0.656390i	−0.611945	−	0.790900i	$-0.709613\pi$
$59$	2.91090	−	5.04183i	0.378967	−	0.656390i	0.990912	+	0.134510i	$0.0429460\pi$
$60$	−0.00264197	−	0.00457603i	−0.000341077	−	0.000590762i
$61$	−2.93403			−0.375664			−0.187832	−	0.982201i	$-0.560146\pi$
$61$	−2.93403			−0.375664			−0.187832	+	0.982201i	$0.560146\pi$
$62$	5.38172	−	9.32142i	0.683480	−	1.18382i
$63$	−1.85598	+	1.88556i	−0.233832	+	0.237558i
$64$	7.99259			0.999074
$65$	0.0192600	−	10.3091i	0.00238891	−	1.27869i
$66$	1.63208	+	2.82685i	0.200895	+	0.347961i
$67$	3.17468			0.387849			0.193924	−	0.981016i	$-0.437878\pi$
$67$	3.17468			0.387849			0.193924	+	0.981016i	$0.437878\pi$
$68$	0.00688536	+	0.0119258i	0.000834973	+	0.00144621i
$69$	0.398944	+	0.690991i	0.0480272	+	0.0831855i
$70$	7.50830	−	7.62794i	0.897413	−	0.911714i
$71$	−3.01045	−	5.21425i	−0.357275	−	0.618818i	0.630230	−	0.776409i	$-0.282961\pi$
$71$	−3.01045	−	5.21425i	−0.357275	−	0.618818i	−0.987505	+	0.157591i	$0.949627\pi$
$72$	2.82712			0.333179
$73$	5.31799	+	9.21103i	0.622424	+	1.07807i	0.989033	+	0.147694i	$0.0471852\pi$
$73$	5.31799	+	9.21103i	0.622424	+	1.07807i	−0.366609	+	0.930375i	$0.619481\pi$
$74$	1.62813	−	2.82001i	0.189267	−	0.327819i
$75$	−1.58765	−	2.74989i	−0.183326	−	0.317530i
$76$	−0.000522686	0	0.000905319i	−5.99562e−5	0	0.000103847i
$77$	−4.28184	+	4.35007i	−0.487961	+	0.495737i
$78$	−4.41315	−	2.55894i	−0.499691	−	0.289743i
$79$	−2.01404	+	3.48841i	−0.226597	+	0.392477i	−0.956797	−	0.290756i	$-0.906093\pi$
$79$	−2.01404	+	3.48841i	−0.226597	+	0.392477i	0.730201	+	0.683233i	$0.239427\pi$
$80$	−11.4476			−1.27988
$81$	1.00000			0.111111
$82$	−16.0757			−1.77527
$83$	16.2573			1.78447			0.892237	−	0.451567i	$-0.149135\pi$
$83$	16.2573			1.78447			0.892237	+	0.451567i	$0.149135\pi$
$84$	−0.00130276	−	0.00471264i	−0.000142143	−	0.000514191i
$85$	10.6530	+	18.4516i	1.15548	+	2.00135i
$86$	5.33327	−	9.23749i	0.575101	−	0.996104i
$87$	3.00672	−	5.20778i	0.322354	−	0.558333i
$88$	6.52230			0.695279
$89$	0.709194	+	1.22836i	0.0751745	+	0.130206i	0.901162	−	0.433482i	$-0.142715\pi$
$89$	0.709194	+	1.22836i	0.0751745	+	0.130206i	−0.825988	+	0.563688i	$0.809382\pi$
$90$	−4.04546			−0.426429
$91$	2.41331	−	9.22908i	0.252984	−	0.967471i
$92$	−0.00147451			−0.000153728
$93$	−3.80370	−	6.58820i	−0.394425	−	0.683164i
$94$	0.381509			0.0393497
$95$	−0.808700	+	1.40071i	−0.0829708	+	0.143710i
$96$	−0.00522698	+	0.00905339i	−0.000533476	+	0.000924008i
$97$	−5.23049	−	9.05948i	−0.531076	−	0.919851i	−0.999342	−	0.0362635i	$-0.988454\pi$
$97$	−5.23049	−	9.05948i	−0.531076	−	0.919851i	0.468266	−	0.883588i	$-0.344879\pi$
$98$	8.49782	−	5.08701i	0.858409	−	0.513865i
$99$	2.30705			0.231867
$100$	0.00586801			0.000586801
$101$	−9.47483			−0.942781			−0.471391	−	0.881925i	$-0.656248\pi$
$101$	−9.47483			−0.942781			−0.471391	+	0.881925i	$0.656248\pi$
$102$	10.5431			1.04392
$103$	−10.1433	+	17.5686i	−0.999444	+	1.73109i	−0.470857	+	0.882210i	$0.656055\pi$
$103$	−10.1433	+	17.5686i	−0.999444	+	1.73109i	−0.528588	+	0.848879i	$0.677278\pi$
$104$	−8.83718	+	5.08016i	−0.866557	+	0.498151i
$105$	−2.01563	−	7.29139i	−0.196705	−	0.711567i
$106$	−3.33898	+	5.78329i	−0.324311	+	0.561723i
$107$	6.68305	+	11.5754i	0.646075	+	1.11903i	0.984052	+	0.177880i	$0.0569239\pi$
$107$	6.68305	+	11.5754i	0.646075	+	1.11903i	−0.337978	+	0.941154i	$0.609743\pi$
$108$	−0.000924008		0.00160043i	−8.89127e−5		0.000154001i
$109$	−0.471097	−	0.815964i	−0.0451229	−	0.0781551i	0.842582	−	0.538568i	$-0.181035\pi$
$109$	−0.471097	−	0.815964i	−0.0451229	−	0.0781551i	−0.887705	+	0.460413i	$0.847701\pi$
$110$	−9.33306			−0.889872
$111$	−1.15073	−	1.99313i	−0.109223	−	0.189179i
$112$	−10.2532	−	2.66065i	−0.968835	−	0.251408i
$113$	−1.28957	−	2.23360i	−0.121313	−	0.210120i	0.798973	−	0.601367i	$-0.205377\pi$
$113$	−1.28957	−	2.23360i	−0.121313	−	0.210120i	−0.920286	+	0.391247i	$0.872044\pi$
$114$	0.400176	+	0.693125i	0.0374799	+	0.0649171i
$115$	−2.28136			−0.212738
$116$	0.00555646	+	0.00962407i	0.000515904	+	0.000893572i
$117$	−3.12586	+	1.79694i	−0.288986	+	0.166127i
$118$	8.23707			0.758284
$119$	5.25302	+	19.0024i	0.481544	+	1.74195i
$120$	−4.04172	+	7.00046i	−0.368957	+	0.639052i
$121$	−5.67753			−0.516139
$122$	−2.07563	−	3.59510i	−0.187919	−	0.325485i
$123$	−5.68100	+	9.83978i	−0.512239	+	0.887223i
$124$	0.0140586			0.00126250
$125$	−5.21726			−0.466646
$126$	−3.62338	−	0.940248i	−0.322796	−	0.0837640i
$127$	−2.06314	+	3.57347i	−0.183074	+	0.317094i	−0.942926	−	0.333003i	$-0.891938\pi$
$127$	−2.06314	+	3.57347i	−0.183074	+	0.317094i	0.759852	+	0.650097i	$0.225272\pi$
$128$	5.66468	+	9.81152i	0.500692	+	0.867224i
$129$	−3.76945	−	6.52888i	−0.331881	−	0.574835i
$130$	12.6455	−	7.26944i	1.10909	−	0.637572i
$131$	3.77229	−	6.53379i	0.329586	−	0.570860i	−0.652844	−	0.757493i	$-0.726424\pi$
$131$	3.77229	−	6.53379i	0.329586	−	0.570860i	0.982430	+	0.186633i	$0.0597574\pi$
$132$	−0.00213173	+	0.00369227i	−0.000185543	+	0.000321371i
$133$	−1.04988	+	1.06661i	−0.0910360	+	0.0924867i
$134$	2.24588	+	3.88997i	0.194014	+	0.336042i
$135$	−1.42962	+	2.47618i	−0.123042	+	0.213116i
$136$	10.5333	−	18.2442i	0.903224	−	1.56443i
$137$	−8.34991	+	14.4625i	−0.713381	+	1.23561i	0.250199	+	0.968194i	$0.419504\pi$
$137$	−8.34991	+	14.4625i	−0.713381	+	1.23561i	−0.963581	+	0.267418i	$0.913829\pi$
$138$	−0.564452	+	0.977660i	−0.0480494	+	0.0832240i
$139$	−5.17295	−	8.95981i	−0.438764	−	0.759961i	0.558831	−	0.829282i	$-0.311250\pi$
$139$	−5.17295	−	8.95981i	−0.438764	−	0.759961i	−0.997594	+	0.0693207i	$0.977917\pi$
$140$	0.0135318	+	0.00351144i	0.00114365	+	0.000296770i
$141$	0.134822	−	0.233518i	0.0113540	−	0.0196658i
$142$	4.25939	−	7.37747i	0.357440	−	0.619104i
$143$	−7.21151	+	4.14562i	−0.603057	+	0.346675i
$144$	2.00185	+	3.46730i	0.166821	+	0.288942i
$145$	8.59695	+	14.8903i	0.713938	+	1.23658i
$146$	−7.52425	+	13.0324i	−0.622711	+	1.07857i
$147$	−0.110659	−	6.99913i	−0.00912699	−	0.577278i
$148$	0.00425315			0.000349606
$149$	−12.2446			−1.00312			−0.501558	−	0.865124i	$-0.667240\pi$
$149$	−12.2446			−1.00312			−0.501558	+	0.865124i	$0.667240\pi$
$150$	2.24632	−	3.89073i	0.183411	−	0.317677i
$151$	−9.04334	−	15.6635i	−0.735936	−	1.27468i	−0.954311	−	0.298814i	$-0.903409\pi$
$151$	−9.04334	−	15.6635i	−0.735936	−	1.27468i	0.218375	−	0.975865i	$-0.429924\pi$
$152$	1.59922			0.129714
$153$	3.72581	−	6.45329i	0.301214	−	0.521718i
$154$	−8.35931	−	2.16920i	−0.673612	−	0.174799i
$155$	21.7514			1.74712
$156$	1.24483e−5	−	0.00666311i	9.96661e−7	−	0.000533475i
$157$	10.9151	+	18.9055i	0.871120	+	1.50882i	0.860839	+	0.508877i	$0.169939\pi$
$157$	10.9151	+	18.9055i	0.871120	+	1.50882i	0.0102810	+	0.999947i	$0.496727\pi$
$158$	−5.69918			−0.453403
$159$	2.35993	+	4.08751i	0.187154	+	0.324161i
$160$	−0.0149452	−	0.0258859i	−0.00118152	−	0.00204646i
$161$	−2.04334	−	0.530235i	−0.161037	−	0.0417884i
$162$	0.707433	+	1.22531i	0.0555812	+	0.0962695i
$163$	−11.3743			−0.890905			−0.445452	−	0.895306i	$-0.646957\pi$
$163$	−11.3743			−0.890905			−0.445452	+	0.895306i	$0.646957\pi$
$164$	−0.0104986	−	0.0181841i	−0.000819802	−	0.00141994i
$165$	−3.29821	+	5.71267i	−0.256765	+	0.444731i
$166$	11.5010	+	19.9203i	0.892649	+	1.54611i
$167$	0.262814	−	0.455207i	0.0203372	−	0.0352250i	−0.855678	−	0.517509i	$-0.826859\pi$
$167$	0.262814	−	0.455207i	0.0203372	−	0.0352250i	0.876015	+	0.482284i	$0.160193\pi$
$168$	−5.24708	+	5.33070i	−0.404821	+	0.411272i
$169$	6.54202	−	11.2340i	0.503232	−	0.864151i
$170$	−15.0726	+	26.1065i	−1.15602	+	2.00228i
$171$	0.565673			0.0432581
$172$	0.0139320			0.00106231
$173$	−9.14517			−0.695295			−0.347647	−	0.937625i	$-0.613019\pi$
$173$	−9.14517			−0.695295			−0.347647	+	0.937625i	$0.613019\pi$
$174$	8.50820			0.645005
$175$	8.13174	+	2.11014i	0.614702	+	0.159512i
$176$	4.61836	+	7.99923i	0.348122	+	0.602964i
$177$	2.91090	−	5.04183i	0.218797	−	0.378967i
