LMFDB - Embedded newform 315.2.k.c.16.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,2,Mod(16,315)] 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([4, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("315.16"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.9
Character	$\chi$	$=$	315.16
Dual form			315.2.k.c.256.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0127903 - 0.0221535i) q^{2} +(-1.71905 - 0.211800i) q^{3} +(0.999673 - 1.73148i) q^{4} +1.00000 q^{5} +(0.0172951 + 0.0407920i) q^{6} +(0.170066 + 2.64028i) q^{7} -0.102306 q^{8} +(2.91028 + 0.728190i) q^{9} +(-0.0127903 - 0.0221535i) q^{10} +3.78014 q^{11} +(-2.08522 + 2.76478i) q^{12} +(-2.77025 - 4.79822i) q^{13} +(0.0563162 - 0.0375376i) q^{14} +(-1.71905 - 0.211800i) q^{15} +(-1.99804 - 3.46070i) q^{16} +(-0.271942 - 0.471017i) q^{17} +(-0.0210915 - 0.0737866i) q^{18} +(3.62126 - 6.27220i) q^{19} +(0.999673 - 1.73148i) q^{20} +(0.266858 - 4.57480i) q^{21} +(-0.0483491 - 0.0837432i) q^{22} +7.25591 q^{23} +(0.175869 + 0.0216683i) q^{24} +1.00000 q^{25} +(-0.0708649 + 0.122742i) q^{26} +(-4.84870 - 1.86819i) q^{27} +(4.74161 + 2.34495i) q^{28} +(-4.04878 + 7.01269i) q^{29} +(0.0172951 + 0.0407920i) q^{30} +(-0.870826 + 1.50832i) q^{31} +(-0.153417 + 0.265726i) q^{32} +(-6.49825 - 0.800632i) q^{33} +(-0.00695644 + 0.0120489i) q^{34} +(0.170066 + 2.64028i) q^{35} +(4.17018 - 4.31116i) q^{36} +(1.67242 - 2.89671i) q^{37} -0.185268 q^{38} +(3.74595 + 8.83513i) q^{39} -0.102306 q^{40} +(0.238169 + 0.412522i) q^{41} +(-0.104761 + 0.0526013i) q^{42} +(-0.279323 + 0.483802i) q^{43} +(3.77890 - 6.54524i) q^{44} +(2.91028 + 0.728190i) q^{45} +(-0.0928054 - 0.160744i) q^{46} +(4.28862 + 7.42811i) q^{47} +(2.70175 + 6.37231i) q^{48} +(-6.94215 + 0.898045i) q^{49} +(-0.0127903 - 0.0221535i) q^{50} +(0.367721 + 0.867300i) q^{51} -11.0774 q^{52} +(-4.26510 - 7.38738i) q^{53} +(0.0206294 + 0.131310i) q^{54} +3.78014 q^{55} +(-0.0173988 - 0.270116i) q^{56} +(-7.55358 + 10.0153i) q^{57} +0.207141 q^{58} +(-0.704208 + 1.21972i) q^{59} +(-2.08522 + 2.76478i) q^{60} +(-0.877009 - 1.51902i) q^{61} +0.0445526 q^{62} +(-1.42768 + 7.80780i) q^{63} -7.98430 q^{64} +(-2.77025 - 4.79822i) q^{65} +(0.0653779 + 0.154199i) q^{66} +(-6.19157 + 10.7241i) q^{67} -1.08741 q^{68} +(-12.4733 - 1.53680i) q^{69} +(0.0563162 - 0.0375376i) q^{70} +10.3293 q^{71} +(-0.297739 - 0.0744980i) q^{72} +(2.91561 + 5.04998i) q^{73} -0.0855629 q^{74} +(-1.71905 - 0.211800i) q^{75} +(-7.24015 - 12.5403i) q^{76} +(0.642874 + 9.98062i) q^{77} +(0.147817 - 0.195990i) q^{78} +(-1.48332 - 2.56918i) q^{79} +(-1.99804 - 3.46070i) q^{80} +(7.93948 + 4.23847i) q^{81} +(0.00609253 - 0.0105526i) q^{82} +(-3.97711 + 6.88856i) q^{83} +(-7.65442 - 5.03536i) q^{84} +(-0.271942 - 0.471017i) q^{85} +0.0142905 q^{86} +(8.44534 - 11.1976i) q^{87} -0.386730 q^{88} +(-9.02021 + 15.6235i) q^{89} +(-0.0210915 - 0.0737866i) q^{90} +(12.1975 - 8.13026i) q^{91} +(7.25354 - 12.5635i) q^{92} +(1.81646 - 2.40843i) q^{93} +(0.109706 - 0.190016i) q^{94} +(3.62126 - 6.27220i) q^{95} +(0.320012 - 0.424303i) q^{96} +(-3.81553 + 6.60869i) q^{97} +(0.108687 + 0.142307i) q^{98} +(11.0013 + 2.75266i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23}+ \cdots - 89 q^{99}+O(q^{100}) $ 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.0127903	−	0.0221535i	−0.00904412	−	0.0156649i	0.861468	−	0.507812i	$-0.169546\pi$
$2$	−0.0127903	−	0.0221535i	−0.00904412	−	0.0156649i	−0.870512	+	0.492147i	$0.836212\pi$
$3$	−1.71905	−	0.211800i	−0.992495	−	0.122283i
$3$	−1.71905	−	0.211800i	−0.992495	−	0.122283i
$4$	0.999673	−	1.73148i	0.499836	−	0.865742i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.0172951	+	0.0407920i	0.00706071	+	0.0166533i
$7$	0.170066	+	2.64028i	0.0642790	+	0.997932i
$7$	0.170066	+	2.64028i	0.0642790	+	0.997932i
$8$	−0.102306			−0.0361706
$9$	2.91028	+	0.728190i	0.970094	+	0.242730i
$10$	−0.0127903	−	0.0221535i	−0.00404465	−	0.00700555i
$11$	3.78014			1.13975			0.569877	−	0.821730i	$-0.306991\pi$
$11$	3.78014			1.13975			0.569877	+	0.821730i	$0.306991\pi$
$12$	−2.08522	+	2.76478i	−0.601951	+	0.798124i
$13$	−2.77025	−	4.79822i	−0.768330	−	1.33079i	−0.938468	−	0.345367i	$-0.887754\pi$
$13$	−2.77025	−	4.79822i	−0.768330	−	1.33079i	0.170137	−	0.985420i	$-0.445579\pi$
$14$	0.0563162	−	0.0375376i	0.0150511	−	0.0100323i
$15$	−1.71905	−	0.211800i	−0.443857	−	0.0546865i
$16$	−1.99804	−	3.46070i	−0.499509	−	0.865175i
$17$	−0.271942	−	0.471017i	−0.0659555	−	0.114238i	0.831162	−	0.556030i	$-0.187676\pi$
$17$	−0.271942	−	0.471017i	−0.0659555	−	0.114238i	−0.897117	+	0.441792i	$0.854343\pi$
$18$	−0.0210915	−	0.0737866i	−0.00497131	−	0.0173917i
$19$	3.62126	−	6.27220i	0.830774	−	1.43894i	−0.0666517	−	0.997776i	$-0.521232\pi$
$19$	3.62126	−	6.27220i	0.830774	−	1.43894i	0.897425	−	0.441166i	$-0.145435\pi$
$20$	0.999673	−	1.73148i	0.223534	−	0.387172i
$21$	0.266858	−	4.57480i	0.0582331	−	0.998303i
$22$	−0.0483491	−	0.0837432i	−0.0103081	−	0.0178541i
$23$	7.25591			1.51296			0.756481	−	0.654016i	$-0.226917\pi$
$23$	7.25591			1.51296			0.756481	+	0.654016i	$0.226917\pi$
$24$	0.175869	+	0.0216683i	0.0358991	+	0.00442303i
$25$	1.00000			0.200000
$26$	−0.0708649	+	0.122742i	−0.0138977	+	0.0240716i
$27$	−4.84870	−	1.86819i	−0.933132	−	0.359534i
$28$	4.74161	+	2.34495i	0.896081	+	0.443154i
$29$	−4.04878	+	7.01269i	−0.751839	+	1.30222i	0.195092	+	0.980785i	$0.437500\pi$
$29$	−4.04878	+	7.01269i	−0.751839	+	1.30222i	−0.946931	+	0.321438i	$0.895834\pi$
$30$	0.0172951	+	0.0407920i	0.00315764	+	0.00744756i
$31$	−0.870826	+	1.50832i	−0.156405	+	0.270901i	−0.933570	−	0.358396i	$-0.883324\pi$
$31$	−0.870826	+	1.50832i	−0.156405	+	0.270901i	0.777165	+	0.629297i	$0.216657\pi$
$32$	−0.153417	+	0.265726i	−0.0271205	+	0.0469741i
$33$	−6.49825	−	0.800632i	−1.13120	−	0.139372i
$34$	−0.00695644	+	0.0120489i	−0.00119302	+	0.00206637i
$35$	0.170066	+	2.64028i	0.0287465	+	0.446289i
$36$	4.17018	−	4.31116i	0.695030	−	0.718526i
$37$	1.67242	−	2.89671i	0.274943	−	0.476216i	−0.695177	−	0.718838i	$-0.744674\pi$
$37$	1.67242	−	2.89671i	0.274943	−	0.476216i	0.970121	+	0.242622i	$0.0780076\pi$
$38$	−0.185268			−0.0300545
$39$	3.74595	+	8.83513i	0.599832	+	1.41475i
$40$	−0.102306			−0.0161760
$41$	0.238169	+	0.412522i	0.0371958	+	0.0644250i	0.884024	−	0.467441i	$-0.154824\pi$
$41$	0.238169	+	0.412522i	0.0371958	+	0.0644250i	−0.846828	+	0.531867i	$0.821491\pi$
$42$	−0.104761	+	0.0526013i	−0.0161650	+	0.00811656i
$43$	−0.279323	+	0.483802i	−0.0425964	+	0.0737791i	−0.886538	−	0.462657i	$-0.846896\pi$
$43$	−0.279323	+	0.483802i	−0.0425964	+	0.0737791i	0.843941	+	0.536436i	$0.180230\pi$
$44$	3.77890	−	6.54524i	0.569690	−	0.986733i
$45$	2.91028	+	0.728190i	0.433839	+	0.108552i
$46$	−0.0928054	−	0.160744i	−0.0136834	−	0.0237004i
$47$	4.28862	+	7.42811i	0.625560	+	1.08350i	0.988432	+	0.151663i	$0.0484628\pi$
$47$	4.28862	+	7.42811i	0.625560	+	1.08350i	−0.362872	+	0.931839i	$0.618204\pi$
$48$	2.70175	+	6.37231i	0.389965	+	0.919764i
$49$	−6.94215	+	0.898045i	−0.991736	+	0.128292i
$50$	−0.0127903	−	0.0221535i	−0.00180882	−	0.00313298i
$51$	0.367721	+	0.867300i	0.0514912	+	0.121446i
$52$	−11.0774			−1.53616
$53$	−4.26510	−	7.38738i	−0.585857	−	1.01473i	−0.994768	−	0.102160i	$-0.967425\pi$
$53$	−4.26510	−	7.38738i	−0.585857	−	1.01473i	0.408911	−	0.912574i	$-0.365909\pi$
$54$	0.0206294	+	0.131310i	0.00280730	+	0.0178691i
$55$	3.78014			0.509713
$56$	−0.0173988	−	0.270116i	−0.00232501	−	0.0360958i
$57$	−7.55358	+	10.0153i	−1.00050	+	1.32655i
$58$	0.207141			0.0271989
$59$	−0.704208	+	1.21972i	−0.0916801	+	0.158795i	−0.908218	−	0.418497i	$-0.862557\pi$
$59$	−0.704208	+	1.21972i	−0.0916801	+	0.158795i	0.816538	+	0.577292i	$0.195890\pi$
$60$	−2.08522	+	2.76478i	−0.269200	+	0.356932i
$61$	−0.877009	−	1.51902i	−0.112289	−	0.194491i	0.804404	−	0.594083i	$-0.202485\pi$
$61$	−0.877009	−	1.51902i	−0.112289	−	0.194491i	−0.916693	+	0.399592i	$0.869152\pi$
$62$	0.0445526			0.00565818
$63$	−1.42768	+	7.80780i	−0.179871	+	0.983690i
$64$	−7.98430			−0.998037
$65$	−2.77025	−	4.79822i	−0.343608	−	0.595146i
$66$	0.0653779	+	0.154199i	0.00804746	+	0.0189806i
$67$	−6.19157	+	10.7241i	−0.756421	+	1.31016i	0.188244	+	0.982122i	$0.439720\pi$
$67$	−6.19157	+	10.7241i	−0.756421	+	1.31016i	−0.944665	+	0.328037i	$0.893613\pi$
$68$	−1.08741			−0.131868
$69$	−12.4733	−	1.53680i	−1.50161	−	0.185009i
$70$	0.0563162	−	0.0375376i	0.00673107	−	0.00448660i
$71$	10.3293			1.22587			0.612934	−	0.790134i	$-0.289989\pi$
$71$	10.3293			1.22587			0.612934	+	0.790134i	$0.289989\pi$
$72$	−0.297739	−	0.0744980i	−0.0350888	−	0.00877968i
$73$	2.91561	+	5.04998i	0.341246	+	0.591055i	0.984664	−	0.174459i	$-0.0558178\pi$
$73$	2.91561	+	5.04998i	0.341246	+	0.591055i	−0.643418	+	0.765515i	$0.722484\pi$
$74$	−0.0855629			−0.00994648
$75$	−1.71905	−	0.211800i	−0.198499	−	0.0244565i
$76$	−7.24015	−	12.5403i	−0.830502	−	1.43847i
$77$	0.642874	+	9.98062i	0.0732622	+	1.13740i
