LMFDB - Embedded newform 1110.2.u.e.401.16

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			401.16
Character	$\chi$	$=$	1110.401
Dual form			1110.2.u.e.191.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.64725 - 0.535321i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.54331 + 0.786252i) q^{6} -2.53955 q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.42686 + 1.76361i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.64725 - 0.535321i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.54331 + 0.786252i) 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} +(-0.786252 - 1.54331i) q^{15} -1.00000 q^{16} +(4.84198 + 4.84198i) q^{17} +(2.96312 - 0.468987i) 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} +(0.786252 + 1.54331i) 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} +(2.43475 - 1.24041i) q^{39} -1.00000i q^{40} +10.4791 q^{41} +(3.91932 - 1.99673i) q^{42} +(-2.78010 + 2.78010i) q^{43} -1.55248i q^{44} +(0.468987 + 2.96312i) 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} +(-5.38394 - 10.5680i) q^{51} +(1.11554 + 1.11554i) q^{52} -5.16143i q^{53} +(-5.13205 - 0.813678i) q^{54} +(1.09777 + 1.09777i) q^{55} +(1.79574 + 1.79574i) q^{56} +(5.43576 - 2.76929i) q^{57} -7.34574i q^{58} +(8.36584 + 8.36584i) q^{59} +(-1.54331 + 0.786252i) 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} +(-2.39595 + 1.22064i) q^{66} -1.98974i q^{67} +(4.84198 - 4.84198i) q^{68} +(-0.952110 - 1.86887i) q^{69} -2.53955 q^{70} +3.37621i q^{71} +(-0.468987 - 2.96312i) 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} +(-11.3368 + 5.77560i) 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} +(-1.89284 - 3.71540i) q^{93} +(7.37349 + 7.37349i) q^{94} -3.52214 q^{95} +(1.54331 - 0.786252i) 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

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
$6$	−1.54331	+	0.786252i	−0.630054	+	0.320986i
$7$	−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	$-0.424804\pi$
$11$	1.55248			0.468089			0.234045	+	0.972226i	$0.424804\pi$
$12$	−0.535321	+	1.64725i	−0.154534	+	0.475520i
$13$	−1.11554	+	1.11554i	−0.309396	+	0.309396i	−0.844675	−	0.535279i	$-0.820206\pi$
$13$	−1.11554	+	1.11554i	−0.309396	+	0.309396i	0.535279	+	0.844675i	$0.320206\pi$
$14$	−1.79574	+	1.79574i	−0.479930	+	0.479930i
$15$	−0.786252	−	1.54331i	−0.203009	−	0.398481i
$16$	−1.00000			−0.250000
$17$	4.84198	+	4.84198i	1.17435	+	1.17435i	0.981161	+	0.193193i	$0.0618843\pi$
$17$	4.84198	+	4.84198i	1.17435	+	1.17435i	0.193193	+	0.981161i	$0.438116\pi$
$18$	2.96312	−	0.468987i	0.698413	−	0.110541i
$19$	−2.49053	+	2.49053i	−0.571367	+	0.571367i	−0.932510	−	0.361143i	$-0.882387\pi$
$19$	−2.49053	+	2.49053i	−0.571367	+	0.571367i	0.361143	+	0.932510i	$0.382387\pi$
$20$	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	$-0.209706\pi$
$23$	0.856269	+	0.856269i	0.178544	+	0.178544i	−0.612177	+	0.790721i	$0.709706\pi$
$24$	0.786252	+	1.54331i	0.160493	+	0.315027i
$25$			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	$-0.511095\pi$
$29$	5.19422	−	5.19422i	0.964543	−	0.964543i	0.999393	+	0.0348499i	$0.0110953\pi$
$30$	−1.64725	−	0.535321i	−0.300745	−	0.0977358i
$31$	1.70231	+	1.70231i	0.305743	+	0.305743i	0.843256	−	0.537513i	$-0.180636\pi$
$31$	1.70231	+	1.70231i	0.305743	+	0.305743i	−0.537513	+	0.843256i	$0.680636\pi$
$32$	−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
$39$	2.43475	−	1.24041i	0.389873	−	0.198624i
$40$		−	1.00000i		−	0.158114i
$41$	10.4791			1.63657			0.818284	−	0.574815i	$-0.194926\pi$
$41$	10.4791			1.63657			0.818284	+	0.574815i	$0.194926\pi$
$42$	3.91932	−	1.99673i	0.604764	−	0.308102i
$43$	−2.78010	+	2.78010i	−0.423961	+	0.423961i	−0.886565	−	0.462604i	$-0.846915\pi$
$43$	−2.78010	+	2.78010i	−0.423961	+	0.423961i	0.462604	+	0.886565i	$0.346915\pi$
$44$		−	1.55248i		−	0.234045i
$45$	0.468987	+	2.96312i	0.0699125	+	0.441715i
$46$	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
$51$	−5.38394	−	10.5680i	−0.753902	−	1.47981i
$52$	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	$-0.115345\pi$
$54$	−5.13205	−	0.813678i	−0.698383	−	0.110728i
$55$	1.09777	+	1.09777i	0.148023	+	0.148023i
$56$	1.79574	+	1.79574i	0.239965	+	0.239965i
$57$	5.43576	−	2.76929i	0.719984	−	0.366802i
$58$		−	7.34574i		−	0.964543i
$59$	8.36584	+	8.36584i	1.08914	+	1.08914i	0.995617	+	0.0935229i	$0.0298128\pi$
$59$	8.36584	+	8.36584i	1.08914	+	1.08914i	0.0935229	+	0.995617i	$0.470187\pi$
$60$	−1.54331	+	0.786252i	−0.199241	+	0.101505i
$61$	7.41355	+	7.41355i	0.949208	+	0.949208i	0.998771	−	0.0495632i	$-0.0157829\pi$
$61$	7.41355	+	7.41355i	0.949208	+	0.949208i	−0.0495632	+	0.998771i	$0.515783\pi$
$62$	2.40742			0.305743
$63$	−6.16315	−	4.47879i	−0.776484	−	0.564275i
$64$			1.00000i			0.125000i
$65$	−1.57762			−0.195679
$66$	−2.39595	+	1.22064i	−0.294921	+	0.150250i
$67$		−	1.98974i		−	0.243085i	−0.992586	−	0.121543i	$-0.961216\pi$
$67$		−	1.98974i		−	0.243085i	0.992586	−	0.121543i	$-0.0387841\pi$
$68$	4.84198	−	4.84198i	0.587177	−	0.587177i
$69$	−0.952110	−	1.86887i	−0.114621	−	0.224985i
$70$	−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	$0.935795\pi$
$72$	−0.468987	−	2.96312i	−0.0552707	−	0.349206i
$73$			0.480190i			0.0562020i	0.999605	+	0.0281010i	$0.00894601\pi$
