LMFDB - Embedded newform 504.2.cs.a.85.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.9
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.a.421.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.972917 - 1.02637i) q^{2} +(-0.120790 - 1.72783i) q^{3} +(-0.106865 + 1.99714i) q^{4} +(2.23744 + 1.29179i) q^{5} +(-1.65588 + 1.80501i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.15378 - 1.83337i) q^{8} +(-2.97082 + 0.417410i) q^{9} +O(q^{10})$	\(q+(-0.972917 - 1.02637i) q^{2} +(-0.120790 - 1.72783i) q^{3} +(-0.106865 + 1.99714i) q^{4} +(2.23744 + 1.29179i) q^{5} +(-1.65588 + 1.80501i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.15378 - 1.83337i) q^{8} +(-2.97082 + 0.417410i) q^{9} +(-0.850996 - 3.55324i) q^{10} +(-3.28096 + 1.89427i) q^{11} +(3.46364 - 0.0565904i) q^{12} +(5.33815 + 3.08198i) q^{13} +(0.402403 - 1.35576i) q^{14} +(1.96174 - 4.02197i) q^{15} +(-3.97716 - 0.426848i) q^{16} +5.86443 q^{17} +(3.31878 + 2.64305i) q^{18} +6.00877i q^{19} +(-2.81899 + 4.33045i) q^{20} +(1.43595 - 0.968524i) q^{21} +(5.13632 + 1.52452i) q^{22} +(1.48115 - 2.56543i) q^{23} +(-3.42792 - 3.49991i) q^{24} +(0.837435 + 1.45048i) q^{25} +(-2.03033 - 8.47742i) q^{26} +(1.08006 + 5.08266i) q^{27} +(-1.78301 + 0.906024i) q^{28} +(-0.798660 + 0.461107i) q^{29} +(-6.03662 + 1.89958i) q^{30} +(-1.65935 + 2.87409i) q^{31} +(3.43134 + 4.49732i) q^{32} +(3.66928 + 5.44015i) q^{33} +(-5.70561 - 6.01907i) q^{34} +2.58358i q^{35} +(-0.516151 - 5.97776i) q^{36} +1.38273i q^{37} +(6.16721 - 5.84603i) q^{38} +(4.68036 - 9.59571i) q^{39} +(7.18728 - 1.31984i) q^{40} +(5.38274 - 9.32318i) q^{41} +(-2.39113 - 0.531523i) q^{42} +(2.62402 - 1.51498i) q^{43} +(-3.43250 - 6.75499i) q^{44} +(-7.18625 - 2.90374i) q^{45} +(-4.07411 + 0.975742i) q^{46} +(-5.21940 - 9.04026i) q^{47} +(-0.257121 + 6.92343i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.673972 - 2.27071i) q^{50} +(-0.708364 - 10.1328i) q^{51} +(-6.72562 + 10.3317i) q^{52} -3.17814i q^{53} +(4.16588 - 6.05355i) q^{54} -9.78796 q^{55} +(2.66463 + 0.948538i) q^{56} +(10.3822 - 0.725798i) q^{57} +(1.25030 + 0.371101i) q^{58} +(2.44834 + 1.41355i) q^{59} +(7.82280 + 4.34767i) q^{60} +(1.28326 - 0.740888i) q^{61} +(4.56428 - 1.09314i) q^{62} +(-1.84690 - 2.36410i) q^{63} +(1.27749 - 7.89734i) q^{64} +(7.96254 + 13.7915i) q^{65} +(2.01369 - 9.05886i) q^{66} +(-6.32775 - 3.65333i) q^{67} +(-0.626700 + 11.7121i) q^{68} +(-4.61154 - 2.24930i) q^{69} +(2.65170 - 2.51361i) q^{70} +1.11085 q^{71} +(-5.63321 + 6.34562i) q^{72} -14.4052 q^{73} +(1.41919 - 1.34529i) q^{74} +(2.40504 - 1.62215i) q^{75} +(-12.0004 - 0.642125i) q^{76} +(-3.28096 - 1.89427i) q^{77} +(-14.4023 + 4.53206i) q^{78} +(2.95269 + 5.11421i) q^{79} +(-8.34727 - 6.09270i) q^{80} +(8.65154 - 2.48010i) q^{81} +(-14.8060 + 3.54601i) q^{82} +(5.77416 - 3.33371i) q^{83} +(1.78083 + 2.97130i) q^{84} +(13.1213 + 7.57561i) q^{85} +(-4.10789 - 1.21926i) q^{86} +(0.893186 + 1.32426i) q^{87} +(-3.59357 + 10.0951i) q^{88} +0.796589 q^{89} +(4.01131 + 10.2008i) q^{90} +6.16397i q^{91} +(4.96524 + 3.23222i) q^{92} +(5.16638 + 2.51993i) q^{93} +(-4.20060 + 14.1524i) q^{94} +(-7.76206 + 13.4443i) q^{95} +(7.35615 - 6.47202i) q^{96} +(6.67562 + 11.5625i) q^{97} +(1.37532 - 0.329387i) q^{98} +(8.95647 - 6.99703i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8	$ 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) $ 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8 + 20 * q^12 + 40 * q^17 - q^18 + 2 * q^20 - 12 * q^22 + 12 * q^23 + 10 * q^24 + 36 * q^25 - 42 * q^26 + 4 * q^30 + 5 * q^32 + 8 * q^33 + 6 * q^34 - 18 * q^36 - 25 * q^38 - 4 * q^39 - 9 * q^40 + 24 * q^41 - 7 * q^42 + 12 * q^46 - 53 * q^48 - 36 * q^49 + 41 * q^50 - 9 * q^52 + 12 * q^54 + 3 * q^56 + 4 * q^57 + 9 * q^58 - 50 * q^60 + 60 * q^62 - 6 * q^64 - 40 * q^65 - 2 * q^66 + 23 * q^68 - 56 * q^71 + 19 * q^72 + 22 * q^74 - 24 * q^76 - 54 * q^78 - 6 * q^80 - 4 * q^81 - 48 * q^82 + 10 * q^84 - 39 * q^86 - 76 * q^87 - 12 * q^88 - 88 * q^89 - 77 * q^90 + 11 * q^92 + 24 * q^94 - 24 * q^95 + 59 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.972917	−	1.02637i	−0.687956	−	0.725752i
$2$	−0.972917	−	1.02637i	−0.687956	−	0.725752i
$3$	−0.120790	−	1.72783i	−0.0697381	−	0.997565i
$3$	−0.120790	−	1.72783i	−0.0697381	−	0.997565i
$4$	−0.106865	+	1.99714i	−0.0534323	+	0.998571i
$5$	2.23744	+	1.29179i	1.00062	+	0.577705i	0.908430	−	0.418036i	$-0.137282\pi$
$5$	2.23744	+	1.29179i	1.00062	+	0.577705i	0.0921849	+	0.995742i	$0.470615\pi$
$6$	−1.65588	+	1.80501i	−0.676008	+	0.736894i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	2.15378	−	1.83337i	0.761474	−	0.648195i
$9$	−2.97082	+	0.417410i	−0.990273	+	0.139137i
$10$	−0.850996	−	3.55324i	−0.269109	−	1.12363i
$11$	−3.28096	+	1.89427i	−0.989248	+	0.571143i	−0.905049	−	0.425306i	$-0.860166\pi$
$11$	−3.28096	+	1.89427i	−0.989248	+	0.571143i	−0.0841987	+	0.996449i	$0.526833\pi$
$12$	3.46364	−	0.0565904i	0.999867	−	0.0163362i
$13$	5.33815	+	3.08198i	1.48054	+	0.854788i	0.999757	−	0.0220532i	$-0.00702032\pi$
$13$	5.33815	+	3.08198i	1.48054	+	0.854788i	0.480780	+	0.876841i	$0.340354\pi$
$14$	0.402403	−	1.35576i	0.107547	−	0.362341i
$15$	1.96174	−	4.02197i	0.506518	−	1.03847i
$16$	−3.97716	−	0.426848i	−0.994290	−	0.106712i
$17$	5.86443			1.42233			0.711167	−	0.703023i	$-0.248167\pi$
$17$	5.86443			1.42233			0.711167	+	0.703023i	$0.248167\pi$
$18$	3.31878	+	2.64305i	0.782243	+	0.622973i
$19$			6.00877i			1.37851i	0.724521	+	0.689253i	$0.242061\pi$
$19$			6.00877i			1.37851i	−0.724521	+	0.689253i	$0.757939\pi$
$20$	−2.81899	+	4.33045i	−0.630345	+	0.968318i
$21$	1.43595	−	0.968524i	0.313351	−	0.211349i
$22$	5.13632	+	1.52452i	1.09507	+	0.325028i
$23$	1.48115	−	2.56543i	0.308841	−	0.534928i	−0.669268	−	0.743021i	$-0.733392\pi$
$23$	1.48115	−	2.56543i	0.308841	−	0.534928i	0.978109	+	0.208093i	$0.0667256\pi$
$24$	−3.42792	−	3.49991i	−0.699721	−	0.714417i
$25$	0.837435	+	1.45048i	0.167487	+	0.290096i
$26$	−2.03033	−	8.47742i	−0.398180	−	1.66256i
$27$	1.08006	+	5.08266i	0.207858	+	0.978159i
$28$	−1.78301	+	0.906024i	−0.336957	+	0.171222i
$29$	−0.798660	+	0.461107i	−0.148307	+	0.0856254i	−0.572317	−	0.820032i	$-0.693955\pi$
$29$	−0.798660	+	0.461107i	−0.148307	+	0.0856254i	0.424010	+	0.905658i	$0.360622\pi$
$30$	−6.03662	+	1.89958i	−1.10213	+	0.346813i
$31$	−1.65935	+	2.87409i	−0.298029	+	0.516201i	−0.975685	−	0.219178i	$-0.929662\pi$
$31$	−1.65935	+	2.87409i	−0.298029	+	0.516201i	0.677656	+	0.735379i	$0.262996\pi$
$32$	3.43134	+	4.49732i	0.606582	+	0.795021i
$33$	3.66928	+	5.44015i	0.638740	+	0.947009i
$34$	−5.70561	−	6.01907i	−0.978504	−	1.03226i
$35$			2.58358i			0.436704i
$36$	−0.516151	−	5.97776i	−0.0860252	−	0.996293i
$37$			1.38273i			0.227320i	0.993520	+	0.113660i	$0.0362575\pi$
$37$			1.38273i			0.227320i	−0.993520	+	0.113660i	$0.963743\pi$
$38$	6.16721	−	5.84603i	1.00045	−	0.948352i
$39$	4.68036	−	9.59571i	0.749457	−	1.53654i
$40$	7.18728	−	1.31984i	1.13641	−	0.208686i
$41$	5.38274	−	9.32318i	0.840643	−	1.45604i	−0.0487091	−	0.998813i	$-0.515511\pi$
$41$	5.38274	−	9.32318i	0.840643	−	1.45604i	0.889352	−	0.457223i	$-0.151156\pi$
$42$	−2.39113	−	0.531523i	−0.368959	−	0.0820158i
$43$	2.62402	−	1.51498i	0.400160	−	0.231032i	−0.286393	−	0.958112i	$-0.592456\pi$
$43$	2.62402	−	1.51498i	0.400160	−	0.231032i	0.686553	+	0.727080i	$0.259123\pi$
$44$	−3.43250	−	6.75499i	−0.517469	−	1.01835i
$45$	−7.18625	−	2.90374i	−1.07126	−	0.432864i
$46$	−4.07411	+	0.975742i	−0.600694	+	0.143865i
$47$	−5.21940	−	9.04026i	−0.761327	−	1.31866i	−0.942167	−	0.335145i	$-0.891215\pi$
$47$	−5.21940	−	9.04026i	−0.761327	−	1.31866i	0.180839	−	0.983513i	$-0.442119\pi$
$48$	−0.257121	+	6.92343i	−0.0371123	+	0.999311i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.673972	−	2.27071i	0.0953141	−	0.321128i
$51$	−0.708364	−	10.1328i	−0.0991908	−	1.41887i
$52$	−6.72562	+	10.3317i	−0.932676	+	1.43275i
$53$		−	3.17814i		−	0.436552i	−0.975887	−	0.218276i	$-0.929957\pi$
$53$		−	3.17814i		−	0.436552i	0.975887	−	0.218276i	$-0.0700433\pi$
$54$	4.16588	−	6.05355i	0.566904	−	0.823784i
$55$	−9.78796			−1.31981
$56$	2.66463	+	0.948538i	0.356077	+	0.126754i
$57$	10.3822	−	0.725798i	1.37515	−	0.0961343i
$58$	1.25030	+	0.371101i	0.164172	+	0.0487280i
$59$	2.44834	+	1.41355i	0.318746	+	0.184028i	0.650834	−	0.759220i	$-0.274420\pi$
$59$	2.44834	+	1.41355i	0.318746	+	0.184028i	−0.332087	+	0.943249i	$0.607753\pi$
$60$	7.82280	+	4.34767i	1.00992	+	0.561282i
$61$	1.28326	−	0.740888i	0.164304	−	0.0948610i	−0.415593	−	0.909551i	$-0.636426\pi$
$61$	1.28326	−	0.740888i	0.164304	−	0.0948610i	0.579897	+	0.814690i	$0.303093\pi$
$62$	4.56428	−	1.09314i	0.579665	−	0.138829i
$63$	−1.84690	−	2.36410i	−0.232687	−	0.297849i
$64$	1.27749	−	7.89734i	0.159687	−	0.987168i
$65$	7.96254	+	13.7915i	0.987632	+	1.71063i
$66$	2.01369	−	9.05886i	0.247869	−	1.11507i
$67$	−6.32775	−	3.65333i	−0.773058	−	0.446325i	0.0609067	−	0.998143i	$-0.480601\pi$
$67$	−6.32775	−	3.65333i	−0.773058	−	0.446325i	−0.833964	+	0.551819i	$0.813934\pi$
$68$	−0.626700	+	11.7121i	−0.0759986	+	1.42030i
$69$	−4.61154	−	2.24930i	−0.555164	−	0.270784i
