LMFDB - Embedded newform 390.2.bn.c.97.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(67,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("390.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.8
Character	$\chi$	$=$	390.97
Dual form			390.2.bn.c.193.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.26528 + 1.84366i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(3.23783 - 1.86936i) q^{7} +1.00000 q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.26528 + 1.84366i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(3.23783 - 1.86936i) q^{7} +1.00000 q^{8} +(-0.866025 + 0.500000i) q^{9} +(-2.22929 + 0.173937i) q^{10} +(6.06028 - 1.62385i) q^{11} +(0.707107 - 0.707107i) q^{12} +(-3.60253 - 0.147508i) q^{13} +3.73872i q^{14} +(-1.45336 + 1.69934i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.09192 + 0.560528i) q^{17} -1.00000i q^{18} +(0.629143 - 2.34800i) q^{19} +(0.964013 - 2.01759i) q^{20} +(2.64368 + 2.64368i) q^{21} +(-1.62385 + 6.06028i) q^{22} +(-6.27100 + 1.68031i) q^{23} +(0.258819 + 0.965926i) q^{24} +(-1.79813 + 4.66548i) q^{25} +(1.92901 - 3.04613i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-3.23783 - 1.86936i) q^{28} +(2.92823 + 1.69061i) q^{29} +(-0.744994 - 2.10831i) q^{30} +(-5.04420 + 5.04420i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.13703 + 5.43350i) q^{33} +(-1.53139 + 1.53139i) q^{34} +(7.54322 + 3.60418i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-2.30606 - 1.33141i) q^{37} +(1.71885 + 1.71885i) q^{38} +(-0.789922 - 3.51796i) q^{39} +(1.26528 + 1.84366i) q^{40} +(-2.05110 - 7.65481i) q^{41} +(-3.61133 + 0.967653i) q^{42} +(0.602337 - 2.24795i) q^{43} +(-4.43644 - 4.43644i) q^{44} +(-2.01759 - 0.964013i) q^{45} +(1.68031 - 6.27100i) q^{46} +8.85955i q^{47} +(-0.965926 - 0.258819i) q^{48} +(3.48902 - 6.04316i) q^{49} +(-3.14136 - 3.88997i) q^{50} +2.16572i q^{51} +(1.67352 + 3.19364i) q^{52} +(-2.17970 + 2.17970i) q^{53} +(0.965926 - 0.258819i) q^{54} +(10.6618 + 9.11845i) q^{55} +(3.23783 - 1.86936i) q^{56} +2.43082 q^{57} +(-2.92823 + 1.69061i) q^{58} +(-3.04462 - 0.815803i) q^{59} +(2.19835 + 0.408973i) q^{60} +(-6.67169 - 11.5557i) q^{61} +(-1.84630 - 6.89050i) q^{62} +(-1.86936 + 3.23783i) q^{63} +1.00000 q^{64} +(-4.28626 - 6.82847i) q^{65} -6.27407 q^{66} +(-5.35325 + 9.27211i) q^{67} +(-0.560528 - 2.09192i) q^{68} +(-3.24611 - 5.62243i) q^{69} +(-6.89292 + 4.73053i) q^{70} +(12.6387 + 3.38653i) q^{71} +(-0.866025 + 0.500000i) q^{72} +2.64120 q^{73} +(2.30606 - 1.33141i) q^{74} +(-4.97190 - 0.529347i) q^{75} +(-2.34800 + 0.629143i) q^{76} +(16.5866 - 16.5866i) q^{77} +(3.44160 + 1.07489i) q^{78} -14.0721i q^{79} +(-2.22929 + 0.173937i) q^{80} +(0.500000 - 0.866025i) q^{81} +(7.65481 + 2.05110i) q^{82} -2.24024i q^{83} +(0.967653 - 3.61133i) q^{84} +(1.61344 + 4.56601i) q^{85} +(1.64561 + 1.64561i) q^{86} +(-0.875126 + 3.26601i) q^{87} +(6.06028 - 1.62385i) q^{88} +(-3.35427 - 12.5183i) q^{89} +(1.84366 - 1.26528i) q^{90} +(-11.9401 + 6.25683i) q^{91} +(4.59069 + 4.59069i) q^{92} +(-6.17785 - 3.56679i) q^{93} +(-7.67260 - 4.42978i) q^{94} +(5.12494 - 1.81095i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-1.75124 - 3.03323i) q^{97} +(3.48902 + 6.04316i) q^{98} +(-4.43644 + 4.43644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8	$ 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8} - 4 q^{11} + 8 q^{13} - 4 q^{15} - 16 q^{16} - 4 q^{17} + 20 q^{19} + 8 q^{21} + 8 q^{22} - 16 q^{23} - 8 q^{25} - 4 q^{26} + 12 q^{28} + 24 q^{29} + 8 q^{30} + 12 q^{31} - 16 q^{32} - 16 q^{34} + 12 q^{35} - 24 q^{37} - 4 q^{38} - 20 q^{39} - 28 q^{41} - 16 q^{42} + 4 q^{43} - 4 q^{44} - 4 q^{46} + 20 q^{49} - 8 q^{50} - 4 q^{52} - 4 q^{53} + 68 q^{55} - 12 q^{56} + 16 q^{57} - 24 q^{58} + 36 q^{59} - 4 q^{60} - 28 q^{61} - 48 q^{62} + 32 q^{64} - 28 q^{65} - 28 q^{67} + 20 q^{68} - 20 q^{69} - 24 q^{70} - 4 q^{71} - 48 q^{73} + 24 q^{74} + 24 q^{75} - 16 q^{76} + 20 q^{77} + 4 q^{78} + 16 q^{81} + 44 q^{82} + 8 q^{84} + 64 q^{85} - 8 q^{86} + 20 q^{87} - 4 q^{88} - 16 q^{89} - 40 q^{91} + 20 q^{92} - 24 q^{93} - 24 q^{94} + 68 q^{95} + 8 q^{97} + 20 q^{98} - 4 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8 - 4 * q^11 + 8 * q^13 - 4 * q^15 - 16 * q^16 - 4 * q^17 + 20 * q^19 + 8 * q^21 + 8 * q^22 - 16 * q^23 - 8 * q^25 - 4 * q^26 + 12 * q^28 + 24 * q^29 + 8 * q^30 + 12 * q^31 - 16 * q^32 - 16 * q^34 + 12 * q^35 - 24 * q^37 - 4 * q^38 - 20 * q^39 - 28 * q^41 - 16 * q^42 + 4 * q^43 - 4 * q^44 - 4 * q^46 + 20 * q^49 - 8 * q^50 - 4 * q^52 - 4 * q^53 + 68 * q^55 - 12 * q^56 + 16 * q^57 - 24 * q^58 + 36 * q^59 - 4 * q^60 - 28 * q^61 - 48 * q^62 + 32 * q^64 - 28 * q^65 - 28 * q^67 + 20 * q^68 - 20 * q^69 - 24 * q^70 - 4 * q^71 - 48 * q^73 + 24 * q^74 + 24 * q^75 - 16 * q^76 + 20 * q^77 + 4 * q^78 + 16 * q^81 + 44 * q^82 + 8 * q^84 + 64 * q^85 - 8 * q^86 + 20 * q^87 - 4 * q^88 - 16 * q^89 - 40 * q^91 + 20 * q^92 - 24 * q^93 - 24 * q^94 + 68 * q^95 + 8 * q^97 + 20 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{12}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.26528	+	1.84366i	0.565850	+	0.824508i
$5$	1.26528	+	1.84366i	0.565850	+	0.824508i
$6$	−0.965926	−	0.258819i	−0.394338	−	0.105662i
$7$	3.23783	−	1.86936i	1.22378	−	0.706552i	0.258062	−	0.966128i	$-0.416916\pi$
$7$	3.23783	−	1.86936i	1.22378	−	0.706552i	0.965723	+	0.259576i	$0.0835829\pi$
$8$	1.00000			0.353553
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	−2.22929	+	0.173937i	−0.704964	+	0.0550037i
$11$	6.06028	−	1.62385i	1.82724	−	0.489609i	0.829610	−	0.558344i	$-0.188563\pi$
$11$	6.06028	−	1.62385i	1.82724	−	0.489609i	0.997635	+	0.0687353i	$0.0218964\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−3.60253	−	0.147508i	−0.999163	−	0.0409113i
$13$	−3.60253	−	0.147508i	−0.999163	−	0.0409113i
$14$			3.73872i			0.999216i
$15$	−1.45336	+	1.69934i	−0.375255	+	0.438768i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.09192	+	0.560528i	0.507365	+	0.135948i	0.503416	−	0.864044i	$-0.332076\pi$
$17$	2.09192	+	0.560528i	0.507365	+	0.135948i	0.00394915	+	0.999992i	$0.498743\pi$
$18$		−	1.00000i		−	0.235702i
$19$	0.629143	−	2.34800i	0.144335	−	0.538667i	−0.855449	−	0.517888i	$-0.826719\pi$
$19$	0.629143	−	2.34800i	0.144335	−	0.538667i	0.999784	−	0.0207794i	$-0.00661478\pi$
$20$	0.964013	−	2.01759i	0.215560	−	0.451147i
$21$	2.64368	+	2.64368i	0.576897	+	0.576897i
$22$	−1.62385	+	6.06028i	−0.346206	+	1.29206i
$23$	−6.27100	+	1.68031i	−1.30759	+	0.350369i	−0.844317	−	0.535844i	$-0.819993\pi$
$23$	−6.27100	+	1.68031i	−1.30759	+	0.350369i	−0.463278	+	0.886213i	$0.653327\pi$
$24$	0.258819	+	0.965926i	0.0528312	+	0.197169i
$25$	−1.79813	+	4.66548i	−0.359626	+	0.933096i
$26$	1.92901	−	3.04613i	0.378310	−	0.597395i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−3.23783	−	1.86936i	−0.611892	−	0.353276i
$29$	2.92823	+	1.69061i	0.543758	+	0.313939i	0.746601	−	0.665272i	$-0.231685\pi$
$29$	2.92823	+	1.69061i	0.543758	+	0.313939i	−0.202842	+	0.979211i	$0.565018\pi$
$30$	−0.744994	−	2.10831i	−0.136017	−	0.384924i
$31$	−5.04420	+	5.04420i	−0.905964	+	0.905964i	−0.995944	−	0.0899793i	$-0.971320\pi$
$31$	−5.04420	+	5.04420i	−0.905964	+	0.905964i	0.0899793	+	0.995944i	$0.471320\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	3.13703	+	5.43350i	0.546088	+	0.945851i
$34$	−1.53139	+	1.53139i	−0.262632	+	0.262632i
$35$	7.54322	+	3.60418i	1.27504	+	0.609217i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	−2.30606	−	1.33141i	−0.379114	−	0.218882i	0.298319	−	0.954466i	$-0.403574\pi$
$37$	−2.30606	−	1.33141i	−0.379114	−	0.218882i	−0.677433	+	0.735585i	$0.736908\pi$
$38$	1.71885	+	1.71885i	0.278835	+	0.278835i
$39$	−0.789922	−	3.51796i	−0.126489	−	0.563324i
$40$	1.26528	+	1.84366i	0.200058	+	0.291508i
$41$	−2.05110	−	7.65481i	−0.320328	−	1.19548i	−0.918926	−	0.394430i	$-0.870942\pi$
$41$	−2.05110	−	7.65481i	−0.320328	−	1.19548i	0.598598	−	0.801050i	$-0.295725\pi$
$42$	−3.61133	+	0.967653i	−0.557240	+	0.149312i
$43$	0.602337	−	2.24795i	0.0918555	−	0.342809i	−0.904668	−	0.426116i	$-0.859882\pi$
$43$	0.602337	−	2.24795i	0.0918555	−	0.342809i	0.996524	+	0.0833069i	$0.0265482\pi$
$44$	−4.43644	−	4.43644i	−0.668818	−	0.668818i
$45$	−2.01759	−	0.964013i	−0.300765	−	0.143707i
$46$	1.68031	−	6.27100i	0.247748	−	0.924609i
$47$			8.85955i			1.29230i	0.763211	+	0.646149i	$0.223622\pi$
$47$			8.85955i			1.29230i	−0.763211	+	0.646149i	$0.776378\pi$
$48$	−0.965926	−	0.258819i	−0.139419	−	0.0373573i
$49$	3.48902	−	6.04316i	0.498432	−	0.863309i
$50$	−3.14136	−	3.88997i	−0.444255	−	0.550125i
$51$			2.16572i			0.303261i
$52$	1.67352	+	3.19364i	0.232076	+	0.442878i
$53$	−2.17970	+	2.17970i	−0.299405	+	0.299405i	−0.840781	−	0.541376i	$-0.817904\pi$
$53$	−2.17970	+	2.17970i	−0.299405	+	0.299405i	0.541376	+	0.840781i	$0.317904\pi$
$54$	0.965926	−	0.258819i	0.131446	−	0.0352208i
$55$	10.6618	+	9.11845i	1.43763	+	1.22953i
$56$	3.23783	−	1.86936i	0.432673	−	0.249804i
$57$	2.43082			0.321970
$58$	−2.92823	+	1.69061i	−0.384495	+	0.221988i
$59$	−3.04462	−	0.815803i	−0.396376	−	0.106209i	0.0551247	−	0.998479i	$-0.482444\pi$
$59$	−3.04462	−	0.815803i	−0.396376	−	0.106209i	−0.451500	+	0.892271i	$0.649111\pi$
$60$	2.19835	+	0.408973i	0.283806	+	0.0527982i
$61$	−6.67169	−	11.5557i	−0.854223	−	1.47956i	−0.877364	−	0.479825i	$-0.840700\pi$
