LMFDB - Embedded newform 165.2.k.c.23.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(23,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("165.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.k (of order $4$, 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:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} + 19 x^{12} - 80 x^{11} + 168 x^{10} + 28 x^{9} + 119 x^{8} - 432 x^{7} + \cdots + 16 $ x^16 - 4x^15 + 8x^14 + 19x^12 - 80x^11 + 168x^10 + 28x^9 + 119x^8 - 432x^7 + 784x^6 + 84x^5 + 169x^4 - 420x^3 + 392x^2 - 112x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.8
Root			$-1.31757 + 1.31757i$ of defining polynomial
Character	$\chi$	$=$	165.23
Dual form			165.2.k.c.122.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.31757 + 1.31757i) q^{2} +(1.52275 + 0.825374i) q^{3} +1.47196i q^{4} +(-1.49219 - 1.66534i) q^{5} +(0.918834 + 3.09381i) q^{6} +(-2.09381 + 2.09381i) q^{7} +(0.695724 - 0.695724i) q^{8} +(1.63751 + 2.51367i) q^{9} +(0.228136 - 4.16026i) q^{10} -1.00000i q^{11} +(-1.21492 + 2.24143i) q^{12} +(0.161681 + 0.161681i) q^{13} -5.51746 q^{14} +(-0.897700 - 3.76751i) q^{15} +4.77725 q^{16} +(-3.37518 - 3.37518i) q^{17} +(-1.15440 + 5.46946i) q^{18} -8.52083i q^{19} +(2.45132 - 2.19645i) q^{20} +(-4.91651 + 1.46016i) q^{21} +(1.31757 - 1.31757i) q^{22} +(-3.15119 + 3.15119i) q^{23} +(1.63364 - 0.485178i) q^{24} +(-0.546726 + 4.97002i) q^{25} +0.426051i q^{26} +(0.418798 + 5.17925i) q^{27} +(-3.08200 - 3.08200i) q^{28} -3.01631 q^{29} +(3.78117 - 6.14672i) q^{30} +5.01096 q^{31} +(4.90290 + 4.90290i) q^{32} +(0.825374 - 1.52275i) q^{33} -8.89405i q^{34} +(6.61126 + 0.362542i) q^{35} +(-3.70003 + 2.41036i) q^{36} +(-4.74287 + 4.74287i) q^{37} +(11.2268 - 11.2268i) q^{38} +(0.112752 + 0.379646i) q^{39} +(-2.19677 - 0.120464i) q^{40} +4.49923i q^{41} +(-8.40169 - 4.55397i) q^{42} +(0.336036 + 0.336036i) q^{43} +1.47196 q^{44} +(1.74264 - 6.47790i) q^{45} -8.30379 q^{46} +(6.15190 + 6.15190i) q^{47} +(7.27454 + 3.94302i) q^{48} -1.76804i q^{49} +(-7.26868 + 5.82798i) q^{50} +(-2.35376 - 7.92533i) q^{51} +(-0.237988 + 0.237988i) q^{52} +(-1.62043 + 1.62043i) q^{53} +(-6.27221 + 7.37580i) q^{54} +(-1.66534 + 1.49219i) q^{55} +2.91342i q^{56} +(7.03287 - 12.9751i) q^{57} +(-3.97419 - 3.97419i) q^{58} -5.16965 q^{59} +(5.54564 - 1.32138i) q^{60} -3.39049 q^{61} +(6.60228 + 6.60228i) q^{62} +(-8.69178 - 1.83450i) q^{63} +3.36529i q^{64} +(0.0279950 - 0.510513i) q^{65} +(3.09381 - 0.918834i) q^{66} +(9.74916 - 9.74916i) q^{67} +(4.96814 - 4.96814i) q^{68} +(-7.39937 + 2.19755i) q^{69} +(8.23310 + 9.18845i) q^{70} -2.23272i q^{71} +(2.88808 + 0.609564i) q^{72} +(5.43376 + 5.43376i) q^{73} -12.4981 q^{74} +(-4.93465 + 7.11683i) q^{75} +12.5423 q^{76} +(2.09381 + 2.09381i) q^{77} +(-0.351651 + 0.648767i) q^{78} +5.93637i q^{79} +(-7.12858 - 7.95576i) q^{80} +(-3.63710 + 8.23235i) q^{81} +(-5.92804 + 5.92804i) q^{82} +(-0.365862 + 0.365862i) q^{83} +(-2.14930 - 7.23692i) q^{84} +(-0.584411 + 10.6572i) q^{85} +0.885499i q^{86} +(-4.59307 - 2.48958i) q^{87} +(-0.695724 - 0.695724i) q^{88} +3.70157 q^{89} +(10.8311 - 6.23903i) q^{90} -0.677057 q^{91} +(-4.63843 - 4.63843i) q^{92} +(7.63043 + 4.13592i) q^{93} +16.2111i q^{94} +(-14.1901 + 12.7147i) q^{95} +(3.41914 + 11.5126i) q^{96} +(4.94287 - 4.94287i) q^{97} +(2.32951 - 2.32951i) q^{98} +(2.51367 - 1.63751i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 2 q^{3} - 8 q^{5} - 4 q^{6} + 8 q^{7} + 16 q^{8} + 6 q^{9} - 4 q^{10} - 4 q^{12} - 24 q^{14} + 8 q^{15} - 4 q^{16} + 8 q^{17} - 32 q^{18} - 20 q^{20} - 8 q^{21} - 4 q^{22} + 14 q^{23} + 12 q^{24}+ \cdots - 4 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 2 * q^3 - 8 * q^5 - 4 * q^6 + 8 * q^7 + 16 * q^8 + 6 * q^9 - 4 * q^10 - 4 * q^12 - 24 * q^14 + 8 * q^15 - 4 * q^16 + 8 * q^17 - 32 * q^18 - 20 * q^20 - 8 * q^21 - 4 * q^22 + 14 * q^23 + 12 * q^24 - 18 * q^25 - 20 * q^27 + 8 * q^28 - 16 * q^29 + 20 * q^30 + 8 * q^31 + 28 * q^32 + 4 * q^33 + 44 * q^36 - 6 * q^37 + 24 * q^38 + 24 * q^39 + 16 * q^40 - 60 * q^42 + 16 * q^43 + 12 * q^44 + 24 * q^45 - 32 * q^46 + 48 * q^47 - 48 * q^48 - 12 * q^50 - 8 * q^51 + 36 * q^52 - 4 * q^53 + 4 * q^54 + 2 * q^55 - 8 * q^57 - 12 * q^58 - 68 * q^59 - 28 * q^60 - 8 * q^61 + 48 * q^62 - 12 * q^63 - 48 * q^65 + 8 * q^66 + 6 * q^67 + 24 * q^68 + 12 * q^69 - 4 * q^70 - 8 * q^72 + 8 * q^74 + 8 * q^75 + 16 * q^76 - 8 * q^77 - 48 * q^78 - 24 * q^80 + 2 * q^81 + 12 * q^82 - 8 * q^83 + 52 * q^84 - 4 * q^85 - 36 * q^87 - 16 * q^88 + 32 * q^89 + 44 * q^90 - 56 * q^91 + 20 * q^92 + 28 * q^93 - 48 * q^95 + 80 * q^96 + 18 * q^97 + 16 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.31757	+	1.31757i	0.931660	+	0.931660i	0.997810	−	0.0661495i	$-0.0210714\pi$
$2$	1.31757	+	1.31757i	0.931660	+	0.931660i	−0.0661495	+	0.997810i	$0.521071\pi$
$3$	1.52275	+	0.825374i	0.879158	+	0.476530i
$3$	1.52275	+	0.825374i	0.879158	+	0.476530i
$4$			1.47196i			0.735981i
$5$	−1.49219	−	1.66534i	−0.667329	−	0.744763i
$5$	−1.49219	−	1.66534i	−0.667329	−	0.744763i
$6$	0.918834	+	3.09381i	0.375112	+	1.26304i
$7$	−2.09381	+	2.09381i	−0.791384	+	0.791384i	−0.981719	−	0.190335i	$-0.939043\pi$
$7$	−2.09381	+	2.09381i	−0.791384	+	0.791384i	0.190335	+	0.981719i	$0.439043\pi$
$8$	0.695724	−	0.695724i	0.245976	−	0.245976i
$9$	1.63751	+	2.51367i	0.545838	+	0.837891i
$10$	0.228136	−	4.16026i	0.0721430	−	1.31559i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−1.21492	+	2.24143i	−0.350717	+	0.647044i
$13$	0.161681	+	0.161681i	0.0448422	+	0.0448422i	0.729172	−	0.684330i	$-0.239905\pi$
$13$	0.161681	+	0.161681i	0.0448422	+	0.0448422i	−0.684330	+	0.729172i	$0.739905\pi$
$14$	−5.51746			−1.47460
$15$	−0.897700	−	3.76751i	−0.231785	−	0.972767i
$16$	4.77725			1.19431
$17$	−3.37518	−	3.37518i	−0.818602	−	0.818602i	0.167304	−	0.985905i	$-0.446494\pi$
$17$	−3.37518	−	3.37518i	−0.818602	−	0.818602i	−0.985905	+	0.167304i	$0.946494\pi$
$18$	−1.15440	+	5.46946i	−0.272094	+	1.28917i
$19$		−	8.52083i		−	1.95481i	−0.211371	−	0.977406i	$-0.567793\pi$
$19$		−	8.52083i		−	1.95481i	0.211371	−	0.977406i	$-0.432207\pi$
$20$	2.45132	−	2.19645i	0.548132	−	0.491141i
$21$	−4.91651	+	1.46016i	−1.07287	+	0.318633i
$22$	1.31757	−	1.31757i	0.280906	−	0.280906i
$23$	−3.15119	+	3.15119i	−0.657068	+	0.657068i	−0.954685	−	0.297617i	$-0.903808\pi$
$23$	−3.15119	+	3.15119i	−0.657068	+	0.657068i	0.297617	+	0.954685i	$0.403808\pi$
$24$	1.63364	−	0.485178i	0.333466	−	0.0990366i
$25$	−0.546726	+	4.97002i	−0.109345	+	0.994004i
$26$			0.426051i			0.0835555i
$27$	0.418798	+	5.17925i	0.0805978	+	0.996747i
$28$	−3.08200	−	3.08200i	−0.582444	−	0.582444i
$29$	−3.01631			−0.560114			−0.280057	−	0.959983i	$-0.590353\pi$
$29$	−3.01631			−0.560114			−0.280057	+	0.959983i	$0.590353\pi$
$30$	3.78117	−	6.14672i	0.690343	−	1.12223i
$31$	5.01096			0.899996			0.449998	−	0.893030i	$-0.351425\pi$
$31$	5.01096			0.899996			0.449998	+	0.893030i	$0.351425\pi$
$32$	4.90290	+	4.90290i	0.866718	+	0.866718i
$33$	0.825374	−	1.52275i	0.143679	−	0.265076i
$34$		−	8.89405i		−	1.52532i
$35$	6.61126	+	0.362542i	1.11751	+	0.0612807i
$36$	−3.70003	+	2.41036i	−0.616672	+	0.401727i
$37$	−4.74287	+	4.74287i	−0.779722	+	0.779722i	−0.979783	−	0.200061i	$-0.935886\pi$
$37$	−4.74287	+	4.74287i	−0.779722	+	0.779722i	0.200061	+	0.979783i	$0.435886\pi$
$38$	11.2268	−	11.2268i	1.82122	−	1.82122i
$39$	0.112752	+	0.379646i	0.0180547	+	0.0607921i
$40$	−2.19677	−	0.120464i	−0.347340	−	0.0190471i
$41$			4.49923i			0.702662i	0.936251	+	0.351331i	$0.114271\pi$
$41$			4.49923i			0.702662i	−0.936251	+	0.351331i	$0.885729\pi$
$42$	−8.40169	−	4.55397i	−1.29641	−	0.702692i
$43$	0.336036	+	0.336036i	0.0512450	+	0.0512450i	0.732265	−	0.681020i	$-0.238463\pi$
$43$	0.336036	+	0.336036i	0.0512450	+	0.0512450i	−0.681020	+	0.732265i	$0.738463\pi$
$44$	1.47196			0.221907
$45$	1.74264	−	6.47790i	0.259777	−	0.965669i
$46$	−8.30379			−1.22433
$47$	6.15190	+	6.15190i	0.897346	+	0.897346i	0.995201	−	0.0978543i	$-0.0311979\pi$
$47$	6.15190	+	6.15190i	0.897346	+	0.897346i	−0.0978543	+	0.995201i	$0.531198\pi$
$48$	7.27454	+	3.94302i	1.04999	+	0.569126i
$49$		−	1.76804i		−	0.252578i
$50$	−7.26868	+	5.82798i	−1.02795	+	0.824201i
$51$	−2.35376	−	7.92533i	−0.329592	−	1.10977i
$52$	−0.237988	+	0.237988i	−0.0330031	+	0.0330031i
$53$	−1.62043	+	1.62043i	−0.222583	+	0.222583i	−0.809585	−	0.587002i	$-0.800308\pi$
$53$	−1.62043	+	1.62043i	−0.222583	+	0.222583i	0.587002	+	0.809585i	$0.300308\pi$
$54$	−6.27221	+	7.37580i	−0.853540	+	1.00372i
$55$	−1.66534	+	1.49219i	−0.224555	+	0.201207i
$56$			2.91342i			0.389322i
$57$	7.03287	−	12.9751i	0.931527	−	1.71859i
$58$	−3.97419	−	3.97419i	−0.521836	−	0.521836i
$59$	−5.16965			−0.673032			−0.336516	−	0.941678i	$-0.609249\pi$
$59$	−5.16965			−0.673032			−0.336516	+	0.941678i	$0.609249\pi$
$60$	5.54564	−	1.32138i	0.715939	−	0.170590i
