LMFDB - Embedded newform 143.2.h.c.92.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(14,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("143.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.h (of order $5$, degree $4$, 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:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			92.6
Character	$\chi$	$=$	143.92
Dual form			143.2.h.c.14.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61320 + 1.17206i) q^{2} +(-0.781399 + 2.40490i) q^{3} +(0.610652 + 1.87939i) q^{4} +(1.47757 - 1.07352i) q^{5} +(-4.07922 + 2.96373i) q^{6} +(-0.624919 - 1.92330i) q^{7} +(0.0147190 - 0.0453005i) q^{8} +(-2.74590 - 1.99502i) q^{9} +O(q^{10})$	\(q+(1.61320 + 1.17206i) q^{2} +(-0.781399 + 2.40490i) q^{3} +(0.610652 + 1.87939i) q^{4} +(1.47757 - 1.07352i) q^{5} +(-4.07922 + 2.96373i) q^{6} +(-0.624919 - 1.92330i) q^{7} +(0.0147190 - 0.0453005i) q^{8} +(-2.74590 - 1.99502i) q^{9} +3.64184 q^{10} +(-2.99848 + 1.41744i) q^{11} -4.99692 q^{12} +(-0.809017 - 0.587785i) q^{13} +(1.24610 - 3.83510i) q^{14} +(1.42713 + 4.39226i) q^{15} +(3.27426 - 2.37889i) q^{16} +(1.34223 - 0.975189i) q^{17} +(-2.09141 - 6.43670i) q^{18} +(-0.610527 + 1.87901i) q^{19} +(2.91985 + 2.12140i) q^{20} +5.11366 q^{21} +(-6.49845 - 1.22777i) q^{22} +3.93925 q^{23} +(0.0974417 + 0.0707955i) q^{24} +(-0.514306 + 1.58287i) q^{25} +(-0.616186 - 1.89642i) q^{26} +(0.806273 - 0.585792i) q^{27} +(3.23304 - 2.34894i) q^{28} +(-2.68126 - 8.25206i) q^{29} +(-2.84573 + 8.75826i) q^{30} +(2.14284 + 1.55686i) q^{31} +7.97494 q^{32} +(-1.06580 - 8.31862i) q^{33} +3.30826 q^{34} +(-2.98807 - 2.17096i) q^{35} +(2.07263 - 6.37890i) q^{36} +(0.429275 + 1.32117i) q^{37} +(-3.18720 + 2.31564i) q^{38} +(2.04573 - 1.48631i) q^{39} +(-0.0268826 - 0.0827360i) q^{40} +(-2.86998 + 8.83290i) q^{41} +(8.24934 + 5.99350i) q^{42} -12.8417 q^{43} +(-4.49496 - 4.76976i) q^{44} -6.19897 q^{45} +(6.35478 + 4.61702i) q^{46} +(-1.90279 + 5.85620i) q^{47} +(3.16248 + 9.73312i) q^{48} +(2.35455 - 1.71068i) q^{49} +(-2.68489 + 1.95069i) q^{50} +(1.29641 + 3.98995i) q^{51} +(0.610652 - 1.87939i) q^{52} +(-9.98909 - 7.25750i) q^{53} +1.98726 q^{54} +(-2.90882 + 5.31330i) q^{55} -0.0963248 q^{56} +(-4.04176 - 2.93651i) q^{57} +(5.34648 - 16.4548i) q^{58} +(-1.23989 - 3.81599i) q^{59} +(-7.38332 + 5.36429i) q^{60} +(12.5865 - 9.14460i) q^{61} +(1.63209 + 5.02305i) q^{62} +(-2.12105 + 6.52793i) q^{63} +(6.31662 + 4.58929i) q^{64} -1.82638 q^{65} +(8.03054 - 14.6687i) q^{66} +6.46440 q^{67} +(2.65240 + 1.92708i) q^{68} +(-3.07813 + 9.47350i) q^{69} +(-2.27586 - 7.00437i) q^{70} +(-2.88721 + 2.09768i) q^{71} +(-0.130792 + 0.0950261i) q^{72} +(0.140323 + 0.431870i) q^{73} +(-0.855982 + 2.63444i) q^{74} +(-3.40477 - 2.47371i) q^{75} -3.90422 q^{76} +(4.59998 + 4.88119i) q^{77} +5.04220 q^{78} +(3.90340 + 2.83598i) q^{79} +(2.28417 - 7.02996i) q^{80} +(-2.36778 - 7.28727i) q^{81} +(-14.9825 + 10.8854i) q^{82} +(-6.13034 + 4.45395i) q^{83} +(3.12267 + 9.61059i) q^{84} +(0.936363 - 2.88183i) q^{85} +(-20.7161 - 15.0511i) q^{86} +21.9405 q^{87} +(0.0200762 + 0.156696i) q^{88} -2.42469 q^{89} +(-10.0001 - 7.26553i) q^{90} +(-0.624919 + 1.92330i) q^{91} +(2.40551 + 7.40341i) q^{92} +(-5.41852 + 3.93678i) q^{93} +(-9.93336 + 7.21701i) q^{94} +(1.11506 + 3.43179i) q^{95} +(-6.23161 + 19.1789i) q^{96} +(13.8540 + 10.0655i) q^{97} +5.80335 q^{98} +(11.0614 + 2.08985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) $ 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	1.61320	+	1.17206i	1.14070	+	0.828768i	0.987217	−	0.159383i	$-0.0509505\pi$
$2$	1.61320	+	1.17206i	1.14070	+	0.828768i	0.153485	+	0.988151i	$0.450950\pi$
$3$	−0.781399	+	2.40490i	−0.451141	+	1.38847i	0.424465	+	0.905444i	$0.360462\pi$
$3$	−0.781399	+	2.40490i	−0.451141	+	1.38847i	−0.875606	+	0.483025i	$0.839538\pi$
$4$	0.610652	+	1.87939i	0.305326	+	0.939697i
$5$	1.47757	−	1.07352i	0.660791	−	0.480093i	−0.206139	−	0.978523i	$-0.566090\pi$
$5$	1.47757	−	1.07352i	0.660791	−	0.480093i	0.866930	+	0.498430i	$0.166090\pi$
$6$	−4.07922	+	2.96373i	−1.66534	+	1.20994i
$7$	−0.624919	−	1.92330i	−0.236197	−	0.726940i	−0.996960	−	0.0779108i	$-0.975175\pi$
$7$	−0.624919	−	1.92330i	−0.236197	−	0.726940i	0.760763	−	0.649030i	$-0.224825\pi$
$8$	0.0147190	−	0.0453005i	0.00520396	−	0.0160161i
$9$	−2.74590	−	1.99502i	−0.915302	−	0.665006i
$10$	3.64184			1.15165
$11$	−2.99848	+	1.41744i	−0.904075	+	0.427375i
$11$	−2.99848	+	1.41744i	−0.904075	+	0.427375i
$12$	−4.99692			−1.44249
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$14$	1.24610	−	3.83510i	0.333035	−	1.02497i
$15$	1.42713	+	4.39226i	0.368484	+	1.13408i
$16$	3.27426	−	2.37889i	0.818564	−	0.594722i
$17$	1.34223	−	0.975189i	0.325539	−	0.236518i	−0.412996	−	0.910733i	$-0.635518\pi$
$17$	1.34223	−	0.975189i	0.325539	−	0.236518i	0.738536	+	0.674215i	$0.235518\pi$
$18$	−2.09141	−	6.43670i	−0.492950	−	1.51715i
$19$	−0.610527	+	1.87901i	−0.140065	+	0.431074i	−0.996343	−	0.0854395i	$-0.972771\pi$
$19$	−0.610527	+	1.87901i	−0.140065	+	0.431074i	0.856279	+	0.516514i	$0.172771\pi$
$20$	2.91985	+	2.12140i	0.652899	+	0.474359i
$21$	5.11366			1.11589
$22$	−6.49845	−	1.22777i	−1.38547	−	0.261761i
$23$	3.93925			0.821390			0.410695	−	0.911773i	$-0.365286\pi$
$23$	3.93925			0.821390			0.410695	+	0.911773i	$0.365286\pi$
$24$	0.0974417	+	0.0707955i	0.0198902	+	0.0144511i
$25$	−0.514306	+	1.58287i	−0.102861	+	0.316574i
$26$	−0.616186	−	1.89642i	−0.120844	−	0.371920i
$27$	0.806273	−	0.585792i	0.155167	−	0.112736i
$28$	3.23304	−	2.34894i	0.610987	−	0.443908i
$29$	−2.68126	−	8.25206i	−0.497897	−	1.53237i	−0.812393	−	0.583110i	$-0.801836\pi$
$29$	−2.68126	−	8.25206i	−0.497897	−	1.53237i	0.314497	−	0.949259i	$-0.398164\pi$
$30$	−2.84573	+	8.75826i	−0.519557	+	1.59903i
$31$	2.14284	+	1.55686i	0.384865	+	0.279621i	0.763348	−	0.645987i	$-0.223554\pi$
$31$	2.14284	+	1.55686i	0.384865	+	0.279621i	−0.378483	+	0.925608i	$0.623554\pi$
$32$	7.97494			1.40978
$33$	−1.06580	−	8.31862i	−0.185532	−	1.44809i
$34$	3.30826			0.567362
$35$	−2.98807	−	2.17096i	−0.505076	−	0.366959i
$36$	2.07263	−	6.37890i	0.345438	−	1.06315i
$37$	0.429275	+	1.32117i	0.0705723	+	0.217199i	0.980122	−	0.198396i	$-0.0635732\pi$
$37$	0.429275	+	1.32117i	0.0705723	+	0.217199i	−0.909550	+	0.415595i	$0.863573\pi$
$38$	−3.18720	+	2.31564i	−0.517033	+	0.375646i
$39$	2.04573	−	1.48631i	0.327579	−	0.238000i
$40$	−0.0268826	−	0.0827360i	−0.00425050	−	0.0130817i
$41$	−2.86998	+	8.83290i	−0.448216	+	1.37947i	0.430701	+	0.902494i	$0.358266\pi$
$41$	−2.86998	+	8.83290i	−0.448216	+	1.37947i	−0.878918	+	0.476973i	$0.841734\pi$
$42$	8.24934	+	5.99350i	1.27290	+	0.924816i
$43$	−12.8417			−1.95834			−0.979168	−	0.203053i	$-0.934914\pi$
$43$	−12.8417			−1.95834			−0.979168	+	0.203053i	$0.934914\pi$
$44$	−4.49496	−	4.76976i	−0.677641	−	0.719068i
$45$	−6.19897			−0.924088
$46$	6.35478	+	4.61702i	0.936961	+	0.680742i
$47$	−1.90279	+	5.85620i	−0.277551	+	0.854214i	0.710982	+	0.703210i	$0.248251\pi$
$47$	−1.90279	+	5.85620i	−0.277551	+	0.854214i	−0.988533	+	0.151004i	$0.951749\pi$
$48$	3.16248	+	9.73312i	0.456465	+	1.40485i
$49$	2.35455	−	1.71068i	0.336364	−	0.244383i
$50$	−2.68489	+	1.95069i	−0.379701	+	0.275869i
$51$	1.29641	+	3.98995i	0.181534	+	0.558704i
$52$	0.610652	−	1.87939i	0.0846823	−	0.260625i
$53$	−9.98909	−	7.25750i	−1.37211	−	0.996894i	−0.997569	−	0.0696824i	$-0.977801\pi$
$53$	−9.98909	−	7.25750i	−1.37211	−	0.996894i	−0.374538	−	0.927212i	$-0.622199\pi$
$54$	1.98726			0.270431
$55$	−2.90882	+	5.31330i	−0.392225	+	0.716445i
$56$	−0.0963248			−0.0128719
$57$	−4.04176	−	2.93651i	−0.535345	−	0.388951i
$58$	5.34648	−	16.4548i	0.702027	−	2.16062i
$59$	−1.23989	−	3.81599i	−0.161420	−	0.496799i	0.837335	−	0.546691i	$-0.184113\pi$
$59$	−1.23989	−	3.81599i	−0.161420	−	0.496799i	−0.998755	+	0.0498911i	$0.984113\pi$
$60$	−7.38332	+	5.36429i	−0.953182	+	0.692527i
$61$	12.5865	−	9.14460i	1.61153	−	1.17085i	0.753124	−	0.657878i	$-0.228546\pi$
$61$	12.5865	−	9.14460i	1.61153	−	1.17085i	0.858408	−	0.512968i	$-0.171454\pi$
$62$	1.63209	+	5.02305i	0.207275	+	0.637928i
$63$	−2.12105	+	6.52793i	−0.267228	+	0.822442i
$64$	6.31662	+	4.58929i	0.789578	+	0.573662i
$65$	−1.82638			−0.226535
$66$	8.03054	−	14.6687i	0.988491	−	1.80560i
$67$	6.46440			0.789753			0.394876	−	0.918734i	$-0.370787\pi$
$67$	6.46440			0.789753			0.394876	+	0.918734i	$0.370787\pi$
$68$	2.65240	+	1.92708i	0.321651	+	0.233693i
$69$	−3.07813	+	9.47350i	−0.370563	+	1.14048i
$70$	−2.27586	−	7.00437i	−0.272017	−	0.837182i
$71$	−2.88721	+	2.09768i	−0.342649	+	0.248949i	−0.745779	−	0.666194i	$-0.767922\pi$
$71$	−2.88721	+	2.09768i	−0.342649	+	0.248949i	0.403130	+	0.915143i	$0.367922\pi$
$72$	−0.130792	+	0.0950261i	−0.0154140	+	0.0111989i