$70$	2.65170	−	2.51361i	0.316939	−	0.300433i
$71$	1.11085			0.131834			0.0659168	−	0.997825i	$-0.479003\pi$
$71$	1.11085			0.131834			0.0659168	+	0.997825i	$0.479003\pi$
$72$	−5.63321	+	6.34562i	−0.663880	+	0.747839i
$73$	−14.4052			−1.68601			−0.843003	−	0.537910i	$-0.819214\pi$
$73$	−14.4052			−1.68601			−0.843003	+	0.537910i	$0.819214\pi$
$74$	1.41919	−	1.34529i	0.164978	−	0.156386i
$75$	2.40504	−	1.62215i	0.277710	−	0.187310i
$76$	−12.0004	−	0.642125i	−1.37654	−	0.0736567i
$77$	−3.28096	−	1.89427i	−0.373901	−	0.215872i
$78$	−14.4023	+	4.53206i	−1.63074	+	0.513154i
$79$	2.95269	+	5.11421i	0.332204	+	0.575394i	0.982944	−	0.183907i	$-0.0588745\pi$
$79$	2.95269	+	5.11421i	0.332204	+	0.575394i	−0.650740	+	0.759301i	$0.725541\pi$
$80$	−8.34727	−	6.09270i	−0.933254	−	0.681184i
$81$	8.65154	−	2.48010i	0.961282	−	0.275566i
$82$	−14.8060	+	3.54601i	−1.63505	+	0.391591i
$83$	5.77416	−	3.33371i	0.633797	−	0.365923i	−0.148424	−	0.988924i	$-0.547420\pi$
$83$	5.77416	−	3.33371i	0.633797	−	0.365923i	0.782221	+	0.623001i	$0.214087\pi$
$84$	1.78083	+	2.97130i	0.194304	+	0.324196i
$85$	13.1213	+	7.57561i	1.42321	+	0.821690i
$86$	−4.10789	−	1.21926i	−0.442965	−	0.131477i
$87$	0.893186	+	1.32426i	0.0957596	+	0.141975i
$88$	−3.59357	+	10.0951i	−0.383075	+	1.07614i
$89$	0.796589			0.0844383			0.0422192	−	0.999108i	$-0.486557\pi$
$89$	0.796589			0.0844383			0.0422192	+	0.999108i	$0.486557\pi$
$90$	4.01131	+	10.2008i	0.422830	+	1.07526i
$91$			6.16397i			0.646159i
$92$	4.96524	+	3.23222i	0.517662	+	0.336982i
$93$	5.16638	+	2.51993i	0.535728	+	0.261304i
$94$	−4.20060	+	14.1524i	−0.433259	+	1.45971i
$95$	−7.76206	+	13.4443i	−0.796370	+	1.37935i
$96$	7.35615	−	6.47202i	0.750784	−	0.660548i
$97$	6.67562	+	11.5625i	0.677807	+	1.17400i	0.975640	+	0.219378i	$0.0704028\pi$
$97$	6.67562	+	11.5625i	0.677807	+	1.17400i	−0.297833	+	0.954618i	$0.596264\pi$
$98$	1.37532	−	0.329387i	0.138928	−	0.0332731i
$99$	8.95647	−	6.99703i	0.900159	−	0.703228i
$100$	−2.98631	+	1.51747i	−0.298631	+	0.151747i
$101$	−7.86466	+	4.54067i	−0.782563	+	0.451813i	−0.837338	−	0.546686i	$-0.815889\pi$
$101$	−7.86466	+	4.54067i	−0.782563	+	0.451813i	0.0547746	+	0.998499i	$0.482556\pi$
$102$	−9.71077	+	10.5854i	−0.961510	+	1.04811i
$103$	6.49109	−	11.2429i	0.639586	−	1.10780i	−0.345937	−	0.938258i	$-0.612439\pi$
$103$	6.49109	−	11.2429i	0.639586	−	1.10780i	0.985524	−	0.169538i	$-0.0542277\pi$
$104$	17.1476	−	3.14892i	1.68146	−	0.308777i
$105$	4.46399	−	0.312070i	0.435641	−	0.0304549i
$106$	−3.26195	+	3.09207i	−0.316828	+	0.300328i
$107$			6.16912i			0.596391i	0.954505	+	0.298196i	$0.0963848\pi$
$107$			6.16912i			0.596391i	−0.954505	+	0.298196i	$0.903615\pi$
$108$	−10.2662	+	1.61388i	−0.987868	+	0.155295i
$109$			5.70927i			0.546849i	0.961894	+	0.273424i	$0.0881563\pi$
$109$			5.70927i			0.546849i	−0.961894	+	0.273424i	$0.911844\pi$
$110$	9.52288	+	10.0461i	0.907971	+	0.957854i
$111$	2.38913	−	0.167020i	0.226767	−	0.0158529i
$112$	−1.61892	−	3.65775i	−0.152973	−	0.345624i
$113$	−7.93542	+	13.7446i	−0.746502	+	1.29298i	0.202988	+	0.979181i	$0.434935\pi$
$113$	−7.93542	+	13.7446i	−0.746502	+	1.29298i	−0.949490	+	0.313798i	$0.898399\pi$
$114$	−10.8459	−	9.94977i	−1.01581	−	0.931881i
$115$	6.62797	−	3.82666i	0.618062	−	0.356838i
$116$	−0.835548	−	1.64431i	−0.0775786	−	0.152671i
$117$	−17.1451	−	6.92782i	−1.58507	−	0.640477i
$118$	−0.931208	−	3.88816i	−0.0857246	−	0.357934i
$119$	2.93222	+	5.07875i	0.268796	+	0.465568i
$120$	−3.14862	−	12.2590i	−0.287429	−	1.11909i
$121$	1.67649	−	2.90376i	0.152408	−	0.263978i
$122$	−2.00893	−	0.596270i	−0.181880	−	0.0539838i
$123$	−16.7591	−	8.17434i	−1.51112	−	0.737055i
$124$	−5.56263	−	3.62111i	−0.499539	−	0.325185i
$125$		−	8.59073i		−	0.768378i
$126$	−0.629560	+	4.19567i	−0.0560857	+	0.373780i
$127$	15.6611			1.38970			0.694850	−	0.719155i	$-0.255471\pi$
$127$	15.6611			1.38970			0.694850	+	0.719155i	$0.255471\pi$
$128$	−9.34848	+	6.37228i	−0.826297	+	0.563235i
$129$	−2.93459	−	4.35088i	−0.258376	−	0.383074i
$130$	6.40829	−	21.5905i	0.562045	−	1.89361i
$131$	3.38467	+	1.95414i	0.295720	+	0.170734i	0.640519	−	0.767943i	$-0.278719\pi$
$131$	3.38467	+	1.95414i	0.295720	+	0.170734i	−0.344799	+	0.938677i	$0.612053\pi$
$132$	−11.2569	+	6.74673i	−0.979786	+	0.587227i
$133$	−5.20374	+	3.00438i	−0.451222	+	0.260513i
$134$	2.40671	+	10.0490i	0.207908	+	0.868100i
$135$	−4.14915	+	12.7674i	−0.357102	+	1.09884i
$136$	12.6307	−	10.7517i	1.08307	−	0.921950i
$137$	−6.03809	−	10.4583i	−0.515869	−	0.893511i	−0.999830	−	0.0184220i	$-0.994136\pi$
$137$	−6.03809	−	10.4583i	−0.515869	−	0.893511i	0.483961	−	0.875089i	$-0.339198\pi$
$138$	2.17803	+	6.92152i	0.185406	+	0.589199i
$139$	12.8116	+	7.39679i	1.08667	+	0.627388i	0.932687	−	0.360686i	$-0.117458\pi$
$139$	12.8116	+	7.39679i	1.08667	+	0.627388i	0.153980	+	0.988074i	$0.450791\pi$
$140$	−5.15977	−	0.276093i	−0.436080	−	0.0233341i
$141$	−14.9896	+	10.1102i	−1.26235	+	0.851434i
$142$	−1.08077	−	1.14014i	−0.0906958	−	0.0956786i
$143$	−23.3524			−1.95282
$144$	11.9936	−	0.392017i	0.999466	−	0.0326681i
$145$	−2.38261			−0.197865
$146$	14.0151	+	14.7851i	1.15990	+	1.22362i
$147$	1.55674	+	0.759310i	0.128398	+	0.0626268i
$148$	−2.76152	−	0.147765i	−0.226995	−	0.0121462i
$149$	−19.8489	−	11.4598i	−1.62609	−	0.938822i	−0.985245	−	0.171149i	$-0.945252\pi$
$149$	−19.8489	−	11.4598i	−1.62609	−	0.938822i	−0.640842	−	0.767673i	$-0.721415\pi$
$150$	−4.00483	−	0.890233i	−0.326993	−	0.0726872i
$151$	−7.42338	−	12.8577i	−0.604106	−	1.04634i	−0.992192	−	0.124719i	$-0.960197\pi$
$151$	−7.42338	−	12.8577i	−0.604106	−	1.04634i	0.388086	−	0.921623i	$-0.373136\pi$
$152$	11.0163	+	12.9415i	0.893540	+	1.04970i
$153$	−17.4222	+	2.44787i	−1.40850	+	0.197899i
$154$	1.24789	+	5.21044i	0.100558	+	0.419869i
$155$	−7.42542	+	4.28707i	−0.596424	+	0.344346i
$156$	18.6638	+	10.3728i	1.49430	+	0.830488i
$157$	8.16658	+	4.71498i	0.651764	+	0.376296i	0.789132	−	0.614224i	$-0.210531\pi$
$157$	8.16658	+	4.71498i	0.651764	+	0.376296i	−0.137368	+	0.990520i	$0.543864\pi$
$158$	2.37634	−	8.00626i	0.189052	−	0.636944i
$159$	−5.49131	+	0.383888i	−0.435489	+	0.0304443i
$160$	1.86785	+	14.4951i	0.147667	+	1.14594i
$161$	2.96230			0.233462
$162$	−10.9627	−	6.46674i	−0.861313	−	0.508075i
$163$		−	12.9469i		−	1.01408i	−0.861923	−	0.507039i	$-0.830740\pi$
$163$		−	12.9469i		−	1.01408i	0.861923	−	0.507039i	$-0.169260\pi$
$164$	18.0445	+	11.7464i	1.40904	+	0.917241i
$165$	1.18229	+	16.9120i	0.0920409	+	1.31660i
$166$	−9.03940	−	2.68299i	−0.701594	−	0.208240i
$167$	3.83453	−	6.64160i	0.296725	−	0.513942i	−0.678660	−	0.734453i	$-0.737439\pi$
$167$	3.83453	−	6.64160i	0.296725	−	0.513942i	0.975385	+	0.220510i	$0.0707723\pi$
$168$	1.31705	−	4.71862i	0.101613	−	0.364049i
$169$	12.4972	+	21.6458i	0.961326	+	1.66506i
$170$	−4.99061	−	20.8378i	−0.382762	−	1.59818i
$171$	−2.50812	−	17.8510i	−0.191801	−	1.36510i
$172$	2.74522	+	5.40245i	0.209321	+	0.411933i
$173$	−2.46639	+	1.42397i	−0.187516	+	0.108263i	−0.590819	−	0.806804i	$-0.701195\pi$
$173$	−2.46639	+	1.42397i	−0.187516	+	0.108263i	0.403303	+	0.915067i	$0.367862\pi$
$174$	0.490178	−	2.20513i	0.0371603	−	0.167170i
$175$	−0.837435	+	1.45048i	−0.0633042	+	0.109646i
$176$	13.8575	−	6.13333i	1.04455	−	0.462317i
$177$	2.14664	−	4.40106i	0.161351	−	0.330804i
$178$	−0.775015	−	0.817594i	−0.0580899	−	0.0612813i
$179$			16.4245i			1.22762i	0.789452	+	0.613812i	$0.210365\pi$
$179$			16.4245i			1.22762i	−0.789452	+	0.613812i	$0.789635\pi$
$180$	6.56714	−	14.0417i	0.489486	−	1.04660i
$181$		−	14.8341i		−	1.10261i	−0.834305	−	0.551303i	$-0.814131\pi$
$181$		−	14.8341i		−	1.10261i	0.834305	−	0.551303i	$-0.185869\pi$
$182$	6.32650	−	5.99703i	0.468951	−	0.444529i
$183$	−1.43514	−	2.12776i	−0.106088	−	0.157289i
$184$	−1.51332	−	8.24085i	−0.111563	−	0.607523i
$185$	−1.78620	+	3.09379i	−0.131324	+	0.227460i
$186$	−2.44008	−	7.75429i	−0.178915	−	0.568572i
$187$	−19.2410	+	11.1088i	−1.40704	+	0.812356i
$188$	18.6125	−	9.45780i	1.35745	−	0.689781i
$189$	−3.86169	+	3.47669i	−0.280896	+	0.252892i
$190$	21.3506	−	5.11344i	1.54894	−	0.370968i
$191$	−6.10923	−	10.5815i	−0.442048	−	0.765650i	0.555793	−	0.831321i	$-0.312415\pi$
$191$	−6.10923	−	10.5815i	−0.442048	−	0.765650i	−0.997841	+	0.0656706i	$0.979081\pi$
$192$	−13.7996	−	1.25338i	−0.995901	−	0.0904548i
$193$	1.43287	−	2.48181i	0.103140	−	0.178644i	−0.809837	−	0.586656i	$-0.800444\pi$
$193$	1.43287	−	2.48181i	0.103140	−	0.178644i	0.912977	+	0.408011i	$0.133778\pi$
$194$	5.37258	−	18.1010i	0.385729	−	1.29958i
$195$	22.8677	−	15.4238i	1.63759	−	1.10452i
$196$	−1.67614	−	1.09112i	−0.119725	−	0.0779371i
$197$			6.89250i			0.491070i	0.969388	+	0.245535i	$0.0789637\pi$
$197$			6.89250i			0.491070i	−0.969388	+	0.245535i	$0.921036\pi$
$198$	−15.8954	−	2.38511i	−1.12964	−	0.169502i
$199$	−18.1104			−1.28381			−0.641905	−	0.766784i	$-0.721856\pi$
$199$	−18.1104			−1.28381			−0.641905	+	0.766784i	$0.721856\pi$
$200$	4.46292	+	1.58868i	0.315576	+	0.112337i
$201$	−5.54801	+	11.3746i	−0.391327	+	0.802301i
$202$	12.3121	+	3.65435i	0.866274	+	0.257119i
$203$	−0.798660	−	0.461107i	−0.0560550	−	0.0323633i
$204$	20.3123	−	0.331871i	1.42214	−	0.0232356i