$61$	−3.39049			−0.434108			−0.217054	−	0.976160i	$-0.569645\pi$
$61$	−3.39049			−0.434108			−0.217054	+	0.976160i	$0.569645\pi$
$62$	6.60228	+	6.60228i	0.838490	+	0.838490i
$63$	−8.69178	−	1.83450i	−1.09506	−	0.231126i
$64$			3.36529i			0.420661i
$65$	0.0279950	−	0.510513i	0.00347235	−	0.0633214i
$66$	3.09381	−	0.918834i	0.380821	−	0.113101i
$67$	9.74916	−	9.74916i	1.19105	−	1.19105i	0.214276	−	0.976773i	$-0.431261\pi$
$67$	9.74916	−	9.74916i	1.19105	−	1.19105i	0.976773	−	0.214276i	$-0.0687392\pi$
$68$	4.96814	−	4.96814i	0.602476	−	0.602476i
$69$	−7.39937	+	2.19755i	−0.890779	+	0.264554i
$70$	8.23310	+	9.18845i	0.984044	+	1.09823i
$71$		−	2.23272i		−	0.264975i	−0.991185	−	0.132488i	$-0.957704\pi$
$71$		−	2.23272i		−	0.264975i	0.991185	−	0.132488i	$-0.0422965\pi$
$72$	2.88808	+	0.609564i	0.340363	+	0.0718378i
$73$	5.43376	+	5.43376i	0.635973	+	0.635973i	0.949560	−	0.313586i	$-0.101531\pi$
$73$	5.43376	+	5.43376i	0.635973	+	0.635973i	−0.313586	+	0.949560i	$0.601531\pi$
$74$	−12.4981			−1.45287
$75$	−4.93465	+	7.11683i	−0.569804	+	0.821780i
$76$	12.5423			1.43871
$77$	2.09381	+	2.09381i	0.238611	+	0.238611i
$78$	−0.351651	+	0.648767i	−0.0398167	+	0.0734585i
$79$			5.93637i			0.667894i	0.942592	+	0.333947i	$0.108381\pi$
$79$			5.93637i			0.667894i	−0.942592	+	0.333947i	$0.891619\pi$
$80$	−7.12858	−	7.95576i	−0.796999	−	0.889480i
$81$	−3.63710	+	8.23235i	−0.404122	+	0.914705i
$82$	−5.92804	+	5.92804i	−0.654642	+	0.654642i
$83$	−0.365862	+	0.365862i	−0.0401586	+	0.0401586i	−0.726901	−	0.686742i	$-0.759040\pi$
$83$	−0.365862	+	0.365862i	−0.0401586	+	0.0401586i	0.686742	+	0.726901i	$0.259040\pi$
$84$	−2.14930	−	7.23692i	−0.234508	−	0.789613i
$85$	−0.584411	+	10.6572i	−0.0633883	+	1.15594i
$86$			0.885499i			0.0954858i
$87$	−4.59307	−	2.48958i	−0.492429	−	0.266911i
$88$	−0.695724	−	0.695724i	−0.0741644	−	0.0741644i
$89$	3.70157			0.392366			0.196183	−	0.980567i	$-0.437145\pi$
$89$	3.70157			0.392366			0.196183	+	0.980567i	$0.437145\pi$
$90$	10.8311	−	6.23903i	1.14170	−	0.657651i
$91$	−0.677057			−0.0709749
$92$	−4.63843	−	4.63843i	−0.483590	−	0.483590i
$93$	7.63043	+	4.13592i	0.791239	+	0.428875i
$94$			16.2111i			1.67204i
$95$	−14.1901	+	12.7147i	−1.45587	+	1.30450i
$96$	3.41914	+	11.5126i	0.348965	+	1.17500i
$97$	4.94287	−	4.94287i	0.501872	−	0.501872i	−0.410147	−	0.912019i	$-0.634523\pi$
$97$	4.94287	−	4.94287i	0.501872	−	0.501872i	0.912019	+	0.410147i	$0.134523\pi$
$98$	2.32951	−	2.32951i	0.235317	−	0.235317i
$99$	2.51367	−	1.63751i	0.252634	−	0.164576i
$100$	−7.31568	−	0.804760i	−0.731568	−	0.0804760i
$101$		−	9.91691i		−	0.986770i	−0.869811	−	0.493385i	$-0.835759\pi$
$101$		−	9.91691i		−	0.986770i	0.869811	−	0.493385i	$-0.164241\pi$
$102$	7.34092	−	13.5434i	0.726860	−	1.34100i
$103$	−5.76598	−	5.76598i	−0.568139	−	0.568139i	0.363468	−	0.931607i	$-0.381593\pi$
$103$	−5.76598	−	5.76598i	−0.568139	−	0.568139i	−0.931607	+	0.363468i	$0.881593\pi$
$104$	0.224971			0.0220602
$105$	9.76804	+	6.00883i	0.953263	+	0.586401i
$106$	−4.27004			−0.414743
$107$	−0.481439	−	0.481439i	−0.0465425	−	0.0465425i	0.683453	−	0.729995i	$-0.260478\pi$
$107$	−0.481439	−	0.481439i	−0.0465425	−	0.0465425i	−0.729995	+	0.683453i	$0.760478\pi$
$108$	−7.62366	+	0.616456i	−0.733587	+	0.0593185i
$109$			2.88151i			0.275999i	0.990432	+	0.137999i	$0.0440672\pi$
$109$			2.88151i			0.275999i	−0.990432	+	0.137999i	$0.955933\pi$
$110$	−4.16026	−	0.228136i	−0.396665	−	0.0217519i
$111$	−11.1368	+	3.30754i	−1.05706	+	0.313938i
$112$	−10.0026	+	10.0026i	−0.945160	+	0.945160i
$113$	−5.89425	+	5.89425i	−0.554485	+	0.554485i	−0.927732	−	0.373247i	$-0.878244\pi$
$113$	−5.89425	+	5.89425i	−0.554485	+	0.554485i	0.373247	+	0.927732i	$0.378244\pi$
$114$	26.3618	−	7.82923i	2.46901	−	0.733274i
$115$	9.94998	+	0.545627i	0.927840	+	0.0508799i
$116$		−	4.43989i		−	0.412234i
$117$	−0.141658	+	0.671168i	−0.0130963	+	0.0620495i
$118$	−6.81136	−	6.81136i	−0.627037	−	0.627037i
$119$	14.1339			1.29566
$120$	−3.24570	−	1.99660i	−0.296290	−	0.182263i
$121$	−1.00000			−0.0909091
$122$	−4.46720	−	4.46720i	−0.404441	−	0.404441i
$123$	−3.71355	+	6.85119i	−0.334840	+	0.617751i
$124$			7.37595i			0.662380i
$125$	9.09260	−	6.50574i	0.813267	−	0.581891i
$126$	−9.03491	−	13.8691i	−0.804894	−	1.23556i
$127$	0.541796	−	0.541796i	0.0480766	−	0.0480766i	−0.682660	−	0.730736i	$-0.739177\pi$
$127$	0.541796	−	0.541796i	0.0480766	−	0.0480766i	0.730736	+	0.682660i	$0.239177\pi$
$128$	5.37181	−	5.37181i	0.474805	−	0.474805i
$129$	0.234342	+	0.789052i	0.0206327	+	0.0694722i
$130$	0.709520	−	0.635750i	0.0622290	−	0.0557589i
$131$		−	20.1139i		−	1.75736i	−0.477413	−	0.878679i	$-0.658425\pi$
$131$		−	20.1139i		−	1.75736i	0.477413	−	0.878679i	$-0.341575\pi$
$132$	2.24143	+	1.21492i	0.195091	+	0.105745i
$133$	17.8410	+	17.8410i	1.54701	+	1.54701i
$134$	25.6903			2.21931
$135$	8.00029	−	8.42587i	0.688555	−	0.725184i
$136$	−4.69639			−0.402712
$137$	10.8866	+	10.8866i	0.930104	+	0.930104i	0.997712	−	0.0676081i	$-0.0215368\pi$
$137$	10.8866	+	10.8866i	0.930104	+	0.930104i	−0.0676081	+	0.997712i	$0.521537\pi$
$138$	−12.6446	−	6.85374i	−1.07638	−	0.583429i
$139$		−	18.8256i		−	1.59677i	−0.602150	−	0.798383i	$-0.705689\pi$
$139$		−	18.8256i		−	1.59677i	0.602150	−	0.798383i	$-0.294311\pi$
$140$	−0.533648	+	9.73153i	−0.0451015	+	0.822465i
$141$	4.29016	+	14.4454i	0.361297	+	1.21652i
$142$	2.94176	−	2.94176i	0.246867	−	0.246867i
$143$	0.161681	−	0.161681i	0.0135204	−	0.0135204i
$144$	7.82282	+	12.0084i	0.651901	+	1.00070i
$145$	4.50091	+	5.02318i	0.373780	+	0.417153i
$146$			14.3187i			1.18502i
$147$	1.45930	−	2.69228i	0.120361	−	0.222056i
$148$	−6.98132	−	6.98132i	−0.573861	−	0.573861i
$149$	−18.1699			−1.48854			−0.744269	−	0.667880i	$-0.767202\pi$
$149$	−18.1699			−1.48854			−0.744269	+	0.667880i	$0.767202\pi$
$150$	−15.8786	+	2.87516i	−1.29648	+	0.234756i
$151$	−5.16859			−0.420614			−0.210307	−	0.977635i	$-0.567446\pi$
$151$	−5.16859			−0.420614			−0.210307	+	0.977635i	$0.567446\pi$
$152$	−5.92814	−	5.92814i	−0.480836	−	0.480836i
$153$	2.95719	−	14.0110i	0.239075	−	1.13272i
$154$			5.51746i			0.444609i
$155$	−7.47732	−	8.34497i	−0.600593	−	0.670284i
$156$	−0.558826	+	0.165966i	−0.0447419	+	0.0132880i
$157$	0.0693025	−	0.0693025i	0.00553094	−	0.00553094i	−0.704336	−	0.709867i	$-0.748755\pi$
$157$	0.0693025	−	0.0693025i	0.00553094	−	0.00553094i	0.709867	+	0.704336i	$0.248755\pi$
$158$	−7.82156	+	7.82156i	−0.622250	+	0.622250i
$159$	−3.80496	+	1.13004i	−0.301753	+	0.0896181i
$160$	0.848935	−	15.4811i	0.0671142	−	1.22389i
$161$		−	13.1959i		−	1.03999i
$162$	−15.6388	+	6.05455i	−1.22870	+	0.475690i
$163$	−12.4108	−	12.4108i	−0.972090	−	0.972090i	0.0275308	−	0.999621i	$-0.491236\pi$
$163$	−12.4108	−	12.4108i	−0.972090	−	0.972090i	−0.999621	+	0.0275308i	$0.991236\pi$
$164$	−6.62270			−0.517146
$165$	−3.76751	+	0.897700i	−0.293300	+	0.0698858i
$166$	−0.964095			−0.0748283
$167$	−5.06115	−	5.06115i	−0.391644	−	0.391644i	0.483629	−	0.875273i	$-0.339318\pi$
$167$	−5.06115	−	5.06115i	−0.391644	−	0.391644i	−0.875273	+	0.483629i	$0.839318\pi$
$168$	−2.40466	+	4.43640i	−0.185524	+	0.342276i
$169$		−	12.9477i		−	0.995978i
$170$	−14.8116	+	13.2716i	−1.13600	+	1.01789i
$171$	21.4186	−	13.9530i	1.63792	−	1.06701i
$172$	−0.494632	+	0.494632i	−0.0377153	+	0.0377153i
$173$	−10.2684	+	10.2684i	−0.780694	+	0.780694i	−0.979948	−	0.199253i	$-0.936148\pi$
$173$	−10.2684	+	10.2684i	−0.780694	+	0.780694i	0.199253	+	0.979948i	$0.436148\pi$
$174$	−2.77149	−	9.33187i	−0.210106	−	0.707447i
$175$	−9.26152	−	11.5510i	−0.700105	−	0.873173i
$176$		−	4.77725i		−	0.360099i
$177$	−7.87207	−	4.26690i	−0.591701	−	0.320720i
$178$	4.87707	+	4.87707i	0.365552	+	0.365552i
$179$	12.8332			0.959200			0.479600	−	0.877487i	$-0.340782\pi$
$179$	12.8332			0.959200			0.479600	+	0.877487i	$0.340782\pi$
$180$	9.53523	+	2.56510i	0.710714	+	0.191191i
$181$	18.9492			1.40848			0.704242	−	0.709960i	$-0.251287\pi$
$181$	18.9492			1.40848			0.704242	+	0.709960i	$0.251287\pi$
$182$	−0.892068	−	0.892068i	−0.0661245	−	0.0661245i
$183$	−5.16286	−	2.79843i	−0.381650	−	0.206866i
$184$			4.38471i			0.323245i
$185$	14.9758	+	0.821225i	1.10104	+	0.0603777i
$186$	4.60425	+	15.5030i	0.337600	+	1.13673i
$187$	−3.37518	+	3.37518i	−0.246818	+	0.246818i
$188$	−9.05537	+	9.05537i	−0.660430	+	0.660430i
$189$	−11.7212	−	9.96746i	−0.852593	−	0.725026i
$190$	−35.4489	−	1.94391i	−2.57173	−	0.141026i
$191$		−	15.8333i		−	1.14566i	−0.819675	−	0.572829i	$-0.805846\pi$
$191$		−	15.8333i		−	1.14566i	0.819675	−	0.572829i	$-0.194154\pi$
$192$	−2.77762	+	5.12448i	−0.200458	+	0.369827i
$193$	7.37312	+	7.37312i	0.530729	+	0.530729i	0.920789	−	0.390061i	$-0.127546\pi$
$193$	7.37312	+	7.37312i	0.530729	+	0.530729i	−0.390061	+	0.920789i	$0.627546\pi$
$194$	13.0251			0.935149
$195$	0.463994	−	0.754276i	0.0332273	−	0.0540148i