$73$	0.140323	+	0.431870i	0.0164236	+	0.0505466i	0.958932	−	0.283635i	$-0.0915403\pi$
$73$	0.140323	+	0.431870i	0.0164236	+	0.0505466i	−0.942509	+	0.334181i	$0.891540\pi$
$74$	−0.855982	+	2.63444i	−0.0995059	+	0.306248i
$75$	−3.40477	−	2.47371i	−0.393149	−	0.285639i
$76$	−3.90422			−0.447845
$77$	4.59998	+	4.88119i	0.524216	+	0.556264i
$78$	5.04220			0.570917
$79$	3.90340	+	2.83598i	0.439166	+	0.319073i	0.785304	−	0.619111i	$-0.212507\pi$
$79$	3.90340	+	2.83598i	0.439166	+	0.319073i	−0.346137	+	0.938184i	$0.612507\pi$
$80$	2.28417	−	7.02996i	0.255378	−	0.785974i
$81$	−2.36778	−	7.28727i	−0.263086	−	0.809697i
$82$	−14.9825	+	10.8854i	−1.65454	+	1.20209i
$83$	−6.13034	+	4.45395i	−0.672892	+	0.488885i	−0.870992	−	0.491297i	$-0.836523\pi$
$83$	−6.13034	+	4.45395i	−0.672892	+	0.488885i	0.198100	+	0.980182i	$0.436523\pi$
$84$	3.12267	+	9.61059i	0.340711	+	1.04860i
$85$	0.936363	−	2.88183i	0.101563	−	0.312578i
$86$	−20.7161	−	15.0511i	−2.23388	−	1.62301i
$87$	21.9405			2.35227
$88$	0.0200762	+	0.156696i	0.00214013	+	0.0167038i
$89$	−2.42469			−0.257016			−0.128508	−	0.991708i	$-0.541019\pi$
$89$	−2.42469			−0.257016			−0.128508	+	0.991708i	$0.541019\pi$
$90$	−10.0001	−	7.26553i	−1.05411	−	0.765854i
$91$	−0.624919	+	1.92330i	−0.0655093	+	0.201617i
$92$	2.40551	+	7.40341i	0.250792	+	0.771858i
$93$	−5.41852	+	3.93678i	−0.561874	+	0.408225i
$94$	−9.93336	+	7.21701i	−1.02455	+	0.744378i
$95$	1.11506	+	3.43179i	0.114402	+	0.352094i
$96$	−6.23161	+	19.1789i	−0.636011	+	1.95744i
$97$	13.8540	+	10.0655i	1.40666	+	1.02200i	0.993798	+	0.111203i	$0.0354703\pi$
$97$	13.8540	+	10.0655i	1.40666	+	1.02200i	0.412861	+	0.910794i	$0.364530\pi$
$98$	5.80335			0.586227
$99$	11.0614	+	2.08985i	1.11171	+	0.210038i
$100$	−3.28890			−0.328890
$101$	2.00155	+	1.45421i	0.199162	+	0.144699i	0.682896	−	0.730515i	$-0.260720\pi$
$101$	2.00155	+	1.45421i	0.199162	+	0.144699i	−0.483735	+	0.875215i	$0.660720\pi$
$102$	−2.58507	+	7.95603i	−0.255960	+	0.787765i
$103$	4.36741	+	13.4415i	0.430334	+	1.32443i	0.897793	+	0.440417i	$0.145169\pi$
$103$	4.36741	+	13.4415i	0.430334	+	1.32443i	−0.467459	+	0.884015i	$0.654831\pi$
$104$	−0.0385349	+	0.0279972i	−0.00377866	+	0.00274536i
$105$	7.55582	−	5.48962i	0.737372	−	0.535732i
$106$	−7.60817	−	23.4155i	−0.738970	−	2.27432i
$107$	1.47259	−	4.53218i	0.142361	−	0.438142i	−0.854301	−	0.519778i	$-0.826015\pi$
$107$	1.47259	−	4.53218i	0.142361	−	0.438142i	0.996662	+	0.0816362i	$0.0260146\pi$
$108$	1.59329	+	1.15759i	0.153314	+	0.111389i
$109$	3.10047			0.296972			0.148486	−	0.988915i	$-0.452560\pi$
$109$	3.10047			0.296972			0.148486	+	0.988915i	$0.452560\pi$
$110$	−10.9200	+	5.16210i	−1.04118	+	0.492187i
$111$	−3.51272			−0.333413
$112$	−6.62147	−	4.81078i	−0.625670	−	0.454576i
$113$	−4.21048	+	12.9585i	−0.396089	+	1.21904i	0.532022	+	0.846731i	$0.321432\pi$
$113$	−4.21048	+	12.9585i	−0.396089	+	1.21904i	−0.928111	+	0.372305i	$0.878568\pi$
$114$	−3.07840	−	9.47434i	−0.288319	−	0.887353i
$115$	5.82053	−	4.22887i	0.542768	−	0.394344i
$116$	13.8716	−	10.0783i	1.28794	−	0.935744i
$117$	1.04884	+	3.22800i	0.0969655	+	0.298429i
$118$	2.47236	−	7.60915i	0.227600	−	0.700479i
$119$	−2.71437	−	1.97211i	−0.248826	−	0.180783i
$120$	0.219978			0.0200811
$121$	6.98172	−	8.50033i	0.634702	−	0.772757i
$122$	31.0224			2.80864
$123$	−18.9996	−	13.8040i	−1.71314	−	1.24467i
$124$	−1.61743	+	4.97795i	−0.145250	+	0.447033i
$125$	3.76123	+	11.5759i	0.336415	+	1.03538i
$126$	−11.0728	+	8.04484i	−0.986441	+	0.716691i
$127$	8.73609	−	6.34714i	0.775203	−	0.563218i	−0.128333	−	0.991731i	$-0.540963\pi$
$127$	8.73609	−	6.34714i	0.775203	−	0.563218i	0.903535	+	0.428514i	$0.140963\pi$
$128$	−0.117744	−	0.362378i	−0.0104072	−	0.0320300i
$129$	10.0345	−	30.8829i	0.883485	−	2.71909i
$130$	−2.94631	−	2.14062i	−0.258409	−	0.187745i
$131$	6.07019			0.530355			0.265178	−	0.964200i	$-0.414569\pi$
$131$	6.07019			0.530355			0.265178	+	0.964200i	$0.414569\pi$
$132$	14.9831	−	7.08284i	1.30412	−	0.616482i
$133$	3.99544			0.346448
$134$	10.4283	+	7.57664i	0.900872	+	0.654522i
$135$	0.562469	−	1.73110i	0.0484096	−	0.148990i
$136$	−0.0244202	−	0.0751577i	−0.00209401	−	0.00644472i
$137$	−14.7712	+	10.7319i	−1.26199	+	0.916890i	−0.998854	−	0.0478684i	$-0.984757\pi$
$137$	−14.7712	+	10.7319i	−1.26199	+	0.916890i	−0.263137	+	0.964758i	$0.584757\pi$
$138$	−16.0691	+	11.6749i	−1.36789	+	0.993831i
$139$	−1.98294	−	6.10287i	−0.168191	−	0.517639i	0.831066	−	0.556173i	$-0.187731\pi$
$139$	−1.98294	−	6.10287i	−0.168191	−	0.517639i	−0.999257	+	0.0385348i	$0.987731\pi$
$140$	2.25542	−	6.94147i	0.190618	−	0.586661i
$141$	−12.5967	−	9.15205i	−1.06084	−	0.770742i
$142$	−7.11623			−0.597181
$143$	3.25897	+	0.615726i	0.272529	+	0.0514896i
$144$	−13.7367			−1.14473
$145$	−12.8205	−	9.31464i	−1.06468	−	0.773539i
$146$	−0.279807	+	0.861157i	−0.0231570	+	0.0712699i
$147$	2.27417	+	6.99917i	0.187570	+	0.577282i
$148$	−2.22087	+	1.61355i	−0.182554	+	0.132633i
$149$	−10.0445	+	7.29778i	−0.822880	+	0.597857i	−0.917536	−	0.397653i	$-0.869825\pi$
$149$	−10.0445	+	7.29778i	−0.822880	+	0.597857i	0.0946562	+	0.995510i	$0.469825\pi$
$150$	−2.59323	−	7.98115i	−0.211737	−	0.651658i
$151$	5.51481	−	16.9729i	0.448789	−	1.38123i	−0.429485	−	0.903074i	$-0.641305\pi$
$151$	5.51481	−	16.9729i	0.448789	−	1.38123i	0.878274	−	0.478157i	$-0.158695\pi$
$152$	0.0761337	+	0.0553144i	0.00617526	+	0.00448659i
$153$	−5.63116			−0.455253
$154$	1.69963	+	13.2657i	0.136960	+	1.06898i
$155$	4.83753			0.388560
$156$	4.04259	+	2.93712i	0.323666	+	0.235157i
$157$	−4.76001	+	14.6498i	−0.379890	+	1.16918i	0.560229	+	0.828337i	$0.310713\pi$
$157$	−4.76001	+	14.6498i	−0.379890	+	1.16918i	−0.940120	+	0.340844i	$0.889287\pi$
$158$	2.97301	+	9.14999i	0.236520	+	0.727934i
$159$	25.2590	−	18.3518i	2.00317	−	1.45539i
$160$	11.7836	−	8.56126i	0.931572	−	0.676827i
$161$	−2.46171	−	7.57637i	−0.194010	−	0.597102i
$162$	4.72139	−	14.5310i	0.370948	−	1.14166i
$163$	−2.68893	−	1.95362i	−0.210613	−	0.153019i	0.477478	−	0.878644i	$-0.341551\pi$
$163$	−2.68893	−	1.95362i	−0.210613	−	0.153019i	−0.688091	+	0.725624i	$0.741551\pi$
$164$	−18.3531			−1.43313
$165$	−10.5050	−	11.1472i	−0.817813	−	0.867810i
$166$	−15.1097			−1.17274
$167$	4.04908	+	2.94183i	0.313327	+	0.227645i	0.733323	−	0.679881i	$-0.237968\pi$
$167$	4.04908	+	2.94183i	0.313327	+	0.227645i	−0.419996	+	0.907526i	$0.637968\pi$
$168$	0.0752681	−	0.231651i	0.00580706	−	0.0178723i
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$	4.88820	−	3.55148i	0.374908	−	0.272386i
$171$	5.42511	−	3.94157i	0.414868	−	0.301419i
$172$	−7.84179	−	24.1346i	−0.597931	−	1.84024i
$173$	5.12198	−	15.7638i	0.389417	−	1.19850i	−0.543808	−	0.839210i	$-0.683018\pi$
$173$	5.12198	−	15.7638i	0.389417	−	1.19850i	0.933225	−	0.359293i	$-0.116982\pi$
$174$	35.3943	+	25.7155i	2.68324	+	1.94948i
$175$	3.36574			0.254426
$176$	−6.44585	+	11.7741i	−0.485874	+	0.887506i
$177$	10.1459			0.762614
$178$	−3.91149	−	2.84187i	−0.293179	−	0.213007i
$179$	6.91562	−	21.2841i	0.516898	−	1.59085i	−0.262905	−	0.964822i	$-0.584681\pi$
$179$	6.91562	−	21.2841i	0.516898	−	1.59085i	0.779803	−	0.626025i	$-0.215319\pi$
$180$	−3.78542	−	11.6503i	−0.282148	−	0.868363i
$181$	−3.27828	+	2.38181i	−0.243673	+	0.177039i	−0.702918	−	0.711271i	$-0.748120\pi$
$181$	−3.27828	+	2.38181i	−0.243673	+	0.177039i	0.459245	+	0.888310i	$0.348120\pi$
$182$	−3.26233	+	2.37023i	−0.241820	+	0.175693i
$183$	12.1568	+	37.4148i	0.898656	+	2.76578i
$184$	0.0579819	−	0.178450i	0.00427448	−	0.0131555i
$185$	2.05259	+	1.49129i	0.150909	+	0.109642i
$186$	−13.3552			−0.979254
$187$	−2.64238	+	4.82662i	−0.193230	+	0.352957i
$188$	−12.1680			−0.887446
$189$	−1.63051	−	1.18464i	−0.118602	−	0.0861696i
$190$	−2.22344	+	6.84305i	−0.161306	+	0.496447i
$191$	0.832738	+	2.56290i	0.0602548	+	0.185445i	0.976653	−	0.214822i	$-0.0689172\pi$
$191$	0.832738	+	2.56290i	0.0602548	+	0.185445i	−0.916398	+	0.400267i	$0.868917\pi$
$192$	−15.9726	+	11.6048i	−1.15272	+	0.837502i
$193$	−4.25463	+	3.09117i	−0.306255	+	0.222507i	−0.730288	−	0.683140i	$-0.760614\pi$
$193$	−4.25463	+	3.09117i	−0.306255	+	0.222507i	0.424033	+	0.905647i	$0.360614\pi$
$194$	10.5518	+	32.4752i	0.757579	+	2.33159i
$195$	1.42713	−	4.39226i	0.102199	−	0.314537i
$196$	4.65285	+	3.38049i	0.332346	+	0.241464i
$197$	−3.83577			−0.273287			−0.136644	−	0.990620i	$-0.543632\pi$
$197$	−3.83577			−0.273287			−0.136644	+	0.990620i	$0.543632\pi$
$198$	15.3947	+	16.3358i	1.09405	+	1.16094i
$199$	−9.11289			−0.645996			−0.322998	−	0.946400i	$-0.604691\pi$
$199$	−9.11289			−0.645996			−0.322998	+	0.946400i	$0.604691\pi$
$200$	0.0641348	+	0.0465966i	0.00453501	+	0.00329488i
$201$	−5.05128	+	15.5462i	−0.356290	+	1.09655i
$202$	1.52448	+	4.69185i	0.107262	+	0.330118i
$203$	−14.1956	+	10.3137i	−0.996339	+	0.723882i
$204$	−6.70703	+	4.87294i	−0.469586	+	0.341174i
