LMFDB - Embedded newform 231.2.i.f.100.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(67,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("231.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.i (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 15x^{8} + 72x^{6} + 120x^{4} + 72x^{2} + 12 $ x^10 + 15x^8 + 72x^6 + 120x^4 + 72x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.2
Root			$-1.21103i$ of defining polynomial
Character	$\chi$	$=$	231.100
Dual form			231.2.i.f.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17616 + 2.03717i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.76671 - 3.06003i) q^{4} +(2.05761 - 3.56389i) q^{5} -2.35232 q^{6} +(2.51585 + 0.818848i) q^{7} +3.60708 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.17616 + 2.03717i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.76671 - 3.06003i) q^{4} +(2.05761 - 3.56389i) q^{5} -2.35232 q^{6} +(2.51585 + 0.818848i) q^{7} +3.60708 q^{8} +(-0.500000 + 0.866025i) q^{9} +(4.84017 + 8.38342i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.76671 - 3.06003i) q^{12} +5.39388 q^{13} +(-4.62717 + 4.16211i) q^{14} +4.11523 q^{15} +(-0.709093 + 1.22819i) q^{16} +(-1.17616 - 2.03717i) q^{17} +(-1.17616 - 2.03717i) q^{18} +(-2.87310 + 4.97636i) q^{19} -14.5408 q^{20} +(0.548780 + 2.58821i) q^{21} +2.35232 q^{22} +(-0.709093 + 1.22819i) q^{23} +(1.80354 + 3.12382i) q^{24} +(-5.96755 - 10.3361i) q^{25} +(-6.34407 + 10.9883i) q^{26} -1.00000 q^{27} +(-1.93907 - 9.14522i) q^{28} -5.13289 q^{29} +(-4.84017 + 8.38342i) q^{30} +(0.266707 + 0.461950i) q^{31} +(1.93907 + 3.35856i) q^{32} +(0.500000 - 0.866025i) q^{33} +5.53341 q^{34} +(8.09493 - 7.28133i) q^{35} +3.53341 q^{36} +(-1.20529 + 2.08763i) q^{37} +(-6.75846 - 11.7060i) q^{38} +(2.69694 + 4.67124i) q^{39} +(7.42198 - 12.8552i) q^{40} +5.68034 q^{41} +(-5.91808 - 1.92619i) q^{42} +3.42461 q^{43} +(-1.76671 + 3.06003i) q^{44} +(2.05761 + 3.56389i) q^{45} +(-1.66802 - 2.88909i) q^{46} +(-4.47135 + 7.74460i) q^{47} -1.41819 q^{48} +(5.65897 + 4.12020i) q^{49} +28.0752 q^{50} +(1.17616 - 2.03717i) q^{51} +(-9.52941 - 16.5054i) q^{52} +(-1.80285 - 3.12263i) q^{53} +(1.17616 - 2.03717i) q^{54} -4.11523 q^{55} +(9.07487 + 2.95365i) q^{56} -5.74620 q^{57} +(6.03711 - 10.4566i) q^{58} +(-0.709093 - 1.22819i) q^{59} +(-7.27040 - 12.5927i) q^{60} +(-1.88214 + 3.25996i) q^{61} -1.25476 q^{62} +(-1.96707 + 1.76936i) q^{63} -11.9590 q^{64} +(11.0985 - 19.2232i) q^{65} +(1.17616 + 2.03717i) q^{66} +(-1.01195 - 1.75274i) q^{67} +(-4.15586 + 7.19816i) q^{68} -1.41819 q^{69} +(5.31237 + 25.0548i) q^{70} +4.10440 q^{71} +(-1.80354 + 3.12382i) q^{72} +(-3.23719 - 5.60698i) q^{73} +(-2.83524 - 4.91077i) q^{74} +(5.96755 - 10.3361i) q^{75} +20.3037 q^{76} +(-0.548780 - 2.58821i) q^{77} -12.6881 q^{78} +(-5.09766 + 8.82941i) q^{79} +(2.91808 + 5.05426i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.68099 + 11.5718i) q^{82} -16.0019 q^{83} +(6.95046 - 6.25189i) q^{84} -9.68034 q^{85} +(-4.02789 + 6.97652i) q^{86} +(-2.56645 - 4.44522i) q^{87} +(-1.80354 - 3.12382i) q^{88} +(4.36999 - 7.56904i) q^{89} -9.68034 q^{90} +(13.5702 + 4.41677i) q^{91} +5.01104 q^{92} +(-0.266707 + 0.461950i) q^{93} +(-10.5180 - 18.2178i) q^{94} +(11.8235 + 20.4788i) q^{95} +(-1.93907 + 3.35856i) q^{96} -17.7919 q^{97} +(-15.0494 + 6.68228i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9} - 2 q^{10} - 5 q^{11} + 10 q^{12} + 10 q^{13} - 10 q^{14} + 8 q^{15} - 16 q^{16} - 2 q^{17} - 2 q^{18} + 3 q^{19} - 16 q^{20} - 2 q^{21} + 4 q^{22} - 16 q^{23} + 6 q^{24} - 7 q^{25} + 10 q^{26} - 10 q^{27} + 4 q^{28} + 2 q^{30} - 5 q^{31} - 4 q^{32} + 5 q^{33} + 40 q^{34} + 26 q^{35} + 20 q^{36} - 15 q^{37} - 6 q^{38} + 5 q^{39} + 6 q^{40} - 44 q^{41} - 14 q^{42} + 6 q^{43} - 10 q^{44} + 4 q^{45} - 16 q^{46} + 2 q^{47} - 32 q^{48} + 31 q^{49} + 68 q^{50} + 2 q^{51} - 40 q^{52} - 6 q^{53} + 2 q^{54} - 8 q^{55} - 12 q^{56} + 6 q^{57} - 12 q^{58} - 16 q^{59} - 8 q^{60} - 12 q^{61} - 8 q^{62} - q^{63} - 8 q^{64} + 28 q^{65} + 2 q^{66} - 7 q^{67} - 10 q^{68} - 32 q^{69} + 32 q^{70} + 48 q^{71} - 6 q^{72} - 17 q^{73} + 36 q^{74} + 7 q^{75} + 60 q^{76} + 2 q^{77} + 20 q^{78} - 7 q^{79} - 16 q^{80} - 5 q^{81} - 8 q^{82} - 24 q^{83} - 28 q^{84} + 4 q^{85} + 18 q^{86} - 6 q^{88} + 6 q^{89} + 4 q^{90} + 11 q^{91} + 136 q^{92} + 5 q^{93} - 82 q^{94} + 18 q^{95} + 4 q^{96} - 28 q^{97} - 38 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9 - 2 * q^10 - 5 * q^11 + 10 * q^12 + 10 * q^13 - 10 * q^14 + 8 * q^15 - 16 * q^16 - 2 * q^17 - 2 * q^18 + 3 * q^19 - 16 * q^20 - 2 * q^21 + 4 * q^22 - 16 * q^23 + 6 * q^24 - 7 * q^25 + 10 * q^26 - 10 * q^27 + 4 * q^28 + 2 * q^30 - 5 * q^31 - 4 * q^32 + 5 * q^33 + 40 * q^34 + 26 * q^35 + 20 * q^36 - 15 * q^37 - 6 * q^38 + 5 * q^39 + 6 * q^40 - 44 * q^41 - 14 * q^42 + 6 * q^43 - 10 * q^44 + 4 * q^45 - 16 * q^46 + 2 * q^47 - 32 * q^48 + 31 * q^49 + 68 * q^50 + 2 * q^51 - 40 * q^52 - 6 * q^53 + 2 * q^54 - 8 * q^55 - 12 * q^56 + 6 * q^57 - 12 * q^58 - 16 * q^59 - 8 * q^60 - 12 * q^61 - 8 * q^62 - q^63 - 8 * q^64 + 28 * q^65 + 2 * q^66 - 7 * q^67 - 10 * q^68 - 32 * q^69 + 32 * q^70 + 48 * q^71 - 6 * q^72 - 17 * q^73 + 36 * q^74 + 7 * q^75 + 60 * q^76 + 2 * q^77 + 20 * q^78 - 7 * q^79 - 16 * q^80 - 5 * q^81 - 8 * q^82 - 24 * q^83 - 28 * q^84 + 4 * q^85 + 18 * q^86 - 6 * q^88 + 6 * q^89 + 4 * q^90 + 11 * q^91 + 136 * q^92 + 5 * q^93 - 82 * q^94 + 18 * q^95 + 4 * q^96 - 28 * q^97 - 38 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.17616	+	2.03717i	−0.831671	+	1.44050i	0.0650412	+	0.997883i	$0.479282\pi$
$2$	−1.17616	+	2.03717i	−0.831671	+	1.44050i	−0.896712	+	0.442614i	$0.854051\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.76671	−	3.06003i	−0.883354	−	1.53001i
$5$	2.05761	−	3.56389i	0.920193	−	1.59382i	0.121077	−	0.992643i	$-0.461365\pi$
$5$	2.05761	−	3.56389i	0.920193	−	1.59382i	0.799115	−	0.601178i	$-0.205302\pi$
$6$	−2.35232			−0.960331
$7$	2.51585	+	0.818848i	0.950901	+	0.309496i
$7$	2.51585	+	0.818848i	0.950901	+	0.309496i
$8$	3.60708			1.27530
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	4.84017	+	8.38342i	1.53060	+	2.65107i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	1.76671	−	3.06003i	0.510004	−	0.883354i
$13$	5.39388			1.49599			0.747997	−	0.663703i	$-0.231016\pi$
$13$	5.39388			1.49599			0.747997	+	0.663703i	$0.231016\pi$
$14$	−4.62717	+	4.16211i	−1.23666	+	1.11237i
$15$	4.11523			1.06255
$16$	−0.709093	+	1.22819i	−0.177273	+	0.307046i
$17$	−1.17616	−	2.03717i	−0.285261	−	0.494086i	0.687412	−	0.726268i	$-0.258747\pi$
$17$	−1.17616	−	2.03717i	−0.285261	−	0.494086i	−0.972672	+	0.232182i	$0.925414\pi$
$18$	−1.17616	−	2.03717i	−0.277224	−	0.480166i
$19$	−2.87310	+	4.97636i	−0.659135	+	1.14165i	0.321706	+	0.946840i	$0.395744\pi$
$19$	−2.87310	+	4.97636i	−0.659135	+	1.14165i	−0.980840	+	0.194815i	$0.937589\pi$
$20$	−14.5408			−3.25142
$21$	0.548780	+	2.58821i	0.119754	+	0.564794i
$22$	2.35232			0.501517
$23$	−0.709093	+	1.22819i	−0.147856	+	0.256094i	−0.930435	−	0.366457i	$-0.880571\pi$
$23$	−0.709093	+	1.22819i	−0.147856	+	0.256094i	0.782579	+	0.622552i	$0.213904\pi$
$24$	1.80354	+	3.12382i	0.368146	+	0.637648i
$25$	−5.96755	−	10.3361i	−1.19351	−	2.06722i
$26$	−6.34407	+	10.9883i	−1.24417	+	2.15497i
$27$	−1.00000			−0.192450
$28$	−1.93907	−	9.14522i	−0.366449	−	1.72828i
$29$	−5.13289			−0.953155			−0.476577	−	0.879133i	$-0.658123\pi$
$29$	−5.13289			−0.953155			−0.476577	+	0.879133i	$0.658123\pi$
$30$	−4.84017	+	8.38342i	−0.883690	+	1.53060i
$31$	0.266707	+	0.461950i	0.0479020	+	0.0829687i	0.888982	−	0.457942i	$-0.151413\pi$
$31$	0.266707	+	0.461950i	0.0479020	+	0.0829687i	−0.841080	+	0.540910i	$0.818080\pi$
$32$	1.93907	+	3.35856i	0.342782	+	0.593716i
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$	5.53341			0.948973
$35$	8.09493	−	7.28133i	1.36829	−	1.23077i
$36$	3.53341			0.588902
$37$	−1.20529	+	2.08763i	−0.198149	+	0.343204i	−0.947928	−	0.318484i	$-0.896826\pi$
$37$	−1.20529	+	2.08763i	−0.198149	+	0.343204i	0.749779	+	0.661688i	$0.230160\pi$
$38$	−6.75846	−	11.7060i	−1.09637	−	1.89896i
$39$	2.69694	+	4.67124i	0.431856	+	0.747997i
$40$	7.42198	−	12.8552i	1.17352	−	2.03259i
$41$	5.68034			0.887119			0.443560	−	0.896245i	$-0.353715\pi$
$41$	5.68034			0.887119			0.443560	+	0.896245i	$0.353715\pi$
$42$	−5.91808	−	1.92619i	−0.913180	−	0.297218i
$43$	3.42461			0.522248			0.261124	−	0.965305i	$-0.415907\pi$
$43$	3.42461			0.522248			0.261124	+	0.965305i	$0.415907\pi$
$44$	−1.76671	+	3.06003i	−0.266341	+	0.461316i
$45$	2.05761	+	3.56389i	0.306731	+	0.531274i
$46$	−1.66802	−	2.88909i	−0.245935	−	0.425973i
$47$	−4.47135	+	7.74460i	−0.652213	+	1.12967i	0.330371	+	0.943851i	$0.392826\pi$
$47$	−4.47135	+	7.74460i	−0.652213	+	1.12967i	−0.982585	+	0.185816i	$0.940507\pi$
$48$	−1.41819			−0.204698
$49$	5.65897	+	4.12020i	0.808425	+	0.588599i
$50$	28.0752			3.97043
$51$	1.17616	−	2.03717i	0.164695	−	0.285261i