$178$	−1.00342	+	1.73797i	−0.0752092	+	0.130266i
$179$	−1.72286			−0.128773			−0.0643863	−	0.997925i	$-0.520509\pi$
$179$	−1.72286			−0.128773			−0.0643863	+	0.997925i	$0.520509\pi$
$180$	−0.00264197	−	0.00457603i	−0.000196921	−	0.000341077i
$181$	−3.97723			−0.295625			−0.147813	−	0.989015i	$-0.547223\pi$
$181$	−3.97723			−0.295625			−0.147813	+	0.989015i	$0.547223\pi$
$182$	13.0157	−	3.57190i	0.964791	−	0.264767i
$183$	−2.93403			−0.216890
$184$	1.12786	+	1.95351i	0.0831471	+	0.144015i
$185$	6.58046			0.483805
$186$	5.38172	−	9.32142i	0.394607	−	0.683480i
$187$	8.59562	−	14.8881i	0.628574	−	1.08872i
$188$	0.000249153	0	0.000431545i	1.81713e−5	0	3.14737e-5i
$189$	−1.85598	+	1.88556i	−0.135003	+	0.137154i
$190$	−2.28840			−0.166018
$191$	25.1534			1.82004			0.910019	−	0.414565i	$-0.136066\pi$
$191$	25.1534			1.82004			0.910019	+	0.414565i	$0.136066\pi$
$192$	7.99259			0.576816
$193$	−18.1553			−1.30685			−0.653425	−	0.756992i	$-0.726668\pi$
$193$	−18.1553			−1.30685			−0.653425	+	0.756992i	$0.726668\pi$
$194$	7.40045	−	12.8180i	0.531322	−	0.920276i
$195$	0.0192600	−	10.3091i	0.00137924	−	0.738254i
$196$	0.0113039	+	0.00629015i	0.000807418	+	0.000449296i
$197$	0.782504	−	1.35534i	0.0557511	−	0.0965638i	−0.836803	−	0.547504i	$-0.815578\pi$
$197$	0.782504	−	1.35534i	0.0557511	−	0.0965638i	0.892554	+	0.450940i	$0.148911\pi$
$198$	1.63208	+	2.82685i	0.115987	+	0.200895i
$199$	7.55805	−	13.0909i	0.535776	−	0.927991i	−0.463349	−	0.886176i	$-0.653352\pi$
$199$	7.55805	−	13.0909i	0.535776	−	0.927991i	0.999125	−	0.0418157i	$-0.0133142\pi$
$200$	−4.48848	−	7.77427i	−0.317383	−	0.549724i
$201$	3.17468			0.223925
$202$	−6.70281	−	11.6096i	−0.471608	−	0.816850i
$203$	4.23917	+	15.3349i	0.297531	+	1.07630i
$204$	0.00688536	+	0.0119258i	0.000482072	+	0.000834973i
$205$	−16.2434	−	28.1344i	−1.13449	−	1.96499i
$206$	−28.7027			−1.99981
$207$	0.398944	+	0.690991i	0.0277285	+	0.0480272i
$208$	−12.4880	−	7.24110i	−0.865888	−	0.502080i
$209$	1.30503			0.0902711
$210$	7.50830	−	7.62794i	0.518122	−	0.526378i
$211$	−8.28852	+	14.3561i	−0.570606	+	0.988318i	0.425898	+	0.904771i	$0.359958\pi$
$211$	−8.28852	+	14.3561i	−0.570606	+	0.988318i	−0.996504	+	0.0835467i	$0.973375\pi$
$212$	−0.00872237			−0.000599055
$213$	−3.01045	−	5.21425i	−0.206273	−	0.357275i
$214$	−9.45562	+	16.3776i	−0.646373	+	1.11955i
$215$	21.5556			1.47008
$216$	2.82712			0.192361
$217$	19.4820	+	5.05548i	1.32253	+	0.343189i
$218$	0.666539	−	1.15448i	0.0451437	−	0.0781912i
$219$	5.31799	+	9.21103i	0.359356	+	0.622424i
$220$	−0.00609515	−	0.0105571i	−0.000410935	−	0.000711760i
$221$	−0.0501943	+	26.8672i	−0.00337644	+	1.80728i
$222$	1.62813	−	2.82001i	0.109273	−	0.189267i
$223$	3.10234	−	5.37341i	0.207748	−	0.359830i	−0.743257	−	0.669006i	$-0.766720\pi$
$223$	3.10234	−	5.37341i	0.207748	−	0.359830i	0.951005	+	0.309176i	$0.100053\pi$
$224$	−0.00736952	−	0.0266587i	−0.000492397	−	0.00178121i
$225$	−1.58765	−	2.74989i	−0.105843	−	0.183326i
$226$	1.82457	−	3.16025i	0.121369	−	0.210217i
$227$	0.770318	−	1.33423i	0.0511278	−	0.0885560i	−0.839329	−	0.543624i	$-0.817052\pi$
$227$	0.770318	−	1.33423i	0.0511278	−	0.0885560i	0.890457	+	0.455068i	$0.150385\pi$
$228$	−0.000522686	0	0.000905319i	−3.46157e−5	0	5.99562e-5i
$229$	10.6720	−	18.4845i	0.705227	−	1.22149i	−0.261383	−	0.965235i	$-0.584179\pi$
$229$	10.6720	−	18.4845i	0.705227	−	1.22149i	0.966610	−	0.256253i	$-0.0824880\pi$
$230$	−1.61391	−	2.79537i	−0.106418	−	0.184321i
$231$	−4.28184	+	4.35007i	−0.281724	+	0.286214i
$232$	8.50034	−	14.7230i	0.558075	−	0.966614i
$233$	−4.31457	+	7.47305i	−0.282657	+	0.489576i	−0.972038	−	0.234823i	$-0.924549\pi$
$233$	−4.31457	+	7.47305i	−0.282657	+	0.489576i	0.689381	+	0.724399i	$0.257882\pi$
$234$	−4.41315	−	2.55894i	−0.288496	−	0.167283i
$235$	0.385489	+	0.667686i	0.0251465	+	0.0435550i
$236$	0.00537939	+	0.00931738i	0.000350169	+	0.000606510i
$237$	−2.01404	+	3.48841i	−0.130826	+	0.226597i
$238$	−19.5677	+	19.8795i	−1.26839	+	1.28860i
$239$	20.3222			1.31454			0.657268	−	0.753657i	$-0.271712\pi$
$239$	20.3222			1.31454			0.657268	+	0.753657i	$0.271712\pi$
$240$	−11.4476			−0.738936
$241$	−13.0577	+	22.6166i	−0.841119	+	1.45686i	0.0478310	+	0.998855i	$0.484769\pi$
$241$	−13.0577	+	22.6166i	−0.841119	+	1.45686i	−0.888950	+	0.458005i	$0.848564\pi$
$242$	−4.01647	−	6.95674i	−0.258189	−	0.447196i
$243$	1.00000			0.0641500
$244$	0.00271107	−	0.00469571i	0.000173558	−	0.000300612i
$245$	17.4893	+	9.73211i	1.11735	+	0.621762i
$246$	−16.0757			−1.02495
$247$	−1.76821	+	1.01648i	−0.112509	+	0.0646770i
$248$	−10.7535	−	18.6256i	−0.682848	−	1.18273i
$249$	16.2573			1.03027
$250$	−3.69087	−	6.39277i	−0.233431	−	0.404314i
$251$	−11.2757	−	19.5301i	−0.711718	−	1.23273i	−0.964212	−	0.265133i	$-0.914584\pi$
$251$	−11.2757	−	19.5301i	−0.711718	−	1.23273i	0.252494	−	0.967599i	$-0.418749\pi$
$252$	−0.00130276	−	0.00471264i	−8.20661e−5	−	0.000296868i
$253$	0.920383	+	1.59415i	0.0578640	+	0.100223i
$254$	−5.83814			−0.366318
$255$	10.6530	+	18.4516i	0.667118	+	1.15548i
$256$	−0.0221762	+	0.0384103i	−0.00138601	+	0.00240064i
$257$	0.536216	+	0.928754i	0.0334483	+	0.0579341i	0.882265	−	0.470753i	$-0.156018\pi$
$257$	0.536216	+	0.928754i	0.0334483	+	0.0579341i	−0.848817	+	0.528687i	$0.822684\pi$
$258$	5.33327	−	9.23749i	0.332035	−	0.575101i
$259$	5.89390	+	1.52944i	0.366229	+	0.0950345i
$260$	0.0164813	+	0.00955656i	0.00102212	+	0.000592673i
$261$	3.00672	−	5.20778i	0.186111	−	0.322354i
$262$	10.6746			0.659477
$263$	15.4691			0.953866			0.476933	−	0.878940i	$-0.341748\pi$
$263$	15.4691			0.953866			0.476933	+	0.878940i	$0.341748\pi$
$264$	6.52230			0.401420
$265$	−13.4952			−0.829006
$266$	−2.04965	−	0.531873i	−0.125672	−	0.0326112i
$267$	0.709194	+	1.22836i	0.0434020	+	0.0751745i
$268$	−0.00293343	+	0.00508085i	−0.000179188	+	0.000310362i
$269$	−1.11891	+	1.93801i	−0.0682212	+	0.118163i	−0.898118	−	0.439754i	$-0.855066\pi$
$269$	−1.11891	+	1.93801i	−0.0682212	+	0.118163i	0.829897	+	0.557916i	$0.188399\pi$
$270$	−4.04546			−0.246199
$271$	−3.07220	−	5.32120i	−0.186623	−	0.323240i	0.757499	−	0.652836i	$-0.226421\pi$
$271$	−3.07220	−	5.32120i	−0.186623	−	0.323240i	−0.944122	+	0.329596i	$0.893088\pi$
$272$	29.8340			1.80895
$273$	2.41331	−	9.22908i	0.146060	−	0.558569i
$274$	−23.6280			−1.42742
$275$	−3.66279	−	6.34414i	−0.220874	−	0.382566i
$276$	−0.00147451			−8.87551e−5
$277$	1.67414	−	2.89969i	0.100589	−	0.174226i	−0.811338	−	0.584577i	$-0.801261\pi$
$277$	1.67414	−	2.89969i	0.100589	−	0.174226i	0.911928	+	0.410351i	$0.134594\pi$
$278$	7.31903	−	12.6769i	0.438966	−	0.760312i
$279$	−3.80370	−	6.58820i	−0.227721	−	0.394425i
$280$	−5.69842	−	20.6136i	−0.340546	−	1.23190i
$281$	−14.2117			−0.847800			−0.423900	−	0.905709i	$-0.639339\pi$
$281$	−14.2117			−0.847800			−0.423900	+	0.905709i	$0.639339\pi$
$282$	0.381509			0.0227186
$283$	14.6283			0.869565			0.434782	−	0.900536i	$-0.356825\pi$
$283$	14.6283			0.869565			0.434782	+	0.900536i	$0.356825\pi$
$284$	0.0111267			0.000660249
$285$	−0.808700	+	1.40071i	−0.0479032	+	0.0829708i
$286$	−10.1813	−	5.90359i	−0.602035	−	0.349087i
$287$	−8.00964	−	28.9743i	−0.472794	−	1.71030i
$288$	−0.00522698	+	0.00905339i	−0.000308003	+	0.000533476i
$289$	−19.2633	−	33.3651i	−1.13314	−	1.96265i
$290$	−12.1635	+	21.0679i	−0.714267	+	1.23715i
$291$	−5.23049	−	9.05948i	−0.306617	−	0.531076i
$292$	−0.0196555			−0.00115025
$293$	−10.7723	−	18.6582i	−0.629324	−	1.09002i	−0.987688	−	0.156439i	$-0.949998\pi$
$293$	−10.7723	−	18.6582i	−0.629324	−	1.09002i	0.358363	−	0.933582i	$-0.383335\pi$
$294$	8.49782	−	5.08701i	0.495603	−	0.296680i
$295$	8.32299	+	14.4158i	0.484583	+	0.839323i
$296$	−3.25326	−	5.63481i	−0.189092	−	0.327517i
$297$	2.30705			0.133868
$298$	−8.66223	−	15.0034i	−0.501790	−	0.869125i
$299$	−2.48871	−	1.44306i	−0.143926	−	0.0834546i
$300$	0.00586801			0.000338790
