LMFDB - Embedded newform 1110.2.u.e.191.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(191,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.u (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			191.3
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.e.401.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.64725 + 0.535321i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.786252 - 1.54331i) q^{6} -2.53955 q^{7} +(0.707107 - 0.707107i) q^{8} +(2.42686 + 1.76361i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.64725 + 0.535321i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.786252 - 1.54331i) q^{6} -2.53955 q^{7} +(0.707107 - 0.707107i) q^{8} +(2.42686 + 1.76361i) q^{9} +1.00000 q^{10} -1.55248 q^{11} +(-0.535321 + 1.64725i) q^{12} +(-1.11554 - 1.11554i) q^{13} +(1.79574 + 1.79574i) q^{14} +(-1.54331 + 0.786252i) q^{15} -1.00000 q^{16} +(-4.84198 + 4.84198i) q^{17} +(-0.468987 - 2.96312i) q^{18} +(-2.49053 - 2.49053i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(-4.18328 - 1.35948i) q^{21} +(1.09777 + 1.09777i) q^{22} +(-0.856269 + 0.856269i) q^{23} +(1.54331 - 0.786252i) q^{24} -1.00000i q^{25} +1.57762i q^{26} +(3.05355 + 4.20426i) q^{27} -2.53955i q^{28} +(-5.19422 - 5.19422i) q^{29} +(1.64725 + 0.535321i) q^{30} +(1.70231 - 1.70231i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.55731 - 0.831073i) q^{33} +6.84760 q^{34} +(1.79574 - 1.79574i) q^{35} +(-1.76361 + 2.42686i) q^{36} +(3.85543 + 4.70486i) q^{37} +3.52214i q^{38} +(-1.24041 - 2.43475i) q^{39} +1.00000i q^{40} -10.4791 q^{41} +(1.99673 + 3.91932i) q^{42} +(-2.78010 - 2.78010i) q^{43} -1.55248i q^{44} +(-2.96312 + 0.468987i) q^{45} +1.21095 q^{46} +10.4277i q^{47} +(-1.64725 - 0.535321i) q^{48} -0.550669 q^{49} +(-0.707107 + 0.707107i) q^{50} +(-10.5680 + 5.38394i) q^{51} +(1.11554 - 1.11554i) q^{52} -5.16143i q^{53} +(0.813678 - 5.13205i) q^{54} +(1.09777 - 1.09777i) q^{55} +(-1.79574 + 1.79574i) q^{56} +(-2.76929 - 5.43576i) q^{57} +7.34574i q^{58} +(-8.36584 + 8.36584i) q^{59} +(-0.786252 - 1.54331i) q^{60} +(7.41355 - 7.41355i) q^{61} -2.40742 q^{62} +(-6.16315 - 4.47879i) q^{63} -1.00000i q^{64} +1.57762 q^{65} +(1.22064 + 2.39595i) q^{66} +1.98974i q^{67} +(-4.84198 - 4.84198i) q^{68} +(-1.86887 + 0.952110i) q^{69} -2.53955 q^{70} +3.37621i q^{71} +(2.96312 - 0.468987i) q^{72} -0.480190i q^{73} +(0.600636 - 6.05304i) q^{74} +(0.535321 - 1.64725i) q^{75} +(2.49053 - 2.49053i) q^{76} +3.94259 q^{77} +(-0.844532 + 2.59873i) q^{78} +(6.52251 + 6.52251i) q^{79} +(0.707107 - 0.707107i) q^{80} +(2.77933 + 8.56010i) q^{81} +(7.40987 + 7.40987i) q^{82} -8.64749i q^{83} +(1.35948 - 4.18328i) q^{84} -6.84760i q^{85} +3.93165i q^{86} +(-5.77560 - 11.3368i) q^{87} +(-1.09777 + 1.09777i) q^{88} +(-10.5685 - 10.5685i) q^{89} +(2.42686 + 1.76361i) q^{90} +(2.83298 + 2.83298i) q^{91} +(-0.856269 - 0.856269i) q^{92} +(3.71540 - 1.89284i) q^{93} +(7.37349 - 7.37349i) q^{94} +3.52214 q^{95} +(0.786252 + 1.54331i) q^{96} +(-5.01332 - 5.01332i) q^{97} +(0.389382 + 0.389382i) q^{98} +(-3.76765 - 2.73797i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) $ 40 * q - 24 * q^7 - 8 * q^9	$ 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) $ 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	1.64725	+	0.535321i	0.951040	+	0.309068i
$3$	1.64725	+	0.535321i	0.951040	+	0.309068i
$4$			1.00000i			0.500000i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−0.786252	−	1.54331i	−0.320986	−	0.630054i
$7$	−2.53955			−0.959861			−0.479930	−	0.877307i	$-0.659338\pi$
$7$	−2.53955			−0.959861			−0.479930	+	0.877307i	$0.659338\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.42686	+	1.76361i	0.808954	+	0.587872i
$10$	1.00000			0.316228
$11$	−1.55248			−0.468089			−0.234045	−	0.972226i	$-0.575196\pi$
$11$	−1.55248			−0.468089			−0.234045	+	0.972226i	$0.575196\pi$
$12$	−0.535321	+	1.64725i	−0.154534	+	0.475520i
$13$	−1.11554	−	1.11554i	−0.309396	−	0.309396i	0.535279	−	0.844675i	$-0.320206\pi$
$13$	−1.11554	−	1.11554i	−0.309396	−	0.309396i	−0.844675	+	0.535279i	$0.820206\pi$
$14$	1.79574	+	1.79574i	0.479930	+	0.479930i
$15$	−1.54331	+	0.786252i	−0.398481	+	0.203009i
$16$	−1.00000			−0.250000
$17$	−4.84198	+	4.84198i	−1.17435	+	1.17435i	−0.193193	+	0.981161i	$0.561884\pi$
$17$	−4.84198	+	4.84198i	−1.17435	+	1.17435i	−0.981161	+	0.193193i	$0.938116\pi$
$18$	−0.468987	−	2.96312i	−0.110541	−	0.698413i
$19$	−2.49053	−	2.49053i	−0.571367	−	0.571367i	0.361143	−	0.932510i	$-0.382387\pi$
$19$	−2.49053	−	2.49053i	−0.571367	−	0.571367i	−0.932510	+	0.361143i	$0.882387\pi$
$20$	−0.707107	−	0.707107i	−0.158114	−	0.158114i
$21$	−4.18328	−	1.35948i	−0.912866	−	0.296662i
$22$	1.09777	+	1.09777i	0.234045	+	0.234045i
$23$	−0.856269	+	0.856269i	−0.178544	+	0.178544i	−0.790721	−	0.612177i	$-0.790294\pi$
$23$	−0.856269	+	0.856269i	−0.178544	+	0.178544i	0.612177	+	0.790721i	$0.290294\pi$
$24$	1.54331	−	0.786252i	0.315027	−	0.160493i
$25$		−	1.00000i		−	0.200000i
$26$			1.57762i			0.309396i
$27$	3.05355	+	4.20426i	0.587656	+	0.809111i
$28$		−	2.53955i		−	0.479930i
$29$	−5.19422	−	5.19422i	−0.964543	−	0.964543i	0.0348499	−	0.999393i	$-0.488905\pi$
$29$	−5.19422	−	5.19422i	−0.964543	−	0.964543i	−0.999393	+	0.0348499i	$0.988905\pi$
$30$	1.64725	+	0.535321i	0.300745	+	0.0977358i
$31$	1.70231	−	1.70231i	0.305743	−	0.305743i	−0.537513	−	0.843256i	$-0.680636\pi$
$31$	1.70231	−	1.70231i	0.305743	−	0.305743i	0.843256	+	0.537513i	$0.180636\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−2.55731	−	0.831073i	−0.445171	−	0.144671i
$34$	6.84760			1.17435
$35$	1.79574	−	1.79574i	0.303535	−	0.303535i
$36$	−1.76361	+	2.42686i	−0.293936	+	0.404477i
$37$	3.85543	+	4.70486i	0.633829	+	0.773474i
$37$	3.85543	+	4.70486i	0.633829	+	0.773474i
$38$			3.52214i			0.571367i
$39$	−1.24041	−	2.43475i	−0.198624	−	0.389873i
$40$			1.00000i			0.158114i
$41$	−10.4791			−1.63657			−0.818284	−	0.574815i	$-0.805074\pi$
$41$	−10.4791			−1.63657			−0.818284	+	0.574815i	$0.805074\pi$
$42$	1.99673	+	3.91932i	0.308102	+	0.604764i
$43$	−2.78010	−	2.78010i	−0.423961	−	0.423961i	0.462604	−	0.886565i	$-0.346915\pi$
$43$	−2.78010	−	2.78010i	−0.423961	−	0.423961i	−0.886565	+	0.462604i	$0.846915\pi$
$44$		−	1.55248i		−	0.234045i
$45$	−2.96312	+	0.468987i	−0.441715	+	0.0699125i
$46$	1.21095			0.178544
$47$			10.4277i			1.52104i	0.649317	+	0.760518i	$0.275055\pi$
$47$			10.4277i			1.52104i	−0.649317	+	0.760518i	$0.724945\pi$
$48$	−1.64725	−	0.535321i	−0.237760	−	0.0772669i
$49$	−0.550669			−0.0786670
$50$	−0.707107	+	0.707107i	−0.100000	+	0.100000i
$51$	−10.5680	+	5.38394i	−1.47981	+	0.753902i
$52$	1.11554	−	1.11554i	0.154698	−	0.154698i
$53$		−	5.16143i		−	0.708978i	−0.935060	−	0.354489i	$-0.884655\pi$
$53$		−	5.16143i		−	0.708978i	0.935060	−	0.354489i	$-0.115345\pi$
$54$	0.813678	−	5.13205i	0.110728	−	0.698383i
$55$	1.09777	−	1.09777i	0.148023	−	0.148023i
$56$	−1.79574	+	1.79574i	−0.239965	+	0.239965i
$57$	−2.76929	−	5.43576i	−0.366802	−	0.719984i
$58$			7.34574i			0.964543i
$59$	−8.36584	+	8.36584i	−1.08914	+	1.08914i	−0.0935229	+	0.995617i	$0.529813\pi$
$59$	−8.36584	+	8.36584i	−1.08914	+	1.08914i	−0.995617	+	0.0935229i	$0.970187\pi$
$60$	−0.786252	−	1.54331i	−0.101505	−	0.199241i
$61$	7.41355	−	7.41355i	0.949208	−	0.949208i	−0.0495632	−	0.998771i	$-0.515783\pi$
$61$	7.41355	−	7.41355i	0.949208	−	0.949208i	0.998771	+	0.0495632i	$0.0157829\pi$
$62$	−2.40742			−0.305743
$63$	−6.16315	−	4.47879i	−0.776484	−	0.564275i
$64$		−	1.00000i		−	0.125000i
$65$	1.57762			0.195679
$66$	1.22064	+	2.39595i	0.150250	+	0.294921i
$67$			1.98974i			0.243085i	0.992586	+	0.121543i	$0.0387841\pi$
$67$			1.98974i			0.243085i	−0.992586	+	0.121543i	$0.961216\pi$
$68$	−4.84198	−	4.84198i	−0.587177	−	0.587177i
$69$	−1.86887	+	0.952110i	−0.224985	+	0.114621i
$70$	−2.53955			−0.303535
$71$			3.37621i			0.400682i	0.979726	+	0.200341i	$0.0642050\pi$
$71$			3.37621i			0.400682i	−0.979726	+	0.200341i	$0.935795\pi$
$72$	2.96312	−	0.468987i	0.349206	−	0.0552707i
$73$		−	0.480190i		−	0.0562020i	−0.999605	−	0.0281010i	$-0.991054\pi$
$73$		−	0.480190i		−	0.0562020i	0.999605	−	0.0281010i	$-0.00894601\pi$
$74$	0.600636	−	6.05304i	0.0698225	−	0.703651i
$75$	0.535321	−	1.64725i	0.0618135	−	0.190208i
$76$	2.49053	−	2.49053i	0.285684	−	0.285684i
$77$	3.94259			0.449300
$78$	−0.844532	+	2.59873i	−0.0956244	+	0.294248i
