LMFDB - Embedded newform 1170.2.j.i.391.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(391,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1170.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.8528759163648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + x^{8} + 9x^{6} - 36x^{5} + 27x^{4} + 27x^{2} - 162x + 243 $ x^10 - 2x^9 + x^8 + 9x^6 - 36x^5 + 27x^4 + 27x^2 - 162x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.5
Root			$-1.13593 + 1.30754i$ of defining polynomial
Character	$\chi$	$=$	1170.391
Dual form			1170.2.j.i.781.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.70033 + 0.329969i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.564403 - 1.63751i) q^{6} +(-0.607060 - 1.05146i) q^{7} +1.00000 q^{8} +(2.78224 + 1.12211i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.70033 + 0.329969i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.564403 - 1.63751i) q^{6} +(-0.607060 - 1.05146i) q^{7} +1.00000 q^{8} +(2.78224 + 1.12211i) q^{9} -1.00000 q^{10} +(1.10706 + 1.91748i) q^{11} +(-1.13593 + 1.30754i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-0.607060 + 1.05146i) q^{14} +(1.13593 - 1.30754i) q^{15} +(-0.500000 - 0.866025i) q^{16} -2.21412 q^{17} +(-0.419344 - 2.97055i) q^{18} +7.12645 q^{19} +(0.500000 + 0.866025i) q^{20} +(-0.685253 - 1.98814i) q^{21} +(1.10706 - 1.91748i) q^{22} +(2.33403 - 4.04266i) q^{23} +(1.70033 + 0.329969i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +(4.36047 + 2.82601i) q^{27} +1.21412 q^{28} +(2.76049 + 4.78132i) q^{29} +(-1.70033 - 0.329969i) q^{30} +(2.37426 - 4.11233i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.24966 + 3.62565i) q^{33} +(1.10706 + 1.91748i) q^{34} -1.21412 q^{35} +(-2.36290 + 1.84844i) q^{36} +0.566835 q^{37} +(-3.56323 - 6.17169i) q^{38} +(-1.13593 + 1.30754i) q^{39} +(0.500000 - 0.866025i) q^{40} +(2.08615 - 3.61332i) q^{41} +(-1.37915 + 1.58752i) q^{42} +(0.823642 + 1.42659i) q^{43} -2.21412 q^{44} +(2.36290 - 1.84844i) q^{45} -4.66806 q^{46} +(0.392940 + 0.680592i) q^{47} +(-0.564403 - 1.63751i) q^{48} +(2.76296 - 4.78558i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-3.76473 - 0.730590i) q^{51} +(-0.500000 - 0.866025i) q^{52} -12.9168 q^{53} +(0.267165 - 5.18928i) q^{54} +2.21412 q^{55} +(-0.607060 - 1.05146i) q^{56} +(12.1173 + 2.35151i) q^{57} +(2.76049 - 4.78132i) q^{58} +(1.17636 - 2.03751i) q^{59} +(0.564403 + 1.63751i) q^{60} +(-1.18105 - 2.04563i) q^{61} -4.74851 q^{62} +(-0.509134 - 3.60660i) q^{63} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +(2.51508 - 2.89506i) q^{66} +(-2.28810 + 3.96311i) q^{67} +(1.10706 - 1.91748i) q^{68} +(5.30257 - 6.10370i) q^{69} +(0.607060 + 1.05146i) q^{70} -5.72281 q^{71} +(2.78224 + 1.12211i) q^{72} +12.6101 q^{73} +(-0.283418 - 0.490894i) q^{74} +(-0.564403 - 1.63751i) q^{75} +(-3.56323 + 6.17169i) q^{76} +(1.34410 - 2.32805i) q^{77} +(1.70033 + 0.329969i) q^{78} +(4.09453 + 7.09193i) q^{79} -1.00000 q^{80} +(6.48173 + 6.24397i) q^{81} -4.17230 q^{82} +(-2.85088 - 4.93788i) q^{83} +(2.06440 + 0.400622i) q^{84} +(-1.10706 + 1.91748i) q^{85} +(0.823642 - 1.42659i) q^{86} +(3.11606 + 9.04069i) q^{87} +(1.10706 + 1.91748i) q^{88} +5.56699 q^{89} +(-2.78224 - 1.12211i) q^{90} +1.21412 q^{91} +(2.33403 + 4.04266i) q^{92} +(5.39396 - 6.20889i) q^{93} +(0.392940 - 0.680592i) q^{94} +(3.56323 - 6.17169i) q^{95} +(-1.13593 + 1.30754i) q^{96} +(7.78996 + 13.4926i) q^{97} -5.52591 q^{98} +(0.928477 + 6.57715i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - q^{3} - 5 q^{4} + 5 q^{5} - q^{6} - 4 q^{7} + 10 q^{8} - q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - q^3 - 5 * q^4 + 5 * q^5 - q^6 - 4 * q^7 + 10 * q^8 - q^9	\( 10 q - 5 q^{2} - q^{3} - 5 q^{4} + 5 q^{5} - q^{6} - 4 q^{7} + 10 q^{8} - q^{9} - 10 q^{10} + 9 q^{11} + 2 q^{12} - 5 q^{13} - 4 q^{14} - 2 q^{15} - 5 q^{16} - 18 q^{17} + 2 q^{18} - 10 q^{19} + 5 q^{20} - 14 q^{21} + 9 q^{22} + 12 q^{23} - q^{24} - 5 q^{25} + 10 q^{26} + 2 q^{27} + 8 q^{28} + 6 q^{29} + q^{30} - 4 q^{31} - 5 q^{32} + 15 q^{33} + 9 q^{34} - 8 q^{35} - q^{36} + 20 q^{37} + 5 q^{38} + 2 q^{39} + 5 q^{40} + 9 q^{41} - 2 q^{42} - q^{43} - 18 q^{44} + q^{45} - 24 q^{46} + 6 q^{47} - q^{48} + 3 q^{49} - 5 q^{50} - 15 q^{51} - 5 q^{52} - 12 q^{53} - q^{54} + 18 q^{55} - 4 q^{56} + 25 q^{57} + 6 q^{58} + 21 q^{59} + q^{60} + 2 q^{61} + 8 q^{62} - 20 q^{63} + 10 q^{64} + 5 q^{65} - 7 q^{67} + 9 q^{68} - 36 q^{69} + 4 q^{70} - 12 q^{71} - q^{72} - 58 q^{73} - 10 q^{74} - q^{75} + 5 q^{76} + 36 q^{77} - q^{78} + 8 q^{79} - 10 q^{80} + 35 q^{81} - 18 q^{82} + 6 q^{83} + 16 q^{84} - 9 q^{85} - q^{86} - 48 q^{87} + 9 q^{88} - 36 q^{89} + q^{90} + 8 q^{91} + 12 q^{92} + 22 q^{93} + 6 q^{94} - 5 q^{95} + 2 q^{96} + 11 q^{97} - 6 q^{98} + 18 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - q^3 - 5 * q^4 + 5 * q^5 - q^6 - 4 * q^7 + 10 * q^8 - q^9 - 10 * q^10 + 9 * q^11 + 2 * q^12 - 5 * q^13 - 4 * q^14 - 2 * q^15 - 5 * q^16 - 18 * q^17 + 2 * q^18 - 10 * q^19 + 5 * q^20 - 14 * q^21 + 9 * q^22 + 12 * q^23 - q^24 - 5 * q^25 + 10 * q^26 + 2 * q^27 + 8 * q^28 + 6 * q^29 + q^30 - 4 * q^31 - 5 * q^32 + 15 * q^33 + 9 * q^34 - 8 * q^35 - q^36 + 20 * q^37 + 5 * q^38 + 2 * q^39 + 5 * q^40 + 9 * q^41 - 2 * q^42 - q^43 - 18 * q^44 + q^45 - 24 * q^46 + 6 * q^47 - q^48 + 3 * q^49 - 5 * q^50 - 15 * q^51 - 5 * q^52 - 12 * q^53 - q^54 + 18 * q^55 - 4 * q^56 + 25 * q^57 + 6 * q^58 + 21 * q^59 + q^60 + 2 * q^61 + 8 * q^62 - 20 * q^63 + 10 * q^64 + 5 * q^65 - 7 * q^67 + 9 * q^68 - 36 * q^69 + 4 * q^70 - 12 * q^71 - q^72 - 58 * q^73 - 10 * q^74 - q^75 + 5 * q^76 + 36 * q^77 - q^78 + 8 * q^79 - 10 * q^80 + 35 * q^81 - 18 * q^82 + 6 * q^83 + 16 * q^84 - 9 * q^85 - q^86 - 48 * q^87 + 9 * q^88 - 36 * q^89 + q^90 + 8 * q^91 + 12 * q^92 + 22 * q^93 + 6 * q^94 - 5 * q^95 + 2 * q^96 + 11 * q^97 - 6 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.70033	+	0.329969i	0.981686	+	0.190508i
$3$	1.70033	+	0.329969i	0.981686	+	0.190508i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−0.564403	−	1.63751i	−0.230417	−	0.668512i
$7$	−0.607060	−	1.05146i	−0.229447	−	0.397414i	0.728197	−	0.685368i	$-0.240358\pi$
$7$	−0.607060	−	1.05146i	−0.229447	−	0.397414i	−0.957644	+	0.287954i	$0.907025\pi$
$8$	1.00000			0.353553
$9$	2.78224	+	1.12211i	0.927414	+	0.374037i
$10$	−1.00000			−0.316228
$11$	1.10706	+	1.91748i	0.333791	+	0.578143i	0.983252	−	0.182252i	$-0.0583387\pi$
$11$	1.10706	+	1.91748i	0.333791	+	0.578143i	−0.649461	+	0.760395i	$0.725005\pi$
$12$	−1.13593	+	1.30754i	−0.327914	+	0.377456i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	−0.607060	+	1.05146i	−0.162244	+	0.281014i
$15$	1.13593	−	1.30754i	0.293295	−	0.337606i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.21412			−0.537003			−0.268501	−	0.963279i	$-0.586528\pi$
$17$	−2.21412			−0.537003			−0.268501	+	0.963279i	$0.586528\pi$
$18$	−0.419344	−	2.97055i	−0.0988403	−	0.700165i
$19$	7.12645			1.63492			0.817460	−	0.575985i	$-0.195381\pi$
$19$	7.12645			1.63492			0.817460	+	0.575985i	$0.195381\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−0.685253	−	1.98814i	−0.149535	−	0.433847i
$22$	1.10706	−	1.91748i	0.236026	−	0.408809i
$23$	2.33403	−	4.04266i	0.486679	−	0.842953i	−0.513204	−	0.858267i	$-0.671541\pi$
$23$	2.33403	−	4.04266i	0.486679	−	0.842953i	0.999883	+	0.0153139i	$0.00487476\pi$
$24$	1.70033	+	0.329969i	0.347078	+	0.0673546i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.00000			0.196116
$27$	4.36047	+	2.82601i	0.839172	+	0.543866i
$28$	1.21412			0.229447
$29$	2.76049	+	4.78132i	0.512611	+	0.887868i	0.999893	+	0.0146235i	$0.00465498\pi$
$29$	2.76049	+	4.78132i	0.512611	+	0.887868i	−0.487282	+	0.873245i	$0.662012\pi$
$30$	−1.70033	−	0.329969i	−0.310436	−	0.0602438i
$31$	2.37426	−	4.11233i	0.426429	−	0.738596i	−0.570124	−	0.821559i	$-0.693105\pi$
$31$	2.37426	−	4.11233i	0.426429	−	0.738596i	0.996553	+	0.0829623i	$0.0264381\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.24966	+	3.62565i	0.217537	+	0.631145i
$34$	1.10706	+	1.91748i	0.189859	+	0.328846i
$35$	−1.21412			−0.205224
$36$	−2.36290	+	1.84844i	−0.393816	+	0.308073i
$37$	0.566835			0.0931872			0.0465936	−	0.998914i	$-0.485163\pi$
$37$	0.566835			0.0931872			0.0465936	+	0.998914i	$0.485163\pi$
$38$	−3.56323	−	6.17169i	−0.578032	−	1.00118i
$39$	−1.13593	+	1.30754i	−0.181894	+	0.209375i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	2.08615	−	3.61332i	0.325802	−	0.564306i	−0.655872	−	0.754872i	$-0.727699\pi$
$41$	2.08615	−	3.61332i	0.325802	−	0.564306i	0.981674	+	0.190566i	$0.0610324\pi$
$42$	−1.37915	+	1.58752i	−0.212807	+	0.244959i
$43$	0.823642	+	1.42659i	0.125604	+	0.217553i	0.921969	−	0.387264i	$-0.126580\pi$
$43$	0.823642	+	1.42659i	0.125604	+	0.217553i	−0.796365	+	0.604817i	$0.793246\pi$
$44$	−2.21412			−0.333791
$45$	2.36290	−	1.84844i	0.352240	−	0.275549i
$46$	−4.66806			−0.688268
$47$	0.392940	+	0.680592i	0.0573162	+	0.0992746i	0.893260	−	0.449541i	$-0.148412\pi$
$47$	0.392940	+	0.680592i	0.0573162	+	0.0992746i	−0.835944	+	0.548815i	$0.815079\pi$
$48$	−0.564403	−	1.63751i	−0.0814646	−	0.236355i
