LMFDB - Embedded newform 630.2.j.i.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(211,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.2
Root			$0.403374 - 1.68443i$ of defining polynomial
Character	$\chi$	$=$	630.211
Dual form			630.2.j.i.421.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.403374 - 1.68443i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.25707 + 1.19154i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-2.67458 + 1.35891i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.403374 - 1.68443i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.25707 + 1.19154i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-2.67458 + 1.35891i) q^{9} +1.00000 q^{10} +(2.25707 + 3.90936i) q^{11} +(1.66044 + 0.492881i) q^{12} +(1.56382 - 2.70861i) q^{13} +(0.500000 - 0.866025i) q^{14} +(1.66044 + 0.492881i) q^{15} +(-0.500000 - 0.866025i) q^{16} +5.34916 q^{17} +(2.51414 + 1.63680i) q^{18} +0.320884 q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.25707 - 1.19154i) q^{21} +(2.25707 - 3.90936i) q^{22} +(0.950321 - 1.64600i) q^{23} +(-0.403374 - 1.68443i) q^{24} +(-0.500000 - 0.866025i) q^{25} -3.12763 q^{26} +(3.36783 + 3.95698i) q^{27} -1.00000 q^{28} +(2.24293 + 3.88487i) q^{29} +(-0.403374 - 1.68443i) q^{30} +(3.51414 - 6.08666i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.67458 - 5.37880i) q^{33} +(-2.67458 - 4.63251i) q^{34} -1.00000 q^{35} +(0.160442 - 2.99571i) q^{36} -1.80675 q^{37} +(-0.160442 - 0.277894i) q^{38} +(-5.19325 - 1.54155i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-2.57795 + 4.46515i) q^{41} +(-1.66044 - 0.492881i) q^{42} +(-2.33502 - 4.04438i) q^{43} -4.51414 q^{44} +(0.160442 - 2.99571i) q^{45} -1.90064 q^{46} +(4.02827 + 6.97717i) q^{47} +(-1.25707 + 1.19154i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-2.15771 - 9.01026i) q^{51} +(1.56382 + 2.70861i) q^{52} +8.24980 q^{53} +(1.74293 - 4.89512i) q^{54} -4.51414 q^{55} +(0.500000 + 0.866025i) q^{56} +(-0.129436 - 0.540506i) q^{57} +(2.24293 - 3.88487i) q^{58} +(6.38197 - 11.0539i) q^{59} +(-1.25707 + 1.19154i) q^{60} +(1.09663 + 1.89941i) q^{61} -7.02827 q^{62} +(-2.51414 - 1.63680i) q^{63} +1.00000 q^{64} +(1.56382 + 2.70861i) q^{65} +(-7.49546 - 2.22493i) q^{66} +(3.48133 - 6.02983i) q^{67} +(-2.67458 + 4.63251i) q^{68} +(-3.15591 - 0.936790i) q^{69} +(0.500000 + 0.866025i) q^{70} -12.0620 q^{71} +(-2.67458 + 1.35891i) q^{72} +2.02827 q^{73} +(0.903374 + 1.56469i) q^{74} +(-1.25707 + 1.19154i) q^{75} +(-0.160442 + 0.277894i) q^{76} +(-2.25707 + 3.90936i) q^{77} +(1.26160 + 5.26826i) q^{78} +(-0.707389 - 1.22523i) q^{79} +1.00000 q^{80} +(5.30675 - 7.26900i) q^{81} +5.15591 q^{82} +(1.80675 + 3.12938i) q^{83} +(0.403374 + 1.68443i) q^{84} +(-2.67458 + 4.63251i) q^{85} +(-2.33502 + 4.04438i) q^{86} +(5.63904 - 5.34511i) q^{87} +(2.25707 + 3.90936i) q^{88} -2.00000 q^{89} +(-2.67458 + 1.35891i) q^{90} +3.12763 q^{91} +(0.950321 + 1.64600i) q^{92} +(-11.6700 - 3.46410i) q^{93} +(4.02827 - 6.97717i) q^{94} +(-0.160442 + 0.277894i) q^{95} +(1.66044 + 0.492881i) q^{96} +(9.17004 + 15.8830i) q^{97} +1.00000 q^{98} +(-11.3492 - 7.38874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} - q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - q^3 - 3 * q^4 - 3 * q^5 - q^6 + 3 * q^7 + 6 * q^8 + 5 * q^9	$ 6 q - 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} - q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9} + 6 q^{10} + 7 q^{11} + 2 q^{12} + 3 q^{14} + 2 q^{15} - 3 q^{16} - 10 q^{17} + 2 q^{18} - 14 q^{19} - 3 q^{20} + q^{21} + 7 q^{22} + 2 q^{23} - q^{24} - 3 q^{25} + 2 q^{27} - 6 q^{28} + 20 q^{29} - q^{30} + 8 q^{31} - 3 q^{32} + 13 q^{33} + 5 q^{34} - 6 q^{35} - 7 q^{36} - 8 q^{37} + 7 q^{38} - 34 q^{39} - 3 q^{40} + 7 q^{41} - 2 q^{42} + 15 q^{43} - 14 q^{44} - 7 q^{45} - 4 q^{46} - 2 q^{47} - q^{48} - 3 q^{49} - 3 q^{50} + q^{51} + 17 q^{54} - 14 q^{55} + 3 q^{56} - 13 q^{57} + 20 q^{58} + 7 q^{59} - q^{60} + 8 q^{61} - 16 q^{62} - 2 q^{63} + 6 q^{64} - 8 q^{66} - 3 q^{67} + 5 q^{68} + 26 q^{69} + 3 q^{70} - 32 q^{71} + 5 q^{72} - 14 q^{73} + 4 q^{74} - q^{75} + 7 q^{76} - 7 q^{77} + 38 q^{78} + 6 q^{79} + 6 q^{80} + 29 q^{81} - 14 q^{82} + 8 q^{83} + q^{84} + 5 q^{85} + 15 q^{86} - 4 q^{87} + 7 q^{88} - 12 q^{89} + 5 q^{90} + 2 q^{92} - 12 q^{93} - 2 q^{94} + 7 q^{95} + 2 q^{96} - 3 q^{97} + 6 q^{98} - 26 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - q^3 - 3 * q^4 - 3 * q^5 - q^6 + 3 * q^7 + 6 * q^8 + 5 * q^9 + 6 * q^10 + 7 * q^11 + 2 * q^12 + 3 * q^14 + 2 * q^15 - 3 * q^16 - 10 * q^17 + 2 * q^18 - 14 * q^19 - 3 * q^20 + q^21 + 7 * q^22 + 2 * q^23 - q^24 - 3 * q^25 + 2 * q^27 - 6 * q^28 + 20 * q^29 - q^30 + 8 * q^31 - 3 * q^32 + 13 * q^33 + 5 * q^34 - 6 * q^35 - 7 * q^36 - 8 * q^37 + 7 * q^38 - 34 * q^39 - 3 * q^40 + 7 * q^41 - 2 * q^42 + 15 * q^43 - 14 * q^44 - 7 * q^45 - 4 * q^46 - 2 * q^47 - q^48 - 3 * q^49 - 3 * q^50 + q^51 + 17 * q^54 - 14 * q^55 + 3 * q^56 - 13 * q^57 + 20 * q^58 + 7 * q^59 - q^60 + 8 * q^61 - 16 * q^62 - 2 * q^63 + 6 * q^64 - 8 * q^66 - 3 * q^67 + 5 * q^68 + 26 * q^69 + 3 * q^70 - 32 * q^71 + 5 * q^72 - 14 * q^73 + 4 * q^74 - q^75 + 7 * q^76 - 7 * q^77 + 38 * q^78 + 6 * q^79 + 6 * q^80 + 29 * q^81 - 14 * q^82 + 8 * q^83 + q^84 + 5 * q^85 + 15 * q^86 - 4 * q^87 + 7 * q^88 - 12 * q^89 + 5 * q^90 + 2 * q^92 - 12 * q^93 - 2 * q^94 + 7 * q^95 + 2 * q^96 - 3 * q^97 + 6 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.403374	−	1.68443i	−0.232888	−	0.972504i
$3$	−0.403374	−	1.68443i	−0.232888	−	0.972504i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−1.25707	+	1.19154i	−0.513196	+	0.486446i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$	−2.67458	+	1.35891i	−0.891526	+	0.452969i
$10$	1.00000			0.316228
$11$	2.25707	+	3.90936i	0.680532	+	1.17872i	0.974819	+	0.222998i	$0.0715845\pi$
$11$	2.25707	+	3.90936i	0.680532	+	1.17872i	−0.294287	+	0.955717i	$0.595082\pi$
$12$	1.66044	+	0.492881i	0.479328	+	0.142282i
$13$	1.56382	−	2.70861i	0.433725	−	0.751233i	−0.563466	−	0.826139i	$-0.690532\pi$
$13$	1.56382	−	2.70861i	0.433725	−	0.751233i	0.997191	+	0.0749063i	$0.0238658\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$	1.66044	+	0.492881i	0.428724	+	0.127261i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	5.34916			1.29736			0.648681	−	0.761061i	$-0.275321\pi$
$17$	5.34916			1.29736			0.648681	+	0.761061i	$0.275321\pi$
$18$	2.51414	+	1.63680i	0.592588	+	0.385798i
$19$	0.320884			0.0736160			0.0368080	−	0.999322i	$-0.488281\pi$
$19$	0.320884			0.0736160			0.0368080	+	0.999322i	$0.488281\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	1.25707	−	1.19154i	0.274315	−	0.260016i
$22$	2.25707	−	3.90936i	0.481209	−	0.833478i
$23$	0.950321	−	1.64600i	0.198156	−	0.343216i	−0.749775	−	0.661693i	$-0.769838\pi$
$23$	0.950321	−	1.64600i	0.198156	−	0.343216i	0.947930	+	0.318478i	$0.103172\pi$
$24$	−0.403374	−	1.68443i	−0.0823383	−	0.343832i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−3.12763			−0.613379
$27$	3.36783	+	3.95698i	0.648139	+	0.761522i
$28$	−1.00000			−0.188982
$29$	2.24293	+	3.88487i	0.416502	+	0.721403i	0.995585	−	0.0938662i	$-0.0299226\pi$
$29$	2.24293	+	3.88487i	0.416502	+	0.721403i	−0.579083	+	0.815269i	$0.696589\pi$
$30$	−0.403374	−	1.68443i	−0.0736456	−	0.307533i
$31$	3.51414	−	6.08666i	0.631158	−	1.09320i	−0.356158	−	0.934426i	$-0.615913\pi$
$31$	3.51414	−	6.08666i	0.631158	−	1.09320i	0.987315	−	0.158771i	$-0.0507532\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	5.67458	−	5.37880i	0.987817	−	0.936328i
$34$	−2.67458	−	4.63251i	−0.458687	−	0.794468i
$35$	−1.00000			−0.169031
$36$	0.160442	−	2.99571i	0.0267404	−	0.499284i
$37$	−1.80675			−0.297027			−0.148514	−	0.988910i	$-0.547449\pi$
$37$	−1.80675			−0.297027			−0.148514	+	0.988910i	$0.547449\pi$
$38$	−0.160442	−	0.277894i	−0.0260272	−	0.0450804i
$39$	−5.19325	−	1.54155i	−0.831586	−	0.246846i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−2.57795	+	4.46515i	−0.402609	+	0.697339i	−0.994040	−	0.109017i	$-0.965230\pi$
$41$	−2.57795	+	4.46515i	−0.402609	+	0.697339i	0.591431	+	0.806355i	$0.298563\pi$
$42$	−1.66044	−	0.492881i	−0.256212	−	0.0760532i
$43$	−2.33502	−	4.04438i	−0.356087	−	0.616762i	0.631216	−	0.775607i	$-0.282556\pi$
$43$	−2.33502	−	4.04438i	−0.356087	−	0.616762i	−0.987303	+	0.158846i	$0.949223\pi$
$44$	−4.51414			−0.680532
$45$	0.160442	−	2.99571i	0.0239173	−	0.446574i
$46$	−1.90064			−0.280234
$47$	4.02827	+	6.97717i	0.587584	+	1.01773i	0.994548	+	0.104281i	$0.0332542\pi$
$47$	4.02827	+	6.97717i	0.587584	+	1.01773i	−0.406964	+	0.913444i	$0.633412\pi$
$48$	−1.25707	+	1.19154i	−0.181442	+	0.171985i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−2.15771	−	9.01026i	−0.302140	−	1.26169i
$52$	1.56382	+	2.70861i	0.216862	+	0.375616i
$53$	8.24980			1.13320			0.566599	−	0.823994i	$-0.308259\pi$
$53$	8.24980			1.13320			0.566599	+	0.823994i	$0.308259\pi$
$54$	1.74293	−	4.89512i	0.237183	−	0.666141i
$55$	−4.51414			−0.608686
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	−0.129436	−	0.540506i	−0.0171443	−	0.0715918i
$58$	2.24293	−	3.88487i	0.294511	−	0.510109i