$52$	−9.52941	−	16.5054i	−1.32149	−	2.28889i
$53$	−1.80285	−	3.12263i	−0.247641	−	0.428927i	0.715230	−	0.698889i	$-0.246322\pi$
$53$	−1.80285	−	3.12263i	−0.247641	−	0.428927i	−0.962871	+	0.269963i	$0.912989\pi$
$54$	1.17616	−	2.03717i	0.160055	−	0.277224i
$55$	−4.11523			−0.554897
$56$	9.07487	+	2.95365i	1.21268	+	0.394699i
$57$	−5.74620			−0.761103
$58$	6.03711	−	10.4566i	0.792711	−	1.37302i
$59$	−0.709093	−	1.22819i	−0.0923161	−	0.159896i	0.816169	−	0.577813i	$-0.196094\pi$
$59$	−0.709093	−	1.22819i	−0.0923161	−	0.159896i	−0.908485	+	0.417917i	$0.862760\pi$
$60$	−7.27040	−	12.5927i	−0.938605	−	1.62571i
$61$	−1.88214	+	3.25996i	−0.240984	+	0.417396i	−0.960995	−	0.276567i	$-0.910803\pi$
$61$	−1.88214	+	3.25996i	−0.240984	+	0.417396i	0.720011	+	0.693962i	$0.244137\pi$
$62$	−1.25476			−0.159355
$63$	−1.96707	+	1.76936i	−0.247827	+	0.222919i
$64$	−11.9590			−1.49487
$65$	11.0985	−	19.2232i	1.37660	−	2.38435i
$66$	1.17616	+	2.03717i	0.144775	+	0.250758i
$67$	−1.01195	−	1.75274i	−0.123629	−	0.214132i	0.797567	−	0.603230i	$-0.206120\pi$
$67$	−1.01195	−	1.75274i	−0.123629	−	0.214132i	−0.921196	+	0.389099i	$0.872787\pi$
$68$	−4.15586	+	7.19816i	−0.503972	+	0.872906i
$69$	−1.41819			−0.170730
$70$	5.31237	+	25.0548i	0.634950	+	2.99462i
$71$	4.10440			0.487103			0.243551	−	0.969888i	$-0.421688\pi$
$71$	4.10440			0.487103			0.243551	+	0.969888i	$0.421688\pi$
$72$	−1.80354	+	3.12382i	−0.212549	+	0.368146i
$73$	−3.23719	−	5.60698i	−0.378885	−	0.656248i	0.612015	−	0.790846i	$-0.290359\pi$
$73$	−3.23719	−	5.60698i	−0.378885	−	0.656248i	−0.990900	+	0.134598i	$0.957026\pi$
$74$	−2.83524	−	4.91077i	−0.329589	−	0.570866i
$75$	5.96755	−	10.3361i	0.689073	−	1.19351i
$76$	20.3037			2.32900
$77$	−0.548780	−	2.58821i	−0.0625393	−	0.294954i
$78$	−12.6881			−1.43665
$79$	−5.09766	+	8.82941i	−0.573532	+	0.993386i	0.422668	+	0.906285i	$0.361094\pi$
$79$	−5.09766	+	8.82941i	−0.573532	+	0.993386i	−0.996199	+	0.0871013i	$0.972240\pi$
$80$	2.91808	+	5.05426i	0.326251	+	0.565084i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.68099	+	11.5718i	−0.737792	+	1.27789i
$83$	−16.0019			−1.75644			−0.878220	−	0.478257i	$-0.841269\pi$
$83$	−16.0019			−1.75644			−0.878220	+	0.478257i	$0.841269\pi$
$84$	6.95046	−	6.25189i	0.758358	−	0.682137i
$85$	−9.68034			−1.04998
$86$	−4.02789	+	6.97652i	−0.434339	+	0.752297i
$87$	−2.56645	−	4.44522i	−0.275152	−	0.476577i
$88$	−1.80354	−	3.12382i	−0.192258	−	0.333001i
$89$	4.36999	−	7.56904i	0.463218	−	0.802317i	−0.535901	−	0.844281i	$-0.680028\pi$
$89$	4.36999	−	7.56904i	0.463218	−	0.802317i	0.999119	+	0.0419638i	$0.0133614\pi$
$90$	−9.68034			−1.02040
$91$	13.5702	+	4.41677i	1.42254	+	0.463003i
$92$	5.01104			0.522437
$93$	−0.266707	+	0.461950i	−0.0276562	+	0.0479020i
$94$	−10.5180	−	18.2178i	−1.08485	−	1.87902i
$95$	11.8235	+	20.4788i	1.21306	+	2.10108i
$96$	−1.93907	+	3.35856i	−0.197905	+	0.342782i
$97$	−17.7919			−1.80650			−0.903248	−	0.429119i	$-0.858824\pi$
$97$	−17.7919			−1.80650			−0.903248	+	0.429119i	$0.858824\pi$
$98$	−15.0494	+	6.68228i	−1.52022	+	0.675012i
$99$	1.00000			0.100504
$100$	−21.0858	+	36.5217i	−2.10858	+	3.65217i
$101$	3.98463	+	6.90159i	0.396486	+	0.686734i	0.993290	−	0.115654i	$-0.0368962\pi$
$101$	3.98463	+	6.90159i	0.396486	+	0.686734i	−0.596804	+	0.802387i	$0.703563\pi$
$102$	2.76671	+	4.79208i	0.273945	+	0.474486i
$103$	8.04663	−	13.9372i	0.792858	−	1.37327i	−0.131332	−	0.991338i	$-0.541926\pi$
$103$	8.04663	−	13.9372i	0.792858	−	1.37327i	0.924190	−	0.381932i	$-0.124741\pi$
$104$	19.4562			1.90783
$105$	10.3533	+	3.36975i	1.01038	+	0.328854i
$106$	8.48178			0.823823
$107$	1.74261	−	3.01829i	0.168464	−	0.291789i	−0.769416	−	0.638748i	$-0.779453\pi$
$107$	1.74261	−	3.01829i	0.168464	−	0.291789i	0.937880	+	0.346960i	$0.112786\pi$
$108$	1.76671	+	3.06003i	0.170001	+	0.294451i
$109$	−3.27875	−	5.67897i	−0.314048	−	0.543946i	0.665187	−	0.746677i	$-0.268352\pi$
$109$	−3.27875	−	5.67897i	−0.314048	−	0.543946i	−0.979235	+	0.202730i	$0.935019\pi$
$110$	4.84017	−	8.38342i	0.461492	−	0.799327i
$111$	−2.41059			−0.228803
$112$	−2.78967	+	2.50929i	−0.263599	+	0.237105i
$113$	2.03211			0.191165			0.0955823	−	0.995422i	$-0.469529\pi$
$113$	2.03211			0.191165			0.0955823	+	0.995422i	$0.469529\pi$
$114$	6.75846	−	11.7060i	0.632987	−	1.09637i
$115$	2.91808	+	5.05426i	0.272112	+	0.471312i
$116$	9.06832	+	15.7068i	0.841972	+	1.45834i
$117$	−2.69694	+	4.67124i	−0.249332	+	0.431856i
$118$	3.33603			0.307106
$119$	−1.29091	−	6.08831i	−0.118337	−	0.558114i
$120$	14.8440			1.35506
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−4.42740	−	7.66848i	−0.400838	−	0.694272i
$123$	2.84017	+	4.91932i	0.256089	+	0.443560i
$124$	0.942386	−	1.63226i	0.0846288	−	0.146581i
$125$	−28.5395			−2.55265
$126$	−1.29091	−	6.08831i	−0.115003	−	0.542389i
$127$	8.42279			0.747402			0.373701	−	0.927549i	$-0.378089\pi$
$127$	8.42279			0.747402			0.373701	+	0.927549i	$0.378089\pi$
$128$	10.1876	−	17.6454i	0.900461	−	1.55964i
$129$	1.71231	+	2.96580i	0.150760	+	0.261124i
$130$	26.1073	+	45.2191i	2.28976	+	3.96598i
$131$	−2.80847	+	4.86442i	−0.245377	+	0.425006i	−0.962238	−	0.272211i	$-0.912245\pi$
$131$	−2.80847	+	4.86442i	−0.245377	+	0.425006i	0.716860	+	0.697217i	$0.245579\pi$
$132$	−3.53341			−0.307544
$133$	−11.3032	+	10.1671i	−0.980109	+	0.881601i
$134$	4.76084			0.411274
$135$	−2.05761	+	3.56389i	−0.177091	+	0.306731i
$136$	−4.24251	−	7.34824i	−0.363792	−	0.630106i
$137$	7.26975	+	12.5916i	0.621097	+	1.07577i	0.989282	+	0.146019i	$0.0466459\pi$
$137$	7.26975	+	12.5916i	0.621097	+	1.07577i	−0.368185	+	0.929752i	$0.620021\pi$
$138$	1.66802	−	2.88909i	0.141991	−	0.245935i
$139$	−11.2314			−0.952636			−0.476318	−	0.879273i	$-0.658029\pi$
$139$	−11.2314			−0.952636			−0.476318	+	0.879273i	$0.658029\pi$
$140$	−36.5824	−	11.9067i	−3.09178	−	1.00630i
$141$	−8.94270			−0.753111
$142$	−4.82743	+	8.36136i	−0.405109	+	0.701670i
$143$	−2.69694	−	4.67124i	−0.225529	−	0.390629i
$144$	−0.709093	−	1.22819i	−0.0590911	−	0.102349i
$145$	−10.5615	+	18.2931i	−0.877086	+	1.51916i
$146$	15.2298			1.26043
$147$	−0.738707	+	6.96091i	−0.0609275	+	0.574126i
$148$	8.51760			0.700142
$149$	−5.92236	+	10.2578i	−0.485179	+	0.840354i	−0.999855	−	0.0170303i	$-0.994579\pi$
$149$	−5.92236	+	10.2578i	−0.485179	+	0.840354i	0.514676	+	0.857385i	$0.327912\pi$
$150$	14.0376	+	24.3138i	1.14616	+	1.98521i
$151$	−4.41422	−	7.64565i	−0.359224	−	0.622194i	0.628608	−	0.777723i	$-0.283625\pi$
$151$	−4.41422	−	7.64565i	−0.359224	−	0.622194i	−0.987831	+	0.155529i	$0.950292\pi$
$152$	−10.3635	+	17.9501i	−0.840592	+	1.45595i
$153$	2.35232			0.190174
$154$	5.91808	+	1.92619i	0.476892	+	0.155217i
$155$	2.19512			0.176316
$156$	9.52941	−	16.5054i	0.762963	−	1.32149i
$157$	−9.69881	−	16.7988i	−0.774050	−	1.34069i	−0.935327	−	0.353784i	$-0.884895\pi$
$157$	−9.69881	−	16.7988i	−0.774050	−	1.34069i	0.161277	−	0.986909i	$-0.448439\pi$
$158$	−11.9913	−	20.7696i	−0.953979	−	1.65234i
$159$	1.80285	−	3.12263i	0.142976	−	0.247641i
$160$	15.9594			1.26170
$161$	−2.78967	+	2.50929i	−0.219857	+	0.197760i
$162$	2.35232			0.184816
$163$	8.41090	−	14.5681i	0.658792	−	1.14106i	−0.322136	−	0.946693i	$-0.604401\pi$
$163$	8.41090	−	14.5681i	0.658792	−	1.14106i	0.980929	−	0.194368i	$-0.0622657\pi$
$164$	−10.0355	−	17.3820i	−0.783640	−	1.35730i
$165$	−2.05761	−	3.56389i	−0.160185	−	0.277449i
$166$	18.8208	−	32.5986i	1.46078	−	2.53014i
$167$	4.59264			0.355389			0.177695	−	0.984086i	$-0.443136\pi$
$167$	4.59264			0.355389			0.177695	+	0.984086i	$0.443136\pi$
$168$	1.97949	+	9.33589i	0.152721	+	0.720280i
$169$	16.0939			1.23800
$170$	11.3856	−	19.7205i	0.873238	−	1.51249i
$171$	−2.87310	−	4.97636i	−0.219712	−	0.380551i
$172$	−6.05029	−	10.4794i	−0.461330	−	0.799047i
$173$	−2.50551	+	4.33968i	−0.190491	+	0.329940i	−0.945413	−	0.325875i	$-0.894341\pi$
$173$	−2.50551	+	4.33968i	−0.190491	+	0.329940i	0.754922	+	0.655814i	$0.227675\pi$
$174$	12.0742			0.915344
$175$	−6.54974	−	30.8906i	−0.495114	−	2.33511i
$176$	1.41819			0.106900
$177$	0.709093	−	1.22819i	0.0532987	−	0.0923161i
$178$	10.2796	+	17.8048i	0.770490	+	1.33453i
$179$	3.85440	+	6.67602i	0.288092	+	0.498989i	0.973354	−	0.229307i	$-0.0736459\pi$
$179$	3.85440	+	6.67602i	0.288092	+	0.498989i	−0.685263	+	0.728296i	$0.740313\pi$
$180$	7.27040	−	12.5927i	0.541904	−	0.938605i
$181$	−1.02451			−0.0761510			−0.0380755	−	0.999275i	$-0.512123\pi$
$181$	−1.02451			−0.0761510			−0.0380755	+	0.999275i	$0.512123\pi$
$182$	−24.9584	+	22.4499i	−1.85004	+	1.66410i
$183$	−3.76428			−0.278264
$184$	−2.55776	+	4.43017i	−0.188560	+	0.326596i
$185$	4.96005	+	8.59107i	0.364670	+	0.631628i
$186$	−0.627380	−	1.08665i	−0.0460018	−	0.0796774i
$187$	−1.17616	+	2.03717i	−0.0860094	+	0.148973i
$188$	31.5983			2.30454
$189$	−2.51585	−	0.818848i	−0.183001	−	0.0595625i
$190$	−55.6252			−4.03547
$191$	1.50588	−	2.60826i	0.108962	−	0.188727i	−0.806388	−	0.591387i	$-0.798581\pi$