$79$	6.52251	+	6.52251i	0.733840	+	0.733840i	0.971378	−	0.237538i	$-0.0763405\pi$
$79$	6.52251	+	6.52251i	0.733840	+	0.733840i	−0.237538	+	0.971378i	$0.576341\pi$
$80$	0.707107	−	0.707107i	0.0790569	−	0.0790569i
$81$	2.77933	+	8.56010i	0.308814	+	0.951122i
$82$	7.40987	+	7.40987i	0.818284	+	0.818284i
$83$		−	8.64749i		−	0.949186i	−0.880205	−	0.474593i	$-0.842595\pi$
$83$		−	8.64749i		−	0.949186i	0.880205	−	0.474593i	$-0.157405\pi$
$84$	1.35948	−	4.18328i	0.148331	−	0.456433i
$85$		−	6.84760i		−	0.742726i
$86$			3.93165i			0.423961i
$87$	−5.77560	−	11.3368i	−0.619210	−	1.21543i
$88$	−1.09777	+	1.09777i	−0.117022	+	0.117022i
$89$	−10.5685	−	10.5685i	−1.12026	−	1.12026i	−0.991702	−	0.128557i	$-0.958965\pi$
$89$	−10.5685	−	10.5685i	−1.12026	−	1.12026i	−0.128557	−	0.991702i	$-0.541035\pi$
$90$	2.42686	+	1.76361i	0.255814	+	0.185901i
$91$	2.83298	+	2.83298i	0.296977	+	0.296977i
$92$	−0.856269	−	0.856269i	−0.0892722	−	0.0892722i
$93$	3.71540	−	1.89284i	0.385269	−	0.196279i
$94$	7.37349	−	7.37349i	0.760518	−	0.760518i
$95$	3.52214			0.361364
$96$	0.786252	+	1.54331i	0.0802465	+	0.157513i
$97$	−5.01332	−	5.01332i	−0.509026	−	0.509026i	0.405202	−	0.914227i	$-0.367201\pi$
$97$	−5.01332	−	5.01332i	−0.509026	−	0.509026i	−0.914227	+	0.405202i	$0.867201\pi$
$98$	0.389382	+	0.389382i	0.0393335	+	0.0393335i
$99$	−3.76765	−	2.73797i	−0.378663	−	0.275176i
$100$	1.00000			0.100000
$101$	3.12753			0.311201			0.155600	−	0.987820i	$-0.450269\pi$
$101$	3.12753			0.311201			0.155600	+	0.987820i	$0.450269\pi$
$102$	11.2797	+	3.66566i	1.11686	+	0.362955i
$103$	−9.44888	+	9.44888i	−0.931026	+	0.931026i	−0.997770	−	0.0667446i	$-0.978739\pi$
$103$	−9.44888	+	9.44888i	−0.931026	+	0.931026i	0.0667446	+	0.997770i	$0.478739\pi$
$104$	−1.57762			−0.154698
$105$	3.91932	−	1.99673i	0.382486	−	0.194861i
$106$	−3.64969	+	3.64969i	−0.354489	+	0.354489i
$107$			1.92564i			0.186159i	0.995659	+	0.0930794i	$0.0296710\pi$
$107$			1.92564i			0.186159i	−0.995659	+	0.0930794i	$0.970329\pi$
$108$	−4.20426	+	3.05355i	−0.404556	+	0.293828i
$109$	−1.77468	−	1.77468i	−0.169983	−	0.169983i	0.616989	−	0.786972i	$-0.288352\pi$
$109$	−1.77468	−	1.77468i	−0.169983	−	0.169983i	−0.786972	+	0.616989i	$0.788352\pi$
$110$	−1.55248			−0.148023
$111$	3.83224	+	9.81396i	0.363741	+	0.931500i
$112$	2.53955			0.239965
$113$	11.3932	+	11.3932i	1.07178	+	1.07178i	0.997216	+	0.0745674i	$0.0237576\pi$
$113$	11.3932	+	11.3932i	1.07178	+	1.07178i	0.0745674	+	0.997216i	$0.476242\pi$
$114$	−1.88548	+	5.80185i	−0.176591	+	0.543393i
$115$		−	1.21095i		−	0.112921i
$116$	5.19422	−	5.19422i	0.482271	−	0.482271i
$117$	−0.739883	−	4.67466i	−0.0684022	−	0.432173i
$118$	11.8311			1.08914
$119$	12.2965	−	12.2965i	1.12722	−	1.12722i
$120$	−0.535321	+	1.64725i	−0.0488679	+	0.150373i
$121$	−8.58982			−0.780893
$122$	−10.4843			−0.949208
$123$	−17.2618	−	5.60971i	−1.55644	−	0.505810i
$124$	1.70231	+	1.70231i	0.152872	+	0.152872i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	1.19102	+	7.52499i	0.106104	+	0.670379i
$127$	14.3170			1.27043			0.635215	−	0.772336i	$-0.280912\pi$
$127$	14.3170			1.27043			0.635215	+	0.772336i	$0.280912\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−3.09127	−	6.06776i	−0.272171	−	0.534236i
$130$	−1.11554	−	1.11554i	−0.0978397	−	0.0978397i
$131$	−0.642612	−	0.642612i	−0.0561453	−	0.0561453i	0.678477	−	0.734622i	$-0.262640\pi$
$131$	−0.642612	−	0.642612i	−0.0561453	−	0.0561453i	−0.734622	+	0.678477i	$0.762640\pi$
$132$	0.831073	−	2.55731i	0.0723356	−	0.222586i
$133$	6.32484	+	6.32484i	0.548433	+	0.548433i
$134$	1.40696	−	1.40696i	0.121543	−	0.121543i
$135$	−5.13205	−	0.813678i	−0.441696	−	0.0700303i
$136$			6.84760i			0.587177i
$137$			22.7686i			1.94525i	0.232373	+	0.972627i	$0.425351\pi$
$137$			22.7686i			1.94525i	−0.232373	+	0.972627i	$0.574649\pi$
$138$	1.99473	+	0.648245i	0.169803	+	0.0551823i
$139$		−	6.95397i		−	0.589828i	−0.955524	−	0.294914i	$-0.904709\pi$
$139$		−	6.95397i		−	0.589828i	0.955524	−	0.294914i	$-0.0952910\pi$
$140$	1.79574	+	1.79574i	0.151767	+	0.151767i
$141$	−5.58216	+	17.1770i	−0.470103	+	1.44657i
$142$	2.38734	−	2.38734i	0.200341	−	0.200341i
$143$	1.73185	+	1.73185i	0.144825	+	0.144825i
$144$	−2.42686	−	1.76361i	−0.202239	−	0.146968i
$145$	7.34574			0.610030
$146$	−0.339546	+	0.339546i	−0.0281010	+	0.0281010i
$147$	−0.907089	−	0.294785i	−0.0748154	−	0.0243134i
$148$	−4.70486	+	3.85543i	−0.386737	+	0.316914i
$149$			15.3710i			1.25924i	0.776904	+	0.629619i	$0.216789\pi$
$149$			15.3710i			1.25924i	−0.776904	+	0.629619i	$0.783211\pi$
$150$	−1.54331	+	0.786252i	−0.126011	+	0.0641972i
$151$			8.84452i			0.719756i	0.932999	+	0.359878i	$0.117182\pi$
$151$			8.84452i			0.719756i	−0.932999	+	0.359878i	$0.882818\pi$
$152$	−3.52214			−0.285684
$153$	−20.2902	+	3.21144i	−1.64037	+	0.259629i
$154$	−2.78784	−	2.78784i	−0.224650	−	0.224650i
$155$			2.40742i			0.193369i
$156$	2.43475	−	1.24041i	0.194936	−	0.0993119i
$157$	4.17933			0.333547			0.166774	−	0.985995i	$-0.446665\pi$
$157$	4.17933			0.333547			0.166774	+	0.985995i	$0.446665\pi$
$158$		−	9.22422i		−	0.733840i
$159$	2.76302	−	8.50217i	0.219122	−	0.674266i
$160$	−1.00000			−0.0790569
$161$	2.17454	−	2.17454i	0.171378	−	0.171378i
$162$	4.08763	−	8.01819i	0.321154	−	0.629968i
$163$	1.54752	−	1.54752i	0.121211	−	0.121211i	−0.643899	−	0.765110i	$-0.722684\pi$
$163$	1.54752	−	1.54752i	0.121211	−	0.121211i	0.765110	+	0.643899i	$0.222684\pi$
$164$		−	10.4791i		−	0.818284i
$165$	2.39595	−	1.22064i	0.186525	−	0.0950265i
$166$	−6.11470	+	6.11470i	−0.474593	+	0.474593i
$167$	−13.7766	+	13.7766i	−1.06607	+	1.06607i	−0.0684095	+	0.997657i	$0.521792\pi$
$167$	−13.7766	+	13.7766i	−1.06607	+	1.06607i	−0.997657	+	0.0684095i	$0.978208\pi$
$168$	−3.91932	+	1.99673i	−0.302382	+	0.154051i
$169$		−	10.5111i		−	0.808548i
$170$	−4.84198	+	4.84198i	−0.371363	+	0.371363i
$171$	−1.65184	−	10.4365i	−0.126319	−	0.798101i
$172$	2.78010	−	2.78010i	0.211980	−	0.211980i
$173$	22.4262			1.70503			0.852517	−	0.522699i	$-0.175075\pi$
$173$	22.4262			1.70503			0.852517	+	0.522699i	$0.175075\pi$
$174$	−3.93233	+	12.1003i	−0.298109	+	0.917319i
$175$			2.53955i			0.191972i
$176$	1.55248			0.117022
$177$	−18.2590	+	9.30222i	−1.37243	+	0.699198i
$178$			14.9461i			1.12026i
$179$	5.77543	+	5.77543i	0.431676	+	0.431676i	0.889198	−	0.457522i	$-0.151263\pi$
$179$	5.77543	+	5.77543i	0.431676	+	0.431676i	−0.457522	+	0.889198i	$0.651263\pi$
$180$	−0.468987	−	2.96312i	−0.0349563	−	0.220858i
$181$	13.1382			0.976553			0.488276	−	0.872689i	$-0.337626\pi$
$181$	13.1382			0.976553			0.488276	+	0.872689i	$0.337626\pi$
$182$		−	4.00644i		−	0.296977i
$183$	16.1806	−	8.24334i	1.19610	−	0.609365i
$184$			1.21095i			0.0892722i
$185$	−6.05304	−	0.600636i	−0.445028	−	0.0441596i
$186$	−3.96563	−	1.28874i	−0.290774	−	0.0944954i
$187$	7.51706	−	7.51706i	0.549702	−	0.549702i
$188$	−10.4277			−0.760518
$189$	−7.75465	−	10.6770i	−0.564068	−	0.776634i
$190$	−2.49053	−	2.49053i	−0.180682	−	0.180682i
$191$	6.53325	−	6.53325i	0.472729	−	0.472729i	−0.430068	−	0.902797i	$-0.641510\pi$
$191$	6.53325	−	6.53325i	0.472729	−	0.472729i	0.902797	+	0.430068i	$0.141510\pi$
$192$	0.535321	−	1.64725i	0.0386335	−	0.118880i
$193$	1.18075	+	1.18075i	0.0849921	+	0.0849921i	0.748325	−	0.663333i	$-0.230859\pi$
$193$	1.18075	+	1.18075i	0.0849921	+	0.0849921i	−0.663333	+	0.748325i	$0.730859\pi$
$194$			7.08991i			0.509026i
$195$	2.59873	+	0.844532i	0.186099	+	0.0604782i
$196$		−	0.550669i		−	0.0393335i
$197$			3.07165i			0.218846i	0.993995	+	0.109423i	$0.0349003\pi$
$197$			3.07165i			0.218846i	−0.993995	+	0.109423i	$0.965100\pi$
$198$	0.728091	+	4.60016i	0.0517432	+	0.326919i
$199$	−1.93640	+	1.93640i	−0.137268	+	0.137268i	−0.772402	−	0.635134i	$-0.780945\pi$
$199$	−1.93640	+	1.93640i	−0.137268	+	0.137268i	0.635134	+	0.772402i	$0.280945\pi$
$200$	−0.707107	−	0.707107i	−0.0500000	−	0.0500000i
$201$	−1.06515	+	3.27760i	−0.0751298	+	0.231184i
$202$	−2.21150	−	2.21150i	−0.155600	−	0.155600i
$203$	13.1910	+	13.1910i	0.925827	+	0.925827i
$204$	−5.38394	−	10.5680i	−0.376951	−	0.739906i
$205$	7.40987	−	7.40987i	0.517528	−	0.517528i
$206$	13.3627			0.931026
$207$	−3.58817	+	0.567919i	−0.249395	+	0.0394731i
$208$	1.11554	+	1.11554i	0.0773490	+	0.0773490i
$209$	3.86649	+	3.86649i	0.267451	+	0.267451i
$210$	−4.18328	−	1.35948i	−0.288674	−	0.0938128i
