LMFDB - Embedded newform 570.2.x.a.217.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(103,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("570.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.x (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			217.9
Character	$\chi$	$=$	570.217
Dual form			570.2.x.a.373.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.47772 + 1.67820i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.44846 - 1.44846i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.47772 + 1.67820i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.44846 - 1.44846i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-1.23855 + 1.86172i) q^{10} -4.77940 q^{11} +(0.707107 - 0.707107i) q^{12} +(-1.64451 + 6.13741i) q^{13} +(1.02422 - 1.77400i) q^{14} +(-1.86172 - 1.23855i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.33143 - 0.624705i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-4.35842 - 0.0647836i) q^{19} +(-2.11884 - 0.714502i) q^{20} +(1.77400 + 1.02422i) q^{21} +(-1.23700 - 4.61654i) q^{22} +(-2.31137 - 0.619330i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-0.632691 + 4.95981i) q^{25} -6.35391 q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.97863 + 0.530173i) q^{28} +(-0.138707 - 0.240248i) q^{29} +(0.714502 - 2.11884i) q^{30} -1.20870i q^{31} +(0.965926 + 0.258819i) q^{32} +(4.61654 - 1.23700i) q^{33} +(1.20684 + 2.09030i) q^{34} +(0.290384 - 4.57122i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.38275 + 2.38275i) q^{37} +(-1.06547 - 4.22668i) q^{38} -6.35391i q^{39} +(0.141759 - 2.23157i) q^{40} +(-8.57196 - 4.94902i) q^{41} +(-0.530173 + 1.97863i) q^{42} +(1.26771 + 4.73117i) q^{43} +(4.13908 - 2.38970i) q^{44} +(2.11884 + 0.714502i) q^{45} -2.39291i q^{46} +(1.36743 - 5.10332i) q^{47} +(-0.258819 + 0.965926i) q^{48} -2.80392i q^{49} +(-4.95456 + 0.672560i) q^{50} +(-2.09030 + 1.20684i) q^{51} +(-1.64451 - 6.13741i) q^{52} +(0.0144909 - 0.0540807i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-7.06261 - 8.02077i) q^{55} +2.04843i q^{56} +(4.22668 - 1.06547i) q^{57} +(0.196162 - 0.196162i) q^{58} +(-5.69599 + 9.86575i) q^{59} +(2.23157 + 0.141759i) q^{60} +(1.79160 + 3.10315i) q^{61} +(1.16752 - 0.312835i) q^{62} +(-1.97863 - 0.530173i) q^{63} +1.00000i q^{64} +(-12.7299 + 6.30955i) q^{65} +(2.38970 + 4.13908i) q^{66} +(13.6853 + 3.66697i) q^{67} +(-1.70672 + 1.70672i) q^{68} +2.39291 q^{69} +(4.49062 - 0.902630i) q^{70} +(8.89740 + 5.13692i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(1.32075 + 4.92912i) q^{73} +(-2.91826 - 1.68486i) q^{74} +(-0.672560 - 4.95456i) q^{75} +(3.80689 - 2.12310i) q^{76} +(6.92277 + 6.92277i) q^{77} +(6.13741 - 1.64451i) q^{78} +(-0.0784953 + 0.135958i) q^{79} +(2.19222 - 0.440644i) q^{80} +(0.500000 - 0.866025i) q^{81} +(2.56180 - 9.56078i) q^{82} +(-9.57920 + 9.57920i) q^{83} -2.04843 q^{84} +(4.49358 + 2.98946i) q^{85} +(-4.24185 + 2.44903i) q^{86} +(0.196162 + 0.196162i) q^{87} +(3.37954 + 3.37954i) q^{88} +(-3.92888 - 6.80502i) q^{89} +(-0.141759 + 2.23157i) q^{90} +(11.2718 - 6.50778i) q^{91} +(2.31137 - 0.619330i) q^{92} +(0.312835 + 1.16752i) q^{93} +5.28335 q^{94} +(-6.33180 - 7.41002i) q^{95} -1.00000 q^{96} +(4.11289 + 15.3495i) q^{97} +(2.70838 - 0.725708i) q^{98} +(-4.13908 + 2.38970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7	$ 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7} - 12 q^{10} + 8 q^{11} - 24 q^{13} + 20 q^{16} + 8 q^{17} + 12 q^{21} + 24 q^{22} + 16 q^{23} - 16 q^{25} + 32 q^{26} + 4 q^{28} + 16 q^{30} - 24 q^{33} - 4 q^{35} - 20 q^{36} - 8 q^{38} - 36 q^{41} + 4 q^{42} - 4 q^{43} + 8 q^{47} - 24 q^{52} - 16 q^{55} - 8 q^{57} + 16 q^{58} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{66} - 36 q^{67} - 16 q^{68} + 48 q^{70} + 72 q^{71} - 16 q^{73} - 8 q^{76} + 24 q^{77} + 24 q^{78} + 8 q^{80} + 20 q^{81} - 24 q^{82} - 40 q^{83} - 48 q^{85} + 16 q^{87} - 72 q^{91} - 16 q^{92} + 16 q^{93} - 16 q^{95} - 40 q^{96} + 36 q^{97} - 48 q^{98}+O(q^{100}) $ 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7 - 12 * q^10 + 8 * q^11 - 24 * q^13 + 20 * q^16 + 8 * q^17 + 12 * q^21 + 24 * q^22 + 16 * q^23 - 16 * q^25 + 32 * q^26 + 4 * q^28 + 16 * q^30 - 24 * q^33 - 4 * q^35 - 20 * q^36 - 8 * q^38 - 36 * q^41 + 4 * q^42 - 4 * q^43 + 8 * q^47 - 24 * q^52 - 16 * q^55 - 8 * q^57 + 16 * q^58 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^66 - 36 * q^67 - 16 * q^68 + 48 * q^70 + 72 * q^71 - 16 * q^73 - 8 * q^76 + 24 * q^77 + 24 * q^78 + 8 * q^80 + 20 * q^81 - 24 * q^82 - 40 * q^83 - 48 * q^85 + 16 * q^87 - 72 * q^91 - 16 * q^92 + 16 * q^93 - 16 * q^95 - 40 * q^96 + 36 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	1.47772	+	1.67820i	0.660856	+	0.750513i
$5$	1.47772	+	1.67820i	0.660856	+	0.750513i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−1.44846	−	1.44846i	−0.547467	−	0.547467i	0.378241	−	0.925707i	$-0.376529\pi$
$7$	−1.44846	−	1.44846i	−0.547467	−	0.547467i	−0.925707	+	0.378241i	$0.876529\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−1.23855	+	1.86172i	−0.391665	+	0.588726i
$11$	−4.77940			−1.44104			−0.720521	−	0.693433i	$-0.756097\pi$
$11$	−4.77940			−1.44104			−0.720521	+	0.693433i	$0.756097\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−1.64451	+	6.13741i	−0.456106	+	1.70221i	0.228711	+	0.973494i	$0.426549\pi$
$13$	−1.64451	+	6.13741i	−0.456106	+	1.70221i	−0.684816	+	0.728716i	$0.740118\pi$
$14$	1.02422	−	1.77400i	0.273733	−	0.474120i
$15$	−1.86172	−	1.23855i	−0.480693	−	0.319793i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.33143	−	0.624705i	0.565455	−	0.151513i	0.0352435	−	0.999379i	$-0.488779\pi$
$17$	2.33143	−	0.624705i	0.565455	−	0.151513i	0.530211	+	0.847866i	$0.322113\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−4.35842	−	0.0647836i	−0.999890	−	0.0148624i
$19$	−4.35842	−	0.0647836i	−0.999890	−	0.0148624i
$20$	−2.11884	−	0.714502i	−0.473787	−	0.159767i
$21$	1.77400	+	1.02422i	0.387117	+	0.223502i
$22$	−1.23700	−	4.61654i	−0.263729	−	0.984250i
$23$	−2.31137	−	0.619330i	−0.481954	−	0.129139i	0.00965820	−	0.999953i	$-0.496926\pi$
$23$	−2.31137	−	0.619330i	−0.481954	−	0.129139i	−0.491612	+	0.870814i	$0.663592\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−0.632691	+	4.95981i	−0.126538	+	0.991962i
$26$	−6.35391			−1.24610
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.97863	+	0.530173i	0.373927	+	0.100193i
$29$	−0.138707	−	0.240248i	−0.0257573	−	0.0446130i	0.852859	−	0.522141i	$-0.174866\pi$
$29$	−0.138707	−	0.240248i	−0.0257573	−	0.0446130i	−0.878617	+	0.477528i	$0.841533\pi$
$30$	0.714502	−	2.11884i	0.130450	−	0.386846i
$31$		−	1.20870i		−	0.217089i	−0.994092	−	0.108545i	$-0.965381\pi$
$31$		−	1.20870i		−	0.217089i	0.994092	−	0.108545i	$-0.0346191\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	4.61654	−	1.23700i	0.803637	−	0.215334i
$34$	1.20684	+	2.09030i	0.206971	+	0.358484i
$35$	0.290384	−	4.57122i	0.0490839	−	0.772677i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−2.38275	+	2.38275i	−0.391722	+	0.391722i	−0.875301	−	0.483579i	$-0.839337\pi$
$37$	−2.38275	+	2.38275i	−0.391722	+	0.391722i	0.483579	+	0.875301i	$0.339337\pi$
$38$	−1.06547	−	4.22668i	−0.172841	−	0.685657i
$39$		−	6.35391i		−	1.01744i
$40$	0.141759	−	2.23157i	0.0224141	−	0.352842i
$41$	−8.57196	−	4.94902i	−1.33871	−	0.772907i	−0.352098	−	0.935963i	$-0.614532\pi$
$41$	−8.57196	−	4.94902i	−1.33871	−	0.772907i	−0.986617	+	0.163056i	$0.947865\pi$
$42$	−0.530173	+	1.97863i	−0.0818075	+	0.305310i
$43$	1.26771	+	4.73117i	0.193324	+	0.721496i	0.992694	+	0.120657i	$0.0385001\pi$
$43$	1.26771	+	4.73117i	0.193324	+	0.721496i	−0.799370	+	0.600839i	$0.794833\pi$
$44$	4.13908	−	2.38970i	0.623990	−	0.360261i
$45$	2.11884	+	0.714502i	0.315858	+	0.106512i
$46$		−	2.39291i		−	0.352815i
$47$	1.36743	−	5.10332i	0.199460	−	0.744396i	−0.791607	−	0.611031i	$-0.790755\pi$
$47$	1.36743	−	5.10332i	0.199460	−	0.744396i	0.991067	−	0.133365i	$-0.0425783\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$		−	2.80392i		−	0.400560i
$50$	−4.95456	+	0.672560i	−0.700681	+	0.0951144i
$51$	−2.09030	+	1.20684i	−0.292701	+	0.168991i
$52$	−1.64451	−	6.13741i	−0.228053	−	0.851105i
$53$	0.0144909	−	0.0540807i	0.00199047	−	0.00742855i	−0.964923	−	0.262531i	$-0.915443\pi$
$53$	0.0144909	−	0.0540807i	0.00199047	−	0.00742855i	0.966914	+	0.255103i	$0.0821093\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−7.06261	−	8.02077i	−0.952322	−	1.08152i
$56$			2.04843i			0.273733i
$57$	4.22668	−	1.06547i	0.559837	−	0.141124i
$58$	0.196162	−	0.196162i	0.0257573	−	0.0257573i
$59$	−5.69599	+	9.86575i	−0.741555	+	1.28441i	0.210232	+	0.977652i	$0.432578\pi$
$59$	−5.69599	+	9.86575i	−0.741555	+	1.28441i	−0.951787	+	0.306759i	$0.900755\pi$
$60$	2.23157	+	0.141759i	0.288094	+	0.0183010i
$61$	1.79160	+	3.10315i	0.229391	+	0.397318i	0.957628	−	0.288008i	$-0.0929931\pi$
$61$	1.79160	+	3.10315i	0.229391	+	0.397318i	−0.728236	+	0.685326i	$0.759660\pi$
$62$	1.16752	−	0.312835i	0.148275	−	0.0397301i
$63$	−1.97863	−	0.530173i	−0.249284	−	0.0667956i
$64$			1.00000i			0.125000i
$65$	−12.7299	+	6.30955i	−1.57895	+	0.782603i
$66$	2.38970	+	4.13908i	0.294151	+	0.509485i
$67$	13.6853	+	3.66697i	1.67193	+	0.447992i	0.965629	−	0.259923i	$-0.0836971\pi$