$73$			0.480190i			0.0562020i	−0.999605	+	0.0281010i	$0.991054\pi$
$74$	−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	−0.237538	−	0.971378i	$-0.576341\pi$
$79$	6.52251	−	6.52251i	0.733840	−	0.733840i	0.971378	+	0.237538i	$0.0763405\pi$
$80$	−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
$87$	−11.3368	+	5.77560i	−1.21543	+	0.619210i
$88$	−1.09777	−	1.09777i	−0.117022	−	0.117022i
$89$	10.5685	−	10.5685i	1.12026	−	1.12026i	0.128557	−	0.991702i	$-0.458965\pi$
$89$	10.5685	−	10.5685i	1.12026	−	1.12026i	0.991702	−	0.128557i	$-0.0410345\pi$
$90$	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
$93$	−1.89284	−	3.71540i	−0.196279	−	0.385269i
$94$	7.37349	+	7.37349i	0.760518	+	0.760518i
$95$	−3.52214			−0.361364
$96$	1.54331	−	0.786252i	0.157513	−	0.0802465i
$97$	−5.01332	+	5.01332i	−0.509026	+	0.509026i	−0.914227	−	0.405202i	$-0.867201\pi$
$97$	−5.01332	+	5.01332i	−0.509026	+	0.509026i	0.405202	+	0.914227i	$0.367201\pi$
$98$	−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	$-0.549731\pi$
$101$	−3.12753			−0.311201			−0.155600	+	0.987820i	$0.549731\pi$
$102$	−11.2797	−	3.66566i	−1.11686	−	0.362955i
$103$	−9.44888	−	9.44888i	−0.931026	−	0.931026i	0.0667446	−	0.997770i	$-0.478739\pi$
$103$	−9.44888	−	9.44888i	−0.931026	−	0.931026i	−0.997770	+	0.0667446i	$0.978739\pi$
$104$	1.57762			0.154698
$105$	1.99673	+	3.91932i	0.194861	+	0.382486i
$106$	−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	−0.786972	−	0.616989i	$-0.788352\pi$
$109$	−1.77468	+	1.77468i	−0.169983	+	0.169983i	0.616989	+	0.786972i	$0.288352\pi$
$110$	1.55248			0.148023
$111$	−8.86946	+	5.68618i	−0.841852	+	0.539708i
$112$	2.53955			0.239965
$113$	−11.3932	+	11.3932i	−1.07178	+	1.07178i	−0.0745674	+	0.997216i	$0.523758\pi$
$113$	−11.3932	+	11.3932i	−1.07178	+	1.07178i	−0.997216	+	0.0745674i	$0.976242\pi$
$114$	1.88548	−	5.80185i	0.176591	−	0.543393i
$115$			1.21095i			0.112921i
$116$	−5.19422	−	5.19422i	−0.482271	−	0.482271i
$117$	−4.67466	+	0.739883i	−0.432173	+	0.0684022i
$118$	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
$126$	−7.52499	+	1.19102i	−0.670379	+	0.106104i
$127$	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
$129$	6.06776	−	3.09127i	0.534236	−	0.272171i
$130$	−1.11554	+	1.11554i	−0.0978397	+	0.0978397i
$131$	0.642612	−	0.642612i	0.0561453	−	0.0561453i	−0.678477	−	0.734622i	$-0.737360\pi$
$131$	0.642612	−	0.642612i	0.0561453	−	0.0561453i	0.734622	+	0.678477i	$0.237360\pi$
$132$	−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
$135$	0.813678	−	5.13205i	0.0700303	−	0.441696i
$136$		−	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	$0.0952910\pi$
$139$			6.95397i			0.589828i	−0.955524	+	0.294914i	$0.904709\pi$
$140$	−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	$0.783211\pi$
$150$	−0.786252	−	1.54331i	−0.0641972	−	0.126011i
$151$		−	8.84452i		−	0.719756i	−0.932999	−	0.359878i	$-0.882818\pi$
$151$		−	8.84452i		−	0.719756i	0.932999	−	0.359878i	$-0.117182\pi$
$152$	3.52214			0.285684
$153$	3.21144	+	20.2902i	0.259629	+	1.64037i
$154$	−2.78784	+	2.78784i	−0.224650	+	0.224650i
$155$			2.40742i			0.193369i
$156$	−1.24041	−	2.43475i	−0.0993119	−	0.194936i
$157$	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
$162$	8.01819	+	4.08763i	0.629968	+	0.321154i
$163$	1.54752	+	1.54752i	0.121211	+	0.121211i	0.765110	−	0.643899i	$-0.222684\pi$
$163$	1.54752	+	1.54752i	0.121211	+	0.121211i	−0.643899	+	0.765110i	$0.722684\pi$
$164$		−	10.4791i		−	0.818284i
$165$	−1.22064	−	2.39595i	−0.0950265	−	0.186525i
$166$	−6.11470	−	6.11470i	−0.474593	−	0.474593i
$167$	13.7766	+	13.7766i	1.06607	+	1.06607i	0.997657	+	0.0684095i	$0.0217924\pi$
$167$	13.7766	+	13.7766i	1.06607	+	1.06607i	0.0684095	+	0.997657i	$0.478208\pi$
$168$	−1.99673	−	3.91932i	−0.154051	−	0.302382i
$169$			10.5111i			0.808548i
$170$	4.84198	+	4.84198i	0.371363	+	0.371363i
$171$	−10.4365	+	1.65184i	−0.798101	+	0.126319i
$172$	2.78010	+	2.78010i	0.211980	+	0.211980i
$173$	−22.4262			−1.70503			−0.852517	−	0.522699i	$-0.824925\pi$
$173$	−22.4262			−1.70503			−0.852517	+	0.522699i	$0.824925\pi$
$174$	−3.93233	+	12.1003i	−0.298109	+	0.917319i
$175$		−	2.53955i		−	0.191972i
$176$	−1.55248			−0.117022
$177$	−9.30222	−	18.2590i	−0.699198	−	1.37243i
$178$		−	14.9461i		−	1.12026i
$179$	−5.77543	+	5.77543i	−0.431676	+	0.431676i	−0.889198	−	0.457522i	$-0.848737\pi$
$179$	−5.77543	+	5.77543i	−0.431676	+	0.431676i	0.457522	+	0.889198i	$0.348737\pi$
$180$	2.96312	−	0.468987i	0.220858	−	0.0349563i
$181$	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
$183$	−8.24334	−	16.1806i	−0.609365	−	1.19610i
$184$		−	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	$-0.358490\pi$
$191$	−6.53325	−	6.53325i	−0.472729	−	0.472729i	−0.902797	+	0.430068i	$0.858490\pi$
$192$	0.535321	−	1.64725i	0.0386335	−	0.118880i
$193$	1.18075	−	1.18075i	0.0849921	−	0.0849921i	−0.663333	−	0.748325i	$-0.730859\pi$
$193$	1.18075	−	1.18075i	0.0849921	−	0.0849921i	0.748325	+	0.663333i	$0.230859\pi$
$194$			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	$0.965100\pi$
$198$	4.60016	−	0.728091i	0.326919	−	0.0517432i
$199$	−1.93640	−	1.93640i	−0.137268	−	0.137268i	0.635134	−	0.772402i	$-0.280945\pi$
