LMFDB - Embedded newform 315.2.u.a.59.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,2,Mod(59,315)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(315, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("315.59"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.u (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.3
Character	$\chi$	$=$	315.59
Dual form			315.2.u.a.299.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26586 + 2.19253i) q^{2} +(-0.586821 - 1.62961i) q^{3} +(-2.20480 - 3.81882i) q^{4} +(1.14318 - 1.92175i) q^{5} +(4.31581 + 0.776236i) q^{6} +(-1.80040 + 1.93870i) q^{7} +6.10041 q^{8} +(-2.31128 + 1.91258i) q^{9} +(2.76640 + 4.93913i) q^{10} -1.42464i q^{11} +(-4.92938 + 5.83393i) q^{12} +(-2.08746 + 3.61559i) q^{13} +(-1.97160 - 6.40156i) q^{14} +(-3.80256 - 0.735214i) q^{15} +(-3.31266 + 5.73769i) q^{16} +(-4.27416 - 2.46769i) q^{17} +(-1.26765 - 7.48862i) q^{18} +(-4.54377 + 2.62335i) q^{19} +(-9.85931 - 0.128519i) q^{20} +(4.21584 + 1.79629i) q^{21} +(3.12356 + 1.80339i) q^{22} +0.477695 q^{23} +(-3.57985 - 9.94130i) q^{24} +(-2.38628 - 4.39382i) q^{25} +(-5.28486 - 9.15364i) q^{26} +(4.47308 + 2.64415i) q^{27} +(11.3731 + 2.60098i) q^{28} +(-1.74963 + 1.01015i) q^{29} +(6.42548 - 7.40655i) q^{30} +(-9.21833 + 5.32221i) q^{31} +(-2.28631 - 3.96000i) q^{32} +(-2.32161 + 0.836008i) q^{33} +(10.8210 - 6.24749i) q^{34} +(1.66752 + 5.67621i) q^{35} +(12.3997 + 4.60951i) q^{36} +(7.03282 - 4.06040i) q^{37} -13.2831i q^{38} +(7.11697 + 1.28005i) q^{39} +(6.97386 - 11.7235i) q^{40} +(-0.421048 + 0.729276i) q^{41} +(-9.27509 + 6.96952i) q^{42} +(-3.70789 + 2.14075i) q^{43} +(-5.44044 + 3.14104i) q^{44} +(1.03331 + 6.62814i) q^{45} +(-0.604694 + 1.04736i) q^{46} +(-4.28080 - 2.47152i) q^{47} +(11.2942 + 2.03135i) q^{48} +(-0.517101 - 6.98087i) q^{49} +(12.6543 + 0.329960i) q^{50} +(-1.51321 + 8.41332i) q^{51} +18.4097 q^{52} +(2.33122 - 4.03778i) q^{53} +(-11.4597 + 6.46025i) q^{54} +(-2.73781 - 1.62862i) q^{55} +(-10.9832 + 11.8268i) q^{56} +(6.94142 + 5.86515i) q^{57} -5.11484i q^{58} +(0.101230 + 0.175335i) q^{59} +(5.57622 + 16.1423i) q^{60} +(-1.54473 - 0.891848i) q^{61} -26.9486i q^{62} +(0.453313 - 7.92430i) q^{63} -1.67406 q^{64} +(4.56193 + 8.14485i) q^{65} +(1.10586 - 6.14847i) q^{66} +(-2.06388 + 1.19158i) q^{67} +21.7630i q^{68} +(-0.280322 - 0.778458i) q^{69} +(-14.5561 - 3.52920i) q^{70} -11.7260i q^{71} +(-14.0998 + 11.6675i) q^{72} +(-4.52420 + 7.83614i) q^{73} +20.5596i q^{74} +(-5.75991 + 6.46710i) q^{75} +(20.0362 + 11.5679i) q^{76} +(2.76194 + 2.56492i) q^{77} +(-11.8156 + 13.9838i) q^{78} +(-0.226118 + 0.391648i) q^{79} +(7.23947 + 12.9253i) q^{80} +(1.68404 - 8.84104i) q^{81} +(-1.06597 - 1.84632i) q^{82} +(-10.6524 + 6.15019i) q^{83} +(-2.43536 - 20.0600i) q^{84} +(-9.62843 + 5.39288i) q^{85} -10.8395i q^{86} +(2.67288 + 2.25845i) q^{87} -8.69087i q^{88} +(1.33067 + 2.30479i) q^{89} +(-15.8404 - 6.12473i) q^{90} +(-3.25126 - 10.5565i) q^{91} +(-1.05322 - 1.82423i) q^{92} +(14.0827 + 11.8991i) q^{93} +(10.8378 - 6.25719i) q^{94} +(-0.152916 + 11.7310i) q^{95} +(-5.11162 + 6.04962i) q^{96} +(-4.69437 - 8.13089i) q^{97} +(15.9604 + 7.70304i) q^{98} +(2.72474 + 3.29274i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 38 q^{4} - 6 q^{5} + 12 q^{6} - 6 q^{9} - 6 q^{10} - 12 q^{14} - 6 q^{15} - 26 q^{16} - 12 q^{19} + 6 q^{20} - 12 q^{21} - 42 q^{24} - 2 q^{25} + 12 q^{26} + 6 q^{29} - 18 q^{30} - 6 q^{31} + 12 q^{34}+ \cdots + 30 q^{99}+O(q^{100}) $ 88 * q - 38 * q^4 - 6 * q^5 + 12 * q^6 - 6 * q^9 - 6 * q^10 - 12 * q^14 - 6 * q^15 - 26 * q^16 - 12 * q^19 + 6 * q^20 - 12 * q^21 - 42 * q^24 - 2 * q^25 + 12 * q^26 + 6 * q^29 - 18 * q^30 - 6 * q^31 + 12 * q^34 - 36 * q^36 - 6 * q^41 + 84 * q^44 - 12 * q^45 - 18 * q^46 + 10 * q^49 + 30 * q^50 - 6 * q^51 - 48 * q^54 - 90 * q^56 - 6 * q^59 + 54 * q^60 + 12 * q^61 - 8 * q^64 + 54 * q^65 + 78 * q^66 - 60 * q^69 - 30 * q^70 + 12 * q^75 + 48 * q^76 + 8 * q^79 + 69 * q^80 + 42 * q^81 + 120 * q^84 - 7 * q^85 - 72 * q^89 - 33 * q^90 + 20 * q^91 - 6 * q^94 - 93 * q^95 - 12 * q^96 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.26586	+	2.19253i	−0.895097	+	1.55035i	−0.0614129	+	0.998112i	$0.519561\pi$
$2$	−1.26586	+	2.19253i	−0.895097	+	1.55035i	−0.833684	+	0.552241i	$0.813773\pi$
$3$	−0.586821	−	1.62961i	−0.338801	−	0.940858i
$3$	−0.586821	−	1.62961i	−0.338801	−	0.940858i
$4$	−2.20480	−	3.81882i	−1.10240	−	1.90941i
$5$	1.14318	−	1.92175i	0.511245	−	0.859435i
$5$	1.14318	−	1.92175i	0.511245	−	0.859435i
$6$	4.31581	+	0.776236i	1.76192	+	0.316897i
$7$	−1.80040	+	1.93870i	−0.680488	+	0.732759i
$7$	−1.80040	+	1.93870i	−0.680488	+	0.732759i
$8$	6.10041			2.15682
$9$	−2.31128	+	1.91258i	−0.770427	+	0.637528i
$10$	2.76640	+	4.93913i	0.874814	+	1.56189i
$11$		−	1.42464i		−	0.429545i	−0.976664	−	0.214772i	$-0.931099\pi$
$11$		−	1.42464i		−	0.429545i	0.976664	−	0.214772i	$-0.0689009\pi$
$12$	−4.92938	+	5.83393i	−1.42299	+	1.68411i
$13$	−2.08746	+	3.61559i	−0.578957	+	1.00278i	0.416642	+	0.909071i	$0.363207\pi$
$13$	−2.08746	+	3.61559i	−0.578957	+	1.00278i	−0.995599	+	0.0937125i	$0.970127\pi$
$14$	−1.97160	−	6.40156i	−0.526933	−	1.71089i
$15$	−3.80256	−	0.735214i	−0.981817	−	0.189832i
$16$	−3.31266	+	5.73769i	−0.828165	+	1.43442i
$17$	−4.27416	−	2.46769i	−1.03664	−	0.598502i	−0.117758	−	0.993042i	$-0.537571\pi$
$17$	−4.27416	−	2.46769i	−1.03664	−	0.598502i	−0.918879	+	0.394540i	$0.870904\pi$
$18$	−1.26765	−	7.48862i	−0.298787	−	1.76508i
$19$	−4.54377	+	2.62335i	−1.04241	+	0.601837i	−0.920515	−	0.390706i	$-0.872231\pi$
$19$	−4.54377	+	2.62335i	−1.04241	+	0.601837i	−0.121896	+	0.992543i	$0.538898\pi$
$20$	−9.85931	−	0.128519i	−2.20461	−	0.0287377i
$21$	4.21584	+	1.79629i	0.919973	+	0.391983i
$22$	3.12356	+	1.80339i	0.665946	+	0.384484i
$23$	0.477695			0.0996063			0.0498031	−	0.998759i	$-0.484141\pi$
$23$	0.477695			0.0996063			0.0498031	+	0.998759i	$0.484141\pi$
$24$	−3.57985	−	9.94130i	−0.730734	−	2.02926i
$25$	−2.38628	−	4.39382i	−0.477256	−	0.878764i
$26$	−5.28486	−	9.15364i	−1.03645	−	1.79518i
$27$	4.47308	+	2.64415i	0.860845	+	0.508867i
$28$	11.3731	+	2.60098i	2.14931	+	0.491539i
$29$	−1.74963	+	1.01015i	−0.324899	+	0.187580i	−0.653574	−	0.756863i	$-0.726731\pi$
$29$	−1.74963	+	1.01015i	−0.324899	+	0.187580i	0.328675	+	0.944443i	$0.393398\pi$
$30$	6.42548	−	7.40655i	1.17313	−	1.35225i
$31$	−9.21833	+	5.32221i	−1.65566	+	0.955897i	−0.680979	+	0.732303i	$0.738446\pi$
$31$	−9.21833	+	5.32221i	−1.65566	+	0.955897i	−0.974682	+	0.223594i	$0.928221\pi$
$32$	−2.28631	−	3.96000i	−0.404166	−	0.700037i
$33$	−2.32161	+	0.836008i	−0.404140	+	0.145530i
$34$	10.8210	−	6.24749i	1.85578	−	1.07144i
$35$	1.66752	+	5.67621i	0.281862	+	0.959455i
$36$	12.3997	+	4.60951i	2.06662	+	0.768251i
$37$	7.03282	−	4.06040i	1.15619	−	0.667526i	0.205801	−	0.978594i	$-0.434020\pi$
$37$	7.03282	−	4.06040i	1.15619	−	0.667526i	0.950388	+	0.311068i	$0.100687\pi$
$38$		−	13.2831i		−	2.15481i
$39$	7.11697	+	1.28005i	1.13963	+	0.204972i
$40$	6.97386	−	11.7235i	1.10266	−	1.85365i
$41$	−0.421048	+	0.729276i	−0.0657566	+	0.113894i	−0.897029	−	0.441971i	$-0.854279\pi$
$41$	−0.421048	+	0.729276i	−0.0657566	+	0.113894i	0.831273	+	0.555865i	$0.187613\pi$
$42$	−9.27509	+	6.96952i	−1.43118	+	1.07542i
$43$	−3.70789	+	2.14075i	−0.565447	+	0.326461i	−0.755329	−	0.655346i	$-0.772523\pi$
$43$	−3.70789	+	2.14075i	−0.565447	+	0.326461i	0.189882	+	0.981807i	$0.439190\pi$
$44$	−5.44044	+	3.14104i	−0.820176	+	0.473529i
$45$	1.03331	+	6.62814i	0.154036	+	0.988065i
$46$	−0.604694	+	1.04736i	−0.0891573	+	0.154425i
$47$	−4.28080	−	2.47152i	−0.624418	−	0.360508i	0.154169	−	0.988045i	$-0.450730\pi$
$47$	−4.28080	−	2.47152i	−0.624418	−	0.360508i	−0.778587	+	0.627536i	$0.784063\pi$
$48$	11.2942	+	2.03135i	1.63017	+	0.293201i
$49$	−0.517101	−	6.98087i	−0.0738715	−	0.997268i
$50$	12.6543	+	0.329960i	1.78959	+	0.0466634i
$51$	−1.51321	+	8.41332i	−0.211892	+	1.17810i
$52$	18.4097			2.55296
$53$	2.33122	−	4.03778i	0.320217	−	0.554632i	−0.660316	−	0.750988i	$-0.729577\pi$
$53$	2.33122	−	4.03778i	0.320217	−	0.554632i	0.980533	+	0.196356i	$0.0629108\pi$
$54$	−11.4597	+	6.46025i	−1.55946	+	0.879129i
$55$	−2.73781	−	1.62862i	−0.369166	−	0.219603i
$56$	−10.9832	+	11.8268i	−1.46769	+	1.58043i
$57$	6.94142	+	5.86515i	0.919413	+	0.776858i
$58$		−	5.11484i		−	0.671611i
$59$	0.101230	+	0.175335i	0.0131790	+	0.0228266i	0.872540	−	0.488543i	$-0.162472\pi$
$59$	0.101230	+	0.175335i	0.0131790	+	0.0228266i	−0.859361	+	0.511370i	$0.829138\pi$
$60$	5.57622	+	16.1423i	0.719887	+	2.08396i
$61$	−1.54473	−	0.891848i	−0.197782	−	0.114189i	0.397839	−	0.917455i	$-0.369760\pi$
$61$	−1.54473	−	0.891848i	−0.197782	−	0.114189i	−0.595620	+	0.803266i	$0.703094\pi$
$62$		−	26.9486i		−	3.42248i
$63$	0.453313	−	7.92430i	0.0571121	−	0.998368i
$64$	−1.67406			−0.209257
$65$	4.56193	+	8.14485i	0.565837	+	1.01024i
$66$	1.10586	−	6.14847i	0.136121	−	0.756824i
$67$	−2.06388	+	1.19158i	−0.252143	+	0.145575i	−0.620745	−	0.784012i	$-0.713170\pi$
$67$	−2.06388	+	1.19158i	−0.252143	+	0.145575i	0.368602	+	0.929587i	$0.379837\pi$
