LMFDB - Embedded newform 570.2.x.a.103.6

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			103.6
Character	$\chi$	$=$	570.103
Dual form			570.2.x.a.487.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.19222 - 0.440644i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.44846 + 1.44846i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.19222 - 0.440644i) 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} +(-2.23157 + 0.141759i) q^{10} -4.77940 q^{11} +(-0.707107 - 0.707107i) q^{12} +(-6.13741 - 1.64451i) q^{13} +(-1.02422 + 1.77400i) q^{14} +(0.141759 + 2.23157i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.624705 - 2.33143i) 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} +(-4.61654 + 1.23700i) q^{22} +(0.619330 - 2.31137i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(4.61167 + 1.93198i) q^{25} -6.35391 q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.530173 + 1.97863i) q^{28} +(0.138707 + 0.240248i) q^{29} +(0.714502 + 2.11884i) q^{30} -1.20870i q^{31} +(0.258819 - 0.965926i) q^{32} +(1.23700 + 4.61654i) q^{33} +(-1.20684 - 2.09030i) q^{34} +(3.81360 - 2.53709i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.38275 + 2.38275i) q^{37} +(4.22668 - 1.06547i) q^{38} +6.35391i q^{39} +(-1.86172 + 1.23855i) q^{40} +(-8.57196 - 4.94902i) q^{41} +(1.97863 + 0.530173i) q^{42} +(-4.73117 + 1.26771i) q^{43} +(-4.13908 + 2.38970i) q^{44} +(2.11884 - 0.714502i) q^{45} -2.39291i q^{46} +(-5.10332 - 1.36743i) q^{47} +(-0.965926 - 0.258819i) q^{48} +2.80392i q^{49} +(4.95456 + 0.672560i) q^{50} +(-2.09030 + 1.20684i) q^{51} +(-6.13741 + 1.64451i) q^{52} +(0.0540807 + 0.0144909i) q^{53} +(0.866025 + 0.500000i) q^{54} +(10.4775 + 2.10601i) q^{55} +2.04843i q^{56} +(-1.06547 - 4.22668i) q^{57} +(0.196162 + 0.196162i) q^{58} +(5.69599 - 9.86575i) q^{59} +(1.23855 + 1.86172i) q^{60} +(1.79160 + 3.10315i) q^{61} +(-0.312835 - 1.16752i) q^{62} +(0.530173 - 1.97863i) q^{63} -1.00000i q^{64} +(12.7299 + 6.30955i) q^{65} +(2.38970 + 4.13908i) q^{66} +(3.66697 - 13.6853i) q^{67} +(-1.70672 - 1.70672i) q^{68} -2.39291 q^{69} +(3.02701 - 3.43767i) q^{70} +(8.89740 + 5.13692i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-4.92912 + 1.32075i) 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} +(1.64451 + 6.13741i) q^{78} +(0.0784953 - 0.135958i) q^{79} +(-1.47772 + 1.67820i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-9.56078 - 2.56180i) q^{82} +(-9.57920 - 9.57920i) q^{83} +2.04843 q^{84} +(0.342160 + 5.38628i) 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} +(1.86172 - 1.23855i) q^{90} +(11.2718 - 6.50778i) q^{91} +(-0.619330 - 2.31137i) q^{92} +(-1.16752 + 0.312835i) q^{93} -5.28335 q^{94} +(-9.52607 - 2.06253i) q^{95} -1.00000 q^{96} +(15.3495 - 4.11289i) q^{97} +(0.725708 + 2.70838i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.19222	−	0.440644i	−0.980391	−	0.197062i
$5$	−2.19222	−	0.440644i	−0.980391	−	0.197062i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−1.44846	+	1.44846i	−0.547467	+	0.547467i	−0.925707	−	0.378241i	$-0.876529\pi$
$7$	−1.44846	+	1.44846i	−0.547467	+	0.547467i	0.378241	+	0.925707i	$0.376529\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	−2.23157	+	0.141759i	−0.705684	+	0.0448282i
$11$	−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
$13$	−6.13741	−	1.64451i	−1.70221	−	0.456106i	−0.728716	−	0.684816i	$-0.759882\pi$
$13$	−6.13741	−	1.64451i	−1.70221	−	0.456106i	−0.973494	+	0.228711i	$0.926549\pi$
$14$	−1.02422	+	1.77400i	−0.273733	+	0.474120i
$15$	0.141759	+	2.23157i	0.0366021	+	0.576189i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.624705	−	2.33143i	−0.151513	−	0.565455i	−0.999379	−	0.0352435i	$-0.988779\pi$
$17$	−0.624705	−	2.33143i	−0.151513	−	0.565455i	0.847866	−	0.530211i	$-0.177887\pi$
$18$	−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
$22$	−4.61654	+	1.23700i	−0.984250	+	0.263729i
$23$	0.619330	−	2.31137i	0.129139	−	0.481954i	−0.870814	−	0.491612i	$-0.836408\pi$
$23$	0.619330	−	2.31137i	0.129139	−	0.481954i	0.999953	+	0.00965820i	$0.00307435\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	4.61167	+	1.93198i	0.922333	+	0.386396i
$26$	−6.35391			−1.24610
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−0.530173	+	1.97863i	−0.100193	+	0.373927i
$29$	0.138707	+	0.240248i	0.0257573	+	0.0446130i	0.878617	−	0.477528i	$-0.158467\pi$
$29$	0.138707	+	0.240248i	0.0257573	+	0.0446130i	−0.852859	+	0.522141i	$0.825134\pi$
$30$	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	$-0.0346191\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	1.23700	+	4.61654i	0.215334	+	0.803637i
$34$	−1.20684	−	2.09030i	−0.206971	−	0.358484i
$35$	3.81360	−	2.53709i	0.644616	−	0.428847i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	2.38275	+	2.38275i	0.391722	+	0.391722i	0.875301	−	0.483579i	$-0.160663\pi$
$37$	2.38275	+	2.38275i	0.391722	+	0.391722i	−0.483579	+	0.875301i	$0.660663\pi$
$38$	4.22668	−	1.06547i	0.685657	−	0.172841i
$39$			6.35391i			1.01744i
$40$	−1.86172	+	1.23855i	−0.294363	+	0.195832i
$41$	−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	$0.947865\pi$
$42$	1.97863	+	0.530173i	0.305310	+	0.0818075i
$43$	−4.73117	+	1.26771i	−0.721496	+	0.193324i	−0.600839	−	0.799370i	$-0.705167\pi$
$43$	−4.73117	+	1.26771i	−0.721496	+	0.193324i	−0.120657	+	0.992694i	$0.538500\pi$
$44$	−4.13908	+	2.38970i	−0.623990	+	0.360261i
$45$	2.11884	−	0.714502i	0.315858	−	0.106512i
$46$		−	2.39291i		−	0.352815i
$47$	−5.10332	−	1.36743i	−0.744396	−	0.199460i	−0.133365	−	0.991067i	$-0.542578\pi$
$47$	−5.10332	−	1.36743i	−0.744396	−	0.199460i	−0.611031	+	0.791607i	$0.709245\pi$
$48$	−0.965926	−	0.258819i	−0.139419	−	0.0373573i
$49$			2.80392i			0.400560i
$50$	4.95456	+	0.672560i	0.700681	+	0.0951144i
$51$	−2.09030	+	1.20684i	−0.292701	+	0.168991i
$52$	−6.13741	+	1.64451i	−0.851105	+	0.228053i
$53$	0.0540807	+	0.0144909i	0.00742855	+	0.00199047i	0.262531	−	0.964923i	$-0.415443\pi$
$53$	0.0540807	+	0.0144909i	0.00742855	+	0.00199047i	−0.255103	+	0.966914i	$0.582109\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	10.4775	+	2.10601i	1.41278	+	0.283975i
$56$			2.04843i			0.273733i
$57$	−1.06547	−	4.22668i	−0.141124	−	0.559837i
$58$	0.196162	+	0.196162i	0.0257573	+	0.0257573i
$59$	5.69599	−	9.86575i	0.741555	−	1.28441i	−0.210232	−	0.977652i	$-0.567422\pi$
$59$	5.69599	−	9.86575i	0.741555	−	1.28441i	0.951787	−	0.306759i	$-0.0992447\pi$
$60$	1.23855	+	1.86172i	0.159896	+	0.240347i
$61$	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	$0.759660\pi$
$62$	−0.312835	−	1.16752i	−0.0397301	−	0.148275i
$63$	0.530173	−	1.97863i	0.0667956	−	0.249284i
$64$		−	1.00000i		−	0.125000i
$65$	12.7299	+	6.30955i	1.57895	+	0.782603i
$66$	2.38970	+	4.13908i	0.294151	+	0.509485i
$67$	3.66697	−	13.6853i	0.447992	−	1.67193i	−0.259923	−	0.965629i	$-0.583697\pi$
$67$	3.66697	−	13.6853i	0.447992	−	1.67193i	0.707914	−	0.706298i	$-0.249636\pi$
$68$	−1.70672	−	1.70672i	−0.206971	−	0.206971i
$69$	−2.39291			−0.288072
$70$	3.02701	−	3.43767i	0.361797	−	0.410881i
$71$	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	$0.457981\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	−4.92912	+	1.32075i	−0.576910	+	0.154582i	−0.535464	−	0.844558i	$-0.679863\pi$
$73$	−4.92912	+	1.32075i	−0.576910	+	0.154582i	−0.0414460	+	0.999141i	$0.513196\pi$
$74$	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
$78$	1.64451	+	6.13741i	0.186204	+	0.694924i
$79$	0.0784953	−	0.135958i	0.00883141	−	0.0152965i	−0.861576	−	0.507629i	$-0.830522\pi$
$79$	0.0784953	−	0.135958i	0.00883141	−	0.0152965i	0.870407	+	0.492332i	$0.163856\pi$
$80$	−1.47772	+	1.67820i	−0.165214	+	0.187628i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−9.56078	−	2.56180i	−1.05581	−	0.282904i
