LMFDB - Embedded newform 234.2.z.a.227.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(41,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("234.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.6
Character	$\chi$	$=$	234.227
Dual form			234.2.z.a.167.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.258819 + 0.965926i) q^{2} +(1.60578 + 0.649218i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.901822 + 3.36565i) q^{5} +(-1.04270 + 1.38303i) q^{6} +(-0.0396662 - 0.0396662i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.15703 + 2.08500i) q^{9} +(-3.01756 - 1.74219i) q^{10} +(-4.98703 - 1.33627i) q^{11} +(-1.06603 - 1.36513i) q^{12} +(2.77745 - 2.29909i) q^{13} +(0.0485810 - 0.0280482i) q^{14} +(-3.63316 + 4.81899i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.83057 + 3.17065i) q^{17} +(-2.57223 + 1.54390i) q^{18} +(0.677531 + 0.181544i) q^{19} +(2.46382 - 2.46382i) q^{20} +(-0.0379430 - 0.0894470i) q^{21} +(2.58148 - 4.47125i) q^{22} +5.78694 q^{23} +(1.59452 - 0.676389i) q^{24} +(-6.18416 - 3.57043i) q^{25} +(1.50189 + 3.27785i) q^{26} +(2.11009 + 4.74842i) q^{27} +(0.0145188 + 0.0541850i) q^{28} +(2.99055 - 1.72660i) q^{29} +(-3.71446 - 4.75661i) q^{30} +(-5.75138 - 1.54108i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-7.14053 - 5.38342i) q^{33} +(-3.53640 + 0.947575i) q^{34} +(0.169274 - 0.0977305i) q^{35} +(-0.825547 - 2.88418i) q^{36} +(7.28892 - 1.95306i) q^{37} +(-0.350716 + 0.607458i) q^{38} +(5.95256 - 1.88865i) q^{39} +(1.74219 + 3.01756i) q^{40} +(2.13130 + 2.13130i) q^{41} +(0.0962195 - 0.0134996i) q^{42} +5.42977i q^{43} +(3.65076 + 3.65076i) q^{44} +(-8.96262 + 5.37951i) q^{45} +(-1.49777 + 5.58976i) q^{46} +(-1.29364 - 4.82793i) q^{47} +(0.240649 + 1.71525i) q^{48} -6.99685i q^{49} +(5.04935 - 5.04935i) q^{50} +(0.881051 + 6.27979i) q^{51} +(-3.55488 + 0.602344i) q^{52} -3.89525i q^{53} +(-5.13276 + 0.809213i) q^{54} +(8.99483 - 15.5795i) q^{55} -0.0560965 q^{56} +(0.970102 + 0.731384i) q^{57} +(0.893752 + 3.33553i) q^{58} +(-0.272879 - 1.01840i) q^{59} +(5.55591 - 2.35679i) q^{60} -3.00390 q^{61} +(2.97713 - 5.15654i) q^{62} +(-0.00285741 - 0.168265i) q^{63} -1.00000i q^{64} +(5.23315 + 11.4213i) q^{65} +(7.04809 - 5.50389i) q^{66} +(7.69542 - 7.69542i) q^{67} -3.66115i q^{68} +(9.29253 + 3.75699i) q^{69} +(0.0505890 + 0.188801i) q^{70} +(3.98742 - 14.8813i) q^{71} +(2.99957 - 0.0509374i) q^{72} +(5.86521 + 5.86521i) q^{73} +7.54605i q^{74} +(-7.61239 - 9.74817i) q^{75} +(-0.495987 - 0.495987i) q^{76} +(0.144812 + 0.250821i) q^{77} +(0.283658 + 6.23855i) q^{78} +(2.76723 - 4.79298i) q^{79} +(-3.36565 + 0.901822i) q^{80} +(0.305580 + 8.99481i) q^{81} +(-2.61030 + 1.50706i) q^{82} +(-15.4261 + 4.13340i) q^{83} +(-0.0118639 + 0.0964349i) q^{84} +(-12.3221 + 3.30170i) q^{85} +(-5.24476 - 1.40533i) q^{86} +(5.92309 - 0.831007i) q^{87} +(-4.47125 + 2.58148i) q^{88} +(4.41179 + 16.4650i) q^{89} +(-2.87651 - 10.0495i) q^{90} +(-0.201367 - 0.0189747i) q^{91} +(-5.01164 - 2.89347i) q^{92} +(-8.23493 - 6.20852i) q^{93} +4.99824 q^{94} +(-1.22203 + 2.11661i) q^{95} +(-1.71909 - 0.211491i) q^{96} +(-1.62729 + 1.62729i) q^{97} +(6.75844 + 1.81092i) q^{98} +(-7.97107 - 13.2803i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	1.60578	+	0.649218i	0.927095	+	0.374826i
$3$	1.60578	+	0.649218i	0.927095	+	0.374826i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.901822	+	3.36565i	−0.403307	+	1.50516i	0.403850	+	0.914825i	$0.367672\pi$
$5$	−0.901822	+	3.36565i	−0.403307	+	1.50516i	−0.807157	+	0.590337i	$0.798995\pi$
$6$	−1.04270	+	1.38303i	−0.425681	+	0.564620i
$7$	−0.0396662	−	0.0396662i	−0.0149924	−	0.0149924i	0.699571	−	0.714563i	$-0.253375\pi$
$7$	−0.0396662	−	0.0396662i	−0.0149924	−	0.0149924i	−0.714563	+	0.699571i	$0.753375\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.15703	+	2.08500i	0.719011	+	0.694999i
$10$	−3.01756	−	1.74219i	−0.954235	−	0.550928i
$11$	−4.98703	−	1.33627i	−1.50365	−	0.402901i	−0.589328	−	0.807894i	$-0.700607\pi$
$11$	−4.98703	−	1.33627i	−1.50365	−	0.402901i	−0.914320	+	0.404993i	$0.867274\pi$
$12$	−1.06603	−	1.36513i	−0.307737	−	0.394078i
$13$	2.77745	−	2.29909i	0.770325	−	0.637652i
$13$	2.77745	−	2.29909i	0.770325	−	0.637652i
$14$	0.0485810	−	0.0280482i	0.0129838	−	0.00749621i
$15$	−3.63316	+	4.81899i	−0.938078	+	1.24426i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.83057	+	3.17065i	0.443979	+	0.768995i	0.997980	−	0.0635211i	$-0.0202330\pi$
$17$	1.83057	+	3.17065i	0.443979	+	0.768995i	−0.554001	+	0.832516i	$0.686900\pi$
$18$	−2.57223	+	1.54390i	−0.606281	+	0.363900i
$19$	0.677531	+	0.181544i	0.155436	+	0.0416491i	0.335698	−	0.941970i	$-0.391028\pi$
$19$	0.677531	+	0.181544i	0.155436	+	0.0416491i	−0.180262	+	0.983619i	$0.557694\pi$
$20$	2.46382	−	2.46382i	0.550928	−	0.550928i
$21$	−0.0379430	−	0.0894470i	−0.00827985	−	0.0195189i
$22$	2.58148	−	4.47125i	0.550373	−	0.953274i
$23$	5.78694			1.20666			0.603330	−	0.797491i	$-0.293840\pi$
$23$	5.78694			1.20666			0.603330	+	0.797491i	$0.293840\pi$
$24$	1.59452	−	0.676389i	0.325480	−	0.138067i
$25$	−6.18416	−	3.57043i	−1.23683	−	0.714085i
$26$	1.50189	+	3.27785i	0.294545	+	0.642840i
$27$	2.11009	+	4.74842i	0.406088	+	0.913834i
$28$	0.0145188	+	0.0541850i	0.00274380	+	0.0102400i
$29$	2.99055	−	1.72660i	0.555332	−	0.320621i	−0.195938	−	0.980616i	$-0.562775\pi$
$29$	2.99055	−	1.72660i	0.555332	−	0.320621i	0.751270	+	0.659995i	$0.229442\pi$
$30$	−3.71446	−	4.75661i	−0.678164	−	0.868434i
$31$	−5.75138	−	1.54108i	−1.03298	−	0.276786i	−0.297778	−	0.954635i	$-0.596245\pi$
$31$	−5.75138	−	1.54108i	−1.03298	−	0.276786i	−0.735201	+	0.677850i	$0.762912\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−7.14053	−	5.38342i	−1.24301	−	0.937134i
$34$	−3.53640	+	0.947575i	−0.606487	+	0.162508i
$35$	0.169274	−	0.0977305i	0.0286126	−	0.0165195i
$36$	−0.825547	−	2.88418i	−0.137591	−	0.480696i
$37$	7.28892	−	1.95306i	1.19829	−	0.321081i	0.396134	−	0.918193i	$-0.370352\pi$
$37$	7.28892	−	1.95306i	1.19829	−	0.321081i	0.802158	+	0.597112i	$0.203685\pi$
$38$	−0.350716	+	0.607458i	−0.0568937	+	0.0985427i
$39$	5.95256	−	1.88865i	0.953173	−	0.302426i
$40$	1.74219	+	3.01756i	0.275464	+	0.477117i
$41$	2.13130	+	2.13130i	0.332854	+	0.332854i	0.853669	−	0.520815i	$-0.174372\pi$
$41$	2.13130	+	2.13130i	0.332854	+	0.332854i	−0.520815	+	0.853669i	$0.674372\pi$
$42$	0.0962195	−	0.0134996i	0.0148470	−	0.00208303i
$43$			5.42977i			0.828032i	0.910270	+	0.414016i	$0.135874\pi$
$43$			5.42977i			0.828032i	−0.910270	+	0.414016i	$0.864126\pi$
$44$	3.65076	+	3.65076i	0.550373	+	0.550373i
$45$	−8.96262	+	5.37951i	−1.33607	+	0.801930i
$46$	−1.49777	+	5.58976i	−0.220834	+	0.824165i
$47$	−1.29364	−	4.82793i	−0.188697	−	0.704226i	−0.993809	−	0.111103i	$-0.964561\pi$
$47$	−1.29364	−	4.82793i	−0.188697	−	0.704226i	0.805112	−	0.593123i	$-0.202105\pi$
$48$	0.240649	+	1.71525i	0.0347347	+	0.247575i
$49$		−	6.99685i		−	0.999550i
$50$	5.04935	−	5.04935i	0.714085	−	0.714085i
$51$	0.881051	+	6.27979i	0.123372	+	0.879346i
$52$	−3.55488	+	0.602344i	−0.492973	+	0.0835300i
$53$		−	3.89525i		−	0.535053i	−0.963550	−	0.267527i	$-0.913794\pi$
$53$		−	3.89525i		−	0.535053i	0.963550	−	0.267527i	$-0.0862064\pi$
$54$	−5.13276	+	0.809213i	−0.698479	+	0.110120i
$55$	8.99483	−	15.5795i	1.21286	−	2.10074i
$56$	−0.0560965			−0.00749621
$57$	0.970102	+	0.731384i	0.128493	+	0.0968742i
$58$	0.893752	+	3.33553i	0.117355	+	0.437976i
$59$	−0.272879	−	1.01840i	−0.0355258	−	0.132584i	0.945885	−	0.324501i	$-0.105196\pi$
$59$	−0.272879	−	1.01840i	−0.0355258	−	0.132584i	−0.981411	+	0.191917i	$0.938530\pi$
$60$	5.55591	−	2.35679i	0.717264	−	0.304260i
$61$	−3.00390			−0.384610			−0.192305	−	0.981335i	$-0.561596\pi$
$61$	−3.00390			−0.384610			−0.192305	+	0.981335i	$0.561596\pi$
$62$	2.97713	−	5.15654i	0.378096	−	0.654882i
$63$	−0.00285741	−	0.168265i	−0.000360000	−	0.0211994i
$64$		−	1.00000i		−	0.125000i
$65$	5.23315	+	11.4213i	0.649092	+	1.41663i
$66$	7.04809	−	5.50389i	0.867560	−	0.677482i
$67$	7.69542	−	7.69542i	0.940145	−	0.940145i	−0.0581622	−	0.998307i	$-0.518524\pi$
$67$	7.69542	−	7.69542i	0.940145	−	0.940145i	0.998307	+	0.0581622i	$0.0185241\pi$
$68$		−	3.66115i		−	0.443979i
$69$	9.29253	+	3.75699i	1.11869	+	0.452288i
$70$	0.0505890	+	0.188801i	0.00604655	+	0.0225660i
$71$	3.98742	−	14.8813i	0.473220	−	1.76608i	−0.154865	−	0.987936i	$-0.549494\pi$
$71$	3.98742	−	14.8813i	0.473220	−	1.76608i	0.628085	−	0.778145i	$-0.283839\pi$
$72$	2.99957	−	0.0509374i	0.353502	−	0.00600303i
$73$	5.86521	+	5.86521i	0.686471	+	0.686471i	0.961450	−	0.274979i	$-0.0886710\pi$
$73$	5.86521	+	5.86521i	0.686471	+	0.686471i	−0.274979	+	0.961450i	$0.588671\pi$
$74$			7.54605i			0.877210i
$75$	−7.61239	−	9.74817i	−0.879003	−	1.12562i
$76$	−0.495987	−	0.495987i	−0.0568937	−	0.0568937i
$77$	0.144812	+	0.250821i	0.0165028	+	0.0285838i
$78$	0.283658	+	6.23855i	0.0321180	+	0.706377i
$79$	2.76723	−	4.79298i	0.311338	−	0.539253i	−0.667314	−	0.744776i	$-0.732556\pi$
$79$	2.76723	−	4.79298i	0.311338	−	0.539253i	0.978652	+	0.205523i	$0.0658896\pi$
$80$	−3.36565	+	0.901822i	−0.376291	+	0.100827i