$68$			21.7630i			2.63915i
$69$	−0.280322	−	0.778458i	−0.0337468	−	0.0937154i
$70$	−14.5561	−	3.52920i	−1.73979	−	0.421820i
$71$		−	11.7260i		−	1.39162i	−0.718223	−	0.695812i	$-0.755044\pi$
$71$		−	11.7260i		−	1.39162i	0.718223	−	0.695812i	$-0.244956\pi$
$72$	−14.0998	+	11.6675i	−1.66167	+	1.37503i
$73$	−4.52420	+	7.83614i	−0.529517	+	0.917150i	0.469890	+	0.882725i	$0.344293\pi$
$73$	−4.52420	+	7.83614i	−0.529517	+	0.917150i	−0.999407	+	0.0344256i	$0.989040\pi$
$74$			20.5596i			2.39000i
$75$	−5.75991	+	6.46710i	−0.665097	+	0.746757i
$76$	20.0362	+	11.5679i	2.29831	+	1.32693i
$77$	2.76194	+	2.56492i	0.314753	+	0.292300i
$78$	−11.8156	+	13.9838i	−1.33786	+	1.58336i
$79$	−0.226118	+	0.391648i	−0.0254403	+	0.0440638i	−0.878465	−	0.477806i	$-0.841432\pi$
$79$	−0.226118	+	0.391648i	−0.0254403	+	0.0440638i	0.853025	+	0.521870i	$0.174765\pi$
$80$	7.23947	+	12.9253i	0.809398	+	1.44510i
$81$	1.68404	−	8.84104i	0.187116	−	0.982338i
$82$	−1.06597	−	1.84632i	−0.117717	−	0.203892i
$83$	−10.6524	+	6.15019i	−1.16926	+	0.675071i	−0.953505	−	0.301378i	$-0.902553\pi$
$83$	−10.6524	+	6.15019i	−1.16926	+	0.675071i	−0.215752	+	0.976448i	$0.569220\pi$
$84$	−2.43536	−	20.0600i	−0.265720	−	2.18873i
$85$	−9.62843	+	5.39288i	−1.04435	+	0.584940i
$86$		−	10.8395i		−	1.16886i
$87$	2.67288	+	2.25845i	0.286563	+	0.242131i
$88$		−	8.69087i		−	0.926450i
$89$	1.33067	+	2.30479i	0.141051	+	0.244307i	0.927893	−	0.372848i	$-0.121619\pi$
$89$	1.33067	+	2.30479i	0.141051	+	0.244307i	−0.786842	+	0.617155i	$0.788285\pi$
$90$	−15.8404	−	6.12473i	−1.66973	−	0.645603i
$91$	−3.25126	−	10.5565i	−0.340825	−	1.10662i
$92$	−1.05322	−	1.82423i	−0.109806	−	0.190189i
$93$	14.0827	+	11.8991i	1.46030	+	1.23388i
$94$	10.8378	−	6.25719i	1.11783	−	0.645380i
$95$	−0.152916	+	11.7310i	−0.0156889	+	1.20357i
$96$	−5.11162	+	6.04962i	−0.521703	+	0.617436i
$97$	−4.69437	−	8.13089i	−0.476641	−	0.825567i	0.523001	−	0.852332i	$-0.324813\pi$
$97$	−4.69437	−	8.13089i	−0.476641	−	0.825567i	−0.999642	+	0.0267656i	$0.991479\pi$
$98$	15.9604	+	7.70304i	1.61224	+	0.778125i
$99$	2.72474	+	3.29274i	0.273847	+	0.330933i
$100$	−11.5179	+	18.8003i	−1.15179	+	1.88003i
$101$	18.4515			1.83600			0.917998	−	0.396585i	$-0.129805\pi$
$101$	18.4515			1.83600			0.917998	+	0.396585i	$0.129805\pi$
$102$	−16.5310	−	13.9678i	−1.63681	−	1.38302i
$103$	18.6900			1.84158			0.920789	−	0.390062i	$-0.127546\pi$
$103$	18.6900			1.84158			0.920789	+	0.390062i	$0.127546\pi$
$104$	−12.7343	+	22.0565i	−1.24871	+	2.16282i
$105$	8.27150	−	6.04833i	0.807215	−	0.590257i
$106$	5.90198	+	10.2225i	0.573251	+	0.992900i
$107$	−0.440832	−	0.763543i	−0.0426168	−	0.0738145i	0.843930	−	0.536453i	$-0.180236\pi$
$107$	−0.440832	−	0.763543i	−0.0426168	−	0.0738145i	−0.886547	+	0.462639i	$0.846903\pi$
$108$	0.235295	−	22.9117i	0.0226413	−	2.20468i
$109$	2.17023	−	3.75895i	0.207870	−	0.360042i	−0.743173	−	0.669099i	$-0.766680\pi$
$109$	2.17023	−	3.75895i	0.207870	−	0.360042i	0.951043	+	0.309057i	$0.100013\pi$
$110$	7.03647	−	3.94112i	0.670901	−	0.375771i
$111$	−10.7439	−	9.07805i	−1.01977	−	0.861650i
$112$	−5.15954	−	16.7524i	−0.487530	−	1.58295i
$113$	4.60460	−	7.97540i	0.433164	−	0.750262i	−0.563980	−	0.825789i	$-0.690730\pi$
$113$	4.60460	−	7.97540i	0.433164	−	0.750262i	0.997144	+	0.0755263i	$0.0240637\pi$
$114$	−21.6464	+	7.79483i	−2.02737	+	0.730053i
$115$	0.546091	−	0.918013i	0.0509233	−	0.0856051i
$116$	7.71517	+	4.45436i	0.716336	+	0.413577i
$117$	−2.09041	−	12.3491i	−0.193258	−	1.14167i
$118$	−0.512569			−0.0471858
$119$	12.4793	−	3.84348i	1.14398	−	0.352331i
$120$	−23.1972	−	4.48511i	−2.11760	−	0.409432i
$121$	8.97041			0.815491
$122$	3.91081	−	2.25791i	0.354068	−	0.204421i
$123$	1.43552	+	0.258190i	0.129436	+	0.0232802i
$124$	40.6491	+	23.4688i	3.65040	+	2.10756i
$125$	−11.1718	−	0.437080i	−0.999236	−	0.0390936i
$126$	16.8004	+	11.0249i	1.49670	+	0.982180i
$127$			8.82849i			0.783401i	0.920093	+	0.391701i	$0.128113\pi$
$127$			8.82849i			0.783401i	−0.920093	+	0.391701i	$0.871887\pi$
$128$	6.69174	−	11.5904i	0.591472	−	1.02446i
$129$	5.66446	+	4.78618i	0.498728	+	0.421400i
$130$	−23.6326	−	0.308057i	−2.07272	−	0.0270184i
$131$	−2.21071			−0.193151			−0.0965753	−	0.995326i	$-0.530789\pi$
$131$	−2.21071			−0.193151			−0.0965753	+	0.995326i	$0.530789\pi$
$132$	8.31124	+	7.02258i	0.723401	+	0.611237i
$133$	3.09474	−	13.5321i	0.268348	−	1.17338i
$134$		−	6.03350i		−	0.521215i
$135$	10.1949	−	5.57343i	0.877441	−	0.479684i
$136$	−26.0741	−	15.0539i	−2.23584	−	1.29086i
$137$	4.83572			0.413143			0.206572	−	0.978431i	$-0.433769\pi$
$137$	4.83572			0.413143			0.206572	+	0.978431i	$0.433769\pi$
$138$	2.06164	+	0.370804i	0.175499	+	0.0315649i
$139$	−1.08200	−	0.624695i	−0.0917743	−	0.0529859i	0.453410	−	0.891302i	$-0.350207\pi$
$139$	−1.08200	−	0.624695i	−0.0917743	−	0.0529859i	−0.545185	+	0.838316i	$0.683541\pi$
$140$	17.9999	−	18.8828i	1.52127	−	1.59589i
$141$	−1.51556	+	8.42638i	−0.127633	+	0.709630i
$142$	25.7097	+	14.8435i	2.15751	+	1.24564i
$143$	5.15090	+	2.97387i	0.430740	+	0.248688i
$144$	−3.31734	−	19.5972i	−0.276445	−	1.63310i
$145$	−0.0588822	+	4.51715i	−0.00488990	+	0.375129i
$146$	−11.4540	−	19.8389i	−0.947938	−	1.64188i
$147$	−11.0727	+	4.93920i	−0.913259	+	0.407378i
$148$	−31.0119	−	17.9047i	−2.54916	−	1.47176i
$149$			3.44380i			0.282127i	0.990001	+	0.141063i	$0.0450522\pi$
$149$			3.44380i			0.282127i	−0.990001	+	0.141063i	$0.954948\pi$
$150$	−6.88810	−	20.8152i	−0.562411	−	1.69956i
$151$	−17.0234			−1.38534			−0.692671	−	0.721254i	$-0.743566\pi$
$151$	−17.0234			−1.38534			−0.692671	+	0.721254i	$0.743566\pi$
$152$	−27.7188	+	16.0035i	−2.24829	+	1.29805i
$153$	14.5985	−	2.47117i	1.18021	−	0.199782i
$154$	−9.11990	+	2.80882i	−0.734903	+	0.226341i
$155$	−0.310234	+	23.7996i	−0.0249186	+	1.91163i
$156$	−10.8032	−	30.0007i	−0.864948	−	2.40198i
$157$	−2.34082	−	4.05442i	−0.186818	−	0.323578i	0.757370	−	0.652986i	$-0.226484\pi$
$157$	−2.34082	−	4.05442i	−0.186818	−	0.323578i	−0.944188	+	0.329408i	$0.893151\pi$
$158$	−0.572467	−	0.991542i	−0.0455430	−	0.0788829i
$159$	−7.94804	−	1.42952i	−0.630320	−	0.113369i
$160$	−10.2238	−	0.133270i	−0.808264	−	0.0105359i
$161$	−0.860043	+	0.926106i	−0.0677809	+	0.0729874i
$162$	17.2525	+	14.8838i	1.35548	+	1.16938i
$163$	−13.9563	+	8.05767i	−1.09314	+	0.631125i	−0.934411	−	0.356197i	$-0.884073\pi$
$163$	−13.9563	+	8.05767i	−1.09314	+	0.631125i	−0.158730	+	0.987322i	$0.550740\pi$
$164$	3.71330			0.289960
$165$	−1.04741	+	5.41727i	−0.0815411	+	0.421734i
$166$		−	31.1411i		−	2.41701i
$167$	−9.83837	−	5.68018i	−0.761316	−	0.439546i	0.0684521	−	0.997654i	$-0.478194\pi$
$167$	−9.83837	−	5.68018i	−0.761316	−	0.439546i	−0.829768	+	0.558108i	$0.811527\pi$
$168$	25.7184	+	10.9581i	1.98421	+	0.845436i
$169$	−2.21497	−	3.83644i	−0.170382	−	0.295111i
$170$	0.364169	−	27.9372i	0.0279305	−	2.14269i
$171$	5.48456	−	14.7536i	0.419414	−	1.12824i
$172$	16.3503	+	9.43983i	1.24670	+	0.719780i
$173$	−11.7421	−	6.77929i	−0.892733	−	0.515420i	−0.0178975	−	0.999840i	$-0.505697\pi$
$173$	−11.7421	−	6.77929i	−0.892733	−	0.515420i	−0.874835	+	0.484420i	$0.839031\pi$
$174$	−8.33521	+	3.00149i	−0.631890	+	0.227543i
$175$	12.8146	+	3.28437i	0.968690	+	0.248275i
$176$	8.17414	+	4.71934i	0.616149	+	0.355734i
$177$	0.226324	−	0.267855i	0.0170116	−	0.0201332i
$178$	−6.73776			−0.505016
$179$	0.777342	+	0.448799i	0.0581013	+	0.0335448i	0.528769	−	0.848766i	$-0.322654\pi$
$179$	0.777342	+	0.448799i	0.0581013	+	0.0335448i	−0.470668	+	0.882310i	$0.655987\pi$
$180$	23.0334	−	18.5597i	1.71681	−	1.38336i
$181$		−	13.4784i		−	1.00184i	−0.865493	−	0.500921i	$-0.832995\pi$
$181$		−	13.4784i		−	1.00184i	0.865493	−	0.500921i	$-0.167005\pi$
$182$	27.2610	+	6.23450i	2.02072	+	0.462132i
$183$	−0.546889	+	3.04066i	−0.0404272	+	0.224772i
$184$	2.91413			0.214833
$185$	0.236683	−	18.1571i	0.0174013	−	1.33494i
$186$	−43.9159	+	15.8140i	−3.22007	+	1.15954i
$187$	−3.51556	+	6.08913i	−0.257083	+	0.445282i
$188$			21.7968i			1.58969i
$189$	−13.1796	+	3.91142i	−0.958672	+	0.284514i
$190$	−25.5269	−	15.1850i	−1.85192	−	1.10164i
$191$	1.71073	+	0.987691i	0.123784	+	0.0714668i	0.560614	−	0.828078i	$-0.310565\pi$
$191$	1.71073	+	0.987691i	0.123784	+	0.0714668i	−0.436829	+	0.899544i	$0.643899\pi$
$192$	0.982371	+	2.72806i	0.0708965	+	0.196881i
$193$	14.3559	−	8.28838i	1.03336	−	0.596611i	0.115414	−	0.993317i	$-0.463180\pi$
$193$	14.3559	−	8.28838i	1.03336	−	0.596611i	0.917945	+	0.396707i	$0.129847\pi$
$194$	23.7696			1.70656
$195$	10.5959	−	12.2137i	0.758789	−	0.874645i
$196$	−25.5186	+	17.3661i	−1.82276	+	1.24044i
$197$	−24.5924			−1.75214			−0.876069	−	0.482186i	$-0.839843\pi$
$197$	−24.5924			−1.75214			−0.876069	+	0.482186i	$0.839843\pi$
$198$	−10.6686	+	1.80594i	−0.758182	+	0.128342i
$199$	0.627348	+	0.362200i	0.0444715	+	0.0256757i	0.522071	−	0.852902i	$-0.325160\pi$
$199$	0.627348	+	0.362200i	0.0444715	+	0.0256757i	−0.477599	+	0.878578i	$0.658493\pi$
$200$	−14.5573	−	26.8041i	−1.02936	−	1.89534i
$201$	3.15295	+	2.66408i	0.222392	+	0.187910i
$202$	−23.3570	+	40.4556i	−1.64339	+	2.84644i
$203$	1.19167	−	5.21069i	0.0836386	−	0.365719i