$83$	−9.57920	−	9.57920i	−1.05145	−	1.05145i	−0.998602	−	0.0528519i	$-0.983169\pi$
$83$	−9.57920	−	9.57920i	−1.05145	−	1.05145i	−0.0528519	−	0.998602i	$-0.516831\pi$
$84$	2.04843			0.223502
$85$	0.342160	+	5.38628i	0.0371125	+	0.584224i
$86$	−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	0.995581	−	0.0939113i	$-0.0299370\pi$
$89$	3.92888	+	6.80502i	0.416461	+	0.721331i	−0.579120	+	0.815242i	$0.696604\pi$
$90$	1.86172	−	1.23855i	0.196242	−	0.130555i
$91$	11.2718	−	6.50778i	1.18161	−	0.682201i
$92$	−0.619330	−	2.31137i	−0.0645696	−	0.240977i
$93$	−1.16752	+	0.312835i	−0.121066	+	0.0324395i
$94$	−5.28335			−0.544936
$95$	−9.52607	−	2.06253i	−0.977354	−	0.211611i
$96$	−1.00000			−0.102062
$97$	15.3495	−	4.11289i	1.55851	−	0.417601i	0.626317	−	0.779568i	$-0.284561\pi$
$97$	15.3495	−	4.11289i	1.55851	−	0.417601i	0.932191	+	0.361967i	$0.117895\pi$
$98$	0.725708	+	2.70838i	0.0733076	+	0.273588i
$99$	4.13908	−	2.38970i	0.415993	−	0.240174i
$100$	4.95981	−	0.632691i	0.495981	−	0.0632691i
$101$	−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	−0.0506874	+	0.998715i	$0.516141\pi$
$103$	−10.6503	+	10.6503i	−1.04940	+	1.04940i	−0.998715	+	0.0506874i	$0.983859\pi$
$104$	−5.50265	+	3.17696i	−0.539579	+	0.311526i
$105$	−3.43767	−	3.02701i	−0.335483	−	0.295406i
$106$	0.0559884			0.00543808
$107$	−5.65689	−	5.65689i	−0.546872	−	0.546872i	0.378663	−	0.925535i	$-0.376384\pi$
$107$	−5.65689	−	5.65689i	−0.546872	−	0.546872i	−0.925535	+	0.378663i	$0.876384\pi$
$108$	0.965926	+	0.258819i	0.0929463	+	0.0249049i
$109$	−4.99236	+	8.64702i	−0.478181	+	0.828234i	−0.999687	−	0.0250137i	$-0.992037\pi$
$109$	−4.99236	+	8.64702i	−0.478181	+	0.828234i	0.521506	+	0.853248i	$0.325370\pi$
$110$	10.6656	−	0.677523i	1.01692	−	0.0645993i
$111$	1.68486	−	2.91826i	0.159920	−	0.276989i
$112$	0.530173	+	1.97863i	0.0500967	+	0.186963i
$113$	−7.87693	+	7.87693i	−0.741000	+	0.741000i	−0.972770	−	0.231771i	$-0.925548\pi$
$113$	−7.87693	+	7.87693i	−0.741000	+	0.741000i	0.231771	+	0.972770i	$0.425548\pi$
$114$	−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
$117$	6.13741	−	1.64451i	0.567403	−	0.152035i
$118$	2.94846	−	11.0038i	0.271428	−	1.01298i
$119$	4.28184	+	2.47212i	0.392516	+	0.226619i
$120$	1.67820	+	1.47772i	0.153198	+	0.134897i
$121$	11.8426			1.07660
$122$	2.53371	+	2.53371i	0.229391	+	0.229391i
$123$	−2.56180	+	9.56078i	−0.230990	+	0.862066i
$124$	−0.604351	−	1.04677i	−0.0542723	−	0.0940025i
$125$	−9.25848	−	6.26742i	−0.828103	−	0.560576i
$126$		−	2.04843i		−	0.182489i
$127$	2.39869	−	8.95204i	0.212850	−	0.794365i	−0.774063	−	0.633109i	$-0.781779\pi$
$127$	2.39869	−	8.95204i	0.212850	−	0.794365i	0.986913	−	0.161257i	$-0.0515547\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	2.44903	+	4.24185i	0.215625	+	0.373474i
$130$	13.9292	+	2.79981i	1.22167	+	0.245560i
$131$	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
$133$	−6.40683	+	6.21916i	−0.555543	+	0.539270i
$134$		−	14.1681i		−	1.22394i
$135$	−1.23855	−	1.86172i	−0.106598	−	0.160231i
$136$	−2.09030	−	1.20684i	−0.179242	−	0.103485i
$137$	−5.11017	−	1.36927i	−0.436591	−	0.116984i	0.0338273	−	0.999428i	$-0.489230\pi$
$137$	−5.11017	−	1.36927i	−0.436591	−	0.116984i	−0.470419	+	0.882443i	$0.655897\pi$
$138$	−2.31137	+	0.619330i	−0.196757	+	0.0527209i
$139$	6.07995	−	3.51026i	0.515695	−	0.297737i	−0.219477	−	0.975618i	$-0.570435\pi$
$139$	6.07995	−	3.51026i	0.515695	−	0.297737i	0.735171	+	0.677881i	$0.237102\pi$
$140$	2.03413	−	4.10399i	0.171915	−	0.346850i
$141$			5.28335i			0.444938i
$142$	9.92377	+	2.65906i	0.832784	+	0.223144i
$143$	29.3331	+	7.85978i	2.45296	+	0.657268i
$144$			1.00000i			0.0833333i
$145$	−0.198213	−	0.587798i	−0.0164607	−	0.0488140i
$146$	−4.41933	+	2.55150i	−0.365746	+	0.211164i
$147$	2.70838	−	0.725708i	0.223383	−	0.0598554i
$148$	3.25490	+	0.872147i	0.267551	+	0.0716900i
$149$	−12.8151	−	7.39882i	−1.04986	−	0.606135i	−0.127248	−	0.991871i	$-0.540614\pi$
$149$	−12.8151	−	7.39882i	−1.04986	−	0.606135i	−0.922609	+	0.385736i	$0.873948\pi$
$150$	−0.632691	−	4.95981i	−0.0516590	−	0.404967i
$151$			12.9082i			1.05045i	0.850962	+	0.525227i	$0.176020\pi$
$151$			12.9082i			1.05045i	−0.850962	+	0.525227i	$0.823980\pi$
$152$	3.12768	−	3.03606i	0.253688	−	0.246257i
$153$	1.70672	+	1.70672i	0.137981	+	0.137981i
$154$	4.89514	−	8.47862i	0.394461	−	0.683227i
$155$	−0.532607	+	2.64974i	−0.0427801	+	0.212832i
$156$	3.17696	+	5.50265i	0.254360	+	0.440564i
$157$	0.683198	+	2.54973i	0.0545251	+	0.203491i	0.987815	−	0.155634i	$-0.0497420\pi$
$157$	0.683198	+	2.54973i	0.0545251	+	0.203491i	−0.933290	+	0.359124i	$0.883075\pi$
$158$	0.0406322	−	0.151641i	0.00323252	−	0.0120639i
$159$		−	0.0559884i		−	0.00444017i
$160$	−0.993018	+	2.00348i	−0.0785050	+	0.158389i
$161$	2.45086	+	4.24501i	0.193154	+	0.334553i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	−13.6829	−	13.6829i	−1.07173	−	1.07173i	−0.997220	−	0.0745108i	$-0.976260\pi$
$163$	−13.6829	−	13.6829i	−1.07173	−	1.07173i	−0.0745108	−	0.997220i	$-0.523740\pi$
$164$	−9.89804			−0.772907
$165$	−0.677523	−	10.6656i	−0.0527451	−	0.830312i
$166$	−11.7321	−	6.77352i	−0.910586	−	0.525727i
$167$	0.244943	−	0.914140i	0.0189543	−	0.0707383i	−0.955801	−	0.294015i	$-0.905009\pi$
$167$	0.244943	−	0.914140i	0.0189543	−	0.0707383i	0.974755	+	0.223276i	$0.0716752\pi$
$168$	1.97863	−	0.530173i	0.152655	−	0.0409038i
$169$	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
$173$	−4.42758	−	16.5240i	−0.336623	−	1.25629i	−0.902099	−	0.431529i	$-0.857974\pi$
$173$	−4.42758	−	16.5240i	−0.336623	−	1.25629i	0.565476	−	0.824765i	$-0.308693\pi$
$174$	0.138707	−	0.240248i	0.0105154	−	0.0182132i
$175$	−9.47821	+	3.88142i	−0.716485	+	0.293408i
$176$	−2.38970	+	4.13908i	−0.180130	+	0.311995i
$177$	−11.0038	−	2.94846i	−0.827097	−	0.221620i
$178$	5.55628	+	5.55628i	0.416461	+	0.416461i
$179$	20.0940			1.50190			0.750948	−	0.660361i	$-0.229597\pi$
$179$	20.0940			1.50190			0.750948	+	0.660361i	$0.229597\pi$
$180$	1.47772	−	1.67820i	0.110143	−	0.125085i
$181$	−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
$185$	−4.17357	−	6.27346i	−0.306847	−	0.461234i
$186$	−1.04677	+	0.604351i	−0.0767527	+	0.0443132i
$187$	2.98571	+	11.1428i	0.218337	+	0.814844i
$188$	−5.10332	+	1.36743i	−0.372198	+	0.0997302i
$189$	−2.04843			−0.149002
$190$	−9.73530	+	0.473277i	−0.706273	+	0.0343351i
$191$	−1.32194			−0.0956522			−0.0478261	−	0.998856i	$-0.515229\pi$
$191$	−1.32194			−0.0956522			−0.0478261	+	0.998856i	$0.515229\pi$
$192$	−0.965926	+	0.258819i	−0.0697097	+	0.0186787i
$193$	6.29234	+	23.4833i	0.452933	+	1.69037i	0.694095	+	0.719884i	$0.255805\pi$
$193$	6.29234	+	23.4833i	0.452933	+	1.69037i	−0.241162	+	0.970485i	$0.577529\pi$
$194$	13.7620	−	7.94550i	0.988055	−	0.570454i
$195$	2.79981	−	13.9292i	0.200499	−	0.997489i
$196$	1.40196	+	2.42827i	0.100140	+	0.173448i
$197$	−8.72758	+	8.72758i	−0.621814	+	0.621814i	−0.945995	−	0.324181i	$-0.894911\pi$
$197$	−8.72758	+	8.72758i	−0.621814	+	0.621814i	0.324181	+	0.945995i	$0.394911\pi$
$198$	3.37954	−	3.37954i	0.240174	−	0.240174i
$199$	−9.76184	+	5.63600i	−0.691998	+	0.399525i	−0.804360	−	0.594142i	$-0.797492\pi$
$199$	−9.76184	+	5.63600i	−0.691998	+	0.399525i	0.112362	+	0.993667i	$0.464158\pi$
$200$	4.62705	−	1.89483i	0.327182	−	0.133984i
$201$	−14.1681			−0.999340
$202$	−3.21868	−	3.21868i	−0.226466	−	0.226466i
$203$	−0.548903	−	0.147078i	−0.0385254	−	0.0103229i
$204$	−1.20684	+	2.09030i	−0.0844955	+	0.146350i
$205$	16.6109	+	14.6265i	1.16015	+	1.02156i
$206$	−7.53088	+	13.0439i	−0.524701	+	0.908809i
$207$	0.619330	+	2.31137i	0.0430464	+	0.160651i
$208$	−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	$0.689171\pi$
$212$	0.0540807	−	0.0144909i	0.00371427	−	0.000995237i
$213$	2.65906	−	9.92377i	0.182196	−	0.679965i
$214$	−6.92824	−	4.00002i	−0.473605	−	0.273436i
