LMFDB - Embedded newform 690.2.i.c.47.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (of order $4$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.4
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	690.47
Dual form			690.2.i.c.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} -1.00000i q^{4} +(1.73205 - 1.41421i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(2.44949 + 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} -1.00000i q^{4} +(1.73205 - 1.41421i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(2.44949 + 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +(0.224745 - 2.22474i) q^{10} +5.65685i q^{11} +(0.292893 + 1.70711i) q^{12} +(-3.44949 + 3.44949i) q^{13} +3.46410 q^{14} +(-2.54258 + 2.92152i) q^{15} -1.00000 q^{16} +(5.19615 - 5.19615i) q^{17} +(1.29289 - 2.70711i) q^{18} +2.44949i q^{19} +(-1.41421 - 1.73205i) q^{20} +(-4.89898 - 3.46410i) q^{21} +(4.00000 + 4.00000i) q^{22} +(0.707107 + 0.707107i) q^{23} +(1.41421 + 1.00000i) q^{24} +(1.00000 - 4.89898i) q^{25} +4.87832i q^{26} +(-4.53553 + 2.53553i) q^{27} +(2.44949 - 2.44949i) q^{28} +2.19275 q^{29} +(0.267949 + 3.86370i) q^{30} +4.89898 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.65685 - 9.65685i) q^{33} -7.34847i q^{34} +(7.70674 + 0.778539i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(-2.44949 - 2.44949i) q^{37} +(1.73205 + 1.73205i) q^{38} +(4.87832 - 6.89898i) q^{39} +(-2.22474 - 0.224745i) q^{40} +8.48528i q^{41} +(-5.91359 + 1.01461i) q^{42} +(2.89898 - 2.89898i) q^{43} +5.65685 q^{44} +(3.48477 - 5.73205i) q^{45} +1.00000 q^{46} +(4.87832 - 4.87832i) q^{47} +(1.70711 - 0.292893i) q^{48} +5.00000i q^{49} +(-2.75699 - 4.17121i) q^{50} +(-7.34847 + 10.3923i) q^{51} +(3.44949 + 3.44949i) q^{52} +(0.953512 + 0.953512i) q^{53} +(-1.41421 + 5.00000i) q^{54} +(8.00000 + 9.79796i) q^{55} -3.46410i q^{56} +(-0.717439 - 4.18154i) q^{57} +(1.55051 - 1.55051i) q^{58} +5.51399 q^{59} +(2.92152 + 2.54258i) q^{60} +0.898979 q^{61} +(3.46410 - 3.46410i) q^{62} +(9.37769 + 4.47871i) q^{63} +1.00000i q^{64} +(-1.09638 + 10.8530i) q^{65} +(-8.00000 - 5.65685i) q^{66} +(-10.8990 - 10.8990i) q^{67} +(-5.19615 - 5.19615i) q^{68} +(-1.41421 - 1.00000i) q^{69} +(6.00000 - 4.89898i) q^{70} -14.6349i q^{71} +(-2.70711 - 1.29289i) q^{72} +(-1.89898 + 1.89898i) q^{73} -3.46410 q^{74} +(-0.272229 + 8.65597i) q^{75} +2.44949 q^{76} +(-13.8564 + 13.8564i) q^{77} +(-1.42883 - 8.32780i) q^{78} +4.44949i q^{79} +(-1.73205 + 1.41421i) q^{80} +(7.00000 - 5.65685i) q^{81} +(6.00000 + 6.00000i) q^{82} +(-1.41421 - 1.41421i) q^{83} +(-3.46410 + 4.89898i) q^{84} +(1.65153 - 16.3485i) q^{85} -4.09978i q^{86} +(-3.74326 + 0.642242i) q^{87} +(4.00000 - 4.00000i) q^{88} -9.12096 q^{89} +(-1.58907 - 6.51727i) q^{90} -16.8990 q^{91} +(0.707107 - 0.707107i) q^{92} +(-8.36308 + 1.43488i) q^{93} -6.89898i q^{94} +(3.46410 + 4.24264i) q^{95} +(1.00000 - 1.41421i) q^{96} +(-0.449490 - 0.449490i) q^{97} +(3.53553 + 3.53553i) q^{98} +(5.65685 + 16.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} - 8 q^{6}+O(q^{10}) $ 8 * q - 8 * q^3 - 8 * q^6	$ 8 q - 8 q^{3} - 8 q^{6} - 8 q^{10} + 8 q^{12} - 8 q^{13} - 8 q^{15} - 8 q^{16} + 16 q^{18} + 32 q^{22} + 8 q^{25} - 8 q^{27} + 16 q^{30} + 32 q^{33} - 8 q^{36} - 8 q^{40} - 16 q^{43} + 8 q^{46} + 8 q^{48} + 8 q^{52} + 64 q^{55} + 32 q^{58} + 8 q^{60} - 32 q^{61} - 64 q^{66} - 48 q^{67} + 48 q^{70} - 16 q^{72} + 24 q^{73} - 8 q^{75} + 8 q^{78} + 56 q^{81} + 48 q^{82} + 72 q^{85} - 32 q^{87} + 32 q^{88} - 8 q^{90} - 96 q^{91} + 8 q^{96} + 16 q^{97}+O(q^{100}) $ 8 * q - 8 * q^3 - 8 * q^6 - 8 * q^10 + 8 * q^12 - 8 * q^13 - 8 * q^15 - 8 * q^16 + 16 * q^18 + 32 * q^22 + 8 * q^25 - 8 * q^27 + 16 * q^30 + 32 * q^33 - 8 * q^36 - 8 * q^40 - 16 * q^43 + 8 * q^46 + 8 * q^48 + 8 * q^52 + 64 * q^55 + 32 * q^58 + 8 * q^60 - 32 * q^61 - 64 * q^66 - 48 * q^67 + 48 * q^70 - 16 * q^72 + 24 * q^73 - 8 * q^75 + 8 * q^78 + 56 * q^81 + 48 * q^82 + 72 * q^85 - 32 * q^87 + 32 * q^88 - 8 * q^90 - 96 * q^91 + 8 * q^96 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.70711	+	0.292893i	−0.985599	+	0.169102i
$3$	−1.70711	+	0.292893i	−0.985599	+	0.169102i
$4$		−	1.00000i		−	0.500000i
$5$	1.73205	−	1.41421i	0.774597	−	0.632456i
$5$	1.73205	−	1.41421i	0.774597	−	0.632456i
$6$	−1.00000	+	1.41421i	−0.408248	+	0.577350i
$7$	2.44949	+	2.44949i	0.925820	+	0.925820i	0.997433	−	0.0716124i	$-0.0228145\pi$
$7$	2.44949	+	2.44949i	0.925820	+	0.925820i	−0.0716124	+	0.997433i	$0.522814\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.82843	−	1.00000i	0.942809	−	0.333333i
$10$	0.224745	−	2.22474i	0.0710706	−	0.703526i
$11$			5.65685i			1.70561i	0.522233	+	0.852803i	$0.325099\pi$
$11$			5.65685i			1.70561i	−0.522233	+	0.852803i	$0.674901\pi$
$12$	0.292893	+	1.70711i	0.0845510	+	0.492799i
$13$	−3.44949	+	3.44949i	−0.956716	+	0.956716i	−0.999101	−	0.0423850i	$-0.986504\pi$
$13$	−3.44949	+	3.44949i	−0.956716	+	0.956716i	0.0423850	+	0.999101i	$0.486504\pi$
$14$	3.46410			0.925820
$15$	−2.54258	+	2.92152i	−0.656492	+	0.754333i
$16$	−1.00000			−0.250000
$17$	5.19615	−	5.19615i	1.26025	−	1.26025i	0.309282	−	0.950971i	$-0.399911\pi$
$17$	5.19615	−	5.19615i	1.26025	−	1.26025i	0.950971	−	0.309282i	$-0.100089\pi$
$18$	1.29289	−	2.70711i	0.304738	−	0.638071i
$19$			2.44949i			0.561951i	0.959715	+	0.280976i	$0.0906580\pi$
$19$			2.44949i			0.561951i	−0.959715	+	0.280976i	$0.909342\pi$
$20$	−1.41421	−	1.73205i	−0.316228	−	0.387298i
$21$	−4.89898	−	3.46410i	−1.06904	−	0.755929i
$22$	4.00000	+	4.00000i	0.852803	+	0.852803i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$	1.41421	+	1.00000i	0.288675	+	0.204124i
$25$	1.00000	−	4.89898i	0.200000	−	0.979796i
$26$			4.87832i			0.956716i
$27$	−4.53553	+	2.53553i	−0.872864	+	0.487964i
$28$	2.44949	−	2.44949i	0.462910	−	0.462910i
$29$	2.19275			0.407184			0.203592	−	0.979056i	$-0.434738\pi$
$29$	2.19275			0.407184			0.203592	+	0.979056i	$0.434738\pi$
$30$	0.267949	+	3.86370i	0.0489206	+	0.705412i
$31$	4.89898			0.879883			0.439941	−	0.898027i	$-0.354999\pi$
$31$	4.89898			0.879883			0.439941	+	0.898027i	$0.354999\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−1.65685	−	9.65685i	−0.288421	−	1.68104i
$34$		−	7.34847i		−	1.26025i
$35$	7.70674	+	0.778539i	1.30268	+	0.131597i
$36$	−1.00000	−	2.82843i	−0.166667	−	0.471405i
$37$	−2.44949	−	2.44949i	−0.402694	−	0.402694i	0.476488	−	0.879181i	$-0.341910\pi$
$37$	−2.44949	−	2.44949i	−0.402694	−	0.402694i	−0.879181	+	0.476488i	$0.841910\pi$
$38$	1.73205	+	1.73205i	0.280976	+	0.280976i
$39$	4.87832	−	6.89898i	0.781156	−	1.10472i
$40$	−2.22474	−	0.224745i	−0.351763	−	0.0355353i
$41$			8.48528i			1.32518i	0.748983	+	0.662589i	$0.230542\pi$
$41$			8.48528i			1.32518i	−0.748983	+	0.662589i	$0.769458\pi$
$42$	−5.91359	+	1.01461i	−0.912487	+	0.156558i
$43$	2.89898	−	2.89898i	0.442090	−	0.442090i	−0.450624	−	0.892714i	$-0.648798\pi$
$43$	2.89898	−	2.89898i	0.442090	−	0.442090i	0.892714	+	0.450624i	$0.148798\pi$
$44$	5.65685			0.852803
$45$	3.48477	−	5.73205i	0.519478	−	0.854484i
$46$	1.00000			0.147442
$47$	4.87832	−	4.87832i	0.711575	−	0.711575i	−0.255289	−	0.966865i	$-0.582171\pi$
$47$	4.87832	−	4.87832i	0.711575	−	0.711575i	0.966865	+	0.255289i	$0.0821707\pi$
$48$	1.70711	−	0.292893i	0.246400	−	0.0422755i
$49$			5.00000i			0.714286i
$50$	−2.75699	−	4.17121i	−0.389898	−	0.589898i
$51$	−7.34847	+	10.3923i	−1.02899	+	1.45521i
$52$	3.44949	+	3.44949i	0.478358	+	0.478358i
$53$	0.953512	+	0.953512i	0.130975	+	0.130975i	0.769555	−	0.638580i	$-0.220478\pi$
$53$	0.953512	+	0.953512i	0.130975	+	0.130975i	−0.638580	+	0.769555i	$0.720478\pi$
$54$	−1.41421	+	5.00000i	−0.192450	+	0.680414i
$55$	8.00000	+	9.79796i	1.07872	+	1.32116i
$56$		−	3.46410i		−	0.462910i
$57$	−0.717439	−	4.18154i	−0.0950271	−	0.553859i
$58$	1.55051	−	1.55051i	0.203592	−	0.203592i
$59$	5.51399			0.717860			0.358930	−	0.933364i	$-0.383142\pi$
$59$	5.51399			0.717860			0.358930	+	0.933364i	$0.383142\pi$
$60$	2.92152	+	2.54258i	0.377167	+	0.328246i
$61$	0.898979			0.115103			0.0575513	−	0.998343i	$-0.481671\pi$
$61$	0.898979			0.115103			0.0575513	+	0.998343i	$0.481671\pi$
$62$	3.46410	−	3.46410i	0.439941	−	0.439941i
$63$	9.37769	+	4.47871i	1.18148	+	0.564265i
$64$			1.00000i			0.125000i
$65$	−1.09638	+	10.8530i	−0.135989	+	1.34615i
$66$	−8.00000	−	5.65685i	−0.984732	−	0.696311i
$67$	−10.8990	−	10.8990i	−1.33152	−	1.33152i	−0.904009	−	0.427513i	$-0.859390\pi$
$67$	−10.8990	−	10.8990i	−1.33152	−	1.33152i	−0.427513	−	0.904009i	$-0.640610\pi$
$68$	−5.19615	−	5.19615i	−0.630126	−	0.630126i
$69$	−1.41421	−	1.00000i	−0.170251	−	0.120386i
$70$	6.00000	−	4.89898i	0.717137	−	0.585540i