$204$	35.4653	−	12.7710i	2.48307	−	0.894148i
$205$	0.920156	+	1.64284i	0.0642665	+	0.114741i
$206$	−23.6589	+	40.9783i	−1.64839	+	2.85510i
$207$	−1.10409	+	0.913632i	−0.0767394	+	0.0635018i
$208$	−13.8301	−	23.9544i	−0.958944	−	1.66094i
$209$	3.73732	+	6.47322i	0.258516	+	0.447762i
$210$	2.79062	+	25.7919i	0.192571	+	1.77981i
$211$	5.83962	−	10.1145i	0.402016	−	0.696312i	−0.591953	−	0.805972i	$-0.701643\pi$
$211$	5.83962	−	10.1145i	0.402016	−	0.696312i	0.993969	+	0.109660i	$0.0349763\pi$
$212$	−20.5594			−1.41203
$213$	−19.1089	+	6.88109i	−1.30932	+	0.471485i
$214$	2.23212			0.152585
$215$	−0.124785	+	9.57291i	−0.00851029	+	0.652867i
$216$	27.2876	+	16.1304i	1.85669	+	1.09753i
$217$	6.27856	−	27.4537i	0.426216	−	1.86368i
$218$	5.49441	+	9.51659i	0.372128	+	0.644545i
$219$	15.4248	+	2.77428i	1.04231	+	0.187468i
$220$	−0.183093	+	14.0460i	−0.0123441	+	0.946978i
$221$	17.8443	−	10.3024i	1.20034	−	0.693014i
$222$	33.5042	−	12.0648i	2.24865	−	0.809736i
$223$	13.2349	+	22.9235i	0.886275	+	1.53507i	0.844245	+	0.535957i	$0.180049\pi$
$223$	13.2349	+	22.9235i	0.886275	+	1.53507i	0.0420295	+	0.999116i	$0.486618\pi$
$224$	11.7935	+	2.69714i	0.787989	+	0.180210i
$225$	13.9189	+	5.59139i	0.927928	+	0.372760i
$226$	11.6575	+	20.1915i	0.775448	+	1.34312i
$227$			7.75247i			0.514550i	0.966338	+	0.257275i	$0.0828246\pi$
$227$			7.75247i			0.514550i	−0.966338	+	0.257275i	$0.917175\pi$
$228$	7.09353	−	39.4395i	0.469781	−	2.61194i
$229$			18.5278i			1.22435i	0.790721	+	0.612177i	$0.209706\pi$
$229$			18.5278i			1.22435i	−0.790721	+	0.612177i	$0.790294\pi$
$230$	1.32150	+	2.35940i	0.0871369	+	0.155574i
$231$	2.55907	−	6.00605i	0.168374	−	0.395169i
$232$	−10.6735	+	6.16233i	−0.700748	+	0.404577i
$233$	−4.75564	−	8.23700i	−0.311552	−	0.539624i	0.667146	−	0.744927i	$-0.267516\pi$
$233$	−4.75564	−	8.23700i	−0.311552	−	0.539624i	−0.978699	+	0.205302i	$0.934182\pi$
$234$	29.7219	+	11.0489i	1.94298	+	0.722289i
$235$	−9.64337	+	5.40125i	−0.629064	+	0.352339i
$236$	0.446381	−	0.773155i	0.0290569	−	0.0503281i
$237$	0.770926	+	0.138658i	0.0500770	+	0.00900679i
$238$	−7.37010	+	32.2266i	−0.477733	+	2.08894i
$239$	−17.6506	−	10.1906i	−1.14173	−	0.659175i	−0.194868	−	0.980829i	$-0.562428\pi$
$239$	−17.6506	−	10.1906i	−1.14173	−	0.659175i	−0.946857	+	0.321654i	$0.895761\pi$
$240$	16.8150	−	19.3824i	1.08540	−	1.25113i
$241$		−	9.04064i		−	0.582359i	−0.956669	−	0.291179i	$-0.905952\pi$
$241$		−	9.04064i		−	0.582359i	0.956669	−	0.291179i	$-0.0940476\pi$
$242$	−11.3553	+	19.6679i	−0.729944	+	1.26430i
$243$	−15.3957	+	2.44377i	−0.987635	+	0.156768i
$244$			7.86537i			0.503529i
$245$	−14.0067	−	6.98665i	−0.894853	−	0.446361i
$246$	−2.38325	+	2.82058i	−0.151951	+	0.179834i
$247$		−	21.9045i		−	1.39375i
$248$	−56.2356	+	32.4676i	−3.57096	+	2.06170i
$249$	16.2735	+	13.7503i	1.03129	+	0.871389i
$250$	15.1002	−	23.9412i	0.955022	−	1.51418i
$251$	4.81421			0.303871			0.151935	−	0.988390i	$-0.451449\pi$
$251$	4.81421			0.303871			0.151935	+	0.988390i	$0.451449\pi$
$252$	−31.2609	+	15.7403i	−1.96925	+	0.991548i
$253$		−	0.680543i		−	0.0427853i
$254$	−19.3567	−	11.1756i	−1.21455	−	0.701220i
$255$	14.4385	+	12.5260i	0.904172	+	0.784406i
$256$	15.2675	+	26.4441i	0.954221	+	1.65276i
$257$		−	0.263682i		−	0.0164480i	−0.999966	−	0.00822401i	$-0.997382\pi$
$257$		−	0.263682i		−	0.0164480i	0.999966	−	0.00822401i	$-0.00261781\pi$
$258$	−17.6643	+	6.36088i	−1.09973	+	0.396011i
$259$	−4.79002	+	20.9449i	−0.297637	+	1.30145i
$260$	21.0456	−	35.3789i	1.30519	−	2.19411i
$261$	2.11190	−	5.68107i	0.130723	−	0.351649i
$262$	2.79845	−	4.84705i	0.172889	−	0.299452i
$263$	9.38115			0.578466			0.289233	−	0.957259i	$-0.406600\pi$
$263$	9.38115			0.578466			0.289233	+	0.957259i	$0.406600\pi$
$264$	−14.1628	+	5.09999i	−0.871658	+	0.313883i
$265$	−5.09463	−	9.09594i	−0.312961	−	0.558759i
$266$	25.7520	+	23.9150i	1.57896	+	1.46632i
$267$	2.97505	−	3.52097i	0.182070	−	0.215480i
$268$	9.10087	+	5.25439i	0.555924	+	0.320963i
$269$	−5.85382	+	10.1391i	−0.356914	+	0.618192i	−0.987444	−	0.157972i	$-0.949504\pi$
$269$	−5.85382	+	10.1391i	−0.356914	+	0.618192i	0.630530	+	0.776165i	$0.282838\pi$
$270$	−0.685441	+	29.4079i	−0.0417146	+	1.78971i
$271$	9.67252	−	5.58443i	0.587564	−	0.339230i	−0.176570	−	0.984288i	$-0.556500\pi$
$271$	9.67252	−	5.58443i	0.587564	−	0.339230i	0.764134	+	0.645058i	$0.223167\pi$
$272$	28.3177	−	16.3492i	1.71701	−	0.991317i
$273$	−15.2950	+	11.4931i	−0.925698	+	0.695592i
$274$	−6.12134	+	10.6025i	−0.369804	+	0.640519i
$275$	−6.25961	+	3.39959i	−0.377468	+	0.205003i
$276$	−2.35474	+	2.78684i	−0.141739	+	0.167748i
$277$		−	10.0334i		−	0.602850i	−0.953490	−	0.301425i	$-0.902538\pi$
$277$		−	10.0334i		−	0.602850i	0.953490	−	0.301425i	$-0.0974623\pi$
$278$	2.73933	−	1.58155i	0.164294	−	0.0948551i
$279$	11.1270	−	29.9320i	0.666156	−	1.79198i
$280$	10.1725	+	34.6272i	0.607925	+	2.06937i
$281$	−11.3034	+	6.52601i	−0.674303	+	0.389309i	−0.797705	−	0.603048i	$-0.793953\pi$
$281$	−11.3034	+	6.52601i	−0.674303	+	0.389309i	0.123402	+	0.992357i	$0.460620\pi$
$282$	−16.5566	−	13.9895i	−0.985933	−	0.833064i
$283$	−6.66995	−	11.5527i	−0.396487	−	0.686736i	0.596803	−	0.802388i	$-0.296438\pi$
$283$	−6.66995	−	11.5527i	−0.396487	−	0.686736i	−0.993290	+	0.115652i	$0.963104\pi$
$284$	−44.7796	+	25.8535i	−2.65718	+	1.53412i
$285$	19.2067	−	6.63478i	1.13770	−	0.393011i
$286$	−13.0406	+	7.52901i	−0.771108	+	0.445200i
$287$	−0.655790	−	2.12927i	−0.0387101	−	0.125687i
$288$	12.8581	+	4.77993i	0.757674	+	0.281660i
$289$	3.67897	+	6.37216i	0.216410	+	0.374833i
$290$	−9.82946	−	5.84718i	−0.577206	−	0.343358i
$291$	−10.4955	+	12.4214i	−0.615254	+	0.728155i
$292$	39.8997			2.33495
$293$	3.97741	+	2.29636i	0.232363	+	0.134155i	0.611662	−	0.791120i	$-0.290501\pi$
$293$	3.97741	+	2.29636i	0.232363	+	0.134155i	−0.379299	+	0.925274i	$0.623835\pi$
$294$	3.18710	−	30.5295i	0.185875	−	1.78052i
$295$	0.452674	+	0.00590073i	0.0263557	+	0.000343553i
$296$	42.9031	−	24.7701i	2.49369	−	1.43973i
$297$	3.76696	−	6.37252i	0.218581	−	0.369771i
$298$	−7.55063	−	4.35936i	−0.437396	−	0.252531i
$299$	−0.997169	+	1.72715i	−0.0576678	+	0.0998835i
$300$	37.3961	+	7.73741i	2.15907	+	0.446719i
$301$	2.52542	−	11.0427i	0.145563	−	0.636490i
$302$	21.5492	−	37.3243i	1.24002	−	2.14777i
$303$	−10.8278	−	30.0689i	−0.622038	−	1.72741i
$304$		−	34.7610i		−	1.99368i
$305$	−3.47981	+	1.94904i	−0.199253	+	0.111602i
$306$	−13.0615	+	35.1357i	−0.746674	+	2.00858i
$307$	−20.6137			−1.17649			−0.588244	−	0.808683i	$-0.700181\pi$
$307$	−20.6137			−1.17649			−0.588244	+	0.808683i	$0.700181\pi$
$308$	3.70545	−	16.2025i	0.211138	−	0.923223i
$309$	−10.9677	−	30.4574i	−0.623929	−	1.73266i
$310$	−51.7887	−	30.8071i	−2.94140	−	1.74973i
$311$	−5.78068	−	10.0124i	−0.327792	−	0.567753i	0.654281	−	0.756251i	$-0.272971\pi$
$311$	−5.78068	−	10.0124i	−0.327792	−	0.567753i	−0.982073	+	0.188499i	$0.939638\pi$
$312$	43.4164	+	7.80882i	2.45797	+	0.442087i
$313$	−14.5202	+	25.1498i	−0.820731	+	1.42155i	0.0844075	+	0.996431i	$0.473100\pi$
$313$	−14.5202	+	25.1498i	−0.820731	+	1.42155i	−0.905139	+	0.425117i	$0.860233\pi$
$314$	11.8526			0.668881
$315$	−14.7103	−	9.93005i	−0.828834	−	0.559495i
$316$	1.99418			0.112181
$317$	−10.8427	+	18.7802i	−0.608988	+	1.05480i	0.382419	+	0.923989i	$0.375091\pi$
$317$	−10.8427	+	18.7802i	−0.608988	+	1.05480i	−0.991407	+	0.130810i	$0.958242\pi$
$318$	13.1954	−	15.6167i	0.739959	−	0.875744i
$319$	1.43910	+	2.49259i	0.0805741	+	0.139559i
$320$	−1.91375	+	3.21712i	−0.106982	+	0.179843i
$321$	−0.985590	+	1.16645i	−0.0550103	+	0.0651048i
$322$	−0.941824	−	3.05799i	−0.0524858	−	0.170415i
$323$	25.8944			1.44080
$324$	−37.4753	+	13.0616i	−2.08196	+	0.725647i
$325$	20.8675	+	0.544119i	1.15752	+	0.0301823i
$326$		−	40.7995i		−	2.25967i
$327$	−7.39917	−	1.33080i	−0.409175	−	0.0735937i
$328$	−2.56856	+	4.44888i	−0.141825	+	0.245648i
$329$	12.4987	−	3.84944i	0.689075	−	0.212227i
$330$	−10.5517	−	9.15399i	−0.580850	−	0.503911i
$331$	−2.97620	+	5.15492i	−0.163587	+	0.283340i	−0.936152	−	0.351594i	$-0.885640\pi$
$331$	−2.97620	+	5.15492i	−0.163587	+	0.283340i	0.772566	+	0.634935i	$0.218973\pi$
$332$	46.9729	+	27.1198i	2.57797	+	1.48839i
$333$	−8.48897	+	22.8356i	−0.465193	+	1.25138i
$334$	24.9080	−	14.3806i	1.36290	−	0.786873i
$335$	−0.0694579	+	5.32846i	−0.00379489	+	0.291125i
$336$	−24.2722	+	18.2387i	−1.32416	+	0.995004i
$337$	−2.43132	−	1.40373i	−0.132443	−	0.0764658i	0.432315	−	0.901723i	$-0.357697\pi$
$337$	−2.43132	−	1.40373i	−0.132443	−	0.0764658i	−0.564757	+	0.825257i	$0.691030\pi$
$338$	11.2154			0.610035
$339$	−15.6989	−	2.82358i	−0.852647	−	0.153356i
$340$	41.8231	+	24.8790i	2.26818	+	1.34925i
$341$	7.58222	+	13.1328i	0.410600	+	0.711181i
$342$	25.4051	+	30.7011i	1.37375	+	1.66012i
$343$	14.4648	+	11.5659i	0.781026	+	0.624499i
$344$	−22.6196	+	13.0594i	−1.21957	+	0.704118i
$345$	−1.81646	−	0.351208i	−0.0977951	−	0.0189084i
$346$	29.7276	−	17.1632i	1.59817	−	0.922701i
$347$	4.94564	+	8.56610i	0.265496	+	0.459852i	0.967693	−	0.252130i	$-0.0811310\pi$
$347$	4.94564	+	8.56610i	0.265496	+	0.459852i	−0.702198	+	0.711982i	$0.747798\pi$