$67$	13.6853	+	3.66697i	1.67193	+	0.447992i	0.706298	+	0.707914i	$0.250364\pi$
$68$	−1.70672	+	1.70672i	−0.206971	+	0.206971i
$69$	2.39291			0.288072
$70$	4.49062	−	0.902630i	0.536731	−	0.107885i
$71$	8.89740	+	5.13692i	1.05593	+	0.609640i	0.924303	−	0.381659i	$-0.124647\pi$
$71$	8.89740	+	5.13692i	1.05593	+	0.609640i	0.131625	+	0.991300i	$0.457981\pi$
$72$	−0.965926	−	0.258819i	−0.113835	−	0.0305021i
$73$	1.32075	+	4.92912i	0.154582	+	0.576910i	0.999141	+	0.0414460i	$0.0131964\pi$
$73$	1.32075	+	4.92912i	0.154582	+	0.576910i	−0.844558	+	0.535464i	$0.820137\pi$
$74$	−2.91826	−	1.68486i	−0.339241	−	0.195861i
$75$	−0.672560	−	4.95456i	−0.0776606	−	0.572103i
$76$	3.80689	−	2.12310i	0.436680	−	0.243537i
$77$	6.92277	+	6.92277i	0.788923	+	0.788923i
$78$	6.13741	−	1.64451i	0.694924	−	0.186204i
$79$	−0.0784953	+	0.135958i	−0.00883141	+	0.0152965i	−0.870407	−	0.492332i	$-0.836144\pi$
$79$	−0.0784953	+	0.135958i	−0.00883141	+	0.0152965i	0.861576	+	0.507629i	$0.169478\pi$
$80$	2.19222	−	0.440644i	0.245098	−	0.0492655i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	2.56180	−	9.56078i	0.282904	−	1.05581i
$83$	−9.57920	+	9.57920i	−1.05145	+	1.05145i	−0.0528519	+	0.998602i	$0.516831\pi$
$83$	−9.57920	+	9.57920i	−1.05145	+	1.05145i	−0.998602	+	0.0528519i	$0.983169\pi$
$84$	−2.04843			−0.223502
$85$	4.49358	+	2.98946i	0.487397	+	0.324252i
$86$	−4.24185	+	2.44903i	−0.457410	+	0.264086i
$87$	0.196162	+	0.196162i	0.0210308	+	0.0210308i
$88$	3.37954	+	3.37954i	0.360261	+	0.360261i
$89$	−3.92888	−	6.80502i	−0.416461	−	0.721331i	0.579120	−	0.815242i	$-0.303396\pi$
$89$	−3.92888	−	6.80502i	−0.416461	−	0.721331i	−0.995581	+	0.0939113i	$0.970063\pi$
$90$	−0.141759	+	2.23157i	−0.0149427	+	0.235228i
$91$	11.2718	−	6.50778i	1.18161	−	0.682201i
$92$	2.31137	−	0.619330i	0.240977	−	0.0645696i
$93$	0.312835	+	1.16752i	0.0324395	+	0.121066i
$94$	5.28335			0.544936
$95$	−6.33180	−	7.41002i	−0.649629	−	0.760252i
$96$	−1.00000			−0.102062
$97$	4.11289	+	15.3495i	0.417601	+	1.55851i	0.779568	+	0.626317i	$0.215439\pi$
$97$	4.11289	+	15.3495i	0.417601	+	1.55851i	−0.361967	+	0.932191i	$0.617895\pi$
$98$	2.70838	−	0.725708i	0.273588	−	0.0733076i
$99$	−4.13908	+	2.38970i	−0.415993	+	0.240174i
$100$	−1.93198	−	4.61167i	−0.193198	−	0.461167i
$101$	−2.27595	−	3.94207i	−0.226466	−	0.392250i	0.730292	−	0.683135i	$-0.239384\pi$
$101$	−2.27595	−	3.94207i	−0.226466	−	0.392250i	−0.956758	+	0.290884i	$0.906050\pi$
$102$	−1.70672	−	1.70672i	−0.168991	−	0.168991i
$103$	10.6503	+	10.6503i	1.04940	+	1.04940i	0.998715	+	0.0506874i	$0.0161412\pi$
$103$	10.6503	+	10.6503i	1.04940	+	1.04940i	0.0506874	+	0.998715i	$0.483859\pi$
$104$	5.50265	−	3.17696i	0.539579	−	0.311526i
$105$	0.902630	+	4.49062i	0.0880876	+	0.438239i
$106$	0.0559884			0.00543808
$107$	5.65689	−	5.65689i	0.546872	−	0.546872i	−0.378663	−	0.925535i	$-0.623616\pi$
$107$	5.65689	−	5.65689i	0.546872	−	0.546872i	0.925535	+	0.378663i	$0.123616\pi$
$108$	0.258819	−	0.965926i	0.0249049	−	0.0929463i
$109$	4.99236	−	8.64702i	0.478181	−	0.828234i	−0.521506	−	0.853248i	$-0.674630\pi$
$109$	4.99236	−	8.64702i	0.478181	−	0.828234i	0.999687	+	0.0250137i	$0.00796293\pi$
$110$	5.91953	−	8.89788i	0.564405	−	0.848380i
$111$	1.68486	−	2.91826i	0.159920	−	0.276989i
$112$	−1.97863	+	0.530173i	−0.186963	+	0.0500967i
$113$	7.87693	+	7.87693i	0.741000	+	0.741000i	0.972770	−	0.231771i	$-0.0744520\pi$
$113$	7.87693	+	7.87693i	0.741000	+	0.741000i	−0.231771	+	0.972770i	$0.574452\pi$
$114$	2.12310	+	3.80689i	0.198847	+	0.356548i
$115$	−2.37620	−	4.79413i	−0.221582	−	0.447055i
$116$	0.240248	+	0.138707i	0.0223065	+	0.0128787i
$117$	1.64451	+	6.13741i	0.152035	+	0.567403i
$118$	−11.0038	−	2.94846i	−1.01298	−	0.271428i
$119$	−4.28184	−	2.47212i	−0.392516	−	0.226619i
$120$	0.440644	+	2.19222i	0.0402251	+	0.200121i
$121$	11.8426			1.07660
$122$	−2.53371	+	2.53371i	−0.229391	+	0.229391i
$123$	9.56078	+	2.56180i	0.862066	+	0.230990i
$124$	0.604351	+	1.04677i	0.0542723	+	0.0940025i
$125$	−9.25848	+	6.26742i	−0.828103	+	0.560576i
$126$		−	2.04843i		−	0.182489i
$127$	8.95204	+	2.39869i	0.794365	+	0.212850i	0.633109	−	0.774063i	$-0.281779\pi$
$127$	8.95204	+	2.39869i	0.794365	+	0.212850i	0.161257	+	0.986913i	$0.448445\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−2.44903	−	4.24185i	−0.215625	−	0.373474i
$130$	−9.38930	−	10.6631i	−0.823496	−	0.935217i
$131$	3.43842	−	5.95552i	0.300416	−	0.520336i	−0.675814	−	0.737072i	$-0.736208\pi$
$131$	3.43842	−	5.95552i	0.300416	−	0.520336i	0.976230	+	0.216736i	$0.0695410\pi$
$132$	−3.37954	+	3.37954i	−0.294151	+	0.294151i
$133$	6.21916	+	6.40683i	0.539270	+	0.555543i
$134$			14.1681i			1.22394i
$135$	−2.23157	−	0.141759i	−0.192063	−	0.0122007i
$136$	−2.09030	−	1.20684i	−0.179242	−	0.103485i
$137$	1.36927	−	5.11017i	0.116984	−	0.436591i	−0.882443	−	0.470419i	$-0.844103\pi$
$137$	1.36927	−	5.11017i	0.116984	−	0.436591i	0.999428	+	0.0338273i	$0.0107696\pi$
$138$	0.619330	+	2.31137i	0.0527209	+	0.196757i
$139$	−6.07995	+	3.51026i	−0.515695	+	0.297737i	−0.735171	−	0.677881i	$-0.762898\pi$
$139$	−6.07995	+	3.51026i	−0.515695	+	0.297737i	0.219477	+	0.975618i	$0.429565\pi$
$140$	2.03413	+	4.10399i	0.171915	+	0.346850i
$141$			5.28335i			0.444938i
$142$	−2.65906	+	9.92377i	−0.223144	+	0.832784i
$143$	7.85978	−	29.3331i	0.657268	−	2.45296i
$144$		−	1.00000i		−	0.0833333i
$145$	0.198213	−	0.587798i	0.0164607	−	0.0488140i
$146$	−4.41933	+	2.55150i	−0.365746	+	0.211164i
$147$	0.725708	+	2.70838i	0.0598554	+	0.223383i
$148$	0.872147	−	3.25490i	0.0716900	−	0.267551i
$149$	12.8151	+	7.39882i	1.04986	+	0.606135i	0.922609	−	0.385736i	$-0.126052\pi$
$149$	12.8151	+	7.39882i	1.04986	+	0.606135i	0.127248	+	0.991871i	$0.459386\pi$
$150$	4.61167	−	1.93198i	0.376541	−	0.157745i
$151$			12.9082i			1.05045i	0.850962	+	0.525227i	$0.176020\pi$
$151$			12.9082i			1.05045i	−0.850962	+	0.525227i	$0.823980\pi$
$152$	3.03606	+	3.12768i	0.246257	+	0.253688i
$153$	1.70672	−	1.70672i	0.137981	−	0.137981i
$154$	−4.89514	+	8.47862i	−0.394461	+	0.683227i
$155$	2.02844	−	1.78612i	0.162928	−	0.143465i
$156$	3.17696	+	5.50265i	0.254360	+	0.440564i
$157$	−2.54973	+	0.683198i	−0.203491	+	0.0545251i	−0.359124	−	0.933290i	$-0.616925\pi$
$157$	−2.54973	+	0.683198i	−0.203491	+	0.0545251i	0.155634	+	0.987815i	$0.450258\pi$
$158$	−0.151641	−	0.0406322i	−0.0120639	−	0.00323252i
$159$			0.0559884i			0.00444017i
$160$	0.993018	+	2.00348i	0.0785050	+	0.158389i
$161$	2.45086	+	4.24501i	0.193154	+	0.334553i
$162$	0.965926	+	0.258819i	0.0758903	+	0.0203347i
$163$	−13.6829	+	13.6829i	−1.07173	+	1.07173i	−0.0745108	+	0.997220i	$0.523740\pi$
$163$	−13.6829	+	13.6829i	−1.07173	+	1.07173i	−0.997220	+	0.0745108i	$0.976260\pi$
$164$	9.89804			0.772907
$165$	8.89788	+	5.91953i	0.692699	+	0.460835i
$166$	−11.7321	−	6.77352i	−0.910586	−	0.525727i
$167$	0.914140	+	0.244943i	0.0707383	+	0.0189543i	0.294015	−	0.955801i	$-0.405009\pi$
$167$	0.914140	+	0.244943i	0.0707383	+	0.0189543i	−0.223276	+	0.974755i	$0.571675\pi$
$168$	−0.530173	−	1.97863i	−0.0409038	−	0.152655i
$169$	−23.7050	−	13.6861i	−1.82346	−	1.05278i
$170$	−1.72457	+	5.11419i	−0.132269	+	0.392241i
$171$	−3.80689	+	2.12310i	−0.291120	+	0.162358i
$172$	−3.46345	−	3.46345i	−0.264086	−	0.264086i
$173$	−16.5240	+	4.42758i	−1.25629	+	0.336623i	−0.824765	−	0.565476i	$-0.808693\pi$
$173$	−16.5240	+	4.42758i	−1.25629	+	0.336623i	−0.431529	+	0.902099i	$0.642026\pi$
$174$	−0.138707	+	0.240248i	−0.0105154	+	0.0182132i
$175$	8.10052	−	6.26766i	0.612342	−	0.473791i
$176$	−2.38970	+	4.13908i	−0.180130	+	0.311995i
$177$	2.94846	−	11.0038i	0.221620	−	0.827097i
$178$	5.55628	−	5.55628i	0.416461	−	0.416461i
$179$	−20.0940			−1.50190			−0.750948	−	0.660361i	$-0.770403\pi$
$179$	−20.0940			−1.50190			−0.750948	+	0.660361i	$0.770403\pi$
$180$	−2.19222	+	0.440644i	−0.163399	+	0.0328437i
$181$	−10.6291	+	6.13673i	−0.790057	+	0.456140i	−0.839983	−	0.542613i	$-0.817435\pi$
$181$	−10.6291	+	6.13673i	−0.790057	+	0.456140i	0.0499253	+	0.998753i	$0.484102\pi$
$182$	9.20339	+	9.20339i	0.682201	+	0.682201i
$183$	−2.53371	−	2.53371i	−0.187297	−	0.187297i
$184$	1.19645	+	2.07232i	0.0882037	+	0.152773i
$185$	−7.51976	−	0.477688i	−0.552864	−	0.0351203i
$186$	−1.04677	+	0.604351i	−0.0767527	+	0.0443132i
$187$	−11.1428	+	2.98571i	−0.814844	+	0.218337i
$188$	1.36743	+	5.10332i	0.0997302	+	0.372198i
$189$	2.04843			0.149002
$190$	5.51874	−	8.03390i	0.400371	−	0.582840i
$191$	−1.32194			−0.0956522			−0.0478261	−	0.998856i	$-0.515229\pi$
$191$	−1.32194			−0.0956522			−0.0478261	+	0.998856i	$0.515229\pi$
$192$	−0.258819	−	0.965926i	−0.0186787	−	0.0697097i
$193$	23.4833	−	6.29234i	1.69037	−	0.452933i	0.719884	−	0.694095i	$-0.244195\pi$
$193$	23.4833	−	6.29234i	1.69037	−	0.452933i	0.970485	+	0.241162i	$0.0775285\pi$
$194$	−13.7620	+	7.94550i	−0.988055	+	0.570454i
$195$	10.6631	−	9.38930i	0.763601	−	0.672381i
$196$	1.40196	+	2.42827i	0.100140	+	0.173448i
$197$	−8.72758	−	8.72758i	−0.621814	−	0.621814i	0.324181	−	0.945995i	$-0.394911\pi$
$197$	−8.72758	−	8.72758i	−0.621814	−	0.621814i	−0.945995	+	0.324181i	$0.894911\pi$
$198$	−3.37954	−	3.37954i	−0.240174	−	0.240174i
$199$	9.76184	−	5.63600i	0.691998	−	0.399525i	−0.112362	−	0.993667i	$-0.535842\pi$
$199$	9.76184	−	5.63600i	0.691998	−	0.399525i	0.804360	+	0.594142i	$0.202508\pi$
$200$	3.95449	−	3.05973i	0.279625	−	0.216356i