$71$		−	14.6349i		−	1.73685i	−0.495822	−	0.868424i	$-0.665133\pi$
$71$		−	14.6349i		−	1.73685i	0.495822	−	0.868424i	$-0.334867\pi$
$72$	−2.70711	−	1.29289i	−0.319036	−	0.152369i
$73$	−1.89898	+	1.89898i	−0.222259	+	0.222259i	−0.809449	−	0.587190i	$-0.800234\pi$
$73$	−1.89898	+	1.89898i	−0.222259	+	0.222259i	0.587190	+	0.809449i	$0.300234\pi$
$74$	−3.46410			−0.402694
$75$	−0.272229	+	8.65597i	−0.0314343	+	0.999506i
$76$	2.44949			0.280976
$77$	−13.8564	+	13.8564i	−1.57908	+	1.57908i
$78$	−1.42883	−	8.32780i	−0.161783	−	0.942938i
$79$			4.44949i			0.500607i	0.968167	+	0.250303i	$0.0805304\pi$
$79$			4.44949i			0.500607i	−0.968167	+	0.250303i	$0.919470\pi$
$80$	−1.73205	+	1.41421i	−0.193649	+	0.158114i
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$	6.00000	+	6.00000i	0.662589	+	0.662589i
$83$	−1.41421	−	1.41421i	−0.155230	−	0.155230i	0.625219	−	0.780449i	$-0.285010\pi$
$83$	−1.41421	−	1.41421i	−0.155230	−	0.155230i	−0.780449	+	0.625219i	$0.785010\pi$
$84$	−3.46410	+	4.89898i	−0.377964	+	0.534522i
$85$	1.65153	−	16.3485i	0.179134	−	1.77324i
$86$		−	4.09978i		−	0.442090i
$87$	−3.74326	+	0.642242i	−0.401320	+	0.0688556i
$88$	4.00000	−	4.00000i	0.426401	−	0.426401i
$89$	−9.12096			−0.966819			−0.483410	−	0.875394i	$-0.660602\pi$
$89$	−9.12096			−0.966819			−0.483410	+	0.875394i	$0.660602\pi$
$90$	−1.58907	−	6.51727i	−0.167503	−	0.686981i
$91$	−16.8990			−1.77149
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$	−8.36308	+	1.43488i	−0.867211	+	0.148790i
$94$		−	6.89898i		−	0.711575i
$95$	3.46410	+	4.24264i	0.355409	+	0.435286i
$96$	1.00000	−	1.41421i	0.102062	−	0.144338i
$97$	−0.449490	−	0.449490i	−0.0456388	−	0.0456388i	0.683919	−	0.729558i	$-0.260274\pi$
$97$	−0.449490	−	0.449490i	−0.0456388	−	0.0456388i	−0.729558	+	0.683919i	$0.760274\pi$
$98$	3.53553	+	3.53553i	0.357143	+	0.357143i
$99$	5.65685	+	16.0000i	0.568535	+	1.60806i
$100$	−4.89898	−	1.00000i	−0.489898	−	0.100000i
$101$			0.635674i			0.0632520i	0.999500	+	0.0316260i	$0.0100685\pi$
$101$			0.635674i			0.0632520i	−0.999500	+	0.0316260i	$0.989931\pi$
$102$	2.15232	+	12.5446i	0.213111	+	1.24210i
$103$	−10.8990	+	10.8990i	−1.07391	+	1.07391i	−0.0768670	+	0.997041i	$0.524492\pi$
$103$	−10.8990	+	10.8990i	−1.07391	+	1.07391i	−0.997041	+	0.0768670i	$0.975508\pi$
$104$	4.87832			0.478358
$105$	−13.3843	+	0.928203i	−1.30617	+	0.0905834i
$106$	1.34847			0.130975
$107$	−7.70674	+	7.70674i	−0.745039	+	0.745039i	−0.973543	−	0.228504i	$-0.926617\pi$
$107$	−7.70674	+	7.70674i	−0.745039	+	0.745039i	0.228504	+	0.973543i	$0.426617\pi$
$108$	2.53553	+	4.53553i	0.243982	+	0.436432i
$109$			13.7980i			1.32160i	0.750560	+	0.660802i	$0.229784\pi$
$109$			13.7980i			1.32160i	−0.750560	+	0.660802i	$0.770216\pi$
$110$	12.5851	+	1.27135i	1.19994	+	0.121218i
$111$	4.89898	+	3.46410i	0.464991	+	0.328798i
$112$	−2.44949	−	2.44949i	−0.231455	−	0.231455i
$113$	−8.02458	−	8.02458i	−0.754889	−	0.754889i	0.220498	−	0.975387i	$-0.429232\pi$
$113$	−8.02458	−	8.02458i	−0.754889	−	0.754889i	−0.975387	+	0.220498i	$0.929232\pi$
$114$	−3.46410	−	2.44949i	−0.324443	−	0.229416i
$115$	2.22474	+	0.224745i	0.207459	+	0.0209576i
$116$		−	2.19275i		−	0.203592i
$117$	−6.30714	+	13.2061i	−0.583095	+	1.22091i
$118$	3.89898	−	3.89898i	0.358930	−	0.358930i
$119$	25.4558			2.33353
$120$	3.86370	−	0.267949i	0.352706	−	0.0244603i
$121$	−21.0000			−1.90909
$122$	0.635674	−	0.635674i	0.0575513	−	0.0575513i
$123$	−2.48528	−	14.4853i	−0.224090	−	1.30609i
$124$		−	4.89898i		−	0.439941i
$125$	−5.19615	−	9.89949i	−0.464758	−	0.885438i
$126$	9.79796	−	3.46410i	0.872872	−	0.308607i
$127$	−3.55051	−	3.55051i	−0.315057	−	0.315057i	0.531808	−	0.846865i	$-0.321513\pi$
$127$	−3.55051	−	3.55051i	−0.315057	−	0.315057i	−0.846865	+	0.531808i	$0.821513\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−4.09978	+	5.79796i	−0.360965	+	0.510482i
$130$	6.89898	+	8.44949i	0.605081	+	0.741069i
$131$			0.142865i			0.0124821i	0.999981	+	0.00624107i	$0.00198661\pi$
$131$			0.142865i			0.0124821i	−0.999981	+	0.00624107i	$0.998013\pi$
$132$	−9.65685	+	1.65685i	−0.840521	+	0.144211i
$133$	−6.00000	+	6.00000i	−0.520266	+	0.520266i
$134$	−15.4135			−1.33152
$135$	−4.26999	+	10.8059i	−0.367502	+	0.930023i
$136$	−7.34847			−0.630126
$137$	13.6814	−	13.6814i	1.16888	−	1.16888i	0.186412	−	0.982472i	$-0.440314\pi$
$137$	13.6814	−	13.6814i	1.16888	−	1.16888i	0.982472	−	0.186412i	$-0.0596860\pi$
$138$	−1.70711	+	0.292893i	−0.145319	+	0.0249327i
$139$			18.6969i			1.58585i	0.609317	+	0.792927i	$0.291444\pi$
$139$			18.6969i			1.58585i	−0.609317	+	0.792927i	$0.708556\pi$
$140$	0.778539	−	7.70674i	0.0657986	−	0.651339i
$141$	−6.89898	+	9.75663i	−0.580999	+	0.821656i
$142$	−10.3485	−	10.3485i	−0.868424	−	0.868424i
$143$	−19.5133	−	19.5133i	−1.63178	−	1.63178i
$144$	−2.82843	+	1.00000i	−0.235702	+	0.0833333i
$145$	3.79796	−	3.10102i	0.315403	−	0.257526i
$146$			2.68556i			0.222259i
$147$	−1.46447	−	8.53553i	−0.120787	−	0.703999i
$148$	−2.44949	+	2.44949i	−0.201347	+	0.201347i
$149$	11.0280			0.903447			0.451724	−	0.892158i	$-0.350809\pi$
$149$	11.0280			0.903447			0.451724	+	0.892158i	$0.350809\pi$
$150$	5.92820	+	6.31319i	0.484036	+	0.515470i
$151$	−0.898979			−0.0731579			−0.0365790	−	0.999331i	$-0.511646\pi$
$151$	−0.898979			−0.0731579			−0.0365790	+	0.999331i	$0.511646\pi$
$152$	1.73205	−	1.73205i	0.140488	−	0.140488i
$153$	9.50079	−	19.8931i	0.768093	−	1.60826i
$154$			19.5959i			1.57908i
$155$	8.48528	−	6.92820i	0.681554	−	0.556487i
$156$	−6.89898	−	4.87832i	−0.552360	−	0.390578i
$157$	−8.44949	−	8.44949i	−0.674343	−	0.674343i	0.284371	−	0.958714i	$-0.408215\pi$
$157$	−8.44949	−	8.44949i	−0.674343	−	0.674343i	−0.958714	+	0.284371i	$0.908215\pi$
$158$	3.14626	+	3.14626i	0.250303	+	0.250303i
$159$	−1.90702	−	1.34847i	−0.151237	−	0.106941i
$160$	−0.224745	+	2.22474i	−0.0177676	+	0.175882i
$161$			3.46410i			0.273009i
$162$	0.949747	−	8.94975i	0.0746192	−	0.703159i
$163$	−4.00000	+	4.00000i	−0.313304	+	0.313304i	−0.846188	−	0.532884i	$-0.821108\pi$
$163$	−4.00000	+	4.00000i	−0.313304	+	0.313304i	0.532884	+	0.846188i	$0.321108\pi$
$164$	8.48528			0.662589
$165$	−16.5266	−	14.3830i	−1.28659	−	1.11972i
$166$	−2.00000			−0.155230
$167$	−5.65685	+	5.65685i	−0.437741	+	0.437741i	−0.891251	−	0.453510i	$-0.850171\pi$
$167$	−5.65685	+	5.65685i	−0.437741	+	0.437741i	0.453510	+	0.891251i	$0.350171\pi$
$168$	1.01461	+	5.91359i	0.0782790	+	0.456243i
$169$		−	10.7980i		−	0.830612i
$170$	−10.3923	−	12.7279i	−0.797053	−	0.976187i
$171$	2.44949	+	6.92820i	0.187317	+	0.529813i
$172$	−2.89898	−	2.89898i	−0.221045	−	0.221045i
$173$	−3.60697	−	3.60697i	−0.274233	−	0.274233i	0.556569	−	0.830801i	$-0.312118\pi$
$173$	−3.60697	−	3.60697i	−0.274233	−	0.274233i	−0.830801	+	0.556569i	$0.812118\pi$
$174$	−2.19275	+	3.10102i	−0.166232	+	0.235088i
$175$	14.4495	−	9.55051i	1.09228	−	0.721951i
$176$		−	5.65685i		−	0.426401i
$177$	−9.41297	+	1.61501i	−0.707522	+	0.121392i
$178$	−6.44949	+	6.44949i	−0.483410	+	0.483410i
$179$	15.2706			1.14138			0.570690	−	0.821166i	$-0.306676\pi$
$179$	15.2706			1.14138			0.570690	+	0.821166i	$0.306676\pi$
$180$	−5.73205	−	3.48477i	−0.427242	−	0.259739i
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	−11.9494	+	11.9494i	−0.885747	+	0.885747i
$183$	−1.53465	+	0.263305i	−0.113445	+	0.0194641i
$184$		−	1.00000i		−	0.0737210i
$185$	−7.70674	−	0.778539i	−0.566611	−	0.0572393i
$186$	−4.89898	+	6.92820i	−0.359211	+	0.508001i
$187$	29.3939	+	29.3939i	2.14949	+	2.14949i
$188$	−4.87832	−	4.87832i	−0.355788	−	0.355788i
$189$	−17.3205	−	4.89898i	−1.25988	−	0.356348i
$190$	5.44949	+	0.550510i	0.395348	+	0.0399382i
$191$		−	17.9562i		−	1.29926i	−0.760249	−	0.649632i	$-0.774923\pi$
$191$		−	17.9562i		−	1.29926i	0.760249	−	0.649632i	$-0.225077\pi$
$192$	−0.292893	−	1.70711i	−0.0211377	−	0.123200i
$193$	1.89898	−	1.89898i	0.136692	−	0.136692i	−0.635450	−	0.772142i	$-0.719185\pi$
$193$	1.89898	−	1.89898i	0.136692	−	0.136692i	0.772142	+	0.635450i	$0.219185\pi$
$194$	−0.635674			−0.0456388
$195$	−1.30714	−	18.8484i	−0.0936063	−	1.34976i
$196$	5.00000			0.357143
$197$	7.70674	−	7.70674i	0.549083	−	0.549083i	−0.377093	−	0.926175i	$-0.623076\pi$
$197$	7.70674	−	7.70674i	0.549083	−	0.549083i	0.926175	+	0.377093i	$0.123076\pi$
$198$	15.3137	+	7.31371i	1.08830	+	0.519763i
$199$			7.55051i			0.535241i	0.963524	+	0.267621i	$0.0862374\pi$
$199$			7.55051i			0.535241i	−0.963524	+	0.267621i	$0.913763\pi$
$200$	−4.17121	+	2.75699i	−0.294949	+	0.194949i
$201$	21.7980	+	15.4135i	1.53751	+	1.08718i
$202$	0.449490	+	0.449490i	0.0316260	+	0.0316260i
$203$	5.37113	+	5.37113i	0.376979	+	0.376979i
$204$	10.3923	+	7.34847i	0.727607	+	0.514496i