$348$	2.73145	−	15.1867i	0.146421	−	0.814090i
$349$	−0.279669	+	0.161467i	−0.0149703	+	0.00864312i	−0.507466	−	0.861671i	$-0.669418\pi$
$349$	−0.279669	+	0.161467i	−0.0149703	+	0.00864312i	0.492496	+	0.870315i	$0.336085\pi$
$350$	−23.4225	+	23.9388i	−1.25199	+	1.27958i
$351$	−18.8975	+	10.6533i	−1.00868	+	0.568629i
$352$	−5.64157	+	3.25716i	−0.300697	+	0.173607i
$353$		−	17.0862i		−	0.909409i	−0.890642	−	0.454704i	$-0.849745\pi$
$353$		−	17.0862i		−	0.909409i	0.890642	−	0.454704i	$-0.150255\pi$
$354$	0.300787	+	0.835290i	0.0159866	+	0.0443952i
$355$	−22.5346	−	13.4050i	−1.19601	−	0.711462i
$356$	5.86771	−	10.1632i	0.310988	−	0.538647i
$357$	−13.5865	−	18.0810i	−0.719074	−	0.956949i
$358$	−1.96801	+	1.13623i	−0.104013	+	0.0600517i
$359$	17.2188	−	9.94126i	0.908772	−	0.524680i	0.0287362	−	0.999587i	$-0.490852\pi$
$359$	17.2188	−	9.94126i	0.908772	−	0.524680i	0.880036	+	0.474907i	$0.157518\pi$
$360$	6.30360	+	40.4344i	0.332229	+	2.13108i
$361$	4.26388	−	7.38525i	0.224415	−	0.388698i
$362$	29.5518	+	17.0618i	1.55321	+	0.896746i
$363$	−5.26403	−	14.6183i	−0.276290	−	0.767262i
$364$	−33.1448	+	35.6908i	−1.73726	+	1.87071i
$365$	9.88716	+	17.6525i	0.517518	+	0.923974i
$366$	−5.97446	−	5.04812i	−0.312290	−	0.263869i
$367$	−31.3681			−1.63740			−0.818702	−	0.574219i	$-0.805306\pi$
$367$	−31.3681			−1.63740			−0.818702	+	0.574219i	$0.805306\pi$
$368$	−1.58244	+	2.74087i	−0.0824904	+	0.142878i
$369$	−0.421642	−	2.49085i	−0.0219498	−	0.129668i
$370$	39.5104	+	23.5033i	2.05405	+	1.22188i
$371$	3.63092	+	11.7892i	0.188508	+	0.612063i
$372$	14.3913	−	80.0143i	0.746152	−	4.14855i
$373$			25.6214i			1.32662i	0.748343	+	0.663312i	$0.230850\pi$
$373$			25.6214i			1.32662i	−0.748343	+	0.663312i	$0.769150\pi$
$374$	−8.90041	−	15.4160i	−0.460229	−	0.797141i
$375$	5.84358	+	18.4622i	0.301761	+	0.953384i
$376$	−26.1146	−	15.0773i	−1.34676	−	0.777551i
$377$		−	8.43460i		−	0.434404i
$378$	8.10754	−	33.8479i	0.417007	−	1.74095i
$379$	−5.00587			−0.257134			−0.128567	−	0.991701i	$-0.541038\pi$
$379$	−5.00587			−0.257134			−0.128567	+	0.991701i	$0.541038\pi$
$380$	45.1356	−	25.2804i	2.31541	−	1.29686i
$381$	14.3870	−	5.18074i	0.737069	−	0.265418i
$382$	−4.33109	+	2.50055i	−0.221598	+	0.127940i
$383$		−	23.0650i		−	1.17857i	−0.807926	−	0.589284i	$-0.799410\pi$
$383$		−	23.0650i		−	1.17857i	0.807926	−	0.589284i	$-0.200590\pi$
$384$	−22.8148	−	4.10343i	−1.16426	−	0.209403i
$385$	8.08655	−	2.37561i	0.412129	−	0.121072i
$386$			41.9677i			2.13610i
$387$	4.47561	−	12.0395i	0.227508	−	0.612003i
$388$	−20.7003	+	35.8539i	−1.05090	+	1.82021i
$389$		−	16.8225i		−	0.852932i	−0.904504	−	0.426466i	$-0.859758\pi$
$389$		−	16.8225i		−	0.852932i	0.904504	−	0.426466i	$-0.140242\pi$
$390$	13.3661	+	38.6928i	0.676819	+	1.95928i
$391$	−2.04175	−	1.17880i	−0.103256	−	0.0596146i
$392$	−3.15452	−	42.5862i	−0.159328	−	2.15093i
$393$	1.29729	+	3.60260i	0.0654397	+	0.181727i
$394$	31.1305	−	53.9197i	1.56833	−	2.71643i
$395$	0.494158	+	0.882268i	0.0248638	+	0.0443917i
$396$	6.56688	−	17.6651i	0.329998	−	0.887705i
$397$	−13.0997	−	22.6893i	−0.657453	−	1.13874i	−0.981273	−	0.192623i	$-0.938301\pi$
$397$	−13.0997	−	22.6893i	−0.657453	−	1.13874i	0.323820	−	0.946119i	$-0.395033\pi$
$398$	−1.58827	+	0.916987i	−0.0796127	+	0.0459644i
$399$	−23.8681	+	2.89768i	−1.19490	+	0.145066i
$400$	33.1153	+	0.863481i	1.65577	+	0.0431740i
$401$			36.2930i			1.81238i	0.422867	+	0.906192i	$0.361024\pi$
$401$			36.2930i			1.81238i	−0.422867	+	0.906192i	$0.638976\pi$
$402$	−9.83227	+	3.54058i	−0.490389	+	0.176588i
$403$		−	44.4396i		−	2.21369i
$404$	−40.6819	−	70.4631i	−2.02400	−	3.50567i
$405$	−15.0651	−	13.3432i	−0.748593	−	0.663030i
$406$	9.91612	+	9.20876i	0.492129	+	0.457023i
$407$	−5.78460	−	10.0192i	−0.286732	−	0.496634i
$408$	−9.23119	+	51.3247i	−0.457012	+	2.54095i
$409$	2.10076	−	1.21287i	0.103876	−	0.0599727i	−0.447162	−	0.894453i	$-0.647565\pi$
$409$	2.10076	−	1.21287i	0.103876	−	0.0599727i	0.551038	+	0.834480i	$0.314232\pi$
$410$	−4.76677	−	0.0621361i	−0.235414	−	0.00306868i
$411$	−2.83770	−	7.88036i	−0.139974	−	0.388709i
$412$	−41.2076	−	71.3736i	−2.03015	−	3.51633i
$413$	−0.522175	−	0.119420i	−0.0256946	−	0.00587626i
$414$	−0.605548	−	3.57728i	−0.0297611	−	0.175813i
$415$	−0.358497	+	27.5021i	−0.0175979	+	1.35003i
$416$	19.0903			0.935980
$417$	−0.383069	+	2.12983i	−0.0187590	+	0.104298i
$418$	−18.9237			−0.925587
$419$	−7.51552	+	13.0173i	−0.367157	+	0.635935i	−0.989120	−	0.147112i	$-0.953002\pi$
$419$	−7.51552	+	13.0173i	−0.367157	+	0.635935i	0.621963	+	0.783047i	$0.286336\pi$
$420$	−41.3345	−	18.2520i	−2.01691	−	0.890607i
$421$	11.1388	+	19.2929i	0.542871	+	0.940281i	0.998738	+	0.0502323i	$0.0159962\pi$
$421$	11.1388	+	19.2929i	0.542871	+	0.940281i	−0.455866	+	0.890048i	$0.650671\pi$
$422$	14.7843	+	25.6071i	0.719687	+	1.24653i
$423$	14.6211	−	2.47501i	0.710903	−	0.120339i
$424$	14.2214	−	24.6321i	0.690650	−	1.19624i
$425$	−0.643230	+	24.6685i	−0.0312012	+	1.19660i
$426$	9.10218	−	50.6074i	0.441002	−	2.45194i
$427$	4.51015	−	1.38907i	0.218262	−	0.0672219i
$428$	−1.94389	+	3.36691i	−0.0939614	+	0.162746i
$429$	1.82361	−	10.1391i	0.0880446	−	0.489521i
$430$	−20.8309	−	12.3915i	−1.00456	−	0.597573i
$431$	−16.8829	−	9.74735i	−0.813221	−	0.469514i	0.0348520	−	0.999392i	$-0.488904\pi$
$431$	−16.8829	−	9.74735i	−0.813221	−	0.469514i	−0.848073	+	0.529879i	$0.822237\pi$
$432$	−29.9891	+	16.9060i	−1.44285	+	0.813391i
$433$	16.9416			0.814161			0.407080	−	0.913392i	$-0.366547\pi$
$433$	16.9416			0.814161			0.407080	+	0.913392i	$0.366547\pi$
$434$	52.2453	+	48.5184i	2.50785	+	2.32896i
$435$	7.39576	−	2.55481i	0.354600	−	0.122494i
$436$	−19.1397			−0.916623
$437$	−2.17053	+	1.25316i	−0.103831	+	0.0599467i
$438$	−25.6083	+	30.3074i	−1.22361	+	1.44815i
$439$	1.43566	+	0.828881i	0.0685205	+	0.0395604i	0.533869	−	0.845567i	$-0.320738\pi$
$439$	1.43566	+	0.828881i	0.0685205	+	0.0395604i	−0.465348	+	0.885128i	$0.654071\pi$
$440$	−16.7017	−	9.93523i	−0.796223	−	0.473643i
$441$	14.5467	+	15.1458i	0.692699	+	0.721227i
$442$			52.1655i			2.48126i
$443$	−18.0449	+	31.2547i	−0.857341	+	1.48496i	0.0171155	+	0.999854i	$0.494552\pi$
$443$	−18.0449	+	31.2547i	−0.857341	+	1.48496i	−0.874456	+	0.485104i	$0.838782\pi$
$444$	−10.9793	+	61.0442i	−0.521056	+	2.89703i
$445$	5.95043	+	0.0775654i	0.282077	+	0.00367695i
$446$	−67.0141			−3.17321
$447$	5.61206	−	2.02089i	0.265441	−	0.0955850i
$448$	3.01397	−	3.24549i	0.142397	−	0.153335i
$449$			26.4059i			1.24617i	0.782154	+	0.623086i	$0.214121\pi$
$449$			26.4059i			1.24617i	−0.782154	+	0.623086i	$0.785879\pi$
$450$	−29.8787	+	23.4398i	−1.40849	+	1.10496i
$451$	1.03895	+	0.599840i	0.0489224	+	0.0282454i
$452$	−40.6088			−1.91008
$453$	9.98968	+	27.7415i	0.469356	+	1.30341i
$454$	−16.9975	−	9.81354i	−0.797734	−	0.460572i
$455$	−24.0037	−	5.81981i	−1.12531	−	0.272837i
$456$	42.3455	+	35.7798i	1.98301	+	1.67554i
$457$	27.5308	+	15.8949i	1.28784	+	0.743532i	0.978268	−	0.207345i	$-0.0664824\pi$
$457$	27.5308	+	15.8949i	1.28784	+	0.743532i	0.309568	+	0.950877i	$0.399816\pi$
$458$	−40.6229	−	23.4536i	−1.89818	−	1.09592i
$459$	−12.5937	−	22.3397i	−0.587825	−	1.04273i
$460$	−4.70974	−	0.0613927i	−0.219593	−	0.00286245i
$461$	5.79487	+	10.0370i	0.269894	+	0.467470i	0.968834	−	0.247710i	$-0.0796780\pi$
$461$	5.79487	+	10.0370i	0.269894	+	0.467470i	−0.698940	+	0.715180i	$0.746345\pi$
$462$	9.92904	+	13.2136i	0.461941	+	0.614754i
$463$	25.9642	+	14.9904i	1.20666	+	0.696664i	0.962028	−	0.272952i	$-0.0880001\pi$
$463$	25.9642	+	14.9904i	1.20666	+	0.696664i	0.244630	+	0.969616i	$0.421333\pi$
$464$		−	13.3851i		−	0.621390i
$465$	38.9662	−	13.4606i	1.80702	−	0.624219i
$466$	24.0799			1.11548
$467$	−2.17113	+	1.25350i	−0.100468	+	0.0580052i	−0.549392	−	0.835565i	$-0.685141\pi$
$467$	−2.17113	+	1.25350i	−0.100468	+	0.0580052i	0.448924	+	0.893570i	$0.351807\pi$
$468$	−42.5500	+	35.2101i	−1.96687	+	1.62759i
$469$	1.40570	−	6.14657i	0.0649091	−	0.283822i
$470$	0.364735	−	27.9806i	0.0168240	−	1.29065i
$471$	−5.23350	+	6.19386i	−0.241147	+	0.285398i
$472$	0.617542	+	1.06961i	0.0284247	+	0.0492329i
$473$	3.04979	+	5.28240i	0.140230	+	0.242885i
$474$	−1.27989	+	1.51476i	−0.0587875	+	0.0695752i
$475$	22.3692	+	13.7045i	1.02637	+	0.628804i
$476$	−42.1919	−	39.1822i	−1.93386	−	1.79591i
$477$	2.33451	+	13.7911i	0.106890	+	0.631451i
$478$	44.6864	−	25.7997i	2.04391	−	1.18005i
$479$	−35.5555			−1.62457			−0.812286	−	0.583260i	$-0.801777\pi$
$479$	−35.5555			−1.62457			−0.812286	+	0.583260i	$0.801777\pi$
$480$	5.78238	+	16.7391i	0.263928	+	0.764031i
$481$			33.9037i			1.54587i
$482$	19.8219	+	11.4442i	0.902862	+	0.521267i
$483$	2.01389	+	0.858079i	0.0916350	+	0.0390440i
$484$	−19.7779	−	34.2564i	−0.898996	−	1.55711i
$485$	−20.9921	−	0.273637i	−0.953201	−	0.0124252i
$486$	14.1307	−	36.8491i	0.640984	−	1.67151i
$487$	15.4460	+	8.91776i	0.699926	+	0.404102i	0.807320	−	0.590114i	$-0.200917\pi$
$487$	15.4460	+	8.91776i	0.699926	+	0.404102i	−0.107394	+	0.994217i	$0.534251\pi$
$488$	−9.42345	−	5.44063i	−0.426580	−	0.246286i
$489$	21.3207	+	18.0149i	0.964157	+	0.814664i
$490$	33.0489	−	21.8659i	1.49300	−	0.987803i
