LMFDB - Embedded newform 630.2.i.g.151.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

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, 2]))

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

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

chi := DirichletCharacter("630.121");

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.i (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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 3 x^{9} - 2 x^{8} + 24 x^{7} - 21 x^{6} + 72 x^{5} - 18 x^{4} + \cdots + 729 $ x^12 - 3x^11 + 7x^10 - 3x^9 - 2x^8 + 24x^7 - 21x^6 + 72x^5 - 18x^4 - 81x^3 + 567x^2 - 729*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.6
Root			$-0.778860 - 1.54705i$ of defining polynomial
Character	$\chi$	$=$	630.151
Dual form			630.2.i.g.121.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.72922 - 0.0990147i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.72922 - 0.0990147i) q^{6} +(1.40545 - 2.24159i) q^{7} +1.00000 q^{8} +(2.98039 - 0.342436i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.72922 - 0.0990147i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.72922 - 0.0990147i) q^{6} +(1.40545 - 2.24159i) q^{7} +1.00000 q^{8} +(2.98039 - 0.342436i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.357242 - 0.618760i) q^{11} +(1.72922 - 0.0990147i) q^{12} +(-0.823772 - 1.42682i) q^{13} +(1.40545 - 2.24159i) q^{14} +(-0.778860 + 1.54705i) q^{15} +1.00000 q^{16} +(-1.61526 + 2.79771i) q^{17} +(2.98039 - 0.342436i) q^{18} +(-0.0769447 - 0.133272i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(2.20837 - 4.01536i) q^{21} +(-0.357242 - 0.618760i) q^{22} +(-1.43903 + 2.49247i) q^{23} +(1.72922 - 0.0990147i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.823772 - 1.42682i) q^{26} +(5.11984 - 0.887250i) q^{27} +(1.40545 - 2.24159i) q^{28} +(-0.602632 + 1.04379i) q^{29} +(-0.778860 + 1.54705i) q^{30} -6.40096 q^{31} +1.00000 q^{32} +(-0.679015 - 1.03460i) q^{33} +(-1.61526 + 2.79771i) q^{34} +(1.23855 + 2.33795i) q^{35} +(2.98039 - 0.342436i) q^{36} +(4.69842 + 8.13791i) q^{37} +(-0.0769447 - 0.133272i) q^{38} +(-1.56576 - 2.38571i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(3.09435 + 5.35958i) q^{41} +(2.20837 - 4.01536i) q^{42} +(4.80435 - 8.32137i) q^{43} +(-0.357242 - 0.618760i) q^{44} +(-1.19364 + 2.75231i) q^{45} +(-1.43903 + 2.49247i) q^{46} -6.29469 q^{47} +(1.72922 - 0.0990147i) q^{48} +(-3.04944 - 6.30087i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-2.51612 + 4.99778i) q^{51} +(-0.823772 - 1.42682i) q^{52} +(-0.576945 + 0.999298i) q^{53} +(5.11984 - 0.887250i) q^{54} +0.714483 q^{55} +(1.40545 - 2.24159i) q^{56} +(-0.146250 - 0.222838i) q^{57} +(-0.602632 + 1.04379i) q^{58} +1.24707 q^{59} +(-0.778860 + 1.54705i) q^{60} -9.20709 q^{61} -6.40096 q^{62} +(3.42118 - 7.16209i) q^{63} +1.00000 q^{64} +1.64754 q^{65} +(-0.679015 - 1.03460i) q^{66} -12.4936 q^{67} +(-1.61526 + 2.79771i) q^{68} +(-2.24160 + 4.45251i) q^{69} +(1.23855 + 2.33795i) q^{70} -3.71448 q^{71} +(2.98039 - 0.342436i) q^{72} +(-1.45160 + 2.51424i) q^{73} +(4.69842 + 8.13791i) q^{74} +(-0.950358 - 1.44804i) q^{75} +(-0.0769447 - 0.133272i) q^{76} +(-1.88909 - 0.0688459i) q^{77} +(-1.56576 - 2.38571i) q^{78} -2.44228 q^{79} +(-0.500000 + 0.866025i) q^{80} +(8.76547 - 2.04119i) q^{81} +(3.09435 + 5.35958i) q^{82} +(2.21659 - 3.83925i) q^{83} +(2.20837 - 4.01536i) q^{84} +(-1.61526 - 2.79771i) q^{85} +(4.80435 - 8.32137i) q^{86} +(-0.938732 + 1.86461i) q^{87} +(-0.357242 - 0.618760i) q^{88} +(-5.52854 - 9.57571i) q^{89} +(-1.19364 + 2.75231i) q^{90} +(-4.35610 - 0.158753i) q^{91} +(-1.43903 + 2.49247i) q^{92} +(-11.0687 + 0.633789i) q^{93} -6.29469 q^{94} +0.153889 q^{95} +(1.72922 - 0.0990147i) q^{96} +(-4.23213 + 7.33026i) q^{97} +(-3.04944 - 6.30087i) q^{98} +(-1.27661 - 1.72182i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9} - 6 q^{10} + 3 q^{11} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} + 8 q^{19} - 6 q^{20} + 5 q^{21} + 3 q^{22} + 11 q^{23} - 6 q^{25} - 2 q^{26} - 27 q^{27} + 4 q^{28} + 13 q^{29} + 3 q^{30} - 42 q^{31} + 12 q^{32} + 17 q^{33} + q^{34} + 4 q^{35} + 4 q^{36} + 18 q^{37} + 8 q^{38} - 24 q^{39} - 6 q^{40} + 5 q^{41} + 5 q^{42} - 11 q^{43} + 3 q^{44} + q^{45} + 11 q^{46} + 46 q^{47} - 6 q^{50} - 27 q^{51} - 2 q^{52} + 2 q^{53} - 27 q^{54} - 6 q^{55} + 4 q^{56} - 44 q^{57} + 13 q^{58} - 2 q^{59} + 3 q^{60} + 2 q^{61} - 42 q^{62} + 9 q^{63} + 12 q^{64} + 4 q^{65} + 17 q^{66} - 4 q^{67} + q^{68} - 24 q^{69} + 4 q^{70} - 30 q^{71} + 4 q^{72} + 22 q^{73} + 18 q^{74} - 3 q^{75} + 8 q^{76} - 31 q^{77} - 24 q^{78} - 54 q^{79} - 6 q^{80} + 52 q^{81} + 5 q^{82} + 6 q^{83} + 5 q^{84} + q^{85} - 11 q^{86} - 28 q^{87} + 3 q^{88} - 18 q^{89} + q^{90} + 14 q^{91} + 11 q^{92} - 38 q^{93} + 46 q^{94} - 16 q^{95} - 4 q^{97} + 63 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9 - 6 * q^10 + 3 * q^11 - 2 * q^13 + 4 * q^14 + 3 * q^15 + 12 * q^16 + q^17 + 4 * q^18 + 8 * q^19 - 6 * q^20 + 5 * q^21 + 3 * q^22 + 11 * q^23 - 6 * q^25 - 2 * q^26 - 27 * q^27 + 4 * q^28 + 13 * q^29 + 3 * q^30 - 42 * q^31 + 12 * q^32 + 17 * q^33 + q^34 + 4 * q^35 + 4 * q^36 + 18 * q^37 + 8 * q^38 - 24 * q^39 - 6 * q^40 + 5 * q^41 + 5 * q^42 - 11 * q^43 + 3 * q^44 + q^45 + 11 * q^46 + 46 * q^47 - 6 * q^50 - 27 * q^51 - 2 * q^52 + 2 * q^53 - 27 * q^54 - 6 * q^55 + 4 * q^56 - 44 * q^57 + 13 * q^58 - 2 * q^59 + 3 * q^60 + 2 * q^61 - 42 * q^62 + 9 * q^63 + 12 * q^64 + 4 * q^65 + 17 * q^66 - 4 * q^67 + q^68 - 24 * q^69 + 4 * q^70 - 30 * q^71 + 4 * q^72 + 22 * q^73 + 18 * q^74 - 3 * q^75 + 8 * q^76 - 31 * q^77 - 24 * q^78 - 54 * q^79 - 6 * q^80 + 52 * q^81 + 5 * q^82 + 6 * q^83 + 5 * q^84 + q^85 - 11 * q^86 - 28 * q^87 + 3 * q^88 - 18 * q^89 + q^90 + 14 * q^91 + 11 * q^92 - 38 * q^93 + 46 * q^94 - 16 * q^95 - 4 * q^97 + 63 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.72922	−	0.0990147i	0.998365	−	0.0571662i
$3$	1.72922	−	0.0990147i	0.998365	−	0.0571662i
$4$	1.00000			0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.72922	−	0.0990147i	0.705950	−	0.0404226i