$49$	2.76296	−	4.78558i	0.394708	−	0.683655i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−3.76473	−	0.730590i	−0.527168	−	0.102303i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	−12.9168			−1.77426			−0.887128	−	0.461523i	$-0.847303\pi$
$53$	−12.9168			−1.77426			−0.887128	+	0.461523i	$0.847303\pi$
$54$	0.267165	−	5.18928i	0.0363566	−	0.706172i
$55$	2.21412			0.298552
$56$	−0.607060	−	1.05146i	−0.0811218	−	0.140507i
$57$	12.1173	+	2.35151i	1.60498	+	0.311465i
$58$	2.76049	−	4.78132i	0.362471	−	0.627818i
$59$	1.17636	−	2.03751i	0.153149	−	0.265261i	−0.779235	−	0.626732i	$-0.784392\pi$
$59$	1.17636	−	2.03751i	0.153149	−	0.265261i	0.932383	+	0.361471i	$0.117725\pi$
$60$	0.564403	+	1.63751i	0.0728642	+	0.211402i
$61$	−1.18105	−	2.04563i	−0.151217	−	0.261916i	0.780458	−	0.625208i	$-0.214986\pi$
$61$	−1.18105	−	2.04563i	−0.151217	−	0.261916i	−0.931675	+	0.363292i	$0.881653\pi$
$62$	−4.74851			−0.603062
$63$	−0.509134	−	3.60660i	−0.0641448	−	0.454389i
$64$	1.00000			0.125000
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$	2.51508	−	2.89506i	0.309584	−	0.356357i
$67$	−2.28810	+	3.96311i	−0.279537	+	0.484171i	−0.971270	−	0.237982i	$-0.923514\pi$
$67$	−2.28810	+	3.96311i	−0.279537	+	0.484171i	0.691733	+	0.722153i	$0.256847\pi$
$68$	1.10706	−	1.91748i	0.134251	−	0.232529i
$69$	5.30257	−	6.10370i	0.638355	−	0.734799i
$70$	0.607060	+	1.05146i	0.0725575	+	0.125673i
$71$	−5.72281			−0.679172			−0.339586	−	0.940575i	$-0.610287\pi$
$71$	−5.72281			−0.679172			−0.339586	+	0.940575i	$0.610287\pi$
$72$	2.78224	+	1.12211i	0.327890	+	0.132242i
$73$	12.6101			1.47590			0.737949	−	0.674857i	$-0.235795\pi$
$73$	12.6101			1.47590			0.737949	+	0.674857i	$0.235795\pi$
$74$	−0.283418	−	0.490894i	−0.0329466	−	0.0570653i
$75$	−0.564403	−	1.63751i	−0.0651717	−	0.189084i
$76$	−3.56323	+	6.17169i	−0.408730	+	0.707941i
$77$	1.34410	−	2.32805i	0.153175	−	0.265306i
$78$	1.70033	+	0.329969i	0.192524	+	0.0373616i
$79$	4.09453	+	7.09193i	0.460670	+	0.797904i	0.998994	−	0.0448337i	$-0.0142758\pi$
$79$	4.09453	+	7.09193i	0.460670	+	0.797904i	−0.538324	+	0.842738i	$0.680942\pi$
$80$	−1.00000			−0.111803
$81$	6.48173	+	6.24397i	0.720193	+	0.693774i
$82$	−4.17230			−0.460754
$83$	−2.85088	−	4.93788i	−0.312925	−	0.542002i	0.666069	−	0.745890i	$-0.267976\pi$
$83$	−2.85088	−	4.93788i	−0.312925	−	0.542002i	−0.978994	+	0.203888i	$0.934642\pi$
$84$	2.06440	+	0.400622i	0.225245	+	0.0437114i
$85$	−1.10706	+	1.91748i	−0.120077	+	0.207980i
$86$	0.823642	−	1.42659i	0.0888156	−	0.153833i
$87$	3.11606	+	9.04069i	0.334077	+	0.969264i
$88$	1.10706	+	1.91748i	0.118013	+	0.204404i
$89$	5.56699			0.590100			0.295050	−	0.955482i	$-0.404664\pi$
$89$	5.56699			0.590100			0.295050	+	0.955482i	$0.404664\pi$
$90$	−2.78224	−	1.12211i	−0.293274	−	0.118281i
$91$	1.21412			0.127274
$92$	2.33403	+	4.04266i	0.243340	+	0.421476i
$93$	5.39396	−	6.20889i	0.559327	−	0.643832i
$94$	0.392940	−	0.680592i	0.0405287	−	0.0701977i
$95$	3.56323	−	6.17169i	0.365579	−	0.633202i
$96$	−1.13593	+	1.30754i	−0.115935	+	0.133451i
$97$	7.78996	+	13.4926i	0.790951	+	1.36997i	0.925379	+	0.379043i	$0.123747\pi$
$97$	7.78996	+	13.4926i	0.790951	+	1.36997i	−0.134428	+	0.990923i	$0.542920\pi$
$98$	−5.52591			−0.558202
$99$	0.928477	+	6.57715i	0.0933155	+	0.661028i
$100$	1.00000			0.100000
$101$	−7.76112	−	13.4427i	−0.772261	−	1.33759i	−0.936321	−	0.351145i	$-0.885793\pi$
$101$	−7.76112	−	13.4427i	−0.772261	−	1.33759i	0.164060	−	0.986450i	$-0.447541\pi$
$102$	1.24966	+	3.62565i	0.123734	+	0.358993i
$103$	−0.947793	+	1.64162i	−0.0933888	+	0.161754i	−0.908935	−	0.416938i	$-0.863103\pi$
$103$	−0.947793	+	1.64162i	−0.0933888	+	0.161754i	0.815546	+	0.578692i	$0.196437\pi$
$104$	−0.500000	+	0.866025i	−0.0490290	+	0.0849208i
$105$	−2.06440	−	0.400622i	−0.201465	−	0.0390967i
$106$	6.45839	+	11.1863i	0.627294	+	1.08651i
$107$	−13.5965			−1.31442			−0.657212	−	0.753706i	$-0.728264\pi$
$107$	−13.5965			−1.31442			−0.657212	+	0.753706i	$0.728264\pi$
$108$	−4.62763	+	2.36327i	−0.445294	+	0.227406i
$109$	3.37794			0.323548			0.161774	−	0.986828i	$-0.448278\pi$
$109$	3.37794			0.323548			0.161774	+	0.986828i	$0.448278\pi$
$110$	−1.10706	−	1.91748i	−0.105554	−	0.182825i
$111$	0.963807	+	0.187038i	0.0914805	+	0.0177529i
$112$	−0.607060	+	1.05146i	−0.0573618	+	0.0993535i
$113$	−2.14975	+	3.72347i	−0.202231	+	0.350275i	−0.949247	−	0.314532i	$-0.898153\pi$
$113$	−2.14975	+	3.72347i	−0.202231	+	0.350275i	0.747016	+	0.664806i	$0.231486\pi$
$114$	−4.02220	−	11.6697i	−0.376713	−	1.09296i
$115$	−2.33403	−	4.04266i	−0.217650	−	0.376980i
$116$	−5.52099			−0.512611
$117$	−2.36290	+	1.84844i	−0.218450	+	0.170888i
$118$	−2.35272			−0.216585
$119$	1.34410	+	2.32805i	0.123214	+	0.213412i
$120$	1.13593	−	1.30754i	0.103695	−	0.119362i
$121$	3.04884	−	5.28074i	0.277167	−	0.480067i
$122$	−1.18105	+	2.04563i	−0.106927	+	0.185203i
$123$	4.73943	−	5.45547i	0.427340	−	0.491903i
$124$	2.37426	+	4.11233i	0.213214	+	0.369298i
$125$	−1.00000			−0.0894427
$126$	−2.86884	+	2.24422i	−0.255577	+	0.199931i
$127$	−7.40317			−0.656925			−0.328463	−	0.944517i	$-0.606530\pi$
$127$	−7.40317			−0.656925			−0.328463	+	0.944517i	$0.606530\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	0.929733	+	2.69745i	0.0818584	+	0.237497i
$130$	0.500000	−	0.866025i	0.0438529	−	0.0759555i
$131$	−0.518764	+	0.898525i	−0.0453246	+	0.0785045i	−0.887798	−	0.460234i	$-0.847766\pi$
$131$	−0.518764	+	0.898525i	−0.0453246	+	0.0785045i	0.842473	+	0.538738i	$0.181099\pi$
$132$	−3.76473	−	0.730590i	−0.327678	−	0.0635897i
$133$	−4.32618	−	7.49317i	−0.375128	−	0.649740i
$134$	4.57621			0.395324
$135$	4.62763	−	2.36327i	0.398283	−	0.203398i
$136$	−2.21412			−0.189859
$137$	−2.78996	−	4.83235i	−0.238362	−	0.412856i	0.721882	−	0.692016i	$-0.243277\pi$
$137$	−2.78996	−	4.83235i	−0.238362	−	0.412856i	−0.960245	+	0.279160i	$0.909944\pi$
$138$	−7.93724	−	1.54031i	−0.675663	−	0.131120i
$139$	−3.69366	+	6.39760i	−0.313292	+	0.542638i	−0.979073	−	0.203510i	$-0.934765\pi$
$139$	−3.69366	+	6.39760i	−0.313292	+	0.542638i	0.665781	+	0.746147i	$0.268099\pi$
$140$	0.607060	−	1.05146i	0.0513059	−	0.0888645i
$141$	0.443554	+	1.28689i	0.0373540	+	0.108376i
$142$	2.86140	+	4.95610i	0.240124	+	0.415906i
$143$	−2.21412			−0.185154
$144$	−0.419344	−	2.97055i	−0.0349453	−	0.247546i
$145$	5.52099			0.458493
$146$	−6.30504	−	10.9206i	−0.521809	−	0.903799i
$147$	6.27703	−	7.22538i	0.517721	−	0.595939i
$148$	−0.283418	+	0.490894i	−0.0232968	+	0.0403512i
$149$	−2.76449	+	4.78825i	−0.226476	+	0.392268i	−0.956761	−	0.290874i	$-0.906054\pi$
$149$	−2.76449	+	4.78825i	−0.226476	+	0.392268i	0.730285	+	0.683143i	$0.239387\pi$
$150$	−1.13593	+	1.30754i	−0.0927480	+	0.106761i
$151$	4.51508	+	7.82034i	0.367432	+	0.636410i	0.989163	−	0.146820i	$-0.0469038\pi$
$151$	4.51508	+	7.82034i	0.367432	+	0.636410i	−0.621732	+	0.783230i	$0.713570\pi$
$152$	7.12645			0.578032
$153$	−6.16021	−	2.48449i	−0.498024	−	0.200859i
$154$	−2.68821			−0.216622
$155$	−2.37426	−	4.11233i	−0.190705	−	0.330310i
$156$	−0.564403	−	1.63751i	−0.0451884	−	0.131106i
$157$	0.349028	−	0.604535i	0.0278555	−	0.0482471i	−0.851762	−	0.523930i	$-0.824466\pi$
$157$	0.349028	−	0.604535i	0.0278555	−	0.0482471i	0.879617	+	0.475682i	$0.157799\pi$
$158$	4.09453	−	7.09193i	0.325743	−	0.564203i
$159$	−21.9628	−	4.26213i	−1.74176	−	0.338009i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−5.66759			−0.446668
$162$	2.16657	−	8.73533i	0.170222	−	0.686312i
$163$	−11.0797			−0.867830			−0.433915	−	0.900954i	$-0.642868\pi$
$163$	−11.0797			−0.867830			−0.433915	+	0.900954i	$0.642868\pi$
$164$	2.08615	+	3.61332i	0.162901	+	0.282153i
$165$	3.76473	+	0.730590i	0.293084	+	0.0568764i
$166$	−2.85088	+	4.93788i	−0.221271	+	0.383253i
$167$	0.808566	−	1.40048i	0.0625687	−	0.108372i	−0.833044	−	0.553206i	$-0.813404\pi$
$167$	0.808566	−	1.40048i	0.0625687	−	0.108372i	0.895613	+	0.444834i	$0.146737\pi$
$168$	−0.685253	−	1.98814i	−0.0528684	−	0.153388i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	2.21412			0.169815
$171$	19.8275	+	7.99667i	1.51625	+	0.611521i
$172$	−1.64728			−0.125604
$173$	−2.61138	−	4.52304i	−0.198539	−	0.343880i	0.749516	−	0.661987i	$-0.230286\pi$
$173$	−2.61138	−	4.52304i	−0.198539	−	0.343880i	−0.948055	+	0.318106i	$0.896953\pi$
$174$	6.27143	−	7.21894i	0.475436	−	0.547266i
$175$	−0.607060	+	1.05146i	−0.0458894	+	0.0794828i
$176$	1.10706	−	1.91748i	0.0834478	−	0.144536i
$177$	2.67251	−	3.07628i	0.200878	−	0.231227i
$178$	−2.78350	−	4.82116i	−0.208632	−	0.361361i
$179$	−1.03753			−0.0775484			−0.0387742	−	0.999248i	$-0.512345\pi$
$179$	−1.03753			−0.0775484			−0.0387742	+	0.999248i	$0.512345\pi$
$180$	0.419344	+	2.97055i	0.0312560	+	0.221412i
$181$	−0.781431			−0.0580833			−0.0290417	−	0.999578i	$-0.509246\pi$
$181$	−0.781431			−0.0580833			−0.0290417	+	0.999578i	$0.509246\pi$
$182$	−0.607060	−	1.05146i	−0.0449983	−	0.0779393i
$183$	−1.33317	−	3.86795i	−0.0985509	−	0.285927i
$184$	2.33403	−	4.04266i	0.172067	−	0.298029i
$185$	0.283418	−	0.490894i	0.0208373	−	0.0360912i
$186$	−8.07403	−	1.56686i	−0.592017	−	0.114888i
$187$	−2.45116	−	4.24554i	−0.179247	−	0.310465i
$188$	−0.785880			−0.0573162
$189$	0.324370	−	6.30041i	0.0235945	−	0.458287i
$190$	−7.12645			−0.517007
$191$	5.03015	+	8.71248i	0.363969	+	0.630413i	0.988610	−	0.150499i	$-0.0480881\pi$
