LMFDB - Embedded newform 315.2.l.c.151.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,2,Mod(121,315)] 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([2, 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("315.121"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (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			151.10
Character	$\chi$	$=$	315.151
Dual form			315.2.l.c.121.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.0255806 q^{2} +(0.676102 + 1.59464i) q^{3} -1.99935 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.0172951 + 0.0407920i) q^{6} +(-2.37158 + 1.17286i) q^{7} -0.102306 q^{8} +(-2.08577 + 2.15628i) q^{9} +(-0.0127903 + 0.0221535i) q^{10} +(-1.89007 - 3.27369i) q^{11} +(-1.35176 - 3.18824i) q^{12} +(-2.77025 - 4.79822i) q^{13} +(-0.0606666 + 0.0300025i) q^{14} +(-1.71905 - 0.211800i) q^{15} +3.99607 q^{16} +(-0.271942 + 0.471017i) q^{17} +(-0.0533554 + 0.0551591i) q^{18} +(3.62126 + 6.27220i) q^{19} +(0.999673 - 1.73148i) q^{20} +(-3.47372 - 2.98886i) q^{21} +(-0.0483491 - 0.0837432i) q^{22} +(-3.62796 + 6.28380i) q^{23} +(-0.0691692 - 0.163141i) q^{24} +(-0.500000 - 0.866025i) 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} +(-0.0439745 - 0.00541797i) q^{30} +1.74165 q^{31} +0.306834 q^{32} +(3.94249 - 5.22733i) 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} +(0.0926341 + 0.160447i) q^{38} +(5.77847 - 7.66166i) q^{39} +(0.0511529 - 0.0885994i) q^{40} +(0.238169 + 0.412522i) q^{41} +(-0.0888600 - 0.0764568i) q^{42} +(-0.279323 + 0.483802i) q^{43} +(3.77890 + 6.54524i) q^{44} +(-0.824510 - 2.88447i) q^{45} +(-0.0928054 + 0.160744i) q^{46} -8.57725 q^{47} +(2.70175 + 6.37231i) q^{48} +(4.24881 - 5.56306i) q^{49} +(-0.0127903 - 0.0221535i) q^{50} +(-0.934964 - 0.115194i) q^{51} +(5.53870 + 9.59330i) q^{52} +(-4.26510 + 7.38738i) q^{53} +(-0.124033 - 0.0477896i) q^{54} +3.78014 q^{55} +(0.242627 - 0.119990i) q^{56} +(-7.55358 + 10.0153i) q^{57} +(-0.103570 + 0.179389i) q^{58} +1.40842 q^{59} +(3.43698 + 0.423461i) q^{60} +1.75402 q^{61} +0.0445526 q^{62} +(2.41757 - 7.56012i) q^{63} -7.98430 q^{64} +5.54051 q^{65} +(0.100851 - 0.133719i) q^{66} +12.3831 q^{67} +(0.543705 - 0.941725i) q^{68} +(-12.4733 - 1.53680i) q^{69} +(0.00435040 - 0.0675400i) q^{70} +10.3293 q^{71} +(0.213387 - 0.220600i) q^{72} +(2.91561 - 5.04998i) q^{73} +(0.0427814 + 0.0740996i) q^{74} +(1.04295 - 1.38284i) q^{75} +(-7.24015 - 12.5403i) q^{76} +(8.32203 + 5.54705i) q^{77} +(0.147817 - 0.195990i) q^{78} +2.96664 q^{79} +(-1.99804 + 3.46070i) q^{80} +(-0.299114 - 8.99503i) q^{81} +(0.00609253 + 0.0105526i) q^{82} +(-3.97711 + 6.88856i) q^{83} +(6.94517 + 5.97575i) q^{84} +(-0.271942 - 0.471017i) q^{85} +(-0.00714526 + 0.0123760i) q^{86} +(-13.9201 - 1.71506i) q^{87} +(0.193365 + 0.334918i) 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} +(1.17754 + 2.77731i) q^{93} -0.219411 q^{94} -7.24252 q^{95} +(0.207451 + 0.489290i) 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} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23}+ \cdots - 89 q^{99}+O(q^{100}) $ 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Character values

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

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

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 $

$2$	0.0255806			0.0180882			0.00904412	−	0.999959i	$-0.497121\pi$
$2$	0.0255806			0.0180882			0.00904412	+	0.999959i	$0.497121\pi$
$3$	0.676102	+	1.59464i	0.390348	+	0.920667i
$3$	0.676102	+	1.59464i	0.390348	+	0.920667i
$4$	−1.99935			−0.999673
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	0.0172951	+	0.0407920i	0.00706071	+	0.0166533i
$7$	−2.37158	+	1.17286i	−0.896374	+	0.443299i
$7$	−2.37158	+	1.17286i	−0.896374	+	0.443299i
$8$	−0.102306			−0.0361706
$9$	−2.08577	+	2.15628i	−0.695257	+	0.718761i
$10$	−0.0127903	+	0.0221535i	−0.00404465	+	0.00700555i
$11$	−1.89007	−	3.27369i	−0.569877	−	0.987056i	−0.996578	−	0.0826628i	$-0.973658\pi$
$11$	−1.89007	−	3.27369i	−0.569877	−	0.987056i	0.426701	−	0.904393i	$-0.359676\pi$
$12$	−1.35176	−	3.18824i	−0.390220	−	0.920366i
$13$	−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	$-0.445579\pi$
$14$	−0.0606666	+	0.0300025i	−0.0162138	+	0.00801849i
$15$	−1.71905	−	0.211800i	−0.443857	−	0.0546865i
$16$	3.99607			0.999019
$17$	−0.271942	+	0.471017i	−0.0659555	+	0.114238i	−0.897117	−	0.441792i	$-0.854343\pi$
$17$	−0.271942	+	0.471017i	−0.0659555	+	0.114238i	0.831162	+	0.556030i	$0.187676\pi$
$18$	−0.0533554	+	0.0551591i	−0.0125760	+	0.0130011i
$19$	3.62126	+	6.27220i	0.830774	+	1.43894i	0.897425	+	0.441166i	$0.145435\pi$
$19$	3.62126	+	6.27220i	0.830774	+	1.43894i	−0.0666517	+	0.997776i	$0.521232\pi$
$20$	0.999673	−	1.73148i	0.223534	−	0.387172i
$21$	−3.47372	−	2.98886i	−0.758028	−	0.652222i
$22$	−0.0483491	−	0.0837432i	−0.0103081	−	0.0178541i
$23$	−3.62796	+	6.28380i	−0.756481	+	1.31026i	0.188154	+	0.982140i	$0.439750\pi$
$23$	−3.62796	+	6.28380i	−0.756481	+	1.31026i	−0.944635	+	0.328124i	$0.893584\pi$
$24$	−0.0691692	−	0.163141i	−0.0141191	−	0.0333011i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−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	$0.895834\pi$
$30$	−0.0439745	−	0.00541797i	−0.00802860	−	0.000989182i
$31$	1.74165			0.312810			0.156405	−	0.987693i	$-0.450009\pi$
$31$	1.74165			0.312810			0.156405	+	0.987693i	$0.450009\pi$
$32$	0.306834			0.0542411
$33$	3.94249	−	5.22733i	0.686300	−	0.909962i
$34$	−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	0.970121	−	0.242622i	$-0.0780076\pi$
$37$	1.67242	+	2.89671i	0.274943	+	0.476216i	−0.695177	+	0.718838i	$0.744674\pi$
$38$	0.0926341	+	0.160447i	0.0150272	+	0.0260279i
$39$	5.77847	−	7.66166i	0.925296	−	1.22685i
$40$	0.0511529	−	0.0885994i	0.00808798	−	0.0140088i
$41$	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	$0.821491\pi$
$42$	−0.0888600	−	0.0764568i	−0.0137114	−	0.0117975i
$43$	−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
$45$	−0.824510	−	2.88447i	−0.122911	−	0.429992i
$46$	−0.0928054	+	0.160744i	−0.0136834	+	0.0237004i
$47$	−8.57725			−1.25112			−0.625560	−	0.780176i	$-0.715129\pi$
$47$	−8.57725			−1.25112			−0.625560	+	0.780176i	$0.715129\pi$
$48$	2.70175	+	6.37231i	0.389965	+	0.919764i
$49$	4.24881	−	5.56306i	0.606972	−	0.794723i
$50$	−0.0127903	−	0.0221535i	−0.00180882	−	0.00313298i
$51$	−0.934964	−	0.115194i	−0.130921	−	0.0161304i
$52$	5.53870	+	9.59330i	0.768079	+	1.33035i
$53$	−4.26510	+	7.38738i	−0.585857	+	1.01473i	0.408911	+	0.912574i	$0.365909\pi$
$53$	−4.26510	+	7.38738i	−0.585857	+	1.01473i	−0.994768	+	0.102160i	$0.967425\pi$
$54$	−0.124033	−	0.0477896i	−0.0168787	−	0.00650334i
$55$	3.78014			0.509713
$56$	0.242627	−	0.119990i	0.0324224	−	0.0160344i
$57$	−7.55358	+	10.0153i	−1.00050	+	1.32655i
$58$	−0.103570	+	0.179389i	−0.0135994	+	0.0235549i
$59$	1.40842			0.183360			0.0916801	−	0.995789i	$-0.470776\pi$
$59$	1.40842			0.183360			0.0916801	+	0.995789i	$0.470776\pi$
$60$	3.43698	+	0.423461i	0.443712	+	0.0546686i
$61$	1.75402			0.224579			0.112289	−	0.993676i	$-0.464182\pi$
$61$	1.75402			0.224579			0.112289	+	0.993676i	$0.464182\pi$
$62$	0.0445526			0.00565818
$63$	2.41757	−	7.56012i	0.304585	−	0.952485i
$64$	−7.98430			−0.998037
$65$	5.54051			0.687216
$66$	0.100851	−	0.133719i	0.0124140	−	0.0164596i
$67$	12.3831			1.51284			0.756421	−	0.654085i	$-0.226946\pi$
$67$	12.3831			1.51284			0.756421	+	0.654085i	$0.226946\pi$
$68$	0.543705	−	0.941725i	0.0659340	−	0.114201i
$69$	−12.4733	−	1.53680i	−1.50161	−	0.185009i
$70$	0.00435040	−	0.0675400i	0.000519973	−	0.00807258i
$71$	10.3293			1.22587			0.612934	−	0.790134i	$-0.289989\pi$
$71$	10.3293			1.22587			0.612934	+	0.790134i	$0.289989\pi$
$72$	0.213387	−	0.220600i	0.0251478	−	0.0259980i
$73$	2.91561	−	5.04998i	0.341246	−	0.591055i	−0.643418	−	0.765515i	$-0.722484\pi$