$199$	−1.93640	−	1.93640i	−0.137268	−	0.137268i	−0.772402	+	0.635134i	$0.780945\pi$
$200$	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
$204$	−10.5680	+	5.38394i	−0.739906	+	0.376951i
$205$	7.40987	+	7.40987i	0.517528	+	0.517528i
$206$	−13.3627			−0.931026
$207$	0.567919	+	3.58817i	0.0394731	+	0.249395i
$208$	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
$216$	−0.813678	+	5.13205i	−0.0553638	+	0.349192i
$217$	−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
$222$	−2.25092	+	10.2924i	−0.151072	+	0.690780i
$223$	−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	$-0.211647\pi$
$227$	2.56107	+	2.56107i	0.169984	+	0.169984i	−0.616988	+	0.786972i	$0.711647\pi$
$228$	−2.76929	−	5.43576i	−0.183401	−	0.359992i
$229$	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	$-0.734231\pi$
$233$	−20.4916			−1.34245			−0.671223	+	0.741255i	$0.734231\pi$
$234$	−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
$237$	−14.2358	+	7.25257i	−0.924717	+	0.471105i
$238$	−17.3898			−1.12722
$239$	−16.0579	−	16.0579i	−1.03870	−	1.03870i	−0.999220	−	0.0394798i	$-0.987430\pi$
$239$	−16.0579	−	16.0579i	−1.03870	−	1.03870i	−0.0394798	−	0.999220i	$-0.512570\pi$
$240$	0.786252	+	1.54331i	0.0507524	+	0.0996203i
$241$	−8.01194	+	8.01194i	−0.516095	+	0.516095i	−0.916387	−	0.400293i	$-0.868908\pi$
$241$	−8.01194	+	8.01194i	−0.516095	+	0.516095i	0.400293	+	0.916387i	$0.368908\pi$
$242$	−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
$246$	−16.1726	+	8.23925i	−1.03113	+	0.525315i
$247$		−	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	$-0.672543\pi$
$251$	5.39840	−	5.39840i	0.340744	−	0.340744i	0.856647	+	0.515903i	$0.172543\pi$
$252$	−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	$-0.443477\pi$
$257$	−12.9474	−	12.9474i	−0.807636	−	0.807636i	−0.984276	+	0.176640i	$0.943477\pi$
$258$	2.10470	−	6.47641i	0.131033	−	0.403204i
$259$	−9.79107	+	11.9482i	−0.608387	+	0.742427i
$260$			1.57762i			0.0978397i
$261$	21.7663	−	3.44506i	1.34730	−	0.213244i
$262$		−	0.908791i		−	0.0561453i
$263$	7.40115			0.456375			0.228187	−	0.973617i	$-0.426720\pi$
$263$	7.40115			0.456375			0.228187	+	0.973617i	$0.426720\pi$
$264$	1.22064	+	2.39595i	0.0751250	+	0.147461i
$265$	3.64969	−	3.64969i	0.224198	−	0.224198i
$266$		−	8.94467i		−	0.548433i
$267$	−23.0665	+	11.7514i	−1.41165	+	0.719175i
$268$	−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
$273$	−6.18319	+	3.15008i	−0.374223	+	0.190651i
$274$	16.0998	+	16.0998i	0.972627	+	0.972627i
$275$			1.55248i			0.0936178i
$276$	−1.86887	+	0.952110i	−0.112493	+	0.0573103i
$277$	7.72665	+	7.72665i	0.464249	+	0.464249i	0.900045	−	0.435796i	$-0.143533\pi$
$277$	7.72665	+	7.72665i	0.464249	+	0.464249i	−0.435796	+	0.900045i	$0.643533\pi$
$278$	4.91720	+	4.91720i	0.294914	+	0.294914i
$279$	1.12905	+	7.13348i	0.0675946	+	0.427070i
$280$			2.53955i			0.151767i
$281$	−3.95236	−	3.95236i	−0.235778	−	0.235778i	0.579321	−	0.815099i	$-0.303318\pi$
$281$	−3.95236	−	3.95236i	−0.235778	−	0.235778i	−0.815099	+	0.579321i	$0.803318\pi$
$282$	−8.19880	−	16.0932i	−0.488231	−	0.958334i
$283$	4.17375	+	4.17375i	0.248104	+	0.248104i	0.820192	−	0.572088i	$-0.193867\pi$
$283$	4.17375	+	4.17375i	0.248104	+	0.248104i	−0.572088	+	0.820192i	$0.693867\pi$
$284$	3.37621			0.200341
$285$	5.80185	+	1.88548i	0.343672	+	0.111686i
$286$			2.44921i			0.144825i
$287$	−26.6123			−1.57088
$288$	−2.96312	+	0.468987i	−0.174603	+	0.0276353i
$289$			29.8896i			1.75821i
$290$	5.19422	−	5.19422i	0.305015	−	0.305015i
$291$	10.9419	−	5.57445i	0.641427	−	0.326780i
$292$	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	$-0.146724\pi$
$294$	0.849853	−	0.432965i	0.0495644	−	0.0252510i
$295$			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	$-0.777562\pi$
$307$		−	22.5433i		−	1.28661i	0.765609	−	0.643306i	$-0.222438\pi$
$308$			3.94259i			0.224650i
$309$	10.5065	+	20.6228i	0.597693	+	1.17319i
$310$	1.70231	+	1.70231i	0.0966845	+	0.0966845i
$311$	6.11792	−	6.11792i	0.346915	−	0.346915i	−0.512044	−	0.858959i	$-0.671112\pi$
$311$	6.11792	−	6.11792i	0.346915	−	0.346915i	0.858959	+	0.512044i	$0.171112\pi$
$312$	−2.59873	−	0.844532i	−0.147124	−	0.0478122i
$313$	3.26673	−	3.26673i	0.184646	−	0.184646i	−0.608731	−	0.793377i	$-0.708321\pi$
$313$	3.26673	−	3.26673i	0.184646	−	0.184646i	0.793377	+	0.608731i	$0.208321\pi$
$314$	2.95524	−	2.95524i	0.166774	−	0.166774i
$315$	−1.19102	−	7.52499i	−0.0671063	−	0.423985i
$316$	−6.52251	−	6.52251i	−0.366920	−	0.366920i
$317$	30.0184			1.68600			0.843001	−	0.537912i	$-0.180787\pi$
$317$	30.0184			1.68600			0.843001	+	0.537912i	$0.180787\pi$
$318$	4.05819	+	7.96570i	0.227572	+	0.446694i
$319$	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
$327$	3.87336	−	1.97331i	0.214197	−	0.109124i
$328$	−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	−0.406833	−	0.913503i	$-0.633367\pi$
$331$	9.21805	−	9.21805i	0.506670	−	0.506670i	0.913503	+	0.406833i	$0.133367\pi$
$332$	−8.64749			−0.474593
$333$	17.6541	−	4.61855i	0.967441	−	0.253095i
$334$	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	$-0.787427\pi$
$337$		−	22.7367i		−	1.23855i	0.785175	−	0.619275i	$-0.212573\pi$
$338$	7.43249	+	7.43249i	0.404274	+	0.404274i
$339$	24.8665	−	12.6684i	1.35056	−	0.688055i