$205$	24.0872	−	13.9067i	1.68232	−	0.971288i
$206$	−17.8547	+	4.27616i	−1.24399	+	0.297934i
$207$	−3.32939	+	8.23966i	−0.231409	+	0.572696i
$208$	−19.9151	−	14.5361i	−1.38087	−	1.00790i
$209$	−11.3822	−	19.7146i	−0.787323	−	1.36368i
$210$	−4.66339	−	4.27808i	−0.321805	−	0.295216i
$211$	−2.14836	−	1.24036i	−0.147899	−	0.0853896i	0.424224	−	0.905557i	$-0.360547\pi$
$211$	−2.14836	−	1.24036i	−0.147899	−	0.0853896i	−0.572123	+	0.820168i	$0.693880\pi$
$212$	6.34721	+	0.339631i	0.435928	+	0.0233260i
$213$	−0.134180	−	1.91936i	−0.00919383	−	0.131513i
$214$	6.33179	−	6.00204i	0.432832	−	0.410291i
$215$	7.82814			0.533875
$216$	11.6446	+	8.96676i	0.792316	+	0.610111i
$217$	−3.31871			−0.225289
$218$	5.85981	−	5.55464i	0.396877	−	0.376208i
$219$	1.74001	+	24.8899i	0.117579	+	1.68190i
$220$	1.04599	−	19.5480i	0.0705204	−	1.31792i
$221$	31.3052	+	18.0741i	2.10582	+	1.21579i
$222$	−2.49585	−	2.28963i	−0.167511	−	0.153670i
$223$	−11.4102	−	19.7631i	−0.764084	−	1.32343i	−0.940730	−	0.339157i	$-0.889858\pi$
$223$	−11.4102	−	19.7631i	−0.764084	−	1.32343i	0.176646	−	0.984274i	$-0.443475\pi$
$224$	−2.17912	+	5.22029i	−0.145599	+	0.348795i
$225$	−3.09331	−	3.95956i	−0.206221	−	0.263971i
$226$	21.8275	−	5.22765i	1.45194	−	0.347738i
$227$	−5.80688	+	3.35260i	−0.385416	+	0.222520i	−0.680172	−	0.733053i	$-0.738095\pi$
$227$	−5.80688	+	3.35260i	−0.385416	+	0.222520i	0.294756	+	0.955573i	$0.404762\pi$
$228$	0.340038	+	20.8122i	0.0225196	+	1.37832i
$229$	6.57019	+	3.79330i	0.434170	+	0.250668i	0.701122	−	0.713042i	$-0.252683\pi$
$229$	6.57019	+	3.79330i	0.434170	+	0.250668i	−0.266951	+	0.963710i	$0.586016\pi$
$230$	−10.3760	−	3.07972i	−0.684176	−	0.203071i
$231$	−2.87667	+	5.89777i	−0.189271	+	0.388045i
$232$	−0.874754	+	2.45736i	−0.0574304	+	0.161334i
$233$	−0.0248225			−0.00162617			−0.000813087	−	1.00000i	$-0.500259\pi$
$233$	−0.0248225			−0.00162617			−0.000813087		1.00000i	$0.500259\pi$
$234$	9.57030	+	24.3374i	0.625630	+	1.59099i
$235$		−	26.9694i		−	1.75929i
$236$	−3.08470	+	4.73862i	−0.200797	+	0.308458i
$237$	8.47986	−	5.71951i	0.550826	−	0.371522i
$238$	2.35986	−	7.95074i	0.152967	−	0.515370i
$239$	5.35802	−	9.28036i	0.346581	−	0.600296i	−0.639058	−	0.769158i	$-0.720676\pi$
$239$	5.35802	−	9.28036i	0.346581	−	0.600296i	0.985640	+	0.168862i	$0.0540092\pi$
$240$	−9.51890	+	15.1586i	−0.614443	+	0.978486i
$241$	−2.74005	−	4.74591i	−0.176502	−	0.305711i	0.764178	−	0.645005i	$-0.223145\pi$
$241$	−2.74005	−	4.74591i	−0.176502	−	0.305711i	−0.940680	+	0.339295i	$0.889812\pi$
$242$	−4.61141	+	1.10443i	−0.296433	+	0.0709951i
$243$	−5.33022	−	14.6488i	−0.341934	−	0.939724i
$244$	1.34252	+	2.64202i	0.0859463	+	0.169138i
$245$	−2.23744	+	1.29179i	−0.142945	+	0.0825293i
$246$	7.91532	+	25.1540i	0.504663	+	1.60376i
$247$	−18.5189	+	32.0757i	−1.17833	+	2.04093i
$248$	1.69539	+	9.23235i	0.107658	+	0.586255i
$249$	−6.45757	−	9.57411i	−0.409232	−	0.606735i
$250$	−8.81725	+	8.35807i	−0.557652	+	0.528610i
$251$			16.3961i			1.03491i	0.855710	+	0.517455i	$0.173121\pi$
$251$			16.3961i			1.03491i	−0.855710	+	0.517455i	$0.826879\pi$
$252$	4.91881	−	3.43588i	0.309856	−	0.216440i
$253$			11.2228i			0.705569i
$254$	−15.2370	−	16.0741i	−0.956053	−	1.00858i
$255$	11.5045	−	23.5865i	0.720438	−	1.47705i
$256$	15.6356	+	3.39528i	0.977225	+	0.212205i
$257$	−13.4549	+	23.3045i	−0.839291	+	1.45370i	0.0511965	+	0.998689i	$0.483697\pi$
$257$	−13.4549	+	23.3045i	−0.839291	+	1.45370i	−0.890488	+	0.455007i	$0.849637\pi$
$258$	−1.61050	+	7.24502i	−0.100265	+	0.451055i
$259$	−1.19748	+	0.691367i	−0.0744079	+	0.0429594i
$260$	−28.3946	+	14.4285i	−1.76096	+	0.894818i
$261$	2.18021	−	1.70323i	0.134951	−	0.105428i
$262$	−1.28734	−	5.37514i	−0.0795319	−	0.332077i
$263$	5.98507	+	10.3664i	0.369055	+	0.639223i	0.989418	−	0.145092i	$-0.0463479\pi$
$263$	5.98507	+	10.3664i	0.369055	+	0.639223i	−0.620363	+	0.784315i	$0.713015\pi$
$264$	17.8766	+	4.98970i	1.10023	+	0.307095i
$265$	4.10549	−	7.11092i	0.252198	−	0.436820i
$266$	8.14642	+	2.41794i	0.499489	+	0.148254i
$267$	−0.0962199	−	1.37637i	−0.00588857	−	0.0842327i
$268$	7.97243	−	12.2470i	0.486994	−	0.748105i
$269$		−	24.4383i		−	1.49003i	−0.667049	−	0.745014i	$-0.732443\pi$
$269$		−	24.4383i		−	1.49003i	0.667049	−	0.745014i	$-0.267557\pi$
$270$	17.1408	−	8.16304i	1.04316	−	0.496787i
$271$	15.6441			0.950310			0.475155	−	0.879902i	$-0.342392\pi$
$271$	15.6441			0.950310			0.475155	+	0.879902i	$0.342392\pi$
$272$	−23.3238	−	2.50322i	−1.41421	−	0.151780i
$273$	10.6503	−	0.744545i	0.644586	−	0.0450619i
$274$	−4.85949	+	16.3723i	−0.293572	+	0.989090i
$275$	−5.49519	−	3.17265i	−0.331373	−	0.191318i
$276$	4.98499	−	8.96953i	0.300061	−	0.539902i
$277$	19.1222	−	11.0402i	1.14894	−	0.663340i	0.200311	−	0.979732i	$-0.435805\pi$
$277$	19.1222	−	11.0402i	1.14894	−	0.663340i	0.948628	+	0.316392i	$0.102472\pi$
$278$	−4.87281	−	20.3459i	−0.292252	−	1.22027i
$279$	3.72997	−	9.23102i	0.223307	−	0.552647i
$280$	4.73666	+	5.56444i	0.283069	+	0.332539i
$281$	−12.0851	−	20.9319i	−0.720934	−	1.24869i	−0.960626	−	0.277845i	$-0.910380\pi$
$281$	−12.0851	−	20.9319i	−0.720934	−	1.24869i	0.239692	−	0.970849i	$-0.422953\pi$
$282$	24.9605	+	5.54846i	1.48637	+	0.330406i
$283$	−26.3574	−	15.2174i	−1.56678	−	0.904582i	−0.996541	−	0.0831048i	$-0.973516\pi$
$283$	−26.3574	−	15.2174i	−1.56678	−	0.904582i	−0.570241	−	0.821477i	$-0.693150\pi$
$284$	−0.118711	+	2.21853i	−0.00704418	+	0.131645i
$285$	24.1671	+	11.7876i	1.43153	+	0.698238i
$286$	22.7199	+	23.9681i	1.34346	+	1.41727i
$287$	10.7655			0.635466
$288$	−12.0711	−	11.9284i	−0.711298	−	0.702891i
$289$	17.3916			1.02303
$290$	2.31808	+	2.44544i	0.136122	+	0.143601i
$291$	19.1718	−	12.9310i	1.12387	−	0.758029i
$292$	1.53941	−	28.7693i	0.0900871	−	1.68360i
$293$	−26.3329	−	15.2033i	−1.53838	−	0.888186i	−0.998934	−	0.0461684i	$-0.985299\pi$
$293$	−26.3329	−	15.2033i	−1.53838	−	0.888186i	−0.539450	−	0.842018i	$-0.681368\pi$
$294$	−0.735250	−	2.33654i	−0.0428807	−	0.136270i
$295$	3.65201	+	6.32547i	0.212628	+	0.368283i
$296$	2.53506	+	2.97810i	0.147348	+	0.173098i
$297$	−13.1716	−	14.6301i	−0.764291	−	0.848926i
$298$	7.54940	+	31.5217i	0.437325	+	1.82600i
$299$	15.8132	−	9.12975i	0.914501	−	0.527987i
$300$	2.98266	+	4.97655i	0.172204	+	0.287321i
$301$	2.62402	+	1.51498i	0.151246	+	0.0873220i
$302$	−5.97437	+	20.1286i	−0.343786	+	1.15827i
$303$	8.79549	+	13.0404i	0.505288	+	0.749149i
$304$	2.56483	−	23.8978i	0.147103	−	1.37063i
$305$	3.82828			0.219207
$306$	19.4627	+	15.5000i	1.11261	+	0.886076i
$307$			0.197326i			0.0112620i	0.999984	+	0.00563100i	$0.00179241\pi$
$307$			0.197326i			0.0112620i	−0.999984	+	0.00563100i	$0.998208\pi$
$308$	4.13374	−	6.35013i	0.235542	−	0.361832i
$309$	−20.2099	−	9.85750i	−1.14970	−	0.560774i
$310$	11.6244	+	3.45026i	0.660223	+	0.195961i
$311$	−3.59510	+	6.22690i	−0.203860	+	0.353095i	−0.949769	−	0.312952i	$-0.898682\pi$
$311$	−3.59510	+	6.22690i	−0.203860	+	0.353095i	0.745909	+	0.666048i	$0.232015\pi$
$312$	−7.51206	−	29.2478i	−0.425287	−	1.65583i
$313$	4.06910	+	7.04789i	0.229999	+	0.398370i	0.957808	−	0.287410i	$-0.0927943\pi$
$313$	4.06910	+	7.04789i	0.229999	+	0.398370i	−0.727808	+	0.685781i	$0.759461\pi$
$314$	−3.10610	−	12.9692i	−0.175287	−	0.731894i
$315$	−1.07841	−	7.67534i	−0.0607615	−	0.432457i
$316$	−10.5294	+	5.35042i	−0.592322	+	0.300985i
$317$	2.77581	−	1.60261i	0.155905	−	0.0900118i	−0.420018	−	0.907516i	$-0.637976\pi$
$317$	2.77581	−	1.60261i	0.155905	−	0.0900118i	0.575923	+	0.817504i	$0.304643\pi$
$318$	5.73660	+	5.26261i	0.321692	+	0.295113i
$319$	1.74692	−	3.02575i	0.0978086	−	0.169409i
$320$	13.0600	−	16.0196i	0.730077	−	0.895523i
$321$	10.6592	−	0.745167i	0.594939	−	0.0415912i
$322$	−2.88207	−	3.04041i	−0.160612	−	0.169435i
$323$			35.2380i			1.96070i
$324$	4.02857	+	17.5434i	0.223809	+	0.974633i
$325$			10.3238i			0.572664i
$326$	−13.2883	+	12.5962i	−0.735969	+	0.697641i
$327$	9.86467	−	0.689622i	0.545517	−	0.0381362i
$328$	−5.49965	−	29.9486i	−0.303667	−	1.65363i
$329$	5.21940	−	9.04026i	0.287755	−	0.498406i
$330$	16.2077	−	17.6674i	0.892202	−	0.972559i
$331$	−10.3987	+	6.00370i	−0.571565	+	0.329993i	−0.757774	−	0.652517i	$-0.773713\pi$
$331$	−10.3987	+	6.00370i	−0.571565	+	0.329993i	0.186209	+	0.982510i	$0.440380\pi$
$332$	6.04085	+	11.8881i	0.331535	+	0.652443i
$333$	−0.577166	−	4.10785i	−0.0316285	−	0.225109i
$334$	−10.5474	+	2.52608i	−0.577128	+	0.138221i
$335$	−9.43865	−	16.3482i	−0.515689	−	0.893199i
$336$	−6.12443	+	3.23904i	−0.334115	+	0.176704i
$337$	−5.90914	+	10.2349i	−0.321892	+	0.557533i	−0.980878	−	0.194622i	$-0.937652\pi$
$337$	−5.90914	+	10.2349i	−0.321892	+	0.557533i	0.658987	+	0.752155i	$0.270985\pi$
$338$	10.0578	−	33.8864i	0.547074	−	1.84318i
$339$	24.7068	+	12.0509i	1.34189	+	0.654514i
$340$	−16.5318	+	25.3956i	−0.896562	+	1.37727i
$341$		−	12.5730i		−	0.680868i
$342$	−15.8815	+	19.9418i	−0.858772	+	1.07833i
$343$	−1.00000			−0.0539949
$344$	2.87403	−	8.07374i	0.154957	−	0.435307i
$345$	−7.41243	−	10.9898i	−0.399072	−	0.591672i
$346$	3.86112	+	1.14602i	0.207575	+	0.0616105i
$347$	10.5125	+	6.06942i	0.564343	+	0.325824i	0.754887	−	0.655855i	$-0.227692\pi$