$81$	0.305580	+	8.99481i	0.0339534	+	0.999423i
$82$	−2.61030	+	1.50706i	−0.288260	+	0.166427i
$83$	−15.4261	+	4.13340i	−1.69323	+	0.453699i	−0.971220	−	0.238184i	$-0.923448\pi$
$83$	−15.4261	+	4.13340i	−1.69323	+	0.453699i	−0.722009	+	0.691883i	$0.756781\pi$
$84$	−0.0118639	+	0.0964349i	−0.00129446	+	0.0105219i
$85$	−12.3221	+	3.30170i	−1.33652	+	0.358120i
$86$	−5.24476	−	1.40533i	−0.565556	−	0.151540i
$87$	5.92309	−	0.831007i	0.635022	−	0.0890933i
$88$	−4.47125	+	2.58148i	−0.476637	+	0.275187i
$89$	4.41179	+	16.4650i	0.467649	+	1.74529i	0.647955	+	0.761679i	$0.275625\pi$
$89$	4.41179	+	16.4650i	0.467649	+	1.74529i	−0.180306	+	0.983611i	$0.557709\pi$
$90$	−2.87651	−	10.0495i	−0.303211	−	1.05932i
$91$	−0.201367	−	0.0189747i	−0.0211090	−	0.00198909i
$92$	−5.01164	−	2.89347i	−0.522500	−	0.301665i
$93$	−8.23493	−	6.20852i	−0.853923	−	0.643794i
$94$	4.99824			0.515529
$95$	−1.22203	+	2.11661i	−0.125377	+	0.217160i
$96$	−1.71909	−	0.211491i	−0.175454	−	0.0215852i
$97$	−1.62729	+	1.62729i	−0.165226	+	0.165226i	−0.784877	−	0.619651i	$-0.787274\pi$
$97$	−1.62729	+	1.62729i	−0.165226	+	0.165226i	0.619651	+	0.784877i	$0.287274\pi$
$98$	6.75844	+	1.81092i	0.682706	+	0.182930i
$99$	−7.97107	−	13.2803i	−0.801123	−	1.33472i
$100$	3.57043	+	6.18416i	0.357043	+	0.618416i
$101$	−1.76164	−	3.05125i	−0.175290	−	0.303611i	0.764972	−	0.644064i	$-0.222753\pi$
$101$	−1.76164	−	3.05125i	−0.175290	−	0.303611i	−0.940262	+	0.340453i	$0.889420\pi$
$102$	−6.29384	−	0.774299i	−0.623183	−	0.0766670i
$103$	−5.20698	+	3.00625i	−0.513059	+	0.296215i	−0.734090	−	0.679052i	$-0.762391\pi$
$103$	−5.20698	+	3.00625i	−0.513059	+	0.296215i	0.221031	+	0.975267i	$0.429058\pi$
$104$	0.338252	−	3.58965i	0.0331683	−	0.351994i
$105$	0.335265	−	0.0470375i	0.0327185	−	0.00459039i
$106$	3.76252	+	1.00816i	0.365448	+	0.0979216i
$107$	−14.5555	−	8.40363i	−1.40714	−	0.812410i	−0.412024	−	0.911173i	$-0.635178\pi$
$107$	−14.5555	−	8.40363i	−1.40714	−	0.812410i	−0.995111	+	0.0987630i	$0.968511\pi$
$108$	0.546815	−	5.16730i	0.0526173	−	0.497224i
$109$	−14.0667	+	14.0667i	−1.34734	+	1.34734i	−0.458806	+	0.888537i	$0.651723\pi$
$109$	−14.0667	+	14.0667i	−1.34734	+	1.34734i	−0.888537	+	0.458806i	$0.848277\pi$
$110$	12.7206	+	12.7206i	1.21286	+	1.21286i
$111$	12.9723	+	1.59592i	1.23128	+	0.151478i
$112$	0.0145188	−	0.0541850i	0.00137190	−	0.00512000i
$113$	−16.9465	−	9.78407i	−1.59419	−	0.920408i	−0.992576	−	0.121623i	$-0.961190\pi$
$113$	−16.9465	−	9.78407i	−1.59419	−	0.920408i	−0.601617	−	0.798785i	$-0.705477\pi$
$114$	−0.957544	+	0.747750i	−0.0896822	+	0.0700332i
$115$	−5.21879	+	19.4768i	−0.486655	+	1.81622i
$116$	−3.45319			−0.320621
$117$	10.7846	+	0.831762i	0.997039	+	0.0768964i
$118$	1.05432			0.0970583
$119$	0.0531556	−	0.198379i	0.00487276	−	0.0181854i
$120$	0.838511	+	5.97658i	0.0765452	+	0.545584i
$121$	13.5586	+	7.82807i	1.23260	+	0.711642i
$122$	0.777466	−	2.90154i	0.0703885	−	0.262693i
$123$	2.03872	+	4.80608i	0.183825	+	0.433349i
$124$	4.21030	+	4.21030i	0.378096	+	0.378096i
$125$	5.27469	−	5.27469i	0.471782	−	0.471782i
$126$	0.163271	+	0.0407902i	0.0145454	+	0.00363388i
$127$	−0.00248320	−	0.00143368i	−0.000220349	−	0.000127218i	0.499890	−	0.866089i	$-0.333374\pi$
$127$	−0.00248320	−	0.00143368i	−0.000220349	−	0.000127218i	−0.500110	+	0.865962i	$0.666707\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−3.52510	+	8.71899i	−0.310368	+	0.767665i
$130$	−12.3865	+	2.09879i	−1.08637	+	0.184076i
$131$	−10.8797	+	6.28138i	−0.950562	+	0.548807i	−0.893255	−	0.449550i	$-0.851584\pi$
$131$	−10.8797	+	6.28138i	−0.950562	+	0.548807i	−0.0573063	+	0.998357i	$0.518251\pi$
$132$	3.49217	+	8.23245i	0.303954	+	0.716542i
$133$	−0.0196739	−	0.0340762i	−0.00170595	−	0.00295479i
$134$	5.44148	+	9.42492i	0.470072	+	0.814189i
$135$	−17.8844	+	2.81960i	−1.53925	+	0.242673i
$136$	3.53640	+	0.947575i	0.303244	+	0.0812539i
$137$	9.94356	−	9.94356i	0.849535	−	0.849535i	−0.140540	−	0.990075i	$-0.544884\pi$
$137$	9.94356	−	9.94356i	0.849535	−	0.849535i	0.990075	+	0.140540i	$0.0448838\pi$
$138$	−6.03405	+	8.00352i	−0.513653	+	0.681305i
$139$	−0.156944	+	0.271834i	−0.0133118	+	0.0230567i	−0.872605	−	0.488427i	$-0.837571\pi$
$139$	−0.156944	+	0.271834i	−0.0133118	+	0.0230567i	0.859293	+	0.511484i	$0.170904\pi$
$140$	−0.195461			−0.0165195
$141$	1.05708	−	8.59243i	0.0890224	−	0.723613i
$142$	13.3422	+	7.70311i	1.11965	+	0.646430i
$143$	−16.9234	+	7.75420i	−1.41521	+	0.648438i
$144$	−0.727143	+	2.91054i	−0.0605953	+	0.242545i
$145$	3.11417	+	11.6222i	0.258617	+	0.965173i
$146$	−7.18339	+	4.14733i	−0.594501	+	0.343235i
$147$	4.54248	−	11.2354i	0.374658	−	0.926678i
$148$	−7.28892	−	1.95306i	−0.599146	−	0.160541i
$149$	5.89166	−	1.57867i	0.482664	−	0.129329i	−0.00927899	−	0.999957i	$-0.502954\pi$
$149$	5.89166	−	1.57867i	0.482664	−	0.129329i	0.491943	+	0.870628i	$0.336287\pi$
$150$	11.3862	−	4.82999i	0.929683	−	0.394367i
$151$	10.8353	−	2.90331i	0.881766	−	0.236268i	0.210597	−	0.977573i	$-0.432459\pi$
$151$	10.8353	−	2.90331i	0.881766	−	0.236268i	0.671169	+	0.741305i	$0.265793\pi$
$152$	0.607458	−	0.350716i	0.0492714	−	0.0284468i
$153$	−2.66218	+	10.6559i	−0.215224	+	0.861481i
$154$	−0.279755	+	0.0749601i	−0.0225433	+	0.00604046i
$155$	10.3734	−	17.9673i	0.833215	−	1.44317i
$156$	−6.09940	−	1.34066i	−0.488342	−	0.107339i
$157$	−6.52002	−	11.2930i	−0.520354	−	0.901280i	−0.999720	−	0.0236645i	$-0.992467\pi$
$157$	−6.52002	−	11.2930i	−0.520354	−	0.901280i	0.479366	−	0.877615i	$-0.340867\pi$
$158$	3.91346	+	3.91346i	0.311338	+	0.311338i
$159$	2.52886	−	6.25490i	0.200552	−	0.496045i
$160$		−	3.48437i		−	0.275464i
$161$	−0.229546	−	0.229546i	−0.0180908	−	0.0180908i
$162$	−8.76741	−	2.03286i	−0.688833	−	0.159717i
$163$	−1.44937	+	5.40913i	−0.113524	+	0.423676i	−0.999172	−	0.0406802i	$-0.987048\pi$
$163$	−1.44937	+	5.40913i	−0.113524	+	0.423676i	0.885649	+	0.464356i	$0.153714\pi$
$164$	−0.780112	−	2.91142i	−0.0609165	−	0.227343i
$165$	24.5582	−	19.1776i	1.91185	−	1.49297i
$166$		−	15.9702i		−	1.23953i
$167$	6.55111	−	6.55111i	0.506940	−	0.506940i	−0.406646	−	0.913586i	$-0.633302\pi$
$167$	6.55111	−	6.55111i	0.506940	−	0.506940i	0.913586	+	0.406646i	$0.133302\pi$
$168$	−0.0900783	−	0.0364188i	−0.00694970	−	0.00280977i
$169$	2.42841	−	12.7712i	0.186801	−	0.982398i
$170$		−	12.7568i		−	0.978402i
$171$	1.08294	+	1.80425i	0.0828144	+	0.137974i
$172$	2.71489	−	4.70232i	0.207008	−	0.358548i
$173$	−9.84649			−0.748615			−0.374307	−	0.927305i	$-0.622120\pi$
$173$	−9.84649			−0.748615			−0.374307	+	0.927305i	$0.622120\pi$
$174$	−0.730318	+	5.93635i	−0.0553653	+	0.450034i
$175$	0.103677	+	0.386927i	0.00783723	+	0.0292490i
$176$	−1.33627	−	4.98703i	−0.100725	−	0.375912i
$177$	0.222980	−	1.81248i	0.0167602	−	0.136234i
$178$	−17.0458			−1.27764
$179$	−7.69779	+	13.3330i	−0.575360	+	0.996553i	0.420642	+	0.907227i	$0.361805\pi$
$179$	−7.69779	+	13.3330i	−0.575360	+	0.996553i	−0.996002	+	0.0893264i	$0.971529\pi$
$180$	10.4516	−	0.177485i	0.779017	−	0.0132289i
$181$			17.1903i			1.27774i	0.769314	+	0.638871i	$0.220598\pi$
$181$			17.1903i			1.27774i	−0.769314	+	0.638871i	$0.779402\pi$
$182$	0.0704457	−	0.189594i	0.00522178	−	0.0140537i
$183$	−4.82359	−	1.95018i	−0.356570	−	0.144162i
$184$	4.09199	−	4.09199i	0.301665	−	0.301665i
$185$			26.2933i			1.93312i
$186$	8.12833	−	6.34745i	0.595998	−	0.465418i
$187$	−4.89229	−	18.2583i	−0.357760	−	1.33518i
$188$	−1.29364	+	4.82793i	−0.0943484	+	0.352113i
$189$	0.104652	−	0.272051i	0.00761234	−	0.0197888i
$190$	−1.72821	−	1.72821i	−0.125377	−	0.125377i
$191$		−	8.54464i		−	0.618269i	−0.951018	−	0.309134i	$-0.899961\pi$
$191$		−	8.54464i		−	0.618269i	0.951018	−	0.309134i	$-0.100039\pi$
$192$	0.649218	−	1.60578i	0.0468533	−	0.115887i
$193$	0.431411	+	0.431411i	0.0310537	+	0.0310537i	0.722463	−	0.691409i	$-0.243010\pi$
$193$	0.431411	+	0.431411i	0.0310537	+	0.0310537i	−0.691409	+	0.722463i	$0.743010\pi$
$194$	−1.15067	−	1.99301i	−0.0826130	−	0.143090i
$195$	0.988372	+	21.7374i	0.0707788	+	1.55665i
$196$	−3.49843	+	6.05945i	−0.249888	+	0.432818i
$197$	−17.3239	+	4.64193i	−1.23428	+	0.330724i	−0.816244	−	0.577707i	$-0.803948\pi$
$197$	−17.3239	+	4.64193i	−1.23428	+	0.330724i	−0.418035	+	0.908431i	$0.637281\pi$
$198$	14.8909	−	4.26226i	1.05825	−	0.302906i
$199$	17.2644	−	9.96763i	1.22384	−	0.706586i	0.258108	−	0.966116i	$-0.416901\pi$
$199$	17.2644	−	9.96763i	1.22384	−	0.706586i	0.965735	+	0.259530i	$0.0835675\pi$
$200$	−6.89754	+	1.84819i	−0.487729	+	0.130687i
$201$	17.3531	−	7.36112i	1.22399	−	0.519213i
$202$	3.40323	−	0.911892i	0.239450	−	0.0641605i
$203$	−0.187111	−	0.0501363i	−0.0131326	−	0.00351888i
$204$	2.37688	−	5.87898i	0.166415	−	0.411611i
$205$	−9.09527	+	5.25116i	−0.635241	+	0.366757i
$206$	−1.55615	−	5.80763i	−0.108422	−	0.404637i
$207$	12.4826	+	12.0658i	0.867602	+	0.838628i
$208$	3.37979	+	1.25580i	0.234346	+	0.0870738i
$209$	−3.13628	−	1.81073i	−0.216941	−	0.125251i
$210$	−0.0413382	+	0.336015i	−0.00285261	+	0.0231872i
$211$	1.45440			0.100125			0.0500623	−	0.998746i	$-0.484058\pi$
$211$	1.45440			0.100125			0.0500623	+	0.998746i	$0.484058\pi$
$212$	−1.94762	+	3.37338i	−0.133763	+	0.231685i