$205$	12.0000	+	14.6969i	0.838116	+	1.02648i
$206$			15.4135i			1.07391i
$207$	2.70711	+	1.29289i	0.188157	+	0.0898623i
$208$	3.44949	−	3.44949i	0.239179	−	0.239179i
$209$	−13.8564			−0.958468
$210$	−8.80776	+	10.1204i	−0.607793	+	0.698377i
$211$	18.6969			1.28715			0.643575	−	0.765383i	$-0.277450\pi$
$211$	18.6969			1.28715			0.643575	+	0.765383i	$0.277450\pi$
$212$	0.953512	−	0.953512i	0.0654875	−	0.0654875i
$213$	4.28648	+	24.9834i	0.293705	+	1.71184i
$214$			10.8990i			0.745039i
$215$	0.921404	−	9.12096i	0.0628392	−	0.622044i
$216$	5.00000	+	1.41421i	0.340207	+	0.0962250i
$217$	12.0000	+	12.0000i	0.814613	+	0.814613i
$218$	9.75663	+	9.75663i	0.660802	+	0.660802i
$219$	2.68556	−	3.79796i	0.181473	−	0.256642i
$220$	9.79796	−	8.00000i	0.660578	−	0.539360i
$221$			35.8481i			2.41141i
$222$	5.91359	−	1.01461i	0.396894	−	0.0680963i
$223$	−12.4495	+	12.4495i	−0.833679	+	0.833679i	−0.988018	−	0.154339i	$-0.950675\pi$
$223$	−12.4495	+	12.4495i	−0.833679	+	0.833679i	0.154339	+	0.988018i	$0.450675\pi$
$224$	−3.46410			−0.231455
$225$	−2.07055	−	14.8564i	−0.138037	−	0.990427i
$226$	−11.3485			−0.754889
$227$	−0.778539	+	0.778539i	−0.0516735	+	0.0516735i	−0.732471	−	0.680798i	$-0.761633\pi$
$227$	−0.778539	+	0.778539i	−0.0516735	+	0.0516735i	0.680798	+	0.732471i	$0.261633\pi$
$228$	−4.18154	+	0.717439i	−0.276929	+	0.0475136i
$229$		−	6.69694i		−	0.442546i	−0.975212	−	0.221273i	$-0.928979\pi$
$229$		−	6.69694i		−	0.442546i	0.975212	−	0.221273i	$-0.0710212\pi$
$230$	1.73205	−	1.41421i	0.114208	−	0.0932505i
$231$	19.5959	−	27.7128i	1.28932	−	1.82337i
$232$	−1.55051	−	1.55051i	−0.101796	−	0.101796i
$233$	3.60697	+	3.60697i	0.236300	+	0.236300i	0.815316	−	0.579016i	$-0.196563\pi$
$233$	3.60697	+	3.60697i	0.236300	+	0.236300i	−0.579016	+	0.815316i	$0.696563\pi$
$234$	4.87832	+	13.7980i	0.318905	+	0.902001i
$235$	1.55051	−	15.3485i	0.101144	−	1.00122i
$236$		−	5.51399i		−	0.358930i
$237$	−1.30323	−	7.59575i	−0.0846536	−	0.493397i
$238$	18.0000	−	18.0000i	1.16677	−	1.16677i
$239$	−13.3636			−0.864419			−0.432210	−	0.901773i	$-0.642266\pi$
$239$	−13.3636			−0.864419			−0.432210	+	0.901773i	$0.642266\pi$
$240$	2.54258	−	2.92152i	0.164123	−	0.188583i
$241$	−9.10102			−0.586248			−0.293124	−	0.956074i	$-0.594695\pi$
$241$	−9.10102			−0.586248			−0.293124	+	0.956074i	$0.594695\pi$
$242$	−14.8492	+	14.8492i	−0.954545	+	0.954545i
$243$	−10.2929	+	11.7071i	−0.660289	+	0.751011i
$244$		−	0.898979i		−	0.0575513i
$245$	7.07107	+	8.66025i	0.451754	+	0.553283i
$246$	−12.0000	−	8.48528i	−0.765092	−	0.541002i
$247$	−8.44949	−	8.44949i	−0.537628	−	0.537628i
$248$	−3.46410	−	3.46410i	−0.219971	−	0.219971i
$249$	2.82843	+	2.00000i	0.179244	+	0.126745i
$250$	−10.6742	−	3.32577i	−0.675098	−	0.210340i
$251$		−	12.8708i		−	0.812397i	−0.913785	−	0.406198i	$-0.866854\pi$
$251$		−	12.8708i		−	0.812397i	0.913785	−	0.406198i	$-0.133146\pi$
$252$	4.47871	−	9.37769i	0.282132	−	0.590739i
$253$	−4.00000	+	4.00000i	−0.251478	+	0.251478i
$254$	−5.02118			−0.315057
$255$	1.96902	+	28.3923i	0.123305	+	1.77800i
$256$	1.00000			0.0625000
$257$	9.61377	−	9.61377i	0.599690	−	0.599690i	−0.340540	−	0.940230i	$-0.610610\pi$
$257$	9.61377	−	9.61377i	0.599690	−	0.599690i	0.940230	+	0.340540i	$0.110610\pi$
$258$	1.20080	+	6.99876i	0.0747583	+	0.435723i
$259$		−	12.0000i		−	0.745644i
$260$	10.8530	+	1.09638i	0.673075	+	0.0679944i
$261$	6.20204	−	2.19275i	0.383897	−	0.135728i
$262$	0.101021	+	0.101021i	0.00624107	+	0.00624107i
$263$	5.65685	+	5.65685i	0.348817	+	0.348817i	0.859669	−	0.510852i	$-0.170670\pi$
$263$	5.65685	+	5.65685i	0.348817	+	0.348817i	−0.510852	+	0.859669i	$0.670670\pi$
$264$	−5.65685	+	8.00000i	−0.348155	+	0.492366i
$265$	3.00000	+	0.303062i	0.184289	+	0.0186169i
$266$			8.48528i			0.520266i
$267$	15.5704	−	2.67147i	0.952896	−	0.163491i
$268$	−10.8990	+	10.8990i	−0.665761	+	0.665761i
$269$	−6.29253			−0.383662			−0.191831	−	0.981428i	$-0.561443\pi$
$269$	−6.29253			−0.383662			−0.191831	+	0.981428i	$0.561443\pi$
$270$	4.62158	+	10.6603i	0.281260	+	0.648762i
$271$	−24.4949			−1.48796			−0.743980	−	0.668202i	$-0.767064\pi$
$271$	−24.4949			−1.48796			−0.743980	+	0.668202i	$0.767064\pi$
$272$	−5.19615	+	5.19615i	−0.315063	+	0.315063i
$273$	28.8484	−	4.94960i	1.74598	−	0.299563i
$274$		−	19.3485i		−	1.16888i
$275$	27.7128	+	5.65685i	1.67115	+	0.341121i
$276$	−1.00000	+	1.41421i	−0.0601929	+	0.0851257i
$277$	−9.44949	−	9.44949i	−0.567765	−	0.567765i	0.363737	−	0.931502i	$-0.381501\pi$
$277$	−9.44949	−	9.44949i	−0.567765	−	0.567765i	−0.931502	+	0.363737i	$0.881501\pi$
$278$	13.2207	+	13.2207i	0.792927	+	0.792927i
$279$	13.8564	−	4.89898i	0.829561	−	0.293294i
$280$	−4.89898	−	6.00000i	−0.292770	−	0.358569i
$281$		−	5.65685i		−	0.337460i	−0.985662	−	0.168730i	$-0.946033\pi$
$281$		−	5.65685i		−	0.337460i	0.985662	−	0.168730i	$-0.0539665\pi$
$282$	2.02066	+	11.7773i	0.120329	+	0.701328i
$283$	5.34847	−	5.34847i	0.317933	−	0.317933i	−0.530039	−	0.847973i	$-0.677823\pi$
$283$	5.34847	−	5.34847i	0.317933	−	0.317933i	0.847973	+	0.530039i	$0.177823\pi$
$284$	−14.6349			−0.868424
$285$	−7.15623	−	6.22803i	−0.423899	−	0.368917i
$286$	−27.5959			−1.63178
$287$	−20.7846	+	20.7846i	−1.22688	+	1.22688i
$288$	−1.29289	+	2.70711i	−0.0761845	+	0.159518i
$289$		−	37.0000i		−	2.17647i
$290$	0.492810	−	4.87832i	0.0289388	−	0.286465i
$291$	0.898979	+	0.635674i	0.0526991	+	0.0372639i
$292$	1.89898	+	1.89898i	0.111129	+	0.111129i
$293$	−13.5386	−	13.5386i	−0.790932	−	0.790932i	0.190714	−	0.981646i	$-0.438920\pi$
$293$	−13.5386	−	13.5386i	−0.790932	−	0.790932i	−0.981646	+	0.190714i	$0.938920\pi$
$294$	−7.07107	−	5.00000i	−0.412393	−	0.291606i
$295$	9.55051	−	7.79796i	0.556052	−	0.454015i
$296$			3.46410i			0.201347i
$297$	−14.3431	−	25.6569i	−0.832274	−	1.48876i
$298$	7.79796	−	7.79796i	0.451724	−	0.451724i
$299$	−4.87832			−0.282120
$300$	8.65597	+	0.272229i	0.499753	+	0.0157171i
$301$	14.2020			0.818592
$302$	−0.635674	+	0.635674i	−0.0365790	+	0.0365790i
$303$	−0.186185	−	1.08516i	−0.0106960	−	0.0623411i
$304$		−	2.44949i		−	0.140488i
$305$	1.55708	−	1.27135i	0.0891580	−	0.0727972i
$306$	−7.34847	−	20.7846i	−0.420084	−	1.18818i
$307$	−22.6969	−	22.6969i	−1.29538	−	1.29538i	−0.931409	−	0.363973i	$-0.881420\pi$
$307$	−22.6969	−	22.6969i	−1.29538	−	1.29538i	−0.363973	−	0.931409i	$-0.618580\pi$
$308$	13.8564	+	13.8564i	0.789542	+	0.789542i
$309$	15.4135	−	21.7980i	0.876843	−	1.24004i
$310$	1.10102	−	10.8990i	0.0625338	−	0.619020i
$311$			14.3492i			0.813669i	0.913502	+	0.406835i	$0.133368\pi$
$311$			14.3492i			0.813669i	−0.913502	+	0.406835i	$0.866632\pi$
$312$	−8.32780	+	1.42883i	−0.471469	+	0.0808913i
$313$	−15.1464	+	15.1464i	−0.856127	+	0.856127i	−0.990879	−	0.134753i	$-0.956976\pi$
$313$	−15.1464	+	15.1464i	−0.856127	+	0.856127i	0.134753	+	0.990879i	$0.456976\pi$
$314$	−11.9494			−0.674343
$315$	22.5765	−	5.50470i	1.27204	−	0.310155i
$316$	4.44949			0.250303
$317$	13.3636	−	13.3636i	0.750574	−	0.750574i	−0.224012	−	0.974586i	$-0.571915\pi$
$317$	13.3636	−	13.3636i	0.750574	−	0.750574i	0.974586	+	0.224012i	$0.0719155\pi$
$318$	−2.30198	+	0.394957i	−0.129089	+	0.0221481i
$319$			12.4041i			0.694495i
$320$	1.41421	+	1.73205i	0.0790569	+	0.0968246i
$321$	10.8990	−	15.4135i	0.608322	−	0.860297i
$322$	2.44949	+	2.44949i	0.136505	+	0.136505i
$323$	12.7279	+	12.7279i	0.708201	+	0.708201i
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$	13.4495	+	20.3485i	0.746043	+	1.12873i
$326$			5.65685i			0.313304i
$327$	−4.04133	−	23.5546i	−0.223486	−	1.30257i
$328$	6.00000	−	6.00000i	0.331295	−	0.331295i
$329$	23.8988			1.31758
$330$	−21.8564	+	1.51575i	−1.20316	+	0.0834393i
$331$	−18.6969			−1.02768			−0.513838	−	0.857887i	$-0.671777\pi$
$331$	−18.6969			−1.02768			−0.513838	+	0.857887i	$0.671777\pi$
$332$	−1.41421	+	1.41421i	−0.0776151	+	0.0776151i
$333$	−9.37769	−	4.47871i	−0.513894	−	0.245432i
$334$			8.00000i			0.437741i
$335$	−34.2911	−	3.46410i	−1.87352	−	0.189264i
$336$	4.89898	+	3.46410i	0.267261	+	0.188982i
$337$	14.4495	+	14.4495i	0.787114	+	0.787114i	0.981020	−	0.193906i	$-0.0621157\pi$
$337$	14.4495	+	14.4495i	0.787114	+	0.787114i	−0.193906	+	0.981020i	$0.562116\pi$
$338$	−7.63531	−	7.63531i	−0.415306	−	0.415306i
$339$	16.0492	+	11.3485i	0.871671	+	0.616364i
$340$	−16.3485	−	1.65153i	−0.886620	−	0.0895668i
$341$			27.7128i			1.50073i
$342$	6.63103	+	3.16693i	0.358565	+	0.171248i
$343$	4.89898	−	4.89898i	0.264520	−	0.264520i
$344$	−4.09978			−0.221045
$345$	−3.86370	+	0.267949i	−0.208015	+	0.0144259i
$346$	−5.10102			−0.274233
$347$	0.142865	−	0.142865i	0.00766937	−	0.00766937i	−0.703262	−	0.710931i	$-0.748274\pi$