$201$	−14.1681			−0.999340
$202$	3.21868	−	3.21868i	0.226466	−	0.226466i
$203$	−0.147078	+	0.548903i	−0.0103229	+	0.0385254i
$204$	1.20684	−	2.09030i	0.0844955	−	0.146350i
$205$	−4.36151	−	21.6987i	−0.304621	−	1.51550i
$206$	−7.53088	+	13.0439i	−0.524701	+	0.908809i
$207$	−2.31137	+	0.619330i	−0.160651	+	0.0430464i
$208$	4.49289	+	4.49289i	0.311526	+	0.311526i
$209$	20.8306	+	0.309626i	1.44088	+	0.0214173i
$210$	−4.10399	+	2.03413i	−0.283202	+	0.140368i
$211$	−1.77725	−	1.02610i	−0.122351	−	0.0706393i	0.437576	−	0.899182i	$-0.355837\pi$
$211$	−1.77725	−	1.02610i	−0.122351	−	0.0706393i	−0.559926	+	0.828542i	$0.689171\pi$
$212$	0.0144909	+	0.0540807i	0.000995237	+	0.00371427i
$213$	−9.92377	−	2.65906i	−0.679965	−	0.182196i
$214$	6.92824	+	4.00002i	0.473605	+	0.273436i
$215$	−6.06651	+	9.11881i	−0.413732	+	0.621897i
$216$	1.00000			0.0680414
$217$	−1.75076	+	1.75076i	−0.118849	+	0.118849i
$218$	9.64449	+	2.58423i	0.653207	+	0.175026i
$219$	−2.55150	−	4.41933i	−0.172414	−	0.298630i
$220$	10.1268	+	3.41489i	0.682747	+	0.230232i
$221$			15.3363i			1.03163i
$222$	3.25490	+	0.872147i	0.218454	+	0.0585347i
$223$	−23.3627	+	6.26002i	−1.56448	+	0.419202i	−0.934079	−	0.357066i	$-0.883777\pi$
$223$	−23.3627	+	6.26002i	−1.56448	+	0.419202i	−0.630403	+	0.776268i	$0.717110\pi$
$224$	−1.02422	−	1.77400i	−0.0684333	−	0.118530i
$225$	1.93198	+	4.61167i	0.128799	+	0.307444i
$226$	−5.56983	+	9.64723i	−0.370500	+	0.641724i
$227$	18.6234	−	18.6234i	1.23608	−	1.23608i	0.274484	−	0.961592i	$-0.411493\pi$
$227$	18.6234	−	18.6234i	1.23608	−	1.23608i	0.961592	−	0.274484i	$-0.0885070\pi$
$228$	−3.12768	+	3.03606i	−0.207135	+	0.201068i
$229$			4.62956i			0.305930i	0.988232	+	0.152965i	$0.0488822\pi$
$229$			4.62956i			0.305930i	−0.988232	+	0.152965i	$0.951118\pi$
$230$	4.01577	−	3.53605i	0.264792	−	0.233160i
$231$	−8.47862	−	4.89514i	−0.557853	−	0.322076i
$232$	−0.0718003	+	0.267962i	−0.00471392	+	0.0175926i
$233$	1.03102	+	3.84781i	0.0675442	+	0.252078i	0.991439	−	0.130567i	$-0.0416798\pi$
$233$	1.03102	+	3.84781i	0.0675442	+	0.252078i	−0.923895	+	0.382645i	$0.875013\pi$
$234$	−5.50265	+	3.17696i	−0.359719	+	0.207684i
$235$	10.5851	−	5.24646i	0.690493	−	0.342241i
$236$		−	11.3920i		−	0.741555i
$237$	0.0406322	−	0.151641i	0.00263934	−	0.00985016i
$238$	1.27967	−	4.77578i	0.0829484	−	0.309568i
$239$		−	3.76301i		−	0.243409i	−0.992566	−	0.121705i	$-0.961164\pi$
$239$		−	3.76301i		−	0.243409i	0.992566	−	0.121705i	$-0.0388360\pi$
$240$	−2.00348	+	0.993018i	−0.129324	+	0.0640990i
$241$	3.01409	−	1.74019i	0.194155	−	0.112095i	−0.399771	−	0.916615i	$-0.630910\pi$
$241$	3.01409	−	1.74019i	0.194155	−	0.112095i	0.593926	+	0.804520i	$0.297577\pi$
$242$	3.06510	+	11.4391i	0.197032	+	0.735333i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	−3.10315	−	1.79160i	−0.198659	−	0.114696i
$245$	4.70553	−	4.14341i	0.300626	−	0.264713i
$246$			9.89804i			0.631076i
$247$	7.56508	−	26.6428i	0.481354	−	1.69524i
$248$	−0.854682	+	0.854682i	−0.0542723	+	0.0542723i
$249$	6.77352	−	11.7321i	0.429254	−	0.743490i
$250$	−8.45014	−	7.32087i	−0.534434	−	0.463013i
$251$	6.87321	+	11.9048i	0.433833	+	0.751422i	0.997200	−	0.0747857i	$-0.0238273\pi$
$251$	6.87321	+	11.9048i	0.433833	+	0.751422i	−0.563366	+	0.826207i	$0.690494\pi$
$252$	1.97863	−	0.530173i	0.124642	−	0.0333978i
$253$	11.0470	+	2.96002i	0.694516	+	0.186095i
$254$			9.26783i			0.581516i
$255$	−5.11419	−	1.72457i	−0.320263	−	0.107997i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.11342	+	2.17399i	0.506101	+	0.135609i	0.502830	−	0.864385i	$-0.332292\pi$
$257$	8.11342	+	2.17399i	0.506101	+	0.135609i	0.00327121	+	0.999995i	$0.498959\pi$
$258$	3.46345	−	3.46345i	0.215625	−	0.215625i
$259$	6.90264			0.428909
$260$	7.86965	−	11.8292i	0.488055	−	0.733615i
$261$	−0.240248	−	0.138707i	−0.0148710	−	0.00858578i
$262$	6.64252	+	1.77986i	0.410376	+	0.109960i
$263$	−8.17641	−	30.5148i	−0.504179	−	1.88162i	−0.470921	−	0.882175i	$-0.656078\pi$
$263$	−8.17641	−	30.5148i	−0.504179	−	1.88162i	−0.0332576	−	0.999447i	$-0.510588\pi$
$264$	−4.13908	−	2.38970i	−0.254743	−	0.147076i
$265$	0.112171	−	0.0555975i	0.00689064	−	0.00341533i
$266$	−4.57889	+	7.66546i	−0.280750	+	0.469999i
$267$	5.55628	+	5.55628i	0.340039	+	0.340039i
$268$	−13.6853	+	3.66697i	−0.835964	+	0.223996i
$269$	15.6519	−	27.1099i	0.954313	−	1.65292i	0.218381	−	0.975864i	$-0.429922\pi$
$269$	15.6519	−	27.1099i	0.954313	−	1.65292i	0.735932	−	0.677055i	$-0.236744\pi$
$270$	−0.440644	−	2.19222i	−0.0268167	−	0.133414i
$271$	1.49243	−	2.58496i	0.0906587	−	0.157025i	−0.817130	−	0.576454i	$-0.804436\pi$
$271$	1.49243	−	2.58496i	0.0906587	−	0.157025i	0.907788	+	0.419428i	$0.137769\pi$
$272$	0.624705	−	2.33143i	0.0378783	−	0.141364i
$273$	−9.20339	+	9.20339i	−0.557015	+	0.557015i
$274$	5.29044			0.319607
$275$	3.02388	−	23.7049i	0.182347	−	1.42946i
$276$	−2.07232	+	1.19645i	−0.124739	+	0.0720181i
$277$	−18.7388	−	18.7388i	−1.12590	−	1.12590i	−0.990837	−	0.135066i	$-0.956875\pi$
$277$	−18.7388	−	18.7388i	−1.12590	−	1.12590i	−0.135066	−	0.990837i	$-0.543125\pi$
$278$	−4.96426	−	4.96426i	−0.297737	−	0.297737i
$279$	−0.604351	−	1.04677i	−0.0361816	−	0.0626683i
$280$	−3.43767	+	3.02701i	−0.205440	+	0.180898i
$281$	−15.2856	+	8.82517i	−0.911865	+	0.526465i	−0.881031	−	0.473059i	$-0.843150\pi$
$281$	−15.2856	+	8.82517i	−0.911865	+	0.526465i	−0.0308340	+	0.999525i	$0.509816\pi$
$282$	−5.10332	+	1.36743i	−0.303898	+	0.0814293i
$283$	−4.06107	−	15.1561i	−0.241406	−	0.900938i	−0.975156	−	0.221519i	$-0.928898\pi$
$283$	−4.06107	−	15.1561i	−0.241406	−	0.900938i	0.733750	−	0.679419i	$-0.237768\pi$
$284$	−10.2738			−0.609640
$285$	8.03390	+	5.51874i	0.475887	+	0.326902i
$286$	30.3679			1.79569
$287$	5.24768	+	19.5846i	0.309761	+	1.15604i
$288$	0.965926	−	0.258819i	0.0569177	−	0.0152511i
$289$	−9.67712	+	5.58709i	−0.569243	+	0.328652i
$290$	0.619071	+	0.0393261i	0.0363531	+	0.00230931i
$291$	−7.94550	−	13.7620i	−0.465773	−	0.806743i
$292$	−3.60836	−	3.60836i	−0.211164	−	0.211164i
$293$	20.9445	+	20.9445i	1.22359	+	1.22359i	0.966347	+	0.257240i	$0.0828133\pi$
$293$	20.9445	+	20.9445i	1.22359	+	1.22359i	0.257240	+	0.966347i	$0.417187\pi$
$294$	−2.42827	+	1.40196i	−0.141619	+	0.0817640i
$295$	−24.9737	+	5.01981i	−1.45403	+	0.292265i
$296$	3.36972			0.195861
$297$	3.37954	−	3.37954i	0.196101	−	0.196101i
$298$	−3.82991	+	14.2934i	−0.221861	+	0.827996i
$299$	7.60216	−	13.1673i	0.439644	−	0.761486i
$300$	3.05973	+	3.95449i	0.176654	+	0.228313i
$301$	5.01668	−	8.68914i	0.289156	−	0.500834i
$302$	−12.4684	+	3.34089i	−0.717474	+	0.192247i
$303$	3.21868	+	3.21868i	0.184909	+	0.184909i
$304$	−2.23531	+	3.74211i	−0.128204	+	0.214625i
$305$	−2.56021	+	7.59225i	−0.146597	+	0.434731i
$306$	2.09030	+	1.20684i	0.119495	+	0.0689903i
$307$	7.22416	+	26.9609i	0.412304	+	1.53874i	0.790174	+	0.612882i	$0.209990\pi$
$307$	7.22416	+	26.9609i	0.412304	+	1.53874i	−0.377870	+	0.925859i	$0.623343\pi$
$308$	−9.45668	−	2.53391i	−0.538844	−	0.144383i
$309$	−13.0439	−	7.53088i	−0.742039	−	0.428417i
$310$	2.25026	+	1.49704i	0.127806	+	0.0850262i
$311$	0.877243			0.0497439			0.0248720	−	0.999691i	$-0.492082\pi$
$311$	0.877243			0.0497439			0.0248720	+	0.999691i	$0.492082\pi$
$312$	−4.49289	+	4.49289i	−0.254360	+	0.254360i
$313$	−20.8053	−	5.57477i	−1.17599	−	0.315105i	−0.382653	−	0.923892i	$-0.624990\pi$
$313$	−20.8053	−	5.57477i	−1.17599	−	0.315105i	−0.793334	+	0.608787i	$0.791656\pi$
$314$	−1.31984	−	2.28603i	−0.0744827	−	0.129008i
$315$	−2.03413	−	4.10399i	−0.114610	−	0.231233i
$316$		−	0.156991i		−	0.00883141i
$317$	4.91216	+	1.31621i	0.275894	+	0.0739256i	0.394113	−	0.919062i	$-0.371052\pi$
$317$	4.91216	+	1.31621i	0.275894	+	0.0739256i	−0.118219	+	0.992988i	$0.537718\pi$
$318$	−0.0540807	+	0.0144909i	−0.00303269	+	0.000812608i
$319$	0.662938	+	1.14824i	0.0371174	+	0.0642892i
$320$	−1.67820	+	1.47772i	−0.0938141	+	0.0826070i
$321$	−4.00002	+	6.92824i	−0.223259	+	0.386697i
$322$	−3.46603	+	3.46603i	−0.193154	+	0.193154i
$323$	−10.2018	+	2.57169i	−0.567644	+	0.143092i
$324$			1.00000i			0.0555556i
$325$	−29.3999	−	12.0396i	−1.63081	−	0.667834i
$326$	−16.7581	−	9.67530i	−0.928146	−	0.535865i
$327$	−2.58423	+	9.64449i	−0.142908	+	0.533342i
$328$	2.56180	+	9.56078i	0.141452	+	0.527906i
$329$	−9.37263	+	5.41129i	−0.516730	+	0.298334i
$330$	−3.41489	+	10.1268i	−0.187983	+	0.557461i
$331$		−	21.9877i		−	1.20855i	−0.796775	−	0.604277i	$-0.793462\pi$
$331$		−	21.9877i		−	1.20855i	0.796775	−	0.604277i	$-0.206538\pi$
$332$	3.50623	−	13.0854i	0.192429	−	0.718157i
$333$	−0.872147	+	3.25490i	−0.0477933	+	0.178367i
$334$			0.946387i			0.0517840i
$335$	14.0692	+	28.3854i	0.768680	+	1.55086i
$336$	1.77400	−	1.02422i	0.0967794	−	0.0558756i
$337$	−8.45993	−	31.5729i	−0.460842	−	1.71988i	−0.670321	−	0.742072i	$-0.733843\pi$
$337$	−8.45993	−	31.5729i	−0.460842	−	1.71988i	0.209479	−	0.977813i	$-0.432823\pi$
$338$	7.08444	−	26.4395i	0.385343	−	1.43812i
$339$	−9.64723	−	5.56983i	−0.523966	−	0.302512i
$340$	−5.38628	−	0.342160i	−0.292112	−	0.0185563i
$341$			5.77687i			0.312835i
$342$	−3.03606	−	3.12768i	−0.164171	−	0.169125i
$343$	−14.2006	+	14.2006i	−0.766760	+	0.766760i
$344$	2.44903	−	4.24185i	0.132043	−	0.228705i
$345$	3.53605	+	4.01577i	0.190374	+	0.216202i
$346$	−8.55344	−	14.8150i	−0.459836	−	0.796459i