$215$	10.9304	−	0.694345i	0.745445	−	0.0473540i
$216$	1.00000			0.0680414
$217$	1.75076	+	1.75076i	0.118849	+	0.118849i
$218$	−2.58423	+	9.64449i	−0.175026	+	0.653207i
$219$	2.55150	+	4.41933i	0.172414	+	0.298630i
$220$	10.1268	−	3.41489i	0.682747	−	0.230232i
$221$			15.3363i			1.03163i
$222$	0.872147	−	3.25490i	0.0585347	−	0.218454i
$223$	−6.26002	−	23.3627i	−0.419202	−	1.56448i	−0.776268	−	0.630403i	$-0.782890\pi$
$223$	−6.26002	−	23.3627i	−0.419202	−	1.56448i	0.357066	−	0.934079i	$-0.383777\pi$
$224$	1.02422	+	1.77400i	0.0684333	+	0.118530i
$225$	−4.95981	+	0.632691i	−0.330654	+	0.0421794i
$226$	−5.56983	+	9.64723i	−0.370500	+	0.641724i
$227$	−18.6234	−	18.6234i	−1.23608	−	1.23608i	−0.961592	−	0.274484i	$-0.911493\pi$
$227$	−18.6234	−	18.6234i	−1.23608	−	1.23608i	−0.274484	−	0.961592i	$-0.588507\pi$
$228$	−3.03606	−	3.12768i	−0.201068	−	0.207135i
$229$		−	4.62956i		−	0.305930i	−0.988232	−	0.152965i	$-0.951118\pi$
$229$		−	4.62956i		−	0.305930i	0.988232	−	0.152965i	$-0.0488822\pi$
$230$	−1.05442	+	5.24578i	−0.0695264	+	0.345897i
$231$	−8.47862	−	4.89514i	−0.557853	−	0.322076i
$232$	0.267962	+	0.0718003i	0.0175926	+	0.00471392i
$233$	−3.84781	+	1.03102i	−0.252078	+	0.0675442i	−0.382645	−	0.923895i	$-0.624987\pi$
$233$	−3.84781	+	1.03102i	−0.252078	+	0.0675442i	0.130567	+	0.991439i	$0.458320\pi$
$234$	5.50265	−	3.17696i	0.359719	−	0.207684i
$235$	10.5851	+	5.24646i	0.690493	+	0.342241i
$236$		−	11.3920i		−	0.741555i
$237$	−0.151641	−	0.0406322i	−0.00985016	−	0.00263934i
$238$	4.77578	+	1.27967i	0.309568	+	0.0829484i
$239$			3.76301i			0.243409i	0.992566	+	0.121705i	$0.0388360\pi$
$239$			3.76301i			0.243409i	−0.992566	+	0.121705i	$0.961164\pi$
$240$	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	$0.297577\pi$
$242$	11.4391	−	3.06510i	0.735333	−	0.197032i
$243$	−0.965926	−	0.258819i	−0.0619642	−	0.0166032i
$244$	3.10315	+	1.79160i	0.198659	+	0.114696i
$245$	1.23553	−	6.14682i	0.0789352	−	0.392706i
$246$			9.89804i			0.631076i
$247$	−26.6428	−	7.56508i	−1.69524	−	0.481354i
$248$	−0.854682	−	0.854682i	−0.0542723	−	0.0542723i
$249$	−6.77352	+	11.7321i	−0.429254	+	0.743490i
$250$	−10.5651	−	3.65760i	−0.668198	−	0.231327i
$251$	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	$0.690494\pi$
$252$	−0.530173	−	1.97863i	−0.0333978	−	0.124642i
$253$	−2.96002	+	11.0470i	−0.186095	+	0.694516i
$254$		−	9.26783i		−	0.581516i
$255$	5.11419	−	1.72457i	0.320263	−	0.107997i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.17399	−	8.11342i	0.135609	−	0.506101i	−0.864385	−	0.502830i	$-0.832292\pi$
$257$	2.17399	−	8.11342i	0.135609	−	0.506101i	0.999995	−	0.00327121i	$-0.00104126\pi$
$258$	3.46345	+	3.46345i	0.215625	+	0.215625i
$259$	−6.90264			−0.428909
$260$	14.1792	−	0.900725i	0.879356	−	0.0558606i
$261$	−0.240248	−	0.138707i	−0.0148710	−	0.00858578i
$262$	1.77986	−	6.64252i	0.109960	−	0.410376i
$263$	30.5148	−	8.17641i	1.88162	−	0.504179i	0.882175	−	0.470921i	$-0.156078\pi$
$263$	30.5148	−	8.17641i	1.88162	−	0.504179i	0.999447	−	0.0332576i	$-0.0105882\pi$
$264$	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
$268$	−3.66697	−	13.6853i	−0.223996	−	0.835964i
$269$	−15.6519	+	27.1099i	−0.954313	+	1.65292i	−0.218381	+	0.975864i	$0.570078\pi$
$269$	−15.6519	+	27.1099i	−0.954313	+	1.65292i	−0.735932	+	0.677055i	$0.763256\pi$
$270$	−1.67820	−	1.47772i	−0.102132	−	0.0899311i
$271$	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	$0.137769\pi$
$272$	−2.33143	−	0.624705i	−0.141364	−	0.0378783i
$273$	−9.20339	−	9.20339i	−0.557015	−	0.557015i
$274$	−5.29044			−0.319607
$275$	−22.0410	−	9.23369i	−1.32912	−	0.556812i
$276$	−2.07232	+	1.19645i	−0.124739	+	0.0720181i
$277$	−18.7388	+	18.7388i	−1.12590	+	1.12590i	−0.135066	+	0.990837i	$0.543125\pi$
$277$	−18.7388	+	18.7388i	−1.12590	+	1.12590i	−0.990837	+	0.135066i	$0.956875\pi$
$278$	4.96426	−	4.96426i	0.297737	−	0.297737i
$279$	0.604351	+	1.04677i	0.0361816	+	0.0626683i
$280$	0.902630	−	4.49062i	0.0539424	−	0.268366i
$281$	−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	$0.509816\pi$
$282$	1.36743	+	5.10332i	0.0814293	+	0.303898i
$283$	15.1561	−	4.06107i	0.900938	−	0.241406i	0.221519	−	0.975156i	$-0.428898\pi$
$283$	15.1561	−	4.06107i	0.900938	−	0.241406i	0.679419	+	0.733750i	$0.262232\pi$
$284$	10.2738			0.609640
$285$	0.473277	+	9.73530i	0.0280345	+	0.576669i
$286$	30.3679			1.79569
$287$	19.5846	−	5.24768i	1.15604	−	0.309761i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	9.67712	−	5.58709i	0.569243	−	0.328652i
$290$	−0.343593	−	0.516468i	−0.0201765	−	0.0303280i
$291$	−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	−0.257240	+	0.966347i	$0.582813\pi$
$293$	−20.9445	+	20.9445i	−1.22359	+	1.22359i	−0.966347	+	0.257240i	$0.917187\pi$
$294$	2.42827	−	1.40196i	0.141619	−	0.0817640i
$295$	−16.8342	+	19.1180i	−0.980122	+	1.11309i
$296$	3.36972			0.195861
$297$	−3.37954	−	3.37954i	−0.196101	−	0.196101i
$298$	−14.2934	−	3.82991i	−0.827996	−	0.221861i
$299$	−7.60216	+	13.1673i	−0.439644	+	0.761486i
$300$	−1.89483	−	4.62705i	−0.109398	−	0.267143i
$301$	5.01668	−	8.68914i	0.289156	−	0.500834i
$302$	3.34089	+	12.4684i	0.192247	+	0.717474i
$303$	−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
$307$	26.9609	−	7.22416i	1.53874	−	0.412304i	0.612882	−	0.790174i	$-0.290010\pi$
$307$	26.9609	−	7.22416i	1.53874	−	0.412304i	0.925859	+	0.377870i	$0.123343\pi$
$308$	2.53391	−	9.45668i	0.144383	−	0.538844i
$309$	13.0439	+	7.53088i	0.742039	+	0.428417i
$310$	0.171345	+	2.69730i	0.00973173	+	0.153197i
$311$	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
$313$	5.57477	−	20.8053i	0.315105	−	1.17599i	−0.608787	−	0.793334i	$-0.708344\pi$
$313$	5.57477	−	20.8053i	0.315105	−	1.17599i	0.923892	−	0.382653i	$-0.124990\pi$
$314$	1.31984	+	2.28603i	0.0744827	+	0.129008i
$315$	−2.03413	+	4.10399i	−0.114610	+	0.231233i
$316$		−	0.156991i		−	0.00883141i
$317$	1.31621	−	4.91216i	0.0739256	−	0.275894i	−0.919062	−	0.394113i	$-0.871052\pi$
$317$	1.31621	−	4.91216i	0.0739256	−	0.275894i	0.992988	+	0.118219i	$0.0377185\pi$
$318$	−0.0144909	−	0.0540807i	−0.000812608	−	0.00303269i
$319$	−0.662938	−	1.14824i	−0.0371174	−	0.0642892i
$320$	−0.440644	+	2.19222i	−0.0246327	+	0.122549i
$321$	−4.00002	+	6.92824i	−0.223259	+	0.386697i
$322$	3.46603	+	3.46603i	0.193154	+	0.193154i
$323$	−2.57169	−	10.2018i	−0.143092	−	0.567644i
$324$		−	1.00000i		−	0.0555556i
$325$	−25.1265	−	19.4413i	−1.39377	−	1.07841i
$326$	−16.7581	−	9.67530i	−0.928146	−	0.535865i
$327$	9.64449	+	2.58423i	0.533342	+	0.142908i
$328$	−9.56078	+	2.56180i	−0.527906	+	0.141452i
$329$	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	$-0.206538\pi$
$332$	−13.0854	−	3.50623i	−0.718157	−	0.192429i
$333$	−3.25490	−	0.872147i	−0.178367	−	0.0477933i
$334$		−	0.946387i		−	0.0517840i
$335$	−14.0692	+	28.3854i	−0.768680	+	1.55086i
$336$	1.77400	−	1.02422i	0.0967794	−	0.0558756i
$337$	−31.5729	+	8.45993i	−1.71988	+	0.460842i	−0.977813	−	0.209479i	$-0.932823\pi$
$337$	−31.5729	+	8.45993i	−1.71988	+	0.460842i	−0.742072	+	0.670321i	$0.766157\pi$
$338$	26.4395	+	7.08444i	1.43812	+	0.385343i
$339$	9.64723	+	5.56983i	0.523966	+	0.302512i
$340$	2.98946	+	4.49358i	0.162126	+	0.243698i
$341$			5.77687i			0.312835i
$342$	−3.12768	+	3.03606i	−0.169125	+	0.164171i
$343$	−14.2006	−	14.2006i	−0.766760	−	0.766760i
$344$	−2.44903	+	4.24185i	−0.132043	+	0.228705i
$345$	5.24578	+	1.05442i	0.282423	+	0.0567681i
$346$	−8.55344	−	14.8150i	−0.459836	−	0.796459i
$347$	6.15382	+	22.9664i	0.330354	+	1.23290i	0.908819	+	0.417191i	$0.136986\pi$
$347$	6.15382	+	22.9664i	0.330354	+	1.23290i	−0.578464	+	0.815708i	$0.696348\pi$
$348$	0.0718003	−	0.267962i	0.00384890	−	0.0143643i
$349$		−	26.3554i		−	1.41077i	−0.708823	−	0.705386i	$-0.750774\pi$
$349$		−	26.3554i		−	1.41077i	0.708823	−	0.705386i	$-0.249226\pi$