$347$	0.142865	−	0.142865i	0.00766937	−	0.00766937i	0.710931	+	0.703262i	$0.248274\pi$
$348$	0.642242	+	3.74326i	0.0344278	+	0.200660i
$349$		−	22.0000i		−	1.17763i	−0.808267	−	0.588817i	$-0.799594\pi$
$349$		−	22.0000i		−	1.17763i	0.808267	−	0.588817i	$-0.200406\pi$
$350$	3.46410	−	16.9706i	0.185164	−	0.907115i
$351$	6.89898	−	24.3916i	0.368240	−	1.30193i
$352$	−4.00000	−	4.00000i	−0.213201	−	0.213201i
$353$	−23.1202	−	23.1202i	−1.23057	−	1.23057i	−0.963747	−	0.266819i	$-0.914027\pi$
$353$	−23.1202	−	23.1202i	−1.23057	−	1.23057i	−0.266819	−	0.963747i	$-0.585973\pi$
$354$	−5.51399	+	7.79796i	−0.293065	+	0.414457i
$355$	−20.6969	−	25.3485i	−1.09848	−	1.34536i
$356$			9.12096i			0.483410i
$357$	−43.4558	+	7.45584i	−2.29993	+	0.394605i
$358$	10.7980	−	10.7980i	0.570690	−	0.570690i
$359$	−26.7272			−1.41061			−0.705304	−	0.708905i	$-0.749189\pi$
$359$	−26.7272			−1.41061			−0.705304	+	0.708905i	$0.749189\pi$
$360$	−6.51727	+	1.58907i	−0.343490	+	0.0837514i
$361$	13.0000			0.684211
$362$	5.65685	−	5.65685i	0.297318	−	0.297318i
$363$	35.8492	−	6.15076i	1.88160	−	0.322831i
$364$			16.8990i			0.885747i
$365$	−0.603566	+	5.97469i	−0.0315921	+	0.312730i
$366$	−0.898979	+	1.27135i	−0.0469904	+	0.0664545i
$367$	19.7980	+	19.7980i	1.03345	+	1.03345i	0.999421	+	0.0340240i	$0.0108323\pi$
$367$	19.7980	+	19.7980i	1.03345	+	1.03345i	0.0340240	+	0.999421i	$0.489168\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$	8.48528	+	24.0000i	0.441726	+	1.24939i
$370$	−6.00000	+	4.89898i	−0.311925	+	0.254686i
$371$			4.67123i			0.242518i
$372$	1.43488	+	8.36308i	0.0743950	+	0.433606i
$373$	12.4495	−	12.4495i	0.644610	−	0.644610i	−0.307075	−	0.951685i	$-0.599350\pi$
$373$	12.4495	−	12.4495i	0.644610	−	0.644610i	0.951685	+	0.307075i	$0.0993503\pi$
$374$	41.5692			2.14949
$375$	11.7699	+	15.3776i	0.607794	+	0.794095i
$376$	−6.89898			−0.355788
$377$	−7.56388	+	7.56388i	−0.389560	+	0.389560i
$378$	−15.7116	+	8.78335i	−0.808115	+	0.451767i
$379$			5.14643i			0.264354i	0.991226	+	0.132177i	$0.0421968\pi$
$379$			5.14643i			0.264354i	−0.991226	+	0.132177i	$0.957803\pi$
$380$	4.24264	−	3.46410i	0.217643	−	0.177705i
$381$	7.10102	+	5.02118i	0.363796	+	0.257243i
$382$	−12.6969	−	12.6969i	−0.649632	−	0.649632i
$383$	4.73545	+	4.73545i	0.241970	+	0.241970i	0.817665	−	0.575695i	$-0.195268\pi$
$383$	4.73545	+	4.73545i	0.241970	+	0.241970i	−0.575695	+	0.817665i	$0.695268\pi$
$384$	−1.41421	−	1.00000i	−0.0721688	−	0.0510310i
$385$	−4.40408	+	43.5959i	−0.224453	+	2.22185i
$386$		−	2.68556i		−	0.136692i
$387$	5.30057	−	11.0985i	0.269443	−	0.564170i
$388$	−0.449490	+	0.449490i	−0.0228194	+	0.0228194i
$389$	−31.1127			−1.57748			−0.788738	−	0.614729i	$-0.789265\pi$
$389$	−31.1127			−1.57748			−0.788738	+	0.614729i	$0.789265\pi$
$390$	−14.2521	−	12.4035i	−0.721683	−	0.628076i
$391$	7.34847			0.371628
$392$	3.53553	−	3.53553i	0.178571	−	0.178571i
$393$	−0.0418441	−	0.243885i	−0.00211075	−	0.0123024i
$394$		−	10.8990i		−	0.549083i
$395$	6.29253	+	7.70674i	0.316611	+	0.387768i
$396$	16.0000	−	5.65685i	0.804030	−	0.284268i
$397$	8.55051	+	8.55051i	0.429138	+	0.429138i	0.888335	−	0.459197i	$-0.151863\pi$
$397$	8.55051	+	8.55051i	0.429138	+	0.429138i	−0.459197	+	0.888335i	$0.651863\pi$
$398$	5.33902	+	5.33902i	0.267621	+	0.267621i
$399$	8.48528	−	12.0000i	0.424795	−	0.600751i
$400$	−1.00000	+	4.89898i	−0.0500000	+	0.244949i
$401$			7.84961i			0.391991i	0.980605	+	0.195995i	$0.0627937\pi$
$401$			7.84961i			0.391991i	−0.980605	+	0.195995i	$0.937206\pi$
$402$	26.3125	−	4.51451i	1.31235	−	0.225163i
$403$	−16.8990	+	16.8990i	−0.841798	+	0.841798i
$404$	0.635674			0.0316260
$405$	4.12436	−	19.6975i	0.204941	−	0.978774i
$406$	7.59592			0.376979
$407$	13.8564	−	13.8564i	0.686837	−	0.686837i
$408$	12.5446	−	2.15232i	0.621051	−	0.106556i
$409$			13.7980i			0.682265i	0.940015	+	0.341133i	$0.110811\pi$
$409$			13.7980i			0.682265i	−0.940015	+	0.341133i	$0.889189\pi$
$410$	18.8776	+	1.90702i	0.932298	+	0.0941812i
$411$	−19.3485	+	27.3629i	−0.954390	+	1.34971i
$412$	10.8990	+	10.8990i	0.536954	+	0.536954i
$413$	13.5065	+	13.5065i	0.664610	+	0.664610i
$414$	2.82843	−	1.00000i	0.139010	−	0.0491473i
$415$	−4.44949	−	0.449490i	−0.218417	−	0.0220646i
$416$		−	4.87832i		−	0.239179i
$417$	−5.47621	−	31.9177i	−0.268171	−	1.56302i
$418$	−9.79796	+	9.79796i	−0.479234	+	0.479234i
$419$	4.38551			0.214246			0.107123	−	0.994246i	$-0.465836\pi$
$419$	4.38551			0.214246			0.107123	+	0.994246i	$0.465836\pi$
$420$	0.928203	+	13.3843i	0.0452917	+	0.653085i
$421$	0.898979			0.0438136			0.0219068	−	0.999760i	$-0.493026\pi$
$421$	0.898979			0.0438136			0.0219068	+	0.999760i	$0.493026\pi$
$422$	13.2207	−	13.2207i	0.643575	−	0.643575i
$423$	8.91964	−	18.6763i	0.433688	−	0.908072i
$424$		−	1.34847i		−	0.0654875i
$425$	−20.2597	−	30.6520i	−0.982739	−	1.48684i
$426$	20.6969	+	14.6349i	1.00277	+	0.709065i
$427$	2.20204	+	2.20204i	0.106564	+	0.106564i
$428$	7.70674	+	7.70674i	0.372519	+	0.372519i
$429$	39.0265	+	27.5959i	1.88422	+	1.33234i
$430$	−5.79796	−	7.10102i	−0.279602	−	0.342442i
$431$		−	22.3417i		−	1.07616i	−0.842893	−	0.538081i	$-0.819150\pi$
$431$		−	22.3417i		−	1.07616i	0.842893	−	0.538081i	$-0.180850\pi$
$432$	4.53553	−	2.53553i	0.218216	−	0.121991i
$433$	29.3485	−	29.3485i	1.41040	−	1.41040i	0.653287	−	0.757110i	$-0.273389\pi$
$433$	29.3485	−	29.3485i	1.41040	−	1.41040i	0.757110	−	0.653287i	$-0.226611\pi$
$434$	16.9706			0.814613
$435$	−5.57525	+	6.40617i	−0.267313	+	0.307152i
$436$	13.7980			0.660802
$437$	−1.73205	+	1.73205i	−0.0828552	+	0.0828552i
$438$	−0.786583	−	4.58454i	−0.0375844	−	0.219058i
$439$		−	16.0000i		−	0.763638i	−0.924237	−	0.381819i	$-0.875298\pi$
$439$		−	16.0000i		−	0.763638i	0.924237	−	0.381819i	$-0.124702\pi$
$440$	1.27135	−	12.5851i	0.0606092	−	0.599969i
$441$	5.00000	+	14.1421i	0.238095	+	0.673435i
$442$	25.3485	+	25.3485i	1.20570	+	1.20570i
$443$	−11.3137	−	11.3137i	−0.537531	−	0.537531i	0.385272	−	0.922803i	$-0.374107\pi$
$443$	−11.3137	−	11.3137i	−0.537531	−	0.537531i	−0.922803	+	0.385272i	$0.874107\pi$
$444$	3.46410	−	4.89898i	0.164399	−	0.232495i
$445$	−15.7980	+	12.8990i	−0.748895	+	0.611470i
$446$			17.6062i			0.833679i
$447$	−18.8259	+	3.23002i	−0.890436	+	0.152775i
$448$	−2.44949	+	2.44949i	−0.115728	+	0.115728i
$449$	−15.1278			−0.713923			−0.356961	−	0.934119i	$-0.616187\pi$
$449$	−15.1278			−0.713923			−0.356961	+	0.934119i	$0.616187\pi$
$450$	−11.9692	−	9.04096i	−0.564232	−	0.426195i
$451$	−48.0000			−2.26023
$452$	−8.02458	+	8.02458i	−0.377444	+	0.377444i
$453$	1.53465	−	0.263305i	0.0721043	−	0.0123711i
$454$			1.10102i			0.0516735i
$455$	−29.2699	+	23.8988i	−1.37219	+	1.12039i
$456$	−2.44949	+	3.46410i	−0.114708	+	0.162221i
$457$	1.55051	+	1.55051i	0.0725298	+	0.0725298i	0.742441	−	0.669911i	$-0.233668\pi$
$457$	1.55051	+	1.55051i	0.0725298	+	0.0725298i	−0.669911	+	0.742441i	$0.733668\pi$
$458$	−4.73545	−	4.73545i	−0.221273	−	0.221273i
$459$	−10.3923	+	36.7423i	−0.485071	+	1.71499i
$460$	0.224745	−	2.22474i	0.0104788	−	0.103729i
$461$			31.4626i			1.46536i	0.680573	+	0.732681i	$0.261731\pi$
$461$			31.4626i			1.46536i	−0.680573	+	0.732681i	$0.738269\pi$
$462$	−5.73951	−	33.4523i	−0.267026	−	1.55634i
$463$	26.0454	−	26.0454i	1.21043	−	1.21043i	0.239548	−	0.970884i	$-0.423001\pi$
$463$	26.0454	−	26.0454i	1.21043	−	1.21043i	0.970884	−	0.239548i	$-0.0769993\pi$
$464$	−2.19275			−0.101796
$465$	−12.4561	+	14.3125i	−0.577636	+	0.663725i
$466$	5.10102			0.236300
$467$	3.60697	−	3.60697i	0.166910	−	0.166910i	−0.618709	−	0.785620i	$-0.712344\pi$
$467$	3.60697	−	3.60697i	0.166910	−	0.166910i	0.785620	+	0.618709i	$0.212344\pi$
$468$	13.2061	+	6.30714i	0.610453	+	0.291548i
$469$		−	53.3939i		−	2.46550i
$470$	−9.75663	−	11.9494i	−0.450040	−	0.551184i
$471$	16.8990	+	11.9494i	0.778664	+	0.550599i
$472$	−3.89898	−	3.89898i	−0.179465	−	0.179465i
$473$	16.3991	+	16.3991i	0.754032	+	0.754032i
$474$	−6.29253	−	4.44949i	−0.289025	−	0.204372i
$475$	12.0000	+	2.44949i	0.550598	+	0.112390i
$476$		−	25.4558i		−	1.16677i
$477$	3.65045	+	1.74343i	0.167143	+	0.0798260i
$478$	−9.44949	+	9.44949i	−0.432210	+	0.432210i
$479$	−26.4415			−1.20814			−0.604071	−	0.796931i	$-0.706456\pi$
$479$	−26.4415			−1.20814			−0.604071	+	0.796931i	$0.706456\pi$
$480$	−0.267949	−	3.86370i	−0.0122302	−	0.176353i
$481$	16.8990			0.770527
$482$	−6.43539	+	6.43539i	−0.293124	+	0.293124i
$483$	−1.01461	−	5.91359i	−0.0461664	−	0.269078i
$484$			21.0000i			0.954545i
$485$	−1.41421	−	0.142865i	−0.0642161	−	0.00648715i
$486$	1.00000	+	15.5563i	0.0453609	+	0.705650i
$487$	19.3485	+	19.3485i	0.876763	+	0.876763i	0.993198	−	0.116435i	$-0.0371468\pi$