$61$	−6.67169	−	11.5557i	−0.854223	−	1.47956i	0.0231412	−	0.999732i	$-0.492633\pi$
$62$	−1.84630	−	6.89050i	−0.234481	−	0.875094i
$63$	−1.86936	+	3.23783i	−0.235517	+	0.407928i
$64$	1.00000			0.125000
$65$	−4.28626	−	6.82847i	−0.531645	−	0.846967i
$66$	−6.27407			−0.772284
$67$	−5.35325	+	9.27211i	−0.654004	+	1.13277i	0.328138	+	0.944630i	$0.393579\pi$
$67$	−5.35325	+	9.27211i	−0.654004	+	1.13277i	−0.982142	+	0.188139i	$0.939755\pi$
$68$	−0.560528	−	2.09192i	−0.0679741	−	0.253683i
$69$	−3.24611	−	5.62243i	−0.390786	−	0.676861i
$70$	−6.89292	+	4.73053i	−0.823861	+	0.565407i
$71$	12.6387	+	3.38653i	1.49994	+	0.401908i	0.913080	−	0.407781i	$-0.133697\pi$
$71$	12.6387	+	3.38653i	1.49994	+	0.401908i	0.586860	+	0.809688i	$0.300364\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	2.64120			0.309130			0.154565	−	0.987983i	$-0.450602\pi$
$73$	2.64120			0.309130			0.154565	+	0.987983i	$0.450602\pi$
$74$	2.30606	−	1.33141i	0.268074	−	0.154773i
$75$	−4.97190	−	0.529347i	−0.574106	−	0.0611237i
$76$	−2.34800	+	0.629143i	−0.269334	+	0.0721677i
$77$	16.5866	−	16.5866i	1.89022	−	1.89022i
$78$	3.44160	+	1.07489i	0.389685	+	0.121707i
$79$		−	14.0721i		−	1.58323i	−0.611019	−	0.791616i	$-0.709240\pi$
$79$		−	14.0721i		−	1.58323i	0.611019	−	0.791616i	$-0.290760\pi$
$80$	−2.22929	+	0.173937i	−0.249243	+	0.0194467i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	7.65481	+	2.05110i	0.845332	+	0.226506i
$83$		−	2.24024i		−	0.245898i	−0.992413	−	0.122949i	$-0.960765\pi$
$83$		−	2.24024i		−	0.245898i	0.992413	−	0.122949i	$-0.0392351\pi$
$84$	0.967653	−	3.61133i	0.105580	−	0.394028i
$85$	1.61344	+	4.56601i	0.175003	+	0.495253i
$86$	1.64561	+	1.64561i	0.177451	+	0.177451i
$87$	−0.875126	+	3.26601i	−0.0938234	+	0.350154i
$88$	6.06028	−	1.62385i	0.646028	−	0.173103i
$89$	−3.35427	−	12.5183i	−0.355552	−	1.32694i	−0.879788	−	0.475366i	$-0.842316\pi$
$89$	−3.35427	−	12.5183i	−0.355552	−	1.32694i	0.524236	−	0.851573i	$-0.324351\pi$
$90$	1.84366	−	1.26528i	0.194338	−	0.133372i
$91$	−11.9401	+	6.25683i	−1.25167	+	0.655894i
$92$	4.59069	+	4.59069i	0.478613	+	0.478613i
$93$	−6.17785	−	3.56679i	−0.640614	−	0.369858i
$94$	−7.67260	−	4.42978i	−0.791368	−	0.456897i
$95$	5.12494	−	1.81095i	0.525807	−	0.185799i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	−1.75124	−	3.03323i	−0.177811	−	0.307978i	0.763319	−	0.646021i	$-0.223568\pi$
$97$	−1.75124	−	3.03323i	−0.177811	−	0.307978i	−0.941131	+	0.338043i	$0.890235\pi$
$98$	3.48902	+	6.04316i	0.352444	+	0.610452i
$99$	−4.43644	+	4.43644i	−0.445879	+	0.445879i
$100$	4.93949	−	0.775513i	0.493949	−	0.0775513i
$101$	3.77878	+	2.18168i	0.376002	+	0.217085i	0.676078	−	0.736831i	$-0.263678\pi$
$101$	3.77878	+	2.18168i	0.376002	+	0.217085i	−0.300075	+	0.953916i	$0.597012\pi$
$102$	−1.87556	−	1.08286i	−0.185709	−	0.107219i
$103$	0.828927	+	0.828927i	0.0816766	+	0.0816766i	0.746765	−	0.665088i	$-0.231606\pi$
$103$	0.828927	+	0.828927i	0.0816766	+	0.0816766i	−0.665088	+	0.746765i	$0.731606\pi$
$104$	−3.60253	−	0.147508i	−0.353257	−	0.0144643i
$105$	−1.52904	+	8.21902i	−0.149219	+	0.802094i
$106$	−0.797827	−	2.97753i	−0.0774918	−	0.289203i
$107$	−0.678228	+	0.181731i	−0.0655667	+	0.0175686i	−0.291453	−	0.956585i	$-0.594139\pi$
$107$	−0.678228	+	0.181731i	−0.0655667	+	0.0175686i	0.225887	+	0.974154i	$0.427472\pi$
$108$	−0.258819	+	0.965926i	−0.0249049	+	0.0929463i
$109$	−3.41724	−	3.41724i	−0.327312	−	0.327312i	0.524252	−	0.851563i	$-0.324345\pi$
$109$	−3.41724	−	3.41724i	−0.327312	−	0.327312i	−0.851563	+	0.524252i	$0.824345\pi$
$110$	−13.2277	+	4.67414i	−1.26121	+	0.445662i
$111$	0.689186	−	2.57208i	0.0654147	−	0.244131i
$112$			3.73872i			0.353276i
$113$	5.73773	+	1.53742i	0.539760	+	0.144628i	0.518392	−	0.855143i	$-0.326531\pi$
$113$	5.73773	+	1.53742i	0.539760	+	0.144628i	0.0213687	+	0.999772i	$0.493198\pi$
$114$	−1.21541	+	2.10515i	−0.113834	+	0.197166i
$115$	−11.0325	−	9.43551i	−1.02879	−	0.879866i
$116$		−	3.38123i		−	0.313939i
$117$	3.19364	−	1.67352i	0.295252	−	0.154717i
$118$	2.22882	−	2.22882i	0.205179	−	0.205179i
$119$	7.82111	−	2.09566i	0.716960	−	0.192109i
$120$	−1.45336	+	1.69934i	−0.132673	+	0.155128i
$121$	24.5639	−	14.1820i	2.23308	−	1.28927i
$122$	13.3434			1.20805
$123$	6.86311	−	3.96242i	0.618826	−	0.357279i
$124$	6.89050	+	1.84630i	0.618785	+	0.165803i
$125$	−10.8767	+	2.58801i	−0.972840	+	0.231478i
$126$	−1.86936	−	3.23783i	−0.166536	−	0.288449i
$127$	−2.54308	−	9.49089i	−0.225661	−	0.842180i	−0.982138	−	0.188160i	$-0.939748\pi$
$127$	−2.54308	−	9.49089i	−0.225661	−	0.842180i	0.756477	−	0.654020i	$-0.226919\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	2.32725			0.204903
$130$	8.05676	−	0.297775i	0.706624	−	0.0261166i
$131$	−2.47841			−0.216539			−0.108270	−	0.994122i	$-0.534531\pi$
$131$	−2.47841			−0.216539			−0.108270	+	0.994122i	$0.534531\pi$
$132$	3.13703	−	5.43350i	0.273044	−	0.472926i
$133$	−2.35219	−	8.77850i	−0.203961	−	0.761193i
$134$	−5.35325	−	9.27211i	−0.462451	−	0.800988i
$135$	0.408973	−	2.19835i	0.0351988	−	0.189204i
$136$	2.09192	+	0.560528i	0.179381	+	0.0480649i
$137$	−2.63445	+	1.52100i	−0.225076	+	0.129948i	−0.608299	−	0.793708i	$-0.708148\pi$
$137$	−2.63445	+	1.52100i	−0.225076	+	0.129948i	0.383222	+	0.923656i	$0.374814\pi$
$138$	6.49222			0.552655
$139$	−4.29170	+	2.47781i	−0.364017	+	0.210165i	−0.670841	−	0.741601i	$-0.734067\pi$
$139$	−4.29170	+	2.47781i	−0.364017	+	0.210165i	0.306824	+	0.951766i	$0.400734\pi$
$140$	−0.650302	−	8.33471i	−0.0549606	−	0.704411i
$141$	−8.55767	+	2.29302i	−0.720686	+	0.193107i
$142$	−9.25218	+	9.25218i	−0.776426	+	0.776426i
$143$	−22.0719	+	4.95603i	−1.84575	+	0.414444i
$144$		−	1.00000i		−	0.0833333i
$145$	0.588120	+	7.53775i	0.0488407	+	0.625976i
$146$	−1.32060	+	2.28735i	−0.109294	+	0.189302i
$147$	6.74027	+	1.80605i	0.555928	+	0.148961i
$148$			2.66281i			0.218882i
$149$	−5.05085	+	18.8500i	−0.413782	+	1.54426i	0.373481	+	0.927638i	$0.378164\pi$
$149$	−5.05085	+	18.8500i	−0.413782	+	1.54426i	−0.787263	+	0.616618i	$0.788503\pi$
$150$	2.94438	−	4.04112i	0.240407	−	0.329956i
$151$	11.0578	+	11.0578i	0.899872	+	0.899872i	0.995424	−	0.0955523i	$-0.0304617\pi$
$151$	11.0578	+	11.0578i	0.899872	+	0.899872i	−0.0955523	+	0.995424i	$0.530462\pi$
$152$	0.629143	−	2.34800i	0.0510303	−	0.190448i
$153$	−2.09192	+	0.560528i	−0.169122	+	0.0453160i
$154$	6.07112	+	22.6577i	0.489225	+	1.82581i
$155$	−15.6821	−	2.91744i	−1.25962	−	0.234334i
$156$	−2.65168	+	2.44307i	−0.212304	+	0.195602i
$157$	−4.65122	−	4.65122i	−0.371208	−	0.371208i	0.496709	−	0.867917i	$-0.334542\pi$
$157$	−4.65122	−	4.65122i	−0.371208	−	0.371208i	−0.867917	+	0.496709i	$0.834542\pi$
$158$	12.1868	+	7.03603i	0.969527	+	0.559757i
$159$	−2.66958	−	1.54128i	−0.211711	−	0.122232i
$160$	0.964013	−	2.01759i	0.0762119	−	0.159505i
$161$	−17.1633	+	17.1633i	−1.35266	+	1.35266i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−6.40658	−	11.0965i	−0.501802	−	0.869147i	−0.999998	−	0.00208226i	$-0.999337\pi$
$163$	−6.40658	−	11.0965i	−0.501802	−	0.869147i	0.498196	−	0.867065i	$-0.333996\pi$
$164$	−5.60371	+	5.60371i	−0.437576	+	0.437576i
$165$	−6.04828	+	12.6585i	−0.470858	+	0.985464i
$166$	1.94010	+	1.12012i	0.150581	+	0.0869380i
$167$	−7.97042	−	4.60173i	−0.616770	−	0.356092i	0.158840	−	0.987304i	$-0.449224\pi$
$167$	−7.97042	−	4.60173i	−0.616770	−	0.356092i	−0.775610	+	0.631212i	$0.782558\pi$
$168$	2.64368	+	2.64368i	0.203964	+	0.203964i
$169$	12.9565	+	1.06280i	0.996653	+	0.0817542i
$170$	−4.76100	−	0.885720i	−0.365152	−	0.0679316i
$171$	0.629143	+	2.34800i	0.0481118	+	0.179556i
$172$	−2.24795	+	0.602337i	−0.171405	+	0.0459277i
$173$	−0.657298	+	2.45307i	−0.0499734	+	0.186503i	−0.986401	−	0.164358i	$-0.947445\pi$
$173$	−0.657298	+	2.45307i	−0.0499734	+	0.186503i	0.936427	+	0.350862i	$0.114111\pi$
$174$	−2.39089	−	2.39089i	−0.181253	−	0.181253i
$175$	2.89943	+	18.4674i	0.219176	+	1.39600i
$176$	−1.62385	+	6.06028i	−0.122402	+	0.456811i
$177$		−	3.15202i		−	0.236920i
$178$	12.5183	+	3.35427i	0.938288	+	0.251413i
$179$	−12.6678	+	21.9412i	−0.946833	+	1.63996i	−0.194795	+	0.980844i	$0.562404\pi$
$179$	−12.6678	+	21.9412i	−0.946833	+	1.63996i	−0.752038	+	0.659120i	$0.770929\pi$
$180$	0.173937	+	2.22929i	0.0129645	+	0.166162i
$181$		−	12.6074i		−	0.937103i	−0.883436	−	0.468551i	$-0.844776\pi$
$181$		−	12.6074i		−	0.937103i	0.883436	−	0.468551i	$-0.155224\pi$
$182$	0.551491	−	13.4689i	0.0408792	−	0.998379i
$183$	9.43520	−	9.43520i	0.697470	−	0.697470i
$184$	−6.27100	+	1.68031i	−0.462305	+	0.123874i
$185$	−0.463161	−	5.93619i	−0.0340523	−	0.436437i
$186$	6.17785	−	3.56679i	0.452982	−	0.261529i
$187$	13.5878			0.993642
$188$	7.67260	−	4.42978i	0.559582	−	0.323075i
$189$	−3.61133	−	0.967653i	−0.262685	−	0.0703864i
$190$	−0.994142	+	5.34380i	−0.0721226	+	0.387680i
$191$	12.5552	+	21.7462i	0.908461	+	1.57350i	0.816203	+	0.577766i	$0.196075\pi$
$191$	12.5552	+	21.7462i	0.908461	+	1.57350i	0.0922583	+	0.995735i	$0.470591\pi$
$192$	0.258819	+	0.965926i	0.0186787	+	0.0697097i
$193$	−7.86874	+	13.6291i	−0.566404	+	0.981041i	0.430513	+	0.902584i	$0.358333\pi$
$193$	−7.86874	+	13.6291i	−0.566404	+	0.981041i	−0.996918	+	0.0784570i	$0.975001\pi$
$194$	3.50248			0.251463
$195$	5.48643	−	5.90755i	0.392891	−	0.423048i
$196$	−6.97804			−0.498432
$197$	−3.57535	+	6.19269i	−0.254733	+	0.441211i	−0.964823	−	0.262900i	$-0.915321\pi$
$197$	−3.57535	+	6.19269i	−0.254733	+	0.441211i	0.710090	+	0.704111i	$0.248654\pi$