$350$	−8.15066	+	6.20231i	−0.435671	+	0.331527i
$351$	−3.17696	−	5.50265i	−0.169573	−	0.293710i
$352$	−1.23700	+	4.61654i	−0.0659322	+	0.246063i
$353$	8.76102	+	8.76102i	0.466302	+	0.466302i	0.900714	−	0.434412i	$-0.143044\pi$
$353$	8.76102	+	8.76102i	0.466302	+	0.466302i	−0.434412	+	0.900714i	$0.643044\pi$
$354$	−11.3920			−0.605477
$355$	−17.2415	−	15.1818i	−0.915085	−	0.805769i
$356$	6.80502	+	3.92888i	0.360666	+	0.208230i
$357$	1.27967	−	4.77578i	0.0677271	−	0.252761i
$358$	19.4093	−	5.20071i	1.02581	−	0.274866i
$359$	17.7464	+	10.2459i	0.936619	+	0.540757i	0.888899	−	0.458104i	$-0.151471\pi$
$359$	17.7464	+	10.2459i	0.936619	+	0.540757i	0.0477199	+	0.998861i	$0.484805\pi$
$360$	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
$363$	−3.06510	−	11.4391i	−0.160876	−	0.600397i
$364$	6.50778	−	11.2718i	0.341100	−	0.590803i
$365$	11.3877	−	0.723397i	0.596059	−	0.0378643i
$366$	1.79160	−	3.10315i	0.0936487	−	0.162204i
$367$	1.34953	+	0.361607i	0.0704451	+	0.0188757i	0.293869	−	0.955846i	$-0.405057\pi$
$367$	1.34953	+	0.361607i	0.0704451	+	0.0188757i	−0.223424	+	0.974721i	$0.571724\pi$
$368$	−1.69204	−	1.69204i	−0.0882037	−	0.0882037i
$369$	9.89804			0.515272
$370$	−5.65505	−	4.97950i	−0.293992	−	0.258872i
$371$	−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	$-0.643155\pi$
$373$	8.99682	−	8.99682i	0.465838	−	0.465838i	0.900563	+	0.434725i	$0.143155\pi$
$374$	5.76795	+	9.99038i	0.298254	+	0.516590i
$375$	−3.65760	+	10.5651i	−0.188878	+	0.545581i
$376$	−4.57551	+	2.64167i	−0.235964	+	0.136234i
$377$	−0.456213	−	1.70261i	−0.0234961	−	0.0876888i
$378$	−1.97863	+	0.530173i	−0.101770	+	0.0272692i
$379$	−27.9212			−1.43421			−0.717107	−	0.696963i	$-0.754534\pi$
$379$	−27.9212			−1.43421			−0.717107	+	0.696963i	$0.754534\pi$
$380$	−9.28108	+	2.97683i	−0.476109	+	0.152708i
$381$	−9.26783			−0.474806
$382$	−1.27690	+	0.342143i	−0.0653317	+	0.0175056i
$383$	5.59098	+	20.8658i	0.285686	+	1.06619i	0.948337	+	0.317266i	$0.102765\pi$
$383$	5.59098	+	20.8658i	0.285686	+	1.06619i	−0.662651	+	0.748929i	$0.730569\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$	−18.2267	+	12.1258i	−0.928919	+	0.617986i
$386$	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	−0.864455	−	0.502709i	$-0.832337\pi$
$389$	−16.9880	+	9.80801i	−0.861324	+	0.497286i	0.00313142	+	0.999995i	$0.499003\pi$
$390$	−0.900725	−	14.1792i	−0.0456100	−	0.717991i
$391$	−5.77570			−0.292090
$392$	1.98267	+	1.98267i	0.100140	+	0.100140i
$393$	−6.64252	−	1.77986i	−0.335071	−	0.0897820i
$394$	−6.17133	+	10.6891i	−0.310907	+	0.538507i
$395$	−0.231988	+	0.263461i	−0.0116726	+	0.0132562i
$396$	2.38970	−	4.13908i	0.120087	−	0.207997i
$397$	1.12530	+	4.19969i	0.0564774	+	0.210777i	0.988398	−	0.151886i	$-0.0485345\pi$
$397$	1.12530	+	4.19969i	0.0564774	+	0.210777i	−0.931921	+	0.362662i	$0.881868\pi$
$398$	−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	$0.534341\pi$
$402$	−13.6853	+	3.66697i	−0.682562	+	0.182892i
$403$	−1.98773	+	7.41830i	−0.0990157	+	0.369532i
$404$	−3.94207	−	2.27595i	−0.196125	−	0.113233i
$405$	−1.47772	+	1.67820i	−0.0734285	+	0.0833903i
$406$	−0.568266			−0.0282026
$407$	−11.3881	−	11.3881i	−0.564487	−	0.564487i
$408$	−0.624705	+	2.33143i	−0.0309275	+	0.115423i
$409$	−19.1608	−	33.1875i	−0.947440	−	1.64101i	−0.750791	−	0.660540i	$-0.770327\pi$
$409$	−19.1608	−	33.1875i	−0.947440	−	1.64101i	−0.196649	−	0.980474i	$-0.563006\pi$
$410$	19.8305	+	9.82894i	0.979358	+	0.485417i
$411$			5.29044i			0.260958i
$412$	−3.89827	+	14.5485i	−0.192054	+	0.716755i
$413$	6.03973	+	22.5406i	0.297196	+	1.10915i
$414$	1.19645	+	2.07232i	0.0588025	+	0.101849i
$415$	16.7787	+	25.2208i	0.823635	+	1.23804i
$416$	−3.17696	+	5.50265i	−0.155763	+	0.269789i
$417$	−4.96426	−	4.96426i	−0.243101	−	0.243101i
$418$	−20.2010	+	5.09228i	−0.988061	+	0.249072i
$419$			20.4732i			1.00018i	0.865972	+	0.500092i	$0.166700\pi$
$419$			20.4732i			1.00018i	−0.865972	+	0.500092i	$0.833300\pi$
$420$	−4.49062	−	0.902630i	−0.219120	−	0.0440438i
$421$	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	$0.540257\pi$
$422$	−1.98226	−	0.531146i	−0.0964951	−	0.0258558i
$423$	5.10332	−	1.36743i	0.248132	−	0.0664868i
$424$	0.0484874	−	0.0279942i	0.00235476	−	0.00135952i
$425$	1.62334	−	11.9587i	0.0787436	−	0.580082i
$426$		−	10.2738i		−	0.497769i
$427$	−7.08986	−	1.89972i	−0.343102	−	0.0919340i
$428$	−7.72745	−	2.07056i	−0.373520	−	0.100084i
$429$		−	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	$0.604612\pi$
$432$	0.965926	−	0.258819i	0.0464731	−	0.0124524i
$433$	−9.05342	−	2.42586i	−0.435080	−	0.116579i	0.0346300	−	0.999400i	$-0.488975\pi$
$433$	−9.05342	−	2.42586i	−0.435080	−	0.116579i	−0.469710	+	0.882821i	$0.655641\pi$
$434$	2.14423	+	1.23797i	0.102926	+	0.0594246i
$435$	−0.516468	+	0.343593i	−0.0247627	+	0.0164740i
$436$			9.98471i			0.478181i
$437$	2.84904	−	10.0338i	0.136288	−	0.479982i
$438$	3.60836	+	3.60836i	0.172414	+	0.172414i
$439$	8.30594	−	14.3863i	0.396421	−	0.686621i	−0.596860	−	0.802345i	$-0.703585\pi$
$439$	8.30594	−	14.3863i	0.396421	−	0.686621i	0.993281	+	0.115724i	$0.0369187\pi$
$440$	8.89788	−	5.91953i	0.424190	−	0.282203i
$441$	−1.40196	−	2.42827i	−0.0667601	−	0.115632i
$442$	3.96932	+	14.8137i	0.188801	+	0.704616i
$443$	4.26848	−	15.9302i	0.202802	−	0.756867i	−0.787307	−	0.616562i	$-0.788525\pi$
$443$	4.26848	−	15.9302i	0.202802	−	0.756867i	0.990108	−	0.140305i	$-0.0448083\pi$
$444$		−	3.36972i		−	0.159920i
$445$	−5.61439	−	16.6494i	−0.266147	−	0.789255i
$446$	−12.0934	−	20.9464i	−0.572640	−	0.991842i
$447$	−3.82991	+	14.2934i	−0.181149	+	0.676056i
$448$	1.44846	+	1.44846i	0.0684333	+	0.0684333i
$449$	8.68803			0.410013			0.205007	−	0.978761i	$-0.434278\pi$
$449$	8.68803			0.410013			0.205007	+	0.978761i	$0.434278\pi$
$450$	−4.62705	+	1.89483i	−0.218121	+	0.0893229i
$451$	40.9688	+	23.6533i	1.92914	+	1.11379i
$452$	−2.88316	+	10.7601i	−0.135612	+	0.506112i
$453$	12.4684	−	3.34089i	0.585815	−	0.156969i
$454$	−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	−0.509458	−	0.860496i	$-0.670154\pi$
$457$	7.50433	−	7.50433i	0.351038	−	0.351038i	0.860496	+	0.509458i	$0.170154\pi$
$458$	−1.19822	−	4.47181i	−0.0559891	−	0.208954i
$459$	1.20684	−	2.09030i	0.0563303	−	0.0975670i
$460$	0.339217	+	5.33994i	0.0158161	+	0.248976i
$461$	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	$-0.0803788\pi$
$462$	−9.45668	−	2.53391i	−0.439964	−	0.117888i
$463$	−14.0645	−	14.0645i	−0.653631	−	0.653631i	0.300234	−	0.953865i	$-0.402935\pi$
$463$	−14.0645	−	14.0645i	−0.653631	−	0.653631i	−0.953865	+	0.300234i	$0.902935\pi$
$464$	0.277415			0.0128787
$465$	2.69730	−	0.171345i	0.125084	−	0.00794592i
$466$	−3.44985	+	1.99177i	−0.159811	+	0.0922671i
$467$	7.41931	−	7.41931i	0.343325	−	0.343325i	−0.514291	−	0.857616i	$-0.671945\pi$
$467$	7.41931	−	7.41931i	0.343325	−	0.343325i	0.857616	+	0.514291i	$0.171945\pi$
$468$	4.49289	−	4.49289i	0.207684	−	0.207684i
$469$	14.5112	+	25.1341i	0.670064	+	1.16059i
$470$	11.5823	+	2.32808i	0.534250	+	0.107386i
$471$	2.28603	−	1.31984i	0.105334	−	0.0608149i
$472$	−2.94846	−	11.0038i	−0.135714	−	0.506491i
$473$	22.6121	−	6.05890i	1.03971	−	0.278588i
$474$	−0.156991			−0.00721082
$475$	19.9744	+	8.71913i	0.916489	+	0.400061i
$476$	4.94425			0.226619
$477$	−0.0540807	+	0.0144909i	−0.00247618	+	0.000663491i
$478$	0.973940	+	3.63479i	0.0445470	+	0.166252i
$479$	16.3256	−	9.42561i	0.745937	−	0.430667i	−0.0782869	−	0.996931i	$-0.524945\pi$
$479$	16.3256	−	9.42561i	0.745937	−	0.430667i	0.824224	+	0.566264i	$0.191612\pi$
$480$	2.19222	+	0.440644i	0.100061	+	0.0201126i
$481$	−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
$485$	−35.4619	+	2.25270i	−1.61024	+	0.102290i
$486$	−1.00000			−0.0453609
$487$	23.7218	+	23.7218i	1.07494	+	1.07494i	0.996955	+	0.0779809i	$0.0248473\pi$