$196$	2.60249			0.185892
$197$	9.03516	+	9.03516i	0.643728	+	0.643728i	0.951470	−	0.307742i	$-0.0995733\pi$
$197$	9.03516	+	9.03516i	0.643728	+	0.643728i	−0.307742	+	0.951470i	$0.599573\pi$
$198$	5.46946	+	1.15440i	0.388698	+	0.0820394i
$199$			11.0729i			0.784936i	0.919766	+	0.392468i	$0.128379\pi$
$199$			11.0729i			0.784936i	−0.919766	+	0.392468i	$0.871621\pi$
$200$	3.07739	+	3.83813i	0.217604	+	0.271397i
$201$	22.8922	−	6.79879i	1.61469	−	0.479550i
$202$	13.0662	−	13.0662i	0.919334	−	0.919334i
$203$	6.31556	−	6.31556i	0.443266	−	0.443266i
$204$	11.6658	−	3.46464i	0.816769	−	0.242574i
$205$	7.49276	−	6.71372i	0.523317	−	0.468906i
$206$		−	15.1941i		−	1.05862i
$207$	−13.0812	−	2.76094i	−0.909204	−	0.191898i
$208$	0.772391	+	0.772391i	0.0535557	+	0.0535557i
$209$	−8.52083			−0.589398
$210$	4.95302	+	20.7871i	0.341791	+	1.43444i
$211$	−2.45739			−0.169174			−0.0845869	−	0.996416i	$-0.526957\pi$
$211$	−2.45739			−0.169174			−0.0845869	+	0.996416i	$0.526957\pi$
$212$	−2.38521	−	2.38521i	−0.163817	−	0.163817i
$213$	1.84283	−	3.39987i	0.126269	−	0.232955i
$214$		−	1.26866i		−	0.0867235i
$215$	0.0581844	−	1.06104i	0.00396815	−	0.0723626i
$216$	3.89469	+	3.31196i	0.265000	+	0.225350i
$217$	−10.4920	+	10.4920i	−0.712242	+	0.712242i
$218$	−3.79658	+	3.79658i	−0.257137	+	0.257137i
$219$	3.78935	+	12.7591i	0.256061	+	0.862181i
$220$	−2.19645	−	2.45132i	−0.148085	−	0.165268i
$221$		−	1.09141i		−	0.0734159i
$222$	−19.0314	−	10.3156i	−1.27730	−	0.692337i
$223$	−2.72361	−	2.72361i	−0.182386	−	0.182386i	0.610009	−	0.792395i	$-0.291166\pi$
$223$	−2.72361	−	2.72361i	−0.182386	−	0.182386i	−0.792395	+	0.610009i	$0.791166\pi$
$224$	−20.5314			−1.37181
$225$	−13.3883	+	6.76419i	−0.892551	+	0.450946i
$226$	−15.5321			−1.03318
$227$	20.3476	+	20.3476i	1.35052	+	1.35052i	0.885084	+	0.465431i	$0.154101\pi$
$227$	20.3476	+	20.3476i	1.35052	+	1.35052i	0.465431	+	0.885084i	$0.345899\pi$
$228$	19.0988	+	10.3521i	1.26485	+	0.685586i
$229$			12.4003i			0.819433i	0.912213	+	0.409716i	$0.134372\pi$
$229$			12.4003i			0.819433i	−0.912213	+	0.409716i	$0.865628\pi$
$230$	12.3909	+	13.8287i	0.817029	+	0.911835i
$231$	1.46016	+	4.91651i	0.0960716	+	0.323483i
$232$	−2.09852	+	2.09852i	−0.137774	+	0.137774i
$233$	−1.83100	+	1.83100i	−0.119953	+	0.119953i	−0.764535	−	0.644582i	$-0.777031\pi$
$233$	−1.83100	+	1.83100i	−0.119953	+	0.119953i	0.644582	+	0.764535i	$0.277031\pi$
$234$	−1.07095	+	0.697664i	−0.0700103	+	0.0456077i
$235$	1.06520	−	19.4248i	0.0694859	−	1.26714i
$236$		−	7.60954i		−	0.495339i
$237$	−4.89973	+	9.03958i	−0.318271	+	0.587184i
$238$	18.6224	+	18.6224i	1.20711	+	1.20711i
$239$	20.2577			1.31036			0.655182	−	0.755471i	$-0.272592\pi$
$239$	20.2577			1.31036			0.655182	+	0.755471i	$0.272592\pi$
$240$	−4.28854	−	17.9983i	−0.276824	−	1.16179i
$241$	2.30059			0.148194			0.0740971	−	0.997251i	$-0.476393\pi$
$241$	2.30059			0.148194			0.0740971	+	0.997251i	$0.476393\pi$
$242$	−1.31757	−	1.31757i	−0.0846964	−	0.0846964i
$243$	−12.3331	+	9.53381i	−0.791171	+	0.611594i
$244$		−	4.99068i		−	0.319496i
$245$	−2.94440	+	2.63826i	−0.188111	+	0.168552i
$246$	−13.9197	+	4.13405i	−0.887491	+	0.263577i
$247$	1.37766	−	1.37766i	0.0876581	−	0.0876581i
$248$	3.48625	−	3.48625i	0.221377	−	0.221377i
$249$	−0.859089	+	0.255142i	−0.0544425	+	0.0161690i
$250$	20.5518	+	3.40836i	1.29981	+	0.215564i
$251$			27.0577i			1.70786i	0.520384	+	0.853932i	$0.325789\pi$
$251$			27.0577i			1.70786i	−0.520384	+	0.853932i	$0.674211\pi$
$252$	2.70032	−	12.7940i	0.170104	−	0.805945i
$253$	3.15119	+	3.15119i	0.198113	+	0.198113i
$254$	1.42770			0.0895821
$255$	−9.68613	+	15.7459i	−0.606569	+	0.986048i
$256$	20.8860			1.30537
$257$	−14.3843	−	14.3843i	−0.897267	−	0.897267i	0.0979266	−	0.995194i	$-0.468779\pi$
$257$	−14.3843	−	14.3843i	−0.897267	−	0.897267i	−0.995194	+	0.0979266i	$0.968779\pi$
$258$	−0.730868	+	1.34839i	−0.0455018	+	0.0839471i
$259$		−	19.8613i		−	1.23412i
$260$	0.751456	+	0.0412076i	0.0466033	+	0.00255559i
$261$	−4.93925	−	7.58201i	−0.305732	−	0.469315i
$262$	26.5014	−	26.5014i	1.63726	−	1.63726i
$263$	1.11325	−	1.11325i	0.0686457	−	0.0686457i	−0.671950	−	0.740596i	$-0.734543\pi$
$263$	1.11325	−	1.11325i	0.0686457	−	0.0686457i	0.740596	+	0.671950i	$0.234543\pi$
$264$	−0.485178	−	1.63364i	−0.0298607	−	0.100544i
$265$	5.11656	+	0.280577i	0.314308	+	0.0172357i
$266$			47.0133i			2.88257i
$267$	5.63656	+	3.05518i	0.344952	+	0.186974i
$268$	14.3504	+	14.3504i	0.876590	+	0.876590i
$269$	3.23597			0.197301			0.0986504	−	0.995122i	$-0.468547\pi$
$269$	3.23597			0.197301			0.0986504	+	0.995122i	$0.468547\pi$
$270$	21.6426	−	0.560737i	1.31712	−	0.0341253i
$271$	−17.4114			−1.05766			−0.528832	−	0.848726i	$-0.677370\pi$
$271$	−17.4114			−1.05766			−0.528832	+	0.848726i	$0.677370\pi$
$272$	−16.1241	−	16.1241i	−0.977666	−	0.977666i
$273$	−1.03099	−	0.558826i	−0.0623981	−	0.0338217i
$274$			28.6876i			1.73308i
$275$	4.97002	+	0.546726i	0.299703	+	0.0329688i
$276$	−3.23471	−	10.8916i	−0.194707	−	0.655597i
$277$	−11.1533	+	11.1533i	−0.670138	+	0.670138i	−0.957748	−	0.287610i	$-0.907139\pi$
$277$	−11.1533	+	11.1533i	−0.670138	+	0.670138i	0.287610	+	0.957748i	$0.407139\pi$
$278$	24.8040	−	24.8040i	1.48764	−	1.48764i
$279$	8.20553	+	12.5959i	0.491252	+	0.754098i
$280$	4.85184	−	4.34738i	0.289953	−	0.259806i
$281$			25.9907i			1.55048i	0.631670	+	0.775238i	$0.282370\pi$
$281$			25.9907i			1.55048i	−0.631670	+	0.775238i	$0.717630\pi$
$282$	−13.3802	+	24.6853i	−0.796779	+	1.46999i
$283$	13.9756	+	13.9756i	0.830762	+	0.830762i	0.987621	−	0.156859i	$-0.0501368\pi$
$283$	13.9756	+	13.9756i	0.830762	+	0.830762i	−0.156859	+	0.987621i	$0.550137\pi$
$284$	3.28648			0.195017
$285$	−32.1023	+	7.64915i	−1.90158	+	0.453096i
$286$	0.426051			0.0251929
$287$	−9.42052	−	9.42052i	−0.556076	−	0.556076i
$288$	−4.29571	+	20.3528i	−0.253127	+	1.19930i
$289$			5.78370i			0.340217i
$290$	−0.688129	+	12.5486i	−0.0404083	+	0.736881i
$291$	11.6065	−	3.44702i	0.680382	−	0.202068i
$292$	−7.99829	+	7.99829i	−0.468064	+	0.468064i
$293$	14.6351	−	14.6351i	0.854994	−	0.854994i	−0.135749	−	0.990743i	$-0.543344\pi$
$293$	14.6351	−	14.6351i	0.854994	−	0.854994i	0.990743	+	0.135749i	$0.0433441\pi$
$294$	5.46998	−	1.62454i	0.319016	−	0.0947450i
$295$	7.71412	+	8.60924i	0.449133	+	0.501249i
$296$			6.59945i			0.383585i
$297$	5.17925	−	0.418798i	0.300530	−	0.0243011i
$298$	−23.9401	−	23.9401i	−1.38681	−	1.38681i
$299$	−1.01897			−0.0589288
$300$	−10.4757	−	7.26362i	−0.604815	−	0.419366i
$301$	−1.40719			−0.0811089
$302$	−6.80996	−	6.80996i	−0.391869	−	0.391869i
$303$	8.18517	−	15.1009i	0.470226	−	0.867527i
$304$		−	40.7061i		−	2.33466i
$305$	5.05927	+	5.64633i	0.289693	+	0.323308i
$306$	22.3567	−	14.5641i	1.27805	−	0.832576i
$307$	−0.137152	+	0.137152i	−0.00782767	+	0.00782767i	−0.711010	−	0.703182i	$-0.751762\pi$
$307$	−0.137152	+	0.137152i	−0.00782767	+	0.00782767i	0.703182	+	0.711010i	$0.251762\pi$
$308$	−3.08200	+	3.08200i	−0.175613	+	0.175613i
$309$	−4.02103	−	13.5392i	−0.228749	−	0.770219i
$310$	1.14318	−	20.8469i	0.0649284	−	1.18403i
$311$		−	18.1688i		−	1.03026i	−0.857113	−	0.515128i	$-0.827745\pi$
$311$		−	18.1688i		−	1.03026i	0.857113	−	0.515128i	$-0.172255\pi$
$312$	0.342573	+	0.185685i	0.0193944	+	0.0105123i
$313$	−15.5417	−	15.5417i	−0.878466	−	0.878466i	0.114910	−	0.993376i	$-0.463342\pi$
$313$	−15.5417	−	15.5417i	−0.878466	−	0.878466i	−0.993376	+	0.114910i	$0.963342\pi$
$314$	0.182621			0.0103059
$315$	9.91472	+	17.2122i	0.558631	+	0.969798i
$316$	−8.73811			−0.491557
$317$	0.878898	+	0.878898i	0.0493638	+	0.0493638i	0.731358	−	0.681994i	$-0.238887\pi$
$317$	0.878898	+	0.878898i	0.0493638	+	0.0493638i	−0.681994	+	0.731358i	$0.738887\pi$
$318$	−6.50220	−	3.52439i	−0.364625	−	0.197638i
$319$			3.01631i			0.168881i
$320$	5.60435	−	5.02165i	0.313293	−	0.280719i
$321$	−0.335742	−	1.13048i	−0.0187393	−	0.0630971i
$322$	17.3865	−	17.3865i	0.968914	−	0.968914i
$323$	−28.7593	+	28.7593i	−1.60021	+	1.60021i
$324$	−12.1177	−	5.35367i	−0.673206	−	0.297426i
$325$	−0.891953	+	0.715162i	−0.0494766	+	0.0396701i
$326$		−	32.7042i		−	1.81132i
$327$	−2.37833	+	4.38781i	−0.131522	+	0.242646i
$328$	3.13022	+	3.13022i	0.172838	+	0.172838i
$329$	−25.7618			−1.42029
$330$	−6.14672	−	3.78117i	−0.338366	−	0.208146i
$331$	−1.81586			−0.0998088			−0.0499044	−	0.998754i	$-0.515892\pi$
$331$	−1.81586			−0.0998088			−0.0499044	+	0.998754i	$0.515892\pi$
$332$	−0.538536	−	0.538536i	−0.0295560	−	0.0295560i
$333$	−19.6885	−	4.15550i	−1.07892	−	0.227720i
$334$		−	13.3368i		−	0.729757i
$335$	−30.7833	−	1.68806i	−1.68187	−	0.0922287i
$336$	−23.4874	+	6.97556i	−1.28134	+	0.380548i
$337$	−0.824320	+	0.824320i	−0.0449036	+	0.0449036i	−0.729202	−	0.684298i	$-0.760109\pi$
$337$	−0.824320	+	0.824320i	−0.0449036	+	0.0449036i	0.684298	+	0.729202i	$0.260109\pi$
$338$	17.0595	−	17.0595i	0.927913	−	0.927913i
