LMFDB - Embedded newform 187.2.g.f.86.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(69,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, 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("187.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.g (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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.6
Character	$\chi$	$=$	187.86
Dual form			187.2.g.f.137.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0881614 - 0.271333i) q^{2} +(-1.31211 + 0.953301i) q^{3} +(1.55218 + 1.12773i) q^{4} +(-1.06412 - 3.27502i) q^{5} +(0.142985 + 0.440062i) q^{6} +(3.21023 + 2.33237i) q^{7} +(0.904452 - 0.657123i) q^{8} +(-0.114211 + 0.351506i) q^{9} +O(q^{10})$	\(q+(0.0881614 - 0.271333i) q^{2} +(-1.31211 + 0.953301i) q^{3} +(1.55218 + 1.12773i) q^{4} +(-1.06412 - 3.27502i) q^{5} +(0.142985 + 0.440062i) q^{6} +(3.21023 + 2.33237i) q^{7} +(0.904452 - 0.657123i) q^{8} +(-0.114211 + 0.351506i) q^{9} -0.982436 q^{10} +(3.31155 + 0.183384i) q^{11} -3.11170 q^{12} +(-0.0509445 + 0.156791i) q^{13} +(0.915868 - 0.665417i) q^{14} +(4.51832 + 3.28275i) q^{15} +(1.08720 + 3.34606i) q^{16} +(0.309017 + 0.951057i) q^{17} +(0.0853062 + 0.0619786i) q^{18} +(1.21922 - 0.885815i) q^{19} +(2.04163 - 6.28348i) q^{20} -6.43562 q^{21} +(0.341709 - 0.882366i) q^{22} -2.81685 q^{23} +(-0.560301 + 1.72443i) q^{24} +(-5.54834 + 4.03110i) q^{25} +(0.0380512 + 0.0276458i) q^{26} +(-1.68877 - 5.19751i) q^{27} +(2.35260 + 7.24054i) q^{28} +(-5.48054 - 3.98185i) q^{29} +(1.28906 - 0.936557i) q^{30} +(2.21098 - 6.80469i) q^{31} +3.23968 q^{32} +(-4.51993 + 2.91628i) q^{33} +0.285296 q^{34} +(4.22250 - 12.9955i) q^{35} +(-0.573680 + 0.416803i) q^{36} +(-0.466100 - 0.338641i) q^{37} +(-0.132863 - 0.408909i) q^{38} +(-0.0826244 - 0.254292i) q^{39} +(-3.11454 - 2.26284i) q^{40} +(1.10710 - 0.804355i) q^{41} +(-0.567373 + 1.74620i) q^{42} -11.1201 q^{43} +(4.93333 + 4.01918i) q^{44} +1.27272 q^{45} +(-0.248337 + 0.764303i) q^{46} +(-10.2448 + 7.44326i) q^{47} +(-4.61633 - 3.35396i) q^{48} +(2.70253 + 8.31753i) q^{49} +(0.604622 + 1.86083i) q^{50} +(-1.31211 - 0.953301i) q^{51} +(-0.255893 + 0.185917i) q^{52} +(-0.967355 + 2.97721i) q^{53} -1.55914 q^{54} +(-2.92330 - 11.0405i) q^{55} +4.43616 q^{56} +(-0.755297 + 2.32457i) q^{57} +(-1.56358 + 1.13601i) q^{58} +(4.58838 + 3.33365i) q^{59} +(3.31121 + 10.1909i) q^{60} +(-2.25257 - 6.93270i) q^{61} +(-1.65141 - 1.19982i) q^{62} +(-1.18649 + 0.862034i) q^{63} +(-1.88879 + 5.81310i) q^{64} +0.567705 q^{65} +(0.392801 + 1.48351i) q^{66} +12.7865 q^{67} +(-0.592882 + 1.82470i) q^{68} +(3.69600 - 2.68530i) q^{69} +(-3.15385 - 2.29141i) q^{70} +(2.57937 + 7.93847i) q^{71} +(0.127684 + 0.392971i) q^{72} +(-4.21542 - 3.06268i) q^{73} +(-0.132977 + 0.0966131i) q^{74} +(3.43715 - 10.5785i) q^{75} +2.89141 q^{76} +(10.2031 + 8.31247i) q^{77} -0.0762820 q^{78} +(2.66455 - 8.20065i) q^{79} +(9.80152 - 7.12122i) q^{80} +(6.27361 + 4.55805i) q^{81} +(-0.120644 - 0.371306i) q^{82} +(-4.73821 - 14.5827i) q^{83} +(-9.98927 - 7.25763i) q^{84} +(2.78590 - 2.02407i) q^{85} +(-0.980365 + 3.01725i) q^{86} +10.9869 q^{87} +(3.11564 - 2.01023i) q^{88} +5.44553 q^{89} +(0.112205 - 0.345332i) q^{90} +(-0.529238 + 0.384514i) q^{91} +(-4.37227 - 3.17664i) q^{92} +(3.58588 + 11.0362i) q^{93} +(1.11641 + 3.43595i) q^{94} +(-4.19846 - 3.05036i) q^{95} +(-4.25080 + 3.08839i) q^{96} +(-0.762547 + 2.34688i) q^{97} +2.49508 q^{98} +(-0.442677 + 1.14309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9 - 10 * q^10 + 3 * q^11 + 28 * q^12 - 13 * q^13 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 9 * q^17 + 2 * q^18 + 10 * q^19 + 19 * q^20 - 50 * q^21 - 25 * q^22 + 38 * q^23 - 17 * q^24 - 28 * q^25 + 20 * q^26 - 16 * q^27 + 31 * q^28 - 45 * q^29 + 68 * q^30 - 13 * q^31 - 40 * q^32 - 29 * q^33 - 4 * q^34 + 13 * q^35 - 25 * q^36 + q^37 + 65 * q^38 - 34 * q^39 - 54 * q^40 + 37 * q^41 + 28 * q^42 - 8 * q^43 - 2 * q^44 + 42 * q^45 + 22 * q^46 - 35 * q^47 + 48 * q^48 - 2 * q^49 - 49 * q^50 - q^51 + 56 * q^52 + 58 * q^53 - 58 * q^54 - 19 * q^55 - 28 * q^56 + 9 * q^57 - 52 * q^58 + 16 * q^59 + 97 * q^60 - 14 * q^61 - 64 * q^62 + 34 * q^63 - 33 * q^64 - 42 * q^65 - 28 * q^66 + 54 * q^67 - 14 * q^68 + 19 * q^69 + 4 * q^70 + 25 * q^71 - 72 * q^72 + 8 * q^73 + 84 * q^74 + 30 * q^75 - 140 * q^76 - 31 * q^77 - 48 * q^78 + 19 * q^79 - 19 * q^80 + 56 * q^81 + 48 * q^82 + 42 * q^83 - 91 * q^84 - 9 * q^85 + 30 * q^86 - 32 * q^87 + 126 * q^88 + 12 * q^89 + 160 * q^90 - 59 * q^91 + 69 * q^92 - 40 * q^93 - 77 * q^94 - 11 * q^95 + 192 * q^96 - 49 * q^97 - 212 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	0.0881614	−	0.271333i	0.0623395	−	0.191861i	−0.915036	−	0.403372i	$-0.867838\pi$
$2$	0.0881614	−	0.271333i	0.0623395	−	0.191861i	0.977376	+	0.211510i	$0.0678382\pi$
$3$	−1.31211	+	0.953301i	−0.757545	+	0.550388i	−0.898156	−	0.439676i	$-0.855093\pi$
$3$	−1.31211	+	0.953301i	−0.757545	+	0.550388i	0.140612	+	0.990065i	$0.455093\pi$
$4$	1.55218	+	1.12773i	0.776092	+	0.563864i
$5$	−1.06412	−	3.27502i	−0.475889	−	1.46463i	−0.844756	−	0.535152i	$-0.820254\pi$
$5$	−1.06412	−	3.27502i	−0.475889	−	1.46463i	0.368867	−	0.929482i	$-0.379746\pi$
$6$	0.142985	+	0.440062i	0.0583733	+	0.179655i
$7$	3.21023	+	2.33237i	1.21335	+	0.881554i	0.995531	−	0.0944344i	$-0.0301043\pi$
$7$	3.21023	+	2.33237i	1.21335	+	0.881554i	0.217824	+	0.975988i	$0.430104\pi$
$8$	0.904452	−	0.657123i	0.319772	−	0.232328i
$9$	−0.114211	+	0.351506i	−0.0380704	+	0.117169i
$10$	−0.982436			−0.310673
$11$	3.31155	+	0.183384i	0.998470	+	0.0552924i
$11$	3.31155	+	0.183384i	0.998470	+	0.0552924i
$12$	−3.11170			−0.898269
$13$	−0.0509445	+	0.156791i	−0.0141294	+	0.0434860i	−0.957873	−	0.287193i	$-0.907278\pi$
$13$	−0.0509445	+	0.156791i	−0.0141294	+	0.0434860i	0.943743	+	0.330679i	$0.107278\pi$
$14$	0.915868	−	0.665417i	0.244776	−	0.177840i
$15$	4.51832	+	3.28275i	1.16662	+	0.847603i
$16$	1.08720	+	3.34606i	0.271801	+	0.836516i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	0.0853062	+	0.0619786i	0.0201069	+	0.0146085i
$19$	1.21922	−	0.885815i	0.279708	−	0.203220i	−0.439082	−	0.898447i	$-0.644696\pi$
$19$	1.21922	−	0.885815i	0.279708	−	0.203220i	0.718790	+	0.695227i	$0.244696\pi$
$20$	2.04163	−	6.28348i	0.456521	−	1.40503i
$21$	−6.43562			−1.40437
$22$	0.341709	−	0.882366i	0.0728526	−	0.188121i
$23$	−2.81685			−0.587353			−0.293677	−	0.955905i	$-0.594879\pi$
$23$	−2.81685			−0.587353			−0.293677	+	0.955905i	$0.594879\pi$
$24$	−0.560301	+	1.72443i	−0.114371	+	0.351998i
$25$	−5.54834	+	4.03110i	−1.10967	+	0.806220i
$26$	0.0380512	+	0.0276458i	0.00746246	+	0.00542179i
$27$	−1.68877	−	5.19751i	−0.325005	−	1.00026i
$28$	2.35260	+	7.24054i	0.444599	+	1.36833i
$29$	−5.48054	−	3.98185i	−1.01771	−	0.739410i	−0.0518984	−	0.998652i	$-0.516527\pi$
$29$	−5.48054	−	3.98185i	−1.01771	−	0.739410i	−0.965812	+	0.259242i	$0.916527\pi$
$30$	1.28906	−	0.936557i	0.235349	−	0.170991i
$31$	2.21098	−	6.80469i	0.397104	−	1.22216i	−0.530208	−	0.847868i	$-0.677886\pi$
$31$	2.21098	−	6.80469i	0.397104	−	1.22216i	0.927311	−	0.374291i	$-0.122114\pi$
$32$	3.23968			0.572699
$33$	−4.51993	+	2.91628i	−0.786818	+	0.507660i
$34$	0.285296			0.0489279
$35$	4.22250	−	12.9955i	0.713732	−	2.19664i
$36$	−0.573680	+	0.416803i	−0.0956134	+	0.0694672i
$37$	−0.466100	−	0.338641i	−0.0766263	−	0.0556723i	0.548813	−	0.835945i	$-0.315080\pi$
$37$	−0.466100	−	0.338641i	−0.0766263	−	0.0556723i	−0.625439	+	0.780273i	$0.715080\pi$
$38$	−0.132863	−	0.408909i	−0.0215532	−	0.0663338i
$39$	−0.0826244	−	0.254292i	−0.0132305	−	0.0407193i
$40$	−3.11454	−	2.26284i	−0.492451	−	0.357787i
$41$	1.10710	−	0.804355i	0.172900	−	0.125619i	−0.497970	−	0.867194i	$-0.665921\pi$
$41$	1.10710	−	0.804355i	0.172900	−	0.125619i	0.670870	+	0.741575i	$0.265921\pi$
$42$	−0.567373	+	1.74620i	−0.0875476	+	0.269444i
$43$	−11.1201			−1.69580			−0.847901	−	0.530155i	$-0.822134\pi$
$43$	−11.1201			−1.69580			−0.847901	+	0.530155i	$0.822134\pi$
$44$	4.93333	+	4.01918i	0.743728	+	0.605914i
$45$	1.27272			0.189727
$46$	−0.248337	+	0.764303i	−0.0366153	+	0.112690i
$47$	−10.2448	+	7.44326i	−1.49435	+	1.08571i	−0.521789	+	0.853075i	$0.674735\pi$
$47$	−10.2448	+	7.44326i	−1.49435	+	1.08571i	−0.972564	+	0.232636i	$0.925265\pi$
$48$	−4.61633	−	3.35396i	−0.666310	−	0.484103i
$49$	2.70253	+	8.31753i	0.386075	+	1.18822i
$50$	0.604622	+	1.86083i	0.0855064	+	0.263162i
$51$	−1.31211	−	0.953301i	−0.183732	−	0.133489i
$52$	−0.255893	+	0.185917i	−0.0354859	+	0.0257820i
$53$	−0.967355	+	2.97721i	−0.132876	+	0.408951i	−0.995254	−	0.0973147i	$-0.968975\pi$
$53$	−0.967355	+	2.97721i	−0.132876	+	0.408951i	0.862377	+	0.506266i	$0.168975\pi$
$54$	−1.55914			−0.212172
$55$	−2.92330	−	11.0405i	−0.394177	−	1.48871i
$56$	4.43616			0.592807
$57$	−0.755297	+	2.32457i	−0.100042	+	0.307896i
$58$	−1.56358	+	1.13601i	−0.205308	+	0.149165i
$59$	4.58838	+	3.33365i	0.597356	+	0.434004i	0.844939	−	0.534862i	$-0.179636\pi$
$59$	4.58838	+	3.33365i	0.597356	+	0.434004i	−0.247584	+	0.968867i	$0.579636\pi$
$60$	3.31121	+	10.1909i	0.427476	+	1.31564i
$61$	−2.25257	−	6.93270i	−0.288412	−	0.887641i	−0.985355	−	0.170515i	$-0.945457\pi$