$340$	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	$-0.587484\pi$
$347$	12.8734	−	12.8734i	0.691078	−	0.691078i	0.962469	+	0.271391i	$0.0874837\pi$
$348$	5.77560	+	11.3368i	0.309605	+	0.607714i
$349$	−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
$351$	8.09641	+	1.28367i	0.432154	+	0.0685174i
$352$	−1.09777	+	1.09777i	−0.0585111	+	0.0585111i
$353$	13.6457	−	13.6457i	0.726286	−	0.726286i	−0.243592	−	0.969878i	$-0.578326\pi$
$353$	13.6457	−	13.6457i	0.726286	−	0.726286i	0.969878	+	0.243592i	$0.0783257\pi$
$354$	−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
$357$	13.6728	+	26.8379i	0.723642	+	1.42041i
$358$			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
$372$	−3.71540	+	1.89284i	−0.192635	+	0.0981393i
$373$		−	26.6336i		−	1.37904i	−0.724268	−	0.689518i	$-0.757822\pi$
$373$		−	26.6336i		−	1.37904i	0.724268	−	0.689518i	$-0.242178\pi$
$374$	10.6307			0.549702
$375$	1.54331	−	0.786252i	0.0796962	−	0.0406019i
$376$	7.37349	−	7.37349i	0.380259	−	0.380259i
$377$			11.5888i			0.596852i
$378$	13.0331	+	2.06638i	0.670351	+	0.106283i
$379$	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	$-0.0556340\pi$
$383$	15.8691	+	15.8691i	0.810874	+	0.810874i	−0.173891	+	0.984765i	$0.555634\pi$
$384$	−0.786252	−	1.54331i	−0.0401233	−	0.0787567i
$385$	−2.78784	−	2.78784i	−0.142081	−	0.142081i
$386$		−	1.66983i		−	0.0849921i
$387$	−11.6499	+	1.84390i	−0.592200	+	0.0937305i
$388$	5.01332	+	5.01332i	0.254513	+	0.254513i
$389$	−8.71629	−	8.71629i	−0.441934	−	0.441934i	0.450728	−	0.892661i	$-0.351164\pi$
$389$	−8.71629	−	8.71629i	−0.441934	−	0.441934i	−0.892661	+	0.450728i	$0.851164\pi$
$390$	2.43475	−	1.24041i	0.123289	−	0.0628104i
$391$			8.29208i			0.419348i
$392$	0.389382	+	0.389382i	0.0196667	+	0.0196667i
$393$	−1.40255	+	0.714539i	−0.0707491	+	0.0360437i
$394$	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	$0.000758675\pi$
$397$			0.0949796i			0.00476689i	−0.999997	+	0.00238345i	$0.999241\pi$
$398$	−2.73848			−0.137268
$399$	−13.8044	+	7.03277i	−0.691085	+	0.352079i
$400$		−	1.00000i		−	0.0500000i
$401$	3.89325	−	3.89325i	0.194420	−	0.194420i	−0.603183	−	0.797603i	$-0.706101\pi$
$401$	3.89325	−	3.89325i	0.194420	−	0.194420i	0.797603	+	0.603183i	$0.206101\pi$
$402$	1.56444	+	3.07079i	0.0780270	+	0.153157i
$403$	−3.79799			−0.189192
$404$			3.12753i			0.155600i
$405$	−4.08763	+	8.01819i	−0.203116	+	0.398427i
$406$			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	0.990544	+	0.137192i	$0.0438078\pi$
$409$	22.8071	+	22.8071i	1.12774	+	1.12774i	0.137192	+	0.990544i	$0.456192\pi$
$410$	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	$0.842321\pi$
$420$	3.91932	−	1.99673i	0.191243	−	0.0974304i
$421$	−14.1201	−	14.1201i	−0.688171	−	0.688171i	0.273657	−	0.961827i	$-0.411767\pi$
$421$	−14.1201	−	14.1201i	−0.688171	−	0.688171i	−0.961827	+	0.273657i	$0.911767\pi$
$422$	−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
$426$	−2.65455	−	5.21054i	−0.128613	−	0.252451i
$427$	−18.8271	−	18.8271i	−0.911107	−	0.911107i
$428$	1.92564			0.0930794
$429$	3.77989	−	1.92570i	0.182495	−	0.0929736i
$430$	−2.78010	+	2.78010i	−0.134068	+	0.134068i
$431$	23.2957	−	23.2957i	1.12211	−	1.12211i	0.130692	−	0.991423i	$-0.458280\pi$
$431$	23.2957	−	23.2957i	1.12211	−	1.12211i	0.991423	−	0.130692i	$-0.0417198\pi$
$432$	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
$438$	−0.377551	−	0.741083i	−0.0180401	−	0.0354103i
$439$	−7.97830	−	7.97830i	−0.380783	−	0.380783i	0.490601	−	0.871384i	$-0.336777\pi$
$439$	−7.97830	−	7.97830i	−0.380783	−	0.380783i	−0.871384	+	0.490601i	$0.836777\pi$
$440$		−	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	$-0.501289\pi$
$443$	−0.170503			−0.00810085			−0.00405043	+	0.999992i	$0.501289\pi$
$444$	5.68618	+	8.86946i	0.269854	+	0.420926i
$445$	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	−0.966361	−	0.257189i	$-0.917204\pi$
$449$	−25.9266	−	25.9266i	−1.22355	−	1.22355i	−0.257189	−	0.966361i	$-0.582796\pi$
$450$	0.468987	+	2.96312i	0.0221083	+	0.139683i
$451$	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	−0.748669	−	0.662944i	$-0.769307\pi$
$457$	−1.83261	+	1.83261i	−0.0857259	+	0.0857259i	0.662944	+	0.748669i	$0.269307\pi$
$458$	9.21757	−	9.21757i	0.430709	−	0.430709i
$459$	5.57174	−	35.1422i	0.260067	−	1.64030i
$460$	1.21095			0.0564607
$461$	11.4366	+	11.4366i	0.532656	+	0.532656i	0.921362	−	0.388706i	$-0.127078\pi$
$461$	11.4366	+	11.4366i	0.532656	+	0.532656i	−0.388706	+	0.921362i	$0.627078\pi$
$462$	6.08465	−	3.09987i	0.283083	−	0.144219i
$463$	−14.6615	+	14.6615i	−0.681376	+	0.681376i	−0.960310	−	0.278934i	$-0.910019\pi$
$463$	−14.6615	+	14.6615i	−0.681376	+	0.681376i	0.278934	+	0.960310i	$0.410019\pi$
$464$	−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	$-0.166558\pi$
$467$	7.91991	+	7.91991i	0.366490	+	0.366490i	−0.499706	+	0.866195i	$0.666558\pi$
$468$	0.739883	+	4.67466i	0.0342011	+	0.216086i
$469$			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	$-0.455769\pi$
$479$	−18.6437	−	18.6437i	−0.851853	−	0.851853i	−0.990361	+	0.138509i	$0.955769\pi$
$480$	1.64725	+	0.535321i	0.0751863	+	0.0244339i
$481$	0.947574	+	9.54937i	0.0432057	+	0.435414i
$482$			11.3306i			0.516095i
$483$	2.41793	+	4.74609i	0.110020	+	0.215954i
$484$			8.58982i			0.390446i