$7$	1.40545	−	2.24159i	0.531209	−	0.847241i
$7$	1.40545	−	2.24159i	0.531209	−	0.847241i
$8$	1.00000			0.353553
$9$	2.98039	−	0.342436i	0.993464	−	0.114145i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−0.357242	−	0.618760i	−0.107712	−	0.186563i	0.807131	−	0.590373i	$-0.201019\pi$
$11$	−0.357242	−	0.618760i	−0.107712	−	0.186563i	−0.914843	+	0.403809i	$0.867686\pi$
$12$	1.72922	−	0.0990147i	0.499182	−	0.0285831i
$13$	−0.823772	−	1.42682i	−0.228473	−	0.395727i	0.728883	−	0.684639i	$-0.240040\pi$
$13$	−0.823772	−	1.42682i	−0.228473	−	0.395727i	−0.957356	+	0.288911i	$0.906707\pi$
$14$	1.40545	−	2.24159i	0.375621	−	0.599090i
$15$	−0.778860	+	1.54705i	−0.201101	+	0.399448i
$16$	1.00000			0.250000
$17$	−1.61526	+	2.79771i	−0.391757	+	0.678543i	−0.992681	−	0.120763i	$-0.961466\pi$
$17$	−1.61526	+	2.79771i	−0.391757	+	0.678543i	0.600924	+	0.799306i	$0.294799\pi$
$18$	2.98039	−	0.342436i	0.702485	−	0.0807130i
$19$	−0.0769447	−	0.133272i	−0.0176523	−	0.0305747i	0.857064	−	0.515209i	$-0.172286\pi$
$19$	−0.0769447	−	0.133272i	−0.0176523	−	0.0305747i	−0.874717	+	0.484635i	$0.838953\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	2.20837	−	4.01536i	0.481906	−	0.876223i
$22$	−0.357242	−	0.618760i	−0.0761641	−	0.131920i
$23$	−1.43903	+	2.49247i	−0.300058	+	0.519716i	−0.976149	−	0.217103i	$-0.930339\pi$
$23$	−1.43903	+	2.49247i	−0.300058	+	0.519716i	0.676091	+	0.736818i	$0.263673\pi$
$24$	1.72922	−	0.0990147i	0.352975	−	0.0202113i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.823772	−	1.42682i	−0.161555	−	0.279821i
$27$	5.11984	−	0.887250i	0.985314	−	0.170751i
$28$	1.40545	−	2.24159i	0.265604	−	0.423620i
$29$	−0.602632	+	1.04379i	−0.111906	+	0.193827i	−0.916539	−	0.399946i	$-0.869029\pi$
$29$	−0.602632	+	1.04379i	−0.111906	+	0.193827i	0.804633	+	0.593773i	$0.202362\pi$
$30$	−0.778860	+	1.54705i	−0.142200	+	0.282452i
$31$	−6.40096			−1.14965			−0.574823	−	0.818278i	$-0.694929\pi$
$31$	−6.40096			−1.14965			−0.574823	+	0.818278i	$0.694929\pi$
$32$	1.00000			0.176777
$33$	−0.679015	−	1.03460i	−0.118201	−	0.180101i
$34$	−1.61526	+	2.79771i	−0.277014	+	0.479803i
$35$	1.23855	+	2.33795i	0.209353	+	0.395185i
$36$	2.98039	−	0.342436i	0.496732	−	0.0570727i
$37$	4.69842	+	8.13791i	0.772416	+	1.33786i	0.936235	+	0.351374i	$0.114285\pi$
$37$	4.69842	+	8.13791i	0.772416	+	1.33786i	−0.163819	+	0.986490i	$0.552381\pi$
$38$	−0.0769447	−	0.133272i	−0.0124821	−	0.0216196i
$39$	−1.56576	−	2.38571i	−0.250722	−	0.382019i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	3.09435	+	5.35958i	0.483257	+	0.837026i	0.999815	−	0.0192264i	$-0.00612034\pi$
$41$	3.09435	+	5.35958i	0.483257	+	0.837026i	−0.516558	+	0.856252i	$0.672787\pi$
$42$	2.20837	−	4.01536i	0.340759	−	0.619583i
$43$	4.80435	−	8.32137i	0.732656	−	1.26900i	−0.223088	−	0.974798i	$-0.571614\pi$
$43$	4.80435	−	8.32137i	0.732656	−	1.26900i	0.955744	−	0.294199i	$-0.0950530\pi$
$44$	−0.357242	−	0.618760i	−0.0538562	−	0.0932817i
$45$	−1.19364	+	2.75231i	−0.177937	+	0.410291i
$46$	−1.43903	+	2.49247i	−0.212173	+	0.367495i