$205$	5.24169	+	16.1323i	0.366095	+	1.12673i
$206$	−8.70871	+	26.8026i	−0.606764	+	1.86743i
$207$	−10.8168	−	7.85887i	−0.751820	−	0.546229i
$208$	−4.04720			−0.280623
$209$	−0.832736	−	6.49955i	−0.0576015	−	0.449583i
$210$	18.6231			1.28512
$211$	3.87608	+	2.81614i	0.266840	+	0.193871i	0.713157	−	0.701004i	$-0.247265\pi$
$211$	3.87608	+	2.81614i	0.266840	+	0.193871i	−0.446317	+	0.894875i	$0.647265\pi$
$212$	7.53984	−	23.2053i	0.517839	−	1.59374i
$213$	−2.78865	−	8.58257i	−0.191075	−	0.588068i
$214$	7.68754	−	5.58533i	0.525509	−	0.381805i
$215$	−18.9745	+	13.7858i	−1.29405	+	0.940183i
$216$	−0.0146691	−	0.0451469i	−0.000998106	−	0.00307186i
$217$	1.65522	−	5.09425i	0.112364	−	0.345820i
$218$	5.00167	+	3.63393i	0.338756	+	0.246121i
$219$	−1.14825			−0.0775917
$220$	−11.7621	−	2.22224i	−0.792998	−	0.149823i
$221$	−1.65909			−0.111603
$222$	−5.66670	−	4.11710i	−0.380324	−	0.276322i
$223$	2.56480	−	7.89364i	0.171752	−	0.528598i	−0.827718	−	0.561144i	$-0.810362\pi$
$223$	2.56480	−	7.89364i	0.171752	−	0.528598i	0.999470	+	0.0325460i	$0.0103616\pi$
$224$	−4.98369	−	15.3382i	−0.332987	−	1.02483i
$225$	4.57009	−	3.32036i	0.304673	−	0.221358i
$226$	−21.9804	+	15.9697i	−1.46212	+	1.06229i
$227$	3.75957	+	11.5708i	0.249532	+	0.767979i	0.994858	+	0.101280i	$0.0322937\pi$
$227$	3.75957	+	11.5708i	0.249532	+	0.767979i	−0.745326	+	0.666700i	$0.767706\pi$
$228$	3.05076	−	9.38926i	0.202041	−	0.621819i
$229$	20.8306	+	15.1344i	1.37653	+	1.00011i	0.997195	+	0.0748459i	$0.0238465\pi$
$229$	20.8306	+	15.1344i	1.37653	+	1.00011i	0.379333	+	0.925260i	$0.376154\pi$
$230$	14.3461			0.945955
$231$	−15.3332	+	7.24832i	−1.00885	+	0.476904i
$232$	−0.413288			−0.0271337
$233$	9.49193	+	6.89629i	0.621837	+	0.451791i	0.853563	−	0.520990i	$-0.174437\pi$
$233$	9.49193	+	6.89629i	0.621837	+	0.451791i	−0.231726	+	0.972781i	$0.574437\pi$
$234$	−2.09141	+	6.43670i	−0.136720	+	0.420780i
$235$	3.47523	+	10.6956i	0.226699	+	0.697707i
$236$	6.41461	−	4.66049i	0.417555	−	0.303372i
$237$	−9.87037	+	7.17124i	−0.641149	+	0.465822i
$238$	−2.06740	−	6.36279i	−0.134009	−	0.412438i
$239$	1.34043	−	4.12541i	0.0867050	−	0.266850i	−0.898298	−	0.439386i	$-0.855196\pi$
$239$	1.34043	−	4.12541i	0.0867050	−	0.266850i	0.985003	+	0.172536i	$0.0551960\pi$
$240$	15.1215	+	10.9864i	0.976089	+	0.709170i
$241$	19.2973			1.24305			0.621525	−	0.783394i	$-0.286513\pi$
$241$	19.2973			1.24305			0.621525	+	0.783394i	$0.286513\pi$
$242$	21.2257	−	5.52974i	1.36444	−	0.355465i
$243$	22.3652			1.43473
$244$	24.8723	+	18.0708i	1.59228	+	1.15686i
$245$	1.64257	−	5.05531i	0.104940	−	0.322972i
$246$	−14.4710	−	44.5373i	−0.922639	−	2.83959i
$247$	1.59838	−	1.16129i	0.101703	−	0.0738912i
$248$	0.102067	−	0.0741562i	0.00648127	−	0.00470892i
$249$	−5.92106	−	18.2232i	−0.375232	−	1.15485i
$250$	−7.49997	+	23.0825i	−0.474340	+	1.45987i
$251$	−6.91027	−	5.02060i	−0.436172	−	0.316898i	0.347940	−	0.937517i	$-0.386881\pi$
$251$	−6.91027	−	5.02060i	−0.436172	−	0.316898i	−0.784112	+	0.620619i	$0.786881\pi$
$252$	−13.5638			−0.854439
$253$	−11.8117	+	5.58366i	−0.742598	+	0.351042i
$254$	21.5322			1.35105
$255$	6.19884	+	4.50372i	0.388186	+	0.282034i
$256$	5.06025	−	15.5739i	0.316266	−	0.973366i
$257$	−5.46992	−	16.8347i	−0.341204	−	1.05012i	−0.963585	−	0.267403i	$-0.913834\pi$
$257$	−5.46992	−	16.8347i	−0.341204	−	1.05012i	0.622381	−	0.782715i	$-0.286166\pi$
$258$	52.3840	−	38.0592i	3.26129	−	2.36946i
$259$	2.27275	−	1.65125i	0.141222	−	0.102604i
$260$	−1.11528	−	3.43249i	−0.0691670	−	0.212874i
$261$	−9.10052	+	28.0085i	−0.563308	+	1.73368i
$262$	9.79241	+	7.11460i	0.604977	+	0.439541i
$263$	−25.9704			−1.60140			−0.800701	−	0.599064i	$-0.795539\pi$
$263$	−25.9704			−1.60140			−0.800701	+	0.599064i	$0.795539\pi$
$264$	−0.392525	−	0.0741608i	−0.0241582	−	0.00456428i
$265$	−22.5507			−1.38528
$266$	6.44542	+	4.68287i	0.395194	+	0.287125i
$267$	1.89465	−	5.83113i	0.115951	−	0.356859i
$268$	3.94750	+	12.1492i	0.241132	+	0.742129i
$269$	−17.0801	+	12.4094i	−1.04139	+	0.756614i	−0.970556	−	0.240875i	$-0.922566\pi$
$269$	−17.0801	+	12.4094i	−1.04139	+	0.756614i	−0.0708331	+	0.997488i	$0.522566\pi$
$270$	2.93632	−	2.13336i	0.178699	−	0.129832i
$271$	−0.315758	−	0.971802i	−0.0191809	−	0.0590328i	0.941008	−	0.338385i	$-0.109880\pi$
$271$	−0.315758	−	0.971802i	−0.0191809	−	0.0590328i	−0.960189	+	0.279352i	$0.909880\pi$
$272$	2.07495	−	6.38604i	0.125812	−	0.387211i
$273$	−4.13704	−	3.00574i	−0.250385	−	0.181915i
$274$	−36.4073			−2.19944
$275$	−0.701493	−	5.47520i	−0.0423016	−	0.330167i
$276$	−19.6841			−1.18484
$277$	1.63775	+	1.18989i	0.0984027	+	0.0714937i	0.635899	−	0.771773i	$-0.280630\pi$
$277$	1.63775	+	1.18989i	0.0984027	+	0.0714937i	−0.537496	+	0.843266i	$0.680630\pi$
$278$	3.95402	−	12.1692i	0.237147	−	0.729862i
$279$	−2.77806	−	8.55000i	−0.166318	−	0.511875i
$280$	−0.142327	+	0.103407i	−0.00850567	+	0.00617973i
$281$	22.9189	−	16.6515i	1.36722	−	0.993347i	0.369276	−	0.929320i	$-0.379606\pi$
$281$	22.9189	−	16.6515i	1.36722	−	0.993347i	0.997948	−	0.0640269i	$-0.0203943\pi$
$282$	−9.59426	−	29.5281i	−0.571330	−	1.75837i
$283$	−3.04057	+	9.35790i	−0.180743	+	0.556270i	−0.999849	−	0.0173724i	$-0.994470\pi$
$283$	−3.04057	+	9.35790i	−0.180743	+	0.556270i	0.819106	+	0.573642i	$0.194470\pi$
$284$	−5.70545	−	4.14525i	−0.338556	−	0.245976i
$285$	−9.12441			−0.540484
$286$	4.53569	+	4.81298i	0.268201	+	0.284597i
$287$	18.7819			1.10866
$288$	−21.8984	−	15.9101i	−1.29038	−	0.937514i
$289$	−4.40269	+	13.5501i	−0.258982	+	0.797065i
$290$	−9.76471	−	30.0527i	−0.573403	−	1.76475i
$291$	−35.0320	+	25.4522i	−2.05361	+	1.49204i
$292$	−0.725966	+	0.527445i	−0.0424839	+	0.0308664i
$293$	−5.69889	−	17.5394i	−0.332933	−	1.02466i	−0.967731	−	0.251984i	$-0.918917\pi$
$293$	−5.69889	−	17.5394i	−0.332933	−	1.02466i	0.634799	−	0.772678i	$-0.281083\pi$
$294$	−4.53473	+	13.9565i	−0.264471	+	0.813958i
$295$	−5.92857	−	4.30736i	−0.345175	−	0.250784i
$296$	0.0661682			0.00384595
$297$	−1.58727	+	2.89933i	−0.0921025	+	0.168236i
$298$	−24.7572			−1.43415
$299$	−3.18692	−	2.31543i	−0.184304	−	0.133905i
$300$	2.56995	−	7.90948i	0.148376	−	0.456654i
$301$	8.02500	+	24.6984i	0.462554	+	1.42359i
$302$	28.7896	−	20.9169i	1.65665	−	1.20363i
$303$	−5.06124	+	3.67721i	−0.290761	+	0.211250i
$304$	2.47093	+	7.60474i	0.141717	+	0.436162i
$305$	8.78052	−	27.0237i	0.502771	−	1.54737i
$306$	−9.08417	−	6.60003i	−0.519307	−	0.377299i
$307$	−16.1262			−0.920370			−0.460185	−	0.887823i	$-0.652217\pi$
$307$	−16.1262			−0.920370			−0.460185	+	0.887823i	$0.652217\pi$
$308$	−6.36470	+	11.6259i	−0.362663	+	0.662446i
$309$	−35.7382			−2.03307
$310$	7.80388	+	5.66985i	0.443231	+	0.322026i
$311$	6.74096	−	20.7465i	0.382245	−	1.17643i	−0.556214	−	0.831039i	$-0.687747\pi$
$311$	6.74096	−	20.7465i	0.382245	−	1.17643i	0.938459	−	0.345390i	$-0.112253\pi$
$312$	−0.0372194	−	0.114550i	−0.00210713	−	0.00648509i
$313$	10.4568	−	7.59733i	0.591055	−	0.429427i	−0.251638	−	0.967822i	$-0.580969\pi$
$313$	10.4568	−	7.59733i	0.591055	−	0.429427i	0.842693	+	0.538395i	$0.180969\pi$
$314$	−24.8492	+	18.0540i	−1.40232	+	1.01885i
$315$	3.87386	+	11.9225i	0.218267	+	0.671757i
$316$	−2.94631	+	9.06782i	−0.165743	+	0.510105i
$317$	3.79665	+	2.75843i	0.213241	+	0.154929i	0.689279	−	0.724496i	$-0.257927\pi$
$317$	3.79665	+	2.75843i	0.213241	+	0.154929i	−0.476038	+	0.879425i	$0.657927\pi$
$318$	62.2570			3.49120
$319$	19.7365	+	20.9431i	1.10503	+	1.17259i
$320$	14.2600			0.797157
$321$	9.74874	+	7.08288i	0.544122	+	0.395328i
$322$	4.90870	−	15.1074i	0.273551	−	0.841905i
$323$	1.01292	+	3.11745i	0.0563604	+	0.173460i
$324$	12.2498	−	8.89998i	0.680543	−	0.494443i
$325$	1.34647	−	0.978268i	0.0746887	−	0.0542646i
$326$	−2.04801	−	6.30314i	−0.113429	−	0.349099i
$327$	−2.42271	+	7.45633i	−0.133976	+	0.412336i
$328$	0.357892	+	0.260023i	0.0197613	+	0.0143574i
$329$	12.4523			0.686519
$330$	−3.88147	−	30.2951i	−0.213668	−	1.66769i
$331$	−11.2076			−0.616027			−0.308014	−	0.951382i	$-0.599664\pi$
$331$	−11.2076			−0.616027			−0.308014	+	0.951382i	$0.599664\pi$
$332$	−12.1142	−	8.80151i	−0.664855	−	0.483046i
$333$	1.45701	−	4.48422i	0.0798438	−	0.245734i
$334$	3.08397	+	9.49148i	0.168747	+	0.519351i
$335$	9.55164	−	6.93967i	0.521862	−	0.379155i
$336$	16.7434	−	12.1648i	0.913430	−	0.663646i
$337$	1.87755	+	5.77850i	0.102277	+	0.314775i	0.989082	−	0.147369i	$-0.0470804\pi$
$337$	1.87755	+	5.77850i	0.102277	+	0.314775i	−0.886805	+	0.462144i	$0.847080\pi$
$338$	−0.616186	+	1.89642i	−0.0335161	+	0.103152i
$339$	−27.8739	−	20.2516i	−1.51390	−	1.09991i
$340$	5.98789			0.324739
$341$	−8.63202	−	1.63087i	−0.467450	−	0.0883165i
$342$	13.3715			0.723048
$343$	−16.2140	−	11.7801i	−0.875472	−	0.636068i
$344$	−0.189017	+	0.581734i	−0.0101911	+	0.0313650i
$345$	5.62183	+	17.3022i	0.302669	+	0.931521i