$485$	−7.08991			−0.321936
$486$	−11.0198	−	11.0256i	−0.499867	−	0.500133i
$487$	8.90792	−	8.90792i	0.403657	−	0.403657i	−0.475863	−	0.879519i	$-0.657864\pi$
$487$	8.90792	−	8.90792i	0.403657	−	0.403657i	0.879519	+	0.475863i	$0.157864\pi$
$488$		−	10.4843i		−	0.474604i
$489$	−1.72073	−	3.37757i	−0.0778142	−	0.152739i
$490$	−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
$495$	0.728091	+	4.60016i	0.0327253	+	0.206762i
$496$	−1.70231	−	1.70231i	−0.0764358	−	0.0764358i
$497$		−	8.57406i		−	0.384599i
$498$	6.79911	+	13.3458i	0.304675	+	0.598038i
$499$	−19.8374	−	19.8374i	−0.888044	−	0.888044i	0.106291	−	0.994335i	$-0.466102\pi$
$499$	−19.8374	−	19.8374i	−0.888044	−	0.888044i	−0.994335	+	0.106291i	$0.966102\pi$
$500$	0.707107	+	0.707107i	0.0316228	+	0.0316228i
$501$	−15.3186	−	30.0684i	−0.684385	−	1.34336i
$502$		−	7.63449i		−	0.340744i
$503$	20.0416	+	20.0416i	0.893611	+	0.893611i	0.994861	−	0.101250i	$-0.0322841\pi$
$503$	20.0416	+	20.0416i	0.893611	+	0.893611i	−0.101250	+	0.994861i	$0.532284\pi$
$504$	1.19102	+	7.52499i	0.0530522	+	0.335190i
$505$	−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	$-0.474117\pi$
$509$	3.66498			0.162447			0.0812237	+	0.996696i	$0.474117\pi$
$510$	−5.38394	−	10.5680i	−0.238405	−	0.467958i
$511$		−	1.21947i		−	0.0539461i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	18.0758	+	2.86589i	0.798067	+	0.126532i
$514$	−18.3104			−0.807636
$515$		−	13.3627i		−	0.588832i
$516$	−3.09127	−	6.06776i	−0.136086	−	0.267118i
$517$			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	$-0.475792\pi$
$521$	3.46852			0.151959			0.0759793	+	0.997109i	$0.475792\pi$
$522$	12.9551	−	17.8271i	0.567027	−	0.780271i
$523$	13.9403	−	13.9403i	0.609567	−	0.609567i	−0.333266	−	0.942833i	$-0.608151\pi$
$523$	13.9403	−	13.9403i	0.609567	−	0.609567i	0.942833	+	0.333266i	$0.108151\pi$
$524$	−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
$531$	5.54863	+	35.0569i	0.240790	+	1.52134i
$532$	−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
$537$	12.6053	−	6.42187i	0.543958	−	0.277124i
$538$	−15.8332	−	15.8332i	−0.682617	−	0.682617i
$539$	−0.854900			−0.0368231
$540$	−5.13205	−	0.813678i	−0.220848	−	0.0350151i
$541$	−5.11347	+	5.11347i	−0.219845	+	0.219845i	−0.808433	−	0.588588i	$-0.799684\pi$
$541$	−5.11347	+	5.11347i	−0.219845	+	0.219845i	0.588588	+	0.808433i	$0.299684\pi$
$542$	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	0.237459	−	0.971398i	$-0.423686\pi$
$547$	−17.1654	−	17.1654i	−0.733939	−	0.733939i	−0.971398	+	0.237459i	$0.923686\pi$
$548$	22.7686			0.972627
$549$	4.91702	+	31.0663i	0.209853	+	1.32588i
$550$	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
$555$	−10.2924	−	2.25092i	−0.436888	−	0.0955462i
$556$	6.95397			0.294914
$557$	21.7065	−	21.7065i	0.919733	−	0.919733i	−0.0772768	−	0.997010i	$-0.524623\pi$
$557$	21.7065	−	21.7065i	0.919733	−	0.919733i	0.997010	+	0.0772768i	$0.0246225\pi$
$558$	5.84249	+	4.24577i	0.247332	+	0.179738i
$559$		−	6.20264i		−	0.262344i
$560$	1.79574	+	1.79574i	0.0758837	+	0.0758837i
$561$	−8.35844	−	16.4065i	−0.352893	−	0.692684i
$562$	−5.58948			−0.235778
$563$	17.3652	+	17.3652i	0.731858	+	0.731858i	0.970988	−	0.239130i	$-0.0768622\pi$
$563$	17.3652	+	17.3652i	0.731858	+	0.731858i	−0.239130	+	0.970988i	$0.576862\pi$
$564$	−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	$-0.752713\pi$
$569$	−0.287563	+	0.287563i	−0.0120553	+	0.0120553i	0.701053	+	0.713109i	$0.252713\pi$
$570$	5.43576	−	2.76929i	0.227679	−	0.115993i
$571$	−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
$573$	7.26450	+	14.2593i	0.303479	+	0.595690i
$574$	−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	−0.989509	−	0.144475i	$-0.953851\pi$
$577$	−20.2984	+	20.2984i	−0.845034	+	0.845034i	0.144475	+	0.989509i	$0.453851\pi$
$578$	21.1352	+	21.1352i	0.879106	+	0.879106i
$579$	−2.57707	+	1.31291i	−0.107099	+	0.0545626i
$580$		−	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	$-0.609797\pi$
$587$	14.6086	−	14.6086i	0.602960	−	0.602960i	0.941097	+	0.338137i	$0.109797\pi$
$588$	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	$-0.218924\pi$
$594$	−7.96738	−	1.26322i	−0.326906	−	0.0518304i
$595$		−	17.3898i		−	0.712914i
$596$	15.3710			0.629619
$597$	2.15314	+	4.22633i	0.0881221	+	0.172972i
$598$	−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	$0.912410\pi$
$600$	−1.54331	+	0.786252i	−0.0630054	+	0.0320986i
$601$	−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
$606$	4.82675	−	2.45903i	0.196073	−	0.0998912i
$607$	−1.58980	−	1.58980i	−0.0645280	−	0.0645280i	0.674106	−	0.738634i	$-0.264529\pi$
$607$	−1.58980	−	1.58980i	−0.0645280	−	0.0645280i	−0.738634	+	0.674106i	$0.764529\pi$
$608$		−	3.52214i		−	0.142842i
$609$	28.7903	−	14.6675i	1.16664	−	0.594355i
$610$	7.41355	+	7.41355i	0.300166	+	0.300166i
$611$	−11.6326	−	11.6326i	−0.470603	−	0.470603i
$612$	20.2902	−	3.21144i	0.820184	−	0.129815i
$613$		−	35.8533i		−	1.44810i	−0.689747	−	0.724051i	$-0.742278\pi$
$613$		−	35.8533i		−	1.44810i	0.689747	−	0.724051i	$-0.257722\pi$
$614$	−15.9405	−	15.9405i	−0.643306	−	0.643306i
$615$	−8.23925	−	16.1726i	−0.332239	−	0.652141i
$616$	2.78784	+	2.78784i	0.112325	+	0.112325i
$617$	22.8071			0.918178			0.459089	−	0.888390i	$-0.348176\pi$