$211$	−24.0332			−1.65451			−0.827257	−	0.561824i	$-0.810100\pi$
$211$	−24.0332			−1.65451			−0.827257	+	0.561824i	$0.810100\pi$
$212$	5.16143			0.354489
$213$	−1.80736	+	5.56146i	−0.123838	+	0.381065i
$214$	1.36163	−	1.36163i	0.0930794	−	0.0930794i
$215$	3.93165			0.268136
$216$	5.13205	+	0.813678i	0.349192	+	0.0553638i
$217$	−4.32310	+	4.32310i	−0.293471	+	0.293471i
$218$			2.50977i			0.169983i
$219$	0.257056	−	0.790993i	0.0173702	−	0.0534504i
$220$	1.09777	+	1.09777i	0.0740114	+	0.0740114i
$221$	10.8029			0.726681
$222$	4.22971	−	9.64933i	0.283880	−	0.647620i
$223$	−19.6653			−1.31688			−0.658442	−	0.752631i	$-0.728784\pi$
$223$	−19.6653			−1.31688			−0.658442	+	0.752631i	$0.728784\pi$
$224$	−1.79574	−	1.79574i	−0.119983	−	0.119983i
$225$	1.76361	−	2.42686i	0.117574	−	0.161791i
$226$		−	16.1124i		−	1.07178i
$227$	−2.56107	+	2.56107i	−0.169984	+	0.169984i	−0.786972	−	0.616988i	$-0.788353\pi$
$227$	−2.56107	+	2.56107i	−0.169984	+	0.169984i	0.616988	+	0.786972i	$0.288353\pi$
$228$	5.43576	−	2.76929i	0.359992	−	0.183401i
$229$	13.0356			0.861418			0.430709	−	0.902491i	$-0.358264\pi$
$229$	13.0356			0.861418			0.430709	+	0.902491i	$0.358264\pi$
$230$	−0.856269	+	0.856269i	−0.0564607	+	0.0564607i
$231$	6.49444	+	2.11055i	0.427303	+	0.138864i
$232$	−7.34574			−0.482271
$233$	20.4916			1.34245			0.671223	−	0.741255i	$-0.265769\pi$
$233$	20.4916			1.34245			0.671223	+	0.741255i	$0.265769\pi$
$234$	−2.78231	+	3.82866i	−0.181885	+	0.250287i
$235$	−7.37349	−	7.37349i	−0.480994	−	0.480994i
$236$	−8.36584	−	8.36584i	−0.544570	−	0.544570i
$237$	7.25257	+	14.2358i	0.471105	+	0.924717i
$238$	−17.3898			−1.12722
$239$	16.0579	−	16.0579i	1.03870	−	1.03870i	0.0394798	−	0.999220i	$-0.487430\pi$
$239$	16.0579	−	16.0579i	1.03870	−	1.03870i	0.999220	−	0.0394798i	$-0.0125701\pi$
$240$	1.54331	−	0.786252i	0.0996203	−	0.0507524i
$241$	−8.01194	−	8.01194i	−0.516095	−	0.516095i	0.400293	−	0.916387i	$-0.368908\pi$
$241$	−8.01194	−	8.01194i	−0.516095	−	0.516095i	−0.916387	+	0.400293i	$0.868908\pi$
$242$	6.07392	+	6.07392i	0.390446	+	0.390446i
$243$	−0.00415661	+	15.5885i	−0.000266647	+	1.00000i
$244$	7.41355	+	7.41355i	0.474604	+	0.474604i
$245$	0.389382	−	0.389382i	0.0248767	−	0.0248767i
$246$	8.23925	+	16.1726i	0.525315	+	1.03113i
$247$			5.55660i			0.353558i
$248$		−	2.40742i		−	0.152872i
$249$	4.62918	−	14.2446i	0.293363	−	0.902714i
$250$		−	1.00000i		−	0.0632456i
$251$	−5.39840	−	5.39840i	−0.340744	−	0.340744i	0.515903	−	0.856647i	$-0.327457\pi$
$251$	−5.39840	−	5.39840i	−0.340744	−	0.340744i	−0.856647	+	0.515903i	$0.827457\pi$
$252$	4.47879	−	6.16315i	0.282137	−	0.388242i
$253$	1.32934	−	1.32934i	0.0835747	−	0.0835747i
$254$	−10.1237	−	10.1237i	−0.635215	−	0.635215i
$255$	3.66566	−	11.2797i	0.229553	−	0.706363i
$256$	1.00000			0.0625000
$257$	12.9474	−	12.9474i	0.807636	−	0.807636i	−0.176640	−	0.984276i	$-0.556523\pi$
$257$	12.9474	−	12.9474i	0.807636	−	0.807636i	0.984276	+	0.176640i	$0.0565227\pi$
$258$	−2.10470	+	6.47641i	−0.131033	+	0.403204i
$259$	−9.79107	−	11.9482i	−0.608387	−	0.742427i
$260$			1.57762i			0.0978397i
$261$	−3.44506	−	21.7663i	−0.213244	−	1.34730i
$262$			0.908791i			0.0561453i
$263$	−7.40115			−0.456375			−0.228187	−	0.973617i	$-0.573280\pi$
$263$	−7.40115			−0.456375			−0.228187	+	0.973617i	$0.573280\pi$
$264$	−2.39595	+	1.22064i	−0.147461	+	0.0751250i
$265$	3.64969	+	3.64969i	0.224198	+	0.224198i
$266$		−	8.94467i		−	0.548433i
$267$	−11.7514	−	23.0665i	−0.719175	−	1.41165i
$268$	−1.98974			−0.121543
$269$		−	22.3915i		−	1.36523i	−0.730776	−	0.682617i	$-0.760842\pi$
$269$		−	22.3915i		−	1.36523i	0.730776	−	0.682617i	$-0.239158\pi$
$270$	3.05355	+	4.20426i	0.185833	+	0.255863i
$271$	18.4875			1.12304			0.561518	−	0.827465i	$-0.310218\pi$
$271$	18.4875			1.12304			0.561518	+	0.827465i	$0.310218\pi$
$272$	4.84198	−	4.84198i	0.293588	−	0.293588i
$273$	3.15008	+	6.18319i	0.190651	+	0.374223i
$274$	16.0998	−	16.0998i	0.972627	−	0.972627i
$275$			1.55248i			0.0936178i
$276$	−0.952110	−	1.86887i	−0.0573103	−	0.112493i
$277$	7.72665	−	7.72665i	0.464249	−	0.464249i	−0.435796	−	0.900045i	$-0.643533\pi$
$277$	7.72665	−	7.72665i	0.464249	−	0.464249i	0.900045	+	0.435796i	$0.143533\pi$
$278$	−4.91720	+	4.91720i	−0.294914	+	0.294914i
$279$	7.13348	−	1.12905i	0.427070	−	0.0675946i
$280$		−	2.53955i		−	0.151767i
$281$	3.95236	−	3.95236i	0.235778	−	0.235778i	−0.579321	−	0.815099i	$-0.696682\pi$
$281$	3.95236	−	3.95236i	0.235778	−	0.235778i	0.815099	+	0.579321i	$0.196682\pi$
$282$	16.0932	−	8.19880i	0.958334	−	0.488231i
$283$	4.17375	−	4.17375i	0.248104	−	0.248104i	−0.572088	−	0.820192i	$-0.693867\pi$
$283$	4.17375	−	4.17375i	0.248104	−	0.248104i	0.820192	+	0.572088i	$0.193867\pi$
$284$	−3.37621			−0.200341
$285$	5.80185	+	1.88548i	0.343672	+	0.111686i
$286$		−	2.44921i		−	0.144825i
$287$	26.6123			1.57088
$288$	0.468987	+	2.96312i	0.0276353	+	0.174603i
$289$		−	29.8896i		−	1.75821i
$290$	−5.19422	−	5.19422i	−0.305015	−	0.305015i
$291$	−5.57445	−	10.9419i	−0.326780	−	0.641427i
$292$	0.480190			0.0281010
$293$		−	15.2274i		−	0.889593i	−0.895632	−	0.444796i	$-0.853276\pi$
$293$		−	15.2274i		−	0.889593i	0.895632	−	0.444796i	$-0.146724\pi$
$294$	0.432965	+	0.849853i	0.0252510	+	0.0495644i
$295$		−	11.8311i		−	0.688833i
$296$	6.05304	+	0.600636i	0.351826	+	0.0349113i
$297$	−4.74056	−	6.52702i	−0.275075	−	0.378736i
$298$	10.8689	−	10.8689i	0.629619	−	0.629619i
$299$	1.91041			0.110482
$300$	1.64725	+	0.535321i	0.0951040	+	0.0309068i
$301$	7.06021	+	7.06021i	0.406944	+	0.406944i
$302$	6.25402	−	6.25402i	0.359878	−	0.359878i
$303$	5.15182	+	1.67423i	0.295964	+	0.0961821i
$304$	2.49053	+	2.49053i	0.142842	+	0.142842i
$305$			10.4843i			0.600332i
$306$	16.6182	+	12.0765i	0.949998	+	0.690369i
$307$			22.5433i			1.28661i	0.765609	+	0.643306i	$0.222438\pi$
$307$			22.5433i			1.28661i	−0.765609	+	0.643306i	$0.777562\pi$
$308$			3.94259i			0.224650i
$309$	−20.6228	+	10.5065i	−1.17319	+	0.597693i
$310$	1.70231	−	1.70231i	0.0966845	−	0.0966845i
$311$	−6.11792	−	6.11792i	−0.346915	−	0.346915i	0.512044	−	0.858959i	$-0.328888\pi$
$311$	−6.11792	−	6.11792i	−0.346915	−	0.346915i	−0.858959	+	0.512044i	$0.828888\pi$
$312$	−2.59873	−	0.844532i	−0.147124	−	0.0478122i
$313$	3.26673	+	3.26673i	0.184646	+	0.184646i	0.793377	−	0.608731i	$-0.208321\pi$
$313$	3.26673	+	3.26673i	0.184646	+	0.184646i	−0.608731	+	0.793377i	$0.708321\pi$
$314$	−2.95524	−	2.95524i	−0.166774	−	0.166774i
$315$	7.52499	−	1.19102i	0.423985	−	0.0671063i
$316$	−6.52251	+	6.52251i	−0.366920	+	0.366920i
$317$	−30.0184			−1.68600			−0.843001	−	0.537912i	$-0.819213\pi$
$317$	−30.0184			−1.68600			−0.843001	+	0.537912i	$0.819213\pi$
$318$	−7.96570	+	4.05819i	−0.446694	+	0.227572i
$319$	8.06390	+	8.06390i	0.451492	+	0.451492i
$320$	0.707107	+	0.707107i	0.0395285	+	0.0395285i
$321$	−1.03084	+	3.17201i	−0.0575357	+	0.177044i
$322$	−3.07526			−0.171378
$323$	24.1182			1.34197
$324$	−8.56010	+	2.77933i	−0.475561	+	0.154407i
$325$	−1.11554	+	1.11554i	−0.0618792	+	0.0618792i
$326$	−2.18852			−0.121211
$327$	−1.97331	−	3.87336i	−0.109124	−	0.214197i
$328$	−7.40987	+	7.40987i	−0.409142	+	0.409142i
$329$		−	26.4817i		−	1.45998i
$330$	−2.55731	−	0.831073i	−0.140776	−	0.0457490i
$331$	9.21805	+	9.21805i	0.506670	+	0.506670i	0.913503	−	0.406833i	$-0.133367\pi$
$331$	9.21805	+	9.21805i	0.506670	+	0.506670i	−0.406833	+	0.913503i	$0.633367\pi$
$332$	8.64749			0.474593
$333$	1.05904	+	18.2175i	0.0580352	+	0.998315i
$334$	19.4831			1.06607
$335$	−1.40696	−	1.40696i	−0.0768704	−	0.0768704i
$336$	4.18328	+	1.35948i	0.228217	+	0.0741655i
$337$			22.7367i			1.23855i	0.785175	+	0.619275i	$0.212573\pi$
$337$			22.7367i			1.23855i	−0.785175	+	0.619275i	$0.787427\pi$
$338$	−7.43249	+	7.43249i	−0.404274	+	0.404274i
$339$	12.6684	+	24.8665i	0.688055	+	1.35056i
$340$	6.84760			0.371363
$341$	−2.64279	+	2.64279i	−0.143115	+	0.143115i
$342$	−6.21171	+	8.54776i	−0.335891	+	0.462210i
$343$	19.1753			1.03537
$344$	−3.93165			−0.211980
$345$	0.648245	−	1.99473i	0.0349003	−	0.107393i
$346$	−15.8577	−	15.8577i	−0.852517	−	0.852517i
$347$	−12.8734	−	12.8734i	−0.691078	−	0.691078i	0.271391	−	0.962469i	$-0.412516\pi$
$347$	−12.8734	−	12.8734i	−0.691078	−	0.691078i	−0.962469	+	0.271391i	$0.912516\pi$
$348$	11.3368	−	5.77560i	0.607714	−	0.309605i
$349$	−17.1933			−0.920336			−0.460168	−	0.887832i	$-0.652211\pi$