$301$	19.3066	+	5.00997i	1.11281	+	0.288770i
$302$	12.7951	−	22.1618i	0.736276	−	1.27527i
$303$	−9.47483			−0.544315
$304$	1.13239	+	1.96136i	0.0649470	+	0.112492i
$305$	4.19456	−	7.26519i	0.240180	−	0.416004i
$306$	10.5431			0.602706
$307$	18.6457			1.06416			0.532082	−	0.846693i	$-0.321410\pi$
$307$	18.6457			1.06416			0.532082	+	0.846693i	$0.321410\pi$
$308$	−0.00300553	−	0.0108723i	−0.000171256	−	0.000619506i
$309$	−10.1433	+	17.5686i	−0.577029	+	0.999444i
$310$	15.3877	+	26.6523i	0.873962	+	1.51375i
$311$	−0.578424	−	1.00186i	−0.0327994	−	0.0568103i	0.849160	−	0.528136i	$-0.177109\pi$
$311$	−0.578424	−	1.00186i	−0.0327994	−	0.0568103i	−0.881959	+	0.471326i	$0.843776\pi$
$312$	−8.83718	+	5.08016i	−0.500307	+	0.287607i
$313$	−6.86004	+	11.8819i	−0.387752	+	0.671607i	−0.992147	−	0.125078i	$-0.960082\pi$
$313$	−6.86004	+	11.8819i	−0.387752	+	0.671607i	0.604394	+	0.796685i	$0.293415\pi$
$314$	−15.4434	+	26.7488i	−0.871523	+	1.50952i
$315$	−2.01563	−	7.29139i	−0.113568	−	0.410823i
$316$	−0.00372197	−	0.00644664i	−0.000209377	−	0.000362652i
$317$	−2.13847	+	3.70393i	−0.120108	+	0.208034i	−0.919810	−	0.392364i	$-0.871658\pi$
$317$	−2.13847	+	3.70393i	−0.120108	+	0.208034i	0.799702	+	0.600397i	$0.204991\pi$
$318$	−3.33898	+	5.78329i	−0.187241	+	0.324311i
$319$	6.93664	−	12.0146i	0.388377	−	0.672689i
$320$	−11.4264	+	19.7911i	−0.638756	+	1.10636i
$321$	6.68305	+	11.5754i	0.373011	+	0.646075i
$322$	−0.795822	−	2.87883i	−0.0443494	−	0.160431i
$323$	2.10759	−	3.65045i	0.117269	−	0.203117i
$324$	−0.000924008		0.00160043i	−5.13338e−5		8.89127e-5i
$325$	9.90417	+	5.74287i	0.549384	+	0.318557i
$326$	−8.04657	−	13.9371i	−0.445658	−	0.771902i
$327$	−0.471097	−	0.815964i	−0.0260517	−	0.0451229i
$328$	−16.0609	+	27.8182i	−0.886813	+	1.53601i
$329$	0.190085	+	0.687619i	0.0104797	+	0.0379097i
$330$	−9.33306			−0.513768
$331$	11.6611			0.640954			0.320477	−	0.947256i	$-0.396157\pi$
$331$	11.6611			0.640954			0.320477	+	0.947256i	$0.396157\pi$
$332$	−0.0150219	+	0.0260187i	−0.000824434	+	0.00142796i
$333$	−1.15073	−	1.99313i	−0.0630598	−	0.109223i
$334$	0.743693			0.0406931
$335$	−4.53860	+	7.86109i	−0.247970	+	0.429497i
$336$	−10.2532	−	2.66065i	−0.559357	−	0.145150i
$337$	−16.2903			−0.887387			−0.443693	−	0.896179i	$-0.646332\pi$
$337$	−16.2903			−0.887387			−0.443693	+	0.896179i	$0.646332\pi$
$338$	18.3931	+	0.0687259i	1.00045	+	0.00373820i
$339$	−1.28957	−	2.23360i	−0.0700400	−	0.121313i
$340$	−0.0393739			−0.00213535
$341$	−8.77531	−	15.1993i	−0.475210	−	0.823087i
$342$	0.400176	+	0.693125i	0.0216390	+	0.0374799i
$343$	13.4026	+	12.7816i	0.723674	+	0.690142i
$344$	−10.6567	−	18.4579i	−0.574570	−	0.995184i
$345$	−2.28136			−0.122824
$346$	−6.46960	−	11.2057i	−0.347808	−	0.602421i
$347$	−12.8556	+	22.2666i	−0.690126	+	1.19533i	0.281670	+	0.959511i	$0.409112\pi$
$347$	−12.8556	+	22.2666i	−0.690126	+	1.19533i	−0.971796	+	0.235822i	$0.924222\pi$
$348$	0.00555646	+	0.00962407i	0.000297857	+	0.000515904i
$349$	−0.908371	+	1.57334i	−0.0486240	+	0.0842192i	−0.889313	−	0.457299i	$-0.848817\pi$
$349$	−0.908371	+	1.57334i	−0.0486240	+	0.0842192i	0.840689	+	0.541518i	$0.182150\pi$
$350$	3.16708	+	11.4567i	0.169288	+	0.612386i
$351$	−3.12586	+	1.79694i	−0.166846	+	0.0959135i
$352$	−0.0120589	+	0.0208866i	−0.000642741	+	0.00111326i
$353$	−0.0624143			−0.00332198			−0.00166099	−	0.999999i	$-0.500529\pi$
$353$	−0.0624143			−0.00332198			−0.00166099	+	0.999999i	$0.500529\pi$
$354$	8.23707			0.437796
$355$	17.2152			0.913691
$356$	−0.00262121			−0.000138924
$357$	5.25302	+	19.0024i	0.278019	+	1.00572i
$358$	−1.21881	−	2.11104i	−0.0644160	−	0.111572i
$359$	−6.71414	+	11.6292i	−0.354359	+	0.613767i	−0.987008	−	0.160671i	$-0.948634\pi$
$359$	−6.71414	+	11.6292i	−0.354359	+	0.613767i	0.632649	+	0.774438i	$0.281967\pi$
$360$	−4.04172	+	7.00046i	−0.213017	+	0.368957i
$361$	−18.6800			−0.983159
$362$	−2.81363	−	4.87334i	−0.147881	−	0.256137i
$363$	−5.67753			−0.297993
$364$	0.0125406	+	0.0123901i	0.000657305	+	0.000649417i
$365$	−30.4109			−1.59178
$366$	−2.07563	−	3.59510i	−0.108495	−	0.187919i
$367$	21.3432			1.11410			0.557052	−	0.830477i	$-0.311932\pi$
$367$	21.3432			1.11410			0.557052	+	0.830477i	$0.311932\pi$
$368$	−1.59725	+	2.76652i	−0.0832623	+	0.144215i
$369$	−5.68100	+	9.83978i	−0.295741	+	0.512239i
$370$	4.65524	+	8.06311i	0.242014	+	0.419181i
$371$	−12.0872	−	3.13657i	−0.627538	−	0.162843i
$372$	0.0140586			0.000728904
$373$	28.7677			1.48953			0.744767	−	0.667325i	$-0.232561\pi$
$373$	28.7677			1.48953			0.744767	+	0.667325i	$0.232561\pi$
$374$	24.3233			1.25773
$375$	−5.21726			−0.269418
$376$	0.381157	−	0.660183i	0.0196567	−	0.0340463i
$377$	−0.0405066	+	21.6817i	−0.00208620	+	1.11666i
$378$	−3.62338	−	0.940248i	−0.186366	−	0.0483611i
$379$	9.71923	−	16.8342i	0.499244	−	0.864715i	−0.500756	−	0.865588i	$-0.666945\pi$
$379$	9.71923	−	16.8342i	0.499244	−	0.864715i	1.00000		0.000873266i	$0.000277969\pi$
$380$	−0.00149449	−	0.00258853i	−7.66657e−5	−	0.000132789i
$381$	−2.06314	+	3.57347i	−0.105698	+	0.183074i
$382$	17.7944	+	30.8208i	0.910440	+	1.57693i
$383$	30.2612			1.54627			0.773137	−	0.634239i	$-0.218687\pi$
$383$	30.2612			1.54627			0.773137	+	0.634239i	$0.218687\pi$
$384$	5.66468	+	9.81152i	0.289075	+	0.500692i
$385$	−4.65015	−	16.8216i	−0.236994	−	0.857307i
$386$	−12.8437	−	22.2459i	−0.653726	−	1.13229i
$387$	−3.76945	−	6.52888i	−0.191612	−	0.331881i
$388$	0.0193321			0.000981438
$389$	0.308324	+	0.534034i	0.0156327	+	0.0270766i	0.873736	−	0.486401i	$-0.161690\pi$
$389$	0.308324	+	0.534034i	0.0156327	+	0.0270766i	−0.858103	+	0.513477i	$0.828357\pi$
$390$	12.6455	−	7.26944i	0.640332	−	0.368102i
$391$	5.94556			0.300680
$392$	−0.312846	−	19.7874i	−0.0158011	−	0.999413i
$393$	3.77229	−	6.53379i	0.190287	−	0.329586i
$394$	2.21428			0.111554
$395$	−5.75863	−	9.97424i	−0.289748	−	0.501858i
$396$	−0.00213173	+	0.00369227i	−0.000107124	+	0.000185543i
$397$	29.5775			1.48445			0.742227	−	0.670149i	$-0.233770\pi$
$397$	29.5775			1.48445			0.742227	+	0.670149i	$0.233770\pi$
$398$	21.3873			1.07205
$399$	−1.04988	+	1.06661i	−0.0525597	+	0.0533972i
$400$	6.35647	−	11.0097i	0.317823	−	0.550486i
$401$	9.92368	+	17.1883i	0.495565	+	0.858344i	0.999987	−	0.00511344i	$-0.00162767\pi$
$401$	9.92368	+	17.1883i	0.495565	+	0.858344i	−0.504422	+	0.863457i	$0.668294\pi$
$402$	2.24588	+	3.88997i	0.112014	+	0.194014i
$403$	23.7284	+	13.7588i	1.18200	+	0.685374i
$404$	0.00875483	−	0.0151638i	0.000435569	−	0.000754427i
$405$	−1.42962	+	2.47618i	−0.0710386	+	0.123042i
$406$	−15.7911	+	16.0427i	−0.783698	+	0.796186i
$407$	−2.65480	−	4.59824i	−0.131593	−	0.227926i
$408$	10.5333	−	18.2442i	0.521477	−	0.903224i
$409$	−11.7662	+	20.3796i	−0.581800	+	1.00771i	0.413466	+	0.910519i	$0.364318\pi$
$409$	−11.7662	+	20.3796i	−0.581800	+	1.00771i	−0.995266	+	0.0971875i	$0.969015\pi$
$410$	22.9822	−	39.8064i	1.13501	−	1.96590i
$411$	−8.34991	+	14.4625i	−0.411871	+	0.713381i
$412$	−0.0187449	−	0.0324671i	−0.000923495	−	0.00159954i
$413$	4.10408	+	14.8462i	0.201949	+	0.730535i
$414$	−0.564452	+	0.977660i	−0.0277413	+	0.0480494i
$415$	−23.2419	+	40.2561i	−1.14090	+	1.97610i
$416$	7.04182e−5	−	0.0376922i	3.45253e−6	−	0.00184801i
$417$	−5.17295	−	8.95981i	−0.253320	−	0.438764i
$418$	0.923225	+	1.59907i	0.0451564	+	0.0782132i
$419$	17.6833	−	30.6285i	0.863888	−	1.49630i	−0.00425910	−	0.999991i	$-0.501356\pi$
$419$	17.6833	−	30.6285i	0.863888	−	1.49630i	0.868147	−	0.496307i	$-0.165311\pi$
$420$	0.0135318	+	0.00351144i	0.000660285	+	0.000171341i
$421$	−10.1261			−0.493514			−0.246757	−	0.969077i	$-0.579365\pi$
$421$	−10.1261			−0.493514			−0.246757	+	0.969077i	$0.579365\pi$
$422$	−23.4543			−1.14174
$423$	0.134822	−	0.233518i	0.00655525	−	0.0113540i
$424$	6.67179	+	11.5559i	0.324011	+	0.561203i
$425$	−23.6612			−1.14773
$426$	4.25939	−	7.37747i	0.206368	−	0.357440i