$347$	−22.9664	+	6.15382i	−1.23290	+	0.330354i	−0.815708	−	0.578464i	$-0.803652\pi$
$347$	−22.9664	+	6.15382i	−1.23290	+	0.330354i	−0.417191	+	0.908819i	$0.636986\pi$
$348$	−0.267962	−	0.0718003i	−0.0143643	−	0.00384890i
$349$			26.3554i			1.41077i	0.708823	+	0.705386i	$0.249226\pi$
$349$			26.3554i			1.41077i	−0.708823	+	0.705386i	$0.750774\pi$
$350$	8.15066	+	6.20231i	0.435671	+	0.331527i
$351$	−3.17696	−	5.50265i	−0.169573	−	0.293710i
$352$	−4.61654	−	1.23700i	−0.246063	−	0.0659322i
$353$	8.76102	−	8.76102i	0.466302	−	0.466302i	−0.434412	−	0.900714i	$-0.643044\pi$
$353$	8.76102	−	8.76102i	0.466302	−	0.466302i	0.900714	+	0.434412i	$0.143044\pi$
$354$	11.3920			0.605477
$355$	4.52710	+	22.5225i	0.240274	+	1.19537i
$356$	6.80502	+	3.92888i	0.360666	+	0.208230i
$357$	4.77578	+	1.27967i	0.252761	+	0.0677271i
$358$	−5.20071	−	19.4093i	−0.274866	−	1.02581i
$359$	−17.7464	−	10.2459i	−0.936619	−	0.540757i	−0.0477199	−	0.998861i	$-0.515195\pi$
$359$	−17.7464	−	10.2459i	−0.936619	−	0.540757i	−0.888899	+	0.458104i	$0.848529\pi$
$360$	−0.993018	−	2.00348i	−0.0523366	−	0.105592i
$361$	18.9916	+	0.564708i	0.999558	+	0.0297215i
$362$	−8.67865	−	8.67865i	−0.456140	−	0.456140i
$363$	−11.4391	+	3.06510i	−0.600397	+	0.160876i
$364$	−6.50778	+	11.2718i	−0.341100	+	0.590803i
$365$	−6.32033	+	9.50034i	−0.330821	+	0.497270i
$366$	1.79160	−	3.10315i	0.0936487	−	0.162204i
$367$	−0.361607	+	1.34953i	−0.0188757	+	0.0704451i	−0.974721	−	0.223424i	$-0.928276\pi$
$367$	−0.361607	+	1.34953i	−0.0188757	+	0.0704451i	0.955846	+	0.293869i	$0.0949431\pi$
$368$	−1.69204	+	1.69204i	−0.0882037	+	0.0882037i
$369$	−9.89804			−0.515272
$370$	−1.48485	−	7.38716i	−0.0771934	−	0.384040i
$371$	−0.0993232	+	0.0573443i	−0.00515660	+	0.00297717i
$372$	−0.854682	−	0.854682i	−0.0443132	−	0.0443132i
$373$	−8.99682	−	8.99682i	−0.465838	−	0.465838i	0.434725	−	0.900563i	$-0.356845\pi$
$373$	−8.99682	−	8.99682i	−0.465838	−	0.465838i	−0.900563	+	0.434725i	$0.856845\pi$
$374$	−5.76795	−	9.99038i	−0.298254	−	0.516590i
$375$	7.32087	−	8.45014i	0.378048	−	0.436363i
$376$	−4.57551	+	2.64167i	−0.235964	+	0.136234i
$377$	1.70261	−	0.456213i	0.0876888	−	0.0234961i
$378$	0.530173	+	1.97863i	0.0272692	+	0.101770i
$379$	27.9212			1.43421			0.717107	−	0.696963i	$-0.245466\pi$
$379$	27.9212			1.43421			0.717107	+	0.696963i	$0.245466\pi$
$380$	9.18851	+	3.25136i	0.471360	+	0.166791i
$381$	−9.26783			−0.474806
$382$	−0.342143	−	1.27690i	−0.0175056	−	0.0653317i
$383$	20.8658	−	5.59098i	1.06619	−	0.285686i	0.317266	−	0.948337i	$-0.397235\pi$
$383$	20.8658	−	5.59098i	1.06619	−	0.285686i	0.748929	+	0.662651i	$0.230569\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	−1.38786	+	21.8477i	−0.0707319	+	1.11346i
$386$	12.1559	+	21.0546i	0.618718	+	1.07165i
$387$	3.46345	+	3.46345i	0.176057	+	0.176057i
$388$	−11.2366	−	11.2366i	−0.570454	−	0.570454i
$389$	16.9880	−	9.80801i	0.861324	−	0.497286i	−0.00313142	−	0.999995i	$-0.500997\pi$
$389$	16.9880	−	9.80801i	0.861324	−	0.497286i	0.864455	+	0.502709i	$0.167663\pi$
$390$	11.8292	+	7.86965i	0.598994	+	0.398495i
$391$	−5.77570			−0.292090
$392$	−1.98267	+	1.98267i	−0.100140	+	0.100140i
$393$	−1.77986	+	6.64252i	−0.0897820	+	0.335071i
$394$	6.17133	−	10.6891i	0.310907	−	0.538507i
$395$	−0.344158	+	0.0691769i	−0.0173165	+	0.00348067i
$396$	2.38970	−	4.13908i	0.120087	−	0.207997i
$397$	−4.19969	+	1.12530i	−0.210777	+	0.0564774i	−0.362662	−	0.931921i	$-0.618132\pi$
$397$	−4.19969	+	1.12530i	−0.210777	+	0.0564774i	0.151886	+	0.988398i	$0.451465\pi$
$398$	7.97051	+	7.97051i	0.399525	+	0.399525i
$399$	−7.66546	−	4.57889i	−0.383753	−	0.229231i
$400$	3.97897	+	3.02783i	0.198949	+	0.151392i
$401$	14.0070	+	8.08697i	0.699478	+	0.403844i	0.807153	−	0.590342i	$-0.201007\pi$
$401$	14.0070	+	8.08697i	0.699478	+	0.403844i	−0.107675	+	0.994186i	$0.534341\pi$
$402$	−3.66697	−	13.6853i	−0.182892	−	0.682562i
$403$	7.41830	+	1.98773i	0.369532	+	0.0990157i
$404$	3.94207	+	2.27595i	0.196125	+	0.113233i
$405$	2.19222	−	0.440644i	0.108932	−	0.0218958i
$406$	−0.568266			−0.0282026
$407$	11.3881	−	11.3881i	0.564487	−	0.564487i
$408$	2.33143	+	0.624705i	0.115423	+	0.0309275i
$409$	19.1608	+	33.1875i	0.947440	+	1.64101i	0.750791	+	0.660540i	$0.229673\pi$
$409$	19.1608	+	33.1875i	0.947440	+	1.64101i	0.196649	+	0.980474i	$0.436994\pi$
$410$	19.8305	−	9.82894i	0.979358	−	0.485417i
$411$			5.29044i			0.260958i
$412$	−14.5485	−	3.89827i	−0.716755	−	0.192054i
$413$	22.5406	−	6.03973i	1.10915	−	0.297196i
$414$	−1.19645	−	2.07232i	−0.0588025	−	0.101849i
$415$	−30.2312	−	1.92042i	−1.48399	−	0.0942696i
$416$	−3.17696	+	5.50265i	−0.155763	+	0.269789i
$417$	4.96426	−	4.96426i	0.243101	−	0.243101i
$418$	5.09228	+	20.2010i	0.249072	+	0.988061i
$419$		−	20.4732i		−	1.00018i	−0.865972	−	0.500092i	$-0.833300\pi$
$419$		−	20.4732i		−	1.00018i	0.865972	−	0.500092i	$-0.166700\pi$
$420$	−3.02701	−	3.43767i	−0.147703	−	0.167741i
$421$	13.7453	+	7.93586i	0.669905	+	0.386770i	0.796041	−	0.605243i	$-0.206924\pi$
$421$	13.7453	+	7.93586i	0.669905	+	0.386770i	−0.126135	+	0.992013i	$0.540257\pi$
$422$	0.531146	−	1.98226i	0.0258558	−	0.0964951i
$423$	−1.36743	−	5.10332i	−0.0664868	−	0.248132i
$424$	−0.0484874	+	0.0279942i	−0.00235476	+	0.00135952i
$425$	1.62334	+	11.9587i	0.0787436	+	0.580082i
$426$		−	10.2738i		−	0.497769i
$427$	1.89972	−	7.08986i	0.0919340	−	0.343102i
$428$	−2.07056	+	7.72745i	−0.100084	+	0.373520i
$429$			30.3679i			1.46617i
$430$	−10.3782	−	3.49967i	−0.500482	−	0.168769i
$431$	−27.0681	+	15.6277i	−1.30382	+	0.752762i	−0.981057	−	0.193717i	$-0.937946\pi$
$431$	−27.0681	+	15.6277i	−1.30382	+	0.752762i	−0.322765	+	0.946479i	$0.604612\pi$
$432$	0.258819	+	0.965926i	0.0124524	+	0.0464731i
$433$	−2.42586	+	9.05342i	−0.116579	+	0.435080i	−0.999400	−	0.0346300i	$-0.988975\pi$
$433$	−2.42586	+	9.05342i	−0.116579	+	0.435080i	0.882821	+	0.469710i	$0.155641\pi$
$434$	−2.14423	−	1.23797i	−0.102926	−	0.0594246i
$435$	−0.0393261	+	0.619071i	−0.00188554	+	0.0296822i
$436$			9.98471i			0.478181i
$437$	10.0338	+	2.84904i	0.479982	+	0.136288i
$438$	3.60836	−	3.60836i	0.172414	−	0.172414i
$439$	−8.30594	+	14.3863i	−0.396421	+	0.686621i	−0.993281	−	0.115724i	$-0.963081\pi$
$439$	−8.30594	+	14.3863i	−0.396421	+	0.686621i	0.596860	+	0.802345i	$0.296415\pi$
$440$	−0.677523	+	10.6656i	−0.0322997	+	0.508460i
$441$	−1.40196	−	2.42827i	−0.0667601	−	0.115632i
$442$	−14.8137	+	3.96932i	−0.704616	+	0.188801i
$443$	−15.9302	−	4.26848i	−0.756867	−	0.202802i	−0.140305	−	0.990108i	$-0.544808\pi$
$443$	−15.9302	−	4.26848i	−0.756867	−	0.202802i	−0.616562	+	0.787307i	$0.711475\pi$
$444$			3.36972i			0.159920i
$445$	5.61439	−	16.6494i	0.266147	−	0.789255i
$446$	−12.0934	−	20.9464i	−0.572640	−	0.991842i
$447$	−14.2934	−	3.82991i	−0.676056	−	0.181149i
$448$	1.44846	−	1.44846i	0.0684333	−	0.0684333i
$449$	−8.68803			−0.410013			−0.205007	−	0.978761i	$-0.565722\pi$
$449$	−8.68803			−0.410013			−0.205007	+	0.978761i	$0.565722\pi$
$450$	−3.95449	+	3.05973i	−0.186417	+	0.144237i
$451$	40.9688	+	23.6533i	1.92914	+	1.11379i
$452$	−10.7601	−	2.88316i	−0.506112	−	0.135612i
$453$	−3.34089	−	12.4684i	−0.156969	−	0.585815i
$454$	22.8089	+	13.1687i	1.07047	+	0.618038i
$455$	27.5779	+	9.29964i	1.29287	+	0.435974i
$456$	−3.74211	−	2.23531i	−0.175240	−	0.104678i
$457$	7.50433	+	7.50433i	0.351038	+	0.351038i	0.860496	−	0.509458i	$-0.170154\pi$
$457$	7.50433	+	7.50433i	0.351038	+	0.351038i	−0.509458	+	0.860496i	$0.670154\pi$
$458$	−4.47181	+	1.19822i	−0.208954	+	0.0559891i
$459$	−1.20684	+	2.09030i	−0.0563303	+	0.0975670i
$460$	4.45492	+	2.96374i	0.207712	+	0.138185i
$461$	15.0407	−	26.0512i	0.700513	−	1.21332i	−0.267774	−	0.963482i	$-0.586288\pi$
$461$	15.0407	−	26.0512i	0.700513	−	1.21332i	0.968287	−	0.249842i	$-0.0803788\pi$
$462$	2.53391	−	9.45668i	0.117888	−	0.439964i
$463$	−14.0645	+	14.0645i	−0.653631	+	0.653631i	−0.953865	−	0.300234i	$-0.902935\pi$
$463$	−14.0645	+	14.0645i	−0.653631	+	0.653631i	0.300234	+	0.953865i	$0.402935\pi$
$464$	−0.277415			−0.0128787
$465$	−1.49704	+	2.25026i	−0.0694236	+	0.104353i
$466$	−3.44985	+	1.99177i	−0.159811	+	0.0922671i
$467$	7.41931	+	7.41931i	0.343325	+	0.343325i	0.857616	−	0.514291i	$-0.171945\pi$
$467$	7.41931	+	7.41931i	0.343325	+	0.343325i	−0.514291	+	0.857616i	$0.671945\pi$
$468$	−4.49289	−	4.49289i	−0.207684	−	0.207684i
$469$	−14.5112	−	25.1341i	−0.670064	−	1.16059i
$470$	7.80731	+	8.86650i	0.360124	+	0.408981i
$471$	2.28603	−	1.31984i	0.105334	−	0.0608149i
$472$	11.0038	−	2.94846i	0.506491	−	0.135714i
$473$	−6.05890	−	22.6121i	−0.278588	−	1.03971i
$474$	0.156991			0.00721082
$475$	3.07885	−	21.5759i	0.141267	−	0.989972i
$476$	4.94425			0.226619
$477$	−0.0144909	−	0.0540807i	−0.000663491	−	0.00247618i
$478$	3.63479	−	0.973940i	0.166252	−	0.0445470i
$479$	−16.3256	+	9.42561i	−0.745937	+	0.430667i	−0.824224	−	0.566264i	$-0.808388\pi$
$479$	−16.3256	+	9.42561i	−0.745937	+	0.430667i	0.0782869	+	0.996931i	$0.475055\pi$
$480$	−1.47772	−	1.67820i	−0.0674484	−	0.0765989i
$481$	−10.7054	−	18.5424i	−0.488126	−	0.845459i
$482$	2.46100	+	2.46100i	0.112095	+	0.112095i
$483$	−3.46603	−	3.46603i	−0.157710	−	0.157710i
$484$	−10.2560	+	5.92131i	−0.466182	+	0.269151i
$485$	−19.6818	+	29.5845i	−0.893706	+	1.34336i
$486$	−1.00000			−0.0453609
$487$	−23.7218	+	23.7218i	−1.07494	+	1.07494i	−0.0779809	+	0.996955i	$0.524847\pi$