$73$	2.91561	−	5.04998i	0.341246	−	0.591055i	0.984664	+	0.174459i	$0.0558178\pi$
$74$	0.0427814	+	0.0740996i	0.00497324	+	0.00861391i
$75$	1.04295	−	1.38284i	0.120430	−	0.159677i
$76$	−7.24015	−	12.5403i	−0.830502	−	1.43847i
$77$	8.32203	+	5.54705i	0.948383	+	0.632145i
$78$	0.147817	−	0.195990i	0.0167370	−	0.0221915i
$79$	2.96664			0.333773			0.166886	−	0.985976i	$-0.446629\pi$
$79$	2.96664			0.333773			0.166886	+	0.985976i	$0.446629\pi$
$80$	−1.99804	+	3.46070i	−0.223387	+	0.386918i
$81$	−0.299114	−	8.99503i	−0.0332349	−	0.999448i
$82$	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	$0.310465\pi$
$84$	6.94517	+	5.97575i	0.757780	+	0.652008i
$85$	−0.271942	−	0.471017i	−0.0294962	−	0.0510889i
$86$	−0.00714526	+	0.0123760i	−0.000770493	+	0.00133453i
$87$	−13.9201	−	1.71506i	−1.49239	−	0.183874i
$88$	0.193365	+	0.334918i	0.0206128	+	0.0357024i
$89$	−9.02021	−	15.6235i	−0.956141	−	1.65608i	−0.731736	−	0.681588i	$-0.761290\pi$
$89$	−9.02021	−	15.6235i	−0.956141	−	1.65608i	−0.224405	−	0.974496i	$-0.572044\pi$
$90$	−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
$93$	1.17754	+	2.77731i	0.122105	+	0.287994i
$94$	−0.219411			−0.0226306
$95$	−7.24252			−0.743067
$96$	0.207451	+	0.489290i	0.0211729	+	0.0499380i
$97$	−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
$101$	1.71240	+	2.96596i	0.170390	+	0.295124i	0.938556	−	0.345126i	$-0.112164\pi$
$101$	1.71240	+	2.96596i	0.170390	+	0.295124i	−0.768166	+	0.640250i	$0.778831\pi$
$102$	−0.0239170	−	0.00294674i	−0.00236813	−	0.000291771i
$103$	−4.71527	+	8.16709i	−0.464610	+	0.804728i	−0.999184	−	0.0403940i	$-0.987139\pi$
$103$	−4.71527	+	8.16709i	−0.464610	+	0.804728i	0.534574	+	0.845122i	$0.320472\pi$
$104$	0.283413	+	0.490886i	0.0277909	+	0.0481353i
$105$	4.32529	−	1.51390i	0.422105	−	0.147742i
$106$	−0.109104	+	0.188974i	−0.0105971	+	0.0183548i
$107$	0.0944380	+	0.163571i	0.00912967	+	0.0158131i	0.870554	−	0.492073i	$-0.163761\pi$
$107$	0.0944380	+	0.163571i	0.00912967	+	0.0158131i	−0.861424	+	0.507886i	$0.830427\pi$
$108$	9.69422	+	3.73516i	0.932827	+	0.359416i
$109$	4.40407	−	7.62807i	0.421833	−	0.730636i	−0.574286	−	0.818655i	$-0.694720\pi$
$109$	4.40407	−	7.62807i	0.421833	−	0.730636i	0.996119	+	0.0880186i	$0.0280535\pi$
$110$	0.0966983			0.00921982
$111$	−3.48849	+	4.62538i	−0.331113	+	0.439021i
$112$	−9.47702	+	4.68683i	−0.895494	+	0.442864i
$113$	−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	$-0.351697\pi$
$114$	−0.193226	+	0.256197i	−0.0180972	+	0.0239950i
$115$	−3.62796	−	6.28380i	−0.338309	−	0.585968i
$116$	8.09490	−	14.0208i	0.751593	−	1.30180i
$117$	16.1244	+	4.03454i	1.49071	+	0.372993i
$118$	0.0360282			0.00331666
$119$	0.0924962	−	1.43600i	0.00847912	−	0.131638i
$120$	0.175869	+	0.0216683i	0.0160546	+	0.00197804i
$121$	−1.64471	+	2.84872i	−0.149519	+	0.258975i
$122$	0.0448689			0.00406224
$123$	−0.496798	+	0.658702i	−0.0447947	+	0.0593932i
$124$	−3.48216			−0.312708
$125$	1.00000			0.0894427
$126$	0.0618429	−	0.193393i	0.00550940	−	0.0172288i
$127$	1.14668			0.101751			0.0508756	−	0.998705i	$-0.483799\pi$
$127$	1.14668			0.101751			0.0508756	+	0.998705i	$0.483799\pi$
$128$	−0.817911			−0.0722938
$129$	−0.960342	−	0.118321i	−0.0845534	−	0.0104176i
$130$	0.141730			0.0124305
$131$	3.18123	−	5.51006i	0.277946	−	0.481416i	−0.692928	−	0.721006i	$-0.743680\pi$
$131$	3.18123	−	5.51006i	0.277946	−	0.481416i	0.970874	+	0.239590i	$0.0770131\pi$
$132$	−7.88241	+	10.4512i	−0.686075	+	0.909664i
$133$	−15.9445	−	10.6278i	−1.38257	−	0.921550i
$134$	0.316769			0.0273646
$135$	4.04225	−	3.26500i	0.347902	−	0.281006i
$136$	0.0278212	−	0.0481878i	0.00238565	−	0.00413207i
$137$	4.27981	+	7.41285i	0.365649	+	0.633322i	0.988880	−	0.148715i	$-0.0475138\pi$
$137$	4.27981	+	7.41285i	0.365649	+	0.633322i	−0.623231	+	0.782038i	$0.714180\pi$
$138$	−0.319075	−	0.0393123i	−0.0271614	−	0.00334649i
$139$	−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	$0.917683\pi$
$140$	−0.340021	+	5.27883i	−0.0287370	+	0.446143i
$141$	−5.79910	−	13.6776i	−0.488372	−	1.15187i
$142$	0.264231			0.0221738
$143$	−10.4719	+	18.1379i	−0.875707	+	1.51677i
$144$	−8.33490	+	8.61667i	−0.694575	+	0.718056i
$145$	−4.04878	−	7.01269i	−0.336233	−	0.582372i
$146$	0.0745831	−	0.129182i	0.00617254	−	0.0106912i
$147$	11.7437	+	3.01413i	0.968606	+	0.248602i
$148$	−3.34374	−	5.79152i	−0.274853	−	0.476060i
$149$	−2.34647	+	4.06421i	−0.192231	+	0.332953i	−0.945989	−	0.324198i	$-0.894906\pi$
$149$	−2.34647	+	4.06421i	−0.192231	+	0.332953i	0.753758	+	0.657152i	$0.228239\pi$
$150$	0.0266793	−	0.0353740i	0.00217836	−	0.00288828i
$151$	7.80627	+	13.5208i	0.635265	+	1.10031i	0.986459	+	0.164008i	$0.0524424\pi$
$151$	7.80627	+	13.5208i	0.635265	+	1.10031i	−0.351194	+	0.936303i	$0.614224\pi$
$152$	−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
$156$	−11.5532	+	15.3183i	−0.924994	+	1.22645i
$157$	−18.5691			−1.48197			−0.740986	−	0.671520i	$-0.765642\pi$
$157$	−18.5691			−1.48197			−0.740986	+	0.671520i	$0.765642\pi$
$158$	0.0758884			0.00603736
$159$	−14.6639	−	1.80670i	−1.16292	−	0.143280i
$160$	−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	0.839209	−	0.543808i	$-0.183018\pi$
$163$	−0.655557	−	1.13546i	−0.0513472	−	0.0889359i	−0.890557	+	0.454872i	$0.849685\pi$
$164$	−0.476183	−	0.824773i	−0.0371836	−	0.0644040i
$165$	2.55576	+	6.02797i	0.198965	+	0.469277i
$166$	−0.101737	+	0.176214i	−0.00789632	+	0.0136768i
$167$	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	$0.691638\pi$
$168$	0.355382	+	0.305777i	0.0274183	+	0.0235912i
$169$	−8.84862	+	15.3263i	−0.680663	+	1.17894i
$170$	−0.00695644	−	0.0120489i	−0.000533535	−	0.000924109i
$171$	−21.0778	−	5.27393i	−1.61186	−	0.403307i
$172$	0.558463	−	0.967287i	0.0425824	−	0.0737549i
$173$	−1.42470			−0.108318			−0.0541592	−	0.998532i	$-0.517248\pi$
$173$	−1.42470			−0.108318			−0.0541592	+	0.998532i	$0.517248\pi$
$174$	−0.356085	−	0.0438723i	−0.0269948	−	0.00332595i
$175$	2.20152	+	1.46742i	0.166419	+	0.110927i
$176$	−7.55285	−	13.0819i	−0.569318	−	0.986087i
$177$	0.952233	+	2.24592i	0.0715742	+	0.168814i
$178$	−0.230743	−	0.399658i	−0.0172949	−	0.0299557i
$179$	−6.28599	+	10.8877i	−0.469837	+	0.813782i	−0.999405	−	0.0344857i	$-0.989021\pi$
$179$	−6.28599	+	10.8877i	−0.469837	+	0.813782i	0.529568	+	0.848267i	$0.322354\pi$
$180$	1.64848	+	5.76706i	0.122871	+	0.429851i
$181$	−14.1730			−1.05347			−0.526735	−	0.850029i	$-0.676584\pi$
$181$	−14.1730			−1.05347			−0.526735	+	0.850029i	$0.676584\pi$
$182$	0.312020	+	0.207977i	0.0231285	+	0.0154163i
$183$	1.18589	+	2.79703i	0.0876639	+	0.206762i
$184$	0.371161	−	0.642869i	0.0273623	−	0.0473930i
$185$	−3.34483			−0.245917
$186$	0.0301221	+	0.0710454i	0.00220866	+	0.00520930i
$187$	2.05595			0.150346
$188$	17.1489			1.25071
$189$	13.6902	−	1.25626i	0.995816	−	0.0913794i
$190$	−0.185268			−0.0134408
$191$	10.1805			0.736632			0.368316	−	0.929701i	$-0.379934\pi$
$191$	10.1805			0.736632			0.368316	+	0.929701i	$0.379934\pi$
$192$	−5.39820	−	12.7321i	−0.389582	−	0.918861i
$193$	−6.85150			−0.493182			−0.246591	−	0.969120i	$-0.579310\pi$
$193$	−6.85150			−0.493182			−0.246591	+	0.969120i	$0.579310\pi$
$194$	−0.0976037	+	0.169055i	−0.00700754	+	0.0121374i
$195$	3.74595	+	8.83513i	0.268253	+	0.632697i
$196$	−8.49483	+	11.1225i	−0.606774	+	0.794463i
$197$	−20.0167			−1.42613			−0.713065	−	0.701098i	$-0.752693\pi$
$197$	−20.0167			−1.42613			−0.713065	+	0.701098i	$0.752693\pi$
$198$	0.281419	+	0.0704147i	0.0199996	+	0.00500415i
$199$	6.47405	−	11.2134i	0.458933	−	0.794896i	−0.539972	−	0.841683i	$-0.681565\pi$
$199$	6.47405	−	11.2134i	0.458933	−	0.794896i	0.998905	+	0.0467876i	$0.0148984\pi$
$200$	0.0511529	+	0.0885994i	0.00361706	+	0.00626493i
$201$	8.37227	+	19.7467i	0.590534	+	1.39282i
$202$	0.0438042	+	0.0758711i	0.00308205	+	0.00533827i
$203$	1.37712	−	21.3798i	0.0966549	−	1.50057i
$204$	1.86932	+	0.230313i	0.130878	+	0.0161252i