$59$	6.38197	−	11.0539i	0.830862	−	1.43909i	−0.0664944	−	0.997787i	$-0.521181\pi$
$59$	6.38197	−	11.0539i	0.830862	−	1.43909i	0.897356	−	0.441308i	$-0.145485\pi$
$60$	−1.25707	+	1.19154i	−0.162287	+	0.153828i
$61$	1.09663	+	1.89941i	0.140409	+	0.243195i	0.927651	−	0.373449i	$-0.121825\pi$
$61$	1.09663	+	1.89941i	0.140409	+	0.243195i	−0.787242	+	0.616644i	$0.788492\pi$
$62$	−7.02827			−0.892592
$63$	−2.51414	−	1.63680i	−0.316751	−	0.206217i
$64$	1.00000			0.125000
$65$	1.56382	+	2.70861i	0.193968	+	0.335962i
$66$	−7.49546	−	2.22493i	−0.922628	−	0.273870i
$67$	3.48133	−	6.02983i	0.425312	−	0.736662i	−0.571138	−	0.820854i	$-0.693498\pi$
$67$	3.48133	−	6.02983i	0.425312	−	0.736662i	0.996449	+	0.0841927i	$0.0268311\pi$
$68$	−2.67458	+	4.63251i	−0.324340	+	0.561774i
$69$	−3.15591	−	0.936790i	−0.379926	−	0.112776i
$70$	0.500000	+	0.866025i	0.0597614	+	0.103510i
$71$	−12.0620			−1.43150			−0.715749	−	0.698358i	$-0.753914\pi$
$71$	−12.0620			−1.43150			−0.715749	+	0.698358i	$0.753914\pi$
$72$	−2.67458	+	1.35891i	−0.315202	+	0.160149i
$73$	2.02827			0.237391			0.118696	−	0.992931i	$-0.462129\pi$
$73$	2.02827			0.237391			0.118696	+	0.992931i	$0.462129\pi$
$74$	0.903374	+	1.56469i	0.105015	+	0.181891i
$75$	−1.25707	+	1.19154i	−0.145154	+	0.137588i
$76$	−0.160442	+	0.277894i	−0.0184040	+	0.0318766i
$77$	−2.25707	+	3.90936i	−0.257217	+	0.445513i
$78$	1.26160	+	5.26826i	0.142849	+	0.596513i
$79$	−0.707389	−	1.22523i	−0.0795875	−	0.137850i	0.823485	−	0.567339i	$-0.192027\pi$
$79$	−0.707389	−	1.22523i	−0.0795875	−	0.137850i	−0.903072	+	0.429489i	$0.858694\pi$
$80$	1.00000			0.111803
$81$	5.30675	−	7.26900i	0.589639	−	0.807667i
$82$	5.15591			0.569375
$83$	1.80675	+	3.12938i	0.198316	+	0.343494i	0.947983	−	0.318322i	$-0.103119\pi$
$83$	1.80675	+	3.12938i	0.198316	+	0.343494i	−0.749666	+	0.661816i	$0.769786\pi$
$84$	0.403374	+	1.68443i	0.0440117	+	0.183786i
$85$	−2.67458	+	4.63251i	−0.290099	+	0.502466i
$86$	−2.33502	+	4.04438i	−0.251792	+	0.436116i
$87$	5.63904	−	5.34511i	0.604568	−	0.573056i
$88$	2.25707	+	3.90936i	0.240604	+	0.416739i
$89$	−2.00000			−0.212000			−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000			−0.212000			−0.106000	+	0.994366i	$0.533804\pi$
$90$	−2.67458	+	1.35891i	−0.281925	+	0.143241i
$91$	3.12763			0.327865
$92$	0.950321	+	1.64600i	0.0990778	+	0.171608i
$93$	−11.6700	−	3.46410i	−1.21013	−	0.359211i
$94$	4.02827	−	6.97717i	0.415485	−	0.719641i
$95$	−0.160442	+	0.277894i	−0.0164610	+	0.0285113i
$96$	1.66044	+	0.492881i	0.169468	+	0.0503044i
$97$	9.17004	+	15.8830i	0.931077	+	1.61267i	0.781485	+	0.623925i	$0.214463\pi$
$97$	9.17004	+	15.8830i	0.931077	+	1.61267i	0.149592	+	0.988748i	$0.452204\pi$
$98$	1.00000			0.101015
$99$	−11.3492	−	7.38874i	−1.14063	−	0.742596i
$100$	1.00000			0.100000
$101$	5.83502	+	10.1066i	0.580606	+	1.00564i	0.995408	+	0.0957276i	$0.0305178\pi$
$101$	5.83502	+	10.1066i	0.580606	+	1.00564i	−0.414801	+	0.909912i	$0.636149\pi$
$102$	−6.72426	+	6.37376i	−0.665801	+	0.631096i
$103$	4.80402	−	8.32080i	0.473354	−	0.819873i	−0.526181	−	0.850373i	$-0.676377\pi$
$103$	4.80402	−	8.32080i	0.473354	−	0.819873i	0.999535	+	0.0304999i	$0.00970992\pi$
$104$	1.56382	−	2.70861i	0.153345	−	0.265601i
$105$	0.403374	+	1.68443i	0.0393653	+	0.164383i
$106$	−4.12490	−	7.14454i	−0.400646	−	0.693939i
$107$	−2.32088			−0.224368			−0.112184	−	0.993687i	$-0.535785\pi$
$107$	−2.32088			−0.224368			−0.112184	+	0.993687i	$0.535785\pi$
$108$	−5.11076	+	0.938136i	−0.491783	+	0.0902722i
$109$	−0.155906			−0.0149331			−0.00746654	−	0.999972i	$-0.502377\pi$
$109$	−0.155906			−0.0149331			−0.00746654	+	0.999972i	$0.502377\pi$
$110$	2.25707	+	3.90936i	0.215203	+	0.372743i
$111$	0.728795	+	3.04333i	0.0691741	+	0.288860i
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	−0.853695	+	1.47864i	−0.0803088	+	0.139099i	−0.903383	−	0.428836i	$-0.858924\pi$
$113$	−0.853695	+	1.47864i	−0.0803088	+	0.139099i	0.823074	+	0.567935i	$0.192257\pi$
$114$	−0.403374	+	0.382348i	−0.0377794	+	0.0358102i
$115$	0.950321	+	1.64600i	0.0886179	+	0.153491i
$116$	−4.48586			−0.416502
$117$	−0.501804	+	9.36947i	−0.0463918	+	0.866208i
$118$	−12.7639			−1.17502
$119$	2.67458	+	4.63251i	0.245178	+	0.424661i
$120$	1.66044	+	0.492881i	0.151577	+	0.0449937i
$121$	−4.68872	+	8.12109i	−0.426247	+	0.738281i
$122$	1.09663	−	1.89941i	0.0992839	−	0.171965i
$123$	8.56108	+	2.54125i	0.771927	+	0.229137i
$124$	3.51414	+	6.08666i	0.315579	+	0.546599i
$125$	1.00000			0.0894427
$126$	−0.160442	+	2.99571i	−0.0142933	+	0.266879i
$127$	15.8259			1.40433			0.702163	−	0.712016i	$-0.252218\pi$
$127$	15.8259			1.40433			0.702163	+	0.712016i	$0.252218\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−5.87056	+	5.56457i	−0.516874	+	0.489933i
$130$	1.56382	−	2.70861i	0.137156	−	0.237561i
$131$	−5.98133	+	10.3600i	−0.522591	+	0.905154i	0.477064	+	0.878869i	$0.341701\pi$
$131$	−5.98133	+	10.3600i	−0.522591	+	0.905154i	−0.999654	+	0.0262853i	$0.991632\pi$
$132$	1.82088	+	7.60373i	0.158488	+	0.661820i
$133$	0.160442	+	0.277894i	0.0139121	+	0.0240965i
$134$	−6.96265			−0.601482
$135$	−5.11076	+	0.938136i	−0.439864	+	0.0807419i
$136$	5.34916			0.458687
$137$	9.23840	+	16.0014i	0.789289	+	1.36709i	0.926403	+	0.376534i	$0.122884\pi$
$137$	9.23840	+	16.0014i	0.789289	+	1.36709i	−0.137113	+	0.990555i	$0.543782\pi$
$138$	0.766669	+	3.20149i	0.0652632	+	0.272529i
$139$	3.50000	−	6.06218i	0.296866	−	0.514187i	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	3.50000	−	6.06218i	0.296866	−	0.514187i	0.975417	+	0.220366i	$0.0707252\pi$
$140$	0.500000	−	0.866025i	0.0422577	−	0.0731925i
$141$	10.1276	−	9.59974i	0.852900	−	0.808444i
$142$	6.03101	+	10.4460i	0.506111	+	0.876610i
$143$	14.1186			1.18065
$144$	2.51414	+	1.63680i	0.209511	+	0.136400i
$145$	−4.48586			−0.372531
$146$	−1.01414	−	1.75654i	−0.0839306	−	0.145372i
$147$	1.66044	+	0.492881i	0.136951	+	0.0406521i
$148$	0.903374	−	1.56469i	0.0742569	−	0.128617i
$149$	−3.15591	+	5.46619i	−0.258542	+	0.447808i	−0.965852	−	0.259096i	$-0.916575\pi$
$149$	−3.15591	+	5.46619i	−0.258542	+	0.447808i	0.707310	+	0.706904i	$0.249909\pi$
$150$	1.66044	+	0.492881i	0.135575	+	0.0402436i
$151$	−6.64177	−	11.5039i	−0.540499	−	0.936173i	−0.998875	−	0.0474141i	$-0.984902\pi$
$151$	−6.64177	−	11.5039i	−0.540499	−	0.936173i	0.458376	−	0.888758i	$-0.348431\pi$
$152$	0.320884			0.0260272
$153$	−14.3067	+	7.26900i	−1.15663	+	0.587664i
$154$	4.51414			0.363760
$155$	3.51414	+	6.08666i	0.282262	+	0.488893i
$156$	3.93165	−	3.72671i	0.314784	−	0.298376i
$157$	−10.0780	+	17.4555i	−0.804308	+	1.39310i	0.112449	+	0.993658i	$0.464131\pi$
$157$	−10.0780	+	17.4555i	−0.804308	+	1.39310i	−0.916757	+	0.399445i	$0.869203\pi$
$158$	−0.707389	+	1.22523i	−0.0562769	+	0.0974744i
$159$	−3.32775	−	13.8962i	−0.263908	−	1.10204i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	1.90064			0.149792
$162$	−8.94852	−	0.961276i	−0.703062	−	0.0755250i
$163$	−19.7639			−1.54803			−0.774016	−	0.633167i	$-0.781755\pi$
$163$	−19.7639			−1.54803			−0.774016	+	0.633167i	$0.781755\pi$
$164$	−2.57795	−	4.46515i	−0.201304	−	0.348669i
$165$	1.82088	+	7.60373i	0.141756	+	0.591949i
$166$	1.80675	−	3.12938i	0.140231	−	0.242887i
$167$	6.03101	−	10.4460i	0.466693	−	0.808336i	−0.532583	−	0.846378i	$-0.678779\pi$
$167$	6.03101	−	10.4460i	0.466693	−	0.808336i	0.999276	+	0.0380414i	$0.0121119\pi$
$168$	1.25707	−	1.19154i	0.0969849	−	0.0919297i
$169$	1.60896	+	2.78680i	0.123766	+	0.214369i
$170$	5.34916			0.410262
$171$	−0.858231	+	0.436052i	−0.0656306	+	0.0333457i
$172$	4.67004			0.356087
$173$	−10.5424	−	18.2600i	−0.801525	−	1.38828i	−0.918612	−	0.395160i	$-0.870689\pi$
$173$	−10.5424	−	18.2600i	−0.801525	−	1.38828i	0.117088	−	0.993122i	$-0.462644\pi$
$174$	−7.44852	−	2.21100i	−0.564671	−	0.167615i
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	2.25707	−	3.90936i	0.170133	−	0.294679i
$177$	−21.1938	−	6.29110i	−1.59302	−	0.472868i
$178$	1.00000	+	1.73205i	0.0749532	+	0.129823i
$179$	−21.3774			−1.59782			−0.798912	−	0.601448i	$-0.794591\pi$
$179$	−21.3774			−1.59782			−0.798912	+	0.601448i	$0.794591\pi$
$180$	2.51414	+	1.63680i	0.187393	+	0.122000i
$181$	−20.7549			−1.54270			−0.771348	−	0.636413i	$-0.780417\pi$
$181$	−20.7549			−1.54270			−0.771348	+	0.636413i	$0.780417\pi$
$182$	−1.56382	−	2.70861i	−0.115918	−	0.200775i
$183$	2.75707	−	2.61336i	0.203808	−	0.193185i
$184$	0.950321	−	1.64600i	0.0700586	−	0.121345i
$185$	0.903374	−	1.56469i	0.0664174	−	0.115038i
$186$	2.83502	+	11.8386i	0.207874	+	0.868049i
$187$	12.0734	+	20.9118i	0.882896	+	1.52922i
$188$	−8.05655			−0.587584
$189$	−1.74293	+	4.89512i	−0.126780	+	0.356068i
$190$	0.320884			0.0232794
$191$	10.2215	+	17.7042i	0.739604	+	1.28103i	0.952674	+	0.303994i	$0.0983204\pi$
$191$	10.2215	+	17.7042i	0.739604	+	1.28103i	−0.213070	+	0.977037i	$0.568346\pi$
$192$	−0.403374	−	1.68443i	−0.0291110	−	0.121563i
$193$	5.53101	−	9.57998i	0.398131	−	0.689582i	−0.595365	−	0.803456i	$-0.702992\pi$
$193$	5.53101	−	9.57998i	0.398131	−	0.689582i	0.993495	+	0.113873i	$0.0363258\pi$
$194$	9.17004	−	15.8830i	0.658371	−	1.14033i
$195$	3.93165	−	3.72671i	0.281551	−	0.266876i