$198$	−1.62385	−	6.06028i	−0.115402	−	0.430686i
$199$	4.83767	+	8.37910i	0.342934	+	0.593978i	0.984976	−	0.172691i	$-0.0552461\pi$
$199$	4.83767	+	8.37910i	0.342934	+	0.593978i	−0.642042	+	0.766669i	$0.721913\pi$
$200$	−1.79813	+	4.66548i	−0.127147	+	0.329899i
$201$	−10.3417	−	2.77105i	−0.729447	−	0.195455i
$202$	−3.77878	+	2.18168i	−0.265874	+	0.153502i
$203$	12.6415			0.887257
$204$	1.87556	−	1.08286i	0.131316	−	0.0758152i
$205$	11.5176	−	13.4670i	0.804425	−	0.940576i
$206$	−1.13234	+	0.303408i	−0.0788936	+	0.0211395i
$207$	4.59069	−	4.59069i	0.319075	−	0.319075i
$208$	1.92901	−	3.04613i	0.133753	−	0.211211i
$209$		−	15.2512i		−	1.05494i
$210$	−6.35336	−	5.43369i	−0.438424	−	0.374961i
$211$	5.84544	−	10.1246i	0.402417	−	0.697006i	−0.591600	−	0.806231i	$-0.701504\pi$
$211$	5.84544	−	10.1246i	0.402417	−	0.697006i	0.994017	+	0.109225i	$0.0348369\pi$
$212$	2.97753	+	0.797827i	0.204498	+	0.0547950i
$213$			13.0846i			0.896540i
$214$	0.181731	−	0.678228i	0.0124228	−	0.0463627i
$215$	4.90657	−	1.73379i	0.334625	−	0.118243i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−6.90282	+	25.7617i	−0.468594	+	1.74882i
$218$	4.66803	−	1.25080i	0.316159	−	0.0847146i
$219$	0.683594	+	2.55121i	0.0461930	+	0.172395i
$220$	2.56593	−	13.7926i	0.172995	−	0.929897i
$221$	−7.45353	−	2.32790i	−0.501379	−	0.156591i
$222$	1.88289	+	1.88289i	0.126371	+	0.126371i
$223$	−1.45640	−	0.840855i	−0.0975280	−	0.0563078i	0.450443	−	0.892805i	$-0.351266\pi$
$223$	−1.45640	−	0.840855i	−0.0975280	−	0.0563078i	−0.547971	+	0.836498i	$0.684599\pi$
$224$	−3.23783	−	1.86936i	−0.216337	−	0.124902i
$225$	−0.775513	−	4.93949i	−0.0517009	−	0.329299i
$226$	−4.20031	+	4.20031i	−0.279401	+	0.279401i
$227$	−4.05722	−	7.02731i	−0.269287	−	0.466419i	0.699391	−	0.714739i	$-0.253455\pi$
$227$	−4.05722	−	7.02731i	−0.269287	−	0.466419i	−0.968678	+	0.248321i	$0.920121\pi$
$228$	−1.21541	−	2.10515i	−0.0804926	−	0.139417i
$229$	17.2603	−	17.2603i	1.14060	−	1.14060i	0.152254	−	0.988341i	$-0.451347\pi$
$229$	17.2603	−	17.2603i	1.14060	−	1.14060i	0.988341	−	0.152254i	$-0.0486532\pi$
$230$	13.6876	−	4.83666i	0.902536	−	0.318920i
$231$	20.3144	+	11.7285i	1.33659	+	0.771679i
$232$	2.92823	+	1.69061i	0.192248	+	0.110994i
$233$	1.35599	+	1.35599i	0.0888341	+	0.0888341i	0.750127	−	0.661293i	$-0.229992\pi$
$233$	1.35599	+	1.35599i	0.0888341	+	0.0888341i	−0.661293	+	0.750127i	$0.729992\pi$
$234$	−0.147508	+	3.60253i	−0.00964289	+	0.235505i
$235$	−16.3340	+	11.2098i	−1.06551	+	0.731248i
$236$	0.815803	+	3.04462i	0.0531043	+	0.198188i
$237$	13.5926	−	3.64212i	0.882933	−	0.236581i
$238$	−2.09566	+	7.82111i	−0.135841	+	0.506967i
$239$	−8.41434	−	8.41434i	−0.544278	−	0.544278i	0.380502	−	0.924780i	$-0.375751\pi$
$239$	−8.41434	−	8.41434i	−0.544278	−	0.544278i	−0.924780	+	0.380502i	$0.875751\pi$
$240$	−0.744994	−	2.10831i	−0.0480891	−	0.136091i
$241$	1.86314	−	6.95332i	0.120015	−	0.447903i	−0.879598	−	0.475718i	$-0.842188\pi$
$241$	1.86314	−	6.95332i	0.120015	−	0.447903i	0.999613	+	0.0278153i	$0.00885502\pi$
$242$			28.3639i			1.82330i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	−6.67169	+	11.5557i	−0.427111	+	0.739779i
$245$	15.5561	−	1.21374i	0.993843	−	0.0775430i
$246$			7.92484i			0.505269i
$247$	−2.61286	+	8.36593i	−0.166252	+	0.532311i
$248$	−5.04420	+	5.04420i	−0.320307	+	0.320307i
$249$	2.16390	−	0.579816i	0.137132	−	0.0367443i
$250$	3.19706	−	10.7135i	0.202200	−	0.677580i
$251$	16.3248	−	9.42513i	1.03041	−	0.594909i	0.113310	−	0.993560i	$-0.463855\pi$
$251$	16.3248	−	9.42513i	1.03041	−	0.594909i	0.917103	+	0.398651i	$0.130521\pi$
$252$	3.73872			0.235517
$253$	−35.2755	+	20.3663i	−2.21775	+	1.28042i
$254$	9.49089	+	2.54308i	0.595511	+	0.159567i
$255$	−3.99283	+	2.74024i	−0.250041	+	0.171600i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.533702	−	1.99180i	−0.0332914	−	0.124245i	0.947280	−	0.320406i	$-0.103819\pi$
$257$	−0.533702	−	1.99180i	−0.0332914	−	0.124245i	−0.980572	+	0.196161i	$0.937153\pi$
$258$	−1.16362	+	2.01546i	−0.0724441	+	0.125477i
$259$	−9.95551			−0.618605
$260$	−3.77050	+	7.12624i	−0.233836	+	0.441951i
$261$	−3.38123			−0.209293
$262$	1.23920	−	2.14636i	0.0765582	−	0.132603i
$263$	5.40492	+	20.1714i	0.333282	+	1.24382i	0.905720	+	0.423877i	$0.139331\pi$
$263$	5.40492	+	20.1714i	0.333282	+	1.24382i	−0.572438	+	0.819948i	$0.694002\pi$
$264$	3.13703	+	5.43350i	0.193071	+	0.334409i
$265$	−6.77656	−	1.26069i	−0.416281	−	0.0774434i
$266$	8.77850	+	2.35219i	0.538244	+	0.144222i
$267$	11.2236	−	6.47996i	0.686874	−	0.396567i
$268$	10.7065			0.654004
$269$	−21.4891	+	12.4067i	−1.31021	+	0.756451i	−0.982131	−	0.188198i	$-0.939735\pi$
$269$	−21.4891	+	12.4067i	−1.31021	+	0.756451i	−0.328081	+	0.944650i	$0.606402\pi$
$270$	1.69934	+	1.45336i	0.103419	+	0.0884484i
$271$	3.46764	−	0.929152i	0.210644	−	0.0564420i	−0.151954	−	0.988388i	$-0.548556\pi$
$271$	3.46764	−	0.929152i	0.210644	−	0.0564420i	0.362598	+	0.931946i	$0.381890\pi$
$272$	−1.53139	+	1.53139i	−0.0928543	+	0.0928543i
$273$	−9.13397	−	9.91389i	−0.552813	−	0.600016i
$274$		−	3.04200i		−	0.183774i
$275$	−3.32116	+	31.1940i	−0.200273	+	1.88107i
$276$	−3.24611	+	5.62243i	−0.195393	+	0.338430i
$277$	14.9207	+	3.99798i	0.896496	+	0.240215i	0.677511	−	0.735513i	$-0.263059\pi$
$277$	14.9207	+	3.99798i	0.896496	+	0.240215i	0.218985	+	0.975728i	$0.429725\pi$
$278$		−	4.95562i		−	0.297219i
$279$	1.84630	−	6.89050i	0.110535	−	0.412523i
$280$	7.54322	+	3.60418i	0.450794	+	0.215391i
$281$	−14.0822	−	14.0822i	−0.840072	−	0.840072i	0.148796	−	0.988868i	$-0.452460\pi$
$281$	−14.0822	−	14.0822i	−0.840072	−	0.840072i	−0.988868	+	0.148796i	$0.952460\pi$
$282$	2.29302	−	8.55767i	0.136547	−	0.509602i
$283$	−8.18213	+	2.19240i	−0.486377	+	0.130324i	−0.493671	−	0.869649i	$-0.664345\pi$
$283$	−8.18213	+	2.19240i	−0.486377	+	0.130324i	0.00729329	+	0.999973i	$0.497678\pi$
$284$	−3.38653	−	12.6387i	−0.200954	−	0.749970i
$285$	3.07567	+	4.48160i	0.182187	+	0.265467i
$286$	6.74391	−	21.5928i	0.398776	−	1.27681i
$287$	−20.9507	−	20.9507i	−1.23668	−	1.23668i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	−10.6605	−	6.15484i	−0.627088	−	0.362049i
$290$	−6.82194	−	3.25955i	−0.400598	−	0.191407i
$291$	2.47662	−	2.47662i	0.145182	−	0.145182i
$292$	−1.32060	−	2.28735i	−0.0772824	−	0.133857i
$293$	−8.85612	−	15.3392i	−0.517380	−	0.896128i	−0.999796	−	0.0201862i	$-0.993574\pi$
$293$	−8.85612	−	15.3392i	−0.517380	−	0.896128i	0.482416	−	0.875942i	$-0.339759\pi$
$294$	−4.93422	+	4.93422i	−0.287770	+	0.287770i
$295$	−2.34824	−	6.64545i	−0.136720	−	0.386913i
$296$	−2.30606	−	1.33141i	−0.134037	−	0.0773864i
$297$	−5.43350	−	3.13703i	−0.315284	−	0.182029i
$298$	−13.7992	−	13.7992i	−0.799365	−	0.799365i
$299$	22.8394	−	5.12835i	1.32083	−	0.296580i
$300$	2.02752	+	4.57047i	0.117059	+	0.263876i
$301$	−2.25197	−	8.40446i	−0.129801	−	0.484425i
$302$	−15.1053	+	4.04744i	−0.869210	+	0.232904i
$303$	−1.12932	+	4.21468i	−0.0648777	+	0.242127i
$304$	1.71885	+	1.71885i	0.0985829	+	0.0985829i
$305$	12.8632	−	26.9215i	0.736544	−	1.54152i
$306$	0.560528	−	2.09192i	0.0320433	−	0.119587i
$307$			7.99719i			0.456424i	0.973612	+	0.228212i	$0.0732879\pi$
$307$			7.99719i			0.456424i	−0.973612	+	0.228212i	$0.926712\pi$
$308$	−22.6577	−	6.07112i	−1.29104	−	0.345934i
$309$	−0.586140	+	1.01522i	−0.0333443	+	0.0577541i
$310$	10.3676	−	12.1224i	0.588841	−	0.688504i
$311$		−	9.83044i		−	0.557433i	−0.960373	−	0.278716i	$-0.910091\pi$
$311$		−	9.83044i		−	0.557433i	0.960373	−	0.278716i	$-0.0899090\pi$
$312$	−0.789922	−	3.51796i	−0.0447205	−	0.199165i
$313$	20.6653	−	20.6653i	1.16807	−	1.16807i	0.185409	−	0.982661i	$-0.440639\pi$
$313$	20.6653	−	20.6653i	1.16807	−	1.16807i	0.982661	−	0.185409i	$-0.0593611\pi$
$314$	6.35369	−	1.70247i	0.358559	−	0.0960757i
$315$	−8.33471	+	0.650302i	−0.469608	+	0.0366404i
$316$	−12.1868	+	7.03603i	−0.685559	+	0.395808i
$317$	−14.5901			−0.819459			−0.409730	−	0.912207i	$-0.634377\pi$
$317$	−14.5901			−0.819459			−0.409730	+	0.912207i	$0.634377\pi$
$318$	2.66958	−	1.54128i	0.149703	−	0.0864308i
$319$	20.4912	+	5.49060i	1.14729	+	0.307415i
$320$	1.26528	+	1.84366i	0.0707313	+	0.103063i
$321$	−0.351076	−	0.608082i	−0.0195952	−	0.0339398i
$322$	−6.28221	−	23.4455i	−0.350094	−	1.30657i
$323$	2.63224	−	4.55917i	0.146462	−	0.253679i
$324$	−1.00000			−0.0555556
$325$	7.16603	−	16.5423i	0.397500	−	0.917602i
$326$	12.8132			0.709655
$327$	2.41635	−	4.18524i	0.133625	−	0.231444i
$328$	−2.05110	−	7.65481i	−0.113253	−	0.422666i
$329$	16.5617	+	28.6857i	0.913076	+	1.58149i
$330$	−7.93845	−	11.5672i	−0.436998	−	0.636755i
$331$	−10.2177	−	2.73783i	−0.561616	−	0.150485i	−0.0331673	−	0.999450i	$-0.510559\pi$
$331$	−10.2177	−	2.73783i	−0.561616	−	0.150485i	−0.528449	+	0.848965i	$0.677226\pi$
$332$	−1.94010	+	1.12012i	−0.106477	+	0.0614745i
$333$	2.66281			0.145921
$334$	7.97042	−	4.60173i	0.436122	−	0.251795i
$335$	−23.8679	+	1.86226i	−1.30405	+	0.101746i
$336$	−3.61133	+	0.967653i	−0.197014	+	0.0527898i
$337$	16.9452	−	16.9452i	0.923062	−	0.923062i	−0.0741830	−	0.997245i	$-0.523635\pi$
$337$	16.9452	−	16.9452i	0.923062	−	0.923062i	0.997245	+	0.0741830i	$0.0236349\pi$
$338$	−7.39866	+	10.6892i	−0.402434	+	0.581418i
$339$			5.94014i			0.322624i
$340$	3.14756	−	3.68029i	0.170700	−	0.199592i
$341$	−22.3783	+	38.7603i	−1.21185	+	2.09899i
$342$	−2.34800	−	0.629143i	−0.126965	−	0.0340202i
$343$			0.0820839i			0.00443212i