$205$	−0.476339			−0.0332689
$206$	−0.120620	+	0.208919i	−0.00840397	+	0.0145561i
$207$	−5.98257	−	20.9295i	−0.415817	−	1.45470i
$208$	−11.0701	−	19.1740i	−0.767576	−	1.32948i
$209$	13.6888	−	23.7098i	0.946878	−	1.64004i
$210$	0.110644	−	0.0387266i	0.00763513	−	0.00267239i
$211$	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	$0.687299\pi$
$212$	8.52742	−	14.7699i	0.585666	−	1.01440i
$213$	6.98369	+	16.4716i	0.478515	+	1.12862i
$214$	0.00241579	+	0.00418426i	0.000165140	+	0.000286030i
$215$	−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
$219$	10.0242	+	1.23505i	0.677370	+	0.0834569i
$220$	−7.55780			−0.509547
$221$	3.01339			0.202703
$222$	−0.0892378	+	0.118320i	−0.00598925	+	0.00794112i
$223$	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
$227$	−4.43111	−	7.67490i	−0.294103	−	0.509401i	0.680673	−	0.732587i	$-0.261687\pi$
$227$	−4.43111	−	7.67490i	−0.294103	−	0.509401i	−0.974776	+	0.223186i	$0.928354\pi$
$228$	15.1022	−	20.0240i	1.00017	−	1.32612i
$229$	−13.1585	+	22.7911i	−0.869536	+	1.50608i	−0.00706468	+	0.999975i	$0.502249\pi$
$229$	−13.1585	+	22.7911i	−0.869536	+	1.50608i	−0.862471	+	0.506106i	$0.831085\pi$
$230$	−0.0928054	−	0.160744i	−0.00611941	−	0.0105991i
$231$	−3.21902	+	17.0210i	−0.211796	+	1.11990i
$232$	0.414213	−	0.717438i	0.0271944	−	0.0471021i
$233$	13.0236	+	22.5576i	0.853208	+	1.47780i	0.878298	+	0.478114i	$0.158679\pi$
$233$	13.0236	+	22.5576i	0.853208	+	1.47780i	−0.0250903	+	0.999685i	$0.507987\pi$
$234$	0.412473	+	0.103206i	0.0269642	+	0.00674680i
$235$	4.28862	−	7.42811i	0.279759	−	0.484557i
$236$	−2.81591			−0.183300
$237$	2.00575	+	4.73073i	0.130287	+	0.307294i
$238$	0.00236611	−	0.0367339i	0.000153372	−	0.00238111i
$239$	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	$0.622668\pi$
$240$	−6.86946	−	0.846367i	−0.443422	−	0.0546328i
$241$	7.14145	+	12.3693i	0.460021	+	0.796780i	0.998961	−	0.0455641i	$-0.0145085\pi$
$241$	7.14145	+	12.3693i	0.460021	+	0.796780i	−0.538940	+	0.842344i	$0.681175\pi$
$242$	−0.0420728	+	0.0728722i	−0.00270454	+	0.00468440i
$243$	14.1416	−	6.55854i	0.907186	−	0.420730i
$244$	−3.50689			−0.224505
$245$	2.69335	+	6.46111i	0.172072	+	0.412785i
$246$	−0.0127084	+	0.0168500i	−0.000810258	+	0.00107432i
$247$	20.0636	−	34.7512i	1.27662	−	2.21117i
$248$	−0.178181			−0.0113145
$249$	−13.6737	−	1.68470i	−0.866537	−	0.106764i
$250$	0.0255806			0.00161786
$251$	−2.23618			−0.141146			−0.0705731	−	0.997507i	$-0.522483\pi$
$251$	−2.23618			−0.141146			−0.0705731	+	0.997507i	$0.522483\pi$
$252$	−4.83355	+	15.1153i	−0.304485	+	0.952174i
$253$	27.4283			1.72440
$254$	0.0293327			0.00184050
$255$	0.567243	−	0.752105i	0.0355221	−	0.0470987i
$256$	15.9477			0.996730
$257$	7.88236	−	13.6527i	0.491688	−	0.851629i	−0.508266	−	0.861200i	$-0.669713\pi$
$257$	7.88236	−	13.6527i	0.491688	−	0.851629i	0.999954	+	0.00957101i	$0.00304659\pi$
$258$	−0.0245662	−	0.00302673i	−0.00152942	−	0.000188436i
$259$	−7.36370	−	4.90828i	−0.457558	−	0.304985i
$260$	−11.0774			−0.686991
$261$	−6.67651	−	23.3572i	−0.413266	−	1.44577i
$262$	0.0813780	−	0.140951i	0.00502755	−	0.00870797i
$263$	6.38973	+	11.0673i	0.394008	+	0.682441i	0.992974	−	0.118333i	$-0.0377550\pi$
$263$	6.38973	+	11.0673i	0.394008	+	0.682441i	−0.598966	+	0.800774i	$0.704422\pi$
$264$	−0.403340	+	0.534787i	−0.0248239	+	0.0329138i
$265$	−4.26510	−	7.38738i	−0.262003	−	0.453803i
$266$	−0.407871	−	0.271867i	−0.0250082	−	0.0166692i
$267$	18.8153	−	24.9471i	1.15148	−	1.52674i
$268$	−24.7582			−1.51235
$269$	9.82818	−	17.0229i	0.599235	−	1.03790i	−0.393700	−	0.919239i	$-0.628805\pi$
$269$	9.82818	−	17.0229i	0.599235	−	1.03790i	0.992934	−	0.118666i	$-0.0378617\pi$
$270$	0.103403	−	0.0835207i	0.00629293	−	0.00508291i
$271$	−1.02524	−	1.77577i	−0.0622791	−	0.107871i	0.833205	−	0.552965i	$-0.186504\pi$
$271$	−1.02524	−	1.77577i	−0.0622791	−	0.107871i	−0.895484	+	0.445094i	$0.853170\pi$
$272$	−1.08670	+	1.88222i	−0.0658908	+	0.114126i
$273$	−4.71809	+	24.9476i	−0.285552	+	1.50990i
$274$	0.109480	+	0.189625i	0.00661394	+	0.0114557i
$275$	−1.89007	+	3.27369i	−0.113975	+	0.197411i
$276$	24.9384	+	3.07259i	1.50112	+	0.184948i
$277$	−3.21007	−	5.56000i	−0.192874	−	0.334068i	0.753327	−	0.657646i	$-0.228448\pi$
$277$	−3.21007	−	5.56000i	−0.192874	−	0.334068i	−0.946202	+	0.323578i	$0.895114\pi$
$278$	−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	$0.800171\pi$
$282$	−0.148345	−	0.349883i	−0.00883379	−	0.0208352i
$283$	9.72939			0.578352			0.289176	−	0.957276i	$-0.406619\pi$
$283$	9.72939			0.578352			0.289176	+	0.957276i	$0.406619\pi$
$284$	−20.6519			−1.22547
$285$	−4.89668	−	11.5492i	−0.290054	−	0.684117i
$286$	−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
$290$	−0.103570	−	0.179389i	−0.00608185	−	0.0105341i
$291$	−13.1182	−	1.61626i	−0.769002	−	0.0947466i
$292$	−5.82931	+	10.0967i	−0.341134	+	0.590862i
$293$	−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	$0.934086\pi$
$294$	0.300412	+	0.0771034i	0.0175204	+	0.00449676i
$295$	−0.704208	+	1.21972i	−0.0410006	+	0.0710151i
$296$	−0.171098	−	0.296350i	−0.00994486	−	0.0172250i
$297$	3.04847	+	19.4042i	0.176890	+	1.12594i
$298$	−0.0600243	+	0.103965i	−0.00347712	+	0.00602254i
$299$	40.2014			2.32491
$300$	−2.08522	+	2.76478i	−0.120390	+	0.159625i
$301$	0.0950069	−	1.47498i	0.00547611	−	0.0850166i
$302$	0.199689	+	0.345872i	0.0114908	+	0.0199027i
$303$	−3.57189	+	4.73595i	−0.205200	+	0.272073i
$304$	14.4708	+	25.0642i	0.829958	+	1.43753i
$305$	−0.877009	+	1.51902i	−0.0502174	+	0.0869790i
$306$	−0.0114713	−	0.0401313i	−0.000655771	−	0.00229416i
$307$	3.58038			0.204343			0.102171	−	0.994767i	$-0.467421\pi$
$307$	3.58038			0.204343			0.102171	+	0.994767i	$0.467421\pi$
$308$	−16.6386	−	11.0905i	−0.948073	−	0.631938i
$309$	−16.2116	−	1.99739i	−0.922246	−	0.113627i
$310$	−0.0222763	+	0.0385837i	−0.00126521	+	0.00219140i
$311$	16.3157			0.925180			0.462590	−	0.886572i	$-0.346920\pi$
$311$	16.3157			0.925180			0.462590	+	0.886572i	$0.346920\pi$
$312$	−0.591171	+	0.783832i	−0.0334685	+	0.0443757i
$313$	−6.87643			−0.388679			−0.194339	−	0.980934i	$-0.562256\pi$
$313$	−6.87643			−0.388679			−0.194339	+	0.980934i	$0.562256\pi$
$314$	−0.475008			−0.0268063
$315$	5.33847	+	5.87373i	0.300789	+	0.330947i
$316$	−5.93133			−0.333663
$317$	−19.9474			−1.12036			−0.560178	−	0.828372i	$-0.689267\pi$
$317$	−19.9474			−1.12036			−0.560178	+	0.828372i	$0.689267\pi$
$318$	−0.375111	−	0.0462164i	−0.0210352	−	0.00259169i
$319$	30.6098			1.71382
$320$	3.99215	−	6.91461i	0.223168	−	0.386538i
$321$	−0.196988	+	0.261186i	−0.0109948	+	0.0145780i
$322$	0.0315661	−	0.490064i	0.00175911	−	0.0273102i
$323$	−3.93908			−0.219177
$324$	0.598032	+	17.9842i	0.0332240	+	0.999121i
$325$	−2.77025	+	4.79822i	−0.153666	+	0.266157i
$326$	−0.0167696	−	0.0290457i	−0.000928780	−	0.00160869i
$327$	15.1416	+	1.86556i	0.837335	+	0.103166i
$328$	−0.0243661	−	0.0422033i	−0.00134539	−	0.00233029i
$329$	20.3416	−	10.0599i	1.12147	−	0.554620i
$330$	0.0653779	+	0.154199i	0.00359894	+	0.00848839i
$331$	−10.8613			−0.596991			−0.298495	−	0.954411i	$-0.596485\pi$
$331$	−10.8613			−0.596991			−0.298495	+	0.954411i	$0.596485\pi$
$332$	7.95162	−	13.7726i	0.436402	−	0.755870i
$333$	−9.73440	−	2.43567i	−0.533442	−	0.133474i
$334$	0.142343	+	0.246546i	0.00778868	+	0.0134904i
$335$	−6.19157	+	10.7241i	−0.338282	+	0.585921i
$336$	−13.8813	−	11.9437i	−0.757284	−	0.651582i
$337$	−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	$0.835713\pi$
$338$	−0.226353	+	0.392055i	−0.0123120	+	0.0213250i
$339$	12.1755	−	16.1434i	0.661282	−	0.876790i
$340$	0.543705	+	0.941725i	0.0294866	+	0.0510722i
$341$	−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
$345$	7.56755	−	10.0338i	0.407423	−	0.540201i
$346$	−0.0364449			−0.00195929
$347$	3.78826			0.203365			0.101682	−	0.994817i	$-0.467577\pi$