$213$	16.0641	−	21.3073i	1.10069	−	1.45995i
$214$	11.8845	−	11.8845i	0.812410	−	0.812410i
$215$	−18.2747	−	4.89669i	−1.24632	−	0.333951i
$216$	4.84970	+	1.86558i	0.329980	+	0.126937i
$217$	0.167007	+	0.289264i	0.0113371	+	0.0196365i
$218$	−9.94664	−	17.2281i	−0.673671	−	1.16683i
$219$	5.61041	+	13.2260i	0.379117	+	0.893731i
$220$	−15.5795	+	8.99483i	−1.05037	+	0.606432i
$221$	12.3739	+	4.59765i	0.832359	+	0.309272i
$222$	−4.89903	+	12.1173i	−0.328801	+	0.813258i
$223$	4.10342	+	1.09951i	0.274786	+	0.0736286i	0.393580	−	0.919290i	$-0.371236\pi$
$223$	4.10342	+	1.09951i	0.274786	+	0.0736286i	−0.118795	+	0.992919i	$0.537903\pi$
$224$	0.0485810	+	0.0280482i	0.00324595	+	0.00187405i
$225$	−5.89511	−	20.5955i	−0.393007	−	1.37303i
$226$	13.8368	−	13.8368i	0.920408	−	0.920408i
$227$	16.5200	+	16.5200i	1.09647	+	1.09647i	0.994820	+	0.101648i	$0.0324117\pi$
$227$	16.5200	+	16.5200i	1.09647	+	1.09647i	0.101648	+	0.994820i	$0.467588\pi$
$228$	−0.474441	−	1.11845i	−0.0314206	−	0.0740711i
$229$	−1.59948	+	5.96935i	−0.105697	+	0.394466i	−0.998423	−	0.0561332i	$-0.982123\pi$
$229$	−1.59948	+	5.96935i	−0.105697	+	0.394466i	0.892727	+	0.450599i	$0.148790\pi$
$230$	−17.4624	−	10.0819i	−1.15144	−	0.664783i
$231$	0.0696976	+	0.496777i	0.00458577	+	0.0326856i
$232$	0.893752	−	3.33553i	0.0586777	−	0.218988i
$233$	−1.20969			−0.0792497			−0.0396249	−	0.999215i	$-0.512616\pi$
$233$	−1.20969			−0.0792497			−0.0396249	+	0.999215i	$0.512616\pi$
$234$	−3.59469	+	10.2019i	−0.234992	+	0.666917i
$235$	17.4157			1.13608
$236$	−0.272879	+	1.01840i	−0.0177629	+	0.0662921i
$237$	7.55524	−	5.89992i	0.490766	−	0.383241i
$238$	0.177862	+	0.102689i	0.0115291	+	0.00665632i
$239$	3.51937	−	13.1345i	0.227649	−	0.849599i	−0.753676	−	0.657246i	$-0.771721\pi$
$239$	3.51937	−	13.1345i	0.227649	−	0.849599i	0.981326	−	0.192353i	$-0.0616119\pi$
$240$	−5.98995	−	0.736913i	−0.386650	−	0.0475675i
$241$	5.04100	+	5.04100i	0.324719	+	0.324719i	0.850574	−	0.525855i	$-0.176255\pi$
$241$	5.04100	+	5.04100i	0.324719	+	0.324719i	−0.525855	+	0.850574i	$0.676255\pi$
$242$	−11.0706	+	11.0706i	−0.711642	+	0.711642i
$243$	−5.34890	+	14.6420i	−0.343132	+	0.939287i
$244$	2.60145	+	1.50195i	0.166541	+	0.0961524i
$245$	23.5489	+	6.30992i	1.50449	+	0.403126i
$246$	−5.16997	+	0.725345i	−0.329625	+	0.0462463i
$247$	2.29919	−	1.05347i	0.146294	−	0.0670310i
$248$	−5.15654	+	2.97713i	−0.327441	+	0.189048i
$249$	−27.4543	−	3.37756i	−1.73984	−	0.214044i
$250$	3.72977	+	6.46015i	0.235891	+	0.408575i
$251$	−2.50999	−	4.34744i	−0.158429	−	0.274408i	0.775873	−	0.630889i	$-0.217310\pi$
$251$	−2.50999	−	4.34744i	−0.158429	−	0.274408i	−0.934302	+	0.356481i	$0.883976\pi$
$252$	−0.0816580	+	0.147151i	−0.00514397	+	0.00926962i
$253$	−28.8597	−	7.73293i	−1.81439	−	0.486165i
$254$	0.00202753	−	0.00202753i	0.000127218	−	0.000127218i
$255$	−21.9301	−	2.69795i	−1.37332	−	0.168952i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.94110			0.308218			0.154109	−	0.988054i	$-0.450749\pi$
$257$	4.94110			0.308218			0.154109	+	0.988054i	$0.450749\pi$
$258$	−7.50954	−	5.66163i	−0.467523	−	0.352478i
$259$	−0.366594	−	0.211653i	−0.0227791	−	0.0131515i
$260$	1.17860	−	12.5077i	0.0730934	−	0.775693i
$261$	10.0507	+	2.51097i	0.622121	+	0.155425i
$262$	−3.25148	−	12.1347i	−0.200877	−	0.749684i
$263$	11.1774	−	6.45325i	0.689226	−	0.397925i	−0.114096	−	0.993470i	$-0.536397\pi$
$263$	11.1774	−	6.45325i	0.689226	−	0.397925i	0.803322	+	0.595545i	$0.203064\pi$
$264$	−8.85577	+	1.24246i	−0.545035	+	0.0764681i
$265$	13.1100	+	3.51282i	0.805342	+	0.215791i
$266$	0.0380071	−	0.0101840i	0.00233037	−	0.000624420i
$267$	−3.60504	+	29.3034i	−0.220625	+	1.79334i
$268$	−10.5121	+	2.81672i	−0.642131	+	0.172058i
$269$	22.4600	−	12.9673i	1.36941	−	0.790630i	0.378558	−	0.925577i	$-0.376420\pi$
$269$	22.4600	−	12.9673i	1.36941	−	0.790630i	0.990853	+	0.134948i	$0.0430866\pi$
$270$	1.90531	−	18.0048i	0.115953	−	1.09574i
$271$	−15.7870	+	4.23012i	−0.958992	+	0.256961i	−0.704174	−	0.710028i	$-0.748682\pi$
$271$	−15.7870	+	4.23012i	−0.958992	+	0.256961i	−0.254819	+	0.966989i	$0.582016\pi$
$272$	−1.83057	+	3.17065i	−0.110995	+	0.192249i
$273$	−0.311031	−	0.161200i	−0.0188245	−	0.00975627i
$274$	7.03116	+	12.1783i	0.424768	+	0.735719i
$275$	26.0696	+	26.0696i	1.57205	+	1.57205i
$276$	−6.16908	−	7.89991i	−0.371335	−	0.475519i
$277$			17.0494i			1.02440i	0.858866	+	0.512201i	$0.171170\pi$
$277$			17.0494i			1.02440i	−0.858866	+	0.512201i	$0.828830\pi$
$278$	−0.221952	−	0.221952i	−0.0133118	−	0.0133118i
$279$	−9.19277	−	15.3158i	−0.550357	−	0.916930i
$280$	0.0505890	−	0.188801i	0.00302327	−	0.0112830i
$281$	−1.03182	−	3.85082i	−0.0615535	−	0.229721i	0.928296	−	0.371843i	$-0.121274\pi$
$281$	−1.03182	−	3.85082i	−0.0615535	−	0.229721i	−0.989849	+	0.142122i	$0.954607\pi$
$282$	8.02606	+	3.24495i	0.477945	+	0.193234i
$283$		−	18.1586i		−	1.07941i	−0.841853	−	0.539707i	$-0.818535\pi$
$283$		−	18.1586i		−	1.07941i	0.841853	−	0.539707i	$-0.181465\pi$
$284$	−10.8938	+	10.8938i	−0.646430	+	0.646430i
$285$	−3.33644	+	2.60544i	−0.197634	+	0.154333i
$286$	−3.10987	−	18.3537i	−0.183891	−	1.08528i
$287$		−	0.169081i		−	0.00998056i
$288$	−2.62317	−	1.45567i	−0.154572	−	0.0857762i
$289$	1.79800	−	3.11423i	0.105765	−	0.183190i
$290$	−12.0322			−0.706556
$291$	−3.66952	+	1.55659i	−0.215111	+	0.0912492i
$292$	−2.14682	−	8.01203i	−0.125633	−	0.468868i
$293$	−5.29384	−	19.7569i	−0.309269	−	1.15421i	−0.929208	−	0.369558i	$-0.879509\pi$
$293$	−5.29384	−	19.7569i	−0.309269	−	1.15421i	0.619938	−	0.784651i	$-0.287158\pi$
$294$	9.67686	+	7.29563i	0.564366	+	0.425490i
$295$	3.67366			0.213888
$296$	3.77302	−	6.53507i	0.219303	−	0.379843i
$297$	−4.17793	−	26.5002i	−0.242428	−	1.53770i
$298$			6.09950i			0.353334i
$299$	16.0729	−	13.3047i	0.929521	−	0.769429i
$300$	1.71844	+	12.2484i	0.0992141	+	0.707159i
$301$	0.215378	−	0.215378i	0.0124142	−	0.0124142i
$302$			11.2175i			0.645497i
$303$	−0.847874	−	6.04332i	−0.0487091	−	0.347179i
$304$	0.181544	+	0.677531i	0.0104123	+	0.0388591i
$305$	2.70898	−	10.1101i	0.155116	−	0.578900i
$306$	−9.60381	−	5.32942i	−0.549013	−	0.304663i
$307$	−6.72055	−	6.72055i	−0.383562	−	0.383562i	0.488822	−	0.872384i	$-0.337427\pi$
$307$	−6.72055	−	6.72055i	−0.383562	−	0.383562i	−0.872384	+	0.488822i	$0.837427\pi$
$308$		−	0.289624i		−	0.0165028i
$309$	−10.3130	+	1.44690i	−0.586683	+	0.0823114i
$310$	14.6703	+	14.6703i	0.833215	+	0.833215i
$311$	1.80968	+	3.13446i	0.102618	+	0.177739i	0.912762	−	0.408491i	$-0.133945\pi$
$311$	1.80968	+	3.13446i	0.102618	+	0.177739i	−0.810145	+	0.586230i	$0.800612\pi$
$312$	2.87362	−	5.54457i	0.162687	−	0.313900i
$313$	−9.03947	+	15.6568i	−0.510941	+	0.884975i	0.488979	+	0.872296i	$0.337370\pi$
$313$	−9.03947	+	15.6568i	−0.510941	+	0.884975i	−0.999920	+	0.0126797i	$0.995964\pi$
$314$	12.5957	−	3.37501i	0.710817	−	0.190463i
$315$	0.568898	+	0.142128i	0.0320538	+	0.00800802i
$316$	−4.79298	+	2.76723i	−0.269626	+	0.155669i
$317$	−10.3161	+	2.76420i	−0.579412	+	0.155253i	−0.536610	−	0.843830i	$-0.680295\pi$
$317$	−10.3161	+	2.76420i	−0.579412	+	0.155253i	−0.0428025	+	0.999084i	$0.513629\pi$
$318$	5.38725	+	4.06158i	0.302102	+	0.227762i
$319$	−17.2212	+	4.61440i	−0.964202	+	0.258357i
$320$	3.36565	+	0.901822i	0.188145	+	0.0504134i
$321$	−17.9171	−	22.9441i	−1.00004	−	1.28061i
$322$	0.281135	−	0.162314i	0.0156671	−	0.00904538i
$323$	0.664659	+	2.48054i	0.0369826	+	0.138021i
$324$	4.23277	−	7.94252i	0.235154	−	0.441251i
$325$	−25.3849	+	4.30125i	−1.40810	+	0.238590i
$326$	−4.84969	−	2.79997i	−0.268600	−	0.155076i
$327$	−31.7202	+	13.4556i	−1.75413	+	0.744096i
$328$	3.01412			0.166427
$329$	−0.140192	+	0.242819i	−0.00772903	+	0.0133871i
$330$	12.1680	+	28.6849i	0.669827	+	1.57905i
$331$	−2.35256	+	2.35256i	−0.129308	+	0.129308i	−0.768799	−	0.639491i	$-0.779145\pi$
$331$	−2.35256	+	2.35256i	−0.129308	+	0.129308i	0.639491	+	0.768799i	$0.279145\pi$
$332$	15.4261	+	4.13340i	0.846615	+	0.226850i
$333$	19.7946	+	10.9846i	1.08474	+	0.601950i
$334$	4.63233	+	8.02344i	0.253470	+	0.439023i
$335$	18.9602	+	32.8399i	1.03590	+	1.79424i
$336$	0.0584919	−	0.0775831i	0.00319099	−	0.00423251i
$337$	−2.50494	+	1.44623i	−0.136453	+	0.0787811i	−0.566672	−	0.823943i	$-0.691769\pi$
$337$	−2.50494	+	1.44623i	−0.136453	+	0.0787811i	0.430220	+	0.902724i	$0.358436\pi$
$338$	11.7075	+	5.65109i	0.636803	+	0.307379i
$339$	−20.8603	−	26.7130i	−1.13298	−	1.45085i
$340$	12.3221	+	3.30170i	0.668261	+	0.179060i
$341$	26.6230	+	15.3708i	1.44172	+	0.832376i
$342$	−2.02305	+	0.579065i	−0.109394	+	0.0313123i
$343$	−0.555202	+	0.555202i	−0.0299781	+	0.0299781i
$344$	3.83943	+	3.83943i	0.207008	+	0.207008i
$345$	−21.0249	+	27.8872i	−1.13194	+	1.50140i
$346$	2.54846	−	9.51098i	0.137006	−	0.511313i
$347$	15.5825	+	8.99658i	0.836514	+	0.482962i	0.856078	−	0.516847i	$-0.172894\pi$
$347$	15.5825	+	8.99658i	0.836514	+	0.482962i	−0.0195637	+	0.999809i	$0.506228\pi$
$348$	−5.54505	−	2.24187i	−0.297246	−	0.120177i
$349$	6.70354	−	25.0179i	0.358832	−	1.33918i	−0.516761	−	0.856130i	$-0.672862\pi$
$349$	6.70354	−	25.0179i	0.358832	−	1.33918i	0.875593	−	0.483050i	$-0.160471\pi$