$349$	−17.1933			−0.920336			−0.460168	+	0.887832i	$0.652211\pi$
$350$	1.79574	−	1.79574i	0.0959861	−	0.0959861i
$351$	1.28367	−	8.09641i	0.0685174	−	0.432154i
$352$	−1.09777	−	1.09777i	−0.0585111	−	0.0585111i
$353$	−13.6457	−	13.6457i	−0.726286	−	0.726286i	0.243592	−	0.969878i	$-0.421674\pi$
$353$	−13.6457	−	13.6457i	−0.726286	−	0.726286i	−0.969878	+	0.243592i	$0.921674\pi$
$354$	19.4888	+	6.33343i	1.03582	+	0.336618i
$355$	−2.38734	−	2.38734i	−0.126707	−	0.126707i
$356$	10.5685	−	10.5685i	0.560130	−	0.560130i
$357$	26.8379	−	13.6728i	1.42041	−	0.723642i
$358$		−	8.16769i		−	0.431676i
$359$			32.6347i			1.72239i	0.508272	+	0.861197i	$0.330284\pi$
$359$			32.6347i			1.72239i	−0.508272	+	0.861197i	$0.669716\pi$
$360$	−1.76361	+	2.42686i	−0.0929507	+	0.127907i
$361$		−	6.59450i		−	0.347079i
$362$	−9.29009	−	9.29009i	−0.488276	−	0.488276i
$363$	−14.1496	−	4.59831i	−0.742660	−	0.241349i
$364$	−2.83298	+	2.83298i	−0.148489	+	0.148489i
$365$	0.339546	+	0.339546i	0.0177726	+	0.0177726i
$366$	−17.2703	−	5.61249i	−0.902735	−	0.293369i
$367$	−12.0728			−0.630194			−0.315097	−	0.949060i	$-0.602037\pi$
$367$	−12.0728			−0.630194			−0.315097	+	0.949060i	$0.602037\pi$
$368$	0.856269	−	0.856269i	0.0446361	−	0.0446361i
$369$	−25.4314	−	18.4812i	−1.32391	−	0.962091i
$370$	3.85543	+	4.70486i	0.200434	+	0.244594i
$371$			13.1077i			0.680520i
$372$	1.89284	+	3.71540i	0.0981393	+	0.192635i
$373$			26.6336i			1.37904i	0.724268	+	0.689518i	$0.242178\pi$
$373$			26.6336i			1.37904i	−0.724268	+	0.689518i	$0.757822\pi$
$374$	−10.6307			−0.549702
$375$	0.786252	+	1.54331i	0.0406019	+	0.0796962i
$376$	7.37349	+	7.37349i	0.380259	+	0.380259i
$377$			11.5888i			0.596852i
$378$	−2.06638	+	13.0331i	−0.106283	+	0.670351i
$379$	20.7514			1.06593			0.532963	−	0.846139i	$-0.321078\pi$
$379$	20.7514			1.06593			0.532963	+	0.846139i	$0.321078\pi$
$380$			3.52214i			0.180682i
$381$	23.5837	+	7.66420i	1.20823	+	0.392649i
$382$	−9.23941			−0.472729
$383$	−15.8691	+	15.8691i	−0.810874	+	0.810874i	−0.984765	−	0.173891i	$-0.944366\pi$
$383$	−15.8691	+	15.8691i	−0.810874	+	0.810874i	0.173891	+	0.984765i	$0.444366\pi$
$384$	−1.54331	+	0.786252i	−0.0787567	+	0.0401233i
$385$	−2.78784	+	2.78784i	−0.142081	+	0.142081i
$386$		−	1.66983i		−	0.0849921i
$387$	−1.84390	−	11.6499i	−0.0937305	−	0.592200i
$388$	5.01332	−	5.01332i	0.254513	−	0.254513i
$389$	8.71629	−	8.71629i	0.441934	−	0.441934i	−0.450728	−	0.892661i	$-0.648836\pi$
$389$	8.71629	−	8.71629i	0.441934	−	0.441934i	0.892661	+	0.450728i	$0.148836\pi$
$390$	−1.24041	−	2.43475i	−0.0628104	−	0.123289i
$391$		−	8.29208i		−	0.419348i
$392$	−0.389382	+	0.389382i	−0.0196667	+	0.0196667i
$393$	−0.714539	−	1.40255i	−0.0360437	−	0.0707491i
$394$	2.17198	−	2.17198i	0.109423	−	0.109423i
$395$	−9.22422			−0.464121
$396$	2.73797	−	3.76765i	0.137588	−	0.189331i
$397$		−	0.0949796i		−	0.00476689i	−0.999997	−	0.00238345i	$-0.999241\pi$
$397$		−	0.0949796i		−	0.00476689i	0.999997	−	0.00238345i	$-0.000758675\pi$
$398$	2.73848			0.137268
$399$	7.03277	+	13.8044i	0.352079	+	0.691085i
$400$			1.00000i			0.0500000i
$401$	−3.89325	−	3.89325i	−0.194420	−	0.194420i	0.603183	−	0.797603i	$-0.293899\pi$
$401$	−3.89325	−	3.89325i	−0.194420	−	0.194420i	−0.797603	+	0.603183i	$0.793899\pi$
$402$	3.07079	−	1.56444i	0.153157	−	0.0780270i
$403$	−3.79799			−0.189192
$404$			3.12753i			0.155600i
$405$	−8.01819	−	4.08763i	−0.398427	−	0.203116i
$406$		−	18.6549i		−	0.925827i
$407$	−5.98546	−	7.30417i	−0.296688	−	0.362054i
$408$	−3.66566	+	11.2797i	−0.181477	+	0.558429i
$409$	22.8071	−	22.8071i	1.12774	−	1.12774i	0.137192	−	0.990544i	$-0.456192\pi$
$409$	22.8071	−	22.8071i	1.12774	−	1.12774i	0.990544	−	0.137192i	$-0.0438078\pi$
$410$	−10.4791			−0.517528
$411$	−12.1885	+	37.5056i	−0.601215	+	1.85001i
$412$	−9.44888	−	9.44888i	−0.465513	−	0.465513i
$413$	21.2455	−	21.2455i	1.04542	−	1.04542i
$414$	2.93880	+	2.13564i	0.144434	+	0.104961i
$415$	6.11470	+	6.11470i	0.300159	+	0.300159i
$416$		−	1.57762i		−	0.0773490i
$417$	3.72260	−	11.4549i	0.182297	−	0.560950i
$418$		−	5.46804i		−	0.267451i
$419$			19.4604i			0.950701i	0.879797	+	0.475350i	$0.157679\pi$
$419$			19.4604i			0.950701i	−0.879797	+	0.475350i	$0.842321\pi$
$420$	1.99673	+	3.91932i	0.0974304	+	0.191243i
$421$	−14.1201	+	14.1201i	−0.688171	+	0.688171i	−0.961827	−	0.273657i	$-0.911767\pi$
$421$	−14.1201	+	14.1201i	−0.688171	+	0.688171i	0.273657	+	0.961827i	$0.411767\pi$
$422$	16.9940	+	16.9940i	0.827257	+	0.827257i
$423$	−18.3904	+	25.3066i	−0.894174	+	1.23045i
$424$	−3.64969	−	3.64969i	−0.177244	−	0.177244i
$425$	4.84198	+	4.84198i	0.234871	+	0.234871i
$426$	5.21054	−	2.65455i	0.252451	−	0.128613i
$427$	−18.8271	+	18.8271i	−0.911107	+	0.911107i
$428$	−1.92564			−0.0930794
$429$	1.92570	+	3.77989i	0.0929736	+	0.182495i
$430$	−2.78010	−	2.78010i	−0.134068	−	0.134068i
$431$	−23.2957	−	23.2957i	−1.12211	−	1.12211i	−0.991423	−	0.130692i	$-0.958280\pi$
$431$	−23.2957	−	23.2957i	−1.12211	−	1.12211i	−0.130692	−	0.991423i	$-0.541720\pi$
$432$	−3.05355	−	4.20426i	−0.146914	−	0.202278i
$433$	−6.51982			−0.313323			−0.156661	−	0.987652i	$-0.550073\pi$
$433$	−6.51982			−0.313323			−0.156661	+	0.987652i	$0.550073\pi$
$434$	6.11378			0.293471
$435$	12.1003	+	3.93233i	0.580163	+	0.188541i
$436$	1.77468	−	1.77468i	0.0849916	−	0.0849916i
$437$	4.26513			0.204029
$438$	−0.741083	+	0.377551i	−0.0354103	+	0.0180401i
$439$	−7.97830	+	7.97830i	−0.380783	+	0.380783i	−0.871384	−	0.490601i	$-0.836777\pi$
$439$	−7.97830	+	7.97830i	−0.380783	+	0.380783i	0.490601	+	0.871384i	$0.336777\pi$
$440$		−	1.55248i		−	0.0740114i
$441$	−1.33640	−	0.971168i	−0.0636380	−	0.0462461i
$442$	−7.63880	−	7.63880i	−0.363341	−	0.363341i
$443$	0.170503			0.00810085			0.00405043	−	0.999992i	$-0.498711\pi$
$443$	0.170503			0.00810085			0.00405043	+	0.999992i	$0.498711\pi$
$444$	−9.81396	+	3.83224i	−0.465750	+	0.181870i
$445$	14.9461			0.708514
$446$	13.9055	+	13.9055i	0.658442	+	0.658442i
$447$	−8.22839	+	25.3198i	−0.389190	+	1.19759i
$448$			2.53955i			0.119983i
$449$	25.9266	−	25.9266i	1.22355	−	1.22355i	0.257189	−	0.966361i	$-0.417204\pi$
$449$	25.9266	−	25.9266i	1.22355	−	1.22355i	0.966361	−	0.257189i	$-0.0827964\pi$
$450$	−2.96312	+	0.468987i	−0.139683	+	0.0221083i
$451$	16.2686			0.766059
$452$	−11.3932	+	11.3932i	−0.535892	+	0.535892i
$453$	−4.73465	+	14.5691i	−0.222453	+	0.684517i
$454$	3.62190			0.169984
$455$	−4.00644			−0.187825
$456$	−5.80185	−	1.88548i	−0.271697	−	0.0882956i
$457$	−1.83261	−	1.83261i	−0.0857259	−	0.0857259i	0.662944	−	0.748669i	$-0.269307\pi$
$457$	−1.83261	−	1.83261i	−0.0857259	−	0.0857259i	−0.748669	+	0.662944i	$0.769307\pi$
$458$	−9.21757	−	9.21757i	−0.430709	−	0.430709i
$459$	−35.1422	−	5.57174i	−1.64030	−	0.260067i
$460$	1.21095			0.0564607
$461$	−11.4366	+	11.4366i	−0.532656	+	0.532656i	−0.921362	−	0.388706i	$-0.872922\pi$
$461$	−11.4366	+	11.4366i	−0.532656	+	0.532656i	0.388706	+	0.921362i	$0.372922\pi$
$462$	−3.09987	−	6.08465i	−0.144219	−	0.283083i
$463$	−14.6615	−	14.6615i	−0.681376	−	0.681376i	0.278934	−	0.960310i	$-0.410019\pi$
$463$	−14.6615	−	14.6615i	−0.681376	−	0.681376i	−0.960310	+	0.278934i	$0.910019\pi$
$464$	5.19422	+	5.19422i	0.241136	+	0.241136i
$465$	−1.28874	+	3.96563i	−0.0597641	+	0.183902i
$466$	−14.4897	−	14.4897i	−0.671223	−	0.671223i
$467$	−7.91991	+	7.91991i	−0.366490	+	0.366490i	−0.866195	−	0.499706i	$-0.833442\pi$
$467$	−7.91991	+	7.91991i	−0.366490	+	0.366490i	0.499706	+	0.866195i	$0.333442\pi$
$468$	4.67466	−	0.739883i	0.216086	−	0.0342011i
$469$		−	5.05305i		−	0.233328i
$470$			10.4277i			0.480994i
$471$	6.88441	+	2.23729i	0.317217	+	0.103089i
$472$			11.8311i			0.544570i
$473$	4.31603	+	4.31603i	0.198451	+	0.198451i
$474$	4.93792	−	15.1946i	0.226806	−	0.697911i
$475$	−2.49053	+	2.49053i	−0.114273	+	0.114273i
$476$	12.2965	+	12.2965i	0.563608	+	0.563608i
$477$	9.10278	−	12.5261i	0.416788	−	0.573530i
$478$	−22.7093			−1.03870
$479$	18.6437	−	18.6437i	0.851853	−	0.851853i	−0.138509	−	0.990361i	$-0.544231\pi$
$479$	18.6437	−	18.6437i	0.851853	−	0.851853i	0.990361	+	0.138509i	$0.0442309\pi$
$480$	−1.64725	−	0.535321i	−0.0751863	−	0.0244339i
$481$	0.947574	−	9.54937i	0.0432057	−	0.435414i
$482$			11.3306i			0.516095i
$483$	4.74609	−	2.41793i	0.215954	−	0.110020i
$484$		−	8.58982i		−	0.390446i
$485$	7.08991			0.321936
$486$	11.0256	−	11.0198i	0.500133	−	0.499867i