$78$	0.147817	−	0.195990i	0.0167370	−	0.0221915i
$79$	−1.48332	−	2.56918i	−0.166886	−	0.289056i	0.770437	−	0.637516i	$-0.220038\pi$
$79$	−1.48332	−	2.56918i	−0.166886	−	0.289056i	−0.937324	+	0.348460i	$0.886705\pi$
$80$	−1.99804	−	3.46070i	−0.223387	−	0.386918i
$81$	7.93948	+	4.23847i	0.882164	+	0.470942i
$82$	0.00609253	−	0.0105526i	0.000672807	−	0.00116534i
$83$	−3.97711	+	6.88856i	−0.436544	+	0.756117i	−0.997420	−	0.0717828i	$-0.977131\pi$
$83$	−3.97711	+	6.88856i	−0.436544	+	0.756117i	0.560876	+	0.827900i	$0.310465\pi$
$84$	−7.65442	−	5.03536i	−0.835166	−	0.549403i
$85$	−0.271942	−	0.471017i	−0.0294962	−	0.0510889i
$86$	0.0142905			0.00154099
$87$	8.44534	−	11.1976i	0.905436	−	1.20051i
$88$	−0.386730			−0.0412255
$89$	−9.02021	+	15.6235i	−0.956141	+	1.65608i	−0.224405	+	0.974496i	$0.572044\pi$
$89$	−9.02021	+	15.6235i	−0.956141	+	1.65608i	−0.731736	+	0.681588i	$0.761290\pi$
$90$	−0.0210915	−	0.0737866i	−0.00222324	−	0.00777780i
$91$	12.1975	−	8.13026i	1.27865	−	0.852283i
$92$	7.25354	−	12.5635i	0.756233	−	1.30983i
$93$	1.81646	−	2.40843i	0.188358	−	0.249743i
$94$	0.109706	−	0.190016i	0.0113153	−	0.0195986i
$95$	3.62126	−	6.27220i	0.371533	−	0.643515i
$96$	0.320012	−	0.424303i	0.0326611	−	0.0433052i
$97$	−3.81553	+	6.60869i	−0.387408	+	0.671011i	−0.992100	−	0.125449i	$-0.959963\pi$
$97$	−3.81553	+	6.60869i	−0.387408	+	0.671011i	0.604692	+	0.796460i	$0.293296\pi$
$98$	0.108687	+	0.142307i	0.0109791	+	0.0143751i
$99$	11.0013	+	2.75266i	1.10567	+	0.276652i
$100$	0.999673	−	1.73148i	0.0999673	−	0.173148i
$101$	−3.42479			−0.340780			−0.170390	−	0.985377i	$-0.554503\pi$
$101$	−3.42479			−0.340780			−0.170390	+	0.985377i	$0.554503\pi$
$102$	0.0145104	−	0.0192393i	0.00143675	−	0.00190498i
$103$	9.43055			0.929219			0.464610	−	0.885516i	$-0.346195\pi$
$103$	9.43055			0.929219			0.464610	+	0.885516i	$0.346195\pi$
$104$	0.283413	+	0.490886i	0.0277909	+	0.0481353i
$105$	0.266858	−	4.57480i	0.0260426	−	0.446455i
$106$	−0.109104	+	0.188974i	−0.0105971	+	0.0183548i
$107$	0.0944380	−	0.163571i	0.00912967	−	0.0158131i	−0.861424	−	0.507886i	$-0.830427\pi$
$107$	0.0944380	−	0.163571i	0.00912967	−	0.0158131i	0.870554	+	0.492073i	$0.163761\pi$
$108$	−8.08186	+	6.52786i	−0.777677	+	0.628144i
$109$	4.40407	+	7.62807i	0.421833	+	0.730636i	0.996119	−	0.0880186i	$-0.0280535\pi$
$109$	4.40407	+	7.62807i	0.421833	+	0.730636i	−0.574286	+	0.818655i	$0.694720\pi$
$110$	−0.0483491	−	0.0837432i	−0.00460991	−	0.00798460i
$111$	−3.48849	+	4.62538i	−0.331113	+	0.439021i
$112$	8.79742	−	5.86393i	0.831278	−	0.554089i
$113$	−5.83704	−	10.1101i	−0.549103	−	0.951074i	−0.998336	−	0.0576593i	$-0.981636\pi$
$113$	−5.83704	−	10.1101i	−0.549103	−	0.951074i	0.449234	−	0.893414i	$-0.351697\pi$
$114$	0.318486	+	0.0392398i	0.0298289	+	0.00367514i
$115$	7.25591			0.676617
$116$	8.09490	+	14.0208i	0.751593	+	1.30180i
$117$	−4.56821	−	15.9814i	−0.422331	−	1.47749i
$118$	0.0360282			0.00331666
$119$	1.19737	−	0.798106i	0.109763	−	0.0731623i
$120$	0.175869	+	0.0216683i	0.0160546	+	0.00197804i
$121$	3.28942			0.299039
$122$	−0.0224344	+	0.0388576i	−0.00203112	+	0.00351800i
$123$	−0.322054	−	0.759590i	−0.0290386	−	0.0684900i
$124$	1.74108	+	3.01564i	0.156354	+	0.270813i
$125$	1.00000			0.0894427
$126$	0.191230	−	0.0682361i	0.0170362	−	0.00607895i
$127$	1.14668			0.101751			0.0508756	−	0.998705i	$-0.483799\pi$
$127$	1.14668			0.101751			0.0508756	+	0.998705i	$0.483799\pi$
$128$	0.408955	+	0.708332i	0.0361469	+	0.0626083i
$129$	0.582640	−	0.772520i	0.0512986	−	0.0680166i
$130$	−0.0708649	+	0.122742i	−0.00621526	+	0.0107651i
$131$	−6.36247			−0.555891			−0.277946	−	0.960597i	$-0.589654\pi$
$131$	−6.36247			−0.555891			−0.277946	+	0.960597i	$0.589654\pi$
$132$	−7.88241	+	10.4512i	−0.686075	+	0.909664i
$133$	17.1762	+	8.49445i	1.48937	+	0.736562i
$134$	0.316769			0.0273646
$135$	−4.84870	−	1.86819i	−0.417309	−	0.160788i
$136$	0.0278212	+	0.0481878i	0.00238565	+	0.00413207i
$137$	−8.55962			−0.731297			−0.365649	−	0.930753i	$-0.619153\pi$
$137$	−8.55962			−0.731297			−0.365649	+	0.930753i	$0.619153\pi$
$138$	0.125492	+	0.295983i	0.0106826	+	0.0251957i
$139$	−3.08779	−	5.34821i	−0.261903	−	0.453630i	0.704844	−	0.709362i	$-0.251017\pi$
$139$	−3.08779	−	5.34821i	−0.261903	−	0.453630i	−0.966748	+	0.255732i	$0.917683\pi$
$140$	4.74161	+	2.34495i	0.400739	+	0.198184i
$141$	−5.79910	−	13.6776i	−0.488372	−	1.15187i
$142$	−0.132116	−	0.228831i	−0.0110869	−	0.0192031i
$143$	−10.4719	−	18.1379i	−0.875707	−	1.51677i
$144$	−3.29480	−	11.5266i	−0.274567	−	0.960547i
$145$	−4.04878	+	7.01269i	−0.336233	+	0.582372i
$146$	0.0745831	−	0.129182i	0.00617254	−	0.0106912i
$147$	12.1241	−	0.0734403i	0.999982	−	0.00605725i
$148$	−3.34374	−	5.79152i	−0.274853	−	0.476060i
$149$	4.69295			0.384461			0.192231	−	0.981350i	$-0.438428\pi$
$149$	4.69295			0.384461			0.192231	+	0.981350i	$0.438428\pi$
$150$	0.0172951	+	0.0407920i	0.00141214	+	0.00333065i
$151$	−15.6125			−1.27053			−0.635265	−	0.772294i	$-0.719109\pi$
$151$	−15.6125			−1.27053			−0.635265	+	0.772294i	$0.719109\pi$
$152$	−0.370476	+	0.641683i	−0.0300496	+	0.0520474i
$153$	−0.448437	−	1.56882i	−0.0362540	−	0.126831i
$154$	0.212883	−	0.141897i	0.0171546	−	0.0114344i
$155$	−0.870826	+	1.50832i	−0.0699464	+	0.121151i
$156$	19.0426	+	2.34619i	1.52463	+	0.187845i
$157$	9.28453	−	16.0813i	0.740986	−	1.28343i	−0.211061	−	0.977473i	$-0.567692\pi$
$157$	9.28453	−	16.0813i	0.740986	−	1.28343i	0.952047	−	0.305953i	$-0.0989749\pi$
$158$	−0.0379442	+	0.0657213i	−0.00301868	+	0.00522851i
$159$	5.76729	+	13.6026i	0.457376	+	1.07876i
$160$	−0.153417	+	0.265726i	−0.0121287	+	0.0210075i
$161$	1.23399	+	19.1576i	0.0972517	+	1.50983i
$162$	−0.00765153	−	0.230099i	−0.000601161	−	0.0180782i
$163$	−0.655557	+	1.13546i	−0.0513472	+	0.0889359i	−0.890557	−	0.454872i	$-0.849685\pi$
$163$	−0.655557	+	1.13546i	−0.0513472	+	0.0889359i	0.839209	+	0.543808i	$0.183018\pi$
$164$	0.952366			0.0743673
$165$	−6.49825	−	0.800632i	−0.505888	−	0.0623291i
$166$	0.203474			0.0157926
$167$	5.56450	+	9.63799i	0.430594	+	0.745810i	0.996925	−	0.0783678i	$-0.0249709\pi$
$167$	5.56450	+	9.63799i	0.430594	+	0.745810i	−0.566331	+	0.824178i	$0.691638\pi$
$168$	−0.0273011	+	0.468028i	−0.00210632	+	0.0361092i
$169$	−8.84862	+	15.3263i	−0.680663	+	1.17894i
$170$	−0.00695644	+	0.0120489i	−0.000533535	+	0.000924109i
$171$	15.1062	−	15.6169i	1.15520	−	1.19426i
$172$	0.558463	+	0.967287i	0.0425824	+	0.0737549i
$173$	0.712352	+	1.23383i	0.0541592	+	0.0938064i	0.891834	−	0.452363i	$-0.149419\pi$
$173$	0.712352	+	1.23383i	0.0541592	+	0.0938064i	−0.837675	+	0.546169i	$0.816085\pi$
$174$	−0.356085	−	0.0438723i	−0.0269948	−	0.00332595i
$175$	0.170066	+	2.64028i	0.0128558	+	0.199586i
$176$	−7.55285	−	13.0819i	−0.569318	−	0.986087i
$177$	1.46891	−	1.94762i	0.110410	−	0.146392i
$178$	0.461486			0.0345898
$179$	−6.28599	−	10.8877i	−0.469837	−	0.813782i	0.529568	−	0.848267i	$-0.322354\pi$
$179$	−6.28599	−	10.8877i	−0.469837	−	0.813782i	−0.999405	+	0.0344857i	$0.989021\pi$
$180$	4.17018	−	4.31116i	0.310827	−	0.321335i
$181$	−14.1730			−1.05347			−0.526735	−	0.850029i	$-0.676584\pi$
$181$	−14.1730			−1.05347			−0.526735	+	0.850029i	$0.676584\pi$
$182$	−0.336124	−	0.166229i	−0.0249152	−	0.0123217i
$183$	1.18589	+	2.79703i	0.0876639	+	0.206762i
$184$	−0.742322			−0.0547247
$185$	1.67242	−	2.89671i	0.122958	−	0.212970i
$186$	−0.0765882	−	0.00943622i	−0.00561572	−	0.000691897i
$187$	−1.02798	−	1.78051i	−0.0751731	−	0.130204i
$188$	17.1489			1.25071
$189$	4.10795	−	13.1196i	0.298810	−	0.954313i
$190$	−0.185268			−0.0134408
$191$	−5.09023	−	8.81654i	−0.368316	−	0.637942i	0.620986	−	0.783821i	$-0.286732\pi$
$191$	−5.09023	−	8.81654i	−0.368316	−	0.637942i	−0.989302	+	0.145879i	$0.953399\pi$
$192$	13.7254	+	1.69107i	0.990547	+	0.122043i
$193$	3.42575	−	5.93357i	0.246591	−	0.427108i	−0.715987	−	0.698114i	$-0.754023\pi$
$193$	3.42575	−	5.93357i	0.246591	−	0.427108i	0.962578	+	0.271006i	$0.0873563\pi$
$194$	0.195207			0.0140151
$195$	3.74595	+	8.83513i	0.268253	+	0.632697i
$196$	−5.38493	+	12.9180i	−0.384638	+	0.922713i
$197$	−20.0167			−1.42613			−0.713065	−	0.701098i	$-0.752693\pi$
$197$	−20.0167			−1.42613			−0.713065	+	0.701098i	$0.752693\pi$
$198$	−0.0797287	−	0.278924i	−0.00566607	−	0.0198222i
$199$	6.47405	+	11.2134i	0.458933	+	0.794896i	0.998905	−	0.0467876i	$-0.0148984\pi$
$199$	6.47405	+	11.2134i	0.458933	+	0.794896i	−0.539972	+	0.841683i	$0.681565\pi$
$200$	−0.102306			−0.00723411
$201$	12.9150	−	17.1239i	0.910954	−	1.20783i
$202$	0.0438042	+	0.0758711i	0.00308205	+	0.00533827i
$203$	−19.2040	−	9.49728i	−1.34786	−	0.666578i
$204$	1.86932	+	0.230313i	0.130878	+	0.0161252i
$205$	0.238169	+	0.412522i	0.0166345	+	0.0288118i
$206$	−0.120620	−	0.208919i	−0.00840397	−	0.0145561i
$207$	21.1167	+	5.28368i	1.46772	+	0.367241i
$208$	−11.0701	+	19.1740i	−0.767576	+	1.32948i
$209$	13.6888	−	23.7098i	0.946878	−	1.64004i
$210$	−0.104761	+	0.0526013i	−0.00722919	+	0.00362984i