$350$	−0.400577			−0.0214117
$351$	16.7777	+	8.33719i	0.895527	+	0.445006i
$352$	5.16296			0.275187
$353$	0.768681	−	2.86876i	0.0409128	−	0.152688i	−0.942448	−	0.334354i	$-0.891482\pi$
$353$	0.768681	−	2.86876i	0.0409128	−	0.152688i	0.983360	+	0.181665i	$0.0581487\pi$
$354$	1.69301	+	0.684485i	0.0899823	+	0.0363800i
$355$	46.4891	+	26.8405i	2.46739	+	1.42455i
$356$	4.41179	−	16.4650i	0.233824	−	0.872645i
$357$	0.214147	−	0.284043i	0.0113339	−	0.0150332i
$358$	−10.8863	−	10.8863i	−0.575360	−	0.575360i
$359$	−0.0334095	+	0.0334095i	−0.00176329	+	0.00176329i	−0.707988	−	0.706225i	$-0.750397\pi$
$359$	−0.0334095	+	0.0334095i	−0.00176329	+	0.00176329i	0.706225	+	0.707988i	$0.250397\pi$
$360$	−2.53364	+	10.1414i	−0.133534	+	0.534500i
$361$	−16.0284	−	9.25400i	−0.843600	−	0.487052i
$362$	−16.6045	−	4.44917i	−0.872714	−	0.233843i
$363$	16.6900	+	21.3726i	0.875996	+	1.12177i
$364$	0.164901	+	0.117116i	0.00864318	+	0.00613854i
$365$	−25.0296	+	14.4508i	−1.31011	+	0.756392i
$366$	3.13217	−	4.15448i	0.163721	−	0.217158i
$367$	4.75005	+	8.22733i	0.247951	+	0.429463i	0.962957	−	0.269655i	$-0.0869096\pi$
$367$	4.75005	+	8.22733i	0.247951	+	0.429463i	−0.715006	+	0.699118i	$0.753576\pi$
$368$	2.89347	+	5.01164i	0.150833	+	0.261250i
$369$	0.153531	+	9.04106i	0.00799253	+	0.470659i
$370$	−25.3973	−	6.80519i	−1.32034	−	0.353785i
$371$	−0.154510	+	0.154510i	−0.00802174	+	0.00802174i
$372$	4.02740	+	9.49420i	0.208811	+	0.492251i
$373$	−13.4290	+	23.2597i	−0.695328	+	1.20434i	0.274743	+	0.961518i	$0.411407\pi$
$373$	−13.4290	+	23.2597i	−0.695328	+	1.20434i	−0.970070	+	0.242825i	$0.921926\pi$
$374$	18.9023			0.977417
$375$	11.8944	−	5.04554i	0.614223	−	0.260551i
$376$	−4.32861	−	2.49912i	−0.223231	−	0.128882i
$377$	4.33651	−	11.6711i	0.223341	−	0.601090i
$378$	0.235695	+	0.171498i	0.0121229	+	0.00882093i
$379$	4.93097	+	18.4026i	0.253287	+	0.945279i	0.969036	+	0.246921i	$0.0794189\pi$
$379$	4.93097	+	18.4026i	0.253287	+	0.945279i	−0.715749	+	0.698358i	$0.753914\pi$
$380$	2.11661	−	1.22203i	0.108580	−	0.0626886i
$381$	−0.00305670	−	0.00391431i	−0.000156600	−	0.000200536i
$382$	8.25349	+	2.21152i	0.422285	+	0.113151i
$383$	−9.24644	+	2.47758i	−0.472471	+	0.126598i	−0.487195	−	0.873293i	$-0.661980\pi$
$383$	−9.24644	+	2.47758i	−0.472471	+	0.126598i	0.0147237	+	0.999892i	$0.495313\pi$
$384$	1.38303	+	1.04270i	0.0705775	+	0.0532101i
$385$	−0.974771	+	0.261189i	−0.0496789	+	0.0133114i
$386$	−0.528369	+	0.305054i	−0.0268933	+	0.0155268i
$387$	−11.3211	+	11.7122i	−0.575481	+	0.595364i
$388$	2.22292	−	0.595628i	0.112851	−	0.0302384i
$389$	−4.60612	+	7.97804i	−0.233540	+	0.404502i	−0.958847	−	0.283922i	$-0.908364\pi$
$389$	−4.60612	+	7.97804i	−0.233540	+	0.404502i	0.725308	+	0.688425i	$0.241698\pi$
$390$	−21.2526	−	4.67137i	−1.07617	−	0.236544i
$391$	10.5934	+	18.3484i	0.535733	+	0.927916i
$392$	−4.94752	−	4.94752i	−0.249888	−	0.249888i
$393$	−21.5483	+	3.02322i	−1.08697	+	0.152501i
$394$		−	17.9351i		−	0.903555i
$395$	13.6359	+	13.6359i	0.686098	+	0.686098i
$396$	0.262988	+	15.4866i	0.0132156	+	0.778233i
$397$	7.23488	−	27.0009i	0.363108	−	1.35514i	−0.506859	−	0.862029i	$-0.669194\pi$
$397$	7.23488	−	27.0009i	0.363108	−	1.35514i	0.869967	−	0.493110i	$-0.164140\pi$
$398$	5.15962	+	19.2560i	0.258629	+	0.965215i
$399$	−0.00946902	−	0.0674915i	−0.000474044	−	0.00337880i
$400$		−	7.14085i		−	0.357043i
$401$	−6.28860	+	6.28860i	−0.314038	+	0.314038i	−0.846472	−	0.532434i	$-0.821278\pi$
$401$	−6.28860	+	6.28860i	−0.314038	+	0.314038i	0.532434	+	0.846472i	$0.321278\pi$
$402$	2.61897	+	18.6670i	0.130623	+	0.931026i
$403$	−19.5172	+	8.94265i	−0.972222	+	0.445465i
$404$			3.52328i			0.175290i
$405$	−30.5489	−	7.08324i	−1.51799	−	0.351969i
$406$	0.0968559	−	0.167759i	0.00480688	−	0.00832576i
$407$	−38.9599			−1.93117
$408$	5.06348	+	3.81748i	0.250680	+	0.188994i
$409$	−9.02175	−	33.6696i	−0.446097	−	1.66486i	−0.713025	−	0.701139i	$-0.752675\pi$
$409$	−9.02175	−	33.6696i	−0.446097	−	1.66486i	0.266928	−	0.963716i	$-0.413991\pi$
$410$	−2.71820	−	10.1445i	−0.134242	−	0.500999i
$411$	22.4227	−	9.51159i	1.10603	−	0.469172i
$412$	6.01250			0.296215
$413$	−0.0295719	+	0.0512200i	−0.00145514	+	0.00252037i
$414$	−14.8854	+	8.93444i	−0.731576	+	0.439104i
$415$		−	55.6462i		−	2.73157i
$416$	−2.08776	+	2.93960i	−0.102361	+	0.144126i
$417$	−0.428496	+	0.334614i	−0.0209835	+	0.0163861i
$418$	2.56076	−	2.56076i	0.125251	−	0.125251i
$419$		−	17.2114i		−	0.840832i	−0.907331	−	0.420416i	$-0.861884\pi$
$419$		−	17.2114i		−	0.840832i	0.907331	−	0.420416i	$-0.138116\pi$
$420$	−0.313867	−	0.126897i	−0.0153151	−	0.00619193i
$421$	−0.986098	−	3.68017i	−0.0480595	−	0.179360i	0.937724	−	0.347381i	$-0.112929\pi$
$421$	−0.986098	−	3.68017i	−0.0480595	−	0.179360i	−0.985783	+	0.168021i	$0.946262\pi$
$422$	−0.376425	+	1.40484i	−0.0183241	+	0.0683864i
$423$	7.27580	−	13.1112i	0.353761	−	0.637491i
$424$	−2.75436	−	2.75436i	−0.133763	−	0.133763i
$425$		−	26.1437i		−	1.26816i
$426$	16.4235	+	21.0314i	0.795723	+	1.01898i
$427$	0.119153	+	0.119153i	0.00576623	+	0.00576623i
$428$	8.40363	+	14.5555i	0.406205	+	0.703568i
$429$	−32.2094	+	1.46452i	−1.55508	+	0.0707075i
$430$	9.45967	−	16.3846i	0.456186	−	0.790137i
$431$	20.9081	−	5.60231i	1.00711	−	0.269854i	0.282687	−	0.959212i	$-0.408774\pi$
$431$	20.9081	−	5.60231i	1.00711	−	0.269854i	0.724420	+	0.689358i	$0.242107\pi$
$432$	−3.05721	+	4.20161i	−0.147090	+	0.202150i
$433$	15.1421	−	8.74227i	0.727681	−	0.420127i	−0.0898923	−	0.995951i	$-0.528652\pi$
$433$	15.1421	−	8.74227i	0.727681	−	0.420127i	0.817573	+	0.575825i	$0.195319\pi$
$434$	−0.322632	+	0.0864490i	−0.0154868	+	0.00414968i
$435$	−2.54470	+	20.6845i	−0.122009	+	0.991744i
$436$	19.2154	−	5.14876i	0.920252	−	0.246581i
$437$	3.92084	+	1.05058i	0.187559	+	0.0502563i
$438$	−14.2274	+	1.99610i	−0.679813	+	0.0953774i
$439$	5.45595	−	3.15000i	0.260398	−	0.150341i	−0.364118	−	0.931353i	$-0.618629\pi$
$439$	5.45595	−	3.15000i	0.260398	−	0.150341i	0.624516	+	0.781012i	$0.285296\pi$
$440$	−4.65607	−	17.3767i	−0.221969	−	0.828401i
$441$	14.5884	−	15.0924i	0.694686	−	0.718688i
$442$	−7.64360	+	10.7623i	−0.363569	+	0.511911i
$443$	−13.9547	−	8.05675i	−0.663007	−	0.382788i	0.130414	−	0.991460i	$-0.458369\pi$
$443$	−13.9547	−	8.05675i	−0.663007	−	0.382788i	−0.793422	+	0.608672i	$0.791703\pi$
$444$	−10.4364	−	7.86828i	−0.495290	−	0.373412i
$445$	−59.3941			−2.81555
$446$	−2.12409	+	3.67903i	−0.100579	+	0.174207i
$447$	10.4856	+	1.28999i	0.495951	+	0.0610143i
$448$	−0.0396662	+	0.0396662i	−0.00187405	+	0.00187405i
$449$	18.3173	+	4.90811i	0.864447	+	0.231628i	0.663685	−	0.748012i	$-0.268991\pi$
$449$	18.3173	+	4.90811i	0.864447	+	0.231628i	0.200762	+	0.979640i	$0.435658\pi$
$450$	21.4195	−	0.363737i	1.00972	−	0.0171467i
$451$	−7.78089	−	13.4769i	−0.366388	−	0.634602i
$452$	9.78407	+	16.9465i	0.460204	+	0.797097i
$453$	19.2840	+	2.37241i	0.906040	+	0.111465i
$454$	−20.2327	+	11.6814i	−0.949570	+	0.548234i
$455$	0.245459	−	0.660617i	0.0115073	−	0.0309702i
$456$	1.20313	−	0.168799i	0.0563418	−	0.00790473i
$457$	16.3542	+	4.38210i	0.765017	+	0.204986i	0.620169	−	0.784468i	$-0.287064\pi$
$457$	16.3542	+	4.38210i	0.765017	+	0.204986i	0.144848	+	0.989454i	$0.453731\pi$
$458$	−5.35197	−	3.08996i	−0.250081	−	0.144384i
$459$	−11.1929	+	15.3827i	−0.522439	+	0.718003i
$460$	14.2580	−	14.2580i	0.664783	−	0.664783i
$461$	9.15894	+	9.15894i	0.426574	+	0.426574i	0.887460	−	0.460885i	$-0.152468\pi$
$461$	9.15894	+	9.15894i	0.426574	+	0.426574i	−0.460885	+	0.887460i	$0.652468\pi$
$462$	−0.497889	−	0.0612527i	−0.0231639	−	0.00284973i
$463$	−4.56925	+	17.0527i	−0.212351	+	0.792505i	0.774731	+	0.632291i	$0.217885\pi$
$463$	−4.56925	+	17.0527i	−0.212351	+	0.792505i	−0.987082	+	0.160214i	$0.948782\pi$
$464$	2.99055	+	1.72660i	0.138833	+	0.0801552i
$465$	28.3221	−	22.1169i	1.31341	−	1.02565i
$466$	0.313092	−	1.16848i	0.0145037	−	0.0541286i
$467$	−21.1177			−0.977210			−0.488605	−	0.872505i	$-0.662494\pi$
$467$	−21.1177			−0.977210			−0.488605	+	0.872505i	$0.662494\pi$
$468$	−8.92388	−	6.11264i	−0.412506	−	0.282557i
$469$	−0.610496			−0.0281901
$470$	−4.50753	+	16.8223i	−0.207917	+	0.775956i
$471$	−3.13807	−	22.3669i	−0.144595	−	1.03061i
$472$	−0.913071	−	0.527162i	−0.0420275	−	0.0242646i
$473$	7.25565	−	27.0784i	0.333615	−	1.24507i
$474$	3.74345	+	8.82482i	0.171942	+	0.405337i
$475$	−3.54177	−	3.54177i	−0.162508	−	0.162508i
$476$	−0.145224	+	0.145224i	−0.00665632	+	0.00665632i
$477$	8.12158	−	8.40218i	0.371861	−	0.384709i
$478$	11.7761	+	6.79891i	0.538624	+	0.310975i
$479$	−14.8553	−	3.98046i	−0.678755	−	0.181872i	−0.0970596	−	0.995279i	$-0.530944\pi$
$479$	−14.8553	−	3.98046i	−0.678755	−	0.181872i	−0.581695	+	0.813407i	$0.697610\pi$
$480$	2.26212	−	5.59512i	0.103251	−	0.255381i
$481$	15.7543	−	22.1824i	0.718336	−	1.01143i
$482$	−6.17394	+	3.56453i	−0.281215	+	0.162360i
$483$	−0.219574	−	0.517625i	−0.00999097	−	0.0235527i
$484$	−7.82807	−	13.5586i	−0.355821	−	0.616300i
$485$	−4.00935	−	6.94439i	−0.182055	−	0.315329i
$486$	−12.7587	−	8.95628i	−0.578748	−	0.406265i
$487$	−15.1707	−	4.06498i	−0.687450	−	0.184202i	−0.101848	−	0.994800i	$-0.532475\pi$