$191$	5.03015	+	8.71248i	0.363969	+	0.630413i	−0.624641	+	0.780912i	$0.714755\pi$
$192$	1.70033	+	0.329969i	0.122711	+	0.0238134i
$193$	3.33379	−	5.77430i	0.239972	−	0.415643i	−0.720734	−	0.693212i	$-0.756195\pi$
$193$	3.33379	−	5.77430i	0.239972	−	0.415643i	0.960706	+	0.277568i	$0.0895285\pi$
$194$	7.78996	−	13.4926i	0.559287	−	0.968713i
$195$	0.564403	+	1.63751i	0.0404178	+	0.117265i
$196$	2.76296	+	4.78558i	0.197354	+	0.341827i
$197$	−8.57128			−0.610679			−0.305339	−	0.952244i	$-0.598770\pi$
$197$	−8.57128			−0.610679			−0.305339	+	0.952244i	$0.598770\pi$
$198$	5.23174	−	4.09266i	0.371803	−	0.290853i
$199$	−24.5886			−1.74304			−0.871518	−	0.490363i	$-0.836864\pi$
$199$	−24.5886			−1.74304			−0.871518	+	0.490363i	$0.836864\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−5.19824	+	5.98360i	−0.366655	+	0.422050i
$202$	−7.76112	+	13.4427i	−0.546071	+	0.945822i
$203$	3.35157	−	5.80509i	0.235234	−	0.407437i
$204$	2.51508	−	2.89506i	0.176091	−	0.202695i
$205$	−2.08615	−	3.61332i	−0.145703	−	0.252365i
$206$	1.89559			0.132072
$207$	11.0302	−	8.62861i	0.766649	−	0.599730i
$208$	1.00000			0.0693375
$209$	7.88941	+	13.6649i	0.545722	+	0.945218i
$210$	0.685253	+	1.98814i	0.0472870	+	0.137194i
$211$	5.44755	−	9.43544i	0.375025	−	0.649563i	−0.615306	−	0.788289i	$-0.710967\pi$
$211$	5.44755	−	9.43544i	0.375025	−	0.649563i	0.990331	+	0.138726i	$0.0443008\pi$
$212$	6.45839	−	11.1863i	0.443564	−	0.768276i
$213$	−9.73066	−	1.88835i	−0.666734	−	0.129387i
$214$	6.79826	+	11.7749i	0.464719	+	0.804917i
$215$	1.64728			0.112344
$216$	4.36047	+	2.82601i	0.296692	+	0.192286i
$217$	−5.76526			−0.391371
$218$	−1.68897	−	2.92538i	−0.114392	−	0.198132i
$219$	21.4413	+	4.16093i	1.44887	+	0.281170i
$220$	−1.10706	+	1.91748i	−0.0746380	+	0.129277i
$221$	1.10706	−	1.91748i	0.0744689	−	0.128984i
$222$	−0.319924	−	0.928200i	−0.0214719	−	0.0622967i
$223$	−12.7461	−	22.0769i	−0.853544	−	1.47838i	−0.877989	−	0.478680i	$-0.841115\pi$
$223$	−12.7461	−	22.0769i	−0.853544	−	1.47838i	0.0244456	−	0.999701i	$-0.492218\pi$
$224$	1.21412			0.0811218
$225$	−0.419344	−	2.97055i	−0.0279563	−	0.198036i
$226$	4.29949			0.285998
$227$	11.5741	+	20.0469i	0.768198	+	1.33056i	0.938539	+	0.345172i	$0.112180\pi$
$227$	11.5741	+	20.0469i	0.768198	+	1.33056i	−0.170342	+	0.985385i	$0.554487\pi$
$228$	−8.09513	+	9.31815i	−0.536113	+	0.617110i
$229$	−10.6161	+	18.3877i	−0.701535	+	1.21509i	0.266393	+	0.963864i	$0.414168\pi$
$229$	−10.6161	+	18.3877i	−0.701535	+	1.21509i	−0.967928	+	0.251229i	$0.919165\pi$
$230$	−2.33403	+	4.04266i	−0.153901	+	0.266565i
$231$	3.05360	−	3.51495i	0.200912	−	0.231267i
$232$	2.76049	+	4.78132i	0.181235	+	0.313909i
$233$	−27.7750			−1.81960			−0.909800	−	0.415046i	$-0.863765\pi$
$233$	−27.7750			−1.81960			−0.909800	+	0.415046i	$0.863765\pi$
$234$	2.78224	+	1.12211i	0.181881	+	0.0733547i
$235$	0.785880			0.0512652
$236$	1.17636	+	2.03751i	0.0765744	+	0.132631i
$237$	4.62193	+	13.4097i	0.300227	+	0.871052i
$238$	1.34410	−	2.32805i	0.0871253	−	0.150905i
$239$	−10.1468	+	17.5747i	−0.656339	+	1.13681i	0.325217	+	0.945639i	$0.394563\pi$
$239$	−10.1468	+	17.5747i	−0.656339	+	1.13681i	−0.981556	+	0.191173i	$0.938771\pi$
$240$	−1.70033	−	0.329969i	−0.109756	−	0.0212994i
$241$	13.2301	+	22.9153i	0.852228	+	1.47610i	0.879193	+	0.476467i	$0.158083\pi$
$241$	13.2301	+	22.9153i	0.852228	+	1.47610i	−0.0269641	+	0.999636i	$0.508584\pi$
$242$	−6.09767			−0.391973
$243$	8.96077	+	12.7556i	0.574834	+	0.818270i
$244$	2.36209			0.151217
$245$	−2.76296	−	4.78558i	−0.176519	−	0.305740i
$246$	−7.09429	−	1.37673i	−0.452315	−	0.0877770i
$247$	−3.56323	+	6.17169i	−0.226723	+	0.392695i
$248$	2.37426	−	4.11233i	0.150765	−	0.261133i
$249$	−3.21810	−	9.33672i	−0.203939	−	0.591690i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−28.7783			−1.81647			−0.908237	−	0.418457i	$-0.862571\pi$
$251$	−28.7783			−1.81647			−0.908237	+	0.418457i	$0.862571\pi$
$252$	3.37797	+	1.36238i	0.212792	+	0.0858217i
$253$	10.3356			0.649797
$254$	3.70159	+	6.41133i	0.232258	+	0.402283i
$255$	−2.51508	+	2.89506i	−0.157500	+	0.181296i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.111537	−	0.193188i	0.00695748	−	0.0120507i	−0.862526	−	0.506013i	$-0.831119\pi$
$257$	0.111537	−	0.193188i	0.00695748	−	0.0120507i	0.869483	+	0.493963i	$0.164452\pi$
$258$	1.87119	−	2.15390i	0.116495	−	0.134096i
$259$	−0.344103	−	0.596004i	−0.0213815	−	0.0370339i
$260$	−1.00000			−0.0620174
$261$	2.31519	+	16.4004i	0.143307	+	1.01516i
$262$	1.03753			0.0640987
$263$	−8.27496	−	14.3327i	−0.510256	−	0.883789i	−0.999929	−	0.0118835i	$-0.996217\pi$
$263$	−8.27496	−	14.3327i	−0.510256	−	0.883789i	0.489673	−	0.871906i	$-0.337116\pi$
$264$	1.24966	+	3.62565i	0.0769111	+	0.223143i
$265$	−6.45839	+	11.1863i	−0.396736	+	0.687167i
$266$	−4.32618	+	7.49317i	−0.265255	+	0.459436i
$267$	9.46572	+	1.83693i	0.579293	+	0.112419i
$268$	−2.28810	−	3.96311i	−0.139768	−	0.242086i
$269$	−2.98389			−0.181931			−0.0909653	−	0.995854i	$-0.528995\pi$
$269$	−2.98389			−0.181931			−0.0909653	+	0.995854i	$0.528995\pi$
$270$	−4.36047	−	2.82601i	−0.265369	−	0.171986i
$271$	3.82022			0.232062			0.116031	−	0.993246i	$-0.462983\pi$
$271$	3.82022			0.232062			0.116031	+	0.993246i	$0.462983\pi$
$272$	1.10706	+	1.91748i	0.0671254	+	0.116265i
$273$	2.06440	+	0.400622i	0.124943	+	0.0242467i
$274$	−2.78996	+	4.83235i	−0.168548	+	0.291933i
$275$	1.10706	−	1.91748i	0.0667582	−	0.115629i
$276$	2.63467	+	7.64401i	0.158589	+	0.460115i
$277$	−1.82597	−	3.16268i	−0.109712	−	0.190027i	0.805941	−	0.591995i	$-0.201660\pi$
$277$	−1.82597	−	3.16268i	−0.109712	−	0.190027i	−0.915654	+	0.401968i	$0.868326\pi$
$278$	7.38732			0.443062
$279$	11.2202	−	8.77732i	0.671738	−	0.525484i
$280$	−1.21412			−0.0725575
$281$	10.1875	+	17.6452i	0.607733	+	1.05262i	0.991613	+	0.129241i	$0.0412541\pi$
$281$	10.1875	+	17.6452i	0.607733	+	1.05262i	−0.383880	+	0.923383i	$0.625413\pi$
$282$	0.892702	−	1.02757i	0.0531596	−	0.0611911i
$283$	−2.38579	+	4.13231i	−0.141821	+	0.245640i	−0.928182	−	0.372126i	$-0.878629\pi$
$283$	−2.38579	+	4.13231i	−0.141821	+	0.245640i	0.786362	+	0.617766i	$0.211962\pi$
$284$	2.86140	−	4.95610i	0.169793	−	0.294090i
$285$	8.09513	−	9.31815i	0.479514	−	0.551960i
$286$	1.10706	+	1.91748i	0.0654618	+	0.113383i
$287$	−5.06567			−0.299017
$288$	−2.36290	+	1.84844i	−0.139235	+	0.108920i
$289$	−12.0977			−0.711628
$290$	−2.76049	−	4.78132i	−0.162102	−	0.280769i
$291$	8.79336	+	25.5123i	0.515476	+	1.49556i
$292$	−6.30504	+	10.9206i	−0.368974	+	0.639082i
$293$	−3.90786	+	6.76861i	−0.228299	+	0.395426i	−0.957304	−	0.289082i	$-0.906650\pi$
$293$	−3.90786	+	6.76861i	−0.228299	+	0.395426i	0.729005	+	0.684509i	$0.239983\pi$
$294$	−9.39587	−	1.82338i	−0.547979	−	0.106342i
$295$	−1.17636	−	2.03751i	−0.0684902	−	0.118629i
$296$	0.566835			0.0329466
$297$	−0.591535	+	11.4897i	−0.0343244	+	0.666699i
$298$	5.52899			0.320286
$299$	2.33403	+	4.04266i	0.134981	+	0.233793i
$300$	1.70033	+	0.329969i	0.0981686	+	0.0190508i
$301$	1.00000	−	1.73205i	0.0576390	−	0.0998337i
$302$	4.51508	−	7.82034i	0.259813	−	0.450010i
$303$	−8.76081	−	25.4179i	−0.503295	−	1.46022i
$304$	−3.56323	−	6.17169i	−0.204365	−	0.353971i
$305$	−2.36209			−0.135253
$306$	0.928477	+	6.57715i	0.0530775	+	0.375990i
$307$	−7.36888			−0.420564			−0.210282	−	0.977641i	$-0.567438\pi$
$307$	−7.36888			−0.420564			−0.210282	+	0.977641i	$0.567438\pi$
$308$	1.34410	+	2.32805i	0.0765874	+	0.132653i
$309$	−2.15324	+	2.47856i	−0.122494	+	0.141000i
$310$	−2.37426	+	4.11233i	−0.134849	+	0.233565i
$311$	0.730659	−	1.26554i	0.0414319	−	0.0717621i	−0.844566	−	0.535452i	$-0.820141\pi$
$311$	0.730659	−	1.26554i	0.0414319	−	0.0717621i	0.885998	+	0.463690i	$0.153475\pi$
$312$	−1.13593	+	1.30754i	−0.0643092	+	0.0740251i
$313$	16.6222	+	28.7904i	0.939540	+	1.62733i	0.766331	+	0.642446i	$0.222080\pi$
$313$	16.6222	+	28.7904i	0.939540	+	1.62733i	0.173209	+	0.984885i	$0.444586\pi$
$314$	−0.698057			−0.0393936
$315$	−3.37797	−	1.36238i	−0.190327	−	0.0767613i
$316$	−8.18905			−0.460670
$317$	−6.03193	−	10.4476i	−0.338787	−	0.586796i	0.645418	−	0.763830i	$-0.276683\pi$
$317$	−6.03193	−	10.4476i	−0.338787	−	0.586796i	−0.984205	+	0.177034i	$0.943350\pi$
$318$	7.29028	+	21.1514i	0.408818	+	1.18611i
$319$	−6.11206	+	10.5864i	−0.342210	+	0.592725i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−23.1186	−	4.48642i	−1.29035	−	0.250408i
$322$	2.83379	+	4.90827i	0.157921	+	0.273527i
$323$	−15.7788			−0.877957
$324$	−8.64830	+	2.49136i	−0.480461	+	0.138409i
$325$	1.00000			0.0554700
$326$	5.53986	+	9.59531i	0.306824	+	0.531435i
$327$	5.74362	+	1.11462i	0.317623	+	0.0616384i
$328$	2.08615	−	3.61332i	0.115188	−	0.199512i
$329$	0.477076	−	0.826321i	0.0263021	−	0.0455565i
$330$	−1.24966	−	3.62565i	−0.0687913	−	0.199585i
$331$	12.6488	+	21.9083i	0.695239	+	1.20419i	0.970100	+	0.242706i	$0.0780349\pi$
$331$	12.6488	+	21.9083i	0.695239	+	1.20419i	−0.274861	+	0.961484i	$0.588632\pi$
$332$	5.70177			0.312925
$333$	1.57707	+	0.636052i	0.0864231	+	0.0348555i
$334$	−1.61713			−0.0884855
$335$	2.28810	+	3.96311i	0.125013	+	0.216528i
$336$	−1.37915	+	1.58752i	−0.0752388	+	0.0866060i
$337$	−1.64867	+	2.85558i	−0.0898087	+	0.155553i	−0.907430	−	0.420203i	$-0.861959\pi$