$211$	6.43285	+	11.1420i	0.442856	+	0.767048i	0.997900	−	0.0647723i	$-0.0206321\pi$
$211$	6.43285	+	11.1420i	0.442856	+	0.767048i	−0.555045	+	0.831821i	$0.687299\pi$
$212$	−17.0548			−1.17133
$213$	−17.7567	−	2.18775i	−1.21667	−	0.149902i
$214$	−0.00483157			−0.000330279
$215$	−0.279323	+	0.483802i	−0.0190497	+	0.0329950i
$216$	0.496050	+	0.191127i	0.0337519	+	0.0130045i
$217$	−4.13047	−	2.04271i	−0.280395	−	0.138668i
$218$	0.112659	−	0.195131i	0.00763022	−	0.0132159i
$219$	−3.94250	−	9.29870i	−0.266409	−	0.628348i
$220$	3.77890	−	6.54524i	0.254773	−	0.441280i
$221$	−1.50670	+	2.60967i	−0.101351	+	0.175546i
$222$	0.147087	+	0.0181222i	0.00987184	+	0.00121628i
$223$	6.20544	−	10.7481i	0.415547	−	0.719749i	−0.579939	−	0.814660i	$-0.696923\pi$
$223$	6.20544	−	10.7481i	0.415547	−	0.719749i	0.995486	+	0.0949115i	$0.0302568\pi$
$224$	−0.727682	−	0.359872i	−0.0486203	−	0.0240450i
$225$	2.91028	+	0.728190i	0.194019	+	0.0485460i
$226$	−0.149315	+	0.258622i	−0.00993230	+	0.0172032i
$227$	8.86221			0.588206			0.294103	−	0.955774i	$-0.404979\pi$
$227$	8.86221			0.588206			0.294103	+	0.955774i	$0.404979\pi$
$228$	9.79016	+	23.0909i	0.648369	+	1.52923i
$229$	26.3169			1.73907			0.869536	−	0.493869i	$-0.164418\pi$
$229$	26.3169			1.73907			0.869536	+	0.493869i	$0.164418\pi$
$230$	−0.0928054	−	0.160744i	−0.00611941	−	0.0105991i
$231$	1.00876	−	17.2934i	0.0663714	−	1.13782i
$232$	0.414213	−	0.717438i	0.0271944	−	0.0471021i
$233$	13.0236	−	22.5576i	0.853208	−	1.47780i	−0.0250903	−	0.999685i	$-0.507987\pi$
$233$	13.0236	−	22.5576i	0.853208	−	1.47780i	0.878298	−	0.478114i	$-0.158679\pi$
$234$	−0.295616	+	0.305609i	−0.0193250	+	0.0199783i
$235$	4.28862	+	7.42811i	0.279759	+	0.484557i
$236$	1.40796	+	2.43865i	0.0916501	+	0.158743i
$237$	2.00575	+	4.73073i	0.130287	+	0.307294i
$238$	−0.0329955	−	0.0163178i	−0.00213878	−	0.00105773i
$239$	9.50084	+	16.4559i	0.614558	+	1.06445i	0.990462	+	0.137787i	$0.0439990\pi$
$239$	9.50084	+	16.4559i	0.614558	+	1.06445i	−0.375904	+	0.926659i	$0.622668\pi$
$240$	2.70175	+	6.37231i	0.174398	+	0.411331i
$241$	−14.2829			−0.920042			−0.460021	−	0.887908i	$-0.652158\pi$
$241$	−14.2829			−0.920042			−0.460021	+	0.887908i	$0.652158\pi$
$242$	−0.0420728	−	0.0728722i	−0.00270454	−	0.00468440i
$243$	−12.7507	−	8.96774i	−0.817956	−	0.575281i
$244$	−3.50689			−0.224505
$245$	−6.94215	+	0.898045i	−0.443518	+	0.0573740i
$246$	−0.0127084	+	0.0168500i	−0.000810258	+	0.00107432i
$247$	−40.1272			−2.55323
$248$	0.0890906	−	0.154309i	0.00565726	−	0.00979866i
$249$	8.29585	−	10.9994i	0.525728	−	0.697061i
$250$	−0.0127903	−	0.0221535i	−0.000808931	−	0.00140111i
$251$	−2.23618			−0.141146			−0.0705731	−	0.997507i	$-0.522483\pi$
$251$	−2.23618			−0.141146			−0.0705731	+	0.997507i	$0.522483\pi$
$252$	12.0919	+	10.2773i	0.761716	+	0.647406i
$253$	27.4283			1.72440
$254$	−0.0146664	−	0.0254029i	−0.000920250	−	0.00159392i
$255$	0.367721	+	0.867300i	0.0230276	+	0.0543124i
$256$	−7.97384	+	13.8111i	−0.498365	+	0.863193i
$257$	−15.7647			−0.983377			−0.491688	−	0.870771i	$-0.663620\pi$
$257$	−15.7647			−0.983377			−0.491688	+	0.870771i	$0.663620\pi$
$258$	−0.0245662	−	0.00302673i	−0.00152942	−	0.000188436i
$259$	7.93254	+	3.92301i	0.492904	+	0.243764i
$260$	−11.0774			−0.686991
$261$	−16.8896	+	17.4606i	−1.04544	+	1.08078i
$262$	0.0813780	+	0.140951i	0.00502755	+	0.00870797i
$263$	−12.7795			−0.788015			−0.394008	−	0.919107i	$-0.628912\pi$
$263$	−12.7795			−0.788015			−0.394008	+	0.919107i	$0.628912\pi$
$264$	0.664809	+	0.0819093i	0.0409161	+	0.00504117i
$265$	−4.26510	−	7.38738i	−0.262003	−	0.453803i
$266$	−0.0315079	−	0.489160i	−0.00193187	−	0.0299923i
$267$	18.8153	−	24.9471i	1.15148	−	1.52674i
$268$	12.3791	+	21.4412i	0.756173	+	1.30973i
$269$	9.82818	+	17.0229i	0.599235	+	1.03790i	0.992934	+	0.118666i	$0.0378617\pi$
$269$	9.82818	+	17.0229i	0.599235	+	1.03790i	−0.393700	+	0.919239i	$0.628805\pi$
$270$	0.0206294	+	0.131310i	0.00125546	+	0.00799129i
$271$	−1.02524	+	1.77577i	−0.0622791	+	0.107871i	−0.895484	−	0.445094i	$-0.853170\pi$
$271$	−1.02524	+	1.77577i	−0.0622791	+	0.107871i	0.833205	+	0.552965i	$0.186504\pi$
$272$	−1.08670	+	1.88222i	−0.0658908	+	0.114126i
$273$	−22.6902	+	11.3929i	−1.37327	+	0.689531i
$274$	0.109480	+	0.189625i	0.00661394	+	0.0114557i
$275$	3.78014			0.227951
$276$	−15.1302	+	20.0610i	−0.910728	+	1.20753i
$277$	6.42013			0.385748			0.192874	−	0.981224i	$-0.438219\pi$
$277$	6.42013			0.385748			0.192874	+	0.981224i	$0.438219\pi$
$278$	−0.0789877	+	0.136811i	−0.00473737	+	0.00820536i
$279$	−3.63269	+	3.75550i	−0.217483	+	0.224836i
$280$	−0.0173988	−	0.270116i	−0.00103978	−	0.0161425i
$281$	−15.3102	+	26.5180i	−0.913327	+	1.58193i	−0.103995	+	0.994578i	$0.533163\pi$
$281$	−15.3102	+	26.5180i	−0.913327	+	1.58193i	−0.809332	+	0.587351i	$0.800171\pi$
$282$	−0.228835	+	0.303412i	−0.0136269	+	0.0180679i
$283$	−4.86470	+	8.42590i	−0.289176	+	0.500868i	−0.973613	−	0.228204i	$-0.926715\pi$
$283$	−4.86470	+	8.42590i	−0.289176	+	0.500868i	0.684437	+	0.729072i	$0.260048\pi$
$284$	10.3260	−	17.8851i	0.612733	−	1.06129i
$285$	−7.55358	+	10.0153i	−0.447436	+	0.593253i
$286$	−0.267879	+	0.463980i	−0.0158400	+	0.0274357i
$287$	−1.04867	+	0.698990i	−0.0619009	+	0.0412601i
$288$	−0.639985	+	0.661620i	−0.0377115	+	0.0389864i
$289$	8.35210	−	14.4663i	0.491300	−	0.850956i
$290$	0.207141			0.0121637
$291$	7.95881	−	10.5526i	0.466554	−	0.618602i
$292$	11.6586			0.682269
$293$	−5.32802	−	9.22840i	−0.311266	−	0.539129i	0.667371	−	0.744726i	$-0.267420\pi$
$293$	−5.32802	−	9.22840i	−0.311266	−	0.539129i	−0.978637	+	0.205597i	$0.934086\pi$
$294$	−0.156698	−	0.267652i	−0.00913884	−	0.0156098i
$295$	−0.704208	+	1.21972i	−0.0410006	+	0.0710151i
$296$	−0.171098	+	0.296350i	−0.00994486	+	0.0172250i
$297$	−18.3287	−	7.06202i	−1.06354	−	0.409780i
$298$	−0.0600243	−	0.103965i	−0.00347712	−	0.00602254i
$299$	−20.1007	−	34.8155i	−1.16245	−	2.01343i
$300$	−2.08522	+	2.76478i	−0.120390	+	0.159625i
$301$	−1.32488	−	0.655213i	−0.0763646	−	0.0377658i
$302$	0.199689	+	0.345872i	0.0114908	+	0.0199027i
$303$	5.88740	+	0.725371i	0.338222	+	0.0416715i
$304$	−28.9416			−1.65992
$305$	−0.877009	−	1.51902i	−0.0502174	−	0.0869790i
$306$	−0.0290191	+	0.0300001i	−0.00165891	+	0.00171499i
$307$	3.58038			0.204343			0.102171	−	0.994767i	$-0.467421\pi$
$307$	3.58038			0.204343			0.102171	+	0.994767i	$0.467421\pi$
$308$	17.9239	+	8.86422i	1.02131	+	0.505086i
$309$	−16.2116	−	1.99739i	−0.922246	−	0.113627i
$310$	0.0445526			0.00253042
$311$	−8.15786	+	14.1298i	−0.462590	+	0.801229i	−0.999089	−	0.0426715i	$-0.986413\pi$
$311$	−8.15786	+	14.1298i	−0.462590	+	0.801229i	0.536499	+	0.843901i	$0.319746\pi$
$312$	−0.383232	−	0.903885i	−0.0216963	−	0.0511724i
$313$	3.43821	+	5.95516i	0.194339	+	0.336606i	0.946684	−	0.322164i	$-0.104410\pi$
$313$	3.43821	+	5.95516i	0.194339	+	0.336606i	−0.752344	+	0.658770i	$0.771077\pi$
$314$	−0.475008			−0.0268063
$315$	−1.42768	+	7.80780i	−0.0804408	+	0.439920i
$316$	−5.93133			−0.333663
$317$	9.97368	+	17.2749i	0.560178	+	0.970256i	0.997480	+	0.0709419i	$0.0226005\pi$
$317$	9.97368	+	17.2749i	0.560178	+	0.970256i	−0.437303	+	0.899314i	$0.644066\pi$
$318$	0.227580	−	0.301748i	0.0127621	−	0.0169212i
$319$	−15.3049	+	26.5089i	−0.856911	+	1.48421i
$320$	−7.98430			−0.446336
$321$	−0.196988	+	0.261186i	−0.0109948	+	0.0145780i
$322$	0.408625	−	0.272369i	0.0227718	−	0.0151785i
$323$	−3.93908			−0.219177
$324$	15.2757	−	9.51000i	0.848652	−	0.528333i
$325$	−2.77025	−	4.79822i	−0.153666	−	0.266157i
$326$	0.0335391			0.00185756
$327$	−5.95520	−	14.0458i	−0.329323	−	0.776736i
$328$	−0.0243661	−	0.0422033i	−0.00134539	−	0.00233029i
$329$	−18.8829	+	12.5864i	−1.04105	+	0.693913i
$330$	0.0653779	+	0.154199i	0.00359894	+	0.00848839i
$331$	5.43065	+	9.40615i	0.298495	+	0.517009i	0.975792	−	0.218701i	$-0.0701820\pi$
$331$	5.43065	+	9.40615i	0.298495	+	0.517009i	−0.677297	+	0.735710i	$0.736849\pi$
$332$	7.95162	+	13.7726i	0.436402	+	0.755870i
$333$	6.97655	−	7.21240i	0.382313	−	0.395237i
$334$	0.142343	−	0.246546i	0.00778868	−	0.0134904i
$335$	−6.19157	+	10.7241i	−0.338282	+	0.585921i
$336$	−16.3652	+	8.21710i	−0.892795	+	0.448280i
$337$	−0.137238	−	0.237703i	−0.00747582	−	0.0129485i	0.862263	−	0.506460i	$-0.169046\pi$
$337$	−0.137238	−	0.237703i	−0.00747582	−	0.0129485i	−0.869739	+	0.493512i	$0.835713\pi$
$338$	0.452707			0.0246240
$339$	7.89287	+	18.6160i	0.428682	+	1.01108i
$340$	−1.08741			−0.0589731
$341$	−3.29184	+	5.70164i	−0.178263	+	0.308761i
$342$	−0.539183	−	0.134910i	−0.0291557	−	0.00729512i
$343$	−3.55172	−	18.1765i	−0.191775	−	0.981439i
$344$	0.0285764	−	0.0494957i	0.00154073	−	0.00266863i
$345$	−12.4733	−	1.53680i	−0.671539	−	0.0827385i
$346$	0.0182224	−	0.0315622i	0.000979644	−	0.00169679i
$347$	−1.89413	+	3.28073i	−0.101682	+	0.176119i	−0.912378	−	0.409349i	$-0.865756\pi$
$347$	−1.89413	+	3.28073i	−0.101682	+	0.176119i	0.810696	+	0.585468i	$0.199089\pi$