$347$	3.78826			0.203365			0.101682	+	0.994817i	$0.467577\pi$
$348$	27.8311	+	3.42900i	1.49190	+	0.183813i
$349$	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
$353$	−2.15744	−	3.73679i	−0.114829	−	0.198889i	0.802883	−	0.596137i	$-0.203299\pi$
$353$	−2.15744	−	3.73679i	−0.114829	−	0.198889i	−0.917711	+	0.397248i	$0.869965\pi$
$354$	0.0243587	+	0.0574521i	0.00129465	+	0.00305354i
$355$	−5.16467	+	8.94548i	−0.274112	+	0.474777i
$356$	18.0345	+	31.2367i	0.955828	+	1.65554i
$357$	2.35245	−	0.823387i	0.124505	−	0.0435783i
$358$	−0.160800	+	0.278513i	−0.00849853	+	0.0147199i
$359$	−13.5903	−	23.5390i	−0.717267	−	1.24234i	−0.962079	−	0.272772i	$-0.912059\pi$
$359$	−13.5903	−	23.5390i	−0.717267	−	1.24234i	0.244811	−	0.969571i	$-0.421274\pi$
$360$	0.0843522	+	0.295098i	0.00444575	+	0.0155530i
$361$	−16.7270	+	28.9721i	−0.880370	+	1.52485i
$362$	−0.362554			−0.0190554
$363$	−5.65469	−	0.696699i	−0.296794	−	0.0365672i
$364$	−24.3871	−	16.2552i	−1.27823	−	0.852004i
$365$	2.91561	+	5.04998i	0.152610	+	0.264328i
$366$	0.0303359	+	0.0715498i	0.00158569	+	0.00373997i
$367$	−6.00761	−	10.4055i	−0.313595	−	0.543162i	0.665543	−	0.746359i	$-0.268200\pi$
$367$	−6.00761	−	10.4055i	−0.313595	−	0.543162i	−0.979138	+	0.203197i	$0.934867\pi$
$368$	−14.4976	+	25.1105i	−0.755738	+	1.30898i
$369$	−1.38628	−	0.346865i	−0.0721669	−	0.0180571i
$370$	−0.0855629			−0.00444820
$371$	1.45070	−	22.5221i	0.0753167	−	1.16929i
$372$	−2.35430	−	5.55281i	−0.122065	−	0.287900i
$373$	4.34193	−	7.52044i	0.224816	−	0.389394i	−0.731448	−	0.681897i	$-0.761155\pi$
$373$	4.34193	−	7.52044i	0.224816	−	0.389394i	0.956264	+	0.292504i	$0.0944884\pi$
$374$	0.0525926			0.00271950
$375$	0.676102	+	1.59464i	0.0349138	+	0.0823470i
$376$	0.877502			0.0452537
$377$	44.8646			2.31064
$378$	0.350204	−	0.0321359i	0.0180126	−	0.00165289i
$379$	12.7019			0.652454			0.326227	−	0.945291i	$-0.394223\pi$
$379$	12.7019			0.652454			0.326227	+	0.945291i	$0.394223\pi$
$380$	14.4803			0.742824
$381$	0.775271	+	1.82854i	0.0397183	+	0.0936790i
$382$	0.260423			0.0133244
$383$	−12.5605	+	21.7554i	−0.641812	+	1.11165i	0.343216	+	0.939256i	$0.388484\pi$
$383$	−12.5605	+	21.7554i	−0.641812	+	1.11165i	−0.985028	+	0.172394i	$0.944850\pi$
$384$	−0.552991	−	1.30428i	−0.0282197	−	0.0665585i
$385$	−8.96490	+	4.43356i	−0.456894	+	0.225955i
$386$	−0.175266			−0.00892079
$387$	−0.460609	−	1.61140i	−0.0234141	−	0.0819120i
$388$	7.62856	−	13.2131i	0.387282	−	0.670791i
$389$	−9.57121	−	16.5778i	−0.485280	−	0.840529i	0.514577	−	0.857444i	$-0.327949\pi$
$389$	−9.57121	−	16.5778i	−0.485280	−	0.840529i	−0.999857	+	0.0169151i	$0.994615\pi$
$390$	0.0958238	+	0.226008i	0.00485223	+	0.0114444i
$391$	−1.97318	−	3.41766i	−0.0997882	−	0.172838i
$392$	−0.434678	+	0.569133i	−0.0219545	+	0.0287456i
$393$	10.9374	+	1.34757i	0.551720	+	0.0679759i
$394$	−0.512039			−0.0257962
$395$	−1.48332	+	2.56918i	−0.0746338	+	0.129270i
$396$	−21.9953	−	5.50351i	−1.10531	−	0.276562i
$397$	−1.80451	−	3.12551i	−0.0905659	−	0.156865i	0.817184	−	0.576378i	$-0.195534\pi$
$397$	−1.80451	−	3.12551i	−0.0905659	−	0.156865i	−0.907749	+	0.419513i	$0.862201\pi$
$398$	0.165610	−	0.286845i	0.00830129	−	0.0143783i
$399$	6.16746	−	32.6113i	0.308759	−	1.63261i
$400$	−1.99804	−	3.46070i	−0.0999019	−	0.173035i
$401$	−1.68008	+	2.90998i	−0.0838989	+	0.145317i	−0.904922	−	0.425579i	$-0.860071\pi$
$401$	−1.68008	+	2.90998i	−0.0838989	+	0.145317i	0.821023	+	0.570896i	$0.193404\pi$
$402$	0.214168	+	0.505133i	0.0106817	+	0.0251937i
$403$	−4.82482	−	8.35683i	−0.240341	−	0.416284i
$404$	−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
$408$	0.0956522	+	0.0117850i	0.00473549	+	0.000583447i
$409$	2.38228			0.117796			0.0588980	−	0.998264i	$-0.481241\pi$
$409$	2.38228			0.117796			0.0588980	+	0.998264i	$0.481241\pi$
$410$	−0.0121851			−0.000601777
$411$	−8.92725	+	11.8366i	−0.440349	+	0.583857i
$412$	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
$416$	−0.850008	−	1.47226i	−0.0416750	−	0.0721833i
$417$	6.44083	−	8.53987i	0.315409	−	0.418199i
$418$	0.350169	−	0.606511i	0.0171273	−	0.0296654i
$419$	−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	$0.857727\pi$
$420$	−8.64774	+	3.02682i	−0.421967	+	0.147694i
$421$	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
$423$	17.8902	−	18.4950i	0.869850	−	0.899256i
$424$	0.436345	−	0.755772i	0.0211908	−	0.0367035i
$425$	0.543883			0.0263822
$426$	0.178647	+	0.421354i	0.00865549	+	0.0204147i
$427$	−4.15980	+	2.05721i	−0.201307	+	0.0995555i
$428$	−0.188814	−	0.327036i	−0.00912668	−	0.0158079i
$429$	−36.0036	−	4.43591i	−1.73827	−	0.214168i
$430$	−0.00714526	−	0.0123760i	−0.000344575	−	0.000596822i
$431$	−11.9751	+	20.7415i	−0.576821	+	0.999082i	0.419021	+	0.907977i	$0.362373\pi$
$431$	−11.9751	+	20.7415i	−0.576821	+	0.999082i	−0.995841	+	0.0911058i	$0.970960\pi$
$432$	−19.3758	−	7.46544i	−0.932216	−	0.359181i
$433$	−15.3737			−0.738813			−0.369406	−	0.929268i	$-0.620439\pi$
$433$	−15.3737			−0.738813			−0.369406	+	0.929268i	$0.620439\pi$
$434$	−0.105660	+	0.0522539i	−0.00507185	+	0.00250827i
$435$	8.44534	−	11.1976i	0.404923	−	0.536886i
$436$	−8.80525	+	15.2511i	−0.421695	+	0.730397i
$437$	−52.5511			−2.51386
$438$	0.256424	+	0.0315933i	0.0122524	+	0.00150959i
$439$	8.50008			0.405687			0.202843	−	0.979211i	$-0.434982\pi$
$439$	8.50008			0.405687			0.202843	+	0.979211i	$0.434982\pi$
$440$	−0.386730			−0.0184366
$441$	3.13349	+	20.7649i	0.149214	+	0.988805i
$442$	0.0770844			0.00366653
$443$	−30.9324			−1.46964			−0.734822	−	0.678260i	$-0.762734\pi$
$443$	−30.9324			−1.46964			−0.734822	+	0.678260i	$0.762734\pi$
$444$	6.97470	−	9.24773i	0.331005	−	0.438878i
$445$	18.0404			0.855198
$446$	0.158739	−	0.274944i	0.00751652	−	0.0130190i
$447$	−8.06743	−	0.993965i	−0.381576	−	0.0470129i
$448$	18.9354	−	9.36445i	0.894615	−	0.442429i
$449$	4.23659			0.199937			0.0999686	−	0.994991i	$-0.468126\pi$
$449$	4.23659			0.199937			0.0999686	+	0.994991i	$0.468126\pi$
$450$	0.0744469	+	0.0186276i	0.00350946	+	0.000878111i
$451$	0.900313	−	1.55939i	0.0423941	−	0.0734287i
$452$	11.6703	+	20.2135i	0.548923	+	0.950762i
$453$	−16.2831	+	21.5897i	−0.765046	+	1.01437i
$454$	−0.113350	−	0.196329i	−0.00531980	−	0.00921417i
$455$	−13.1398	+	6.49823i	−0.616002	+	0.304642i
$456$	0.772776	−	1.02462i	0.0361885	−	0.0479822i
$457$	39.3982			1.84297			0.921485	−	0.388414i	$-0.126977\pi$
$457$	39.3982			1.84297			0.921485	+	0.388414i	$0.126977\pi$
$458$	−0.336602	+	0.583012i	−0.0157284	+	0.0272424i
$459$	2.19851	−	1.77578i	0.102618	−	0.0828862i
$460$	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	$0.209221\pi$
$462$	−0.0823447	+	0.435409i	−0.00383102	+	0.0202571i
$463$	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	$0.688549\pi$
$464$	−16.1792	+	28.0232i	−0.751101	+	1.30094i
$465$	−2.99399	−	0.368881i	−0.138843	−	0.0171065i
$466$	0.333153	+	0.577038i	0.0154330	+	0.0267308i
$467$	11.2057	+	19.4088i	0.518536	+	0.898131i	0.999768	+	0.0215379i	$0.00685627\pi$
$467$	11.2057	+	19.4088i	0.518536	+	0.898131i	−0.481232	+	0.876593i	$0.659810\pi$
$468$	−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
$471$	−12.5546	−	29.6110i	−0.578485	−	1.36440i
$472$	−0.144089			−0.00663224
$473$	2.11176			0.0970987
$474$	0.0513083	+	0.121015i	0.00235667	+	0.00555840i
$475$	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
$479$	15.0652	+	26.0938i	0.688349	+	1.19226i	0.972372	+	0.233438i	$0.0749975\pi$
$479$	15.0652	+	26.0938i	0.688349	+	1.19226i	−0.284023	+	0.958817i	$0.591669\pi$
$480$	−0.527463	−	0.0649873i	−0.0240753	−	0.00296625i
$481$	9.26603	−	16.0492i	0.422495	−	0.731782i
$482$	0.182683	+	0.316416i	0.00832097	+	0.0144123i
$483$	31.3839	−	10.9848i	1.42802	−	0.499824i
$484$	3.28835	−	5.69559i	0.149470	−	0.258890i
$485$	−3.81553	−	6.60869i	−0.173254	−	0.300085i
$486$	0.361752	−	0.167772i	0.0164094	−	0.00761027i