$491$	−6.13294	−	3.54085i	−0.276776	−	0.159796i	0.355187	−	0.934795i	$-0.384417\pi$
$491$	−6.13294	−	3.54085i	−0.276776	−	0.159796i	−0.631963	+	0.774999i	$0.717750\pi$
$492$	−2.17904	−	6.05124i	−0.0982388	−	0.272811i
$493$	9.97095			0.449069
$494$	48.0263	+	27.7280i	2.16081	+	1.24754i
$495$	9.44271	−	1.47209i	0.424418	−	0.0661655i
$496$		−	70.5226i		−	3.16656i
$497$	22.7333	+	21.1116i	1.01973	+	0.946984i
$498$	−50.7479	+	18.2742i	−2.27407	+	0.818888i
$499$	22.9705			1.02830			0.514149	−	0.857701i	$-0.328108\pi$
$499$	22.9705			1.02830			0.514149	+	0.857701i	$0.328108\pi$
$500$	22.9624	+	43.6267i	1.02691	+	1.95105i
$501$	−3.48314	+	19.3660i	−0.155615	+	0.865209i
$502$	−6.09411	+	10.5553i	−0.271994	+	0.471107i
$503$			5.23692i			0.233503i	0.993161	+	0.116751i	$0.0372481\pi$
$503$			5.23692i			0.233503i	−0.993161	+	0.116751i	$0.962752\pi$
$504$	2.76540	−	48.3414i	0.123181	−	2.15330i
$505$	21.0934	−	35.4593i	0.938645	−	1.57792i
$506$	1.49211	+	0.861471i	0.0663324	+	0.0382970i
$507$	−4.95213	+	5.86086i	−0.219932	+	0.260290i
$508$	33.7144	−	19.4650i	1.49583	−	0.863620i
$509$	−9.71710			−0.430703			−0.215351	−	0.976537i	$-0.569090\pi$
$509$	−9.71710			−0.430703			−0.215351	+	0.976537i	$0.569090\pi$
$510$	−45.7406	+	15.8007i	−2.02543	+	0.699668i
$511$	−7.04653	−	22.8793i	−0.311720	−	1.01212i
$512$	−50.5392			−2.23354
$513$	−27.2612	−	0.279963i	−1.20361	−	0.0123607i
$514$	0.578131	+	0.333784i	0.0255003	+	0.0147226i
$515$	21.3660	−	35.9175i	0.941498	−	1.58272i
$516$	5.78859	−	32.1841i	0.254829	−	1.41683i
$517$	−3.52102	+	6.09859i	−0.154854	+	0.268216i
$518$	−39.8588	−	37.0155i	−1.75130	−	1.62637i
$519$	−4.15712	+	23.1133i	−0.182477	+	1.01456i
$520$	27.8296	+	49.6869i	1.22041	+	2.17891i
$521$	−2.77492	+	4.80630i	−0.121571	+	0.210568i	−0.920387	−	0.391007i	$-0.872127\pi$
$521$	−2.77492	+	4.80630i	−0.121571	+	0.210568i	0.798816	+	0.601575i	$0.205460\pi$
$522$	9.78255	+	11.8218i	0.428171	+	0.517427i
$523$	−3.79740	−	6.57728i	−0.166049	−	0.287605i	0.770979	−	0.636861i	$-0.219768\pi$
$523$	−3.79740	−	6.57728i	−0.166049	−	0.287605i	−0.937027	+	0.349257i	$0.886434\pi$
$524$	4.87417	+	8.44230i	0.212929	+	0.368804i
$525$	−2.16761	−	22.8101i	−0.0946021	−	0.995515i
$526$	−11.8752	+	20.5685i	−0.517784	+	0.896827i
$527$	52.5342			2.28843
$528$	2.89394	−	16.0901i	0.125943	−	0.700232i
$529$	−22.7718			−0.990079
$530$	26.3922	+	0.344029i	1.14640	+	0.0149437i
$531$	−0.569313	−	0.211638i	−0.0247061	−	0.00918430i
$532$	−58.4998	+	18.0172i	−2.53629	+	0.781145i
$533$	−1.75784	−	3.04467i	−0.0761405	−	0.131879i
$534$	3.95386	+	10.9799i	0.171100	+	0.475148i
$535$	−1.97129	−	0.0256963i	−0.0852264	−	0.00111095i
$536$	−12.5905	+	7.26913i	−0.543827	+	0.313979i
$537$	0.275208	−	1.53013i	0.0118761	−	0.0660301i
$538$	−14.8202	−	25.6694i	−0.638945	−	1.10668i
$539$	−9.94522	+	0.736681i	−0.428371	+	0.0317311i
$540$	−43.7617	−	26.6444i	−1.88320	−	1.14659i
$541$	−16.8986	−	29.2693i	−0.726530	−	1.25839i	−0.958341	−	0.285626i	$-0.907799\pi$
$541$	−16.8986	−	29.2693i	−0.726530	−	1.25839i	0.231812	−	0.972761i	$-0.425535\pi$
$542$			28.2764i			1.21458i
$543$	−21.9646	+	7.90942i	−0.942591	+	0.339426i
$544$			22.5676i			0.967578i
$545$	−4.74281	−	8.46780i	−0.203160	−	0.362721i
$546$	−5.83753	−	48.0835i	−0.249823	−	2.05778i
$547$	−14.5277	+	8.38754i	−0.621158	+	0.358626i	−0.777320	−	0.629106i	$-0.783421\pi$
$547$	−14.5277	+	8.38754i	−0.621158	+	0.358626i	0.156162	+	0.987731i	$0.450088\pi$
$548$	−10.6618	−	18.4667i	−0.455449	−	0.788860i
$549$	5.27603	−	0.893107i	0.225175	−	0.0381169i
$550$	0.470074	−	18.0278i	0.0200440	−	0.768707i
$551$	5.29995	−	9.17978i	0.225786	−	0.391072i
$552$	−1.71008	−	4.74891i	−0.0727857	−	0.202127i
$553$	−0.352184	−	1.14350i	−0.0149764	−	0.0486265i
$554$	21.9986	+	12.7009i	0.934631	+	0.539609i
$555$	−29.7280	+	10.2693i	−1.26188	+	0.435907i
$556$			5.50930i			0.233646i
$557$	3.36711	−	5.83201i	0.142669	−	0.247110i	−0.785832	−	0.618440i	$-0.787765\pi$
$557$	3.36711	−	5.83201i	0.142669	−	0.247110i	0.928501	+	0.371330i	$0.121098\pi$
$558$	51.5416	+	62.2859i	2.18193	+	2.63677i
$559$		−	17.8749i		−	0.756028i
$560$	−38.0923	−	9.23564i	−1.60969	−	0.390277i
$561$	11.9859	+	2.15578i	0.506047	+	0.0910169i
$562$		−	33.0440i		−	1.39388i
$563$	39.7410	−	22.9445i	1.67488	−	0.966995i	0.710045	−	0.704156i	$-0.248675\pi$
$563$	39.7410	−	22.9445i	1.67488	−	0.966995i	0.964840	−	0.262839i	$-0.0846587\pi$
$564$	35.5203	−	12.7908i	1.49568	−	0.538591i
$565$	−10.0629	−	17.9662i	−0.423348	−	0.755845i
$566$	33.7728			1.41958
$567$	14.1082	+	19.1823i	0.592487	+	0.805580i
$568$		−	71.5336i		−	3.00148i
$569$	−22.4961	−	12.9881i	−0.943085	−	0.544491i	−0.0521592	−	0.998639i	$-0.516610\pi$
$569$	−22.4961	−	12.9881i	−0.943085	−	0.544491i	−0.890926	+	0.454148i	$0.849944\pi$
$570$	−9.76595	+	50.5099i	−0.409051	+	2.11563i
$571$	13.5772	+	23.5163i	0.568187	+	0.984128i	0.996745	+	0.0806144i	$0.0256882\pi$
$571$	13.5772	+	23.5163i	0.568187	+	0.984128i	−0.428559	+	0.903514i	$0.640978\pi$
$572$		−	26.2271i		−	1.09661i
$573$	0.605661	−	3.36743i	0.0253019	−	0.140676i
$574$	5.49864	+	1.25752i	0.229509	+	0.0524878i
$575$	−1.13991	−	2.09891i	−0.0475377	−	0.0875304i
$576$	3.86921	−	3.20177i	0.161217	−	0.133407i
$577$	−6.23651	+	10.8020i	−0.259629	+	0.449691i	−0.966143	−	0.258008i	$-0.916934\pi$
$577$	−6.23651	+	10.8020i	−0.259629	+	0.449691i	0.706513	+	0.707700i	$0.250267\pi$
$578$	−18.6282			−0.774832
$579$	−21.9312	−	18.5308i	−0.911430	−	0.770112i
$580$	17.3800	−	9.73453i	0.721665	−	0.404205i
$581$	7.25532	−	31.7247i	0.301001	−	1.31616i
$582$	−13.9485	−	38.7353i	−0.578185	−	1.60563i
$583$	−5.75238	−	3.32114i	−0.238239	−	0.137548i
$584$	−27.5994	+	47.8036i	−1.14207	+	1.97813i
$585$	−26.1216	−	10.1000i	−1.08000	−	0.417582i
$586$	−10.0697	+	5.81373i	−0.415974	+	0.240163i
$587$	14.4358	−	8.33452i	0.595830	−	0.344002i	−0.171569	−	0.985172i	$-0.554884\pi$
$587$	14.4358	−	8.33452i	0.595830	−	0.344002i	0.767399	+	0.641170i	$0.221550\pi$
$588$	43.2749	+	31.3946i	1.78463	+	1.29469i
$589$	27.9240	−	48.3657i	1.15059	−	1.99288i
$590$	−0.585959	+	0.985033i	−0.0241235	+	0.0405532i
$591$	14.4314	+	40.0762i	0.593627	+	1.64851i
$592$			53.8029i			2.21128i
$593$	−0.329806	+	0.190413i	−0.0135435	+	0.00781934i	−0.506756	−	0.862089i	$-0.669156\pi$
$593$	−0.329806	+	0.190413i	−0.0135435	+	0.00781934i	0.493213	+	0.869909i	$0.335822\pi$
$594$	9.20353	+	16.3259i	0.377625	+	0.669859i
$595$	6.87988	−	28.3760i	0.282048	−	1.16330i
$596$	13.1512	−	7.59287i	0.538696	−	0.311016i
$597$	0.222104	−	1.23488i	0.00909012	−	0.0505403i
$598$	−2.52455	−	4.37265i	−0.103237	−	0.178811i
$599$	18.1887	−	10.5012i	0.743169	−	0.429069i	−0.0800517	−	0.996791i	$-0.525509\pi$
$599$	18.1887	−	10.5012i	0.743169	−	0.429069i	0.823220	+	0.567722i	$0.192175\pi$
$600$	−35.1378	+	39.4520i	−1.43449	+	1.61062i
$601$	3.49714	−	2.01907i	0.142651	−	0.0823597i	−0.426976	−	0.904263i	$-0.640421\pi$
$601$	3.49714	−	2.01907i	0.142651	−	0.0823597i	0.569627	+	0.821903i	$0.307088\pi$
$602$	21.0146	+	19.5155i	0.856491	+	0.795394i
$603$	2.49121	−	6.70143i	0.101450	−	0.272903i
$604$	37.5331	+	65.0092i	1.52720	+	2.64519i
$605$	10.2548	−	17.2389i	0.416916	−	0.700862i
$606$	79.6333	+	14.3227i	3.23488	+	0.581822i
$607$	−17.7673			−0.721154			−0.360577	−	0.932729i	$-0.617420\pi$
$607$	−17.7673			−0.721154			−0.360577	+	0.932729i	$0.617420\pi$
$608$	20.7769	+	11.9956i	0.842615	+	0.486484i
$609$	−9.19071	+	1.11579i	−0.372426	+	0.0452141i
$610$	0.131615	−	10.0968i	0.00532892	−	0.408808i
$611$	17.8720	−	10.3184i	0.723023	−	0.417437i
$612$	−41.6236	−	50.3004i	−1.68253	−	2.03327i
$613$	12.3044	+	7.10394i	0.496969	+	0.286925i	0.727461	−	0.686149i	$-0.240700\pi$
$613$	12.3044	+	7.10394i	0.496969	+	0.286925i	−0.230492	+	0.973074i	$0.574034\pi$
$614$	26.0941	−	45.1963i	1.05307	−	1.82397i
$615$	2.13723	−	2.46355i	0.0861815	−	0.0993401i
$616$	16.8490	+	15.6471i	0.678865	+	0.630438i
$617$	−16.5509	+	28.6670i	−0.666314	+	1.15409i	0.312614	+	0.949880i	$0.398795\pi$
$617$	−16.5509	+	28.6670i	−0.666314	+	1.15409i	−0.978927	+	0.204209i	$0.934538\pi$
$618$	80.6624	+	14.5078i	3.24472	+	0.583591i
$619$			41.1655i			1.65458i	0.561773	+	0.827291i	$0.310119\pi$
$619$			41.1655i			1.65458i	−0.561773	+	0.827291i	$0.689881\pi$
$620$	91.5704	−	51.2886i	3.67756	−	2.05980i
$621$	2.13677	+	1.26310i	0.0857456	+	0.0506863i
$622$	29.2701			1.17362
$623$	−6.86402	−	1.56978i	−0.275001	−	0.0628918i
$624$	−30.9206	+	36.5946i	−1.23782	+	1.46496i
$625$	−13.6113	+	20.9698i	−0.544453	+	0.838791i
$626$	−36.7611	−	63.6721i	−1.46927	−	2.54485i
$627$	8.35572	−	9.88901i	0.333695	−	0.394929i
$628$	−10.3221	+	17.8783i	−0.411895	+	0.713424i
$629$	−40.0792			−1.59806
$630$	40.3932	−	19.6828i	1.60930	−	0.784183i
$631$	10.0626			0.400586			0.200293	−	0.979736i	$-0.435811\pi$
$631$	10.0626			0.400586			0.200293	+	0.979736i	$0.435811\pi$
$632$	−1.37941	+	2.38921i	−0.0548701	+	0.0950378i
$633$	−19.9096	−	3.58091i	−0.791334	−	0.142328i
$634$	−27.4507	−	47.5461i	−1.09021	−	1.88830i
$635$	16.9662	+	10.0925i	0.673282	+	0.400510i
$636$	12.0647	+	33.5039i	0.478397	+	1.32852i
$637$	26.3194	+	12.7027i	1.04281	+	0.503298i