$61$	−2.25257	−	6.93270i	−0.288412	−	0.887641i	0.696943	−	0.717126i	$-0.254543\pi$
$62$	−1.65141	−	1.19982i	−0.209730	−	0.152378i
$63$	−1.18649	+	0.862034i	−0.149483	+	0.108606i
$64$	−1.88879	+	5.81310i	−0.236099	+	0.726637i
$65$	0.567705			0.0704151
$66$	0.392801	+	1.48351i	0.0483505	+	0.182607i
$67$	12.7865			1.56212			0.781062	−	0.624454i	$-0.214678\pi$
$67$	12.7865			1.56212			0.781062	+	0.624454i	$0.214678\pi$
$68$	−0.592882	+	1.82470i	−0.0718975	+	0.221278i
$69$	3.69600	−	2.68530i	0.444946	−	0.323272i
$70$	−3.15385	−	2.29141i	−0.376957	−	0.273875i
$71$	2.57937	+	7.93847i	0.306114	+	0.942123i	0.979259	+	0.202612i	$0.0649432\pi$
$71$	2.57937	+	7.93847i	0.306114	+	0.942123i	−0.673145	+	0.739511i	$0.735057\pi$
$72$	0.127684	+	0.392971i	0.0150477	+	0.0463121i
$73$	−4.21542	−	3.06268i	−0.493378	−	0.358460i	0.313104	−	0.949719i	$-0.398631\pi$
$73$	−4.21542	−	3.06268i	−0.493378	−	0.358460i	−0.806482	+	0.591259i	$0.798631\pi$
$74$	−0.132977	+	0.0966131i	−0.0154582	+	0.0112310i
$75$	3.43715	−	10.5785i	0.396888	−	1.22150i
$76$	2.89141			0.331668
$77$	10.2031	+	8.31247i	1.16276	+	0.947294i
$78$	−0.0762820			−0.00863724
$79$	2.66455	−	8.20065i	0.299786	−	0.922646i	−0.681786	−	0.731552i	$-0.738796\pi$
$79$	2.66455	−	8.20065i	0.299786	−	0.922646i	0.981572	−	0.191094i	$-0.0612035\pi$
$80$	9.80152	−	7.12122i	1.09584	−	0.796177i
$81$	6.27361	+	4.55805i	0.697068	+	0.506450i
$82$	−0.120644	−	0.371306i	−0.0133230	−	0.0410038i
$83$	−4.73821	−	14.5827i	−0.520086	−	1.60066i	−0.773834	−	0.633389i	$-0.781663\pi$
$83$	−4.73821	−	14.5827i	−0.520086	−	1.60066i	0.253748	−	0.967270i	$-0.418337\pi$
$84$	−9.98927	−	7.25763i	−1.08992	−	0.791872i
$85$	2.78590	−	2.02407i	0.302173	−	0.219542i
$86$	−0.980365	+	3.01725i	−0.105716	+	0.325359i
$87$	10.9869			1.17792
$88$	3.11564	−	2.01023i	0.332129	−	0.214292i
$89$	5.44553			0.577225			0.288613	−	0.957446i	$-0.406806\pi$
$89$	5.44553			0.577225			0.288613	+	0.957446i	$0.406806\pi$
$90$	0.112205	−	0.345332i	0.0118275	−	0.0364012i
$91$	−0.529238	+	0.384514i	−0.0554793	+	0.0403080i
$92$	−4.37227	−	3.17664i	−0.455840	−	0.331187i
$93$	3.58588	+	11.0362i	0.371839	+	1.14440i
$94$	1.11641	+	3.43595i	0.115149	+	0.354391i
$95$	−4.19846	−	3.05036i	−0.430753	−	0.312960i
$96$	−4.25080	+	3.08839i	−0.433845	+	0.315207i
$97$	−0.762547	+	2.34688i	−0.0774250	+	0.238289i	−0.982276	−	0.187438i	$-0.939982\pi$
$97$	−0.762547	+	2.34688i	−0.0774250	+	0.238289i	0.904852	+	0.425727i	$0.139982\pi$
$98$	2.49508			0.252041
$99$	−0.442677	+	1.14309i	−0.0444907	+	0.114884i
$100$	−13.1580			−1.31580
$101$	−1.60367	+	4.93558i	−0.159571	+	0.491108i	−0.998595	−	0.0529853i	$-0.983126\pi$
$101$	−1.60367	+	4.93558i	−0.159571	+	0.491108i	0.839025	+	0.544094i	$0.183126\pi$
$102$	−0.374339	+	0.271973i	−0.0370651	+	0.0269294i
$103$	−12.5896	−	9.14689i	−1.24049	−	0.901270i	−0.242860	−	0.970061i	$-0.578086\pi$
$103$	−12.5896	−	9.14689i	−1.24049	−	0.901270i	−0.997631	+	0.0687915i	$0.978086\pi$
$104$	0.0569541	+	0.175287i	0.00558481	+	0.0171883i
$105$	6.84827	+	21.0768i	0.668322	+	2.05688i
$106$	0.722532	+	0.524951i	0.0701785	+	0.0509877i
$107$	3.44959	−	2.50628i	0.333485	−	0.242291i	−0.408423	−	0.912793i	$-0.633921\pi$
$107$	3.44959	−	2.50628i	0.333485	−	0.242291i	0.741908	+	0.670502i	$0.233921\pi$
$108$	3.24009	−	9.97197i	0.311778	−	0.959554i
$109$	−8.09415			−0.775279			−0.387640	−	0.921811i	$-0.626709\pi$
$109$	−8.09415			−0.775279			−0.387640	+	0.921811i	$0.626709\pi$
$110$	−3.25339	−	0.180163i	−0.310198	−	0.0171779i
$111$	0.934399			0.0886893
$112$	−4.31409	+	13.2774i	−0.407643	+	1.25460i
$113$	−8.31895	+	6.04407i	−0.782581	+	0.568578i	−0.905752	−	0.423807i	$-0.860693\pi$
$113$	−8.31895	+	6.04407i	−0.782581	+	0.568578i	0.123172	+	0.992385i	$0.460693\pi$
$114$	0.564143	+	0.409874i	0.0528369	+	0.0383882i
$115$	2.99746	+	9.22523i	0.279515	+	0.860258i
$116$	−4.01637	−	12.3611i	−0.372911	−	1.14770i
$117$	−0.0492945	−	0.0358146i	−0.00455728	−	0.00331106i
$118$	1.30905	−	0.951079i	0.120508	−	0.0875539i
$119$	−1.22620	+	3.77386i	−0.112406	+	0.345949i
$120$	6.24377			0.569976
$121$	10.9327	+	1.21457i	0.993886	+	0.110416i
$122$	−2.07966			−0.188284
$123$	−0.685840	+	2.11080i	−0.0618401	+	0.190324i
$124$	11.1057	−	8.06876i	0.997321	−	0.724596i
$125$	5.17654	+	3.76097i	0.463003	+	0.336392i
$126$	0.129296	+	0.397931i	0.0115186	+	0.0354505i
$127$	2.10771	+	6.48687i	0.187029	+	0.575616i	0.999977	−	0.00671950i	$-0.00213890\pi$
$127$	2.10771	+	6.48687i	0.187029	+	0.575616i	−0.812948	+	0.582336i	$0.802139\pi$
$128$	6.65267	+	4.83345i	0.588019	+	0.427221i
$129$	14.5908	−	10.6008i	1.28465	−	0.933350i
$130$	0.0500497	−	0.154037i	0.00438964	−	0.0135099i
$131$	9.27978			0.810778			0.405389	−	0.914144i	$-0.367136\pi$
$131$	9.27978			0.810778			0.405389	+	0.914144i	$0.367136\pi$
$132$	−10.3045	−	0.570635i	−0.896895	−	0.0496674i
$133$	5.98003			0.518534
$134$	1.12728	−	3.46941i	0.0973820	−	0.299711i
$135$	−15.2249	+	11.0615i	−1.31035	+	0.952026i
$136$	0.904452	+	0.657123i	0.0775561	+	0.0563478i
$137$	1.72194	+	5.29959i	0.147115	+	0.452774i	0.997277	−	0.0737474i	$-0.0234959\pi$
$137$	1.72194	+	5.29959i	0.147115	+	0.452774i	−0.850162	+	0.526522i	$0.823496\pi$
$138$	−0.402766	−	1.23959i	−0.0342857	−	0.105521i
$139$	9.83537	+	7.14582i	0.834225	+	0.606100i	0.920752	−	0.390149i	$-0.127577\pi$
$139$	9.83537	+	7.14582i	0.834225	+	0.606100i	−0.0865262	+	0.996250i	$0.527577\pi$
$140$	21.2095	−	15.4096i	1.79253	−	1.30235i
$141$	6.34655	−	19.5327i	0.534476	−	1.64495i
$142$	2.38137			0.199840
$143$	−0.197458	+	0.509879i	−0.0165123	+	0.0426382i
$144$	−1.30033			−0.108361
$145$	−7.20868	+	22.1860i	−0.598649	+	1.84245i
$146$	−1.20264	+	0.873772i	−0.0995315	+	0.0723139i
$147$	−11.4751	−	8.33715i	−0.946451	−	0.687637i
$148$	−0.341578	−	1.05127i	−0.0280775	−	0.0864137i
$149$	−6.59634	−	20.3014i	−0.540393	−	1.66316i	−0.731699	−	0.681628i	$-0.761272\pi$
$149$	−6.59634	−	20.3014i	−0.540393	−	1.66316i	0.191306	−	0.981530i	$-0.438728\pi$
$150$	−2.56726	−	1.86523i	−0.209616	−	0.152295i
$151$	−6.08281	+	4.41942i	−0.495012	+	0.359647i	−0.807109	−	0.590403i	$-0.798969\pi$
$151$	−6.08281	+	4.41942i	−0.495012	+	0.359647i	0.312096	+	0.950050i	$0.398969\pi$
$152$	0.520636	−	1.60235i	0.0422292	−	0.129968i
$153$	−0.369595			−0.0298800
$154$	3.15497	−	2.03561i	0.254235	−	0.164034i
$155$	−24.6383			−1.97899
$156$	0.158524	−	0.487886i	0.0126920	−	0.0390621i
$157$	−7.46614	+	5.42447i	−0.595862	+	0.432919i	−0.844408	−	0.535701i	$-0.820047\pi$
$157$	−7.46614	+	5.42447i	−0.595862	+	0.432919i	0.248545	+	0.968620i	$0.420047\pi$
$158$	−1.99020	−	1.44596i	−0.158332	−	0.115035i
$159$	−1.56891	−	4.82860i	−0.124422	−	0.382933i
$160$	−3.44740	−	10.6100i	−0.272541	−	0.838795i
$161$	−9.04274	−	6.56993i	−0.712668	−	0.517783i
$162$	1.78984	−	1.30039i	0.140623	−	0.102169i
$163$	−3.22611	+	9.92895i	−0.252689	+	0.777696i	0.741588	+	0.670856i	$0.234073\pi$
$163$	−3.22611	+	9.92895i	−0.252689	+	0.777696i	−0.994276	+	0.106840i	$0.965927\pi$
$164$	2.62552			0.205018
$165$	14.3606	+	11.6996i	1.11797	+	0.910811i
$166$	−4.37449			−0.339527
$167$	2.07338	−	6.38120i	0.160443	−	0.493792i	−0.838229	−	0.545319i	$-0.816409\pi$
$167$	2.07338	−	6.38120i	0.160443	−	0.493792i	0.998672	+	0.0515266i	$0.0164087\pi$
$168$	−5.82071	+	4.22899i	−0.449077	+	0.326274i
$169$	10.4952	+	7.62523i	0.807326	+	0.586556i
$170$	−0.303589	−	0.934352i	−0.0232842	−	0.0716615i
$171$	0.172121	+	0.529733i	0.0131624	+	0.0405097i
$172$	−17.2605	−	12.5405i	−1.31610	−	0.956202i
$173$	−15.5111	+	11.2695i	−1.17929	+	0.856802i	−0.992091	−	0.125520i	$-0.959940\pi$
$173$	−15.5111	+	11.2695i	−1.17929	+	0.856802i	−0.187196	+	0.982323i	$0.559940\pi$
$174$	0.968625	−	2.98112i	0.0734313	−	0.225998i
$175$	−27.2135			−2.05715
$176$	2.98671	+	11.2800i	0.225132	+	0.850265i
$177$	−9.19841			−0.691395
$178$	0.480086	−	1.47755i	0.0359840	−	0.110747i
$179$	13.8567	−	10.0675i	1.03570	−	0.752477i	0.0662554	−	0.997803i	$-0.478895\pi$
$179$	13.8567	−	10.0675i	1.03570	−	0.752477i	0.969441	+	0.245325i	$0.0788948\pi$
$180$	1.97550	+	1.43529i	0.147245	+	0.106980i
$181$	2.25604	+	6.94339i	0.167690	+	0.516098i	0.999224	−	0.0393757i	$-0.0125369\pi$
$181$	2.25604	+	6.94339i	0.167690	+	0.516098i	−0.831534	+	0.555474i	$0.812537\pi$
$182$	0.0576730	+	0.177499i	0.00427500	+	0.0131571i
$183$	9.56456	+	6.94906i	0.707032	+	0.513689i
$184$	−2.54770	+	1.85101i	−0.187819	+	0.136459i
$185$	−0.613072	+	1.88684i	−0.0450740	+	0.138723i
$186$	3.31062			0.242747
$187$	0.848917	+	3.20614i	0.0620790	+	0.234456i
$188$	−24.2957			−1.77195
$189$	6.70117	−	20.6241i	0.487438	−	1.50018i
$190$	−1.19780	+	0.870256i	−0.0868979	+	0.0631350i
$191$	−13.2449	−	9.62297i	−0.958366	−	0.696293i	−0.00559509	−	0.999984i	$-0.501781\pi$
$191$	−13.2449	−	9.62297i	−0.958366	−	0.696293i	−0.952771	+	0.303691i	$0.901781\pi$
$192$	−3.06334	−	9.42799i	−0.221077	−	0.680406i
$193$	−0.320351	−	0.985940i	−0.0230594	−	0.0709695i	0.938865	−	0.344287i	$-0.111879\pi$
$193$	−0.320351	−	0.985940i	−0.0230594	−	0.0709695i	−0.961924	+	0.273317i	$0.911879\pi$
$194$	0.569559	+	0.413808i	0.0408919	+	0.0297097i
$195$	−0.744889	+	0.541193i	−0.0533426	+	0.0387557i
$196$	−5.18509	+	15.9581i	−0.370363	+	1.13986i