$487$	−17.0000	+	29.4448i	−0.770343	+	1.33427i	0.167032	+	0.985951i	$0.446582\pi$
$487$	−17.0000	+	29.4448i	−0.770343	+	1.33427i	−0.937375	+	0.348322i	$0.886752\pi$
$488$	−0.179446			−0.00812315
$489$	1.36743	−	1.81306i	0.0618372	−	0.0819896i
$490$	0.0688975	+	0.165279i	0.00311247	+	0.00746655i
$491$	−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	$0.942899\pi$
$492$	0.993270	−	1.31697i	0.0447801	−	0.0593737i
$493$	−2.20206	−	3.81408i	−0.0991759	−	0.171778i
$494$	0.513240	−	0.888958i	0.0230918	−	0.0399961i
$495$	−7.88450	+	8.15104i	−0.354382	+	0.366362i
$496$	6.95977			0.312503
$497$	−24.4969	+	12.1149i	−1.09884	+	0.543426i
$498$	−0.349782	−	0.0430957i	−0.0156741	−	0.00193117i
$499$	−0.409572	+	0.709399i	−0.0183349	+	0.0317570i	−0.875047	−	0.484037i	$-0.839170\pi$
$499$	−0.409572	+	0.709399i	−0.0183349	+	0.0317570i	0.856712	+	0.515794i	$0.172503\pi$
$500$	−1.99935			−0.0894135
$501$	−11.6070	+	15.3897i	−0.518562	+	0.687559i
$502$	−0.0572028			−0.00255309
$503$	13.5639			0.604783			0.302392	−	0.953184i	$-0.402215\pi$
$503$	13.5639			0.604783			0.302392	+	0.953184i	$0.402215\pi$
$504$	−0.247331	+	0.773444i	−0.0110170	+	0.0344519i
$505$	−3.42479			−0.152401
$506$	0.701634			0.0311914
$507$	−30.4225	−	3.74827i	−1.35111	−	0.166467i
$508$	−2.29260			−0.101718
$509$	−17.4596	+	30.2408i	−0.773881	+	1.34040i	0.161540	+	0.986866i	$0.448354\pi$
$509$	−17.4596	+	30.2408i	−0.773881	+	1.34040i	−0.935421	+	0.353536i	$0.884979\pi$
$510$	0.0145104	−	0.0192393i	0.000642533	−	0.000851932i
$511$	−0.991693	+	15.3960i	−0.0438699	+	0.681080i
$512$	2.04377			0.0903229
$513$	−5.84070	−	37.1772i	−0.257873	−	1.64141i
$514$	0.201636	−	0.349244i	0.00889378	−	0.0154045i
$515$	−4.71527	−	8.16709i	−0.207780	−	0.359885i
$516$	1.92006	+	0.236565i	0.0845257	+	0.0104142i
$517$	16.2116	+	28.0793i	0.712984	+	1.23493i
$518$	−0.188368	−	0.125557i	−0.00827642	−	0.00551665i
$519$	−0.963246	−	2.27190i	−0.0422818	−	0.0997251i
$520$	−0.566826			−0.0248570
$521$	1.55141	−	2.68713i	0.0679687	−	0.117725i	−0.830038	−	0.557706i	$-0.811682\pi$
$521$	1.55141	−	2.68713i	0.0679687	−	0.117725i	0.898007	+	0.439981i	$0.145015\pi$
$522$	−0.170789	−	0.597491i	−0.00747525	−	0.0261515i
$523$	−5.99060	−	10.3760i	−0.261951	−	0.453712i	0.704810	−	0.709396i	$-0.251032\pi$
$523$	−5.99060	−	10.3760i	−0.261951	−	0.453712i	−0.966760	+	0.255685i	$0.917699\pi$
$524$	−6.36039	+	11.0165i	−0.277855	+	0.481259i
$525$	−0.851563	+	4.50276i	−0.0371653	+	0.196517i
$526$	0.163453	+	0.283110i	0.00712691	+	0.0123442i
$527$	−0.473628	+	0.820348i	−0.0206316	+	0.0357349i
$528$	15.7545	−	20.8888i	0.685626	−	0.909069i
$529$	−14.8241	−	25.6761i	−0.644527	−	1.11635i
$530$	−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
$534$	0.481306	−	0.638162i	0.0208282	−	0.0276160i
$535$	−0.188876			−0.00816583
$536$	−1.26687			−0.0547203
$537$	−21.6119	−	2.66274i	−0.932622	−	0.114906i
$538$	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	0.877954	−	0.478745i	$-0.158908\pi$
$541$	0.566880	+	0.981865i	0.0243721	+	0.0422137i	−0.853582	+	0.520958i	$0.825575\pi$
$542$	−0.0262264	−	0.0454254i	−0.00112652	−	0.00195119i
$543$	−9.58240	−	22.6009i	−0.411220	−	0.969896i
$544$	−0.0834409	+	0.144524i	−0.00357750	+	0.00619641i
$545$	4.40407	+	7.62807i	0.188650	+	0.326751i
$546$	−0.120692	+	0.638175i	−0.00516513	+	0.0273114i
$547$	−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
$549$	−3.65848	+	3.78216i	−0.156140	+	0.161419i
$550$	−0.0483491	+	0.0837432i	−0.00206161	+	0.00357082i
$551$	−58.6467			−2.49843
$552$	1.27609	+	0.157224i	0.0543140	+	0.00669188i
$553$	−7.03562	+	3.47944i	−0.299185	+	0.147961i
$554$	−0.0821155	−	0.142228i	−0.00348875	−	0.00604270i
$555$	−2.26145	−	5.33381i	−0.0959931	−	0.226408i
$556$	6.17357	+	10.6929i	0.261818	+	0.453481i
$557$	−6.94094	+	12.0221i	−0.294097	+	0.509391i	−0.974774	−	0.223192i	$-0.928352\pi$
$557$	−6.94094	+	12.0221i	−0.294097	+	0.509391i	0.680677	+	0.732583i	$0.261686\pi$
$558$	−0.0929265	+	0.0960680i	−0.00393389	+	0.00406688i
$559$	3.09518			0.130912
$560$	0.679598	−	10.5508i	0.0287182	−	0.445851i
$561$	1.39003	+	3.27851i	0.0586873	+	0.138419i
$562$	−0.391643	+	0.678346i	−0.0165205	+	0.0286143i
$563$	22.2662			0.938408			0.469204	−	0.883090i	$-0.344541\pi$
$563$	22.2662			0.938408			0.469204	+	0.883090i	$0.344541\pi$
$564$	11.5944	+	27.3463i	0.488212	+	1.15149i
$565$	11.6741			0.491132
$566$	0.248884			0.0104614
$567$	11.2593	+	20.9816i	0.472845	+	0.881146i
$568$	−1.05675			−0.0443403
$569$	0.0987691			0.00414062			0.00207031	−	0.999998i	$-0.499341\pi$
$569$	0.0987691			0.00414062			0.00207031	+	0.999998i	$0.499341\pi$
$570$	−0.125260	−	0.295437i	−0.00524657	−	0.0123745i
$571$	34.9761			1.46370			0.731852	−	0.681463i	$-0.238656\pi$
$571$	34.9761			1.46370			0.731852	+	0.681463i	$0.238656\pi$
$572$	20.9370	−	36.2640i	0.875421	−	1.51627i
$573$	6.88303	+	16.2342i	0.287543	+	0.678193i
$574$	−0.0268256	−	0.0178806i	−0.00111968	−	0.000746322i
$575$	7.25591			0.302592
$576$	16.6534	−	17.2164i	0.693893	−	0.717350i
$577$	9.85646	−	17.0719i	0.410330	−	0.710712i	−0.584596	−	0.811325i	$-0.698747\pi$
$577$	9.85646	−	17.0719i	0.410330	−	0.710712i	0.994926	+	0.100612i	$0.0320802\pi$
$578$	0.213652	+	0.370056i	0.00888675	+	0.0153923i
$579$	−4.63232	−	10.9257i	−0.192512	−	0.454057i
$580$	8.09490	+	14.0208i	0.336123	+	0.582181i
$581$	1.35274	−	21.0014i	0.0561213	−	0.871283i
$582$	−0.335572	−	0.0413449i	−0.0139099	−	0.00171380i
$583$	32.2453			1.33547
$584$	−0.298283	+	0.516642i	−0.0123431	+	0.0213788i
$585$	−11.5562	+	11.9469i	−0.477792	+	0.493944i
$586$	−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	$-0.0195997\pi$
$588$	−23.4798	−	6.02629i	−0.968289	−	0.248520i
$589$	6.30697	+	10.9240i	0.259874	+	0.450116i
$590$	−0.0180141	+	0.0312013i	−0.000741628	+	0.00128454i
$591$	−13.5333	−	31.9195i	−0.556687	−	1.31299i
$592$	6.68310	+	11.5755i	0.274674	+	0.475749i
$593$	2.17116	+	3.76056i	0.0891589	+	0.154428i	0.907156	−	0.420795i	$-0.138249\pi$
$593$	2.17116	+	3.76056i	0.0891589	+	0.154428i	−0.817997	+	0.575223i	$0.804915\pi$
$594$	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
$597$	22.2585	+	2.74240i	0.910978	+	0.112239i
$598$	1.02838			0.0420535
$599$	−38.5844			−1.57652			−0.788258	−	0.615345i	$-0.789017\pi$
$599$	−38.5844			−1.57652			−0.788258	+	0.615345i	$0.789017\pi$
$600$	−0.106700	+	0.141473i	−0.00435600	+	0.00577561i
$601$	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
$605$	−1.64471	−	2.84872i	−0.0668670	−	0.115817i
$606$	−0.0913712	+	0.121149i	−0.00371170	+	0.00492133i
$607$	−5.35336	+	9.27229i	−0.217286	+	0.376351i	−0.953977	−	0.299879i	$-0.903054\pi$
$607$	−5.35336	+	9.27229i	−0.217286	+	0.376351i	0.736691	+	0.676229i	$0.236387\pi$
$608$	1.11112	+	1.92452i	0.0450620	+	0.0780498i
$609$	35.0242	−	12.2589i	1.41925	−	0.496756i
$610$	−0.0224344	+	0.0388576i	−0.000908344	+	0.00157330i
$611$	23.7612	+	41.1555i	0.961274	+	1.66497i
$612$	0.896581	+	3.13661i	0.0362422	+	0.126790i
$613$	−14.1382	+	24.4882i	−0.571038	+	0.989067i	0.425421	+	0.904995i	$0.360126\pi$
$613$	−14.1382	+	24.4882i	−0.571038	+	0.989067i	−0.996460	+	0.0840720i	$0.973207\pi$
$614$	0.0915883			0.00369620
$615$	−0.322054	−	0.759590i	−0.0129865	−	0.0306296i
$616$	−0.851392	−	0.567496i	−0.0343036	−	0.0228651i
$617$	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	$0.567850\pi$
$618$	−0.414703	−	0.0510944i	−0.0166818	−	0.00205532i
$619$	−3.26092	−	5.64807i	−0.131067	−	0.227015i	0.793021	−	0.609194i	$-0.208507\pi$
$619$	−3.26092	−	5.64807i	−0.131067	−	0.227015i	−0.924088	+	0.382179i	$0.875174\pi$
$620$	1.74108	−	3.01564i	0.0699236	−	0.121111i
$621$	29.3302	−	23.6905i	1.17698	−	0.950668i
$622$	0.417367			0.0167349
$623$	39.7163	+	26.4729i	1.59120	+	1.06061i
$624$	23.0912	−	30.6165i	0.924388	−	1.22564i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−0.175903			−0.00703051
$627$	47.0637	+	5.79859i	1.87954	+	0.231573i