$487$	−23.7218	+	23.7218i	−1.07494	+	1.07494i	−0.996955	+	0.0779809i	$0.975153\pi$
$488$	0.927403	−	3.46111i	0.0419815	−	0.156677i
$489$	9.67530	−	16.7581i	0.437532	−	0.757828i
$490$	5.22011	+	3.47280i	0.235820	+	0.156885i
$491$	8.32670	−	14.4223i	0.375779	−	0.650868i	−0.614665	−	0.788789i	$-0.710709\pi$
$491$	8.32670	−	14.4223i	0.375779	−	0.650868i	0.990443	+	0.137921i	$0.0440420\pi$
$492$	−9.56078	+	2.56180i	−0.431033	+	0.115495i
$493$	−0.473471	−	0.473471i	−0.0213241	−	0.0213241i
$494$	27.6930	+	0.411629i	1.24597	+	0.0185201i
$495$	−10.1268	−	3.41489i	−0.455165	−	0.153488i
$496$	−1.04677	−	0.604351i	−0.0470012	−	0.0271362i
$497$	−5.44692	−	20.3282i	−0.244328	−	0.911843i
$498$	13.0854	+	3.50623i	0.586372	+	0.157118i
$499$	23.3473	+	13.4796i	1.04517	+	0.603429i	0.921293	−	0.388869i	$-0.127134\pi$
$499$	23.3473	+	13.4796i	1.04517	+	0.603429i	0.123876	+	0.992298i	$0.460467\pi$
$500$	4.88436	−	10.0570i	0.218435	−	0.449762i
$501$	−0.946387			−0.0422815
$502$	−9.72019	+	9.72019i	−0.433833	+	0.433833i
$503$	2.14125	+	0.573747i	0.0954737	+	0.0255821i	0.306240	−	0.951954i	$-0.400929\pi$
$503$	2.14125	+	0.573747i	0.0954737	+	0.0255821i	−0.210766	+	0.977537i	$0.567596\pi$
$504$	1.02422	+	1.77400i	0.0456222	+	0.0790200i
$505$	3.25235	−	9.64477i	0.144727	−	0.429187i
$506$			11.4367i			0.508421i
$507$	26.4395	+	7.08444i	1.17422	+	0.314631i
$508$	−8.95204	+	2.39869i	−0.397183	+	0.106425i
$509$	12.1764	+	21.0902i	0.539710	+	0.934805i	0.998919	+	0.0464769i	$0.0147994\pi$
$509$	12.1764	+	21.0902i	0.539710	+	0.934805i	−0.459210	+	0.888328i	$0.651867\pi$
$510$	0.342160	−	5.38628i	0.0151511	−	0.238509i
$511$	5.22657	−	9.05269i	0.231210	−	0.400468i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	3.12768	−	3.03606i	0.138090	−	0.134045i
$514$			8.39963i			0.370492i
$515$	−2.13514	+	33.6114i	−0.0940856	+	1.48109i
$516$	4.24185	+	2.44903i	0.186737	+	0.107813i
$517$	−6.53549	+	24.3908i	−0.287431	+	1.07271i
$518$	1.78653	+	6.66744i	0.0784958	+	0.292950i
$519$	14.8150	−	8.55344i	0.650306	−	0.375454i
$520$	13.4629	+	4.53988i	0.590388	+	0.199087i
$521$		−	8.85907i		−	0.388123i	−0.980989	−	0.194062i	$-0.937834\pi$
$521$		−	8.85907i		−	0.388123i	0.980989	−	0.194062i	$-0.0621661\pi$
$522$	0.0718003	−	0.267962i	0.00314261	−	0.0117284i
$523$	−6.19582	+	23.1231i	−0.270924	+	1.01110i	0.687600	+	0.726090i	$0.258664\pi$
$523$	−6.19582	+	23.1231i	−0.270924	+	1.01110i	−0.958524	+	0.285013i	$0.908002\pi$
$524$			6.87684i			0.300416i
$525$	−6.20231	+	8.15066i	−0.270691	+	0.355724i
$526$	27.3588	−	15.7956i	1.19290	−	0.688721i
$527$	−0.755082	−	2.81800i	−0.0328919	−	0.122754i
$528$	1.23700	−	4.61654i	0.0538335	−	0.200909i
$529$	−14.9597	−	8.63700i	−0.650422	−	0.375522i
$530$	0.0827352	+	0.0939596i	0.00359379	+	0.00408134i
$531$			11.3920i			0.494370i
$532$	−8.58937	−	2.43890i	−0.372396	−	0.105740i
$533$	44.4709	−	44.4709i	1.92625	−	1.92625i
$534$	−3.92888	+	6.80502i	−0.170019	+	0.294482i
$535$	17.8527	+	1.13408i	0.771838	+	0.0490305i
$536$	−7.08404	−	12.2699i	−0.305984	−	0.529980i
$537$	19.4093	−	5.20071i	0.837574	−	0.224427i
$538$	30.2371	+	8.10202i	1.30362	+	0.349303i
$539$			13.4011i			0.577224i
$540$	2.00348	−	0.993018i	0.0862159	−	0.0427327i
$541$	−15.4330	−	26.7307i	−0.663516	−	1.14924i	−0.979685	−	0.200541i	$-0.935730\pi$
$541$	−15.4330	−	26.7307i	−0.663516	−	1.14924i	0.316169	−	0.948703i	$-0.397603\pi$
$542$	2.88315	+	0.772539i	0.123842	+	0.0331834i
$543$	8.67865	−	8.67865i	0.372437	−	0.372437i
$544$	2.41367			0.103485
$545$	21.8887	−	4.39970i	0.937609	−	0.188463i
$546$	−11.2718	−	6.50778i	−0.482389	−	0.278507i
$547$	−18.8257	−	5.04432i	−0.804927	−	0.215680i	−0.167181	−	0.985926i	$-0.553466\pi$
$547$	−18.8257	−	5.04432i	−0.804927	−	0.215680i	−0.637746	+	0.770247i	$0.720133\pi$
$548$	1.36927	+	5.11017i	0.0584921	+	0.218296i
$549$	3.10315	+	1.79160i	0.132439	+	0.0764638i
$550$	23.6798	−	3.21443i	1.00971	−	0.137064i
$551$	0.588981	+	1.05609i	0.0250914	+	0.0449909i
$552$	−1.69204	−	1.69204i	−0.0720181	−	0.0720181i
$553$	0.310627	−	0.0832322i	0.0132092	−	0.00353940i
$554$	13.2503	−	22.9502i	0.562951	−	0.975060i
$555$	7.38716	−	1.48485i	0.313568	−	0.0630282i
$556$	3.51026	−	6.07995i	0.148868	−	0.257847i
$557$	−7.01900	+	26.1952i	−0.297404	+	1.10993i	0.641885	+	0.766801i	$0.278153\pi$
$557$	−7.01900	+	26.1952i	−0.297404	+	1.10993i	−0.939289	+	0.343127i	$0.888514\pi$
$558$	0.854682	−	0.854682i	0.0361816	−	0.0361816i
$559$	−31.1219			−1.31631
$560$	−3.81360	−	2.53709i	−0.161154	−	0.107212i
$561$	9.99038	−	5.76795i	0.421794	−	0.243523i
$562$	−12.4807	−	12.4807i	−0.526465	−	0.526465i
$563$	−8.70101	−	8.70101i	−0.366704	−	0.366704i	0.499570	−	0.866274i	$-0.333491\pi$
$563$	−8.70101	−	8.70101i	−0.366704	−	0.366704i	−0.866274	+	0.499570i	$0.833491\pi$
$564$	−2.64167	−	4.57551i	−0.111235	−	0.192664i
$565$	−1.57915	+	24.8589i	−0.0664353	+	1.04582i
$566$	13.5886	−	7.84539i	0.571172	−	0.329766i
$567$	−1.97863	+	0.530173i	−0.0830948	+	0.0222652i
$568$	−2.65906	−	9.92377i	−0.111572	−	0.416392i
$569$	−43.0899			−1.80642			−0.903210	−	0.429198i	$-0.858796\pi$
$569$	−43.0899			−1.80642			−0.903210	+	0.429198i	$0.858796\pi$
$570$	−3.25136	+	9.18851i	−0.136185	+	0.384864i
$571$	24.8314			1.03916			0.519581	−	0.854421i	$-0.326088\pi$
$571$	24.8314			1.03916			0.519581	+	0.854421i	$0.326088\pi$
$572$	7.85978	+	29.3331i	0.328634	+	1.22648i
$573$	1.27690	−	0.342143i	0.0533431	−	0.0142932i
$574$	−17.5591	+	10.1377i	−0.732902	+	0.423141i
$575$	4.53414	−	11.0721i	0.189087	−	0.461739i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	32.5940	+	32.5940i	1.35691	+	1.35691i	0.877706	+	0.479200i	$0.159073\pi$
$577$	32.5940	+	32.5940i	1.35691	+	1.35691i	0.479200	+	0.877706i	$0.340927\pi$
$578$	−7.90134	−	7.90134i	−0.328652	−	0.328652i
$579$	−21.0546	+	12.1559i	−0.874999	+	0.505181i
$580$	0.122241	+	0.608155i	0.00507579	+	0.0252523i
$581$	27.7502			1.15127
$582$	11.2366	−	11.2366i	0.465773	−	0.465773i
$583$	−0.0692576	+	0.258473i	−0.00286836	+	0.0107049i
$584$	2.55150	−	4.41933i	0.105582	−	0.182873i
$585$	−7.86965	+	11.8292i	−0.325370	+	0.489076i
$586$	−14.8100	+	25.6516i	−0.611794	+	1.05966i
$587$	−10.1284	+	2.71390i	−0.418044	+	0.112014i	−0.461708	−	0.887032i	$-0.652763\pi$
$587$	−10.1284	+	2.71390i	−0.418044	+	0.112014i	0.0436647	+	0.999046i	$0.486097\pi$
$588$	−1.98267	−	1.98267i	−0.0817640	−	0.0817640i
$589$	−0.0783041	+	5.26803i	−0.00322646	+	0.217065i
$590$	−11.3124	−	22.8236i	−0.465726	−	0.939631i
$591$	10.6891	+	6.17133i	0.439689	+	0.253855i
$592$	0.872147	+	3.25490i	0.0358450	+	0.133775i
$593$	15.6477	+	4.19280i	0.642575	+	0.172178i	0.565370	−	0.824838i	$-0.308733\pi$
$593$	15.6477	+	4.19280i	0.642575	+	0.172178i	0.0772058	+	0.997015i	$0.475400\pi$
$594$	4.13908	+	2.38970i	0.169828	+	0.0980505i
$595$	−2.17865	−	10.8389i	−0.0893161	−	0.444351i
$596$	−14.7976			−0.606135
$597$	−7.97051	+	7.97051i	−0.326211	+	0.326211i
$598$	14.6862	+	3.93517i	0.600565	+	0.160921i
$599$	−7.30723	−	12.6565i	−0.298565	−	0.517130i	0.677243	−	0.735760i	$-0.263175\pi$
$599$	−7.30723	−	12.6565i	−0.298565	−	0.517130i	−0.975808	+	0.218630i	$0.929841\pi$
$600$	−3.02783	+	3.97897i	−0.123611	+	0.162441i
$601$			2.25779i			0.0920973i	0.998939	+	0.0460487i	$0.0146629\pi$
$601$			2.25779i			0.0920973i	−0.998939	+	0.0460487i	$0.985337\pi$
$602$	9.69148	+	2.59682i	0.394995	+	0.105839i
$603$	13.6853	−	3.66697i	0.557309	−	0.149331i
$604$	−6.45410	−	11.1788i	−0.262614	−	0.454860i
$605$	17.5001	+	19.8743i	0.711479	+	0.808003i
$606$	−2.27595	+	3.94207i	−0.0924543	+	0.160136i
$607$	18.6048	−	18.6048i	0.755144	−	0.755144i	−0.220290	−	0.975434i	$-0.570700\pi$
$607$	18.6048	−	18.6048i	0.755144	−	0.755144i	0.975434	+	0.220290i	$0.0707004\pi$
$608$	−4.19314	−	1.19062i	−0.170054	−	0.0482859i
$609$		−	0.568266i		−	0.0230273i
$610$	−7.99618	−	0.507953i	−0.323756	−	0.0205664i
$611$	29.0724	+	16.7850i	1.17614	+	0.679047i
$612$	−0.624705	+	2.33143i	−0.0252522	+	0.0942425i
$613$	−4.43051	−	16.5349i	−0.178947	−	0.667839i	−0.995846	−	0.0910575i	$-0.970975\pi$
$613$	−4.43051	−	16.5349i	−0.178947	−	0.667839i	0.816899	−	0.576781i	$-0.195691\pi$
$614$	−24.1725	+	13.9560i	−0.975523	+	0.563218i
$615$	9.82894	+	19.8305i	0.396341	+	0.799643i
$616$		−	9.79027i		−	0.394461i
$617$	−5.19367	+	19.3830i	−0.209089	+	0.780332i	0.779075	+	0.626931i	$0.215689\pi$
$617$	−5.19367	+	19.3830i	−0.209089	+	0.780332i	−0.988164	+	0.153401i	$0.950977\pi$
$618$	3.89827	−	14.5485i	0.156811	−	0.585228i
$619$			24.5228i			0.985656i	0.870127	+	0.492828i	$0.164037\pi$
$619$			24.5228i			0.985656i	−0.870127	+	0.492828i	$0.835963\pi$
$620$	−0.863620	+	2.56105i	−0.0346838	+	0.102854i
$621$	2.07232	−	1.19645i	0.0831593	−	0.0480120i
$622$	0.227047	+	0.847352i	0.00910377	+	0.0339757i
$623$	−4.16598	+	15.5476i	−0.166906	+	0.622903i
$624$	−5.50265	−	3.17696i	−0.220282	−	0.127180i
$625$	−24.1994	−	6.27605i	−0.967976	−	0.251042i
$626$		−	21.5393i		−	0.860882i
$627$	−20.2010	+	5.09228i	−0.806748	+	0.203366i
$628$	1.86653	−	1.86653i	0.0744827	−	0.0744827i
$629$	−4.06670	+	7.04373i	−0.162150	+	0.280852i
$630$	3.43767	−	3.02701i	0.136960	−	0.120599i
$631$	−13.8015	−	23.9048i	−0.549428	−	0.951636i	−0.998314	−	0.0580475i	$-0.981513\pi$
$631$	−13.8015	−	23.9048i	−0.549428	−	0.951636i	0.448886	−	0.893589i	$-0.351821\pi$
$632$	0.151641	−	0.0406322i	0.00603197	−	0.00161626i