$427$	5.44551	−	5.53228i	0.263527	−	0.267726i
$428$	−0.0247008			−0.00119396
$429$	−7.21151	+	4.14562i	−0.348175	+	0.200153i
$430$	15.2491	+	26.4123i	0.735379	+	1.27371i
$431$	−6.24300			−0.300715			−0.150357	−	0.988632i	$-0.548042\pi$
$431$	−6.24300			−0.300715			−0.150357	+	0.988632i	$0.548042\pi$
$432$	2.00185	+	3.46730i	0.0963139	+	0.166821i
$433$	16.9222	+	29.3101i	0.813229	+	1.40855i	0.910593	+	0.413305i	$0.135626\pi$
$433$	16.9222	+	29.3101i	0.813229	+	1.40855i	−0.0973634	+	0.995249i	$0.531041\pi$
$434$	7.58769	+	27.4479i	0.364221	+	1.31754i
$435$	8.59695	+	14.8903i	0.412192	+	0.713938i
$436$	0.00174119			8.33878e−5
$437$	0.225672	+	0.390875i	0.0107953	+	0.0186981i
$438$	−7.52425	+	13.0324i	−0.359522	+	0.622711i
$439$	−4.43741	−	7.68582i	−0.211786	−	0.366824i	0.740488	−	0.672070i	$-0.234595\pi$
$439$	−4.43741	−	7.68582i	−0.211786	−	0.366824i	−0.952274	+	0.305246i	$0.901261\pi$
$440$	−9.32444	+	16.1504i	−0.444525	+	0.769940i
$441$	−0.110659	−	6.99913i	−0.00526947	−	0.333292i
$442$	−32.9561	+	18.9452i	−1.56756	+	0.901132i
$443$	5.95160	−	10.3085i	0.282769	−	0.489770i	−0.689297	−	0.724479i	$-0.742080\pi$
$443$	5.95160	−	10.3085i	0.282769	−	0.489770i	0.972066	+	0.234709i	$0.0754136\pi$
$444$	0.00425315			0.000201845
$445$	−4.05553			−0.192250
$446$	8.77879			0.415688
$447$	−12.2446			−0.579149
$448$	−14.8341	+	15.0705i	−0.700846	+	0.712014i
$449$	2.97292	+	5.14925i	0.140301	+	0.243008i	0.927610	−	0.373550i	$-0.121860\pi$
$449$	2.97292	+	5.14925i	0.140301	+	0.243008i	−0.787309	+	0.616558i	$0.788526\pi$
$450$	2.24632	−	3.89073i	0.105892	−	0.183411i
$451$	−13.1063	+	22.7009i	−0.617154	+	1.06894i
$452$	0.00476630			0.000224188
$453$	−9.04334	−	15.6635i	−0.424893	−	0.735936i
$454$	2.17980			0.102303
$455$	19.4028	+	19.1699i	0.909615	+	0.898700i
$456$	1.59922			0.0748905
$457$	−6.05613	−	10.4895i	−0.283294	−	0.490679i	0.688900	−	0.724856i	$-0.258094\pi$
$457$	−6.05613	−	10.4895i	−0.283294	−	0.490679i	−0.972194	+	0.234177i	$0.924761\pi$
$458$	30.1990			1.41110
$459$	3.72581	−	6.45329i	0.173906	−	0.301214i
$460$	0.00210800	−	0.00365115i	9.82858e−5	−	0.000170236i
$461$	−2.55673	−	4.42839i	−0.119079	−	0.206251i	0.800324	−	0.599568i	$-0.204661\pi$
$461$	−2.55673	−	4.42839i	−0.119079	−	0.206251i	−0.919403	+	0.393317i	$0.871327\pi$
$462$	−8.35931	−	2.16920i	−0.388910	−	0.100920i
$463$	−38.9344			−1.80944			−0.904718	−	0.426010i	$-0.859919\pi$
$463$	−38.9344			−1.80944			−0.904718	+	0.426010i	$0.859919\pi$
$464$	24.0759			1.11770
$465$	21.7514			1.00870
$466$	−12.2091			−0.565575
$467$	7.02626	−	12.1698i	0.325136	−	0.563153i	−0.656404	−	0.754410i	$-0.727923\pi$
$467$	7.02626	−	12.1698i	0.325136	−	0.563153i	0.981540	+	0.191257i	$0.0612564\pi$
$468$	1.24483e−5	−	0.00666311i	5.75423e−7	−	0.000308002i
$469$	−5.89215	+	5.98604i	−0.272074	+	0.276410i
$470$	−0.545415	+	0.944687i	−0.0251581	+	0.0435752i
$471$	10.9151	+	18.9055i	0.502941	+	0.871120i
$472$	8.22946	−	14.2538i	0.378792	−	0.656087i
$473$	−8.69630	−	15.0624i	−0.399856	−	0.692571i
$474$	−5.69918			−0.261772
$475$	−0.898091	−	1.55554i	−0.0412073	−	0.0713731i
$476$	−0.0352659	−	0.00915132i	−0.00161641	−	0.000419450i
$477$	2.35993	+	4.08751i	0.108054	+	0.187154i
$478$	14.3766	+	24.9011i	0.657572	+	1.13895i
$479$	−32.2735			−1.47462			−0.737308	−	0.675557i	$-0.763903\pi$
$479$	−32.2735			−1.47462			−0.737308	+	0.675557i	$0.763903\pi$
$480$	−0.0149452	−	0.0258859i	−0.000682153	−	0.00118152i
$481$	7.17856	+	4.16244i	0.327314	+	0.189791i
$482$	−36.9497			−1.68301
$483$	−2.04334	−	0.530235i	−0.0929750	−	0.0241265i
$484$	0.00524608	−	0.00908648i	0.000238458	−	0.000413022i
$485$	29.9106			1.35817
$486$	0.707433	+	1.22531i	0.0320898	+	0.0555812i
$487$	6.14080	−	10.6362i	0.278266	−	0.481971i	−0.692688	−	0.721238i	$-0.743574\pi$
$487$	6.14080	−	10.6362i	0.278266	−	0.481971i	0.970954	+	0.239266i	$0.0769069\pi$
$488$	−8.29485			−0.375490
$489$	−11.3743			−0.514364
$490$	0.447665	+	28.3147i	0.0202235	+	1.27913i
$491$	−10.8531	+	18.7981i	−0.489792	+	0.848345i	−0.999931	−	0.0117472i	$-0.996261\pi$
$491$	−10.8531	+	18.7981i	−0.489792	+	0.848345i	0.510139	+	0.860092i	$0.329594\pi$
$492$	−0.0104986	−	0.0181841i	−0.000473313	−	0.000819802i
$493$	−22.4049	−	38.8064i	−1.00907	−	1.74775i
$494$	−2.49640	−	1.44752i	−0.112318	−	0.0651270i
$495$	−3.29821	+	5.71267i	−0.148244	+	0.256765i
$496$	15.2288	−	26.3771i	0.683795	−	1.18437i
$497$	15.4191	+	4.00118i	0.691642	+	0.179478i
$498$	11.5010	+	19.9203i	0.515371	+	0.892649i
$499$	−4.93997	+	8.55628i	−0.221143	+	0.383032i	−0.955155	−	0.296105i	$-0.904312\pi$
$499$	−4.93997	+	8.55628i	−0.221143	+	0.383032i	0.734012	+	0.679136i	$0.237646\pi$
$500$	0.00482079	−	0.00834986i	0.000215592	−	0.000373417i
$501$	0.262814	−	0.455207i	0.0117417	−	0.0203372i
$502$	15.9537	−	27.6326i	0.712047	−	1.23330i
$503$	−17.2279	−	29.8396i	−0.768155	−	1.33048i	−0.938562	−	0.345110i	$-0.887842\pi$
$503$	−17.2279	−	29.8396i	−0.768155	−	1.33048i	0.170407	−	0.985374i	$-0.445492\pi$
$504$	−5.24708	+	5.33070i	−0.233724	+	0.237448i
$505$	13.5455	−	23.4614i	0.602765	−	1.04402i
$506$	−1.30222	+	2.25551i	−0.0578907	+	0.100270i
$507$	6.54202	−	11.2340i	0.290541	−	0.498918i
$508$	−0.00381272	−	0.00660383i	−0.000169162	−	0.000292998i
$509$	−5.43324	−	9.41065i	−0.240824	−	0.417120i	0.720125	−	0.693844i	$-0.244084\pi$
$509$	−5.43324	−	9.41065i	−0.240824	−	0.417120i	−0.960949	+	0.276725i	$0.910751\pi$
$510$	−15.0726	+	26.1065i	−0.667426	+	1.15602i
$511$	−27.2380	−	7.06813i	−1.20494	−	0.312676i
$512$	22.5960			0.998610
$513$	0.565673			0.0249751
$514$	−0.758675	+	1.31406i	−0.0334637	+	0.0579608i
$515$	−29.0021	−	50.2331i	−1.27798	−	2.21353i
$516$	0.0139320			0.000613322
$517$	0.311040	−	0.538737i	0.0136795	−	0.0236936i
$518$	2.29551	+	8.30383i	0.100859	+	0.364849i
$519$	−9.14517			−0.401429
$520$	0.0544503	−	29.1452i	0.00238780	−	1.27810i
$521$	19.0141	+	32.9334i	0.833024	+	1.44284i	0.895630	+	0.444801i	$0.146726\pi$
$521$	19.0141	+	32.9334i	0.833024	+	1.44284i	−0.0626059	+	0.998038i	$0.519941\pi$
$522$	8.50820			0.372394
$523$	−13.6142	−	23.5805i	−0.595307	−	1.03110i	−0.993503	−	0.113802i	$-0.963697\pi$
$523$	−13.6142	−	23.5805i	−0.595307	−	1.03110i	0.398196	−	0.917300i	$-0.369636\pi$
$524$	0.00697125	+	0.0120746i	0.000304540	+	0.000527479i
$525$	8.13174	+	2.11014i	0.354898	+	0.0920942i
$526$	10.9434	+	18.9545i	0.477153	+	0.826453i
$527$	−56.6874			−2.46934
$528$	4.61836	+	7.99923i	0.200988	+	0.348122i
$529$	11.1817	−	19.3673i	0.486160	−	0.842054i
$530$	−9.54698	−	16.5359i	−0.414694	−	0.718272i
$531$	2.91090	−	5.04183i	0.126322	−	0.218797i
$532$	−0.000736936	−	0.00266581i	−3.19502e−5	−	0.000115578i
$533$	0.0765348	−	40.9662i	0.00331509	−	1.77444i
$534$	−1.00342	+	1.73797i	−0.0434220	+	0.0752092i
$535$	−38.2170			−1.65226
$536$	8.97520			0.387670
$537$	−1.72286			−0.0743469
$538$	−3.16622			−0.136505
$539$	−0.255295	−	16.1473i	−0.0109963	−	0.695514i
$540$	−0.00264197	−	0.00457603i	−0.000113692	−	0.000196921i
$541$	−19.4083	+	33.6162i	−0.834430	+	1.44528i	0.0600635	+	0.998195i	$0.480870\pi$
$541$	−19.4083	+	33.6162i	−0.834430	+	1.44528i	−0.894494	+	0.447081i	$0.852464\pi$
$542$	4.34675	−	7.52879i	0.186709	−	0.323389i
$543$	−3.97723			−0.170679
$544$	0.0389495	+	0.0674625i	0.00166994	+	0.00289243i
$545$	2.69397			0.115397
$546$	13.0157	−	3.57190i	0.557023	−	0.152863i
$547$	−8.34899			−0.356977			−0.178489	−	0.983942i	$-0.557121\pi$
$547$	−8.34899			−0.356977			−0.178489	+	0.983942i	$0.557121\pi$
$548$	−0.0154308	−	0.0267269i	−0.000659170	−	0.00114172i
$549$	−2.93403			−0.125221
$550$	5.18236	−	8.97611i	0.220976	−	0.382742i
$551$	1.70082	−	2.94590i	0.0724572	−	0.125500i
$552$	1.12786	+	1.95351i	0.0480050	+	0.0831471i
$553$	−2.83959	−	10.2720i	−0.120752	−	0.436810i
$554$	4.73736			0.201271
$555$	6.58046			0.279325
$556$	0.0191194			0.000810843
$557$	20.3402			0.861842			0.430921	−	0.902390i	$-0.358189\pi$