$339$	−13.8404	+	4.11049i	−0.751708	+	0.223251i
$340$	−15.6871	−	0.860232i	−0.850751	−	0.0466526i
$341$		−	5.01096i		−	0.271359i
$342$	46.6044	+	9.83641i	2.52008	+	0.531892i
$343$	−10.9547	−	10.9547i	−0.591498	−	0.591498i
$344$	0.467576			0.0252100
$345$	14.7009	+	9.04331i	0.791472	+	0.486875i
$346$	−27.0587			−1.45468
$347$	−10.0480	−	10.0480i	−0.539406	−	0.539406i	0.383949	−	0.923354i	$-0.374564\pi$
$347$	−10.0480	−	10.0480i	−0.539406	−	0.539406i	−0.923354	+	0.383949i	$0.874564\pi$
$348$	3.66457	−	6.76083i	0.196442	−	0.362419i
$349$		−	1.50331i		−	0.0804702i	−0.999190	−	0.0402351i	$-0.987189\pi$
$349$		−	1.50331i		−	0.0804702i	0.999190	−	0.0402351i	$-0.0128107\pi$
$350$	3.01653	−	27.4219i	0.161241	−	1.46576i
$351$	−0.769674	+	0.905098i	−0.0410822	+	0.0483105i
$352$	4.90290	−	4.90290i	0.261325	−	0.261325i
$353$	10.4384	−	10.4384i	0.555578	−	0.555578i	−0.372467	−	0.928045i	$-0.621488\pi$
$353$	10.4384	−	10.4384i	0.555578	−	0.555578i	0.928045	+	0.372467i	$0.121488\pi$
$354$	−4.75005	−	15.9939i	−0.252463	−	0.850066i
$355$	−3.71824	+	3.33165i	−0.197344	+	0.176825i
$356$			5.44858i			0.288774i
$357$	21.5224	+	11.6658i	1.13909	+	0.617419i
$358$	16.9086	+	16.9086i	0.893649	+	0.893649i
$359$	−14.3901			−0.759480			−0.379740	−	0.925093i	$-0.623987\pi$
$359$	−14.3901			−0.759480			−0.379740	+	0.925093i	$0.623987\pi$
$360$	−3.29444	−	5.71923i	−0.173632	−	0.301430i
$361$	−53.6045			−2.82129
$362$	24.9669	+	24.9669i	1.31223	+	1.31223i
$363$	−1.52275	−	0.825374i	−0.0799235	−	0.0433209i
$364$		−	0.996603i		−	0.0522362i
$365$	0.940853	−	17.1573i	0.0492465	−	0.898053i
$366$	−3.11530	−	10.4895i	−0.162839	−	0.548296i
$367$	−23.9839	+	23.9839i	−1.25195	+	1.25195i	−0.297104	+	0.954845i	$0.596021\pi$
$367$	−23.9839	+	23.9839i	−1.25195	+	1.25195i	−0.954845	+	0.297104i	$0.903979\pi$
$368$	−15.0540	+	15.0540i	−0.784744	+	0.784744i
$369$	−11.3096	+	7.36756i	−0.588754	+	0.383540i
$370$	18.6495	+	20.8136i	0.969543	+	1.08205i
$371$		−	6.78572i		−	0.352297i
$372$	−6.08792	+	11.2317i	−0.315644	+	0.582337i
$373$	−16.6266	−	16.6266i	−0.860894	−	0.860894i	0.130548	−	0.991442i	$-0.458326\pi$
$373$	−16.6266	−	16.6266i	−0.860894	−	0.860894i	−0.991442	+	0.130548i	$0.958326\pi$
$374$	−8.89405			−0.459900
$375$	19.2154	−	2.40179i	0.992279	−	0.124028i
$376$	8.56004			0.441451
$377$	−0.487680	−	0.487680i	−0.0251168	−	0.0251168i
$378$	−2.31070	−	28.5763i	−0.118850	−	1.46980i
$379$			27.3979i			1.40733i	0.710530	+	0.703667i	$0.248455\pi$
$379$			27.3979i			1.40733i	−0.710530	+	0.703667i	$0.751545\pi$
$380$	−18.7156	−	20.8873i	−0.960089	−	1.07150i
$381$	1.27220	−	0.377833i	0.0651769	−	0.0193570i
$382$	20.8615	−	20.8615i	1.06736	−	1.06736i
$383$	17.6188	−	17.6188i	0.900277	−	0.900277i	−0.0951829	−	0.995460i	$-0.530344\pi$
$383$	17.6188	−	17.6188i	0.900277	−	0.900277i	0.995460	+	0.0951829i	$0.0303436\pi$
$384$	12.6137	−	3.74615i	0.643688	−	0.191170i
$385$	0.362542	−	6.61126i	0.0184768	−	0.336941i
$386$			19.4291i			0.988917i
$387$	−0.294420	+	1.39495i	−0.0149662	+	0.0709091i
$388$	7.27572	+	7.27572i	0.369369	+	0.369369i
$389$	19.7634			1.00204			0.501022	−	0.865434i	$-0.332957\pi$
$389$	19.7634			1.00204			0.501022	+	0.865434i	$0.332957\pi$
$390$	1.60515	−	0.382466i	0.0812800	−	0.0193669i
$391$	21.2716			1.07575
$392$	−1.23007	−	1.23007i	−0.0621279	−	0.0621279i
$393$	16.6015	−	30.6283i	0.837434	−	1.54500i
$394$			23.8088i			1.19947i
$395$	9.88608	−	8.85820i	0.497423	−	0.445705i
$396$	2.41036	+	3.70003i	0.121125	+	0.185934i
$397$	−1.41299	+	1.41299i	−0.0709160	+	0.0709160i	−0.741675	−	0.670759i	$-0.765968\pi$
$397$	−1.41299	+	1.41299i	−0.0709160	+	0.0709160i	0.670759	+	0.741675i	$0.265968\pi$
$398$	−14.5893	+	14.5893i	−0.731294	+	0.731294i
$399$	12.4418	+	41.8927i	0.622868	+	2.09726i
$400$	−2.61185	+	23.7430i	−0.130592	+	1.18715i
$401$			24.4929i			1.22312i	0.791199	+	0.611559i	$0.209457\pi$
$401$			24.4929i			1.22312i	−0.791199	+	0.611559i	$0.790543\pi$
$402$	39.1199	+	21.2041i	1.95112	+	1.05757i
$403$	0.810178	+	0.810178i	0.0403578	+	0.0403578i
$404$	14.5973			0.726244
$405$	19.1369	−	6.22724i	0.950921	−	0.309434i
$406$	16.6423			0.825946
$407$	4.74287	+	4.74287i	0.235095	+	0.235095i
$408$	−7.15141	−	3.87628i	−0.354048	−	0.191904i
$409$		−	22.4416i		−	1.10966i	−0.831962	−	0.554832i	$-0.812782\pi$
$409$		−	22.4416i		−	1.10966i	0.831962	−	0.554832i	$-0.187218\pi$
$410$	18.7180	+	1.02644i	0.924415	+	0.0506921i
$411$	7.59200	+	25.5630i	0.374486	+	1.26093i
$412$	8.48731	−	8.48731i	0.418140	−	0.418140i
$413$	10.8242	−	10.8242i	0.532626	−	0.532626i
$414$	−13.5976	−	20.8730i	−0.668285	−	1.02585i
$415$	1.15522	+	0.0633489i	0.0567076	+	0.00310967i
$416$			1.58541i			0.0777312i
$417$	15.5382	−	28.6666i	0.760907	−	1.40381i
$418$	−11.2268	−	11.2268i	−0.549119	−	0.549119i
$419$	2.45688			0.120027			0.0600133	−	0.998198i	$-0.480886\pi$
$419$	2.45688			0.120027			0.0600133	+	0.998198i	$0.480886\pi$
$420$	−8.84477	+	14.3782i	−0.431580	+	0.701584i
$421$	−0.919497			−0.0448135			−0.0224068	−	0.999749i	$-0.507133\pi$
$421$	−0.919497			−0.0448135			−0.0224068	+	0.999749i	$0.507133\pi$
$422$	−3.23778	−	3.23778i	−0.157612	−	0.157612i
$423$	−5.39003	+	25.5377i	−0.262072	+	1.24168i
$424$			2.25474i			0.109500i
$425$	18.6200	−	14.9294i	0.903203	−	0.724183i
$426$	6.90760	−	2.05150i	0.334674	−	0.0993955i
$427$	7.09903	−	7.09903i	0.343546	−	0.343546i
$428$	0.708660	−	0.708660i	0.0342544	−	0.0342544i
$429$	0.379646	−	0.112752i	0.0183295	−	0.00544371i
$430$	1.47466	−	1.32133i	0.0711143	−	0.0637204i
$431$		−	14.3343i		−	0.690458i	−0.938518	−	0.345229i	$-0.887801\pi$
$431$		−	14.3343i		−	0.690458i	0.938518	−	0.345229i	$-0.112199\pi$
$432$	2.00070	+	24.7426i	0.0962589	+	1.19043i
$433$	−2.60099	−	2.60099i	−0.124995	−	0.124995i	0.641842	−	0.766837i	$-0.278171\pi$
$433$	−2.60099	−	2.60099i	−0.124995	−	0.124995i	−0.766837	+	0.641842i	$0.778171\pi$
$434$	−27.6478			−1.32714
$435$	2.70774	+	11.3640i	0.129826	+	0.544861i
$436$	−4.24148			−0.203130
$437$	26.8507	+	26.8507i	1.28444	+	1.28444i
$438$	−11.8183	+	21.8037i	−0.564699	+	1.04182i
$439$		−	10.0523i		−	0.479772i	−0.970801	−	0.239886i	$-0.922890\pi$
$439$		−	10.0523i		−	0.479772i	0.970801	−	0.239886i	$-0.0771101\pi$
$440$	−0.120464	+	2.19677i	−0.00574291	+	0.104727i
$441$	4.44428	−	2.89520i	0.211632	−	0.137866i
$442$	1.43800	−	1.43800i	0.0683986	−	0.0683986i
$443$	−10.7107	+	10.7107i	−0.508879	+	0.508879i	−0.914182	−	0.405303i	$-0.867166\pi$
$443$	−10.7107	+	10.7107i	−0.508879	+	0.508879i	0.405303	+	0.914182i	$0.367166\pi$
$444$	−4.86858	−	16.3930i	−0.231053	−	0.777977i
$445$	−5.52346	−	6.16438i	−0.261837	−	0.292220i
$446$		−	7.17706i		−	0.339844i
$447$	−27.6682	−	14.9970i	−1.30866	−	0.709333i
$448$	−7.04626	−	7.04626i	−0.332904	−	0.332904i
$449$	−25.8564			−1.22024			−0.610120	−	0.792309i	$-0.708879\pi$
$449$	−25.8564			−1.22024			−0.610120	+	0.792309i	$0.708879\pi$
$450$	−26.5522	−	8.72767i	−1.25168	−	0.411426i
$451$	4.49923			0.211861
$452$	−8.67612	−	8.67612i	−0.408090	−	0.408090i
$453$	−7.87045	−	4.26602i	−0.369786	−	0.200435i
$454$			53.6185i			2.51644i
$455$	1.01030	+	1.12753i	0.0473636	+	0.0528595i
$456$	−4.13412	−	13.9200i	−0.193598	−	0.651864i
$457$	−13.9683	+	13.9683i	−0.653409	+	0.653409i	−0.953812	−	0.300403i	$-0.902879\pi$
$457$	−13.9683	+	13.9683i	−0.653409	+	0.653409i	0.300403	+	0.953812i	$0.402879\pi$
$458$	−16.3382	+	16.3382i	−0.763433	+	0.763433i
$459$	16.0674	−	18.8944i	0.749961	−	0.881916i
$460$	−0.803142	+	14.6460i	−0.0374467	+	0.682873i
$461$		−	0.0529299i		−	0.00246519i	−0.999999	−	0.00123260i	$-0.999608\pi$
$461$		−	0.0529299i		−	0.00246519i	0.999999	−	0.00123260i	$-0.000392348\pi$
$462$	−4.55397	+	8.40169i	−0.211870	+	0.390882i
$463$	2.46604	+	2.46604i	0.114607	+	0.114607i	0.762084	−	0.647478i	$-0.224176\pi$
$463$	2.46604	+	2.46604i	0.114607	+	0.114607i	−0.647478	+	0.762084i	$0.724176\pi$
$464$	−14.4097			−0.668952
$465$	−4.49834	−	18.8789i	−0.208606	−	0.875486i
$466$	−4.82492			−0.223510
$467$	−13.3103	−	13.3103i	−0.615928	−	0.615928i	0.328557	−	0.944484i	$-0.393438\pi$
$467$	−13.3103	−	13.3103i	−0.615928	−	0.615928i	−0.944484	+	0.328557i	$0.893438\pi$
$468$	−0.987934	−	0.208515i	−0.0456673	−	0.00963863i
$469$			40.8257i			1.88515i
$470$	26.9970	−	24.1900i	1.24528	−	1.11580i
$471$	0.162731	−	0.0483296i	0.00749823	−	0.00222691i
$472$	−3.59665	+	3.59665i	−0.165549	+	0.165549i
$473$	0.336036	−	0.336036i	0.0154509	−	0.0154509i
$474$	−18.3660	+	5.45454i	−0.843577	+	0.250535i
$475$	42.3487	+	4.65855i	1.94309	+	0.213749i
$476$			20.8046i			0.953579i
$477$	−6.72670	−	1.41975i	−0.307994	−	0.0650059i
$478$	26.6909	+	26.6909i	1.22081	+	1.22081i
$479$	15.7954			0.721710			0.360855	−	0.932622i	$-0.382485\pi$
$479$	15.7954			0.721710			0.360855	+	0.932622i	$0.382485\pi$
$480$	14.0704	−	22.8731i	0.642222	−	1.04401i
$481$	−1.53366			−0.0699290
$482$	3.03119	+	3.03119i	0.138067	+	0.138067i