$347$	10.5125	+	6.06942i	0.564343	+	0.325824i	−0.190544	+	0.981679i	$0.561025\pi$
$348$	−2.74018	+	1.64230i	−0.146889	+	0.0880367i
$349$	−15.8670	+	9.16083i	−0.849342	+	0.490368i	−0.860429	−	0.509570i	$-0.829804\pi$
$349$	−15.8670	+	9.16083i	−0.849342	+	0.490368i	0.0110865	+	0.999939i	$0.496471\pi$
$350$	2.30348	−	0.551680i	0.123126	−	0.0294885i
$351$	−9.89916	+	30.4607i	−0.528378	+	1.62587i
$352$	−19.7772	−	8.25567i	−1.05413	−	0.440029i
$353$	0.920462	+	1.59429i	0.0489913	+	0.0848554i	0.889481	−	0.456972i	$-0.151066\pi$
$353$	0.920462	+	1.59429i	0.0489913	+	0.0848554i	−0.840490	+	0.541827i	$0.817733\pi$
$354$	−6.60562	+	2.07862i	−0.351084	+	0.110478i
$355$	2.48547	+	1.43498i	0.131915	+	0.0761610i
$356$	−0.0851272	+	1.59090i	−0.00451173	+	0.0843177i
$357$	8.42105	−	5.67984i	0.445689	−	0.300609i
$358$	16.8576	−	15.9797i	0.890951	−	0.844552i
$359$	15.4249			0.814095			0.407048	−	0.913407i	$-0.366558\pi$
$359$	15.4249			0.814095			0.407048	+	0.913407i	$0.366558\pi$
$360$	−20.8012	+	6.92106i	−1.09632	+	0.364772i
$361$	−17.1053			−0.900278
$362$	−15.2252	+	14.4323i	−0.800219	+	0.758545i
$363$	−5.21972	−	2.54595i	−0.273964	−	0.133628i
$364$	−12.3103	−	0.658710i	−0.645236	−	0.0345258i
$365$	−32.2309	−	18.6085i	−1.68704	−	0.974014i
$366$	−0.787598	+	3.54311i	−0.0411684	+	0.185201i
$367$	15.3951	+	26.6651i	0.803618	+	1.39191i	0.917220	+	0.398381i	$0.130428\pi$
$367$	15.3951	+	26.6651i	0.803618	+	1.39191i	−0.113602	+	0.993526i	$0.536239\pi$
$368$	−6.98581	+	9.57088i	−0.364161	+	0.498917i
$369$	−12.0996	+	29.9443i	−0.629878	+	1.55884i
$370$	4.91319	−	1.17670i	0.255425	−	0.0611737i
$371$	2.75235	−	1.58907i	0.142895	−	0.0825005i
$372$	−5.58476	+	10.0487i	−0.289556	+	0.521001i
$373$	−8.72935	−	5.03989i	−0.451989	−	0.260956i	0.256681	−	0.966496i	$-0.417371\pi$
$373$	−8.72935	−	5.03989i	−0.451989	−	0.260956i	−0.708670	+	0.705540i	$0.750704\pi$
$374$	30.1216	+	8.94042i	1.55755	+	0.462298i
$375$	−14.8433	+	1.03767i	−0.766507	+	0.0535852i
$376$	−27.8156	−	9.90159i	−1.43448	−	0.510636i
$377$	−5.68449			−0.292766
$378$	7.32547	+	0.580981i	0.376781	+	0.0298824i
$379$		−	7.97134i		−	0.409460i	−0.978818	−	0.204730i	$-0.934368\pi$
$379$		−	7.97134i		−	0.409460i	0.978818	−	0.204730i	$-0.0656317\pi$
$380$	−26.0207	−	16.9387i	−1.33483	−	0.868935i
$381$	−1.89171	−	27.0598i	−0.0969150	−	1.38632i
$382$	−4.91674	+	16.5652i	−0.251562	+	0.847551i
$383$	−5.12300	+	8.87330i	−0.261773	+	0.453404i	−0.966713	−	0.255863i	$-0.917641\pi$
$383$	−5.12300	+	8.87330i	−0.261773	+	0.453404i	0.704940	+	0.709267i	$0.250974\pi$
$384$	12.1394	+	15.3829i	0.619488	+	0.785006i
$385$	−4.89398	−	8.47663i	−0.249420	−	0.432009i
$386$	−3.94131	+	0.943938i	−0.200608	+	0.0480452i
$387$	−7.16313	+	5.59603i	−0.364123	+	0.284462i
$388$	−23.8054	+	12.0966i	−1.20854	+	0.614109i
$389$	12.6279	−	7.29074i	0.640261	−	0.369655i	−0.144454	−	0.989512i	$-0.546143\pi$
$389$	12.6279	−	7.29074i	0.640261	−	0.369655i	0.784715	+	0.619857i	$0.212809\pi$
$390$	−38.0789	−	8.46455i	−1.92820	−	0.428619i
$391$	8.68610	−	15.0448i	0.439275	−	0.760847i
$392$	0.510859	+	2.78191i	0.0258023	+	0.140508i
$393$	2.96760	−	6.08419i	0.149695	−	0.306907i
$394$	7.07424	−	6.70583i	0.356395	−	0.337835i
$395$			15.2570i			0.767664i
$396$	13.0169	+	18.6351i	0.654126	+	0.936448i
$397$		−	19.6768i		−	0.987549i	−0.869590	−	0.493774i	$-0.835617\pi$
$397$		−	19.6768i		−	0.987549i	0.869590	−	0.493774i	$-0.164383\pi$
$398$	17.6199	+	18.5879i	0.883206	+	0.931728i
$399$	5.81964	+	8.62831i	0.291346	+	0.431956i
$400$	−2.71148	−	6.12625i	−0.135574	−	0.306313i
$401$	14.3891	−	24.9226i	0.718555	−	1.24457i	−0.243017	−	0.970022i	$-0.578137\pi$
$401$	14.3891	−	24.9226i	0.718555	−	1.24457i	0.961572	−	0.274552i	$-0.0885296\pi$
$402$	17.0723	−	5.37222i	0.851488	−	0.267942i
$403$	−17.7158	+	10.2282i	−0.882485	+	0.509503i
$404$	−8.22790	−	16.1921i	−0.409354	−	0.805587i
$405$	22.5611	+	5.62688i	1.12107	+	0.279602i
$406$	0.303765	+	1.26834i	0.0150756	+	0.0629466i
$407$	−2.61926	−	4.53670i	−0.129832	−	0.224876i
$408$	−20.1028	−	20.5250i	−0.995236	−	1.01614i
$409$	17.8856	−	30.9787i	0.884384	−	1.53180i	0.0379655	−	0.999279i	$-0.487912\pi$
$409$	17.8856	−	30.9787i	0.884384	−	1.53180i	0.846418	−	0.532519i	$-0.178754\pi$
$410$	−37.7082	−	11.1922i	−1.86228	−	0.552744i
$411$	−17.3408	+	11.6961i	−0.855360	+	0.576925i
$412$	21.7600	+	14.1651i	1.07204	+	0.697865i
$413$			2.82710i			0.139112i
$414$	11.6962	−	4.59932i	0.574835	−	0.226044i
$415$	17.2258			0.845582
$416$	4.45637	+	34.5827i	0.218491	+	1.69556i
$417$	11.2329	−	23.0298i	0.550078	−	1.12777i
$418$	−9.16046	+	30.8630i	−0.448053	+	1.50956i
$419$	−30.4740	−	17.5942i	−1.48875	−	0.859532i	−0.488836	−	0.872376i	$-0.662578\pi$
$419$	−30.4740	−	17.5942i	−1.48875	−	0.859532i	−0.999918	+	0.0128436i	$0.995912\pi$
$420$	0.146206	+	8.94858i	0.00713410	+	0.436646i
$421$	−1.24610	+	0.719438i	−0.0607314	+	0.0350633i	−0.530058	−	0.847961i	$-0.677830\pi$
$421$	−1.24610	+	0.719438i	−0.0607314	+	0.0350633i	0.469327	+	0.883025i	$0.344497\pi$
$422$	0.817113	+	3.41177i	0.0397764	+	0.166082i
$423$	19.2794	+	24.6784i	0.937396	+	1.19990i
$424$	−5.82672	−	6.84501i	−0.282971	−	0.332423i
$425$	4.91108	+	8.50625i	0.238223	+	0.412614i
$426$	−1.83943	+	2.00510i	−0.0891207	+	0.0971474i
$427$	1.28326	+	0.740888i	0.0621011	+	0.0358541i
$428$	−12.3206	−	0.659261i	−0.595539	−	0.0318666i
$429$	2.82073	+	40.3490i	0.136186	+	1.94807i
$430$	−7.61613	−	8.03456i	−0.367282	−	0.387461i
$431$	10.3139			0.496803			0.248401	−	0.968657i	$-0.420095\pi$
$431$	10.3139			0.496803			0.248401	+	0.968657i	$0.420095\pi$
$432$	−2.12605	−	20.6756i	−0.102289	−	0.994755i
$433$	−34.1533			−1.64130			−0.820652	−	0.571428i	$-0.806390\pi$
$433$	−34.1533			−1.64130			−0.820652	+	0.571428i	$0.806390\pi$
$434$	3.22883	+	3.40622i	0.154989	+	0.163504i
$435$	0.287795	+	4.11675i	0.0137987	+	0.197383i
$436$	−11.4022	−	0.610119i	−0.546067	−	0.0292194i
$437$	15.4150	+	8.89988i	0.737402	+	0.425739i
$438$	23.8533	−	26.0016i	1.13975	−	1.24241i
$439$	−13.9673	−	24.1921i	−0.666623	−	1.15462i	−0.978843	−	0.204614i	$-0.934406\pi$
$439$	−13.9673	−	24.1921i	−0.666623	−	1.15462i	0.312220	−	0.950010i	$-0.398927\pi$
$440$	−21.0811	+	17.9450i	−1.00500	+	0.855493i
$441$	1.12392	−	2.78151i	0.0535201	−	0.132453i
$442$	−11.9067	−	49.7153i	−0.566345	−	2.36471i
$443$	−22.1026	+	12.7610i	−1.05013	+	0.606291i	−0.922685	−	0.385555i	$-0.874010\pi$
$443$	−22.1026	+	12.7610i	−1.05013	+	0.606291i	−0.127442	+	0.991846i	$0.540677\pi$
$444$	0.0782494	+	4.78929i	0.00371355	+	0.227290i
$445$	1.78232	+	1.02903i	0.0844902	+	0.0487805i
$446$	−9.18299	+	30.9389i	−0.434827	+	1.46500i
$447$	−17.4031	+	35.6799i	−0.823136	+	1.68760i
$448$	7.47805	−	2.84233i	0.353304	−	0.134287i
$449$	22.1326			1.04450			0.522250	−	0.852793i	$-0.325093\pi$
$449$	22.1326			1.04450			0.522250	+	0.852793i	$0.325093\pi$
$450$	−1.05443	+	7.02721i	−0.0497064	+	0.331266i
$451$			40.7854i			1.92051i
$452$	−26.6018	−	17.3170i	−1.25124	−	0.814522i
$453$	−21.3192	+	14.3794i	−1.00167	+	0.675605i
$454$	9.09061	+	2.69819i	0.426644	+	0.126632i
$455$	−7.96254	+	13.7915i	−0.373290	+	0.646557i
$456$	21.0302	−	20.5976i	0.984827	−	0.964569i
$457$	1.20245	+	2.08271i	0.0562484	+	0.0974251i	0.892779	−	0.450496i	$-0.148753\pi$
$457$	1.20245	+	2.08271i	0.0562484	+	0.0974251i	−0.836530	+	0.547921i	$0.815419\pi$
$458$	−2.49893	−	10.4340i	−0.116767	−	0.487549i
$459$	6.33394	+	29.8069i	0.295643	+	1.39127i
$460$	6.93410	+	13.6459i	0.323304	+	0.636246i
$461$	−18.8610	+	10.8894i	−0.878446	+	0.507171i	−0.870146	−	0.492795i	$-0.835975\pi$
$461$	−18.8610	+	10.8894i	−0.878446	+	0.507171i	−0.00830024	+	0.999966i	$0.502642\pi$
$462$	8.85205	−	2.78552i	0.411834	−	0.129594i
$463$	10.2768	−	17.8000i	0.477604	−	0.827234i	−0.522067	−	0.852905i	$-0.674839\pi$
$463$	10.2768	−	17.8000i	0.477604	−	0.827234i	0.999670	+	0.0256705i	$0.00817208\pi$
$464$	3.37322	−	1.49299i	0.156598	−	0.0693103i
$465$	8.30426	+	12.3121i	0.385101	+	0.570958i
$466$	0.0241502	+	0.0254770i	0.00111874	+	0.00118020i
$467$			6.30020i			0.291538i	0.989319	+	0.145769i	$0.0465657\pi$
$467$			6.30020i			0.291538i	−0.989319	+	0.145769i	$0.953434\pi$
$468$	15.6681	−	33.5009i	0.724256	−	1.54858i
$469$		−	7.30665i		−	0.337390i
$470$	−27.6806	+	26.2390i	−1.27681	+	1.21032i
$471$	7.16025	−	14.6800i	0.329927	−	0.676419i
$472$	7.86473	−	1.44425i	0.362003	−	0.0664769i
$473$	−5.73955	+	9.94120i	−0.263905	+	0.457097i
$474$	−14.1205	−	3.13885i	−0.648577	−	0.144172i
$475$	−8.71560	+	5.03195i	−0.399899	+	0.230882i
$476$	−10.4563	+	5.31332i	−0.479265	+	0.243535i
$477$	1.32659	+	9.44169i	0.0607403	+	0.432305i
$478$	−14.7380	+	3.52972i	−0.674099	+	0.161446i
$479$	−1.64205	−	2.84412i	−0.0750274	−	0.129951i	0.826071	−	0.563566i	$-0.190571\pi$
$479$	−1.64205	−	2.84412i	−0.0750274	−	0.129951i	−0.901098	+	0.433615i	$0.857238\pi$
$480$	24.8195	−	4.97820i	1.13285	−	0.227222i
$481$	−4.26156	+	7.38124i	−0.194310	+	0.336556i
$482$	−2.20521	+	7.42967i	−0.100444	+	0.338412i
$483$	−0.357816	−	5.11836i	−0.0162812	−	0.232893i
$484$	5.62007	+	3.65849i	0.255458	+	0.166295i
$485$			34.4940i			1.56629i
$486$	−9.84926	+	19.7229i	−0.446772	+	0.894648i