$337$	−1.64867	+	2.85558i	−0.0898087	+	0.155553i	0.817621	+	0.575756i	$0.195292\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$	−4.88391	+	5.62178i	−0.265257	+	0.305333i
$340$	−1.10706	−	1.91748i	−0.0600387	−	0.103990i
$341$	10.5138			0.569353
$342$	−2.98843	−	21.1695i	−0.161596	−	1.14471i
$343$	−15.2080			−0.821153
$344$	0.823642	+	1.42659i	0.0444078	+	0.0769166i
$345$	−2.63467	−	7.64401i	−0.141846	−	0.411540i
$346$	−2.61138	+	4.52304i	−0.140389	+	0.243160i
$347$	−3.59293	+	6.22314i	−0.192879	+	0.334076i	−0.946203	−	0.323573i	$-0.895116\pi$
$347$	−3.59293	+	6.22314i	−0.192879	+	0.334076i	0.753324	+	0.657649i	$0.228449\pi$
$348$	−9.38750	−	1.82175i	−0.503223	−	0.0976562i
$349$	4.02091	+	6.96442i	0.215234	+	0.372797i	0.953345	−	0.301883i	$-0.0976151\pi$
$349$	4.02091	+	6.96442i	0.215234	+	0.372797i	−0.738111	+	0.674680i	$0.764282\pi$
$350$	1.21412			0.0648974
$351$	−4.62763	+	2.36327i	−0.247005	+	0.126142i
$352$	−2.21412			−0.118013
$353$	−4.13406	−	7.16041i	−0.220034	−	0.381110i	0.734784	−	0.678301i	$-0.237283\pi$
$353$	−4.13406	−	7.16041i	−0.220034	−	0.381110i	−0.954818	+	0.297191i	$0.903950\pi$
$354$	−4.00039	−	0.776323i	−0.212618	−	0.0412611i
$355$	−2.86140	+	4.95610i	−0.151868	+	0.263042i
$356$	−2.78350	+	4.82116i	−0.147525	+	0.255521i
$357$	1.51723	+	4.40197i	0.0803005	+	0.232977i
$358$	0.518764	+	0.898525i	0.0274175	+	0.0474885i
$359$	21.6643			1.14340			0.571700	−	0.820463i	$-0.306284\pi$
$359$	21.6643			1.14340			0.571700	+	0.820463i	$0.306284\pi$
$360$	2.36290	−	1.84844i	0.124536	−	0.0974211i
$361$	31.7863			1.67297
$362$	0.390716	+	0.676739i	0.0205356	+	0.0355686i
$363$	6.92651	−	7.97298i	0.363547	−	0.418473i
$364$	−0.607060	+	1.05146i	−0.0318186	+	0.0551114i
$365$	6.30504	−	10.9206i	0.330021	−	0.571613i
$366$	−2.68316	+	3.08854i	−0.140251	+	0.161440i
$367$	−8.90147	−	15.4178i	−0.464653	−	0.804802i	0.534533	−	0.845148i	$-0.320488\pi$
$367$	−8.90147	−	15.4178i	−0.464653	−	0.804802i	−0.999186	+	0.0403452i	$0.987154\pi$
$368$	−4.66806			−0.243340
$369$	9.85872	−	7.71223i	0.513224	−	0.401483i
$370$	−0.566835			−0.0294684
$371$	7.84126	+	13.5815i	0.407098	+	0.705114i
$372$	2.68008	+	7.77575i	0.138955	+	0.403154i
$373$	11.7603	−	20.3695i	0.608927	−	1.05469i	−0.382491	−	0.923959i	$-0.624934\pi$
$373$	11.7603	−	20.3695i	0.608927	−	1.05469i	0.991418	−	0.130733i	$-0.0417331\pi$
$374$	−2.45116	+	4.24554i	−0.126747	+	0.219532i
$375$	−1.70033	−	0.329969i	−0.0878046	−	0.0170395i
$376$	0.392940	+	0.680592i	0.0202643	+	0.0350989i
$377$	−5.52099			−0.284345
$378$	−5.61850	+	2.86929i	−0.288984	+	0.147580i
$379$	−32.2403			−1.65607			−0.828036	−	0.560675i	$-0.810542\pi$
$379$	−32.2403			−1.65607			−0.828036	+	0.560675i	$0.810542\pi$
$380$	3.56323	+	6.17169i	0.182790	+	0.316601i
$381$	−12.5878	−	2.44281i	−0.644894	−	0.125149i
$382$	5.03015	−	8.71248i	0.257365	−	0.445769i
$383$	−12.4881	+	21.6300i	−0.638110	+	1.10524i	0.347737	+	0.937592i	$0.386950\pi$
$383$	−12.4881	+	21.6300i	−0.638110	+	1.10524i	−0.985847	+	0.167647i	$0.946383\pi$
$384$	−0.564403	−	1.63751i	−0.0288021	−	0.0835640i
$385$	−1.34410	−	2.32805i	−0.0685018	−	0.118649i
$386$	−6.66759			−0.339371
$387$	0.690778	+	4.89334i	0.0351142	+	0.248742i
$388$	−15.5799			−0.790951
$389$	16.6601	+	28.8561i	0.844698	+	1.46306i	0.885883	+	0.463909i	$0.153553\pi$
$389$	16.6601	+	28.8561i	0.844698	+	1.46306i	−0.0411849	+	0.999152i	$0.513113\pi$
$390$	1.13593	−	1.30754i	0.0575199	−	0.0662101i
$391$	−5.16782	+	8.95093i	−0.261348	+	0.452668i
$392$	2.76296	−	4.78558i	0.139550	−	0.241708i
$393$	−1.17855	+	1.35661i	−0.0594502	+	0.0684321i
$394$	4.28564	+	7.42295i	0.215908	+	0.373963i
$395$	8.18905			0.412036
$396$	−6.16021	−	2.48449i	−0.309562	−	0.124850i
$397$	−0.700030			−0.0351335			−0.0175668	−	0.999846i	$-0.505592\pi$
$397$	−0.700030			−0.0351335			−0.0175668	+	0.999846i	$0.505592\pi$
$398$	12.2943	+	21.2943i	0.616256	+	1.06739i
$399$	−4.88343	−	14.1684i	−0.244477	−	0.709305i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	11.0964	−	19.2195i	0.554127	−	0.959776i	−0.443844	−	0.896104i	$-0.646386\pi$
$401$	11.0964	−	19.2195i	0.554127	−	0.959776i	0.997971	−	0.0636718i	$-0.0202811\pi$
$402$	7.78106	+	1.51001i	0.388084	+	0.0753123i
$403$	2.37426	+	4.11233i	0.118270	+	0.204850i
$404$	15.5222			0.772261
$405$	8.64830	−	2.49136i	0.429738	−	0.123797i
$406$	−6.70314			−0.332671
$407$	0.627521	+	1.08690i	0.0311050	+	0.0538755i
$408$	−3.76473	−	0.730590i	−0.186382	−	0.0361696i
$409$	17.4711	−	30.2608i	0.863890	−	1.49630i	−0.00425608	−	0.999991i	$-0.501355\pi$
$409$	17.4711	−	30.2608i	0.863890	−	1.49630i	0.868146	−	0.496310i	$-0.165312\pi$
$410$	−2.08615	+	3.61332i	−0.103028	+	0.178449i
$411$	−3.14933	−	9.13719i	−0.155345	−	0.450704i
$412$	−0.947793	−	1.64162i	−0.0466944	−	0.0808771i
$413$	−2.85648			−0.140558
$414$	−12.9877	−	5.23809i	−0.638309	−	0.257438i
$415$	−5.70177			−0.279889
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	−8.39145	+	9.65924i	−0.410931	+	0.473015i
$418$	7.88941	−	13.6649i	0.385884	−	0.668370i
$419$	−14.6982	+	25.4581i	−0.718056	+	1.24371i	0.243713	+	0.969847i	$0.421634\pi$
$419$	−14.6982	+	25.4581i	−0.718056	+	1.24371i	−0.961769	+	0.273862i	$0.911699\pi$
$420$	1.37915	−	1.58752i	0.0672956	−	0.0774628i
$421$	−20.0782	−	34.7765i	−0.978553	−	1.69490i	−0.667675	−	0.744453i	$-0.732711\pi$
$421$	−20.0782	−	34.7765i	−0.978553	−	1.69490i	−0.310877	−	0.950450i	$-0.600623\pi$
$422$	−10.8951			−0.530366
$423$	0.329554	+	2.33449i	0.0160235	+	0.113507i
$424$	−12.9168			−0.627294
$425$	1.10706	+	1.91748i	0.0537003	+	0.0930116i
$426$	3.22997	+	9.37117i	0.156493	+	0.454035i
$427$	−1.43393	+	2.48364i	−0.0693927	+	0.120192i
$428$	6.79826	−	11.7749i	0.328606	−	0.569162i
$429$	−3.76473	−	0.730590i	−0.181763	−	0.0352732i
$430$	−0.823642	−	1.42659i	−0.0397195	−	0.0687963i
$431$	13.2965			0.640472			0.320236	−	0.947338i	$-0.396238\pi$
$431$	13.2965			0.640472			0.320236	+	0.947338i	$0.396238\pi$
$432$	0.267165	−	5.18928i	0.0128540	−	0.249669i
$433$	16.6047			0.797970			0.398985	−	0.916958i	$-0.369363\pi$
$433$	16.6047			0.797970			0.398985	+	0.916958i	$0.369363\pi$
$434$	2.88263	+	4.99286i	0.138371	+	0.239665i
$435$	9.38750	+	1.82175i	0.450096	+	0.0873464i
$436$	−1.68897	+	2.92538i	−0.0808871	+	0.140101i
$437$	16.6334	−	28.8098i	0.795682	−	1.37816i
$438$	−7.11717	−	20.6492i	−0.340071	−	0.986655i
$439$	5.01385	+	8.68425i	0.239298	+	0.414476i	0.960513	−	0.278235i	$-0.0897494\pi$
$439$	5.01385	+	8.68425i	0.239298	+	0.414476i	−0.721215	+	0.692711i	$0.756416\pi$
$440$	2.21412			0.105554
$441$	13.0572	−	10.2143i	0.621770	−	0.486395i
$442$	−2.21412			−0.105315
$443$	−6.81935	−	11.8115i	−0.323997	−	0.561179i	0.657312	−	0.753619i	$-0.271693\pi$
$443$	−6.81935	−	11.8115i	−0.323997	−	0.561179i	−0.981309	+	0.192439i	$0.938360\pi$
$444$	−0.643883	+	0.741162i	−0.0305573	+	0.0351740i
$445$	2.78350	−	4.82116i	0.131950	−	0.228545i
$446$	−12.7461	+	22.0769i	−0.603547	+	1.04537i
$447$	−6.28052	+	7.22940i	−0.297059	+	0.341939i
$448$	−0.607060	−	1.05146i	−0.0286809	−	0.0496767i
$449$	−35.9670			−1.69739			−0.848693	−	0.528885i	$-0.822610\pi$
$449$	−35.9670			−1.69739			−0.848693	+	0.528885i	$0.822610\pi$
$450$	−2.36290	+	1.84844i	−0.111388	+	0.0871361i
$451$	9.23797			0.434999
$452$	−2.14975	−	3.72347i	−0.101116	−	0.175137i
$453$	5.09665	+	14.7870i	0.239461	+	0.694753i
$454$	11.5741	−	20.0469i	0.543198	−	0.940846i
$455$	0.607060	−	1.05146i	0.0284594	−	0.0492931i
$456$	12.1173	+	2.35151i	0.567446	+	0.110119i
$457$	−21.0006	−	36.3740i	−0.982364	−	1.70150i	−0.653109	−	0.757264i	$-0.726536\pi$
$457$	−21.0006	−	36.3740i	−0.982364	−	1.70150i	−0.329255	−	0.944241i	$-0.606798\pi$
$458$	21.2323			0.992120
$459$	−9.65459	−	6.25713i	−0.450638	−	0.292058i
$460$	4.66806			0.217650
$461$	−5.59495	−	9.69073i	−0.260583	−	0.451342i	0.705814	−	0.708397i	$-0.250581\pi$
$461$	−5.59495	−	9.69073i	−0.260583	−	0.451342i	−0.966397	+	0.257055i	$0.917248\pi$
$462$	−4.57084	−	0.887024i	−0.212655	−	0.0412681i
$463$	14.7571	−	25.5601i	0.685823	−	1.18788i	−0.287355	−	0.957824i	$-0.592776\pi$
$463$	14.7571	−	25.5601i	0.685823	−	1.18788i	0.973177	−	0.230056i	$-0.0738908\pi$
$464$	2.76049	−	4.78132i	0.128153	−	0.221967i
$465$	−2.68008	−	7.77575i	−0.124286	−	0.360592i
$466$	13.8875	+	24.0539i	0.643326	+	1.11427i
$467$	−22.5804			−1.04490			−0.522448	−	0.852671i	$-0.674981\pi$
$467$	−22.5804			−1.04490			−0.522448	+	0.852671i	$0.674981\pi$
$468$	−0.419344	−	2.97055i	−0.0193842	−	0.137314i
$469$	5.55607			0.256555
$470$	−0.392940	−	0.680592i	−0.0181250	−	0.0313934i
$471$	0.792941	−	0.912740i	0.0365368	−	0.0420568i
$472$	1.17636	−	2.03751i	0.0541463	−	0.0937841i
$473$	−1.82364	+	3.15864i	−0.0838512	+	0.145234i
$474$	9.30216	−	10.7075i	0.427262	−	0.491814i
$475$	−3.56323	−	6.17169i	−0.163492	−	0.283177i
$476$	−2.68821			−0.123214
$477$	−35.9376	−	14.4941i	−1.64547	−	0.663638i
$478$	20.2935			0.928204
$479$	2.37648	+	4.11618i	0.108584	+	0.188073i	0.915197	−	0.403007i	$-0.132035\pi$
$479$	2.37648	+	4.11618i	0.108584	+	0.188073i	−0.806613	+	0.591080i	$0.798702\pi$
$480$	0.564403	+	1.63751i	0.0257614	+	0.0747419i
$481$	−0.283418	+	0.490894i	−0.0129227	+	0.0223828i
$482$	13.2301	−	22.9153i	0.602617	−	1.04376i