$483$	10.8916	−	20.0941i	0.495585	−	0.914312i
$484$		−	1.47196i		−	0.0669074i
$485$	−15.6073	−	0.855855i	−0.708690	−	0.0388624i
$486$	−28.8112	−	3.68830i	−1.30690	−	0.167305i
$487$	19.8992	−	19.8992i	0.901717	−	0.901717i	−0.0938674	−	0.995585i	$-0.529923\pi$
$487$	19.8992	−	19.8992i	0.901717	−	0.901717i	0.995585	+	0.0938674i	$0.0299230\pi$
$488$	−2.35885	+	2.35885i	−0.106780	+	0.106780i
$489$	−8.65496	−	29.1421i	−0.391391	−	1.31785i
$490$	−7.35552	−	0.403354i	−0.332289	−	0.0182217i
$491$			15.0149i			0.677611i	0.940856	+	0.338806i	$0.110023\pi$
$491$			15.0149i			0.677611i	−0.940856	+	0.338806i	$0.889977\pi$
$492$	−10.0847	−	5.46621i	−0.454653	−	0.246436i
$493$	10.1806	+	10.1806i	0.458510	+	0.458510i
$494$	3.63031			0.163335
$495$	−6.47790	−	1.74264i	−0.291160	−	0.0783257i
$496$	23.9386			1.07488
$497$	4.67488	+	4.67488i	0.209697	+	0.209697i
$498$	−1.46807	−	0.795740i	−0.0657859	−	0.0356580i
$499$			5.53151i			0.247625i	0.992306	+	0.123812i	$0.0395121\pi$
$499$			5.53151i			0.247625i	−0.992306	+	0.123812i	$0.960488\pi$
$500$	9.57621	+	13.3840i	0.428261	+	0.598549i
$501$	−3.52950	−	11.8842i	−0.157687	−	0.530947i
$502$	−35.6503	+	35.6503i	−1.59115	+	1.59115i
$503$	−29.2941	+	29.2941i	−1.30616	+	1.30616i	−0.381993	+	0.924165i	$0.624762\pi$
$503$	−29.2941	+	29.2941i	−1.30616	+	1.30616i	−0.924165	+	0.381993i	$0.875238\pi$
$504$	−7.32339	+	4.77077i	−0.326210	+	0.212507i
$505$	−16.5150	+	14.7979i	−0.734910	+	0.658500i
$506$			8.30379i			0.369149i
$507$	10.6867	−	19.7161i	0.474614	−	0.875622i
$508$	0.797503	+	0.797503i	0.0353835	+	0.0353835i
$509$	−12.2904			−0.544763			−0.272382	−	0.962189i	$-0.587811\pi$
$509$	−12.2904			−0.544763			−0.272382	+	0.962189i	$0.587811\pi$
$510$	−33.5084	+	7.98419i	−1.48378	+	0.353546i
$511$	−22.7545			−1.00660
$512$	16.7751	+	16.7751i	0.741361	+	0.741361i
$513$	44.1315	−	3.56851i	1.94845	−	0.157553i
$514$		−	37.9045i		−	1.67190i
$515$	−0.998377	+	18.2063i	−0.0439937	+	0.802264i
$516$	−1.16146	+	0.344943i	−0.0511302	+	0.0151852i
$517$	6.15190	−	6.15190i	0.270560	−	0.270560i
$518$	26.1686	−	26.1686i	1.14978	−	1.14978i
$519$	−24.1115	+	7.16092i	−1.05838	+	0.314329i
$520$	−0.335699	−	0.374653i	−0.0147214	−	0.0164296i
$521$		−	9.03181i		−	0.395691i	−0.980233	−	0.197845i	$-0.936606\pi$
$521$		−	9.03181i		−	0.395691i	0.980233	−	0.197845i	$-0.0633944\pi$
$522$	3.48201	−	16.4976i	0.152404	−	0.722080i
$523$	−3.54962	−	3.54962i	−0.155214	−	0.155214i	0.625228	−	0.780442i	$-0.285006\pi$
$523$	−3.54962	−	3.54962i	−0.155214	−	0.155214i	−0.780442	+	0.625228i	$0.785006\pi$
$524$	29.6069			1.29338
$525$	−4.56905	−	25.2335i	−0.199410	−	1.10128i
$526$	2.93355			0.127909
$527$	−16.9129	−	16.9129i	−0.736738	−	0.736738i
$528$	3.94302	−	7.27454i	0.171598	−	0.316584i
$529$			3.14005i			0.136524i
$530$	6.37173	+	7.11108i	0.276770	+	0.308886i
$531$	−8.46538	−	12.9948i	−0.367366	−	0.563927i
$532$	−26.2612	+	26.2612i	−1.13857	+	1.13857i
$533$	−0.727440	+	0.727440i	−0.0315089	+	0.0315089i
$534$	3.40113	+	11.4519i	0.147181	+	0.495574i
$535$	−0.0833609	+	1.52016i	−0.00360401	+	0.0657222i
$536$		−	13.5654i		−	0.585938i
$537$	19.5417	+	10.5922i	0.843289	+	0.457088i
$538$	4.26361	+	4.26361i	0.183817	+	0.183817i
$539$	−1.76804			−0.0761550
$540$	12.4026	+	11.7761i	0.533722	+	0.506764i
$541$	6.29034			0.270443			0.135221	−	0.990815i	$-0.456825\pi$
$541$	6.29034			0.270443			0.135221	+	0.990815i	$0.456825\pi$
$542$	−22.9406	−	22.9406i	−0.985384	−	0.985384i
$543$	28.8549	+	15.6402i	1.23828	+	0.671185i
$544$		−	33.0963i		−	1.41899i
$545$	4.79870	−	4.29977i	0.205554	−	0.184182i
$546$	−0.622103	−	2.09468i	−0.0266236	−	0.0896441i
$547$	10.6433	−	10.6433i	0.455076	−	0.455076i	−0.441959	−	0.897035i	$-0.645716\pi$
$547$	10.6433	−	10.6433i	0.455076	−	0.455076i	0.897035	+	0.441959i	$0.145716\pi$
$548$	−16.0247	+	16.0247i	−0.684539	+	0.684539i
$549$	−5.55198	−	8.52259i	−0.236953	−	0.363735i
$550$	5.82798	+	7.26868i	0.248506	+	0.309937i
$551$			25.7014i			1.09492i
$552$	−3.61903	+	6.67680i	−0.154036	+	0.284184i
$553$	−12.4296	−	12.4296i	−0.528560	−	0.528560i
$554$	−29.3905			−1.24868
$555$	22.1265	+	13.6111i	0.939216	+	0.577760i
$556$	27.7106			1.17519
$557$	7.68611	+	7.68611i	0.325671	+	0.325671i	0.850938	−	0.525267i	$-0.176034\pi$
$557$	7.68611	+	7.68611i	0.325671	+	0.325671i	−0.525267	+	0.850938i	$0.676034\pi$
$558$	−5.78464	+	27.4073i	−0.244883	+	1.16024i
$559$			0.108661i			0.00459588i
$560$	31.5837	+	1.73195i	1.33465	+	0.0731883i
$561$	−7.92533	+	2.35376i	−0.334608	+	0.0993757i
$562$	−34.2445	+	34.2445i	−1.44452	+	1.44452i
$563$	−0.0543618	+	0.0543618i	−0.00229108	+	0.00229108i	−0.708251	−	0.705960i	$-0.750516\pi$
$563$	−0.0543618	+	0.0543618i	−0.00229108	+	0.00229108i	0.705960	+	0.708251i	$0.250516\pi$
$564$	−21.2631	+	6.31496i	−0.895338	+	0.265908i
$565$	18.6113	+	1.02059i	0.782983	+	0.0429364i
$566$			36.8275i			1.54798i
$567$	−9.62156	−	24.8523i	−0.404068	−	1.04370i
$568$	−1.55336	−	1.55336i	−0.0651774	−	0.0651774i
$569$	8.63090			0.361826			0.180913	−	0.983499i	$-0.442095\pi$
$569$	8.63090			0.361826			0.180913	+	0.983499i	$0.442095\pi$
$570$	−52.3752	−	32.2187i	−2.19375	−	1.34949i
$571$	44.5130			1.86281			0.931405	−	0.363984i	$-0.118584\pi$
$571$	44.5130			1.86281			0.931405	+	0.363984i	$0.118584\pi$
$572$	0.237988	+	0.237988i	0.00995080	+	0.00995080i
$573$	13.0684	−	24.1101i	0.545941	−	1.00722i
$574$		−	24.8243i		−	1.03615i
$575$	−13.9386	−	17.3843i	−0.581281	−	0.724975i
$576$	−8.45923	+	5.51070i	−0.352468	+	0.229613i
$577$	−20.3357	+	20.3357i	−0.846587	+	0.846587i	−0.989706	−	0.143119i	$-0.954287\pi$
$577$	−20.3357	+	20.3357i	−0.846587	+	0.846587i	0.143119	+	0.989706i	$0.454287\pi$
$578$	−7.62041	+	7.62041i	−0.316967	+	0.316967i
$579$	5.14181	+	17.3130i	0.213686	+	0.719502i
$580$	−7.39394	+	6.62517i	−0.307017	+	0.275095i
$581$		−	1.53209i		−	0.0635617i
$582$	19.8339	+	10.7506i	0.822144	+	0.445627i
$583$	1.62043	+	1.62043i	0.0671113	+	0.0671113i
$584$	7.56079			0.312868
$585$	1.32910	−	0.765602i	0.0549517	−	0.0316538i
$586$	38.5655			1.59313
$587$	−0.959751	−	0.959751i	−0.0396132	−	0.0396132i	0.687023	−	0.726636i	$-0.258917\pi$
$587$	−0.959751	−	0.959751i	−0.0396132	−	0.0396132i	−0.726636	+	0.687023i	$0.758917\pi$
$588$	3.96294	+	2.14803i	0.163429	+	0.0885834i
$589$		−	42.6976i		−	1.75932i
$590$	−1.17938	+	21.5071i	−0.0485545	+	0.885433i
$591$	6.30087	+	21.2156i	0.259183	+	0.872695i
$592$	−22.6579	+	22.6579i	−0.931232	+	0.931232i
$593$	−17.7549	+	17.7549i	−0.729108	+	0.729108i	−0.970442	−	0.241334i	$-0.922415\pi$
$593$	−17.7549	+	17.7549i	−0.729108	+	0.729108i	0.241334	+	0.970442i	$0.422415\pi$
$594$	7.37580	+	6.27221i	0.302633	+	0.257352i
$595$	−21.0906	−	23.5378i	−0.864629	−	0.964958i
$596$		−	26.7454i		−	1.09554i
$597$	−9.13928	+	16.8612i	−0.374046	+	0.690083i
$598$	−1.34257	−	1.34257i	−0.0549016	−	0.0549016i
$599$	44.2947			1.80983			0.904915	−	0.425592i	$-0.139934\pi$
$599$	44.2947			1.80983			0.904915	+	0.425592i	$0.139934\pi$
$600$	1.51819	+	8.38450i	0.0619799	+	0.342296i
$601$	−22.9340			−0.935497			−0.467748	−	0.883862i	$-0.654935\pi$
$601$	−22.9340			−0.935497			−0.467748	+	0.883862i	$0.654935\pi$
$602$	−1.85406	−	1.85406i	−0.0755659	−	0.0755659i
$603$	40.4706	+	8.54180i	1.64809	+	0.347849i
$604$		−	7.60797i		−	0.309564i
$605$	1.49219	+	1.66534i	0.0606662	+	0.0677058i
$606$	30.6810	−	9.11200i	1.24633	−	0.370150i
$607$	10.8599	−	10.8599i	0.440790	−	0.440790i	−0.451487	−	0.892278i	$-0.649106\pi$
$607$	10.8599	−	10.8599i	0.440790	−	0.440790i	0.892278	+	0.451487i	$0.149106\pi$
$608$	41.7767	−	41.7767i	1.69427	−	1.69427i
$609$	14.8297	−	4.40430i	0.600930	−	0.178471i
$610$	−0.773494	+	14.1053i	−0.0313179	+	0.571108i
$611$			1.98929i			0.0804780i
$612$	20.6237	+	4.35288i	0.833663	+	0.175955i
$613$	6.73269	+	6.73269i	0.271931	+	0.271931i	0.829877	−	0.557946i	$-0.188410\pi$
$613$	6.73269	+	6.73269i	0.271931	+	0.271931i	−0.557946	+	0.829877i	$0.688410\pi$
$614$	−0.361414			−0.0145855
$615$	16.9509	−	4.03896i	0.683526	−	0.162867i
$616$	2.91342			0.117385
$617$	−14.3232	−	14.3232i	−0.576631	−	0.576631i	0.357343	−	0.933973i	$-0.383683\pi$
$617$	−14.3232	−	14.3232i	−0.576631	−	0.576631i	−0.933973	+	0.357343i	$0.883683\pi$
$618$	12.5408	−	23.1368i	0.504466	−	0.930698i
$619$		−	17.4592i		−	0.701743i	−0.936424	−	0.350871i	$-0.885885\pi$
$619$		−	17.4592i		−	0.701743i	0.936424	−	0.350871i	$-0.114115\pi$
$620$	12.2835	−	11.0063i	0.493317	−	0.442025i
$621$	−17.6405	−	15.0011i	−0.707888	−	0.601972i
$622$	23.9385	−	23.9385i	0.959848	−	0.959848i
$623$	−7.75037	+	7.75037i	−0.310512	+	0.310512i
$624$	0.538644	+	1.81367i	0.0215630	+	0.0726048i
$625$	−24.4022	−	5.43447i	−0.976087	−	0.217379i
$626$		−	40.9543i		−	1.63686i
$627$	−12.9751	−	7.03287i	−0.518174	−	0.280866i
$628$	0.102011	+	0.102011i	0.00407067	+	0.00407067i
$629$	32.0161			1.27656
$630$	−9.61492	+	35.7415i	−0.383068	+	1.42398i