$346$	26.7388	−	19.4269i	1.43749	−	1.04440i
$347$	6.14470	−	4.46438i	0.329865	−	0.239661i	−0.410509	−	0.911857i	$-0.634649\pi$
$347$	6.14470	−	4.46438i	0.329865	−	0.239661i	0.740373	+	0.672196i	$0.234649\pi$
$348$	13.3980	+	41.2349i	0.718209	+	2.21042i
$349$	6.94701	−	21.3807i	0.371865	−	1.14448i	−0.573705	−	0.819062i	$-0.694494\pi$
$349$	6.94701	−	21.3807i	0.371865	−	1.14448i	0.945570	−	0.325420i	$-0.105506\pi$
$350$	5.42960	+	3.94483i	0.290224	+	0.210860i
$351$	−0.996609			−0.0531950
$352$	−23.9127	+	11.3040i	−1.27455	+	0.602506i
$353$	12.4405			0.662142			0.331071	−	0.943606i	$-0.392590\pi$
$353$	12.4405			0.662142			0.331071	+	0.943606i	$0.392590\pi$
$354$	16.3673	+	11.8916i	0.869915	+	0.632030i
$355$	−2.01416	+	6.19896i	−0.106901	+	0.329006i
$356$	−1.48064	−	4.55694i	−0.0784738	−	0.241518i
$357$	6.86373	−	4.98679i	0.363267	−	0.263929i
$358$	36.1024	−	26.2299i	1.90807	−	1.38629i
$359$	−0.625944	−	1.92646i	−0.0330361	−	0.101675i	0.933179	−	0.359413i	$-0.117023\pi$
$359$	−0.625944	−	1.92646i	−0.0330361	−	0.101675i	−0.966215	+	0.257738i	$0.917023\pi$
$360$	−0.0912427	+	0.280816i	−0.00480892	+	0.0148003i
$361$	12.2134	+	8.87355i	0.642810	+	0.467029i
$362$	−8.08013			−0.424682
$363$	14.9869	+	23.4325i	0.786610	+	1.22989i
$364$	−3.99626			−0.209461
$365$	0.670959	+	0.487480i	0.0351196	+	0.0255159i
$366$	−24.2409	+	74.6058i	−1.26709	+	3.89971i
$367$	−7.41086	−	22.8083i	−0.386844	−	1.19058i	−0.935134	−	0.354294i	$-0.884721\pi$
$367$	−7.41086	−	22.8083i	−0.386844	−	1.19058i	0.548290	−	0.836288i	$-0.315279\pi$
$368$	12.8981	−	9.37103i	0.672361	−	0.488499i
$369$	25.5025	−	18.5286i	1.32761	−	0.964563i
$370$	1.56335	+	4.81150i	0.0812747	+	0.250138i
$371$	−7.71600	+	23.7474i	−0.400595	+	1.23290i
$372$	−10.7076	−	7.77952i	−0.555163	−	0.403350i
$373$	3.81762			0.197669			0.0988343	−	0.995104i	$-0.468489\pi$
$373$	3.81762			0.197669			0.0988343	+	0.995104i	$0.468489\pi$
$374$	−9.91974	+	4.68927i	−0.512937	+	0.242476i
$375$	−30.7779			−1.58936
$376$	0.237281	+	0.172395i	0.0122368	+	0.00889059i
$377$	−2.68126	+	8.25206i	−0.138092	+	0.425003i
$378$	−1.24188	−	3.82210i	−0.0638752	−	0.196588i
$379$	−5.70403	+	4.14422i	−0.292996	+	0.212874i	−0.724566	−	0.689205i	$-0.757960\pi$
$379$	−5.70403	+	4.14422i	−0.292996	+	0.212874i	0.431570	+	0.902080i	$0.357960\pi$
$380$	−5.76878	+	4.19126i	−0.295932	+	0.215007i
$381$	8.43786	+	25.9691i	0.432285	+	1.33044i
$382$	−1.66049	+	5.11048i	−0.0849583	+	0.261475i
$383$	−22.7252	−	16.5109i	−1.16121	−	0.843665i	−0.171276	−	0.985223i	$-0.554789\pi$
$383$	−22.7252	−	16.5109i	−1.16121	−	0.843665i	−0.989930	+	0.141558i	$0.954789\pi$
$384$	0.963488			0.0491678
$385$	12.0369	+	2.27416i	0.613456	+	0.115902i
$386$	−10.4866			−0.533752
$387$	35.2620	+	25.6193i	1.79247	+	1.30230i
$388$	−10.4571	+	32.1836i	−0.530878	+	1.63388i
$389$	0.886008	+	2.72685i	0.0449224	+	0.138257i	0.971002	−	0.239071i	$-0.0768429\pi$
$389$	0.886008	+	2.72685i	0.0449224	+	0.138257i	−0.926080	+	0.377328i	$0.876843\pi$
$390$	7.45022	−	5.41290i	0.377257	−	0.274093i
$391$	5.28739	−	3.84152i	0.267395	−	0.194274i
$392$	−0.0428379	−	0.131842i	−0.00216364	−	0.00665900i
$393$	−4.74324	+	14.5982i	−0.239265	+	0.736382i
$394$	−6.18785	−	4.49573i	−0.311739	−	0.226492i
$395$	8.81204			0.443382
$396$	2.82699	+	22.0648i	0.142061	+	1.10880i
$397$	−2.35269			−0.118078			−0.0590391	−	0.998256i	$-0.518804\pi$
$397$	−2.35269			−0.118078			−0.0590391	+	0.998256i	$0.518804\pi$
$398$	−14.7009	−	10.6808i	−0.736889	−	0.535381i
$399$	−3.12203	+	9.60862i	−0.156297	+	0.481033i
$400$	2.08150	+	6.40620i	0.104075	+	0.320310i
$401$	31.6084	−	22.9648i	1.57845	−	1.14681i	0.659998	−	0.751267i	$-0.270557\pi$
$401$	31.6084	−	22.9648i	1.57845	−	1.14681i	0.918448	−	0.395541i	$-0.129443\pi$
$402$	−26.3698	+	19.1587i	−1.31520	+	0.955552i
$403$	−0.818492	−	2.51906i	−0.0407720	−	0.125483i
$404$	−1.51079	+	4.64972i	−0.0751644	+	0.231332i
$405$	−11.3216	−	8.22562i	−0.562575	−	0.408735i
$406$	−34.9886			−1.73646
$407$	−3.15985	−	3.35303i	−0.156628	−	0.166204i
$408$	0.199829			0.00989299
$409$	−16.2713	−	11.8218i	−0.804563	−	0.584549i	0.107686	−	0.994185i	$-0.465656\pi$
$409$	−16.2713	−	11.8218i	−0.804563	−	0.584549i	−0.912249	+	0.409636i	$0.865656\pi$
$410$	−10.4520	+	32.1680i	−0.516189	+	1.58867i
$411$	−14.2670	−	43.9092i	−0.703738	−	2.16588i
$412$	−22.5949	+	16.4162i	−1.11317	+	0.808768i
$413$	−6.56447	+	4.76937i	−0.323017	+	0.234685i
$414$	−8.23859	−	25.3558i	−0.404905	−	1.24617i
$415$	−4.27662	+	13.1621i	−0.209931	+	0.646101i
$416$	−6.45186	−	4.68755i	−0.316329	−	0.229826i
$417$	16.2263			0.794603
$418$	6.27447	−	11.4611i	0.306894	−	0.560579i
$419$	9.20303			0.449597			0.224799	−	0.974405i	$-0.427828\pi$
$419$	9.20303			0.449597			0.224799	+	0.974405i	$0.427828\pi$
$420$	14.9311	+	10.8481i	0.728565	+	0.529334i
$421$	5.70020	−	17.5434i	0.277811	−	0.855013i	−0.710651	−	0.703544i	$-0.751600\pi$
$421$	5.70020	−	17.5434i	0.277811	−	0.855013i	0.988462	−	0.151469i	$-0.0484004\pi$
$422$	2.95221	+	9.08596i	0.143711	+	0.442298i
$423$	16.9081	−	12.2845i	0.822100	−	0.597290i
$424$	−0.475798	+	0.345687i	−0.0231068	+	0.0167881i
$425$	0.853281	+	2.62613i	0.0413902	+	0.127386i
$426$	5.56062	−	17.1138i	0.269413	−	0.829167i
$427$	−25.4534	−	18.4930i	−1.23178	−	0.894937i
$428$	9.41699			0.455187
$429$	−4.02731	+	7.35637i	−0.194441	+	0.355169i
$430$	−46.7673			−2.25532
$431$	−0.476224	−	0.345997i	−0.0229389	−	0.0166661i	0.576257	−	0.817269i	$-0.304513\pi$
$431$	−0.476224	−	0.345997i	−0.0229389	−	0.0166661i	−0.599196	+	0.800603i	$0.704513\pi$
$432$	1.24641	−	3.83607i	0.0599681	−	0.184563i
$433$	3.27316	+	10.0738i	0.157298	+	0.484114i	0.998386	−	0.0567839i	$-0.0180846\pi$
$433$	3.27316	+	10.0738i	0.157298	+	0.484114i	−0.841088	+	0.540898i	$0.818085\pi$
$434$	8.64093	−	6.27801i	0.414778	−	0.301354i
$435$	32.4187	−	23.5536i	1.55436	−	1.12931i
$436$	1.89331	+	5.82702i	0.0906732	+	0.279063i
$437$	−2.40502	+	7.40189i	−0.115048	+	0.354080i
$438$	−1.85236	−	1.34581i	−0.0885090	−	0.0643055i
$439$	−3.40730			−0.162621			−0.0813107	−	0.996689i	$-0.525911\pi$
$439$	−3.40730			−0.162621			−0.0813107	+	0.996689i	$0.525911\pi$
$440$	0.197880	+	0.209977i	0.00943357	+	0.0100103i
$441$	−9.87819			−0.470390
$442$	−2.67644	−	1.94455i	−0.127305	−	0.0924926i
$443$	10.8325	−	33.3389i	0.514667	−	1.58398i	−0.269221	−	0.963078i	$-0.586766\pi$
$443$	10.8325	−	33.3389i	0.514667	−	1.58398i	0.783888	−	0.620903i	$-0.213234\pi$
$444$	−2.14505	−	6.60179i	−0.101800	−	0.313307i
$445$	−3.58266	+	2.60295i	−0.169834	+	0.123392i
$446$	13.3893	−	9.72790i	0.634002	−	0.460630i
$447$	−9.70163	−	29.8586i	−0.458871	−	1.41226i
$448$	4.87923	−	15.0167i	0.230522	−	0.709473i
$449$	−11.7951	−	8.56962i	−0.556643	−	0.404425i	0.273585	−	0.961848i	$-0.411790\pi$
$449$	−11.7951	−	8.56962i	−0.556643	−	0.404425i	−0.830229	+	0.557423i	$0.811790\pi$
$450$	11.2641			0.530995
$451$	−3.91455	−	30.5533i	−0.184329	−	1.43870i
$452$	−26.9253			−1.26646
$453$	36.5087	+	26.5251i	1.71533	+	1.24626i
$454$	−7.49666	+	23.0723i	−0.351836	+	1.08284i
$455$	1.14134	+	3.51269i	0.0535069	+	0.164677i
$456$	−0.192516	+	0.139871i	−0.00901540	+	0.00655007i
$457$	−18.8001	+	13.6591i	−0.879433	+	0.638945i	−0.933101	−	0.359614i	$-0.882909\pi$
$457$	−18.8001	+	13.6591i	−0.879433	+	0.638945i	0.0536687	+	0.998559i	$0.482909\pi$
$458$	15.8656	+	48.8293i	0.741351	+	2.28165i
$459$	0.510949	−	1.57254i	0.0238490	−	0.0733998i
$460$	11.5020	+	8.35671i	0.536285	+	0.389634i
$461$	−30.5934			−1.42488			−0.712438	−	0.701735i	$-0.752409\pi$
$461$	−30.5934			−1.42488			−0.712438	+	0.701735i	$0.752409\pi$
$462$	−33.2309	−	6.27839i	−1.54604	−	0.292097i
$463$	5.99110			0.278430			0.139215	−	0.990262i	$-0.455542\pi$
$463$	5.99110			0.278430			0.139215	+	0.990262i	$0.455542\pi$
$464$	−28.4098	−	20.6409i	−1.31889	−	0.958232i
$465$	−3.78004	+	11.6338i	−0.175295	+	0.539503i
$466$	7.22951	+	22.2501i	0.334900	+	1.03072i
$467$	−23.2110	+	16.8638i	−1.07408	+	0.780363i	−0.976641	−	0.214879i	$-0.931064\pi$
$467$	−23.2110	+	16.8638i	−1.07408	+	0.780363i	−0.0974364	+	0.995242i	$0.531064\pi$
$468$	−5.42622	+	3.94238i	−0.250827	+	0.182236i
$469$	−4.03973	−	12.4330i	−0.186537	−	0.574103i
$470$	−6.92967	+	21.3273i	−0.319642	+	0.983756i
$471$	−31.5118	−	22.8947i	−1.45199	−	1.05493i
$472$	−0.191116			−0.00879683
$473$	38.5054	−	18.2023i	1.77048	−	0.836943i
$474$	−24.3279			−1.11742
$475$	−2.66023	−	1.93277i	−0.122060	−	0.0886817i
$476$	2.04883	−	6.30565i	0.0939080	−	0.289019i
$477$	12.9503	+	39.8568i	0.592952	+	1.82492i
$478$	6.99757	−	5.08404i	0.320062	−	0.232538i
$479$	−27.2611	+	19.8064i	−1.24559	+	0.904976i	−0.997958	−	0.0638770i	$-0.979653\pi$
$479$	−27.2611	+	19.8064i	−1.24559	+	0.904976i	−0.247635	+	0.968853i	$0.579653\pi$
$480$	11.3813	+	35.0280i	0.519483	+	1.59880i
$481$	0.429275	−	1.32117i	0.0195732	−	0.0602403i