$191$	1.50588	−	2.60826i	0.108962	−	0.188727i	0.915350	+	0.402659i	$0.131914\pi$
$192$	−5.97949	−	10.3568i	−0.431533	−	0.747437i
$193$	1.30043	+	2.25241i	0.0936069	+	0.162132i	0.909026	−	0.416739i	$-0.136827\pi$
$193$	1.30043	+	2.25241i	0.0936069	+	0.162132i	−0.815419	+	0.578871i	$0.803494\pi$
$194$	20.9262	−	36.2452i	1.50241	−	2.60225i
$195$	22.1970			1.58956
$196$	2.61016	−	24.5958i	0.186440	−	1.75684i
$197$	−10.5474			−0.751474			−0.375737	−	0.926726i	$-0.622610\pi$
$197$	−10.5474			−0.751474			−0.375737	+	0.926726i	$0.622610\pi$
$198$	−1.17616	+	2.03717i	−0.0835861	+	0.144775i
$199$	3.64864	+	6.31963i	0.258645	+	0.447987i	0.965879	−	0.258993i	$-0.0833906\pi$
$199$	3.64864	+	6.31963i	0.258645	+	0.447987i	−0.707234	+	0.706980i	$0.750057\pi$
$200$	−21.5254	−	37.2831i	−1.52208	−	2.63632i
$201$	1.01195	−	1.75274i	0.0713772	−	0.123629i
$202$	−18.7463			−1.31898
$203$	−12.9136	−	4.20306i	−0.906356	−	0.294997i
$204$	−8.31172			−0.581937
$205$	11.6879	−	20.2441i	0.816321	−	1.41391i
$206$	18.9283	+	32.7847i	1.31879	+	2.28422i
$207$	−0.709093	−	1.22819i	−0.0492854	−	0.0853648i
$208$	−3.82476	+	6.62469i	−0.265200	+	0.459339i
$209$	5.74620			0.397473
$210$	−19.0419	+	17.1280i	−1.31401	+	1.18195i
$211$	−13.7787			−0.948562			−0.474281	−	0.880374i	$-0.657292\pi$
$211$	−13.7787			−0.948562			−0.474281	+	0.880374i	$0.657292\pi$
$212$	−6.37023	+	11.0336i	−0.437509	+	0.757788i
$213$	2.05220	+	3.55451i	0.140614	+	0.243551i
$214$	4.09917	+	7.09998i	0.280214	+	0.485344i
$215$	7.04653	−	12.2049i	0.480569	−	0.832370i
$216$	−3.60708			−0.245431
$217$	0.292727	+	1.38059i	0.0198716	+	0.0937205i
$218$	15.4254			1.04474
$219$	3.23719	−	5.60698i	0.218749	−	0.378885i
$220$	7.27040	+	12.5927i	0.490170	+	0.849000i
$221$	−6.34407	−	10.9883i	−0.426748	−	0.739150i
$222$	2.83524	−	4.91077i	0.190289	−	0.329589i
$223$	6.91667			0.463174			0.231587	−	0.972814i	$-0.425608\pi$
$223$	6.91667			0.463174			0.231587	+	0.972814i	$0.425608\pi$
$224$	2.12824	+	10.0374i	0.142199	+	0.670654i
$225$	11.9351			0.795673
$226$	−2.39009	+	4.13975i	−0.158986	+	0.275372i
$227$	2.99240	+	5.18299i	0.198612	+	0.344007i	0.948079	−	0.318036i	$-0.103023\pi$
$227$	2.99240	+	5.18299i	0.198612	+	0.344007i	−0.749466	+	0.662043i	$0.769690\pi$
$228$	10.1519	+	17.5835i	0.672323	+	1.16450i
$229$	−11.2761	+	19.5308i	−0.745147	+	1.29063i	0.204979	+	0.978766i	$0.434287\pi$
$229$	−11.2761	+	19.5308i	−0.745147	+	1.29063i	−0.950126	+	0.311866i	$0.899046\pi$
$230$	−13.7285			−0.905232
$231$	1.96707	−	1.76936i	0.129424	−	0.116416i
$232$	−18.5148			−1.21555
$233$	−6.46621	+	11.1998i	−0.423615	+	0.733724i	−0.996290	−	0.0860593i	$-0.972573\pi$
$233$	−6.46621	+	11.1998i	−0.423615	+	0.733724i	0.572675	+	0.819783i	$0.305906\pi$
$234$	−6.34407	−	10.9883i	−0.414725	−	0.718324i
$235$	18.4006	+	31.8708i	1.20032	+	2.07902i
$236$	−2.50552	+	4.33969i	−0.163095	+	0.282490i
$237$	−10.1953			−0.662257
$238$	13.9212	+	4.53103i	0.902379	+	0.293703i
$239$	25.5349			1.65172			0.825858	−	0.563877i	$-0.190691\pi$
$239$	25.5349			1.65172			0.825858	+	0.563877i	$0.190691\pi$
$240$	−2.91808	+	5.05426i	−0.188361	+	0.326251i
$241$	6.40928	+	11.1012i	0.412858	+	0.715092i	0.995201	−	0.0978519i	$-0.0311971\pi$
$241$	6.40928	+	11.1012i	0.412858	+	0.715092i	−0.582343	+	0.812943i	$0.697864\pi$
$242$	−1.17616	−	2.03717i	−0.0756065	−	0.130954i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	13.3008			0.851495
$245$	26.3279	−	11.6902i	1.68203	−	0.746859i
$246$	−13.3620			−0.851928
$247$	−15.4972	+	26.8419i	−0.986061	+	1.70791i
$248$	0.962034	+	1.66629i	0.0610892	+	0.105810i
$249$	−8.00096	−	13.8581i	−0.507040	−	0.878220i
$250$	33.5670	−	58.1398i	2.12297	−	3.67708i
$251$	2.91189			0.183797			0.0918985	−	0.995768i	$-0.470706\pi$
$251$	2.91189			0.183797			0.0918985	+	0.995768i	$0.470706\pi$
$252$	8.88953	+	2.89333i	0.559988	+	0.182263i
$253$	1.41819			0.0891606
$254$	−9.90655	+	17.1587i	−0.621592	+	1.07663i
$255$	−4.84017	−	8.38342i	−0.303103	−	0.524990i
$256$	12.0054	+	20.7940i	0.750338	+	1.29962i
$257$	−11.2865	+	19.5487i	−0.704030	+	1.21942i	0.263011	+	0.964793i	$0.415285\pi$
$257$	−11.2865	+	19.5487i	−0.704030	+	1.21942i	−0.967041	+	0.254622i	$0.918049\pi$
$258$	−8.05579			−0.501531
$259$	−4.74178	+	4.26520i	−0.294640	+	0.265027i
$260$	−78.4313			−4.86411
$261$	2.56645	−	4.44522i	0.158859	−	0.275152i
$262$	−6.60643	−	11.4427i	−0.408147	−	0.706931i
$263$	−6.21182	−	10.7592i	−0.383038	−	0.663440i	0.608457	−	0.793587i	$-0.291789\pi$
$263$	−6.21182	−	10.7592i	−0.383038	−	0.663440i	−0.991495	+	0.130146i	$0.958455\pi$
$264$	1.80354	−	3.12382i	0.111000	−	0.192258i
$265$	−14.8383			−0.911509
$266$	−7.41781	−	34.9846i	−0.454815	−	2.14505i
$267$	8.73998			0.534878
$268$	−3.57562	+	6.19316i	−0.218416	+	0.378308i
$269$	5.01468	+	8.68568i	0.305750	+	0.529575i	0.977428	−	0.211268i	$-0.0677594\pi$
$269$	5.01468	+	8.68568i	0.305750	+	0.529575i	−0.671678	+	0.740843i	$0.734426\pi$
$270$	−4.84017	−	8.38342i	−0.294563	−	0.510198i
$271$	−11.8971	+	20.6064i	−0.722699	+	1.25175i	0.237215	+	0.971457i	$0.423765\pi$
$271$	−11.8971	+	20.6064i	−0.722699	+	1.25175i	−0.959914	+	0.280295i	$0.909568\pi$
$272$	3.33603			0.202277
$273$	2.96005	+	13.9605i	0.179151	+	0.844928i
$274$	−34.2016			−2.06619
$275$	−5.96755	+	10.3361i	−0.359857	+	0.623290i
$276$	2.50552	+	4.33969i	0.150815	+	0.261219i
$277$	−4.78104	−	8.28101i	−0.287265	−	0.497557i	0.685891	−	0.727704i	$-0.259413\pi$
$277$	−4.78104	−	8.28101i	−0.287265	−	0.497557i	−0.973156	+	0.230147i	$0.926079\pi$
$278$	13.2099	−	22.8803i	0.792280	−	1.37227i
$279$	−0.533414			−0.0319347
$280$	29.1991	−	26.2644i	1.74498	−	1.56960i
$281$	−7.42481			−0.442927			−0.221464	−	0.975169i	$-0.571083\pi$
$281$	−7.42481			−0.442927			−0.221464	+	0.975169i	$0.571083\pi$
$282$	10.5180	−	18.2178i	0.626341	−	1.08485i
$283$	12.2038	+	21.1376i	0.725440	+	1.25650i	0.958793	+	0.284106i	$0.0916969\pi$
$283$	12.2038	+	21.1376i	0.725440	+	1.25650i	−0.233353	+	0.972392i	$0.574970\pi$
$284$	−7.25127	−	12.5596i	−0.430284	−	0.745273i
$285$	−11.8235	+	20.4788i	−0.700361	+	1.21306i
$286$	12.6881			0.750265
$287$	14.2909	+	4.65133i	0.843563	+	0.274560i
$288$	−3.87813			−0.228521
$289$	5.73329	−	9.93035i	0.337253	−	0.584139i
$290$	−24.8441	−	43.0312i	−1.45889	−	2.52688i
$291$	−8.89596	−	15.4083i	−0.521490	−	0.903248i
$292$	−11.4383	+	19.8118i	−0.669379	+	1.15940i
$293$	31.4484			1.83723			0.918617	−	0.395148i	$-0.129307\pi$
$293$	31.4484			1.83723			0.918617	+	0.395148i	$0.129307\pi$
$294$	−13.3117	−	9.69202i	−0.776356	−	0.565250i
$295$	−5.83616			−0.339794
$296$	−4.34759	+	7.53025i	−0.252699	+	0.437687i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	−13.9313	−	24.1297i	−0.807018	−	1.39780i
$299$	−3.82476	+	6.62469i	−0.221192	+	0.383116i
$300$	−42.1716			−2.43478
$301$	8.61580	+	2.80424i	0.496607	+	0.161634i
$302$	20.7673			1.19502
$303$	−3.98463	+	6.90159i	−0.228911	+	0.396486i
$304$	−4.07459	−	7.05740i	−0.233694	−	0.404770i
$305$	7.74544	+	13.4155i	0.443503	+	0.768169i
$306$	−2.76671	+	4.79208i	−0.158162	+	0.273945i
$307$	−0.934896			−0.0533573			−0.0266787	−	0.999644i	$-0.508493\pi$
$307$	−0.934896			−0.0533573			−0.0266787	+	0.999644i	$0.508493\pi$
$308$	−6.95046	+	6.25189i	−0.396039	+	0.356235i
$309$	16.0933			0.915514
$310$	−2.58181	+	4.47183i	−0.146637	+	0.253983i
$311$	−6.98248	−	12.0940i	−0.395940	−	0.685789i	0.597280	−	0.802033i	$-0.296248\pi$
$311$	−6.98248	−	12.0940i	−0.395940	−	0.685789i	−0.993221	+	0.116244i	$0.962915\pi$
$312$	9.72808	+	16.8495i	0.550744	+	0.953917i
$313$	−2.30189	+	3.98699i	−0.130111	+	0.225358i	−0.923719	−	0.383071i	$-0.874867\pi$
$313$	−2.30189	+	3.98699i	−0.130111	+	0.225358i	0.793608	+	0.608429i	$0.208200\pi$
$314$	45.6294			2.57502
$315$	2.25835	+	10.6511i	0.127244	+	0.600120i
$316$	36.0243			2.02652
$317$	11.9989	−	20.7828i	0.673927	−	1.16728i	−0.302854	−	0.953037i	$-0.597939\pi$
$317$	11.9989	−	20.7828i	0.673927	−	1.16728i	0.976781	−	0.214239i	$-0.0687273\pi$
$318$	4.24089	+	7.34543i	0.237817	+	0.411911i
$319$	2.56645	+	4.44522i	0.143693	+	0.248884i
$320$	−24.6070	+	42.6205i	−1.37557	+	2.38256i
$321$	3.48522			0.194526
$322$	−1.83075	−	8.63435i	−0.102024	−	0.481174i
$323$	13.5169			0.752101
$324$	−1.76671	+	3.06003i	−0.0981504	+	0.170001i
$325$	−32.1882	−	55.7517i	−1.78548	−	3.09255i
$326$	19.7851	+	34.2689i	1.09580	+	1.89798i
$327$	3.27875	−	5.67897i	0.181315	−	0.314048i
$328$	20.4894			1.13134
$329$	−17.5909	+	15.8229i	−0.969817	+	0.872344i
$330$	9.68034			0.532885
$331$	16.5305	−	28.6316i	0.908597	−	1.57374i	0.0925818	−	0.995705i	$-0.470488\pi$
$331$	16.5305	−	28.6316i	0.908597	−	1.57374i	0.816015	−	0.578031i	$-0.196179\pi$
$332$	28.2707	+	48.9663i	1.55156	+	2.68738i
$333$	−1.20529	−	2.08763i	−0.0660496	−	0.114401i
$334$	−5.40168	+	9.35599i	−0.295567	+	0.511937i
$335$	−8.32878			−0.455050
$336$	−3.56794	−	1.16128i	−0.194647	−	0.0633530i
$337$	10.2250			0.556991			0.278495	−	0.960438i	$-0.410164\pi$