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	−13.6080			−0.969532			−0.484766	−	0.874644i	$-0.661095\pi$
$197$	−13.6080			−0.969532			−0.484766	+	0.874644i	$0.661095\pi$
$198$	−0.724258	+	13.5230i	−0.0514708	+	0.961040i
$199$	19.9572			1.41473			0.707364	−	0.706850i	$-0.249884\pi$
$199$	19.9572			1.41473			0.707364	+	0.706850i	$0.249884\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−11.5611	−	3.43176i	−0.815456	−	0.242058i
$202$	5.83502	−	10.1066i	0.410551	−	0.711095i
$203$	−2.24293	+	3.88487i	−0.157423	+	0.272665i
$204$	8.88197	+	2.63650i	0.621862	+	0.184592i
$205$	−2.57795	−	4.46515i	−0.180052	−	0.311859i
$206$	−9.60803			−0.669423
$207$	−0.304943	+	5.69377i	−0.0211950	+	0.395744i
$208$	−3.12763			−0.216862
$209$	0.724258	+	1.25445i	0.0500980	+	0.0867723i
$210$	1.25707	−	1.19154i	0.0867460	−	0.0822244i
$211$	−4.97173	+	8.61128i	−0.342268	+	0.592825i	−0.984853	−	0.173389i	$-0.944528\pi$
$211$	−4.97173	+	8.61128i	−0.342268	+	0.592825i	0.642586	+	0.766214i	$0.277862\pi$
$212$	−4.12490	+	7.14454i	−0.283299	+	0.490689i
$213$	4.86550	+	20.3176i	0.333379	+	1.39214i
$214$	1.16044	+	2.00994i	0.0793262	+	0.137397i
$215$	4.67004			0.318494
$216$	3.36783	+	3.95698i	0.229152	+	0.269239i
$217$	7.02827			0.477110
$218$	0.0779530	+	0.135018i	0.00527964	+	0.00914461i
$219$	−0.818153	−	3.41648i	−0.0552856	−	0.230864i
$220$	2.25707	−	3.90936i	0.152172	−	0.263569i
$221$	8.36510	−	14.4888i	0.562697	−	0.974621i
$222$	2.27121	−	2.15282i	0.152433	−	0.144488i
$223$	−10.5734	−	18.3137i	−0.708048	−	1.22638i	−0.965580	−	0.260106i	$-0.916243\pi$
$223$	−10.5734	−	18.3137i	−0.708048	−	1.22638i	0.257532	−	0.966270i	$-0.417091\pi$
$224$	−1.00000			−0.0668153
$225$	2.51414	+	1.63680i	0.167609	+	0.109120i
$226$	1.70739			0.113574
$227$	−9.45992	−	16.3851i	−0.627877	−	1.08751i	−0.987977	−	0.154601i	$-0.950591\pi$
$227$	−9.45992	−	16.3851i	−0.627877	−	1.08751i	0.360100	−	0.932914i	$-0.382743\pi$
$228$	0.532810	+	0.158158i	0.0352862	+	0.0104743i
$229$	−7.83775	+	13.5754i	−0.517933	+	0.897087i	0.481850	+	0.876254i	$0.339965\pi$
$229$	−7.83775	+	13.5754i	−0.517933	+	0.897087i	−0.999783	+	0.0208329i	$0.993368\pi$
$230$	0.950321	−	1.64600i	0.0626623	−	0.108534i
$231$	7.49546	+	2.22493i	0.493165	+	0.146390i
$232$	2.24293	+	3.88487i	0.147256	+	0.255054i
$233$	−21.6555			−1.41870			−0.709350	−	0.704857i	$-0.751011\pi$
$233$	−21.6555			−1.41870			−0.709350	+	0.704857i	$0.751011\pi$
$234$	8.36510	−	4.25016i	0.546844	−	0.277842i
$235$	−8.05655			−0.525551
$236$	6.38197	+	11.0539i	0.415431	+	0.719547i
$237$	−1.77847	+	1.68577i	−0.115524	+	0.109503i
$238$	2.67458	−	4.63251i	0.173367	−	0.300281i
$239$	1.45759	−	2.52462i	0.0942836	−	0.163304i	−0.815026	−	0.579425i	$-0.803277\pi$
$239$	1.45759	−	2.52462i	0.0942836	−	0.163304i	0.909309	+	0.416121i	$0.136611\pi$
$240$	−0.403374	−	1.68443i	−0.0260377	−	0.108729i
$241$	−0.375100	−	0.649692i	−0.0241623	−	0.0418503i	0.853691	−	0.520779i	$-0.174359\pi$
$241$	−0.375100	−	0.649692i	−0.0241623	−	0.0418503i	−0.877854	+	0.478929i	$0.841025\pi$
$242$	9.37743			0.602804
$243$	−14.3847	−	6.00670i	−0.922779	−	0.385330i
$244$	−2.19325			−0.140409
$245$	−0.500000	−	0.866025i	−0.0319438	−	0.0553283i
$246$	−2.07976	−	8.68474i	−0.132600	−	0.553719i
$247$	0.501804	−	0.869151i	0.0319290	−	0.0553027i
$248$	3.51414	−	6.08666i	0.223148	−	0.386504i
$249$	4.54241	−	4.30564i	0.287864	−	0.272859i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	4.02827			0.254262			0.127131	−	0.991886i	$-0.459423\pi$
$251$	4.02827			0.254262			0.127131	+	0.991886i	$0.459423\pi$
$252$	2.67458	−	1.35891i	0.168483	−	0.0856030i
$253$	8.57976			0.539405
$254$	−7.91297	−	13.7057i	−0.496504	−	0.859970i
$255$	8.88197	+	2.63650i	0.556210	+	0.165104i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.43438	−	9.41262i	0.338987	−	0.587143i	−0.645255	−	0.763967i	$-0.723249\pi$
$257$	5.43438	−	9.41262i	0.338987	−	0.587143i	0.984243	+	0.176824i	$0.0565823\pi$
$258$	7.75434	+	2.30177i	0.482764	+	0.143302i
$259$	−0.903374	−	1.56469i	−0.0561329	−	0.0972251i
$260$	−3.12763			−0.193968
$261$	−11.2781	−	7.34246i	−0.698095	−	0.454487i
$262$	11.9627			0.739055
$263$	−2.42711	−	4.20388i	−0.149662	−	0.259222i	0.781440	−	0.623980i	$-0.214485\pi$
$263$	−2.42711	−	4.20388i	−0.149662	−	0.259222i	−0.931103	+	0.364757i	$0.881152\pi$
$264$	5.67458	−	5.37880i	0.349246	−	0.331042i
$265$	−4.12490	+	7.14454i	−0.253391	+	0.438885i
$266$	0.160442	−	0.277894i	0.00983735	−	0.0170388i
$267$	0.806748	+	3.36885i	0.0493721	+	0.206170i
$268$	3.48133	+	6.02983i	0.212656	+	0.368331i
$269$	29.9873			1.82836			0.914180	−	0.405309i	$-0.132836\pi$
$269$	29.9873			1.82836			0.914180	+	0.405309i	$0.132836\pi$
$270$	3.36783	+	3.95698i	0.204960	+	0.240814i
$271$	16.9289			1.02836			0.514179	−	0.857683i	$-0.328097\pi$
$271$	16.9289			1.02836			0.514179	+	0.857683i	$0.328097\pi$
$272$	−2.67458	−	4.63251i	−0.162170	−	0.280887i
$273$	−1.26160	−	5.26826i	−0.0763558	−	0.318850i
$274$	9.23840	−	16.0014i	0.558112	−	0.966678i
$275$	2.25707	−	3.90936i	0.136106	−	0.235743i
$276$	2.38924	−	2.26470i	0.143815	−	0.136319i
$277$	−15.9909	−	27.6971i	−0.960802	−	1.66416i	−0.720495	−	0.693460i	$-0.756085\pi$
$277$	−15.9909	−	27.6971i	−0.960802	−	1.66416i	−0.240307	−	0.970697i	$-0.577248\pi$
$278$	−7.00000			−0.419832
$279$	−1.12763	+	21.0546i	−0.0675096	+	1.26051i
$280$	−1.00000			−0.0597614
$281$	−7.46719	−	12.9336i	−0.445455	−	0.771551i	0.552629	−	0.833428i	$-0.313625\pi$
$281$	−7.46719	−	12.9336i	−0.445455	−	0.771551i	−0.998084	+	0.0618766i	$0.980291\pi$
$282$	−13.3774	−	3.97092i	−0.796614	−	0.236465i
$283$	−14.2498	+	24.6814i	−0.847063	+	1.46716i	0.0367551	+	0.999324i	$0.488298\pi$
$283$	−14.2498	+	24.6814i	−0.847063	+	1.46716i	−0.883818	+	0.467831i	$0.845035\pi$
$284$	6.03101	−	10.4460i	0.357874	−	0.619857i
$285$	0.532810	+	0.158158i	0.0315610	+	0.00936846i
$286$	−7.05928	−	12.2270i	−0.417424	−	0.723000i
$287$	−5.15591			−0.304344
$288$	0.160442	−	2.99571i	0.00945415	−	0.176524i
$289$	11.6135			0.683147
$290$	2.24293	+	3.88487i	0.131709	+	0.228128i
$291$	23.0547	−	21.8530i	1.35149	−	1.28105i
$292$	−1.01414	+	1.75654i	−0.0593479	+	0.102794i
$293$	15.6486	−	27.1042i	0.914203	−	1.58345i	0.106139	−	0.994351i	$-0.466151\pi$
$293$	15.6486	−	27.1042i	0.914203	−	1.58345i	0.808064	−	0.589095i	$-0.200516\pi$
$294$	−0.403374	−	1.68443i	−0.0235252	−	0.0982377i
$295$	6.38197	+	11.0539i	0.371573	+	0.643583i
$296$	−1.80675			−0.105015
$297$	−7.86783	+	22.0972i	−0.456538	+	1.28221i
$298$	6.31181			0.365633
$299$	−2.97225	−	5.14810i	−0.171890	−	0.297722i
$300$	−0.403374	−	1.68443i	−0.0232888	−	0.0972504i
$301$	2.33502	−	4.04438i	0.134588	−	0.233114i
$302$	−6.64177	+	11.5039i	−0.382191	+	0.661974i
$303$	14.6700	−	13.9054i	0.842772	−	0.798843i
$304$	−0.160442	−	0.277894i	−0.00920199	−	0.0159383i
$305$	−2.19325			−0.125585
$306$	13.4485	+	8.75550i	0.768801	+	0.500519i
$307$	−10.3829			−0.592583			−0.296292	−	0.955098i	$-0.595750\pi$
$307$	−10.3829			−0.592583			−0.296292	+	0.955098i	$0.595750\pi$
$308$	−2.25707	−	3.90936i	−0.128608	−	0.222756i
$309$	−15.9536	−	4.73561i	−0.907568	−	0.269400i
$310$	3.51414	−	6.08666i	0.199590	−	0.345699i
$311$	−2.67912	+	4.64036i	−0.151919	+	0.263131i	−0.931933	−	0.362631i	$-0.881879\pi$
$311$	−2.67912	+	4.64036i	−0.151919	+	0.263131i	0.780014	+	0.625762i	$0.215212\pi$
$312$	−5.19325	−	1.54155i	−0.294010	−	0.0872731i
$313$	6.64631	+	11.5117i	0.375671	+	0.650682i	0.990427	−	0.138036i	$-0.0440788\pi$
$313$	6.64631	+	11.5117i	0.375671	+	0.650682i	−0.614756	+	0.788717i	$0.710745\pi$
$314$	20.1559			1.13746
$315$	2.67458	−	1.35891i	0.150695	−	0.0765657i
$316$	1.41478			0.0795875
$317$	−16.1814	−	28.0271i	−0.908841	−	1.57416i	−0.815677	−	0.578507i	$-0.803635\pi$
$317$	−16.1814	−	28.0271i	−0.908841	−	1.57416i	−0.0931635	−	0.995651i	$-0.529698\pi$
$318$	−10.3706	+	9.83001i	−0.581552	+	0.551239i
$319$	−10.1249	+	17.5368i	−0.566886	+	0.981875i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	0.936184	+	3.90936i	0.0522527	+	0.218199i
$322$	−0.950321	−	1.64600i	−0.0529593	−	0.0917282i
$323$	1.71646			0.0955065
$324$	3.64177	+	8.23028i	0.202320	+	0.457238i
$325$	−3.12763			−0.173490
$326$	9.88197	+	17.1161i	0.547312	+	0.947972i
$327$	0.0628884	+	0.262612i	0.00347773	+	0.0145225i
$328$	−2.57795	+	4.46515i	−0.142344	+	0.246546i
$329$	−4.02827	+	6.97717i	−0.222086	+	0.384664i
$330$	5.67458	−	5.37880i	0.312375	−	0.296093i
$331$	−1.80675	−	3.12938i	−0.0993078	−	0.172006i	0.812091	−	0.583531i	$-0.198330\pi$
$331$	−1.80675	−	3.12938i	−0.0993078	−	0.172006i	−0.911398	+	0.411525i	$0.864996\pi$
$332$	−3.61350			−0.198316
$333$	4.83229	−	2.45520i	0.264808	−	0.134544i
$334$	−12.0620			−0.660004
$335$	3.48133	+	6.02983i	0.190205	+	0.329445i
$336$	−1.66044	−	0.492881i	−0.0905846	−	0.0268889i
$337$	−8.17277	+	14.1557i	−0.445199	+	0.771108i	−0.998066	−	0.0621617i	$-0.980201\pi$
$337$	−8.17277	+	14.1557i	−0.445199	+	0.771108i	0.552867	+	0.833270i	$0.313534\pi$
$338$	1.60896	−	2.78680i	0.0875158	−	0.151582i
$339$	2.83502	+	0.841540i	0.153977	+	0.0457062i
$340$	−2.67458	−	4.63251i	−0.145049	−	0.251233i
$341$	31.7266			1.71809
$342$	0.806748	+	0.525224i	0.0436239	+	0.0284009i
$343$	−1.00000			−0.0539949