$487$	19.3485	+	19.3485i	0.876763	+	0.876763i	−0.116435	+	0.993198i	$0.537147\pi$
$488$	−0.635674	−	0.635674i	−0.0287756	−	0.0287756i
$489$	5.65685	−	8.00000i	0.255812	−	0.361773i
$490$	11.1237	+	1.12372i	0.502519	+	0.0507647i
$491$		−	25.3130i		−	1.14236i	−0.820825	−	0.571179i	$-0.806486\pi$
$491$		−	25.3130i		−	1.14236i	0.820825	−	0.571179i	$-0.193514\pi$
$492$	−14.4853	+	2.48528i	−0.653047	+	0.112045i
$493$	11.3939	−	11.3939i	0.513154	−	0.513154i
$494$	−11.9494			−0.537628
$495$	32.4254	+	19.7128i	1.45741	+	0.886025i
$496$	−4.89898			−0.219971
$497$	35.8481	−	35.8481i	1.60801	−	1.60801i
$498$	3.41421	−	0.585786i	0.152995	−	0.0262497i
$499$		−	33.7980i		−	1.51300i	−0.653991	−	0.756502i	$-0.726907\pi$
$499$		−	33.7980i		−	1.51300i	0.653991	−	0.756502i	$-0.273093\pi$
$500$	−9.89949	+	5.19615i	−0.442719	+	0.232379i
$501$	8.00000	−	11.3137i	0.357414	−	0.505459i
$502$	−9.10102	−	9.10102i	−0.406198	−	0.406198i
$503$	1.90702	+	1.90702i	0.0850300	+	0.0850300i	0.748342	−	0.663313i	$-0.230850\pi$
$503$	1.90702	+	1.90702i	0.0850300	+	0.0850300i	−0.663313	+	0.748342i	$0.730850\pi$
$504$	−3.46410	−	9.79796i	−0.154303	−	0.436436i
$505$	0.898979	+	1.10102i	0.0400041	+	0.0489948i
$506$			5.65685i			0.251478i
$507$	3.16265	+	18.4333i	0.140458	+	0.818650i
$508$	−3.55051	+	3.55051i	−0.157528	+	0.157528i
$509$	19.8632			0.880421			0.440211	−	0.897895i	$-0.354904\pi$
$509$	19.8632			0.880421			0.440211	+	0.897895i	$0.354904\pi$
$510$	21.4687	+	18.6841i	0.950650	+	0.827345i
$511$	−9.30306			−0.411543
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−6.21076	−	11.1097i	−0.274212	−	0.490507i
$514$		−	13.5959i		−	0.599690i
$515$	−3.46410	+	34.2911i	−0.152647	+	1.51105i
$516$	5.79796	+	4.09978i	0.255241	+	0.180483i
$517$	27.5959	+	27.5959i	1.21367	+	1.21367i
$518$	−8.48528	−	8.48528i	−0.372822	−	0.372822i
$519$	7.21393	+	5.10102i	0.316656	+	0.223910i
$520$	8.44949	−	6.89898i	0.370535	−	0.302540i
$521$		−	19.8632i		−	0.870223i	−0.900377	−	0.435111i	$-0.856709\pi$
$521$		−	19.8632i		−	0.870223i	0.900377	−	0.435111i	$-0.143291\pi$
$522$	2.83500	−	5.93602i	0.124084	−	0.259812i
$523$	−22.2474	+	22.2474i	−0.972813	+	0.972813i	−0.999640	−	0.0268271i	$-0.991460\pi$
$523$	−22.2474	+	22.2474i	−0.972813	+	0.972813i	0.0268271	+	0.999640i	$0.491460\pi$
$524$	0.142865			0.00624107
$525$	−21.8695	+	20.5359i	−0.954465	+	0.896260i
$526$	8.00000			0.348817
$527$	25.4558	−	25.4558i	1.10887	−	1.10887i
$528$	1.65685	+	9.65685i	0.0721053	+	0.420261i
$529$			1.00000i			0.0434783i
$530$	2.33562	−	1.90702i	0.101453	−	0.0828358i
$531$	15.5959	−	5.51399i	0.676805	−	0.239287i
$532$	6.00000	+	6.00000i	0.260133	+	0.260133i
$533$	−29.2699	−	29.2699i	−1.26782	−	1.26782i
$534$	9.12096	−	12.8990i	0.394702	−	0.558193i
$535$	−2.44949	+	24.2474i	−0.105901	+	1.04831i
$536$			15.4135i			0.665761i
$537$	−26.0686	+	4.47266i	−1.12494	+	0.193010i
$538$	−4.44949	+	4.44949i	−0.191831	+	0.191831i
$539$	−28.2843			−1.21829
$540$	10.8059	+	4.26999i	0.465011	+	0.183751i
$541$	18.6969			0.803844			0.401922	−	0.915674i	$-0.368342\pi$
$541$	18.6969			0.803844			0.401922	+	0.915674i	$0.368342\pi$
$542$	−17.3205	+	17.3205i	−0.743980	+	0.743980i
$543$	−13.6569	+	2.34315i	−0.586072	+	0.100554i
$544$			7.34847i			0.315063i
$545$	19.5133	+	23.8988i	0.835856	+	1.02371i
$546$	16.8990	−	23.8988i	0.723210	−	1.02277i
$547$	−11.5959	−	11.5959i	−0.495806	−	0.495806i	0.414324	−	0.910130i	$-0.364018\pi$
$547$	−11.5959	−	11.5959i	−0.495806	−	0.495806i	−0.910130	+	0.414324i	$0.864018\pi$
$548$	−13.6814	−	13.6814i	−0.584442	−	0.584442i
$549$	2.54270	−	0.898979i	0.108520	−	0.0383675i
$550$	23.5959	−	15.5959i	1.00613	−	0.665012i
$551$			5.37113i			0.228818i
$552$	0.292893	+	1.70711i	0.0124664	+	0.0726593i
$553$	−10.8990	+	10.8990i	−0.463472	+	0.463472i
$554$	−13.3636			−0.567765
$555$	13.3843	−	0.928203i	0.568130	−	0.0394000i
$556$	18.6969			0.792927
$557$	−21.1024	+	21.1024i	−0.894139	+	0.894139i	−0.994910	−	0.100770i	$-0.967869\pi$
$557$	−21.1024	+	21.1024i	−0.894139	+	0.894139i	0.100770	+	0.994910i	$0.467869\pi$
$558$	6.33386	−	13.2621i	0.268134	−	0.561428i
$559$			20.0000i			0.845910i
$560$	−7.70674	−	0.778539i	−0.325669	−	0.0328993i
$561$	−58.7878	−	41.5692i	−2.48202	−	1.75505i
$562$	−4.00000	−	4.00000i	−0.168730	−	0.168730i
$563$	26.5843	+	26.5843i	1.12040	+	1.12040i	0.991682	+	0.128714i	$0.0410850\pi$
$563$	26.5843	+	26.5843i	1.12040	+	1.12040i	0.128714	+	0.991682i	$0.458915\pi$
$564$	9.75663	+	6.89898i	0.410828	+	0.290499i
$565$	−25.2474	−	2.55051i	−1.06217	−	0.107301i
$566$		−	7.56388i		−	0.317933i
$567$	31.0028	+	3.29002i	1.30200	+	0.138168i
$568$	−10.3485	+	10.3485i	−0.434212	+	0.434212i
$569$	23.8988			1.00189			0.500944	−	0.865480i	$-0.332986\pi$
$569$	23.8988			1.00189			0.500944	+	0.865480i	$0.332986\pi$
$570$	−9.46410	+	0.656339i	−0.396408	+	0.0274910i
$571$	21.5505			0.901861			0.450930	−	0.892559i	$-0.351092\pi$
$571$	21.5505			0.901861			0.450930	+	0.892559i	$0.351092\pi$
$572$	−19.5133	+	19.5133i	−0.815890	+	0.815890i
$573$	5.25924	+	30.6531i	0.219708	+	1.28055i
$574$			29.3939i			1.22688i
$575$	4.17121	−	2.75699i	0.173951	−	0.114975i
$576$	1.00000	+	2.82843i	0.0416667	+	0.117851i
$577$	−0.797959	−	0.797959i	−0.0332195	−	0.0332195i	0.690302	−	0.723521i	$-0.257478\pi$
$577$	−0.797959	−	0.797959i	−0.0332195	−	0.0332195i	−0.723521	+	0.690302i	$0.757478\pi$
$578$	−26.1630	−	26.1630i	−1.08824	−	1.08824i
$579$	−2.68556	+	3.79796i	−0.111608	+	0.157838i
$580$	−3.10102	−	3.79796i	−0.128763	−	0.157702i
$581$		−	6.92820i		−	0.287430i
$582$	1.08516	−	0.186185i	0.0449815	−	0.00771761i
$583$	−5.39388	+	5.39388i	−0.223392	+	0.223392i
$584$	2.68556			0.111129
$585$	7.75199	+	31.7933i	0.320505	+	1.31449i
$586$	−19.1464			−0.790932
$587$	−13.9993	+	13.9993i	−0.577812	+	0.577812i	−0.934300	−	0.356488i	$-0.883974\pi$
$587$	−13.9993	+	13.9993i	−0.577812	+	0.577812i	0.356488	+	0.934300i	$0.383974\pi$
$588$	−8.53553	+	1.46447i	−0.351999	+	0.0603936i
$589$			12.0000i			0.494451i
$590$	1.23924	−	12.2672i	0.0510187	−	0.505033i
$591$	−10.8990	+	15.4135i	−0.448324	+	0.634026i
$592$	2.44949	+	2.44949i	0.100673	+	0.100673i
$593$	11.1708	+	11.1708i	0.458732	+	0.458732i	0.898239	−	0.439507i	$-0.144847\pi$
$593$	11.1708	+	11.1708i	0.458732	+	0.458732i	−0.439507	+	0.898239i	$0.644847\pi$
$594$	−28.2843	−	8.00000i	−1.16052	−	0.328244i
$595$	44.0908	−	36.0000i	1.80755	−	1.47586i
$596$		−	11.0280i		−	0.451724i
$597$	−2.21149	−	12.8895i	−0.0905104	−	0.527533i
$598$	−3.44949	+	3.44949i	−0.141060	+	0.141060i
$599$	−3.32124			−0.135702			−0.0678510	−	0.997695i	$-0.521614\pi$
$599$	−3.32124			−0.135702			−0.0678510	+	0.997695i	$0.521614\pi$
$600$	6.31319	−	5.92820i	0.257735	−	0.242018i
$601$	−16.2020			−0.660895			−0.330448	−	0.943824i	$-0.607200\pi$
$601$	−16.2020			−0.660895			−0.330448	+	0.943824i	$0.607200\pi$
$602$	10.0424	−	10.0424i	0.409296	−	0.409296i
$603$	−41.7259	−	19.9280i	−1.69921	−	0.811530i
$604$			0.898979i			0.0365790i
$605$	−36.3731	+	29.6985i	−1.47878	+	1.20742i
$606$	−0.898979	−	0.635674i	−0.0365185	−	0.0258225i
$607$	−7.34847	−	7.34847i	−0.298265	−	0.298265i	0.542069	−	0.840334i	$-0.317641\pi$
$607$	−7.34847	−	7.34847i	−0.298265	−	0.298265i	−0.840334	+	0.542069i	$0.817641\pi$
$608$	−1.73205	−	1.73205i	−0.0702439	−	0.0702439i
$609$	−10.7423	−	7.59592i	−0.435298	−	0.307802i
$610$	0.202041	−	2.00000i	0.00818040	−	0.0809776i
$611$			33.6554i			1.36155i
$612$	−19.8931	−	9.50079i	−0.804131	−	0.384047i
$613$	3.34847	−	3.34847i	0.135243	−	0.135243i	−0.636244	−	0.771488i	$-0.719513\pi$
$613$	3.34847	−	3.34847i	0.135243	−	0.135243i	0.771488	+	0.636244i	$0.219513\pi$
$614$	−32.0983			−1.29538
$615$	−24.7899	−	21.5745i	−0.999626	−	0.869969i
$616$	19.5959			0.789542
$617$	−18.4169	+	18.4169i	−0.741436	+	0.741436i	−0.972854	−	0.231418i	$-0.925663\pi$
$617$	−18.4169	+	18.4169i	−0.741436	+	0.741436i	0.231418	+	0.972854i	$0.425663\pi$
$618$	−4.51451	−	26.3125i	−0.181600	−	1.05844i
$619$			30.0454i			1.20763i	0.797126	+	0.603813i	$0.206353\pi$
$619$			30.0454i			1.20763i	−0.797126	+	0.603813i	$0.793647\pi$
$620$	−6.92820	−	8.48528i	−0.278243	−	0.340777i
$621$	−5.00000	−	1.41421i	−0.200643	−	0.0567504i
$622$	10.1464	+	10.1464i	0.406835	+	0.406835i
$623$	−22.3417	−	22.3417i	−0.895101	−	0.895101i
$624$	−4.87832	+	6.89898i	−0.195289	+	0.276180i
$625$	−23.0000	−	9.79796i	−0.920000	−	0.391918i
$626$			21.4203i			0.856127i
$627$	23.6544	−	4.05845i	0.944664	−	0.162079i
$628$	−8.44949	+	8.44949i	−0.337171	+	0.337171i
$629$	−25.4558			−1.01499
$630$	12.0716	−	19.8564i	0.480943	−	0.791098i
$631$	24.4495			0.973319			0.486659	−	0.873592i	$-0.338215\pi$
$631$	24.4495			0.973319			0.486659	+	0.873592i	$0.338215\pi$
$632$	3.14626	−	3.14626i	0.125152	−	0.125152i