$197$	5.09462			0.362977			0.181488	−	0.983393i	$-0.441909\pi$
$197$	5.09462			0.362977			0.181488	+	0.983393i	$0.441909\pi$
$198$	0.271130	+	0.220889i	0.0192684	+	0.0156979i
$199$	6.40778			0.454235			0.227118	−	0.973867i	$-0.427070\pi$
$199$	6.40778			0.454235			0.227118	+	0.973867i	$0.427070\pi$
$200$	−2.36927	+	7.29188i	−0.167533	+	0.515613i
$201$	−16.7773	+	12.1894i	−1.18338	+	0.859775i
$202$	1.19780	+	0.870255i	0.0842772	+	0.0612309i
$203$	−8.30667	−	25.5653i	−0.583014	−	1.79433i
$204$	−0.961567	−	2.95940i	−0.0673231	−	0.207199i
$205$	−3.81236	−	2.76984i	−0.266267	−	0.193454i
$206$	−3.59177	+	2.60957i	−0.250251	+	0.181818i
$207$	0.321716	−	0.990139i	0.0223608	−	0.0688194i
$208$	−0.580019			−0.0402171
$209$	4.19995	−	2.70984i	0.290517	−	0.187443i
$210$	6.32258			0.436300
$211$	7.37227	−	22.6895i	0.507528	−	1.56201i	−0.288952	−	0.957344i	$-0.593307\pi$
$211$	7.37227	−	22.6895i	0.507528	−	1.56201i	0.796479	−	0.604666i	$-0.206693\pi$
$212$	−4.85900	+	3.53027i	−0.333717	+	0.242460i
$213$	−10.9522	−	7.95721i	−0.750429	−	0.545219i
$214$	−0.375914	−	1.15694i	−0.0256970	−	0.0790871i
$215$	11.8331	+	36.4186i	0.807013	+	2.48373i
$216$	−4.94282	−	3.59117i	−0.336316	−	0.244348i
$217$	22.9688	−	16.6878i	1.55923	−	1.13284i
$218$	−0.713592	+	2.19621i	−0.0483306	+	0.148746i
$219$	8.45074			0.571048
$220$	7.91324	−	20.4337i	0.533510	−	1.37764i
$221$	−0.164860			−0.0110897
$222$	0.0823780	−	0.253533i	0.00552885	−	0.0170160i
$223$	22.9786	−	16.6949i	1.53876	−	1.11797i	0.587654	−	0.809112i	$-0.300052\pi$
$223$	22.9786	−	16.6949i	1.53876	−	1.11797i	0.951107	−	0.308863i	$-0.0999483\pi$
$224$	10.4001	+	7.55613i	0.694887	+	0.504865i
$225$	−0.783274	−	2.41067i	−0.0522183	−	0.160711i
$226$	0.906545	+	2.79006i	0.0603025	+	0.185592i
$227$	9.49717	+	6.90010i	0.630350	+	0.457976i	0.856521	−	0.516112i	$-0.172621\pi$
$227$	9.49717	+	6.90010i	0.630350	+	0.457976i	−0.226172	+	0.974087i	$0.572621\pi$
$228$	−3.79384	+	2.75639i	−0.251253	+	0.182546i
$229$	1.28869	−	3.96618i	0.0851591	−	0.262093i	−0.899405	−	0.437116i	$-0.856000\pi$
$229$	1.28869	−	3.96618i	0.0851591	−	0.262093i	0.984564	+	0.175023i	$0.0560000\pi$
$230$	2.76737			0.182475
$231$	−21.3119	−	1.18019i	−1.40222	−	0.0776508i
$232$	−7.57345			−0.497221
$233$	0.233466	−	0.718535i	0.0152949	−	0.0470728i	−0.943118	−	0.332459i	$-0.892122\pi$
$233$	0.233466	−	0.718535i	0.0152949	−	0.0470728i	0.958413	+	0.285386i	$0.0921218\pi$
$234$	−0.0140635	+	0.0102178i	−0.000919363	+	0.000667956i
$235$	35.2785	+	25.6313i	2.30131	+	1.67200i
$236$	3.36256	+	10.3489i	0.218884	+	0.673655i
$237$	4.32151	+	13.3002i	0.280712	+	0.863944i
$238$	0.915868	+	0.665417i	0.0593669	+	0.0431326i
$239$	4.76455	−	3.46164i	0.308193	−	0.223915i	−0.422928	−	0.906163i	$-0.638998\pi$
$239$	4.76455	−	3.46164i	0.308193	−	0.223915i	0.731121	+	0.682248i	$0.238998\pi$
$240$	−6.07197	+	18.6876i	−0.391944	+	1.20628i
$241$	−29.6453			−1.90962			−0.954812	−	0.297211i	$-0.903943\pi$
$241$	−29.6453			−1.90962			−0.954812	+	0.297211i	$0.903943\pi$
$242$	1.29340	−	2.85933i	0.0831429	−	0.183805i
$243$	3.81812			0.244933
$244$	4.32179	−	13.3011i	0.276675	−	0.851517i
$245$	24.3643	−	17.7017i	1.55658	−	1.13092i
$246$	0.512264	+	0.372182i	0.0326608	+	0.0237294i
$247$	0.0767752	+	0.236290i	0.00488509	+	0.0150348i
$248$	−2.47179	−	7.60740i	−0.156959	−	0.483071i
$249$	20.1187	+	14.6171i	1.27497	+	0.926322i
$250$	1.47685	−	1.07299i	0.0934040	−	0.0678620i
$251$	−4.80609	+	14.7916i	−0.303358	+	0.933640i	0.676927	+	0.736050i	$0.263311\pi$
$251$	−4.80609	+	14.7916i	−0.303358	+	0.933640i	−0.980285	+	0.197590i	$0.936689\pi$
$252$	−2.81379			−0.177252
$253$	−9.32813	−	0.516565i	−0.586455	−	0.0324761i
$254$	1.94592			0.122098
$255$	−1.72584	+	5.31160i	−0.108077	+	0.332625i
$256$	−7.99185	+	5.80642i	−0.499491	+	0.362901i
$257$	−2.00093	−	1.45376i	−0.124814	−	0.0906829i	0.523627	−	0.851948i	$-0.324579\pi$
$257$	−2.00093	−	1.45376i	−0.124814	−	0.0906829i	−0.648441	+	0.761265i	$0.724579\pi$
$258$	−1.59001	−	4.89354i	−0.0989896	−	0.304659i
$259$	−0.706452	−	2.17424i	−0.0438968	−	0.135100i
$260$	0.881183	+	0.640217i	0.0546486	+	0.0397045i
$261$	2.02558	−	1.47167i	0.125380	−	0.0910942i
$262$	0.818119	−	2.51791i	0.0505435	−	0.155557i
$263$	8.87272			0.547115			0.273558	−	0.961856i	$-0.411800\pi$
$263$	8.87272			0.547115			0.273558	+	0.961856i	$0.411800\pi$
$264$	−2.17170	+	5.60779i	−0.133659	+	0.345135i
$265$	10.7798			0.662199
$266$	0.527208	−	1.62258i	0.0323252	−	0.0994867i
$267$	−7.14512	+	5.19123i	−0.437274	+	0.317698i
$268$	19.8471	+	14.4197i	1.21235	+	0.880825i
$269$	−2.24801	−	6.91866i	−0.137064	−	0.421838i	0.858842	−	0.512241i	$-0.171185\pi$
$269$	−2.24801	−	6.91866i	−0.137064	−	0.421838i	−0.995905	+	0.0904028i	$0.971185\pi$
$270$	1.65911	+	5.10622i	0.100970	+	0.310755i
$271$	7.31071	+	5.31154i	0.444094	+	0.322653i	0.787260	−	0.616622i	$-0.211499\pi$
$271$	7.31071	+	5.31154i	0.444094	+	0.322653i	−0.343165	+	0.939275i	$0.611499\pi$
$272$	−2.84633	+	2.06798i	−0.172584	+	0.125390i
$273$	0.327859	−	1.00905i	0.0198429	−	0.0610703i
$274$	1.58976			0.0960410
$275$	−19.1128	+	12.3317i	−1.15255	+	0.743631i
$276$	8.76517			0.527601
$277$	−0.130401	+	0.401333i	−0.00783504	+	0.0241138i	−0.954898	−	0.296935i	$-0.904035\pi$
$277$	−0.130401	+	0.401333i	−0.00783504	+	0.0241138i	0.947063	+	0.321049i	$0.104035\pi$
$278$	2.80600	−	2.03868i	0.168292	−	0.122272i
$279$	2.13937	+	1.55435i	0.128081	+	0.0930562i
$280$	−4.72060	−	14.5285i	−0.282110	−	0.868245i
$281$	2.30508	+	7.09432i	0.137510	+	0.423212i	0.995972	−	0.0896652i	$-0.0285797\pi$
$281$	2.30508	+	7.09432i	0.137510	+	0.423212i	−0.858462	+	0.512877i	$0.828580\pi$
$282$	−4.74034	−	3.44406i	−0.282283	−	0.205091i
$283$	−18.9986	+	13.8033i	−1.12935	+	0.820521i	−0.985600	−	0.169092i	$-0.945916\pi$
$283$	−18.9986	+	13.8033i	−1.12935	+	0.820521i	−0.143751	+	0.989614i	$0.545916\pi$
$284$	−4.94879	+	15.2308i	−0.293656	+	0.903782i
$285$	8.41673			0.498564
$286$	0.120939	+	0.0985285i	0.00715126	+	0.00582611i
$287$	5.43010			0.320529
$288$	−0.370007	+	1.13877i	−0.0218029	+	0.0671024i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	5.38428	+	3.91191i	0.316176	+	0.229715i
$291$	−1.23674	−	3.80629i	−0.0724989	−	0.223129i
$292$	−3.08924	−	9.50770i	−0.180784	−	0.556396i
$293$	4.15233	+	3.01685i	0.242582	+	0.176246i	0.702433	−	0.711750i	$-0.252097\pi$
$293$	4.15233	+	3.01685i	0.242582	+	0.176246i	−0.459851	+	0.887996i	$0.652097\pi$
$294$	−3.27381	+	2.37856i	−0.190932	+	0.138720i
$295$	6.03520	−	18.5744i	0.351383	−	1.08145i
$296$	−0.644094			−0.0374372
$297$	−4.63932	−	17.5215i	−0.269201	−	1.01670i
$298$	−6.08999			−0.352784
$299$	0.143503	−	0.441656i	0.00829897	−	0.0255416i
$300$	17.2647	−	12.5436i	0.996780	−	0.724203i
$301$	−35.6982	−	25.9362i	−2.05761	−	1.49494i
$302$	0.662865	+	2.04009i	0.0381436	+	0.117394i
$303$	−2.60091	−	8.00478i	−0.149418	−	0.459862i
$304$	4.28953	+	3.11653i	0.246022	+	0.178745i
$305$	−20.3077	+	14.7544i	−1.16282	+	0.844836i
$306$	−0.0325841	+	0.100283i	−0.00186271	+	0.00573282i
$307$	28.3756			1.61948			0.809739	−	0.586790i	$-0.199609\pi$
$307$	28.3756			1.61948			0.809739	+	0.586790i	$0.199609\pi$
$308$	6.46294	+	24.4089i	0.368260	+	1.39082i
$309$	25.2386			1.43578
$310$	−2.17214	+	6.68517i	−0.123370	+	0.379692i
$311$	−14.1859	+	10.3066i	−0.804407	+	0.584436i	−0.912204	−	0.409737i	$-0.865621\pi$
$311$	−14.1859	+	10.3066i	−0.804407	+	0.584436i	0.107796	+	0.994173i	$0.465621\pi$
$312$	−0.241831	−	0.175700i	−0.0136910	−	0.00994707i
$313$	9.38539	+	28.8852i	0.530493	+	1.63269i	0.753190	+	0.657803i	$0.228514\pi$
$313$	9.38539	+	28.8852i	0.530493	+	1.63269i	−0.222697	+	0.974888i	$0.571486\pi$
$314$	0.813611	+	2.50404i	0.0459147	+	0.141311i
$315$	4.08574	+	2.96847i	0.230206	+	0.167254i
$316$	13.3840	−	9.72404i	0.752908	−	0.547020i
$317$	1.23427	−	3.79870i	0.0693236	−	0.213356i	−0.910393	−	0.413745i	$-0.864221\pi$
$317$	1.23427	−	3.79870i	0.0693236	−	0.213356i	0.979716	+	0.200389i	$0.0642205\pi$
$318$	−1.44847			−0.0812264
$319$	−17.4189	−	14.1911i	−0.975270	−	0.794551i
$320$	21.0479			1.17661
$321$	−2.13700	+	6.57700i	−0.119275	+	0.367092i
$322$	−2.57986	+	1.87438i	−0.143770	+	0.104455i
$323$	1.21922	+	0.885815i	0.0678392	+	0.0492881i
$324$	4.59757	+	14.1499i	0.255421	+	0.786104i
$325$	−0.349383	−	1.07529i	−0.0193803	−	0.0596464i
$326$	2.40963	+	1.75070i	0.133457	+	0.0969624i
$327$	10.6204	−	7.71616i	0.587309	−	0.426705i
$328$	0.472758	−	1.45500i	0.0261037	−	0.0803389i
$329$	−50.2485			−2.77029
$330$	4.44054	−	2.86506i	0.244444	−	0.157717i
$331$	18.6689			1.02614			0.513068	−	0.858348i	$-0.328509\pi$
$331$	18.6689			1.02614			0.513068	+	0.858348i	$0.328509\pi$
$332$	9.09075	−	27.9785i	0.498920	−	1.53552i
$333$	0.172268	−	0.125160i	0.00944025	−	0.00685874i
$334$	−1.54864	−	1.12515i	−0.0847377	−	0.0615655i
$335$	−13.6064	−	41.8762i	−0.743397	−	2.28794i
$336$	−6.99682	−	21.5340i	−0.381708	−	1.17478i
$337$	−26.9729	−	19.5970i	−1.46931	−	1.06752i	−0.980813	−	0.194948i	$-0.937546\pi$
$337$	−26.9729	−	19.5970i	−1.46931	−	1.06752i	−0.488495	−	0.872567i	$-0.662454\pi$
$338$	2.99425	−	2.17545i	0.162866	−	0.118329i
$339$	5.15352	−	15.8609i	0.279901	−	0.861447i