$487$	32.9889			1.49487			0.747434	−	0.664336i	$-0.231286\pi$
$487$	32.9889			1.49487			0.747434	+	0.664336i	$0.231286\pi$
$488$	1.40552	−	3.94839i	0.0636249	−	0.178735i
$489$	−22.3700	+	1.56385i	−1.01161	+	0.0707198i
$490$	3.50270	+	1.03964i	0.158236	+	0.0469661i
$491$	−1.70162	−	0.982430i	−0.0767930	−	0.0443364i	0.461112	−	0.887342i	$-0.347451\pi$
$491$	−1.70162	−	0.982430i	−0.0767930	−	0.0443364i	−0.537905	+	0.843006i	$0.680784\pi$
$492$	18.1163	−	32.5967i	0.816745	−	1.46957i
$493$	−4.68369	+	2.70413i	−0.210943	+	0.121788i
$494$	50.9389	−	12.1998i	2.29185	−	0.548893i
$495$	29.0783	−	4.08559i	1.30697	−	0.183634i
$496$	7.82631	−	10.7224i	0.351412	−	0.481450i
$497$	0.555425	+	0.962025i	0.0249142	+	0.0431527i
$498$	−3.54389	+	15.9427i	−0.158806	+	0.714408i
$499$	−8.92030	−	5.15014i	−0.399328	−	0.230552i	0.286866	−	0.957971i	$-0.407386\pi$
$499$	−8.92030	−	5.15014i	−0.399328	−	0.230552i	−0.686194	+	0.727419i	$0.740720\pi$
$500$	17.1569	+	0.918045i	0.767280	+	0.0410562i
$501$	−11.9387	−	5.82319i	−0.533384	−	0.260161i
$502$	16.8284	−	15.9520i	0.751089	−	0.711973i
$503$	17.9406			0.799931			0.399966	−	0.916530i	$-0.369022\pi$
$503$	17.9406			0.799931			0.399966	+	0.916530i	$0.369022\pi$
$504$	−8.31208	−	1.70569i	−0.370249	−	0.0759775i
$505$	−23.4623			−1.04406
$506$	11.5187	−	10.9188i	0.512068	−	0.485401i
$507$	35.8909	−	24.2077i	1.59397	−	1.07510i
$508$	−1.67362	+	31.2775i	−0.0742549	+	1.38771i
$509$	1.19295	+	0.688750i	0.0528766	+	0.0305283i	0.526205	−	0.850358i	$-0.323614\pi$
$509$	1.19295	+	0.688750i	0.0528766	+	0.0305283i	−0.473329	+	0.880886i	$0.656948\pi$
$510$	−35.4014	+	11.1399i	−1.56760	+	0.493285i
$511$	−7.20262	−	12.4753i	−0.318625	−	0.551875i
$512$	−11.7273	−	19.3512i	−0.518280	−	0.855211i
$513$	−30.5405	+	6.48983i	−1.34840	+	0.286533i
$514$	37.0095	−	8.86371i	1.63242	−	0.390961i
$515$	29.0469	−	16.7702i	1.27996	−	0.738985i
$516$	9.00294	−	5.39584i	0.396332	−	0.237539i
$517$	34.2493	+	19.7739i	1.50628	+	0.869653i
$518$	1.87465	+	0.556416i	0.0823673	+	0.0244475i
$519$	2.75830	+	4.08952i	0.121076	+	0.179510i
$520$	42.4345	+	15.1055i	1.86088	+	0.662422i
$521$	1.24336			0.0544727			0.0272364	−	0.999629i	$-0.491329\pi$
$521$	1.24336			0.0544727			0.0272364	+	0.999629i	$0.491329\pi$
$522$	−3.86930	−	0.580589i	−0.169355	−	0.0254117i
$523$		−	28.3398i		−	1.23921i	−0.784913	−	0.619606i	$-0.787293\pi$
$523$		−	28.3398i		−	1.23921i	0.784913	−	0.619606i	$-0.212707\pi$
$524$	−4.26440	+	6.55084i	−0.186291	+	0.286175i
$525$	2.60734	+	1.27175i	0.113794	+	0.0555035i
$526$	4.81682	−	16.2286i	0.210023	−	0.707600i
$527$	−9.73117	+	16.8549i	−0.423896	+	0.734210i
$528$	−12.2712	−	23.2026i	−0.534036	−	1.00976i
$529$	7.11239	+	12.3190i	0.309235	+	0.535610i
$530$	−11.2927	+	2.70459i	−0.490525	+	0.117480i
$531$	−7.86360	−	3.17744i	−0.341251	−	0.137889i
$532$	−5.44409	−	10.7137i	−0.236031	−	0.464497i
$533$	57.4678	−	33.1790i	2.48921	−	1.43714i
$534$	−1.31905	+	1.43786i	−0.0570810	+	0.0622221i
$535$	−7.96920	+	13.8031i	−0.344538	+	0.596758i
$536$	−20.3265	+	3.73267i	−0.877969	+	0.161227i
$537$	28.3788	−	1.98391i	1.22464	−	0.0856122i
$538$	−25.0827	+	23.7764i	−1.08139	+	1.02507i
$539$		−	3.78853i		−	0.163184i
$540$	−25.0549	−	9.65084i	−1.07819	−	0.415306i
$541$			2.43835i			0.104833i	0.998625	+	0.0524164i	$0.0166923\pi$
$541$			2.43835i			0.104833i	−0.998625	+	0.0524164i	$0.983308\pi$
$542$	−15.2204	−	16.0566i	−0.653771	−	0.689689i
$543$	−25.6308	+	1.79180i	−1.09992	+	0.0768937i
$544$	20.1229	+	26.3742i	0.862762	+	1.13079i
$545$	−7.37517	+	12.7742i	−0.315917	+	0.547185i
$546$	−11.1260	−	10.2068i	−0.476151	−	0.436809i
$547$	19.4786	−	11.2460i	0.832843	−	0.480842i	−0.0219819	−	0.999758i	$-0.506998\pi$
$547$	19.4786	−	11.2460i	0.832843	−	0.480842i	0.854825	+	0.518916i	$0.173664\pi$
$548$	21.5319	−	10.9413i	0.919799	−	0.467390i
$549$	−3.50307	+	2.73669i	−0.149507	+	0.116799i
$550$	2.09006	+	8.72682i	0.0891204	+	0.372113i
$551$	−2.77068	−	4.79896i	−0.118035	−	0.204443i
$552$	−14.0560	+	3.61017i	−0.598264	+	0.153659i
$553$	−2.95269	+	5.11421i	−0.125561	+	0.217478i
$554$	−29.9356	−	8.88520i	−1.27184	−	0.377496i
$555$	5.56131	+	2.71256i	0.236064	+	0.115142i
$556$	−16.1416	+	24.7962i	−0.684554	+	1.05159i
$557$		−	21.3600i		−	0.905054i	−0.891751	−	0.452527i	$-0.850523\pi$
$557$		−	21.3600i		−	0.905054i	0.891751	−	0.452527i	$-0.149477\pi$
$558$	−13.1034	+	5.15269i	−0.554710	+	0.218131i
$559$	18.6766			0.789935
$560$	1.10279	−	10.2753i	0.0466016	−	0.434211i
$561$	21.5183	+	31.9034i	0.908502	+	1.34696i
$562$	−9.72611	+	32.7687i	−0.410271	+	1.38227i
$563$	−0.0341382	−	0.0197097i	−0.00143875	−	0.000830665i	0.499280	−	0.866440i	$-0.333598\pi$
$563$	−0.0341382	−	0.0197097i	−0.00143875	−	0.000830665i	−0.500719	+	0.865610i	$0.666931\pi$
$564$	−18.5897	−	31.0168i	−0.782768	−	1.30604i
$565$	−35.5101	+	20.5018i	−1.49392	+	0.862516i
$566$	10.0248	+	41.8577i	0.421375	+	1.75941i
$567$	6.47360	+	6.25240i	0.271866	+	0.262576i
$568$	2.39252	−	2.03660i	0.100388	−	0.0854539i
$569$	−14.0425	−	24.3223i	−0.588693	−	1.01965i	−0.994404	−	0.105644i	$-0.966309\pi$
$569$	−14.0425	−	24.3223i	−0.588693	−	1.01965i	0.405711	−	0.914001i	$-0.367024\pi$
$570$	−11.4141	−	36.2727i	−0.478084	−	1.51929i
$571$	−17.6951	−	10.2163i	−0.740517	−	0.427538i	0.0817404	−	0.996654i	$-0.473952\pi$
$571$	−17.6951	−	10.2163i	−0.740517	−	0.427538i	−0.822257	+	0.569116i	$0.807286\pi$
$572$	2.49554	−	46.6380i	0.104344	−	1.95003i
$573$	−17.5451	+	11.8339i	−0.732958	+	0.494367i
$574$	−10.4739	−	11.0494i	−0.437173	−	0.461191i
$575$	4.96147			0.206907
$576$	−0.498776	+	23.9948i	−0.0207823	+	0.999784i
$577$	27.1462			1.13011			0.565055	−	0.825053i	$-0.308855\pi$
$577$	27.1462			1.13011			0.565055	+	0.825053i	$0.308855\pi$
$578$	−16.9206	−	17.8502i	−0.703803	−	0.742469i
$579$	−4.46123	−	2.17599i	−0.185402	−	0.0904310i
$580$	0.254617	−	4.75841i	0.0105724	−	0.197582i
$581$	5.77416	+	3.33371i	0.239553	+	0.138306i
$582$	−31.9245	−	7.09650i	−1.32331	−	0.294159i
$583$	6.02025	+	10.4274i	0.249333	+	0.431858i
$584$	−31.0256	+	26.4102i	−1.28385	+	1.09286i
$585$	−29.4120	−	37.6485i	−1.21604	−	1.55657i
$586$	10.0155	+	41.8188i	0.413738	+	1.72752i
$587$	22.3876	−	12.9255i	0.924034	−	0.533491i	0.0391144	−	0.999235i	$-0.487546\pi$
$587$	22.3876	−	12.9255i	0.924034	−	0.533491i	0.884920	+	0.465743i	$0.154213\pi$
$588$	−1.68281	+	3.02789i	−0.0693980	+	0.124868i
$589$	−17.2697	−	9.97067i	−0.711586	−	0.410834i
$590$	2.93916	−	9.90246i	0.121003	−	0.407678i
$591$	11.9091	−	0.832544i	0.489875	−	0.0342463i
$592$	0.590217	−	5.49935i	0.0242578	−	0.226022i
$593$	22.5593			0.926400			0.463200	−	0.886254i	$-0.346701\pi$
$593$	22.5593			0.926400			0.463200	+	0.886254i	$0.346701\pi$
$594$	−2.20106	+	27.7528i	−0.0903108	+	1.13871i
$595$			15.1512i			0.621139i
$596$	25.0080	−	38.4165i	1.02437	−	1.57360i
$597$	2.18755	+	31.2917i	0.0895305	+	1.28068i
$598$	−24.7554	−	7.34767i	−1.01232	−	0.300469i
$599$	−13.0190	+	22.5496i	−0.531944	+	0.921353i	0.467361	+	0.884067i	$0.345205\pi$
$599$	−13.0190	+	22.5496i	−0.531944	+	0.921353i	−0.999305	+	0.0372869i	$0.988128\pi$
$600$	2.20590	−	7.90308i	0.0900554	−	0.322642i
$601$	−13.1999	−	22.8630i	−0.538437	−	0.932600i	−0.998988	−	0.0449672i	$-0.985682\pi$
$601$	−13.1999	−	22.8630i	−0.538437	−	0.932600i	0.460552	−	0.887633i	$-0.347652\pi$
$602$	−0.998029	−	4.16717i	−0.0406766	−	0.169841i
$603$	20.3235	+	8.21211i	0.827638	+	0.334423i
$604$	26.4719	−	13.4515i	1.07713	−	0.547334i
$605$	7.50209	−	4.33133i	0.305003	−	0.176094i
$606$	4.82694	−	21.7146i	0.196081	−	0.882096i
$607$	−9.00326	+	15.5941i	−0.365431	+	0.632945i	−0.988845	−	0.148947i	$-0.952412\pi$
$607$	−9.00326	+	15.5941i	−0.365431	+	0.632945i	0.623414	+	0.781892i	$0.285745\pi$
$608$	−27.0233	+	20.6181i	−1.09594	+	0.836176i
$609$	−0.700246	+	1.43565i	−0.0283754	+	0.0581754i
$610$	−3.72460	−	3.92923i	−0.150805	−	0.159090i
$611$		−	64.3444i		−	2.60309i
$612$	−3.02694	−	35.0562i	−0.122357	−	1.41706i
$613$		−	29.0859i		−	1.17477i	−0.809308	−	0.587385i	$-0.800158\pi$
$613$		−	29.0859i		−	1.17477i	0.809308	−	0.587385i	$-0.199842\pi$
$614$	0.202529	−	0.191982i	0.00817341	−	0.00774776i
$615$	−26.9380	−	39.9388i	−1.08624	−	1.61049i
$616$	−10.5394	+	1.93541i	−0.424643	+	0.0779798i
$617$	0.464348	−	0.804275i	0.0186940	−	0.0323789i	−0.856527	−	0.516102i	$-0.827383\pi$
$617$	0.464348	−	0.804275i	0.0186940	−	0.0323789i	0.875221	+	0.483723i	$0.160716\pi$
$618$	9.54515	+	30.3334i	0.383962	+	1.22019i
$619$	−1.71547	+	0.990425i	−0.0689504	+	0.0398086i	−0.534079	−	0.845435i	$-0.679341\pi$
$619$	−1.71547	+	0.990425i	−0.0689504	+	0.0398086i	0.465128	+	0.885243i	$0.346008\pi$
$620$	−7.76837	−	15.2878i	−0.311985	−	0.613971i
$621$	14.6389	+	4.75737i	0.587440	+	0.190907i
$622$	9.88883	−	2.36836i	0.396506	−	0.0949625i
$623$	0.398295	+	0.689867i	0.0159573	+	0.0276389i
$624$	−22.7104	+	36.1659i	−0.909145	+	1.44779i
$625$	15.2846	−	26.4737i	0.611383	−	1.05895i
$626$	3.27483	−	11.0334i	0.130889	−	0.440984i
$627$	−32.6886	+	22.0479i	−1.30546	+	0.880507i
$628$	−10.2892	+	15.8060i	−0.410584	+	0.630726i
$629$			8.10895i			0.323325i
$630$	−6.82853	+	8.57432i	−0.272055	+	0.341609i