$487$	8.90792	+	8.90792i	0.403657	+	0.403657i	0.879519	−	0.475863i	$-0.157864\pi$
$487$	8.90792	+	8.90792i	0.403657	+	0.403657i	−0.475863	+	0.879519i	$0.657864\pi$
$488$		−	10.4843i		−	0.474604i
$489$	3.37757	−	1.72073i	0.152739	−	0.0778142i
$490$	−0.550669			−0.0248767
$491$			0.432806i			0.0195322i	0.999952	+	0.00976612i	$0.00310870\pi$
$491$			0.432806i			0.0195322i	−0.999952	+	0.00976612i	$0.996891\pi$
$492$	5.60971	−	17.2618i	0.252905	−	0.778220i
$493$	50.3007			2.26543
$494$	3.92911	−	3.92911i	0.176779	−	0.176779i
$495$	4.60016	−	0.728091i	0.206762	−	0.0327253i
$496$	−1.70231	+	1.70231i	−0.0764358	+	0.0764358i
$497$		−	8.57406i		−	0.384599i
$498$	−13.3458	+	6.79911i	−0.598038	+	0.304675i
$499$	−19.8374	+	19.8374i	−0.888044	+	0.888044i	−0.994335	−	0.106291i	$-0.966102\pi$
$499$	−19.8374	+	19.8374i	−0.888044	+	0.888044i	0.106291	+	0.994335i	$0.466102\pi$
$500$	−0.707107	+	0.707107i	−0.0316228	+	0.0316228i
$501$	−30.0684	+	15.3186i	−1.34336	+	0.684385i
$502$			7.63449i			0.340744i
$503$	−20.0416	+	20.0416i	−0.893611	+	0.893611i	−0.994861	−	0.101250i	$-0.967716\pi$
$503$	−20.0416	+	20.0416i	−0.893611	+	0.893611i	0.101250	+	0.994861i	$0.467716\pi$
$504$	−7.52499	+	1.19102i	−0.335190	+	0.0530522i
$505$	−2.21150	+	2.21150i	−0.0984104	+	0.0984104i
$506$	−1.87997			−0.0835747
$507$	5.62683	−	17.3144i	0.249896	−	0.768962i
$508$			14.3170i			0.635215i
$509$	−3.66498			−0.162447			−0.0812237	−	0.996696i	$-0.525883\pi$
$509$	−3.66498			−0.162447			−0.0812237	+	0.996696i	$0.525883\pi$
$510$	−10.5680	+	5.38394i	−0.467958	+	0.238405i
$511$			1.21947i			0.0539461i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	2.86589	−	18.0758i	0.126532	−	0.798067i
$514$	−18.3104			−0.807636
$515$		−	13.3627i		−	0.588832i
$516$	6.06776	−	3.09127i	0.267118	−	0.136086i
$517$		−	16.1887i		−	0.711980i
$518$	−1.52535	+	15.3720i	−0.0670199	+	0.675407i
$519$	36.9416	+	12.0052i	1.62156	+	0.526971i
$520$	1.11554	−	1.11554i	0.0489198	−	0.0489198i
$521$	−3.46852			−0.151959			−0.0759793	−	0.997109i	$-0.524208\pi$
$521$	−3.46852			−0.151959			−0.0759793	+	0.997109i	$0.524208\pi$
$522$	−12.9551	+	17.8271i	−0.567027	+	0.780271i
$523$	13.9403	+	13.9403i	0.609567	+	0.609567i	0.942833	−	0.333266i	$-0.108151\pi$
$523$	13.9403	+	13.9403i	0.609567	+	0.609567i	−0.333266	+	0.942833i	$0.608151\pi$
$524$	0.642612	−	0.642612i	0.0280726	−	0.0280726i
$525$	−1.35948	+	4.18328i	−0.0593324	+	0.182573i
$526$	5.23341	+	5.23341i	0.228187	+	0.228187i
$527$			16.4851i			0.718101i
$528$	2.55731	+	0.831073i	0.111293	+	0.0361678i
$529$			21.5336i			0.936244i
$530$		−	5.16143i		−	0.224198i
$531$	−35.0569	+	5.54863i	−1.52134	+	0.240790i
$532$	−6.32484	+	6.32484i	−0.274217	+	0.274217i
$533$	11.6899	+	11.6899i	0.506348	+	0.506348i
$534$	−8.00097	+	24.6200i	−0.346236	+	1.06541i
$535$	−1.36163	−	1.36163i	−0.0588686	−	0.0588686i
$536$	1.40696	+	1.40696i	0.0607713	+	0.0607713i
$537$	6.42187	+	12.6053i	0.277124	+	0.543958i
$538$	−15.8332	+	15.8332i	−0.682617	+	0.682617i
$539$	0.854900			0.0368231
$540$	0.813678	−	5.13205i	0.0350151	−	0.220848i
$541$	−5.11347	−	5.11347i	−0.219845	−	0.219845i	0.588588	−	0.808433i	$-0.299684\pi$
$541$	−5.11347	−	5.11347i	−0.219845	−	0.219845i	−0.808433	+	0.588588i	$0.799684\pi$
$542$	−13.0726	−	13.0726i	−0.561518	−	0.561518i
$543$	21.6419	+	7.03314i	0.928741	+	0.301821i
$544$	−6.84760			−0.293588
$545$	2.50977			0.107507
$546$	2.14473	−	6.59961i	0.0917861	−	0.282437i
$547$	−17.1654	+	17.1654i	−0.733939	+	0.733939i	−0.971398	−	0.237459i	$-0.923686\pi$
$547$	−17.1654	+	17.1654i	−0.733939	+	0.733939i	0.237459	+	0.971398i	$0.423686\pi$
$548$	−22.7686			−0.972627
$549$	31.0663	−	4.91702i	1.32588	−	0.209853i
$550$	1.09777	−	1.09777i	0.0468089	−	0.0468089i
$551$			25.8728i			1.10222i
$552$	−0.648245	+	1.99473i	−0.0275911	+	0.0849014i
$553$	−16.5643	−	16.5643i	−0.704384	−	0.704384i
$554$	−10.9271			−0.464249
$555$	−9.64933	−	4.22971i	−0.409591	−	0.179541i
$556$	6.95397			0.294914
$557$	−21.7065	−	21.7065i	−0.919733	−	0.919733i	0.0772768	−	0.997010i	$-0.475377\pi$
$557$	−21.7065	−	21.7065i	−0.919733	−	0.919733i	−0.997010	+	0.0772768i	$0.975377\pi$
$558$	−5.84249	−	4.24577i	−0.247332	−	0.179738i
$559$			6.20264i			0.262344i
$560$	−1.79574	+	1.79574i	−0.0758837	+	0.0758837i
$561$	16.4065	−	8.35844i	0.692684	−	0.352893i
$562$	−5.58948			−0.235778
$563$	−17.3652	+	17.3652i	−0.731858	+	0.731858i	−0.970988	−	0.239130i	$-0.923138\pi$
$563$	−17.3652	+	17.3652i	−0.731858	+	0.731858i	0.239130	+	0.970988i	$0.423138\pi$
$564$	−17.1770	−	5.58216i	−0.723283	−	0.235052i
$565$	−16.1124			−0.677855
$566$	−5.90258			−0.248104
$567$	−7.05825	−	21.7388i	−0.296419	−	0.912945i
$568$	2.38734	+	2.38734i	0.100171	+	0.100171i
$569$	0.287563	+	0.287563i	0.0120553	+	0.0120553i	0.713109	−	0.701053i	$-0.247287\pi$
$569$	0.287563	+	0.287563i	0.0120553	+	0.0120553i	−0.701053	+	0.713109i	$0.747287\pi$
$570$	−2.76929	−	5.43576i	−0.115993	−	0.227679i
$571$	−27.3088			−1.14284			−0.571420	−	0.820658i	$-0.693607\pi$
$571$	−27.3088			−1.14284			−0.571420	+	0.820658i	$0.693607\pi$
$572$	−1.73185	+	1.73185i	−0.0724125	+	0.0724125i
$573$	14.2593	−	7.26450i	0.595690	−	0.303479i
$574$	−18.8178	−	18.8178i	−0.785438	−	0.785438i
$575$	0.856269	+	0.856269i	0.0357089	+	0.0357089i
$576$	1.76361	−	2.42686i	0.0734839	−	0.101119i
$577$	−20.2984	−	20.2984i	−0.845034	−	0.845034i	0.144475	−	0.989509i	$-0.453851\pi$
$577$	−20.2984	−	20.2984i	−0.845034	−	0.845034i	−0.989509	+	0.144475i	$0.953851\pi$
$578$	−21.1352	+	21.1352i	−0.879106	+	0.879106i
$579$	1.31291	+	2.57707i	0.0545626	+	0.107099i
$580$			7.34574i			0.305015i
$581$			21.9608i			0.911086i
$582$	−3.79538	+	11.6788i	−0.157323	+	0.484104i
$583$			8.01300i			0.331865i
$584$	−0.339546	−	0.339546i	−0.0140505	−	0.0140505i
$585$	3.82866	+	2.78231i	0.158296	+	0.115034i
$586$	−10.7674	+	10.7674i	−0.444796	+	0.444796i
$587$	−14.6086	−	14.6086i	−0.602960	−	0.602960i	0.338137	−	0.941097i	$-0.390203\pi$
$587$	−14.6086	−	14.6086i	−0.602960	−	0.602960i	−0.941097	+	0.338137i	$0.890203\pi$
$588$	0.294785	−	0.907089i	0.0121567	−	0.0374077i
$589$	−8.47930			−0.349383
$590$	−8.36584	+	8.36584i	−0.344416	+	0.344416i
$591$	−1.64432	+	5.05977i	−0.0676382	+	0.208131i
$592$	−3.85543	−	4.70486i	−0.158457	−	0.193368i
$593$		−	30.9176i		−	1.26963i	−0.772663	−	0.634817i	$-0.781076\pi$
$593$		−	30.9176i		−	1.26963i	0.772663	−	0.634817i	$-0.218924\pi$
$594$	−1.26322	+	7.96738i	−0.0518304	+	0.326906i
$595$			17.3898i			0.712914i
$596$	−15.3710			−0.629619
$597$	−4.22633	+	2.15314i	−0.172972	+	0.0881221i
$598$	−1.35086	−	1.35086i	−0.0552409	−	0.0552409i
$599$			13.3000i			0.543423i	0.962379	+	0.271712i	$0.0875897\pi$
$599$			13.3000i			0.543423i	−0.962379	+	0.271712i	$0.912410\pi$
$600$	−0.786252	−	1.54331i	−0.0320986	−	0.0630054i
$601$	−13.2105			−0.538866			−0.269433	−	0.963019i	$-0.586836\pi$
$601$	−13.2105			−0.538866			−0.269433	+	0.963019i	$0.586836\pi$
$602$		−	9.98464i		−	0.406944i
$603$	−3.50913	+	4.82883i	−0.142903	+	0.196645i
$604$	−8.84452			−0.359878
$605$	6.07392	−	6.07392i	0.246940	−	0.246940i
$606$	−2.45903	−	4.82675i	−0.0998912	−	0.196073i
$607$	−1.58980	+	1.58980i	−0.0645280	+	0.0645280i	−0.738634	−	0.674106i	$-0.764529\pi$
$607$	−1.58980	+	1.58980i	−0.0645280	+	0.0645280i	0.674106	+	0.738634i	$0.264529\pi$
$608$		−	3.52214i		−	0.142842i
$609$	14.6675	+	28.7903i	0.594355	+	1.16664i
$610$	7.41355	−	7.41355i	0.300166	−	0.300166i
$611$	11.6326	−	11.6326i	0.470603	−	0.470603i
$612$	−3.21144	−	20.2902i	−0.129815	−	0.820184i
$613$			35.8533i			1.44810i	0.689747	+	0.724051i	$0.257722\pi$
$613$			35.8533i			1.44810i	−0.689747	+	0.724051i	$0.742278\pi$
$614$	15.9405	−	15.9405i	0.643306	−	0.643306i
$615$	16.1726	−	8.23925i	0.652141	−	0.332239i
$616$	2.78784	−	2.78784i	0.112325	−	0.112325i
$617$	−22.8071			−0.918178			−0.459089	−	0.888390i	$-0.651824\pi$
$617$	−22.8071			−0.918178			−0.459089	+	0.888390i	$0.651824\pi$
$618$	22.0118	+	7.15335i	0.885443	+	0.287750i
$619$			33.8714i			1.36141i	0.732559	+	0.680704i	$0.238326\pi$
$619$			33.8714i			1.36141i	−0.732559	+	0.680704i	$0.761674\pi$
$620$	−2.40742			−0.0966845
$621$	−6.21464	−	0.985321i	−0.249385	−	0.0395396i
$622$			8.65204i			0.346915i
$623$	26.8393	+	26.8393i	1.07529	+	1.07529i
$624$	1.24041	+	2.43475i	0.0496559	+	0.0974681i
$625$	−1.00000			−0.0400000
$626$		−	4.61985i		−	0.184646i