$633$	1.98226	+	0.531146i	0.0787879	+	0.0211112i
$634$			5.08544i			0.201969i
$635$	9.20313	+	18.5679i	0.365215	+	0.736844i
$636$	−0.0279942	−	0.0484874i	−0.00111004	−	0.00192265i
$637$	17.2088	+	4.61109i	0.681838	+	0.182698i
$638$	−0.937536	+	0.937536i	−0.0371174	+	0.0371174i
$639$	10.2738			0.406427
$640$	−1.86172	−	1.23855i	−0.0735908	−	0.0489581i
$641$	13.5953	+	7.84926i	0.536983	+	0.310027i	0.743855	−	0.668341i	$-0.232995\pi$
$641$	13.5953	+	7.84926i	0.536983	+	0.310027i	−0.206872	+	0.978368i	$0.566329\pi$
$642$	−7.72745	−	2.07056i	−0.304978	−	0.0817186i
$643$	−2.24598	−	8.38212i	−0.0885728	−	0.330558i	0.907394	−	0.420281i	$-0.138069\pi$
$643$	−2.24598	−	8.38212i	−0.0885728	−	0.330558i	−0.995967	+	0.0897228i	$0.971402\pi$
$644$	−4.24501	−	2.45086i	−0.167277	−	0.0965772i
$645$	3.49967	−	10.3782i	0.137800	−	0.408642i
$646$	−5.12448	−	9.18859i	−0.201620	−	0.361520i
$647$	−13.1498	−	13.1498i	−0.516971	−	0.516971i	0.399682	−	0.916654i	$-0.369120\pi$
$647$	−13.1498	−	13.1498i	−0.516971	−	0.516971i	−0.916654	+	0.399682i	$0.869120\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	27.2234	−	47.1523i	1.06861	−	1.85089i
$650$	4.02006	−	31.5142i	0.157680	−	1.23609i
$651$	1.23797	−	2.14423i	0.0485200	−	0.0840391i
$652$	5.00831	−	18.6913i	0.196140	−	0.732006i
$653$	−10.3380	+	10.3380i	−0.404558	+	0.404558i	−0.879836	−	0.475278i	$-0.842348\pi$
$653$	−10.3380	+	10.3380i	−0.404558	+	0.404558i	0.475278	+	0.879836i	$0.342348\pi$
$654$	−9.98471			−0.390433
$655$	15.0756	−	3.03024i	0.589051	−	0.118401i
$656$	−8.57196	+	4.94902i	−0.334679	+	0.193227i
$657$	3.60836	+	3.60836i	0.140776	+	0.140776i
$658$	−7.65272	−	7.65272i	−0.298334	−	0.298334i
$659$	10.8391	+	18.7738i	0.422230	+	0.731324i	0.996157	−	0.0875825i	$-0.0279141\pi$
$659$	10.8391	+	18.7738i	0.422230	+	0.731324i	−0.573927	+	0.818906i	$0.694581\pi$
$660$	−10.6656	−	0.677523i	−0.415156	−	0.0263726i
$661$	−9.11501	+	5.26256i	−0.354533	+	0.204690i	−0.666680	−	0.745344i	$-0.732285\pi$
$661$	−9.11501	+	5.26256i	−0.354533	+	0.204690i	0.312147	+	0.950034i	$0.398952\pi$
$662$	21.2385	−	5.69084i	0.825457	−	0.221181i
$663$	−3.96932	−	14.8137i	−0.154156	−	0.575316i
$664$	13.5470			0.525727
$665$	−1.56176	+	19.9045i	−0.0605623	+	0.771863i
$666$	−3.36972			−0.130574
$667$	0.171811	+	0.641209i	0.00665257	+	0.0248277i
$668$	−0.914140	+	0.244943i	−0.0353691	+	0.00947713i
$669$	20.9464	−	12.0934i	0.809835	−	0.467559i
$670$	−23.7768	+	20.9365i	−0.918579	+	0.808846i
$671$	−8.56279	−	14.8312i	−0.330563	−	0.572551i
$672$	1.44846	+	1.44846i	0.0558756	+	0.0558756i
$673$	4.64564	+	4.64564i	0.179076	+	0.179076i	0.790953	−	0.611877i	$-0.209585\pi$
$673$	4.64564	+	4.64564i	0.179076	+	0.179076i	−0.611877	+	0.790953i	$0.709585\pi$
$674$	28.3075	−	16.3433i	1.09036	−	0.629522i
$675$	−3.05973	−	3.95449i	−0.117769	−	0.152209i
$676$	27.3722			1.05278
$677$	−13.2614	+	13.2614i	−0.509675	+	0.509675i	−0.914427	−	0.404751i	$-0.867358\pi$
$677$	−13.2614	+	13.2614i	−0.509675	+	0.509675i	0.404751	+	0.914427i	$0.367358\pi$
$678$	2.88316	−	10.7601i	0.110727	−	0.413239i
$679$	16.2758	−	28.1906i	0.624609	−	1.08185i
$680$	−1.06357	−	5.29131i	−0.0407861	−	0.202912i
$681$	−13.1687	+	22.8089i	−0.504626	+	0.874037i
$682$	−5.58003	+	1.49516i	−0.213670	+	0.0572528i
$683$	20.6154	+	20.6154i	0.788826	+	0.788826i	0.981302	−	0.192476i	$-0.0616517\pi$
$683$	20.6154	+	20.6154i	0.788826	+	0.788826i	−0.192476	+	0.981302i	$0.561652\pi$
$684$	2.23531	−	3.74211i	0.0854693	−	0.143083i
$685$	10.5993	−	5.25350i	0.404977	−	0.200726i
$686$	−17.3921	−	10.0413i	−0.664034	−	0.383380i
$687$	−1.19822	−	4.47181i	−0.0457149	−	0.170610i
$688$	4.73117	+	1.26771i	0.180374	+	0.0483311i
$689$	0.308085	+	0.177873i	0.0117371	+	0.00677641i
$690$	−2.96374	+	4.45492i	−0.112828	+	0.169596i
$691$	−6.94649			−0.264257			−0.132129	−	0.991233i	$-0.542181\pi$
$691$	−6.94649			−0.264257			−0.132129	+	0.991233i	$0.542181\pi$
$692$	12.0964	−	12.0964i	0.459836	−	0.459836i
$693$	9.45668	+	2.53391i	0.359229	+	0.0962552i
$694$	−11.8883	−	20.5911i	−0.451272	−	0.781627i
$695$	−14.8754	−	5.01618i	−0.564255	−	0.190274i
$696$		−	0.277415i		−	0.0105154i
$697$	−23.0766	−	6.18335i	−0.874088	−	0.234211i
$698$	−25.4574	+	6.82128i	−0.963575	+	0.258189i
$699$	−1.99177	−	3.44985i	−0.0753358	−	0.130485i
$700$	−3.88142	+	9.47821i	−0.146704	+	0.358243i
$701$	22.3233	−	38.6651i	0.843140	−	1.46036i	−0.0440861	−	0.999028i	$-0.514038\pi$
$701$	22.3233	−	38.6651i	0.843140	−	1.46036i	0.887226	−	0.461334i	$-0.152629\pi$
$702$	4.49289	−	4.49289i	0.169573	−	0.169573i
$703$	10.5394	−	10.2307i	0.397500	−	0.385856i
$704$		−	4.77940i		−	0.180130i
$705$	−8.86650	+	7.80731i	−0.333932	+	0.294040i
$706$	10.7300	+	6.19497i	0.403829	+	0.233151i
$707$	−2.41330	+	9.00656i	−0.0907615	+	0.338727i
$708$	2.94846	+	11.0038i	0.110810	+	0.413549i
$709$	6.31333	−	3.64500i	0.237102	−	0.136891i	−0.376742	−	0.926318i	$-0.622956\pi$
$709$	6.31333	−	3.64500i	0.237102	−	0.136891i	0.613844	+	0.789427i	$0.289622\pi$
$710$	−20.5834	+	10.2021i	−0.772481	+	0.382878i
$711$			0.156991i			0.00588761i
$712$	−2.03374	+	7.59002i	−0.0762176	+	0.284448i
$713$	−0.748586	+	2.79376i	−0.0280348	+	0.104627i
$714$			4.94425i			0.185034i
$715$	60.8413	−	30.1558i	2.27533	−	1.12776i
$716$	17.4019	−	10.0470i	0.650340	−	0.375474i
$717$	0.973940	+	3.63479i	0.0363724	+	0.135744i
$718$	5.30366	−	19.7935i	0.197931	−	0.738688i
$719$	20.5521	+	11.8657i	0.766462	+	0.442517i	0.831611	−	0.555358i	$-0.187419\pi$
$719$	20.5521	+	11.8657i	0.766462	+	0.442517i	−0.0651489	+	0.997876i	$0.520752\pi$
$720$	1.67820	−	1.47772i	0.0625427	−	0.0550713i
$721$		−	30.8530i		−	1.14903i
$722$	4.36992	+	18.4906i	0.162632	+	0.688150i
$723$	−2.46100	+	2.46100i	−0.0915255	+	0.0915255i
$724$	6.13673	−	10.6291i	0.228070	−	0.395029i
$725$	1.27935	−	0.535960i	0.0475137	−	0.0199050i
$726$	−5.92131	−	10.2560i	−0.219760	−	0.380636i
$727$	5.84531	−	1.56625i	0.216791	−	0.0580889i	−0.148789	−	0.988869i	$-0.547537\pi$
$727$	5.84531	−	1.56625i	0.216791	−	0.0580889i	0.365580	+	0.930780i	$0.380871\pi$
$728$	−12.5721	−	3.36867i	−0.465952	−	0.124851i
$729$		−	1.00000i		−	0.0370370i
$730$	−10.8124	−	3.64610i	−0.400186	−	0.134948i
$731$	5.91116	+	10.2384i	0.218632	+	0.378682i
$732$	3.46111	+	0.927403i	0.127926	+	0.0342778i
$733$	−22.5054	+	22.5054i	−0.831254	+	0.831254i	−0.987688	−	0.156434i	$-0.950000\pi$
$733$	−22.5054	+	22.5054i	−0.831254	+	0.831254i	0.156434	+	0.987688i	$0.450000\pi$
$734$	−1.39714			−0.0515694
$735$	−3.47280	+	5.22011i	−0.128096	+	0.192547i
$736$	−2.07232	−	1.19645i	−0.0763867	−	0.0441019i
$737$	−65.4076	−	17.5259i	−2.40932	−	0.645575i
$738$	−2.56180	−	9.56078i	−0.0943012	−	0.351937i
$739$	36.3104	+	20.9638i	1.33570	+	0.771166i	0.986166	−	0.165759i	$-0.0530074\pi$
$739$	36.3104	+	20.9638i	1.33570	+	0.771166i	0.349532	+	0.936925i	$0.386341\pi$
$740$	6.75115	−	3.34619i	0.248177	−	0.123008i
$741$	−0.411629	+	27.6930i	−0.0151216	+	1.01733i
$742$	−0.0810970	−	0.0810970i	−0.00297717	−	0.00297717i
$743$	−27.5549	+	7.38331i	−1.01089	+	0.270867i	−0.726002	−	0.687693i	$-0.758624\pi$
$743$	−27.5549	+	7.38331i	−1.01089	+	0.270867i	−0.284889	+	0.958560i	$0.591957\pi$
$744$	0.604351	−	1.04677i	0.0221566	−	0.0383763i
$745$	6.52049	+	32.4397i	0.238892	+	1.18850i
$746$	6.36171	−	11.0188i	0.232919	−	0.403427i
$747$	−3.50623	+	13.0854i	−0.128286	+	0.478771i
$748$	8.15711	−	8.15711i	0.298254	−	0.298254i
$749$	−16.3876			−0.598788
$750$	10.0570	+	4.88436i	0.367229	+	0.178352i
$751$	42.2107	−	24.3703i	1.54029	−	0.889286i	0.541469	−	0.840721i	$-0.317868\pi$
$751$	42.2107	−	24.3703i	1.54029	−	0.889286i	0.998820	−	0.0485654i	$-0.0154649\pi$
$752$	−3.73589	−	3.73589i	−0.136234	−	0.136234i
$753$	−9.72019	−	9.72019i	−0.354224	−	0.354224i
$754$	0.881335	+	1.52652i	0.0320963	+	0.0555925i
$755$	−21.6625	+	19.0747i	−0.788380	+	0.694200i
$756$	−1.77400	+	1.02422i	−0.0645196	+	0.0372504i
$757$	−49.3664	+	13.2277i	−1.79425	+	0.480768i	−0.993057	−	0.117635i	$-0.962469\pi$
$757$	−49.3664	+	13.2277i	−1.79425	+	0.480768i	−0.801195	+	0.598403i	$0.795802\pi$
$758$	7.22653	+	26.9698i	0.262479	+	0.979586i
$759$	−11.4367			−0.415124
$760$	−0.762415	+	9.71693i	−0.0276557	+	0.352470i
$761$	−46.7132			−1.69335			−0.846677	−	0.532108i	$-0.821400\pi$
$761$	−46.7132			−1.69335			−0.846677	+	0.532108i	$0.821400\pi$
$762$	−2.39869	−	8.95204i	−0.0868954	−	0.324298i
$763$	−19.7561	+	5.29363i	−0.715219	+	0.191642i
$764$	1.14483	−	0.660970i	0.0414186	−	0.0239131i
$765$	5.38628	+	0.342160i	0.194741	+	0.0123708i
$766$	10.8010	+	18.7078i	0.390254	+	0.675940i
$767$	−51.1830	−	51.1830i	−1.84811	−	1.84811i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−5.10923	+	2.94981i	−0.184243	+	0.106373i	−0.589285	−	0.807925i	$-0.700590\pi$
$769$	−5.10923	+	2.94981i	−0.184243	+	0.106373i	0.405041	+	0.914298i	$0.367257\pi$
$770$	−21.4624	+	4.31402i	−0.773453	+	0.155467i
$771$	−8.39963			−0.302505
$772$	−17.1910	+	17.1910i	−0.618718	+	0.618718i
$773$	2.40665	−	8.98173i	0.0865611	−	0.323050i	−0.909044	−	0.416700i	$-0.863187\pi$
$773$	2.40665	−	8.98173i	0.0865611	−	0.323050i	0.995605	+	0.0936494i	$0.0298533\pi$
$774$	−2.44903	+	4.24185i	−0.0880286	+	0.152470i
$775$	5.99493	+	0.764735i	0.215344	+	0.0274701i
$776$	7.94550	−	13.7620i	0.285227	−	0.494027i
$777$	−6.66744	+	1.78653i	−0.239193	+	0.0640916i
$778$	13.8706	+	13.8706i	0.497286	+	0.497286i