$631$	11.4177			0.454532			0.227266	−	0.973833i	$-0.427021\pi$
$631$	11.4177			0.454532			0.227266	+	0.973833i	$0.427021\pi$
$632$	4.13007	+	4.13007i	0.164286	+	0.164286i
$633$	−3.74198	−	2.02827i	−0.148730	−	0.0806164i
$634$			2.31601i			0.0919807i
$635$	−1.71074	−	0.0938117i	−0.0678886	−	0.00372280i
$636$	−1.66338	−	5.60076i	−0.0659573	−	0.222085i
$637$	0.285859	−	0.285859i	0.0113261	−	0.0113261i
$638$	−3.97419	+	3.97419i	−0.157340	+	0.157340i
$639$	5.61233	−	3.65611i	0.222020	−	0.144634i
$640$	−16.9617	−	0.930126i	−0.670469	−	0.0367665i
$641$			49.6654i			1.96166i	0.194855	+	0.980832i	$0.437576\pi$
$641$			49.6654i			1.96166i	−0.194855	+	0.980832i	$0.562424\pi$
$642$	1.04712	−	1.93184i	0.0413264	−	0.0762437i
$643$	−20.8135	−	20.8135i	−0.820803	−	0.820803i	0.165420	−	0.986223i	$-0.447102\pi$
$643$	−20.8135	−	20.8135i	−0.820803	−	0.820803i	−0.986223	+	0.165420i	$0.947102\pi$
$644$	19.4239			0.765410
$645$	0.964359	−	1.56768i	0.0379716	−	0.0617272i
$646$	−75.7847			−2.98171
$647$	4.95430	+	4.95430i	0.194774	+	0.194774i	0.797755	−	0.602982i	$-0.206021\pi$
$647$	4.95430	+	4.95430i	0.194774	+	0.194774i	−0.602982	+	0.797755i	$0.706021\pi$
$648$	3.19703	+	8.25785i	0.125591	+	0.324399i
$649$			5.16965i			0.202927i
$650$	−2.11748	−	0.232933i	−0.0830544	−	0.00913638i
$651$	−24.6365	+	7.31682i	−0.965579	+	0.286769i
$652$	18.2683	−	18.2683i	0.715440	−	0.715440i
$653$	−6.32930	+	6.32930i	−0.247684	+	0.247684i	−0.820020	−	0.572335i	$-0.806038\pi$
$653$	−6.32930	+	6.32930i	−0.247684	+	0.247684i	0.572335	+	0.820020i	$0.306038\pi$
$654$	−8.91483	+	2.64763i	−0.348598	+	0.103531i
$655$	−33.4965	+	30.0138i	−1.30882	+	1.17274i
$656$			21.4940i			0.839198i
$657$	−4.76083	+	22.5565i	−0.185738	+	0.880014i
$658$	−33.9428	−	33.9428i	−1.32323	−	1.32323i
$659$	4.08497			0.159128			0.0795639	−	0.996830i	$-0.474647\pi$
$659$	4.08497			0.159128			0.0795639	+	0.996830i	$0.474647\pi$
$660$	−1.32138	−	5.54564i	−0.0514347	−	0.215864i
$661$	1.41024			0.0548519			0.0274259	−	0.999624i	$-0.491269\pi$
$661$	1.41024			0.0548519			0.0274259	+	0.999624i	$0.491269\pi$
$662$	−2.39252	−	2.39252i	−0.0929879	−	0.0929879i
$663$	0.900818	−	1.66193i	0.0349849	−	0.0645441i
$664$			0.509078i			0.0197561i
$665$	3.08915	−	56.3334i	0.119792	−	2.18452i
$666$	−20.4658	−	31.4161i	−0.793033	−	1.21735i
$667$	9.50495	−	9.50495i	0.368033	−	0.368033i
$668$	7.44983	−	7.44983i	0.288242	−	0.288242i
$669$	−1.89937	−	6.39536i	−0.0734338	−	0.247259i
$670$	−38.3349	−	42.7832i	−1.48101	−	1.65286i
$671$			3.39049i			0.130889i
$672$	−31.2642	−	16.9461i	−1.20604	−	0.653711i
$673$	18.1505	+	18.1505i	0.699650	+	0.699650i	0.964335	−	0.264685i	$-0.0852680\pi$
$673$	18.1505	+	18.1505i	0.699650	+	0.699650i	−0.264685	+	0.964335i	$0.585268\pi$
$674$	−2.17219			−0.0836698
$675$	−25.9699	−	0.750192i	−0.999583	−	0.0288749i
$676$	19.0586			0.733022
$677$	−32.0068	−	32.0068i	−1.23012	−	1.23012i	−0.963916	−	0.266205i	$-0.914230\pi$
$677$	−32.0068	−	32.0068i	−1.23012	−	1.23012i	−0.266205	−	0.963916i	$-0.585770\pi$
$678$	−23.6515	−	12.8198i	−0.908331	−	0.492343i
$679$			20.6988i			0.794347i
$680$	7.00791	+	7.82109i	0.268741	+	0.299925i
$681$	14.1898	+	47.7785i	0.543755	+	1.83088i
$682$	6.60228	−	6.60228i	0.252814	−	0.252814i
$683$	−0.422561	+	0.422561i	−0.0161689	+	0.0161689i	−0.715145	−	0.698976i	$-0.753639\pi$
$683$	−0.422561	+	0.422561i	−0.0161689	+	0.0161689i	0.698976	+	0.715145i	$0.253639\pi$
$684$	20.5383	+	31.5273i	0.785300	+	1.20548i
$685$	1.88501	−	34.3748i	0.0720224	−	1.31339i
$686$		−	28.8671i		−	1.10215i
$687$	−10.2349	+	18.8825i	−0.390484	+	0.720411i
$688$	1.60533	+	1.60533i	0.0612025	+	0.0612025i
$689$	−0.523985			−0.0199622
$690$	7.45432	+	31.2846i	0.283781	+	1.19099i
$691$	33.4110			1.27101			0.635507	−	0.772095i	$-0.280791\pi$
$691$	33.4110			1.27101			0.635507	+	0.772095i	$0.280791\pi$
$692$	−15.1148	−	15.1148i	−0.574577	−	0.574577i
$693$	−1.83450	+	8.69178i	−0.0696871	+	0.330173i
$694$		−	26.4779i		−	1.00509i
$695$	−31.3510	+	28.0914i	−1.18921	+	1.06557i
$696$	−4.92757	+	1.46345i	−0.186779	+	0.0554718i
$697$	15.1857	−	15.1857i	0.575200	−	0.575200i
$698$	1.98071	−	1.98071i	0.0749709	−	0.0749709i
$699$	−4.29940	+	1.27689i	−0.162618	+	0.0482963i
$700$	17.0026	−	13.6326i	0.642639	−	0.515264i
$701$		−	5.59359i		−	0.211267i	−0.994405	−	0.105634i	$-0.966313\pi$
$701$		−	5.59359i		−	0.211267i	0.994405	−	0.105634i	$-0.0336871\pi$
$702$	−2.20662	+	0.178429i	−0.0832836	+	0.00673438i
$703$	40.4131	+	40.4131i	1.52421	+	1.52421i
$704$	3.36529			0.126834
$705$	17.6548	−	28.6999i	0.664917	−	1.08090i
$706$	27.5065			1.03522
$707$	20.7641	+	20.7641i	0.780914	+	0.780914i
$708$	6.28072	−	11.5874i	0.236044	−	0.435481i
$709$		−	7.90281i		−	0.296796i	−0.988928	−	0.148398i	$-0.952588\pi$
$709$		−	7.90281i		−	0.296796i	0.988928	−	0.148398i	$-0.0474117\pi$
$710$	−9.28870	−	0.509364i	−0.348599	−	0.0191161i
$711$	−14.9221	+	9.72089i	−0.559622	+	0.364562i
$712$	2.57527	−	2.57527i	0.0965124	−	0.0965124i
$713$	−15.7905	+	15.7905i	−0.591358	+	0.591358i
$714$	12.9868	+	43.7277i	0.486017	+	1.63647i
$715$	−0.510513	−	0.0279950i	−0.0190921	−	0.00104695i
$716$			18.8900i			0.705953i
$717$	30.8474	+	16.7202i	1.15202	+	0.624428i
$718$	−18.9599	−	18.9599i	−0.707577	−	0.707577i
$719$	2.71116			0.101109			0.0505547	−	0.998721i	$-0.483901\pi$
$719$	2.71116			0.101109			0.0505547	+	0.998721i	$0.483901\pi$
$720$	8.32502	−	30.9466i	0.310255	−	1.15331i
$721$	24.1457			0.899232
$722$	−70.6275	−	70.6275i	−2.62848	−	2.62848i
$723$	3.50322	+	1.89885i	0.130286	+	0.0706190i
$724$			27.8926i			1.03662i
$725$	1.64909	−	14.9911i	0.0612458	−	0.556756i
$726$	−0.918834	−	3.09381i	−0.0341011	−	0.114822i
$727$	−28.7249	+	28.7249i	−1.06535	+	1.06535i	−0.0676395	+	0.997710i	$0.521547\pi$
$727$	−28.7249	+	28.7249i	−1.06535	+	1.06535i	−0.997710	+	0.0676395i	$0.978453\pi$
$728$	−0.471045	+	0.471045i	−0.0174581	+	0.0174581i
$729$	−26.6492	+	4.33812i	−0.987008	+	0.160671i
$730$	23.8455	−	21.3662i	0.882561	−	0.790799i
$731$		−	2.26836i		−	0.0838984i
$732$	4.11918	−	7.59954i	0.152249	−	0.280887i
$733$	−28.0365	−	28.0365i	−1.03555	−	1.03555i	−0.999344	−	0.0362092i	$-0.988472\pi$
$733$	−28.0365	−	28.0365i	−1.03555	−	1.03555i	−0.0362092	−	0.999344i	$-0.511528\pi$
$734$	−63.2007			−2.33278
$735$	−6.66112	+	1.58717i	−0.245699	+	0.0585437i
$736$	−30.8999			−1.13899
$737$	−9.74916	−	9.74916i	−0.359115	−	0.359115i
$738$	−24.6084	−	5.19390i	−0.905847	−	0.191190i
$739$		−	14.9125i		−	0.548565i	−0.961649	−	0.274282i	$-0.911560\pi$
$739$		−	14.9125i		−	0.548565i	0.961649	−	0.274282i	$-0.0884403\pi$
$740$	−1.20881	+	22.0438i	−0.0444368	+	0.810345i
$741$	3.23490	−	0.960739i	0.118837	−	0.0352936i
$742$	8.94064	−	8.94064i	0.328221	−	0.328221i
$743$	8.00940	−	8.00940i	0.293836	−	0.293836i	−0.544757	−	0.838594i	$-0.683378\pi$
$743$	8.00940	−	8.00940i	0.293836	−	0.293836i	0.838594	+	0.544757i	$0.183378\pi$
$744$	8.18613	−	2.43121i	0.300118	−	0.0891326i
$745$	27.1130	+	30.2591i	0.993344	+	1.10861i
$746$		−	43.8133i		−	1.60412i
$747$	−1.51876	−	0.320553i	−0.0555686	−	0.0117284i
$748$	−4.96814	−	4.96814i	−0.181653	−	0.181653i
$749$	2.01608			0.0736659
$750$	28.4821	+	22.1530i	1.04002	+	0.808915i
$751$	−14.6500			−0.534587			−0.267294	−	0.963615i	$-0.586129\pi$
$751$	−14.6500			−0.534587			−0.267294	+	0.963615i	$0.586129\pi$
$752$	29.3892	+	29.3892i	1.07171	+	1.07171i
$753$	−22.3327	+	41.2020i	−0.813849	+	1.50148i
$754$		−	1.28510i		−	0.0468006i
$755$	7.71253	+	8.60746i	0.280688	+	0.313258i
$756$	14.6717	−	17.2532i	0.533605	−	0.627493i
$757$	28.2615	−	28.2615i	1.02718	−	1.02718i	0.0275615	−	0.999620i	$-0.491226\pi$
$757$	28.2615	−	28.2615i	1.02718	−	1.02718i	0.999620	−	0.0275615i	$-0.00877422\pi$
$758$	−36.0985	+	36.0985i	−1.31116	+	1.31116i
$759$	2.19755	+	7.39937i	0.0797660	+	0.268580i
$760$	−1.02646	+	18.7183i	−0.0372335	+	0.678985i
$761$			3.35785i			0.121722i	0.998146	+	0.0608610i	$0.0193846\pi$
$761$			3.35785i			0.121722i	−0.998146	+	0.0608610i	$0.980615\pi$
$762$	2.17403	+	1.17839i	0.0787568	+	0.0426886i
$763$	−6.03332	−	6.03332i	−0.218421	−	0.218421i
$764$	23.3061			0.843184
$765$	−27.7458	+	15.9824i	−1.00315	+	0.577844i
$766$	46.4278			1.67750
$767$	−0.835835	−	0.835835i	−0.0301802	−	0.0301802i
$768$	31.8041	+	17.2388i	1.14763	+	0.622051i
$769$			16.5162i			0.595588i	0.954630	+	0.297794i	$0.0962508\pi$
$769$			16.5162i			0.595588i	−0.954630	+	0.297794i	$0.903749\pi$
$770$	9.18845	−	8.23310i	0.331129	−	0.296700i
$771$	−10.0312	−	33.7760i	−0.361265	−	1.21641i
$772$	−10.8530	+	10.8530i	−0.390606	+	0.390606i
$773$	−18.4182	+	18.4182i	−0.662457	+	0.662457i	−0.955959	−	0.293502i	$-0.905179\pi$
$773$	−18.4182	+	18.4182i	−0.662457	+	0.662457i	0.293502	+	0.955959i	$0.405179\pi$
$774$	−2.22585	+	1.45002i	−0.0800066	+	0.0521198i
$775$	−2.73962	+	24.9046i	−0.0984102	+	0.894599i
$776$		−	6.87774i		−	0.246897i