$631$	12.1623			0.484173			0.242087	−	0.970255i	$-0.422168\pi$
$631$	12.1623			0.484173			0.242087	+	0.970255i	$0.422168\pi$
$632$	15.7357	+	5.60148i	0.625932	+	0.222815i
$633$	−1.88363	+	3.86183i	−0.0748675	+	0.153494i
$634$	−4.34550	−	1.28979i	−0.172582	−	0.0512242i
$635$	35.0409	+	20.2309i	1.39055	+	0.802837i
$636$	−0.179852	−	11.0079i	−0.00713161	−	0.436493i
$637$	−5.33815	+	3.08198i	−0.211505	+	0.122113i
$638$	−4.80514	+	1.15082i	−0.190237	+	0.0455615i
$639$	−3.30014	+	0.463680i	−0.130551	+	0.0183429i
$640$	−29.1483	+	2.18136i	−1.15219	+	0.0862257i
$641$	−2.24823	−	3.89404i	−0.0887996	−	0.153805i	0.818204	−	0.574928i	$-0.194970\pi$
$641$	−2.24823	−	3.89404i	−0.0887996	−	0.153805i	−0.907004	+	0.421122i	$0.861636\pi$
$642$	−11.1353	−	10.2153i	−0.439477	−	0.403166i
$643$	17.9934	+	10.3885i	0.709590	+	0.409682i	0.810909	−	0.585172i	$-0.198973\pi$
$643$	17.9934	+	10.3885i	0.709590	+	0.409682i	−0.101319	+	0.994854i	$0.532306\pi$
$644$	−0.316565	+	5.91613i	−0.0124744	+	0.233128i
$645$	−0.945560	−	13.5257i	−0.0372314	−	0.532575i
$646$	36.1672	−	34.2837i	1.42298	−	1.34887i
$647$	3.23345			0.127120			0.0635601	−	0.997978i	$-0.479755\pi$
$647$	3.23345			0.127120			0.0635601	+	0.997978i	$0.479755\pi$
$648$	14.0865	−	21.2031i	0.553371	−	0.832935i
$649$	−10.7105			−0.420426
$650$	10.5961	−	10.0442i	0.415612	−	0.393968i
$651$	0.400866	+	5.73418i	0.0157112	+	0.224740i
$652$	25.8567	+	1.38356i	1.01263	+	0.0541845i
$653$	−0.425057	−	0.245407i	−0.0166338	−	0.00960351i	0.491660	−	0.870787i	$-0.336390\pi$
$653$	−0.425057	−	0.245407i	−0.0166338	−	0.00960351i	−0.508294	+	0.861184i	$0.669724\pi$
$654$	−10.3053	−	9.45384i	−0.402969	−	0.369674i
$655$	5.04867	+	8.74456i	0.197268	+	0.341678i
$656$	−25.3876	+	34.7822i	−0.991219	+	1.35802i
$657$	42.7954	−	6.01288i	1.66961	−	0.234585i
$658$	−14.3567	+	3.43840i	−0.559682	+	0.134043i
$659$	−42.2541	+	24.3954i	−1.64599	+	0.950311i	−0.667342	+	0.744752i	$0.732568\pi$
$659$	−42.2541	+	24.3954i	−1.64599	+	0.950311i	−0.978645	+	0.205559i	$0.934099\pi$
$660$	−33.9020	+	0.553905i	−1.31963	+	0.0215607i
$661$	28.3317	+	16.3573i	1.10198	+	0.636226i	0.936739	−	0.350028i	$-0.113828\pi$
$661$	28.3317	+	16.3573i	1.10198	+	0.636226i	0.165237	+	0.986254i	$0.447161\pi$
$662$	16.2791	+	4.83181i	0.632705	+	0.187794i
$663$	27.4477	−	56.2734i	1.06598	−	2.18548i
$664$	6.32431	−	17.7663i	0.245431	−	0.689465i
$665$	−15.5241			−0.601999
$666$	−3.65463	+	4.58898i	−0.141614	+	0.177820i
$667$			2.73187i			0.105778i
$668$	12.8544	+	8.36785i	0.497353	+	0.323762i
$669$	−32.7690	+	22.1021i	−1.26692	+	0.854517i
$670$	−7.59628	+	25.5930i	−0.293470	+	0.988744i
$671$	−2.80688	+	4.86165i	−0.108358	+	0.187682i
$672$	9.28301	+	3.13460i	0.358100	+	0.120920i
$673$	9.34989	+	16.1945i	0.360412	+	0.624252i	0.988029	−	0.154271i	$-0.0493028\pi$
$673$	9.34989	+	16.1945i	0.360412	+	0.624252i	−0.627617	+	0.778523i	$0.715969\pi$
$674$	16.2539	−	3.89279i	0.626078	−	0.149945i
$675$	−6.46783	+	5.82301i	−0.248947	+	0.224128i
$676$	−44.5654	+	22.6456i	−1.71405	+	0.870984i
$677$	7.45485	−	4.30406i	0.286513	−	0.165418i	−0.349855	−	0.936804i	$-0.613769\pi$
$677$	7.45485	−	4.30406i	0.286513	−	0.165418i	0.636368	+	0.771385i	$0.280436\pi$
$678$	−11.6690	−	37.0828i	−0.448147	−	1.42416i
$679$	−6.67562	+	11.5625i	−0.256187	+	0.443729i
$680$	42.1493	−	7.74014i	1.61635	−	0.296821i
$681$	6.49415	+	9.62836i	0.248856	+	0.368959i
$682$	−12.9046	+	12.2325i	−0.494141	+	0.468407i
$683$		−	6.41339i		−	0.245402i	−0.992444	−	0.122701i	$-0.960844\pi$
$683$		−	6.41339i		−	0.245402i	0.992444	−	0.122701i	$-0.0391556\pi$
$684$	35.9190	−	3.10143i	1.37340	−	0.118586i
$685$		−	31.1998i		−	1.19208i
$686$	0.972917	+	1.02637i	0.0371461	+	0.0391869i
$687$	5.76058	−	11.8104i	0.219780	−	0.450594i
$688$	−11.0828	+	4.90526i	−0.422529	+	0.187011i
$689$	9.79499	−	16.9654i	0.373159	−	0.646331i
$690$	−4.06792	+	18.3001i	−0.154863	+	0.696672i
$691$	4.70510	−	2.71649i	0.178990	−	0.103340i	−0.407828	−	0.913059i	$-0.633714\pi$
$691$	4.70510	−	2.71649i	0.178990	−	0.103340i	0.586818	+	0.809719i	$0.300380\pi$
$692$	−2.58031	−	5.07791i	−0.0980886	−	0.193033i
$693$	10.5378	+	4.25802i	0.400299	+	0.161749i
$694$	−3.99837	−	16.6948i	−0.151776	−	0.633726i
$695$	19.1102	+	33.0998i	0.724890	+	1.25555i
$696$	4.35157	+	1.21461i	0.164946	+	0.0460395i
$697$	31.5667	−	54.6752i	1.19567	−	2.07097i
$698$	24.8397	+	7.37269i	0.940196	+	0.279060i
$699$	0.00299830	+	0.0428891i	0.000113406	+	0.00162221i
$700$	−2.80733	−	1.82748i	−0.106107	−	0.0690724i
$701$		−	18.6990i		−	0.706252i	−0.935576	−	0.353126i	$-0.885119\pi$
$701$		−	18.6990i		−	0.706252i	0.935576	−	0.353126i	$-0.114881\pi$
$702$	40.8950	−	19.4756i	1.54348	−	0.735059i
$703$	−8.30852			−0.313362
$704$	10.7683	+	28.3308i	0.405844	+	1.06776i
$705$	−46.5987	+	3.25763i	−1.75501	+	0.122690i
$706$	0.740793	−	2.49584i	0.0278801	−	0.0939323i
$707$	−7.86466	−	4.54067i	−0.295781	−	0.170769i
$708$	8.56015	+	4.75747i	0.321710	+	0.178797i
$709$	2.51650	−	1.45290i	0.0945092	−	0.0545649i	−0.452000	−	0.892018i	$-0.649289\pi$
$709$	2.51650	−	1.45290i	0.0945092	−	0.0545649i	0.546510	+	0.837453i	$0.315956\pi$
$710$	−0.945329	−	3.94712i	−0.0354776	−	0.148133i
$711$	−10.9066	−	13.9609i	−0.409031	−	0.523576i
$712$	1.71567	−	1.46044i	0.0642976	−	0.0547325i
$713$	4.91550	+	8.51390i	0.184087	+	0.318848i
$714$	−14.0226	−	3.11708i	−0.524783	−	0.116654i
$715$	−52.2496	−	30.1663i	−1.95403	−	1.12816i
$716$	−32.8021	−	1.75520i	−1.22587	−	0.0655948i
$717$	−16.6821	−	8.13679i	−0.623005	−	0.303874i
$718$	−15.0072	−	15.8316i	−0.560062	−	0.590831i
$719$	42.0676			1.56886			0.784428	−	0.620220i	$-0.212957\pi$
$719$	42.0676			1.56886			0.784428	+	0.620220i	$0.212957\pi$
$720$	27.3414	+	14.6161i	1.01895	+	0.544709i
$721$	12.9822			0.483482
$722$	16.6420	+	17.5563i	0.619352	+	0.653379i
$723$	−7.86917	+	5.30761i	−0.292657	+	0.197392i
$724$	29.6257	+	1.58524i	1.10103	+	0.0589148i
$725$	−1.33765	−	0.772294i	−0.0496792	−	0.0286823i
$726$	2.46528	+	7.83435i	0.0914950	+	0.290760i
$727$	11.1312	+	19.2798i	0.412834	+	0.715049i	0.995198	−	0.0978786i	$-0.0312057\pi$
$727$	11.1312	+	19.2798i	0.412834	+	0.715049i	−0.582365	+	0.812928i	$0.697872\pi$
$728$	11.3008	+	13.2758i	0.418837	+	0.492034i
$729$	−24.6669	+	10.9792i	−0.913590	+	0.406636i
$730$	12.2588	+	51.1853i	0.453718	+	1.89445i
$731$	15.3884	−	8.88450i	0.569161	−	0.328605i
$732$	4.40281	−	2.63879i	0.162732	−	0.0975324i
$733$	−36.8029	−	21.2482i	−1.35935	−	0.784819i	−0.369811	−	0.929107i	$-0.620578\pi$
$733$	−36.8029	−	21.2482i	−1.35935	−	0.784819i	−0.989536	+	0.144288i	$0.953911\pi$
$734$	12.3901	−	41.7440i	0.457326	−	1.54080i
$735$	2.50226	+	3.70990i	0.0922971	+	0.136842i
$736$	16.6199	−	2.14166i	0.612617	−	0.0789425i
$737$	27.6815			1.01966
$738$	42.5058	−	16.7147i	1.56466	−	0.615277i
$739$		−	6.70019i		−	0.246470i	−0.992377	−	0.123235i	$-0.960673\pi$
$739$		−	6.70019i		−	0.246470i	0.992377	−	0.123235i	$-0.0393270\pi$
$740$	−5.98786	−	3.89791i	−0.220118	−	0.143290i
$741$	57.6584	+	28.1232i	2.11813	+	1.03313i
$742$	−4.30879	−	1.27889i	−0.158181	−	0.0469497i
$743$	−10.7687	+	18.6519i	−0.395065	+	0.684272i	−0.993109	−	0.117190i	$-0.962611\pi$
$743$	−10.7687	+	18.6519i	−0.395065	+	0.684272i	0.598045	+	0.801463i	$0.295945\pi$
$744$	15.7472	−	4.04453i	0.577319	−	0.148280i
$745$	−29.6072	−	51.2812i	−1.08473	−	1.87880i
$746$	3.32015	+	13.8629i	0.121559	+	0.507558i
$747$	−15.7625	+	12.3141i	−0.576719	+	0.450548i
$748$	−20.1297	−	39.6142i	−0.736014	−	1.44844i
$749$	−5.34261	+	3.08456i	−0.195215	+	0.112707i
$750$	15.5064	+	14.2252i	0.566213	+	0.519430i
$751$	12.4108	−	21.4962i	0.452877	−	0.784406i	−0.545686	−	0.837990i	$-0.683731\pi$
$751$	12.4108	−	21.4962i	0.452877	−	0.784406i	0.998563	+	0.0535833i	$0.0170643\pi$
$752$	16.8996	+	38.1825i	0.616264	+	1.39237i
$753$	28.3297	−	1.98048i	1.03239	−	0.0721727i
$754$	5.53054	+	5.83438i	0.201410	+	0.212476i
$755$		−	38.3577i		−	1.39598i
$756$	−6.53077	−	8.08387i	−0.237522	−	0.294008i
$757$			41.6074i			1.51225i	0.654428	+	0.756124i	$0.272909\pi$
$757$			41.6074i			1.51225i	−0.654428	+	0.756124i	$0.727091\pi$
$758$	−8.18153	+	7.75545i	−0.297167	+	0.281691i
$759$	19.3911	−	1.35560i	0.703851	−	0.0492050i
$760$	7.93064	+	43.1867i	0.287674	+	1.56655i
$761$	−18.4049	+	31.8783i	−0.667178	+	1.15559i	0.311511	+	0.950242i	$0.399165\pi$
$761$	−18.4049	+	31.8783i	−0.667178	+	1.15559i	−0.978690	+	0.205345i	$0.934169\pi$
$762$	−25.9329	+	28.2685i	−0.939449	+	1.02406i
$763$	−4.94437	+	2.85463i	−0.178998	+	0.103345i
$764$	21.7856	−	11.0702i	0.788176	−	0.400506i
$765$	−42.1433	−	17.0288i	−1.52369	−	0.615677i
$766$	14.0915	−	3.37490i	0.509148	−	0.121940i
$767$	8.71306	+	15.0915i	0.314610	+	0.544921i
$768$	3.97786	−	27.4258i	0.143539	−	0.989645i
$769$	−7.47392	+	12.9452i	−0.269516	+	0.466816i	−0.968737	−	0.248090i	$-0.920197\pi$
$769$	−7.47392	+	12.9452i	−0.269516	+	0.466816i	0.699221	+	0.714906i	$0.253531\pi$
$770$	−3.93870	+	13.2701i	−0.141941	+	0.478221i
$771$	41.8915	+	20.4328i	1.50869	+	0.735870i
$772$	4.80340	+	3.12687i	0.172878	+	0.112538i
$773$		−	7.05545i		−	0.253767i	−0.991918	−	0.126883i	$-0.959503\pi$
$773$		−	7.05545i		−	0.253767i	0.991918	−	0.126883i	$-0.0404974\pi$