$617$	22.8071			0.918178			0.459089	+	0.888390i	$0.348176\pi$
$618$	22.0118	+	7.15335i	0.885443	+	0.287750i
$619$		−	33.8714i		−	1.36141i	−0.732559	−	0.680704i	$-0.761674\pi$
$619$		−	33.8714i		−	1.36141i	0.732559	−	0.680704i	$-0.238326\pi$
$620$	2.40742			0.0966845
$621$	0.985321	−	6.21464i	0.0395396	−	0.249385i
$622$		−	8.65204i		−	0.346915i
$623$	−26.8393	+	26.8393i	−1.07529	+	1.07529i
$624$	−2.43475	+	1.24041i	−0.0974681	+	0.0496559i
$625$	−1.00000			−0.0400000
$626$		−	4.61985i		−	0.184646i
$627$	8.43889	−	4.29926i	0.337017	−	0.171696i
$628$		−	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	0.625027	−	0.780603i	$-0.285088\pi$
$631$	−3.90804	−	3.90804i	−0.155576	−	0.155576i	−0.780603	+	0.625027i	$0.785088\pi$
$632$	−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	$0.798562\pi$
$642$	−1.51404	−	2.97186i	−0.0597544	−	0.117290i
$643$	−16.6932	−	16.6932i	−0.658317	−	0.658317i	0.296664	−	0.954982i	$-0.404126\pi$
$643$	−16.6932	−	16.6932i	−0.658317	−	0.658317i	−0.954982	+	0.296664i	$0.904126\pi$
$644$	−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	$-0.738594\pi$
$647$	1.28867	−	1.28867i	0.0506627	−	0.0506627i	0.731984	+	0.681322i	$0.238594\pi$
$648$	4.08763	−	8.01819i	0.160577	−	0.314984i
$649$	12.9878	+	12.9878i	0.509814	+	0.509814i
$650$	−1.57762			−0.0618792
$651$	4.80698	+	9.43547i	0.188400	+	0.369805i
$652$	1.54752	−	1.54752i	0.0606056	−	0.0606056i
$653$	8.09056	−	8.09056i	0.316608	−	0.316608i	−0.530855	−	0.847463i	$-0.678129\pi$
$653$	8.09056	−	8.09056i	0.316608	−	0.316608i	0.847463	+	0.530855i	$0.178129\pi$
$654$	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	$-0.421021\pi$
$659$	12.6087			0.491164			0.245582	+	0.969376i	$0.421021\pi$
$660$	−2.39595	+	1.22064i	−0.0932623	+	0.0475133i
$661$	−2.03012	−	2.03012i	−0.0789624	−	0.0789624i	0.666523	−	0.745485i	$-0.267782\pi$
$661$	−2.03012	−	2.03012i	−0.0789624	−	0.0789624i	−0.745485	+	0.666523i	$0.767782\pi$
$662$		−	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
$666$	9.21756	−	15.7492i	0.357173	−	0.610268i
$667$	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
$672$	−3.91932	+	1.99673i	−0.151191	+	0.0770255i
$673$	−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	$-0.723262\pi$
$677$	−33.5797			−1.29057			−0.645286	+	0.763941i	$0.723262\pi$
$678$	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
$681$	−2.84773	−	5.58972i	−0.109125	−	0.214198i
$682$	3.73747			0.143115
$683$	−18.5669	−	18.5669i	−0.710442	−	0.710442i	0.256186	−	0.966628i	$-0.417534\pi$
$683$	−18.5669	−	18.5669i	−0.710442	−	0.710442i	−0.966628	+	0.256186i	$0.917534\pi$
$684$	1.65184	+	10.4365i	0.0631597	+	0.399050i
$685$	−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
$690$	−0.952110	−	1.86887i	−0.0362462	−	0.0711465i
$691$			14.7237i			0.560118i	0.959983	+	0.280059i	$0.0903540\pi$
$691$			14.7237i			0.560118i	−0.959983	+	0.280059i	$0.909646\pi$
$692$			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	$-0.261594\pi$
$701$	−1.36351	−	1.36351i	−0.0514990	−	0.0514990i	−0.732387	+	0.680888i	$0.761594\pi$
$702$	6.63272	−	4.81733i	0.250336	−	0.181818i
$703$	2.11553	+	21.3197i	0.0797886	+	0.804086i
$704$			1.55248i			0.0585111i
$705$	16.0932	−	8.19880i	0.606104	−	0.308785i
$706$		−	19.2979i		−	0.726286i
$707$	7.94253			0.298710
$708$	−18.2590	+	9.30222i	−0.686217	+	0.349599i
$709$	5.92223	−	5.92223i	0.222414	−	0.222414i	−0.587100	−	0.809514i	$-0.699731\pi$
$709$	5.92223	−	5.92223i	0.222414	−	0.222414i	0.809514	+	0.587100i	$0.199731\pi$
$710$			3.37621i			0.126707i
$711$	27.3324	−	4.32604i	1.02505	−	0.162239i
$712$	−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
$717$	17.8553	+	35.0475i	0.666817	+	1.30887i
$718$	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	$0.810598\pi$
$720$	−0.468987	−	2.96312i	−0.0174781	−	0.110429i
$721$	23.9959	+	23.9959i	0.893655	+	0.893655i
$722$	4.66301	+	4.66301i	0.173539	+	0.173539i
$723$	17.4866	−	8.90871i	0.650335	−	0.331318i
$724$		−	13.1382i		−	0.488276i
$725$	5.19422	+	5.19422i	0.192909	+	0.192909i
$726$	13.2568	−	6.75377i	0.492004	−	0.250656i
$727$	−0.0366111	−	0.0366111i	−0.00135783	−	0.00135783i	0.706428	−	0.707785i	$-0.250306\pi$
$727$	−0.0366111	−	0.0366111i	−0.00135783	−	0.00135783i	−0.707785	+	0.706428i	$0.750306\pi$
$728$	−4.00644			−0.148489
$729$	−8.35167	+	25.6759i	−0.309321	+	0.950958i
$730$			0.480190i			0.0177726i
$731$	−26.9224			−0.995760
$732$	−16.1806	+	8.24334i	−0.598052	+	0.304683i
$733$			23.8385i			0.880494i	0.897877	+	0.440247i	$0.145109\pi$
$733$			23.8385i			0.880494i	−0.897877	+	0.440247i	$0.854891\pi$
$734$	−8.53674	+	8.53674i	−0.315097	+	0.315097i
$735$	0.432965	+	0.849853i	0.0159701	+	0.0313473i
$736$	−1.21095			−0.0446361
$737$		−	3.08902i		−	0.113786i
$738$	31.0509	−	4.91459i	1.14300	−	0.180908i
$739$		−	38.4233i		−	1.41343i	−0.707501	−	0.706713i	$-0.750177\pi$
$739$		−	38.4233i		−	1.41343i	0.707501	−	0.706713i	$-0.249823\pi$
$740$	−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	$-0.638532\pi$
$743$	−22.9840			−0.843202			−0.421601	+	0.906782i	$0.638532\pi$
$744$	−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	$0.0730385\pi$
$751$			12.4662i			0.454898i	−0.973790	+	0.227449i	$0.926962\pi$
$752$		−	10.4277i		−	0.380259i