$344$	0.602337	−	2.24795i	0.0324758	−	0.121201i
$345$	6.25858	−	13.0987i	0.336951	−	0.705208i
$346$	−1.79577	−	1.79577i	−0.0965413	−	0.0965413i
$347$	9.26376	−	34.5728i	0.497305	−	1.85597i	−0.0194133	−	0.999812i	$-0.506180\pi$
$347$	9.26376	−	34.5728i	0.497305	−	1.85597i	0.516718	−	0.856156i	$-0.327154\pi$
$348$	3.26601	−	0.875126i	0.175077	−	0.0469117i
$349$	−2.61785	−	9.76996i	−0.140130	−	0.522974i	−0.999924	−	0.0123320i	$-0.996075\pi$
$349$	−2.61785	−	9.76996i	−0.140130	−	0.522974i	0.859794	−	0.510642i	$-0.170592\pi$
$350$	−17.4429	−	6.72272i	−0.932364	−	0.359344i
$351$	2.44307	+	2.65168i	0.130402	+	0.141536i
$352$	−4.43644	−	4.43644i	−0.236463	−	0.236463i
$353$	7.34797	+	4.24235i	0.391093	+	0.225798i	0.682634	−	0.730761i	$-0.260834\pi$
$353$	7.34797	+	4.24235i	0.391093	+	0.225798i	−0.291540	+	0.956558i	$0.594168\pi$
$354$	2.72973	+	1.57601i	0.145084	+	0.0837640i
$355$	9.74792	+	27.5864i	0.517366	+	1.46413i
$356$	−9.16404	+	9.16404i	−0.485693	+	0.485693i
$357$	4.04850	+	7.01222i	0.214270	+	0.371126i
$358$	−12.6678	−	21.9412i	−0.669512	−	1.15963i
$359$	17.2160	−	17.2160i	0.908627	−	0.908627i	−0.0875342	−	0.996162i	$-0.527899\pi$
$359$	17.2160	−	17.2160i	0.908627	−	0.908627i	0.996162	+	0.0875342i	$0.0278987\pi$
$360$	−2.01759	−	0.964013i	−0.106336	−	0.0508079i
$361$	11.3372	+	6.54555i	0.596696	+	0.344503i
$362$	10.9184	+	6.30371i	0.573856	+	0.331316i
$363$	20.0563	+	20.0563i	1.05268	+	1.05268i
$364$	11.3886	+	7.21204i	0.596927	+	0.378014i
$365$	3.34186	+	4.86947i	0.174921	+	0.254880i
$366$	3.45352	+	12.8887i	0.180519	+	0.673704i
$367$	−23.9130	+	6.40747i	−1.24825	+	0.334467i	−0.821659	−	0.569979i	$-0.806951\pi$
$367$	−23.9130	+	6.40747i	−1.24825	+	0.334467i	−0.426588	+	0.904446i	$0.640285\pi$
$368$	1.68031	−	6.27100i	0.0875922	−	0.326899i
$369$	5.60371	+	5.60371i	0.291717	+	0.291717i
$370$	5.37247	+	2.56698i	0.279301	+	0.133451i
$371$	−2.98285	+	11.1322i	−0.154862	+	0.577953i
$372$			7.13357i			0.369858i
$373$	9.62574	+	2.57921i	0.498402	+	0.133546i	0.499258	−	0.866453i	$-0.333606\pi$
$373$	9.62574	+	2.57921i	0.498402	+	0.133546i	−0.000856279		1.00000i	$0.500273\pi$
$374$	−6.79392	+	11.7674i	−0.351305	+	0.608479i
$375$	−5.31491	−	9.83624i	−0.274461	−	0.507941i
$376$			8.85955i			0.456897i
$377$	−10.2997	−	6.52243i	−0.530459	−	0.335922i
$378$	2.64368	−	2.64368i	0.135976	−	0.135976i
$379$	−10.0848	+	2.70222i	−0.518023	+	0.138804i	−0.508352	−	0.861149i	$-0.669745\pi$
$379$	−10.0848	+	2.70222i	−0.518023	+	0.138804i	−0.00967124	+	0.999953i	$0.503078\pi$
$380$	−4.13080	−	3.53285i	−0.211905	−	0.181231i
$381$	8.50930	−	4.91284i	0.435944	−	0.251693i
$382$	−25.1104			−1.28476
$383$	28.1313	−	16.2416i	1.43744	−	0.829907i	0.439770	−	0.898111i	$-0.355060\pi$
$383$	28.1313	−	16.2416i	1.43744	−	0.829907i	0.997671	+	0.0682035i	$0.0217267\pi$
$384$	−0.965926	−	0.258819i	−0.0492922	−	0.0132078i
$385$	51.5667	+	9.59328i	2.62808	+	0.488919i
$386$	−7.86874	−	13.6291i	−0.400508	−	0.693701i
$387$	0.602337	+	2.24795i	0.0306185	+	0.114270i
$388$	−1.75124	+	3.03323i	−0.0889056	+	0.153989i
$389$	1.54320			0.0782435			0.0391218	−	0.999234i	$-0.487544\pi$
$389$	1.54320			0.0782435			0.0391218	+	0.999234i	$0.487544\pi$
$390$	2.37287	+	7.70516i	0.120155	+	0.390166i
$391$	−14.0603			−0.711060
$392$	3.48902	−	6.04316i	0.176222	−	0.305226i
$393$	−0.641459	−	2.39396i	−0.0323573	−	0.120759i
$394$	−3.57535	−	6.19269i	−0.180123	−	0.311983i
$395$	25.9440	−	17.8051i	1.30539	−	0.895872i
$396$	6.06028	+	1.62385i	0.304541	+	0.0816014i
$397$	−30.4129	+	17.5589i	−1.52638	+	0.881255i	−0.526869	+	0.849947i	$0.676634\pi$
$397$	−30.4129	+	17.5589i	−1.52638	+	0.881255i	−0.999510	+	0.0313085i	$0.990033\pi$
$398$	−9.67535			−0.484981
$399$	7.87059	−	4.54409i	0.394022	−	0.227489i
$400$	−3.14136	−	3.88997i	−0.157068	−	0.194498i
$401$	−11.6976	+	3.13438i	−0.584153	+	0.156523i	−0.538779	−	0.842447i	$-0.681114\pi$
$401$	−11.6976	+	3.13438i	−0.584153	+	0.156523i	−0.0453732	+	0.998970i	$0.514448\pi$
$402$	7.57065	−	7.57065i	0.377589	−	0.377589i
$403$	18.9159	−	17.4278i	0.942270	−	0.868142i
$404$		−	4.36336i		−	0.217085i
$405$	2.22929	−	0.173937i	0.110774	−	0.00864300i
$406$	−6.32073	+	10.9478i	−0.313693	+	0.543332i
$407$	−16.1374	−	4.32400i	−0.799901	−	0.214333i
$408$			2.16572i			0.107219i
$409$	3.34657	−	12.4896i	0.165477	−	0.617569i	−0.832502	−	0.554023i	$-0.813092\pi$
$409$	3.34657	−	12.4896i	0.165477	−	0.617569i	0.997979	−	0.0635468i	$-0.0202412\pi$
$410$	5.90396	+	16.7080i	0.291576	+	0.825152i
$411$	−2.15102	−	2.15102i	−0.106102	−	0.106102i
$412$	0.303408	−	1.13234i	0.0149479	−	0.0557862i
$413$	−11.3830	+	3.05006i	−0.560120	+	0.150084i
$414$	1.68031	+	6.27100i	0.0825828	+	0.308203i
$415$	4.13023	−	2.83453i	0.202745	−	0.139141i
$416$	1.67352	+	3.19364i	0.0820511	+	0.156581i
$417$	−3.50416	−	3.50416i	−0.171599	−	0.171599i
$418$	13.2079	+	7.62558i	0.646019	+	0.372979i
$419$	29.4352	+	16.9944i	1.43800	+	0.830232i	0.997711	−	0.0676215i	$-0.0215410\pi$
$419$	29.4352	+	16.9944i	1.43800	+	0.830232i	0.440294	+	0.897854i	$0.354874\pi$
$420$	7.88240	−	2.78532i	0.384622	−	0.135910i
$421$	−13.6957	+	13.6957i	−0.667488	+	0.667488i	−0.957134	−	0.289646i	$-0.906462\pi$
$421$	−13.6957	+	13.6957i	−0.667488	+	0.667488i	0.289646	+	0.957134i	$0.406462\pi$
$422$	5.84544	+	10.1246i	0.284552	+	0.492858i
$423$	−4.42978	−	7.67260i	−0.215383	−	0.373054i
$424$	−2.17970	+	2.17970i	−0.105856	+	0.105856i
$425$	−6.37669	+	8.75191i	−0.309315	+	0.424530i
$426$	−11.3316	−	6.54228i	−0.549016	−	0.316975i
$427$	−43.2036	−	24.9436i	−2.09077	−	1.20711i
$428$	0.496497	+	0.496497i	0.0239991	+	0.0239991i
$429$	−10.4998	−	20.0371i	−0.506934	−	0.967401i
$430$	−0.951783	+	5.11611i	−0.0458990	+	0.246721i
$431$	6.77487	+	25.2842i	0.326334	+	1.21789i	0.912964	+	0.408040i	$0.133788\pi$
$431$	6.77487	+	25.2842i	0.326334	+	1.21789i	−0.586630	+	0.809855i	$0.699546\pi$
$432$	0.965926	−	0.258819i	0.0464731	−	0.0124524i
$433$	0.696777	−	2.60041i	0.0334850	−	0.124968i	−0.947160	−	0.320761i	$-0.896061\pi$
$433$	0.696777	−	2.60041i	0.0334850	−	0.124968i	0.980645	+	0.195793i	$0.0627281\pi$
$434$	−18.8588	−	18.8588i	−0.905254	−	0.905254i
$435$	−7.12869	+	2.51899i	−0.341794	+	0.120776i
$436$	−1.25080	+	4.66803i	−0.0599022	+	0.223558i
$437$			15.7814i			0.754929i
$438$	−2.55121	−	0.683594i	−0.121901	−	0.0326634i
$439$	−2.71924	+	4.70986i	−0.129782	+	0.224789i	−0.923592	−	0.383377i	$-0.874761\pi$
$439$	−2.71924	+	4.70986i	−0.129782	+	0.224789i	0.793810	+	0.608166i	$0.208094\pi$
$440$	10.6618	+	9.11845i	0.508280	+	0.434705i
$441$			6.97804i			0.332288i
$442$	5.74278	−	5.29100i	0.273156	−	0.251667i
$443$	15.6158	−	15.6158i	0.741928	−	0.741928i	−0.231021	−	0.972949i	$-0.574206\pi$
$443$	15.6158	−	15.6158i	0.741928	−	0.741928i	0.972949	+	0.231021i	$0.0742065\pi$
$444$	−2.57208	+	0.689186i	−0.122065	+	0.0327073i
$445$	18.8354	−	22.0233i	0.892882	−	1.04400i
$446$	1.45640	−	0.840855i	0.0689627	−	0.0398156i
$447$	−19.5150			−0.923028
$448$	3.23783	−	1.86936i	0.152973	−	0.0883190i
$449$	0.941399	+	0.252247i	0.0444274	+	0.0119043i	0.280964	−	0.959718i	$-0.409346\pi$
$449$	0.941399	+	0.252247i	0.0444274	+	0.0119043i	−0.236537	+	0.971623i	$0.576012\pi$
$450$	4.66548	+	1.79813i	0.219933	+	0.0847648i
$451$	−24.8605	−	43.0596i	−1.17063	−	2.02760i
$452$	−1.53742	−	5.73773i	−0.0723142	−	0.269880i
$453$	−7.81906	+	13.5430i	−0.367371	+	0.636306i
$454$	8.11444			0.380829
$455$	−26.6430	−	14.0968i	−1.24905	−	0.660870i
$456$	2.43082			0.113834
$457$	2.19918	−	3.80909i	0.102873	−	0.178181i	−0.809994	−	0.586438i	$-0.800530\pi$
$457$	2.19918	−	3.80909i	0.102873	−	0.178181i	0.912867	+	0.408256i	$0.133863\pi$
$458$	6.31772	+	23.5781i	0.295208	+	1.10173i
$459$	−1.08286	−	1.87556i	−0.0505435	−	0.0875439i
$460$	−2.65514	+	14.2722i	−0.123797	+	0.665443i
$461$	−8.41586	−	2.25502i	−0.391966	−	0.105027i	0.0574528	−	0.998348i	$-0.481702\pi$
$461$	−8.41586	−	2.25502i	−0.391966	−	0.105027i	−0.449419	+	0.893321i	$0.648369\pi$
$462$	−20.3144	+	11.7285i	−0.945109	+	0.545659i
$463$	−37.4495			−1.74043			−0.870214	−	0.492674i	$-0.836019\pi$
$463$	−37.4495			−1.74043			−0.870214	+	0.492674i	$0.836019\pi$
$464$	−2.92823	+	1.69061i	−0.135940	+	0.0784848i
$465$	−1.24079	−	15.9028i	−0.0575403	−	0.737475i
$466$	−1.85232	+	0.496328i	−0.0858071	+	0.0229920i
$467$	10.7112	−	10.7112i	0.495656	−	0.495656i	−0.414427	−	0.910083i	$-0.636018\pi$
$467$	10.7112	−	10.7112i	0.495656	−	0.495656i	0.910083	+	0.414427i	$0.136018\pi$
$468$	−3.04613	−	1.92901i	−0.140807	−	0.0891686i
$469$			40.0287i			1.84835i
$470$	−1.54100	−	19.7505i	−0.0710812	−	0.911024i
$471$	3.28891	−	5.69656i	0.151545	−	0.262484i
$472$	−3.04462	−	0.815803i	−0.140140	−	0.0375504i
$473$		−	14.6013i		−	0.671370i
$474$	−3.64212	+	13.5926i	−0.167288	+	0.624328i
$475$	9.82325	+	7.15726i	0.450721	+	0.328398i
$476$	−5.72545	−	5.72545i	−0.262426	−	0.262426i
$477$	0.797827	−	2.97753i	0.0365300	−	0.136332i
$478$	11.4942	−	3.07986i	0.525732	−	0.140870i
$479$	8.97663	+	33.5012i	0.410152	+	1.53071i	0.794351	+	0.607459i	$0.207811\pi$
$479$	8.97663	+	33.5012i	0.410152	+	1.53071i	−0.384198	+	0.923251i	$0.625522\pi$
$480$	2.19835	+	0.408973i	0.100340	+	0.0186670i
$481$	8.11127	+	5.13659i	0.369842	+	0.234209i
$482$	5.09018	+	5.09018i	0.231851	+	0.231851i
$483$	−21.0207	−	12.1363i	−0.956475	−	0.552221i
$484$	−24.5639	−	14.1820i	−1.11654	−	0.644635i