$487$	−15.1707	−	4.06498i	−0.687450	−	0.184202i	−0.585603	+	0.810598i	$0.699142\pi$
$488$	−2.12408	+	2.12408i	−0.0961524	+	0.0961524i
$489$	−5.83907	+	7.74489i	−0.264052	+	0.350236i
$490$	−12.1898	+	21.1134i	−0.550680	+	0.953806i
$491$	−6.39468			−0.288588			−0.144294	−	0.989535i	$-0.546091\pi$
$491$	−6.39468			−0.288588			−0.144294	+	0.989535i	$0.546091\pi$
$492$	0.637458	−	5.18154i	0.0287388	−	0.233602i
$493$	10.9489	+	6.32132i	0.493112	+	0.284698i
$494$	0.422503	+	2.49351i	0.0190093	+	0.112188i
$495$	51.8854	−	14.8513i	2.33207	−	0.667517i
$496$	−1.54108	−	5.75138i	−0.0691964	−	0.258245i
$497$	−0.748449	+	0.432117i	−0.0335725	+	0.0193831i
$498$	10.3682	−	25.6446i	0.464608	−	1.14916i
$499$	7.39299	+	1.98095i	0.330956	+	0.0886794i	0.420471	−	0.907306i	$-0.361865\pi$
$499$	7.39299	+	1.98095i	0.330956	+	0.0886794i	−0.0895148	+	0.995985i	$0.528532\pi$
$500$	−7.20536	+	1.93067i	−0.322233	+	0.0863422i
$501$	14.7727	−	6.26652i	0.659996	−	0.279967i
$502$	4.84894	−	1.29927i	0.216419	−	0.0579892i
$503$	−6.97222	+	4.02541i	−0.310876	+	0.179484i	−0.647318	−	0.762220i	$-0.724110\pi$
$503$	−6.97222	+	4.02541i	−0.310876	+	0.179484i	0.336442	+	0.941704i	$0.390776\pi$
$504$	−0.121002	−	0.116961i	−0.00538985	−	0.00520985i
$505$	11.8581	−	3.17737i	0.527679	−	0.141391i
$506$	14.9389	−	25.8749i	0.664114	−	1.15028i
$507$	12.1908	−	18.9311i	0.541410	−	0.840758i
$508$	0.00143368	+	0.00248320i	6.36092e−5	+	0.000110174i
$509$	22.8937	+	22.8937i	1.01474	+	1.01474i	0.999890	+	0.0148538i	$0.00472829\pi$
$509$	22.8937	+	22.8937i	1.01474	+	1.01474i	0.0148538	+	0.999890i	$0.495272\pi$
$510$	8.28194	−	20.4846i	0.366731	−	0.907072i
$511$		−	0.465301i		−	0.0205837i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	0.567608	+	3.60028i	0.0250605	+	0.158956i
$514$	−1.27885	+	4.77274i	−0.0564077	+	0.210517i
$515$	−5.42221	−	20.2359i	−0.238931	−	0.891702i
$516$	7.41233	−	5.78832i	0.326309	−	0.254817i
$517$			25.8057i			1.13493i
$518$	0.299323	−	0.299323i	0.0131515	−	0.0131515i
$519$	−15.8113	−	6.39252i	−0.694037	−	0.280600i
$520$	11.7764	+	4.37566i	0.516431	+	0.191885i
$521$			3.95332i			0.173198i	0.996243	+	0.0865990i	$0.0275999\pi$
$521$			3.95332i			0.173198i	−0.996243	+	0.0865990i	$0.972400\pi$
$522$	−5.02671	+	9.05831i	−0.220013	+	0.396472i
$523$	−19.7397	+	34.1901i	−0.863155	+	1.49503i	0.00571276	+	0.999984i	$0.498182\pi$
$523$	−19.7397	+	34.1901i	−0.863155	+	1.49503i	−0.868868	+	0.495044i	$0.835152\pi$
$524$	12.5628			0.548807
$525$	−0.0847183	+	0.688627i	−0.00369741	+	0.0300542i
$526$	3.34045	+	12.4667i	0.145650	+	0.543575i
$527$	−5.64211	−	21.0566i	−0.245774	−	0.917242i
$528$	1.09192	−	8.87559i	0.0475196	−	0.386261i
$529$	10.4887			0.456031
$530$	−6.78625	+	11.7541i	−0.294776	+	0.510567i
$531$	1.53475	−	2.76567i	0.0666024	−	0.120020i
$532$			0.0393479i			0.00170595i
$533$	10.8196	+	1.01953i	0.468650	+	0.0441608i
$534$	−27.3718	−	11.0665i	−1.18449	−	0.478893i
$535$	41.4101	−	41.4101i	1.79032	−	1.79032i
$536$		−	10.8830i		−	0.470072i
$537$	−21.0169	+	16.4122i	−0.906948	+	0.708240i
$538$	6.71236	+	25.0509i	0.289391	+	1.08002i
$539$	−9.34970	+	34.8935i	−0.402720	+	1.50297i
$540$	16.8982	+	6.50037i	0.727182	+	0.279731i
$541$	8.65093	+	8.65093i	0.371933	+	0.371933i	0.868181	−	0.496248i	$-0.165289\pi$
$541$	8.65093	+	8.65093i	0.371933	+	0.371933i	−0.496248	+	0.868181i	$0.665289\pi$
$542$		−	16.3439i		−	0.702031i
$543$	−11.1602	+	27.6037i	−0.478931	+	1.18459i
$544$	−2.58882	−	2.58882i	−0.110995	−	0.110995i
$545$	−34.6578	−	60.0291i	−1.48458	−	2.57136i
$546$	0.236208	−	0.258711i	0.0101088	−	0.0110718i
$547$	12.5519	−	21.7406i	0.536681	−	0.929559i	−0.462399	−	0.886672i	$-0.653011\pi$
$547$	12.5519	−	21.7406i	0.536681	−	0.929559i	0.999080	−	0.0428870i	$-0.0136556\pi$
$548$	−13.5832	+	3.63959i	−0.580243	+	0.155476i
$549$	−6.47951	−	6.26312i	−0.276539	−	0.267303i
$550$	−31.9286	+	18.4340i	−1.36144	+	0.786027i
$551$	2.33965	−	0.626906i	0.0996723	−	0.0267071i
$552$	9.22740	−	3.91422i	0.392744	−	0.166600i
$553$	−0.299885	+	0.0803539i	−0.0127524	+	0.00341700i
$554$	−16.4685	−	4.41272i	−0.699680	−	0.187479i
$555$	−17.0700	+	42.2211i	−0.724583	+	1.79218i
$556$	0.271834	−	0.156944i	0.0115283	−	0.00665589i
$557$	2.76078	+	10.3034i	0.116978	+	0.436567i	0.999427	−	0.0338399i	$-0.0107736\pi$
$557$	2.76078	+	10.3034i	0.116978	+	0.436567i	−0.882449	+	0.470407i	$0.844107\pi$
$558$	17.1731	−	4.91553i	0.726997	−	0.208091i
$559$	12.4835	+	15.0809i	0.527996	+	0.637854i
$560$	0.169274	+	0.0977305i	0.00715314	+	0.00412987i
$561$	3.99767	−	32.4948i	0.168782	−	1.37193i
$562$	3.98666			0.168167
$563$	−14.9323	+	25.8635i	−0.629322	+	1.09002i	0.358366	+	0.933581i	$0.383334\pi$
$563$	−14.9323	+	25.8635i	−0.629322	+	1.09002i	−0.987688	+	0.156437i	$0.949999\pi$
$564$	−5.21168	+	6.91272i	−0.219451	+	0.291078i
$565$	48.2124	−	48.2124i	2.02831	−	2.02831i
$566$	17.5398	+	4.69978i	0.737254	+	0.197547i
$567$	0.344669	−	0.368911i	0.0144747	−	0.0154928i
$568$	−7.70311	−	13.3422i	−0.323215	−	0.559825i
$569$	22.5294	+	39.0221i	0.944482	+	1.63589i	0.756785	+	0.653664i	$0.226769\pi$
$569$	22.5294	+	39.0221i	0.944482	+	1.63589i	0.187697	+	0.982227i	$0.439898\pi$
$570$	−1.65313	−	3.89709i	−0.0692419	−	0.163231i
$571$	−23.2043	+	13.3970i	−0.971071	+	0.560648i	−0.899562	−	0.436792i	$-0.856115\pi$
$571$	−23.2043	+	13.3970i	−0.971071	+	0.560648i	−0.0715081	+	0.997440i	$0.522781\pi$
$572$	18.5332	+	1.74638i	0.774912	+	0.0730198i
$573$	5.54733	−	13.7208i	0.231743	−	0.573194i
$574$	0.163320	+	0.0437615i	0.00681685	+	0.00182657i
$575$	−35.7874	−	20.6619i	−1.49244	−	0.861659i
$576$	2.08500	−	2.15703i	0.0868748	−	0.0898764i
$577$	−20.9051	+	20.9051i	−0.870292	+	0.870292i	−0.992504	−	0.122212i	$-0.961001\pi$
$577$	−20.9051	+	20.9051i	−0.870292	+	0.870292i	0.122212	+	0.992504i	$0.461001\pi$
$578$	2.54276	+	2.54276i	0.105765	+	0.105765i
$579$	0.412670	+	0.972830i	0.0171500	+	0.0404294i
$580$	3.11417	−	11.6222i	0.129309	−	0.482587i
$581$	0.775849	+	0.447937i	0.0321876	+	0.0185835i
$582$	−0.553813	−	3.94736i	−0.0229563	−	0.163623i
$583$	−5.20511	+	19.4257i	−0.215574	+	0.804532i
$584$	8.29466			0.343235
$585$	−12.5252	+	35.5471i	−0.517854	+	1.46969i
$586$	20.4538			0.844940
$587$	6.48426	−	24.1996i	0.267634	−	0.998824i	−0.692984	−	0.720953i	$-0.743704\pi$
$587$	6.48426	−	24.1996i	0.267634	−	0.998824i	0.960618	−	0.277871i	$-0.0896289\pi$
$588$	−9.55159	+	7.45888i	−0.393901	+	0.307599i
$589$	−3.61697	−	2.08826i	−0.149035	−	0.0860451i
$590$	−0.950812	+	3.54848i	−0.0391443	+	0.146089i
$591$	−30.8320	−	3.79310i	−1.26826	−	0.156027i
$592$	5.33586	+	5.33586i	0.219303	+	0.219303i
$593$	13.5809	−	13.5809i	0.557700	−	0.557700i	−0.370952	−	0.928652i	$-0.620969\pi$
$593$	13.5809	−	13.5809i	0.557700	−	0.557700i	0.928652	+	0.370952i	$0.120969\pi$
$594$	26.6786	+	2.82318i	1.09463	+	0.115837i
$595$	0.619738	+	0.357806i	0.0254068	+	0.0146686i
$596$	−5.89166	−	1.57867i	−0.241332	−	0.0646647i
$597$	34.1940	−	4.79740i	1.39947	−	0.196344i
$598$	8.69135	+	18.9688i	0.355416	+	0.775690i
$599$	12.8779	−	7.43506i	0.526176	−	0.303788i	−0.213282	−	0.976991i	$-0.568415\pi$
$599$	12.8779	−	7.43506i	0.526176	−	0.303788i	0.739458	+	0.673203i	$0.235082\pi$
$600$	−12.2758	−	1.51022i	−0.501156	−	0.0616547i
$601$	11.5545	+	20.0130i	0.471318	+	0.816346i	0.999462	−	0.0328085i	$-0.0104452\pi$
$601$	11.5545	+	20.0130i	0.471318	+	0.816346i	−0.528144	+	0.849155i	$0.677112\pi$
$602$	0.152295	+	0.263783i	0.00620710	+	0.0107510i
$603$	32.6442	−	0.554350i	1.32937	−	0.0225749i
$604$	−10.8353	−	2.90331i	−0.440883	−	0.118134i
$605$	−38.5740	+	38.5740i	−1.56825	+	1.56825i
$606$	6.05684	+	0.745142i	0.246042	+	0.0302693i
$607$	−14.9349	+	25.8680i	−0.606188	+	1.04995i	0.385675	+	0.922635i	$0.373969\pi$
$607$	−14.9349	+	25.8680i	−0.606188	+	1.04995i	−0.991863	+	0.127313i	$0.959365\pi$
$608$	−0.701432			−0.0284468
$609$	−0.267909	−	0.201984i	−0.0108562	−	0.00818479i
$610$	9.06443	+	5.23335i	0.367008	+	0.211892i
$611$	−14.6928	−	10.4351i	−0.594409	−	0.422160i
$612$	7.63348	−	7.89721i	0.308565	−	0.319226i
$613$	−8.88349	−	33.1536i	−0.358801	−	1.33906i	−0.875633	−	0.482977i	$-0.839556\pi$
$613$	−8.88349	−	33.1536i	−0.358801	−	1.33906i	0.516832	−	0.856087i	$-0.327111\pi$
$614$	8.23095	−	4.75214i	0.332174	−	0.191781i
$615$	−18.0141	+	2.52737i	−0.726399	+	0.101913i
$616$	0.279755	+	0.0749601i	0.0112716	+	0.00302023i
$617$	2.65490	−	0.711378i	0.106882	−	0.0286390i	−0.204982	−	0.978766i	$-0.565713\pi$
$617$	2.65490	−	0.711378i	0.106882	−	0.0286390i	0.311864	+	0.950127i	$0.399047\pi$
$618$	1.27159	−	10.3360i	0.0511508	−	0.415776i
$619$	−17.6710	+	4.73494i	−0.710259	+	0.190313i	−0.595821	−	0.803117i	$-0.703173\pi$
$619$	−17.6710	+	4.73494i	−0.710259	+	0.190313i	−0.114438	+	0.993430i	$0.536507\pi$
$620$	−17.9673	+	10.3734i	−0.721585	+	0.416607i
$621$	12.2110	+	27.4788i	0.490010	+	1.10269i
$622$	−3.49603	+	0.936759i	−0.140178	+	0.0375606i
$623$	0.478106	−	0.828104i	0.0191549	−	0.0331773i
$624$	4.61190	+	4.21075i	0.184624	+	0.168565i
$625$	−4.85624	−	8.41125i	−0.194250	−	0.336450i
$626$	−12.7837	−	12.7837i	−0.510941	−	0.510941i
$627$	−3.86060	−	4.94376i	−0.154178	−	0.197435i