$557$	20.3402			0.861842			0.430921	+	0.902390i	$0.358189\pi$
$558$	5.38172	−	9.32142i	0.227827	−	0.394607i
$559$	23.5148	+	13.6349i	0.994569	+	0.576695i
$560$	21.2465	−	21.5850i	0.897827	−	0.912134i
$561$	8.59562	−	14.8881i	0.362908	−	0.628574i
$562$	−10.0538	−	17.4138i	−0.424096	−	0.734555i
$563$	1.82692	−	3.16432i	0.0769955	−	0.133360i	−0.824957	−	0.565196i	$-0.808801\pi$
$563$	1.82692	−	3.16432i	0.0769955	−	0.133360i	0.901952	+	0.431836i	$0.142134\pi$
$564$	0.000249153	0	0.000431545i	1.04912e−5	0	1.81713e-5i
$565$	7.37442			0.310244
$566$	10.3486	+	17.9243i	0.434983	+	0.753413i
$567$	−1.85598	+	1.88556i	−0.0779439	+	0.0791860i
$568$	−8.51090	−	14.7413i	−0.357109	−	0.618532i
$569$	−2.69407	−	4.66627i	−0.112941	−	0.195620i	0.804014	−	0.594611i	$-0.202694\pi$
$569$	−2.69407	−	4.66627i	−0.112941	−	0.195620i	−0.916955	+	0.398991i	$0.869361\pi$
$570$	−2.28840			−0.0958507
$571$	−3.46902	−	6.00851i	−0.145174	−	0.251448i	0.784264	−	0.620427i	$-0.213041\pi$
$571$	−3.46902	−	6.00851i	−0.145174	−	0.251448i	−0.929438	+	0.368979i	$0.879707\pi$
$572$	2.87188e−5	−	0.0153721i	1.20079e−6	−	0.000642740i
$573$	25.1534			1.05080
$574$	29.8363	−	30.3117i	1.24534	−	1.26519i
$575$	1.26677	−	2.19411i	0.0528279	−	0.0915005i
$576$	7.99259			0.333025
$577$	−4.66974	−	8.08823i	−0.194404	−	0.336718i	0.752301	−	0.658820i	$-0.228944\pi$
$577$	−4.66974	−	8.08823i	−0.194404	−	0.336718i	−0.946705	+	0.322102i	$0.895611\pi$
$578$	27.2550	−	47.2071i	1.13366	−	1.96356i
$579$	−18.1553			−0.754510
$580$	−0.0317746			−0.00131937
$581$	−30.1733	+	30.6541i	−1.25180	+	1.27175i
$582$	7.40045	−	12.8180i	0.306759	−	0.531322i
$583$	5.44446	+	9.43009i	0.225487	+	0.390554i
$584$	15.0346	+	26.0407i	0.622136	+	1.07757i
$585$	0.0192600	−	10.3091i	0.000796302	−	0.426231i
$586$	15.2414	−	26.3988i	0.629615	−	1.09053i
$587$	−11.8226	+	20.4774i	−0.487972	+	0.845192i	−0.999904	−	0.0138340i	$-0.995596\pi$
$587$	−11.8226	+	20.4774i	−0.487972	+	0.845192i	0.511933	+	0.859026i	$0.328930\pi$
$588$	0.0113039	+	0.00629015i	0.000466163	+	0.000259401i
$589$	−2.15165	−	3.72676i	−0.0886571	−	0.153559i
$590$	−11.7759	+	20.3965i	−0.484807	+	0.839710i
$591$	0.782504	−	1.35534i	0.0321879	−	0.0557511i
$592$	4.60718	−	7.97987i	0.189354	−	0.327971i
$593$	6.02330	−	10.4327i	0.247347	−	0.428418i	−0.715442	−	0.698673i	$-0.753774\pi$
$593$	6.02330	−	10.4327i	0.247347	−	0.428418i	0.962789	+	0.270254i	$0.0871078\pi$
$594$	1.63208	+	2.82685i	0.0669652	+	0.115987i
$595$	−54.5633	−	14.1589i	−2.23688	−	0.580458i
$596$	0.0113141	−	0.0195966i	0.000463444	−	0.000802708i
$597$	7.55805	−	13.0909i	0.309330	−	0.535776i
$598$	0.00760434	−	4.07032i	0.000310964	−	0.166448i
$599$	3.07545	+	5.32684i	0.125660	+	0.217649i	0.921991	−	0.387212i	$-0.126562\pi$
$599$	3.07545	+	5.32684i	0.125660	+	0.217649i	−0.796331	+	0.604861i	$0.793229\pi$
$600$	−4.48848	−	7.77427i	−0.183241	−	0.317383i
$601$	2.33860	−	4.05057i	0.0953934	−	0.165226i	−0.814379	−	0.580333i	$-0.802922\pi$
$601$	2.33860	−	4.05057i	0.0953934	−	0.165226i	0.909773	+	0.415107i	$0.136256\pi$
$602$	7.51937	+	27.2008i	0.306467	+	1.10862i
$603$	3.17468			0.129283
$604$	0.0334245			0.00136002
$605$	8.11673	−	14.0586i	0.329992	−	0.571563i
$606$	−6.70281	−	11.6096i	−0.272283	−	0.471608i
$607$	−15.3001			−0.621011			−0.310505	−	0.950572i	$-0.600498\pi$
$607$	−15.3001			−0.621011			−0.310505	+	0.950572i	$0.600498\pi$
$608$	−0.00295676	+	0.00512126i	−0.000119912	+	0.000207694i
$609$	4.23917	+	15.3349i	0.171780	+	0.621401i
$610$	11.8695			0.480582
$611$	−0.00181633	+	0.972211i	−7.34807e−5	+	0.0393315i
$612$	0.00688536	+	0.0119258i	0.000278324	+	0.000482072i
$613$	11.5283			0.465622			0.232811	−	0.972522i	$-0.425208\pi$
$613$	11.5283			0.465622			0.232811	+	0.972522i	$0.425208\pi$
$614$	13.1906	+	22.8467i	0.532328	+	0.922019i
$615$	−16.2434	−	28.1344i	−0.654997	−	1.13449i
$616$	−12.1053	+	12.2982i	−0.487735	+	0.495508i
$617$	10.2940	+	17.8298i	0.414423	+	0.717801i	0.995368	−	0.0961418i	$-0.0306502\pi$
$617$	10.2940	+	17.8298i	0.414423	+	0.717801i	−0.580945	+	0.813943i	$0.697317\pi$
$618$	−28.7027			−1.15459
$619$	−9.83404	−	17.0331i	−0.395263	−	0.684616i	0.597871	−	0.801592i	$-0.296013\pi$
$619$	−9.83404	−	17.0331i	−0.395263	−	0.684616i	−0.993135	+	0.116976i	$0.962680\pi$
$620$	−0.0200985	+	0.0348116i	−0.000807175	+	0.00139807i
$621$	0.398944	+	0.690991i	0.0160091	+	0.0277285i
$622$	0.818393	−	1.41750i	0.0328146	−	0.0568365i
$623$	−3.63240	−	0.942589i	−0.145529	−	0.0377640i
$624$	−12.4880	−	7.24110i	−0.499921	−	0.289876i
$625$	15.3970	−	26.6684i	0.615879	−	1.06673i
$626$	−19.4121			−0.775863
$627$	1.30503			0.0521180
$628$	−0.0403426			−0.00160984
$629$	−17.1496			−0.683801
$630$	7.50830	−	7.62794i	0.299138	−	0.303905i
$631$	21.7095	+	37.6019i	0.864241	+	1.49691i	0.867799	+	0.496916i	$0.165534\pi$
$631$	21.7095	+	37.6019i	0.864241	+	1.49691i	−0.00355775	+	0.999994i	$0.501132\pi$
$632$	−5.69392	+	9.86215i	−0.226492	+	0.392295i
$633$	−8.28852	+	14.3561i	−0.329439	+	0.570606i
$634$	−6.05129			−0.240328
$635$	−5.89904	−	10.2174i	−0.234096	−	0.405467i
$636$	−0.00872237			−0.000345864
$637$	12.9229	+	21.6794i	0.512024	+	0.858971i
$638$	19.6288			0.777113
$639$	−3.01045	−	5.21425i	−0.119092	−	0.206273i
$640$	−32.3935			−1.28046
$641$	−13.4905	+	23.3663i	−0.532844	+	0.922912i	0.466421	+	0.884563i	$0.345543\pi$
$641$	−13.4905	+	23.3663i	−0.532844	+	0.922912i	−0.999264	+	0.0383494i	$0.987790\pi$
$642$	−9.45562	+	16.3776i	−0.373184	+	0.646373i
$643$	−2.55705	−	4.42895i	−0.100840	−	0.174661i	0.811191	−	0.584782i	$-0.198820\pi$
$643$	−2.55705	−	4.42895i	−0.100840	−	0.174661i	−0.912031	+	0.410121i	$0.865486\pi$
$644$	0.00273666	−	0.00278027i	0.000107840	−	0.000109558i
$645$	21.5556			0.848750
$646$	5.96392			0.234647
$647$	19.5448			0.768384			0.384192	−	0.923253i	$-0.374480\pi$
$647$	19.5448			0.768384			0.384192	+	0.923253i	$0.374480\pi$
$648$	2.82712			0.111060
$649$	6.71559	−	11.6317i	0.263610	−	0.456586i
$650$	−0.0302625	+	16.1984i	−0.00118699	+	0.635353i
$651$	19.4820	+	5.05548i	0.763561	+	0.198140i
$652$	0.0105100	−	0.0182038i	0.000411602	−	0.000712915i
$653$	−7.68131	−	13.3044i	−0.300593	−	0.520642i	0.675677	−	0.737197i	$-0.263851\pi$
$653$	−7.68131	−	13.3044i	−0.300593	−	0.520642i	−0.976270	+	0.216555i	$0.930518\pi$
$654$	0.666539	−	1.15448i	0.0260637	−	0.0451437i
$655$	10.7859	+	18.6817i	0.421440	+	0.729956i
$656$	−45.4900			−1.77608
$657$	5.31799	+	9.21103i	0.207475	+	0.359356i
$658$	−0.708075	+	0.719358i	−0.0276036	+	0.0280435i
$659$	−8.71206	−	15.0897i	−0.339374	−	0.587813i	0.644941	−	0.764232i	$-0.276882\pi$
$659$	−8.71206	−	15.0897i	−0.339374	−	0.587813i	−0.984315	+	0.176420i	$0.943548\pi$
$660$	−0.00609515	−	0.0105571i	−0.000237253	−	0.000410935i
$661$	16.7166			0.650202			0.325101	−	0.945679i	$-0.394602\pi$
$661$	16.7166			0.650202			0.325101	+	0.945679i	$0.394602\pi$
$662$	8.24948	+	14.2885i	0.320625	+	0.555339i
$663$	−0.0501943	+	26.8672i	−0.00194939	+	1.04343i
$664$	45.9614			1.78365
$665$	−1.14019	−	4.12454i	−0.0442145	−	0.159943i
$666$	1.62813	−	2.82001i	0.0630889	−	0.109273i
$667$	4.79804			0.185781
$668$	0.000485684	0	0.000841230i	1.87917e−5	0	3.25482e-5i
$669$	3.10234	−	5.37341i	0.119943	−	0.207748i
$670$	−12.8430			−0.496170
$671$	−6.76895			−0.261312
$672$	−0.00736952	−	0.0266587i	−0.000284285	−	0.00102838i
$673$	−15.0178	+	26.0116i	−0.578894	+	1.00267i	0.416713	+	0.909038i	$0.363182\pi$
$673$	−15.0178	+	26.0116i	−0.578894	+	1.00267i	−0.995607	+	0.0936354i	$0.970151\pi$
$674$	−11.5243	−	19.9606i	−0.443898	−	0.768854i
$675$	−1.58765	−	2.74989i	−0.0611087	−	0.105843i
$676$	0.0119343	+	0.0208503i	0.000459011	+	0.000801935i
$677$	1.91898	−	3.32377i	0.0737525	−	0.127743i	−0.826791	−	0.562510i	$-0.809836\pi$
$677$	1.91898	−	3.32377i	0.0737525	−	0.127743i	0.900543	+	0.434767i	$0.143169\pi$
$678$	1.82457	−	3.16025i	0.0700723	−	0.121369i
$679$	26.7899	+	6.95184i	1.02810	+	0.266787i