$485$	3.37643	−	7.06657i	0.153316	−	0.320876i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	16.1881	+	28.0386i	0.733554	+	1.27055i	0.955355	+	0.295460i	$0.0954730\pi$
$487$	16.1881	+	28.0386i	0.733554	+	1.27055i	−0.221801	+	0.975092i	$0.571194\pi$
$488$	−6.67169	−	11.5557i	−0.302013	−	0.523103i
$489$	9.06027	−	9.06027i	0.409720	−	0.409720i
$490$	−6.72692	+	14.0789i	−0.303891	+	0.636018i
$491$	−4.60222	−	2.65709i	−0.207695	−	0.119913i	0.392545	−	0.919733i	$-0.371595\pi$
$491$	−4.60222	−	2.65709i	−0.207695	−	0.119913i	−0.600240	+	0.799820i	$0.704928\pi$
$492$	−6.86311	−	3.96242i	−0.309413	−	0.178640i
$493$	5.17799	+	5.17799i	0.233205	+	0.233205i
$494$	−5.93868	−	6.44576i	−0.267194	−	0.290009i
$495$	−13.7926	−	2.56593i	−0.619931	−	0.115330i
$496$	−1.84630	−	6.89050i	−0.0829015	−	0.309393i
$497$	47.2527	−	12.6613i	2.11957	−	0.567937i
$498$	−0.579816	+	2.16390i	−0.0259822	+	0.0969668i
$499$	24.6981	+	24.6981i	1.10564	+	1.10564i	0.993717	+	0.111922i	$0.0357007\pi$
$499$	24.6981	+	24.6981i	1.10564	+	1.10564i	0.111922	+	0.993717i	$0.464299\pi$
$500$	7.67962	+	8.12548i	0.343443	+	0.363383i
$501$	2.38203	−	8.88985i	0.106421	−	0.397169i
$502$			18.8503i			0.841328i
$503$	4.16280	+	1.11542i	0.185610	+	0.0497340i	0.350427	−	0.936590i	$-0.386037\pi$
$503$	4.16280	+	1.11542i	0.185610	+	0.0497340i	−0.164817	+	0.986324i	$0.552703\pi$
$504$	−1.86936	+	3.23783i	−0.0832680	+	0.144224i
$505$	0.758949	+	9.72720i	0.0337728	+	0.432855i
$506$		−	40.7326i		−	1.81079i
$507$	2.32679	+	12.7901i	0.103337	+	0.568027i
$508$	−6.94781	+	6.94781i	−0.308259	+	0.308259i
$509$	−16.9265	+	4.53544i	−0.750254	+	0.201030i	−0.613631	−	0.789593i	$-0.710292\pi$
$509$	−16.9265	+	4.53544i	−0.750254	+	0.201030i	−0.136623	+	0.990623i	$0.543625\pi$
$510$	−0.376698	−	4.82801i	−0.0166805	−	0.213788i
$511$	8.55177	−	4.93737i	0.378308	−	0.218416i
$512$	1.00000			0.0441942
$513$	−2.10515	+	1.21541i	−0.0929449	+	0.0536617i
$514$	1.99180	+	0.533702i	0.0878546	+	0.0235406i
$515$	−0.479431	+	2.57708i	−0.0211263	+	0.113560i
$516$	−1.16362	−	2.01546i	−0.0512257	−	0.0887256i
$517$	14.3866	+	53.6914i	0.632721	+	2.36135i
$518$	4.97776	−	8.62173i	0.218710	−	0.378817i
$519$	−2.53960			−0.111476
$520$	−4.28626	−	6.82847i	−0.187965	−	0.299448i
$521$	9.82425			0.430408			0.215204	−	0.976569i	$-0.430958\pi$
$521$	9.82425			0.430408			0.215204	+	0.976569i	$0.430958\pi$
$522$	1.69061	−	2.92823i	0.0739961	−	0.128165i
$523$	6.49113	+	24.2252i	0.283837	+	1.05930i	0.949685	+	0.313207i	$0.101403\pi$
$523$	6.49113	+	24.2252i	0.283837	+	1.05930i	−0.665848	+	0.746088i	$0.731930\pi$
$524$	1.23920	+	2.14636i	0.0541349	+	0.0937643i
$525$	−17.0877	+	7.58034i	−0.745768	+	0.330833i
$526$	−20.1714	−	5.40492i	−0.879517	−	0.235666i
$527$	−13.3795	+	7.72464i	−0.582819	+	0.336491i
$528$	−6.27407			−0.273044
$529$	16.5835	−	9.57447i	0.721020	−	0.416281i
$530$	4.48006	−	5.23833i	0.194602	−	0.227538i
$531$	3.04462	−	0.815803i	0.132125	−	0.0354028i
$532$	−6.42631	+	6.42631i	−0.278616	+	0.278616i
$533$	6.26001	+	27.8792i	0.271151	+	1.20758i
$534$			12.9599i			0.560830i
$535$	−1.19320	−	1.02048i	−0.0515864	−	0.0441191i
$536$	−5.35325	+	9.27211i	−0.231225	+	0.400494i
$537$	−24.4722	−	6.55732i	−1.05606	−	0.282969i
$538$		−	24.8135i		−	1.06978i
$539$	11.3313	−	42.2889i	0.488073	−	1.82151i
$540$	−2.10831	+	0.744994i	−0.0907274	+	0.0320594i
$541$	9.69896	+	9.69896i	0.416991	+	0.416991i	0.884165	−	0.467174i	$-0.154728\pi$
$541$	9.69896	+	9.69896i	0.416991	+	0.416991i	−0.467174	+	0.884165i	$0.654728\pi$
$542$	−0.929152	+	3.46764i	−0.0399105	+	0.148948i
$543$	12.1778	−	3.26304i	0.522601	−	0.140031i
$544$	−0.560528	−	2.09192i	−0.0240325	−	0.0896904i
$545$	1.97645	−	10.6240i	0.0846616	−	0.455081i
$546$	13.1527	−	2.95330i	0.562882	−	0.126390i
$547$	−13.3292	−	13.3292i	−0.569917	−	0.569917i	0.362188	−	0.932105i	$-0.382030\pi$
$547$	−13.3292	−	13.3292i	−0.569917	−	0.569917i	−0.932105	+	0.362188i	$0.882030\pi$
$548$	2.63445	+	1.52100i	0.112538	+	0.0649739i
$549$	11.5557	+	6.67169i	0.493186	+	0.284741i
$550$	−25.3543	−	18.4732i	−1.08111	−	0.787701i
$551$	5.81183	−	5.81183i	0.247592	−	0.247592i
$552$	−3.24611	−	5.62243i	−0.138164	−	0.239306i
$553$	−26.3058	−	45.5629i	−1.11864	−	1.93753i
$554$	−10.9227	+	10.9227i	−0.464060	+	0.464060i
$555$	5.61404	−	1.98378i	0.238303	−	0.0842067i
$556$	4.29170	+	2.47781i	0.182008	+	0.105083i
$557$	12.7757	+	7.37604i	0.541323	+	0.312533i	0.745615	−	0.666377i	$-0.232156\pi$
$557$	12.7757	+	7.37604i	0.541323	+	0.312533i	−0.204292	+	0.978910i	$0.565489\pi$
$558$	5.04420	+	5.04420i	0.213538	+	0.213538i
$559$	−2.50153	+	8.00947i	−0.105803	+	0.338764i
$560$	−6.89292	+	4.73053i	−0.291279	+	0.199901i
$561$	3.51679	+	13.1249i	0.148479	+	0.554132i
$562$	19.2366	−	5.15443i	0.811447	−	0.217427i
$563$	1.75955	−	6.56675i	0.0741564	−	0.276755i	−0.918884	−	0.394527i	$-0.870908\pi$
$563$	1.75955	−	6.56675i	0.0741564	−	0.276755i	0.993041	+	0.117772i	$0.0375751\pi$
$564$	6.26465	+	6.26465i	0.263789	+	0.263789i
$565$	4.42536	+	12.5237i	0.186176	+	0.526875i
$566$	2.19240	−	8.18213i	0.0921533	−	0.343921i
$567$		−	3.73872i		−	0.157012i
$568$	12.6387	+	3.38653i	0.530309	+	0.142096i
$569$	−1.15885	+	2.00719i	−0.0485815	+	0.0841457i	−0.889294	−	0.457337i	$-0.848803\pi$
$569$	−1.15885	+	2.00719i	−0.0485815	+	0.0841457i	0.840712	+	0.541482i	$0.182137\pi$
$570$	−5.41902	+	0.422810i	−0.226978	+	0.0177096i
$571$			42.3870i			1.77384i	0.461922	+	0.886920i	$0.347160\pi$
$571$			42.3870i			1.77384i	−0.461922	+	0.886920i	$0.652840\pi$
$572$	15.3280	+	16.6368i	0.640896	+	0.695620i
$573$	−17.7557	+	17.7557i	−0.741755	+	0.741755i
$574$	28.6192	−	7.66849i	1.19454	−	0.320077i
$575$	3.43664	−	32.2787i	0.143318	−	1.34611i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	24.8803			1.03578			0.517890	−	0.855447i	$-0.326718\pi$
$577$	24.8803			1.03578			0.517890	+	0.855447i	$0.326718\pi$
$578$	10.6605	−	6.15484i	0.443418	−	0.256007i
$579$	−15.2012	−	4.07316i	−0.631742	−	0.169275i
$580$	6.23382	−	4.27820i	0.258845	−	0.177643i
$581$	−4.18781	−	7.25350i	−0.173740	−	0.300926i
$582$	0.906507	+	3.38313i	0.0375759	+	0.140235i
$583$	−9.67011	+	16.7491i	−0.400495	+	0.693678i
$584$	2.64120			0.109294
$585$	7.12624	+	3.77050i	0.294634	+	0.155891i
$586$	17.7122			0.731686
$587$	−13.4435	+	23.2849i	−0.554874	+	0.961070i	0.443039	+	0.896502i	$0.353900\pi$
$587$	−13.4435	+	23.2849i	−0.554874	+	0.961070i	−0.997913	+	0.0645679i	$0.979433\pi$
$588$	−1.80605	−	6.74027i	−0.0744803	−	0.277964i
$589$	8.67023	+	15.0173i	0.357250	+	0.618776i
$590$	6.92925	+	1.28909i	0.285273	+	0.0530711i
$591$	−6.90704	−	1.85074i	−0.284118	−	0.0761291i
$592$	2.30606	−	1.33141i	0.0947786	−	0.0547204i
$593$	4.62412			0.189890			0.0949449	−	0.995483i	$-0.469732\pi$
$593$	4.62412			0.189890			0.0949449	+	0.995483i	$0.469732\pi$
$594$	5.43350	−	3.13703i	0.222939	−	0.128714i
$595$	13.7596	+	11.7678i	0.564087	+	0.482434i
$596$	18.8500	−	5.05085i	0.772128	−	0.206891i
$597$	−6.84150	+	6.84150i	−0.280004	+	0.280004i
$598$	−6.97840	+	22.3436i	−0.285368	+	0.913699i
$599$			39.3499i			1.60779i	0.594769	+	0.803897i	$0.297243\pi$
$599$			39.3499i			1.60779i	−0.594769	+	0.803897i	$0.702757\pi$
$600$	−4.97190	−	0.529347i	−0.202977	−	0.0216105i
$601$	−11.1291	+	19.2762i	−0.453966	+	0.786292i	−0.998628	−	0.0523635i	$-0.983325\pi$
$601$	−11.1291	+	19.2762i	−0.453966	+	0.786292i	0.544662	+	0.838656i	$0.316658\pi$
$602$	8.40446	+	2.25197i	0.342540	+	0.0917834i
$603$		−	10.7065i		−	0.436003i
$604$	4.04744	−	15.1053i	0.164688	−	0.614624i
$605$	57.2269	+	27.3432i	2.32660	+	1.11166i
$606$	−3.08536	−	3.08536i	−0.125334	−	0.125334i
$607$	−7.16807	+	26.7516i	−0.290943	+	1.08581i	0.653444	+	0.756975i	$0.273324\pi$
$607$	−7.16807	+	26.7516i	−0.290943	+	1.08581i	−0.944386	+	0.328838i	$0.893343\pi$
$608$	−2.34800	+	0.629143i	−0.0952238	+	0.0255151i
$609$	3.27185	+	12.2107i	0.132582	+	0.494803i
$610$	16.8831	+	24.6006i	0.683578	+	0.996050i
$611$	1.30685	−	31.9168i	0.0528697	−	1.29122i
$612$	1.53139	+	1.53139i	0.0619029	+	0.0619029i
$613$	7.86406	+	4.54032i	0.317626	+	0.183382i	0.650334	−	0.759648i	$-0.274629\pi$
$613$	7.86406	+	4.54032i	0.317626	+	0.183382i	−0.332708	+	0.943030i	$0.607962\pi$
$614$	−6.92577	−	3.99859i	−0.279501	−	0.161370i
$615$	15.9891	+	7.63965i	0.644743	+	0.308060i
$616$	16.5866	−	16.5866i	0.668293	−	0.668293i
$617$	19.9985	+	34.6385i	0.805110	+	1.39449i	0.916217	+	0.400683i	$0.131227\pi$
$617$	19.9985	+	34.6385i	0.805110	+	1.39449i	−0.111106	+	0.993809i	$0.535439\pi$
$618$	−0.586140	−	1.01522i	−0.0235780	−	0.0408383i
$619$	−9.63249	+	9.63249i	−0.387163	+	0.387163i	−0.873674	−	0.486512i	$-0.838269\pi$
$619$	−9.63249	+	9.63249i	−0.387163	+	0.387163i	0.486512	+	0.873674i	$0.338269\pi$
$620$	5.31446	+	15.0398i	0.213434	+	0.604013i
$621$	5.62243	+	3.24611i	0.225620	+	0.130262i
$622$	8.51341	+	4.91522i	0.341357	+	0.197082i
$623$	−34.2618	−	34.2618i	−1.37267	−	1.37267i
$624$	3.44160	+	1.07489i	0.137774	+	0.0430299i
$625$	−18.5334	−	16.7783i	−0.741338	−	0.671132i
$626$	7.56402	+	28.2293i	0.302319	+	1.12827i
$627$	14.7315	−	3.94729i	0.588319	−	0.157640i
$628$	−1.70247	+	6.35369i	−0.0679358	+	0.253540i
$629$	−4.07781	−	4.07781i	−0.162593	−	0.162593i
$630$	3.60418	−	7.54322i	0.143594	−	0.300529i
$631$	3.96816	−	14.8094i	0.157970	−	0.589551i	−0.840863	−	0.541248i	$-0.817952\pi$
$631$	3.96816	−	14.8094i	0.157970	−	0.589551i	0.998833	−	0.0483032i	$-0.0153814\pi$
$632$		−	14.0721i		−	0.559757i