$348$	−10.9460	−	25.8170i	−0.586765	−	1.38393i
$349$	14.3243	−	24.8104i	0.766763	−	1.32807i	−0.172547	−	0.985001i	$-0.555200\pi$
$349$	14.3243	−	24.8104i	0.766763	−	1.32807i	0.939310	−	0.343070i	$-0.111467\pi$
$350$	0.0563162	−	0.0375376i	0.00301023	−	0.00200647i
$351$	4.46812	+	28.4405i	0.238491	+	1.51804i
$352$	−0.579937	+	1.00448i	−0.0309107	+	0.0535389i
$353$	4.31487			0.229658			0.114829	−	0.993385i	$-0.463368\pi$
$353$	4.31487			0.229658			0.114829	+	0.993385i	$0.463368\pi$
$354$	−0.0619343	−	0.00763076i	−0.00329177	−	0.000405570i
$355$	10.3293			0.548225
$356$	18.0345	+	31.2367i	0.955828	+	1.65554i
$357$	−2.22738	+	1.11838i	−0.117885	+	0.0591912i
$358$	−0.160800	+	0.278513i	−0.00849853	+	0.0147199i
$359$	−13.5903	+	23.5390i	−0.717267	+	1.24234i	0.244811	+	0.969571i	$0.421274\pi$
$359$	−13.5903	+	23.5390i	−0.717267	+	1.24234i	−0.962079	+	0.272772i	$0.912059\pi$
$360$	−0.297739	−	0.0744980i	−0.0156922	−	0.00392639i
$361$	−16.7270	−	28.9721i	−0.880370	−	1.52485i
$362$	0.181277	+	0.313981i	0.00952772	+	0.0165025i
$363$	−5.65469	−	0.696699i	−0.296794	−	0.0365672i
$364$	−1.88389	−	29.2474i	−0.0987427	−	1.53298i
$365$	2.91561	+	5.04998i	0.152610	+	0.264328i
$366$	0.0467960	−	0.0620466i	0.00244607	−	0.00324323i
$367$	12.0152			0.627189			0.313595	−	0.949557i	$-0.398467\pi$
$367$	12.0152			0.627189			0.313595	+	0.949557i	$0.398467\pi$
$368$	−14.4976	−	25.1105i	−0.755738	−	1.30898i
$369$	0.392746	+	1.37399i	0.0204456	+	0.0715269i
$370$	−0.0855629			−0.00444820
$371$	18.7794	−	12.5174i	0.974978	−	0.649872i
$372$	−2.35430	−	5.55281i	−0.122065	−	0.287900i
$373$	−8.68386			−0.449633			−0.224816	−	0.974401i	$-0.572178\pi$
$373$	−8.68386			−0.449633			−0.224816	+	0.974401i	$0.572178\pi$
$374$	−0.0262963	+	0.0455465i	−0.00135975	+	0.00235515i
$375$	−1.71905	−	0.211800i	−0.0887715	−	0.0109373i
$376$	−0.438751	−	0.759939i	−0.0226269	−	0.0391909i
$377$	44.8646			2.31064
$378$	−0.343188	+	0.0767988i	−0.0176517	+	0.00395011i
$379$	12.7019			0.652454			0.326227	−	0.945291i	$-0.394223\pi$
$379$	12.7019			0.652454			0.326227	+	0.945291i	$0.394223\pi$
$380$	−7.24015	−	12.5403i	−0.371412	−	0.643304i
$381$	−1.97120	−	0.242866i	−0.100988	−	0.0124424i
$382$	−0.130211	+	0.225533i	−0.00666219	+	0.0115393i
$383$	25.1210			1.28362			0.641812	−	0.766862i	$-0.278183\pi$
$383$	25.1210			1.28362			0.641812	+	0.766862i	$0.278183\pi$
$384$	−0.552991	−	1.30428i	−0.0282197	−	0.0665585i
$385$	0.642874	+	9.98062i	0.0327639	+	0.508659i
$386$	−0.175266			−0.00892079
$387$	−1.16521	+	1.20460i	−0.0592309	+	0.0612332i
$388$	7.62856	+	13.2131i	0.387282	+	0.670791i
$389$	19.1424			0.970559			0.485280	−	0.874359i	$-0.338718\pi$
$389$	19.1424			0.970559			0.485280	+	0.874359i	$0.338718\pi$
$390$	0.147817	−	0.195990i	0.00748501	−	0.00992434i
$391$	−1.97318	−	3.41766i	−0.0997882	−	0.172838i
$392$	0.710223	−	0.0918752i	0.0358717	−	0.00464040i
$393$	10.9374	+	1.34757i	0.551720	+	0.0679759i
$394$	0.256020	+	0.443439i	0.0128981	+	0.0223401i
$395$	−1.48332	−	2.56918i	−0.0746338	−	0.129270i
$396$	15.7638	−	16.2968i	0.792163	−	0.818943i
$397$	−1.80451	+	3.12551i	−0.0905659	+	0.156865i	−0.907749	−	0.419513i	$-0.862201\pi$
$397$	−1.80451	+	3.12551i	−0.0905659	+	0.156865i	0.817184	+	0.576378i	$0.195534\pi$
$398$	0.165610	−	0.286845i	0.00830129	−	0.0143783i
$399$	−27.7277	−	18.2403i	−1.38812	−	0.913158i
$400$	−1.99804	−	3.46070i	−0.0999019	−	0.173035i
$401$	3.36015			0.167798			0.0838989	−	0.996474i	$-0.473263\pi$
$401$	3.36015			0.167798			0.0838989	+	0.996474i	$0.473263\pi$
$402$	−0.544542	−	0.0670915i	−0.0271593	−	0.00334622i
$403$	9.64964			0.480683
$404$	−3.42367	+	5.92998i	−0.170334	+	0.295027i
$405$	7.93948	+	4.23847i	0.394516	+	0.210611i
$406$	0.0352276	+	0.546909i	0.00174832	+	0.0271426i
$407$	6.32196	−	10.9499i	0.313368	−	0.542769i
$408$	−0.0376200	−	0.0887298i	−0.00186247	−	0.00439278i
$409$	−1.19114	+	2.06311i	−0.0588980	+	0.102014i	−0.893971	−	0.448125i	$-0.852092\pi$
$409$	−1.19114	+	2.06311i	−0.0588980	+	0.102014i	0.835073	+	0.550139i	$0.185425\pi$
$410$	0.00609253	−	0.0105526i	0.000300888	−	0.000521154i
$411$	14.7144	+	1.81292i	0.725809	+	0.0894250i
$412$	9.42746	−	16.3288i	0.464458	−	0.804464i
$413$	−3.34017	−	1.65187i	−0.164359	−	0.0812833i
$414$	−0.153038	−	0.535389i	−0.00752141	−	0.0263129i
$415$	−3.97711	+	6.88856i	−0.195229	+	0.338146i
$416$	1.70002			0.0833501
$417$	4.17533	+	9.84785i	0.204467	+	0.482252i
$418$	−0.700339			−0.0342547
$419$	−1.56715	−	2.71438i	−0.0765602	−	0.132606i	0.825203	−	0.564836i	$-0.191060\pi$
$419$	−1.56715	−	2.71438i	−0.0765602	−	0.132606i	−0.901764	+	0.432229i	$0.857727\pi$
$420$	−7.65442	−	5.03536i	−0.373498	−	0.245701i
$421$	6.68047	−	11.5709i	0.325586	−	0.563932i	−0.656044	−	0.754722i	$-0.727772\pi$
$421$	6.68047	−	11.5709i	0.325586	−	0.563932i	0.981631	+	0.190790i	$0.0611050\pi$
$422$	0.164556	−	0.285020i	0.00801048	−	0.0138746i
$423$	7.07203	+	24.7408i	0.343854	+	1.20294i
$424$	0.436345	+	0.755772i	0.0211908	+	0.0367035i
$425$	−0.271942	−	0.471017i	−0.0131911	−	0.0228477i
$426$	0.178647	+	0.421354i	0.00865549	+	0.0204147i
$427$	3.86150	−	2.57388i	0.186871	−	0.124559i
$428$	−0.188814	−	0.327036i	−0.00912668	−	0.0158079i
$429$	14.1602	+	33.3980i	0.683661	+	1.61247i
$430$	0.0142905			0.000689150
$431$	−11.9751	−	20.7415i	−0.576821	−	0.999082i	−0.995841	−	0.0911058i	$-0.970960\pi$
$431$	−11.9751	−	20.7415i	−0.576821	−	0.999082i	0.419021	−	0.907977i	$-0.362373\pi$
$432$	3.22262	+	20.5126i	0.155048	+	0.986913i
$433$	−15.3737			−0.738813			−0.369406	−	0.929268i	$-0.620439\pi$
$433$	−15.3737			−0.738813			−0.369406	+	0.929268i	$0.620439\pi$
$434$	0.00757689	+	0.117631i	0.000363702	+	0.00564648i
$435$	8.44534	−	11.1976i	0.404923	−	0.536886i
$436$	17.6105			0.843390
$437$	26.2755	−	45.5106i	1.25693	−	2.17706i
$438$	−0.155573	+	0.206273i	−0.00743356	+	0.00985612i
$439$	−4.25004	−	7.36128i	−0.202843	−	0.351335i	0.746600	−	0.665273i	$-0.231685\pi$
$439$	−4.25004	−	7.36128i	−0.202843	−	0.351335i	−0.949443	+	0.313938i	$0.898352\pi$
$440$	−0.386730			−0.0184366
$441$	−20.8576	−	2.44164i	−0.993218	−	0.116269i
$442$	0.0770844			0.00366653
$443$	15.4662	+	26.7883i	0.734822	+	1.27275i	0.954801	+	0.297245i	$0.0960677\pi$
$443$	15.4662	+	26.7883i	0.734822	+	1.27275i	−0.219979	+	0.975505i	$0.570599\pi$
$444$	4.52141	+	10.6641i	0.214577	+	0.506097i
$445$	−9.02021	+	15.6235i	−0.427599	+	0.740623i
$446$	−0.317478			−0.0150330
$447$	−8.06743	−	0.993965i	−0.381576	−	0.0470129i
$448$	−1.35786	−	21.0808i	−0.0641529	−	0.995973i
$449$	4.23659			0.199937			0.0999686	−	0.994991i	$-0.468126\pi$
$449$	4.23659			0.199937			0.0999686	+	0.994991i	$0.468126\pi$
$450$	−0.0210915	−	0.0737866i	−0.000994263	−	0.00347834i
$451$	0.900313	+	1.55939i	0.0423941	+	0.0734287i
$452$	−23.3405			−1.09785
$453$	26.8388	+	3.30673i	1.26099	+	0.155364i
$454$	−0.113350	−	0.196329i	−0.00531980	−	0.00921417i
$455$	12.1975	−	8.13026i	0.571829	−	0.381153i
$456$	0.772776	−	1.02462i	0.0361885	−	0.0479822i
$457$	−19.6991	−	34.1198i	−0.921485	−	1.59606i	−0.797119	−	0.603823i	$-0.793644\pi$
$457$	−19.6991	−	34.1198i	−0.921485	−	1.59606i	−0.124366	−	0.992236i	$-0.539690\pi$
$458$	−0.336602	−	0.583012i	−0.0157284	−	0.0272424i
$459$	0.438612	+	2.79186i	0.0204727	+	0.130313i
$460$	7.25354	−	12.5635i	0.338198	−	0.585776i
$461$	−2.86184	+	4.95686i	−0.133289	+	0.230864i	−0.924943	−	0.380107i	$-0.875887\pi$
$461$	−2.86184	+	4.95686i	−0.133289	+	0.230864i	0.791653	+	0.610971i	$0.209221\pi$
$462$	−0.396010	+	0.198840i	−0.0184241	+	0.00925088i
$463$	9.45324	+	16.3735i	0.439329	+	0.760941i	0.997638	−	0.0686927i	$-0.0218828\pi$
$463$	9.45324	+	16.3735i	0.439329	+	0.760941i	−0.558309	+	0.829633i	$0.688549\pi$
$464$	32.3584			1.50220
$465$	1.81646	−	2.40843i	0.0842362	−	0.111688i
$466$	−0.666306			−0.0308661
$467$	11.2057	−	19.4088i	0.518536	−	0.898131i	−0.481232	−	0.876593i	$-0.659810\pi$
$467$	11.2057	−	19.4088i	0.518536	−	0.898131i	0.999768	−	0.0215379i	$-0.00685627\pi$
$468$	−32.2383	−	8.06644i	−1.49022	−	0.372871i
$469$	−29.3676	−	14.5237i	−1.35607	−	0.670641i
$470$	0.109706	−	0.190016i	0.00506035	−	0.00876478i
$471$	−19.3666	+	25.6781i	−0.892366	+	1.18318i
$472$	0.0720446	−	0.124785i	0.00331612	−	0.00574369i
$473$	−1.05588	+	1.82884i	−0.0485494	+	0.0840900i
$474$	0.0791479	−	0.104942i	0.00363538	−	0.00482014i
$475$	3.62126	−	6.27220i	0.166155	−	0.287788i
$476$	−0.184932	−	2.87107i	−0.00847634	−	0.131595i
$477$	−7.03324	−	24.6052i	−0.322030	−	1.12659i
$478$	0.243038	−	0.420953i	0.0111163	−	0.0192540i
$479$	−30.1305			−1.37670			−0.688349	−	0.725380i	$-0.741664\pi$
$479$	−30.1305			−1.37670			−0.688349	+	0.725380i	$0.741664\pi$
$480$	0.320012	−	0.424303i	0.0146065	−	0.0193667i
$481$	−18.5321			−0.844989
$482$	0.182683	+	0.316416i	0.00832097	+	0.0144123i
$483$	1.93630	−	33.1943i	0.0881045	−	1.51039i
$484$	3.28835	−	5.69559i	0.149470	−	0.258890i
$485$	−3.81553	+	6.60869i	−0.173254	+	0.300085i
$486$	−0.0355814	+	0.397172i	−0.00161401	+	0.0180161i