$487$	23.7218	+	23.7218i	1.07494	+	1.07494i	0.0779809	+	0.996955i	$0.475153\pi$
$488$	3.46111	+	0.927403i	0.156677	+	0.0419815i
$489$	−9.67530	+	16.7581i	−0.437532	+	0.757828i
$490$	−0.397482	−	6.25715i	−0.0179564	−	0.282669i
$491$	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	$0.0440420\pi$
$492$	2.56180	+	9.56078i	0.115495	+	0.431033i
$493$	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
$497$	−20.3282	+	5.44692i	−0.911843	+	0.244328i
$498$	−3.50623	+	13.0854i	−0.157118	+	0.586372i
$499$	−23.3473	−	13.4796i	−1.04517	−	0.603429i	−0.123876	−	0.992298i	$-0.539533\pi$
$499$	−23.3473	−	13.4796i	−1.04517	−	0.603429i	−0.921293	+	0.388869i	$0.872866\pi$
$500$	−11.1518	−	0.798511i	−0.498723	−	0.0357105i
$501$	−0.946387			−0.0422815
$502$	9.72019	+	9.72019i	0.433833	+	0.433833i
$503$	−0.573747	+	2.14125i	−0.0255821	+	0.0954737i	−0.977537	−	0.210766i	$-0.932404\pi$
$503$	−0.573747	+	2.14125i	−0.0255821	+	0.0954737i	0.951954	+	0.306240i	$0.0990709\pi$
$504$	−1.02422	−	1.77400i	−0.0456222	−	0.0790200i
$505$	3.25235	+	9.64477i	0.144727	+	0.429187i
$506$			11.4367i			0.508421i
$507$	7.08444	−	26.4395i	0.314631	−	1.17422i
$508$	−2.39869	−	8.95204i	−0.106425	−	0.397183i
$509$	−12.1764	−	21.0902i	−0.539710	−	0.934805i	−0.998919	−	0.0464769i	$-0.985201\pi$
$509$	−12.1764	−	21.0902i	−0.539710	−	0.934805i	0.459210	−	0.888328i	$-0.348133\pi$
$510$	4.49358	−	2.98946i	0.198979	−	0.132376i
$511$	5.22657	−	9.05269i	0.231210	−	0.400468i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	3.03606	+	3.12768i	0.134045	+	0.138090i
$514$		−	8.39963i		−	0.370492i
$515$	28.0407	−	18.6548i	1.23562	−	0.822027i
$516$	4.24185	+	2.44903i	0.186737	+	0.107813i
$517$	24.3908	+	6.53549i	1.07271	+	0.287431i
$518$	−6.66744	+	1.78653i	−0.292950	+	0.0784958i
$519$	−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	$-0.0621661\pi$
$522$	−0.267962	−	0.0718003i	−0.0117284	−	0.00314261i
$523$	−23.1231	−	6.19582i	−1.01110	−	0.270924i	−0.285013	−	0.958524i	$-0.591998\pi$
$523$	−23.1231	−	6.19582i	−1.01110	−	0.270924i	−0.726090	+	0.687600i	$0.758664\pi$
$524$		−	6.87684i		−	0.300416i
$525$	6.20231	+	8.15066i	0.270691	+	0.355724i
$526$	27.3588	−	15.7956i	1.19290	−	0.688721i
$527$	−2.81800	+	0.755082i	−0.122754	+	0.0328919i
$528$	4.61654	+	1.23700i	0.200909	+	0.0538335i
$529$	14.9597	+	8.63700i	0.650422	+	0.375522i
$530$	−0.122739	−	0.0246710i	−0.00533144	−	0.00107164i
$531$			11.3920i			0.494370i
$532$	−2.43890	+	8.58937i	−0.105740	+	0.372396i
$533$	44.4709	+	44.4709i	1.92625	+	1.92625i
$534$	3.92888	−	6.80502i	0.170019	−	0.294482i
$535$	9.90847	+	14.8938i	0.428381	+	0.643916i
$536$	−7.08404	−	12.2699i	−0.305984	−	0.529980i
$537$	−5.20071	−	19.4093i	−0.224427	−	0.837574i
$538$	−8.10202	+	30.2371i	−0.349303	+	1.30362i
$539$		−	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	$-0.397603\pi$
$542$	0.772539	−	2.88315i	0.0331834	−	0.123842i
$543$	8.67865	+	8.67865i	0.372437	+	0.372437i
$544$	−2.41367			−0.103485
$545$	14.7546	−	16.7563i	0.632018	−	0.717762i
$546$	−11.2718	−	6.50778i	−0.482389	−	0.278507i
$547$	−5.04432	+	18.8257i	−0.215680	+	0.804927i	0.770247	+	0.637746i	$0.220133\pi$
$547$	−5.04432	+	18.8257i	−0.215680	+	0.804927i	−0.985926	+	0.167181i	$0.946534\pi$
$548$	−5.11017	+	1.36927i	−0.218296	+	0.0584921i
$549$	−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
$553$	0.0832322	+	0.310627i	0.00353940	+	0.0132092i
$554$	−13.2503	+	22.9502i	−0.562951	+	0.975060i
$555$	−4.97950	+	5.65505i	−0.211368	+	0.240043i
$556$	3.51026	−	6.07995i	0.148868	−	0.257847i
$557$	26.1952	+	7.01900i	1.10993	+	0.297404i	0.766801	−	0.641885i	$-0.221847\pi$
$557$	26.1952	+	7.01900i	1.10993	+	0.297404i	0.343127	+	0.939289i	$0.388514\pi$
$558$	0.854682	+	0.854682i	0.0361816	+	0.0361816i
$559$	31.1219			1.31631
$560$	−0.290384	−	4.57122i	−0.0122710	−	0.193169i
$561$	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	$-0.666509\pi$
$563$	8.70101	−	8.70101i	0.366704	−	0.366704i	0.866274	+	0.499570i	$0.166509\pi$
$564$	2.64167	+	4.57551i	0.111235	+	0.192664i
$565$	20.7389	−	13.7971i	0.872492	−	0.580446i
$566$	13.5886	−	7.84539i	0.571172	−	0.329766i
$567$	0.530173	+	1.97863i	0.0222652	+	0.0830948i
$568$	9.92377	−	2.65906i	0.416392	−	0.111572i
$569$	43.0899			1.80642			0.903210	−	0.429198i	$-0.141204\pi$
$569$	43.0899			1.80642			0.903210	+	0.429198i	$0.141204\pi$
$570$	2.97683	+	9.28108i	0.124686	+	0.388742i
$571$	24.8314			1.03916			0.519581	−	0.854421i	$-0.326088\pi$
$571$	24.8314			1.03916			0.519581	+	0.854421i	$0.326088\pi$
$572$	29.3331	−	7.85978i	1.22648	−	0.328634i
$573$	0.342143	+	1.27690i	0.0142932	+	0.0533431i
$574$	17.5591	−	10.1377i	0.732902	−	0.423141i
$575$	7.32166	−	9.46274i	0.305334	−	0.394624i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	32.5940	−	32.5940i	1.35691	−	1.35691i	0.479200	−	0.877706i	$-0.340927\pi$
$577$	32.5940	−	32.5940i	1.35691	−	1.35691i	0.877706	−	0.479200i	$-0.159073\pi$
$578$	7.90134	−	7.90134i	0.328652	−	0.328652i
$579$	21.0546	−	12.1559i	0.874999	−	0.505181i
$580$	−0.465557	−	0.409941i	−0.0193312	−	0.0170219i
$581$	27.7502			1.15127
$582$	−11.2366	−	11.2366i	−0.465773	−	0.465773i
$583$	−0.258473	−	0.0692576i	−0.0107049	−	0.00286836i
$584$	−2.55150	+	4.41933i	−0.105582	+	0.182873i
$585$	−14.1792	+	0.900725i	−0.586238	+	0.0372404i
$586$	−14.8100	+	25.6516i	−0.611794	+	1.05966i
$587$	2.71390	+	10.1284i	0.112014	+	0.418044i	0.999046	−	0.0436647i	$-0.0139033\pi$
$587$	2.71390	+	10.1284i	0.112014	+	0.418044i	−0.887032	+	0.461708i	$0.847237\pi$
$588$	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
$592$	3.25490	−	0.872147i	0.133775	−	0.0358450i
$593$	−4.19280	+	15.6477i	−0.172178	+	0.642575i	0.824838	+	0.565370i	$0.191267\pi$
$593$	−4.19280	+	15.6477i	−0.172178	+	0.642575i	−0.997015	+	0.0772058i	$0.975400\pi$
$594$	−4.13908	−	2.38970i	−0.169828	−	0.0980505i
$595$	−8.29742	−	7.30621i	−0.340161	−	0.299525i
$596$	−14.7976			−0.606135
$597$	7.97051	+	7.97051i	0.326211	+	0.326211i
$598$	−3.93517	+	14.6862i	−0.160921	+	0.600565i
$599$	7.30723	+	12.6565i	0.298565	+	0.517130i	0.975808	−	0.218630i	$-0.0701586\pi$
$599$	7.30723	+	12.6565i	0.298565	+	0.517130i	−0.677243	+	0.735760i	$0.736825\pi$
$600$	−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	$0.985337\pi$
$602$	2.59682	−	9.69148i	0.105839	−	0.394995i
$603$	3.66697	+	13.6853i	0.149331	+	0.557309i
$604$	6.45410	+	11.1788i	0.262614	+	0.454860i
$605$	−25.9616	−	5.21838i	−1.05549	−	0.212157i
$606$	−2.27595	+	3.94207i	−0.0924543	+	0.160136i
$607$	−18.6048	−	18.6048i	−0.755144	−	0.755144i	0.220290	−	0.975434i	$-0.429300\pi$
$607$	−18.6048	−	18.6048i	−0.755144	−	0.755144i	−0.975434	+	0.220290i	$0.929300\pi$
$608$	1.19062	−	4.19314i	0.0482859	−	0.170054i
$609$			0.568266i			0.0230273i
$610$	−4.43799	−	6.67092i	−0.179689	−	0.270098i
$611$	29.0724	+	16.7850i	1.17614	+	0.679047i
$612$	2.33143	+	0.624705i	0.0942425	+	0.0252522i
$613$	16.5349	−	4.43051i	0.667839	−	0.178947i	0.0910575	−	0.995846i	$-0.470975\pi$
$613$	16.5349	−	4.43051i	0.667839	−	0.178947i	0.576781	+	0.816899i	$0.304309\pi$
$614$	24.1725	−	13.9560i	0.975523	−	0.563218i
$615$	9.82894	−	19.8305i	0.396341	−	0.799643i
$616$		−	9.79027i		−	0.394461i
$617$	19.3830	+	5.19367i	0.780332	+	0.209089i	0.626931	−	0.779075i	$-0.284311\pi$
$617$	19.3830	+	5.19367i	0.780332	+	0.209089i	0.153401	+	0.988164i	$0.450977\pi$
$618$	14.5485	+	3.89827i	0.585228	+	0.156811i
$619$		−	24.5228i		−	0.985656i	−0.870127	−	0.492828i	$-0.835963\pi$
$619$		−	24.5228i		−	0.985656i	0.870127	−	0.492828i	$-0.164037\pi$
$620$	0.863620	+	2.56105i	0.0346838	+	0.102854i
$621$	2.07232	−	1.19645i	0.0831593	−	0.0480120i
$622$	0.847352	−	0.227047i	0.0339757	−	0.00910377i
$623$	−15.5476	−	4.16598i	−0.622903	−	0.166906i
$624$	5.50265	+	3.17696i	0.220282	+	0.127180i
$625$	17.5349	+	17.8193i	0.701397	+	0.712771i