$628$			13.0400i			0.520354i
$629$	19.5354	+	19.5354i	0.778927	+	0.778927i
$630$	−0.284527	+	0.512727i	−0.0113358	+	0.0204276i
$631$	−8.90171	+	33.2216i	−0.354371	+	1.32253i	0.526902	+	0.849926i	$0.323353\pi$
$631$	−8.90171	+	33.2216i	−0.354371	+	1.32253i	−0.881274	+	0.472606i	$0.843313\pi$
$632$	−1.43242	−	5.34588i	−0.0569788	−	0.212648i
$633$	2.33543	+	0.944219i	0.0928251	+	0.0375293i
$634$		−	10.6801i		−	0.424159i
$635$	0.00706466	−	0.00706466i	0.000280353	−	0.000280353i
$636$	−5.31751	+	4.15247i	−0.210853	+	0.164656i
$637$	−16.0864	−	19.4334i	−0.637365	−	0.769979i
$638$		−	17.8287i		−	0.705845i
$639$	39.6284	−	23.7856i	1.56767	−	0.940944i
$640$	−1.74219	+	3.01756i	−0.0688660	+	0.119279i
$641$	−13.5556			−0.535415			−0.267707	−	0.963500i	$-0.586266\pi$
$641$	−13.5556			−0.535415			−0.267707	+	0.963500i	$0.586266\pi$
$642$	26.7995	−	11.3682i	1.05769	−	0.448669i
$643$	10.3126	+	38.4870i	0.406688	+	1.51778i	0.800922	+	0.598769i	$0.204343\pi$
$643$	10.3126	+	38.4870i	0.406688	+	1.51778i	−0.394234	+	0.919010i	$0.628990\pi$
$644$	0.0840197	+	0.313566i	0.00331084	+	0.0123562i
$645$	−26.1660	−	19.7272i	−1.03029	−	0.776759i
$646$	−2.56805			−0.101038
$647$	11.0797	−	19.1906i	0.435588	−	0.754460i	−0.561756	−	0.827303i	$-0.689874\pi$
$647$	11.0797	−	19.1906i	0.435588	−	0.754460i	0.997343	+	0.0728432i	$0.0232073\pi$
$648$	6.57637	+	6.14421i	0.258344	+	0.241368i
$649$			5.44343i			0.213673i
$650$	2.41541	−	25.6332i	0.0947400	−	1.00542i
$651$	0.0803799	+	0.572917i	0.00315034	+	0.0224544i
$652$	3.95976	−	3.95976i	0.155076	−	0.155076i
$653$			34.0991i			1.33440i	0.744879	+	0.667200i	$0.232507\pi$
$653$			34.0991i			1.33440i	−0.744879	+	0.667200i	$0.767493\pi$
$654$	−4.78729	−	34.1220i	−0.187198	−	1.33427i
$655$	−11.3294	−	42.2818i	−0.442675	−	1.65209i
$656$	−0.780112	+	2.91142i	−0.0304582	+	0.113672i
$657$	0.422508	+	24.8804i	0.0164836	+	0.970676i
$658$	−0.198261	−	0.198261i	−0.00772903	−	0.00772903i
$659$			5.70080i			0.222072i	0.993816	+	0.111036i	$0.0354168\pi$
$659$			5.70080i			0.222072i	−0.993816	+	0.111036i	$0.964583\pi$
$660$	−30.8568	+	4.32919i	−1.20110	+	0.168514i
$661$	6.48873	+	6.48873i	0.252382	+	0.252382i	0.821947	−	0.569564i	$-0.192888\pi$
$661$	6.48873	+	6.48873i	0.252382	+	0.252382i	−0.569564	+	0.821947i	$0.692888\pi$
$662$	−1.66351	−	2.88129i	−0.0646542	−	0.111984i
$663$	16.8848	+	15.4162i	0.655753	+	0.598714i
$664$	−7.98511	+	13.8306i	−0.309882	+	0.536732i
$665$	0.132431	−	0.0354848i	0.00513545	−	0.00137604i
$666$	−15.7335	+	16.2771i	−0.609660	+	0.630724i
$667$	17.3062	−	9.99171i	0.670097	−	0.386881i
$668$	−8.94898	+	2.39787i	−0.346246	+	0.0927765i
$669$	5.87536	+	4.42958i	0.227154	+	0.171257i
$670$	−36.6282	+	9.81450i	−1.41507	+	0.379167i
$671$	14.9805	+	4.01402i	0.578318	+	0.154960i
$672$	0.0598007	+	0.0765788i	0.00230686	+	0.00295409i
$673$	26.7361	−	15.4361i	1.03060	−	0.595018i	0.113444	−	0.993544i	$-0.463812\pi$
$673$	26.7361	−	15.4361i	1.03060	−	0.595018i	0.917157	+	0.398527i	$0.130478\pi$
$674$	−0.748623	−	2.79390i	−0.0288359	−	0.107617i
$675$	3.90472	−	36.8989i	0.150293	−	1.42024i
$676$	−8.48865	+	9.84595i	−0.326487	+	0.378691i
$677$	−3.80387	−	2.19617i	−0.146195	−	0.0844055i	0.425118	−	0.905138i	$-0.360232\pi$
$677$	−3.80387	−	2.19617i	−0.146195	−	0.0844055i	−0.571313	+	0.820732i	$0.693566\pi$
$678$	31.2018	−	13.2357i	1.19830	−	0.508313i
$679$	0.129097			0.00495427
$680$	−6.37840	+	11.0477i	−0.244601	+	0.423661i
$681$	15.8023	+	37.2524i	0.605546	+	1.42752i
$682$	−21.7376	+	21.7376i	−0.832376	+	0.832376i
$683$	−11.2191	−	3.00615i	−0.429287	−	0.115027i	0.0377045	−	0.999289i	$-0.487995\pi$
$683$	−11.2191	−	3.00615i	−0.429287	−	0.115027i	−0.466991	+	0.884262i	$0.654662\pi$
$684$	−0.0357291	−	2.10399i	−0.00136614	−	0.0804482i
$685$	24.4992	+	42.4338i	0.936065	+	1.62131i
$686$	−0.392587	−	0.679981i	−0.0149890	−	0.0259618i
$687$	−6.44382	+	8.54702i	−0.245847	+	0.326089i
$688$	−4.70232	+	2.71489i	−0.179274	+	0.103504i
$689$	−8.95551	−	10.8188i	−0.341178	−	0.412165i
$690$	−21.4954	−	27.5262i	−0.818315	−	1.04791i
$691$	−10.2662	−	2.75083i	−0.390545	−	0.104646i	0.0582023	−	0.998305i	$-0.481463\pi$
$691$	−10.2662	−	2.75083i	−0.390545	−	0.104646i	−0.448748	+	0.893658i	$0.648130\pi$
$692$	8.52731	+	4.92325i	0.324160	+	0.187154i
$693$	−0.210598	+	0.842962i	−0.00799995	+	0.0320215i
$694$	−12.7231	+	12.7231i	−0.482962	+	0.482962i
$695$	−0.773362	−	0.773362i	−0.0293353	−	0.0293353i
$696$	3.60065	−	4.77587i	0.136482	−	0.181029i
$697$	−2.85610	+	10.6591i	−0.108183	+	0.403743i
$698$	22.4305	+	12.9502i	0.849006	+	0.490174i
$699$	−1.94250	−	0.785355i	−0.0734720	−	0.0297049i
$700$	0.103677	−	0.386927i	0.00391862	−	0.0146245i
$701$	−10.2778			−0.388185			−0.194093	−	0.980983i	$-0.562176\pi$
$701$	−10.2778			−0.388185			−0.194093	+	0.980983i	$0.562176\pi$
$702$	−12.3955	+	14.0482i	−0.467838	+	0.530215i
$703$	5.29304			0.199631
$704$	−1.33627	+	4.98703i	−0.0503626	+	0.187956i
$705$	27.9658	+	11.3066i	1.05325	+	0.425832i
$706$	2.57206	+	1.48498i	0.0968006	+	0.0558879i
$707$	−0.0511539	+	0.190909i	−0.00192384	+	0.00717988i
$708$	−1.09934	+	1.45816i	−0.0413159	+	0.0548011i
$709$	−25.6372	−	25.6372i	−0.962826	−	0.962826i	0.0365077	−	0.999333i	$-0.488377\pi$
$709$	−25.6372	−	25.6372i	−0.962826	−	0.962826i	−0.999333	+	0.0365077i	$0.988377\pi$
$710$	−37.9582	+	37.9582i	−1.42455	+	1.42455i
$711$	15.9624	−	4.56896i	0.598635	−	0.171349i
$712$	14.7621	+	8.52292i	0.553235	+	0.319410i
$713$	−33.2829	−	8.91813i	−1.24645	−	0.333986i
$714$	0.218939	+	0.280366i	0.00819360	+	0.0104924i
$715$	−10.8360	−	63.9511i	−0.405242	−	2.39164i
$716$	13.3330	−	7.69779i	0.498276	−	0.287680i
$717$	14.1785	−	18.8062i	0.529504	−	0.702330i
$718$	−0.0236241	−	0.0409182i	−0.000881644	−	0.00152705i
$719$	−0.703567	−	1.21861i	−0.0262386	−	0.0454466i	0.852608	−	0.522551i	$-0.175020\pi$
$719$	−0.703567	−	1.21861i	−0.0262386	−	0.0454466i	−0.878847	+	0.477105i	$0.841686\pi$
$720$	−9.14010	−	5.07210i	−0.340632	−	0.189026i
$721$	0.325787	+	0.0872945i	0.0121330	+	0.00325102i
$722$	13.0871	−	13.0871i	0.487052	−	0.487052i
$723$	4.82201	+	11.3674i	0.179333	+	0.422759i
$724$	8.59513	−	14.8872i	0.319436	−	0.553279i
$725$	−24.6587			−0.915803
$726$	−24.9640	+	10.5896i	−0.926502	+	0.393018i
$727$	32.7077	+	18.8838i	1.21306	+	0.700361i	0.963425	−	0.267978i	$-0.0863555\pi$
$727$	32.7077	+	18.8838i	1.21306	+	0.700361i	0.249636	+	0.968340i	$0.419689\pi$
$728$	−0.155805	+	0.128971i	−0.00577451	+	0.00477997i
$729$	−18.0950	+	20.0392i	−0.670185	+	0.742194i
$730$	−7.48031	−	27.9169i	−0.276859	−	1.03325i
$731$	−17.2159	+	9.93959i	−0.636752	+	0.367629i
$732$	3.20226	+	4.10070i	0.118359	+	0.151566i
$733$	32.1810	+	8.62288i	1.18863	+	0.318493i	0.798346	−	0.602199i	$-0.205709\pi$
$733$	32.1810	+	8.62288i	1.18863	+	0.318493i	0.390288	+	0.920693i	$0.372375\pi$
$734$	−9.17639	+	2.45881i	−0.338707	+	0.0907562i
$735$	33.7178	+	25.4207i	1.24370	+	0.937656i
$736$	−5.58976	+	1.49777i	−0.206041	+	0.0552086i
$737$	−48.6605	+	28.0941i	−1.79243	+	1.03486i
$738$	−8.77273	−	2.19170i	−0.322929	−	0.0806775i
$739$	−23.0630	+	6.17972i	−0.848388	+	0.227325i	−0.656719	−	0.754135i	$-0.728056\pi$
$739$	−23.0630	+	6.17972i	−0.848388	+	0.227325i	−0.191668	+	0.981460i	$0.561390\pi$
$740$	13.1466	−	22.7706i	0.483280	−	0.837065i
$741$	4.37592	−	0.198967i	0.160753	−	0.00730924i
$742$	−0.109255	−	0.189235i	−0.00401087	−	0.00694703i
$743$	8.52596	+	8.52596i	0.312787	+	0.312787i	0.845988	−	0.533201i	$-0.179011\pi$
$743$	8.52596	+	8.52596i	0.312787	+	0.312787i	−0.533201	+	0.845988i	$0.679011\pi$
$744$	−10.2131	+	1.43289i	−0.374429	+	0.0525322i
$745$			21.2529i			0.778647i
$746$	−18.9915	−	18.9915i	−0.695328	−	0.695328i
$747$	−41.8926	−	23.2474i	−1.53277	−	0.850577i
$748$	−4.89229	+	18.2583i	−0.178880	+	0.667588i
$749$	0.244022	+	0.910702i	0.00891637	+	0.0332763i
$750$	1.79513	+	12.7950i	0.0655488	+	0.467206i
$751$			30.0994i			1.09834i	0.835710	+	0.549171i	$0.185056\pi$
$751$			30.0994i			1.09834i	−0.835710	+	0.549171i	$0.814944\pi$
$752$	3.53429	−	3.53429i	0.128882	−	0.128882i
$753$	−1.20805	−	8.61054i	−0.0440240	−	0.313786i
$754$	10.1510	+	7.20944i	0.369678	+	0.262552i
$755$			39.0861i			1.42249i
$756$	−0.226657	+	0.183277i	−0.00824344	+	0.00666572i
$757$	25.3503	−	43.9080i	0.921371	−	1.59586i	0.124076	−	0.992273i	$-0.460403\pi$
$757$	25.3503	−	43.9080i	0.921371	−	1.59586i	0.797296	−	0.603589i	$-0.206263\pi$
$758$	−19.0518			−0.691992
$759$	−41.3218	−	31.1536i	−1.49989	−	1.13080i
$760$	0.632567	+	2.36077i	0.0229456	+	0.0856342i
$761$	−3.85658	−	14.3930i	−0.139801	−	0.521744i	−0.999932	−	0.0116709i	$-0.996285\pi$
$761$	−3.85658	−	14.3930i	−0.139801	−	0.521744i	0.860131	−	0.510073i	$-0.170382\pi$
$762$	0.00457206	−	0.00193945i	0.000165628	−	7.02588e-5i
$763$	1.11594			0.0403998
$764$	−4.27232	+	7.39988i	−0.154567	+	0.267718i
$765$	−33.4633	−	18.5697i	−1.20987	−	0.671389i
$766$		−	9.57262i		−	0.345873i
$767$	−3.09929	−	2.20117i	−0.111909	−	0.0794798i
$768$	−1.36513	+	1.06603i	−0.0492598	+	0.0384672i
$769$	−18.7823	+	18.7823i	−0.677307	+	0.677307i	−0.959390	−	0.282083i	$-0.908975\pi$
$769$	−18.7823	+	18.7823i	−0.677307	+	0.677307i	0.282083	+	0.959390i	$0.408975\pi$