$340$	6.60684			0.358306
$341$	8.56964	−	22.1286i	0.464072	−	1.19833i
$342$	0.158908			0.00859279
$343$	−2.14041	+	6.58751i	−0.115571	+	0.355692i
$344$	−10.0576	+	7.30728i	−0.542270	+	0.393982i
$345$	−12.7274	−	9.24700i	−0.685221	−	0.497842i
$346$	1.69030	+	5.20221i	0.0908711	+	0.279672i
$347$	8.70275	+	26.7843i	0.467188	+	1.43786i	0.856210	+	0.516628i	$0.172813\pi$
$347$	8.70275	+	26.7843i	0.467188	+	1.43786i	−0.389022	+	0.921229i	$0.627187\pi$
$348$	17.0538	+	12.3903i	0.914178	+	0.664189i
$349$	−18.9604	+	13.7755i	−1.01493	+	0.737386i	−0.965236	−	0.261378i	$-0.915823\pi$
$349$	−18.9604	+	13.7755i	−1.01493	+	0.737386i	−0.0496888	+	0.998765i	$0.515823\pi$
$350$	−2.39918	+	7.38392i	−0.128242	+	0.394687i
$351$	0.900956			0.0480895
$352$	10.7283	+	0.594105i	0.571823	+	0.0316659i
$353$	13.2319			0.704261			0.352131	−	0.935951i	$-0.385457\pi$
$353$	13.2319			0.704261			0.352131	+	0.935951i	$0.385457\pi$
$354$	−0.810945	+	2.49583i	−0.0431012	+	0.132652i
$355$	23.2539	−	16.8950i	1.23419	−	0.896691i
$356$	8.45248	+	6.14108i	0.447980	+	0.325477i
$357$	−1.98872	−	6.12064i	−0.105254	−	0.323939i
$358$	−1.51001	−	4.64733i	−0.0798065	−	0.245619i
$359$	10.3350	+	7.50883i	0.545462	+	0.396301i	0.826109	−	0.563510i	$-0.190549\pi$
$359$	10.3350	+	7.50883i	0.545462	+	0.396301i	−0.280648	+	0.959811i	$0.590549\pi$
$360$	1.15112	−	0.836336i	0.0606693	−	0.0440788i
$361$	−5.16949	+	15.9101i	−0.272079	+	0.837372i
$362$	2.08287			0.109473
$363$	−15.5028	+	8.82854i	−0.813684	+	0.463378i
$364$	−1.25510			−0.0657853
$365$	−5.54464	+	17.0647i	−0.290220	+	0.893205i
$366$	2.72873	−	1.98254i	0.142633	−	0.103629i
$367$	0.683309	+	0.496453i	0.0356685	+	0.0259147i	0.605477	−	0.795863i	$-0.292983\pi$
$367$	0.683309	+	0.496453i	0.0356685	+	0.0259147i	−0.569808	+	0.821778i	$0.692983\pi$
$368$	−3.06248	−	9.42535i	−0.159643	−	0.491330i
$369$	0.156292	+	0.481018i	0.00813626	+	0.0250408i
$370$	0.457913	+	0.332693i	0.0238058	+	0.0172959i
$371$	−10.0494	+	7.30132i	−0.521739	+	0.379066i
$372$	−6.87989	+	21.1741i	−0.356706	+	1.09783i
$373$	27.0083			1.39844			0.699220	−	0.714907i	$-0.253531\pi$
$373$	27.0083			1.39844			0.699220	+	0.714907i	$0.253531\pi$
$374$	0.944774	+	0.0523188i	0.0488531	+	0.00270534i
$375$	−10.3775			−0.535892
$376$	−4.37476	+	13.4641i	−0.225611	+	0.694360i
$377$	0.903520	−	0.656446i	0.0465337	−	0.0338087i
$378$	−5.00521	−	3.63650i	−0.257440	−	0.187041i
$379$	2.20413	+	6.78362i	0.113219	+	0.348451i	0.991571	−	0.129562i	$-0.0413571\pi$
$379$	2.20413	+	6.78362i	0.113219	+	0.348451i	−0.878353	+	0.478013i	$0.841357\pi$
$380$	−3.07681	−	9.46944i	−0.157837	−	0.485772i
$381$	−8.94947	−	6.50217i	−0.458495	−	0.333116i
$382$	−3.77872	+	2.74540i	−0.193336	+	0.140467i
$383$	0.334002	−	1.02795i	0.0170667	−	0.0525259i	−0.942160	−	0.335162i	$-0.891209\pi$
$383$	0.334002	−	1.02795i	0.0170667	−	0.0525259i	0.959227	+	0.282636i	$0.0912089\pi$
$384$	−13.3367			−0.680588
$385$	16.3662	−	42.2610i	0.834098	−	2.15382i
$386$	−0.295761			−0.0150538
$387$	1.27004	−	3.90879i	0.0645599	−	0.198695i
$388$	−3.83026	+	2.78284i	−0.194452	+	0.141278i
$389$	14.9644	+	10.8723i	0.758725	+	0.551246i	0.898519	−	0.438935i	$-0.144644\pi$
$389$	14.9644	+	10.8723i	0.758725	+	0.551246i	−0.139794	+	0.990181i	$0.544644\pi$
$390$	0.0811731	+	0.249825i	0.00411036	+	0.0126504i
$391$	−0.870453	−	2.67898i	−0.0440207	−	0.135482i
$392$	7.90994	+	5.74691i	0.399512	+	0.290263i
$393$	−12.1761	+	8.84642i	−0.614201	+	0.446243i
$394$	0.449149	−	1.38234i	0.0226278	−	0.0696412i
$395$	−29.6927			−1.49400
$396$	−1.97621	+	1.27506i	−0.0993081	+	0.0640742i
$397$	9.66212			0.484928			0.242464	−	0.970160i	$-0.422044\pi$
$397$	9.66212			0.484928			0.242464	+	0.970160i	$0.422044\pi$
$398$	0.564919	−	1.73864i	0.0283168	−	0.0871502i
$399$	−7.84643	+	5.70077i	−0.392813	+	0.285395i
$400$	−19.5205	−	14.1825i	−0.976025	−	0.709123i
$401$	9.43048	+	29.0240i	0.470936	+	1.44939i	0.851362	+	0.524579i	$0.175777\pi$
$401$	9.43048	+	29.0240i	0.470936	+	1.44939i	−0.380426	+	0.924811i	$0.624223\pi$
$402$	1.82828	+	5.62687i	0.0911863	+	0.280643i
$403$	0.954277	+	0.693323i	0.0475359	+	0.0345369i
$404$	−8.05518	+	5.85243i	−0.400760	+	0.291169i
$405$	8.25183	−	25.3965i	0.410037	−	1.26196i
$406$	−7.66904			−0.380608
$407$	−1.48141	−	1.20690i	−0.0734309	−	0.0598240i
$408$	−1.81317			−0.0897654
$409$	−4.49029	+	13.8197i	−0.222031	+	0.683340i	0.776549	+	0.630057i	$0.216969\pi$
$409$	−4.49029	+	13.8197i	−0.222031	+	0.683340i	−0.998579	+	0.0532832i	$0.983031\pi$
$410$	−1.08765	+	0.790227i	−0.0537154	+	0.0390265i
$411$	−7.31147	−	5.31209i	−0.360648	−	0.262026i
$412$	−9.22620	−	28.3953i	−0.454542	−	1.39894i
$413$	6.95445	+	21.4036i	0.342206	+	1.05320i
$414$	−0.240294	−	0.174584i	−0.0118098	−	0.00858034i
$415$	−42.7166	+	31.0355i	−2.09688	+	1.52347i
$416$	−0.165043	+	0.507952i	−0.00809192	+	0.0249044i
$417$	−19.7172			−0.965554
$418$	−0.364994	−	1.37849i	−0.0178524	−	0.0674241i
$419$	−34.5617			−1.68845			−0.844224	−	0.535990i	$-0.819939\pi$
$419$	−34.5617			−1.68845			−0.844224	+	0.535990i	$0.819939\pi$
$420$	−13.1391	+	40.4381i	−0.641124	+	1.97318i
$421$	0.547763	−	0.397973i	0.0266963	−	0.0193960i	−0.574357	−	0.818605i	$-0.694748\pi$
$421$	0.547763	−	0.397973i	0.0266963	−	0.0193960i	0.601053	+	0.799209i	$0.294748\pi$
$422$	−5.50646	−	4.00068i	−0.268050	−	0.194750i
$423$	−1.44628	−	4.45120i	−0.0703207	−	0.216425i
$424$	1.08147	+	3.32842i	0.0525207	+	0.161642i
$425$	−5.54834	−	4.03110i	−0.269134	−	0.195537i
$426$	−3.12461	+	2.27016i	−0.151388	+	0.109990i
$427$	8.93835	−	27.5094i	0.432557	−	1.33127i
$428$	8.18080			0.395434
$429$	−0.226982	−	0.857252i	−0.0109588	−	0.0413885i
$430$	10.9248			0.526841
$431$	−6.09775	+	18.7669i	−0.293718	+	0.903972i	0.689931	+	0.723876i	$0.257641\pi$
$431$	−6.09775	+	18.7669i	−0.293718	+	0.903972i	−0.983649	+	0.180097i	$0.942359\pi$
$432$	15.5552	−	11.3015i	0.748398	−	0.543743i
$433$	−1.70519	−	1.23890i	−0.0819464	−	0.0595375i	0.546058	−	0.837748i	$-0.316128\pi$
$433$	−1.70519	−	1.23890i	−0.0819464	−	0.0595375i	−0.628004	+	0.778210i	$0.716128\pi$
$434$	−2.50299	−	7.70343i	−0.120148	−	0.369776i
$435$	−11.6914	−	35.9825i	−0.560561	−	1.72523i
$436$	−12.5636	−	9.12801i	−0.601688	−	0.437152i
$437$	−3.43435	+	2.49520i	−0.164287	+	0.119362i
$438$	0.745029	−	2.29296i	0.0355989	−	0.109562i
$439$	30.1117			1.43715			0.718576	−	0.695449i	$-0.244794\pi$
$439$	30.1117			1.43715			0.718576	+	0.695449i	$0.244794\pi$
$440$	−9.89898	−	8.06468i	−0.471915	−	0.384468i
$441$	−3.23232			−0.153920
$442$	−0.0145343	+	0.0447319i	−0.000691325	+	0.00212768i
$443$	0.826546	−	0.600521i	0.0392704	−	0.0285316i	−0.567977	−	0.823044i	$-0.692274\pi$
$443$	0.826546	−	0.600521i	0.0392704	−	0.0285316i	0.607247	+	0.794513i	$0.292274\pi$
$444$	1.45036	+	1.05375i	0.0688311	+	0.0500087i
$445$	−5.79470	−	17.8342i	−0.274695	−	0.845424i
$446$	−2.50406	−	7.70670i	−0.118571	−	0.364923i
$447$	28.0085	+	20.3493i	1.32476	+	0.962491i
$448$	−19.6218	+	14.2560i	−0.927041	+	0.673535i
$449$	6.66300	−	20.5066i	0.314447	−	0.967767i	−0.661535	−	0.749914i	$-0.730095\pi$
$449$	6.66300	−	20.5066i	0.314447	−	0.967767i	0.975982	−	0.217853i	$-0.0699053\pi$
$450$	−0.723149			−0.0340896
$451$	3.81372	−	2.46064i	0.179581	−	0.115867i
$452$	−19.7286			−0.927956
$453$	3.76826	−	11.5975i	0.177048	−	0.544898i
$454$	2.70951	−	1.96857i	0.127164	−	0.0923898i
$455$	1.82246	+	1.32410i	0.0854385	+	0.0620747i
$456$	0.844395	+	2.59878i	0.0395424	+	0.121699i
$457$	−8.62619	−	26.5487i	−0.403516	−	1.24190i	−0.922128	−	0.386885i	$-0.873551\pi$
$457$	−8.62619	−	26.5487i	−0.403516	−	1.24190i	0.518612	−	0.855010i	$-0.326449\pi$
$458$	−0.962543	−	0.699329i	−0.0449767	−	0.0326775i
$459$	4.42127	−	3.21224i	0.206367	−	0.149934i
$460$	−5.75095	+	17.6996i	−0.268139	+	0.825248i
$461$	16.0983			0.749772			0.374886	−	0.927071i	$-0.377682\pi$
$461$	16.0983			0.749772			0.374886	+	0.927071i	$0.377682\pi$
$462$	−2.19911	+	5.67857i	−0.102312	+	0.264191i
$463$	26.7979			1.24541			0.622703	−	0.782458i	$-0.286034\pi$
$463$	26.7979			1.24541			0.622703	+	0.782458i	$0.286034\pi$
$464$	7.36506	−	22.6673i	0.341914	−	1.05230i
$465$	32.3280	−	23.4877i	1.49918	−	1.08922i
$466$	−0.174379	−	0.126694i	−0.00807797	−	0.00586899i
$467$	−0.971024	−	2.98851i	−0.0449336	−	0.138292i	0.926073	−	0.377345i	$-0.123163\pi$
$467$	−0.971024	−	2.98851i	−0.0449336	−	0.138292i	−0.971006	+	0.239053i	$0.923163\pi$
$468$	−0.0361251	−	0.111182i	−0.00166988	−	0.00513937i
$469$	41.0478	+	29.8229i	1.89541	+	1.37710i
$470$	10.0648	−	7.31252i	0.464256	−	0.337301i
$471$	4.62521	−	14.2349i	0.213119	−	0.655912i
$472$	6.34058			0.291849
$473$	−36.8248	−	2.03925i	−1.69321	−	0.0937649i
$474$	3.98979			0.183257
$475$	−3.19383	+	9.82960i	−0.146543	+	0.451013i
$476$	−6.15918	+	4.47490i	−0.282305	+	0.205107i
$477$	−0.936025	−	0.680062i	−0.0428577	−	0.0311379i
$478$	−0.519209	−	1.59796i	−0.0237481	−	0.0730891i
$479$	−6.21997	−	19.1431i	−0.284198	−	0.874670i	−0.986638	−	0.162928i	$-0.947906\pi$
$479$	−6.21997	−	19.1431i	−0.284198	−	0.874670i	0.702440	−	0.711743i	$-0.252094\pi$
$480$	14.6379	+	10.6350i	0.668125	+	0.485421i
$481$	0.0768411	−	0.0558283i	0.00350365	−	0.00254555i
$482$	−2.61357	+	8.04375i	−0.119045	+	0.366383i