$483$	−9.63676	−	1.87013i	−0.438488	−	0.0850937i
$484$	3.04884	+	5.28074i	0.138584	+	0.240034i
$485$	15.5799			0.707448
$486$	6.56627	−	14.1380i	0.297852	−	0.641314i
$487$	−4.26734			−0.193372			−0.0966859	−	0.995315i	$-0.530824\pi$
$487$	−4.26734			−0.193372			−0.0966859	+	0.995315i	$0.530824\pi$
$488$	−1.18105	−	2.04563i	−0.0534634	−	0.0926013i
$489$	−18.8392	−	3.65596i	−0.851936	−	0.165328i
$490$	−2.76296	+	4.78558i	−0.124818	+	0.216191i
$491$	−19.3194	+	33.4622i	−0.871874	+	1.51013i	−0.0118171	+	0.999930i	$0.503762\pi$
$491$	−19.3194	+	33.4622i	−0.871874	+	1.51013i	−0.860056	+	0.510199i	$0.829572\pi$
$492$	2.35486	+	6.83220i	0.106165	+	0.308019i
$493$	−6.11206	−	10.5864i	−0.275274	−	0.476788i
$494$	7.12645			0.320634
$495$	6.16021	+	2.48449i	0.276881	+	0.111669i
$496$	−4.74851			−0.213214
$497$	3.47409	+	6.01729i	0.155834	+	0.269913i
$498$	−6.47679	+	7.45531i	−0.290232	+	0.334081i
$499$	−10.9349	+	18.9398i	−0.489514	+	0.847863i	−0.999927	−	0.0120660i	$-0.996159\pi$
$499$	−10.9349	+	18.9398i	−0.489514	+	0.847863i	0.510413	+	0.859929i	$0.329492\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	1.83694	−	2.11447i	0.0820685	−	0.0944676i
$502$	14.3892	+	24.9228i	0.642220	+	1.11236i
$503$	−29.7478			−1.32639			−0.663194	−	0.748448i	$-0.730799\pi$
$503$	−29.7478			−1.32639			−0.663194	+	0.748448i	$0.730799\pi$
$504$	−0.509134	−	3.60660i	−0.0226786	−	0.160651i
$505$	−15.5222			−0.690731
$506$	−5.16782	−	8.95093i	−0.229738	−	0.397918i
$507$	−0.564403	−	1.63751i	−0.0250660	−	0.0727245i
$508$	3.70159	−	6.41133i	0.164231	−	0.284457i
$509$	14.3072	−	24.7807i	0.634154	−	1.09839i	−0.352540	−	0.935797i	$-0.614682\pi$
$509$	14.3072	−	24.7807i	0.634154	−	1.09839i	0.986694	−	0.162590i	$-0.0519847\pi$
$510$	3.76473	+	0.730590i	0.166705	+	0.0323511i
$511$	−7.65507	−	13.2590i	−0.338640	−	0.586542i
$512$	1.00000			0.0441942
$513$	31.0747	+	20.1394i	1.37198	+	0.889178i
$514$	−0.223074			−0.00983936
$515$	0.947793	+	1.64162i	0.0417647	+	0.0723386i
$516$	−2.80093	−	0.543552i	−0.123304	−	0.0239286i
$517$	−0.870017	+	1.50691i	−0.0382633	+	0.0662740i
$518$	−0.344103	+	0.596004i	−0.0151190	+	0.0261869i
$519$	−2.94774	−	8.55233i	−0.129391	−	0.375406i
$520$	0.500000	+	0.866025i	0.0219265	+	0.0379777i
$521$	31.8530			1.39550			0.697752	−	0.716339i	$-0.254184\pi$
$521$	31.8530			1.39550			0.697752	+	0.716339i	$0.254184\pi$
$522$	13.0455	−	10.2052i	0.570987	−	0.446669i
$523$	14.8839			0.650828			0.325414	−	0.945572i	$-0.394496\pi$
$523$	14.8839			0.650828			0.325414	+	0.945572i	$0.394496\pi$
$524$	−0.518764	−	0.898525i	−0.0226623	−	0.0392523i
$525$	−1.37915	+	1.58752i	−0.0601910	+	0.0692848i
$526$	−8.27496	+	14.3327i	−0.360806	+	0.624934i
$527$	−5.25689	+	9.10519i	−0.228994	+	0.396628i
$528$	2.51508	−	2.89506i	0.109455	−	0.125991i
$529$	0.604597	+	1.04719i	0.0262868	+	0.0455301i
$530$	12.9168			0.561069
$531$	5.55923	−	4.34884i	0.241250	−	0.188724i
$532$	8.65237			0.375128
$533$	2.08615	+	3.61332i	0.0903612	+	0.156510i
$534$	−3.14203	−	9.11602i	−0.135969	−	0.394489i
$535$	−6.79826	+	11.7749i	−0.293914	+	0.509074i
$536$	−2.28810	+	3.96311i	−0.0988311	+	0.171180i
$537$	−1.76414	−	0.342352i	−0.0761282	−	0.0147736i
$538$	1.49194	+	2.58412i	0.0643222	+	0.111409i
$539$	12.2350			0.527000
$540$	−0.267165	+	5.18928i	−0.0114970	+	0.223311i
$541$	−17.6225			−0.757649			−0.378825	−	0.925468i	$-0.623672\pi$
$541$	−17.6225			−0.757649			−0.378825	+	0.925468i	$0.623672\pi$
$542$	−1.91011	−	3.30841i	−0.0820462	−	0.142108i
$543$	−1.32869	−	0.257848i	−0.0570196	−	0.0110653i
$544$	1.10706	−	1.91748i	0.0474648	−	0.0822114i
$545$	1.68897	−	2.92538i	0.0723476	−	0.125310i
$546$	−0.685253	−	1.98814i	−0.0293261	−	0.0850844i
$547$	6.68044	+	11.5709i	0.285635	+	0.494734i	0.972763	−	0.231802i	$-0.0744622\pi$
$547$	6.68044	+	11.5709i	0.285635	+	0.494734i	−0.687128	+	0.726536i	$0.741129\pi$
$548$	5.57992			0.238362
$549$	−0.990528	−	7.01670i	−0.0422747	−	0.299465i
$550$	−2.21412			−0.0944104
$551$	19.6725	+	34.0738i	0.838078	+	1.45159i
$552$	5.30257	−	6.10370i	0.225693	−	0.259791i
$553$	4.97124	−	8.61045i	0.211399	−	0.366153i
$554$	−1.82597	+	3.16268i	−0.0775782	+	0.134369i
$555$	0.643883	−	0.741162i	0.0273313	−	0.0314606i
$556$	−3.69366	−	6.39760i	−0.156646	−	0.271319i
$557$	30.8961			1.30911			0.654554	−	0.756015i	$-0.272857\pi$
$557$	30.8961			1.30911			0.654554	+	0.756015i	$0.272857\pi$
$558$	−13.2115	−	5.32836i	−0.559288	−	0.225567i
$559$	−1.64728			−0.0696727
$560$	0.607060	+	1.05146i	0.0256530	+	0.0444322i
$561$	−2.76689	−	8.02762i	−0.116818	−	0.338926i
$562$	10.1875	−	17.6452i	0.429732	−	0.744318i
$563$	22.9532	−	39.7561i	0.967361	−	1.67552i	0.264228	−	0.964460i	$-0.414883\pi$
$563$	22.9532	−	39.7561i	0.967361	−	1.67552i	0.703133	−	0.711058i	$-0.251784\pi$
$564$	−1.33626	−	0.259316i	−0.0562665	−	0.0109192i
$565$	2.14975	+	3.72347i	0.0904405	+	0.156648i
$566$	4.77158			0.200564
$567$	2.63047	−	10.6057i	0.110470	−	0.445399i
$568$	−5.72281			−0.240124
$569$	−13.0937	−	22.6789i	−0.548916	−	0.950750i	−0.998349	−	0.0574360i	$-0.981707\pi$
$569$	−13.0937	−	22.6789i	−0.548916	−	0.950750i	0.449434	−	0.893314i	$-0.351626\pi$
$570$	−12.1173	−	2.35151i	−0.507539	−	0.0984938i
$571$	2.41447	−	4.18198i	0.101042	−	0.175010i	−0.811072	−	0.584946i	$-0.801116\pi$
$571$	2.41447	−	4.18198i	0.101042	−	0.175010i	0.912114	+	0.409936i	$0.134449\pi$
$572$	1.10706	−	1.91748i	0.0462885	−	0.0801740i
$573$	5.67807	+	16.4739i	0.237205	+	0.688206i
$574$	2.53284	+	4.38700i	0.105719	+	0.183110i
$575$	−4.66806			−0.194672
$576$	2.78224	+	1.12211i	0.115927	+	0.0467546i
$577$	8.63436			0.359453			0.179726	−	0.983717i	$-0.442479\pi$
$577$	8.63436			0.359453			0.179726	+	0.983717i	$0.442479\pi$
$578$	6.04884	+	10.4769i	0.251598	+	0.435781i
$579$	7.57388	−	8.71816i	0.314760	−	0.362315i
$580$	−2.76049	+	4.78132i	−0.114623	+	0.198533i
$581$	−3.46131	+	5.99517i	−0.143599	+	0.248722i
$582$	17.6976	−	20.3714i	0.733591	−	0.844423i
$583$	−14.2997	−	24.7677i	−0.592231	−	1.02577i
$584$	12.6101			0.521809
$585$	0.419344	+	2.97055i	0.0173377	+	0.122817i
$586$	7.81571			0.322864
$587$	−3.67199	−	6.36007i	−0.151559	−	0.262508i	0.780242	−	0.625478i	$-0.215096\pi$
$587$	−3.67199	−	6.36007i	−0.151559	−	0.262508i	−0.931801	+	0.362970i	$0.881763\pi$
$588$	3.11884	+	9.04876i	0.128619	+	0.373164i
$589$	16.9200	−	29.3063i	0.697177	−	1.20755i
$590$	−1.17636	+	2.03751i	−0.0484299	+	0.0838830i
$591$	−14.5740	−	2.82826i	−0.599495	−	0.116339i
$592$	−0.283418	−	0.490894i	−0.0116484	−	0.0201756i
$593$	40.6821			1.67062			0.835308	−	0.549783i	$-0.185289\pi$
$593$	40.6821			1.67062			0.835308	+	0.549783i	$0.185289\pi$
$594$	10.2461	−	5.23256i	0.420404	−	0.214694i
$595$	2.68821			0.110206
$596$	−2.76449	−	4.78825i	−0.113238	−	0.196134i
$597$	−41.8086	−	8.11345i	−1.71111	−	0.332062i
$598$	2.33403	−	4.04266i	0.0954456	−	0.165317i
$599$	−3.55295	+	6.15388i	−0.145169	+	0.251441i	−0.929436	−	0.368983i	$-0.879706\pi$
$599$	−3.55295	+	6.15388i	−0.145169	+	0.251441i	0.784267	+	0.620424i	$0.213039\pi$
$600$	−0.564403	−	1.63751i	−0.0230417	−	0.0668512i
$601$	−15.9902	−	27.6958i	−0.652252	−	1.12973i	−0.982575	−	0.185866i	$-0.940491\pi$
$601$	−15.9902	−	27.6958i	−0.652252	−	1.12973i	0.330323	−	0.943868i	$-0.392842\pi$
$602$	−2.00000			−0.0815139
$603$	−10.8131	+	8.45883i	−0.440344	+	0.344470i
$604$	−9.03015			−0.367432
$605$	−3.04884	−	5.28074i	−0.123953	−	0.214693i
$606$	−17.6321	+	20.2960i	−0.716256	+	0.824470i
$607$	−7.30880	+	12.6592i	−0.296655	+	0.513822i	−0.975369	−	0.220581i	$-0.929205\pi$
$607$	−7.30880	+	12.6592i	−0.296655	+	0.513822i	0.678713	+	0.734403i	$0.262538\pi$
$608$	−3.56323	+	6.17169i	−0.144508	+	0.250295i
$609$	7.61427	−	8.76465i	0.308546	−	0.355162i
$610$	1.18105	+	2.04563i	0.0478191	+	0.0828251i
$611$	−0.785880			−0.0317933
$612$	5.23174	−	4.09266i	0.211480	−	0.165436i
$613$	33.4584			1.35137			0.675687	−	0.737189i	$-0.263847\pi$
$613$	33.4584			1.35137			0.675687	+	0.737189i	$0.263847\pi$
$614$	3.68444	+	6.38163i	0.148692	+	0.257542i
$615$	−2.35486	−	6.83220i	−0.0949572	−	0.275501i
$616$	1.34410	−	2.32805i	0.0541555	−	0.0938000i
$617$	4.73951	−	8.20906i	0.190805	−	0.330485i	−0.754712	−	0.656056i	$-0.772223\pi$
$617$	4.73951	−	8.20906i	0.190805	−	0.330485i	0.945517	+	0.325572i	$0.105557\pi$
$618$	3.22312	+	0.625484i	0.129653	+	0.0251606i
$619$	−21.7491	−	37.6705i	−0.874169	−	1.51410i	−0.857646	−	0.514241i	$-0.828074\pi$
$619$	−21.7491	−	37.6705i	−0.874169	−	1.51410i	−0.0165228	−	0.999863i	$-0.505260\pi$
$620$	4.74851			0.190705
$621$	21.6021	−	11.0319i	0.866861	−	0.442694i
$622$	−1.46132			−0.0585935
$623$	−3.37950	−	5.85346i	−0.135397	−	0.234514i
$624$	1.70033	+	0.329969i	0.0680677	+	0.0132093i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	16.6222	−	28.7904i	0.664355	−	1.15070i
$627$	8.90562	+	25.8380i	0.355656	+	1.03187i
$628$	0.349028	+	0.604535i	0.0139277	+	0.0241236i
$629$	−1.25504			−0.0500418
$630$	0.509134	+	3.60660i	0.0202844	+	0.143690i
$631$	25.5585			1.01747			0.508733	−	0.860924i	$-0.330114\pi$
$631$	25.5585			1.01747			0.508733	+	0.860924i	$0.330114\pi$
$632$	4.09453	+	7.09193i	0.162871	+	0.282102i
$633$	12.3760	−	14.2458i	0.491903	−	0.566221i
$634$	−6.03193	+	10.4476i	−0.239558	+	0.414927i
$635$	−3.70159	+	6.41133i	−0.146893	+	0.254426i