$482$	31.1304	+	22.6175i	1.41795	+	1.03020i
$483$	20.1440			0.916584
$484$	20.2389	+	7.93066i	0.919949	+	0.360484i
$485$	31.2758			1.42016
$486$	36.0794	+	26.2132i	1.63659	+	1.18905i
$487$	9.08381	−	27.9571i	0.411627	−	1.26686i	−0.503607	−	0.863933i	$-0.667994\pi$
$487$	9.08381	−	27.9571i	0.411627	−	1.26686i	0.915233	−	0.402924i	$-0.132006\pi$
$488$	−0.228995	−	0.704773i	−0.0103661	−	0.0319036i
$489$	6.79938	−	4.94004i	0.307479	−	0.223396i
$490$	8.57488	−	6.23002i	0.387374	−	0.281443i
$491$	3.77475	+	11.6175i	0.170352	+	0.524290i	0.999391	−	0.0349011i	$-0.0111116\pi$
$491$	3.77475	+	11.6175i	0.170352	+	0.524290i	−0.829038	+	0.559192i	$0.811112\pi$
$492$	14.3411	−	44.1373i	0.646546	−	1.98986i
$493$	−11.6462	−	8.46145i	−0.524518	−	0.381085i
$494$	3.93960			0.177251
$495$	18.5875	−	8.78668i	0.835444	−	0.394932i
$496$	10.7198			0.481334
$497$	5.83875	+	4.24210i	0.261904	+	0.190284i
$498$	11.8067	−	36.3373i	0.529071	−	1.62831i
$499$	8.24133	+	25.3642i	0.368932	+	1.13546i	0.947482	+	0.319810i	$0.103619\pi$
$499$	8.24133	+	25.3642i	0.368932	+	1.13546i	−0.578549	+	0.815647i	$0.696381\pi$
$500$	−19.4589	+	14.1377i	−0.870227	+	0.632257i
$501$	−10.2387	+	7.43888i	−0.457433	+	0.332345i
$502$	−5.26319	−	16.1984i	−0.234908	−	0.722971i
$503$	−6.87789	+	21.1680i	−0.306670	+	0.943833i	0.672379	+	0.740207i	$0.265273\pi$
$503$	−6.87789	+	21.1680i	−0.306670	+	0.943833i	−0.979049	+	0.203626i	$0.934727\pi$
$504$	0.264499	+	0.192170i	0.0117817	+	0.00855991i
$505$	4.51856			0.201073
$506$	−25.5990	−	4.83649i	−1.13801	−	0.215008i
$507$	−2.52866			−0.112302
$508$	17.2635	+	12.5427i	0.765944	+	0.556491i
$509$	−0.0755376	+	0.232481i	−0.00334815	+	0.0103045i	−0.952717	−	0.303860i	$-0.901724\pi$
$509$	−0.0755376	+	0.232481i	−0.00334815	+	0.0103045i	0.949368	+	0.314165i	$0.101724\pi$
$510$	4.72133	+	14.5308i	0.209064	+	0.643433i
$511$	0.742927	−	0.539768i	0.0328651	−	0.0238779i
$512$	25.8001	−	18.7449i	1.14021	−	0.828413i
$513$	0.608457	+	1.87264i	0.0268640	+	0.0826790i
$514$	10.9071	−	33.5687i	0.481092	−	1.48065i
$515$	20.8829	+	15.1723i	0.920211	+	0.668573i
$516$	64.1688			2.82487
$517$	−2.59534	−	20.2568i	−0.114143	−	0.890891i
$518$	5.60175			0.246127
$519$	33.9081	+	24.6357i	1.48840	+	1.08139i
$520$	−0.0268826	+	0.0827360i	−0.00117888	+	0.00362821i
$521$	−8.07927	−	24.8654i	−0.353959	−	1.08938i	−0.956610	−	0.291370i	$-0.905889\pi$
$521$	−8.07927	−	24.8654i	−0.353959	−	1.08938i	0.602651	−	0.798005i	$-0.294111\pi$
$522$	−47.5084	+	34.5169i	−2.07939	+	1.51076i
$523$	14.4741	−	10.5160i	0.632908	−	0.459834i	−0.224499	−	0.974474i	$-0.572074\pi$
$523$	14.4741	−	10.5160i	0.632908	−	0.459834i	0.857406	+	0.514640i	$0.172074\pi$
$524$	3.70678	+	11.4083i	0.161931	+	0.498373i
$525$	−2.62999	+	8.09427i	−0.114782	+	0.353263i
$526$	−41.8953	−	30.4387i	−1.82672	−	1.32719i
$527$	4.39443			0.191424
$528$	−23.2788	−	24.7019i	−1.01308	−	1.07501i
$529$	−7.48231			−0.325318
$530$	−36.3787	−	26.4307i	−1.58019	−	1.14807i
$531$	−4.20834	+	12.9519i	−0.182626	+	0.562066i
$532$	2.43982	+	7.50900i	0.105780	+	0.325557i
$533$	7.51372	−	5.45904i	0.325455	−	0.236457i
$534$	9.89084	−	7.18612i	0.428019	−	0.310974i
$535$	−2.68952	−	8.27748i	−0.116278	−	0.357867i
$536$	0.0951497	−	0.292841i	0.00410984	−	0.0126488i
$537$	45.7822	+	33.2627i	1.97565	+	1.43539i
$538$	−42.0980			−1.81497
$539$	−4.63526	+	8.46686i	−0.199655	+	0.364693i
$540$	3.59690			0.154786
$541$	8.50623	+	6.18014i	0.365712	+	0.265705i	0.755430	−	0.655229i	$-0.227428\pi$
$541$	8.50623	+	6.18014i	0.365712	+	0.265705i	−0.389719	+	0.920934i	$0.627428\pi$
$542$	0.629627	−	1.93779i	0.0270448	−	0.0832353i
$543$	−3.16637	−	9.74509i	−0.135882	−	0.418202i
$544$	10.7042	−	7.77708i	0.458940	−	0.333439i
$545$	4.58118	−	3.32842i	0.196236	−	0.142574i
$546$	−3.15097	−	9.69768i	−0.134849	−	0.415022i
$547$	1.66419	−	5.12185i	0.0711556	−	0.218994i	−0.909154	−	0.416459i	$-0.863271\pi$
$547$	1.66419	−	5.12185i	0.0711556	−	0.218994i	0.980310	+	0.197465i	$0.0632708\pi$
$548$	−29.1896	−	21.2075i	−1.24692	−	0.905939i
$549$	−52.8049			−2.25366
$550$	5.28559	−	9.65476i	0.225378	−	0.411680i
$551$	17.1427			0.730302
$552$	0.383847	+	0.278881i	0.0163376	+	0.0118700i
$553$	3.01515	−	9.27968i	0.128217	−	0.394612i
$554$	1.24739	+	3.83906i	0.0529963	+	0.163106i
$555$	−5.19030	+	3.77098i	−0.220316	+	0.160069i
$556$	10.2588	−	7.45346i	0.435070	−	0.316097i
$557$	7.57752	+	23.3212i	0.321070	+	0.988152i	0.973183	+	0.230030i	$0.0738826\pi$
$557$	7.57752	+	23.3212i	0.321070	+	0.988152i	−0.652113	+	0.758121i	$0.726117\pi$
$558$	5.53951	−	17.0489i	0.234506	−	0.721736i
$559$	10.3891	+	7.54814i	0.439413	+	0.319252i
$560$	−14.9482			−0.631676
$561$	−9.54278	−	10.1262i	−0.402897	−	0.427527i
$562$	56.4891			2.38285
$563$	−10.9412	−	7.94925i	−0.461117	−	0.335021i	0.332852	−	0.942979i	$-0.391989\pi$
$563$	−10.9412	−	7.94925i	−0.461117	−	0.335021i	−0.793969	+	0.607958i	$0.791989\pi$
$564$	9.50810	−	29.2629i	0.400363	−	1.23219i
$565$	7.68994	+	23.6672i	0.323518	+	0.995687i
$566$	−15.8730	+	11.5324i	−0.667192	+	0.484744i
$567$	−12.5360	+	9.10791i	−0.526461	+	0.382496i
$568$	0.0525291	+	0.161668i	0.00220407	+	0.00678343i
$569$	−4.43218	+	13.6408i	−0.185807	+	0.571854i	−0.999961	−	0.00879409i	$-0.997201\pi$
$569$	−4.43218	+	13.6408i	−0.185807	+	0.571854i	0.814155	+	0.580648i	$0.197201\pi$
$570$	−14.7195	−	10.6943i	−0.616530	−	0.447936i
$571$	4.77684			0.199905			0.0999523	−	0.994992i	$-0.468131\pi$
$571$	4.77684			0.199905			0.0999523	+	0.994992i	$0.468131\pi$
$572$	0.832906	+	6.50088i	0.0348256	+	0.271816i
$573$	−6.81422			−0.284668
$574$	30.2988	+	22.0134i	1.26465	+	0.918821i
$575$	−2.02598	+	6.23533i	−0.0844892	+	0.260031i
$576$	−8.18912	−	25.2035i	−0.341214	−	1.05015i
$577$	−35.8098	+	26.0173i	−1.49078	+	1.08312i	−0.516902	+	0.856044i	$0.672915\pi$
$577$	−35.8098	+	26.0173i	−1.49078	+	1.08312i	−0.973878	+	0.227071i	$0.927085\pi$
$578$	−22.9839	+	16.6988i	−0.956003	+	0.694577i
$579$	−4.10938	−	12.6474i	−0.170780	−	0.525607i
$580$	9.67702	−	29.7828i	0.401816	−	1.23666i
$581$	12.3973	+	9.00714i	0.514325	+	0.373679i
$582$	−86.3449			−3.57911
$583$	40.2391	+	7.60248i	1.66653	+	0.314863i
$584$	0.0216293			0.000895029
$585$	5.01507	+	3.64366i	0.207348	+	0.150647i
$586$	11.3637	−	34.9739i	0.469430	−	1.44476i
$587$	7.89094	+	24.2858i	0.325694	+	1.00238i	0.971126	+	0.238565i	$0.0766771\pi$
$587$	7.89094	+	24.2858i	0.325694	+	1.00238i	−0.645433	+	0.763817i	$0.723323\pi$
$588$	−11.7655	+	8.54812i	−0.485200	+	0.352518i
$589$	−4.23363	+	3.07591i	−0.174444	+	0.126741i
$590$	−4.51548	−	13.8972i	−0.185899	−	0.572140i
$591$	2.99727	−	9.22464i	0.123291	−	0.379451i
$592$	4.54847	+	3.30466i	0.186941	+	0.135821i
$593$	−16.5202			−0.678404			−0.339202	−	0.940714i	$-0.610157\pi$
$593$	−16.5202			−0.678404			−0.339202	+	0.940714i	$0.610157\pi$
$594$	−5.95874	+	2.81682i	−0.244490	+	0.115576i
$595$	−6.12778			−0.251215
$596$	−19.8491	−	14.4212i	−0.813052	−	0.590717i
$597$	7.12081	−	21.9156i	0.291435	−	0.896946i
$598$	−2.42731	−	7.47049i	−0.0992601	−	0.305491i
$599$	−2.93223	+	2.13039i	−0.119808	+	0.0870453i	−0.646076	−	0.763273i	$-0.723591\pi$
$599$	−2.93223	+	2.13039i	−0.119808	+	0.0870453i	0.526268	+	0.850319i	$0.323591\pi$
$600$	−0.162175	+	0.117827i	−0.00662077	+	0.00481027i
$601$	6.60616	+	20.3317i	0.269471	+	0.829346i	0.990630	+	0.136576i	$0.0436097\pi$
$601$	6.60616	+	20.3317i	0.269471	+	0.829346i	−0.721159	+	0.692770i	$0.756390\pi$
$602$	−16.0020	+	49.2491i	−0.652193	+	2.00724i
$603$	−17.7506	−	12.8966i	−0.722862	−	0.525190i
$604$	35.2663			1.43497
$605$	1.19073	−	20.0549i	0.0484099	−	0.815347i
$606$	−12.4747			−0.506748
$607$	−14.0920	−	10.2384i	−0.571977	−	0.415565i	0.263846	−	0.964565i	$-0.415009\pi$
$607$	−14.0920	−	10.2384i	−0.571977	−	0.415565i	−0.835823	+	0.548999i	$0.815009\pi$
$608$	−4.86892	+	14.9850i	−0.197461	+	0.607722i
$609$	−13.7110	−	42.1982i	−0.555599	−	1.70996i
$610$	45.8379	−	33.3032i	1.85592	−	1.34841i
$611$	4.98158	−	3.61933i	0.201533	−	0.146422i
$612$	−3.43868	−	10.5832i	−0.139001	−	0.427800i
$613$	−4.16037	+	12.8043i	−0.168036	+	0.517161i	−0.999247	−	0.0387954i	$-0.987648\pi$
$613$	−4.16037	+	12.8043i	−0.168036	+	0.517161i	0.831211	+	0.555957i	$0.187648\pi$
$614$	−26.0147	−	18.9008i	−1.04987	−	0.762773i
$615$	−42.8923			−1.72958
$616$	0.288828	−	0.136535i	0.0116372	−	0.00550114i
$617$	37.8461			1.52363			0.761813	−	0.647797i	$-0.224310\pi$
$617$	37.8461			1.52363			0.761813	+	0.647797i	$0.224310\pi$
$618$	−57.6527	−	41.8871i	−2.31913	−	1.68495i
$619$	4.55254	−	14.0113i	0.182982	−	0.563160i	−0.816926	−	0.576743i	$-0.804324\pi$
$619$	4.55254	−	14.0113i	0.182982	−	0.563160i	0.999908	+	0.0135823i	$0.00432352\pi$
$620$	2.95405	+	9.09163i	0.118637	+	0.365129i
$621$	3.17611	−	2.30758i	0.127453	−	0.0926000i
$622$	35.1906	−	25.5675i	1.41101	−	1.02516i