$487$	−17.0000	−	29.4448i	−0.770343	−	1.33427i	−0.937375	−	0.348322i	$-0.886752\pi$
$487$	−17.0000	−	29.4448i	−0.770343	−	1.33427i	0.167032	−	0.985951i	$-0.446582\pi$
$488$	0.0897231	+	0.155405i	0.00406157	+	0.00703485i
$489$	1.36743	−	1.81306i	0.0618372	−	0.0819896i
$490$	0.108687	+	0.142307i	0.00490999	+	0.00642876i
$491$	−7.47750	−	12.9514i	−0.337455	−	0.584489i	0.646498	−	0.762915i	$-0.276233\pi$
$491$	−7.47750	−	12.9514i	−0.337455	−	0.584489i	−0.983953	+	0.178426i	$0.942899\pi$
$492$	−1.63717	−	0.201711i	−0.0738092	−	0.00909383i
$493$	4.40412			0.198352
$494$	0.513240	+	0.888958i	0.0230918	+	0.0399961i
$495$	11.0013	+	2.75266i	0.494470	+	0.123723i
$496$	6.95977			0.312503
$497$	1.75667	+	27.2724i	0.0787976	+	1.22333i
$498$	−0.349782	−	0.0430957i	−0.0156741	−	0.00193117i
$499$	0.819143			0.0366699			0.0183349	−	0.999832i	$-0.494163\pi$
$499$	0.819143			0.0366699			0.0183349	+	0.999832i	$0.494163\pi$
$500$	0.999673	−	1.73148i	0.0447067	−	0.0774343i
$501$	−7.52434	−	17.7468i	−0.336163	−	0.792867i
$502$	0.0286014	+	0.0495391i	0.00127654	+	0.00221104i
$503$	13.5639			0.604783			0.302392	−	0.953184i	$-0.402215\pi$
$503$	13.5639			0.604783			0.302392	+	0.953184i	$0.402215\pi$
$504$	0.146060	−	0.798783i	0.00650604	−	0.0355806i
$505$	−3.42479			−0.152401
$506$	−0.350817	−	0.607633i	−0.0155957	−	0.0270126i
$507$	18.4573	−	24.4725i	0.819719	−	1.08686i
$508$	1.14630	−	1.98545i	0.0508589	−	0.0880903i
$509$	34.9191			1.54776			0.773881	−	0.633330i	$-0.218313\pi$
$509$	34.9191			1.54776			0.773881	+	0.633330i	$0.218313\pi$
$510$	0.0145104	−	0.0192393i	0.000642533	−	0.000851932i
$511$	−12.8375	+	8.55685i	−0.567898	+	0.378533i
$512$	2.04377			0.0903229
$513$	−29.2761	+	23.6468i	−1.29257	+	1.04403i
$514$	0.201636	+	0.349244i	0.00889378	+	0.0154045i
$515$	9.43055			0.415560
$516$	−0.755157	−	1.78110i	−0.0332439	−	0.0784085i
$517$	16.2116	+	28.0793i	0.712984	+	1.23493i
$518$	−0.0145514	−	0.225910i	−0.000639350	−	0.00992591i
$519$	−0.963246	−	2.27190i	−0.0422818	−	0.0997251i
$520$	0.283413	+	0.490886i	0.0124285	+	0.0215268i
$521$	1.55141	+	2.68713i	0.0679687	+	0.117725i	0.898007	−	0.439981i	$-0.145015\pi$
$521$	1.55141	+	2.68713i	0.0679687	+	0.117725i	−0.830038	+	0.557706i	$0.811682\pi$
$522$	0.602837	+	0.150838i	0.0263855	+	0.00660198i
$523$	−5.99060	+	10.3760i	−0.261951	+	0.453712i	−0.966760	−	0.255685i	$-0.917699\pi$
$523$	−5.99060	+	10.3760i	−0.261951	+	0.453712i	0.704810	+	0.709396i	$0.251032\pi$
$524$	−6.36039	+	11.0165i	−0.277855	+	0.481259i
$525$	0.266858	−	4.57480i	0.0116466	−	0.199661i
$526$	0.163453	+	0.283110i	0.00712691	+	0.0123442i
$527$	0.947256			0.0412631
$528$	10.2130	+	24.0882i	0.444464	+	1.04830i
$529$	29.6482			1.28905
$530$	−0.109104	+	0.188974i	−0.00473918	+	0.00820850i
$531$	−2.93763	+	3.03694i	−0.127482	+	0.131792i
$532$	31.8786	−	21.2487i	1.38211	−	0.921248i
$533$	1.31958	−	2.28558i	0.0571574	−	0.0989994i
$534$	−0.793318	−	0.0977425i	−0.0343302	−	0.00422973i
$535$	0.0944380	−	0.163571i	0.00408291	−	0.00707181i
$536$	0.633434	−	1.09714i	0.0273602	−	0.0473892i
$537$	8.49995	+	20.0478i	0.366800	+	0.865127i
$538$	0.251411	−	0.435457i	0.0108391	−	0.0187739i
$539$	−26.2423	+	3.39473i	−1.13034	+	0.146221i
$540$	−8.08186	+	6.52786i	−0.347788	+	0.280914i
$541$	0.566880	−	0.981865i	0.0243721	−	0.0422137i	−0.853582	−	0.520958i	$-0.825575\pi$
$541$	0.566880	−	0.981865i	0.0243721	−	0.0422137i	0.877954	+	0.478745i	$0.158908\pi$
$542$	0.0524527			0.00225304
$543$	24.3641	+	3.00184i	1.04556	+	0.128821i
$544$	0.166882			0.00715500
$545$	4.40407	+	7.62807i	0.188650	+	0.326751i
$546$	0.542607	+	0.356947i	0.0232214	+	0.0152759i
$547$	−3.51151	+	6.08211i	−0.150141	+	0.260052i	−0.931279	−	0.364306i	$-0.881306\pi$
$547$	−3.51151	+	6.08211i	−0.150141	+	0.260052i	0.781138	+	0.624358i	$0.214640\pi$
$548$	−8.55682	+	14.8208i	−0.365529	+	0.633115i
$549$	−1.44621	−	5.05941i	−0.0617225	−	0.215931i
$550$	−0.0483491	−	0.0837432i	−0.00206161	−	0.00357082i
$551$	29.3233	+	50.7895i	1.24922	+	2.16371i
$552$	1.27609	+	0.157224i	0.0543140	+	0.00669188i
$553$	6.53110	−	4.35331i	0.277731	−	0.185121i
$554$	−0.0821155	−	0.142228i	−0.00348875	−	0.00604270i
$555$	−3.48849	+	4.62538i	−0.148078	+	0.196336i
$556$	−12.3471			−0.523635
$557$	−6.94094	−	12.0221i	−0.294097	−	0.509391i	0.680677	−	0.732583i	$-0.261686\pi$
$557$	−6.94094	−	12.0221i	−0.294097	−	0.509391i	−0.974774	+	0.223192i	$0.928352\pi$
$558$	0.129661	+	0.0324427i	0.00548897	+	0.00137341i
$559$	3.09518			0.130912
$560$	8.79742	−	5.86393i	0.371759	−	0.247796i
$561$	1.39003	+	3.27851i	0.0586873	+	0.138419i
$562$	0.783287			0.0330410
$563$	−11.1331	+	19.2831i	−0.469204	+	0.812685i	−0.999380	−	0.0352025i	$-0.988792\pi$
$563$	−11.1331	+	19.2831i	−0.469204	+	0.812685i	0.530176	+	0.847887i	$0.322126\pi$
$564$	−29.4798	−	3.63213i	−1.24132	−	0.152940i
$565$	−5.83704	−	10.1101i	−0.245566	−	0.425333i
$566$	0.248884			0.0104614
$567$	−9.84052	+	21.6833i	−0.413263	+	0.910612i
$568$	−1.05675			−0.0443403
$569$	−0.0493845	−	0.0855365i	−0.00207031	−	0.00358588i	0.864988	−	0.501792i	$-0.167326\pi$
$569$	−0.0493845	−	0.0855365i	−0.00207031	−	0.00358588i	−0.867059	+	0.498206i	$0.833992\pi$
$570$	0.318486	+	0.0392398i	0.0133399	+	0.00164357i
$571$	−17.4881	+	30.2902i	−0.731852	+	1.26761i	0.224238	+	0.974534i	$0.428011\pi$
$571$	−17.4881	+	30.2902i	−0.731852	+	1.26761i	−0.956091	+	0.293071i	$0.905323\pi$
$572$	−41.8740			−1.75084
$573$	6.88303	+	16.2342i	0.287543	+	0.678193i
$574$	0.0288979	+	0.0142913i	0.00120617	+	0.000596509i
$575$	7.25591			0.302592
$576$	−23.2366	−	5.81408i	−0.968190	−	0.242253i
$577$	9.85646	+	17.0719i	0.410330	+	0.710712i	0.994926	−	0.100612i	$-0.0320802\pi$
$577$	9.85646	+	17.0719i	0.410330	+	0.710712i	−0.584596	+	0.811325i	$0.698747\pi$
$578$	−0.427304			−0.0177735
$579$	−7.14577	+	9.47455i	−0.296968	+	0.393749i
$580$	8.09490	+	14.0208i	0.336123	+	0.582181i
$581$	−18.8641	−	9.32917i	−0.782614	−	0.387039i
$582$	−0.335572	−	0.0413449i	−0.0139099	−	0.00171380i
$583$	−16.1227	−	27.9253i	−0.667733	−	1.15655i
$584$	−0.298283	−	0.516642i	−0.0123431	−	0.0213788i
$585$	−4.56821	−	15.9814i	−0.188872	−	0.660752i
$586$	−0.136294	+	0.236068i	−0.00563026	+	0.00975189i
$587$	13.3822	−	23.1787i	0.552344	−	0.956687i	−0.445761	−	0.895152i	$-0.647067\pi$
$587$	13.3822	−	23.1787i	0.552344	−	0.956687i	0.998105	−	0.0615355i	$-0.0195997\pi$
$588$	11.9930	−	21.0662i	0.494583	−	0.868754i
$589$	6.30697	+	10.9240i	0.259874	+	0.450116i
$590$	0.0360282			0.00148326
$591$	34.4097	+	4.23953i	1.41543	+	0.174391i
$592$	−13.3662			−0.549347
$593$	2.17116	−	3.76056i	0.0891589	−	0.154428i	−0.817997	−	0.575223i	$-0.804915\pi$
$593$	2.17116	−	3.76056i	0.0891589	−	0.154428i	0.907156	+	0.420795i	$0.138249\pi$
$594$	0.0779819	+	0.496371i	0.00319964	+	0.0203663i
$595$	1.19737	−	0.798106i	0.0490873	−	0.0327192i
$596$	4.69141	−	8.12577i	0.192168	−	0.332844i
$597$	−8.75424	−	20.6476i	−0.358287	−	0.845050i
$598$	−0.514189	+	0.890602i	−0.0210268	+	0.0364194i
$599$	19.2922	−	33.4151i	0.788258	−	1.36530i	−0.138775	−	0.990324i	$-0.544317\pi$
$599$	19.2922	−	33.4151i	0.788258	−	1.36530i	0.927033	−	0.374979i	$-0.122350\pi$
$600$	0.175869	+	0.0216683i	0.00717982	+	0.000884606i
$601$	22.6721	−	39.2693i	0.924815	−	1.60183i	0.132957	−	0.991122i	$-0.457553\pi$
$601$	22.6721	−	39.2693i	0.924815	−	1.60183i	0.791858	−	0.610705i	$-0.209114\pi$
$602$	0.00243034	+	0.0377310i	9.90531e−5	+	0.00153780i
$603$	−25.8284	+	26.7016i	−1.05181	+	1.08737i
$604$	−15.6074	+	27.0328i	−0.635057	+	1.09995i
$605$	3.28942			0.133734
$606$	−0.0592323	−	0.139704i	−0.00240615	−	0.00567509i
$607$	10.7067			0.434572			0.217286	−	0.976108i	$-0.430280\pi$
$607$	10.7067			0.434572			0.217286	+	0.976108i	$0.430280\pi$
$608$	1.11112	+	1.92452i	0.0450620	+	0.0780498i
$609$	31.0012	+	20.3937i	1.25623	+	0.826395i
$610$	−0.0224344	+	0.0388576i	−0.000908344	+	0.00157330i
$611$	23.7612	−	41.1555i	0.961274	−	1.66497i
$612$	−3.16467	−	0.791841i	−0.127924	−	0.0320083i
$613$	−14.1382	−	24.4882i	−0.571038	−	0.989067i	−0.996460	−	0.0840720i	$-0.973207\pi$
$613$	−14.1382	−	24.4882i	−0.571038	−	0.989067i	0.425421	−	0.904995i	$-0.360126\pi$
$614$	−0.0457942	−	0.0793178i	−0.00184810	−	0.00320101i
$615$	−0.322054	−	0.759590i	−0.0129865	−	0.0306296i
$616$	−0.0657697	−	1.02107i	−0.00264994	−	0.0411403i
$617$	18.3974	+	31.8653i	0.740653	+	1.28285i	0.952198	+	0.305480i	$0.0988170\pi$
$617$	18.3974	+	31.8653i	0.740653	+	1.28285i	−0.211546	+	0.977368i	$0.567850\pi$
$618$	0.163102	+	0.384691i	0.00656094	+	0.0154745i
$619$	6.52183			0.262135			0.131067	−	0.991373i	$-0.458160\pi$
$619$	6.52183			0.262135			0.131067	+	0.991373i	$0.458160\pi$
$620$	1.74108	+	3.01564i	0.0699236	+	0.121111i
$621$	−35.1817	−	13.5554i	−1.41179	−	0.543961i
$622$	0.417367			0.0167349
$623$	−42.7844	−	21.1589i	−1.71412	−	0.847712i
$624$	23.0912	−	30.6165i	0.924388	−	1.22564i
$625$	1.00000			0.0400000
$626$	0.0879517	−	0.152337i	0.00351526	−	0.00608860i