$636$	14.6725	−	16.8893i	0.581803	−	0.669703i
$637$	2.76296	+	4.78558i	0.109472	+	0.189612i
$638$	12.2241			0.483958
$639$	−15.9222	−	6.42163i	−0.629874	−	0.254036i
$640$	−1.00000			−0.0395285
$641$	−20.7069	−	35.8654i	−0.817873	−	1.41660i	−0.907246	−	0.420600i	$-0.861820\pi$
$641$	−20.7069	−	35.8654i	−0.817873	−	1.41660i	0.0893726	−	0.995998i	$-0.471514\pi$
$642$	7.67392	+	22.2645i	0.302865	+	0.878708i
$643$	19.0663	−	33.0238i	0.751901	−	1.30233i	−0.194999	−	0.980803i	$-0.562470\pi$
$643$	19.0663	−	33.0238i	0.751901	−	1.30233i	0.946900	−	0.321528i	$-0.104196\pi$
$644$	2.83379	−	4.90827i	0.111667	−	0.193413i
$645$	2.80093	+	0.543552i	0.110286	+	0.0214023i
$646$	7.88941	+	13.6649i	0.310405	+	0.537637i
$647$	−11.4804			−0.451342			−0.225671	−	0.974204i	$-0.572457\pi$
$647$	−11.4804			−0.451342			−0.225671	+	0.974204i	$0.572457\pi$
$648$	6.48173	+	6.24397i	0.254627	+	0.245286i
$649$	5.20919			0.204479
$650$	−0.500000	−	0.866025i	−0.0196116	−	0.0339683i
$651$	−9.80284	−	1.90236i	−0.384204	−	0.0745592i
$652$	5.53986	−	9.59531i	0.216957	−	0.375781i
$653$	15.1287	−	26.2037i	0.592032	−	1.02543i	−0.401927	−	0.915672i	$-0.631659\pi$
$653$	15.1287	−	26.2037i	0.592032	−	1.02543i	0.993958	−	0.109757i	$-0.0350074\pi$
$654$	−1.90652	−	5.53143i	−0.0745509	−	0.216296i
$655$	0.518764	+	0.898525i	0.0202698	+	0.0351083i
$656$	−4.17230			−0.162901
$657$	35.0843	+	14.1499i	1.36877	+	0.552040i
$658$	−0.954153			−0.0371967
$659$	14.6532	+	25.3801i	0.570808	+	0.988669i	0.996483	+	0.0837929i	$0.0267034\pi$
$659$	14.6532	+	25.3801i	0.570808	+	0.988669i	−0.425675	+	0.904876i	$0.639963\pi$
$660$	−2.51508	+	2.89506i	−0.0978992	+	0.112690i
$661$	16.4823	−	28.5483i	0.641089	−	1.11040i	−0.344101	−	0.938933i	$-0.611816\pi$
$661$	16.4823	−	28.5483i	0.641089	−	1.11040i	0.985190	−	0.171466i	$-0.0548503\pi$
$662$	12.6488	−	21.9083i	0.491608	−	0.851491i
$663$	2.51508	−	2.89506i	0.0976775	−	0.112435i
$664$	−2.85088	−	4.93788i	−0.110636	−	0.191627i
$665$	−8.65237			−0.335524
$666$	−0.237699	−	1.68381i	−0.00921065	−	0.0652464i
$667$	25.7723			0.997908
$668$	0.808566	+	1.40048i	0.0312844	+	0.0541861i
$669$	−14.3879	−	41.7439i	−0.556269	−	1.61391i
$670$	2.28810	−	3.96311i	0.0883972	−	0.153108i
$671$	2.61498	−	4.52927i	0.100950	−	0.174851i
$672$	2.06440	+	0.400622i	0.0796361	+	0.0154543i
$673$	18.4504	+	31.9571i	0.711212	+	1.23186i	0.964402	+	0.264439i	$0.0851868\pi$
$673$	18.4504	+	31.9571i	0.711212	+	1.23186i	−0.253190	+	0.967416i	$0.581480\pi$
$674$	3.29734			0.127009
$675$	0.267165	−	5.18928i	0.0102832	−	0.199735i
$676$	1.00000			0.0384615
$677$	21.9030	+	37.9371i	0.841800	+	1.45804i	0.888371	+	0.459125i	$0.151837\pi$
$677$	21.9030	+	37.9371i	0.841800	+	1.45804i	−0.0465714	+	0.998915i	$0.514830\pi$
$678$	7.31056	+	1.41870i	0.280760	+	0.0544848i
$679$	9.45794	−	16.3816i	0.362963	−	0.628670i
$680$	−1.10706	+	1.91748i	−0.0424538	+	0.0735321i
$681$	13.0649	+	37.9054i	0.500647	+	1.45254i
$682$	−5.25689	−	9.10519i	−0.201297	−	0.348656i
$683$	−22.1528			−0.847653			−0.423826	−	0.905743i	$-0.639313\pi$
$683$	−22.1528			−0.847653			−0.423826	+	0.905743i	$0.639313\pi$
$684$	−16.8391	+	13.1728i	−0.643858	+	0.503674i
$685$	−5.57992			−0.213198
$686$	7.60398	+	13.1705i	0.290321	+	0.502851i
$687$	−24.1183	+	27.7622i	−0.920171	+	1.05919i
$688$	0.823642	−	1.42659i	0.0314011	−	0.0543882i
$689$	6.45839	−	11.1863i	0.246045	−	0.426163i
$690$	−5.30257	+	6.10370i	−0.201866	+	0.232364i
$691$	−13.4454	−	23.2880i	−0.511485	−	0.885919i	−0.999911	−	0.0133133i	$-0.995762\pi$
$691$	−13.4454	−	23.2880i	−0.511485	−	0.885919i	0.488426	−	0.872605i	$-0.337571\pi$
$692$	5.22276			0.198539
$693$	6.35196	−	4.96898i	0.241291	−	0.188756i
$694$	7.18586			0.272772
$695$	3.69366	+	6.39760i	0.140108	+	0.242675i
$696$	3.11606	+	9.04069i	0.118114	+	0.342686i
$697$	−4.61899	+	8.00032i	−0.174957	+	0.303034i
$698$	4.02091	−	6.96442i	0.152194	−	0.263607i
$699$	−47.2267	−	9.16488i	−1.78628	−	0.346648i
$700$	−0.607060	−	1.05146i	−0.0229447	−	0.0397414i
$701$	41.0685			1.55113			0.775567	−	0.631265i	$-0.217464\pi$
$701$	41.0685			1.55113			0.775567	+	0.631265i	$0.217464\pi$
$702$	4.36047	+	2.82601i	0.164575	+	0.106661i
$703$	4.03953			0.152354
$704$	1.10706	+	1.91748i	0.0417239	+	0.0722679i
$705$	1.33626	+	0.259316i	0.0503263	+	0.00976640i
$706$	−4.13406	+	7.16041i	−0.155588	+	0.269485i
$707$	−9.42293	+	16.3210i	−0.354386	+	0.613814i
$708$	1.32788	+	3.85260i	0.0499048	+	0.144790i
$709$	−17.1461	−	29.6979i	−0.643935	−	1.11533i	−0.984546	−	0.175124i	$-0.943967\pi$
$709$	−17.1461	−	29.6979i	−0.643935	−	1.11533i	0.340612	−	0.940204i	$-0.389366\pi$
$710$	5.72281			0.214773
$711$	3.43403	+	24.3260i	0.128786	+	0.912295i
$712$	5.56699			0.208632
$713$	−11.0832	−	19.1966i	−0.415068	−	0.718919i
$714$	3.05360	−	3.51495i	0.114278	−	0.131544i
$715$	−1.10706	+	1.91748i	−0.0414017	+	0.0717098i
$716$	0.518764	−	0.898525i	0.0193871	−	0.0335795i
$717$	−23.0519	+	26.5347i	−0.860890	+	0.990955i
$718$	−10.8322	−	18.7619i	−0.404253	−	0.700187i
$719$	14.8980			0.555601			0.277800	−	0.960639i	$-0.410395\pi$
$719$	14.8980			0.555601			0.277800	+	0.960639i	$0.410395\pi$
$720$	−2.78224	−	1.12211i	−0.103688	−	0.0418186i
$721$	2.30147			0.0857111
$722$	−15.8932	−	27.5278i	−0.591483	−	1.02448i
$723$	14.9343	+	43.3291i	0.555412	+	1.61143i
$724$	0.390716	−	0.676739i	0.0145208	−	0.0251508i
$725$	2.76049	−	4.78132i	0.102522	−	0.177574i
$726$	−10.3681	−	2.01204i	−0.384795	−	0.0746739i
$727$	−5.94269	−	10.2930i	−0.220402	−	0.381747i	0.734528	−	0.678578i	$-0.237404\pi$
$727$	−5.94269	−	10.2930i	−0.220402	−	0.381747i	−0.954930	+	0.296831i	$0.904070\pi$
$728$	1.21412			0.0449983
$729$	11.0273	+	24.6455i	0.408419	+	0.912794i
$730$	−12.6101			−0.466720
$731$	−1.82364	−	3.15864i	−0.0674498	−	0.116827i
$732$	4.01633	+	0.779416i	0.148448	+	0.0288080i
$733$	−9.25612	+	16.0321i	−0.341883	+	0.592158i	−0.984782	−	0.173792i	$-0.944398\pi$
$733$	−9.25612	+	16.0321i	−0.341883	+	0.592158i	0.642900	+	0.765950i	$0.277731\pi$
$734$	−8.90147	+	15.4178i	−0.328559	+	0.569081i
$735$	−3.11884	−	9.04876i	−0.115040	−	0.333768i
$736$	2.33403	+	4.04266i	0.0860335	+	0.149014i
$737$	−10.1323			−0.373227
$738$	−11.6083	−	4.68179i	−0.427309	−	0.172339i
$739$	−14.3670			−0.528497			−0.264249	−	0.964455i	$-0.585124\pi$
$739$	−14.3670			−0.528497			−0.264249	+	0.964455i	$0.585124\pi$
$740$	0.283418	+	0.490894i	0.0104186	+	0.0180456i
$741$	−8.09513	+	9.31815i	−0.297382	+	0.342311i
$742$	7.84126	−	13.5815i	0.287862	−	0.498591i
$743$	−1.80009	+	3.11784i	−0.0660388	+	0.114383i	−0.897154	−	0.441717i	$-0.854369\pi$
$743$	−1.80009	+	3.11784i	−0.0660388	+	0.114383i	0.831116	+	0.556100i	$0.187703\pi$
$744$	5.39396	−	6.20889i	0.197752	−	0.227629i
$745$	2.76449	+	4.78825i	0.101283	+	0.175428i
$746$	−23.5207			−0.861153
$747$	−2.39100	−	16.9374i	−0.0874821	−	0.619706i
$748$	4.90233			0.179247
$749$	8.25390	+	14.2962i	0.301591	+	0.522371i
$750$	0.564403	+	1.63751i	0.0206091	+	0.0597935i
$751$	13.2668	−	22.9788i	0.484112	−	0.838507i	−0.515721	−	0.856757i	$-0.672476\pi$
$751$	13.2668	−	22.9788i	0.484112	−	0.838507i	0.999833	+	0.0182493i	$0.00580926\pi$
$752$	0.392940	−	0.680592i	0.0143291	−	0.0248187i
$753$	−48.9327	−	9.49595i	−1.78321	−	0.346052i
$754$	2.76049	+	4.78132i	0.100531	+	0.174125i
$755$	9.03015			0.328641
$756$	5.29413	+	3.43112i	0.192546	+	0.124788i
$757$	−6.56678			−0.238674			−0.119337	−	0.992854i	$-0.538077\pi$
$757$	−6.56678			−0.238674			−0.119337	+	0.992854i	$0.538077\pi$
$758$	16.1201	+	27.9209i	0.585510	+	1.01413i
$759$	17.5740	+	3.41044i	0.637896	+	0.123791i
$760$	3.56323	−	6.17169i	0.129252	−	0.223871i
$761$	−1.65657	+	2.86926i	−0.0600505	+	0.104010i	−0.894488	−	0.447092i	$-0.852460\pi$
$761$	−1.65657	+	2.86926i	−0.0600505	+	0.104010i	0.834437	+	0.551103i	$0.185793\pi$
$762$	4.17837	+	12.1228i	0.151367	+	0.439162i
$763$	−2.05061	−	3.55177i	−0.0742372	−	0.128583i
$764$	−10.0603			−0.363969
$765$	−5.23174	+	4.09266i	−0.189154	+	0.147970i
$766$	24.9761			0.902424
$767$	1.17636	+	2.03751i	0.0424758	+	0.0735703i
$768$	−1.13593	+	1.30754i	−0.0409892	+	0.0471819i
$769$	−4.08283	+	7.07167i	−0.147231	+	0.255011i	−0.930203	−	0.367046i	$-0.880369\pi$
$769$	−4.08283	+	7.07167i	−0.147231	+	0.255011i	0.782972	+	0.622057i	$0.213703\pi$
$770$	−1.34410	+	2.32805i	−0.0484381	+	0.0838973i
$771$	0.253395	−	0.291679i	0.00912581	−	0.0105046i
$772$	3.33379	+	5.77430i	0.119986	+	0.207822i
$773$	−39.5554			−1.42271			−0.711355	−	0.702833i	$-0.751918\pi$
$773$	−39.5554			−1.42271			−0.711355	+	0.702833i	$0.751918\pi$
$774$	3.89236	−	3.04490i	0.139908	−	0.109447i
$775$	−4.74851			−0.170572
$776$	7.78996	+	13.4926i	0.279643	+	0.484356i
$777$	−0.388426	−	1.12695i	−0.0139347	−	0.0404290i
$778$	16.6601	−	28.8561i	0.597292	−	1.03454i
$779$	14.8669	−	25.7502i	0.532660	−	0.922595i
$780$	−1.70033	−	0.329969i	−0.0608816	−	0.0118148i
$781$	−6.33549	−	10.9734i	−0.226702	−	0.392659i
$782$	10.3356			0.369602
$783$	−1.47501	+	28.6500i	−0.0527127	+	1.02387i
$784$	−5.52591			−0.197354
$785$	−0.349028	−	0.604535i	−0.0124574	−	0.0215768i
$786$	1.76414	+	0.342352i	0.0629247	+	0.0122113i
$787$	−12.3222	+	21.3426i	−0.439238	+	0.760783i	−0.997631	−	0.0687937i	$-0.978085\pi$