$344$	−2.33502	−	4.04438i	−0.125896	−	0.218058i
$345$	2.38924	−	2.26470i	0.128632	−	0.121927i
$346$	−10.5424	+	18.2600i	−0.566764	+	0.981663i
$347$	18.5096	−	32.0596i	0.993647	−	1.72105i	0.399363	−	0.916793i	$-0.369231\pi$
$347$	18.5096	−	32.0596i	0.993647	−	1.72105i	0.594284	−	0.804255i	$-0.297435\pi$
$348$	1.80948	+	7.55610i	0.0969983	+	0.405050i
$349$	−10.1586	−	17.5953i	−0.543779	−	0.941854i	−0.998683	−	0.0513127i	$-0.983659\pi$
$349$	−10.1586	−	17.5953i	−0.543779	−	0.941854i	0.454903	−	0.890541i	$-0.349674\pi$
$350$	−1.00000			−0.0534522
$351$	15.9846	−	2.93415i	0.853194	−	0.156613i
$352$	−4.51414			−0.240604
$353$	11.7835	+	20.4097i	0.627174	+	1.08630i	0.988116	+	0.153710i	$0.0491220\pi$
$353$	11.7835	+	20.4097i	0.627174	+	1.08630i	−0.360942	+	0.932588i	$0.617545\pi$
$354$	5.14864	+	21.4999i	0.273647	+	1.14271i
$355$	6.03101	−	10.4460i	0.320093	−	0.554417i
$356$	1.00000	−	1.73205i	0.0529999	−	0.0917985i
$357$	6.72426	−	6.37376i	0.355885	−	0.337335i
$358$	10.6887	+	18.5134i	0.564916	+	0.978464i
$359$	−30.3173			−1.60008			−0.800042	−	0.599944i	$-0.795190\pi$
$359$	−30.3173			−1.60008			−0.800042	+	0.599944i	$0.795190\pi$
$360$	0.160442	−	2.99571i	0.00845605	−	0.157888i
$361$	−18.8970			−0.994581
$362$	10.3774	+	17.9742i	0.545426	+	0.944705i
$363$	15.5707	+	4.62196i	0.817249	+	0.242590i
$364$	−1.56382	+	2.70861i	−0.0819662	+	0.141970i
$365$	−1.01414	+	1.75654i	−0.0530824	+	0.0919413i
$366$	−3.64177	−	1.08101i	−0.190358	−	0.0565054i
$367$	−6.41751	−	11.1155i	−0.334991	−	0.580222i	0.648492	−	0.761222i	$-0.275400\pi$
$367$	−6.41751	−	11.1155i	−0.334991	−	0.580222i	−0.983483	+	0.181000i	$0.942067\pi$
$368$	−1.90064			−0.0990778
$369$	0.827225	−	15.4456i	0.0430636	−	0.804065i
$370$	−1.80675			−0.0939283
$371$	4.12490	+	7.14454i	0.214154	+	0.370926i
$372$	8.83502	−	8.37450i	0.458075	−	0.434198i
$373$	−2.74113	+	4.74777i	−0.141930	+	0.245830i	−0.928223	−	0.372023i	$-0.878664\pi$
$373$	−2.74113	+	4.74777i	−0.141930	+	0.245830i	0.786293	+	0.617853i	$0.211998\pi$
$374$	12.0734	−	20.9118i	0.624302	−	1.08132i
$375$	−0.403374	−	1.68443i	−0.0208301	−	0.0869834i
$376$	4.02827	+	6.97717i	0.207742	+	0.359820i
$377$	14.0301			0.722588
$378$	5.11076	−	0.938136i	0.262869	−	0.0482525i
$379$	−12.2781			−0.630682			−0.315341	−	0.948978i	$-0.602119\pi$
$379$	−12.2781			−0.630682			−0.315341	+	0.948978i	$0.602119\pi$
$380$	−0.160442	−	0.277894i	−0.00823051	−	0.0142557i
$381$	−6.38377	−	26.6576i	−0.327051	−	1.36571i
$382$	10.2215	−	17.7042i	0.522979	−	0.905826i
$383$	9.83502	−	17.0348i	0.502546	−	0.870435i	−0.497450	−	0.867493i	$-0.665730\pi$
$383$	9.83502	−	17.0348i	0.502546	−	0.870435i	0.999996	−	0.00294250i	$-0.000936630\pi$
$384$	−1.25707	+	1.19154i	−0.0641495	+	0.0608058i
$385$	−2.25707	−	3.90936i	−0.115031	−	0.199239i
$386$	−11.0620			−0.563042
$387$	11.7411	+	7.64393i	0.596835	+	0.388563i
$388$	−18.3401			−0.931077
$389$	0.934380	+	1.61839i	0.0473749	+	0.0820558i	0.888740	−	0.458411i	$-0.151581\pi$
$389$	0.934380	+	1.61839i	0.0473749	+	0.0820558i	−0.841366	+	0.540466i	$0.818248\pi$
$390$	−5.19325	−	1.54155i	−0.262971	−	0.0780594i
$391$	5.08342	−	8.80474i	0.257079	−	0.445275i
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$	19.8633	+	5.89616i	1.00197	+	0.297422i
$394$	6.80402	+	11.7849i	0.342781	+	0.593715i
$395$	1.41478			0.0711852
$396$	12.0734	−	6.13429i	0.606712	−	0.308260i
$397$	14.9855			0.752099			0.376049	−	0.926600i	$-0.377282\pi$
$397$	14.9855			0.752099			0.376049	+	0.926600i	$0.377282\pi$
$398$	−9.97859	−	17.2834i	−0.500182	−	0.866340i
$399$	0.403374	−	0.382348i	0.0201939	−	0.0191414i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−15.7835	+	27.3379i	−0.788192	+	1.36519i	0.138881	+	0.990309i	$0.455649\pi$
$401$	−15.7835	+	27.3379i	−0.788192	+	1.36519i	−0.927073	+	0.374880i	$0.877684\pi$
$402$	2.80855	+	11.7281i	0.140078	+	0.584943i
$403$	−10.9909	−	19.0368i	−0.547497	−	0.948293i
$404$	−11.6700			−0.580606
$405$	3.64177	+	8.23028i	0.180961	+	0.408966i
$406$	4.48586			0.222630
$407$	−4.07795	−	7.06322i	−0.202137	−	0.350111i
$408$	−2.15771	−	9.01026i	−0.106823	−	0.446074i
$409$	−11.2571	+	19.4978i	−0.556626	+	0.964105i	0.441149	+	0.897434i	$0.354571\pi$
$409$	−11.2571	+	19.4978i	−0.556626	+	0.964105i	−0.997775	+	0.0666709i	$0.978762\pi$
$410$	−2.57795	+	4.46515i	−0.127316	+	0.220518i
$411$	23.2266	−	22.0159i	1.14568	−	1.08597i
$412$	4.80402	+	8.32080i	0.236677	+	0.409936i
$413$	12.7639			0.628072
$414$	5.08342	−	2.58279i	0.249836	−	0.126937i
$415$	−3.61350			−0.177380
$416$	1.56382	+	2.70861i	0.0766724	+	0.132800i
$417$	−11.6231	−	3.45017i	−0.569185	−	0.168955i
$418$	0.724258	−	1.25445i	0.0354246	−	0.0613573i
$419$	−5.98133	+	10.3600i	−0.292207	+	0.506117i	−0.974331	−	0.225119i	$-0.927723\pi$
$419$	−5.98133	+	10.3600i	−0.292207	+	0.506117i	0.682124	+	0.731236i	$0.261056\pi$
$420$	−1.66044	−	0.492881i	−0.0810213	−	0.0240501i
$421$	−7.43618	−	12.8798i	−0.362417	−	0.627725i	0.625941	−	0.779871i	$-0.284715\pi$
$421$	−7.43618	−	12.8798i	−0.362417	−	0.627725i	−0.988358	+	0.152145i	$0.951382\pi$
$422$	9.94345			0.484040
$423$	−20.2553	−	13.1870i	−0.984845	−	0.641172i
$424$	8.24980			0.400646
$425$	−2.67458	−	4.63251i	−0.129736	−	0.224710i
$426$	15.1628	−	14.3724i	0.734639	−	0.696346i
$427$	−1.09663	+	1.89941i	−0.0530695	+	0.0919190i
$428$	1.16044	−	2.00994i	0.0560921	−	0.0971544i
$429$	−5.69506	−	23.7817i	−0.274960	−	1.14819i
$430$	−2.33502	−	4.04438i	−0.112605	−	0.195037i
$431$	−14.2553			−0.686652			−0.343326	−	0.939216i	$-0.611554\pi$
$431$	−14.2553			−0.686652			−0.343326	+	0.939216i	$0.611554\pi$
$432$	1.74293	−	4.89512i	0.0838568	−	0.235517i
$433$	−6.42571			−0.308800			−0.154400	−	0.988008i	$-0.549344\pi$
$433$	−6.42571			−0.308800			−0.154400	+	0.988008i	$0.549344\pi$
$434$	−3.51414	−	6.08666i	−0.168684	−	0.292169i
$435$	1.80948	+	7.55610i	0.0867579	+	0.362287i
$436$	0.0779530	−	0.135018i	0.00373327	−	0.00646621i
$437$	0.304943	−	0.528177i	0.0145874	−	0.0252661i
$438$	−2.54968	+	2.41678i	−0.121828	+	0.115478i
$439$	−1.33683	−	2.31545i	−0.0638032	−	0.110510i	0.832359	−	0.554236i	$-0.186990\pi$
$439$	−1.33683	−	2.31545i	−0.0638032	−	0.110510i	−0.896162	+	0.443726i	$0.853656\pi$
$440$	−4.51414			−0.215203
$441$	0.160442	−	2.99571i	0.00764011	−	0.142653i
$442$	−16.7302			−0.795774
$443$	4.07068	+	7.05063i	0.193404	+	0.334986i	0.946376	−	0.323067i	$-0.104714\pi$
$443$	4.07068	+	7.05063i	0.193404	+	0.334986i	−0.752972	+	0.658052i	$0.771381\pi$
$444$	−3.00000	−	0.890511i	−0.142374	−	0.0422618i
$445$	1.00000	−	1.73205i	0.0474045	−	0.0821071i
$446$	−10.5734	+	18.3137i	−0.500666	+	0.867179i
$447$	10.4804	+	3.11097i	0.495706	+	0.147144i
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	−22.2643			−1.05072			−0.525360	−	0.850880i	$-0.676069\pi$
$449$	−22.2643			−1.05072			−0.525360	+	0.850880i	$0.676069\pi$
$450$	0.160442	−	2.99571i	0.00756332	−	0.141219i
$451$	−23.2745			−1.09595
$452$	−0.853695	−	1.47864i	−0.0401544	−	0.0695495i
$453$	−16.6983	+	15.8279i	−0.784555	+	0.743661i
$454$	−9.45992	+	16.3851i	−0.443976	+	0.768989i
$455$	−1.56382	+	2.70861i	−0.0733128	+	0.126982i
$456$	−0.129436	−	0.540506i	−0.00606141	−	0.0253115i
$457$	15.9271	+	27.5866i	0.745039	+	1.29045i	0.950177	+	0.311712i	$0.100902\pi$
$457$	15.9271	+	27.5866i	0.745039	+	1.29045i	−0.205138	+	0.978733i	$0.565764\pi$
$458$	15.6755			0.732468
$459$	18.0151	+	21.1665i	0.840871	+	0.987969i
$460$	−1.90064			−0.0886179
$461$	−1.19052	−	2.06204i	−0.0554481	−	0.0960389i	0.836969	−	0.547250i	$-0.184325\pi$
$461$	−1.19052	−	2.06204i	−0.0554481	−	0.0960389i	−0.892417	+	0.451211i	$0.850992\pi$
$462$	−1.82088	−	7.60373i	−0.0847152	−	0.353757i
$463$	17.1559	−	29.7149i	0.797303	−	1.38097i	−0.124064	−	0.992274i	$-0.539593\pi$
$463$	17.1559	−	29.7149i	0.797303	−	1.38097i	0.921367	−	0.388694i	$-0.127074\pi$
$464$	2.24293	−	3.88487i	0.104125	−	0.180351i
$465$	8.83502	−	8.37450i	0.409714	−	0.388358i
$466$	10.8278	+	18.7542i	0.501586	+	0.868772i
$467$	−38.5899			−1.78573			−0.892863	−	0.450327i	$-0.851307\pi$
$467$	−38.5899			−1.78573			−0.892863	+	0.450327i	$0.851307\pi$
$468$	−7.86330	−	5.11931i	−0.363481	−	0.236640i
$469$	6.96265			0.321505
$470$	4.02827	+	6.97717i	0.185810	+	0.321833i
$471$	33.4677	+	9.93446i	1.54211	+	0.457756i
$472$	6.38197	−	11.0539i	0.293754	−	0.508797i
$473$	10.5406	−	18.2569i	0.484658	−	0.839452i
$474$	2.34916	+	0.697317i	0.107900	+	0.0320288i
$475$	−0.160442	−	0.277894i	−0.00736160	−	0.0127507i
$476$	−5.34916			−0.245178
$477$	−22.0647	+	11.2107i	−1.01028	+	0.513303i
$478$	−2.91518			−0.133337
$479$	2.56382	+	4.44066i	0.117144	+	0.202899i	0.918635	−	0.395108i	$-0.129293\pi$
$479$	2.56382	+	4.44066i	0.117144	+	0.202899i	−0.801491	+	0.598007i	$0.795960\pi$
$480$	−1.25707	+	1.19154i	−0.0573771	+	0.0543863i
$481$	−2.82542	+	4.89377i	−0.128828	+	0.223137i
$482$	−0.375100	+	0.649692i	−0.0170853	+	0.0295927i
$483$	−0.766669	−	3.20149i	−0.0348847	−	0.145673i
$484$	−4.68872	−	8.12109i	−0.213123	−	0.369141i
$485$	−18.3401			−0.832780
$486$	1.99040	+	15.4609i	0.0902863	+	0.701319i
$487$	−11.7831			−0.533945			−0.266972	−	0.963704i	$-0.586023\pi$
$487$	−11.7831			−0.533945			−0.266972	+	0.963704i	$0.586023\pi$