$337$	10.2250			0.556991			0.278495	+	0.960438i	$0.410164\pi$
$338$	−18.9291	+	32.7861i	−1.02961	+	1.78333i
$339$	1.01605	+	1.75986i	0.0551845	+	0.0955823i
$340$	17.1023	+	29.6221i	0.927503	+	1.60648i
$341$	0.266707	−	0.461950i	0.0144430	−	0.0250160i
$342$	13.5169			0.730911
$343$	10.8633	+	14.9996i	0.586563	+	0.809904i
$344$	12.3529			0.666021
$345$	−2.91808	+	5.05426i	−0.157104	+	0.272112i
$346$	−5.89377	−	10.2083i	−0.316851	−	0.548802i
$347$	−10.1198	−	17.5280i	−0.543258	−	0.940951i	−0.998714	−	0.0506928i	$-0.983857\pi$
$347$	−10.1198	−	17.5280i	−0.543258	−	0.940951i	0.455456	−	0.890258i	$-0.349476\pi$
$348$	−9.06832	+	15.7068i	−0.486113	+	0.841972i
$349$	12.9206			0.691625			0.345813	−	0.938304i	$-0.387603\pi$
$349$	12.9206			0.691625			0.345813	+	0.938304i	$0.387603\pi$
$350$	70.6329	+	22.9893i	3.77549	+	1.22883i
$351$	−5.39388			−0.287904
$352$	1.93907	−	3.35856i	0.103353	−	0.179012i
$353$	1.70945	+	2.96086i	0.0909851	+	0.157591i	0.907926	−	0.419131i	$-0.137665\pi$
$353$	1.70945	+	2.96086i	0.0909851	+	0.157591i	−0.816941	+	0.576722i	$0.804332\pi$
$354$	1.66802	+	2.88909i	0.0886540	+	0.153553i
$355$	8.44527	−	14.6276i	0.448228	−	0.776354i
$356$	−30.8820			−1.63674
$357$	4.62717	−	4.16211i	0.244896	−	0.220282i
$358$	−18.1336			−0.958390
$359$	−12.0213	+	20.8214i	−0.634458	+	1.09891i	0.352172	+	0.935935i	$0.385443\pi$
$359$	−12.0213	+	20.8214i	−0.634458	+	1.09891i	−0.986630	+	0.162978i	$0.947890\pi$
$360$	7.42198	+	12.8552i	0.391173	+	0.677531i
$361$	−7.00942	−	12.1407i	−0.368917	−	0.638982i
$362$	1.20499	−	2.08710i	0.0633326	−	0.109695i
$363$	−1.00000			−0.0524864
$364$	−10.4591	−	49.3282i	−0.548206	−	2.58550i
$365$	−26.6436			−1.39459
$366$	4.42740	−	7.66848i	0.231424	−	0.400838i
$367$	−5.99888	−	10.3904i	−0.313139	−	0.542373i	0.665901	−	0.746040i	$-0.268047\pi$
$367$	−5.99888	−	10.3904i	−0.313139	−	0.542373i	−0.979040	+	0.203667i	$0.934714\pi$
$368$	−1.00563	−	1.74180i	−0.0524219	−	0.0907974i
$369$	−2.84017	+	4.91932i	−0.147853	+	0.256089i
$370$	−23.3353			−1.21314
$371$	−1.97874	−	9.33233i	−0.102731	−	0.484510i
$372$	1.88477			0.0977209
$373$	17.1569	−	29.7166i	0.888350	−	1.53867i	0.0465247	−	0.998917i	$-0.485185\pi$
$373$	17.1569	−	29.7166i	0.888350	−	1.53867i	0.841825	−	0.539750i	$-0.181481\pi$
$374$	−2.76671	−	4.79208i	−0.143063	−	0.247792i
$375$	−14.2698	−	24.7159i	−0.736887	−	1.27633i
$376$	−16.1285	+	27.9354i	−0.831765	+	1.44066i
$377$	−27.6862			−1.42591
$378$	4.62717	−	4.16211i	0.237996	−	0.214076i
$379$	30.7107			1.57750			0.788752	−	0.614711i	$-0.210728\pi$
$379$	30.7107			1.57750			0.788752	+	0.614711i	$0.210728\pi$
$380$	41.7772	−	72.3602i	2.14312	−	3.71200i
$381$	4.21139	+	7.29435i	0.215756	+	0.373701i
$382$	3.54232	+	6.13547i	0.181241	+	0.313918i
$383$	2.67396	−	4.63143i	0.136633	−	0.236655i	−0.789587	−	0.613638i	$-0.789705\pi$
$383$	2.67396	−	4.63143i	0.136633	−	0.236655i	0.926220	+	0.376983i	$0.123039\pi$
$384$	20.3751			1.03976
$385$	−10.3533	−	3.36975i	−0.527652	−	0.171738i
$386$	−6.11805			−0.311401
$387$	−1.71231	+	2.96580i	−0.0870414	+	0.150760i
$388$	31.4331	+	54.4438i	1.59577	+	2.76396i
$389$	13.1577	+	22.7899i	0.667124	+	1.15549i	0.978705	+	0.205273i	$0.0658084\pi$
$389$	13.1577	+	22.7899i	0.667124	+	1.15549i	−0.311580	+	0.950220i	$0.600858\pi$
$390$	−26.1073	+	45.2191i	−1.32199	+	2.28976i
$391$	3.33603			0.168710
$392$	20.4124	+	14.8619i	1.03098	+	0.750638i
$393$	−5.61695			−0.283337
$394$	12.4055	−	21.4869i	0.624979	−	1.08250i
$395$	20.9780	+	36.3350i	1.05552	+	1.82821i
$396$	−1.76671	−	3.06003i	−0.0887804	−	0.153772i
$397$	13.9665	−	24.1907i	0.700958	−	1.21409i	−0.267173	−	0.963649i	$-0.586089\pi$
$397$	13.9665	−	24.1907i	0.700958	−	1.21409i	0.968131	−	0.250446i	$-0.0805772\pi$
$398$	−17.1656			−0.860431
$399$	−14.4566	−	4.70527i	−0.723733	−	0.235558i
$400$	16.9262			0.846310
$401$	17.2750	−	29.9212i	0.862673	−	1.49419i	−0.00666724	−	0.999978i	$-0.502122\pi$
$401$	17.2750	−	29.9212i	0.862673	−	1.49419i	0.869340	−	0.494215i	$-0.164544\pi$
$402$	2.38042	+	4.12301i	0.118725	+	0.205637i
$403$	1.43859	+	2.49170i	0.0716611	+	0.124121i
$404$	14.0794	−	24.3862i	0.700474	−	1.21326i
$405$	−4.11523			−0.204487
$406$	23.7508	−	21.3637i	1.17873	−	1.06026i
$407$	2.41059			0.119488
$408$	4.24251	−	7.34824i	0.210035	−	0.363792i
$409$	−11.5168	−	19.9477i	−0.569470	−	0.986350i	−0.996618	−	0.0821689i	$-0.973815\pi$
$409$	−11.5168	−	19.9477i	−0.569470	−	0.986350i	0.427149	−	0.904181i	$-0.359518\pi$
$410$	27.4938	+	47.6206i	1.35782	+	2.35181i
$411$	−7.26975	+	12.5916i	−0.358590	+	0.621097i
$412$	−56.8642			−2.80150
$413$	−0.778272	−	3.67057i	−0.0382963	−	0.180617i
$414$	3.33603			0.163957
$415$	−32.9258	+	57.0291i	−1.61626	+	2.79945i
$416$	10.4591	+	18.1157i	0.512799	+	0.888195i
$417$	−5.61571	−	9.72669i	−0.275002	−	0.476318i
$418$	−6.75846	+	11.7060i	−0.330567	+	0.572559i
$419$	−16.6360			−0.812721			−0.406360	−	0.913713i	$-0.633202\pi$
$419$	−16.6360			−0.812721			−0.406360	+	0.913713i	$0.633202\pi$
$420$	−7.97970	−	37.6347i	−0.389370	−	1.83638i
$421$	−18.2848			−0.891148			−0.445574	−	0.895245i	$-0.647000\pi$
$421$	−18.2848			−0.891148			−0.445574	+	0.895245i	$0.647000\pi$
$422$	16.2059	−	28.0695i	0.788891	−	1.36640i
$423$	−4.47135	−	7.74460i	−0.217404	−	0.376556i
$424$	−6.50304	−	11.2636i	−0.315815	−	0.547008i
$425$	−14.0376	+	24.3138i	−0.680923	+	1.17939i
$426$	−9.65487			−0.467780
$427$	−7.40460	+	6.66038i	−0.358334	+	0.322319i
$428$	−12.3147			−0.595254
$429$	2.69694	−	4.67124i	0.130210	−	0.225529i
$430$	16.5757	+	28.7100i	0.799351	+	1.38452i
$431$	−11.2815	−	19.5401i	−0.543410	−	0.941214i	−0.998705	−	0.0508732i	$-0.983800\pi$
$431$	−11.2815	−	19.5401i	−0.543410	−	0.941214i	0.455295	−	0.890341i	$-0.349534\pi$
$432$	0.709093	−	1.22819i	0.0341163	−	0.0590911i
$433$	3.56968			0.171548			0.0857740	−	0.996315i	$-0.472664\pi$
$433$	3.56968			0.171548			0.0857740	+	0.996315i	$0.472664\pi$
$434$	−3.15679	−	1.02746i	−0.151531	−	0.0493196i
$435$	−21.1230			−1.01277
$436$	−11.5852	+	20.0661i	−0.554830	+	0.960994i
$437$	−4.07459	−	7.05740i	−0.194914	−	0.337601i
$438$	7.61492	+	13.1894i	0.363855	+	0.630215i
$439$	−13.0380	+	22.5825i	−0.622270	+	1.07780i	0.366792	+	0.930303i	$0.380456\pi$
$439$	−13.0380	+	22.5825i	−0.622270	+	1.07780i	−0.989062	+	0.147500i	$0.952877\pi$
$440$	−14.8440			−0.707658
$441$	−6.39768	+	2.84072i	−0.304651	+	0.135272i
$442$	29.8466			1.41966
$443$	7.56976	−	13.1112i	0.359650	−	0.622932i	−0.628252	−	0.778010i	$-0.716229\pi$
$443$	7.56976	−	13.1112i	0.359650	−	0.622932i	0.987902	+	0.155077i	$0.0495627\pi$
$444$	4.25880	+	7.37645i	0.202114	+	0.350071i
$445$	−17.9835	−	31.1483i	−0.852499	−	1.47657i
$446$	−8.13511	+	14.0904i	−0.385209	+	0.667201i
$447$	−11.8447			−0.560236
$448$	−30.0870	−	9.79260i	−1.42148	−	0.462657i
$449$	−9.40928			−0.444052			−0.222026	−	0.975041i	$-0.571267\pi$
$449$	−9.40928			−0.444052			−0.222026	+	0.975041i	$0.571267\pi$
$450$	−14.0376	+	24.3138i	−0.661738	+	1.14616i
$451$	−2.84017	−	4.91932i	−0.133738	−	0.231642i
$452$	−3.59014	−	6.21831i	−0.168866	−	0.292484i
$453$	4.41422	−	7.64565i	0.207398	−	0.359224i
$454$	−14.0782			−0.660721
$455$	43.6631	−	39.2746i	2.04696	−	1.84122i
$456$	−20.7270			−0.970632
$457$	6.36625	−	11.0267i	0.297800	−	0.515806i	−0.677832	−	0.735217i	$-0.737080\pi$
$457$	6.36625	−	11.0267i	0.297800	−	0.515806i	0.975632	+	0.219411i	$0.0704136\pi$
$458$	−26.5251	−	45.9428i	−1.23943	−	2.14676i
$459$	1.17616	+	2.03717i	0.0548985	+	0.0950869i
$460$	10.3108	−	17.8588i	0.480743	−	0.832671i
$461$	−20.9096			−0.973858			−0.486929	−	0.873441i	$-0.661883\pi$
$461$	−20.9096			−0.973858			−0.486929	+	0.873441i	$0.661883\pi$
$462$	1.29091	+	6.08831i	0.0600584	+	0.283254i
$463$	14.8590			0.690555			0.345277	−	0.938501i	$-0.387785\pi$
$463$	14.8590			0.690555			0.345277	+	0.938501i	$0.387785\pi$
$464$	3.63970	−	6.30415i	0.168969	−	0.292663i
$465$	1.09756	+	1.90103i	0.0508981	+	0.0881581i
$466$	−15.2106	−	26.3455i	−0.704617	−	1.22043i
$467$	1.35089	−	2.33982i	0.0625120	−	0.108274i	−0.833076	−	0.553159i	$-0.813422\pi$
$467$	1.35089	−	2.33982i	0.0625120	−	0.108274i	0.895588	+	0.444885i	$0.146756\pi$
$468$	19.0588			0.880994
$469$	−1.11067	−	5.23826i	−0.0512860	−	0.241880i
$470$	−86.5683			−3.99310
$471$	9.69881	−	16.7988i	0.446898	−	0.774050i
$472$	−2.55776	−	4.43017i	−0.117730	−	0.203915i
$473$	−1.71231	−	2.96580i	−0.0787319	−	0.136368i
$474$	11.9913	−	20.7696i	0.550780	−	0.953979i
$475$	68.5815			3.14673
$476$	−16.3497	+	14.7065i	−0.749388	+	0.674069i
$477$	3.60571			0.165094
$478$	−30.0332	+	52.0190i	−1.37369	+	2.37929i
$479$	18.0688	+	31.2960i	0.825582	+	1.42995i	0.901473	+	0.432835i	$0.142487\pi$
$479$	18.0688	+	31.2960i	0.825582	+	1.42995i	−0.0758910	+	0.997116i	$0.524180\pi$
$480$	7.97970	+	13.8212i	0.364222	+	0.630851i
$481$	−6.50120	+	11.2604i	−0.296429	+	0.513431i
$482$	−30.1534			−1.37345
$483$	−3.56794	−	1.16128i	−0.162347	−	0.0528401i
$484$	3.53341			0.160610
$485$	−36.6089	+	63.4085i	−1.66232	+	2.87923i