$627$	−28.5536	+	37.8591i	−1.14032	+	1.51195i
$628$	−18.5630	−	32.1520i	−0.740744	−	1.28301i
$629$	−1.81920			−0.0725362
$630$	0.191230	−	0.0682361i	0.00761880	−	0.00271859i
$631$	2.81008			0.111867			0.0559337	−	0.998434i	$-0.482186\pi$
$631$	2.81008			0.111867			0.0559337	+	0.998434i	$0.482186\pi$
$632$	0.151752	+	0.262842i	0.00603637	+	0.0104553i
$633$	−8.69853	−	20.5162i	−0.345735	−	0.815445i
$634$	0.255133	−	0.441903i	0.0101326	−	0.0175502i
$635$	1.14668			0.0455045
$636$	29.3182	+	3.61221i	1.16254	+	0.143233i
$637$	23.5406	+	30.8222i	0.932711	+	1.22122i
$638$	0.783019			0.0310000
$639$	30.0613	+	7.52172i	1.18921	+	0.297555i
$640$	0.408955	+	0.708332i	0.0161654	+	0.0279993i
$641$	−1.71362			−0.0676838			−0.0338419	−	0.999427i	$-0.510774\pi$
$641$	−1.71362			−0.0676838			−0.0338419	+	0.999427i	$0.510774\pi$
$642$	0.00830572	+	0.00102333i	0.000327801	+	4.03874e-5i
$643$	−10.4993	−	18.1854i	−0.414054	−	0.717162i	0.581275	−	0.813707i	$-0.302554\pi$
$643$	−10.4993	−	18.1854i	−0.414054	−	0.717162i	−0.995329	+	0.0965451i	$0.969221\pi$
$644$	34.4047	+	17.0147i	1.35574	+	0.670475i
$645$	0.582640	−	0.772520i	0.0229414	−	0.0304179i
$646$	0.0503821	+	0.0872644i	0.00198226	+	0.00343337i
$647$	−1.23228	−	2.13437i	−0.0484458	−	0.0839105i	0.840786	−	0.541368i	$-0.182093\pi$
$647$	−1.23228	−	2.13437i	−0.0484458	−	0.0839105i	−0.889231	+	0.457458i	$0.848760\pi$
$648$	−0.812255	−	0.433620i	−0.0319084	−	0.0170342i
$649$	−2.66200	+	4.61072i	−0.104493	+	0.180987i
$650$	−0.0708649	+	0.122742i	−0.00277955	+	0.00481432i
$651$	6.66785	+	4.38636i	0.261334	+	0.171915i
$652$	1.31068	+	2.27017i	0.0513304	+	0.0889068i
$653$	−33.5479			−1.31283			−0.656416	−	0.754399i	$-0.727928\pi$
$653$	−33.5479			−1.31283			−0.656416	+	0.754399i	$0.727928\pi$
$654$	−0.234995	+	0.311579i	−0.00918903	+	0.0121837i
$655$	−6.36247			−0.248602
$656$	0.951743	−	1.64847i	0.0371593	−	0.0643618i
$657$	4.80789	+	16.8200i	0.187574	+	0.656210i
$658$	0.520352	+	0.257338i	0.0202854	+	0.0100321i
$659$	5.81556	−	10.0728i	0.226542	−	0.392382i	−0.730239	−	0.683192i	$-0.760591\pi$
$659$	5.81556	−	10.0728i	0.226542	−	0.392382i	0.956781	+	0.290809i	$0.0939246\pi$
$660$	−7.88241	+	10.4512i	−0.306822	+	0.406814i
$661$	21.0430	−	36.4476i	0.818479	−	1.41765i	−0.0883238	−	0.996092i	$-0.528151\pi$
$661$	21.0430	−	36.4476i	0.818479	−	1.41765i	0.906803	−	0.421555i	$-0.138516\pi$
$662$	0.138919	−	0.240615i	0.00539925	−	0.00935178i
$663$	3.14282	−	4.16705i	0.122057	−	0.161835i
$664$	0.406881	−	0.704739i	0.0157901	−	0.0273492i
$665$	17.1762	+	8.49445i	0.666066	+	0.329401i
$666$	−0.249012	−	0.0623060i	−0.00964902	−	0.00241431i
$667$	−29.3776	+	50.8834i	−1.13750	+	1.97021i
$668$	22.2507			0.860906
$669$	−12.9439	+	17.1623i	−0.500441	+	0.663533i
$670$	0.316769			0.0122378
$671$	−3.31521	−	5.74211i	−0.127982	−	0.221672i
$672$	1.17470	+	0.772762i	0.0453151	+	0.0298100i
$673$	−4.35702	+	7.54659i	−0.167951	+	0.290899i	−0.937699	−	0.347448i	$-0.887048\pi$
$673$	−4.35702	+	7.54659i	−0.167951	+	0.290899i	0.769748	+	0.638347i	$0.220382\pi$
$674$	−0.00351063	+	0.00608059i	−0.000135224	+	0.000234216i
$675$	−4.84870	−	1.86819i	−0.186626	−	0.0719068i
$676$	17.6915	+	30.6425i	0.680440	+	1.17856i
$677$	−5.73561	−	9.93437i	−0.220437	−	0.381809i	0.734503	−	0.678605i	$-0.237415\pi$
$677$	−5.73561	−	9.93437i	−0.220437	−	0.381809i	−0.954941	+	0.296796i	$0.904082\pi$
$678$	0.311457	−	0.412959i	0.0119614	−	0.0158596i
$679$	−18.0977	−	8.95015i	−0.694525	−	0.343475i
$680$	0.0278212	+	0.0481878i	0.00106689	+	0.00184792i
$681$	−15.2346	−	1.87701i	−0.583791	−	0.0719273i
$682$	0.168415			0.00644893
$683$	17.5055	+	30.3205i	0.669831	+	1.16018i	0.977951	+	0.208834i	$0.0669667\pi$
$683$	17.5055	+	30.3205i	0.669831	+	1.16018i	−0.308120	+	0.951347i	$0.599700\pi$
$684$	−11.9392	−	41.7680i	−0.456505	−	1.59704i
$685$	−8.55962			−0.327046
$686$	−0.357245	+	0.311166i	−0.0136397	+	0.0118804i
$687$	−45.2402	−	5.57392i	−1.72602	−	0.212658i
$688$	2.23239			0.0851091
$689$	−23.6309	+	40.9298i	−0.900264	+	1.55930i
$690$	0.125492	+	0.295983i	0.00477739	+	0.0112679i
$691$	−1.92339	−	3.33141i	−0.0731692	−	0.126733i	0.827119	−	0.562026i	$-0.189978\pi$
$691$	−1.92339	−	3.33141i	−0.0731692	−	0.126733i	−0.900289	+	0.435293i	$0.856645\pi$
$692$	2.84848			0.108283
$693$	−5.39684	+	29.5145i	−0.205009	+	1.12116i
$694$	0.0969062			0.00367851
$695$	−3.08779	−	5.34821i	−0.117127	−	0.202869i
$696$	−0.864008	+	1.14558i	−0.0327501	+	0.0434232i
$697$	0.129536	−	0.224364i	0.00490654	−	0.00849838i
$698$	−0.732850			−0.0277388
$699$	−27.1660	+	36.0193i	−1.02751	+	1.36238i
$700$	4.74161	+	2.34495i	0.179216	+	0.0886307i
$701$	6.90316			0.260729			0.130364	−	0.991466i	$-0.458385\pi$
$701$	6.90316			0.260729			0.130364	+	0.991466i	$0.458385\pi$
$702$	0.572907	−	0.462747i	0.0216230	−	0.0174653i
$703$	−12.1125	−	20.9795i	−0.456832	−	0.791255i
$704$	−30.1817			−1.13752
$705$	−5.79910	−	13.6776i	−0.218407	−	0.515130i
$706$	−0.0551886	−	0.0955895i	−0.00207705	−	0.00359756i
$707$	−0.582442	−	9.04242i	−0.0219050	−	0.340075i
$708$	−1.90384	−	4.49037i	−0.0715508	−	0.168758i
$709$	−5.27133	−	9.13021i	−0.197969	−	0.342892i	0.749901	−	0.661550i	$-0.230101\pi$
$709$	−5.27133	−	9.13021i	−0.197969	−	0.342892i	−0.947870	+	0.318658i	$0.896768\pi$
$710$	−0.132116	−	0.228831i	−0.00495821	−	0.00858787i
$711$	−2.44602	−	8.55718i	−0.0917330	−	0.320919i
$712$	0.922820	−	1.59837i	0.0345841	−	0.0599015i
$713$	−6.31864	+	10.9442i	−0.236635	+	0.409863i
$714$	0.0532650	+	0.0350397i	0.00199339	+	0.00131133i
$715$	−10.4719	−	18.1379i	−0.391628	−	0.678320i
$716$	−25.1357			−0.939367
$717$	−12.8471	−	30.3009i	−0.479783	−	1.13161i
$718$	0.695296			0.0259482
$719$	−17.8806	+	30.9701i	−0.666835	+	1.15499i	0.311950	+	0.950099i	$0.399018\pi$
$719$	−17.8806	+	30.9701i	−0.666835	+	1.15499i	−0.978784	+	0.204893i	$0.934315\pi$
$720$	−3.29480	−	11.5266i	−0.122790	−	0.429570i
$721$	1.60382	+	24.8993i	0.0597293	+	0.927298i
$722$	−0.427888	+	0.741124i	−0.0159243	+	0.0275818i
$723$	24.5530	+	3.02511i	0.913138	+	0.112505i
$724$	−14.1684	+	24.5403i	−0.526563	+	0.912034i
$725$	−4.04878	+	7.01269i	−0.150368	+	0.260445i
$726$	0.0568910	+	0.134182i	0.00211142	+	0.00497996i
$727$	−19.2427	+	33.3294i	−0.713674	+	1.23612i	0.249795	+	0.968299i	$0.419637\pi$
$727$	−19.2427	+	33.3294i	−0.713674	+	1.23612i	−0.963469	+	0.267820i	$0.913697\pi$
$728$	−1.24788	+	0.831773i	−0.0462494	+	0.0308276i
$729$	20.0197	+	18.1166i	0.741471	+	0.670985i
$730$	0.0745831	−	0.129182i	0.00276044	−	0.00478123i
$731$	0.303838			0.0112379
$732$	6.02852	+	0.742758i	0.222821	+	0.0274531i
$733$	41.6428			1.53811			0.769056	−	0.639182i	$-0.220727\pi$
$733$	41.6428			1.53811			0.769056	+	0.639182i	$0.220727\pi$
$734$	−0.153678	−	0.266179i	−0.00567238	−	0.00982484i
$735$	12.1241	−	0.0734403i	0.447205	−	0.00270889i
$736$	−1.11318	+	1.92808i	−0.0410323	+	0.0710701i
$737$	−23.4050	+	40.5386i	−0.862133	+	1.49326i
$738$	0.0254152	−	0.0262744i	0.000935548	−	0.000967175i
$739$	−22.4915	−	38.9565i	−0.827364	−	1.43304i	−0.900099	−	0.435685i	$-0.856506\pi$
$739$	−22.4915	−	38.9565i	−0.827364	−	1.43304i	0.0727349	−	0.997351i	$-0.476827\pi$
$740$	−3.34374	−	5.79152i	−0.122918	−	0.212901i
$741$	68.9808	+	8.49894i	2.53407	+	0.312216i
$742$	−0.517499	−	0.255927i	−0.0189980	−	0.00939539i
$743$	−2.24629	−	3.89069i	−0.0824083	−	0.142735i	0.821876	−	0.569667i	$-0.192928\pi$
$743$	−2.24629	−	3.89069i	−0.0824083	−	0.142735i	−0.904284	+	0.426932i	$0.859595\pi$
$744$	−0.185834	+	0.246397i	−0.00681301	+	0.00903334i
$745$	4.69295			0.171936
$746$	0.111069	+	0.192378i	0.00406653	+	0.00704344i
$747$	−16.5907	+	17.1515i	−0.607021	+	0.627542i
$748$	−4.11056			−0.150297
$749$	0.447935	+	0.221525i	0.0163672	+	0.00809434i
$750$	0.0172951	+	0.0407920i	0.000631529	+	0.00148951i
$751$	42.2660			1.54231			0.771154	−	0.636649i	$-0.219680\pi$
$751$	42.2660			1.54231			0.771154	+	0.636649i	$0.219680\pi$
$752$	17.1377	−	29.6833i	0.624946	−	1.08244i
$753$	3.84410	+	0.473621i	0.140087	+	0.0172597i
$754$	−0.573832	−	0.993906i	−0.0208977	−	0.0361959i
$755$	−15.6125			−0.568198
$756$	−18.6098	−	20.2282i	−0.676833	−	0.735692i
$757$	−25.4479			−0.924918			−0.462459	−	0.886641i	$-0.653033\pi$
$757$	−25.4479			−0.924918			−0.462459	+	0.886641i	$0.653033\pi$
$758$	−0.162462	−	0.281392i	−0.00590087	−	0.0102206i
$759$	−47.1507	−	5.80931i	−1.71146	−	0.210865i
$760$	−0.370476	+	0.641683i	−0.0134386	+	0.0232763i
$761$	−29.8303			−1.08135			−0.540673	−	0.841233i	$-0.681830\pi$
$761$	−29.8303			−1.08135			−0.540673	+	0.841233i	$0.681830\pi$
$762$	0.0198319	+	0.0467752i	0.000718435	+	0.00169449i
$763$	−19.3913	+	12.9252i	−0.702010	+	0.467925i
$764$	−20.3543			−0.736391
$765$	−0.448437	−	1.56882i	−0.0162133	−	0.0567207i
$766$	−0.321306	−	0.556518i	−0.0116092	−	0.0201078i
$767$	7.80334			0.281762
$768$	16.6326	−	22.0531i	0.600178	−	0.795774i
$769$	9.71584	+	16.8283i	0.350362	+	0.606845i	0.986313	−	0.164885i	$-0.0527252\pi$