$626$		−	21.5393i		−	0.860882i
$627$	5.09228	+	20.2010i	0.203366	+	0.806748i
$628$	1.86653	+	1.86653i	0.0744827	+	0.0744827i
$629$	4.06670	−	7.04373i	0.162150	−	0.280852i
$630$	−0.902630	+	4.49062i	−0.0359616	+	0.178910i
$631$	−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	$-0.351821\pi$
$632$	−0.0406322	−	0.151641i	−0.00161626	−	0.00603197i
$633$	−0.531146	+	1.98226i	−0.0211112	+	0.0787879i
$634$		−	5.08544i		−	0.201969i
$635$	−9.20313	+	18.5679i	−0.365215	+	0.736844i
$636$	−0.0279942	−	0.0484874i	−0.00111004	−	0.00192265i
$637$	4.61109	−	17.2088i	0.182698	−	0.681838i
$638$	−0.937536	−	0.937536i	−0.0371174	−	0.0371174i
$639$	−10.2738			−0.406427
$640$	0.141759	+	2.23157i	0.00560352	+	0.0882105i
$641$	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	$0.566329\pi$
$642$	−2.07056	+	7.72745i	−0.0817186	+	0.304978i
$643$	8.38212	−	2.24598i	0.330558	−	0.0885728i	−0.0897228	−	0.995967i	$-0.528598\pi$
$643$	8.38212	−	2.24598i	0.330558	−	0.0885728i	0.420281	+	0.907394i	$0.361931\pi$
$644$	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	−0.916654	−	0.399682i	$-0.869120\pi$
$647$	−13.1498	+	13.1498i	−0.516971	+	0.516971i	0.399682	+	0.916654i	$0.369120\pi$
$648$	−0.258819	−	0.965926i	−0.0101674	−	0.0379452i
$649$	−27.2234	+	47.1523i	−1.06861	+	1.85089i
$650$	−29.3021	−	12.2756i	−1.14932	−	0.481489i
$651$	1.23797	−	2.14423i	0.0485200	−	0.0840391i
$652$	−18.6913	−	5.00831i	−0.732006	−	0.196140i
$653$	−10.3380	−	10.3380i	−0.404558	−	0.404558i	0.475278	−	0.879836i	$-0.342348\pi$
$653$	−10.3380	−	10.3380i	−0.404558	−	0.404558i	−0.879836	+	0.475278i	$0.842348\pi$
$654$	9.98471			0.390433
$655$	−10.1620	+	11.5407i	−0.397064	+	0.450933i
$656$	−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	0.573927	−	0.818906i	$-0.305419\pi$
$659$	−10.8391	−	18.7738i	−0.422230	−	0.731324i	−0.996157	+	0.0875825i	$0.972086\pi$
$660$	−5.91953	−	8.89788i	−0.230417	−	0.346350i
$661$	−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	$0.398952\pi$
$662$	−5.69084	−	21.2385i	−0.221181	−	0.825457i
$663$	14.8137	−	3.96932i	0.575316	−	0.154156i
$664$	−13.5470			−0.525727
$665$	16.7856	−	10.8106i	0.650919	−	0.419219i
$666$	−3.36972			−0.130574
$667$	0.641209	−	0.171811i	0.0248277	−	0.00665257i
$668$	−0.244943	−	0.914140i	−0.00947713	−	0.0353691i
$669$	−20.9464	+	12.0934i	−0.809835	+	0.467559i
$670$	−6.24308	+	31.0596i	−0.241191	+	1.19994i
$671$	−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	$-0.790415\pi$
$673$	−4.64564	+	4.64564i	−0.179076	+	0.179076i	0.611877	+	0.790953i	$0.290415\pi$
$674$	−28.3075	+	16.3433i	−1.09036	+	0.629522i
$675$	1.89483	+	4.62705i	0.0729319	+	0.178095i
$676$	27.3722			1.05278
$677$	13.2614	+	13.2614i	0.509675	+	0.509675i	0.914427	−	0.404751i	$-0.132642\pi$
$677$	13.2614	+	13.2614i	0.509675	+	0.509675i	−0.404751	+	0.914427i	$0.632642\pi$
$678$	10.7601	+	2.88316i	0.413239	+	0.110727i
$679$	−16.2758	+	28.1906i	−0.624609	+	1.08185i
$680$	4.05062	+	3.56673i	0.155334	+	0.136778i
$681$	−13.1687	+	22.8089i	−0.504626	+	0.874037i
$682$	1.49516	+	5.58003i	0.0572528	+	0.213670i
$683$	−20.6154	+	20.6154i	−0.788826	+	0.788826i	−0.981302	−	0.192476i	$-0.938348\pi$
$683$	−20.6154	+	20.6154i	−0.788826	+	0.788826i	0.192476	+	0.981302i	$0.438348\pi$
$684$	−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
$687$	−4.47181	+	1.19822i	−0.170610	+	0.0457149i
$688$	−1.26771	+	4.73117i	−0.0483311	+	0.180374i
$689$	−0.308085	−	0.177873i	−0.0117371	−	0.00677641i
$690$	5.33994	−	0.339217i	0.203288	−	0.0129138i
$691$	−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
$693$	−2.53391	+	9.45668i	−0.0962552	+	0.359229i
$694$	11.8883	+	20.5911i	0.451272	+	0.781627i
$695$	−14.8754	+	5.01618i	−0.564255	+	0.190274i
$696$		−	0.277415i		−	0.0105154i
$697$	−6.18335	+	23.0766i	−0.234211	+	0.874088i
$698$	−6.82128	−	25.4574i	−0.258189	−	0.963575i
$699$	1.99177	+	3.44985i	0.0753358	+	0.130485i
$700$	−6.26766	+	8.10052i	−0.236895	+	0.306171i
$701$	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
$703$	10.2307	+	10.5394i	0.385856	+	0.397500i
$704$			4.77940i			0.180130i
$705$	2.32808	−	11.5823i	0.0876804	−	0.436213i
$706$	10.7300	+	6.19497i	0.403829	+	0.233151i
$707$	9.00656	+	2.41330i	0.338727	+	0.0907615i
$708$	−11.0038	+	2.94846i	−0.413549	+	0.110810i
$709$	−6.31333	+	3.64500i	−0.237102	+	0.136891i	−0.613844	−	0.789427i	$-0.710378\pi$
$709$	−6.31333	+	3.64500i	−0.237102	+	0.136891i	0.376742	+	0.926318i	$0.377044\pi$
$710$	−20.5834	−	10.2021i	−0.772481	−	0.382878i
$711$			0.156991i			0.00588761i
$712$	7.59002	+	2.03374i	0.284448	+	0.0762176i
$713$	−2.79376	−	0.748586i	−0.104627	−	0.0280348i
$714$		−	4.94425i		−	0.185034i
$715$	−60.8413	−	30.1558i	−2.27533	−	1.12776i
$716$	17.4019	−	10.0470i	0.650340	−	0.375474i
$717$	3.63479	−	0.973940i	0.135744	−	0.0363724i
$718$	19.7935	+	5.30366i	0.738688	+	0.197931i
$719$	−20.5521	−	11.8657i	−0.766462	−	0.442517i	0.0651489	−	0.997876i	$-0.479248\pi$
$719$	−20.5521	−	11.8657i	−0.766462	−	0.442517i	−0.831611	+	0.555358i	$0.812581\pi$
$720$	0.440644	−	2.19222i	0.0164218	−	0.0816993i
$721$		−	30.8530i		−	1.14903i
$722$	18.4906	−	4.36992i	0.688150	−	0.162632i
$723$	−2.46100	−	2.46100i	−0.0915255	−	0.0915255i
$724$	−6.13673	+	10.6291i	−0.228070	+	0.395029i
$725$	0.175518	+	1.37593i	0.00651857	+	0.0511006i
$726$	−5.92131	−	10.2560i	−0.219760	−	0.380636i
$727$	−1.56625	−	5.84531i	−0.0580889	−	0.216791i	0.930780	−	0.365580i	$-0.119129\pi$
$727$	−1.56625	−	5.84531i	−0.0580889	−	0.216791i	−0.988869	+	0.148789i	$0.952463\pi$
$728$	3.36867	−	12.5721i	0.124851	−	0.465952i
$729$			1.00000i			0.0370370i
$730$	10.8124	−	3.64610i	0.400186	−	0.134948i
$731$	5.91116	+	10.2384i	0.218632	+	0.378682i
$732$	0.927403	−	3.46111i	0.0342778	−	0.127926i
$733$	−22.5054	−	22.5054i	−0.831254	−	0.831254i	0.156434	−	0.987688i	$-0.450000\pi$
$733$	−22.5054	−	22.5054i	−0.831254	−	0.831254i	−0.987688	+	0.156434i	$0.950000\pi$
$734$	1.39714			0.0515694
$735$	−6.25715	+	0.397482i	−0.230798	+	0.0146613i
$736$	−2.07232	−	1.19645i	−0.0763867	−	0.0441019i
$737$	−17.5259	+	65.4076i	−0.645575	+	2.40932i
$738$	9.56078	−	2.56180i	0.351937	−	0.0943012i
$739$	−36.3104	−	20.9638i	−1.33570	−	0.771166i	−0.349532	−	0.936925i	$-0.613659\pi$
$739$	−36.3104	−	20.9638i	−1.33570	−	0.771166i	−0.986166	+	0.165759i	$0.946993\pi$
$740$	−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
$743$	−7.38331	−	27.5549i	−0.270867	−	1.01089i	−0.958560	−	0.284889i	$-0.908043\pi$
$743$	−7.38331	−	27.5549i	−0.270867	−	1.01089i	0.687693	−	0.726002i	$-0.258624\pi$
$744$	−0.604351	+	1.04677i	−0.0221566	+	0.0383763i
$745$	24.8334	+	21.8668i	0.909824	+	0.801136i
$746$	6.36171	−	11.0188i	0.232919	−	0.403427i
$747$	13.0854	+	3.50623i	0.478771	+	0.128286i
$748$	8.15711	+	8.15711i	0.298254	+	0.298254i
$749$	16.3876			0.598788
$750$	−0.798511	+	11.1518i	−0.0291575	+	0.407206i
$751$	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
$755$	5.68792	−	28.2976i	0.207005	−	1.02986i
$756$	−1.77400	+	1.02422i	−0.0645196	+	0.0372504i
$757$	13.2277	+	49.3664i	0.480768	+	1.79425i	0.598403	+	0.801195i	$0.295802\pi$
$757$	13.2277	+	49.3664i	0.480768	+	1.79425i	−0.117635	+	0.993057i	$0.537531\pi$
$758$	−26.9698	+	7.22653i	−0.979586	+	0.262479i
$759$	11.4367			0.415124
$760$	−8.19438	+	5.27752i	−0.297241	+	0.191436i
$761$	−46.7132			−1.69335			−0.846677	−	0.532108i	$-0.821400\pi$
$761$	−46.7132			−1.69335			−0.846677	+	0.532108i	$0.821400\pi$
$762$	−8.95204	+	2.39869i	−0.324298	+	0.0868954i
$763$	−5.29363	−	19.7561i	−0.191642	−	0.715219i
$764$	−1.14483	+	0.660970i	−0.0414186	+	0.0239131i
$765$	−2.98946	−	4.49358i	−0.108084	−	0.162466i
$766$	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	−0.405041	−	0.914298i	$-0.632743\pi$
$769$	5.10923	−	2.94981i	0.184243	−	0.106373i	0.589285	+	0.807925i	$0.299410\pi$