$486$	1.17616	+	2.03717i	0.0533517	+	0.0924079i
$487$	10.6509	+	18.4479i	0.482639	+	0.835956i	0.999801	−	0.0199316i	$-0.00634484\pi$
$487$	10.6509	+	18.4479i	0.482639	+	0.835956i	−0.517162	+	0.855888i	$0.673012\pi$
$488$	−6.78904	+	11.7590i	−0.307325	+	0.532303i
$489$	16.8218			0.760708
$490$	−7.15093	+	67.3840i	−0.323046	+	3.04410i
$491$	−19.8401			−0.895372			−0.447686	−	0.894191i	$-0.647752\pi$
$491$	−19.8401			−0.895372			−0.447686	+	0.894191i	$0.647752\pi$
$492$	10.0355	−	17.3820i	0.452435	−	0.783640i
$493$	6.03711	+	10.4566i	0.271898	+	0.470941i
$494$	−36.4543	−	63.1407i	−1.64016	−	2.84083i
$495$	2.05761	−	3.56389i	0.0924829	−	0.160185i
$496$	−0.756481			−0.0339670
$497$	10.3260	+	3.36088i	0.463186	+	0.150756i
$498$	37.6417			1.68676
$499$	−3.26671	+	5.65810i	−0.146238	+	0.253291i	−0.929834	−	0.367979i	$-0.880050\pi$
$499$	−3.26671	+	5.65810i	−0.146238	+	0.253291i	0.783596	+	0.621270i	$0.213383\pi$
$500$	50.4209	+	87.3316i	2.25489	+	3.90559i
$501$	2.29632	+	3.97734i	0.102592	+	0.177695i
$502$	−3.42485	+	5.93202i	−0.152859	+	0.264759i
$503$	−16.7339			−0.746127			−0.373064	−	0.927806i	$-0.621693\pi$
$503$	−16.7339			−0.746127			−0.373064	+	0.927806i	$0.621693\pi$
$504$	−7.09537	+	6.38224i	−0.316053	+	0.284288i
$505$	32.7954			1.45937
$506$	−1.66802	+	2.88909i	−0.0741523	+	0.128436i
$507$	8.04697	+	13.9378i	0.357379	+	0.618998i
$508$	−14.8806	−	25.7740i	−0.660220	−	1.14353i
$509$	13.4161	−	23.2374i	0.594659	−	1.02998i	−0.398936	−	0.916979i	$-0.630620\pi$
$509$	13.4161	−	23.2374i	0.594659	−	1.02998i	0.993595	−	0.113001i	$-0.0360464\pi$
$510$	22.7713			1.00833
$511$	−3.55301	−	16.7571i	−0.157176	−	0.741290i
$512$	−15.7309			−0.695216
$513$	2.87310	−	4.97636i	0.126850	−	0.219712i
$514$	−26.5494	−	45.9849i	−1.17104	−	2.02830i
$515$	−33.1137	−	57.3546i	−1.45916	−	2.52735i
$516$	6.05029	−	10.4794i	0.266349	−	0.461330i
$517$	8.94270			0.393299
$518$	−3.11184	−	14.6764i	−0.136726	−	0.644843i
$519$	−5.01103			−0.219960
$520$	40.0333	−	69.3397i	1.75558	−	3.04075i
$521$	13.3226	+	23.0753i	0.583672	+	1.01095i	0.995040	+	0.0994795i	$0.0317178\pi$
$521$	13.3226	+	23.0753i	0.583672	+	1.01095i	−0.411368	+	0.911469i	$0.634949\pi$
$522$	6.03711	+	10.4566i	0.264237	+	0.457672i
$523$	−2.60698	+	4.51542i	−0.113995	+	0.197446i	−0.917378	−	0.398018i	$-0.869698\pi$
$523$	−2.60698	+	4.51542i	−0.113995	+	0.197446i	0.803382	+	0.595463i	$0.203032\pi$
$524$	19.8470			0.867020
$525$	23.4771	−	21.1175i	1.02463	−	0.921644i
$526$	29.2244			1.27424
$527$	0.627380	−	1.08665i	0.0273291	−	0.0473354i
$528$	0.709093	+	1.22819i	0.0308593	+	0.0534499i
$529$	10.4944	+	18.1768i	0.456277	+	0.790295i
$530$	17.4522	−	30.2281i	0.758076	−	1.31303i
$531$	1.41819			0.0615441
$532$	51.0810	+	16.6257i	2.21464	+	0.720814i
$533$	30.6391			1.32712
$534$	−10.2796	+	17.8048i	−0.444842	+	0.770490i
$535$	−7.17123	−	12.4209i	−0.310039	−	0.537004i
$536$	−3.65017	−	6.32228i	−0.157663	−	0.273081i
$537$	−3.85440	+	6.67602i	−0.166330	+	0.288092i
$538$	−23.5923			−1.01713
$539$	0.738707	−	6.96091i	0.0318184	−	0.299828i
$540$	14.5408			0.625737
$541$	20.1050	−	34.8230i	0.864384	−	1.49716i	−0.00327439	−	0.999995i	$-0.501042\pi$
$541$	20.1050	−	34.8230i	0.864384	−	1.49716i	0.867658	−	0.497162i	$-0.165624\pi$
$542$	−27.9859	−	48.4729i	−1.20210	−	2.08209i
$543$	−0.512254	−	0.887249i	−0.0219829	−	0.0380755i
$544$	4.56131	−	7.90042i	0.195564	−	0.338728i
$545$	−26.9856			−1.15594
$546$	−31.9214	−	10.3897i	−1.36611	−	0.444637i
$547$	0.770709			0.0329531			0.0164766	−	0.999864i	$-0.494755\pi$
$547$	0.770709			0.0329531			0.0164766	+	0.999864i	$0.494755\pi$
$548$	25.6870	−	44.4913i	1.09730	−	1.90057i
$549$	−1.88214	−	3.25996i	−0.0803278	−	0.139132i
$550$	−14.0376	−	24.3138i	−0.598565	−	1.03674i
$551$	14.7473	−	25.5431i	0.628257	−	1.08817i
$552$	−5.11552			−0.217731
$553$	−20.0549	+	18.0392i	−0.852820	+	0.767106i
$554$	22.4931			0.955640
$555$	−4.96005	+	8.59107i	−0.210543	+	0.364670i
$556$	19.8426	+	34.3684i	0.841515	+	1.45755i
$557$	−10.1450	−	17.5717i	−0.429858	−	0.744536i	0.567002	−	0.823716i	$-0.308103\pi$
$557$	−10.1450	−	17.5717i	−0.429858	−	0.744536i	−0.996860	+	0.0791802i	$0.974770\pi$
$558$	0.627380	−	1.08665i	0.0265591	−	0.0460018i
$559$	18.4720			0.781280
$560$	3.20277	+	15.1052i	0.135342	+	0.638312i
$561$	−2.35232			−0.0993151
$562$	8.73277	−	15.1256i	0.368370	−	0.638035i
$563$	−6.82710	−	11.8249i	−0.287728	−	0.498360i	0.685539	−	0.728036i	$-0.259567\pi$
$563$	−6.82710	−	11.8249i	−0.287728	−	0.498360i	−0.973267	+	0.229676i	$0.926233\pi$
$564$	15.7991	+	27.3649i	0.665263	+	1.15227i
$565$	4.18129	−	7.24221i	0.175908	−	0.304682i
$566$	−57.4144			−2.41331
$567$	−0.548780	−	2.58821i	−0.0230466	−	0.108695i
$568$	14.8049			0.621200
$569$	−2.63364	+	4.56160i	−0.110408	+	0.191232i	−0.915935	−	0.401327i	$-0.868549\pi$
$569$	−2.63364	+	4.56160i	−0.110408	+	0.191232i	0.805527	+	0.592559i	$0.201882\pi$
$570$	−27.8126	−	48.1728i	−1.16494	−	2.01774i
$571$	−3.14553	−	5.44822i	−0.131636	−	0.228001i	0.792671	−	0.609649i	$-0.208690\pi$
$571$	−3.14553	−	5.44822i	−0.131636	−	0.228001i	−0.924307	+	0.381649i	$0.875356\pi$
$572$	−9.52941	+	16.5054i	−0.398444	+	0.690126i
$573$	3.01176			0.125818
$574$	−26.2839	+	23.6422i	−1.09707	+	0.986806i
$575$	16.9262			0.705871
$576$	5.97949	−	10.3568i	0.249146	−	0.431533i
$577$	1.61988	+	2.80571i	0.0674365	+	0.116803i	0.897772	−	0.440460i	$-0.145185\pi$
$577$	1.61988	+	2.80571i	0.0674365	+	0.116803i	−0.830336	+	0.557263i	$0.811851\pi$
$578$	13.4865	+	23.3594i	0.560966	+	0.971622i
$579$	−1.30043	+	2.25241i	−0.0540440	+	0.0936069i
$580$	74.6364			3.09911
$581$	−40.2584	−	13.1032i	−1.67020	−	0.543610i
$582$	41.8523			1.73483
$583$	−1.80285	+	3.12263i	−0.0746665	+	0.129326i
$584$	−11.6768	−	20.2249i	−0.483190	−	0.836910i
$585$	11.0985	+	19.2232i	0.458867	+	0.794782i
$586$	−36.9884	+	64.0657i	−1.52797	+	2.64653i
$587$	17.5888			0.725967			0.362984	−	0.931795i	$-0.381758\pi$
$587$	17.5888			0.725967			0.362984	+	0.931795i	$0.381758\pi$
$588$	22.6057	−	10.0374i	0.932242	−	0.413937i
$589$	−3.06510			−0.126295
$590$	6.86426	−	11.8892i	0.282597	−	0.489473i
$591$	−5.27372	−	9.13435i	−0.216932	−	0.375737i
$592$	−1.70933	−	2.96065i	−0.0702530	−	0.121682i
$593$	10.8144	−	18.7310i	0.444093	−	0.769191i	−0.553896	−	0.832586i	$-0.686859\pi$
$593$	10.8144	−	18.7310i	0.444093	−	0.769191i	0.997989	+	0.0633947i	$0.0201927\pi$
$594$	−2.35232			−0.0965169
$595$	−24.3542	−	7.92673i	−0.998427	−	0.324964i
$596$	41.8523			1.71434
$597$	−3.64864	+	6.31963i	−0.149329	+	0.258645i
$598$	−8.99707	−	15.5834i	−0.367918	−	0.637252i
$599$	−1.35274	−	2.34301i	−0.0552713	−	0.0957326i	0.837066	−	0.547102i	$-0.184269\pi$
$599$	−1.35274	−	2.34301i	−0.0552713	−	0.0957326i	−0.892337	+	0.451369i	$0.850936\pi$
$600$	21.5254	−	37.2831i	0.878772	−	1.52208i
$601$	10.8157			0.441182			0.220591	−	0.975366i	$-0.429201\pi$
$601$	10.8157			0.441182			0.220591	+	0.975366i	$0.429201\pi$
$602$	−15.8463	+	14.2536i	−0.645846	+	0.580934i
$603$	2.02389			0.0824193
$604$	−15.5973	+	27.0152i	−0.634643	+	1.09923i
$605$	2.05761	+	3.56389i	0.0836539	+	0.144893i
$606$	−9.37314	−	16.2348i	−0.380758	−	0.659492i
$607$	−5.11853	+	8.86555i	−0.207755	+	0.359842i	−0.951007	−	0.309170i	$-0.899949\pi$
$607$	−5.11853	+	8.86555i	−0.207755	+	0.359842i	0.743252	+	0.669011i	$0.233282\pi$
$608$	−22.2845			−0.903757
$609$	−2.81683	−	13.2850i	−0.114144	−	0.538336i
$610$	−36.4395			−1.47539
$611$	−24.1179	+	41.7735i	−0.975707	+	1.68997i
$612$	−4.15586	−	7.19816i	−0.167991	−	0.290969i
$613$	−2.69062	−	4.66028i	−0.108673	−	0.188227i	0.806560	−	0.591152i	$-0.201327\pi$
$613$	−2.69062	−	4.66028i	−0.108673	−	0.188227i	−0.915233	+	0.402925i	$0.867993\pi$
$614$	1.09959	−	1.90454i	0.0443757	−	0.0768610i
$615$	23.3759			0.942606
$616$	−1.97949	−	9.33589i	−0.0797561	−	0.376154i
$617$	40.7869			1.64202			0.821009	−	0.570916i	$-0.193412\pi$
$617$	40.7869			1.64202			0.821009	+	0.570916i	$0.193412\pi$
$618$	−18.9283	+	32.7847i	−0.761406	+	1.31879i
$619$	14.5211	+	25.1512i	0.583650	+	1.01091i	0.995042	+	0.0994536i	$0.0317095\pi$
$619$	14.5211	+	25.1512i	0.583650	+	1.01091i	−0.411392	+	0.911459i	$0.634957\pi$
$620$	−3.87813	−	6.71712i	−0.155750	−	0.269766i
$621$	0.709093	−	1.22819i	0.0284549	−	0.0492854i
$622$	32.8501			1.31717
$623$	17.1921	−	15.4642i	0.688788	−	0.619560i
$624$	−7.64953			−0.306226
$625$	−28.8855	+	50.0312i	−1.15542	+	2.00125i
$626$	−5.41478	−	9.37868i	−0.216418	−	0.374848i
$627$	2.87310	+	4.97636i	0.114741	+	0.198737i
$628$	−34.2699	+	59.3573i	−1.36752	+	2.36861i
$629$	5.67047			0.226096
$630$	−24.3542	−	7.92673i	−0.970296	−	0.315808i
$631$	−47.0360			−1.87247			−0.936236	−	0.351371i	$-0.885715\pi$
$631$	−47.0360			−1.87247			−0.936236	+	0.351371i	$0.885715\pi$
$632$	−18.3877	+	31.8484i	−0.731423	+	1.26686i
$633$	−6.88933	−	11.9327i	−0.273826	−	0.474281i
$634$	28.2253	+	48.8877i	1.12097	+	1.94158i
$635$	17.3308	−	30.0179i	0.687754	−	1.19122i
$636$	−12.7405			−0.505192