$633$	−31.9177	+	5.47621i	−1.26861	+	0.217660i
$634$		−	18.8990i		−	0.750574i
$635$	−11.1708	−	1.12848i	−0.443301	−	0.0447825i
$636$	−1.34847	+	1.90702i	−0.0534703	+	0.0756184i
$637$	−17.2474	−	17.2474i	−0.683369	−	0.683369i
$638$	8.77101	+	8.77101i	0.347248	+	0.347248i
$639$	−14.6349	−	41.3939i	−0.578949	−	1.63752i
$640$	2.22474	+	0.224745i	0.0879408	+	0.00888382i
$641$		−	20.4347i		−	0.807121i	−0.914953	−	0.403560i	$-0.867773\pi$
$641$		−	20.4347i		−	0.807121i	0.914953	−	0.403560i	$-0.132227\pi$
$642$	−3.19224	−	18.6057i	−0.125988	−	0.734309i
$643$	−22.8990	+	22.8990i	−0.903048	+	0.903048i	−0.995699	−	0.0926510i	$-0.970466\pi$
$643$	−22.8990	+	22.8990i	−0.903048	+	0.903048i	0.0926510	+	0.995699i	$0.470466\pi$
$644$	3.46410			0.136505
$645$	1.09853	+	15.8403i	0.0432546	+	0.623712i
$646$	18.0000			0.708201
$647$	34.4339	−	34.4339i	1.35374	−	1.35374i	0.472300	−	0.881438i	$-0.343424\pi$
$647$	34.4339	−	34.4339i	1.35374	−	1.35374i	0.881438	−	0.472300i	$-0.156576\pi$
$648$	−8.94975	−	0.949747i	−0.351579	−	0.0373096i
$649$			31.1918i			1.22439i
$650$	23.8988	+	4.87832i	0.937387	+	0.191343i
$651$	−24.0000	−	16.9706i	−0.940634	−	0.665129i
$652$	4.00000	+	4.00000i	0.156652	+	0.156652i
$653$	16.1920	+	16.1920i	0.633643	+	0.633643i	0.948980	−	0.315337i	$-0.102118\pi$
$653$	16.1920	+	16.1920i	0.633643	+	0.633643i	−0.315337	+	0.948980i	$0.602118\pi$
$654$	−19.5133	−	13.7980i	−0.763029	−	0.539543i
$655$	0.202041	+	0.247449i	0.00789440	+	0.00966862i
$656$		−	8.48528i		−	0.331295i
$657$	−3.47215	+	7.27010i	−0.135461	+	0.283634i
$658$	16.8990	−	16.8990i	0.658791	−	0.658791i
$659$	9.75663			0.380064			0.190032	−	0.981778i	$-0.439141\pi$
$659$	9.75663			0.380064			0.190032	+	0.981778i	$0.439141\pi$
$660$	−14.3830	+	16.5266i	−0.559858	+	0.643297i
$661$	16.8990			0.657294			0.328647	−	0.944453i	$-0.393407\pi$
$661$	16.8990			0.657294			0.328647	+	0.944453i	$0.393407\pi$
$662$	−13.2207	+	13.2207i	−0.513838	+	0.513838i
$663$	−10.4997	−	61.1966i	−0.407774	−	2.37668i
$664$			2.00000i			0.0776151i
$665$	−1.90702	+	18.8776i	−0.0739512	+	0.732041i
$666$	−9.79796	+	3.46410i	−0.379663	+	0.134231i
$667$	1.55051	+	1.55051i	0.0600360	+	0.0600360i
$668$	5.65685	+	5.65685i	0.218870	+	0.218870i
$669$	17.6062	−	24.8990i	0.680696	−	0.962650i
$670$	−26.6969	+	21.7980i	−1.03139	+	0.842129i
$671$			5.08540i			0.196320i
$672$	5.91359	−	1.01461i	0.228122	−	0.0391395i
$673$	3.00000	−	3.00000i	0.115642	−	0.115642i	−0.646918	−	0.762560i	$-0.723942\pi$
$673$	3.00000	−	3.00000i	0.115642	−	0.115642i	0.762560	+	0.646918i	$0.223942\pi$
$674$	20.4347			0.787114
$675$	7.88599	+	24.7550i	0.303532	+	0.952821i
$676$	−10.7980			−0.415306
$677$	8.51739	−	8.51739i	0.327350	−	0.327350i	−0.524228	−	0.851578i	$-0.675646\pi$
$677$	8.51739	−	8.51739i	0.327350	−	0.327350i	0.851578	+	0.524228i	$0.175646\pi$
$678$	19.3730	−	3.32389i	0.744017	−	0.127653i
$679$		−	2.20204i		−	0.0845066i
$680$	−12.7279	+	10.3923i	−0.488094	+	0.398527i
$681$	1.10102	−	1.55708i	0.0421912	−	0.0596674i
$682$	19.5959	+	19.5959i	0.750366	+	0.750366i
$683$	−4.24264	−	4.24264i	−0.162340	−	0.162340i	0.621262	−	0.783603i	$-0.286620\pi$
$683$	−4.24264	−	4.24264i	−0.162340	−	0.162340i	−0.783603	+	0.621262i	$0.786620\pi$
$684$	6.92820	−	2.44949i	0.264906	−	0.0936586i
$685$	4.34847	−	43.0454i	0.166146	−	1.64468i
$686$		−	6.92820i		−	0.264520i
$687$	1.96149	+	11.4324i	0.0748354	+	0.436173i
$688$	−2.89898	+	2.89898i	−0.110523	+	0.110523i
$689$	−6.57826			−0.250612
$690$	−2.54258	+	2.92152i	−0.0967944	+	0.111220i
$691$	−28.0000			−1.06517			−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000			−1.06517			−0.532585	+	0.846376i	$0.678779\pi$
$692$	−3.60697	+	3.60697i	−0.137116	+	0.137116i
$693$	−25.3354	+	53.0482i	−0.962413	+	2.01514i
$694$		−	0.202041i		−	0.00766937i
$695$	26.4415	+	32.3840i	1.00298	+	1.22840i
$696$	3.10102	+	2.19275i	0.117544	+	0.0831161i
$697$	44.0908	+	44.0908i	1.67006	+	1.67006i
$698$	−15.5563	−	15.5563i	−0.588817	−	0.588817i
$699$	−7.21393	−	5.10102i	−0.272856	−	0.192938i
$700$	−9.55051	−	14.4495i	−0.360975	−	0.546139i
$701$		−	36.1339i		−	1.36476i	−0.730999	−	0.682379i	$-0.760945\pi$
$701$		−	36.1339i		−	1.36476i	0.730999	−	0.682379i	$-0.239055\pi$
$702$	−12.3691	−	22.1258i	−0.466843	−	0.835083i
$703$	6.00000	−	6.00000i	0.226294	−	0.226294i
$704$	−5.65685			−0.213201
$705$	1.84858	+	26.6556i	0.0696214	+	1.00391i
$706$	−32.6969			−1.23057
$707$	−1.55708	+	1.55708i	−0.0585600	+	0.0585600i
$708$	1.61501	+	9.41297i	0.0606958	+	0.353761i
$709$		−	16.8990i		−	0.634654i	−0.948316	−	0.317327i	$-0.897215\pi$
$709$		−	16.8990i		−	0.634654i	0.948316	−	0.317327i	$-0.102785\pi$
$710$	−32.5590	−	3.28913i	−1.22192	−	0.123439i
$711$	4.44949	+	12.5851i	0.166869	+	0.471977i
$712$	6.44949	+	6.44949i	0.241705	+	0.241705i
$713$	3.46410	+	3.46410i	0.129732	+	0.129732i
$714$	−25.4558	+	36.0000i	−0.952661	+	1.34727i
$715$	−61.3939	−	6.20204i	−2.29600	−	0.231943i
$716$		−	15.2706i		−	0.570690i
$717$	22.8131	−	3.91411i	0.851970	−	0.146175i
$718$	−18.8990	+	18.8990i	−0.705304	+	0.705304i
$719$	−1.76416			−0.0657920			−0.0328960	−	0.999459i	$-0.510473\pi$
$719$	−1.76416			−0.0657920			−0.0328960	+	0.999459i	$0.510473\pi$
$720$	−3.48477	+	5.73205i	−0.129870	+	0.213621i
$721$	−53.3939			−1.98849
$722$	9.19239	−	9.19239i	0.342105	−	0.342105i
$723$	15.5364	−	2.66563i	0.577805	−	0.0991357i
$724$		−	8.00000i		−	0.297318i
$725$	2.19275	−	10.7423i	0.0814368	−	0.398957i
$726$	21.0000	−	29.6985i	0.779383	−	1.10221i
$727$	24.2474	+	24.2474i	0.899288	+	0.899288i	0.995373	−	0.0960850i	$-0.0306321\pi$
$727$	24.2474	+	24.2474i	0.899288	+	0.899288i	−0.0960850	+	0.995373i	$0.530632\pi$
$728$	11.9494	+	11.9494i	0.442874	+	0.442874i
$729$	14.1421	−	23.0000i	0.523783	−	0.851852i
$730$	3.79796	+	4.65153i	0.140569	+	0.172161i
$731$		−	30.1271i		−	1.11429i
$732$	0.263305	+	1.53465i	0.00973203	+	0.0567224i
$733$	−25.1464	+	25.1464i	−0.928805	+	0.928805i	−0.997629	−	0.0688243i	$-0.978075\pi$
$733$	−25.1464	+	25.1464i	−0.928805	+	0.928805i	0.0688243	+	0.997629i	$0.478075\pi$
$734$	27.9985			1.03345
$735$	−14.6076	−	12.7129i	−0.538809	−	0.468923i
$736$	−1.00000			−0.0368605
$737$	61.6539	−	61.6539i	2.27105	−	2.27105i
$738$	22.9706	+	10.9706i	0.845558	+	0.403832i
$739$			30.6969i			1.12921i	0.825363	+	0.564603i	$0.190971\pi$
$739$			30.6969i			1.12921i	−0.825363	+	0.564603i	$0.809029\pi$
$740$	−0.778539	+	7.70674i	−0.0286197	+	0.283305i
$741$	16.8990	+	11.9494i	0.620800	+	0.438972i
$742$	3.30306	+	3.30306i	0.121259	+	0.121259i
$743$	−10.6780	−	10.6780i	−0.391739	−	0.391739i	0.483568	−	0.875307i	$-0.339341\pi$
$743$	−10.6780	−	10.6780i	−0.391739	−	0.391739i	−0.875307	+	0.483568i	$0.839341\pi$
$744$	6.92820	+	4.89898i	0.254000	+	0.179605i
$745$	19.1010	−	15.5959i	0.699807	−	0.571390i
$746$		−	17.6062i		−	0.644610i
$747$	−5.41421	−	2.58579i	−0.198096	−	0.0946090i
$748$	29.3939	−	29.3939i	1.07475	−	1.07475i
$749$	−37.7552			−1.37954
$750$	19.1962	+	2.55103i	0.700944	+	0.0931503i
$751$	−42.2474			−1.54163			−0.770816	−	0.637058i	$-0.780151\pi$
$751$	−42.2474			−1.54163			−0.770816	+	0.637058i	$0.780151\pi$
$752$	−4.87832	+	4.87832i	−0.177894	+	0.177894i
$753$	3.76977	+	21.9718i	0.137378	+	0.800697i
$754$			10.6969i			0.389560i
$755$	−1.55708	+	1.27135i	−0.0566679	+	0.0462691i
$756$	−4.89898	+	17.3205i	−0.178174	+	0.629941i
$757$	−25.3485	−	25.3485i	−0.921306	−	0.921306i	0.0758160	−	0.997122i	$-0.475844\pi$
$757$	−25.3485	−	25.3485i	−0.921306	−	0.921306i	−0.997122	+	0.0758160i	$0.975844\pi$
$758$	3.63907	+	3.63907i	0.132177	+	0.132177i
$759$	5.65685	−	8.00000i	0.205331	−	0.290382i
$760$	0.550510	−	5.44949i	0.0199691	−	0.197674i
$761$			42.1407i			1.52760i	0.645454	+	0.763799i	$0.276668\pi$
$761$			42.1407i			1.52760i	−0.645454	+	0.763799i	$0.723332\pi$
$762$	8.57169	−	1.47067i	0.310520	−	0.0532767i
$763$	−33.7980	+	33.7980i	−1.22357	+	1.22357i
$764$	−17.9562			−0.649632
$765$	−11.6772	−	47.8920i	−0.422191	−	1.73154i
$766$	6.69694			0.241970
$767$	−19.0205	+	19.0205i	−0.686789	+	0.686789i
$768$	−1.70711	+	0.292893i	−0.0615999	+	0.0105689i
$769$			28.6969i			1.03484i	0.855732	+	0.517419i	$0.173107\pi$
$769$			28.6969i			1.03484i	−0.855732	+	0.517419i	$0.826893\pi$
$770$	27.7128	+	33.9411i	0.998700	+	1.22315i
$771$	−13.5959	+	19.2275i	−0.489645	+	0.692463i
$772$	−1.89898	−	1.89898i	−0.0683458	−	0.0683458i
$773$	−26.7593	−	26.7593i	−0.962465	−	0.962465i	0.0368554	−	0.999321i	$-0.488266\pi$
$773$	−26.7593	−	26.7593i	−0.962465	−	0.962465i	−0.999321	+	0.0368554i	$0.988266\pi$
$774$	−4.09978	−	11.5959i	−0.147363	−	0.416807i
$775$	4.89898	−	24.0000i	0.175977	−	0.862105i
$776$			0.635674i			0.0228194i