$770$	−14.4673	+	16.4300i	−0.521364	+	0.592096i
$771$	−8.39963			−0.302505
$772$	17.1910	+	17.1910i	0.618718	+	0.618718i
$773$	8.98173	+	2.40665i	0.323050	+	0.0865611i	0.416700	−	0.909044i	$-0.363187\pi$
$773$	8.98173	+	2.40665i	0.323050	+	0.0865611i	−0.0936494	+	0.995605i	$0.529853\pi$
$774$	2.44903	−	4.24185i	0.0880286	−	0.152470i
$775$	2.33519	−	5.57413i	0.0838824	−	0.200229i
$776$	7.94550	−	13.7620i	0.285227	−	0.494027i
$777$	1.78653	+	6.66744i	0.0640916	+	0.239193i
$778$	−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
$782$	−5.57890	+	1.49486i	−0.199501	+	0.0534561i
$783$	−0.0718003	+	0.267962i	−0.00256593	+	0.00957619i
$784$	2.42827	+	1.40196i	0.0867239	+	0.0500700i
$785$	−0.374198	−	5.89062i	−0.0133557	−	0.210245i
$786$	−6.87684			−0.245289
$787$	0.777955	+	0.777955i	0.0277311	+	0.0277311i	0.720836	−	0.693105i	$-0.243758\pi$
$787$	0.777955	+	0.777955i	0.0277311	+	0.0277311i	−0.693105	+	0.720836i	$0.743758\pi$
$788$	−3.19451	+	11.9221i	−0.113800	+	0.424707i
$789$	−15.7956	−	27.3588i	−0.562339	−	0.973999i
$790$	−0.155894	+	0.314527i	−0.00554648	+	0.0111904i
$791$		−	22.8189i		−	0.811345i
$792$	1.23700	−	4.61654i	0.0439548	−	0.164042i
$793$	−5.89263	−	21.9916i	−0.209254	−	0.780945i
$794$	2.17392	+	3.76534i	0.0771496	+	0.133627i
$795$	−0.0246710	+	0.122739i	−0.000874989	+	0.00435310i
$796$	−5.63600	+	9.76184i	−0.199763	+	0.345999i
$797$	18.2358	+	18.2358i	0.645944	+	0.645944i	0.952010	−	0.306066i	$-0.0990128\pi$
$797$	18.2358	+	18.2358i	0.645944	+	0.645944i	−0.306066	+	0.952010i	$0.599013\pi$
$798$	8.58937	+	2.43890i	0.304060	+	0.0863361i
$799$			12.7523i			0.451143i
$800$	3.05973	−	3.95449i	0.108178	−	0.139812i
$801$	−6.80502	−	3.92888i	−0.240444	−	0.138820i
$802$	15.6228	+	4.18612i	0.551661	+	0.147817i
$803$	23.5582	−	6.31240i	0.831351	−	0.222760i
$804$	−12.2699	+	7.08404i	−0.432727	+	0.249835i
$805$	−3.50228	−	10.3859i	−0.123439	−	0.366057i
$806$			7.67999i			0.270516i
$807$	30.2371	+	8.10202i	1.06440	+	0.285205i
$808$	−4.39680	−	1.17812i	−0.154679	−	0.0414461i
$809$		−	54.6709i		−	1.92213i	−0.276328	−	0.961063i	$-0.589118\pi$
$809$		−	54.6709i		−	1.92213i	0.276328	−	0.961063i	$-0.410882\pi$
$810$	−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	$0.374534\pi$
$812$	−0.548903	+	0.147078i	−0.0192627	+	0.00516143i
$813$	−2.88315	−	0.772539i	−0.101117	−	0.0270941i
$814$	−13.9475	−	8.05260i	−0.488860	−	0.282244i
$815$	23.9667	+	36.0253i	0.839518	+	1.26191i
$816$			2.41367i			0.0844955i
$817$	−20.7025	+	5.21872i	−0.724290	+	0.182580i
$818$	−27.0974	−	27.0974i	−0.947440	−	0.947440i
$819$	−6.50778	+	11.2718i	−0.227400	+	0.393869i
$820$	21.6987	+	4.36151i	0.757751	+	0.152311i
$821$	−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	$-0.419009\pi$
$822$	1.36927	+	5.11017i	0.0477586	+	0.178238i
$823$	−2.55319	+	9.52863i	−0.0889986	+	0.332147i	−0.996041	−	0.0888913i	$-0.971668\pi$
$823$	−2.55319	+	9.52863i	−0.0889986	+	0.332147i	0.907043	+	0.421039i	$0.138334\pi$
$824$			15.0618i			0.524701i
$825$	−3.21443	+	23.6798i	−0.111912	+	0.824425i
$826$	11.6679	+	20.2093i	0.405977	+	0.703172i
$827$	−2.90165	+	10.8291i	−0.100900	+	0.376565i	−0.997848	−	0.0655719i	$-0.979113\pi$
$827$	−2.90165	+	10.8291i	−0.100900	+	0.376565i	0.896948	+	0.442137i	$0.145779\pi$
$828$	1.69204	+	1.69204i	0.0588025	+	0.0588025i
$829$	−32.8630			−1.14138			−0.570689	−	0.821166i	$-0.693324\pi$
$829$	−32.8630			−1.14138			−0.570689	+	0.821166i	$0.693324\pi$
$830$	22.7346	+	20.0187i	0.789130	+	0.694860i
$831$	22.9502	+	13.2503i	0.796133	+	0.459648i
$832$	−1.64451	+	6.13741i	−0.0570132	+	0.212776i
$833$	6.53715	−	1.75162i	0.226499	−	0.0606902i
$834$	−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
$838$	5.29887	+	19.7756i	0.183046	+	0.683138i
$839$	10.7505	−	18.6204i	0.371148	−	0.642847i	−0.618594	−	0.785711i	$-0.712298\pi$
$839$	10.7505	−	18.6204i	0.371148	−	0.642847i	0.989742	+	0.142863i	$0.0456309\pi$
$840$	−4.57122	+	0.290384i	−0.157722	+	0.0100192i
$841$	14.4615	−	25.0481i	0.498673	−	0.863727i
$842$	15.3309	+	4.10790i	0.528338	+	0.141568i
$843$	12.4807	+	12.4807i	0.429857	+	0.429857i
$844$	−2.05219			−0.0706393
$845$	−45.9359	−	40.4484i	−1.58024	−	1.39147i
$846$	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
$850$	−1.52711	−	11.9714i	−0.0523794	−	0.410614i
$851$	6.98313	−	4.03171i	0.239379	−	0.138205i
$852$	−2.65906	−	9.92377i	−0.0910981	−	0.339983i
$853$	53.0752	−	14.2214i	1.81726	−	0.486933i	0.820816	−	0.571193i	$-0.193519\pi$
$853$	53.0752	−	14.2214i	1.81726	−	0.486933i	0.996444	+	0.0842602i	$0.0268527\pi$
$854$	−7.33996			−0.251168
$855$	9.28108	−	2.97683i	0.317406	−	0.101805i
$856$	−8.00004			−0.273436
$857$	8.25202	−	2.21112i	0.281883	−	0.0755304i	−0.115107	−	0.993353i	$-0.536721\pi$
$857$	8.25202	−	2.21112i	0.281883	−	0.0755304i	0.396991	+	0.917823i	$0.370055\pi$
$858$	−7.85978	−	29.3331i	−0.268328	−	1.00142i
$859$	−5.45192	+	3.14767i	−0.186017	+	0.107397i	−0.590117	−	0.807318i	$-0.700918\pi$
$859$	−5.45192	+	3.14767i	−0.186017	+	0.107397i	0.404100	+	0.914715i	$0.367585\pi$
$860$	9.11881	−	6.06651i	0.310949	−	0.206866i
$861$	−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	$-0.870622\pi$
$863$	−15.3692	+	15.3692i	−0.523175	+	0.523175i	0.395354	+	0.918529i	$0.370622\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	2.42506	+	38.1752i	0.0824544	+	1.29800i
$866$	−9.37279			−0.318500
$867$	−7.90134	−	7.90134i	−0.268344	−	0.268344i
$868$	2.39158	+	0.640822i	0.0811755	+	0.0217509i
$869$	−0.375160	+	0.649796i	−0.0127264	+	0.0220428i
$870$	−0.409941	+	0.465557i	−0.0138983	+	0.0157839i
$871$	−45.0114	+	77.9620i	−1.52515	+	2.64164i
$872$	2.58423	+	9.64449i	0.0875132	+	0.326604i
$873$	−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
$877$	−12.9452	+	3.46866i	−0.437128	+	0.117128i	−0.470670	−	0.882309i	$-0.655988\pi$
$877$	−12.9452	+	3.46866i	−0.437128	+	0.117128i	0.0335420	+	0.999437i	$0.489321\pi$
$878$	4.29947	−	16.0458i	0.145100	−	0.541521i
$879$	25.6516	+	14.8100i	0.865207	+	0.499528i
$880$	7.06261	−	8.02077i	0.238080	−	0.270380i
$881$	−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
$883$	−3.81853	+	14.2509i	−0.128504	+	0.479582i	−0.999940	−	0.0109258i	$-0.996522\pi$
$883$	−3.81853	+	14.2509i	−0.128504	+	0.479582i	0.871437	+	0.490508i	$0.163189\pi$
$884$	7.66813	+	13.2816i	0.257907	+	0.446708i
$885$	22.8236	+	11.3124i	0.767206	+	0.380264i
$886$		−	16.4922i		−	0.554065i
$887$	−10.5282	+	39.2917i	−0.353502	+	1.31929i	0.528857	+	0.848711i	$0.322621\pi$
$887$	−10.5282	+	39.2917i	−0.353502	+	1.31929i	−0.882359	+	0.470577i	$0.844046\pi$
$888$	−0.872147	−	3.25490i	−0.0292673	−	0.109227i
$889$	9.49227	+	16.4411i	0.318360	+	0.551417i
$890$	−9.73225	−	14.6289i	−0.326226	−	0.490363i
$891$	−2.38970	+	4.13908i	−0.0800579	+	0.138664i
$892$	−17.1027	−	17.1027i	−0.572640	−	0.572640i
$893$	−22.1538	−	6.29045i	−0.741349	−	0.210502i
$894$			14.7976i			0.494907i
$895$	−44.0505	−	8.85430i	−1.47245	−	0.295967i
$896$	1.77400	+	1.02422i	0.0592650	+	0.0342167i
$897$	14.6862	+	3.93517i	0.490359	+	0.131391i
$898$	8.39199	−	2.24863i	0.280044	−	0.0750377i
$899$	0.290389	−	0.167656i	0.00968501	−	0.00559164i
$900$	−3.97897	+	3.02783i	−0.132632	+	0.100928i
$901$		−	0.135138i		−	0.00450209i
$902$	45.6947	+	12.2439i	1.52147	+	0.407676i
$903$	−9.69148	−	2.59682i	−0.322512	−	0.0864169i
$904$			11.1397i			0.370500i
$905$	26.0055	−	8.76941i	0.864453	−	0.291505i
$906$	11.1788	−	6.45410i	0.371392	−	0.214423i
$907$	7.10859	−	1.90474i	0.236037	−	0.0632459i	−0.138862	−	0.990312i	$-0.544344\pi$
$907$	7.10859	−	1.90474i	0.236037	−	0.0632459i	0.374898	+	0.927066i	$0.377678\pi$
$908$	−25.4400	−	6.81662i	−0.844255	−	0.226218i
$909$	3.94207	+	2.27595i	0.130750	+	0.0754886i
$910$	−24.2313	+	16.1204i	−0.803259	+	0.534388i
$911$			9.26255i			0.306882i	0.988158	+	0.153441i	$0.0490355\pi$