$483$	18.1282			0.824860
$484$	15.5999	+	14.2144i	0.709088	+	0.646109i
$485$	8.49752			0.385853
$486$	0.336611	−	1.03598i	0.0152690	−	0.0469931i
$487$	−9.13273	+	6.63532i	−0.413844	+	0.300675i	−0.775156	−	0.631770i	$-0.782329\pi$
$487$	−9.13273	+	6.63532i	−0.413844	+	0.300675i	0.361312	+	0.932445i	$0.382329\pi$
$488$	−6.59298	−	4.79008i	−0.298450	−	0.216837i
$489$	−5.23228	−	16.1033i	−0.236612	−	0.728216i
$490$	−2.65506	−	8.17144i	−0.119943	−	0.369148i
$491$	0.112275	+	0.0815724i	0.00506689	+	0.00368131i	0.590316	−	0.807172i	$-0.299003\pi$
$491$	0.112275	+	0.0815724i	0.00506689	+	0.00368131i	−0.585249	+	0.810854i	$0.699003\pi$
$492$	−3.44496	+	2.50291i	−0.155311	+	0.112840i
$493$	2.09338	−	6.44276i	0.0942811	−	0.290167i
$494$	0.0708818			0.00318913
$495$	4.21469	+	0.233397i	0.189436	+	0.0104904i
$496$	25.1727			1.13029
$497$	−10.2351	+	31.5004i	−0.459107	+	1.41299i
$498$	5.73980	−	4.17021i	0.257207	−	0.186872i
$499$	−18.4683	−	13.4180i	−0.826754	−	0.600672i	0.0918851	−	0.995770i	$-0.470711\pi$
$499$	−18.4683	−	13.4180i	−0.826754	−	0.600672i	−0.918639	+	0.395098i	$0.870711\pi$
$500$	3.79358	+	11.6755i	0.169654	+	0.522142i
$501$	3.36271	+	10.3494i	0.150235	+	0.462375i
$502$	3.58975	+	2.60810i	0.160218	+	0.116405i
$503$	9.79177	−	7.11413i	0.436593	−	0.317204i	−0.347687	−	0.937611i	$-0.613033\pi$
$503$	9.79177	−	7.11413i	0.436593	−	0.317204i	0.784280	+	0.620407i	$0.213033\pi$
$504$	−0.506659	+	1.55934i	−0.0225684	+	0.0694584i
$505$	17.8706			0.795232
$506$	−0.962542	+	2.48549i	−0.0427902	+	0.110493i
$507$	−21.0400			−0.934419
$508$	−4.04387	+	12.4457i	−0.179418	+	0.552190i
$509$	−30.1544	+	21.9084i	−1.33657	+	0.971074i	−0.337006	+	0.941502i	$0.609414\pi$
$509$	−30.1544	+	21.9084i	−1.33657	+	0.971074i	−0.999563	+	0.0295717i	$0.990586\pi$
$510$	1.28906	+	0.936557i	0.0570805	+	0.0414714i
$511$	−6.38917	−	19.6639i	−0.282640	−	0.869878i
$512$	5.95309	+	18.3217i	0.263092	+	0.809713i
$513$	−6.66302	−	4.84097i	−0.294179	−	0.213734i
$514$	−0.570857	+	0.414752i	−0.0251794	+	0.0182939i
$515$	−16.5594	+	50.9646i	−0.729695	+	2.24577i
$516$	34.6024			1.52329
$517$	−35.2910	+	22.7700i	−1.55210	+	1.00142i
$518$	−0.652224			−0.0286571
$519$	9.60901	−	29.5735i	0.421789	−	1.29813i
$520$	0.513462	−	0.373052i	0.0225168	−	0.0163594i
$521$	−9.23463	−	6.70935i	−0.404576	−	0.293942i	0.366826	−	0.930290i	$-0.380444\pi$
$521$	−9.23463	−	6.70935i	−0.404576	−	0.293942i	−0.771402	+	0.636348i	$0.780444\pi$
$522$	−0.220735	−	0.679352i	−0.00966130	−	0.0297344i
$523$	3.87290	+	11.9196i	0.169350	+	0.521206i	0.999330	−	0.0365864i	$-0.0116484\pi$
$523$	3.87290	+	11.9196i	0.169350	+	0.521206i	−0.829980	+	0.557793i	$0.811648\pi$
$524$	14.4039	+	10.4651i	0.629239	+	0.457169i
$525$	35.7070	−	25.9426i	1.55838	−	1.13223i
$526$	0.782232	−	2.40746i	0.0341069	−	0.104970i
$527$	7.15488			0.311671
$528$	−14.6722	−	11.9534i	−0.638524	−	0.520204i
$529$	−15.0654			−0.655016
$530$	0.950364	−	2.92492i	0.0412812	−	0.127050i
$531$	−1.69584	+	1.23210i	−0.0735933	+	0.0534687i
$532$	9.28211	+	6.74385i	0.402431	+	0.292383i
$533$	0.0697149	+	0.214560i	0.00301969	+	0.00929365i
$534$	0.778629	+	2.39637i	0.0336946	+	0.103701i
$535$	−11.8789	−	8.63051i	−0.513569	−	0.373130i
$536$	11.5648	−	8.40232i	0.499523	−	0.362925i
$537$	−8.58410	+	26.4191i	−0.370431	+	1.14007i
$538$	−2.07545			−0.0894789
$539$	7.42426	+	28.0395i	0.319785	+	1.20775i
$540$	−36.1063			−1.55377
$541$	−7.47066	+	22.9923i	−0.321189	+	0.988518i	0.651943	+	0.758268i	$0.273954\pi$
$541$	−7.47066	+	22.9923i	−0.321189	+	0.988518i	−0.973132	+	0.230250i	$0.926046\pi$
$542$	2.08572	−	1.51536i	0.0895893	−	0.0650905i
$543$	−9.57931	−	6.95978i	−0.411087	−	0.298673i
$544$	1.00111	+	3.08111i	0.0429224	+	0.132102i
$545$	8.61314	+	26.5085i	0.368947	+	1.13550i
$546$	−0.244883	−	0.177918i	−0.0104800	−	0.00761419i
$547$	7.28513	−	5.29296i	0.311490	−	0.226311i	−0.421046	−	0.907039i	$-0.638337\pi$
$547$	7.28513	−	5.29296i	0.311490	−	0.226311i	0.732535	+	0.680729i	$0.238337\pi$
$548$	−3.30372	+	10.1678i	−0.141128	+	0.434348i
$549$	2.69415			0.114984
$550$	1.66099	+	6.27312i	0.0708248	+	0.267487i
$551$	−10.2092			−0.434925
$552$	1.57828	−	4.85745i	0.0671761	−	0.206747i
$553$	27.6808	−	20.1113i	1.17711	−	0.855219i
$554$	0.0973986	+	0.0707642i	0.00413807	+	0.00300648i
$555$	−0.994312	−	3.06018i	−0.0422062	−	0.129897i
$556$	7.20778	+	22.1833i	0.305678	+	0.940780i
$557$	−14.6870	−	10.6708i	−0.622309	−	0.452134i	0.231418	−	0.972854i	$-0.425664\pi$
$557$	−14.6870	−	10.6708i	−0.622309	−	0.452134i	−0.853727	+	0.520720i	$0.825664\pi$
$558$	0.610355	−	0.443449i	0.0258384	−	0.0187727i
$559$	0.566508	−	1.74353i	0.0239607	−	0.0737436i
$560$	48.0745			2.03152
$561$	−4.17029	−	3.39752i	−0.176070	−	0.143444i
$562$	2.12814			0.0897703
$563$	0.194317	−	0.598046i	0.00818948	−	0.0252046i	−0.946878	−	0.321592i	$-0.895782\pi$
$563$	0.194317	−	0.598046i	0.00818948	−	0.0252046i	0.955068	+	0.296388i	$0.0957820\pi$
$564$	31.8786	−	23.1611i	1.34233	−	0.975260i
$565$	28.6468	+	20.8131i	1.20518	+	0.875615i
$566$	2.07035	+	6.37187i	0.0870232	+	0.267830i
$567$	9.50871	+	29.2648i	0.399328	+	1.22901i
$568$	7.54946	+	5.48501i	0.316768	+	0.230146i
$569$	15.5481	−	11.2964i	0.651811	−	0.473568i	−0.212077	−	0.977253i	$-0.568023\pi$
$569$	15.5481	−	11.2964i	0.651811	−	0.473568i	0.863887	+	0.503685i	$0.168023\pi$
$570$	0.742031	−	2.28374i	0.0310803	−	0.0956552i
$571$	15.8787			0.664504			0.332252	−	0.943191i	$-0.392192\pi$
$571$	15.8787			0.664504			0.332252	+	0.943191i	$0.392192\pi$
$572$	−0.881496	+	0.568747i	−0.0368572	+	0.0237805i
$573$	26.5523			1.10924
$574$	0.478726	−	1.47337i	0.0199816	−	0.0614971i
$575$	15.6288	−	11.3550i	0.651766	−	0.473536i
$576$	−1.82762	−	1.32784i	−0.0761508	−	0.0553268i
$577$	−3.95056	−	12.1586i	−0.164464	−	0.506168i	0.834532	−	0.550959i	$-0.185738\pi$
$577$	−3.95056	−	12.1586i	−0.164464	−	0.506168i	−0.998996	+	0.0447907i	$0.985738\pi$
$578$	0.0881614	+	0.271333i	0.00366703	+	0.0112860i
$579$	1.36023	+	0.988267i	0.0565293	+	0.0410710i
$580$	−36.2090	+	26.3074i	−1.50350	+	1.09236i
$581$	18.8015	−	57.8651i	0.780019	−	2.40065i
$582$	−1.14181			−0.0473293
$583$	−3.74942	+	9.68179i	−0.155285	+	0.400979i
$584$	−5.82520			−0.241049
$585$	−0.0648383	+	0.199552i	−0.00268073	+	0.00825044i
$586$	1.18465	−	0.860695i	0.0489372	−	0.0355550i
$587$	12.4711	+	9.06079i	0.514738	+	0.373979i	0.814618	−	0.579998i	$-0.196947\pi$
$587$	12.4711	+	9.06079i	0.514738	+	0.373979i	−0.299880	+	0.953977i	$0.596947\pi$
$588$	−8.40944	−	25.8816i	−0.346800	−	1.06734i
$589$	−3.33203	−	10.2549i	−0.137294	−	0.422547i
$590$	−4.50779	−	3.27510i	−0.185583	−	0.134834i
$591$	−6.68468	+	4.85671i	−0.274971	+	0.199778i
$592$	0.626371	−	1.92777i	0.0257437	−	0.0792309i
$593$	−31.9827			−1.31337			−0.656687	−	0.754164i	$-0.728043\pi$
$593$	−31.9827			−1.31337			−0.656687	+	0.754164i	$0.728043\pi$
$594$	−5.16317	−	0.285922i	−0.211848	−	0.0117315i
$595$	13.6643			0.560181
$596$	12.6558	−	38.9505i	0.518401	−	1.59547i
$597$	−8.40769	+	6.10854i	−0.344104	+	0.250006i
$598$	−0.107184	−	0.0778740i	−0.00438310	−	0.00318451i
$599$	2.34949	+	7.23098i	0.0959975	+	0.295450i	0.987512	−	0.157542i	$-0.0503568\pi$
$599$	2.34949	+	7.23098i	0.0959975	+	0.295450i	−0.891515	+	0.452991i	$0.850357\pi$
$600$	−3.84261	−	11.8263i	−0.156874	−	0.482808i
$601$	−10.8569	−	7.88799i	−0.442862	−	0.321758i	0.343909	−	0.939003i	$-0.388249\pi$
$601$	−10.8569	−	7.88799i	−0.442862	−	0.321758i	−0.786771	+	0.617245i	$0.788249\pi$
$602$	−10.1846	+	7.39952i	−0.415092	+	0.301582i
$603$	−1.46037	+	4.49454i	−0.0594707	+	0.183032i
$604$	−14.4256			−0.586967
$605$	−7.65599	−	37.0974i	−0.311260	−	1.50822i
$606$	−2.40126			−0.0975445
$607$	−1.11456	+	3.43026i	−0.0452385	+	0.139230i	−0.971125	−	0.238573i	$-0.923320\pi$
$607$	−1.11456	+	3.43026i	−0.0452385	+	0.139230i	0.925886	+	0.377803i	$0.123320\pi$
$608$	3.94988	−	2.86975i	0.160189	−	0.116384i
$609$	35.2707	+	25.6256i	1.42924	+	1.03840i
$610$	2.21301	+	6.81093i	0.0896020	+	0.275767i
$611$	−0.645121	−	1.98548i	−0.0260988	−	0.0803239i
$612$	−0.573680	−	0.416803i	−0.0231897	−	0.0168483i
$613$	−1.31046	+	0.952102i	−0.0529288	+	0.0384551i	−0.613935	−	0.789357i	$-0.710414\pi$
$613$	−1.31046	+	0.952102i	−0.0529288	+	0.0384551i	0.561006	+	0.827812i	$0.310414\pi$
$614$	2.50163	−	7.69922i	0.100958	−	0.310715i
$615$	7.64272			0.308184
$616$	14.6906	+	0.813521i	0.591900	+	0.0327777i
$617$	1.05207			0.0423546			0.0211773	−	0.999776i	$-0.493259\pi$
$617$	1.05207			0.0423546			0.0211773	+	0.999776i	$0.493259\pi$
$618$	2.22507	−	6.84808i	0.0895056	−	0.275470i
$619$	−15.8036	+	11.4820i	−0.635201	+	0.461500i	−0.858198	−	0.513319i	$-0.828416\pi$
$619$	−15.8036	+	11.4820i	−0.635201	+	0.461500i	0.222997	+	0.974819i	$0.428416\pi$
$620$	−38.2431	−	27.7853i	−1.53588	−	1.11588i
$621$	4.75702	+	14.6406i	0.190892	+	0.587507i
$622$	1.54589	+	4.75775i	0.0619843	+	0.190768i
$623$	17.4814	+	12.7010i	0.700379	+	0.508855i
$624$	0.761047	−	0.552933i	0.0304663	−	0.0221350i
$625$	−3.78756	+	11.6569i	−0.151502	+	0.466276i
$626$	8.66495			0.346321
$627$	−2.92749	+	7.55941i	−0.116913	+	0.301894i
$628$	−17.7061			−0.706552
$629$	0.178034	−	0.547933i	0.00709869	−	0.0218475i