$623$	1.51523	+	4.66341i	0.0607066	+	0.186836i
$624$	3.16248	−	9.73312i	0.126601	−	0.389637i
$625$	11.2521	+	8.17513i	0.450084	+	0.327005i
$626$	25.7734			1.03011
$627$	16.2815	+	3.07610i	0.650219	+	0.122848i
$628$	−30.4395			−1.21467
$629$	1.86458	+	1.35470i	0.0743457	+	0.0540153i
$630$	−7.72454	+	23.7737i	−0.307753	+	0.947167i
$631$	−4.26102	−	13.1141i	−0.169629	−	0.522063i	0.829719	−	0.558182i	$-0.188501\pi$
$631$	−4.26102	−	13.1141i	−0.169629	−	0.522063i	−0.999348	+	0.0361182i	$0.988501\pi$
$632$	0.185926	−	0.135083i	0.00739572	−	0.00537331i
$633$	−9.80130	+	7.12106i	−0.389567	+	0.283037i
$634$	2.89171	+	8.89977i	0.114844	+	0.353455i
$635$	6.09443	−	18.7567i	0.241850	−	0.744339i
$636$	49.9147	+	36.2651i	1.97925	+	1.43801i
$637$	−2.91038			−0.115313
$638$	7.29238	+	56.9175i	0.288708	+	2.25339i
$639$	12.1129			0.479179
$640$	−0.562995	−	0.409040i	−0.0222543	−	0.0161687i
$641$	−3.29558	+	10.1428i	−0.130168	+	0.400615i	−0.994807	−	0.101778i	$-0.967547\pi$
$641$	−3.29558	+	10.1428i	−0.130168	+	0.400615i	0.864639	+	0.502393i	$0.167547\pi$
$642$	7.42511	+	22.8521i	0.293046	+	0.901902i
$643$	13.2324	−	9.61389i	0.521834	−	0.379135i	−0.295460	−	0.955355i	$-0.595473\pi$
$643$	13.2324	−	9.61389i	0.521834	−	0.379135i	0.817294	+	0.576220i	$0.195473\pi$
$644$	12.7357	−	9.25306i	0.501859	−	0.364622i
$645$	−18.3268	−	56.4040i	−0.721616	−	2.22090i
$646$	−2.01978	+	6.21625i	−0.0794673	+	0.244575i
$647$	23.5242	+	17.0913i	0.924832	+	0.671930i	0.944722	−	0.327872i	$-0.106332\pi$
$647$	23.5242	+	17.0913i	0.924832	+	0.671930i	−0.0198900	+	0.999802i	$0.506332\pi$
$648$	−0.364968			−0.0143373
$649$	9.12672	+	9.68468i	0.358255	+	0.380157i
$650$	3.31870			0.130170
$651$	10.9578	+	7.96128i	0.429469	+	0.312027i
$652$	2.02962	−	6.24654i	0.0794862	−	0.244633i
$653$	2.00232	+	6.16252i	0.0783570	+	0.241158i	0.982560	−	0.185944i	$-0.0595344\pi$
$653$	2.00232	+	6.16252i	0.0783570	+	0.241158i	−0.904203	+	0.427102i	$0.859534\pi$
$654$	−12.6475	+	9.18897i	−0.494558	+	0.359317i
$655$	8.96916	−	6.51648i	0.350454	−	0.254620i
$656$	11.6154	+	35.7486i	0.453506	+	1.39575i
$657$	0.476274	−	1.46582i	0.0185812	−	0.0571871i
$658$	20.0881	+	14.5948i	0.783114	+	0.568965i
$659$	10.0364			0.390964			0.195482	−	0.980707i	$-0.437373\pi$
$659$	10.0364			0.390964			0.195482	+	0.980707i	$0.437373\pi$
$660$	14.5351	−	26.5501i	0.565779	−	1.03346i
$661$	16.0229			0.623220			0.311610	−	0.950210i	$-0.399132\pi$
$661$	16.0229			0.623220			0.311610	+	0.950210i	$0.399132\pi$
$662$	−18.0801	−	13.1360i	−0.702703	−	0.510544i
$663$	1.29641	−	3.98995i	0.0503485	−	0.154957i
$664$	0.111534	+	0.343265i	0.00432834	+	0.0133213i
$665$	5.90355	−	4.28918i	0.228930	−	0.166327i
$666$	7.60620	−	5.52623i	0.294734	−	0.214137i
$667$	−10.5621	−	32.5069i	−0.408968	−	1.25867i
$668$	−3.05627	+	9.40625i	−0.118251	+	0.363939i
$669$	16.9793	+	12.3362i	0.656457	+	0.476944i
$670$	23.5423			0.909520
$671$	−24.7783	+	45.2605i	−0.956555	+	1.74726i
$672$	40.7812			1.57317
$673$	−35.9534	−	26.1217i	−1.38590	−	1.00692i	−0.996301	−	0.0859325i	$-0.972613\pi$
$673$	−35.9534	−	26.1217i	−1.38590	−	1.00692i	−0.389601	−	0.920984i	$-0.627387\pi$
$674$	−3.74387	+	11.5224i	−0.144208	+	0.443828i
$675$	0.512562	+	1.57750i	0.0197285	+	0.0607181i
$676$	−1.59871	+	1.16153i	−0.0614888	+	0.0446742i
$677$	−22.8611	+	16.6095i	−0.878622	+	0.638356i	−0.932887	−	0.360170i	$-0.882719\pi$
$677$	−22.8611	+	16.6095i	−0.878622	+	0.638356i	0.0542646	+	0.998527i	$0.482719\pi$
$678$	−21.2301	−	65.3394i	−0.815336	−	2.50935i
$679$	10.7014	−	32.9355i	0.410682	−	1.26395i
$680$	−0.116766	−	0.0848354i	−0.00447777	−	0.00325329i
$681$	−30.7643			−1.17889
$682$	−12.0137	−	12.7481i	−0.460027	−	0.488150i
$683$	6.47639			0.247812			0.123906	−	0.992294i	$-0.460458\pi$
$683$	6.47639			0.247812			0.123906	+	0.992294i	$0.460458\pi$
$684$	10.7206	+	7.78899i	0.409913	+	0.297819i
$685$	−10.3046	+	31.7144i	−0.393720	+	1.21175i
$686$	−12.3493	−	38.0073i	−0.471500	−	1.45113i
$687$	−52.6736	+	38.2696i	−2.00962	+	1.46008i
$688$	−42.0469	+	30.5489i	−1.60302	+	1.16466i
$689$	3.81549	+	11.7429i	0.145359	+	0.447368i
$690$	−11.2100	+	34.5010i	−0.426759	+	1.31343i
$691$	28.8077	+	20.9300i	1.09590	+	0.796216i	0.980385	−	0.197090i	$-0.0631491\pi$
$691$	28.8077	+	20.9300i	1.09590	+	0.796216i	0.115512	+	0.993306i	$0.463149\pi$
$692$	32.7542			1.24513
$693$	−2.89304	−	22.5803i	−0.109897	−	0.857756i
$694$	15.1451			0.574900
$695$	−9.48150	−	6.88871i	−0.359654	−	0.261304i
$696$	0.322943	−	0.993915i	0.0122411	−	0.0376743i
$697$	4.76157	+	14.6546i	0.180357	+	0.555082i
$698$	36.2662	−	26.3490i	1.37270	−	0.997323i
$699$	−24.0019	+	17.4384i	−0.907834	+	0.659580i
$700$	2.05530	+	6.32556i	0.0776830	+	0.239084i
$701$	1.68011	−	5.17084i	0.0634567	−	0.195300i	−0.914302	−	0.405034i	$-0.867260\pi$
$701$	1.68011	−	5.17084i	0.0634567	−	0.195300i	0.977758	+	0.209734i	$0.0672598\pi$
$702$	−1.60772	−	1.16808i	−0.0606797	−	0.0440864i
$703$	−2.74458			−0.103514
$704$	−25.4453	−	4.80745i	−0.959006	−	0.181187i
$705$	−28.4375			−1.07102
$706$	20.0690	+	14.5810i	0.755307	+	0.548762i
$707$	1.54608	−	4.75835i	0.0581464	−	0.178956i
$708$	6.19563	+	19.0682i	0.232846	+	0.716626i
$709$	4.24545	−	3.08450i	0.159441	−	0.115841i	−0.505204	−	0.863000i	$-0.668583\pi$
$709$	4.24545	−	3.08450i	0.159441	−	0.115841i	0.664645	+	0.747159i	$0.268583\pi$
$710$	−10.5148	+	7.63942i	−0.394612	+	0.286702i
$711$	−5.06052	−	15.5747i	−0.189784	−	0.584096i
$712$	−0.0356890	+	0.109840i	−0.00133750	+	0.00411641i
$713$	8.44118	+	6.13288i	0.316125	+	0.229678i
$714$	16.9173			0.633115
$715$	5.47636	−	2.58879i	0.204804	−	0.0968153i
$716$	44.2242			1.65274
$717$	8.87378	+	6.44718i	0.331397	+	0.240774i
$718$	1.24815	−	3.84140i	0.0465804	−	0.143360i
$719$	−11.7173	−	36.0622i	−0.436982	−	1.34489i	−0.891042	−	0.453921i	$-0.850025\pi$
$719$	−11.7173	−	36.0622i	−0.436982	−	1.34489i	0.454060	−	0.890971i	$-0.349975\pi$
$720$	−20.2970	+	14.7466i	−0.756425	+	0.549575i
$721$	23.1228	−	16.7997i	0.861140	−	0.625654i
$722$	9.30230	+	28.6295i	0.346196	+	1.06548i
$723$	−15.0789	+	46.4081i	−0.560791	+	1.72594i
$724$	−6.47826	−	4.70673i	−0.240763	−	0.174924i
$725$	14.4409			0.536323
$726$	−3.28731	+	55.3667i	−0.122003	+	2.05485i
$727$	−39.1558			−1.45221			−0.726104	−	0.687585i	$-0.758671\pi$
$727$	−39.1558			−1.45221			−0.726104	+	0.687585i	$0.758671\pi$
$728$	0.0779284	+	0.0566183i	0.00288822	+	0.00209841i
$729$	−10.3728	+	31.9241i	−0.384177	+	1.18238i
$730$	0.511034	+	1.57280i	0.0189142	+	0.0582120i
$731$	−17.2365	+	12.5231i	−0.637515	+	0.463182i
$732$	−62.8935	+	45.6948i	−2.32461	+	1.68893i
$733$	11.8382	+	36.4343i	0.437255	+	1.34573i	0.890758	+	0.454478i	$0.150174\pi$
$733$	11.8382	+	36.4343i	0.437255	+	1.34573i	−0.453503	+	0.891255i	$0.649826\pi$
$734$	14.7774	−	45.4801i	0.545444	−	1.67870i
$735$	10.8740	+	7.90042i	0.401093	+	0.291411i
$736$	31.4153			1.15798
$737$	−19.3834	+	9.16292i	−0.713995	+	0.337520i
$738$	62.8571			2.31380
$739$	−25.4594	−	18.4973i	−0.936537	−	0.680434i	0.0110473	−	0.999939i	$-0.496483\pi$
$739$	−25.4594	−	18.4973i	−0.936537	−	0.680434i	−0.947585	+	0.319505i	$0.896483\pi$
$740$	−1.54931	+	4.76829i	−0.0569538	+	0.175286i
$741$	1.54382	+	4.75138i	0.0567135	+	0.174546i
$742$	−40.2807	+	29.2656i	−1.47875	+	1.07437i
$743$	4.59211	−	3.33636i	0.168468	−	0.122399i	−0.500356	−	0.865820i	$-0.666798\pi$
$743$	4.59211	−	3.33636i	0.168468	−	0.122399i	0.668825	+	0.743420i	$0.266798\pi$
$744$	0.0985829	+	0.303407i	0.00361422	+	0.0111234i
$745$	−7.00722	+	21.5660i	−0.256725	+	0.790117i
$746$	6.15856	+	4.47446i	0.225481	+	0.163821i
$747$	25.7190			0.941010
$748$	−10.6847	−	2.01869i	−0.390671	−	0.0738105i
$749$	−9.63700			−0.352128
$750$	−49.6507	−	36.0734i	−1.81299	−	1.31721i
$751$	−1.50469	+	4.63096i	−0.0549069	+	0.168986i	−0.974749	−	0.223302i	$-0.928316\pi$
$751$	−1.50469	+	4.63096i	−0.0549069	+	0.168986i	0.919842	+	0.392288i	$0.128316\pi$
$752$	7.70099	+	23.7012i	0.280826	+	0.864294i
$753$	17.4737	−	12.6954i	0.636778	−	0.462646i
$754$	−13.9973	+	10.1696i	−0.509750	+	0.370355i
$755$	−10.0722	−	30.9989i	−0.366563	−	1.12817i
$756$	1.23072	−	3.78778i	0.0447610	−	0.137760i
$757$	−22.7250	−	16.5107i	−0.825956	−	0.600092i	0.0924566	−	0.995717i	$-0.470528\pi$
$757$	−22.7250	−	16.5107i	−0.825956	−	0.600092i	−0.918412	+	0.395625i	$0.870528\pi$
$758$	−14.0590			−0.510645
$759$	−4.19845	−	32.7691i	−0.152394	−	1.18944i
$760$	0.171874			0.00623454
$761$	7.86385	+	5.71342i	0.285064	+	0.207111i	0.721123	−	0.692807i	$-0.243626\pi$
$761$	7.86385	+	5.71342i	0.285064	+	0.207111i	−0.436059	+	0.899918i	$0.643626\pi$
$762$	−16.8253	+	51.7828i	−0.609515	+	1.87589i
$763$	−1.93755	−	5.96316i	−0.0701439	−	0.215881i
$764$	−4.30819	+	3.13009i	−0.155865	+	0.113243i
$765$	−8.32046	+	6.04517i	−0.300827	+	0.218564i
$766$	−17.3086	−	53.2705i	−0.625386	−	1.92474i