$680$	30.1174	+	52.1648i	1.15495	+	2.00043i
$681$	0.770318	−	1.33423i	0.0295187	−	0.0511278i
$682$	12.4159	−	21.5050i	0.475429	−	0.823468i
$683$	−13.9784	+	24.2113i	−0.534868	+	0.926419i	0.464301	+	0.885677i	$0.346305\pi$
$683$	−13.9784	+	24.2113i	−0.534868	+	0.926419i	−0.999170	+	0.0407419i	$0.987028\pi$
$684$	−0.000522686	0	0.000905319i	−1.99854e−5	0	3.46157e-5i
$685$	−23.8745	−	41.3518i	−0.912197	−	1.57997i
$686$	−6.17996	+	25.4645i	−0.235952	+	0.972240i
$687$	10.6720	−	18.4845i	0.407163	−	0.705227i
$688$	15.0917	−	26.1396i	0.575366	−	0.996563i
$689$	−14.7218	−	8.53636i	−0.560857	−	0.325209i
$690$	−1.61391	−	2.79537i	−0.0614405	−	0.106418i
$691$	8.97353	+	15.5426i	0.341369	+	0.591269i	0.984687	−	0.174330i	$-0.0557760\pi$
$691$	8.97353	+	15.5426i	0.341369	+	0.591269i	−0.643318	+	0.765599i	$0.722443\pi$
$692$	0.00845022	−	0.0146362i	0.000321229	−	0.000556385i
$693$	−4.28184	+	4.35007i	−0.162654	+	0.165246i
$694$	−36.3780			−1.38089
$695$	29.5815			1.12209
$696$	8.50034	−	14.7230i	0.322205	−	0.558075i
$697$	42.3327	+	73.3223i	1.60346	+	2.77728i
$698$	−2.57045			−0.0972929
$699$	−4.31457	+	7.47305i	−0.163192	+	0.282657i
$700$	−0.0108909	+	0.0110645i	−0.000411638	+	0.000418198i
$701$	35.0636			1.32433			0.662167	−	0.749356i	$-0.269637\pi$
$701$	35.0636			1.32433			0.662167	+	0.749356i	$0.269637\pi$
$702$	−4.41315	−	2.55894i	−0.166564	−	0.0965808i
$703$	−0.650938	−	1.12746i	−0.0245506	−	0.0425229i
$704$	18.4393			0.694957
$705$	0.385489	+	0.667686i	0.0145183	+	0.0251465i
$706$	−0.0441540	−	0.0764769i	−0.00166176	−	0.00287825i
$707$	17.5851	−	17.8654i	0.661357	−	0.671896i
$708$	0.00537939	+	0.00931738i	0.000202170	+	0.000350169i
$709$	−7.64503			−0.287115			−0.143558	−	0.989642i	$-0.545854\pi$
$709$	−7.64503			−0.287115			−0.143558	+	0.989642i	$0.545854\pi$
$710$	12.1786	+	21.0940i	0.457056	+	0.791645i
$711$	−2.01404	+	3.48841i	−0.0755322	+	0.130826i
$712$	2.00498	+	3.47272i	0.0751397	+	0.130146i
$713$	3.03492	−	5.25664i	0.113659	−	0.196863i
$714$	−19.5677	+	19.8795i	−0.732303	+	0.743973i
$715$	0.0444337	−	23.7837i	0.00166173	−	0.889460i
$716$	0.00159194	−	0.00275732i	5.94935e−5	−	0.000103046i
$717$	20.3222			0.758948
$718$	−18.9992			−0.709045
$719$	27.9531			1.04247			0.521237	−	0.853412i	$-0.325471\pi$
$719$	27.9531			1.04247			0.521237	+	0.853412i	$0.325471\pi$
$720$	−11.4476			−0.426625
$721$	−14.3010	−	51.7328i	−0.532596	−	1.92663i
$722$	−13.2149	−	22.8888i	−0.491806	−	0.851834i
$723$	−13.0577	+	22.6166i	−0.485620	+	0.841119i
$724$	0.00367499	−	0.00636528i	0.000136580	−	0.000236564i
$725$	−19.0945			−0.709151
$726$	−4.01647	−	6.95674i	−0.149065	−	0.258189i
$727$	−9.94798			−0.368950			−0.184475	−	0.982837i	$-0.559058\pi$
$727$	−9.94798			−0.368950			−0.184475	+	0.982837i	$0.559058\pi$
$728$	6.82272	−	26.0917i	0.252867	−	0.967023i
$729$	1.00000			0.0370370
$730$	−21.5137	−	37.2628i	−0.796258	−	1.37916i
$731$	−56.1770			−2.07778
$732$	0.00271107	−	0.00469571i	0.000100204	−	0.000173558i
$733$	−15.9308	+	27.5929i	−0.588416	+	1.01917i	0.406024	+	0.913863i	$0.366915\pi$
$733$	−15.9308	+	27.5929i	−0.588416	+	1.01917i	−0.994440	+	0.105304i	$0.966418\pi$
$734$	15.0989	+	26.1520i	0.557310	+	0.965289i
$735$	17.4893	+	9.73211i	0.645103	+	0.358974i
$736$	−0.00834108			−0.000307456
$737$	7.32414			0.269788
$738$	−16.0757			−0.591755
$739$	−18.1484			−0.667598			−0.333799	−	0.942644i	$-0.608331\pi$
$739$	−18.1484			−0.667598			−0.333799	+	0.942644i	$0.608331\pi$
$740$	−0.00608040	+	0.0105316i	−0.000223520	+	0.000387148i
$741$	−1.76821	+	1.01648i	−0.0649570	+	0.0373413i
$742$	−4.70763	−	17.0295i	−0.172823	−	0.625174i
$743$	−12.8238	+	22.2115i	−0.470460	+	0.814861i	−0.999429	−	0.0337802i	$-0.989245\pi$
$743$	−12.8238	+	22.2115i	−0.470460	+	0.814861i	0.528969	+	0.848641i	$0.322579\pi$
$744$	−10.7535	−	18.6256i	−0.394243	−	0.682848i
$745$	17.5052	−	30.3198i	0.641340	−	1.11083i
$746$	20.3512	+	35.2493i	0.745111	+	1.29057i
$747$	16.2573			0.594825
$748$	0.0158849	+	0.0275134i	0.000580808	+	0.00100599i
$749$	−34.2297	−	8.88242i	−1.25072	−	0.324557i
$750$	−3.69087	−	6.39277i	−0.134771	−	0.233431i
$751$	25.2869	+	43.7983i	0.922734	+	1.59822i	0.795166	+	0.606392i	$0.207384\pi$
$751$	25.2869	+	43.7983i	0.922734	+	1.59822i	0.127567	+	0.991830i	$0.459283\pi$
$752$	1.07957			0.0393678
$753$	−11.2757	−	19.5301i	−0.410911	−	0.711718i
$754$	−26.5955	+	15.2887i	−0.968550	+	0.556782i
$755$	51.7143			1.88208
$756$	−0.00130276	−	0.00471264i	−4.73809e−5	−	0.000171397i
$757$	0.651718	−	1.12881i	0.0236871	−	0.0410272i	−0.853939	−	0.520373i	$-0.825793\pi$
$757$	0.651718	−	1.12881i	0.0236871	−	0.0410272i	0.877626	+	0.479346i	$0.159126\pi$
$758$	27.5028			0.998948
$759$	0.920383	+	1.59415i	0.0334078	+	0.0578640i
$760$	−2.28629	+	3.95997i	−0.0829325	+	0.143643i
$761$	15.3520			0.556510			0.278255	−	0.960507i	$-0.410244\pi$
$761$	15.3520			0.556510			0.278255	+	0.960507i	$0.410244\pi$
$762$	−5.83814			−0.211494
$763$	2.41289	+	0.626134i	0.0873526	+	0.0226676i
$764$	−0.0232420	+	0.0402563i	−0.000840866	+	0.00145642i
$765$	10.6530	+	18.4516i	0.385161	+	0.667118i
$766$	21.4078	+	37.0793i	0.773494	+	1.33973i
$767$	−0.0392158	+	20.9908i	−0.00141600	+	0.757933i
$768$	−0.0221762	+	0.0384103i	−0.000800214	+	0.00138601i
$769$	−9.84042	+	17.0441i	−0.354855	+	0.614626i	−0.987093	−	0.160148i	$-0.948803\pi$
$769$	−9.84042	+	17.0441i	−0.354855	+	0.614626i	0.632239	+	0.774774i	$0.282136\pi$
$770$	17.3220	−	17.5980i	0.624241	−	0.634189i
$771$	0.536216	+	0.928754i	0.0193114	+	0.0334483i
$772$	0.0167757	−	0.0290563i	0.000603770	−	0.00104576i
$773$	9.18054	−	15.9012i	0.330201	−	0.571925i	−0.652350	−	0.757918i	$-0.726217\pi$
$773$	9.18054	−	15.9012i	0.330201	−	0.571925i	0.982551	+	0.185993i	$0.0595502\pi$
$774$	5.33327	−	9.23749i	0.191700	−	0.332035i
$775$	−12.0779	+	20.9195i	−0.433851	+	0.751451i
$776$	−14.7872	−	25.6122i	−0.530831	−	0.919426i
$777$	5.89390	+	1.52944i	0.211442	+	0.0548682i
$778$	−0.436238	+	0.755586i	−0.0156399	+	0.0270891i
$779$	−3.21359	+	5.56610i	−0.115139	+	0.199426i
$780$	0.0164813	+	0.00955656i	0.000590124	+	0.000342180i
$781$	−6.94525	−	12.0295i	−0.248521	−	0.430450i
$782$	4.20609	+	7.28515i	0.150409	+	0.260517i
$783$	3.00672	−	5.20778i	0.107451	−	0.186111i
$784$	24.0465	−	14.3949i	0.858805	−	0.514102i
$785$	−62.4180			−2.22779
$786$	10.6746			0.380749
$787$	1.61200	−	2.79206i	0.0574615	−	0.0995262i	−0.835864	−	0.548937i	$-0.815033\pi$
$787$	1.61200	−	2.79206i	0.0574615	−	0.0995262i	0.893325	+	0.449411i	$0.148366\pi$
$788$	0.00144608	+	0.00250469i	5.15145e−5	+	8.92257e-5i
$789$	15.4691			0.550715
$790$	8.14769	−	14.1122i	0.289882	−	0.502090i
$791$	6.60502	+	1.71397i	0.234847	+	0.0609417i
$792$	6.52230			0.231760
$793$	9.17137	−	5.27227i	0.325685	−	0.187224i
$794$	20.9241	+	36.2417i	0.742570	+	1.28617i
$795$	−13.4952			−0.478627
$796$	0.0139674	+	0.0241923i	0.000495062	+	0.000857472i
$797$	−7.59673	−	13.1579i	−0.269090	−	0.466078i	0.699537	−	0.714596i	$-0.253390\pi$
$797$	−7.59673	−	13.1579i	−0.269090	−	0.466078i	−0.968627	+	0.248519i	$0.920056\pi$
$798$	−2.04965	−	0.531873i	−0.0725567	−	0.0188281i
$799$	−1.00464	−	1.74009i	−0.0355416	−	0.0615599i
$800$	0.0331945			0.00117360
$801$	0.709194	+	1.22836i	0.0250582	+	0.0434020i
$802$	−14.0407	+	24.3192i	−0.495794	+	0.858740i
$803$	12.2689	+	21.2503i	0.432959	+	0.749906i
$804$	−0.00293343	+	0.00508085i	−0.000103454	+	0.000179188i
$805$	4.23416	−	4.30164i	0.149235	−	0.151613i
$806$	−0.0725029	+	38.8081i	−0.00255381	+	1.36696i
$807$	−1.11891	+	1.93801i	−0.0393875	+	0.0682212i
$808$	−26.7865			−0.942345
$809$	−29.0109			−1.01997			−0.509984	−	0.860184i	$-0.670349\pi$
$809$	−29.0109			−1.01997			−0.509984	+	0.860184i	$0.670349\pi$
$810$	−4.04546			−0.142143
$811$	−20.5902			−0.723020			−0.361510	−	0.932368i	$-0.617739\pi$
$811$	−20.5902			−0.723020			−0.361510	+	0.932368i	$0.617739\pi$