$637$	30.5238	+	22.2238i	1.20940	+	0.880541i
$638$	−12.0742			−0.478023
$639$	−2.05220	+	3.55451i	−0.0811838	+	0.140614i
$640$	−41.9241	−	72.6147i	−1.65720	−	2.87035i
$641$	24.7949	+	42.9460i	0.979340	+	1.69627i	0.664798	+	0.747024i	$0.268518\pi$
$641$	24.7949	+	42.9460i	0.979340	+	1.69627i	0.314543	+	0.949243i	$0.398149\pi$
$642$	−4.09917	+	7.09998i	−0.161781	+	0.280214i
$643$	−14.5294			−0.572982			−0.286491	−	0.958083i	$-0.592489\pi$
$643$	−14.5294			−0.572982			−0.286491	+	0.958083i	$0.592489\pi$
$644$	12.6070	+	4.10328i	0.496786	+	0.161692i
$645$	14.0931			0.554914
$646$	−15.8981	+	27.5362i	−0.625501	+	1.08340i
$647$	−2.74544	−	4.75524i	−0.107934	−	0.186948i	0.806999	−	0.590553i	$-0.201090\pi$
$647$	−2.74544	−	4.75524i	−0.107934	−	0.186948i	−0.914933	+	0.403605i	$0.867757\pi$
$648$	−1.80354	−	3.12382i	−0.0708498	−	0.122715i
$649$	−0.709093	+	1.22819i	−0.0278343	+	0.0482105i
$650$	151.434			5.93974
$651$	−1.04926	+	0.943803i	−0.0411238	+	0.0369906i
$652$	−59.4384			−2.32779
$653$	18.6217	−	32.2537i	0.728722	−	1.26218i	−0.228702	−	0.973497i	$-0.573448\pi$
$653$	18.6217	−	32.2537i	0.728722	−	1.26218i	0.957424	−	0.288687i	$-0.0932186\pi$
$654$	7.71268	+	13.3588i	0.301590	+	0.522369i
$655$	11.5575	+	20.0182i	0.451589	+	0.782175i
$656$	−4.02789	+	6.97651i	−0.157263	+	0.272387i
$657$	6.47439			0.252590
$658$	−11.5442	−	54.4459i	−0.450039	−	2.12252i
$659$	−40.8470			−1.59117			−0.795587	−	0.605839i	$-0.792837\pi$
$659$	−40.8470			−1.59117			−0.795587	+	0.605839i	$0.792837\pi$
$660$	−7.27040	+	12.5927i	−0.283000	+	0.490170i
$661$	14.2196	+	24.6291i	0.553080	+	0.957962i	0.998050	+	0.0624167i	$0.0198808\pi$
$661$	14.2196	+	24.6291i	0.553080	+	0.957962i	−0.444971	+	0.895545i	$0.646786\pi$
$662$	38.8850	+	67.3507i	1.51131	+	2.61766i
$663$	6.34407	−	10.9883i	0.246383	−	0.426748i
$664$	−57.7203			−2.23998
$665$	12.9770	+	61.2033i	0.503225	+	2.37336i
$666$	5.67047			0.219726
$667$	3.63970	−	6.30415i	0.140930	−	0.244098i
$668$	−8.11385	−	14.0536i	−0.313934	−	0.543750i
$669$	3.45833	+	5.99001i	0.133707	+	0.231587i
$670$	9.79598	−	16.9671i	0.378452	−	0.655497i
$671$	3.76428			0.145319
$672$	−7.62855	+	6.86183i	−0.294278	+	0.264701i
$673$	29.3236			1.13034			0.565171	−	0.824974i	$-0.308810\pi$
$673$	29.3236			1.13034			0.565171	+	0.824974i	$0.308810\pi$
$674$	−12.0262	+	20.8300i	−0.463233	+	0.802343i
$675$	5.96755	+	10.3361i	0.229691	+	0.397837i
$676$	−28.4333	−	49.2479i	−1.09359	−	1.89415i
$677$	22.7424	−	39.3910i	0.874063	−	1.51392i	0.0163048	−	0.999867i	$-0.494810\pi$
$677$	22.7424	−	39.3910i	0.874063	−	1.51392i	0.857758	−	0.514054i	$-0.171857\pi$
$678$	−4.78017			−0.183581
$679$	−44.7618	−	14.5689i	−1.71780	−	0.559103i
$680$	−34.9178			−1.33904
$681$	−2.99240	+	5.18299i	−0.114669	+	0.198612i
$682$	0.627380	+	1.08665i	0.0240236	+	0.0416102i
$683$	−14.9038	−	25.8141i	−0.570277	−	0.987748i	−0.996537	−	0.0831477i	$-0.973503\pi$
$683$	−14.9038	−	25.8141i	−0.570277	−	0.987748i	0.426261	−	0.904600i	$-0.359831\pi$
$684$	−10.1519	+	17.5835i	−0.388166	+	0.672323i
$685$	59.8334			2.28611
$686$	−43.3338	+	4.48842i	−1.65449	+	0.171369i
$687$	−22.5522			−0.860422
$688$	−2.42837	+	4.20606i	−0.0925807	+	0.160355i
$689$	−9.72437	−	16.8431i	−0.370469	−	0.641671i
$690$	−6.86426	−	11.8892i	−0.261318	−	0.452616i
$691$	−7.92243	+	13.7220i	−0.301383	+	0.522011i	−0.976450	−	0.215746i	$-0.930782\pi$
$691$	−7.92243	+	13.7220i	−0.301383	+	0.522011i	0.675066	+	0.737757i	$0.264115\pi$
$692$	17.7060			0.673083
$693$	2.51585	+	0.818848i	0.0955691	+	0.0311055i
$694$	47.6100			1.80725
$695$	−23.1099	+	40.0276i	−0.876609	+	1.51833i
$696$	−9.25739	−	16.0343i	−0.350900	−	0.607777i
$697$	−6.68099	−	11.5718i	−0.253060	−	0.438313i
$698$	−15.1967	+	26.3215i	−0.575205	+	0.996284i
$699$	−12.9324			−0.489149
$700$	−82.9544	+	74.6170i	−3.13538	+	2.82026i
$701$	3.22320			0.121739			0.0608693	−	0.998146i	$-0.480613\pi$
$701$	3.22320			0.121739			0.0608693	+	0.998146i	$0.480613\pi$
$702$	6.34407	−	10.9883i	0.239441	−	0.414725i
$703$	−6.92585	−	11.9959i	−0.261214	−	0.452435i
$704$	5.97949	+	10.3568i	0.225361	+	0.390336i
$705$	−18.4006	+	31.8708i	−0.693007	+	1.20032i
$706$	−8.04237			−0.302679
$707$	4.37337	+	20.6262i	0.164478	+	0.775726i
$708$	−5.01104			−0.188326
$709$	4.11143	−	7.12120i	0.154408	−	0.267442i	−0.778435	−	0.627725i	$-0.783986\pi$
$709$	4.11143	−	7.12120i	0.154408	−	0.267442i	0.932843	+	0.360282i	$0.117320\pi$
$710$	19.8660	+	34.4089i	0.745557	+	1.29134i
$711$	−5.09766	−	8.82941i	−0.191177	−	0.331129i
$712$	15.7629	−	27.3022i	0.590740	−	1.02319i
$713$	−0.756481			−0.0283304
$714$	3.03663	+	14.3216i	0.113643	+	0.535974i
$715$	−22.1970			−0.830122
$716$	13.6192	−	23.5891i	0.508973	−	0.881568i
$717$	12.7675	+	22.1139i	0.476810	+	0.825858i
$718$	−28.2779	−	48.9787i	−1.05532	−	1.82787i
$719$	6.94650	−	12.0317i	0.259061	−	0.448706i	−0.706930	−	0.707284i	$-0.749920\pi$
$719$	6.94650	−	12.0317i	0.259061	−	0.448706i	0.965991	+	0.258577i	$0.0832537\pi$
$720$	−5.83616			−0.217501
$721$	31.6565	−	28.4748i	1.17895	−	1.06046i
$722$	32.9768			1.22727
$723$	−6.40928	+	11.1012i	−0.238364	+	0.412858i
$724$	1.81000	+	3.13502i	0.0672683	+	0.116512i
$725$	30.6308	+	53.0541i	1.13760	+	1.97038i
$726$	1.17616	−	2.03717i	0.0436514	−	0.0756065i
$727$	−29.6073			−1.09807			−0.549036	−	0.835798i	$-0.685005\pi$
$727$	−29.6073			−1.09807			−0.549036	+	0.835798i	$0.685005\pi$
$728$	48.9487	+	15.9317i	1.81416	+	0.590466i
$729$	1.00000			0.0370370
$730$	31.3371	−	54.2775i	1.15984	−	2.00890i
$731$	−4.02789	−	6.97652i	−0.148977	−	0.258036i
$732$	6.65039	+	11.5188i	0.245805	+	0.425747i
$733$	−6.07357	+	10.5197i	−0.224332	+	0.388555i	−0.956119	−	0.292979i	$-0.905353\pi$
$733$	−6.07357	+	10.5197i	−0.224332	+	0.388555i	0.731787	+	0.681534i	$0.238687\pi$
$734$	28.2226			1.04171
$735$	23.2880	+	16.9555i	0.858990	+	0.625415i
$736$	−5.49992			−0.202730
$737$	−1.01195	+	1.75274i	−0.0372755	+	0.0645631i
$738$	−6.68099	−	11.5718i	−0.245931	−	0.425964i
$739$	−19.4342	−	33.6611i	−0.714900	−	1.23824i	−0.962998	−	0.269508i	$-0.913139\pi$
$739$	−19.4342	−	33.6611i	−0.714900	−	1.23824i	0.248098	−	0.968735i	$-0.420194\pi$
$740$	17.5259	−	30.3558i	0.644266	−	1.11590i
$741$	−30.9943			−1.13860
$742$	21.3389	+	6.94529i	0.783374	+	0.254970i
$743$	33.6200			1.23340			0.616699	−	0.787199i	$-0.288469\pi$
$743$	33.6200			1.23340			0.616699	+	0.787199i	$0.288469\pi$
$744$	−0.962034	+	1.66629i	−0.0352699	+	0.0610892i
$745$	24.3719	+	42.2133i	0.892916	+	1.54658i
$746$	40.3585	+	69.9030i	1.47763	+	2.55933i
$747$	8.00096	−	13.8581i	0.292740	−	0.507040i
$748$	8.31172			0.303907
$749$	6.85565	−	6.16661i	0.250500	−	0.225323i
$750$	67.1341			2.45139
$751$	−5.54257	+	9.60002i	−0.202251	+	0.350310i	−0.949253	−	0.314512i	$-0.898159\pi$
$751$	−5.54257	+	9.60002i	−0.202251	+	0.350310i	0.747002	+	0.664822i	$0.231492\pi$
$752$	−6.34121	−	10.9833i	−0.231240	−	0.400519i
$753$	1.45595	+	2.52177i	0.0530576	+	0.0918985i
$754$	32.5634	−	56.4015i	1.18589	−	2.05402i
$755$	−36.3310			−1.32222
$756$	1.93907	+	9.14522i	0.0705232	+	0.332609i
$757$	−15.4683			−0.562205			−0.281102	−	0.959678i	$-0.590700\pi$
$757$	−15.4683			−0.562205			−0.281102	+	0.959678i	$0.590700\pi$
$758$	−36.1207	+	62.5630i	−1.31196	+	2.27239i
$759$	0.709093	+	1.22819i	0.0257385	+	0.0445803i
$760$	42.6482	+	73.8688i	1.54701	+	2.67950i
$761$	23.6321	−	40.9320i	0.856663	−	1.48378i	−0.0184313	−	0.999830i	$-0.505867\pi$
$761$	23.6321	−	40.9320i	0.856663	−	1.48378i	0.875094	−	0.483953i	$-0.160799\pi$
$762$	−19.8131			−0.717753
$763$	−3.59863	−	16.9722i	−0.130279	−	0.614436i
$764$	−10.6418			−0.385007
$765$	4.84017	−	8.38342i	0.174997	−	0.303103i
$766$	6.29001	+	10.8946i	0.227267	+	0.393639i
$767$	−3.82476	−	6.62469i	−0.138104	−	0.239204i
$768$	−12.0054	+	20.7940i	−0.433208	+	0.750338i
$769$	38.4854			1.38782			0.693910	−	0.720062i	$-0.255887\pi$
$769$	38.4854			1.38782			0.693910	+	0.720062i	$0.255887\pi$
$770$	19.0419	−	17.1280i	0.686221	−	0.617251i
$771$	−22.5729			−0.812944
$772$	4.59495	−	7.95869i	0.165376	−	0.286440i
$773$	−20.9108	−	36.2186i	−0.752109	−	1.30269i	−0.946799	−	0.321826i	$-0.895703\pi$
$773$	−20.9108	−	36.2186i	−0.752109	−	1.30269i	0.194690	−	0.980865i	$-0.437630\pi$
$774$	−4.02789	−	6.97652i	−0.144780	−	0.250766i
$775$	3.18317	−	5.51342i	0.114343	−	0.198048i
$776$	−64.1769			−2.30382
$777$	−6.06466	−	1.97390i	−0.217569	−	0.0708134i
$778$	−61.9025			−2.21931
$779$	−16.3202	+	28.2674i	−0.584731	+	1.01278i
$780$	−39.2157	−	67.9235i	−1.40415	−	2.43205i
$781$	−2.05220	−	3.55451i	−0.0734335	−	0.127191i
$782$	−3.92371	+	6.79606i	−0.140311	+	0.243027i
$783$	5.13289			0.183435
$784$	−9.07311	+	4.02867i	−0.324039	+	0.143881i
$785$	−79.8257			−2.84910
$786$	6.60643	−	11.4427i	0.235644	−	0.408147i
$787$	12.3508	+	21.3922i	0.440259	+	0.762551i	0.997708	−	0.0676599i	$-0.0215533\pi$
$787$	12.3508	+	21.3922i	0.440259	+	0.762551i	−0.557449	+	0.830211i	$0.688220\pi$
$788$	18.6342	+	32.2754i	0.663817	+	1.14977i