$753$	−11.7824	+	6.00264i	−0.429374	+	0.218748i
$754$	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	−0.351710	−	0.936109i	$-0.614400\pi$
$757$	16.0789	−	16.0789i	0.584398	−	0.584398i	0.936109	+	0.351710i	$0.114400\pi$
$758$	14.6734	−	14.6734i	0.532963	−	0.532963i
$759$	−1.47813	−	2.90137i	−0.0536526	−	0.105313i
$760$	2.49053	+	2.49053i	0.0903411	+	0.0903411i
$761$	−29.9383			−1.08526			−0.542632	−	0.839971i	$-0.682572\pi$
$761$	−29.9383			−1.08526			−0.542632	+	0.839971i	$0.682572\pi$
$762$	−22.0956	+	11.2568i	−0.800439	+	0.407790i
$763$	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	−0.999973	−	0.00735452i	$-0.997659\pi$
$769$	−27.9340	−	27.9340i	−1.00733	−	1.00733i	−0.00735452	−	0.999973i	$-0.502341\pi$
$770$	−3.94259			−0.142081
$771$	14.3966	+	28.2586i	0.518480	+	1.01771i
$772$	−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
$777$	22.5245	−	14.4404i	0.808061	−	0.518045i
$778$	−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
$783$	−37.6987	−	5.97707i	−1.34724	−	0.213603i
$784$	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
$792$	−0.728091	−	4.60016i	−0.0258716	−	0.163460i
$793$	−16.5403			−0.587363
$794$	0.0671608	+	0.0671608i	0.00238345	+	0.00238345i
$795$	−7.96570	+	4.05819i	−0.282514	+	0.143929i
$796$	−1.93640	+	1.93640i	−0.0686339	+	0.0686339i
$797$	−4.77954	+	4.77954i	−0.169300	+	0.169300i	−0.786672	−	0.617372i	$-0.788198\pi$
$797$	−4.77954	+	4.77954i	−0.169300	+	0.169300i	0.617372	+	0.786672i	$0.288198\pi$
$798$	−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
$801$	44.2871	−	7.00954i	1.56481	−	0.247670i
$802$		−	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	$-0.564551\pi$
$809$	22.1315	−	22.1315i	0.778101	−	0.778101i	0.979508	+	0.201406i	$0.0645512\pi$
$810$	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
$816$	5.38394	+	10.5680i	0.188476	+	0.369953i
$817$		−	13.8478i		−	0.484475i
$818$	32.2541			1.12774
$819$	11.8716	−	1.87897i	0.414826	−	0.0656566i
$820$	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	$0.950914\pi$
$822$	−17.9019	−	35.1390i	−0.624399	−	1.22561i
$823$	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	0.959865	+	0.280461i	$0.0904874\pi$
$827$	35.6688	+	35.6688i	1.24033	+	1.24033i	0.280461	+	0.959865i	$0.409513\pi$
$828$	3.58817	−	0.567919i	0.124698	−	0.0197365i
$829$	13.6682	+	13.6682i	0.474716	+	0.474716i	0.903437	−	0.428721i	$-0.141036\pi$
$829$	13.6682	+	13.6682i	0.474716	+	0.474716i	−0.428721	+	0.903437i	$0.641036\pi$
$830$		−	8.64749i		−	0.300159i
$831$	−8.59148	−	16.8639i	−0.298035	−	0.585004i
$832$	−1.11554	−	1.11554i	−0.0386745	−	0.0386745i
$833$	−2.66633	−	2.66633i	−0.0923828	−	0.0923828i
$834$	−5.46757	−	10.7321i	−0.189327	−	0.371623i
$835$			19.4831i			0.674240i
$836$	3.86649	+	3.86649i	0.133725	+	0.133725i
$837$	1.95887	−	12.3550i	0.0677084	−	0.427052i
$838$	13.7606	+	13.7606i	0.475350	+	0.475350i
$839$	−19.8742			−0.686135			−0.343067	−	0.939311i	$-0.611466\pi$
$839$	−19.8742			−0.686135			−0.343067	+	0.939311i	$0.611466\pi$
$840$	1.35948	−	4.18328i	0.0469064	−	0.144337i
$841$		−	24.9599i		−	0.860685i
$842$	−19.9688			−0.688171
$843$	4.39474	+	8.62631i	0.151363	+	0.297106i
$844$			24.0332i			0.827257i
$845$	−7.43249	+	7.43249i	−0.255685	+	0.255685i
$846$	4.89046	+	30.8985i	0.168137	+	1.06231i
$847$	21.8143			0.749548
$848$			5.16143i			0.177244i
$849$	−4.64092	−	9.10951i	−0.159276	−	0.312638i
$850$			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	0.999335	−	0.0364533i	$-0.0116060\pi$
$853$	28.1221	+	28.1221i	0.962882	+	0.962882i	−0.0364533	+	0.999335i	$0.511606\pi$
$854$	−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	$-0.138002\pi$
$857$	14.2681	+	14.2681i	0.487389	+	0.487389i	−0.420092	+	0.907481i	$0.638002\pi$
$858$	1.31111	−	4.03446i	0.0447607	−	0.137734i
$859$	11.9927	−	11.9927i	0.409185	−	0.409185i	−0.472269	−	0.881454i	$-0.656565\pi$
$859$	11.9927	−	11.9927i	0.409185	−	0.409185i	0.881454	+	0.472269i	$0.156565\pi$
$860$			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	$-0.0995277\pi$
$864$	5.13205	+	0.813678i	0.174596	+	0.0276819i
$865$	−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
$870$	−11.3368	+	5.77560i	−0.384352	+	0.195811i
$871$	2.21964	+	2.21964i	0.0752097	+	0.0752097i
$872$	2.50977			0.0849916
$873$	−21.0082	+	3.32508i	−0.711020	+	0.112537i
$874$	−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	$-0.350730\pi$
$881$	26.8290			0.903891			0.451946	+	0.892045i	$0.350730\pi$
$882$	−1.63170	+	0.258257i	−0.0549420	+	0.00869596i
$883$	32.1258	+	32.1258i	1.08112	+	1.08112i	0.996405	+	0.0847128i	$0.0269973\pi$
$883$	32.1258	+	32.1258i	1.08112	+	1.08112i	0.0847128	+	0.996405i	$0.473003\pi$
$884$			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	$-0.109540\pi$
$887$	56.0728			1.88274			0.941370	+	0.337377i	$0.109540\pi$
$888$	10.2924	+	2.25092i	0.345390	+	0.0755359i
$889$	−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
$894$	−12.0854	−	23.7222i	−0.404198	−	0.793387i
$895$	−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
$903$	−15.4094	+	7.85045i	−0.512793	+	0.261247i
$904$	16.1124			0.535892
$905$	9.29009	+	9.29009i	0.308813	+	0.308813i
$906$	6.95402	+	13.6498i	0.231032	+	0.453485i
$907$	29.0323	−	29.0323i	0.964003	−	0.964003i	−0.0353712	−	0.999374i	$-0.511261\pi$