$638$	−7.28679			−0.288487
$639$	22.4270	+	27.1022i	0.887200	+	1.07215i
$640$	−14.6241	−	26.1098i	−0.578068	−	1.03208i
$641$			39.1652i			1.54693i	0.633837	+	0.773466i	$0.281479\pi$
$641$			39.1652i			1.54693i	−0.633837	+	0.773466i	$0.718521\pi$
$642$	−1.30986	−	3.63750i	−0.0516959	−	0.143561i
$643$	7.40682	−	12.8290i	0.292097	−	0.505926i	−0.682209	−	0.731157i	$-0.738980\pi$
$643$	7.40682	−	12.8290i	0.292097	−	0.505926i	0.974305	+	0.225231i	$0.0723138\pi$
$644$	5.43285	+	1.24247i	0.214084	+	0.0489603i
$645$	15.6734	−	5.41424i	0.617138	−	0.213185i
$646$	−32.7786	+	56.7743i	−1.28966	+	2.23375i
$647$	23.0628	+	13.3153i	0.906691	+	0.523478i	0.879365	−	0.476148i	$-0.157967\pi$
$647$	23.0628	+	13.3153i	0.906691	+	0.523478i	0.0273261	+	0.999627i	$0.491301\pi$
$648$	10.2733	−	53.9339i	0.403575	−	2.11873i
$649$	0.249789	−	0.144216i	0.00980506	−	0.00566096i
$650$	−27.6083	+	45.0639i	−1.08289	+	1.76755i
$651$	−48.4233	+	5.87878i	−1.89786	+	0.230408i
$652$	61.5415	+	35.5310i	2.41015	+	1.39150i
$653$	21.3302			0.834716			0.417358	−	0.908742i	$-0.362956\pi$
$653$	21.3302			0.834716			0.417358	+	0.908742i	$0.362956\pi$
$654$	12.2841	−	14.5383i	0.480348	−	0.568493i
$655$	−2.52724	+	4.24844i	−0.0987474	+	0.166000i
$656$	−2.78957	−	4.83168i	−0.108915	−	0.188646i
$657$	−4.53058	−	26.7644i	−0.176755	−	1.04418i
$658$	−7.38155	+	32.2766i	−0.287763	+	1.25827i
$659$	−3.91124	+	2.25816i	−0.152360	+	0.0879653i	−0.574242	−	0.818686i	$-0.694703\pi$
$659$	−3.91124	+	2.25816i	−0.152360	+	0.0879653i	0.421882	+	0.906651i	$0.361370\pi$
$660$	22.9969	−	7.94409i	0.895154	−	0.309223i
$661$	−29.3391	+	16.9389i	−1.14116	+	0.658848i	−0.946717	−	0.322067i	$-0.895622\pi$
$661$	−29.3391	+	16.9389i	−1.14116	+	0.658848i	−0.194441	+	0.980914i	$0.562289\pi$
$662$	−7.53489	−	13.0508i	−0.292852	−	0.507234i
$663$	−27.2603	−	23.0336i	−1.05870	−	0.894551i
$664$	−64.9842	+	37.5186i	−2.52187	+	1.45601i
$665$	−22.4675	−	21.4169i	−0.871251	−	0.830512i
$666$	−39.3219	−	47.5190i	−1.52369	−	1.84132i
$667$	−0.835791	+	0.482544i	−0.0323620	+	0.0186842i
$668$			50.0946i			1.93822i
$669$	29.5900	−	35.0198i	1.14401	−	1.35394i
$670$	−11.5949	−	6.89737i	−0.447950	−	0.266469i
$671$	−1.27056	+	2.20068i	−0.0490495	+	0.0849561i
$672$	−2.52540	−	20.8016i	−0.0974195	−	0.802441i
$673$	0.00944408	−	0.00545254i	0.000364043	−	0.000210180i	−0.499818	−	0.866130i	$-0.666600\pi$
$673$	0.00944408	−	0.00545254i	0.000364043	−	0.000210180i	0.500182	+	0.865920i	$0.333266\pi$
$674$	6.15542	−	3.55384i	0.237098	−	0.136889i
$675$	0.943890	−	25.9636i	0.0363303	−	0.999340i
$676$	−9.76712	+	16.9172i	−0.375659	+	0.650660i
$677$	−30.4790	−	17.5970i	−1.17140	−	0.676309i	−0.217392	−	0.976084i	$-0.569755\pi$
$677$	−30.4790	−	17.5970i	−1.17140	−	0.676309i	−0.954010	+	0.299775i	$0.903088\pi$
$678$	26.0634	−	30.8461i	1.00096	−	1.18464i
$679$	24.2151	+	5.53791i	0.929290	+	0.212525i
$680$	−58.7373	+	32.8987i	−2.25247	+	1.26161i
$681$	12.6335	−	4.54932i	0.484118	−	0.174330i
$682$	−38.3921			−1.47011
$683$	13.2893	−	23.0177i	0.508499	−	0.880746i	−0.491452	−	0.870904i	$-0.663534\pi$
$683$	13.2893	−	23.0177i	0.508499	−	0.880746i	0.999952	−	0.00984199i	$-0.00313285\pi$
$684$	−68.4337	+	11.5842i	−2.61663	+	0.442933i
$685$	5.52810	−	9.29307i	0.211218	−	0.355070i
$686$	−43.6689	+	17.0738i	−1.66729	+	0.651879i
$687$	30.1932	−	10.8725i	1.15194	−	0.414813i
$688$		−	28.3663i		−	1.08145i
$689$	9.73264	+	16.8574i	0.370784	+	0.642217i
$690$	3.06942	−	3.53807i	0.116851	−	0.134692i
$691$	2.84810	+	1.64435i	0.108347	+	0.0625540i	0.553194	−	0.833052i	$-0.313409\pi$
$691$	2.84810	+	1.64435i	0.108347	+	0.0625540i	−0.444847	+	0.895606i	$0.646742\pi$
$692$			59.7878i			2.27279i
$693$	−11.2893	−	0.645808i	−0.428843	−	0.0245322i
$694$	−25.0419			−0.950578
$695$	−2.43743	+	1.36521i	−0.0924572	+	0.0517852i
$696$	16.3056	+	13.7775i	0.618064	+	0.522233i
$697$	3.59925	−	2.07803i	0.136331	−	0.0787109i
$698$		−	0.817576i		−	0.0309457i
$699$	−10.6324	+	12.5835i	−0.402155	+	0.475952i
$700$	−15.7111	−	56.1778i	−0.593823	−	2.12332i
$701$		−	39.7933i		−	1.50297i	−0.659749	−	0.751486i	$-0.729337\pi$
$701$		−	39.7933i		−	1.50297i	0.659749	−	0.751486i	$-0.270663\pi$
$702$	0.563999	−	54.9189i	0.0212868	−	2.07278i
$703$	−21.3037	+	36.8990i	−0.803483	+	1.39167i
$704$			2.38492i			0.0898852i
$705$	14.4609	+	12.5454i	0.544629	+	0.472487i
$706$	37.4621	+	21.6288i	1.40991	+	0.814009i
$707$	−33.2202	+	35.7719i	−1.24937	+	1.34534i
$708$	−1.52189	−	0.273725i	−0.0571961	−	0.0102872i
$709$	1.54464	−	2.67540i	0.0580103	−	0.100477i	−0.835562	−	0.549396i	$-0.814858\pi$
$709$	1.54464	−	2.67540i	0.0580103	−	0.100477i	0.893572	+	0.448920i	$0.148191\pi$
$710$	57.9164	−	32.4390i	2.17356	−	1.21741i
$711$	−0.226437	−	1.33768i	−0.00849206	−	0.0501669i
$712$	8.11762	+	14.0601i	0.304221	+	0.526926i
$713$	−4.40355	+	2.54239i	−0.164914	+	0.0952133i
$714$	56.8418	−	6.90083i	2.12725	−	0.258257i
$715$	11.6035	−	6.49910i	0.433945	−	0.243052i
$716$		−	3.95804i		−	0.147919i
$717$	−6.24897	+	34.7438i	−0.233372	+	1.29753i
$718$			50.3369i			1.87856i
$719$	−10.5791	−	18.3235i	−0.394532	−	0.683350i	0.598509	−	0.801116i	$-0.295760\pi$
$719$	−10.5791	−	18.3235i	−0.394532	−	0.683350i	−0.993041	+	0.117766i	$0.962427\pi$
$720$	−41.4532	−	16.0280i	−1.54487	−	0.597327i
$721$	−33.6495	+	36.2342i	−1.25317	+	1.34943i
$722$	10.7949	+	18.6974i	0.401746	+	0.695844i
$723$	−14.7327	+	5.30524i	−0.547917	+	0.197304i
$724$	−51.4716	+	29.7171i	−1.91293	+	1.10443i
$725$	8.61354	+	5.27707i	0.319899	+	0.195986i
$726$	38.7146	+	6.96315i	1.43683	+	0.258427i
$727$	4.31669	+	7.47672i	0.160097	+	0.277296i	0.934903	−	0.354903i	$-0.115486\pi$
$727$	4.31669	+	7.47672i	0.160097	+	0.277296i	−0.774806	+	0.632199i	$0.782153\pi$
$728$	−19.8340	−	64.3987i	−0.735097	−	2.38677i
$729$	13.0169	+	23.6550i	0.482109	+	0.876111i
$730$	−51.2194	−	0.667659i	−1.89572	−	0.0247112i
$731$	21.1308			0.781551
$732$	12.8175	−	4.61557i	0.473749	−	0.170596i
$733$	5.15980			0.190581			0.0952907	−	0.995449i	$-0.469622\pi$
$733$	5.15980			0.190581			0.0952907	+	0.995449i	$0.469622\pi$
$734$	39.7076	−	68.7756i	1.46564	−	2.53855i
$735$	−3.16613	+	26.9254i	−0.116785	+	0.993157i
$736$	−1.09216	−	1.89167i	−0.0402575	−	0.0697280i
$737$	1.69757	+	2.94028i	0.0625309	+	0.108307i
$738$	5.99501	+	2.22860i	0.220679	+	0.0820359i
$739$	−7.92896	+	13.7334i	−0.291671	+	0.505190i	−0.974205	−	0.225664i	$-0.927545\pi$
$739$	−7.92896	+	13.7334i	−0.291671	+	0.505190i	0.682534	+	0.730854i	$0.260878\pi$
$740$	−69.8606	+	39.1289i	−2.56813	+	1.43841i
$741$	−35.6959	+	12.8540i	−1.31132	+	0.472205i
$742$	−30.4443	−	6.96251i	−1.11765	−	0.255602i
$743$	14.5897	−	25.2701i	0.535243	−	0.927069i	−0.463908	−	0.885883i	$-0.653553\pi$
$743$	14.5897	−	25.2701i	0.535243	−	0.927069i	0.999152	−	0.0411854i	$-0.0131134\pi$
$744$	85.9099	+	72.5896i	3.14961	+	2.66126i
$745$	6.61813	+	3.93688i	0.242470	+	0.144236i
$746$	−56.1756	−	32.4330i	−2.05674	−	1.18746i
$747$	12.8580	−	34.5885i	0.470450	−	1.26553i
$748$	31.0044			1.13363
$749$	2.27395	+	0.520045i	0.0830885	+	0.0190020i
$750$	−47.8761	−	10.5583i	−1.74819	−	0.385535i
$751$	−27.9822			−1.02109			−0.510543	−	0.859852i	$-0.670556\pi$
$751$	−27.9822			−1.02109			−0.510543	+	0.859852i	$0.670556\pi$
$752$	28.3616	−	16.3746i	1.03424	−	0.597120i
$753$	−2.82508	−	7.84531i	−0.102952	−	0.285899i
$754$	18.4931	+	10.6770i	0.673480	+	0.388834i
$755$	−19.4608	+	32.7147i	−0.708250	+	1.19061i
$756$	43.9953	+	41.7065i	1.60009	+	1.51685i
$757$			12.4434i			0.452263i	0.974097	+	0.226132i	$0.0726079\pi$
$757$			12.4434i			0.452263i	−0.974097	+	0.226132i	$0.927392\pi$
$758$	6.33672	−	10.9755i	0.230160	−	0.398649i
$759$	−1.10902	+	0.399357i	−0.0402549	+	0.0144957i
$760$	−0.932850	+	71.5636i	−0.0338380	+	2.59588i
$761$	−21.0307			−0.762362			−0.381181	−	0.924500i	$-0.624483\pi$
$761$	−21.0307			−0.762362			−0.381181	+	0.924500i	$0.624483\pi$
$762$	−6.85299	+	38.1021i	−0.248258	+	1.38029i
$763$	3.38018	+	10.9750i	0.122371	+	0.397323i
$764$		−	8.71063i		−	0.315140i
$765$	11.9397	−	30.8796i	0.431679	−	1.11646i
$766$	50.5708	+	29.1971i	1.82720	+	1.05493i
$767$	−0.845251			−0.0305202
$768$	34.1344	−	40.3982i	1.23172	−	1.45774i
$769$	11.8574	+	6.84585i	0.427588	+	0.246868i	0.698318	−	0.715787i	$-0.253932\pi$
$769$	11.8574	+	6.84585i	0.427588	+	0.246868i	−0.270731	+	0.962655i	$0.587265\pi$
$770$	−5.02783	+	20.7372i	−0.181190	+	0.747317i
$771$	−0.429700	+	0.154734i	−0.0154753	+	0.00557262i
$772$	−63.3036	−	36.5484i	−2.27835	−	1.31540i
$773$	−0.308779	−	0.178273i	−0.0111060	−	0.00641205i	0.494437	−	0.869214i	$-0.335374\pi$
$773$	−0.308779	−	0.178273i	−0.0111060	−	0.00641205i	−0.505543	+	0.862802i	$0.668708\pi$
$774$	20.7315	+	25.0532i	0.745180	+	0.900520i
$775$	45.3824	+	27.8034i	1.63018	+	0.998729i
$776$	−28.6376	−	49.6017i	−1.02803	−	1.78060i
$777$	36.9429	−	4.48502i	1.32532	−	0.160899i
$778$	36.8838	+	21.2948i	1.32235	+	0.763457i
$779$		−	4.41821i		−	0.158299i
$780$	−70.0039	−	13.5351i	−2.50654	−	0.484633i
$781$	−16.7054			−0.597765
$782$	5.16912	−	2.98439i	0.184847	−	0.106722i
$783$	−10.4972	−	0.107803i	−0.375141	−	0.00385257i