$628$	37.1260			1.48149
$629$	−1.81920			−0.0725362
$630$	0.136561	+	0.150254i	0.00544074	+	0.00598625i
$631$	2.81008			0.111867			0.0559337	−	0.998434i	$-0.482186\pi$
$631$	2.81008			0.111867			0.0559337	+	0.998434i	$0.482186\pi$
$632$	−0.303504			−0.0120727
$633$	−13.4183	+	17.7912i	−0.533329	+	0.707138i
$634$	−0.510266			−0.0202653
$635$	−0.573339	+	0.993052i	−0.0227523	+	0.0394081i
$636$	29.3182	+	3.61221i	1.16254	+	0.143233i
$637$	−38.4631	−	4.97563i	−1.52396	−	0.197142i
$638$	0.783019			0.0310000
$639$	−21.5447	+	22.2730i	−0.852293	+	0.881106i
$640$	0.408955	−	0.708332i	0.0161654	−	0.0279993i
$641$	0.856808	+	1.48403i	0.0338419	+	0.0586159i	0.882450	−	0.470406i	$-0.155892\pi$
$641$	0.856808	+	1.48403i	0.0338419	+	0.0586159i	−0.848608	+	0.529022i	$0.822559\pi$
$642$	−0.00503909	+	0.00668130i	−0.000198877	+	0.000263690i
$643$	−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	$0.969221\pi$
$644$	−2.46716	+	38.3027i	−0.0972199	+	1.50934i
$645$	0.582640	−	0.772520i	0.0229414	−	0.0304179i
$646$	−0.100764			−0.00396452
$647$	−1.23228	+	2.13437i	−0.0484458	+	0.0839105i	−0.889231	−	0.457458i	$-0.848760\pi$
$647$	−1.23228	+	2.13437i	−0.0484458	+	0.0839105i	0.840786	+	0.541368i	$0.182093\pi$
$648$	0.0306011	+	0.920244i	0.00120212	+	0.0361506i
$649$	−2.66200	−	4.61072i	−0.104493	−	0.180987i
$650$	−0.0708649	+	0.122742i	−0.00277955	+	0.00481432i
$651$	−6.05002	−	5.20555i	−0.237119	−	0.204021i
$652$	1.31068	+	2.27017i	0.0513304	+	0.0889068i
$653$	16.7740	−	29.0534i	0.656416	−	1.13695i	−0.325121	−	0.945672i	$-0.605405\pi$
$653$	16.7740	−	29.0534i	0.656416	−	1.13695i	0.981537	−	0.191273i	$-0.0612616\pi$
$654$	0.387333	+	0.0477222i	0.0151459	+	0.00186609i
$655$	3.18123	+	5.51006i	0.124301	+	0.215296i
$656$	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	$0.0939246\pi$
$660$	−5.10984	−	12.0520i	−0.198900	−	0.469123i
$661$	−42.0861			−1.63696			−0.818479	−	0.574537i	$-0.805182\pi$
$661$	−42.0861			−1.63696			−0.818479	+	0.574537i	$0.805182\pi$
$662$	−0.277839			−0.0107985
$663$	2.03736	+	4.80528i	0.0791245	+	0.186622i
$664$	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
$668$	−11.1254	−	19.2697i	−0.430453	−	0.745566i
$669$	21.3350	+	2.62862i	0.824857	+	0.101628i
$670$	−0.158384	+	0.274330i	−0.00611892	+	0.0105983i
$671$	−3.31521	−	5.74211i	−0.127982	−	0.221672i
$672$	−1.06586	−	0.917082i	−0.0411163	−	0.0353772i
$673$	−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
$675$	0.806446	+	5.13319i	0.0310401	+	0.197577i
$676$	17.6915	−	30.6425i	0.680440	−	1.17856i
$677$	11.4712			0.440875			0.220437	−	0.975401i	$-0.429252\pi$
$677$	11.4712			0.440875			0.220437	+	0.975401i	$0.429252\pi$
$678$	0.311457	−	0.412959i	0.0119614	−	0.0158596i
$679$	1.29779	−	20.1481i	0.0498045	−	0.773214i
$680$	0.0278212	+	0.0481878i	0.00106689	+	0.00184792i
$681$	9.24284	−	12.2550i	0.354187	−	0.469614i
$682$	−0.0842074	−	0.145851i	−0.00322447	−	0.00558494i
$683$	17.5055	−	30.3205i	0.669831	−	1.16018i	−0.308120	−	0.951347i	$-0.599700\pi$
$683$	17.5055	−	30.3205i	0.669831	−	1.16018i	0.977951	−	0.208834i	$-0.0669667\pi$
$684$	42.1417	+	10.5444i	1.61133	+	0.403175i
$685$	−8.55962			−0.327046
$686$	−0.0908552	+	0.464967i	−0.00346887	+	0.0177525i
$687$	−45.2402	−	5.57392i	−1.72602	−	0.212658i
$688$	−1.11620	+	1.93331i	−0.0425546	+	0.0737067i
$689$	47.2617			1.80053
$690$	0.193583	−	0.256671i	0.00736957	−	0.00977128i
$691$	3.84678			0.146338			0.0731692	−	0.997320i	$-0.476689\pi$
$691$	3.84678			0.146338			0.0731692	+	0.997320i	$0.476689\pi$
$692$	2.84848			0.108283
$693$	−29.3189	+	6.37477i	−1.11373	+	0.242157i
$694$	0.0969062			0.00367851
$695$	6.17559			0.234253
$696$	1.42411	+	0.175460i	0.0539807	+	0.00665081i
$697$	−0.259073			−0.00981308
$698$	0.366425	−	0.634666i	0.0138694	−	0.0240225i
$699$	−27.1660	+	36.0193i	−1.02751	+	1.36238i
$700$	−4.40159	−	2.93388i	−0.166365	−	0.110890i
$701$	6.90316			0.260729			0.130364	−	0.991466i	$-0.458385\pi$
$701$	6.90316			0.260729			0.130364	+	0.991466i	$0.458385\pi$
$702$	0.114297	+	0.727526i	0.00431388	+	0.0274587i
$703$	−12.1125	+	20.9795i	−0.456832	+	0.791255i
$704$	15.0909	+	26.1381i	0.568758	+	0.985119i
$705$	14.7447	+	1.81666i	0.555319	+	0.0684193i
$706$	−0.0551886	−	0.0955895i	−0.00207705	−	0.00359756i
$707$	−7.53974	−	5.02562i	−0.283561	−	0.189008i
$708$	−1.90384	−	4.49037i	−0.0715508	−	0.168758i
$709$	10.5427			0.395938			0.197969	−	0.980208i	$-0.436565\pi$
$709$	10.5427			0.395938			0.197969	+	0.980208i	$0.436565\pi$
$710$	−0.132116	+	0.228831i	−0.00495821	+	0.00858787i
$711$	−6.18773	+	6.39691i	−0.232058	+	0.239903i
$712$	0.922820	+	1.59837i	0.0345841	+	0.0599015i
$713$	−6.31864	+	10.9442i	−0.236635	+	0.409863i
$714$	0.0601772	−	0.0210628i	0.00225207	−	0.000788254i
$715$	−10.4719	−	18.1379i	−0.391628	−	0.678320i
$716$	12.5679	−	21.7682i	0.469683	−	0.813515i
$717$	−19.8178	+	26.2763i	−0.740109	+	0.981308i
$718$	−0.347648	−	0.602144i	−0.0129741	−	0.0224718i
$719$	−17.8806	−	30.9701i	−0.666835	−	1.15499i	−0.978784	−	0.204893i	$-0.934315\pi$
$719$	−17.8806	−	30.9701i	−0.666835	−	1.15499i	0.311950	−	0.950099i	$-0.399018\pi$
$720$	−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
$723$	−14.8963	+	19.7510i	−0.554001	+	0.734548i
$724$	28.3367			1.05313
$725$	8.09755			0.300736
$726$	−0.144651	−	0.0178220i	−0.00536849	−	0.000661437i
$727$	−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
$731$	−0.151919	−	0.263132i	−0.00561893	−	0.00973228i
$732$	−2.37101	−	5.59223i	−0.0876352	−	0.206695i
$733$	−20.8214	+	36.0637i	−0.769056	+	1.33204i	0.169020	+	0.985613i	$0.445940\pi$
$733$	−20.8214	+	36.0637i	−0.769056	+	1.33204i	−0.938075	+	0.346431i	$0.887393\pi$
$734$	−0.153678	−	0.266179i	−0.00567238	−	0.00982484i
$735$	−8.48218	+	8.66329i	−0.312870	+	0.319550i
$736$	−1.11318	+	1.92808i	−0.0410323	+	0.0710701i
$737$	−23.4050	−	40.5386i	−0.862133	−	1.49326i
$738$	−0.0354619	−	0.00887303i	−0.00130537	−	0.000326621i
$739$	−22.4915	+	38.9565i	−0.827364	+	1.43304i	0.0727349	+	0.997351i	$0.476827\pi$
$739$	−22.4915	+	38.9565i	−0.827364	+	1.43304i	−0.900099	+	0.435685i	$0.856506\pi$
$740$	6.68747			0.245836
$741$	68.9808	+	8.49894i	2.53407	+	0.312216i
$742$	0.0371099	−	0.576131i	0.00136235	−	0.0211504i
$743$	−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	$0.859595\pi$
$744$	−0.120469	−	0.284135i	−0.00441660	−	0.0104169i
$745$	−2.34647	−	4.06421i	−0.0859682	−	0.148901i
$746$	0.111069	−	0.192378i	0.00406653	−	0.00704344i
$747$	−6.55833	−	22.9437i	−0.239957	−	0.839467i
$748$	−4.11056			−0.150297
$749$	−0.415814	−	0.277161i	−0.0151935	−	0.0101272i
$750$	0.0172951	+	0.0407920i	0.000631529	+	0.00148951i
$751$	−21.1330	+	36.6034i	−0.771154	+	1.33568i	0.165778	+	0.986163i	$0.446987\pi$
$751$	−21.1330	+	36.6034i	−0.771154	+	1.33568i	−0.936931	+	0.349514i	$0.886347\pi$
$752$	−34.2753			−1.24989
$753$	−1.51188	−	3.56590i	−0.0550961	−	0.129949i
$754$	1.14766			0.0417955
$755$	−15.6125			−0.568198
$756$	−27.3715	+	2.51170i	−0.995490	+	0.0913495i
$757$	−25.4479			−0.924918			−0.462459	−	0.886641i	$-0.653033\pi$
$757$	−25.4479			−0.924918			−0.462459	+	0.886641i	$0.653033\pi$
$758$	0.324923			0.0118017
$759$	18.5444	+	43.7384i	0.673117	+	1.58760i
$760$	0.740952			0.0268771
$761$	14.9151	−	25.8338i	0.540673	−	0.936473i	−0.458193	−	0.888853i	$-0.651503\pi$
$761$	14.9151	−	25.8338i	0.540673	−	0.936473i	0.998866	−	0.0476201i	$-0.0151637\pi$
$762$	0.0198319	+	0.0467752i	0.000718435	+	0.00169449i
$763$	−1.49797	+	23.2559i	−0.0542300	+	0.841922i
$764$	−20.3543			−0.736391
$765$	1.58285	+	0.396050i	0.0572282	+	0.0143192i
$766$	−0.321306	+	0.556518i	−0.0116092	+	0.0201078i
$767$	−3.90167	−	6.75789i	−0.140881	−	0.244013i
$768$	10.7823	+	25.4308i	0.389071	+	0.917657i
$769$	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	$0.719392\pi$
$770$	−0.229328	+	0.113413i	−0.00826440	+	0.00408713i