$777$	16.3930	−	30.2437i	0.588095	−	1.08499i
$778$	26.0396	+	26.0396i	0.933565	+	0.933565i
$779$	38.3372			1.37357
$780$	1.11027	+	0.682982i	0.0397539	+	0.0244547i
$781$	−2.23272			−0.0798930
$782$	28.0268	+	28.0268i	1.00224	+	1.00224i
$783$	−1.26322	−	15.6222i	−0.0451440	−	0.558292i
$784$		−	8.44639i		−	0.301657i
$785$	−0.218825	−	0.0119997i	−0.00781020	−	0.000428287i
$786$	62.2284	−	18.4813i	2.21962	−	0.659207i
$787$	6.14166	−	6.14166i	0.218926	−	0.218926i	−0.589119	−	0.808046i	$-0.700525\pi$
$787$	6.14166	−	6.14166i	0.218926	−	0.218926i	0.808046	+	0.589119i	$0.200525\pi$
$788$	−13.2994	+	13.2994i	−0.473772	+	0.473772i
$789$	2.61404	−	0.776347i	0.0930622	−	0.0276387i
$790$	24.6968	+	1.35430i	0.878674	+	0.0481838i
$791$		−	24.6828i		−	0.877621i
$792$	0.609564	−	2.88808i	0.0216599	−	0.102623i
$793$	−0.548178	−	0.548178i	−0.0194664	−	0.0194664i
$794$	−3.72342			−0.132139
$795$	7.55964	+	4.65032i	0.268113	+	0.164930i
$796$	−16.2989			−0.577698
$797$	−28.9739	−	28.9739i	−1.02631	−	1.02631i	−0.999644	−	0.0266641i	$-0.991512\pi$
$797$	−28.9739	−	28.9739i	−1.02631	−	1.02631i	−0.0266641	−	0.999644i	$-0.508488\pi$
$798$	−38.8036	+	71.5893i	−1.37363	+	2.53423i
$799$		−	41.5275i		−	1.46914i
$800$	−27.0480	+	21.6870i	−0.956293	+	0.766750i
$801$	6.06138	+	9.30454i	0.214168	+	0.328760i
$802$	−32.2710	+	32.2710i	−1.13953	+	1.13953i
$803$	5.43376	−	5.43376i	0.191753	−	0.191753i
$804$	10.0076	+	33.6965i	0.352940	+	1.18838i
$805$	−21.9758	+	19.6909i	−0.774544	+	0.694012i
$806$			2.13493i			0.0751996i
$807$	4.92757	+	2.67089i	0.173459	+	0.0940198i
$808$	−6.89943	−	6.89943i	−0.242721	−	0.242721i
$809$	27.5336			0.968031			0.484016	−	0.875059i	$-0.339178\pi$
$809$	27.5336			0.968031			0.484016	+	0.875059i	$0.339178\pi$
$810$	33.4190	+	17.0094i	1.17422	+	0.597648i
$811$	12.6038			0.442580			0.221290	−	0.975208i	$-0.428973\pi$
$811$	12.6038			0.442580			0.221290	+	0.975208i	$0.428973\pi$
$812$	9.29627	+	9.29627i	0.326235	+	0.326235i
$813$	−26.5131	−	14.3709i	−0.929854	−	0.504009i
$814$			12.4981i			0.438057i
$815$	−2.14893	+	39.1876i	−0.0752737	+	1.37268i
$816$	−11.2445	−	37.8613i	−0.393636	−	1.32541i
$817$	2.86330	−	2.86330i	0.100174	−	0.100174i
$818$	29.5683	−	29.5683i	1.03383	−	1.03383i
$819$	−1.10869	−	1.70190i	−0.0387408	−	0.0594692i
$820$	9.88235	+	11.0291i	0.345106	+	0.385152i
$821$			17.3304i			0.604836i	0.953175	+	0.302418i	$0.0977938\pi$
$821$			17.3304i			0.604836i	−0.953175	+	0.302418i	$0.902206\pi$
$822$	−23.6780	+	43.6839i	−0.825866	+	1.52365i
$823$	−20.4085	−	20.4085i	−0.711397	−	0.711397i	0.255430	−	0.966828i	$-0.417783\pi$
$823$	−20.4085	−	20.4085i	−0.711397	−	0.711397i	−0.966828	+	0.255430i	$0.917783\pi$
$824$	−8.02306			−0.279496
$825$	7.11683	+	4.93465i	0.247776	+	0.171803i
$826$	28.5233			0.992454
$827$	−13.1570	−	13.1570i	−0.457513	−	0.457513i	0.440325	−	0.897838i	$-0.354863\pi$
$827$	−13.1570	−	13.1570i	−0.457513	−	0.457513i	−0.897838	+	0.440325i	$0.854863\pi$
$828$	4.06400	−	19.2550i	0.141234	−	0.669157i
$829$		−	25.7974i		−	0.895980i	−0.894039	−	0.447990i	$-0.852140\pi$
$829$		−	25.7974i		−	0.895980i	0.894039	−	0.447990i	$-0.147860\pi$
$830$	1.43862	+	1.60555i	0.0499351	+	0.0557294i
$831$	−26.1893	+	7.77801i	−0.908498	+	0.269816i
$832$	−0.544103	+	0.544103i	−0.0188634	+	0.0188634i
$833$	−5.96747	+	5.96747i	−0.206760	+	0.206760i
$834$	58.2427	−	17.2976i	2.01678	−	0.598967i
$835$	−0.876336	+	15.9808i	−0.0303269	+	0.553037i
$836$		−	12.5423i		−	0.433786i
$837$	2.09858	+	25.9530i	0.0725377	+	0.897068i
$838$	3.23710	+	3.23710i	0.111824	+	0.111824i
$839$	17.9282			0.618949			0.309475	−	0.950908i	$-0.399847\pi$
$839$	17.9282			0.618949			0.309475	+	0.950908i	$0.399847\pi$
$840$	10.9763	−	2.61538i	0.378720	−	0.0902391i
$841$	−19.9019			−0.686272
$842$	−1.21150	−	1.21150i	−0.0417510	−	0.0417510i
$843$	−21.4521	+	39.5773i	−0.738848	+	1.36311i
$844$		−	3.61719i		−	0.124509i
$845$	−21.5624	+	19.3205i	−0.741768	+	0.664645i
$846$	−40.7493	+	26.5459i	−1.40099	+	0.912665i
$847$	2.09381	−	2.09381i	0.0719440	−	0.0719440i
$848$	−7.74119	+	7.74119i	−0.265834	+	0.265834i
$849$	9.74618	+	32.8164i	0.334488	+	1.12625i
$850$	44.2036	+	4.86261i	1.51617	+	0.166786i
$851$		−	29.8913i		−	1.02466i
$852$	5.00448	+	2.71258i	0.171451	+	0.0929314i
$853$	−9.62668	−	9.62668i	−0.329611	−	0.329611i	0.522827	−	0.852439i	$-0.324877\pi$
$853$	−9.62668	−	9.62668i	−0.329611	−	0.329611i	−0.852439	+	0.522827i	$0.824877\pi$
$854$	18.7069			0.640137
$855$	−55.1971	−	14.8487i	−1.88770	−	0.507815i
$856$	−0.669897			−0.0228966
$857$	18.5942	+	18.5942i	0.635167	+	0.635167i	0.949359	−	0.314193i	$-0.101734\pi$
$857$	18.5942	+	18.5942i	0.635167	+	0.635167i	−0.314193	+	0.949359i	$0.601734\pi$
$858$	0.648767	+	0.351651i	0.0221486	+	0.0120052i
$859$			52.8538i			1.80335i	0.432416	+	0.901674i	$0.357661\pi$
$859$			52.8538i			1.80335i	−0.432416	+	0.901674i	$0.642339\pi$
$860$	1.56182	+	0.0856453i	0.0532575	+	0.00292048i
$861$	−6.56961	−	22.1205i	−0.223892	−	0.753865i
$862$	18.8864	−	18.8864i	0.643273	−	0.643273i
$863$	33.0543	−	33.0543i	1.12518	−	1.12518i	0.134233	−	0.990950i	$-0.457143\pi$
$863$	33.0543	−	33.0543i	1.12518	−	1.12518i	0.990950	−	0.134233i	$-0.0428570\pi$
$864$	−23.3400	+	27.4466i	−0.794043	+	0.933754i
$865$	32.4229	+	1.77797i	1.10241	+	0.0604530i
$866$		−	6.85394i		−	0.232907i
$867$	−4.77372	+	8.80710i	−0.162124	+	0.299105i
$868$	−15.4438	−	15.4438i	−0.524197	−	0.524197i
$869$	5.93637			0.201378
$870$	−11.4052	+	18.5404i	−0.386671	+	0.628579i
$871$	3.15251			0.106819
$872$	2.00474	+	2.00474i	0.0678889	+	0.0678889i
$873$	20.5188	+	4.33073i	0.694455	+	0.146573i
$874$			70.7552i			2.39333i
$875$	−5.41638	+	32.6599i	−0.183107	+	1.10411i
$876$	−18.7810	+	5.57778i	−0.634550	+	0.188456i
$877$	7.28035	−	7.28035i	0.245840	−	0.245840i	−0.573421	−	0.819261i	$-0.694384\pi$
$877$	7.28035	−	7.28035i	0.245840	−	0.245840i	0.819261	+	0.573421i	$0.194384\pi$
$878$	13.2446	−	13.2446i	0.446984	−	0.446984i
$879$	34.3651	−	10.2061i	1.15911	−	0.344245i
$880$	−7.95576	+	7.12858i	−0.268188	+	0.240304i
$881$		−	29.9331i		−	1.00847i	−0.863566	−	0.504236i	$-0.831774\pi$
$881$		−	29.9331i		−	1.00847i	0.863566	−	0.504236i	$-0.168226\pi$
$882$	9.67025	+	2.04102i	0.325614	+	0.0687248i
$883$	13.3384	+	13.3384i	0.448872	+	0.448872i	0.894979	−	0.446107i	$-0.147190\pi$
$883$	13.3384	+	13.3384i	0.448872	+	0.448872i	−0.446107	+	0.894979i	$0.647190\pi$
$884$	1.60651			0.0540327
$885$	4.64080	+	19.4767i	0.155999	+	0.654703i
$886$	−28.2240			−0.948205
$887$	−18.3918	−	18.3918i	−0.617537	−	0.617537i	0.327362	−	0.944899i	$-0.393840\pi$
$887$	−18.3918	−	18.3918i	−0.617537	−	0.617537i	−0.944899	+	0.327362i	$0.893840\pi$
$888$	−5.44702	+	10.0493i	−0.182790	+	0.337232i
$889$			2.26883i			0.0760941i
$890$	0.844462	−	15.3995i	0.0283064	−	0.516193i
$891$	8.23235	+	3.63710i	0.275794	+	0.121847i
$892$	4.00905	−	4.00905i	0.134233	−	0.134233i
$893$	52.4193	−	52.4193i	1.75414	−	1.75414i
$894$	−16.6951	−	56.2142i	−0.558369	−	1.88008i
$895$	−19.1496	−	21.3717i	−0.640102	−	0.714377i
$896$			22.4950i			0.751507i
$897$	−1.55164	−	0.841035i	−0.0518077	−	0.0280813i
$898$	−34.0676	−	34.0676i	−1.13685	−	1.13685i
$899$	−15.1146			−0.504101
$900$	−9.95663	−	19.7070i	−0.331888	−	0.656901i
$901$	10.9385			0.364414
$902$	5.92804	+	5.92804i	0.197382	+	0.197382i
$903$	−2.14279	−	1.16146i	−0.0713075	−	0.0386508i
$904$			8.20154i			0.272779i
$905$	−28.2759	−	31.5569i	−0.939922	−	1.04899i
$906$	−4.74907	−	15.9906i	−0.157777	−	0.531252i
$907$	24.1125	−	24.1125i	0.800643	−	0.800643i	−0.182553	−	0.983196i	$-0.558436\pi$
$907$	24.1125	−	24.1125i	0.800643	−	0.800643i	0.983196	+	0.182553i	$0.0584360\pi$
$908$	−29.9509	+	29.9509i	−0.993954	+	0.993954i
$909$	24.9279	−	16.2391i	0.826805	−	0.538616i
$910$	−0.154461	+	2.81673i	−0.00512034	+	0.0933738i
$911$		−	36.8662i		−	1.22143i	−0.791850	−	0.610715i	$-0.790882\pi$
$911$		−	36.8662i		−	1.22143i	0.791850	−	0.610715i	$-0.209118\pi$
$912$	33.5978	−	61.9851i	1.11253	−	2.05253i
$913$	0.365862	+	0.365862i	0.0121083	+	0.0121083i
$914$	−36.8083			−1.21751
$915$	3.04365	+	12.7737i	0.100620	+	0.422286i
$916$	−18.2527			−0.603087
$917$	42.1146	+	42.1146i	1.39075	+	1.39075i
$918$	46.0645	−	3.72481i	1.52035	−	0.122937i
$919$			36.9865i			1.22007i	0.792374	+	0.610035i	$0.208845\pi$
$919$			36.9865i			1.22007i	−0.792374	+	0.610035i	$0.791155\pi$
$920$	7.30204	−	6.54283i	0.240741	−	0.215711i
$921$	−0.322049	+	0.0956459i	−0.0106119	+	0.00315164i
$922$	0.0697387	−	0.0697387i	0.00229672	−	0.00229672i
$923$	0.360988	−	0.360988i	0.0118821	−	0.0118821i
$924$	−7.23692	+	2.14930i	−0.238077	+	0.0707069i
$925$	−20.9791	−	26.1652i	−0.689788	−	0.860306i
$926$			6.49835i			0.213549i
$927$	5.05191	−	23.9356i	0.165926	−	0.786150i
$928$	−14.7886	−	14.7886i	−0.485461	−	0.485461i
$929$	40.7878			1.33820			0.669102	−	0.743170i	$-0.266679\pi$
$929$	40.7878			1.33820			0.669102	+	0.743170i	$0.266679\pi$