$627$	4.29926	+	8.43889i	0.171696	+	0.337017i
$628$			4.17933i			0.166774i
$629$	−41.4488	−	4.11292i	−1.65267	−	0.163993i
$630$	−6.16315	−	4.47879i	−0.245546	−	0.178439i
$631$	−3.90804	+	3.90804i	−0.155576	+	0.155576i	−0.780603	−	0.625027i	$-0.785088\pi$
$631$	−3.90804	+	3.90804i	−0.155576	+	0.155576i	0.625027	+	0.780603i	$0.285088\pi$
$632$	9.22422			0.366920
$633$	−39.5887	−	12.8655i	−1.57351	−	0.511357i
$634$	21.2262	+	21.2262i	0.843001	+	0.843001i
$635$	−10.1237	+	10.1237i	−0.401745	+	0.401745i
$636$	8.50217	+	2.76302i	0.337133	+	0.109561i
$637$	0.614295	+	0.614295i	0.0243393	+	0.0243393i
$638$		−	11.4041i		−	0.451492i
$639$	−5.95433	+	8.19360i	−0.235550	+	0.324134i
$640$		−	1.00000i		−	0.0395285i
$641$			29.9478i			1.18287i	0.806353	+	0.591434i	$0.201438\pi$
$641$			29.9478i			1.18287i	−0.806353	+	0.591434i	$0.798562\pi$
$642$	2.97186	−	1.51404i	0.117290	−	0.0597544i
$643$	−16.6932	+	16.6932i	−0.658317	+	0.658317i	−0.954982	−	0.296664i	$-0.904126\pi$
$643$	−16.6932	+	16.6932i	−0.658317	+	0.658317i	0.296664	+	0.954982i	$0.404126\pi$
$644$	2.17454	+	2.17454i	0.0856889	+	0.0856889i
$645$	6.47641	+	2.10470i	0.255008	+	0.0828723i
$646$	−17.0542	−	17.0542i	−0.670987	−	0.670987i
$647$	−1.28867	−	1.28867i	−0.0506627	−	0.0506627i	0.681322	−	0.731984i	$-0.261406\pi$
$647$	−1.28867	−	1.28867i	−0.0506627	−	0.0506627i	−0.731984	+	0.681322i	$0.761406\pi$
$648$	8.01819	+	4.08763i	0.314984	+	0.160577i
$649$	12.9878	−	12.9878i	0.509814	−	0.509814i
$650$	1.57762			0.0618792
$651$	−9.43547	+	4.80698i	−0.369805	+	0.188400i
$652$	1.54752	+	1.54752i	0.0606056	+	0.0606056i
$653$	−8.09056	−	8.09056i	−0.316608	−	0.316608i	0.530855	−	0.847463i	$-0.321871\pi$
$653$	−8.09056	−	8.09056i	−0.316608	−	0.316608i	−0.847463	+	0.530855i	$0.821871\pi$
$654$	−1.34353	+	4.13422i	−0.0525363	+	0.161661i
$655$	0.908791			0.0355094
$656$	10.4791			0.409142
$657$	0.846870	−	1.16536i	0.0330396	−	0.0454649i
$658$	−18.7254	+	18.7254i	−0.729991	+	0.729991i
$659$	−12.6087			−0.491164			−0.245582	−	0.969376i	$-0.578979\pi$
$659$	−12.6087			−0.491164			−0.245582	+	0.969376i	$0.578979\pi$
$660$	1.22064	+	2.39595i	0.0475133	+	0.0932623i
$661$	−2.03012	+	2.03012i	−0.0789624	+	0.0789624i	−0.745485	−	0.666523i	$-0.767782\pi$
$661$	−2.03012	+	2.03012i	−0.0789624	+	0.0789624i	0.666523	+	0.745485i	$0.267782\pi$
$662$		−	13.0363i		−	0.506670i
$663$	17.7951	+	5.78301i	0.691103	+	0.224594i
$664$	−6.11470	−	6.11470i	−0.237296	−	0.237296i
$665$	−8.94467			−0.346860
$666$	12.1329	−	13.6306i	0.470140	−	0.528175i
$667$	8.89530			0.344427
$668$	−13.7766	−	13.7766i	−0.533033	−	0.533033i
$669$	−32.3936	−	10.5272i	−1.25241	−	0.407007i
$670$			1.98974i			0.0768704i
$671$	−11.5094	+	11.5094i	−0.444314	+	0.444314i
$672$	−1.99673	−	3.91932i	−0.0770255	−	0.151191i
$673$	−40.7016			−1.56893			−0.784466	−	0.620172i	$-0.787063\pi$
$673$	−40.7016			−1.56893			−0.784466	+	0.620172i	$0.787063\pi$
$674$	16.0773	−	16.0773i	0.619275	−	0.619275i
$675$	4.20426	−	3.05355i	0.161822	−	0.117531i
$676$	10.5111			0.404274
$677$	33.5797			1.29057			0.645286	−	0.763941i	$-0.276738\pi$
$677$	33.5797			1.29057			0.645286	+	0.763941i	$0.276738\pi$
$678$	8.62533	−	26.5412i	0.331254	−	1.01931i
$679$	12.7316	+	12.7316i	0.488594	+	0.488594i
$680$	−4.84198	−	4.84198i	−0.185682	−	0.185682i
$681$	−5.58972	+	2.84773i	−0.214198	+	0.109125i
$682$	3.73747			0.143115
$683$	18.5669	−	18.5669i	0.710442	−	0.710442i	−0.256186	−	0.966628i	$-0.582466\pi$
$683$	18.5669	−	18.5669i	0.710442	−	0.710442i	0.966628	+	0.256186i	$0.0824658\pi$
$684$	10.4365	−	1.65184i	0.399050	−	0.0631597i
$685$	−16.0998	−	16.0998i	−0.615143	−	0.615143i
$686$	−13.5590	−	13.5590i	−0.517685	−	0.517685i
$687$	21.4729	+	6.97824i	0.819243	+	0.266236i
$688$	2.78010	+	2.78010i	0.105990	+	0.105990i
$689$	−5.75781	+	5.75781i	−0.219355	+	0.219355i
$690$	−1.86887	+	0.952110i	−0.0711465	+	0.0362462i
$691$		−	14.7237i		−	0.560118i	−0.959983	−	0.280059i	$-0.909646\pi$
$691$		−	14.7237i		−	0.560118i	0.959983	−	0.280059i	$-0.0903540\pi$
$692$			22.4262i			0.852517i
$693$	9.56814	+	6.95322i	0.363463	+	0.264131i
$694$			18.2057i			0.691078i
$695$	4.91720	+	4.91720i	0.186520	+	0.186520i
$696$	−12.1003	−	3.93233i	−0.458659	−	0.149054i
$697$	50.7398	−	50.7398i	1.92191	−	1.92191i
$698$	12.1575	+	12.1575i	0.460168	+	0.460168i
$699$	33.7547	+	10.9696i	1.27672	+	0.414907i
$700$	−2.53955			−0.0959861
$701$	1.36351	−	1.36351i	0.0514990	−	0.0514990i	−0.680888	−	0.732387i	$-0.738406\pi$
$701$	1.36351	−	1.36351i	0.0514990	−	0.0514990i	0.732387	+	0.680888i	$0.238406\pi$
$702$	−6.63272	+	4.81733i	−0.250336	+	0.181818i
$703$	2.11553	−	21.3197i	0.0797886	−	0.804086i
$704$			1.55248i			0.0585111i
$705$	−8.19880	−	16.0932i	−0.308785	−	0.606104i
$706$			19.2979i			0.726286i
$707$	−7.94253			−0.298710
$708$	−9.30222	−	18.2590i	−0.349599	−	0.686217i
$709$	5.92223	+	5.92223i	0.222414	+	0.222414i	0.809514	−	0.587100i	$-0.199731\pi$
$709$	5.92223	+	5.92223i	0.222414	+	0.222414i	−0.587100	+	0.809514i	$0.699731\pi$
$710$			3.37621i			0.126707i
$711$	4.32604	+	27.3324i	0.162239	+	1.02505i
$712$	−14.9461			−0.560130
$713$			2.91526i			0.109177i
$714$	−28.6454	−	9.30915i	−1.07203	−	0.348386i
$715$	−2.44921			−0.0915953
$716$	−5.77543	+	5.77543i	−0.215838	+	0.215838i
$717$	35.0475	−	17.8553i	1.30887	−	0.666817i
$718$	23.0762	−	23.0762i	0.861197	−	0.861197i
$719$			30.0602i			1.12106i	0.828135	+	0.560529i	$0.189402\pi$
$719$			30.0602i			1.12106i	−0.828135	+	0.560529i	$0.810598\pi$
$720$	2.96312	−	0.468987i	0.110429	−	0.0174781i
$721$	23.9959	−	23.9959i	0.893655	−	0.893655i
$722$	−4.66301	+	4.66301i	−0.173539	+	0.173539i
$723$	−8.90871	−	17.4866i	−0.331318	−	0.650335i
$724$			13.1382i			0.488276i
$725$	−5.19422	+	5.19422i	−0.192909	+	0.192909i
$726$	6.75377	+	13.2568i	0.250656	+	0.492004i
$727$	−0.0366111	+	0.0366111i	−0.00135783	+	0.00135783i	−0.707785	−	0.706428i	$-0.750306\pi$
$727$	−0.0366111	+	0.0366111i	−0.00135783	+	0.00135783i	0.706428	+	0.707785i	$0.250306\pi$
$728$	4.00644			0.148489
$729$	−8.35167	+	25.6759i	−0.309321	+	0.950958i
$730$		−	0.480190i		−	0.0177726i
$731$	26.9224			0.995760
$732$	8.24334	+	16.1806i	0.304683	+	0.598052i
$733$		−	23.8385i		−	0.880494i	−0.897877	−	0.440247i	$-0.854891\pi$
$733$		−	23.8385i		−	0.880494i	0.897877	−	0.440247i	$-0.145109\pi$
$734$	8.53674	+	8.53674i	0.315097	+	0.315097i
$735$	0.849853	−	0.432965i	0.0313473	−	0.0159701i
$736$	−1.21095			−0.0446361
$737$		−	3.08902i		−	0.113786i
$738$	4.91459	+	31.0509i	0.180908	+	1.14300i
$739$			38.4233i			1.41343i	0.707501	+	0.706713i	$0.249823\pi$
$739$			38.4233i			1.41343i	−0.707501	+	0.706713i	$0.750177\pi$
$740$	0.600636	−	6.05304i	0.0220798	−	0.222514i
$741$	−2.97456	+	9.15310i	−0.109273	+	0.336248i
$742$	9.26857	−	9.26857i	0.340260	−	0.340260i
$743$	22.9840			0.843202			0.421601	−	0.906782i	$-0.361468\pi$
$743$	22.9840			0.843202			0.421601	+	0.906782i	$0.361468\pi$
$744$	1.28874	−	3.96563i	0.0472477	−	0.145387i
$745$	−10.8689	−	10.8689i	−0.398206	−	0.398206i
$746$	18.8328	−	18.8328i	0.689518	−	0.689518i
$747$	15.2508	−	20.9863i	0.557999	−	0.767848i
$748$	7.51706	+	7.51706i	0.274851	+	0.274851i
$749$		−	4.89027i		−	0.178687i
$750$	0.535321	−	1.64725i	0.0195472	−	0.0601491i
$751$		−	12.4662i		−	0.454898i	−0.973790	−	0.227449i	$-0.926962\pi$
$751$		−	12.4662i		−	0.454898i	0.973790	−	0.227449i	$-0.0730385\pi$
$752$		−	10.4277i		−	0.380259i
$753$	−6.00264	−	11.7824i	−0.218748	−	0.429374i
$754$	8.19449	−	8.19449i	0.298426	−	0.298426i
$755$	−6.25402	−	6.25402i	−0.227607	−	0.227607i
$756$	10.6770	−	7.75465i	0.388317	−	0.282034i
$757$	16.0789	+	16.0789i	0.584398	+	0.584398i	0.936109	−	0.351710i	$-0.114400\pi$
$757$	16.0789	+	16.0789i	0.584398	+	0.584398i	−0.351710	+	0.936109i	$0.614400\pi$
$758$	−14.6734	−	14.6734i	−0.532963	−	0.532963i
$759$	2.90137	−	1.47813i	0.105313	−	0.0536526i
$760$	2.49053	−	2.49053i	0.0903411	−	0.0903411i
$761$	29.9383			1.08526			0.542632	−	0.839971i	$-0.317428\pi$
$761$	29.9383			1.08526			0.542632	+	0.839971i	$0.317428\pi$
$762$	−11.2568	−	22.0956i	−0.407790	−	0.800439i
$763$	4.50688	+	4.50688i	0.163160	+	0.163160i
$764$	6.53325	+	6.53325i	0.236365	+	0.236365i
$765$	12.0765	−	16.6182i	0.436628	−	0.600832i
$766$	22.4423			0.810874
$767$	18.6649			0.673952
$768$	1.64725	+	0.535321i	0.0594400	+	0.0193167i
$769$	−27.9340	+	27.9340i	−1.00733	+	1.00733i	−0.00735452	+	0.999973i	$0.502341\pi$