$488$	1.09663	+	1.89941i	0.0496419	+	0.0859824i
$489$	7.97225	+	33.2909i	0.360518	+	1.50547i
$490$	−0.500000	+	0.866025i	−0.0225877	+	0.0391230i
$491$	−17.6532	+	30.5762i	−0.796677	+	1.37988i	0.125093	+	0.992145i	$0.460077\pi$
$491$	−17.6532	+	30.5762i	−0.796677	+	1.37988i	−0.921769	+	0.387739i	$0.873256\pi$
$492$	−6.48133	+	6.14349i	−0.292201	+	0.276970i
$493$	11.9978	+	20.7808i	0.540354	+	0.935920i
$494$	−1.00361			−0.0451545
$495$	12.0734	−	6.13429i	0.542660	−	0.275716i
$496$	−7.02827			−0.315579
$497$	−6.03101	−	10.4460i	−0.270528	−	0.468568i
$498$	−6.00000	−	1.78102i	−0.268866	−	0.0798095i
$499$	15.9554	−	27.6355i	0.714261	−	1.23714i	−0.248983	−	0.968508i	$-0.580096\pi$
$499$	15.9554	−	27.6355i	0.714261	−	1.23714i	0.963244	−	0.268629i	$-0.0865704\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−20.0283	−	5.94513i	−0.894797	−	0.265609i
$502$	−2.01414	−	3.48859i	−0.0898953	−	0.155703i
$503$	36.6236			1.63297			0.816483	−	0.577369i	$-0.195921\pi$
$503$	36.6236			1.63297			0.816483	+	0.577369i	$0.195921\pi$
$504$	−2.51414	−	1.63680i	−0.111989	−	0.0729089i
$505$	−11.6700			−0.519310
$506$	−4.28988	−	7.43029i	−0.190708	−	0.330317i
$507$	4.04514	−	3.83429i	0.179651	−	0.170287i
$508$	−7.91297	+	13.7057i	−0.351081	+	0.608091i
$509$	12.2243	−	21.1730i	0.541831	−	0.938478i	−0.456968	−	0.889483i	$-0.651065\pi$
$509$	12.2243	−	21.1730i	0.541831	−	0.938478i	0.998799	−	0.0489954i	$-0.0156020\pi$
$510$	−2.15771	−	9.01026i	−0.0955450	−	0.398981i
$511$	1.01414	+	1.75654i	0.0448628	+	0.0777046i
$512$	1.00000			0.0441942
$513$	1.08068	+	1.26973i	0.0477134	+	0.0560601i
$514$	−10.8688			−0.479400
$515$	4.80402	+	8.32080i	0.211690	+	0.366658i
$516$	−1.88377	−	7.86634i	−0.0829285	−	0.346296i
$517$	−18.1842	+	31.4959i	−0.799739	+	1.38519i
$518$	−0.903374	+	1.56469i	−0.0396920	+	0.0687485i
$519$	−26.5051	+	25.1235i	−1.16344	+	1.10280i
$520$	1.56382	+	2.70861i	0.0685779	+	0.118780i
$521$	−4.34555			−0.190382			−0.0951910	−	0.995459i	$-0.530346\pi$
$521$	−4.34555			−0.190382			−0.0951910	+	0.995459i	$0.530346\pi$
$522$	−0.719722	+	13.4383i	−0.0315014	+	0.588180i
$523$	9.18964			0.401835			0.200918	−	0.979608i	$-0.435608\pi$
$523$	9.18964			0.401835			0.200918	+	0.979608i	$0.435608\pi$
$524$	−5.98133	−	10.3600i	−0.261295	−	0.452577i
$525$	−1.66044	−	0.492881i	−0.0724676	−	0.0215111i
$526$	−2.42711	+	4.20388i	−0.105827	+	0.183298i
$527$	18.7977	−	32.5585i	0.818840	−	1.41827i
$528$	−7.49546	−	2.22493i	−0.326198	−	0.0968277i
$529$	9.69378	+	16.7901i	0.421469	+	0.730005i
$530$	8.24980			0.358348
$531$	−2.04787	+	38.2370i	−0.0888702	+	1.65934i
$532$	−0.320884			−0.0139121
$533$	8.06289	+	13.9653i	0.349242	+	0.604906i
$534$	2.51414	−	2.38309i	0.108797	−	0.103126i
$535$	1.16044	−	2.00994i	0.0501703	−	0.0868975i
$536$	3.48133	−	6.02983i	0.150370	−	0.260449i
$537$	8.62310	+	36.0087i	0.372114	+	1.55389i
$538$	−14.9937	−	25.9698i	−0.646423	−	1.11964i
$539$	−4.51414			−0.194438
$540$	1.74293	−	4.89512i	0.0750038	−	0.210652i
$541$	10.5852			0.455094			0.227547	−	0.973767i	$-0.426929\pi$
$541$	10.5852			0.455094			0.227547	+	0.973767i	$0.426929\pi$
$542$	−8.46446	−	14.6609i	−0.363580	−	0.629738i
$543$	8.37197	+	34.9600i	0.359276	+	1.50028i
$544$	−2.67458	+	4.63251i	−0.114672	+	0.198617i
$545$	0.0779530	−	0.135018i	0.00333914	−	0.00578356i
$546$	−3.93165	+	3.72671i	−0.168259	+	0.159489i
$547$	−6.82088	−	11.8141i	−0.291640	−	0.505135i	0.682558	−	0.730832i	$-0.260868\pi$
$547$	−6.82088	−	11.8141i	−0.291640	−	0.505135i	−0.974198	+	0.225696i	$0.927534\pi$
$548$	−18.4768			−0.789289
$549$	−5.51414	−	3.58992i	−0.235338	−	0.153214i
$550$	−4.51414			−0.192483
$551$	0.719722	+	1.24660i	0.0306612	+	0.0531067i
$552$	−3.15591	−	0.936790i	−0.134324	−	0.0398724i
$553$	0.707389	−	1.22523i	0.0300813	−	0.0521023i
$554$	−15.9909	+	27.6971i	−0.679389	+	1.17674i
$555$	−3.00000	−	0.890511i	−0.127343	−	0.0378001i
$556$	3.50000	+	6.06218i	0.148433	+	0.257094i
$557$	−12.8296			−0.543606			−0.271803	−	0.962353i	$-0.587620\pi$
$557$	−12.8296			−0.543606			−0.271803	+	0.962353i	$0.587620\pi$
$558$	18.7977	−	9.55077i	0.795769	−	0.404316i
$559$	−14.6062			−0.617775
$560$	0.500000	+	0.866025i	0.0211289	+	0.0365963i
$561$	30.3542	−	28.7720i	1.28156	−	1.21476i
$562$	−7.46719	+	12.9336i	−0.314984	+	0.545569i
$563$	−14.4039	+	24.9483i	−0.607052	+	1.05145i	0.384671	+	0.923054i	$0.374315\pi$
$563$	−14.4039	+	24.9483i	−0.607052	+	1.05145i	−0.991724	+	0.128392i	$0.959019\pi$
$564$	3.24980	+	13.5707i	0.136841	+	0.571428i
$565$	−0.853695	−	1.47864i	−0.0359152	−	0.0622070i
$566$	28.4996			1.19793
$567$	8.94852	+	0.961276i	0.375802	+	0.0403698i
$568$	−12.0620			−0.506111
$569$	21.8250	+	37.8020i	0.914952	+	1.58474i	0.806971	+	0.590591i	$0.201105\pi$
$569$	21.8250	+	37.8020i	0.914952	+	1.58474i	0.107982	+	0.994153i	$0.465561\pi$
$570$	−0.129436	−	0.540506i	−0.00542149	−	0.0226393i
$571$	−14.1673	+	24.5385i	−0.592884	+	1.02690i	0.400958	+	0.916096i	$0.368677\pi$
$571$	−14.1673	+	24.5385i	−0.592884	+	1.02690i	−0.993842	+	0.110808i	$0.964656\pi$
$572$	−7.05928	+	12.2270i	−0.295163	+	0.511238i
$573$	25.6983	−	24.3588i	1.07356	−	1.01760i
$574$	2.57795	+	4.46515i	0.107602	+	0.186372i
$575$	−1.90064			−0.0792622
$576$	−2.67458	+	1.35891i	−0.111441	+	0.0566211i
$577$	13.8778			0.577742			0.288871	−	0.957368i	$-0.406720\pi$
$577$	13.8778			0.577742			0.288871	+	0.957368i	$0.406720\pi$
$578$	−5.80675	−	10.0576i	−0.241529	−	0.418340i
$579$	−18.3678	−	5.45225i	−0.763341	−	0.226588i
$580$	2.24293	−	3.88487i	0.0931327	−	0.161311i
$581$	−1.80675	+	3.12938i	−0.0749565	+	0.129829i
$582$	−30.4527	−	9.03948i	−1.26230	−	0.374698i
$583$	18.6204	+	32.2514i	0.771177	+	1.33572i
$584$	2.02827			0.0839306
$585$	−7.86330	−	5.11931i	−0.325107	−	0.211657i
$586$	−31.2973			−1.29288
$587$	−16.5689	−	28.6981i	−0.683871	−	1.18450i	−0.973790	−	0.227448i	$-0.926962\pi$
$587$	−16.5689	−	28.6981i	−0.683871	−	1.18450i	0.289919	−	0.957051i	$-0.406372\pi$
$588$	−1.25707	+	1.19154i	−0.0518406	+	0.0491385i
$589$	1.12763	−	1.95312i	0.0464633	−	0.0804767i
$590$	6.38197	−	11.0539i	0.262741	−	0.455082i
$591$	5.48912	+	22.9217i	0.225792	+	0.942873i
$592$	0.903374	+	1.56469i	0.0371284	+	0.0643083i
$593$	−21.7639			−0.893738			−0.446869	−	0.894599i	$-0.647461\pi$
$593$	−21.7639			−0.893738			−0.446869	+	0.894599i	$0.647461\pi$
$594$	23.0707	−	4.23488i	0.946602	−	0.173759i
$595$	−5.34916			−0.219294
$596$	−3.15591	−	5.46619i	−0.129271	−	0.223904i
$597$	−8.05021	−	33.6164i	−0.329473	−	1.37583i
$598$	−2.97225	+	5.14810i	−0.121545	+	0.210521i
$599$	−8.40571	+	14.5591i	−0.343448	+	0.594869i	−0.985071	−	0.172151i	$-0.944928\pi$
$599$	−8.40571	+	14.5591i	−0.343448	+	0.594869i	0.641623	+	0.767020i	$0.278262\pi$
$600$	−1.25707	+	1.19154i	−0.0513196	+	0.0486446i
$601$	−16.8615	−	29.2050i	−0.687795	−	1.19130i	−0.972550	−	0.232695i	$-0.925246\pi$
$601$	−16.8615	−	29.2050i	−0.687795	−	1.19130i	0.284755	−	0.958600i	$-0.408088\pi$
$602$	−4.67004			−0.190337
$603$	−1.11710	+	20.8581i	−0.0454920	+	0.849406i
$604$	13.2835			0.540499
$605$	−4.68872	−	8.12109i	−0.190623	−	0.330169i
$606$	−19.3774	−	5.75194i	−0.787154	−	0.233657i
$607$	0.0565477	−	0.0979435i	0.00229520	−	0.00397540i	−0.864876	−	0.501986i	$-0.832603\pi$
$607$	0.0565477	−	0.0979435i	0.00229520	−	0.00397540i	0.867171	+	0.498011i	$0.165936\pi$
$608$	−0.160442	+	0.277894i	−0.00650679	+	0.0112701i
$609$	7.44852	+	2.21100i	0.301829	+	0.0895941i
$610$	1.09663	+	1.89941i	0.0444011	+	0.0769050i
$611$	25.1979			1.01940
$612$	0.858231	−	16.0245i	0.0346919	−	0.647752i
$613$	10.6418			0.429817			0.214909	−	0.976634i	$-0.431055\pi$
$613$	10.6418			0.429817			0.214909	+	0.976634i	$0.431055\pi$
$614$	5.19145	+	8.99185i	0.209510	+	0.362882i
$615$	−6.48133	+	6.14349i	−0.261352	+	0.247730i
$616$	−2.25707	+	3.90936i	−0.0909399	+	0.157512i
$617$	12.6249	−	21.8670i	0.508259	−	0.880331i	−0.491695	−	0.870768i	$-0.663622\pi$
$617$	12.6249	−	21.8670i	0.508259	−	0.880331i	0.999954	−	0.00956347i	$-0.00304419\pi$
$618$	3.87563	+	16.1840i	0.155901	+	0.651017i
$619$	−11.1700	−	19.3471i	−0.448962	−	0.777625i	0.549357	−	0.835588i	$-0.314873\pi$
$619$	−11.1700	−	19.3471i	−0.448962	−	0.777625i	−0.998319	+	0.0579630i	$0.981539\pi$
$620$	−7.02827			−0.282262
$621$	9.71373	−	1.78306i	0.389799	−	0.0715518i
$622$	5.35823			0.214845
$623$	−1.00000	−	1.73205i	−0.0400642	−	0.0693932i
$624$	1.26160	+	5.26826i	0.0505046	+	0.210899i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	6.64631	−	11.5117i	0.265640	−	0.460102i
$627$	1.82088	−	1.72597i	0.0727191	−	0.0689287i
$628$	−10.0780	−	17.4555i	−0.402154	−	0.696551i
$629$	−9.66458			−0.385352
$630$	−2.51414	−	1.63680i	−0.100166	−	0.0652117i
$631$	35.5333			1.41456			0.707280	−	0.706934i	$-0.249922\pi$
$631$	35.5333			1.41456			0.707280	+	0.706934i	$0.249922\pi$
$632$	−0.707389	−	1.22523i	−0.0281384	−	0.0487372i
$633$	16.5105	+	4.90094i	0.656235	+	0.194795i
$634$	−16.1814	+	28.0271i	−0.642647	+	1.11310i
$635$	−7.91297	+	13.7057i	−0.314017	+	0.543893i
$636$	13.6983	+	4.06617i	0.543174	+	0.161234i
$637$	1.56382	+	2.70861i	0.0619606	+	0.107319i
$638$	20.2498			0.801697
$639$	32.2608	−	16.3911i	1.27622	−	0.648424i