$787$	−12.3222	+	21.3426i	−0.439238	+	0.760783i	0.558393	+	0.829577i	$0.311418\pi$
$788$	4.28564	−	7.42295i	0.152670	−	0.264432i
$789$	−9.34084	−	27.1007i	−0.332543	−	0.964811i
$790$	−4.09453	−	7.09193i	−0.145677	−	0.252319i
$791$	5.22010			0.185605
$792$	0.928477	+	6.57715i	0.0329920	+	0.233709i
$793$	2.36209			0.0838803
$794$	0.350015	+	0.606244i	0.0124216	+	0.0215148i
$795$	−14.6725	+	16.8893i	−0.520380	+	0.599001i
$796$	12.2943	−	21.2943i	0.435759	−	0.754757i
$797$	16.8516	−	29.1879i	0.596916	−	1.03389i	−0.396358	−	0.918096i	$-0.629726\pi$
$797$	16.8516	−	29.1879i	0.596916	−	1.03389i	0.993273	−	0.115792i	$-0.0369407\pi$
$798$	−9.82845	+	11.3134i	−0.347923	+	0.400488i
$799$	−0.870017	−	1.50691i	−0.0307790	−	0.0533107i
$800$	1.00000			0.0353553
$801$	15.4887	+	6.24679i	0.547267	+	0.220719i
$802$	−22.1928			−0.783654
$803$	13.9601	+	24.1796i	0.492641	+	0.853280i
$804$	−2.58283	−	7.49360i	−0.0910893	−	0.264279i
$805$	−2.83379	+	4.90827i	−0.0998781	+	0.172994i
$806$	2.37426	−	4.11233i	0.0836296	−	0.144851i
$807$	−5.07359	−	0.984589i	−0.178599	−	0.0346592i
$808$	−7.76112	−	13.4427i	−0.273035	−	0.472911i
$809$	4.55422			0.160118			0.0800589	−	0.996790i	$-0.474489\pi$
$809$	4.55422			0.160118			0.0800589	+	0.996790i	$0.474489\pi$
$810$	−6.48173	−	6.24397i	−0.227745	−	0.219391i
$811$	1.95039			0.0684873			0.0342437	−	0.999414i	$-0.489098\pi$
$811$	1.95039			0.0684873			0.0342437	+	0.999414i	$0.489098\pi$
$812$	3.35157	+	5.80509i	0.117617	+	0.203719i
$813$	6.49563	+	1.26055i	0.227812	+	0.0442095i
$814$	0.627521	−	1.08690i	0.0219946	−	0.0380957i
$815$	−5.53986	+	9.59531i	−0.194053	+	0.336109i
$816$	1.24966	+	3.62565i	0.0437467	+	0.126923i
$817$	5.86965	+	10.1665i	0.205353	+	0.355682i
$818$	−34.9422			−1.22172
$819$	3.37797	+	1.36238i	0.118036	+	0.0476053i
$820$	4.17230			0.145703
$821$	−13.0156	−	22.5437i	−0.454248	−	0.786780i	0.544397	−	0.838828i	$-0.316759\pi$
$821$	−13.0156	−	22.5437i	−0.454248	−	0.786780i	−0.998645	+	0.0520477i	$0.983425\pi$
$822$	−6.33838	+	7.29599i	−0.221076	+	0.254477i
$823$	−18.1679	+	31.4678i	−0.633294	+	1.09690i	0.353580	+	0.935404i	$0.384964\pi$
$823$	−18.1679	+	31.4678i	−0.633294	+	1.09690i	−0.986874	+	0.161493i	$0.948369\pi$
$824$	−0.947793	+	1.64162i	−0.0330179	+	0.0571887i
$825$	2.51508	−	2.89506i	0.0875637	−	0.100793i
$826$	1.42824	+	2.47378i	0.0496948	+	0.0860739i
$827$	16.7597			0.582793			0.291397	−	0.956602i	$-0.405880\pi$
$827$	16.7597			0.582793			0.291397	+	0.956602i	$0.405880\pi$
$828$	1.95752	+	13.8667i	0.0680286	+	0.481901i
$829$	−47.6817			−1.65605			−0.828027	−	0.560689i	$-0.810536\pi$
$829$	−47.6817			−1.65605			−0.828027	+	0.560689i	$0.810536\pi$
$830$	2.85088	+	4.93788i	0.0989556	+	0.171396i
$831$	−2.06117	−	5.98011i	−0.0715013	−	0.207448i
$832$	−0.500000	+	0.866025i	−0.0173344	+	0.0300240i
$833$	−6.11752	+	10.5958i	−0.211959	+	0.367124i
$834$	12.5609	+	2.43758i	0.434947	+	0.0844066i
$835$	−0.808566	−	1.40048i	−0.0279816	−	0.0484655i
$836$	−15.7788			−0.545722
$837$	21.9744	−	11.2220i	0.759545	−	0.387889i
$838$	29.3965			1.01548
$839$	26.5245	+	45.9417i	0.915727	+	1.58608i	0.805834	+	0.592141i	$0.201717\pi$
$839$	26.5245	+	45.9417i	0.915727	+	1.58608i	0.109892	+	0.993943i	$0.464949\pi$
$840$	−2.06440	−	0.400622i	−0.0712287	−	0.0138228i
$841$	−0.740656	+	1.28285i	−0.0255398	+	0.0442363i
$842$	−20.0782	+	34.7765i	−0.691941	+	1.19848i
$843$	11.4997	+	33.3642i	0.396070	+	1.14912i
$844$	5.44755	+	9.43544i	0.187513	+	0.324781i
$845$	−1.00000			−0.0344010
$846$	1.85695	−	1.45265i	0.0638434	−	0.0499431i
$847$	−7.40331			−0.254381
$848$	6.45839	+	11.1863i	0.221782	+	0.384138i
$849$	−5.42016	+	6.23905i	−0.186020	+	0.214124i
$850$	1.10706	−	1.91748i	0.0379718	−	0.0657692i
$851$	1.32301	−	2.29152i	0.0453523	−	0.0785524i
$852$	6.50069	−	7.48282i	0.222710	−	0.256357i
$853$	16.5256	+	28.6232i	0.565827	+	0.980040i	0.996972	+	0.0777580i	$0.0247762\pi$
$853$	16.5256	+	28.6232i	0.565827	+	0.980040i	−0.431146	+	0.902282i	$0.641891\pi$
$854$	2.86786			0.0981361
$855$	16.8391	−	13.1728i	0.575884	−	0.450500i
$856$	−13.5965			−0.464719
$857$	−6.83856	−	11.8447i	−0.233601	−	0.404608i	0.725264	−	0.688470i	$-0.241718\pi$
$857$	−6.83856	−	11.8447i	−0.233601	−	0.404608i	−0.958865	+	0.283862i	$0.908384\pi$
$858$	1.24966	+	3.62565i	0.0426626	+	0.123778i
$859$	−24.2773	+	42.0495i	−0.828330	+	1.43471i	0.0710167	+	0.997475i	$0.477376\pi$
$859$	−24.2773	+	42.0495i	−0.828330	+	1.43471i	−0.899347	+	0.437235i	$0.855958\pi$
$860$	−0.823642	+	1.42659i	−0.0280860	+	0.0486463i
$861$	−8.61331	−	1.67151i	−0.293541	−	0.0569650i
$862$	−6.64827	−	11.5151i	−0.226441	−	0.392207i
$863$	−19.5932			−0.666959			−0.333480	−	0.942757i	$-0.608223\pi$
$863$	−19.5932			−0.666959			−0.333480	+	0.942757i	$0.608223\pi$
$864$	−4.62763	+	2.36327i	−0.157435	+	0.0804000i
$865$	−5.22276			−0.177579
$866$	−8.30234	−	14.3801i	−0.282125	−	0.488655i
$867$	−20.5700	−	3.99185i	−0.698595	−	0.135570i
$868$	2.88263	−	4.99286i	0.0978428	−	0.169469i
$869$	−9.06577	+	15.7024i	−0.307535	+	0.532666i
$870$	−3.11606	−	9.04069i	−0.105644	−	0.306508i
$871$	−2.28810	−	3.96311i	−0.0775295	−	0.134285i
$872$	3.37794			0.114392
$873$	6.53334	+	46.2809i	0.221120	+	1.56637i
$874$	−33.2667			−1.12526
$875$	0.607060	+	1.05146i	0.0205224	+	0.0355458i
$876$	−14.3241	+	16.4882i	−0.483967	+	0.557086i
$877$	−16.6079	+	28.7657i	−0.560808	+	0.971348i	0.436618	+	0.899647i	$0.356176\pi$
$877$	−16.6079	+	28.7657i	−0.560808	+	0.971348i	−0.997426	+	0.0717012i	$0.977157\pi$
$878$	5.01385	−	8.68425i	0.169209	−	0.293079i
$879$	−8.87807	+	10.2194i	−0.299450	+	0.344692i
$880$	−1.10706	−	1.91748i	−0.0373190	−	0.0646384i
$881$	−10.2452			−0.345170			−0.172585	−	0.984995i	$-0.555212\pi$
$881$	−10.2452			−0.345170			−0.172585	+	0.984995i	$0.555212\pi$
$882$	−15.3744	−	6.20069i	−0.517684	−	0.208788i
$883$	−21.7252			−0.731110			−0.365555	−	0.930790i	$-0.619121\pi$
$883$	−21.7252			−0.731110			−0.365555	+	0.930790i	$0.619121\pi$
$884$	1.10706	+	1.91748i	0.0372345	+	0.0644920i
$885$	−1.32788	−	3.85260i	−0.0446362	−	0.129504i
$886$	−6.81935	+	11.8115i	−0.229100	+	0.396814i
$887$	18.4535	−	31.9623i	0.619607	−	1.07319i	−0.369951	−	0.929051i	$-0.620625\pi$
$887$	18.4535	−	31.9623i	0.619607	−	1.07319i	0.989557	−	0.144139i	$-0.0460412\pi$
$888$	0.963807	+	0.187038i	0.0323432	+	0.00627658i
$889$	4.49417	+	7.78413i	0.150730	+	0.261071i
$890$	−5.56699			−0.186606
$891$	−4.79704	+	19.3411i	−0.160707	+	0.647950i
$892$	25.4923			0.853544
$893$	2.80027	+	4.85021i	0.0937075	+	0.162306i
$894$	9.40110	+	1.82439i	0.314420	+	0.0610169i
$895$	−0.518764	+	0.898525i	−0.0173404	+	0.0300344i
$896$	−0.607060	+	1.05146i	−0.0202804	+	0.0351268i
$897$	2.63467	+	7.64401i	0.0879691	+	0.255226i
$898$	17.9835	+	31.1483i	0.600117	+	1.03943i
$899$	26.2165			0.874368
$900$	2.78224	+	1.12211i	0.0927414	+	0.0374037i
$901$	28.5993			0.952781
$902$	−4.61899	−	8.00032i	−0.153795	−	0.266382i
$903$	2.27185	−	2.61509i	0.0756025	−	0.0870247i
$904$	−2.14975	+	3.72347i	−0.0714995	+	0.123841i
$905$	−0.390716	+	0.676739i	−0.0129878	+	0.0224956i
$906$	10.2576	−	11.8073i	0.340785	−	0.392272i
$907$	−8.97051	−	15.5374i	−0.297861	−	0.515910i	0.677786	−	0.735260i	$-0.262940\pi$
$907$	−8.97051	−	15.5374i	−0.297861	−	0.515910i	−0.975646	+	0.219350i	$0.929606\pi$
$908$	−23.1481			−0.768198
$909$	−6.50916	−	46.1096i	−0.215895	−	1.52936i
$910$	−1.21412			−0.0402477
$911$	−13.2403	−	22.9328i	−0.438670	−	0.759798i	0.558917	−	0.829223i	$-0.311217\pi$
$911$	−13.2403	−	22.9328i	−0.438670	−	0.759798i	−0.997587	+	0.0694250i	$0.977884\pi$
$912$	−4.02220	−	11.6697i	−0.133188	−	0.386421i
$913$	6.31220	−	10.9330i	0.208903	−	0.361831i
$914$	−21.0006	+	36.3740i	−0.694636	+	1.20315i
$915$	−4.01633	−	0.779416i	−0.132776	−	0.0257667i
$916$	−10.6161	−	18.3877i	−0.350767	−	0.607547i
$917$	1.25968			0.0415984
$918$	−0.591535	+	11.4897i	−0.0195236	+	0.379216i
$919$	40.5779			1.33854			0.669271	−	0.743019i	$-0.266607\pi$
$919$	40.5779			1.33854			0.669271	+	0.743019i	$0.266607\pi$
$920$	−2.33403	−	4.04266i	−0.0769507	−	0.133283i
$921$	−12.5295	−	2.43150i	−0.412862	−	0.0801206i
$922$	−5.59495	+	9.69073i	−0.184260	+	0.319147i
$923$	2.86140	−	4.95610i	0.0941843	−	0.163132i
$924$	1.51723	+	4.40197i	0.0499133	+	0.144814i
$925$	−0.283418	−	0.490894i	−0.00931872	−	0.0161405i
$926$	−29.5143			−0.969900
$927$	−4.47907	+	3.50387i	−0.147112	+	0.115082i
$928$	−5.52099			−0.181235
$929$	5.01659	+	8.68899i	0.164589	+	0.285077i	0.936509	−	0.350643i	$-0.114037\pi$
$929$	5.01659	+	8.68899i	0.164589	+	0.285077i	−0.771920	+	0.635719i	$0.780704\pi$
$930$	−5.39396	+	6.20889i	−0.176875	+	0.203597i
$931$	19.6901	−	34.1042i	0.645316	−	1.11772i
$932$	13.8875	−	24.0539i	0.454900	−	0.787910i
$933$	1.65995	−	1.91074i	0.0543443	−	0.0625547i
$934$	11.2902	+	19.5552i	0.369427	+	0.639866i
$935$	−4.90233			−0.160323
$936$	−2.36290	+	1.84844i	−0.0772337	+	0.0604180i
$937$	6.84218			0.223524			0.111762	−	0.993735i	$-0.464351\pi$
$937$	6.84218			0.223524			0.111762	+	0.993735i	$0.464351\pi$
$938$	−2.77803	−	4.81169i	−0.0907060	−	0.157107i
$939$	18.7632	+	54.4380i	0.612314	+	1.77652i
$940$	−0.392940	+	0.680592i	−0.0128163	+	0.0221985i
$941$	−15.7075	+	27.2061i	−0.512048	+	0.886894i	0.487854	+	0.872925i	$0.337780\pi$