$630$	1.16565	−	0.846893i	0.0464405	−	0.0337410i
$631$	13.4332	+	9.75981i	0.534768	+	0.388532i	0.822138	−	0.569288i	$-0.192781\pi$
$631$	13.4332	+	9.75981i	0.534768	+	0.388532i	−0.287370	+	0.957820i	$0.592781\pi$
$632$	−2.97888	−	9.16804i	−0.118493	−	0.364685i
$633$	11.9567	+	36.7990i	0.475237	+	1.46263i
$634$	−0.921897	−	0.669797i	−0.0366132	−	0.0266011i
$635$	19.0018	−	13.8056i	0.754062	−	0.547858i
$636$	3.01011	−	9.26418i	0.119359	−	0.367348i
$637$	−1.44179			−0.0571258
$638$	−5.38619	+	3.47521i	−0.213241	+	0.137585i
$639$	−3.08501			−0.122041
$640$	8.75042	−	26.9310i	0.345891	−	1.06454i
$641$	28.1729	−	20.4688i	1.11276	−	0.808470i	0.129667	−	0.991558i	$-0.458609\pi$
$641$	28.1729	−	20.4688i	1.11276	−	0.808470i	0.983097	+	0.183088i	$0.0586093\pi$
$642$	1.59616	+	1.15968i	0.0629952	+	0.0457687i
$643$	−1.59967	−	4.92327i	−0.0630847	−	0.194155i	0.914547	−	0.404480i	$-0.132548\pi$
$643$	−1.59967	−	4.92327i	−0.0630847	−	0.194155i	−0.977631	+	0.210326i	$0.932548\pi$
$644$	−6.62690	−	20.3955i	−0.261136	−	0.803695i
$645$	−50.2442	−	36.5046i	−1.97836	−	1.43737i
$646$	0.347839	−	0.252720i	0.0136855	−	0.00994313i
$647$	−7.79090	+	23.9779i	−0.306292	+	0.942670i	0.672900	+	0.739733i	$0.265048\pi$
$647$	−7.79090	+	23.9779i	−0.306292	+	0.942670i	−0.979192	+	0.202936i	$0.934952\pi$
$648$	8.66938			0.340565
$649$	14.5833	+	11.8810i	0.572445	+	0.466370i
$650$	−0.322564			−0.0126520
$651$	−14.2290	+	43.7924i	−0.557679	+	1.71636i
$652$	−16.2047	+	11.7734i	−0.634624	+	0.461082i
$653$	17.2722	+	12.5490i	0.675912	+	0.491079i	0.871999	−	0.489508i	$-0.162824\pi$
$653$	17.2722	+	12.5490i	0.675912	+	0.491079i	−0.196087	+	0.980586i	$0.562824\pi$
$654$	−1.15734	−	3.56193i	−0.0452556	−	0.139282i
$655$	−9.87479	−	30.3915i	−0.385840	−	1.18749i
$656$	3.89506	+	2.82993i	0.152077	+	0.110490i
$657$	1.55800	−	1.13195i	0.0607834	−	0.0441617i
$658$	−4.42998	+	13.6341i	−0.172699	+	0.531512i
$659$	−37.2595			−1.45142			−0.725712	−	0.687998i	$-0.758490\pi$
$659$	−37.2595			−1.45142			−0.725712	+	0.687998i	$0.758490\pi$
$660$	9.09641	+	34.3548i	0.354077	+	1.33726i
$661$	5.60642			0.218064			0.109032	−	0.994038i	$-0.465225\pi$
$661$	5.60642			0.218064			0.109032	+	0.994038i	$0.465225\pi$
$662$	1.64588	−	5.06549i	0.0639688	−	0.196876i
$663$	0.216313	−	0.157161i	0.00840092	−	0.00610362i
$664$	−13.8681	−	10.0758i	−0.538187	−	0.391016i
$665$	−6.36346	−	19.5847i	−0.246765	−	0.759463i
$666$	−0.0187727	−	0.0577764i	−0.000727427	−	0.00223879i
$667$	15.4378	+	11.2162i	0.597755	+	0.434295i
$668$	10.4145	−	7.56659i	0.402950	−	0.292760i
$669$	−14.2351	+	43.8110i	−0.550359	+	1.69383i
$670$	−12.5619			−0.485310
$671$	−6.18815	−	23.3711i	−0.238891	−	0.902230i
$672$	−20.8493			−0.804280
$673$	8.89255	−	27.3685i	0.342783	−	1.05498i	−0.619977	−	0.784620i	$-0.712858\pi$
$673$	8.89255	−	27.3685i	0.342783	−	1.05498i	0.962760	−	0.270357i	$-0.0871417\pi$
$674$	−7.69528	+	5.59095i	−0.296411	+	0.215355i
$675$	30.3216	+	22.0299i	1.16708	+	0.847932i
$676$	7.69135	+	23.6715i	0.295821	+	0.910444i
$677$	0.513607	+	1.58072i	0.0197395	+	0.0607520i	0.960441	−	0.278483i	$-0.0898317\pi$
$677$	0.513607	+	1.58072i	0.0197395	+	0.0607520i	−0.940702	+	0.339235i	$0.889832\pi$
$678$	−3.84925	−	2.79664i	−0.147829	−	0.107404i
$679$	−7.92175	+	5.75549i	−0.304009	+	0.220875i
$680$	1.18965	−	3.66136i	0.0456209	−	0.140407i
$681$	−19.0392			−0.729583
$682$	−5.24872	−	4.27612i	−0.200984	−	0.163741i
$683$	−26.8129			−1.02597			−0.512983	−	0.858399i	$-0.671460\pi$
$683$	−26.8129			−1.02597			−0.512983	+	0.858399i	$0.671460\pi$
$684$	−0.330232	+	1.01635i	−0.0126267	+	0.0388611i
$685$	15.5239	−	11.2788i	0.593138	−	0.430940i
$686$	1.59871	+	1.16153i	0.0610389	+	0.0443474i
$687$	2.09007	+	6.43256i	0.0797410	+	0.245418i
$688$	−12.0898	−	37.2086i	−0.460920	−	1.41857i
$689$	−0.417518	−	0.303345i	−0.0159062	−	0.0115565i
$690$	−3.63108	+	2.63814i	−0.138233	+	0.100432i
$691$	−13.3790	+	41.1762i	−0.508960	+	1.56642i	0.285050	+	0.958513i	$0.407990\pi$
$691$	−13.3790	+	41.1762i	−0.508960	+	1.56642i	−0.794010	+	0.607905i	$0.792010\pi$
$692$	−36.7850			−1.39836
$693$	−4.08720	+	2.63709i	−0.155260	+	0.100175i
$694$	8.03471			0.304993
$695$	12.9367	−	39.8151i	0.490717	−	1.51027i
$696$	9.93716	−	7.21977i	0.376667	−	0.273665i
$697$	1.10710	+	0.804355i	0.0419344	+	0.0304671i
$698$	2.06618	+	6.35904i	0.0782060	+	0.240693i
$699$	0.378647	+	1.16536i	0.0143218	+	0.0440778i
$700$	−42.2404	−	30.6894i	−1.59654	−	1.15995i
$701$	11.6165	−	8.43985i	0.438748	−	0.318769i	−0.346389	−	0.938091i	$-0.612592\pi$
$701$	11.6165	−	8.43985i	0.438748	−	0.318769i	0.785137	+	0.619322i	$0.212592\pi$
$702$	0.0794296	−	0.244459i	0.00299788	−	0.00922651i
$703$	−0.868251			−0.0327467
$704$	−7.32086	+	18.9040i	−0.275915	+	0.712471i
$705$	−70.7235			−2.66360
$706$	1.16654	−	3.59024i	0.0439033	−	0.135120i
$707$	−16.6597	+	12.1040i	−0.626554	+	0.455218i
$708$	−14.2776	−	10.3733i	−0.536586	−	0.389853i
$709$	−4.05474	−	12.4792i	−0.152279	−	0.468667i	0.845596	−	0.533823i	$-0.179245\pi$
$709$	−4.05474	−	12.4792i	−0.152279	−	0.468667i	−0.997875	+	0.0651566i	$0.979245\pi$
$710$	−2.53406	−	7.79904i	−0.0951016	−	0.292693i
$711$	2.57826	+	1.87321i	0.0966922	+	0.0702510i
$712$	4.92522	−	3.57838i	0.184581	−	0.134106i
$713$	−6.22799	+	19.1678i	−0.233240	+	0.717839i
$714$	−1.83606			−0.0687128
$715$	1.87998	+	0.104108i	0.0703074	+	0.00389342i
$716$	32.8615			1.22809
$717$	−2.95160	+	9.08409i	−0.110230	+	0.339252i
$718$	2.94855	−	2.14224i	0.110039	−	0.0799478i
$719$	8.32306	+	6.04706i	0.310398	+	0.225517i	0.732067	−	0.681232i	$-0.238556\pi$
$719$	8.32306	+	6.04706i	0.310398	+	0.225517i	−0.421669	+	0.906750i	$0.638556\pi$
$720$	1.38371	+	4.25862i	0.0515678	+	0.158709i
$721$	−19.0817	−	58.7273i	−0.710638	−	2.18712i
$722$	3.86118	+	2.80531i	0.143698	+	0.104403i
$723$	38.8978	−	28.2609i	1.44663	−	1.05103i
$724$	−4.32846	+	13.3216i	−0.160866	+	0.495094i
$725$	46.4591			1.72545
$726$	1.02873	+	4.98475i	0.0381797	+	0.185001i
$727$	39.1072			1.45041			0.725203	−	0.688535i	$-0.241746\pi$
$727$	39.1072			1.45041			0.725203	+	0.688535i	$0.241746\pi$
$728$	−0.225998	+	0.695549i	−0.00837603	+	0.0257788i
$729$	−23.8306	+	17.3140i	−0.882616	+	0.641258i
$730$	4.14138	+	3.00889i	0.153279	+	0.111364i
$731$	−3.43631	−	10.5759i	−0.127096	−	0.391162i
$732$	7.00931	+	21.5724i	0.259072	+	0.797340i
$733$	−26.9744	−	19.5980i	−0.996322	−	0.723870i	−0.0350256	−	0.999386i	$-0.511151\pi$
$733$	−26.9744	−	19.5980i	−0.996322	−	0.723870i	−0.961296	+	0.275516i	$0.911151\pi$
$734$	0.194946	−	0.141636i	0.00719558	−	0.00522789i
$735$	−15.0935	+	46.4530i	−0.556731	+	1.71344i
$736$	−9.12567			−0.336377
$737$	42.3432	+	2.34485i	1.55973	+	0.0863735i
$738$	0.144295			0.00531158
$739$	2.31006	−	7.10963i	0.0849769	−	0.261532i	−0.899535	−	0.436848i	$-0.856095\pi$
$739$	2.31006	−	7.10963i	0.0849769	−	0.261532i	0.984512	+	0.175316i	$0.0560947\pi$
$740$	−3.07945	+	2.23735i	−0.113203	+	0.0822466i
$741$	−0.325993	−	0.236847i	−0.0119756	−	0.00870081i
$742$	1.09512	+	3.37043i	0.0402031	+	0.123732i
$743$	11.6632	+	35.8957i	0.427882	+	1.31689i	0.900207	+	0.435461i	$0.143415\pi$
$743$	11.6632	+	35.8957i	0.427882	+	1.31689i	−0.472325	+	0.881424i	$0.656585\pi$
$744$	10.4954	+	7.62535i	0.384780	+	0.279559i
$745$	−59.4684	+	43.2063i	−2.17875	+	1.58296i
$746$	2.38109	−	7.32826i	0.0871781	−	0.268306i
$747$	5.66706			0.207347
$748$	−2.29798	+	5.93387i	−0.0840225	+	0.216964i
$749$	16.9196			0.618227
$750$	−0.914895	+	2.81576i	−0.0334073	+	0.102817i
$751$	−13.7519	+	9.99132i	−0.501813	+	0.364588i	−0.809709	−	0.586832i	$-0.800375\pi$
$751$	−13.7519	+	9.99132i	−0.501813	+	0.364588i	0.307896	+	0.951420i	$0.400375\pi$
$752$	−36.0438	−	26.1873i	−1.31438	−	0.954953i
$753$	−7.79477	−	23.9899i	−0.284057	−	0.874239i
$754$	−0.0984598	−	0.303028i	−0.00358569	−	0.0110356i
$755$	20.9465	+	15.2186i	0.762323	+	0.553860i
$756$	33.6598	−	24.4553i	1.22420	−	0.889430i
$757$	14.4481	−	44.4666i	0.525125	−	1.61617i	−0.238944	−	0.971033i	$-0.576801\pi$
$757$	14.4481	−	44.4666i	0.525125	−	1.61617i	0.764069	−	0.645134i	$-0.223199\pi$
$758$	2.03494			0.0739123
$759$	12.7319	−	8.21473i	0.462140	−	0.298176i
$760$	−5.80176			−0.210452
$761$	8.79928	−	27.0814i	0.318974	−	0.981700i	−0.655114	−	0.755530i	$-0.727379\pi$
$761$	8.79928	−	27.0814i	0.318974	−	0.981700i	0.974088	−	0.226170i	$-0.0726206\pi$
$762$	−2.55325	+	1.85505i	−0.0924946	+	0.0672012i
$763$	−25.9841	−	18.8786i	−0.940689	−	0.683450i
$764$	−9.70641	−	29.8732i	−0.351165	−	1.08078i
$765$	0.393294	+	1.21043i	0.0142196	+	0.0437633i
$766$	−0.249471	−	0.181252i	−0.00901377	−	0.00654889i
$767$	−0.756438	+	0.549585i	−0.0273134	+	0.0198444i
$768$	4.95089	−	15.2373i	0.178650	−	0.549828i
$769$	2.70949			0.0977067			0.0488534	−	0.998806i	$-0.484443\pi$
$769$	2.70949			0.0977067			0.0488534	+	0.998806i	$0.484443\pi$
$770$	−10.0239	−	8.16647i	−0.361237	−	0.294299i
$771$	4.01129			0.144463
$772$	0.614628	−	1.89163i	0.0221209	−	0.0680813i
$773$	30.4682	−	22.1364i	1.09586	−	0.796192i	0.115484	−	0.993309i	$-0.463158\pi$
$773$	30.4682	−	22.1364i	1.09586	−	0.796192i	0.980380	+	0.197117i	$0.0631579\pi$
$774$	−0.948615	−	0.689209i	−0.0340972	−	0.0247731i