$777$	3.51472	+	20.4853i	0.126090	+	0.734905i
$778$	−22.0000	+	22.0000i	−0.788738	+	0.788738i
$779$	−20.7846			−0.744686
$780$	−18.8484	+	1.30714i	−0.674880	+	0.0468031i
$781$	82.7878			2.96238
$782$	5.19615	−	5.19615i	0.185814	−	0.185814i
$783$	−9.94530	+	5.55980i	−0.355416	+	0.198691i
$784$		−	5.00000i		−	0.178571i
$785$	−26.5843	−	2.68556i	−0.948835	−	0.0958518i
$786$	−0.202041	−	0.142865i	−0.00720656	−	0.00509581i
$787$	21.1010	+	21.1010i	0.752170	+	0.752170i	0.974884	−	0.222714i	$-0.0714915\pi$
$787$	21.1010	+	21.1010i	0.752170	+	0.752170i	−0.222714	+	0.974884i	$0.571492\pi$
$788$	−7.70674	−	7.70674i	−0.274541	−	0.274541i
$789$	−11.3137	−	8.00000i	−0.402779	−	0.284808i
$790$	9.89898	+	1.00000i	0.352190	+	0.0355784i
$791$		−	39.3123i		−	1.39778i
$792$	7.31371	−	15.3137i	0.259881	−	0.544149i
$793$	−3.10102	+	3.10102i	−0.110120	+	0.110120i
$794$	12.0922			0.429138
$795$	−5.21009	+	0.361321i	−0.184783	+	0.0128147i
$796$	7.55051			0.267621
$797$	0.667783	−	0.667783i	0.0236541	−	0.0236541i	−0.695181	−	0.718835i	$-0.744676\pi$
$797$	0.667783	−	0.667783i	0.0236541	−	0.0236541i	0.718835	+	0.695181i	$0.244676\pi$
$798$	−2.48528	−	14.4853i	−0.0879780	−	0.512773i
$799$		−	50.6969i		−	1.79353i
$800$	2.75699	+	4.17121i	0.0974745	+	0.147474i
$801$	−25.7980	+	9.12096i	−0.911526	+	0.322273i
$802$	5.55051	+	5.55051i	0.195995	+	0.195995i
$803$	−10.7423	−	10.7423i	−0.379086	−	0.379086i
$804$	15.4135	−	21.7980i	0.543592	−	0.768755i
$805$	4.89898	+	6.00000i	0.172666	+	0.211472i
$806$			23.8988i			0.841798i
$807$	10.7420	−	1.84304i	0.378137	−	0.0648780i
$808$	0.449490	−	0.449490i	0.0158130	−	0.0158130i
$809$	−8.48528			−0.298327			−0.149163	−	0.988813i	$-0.547658\pi$
$809$	−8.48528			−0.298327			−0.149163	+	0.988813i	$0.547658\pi$
$810$	−11.0118	−	16.8446i	−0.386917	−	0.591858i
$811$	−31.5959			−1.10948			−0.554741	−	0.832023i	$-0.687183\pi$
$811$	−31.5959			−1.10948			−0.554741	+	0.832023i	$0.687183\pi$
$812$	5.37113	−	5.37113i	0.188490	−	0.188490i
$813$	41.8154	−	7.17439i	1.46653	−	0.251617i
$814$		−	19.5959i		−	0.686837i
$815$	−1.27135	+	12.5851i	−0.0445334	+	0.440835i
$816$	7.34847	−	10.3923i	0.257248	−	0.363803i
$817$	7.10102	+	7.10102i	0.248433	+	0.248433i
$818$	9.75663	+	9.75663i	0.341133	+	0.341133i
$819$	−47.7975	+	16.8990i	−1.67018	+	0.590498i
$820$	14.6969	−	12.0000i	0.513239	−	0.419058i
$821$			31.7484i			1.10803i	0.832508	+	0.554013i	$0.186904\pi$
$821$			31.7484i			1.10803i	−0.832508	+	0.554013i	$0.813096\pi$
$822$	5.66704	+	33.0299i	0.197661	+	1.15205i
$823$	29.1464	−	29.1464i	1.01598	−	1.01598i	0.0161104	−	0.999870i	$-0.494872\pi$
$823$	29.1464	−	29.1464i	1.01598	−	1.01598i	0.999870	−	0.0161104i	$-0.00512832\pi$
$824$	15.4135			0.536954
$825$	−48.9656	−	1.53996i	−1.70476	−	0.0536145i
$826$	19.1010			0.664610
$827$	−14.9207	+	14.9207i	−0.518843	+	0.518843i	−0.917221	−	0.398378i	$-0.869573\pi$
$827$	−14.9207	+	14.9207i	−0.518843	+	0.518843i	0.398378	+	0.917221i	$0.369573\pi$
$828$	1.29289	−	2.70711i	0.0449311	−	0.0940785i
$829$		−	32.8990i		−	1.14263i	−0.820731	−	0.571314i	$-0.806434\pi$
$829$		−	32.8990i		−	1.14263i	0.820731	−	0.571314i	$-0.193566\pi$
$830$	−3.46410	+	2.82843i	−0.120241	+	0.0981761i
$831$	18.8990	+	13.3636i	0.655598	+	0.463578i
$832$	−3.44949	−	3.44949i	−0.119590	−	0.119590i
$833$	25.9808	+	25.9808i	0.900180	+	0.900180i
$834$	−26.4415	−	18.6969i	−0.915593	−	0.647422i
$835$	−1.79796	+	17.7980i	−0.0622209	+	0.615924i
$836$			13.8564i			0.479234i
$837$	−22.2195	+	12.4215i	−0.768018	+	0.429351i
$838$	3.10102	−	3.10102i	0.107123	−	0.107123i
$839$	27.9985			0.966617			0.483309	−	0.875450i	$-0.339435\pi$
$839$	27.9985			0.966617			0.483309	+	0.875450i	$0.339435\pi$
$840$	10.1204	+	8.80776i	0.349188	+	0.303897i
$841$	−24.1918			−0.834201
$842$	0.635674	−	0.635674i	0.0219068	−	0.0219068i
$843$	1.65685	+	9.65685i	0.0570651	+	0.332600i
$844$		−	18.6969i		−	0.643575i
$845$	−15.2706	−	18.7026i	−0.525325	−	0.643389i
$846$	−6.89898	−	19.5133i	−0.237192	−	0.670880i
$847$	−51.4393	−	51.4393i	−1.76747	−	1.76747i
$848$	−0.953512	−	0.953512i	−0.0327437	−	0.0327437i
$849$	−7.56388	+	10.6969i	−0.259592	+	0.367118i
$850$	−36.0000	−	7.34847i	−1.23479	−	0.252050i
$851$		−	3.46410i		−	0.118748i
$852$	24.9834	−	4.28648i	0.855918	−	0.146852i
$853$	5.24745	−	5.24745i	0.179669	−	0.179669i	−0.611542	−	0.791212i	$-0.709451\pi$
$853$	5.24745	−	5.24745i	0.179669	−	0.179669i	0.791212	+	0.611542i	$0.209451\pi$
$854$	3.11416			0.106564
$855$	14.0406	+	8.53590i	0.480178	+	0.291922i
$856$	10.8990			0.372519
$857$	−9.89949	+	9.89949i	−0.338160	+	0.338160i	−0.855675	−	0.517514i	$-0.826857\pi$
$857$	−9.89949	+	9.89949i	−0.338160	+	0.338160i	0.517514	+	0.855675i	$0.326857\pi$
$858$	47.1092	−	8.08266i	1.60828	−	0.275937i
$859$		−	44.8990i		−	1.53193i	−0.642880	−	0.765967i	$-0.722261\pi$
$859$		−	44.8990i		−	1.53193i	0.642880	−	0.765967i	$-0.277739\pi$
$860$	−9.12096	−	0.921404i	−0.311022	−	0.0314196i
$861$	29.3939	−	41.5692i	1.00174	−	1.41668i
$862$	−15.7980	−	15.7980i	−0.538081	−	0.538081i
$863$	−5.65685	−	5.65685i	−0.192562	−	0.192562i	0.604240	−	0.796802i	$-0.293477\pi$
$863$	−5.65685	−	5.65685i	−0.192562	−	0.192562i	−0.796802	+	0.604240i	$0.793477\pi$
$864$	1.41421	−	5.00000i	0.0481125	−	0.170103i
$865$	−11.3485	−	1.14643i	−0.385860	−	0.0389797i
$866$		−	41.5050i		−	1.41040i
$867$	10.8370	+	63.1630i	0.368045	+	2.14513i
$868$	12.0000	−	12.0000i	0.407307	−	0.407307i
$869$	−25.1701			−0.853838
$870$	0.587546	+	8.47215i	0.0199197	+	0.287233i
$871$	75.1918			2.54778
$872$	9.75663	−	9.75663i	0.330401	−	0.330401i
$873$	−1.72084	−	0.821859i	−0.0582416	−	0.0278157i
$874$			2.44949i			0.0828552i
$875$	11.5208	−	36.9766i	0.389474	−	1.25004i
$876$	−3.79796	−	2.68556i	−0.128321	−	0.0907367i
$877$	−13.2474	−	13.2474i	−0.447335	−	0.447335i	0.447133	−	0.894468i	$-0.352445\pi$
$877$	−13.2474	−	13.2474i	−0.447335	−	0.447335i	−0.894468	+	0.447133i	$0.852445\pi$
$878$	−11.3137	−	11.3137i	−0.381819	−	0.381819i
$879$	27.0771	+	19.1464i	0.913289	+	0.645793i
$880$	−8.00000	−	9.79796i	−0.269680	−	0.330289i
$881$		−	22.6274i		−	0.762337i	−0.924506	−	0.381169i	$-0.875522\pi$
$881$		−	22.6274i		−	0.762337i	0.924506	−	0.381169i	$-0.124478\pi$
$882$	13.5355	+	6.46447i	0.455765	+	0.217670i
$883$	−17.3939	+	17.3939i	−0.585351	+	0.585351i	−0.936369	−	0.351018i	$-0.885836\pi$
$883$	−17.3939	+	17.3939i	−0.585351	+	0.585351i	0.351018	+	0.936369i	$0.385836\pi$
$884$	35.8481			1.20570
$885$	−14.0198	+	16.1092i	−0.471269	+	0.541506i
$886$	−16.0000			−0.537531
$887$	−25.1701	+	25.1701i	−0.845130	+	0.845130i	−0.989521	−	0.144391i	$-0.953878\pi$
$887$	−25.1701	+	25.1701i	−0.845130	+	0.845130i	0.144391	+	0.989521i	$0.453878\pi$
$888$	−1.01461	−	5.91359i	−0.0340481	−	0.198447i
$889$		−	17.3939i		−	0.583372i
$890$	−2.04989	+	20.2918i	−0.0687124	+	0.680183i
$891$	32.0000	+	39.5980i	1.07204	+	1.32658i
$892$	12.4495	+	12.4495i	0.416840	+	0.416840i
$893$	11.9494	+	11.9494i	0.399871	+	0.399871i
$894$	−11.0280	+	15.5959i	−0.368831	+	0.521606i
$895$	26.4495	−	21.5959i	0.884109	−	0.721872i
$896$			3.46410i			0.115728i
$897$	8.32780	−	1.42883i	0.278057	−	0.0477071i
$898$	−10.6969	+	10.6969i	−0.356961	+	0.356961i
$899$	10.7423			0.358274
$900$	−14.8564	+	2.07055i	−0.495214	+	0.0690184i
$901$	9.90918			0.330123
$902$	−33.9411	+	33.9411i	−1.13012	+	1.13012i
$903$	−24.2444	+	4.15968i	−0.806803	+	0.138426i
$904$			11.3485i			0.377444i
$905$	13.8564	−	11.3137i	0.460603	−	0.376080i
$906$	0.898979	−	1.27135i	0.0298666	−	0.0422377i
$907$	3.55051	+	3.55051i	0.117893	+	0.117893i	0.763592	−	0.645699i	$-0.223434\pi$
$907$	3.55051	+	3.55051i	0.117893	+	0.117893i	−0.645699	+	0.763592i	$0.723434\pi$
$908$	0.778539	+	0.778539i	0.0258367	+	0.0258367i
$909$	0.635674	+	1.79796i	0.0210840	+	0.0596345i
$910$	−3.79796	+	37.5959i	−0.125901	+	1.24629i
$911$			22.0560i			0.730747i	0.930861	+	0.365373i	$0.119059\pi$
$911$			22.0560i			0.730747i	−0.930861	+	0.365373i	$0.880941\pi$
$912$	0.717439	+	4.18154i	0.0237568	+	0.138465i
$913$	8.00000	−	8.00000i	0.264761	−	0.264761i
$914$	2.19275			0.0725298
$915$	−2.28573	+	2.62639i	−0.0755639	+	0.0868256i
$916$	−6.69694			−0.221273
$917$	−0.349945	+	0.349945i	−0.0115562	+	0.0115562i
$918$	18.6323	+	33.3292i	0.614957	+	1.10003i
$919$			27.5505i			0.908807i	0.890796	+	0.454404i	$0.150148\pi$
$919$			27.5505i			0.908807i	−0.890796	+	0.454404i	$0.849852\pi$
$920$	−1.41421	−	1.73205i	−0.0466252	−	0.0571040i
$921$	45.3939	+	32.0983i	1.49578	+	1.05768i
$922$	22.2474	+	22.2474i	0.732681	+	0.732681i
$923$	50.4831	+	50.4831i	1.66167	+	1.66167i
$924$	−27.7128	−	19.5959i	−0.911685	−	0.644658i
$925$	−14.4495	+	9.55051i	−0.475096	+	0.314019i