$767$	−1.23989	+	3.81599i	−0.0447698	+	0.137787i
$768$	33.4995	+	24.3388i	1.20881	+	0.878251i
$769$	18.3552			0.661905			0.330952	−	0.943647i	$-0.392630\pi$
$769$	18.3552			0.661905			0.330952	+	0.943647i	$0.392630\pi$
$770$	16.7524	+	17.7765i	0.603714	+	0.640622i
$771$	44.7599			1.61199
$772$	−8.40762	−	6.10850i	−0.302597	−	0.219850i
$773$	−7.36982	+	22.6820i	−0.265074	+	0.815814i	0.726602	+	0.687058i	$0.241098\pi$
$773$	−7.36982	+	22.6820i	−0.265074	+	0.815814i	−0.991676	+	0.128756i	$0.958902\pi$
$774$	26.8572	+	82.6580i	0.965362	+	2.97108i
$775$	−3.56639	+	2.59113i	−0.128109	+	0.0930763i
$776$	0.659889	−	0.479438i	0.0236886	−	0.0172108i
$777$	2.19517	+	6.75603i	0.0787512	+	0.242371i
$778$	−1.76672	+	5.43740i	−0.0633399	+	0.194940i
$779$	−14.8449	−	10.7855i	−0.531874	−	0.386429i
$780$	9.12628			0.326773
$781$	5.68389	−	10.3823i	0.203386	−	0.371508i
$782$	13.0321			0.466026
$783$	−6.99581	−	5.08276i	−0.250010	−	0.181643i
$784$	3.63988	−	11.2024i	0.129996	−	0.400086i
$785$	8.69360	+	26.7561i	0.310288	+	0.954968i
$786$	−24.7617	+	17.9904i	−0.883220	+	0.641697i
$787$	−6.82159	+	4.95617i	−0.243163	+	0.176668i	−0.702691	−	0.711495i	$-0.748019\pi$
$787$	−6.82159	+	4.95617i	−0.243163	+	0.176668i	0.459528	+	0.888163i	$0.348019\pi$
$788$	−2.34232	−	7.20893i	−0.0834418	−	0.256807i
$789$	20.2932	−	62.4561i	0.722458	−	2.22350i
$790$	14.2155	+	10.3282i	0.505767	+	0.367461i
$791$	27.5544			0.979721
$792$	0.257483	−	0.470324i	0.00914928	−	0.0167122i
$793$	−15.5577			−0.552471
$794$	−3.79535	−	2.75749i	−0.134692	−	0.0978595i
$795$	17.6211	−	54.2321i	0.624956	−	1.92342i
$796$	−5.56481	−	17.1267i	−0.197239	−	0.607041i
$797$	15.6310	−	11.3566i	0.553679	−	0.402271i	−0.275461	−	0.961312i	$-0.588831\pi$
$797$	15.6310	−	11.3566i	0.553679	−	0.402271i	0.829140	+	0.559041i	$0.188831\pi$
$798$	−16.2983	+	11.8414i	−0.576953	+	0.419181i
$799$	3.15691	+	9.71596i	0.111683	+	0.343726i
$800$	−4.10156	+	12.6233i	−0.145012	+	0.446301i
$801$	6.65796	+	4.83729i	0.235247	+	0.170917i
$802$	77.9065			2.75097
$803$	−1.03291	−	1.09605i	−0.0364505	−	0.0386788i
$804$	−32.3021			−1.13921
$805$	−11.7708	−	8.55195i	−0.414865	−	0.301417i
$806$	1.63209	−	5.02305i	0.0574879	−	0.176929i
$807$	−16.4970	−	50.7725i	−0.580721	−	1.78728i
$808$	0.0953373	−	0.0692666i	0.00335395	−	0.00243679i
$809$	29.5316	−	21.4560i	1.03828	−	0.754352i	0.0683283	−	0.997663i	$-0.478233\pi$
$809$	29.5316	−	21.4560i	1.03828	−	0.754352i	0.969948	+	0.243311i	$0.0782335\pi$
$810$	−8.62307	−	26.5391i	−0.302984	−	0.932488i
$811$	−9.77860	+	30.0954i	−0.343373	+	1.05679i	0.619076	+	0.785331i	$0.287507\pi$
$811$	−9.77860	+	30.0954i	−0.343373	+	1.05679i	−0.962449	+	0.271463i	$0.912493\pi$
$812$	−28.0522	−	20.3811i	−0.984439	−	0.715237i
$813$	2.58382			0.0906185
$814$	−1.16753	−	9.11262i	−0.0409218	−	0.319397i
$815$	−6.07034			−0.212635
$816$	13.7364	+	9.98009i	0.480871	+	0.349373i
$817$	7.84019	−	24.1296i	0.274293	−	0.844188i
$818$	−12.3930	−	38.1417i	−0.433310	−	1.33359i
$819$	5.55299	−	4.03448i	0.194037	−	0.140976i
$820$	−27.1180	+	19.7024i	−0.947003	+	0.688038i
$821$	1.41680	+	4.36047i	0.0494468	+	0.152182i	0.972731	−	0.231936i	$-0.0745059\pi$
$821$	1.41680	+	4.36047i	0.0494468	+	0.152182i	−0.923284	+	0.384117i	$0.874506\pi$
$822$	28.4486	−	87.5558i	0.992259	−	3.05386i
$823$	40.6759	+	29.5528i	1.41787	+	1.03014i	0.992118	+	0.125306i	$0.0399913\pi$
$823$	40.6759	+	29.5528i	1.41787	+	1.03014i	0.425755	+	0.904839i	$0.360009\pi$
$824$	0.673191			0.0234517
$825$	13.7155	+	2.59130i	0.477511	+	0.0902173i
$826$	−16.1797			−0.562965
$827$	−34.9703	−	25.4074i	−1.21604	−	0.883503i	−0.220273	−	0.975438i	$-0.570695\pi$
$827$	−34.9703	−	25.4074i	−1.21604	−	0.883503i	−0.995765	+	0.0919352i	$0.970695\pi$
$828$	8.16461	−	25.1281i	0.283740	−	0.873261i
$829$	−1.49923	−	4.61416i	−0.0520705	−	0.160256i	0.921640	−	0.388046i	$-0.126850\pi$
$829$	−1.49923	−	4.61416i	−0.0520705	−	0.160256i	−0.973710	+	0.227790i	$0.926850\pi$
$830$	−22.3257	+	16.2206i	−0.774937	+	0.563025i
$831$	−4.14131	+	3.00883i	−0.143660	+	0.104375i
$832$	−2.41273	−	7.42563i	−0.0836465	−	0.257438i
$833$	1.49211	−	4.59226i	0.0516987	−	0.159112i
$834$	26.1761	+	19.0181i	0.906405	+	0.658542i
$835$	9.14092			0.316335
$836$	11.7067	−	5.53401i	0.404885	−	0.191398i
$837$	2.63971			0.0912418
$838$	14.8463	+	10.7865i	0.512856	+	0.372612i
$839$	−3.74410	+	11.5231i	−0.129261	+	0.397823i	−0.994653	−	0.103271i	$-0.967069\pi$
$839$	−3.74410	+	11.5231i	−0.129261	+	0.397823i	0.865393	+	0.501094i	$0.167069\pi$
$840$	−0.137468	−	0.423084i	−0.00474311	−	0.0145978i
$841$	−37.4458	+	27.2060i	−1.29123	+	0.938137i
$842$	29.7574	−	21.6200i	1.02551	−	0.745074i
$843$	22.1365	+	68.1290i	0.762420	+	2.34649i
$844$	−2.92570	+	9.00437i	−0.100707	+	0.309943i
$845$	1.47757	+	1.07352i	0.0508301	+	0.0369302i
$846$	41.6741			1.43279
$847$	−20.7117	−	8.11594i	−0.711663	−	0.278867i
$848$	−49.9716			−1.71603
$849$	−20.1289	−	14.6245i	−0.690823	−	0.501912i
$850$	−1.70146	+	5.23655i	−0.0583595	+	0.179612i
$851$	1.69102	+	5.20443i	0.0579674	+	0.178405i
$852$	14.4272	−	10.4819i	0.494266	−	0.359105i
$853$	−16.4419	+	11.9457i	−0.562959	+	0.409014i	−0.832541	−	0.553964i	$-0.813115\pi$
$853$	−16.4419	+	11.9457i	−0.562959	+	0.409014i	0.269581	+	0.962978i	$0.413115\pi$
$854$	−19.3865	−	59.6655i	−0.663392	−	2.04171i
$855$	3.78464	−	11.6479i	0.129432	−	0.398351i
$856$	−0.183635	−	0.133418i	−0.00627650	−	0.00456015i
$857$	5.07138			0.173235			0.0866175	−	0.996242i	$-0.472394\pi$
$857$	5.07138			0.173235			0.0866175	+	0.996242i	$0.472394\pi$
$858$	−15.1189	+	7.14702i	−0.516151	+	0.243995i
$859$	31.1183			1.06174			0.530871	−	0.847452i	$-0.321865\pi$
$859$	31.1183			1.06174			0.530871	+	0.847452i	$0.321865\pi$
$860$	−37.4958	−	27.2423i	−1.27860	−	0.928954i
$861$	−14.6761	+	45.1685i	−0.500161	+	1.53934i
$862$	−0.362715	−	1.11632i	−0.0123541	−	0.0380220i
$863$	−30.0253	+	21.8147i	−1.02207	+	0.742581i	−0.966707	−	0.255886i	$-0.917633\pi$
$863$	−30.0253	+	21.8147i	−1.02207	+	0.742581i	−0.0553673	+	0.998466i	$0.517633\pi$
$864$	6.42998	−	4.67166i	0.218752	−	0.158933i
$865$	−9.35469	−	28.7908i	−0.318069	−	0.978916i
$866$	−6.52675	+	20.0873i	−0.221788	+	0.682593i
$867$	−29.1464	−	21.1761i	−0.989862	−	0.719177i
$868$	10.5849			0.359274
$869$	−15.7241	−	2.97079i	−0.533403	−	0.100777i
$870$	79.9038			2.70899
$871$	−5.22981	−	3.79968i	−0.177205	−	0.128747i
$872$	0.0456360	−	0.140453i	0.00154543	−	0.00475634i
$873$	−17.9609	−	55.2778i	−0.607883	−	1.87087i
$874$	−12.5552	+	9.12188i	−0.424686	+	0.308552i
$875$	19.9135	−	14.4680i	0.673199	−	0.489107i
$876$	−0.701183	−	2.15802i	−0.0236908	−	0.0729127i
$877$	−10.0380	+	30.8938i	−0.338959	+	1.04321i	0.625779	+	0.780000i	$0.284781\pi$
$877$	−10.0380	+	30.8938i	−0.338959	+	1.04321i	−0.964739	+	0.263210i	$0.915219\pi$
$878$	−5.49664	−	3.99354i	−0.185503	−	0.134775i
$879$	46.6336			1.57291
$880$	3.11552	+	24.3169i	0.105024	+	0.819721i
$881$	4.44712			0.149827			0.0749137	−	0.997190i	$-0.476132\pi$
$881$	4.44712			0.149827			0.0749137	+	0.997190i	$0.476132\pi$
$882$	−15.9354	−	11.5778i	−0.536574	−	0.389844i
$883$	7.83018	−	24.0988i	0.263507	−	0.810990i	−0.728527	−	0.685017i	$-0.759795\pi$
$883$	7.83018	−	24.0988i	0.263507	−	0.810990i	0.992034	−	0.125973i	$-0.0402052\pi$
$884$	−1.01313	−	3.11809i	−0.0340752	−	0.104873i
$885$	14.9913	−	10.8918i	0.503928	−	0.366125i
$886$	56.5500	−	41.0860i	1.89983	−	1.38031i
$887$	−11.0756	−	34.0873i	−0.371884	−	1.14454i	−0.945557	−	0.325456i	$-0.894482\pi$
$887$	−11.0756	−	34.0873i	−0.371884	−	1.14454i	0.573673	−	0.819084i	$-0.305518\pi$
$888$	−0.0517038	+	0.159128i	−0.00173507	+	0.00533998i
$889$	−17.6668	−	12.8357i	−0.592526	−	0.430496i
$890$	−8.83033			−0.295993
$891$	17.4290	+	18.4945i	0.583894	+	0.619590i
$892$	16.4015			0.549162
$893$	−9.84214	−	7.15073i	−0.329355	−	0.239290i
$894$	19.3452	−	59.5385i	0.647002	−	1.99127i
$895$	−12.6306	−	38.8729i	−0.422193	−	1.29938i
$896$	−0.623383	+	0.452914i	−0.0208258	+	0.0151308i
$897$	8.05864	−	5.85494i	0.269070	−	0.195491i
$898$	−8.98368	−	27.6489i	−0.299789	−	0.922657i
$899$	7.10183	−	21.8572i	0.236859	−	0.728978i
$900$	9.03101	+	6.56141i	0.301034	+	0.218714i
$901$	−20.4851			−0.682458
$902$	29.4952	−	53.8765i	0.982083	−	1.79389i
$903$	−65.6680			−2.18529
$904$	0.525053	+	0.381474i	0.0174630	+	0.0126876i
$905$	−2.28698	+	7.03861i	−0.0760219	+	0.233971i
$906$	27.8068	+	85.5805i	0.923819	+	2.84322i
$907$	42.0535	−	30.5536i	1.39636	−	1.01452i	0.401229	−	0.915978i	$-0.368583\pi$
$907$	42.0535	−	30.5536i	1.39636	−	1.01452i	0.995133	−	0.0985385i	$-0.0314167\pi$
$908$	−19.4503	+	14.1314i	−0.645480	+	0.468968i
$909$	−2.59489	−	7.98625i	−0.0860671	−	0.264887i
$910$	−2.27586	+	7.00437i	−0.0754439	+	0.232192i
$911$	30.3349	+	22.0396i	1.00504	+	0.730205i	0.963163	−	0.268917i	$-0.0866658\pi$