$769$	9.71584	+	16.8283i	0.350362	+	0.606845i	−0.635951	+	0.771730i	$0.719392\pi$
$770$	0.212883	−	0.141897i	0.00767176	−	0.00511362i
$771$	27.1004	+	3.33896i	0.975997	+	0.120250i
$772$	−6.84926	−	11.8633i	−0.246510	−	0.426968i
$773$	16.1602	+	27.9902i	0.581241	+	1.00674i	0.995333	+	0.0965036i	$0.0307659\pi$
$773$	16.1602	+	27.9902i	0.581241	+	1.00674i	−0.414092	+	0.910235i	$0.635901\pi$
$774$	0.0415894	+	0.0104062i	0.00149490	+	0.000374044i
$775$	−0.870826	+	1.50832i	−0.0312810	+	0.0541803i
$776$	0.390351	−	0.676107i	0.0140128	−	0.0242708i
$777$	−12.8056	−	8.42397i	−0.459397	−	0.302208i
$778$	−0.244838	−	0.424071i	−0.00877785	−	0.0152037i
$779$	3.44989			0.123605
$780$	19.0426	+	2.34619i	0.681835	+	0.0840070i
$781$	39.0463			1.39719
$782$	−0.0504753	+	0.0874258i	−0.00180499	+	0.00312634i
$783$	32.7323	−	26.4385i	1.16976	−	0.944834i
$784$	16.9785	+	22.2304i	0.606377	+	0.793943i
$785$	9.28453	−	16.0813i	0.331379	−	0.573965i
$786$	−0.110040	−	0.259538i	−0.00392499	−	0.00925740i
$787$	−13.0951	+	22.6813i	−0.466788	+	0.808501i	−0.999280	−	0.0379339i	$-0.987922\pi$
$787$	−13.0951	+	22.6813i	−0.466788	+	0.808501i	0.532492	+	0.846435i	$0.321256\pi$
$788$	−20.0101	+	34.6586i	−0.712831	+	1.23466i
$789$	21.9686	+	2.70669i	0.782102	+	0.0963606i
$790$	−0.0379442	+	0.0657213i	−0.00134999	+	0.00233826i
$791$	25.7007	−	17.1308i	0.913811	−	0.609101i
$792$	−1.12549	−	0.281613i	−0.0399926	−	0.0100067i
$793$	−4.85907	+	8.41616i	−0.172551	+	0.298867i
$794$	0.0923211			0.00327635
$795$	5.76729	+	13.6026i	0.204545	+	0.482436i
$796$	25.8877			0.917566
$797$	9.92568	+	17.1918i	0.351586	+	0.608964i	0.986527	−	0.163596i	$-0.0523092\pi$
$797$	9.92568	+	17.1918i	0.351586	+	0.608964i	−0.634942	+	0.772560i	$0.718976\pi$
$798$	−0.0494402	+	0.847565i	−0.00175017	+	0.0300035i
$799$	2.33251	−	4.04003i	0.0825183	−	0.142926i
$800$	−0.153417	+	0.265726i	−0.00542411	+	0.00939483i
$801$	−37.6282	+	38.9003i	−1.32953	+	1.37447i
$802$	−0.0429774	−	0.0744390i	−0.00151758	−	0.00262853i
$803$	11.0214	+	19.0896i	0.388936	+	0.673657i
$804$	−16.7391	−	39.4805i	−0.590341	−	1.39237i
$805$	1.23399	+	19.1576i	0.0434923	+	0.675218i
$806$	−0.123422	−	0.213773i	−0.00434735	−	0.00752984i
$807$	−13.2897	−	31.3449i	−0.467820	−	1.10339i
$808$	0.350376			0.0123262
$809$	−1.09725	−	1.90050i	−0.0385774	−	0.0668180i	0.846092	−	0.533037i	$-0.178949\pi$
$809$	−1.09725	−	1.90050i	−0.0385774	−	0.0668180i	−0.884669	+	0.466219i	$0.845616\pi$
$810$	−0.00765153	−	0.230099i	−0.000268847	−	0.00808484i
$811$	−21.8077			−0.765773			−0.382887	−	0.923795i	$-0.625070\pi$
$811$	−21.8077			−0.765773			−0.382887	+	0.923795i	$0.625070\pi$
$812$	−35.6421	+	23.7573i	−1.25079	+	0.833717i
$813$	2.13855	−	2.83550i	0.0750024	−	0.0994454i
$814$	−0.323439			−0.0113365
$815$	−0.655557	+	1.13546i	−0.0229632	+	0.0397734i
$816$	2.26675	−	3.00547i	0.0793520	−	0.105212i
$817$	2.02300	+	3.50394i	0.0707759	+	0.122587i
$818$	0.0609402			0.00213072
$819$	41.4186	−	14.7792i	1.44728	−	0.516429i
$820$	0.952366			0.0332581
$821$	−22.0670	−	38.2212i	−0.770144	−	1.33393i	−0.937484	−	0.348029i	$-0.886851\pi$
$821$	−22.0670	−	38.2212i	−0.770144	−	1.33393i	0.167340	−	0.985899i	$-0.446482\pi$
$822$	−0.148040	−	0.349164i	−0.00516348	−	0.0121785i
$823$	−16.7786	+	29.0615i	−0.584867	+	1.01302i	0.410025	+	0.912074i	$0.365520\pi$
$823$	−16.7786	+	29.0615i	−0.584867	+	1.01302i	−0.994892	+	0.100945i	$0.967813\pi$
$824$	−0.964800			−0.0336104
$825$	−6.49825	−	0.800632i	−0.226240	−	0.0278744i
$826$	0.00612718	+	0.0951245i	0.000213192	+	0.00330980i
$827$	−4.29754			−0.149440			−0.0747201	−	0.997205i	$-0.523806\pi$
$827$	−4.29754			−0.149440			−0.0747201	+	0.997205i	$0.523806\pi$
$828$	30.2584	−	31.2814i	1.05155	−	1.08710i
$829$	−11.9899	−	20.7671i	−0.416427	−	0.721273i	0.579150	−	0.815221i	$-0.303385\pi$
$829$	−11.9899	−	20.7671i	−0.416427	−	0.721273i	−0.995577	+	0.0939481i	$0.970051\pi$
$830$	0.203474			0.00706268
$831$	−11.0365	−	1.35978i	−0.382853	−	0.0471703i
$832$	22.1185	+	38.3104i	0.766822	+	1.32818i
$833$	2.31086	+	3.02566i	0.0800664	+	0.104833i
$834$	0.164760	−	0.218455i	0.00570519	−	0.00756449i
$835$	5.56450	+	9.63799i	0.192567	+	0.333536i
$836$	−27.3687	−	47.4041i	−0.946568	−	1.63950i
$837$	7.04020	−	5.68649i	0.243345	−	0.196554i
$838$	−0.0400887	+	0.0694356i	−0.00138484	+	0.00239861i
$839$	24.2851	−	42.0630i	0.838414	−	1.45218i	−0.0528059	−	0.998605i	$-0.516816\pi$
$839$	24.2851	−	42.0630i	0.838414	−	1.45218i	0.891220	−	0.453571i	$-0.149850\pi$
$840$	−0.0273011	+	0.468028i	−0.000941977	+	0.0161485i
$841$	−18.2852	−	31.6708i	−0.630523	−	1.09210i
$842$	−0.341782			−0.0117786
$843$	31.9354	−	42.3431i	1.09992	−	1.45837i
$844$	25.7230			0.885421
$845$	−8.84862	+	15.3263i	−0.304402	+	0.527239i
$846$	0.457642	−	0.473113i	0.0157341	−	0.0162660i
$847$	0.559420	+	8.68500i	0.0192219	+	0.298420i
$848$	−17.0437	+	29.5205i	−0.585282	+	1.01374i
$849$	10.1473	−	13.4542i	0.348253	−	0.461748i
$850$	−0.00695644	+	0.0120489i	−0.000238604	+	0.000413274i
$851$	12.1349	−	21.0183i	0.415979	−	0.720496i
$852$	−21.5389	+	28.5584i	−0.737912	+	0.978394i
$853$	−8.37813	+	14.5113i	−0.286862	+	0.496859i	−0.973059	−	0.230556i	$-0.925945\pi$
$853$	−8.37813	+	14.5113i	−0.286862	+	0.496859i	0.686197	+	0.727416i	$0.259279\pi$
$854$	−0.106410	−	0.0526248i	−0.00364128	−	0.00180078i
$855$	15.1062	−	15.6169i	0.516622	−	0.534087i
$856$	−0.00966156	+	0.0167343i	−0.000330225	+	0.000571967i
$857$	−10.4552			−0.357143			−0.178571	−	0.983927i	$-0.557148\pi$
$857$	−10.4552			−0.357143			−0.178571	+	0.983927i	$0.557148\pi$
$858$	0.558768	−	0.740869i	0.0190760	−	0.0252928i
$859$	13.4320			0.458295			0.229147	−	0.973392i	$-0.426406\pi$
$859$	13.4320			0.458295			0.229147	+	0.973392i	$0.426406\pi$
$860$	0.558463	+	0.967287i	0.0190434	+	0.0329842i
$861$	1.95076	−	0.979493i	0.0664817	−	0.0333810i
$862$	−0.306331	+	0.530581i	−0.0104337	+	0.0180716i
$863$	15.5326	−	26.9033i	0.528737	−	0.915799i	−0.470702	−	0.882292i	$-0.655999\pi$
$863$	15.5326	−	26.9033i	0.528737	−	0.915799i	0.999439	−	0.0335063i	$-0.0106674\pi$
$864$	1.24030	−	1.00181i	0.0421958	−	0.0340823i
$865$	0.712352	+	1.23383i	0.0242207	+	0.0419515i
$866$	0.196635	+	0.340581i	0.00668191	+	0.0115734i
$867$	−17.4216	+	23.0993i	−0.591670	+	0.784493i
$868$	−7.66604	+	5.10980i	−0.260202	+	0.173438i
$869$	−5.60714	−	9.71186i	−0.190209	−	0.329452i
$870$	−0.356085	−	0.0438723i	−0.0120724	−	0.00148741i
$871$	68.6089			2.32472
$872$	−0.450562	−	0.780396i	−0.0152579	−	0.0264275i
$873$	−15.9166	+	16.4547i	−0.538697	+	0.556908i
$874$	−1.34429			−0.0454713
$875$	0.170066	+	2.64028i	0.00574929	+	0.0892577i
$876$	−20.0418	−	2.46929i	−0.677148	−	0.0834296i
$877$	−10.6455			−0.359472			−0.179736	−	0.983715i	$-0.557524\pi$
$877$	−10.6455			−0.359472			−0.179736	+	0.983715i	$0.557524\pi$
$878$	−0.108719	+	0.188306i	−0.00366908	+	0.00635503i
$879$	7.20457	+	16.9926i	0.243004	+	0.573145i
$880$	−7.55285	−	13.0819i	−0.254607	−	0.440991i
$881$	−37.4454			−1.26157			−0.630785	−	0.775958i	$-0.717267\pi$
$881$	−37.4454			−1.26157			−0.630785	+	0.775958i	$0.717267\pi$
$882$	0.212684	+	0.493297i	0.00716145	+	0.0166102i
$883$	−1.93626			−0.0651605			−0.0325802	−	0.999469i	$-0.510372\pi$
$883$	−1.93626			−0.0651605			−0.0325802	+	0.999469i	$0.510372\pi$
$884$	3.01240	+	5.21764i	0.101318	+	0.175488i
$885$	1.46891	−	1.94762i	0.0493768	−	0.0654685i
$886$	0.395636	−	0.685261i	0.0132916	−	0.0230218i
$887$	27.1683			0.912224			0.456112	−	0.889922i	$-0.349242\pi$
$887$	27.1683			0.912224			0.456112	+	0.889922i	$0.349242\pi$
$888$	0.356893	−	0.473203i	0.0119765	−	0.0158796i
$889$	0.195011	+	3.02755i	0.00654046	+	0.101541i
$890$	0.461486			0.0154690
$891$	30.0123	+	16.0220i	1.00545	+	0.536757i
$892$	−12.4068	−	21.4892i	−0.415411	−	0.719513i
$893$	62.1209			2.07880
$894$	0.0811651	+	0.191435i	0.00271457	+	0.00640253i
$895$	−6.28599	−	10.8877i	−0.210118	−	0.363934i
$896$	−1.80064	+	1.20022i	−0.0601553	+	0.0400965i
$897$	27.1803	+	64.1069i	0.907523	+	2.14047i
$898$	−0.0541874	−	0.0938553i	−0.00180826	−	0.00313199i
$899$	−7.05156	−	12.2137i	−0.235183	−	0.407348i
$900$	4.17018	−	4.31116i	0.139006	−	0.143705i
$901$	−2.31972	+	4.01787i	−0.0772811	+	0.133855i
$902$	0.0230306	−	0.0398901i	0.000766834	−	0.00132820i
$903$	2.13876	+	1.40695i	0.0711734	+	0.0468205i
$904$	0.597163	+	1.03432i	0.0198614	+	0.0344009i
$905$	−14.1730			−0.471127
$906$	−0.270021	−	0.636866i	−0.00897084	−	0.0211585i
$907$	55.9188			1.85675			0.928376	−	0.371642i	$-0.121205\pi$
$907$	55.9188			1.85675			0.928376	+	0.371642i	$0.121205\pi$
$908$	8.85931	−	15.3448i	0.294007	−	0.509234i
$909$	−9.96712	−	2.49390i	−0.330588	−	0.0827174i
$910$	−0.336124	−	0.166229i	−0.0111424	−	0.00551043i
$911$	4.38364	−	7.59269i	0.145237	−	0.251557i	−0.784225	−	0.620477i	$-0.786939\pi$
$911$	4.38364	−	7.59269i	0.145237	−	0.251557i	0.929461	+	0.368920i	$0.120272\pi$
$912$	49.7522	+	6.12983i	1.64746	+	0.202979i
$913$	−15.0340	+	26.0397i	−0.497553	+	0.861787i
$914$	−0.503916	+	0.872807i	−0.0166680	+	0.0288699i