$771$	27.1004	+	3.33896i	0.975997	+	0.120250i
$772$	13.6985			0.493021
$773$	16.1602	−	27.9902i	0.581241	−	1.00674i	−0.414092	−	0.910235i	$-0.635901\pi$
$773$	16.1602	−	27.9902i	0.581241	−	1.00674i	0.995333	−	0.0965036i	$-0.0307659\pi$
$774$	−0.0117827	−	0.0412206i	−0.000423520	−	0.00148164i
$775$	−0.870826	−	1.50832i	−0.0312810	−	0.0541803i
$776$	0.390351	−	0.676107i	0.0140128	−	0.0242708i
$777$	2.84834	−	15.0610i	0.102183	−	0.540309i
$778$	−0.244838	−	0.424071i	−0.00877785	−	0.0152037i
$779$	−1.72495	+	2.98769i	−0.0618026	+	0.107045i
$780$	−7.48945	−	17.6645i	−0.268165	−	0.632490i
$781$	−19.5232	−	33.8151i	−0.698594	−	1.21000i
$782$	−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
$786$	0.279786	+	0.0344717i	0.00997964	+	0.00122956i
$787$	26.1901			0.933577			0.466788	−	0.884369i	$-0.345411\pi$
$787$	26.1901			0.933577			0.466788	+	0.884369i	$0.345411\pi$
$788$	40.0203			1.42566
$789$	−13.3283	+	17.6720i	−0.474502	+	0.629140i
$790$	−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
$794$	−0.0461606	−	0.0799525i	−0.00163818	−	0.00283741i
$795$	8.89658	−	11.7959i	0.315529	−	0.418359i
$796$	−12.9439	+	22.4194i	−0.458783	+	0.794636i
$797$	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	$0.718976\pi$
$798$	0.157768	−	0.834218i	0.00558491	−	0.0295310i
$799$	2.33251	−	4.04003i	0.0825183	−	0.142926i
$800$	−0.153417	−	0.265726i	−0.00542411	−	0.00939483i
$801$	52.5027	+	13.1369i	1.85509	+	0.464168i
$802$	−0.0429774	+	0.0744390i	−0.00151758	+	0.00262853i
$803$	−22.0428			−0.777873
$804$	−16.7391	−	39.4805i	−0.590341	−	1.39237i
$805$	15.9740	+	10.6475i	0.563010	+	0.375274i
$806$	−0.123422	−	0.213773i	−0.00434735	−	0.00752984i
$807$	33.7903	+	4.16321i	1.18948	+	0.146552i
$808$	−0.175188	−	0.303435i	−0.00616310	−	0.0106748i
$809$	−1.09725	+	1.90050i	−0.0385774	+	0.0668180i	−0.884669	−	0.466219i	$-0.845616\pi$
$809$	−1.09725	+	1.90050i	−0.0385774	+	0.0668180i	0.846092	+	0.533037i	$0.178949\pi$
$810$	0.203097	+	0.108423i	0.00713610	+	0.00380959i
$811$	−21.8077			−0.765773			−0.382887	−	0.923795i	$-0.625070\pi$
$811$	−21.8077			−0.765773			−0.382887	+	0.923795i	$0.625070\pi$
$812$	−2.75334	+	42.7456i	−0.0966233	+	1.50008i
$813$	2.13855	−	2.83550i	0.0750024	−	0.0994454i
$814$	0.161720	−	0.280107i	0.00566827	−	0.00981773i
$815$	1.31111			0.0459263
$816$	−3.73619	−	0.460325i	−0.130793	−	0.0161146i
$817$	−4.04600			−0.141552
$818$	0.0609402			0.00213072
$819$	−42.9724	+	9.34344i	−1.50158	+	0.326486i
$820$	0.952366			0.0332581
$821$	44.1340			1.54029			0.770144	−	0.637870i	$-0.220184\pi$
$821$	44.1340			1.54029			0.770144	+	0.637870i	$0.220184\pi$
$822$	−0.228365	+	0.302788i	−0.00796514	+	0.0105609i
$823$	33.5573			1.16973			0.584867	−	0.811129i	$-0.301147\pi$
$823$	33.5573			1.16973			0.584867	+	0.811129i	$0.301147\pi$
$824$	0.482400	−	0.835541i	0.0168052	−	0.0291074i
$825$	−6.49825	−	0.800632i	−0.226240	−	0.0278744i
$826$	−0.0854438	+	0.0422559i	−0.00297297	+	0.00147027i
$827$	−4.29754			−0.149440			−0.0747201	−	0.997205i	$-0.523806\pi$
$827$	−4.29754			−0.149440			−0.0747201	+	0.997205i	$0.523806\pi$
$828$	11.9612	+	41.8453i	0.415681	+	1.45422i
$829$	−11.9899	+	20.7671i	−0.416427	+	0.721273i	−0.995577	−	0.0939481i	$-0.970051\pi$
$829$	−11.9899	+	20.7671i	−0.416427	+	0.721273i	0.579150	+	0.815221i	$0.303385\pi$
$830$	−0.101737	−	0.176214i	−0.00353134	−	0.00611646i
$831$	6.69588	−	8.87803i	0.232277	−	0.307976i
$832$	22.1185	+	38.3104i	0.766822	+	1.32818i
$833$	1.46487	+	3.51409i	0.0507546	+	0.121756i
$834$	0.164760	−	0.218455i	0.00570519	−	0.00756449i
$835$	−11.1290			−0.385135
$836$	−27.3687	+	47.4041i	−0.946568	+	1.63950i
$837$	−8.44474	−	3.25374i	−0.291893	−	0.112466i
$838$	−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	$-0.149850\pi$
$840$	−0.442502	+	0.154881i	−0.0152678	+	0.00534391i
$841$	−18.2852	−	31.6708i	−0.630523	−	1.09210i
$842$	0.170891	−	0.295992i	0.00588929	−	0.0102005i
$843$	−52.6379	−	6.48537i	−1.81295	−	0.223368i
$844$	−12.8615	−	22.2768i	−0.442711	−	0.766797i
$845$	−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
$849$	6.57806	+	15.5149i	0.225759	+	0.532470i
$850$	0.0139129			0.000477208
$851$	−24.2698			−0.831958
$852$	−13.9628	−	32.9325i	−0.478358	−	1.12825i
$853$	−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
$857$	5.22760	+	9.05447i	0.178571	+	0.309295i	0.941391	−	0.337316i	$-0.109519\pi$
$857$	5.22760	+	9.05447i	0.178571	+	0.309295i	−0.762820	+	0.646611i	$0.776186\pi$
$858$	−0.920995	−	0.113473i	−0.0314423	−	0.00387392i
$859$	−6.71601	+	11.6325i	−0.229147	+	0.396895i	−0.957556	−	0.288248i	$-0.906927\pi$
$859$	−6.71601	+	11.6325i	−0.229147	+	0.396895i	0.728408	+	0.685143i	$0.240260\pi$
$860$	0.558463	+	0.967287i	0.0190434	+	0.0329842i
$861$	0.405633	−	2.14484i	0.0138239	−	0.0730959i
$862$	−0.306331	+	0.530581i	−0.0104337	+	0.0180716i
$863$	15.5326	+	26.9033i	0.528737	+	0.915799i	0.999439	+	0.0335063i	$0.0106674\pi$
$863$	15.5326	+	26.9033i	0.528737	+	0.915799i	−0.470702	+	0.882292i	$0.655999\pi$
$864$	−1.48774	−	0.573225i	−0.0506141	−	0.0195015i
$865$	0.712352	−	1.23383i	0.0242207	−	0.0419515i
$866$	−0.393269			−0.0133638
$867$	−17.4216	+	23.0993i	−0.591670	+	0.784493i
$868$	8.25824	−	4.08409i	0.280303	−	0.138623i
$869$	−5.60714	−	9.71186i	−0.190209	−	0.329452i
$870$	0.216037	−	0.286443i	0.00732435	−	0.00971132i
$871$	−34.3045	−	59.4171i	−1.16236	−	2.01327i
$872$	−0.450562	+	0.780396i	−0.0152579	+	0.0264275i
$873$	−6.29189	−	22.0116i	−0.212948	−	0.744979i
$874$	−1.34429			−0.0454713
$875$	−2.37158	+	1.17286i	−0.0801741	+	0.0396498i
$876$	−20.0418	−	2.46929i	−0.677148	−	0.0834296i
$877$	5.32274	−	9.21925i	0.179736	−	0.311312i	−0.762054	−	0.647513i	$-0.775809\pi$
$877$	5.32274	−	9.21925i	0.179736	−	0.311312i	0.941790	+	0.336201i	$0.109142\pi$
$878$	0.217437			0.00733816
$879$	11.1137	−	14.7356i	0.374856	−	0.497020i
$880$	15.1057			0.509213
$881$	−37.4454			−1.26157			−0.630785	−	0.775958i	$-0.717267\pi$
$881$	−37.4454			−1.26157			−0.630785	+	0.775958i	$0.717267\pi$
$882$	0.0801567	+	0.531179i	0.00269902	+	0.0178857i
$883$	−1.93626			−0.0651605			−0.0325802	−	0.999469i	$-0.510372\pi$
$883$	−1.93626			−0.0651605			−0.0325802	+	0.999469i	$0.510372\pi$
$884$	−6.02481			−0.202636
$885$	−2.42114	−	0.298302i	−0.0813858	−	0.0100273i
$886$	−0.791271			−0.0265833
$887$	−13.5842	+	23.5285i	−0.456112	+	0.790009i	−0.998751	−	0.0499568i	$-0.984092\pi$
$887$	−13.5842	+	23.5285i	−0.456112	+	0.790009i	0.542640	+	0.839966i	$0.317425\pi$
$888$	0.356893	−	0.473203i	0.0119765	−	0.0158796i
$889$	−2.71944	+	1.34489i	−0.0912071	+	0.0451062i
$890$	0.461486			0.0154690
$891$	−28.8816	+	17.9804i	−0.967571	+	0.602367i
$892$	−12.4068	+	21.4892i	−0.415411	+	0.719513i
$893$	−31.0604	−	53.7982i	−1.03940	−	1.80029i
$894$	−0.206370	−	0.0254263i	−0.00690204	−	0.000850382i
$895$	−6.28599	−	10.8877i	−0.210118	−	0.363934i
$896$	1.93974	−	0.959293i	0.0648023	−	0.0320477i
$897$	27.1803	+	64.1069i	0.907523	+	2.14047i
$898$	0.108375			0.00361651
$899$	−7.05156	+	12.2137i	−0.235183	+	0.407348i
$900$	−5.81866	−	1.45590i	−0.193955	−	0.0485301i
$901$	−2.31972	−	4.01787i	−0.0772811	−	0.133855i
$902$	0.0230306	−	0.0398901i	0.000766834	−	0.00132820i
$903$	2.41630	−	0.845737i	0.0804096	−	0.0281444i
$904$	0.597163	+	1.03432i	0.0198614	+	0.0344009i
$905$	7.08650	−	12.2742i	0.235563	−	0.408008i
$906$	−0.416532	+	0.552278i	−0.0138383	+	0.0183482i
$907$	−27.9594	−	48.4271i	−0.928376	−	1.60799i	−0.786040	−	0.618176i	$-0.787872\pi$
$907$	−27.9594	−	48.4271i	−0.928376	−	1.60799i	−0.142337	−	0.989818i	$-0.545462\pi$
$908$	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	$0.120272\pi$
$912$	−30.1847	+	40.0217i	−0.999515	+	1.32525i
$913$	30.0680			0.995106
$914$	1.00783			0.0333361
$915$	−3.01525	−	0.371500i	−0.0996810	−	0.0122814i
$916$	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	0.938350	−	0.345686i	$-0.112354\pi$