$930$	18.9473	−	30.8010i	0.621306	−	1.01001i
$931$	−15.0652			−0.493742
$932$	−2.69516	−	2.69516i	−0.0882829	−	0.0882829i
$933$	14.9960	−	27.6664i	0.490948	−	0.905757i
$934$		−	35.0744i		−	1.14767i
$935$	10.6572	+	0.584411i	0.348529	+	0.0191123i
$936$	0.368393	+	0.565502i	0.0120413	+	0.0184840i
$937$	−3.15650	+	3.15650i	−0.103119	+	0.103119i	−0.756784	−	0.653665i	$-0.773230\pi$
$937$	−3.15650	+	3.15650i	−0.103119	+	0.103119i	0.653665	+	0.756784i	$0.273230\pi$
$938$	−53.7905	+	53.7905i	−1.75632	+	1.75632i
$939$	−10.8383	−	36.4937i	−0.353695	−	1.19093i
$940$	28.5926	+	1.56793i	0.932588	+	0.0511403i
$941$			57.5077i			1.87470i	0.348394	+	0.937348i	$0.386727\pi$
$941$			57.5077i			1.87470i	−0.348394	+	0.937348i	$0.613273\pi$
$942$	0.278086	+	0.150731i	0.00906053	+	0.00491108i
$943$	−14.1779	−	14.1779i	−0.461697	−	0.461697i
$944$	−24.6967			−0.803810
$945$	0.891092	+	34.3932i	0.0289872	+	1.11881i
$946$	0.885499			0.0287900
$947$	27.6497	+	27.6497i	0.898494	+	0.898494i	0.995303	−	0.0968091i	$-0.0308636\pi$
$947$	27.6497	+	27.6497i	0.898494	+	0.898494i	−0.0968091	+	0.995303i	$0.530864\pi$
$948$	−13.3059	−	7.21222i	−0.432157	−	0.234242i
$949$			1.75707i			0.0570369i
$950$	49.6592	+	61.9352i	1.61116	+	2.00944i
$951$	0.612919	+	2.06376i	0.0198753	+	0.0669220i
$952$	9.83332	−	9.83332i	0.318700	−	0.318700i
$953$	−1.83684	+	1.83684i	−0.0595012	+	0.0595012i	−0.736231	−	0.676730i	$-0.763396\pi$
$953$	−1.83684	+	1.83684i	−0.0595012	+	0.0595012i	0.676730	+	0.736231i	$0.263396\pi$
$954$	−6.99226	−	10.7335i	−0.226383	−	0.347510i
$955$	−26.3679	+	23.6264i	−0.853245	+	0.764531i
$956$			29.8186i			0.964403i
$957$	−2.48958	+	4.59307i	−0.0804768	+	0.148473i
$958$	20.8115	+	20.8115i	0.672389	+	0.672389i
$959$	−45.5888			−1.47214
$960$	12.6788	−	3.02102i	0.409205	−	0.0975029i
$961$	−5.89023			−0.190007
$962$	−2.02070	−	2.02070i	−0.0651500	−	0.0651500i
$963$	0.421817	−	1.99854i	0.0135928	−	0.0644021i
$964$			3.38639i			0.109068i
$965$	1.27665	−	23.2809i	0.0410969	−	0.749438i
$966$	40.8257	−	12.1249i	1.31354	−	0.390112i
$967$	5.45469	−	5.45469i	0.175411	−	0.175411i	−0.613941	−	0.789352i	$-0.710417\pi$
$967$	5.45469	−	5.45469i	0.175411	−	0.175411i	0.789352	+	0.613941i	$0.210417\pi$
$968$	−0.695724	+	0.695724i	−0.0223614	+	0.0223614i
$969$	−67.5304	+	20.0560i	−2.16939	+	0.644290i
$970$	−19.4360	−	21.6913i	−0.624051	−	0.696465i
$971$		−	30.2021i		−	0.969231i	−0.874727	−	0.484615i	$-0.838960\pi$
$971$		−	30.2021i		−	0.969231i	0.874727	−	0.484615i	$-0.161040\pi$
$972$	−14.0334	−	18.1539i	−0.450122	−	0.582288i
$973$	39.4171	+	39.4171i	1.26366	+	1.26366i
$974$	52.4370			1.68019
$975$	−1.94849	+	0.352816i	−0.0624018	+	0.0112992i
$976$	−16.1972			−0.518461
$977$	−21.7515	−	21.7515i	−0.695892	−	0.695892i	0.267630	−	0.963522i	$-0.413760\pi$
$977$	−21.7515	−	21.7515i	−0.695892	−	0.695892i	−0.963522	+	0.267630i	$0.913760\pi$
$978$	26.9932	−	49.8001i	0.863146	−	1.59243i
$979$		−	3.70157i		−	0.118303i
$980$	−3.88342	−	4.33404i	−0.124051	−	0.138446i
$981$	−7.24317	+	4.71851i	−0.231257	+	0.150651i
$982$	−19.7831	+	19.7831i	−0.631303	+	0.631303i
$983$	13.0850	−	13.0850i	0.417347	−	0.417347i	−0.466941	−	0.884288i	$-0.654644\pi$
$983$	13.0850	−	13.0850i	0.417347	−	0.417347i	0.884288	+	0.466941i	$0.154644\pi$
$984$	2.18293	+	7.35014i	0.0695893	+	0.234314i
$985$	1.56443	−	28.5288i	0.0498470	−	0.909004i
$986$			26.8272i			0.854352i
$987$	−39.2286	−	21.2631i	−1.24866	−	0.676812i
$988$	2.02786	+	2.02786i	0.0645148	+	0.0645148i
$989$	−2.11782			−0.0673428
$990$	−6.23903	−	10.8311i	−0.198289	−	0.344235i
$991$	−40.4113			−1.28371			−0.641853	−	0.766828i	$-0.721834\pi$
$991$	−40.4113			−1.28371			−0.641853	+	0.766828i	$0.721834\pi$
$992$	24.5683	+	24.5683i	0.780043	+	0.780043i
$993$	−2.76510	−	1.49877i	−0.0877477	−	0.0475619i
$994$			12.3189i			0.390733i
$995$	18.4401	−	16.5229i	0.584592	−	0.523810i
$996$	−0.375560	−	1.26455i	−0.0119001	−	0.0400687i
$997$	9.17711	−	9.17711i	0.290642	−	0.290642i	−0.546692	−	0.837334i	$-0.684113\pi$
$997$	9.17711	−	9.17711i	0.290642	−	0.290642i	0.837334	+	0.546692i	$0.184113\pi$
$998$	−7.28814	+	7.28814i	−0.230702	+	0.230702i
$999$	−26.5508	−	22.5782i	−0.840029	−	0.714342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.k.c.23.8	✓	16
3.2	odd	2		165.2.k.d.23.1	yes	16
5.2	odd	4		165.2.k.d.122.1	yes	16
5.3	odd	4		825.2.k.i.782.8		16
5.4	even	2		825.2.k.j.518.1		16
15.2	even	4	inner	165.2.k.c.122.8	yes	16
15.8	even	4		825.2.k.j.782.1		16
15.14	odd	2		825.2.k.i.518.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.k.c.23.8	✓	16	1.1	even	1	trivial
165.2.k.c.122.8	yes	16	15.2	even	4	inner
165.2.k.d.23.1	yes	16	3.2	odd	2
165.2.k.d.122.1	yes	16	5.2	odd	4
825.2.k.i.518.8		16	15.14	odd	2
825.2.k.i.782.8		16	5.3	odd	4
825.2.k.j.518.1		16	5.4	even	2
825.2.k.j.782.1		16	15.8	even	4

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31757 + 1.31757i) q^{2} +(1.52275 + 0.825374i) q^{3} +1.47196i q^{4} +(-1.49219 - 1.66534i) q^{5} +(0.918834 + 3.09381i) q^{6} +(-2.09381 + 2.09381i) q^{7} +(0.695724 - 0.695724i) q^{8} +(1.63751 + 2.51367i) q^{9} +(0.228136 - 4.16026i) q^{10} -1.00000i q^{11} +(-1.21492 + 2.24143i) q^{12} +(0.161681 + 0.161681i) q^{13} -5.51746 q^{14} +(-0.897700 - 3.76751i) q^{15} +4.77725 q^{16} +(-3.37518 - 3.37518i) q^{17} +(-1.15440 + 5.46946i) q^{18} -8.52083i q^{19} +(2.45132 - 2.19645i) q^{20} +(-4.91651 + 1.46016i) q^{21} +(1.31757 - 1.31757i) q^{22} +(-3.15119 + 3.15119i) q^{23} +(1.63364 - 0.485178i) q^{24} +(-0.546726 + 4.97002i) q^{25} +0.426051i q^{26} +(0.418798 + 5.17925i) q^{27} +(-3.08200 - 3.08200i) q^{28} -3.01631 q^{29} +(3.78117 - 6.14672i) q^{30} +5.01096 q^{31} +(4.90290 + 4.90290i) q^{32} +(0.825374 - 1.52275i) q^{33} -8.89405i q^{34} +(6.61126 + 0.362542i) q^{35} +(-3.70003 + 2.41036i) q^{36} +(-4.74287 + 4.74287i) q^{37} +(11.2268 - 11.2268i) q^{38} +(0.112752 + 0.379646i) q^{39} +(-2.19677 - 0.120464i) q^{40} +4.49923i q^{41} +(-8.40169 - 4.55397i) q^{42} +(0.336036 + 0.336036i) q^{43} +1.47196 q^{44} +(1.74264 - 6.47790i) q^{45} -8.30379 q^{46} +(6.15190 + 6.15190i) q^{47} +(7.27454 + 3.94302i) q^{48} -1.76804i q^{49} +(-7.26868 + 5.82798i) q^{50} +(-2.35376 - 7.92533i) q^{51} +(-0.237988 + 0.237988i) q^{52} +(-1.62043 + 1.62043i) q^{53} +(-6.27221 + 7.37580i) q^{54} +(-1.66534 + 1.49219i) q^{55} +2.91342i q^{56} +(7.03287 - 12.9751i) q^{57} +(-3.97419 - 3.97419i) q^{58} -5.16965 q^{59} +(5.54564 - 1.32138i) q^{60} -3.39049 q^{61} +(6.60228 + 6.60228i) q^{62} +(-8.69178 - 1.83450i) q^{63} +3.36529i q^{64} +(0.0279950 - 0.510513i) q^{65} +(3.09381 - 0.918834i) q^{66} +(9.74916 - 9.74916i) q^{67} +(4.96814 - 4.96814i) q^{68} +(-7.39937 + 2.19755i) q^{69} +(8.23310 + 9.18845i) q^{70} -2.23272i q^{71} +(2.88808 + 0.609564i) q^{72} +(5.43376 + 5.43376i) q^{73} -12.4981 q^{74} +(-4.93465 + 7.11683i) q^{75} +12.5423 q^{76} +(2.09381 + 2.09381i) q^{77} +(-0.351651 + 0.648767i) q^{78} +5.93637i q^{79} +(-7.12858 - 7.95576i) q^{80} +(-3.63710 + 8.23235i) q^{81} +(-5.92804 + 5.92804i) q^{82} +(-0.365862 + 0.365862i) q^{83} +(-2.14930 - 7.23692i) q^{84} +(-0.584411 + 10.6572i) q^{85} +0.885499i q^{86} +(-4.59307 - 2.48958i) q^{87} +(-0.695724 - 0.695724i) q^{88} +3.70157 q^{89} +(10.8311 - 6.23903i) q^{90} -0.677057 q^{91} +(-4.63843 - 4.63843i) q^{92} +(7.63043 + 4.13592i) q^{93} +16.2111i q^{94} +(-14.1901 + 12.7147i) q^{95} +(3.41914 + 11.5126i) q^{96} +(4.94287 - 4.94287i) q^{97} +(2.32951 - 2.32951i) q^{98} +(2.51367 - 1.63751i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 2 q^{3} - 8 q^{5} - 4 q^{6} + 8 q^{7} + 16 q^{8} + 6 q^{9} - 4 q^{10} - 4 q^{12} - 24 q^{14} + 8 q^{15} - 4 q^{16} + 8 q^{17} - 32 q^{18} - 20 q^{20} - 8 q^{21} - 4 q^{22} + 14 q^{23} + 12 q^{24}+ \cdots - 4 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 8 * q^5 - 4 * q^6 + 8 * q^7 + 16 * q^8 + 6 * q^9 - 4 * q^10 - 4 * q^12 - 24 * q^14 + 8 * q^15 - 4 * q^16 + 8 * q^17 - 32 * q^18 - 20 * q^20 - 8 * q^21 - 4 * q^22 + 14 * q^23 + 12 * q^24 - 18 * q^25 - 20 * q^27 + 8 * q^28 - 16 * q^29 + 20 * q^30 + 8 * q^31 + 28 * q^32 + 4 * q^33 + 44 * q^36 - 6 * q^37 + 24 * q^38 + 24 * q^39 + 16 * q^40 - 60 * q^42 + 16 * q^43 + 12 * q^44 + 24 * q^45 - 32 * q^46 + 48 * q^47 - 48 * q^48 - 12 * q^50 - 8 * q^51 + 36 * q^52 - 4 * q^53 + 4 * q^54 + 2 * q^55 - 8 * q^57 - 12 * q^58 - 68 * q^59 - 28 * q^60 - 8 * q^61 + 48 * q^62 - 12 * q^63 - 48 * q^65 + 8 * q^66 + 6 * q^67 + 24 * q^68 + 12 * q^69 - 4 * q^70 - 8 * q^72 + 8 * q^74 + 8 * q^75 + 16 * q^76 - 8 * q^77 - 48 * q^78 - 24 * q^80 + 2 * q^81 + 12 * q^82 - 8 * q^83 + 52 * q^84 - 4 * q^85 - 36 * q^87 - 16 * q^88 + 32 * q^89 + 44 * q^90 - 56 * q^91 + 20 * q^92 + 28 * q^93 - 48 * q^95 + 80 * q^96 + 18 * q^97 + 16 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

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