$774$	12.7127	+	1.90754i	0.456949	+	0.0685652i
$775$	−5.55841			−0.199664
$776$	35.5762	+	12.6642i	1.27711	+	0.454617i
$777$	1.33921	+	1.98554i	0.0480439	+	0.0712309i
$778$	−19.7689	−	5.86762i	−0.708750	−	0.210364i
$779$	56.0208	+	32.3436i	2.00715	+	1.15883i
$780$	28.3598	+	47.3183i	1.01544	+	1.69427i
$781$	−3.64466	+	2.10425i	−0.130416	+	0.0752959i
$782$	−23.8923	+	5.72217i	−0.854388	+	0.204624i
$783$	−3.20625	−	3.56130i	−0.114582	−	0.127270i
$784$	2.35824	−	3.23090i	0.0842229	−	0.115389i
$785$	12.1815	+	21.0990i	0.434776	+	0.753055i
$786$	−9.13185	+	2.87356i	−0.325722	+	0.102497i
$787$	−1.74646	−	1.00832i	−0.0622544	−	0.0359426i	0.468550	−	0.883437i	$-0.344777\pi$
$787$	−1.74646	−	1.00832i	−0.0622544	−	0.0359426i	−0.530804	+	0.847495i	$0.678110\pi$
$788$	−13.7653	−	0.736564i	−0.490369	−	0.0262390i
$789$	17.1886	−	11.5934i	0.611929	−	0.412735i
$790$	15.6593	−	14.8438i	0.557134	−	0.528119i
$791$	−15.8708			−0.564302
$792$	6.46206	−	31.4906i	0.229619	−	1.11897i
$793$	9.13361			0.324344
$794$	−20.1956	+	19.1439i	−0.716715	+	0.679390i
$795$	−12.7824	−	6.23468i	−0.453345	−	0.221121i
$796$	1.93536	−	36.1690i	0.0685970	−	1.28198i
$797$	−7.67198	−	4.42942i	−0.271755	−	0.156898i	0.357930	−	0.933749i	$-0.383483\pi$
$797$	−7.67198	−	4.42942i	−0.271755	−	0.156898i	−0.629685	+	0.776850i	$0.716816\pi$
$798$	3.19380	−	14.3677i	0.113059	−	0.508612i
$799$	−30.6088	−	53.0160i	−1.08286	−	1.87557i
$800$	−3.64975	+	8.74331i	−0.129038	+	0.309123i
$801$	−2.36652	+	0.332504i	−0.0836170	+	0.0117485i
$802$	−39.5791	+	9.47913i	−1.39759	+	0.334720i
$803$	47.2631	−	27.2873i	1.66788	−	0.962950i
$804$	−22.1238	−	12.2957i	−0.780246	−	0.433637i
$805$	6.62797	+	3.82666i	0.233605	+	0.134872i
$806$	27.7339	+	8.23171i	0.976884	+	0.289950i
$807$	−42.2253	+	2.95190i	−1.48640	+	0.103912i
$808$	−8.61399	+	24.1984i	−0.303039	+	0.851298i
$809$	8.72690			0.306822			0.153411	−	0.988163i	$-0.450974\pi$
$809$	8.72690			0.306822			0.153411	+	0.988163i	$0.450974\pi$
$810$	−16.1748	−	28.6305i	−0.568325	−	1.00597i
$811$			27.6190i			0.969833i	0.874561	+	0.484916i	$0.161150\pi$
$811$			27.6190i			0.969833i	−0.874561	+	0.484916i	$0.838850\pi$
$812$	1.00624	−	1.54576i	0.0353123	−	0.0542456i
$813$	−1.88965	−	27.0304i	−0.0662728	−	0.947996i
$814$	−2.10800	+	7.10216i	−0.0738853	+	0.248931i
$815$	16.7246	−	28.9679i	0.585838	−	1.01470i
$816$	−1.50787	+	40.6020i	−0.0527861	+	1.42135i
$817$	9.10317	+	15.7671i	0.318479	+	0.551623i
$818$	−49.1967	+	11.7825i	−1.72012	+	0.411966i
$819$	−2.57290	−	18.3120i	−0.0899044	−	0.639874i
$820$	25.1997	+	49.5916i	0.880010	+	1.73181i
$821$	−3.41856	+	1.97371i	−0.119309	+	0.0688828i	−0.558467	−	0.829527i	$-0.688610\pi$
$821$	−3.41856	+	1.97371i	−0.119309	+	0.0688828i	0.439158	+	0.898410i	$0.355277\pi$
$822$	28.8757	+	6.41877i	1.00715	+	0.223880i
$823$	−19.3464	+	33.5090i	−0.674375	+	1.16805i	0.302276	+	0.953220i	$0.402253\pi$
$823$	−19.3464	+	33.5090i	−0.674375	+	1.16805i	−0.976651	+	0.214831i	$0.931080\pi$
$824$	−6.63207	−	36.1153i	−0.231039	−	1.25814i
$825$	−4.81805	+	9.87800i	−0.167743	+	0.343908i
$826$	2.90164	−	2.75053i	0.100961	−	0.0957032i
$827$		−	12.7930i		−	0.444858i	−0.974949	−	0.222429i	$-0.928602\pi$
$827$		−	12.7930i		−	0.444858i	0.974949	−	0.222429i	$-0.0713985\pi$
$828$	−16.1000	−	7.52980i	−0.559513	−	0.261679i
$829$			51.1880i			1.77783i	0.458069	+	0.888917i	$0.348541\pi$
$829$			51.1880i			1.77783i	−0.458069	+	0.888917i	$0.651459\pi$
$830$	−16.7593	−	17.6800i	−0.581724	−	0.613683i
$831$	−21.3854	−	31.7064i	−0.741850	−	1.09988i
$832$	31.1589	−	38.2200i	1.08024	−	1.32504i
$833$	−2.93222	+	5.07875i	−0.101595	+	0.175968i
$834$	−34.5658	+	10.8770i	−1.19691	+	0.376639i
$835$	17.1591	−	9.90680i	0.593814	−	0.342839i
$836$	40.5891	−	20.6251i	1.40380	−	0.713334i
$837$	−16.4002	−	5.32975i	−0.566874	−	0.184223i
$838$	11.5906	+	48.3953i	0.400390	+	1.67179i
$839$	−14.7980	−	25.6308i	−0.510883	−	0.884875i	−0.999920	−	0.0126122i	$-0.995985\pi$
$839$	−14.7980	−	25.6308i	−0.510883	−	0.884875i	0.489038	−	0.872263i	$-0.337348\pi$
$840$	9.04229	−	8.85629i	0.311989	−	0.305571i
$841$	−14.0748	+	24.3782i	−0.485337	+	0.840628i
$842$	1.95076	+	0.579008i	0.0672278	+	0.0199539i
$843$	−34.7071	+	23.4093i	−1.19538	+	0.806260i
$844$	2.70675	−	4.15803i	0.0931702	−	0.143125i
$845$			64.5751i			2.22145i
$846$	6.57185	−	43.7977i	0.225945	−	1.50580i
$847$	3.35297			0.115210
$848$	−1.35658	+	12.6400i	−0.0465853	+	0.434059i
$849$	−23.1095	+	47.3792i	−0.793115	+	1.62605i
$850$	3.95247	−	13.3165i	0.135568	−	0.456751i
$851$	3.54730	+	2.04803i	0.121600	+	0.0702057i
$852$	3.84759	−	0.0628635i	0.131816	−	0.00215367i
$853$	−2.72307	+	1.57217i	−0.0932362	+	0.0538300i	−0.545893	−	0.837855i	$-0.683810\pi$
$853$	−2.72307	+	1.57217i	−0.0932362	+	0.0538300i	0.452657	+	0.891685i	$0.350476\pi$
$854$	−0.488077	−	2.03792i	−0.0167017	−	0.0697360i
$855$	17.4479	−	43.1805i	0.596706	−	1.47674i
$856$	11.3103	+	13.2869i	0.386578	+	0.454137i
$857$	25.6134	+	44.3637i	0.874937	+	1.51544i	0.856829	+	0.515600i	$0.172431\pi$
$857$	25.6134	+	44.3637i	0.874937	+	1.51544i	0.0181078	+	0.999836i	$0.494236\pi$
$858$	38.6686	−	42.1514i	1.32013	−	1.43902i
$859$	25.0984	+	14.4905i	0.856345	+	0.494411i	0.862787	−	0.505568i	$-0.168717\pi$
$859$	25.0984	+	14.4905i	0.856345	+	0.494411i	−0.00644157	+	0.999979i	$0.502050\pi$
$860$	−0.836551	+	15.6339i	−0.0285262	+	0.533112i
$861$	−1.30036	−	18.6010i	−0.0443162	−	0.633919i
$862$	−10.0346	−	10.5859i	−0.341779	−	0.360556i
$863$	−34.5098			−1.17473			−0.587364	−	0.809323i	$-0.699834\pi$
$863$	−34.5098			−1.17473			−0.587364	+	0.809323i	$0.699834\pi$
$864$	−19.1523	+	22.2977i	−0.651575	+	0.758585i
$865$	−7.35789			−0.250176
$866$	33.2284	+	35.0539i	1.12915	+	1.19118i
$867$	−2.10073	−	30.0498i	−0.0713444	−	1.02054i
$868$	0.354652	−	6.62793i	0.0120377	−	0.224967i
$869$	−19.3754	−	11.1864i	−0.657264	−	0.379472i
$870$	3.94531	−	4.30064i	0.133758	−	0.145805i
$871$	−22.5190	−	39.0040i	−0.763027	−	1.32160i
$872$	10.4672	+	12.2965i	0.354465	+	0.416411i
$873$	−24.6584	−	31.5637i	−0.834560	−	1.06827i
$874$	−5.86300	−	24.4804i	−0.198319	−	0.828061i
$875$	7.43979	−	4.29536i	0.251511	−	0.145210i
$876$	−49.8945	+	0.815198i	−1.68578	+	0.0275430i
$877$	−15.6480	−	9.03435i	−0.528394	−	0.305068i	0.211968	−	0.977277i	$-0.432013\pi$
$877$	−15.6480	−	9.03435i	−0.528394	−	0.305068i	−0.740362	+	0.672208i	$0.765346\pi$
$878$	−11.2410	+	37.8725i	−0.379364	+	1.27813i
$879$	−23.0880	+	47.3353i	−0.778740	+	1.59658i
$880$	38.9283	+	4.17797i	1.31227	+	0.140839i
$881$	−7.76180			−0.261502			−0.130751	−	0.991415i	$-0.541739\pi$
$881$	−7.76180			−0.261502			−0.130751	+	0.991415i	$0.541739\pi$
$882$	−3.94834	+	1.55262i	−0.132947	+	0.0522794i
$883$			42.6856i			1.43648i	0.695794	+	0.718242i	$0.255053\pi$
$883$			42.6856i			1.43648i	−0.695794	+	0.718242i	$0.744947\pi$
$884$	−39.4419	+	60.5895i	−1.32658	+	2.03785i
$885$	10.4882	−	7.07412i	0.352558	−	0.237794i
$886$	34.6015	+	10.2701i	1.16246	+	0.345030i
$887$	7.10271	−	12.3023i	0.238486	−	0.413069i	−0.721794	−	0.692108i	$-0.756682\pi$
$887$	7.10271	−	12.3023i	0.238486	−	0.413069i	0.960280	+	0.279038i	$0.0900156\pi$
$888$	4.83945	−	4.73989i	0.162401	−	0.159060i
$889$	7.83056	+	13.5629i	0.262629	+	0.454886i
$890$	−0.677894	−	2.83048i	−0.0227231	−	0.0948778i
$891$	−23.6874	+	24.5254i	−0.793559	+	0.821633i
$892$	40.6890	−	20.6758i	1.36237	−	0.692278i
$893$	54.3208	−	31.3621i	1.81778	−	1.04949i
$894$	53.5524	−	16.8516i	1.79106	−	0.563602i
$895$	−21.2170	+	36.7489i	−0.709206	+	1.22838i
$896$	−10.1928	−	4.90988i	−0.340517	−	0.164028i
$897$	−17.6848	−	26.2198i	−0.590477	−	0.875453i
$898$	−21.5331	−	22.7162i	−0.718570	−	0.758048i
$899$		−	3.06056i		−	0.102075i
$900$	8.23838	−	5.75465i	0.274613	−	0.191822i
$901$		−	18.6380i		−	0.620922i
$902$	41.8608	−	39.6808i	1.39381	−	1.32123i
$903$	2.30068	−	4.71687i	0.0765618	−	0.156968i
$904$	8.10777	+	44.1513i	0.269660	+	1.46845i
$905$	19.1625	−	33.1904i	0.636982	−	1.10328i
$906$	35.5004	+	7.89140i	1.17942	+	0.262174i
$907$	20.8364	−	12.0299i	0.691861	−	0.399446i	−0.112448	−	0.993658i	$-0.535869\pi$
$907$	20.8364	−	12.0299i	0.691861	−	0.399446i	0.804309	+	0.594212i	$0.202536\pi$
$908$	−6.07508	−	11.9554i	−0.201608	−	0.396755i
$909$	21.4692	−	16.7723i	0.712088	−	0.556302i
$910$	21.9021	−	5.24551i	0.726047	−	0.173887i
$911$	−9.06752	−	15.7054i	−0.300420	−	0.520344i	0.675811	−	0.737075i	$-0.263794\pi$
$911$	−9.06752	−	15.7054i	−0.300420	−	0.520344i	−0.976231	+	0.216732i	$0.930460\pi$
$912$	−41.6013	−	1.54498i	−1.37756	−	0.0511595i
$913$	−12.6299	+	21.8756i	−0.417988	+	0.723977i
$914$	0.967741	−	3.26046i	0.0320100	−	0.107847i
$915$	−0.462418	−	6.61464i	−0.0152871	−	0.218673i
$916$	−8.27788	+	12.7162i	−0.273509	+	0.420156i
$917$			3.90828i			0.129063i
$918$	24.4305	−	35.5006i	0.806327	−	1.17170i
$919$	17.3492			0.572297			0.286149	−	0.958185i	$-0.407625\pi$
$919$	17.3492			0.572297			0.286149	+	0.958185i	$0.407625\pi$
$920$	7.25947	−	20.3933i	0.239338	−	0.672348i
$921$	0.340947	−	0.0238350i	0.0112346	−	0.000785390i
$922$	29.5268	+	8.76387i	0.972413	+	0.288623i
$923$	5.92989	+	3.42362i	0.195185	+	0.112690i
$924$	−11.4713	−	6.37538i	−0.377377	−	0.209735i