$640$	1.00000			0.0395285
$641$	8.25980	+	14.3064i	0.326243	+	0.565069i	0.981763	−	0.190109i	$-0.0608841\pi$
$641$	8.25980	+	14.3064i	0.326243	+	0.565069i	−0.655521	+	0.755177i	$0.727551\pi$
$642$	2.91751	−	2.76544i	0.115145	−	0.109143i
$643$	7.17277	−	12.4236i	0.282867	−	0.489939i	−0.689223	−	0.724549i	$-0.742048\pi$
$643$	7.17277	−	12.4236i	0.282867	−	0.489939i	0.972090	+	0.234610i	$0.0753813\pi$
$644$	−0.950321	+	1.64600i	−0.0374479	+	0.0648616i
$645$	−1.88377	−	7.86634i	−0.0741735	−	0.309737i
$646$	−0.858231	−	1.48650i	−0.0337666	−	0.0584855i
$647$	−16.2317			−0.638132			−0.319066	−	0.947732i	$-0.603369\pi$
$647$	−16.2317			−0.638132			−0.319066	+	0.947732i	$0.603369\pi$
$648$	5.30675	−	7.26900i	0.208469	−	0.285553i
$649$	57.6182			2.26171
$650$	1.56382	+	2.70861i	0.0613379	+	0.106240i
$651$	−2.83502	−	11.8386i	−0.111113	−	0.463991i
$652$	9.88197	−	17.1161i	0.387008	−	0.670317i
$653$	−10.0848	+	17.4674i	−0.394650	+	0.683553i	−0.993056	−	0.117639i	$-0.962467\pi$
$653$	−10.0848	+	17.4674i	−0.394650	+	0.683553i	0.598407	+	0.801192i	$0.295801\pi$
$654$	0.195984	−	0.185769i	0.00766360	−	0.00726414i
$655$	−5.98133	−	10.3600i	−0.233710	−	0.404797i
$656$	5.15591			0.201304
$657$	−5.42478	+	2.75623i	−0.211641	+	0.107531i
$658$	8.05655			0.314077
$659$	19.0475	+	32.9912i	0.741984	+	1.28515i	0.951591	+	0.307369i	$0.0994485\pi$
$659$	19.0475	+	32.9912i	0.741984	+	1.28515i	−0.209606	+	0.977786i	$0.567218\pi$
$660$	−7.49546	−	2.22493i	−0.291761	−	0.0866053i
$661$	−12.1559	+	21.0546i	−0.472810	+	0.818931i	−0.999516	−	0.0311168i	$-0.990094\pi$
$661$	−12.1559	+	21.0546i	−0.472810	+	0.818931i	0.526706	+	0.850048i	$0.323427\pi$
$662$	−1.80675	+	3.12938i	−0.0702212	+	0.121627i
$663$	−27.7795	−	8.24599i	−1.07887	−	0.320248i
$664$	1.80675	+	3.12938i	0.0701154	+	0.121443i
$665$	−0.320884			−0.0124434
$666$	−4.54241	−	2.95729i	−0.176015	−	0.114592i
$667$	8.52602			0.330129
$668$	6.03101	+	10.4460i	0.233347	+	0.404168i
$669$	−26.5830	+	25.1974i	−1.02776	+	0.974188i
$670$	3.48133	−	6.02983i	0.134495	−	0.232953i
$671$	−4.95032	+	8.57421i	−0.191105	+	0.331004i
$672$	0.403374	+	1.68443i	0.0155605	+	0.0649781i
$673$	14.7694	+	25.5814i	0.569319	+	0.986089i	0.996633	+	0.0819858i	$0.0261262\pi$
$673$	14.7694	+	25.5814i	0.569319	+	0.986089i	−0.427315	+	0.904103i	$0.640540\pi$
$674$	16.3455			0.629607
$675$	1.74293	−	4.89512i	0.0670855	−	0.188413i
$676$	−3.21792			−0.123766
$677$	−6.36149	−	11.0184i	−0.244492	−	0.423472i	0.717497	−	0.696562i	$-0.245288\pi$
$677$	−6.36149	−	11.0184i	−0.244492	−	0.423472i	−0.961989	+	0.273089i	$0.911955\pi$
$678$	−0.688716	−	2.87597i	−0.0264500	−	0.110451i
$679$	−9.17004	+	15.8830i	−0.351914	+	0.609533i
$680$	−2.67458	+	4.63251i	−0.102565	+	0.177649i
$681$	−23.7835	+	22.5438i	−0.911387	+	0.863882i
$682$	−15.8633	−	27.4760i	−0.607437	−	1.05211i
$683$	−1.42385			−0.0544822			−0.0272411	−	0.999629i	$-0.508672\pi$
$683$	−1.42385			−0.0544822			−0.0272411	+	0.999629i	$0.508672\pi$
$684$	0.0514834	−	0.961276i	0.00196852	−	0.0367553i
$685$	−18.4768			−0.705962
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	26.0283	+	7.72616i	0.993041	+	0.294771i
$688$	−2.33502	+	4.04438i	−0.0890219	+	0.154190i
$689$	12.9012	−	22.3455i	0.491495	−	0.851295i
$690$	−3.15591	−	0.936790i	−0.120143	−	0.0356630i
$691$	−23.6700	−	40.9977i	−0.900451	−	1.55963i	−0.826910	−	0.562334i	$-0.809903\pi$
$691$	−23.6700	−	40.9977i	−0.900451	−	1.55963i	−0.0735410	−	0.997292i	$-0.523430\pi$
$692$	21.0848			0.801525
$693$	0.724258	−	13.5230i	0.0275123	−	0.513697i
$694$	−37.0192			−1.40523
$695$	3.50000	+	6.06218i	0.132763	+	0.229952i
$696$	5.63904	−	5.34511i	0.213747	−	0.202606i
$697$	−13.7899	+	23.8848i	−0.522329	+	0.904700i
$698$	−10.1586	+	17.5953i	−0.384510	+	0.665991i
$699$	8.73526	+	36.4771i	0.330398	+	1.37969i
$700$	0.500000	+	0.866025i	0.0188982	+	0.0327327i
$701$	−1.95719			−0.0739220			−0.0369610	−	0.999317i	$-0.511768\pi$
$701$	−1.95719			−0.0739220			−0.0369610	+	0.999317i	$0.511768\pi$
$702$	−10.5333	−	12.3760i	−0.397555	−	0.467101i
$703$	−0.579757			−0.0218660
$704$	2.25707	+	3.90936i	0.0850665	+	0.147339i
$705$	3.24980	+	13.5707i	0.122395	+	0.511100i
$706$	11.7835	−	20.4097i	0.443479	−	0.768129i
$707$	−5.83502	+	10.1066i	−0.219449	+	0.380096i
$708$	16.0451	−	15.2088i	0.603013	−	0.571582i
$709$	−7.33683	−	12.7078i	−0.275540	−	0.477250i	0.694731	−	0.719270i	$-0.255523\pi$
$709$	−7.33683	−	12.7078i	−0.275540	−	0.477250i	−0.970271	+	0.242020i	$0.922190\pi$
$710$	−12.0620			−0.452679
$711$	3.55695	+	2.31571i	0.133396	+	0.0868459i
$712$	−2.00000			−0.0749532
$713$	−6.67912	−	11.5686i	−0.250135	−	0.433246i
$714$	−8.88197	−	2.63650i	−0.332399	−	0.0986684i
$715$	−7.05928	+	12.2270i	−0.264002	+	0.457265i
$716$	10.6887	−	18.5134i	0.399456	−	0.691878i
$717$	−4.84049	−	1.43684i	−0.180771	−	0.0536596i
$718$	15.1586	+	26.2555i	0.565715	+	0.979848i
$719$	−40.2690			−1.50178			−0.750890	−	0.660427i	$-0.770375\pi$
$719$	−40.2690			−1.50178			−0.750890	+	0.660427i	$0.770375\pi$
$720$	−2.67458	+	1.35891i	−0.0996757	+	0.0506434i
$721$	9.60803			0.357822
$722$	9.44852	+	16.3653i	0.351637	+	0.609054i
$723$	−0.943053	+	0.893897i	−0.0350725	+	0.0332444i
$724$	10.3774	−	17.9742i	0.385674	−	0.668007i
$725$	2.24293	−	3.88487i	0.0833004	−	0.144281i
$726$	−3.78261	−	15.7956i	−0.140386	−	0.586229i
$727$	−9.79494	−	16.9653i	−0.363274	−	0.629210i	0.625223	−	0.780446i	$-0.285008\pi$
$727$	−9.79494	−	16.9653i	−0.363274	−	0.629210i	−0.988498	+	0.151236i	$0.951675\pi$
$728$	3.12763			0.115918
$729$	−4.31542	+	26.6529i	−0.159830	+	0.987144i
$730$	2.02827			0.0750698
$731$	−12.4904	−	21.6340i	−0.461974	−	0.800163i
$732$	0.884701	+	3.69437i	0.0326995	+	0.136548i
$733$	−5.59755	+	9.69525i	−0.206750	+	0.358102i	−0.950689	−	0.310146i	$-0.899622\pi$
$733$	−5.59755	+	9.69525i	−0.206750	+	0.358102i	0.743939	+	0.668248i	$0.232955\pi$
$734$	−6.41751	+	11.1155i	−0.236875	+	0.410279i
$735$	−1.25707	+	1.19154i	−0.0463677	+	0.0439508i
$736$	0.950321	+	1.64600i	0.0350293	+	0.0606725i
$737$	31.4304			1.15775
$738$	−13.7899	+	7.00639i	−0.507612	+	0.257909i
$739$	3.04281			0.111932			0.0559658	−	0.998433i	$-0.482176\pi$
$739$	3.04281			0.111932			0.0559658	+	0.998433i	$0.482176\pi$
$740$	0.903374	+	1.56469i	0.0332087	+	0.0575191i
$741$	−1.66643	−	0.494659i	−0.0612180	−	0.0181718i
$742$	4.12490	−	7.14454i	0.151430	−	0.262284i
$743$	−10.2270	+	17.7137i	−0.375192	+	0.649851i	−0.990356	−	0.138548i	$-0.955757\pi$
$743$	−10.2270	+	17.7137i	−0.375192	+	0.649851i	0.615164	+	0.788399i	$0.289090\pi$
$744$	−11.6700	−	3.46410i	−0.427845	−	0.127000i
$745$	−3.15591	−	5.46619i	−0.115623	−	0.200266i
$746$	5.48225			0.200720
$747$	−9.08482	−	5.91457i	−0.332396	−	0.216403i
$748$	−24.1468			−0.882896
$749$	−1.16044	−	2.00994i	−0.0424016	−	0.0734418i
$750$	−1.25707	+	1.19154i	−0.0459017	+	0.0435091i
$751$	−8.19052	+	14.1864i	−0.298876	+	0.517669i	−0.975879	−	0.218311i	$-0.929945\pi$
$751$	−8.19052	+	14.1864i	−0.298876	+	0.517669i	0.677003	+	0.735980i	$0.263278\pi$
$752$	4.02827	−	6.97717i	0.146896	−	0.254431i
$753$	−1.62490	−	6.78533i	−0.0592147	−	0.247271i
$754$	−7.01506	−	12.1504i	−0.255474	−	0.442493i
$755$	13.2835			0.483437
$756$	−3.36783	−	3.95698i	−0.122487	−	0.143914i
$757$	43.0721			1.56548			0.782742	−	0.622347i	$-0.213821\pi$
$757$	43.0721			1.56548			0.782742	+	0.622347i	$0.213821\pi$
$758$	6.13904	+	10.6331i	0.222980	+	0.386212i
$759$	−3.46085	−	14.4520i	−0.125621	−	0.524573i
$760$	−0.160442	+	0.277894i	−0.00581985	+	0.0100803i
$761$	9.40571	−	16.2912i	0.340957	−	0.590554i	−0.643654	−	0.765317i	$-0.722582\pi$
$761$	9.40571	−	16.2912i	0.340957	−	0.590554i	0.984611	+	0.174762i	$0.0559158\pi$
$762$	−19.8943	+	18.8573i	−0.720694	+	0.683129i
$763$	−0.0779530	−	0.135018i	−0.00282209	−	0.00488800i
$764$	−20.4431			−0.739604
$765$	0.858231	−	16.0245i	0.0310294	−	0.579367i
$766$	−19.6700			−0.710708
$767$	−19.9604	−	34.5725i	−0.720730	−	1.24834i
$768$	1.66044	+	0.492881i	0.0599160	+	0.0177853i
$769$	1.43892	−	2.49228i	0.0518886	−	0.0898738i	−0.838914	−	0.544263i	$-0.816809\pi$
$769$	1.43892	−	2.49228i	0.0518886	−	0.0898738i	0.890803	+	0.454390i	$0.150143\pi$
$770$	−2.25707	+	3.90936i	−0.0813391	+	0.140883i
$771$	−18.0469	−	5.35700i	−0.649945	−	0.192928i
$772$	5.53101	+	9.57998i	0.199065	+	0.344791i
$773$	−29.1842			−1.04968			−0.524841	−	0.851200i	$-0.675875\pi$
$773$	−29.1842			−1.04968			−0.524841	+	0.851200i	$0.675875\pi$
$774$	0.749272	−	13.9901i	0.0269320	−	0.502863i
$775$	−7.02827			−0.252463
$776$	9.17004	+	15.8830i	0.329185	+	0.570166i
$777$	−2.27121	+	2.15282i	−0.0814790	+	0.0772320i
$778$	0.934380	−	1.61839i	0.0334991	−	0.0580222i
$779$	−0.827225	+	1.43280i	−0.0296384	+	0.0513352i
$780$	1.26160	+	5.26826i	0.0451727	+	0.188634i
$781$	−27.2248	−	47.1547i	−0.974179	−	1.68733i
$782$	−10.1668			−0.363565
$783$	−7.81855	+	21.9588i	−0.279412	+	0.784745i
$784$	1.00000			0.0357143
$785$	−10.0780	−	17.4555i	−0.359698	−	0.623014i
$786$	−4.82542	−	20.1502i	−0.172117	−	0.718734i
$787$	20.4485	−	35.4179i	0.728911	−	1.26251i	−0.228433	−	0.973560i	$-0.573360\pi$
$787$	20.4485	−	35.4179i	0.728911	−	1.26251i	0.957344	−	0.288951i	$-0.0933065\pi$