$633$	11.2925	+	3.02582i	0.448838	+	0.120266i
$634$	7.29503	−	12.6354i	0.289723	−	0.501814i
$635$	14.2802	−	16.6972i	0.566693	−	0.662608i
$636$			3.08257i			0.122232i
$637$	−13.4607	+	21.2560i	−0.533334	+	0.842195i
$638$	−15.0006	+	15.0006i	−0.593879	+	0.593879i
$639$	−12.6387	+	3.38653i	−0.499980	+	0.133969i
$640$	−2.22929	+	0.173937i	−0.0881205	+	0.00687546i
$641$	−15.5266	+	8.96429i	−0.613264	+	0.354068i	−0.774242	−	0.632890i	$-0.781869\pi$
$641$	−15.5266	+	8.96429i	−0.613264	+	0.354068i	0.160978	+	0.986958i	$0.448535\pi$
$642$	0.702153			0.0277118
$643$	29.7295	−	17.1643i	1.17242	−	0.676894i	0.218168	−	0.975911i	$-0.429992\pi$
$643$	29.7295	−	17.1643i	1.17242	−	0.676894i	0.954248	+	0.299017i	$0.0966587\pi$
$644$	23.4455	+	6.28221i	0.923884	+	0.247554i
$645$	2.94462	+	4.29065i	0.115944	+	0.168944i
$646$	2.63224	+	4.55917i	0.103564	+	0.179378i
$647$	−5.54154	−	20.6813i	−0.217861	−	0.813067i	−0.985140	−	0.171754i	$-0.945057\pi$
$647$	−5.54154	−	20.6813i	−0.217861	−	0.813067i	0.767279	−	0.641313i	$-0.221610\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−19.7760			−0.776276
$650$	10.7430	+	14.4771i	0.421377	+	0.567839i
$651$	−26.6704			−1.04530
$652$	−6.40658	+	11.0965i	−0.250901	+	0.434573i
$653$	−5.41467	−	20.2078i	−0.211892	−	0.790793i	−0.987237	−	0.159255i	$-0.949091\pi$
$653$	−5.41467	−	20.2078i	−0.211892	−	0.790793i	0.775345	−	0.631538i	$-0.217576\pi$
$654$	2.41635	+	4.18524i	0.0944868	+	0.163656i
$655$	−3.13588	−	4.56933i	−0.122529	−	0.178538i
$656$	7.65481	+	2.05110i	0.298870	+	0.0800820i
$657$	−2.28735	+	1.32060i	−0.0892380	+	0.0515216i
$658$	−33.1234			−1.29128
$659$	−21.0775	+	12.1691i	−0.821065	+	0.474042i	−0.850783	−	0.525516i	$-0.823872\pi$
$659$	−21.0775	+	12.1691i	−0.821065	+	0.474042i	0.0297188	+	0.999558i	$0.490539\pi$
$660$	13.9867	−	1.09129i	0.544433	−	0.0424785i
$661$	−20.9303	+	5.60825i	−0.814093	+	0.218135i	−0.641762	−	0.766904i	$-0.721796\pi$
$661$	−20.9303	+	5.60825i	−0.814093	+	0.218135i	−0.172330	+	0.985039i	$0.555130\pi$
$662$	7.47988	−	7.47988i	0.290714	−	0.290714i
$663$	0.319460	−	7.80206i	0.0124068	−	0.303007i
$664$		−	2.24024i		−	0.0869380i
$665$	13.2084	−	15.4439i	0.512198	−	0.598889i
$666$	−1.33141	+	2.30606i	−0.0515909	+	0.0893581i
$667$	−21.2037	−	5.68151i	−0.821010	−	0.219989i
$668$			9.20345i			0.356092i
$669$	0.435258	−	1.62441i	0.0168281	−	0.0628032i
$670$	10.3212	−	21.6014i	0.398743	−	0.834534i
$671$	−59.1971	−	59.1971i	−2.28528	−	2.28528i
$672$	0.967653	−	3.61133i	0.0373280	−	0.139310i
$673$	22.1884	−	5.94537i	0.855301	−	0.229177i	0.195580	−	0.980688i	$-0.437341\pi$
$673$	22.1884	−	5.94537i	0.855301	−	0.229177i	0.659721	+	0.751511i	$0.270674\pi$
$674$	6.20236	+	23.1475i	0.238906	+	0.891609i
$675$	4.57047	−	2.02752i	0.175917	−	0.0780394i
$676$	−5.55783	−	11.7520i	−0.213763	−	0.452002i
$677$	−14.4223	−	14.4223i	−0.554294	−	0.554294i	0.373383	−	0.927677i	$-0.378198\pi$
$677$	−14.4223	−	14.4223i	−0.554294	−	0.554294i	−0.927677	+	0.373383i	$0.878198\pi$
$678$	−5.14431	−	2.97007i	−0.197566	−	0.114065i
$679$	−11.3404	−	6.54739i	−0.435205	−	0.251266i
$680$	1.61344	+	4.56601i	0.0618728	+	0.175098i
$681$	5.73777	−	5.73777i	0.219872	−	0.219872i
$682$	−22.3783	−	38.7603i	−0.856908	−	1.48421i
$683$	5.89765	+	10.2150i	0.225667	+	0.390867i	0.956519	−	0.291669i	$-0.0942104\pi$
$683$	5.89765	+	10.2150i	0.225667	+	0.390867i	−0.730852	+	0.682536i	$0.760877\pi$
$684$	1.71885	−	1.71885i	0.0657219	−	0.0657219i
$685$	−6.13752	−	2.93253i	−0.234502	−	0.112046i
$686$	−0.0710868	−	0.0410420i	−0.00271411	−	0.00156699i
$687$	21.1395	+	12.2049i	0.806523	+	0.465646i
$688$	1.64561	+	1.64561i	0.0627384	+	0.0627384i
$689$	8.17397	−	7.53093i	0.311404	−	0.286905i
$690$	8.21448	+	11.9694i	0.312720	+	0.455668i
$691$	0.964968	+	3.60131i	0.0367091	+	0.137000i	0.981848	−	0.189667i	$-0.0607409\pi$
$691$	0.964968	+	3.60131i	0.0367091	+	0.137000i	−0.945139	+	0.326668i	$0.894074\pi$
$692$	2.45307	−	0.657298i	0.0932517	−	0.0249867i
$693$	−6.07112	+	22.6577i	−0.230623	+	0.860696i
$694$	25.3091	+	25.3091i	0.960719	+	0.960719i
$695$	−9.99843	−	4.77728i	−0.379262	−	0.181213i
$696$	−0.875126	+	3.26601i	−0.0331716	+	0.123798i
$697$		−	17.1630i		−	0.650093i
$698$	9.76996	+	2.61785i	0.369798	+	0.0990872i
$699$	−0.958832	+	1.66075i	−0.0362664	+	0.0628152i
$700$	14.5435	−	11.7447i	0.549693	−	0.443907i
$701$		−	15.8648i		−	0.599204i	−0.954064	−	0.299602i	$-0.903146\pi$
$701$		−	15.8648i		−	0.599204i	0.954064	−	0.299602i	$-0.0968538\pi$
$702$	−3.51796	+	0.789922i	−0.132777	+	0.0298137i
$703$	−4.57698	+	4.57698i	−0.172624	+	0.172624i
$704$	6.06028	−	1.62385i	0.228406	−	0.0612011i
$705$	−15.0554	−	12.8761i	−0.567019	−	0.484941i
$706$	−7.34797	+	4.24235i	−0.276545	+	0.159663i
$707$	16.3134			0.613528
$708$	−2.72973	+	1.57601i	−0.102590	+	0.0592301i
$709$	−23.0138	−	6.16653i	−0.864302	−	0.231589i	−0.200680	−	0.979657i	$-0.564315\pi$
$709$	−23.0138	−	6.16653i	−0.864302	−	0.231589i	−0.663622	+	0.748068i	$0.730982\pi$
$710$	−28.7644	−	5.35124i	−1.07951	−	0.200828i
$711$	7.03603	+	12.1868i	0.263872	+	0.457040i
$712$	−3.35427	−	12.5183i	−0.125707	−	0.469144i
$713$	23.1564	−	40.1080i	0.867212	−	1.50206i
$714$	−8.09701			−0.303023
$715$	−37.0643	−	34.4222i	−1.38613	−	1.28732i
$716$	25.3355			0.946833
$717$	5.94983	−	10.3054i	0.222201	−	0.384863i
$718$	6.30150	+	23.5175i	0.235170	+	0.877667i
$719$	−6.87314	−	11.9046i	−0.256325	−	0.443968i	0.708930	−	0.705279i	$-0.249178\pi$
$719$	−6.87314	−	11.9046i	−0.256325	−	0.443968i	−0.965255	+	0.261312i	$0.915845\pi$
$720$	1.84366	−	1.26528i	0.0687090	−	0.0471542i
$721$	4.23349	+	1.13436i	0.157663	+	0.0422458i
$722$	−11.3372	+	6.54555i	−0.421928	+	0.243600i
$723$	7.19860			0.267719
$724$	−10.9184	+	6.30371i	−0.405777	+	0.234276i
$725$	−13.1529	+	10.6217i	−0.488485	+	0.394478i
$726$	−27.3975	+	7.34113i	−1.01681	+	0.272455i
$727$	22.8501	−	22.8501i	0.847462	−	0.847462i	−0.142354	−	0.989816i	$-0.545467\pi$
$727$	22.8501	−	22.8501i	0.847462	−	0.847462i	0.989816	+	0.142354i	$0.0454670\pi$
$728$	−11.9401	+	6.25683i	−0.442531	+	0.231894i
$729$			1.00000i			0.0370370i
$730$	−5.88802	+	0.459403i	−0.217925	+	0.0170033i
$731$	2.52008	−	4.36491i	0.0932085	−	0.161442i
$732$	−12.8887	−	3.45352i	−0.476381	−	0.127646i
$733$			11.6905i			0.431800i	0.976415	+	0.215900i	$0.0692686\pi$
$733$			11.6905i			0.431800i	−0.976415	+	0.215900i	$0.930731\pi$
$734$	6.40747	−	23.9130i	0.236504	−	0.882645i
$735$	5.19860	+	14.7119i	0.191753	+	0.542657i
$736$	4.59069	+	4.59069i	0.169215	+	0.169215i
$737$	−17.3857	+	64.8845i	−0.640412	+	2.39005i
$738$	−7.65481	+	2.05110i	−0.281777	+	0.0755020i
$739$	−1.51977	−	5.67185i	−0.0559056	−	0.208643i	0.932323	−	0.361626i	$-0.117778\pi$
$739$	−1.51977	−	5.67185i	−0.0559056	−	0.208643i	−0.988229	+	0.152984i	$0.951112\pi$
$740$	−4.90931	+	3.36920i	−0.180470	+	0.123854i
$741$	−8.75712	−	0.358566i	−0.321701	−	0.0131722i
$742$	−8.14930	−	8.14930i	−0.299170	−	0.299170i
$743$	20.3325	+	11.7389i	0.745925	+	0.430660i	0.824220	−	0.566270i	$-0.191614\pi$
$743$	20.3325	+	11.7389i	0.745925	+	0.430660i	−0.0782945	+	0.996930i	$0.524947\pi$
$744$	−6.17785	−	3.56679i	−0.226491	−	0.130765i
$745$	−41.1437	+	14.5385i	−1.50739	+	0.532651i
$746$	−7.04653	+	7.04653i	−0.257992	+	0.257992i
$747$	1.12012	+	1.94010i	0.0409830	+	0.0709846i
$748$	−6.79392	−	11.7674i	−0.248410	−	0.430260i
$749$	−1.85626	+	1.85626i	−0.0678264	+	0.0678264i
$750$	11.1759	+	0.315272i	0.408086	+	0.0115121i
$751$	24.4643	+	14.1244i	0.892714	+	0.515408i	0.874829	−	0.484432i	$-0.160974\pi$
$751$	24.4643	+	14.1244i	0.892714	+	0.515408i	0.0178845	+	0.999840i	$0.494307\pi$
$752$	−7.67260	−	4.42978i	−0.279791	−	0.161537i
$753$	13.3291	+	13.3291i	0.485741	+	0.485741i
$754$	10.7984	−	5.65855i	0.393255	−	0.206072i
$755$	−6.39557	+	34.3780i	−0.232759	+	1.25114i
$756$	0.967653	+	3.61133i	0.0351932	+	0.131343i
$757$	24.8168	−	6.64965i	0.901983	−	0.241686i	0.222115	−	0.975020i	$-0.428704\pi$
$757$	24.8168	−	6.64965i	0.901983	−	0.241686i	0.679868	+	0.733335i	$0.262037\pi$
$758$	2.70222	−	10.0848i	0.0981492	−	0.366298i
$759$	−28.8023	−	28.8023i	−1.04546	−	1.04546i
$760$	5.12494	−	1.81095i	0.185901	−	0.0656900i
$761$	−3.00974	+	11.2325i	−0.109103	+	0.407178i	−0.998778	−	0.0494158i	$-0.984264\pi$
$761$	−3.00974	+	11.2325i	−0.109103	+	0.407178i	0.889675	+	0.456594i	$0.150931\pi$
$762$			9.82569i			0.355947i
$763$	−17.4525	−	4.67638i	−0.631822	−	0.169296i
$764$	12.5552	−	21.7462i	0.454231	−	0.786750i
$765$	−3.68029	−	3.14756i	−0.133061	−	0.113800i
$766$			32.4832i			1.17367i
$767$	10.8480	+	3.38806i	0.391699	+	0.122336i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−42.3503	+	11.3477i	−1.52719	+	0.409209i	−0.922101	−	0.386949i	$-0.873529\pi$
$769$	−42.3503	+	11.3477i	−1.52719	+	0.409209i	−0.605089	+	0.796158i	$0.706862\pi$
$770$	−34.0914	+	39.8614i	−1.22857	+	1.43651i
$771$	1.78580	−	1.03103i	0.0643140	−	0.0371317i
$772$	15.7375			0.566404
$773$	−11.0535	+	6.38173i	−0.397566	+	0.229535i	−0.685433	−	0.728136i	$-0.740387\pi$
$773$	−11.0535	+	6.38173i	−0.397566	+	0.229535i	0.287867	+	0.957670i	$0.407054\pi$
$774$	−2.24795	−	0.602337i	−0.0808009	−	0.0216505i
$775$	−14.4635	−	32.6037i	−0.519543	−	1.17116i
$776$	−1.75124	−	3.03323i	−0.0628658	−	0.108887i
$777$	−2.57668	−	9.61629i	−0.0924377	−	0.344982i
$778$	−0.771602	+	1.33645i	−0.0276633	+	0.0479142i
$779$	−19.2639			−0.690200
$780$	−7.85930	−	1.79761i	−0.281408	−	0.0643649i
$781$	82.0934			2.93753