$784$	41.7671	+	20.1583i	1.49168	+	0.719939i
$785$	−10.4676	−	0.136448i	−0.373604	−	0.00487003i
$786$	−9.54101	−	1.71603i	−0.340317	−	0.0612089i
$787$	−5.29263	−	9.16710i	−0.188662	−	0.326772i	0.756143	−	0.654407i	$-0.227082\pi$
$787$	−5.29263	−	9.16710i	−0.188662	−	0.326772i	−0.944804	+	0.327635i	$0.893748\pi$
$788$	54.2213	+	93.9140i	1.93155	+	3.34555i
$789$	−5.50506	−	15.2876i	−0.195985	−	0.544255i
$790$	−2.55993	−	0.0333694i	−0.0910783	−	0.00118723i
$791$	7.17176	+	23.2859i	0.254998	+	0.827950i
$792$	16.6220	+	20.0870i	0.590638	+	0.713762i
$793$	6.44910	−	3.72339i	0.229014	−	0.132222i
$794$	66.3293			2.35394
$795$	−11.8332	+	13.6400i	−0.419681	+	0.483760i
$796$		−	3.19431i		−	0.113219i
$797$	−32.2113	−	18.5972i	−1.14098	−	0.658747i	−0.194309	−	0.980940i	$-0.562247\pi$
$797$	−32.2113	−	18.5972i	−1.14098	−	0.658747i	−0.946674	+	0.322193i	$0.895580\pi$
$798$	23.8604	−	55.9996i	0.844648	−	1.98237i
$799$	12.1979	+	21.1273i	0.431530	+	0.747432i
$800$	−11.9438	+	19.4953i	−0.422276	+	0.689264i
$801$	−7.48365	−	2.78199i	−0.264422	−	0.0982969i
$802$	−79.5735	−	45.9418i	−2.80984	−	1.62226i
$803$	11.1637	+	6.44534i	0.393957	+	0.227451i
$804$	3.22204	−	17.9143i	0.113633	−	0.631788i
$805$	0.796565	+	2.71150i	0.0280752	+	0.0955677i
$806$	97.4351	+	56.2542i	3.43201	+	1.98147i
$807$	19.9580	+	3.58962i	0.702554	+	0.126360i
$808$	112.562			3.95991
$809$	27.2837	+	15.7522i	0.959243	+	0.553819i	0.895940	−	0.444175i	$-0.146503\pi$
$809$	27.2837	+	15.7522i	0.959243	+	0.553819i	0.0633032	+	0.997994i	$0.479836\pi$
$810$	48.3258	−	16.1402i	1.69799	−	0.567108i
$811$		−	1.59210i		−	0.0559062i	−0.999609	−	0.0279531i	$-0.991101\pi$
$811$		−	1.59210i		−	0.0559062i	0.999609	−	0.0279531i	$-0.00889891\pi$
$812$	−22.5261	+	6.93775i	−0.790510	+	0.243467i
$813$	−14.7765	−	12.4854i	−0.518235	−	0.437882i
$814$	29.2900			1.02661
$815$	−0.469685	+	36.0319i	−0.0164524	+	1.26214i
$816$	−43.2603	−	36.5528i	−1.51441	−	1.27960i
$817$	11.2318	−	19.4541i	0.392953	−	0.680614i
$818$			6.14130i			0.214726i
$819$	27.7047	+	18.1806i	0.968081	+	0.635283i
$820$	4.24496	−	7.13604i	0.148241	−	0.249201i
$821$	−22.0104	−	12.7077i	−0.768170	−	0.443503i	0.0640515	−	0.997947i	$-0.479598\pi$
$821$	−22.0104	−	12.7077i	−0.768170	−	0.443503i	−0.832221	+	0.554443i	$0.812931\pi$
$822$	20.8701	+	3.75366i	0.727927	+	0.130924i
$823$	−17.0924	+	9.86828i	−0.595802	+	0.343986i	−0.767388	−	0.641183i	$-0.778444\pi$
$823$	−17.0924	+	9.86828i	−0.595802	+	0.343986i	0.171586	+	0.985169i	$0.445111\pi$
$824$	114.016			3.97195
$825$	9.21328	+	8.20579i	0.320765	+	0.285689i
$826$	0.922831	−	0.993717i	0.0321094	−	0.0345759i
$827$	11.0429			0.383998			0.191999	−	0.981395i	$-0.438503\pi$
$827$	11.0429			0.383998			0.191999	+	0.981395i	$0.438503\pi$
$828$	5.92328	+	2.20194i	0.205848	+	0.0765226i
$829$	−18.4118	−	10.6300i	−0.639467	−	0.369196i	0.144942	−	0.989440i	$-0.453700\pi$
$829$	−18.4118	−	10.6300i	−0.639467	−	0.369196i	−0.784409	+	0.620244i	$0.787034\pi$
$830$	−59.8455	−	35.5998i	−2.07727	−	1.23569i
$831$	−16.3506	+	5.88783i	−0.567196	+	0.204246i
$832$	3.49452	−	6.05269i	0.121151	−	0.209839i
$833$	−15.0164	+	31.1134i	−0.520289	+	1.07802i
$834$	−4.18481	−	3.53596i	−0.144908	−	0.122440i
$835$	−22.1629	+	12.4135i	−0.766980	+	0.429585i
$836$	16.4800	−	28.5443i	0.569974	−	0.987225i
$837$	−55.3071	−	0.567985i	−1.91169	−	0.0196324i
$838$	−19.0272	−	32.9560i	−0.657283	−	1.13845i
$839$	17.8301	+	30.8827i	0.615564	+	1.06619i	0.990285	+	0.139051i	$0.0444051\pi$
$839$	17.8301	+	30.8827i	0.615564	+	1.06619i	−0.374721	+	0.927137i	$0.622262\pi$
$840$	50.4595	−	36.8973i	1.74102	−	1.27308i
$841$	−12.4592	+	21.5799i	−0.429627	+	0.744136i
$842$	−56.4005			−1.94369
$843$	17.2679	+	14.5905i	0.594740	+	0.502525i
$844$	−51.5007			−1.77273
$845$	−9.90481	−	0.129112i	−0.340736	−	0.00444158i
$846$	−13.0817	+	35.1903i	−0.449759	+	1.20987i
$847$	−16.1503	+	17.3909i	−0.554932	+	0.597559i
$848$	15.4450	+	26.7516i	0.530385	+	0.918654i
$849$	−14.9123	+	17.6488i	−0.511790	+	0.605705i
$850$	−53.2722	−	32.6371i	−1.82722	−	1.11944i
$851$	3.35954	−	1.93963i	0.115164	−	0.0664898i
$852$	68.4089	+	57.8021i	2.34365	+	1.98027i
$853$	12.0777	+	20.9192i	0.413534	+	0.716261i	0.995273	−	0.0971139i	$-0.0309611\pi$
$853$	12.0777	+	20.9192i	0.413534	+	0.716261i	−0.581740	+	0.813375i	$0.697628\pi$
$854$	−2.66363	+	11.6470i	−0.0911476	+	0.398553i
$855$	−22.0830	−	27.4060i	−0.755223	−	0.937266i
$856$	−2.68925	−	4.65792i	−0.0919167	−	0.159204i
$857$		−	53.8243i		−	1.83860i	−0.393553	−	0.919302i	$-0.628754\pi$
$857$		−	53.8243i		−	1.83860i	0.393553	−	0.919302i	$-0.371246\pi$
$858$	19.9219	+	16.8330i	0.680122	+	0.574669i
$859$			17.2017i			0.586913i	0.955972	+	0.293457i	$0.0948056\pi$
$859$			17.2017i			0.586913i	−0.955972	+	0.293457i	$0.905194\pi$
$860$	36.8323	−	20.6298i	1.25597	−	0.703470i
$861$	−3.08506	+	2.31819i	−0.105139	+	0.0790037i
$862$	42.7428	−	24.6775i	1.45582	−	0.840521i
$863$	−14.6092	−	25.3039i	−0.497304	−	0.861356i	0.502691	−	0.864466i	$-0.332343\pi$
$863$	−14.6092	−	25.3039i	−0.497304	−	0.861356i	−0.999995	+	0.00310991i	$0.999010\pi$
$864$	0.243995	−	23.7588i	0.00830086	−	0.808290i
$865$	−26.4514	+	14.8154i	−0.899375	+	0.503740i
$866$	−21.4457	+	37.1450i	−0.728753	+	1.26224i
$867$	8.22527	−	9.73462i	0.279345	−	0.330605i
$868$	−118.684	+	36.5531i	−4.02838	+	1.24069i
$869$	0.557957	+	0.322137i	0.0189274	+	0.0109277i
$870$	−3.76050	+	19.4495i	−0.127493	+	0.659399i
$871$		−	9.94951i		−	0.337126i
$872$	13.2393	−	22.9311i	0.448339	−	0.776545i
$873$	26.4010	+	9.81439i	0.893539	+	0.332167i
$874$		−	6.34529i		−	0.214633i
$875$	20.9611	−	20.8718i	0.708614	−	0.705596i
$876$	−23.4140	−	65.0211i	−0.791086	−	2.19686i
$877$			32.6729i			1.10329i	0.834081	+	0.551643i	$0.185999\pi$
$877$			32.6729i			1.10329i	−0.834081	+	0.551643i	$0.814001\pi$
$878$	−3.63470	+	2.09849i	−0.122665	+	0.0708207i
$879$	1.40815	−	7.82919i	0.0474957	−	0.264072i
$880$	18.4139	−	10.3136i	0.620733	−	0.347672i
$881$	51.6741			1.74094			0.870472	−	0.492217i	$-0.163814\pi$
$881$	51.6741			1.74094			0.870472	+	0.492217i	$0.163814\pi$
$882$	−51.6216	+	12.7216i	−1.73819	+	0.428360i
$883$		−	18.8576i		−	0.634610i	−0.948324	−	0.317305i	$-0.897222\pi$
$883$		−	18.8576i		−	0.634610i	0.948324	−	0.317305i	$-0.102778\pi$
$884$	−78.6860	−	45.4294i	−2.64650	−	1.52796i
$885$	−0.256023	−	0.741147i	−0.00860612	−	0.0249134i
$886$	−45.6847	−	79.1282i	−1.53481	−	2.65836i
$887$		−	38.4610i		−	1.29139i	−0.763594	−	0.645697i	$-0.776567\pi$
$887$		−	38.4610i		−	1.29139i	0.763594	−	0.645697i	$-0.223433\pi$
$888$	−65.5421	−	55.3798i	−2.19945	−	1.85842i
$889$	−17.1158	−	15.8948i	−0.574044	−	0.533095i
$890$	−7.70246	+	12.9483i	−0.258187	+	0.434028i
$891$	−12.5953	−	2.39915i	−0.421958	−	0.0803746i
$892$	58.3605	−	101.083i	1.95406	−	3.38452i
$893$	25.9346			0.867868
$894$	−2.67320	+	14.8628i	−0.0894052	+	0.497086i
$895$	1.75112	−	0.980804i	0.0585336	−	0.0327846i
$896$	10.4225	+	33.8407i	0.348192	+	1.13054i
$897$	3.39974	+	0.611473i	0.113514	+	0.0204165i
$898$	−57.8958	−	33.4261i	−1.93201	−	1.11544i
$899$	10.7525	−	18.6238i	0.358615	−	0.621139i
$900$	−9.33586	−	65.4817i	−0.311195	−	2.18272i
$901$	−19.9280	+	11.5054i	−0.663897	+	0.383301i
$902$	−2.63034	+	1.51863i	−0.0875807	+	0.0505647i
$903$	−19.4773	+	2.36462i	−0.648163	+	0.0786896i
$904$	28.0899	−	48.6532i	0.934257	−	1.61818i
$905$	−25.9022	−	15.4082i	−0.861018	−	0.512187i
$906$	−73.4697	−	13.2142i	−2.44087	−	0.439011i
$907$			6.55889i			0.217784i	0.994054	+	0.108892i	$0.0347303\pi$
$907$			6.55889i			0.217784i	−0.994054	+	0.108892i	$0.965270\pi$
$908$	29.6053	−	17.0926i	0.982486	−	0.567239i
$909$	−42.6467	+	35.2901i	−1.41450	+	1.17050i
$910$	43.1454	−	45.2618i	1.43026	−	1.50042i
$911$	40.3423	−	23.2916i	1.33660	−	0.771686i	0.350298	−	0.936638i	$-0.386080\pi$
$911$	40.3423	−	23.2916i	1.33660	−	0.771686i	0.986302	+	0.164952i	$0.0527469\pi$
$912$	−56.6470	+	20.3985i	−1.87577	+	0.675462i
$913$	8.76179	+	15.1759i	0.289973	+	0.502248i
$914$	−69.7001	+	40.2414i	−2.30548	+	1.33107i
$915$	5.21821	+	4.52701i	0.172509	+	0.149658i
$916$	70.7544	−	40.8501i	2.33779	−	1.34972i
$917$	3.98017	−	4.28590i	0.131437	−	0.141533i
$918$	64.9224	+	0.666731i	2.14276	+	0.0220054i
$919$	−25.8448	−	44.7644i	−0.852540	−	1.47664i	−0.878909	−	0.476990i	$-0.841728\pi$
$919$	−25.8448	−	44.7644i	−0.852540	−	1.47664i	0.0263686	−	0.999652i	$-0.491606\pi$
$920$	3.33138	−	5.60025i	0.109832	−	0.184635i
$921$	12.0966	+	33.5924i	0.398596	+	1.10691i
$922$	−29.3420			−0.966326
$923$	42.3965	+	24.4776i	1.39550	+	0.805691i
$924$	−28.5782	+	3.46951i	−0.940155	+	0.114139i
$925$	−34.6230	−	21.2117i	−1.13840	−	0.697436i
$926$	−65.7340	+	37.9515i	−2.16015	+	1.24716i
$927$	−43.1978	+	35.7461i	−1.41880	+	1.17406i
$928$	8.00041	+	4.61904i	0.262626	+	0.151627i
$929$	22.6296	−	39.1956i	0.742452	−	1.28596i	−0.208923	−	0.977932i	$-0.566996\pi$
$929$	22.6296	−	39.1956i	0.742452	−	1.28596i	0.951376	−	0.308033i	$-0.0996707\pi$
$930$	−19.8130	+	102.474i	−0.649695	+	3.36025i
$931$	20.6628	+	30.3629i	0.677197	+	0.995105i
$932$	−20.9704	+	36.3218i	−0.686909	+	1.18976i
$933$	−12.9242	+	15.2958i	−0.423118	+	0.500761i