$779$	37.0396	+	22.1252i	1.32708	+	0.792719i
$780$	−4.53988	+	13.4629i	−0.162554	+	0.482050i
$781$	−42.5242	−	24.5514i	−1.52164	−	0.878517i
$782$	−1.49486	−	5.57890i	−0.0534561	−	0.199501i
$783$	0.267962	+	0.0718003i	0.00957619	+	0.00256593i
$784$	−2.42827	−	1.40196i	−0.0867239	−	0.0500700i
$785$	−4.91433	−	3.26937i	−0.175400	−	0.116689i
$786$	−6.87684			−0.245289
$787$	−0.777955	+	0.777955i	−0.0277311	+	0.0277311i	−0.720836	−	0.693105i	$-0.756242\pi$
$787$	−0.777955	+	0.777955i	−0.0277311	+	0.0277311i	0.693105	+	0.720836i	$0.256242\pi$
$788$	11.9221	+	3.19451i	0.424707	+	0.113800i
$789$	15.7956	+	27.3588i	0.562339	+	0.973999i
$790$	−0.155894	−	0.314527i	−0.00554648	−	0.0111904i
$791$		−	22.8189i		−	0.811345i
$792$	4.61654	+	1.23700i	0.164042	+	0.0439548i
$793$	−21.9916	+	5.89263i	−0.780945	+	0.209254i
$794$	−2.17392	−	3.76534i	−0.0771496	−	0.133627i
$795$	−0.0939596	+	0.0827352i	−0.00333240	+	0.00293431i
$796$	−5.63600	+	9.76184i	−0.199763	+	0.345999i
$797$	−18.2358	+	18.2358i	−0.645944	+	0.645944i	−0.952010	−	0.306066i	$-0.900987\pi$
$797$	−18.2358	+	18.2358i	−0.645944	+	0.645944i	0.306066	+	0.952010i	$0.400987\pi$
$798$	2.43890	−	8.58937i	0.0863361	−	0.304060i
$799$		−	12.7523i		−	0.451143i
$800$	−1.89483	+	4.62705i	−0.0669922	+	0.163591i
$801$	−6.80502	−	3.92888i	−0.240444	−	0.138820i
$802$	−4.18612	+	15.6228i	−0.147817	+	0.551661i
$803$	−6.31240	−	23.5582i	−0.222760	−	0.831351i
$804$	12.2699	−	7.08404i	0.432727	−	0.249835i
$805$	−3.50228	+	10.3859i	−0.123439	+	0.366057i
$806$			7.67999i			0.270516i
$807$	−8.10202	+	30.2371i	−0.285205	+	1.06440i
$808$	−1.17812	+	4.39680i	−0.0414461	+	0.154679i
$809$			54.6709i			1.92213i	0.276328	+	0.961063i	$0.410882\pi$
$809$			54.6709i			1.92213i	−0.276328	+	0.961063i	$0.589118\pi$
$810$	0.993018	+	2.00348i	0.0348911	+	0.0703950i
$811$	−6.36672	+	3.67583i	−0.223566	+	0.129076i	−0.607600	−	0.794243i	$-0.707868\pi$
$811$	−6.36672	+	3.67583i	−0.223566	+	0.129076i	0.384034	+	0.923319i	$0.374534\pi$
$812$	−0.147078	−	0.548903i	−0.00516143	−	0.0192627i
$813$	−0.772539	+	2.88315i	−0.0270941	+	0.101117i
$814$	13.9475	+	8.05260i	0.488860	+	0.282244i
$815$	−43.1822	−	2.74313i	−1.51261	−	0.0960875i
$816$			2.41367i			0.0844955i
$817$	−5.21872	−	20.7025i	−0.182580	−	0.724290i
$818$	−27.0974	+	27.0974i	−0.947440	+	0.947440i
$819$	6.50778	−	11.2718i	0.227400	−	0.393869i
$820$	14.6265	+	16.6109i	0.510781	+	0.580077i
$821$	−20.4093	−	35.3500i	−0.712290	−	1.23372i	−0.963995	−	0.265919i	$-0.914325\pi$
$821$	−20.4093	−	35.3500i	−0.712290	−	1.23372i	0.251705	−	0.967804i	$-0.419009\pi$
$822$	−5.11017	+	1.36927i	−0.178238	+	0.0477586i
$823$	9.52863	+	2.55319i	0.332147	+	0.0889986i	0.421039	−	0.907043i	$-0.361666\pi$
$823$	9.52863	+	2.55319i	0.332147	+	0.0889986i	−0.0888913	+	0.996041i	$0.528332\pi$
$824$		−	15.0618i		−	0.524701i
$825$	3.21443	+	23.6798i	0.111912	+	0.824425i
$826$	11.6679	+	20.2093i	0.405977	+	0.703172i
$827$	−10.8291	−	2.90165i	−0.376565	−	0.100900i	0.0655719	−	0.997848i	$-0.479113\pi$
$827$	−10.8291	−	2.90165i	−0.376565	−	0.100900i	−0.442137	+	0.896948i	$0.645779\pi$
$828$	1.69204	−	1.69204i	0.0588025	−	0.0588025i
$829$	32.8630			1.14138			0.570689	−	0.821166i	$-0.306676\pi$
$829$	32.8630			1.14138			0.570689	+	0.821166i	$0.306676\pi$
$830$	−5.96942	−	29.6981i	−0.207202	−	1.03084i
$831$	22.9502	+	13.2503i	0.796133	+	0.459648i
$832$	−6.13741	−	1.64451i	−0.212776	−	0.0570132i
$833$	−1.75162	−	6.53715i	−0.0606902	−	0.226499i
$834$	6.07995	+	3.51026i	0.210532	+	0.121550i
$835$	0.939780	+	1.89606i	0.0325224	+	0.0656160i
$836$	−18.1946	+	10.1472i	−0.629275	+	0.350947i
$837$	0.854682	+	0.854682i	0.0295421	+	0.0295421i
$838$	19.7756	−	5.29887i	0.683138	−	0.183046i
$839$	−10.7505	+	18.6204i	−0.371148	+	0.642847i	−0.989742	−	0.142863i	$-0.954369\pi$
$839$	−10.7505	+	18.6204i	−0.371148	+	0.642847i	0.618594	+	0.785711i	$0.287702\pi$
$840$	2.53709	−	3.81360i	0.0875380	−	0.131582i
$841$	14.4615	−	25.0481i	0.498673	−	0.863727i
$842$	−4.10790	+	15.3309i	−0.141568	+	0.528338i
$843$	12.4807	−	12.4807i	0.429857	−	0.429857i
$844$	2.05219			0.0706393
$845$	−12.0614	−	60.0059i	−0.414924	−	2.06426i
$846$	4.57551	−	2.64167i	0.157309	−	0.0908226i
$847$	−17.1536	−	17.1536i	−0.589404	−	0.589404i
$848$	−0.0395898	−	0.0395898i	−0.00135952	−	0.00135952i
$849$	7.84539	+	13.5886i	0.269253	+	0.466360i
$850$	−11.1311	+	4.66316i	−0.381792	+	0.159945i
$851$	6.98313	−	4.03171i	0.239379	−	0.138205i
$852$	9.92377	−	2.65906i	0.339983	−	0.0910981i
$853$	−14.2214	−	53.0752i	−0.486933	−	1.81726i	−0.571193	−	0.820816i	$-0.693519\pi$
$853$	−14.2214	−	53.0752i	−0.486933	−	1.81726i	0.0842602	−	0.996444i	$-0.473147\pi$
$854$	7.33996			0.251168
$855$	−9.18851	−	3.25136i	−0.314240	−	0.111194i
$856$	−8.00004			−0.273436
$857$	2.21112	+	8.25202i	0.0755304	+	0.281883i	0.993353	−	0.115107i	$-0.0367212\pi$
$857$	2.21112	+	8.25202i	0.0755304	+	0.281883i	−0.917823	+	0.396991i	$0.870055\pi$
$858$	−29.3331	+	7.85978i	−1.00142	+	0.268328i
$859$	5.45192	−	3.14767i	0.186017	−	0.107397i	−0.404100	−	0.914715i	$-0.632415\pi$
$859$	5.45192	−	3.14767i	0.186017	−	0.107397i	0.590117	+	0.807318i	$0.299082\pi$
$860$	0.694345	−	10.9304i	0.0236770	−	0.372723i
$861$	−10.1377	−	17.5591i	−0.345493	−	0.598412i
$862$	−22.1010	−	22.1010i	−0.752762	−	0.752762i
$863$	15.3692	+	15.3692i	0.523175	+	0.523175i	0.918529	−	0.395354i	$-0.129378\pi$
$863$	15.3692	+	15.3692i	0.523175	+	0.523175i	−0.395354	+	0.918529i	$0.629378\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−31.8481	−	21.1877i	−1.08287	−	0.720405i
$866$	−9.37279			−0.318500
$867$	7.90134	−	7.90134i	0.268344	−	0.268344i
$868$	0.640822	−	2.39158i	0.0217509	−	0.0811755i
$869$	0.375160	−	0.649796i	0.0127264	−	0.0220428i
$870$	−0.608155	+	0.122241i	−0.0206184	+	0.00414437i
$871$	−45.0114	+	77.9620i	−1.52515	+	2.64164i
$872$	−9.64449	+	2.58423i	−0.326604	+	0.0875132i
$873$	11.2366	+	11.2366i	0.380302	+	0.380302i
$874$	−0.155021	+	10.4293i	−0.00524367	+	0.352776i
$875$	22.4887	+	4.33242i	0.760255	+	0.146463i
$876$	4.41933	+	2.55150i	0.149315	+	0.0862072i
$877$	−3.46866	−	12.9452i	−0.117128	−	0.437128i	0.882309	−	0.470670i	$-0.155988\pi$
$877$	−3.46866	−	12.9452i	−0.117128	−	0.437128i	−0.999437	+	0.0335420i	$0.989321\pi$
$878$	−16.0458	−	4.29947i	−0.541521	−	0.145100i
$879$	−25.6516	−	14.8100i	−0.865207	−	0.499528i
$880$	−10.4775	+	2.10601i	−0.353196	+	0.0709936i
$881$	−25.5112			−0.859494			−0.429747	−	0.902949i	$-0.641397\pi$
$881$	−25.5112			−0.859494			−0.429747	+	0.902949i	$0.641397\pi$
$882$	1.98267	−	1.98267i	0.0667601	−	0.0667601i
$883$	14.2509	+	3.81853i	0.479582	+	0.128504i	0.490508	−	0.871437i	$-0.336811\pi$
$883$	14.2509	+	3.81853i	0.479582	+	0.128504i	−0.0109258	+	0.999940i	$0.503478\pi$
$884$	−7.66813	−	13.2816i	−0.257907	−	0.446708i
$885$	22.8236	−	11.3124i	0.767206	−	0.380264i
$886$		−	16.4922i		−	0.554065i
$887$	−39.2917	−	10.5282i	−1.31929	−	0.353502i	−0.470577	−	0.882359i	$-0.655954\pi$
$887$	−39.2917	−	10.5282i	−1.31929	−	0.353502i	−0.848711	+	0.528857i	$0.822621\pi$
$888$	−3.25490	+	0.872147i	−0.109227	+	0.0292673i
$889$	−9.49227	−	16.4411i	−0.318360	−	0.551417i
$890$	17.5352	+	1.11391i	0.587780	+	0.0373384i
$891$	−2.38970	+	4.13908i	−0.0800579	+	0.138664i
$892$	17.1027	−	17.1027i	0.572640	−	0.572640i
$893$	−6.29045	+	22.1538i	−0.210502	+	0.741349i
$894$		−	14.7976i		−	0.494907i
$895$	−29.6933	−	33.7217i	−0.992538	−	1.12719i
$896$	1.77400	+	1.02422i	0.0592650	+	0.0342167i
$897$	−3.93517	+	14.6862i	−0.131391	+	0.490359i
$898$	−2.24863	−	8.39199i	−0.0750377	−	0.280044i
$899$	−0.290389	+	0.167656i	−0.00968501	+	0.00559164i
$900$	−3.97897	−	3.02783i	−0.132632	−	0.100928i
$901$		−	0.135138i		−	0.00450209i
$902$	−12.2439	+	45.6947i	−0.407676	+	1.52147i
$903$	−2.59682	+	9.69148i	−0.0864169	+	0.322512i
$904$		−	11.1397i		−	0.370500i
$905$	−26.0055	−	8.76941i	−0.864453	−	0.291505i
$906$	11.1788	−	6.45410i	0.371392	−	0.214423i
$907$	1.90474	+	7.10859i	0.0632459	+	0.236037i	0.990312	−	0.138862i	$-0.0443443\pi$
$907$	1.90474	+	7.10859i	0.0632459	+	0.236037i	−0.927066	+	0.374898i	$0.877678\pi$
$908$	−6.81662	+	25.4400i	−0.226218	+	0.844255i
$909$	−3.94207	−	2.27595i	−0.130750	−	0.0754886i
$910$	−1.84508	+	29.0451i	−0.0611636	+	0.962837i
$911$			9.26255i			0.306882i	0.988158	+	0.153441i	$0.0490355\pi$
$911$			9.26255i			0.306882i	−0.988158	+	0.153441i	$0.950965\pi$
$912$	1.19062	−	4.19314i	0.0394253	−	0.138849i
$913$	45.7828	−	45.7828i	1.51519	−	1.51519i
$914$	−5.30636	+	9.19089i	−0.175519	+	0.304008i
$915$	0.507953	−	7.99618i	0.0167924	−	0.264346i
$916$	−2.31478	−	4.00932i	−0.0764825	−	0.132472i
$917$	−13.6068	+	3.64592i	−0.449335	+	0.120399i
$918$	−2.33143	−	0.624705i	−0.0769486	−	0.0206183i
$919$			54.6922i			1.80413i	0.431600	+	0.902065i	$0.357949\pi$
$919$			54.6922i			1.80413i	−0.431600	+	0.902065i	$0.642051\pi$
$920$	−1.70974	+	5.07019i	−0.0563683	+	0.167159i
$921$	−13.9560	−	24.1725i	−0.459866	−	0.796511i
$922$	29.0563	+	7.78561i	0.956919	+	0.256406i
$923$	−46.1593	+	46.1593i	−1.51935	+	1.51935i
$924$	9.79027			0.322076
$925$	−10.3104	−	13.3255i	−0.339005	−	0.438141i
$926$	−17.2254	−	9.94508i	−0.566061	−	0.326816i
$927$	14.5485	+	3.89827i	0.477837	+	0.128036i
$928$	−0.0718003	−	0.267962i	−0.00235696	−	0.00879629i
$929$	22.4098	+	12.9383i	0.735241	+	0.424491i	0.820336	−	0.571881i	$-0.193786\pi$