$788$	6.80402	−	11.7849i	0.242383	−	0.419820i
$789$	−6.10209	+	5.78402i	−0.217240	+	0.205917i
$790$	−0.707389	−	1.22523i	−0.0251678	−	0.0435919i
$791$	−1.70739			−0.0607078
$792$	−11.3492	−	7.38874i	−0.403275	−	0.262547i
$793$	6.85969			0.243595
$794$	−7.49273	−	12.9778i	−0.265907	−	0.460565i
$795$	13.6983	+	4.06617i	0.485829	+	0.144212i
$796$	−9.97859	+	17.2834i	−0.353682	+	0.612595i
$797$	19.2125	−	33.2769i	0.680540	−	1.17873i	−0.294276	−	0.955720i	$-0.595079\pi$
$797$	19.2125	−	33.2769i	0.680540	−	1.17873i	0.974816	−	0.223009i	$-0.0715881\pi$
$798$	−0.532810	−	0.158158i	−0.0188613	−	0.00559873i
$799$	21.5479	+	37.3220i	0.762309	+	1.32036i
$800$	1.00000			0.0353553
$801$	5.34916	−	2.71781i	0.189003	−	0.0960292i
$802$	31.5671			1.11467
$803$	4.57795	+	7.92925i	0.161552	+	0.279817i
$804$	8.75253	−	8.29631i	0.308678	−	0.292588i
$805$	−0.950321	+	1.64600i	−0.0334944	+	0.0580140i
$806$	−10.9909	+	19.0368i	−0.387139	+	0.670544i
$807$	−12.0961	−	50.5114i	−0.425803	−	1.77809i
$808$	5.83502	+	10.1066i	0.205275	+	0.355547i
$809$	35.5188			1.24877			0.624387	−	0.781115i	$-0.285349\pi$
$809$	35.5188			1.24877			0.624387	+	0.781115i	$0.285349\pi$
$810$	5.30675	−	7.26900i	0.186460	−	0.255407i
$811$	5.16137			0.181240			0.0906201	−	0.995886i	$-0.471115\pi$
$811$	5.16137			0.181240			0.0906201	+	0.995886i	$0.471115\pi$
$812$	−2.24293	−	3.88487i	−0.0787115	−	0.136332i
$813$	−6.82868	−	28.5155i	−0.239492	−	1.00008i
$814$	−4.07795	+	7.06322i	−0.142932	+	0.247566i
$815$	9.88197	−	17.1161i	0.346150	−	0.599550i
$816$	−6.72426	+	6.37376i	−0.235396	+	0.223126i
$817$	−0.749272	−	1.29778i	−0.0262137	−	0.0454035i
$818$	22.5141			0.787188
$819$	−8.36510	+	4.25016i	−0.292300	+	0.148513i
$820$	5.15591			0.180052
$821$	−7.20559	−	12.4804i	−0.251477	−	0.435570i	0.712456	−	0.701717i	$-0.247583\pi$
$821$	−7.20559	−	12.4804i	−0.251477	−	0.435570i	−0.963933	+	0.266147i	$0.914250\pi$
$822$	−30.6796	−	9.10686i	−1.07008	−	0.317638i
$823$	20.3560	−	35.2577i	0.709566	−	1.22901i	−0.255452	−	0.966822i	$-0.582224\pi$
$823$	20.3560	−	35.2577i	0.709566	−	1.22901i	0.965018	−	0.262183i	$-0.0844425\pi$
$824$	4.80402	−	8.32080i	0.167356	−	0.289869i
$825$	−7.49546	−	2.22493i	−0.260959	−	0.0774622i
$826$	−6.38197	−	11.0539i	−0.222057	−	0.384614i
$827$	29.0475			1.01008			0.505040	−	0.863096i	$-0.331478\pi$
$827$	29.0475			1.01008			0.505040	+	0.863096i	$0.331478\pi$
$828$	−4.77847	−	3.11097i	−0.166063	−	0.108114i
$829$	35.1414			1.22051			0.610255	−	0.792205i	$-0.291067\pi$
$829$	35.1414			1.22051			0.610255	+	0.792205i	$0.291067\pi$
$830$	1.80675	+	3.12938i	0.0627131	+	0.108622i
$831$	−40.2034	+	38.1078i	−1.39464	+	1.32195i
$832$	1.56382	−	2.70861i	0.0542156	−	0.0939041i
$833$	−2.67458	+	4.63251i	−0.0926687	+	0.160507i
$834$	2.82362	+	11.7910i	0.0977738	+	0.408288i
$835$	6.03101	+	10.4460i	0.208712	+	0.361499i
$836$	−1.44852			−0.0500980
$837$	35.9198	−	6.59348i	1.24157	−	0.227904i
$838$	11.9627			0.413243
$839$	−3.95032	−	6.84216i	−0.136380	−	0.236217i	0.789744	−	0.613437i	$-0.210214\pi$
$839$	−3.95032	−	6.84216i	−0.136380	−	0.236217i	−0.926124	+	0.377220i	$0.876880\pi$
$840$	0.403374	+	1.68443i	0.0139177	+	0.0581182i
$841$	4.43852	−	7.68774i	0.153052	−	0.265094i
$842$	−7.43618	+	12.8798i	−0.256268	+	0.443869i
$843$	−18.7735	+	17.7950i	−0.646595	+	0.612892i
$844$	−4.97173	−	8.61128i	−0.171134	−	0.296413i
$845$	−3.21792			−0.110700
$846$	−1.29261	+	24.1351i	−0.0444409	+	0.829780i
$847$	−9.37743			−0.322212
$848$	−4.12490	−	7.14454i	−0.141650	−	0.245344i
$849$	47.3219	+	14.0469i	1.62408	+	0.482089i
$850$	−2.67458	+	4.63251i	−0.0917373	+	0.158894i
$851$	−1.71699	+	2.97391i	−0.0588577	+	0.101944i
$852$	−20.0283	−	5.94513i	−0.686157	−	0.203677i
$853$	22.7977	+	39.4867i	0.780578	+	1.35200i	0.931606	+	0.363470i	$0.118408\pi$
$853$	22.7977	+	39.4867i	0.780578	+	1.35200i	−0.151028	+	0.988529i	$0.548258\pi$
$854$	2.19325			0.0750516
$855$	0.0514834	−	0.961276i	0.00176070	−	0.0328749i
$856$	−2.32088			−0.0793262
$857$	5.52374	+	9.56739i	0.188687	+	0.326816i	0.944813	−	0.327611i	$-0.106243\pi$
$857$	5.52374	+	9.56739i	0.188687	+	0.326816i	−0.756126	+	0.654427i	$0.772910\pi$
$858$	−17.7480	+	16.8229i	−0.605907	+	0.574324i
$859$	21.5041	−	37.2463i	0.733712	−	1.27083i	−0.221575	−	0.975143i	$-0.571120\pi$
$859$	21.5041	−	37.2463i	0.733712	−	1.27083i	0.955286	−	0.295682i	$-0.0955470\pi$
$860$	−2.33502	+	4.04438i	−0.0796236	+	0.137912i
$861$	2.07976	+	8.68474i	0.0708779	+	0.295975i
$862$	7.12763	+	12.3454i	0.242768	+	0.420487i
$863$	−10.2662			−0.349465			−0.174733	−	0.984616i	$-0.555906\pi$
$863$	−10.2662			−0.349465			−0.174733	+	0.984616i	$0.555906\pi$
$864$	−5.11076	+	0.938136i	−0.173872	+	0.0319161i
$865$	21.0848			0.716905
$866$	3.21285	+	5.56483i	0.109177	+	0.189100i
$867$	−4.68458	−	19.5621i	−0.159097	−	0.664363i
$868$	−3.51414	+	6.08666i	−0.119278	+	0.206595i
$869$	3.19325	−	5.53088i	0.108324	−	0.187622i
$870$	5.63904	−	5.34511i	0.191181	−	0.181216i
$871$	−10.8883	−	18.8591i	−0.368936	−	0.639016i
$872$	−0.155906			−0.00527964
$873$	−46.1095	−	30.0191i	−1.56057	−	1.01599i
$874$	−0.609886			−0.0206297
$875$	0.500000	+	0.866025i	0.0169031	+	0.0292770i
$876$	3.36783	+	0.999697i	0.113788	+	0.0337766i
$877$	4.41205	−	7.64189i	0.148984	−	0.258048i	−0.781868	−	0.623444i	$-0.785733\pi$
$877$	4.41205	−	7.64189i	0.148984	−	0.258048i	0.930852	+	0.365396i	$0.119066\pi$
$878$	−1.33683	+	2.31545i	−0.0451157	+	0.0781427i
$879$	−51.9673	−	15.4258i	−1.75281	−	0.520300i
$880$	2.25707	+	3.90936i	0.0760858	+	0.131784i
$881$	50.2179			1.69188			0.845942	−	0.533274i	$-0.179039\pi$
$881$	50.2179			1.69188			0.845942	+	0.533274i	$0.179039\pi$
$882$	−2.67458	+	1.35891i	−0.0900578	+	0.0457568i
$883$	−7.81036			−0.262839			−0.131420	−	0.991327i	$-0.541954\pi$
$883$	−7.81036			−0.262839			−0.131420	+	0.991327i	$0.541954\pi$
$884$	8.36510	+	14.4888i	0.281349	+	0.487310i
$885$	16.0451	−	15.2088i	0.539352	−	0.511238i
$886$	4.07068	−	7.05063i	0.136757	−	0.236871i
$887$	−2.50867	+	4.34515i	−0.0842330	+	0.145896i	−0.905064	−	0.425275i	$-0.860177\pi$
$887$	−2.50867	+	4.34515i	−0.0842330	+	0.145896i	0.820831	+	0.571171i	$0.193511\pi$
$888$	0.728795	+	3.04333i	0.0244567	+	0.102128i
$889$	7.91297	+	13.7057i	0.265393	+	0.459674i
$890$	−2.00000			−0.0670402
$891$	40.3948	+	4.33933i	1.35328	+	0.145373i
$892$	21.1468			0.708048
$893$	1.29261	+	2.23887i	0.0432556	+	0.0749208i
$894$	−2.54602	−	10.6318i	−0.0851516	−	0.355580i
$895$	10.6887	−	18.5134i	0.357284	−	0.618835i
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$	−7.47265	+	7.08315i	−0.249505	+	0.236499i
$898$	11.1322	+	19.2815i	0.371485	+	0.643431i
$899$	31.5279			1.05151
$900$	−2.67458	+	1.35891i	−0.0891526	+	0.0452969i
$901$	44.1295			1.47017
$902$	11.6372	+	20.1563i	0.387477	+	0.671131i
$903$	−7.75434	−	2.30177i	−0.258048	−	0.0765983i
$904$	−0.853695	+	1.47864i	−0.0283935	+	0.0491789i
$905$	10.3774	−	17.9742i	0.344958	−	0.597484i
$906$	22.0565	+	6.54720i	0.732780	+	0.217516i
$907$	−15.5096	−	26.8634i	−0.514988	−	0.891985i	−0.999849	−	0.0173938i	$-0.994463\pi$
$907$	−15.5096	−	26.8634i	−0.514988	−	0.891985i	0.484861	−	0.874591i	$-0.338870\pi$
$908$	18.9198			0.627877
$909$	−29.3401	−	19.1015i	−0.973149	−	0.633558i
$910$	3.12763			0.103680
$911$	−14.8004	−	25.6351i	−0.490359	−	0.849327i	0.509579	−	0.860424i	$-0.329801\pi$
$911$	−14.8004	−	25.6351i	−0.490359	−	0.849327i	−0.999938	+	0.0110965i	$0.996468\pi$
$912$	−0.403374	+	0.382348i	−0.0133570	+	0.0126608i
$913$	−8.15591	+	14.1264i	−0.269921	+	0.467517i
$914$	15.9271	−	27.5866i	0.526822	−	0.912483i
$915$	0.884701	+	3.69437i	0.0292473	+	0.122132i
$916$	−7.83775	−	13.5754i	−0.258967	−	0.448543i
$917$	−11.9627			−0.395042
$918$	9.32322	−	26.1848i	0.307712	−	0.864226i
$919$	47.8836			1.57953			0.789766	−	0.613408i	$-0.210202\pi$
$919$	47.8836			1.57953			0.789766	+	0.613408i	$0.210202\pi$
$920$	0.950321	+	1.64600i	0.0313312	+	0.0542671i
$921$	4.18819	+	17.4892i	0.138005	+	0.576289i
$922$	−1.19052	+	2.06204i	−0.0392077	+	0.0679097i
$923$	−18.8628	+	32.6713i	−0.620876	+	1.07539i
$924$	−5.67458	+	5.37880i	−0.186680	+	0.176949i
$925$	0.903374	+	1.56469i	0.0297027	+	0.0514467i
$926$	−34.3118			−1.12756
$927$	−1.54153	+	28.7828i	−0.0506306	+	0.945353i
$928$	−4.48586			−0.147256
$929$	3.15591	+	5.46619i	0.103542	+	0.179340i	0.913142	−	0.407643i	$-0.133649\pi$
$929$	3.15591	+	5.46619i	0.103542	+	0.179340i	−0.809600	+	0.586982i	$0.800316\pi$
$930$	−11.6700	−	3.46410i	−0.382676	−	0.113592i
$931$	−0.160442	+	0.277894i	−0.00525828	+	0.00910761i
$932$	10.8278	−	18.7542i	0.354675	−	0.614315i
$933$	8.89703	+	2.64097i	0.291276	+	0.0864615i
$934$	19.2949	+	33.4198i	0.631350	+	1.09353i
$935$	−24.1468			−0.789686
$936$	−0.501804	+	9.36947i	−0.0164020	+	0.306251i
$937$	10.1504			0.331600			0.165800	−	0.986159i	$-0.446979\pi$
$937$	10.1504			0.331600			0.165800	+	0.986159i	$0.446979\pi$
$938$	−3.48133	−	6.02983i	−0.113669	−	0.196881i
$939$	16.7097	−	15.8387i	0.545301	−	0.516878i
$940$	4.02827	−	6.97717i	0.131388	−	0.227570i
$941$	−11.4202	+	19.7804i	−0.372289	+	0.644824i	−0.989917	−	0.141646i	$-0.954760\pi$
$941$	−11.4202	+	19.7804i	−0.372289	+	0.644824i	0.617628	+	0.786470i	$0.288094\pi$