$926$		−	36.8338i		−	1.21043i
$927$	−19.9280	+	41.7259i	−0.654521	+	1.37046i
$928$	−1.55051	+	1.55051i	−0.0508980	+	0.0508980i
$929$	41.5692			1.36384			0.681921	−	0.731426i	$-0.261145\pi$
$929$	41.5692			1.36384			0.681921	+	0.731426i	$0.261145\pi$
$930$	1.31268	+	18.9282i	0.0430444	+	0.620680i
$931$	−12.2474			−0.401394
$932$	3.60697	−	3.60697i	0.118150	−	0.118150i
$933$	−4.20279	−	24.4956i	−0.137593	−	0.801951i
$934$		−	5.10102i		−	0.166910i
$935$	92.4809	+	9.34247i	3.02445	+	0.305531i
$936$	13.7980	−	4.87832i	0.451000	−	0.159453i
$937$	39.1464	+	39.1464i	1.27886	+	1.27886i	0.941307	+	0.337551i	$0.109598\pi$
$937$	39.1464	+	39.1464i	1.27886	+	1.27886i	0.337551	+	0.941307i	$0.390402\pi$
$938$	−37.7552	−	37.7552i	−1.23275	−	1.23275i
$939$	21.4203	−	30.2929i	0.699025	−	0.988570i
$940$	−15.3485	−	1.55051i	−0.500612	−	0.0505721i
$941$		−	34.9267i		−	1.13858i	−0.822137	−	0.569290i	$-0.807218\pi$
$941$		−	34.9267i		−	1.13858i	0.822137	−	0.569290i	$-0.192782\pi$
$942$	20.3989	−	3.49989i	0.664631	−	0.114033i
$943$	−6.00000	+	6.00000i	−0.195387	+	0.195387i
$944$	−5.51399			−0.179465
$945$	−36.9282	+	16.0096i	−1.20127	+	0.520793i
$946$	23.1918			0.754032
$947$	−25.4558	+	25.4558i	−0.827204	+	0.827204i	−0.987129	−	0.159925i	$-0.948875\pi$
$947$	−25.4558	+	25.4558i	−0.827204	+	0.827204i	0.159925	+	0.987129i	$0.448875\pi$
$948$	−7.59575	+	1.30323i	−0.246699	+	0.0423268i
$949$		−	13.1010i		−	0.425277i
$950$	10.2173	−	6.75323i	0.331494	−	0.219104i
$951$	−18.8990	+	26.7272i	−0.612841	+	0.866689i
$952$	−18.0000	−	18.0000i	−0.583383	−	0.583383i
$953$	35.3874	+	35.3874i	1.14631	+	1.14631i	0.987272	+	0.159040i	$0.0508398\pi$
$953$	35.3874	+	35.3874i	1.14631	+	1.14631i	0.159040	+	0.987272i	$0.449160\pi$
$954$	3.81405	−	1.34847i	0.123484	−	0.0436583i
$955$	−25.3939	−	31.1010i	−0.821727	−	1.00641i
$956$			13.3636i			0.432210i
$957$	−3.63307	−	21.1751i	−0.117441	−	0.684494i
$958$	−18.6969	+	18.6969i	−0.604071	+	0.604071i
$959$	67.0251			2.16435
$960$	−2.92152	−	2.54258i	−0.0942916	−	0.0820615i
$961$	−7.00000			−0.225806
$962$	11.9494	−	11.9494i	0.385264	−	0.385264i
$963$	−14.0912	+	29.5047i	−0.454083	+	0.950776i
$964$			9.10102i			0.293124i
$965$	0.603566	−	5.97469i	0.0194295	−	0.192332i
$966$	−4.89898	−	3.46410i	−0.157622	−	0.111456i
$967$	2.44949	+	2.44949i	0.0787703	+	0.0787703i	0.745394	−	0.666624i	$-0.232261\pi$
$967$	2.44949	+	2.44949i	0.0787703	+	0.0787703i	−0.666624	+	0.745394i	$0.732261\pi$
$968$	14.8492	+	14.8492i	0.477273	+	0.477273i
$969$	−25.4558	−	18.0000i	−0.817760	−	0.578243i
$970$	−1.10102	+	0.898979i	−0.0353516	+	0.0288645i
$971$		−	29.5556i		−	0.948485i	−0.880394	−	0.474242i	$-0.842722\pi$
$971$		−	29.5556i		−	0.948485i	0.880394	−	0.474242i	$-0.157278\pi$
$972$	11.7071	+	10.2929i	0.375506	+	0.330145i
$973$	−45.7980	+	45.7980i	−1.46822	+	1.46822i
$974$	27.3629			0.876763
$975$	−28.9196	−	30.7977i	−0.926170	−	0.986317i
$976$	−0.898979			−0.0287756
$977$	−22.4524	+	22.4524i	−0.718317	+	0.718317i	−0.968261	−	0.249943i	$-0.919588\pi$
$977$	−22.4524	+	22.4524i	−0.718317	+	0.718317i	0.249943	+	0.968261i	$0.419588\pi$
$978$	−1.65685	−	9.65685i	−0.0529804	−	0.308792i
$979$		−	51.5959i		−	1.64901i
$980$	8.66025	−	7.07107i	0.276642	−	0.225877i
$981$	13.7980	+	39.0265i	0.440535	+	1.24602i
$982$	−17.8990	−	17.8990i	−0.571179	−	0.571179i
$983$	39.0265	+	39.0265i	1.24475	+	1.24475i	0.958007	+	0.286746i	$0.0925736\pi$
$983$	39.0265	+	39.0265i	1.24475	+	1.24475i	0.286746	+	0.958007i	$0.407426\pi$
$984$	−8.48528	+	12.0000i	−0.270501	+	0.382546i
$985$	2.44949	−	24.2474i	0.0780472	−	0.772588i
$986$		−	16.1134i		−	0.513154i
$987$	−40.7977	+	6.99979i	−1.29861	+	0.222806i
$988$	−8.44949	+	8.44949i	−0.268814	+	0.268814i
$989$	4.09978			0.130365
$990$	36.8673	−	8.98914i	1.17172	−	0.285694i
$991$	−13.7980			−0.438307			−0.219153	−	0.975690i	$-0.570329\pi$
$991$	−13.7980			−0.438307			−0.219153	+	0.975690i	$0.570329\pi$
$992$	−3.46410	+	3.46410i	−0.109985	+	0.109985i
$993$	31.9177	−	5.47621i	1.01288	−	0.173782i
$994$		−	50.6969i		−	1.60801i
$995$	10.6780	+	13.0779i	0.338516	+	0.414596i
$996$	2.00000	−	2.82843i	0.0633724	−	0.0896221i
$997$	5.44949	+	5.44949i	0.172587	+	0.172587i	0.788115	−	0.615528i	$-0.211057\pi$
$997$	5.44949	+	5.44949i	0.172587	+	0.172587i	−0.615528	+	0.788115i	$0.711057\pi$
$998$	−23.8988	−	23.8988i	−0.756502	−	0.756502i
$999$	17.3205	+	4.89898i	0.547997	+	0.154997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.c.47.4	yes	8
3.2	odd	2	inner	690.2.i.c.47.1	✓	8
5.3	odd	4	inner	690.2.i.c.323.1	yes	8
15.8	even	4	inner	690.2.i.c.323.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.c.47.1	✓	8	3.2	odd	2	inner
690.2.i.c.47.4	yes	8	1.1	even	1	trivial
690.2.i.c.323.1	yes	8	5.3	odd	4	inner
690.2.i.c.323.4	yes	8	15.8	even	4	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} -1.00000i q^{4} +(1.73205 - 1.41421i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(2.44949 + 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} -1.00000i q^{4} +(1.73205 - 1.41421i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(2.44949 + 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +(0.224745 - 2.22474i) q^{10} +5.65685i q^{11} +(0.292893 + 1.70711i) q^{12} +(-3.44949 + 3.44949i) q^{13} +3.46410 q^{14} +(-2.54258 + 2.92152i) q^{15} -1.00000 q^{16} +(5.19615 - 5.19615i) q^{17} +(1.29289 - 2.70711i) q^{18} +2.44949i q^{19} +(-1.41421 - 1.73205i) q^{20} +(-4.89898 - 3.46410i) q^{21} +(4.00000 + 4.00000i) q^{22} +(0.707107 + 0.707107i) q^{23} +(1.41421 + 1.00000i) q^{24} +(1.00000 - 4.89898i) q^{25} +4.87832i q^{26} +(-4.53553 + 2.53553i) q^{27} +(2.44949 - 2.44949i) q^{28} +2.19275 q^{29} +(0.267949 + 3.86370i) q^{30} +4.89898 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.65685 - 9.65685i) q^{33} -7.34847i q^{34} +(7.70674 + 0.778539i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(-2.44949 - 2.44949i) q^{37} +(1.73205 + 1.73205i) q^{38} +(4.87832 - 6.89898i) q^{39} +(-2.22474 - 0.224745i) q^{40} +8.48528i q^{41} +(-5.91359 + 1.01461i) q^{42} +(2.89898 - 2.89898i) q^{43} +5.65685 q^{44} +(3.48477 - 5.73205i) q^{45} +1.00000 q^{46} +(4.87832 - 4.87832i) q^{47} +(1.70711 - 0.292893i) q^{48} +5.00000i q^{49} +(-2.75699 - 4.17121i) q^{50} +(-7.34847 + 10.3923i) q^{51} +(3.44949 + 3.44949i) q^{52} +(0.953512 + 0.953512i) q^{53} +(-1.41421 + 5.00000i) q^{54} +(8.00000 + 9.79796i) q^{55} -3.46410i q^{56} +(-0.717439 - 4.18154i) q^{57} +(1.55051 - 1.55051i) q^{58} +5.51399 q^{59} +(2.92152 + 2.54258i) q^{60} +0.898979 q^{61} +(3.46410 - 3.46410i) q^{62} +(9.37769 + 4.47871i) q^{63} +1.00000i q^{64} +(-1.09638 + 10.8530i) q^{65} +(-8.00000 - 5.65685i) q^{66} +(-10.8990 - 10.8990i) q^{67} +(-5.19615 - 5.19615i) q^{68} +(-1.41421 - 1.00000i) q^{69} +(6.00000 - 4.89898i) q^{70} -14.6349i q^{71} +(-2.70711 - 1.29289i) q^{72} +(-1.89898 + 1.89898i) q^{73} -3.46410 q^{74} +(-0.272229 + 8.65597i) q^{75} +2.44949 q^{76} +(-13.8564 + 13.8564i) q^{77} +(-1.42883 - 8.32780i) q^{78} +4.44949i q^{79} +(-1.73205 + 1.41421i) q^{80} +(7.00000 - 5.65685i) q^{81} +(6.00000 + 6.00000i) q^{82} +(-1.41421 - 1.41421i) q^{83} +(-3.46410 + 4.89898i) q^{84} +(1.65153 - 16.3485i) q^{85} -4.09978i q^{86} +(-3.74326 + 0.642242i) q^{87} +(4.00000 - 4.00000i) q^{88} -9.12096 q^{89} +(-1.58907 - 6.51727i) q^{90} -16.8990 q^{91} +(0.707107 - 0.707107i) q^{92} +(-8.36308 + 1.43488i) q^{93} -6.89898i q^{94} +(3.46410 + 4.24264i) q^{95} +(1.00000 - 1.41421i) q^{96} +(-0.449490 - 0.449490i) q^{97} +(3.53553 + 3.53553i) q^{98} +(5.65685 + 16.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} - 8 q^{6}+O(q^{10}) \) 8 * q - 8 * q^3 - 8 * q^6	\( 8 q - 8 q^{3} - 8 q^{6} - 8 q^{10} + 8 q^{12} - 8 q^{13} - 8 q^{15} - 8 q^{16} + 16 q^{18} + 32 q^{22} + 8 q^{25} - 8 q^{27} + 16 q^{30} + 32 q^{33} - 8 q^{36} - 8 q^{40} - 16 q^{43} + 8 q^{46} + 8 q^{48} + 8 q^{52} + 64 q^{55} + 32 q^{58} + 8 q^{60} - 32 q^{61} - 64 q^{66} - 48 q^{67} + 48 q^{70} - 16 q^{72} + 24 q^{73} - 8 q^{75} + 8 q^{78} + 56 q^{81} + 48 q^{82} + 72 q^{85} - 32 q^{87} + 32 q^{88} - 8 q^{90} - 96 q^{91} + 8 q^{96} + 16 q^{97}+O(q^{100}) \) 8 * q - 8 * q^3 - 8 * q^6 - 8 * q^10 + 8 * q^12 - 8 * q^13 - 8 * q^15 - 8 * q^16 + 16 * q^18 + 32 * q^22 + 8 * q^25 - 8 * q^27 + 16 * q^30 + 32 * q^33 - 8 * q^36 - 8 * q^40 - 16 * q^43 + 8 * q^46 + 8 * q^48 + 8 * q^52 + 64 * q^55 + 32 * q^58 + 8 * q^60 - 32 * q^61 - 64 * q^66 - 48 * q^67 + 48 * q^70 - 16 * q^72 + 24 * q^73 - 8 * q^75 + 8 * q^78 + 56 * q^81 + 48 * q^82 + 72 * q^85 - 32 * q^87 + 32 * q^88 - 8 * q^90 - 96 * q^91 + 8 * q^96 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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