$929$	22.4098	+	12.9383i	0.735241	+	0.424491i	−0.0850956	+	0.996373i	$0.527120\pi$
$930$	−2.56105	−	0.863620i	−0.0839801	−	0.0283192i
$931$	−0.181648	+	12.2207i	−0.00595328	+	0.400516i
$932$	−2.81679	−	2.81679i	−0.0922671	−	0.0922671i
$933$	−0.847352	+	0.227047i	−0.0277411	+	0.00743320i
$934$	−5.24624	+	9.08676i	−0.171662	+	0.297328i
$935$	−21.4766	−	14.2878i	−0.702359	−	0.467261i
$936$	3.17696	−	5.50265i	0.103842	−	0.179860i
$937$	5.28196	−	19.7126i	0.172554	−	0.643981i	−0.824401	−	0.566006i	$-0.808488\pi$
$937$	5.28196	−	19.7126i	0.172554	−	0.643981i	0.996955	−	0.0779750i	$-0.0248454\pi$
$938$	20.5219	−	20.5219i	0.670064	−	0.670064i
$939$	21.5393			0.702907
$940$	−6.54370	+	9.83610i	−0.213432	+	0.320818i
$941$	−7.49515	+	4.32733i	−0.244335	+	0.141067i	−0.617168	−	0.786832i	$-0.711720\pi$
$941$	−7.49515	+	4.32733i	−0.244335	+	0.141067i	0.372833	+	0.927899i	$0.378387\pi$
$942$	1.86653	+	1.86653i	0.0608149	+	0.0608149i
$943$	16.7479	+	16.7479i	0.545387	+	0.545387i
$944$	5.69599	+	9.86575i	0.185389	+	0.321103i
$945$	3.02701	+	3.43767i	0.0984686	+	0.111828i
$946$	20.2735	−	11.7049i	0.659147	−	0.380559i
$947$	58.6155	−	15.7060i	1.90475	−	0.510376i	0.909173	−	0.416419i	$-0.136715\pi$
$947$	58.6155	−	15.7060i	1.90475	−	0.510376i	0.995576	−	0.0939567i	$-0.0299515\pi$
$948$	0.0406322	+	0.151641i	0.00131967	+	0.00492508i
$949$	−32.4240			−1.05253
$950$	21.6376	−	2.61032i	0.702017	−	0.0846901i
$951$	−5.08544			−0.164907
$952$	1.27967	+	4.77578i	0.0414742	+	0.154784i
$953$	−13.3204	+	3.56920i	−0.431491	+	0.115618i	−0.468026	−	0.883715i	$-0.655035\pi$
$953$	−13.3204	+	3.56920i	−0.431491	+	0.115618i	0.0365351	+	0.999332i	$0.488368\pi$
$954$	0.0484874	−	0.0279942i	0.00156984	−	0.000906346i
$955$	−1.95346	−	2.21848i	−0.0632124	−	0.0717882i
$956$	1.88151	+	3.25887i	0.0608523	+	0.105399i
$957$	−0.937536	−	0.937536i	−0.0303062	−	0.0303062i
$958$	−13.3298	−	13.3298i	−0.430667	−	0.430667i
$959$	−9.38521	+	5.41855i	−0.303064	+	0.174974i
$960$	1.23855	−	1.86172i	0.0399741	−	0.0600866i
$961$	29.5390			0.952872
$962$	15.1398	−	15.1398i	0.488126	−	0.488126i
$963$	2.07056	−	7.72745i	0.0667230	−	0.249014i
$964$	−1.74019	+	3.01409i	−0.0560477	+	0.0970775i
$965$	45.2616	+	30.1114i	1.45702	+	0.969319i
$966$	2.45086	−	4.24501i	0.0788550	−	0.136581i
$967$	6.60146	−	1.76886i	0.212289	−	0.0568826i	−0.151107	−	0.988517i	$-0.548284\pi$
$967$	6.60146	−	1.76886i	0.212289	−	0.0568826i	0.363396	+	0.931635i	$0.381617\pi$
$968$	−8.37400	−	8.37400i	−0.269151	−	0.269151i
$969$	9.18859	−	5.12448i	0.295180	−	0.164622i
$970$	−33.6705	−	11.3541i	−1.08109	−	0.364560i
$971$	24.0175	+	13.8665i	0.770758	+	0.444997i	0.833145	−	0.553055i	$-0.186538\pi$
$971$	24.0175	+	13.8665i	0.770758	+	0.444997i	−0.0623869	+	0.998052i	$0.519871\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	13.8911	+	3.72210i	0.445327	+	0.119325i
$974$	−29.0531	−	16.7738i	−0.930922	−	0.537468i
$975$	31.5142	+	4.02006i	1.00926	+	0.128745i
$976$	3.58321			0.114696
$977$	20.5134	−	20.5134i	0.656281	−	0.656281i	−0.298217	−	0.954498i	$-0.596392\pi$
$977$	20.5134	−	20.5134i	0.656281	−	0.656281i	0.954498	+	0.298217i	$0.0963918\pi$
$978$	18.6913	+	5.00831i	0.597680	+	0.160148i
$979$	18.7777	+	32.5239i	0.600137	+	1.03947i
$980$	−2.00341	+	5.94107i	−0.0639965	+	0.189780i
$981$		−	9.98471i		−	0.318787i
$982$	16.0859	+	4.31022i	0.513323	+	0.137545i
$983$	−0.196689	+	0.0527027i	−0.00627341	+	0.00168096i	−0.261954	−	0.965080i	$-0.584367\pi$
$983$	−0.196689	+	0.0527027i	−0.00627341	+	0.00168096i	0.255681	+	0.966761i	$0.417700\pi$
$984$	−4.94902	−	8.57196i	−0.157769	−	0.273264i
$985$	1.74969	−	27.5435i	0.0557496	−	0.877609i
$986$	0.334795	−	0.579881i	0.0106620	−	0.0184672i
$987$	7.65272	−	7.65272i	0.243589	−	0.243589i
$988$	6.76987	+	26.8559i	0.215378	+	0.854400i
$989$		−	11.7206i		−	0.372694i
$990$	0.677523	−	10.6656i	0.0215331	−	0.338974i
$991$	−1.37747	−	0.795281i	−0.0437567	−	0.0252629i	0.477962	−	0.878380i	$-0.341376\pi$
$991$	−1.37747	−	0.795281i	−0.0437567	−	0.0252629i	−0.521719	+	0.853118i	$0.674709\pi$
$992$	0.312835	−	1.16752i	0.00993253	−	0.0370687i
$993$	5.69084	+	21.2385i	0.180593	+	0.673983i
$994$	18.2257	−	10.5226i	0.578085	−	0.333758i
$995$	23.8836	+	8.05386i	0.757160	+	0.255325i
$996$			13.5470i			0.429254i
$997$	−6.70603	+	25.0272i	−0.212382	+	0.792620i	0.774690	+	0.632341i	$0.217906\pi$
$997$	−6.70603	+	25.0272i	−0.212382	+	0.792620i	−0.987072	+	0.160279i	$0.948761\pi$
$998$	−6.97754	+	26.0405i	−0.220870	+	0.824299i
$999$		−	3.36972i		−	0.106613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.x.a.217.9	yes	40
5.3	odd	4	inner	570.2.x.a.103.6	✓	40
19.12	odd	6	inner	570.2.x.a.487.6	yes	40
95.88	even	12	inner	570.2.x.a.373.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.a.103.6	✓	40	5.3	odd	4	inner
570.2.x.a.217.9	yes	40	1.1	even	1	trivial
570.2.x.a.373.9	yes	40	95.88	even	12	inner
570.2.x.a.487.6	yes	40	19.12	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.47772 + 1.67820i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.44846 - 1.44846i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.47772 + 1.67820i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.44846 - 1.44846i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-1.23855 + 1.86172i) q^{10} -4.77940 q^{11} +(0.707107 - 0.707107i) q^{12} +(-1.64451 + 6.13741i) q^{13} +(1.02422 - 1.77400i) q^{14} +(-1.86172 - 1.23855i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.33143 - 0.624705i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-4.35842 - 0.0647836i) q^{19} +(-2.11884 - 0.714502i) q^{20} +(1.77400 + 1.02422i) q^{21} +(-1.23700 - 4.61654i) q^{22} +(-2.31137 - 0.619330i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-0.632691 + 4.95981i) q^{25} -6.35391 q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.97863 + 0.530173i) q^{28} +(-0.138707 - 0.240248i) q^{29} +(0.714502 - 2.11884i) q^{30} -1.20870i q^{31} +(0.965926 + 0.258819i) q^{32} +(4.61654 - 1.23700i) q^{33} +(1.20684 + 2.09030i) q^{34} +(0.290384 - 4.57122i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.38275 + 2.38275i) q^{37} +(-1.06547 - 4.22668i) q^{38} -6.35391i q^{39} +(0.141759 - 2.23157i) q^{40} +(-8.57196 - 4.94902i) q^{41} +(-0.530173 + 1.97863i) q^{42} +(1.26771 + 4.73117i) q^{43} +(4.13908 - 2.38970i) q^{44} +(2.11884 + 0.714502i) q^{45} -2.39291i q^{46} +(1.36743 - 5.10332i) q^{47} +(-0.258819 + 0.965926i) q^{48} -2.80392i q^{49} +(-4.95456 + 0.672560i) q^{50} +(-2.09030 + 1.20684i) q^{51} +(-1.64451 - 6.13741i) q^{52} +(0.0144909 - 0.0540807i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-7.06261 - 8.02077i) q^{55} +2.04843i q^{56} +(4.22668 - 1.06547i) q^{57} +(0.196162 - 0.196162i) q^{58} +(-5.69599 + 9.86575i) q^{59} +(2.23157 + 0.141759i) q^{60} +(1.79160 + 3.10315i) q^{61} +(1.16752 - 0.312835i) q^{62} +(-1.97863 - 0.530173i) q^{63} +1.00000i q^{64} +(-12.7299 + 6.30955i) q^{65} +(2.38970 + 4.13908i) q^{66} +(13.6853 + 3.66697i) q^{67} +(-1.70672 + 1.70672i) q^{68} +2.39291 q^{69} +(4.49062 - 0.902630i) q^{70} +(8.89740 + 5.13692i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(1.32075 + 4.92912i) q^{73} +(-2.91826 - 1.68486i) q^{74} +(-0.672560 - 4.95456i) q^{75} +(3.80689 - 2.12310i) q^{76} +(6.92277 + 6.92277i) q^{77} +(6.13741 - 1.64451i) q^{78} +(-0.0784953 + 0.135958i) q^{79} +(2.19222 - 0.440644i) q^{80} +(0.500000 - 0.866025i) q^{81} +(2.56180 - 9.56078i) q^{82} +(-9.57920 + 9.57920i) q^{83} -2.04843 q^{84} +(4.49358 + 2.98946i) q^{85} +(-4.24185 + 2.44903i) q^{86} +(0.196162 + 0.196162i) q^{87} +(3.37954 + 3.37954i) q^{88} +(-3.92888 - 6.80502i) q^{89} +(-0.141759 + 2.23157i) q^{90} +(11.2718 - 6.50778i) q^{91} +(2.31137 - 0.619330i) q^{92} +(0.312835 + 1.16752i) q^{93} +5.28335 q^{94} +(-6.33180 - 7.41002i) q^{95} -1.00000 q^{96} +(4.11289 + 15.3495i) q^{97} +(2.70838 - 0.725708i) q^{98} +(-4.13908 + 2.38970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7	\( 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7} - 12 q^{10} + 8 q^{11} - 24 q^{13} + 20 q^{16} + 8 q^{17} + 12 q^{21} + 24 q^{22} + 16 q^{23} - 16 q^{25} + 32 q^{26} + 4 q^{28} + 16 q^{30} - 24 q^{33} - 4 q^{35} - 20 q^{36} - 8 q^{38} - 36 q^{41} + 4 q^{42} - 4 q^{43} + 8 q^{47} - 24 q^{52} - 16 q^{55} - 8 q^{57} + 16 q^{58} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{66} - 36 q^{67} - 16 q^{68} + 48 q^{70} + 72 q^{71} - 16 q^{73} - 8 q^{76} + 24 q^{77} + 24 q^{78} + 8 q^{80} + 20 q^{81} - 24 q^{82} - 40 q^{83} - 48 q^{85} + 16 q^{87} - 72 q^{91} - 16 q^{92} + 16 q^{93} - 16 q^{95} - 40 q^{96} + 36 q^{97} - 48 q^{98}+O(q^{100}) \) 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7 - 12 * q^10 + 8 * q^11 - 24 * q^13 + 20 * q^16 + 8 * q^17 + 12 * q^21 + 24 * q^22 + 16 * q^23 - 16 * q^25 + 32 * q^26 + 4 * q^28 + 16 * q^30 - 24 * q^33 - 4 * q^35 - 20 * q^36 - 8 * q^38 - 36 * q^41 + 4 * q^42 - 4 * q^43 + 8 * q^47 - 24 * q^52 - 16 * q^55 - 8 * q^57 + 16 * q^58 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^66 - 36 * q^67 - 16 * q^68 + 48 * q^70 + 72 * q^71 - 16 * q^73 - 8 * q^76 + 24 * q^77 + 24 * q^78 + 8 * q^80 + 20 * q^81 - 24 * q^82 - 40 * q^83 - 48 * q^85 + 16 * q^87 - 72 * q^91 - 16 * q^92 + 16 * q^93 - 16 * q^95 - 40 * q^96 + 36 * q^97 - 48 * q^98

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