$769$	−27.9340	+	27.9340i	−1.00733	+	1.00733i	−0.999973	+	0.00735452i	$0.997659\pi$
$770$	3.94259			0.142081
$771$	28.2586	−	14.3966i	1.01771	−	0.518480i
$772$	−1.18075	+	1.18075i	−0.0424961	+	0.0424961i
$773$			1.29800i			0.0466858i	0.999728	+	0.0233429i	$0.00743094\pi$
$773$			1.29800i			0.0466858i	−0.999728	+	0.0233429i	$0.992569\pi$
$774$	−6.93392	+	9.54158i	−0.249235	+	0.342965i
$775$	−1.70231	−	1.70231i	−0.0611486	−	0.0611486i
$776$	−7.08991			−0.254513
$777$	−9.73219	−	24.9231i	−0.349140	−	0.894111i
$778$	−12.3267			−0.441934
$779$	26.0986	+	26.0986i	0.935081	+	0.935081i
$780$	−0.844532	+	2.59873i	−0.0302391	+	0.0930494i
$781$		−	5.24148i		−	0.187555i
$782$	−5.86338	+	5.86338i	−0.209674	+	0.209674i
$783$	5.97707	−	37.6987i	0.213603	−	1.34724i
$784$	0.550669			0.0196667
$785$	−2.95524	+	2.95524i	−0.105477	+	0.105477i
$786$	−0.486495	+	1.49701i	−0.0173527	+	0.0533964i
$787$	−3.84246			−0.136969			−0.0684844	−	0.997652i	$-0.521816\pi$
$787$	−3.84246			−0.136969			−0.0684844	+	0.997652i	$0.521816\pi$
$788$	−3.07165			−0.109423
$789$	−12.1915	−	3.96199i	−0.434031	−	0.141051i
$790$	6.52251	+	6.52251i	0.232061	+	0.232061i
$791$	−28.9337	−	28.9337i	−1.02876	−	1.02876i
$792$	−4.60016	+	0.728091i	−0.163460	+	0.0258716i
$793$	−16.5403			−0.587363
$794$	−0.0671608	+	0.0671608i	−0.00238345	+	0.00238345i
$795$	4.05819	+	7.96570i	0.143929	+	0.282514i
$796$	−1.93640	−	1.93640i	−0.0686339	−	0.0686339i
$797$	4.77954	+	4.77954i	0.169300	+	0.169300i	0.786672	−	0.617372i	$-0.211802\pi$
$797$	4.77954	+	4.77954i	0.169300	+	0.169300i	−0.617372	+	0.786672i	$0.711802\pi$
$798$	4.78827	−	14.7341i	0.169503	−	0.521582i
$799$	−50.4907	−	50.4907i	−1.78623	−	1.78623i
$800$	0.707107	−	0.707107i	0.0250000	−	0.0250000i
$801$	−7.00954	−	44.2871i	−0.247670	−	1.56481i
$802$			5.50588i			0.194420i
$803$			0.745484i			0.0263075i
$804$	−3.27760	−	1.06515i	−0.115592	−	0.0375649i
$805$			3.07526i			0.108389i
$806$	2.68559	+	2.68559i	0.0945958	+	0.0945958i
$807$	11.9866	−	36.8844i	0.421950	−	1.29839i
$808$	2.21150	−	2.21150i	0.0778002	−	0.0778002i
$809$	−22.1315	−	22.1315i	−0.778101	−	0.778101i	0.201406	−	0.979508i	$-0.435449\pi$
$809$	−22.1315	−	22.1315i	−0.778101	−	0.778101i	−0.979508	+	0.201406i	$0.935449\pi$
$810$	2.77933	+	8.56010i	0.0976556	+	0.300771i
$811$	−53.7835			−1.88859			−0.944297	−	0.329094i	$-0.893257\pi$
$811$	−53.7835			−1.88859			−0.944297	+	0.329094i	$0.893257\pi$
$812$	−13.1910	+	13.1910i	−0.462913	+	0.462913i
$813$	30.4535	+	9.89675i	1.06805	+	0.347094i
$814$	−0.932473	+	9.39719i	−0.0326832	+	0.329371i
$815$			2.18852i			0.0766607i
$816$	10.5680	−	5.38394i	0.369953	−	0.188476i
$817$			13.8478i			0.484475i
$818$	−32.2541			−1.12774
$819$	1.87897	+	11.8716i	0.0656566	+	0.414826i
$820$	7.40987	+	7.40987i	0.258764	+	0.258764i
$821$			8.80205i			0.307194i	0.988134	+	0.153597i	$0.0490857\pi$
$821$			8.80205i			0.307194i	−0.988134	+	0.153597i	$0.950914\pi$
$822$	35.1390	−	17.9019i	1.22561	−	0.624399i
$823$	32.0302			1.11650			0.558251	−	0.829672i	$-0.311473\pi$
$823$	32.0302			1.11650			0.558251	+	0.829672i	$0.311473\pi$
$824$			13.3627i			0.465513i
$825$	−0.831073	+	2.55731i	−0.0289342	+	0.0890343i
$826$	−30.0457			−1.04542
$827$	−35.6688	+	35.6688i	−1.24033	+	1.24033i	−0.280461	+	0.959865i	$0.590487\pi$
$827$	−35.6688	+	35.6688i	−1.24033	+	1.24033i	−0.959865	+	0.280461i	$0.909513\pi$
$828$	−0.567919	−	3.58817i	−0.0197365	−	0.124698i
$829$	13.6682	−	13.6682i	0.474716	−	0.474716i	−0.428721	−	0.903437i	$-0.641036\pi$
$829$	13.6682	−	13.6682i	0.474716	−	0.474716i	0.903437	+	0.428721i	$0.141036\pi$
$830$		−	8.64749i		−	0.300159i
$831$	16.8639	−	8.59148i	0.585004	−	0.298035i
$832$	−1.11554	+	1.11554i	−0.0386745	+	0.0386745i
$833$	2.66633	−	2.66633i	0.0923828	−	0.0923828i
$834$	−10.7321	+	5.46757i	−0.371623	+	0.189327i
$835$		−	19.4831i		−	0.674240i
$836$	−3.86649	+	3.86649i	−0.133725	+	0.133725i
$837$	12.3550	+	1.95887i	0.427052	+	0.0677084i
$838$	13.7606	−	13.7606i	0.475350	−	0.475350i
$839$	19.8742			0.686135			0.343067	−	0.939311i	$-0.388534\pi$
$839$	19.8742			0.686135			0.343067	+	0.939311i	$0.388534\pi$
$840$	1.35948	−	4.18328i	0.0469064	−	0.144337i
$841$			24.9599i			0.860685i
$842$	19.9688			0.688171
$843$	8.62631	−	4.39474i	0.297106	−	0.151363i
$844$		−	24.0332i		−	0.827257i
$845$	7.43249	+	7.43249i	0.255685	+	0.255685i
$846$	30.8985	−	4.89046i	1.06231	−	0.168137i
$847$	21.8143			0.749548
$848$			5.16143i			0.177244i
$849$	9.10951	−	4.64092i	0.312638	−	0.159276i
$850$		−	6.84760i		−	0.234871i
$851$	−7.32990	−	0.727338i	−0.251266	−	0.0249328i
$852$	−5.56146	−	1.80736i	−0.190532	−	0.0619190i
$853$	28.1221	−	28.1221i	0.962882	−	0.962882i	−0.0364533	−	0.999335i	$-0.511606\pi$
$853$	28.1221	−	28.1221i	0.962882	−	0.962882i	0.999335	+	0.0364533i	$0.0116060\pi$
$854$	26.6255			0.911107
$855$	8.54776	+	6.21171i	0.292327	+	0.212436i
$856$	1.36163	+	1.36163i	0.0465397	+	0.0465397i
$857$	−14.2681	+	14.2681i	−0.487389	+	0.487389i	−0.907481	−	0.420092i	$-0.861998\pi$
$857$	−14.2681	+	14.2681i	−0.487389	+	0.487389i	0.420092	+	0.907481i	$0.361998\pi$
$858$	1.31111	−	4.03446i	0.0447607	−	0.137734i
$859$	11.9927	+	11.9927i	0.409185	+	0.409185i	0.881454	−	0.472269i	$-0.156565\pi$
$859$	11.9927	+	11.9927i	0.409185	+	0.409185i	−0.472269	+	0.881454i	$0.656565\pi$
$860$			3.93165i			0.134068i
$861$	43.8372	+	14.2461i	1.49397	+	0.485507i
$862$			32.9451i			1.12211i
$863$		−	18.0730i		−	0.615211i	−0.951514	−	0.307605i	$-0.900472\pi$
$863$		−	18.0730i		−	0.615211i	0.951514	−	0.307605i	$-0.0995277\pi$
$864$	−0.813678	+	5.13205i	−0.0276819	+	0.174596i
$865$	−15.8577	+	15.8577i	−0.539179	+	0.539179i
$866$	4.61021	+	4.61021i	0.156661	+	0.156661i
$867$	16.0005	−	49.2357i	0.543407	−	1.67213i
$868$	−4.32310	−	4.32310i	−0.146735	−	0.146735i
$869$	−10.1260	−	10.1260i	−0.343502	−	0.343502i
$870$	−5.77560	−	11.3368i	−0.195811	−	0.384352i
$871$	2.21964	−	2.21964i	0.0752097	−	0.0752097i
$872$	−2.50977			−0.0849916
$873$	−3.32508	−	21.0082i	−0.112537	−	0.711020i
$874$	−3.01590	−	3.01590i	−0.102014	−	0.102014i
$875$	−1.79574	−	1.79574i	−0.0607069	−	0.0607069i
$876$	0.790993	+	0.257056i	0.0267252	+	0.00868511i
$877$	−54.1088			−1.82712			−0.913562	−	0.406698i	$-0.866680\pi$
$877$	−54.1088			−1.82712			−0.913562	+	0.406698i	$0.866680\pi$
$878$	11.2830			0.380783
$879$	8.15153	−	25.0833i	0.274944	−	0.846038i
$880$	−1.09777	+	1.09777i	−0.0370057	+	0.0370057i
$881$	−26.8290			−0.903891			−0.451946	−	0.892045i	$-0.649270\pi$
$881$	−26.8290			−0.903891			−0.451946	+	0.892045i	$0.649270\pi$
$882$	0.258257	+	1.63170i	0.00869596	+	0.0549420i
$883$	32.1258	−	32.1258i	1.08112	−	1.08112i	0.0847128	−	0.996405i	$-0.473003\pi$
$883$	32.1258	−	32.1258i	1.08112	−	1.08112i	0.996405	−	0.0847128i	$-0.0269973\pi$
$884$			10.8029i			0.363341i
$885$	6.33343	−	19.4888i	0.212896	−	0.655107i
$886$	−0.120564	−	0.120564i	−0.00405043	−	0.00405043i
$887$	−56.0728			−1.88274			−0.941370	−	0.337377i	$-0.890460\pi$
$887$	−56.0728			−1.88274			−0.941370	+	0.337377i	$0.890460\pi$
$888$	9.64933	+	4.22971i	0.323810	+	0.141940i
$889$	−36.3588			−1.21944
$890$	−10.5685	−	10.5685i	−0.354257	−	0.354257i
$891$	−4.31484	−	13.2893i	−0.144552	−	0.445210i
$892$		−	19.6653i		−	0.658442i
$893$	25.9705	−	25.9705i	0.869070	−	0.869070i
$894$	23.7222	−	12.0854i	0.793387	−	0.404198i
$895$	−8.16769			−0.273016
$896$	1.79574	−	1.79574i	0.0599913	−	0.0599913i
$897$	3.14692	+	1.02268i	0.105073	+	0.0341464i
$898$	−36.6657			−1.22355
$899$	−17.6843			−0.589805
$900$	2.42686	+	1.76361i	0.0808954	+	0.0587872i
$901$	24.9916	+	24.9916i	0.832590	+	0.832590i
$902$	−11.5036	−	11.5036i	−0.383030	−	0.383030i
$903$	7.85045	+	15.4094i	0.261247	+	0.512793i
$904$	16.1124			0.535892
$905$	−9.29009	+	9.29009i	−0.308813	+	0.308813i
$906$	13.6498	−	6.95402i	0.453485	−	0.231032i
$907$	29.0323	+	29.0323i	0.964003	+	0.964003i	0.999374	−	0.0353712i	$-0.0112613\pi$
$907$	29.0323	+	29.0323i	0.964003	+	0.964003i	−0.0353712	+	0.999374i	$0.511261\pi$
$908$	−2.56107	−	2.56107i	−0.0849921	−	0.0849921i
$909$	7.59009	+	5.51576i	0.251747	+	0.182946i
$910$	2.83298	+	2.83298i	0.0939125	+	0.0939125i
$911$	−23.5290	+	23.5290i	−0.779551	+	0.779551i	−0.979754	−	0.200203i	$-0.935840\pi$
$911$	−23.5290	+	23.5290i	−0.779551	+	0.779551i	0.200203	+	0.979754i	$0.435840\pi$
$912$	2.76929	+	5.43576i	0.0917005	+	0.179996i