$775$	15.1632	+	46.6674i	0.544677	+	1.67634i
$776$	0.852501	+	2.62373i	0.0306030	+	0.0941863i
$777$	2.99964	+	2.17937i	0.107612	+	0.0781844i
$778$	4.26929	−	3.10182i	0.153061	−	0.111206i
$779$	0.637288	−	1.96137i	0.0228332	−	0.0702734i
$780$	−1.76652			−0.0632517
$781$	7.08591	+	26.7617i	0.253554	+	0.957608i
$782$	−0.803636			−0.0287380
$783$	−11.4403	+	35.2096i	−0.408843	+	1.25829i
$784$	−24.8928	+	18.0857i	−0.889028	+	0.645917i
$785$	25.7101	+	18.6795i	0.917633	+	0.666699i
$786$	1.32687	+	4.08368i	0.0473278	+	0.145660i
$787$	−7.59168	−	23.3648i	−0.270614	−	0.832865i	−0.990347	−	0.138613i	$-0.955735\pi$
$787$	−7.59168	−	23.3648i	−0.270614	−	0.832865i	0.719732	−	0.694252i	$-0.244265\pi$
$788$	7.90779	+	5.74535i	0.281703	+	0.204670i
$789$	−11.6419	+	8.45837i	−0.414464	+	0.301126i
$790$	−2.61775	+	8.05662i	−0.0931355	+	0.286642i
$791$	−40.8028			−1.45078
$792$	0.350768	+	1.32476i	0.0124640	+	0.0470733i
$793$	1.20174			0.0426750
$794$	0.851826	−	2.62165i	0.0302302	−	0.0930389i
$795$	−14.1443	+	10.2764i	−0.501645	+	0.364467i
$796$	9.94606	+	7.22623i	0.352529	+	0.256127i
$797$	−2.59415	−	7.98399i	−0.0918897	−	0.282807i	0.894541	−	0.446986i	$-0.147503\pi$
$797$	−2.59415	−	7.98399i	−0.0918897	−	0.282807i	−0.986431	+	0.164179i	$0.947503\pi$
$798$	0.855053	+	2.63158i	0.0302686	+	0.0931571i
$799$	−10.2448	−	7.44326i	−0.362434	−	0.263324i
$800$	−17.9748	+	13.0595i	−0.635505	+	0.461722i
$801$	−0.621941	+	1.91414i	−0.0219752	+	0.0676328i
$802$	8.70658			0.307440
$803$	−13.3979	−	10.9153i	−0.472803	−	0.385191i
$804$	−39.7878			−1.40321
$805$	−11.8941	+	36.6064i	−0.419213	+	1.29020i
$806$	0.272252	−	0.197802i	0.00958966	−	0.00696729i
$807$	9.54519	+	6.93499i	0.336007	+	0.244123i
$808$	1.79284	+	5.51780i	0.0630719	+	0.194115i
$809$	9.10193	+	28.0129i	0.320007	+	0.984880i	0.973644	+	0.228072i	$0.0732422\pi$
$809$	9.10193	+	28.0129i	0.320007	+	0.984880i	−0.653637	+	0.756808i	$0.726758\pi$
$810$	−6.16342	−	4.47799i	−0.216561	−	0.157340i
$811$	−14.3870	+	10.4528i	−0.505197	+	0.367047i	−0.810999	−	0.585048i	$-0.801076\pi$
$811$	−14.3870	+	10.4528i	−0.505197	+	0.367047i	0.305801	+	0.952095i	$0.401076\pi$
$812$	15.9372	−	49.0498i	0.559287	−	1.72131i
$813$	−14.6559			−0.514006
$814$	−0.458076	+	0.295554i	−0.0160556	+	0.0103591i
$815$	35.9505			1.25929
$816$	1.76328	−	5.42682i	0.0617272	−	0.189977i
$817$	−13.5579	+	9.85036i	−0.474330	+	0.344621i
$818$	3.35387	+	2.43673i	0.117265	+	0.0851983i
$819$	−0.0747141	−	0.229946i	−0.00261072	−	0.00803498i
$820$	−2.79386	−	8.59862i	−0.0975659	−	0.300277i
$821$	4.25094	+	3.08849i	0.148359	+	0.107789i	0.659489	−	0.751715i	$-0.270773\pi$
$821$	4.25094	+	3.08849i	0.148359	+	0.107789i	−0.511130	+	0.859503i	$0.670773\pi$
$822$	−2.08594	+	1.51552i	−0.0727554	+	0.0528599i
$823$	8.03569	−	24.7313i	0.280107	−	0.862080i	−0.707716	−	0.706497i	$-0.750274\pi$
$823$	8.03569	−	24.7313i	0.280107	−	0.862080i	0.987823	−	0.155583i	$-0.0497256\pi$
$824$	−17.3973			−0.606065
$825$	13.3222	−	34.4008i	0.463820	−	1.19768i
$826$	6.42062			0.223402
$827$	4.79534	−	14.7585i	0.166750	−	0.513204i	−0.832411	−	0.554159i	$-0.813040\pi$
$827$	4.79534	−	14.7585i	0.166750	−	0.513204i	0.999161	+	0.0409548i	$0.0130400\pi$
$828$	1.61597	−	1.17407i	0.0561588	−	0.0408018i
$829$	−18.2547	−	13.2628i	−0.634012	−	0.460637i	0.223776	−	0.974641i	$-0.428162\pi$
$829$	−18.2547	−	13.2628i	−0.634012	−	0.460637i	−0.857788	+	0.514004i	$0.828162\pi$
$830$	4.65498	+	14.3266i	0.161577	+	0.497282i
$831$	−0.211491	−	0.650903i	−0.00733655	−	0.0225796i
$832$	−0.815218	−	0.592290i	−0.0282626	−	0.0205340i
$833$	−7.07531	+	5.14051i	−0.245145	+	0.178108i
$834$	−1.73829	+	5.34992i	−0.0601922	+	0.185252i
$835$	−23.1049			−0.799577
$836$	9.57506	+	0.530239i	0.331160	+	0.0183387i
$837$	−39.1013			−1.35154
$838$	−3.04701	+	9.37773i	−0.105257	+	0.323948i
$839$	7.03034	−	5.10784i	0.242714	−	0.176342i	−0.459777	−	0.888034i	$-0.652071\pi$
$839$	7.03034	−	5.10784i	0.242714	−	0.176342i	0.702492	+	0.711692i	$0.252071\pi$
$840$	20.0440	+	14.5628i	0.691583	+	0.502464i
$841$	5.21973	+	16.0647i	0.179991	+	0.553955i
$842$	−0.0596916	−	0.183712i	−0.00205711	−	0.00633113i
$843$	−9.78754	−	7.11106i	−0.337101	−	0.244918i
$844$	37.0307	−	26.9044i	1.27465	−	0.926087i
$845$	13.8046	−	42.4863i	0.474894	−	1.46157i
$846$	−1.33526			−0.0459073
$847$	32.2638	+	29.3983i	1.10860	+	1.01014i
$848$	−11.0137			−0.378210
$849$	11.7695	−	36.2228i	0.403928	−	1.24316i
$850$	−1.58292	+	1.15006i	−0.0542937	+	0.0394467i
$851$	1.31293	+	0.953901i	0.0450067	+	0.0326993i
$852$	−8.02620	−	24.7021i	−0.274973	−	0.846280i
$853$	−14.2782	−	43.9439i	−0.488878	−	1.50461i	−0.826285	−	0.563252i	$-0.809550\pi$
$853$	−14.2782	−	43.9439i	−0.488878	−	1.50461i	0.337407	−	0.941359i	$-0.390450\pi$
$854$	−6.67619	−	4.85054i	−0.228455	−	0.165982i
$855$	1.55173	−	1.12740i	0.0530681	−	0.0385562i
$856$	1.47306	−	4.53361i	0.0503481	−	0.154956i
$857$	20.6125			0.704109			0.352054	−	0.935980i	$-0.385483\pi$
$857$	20.6125			0.704109			0.352054	+	0.935980i	$0.385483\pi$
$858$	−0.252612	−	0.0139889i	−0.00862402	−	0.000477573i
$859$	−7.78645			−0.265670			−0.132835	−	0.991138i	$-0.542408\pi$
$859$	−7.78645			−0.265670			−0.132835	+	0.991138i	$0.542408\pi$
$860$	−22.7031	+	69.8730i	−0.774170	+	2.38265i
$861$	−7.12487	+	5.17652i	−0.242815	+	0.176415i
$862$	4.55451	+	3.30904i	0.155127	+	0.112706i
$863$	−0.620351	−	1.90924i	−0.0211170	−	0.0649914i	0.939943	−	0.341332i	$-0.110878\pi$
$863$	−0.620351	−	1.90924i	−0.0211170	−	0.0649914i	−0.961060	+	0.276341i	$0.910878\pi$
$864$	−5.47108	−	16.8382i	−0.186130	−	0.572849i
$865$	53.4134	+	38.8071i	1.81611	+	1.31948i
$866$	−0.486486	+	0.353453i	−0.0165315	+	0.0120108i
$867$	0.501180	−	1.54247i	0.0170210	−	0.0523851i
$868$	54.4712			1.84887
$869$	10.3277	−	26.6682i	0.350342	−	0.904658i
$870$	−10.7940			−0.365950
$871$	−0.651403	+	2.00481i	−0.0220719	+	0.0679304i
$872$	−7.32077	+	5.31885i	−0.247913	+	0.180119i
$873$	−0.737851	−	0.536080i	−0.0249725	−	0.0181436i
$874$	0.374254	+	1.15183i	0.0126593	+	0.0389614i
$875$	7.84591	+	24.1472i	0.265240	+	0.816325i
$876$	13.1171	+	9.53013i	0.443186	+	0.321993i
$877$	19.7181	−	14.3260i	0.665833	−	0.483756i	−0.202794	−	0.979221i	$-0.565002\pi$
$877$	19.7181	−	14.3260i	0.665833	−	0.483756i	0.868628	+	0.495465i	$0.165002\pi$
$878$	2.65469	−	8.17029i	0.0895914	−	0.275734i
$879$	−8.32426			−0.280770
$880$	33.7642	−	21.7849i	1.13819	−	0.734367i
$881$	−0.704816			−0.0237459			−0.0118729	−	0.999930i	$-0.503779\pi$
$881$	−0.704816			−0.0237459			−0.0118729	+	0.999930i	$0.503779\pi$
$882$	−0.284966	+	0.877035i	−0.00959530	+	0.0295313i
$883$	−1.90625	+	1.38497i	−0.0641503	+	0.0466079i	−0.619398	−	0.785077i	$-0.712623\pi$
$883$	−1.90625	+	1.38497i	−0.0641503	+	0.0466079i	0.555248	+	0.831685i	$0.312623\pi$
$884$	−0.255893	−	0.185917i	−0.00860660	−	0.00625306i
$885$	9.78820	+	30.1250i	0.329027	+	1.01264i
$886$	−0.0900716	−	0.277212i	−0.00302602	−	0.00931312i
$887$	−9.69821	−	7.04616i	−0.325634	−	0.236587i	0.412942	−	0.910757i	$-0.364501\pi$
$887$	−9.69821	−	7.04616i	−0.325634	−	0.236587i	−0.738576	+	0.674170i	$0.764501\pi$
$888$	0.845119	−	0.614015i	0.0283603	−	0.0206050i
$889$	−8.36354	+	25.7403i	−0.280504	+	0.863303i
$890$	−5.34989			−0.179329
$891$	19.9395	+	16.2447i	0.667999	+	0.544217i
$892$	54.4944			1.82461
$893$	−5.89727	+	18.1499i	−0.197345	+	0.607364i
$894$	7.99071	−	5.80559i	0.267249	−	0.194168i
$895$	−47.7163	−	34.6679i	−1.59498	−	1.15882i
$896$	10.0832	+	31.0330i	0.336857	+	1.03674i
$897$	0.232740	+	0.716301i	0.00777097	+	0.0239166i
$898$	−4.97670	−	3.61579i	−0.166075	−	0.120660i
$899$	−39.2126	+	28.4896i	−1.30781	+	0.950182i
$900$	1.50280	−	4.62513i	0.0500932	−	0.154171i
$901$	−3.13043			−0.104290
$902$	−0.331429	−	1.25172i	−0.0110354	−	0.0416778i
$903$	71.5649			2.38153
$904$	−3.55239	+	10.9331i	−0.118151	+	0.363631i
$905$	20.3391	−	14.7772i	0.676093	−	0.491210i
$906$	−2.81457	−	2.04490i	−0.0935078	−	0.0679374i
$907$	1.28275	+	3.94789i	0.0425929	+	0.131088i	0.970092	−	0.242739i	$-0.0780457\pi$
$907$	1.28275	+	3.94789i	0.0425929	+	0.131088i	−0.927499	+	0.373826i	$0.878046\pi$
$908$	6.95993	+	21.4205i	0.230973	+	0.710863i
$909$	−1.55173	−	1.12740i	−0.0514676	−	0.0373934i
$910$	0.519943	−	0.377760i	0.0172359	−	0.0125226i
$911$	15.3184	−	47.1451i	0.507520	−	1.56199i	−0.288973	−	0.957337i	$-0.593314\pi$
$911$	15.3184	−	47.1451i	0.507520	−	1.56199i	0.796493	−	0.604648i	$-0.206686\pi$
$912$	−8.59931			−0.284752
$913$	−13.0166	−	49.1603i	−0.430786	−	1.62697i
$914$	−7.96403			−0.263427
$915$	12.5805	−	38.7188i	0.415898	−	1.28000i
$916$	6.47306	−	4.70296i	0.213876	−	0.155390i
$917$	29.7903	+	21.6439i	0.983761	+	0.714744i
$918$	−0.481801	−	1.48283i	−0.0159018	−	0.0489407i
$919$	8.19773	+	25.2300i	0.270418	+	0.832262i	0.990395	+	0.138264i	$0.0441522\pi$
$919$	8.19773	+	25.2300i	0.270418	+	0.832262i	−0.719977	+	0.693998i	$0.755848\pi$
$920$	8.77317	+	6.37408i	0.289243	+	0.210147i
$921$	−37.2317	+	27.0504i	−1.22683	+	0.891342i
$922$	1.41925	−	4.36800i	0.0467405	−	0.143852i
$923$	−1.37608			−0.0452944
$924$	−31.7491	−	25.8659i	−1.04447	−	0.850925i
$925$	3.95118			0.129914
$926$	2.36255	−	7.27117i	0.0776381	−	0.238945i
$927$	4.65306	−	3.38065i	0.152827	−	0.111035i