$770$		−	1.00916i		−	0.0363675i
$771$	7.93431	+	3.20785i	0.285747	+	0.115528i
$772$	−0.157908	−	0.589319i	−0.00568322	−	0.0212101i
$773$	11.3267	−	42.2718i	0.407393	−	1.52041i	−0.392206	−	0.919877i	$-0.628288\pi$
$773$	11.3267	−	42.2718i	0.407393	−	1.52041i	0.799599	−	0.600534i	$-0.205045\pi$
$774$	−8.38300	−	13.9666i	−0.301321	−	0.502020i
$775$	30.0651	+	30.0651i	1.07997	+	1.07997i
$776$			2.30133i			0.0826130i
$777$	−0.451259	−	0.577867i	−0.0161888	−	0.0207309i
$778$	−6.51404	−	6.51404i	−0.233540	−	0.233540i
$779$	1.05710	+	1.83095i	0.0378745	+	0.0656006i
$780$	10.0128	−	19.3194i	0.358515	−	0.691744i
$781$	−39.7708	+	68.8851i	−1.42311	+	2.46490i
$782$	−20.4649	+	5.48356i	−0.731824	+	0.196092i
$783$	14.5090	+	10.5571i	0.518508	+	0.377281i
$784$	6.05945	−	3.49843i	0.216409	−	0.124944i
$785$	43.8881	−	11.7598i	1.56643	−	0.419725i
$786$	2.65691	−	21.5965i	0.0947688	−	0.770323i
$787$	14.8005	−	3.96579i	0.527582	−	0.141365i	0.0148105	−	0.999890i	$-0.495285\pi$
$787$	14.8005	−	3.96579i	0.527582	−	0.141365i	0.512771	+	0.858525i	$0.328619\pi$
$788$	17.3239	+	4.64193i	0.617139	+	0.165362i
$789$	22.1379	−	3.10594i	0.788130	−	0.110574i
$790$	−16.7005	+	9.64206i	−0.594179	+	0.343049i
$791$	0.284107	+	1.06030i	0.0101017	+	0.0376999i
$792$	−15.0270	−	3.75421i	−0.533962	−	0.133400i
$793$	−8.34317	+	6.90622i	−0.296274	+	0.245247i
$794$	24.2084	+	13.9767i	0.859123	+	0.496015i
$795$	18.7712	+	14.1521i	0.665745	+	0.501922i
$796$	−19.9353			−0.706586
$797$	14.8679	−	25.7520i	0.526650	−	0.912184i	−0.472868	−	0.881133i	$-0.656781\pi$
$797$	14.8679	−	25.7520i	0.526650	−	0.912184i	0.999518	−	0.0310506i	$-0.00988531\pi$
$798$	0.0676425	+	0.00832171i	0.00239452	+	0.000294585i
$799$	12.9396	−	12.9396i	0.457769	−	0.457769i
$800$	6.89754	+	1.84819i	0.243865	+	0.0653433i
$801$	−24.8131	+	44.7142i	−0.876729	+	1.57990i
$802$	−4.44671	−	7.70193i	−0.157019	−	0.271965i
$803$	−21.4125	−	37.0875i	−0.755630	−	1.30879i
$804$	−18.7088	−	2.30165i	−0.659808	−	0.0811728i
$805$	0.979580	−	0.565561i	0.0345257	−	0.0199334i
$806$	−3.58651	−	21.1667i	−0.126330	−	0.745565i
$807$	44.4843	−	6.24113i	1.56592	−	0.219698i
$808$	−3.40323	−	0.911892i	−0.119725	−	0.0320803i
$809$	−25.6350	−	14.8004i	−0.901280	−	0.520354i	−0.0236649	−	0.999720i	$-0.507533\pi$
$809$	−25.6350	−	14.8004i	−0.901280	−	0.520354i	−0.877615	+	0.479366i	$0.840867\pi$
$810$	14.7485	−	27.6747i	0.518211	−	0.972390i
$811$	−24.2773	+	24.2773i	−0.852492	+	0.852492i	−0.990440	−	0.137948i	$-0.955949\pi$
$811$	−24.2773	+	24.2773i	−0.852492	+	0.852492i	0.137948	+	0.990440i	$0.455949\pi$
$812$	0.136975	+	0.136975i	0.00480688	+	0.00480688i
$813$	−28.0967	−	3.45659i	−0.985393	−	0.121228i
$814$	10.0836	−	37.6324i	0.353429	−	1.31902i
$815$	−16.8981	−	9.75615i	−0.591916	−	0.341743i
$816$	−4.99793	+	3.90291i	−0.174963	+	0.136629i
$817$	−0.985742	+	3.67884i	−0.0344868	+	0.128706i
$818$	34.8574			1.21876
$819$	−0.394792	−	0.460778i	−0.0137952	−	0.0161009i
$820$	10.5023			0.366757
$821$	−10.6905	+	39.8975i	−0.373101	+	1.39243i	0.482999	+	0.875621i	$0.339547\pi$
$821$	−10.6905	+	39.8975i	−0.373101	+	1.39243i	−0.856100	+	0.516810i	$0.827119\pi$
$822$	3.38408	+	24.1204i	0.118033	+	0.841296i
$823$	−10.9875	−	6.34364i	−0.383001	−	0.221126i	0.296122	−	0.955150i	$-0.404306\pi$
$823$	−10.9875	−	6.34364i	−0.383001	−	0.221126i	−0.679123	+	0.734025i	$0.737640\pi$
$824$	−1.55615	+	5.80763i	−0.0542110	+	0.202318i
$825$	24.9371	+	58.7867i	0.868197	+	2.04669i
$826$	−0.0418210	−	0.0418210i	−0.00145514	−	0.00145514i
$827$	36.0824	−	36.0824i	1.25471	−	1.25471i	0.301123	−	0.953585i	$-0.402639\pi$
$827$	36.0824	−	36.0824i	1.25471	−	1.25471i	0.953585	−	0.301123i	$-0.0973614\pi$
$828$	−4.77739	−	16.6906i	−0.166026	−	0.580037i
$829$	46.6421	+	26.9288i	1.61995	+	0.935276i	0.986932	+	0.161136i	$0.0515159\pi$
$829$	46.6421	+	26.9288i	1.61995	+	0.935276i	0.633014	+	0.774140i	$0.281817\pi$
$830$	53.7501	+	14.4023i	1.86569	+	0.499911i
$831$	−11.0688	+	27.3776i	−0.383972	+	0.949718i
$832$	−2.29909	−	2.77745i	−0.0797065	−	0.0962906i
$833$	22.1845	−	12.8083i	0.768649	−	0.443780i
$834$	−0.212310	−	0.500500i	−0.00735168	−	0.0173309i
$835$	16.1408	+	27.9566i	0.558575	+	0.967480i
$836$	1.81073	+	3.13628i	0.0626255	+	0.108471i
$837$	−4.81827	−	30.5618i	−0.166544	−	1.05637i
$838$	16.6249	+	4.45464i	0.574299	+	0.153883i
$839$	5.67674	−	5.67674i	0.195983	−	0.195983i	−0.602293	−	0.798275i	$-0.705746\pi$
$839$	5.67674	−	5.67674i	0.195983	−	0.195983i	0.798275	+	0.602293i	$0.205746\pi$
$840$	0.203807	−	0.270329i	0.00703203	−	0.00932722i
$841$	−8.53773	+	14.7878i	−0.294404	+	0.509924i
$842$	3.80999			0.131301
$843$	0.843142	−	6.85343i	0.0290394	−	0.236045i
$844$	−1.25954	−	0.727198i	−0.0433553	−	0.0250312i
$845$	40.7932	+	19.6905i	1.40333	+	0.677374i
$846$	10.7814	+	10.4213i	0.370671	+	0.358292i
$847$	−0.227309	−	0.848328i	−0.00781042	−	0.0291489i
$848$	3.37338	−	1.94762i	0.115842	−	0.0668817i
$849$	11.7889	−	29.1586i	0.404593	−	1.00072i
$850$	25.2529	+	6.76649i	0.866167	+	0.232089i
$851$	42.1806	−	11.3023i	1.44593	−	0.387436i
$852$	−24.5655	+	10.4206i	−0.841601	+	0.357004i
$853$	−5.95946	+	1.59683i	−0.204048	+	0.0546745i	−0.359395	−	0.933185i	$-0.617017\pi$
$853$	−5.95946	+	1.59683i	−0.204048	+	0.0546745i	0.155347	+	0.987860i	$0.450350\pi$
$854$	−0.145932	+	0.0842540i	−0.00499370	+	0.00288311i
$855$	−7.04907	+	2.01768i	−0.241073	+	0.0690032i
$856$	−16.2346	+	4.35004i	−0.554886	+	0.148681i
$857$	−19.6661	+	34.0626i	−0.671780	+	1.16356i	0.305619	+	0.952154i	$0.401137\pi$
$857$	−19.6661	+	34.0626i	−0.671780	+	1.16356i	−0.977399	+	0.211404i	$0.932197\pi$
$858$	6.92179	−	31.4909i	0.236306	−	1.07508i
$859$	−7.03986	−	12.1934i	−0.240197	−	0.416033i	0.720573	−	0.693379i	$-0.243879\pi$
$859$	−7.03986	−	12.1934i	−0.240197	−	0.416033i	−0.960770	+	0.277345i	$0.910545\pi$
$860$	13.3780	+	13.3780i	0.456186	+	0.456186i
$861$	0.109771	−	0.271507i	0.00374097	−	0.00925293i
$862$			21.6457i			0.737254i
$863$	20.5132	+	20.5132i	0.698277	+	0.698277i	0.964039	−	0.265762i	$-0.0856234\pi$
$863$	20.5132	+	20.5132i	0.698277	+	0.698277i	−0.265762	+	0.964039i	$0.585623\pi$
$864$	−3.26718	−	4.04049i	−0.111152	−	0.137460i
$865$	8.87978	−	33.1398i	0.301922	−	1.12679i
$866$	4.52533	+	16.8888i	0.153777	+	0.573904i
$867$	4.90900	−	3.83346i	0.166718	−	0.130191i
$868$		−	0.334013i		−	0.0113371i
$869$	−20.2050	+	20.2050i	−0.685408	+	0.685408i
$870$	−19.3210	−	7.81152i	−0.655044	−	0.264835i
$871$	3.68118	−	39.0660i	0.124732	−	1.32370i
$872$			19.8933i			0.673671i
$873$	−6.90300	+	0.117224i	−0.233631	+	0.00396743i
$874$	−2.02957	+	3.51533i	−0.0686514	+	0.118908i
$875$	−0.418453			−0.0141463
$876$	1.75424	−	14.2593i	0.0592704	−	0.481776i
$877$	2.00216	+	7.47216i	0.0676081	+	0.252317i	0.991456	−	0.130444i	$-0.0416401\pi$
$877$	2.00216	+	7.47216i	0.0676081	+	0.252317i	−0.923848	+	0.382760i	$0.874973\pi$
$878$	1.63056	+	6.08532i	0.0550287	+	0.205370i
$879$	4.32579	−	35.1620i	0.145905	−	1.18598i
$880$	17.9897			0.606432
$881$	20.3481	−	35.2439i	0.685544	−	1.18740i	−0.287722	−	0.957714i	$-0.592898\pi$
$881$	20.3481	−	35.2439i	0.685544	−	1.18740i	0.973266	−	0.229682i	$-0.0737688\pi$
$882$	10.8024	+	17.9975i	0.363736	+	0.606009i
$883$		−	18.4296i		−	0.620206i	−0.950703	−	0.310103i	$-0.899636\pi$
$883$		−	18.4296i		−	0.620206i	0.950703	−	0.310103i	$-0.100364\pi$
$884$	−8.41729	−	10.1686i	−0.283104	−	0.342008i
$885$	5.89907	+	2.38500i	0.198295	+	0.0801710i
$886$	11.3940	−	11.3940i	0.382788	−	0.382788i
$887$			17.5993i			0.590927i	0.955354	+	0.295463i	$0.0954740\pi$
$887$			17.5993i			0.590927i	−0.955354	+	0.295463i	$0.904526\pi$
$888$	10.3013	−	8.04434i	0.345690	−	0.269951i
$889$	4.16307e−5	0	0.000155368i	1.39625e−6	0	5.21087e-6i
$890$	15.3723	−	57.3703i	0.515281	−	1.92306i
$891$	10.4956	−	45.2658i	0.351615	−	1.51646i
$892$	−3.00391	−	3.00391i	−0.100579	−	0.100579i
$893$		−	3.50593i		−	0.117321i
$894$	−3.95990	+	9.79442i	−0.132439	+	0.327575i
$895$	−37.9320	−	37.9320i	−1.26793	−	1.26793i
$896$	−0.0280482	−	0.0485810i	−0.000937026	−	0.00162298i
$897$	34.4471	−	10.9295i	1.15016	−	0.364926i
$898$	−9.48174	+	16.4229i	−0.316410	+	0.548038i
$899$	−19.8606	+	5.32164i	−0.662389	+	0.177487i
$900$	−5.19243	+	20.7838i	−0.173081	+	0.692792i
$901$	12.3505	−	7.13054i	0.411453	−	0.237553i
$902$	15.0315	−	4.02768i	0.500495	−	0.134107i
$903$	0.485677	−	0.206022i	0.0161623	−	0.00685598i
$904$	−18.9014	+	5.06461i	−0.628650	+	0.168446i
$905$	−57.8564	−	15.5026i	−1.92321	−	0.515323i
$906$	−7.28263	+	18.0129i	−0.241949	+	0.598437i
$907$	−31.5177	+	18.1967i	−1.04653	+	0.604213i	−0.921675	−	0.387963i	$-0.873179\pi$
$907$	−31.5177	+	18.1967i	−1.04653	+	0.604213i	−0.124852	+	0.992175i	$0.539846\pi$
$908$	−6.04673	−	22.5667i	−0.200668	−	0.748902i
$909$	2.56193	−	10.2547i	0.0849739	−	0.340126i
$910$	0.574578	+	0.408076i	0.0190471	+	0.0135276i
$911$	30.6958	+	17.7222i	1.01700	+	0.587164i	0.913233	−	0.407438i	$-0.133578\pi$
$911$	30.6958	+	17.7222i	1.01700	+	0.587164i	0.103765	+	0.994602i	$0.466911\pi$
$912$	−0.148346	+	1.20583i	−0.00491224	+	0.0399289i
$913$	82.4536			2.72882
$914$	−8.46556	+	14.6628i	−0.280016	+	0.485002i