$915$	1.18589	+	2.79703i	0.0392045	+	0.0924670i
$916$	26.3083	−	45.5674i	0.869252	−	1.50559i
$917$	−1.08204	−	16.7987i	−0.0357322	−	0.554742i
$918$	0.0562394	−	0.0454255i	0.00185618	−	0.00149927i
$919$	5.14755	−	8.91582i	0.169802	−	0.294106i	−0.768548	−	0.639792i	$-0.779021\pi$
$919$	5.14755	−	8.91582i	0.169802	−	0.294106i	0.938350	+	0.345686i	$0.112354\pi$
$920$	−0.742322			−0.0244736
$921$	−6.15485	−	0.758323i	−0.202809	−	0.0249876i
$922$	0.146416			0.00482194
$923$	−28.6149	−	49.5625i	−0.941871	−	1.63137i
$924$	−28.9348	−	19.0344i	−0.951883	−	0.626184i
$925$	1.67242	−	2.89671i	0.0549887	−	0.0952432i
$926$	0.241820	−	0.418844i	0.00794669	−	0.0137641i
$927$	27.4455	+	6.86723i	0.901430	+	0.225549i
$928$	−1.24230	−	2.15173i	−0.0407805	−	0.0706339i
$929$	−18.7180	−	32.4206i	−0.614119	−	1.06368i	−0.990538	−	0.137235i	$-0.956178\pi$
$929$	−18.7180	−	32.4206i	−0.614119	−	1.06368i	0.376420	−	0.926449i	$-0.377155\pi$
$930$	−0.0765882	−	0.00943622i	−0.00251143	−	0.000309426i
$931$	−19.5066	+	46.7947i	−0.639304	+	1.53363i
$932$	−26.0388	−	45.1005i	−0.852928	−	1.47732i
$933$	17.0165	−	22.5621i	0.557095	−	0.738650i
$934$	−0.573296			−0.0187588
$935$	−1.02798	−	1.78051i	−0.0336184	−	0.0582288i
$936$	0.467354	+	1.63499i	0.0152759	+	0.0534415i
$937$	−20.0462			−0.654882			−0.327441	−	0.944872i	$-0.606186\pi$
$937$	−20.0462			−0.654882			−0.327441	+	0.944872i	$0.606186\pi$
$938$	0.0538717	+	0.836358i	0.00175897	+	0.0273081i
$939$	−4.64917	−	10.9654i	−0.151720	−	0.357844i
$940$	17.1489			0.559335
$941$	4.82903	−	8.36413i	0.157422	−	0.272663i	−0.776516	−	0.630097i	$-0.783015\pi$
$941$	4.82903	−	8.36413i	0.157422	−	0.272663i	0.933938	+	0.357434i	$0.116348\pi$
$942$	0.816564	+	0.100607i	0.0266051	+	0.00327794i
$943$	1.72814	+	2.99322i	0.0562759	+	0.0974726i
$944$	5.62813			0.183180
$945$	4.10795	−	13.1196i	0.133632	−	0.426782i
$946$	0.0540201			0.00175635
$947$	−8.28334	−	14.3472i	−0.269172	−	0.466220i	0.699476	−	0.714656i	$-0.253417\pi$
$947$	−8.28334	−	14.3472i	−0.269172	−	0.466220i	−0.968648	+	0.248436i	$0.920083\pi$
$948$	10.1963	+	1.25625i	0.331159	+	0.0408012i
$949$	16.1539	−	27.9795i	0.524379	−	0.908251i
$950$	−0.185268			−0.00601089
$951$	−13.4865	−	31.8089i	−0.437328	−	1.03147i
$952$	−0.122498	+	0.0816509i	−0.00397017	+	0.00264632i
$953$	22.6180			0.732669			0.366335	−	0.930483i	$-0.380613\pi$
$953$	22.6180			0.732669			0.366335	+	0.930483i	$0.380613\pi$
$954$	−0.455132	+	0.470519i	−0.0147355	+	0.0152336i
$955$	−5.09023	−	8.81654i	−0.164716	−	0.285296i
$956$	37.9909			1.22871
$957$	31.9245	−	42.3286i	1.03197	−	1.36829i
$958$	0.385379	+	0.667495i	0.0124510	+	0.0215658i
$959$	−1.45570	−	22.5998i	−0.0470071	−	0.729785i
$960$	13.7254	+	1.69107i	0.442986	+	0.0545791i
$961$	13.9833	+	24.2198i	0.451075	+	0.781285i
$962$	0.237031	+	0.410550i	0.00764219	+	0.0132367i
$963$	0.393952	−	0.407270i	0.0126949	−	0.0131241i
$964$	−14.2782	+	24.7306i	−0.459871	+	0.796519i
$965$	3.42575	−	5.93357i	0.110279	−	0.191009i
$966$	−0.760136	+	0.381670i	−0.0244570	+	0.0122800i
$967$	−16.1629	−	27.9950i	−0.519764	−	0.900258i	−0.999736	−	0.0229741i	$-0.992686\pi$
$967$	−16.1629	−	27.9950i	−0.519764	−	0.900258i	0.479972	−	0.877284i	$-0.340647\pi$
$968$	−0.336527			−0.0108164
$969$	6.77149	+	0.834297i	0.217532	+	0.0268015i
$970$	0.195207			0.00626773
$971$	19.6527	−	34.0395i	0.630686	−	1.09238i	−0.356726	−	0.934209i	$-0.616107\pi$
$971$	19.6527	−	34.0395i	0.630686	−	1.09238i	0.987412	−	0.158171i	$-0.0505597\pi$
$972$	−28.2740	+	13.1128i	−0.906889	+	0.420593i
$973$	13.5957	−	9.06219i	0.435857	−	0.290520i
$974$	−0.434870	+	0.753218i	−0.0139341	+	0.0241347i
$975$	3.74595	+	8.83513i	0.119966	+	0.282951i
$976$	−3.50459	+	6.07013i	−0.112179	+	0.194300i
$977$	−14.9663	+	25.9223i	−0.478813	+	0.829328i	−0.999705	−	0.0242942i	$-0.992266\pi$
$977$	−14.9663	+	25.9223i	−0.478813	+	0.829328i	0.520892	+	0.853623i	$0.325599\pi$
$978$	−0.0576555	−	0.00710358i	−0.00184362	−	0.000227147i
$979$	−34.0976	+	59.0588i	−1.08976	+	1.88753i
$980$	−5.38493	+	12.9180i	−0.172015	+	0.412650i
$981$	7.26240	+	25.4068i	0.231870	+	0.811177i
$982$	−0.191279	+	0.331305i	−0.00610396	+	0.0105724i
$983$	0.568902			0.0181451			0.00907257	−	0.999959i	$-0.497112\pi$
$983$	0.568902			0.0181451			0.00907257	+	0.999959i	$0.497112\pi$
$984$	0.0329480	+	0.0777105i	0.00105034	+	0.00247732i
$985$	−20.0167			−0.637785
$986$	−0.0563301	−	0.0975667i	−0.00179392	−	0.00310716i
$987$	35.1266	−	17.6373i	1.11809	−	0.561403i
$988$	−40.1141	+	69.4797i	−1.27620	+	2.21044i
$989$	−2.02674	+	3.51042i	−0.0644467	+	0.111625i
$990$	−0.0797287	−	0.278924i	−0.00253394	−	0.00886477i
$991$	−6.46835	−	11.2035i	−0.205474	−	0.355891i	0.744810	−	0.667277i	$-0.232540\pi$
$991$	−6.46835	−	11.2035i	−0.205474	−	0.355891i	−0.950284	+	0.311386i	$0.899207\pi$
$992$	−0.267199	−	0.462802i	−0.00848357	−	0.0146940i
$993$	−7.34334	−	17.3199i	−0.233034	−	0.549630i
$994$	0.581709	−	0.387739i	0.0184507	−	0.0122983i
$995$	6.47405	+	11.2134i	0.205241	+	0.355488i
$996$	−10.7522	−	25.3600i	−0.340697	−	0.803562i
$997$	10.7662			0.340970			0.170485	−	0.985360i	$-0.445466\pi$
$997$	10.7662			0.340970			0.170485	+	0.985360i	$0.445466\pi$
$998$	−0.0104771	−	0.0181469i	−0.000331647	−	0.000574429i
$999$	−13.5206	+	10.9209i	−0.427774	+	0.345521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.c.16.9	✓	36
3.2	odd	2		945.2.k.c.856.10		36
7.4	even	3		315.2.l.c.151.10	yes	36
9.4	even	3		315.2.l.c.121.10	yes	36
9.5	odd	6		945.2.l.c.226.9		36
21.11	odd	6		945.2.l.c.46.9		36
63.4	even	3	inner	315.2.k.c.256.9	yes	36
63.32	odd	6		945.2.k.c.361.10		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.9	✓	36	1.1	even	1	trivial
315.2.k.c.256.9	yes	36	63.4	even	3	inner
315.2.l.c.121.10	yes	36	9.4	even	3
315.2.l.c.151.10	yes	36	7.4	even	3
945.2.k.c.361.10		36	63.32	odd	6
945.2.k.c.856.10		36	3.2	odd	2
945.2.l.c.46.9		36	21.11	odd	6
945.2.l.c.226.9		36	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.0127903 - 0.0221535i) q^{2} +(-1.71905 - 0.211800i) q^{3} +(0.999673 - 1.73148i) q^{4} +1.00000 q^{5} +(0.0172951 + 0.0407920i) q^{6} +(0.170066 + 2.64028i) q^{7} -0.102306 q^{8} +(2.91028 + 0.728190i) q^{9} +(-0.0127903 - 0.0221535i) q^{10} +3.78014 q^{11} +(-2.08522 + 2.76478i) q^{12} +(-2.77025 - 4.79822i) q^{13} +(0.0563162 - 0.0375376i) q^{14} +(-1.71905 - 0.211800i) q^{15} +(-1.99804 - 3.46070i) q^{16} +(-0.271942 - 0.471017i) q^{17} +(-0.0210915 - 0.0737866i) q^{18} +(3.62126 - 6.27220i) q^{19} +(0.999673 - 1.73148i) q^{20} +(0.266858 - 4.57480i) q^{21} +(-0.0483491 - 0.0837432i) q^{22} +7.25591 q^{23} +(0.175869 + 0.0216683i) q^{24} +1.00000 q^{25} +(-0.0708649 + 0.122742i) q^{26} +(-4.84870 - 1.86819i) q^{27} +(4.74161 + 2.34495i) q^{28} +(-4.04878 + 7.01269i) q^{29} +(0.0172951 + 0.0407920i) q^{30} +(-0.870826 + 1.50832i) q^{31} +(-0.153417 + 0.265726i) q^{32} +(-6.49825 - 0.800632i) q^{33} +(-0.00695644 + 0.0120489i) q^{34} +(0.170066 + 2.64028i) q^{35} +(4.17018 - 4.31116i) q^{36} +(1.67242 - 2.89671i) q^{37} -0.185268 q^{38} +(3.74595 + 8.83513i) q^{39} -0.102306 q^{40} +(0.238169 + 0.412522i) q^{41} +(-0.104761 + 0.0526013i) q^{42} +(-0.279323 + 0.483802i) q^{43} +(3.77890 - 6.54524i) q^{44} +(2.91028 + 0.728190i) q^{45} +(-0.0928054 - 0.160744i) q^{46} +(4.28862 + 7.42811i) q^{47} +(2.70175 + 6.37231i) q^{48} +(-6.94215 + 0.898045i) q^{49} +(-0.0127903 - 0.0221535i) q^{50} +(0.367721 + 0.867300i) q^{51} -11.0774 q^{52} +(-4.26510 - 7.38738i) q^{53} +(0.0206294 + 0.131310i) q^{54} +3.78014 q^{55} +(-0.0173988 - 0.270116i) q^{56} +(-7.55358 + 10.0153i) q^{57} +0.207141 q^{58} +(-0.704208 + 1.21972i) q^{59} +(-2.08522 + 2.76478i) q^{60} +(-0.877009 - 1.51902i) q^{61} +0.0445526 q^{62} +(-1.42768 + 7.80780i) q^{63} -7.98430 q^{64} +(-2.77025 - 4.79822i) q^{65} +(0.0653779 + 0.154199i) q^{66} +(-6.19157 + 10.7241i) q^{67} -1.08741 q^{68} +(-12.4733 - 1.53680i) q^{69} +(0.0563162 - 0.0375376i) q^{70} +10.3293 q^{71} +(-0.297739 - 0.0744980i) q^{72} +(2.91561 + 5.04998i) q^{73} -0.0855629 q^{74} +(-1.71905 - 0.211800i) q^{75} +(-7.24015 - 12.5403i) q^{76} +(0.642874 + 9.98062i) q^{77} +(0.147817 - 0.195990i) q^{78} +(-1.48332 - 2.56918i) q^{79} +(-1.99804 - 3.46070i) q^{80} +(7.93948 + 4.23847i) q^{81} +(0.00609253 - 0.0105526i) q^{82} +(-3.97711 + 6.88856i) q^{83} +(-7.65442 - 5.03536i) q^{84} +(-0.271942 - 0.471017i) q^{85} +0.0142905 q^{86} +(8.44534 - 11.1976i) q^{87} -0.386730 q^{88} +(-9.02021 + 15.6235i) q^{89} +(-0.0210915 - 0.0737866i) q^{90} +(12.1975 - 8.13026i) q^{91} +(7.25354 - 12.5635i) q^{92} +(1.81646 - 2.40843i) q^{93} +(0.109706 - 0.190016i) q^{94} +(3.62126 - 6.27220i) q^{95} +(0.320012 - 0.424303i) q^{96} +(-3.81553 + 6.60869i) q^{97} +(0.108687 + 0.142307i) q^{98} +(11.0013 + 2.75266i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23}+ \cdots - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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