$812$	−0.0284594	−	0.00738508i	−0.000998730	−	0.000259165i
$813$	−3.07220	−	5.32120i	−0.107747	−	0.186623i
$814$	3.75618	−	6.50590i	0.131654	−	0.228032i
$815$	16.2610	−	28.1649i	0.569598	−	0.986572i
$816$	29.8340			1.04440
$817$	−2.13227	−	3.69321i	−0.0745988	−	0.129209i
$818$	−33.2951			−1.16414
$819$	2.41331	−	9.22908i	0.0843279	−	0.322490i
$820$	0.0600361			0.00209655
$821$	−0.143029	−	0.247733i	−0.00499174	−	0.00864595i	0.863519	−	0.504317i	$-0.168256\pi$
$821$	−0.143029	−	0.247733i	−0.00499174	−	0.00864595i	−0.868510	+	0.495671i	$0.834922\pi$
$822$	−23.6280			−0.824122
$823$	−11.2907	+	19.5560i	−0.393568	+	0.681681i	−0.992917	−	0.118807i	$-0.962093\pi$
$823$	−11.2907	+	19.5560i	−0.393568	+	0.681681i	0.599349	+	0.800488i	$0.295426\pi$
$824$	−28.6762	+	49.6686i	−0.998982	+	1.73029i
$825$	−3.66279	−	6.34414i	−0.127522	−	0.220874i
$826$	−15.2879	+	15.5315i	−0.531933	+	0.540409i
$827$	27.6090			0.960060			0.480030	−	0.877252i	$-0.340626\pi$
$827$	27.6090			0.960060			0.480030	+	0.877252i	$0.340626\pi$
$828$	−0.00147451			−5.12428e−5
$829$	30.1954			1.04873			0.524366	−	0.851493i	$-0.324303\pi$
$829$	30.1954			1.04873			0.524366	+	0.851493i	$0.324303\pi$
$830$	−65.7683			−2.28285
$831$	1.67414	−	2.89969i	0.0580752	−	0.100589i
$832$	−24.9837	+	14.3622i	−0.866155	+	0.497920i
$833$	−45.5797	−	25.3633i	−1.57924	−	0.878786i
$834$	7.31903	−	12.6769i	0.253437	−	0.438966i
$835$	0.751450	+	1.30155i	0.0260050	+	0.0450420i
$836$	−0.00120586	+	0.00208862i	−4.17056e−5	+	7.22363e-5i
$837$	−3.80370	−	6.58820i	−0.131475	−	0.227721i
$838$	50.0392			1.72857
$839$	25.9928	+	45.0209i	0.897372	+	1.55429i	0.830841	+	0.556509i	$0.187860\pi$
$839$	25.9928	+	45.0209i	0.897372	+	1.55429i	0.0665306	+	0.997784i	$0.478807\pi$
$840$	−5.69842	−	20.6136i	−0.196614	−	0.711238i
$841$	−3.58067	−	6.20190i	−0.123471	−	0.213859i
$842$	−7.16351	−	12.4076i	−0.246871	−	0.427593i
$843$	−14.2117			−0.489477
$844$	−0.0153173	−	0.0265304i	−0.000527244	−	0.000913214i
$845$	18.4647	+	32.2596i	0.635205	+	1.10976i
$846$	0.381509			0.0131166
$847$	10.5374	−	10.7053i	0.362069	−	0.367839i
$848$	−9.44842	+	16.3651i	−0.324460	+	0.561981i
$849$	14.6283			0.502044
$850$	−16.7387	−	28.9923i	−0.574132	−	0.994427i
$851$	0.918155	−	1.59029i	0.0314740	−	0.0545145i
$852$	0.0111267			0.000381195
$853$	11.5389			0.395085			0.197542	−	0.980294i	$-0.436704\pi$
$853$	11.5389			0.395085			0.197542	+	0.980294i	$0.436704\pi$
$854$	10.6311	+	2.75872i	0.363789	+	0.0944013i
$855$	−0.808700	+	1.40071i	−0.0276569	+	0.0479032i
$856$	18.8938	+	32.7250i	0.645776	+	1.11852i
$857$	3.43142	+	5.94339i	0.117215	+	0.203022i	0.918663	−	0.395042i	$-0.129270\pi$
$857$	3.43142	+	5.94339i	0.117215	+	0.203022i	−0.801448	+	0.598064i	$0.795937\pi$
$858$	−10.1813	−	5.90359i	−0.347585	−	0.201545i
$859$	−6.60534	+	11.4408i	−0.225371	+	0.390355i	−0.956431	−	0.291959i	$-0.905693\pi$
$859$	−6.60534	+	11.4408i	−0.225371	+	0.390355i	0.731059	+	0.682314i	$0.239026\pi$
$860$	−0.0199175	+	0.0344982i	−0.000679182	+	0.00117638i
$861$	−8.00964	−	28.9743i	−0.272968	−	0.987442i
$862$	−4.41650	−	7.64961i	−0.150427	−	0.260547i
$863$	11.4551	−	19.8408i	0.389937	−	0.675390i	−0.602504	−	0.798116i	$-0.705830\pi$
$863$	11.4551	−	19.8408i	0.389937	−	0.675390i	0.992441	+	0.122726i	$0.0391635\pi$
$864$	−0.00522698	+	0.00905339i	−0.000177825	+	0.000308003i
$865$	13.0742	−	22.6451i	0.444535	−	0.769957i
$866$	−23.9427	+	41.4699i	−0.813605	+	1.40920i
$867$	−19.2633	−	33.3651i	−0.654217	−	1.13314i
$868$	−0.0260925	+	0.0265083i	−0.000885637	+	0.000899750i
$869$	−4.64648	+	8.04793i	−0.157621	+	0.273007i
$870$	−12.1635	+	21.0679i	−0.412382	+	0.714267i
$871$	−9.92361	+	5.70471i	−0.336249	+	0.193297i
$872$	−1.33185	−	2.30683i	−0.0451020	−	0.0781190i
$873$	−5.23049	−	9.05948i	−0.177025	−	0.306617i
$874$	−0.319295	+	0.553036i	−0.0108003	+	0.0187067i
$875$	9.68315	−	9.83745i	0.327350	−	0.332567i
$876$	−0.0196555			−0.000664097
$877$	−28.5019			−0.962440			−0.481220	−	0.876600i	$-0.659806\pi$
$877$	−28.5019			−0.962440			−0.481220	+	0.876600i	$0.659806\pi$
$878$	6.27834	−	10.8744i	0.211884	−	0.366993i
$879$	−10.7723	−	18.6582i	−0.363341	−	0.629324i
$880$	−26.4101			−0.890283
$881$	15.9035	−	27.5457i	0.535804	−	0.928039i	−0.463320	−	0.886191i	$-0.653342\pi$
$881$	15.9035	−	27.5457i	0.535804	−	0.928039i	0.999124	−	0.0418483i	$-0.0133246\pi$
$882$	8.49782	−	5.08701i	0.286136	−	0.171288i
$883$	11.0073			0.370427			0.185213	−	0.982698i	$-0.440702\pi$
$883$	11.0073			0.370427			0.185213	+	0.982698i	$0.440702\pi$
$884$	−0.0429526	−	0.0249058i	−0.00144465	−	0.000837673i
$885$	8.32299	+	14.4158i	0.279774	+	0.484583i
$886$	16.8414			0.565799
$887$	11.1025	+	19.2302i	0.372787	+	0.645686i	0.989993	−	0.141116i	$-0.0450690\pi$
$887$	11.1025	+	19.2302i	0.372787	+	0.645686i	−0.617206	+	0.786801i	$0.711736\pi$
$888$	−3.25326	−	5.63481i	−0.109172	−	0.189092i
$889$	−2.90883	−	10.5225i	−0.0975589	−	0.352912i
$890$	−2.86901	−	4.96928i	−0.0961696	−	0.166571i
$891$	2.30705			0.0772890
$892$	0.00573317	+	0.00993015i	0.000191961	+	0.000332486i
$893$	0.0762650	−	0.132095i	0.00255211	−	0.00442038i
$894$	−8.66223	−	15.0034i	−0.289708	−	0.501790i
$895$	2.46304	−	4.26611i	0.0823304	−	0.142600i
$896$	−29.0137	−	7.52892i	−0.969281	−	0.251523i
$897$	−2.48871	−	1.44306i	−0.0830957	−	0.0481825i
$898$	−4.20628	+	7.28550i	−0.140366	+	0.243120i
$899$	−45.7465			−1.52573
$900$	0.00586801			0.000195600
$901$	35.1706			1.17170
$902$	−37.0875			−1.23488
$903$	19.3066	+	5.00997i	0.642484	+	0.166721i
$904$	−3.64577	−	6.31467i	−0.121257	−	0.210023i
$905$	5.68595	−	9.84835i	0.189007	−	0.327370i
$906$	12.7951	−	22.1618i	0.425089	−	0.736276i
$907$	1.59043			0.0528092			0.0264046	−	0.999651i	$-0.491594\pi$
$907$	1.59043			0.0528092			0.0264046	+	0.999651i	$0.491594\pi$
$908$	0.00142356	+	0.00246568i	4.72425e−5	+	8.18265e-5i
$909$	−9.47483			−0.314260
$910$	−9.76294	+	37.3358i	−0.323638	+	1.23767i
$911$	−2.61896			−0.0867699			−0.0433849	−	0.999058i	$-0.513814\pi$
$911$	−2.61896			−0.0867699			−0.0433849	+	0.999058i	$0.513814\pi$
$912$	1.13239	+	1.96136i	0.0374972	+	0.0649470i
$913$	37.5065			1.24128
$914$	8.56862	−	14.8413i	0.283425	−	0.490906i
$915$	4.19456	−	7.26519i	0.138668	−	0.240180i
$916$	0.0197221	+	0.0341596i	0.000651635	+	0.00112867i
$917$	5.31855	+	19.2395i	0.175634	+	0.635343i
$918$	10.5431			0.347973
$919$	20.1784			0.665623			0.332811	−	0.942993i	$-0.392003\pi$
$919$	20.1784			0.665623			0.332811	+	0.942993i	$0.392003\pi$
$920$	−6.44967			−0.212639
$921$	18.6457			0.614396
$922$	3.61743	−	6.26558i	0.119134	−	0.206346i
$923$	18.7799	+	10.8894i	0.618149	+	0.358430i
$924$	−0.00300553	−	0.0108723i	−9.88746e−5	−	0.000357672i
$925$	−3.65392	+	6.32878i	−0.120140	+	0.208089i
$926$	−27.5435	−	47.7068i	−0.905136	−	1.56774i
$927$	−10.1433	+	17.5686i	−0.333148	+	0.577029i
$928$	0.0314321	+	0.0544419i	0.00103181	+	0.00178714i
$929$	−32.8102			−1.07647			−0.538234	−	0.842796i	$-0.680908\pi$
$929$	−32.8102			−1.07647			−0.538234	+	0.842796i	$0.680908\pi$
$930$	15.3877	+	26.6523i	0.504582	+	0.873962i
$931$	−0.0625967	−	3.95921i	−0.00205152	−	0.129758i
$932$	−0.00797339	−	0.0138103i	−0.000261177	−	0.000452372i
$933$	−0.578424	−	1.00186i	−0.0189368	−	0.0327994i
$934$	19.8824			0.650573
$935$	24.5770	+	42.5687i	0.803755	+	1.39214i
$936$	−8.83718	+	5.08016i	−0.288852	+	0.166050i
$937$	48.1088			1.57165			0.785823	−	0.618452i	$-0.212240\pi$
$937$	48.1088			1.57165			0.785823	+	0.618452i	$0.212240\pi$
$938$	−11.5031	−	2.98499i	−0.375589	−	0.0974633i
$939$	−6.86004	+	11.8819i	−0.223869	+	0.387752i
$940$	−0.00142478			−4.64712e−5
$941$	5.25163	+	9.09609i	0.171198	+	0.296524i	0.938839	−	0.344356i	$-0.111903\pi$
$941$	5.25163	+	9.09609i	0.171198	+	0.296524i	−0.767641	+	0.640880i	$0.778569\pi$
$942$	−15.4434	+	26.7488i	−0.503174	+	0.871523i
$943$	−9.06560			−0.295217
$944$	23.3087			0.758634
$945$	−2.01563	−	7.29139i	−0.0655684	−	0.237189i