$911$	30.3349	+	22.0396i	1.00504	+	0.730205i	0.0418783	+	0.999123i	$0.486666\pi$
$912$	−20.2194			−0.669531
$913$	12.0685	−	22.0445i	0.399408	−	0.729565i
$914$	−46.3375			−1.53271
$915$	58.1281	+	42.2325i	1.92166	+	1.39616i
$916$	−15.7231	+	48.3908i	−0.519507	+	1.59888i
$917$	−3.79338	−	11.6748i	−0.125268	−	0.385537i
$918$	2.66736	−	1.93795i	0.0880361	−	0.0639620i
$919$	−44.9636	+	32.6680i	−1.48321	+	1.07762i	−0.506710	+	0.862116i	$0.669139\pi$
$919$	−44.9636	+	32.6680i	−1.48321	+	1.07762i	−0.976503	+	0.215502i	$0.930861\pi$
$920$	−0.105897	−	0.325918i	−0.00349132	−	0.0107452i
$921$	12.6010	−	38.7818i	0.415216	−	1.27790i
$922$	−49.3531	−	35.8571i	−1.62536	−	1.18089i
$923$	3.56879			0.117468
$924$	−22.9857	−	24.3909i	−0.756174	−	0.802403i
$925$	−2.31202			−0.0760189
$926$	9.66481	+	7.02189i	0.317605	+	0.230754i
$927$	14.8235	−	45.6222i	0.486869	−	1.49843i
$928$	−21.3828	−	65.8096i	−0.701926	−	2.16031i
$929$	−17.4271	+	12.6615i	−0.571765	+	0.415412i	−0.835746	−	0.549116i	$-0.814964\pi$
$929$	−17.4271	+	12.6615i	−0.571765	+	0.415412i	0.263981	+	0.964528i	$0.414964\pi$
$930$	−19.7334	+	14.3371i	−0.647083	+	0.470133i
$931$	1.77687	+	5.46863i	0.0582344	+	0.179227i
$932$	−7.16459	+	22.0503i	−0.234684	+	0.722282i
$933$	44.6260	+	32.4227i	1.46099	+	1.06147i
$934$	−57.2092			−1.87194
$935$	1.27716	+	9.96834i	0.0417677	+	0.325999i
$936$	0.161668			0.00528429
$937$	7.57687	+	5.50492i	0.247525	+	0.179838i	0.704629	−	0.709576i	$-0.251113\pi$
$937$	7.57687	+	5.50492i	0.247525	+	0.179838i	−0.457104	+	0.889413i	$0.651113\pi$
$938$	8.05530	−	24.7917i	0.263015	−	0.809477i
$939$	10.0999	+	31.0842i	0.329597	+	1.01439i
$940$	−17.9792	+	13.0626i	−0.586417	+	0.426057i
$941$	11.0450	−	8.02463i	0.360055	−	0.261596i	−0.393020	−	0.919530i	$-0.628570\pi$
$941$	11.0450	−	8.02463i	0.360055	−	0.261596i	0.753075	+	0.657934i	$0.228570\pi$
$942$	−24.0009	−	73.8672i	−0.781992	−	2.40672i
$943$	−11.3056	+	34.7950i	−0.368161	+	1.13308i
$944$	−13.1375	−	9.54497i	−0.427590	−	0.310662i
$945$	−3.68093			−0.119741
$946$	83.4509	+	15.7666i	2.71322	+	0.512616i
$947$	23.0149			0.747885			0.373942	−	0.927452i	$-0.378006\pi$
$947$	23.0149			0.747885			0.373942	+	0.927452i	$0.378006\pi$
$948$	−19.5050	−	14.1712i	−0.633491	−	0.460259i
$949$	0.140323	−	0.431870i	0.00455508	−	0.0140191i
$950$	−2.02616	−	6.23588i	−0.0657373	−	0.202319i
$951$	−9.60044	+	6.97513i	−0.311316	+	0.226184i
$952$	−0.129290	+	0.0939349i	−0.00419032	+	0.00304445i
$953$	12.1947	+	37.5314i	0.395024	+	1.21576i	0.928943	+	0.370224i	$0.120719\pi$
$953$	12.1947	+	37.5314i	0.395024	+	1.21576i	−0.533918	+	0.845536i	$0.679281\pi$
$954$	−25.8231	+	79.4752i	−0.836053	+	2.57311i
$955$	3.98176	+	2.89292i	0.128847	+	0.0936126i
$956$	8.57180			0.277232
$957$	−65.7880	+	31.0994i	−2.12663	+	1.00530i
$958$	−67.1917			−2.17087
$959$	29.8716	+	21.7030i	0.964603	+	0.700825i
$960$	−11.1427	+	34.2938i	−0.359630	+	1.10683i
$961$	−7.41159	−	22.8105i	−0.239084	−	0.735824i
$962$	2.24099	−	1.62817i	0.0722524	−	0.0524945i
$963$	−13.0854	+	9.50708i	−0.421670	+	0.306361i
$964$	11.7840	+	36.2673i	0.379536	+	1.16809i
$965$	−2.96810	+	9.13486i	−0.0955464	+	0.294061i
$966$	32.4962	+	23.6099i	1.04555	+	0.759635i
$967$	−18.3171			−0.589037			−0.294518	−	0.955646i	$-0.595159\pi$
$967$	−18.3171			−0.589037			−0.294518	+	0.955646i	$0.595159\pi$
$968$	−0.282305	−	0.441392i	−0.00907363	−	0.0141869i
$969$	−8.28865			−0.266270
$970$	50.4540	+	36.6570i	1.61998	+	1.17698i
$971$	−1.91786	+	5.90256i	−0.0615470	+	0.189422i	−0.977102	−	0.212770i	$-0.931752\pi$
$971$	−1.91786	+	5.90256i	−0.0615470	+	0.189422i	0.915555	+	0.402192i	$0.131752\pi$
$972$	13.6573	+	42.0330i	0.438059	+	1.34821i
$973$	−10.4985	+	7.62760i	−0.336566	+	0.244530i
$974$	47.4212	−	34.4535i	1.51947	−	1.10396i
$975$	1.30051	+	4.00254i	0.0416495	+	0.128184i
$976$	19.4573	−	59.8836i	0.622815	−	1.91683i
$977$	−0.288159	−	0.209360i	−0.00921903	−	0.00669802i	0.583166	−	0.812353i	$-0.301814\pi$
$977$	−0.288159	−	0.209360i	−0.00921903	−	0.00669802i	−0.592385	+	0.805655i	$0.701814\pi$
$978$	16.7587			0.535885
$979$	7.27037	−	3.43685i	0.232362	−	0.109842i
$980$	10.5040			0.335536
$981$	−8.51361	−	6.18550i	−0.271819	−	0.197488i
$982$	−7.52693	+	23.1655i	−0.240194	+	0.739241i
$983$	8.35079	+	25.7011i	0.266349	+	0.819737i	0.991380	+	0.131021i	$0.0418255\pi$
$983$	8.35079	+	25.7011i	0.266349	+	0.819737i	−0.725031	+	0.688716i	$0.758174\pi$
$984$	−0.904986	+	0.657511i	−0.0288499	+	0.0209607i
$985$	−5.66763	+	4.11778i	−0.180586	+	0.131203i
$986$	−8.87029	−	27.2999i	−0.282488	−	0.869407i
$987$	−9.73024	+	29.9466i	−0.309717	+	0.953211i
$988$	3.15858	+	2.29484i	0.100488	+	0.0730087i
$989$	−50.5865			−1.60856
$990$	40.2837	+	7.61090i	1.28030	+	0.241890i
$991$	16.0927			0.511203			0.255602	−	0.966782i	$-0.417726\pi$
$991$	16.0927			0.511203			0.255602	+	0.966782i	$0.417726\pi$
$992$	17.0890	+	12.4159i	0.542577	+	0.394205i
$993$	8.75763	−	26.9532i	0.277915	−	0.855335i
$994$	4.44707	+	13.6867i	0.141052	+	0.434115i
$995$	−13.4650	+	9.78288i	−0.426868	+	0.310138i
$996$	30.6328	−	22.2560i	0.970637	−	0.705209i
$997$	10.4546	+	32.1759i	0.331100	+	1.01902i	0.968611	+	0.248580i	$0.0799638\pi$
$997$	10.4546	+	32.1759i	0.331100	+	1.01902i	−0.637512	+	0.770441i	$0.720036\pi$
$998$	−16.4334	+	50.5767i	−0.520189	+	1.60098i
$999$	1.12004	+	0.813760i	0.0354366	+	0.0257462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.h.c.92.6	yes	28
11.3	even	5	inner	143.2.h.c.14.6	✓	28
11.5	even	5		1573.2.a.s.1.3		14
11.6	odd	10		1573.2.a.r.1.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.c.14.6	✓	28	11.3	even	5	inner
143.2.h.c.92.6	yes	28	1.1	even	1	trivial
1573.2.a.r.1.12		14	11.6	odd	10
1573.2.a.s.1.3		14	11.5	even	5

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61320 + 1.17206i) q^{2} +(-0.781399 + 2.40490i) q^{3} +(0.610652 + 1.87939i) q^{4} +(1.47757 - 1.07352i) q^{5} +(-4.07922 + 2.96373i) q^{6} +(-0.624919 - 1.92330i) q^{7} +(0.0147190 - 0.0453005i) q^{8} +(-2.74590 - 1.99502i) q^{9} +O(q^{10})\)	\(q+(1.61320 + 1.17206i) q^{2} +(-0.781399 + 2.40490i) q^{3} +(0.610652 + 1.87939i) q^{4} +(1.47757 - 1.07352i) q^{5} +(-4.07922 + 2.96373i) q^{6} +(-0.624919 - 1.92330i) q^{7} +(0.0147190 - 0.0453005i) q^{8} +(-2.74590 - 1.99502i) q^{9} +3.64184 q^{10} +(-2.99848 + 1.41744i) q^{11} -4.99692 q^{12} +(-0.809017 - 0.587785i) q^{13} +(1.24610 - 3.83510i) q^{14} +(1.42713 + 4.39226i) q^{15} +(3.27426 - 2.37889i) q^{16} +(1.34223 - 0.975189i) q^{17} +(-2.09141 - 6.43670i) q^{18} +(-0.610527 + 1.87901i) q^{19} +(2.91985 + 2.12140i) q^{20} +5.11366 q^{21} +(-6.49845 - 1.22777i) q^{22} +3.93925 q^{23} +(0.0974417 + 0.0707955i) q^{24} +(-0.514306 + 1.58287i) q^{25} +(-0.616186 - 1.89642i) q^{26} +(0.806273 - 0.585792i) q^{27} +(3.23304 - 2.34894i) q^{28} +(-2.68126 - 8.25206i) q^{29} +(-2.84573 + 8.75826i) q^{30} +(2.14284 + 1.55686i) q^{31} +7.97494 q^{32} +(-1.06580 - 8.31862i) q^{33} +3.30826 q^{34} +(-2.98807 - 2.17096i) q^{35} +(2.07263 - 6.37890i) q^{36} +(0.429275 + 1.32117i) q^{37} +(-3.18720 + 2.31564i) q^{38} +(2.04573 - 1.48631i) q^{39} +(-0.0268826 - 0.0827360i) q^{40} +(-2.86998 + 8.83290i) q^{41} +(8.24934 + 5.99350i) q^{42} -12.8417 q^{43} +(-4.49496 - 4.76976i) q^{44} -6.19897 q^{45} +(6.35478 + 4.61702i) q^{46} +(-1.90279 + 5.85620i) q^{47} +(3.16248 + 9.73312i) q^{48} +(2.35455 - 1.71068i) q^{49} +(-2.68489 + 1.95069i) q^{50} +(1.29641 + 3.98995i) q^{51} +(0.610652 - 1.87939i) q^{52} +(-9.98909 - 7.25750i) q^{53} +1.98726 q^{54} +(-2.90882 + 5.31330i) q^{55} -0.0963248 q^{56} +(-4.04176 - 2.93651i) q^{57} +(5.34648 - 16.4548i) q^{58} +(-1.23989 - 3.81599i) q^{59} +(-7.38332 + 5.36429i) q^{60} +(12.5865 - 9.14460i) q^{61} +(1.63209 + 5.02305i) q^{62} +(-2.12105 + 6.52793i) q^{63} +(6.31662 + 4.58929i) q^{64} -1.82638 q^{65} +(8.03054 - 14.6687i) q^{66} +6.46440 q^{67} +(2.65240 + 1.92708i) q^{68} +(-3.07813 + 9.47350i) q^{69} +(-2.27586 - 7.00437i) q^{70} +(-2.88721 + 2.09768i) q^{71} +(-0.130792 + 0.0950261i) q^{72} +(0.140323 + 0.431870i) q^{73} +(-0.855982 + 2.63444i) q^{74} +(-3.40477 - 2.47371i) q^{75} -3.90422 q^{76} +(4.59998 + 4.88119i) q^{77} +5.04220 q^{78} +(3.90340 + 2.83598i) q^{79} +(2.28417 - 7.02996i) q^{80} +(-2.36778 - 7.28727i) q^{81} +(-14.9825 + 10.8854i) q^{82} +(-6.13034 + 4.45395i) q^{83} +(3.12267 + 9.61059i) q^{84} +(0.936363 - 2.88183i) q^{85} +(-20.7161 - 15.0511i) q^{86} +21.9405 q^{87} +(0.0200762 + 0.156696i) q^{88} -2.42469 q^{89} +(-10.0001 - 7.26553i) q^{90} +(-0.624919 + 1.92330i) q^{91} +(2.40551 + 7.40341i) q^{92} +(-5.41852 + 3.93678i) q^{93} +(-9.93336 + 7.21701i) q^{94} +(1.11506 + 3.43179i) q^{95} +(-6.23161 + 19.1789i) q^{96} +(13.8540 + 10.0655i) q^{97} +5.80335 q^{98} +(11.0614 + 2.08985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more