$919$	5.14755	+	8.91582i	0.169802	+	0.294106i	−0.768548	+	0.639792i	$0.779021\pi$
$920$	0.371161	+	0.642869i	0.0122368	+	0.0211948i
$921$	2.42070	+	5.70942i	0.0797648	+	0.188132i
$922$	−0.0732078	+	0.126800i	−0.00241097	+	0.00417592i
$923$	−28.6149	−	49.5625i	−0.941871	−	1.63137i
$924$	6.43594	−	34.0309i	0.211727	−	1.11954i
$925$	1.67242	−	2.89671i	0.0549887	−	0.0952432i
$926$	0.241820	+	0.418844i	0.00794669	+	0.0137641i
$927$	−7.77558	−	27.2022i	−0.255384	−	0.893436i
$928$	−1.24230	+	2.15173i	−0.0407805	+	0.0706339i
$929$	37.4361			1.22824			0.614119	−	0.789214i	$-0.289512\pi$
$929$	37.4361			1.22824			0.614119	+	0.789214i	$0.289512\pi$
$930$	−0.0765882	−	0.00943622i	−0.00251143	−	0.000309426i
$931$	50.2787	+	6.50411i	1.64782	+	0.213164i
$932$	−26.0388	−	45.1005i	−0.852928	−	1.47732i
$933$	11.0311	+	26.0178i	0.361142	+	0.851783i
$934$	0.286648	+	0.496489i	0.00937941	+	0.0162456i
$935$	−1.02798	+	1.78051i	−0.0336184	+	0.0582288i
$936$	−1.64962	−	0.412757i	−0.0539196	−	0.0134914i
$937$	−20.0462			−0.654882			−0.327441	−	0.944872i	$-0.606186\pi$
$937$	−20.0462			−0.654882			−0.327441	+	0.944872i	$0.606186\pi$
$938$	−0.751243	+	0.371525i	−0.0245290	+	0.0121307i
$939$	−4.64917	−	10.9654i	−0.151720	−	0.357844i
$940$	−8.57444	+	14.8514i	−0.279667	+	0.484398i
$941$	−9.65806			−0.314844			−0.157422	−	0.987531i	$-0.550318\pi$
$941$	−9.65806			−0.314844			−0.157422	+	0.987531i	$0.550318\pi$
$942$	−0.321154	−	0.757469i	−0.0104638	−	0.0246797i
$943$	−3.45627			−0.112552
$944$	5.62813			0.183180
$945$	−5.75715	+	12.4842i	−0.187280	+	0.406111i
$946$	0.0540201			0.00175635
$947$	16.5667			0.538345			0.269172	−	0.963092i	$-0.413250\pi$
$947$	16.5667			0.538345			0.269172	+	0.963092i	$0.413250\pi$
$948$	−4.01019	−	9.45835i	−0.130245	−	0.307193i
$949$	−32.3079			−1.04876
$950$	0.0926341	−	0.160447i	0.00300545	−	0.00520559i
$951$	−13.4865	−	31.8089i	−0.437328	−	1.03147i
$952$	−0.00946290	+	0.146912i	−0.000306694	+	0.00476143i
$953$	22.6180			0.732669			0.366335	−	0.930483i	$-0.380613\pi$
$953$	22.6180			0.732669			0.366335	+	0.930483i	$0.380613\pi$
$954$	−0.179915	−	0.629416i	−0.00582496	−	0.0203781i
$955$	−5.09023	+	8.81654i	−0.164716	+	0.285296i
$956$	−18.9955	−	32.9011i	−0.614357	−	1.06410i
$957$	20.6954	+	48.8118i	0.668987	+	1.57786i
$958$	0.385379	+	0.667495i	0.0124510	+	0.0215658i
$959$	−18.8441	−	12.5606i	−0.608509	−	0.405602i
$960$	13.7254	+	1.69107i	0.442986	+	0.0545791i
$961$	−27.9666			−0.902150
$962$	0.237031	−	0.410550i	0.00764219	−	0.0132367i
$963$	−0.549683	−	0.137538i	−0.0177133	−	0.00443209i
$964$	−14.2782	−	24.7306i	−0.459871	−	0.796519i
$965$	3.42575	−	5.93357i	0.110279	−	0.191009i
$966$	0.802820	−	0.280997i	0.0258303	−	0.00904093i
$967$	−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	$-0.340647\pi$
$968$	0.168264	−	0.291441i	0.00540820	−	0.00936727i
$969$	−2.66322	−	6.28143i	−0.0855551	−	0.201789i
$970$	−0.0976037	−	0.169055i	−0.00313386	−	0.00542801i
$971$	19.6527	+	34.0395i	0.630686	+	1.09238i	0.987412	+	0.158171i	$0.0505597\pi$
$971$	19.6527	+	34.0395i	0.630686	+	1.09238i	−0.356726	+	0.934209i	$0.616107\pi$
$972$	−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
$975$	−9.52443	−	1.17348i	−0.305026	−	0.0375814i
$976$	7.00918			0.224358
$977$	29.9325			0.957626			0.478813	−	0.877917i	$-0.341067\pi$
$977$	29.9325			0.957626			0.478813	+	0.877917i	$0.341067\pi$
$978$	0.0349796	−	0.0463794i	0.00111853	−	0.00148305i
$979$	−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
$983$	−0.284451	−	0.492683i	−0.00907257	−	0.0157142i	0.861453	−	0.507836i	$-0.169555\pi$
$983$	−0.284451	−	0.492683i	−0.00907257	−	0.0157142i	−0.870526	+	0.492122i	$0.836221\pi$
$984$	0.0508253	−	0.0673890i	0.00162025	−	0.00214828i
$985$	10.0083	−	17.3350i	0.318892	−	0.552338i
$986$	−0.0563301	−	0.0975667i	−0.00179392	−	0.00310716i
$987$	29.7950	+	25.6361i	0.948384	+	0.816008i
$988$	−40.1141	+	69.4797i	−1.27620	+	2.21044i
$989$	−2.02674	−	3.51042i	−0.0644467	−	0.111625i
$990$	−0.201690	+	0.208509i	−0.00641014	+	0.00662685i
$991$	−6.46835	+	11.2035i	−0.205474	+	0.355891i	−0.950284	−	0.311386i	$-0.899207\pi$
$991$	−6.46835	+	11.2035i	−0.205474	+	0.355891i	0.744810	+	0.667277i	$0.232540\pi$
$992$	0.534398			0.0169671
$993$	−7.34334	−	17.3199i	−0.233034	−	0.549630i
$994$	−0.626646	+	0.309906i	−0.0198760	+	0.00982961i
$995$	6.47405	+	11.2134i	0.205241	+	0.355488i
$996$	27.3385	+	3.36830i	0.866253	+	0.106729i
$997$	−5.38312	−	9.32384i	−0.170485	−	0.295289i	0.768104	−	0.640325i	$-0.221200\pi$
$997$	−5.38312	−	9.32384i	−0.170485	−	0.295289i	−0.938590	+	0.345036i	$0.887867\pi$
$998$	−0.0104771	+	0.0181469i	−0.000331647	+	0.000574429i
$999$	−2.69742	−	17.1697i	−0.0853427	−	0.543224i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.9	✓	36	7.2	even	3
315.2.k.c.256.9	yes	36	9.4	even	3
315.2.l.c.121.10	yes	36	63.58	even	3	inner
315.2.l.c.151.10	yes	36	1.1	even	1	trivial
945.2.k.c.361.10		36	9.5	odd	6
945.2.k.c.856.10		36	21.2	odd	6
945.2.l.c.46.9		36	3.2	odd	2
945.2.l.c.226.9		36	63.23	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.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.0255806 q^{2} +(0.676102 + 1.59464i) q^{3} -1.99935 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.0172951 + 0.0407920i) q^{6} +(-2.37158 + 1.17286i) q^{7} -0.102306 q^{8} +(-2.08577 + 2.15628i) q^{9} +(-0.0127903 + 0.0221535i) q^{10} +(-1.89007 - 3.27369i) q^{11} +(-1.35176 - 3.18824i) q^{12} +(-2.77025 - 4.79822i) q^{13} +(-0.0606666 + 0.0300025i) q^{14} +(-1.71905 - 0.211800i) q^{15} +3.99607 q^{16} +(-0.271942 + 0.471017i) q^{17} +(-0.0533554 + 0.0551591i) q^{18} +(3.62126 + 6.27220i) q^{19} +(0.999673 - 1.73148i) q^{20} +(-3.47372 - 2.98886i) q^{21} +(-0.0483491 - 0.0837432i) q^{22} +(-3.62796 + 6.28380i) q^{23} +(-0.0691692 - 0.163141i) q^{24} +(-0.500000 - 0.866025i) 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} +(-0.0439745 - 0.00541797i) q^{30} +1.74165 q^{31} +0.306834 q^{32} +(3.94249 - 5.22733i) 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} +(0.0926341 + 0.160447i) q^{38} +(5.77847 - 7.66166i) q^{39} +(0.0511529 - 0.0885994i) q^{40} +(0.238169 + 0.412522i) q^{41} +(-0.0888600 - 0.0764568i) q^{42} +(-0.279323 + 0.483802i) q^{43} +(3.77890 + 6.54524i) q^{44} +(-0.824510 - 2.88447i) q^{45} +(-0.0928054 + 0.160744i) q^{46} -8.57725 q^{47} +(2.70175 + 6.37231i) q^{48} +(4.24881 - 5.56306i) q^{49} +(-0.0127903 - 0.0221535i) q^{50} +(-0.934964 - 0.115194i) q^{51} +(5.53870 + 9.59330i) q^{52} +(-4.26510 + 7.38738i) q^{53} +(-0.124033 - 0.0477896i) q^{54} +3.78014 q^{55} +(0.242627 - 0.119990i) q^{56} +(-7.55358 + 10.0153i) q^{57} +(-0.103570 + 0.179389i) q^{58} +1.40842 q^{59} +(3.43698 + 0.423461i) q^{60} +1.75402 q^{61} +0.0445526 q^{62} +(2.41757 - 7.56012i) q^{63} -7.98430 q^{64} +5.54051 q^{65} +(0.100851 - 0.133719i) q^{66} +12.3831 q^{67} +(0.543705 - 0.941725i) q^{68} +(-12.4733 - 1.53680i) q^{69} +(0.00435040 - 0.0675400i) q^{70} +10.3293 q^{71} +(0.213387 - 0.220600i) q^{72} +(2.91561 - 5.04998i) q^{73} +(0.0427814 + 0.0740996i) q^{74} +(1.04295 - 1.38284i) q^{75} +(-7.24015 - 12.5403i) q^{76} +(8.32203 + 5.54705i) q^{77} +(0.147817 - 0.195990i) q^{78} +2.96664 q^{79} +(-1.99804 + 3.46070i) q^{80} +(-0.299114 - 8.99503i) q^{81} +(0.00609253 + 0.0105526i) q^{82} +(-3.97711 + 6.88856i) q^{83} +(6.94517 + 5.97575i) q^{84} +(-0.271942 - 0.471017i) q^{85} +(-0.00714526 + 0.0123760i) q^{86} +(-13.9201 - 1.71506i) q^{87} +(0.193365 + 0.334918i) 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} +(1.17754 + 2.77731i) q^{93} -0.219411 q^{94} -7.24252 q^{95} +(0.207451 + 0.489290i) q^{96} +(-3.81553 + 6.60869i) q^{97} +(0.108687 - 0.142307i) q^{98} +(11.0013 + 2.75266i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23}+ \cdots - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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