$782$	7.03015	−	12.1766i	0.251398	−	0.435434i
$783$	−0.875126	−	3.26601i	−0.0312745	−	0.116718i
$784$	3.48902	+	6.04316i	0.124608	+	0.215827i
$785$	2.69015	−	14.4603i	0.0960157	−	0.516112i
$786$	2.39396	+	0.641459i	0.0853896	+	0.0228801i
$787$	−3.79581	+	2.19151i	−0.135306	+	0.0781189i	−0.566125	−	0.824319i	$-0.691558\pi$
$787$	−3.79581	+	2.19151i	−0.135306	+	0.0781189i	0.430819	+	0.902438i	$0.358225\pi$
$788$	7.15070			0.254733
$789$	−18.0852	+	10.4415i	−0.643851	+	0.371728i
$790$	2.44765	+	31.3708i	0.0870836	+	1.11612i
$791$	21.4518	−	5.74799i	0.762738	−	0.204375i
$792$	−4.43644	+	4.43644i	−0.157642	+	0.157642i
$793$	22.3304	+	42.6140i	0.792977	+	1.51327i
$794$		−	35.1178i		−	1.24628i
$795$	−0.536172	−	6.87194i	−0.0190161	−	0.243723i
$796$	4.83767	−	8.37910i	0.171467	−	0.296989i
$797$	−17.7223	−	4.74868i	−0.627757	−	0.168207i	−0.0691054	−	0.997609i	$-0.522014\pi$
$797$	−17.7223	−	4.74868i	−0.627757	−	0.168207i	−0.558652	+	0.829402i	$0.688681\pi$
$798$			9.08817i			0.321718i
$799$	−4.96603	+	18.5335i	−0.175686	+	0.655667i
$800$	4.93949	−	0.775513i	0.174637	−	0.0274185i
$801$	9.16404	+	9.16404i	0.323796	+	0.323796i
$802$	3.13438	−	11.6976i	0.110679	−	0.413058i
$803$	16.0065	−	4.28892i	0.564855	−	0.151353i
$804$	2.77105	+	10.3417i	0.0977273	+	0.364723i
$805$	−53.3597	−	9.92685i	−1.88068	−	0.349875i
$806$	5.63497	+	25.0956i	0.198483	+	0.883955i
$807$	−17.5458	−	17.5458i	−0.617640	−	0.617640i
$808$	3.77878	+	2.18168i	0.132937	+	0.0767512i
$809$	13.5851	+	7.84336i	0.477627	+	0.275758i	0.719427	−	0.694568i	$-0.244405\pi$
$809$	13.5851	+	7.84336i	0.477627	+	0.275758i	−0.241800	+	0.970326i	$0.577738\pi$
$810$	−0.964013	+	2.01759i	−0.0338719	+	0.0708910i
$811$	−12.4394	+	12.4394i	−0.436808	+	0.436808i	−0.890936	−	0.454128i	$-0.849951\pi$
$811$	−12.4394	+	12.4394i	−0.436808	+	0.436808i	0.454128	+	0.890936i	$0.349951\pi$
$812$	−6.32073	−	10.9478i	−0.221814	−	0.384194i
$813$	1.79498	+	3.10900i	0.0629528	+	0.109037i
$814$	11.8134	−	11.8134i	0.414059	−	0.414059i
$815$	12.3520	−	25.8517i	0.432673	−	0.905547i
$816$	−1.87556	−	1.08286i	−0.0656579	−	0.0379076i
$817$	−4.89922	−	2.82857i	−0.171402	−	0.0989590i
$818$	9.14300	+	9.14300i	0.319677	+	0.319677i
$819$	7.21204	−	11.3886i	0.252009	−	0.397951i
$820$	−17.4216	−	3.24105i	−0.608388	−	0.113182i
$821$	3.94197	+	14.7116i	0.137576	+	0.513439i	0.999974	+	0.00720903i	$0.00229473\pi$
$821$	3.94197	+	14.7116i	0.137576	+	0.513439i	−0.862398	+	0.506230i	$0.831039\pi$
$822$	2.93835	−	0.787328i	0.102487	−	0.0274612i
$823$	3.57064	−	13.3258i	0.124465	−	0.464509i	−0.875355	−	0.483480i	$-0.839372\pi$
$823$	3.57064	−	13.3258i	0.124465	−	0.464509i	0.999820	+	0.0189713i	$0.00603912\pi$
$824$	0.828927	+	0.828927i	0.0288770	+	0.0288770i
$825$	−30.9907	+	4.86562i	−1.07896	+	0.169399i
$826$	3.05006	−	11.3830i	0.106125	−	0.396065i
$827$		−	8.07581i		−	0.280823i	−0.990093	−	0.140412i	$-0.955157\pi$
$827$		−	8.07581i		−	0.280823i	0.990093	−	0.140412i	$-0.0448426\pi$
$828$	−6.27100	−	1.68031i	−0.217932	−	0.0583948i
$829$	−1.62013	+	2.80615i	−0.0562696	+	0.0974618i	−0.892788	−	0.450477i	$-0.851254\pi$
$829$	−1.62013	+	2.80615i	−0.0562696	+	0.0974618i	0.836518	+	0.547939i	$0.184587\pi$
$830$	0.389660	+	4.99414i	0.0135253	+	0.173349i
$831$			15.4470i			0.535851i
$832$	−3.60253	−	0.147508i	−0.124895	−	0.00511392i
$833$	10.6861	−	10.6861i	0.370252	−	0.370252i
$834$	4.78677	−	1.28261i	0.165752	−	0.0444131i
$835$	−1.60082	−	20.5172i	−0.0553987	−	0.710027i
$836$	−13.2079	+	7.62558i	−0.456804	+	0.263736i
$837$	7.13357			0.246572
$838$	−29.4352	+	16.9944i	−1.01682	+	0.587063i
$839$	4.32851	+	1.15982i	0.149437	+	0.0400415i	0.332762	−	0.943011i	$-0.392019\pi$
$839$	4.32851	+	1.15982i	0.149437	+	0.0400415i	−0.183325	+	0.983052i	$0.558686\pi$
$840$	−1.52904	+	8.21902i	−0.0527568	+	0.283583i
$841$	−8.78365	−	15.2137i	−0.302885	−	0.524611i
$842$	−5.01298	−	18.7087i	−0.172759	−	0.644744i
$843$	9.95760	−	17.2471i	0.342958	−	0.594021i
$844$	−11.6909			−0.402417
$845$	14.4341	+	25.2320i	0.496549	+	0.868008i
$846$	8.85955			0.304598
$847$	53.0224	−	91.8375i	1.82187	−	3.15558i
$848$	−0.797827	−	2.97753i	−0.0273975	−	0.102249i
$849$	−4.23538	−	7.33590i	−0.145358	−	0.251767i
$850$	−4.39104	−	9.89833i	−0.150611	−	0.339510i
$851$	16.6985	+	4.47435i	0.572417	+	0.153379i
$852$	11.3316	−	6.54228i	0.388213	−	0.224135i
$853$	−31.8106			−1.08918			−0.544588	−	0.838704i	$-0.683314\pi$
$853$	−31.8106			−1.08918			−0.544588	+	0.838704i	$0.683314\pi$
$854$	43.2036	−	24.9436i	1.47840	−	0.853553i
$855$	−3.53285	+	4.13080i	−0.120821	+	0.141270i
$856$	−0.678228	+	0.181731i	−0.0231813	+	0.00621142i
$857$	−11.4854	+	11.4854i	−0.392335	+	0.392335i	−0.875519	−	0.483184i	$-0.839480\pi$
$857$	−11.4854	+	11.4854i	−0.392335	+	0.392335i	0.483184	+	0.875519i	$0.339480\pi$
$858$	22.6025	+	0.925475i	0.771638	+	0.0315952i
$859$			6.12613i			0.209021i	0.994524	+	0.104510i	$0.0333276\pi$
$859$			6.12613i			0.209021i	−0.994524	+	0.104510i	$0.966672\pi$
$860$	−3.95479	−	3.38232i	−0.134857	−	0.115336i
$861$	14.8144	−	25.6593i	0.504873	−	0.874466i
$862$	−25.2842	−	6.77487i	−0.861182	−	0.230753i
$863$			32.2134i			1.09656i	0.836296	+	0.548279i	$0.184717\pi$
$863$			32.2134i			1.09656i	−0.836296	+	0.548279i	$0.815283\pi$
$864$	−0.258819	+	0.965926i	−0.00880520	+	0.0328615i
$865$	−5.35428	+	1.89199i	−0.182051	+	0.0643296i
$866$	1.90363	+	1.90363i	0.0646880	+	0.0646880i
$867$	3.18598	−	11.8902i	0.108201	−	0.403813i
$868$	25.7617	−	6.90282i	0.874408	−	0.234297i
$869$	−22.8509	−	85.2807i	−0.775164	−	2.89295i
$870$	1.38283	−	7.43312i	0.0468824	−	0.252006i
$871$	20.6530	−	32.6134i	0.699800	−	1.10506i
$872$	−3.41724	−	3.41724i	−0.115722	−	0.115722i
$873$	3.03323	+	1.75124i	0.102659	+	0.0592704i
$874$	−13.6671	−	7.89072i	−0.462298	−	0.266908i
$875$	−30.3789	+	28.7120i	−1.02699	+	0.970642i
$876$	1.86761	−	1.86761i	0.0631008	−	0.0631008i
$877$	−0.150169	−	0.260101i	−0.00507085	−	0.00878298i	0.863479	−	0.504385i	$-0.168281\pi$
$877$	−0.150169	−	0.260101i	−0.00507085	−	0.00878298i	−0.868550	+	0.495602i	$0.834947\pi$
$878$	−2.71924	−	4.70986i	−0.0917699	−	0.158950i
$879$	12.5244	−	12.5244i	0.422439	−	0.422439i
$880$	−13.2277	+	4.67414i	−0.445906	+	0.157565i
$881$	−13.5261	−	7.80932i	−0.455707	−	0.263103i	0.254530	−	0.967065i	$-0.418079\pi$
$881$	−13.5261	−	7.80932i	−0.455707	−	0.263103i	−0.710237	+	0.703962i	$0.751412\pi$
$882$	−6.04316	−	3.48902i	−0.203484	−	0.117481i
$883$	21.3639	+	21.3639i	0.718951	+	0.718951i	0.968390	−	0.249439i	$-0.0802462\pi$
$883$	21.3639	+	21.3639i	0.718951	+	0.718951i	−0.249439	+	0.968390i	$0.580246\pi$
$884$	1.71075	+	7.61890i	0.0575387	+	0.256251i
$885$	5.81124	−	3.98819i	0.195343	−	0.134062i
$886$	5.71577	+	21.3316i	0.192025	+	0.716648i
$887$	−18.4656	+	4.94784i	−0.620014	+	0.166132i	−0.555134	−	0.831761i	$-0.687333\pi$
$887$	−18.4656	+	4.94784i	−0.620014	+	0.166132i	−0.0648796	+	0.997893i	$0.520666\pi$
$888$	0.689186	−	2.57208i	0.0231276	−	0.0863133i
$889$	−25.9759	−	25.9759i	−0.871205	−	0.871205i
$890$	9.65505	+	27.3236i	0.323638	+	0.915888i
$891$	1.62385	−	6.06028i	0.0544010	−	0.203027i
$892$			1.68171i			0.0563078i
$893$	20.8022	+	5.57393i	0.696119	+	0.186524i
$894$	9.75750	−	16.9005i	0.326340	−	0.565237i
$895$	−56.4803	+	4.40679i	−1.88793	+	0.147303i
$896$			3.73872i			0.124902i
$897$	10.8649	+	20.7338i	0.362767	+	0.692282i
$898$	−0.689152	+	0.689152i	−0.0229973	+	0.0229973i
$899$	−23.2983	+	6.24277i	−0.777043	+	0.208208i
$900$	−3.88997	+	3.14136i	−0.129666	+	0.104712i
$901$	−5.78155	+	3.33798i	−0.192611	+	0.111204i
$902$	49.7210			1.65553
$903$	7.53524	−	4.35047i	0.250757	−	0.144775i
$904$	5.73773	+	1.53742i	0.190834	+	0.0511338i
$905$	23.2438	−	15.9519i	0.772649	−	0.530260i
$906$	−7.81906	−	13.5430i	−0.259771	−	0.449936i
$907$	−10.2772	−	38.3551i	−0.341250	−	1.27356i	−0.896933	−	0.442167i	$-0.854210\pi$
$907$	−10.2772	−	38.3551i	−0.341250	−	1.27356i	0.555683	−	0.831394i	$-0.312457\pi$
$908$	−4.05722	+	7.02731i	−0.134644	+	0.233209i
$909$	−4.36336			−0.144723
$910$	25.5297	−	16.0251i	0.846303	−	0.531228i
$911$	19.2539			0.637911			0.318956	−	0.947770i	$-0.396668\pi$
$911$	19.2539			0.637911			0.318956	+	0.947770i	$0.396668\pi$
$912$	−1.21541	+	2.10515i	−0.0402463	+	0.0697086i
$913$	−3.63780	−	13.5765i	−0.120394	−	0.449316i
$914$	2.19918	+	3.80909i	0.0727423	+	0.125993i
$915$	29.3334	+	5.45709i	0.969733	+	0.180406i
$916$	−23.5781	−	6.31772i	−0.779041	−	0.208743i
$917$	−8.02466	+	4.63304i	−0.264997	+	0.152996i
$918$	2.16572			0.0714793
$919$	5.45430	−	3.14904i	0.179921	−	0.103877i	−0.407335	−	0.913279i	$-0.633542\pi$
$919$	5.45430	−	3.14904i	0.179921	−	0.103877i	0.587255	+	0.809402i	$0.300208\pi$
$920$	−11.0325	−	9.43551i	−0.363730	−	0.311079i
$921$	−7.72469	+	2.06982i	−0.254537	+	0.0682030i
$922$	6.16084	−	6.16084i	0.202896	−	0.202896i
$923$	−45.0319	−	14.0644i	−1.48224	−	0.462936i
$924$		−	23.4570i		−	0.771679i
$925$	10.3583	−	8.36485i	0.340577	−	0.275034i
$926$	18.7248	−	32.4323i	0.615334	−	1.06579i
$927$	−1.13234	−	0.303408i	−0.0371908	−	0.00996524i
$928$		−	3.38123i		−	0.110994i
$929$	0.336633	−	1.25633i	0.0110446	−	0.0412189i	−0.960184	−	0.279370i	$-0.909875\pi$
$929$	0.336633	−	1.25633i	0.0110446	−	0.0412189i	0.971228	+	0.238151i	$0.0765412\pi$
$930$	14.3926	+	6.87685i	0.471953	+	0.225501i
$931$	−11.9942	−	11.9942i	−0.393095	−	0.393095i
$932$	0.496328	−	1.85232i	0.0162578	−	0.0606748i