$915$	10.9136	−	14.4758i	0.360794	−	0.478554i
$916$	4.36987	−	4.36987i	0.144384	−	0.144384i
$917$	0.680714	+	0.182397i	0.0224791	+	0.00602327i
$918$	−11.9616	−	14.7928i	−0.394792	−	0.488236i
$919$	−9.39060	−	16.2650i	−0.309767	−	0.536533i	0.668544	−	0.743673i	$-0.266918\pi$
$919$	−9.39060	−	16.2650i	−0.309767	−	0.536533i	−0.978311	+	0.207140i	$0.933584\pi$
$920$	10.0819	+	17.4624i	0.332391	+	0.575719i
$921$	−6.42859	−	15.1548i	−0.211829	−	0.499367i
$922$	−11.2174	+	6.47635i	−0.369424	+	0.213287i
$923$	−23.1384	−	50.4993i	−0.761611	−	1.66221i
$924$	0.188029	−	0.465071i	0.00618569	−	0.0152997i
$925$	−52.0491	−	13.9465i	−1.71137	−	0.458559i
$926$	−15.2890	−	8.82711i	−0.502428	−	0.290077i
$927$	−17.4996	−	4.37195i	−0.574764	−	0.143594i
$928$	−2.44178	+	2.44178i	−0.0801552	+	0.0801552i
$929$	−4.30437	−	4.30437i	−0.141222	−	0.141222i	0.632962	−	0.774183i	$-0.281839\pi$
$929$	−4.30437	−	4.30437i	−0.141222	−	0.141222i	−0.774183	+	0.632962i	$0.781839\pi$
$930$	14.0330	+	33.0813i	0.460159	+	1.08478i
$931$	1.27024	−	4.74059i	0.0416303	−	0.155366i
$932$	1.04763	+	0.604847i	0.0343161	+	0.0198124i
$933$	0.870995	+	6.20811i	0.0285151	+	0.203245i
$934$	5.46566	−	20.3981i	0.178842	−	0.667447i
$935$	65.8628			2.15394
$936$	8.21403	−	7.03774i	0.268484	−	0.230036i
$937$	−10.2331			−0.334301			−0.167150	−	0.985931i	$-0.553457\pi$
$937$	−10.2331			−0.334301			−0.167150	+	0.985931i	$0.553457\pi$
$938$	0.158008	−	0.589694i	0.00515914	−	0.0192542i
$939$	−24.6800	+	19.2728i	−0.805403	+	0.628943i
$940$	−15.0825	−	8.70787i	−0.491936	−	0.284019i
$941$	−9.66473	+	36.0693i	−0.315061	+	1.17582i	0.608871	+	0.793269i	$0.291623\pi$
$941$	−9.66473	+	36.0693i	−0.315061	+	1.17582i	−0.923932	+	0.382556i	$0.875044\pi$
$942$	22.4170	+	2.75785i	0.730385	+	0.0898555i
$943$	12.3337	+	12.3337i	0.401642	+	0.401642i
$944$	0.745519	−	0.745519i	0.0242646	−	0.0242646i
$945$	0.821250	+	0.597564i	0.0267153	+	0.0194388i
$946$	24.2779	+	14.0168i	0.789342	+	0.455727i
$947$	−22.7358	−	6.09203i	−0.738813	−	0.197964i	−0.130262	−	0.991480i	$-0.541582\pi$
$947$	−22.7358	−	6.09203i	−0.738813	−	0.197964i	−0.608550	+	0.793515i	$0.708249\pi$
$948$	−9.49299	+	1.33186i	−0.308318	+	0.0432569i
$949$	29.7749	+	2.80568i	0.966535	+	0.0910763i
$950$	4.33777	−	2.50441i	0.140736	−	0.0812539i
$951$	−18.3600	−	2.25873i	−0.595363	−	0.0732445i
$952$	−0.102689	−	0.177862i	−0.00332816	−	0.00576454i
$953$	−23.3774	−	40.4908i	−0.757267	−	1.31163i	−0.944239	−	0.329260i	$-0.893201\pi$
$953$	−23.3774	−	40.4908i	−0.757267	−	1.31163i	0.186972	−	0.982365i	$-0.440133\pi$
$954$	6.01386	+	10.0195i	0.194706	+	0.324393i
$955$	28.7582	+	7.70575i	0.930595	+	0.249352i
$956$	−9.61511	+	9.61511i	−0.310975	+	0.310975i
$957$	−30.6491	−	3.77060i	−0.990746	−	0.121886i
$958$	7.68966	−	13.3189i	0.248442	−	0.430313i
$959$	−0.788846			−0.0254732
$960$	4.81899	+	3.63316i	0.155532	+	0.117260i
$961$	3.85665	+	2.22664i	0.124408	+	0.0718270i
$962$	17.3490	+	20.9587i	0.559355	+	0.675737i
$963$	−13.8752	−	48.4751i	−0.447122	−	1.56209i
$964$	−1.84513	−	6.88614i	−0.0594278	−	0.221788i
$965$	−1.84103	+	1.06292i	−0.0592650	+	0.0342167i
$966$	0.556817	−	0.0781211i	0.0179153	−	0.00251351i
$967$	−44.7620	−	11.9939i	−1.43945	−	0.385699i	−0.547108	−	0.837062i	$-0.684271\pi$
$967$	−44.7620	−	11.9939i	−1.43945	−	0.385699i	−0.892340	+	0.451363i	$0.850938\pi$
$968$	15.1227	−	4.05211i	0.486061	−	0.130240i
$969$	−0.543118	+	4.41470i	−0.0174475	+	0.141821i
$970$	7.74546	−	2.07539i	0.248692	−	0.0666368i
$971$	10.9829	−	6.34097i	0.352458	−	0.203491i	−0.313310	−	0.949651i	$-0.601438\pi$
$971$	10.9829	−	6.34097i	0.352458	−	0.203491i	0.665767	+	0.746160i	$0.268104\pi$
$972$	11.9533	−	10.0059i	0.383402	−	0.320940i
$973$	0.0170080	−	0.00455727i	0.000545251	−	0.000146099i
$974$	7.85293	−	13.6017i	0.251624	−	0.435826i
$975$	−43.5549	−	9.57348i	−1.39487	−	0.306597i
$976$	−1.50195	−	2.60145i	−0.0480762	−	0.0832705i
$977$	−42.6741	−	42.6741i	−1.36526	−	1.36526i	−0.867058	−	0.498206i	$-0.833992\pi$
$977$	−42.6741	−	42.6741i	−1.36526	−	1.36526i	−0.498206	−	0.867058i	$-0.666008\pi$
$978$	−5.96973	−	7.64463i	−0.190891	−	0.244448i
$979$		−	88.0070i		−	2.81272i
$980$	−17.2390	−	17.2390i	−0.550680	−	0.550680i
$981$	−59.6712	+	1.01331i	−1.90516	+	0.0323525i
$982$	1.65507	−	6.17679i	0.0528153	−	0.197109i
$983$	5.89349	+	21.9948i	0.187973	+	0.701525i	0.993975	+	0.109611i	$0.0349607\pi$
$983$	5.89349	+	21.9948i	0.187973	+	0.701525i	−0.806001	+	0.591914i	$0.798373\pi$
$984$	4.84000	+	1.95682i	0.154294	+	0.0623811i
$985$		−	62.4924i		−	1.99117i
$986$	−8.93970	+	8.93970i	−0.284698	+	0.284698i
$987$	−0.382759	+	0.298899i	−0.0121834	+	0.00951405i
$988$	−2.51790	−	0.237261i	−0.0801049	−	0.00754827i
$989$			31.4218i			0.999154i
$990$	0.916347	+	53.9612i	0.0291234	+	1.71500i
$991$	14.2272	−	24.6423i	0.451942	−	0.782787i	−0.546564	−	0.837417i	$-0.684065\pi$
$991$	14.2272	−	24.6423i	0.451942	−	0.782787i	0.998507	+	0.0546299i	$0.0173979\pi$
$992$	5.95427			0.189048
$993$	−5.30501	+	2.25036i	−0.168349	+	0.0714130i
$994$	−0.223680	−	0.834786i	−0.00709471	−	0.0264778i
$995$	17.9781	+	67.0950i	0.569943	+	2.12705i
$996$	22.0873	+	16.6522i	0.699863	+	0.527644i
$997$	−16.7316			−0.529896			−0.264948	−	0.964263i	$-0.585355\pi$
$997$	−16.7316			−0.529896			−0.264948	+	0.964263i	$0.585355\pi$
$998$	−3.82690	+	6.62838i	−0.121138	+	0.209818i
$999$	24.6543	+	30.4897i	0.780027	+	0.964653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.z.a.227.6	yes	56
3.2	odd	2		702.2.bc.a.305.14		56
9.4	even	3		702.2.bb.a.71.7		56
9.5	odd	6		234.2.y.a.149.8	yes	56
13.11	odd	12		234.2.y.a.11.8	✓	56
39.11	even	12		702.2.bb.a.89.7		56
117.50	even	12	inner	234.2.z.a.167.6	yes	56
117.76	odd	12		702.2.bc.a.557.14		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.8	✓	56	13.11	odd	12
234.2.y.a.149.8	yes	56	9.5	odd	6
234.2.z.a.167.6	yes	56	117.50	even	12	inner
234.2.z.a.227.6	yes	56	1.1	even	1	trivial
702.2.bb.a.71.7		56	9.4	even	3
702.2.bb.a.89.7		56	39.11	even	12
702.2.bc.a.305.14		56	3.2	odd	2
702.2.bc.a.557.14		56	117.76	odd	12

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.60578 + 0.649218i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.901822 + 3.36565i) q^{5} +(-1.04270 + 1.38303i) q^{6} +(-0.0396662 - 0.0396662i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.15703 + 2.08500i) q^{9} +(-3.01756 - 1.74219i) q^{10} +(-4.98703 - 1.33627i) q^{11} +(-1.06603 - 1.36513i) q^{12} +(2.77745 - 2.29909i) q^{13} +(0.0485810 - 0.0280482i) q^{14} +(-3.63316 + 4.81899i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.83057 + 3.17065i) q^{17} +(-2.57223 + 1.54390i) q^{18} +(0.677531 + 0.181544i) q^{19} +(2.46382 - 2.46382i) q^{20} +(-0.0379430 - 0.0894470i) q^{21} +(2.58148 - 4.47125i) q^{22} +5.78694 q^{23} +(1.59452 - 0.676389i) q^{24} +(-6.18416 - 3.57043i) q^{25} +(1.50189 + 3.27785i) q^{26} +(2.11009 + 4.74842i) q^{27} +(0.0145188 + 0.0541850i) q^{28} +(2.99055 - 1.72660i) q^{29} +(-3.71446 - 4.75661i) q^{30} +(-5.75138 - 1.54108i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-7.14053 - 5.38342i) q^{33} +(-3.53640 + 0.947575i) q^{34} +(0.169274 - 0.0977305i) q^{35} +(-0.825547 - 2.88418i) q^{36} +(7.28892 - 1.95306i) q^{37} +(-0.350716 + 0.607458i) q^{38} +(5.95256 - 1.88865i) q^{39} +(1.74219 + 3.01756i) q^{40} +(2.13130 + 2.13130i) q^{41} +(0.0962195 - 0.0134996i) q^{42} +5.42977i q^{43} +(3.65076 + 3.65076i) q^{44} +(-8.96262 + 5.37951i) q^{45} +(-1.49777 + 5.58976i) q^{46} +(-1.29364 - 4.82793i) q^{47} +(0.240649 + 1.71525i) q^{48} -6.99685i q^{49} +(5.04935 - 5.04935i) q^{50} +(0.881051 + 6.27979i) q^{51} +(-3.55488 + 0.602344i) q^{52} -3.89525i q^{53} +(-5.13276 + 0.809213i) q^{54} +(8.99483 - 15.5795i) q^{55} -0.0560965 q^{56} +(0.970102 + 0.731384i) q^{57} +(0.893752 + 3.33553i) q^{58} +(-0.272879 - 1.01840i) q^{59} +(5.55591 - 2.35679i) q^{60} -3.00390 q^{61} +(2.97713 - 5.15654i) q^{62} +(-0.00285741 - 0.168265i) q^{63} -1.00000i q^{64} +(5.23315 + 11.4213i) q^{65} +(7.04809 - 5.50389i) q^{66} +(7.69542 - 7.69542i) q^{67} -3.66115i q^{68} +(9.29253 + 3.75699i) q^{69} +(0.0505890 + 0.188801i) q^{70} +(3.98742 - 14.8813i) q^{71} +(2.99957 - 0.0509374i) q^{72} +(5.86521 + 5.86521i) q^{73} +7.54605i q^{74} +(-7.61239 - 9.74817i) q^{75} +(-0.495987 - 0.495987i) q^{76} +(0.144812 + 0.250821i) q^{77} +(0.283658 + 6.23855i) q^{78} +(2.76723 - 4.79298i) q^{79} +(-3.36565 + 0.901822i) q^{80} +(0.305580 + 8.99481i) q^{81} +(-2.61030 + 1.50706i) q^{82} +(-15.4261 + 4.13340i) q^{83} +(-0.0118639 + 0.0964349i) q^{84} +(-12.3221 + 3.30170i) q^{85} +(-5.24476 - 1.40533i) q^{86} +(5.92309 - 0.831007i) q^{87} +(-4.47125 + 2.58148i) q^{88} +(4.41179 + 16.4650i) q^{89} +(-2.87651 - 10.0495i) q^{90} +(-0.201367 - 0.0189747i) q^{91} +(-5.01164 - 2.89347i) q^{92} +(-8.23493 - 6.20852i) q^{93} +4.99824 q^{94} +(-1.22203 + 2.11661i) q^{95} +(-1.71909 - 0.211491i) q^{96} +(-1.62729 + 1.62729i) q^{97} +(6.75844 + 1.81092i) q^{98} +(-7.97107 - 13.2803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Introduction

L-functions

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