$946$	12.3041	−	21.3113i	0.400041	−	0.692891i
$947$	0.314804	+	0.545257i	0.0102298	+	0.0177185i	0.871095	−	0.491115i	$-0.163410\pi$
$947$	0.314804	+	0.545257i	0.0102298	+	0.0177185i	−0.860865	+	0.508833i	$0.830077\pi$
$948$	−0.00372197	−	0.00644664i	−0.000120884	−	0.000209377i
$949$	−33.1750	−	19.2363i	−1.07690	−	0.624437i
$950$	1.27068	−	2.20088i	0.0412263	−	0.0714060i
$951$	−2.13847	+	3.70393i	−0.0693446	+	0.120108i
$952$	14.8509	+	53.7221i	0.481321	+	1.74114i
$953$	10.6206	+	18.3954i	0.344034	+	0.595885i	0.985178	−	0.171536i	$-0.0548730\pi$
$953$	10.6206	+	18.3954i	0.344034	+	0.595885i	−0.641144	+	0.767421i	$0.721540\pi$
$954$	−3.33898	+	5.78329i	−0.108104	+	0.187241i
$955$	−35.9600	+	62.2845i	−1.16364	+	2.01548i
$956$	−0.0187779	+	0.0325243i	−0.000607321	+	0.00105191i
$957$	6.93664	−	12.0146i	0.224230	−	0.388377i
$958$	−22.8314	−	39.5451i	−0.737648	−	1.27764i
$959$	−11.7725	−	42.5864i	−0.380155	−	1.37518i
$960$	−11.4264	+	19.7911i	−0.368786	+	0.638756i
$961$	−13.4362	+	23.2722i	−0.433427	+	0.750717i
$962$	−0.0219343	+	11.7406i	−0.000707190	+	0.378533i
$963$	6.68305	+	11.5754i	0.215358	+	0.373011i
$964$	−0.0241308	−	0.0417958i	−0.000777201	−	0.00134615i
$965$	25.9553	−	44.9559i	0.835531	−	1.44718i
$966$	−0.795822	−	2.87883i	−0.0256051	−	0.0926248i
$967$	15.0353			0.483502			0.241751	−	0.970338i	$-0.422278\pi$
$967$	15.0353			0.483502			0.241751	+	0.970338i	$0.422278\pi$
$968$	−16.0511			−0.515900
$969$	2.10759	−	3.65045i	0.0677055	−	0.117269i
$970$	21.1597	+	36.6497i	0.679398	+	1.17675i
$971$	−7.88140			−0.252926			−0.126463	−	0.991971i	$-0.540363\pi$
$971$	−7.88140			−0.252926			−0.126463	+	0.991971i	$0.540363\pi$
$972$	−0.000924008		0.00160043i	−2.96376e−5		5.13338e-5i
$973$	26.4951	+	6.87535i	0.849395	+	0.220414i
$974$	17.3768			0.556790
$975$	9.90417	+	5.74287i	0.317187	+	0.183919i
$976$	−5.87348	−	10.1732i	−0.188005	−	0.325635i
$977$	17.9482			0.574213			0.287107	−	0.957899i	$-0.407307\pi$
$977$	17.9482			0.574213			0.287107	+	0.957899i	$0.407307\pi$
$978$	−8.04657	−	13.9371i	−0.257301	−	0.445658i
$979$	1.63615	+	2.83389i	0.0522914	+	0.0905714i
$980$	−0.0317358	+	0.0189979i	−0.00101376	+	0.000606864i
$981$	−0.471097	−	0.815964i	−0.0150410	−	0.0260517i
$982$	−30.7113			−0.980037
$983$	2.92791	+	5.07129i	0.0933858	+	0.161749i	0.908934	−	0.416941i	$-0.136898\pi$
$983$	2.92791	+	5.07129i	0.0933858	+	0.161749i	−0.815548	+	0.578689i	$0.803564\pi$
$984$	−16.0609	+	27.8182i	−0.512002	+	0.886813i
$985$	2.23737	+	3.87525i	0.0712887	+	0.123476i
$986$	31.7000	−	54.9059i	1.00953	−	1.74856i
$987$	0.190085	+	0.687619i	0.00605048	+	0.0218872i
$988$	7.04166e−6	−	0.00376914i	2.24025e−7	−	0.000119912i
$989$	3.00760	−	5.20931i	0.0956360	−	0.165646i
$990$	−9.33306			−0.296624
$991$	51.2028			1.62651			0.813255	−	0.581908i	$-0.197694\pi$
$991$	51.2028			1.62651			0.813255	+	0.581908i	$0.197694\pi$
$992$	0.0795274			0.00252500
$993$	11.6611			0.370055
$994$	6.00531	+	21.7238i	0.190477	+	0.689036i
$995$	21.6104	+	37.4302i	0.685094	+	1.18662i
$996$	−0.0150219	+	0.0260187i	−0.000475987	+	0.000824434i
$997$	−2.52862	+	4.37970i	−0.0800822	+	0.138707i	−0.903285	−	0.429041i	$-0.858852\pi$
$997$	−2.52862	+	4.37970i	−0.0800822	+	0.138707i	0.823203	+	0.567747i	$0.192185\pi$
$998$	−13.9788			−0.442491
$999$	−1.15073	−	1.99313i	−0.0364076	−	0.0630598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.j.c.100.7	✓	20
3.2	odd	2		819.2.n.f.100.4		20
7.4	even	3		273.2.l.c.256.4	yes	20
13.3	even	3		273.2.l.c.16.4	yes	20
21.11	odd	6		819.2.s.f.802.7		20
39.29	odd	6		819.2.s.f.289.7		20
91.81	even	3	inner	273.2.j.c.172.7	yes	20
273.263	odd	6		819.2.n.f.172.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.7	✓	20	1.1	even	1	trivial
273.2.j.c.172.7	yes	20	91.81	even	3	inner
273.2.l.c.16.4	yes	20	13.3	even	3
273.2.l.c.256.4	yes	20	7.4	even	3
819.2.n.f.100.4		20	3.2	odd	2
819.2.n.f.172.4		20	273.263	odd	6
819.2.s.f.289.7		20	39.29	odd	6
819.2.s.f.802.7		20	21.11	odd	6

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707433 + 1.22531i) q^{2} +1.00000 q^{3} +(-0.000924008 + 0.00160043i) q^{4} +(-1.42962 + 2.47618i) q^{5} +(0.707433 + 1.22531i) q^{6} +(-1.85598 + 1.88556i) q^{7} +2.82712 q^{8} +1.00000 q^{9} -4.04546 q^{10} +2.30705 q^{11} +(-0.000924008 + 0.00160043i) q^{12} +(-3.12586 + 1.79694i) q^{13} +(-3.62338 - 0.940248i) q^{14} +(-1.42962 + 2.47618i) q^{15} +(2.00185 + 3.46730i) q^{16} +(3.72581 - 6.45329i) q^{17} +(0.707433 + 1.22531i) q^{18} +0.565673 q^{19} +(-0.00264197 - 0.00457603i) q^{20} +(-1.85598 + 1.88556i) q^{21} +(1.63208 + 2.82685i) q^{22} +(0.398944 + 0.690991i) q^{23} +2.82712 q^{24} +(-1.58765 - 2.74989i) q^{25} +(-4.41315 - 2.55894i) q^{26} +1.00000 q^{27} +(-0.00130276 - 0.00471264i) q^{28} +(3.00672 - 5.20778i) q^{29} -4.04546 q^{30} +(-3.80370 - 6.58820i) q^{31} +(-0.00522698 + 0.00905339i) q^{32} +2.30705 q^{33} +10.5431 q^{34} +(-2.01563 - 7.29139i) q^{35} +(-0.000924008 + 0.00160043i) q^{36} +(-1.15073 - 1.99313i) q^{37} +(0.400176 + 0.693125i) q^{38} +(-3.12586 + 1.79694i) q^{39} +(-4.04172 + 7.00046i) q^{40} +(-5.68100 + 9.83978i) q^{41} +(-3.62338 - 0.940248i) q^{42} +(-3.76945 - 6.52888i) q^{43} +(-0.00213173 + 0.00369227i) q^{44} +(-1.42962 + 2.47618i) q^{45} +(-0.564452 + 0.977660i) q^{46} +(0.134822 - 0.233518i) q^{47} +(2.00185 + 3.46730i) q^{48} +(-0.110659 - 6.99913i) q^{49} +(2.24632 - 3.89073i) q^{50} +(3.72581 - 6.45329i) q^{51} +(1.24483e-5 - 0.00666311i) q^{52} +(2.35993 + 4.08751i) q^{53} +(0.707433 + 1.22531i) q^{54} +(-3.29821 + 5.71267i) q^{55} +(-5.24708 + 5.33070i) q^{56} +0.565673 q^{57} +8.50820 q^{58} +(2.91090 - 5.04183i) q^{59} +(-0.00264197 - 0.00457603i) q^{60} -2.93403 q^{61} +(5.38172 - 9.32142i) q^{62} +(-1.85598 + 1.88556i) q^{63} +7.99259 q^{64} +(0.0192600 - 10.3091i) q^{65} +(1.63208 + 2.82685i) q^{66} +3.17468 q^{67} +(0.00688536 + 0.0119258i) q^{68} +(0.398944 + 0.690991i) q^{69} +(7.50830 - 7.62794i) q^{70} +(-3.01045 - 5.21425i) q^{71} +2.82712 q^{72} +(5.31799 + 9.21103i) q^{73} +(1.62813 - 2.82001i) q^{74} +(-1.58765 - 2.74989i) q^{75} +(-0.000522686 + 0.000905319i) q^{76} +(-4.28184 + 4.35007i) q^{77} +(-4.41315 - 2.55894i) q^{78} +(-2.01404 + 3.48841i) q^{79} -11.4476 q^{80} +1.00000 q^{81} -16.0757 q^{82} +16.2573 q^{83} +(-0.00130276 - 0.00471264i) q^{84} +(10.6530 + 18.4516i) q^{85} +(5.33327 - 9.23749i) q^{86} +(3.00672 - 5.20778i) q^{87} +6.52230 q^{88} +(0.709194 + 1.22836i) q^{89} -4.04546 q^{90} +(2.41331 - 9.22908i) q^{91} -0.00147451 q^{92} +(-3.80370 - 6.58820i) q^{93} +0.381509 q^{94} +(-0.808700 + 1.40071i) q^{95} +(-0.00522698 + 0.00905339i) q^{96} +(-5.23049 - 9.05948i) q^{97} +(8.49782 - 5.08701i) q^{98} +2.30705 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) \) 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9 + 8 * q^10 + 16 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 - 20 * q^16 - 14 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 - 14 * q^23 - 12 * q^24 - 32 * q^25 + 4 * q^26 + 20 * q^27 + 13 * q^28 - 9 * q^29 + 8 * q^30 - 9 * q^31 + 17 * q^32 + 16 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 + 18 * q^37 + 22 * q^38 - 5 * q^39 - 9 * q^40 - q^41 - 9 * q^42 - 11 * q^43 + 8 * q^44 - 10 * q^46 + 13 * q^47 - 20 * q^48 - 21 * q^49 + 5 * q^50 - 2 * q^52 - 6 * q^53 - 19 * q^55 - 5 * q^56 - 14 * q^57 - 15 * q^59 + 12 * q^60 + 22 * q^62 - 9 * q^63 + 72 * q^64 - 27 * q^65 - 9 * q^66 + 44 * q^67 + 39 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 - 12 * q^72 - 3 * q^74 - 32 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 - 96 * q^80 + 20 * q^81 + 26 * q^82 + 40 * q^83 + 13 * q^84 - 16 * q^85 + 4 * q^86 - 9 * q^87 + 24 * q^88 + 2 * q^89 + 8 * q^90 + 9 * q^91 + 66 * q^92 - 9 * q^93 + 88 * q^94 - 36 * q^95 + 17 * q^96 + 21 * q^97 - 79 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more