$941$	−15.7075	+	27.2061i	−0.512048	+	0.886894i	−0.999902	+	0.0139687i	$0.995553\pi$
$942$	−1.18693	−	0.230337i	−0.0386722	−	0.00750478i
$943$	−9.73828	−	16.8672i	−0.317122	−	0.549272i
$944$	−2.35272			−0.0765744
$945$	−5.29413	−	3.43112i	−0.172218	−	0.111614i
$946$	3.64728			0.118583
$947$	16.1942	+	28.0492i	0.526242	+	0.911478i	0.999533	+	0.0305715i	$0.00973273\pi$
$947$	16.1942	+	28.0492i	0.526242	+	0.911478i	−0.473291	+	0.880906i	$0.656934\pi$
$948$	−13.9241	−	2.70213i	−0.452233	−	0.0877611i
$949$	−6.30504	+	10.9206i	−0.204670	+	0.354499i
$950$	−3.56323	+	6.17169i	−0.115606	+	0.200236i
$951$	−6.80888	−	19.7547i	−0.220793	−	0.640591i
$952$	1.34410	+	2.32805i	0.0435626	+	0.0754527i
$953$	11.5359			0.373683			0.186842	−	0.982390i	$-0.440175\pi$
$953$	11.5359			0.373683			0.186842	+	0.982390i	$0.440175\pi$
$954$	5.41657	+	38.3699i	0.175368	+	1.24227i
$955$	10.0603			0.325544
$956$	−10.1468	−	17.5747i	−0.328170	−	0.568406i
$957$	−13.8857	+	15.9836i	−0.448861	+	0.516676i
$958$	2.37648	−	4.11618i	0.0767806	−	0.132988i
$959$	−3.38735	+	5.86705i	−0.109383	+	0.189457i
$960$	1.13593	−	1.30754i	0.0366619	−	0.0422008i
$961$	4.22582	+	7.31934i	0.136317	+	0.236108i
$962$	0.566835			0.0182755
$963$	−37.8288	−	15.2568i	−1.21902	−	0.491643i
$964$	−26.4603			−0.852228
$965$	−3.33379	−	5.77430i	−0.107319	−	0.185881i
$966$	3.19881	+	9.28075i	0.102920	+	0.298603i
$967$	−9.56105	+	16.5602i	−0.307463	+	0.532541i	−0.977807	−	0.209509i	$-0.932813\pi$
$967$	−9.56105	+	16.5602i	−0.307463	+	0.532541i	0.670344	+	0.742051i	$0.266147\pi$
$968$	3.04884	−	5.28074i	0.0979933	−	0.169729i
$969$	−26.8292	−	5.20652i	−0.861878	−	0.167257i
$970$	−7.78996	−	13.4926i	−0.250121	−	0.433221i
$971$	0.228531			0.00733391			0.00366696	−	0.999993i	$-0.498833\pi$
$971$	0.228531			0.00733391			0.00366696	+	0.999993i	$0.498833\pi$
$972$	−15.5270	+	1.38247i	−0.498030	+	0.0443426i
$973$	8.96909			0.287536
$974$	2.13367	+	3.69563i	0.0683672	+	0.118416i
$975$	1.70033	+	0.329969i	0.0544541	+	0.0105675i
$976$	−1.18105	+	2.04563i	−0.0378043	+	0.0654790i
$977$	0.329764	−	0.571168i	0.0105501	−	0.0182733i	−0.860702	−	0.509109i	$-0.829975\pi$
$977$	0.329764	−	0.571168i	0.0105501	−	0.0182733i	0.871252	+	0.490836i	$0.163308\pi$
$978$	6.25343	+	18.1432i	0.199963	+	0.580155i
$979$	6.16299	+	10.6746i	0.196970	+	0.341162i
$980$	5.52591			0.176519
$981$	9.39825	+	3.79043i	0.300063	+	0.121019i
$982$	38.6389			1.23302
$983$	−8.43602	−	14.6116i	−0.269067	−	0.466038i	0.699554	−	0.714580i	$-0.253382\pi$
$983$	−8.43602	−	14.6116i	−0.269067	−	0.466038i	−0.968621	+	0.248542i	$0.920049\pi$
$984$	4.73943	−	5.45547i	0.151087	−	0.173914i
$985$	−4.28564	+	7.42295i	−0.136552	+	0.236515i
$986$	−6.11206	+	10.5864i	−0.194648	+	0.337140i
$987$	1.08385	−	1.24760i	0.0344992	−	0.0397114i
$988$	−3.56323	−	6.17169i	−0.113361	−	0.196348i
$989$	7.68963			0.244516
$990$	−0.928477	−	6.57715i	−0.0295089	−	0.209035i
$991$	−36.9068			−1.17238			−0.586192	−	0.810172i	$-0.699373\pi$
$991$	−36.9068			−1.17238			−0.586192	+	0.810172i	$0.699373\pi$
$992$	2.37426	+	4.11233i	0.0753827	+	0.130567i
$993$	14.2780	+	41.4251i	0.453099	+	1.31458i
$994$	3.47409	−	6.01729i	0.110191	−	0.190857i
$995$	−12.2943	+	21.2943i	−0.389755	+	0.675075i
$996$	9.69488	+	1.88140i	0.307194	+	0.0596146i
$997$	−11.5484	−	20.0024i	−0.365742	−	0.633484i	0.623153	−	0.782100i	$-0.285851\pi$
$997$	−11.5484	−	20.0024i	−0.365742	−	0.633484i	−0.988895	+	0.148616i	$0.952518\pi$
$998$	21.8698			0.692277
$999$	2.47167	+	1.60188i	0.0782001	+	0.0506814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.j.i.391.5	✓	10
3.2	odd	2		3510.2.j.j.1171.2		10
9.2	odd	6		3510.2.j.j.2341.2		10
9.7	even	3	inner	1170.2.j.i.781.5	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.j.i.391.5	✓	10	1.1	even	1	trivial
1170.2.j.i.781.5	yes	10	9.7	even	3	inner
3510.2.j.j.1171.2		10	3.2	odd	2
3510.2.j.j.2341.2		10	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.70033 + 0.329969i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.564403 - 1.63751i) q^{6} +(-0.607060 - 1.05146i) q^{7} +1.00000 q^{8} +(2.78224 + 1.12211i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.70033 + 0.329969i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.564403 - 1.63751i) q^{6} +(-0.607060 - 1.05146i) q^{7} +1.00000 q^{8} +(2.78224 + 1.12211i) q^{9} -1.00000 q^{10} +(1.10706 + 1.91748i) q^{11} +(-1.13593 + 1.30754i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-0.607060 + 1.05146i) q^{14} +(1.13593 - 1.30754i) q^{15} +(-0.500000 - 0.866025i) q^{16} -2.21412 q^{17} +(-0.419344 - 2.97055i) q^{18} +7.12645 q^{19} +(0.500000 + 0.866025i) q^{20} +(-0.685253 - 1.98814i) q^{21} +(1.10706 - 1.91748i) q^{22} +(2.33403 - 4.04266i) q^{23} +(1.70033 + 0.329969i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +(4.36047 + 2.82601i) q^{27} +1.21412 q^{28} +(2.76049 + 4.78132i) q^{29} +(-1.70033 - 0.329969i) q^{30} +(2.37426 - 4.11233i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.24966 + 3.62565i) q^{33} +(1.10706 + 1.91748i) q^{34} -1.21412 q^{35} +(-2.36290 + 1.84844i) q^{36} +0.566835 q^{37} +(-3.56323 - 6.17169i) q^{38} +(-1.13593 + 1.30754i) q^{39} +(0.500000 - 0.866025i) q^{40} +(2.08615 - 3.61332i) q^{41} +(-1.37915 + 1.58752i) q^{42} +(0.823642 + 1.42659i) q^{43} -2.21412 q^{44} +(2.36290 - 1.84844i) q^{45} -4.66806 q^{46} +(0.392940 + 0.680592i) q^{47} +(-0.564403 - 1.63751i) q^{48} +(2.76296 - 4.78558i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-3.76473 - 0.730590i) q^{51} +(-0.500000 - 0.866025i) q^{52} -12.9168 q^{53} +(0.267165 - 5.18928i) q^{54} +2.21412 q^{55} +(-0.607060 - 1.05146i) q^{56} +(12.1173 + 2.35151i) q^{57} +(2.76049 - 4.78132i) q^{58} +(1.17636 - 2.03751i) q^{59} +(0.564403 + 1.63751i) q^{60} +(-1.18105 - 2.04563i) q^{61} -4.74851 q^{62} +(-0.509134 - 3.60660i) q^{63} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +(2.51508 - 2.89506i) q^{66} +(-2.28810 + 3.96311i) q^{67} +(1.10706 - 1.91748i) q^{68} +(5.30257 - 6.10370i) q^{69} +(0.607060 + 1.05146i) q^{70} -5.72281 q^{71} +(2.78224 + 1.12211i) q^{72} +12.6101 q^{73} +(-0.283418 - 0.490894i) q^{74} +(-0.564403 - 1.63751i) q^{75} +(-3.56323 + 6.17169i) q^{76} +(1.34410 - 2.32805i) q^{77} +(1.70033 + 0.329969i) q^{78} +(4.09453 + 7.09193i) q^{79} -1.00000 q^{80} +(6.48173 + 6.24397i) q^{81} -4.17230 q^{82} +(-2.85088 - 4.93788i) q^{83} +(2.06440 + 0.400622i) q^{84} +(-1.10706 + 1.91748i) q^{85} +(0.823642 - 1.42659i) q^{86} +(3.11606 + 9.04069i) q^{87} +(1.10706 + 1.91748i) q^{88} +5.56699 q^{89} +(-2.78224 - 1.12211i) q^{90} +1.21412 q^{91} +(2.33403 + 4.04266i) q^{92} +(5.39396 - 6.20889i) q^{93} +(0.392940 - 0.680592i) q^{94} +(3.56323 - 6.17169i) q^{95} +(-1.13593 + 1.30754i) q^{96} +(7.78996 + 13.4926i) q^{97} -5.52591 q^{98} +(0.928477 + 6.57715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - q^{3} - 5 q^{4} + 5 q^{5} - q^{6} - 4 q^{7} + 10 q^{8} - q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - q^3 - 5 * q^4 + 5 * q^5 - q^6 - 4 * q^7 + 10 * q^8 - q^9	\( 10 q - 5 q^{2} - q^{3} - 5 q^{4} + 5 q^{5} - q^{6} - 4 q^{7} + 10 q^{8} - q^{9} - 10 q^{10} + 9 q^{11} + 2 q^{12} - 5 q^{13} - 4 q^{14} - 2 q^{15} - 5 q^{16} - 18 q^{17} + 2 q^{18} - 10 q^{19} + 5 q^{20} - 14 q^{21} + 9 q^{22} + 12 q^{23} - q^{24} - 5 q^{25} + 10 q^{26} + 2 q^{27} + 8 q^{28} + 6 q^{29} + q^{30} - 4 q^{31} - 5 q^{32} + 15 q^{33} + 9 q^{34} - 8 q^{35} - q^{36} + 20 q^{37} + 5 q^{38} + 2 q^{39} + 5 q^{40} + 9 q^{41} - 2 q^{42} - q^{43} - 18 q^{44} + q^{45} - 24 q^{46} + 6 q^{47} - q^{48} + 3 q^{49} - 5 q^{50} - 15 q^{51} - 5 q^{52} - 12 q^{53} - q^{54} + 18 q^{55} - 4 q^{56} + 25 q^{57} + 6 q^{58} + 21 q^{59} + q^{60} + 2 q^{61} + 8 q^{62} - 20 q^{63} + 10 q^{64} + 5 q^{65} - 7 q^{67} + 9 q^{68} - 36 q^{69} + 4 q^{70} - 12 q^{71} - q^{72} - 58 q^{73} - 10 q^{74} - q^{75} + 5 q^{76} + 36 q^{77} - q^{78} + 8 q^{79} - 10 q^{80} + 35 q^{81} - 18 q^{82} + 6 q^{83} + 16 q^{84} - 9 q^{85} - q^{86} - 48 q^{87} + 9 q^{88} - 36 q^{89} + q^{90} + 8 q^{91} + 12 q^{92} + 22 q^{93} + 6 q^{94} - 5 q^{95} + 2 q^{96} + 11 q^{97} - 6 q^{98} + 18 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - q^3 - 5 * q^4 + 5 * q^5 - q^6 - 4 * q^7 + 10 * q^8 - q^9 - 10 * q^10 + 9 * q^11 + 2 * q^12 - 5 * q^13 - 4 * q^14 - 2 * q^15 - 5 * q^16 - 18 * q^17 + 2 * q^18 - 10 * q^19 + 5 * q^20 - 14 * q^21 + 9 * q^22 + 12 * q^23 - q^24 - 5 * q^25 + 10 * q^26 + 2 * q^27 + 8 * q^28 + 6 * q^29 + q^30 - 4 * q^31 - 5 * q^32 + 15 * q^33 + 9 * q^34 - 8 * q^35 - q^36 + 20 * q^37 + 5 * q^38 + 2 * q^39 + 5 * q^40 + 9 * q^41 - 2 * q^42 - q^43 - 18 * q^44 + q^45 - 24 * q^46 + 6 * q^47 - q^48 + 3 * q^49 - 5 * q^50 - 15 * q^51 - 5 * q^52 - 12 * q^53 - q^54 + 18 * q^55 - 4 * q^56 + 25 * q^57 + 6 * q^58 + 21 * q^59 + q^60 + 2 * q^61 + 8 * q^62 - 20 * q^63 + 10 * q^64 + 5 * q^65 - 7 * q^67 + 9 * q^68 - 36 * q^69 + 4 * q^70 - 12 * q^71 - q^72 - 58 * q^73 - 10 * q^74 - q^75 + 5 * q^76 + 36 * q^77 - q^78 + 8 * q^79 - 10 * q^80 + 35 * q^81 - 18 * q^82 + 6 * q^83 + 16 * q^84 - 9 * q^85 - q^86 - 48 * q^87 + 9 * q^88 - 36 * q^89 + q^90 + 8 * q^91 + 12 * q^92 + 22 * q^93 + 6 * q^94 - 5 * q^95 + 2 * q^96 + 11 * q^97 - 6 * q^98 + 18 * q^99

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