$911$			9.26255i			0.306882i	−0.988158	+	0.153441i	$0.950965\pi$
$912$	−4.19314	−	1.19062i	−0.138849	−	0.0394253i
$913$	45.7828	+	45.7828i	1.51519	+	1.51519i
$914$	5.30636	−	9.19089i	0.175519	−	0.304008i
$915$	−6.67092	+	4.43799i	−0.220534	+	0.146715i
$916$	−2.31478	−	4.00932i	−0.0764825	−	0.132472i
$917$	3.64592	+	13.6068i	0.120399	+	0.449335i
$918$	0.624705	−	2.33143i	0.0206183	−	0.0769486i
$919$		−	54.6922i		−	1.80413i	−0.431600	−	0.902065i	$-0.642051\pi$
$919$		−	54.6922i		−	1.80413i	0.431600	−	0.902065i	$-0.357949\pi$
$920$	1.70974	+	5.07019i	0.0563683	+	0.167159i
$921$	−13.9560	−	24.1725i	−0.459866	−	0.796511i
$922$	7.78561	−	29.0563i	0.256406	−	0.956919i
$923$	−46.1593	−	46.1593i	−1.51935	−	1.51935i
$924$	−9.79027			−0.322076
$925$	6.38503	+	15.5919i	0.209938	+	0.512657i
$926$	−17.2254	−	9.94508i	−0.566061	−	0.326816i
$927$	3.89827	−	14.5485i	0.128036	−	0.477837i
$928$	0.267962	−	0.0718003i	0.00879629	−	0.00235696i
$929$	−22.4098	−	12.9383i	−0.735241	−	0.424491i	0.0850956	−	0.996373i	$-0.472880\pi$
$929$	−22.4098	−	12.9383i	−0.735241	−	0.424491i	−0.820336	+	0.571881i	$0.806214\pi$
$930$	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
$933$	−0.227047	−	0.847352i	−0.00743320	−	0.0277411i
$934$	5.24624	−	9.08676i	0.171662	−	0.297328i
$935$	−1.63532	−	25.7432i	−0.0534807	−	0.841892i
$936$	3.17696	−	5.50265i	0.103842	−	0.179860i
$937$	−19.7126	−	5.28196i	−0.643981	−	0.172554i	−0.0779750	−	0.996955i	$-0.524845\pi$
$937$	−19.7126	−	5.28196i	−0.643981	−	0.172554i	−0.566006	+	0.824401i	$0.691512\pi$
$938$	20.5219	+	20.5219i	0.670064	+	0.670064i
$939$	−21.5393			−0.702907
$940$	11.7902	−	0.748963i	0.384553	−	0.0244285i
$941$	−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
$945$	4.49062	+	0.902630i	0.146080	+	0.0293625i
$946$	20.2735	−	11.7049i	0.659147	−	0.380559i
$947$	−15.7060	−	58.6155i	−0.510376	−	1.90475i	−0.416419	−	0.909173i	$-0.636715\pi$
$947$	−15.7060	−	58.6155i	−0.510376	−	1.90475i	−0.0939567	−	0.995576i	$-0.529952\pi$
$948$	−0.151641	+	0.0406322i	−0.00492508	+	0.00131967i
$949$	32.4240			1.05253
$950$	21.5505	+	3.25227i	0.699190	+	0.105518i
$951$	−5.08544			−0.164907
$952$	4.77578	−	1.27967i	0.154784	−	0.0414742i
$953$	−3.56920	−	13.3204i	−0.115618	−	0.431491i	0.883715	−	0.468026i	$-0.155035\pi$
$953$	−3.56920	−	13.3204i	−0.115618	−	0.431491i	−0.999332	+	0.0365351i	$0.988368\pi$
$954$	−0.0484874	+	0.0279942i	−0.00156984	+	0.000906346i
$955$	2.89798	+	0.582505i	0.0937766	+	0.0188494i
$956$	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
$960$	2.23157	−	0.141759i	0.0720236	−	0.00457526i
$961$	29.5390			0.952872
$962$	−15.1398	−	15.1398i	−0.488126	−	0.488126i
$963$	7.72745	+	2.07056i	0.249014	+	0.0667230i
$964$	1.74019	−	3.01409i	0.0560477	−	0.0970775i
$965$	−3.44641	−	54.2534i	−0.110944	−	1.74648i
$966$	2.45086	−	4.24501i	0.0788550	−	0.136581i
$967$	−1.76886	−	6.60146i	−0.0568826	−	0.212289i	0.931635	−	0.363396i	$-0.118383\pi$
$967$	−1.76886	−	6.60146i	−0.0568826	−	0.212289i	−0.988517	+	0.151107i	$0.951716\pi$
$968$	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	$0.519871\pi$
$972$	−0.965926	+	0.258819i	−0.0309821	+	0.00830162i
$973$	−3.72210	+	13.8911i	−0.119325	+	0.445327i
$974$	29.0531	+	16.7738i	0.930922	+	0.537468i
$975$	−12.2756	+	29.3021i	−0.393134	+	0.938419i
$976$	3.58321			0.114696
$977$	−20.5134	−	20.5134i	−0.656281	−	0.656281i	0.298217	−	0.954498i	$-0.403608\pi$
$977$	−20.5134	−	20.5134i	−0.656281	−	0.656281i	−0.954498	+	0.298217i	$0.903608\pi$
$978$	−5.00831	+	18.6913i	−0.160148	+	0.597680i
$979$	−18.7777	−	32.5239i	−0.600137	−	1.03947i
$980$	−2.00341	−	5.94107i	−0.0639965	−	0.189780i
$981$		−	9.98471i		−	0.318787i
$982$	4.31022	−	16.0859i	0.137545	−	0.513323i
$983$	−0.0527027	−	0.196689i	−0.00168096	−	0.00627341i	0.965080	−	0.261954i	$-0.0843670\pi$
$983$	−0.0527027	−	0.196689i	−0.00168096	−	0.00627341i	−0.966761	+	0.255681i	$0.917700\pi$
$984$	4.94902	+	8.57196i	0.157769	+	0.273264i
$985$	22.9785	−	15.2870i	0.732157	−	0.487085i
$986$	0.334795	−	0.579881i	0.0106620	−	0.0184672i
$987$	−7.65272	−	7.65272i	−0.243589	−	0.243589i
$988$	−26.8559	+	6.76987i	−0.854400	+	0.215378i
$989$			11.7206i			0.372694i
$990$	−8.89788	+	5.91953i	−0.282793	+	0.188135i
$991$	−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	$0.674709\pi$
$992$	−1.16752	−	0.312835i	−0.0370687	−	0.00993253i
$993$	−21.2385	+	5.69084i	−0.673983	+	0.180593i
$994$	−18.2257	+	10.5226i	−0.578085	+	0.333758i
$995$	23.8836	−	8.05386i	0.757160	−	0.255325i
$996$			13.5470i			0.429254i
$997$	25.0272	+	6.70603i	0.792620	+	0.212382i	0.632341	−	0.774690i	$-0.282094\pi$
$997$	25.0272	+	6.70603i	0.792620	+	0.212382i	0.160279	+	0.987072i	$0.448761\pi$
$998$	−26.0405	−	6.97754i	−0.824299	−	0.220870i
$999$			3.36972i			0.106613i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.a.103.6	✓	40	1.1	even	1	trivial
570.2.x.a.217.9	yes	40	5.2	odd	4	inner
570.2.x.a.373.9	yes	40	19.12	odd	6	inner
570.2.x.a.487.6	yes	40	95.12	even	12	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)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.19222 - 0.440644i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.44846 + 1.44846i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.19222 - 0.440644i) 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} +(-2.23157 + 0.141759i) q^{10} -4.77940 q^{11} +(-0.707107 - 0.707107i) q^{12} +(-6.13741 - 1.64451i) q^{13} +(-1.02422 + 1.77400i) q^{14} +(0.141759 + 2.23157i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.624705 - 2.33143i) 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} +(-4.61654 + 1.23700i) q^{22} +(0.619330 - 2.31137i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(4.61167 + 1.93198i) q^{25} -6.35391 q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.530173 + 1.97863i) q^{28} +(0.138707 + 0.240248i) q^{29} +(0.714502 + 2.11884i) q^{30} -1.20870i q^{31} +(0.258819 - 0.965926i) q^{32} +(1.23700 + 4.61654i) q^{33} +(-1.20684 - 2.09030i) q^{34} +(3.81360 - 2.53709i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.38275 + 2.38275i) q^{37} +(4.22668 - 1.06547i) q^{38} +6.35391i q^{39} +(-1.86172 + 1.23855i) q^{40} +(-8.57196 - 4.94902i) q^{41} +(1.97863 + 0.530173i) q^{42} +(-4.73117 + 1.26771i) q^{43} +(-4.13908 + 2.38970i) q^{44} +(2.11884 - 0.714502i) q^{45} -2.39291i q^{46} +(-5.10332 - 1.36743i) q^{47} +(-0.965926 - 0.258819i) q^{48} +2.80392i q^{49} +(4.95456 + 0.672560i) q^{50} +(-2.09030 + 1.20684i) q^{51} +(-6.13741 + 1.64451i) q^{52} +(0.0540807 + 0.0144909i) q^{53} +(0.866025 + 0.500000i) q^{54} +(10.4775 + 2.10601i) q^{55} +2.04843i q^{56} +(-1.06547 - 4.22668i) q^{57} +(0.196162 + 0.196162i) q^{58} +(5.69599 - 9.86575i) q^{59} +(1.23855 + 1.86172i) q^{60} +(1.79160 + 3.10315i) q^{61} +(-0.312835 - 1.16752i) q^{62} +(0.530173 - 1.97863i) q^{63} -1.00000i q^{64} +(12.7299 + 6.30955i) q^{65} +(2.38970 + 4.13908i) q^{66} +(3.66697 - 13.6853i) q^{67} +(-1.70672 - 1.70672i) q^{68} -2.39291 q^{69} +(3.02701 - 3.43767i) q^{70} +(8.89740 + 5.13692i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-4.92912 + 1.32075i) 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} +(1.64451 + 6.13741i) q^{78} +(0.0784953 - 0.135958i) q^{79} +(-1.47772 + 1.67820i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-9.56078 - 2.56180i) q^{82} +(-9.57920 - 9.57920i) q^{83} +2.04843 q^{84} +(0.342160 + 5.38628i) 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} +(1.86172 - 1.23855i) q^{90} +(11.2718 - 6.50778i) q^{91} +(-0.619330 - 2.31137i) q^{92} +(-1.16752 + 0.312835i) q^{93} -5.28335 q^{94} +(-9.52607 - 2.06253i) q^{95} -1.00000 q^{96} +(15.3495 - 4.11289i) q^{97} +(0.725708 + 2.70838i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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