$789$	6.21182	−	10.7592i	0.221147	−	0.383038i
$790$	−98.6941			−3.51138
$791$	5.11247	+	1.66399i	0.181779	+	0.0591646i
$792$	3.60708			0.128172
$793$	−10.1520	+	17.5839i	−0.360510	+	0.624421i
$794$	32.8537	+	56.9042i	1.16593	+	2.01945i
$795$	−7.41915	−	12.8503i	−0.263130	−	0.455755i
$796$	12.8922	−	22.3299i	0.456951	−	0.791462i
$797$	−5.08051			−0.179961			−0.0899804	−	0.995944i	$-0.528680\pi$
$797$	−5.08051			−0.179961			−0.0899804	+	0.995944i	$0.528680\pi$
$798$	26.5887	−	23.9163i	0.941229	−	0.846629i
$799$	21.0361			0.744204
$800$	23.1430	−	40.0848i	0.818227	−	1.41721i
$801$	4.36999	+	7.56904i	0.154406	+	0.267439i
$802$	40.6364	+	70.3842i	1.43492	+	2.48535i
$803$	−3.23719	+	5.60698i	−0.114238	+	0.197866i
$804$	−7.15125			−0.252205
$805$	3.20277	+	15.1052i	0.112883	+	0.532389i
$806$	−6.76803			−0.238394
$807$	−5.01468	+	8.68568i	−0.176525	+	0.305750i
$808$	14.3729	+	24.8946i	0.505637	+	0.875789i
$809$	12.3474	+	21.3862i	0.434110	+	0.751900i	0.997223	−	0.0744799i	$-0.0237297\pi$
$809$	12.3474	+	21.3862i	0.434110	+	0.751900i	−0.563113	+	0.826380i	$0.690396\pi$
$810$	4.84017	−	8.38342i	0.170066	−	0.294563i
$811$	30.9575			1.08706			0.543532	−	0.839388i	$-0.317087\pi$
$811$	30.9575			1.08706			0.543532	+	0.839388i	$0.317087\pi$
$812$	9.95303	+	46.9415i	0.349283	+	1.64732i
$813$	−23.7943			−0.834501
$814$	−2.83524	+	4.91077i	−0.0993749	+	0.172122i
$815$	−34.6128	−	59.9510i	−1.21243	−	2.09999i
$816$	1.66802	+	2.88909i	0.0583922	+	0.101138i
$817$	−9.83926	+	17.0421i	−0.344232	+	0.596227i
$818$	54.1825			1.89445
$819$	−10.6101	+	9.54373i	−0.370748	+	0.333485i
$820$	−82.5966			−2.88440
$821$	−4.59321	+	7.95567i	−0.160304	+	0.277655i	−0.934978	−	0.354706i	$-0.884581\pi$
$821$	−4.59321	+	7.95567i	−0.160304	+	0.277655i	0.774674	+	0.632361i	$0.217914\pi$
$822$	−17.1008	−	29.6194i	−0.596458	−	1.03310i
$823$	−3.90309	−	6.76035i	−0.136053	−	0.235651i	0.789946	−	0.613176i	$-0.210108\pi$
$823$	−3.90309	−	6.76035i	−0.136053	−	0.235651i	−0.925999	+	0.377525i	$0.876775\pi$
$824$	29.0249	−	50.2725i	1.01113	−	1.75133i
$825$	−11.9351			−0.415527
$826$	8.39294	+	2.73170i	0.292028	+	0.0950481i
$827$	12.3641			0.429942			0.214971	−	0.976620i	$-0.431034\pi$
$827$	12.3641			0.429942			0.214971	+	0.976620i	$0.431034\pi$
$828$	−2.50552	+	4.33969i	−0.0870728	+	0.150815i
$829$	17.0018	+	29.4480i	0.590498	+	1.02277i	0.994165	+	0.107866i	$0.0344018\pi$
$829$	17.0018	+	29.4480i	0.590498	+	1.02277i	−0.403668	+	0.914906i	$0.632265\pi$
$830$	−77.4520	−	134.151i	−2.68840	−	4.65644i
$831$	4.78104	−	8.28101i	0.165852	−	0.287265i
$832$	−64.5054			−2.23632
$833$	1.73768	−	16.3743i	0.0602069	−	0.567336i
$834$	26.4199			0.914846
$835$	9.44988	−	16.3677i	0.327027	−	0.566427i
$836$	−10.1519	−	17.5835i	−0.351109	−	0.608139i
$837$	−0.266707	−	0.461950i	−0.00921874	−	0.0159673i
$838$	19.5666	−	33.8903i	0.675916	−	1.17072i
$839$	−2.18419			−0.0754067			−0.0377034	−	0.999289i	$-0.512004\pi$
$839$	−2.18419			−0.0754067			−0.0377034	+	0.999289i	$0.512004\pi$
$840$	37.3451	+	12.1550i	1.28853	+	0.419386i
$841$	−2.65339			−0.0914962
$842$	21.5059	−	37.2493i	0.741142	−	1.28370i
$843$	−3.71241	−	6.43008i	−0.127862	−	0.221464i
$844$	24.3428	+	42.1631i	0.837915	+	1.45131i
$845$	33.1151	−	57.3571i	1.13919	−	1.97314i
$846$	21.0361			0.723236
$847$	−1.96707	+	1.76936i	−0.0675892	+	0.0607960i
$848$	5.11356			0.175600
$849$	−12.2038	+	21.1376i	−0.418833	+	0.725440i
$850$	−33.0209	−	57.1939i	−1.13261	−	1.96173i
$851$	−1.70933	−	2.96065i	−0.0585951	−	0.101490i
$852$	7.25127	−	12.5596i	0.248424	−	0.430284i
$853$	−39.9771			−1.36879			−0.684395	−	0.729111i	$-0.739934\pi$
$853$	−39.9771			−1.36879			−0.684395	+	0.729111i	$0.739934\pi$
$854$	−4.85934	−	22.9181i	−0.166283	−	0.784241i
$855$	−23.6469			−0.808708
$856$	6.28573	−	10.8872i	0.214842	−	0.372117i
$857$	−1.22537	−	2.12240i	−0.0418578	−	0.0724998i	0.844338	−	0.535812i	$-0.179994\pi$
$857$	−1.22537	−	2.12240i	−0.0418578	−	0.0724998i	−0.886195	+	0.463312i	$0.846661\pi$
$858$	6.34407	+	10.9883i	0.216583	+	0.375133i
$859$	14.5621	−	25.2223i	0.496852	−	0.860573i	−0.503142	−	0.864204i	$-0.667823\pi$
$859$	14.5621	−	25.2223i	0.496852	−	0.860573i	0.999993	+	0.00363134i	$0.00115589\pi$
$860$	−49.7966			−1.69805
$861$	3.11725	+	14.7019i	0.106236	+	0.501040i
$862$	53.0753			1.80775
$863$	−8.93455	+	15.4751i	−0.304136	+	0.526778i	−0.977068	−	0.212925i	$-0.931701\pi$
$863$	−8.93455	+	15.4751i	−0.304136	+	0.526778i	0.672933	+	0.739704i	$0.265034\pi$
$864$	−1.93907	−	3.35856i	−0.0659684	−	0.114261i
$865$	10.3108	+	17.8588i	0.350576	+	0.607216i
$866$	−4.19852	+	7.27205i	−0.142672	+	0.247114i
$867$	11.4666			0.389426
$868$	3.70747	−	3.33485i	0.125840	−	0.113192i
$869$	10.1953			0.345853
$870$	24.8441	−	43.0312i	0.842293	−	1.45889i
$871$	−5.45832	−	9.45408i	−0.184948	−	0.320339i
$872$	−11.8267	−	20.4845i	−0.400504	−	0.693693i
$873$	8.89596	−	15.4083i	0.301083	−	0.521490i
$874$	19.1695			0.648418
$875$	−71.8010	−	23.3695i	−2.42732	−	0.790034i
$876$	−22.8767			−0.772932
$877$	11.4450	−	19.8233i	0.386470	−	0.669385i	−0.605502	−	0.795844i	$-0.707028\pi$
$877$	11.4450	−	19.8233i	0.386470	−	0.669385i	0.991972	+	0.126458i	$0.0403610\pi$
$878$	−30.6696	−	53.1213i	−1.03505	−	1.79276i
$879$	15.7242	+	27.2351i	0.530364	+	0.918617i
$880$	2.91808	−	5.05426i	0.0983685	−	0.170379i
$881$	22.5442			0.759533			0.379766	−	0.925082i	$-0.376004\pi$
$881$	22.5442			0.759533			0.379766	+	0.925082i	$0.376004\pi$
$882$	1.73768	−	16.3743i	0.0585106	−	0.551351i
$883$	44.0121			1.48112			0.740562	−	0.671988i	$-0.234559\pi$
$883$	44.0121			1.48112			0.740562	+	0.671988i	$0.234559\pi$
$884$	−22.4162	+	38.8260i	−0.753939	+	1.30586i
$885$	−2.91808	−	5.05426i	−0.0980902	−	0.169897i
$886$	17.8065	+	30.8418i	0.598221	+	1.03615i
$887$	−0.907958	+	1.57263i	−0.0304863	+	0.0528038i	−0.880866	−	0.473366i	$-0.843039\pi$
$887$	−0.907958	+	1.57263i	−0.0304863	+	0.0528038i	0.850380	+	0.526169i	$0.176372\pi$
$888$	−8.69518			−0.291791
$889$	21.1905	+	6.89699i	0.710705	+	0.231318i
$890$	84.6059			2.83600
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$	−12.2197	−	21.1652i	−0.409147	−	0.708663i
$893$	−25.6933	−	44.5021i	−0.859793	−	1.48920i
$894$	13.9313	−	24.1297i	0.465932	−	0.807018i
$895$	31.7235			1.06040
$896$	40.0792	−	36.0510i	1.33895	−	1.20438i
$897$	−7.64953			−0.255410
$898$	11.0668	−	19.1683i	0.369305	−	0.639655i
$899$	−1.36898	−	2.37114i	−0.0456580	−	0.0790820i
$900$	−21.0858	−	36.5217i	−0.702861	−	1.21739i
$901$	−4.24089	+	7.34543i	−0.141284	+	0.244712i
$902$	13.3620			0.444905
$903$	1.87936	+	8.86362i	0.0625411	+	0.294963i
$904$	7.32998			0.243792
$905$	−2.10804	+	3.65123i	−0.0700736	+	0.121371i
$906$	10.3837	+	17.9850i	0.344974	+	0.597512i
$907$	20.8205	+	36.0621i	0.691333	+	1.19742i	0.971401	+	0.237443i	$0.0763093\pi$
$907$	20.8205	+	36.0621i	0.691333	+	1.19742i	−0.280069	+	0.959980i	$0.590357\pi$
$908$	10.5734	−	18.3136i	0.350890	−	0.607759i
$909$	−7.96927			−0.264324
$910$	28.6543	+	135.142i	0.949881	+	4.47993i
$911$	−7.61048			−0.252147			−0.126073	−	0.992021i	$-0.540237\pi$
$911$	−7.61048			−0.252147			−0.126073	+	0.992021i	$0.540237\pi$
$912$	4.07459	−	7.05740i	0.134923	−	0.233694i
$913$	8.00096	+	13.8581i	0.264793	+	0.458635i
$914$	14.9755	+	25.9383i	0.495344	+	0.857961i
$915$	−7.74544	+	13.4155i	−0.256056	+	0.443503i
$916$	79.6864			2.63291
$917$	−11.0489	+	9.93842i	−0.364867	+	0.328196i
$918$	−5.53341			−0.182630
$919$	10.1444	−	17.5705i	0.334631	−	0.579599i	−0.648783	−	0.760974i	$-0.724722\pi$
$919$	10.1444	−	17.5705i	0.334631	−	0.579599i	0.983414	+	0.181375i	$0.0580549\pi$
$920$	10.5258	+	18.2311i	0.347024	+	0.601063i
$921$	−0.467448	−	0.809643i	−0.0154029	−	0.0266787i
$922$	24.5931	−	42.5965i	0.809930	−	1.40284i
$923$	22.1386			0.728702
$924$	−8.88953	−	2.89333i	−0.292444	−	0.0951836i
$925$	28.7706			0.945971
$926$	−17.4765	+	30.2702i	−0.574314	+	0.994742i
$927$	8.04663	+	13.9372i	0.264286	+	0.457757i
$928$	−9.95303	−	17.2391i	−0.326724	−	0.565903i
$929$	−19.6088	+	33.9634i	−0.643344	+	1.11430i	0.341337	+	0.939941i	$0.389120\pi$
$929$	−19.6088	+	33.9634i	−0.643344	+	1.11430i	−0.984681	+	0.174364i	$0.944213\pi$
$930$	−5.16363			−0.169322
$931$	−36.7624	+	16.3233i	−1.20484	+	0.534976i
$932$	45.6956			1.49681
$933$	6.98248	−	12.0940i	0.228596	−	0.395940i
$934$	3.17774	+	5.50400i	0.103979	+	0.180097i
$935$	4.84017	+	8.38342i	0.158290	+	0.274167i
$936$	−9.72808	+	16.8495i	−0.317972	+	0.550744i
$937$	−48.0166			−1.56863			−0.784317	−	0.620360i	$-0.786986\pi$
$937$	−48.0166			−1.56863			−0.784317	+	0.620360i	$0.786986\pi$
$938$	11.9776	+	3.89841i	0.391081	+	0.127288i
$939$	−4.60378			−0.150239
$940$	65.0170	−	112.613i	2.12062	−	3.67302i
$941$	16.3003	+	28.2330i	0.531376	+	0.920370i	0.999329	+	0.0366172i	$0.0116582\pi$
$941$	16.3003	+	28.2330i	0.531376	+	0.920370i	−0.467953	+	0.883753i	$0.655008\pi$
$942$	22.8147	+	39.5163i	0.743344	+	1.28751i
$943$	−4.02789	+	6.97651i	−0.131166	+	0.227186i