$907$	29.0323	−	29.0323i	0.964003	−	0.964003i	0.999374	+	0.0353712i	$0.0112613\pi$
$908$	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	$-0.0641602\pi$
$911$	23.5290	+	23.5290i	0.779551	+	0.779551i	−0.200203	+	0.979754i	$0.564160\pi$
$912$	−5.43576	+	2.76929i	−0.179996	+	0.0917005i
$913$		−	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	0.448976	−	0.893544i	$-0.351789\pi$
$919$	−13.4771	−	13.4771i	−0.444568	−	0.444568i	−0.893544	+	0.448976i	$0.851789\pi$
$920$	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
$927$	−6.26695	−	39.5953i	−0.205834	−	1.30048i
$928$			7.34574i			0.241136i
$929$	−48.7123			−1.59820			−0.799099	−	0.601200i	$-0.794690\pi$
$929$	−48.7123			−1.59820			−0.799099	+	0.601200i	$0.794690\pi$
$930$	−1.89284	−	3.71540i	−0.0620688	−	0.121833i
$931$	1.37146	−	1.37146i	0.0449477	−	0.0449477i
$932$			20.4916i			0.671223i
$933$	−13.3528	+	6.80269i	−0.437151	+	0.222710i
$934$	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
$939$	−7.12986	+	3.63237i	−0.232674	+	0.118538i
$940$	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	$-0.238263\pi$
$942$	−6.45001	+	3.28601i	−0.210153	+	0.107064i
$943$	8.97296	+	8.97296i	0.292200	+	0.292200i
$944$	−8.36584	−	8.36584i	−0.272285	−	0.272285i
$945$	−2.06638	+	13.0331i	−0.0672193	+	0.423967i
$946$			6.10379i			0.198451i
$947$	−34.4729	−	34.4729i	−1.12022	−	1.12022i	−0.991708	−	0.128510i	$-0.958981\pi$
$947$	−34.4729	−	34.4729i	−1.12022	−	1.12022i	−0.128510	−	0.991708i	$-0.541019\pi$
$948$	7.25257	+	14.2358i	0.235552	+	0.462359i
$949$	−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	$-0.735695\pi$
$953$	−41.6524			−1.34925			−0.674627	+	0.738159i	$0.735695\pi$
$954$	−2.42065	−	15.2939i	−0.0783714	−	0.495159i
$955$		−	9.23941i		−	0.298980i
$956$	−16.0579	+	16.0579i	−0.519350	+	0.519350i
$957$	−17.6000	+	8.96648i	−0.568928	+	0.289845i
$958$	−26.3662			−0.851853
$959$		−	57.8221i		−	1.86717i
$960$	1.54331	−	0.786252i	0.0498101	−	0.0253762i
$961$		−	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	−0.934095	−	0.357024i	$-0.883792\pi$
$967$	−17.9450	+	17.9450i	−0.577071	+	0.577071i	0.357024	+	0.934095i	$0.383792\pi$
$968$	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
$975$	1.24041	+	2.43475i	0.0397248	+	0.0779745i
$976$	−7.41355	−	7.41355i	−0.237302	−	0.237302i
$977$	−7.77719	+	7.77719i	−0.248814	+	0.248814i	−0.820484	−	0.571670i	$-0.806296\pi$
$977$	−7.77719	+	7.77719i	−0.248814	+	0.248814i	0.571670	+	0.820484i	$0.306296\pi$
$978$	−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
$981$	−7.43674	+	1.17705i	−0.237437	+	0.0375803i
$982$	0.306040	+	0.306040i	0.00976612	+	0.00976612i
$983$	4.10130			0.130811			0.0654056	−	0.997859i	$-0.479166\pi$
$983$	4.10130			0.130811			0.0654056	+	0.997859i	$0.479166\pi$
$984$	8.23925	+	16.1726i	0.262658	+	0.515563i
$985$	−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	0.925091	+	0.379744i	$0.123988\pi$
$991$	41.0764	+	41.0764i	1.30484	+	1.30484i	0.379744	+	0.925091i	$0.376012\pi$
$992$	−2.40742			−0.0764358
$993$	−20.1191	+	10.2498i	−0.638459	+	0.325268i
$994$	−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	−0.632434	−	0.774614i	$-0.717944\pi$
$997$	4.48937	−	4.48937i	0.142180	−	0.142180i	0.774614	+	0.632434i	$0.217944\pi$
$998$	−28.0543			−0.888044
$999$	−31.5532	−	1.84273i	−0.998299	−	0.0583014i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.e.191.3	✓	40	37.6	odd	4	inner
1110.2.u.e.191.16	yes	40	111.80	even	4	inner
1110.2.u.e.401.3	yes	40	3.2	odd	2	inner
1110.2.u.e.401.16	yes	40	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.64725 - 0.535321i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.54331 + 0.786252i) q^{6} -2.53955 q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.42686 + 1.76361i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.64725 - 0.535321i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.54331 + 0.786252i) 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} +(-0.786252 - 1.54331i) q^{15} -1.00000 q^{16} +(4.84198 + 4.84198i) q^{17} +(2.96312 - 0.468987i) 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} +(0.786252 + 1.54331i) 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} +(2.43475 - 1.24041i) q^{39} -1.00000i q^{40} +10.4791 q^{41} +(3.91932 - 1.99673i) q^{42} +(-2.78010 + 2.78010i) q^{43} -1.55248i q^{44} +(0.468987 + 2.96312i) 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} +(-5.38394 - 10.5680i) q^{51} +(1.11554 + 1.11554i) q^{52} -5.16143i q^{53} +(-5.13205 - 0.813678i) q^{54} +(1.09777 + 1.09777i) q^{55} +(1.79574 + 1.79574i) q^{56} +(5.43576 - 2.76929i) q^{57} -7.34574i q^{58} +(8.36584 + 8.36584i) q^{59} +(-1.54331 + 0.786252i) 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} +(-2.39595 + 1.22064i) q^{66} -1.98974i q^{67} +(4.84198 - 4.84198i) q^{68} +(-0.952110 - 1.86887i) q^{69} -2.53955 q^{70} +3.37621i q^{71} +(-0.468987 - 2.96312i) 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} +(-11.3368 + 5.77560i) 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} +(-1.89284 - 3.71540i) q^{93} +(7.37349 + 7.37349i) q^{94} -3.52214 q^{95} +(1.54331 - 0.786252i) 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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