$933$	9.49547	−	2.54430i	0.310868	−	0.0832968i
$934$	3.92058	+	14.6318i	0.128285	+	0.478767i
$935$	17.1924	+	25.0513i	0.562253	+	0.819266i
$936$	3.19364	−	1.67352i	0.104387	−	0.0547007i
$937$	7.90659	+	7.90659i	0.258297	+	0.258297i	0.824361	−	0.566064i	$-0.191535\pi$
$937$	7.90659	+	7.90659i	0.258297	+	0.258297i	−0.566064	+	0.824361i	$0.691535\pi$
$938$	−34.6658	−	20.0143i	−1.13188	−	0.653491i
$939$	25.3097	+	14.6126i	0.825951	+	0.476863i
$940$	17.8750	+	8.54072i	0.583017	+	0.278568i
$941$	22.8842	−	22.8842i	0.746005	−	0.746005i	−0.227722	−	0.973726i	$-0.573128\pi$
$941$	22.8842	−	22.8842i	0.746005	−	0.746005i	0.973726	+	0.227722i	$0.0731276\pi$
$942$	3.28891	+	5.69656i	0.107158	+	0.185604i
$943$	25.7249	+	44.5568i	0.837718	+	1.45097i
$944$	2.22882	−	2.22882i	0.0725418	−	0.0725418i
$945$	−2.78532	−	7.88240i	−0.0906066	−	0.256414i
$946$	12.6451	+	7.30066i	0.411128	+	0.237365i
$947$	5.89383	+	3.40280i	0.191524	+	0.110576i	0.592696	−	0.805426i	$-0.298064\pi$
$947$	5.89383	+	3.40280i	0.191524	+	0.110576i	−0.401172	+	0.916003i	$0.631397\pi$
$948$	−9.95045	−	9.95045i	−0.323176	−	0.323176i
$949$	−9.51503	−	0.389599i	−0.308871	−	0.0126469i
$950$	−11.1100	+	4.92855i	−0.360456	+	0.159903i
$951$	−3.77618	−	14.0929i	−0.122451	−	0.456994i
$952$	7.82111	−	2.09566i	0.253484	−	0.0679207i
$953$	−8.61808	+	32.1631i	−0.279167	+	1.04186i	0.673830	+	0.738886i	$0.264648\pi$
$953$	−8.61808	+	32.1631i	−0.279167	+	1.04186i	−0.952997	+	0.302979i	$0.902019\pi$
$954$	2.17970	+	2.17970i	0.0705705	+	0.0705705i
$955$	−24.2067	+	50.6625i	−0.783311	+	1.63940i
$956$	−3.07986	+	11.4942i	−0.0996098	+	0.371749i
$957$			21.2140i			0.685753i
$958$	−33.5012	−	8.97663i	−1.08238	−	0.290022i
$959$	−5.68660	+	9.84948i	−0.183630	+	0.318056i
$960$	−1.45336	+	1.69934i	−0.0469069	+	0.0548460i
$961$		−	19.8878i		−	0.641543i
$962$	−8.50406	+	4.45627i	−0.274182	+	0.143676i
$963$	0.496497	−	0.496497i	0.0159994	−	0.0159994i
$964$	−6.95332	+	1.86314i	−0.223951	+	0.0600076i
$965$	−35.0835	+	2.73733i	−1.12938	+	0.0881178i
$966$	21.0207	−	12.1363i	0.676330	−	0.390479i
$967$	59.2392			1.90500			0.952502	−	0.304533i	$-0.0985005\pi$
$967$	59.2392			1.90500			0.952502	+	0.304533i	$0.0985005\pi$
$968$	24.5639	−	14.1820i	0.789513	−	0.455826i
$969$	5.08509	+	1.36255i	0.163357	+	0.0437713i
$970$	4.43161	+	6.45736i	0.142291	+	0.207333i
$971$	−6.51004	−	11.2757i	−0.208917	−	0.361855i	0.742457	−	0.669894i	$-0.233661\pi$
$971$	−6.51004	−	11.2757i	−0.208917	−	0.361855i	−0.951374	+	0.308039i	$0.900327\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	−9.26385	+	16.0455i	−0.296985	+	0.514394i
$974$	−32.3762			−1.03740
$975$	17.8334	+	2.64038i	0.571124	+	0.0845599i
$976$	13.3434			0.427111
$977$	14.9647	−	25.9196i	0.478762	−	0.829241i	−0.520941	−	0.853593i	$-0.674419\pi$
$977$	14.9647	−	25.9196i	0.478762	−	0.829241i	0.999703	+	0.0243520i	$0.00775226\pi$
$978$	3.31629	+	12.3766i	0.106043	+	0.395759i
$979$	−40.6557	−	70.4177i	−1.29936	−	2.25056i
$980$	−8.82918	−	12.8651i	−0.282038	−	0.410961i
$981$	4.66803	+	1.25080i	0.149039	+	0.0399348i
$982$	4.60222	−	2.65709i	0.146863	−	0.0847912i
$983$	43.9501			1.40179			0.700895	−	0.713265i	$-0.252784\pi$
$983$	43.9501			1.40179			0.700895	+	0.713265i	$0.252784\pi$
$984$	6.86311	−	3.96242i	0.218788	−	0.126317i
$985$	−15.9410	+	1.24377i	−0.507923	+	0.0396298i
$986$	−7.07326	+	1.89527i	−0.225258	+	0.0603578i
$987$	−23.4218	+	23.4218i	−0.745524	+	0.745524i
$988$	8.55153	−	1.92016i	0.272060	−	0.0610885i
$989$			15.1090i			0.480439i
$990$	9.11845	−	10.6618i	0.289804	−	0.338853i
$991$	−11.4354	+	19.8067i	−0.363258	+	0.629181i	−0.988495	−	0.151254i	$-0.951669\pi$
$991$	−11.4354	+	19.8067i	−0.363258	+	0.629181i	0.625237	+	0.780435i	$0.285002\pi$
$992$	6.89050	+	1.84630i	0.218774	+	0.0586202i
$993$		−	10.5781i		−	0.335687i
$994$	−12.6613	+	47.2527i	−0.401592	+	1.49876i
$995$	−9.32716	+	19.5209i	−0.295691	+	0.618854i
$996$	−1.58409	−	1.58409i	−0.0501937	−	0.0501937i
$997$	6.57973	−	24.5559i	0.208382	−	0.777692i	−0.780010	−	0.625767i	$-0.784786\pi$
$997$	6.57973	−	24.5559i	0.208382	−	0.777692i	0.988392	−	0.151925i	$-0.0485473\pi$
$998$	−33.7382	+	9.04013i	−1.06797	+	0.286160i
$999$	0.689186	+	2.57208i	0.0218049	+	0.0813769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bn.c.97.8	yes	32
5.3	odd	4		390.2.bd.c.253.2	yes	32
13.11	odd	12		390.2.bd.c.37.2	✓	32
65.63	even	12	inner	390.2.bn.c.193.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.c.37.2	✓	32	13.11	odd	12
390.2.bd.c.253.2	yes	32	5.3	odd	4
390.2.bn.c.97.8	yes	32	1.1	even	1	trivial
390.2.bn.c.193.8	yes	32	65.63	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.26528 + 1.84366i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(3.23783 - 1.86936i) q^{7} +1.00000 q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.26528 + 1.84366i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(3.23783 - 1.86936i) q^{7} +1.00000 q^{8} +(-0.866025 + 0.500000i) q^{9} +(-2.22929 + 0.173937i) q^{10} +(6.06028 - 1.62385i) q^{11} +(0.707107 - 0.707107i) q^{12} +(-3.60253 - 0.147508i) q^{13} +3.73872i q^{14} +(-1.45336 + 1.69934i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.09192 + 0.560528i) q^{17} -1.00000i q^{18} +(0.629143 - 2.34800i) q^{19} +(0.964013 - 2.01759i) q^{20} +(2.64368 + 2.64368i) q^{21} +(-1.62385 + 6.06028i) q^{22} +(-6.27100 + 1.68031i) q^{23} +(0.258819 + 0.965926i) q^{24} +(-1.79813 + 4.66548i) q^{25} +(1.92901 - 3.04613i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-3.23783 - 1.86936i) q^{28} +(2.92823 + 1.69061i) q^{29} +(-0.744994 - 2.10831i) q^{30} +(-5.04420 + 5.04420i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.13703 + 5.43350i) q^{33} +(-1.53139 + 1.53139i) q^{34} +(7.54322 + 3.60418i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-2.30606 - 1.33141i) q^{37} +(1.71885 + 1.71885i) q^{38} +(-0.789922 - 3.51796i) q^{39} +(1.26528 + 1.84366i) q^{40} +(-2.05110 - 7.65481i) q^{41} +(-3.61133 + 0.967653i) q^{42} +(0.602337 - 2.24795i) q^{43} +(-4.43644 - 4.43644i) q^{44} +(-2.01759 - 0.964013i) q^{45} +(1.68031 - 6.27100i) q^{46} +8.85955i q^{47} +(-0.965926 - 0.258819i) q^{48} +(3.48902 - 6.04316i) q^{49} +(-3.14136 - 3.88997i) q^{50} +2.16572i q^{51} +(1.67352 + 3.19364i) q^{52} +(-2.17970 + 2.17970i) q^{53} +(0.965926 - 0.258819i) q^{54} +(10.6618 + 9.11845i) q^{55} +(3.23783 - 1.86936i) q^{56} +2.43082 q^{57} +(-2.92823 + 1.69061i) q^{58} +(-3.04462 - 0.815803i) q^{59} +(2.19835 + 0.408973i) q^{60} +(-6.67169 - 11.5557i) q^{61} +(-1.84630 - 6.89050i) q^{62} +(-1.86936 + 3.23783i) q^{63} +1.00000 q^{64} +(-4.28626 - 6.82847i) q^{65} -6.27407 q^{66} +(-5.35325 + 9.27211i) q^{67} +(-0.560528 - 2.09192i) q^{68} +(-3.24611 - 5.62243i) q^{69} +(-6.89292 + 4.73053i) q^{70} +(12.6387 + 3.38653i) q^{71} +(-0.866025 + 0.500000i) q^{72} +2.64120 q^{73} +(2.30606 - 1.33141i) q^{74} +(-4.97190 - 0.529347i) q^{75} +(-2.34800 + 0.629143i) q^{76} +(16.5866 - 16.5866i) q^{77} +(3.44160 + 1.07489i) q^{78} -14.0721i q^{79} +(-2.22929 + 0.173937i) q^{80} +(0.500000 - 0.866025i) q^{81} +(7.65481 + 2.05110i) q^{82} -2.24024i q^{83} +(0.967653 - 3.61133i) q^{84} +(1.61344 + 4.56601i) q^{85} +(1.64561 + 1.64561i) q^{86} +(-0.875126 + 3.26601i) q^{87} +(6.06028 - 1.62385i) q^{88} +(-3.35427 - 12.5183i) q^{89} +(1.84366 - 1.26528i) q^{90} +(-11.9401 + 6.25683i) q^{91} +(4.59069 + 4.59069i) q^{92} +(-6.17785 - 3.56679i) q^{93} +(-7.67260 - 4.42978i) q^{94} +(5.12494 - 1.81095i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-1.75124 - 3.03323i) q^{97} +(3.48902 + 6.04316i) q^{98} +(-4.43644 + 4.43644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8	\( 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8} - 4 q^{11} + 8 q^{13} - 4 q^{15} - 16 q^{16} - 4 q^{17} + 20 q^{19} + 8 q^{21} + 8 q^{22} - 16 q^{23} - 8 q^{25} - 4 q^{26} + 12 q^{28} + 24 q^{29} + 8 q^{30} + 12 q^{31} - 16 q^{32} - 16 q^{34} + 12 q^{35} - 24 q^{37} - 4 q^{38} - 20 q^{39} - 28 q^{41} - 16 q^{42} + 4 q^{43} - 4 q^{44} - 4 q^{46} + 20 q^{49} - 8 q^{50} - 4 q^{52} - 4 q^{53} + 68 q^{55} - 12 q^{56} + 16 q^{57} - 24 q^{58} + 36 q^{59} - 4 q^{60} - 28 q^{61} - 48 q^{62} + 32 q^{64} - 28 q^{65} - 28 q^{67} + 20 q^{68} - 20 q^{69} - 24 q^{70} - 4 q^{71} - 48 q^{73} + 24 q^{74} + 24 q^{75} - 16 q^{76} + 20 q^{77} + 4 q^{78} + 16 q^{81} + 44 q^{82} + 8 q^{84} + 64 q^{85} - 8 q^{86} + 20 q^{87} - 4 q^{88} - 16 q^{89} - 40 q^{91} + 20 q^{92} - 24 q^{93} - 24 q^{94} + 68 q^{95} + 8 q^{97} + 20 q^{98} - 4 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8 - 4 * q^11 + 8 * q^13 - 4 * q^15 - 16 * q^16 - 4 * q^17 + 20 * q^19 + 8 * q^21 + 8 * q^22 - 16 * q^23 - 8 * q^25 - 4 * q^26 + 12 * q^28 + 24 * q^29 + 8 * q^30 + 12 * q^31 - 16 * q^32 - 16 * q^34 + 12 * q^35 - 24 * q^37 - 4 * q^38 - 20 * q^39 - 28 * q^41 - 16 * q^42 + 4 * q^43 - 4 * q^44 - 4 * q^46 + 20 * q^49 - 8 * q^50 - 4 * q^52 - 4 * q^53 + 68 * q^55 - 12 * q^56 + 16 * q^57 - 24 * q^58 + 36 * q^59 - 4 * q^60 - 28 * q^61 - 48 * q^62 + 32 * q^64 - 28 * q^65 - 28 * q^67 + 20 * q^68 - 20 * q^69 - 24 * q^70 - 4 * q^71 - 48 * q^73 + 24 * q^74 + 24 * q^75 - 16 * q^76 + 20 * q^77 + 4 * q^78 + 16 * q^81 + 44 * q^82 + 8 * q^84 + 64 * q^85 - 8 * q^86 + 20 * q^87 - 4 * q^88 - 16 * q^89 - 40 * q^91 + 20 * q^92 - 24 * q^93 - 24 * q^94 + 68 * q^95 + 8 * q^97 + 20 * q^98 - 4 * q^99

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