$934$		−	6.34703i		−	0.207681i
$935$	7.68290	+	13.7170i	0.251258	+	0.448595i
$936$	−12.7523	−	75.3344i	−0.416823	−	2.46238i
$937$	16.0761			0.525184			0.262592	−	0.964907i	$-0.415423\pi$
$937$	16.0761			0.525184			0.262592	+	0.964907i	$0.415423\pi$
$938$	11.6971	+	10.8627i	0.381925	+	0.354680i
$939$	49.5052	+	8.90393i	1.61554	+	0.290569i
$940$	41.8881	+	24.9176i	1.36624	+	0.812724i
$941$	−11.8241	−	20.4800i	−0.385456	−	0.667629i	0.606376	−	0.795178i	$-0.292622\pi$
$941$	−11.8241	−	20.4800i	−0.385456	−	0.667629i	−0.991832	+	0.127549i	$0.959289\pi$
$942$	−6.95536	−	19.3152i	−0.226618	−	0.629322i
$943$	−0.201132	+	0.348371i	−0.00654977	+	0.0113445i
$944$	−1.34136			−0.0436574
$945$	−7.54981	+	29.7993i	−0.245595	+	0.969372i
$946$	−15.4424			−0.502077
$947$	14.2698	−	24.7160i	0.463707	−	0.803163i	−0.535436	−	0.844576i	$-0.679853\pi$
$947$	14.2698	−	24.7160i	0.463707	−	0.803163i	0.999142	+	0.0414127i	$0.0131858\pi$
$948$	−1.17023	−	3.24974i	−0.0380072	−	0.105547i
$949$	−18.8881	−	32.7152i	−0.613135	−	1.06198i
$950$	−58.3637	+	31.6973i	−1.89357	+	1.02840i
$951$	36.9672	+	6.64886i	1.19874	+	0.215604i
$952$	76.1289	−	23.4468i	2.46735	−	0.759914i
$953$	−60.3601			−1.95525			−0.977627	−	0.210346i	$-0.932541\pi$
$953$	−60.3601			−1.95525			−0.977627	+	0.210346i	$0.932541\pi$
$954$	−33.1926	−	12.3391i	−1.07465	−	0.399493i
$955$	3.85377	−	2.15850i	0.124705	−	0.0698473i
$956$			89.8728i			2.90669i
$957$	3.21747	−	3.80789i	0.104006	−	0.123091i
$958$	45.0082	−	77.9565i	1.45415	−	2.51866i
$959$	−8.70624	+	9.37500i	−0.281139	+	0.302735i
$960$	6.36569	+	1.23079i	0.205452	+	0.0397236i
$961$	41.1518	−	71.2770i	1.32748	−	2.29926i
$962$	−74.3349	−	42.9173i	−2.39665	−	1.38371i
$963$	2.47923	+	0.921635i	0.0798919	+	0.0296993i
$964$	−34.5245	+	19.9328i	−1.11196	+	0.641991i
$965$	0.483134	−	37.0636i	0.0155526	−	1.19312i
$966$	−4.43066	+	3.32930i	−0.142554	+	0.107119i
$967$	−20.6715	−	11.9347i	−0.664752	−	0.383795i	0.129333	−	0.991601i	$-0.458716\pi$
$967$	−20.6715	−	11.9347i	−0.664752	−	0.383795i	−0.794085	+	0.607807i	$0.792050\pi$
$968$	54.7231			1.75887
$969$	−15.1954	−	42.1979i	−0.488146	−	1.35559i
$970$	27.1730	−	45.6794i	0.872471	−	1.46668i
$971$	21.2234	+	36.7601i	0.681092	+	1.17969i	0.974648	+	0.223745i	$0.0718282\pi$
$971$	21.2234	+	36.7601i	0.681092	+	1.17969i	−0.293555	+	0.955942i	$0.594839\pi$
$972$	43.2767	+	53.4054i	1.38810	+	1.71298i
$973$	3.15914	−	0.972975i	0.101277	−	0.0311922i
$974$	−39.1049	+	22.5772i	−1.25300	+	0.723422i
$975$	−11.3588	−	34.3253i	−0.363772	−	1.09929i
$976$	10.2343	−	5.90878i	0.327592	−	0.189135i
$977$	3.50206	+	6.06575i	0.112041	+	0.194060i	0.916593	−	0.399822i	$-0.130928\pi$
$977$	3.50206	+	6.06575i	0.112041	+	0.194060i	−0.804552	+	0.593882i	$0.797595\pi$
$978$	−66.4874	+	23.9420i	−2.12603	+	0.765581i
$979$	3.28349	−	1.89572i	0.104941	−	0.0605875i
$980$	4.20108	+	68.8931i	0.134199	+	2.20071i
$981$	2.17329	+	12.8387i	0.0693879	+	0.409909i
$982$	15.5269	−	8.96444i	0.495482	−	0.286067i
$983$		−	28.5269i		−	0.909866i	−0.890526	−	0.454933i	$-0.849663\pi$
$983$		−	28.5269i		−	0.909866i	0.890526	−	0.454933i	$-0.150337\pi$
$984$	8.75724	+	1.57507i	0.279171	+	0.0502112i
$985$	−28.1136	+	47.2606i	−0.895773	+	1.50585i
$986$	−12.6218	+	21.8616i	−0.401961	+	0.696216i
$987$	−13.6076	−	18.1091i	−0.433135	−	0.576419i
$988$	−83.6493	+	48.2950i	−2.66124	+	1.53647i
$989$	−1.77124	+	1.02263i	−0.0563221	+	0.0325176i
$990$	−8.72553	+	22.5669i	−0.277315	+	0.717223i
$991$	28.9247	−	50.0991i	0.918824	−	1.59145i	0.117620	−	0.993059i	$-0.462474\pi$
$991$	28.9247	−	50.0991i	0.918824	−	1.59145i	0.801204	−	0.598391i	$-0.204193\pi$
$992$	42.1519	+	24.3364i	1.33833	+	0.772682i
$993$	10.1470	+	1.82503i	0.322006	+	0.0579156i
$994$	−75.0649	+	23.1191i	−2.38091	+	0.733293i
$995$	1.41323	−	0.791550i	0.0448024	−	0.0250938i
$996$	16.6301	−	92.4621i	0.526945	−	2.92977i
$997$	2.21323			0.0700937			0.0350469	−	0.999386i	$-0.488842\pi$
$997$	2.21323			0.0700937			0.0350469	+	0.999386i	$0.488842\pi$
$998$	−29.0773	+	50.3634i	−0.920427	+	1.59423i
$999$	42.1947	+	0.433325i	1.33498	+	0.0137098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.u.a.59.3	✓	88
3.2	odd	2		945.2.u.a.584.42		88
5.4	even	2	inner	315.2.u.a.59.42	yes	88
7.5	odd	6		315.2.bq.a.194.42	yes	88
9.2	odd	6		315.2.bq.a.164.3	yes	88
9.7	even	3		945.2.bq.a.899.42		88
15.14	odd	2		945.2.u.a.584.3		88
21.5	even	6		945.2.bq.a.719.3		88
35.19	odd	6		315.2.bq.a.194.3	yes	88
45.29	odd	6		315.2.bq.a.164.42	yes	88
45.34	even	6		945.2.bq.a.899.3		88
63.47	even	6	inner	315.2.u.a.299.42	yes	88
63.61	odd	6		945.2.u.a.89.3		88
105.89	even	6		945.2.bq.a.719.42		88
315.124	odd	6		945.2.u.a.89.42		88
315.299	even	6	inner	315.2.u.a.299.3	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.u.a.59.3	✓	88	1.1	even	1	trivial
315.2.u.a.59.42	yes	88	5.4	even	2	inner
315.2.u.a.299.3	yes	88	315.299	even	6	inner
315.2.u.a.299.42	yes	88	63.47	even	6	inner
315.2.bq.a.164.3	yes	88	9.2	odd	6
315.2.bq.a.164.42	yes	88	45.29	odd	6
315.2.bq.a.194.3	yes	88	35.19	odd	6
315.2.bq.a.194.42	yes	88	7.5	odd	6
945.2.u.a.89.3		88	63.61	odd	6
945.2.u.a.89.42		88	315.124	odd	6
945.2.u.a.584.3		88	15.14	odd	2
945.2.u.a.584.42		88	3.2	odd	2
945.2.bq.a.719.3		88	21.5	even	6
945.2.bq.a.719.42		88	105.89	even	6
945.2.bq.a.899.3		88	45.34	even	6
945.2.bq.a.899.42		88	9.7	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26586 + 2.19253i) q^{2} +(-0.586821 - 1.62961i) q^{3} +(-2.20480 - 3.81882i) q^{4} +(1.14318 - 1.92175i) q^{5} +(4.31581 + 0.776236i) q^{6} +(-1.80040 + 1.93870i) q^{7} +6.10041 q^{8} +(-2.31128 + 1.91258i) q^{9} +(2.76640 + 4.93913i) q^{10} -1.42464i q^{11} +(-4.92938 + 5.83393i) q^{12} +(-2.08746 + 3.61559i) q^{13} +(-1.97160 - 6.40156i) q^{14} +(-3.80256 - 0.735214i) q^{15} +(-3.31266 + 5.73769i) q^{16} +(-4.27416 - 2.46769i) q^{17} +(-1.26765 - 7.48862i) q^{18} +(-4.54377 + 2.62335i) q^{19} +(-9.85931 - 0.128519i) q^{20} +(4.21584 + 1.79629i) q^{21} +(3.12356 + 1.80339i) q^{22} +0.477695 q^{23} +(-3.57985 - 9.94130i) q^{24} +(-2.38628 - 4.39382i) q^{25} +(-5.28486 - 9.15364i) q^{26} +(4.47308 + 2.64415i) q^{27} +(11.3731 + 2.60098i) q^{28} +(-1.74963 + 1.01015i) q^{29} +(6.42548 - 7.40655i) q^{30} +(-9.21833 + 5.32221i) q^{31} +(-2.28631 - 3.96000i) q^{32} +(-2.32161 + 0.836008i) q^{33} +(10.8210 - 6.24749i) q^{34} +(1.66752 + 5.67621i) q^{35} +(12.3997 + 4.60951i) q^{36} +(7.03282 - 4.06040i) q^{37} -13.2831i q^{38} +(7.11697 + 1.28005i) q^{39} +(6.97386 - 11.7235i) q^{40} +(-0.421048 + 0.729276i) q^{41} +(-9.27509 + 6.96952i) q^{42} +(-3.70789 + 2.14075i) q^{43} +(-5.44044 + 3.14104i) q^{44} +(1.03331 + 6.62814i) q^{45} +(-0.604694 + 1.04736i) q^{46} +(-4.28080 - 2.47152i) q^{47} +(11.2942 + 2.03135i) q^{48} +(-0.517101 - 6.98087i) q^{49} +(12.6543 + 0.329960i) q^{50} +(-1.51321 + 8.41332i) q^{51} +18.4097 q^{52} +(2.33122 - 4.03778i) q^{53} +(-11.4597 + 6.46025i) q^{54} +(-2.73781 - 1.62862i) q^{55} +(-10.9832 + 11.8268i) q^{56} +(6.94142 + 5.86515i) q^{57} -5.11484i q^{58} +(0.101230 + 0.175335i) q^{59} +(5.57622 + 16.1423i) q^{60} +(-1.54473 - 0.891848i) q^{61} -26.9486i q^{62} +(0.453313 - 7.92430i) q^{63} -1.67406 q^{64} +(4.56193 + 8.14485i) q^{65} +(1.10586 - 6.14847i) q^{66} +(-2.06388 + 1.19158i) q^{67} +21.7630i q^{68} +(-0.280322 - 0.778458i) q^{69} +(-14.5561 - 3.52920i) q^{70} -11.7260i q^{71} +(-14.0998 + 11.6675i) q^{72} +(-4.52420 + 7.83614i) q^{73} +20.5596i q^{74} +(-5.75991 + 6.46710i) q^{75} +(20.0362 + 11.5679i) q^{76} +(2.76194 + 2.56492i) q^{77} +(-11.8156 + 13.9838i) q^{78} +(-0.226118 + 0.391648i) q^{79} +(7.23947 + 12.9253i) q^{80} +(1.68404 - 8.84104i) q^{81} +(-1.06597 - 1.84632i) q^{82} +(-10.6524 + 6.15019i) q^{83} +(-2.43536 - 20.0600i) q^{84} +(-9.62843 + 5.39288i) q^{85} -10.8395i q^{86} +(2.67288 + 2.25845i) q^{87} -8.69087i q^{88} +(1.33067 + 2.30479i) q^{89} +(-15.8404 - 6.12473i) q^{90} +(-3.25126 - 10.5565i) q^{91} +(-1.05322 - 1.82423i) q^{92} +(14.0827 + 11.8991i) q^{93} +(10.8378 - 6.25719i) q^{94} +(-0.152916 + 11.7310i) q^{95} +(-5.11162 + 6.04962i) q^{96} +(-4.69437 - 8.13089i) q^{97} +(15.9604 + 7.70304i) q^{98} +(2.72474 + 3.29274i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 38 q^{4} - 6 q^{5} + 12 q^{6} - 6 q^{9} - 6 q^{10} - 12 q^{14} - 6 q^{15} - 26 q^{16} - 12 q^{19} + 6 q^{20} - 12 q^{21} - 42 q^{24} - 2 q^{25} + 12 q^{26} + 6 q^{29} - 18 q^{30} - 6 q^{31} + 12 q^{34}+ \cdots + 30 q^{99}+O(q^{100}) \) 88 * q - 38 * q^4 - 6 * q^5 + 12 * q^6 - 6 * q^9 - 6 * q^10 - 12 * q^14 - 6 * q^15 - 26 * q^16 - 12 * q^19 + 6 * q^20 - 12 * q^21 - 42 * q^24 - 2 * q^25 + 12 * q^26 + 6 * q^29 - 18 * q^30 - 6 * q^31 + 12 * q^34 - 36 * q^36 - 6 * q^41 + 84 * q^44 - 12 * q^45 - 18 * q^46 + 10 * q^49 + 30 * q^50 - 6 * q^51 - 48 * q^54 - 90 * q^56 - 6 * q^59 + 54 * q^60 + 12 * q^61 - 8 * q^64 + 54 * q^65 + 78 * q^66 - 60 * q^69 - 30 * q^70 + 12 * q^75 + 48 * q^76 + 8 * q^79 + 69 * q^80 + 42 * q^81 + 120 * q^84 - 7 * q^85 - 72 * q^89 - 33 * q^90 + 20 * q^91 - 6 * q^94 - 93 * q^95 - 12 * q^96 + 30 * q^99

Introduction

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