$942$	−8.13036	−	33.9511i	−0.264902	−	1.10619i
$943$	4.89977	+	8.48664i	0.159558	+	0.276363i
$944$	−12.7639			−0.415431
$945$	−3.36783	−	3.95698i	−0.109556	−	0.128721i
$946$	−21.0812			−0.685409
$947$	4.30675	+	7.45951i	0.139950	+	0.242401i	0.927478	−	0.373879i	$-0.121972\pi$
$947$	4.30675	+	7.45951i	0.139950	+	0.242401i	−0.787527	+	0.616280i	$0.788639\pi$
$948$	−0.570685	−	2.38309i	−0.0185350	−	0.0773991i
$949$	3.17185	−	5.49380i	0.102963	−	0.178336i
$950$	−0.160442	+	0.277894i	−0.00520543	+	0.00901608i
$951$	−40.6824	+	38.5618i	−1.31922	+	1.25045i
$952$	2.67458	+	4.63251i	0.0866836	+	0.150140i
$953$	−12.6382			−0.409390			−0.204695	−	0.978826i	$-0.565620\pi$
$953$	−12.6382			−0.409390			−0.204695	+	0.978826i	$0.565620\pi$
$954$	20.7411	+	13.5033i	0.671519	+	0.437185i
$955$	−20.4431			−0.661522
$956$	1.45759	+	2.52462i	0.0471418	+	0.0816520i
$957$	33.6236	+	9.98074i	1.08690	+	0.322631i
$958$	2.56382	−	4.44066i	0.0828331	−	0.143471i
$959$	−9.23840	+	16.0014i	−0.298323	+	0.516711i
$960$	1.66044	+	0.492881i	0.0535905	+	0.0159077i
$961$	−9.19832	−	15.9320i	−0.296720	−	0.513934i
$962$	5.65084			0.182190
$963$	6.20739	−	3.15386i	0.200030	−	0.101632i
$964$	0.750200			0.0241623
$965$	5.53101	+	9.57998i	0.178049	+	0.308391i
$966$	−2.38924	+	2.26470i	−0.0768724	+	0.0728655i
$967$	2.21245	−	3.83208i	0.0711477	−	0.123231i	−0.828257	−	0.560349i	$-0.810667\pi$
$967$	2.21245	−	3.83208i	0.0711477	−	0.123231i	0.899405	+	0.437117i	$0.144000\pi$
$968$	−4.68872	+	8.12109i	−0.150701	+	0.261022i
$969$	−0.692376	−	2.89125i	−0.0222423	−	0.0928804i
$970$	9.17004	+	15.8830i	0.294432	+	0.509972i
$971$	20.7730			0.666638			0.333319	−	0.942814i	$-0.391831\pi$
$971$	20.7730			0.666638			0.333319	+	0.942814i	$0.391831\pi$
$972$	12.3943	−	9.45417i	0.397547	−	0.303243i
$973$	7.00000			0.224410
$974$	5.89157	+	10.2045i	0.188778	+	0.326973i
$975$	1.26160	+	5.26826i	0.0404037	+	0.168719i
$976$	1.09663	−	1.89941i	0.0351021	−	0.0607987i
$977$	−5.17277	+	8.95951i	−0.165492	+	0.286640i	−0.936830	−	0.349786i	$-0.886254\pi$
$977$	−5.17277	+	8.95951i	−0.165492	+	0.286640i	0.771338	+	0.636426i	$0.219588\pi$
$978$	24.8446	−	23.5496i	0.794443	−	0.753034i
$979$	−4.51414	−	7.81871i	−0.144272	−	0.249887i
$980$	1.00000			0.0319438
$981$	0.416983	−	0.211862i	0.0133132	−	0.00676422i
$982$	35.3063			1.12667
$983$	−10.9717	−	19.0036i	−0.349944	−	0.606120i	0.636295	−	0.771446i	$-0.280466\pi$
$983$	−10.9717	−	19.0036i	−0.349944	−	0.606120i	−0.986239	+	0.165325i	$0.947133\pi$
$984$	8.56108	+	2.54125i	0.272917	+	0.0810120i
$985$	6.80402	−	11.7849i	0.216794	−	0.375498i
$986$	11.9978	−	20.7808i	0.382088	−	0.661795i
$987$	13.3774	+	3.97092i	0.425808	+	0.126396i
$988$	0.501804	+	0.869151i	0.0159645	+	0.0276514i
$989$	−8.87608			−0.282243
$990$	−11.3492	−	7.38874i	−0.360700	−	0.234830i
$991$	−11.0848			−0.352121			−0.176060	−	0.984379i	$-0.556335\pi$
$991$	−11.0848			−0.352121			−0.176060	+	0.984379i	$0.556335\pi$
$992$	3.51414	+	6.08666i	0.111574	+	0.193252i
$993$	−4.54241	+	4.30564i	−0.144149	+	0.136635i
$994$	−6.03101	+	10.4460i	−0.191292	+	0.331327i
$995$	−9.97859	+	17.2834i	−0.316343	+	0.547922i
$996$	1.45759	+	6.08666i	0.0461855	+	0.192863i
$997$	−24.0812	−	41.7099i	−0.762660	−	1.32097i	−0.941475	−	0.337083i	$-0.890560\pi$
$997$	−24.0812	−	41.7099i	−0.762660	−	1.32097i	0.178815	−	0.983883i	$-0.442774\pi$
$998$	−31.9108			−1.01012
$999$	−6.08482	−	7.14927i	−0.192515	−	0.226193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.j.i.211.2	✓	6
3.2	odd	2		1890.2.j.k.631.1		6
9.2	odd	6		1890.2.j.k.1261.1		6
9.4	even	3		5670.2.a.bs.1.1		3
9.5	odd	6		5670.2.a.bo.1.3		3
9.7	even	3	inner	630.2.j.i.421.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.i.211.2	✓	6	1.1	even	1	trivial
630.2.j.i.421.2	yes	6	9.7	even	3	inner
1890.2.j.k.631.1		6	3.2	odd	2
1890.2.j.k.1261.1		6	9.2	odd	6
5670.2.a.bo.1.3		3	9.5	odd	6
5670.2.a.bs.1.1		3	9.4	even	3

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.403374 - 1.68443i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.25707 + 1.19154i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-2.67458 + 1.35891i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.403374 - 1.68443i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.25707 + 1.19154i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-2.67458 + 1.35891i) q^{9} +1.00000 q^{10} +(2.25707 + 3.90936i) q^{11} +(1.66044 + 0.492881i) q^{12} +(1.56382 - 2.70861i) q^{13} +(0.500000 - 0.866025i) q^{14} +(1.66044 + 0.492881i) q^{15} +(-0.500000 - 0.866025i) q^{16} +5.34916 q^{17} +(2.51414 + 1.63680i) q^{18} +0.320884 q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.25707 - 1.19154i) q^{21} +(2.25707 - 3.90936i) q^{22} +(0.950321 - 1.64600i) q^{23} +(-0.403374 - 1.68443i) q^{24} +(-0.500000 - 0.866025i) q^{25} -3.12763 q^{26} +(3.36783 + 3.95698i) q^{27} -1.00000 q^{28} +(2.24293 + 3.88487i) q^{29} +(-0.403374 - 1.68443i) q^{30} +(3.51414 - 6.08666i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.67458 - 5.37880i) q^{33} +(-2.67458 - 4.63251i) q^{34} -1.00000 q^{35} +(0.160442 - 2.99571i) q^{36} -1.80675 q^{37} +(-0.160442 - 0.277894i) q^{38} +(-5.19325 - 1.54155i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-2.57795 + 4.46515i) q^{41} +(-1.66044 - 0.492881i) q^{42} +(-2.33502 - 4.04438i) q^{43} -4.51414 q^{44} +(0.160442 - 2.99571i) q^{45} -1.90064 q^{46} +(4.02827 + 6.97717i) q^{47} +(-1.25707 + 1.19154i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-2.15771 - 9.01026i) q^{51} +(1.56382 + 2.70861i) q^{52} +8.24980 q^{53} +(1.74293 - 4.89512i) q^{54} -4.51414 q^{55} +(0.500000 + 0.866025i) q^{56} +(-0.129436 - 0.540506i) q^{57} +(2.24293 - 3.88487i) q^{58} +(6.38197 - 11.0539i) q^{59} +(-1.25707 + 1.19154i) q^{60} +(1.09663 + 1.89941i) q^{61} -7.02827 q^{62} +(-2.51414 - 1.63680i) q^{63} +1.00000 q^{64} +(1.56382 + 2.70861i) q^{65} +(-7.49546 - 2.22493i) q^{66} +(3.48133 - 6.02983i) q^{67} +(-2.67458 + 4.63251i) q^{68} +(-3.15591 - 0.936790i) q^{69} +(0.500000 + 0.866025i) q^{70} -12.0620 q^{71} +(-2.67458 + 1.35891i) q^{72} +2.02827 q^{73} +(0.903374 + 1.56469i) q^{74} +(-1.25707 + 1.19154i) q^{75} +(-0.160442 + 0.277894i) q^{76} +(-2.25707 + 3.90936i) q^{77} +(1.26160 + 5.26826i) q^{78} +(-0.707389 - 1.22523i) q^{79} +1.00000 q^{80} +(5.30675 - 7.26900i) q^{81} +5.15591 q^{82} +(1.80675 + 3.12938i) q^{83} +(0.403374 + 1.68443i) q^{84} +(-2.67458 + 4.63251i) q^{85} +(-2.33502 + 4.04438i) q^{86} +(5.63904 - 5.34511i) q^{87} +(2.25707 + 3.90936i) q^{88} -2.00000 q^{89} +(-2.67458 + 1.35891i) q^{90} +3.12763 q^{91} +(0.950321 + 1.64600i) q^{92} +(-11.6700 - 3.46410i) q^{93} +(4.02827 - 6.97717i) q^{94} +(-0.160442 + 0.277894i) q^{95} +(1.66044 + 0.492881i) q^{96} +(9.17004 + 15.8830i) q^{97} +1.00000 q^{98} +(-11.3492 - 7.38874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} - q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - q^3 - 3 * q^4 - 3 * q^5 - q^6 + 3 * q^7 + 6 * q^8 + 5 * q^9	\( 6 q - 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} - q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9} + 6 q^{10} + 7 q^{11} + 2 q^{12} + 3 q^{14} + 2 q^{15} - 3 q^{16} - 10 q^{17} + 2 q^{18} - 14 q^{19} - 3 q^{20} + q^{21} + 7 q^{22} + 2 q^{23} - q^{24} - 3 q^{25} + 2 q^{27} - 6 q^{28} + 20 q^{29} - q^{30} + 8 q^{31} - 3 q^{32} + 13 q^{33} + 5 q^{34} - 6 q^{35} - 7 q^{36} - 8 q^{37} + 7 q^{38} - 34 q^{39} - 3 q^{40} + 7 q^{41} - 2 q^{42} + 15 q^{43} - 14 q^{44} - 7 q^{45} - 4 q^{46} - 2 q^{47} - q^{48} - 3 q^{49} - 3 q^{50} + q^{51} + 17 q^{54} - 14 q^{55} + 3 q^{56} - 13 q^{57} + 20 q^{58} + 7 q^{59} - q^{60} + 8 q^{61} - 16 q^{62} - 2 q^{63} + 6 q^{64} - 8 q^{66} - 3 q^{67} + 5 q^{68} + 26 q^{69} + 3 q^{70} - 32 q^{71} + 5 q^{72} - 14 q^{73} + 4 q^{74} - q^{75} + 7 q^{76} - 7 q^{77} + 38 q^{78} + 6 q^{79} + 6 q^{80} + 29 q^{81} - 14 q^{82} + 8 q^{83} + q^{84} + 5 q^{85} + 15 q^{86} - 4 q^{87} + 7 q^{88} - 12 q^{89} + 5 q^{90} + 2 q^{92} - 12 q^{93} - 2 q^{94} + 7 q^{95} + 2 q^{96} - 3 q^{97} + 6 q^{98} - 26 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - q^3 - 3 * q^4 - 3 * q^5 - q^6 + 3 * q^7 + 6 * q^8 + 5 * q^9 + 6 * q^10 + 7 * q^11 + 2 * q^12 + 3 * q^14 + 2 * q^15 - 3 * q^16 - 10 * q^17 + 2 * q^18 - 14 * q^19 - 3 * q^20 + q^21 + 7 * q^22 + 2 * q^23 - q^24 - 3 * q^25 + 2 * q^27 - 6 * q^28 + 20 * q^29 - q^30 + 8 * q^31 - 3 * q^32 + 13 * q^33 + 5 * q^34 - 6 * q^35 - 7 * q^36 - 8 * q^37 + 7 * q^38 - 34 * q^39 - 3 * q^40 + 7 * q^41 - 2 * q^42 + 15 * q^43 - 14 * q^44 - 7 * q^45 - 4 * q^46 - 2 * q^47 - q^48 - 3 * q^49 - 3 * q^50 + q^51 + 17 * q^54 - 14 * q^55 + 3 * q^56 - 13 * q^57 + 20 * q^58 + 7 * q^59 - q^60 + 8 * q^61 - 16 * q^62 - 2 * q^63 + 6 * q^64 - 8 * q^66 - 3 * q^67 + 5 * q^68 + 26 * q^69 + 3 * q^70 - 32 * q^71 + 5 * q^72 - 14 * q^73 + 4 * q^74 - q^75 + 7 * q^76 - 7 * q^77 + 38 * q^78 + 6 * q^79 + 6 * q^80 + 29 * q^81 - 14 * q^82 + 8 * q^83 + q^84 + 5 * q^85 + 15 * q^86 - 4 * q^87 + 7 * q^88 - 12 * q^89 + 5 * q^90 + 2 * q^92 - 12 * q^93 - 2 * q^94 + 7 * q^95 + 2 * q^96 - 3 * q^97 + 6 * q^98 - 26 * q^99

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