$913$			13.4250i			0.444303i
$914$			2.59170i			0.0857259i
$915$	−5.61249	+	17.2703i	−0.185543	+	0.570939i
$916$			13.0356i			0.430709i
$917$	1.63195	+	1.63195i	0.0538917	+	0.0538917i
$918$	20.9095	+	28.7891i	0.690116	+	0.950182i
$919$	−13.4771	+	13.4771i	−0.444568	+	0.444568i	−0.893544	−	0.448976i	$-0.851789\pi$
$919$	−13.4771	+	13.4771i	−0.444568	+	0.444568i	0.448976	+	0.893544i	$0.351789\pi$
$920$	−0.856269	−	0.856269i	−0.0282303	−	0.0282303i
$921$	−12.0679	+	37.1344i	−0.397650	+	1.22362i
$922$	16.1738			0.532656
$923$	3.76631	−	3.76631i	0.123970	−	0.123970i
$924$	−2.11055	+	6.49444i	−0.0694321	+	0.213651i
$925$	4.70486	−	3.85543i	0.154695	−	0.126766i
$926$			20.7344i			0.681376i
$927$	−39.5953	+	6.26695i	−1.30048	+	0.205834i
$928$		−	7.34574i		−	0.241136i
$929$	48.7123			1.59820			0.799099	−	0.601200i	$-0.205310\pi$
$929$	48.7123			1.59820			0.799099	+	0.601200i	$0.205310\pi$
$930$	3.71540	−	1.89284i	0.121833	−	0.0620688i
$931$	1.37146	+	1.37146i	0.0449477	+	0.0449477i
$932$			20.4916i			0.671223i
$933$	−6.80269	−	13.3528i	−0.222710	−	0.437151i
$934$	11.2004			0.366490
$935$			10.6307i			0.347662i
$936$	−3.82866	−	2.78231i	−0.125144	−	0.0909426i
$937$	24.3402			0.795161			0.397581	−	0.917567i	$-0.369850\pi$
$937$	24.3402			0.795161			0.397581	+	0.917567i	$0.369850\pi$
$938$	−3.57305	+	3.57305i	−0.116664	+	0.116664i
$939$	3.63237	+	7.12986i	0.118538	+	0.232674i
$940$	7.37349	−	7.37349i	0.240497	−	0.240497i
$941$		−	41.7533i		−	1.36112i	−0.732694	−	0.680559i	$-0.761737\pi$
$941$		−	41.7533i		−	1.36112i	0.732694	−	0.680559i	$-0.238263\pi$
$942$	−3.28601	−	6.45001i	−0.107064	−	0.210153i
$943$	8.97296	−	8.97296i	0.292200	−	0.292200i
$944$	8.36584	−	8.36584i	0.272285	−	0.272285i
$945$	13.0331	+	2.06638i	0.423967	+	0.0672193i
$946$		−	6.10379i		−	0.198451i
$947$	34.4729	−	34.4729i	1.12022	−	1.12022i	0.128510	−	0.991708i	$-0.458981\pi$
$947$	34.4729	−	34.4729i	1.12022	−	1.12022i	0.991708	−	0.128510i	$-0.0410195\pi$
$948$	−14.2358	+	7.25257i	−0.462359	+	0.235552i
$949$	−0.535673	+	0.535673i	−0.0173887	+	0.0173887i
$950$	3.52214			0.114273
$951$	−49.4478	−	16.0695i	−1.60346	−	0.521089i
$952$		−	17.3898i		−	0.563608i
$953$	41.6524			1.34925			0.674627	−	0.738159i	$-0.264305\pi$
$953$	41.6524			1.34925			0.674627	+	0.738159i	$0.264305\pi$
$954$	−15.2939	+	2.42065i	−0.495159	+	0.0783714i
$955$			9.23941i			0.298980i
$956$	16.0579	+	16.0579i	0.519350	+	0.519350i
$957$	8.96648	+	17.6000i	0.289845	+	0.568928i
$958$	−26.3662			−0.851853
$959$		−	57.8221i		−	1.86717i
$960$	0.786252	+	1.54331i	0.0253762	+	0.0498101i
$961$			25.2043i			0.813042i
$962$	−7.42246	+	6.08239i	−0.239310	+	0.196104i
$963$	−3.39609	+	4.67327i	−0.109437	+	0.150594i
$964$	8.01194	−	8.01194i	0.258047	−	0.258047i
$965$	−1.66983			−0.0537537
$966$	−5.06573	−	1.64625i	−0.162987	−	0.0529673i
$967$	−17.9450	−	17.9450i	−0.577071	−	0.577071i	0.357024	−	0.934095i	$-0.383792\pi$
$967$	−17.9450	−	17.9450i	−0.577071	−	0.577071i	−0.934095	+	0.357024i	$0.883792\pi$
$968$	−6.07392	+	6.07392i	−0.195223	+	0.195223i
$969$	39.7288	+	12.9110i	1.27627	+	0.414761i
$970$	−5.01332	−	5.01332i	−0.160968	−	0.160968i
$971$			14.9163i			0.478687i	0.970935	+	0.239343i	$0.0769321\pi$
$971$			14.9163i			0.478687i	−0.970935	+	0.239343i	$0.923068\pi$
$972$	−15.5885	−	0.00415661i	−0.500000	−	0.000133323i
$973$			17.6600i			0.566153i
$974$		−	12.5977i		−	0.403657i
$975$	−2.43475	+	1.24041i	−0.0779745	+	0.0397248i
$976$	−7.41355	+	7.41355i	−0.237302	+	0.237302i
$977$	7.77719	+	7.77719i	0.248814	+	0.248814i	0.820484	−	0.571670i	$-0.193704\pi$
$977$	7.77719	+	7.77719i	0.248814	+	0.248814i	−0.571670	+	0.820484i	$0.693704\pi$
$978$	−3.60505	−	1.17156i	−0.115277	−	0.0374625i
$979$	16.4073	+	16.4073i	0.524381	+	0.524381i
$980$	0.389382	+	0.389382i	0.0124383	+	0.0124383i
$981$	−1.17705	−	7.43674i	−0.0375803	−	0.237437i
$982$	0.306040	−	0.306040i	0.00976612	−	0.00976612i
$983$	−4.10130			−0.130811			−0.0654056	−	0.997859i	$-0.520834\pi$
$983$	−4.10130			−0.130811			−0.0654056	+	0.997859i	$0.520834\pi$
$984$	−16.1726	+	8.23925i	−0.515563	+	0.262658i
$985$	−2.17198	−	2.17198i	−0.0692052	−	0.0692052i
$986$	−35.5679	−	35.5679i	−1.13271	−	1.13271i
$987$	14.1762	−	43.6220i	0.451234	−	1.38850i
$988$	−5.55660			−0.176779
$989$	4.76102			0.151392
$990$	−3.76765	−	2.73797i	−0.119744	−	0.0870184i
$991$	41.0764	−	41.0764i	1.30484	−	1.30484i	0.379744	−	0.925091i	$-0.376012\pi$
$991$	41.0764	−	41.0764i	1.30484	−	1.30484i	0.925091	−	0.379744i	$-0.123988\pi$
$992$	2.40742			0.0764358
$993$	10.2498	+	20.1191i	0.325268	+	0.638459i
$994$	−6.06278	+	6.06278i	−0.192300	+	0.192300i
$995$		−	2.73848i		−	0.0868158i
$996$	14.2446	+	4.62918i	0.451357	+	0.146681i
$997$	4.48937	+	4.48937i	0.142180	+	0.142180i	0.774614	−	0.632434i	$-0.217944\pi$
$997$	4.48937	+	4.48937i	0.142180	+	0.142180i	−0.632434	+	0.774614i	$0.717944\pi$
$998$	28.0543			0.888044
$999$	−8.00772	+	30.5757i	−0.253353	+	0.967374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.e.191.3	✓	40
3.2	odd	2	inner	1110.2.u.e.191.16	yes	40
37.31	odd	4	inner	1110.2.u.e.401.16	yes	40
111.68	even	4	inner	1110.2.u.e.401.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.e.191.3	✓	40	1.1	even	1	trivial
1110.2.u.e.191.16	yes	40	3.2	odd	2	inner
1110.2.u.e.401.3	yes	40	111.68	even	4	inner
1110.2.u.e.401.16	yes	40	37.31	odd	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.64725 + 0.535321i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.786252 - 1.54331i) q^{6} -2.53955 q^{7} +(0.707107 - 0.707107i) q^{8} +(2.42686 + 1.76361i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.64725 + 0.535321i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.786252 - 1.54331i) q^{6} -2.53955 q^{7} +(0.707107 - 0.707107i) q^{8} +(2.42686 + 1.76361i) q^{9} +1.00000 q^{10} -1.55248 q^{11} +(-0.535321 + 1.64725i) q^{12} +(-1.11554 - 1.11554i) q^{13} +(1.79574 + 1.79574i) q^{14} +(-1.54331 + 0.786252i) q^{15} -1.00000 q^{16} +(-4.84198 + 4.84198i) q^{17} +(-0.468987 - 2.96312i) q^{18} +(-2.49053 - 2.49053i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(-4.18328 - 1.35948i) q^{21} +(1.09777 + 1.09777i) q^{22} +(-0.856269 + 0.856269i) q^{23} +(1.54331 - 0.786252i) q^{24} -1.00000i q^{25} +1.57762i q^{26} +(3.05355 + 4.20426i) q^{27} -2.53955i q^{28} +(-5.19422 - 5.19422i) q^{29} +(1.64725 + 0.535321i) q^{30} +(1.70231 - 1.70231i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.55731 - 0.831073i) q^{33} +6.84760 q^{34} +(1.79574 - 1.79574i) q^{35} +(-1.76361 + 2.42686i) q^{36} +(3.85543 + 4.70486i) q^{37} +3.52214i q^{38} +(-1.24041 - 2.43475i) q^{39} +1.00000i q^{40} -10.4791 q^{41} +(1.99673 + 3.91932i) q^{42} +(-2.78010 - 2.78010i) q^{43} -1.55248i q^{44} +(-2.96312 + 0.468987i) q^{45} +1.21095 q^{46} +10.4277i q^{47} +(-1.64725 - 0.535321i) q^{48} -0.550669 q^{49} +(-0.707107 + 0.707107i) q^{50} +(-10.5680 + 5.38394i) q^{51} +(1.11554 - 1.11554i) q^{52} -5.16143i q^{53} +(0.813678 - 5.13205i) q^{54} +(1.09777 - 1.09777i) q^{55} +(-1.79574 + 1.79574i) q^{56} +(-2.76929 - 5.43576i) q^{57} +7.34574i q^{58} +(-8.36584 + 8.36584i) q^{59} +(-0.786252 - 1.54331i) q^{60} +(7.41355 - 7.41355i) q^{61} -2.40742 q^{62} +(-6.16315 - 4.47879i) q^{63} -1.00000i q^{64} +1.57762 q^{65} +(1.22064 + 2.39595i) q^{66} +1.98974i q^{67} +(-4.84198 - 4.84198i) q^{68} +(-1.86887 + 0.952110i) q^{69} -2.53955 q^{70} +3.37621i q^{71} +(2.96312 - 0.468987i) q^{72} -0.480190i q^{73} +(0.600636 - 6.05304i) q^{74} +(0.535321 - 1.64725i) q^{75} +(2.49053 - 2.49053i) q^{76} +3.94259 q^{77} +(-0.844532 + 2.59873i) q^{78} +(6.52251 + 6.52251i) q^{79} +(0.707107 - 0.707107i) q^{80} +(2.77933 + 8.56010i) q^{81} +(7.40987 + 7.40987i) q^{82} -8.64749i q^{83} +(1.35948 - 4.18328i) q^{84} -6.84760i q^{85} +3.93165i q^{86} +(-5.77560 - 11.3368i) q^{87} +(-1.09777 + 1.09777i) q^{88} +(-10.5685 - 10.5685i) q^{89} +(2.42686 + 1.76361i) q^{90} +(2.83298 + 2.83298i) q^{91} +(-0.856269 - 0.856269i) q^{92} +(3.71540 - 1.89284i) q^{93} +(7.37349 - 7.37349i) q^{94} +3.52214 q^{95} +(0.786252 + 1.54331i) q^{96} +(-5.01332 - 5.01332i) q^{97} +(0.389382 + 0.389382i) q^{98} +(-3.76765 - 2.73797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) \) 40 * q - 24 * q^7 - 8 * q^9	\( 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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