$925$	−2.00563	+	1.15795i	−0.0659446	+	0.0380732i
$926$	−28.2678	+	6.77009i	−0.928938	+	0.222479i
$927$	−14.5910	+	36.1101i	−0.479230	+	1.18601i
$928$	−4.81422	−	2.00961i	−0.158035	−	0.0659688i
$929$	18.9924	+	32.8958i	0.623121	+	1.07928i	0.988901	+	0.148576i	$0.0474690\pi$
$929$	18.9924	+	32.8958i	0.623121	+	1.07928i	−0.365780	+	0.930701i	$0.619198\pi$
$930$	4.55735	−	20.5018i	0.149442	−	0.672282i
$931$	−5.20374	−	3.00438i	−0.170546	−	0.0984647i
$932$	0.00265264	−	0.0495740i	8.68902e−5	−	0.00162385i
$933$	11.1933	+	5.45959i	0.366452	+	0.178739i
$934$	6.46632	−	6.12957i	0.211585	−	0.200566i
$935$	−57.4009			−1.87721
$936$	−49.6280	+	16.5124i	−1.62214	+	0.539726i
$937$	−11.7748			−0.384665			−0.192333	−	0.981330i	$-0.561605\pi$
$937$	−11.7748			−0.384665			−0.192333	+	0.981330i	$0.561605\pi$
$938$	−7.49932	+	7.10877i	−0.244861	+	0.232110i
$939$	11.6861	−	7.88204i	0.381361	−	0.257221i
$940$	53.8618	+	2.88208i	1.75678	+	0.0940030i
$941$	8.34865	+	4.82009i	0.272158	+	0.157131i	0.629868	−	0.776702i	$-0.283109\pi$
$941$	8.34865	+	4.82009i	0.272158	+	0.157131i	−0.357710	+	0.933833i	$0.616442\pi$
$942$	−22.0334	+	6.93337i	−0.717888	+	0.225901i
$943$	−15.9453	−	27.6180i	−0.519250	−	0.899367i
$944$	−9.13406	−	6.66697i	−0.297288	−	0.216991i
$945$	−13.1315	+	2.79042i	−0.427166	+	0.0907723i
$946$	15.7874	−	3.78106i	0.513294	−	0.122933i
$947$	−37.2981	+	21.5341i	−1.21203	+	0.699764i	−0.963200	−	0.268785i	$-0.913378\pi$
$947$	−37.2981	+	21.5341i	−1.21203	+	0.699764i	−0.248826	+	0.968548i	$0.580045\pi$
$948$	10.5165	+	17.5467i	0.341559	+	0.569890i
$949$	−76.8973	−	44.3967i	−2.49619	−	1.44118i
$950$	13.6442	+	4.04974i	0.442676	+	0.131391i
$951$	−3.10434	−	4.60256i	−0.100665	−	0.149248i
$952$	15.6266	+	5.56264i	0.506460	+	0.180286i
$953$	−10.2888			−0.333287			−0.166643	−	0.986017i	$-0.553293\pi$
$953$	−10.2888			−0.333287			−0.166643	+	0.986017i	$0.553293\pi$
$954$	8.40000	−	10.5476i	0.271960	−	0.341490i
$955$		−	31.5673i		−	1.02149i
$956$	17.9616	+	11.6925i	0.580920	+	0.378161i
$957$	−5.43900	−	2.65290i	−0.175818	−	0.0857562i
$958$	−1.32153	+	4.45245i	−0.0426968	+	0.143852i
$959$	6.03809	−	10.4583i	0.194980	−	0.337716i
$960$	−29.2567	−	20.6305i	−0.944257	−	0.665848i
$961$	9.99309	+	17.3085i	0.322358	+	0.558340i
$962$	11.7220	−	2.80740i	0.377933	−	0.0905143i
$963$	−2.57505	−	18.3273i	−0.0829798	−	0.590590i
$964$	9.77107	−	4.96510i	0.314705	−	0.159915i
$965$	6.41194	−	3.70194i	0.206408	−	0.119170i
$966$	−4.90520	+	5.34699i	−0.157822	+	0.172037i
$967$	−12.8668	+	22.2859i	−0.413768	+	0.716667i	−0.995298	−	0.0968575i	$-0.969121\pi$
$967$	−12.8668	+	22.2859i	−0.413768	+	0.716667i	0.581530	+	0.813525i	$0.302454\pi$
$968$	−1.71290	−	9.32767i	−0.0550546	−	0.299803i
$969$	60.8854	−	4.25640i	1.95592	−	0.136735i
$970$	35.4035	−	33.5598i	1.13674	−	1.07754i
$971$			0.210109i			0.00674270i	0.999994	+	0.00337135i	$0.00107314\pi$
$971$			0.210109i			0.00674270i	−0.999994	+	0.00337135i	$0.998927\pi$
$972$	29.8255	−	9.07976i	0.956652	−	0.291233i
$973$			14.7936i			0.474260i
$974$	−32.0954	−	33.8587i	−1.02840	−	1.08490i
$975$	17.8379	−	1.24702i	0.571270	−	0.0399365i
$976$	−5.41996	+	2.39887i	−0.173489	+	0.0767861i
$977$	−9.66357	+	16.7378i	−0.309165	+	0.535490i	−0.978180	−	0.207759i	$-0.933383\pi$
$977$	−9.66357	+	16.7378i	−0.309165	+	0.535490i	0.669015	+	0.743249i	$0.266716\pi$
$978$	23.3693	+	21.4384i	0.747267	+	0.685525i
$979$	−2.61358	+	1.50895i	−0.0835304	+	0.0482263i
$980$	−2.34078	−	4.60654i	−0.0747736	−	0.147151i
$981$	−2.38310	−	16.9612i	−0.0760867	−	0.541530i
$982$	0.647199	+	2.70231i	0.0206529	+	0.0862342i
$983$	−0.300861	−	0.521107i	−0.00959599	−	0.0166207i	0.861188	−	0.508287i	$-0.169721\pi$
$983$	−0.300861	−	0.521107i	−0.00959599	−	0.0166207i	−0.870784	+	0.491667i	$0.836388\pi$
$984$	−51.0819	+	13.1200i	−1.62843	+	0.418249i
$985$	−8.90365	+	15.4216i	−0.283694	+	0.491372i
$986$	7.33228	+	2.17630i	0.233507	+	0.0693074i
$987$	−16.2505	−	7.92628i	−0.517260	−	0.252296i
$988$	−62.0807	−	40.4127i	−1.97505	−	1.28570i
$989$		−	8.97565i		−	0.285409i
$990$	−32.4841	−	25.8701i	−1.03241	−	0.822205i
$991$	−29.4630			−0.935924			−0.467962	−	0.883749i	$-0.655012\pi$
$991$	−29.4630			−0.935924			−0.467962	+	0.883749i	$0.655012\pi$
$992$	−18.6195	+	2.39933i	−0.591169	+	0.0761788i
$993$	11.6294	+	17.2421i	0.369049	+	0.547160i
$994$	0.447009	−	1.50604i	0.0141783	−	0.0477687i
$995$	−40.5209	−	23.3948i	−1.28460	−	0.741664i
$996$	19.8110	−	11.8735i	0.627734	−	0.376228i
$997$	−17.6253	+	10.1760i	−0.558200	+	0.322277i	−0.752423	−	0.658681i	$-0.771115\pi$
$997$	−17.6253	+	10.1760i	−0.558200	+	0.322277i	0.194223	+	0.980957i	$0.437781\pi$
$998$	3.39277	+	14.1662i	0.107396	+	0.448422i
$999$	−7.02797	+	1.49343i	−0.222355	+	0.0472502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.a.85.9	✓	72
8.5	even	2	inner	504.2.cs.a.85.15	yes	72
9.7	even	3	inner	504.2.cs.a.421.15	yes	72
72.61	even	6	inner	504.2.cs.a.421.9	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.a.85.9	✓	72	1.1	even	1	trivial
504.2.cs.a.85.15	yes	72	8.5	even	2	inner
504.2.cs.a.421.9	yes	72	72.61	even	6	inner
504.2.cs.a.421.15	yes	72	9.7	even	3	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.972917 - 1.02637i) q^{2} +(-0.120790 - 1.72783i) q^{3} +(-0.106865 + 1.99714i) q^{4} +(2.23744 + 1.29179i) q^{5} +(-1.65588 + 1.80501i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.15378 - 1.83337i) q^{8} +(-2.97082 + 0.417410i) q^{9} +O(q^{10})\)	\(q+(-0.972917 - 1.02637i) q^{2} +(-0.120790 - 1.72783i) q^{3} +(-0.106865 + 1.99714i) q^{4} +(2.23744 + 1.29179i) q^{5} +(-1.65588 + 1.80501i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.15378 - 1.83337i) q^{8} +(-2.97082 + 0.417410i) q^{9} +(-0.850996 - 3.55324i) q^{10} +(-3.28096 + 1.89427i) q^{11} +(3.46364 - 0.0565904i) q^{12} +(5.33815 + 3.08198i) q^{13} +(0.402403 - 1.35576i) q^{14} +(1.96174 - 4.02197i) q^{15} +(-3.97716 - 0.426848i) q^{16} +5.86443 q^{17} +(3.31878 + 2.64305i) q^{18} +6.00877i q^{19} +(-2.81899 + 4.33045i) q^{20} +(1.43595 - 0.968524i) q^{21} +(5.13632 + 1.52452i) q^{22} +(1.48115 - 2.56543i) q^{23} +(-3.42792 - 3.49991i) q^{24} +(0.837435 + 1.45048i) q^{25} +(-2.03033 - 8.47742i) q^{26} +(1.08006 + 5.08266i) q^{27} +(-1.78301 + 0.906024i) q^{28} +(-0.798660 + 0.461107i) q^{29} +(-6.03662 + 1.89958i) q^{30} +(-1.65935 + 2.87409i) q^{31} +(3.43134 + 4.49732i) q^{32} +(3.66928 + 5.44015i) q^{33} +(-5.70561 - 6.01907i) q^{34} +2.58358i q^{35} +(-0.516151 - 5.97776i) q^{36} +1.38273i q^{37} +(6.16721 - 5.84603i) q^{38} +(4.68036 - 9.59571i) q^{39} +(7.18728 - 1.31984i) q^{40} +(5.38274 - 9.32318i) q^{41} +(-2.39113 - 0.531523i) q^{42} +(2.62402 - 1.51498i) q^{43} +(-3.43250 - 6.75499i) q^{44} +(-7.18625 - 2.90374i) q^{45} +(-4.07411 + 0.975742i) q^{46} +(-5.21940 - 9.04026i) q^{47} +(-0.257121 + 6.92343i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.673972 - 2.27071i) q^{50} +(-0.708364 - 10.1328i) q^{51} +(-6.72562 + 10.3317i) q^{52} -3.17814i q^{53} +(4.16588 - 6.05355i) q^{54} -9.78796 q^{55} +(2.66463 + 0.948538i) q^{56} +(10.3822 - 0.725798i) q^{57} +(1.25030 + 0.371101i) q^{58} +(2.44834 + 1.41355i) q^{59} +(7.82280 + 4.34767i) q^{60} +(1.28326 - 0.740888i) q^{61} +(4.56428 - 1.09314i) q^{62} +(-1.84690 - 2.36410i) q^{63} +(1.27749 - 7.89734i) q^{64} +(7.96254 + 13.7915i) q^{65} +(2.01369 - 9.05886i) q^{66} +(-6.32775 - 3.65333i) q^{67} +(-0.626700 + 11.7121i) q^{68} +(-4.61154 - 2.24930i) q^{69} +(2.65170 - 2.51361i) q^{70} +1.11085 q^{71} +(-5.63321 + 6.34562i) q^{72} -14.4052 q^{73} +(1.41919 - 1.34529i) q^{74} +(2.40504 - 1.62215i) q^{75} +(-12.0004 - 0.642125i) q^{76} +(-3.28096 - 1.89427i) q^{77} +(-14.4023 + 4.53206i) q^{78} +(2.95269 + 5.11421i) q^{79} +(-8.34727 - 6.09270i) q^{80} +(8.65154 - 2.48010i) q^{81} +(-14.8060 + 3.54601i) q^{82} +(5.77416 - 3.33371i) q^{83} +(1.78083 + 2.97130i) q^{84} +(13.1213 + 7.57561i) q^{85} +(-4.10789 - 1.21926i) q^{86} +(0.893186 + 1.32426i) q^{87} +(-3.59357 + 10.0951i) q^{88} +0.796589 q^{89} +(4.01131 + 10.2008i) q^{90} +6.16397i q^{91} +(4.96524 + 3.23222i) q^{92} +(5.16638 + 2.51993i) q^{93} +(-4.20060 + 14.1524i) q^{94} +(-7.76206 + 13.4443i) q^{95} +(7.35615 - 6.47202i) q^{96} +(6.67562 + 11.5625i) q^{97} +(1.37532 - 0.329387i) q^{98} +(8.95647 - 6.99703i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8	\( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) \) 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8 + 20 * q^12 + 40 * q^17 - q^18 + 2 * q^20 - 12 * q^22 + 12 * q^23 + 10 * q^24 + 36 * q^25 - 42 * q^26 + 4 * q^30 + 5 * q^32 + 8 * q^33 + 6 * q^34 - 18 * q^36 - 25 * q^38 - 4 * q^39 - 9 * q^40 + 24 * q^41 - 7 * q^42 + 12 * q^46 - 53 * q^48 - 36 * q^49 + 41 * q^50 - 9 * q^52 + 12 * q^54 + 3 * q^56 + 4 * q^57 + 9 * q^58 - 50 * q^60 + 60 * q^62 - 6 * q^64 - 40 * q^65 - 2 * q^66 + 23 * q^68 - 56 * q^71 + 19 * q^72 + 22 * q^74 - 24 * q^76 - 54 * q^78 - 6 * q^80 - 4 * q^81 - 48 * q^82 + 10 * q^84 - 39 * q^86 - 76 * q^87 - 12 * q^88 - 88 * q^89 - 77 * q^90 + 11 * q^92 + 24 * q^94 - 24 * q^95 + 59 * q^96

Introduction

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