$944$	2.01125			0.0654607
$945$	−8.09493	+	7.28133i	−0.263328	+	0.236862i
$946$	8.05579			0.261916
$947$	13.0429	−	22.5909i	0.423837	−	0.734107i	−0.572474	−	0.819923i	$-0.694016\pi$
$947$	13.0429	−	22.5909i	0.423837	−	0.734107i	0.996311	+	0.0858159i	$0.0273497\pi$
$948$	18.0121	+	31.1980i	0.585007	+	1.01326i
$949$	−17.4610	−	30.2434i	−0.566809	−	0.981742i
$950$	−80.6628	+	139.712i	−2.61705	+	4.53286i
$951$	23.9979			0.778184
$952$	−4.65641	−	21.9610i	−0.150915	−	0.711761i
$953$	−6.67910			−0.216357			−0.108179	−	0.994131i	$-0.534502\pi$
$953$	−6.67910			−0.216357			−0.108179	+	0.994131i	$0.534502\pi$
$954$	−4.24089	+	7.34543i	−0.137304	+	0.237817i
$955$	−6.19704	−	10.7336i	−0.200532	−	0.347331i
$956$	−45.1127	−	78.1375i	−1.45905	−	2.52715i
$957$	−2.56645	+	4.44522i	−0.0829615	+	0.143693i
$958$	−85.0070			−2.74645
$959$	7.97899	+	37.6313i	0.257655	+	1.21518i
$960$	−49.2140			−1.58837
$961$	15.3577	−	26.6004i	0.495411	−	0.858077i
$962$	−15.2929	−	26.4881i	−0.493064	−	0.854011i
$963$	1.74261	+	3.01829i	0.0561548	+	0.0972629i
$964$	22.6467	−	39.2252i	0.729400	−	1.26336i
$965$	10.7031			0.344546
$966$	6.56220	−	5.90265i	0.211135	−	0.189915i
$967$	−41.4741			−1.33372			−0.666859	−	0.745184i	$-0.732362\pi$
$967$	−41.4741			−1.33372			−0.666859	+	0.745184i	$0.732362\pi$
$968$	−1.80354	+	3.12382i	−0.0579680	+	0.100404i
$969$	6.75846	+	11.7060i	0.217113	+	0.376051i
$970$	−86.1159	−	149.157i	−2.76501	−	4.78915i
$971$	−23.0509	+	39.9253i	−0.739738	+	1.28126i	0.212876	+	0.977079i	$0.431717\pi$
$971$	−23.0509	+	39.9253i	−0.739738	+	1.28126i	−0.952613	+	0.304184i	$0.901616\pi$
$972$	−3.53341			−0.113334
$973$	−28.2565	−	9.19683i	−0.905863	−	0.294837i
$974$	−50.1088			−1.60559
$975$	32.1882	−	55.7517i	1.03085	−	1.78548i
$976$	−2.66923	−	4.62324i	−0.0854399	−	0.147986i
$977$	15.5916	+	27.0054i	0.498819	+	0.863979i	0.999999	−	0.00136350i	$-0.000434015\pi$
$977$	15.5916	+	27.0054i	0.498819	+	0.863979i	−0.501180	+	0.865343i	$0.667101\pi$
$978$	−19.7851	+	34.2689i	−0.632659	+	1.09580i
$979$	−8.73998			−0.279331
$980$	−82.2860	−	59.9109i	−2.62853	−	1.91378i
$981$	6.55751			0.209365
$982$	23.3352	−	40.4177i	0.744655	−	1.28978i
$983$	4.78448	+	8.28697i	0.152601	+	0.264313i	0.932183	−	0.361987i	$-0.117902\pi$
$983$	4.78448	+	8.28697i	0.152601	+	0.264313i	−0.779582	+	0.626301i	$0.784568\pi$
$984$	10.2447	+	17.7444i	0.326590	+	0.565670i
$985$	−21.7026	+	37.5899i	−0.691501	+	1.19771i
$986$	−28.4024			−0.904518
$987$	−22.4985	−	7.32271i	−0.716134	−	0.233085i
$988$	109.516			3.48416
$989$	−2.42837	+	4.20606i	−0.0772177	+	0.133745i
$990$	4.84017	+	8.38342i	0.153831	+	0.266442i
$991$	27.5493	+	47.7168i	0.875133	+	1.51577i	0.856621	+	0.515946i	$0.172559\pi$
$991$	27.5493	+	47.7168i	0.875133	+	1.51577i	0.0185115	+	0.999829i	$0.494107\pi$
$992$	−1.03433	+	1.79150i	−0.0328399	+	0.0568803i
$993$	33.0609			1.04916
$994$	−18.9918	+	17.0830i	−0.602382	+	0.541839i
$995$	30.0300			0.952014
$996$	−28.2707	+	48.9663i	−0.895792	+	1.55156i
$997$	−28.6774	−	49.6707i	−0.908222	−	1.57309i	−0.816533	−	0.577299i	$-0.804107\pi$
$997$	−28.6774	−	49.6707i	−0.908222	−	1.57309i	−0.0916894	−	0.995788i	$-0.529227\pi$
$998$	−7.68434	−	13.3097i	−0.243244	−	0.421310i
$999$	1.20529	−	2.08763i	0.0381338	−	0.0660496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.i.f.100.2	yes	10
3.2	odd	2		693.2.i.j.100.4		10
7.2	even	3		1617.2.a.ba.1.4		5
7.4	even	3	inner	231.2.i.f.67.2	✓	10
7.5	odd	6		1617.2.a.bb.1.4		5
21.2	odd	6		4851.2.a.ca.1.2		5
21.5	even	6		4851.2.a.bz.1.2		5
21.11	odd	6		693.2.i.j.298.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.f.67.2	✓	10	7.4	even	3	inner
231.2.i.f.100.2	yes	10	1.1	even	1	trivial
693.2.i.j.100.4		10	3.2	odd	2
693.2.i.j.298.4		10	21.11	odd	6
1617.2.a.ba.1.4		5	7.2	even	3
1617.2.a.bb.1.4		5	7.5	odd	6
4851.2.a.bz.1.2		5	21.5	even	6
4851.2.a.ca.1.2		5	21.2	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17616 + 2.03717i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.76671 - 3.06003i) q^{4} +(2.05761 - 3.56389i) q^{5} -2.35232 q^{6} +(2.51585 + 0.818848i) q^{7} +3.60708 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.17616 + 2.03717i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.76671 - 3.06003i) q^{4} +(2.05761 - 3.56389i) q^{5} -2.35232 q^{6} +(2.51585 + 0.818848i) q^{7} +3.60708 q^{8} +(-0.500000 + 0.866025i) q^{9} +(4.84017 + 8.38342i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.76671 - 3.06003i) q^{12} +5.39388 q^{13} +(-4.62717 + 4.16211i) q^{14} +4.11523 q^{15} +(-0.709093 + 1.22819i) q^{16} +(-1.17616 - 2.03717i) q^{17} +(-1.17616 - 2.03717i) q^{18} +(-2.87310 + 4.97636i) q^{19} -14.5408 q^{20} +(0.548780 + 2.58821i) q^{21} +2.35232 q^{22} +(-0.709093 + 1.22819i) q^{23} +(1.80354 + 3.12382i) q^{24} +(-5.96755 - 10.3361i) q^{25} +(-6.34407 + 10.9883i) q^{26} -1.00000 q^{27} +(-1.93907 - 9.14522i) q^{28} -5.13289 q^{29} +(-4.84017 + 8.38342i) q^{30} +(0.266707 + 0.461950i) q^{31} +(1.93907 + 3.35856i) q^{32} +(0.500000 - 0.866025i) q^{33} +5.53341 q^{34} +(8.09493 - 7.28133i) q^{35} +3.53341 q^{36} +(-1.20529 + 2.08763i) q^{37} +(-6.75846 - 11.7060i) q^{38} +(2.69694 + 4.67124i) q^{39} +(7.42198 - 12.8552i) q^{40} +5.68034 q^{41} +(-5.91808 - 1.92619i) q^{42} +3.42461 q^{43} +(-1.76671 + 3.06003i) q^{44} +(2.05761 + 3.56389i) q^{45} +(-1.66802 - 2.88909i) q^{46} +(-4.47135 + 7.74460i) q^{47} -1.41819 q^{48} +(5.65897 + 4.12020i) q^{49} +28.0752 q^{50} +(1.17616 - 2.03717i) q^{51} +(-9.52941 - 16.5054i) q^{52} +(-1.80285 - 3.12263i) q^{53} +(1.17616 - 2.03717i) q^{54} -4.11523 q^{55} +(9.07487 + 2.95365i) q^{56} -5.74620 q^{57} +(6.03711 - 10.4566i) q^{58} +(-0.709093 - 1.22819i) q^{59} +(-7.27040 - 12.5927i) q^{60} +(-1.88214 + 3.25996i) q^{61} -1.25476 q^{62} +(-1.96707 + 1.76936i) q^{63} -11.9590 q^{64} +(11.0985 - 19.2232i) q^{65} +(1.17616 + 2.03717i) q^{66} +(-1.01195 - 1.75274i) q^{67} +(-4.15586 + 7.19816i) q^{68} -1.41819 q^{69} +(5.31237 + 25.0548i) q^{70} +4.10440 q^{71} +(-1.80354 + 3.12382i) q^{72} +(-3.23719 - 5.60698i) q^{73} +(-2.83524 - 4.91077i) q^{74} +(5.96755 - 10.3361i) q^{75} +20.3037 q^{76} +(-0.548780 - 2.58821i) q^{77} -12.6881 q^{78} +(-5.09766 + 8.82941i) q^{79} +(2.91808 + 5.05426i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.68099 + 11.5718i) q^{82} -16.0019 q^{83} +(6.95046 - 6.25189i) q^{84} -9.68034 q^{85} +(-4.02789 + 6.97652i) q^{86} +(-2.56645 - 4.44522i) q^{87} +(-1.80354 - 3.12382i) q^{88} +(4.36999 - 7.56904i) q^{89} -9.68034 q^{90} +(13.5702 + 4.41677i) q^{91} +5.01104 q^{92} +(-0.266707 + 0.461950i) q^{93} +(-10.5180 - 18.2178i) q^{94} +(11.8235 + 20.4788i) q^{95} +(-1.93907 + 3.35856i) q^{96} -17.7919 q^{97} +(-15.0494 + 6.68228i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9} - 2 q^{10} - 5 q^{11} + 10 q^{12} + 10 q^{13} - 10 q^{14} + 8 q^{15} - 16 q^{16} - 2 q^{17} - 2 q^{18} + 3 q^{19} - 16 q^{20} - 2 q^{21} + 4 q^{22} - 16 q^{23} + 6 q^{24} - 7 q^{25} + 10 q^{26} - 10 q^{27} + 4 q^{28} + 2 q^{30} - 5 q^{31} - 4 q^{32} + 5 q^{33} + 40 q^{34} + 26 q^{35} + 20 q^{36} - 15 q^{37} - 6 q^{38} + 5 q^{39} + 6 q^{40} - 44 q^{41} - 14 q^{42} + 6 q^{43} - 10 q^{44} + 4 q^{45} - 16 q^{46} + 2 q^{47} - 32 q^{48} + 31 q^{49} + 68 q^{50} + 2 q^{51} - 40 q^{52} - 6 q^{53} + 2 q^{54} - 8 q^{55} - 12 q^{56} + 6 q^{57} - 12 q^{58} - 16 q^{59} - 8 q^{60} - 12 q^{61} - 8 q^{62} - q^{63} - 8 q^{64} + 28 q^{65} + 2 q^{66} - 7 q^{67} - 10 q^{68} - 32 q^{69} + 32 q^{70} + 48 q^{71} - 6 q^{72} - 17 q^{73} + 36 q^{74} + 7 q^{75} + 60 q^{76} + 2 q^{77} + 20 q^{78} - 7 q^{79} - 16 q^{80} - 5 q^{81} - 8 q^{82} - 24 q^{83} - 28 q^{84} + 4 q^{85} + 18 q^{86} - 6 q^{88} + 6 q^{89} + 4 q^{90} + 11 q^{91} + 136 q^{92} + 5 q^{93} - 82 q^{94} + 18 q^{95} + 4 q^{96} - 28 q^{97} - 38 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9 - 2 * q^10 - 5 * q^11 + 10 * q^12 + 10 * q^13 - 10 * q^14 + 8 * q^15 - 16 * q^16 - 2 * q^17 - 2 * q^18 + 3 * q^19 - 16 * q^20 - 2 * q^21 + 4 * q^22 - 16 * q^23 + 6 * q^24 - 7 * q^25 + 10 * q^26 - 10 * q^27 + 4 * q^28 + 2 * q^30 - 5 * q^31 - 4 * q^32 + 5 * q^33 + 40 * q^34 + 26 * q^35 + 20 * q^36 - 15 * q^37 - 6 * q^38 + 5 * q^39 + 6 * q^40 - 44 * q^41 - 14 * q^42 + 6 * q^43 - 10 * q^44 + 4 * q^45 - 16 * q^46 + 2 * q^47 - 32 * q^48 + 31 * q^49 + 68 * q^50 + 2 * q^51 - 40 * q^52 - 6 * q^53 + 2 * q^54 - 8 * q^55 - 12 * q^56 + 6 * q^57 - 12 * q^58 - 16 * q^59 - 8 * q^60 - 12 * q^61 - 8 * q^62 - q^63 - 8 * q^64 + 28 * q^65 + 2 * q^66 - 7 * q^67 - 10 * q^68 - 32 * q^69 + 32 * q^70 + 48 * q^71 - 6 * q^72 - 17 * q^73 + 36 * q^74 + 7 * q^75 + 60 * q^76 + 2 * q^77 + 20 * q^78 - 7 * q^79 - 16 * q^80 - 5 * q^81 - 8 * q^82 - 24 * q^83 - 28 * q^84 + 4 * q^85 + 18 * q^86 - 6 * q^88 + 6 * q^89 + 4 * q^90 + 11 * q^91 + 136 * q^92 + 5 * q^93 - 82 * q^94 + 18 * q^95 + 4 * q^96 - 28 * q^97 - 38 * q^98 + 10 * q^99

Introduction

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