$928$	−17.7552	−	12.8999i	−0.582842	−	0.423459i
$929$	6.20095	+	19.0846i	0.203447	+	0.626145i	0.999774	+	0.0212781i	$0.00677353\pi$
$929$	6.20095	+	19.0846i	0.203447	+	0.626145i	−0.796327	+	0.604866i	$0.793226\pi$
$930$	−3.52290	−	10.8424i	−0.115520	−	0.355535i
$931$	10.6628	+	7.74695i	0.349458	+	0.253896i
$932$	1.17269	−	0.852012i	0.0384129	−	0.0279086i
$933$	8.78804	−	27.0468i	0.287708	−	0.885473i
$934$	−0.896487			−0.0293339
$935$	9.59683	−	6.19194i	0.313850	−	0.202498i
$936$	−0.0681191			−0.00222654
$937$	7.00299	−	21.5530i	0.228778	−	0.704106i	−0.769108	−	0.639119i	$-0.779299\pi$
$937$	7.00299	−	21.5530i	0.228778	−	0.704106i	0.997886	−	0.0649873i	$-0.0207007\pi$
$938$	11.7108	−	8.50838i	0.382370	−	0.277808i
$939$	−39.8509	−	28.9534i	−1.30049	−	0.944859i
$940$	25.8536	+	79.5691i	0.843250	+	2.59526i
$941$	−14.7675	−	45.4498i	−0.481408	−	1.48162i	−0.837116	−	0.547025i	$-0.815760\pi$
$941$	−14.7675	−	45.4498i	−0.481408	−	1.48162i	0.355708	−	0.934597i	$-0.384240\pi$
$942$	−3.45464	−	2.50995i	−0.112558	−	0.0817785i
$943$	−3.11853	+	2.26574i	−0.101553	+	0.0737828i
$944$	−6.16612	+	18.9774i	−0.200690	+	0.617660i
$945$	−74.6751			−2.42918
$946$	−3.79985	+	9.81201i	−0.123544	+	0.319016i
$947$	9.65655			0.313796			0.156898	−	0.987615i	$-0.449851\pi$
$947$	9.65655			0.313796			0.156898	+	0.987615i	$0.449851\pi$
$948$	−8.29128	+	25.5179i	−0.269288	+	0.828784i
$949$	0.694953	−	0.504913i	0.0225591	−	0.0163902i
$950$	2.38552	+	1.73318i	0.0773965	+	0.0562319i
$951$	2.00181	+	6.16093i	0.0649130	+	0.199782i
$952$	1.37085	+	4.21904i	0.0444294	+	0.136740i
$953$	41.2841	+	29.9946i	1.33732	+	0.971622i	0.999538	+	0.0303984i	$0.00967761\pi$
$953$	41.2841	+	29.9946i	1.33732	+	0.971622i	0.337785	+	0.941223i	$0.390322\pi$
$954$	−0.267045	+	0.194019i	−0.00864589	+	0.00628161i
$955$	−17.4213	+	53.6173i	−0.563740	+	1.73501i
$956$	11.2993			0.365444
$957$	36.3838	+	2.01483i	1.17612	+	0.0651302i
$958$	−5.74252			−0.185532
$959$	−6.83278	+	21.0291i	−0.220642	+	0.679066i
$960$	−27.6171	+	20.0650i	−0.891338	+	0.647595i
$961$	−16.3359	−	11.8687i	−0.526964	−	0.382862i
$962$	−0.00837364	−	0.0257714i	−0.000269977	−	0.000830904i
$963$	0.486989	+	1.49880i	0.0156930	+	0.0482981i
$964$	−46.0150	−	33.4319i	−1.48204	−	1.07677i
$965$	−2.88808	+	2.09832i	−0.0929707	+	0.0675472i
$966$	1.59820	−	4.91877i	0.0514214	−	0.158259i
$967$	−16.6931			−0.536815			−0.268408	−	0.963305i	$-0.586497\pi$
$967$	−16.6931			−0.536815			−0.268408	+	0.963305i	$0.586497\pi$
$968$	10.6863	−	6.08563i	0.343469	−	0.195600i
$969$	−2.44419			−0.0785188
$970$	0.749154	−	2.30566i	0.0240539	−	0.0740302i
$971$	−27.4342	+	19.9321i	−0.880405	+	0.639652i	−0.933359	−	0.358945i	$-0.883136\pi$
$971$	−27.4342	+	19.9321i	−0.880405	+	0.639652i	0.0529537	+	0.998597i	$0.483136\pi$
$972$	5.92643	+	4.30580i	0.190090	+	0.138109i
$973$	14.9072	+	45.8795i	0.477901	+	1.47083i
$974$	0.995226	+	3.06299i	0.0318891	+	0.0981445i
$975$	1.48350	+	1.07783i	0.0475101	+	0.0345181i
$976$	20.7483	−	15.0745i	0.664136	−	0.482523i
$977$	−5.06120	+	15.5768i	−0.161922	+	0.498345i	−0.998796	−	0.0490504i	$-0.984380\pi$
$977$	−5.06120	+	15.5768i	−0.161922	+	0.498345i	0.836874	+	0.547395i	$0.184380\pi$
$978$	−4.83064			−0.154467
$979$	18.0332	+	0.998624i	0.576342	+	0.0319162i
$980$	57.7805			1.84573
$981$	0.924443	−	2.84514i	0.0295152	−	0.0908385i
$982$	0.0320316	−	0.0232723i	0.00102217	−	0.000742649i
$983$	25.5178	+	18.5397i	0.813891	+	0.591326i	0.914956	−	0.403554i	$-0.132225\pi$
$983$	25.5178	+	18.5397i	0.813891	+	0.591326i	−0.101065	+	0.994880i	$0.532225\pi$
$984$	0.766744	+	2.35980i	0.0244429	+	0.0752275i
$985$	−5.42128	−	16.6850i	−0.172736	−	0.531628i
$986$	−1.56358	−	1.13601i	−0.0497945	−	0.0361778i
$987$	65.9314	−	47.9020i	2.09862	−	1.52474i
$988$	−0.147301	+	0.453347i	−0.00468628	+	0.0144229i
$989$	31.3237			0.996034
$990$	0.434902	−	1.12301i	0.0138221	−	0.0356916i
$991$	7.57603			0.240661			0.120330	−	0.992734i	$-0.461605\pi$
$991$	7.57603			0.240661			0.120330	+	0.992734i	$0.461605\pi$
$992$	7.16285	−	22.0450i	0.227421	−	0.699929i
$993$	−24.4956	+	17.7971i	−0.777344	+	0.564773i
$994$	7.64476	+	5.55424i	0.242477	+	0.176170i
$995$	−6.81864	−	20.9856i	−0.216165	−	0.665289i
$996$	14.7439	+	45.3769i	0.467177	+	1.43782i
$997$	−26.3330	−	19.1320i	−0.833973	−	0.605917i	0.0867075	−	0.996234i	$-0.472365\pi$
$997$	−26.3330	−	19.1320i	−0.833973	−	0.605917i	−0.920681	+	0.390317i	$0.872365\pi$
$998$	−5.26894	+	3.82811i	−0.166785	+	0.121177i
$999$	−0.972955	+	2.99445i	−0.0307829	+	0.0947401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.f.86.6	✓	36
11.4	even	5		2057.2.a.bd.1.10		18
11.5	even	5	inner	187.2.g.f.137.6	yes	36
11.7	odd	10		2057.2.a.be.1.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.f.86.6	✓	36	1.1	even	1	trivial
187.2.g.f.137.6	yes	36	11.5	even	5	inner
2057.2.a.bd.1.10		18	11.4	even	5
2057.2.a.be.1.9		18	11.7	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0881614 - 0.271333i) q^{2} +(-1.31211 + 0.953301i) q^{3} +(1.55218 + 1.12773i) q^{4} +(-1.06412 - 3.27502i) q^{5} +(0.142985 + 0.440062i) q^{6} +(3.21023 + 2.33237i) q^{7} +(0.904452 - 0.657123i) q^{8} +(-0.114211 + 0.351506i) q^{9} +O(q^{10})\)	\(q+(0.0881614 - 0.271333i) q^{2} +(-1.31211 + 0.953301i) q^{3} +(1.55218 + 1.12773i) q^{4} +(-1.06412 - 3.27502i) q^{5} +(0.142985 + 0.440062i) q^{6} +(3.21023 + 2.33237i) q^{7} +(0.904452 - 0.657123i) q^{8} +(-0.114211 + 0.351506i) q^{9} -0.982436 q^{10} +(3.31155 + 0.183384i) q^{11} -3.11170 q^{12} +(-0.0509445 + 0.156791i) q^{13} +(0.915868 - 0.665417i) q^{14} +(4.51832 + 3.28275i) q^{15} +(1.08720 + 3.34606i) q^{16} +(0.309017 + 0.951057i) q^{17} +(0.0853062 + 0.0619786i) q^{18} +(1.21922 - 0.885815i) q^{19} +(2.04163 - 6.28348i) q^{20} -6.43562 q^{21} +(0.341709 - 0.882366i) q^{22} -2.81685 q^{23} +(-0.560301 + 1.72443i) q^{24} +(-5.54834 + 4.03110i) q^{25} +(0.0380512 + 0.0276458i) q^{26} +(-1.68877 - 5.19751i) q^{27} +(2.35260 + 7.24054i) q^{28} +(-5.48054 - 3.98185i) q^{29} +(1.28906 - 0.936557i) q^{30} +(2.21098 - 6.80469i) q^{31} +3.23968 q^{32} +(-4.51993 + 2.91628i) q^{33} +0.285296 q^{34} +(4.22250 - 12.9955i) q^{35} +(-0.573680 + 0.416803i) q^{36} +(-0.466100 - 0.338641i) q^{37} +(-0.132863 - 0.408909i) q^{38} +(-0.0826244 - 0.254292i) q^{39} +(-3.11454 - 2.26284i) q^{40} +(1.10710 - 0.804355i) q^{41} +(-0.567373 + 1.74620i) q^{42} -11.1201 q^{43} +(4.93333 + 4.01918i) q^{44} +1.27272 q^{45} +(-0.248337 + 0.764303i) q^{46} +(-10.2448 + 7.44326i) q^{47} +(-4.61633 - 3.35396i) q^{48} +(2.70253 + 8.31753i) q^{49} +(0.604622 + 1.86083i) q^{50} +(-1.31211 - 0.953301i) q^{51} +(-0.255893 + 0.185917i) q^{52} +(-0.967355 + 2.97721i) q^{53} -1.55914 q^{54} +(-2.92330 - 11.0405i) q^{55} +4.43616 q^{56} +(-0.755297 + 2.32457i) q^{57} +(-1.56358 + 1.13601i) q^{58} +(4.58838 + 3.33365i) q^{59} +(3.31121 + 10.1909i) q^{60} +(-2.25257 - 6.93270i) q^{61} +(-1.65141 - 1.19982i) q^{62} +(-1.18649 + 0.862034i) q^{63} +(-1.88879 + 5.81310i) q^{64} +0.567705 q^{65} +(0.392801 + 1.48351i) q^{66} +12.7865 q^{67} +(-0.592882 + 1.82470i) q^{68} +(3.69600 - 2.68530i) q^{69} +(-3.15385 - 2.29141i) q^{70} +(2.57937 + 7.93847i) q^{71} +(0.127684 + 0.392971i) q^{72} +(-4.21542 - 3.06268i) q^{73} +(-0.132977 + 0.0966131i) q^{74} +(3.43715 - 10.5785i) q^{75} +2.89141 q^{76} +(10.2031 + 8.31247i) q^{77} -0.0762820 q^{78} +(2.66455 - 8.20065i) q^{79} +(9.80152 - 7.12122i) q^{80} +(6.27361 + 4.55805i) q^{81} +(-0.120644 - 0.371306i) q^{82} +(-4.73821 - 14.5827i) q^{83} +(-9.98927 - 7.25763i) q^{84} +(2.78590 - 2.02407i) q^{85} +(-0.980365 + 3.01725i) q^{86} +10.9869 q^{87} +(3.11564 - 2.01023i) q^{88} +5.44553 q^{89} +(0.112205 - 0.345332i) q^{90} +(-0.529238 + 0.384514i) q^{91} +(-4.37227 - 3.17664i) q^{92} +(3.58588 + 11.0362i) q^{93} +(1.11641 + 3.43595i) q^{94} +(-4.19846 - 3.05036i) q^{95} +(-4.25080 + 3.08839i) q^{96} +(-0.762547 + 2.34688i) q^{97} +2.49508 q^{98} +(-0.442677 + 1.14309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9 - 10 * q^10 + 3 * q^11 + 28 * q^12 - 13 * q^13 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 9 * q^17 + 2 * q^18 + 10 * q^19 + 19 * q^20 - 50 * q^21 - 25 * q^22 + 38 * q^23 - 17 * q^24 - 28 * q^25 + 20 * q^26 - 16 * q^27 + 31 * q^28 - 45 * q^29 + 68 * q^30 - 13 * q^31 - 40 * q^32 - 29 * q^33 - 4 * q^34 + 13 * q^35 - 25 * q^36 + q^37 + 65 * q^38 - 34 * q^39 - 54 * q^40 + 37 * q^41 + 28 * q^42 - 8 * q^43 - 2 * q^44 + 42 * q^45 + 22 * q^46 - 35 * q^47 + 48 * q^48 - 2 * q^49 - 49 * q^50 - q^51 + 56 * q^52 + 58 * q^53 - 58 * q^54 - 19 * q^55 - 28 * q^56 + 9 * q^57 - 52 * q^58 + 16 * q^59 + 97 * q^60 - 14 * q^61 - 64 * q^62 + 34 * q^63 - 33 * q^64 - 42 * q^65 - 28 * q^66 + 54 * q^67 - 14 * q^68 + 19 * q^69 + 4 * q^70 + 25 * q^71 - 72 * q^72 + 8 * q^73 + 84 * q^74 + 30 * q^75 - 140 * q^76 - 31 * q^77 - 48 * q^78 + 19 * q^79 - 19 * q^80 + 56 * q^81 + 48 * q^82 + 42 * q^83 - 91 * q^84 - 9 * q^85 + 30 * q^86 - 32 * q^87 + 126 * q^88 + 12 * q^89 + 160 * q^90 - 59 * q^91 + 69 * q^92 - 40 * q^93 - 77 * q^94 - 11 * q^95 + 192 * q^96 - 49 * q^97 - 212 * q^98 + 38 * q^99

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