$47$	−6.29469			−0.918175			−0.459087	−	0.888391i	$-0.651824\pi$
$47$	−6.29469			−0.918175			−0.459087	+	0.888391i	$0.651824\pi$
$48$	1.72922	−	0.0990147i	0.249591	−	0.0142915i
$49$	−3.04944	−	6.30087i	−0.435635	−	0.900124i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−2.51612	+	4.99778i	−0.352327	+	0.699829i
$52$	−0.823772	−	1.42682i	−0.114237	−	0.197864i
$53$	−0.576945	+	0.999298i	−0.0792495	+	0.137264i	−0.902926	−	0.429795i	$-0.858586\pi$
$53$	−0.576945	+	0.999298i	−0.0792495	+	0.137264i	0.823677	+	0.567059i	$0.191919\pi$
$54$	5.11984	−	0.887250i	0.696722	−	0.120739i
$55$	0.714483			0.0963409
$56$	1.40545	−	2.24159i	0.187811	−	0.299545i
$57$	−0.146250	−	0.222838i	−0.0193713	−	0.0295156i
$58$	−0.602632	+	1.04379i	−0.0791295	+	0.137056i
$59$	1.24707			0.162354			0.0811772	−	0.996700i	$-0.474132\pi$
$59$	1.24707			0.162354			0.0811772	+	0.996700i	$0.474132\pi$
$60$	−0.778860	+	1.54705i	−0.100550	+	0.199724i
$61$	−9.20709			−1.17885			−0.589423	−	0.807824i	$-0.700645\pi$
$61$	−9.20709			−1.17885			−0.589423	+	0.807824i	$0.700645\pi$
$62$	−6.40096			−0.812922
$63$	3.42118	−	7.16209i	0.431028	−	0.902339i
$64$	1.00000			0.125000
$65$	1.64754			0.204353
$66$	−0.679015	−	1.03460i	−0.0835810	−	0.127350i
$67$	−12.4936			−1.52634			−0.763170	−	0.646198i	$-0.776358\pi$
$67$	−12.4936			−1.52634			−0.763170	+	0.646198i	$0.776358\pi$
$68$	−1.61526	+	2.79771i	−0.195879	+	0.339272i
$69$	−2.24160	+	4.45251i	−0.269857	+	0.536019i
$70$	1.23855	+	2.33795i	0.148035	+	0.279438i
$71$	−3.71448			−0.440828			−0.220414	−	0.975406i	$-0.570741\pi$
$71$	−3.71448			−0.440828			−0.220414	+	0.975406i	$0.570741\pi$
$72$	2.98039	−	0.342436i	0.351243	−	0.0403565i
$73$	−1.45160	+	2.51424i	−0.169896	+	0.294269i	−0.938383	−	0.345596i	$-0.887677\pi$
$73$	−1.45160	+	2.51424i	−0.169896	+	0.294269i	0.768487	+	0.639866i	$0.221010\pi$
$74$	4.69842	+	8.13791i	0.546181	+	0.946013i
$75$	−0.950358	−	1.44804i	−0.109738	−	0.167205i
$76$	−0.0769447	−	0.133272i	−0.00882616	−	0.0152874i
$77$	−1.88909	−	0.0688459i	−0.215282	−	0.00784571i
$78$	−1.56576	−	2.38571i	−0.177287	−	0.270128i
$79$	−2.44228			−0.274778			−0.137389	−	0.990517i	$-0.543871\pi$
$79$	−2.44228			−0.274778			−0.137389	+	0.990517i	$0.543871\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	8.76547	−	2.04119i	0.973942	−	0.226799i
$82$	3.09435	+	5.35958i	0.341714	+	0.591867i
$83$	2.21659	−	3.83925i	0.243303	−	0.421413i	−0.718350	−	0.695682i	$-0.755102\pi$
$83$	2.21659	−	3.83925i	0.243303	−	0.421413i	0.961653	+	0.274269i	$0.0884358\pi$
$84$	2.20837	−	4.01536i	0.240953	−	0.438111i
$85$	−1.61526	−	2.79771i	−0.175199	−	0.303454i
$86$	4.80435	−	8.32137i	0.518066	−	0.897317i
$87$	−0.938732	+	1.86461i	−0.100643	+	0.199907i
$88$	−0.357242	−	0.618760i	−0.0380821	−	0.0659601i
$89$	−5.52854	−	9.57571i	−0.586024	−	1.01502i	−0.994747	−	0.102365i	$-0.967359\pi$
$89$	−5.52854	−	9.57571i	−0.586024	−	1.01502i	0.408723	−	0.912659i	$-0.365974\pi$
$90$	−1.19364	+	2.75231i	−0.125820	+	0.290119i
$91$	−4.35610	−	0.158753i	−0.456643	−	0.0166419i
$92$	−1.43903	+	2.49247i	−0.150029	+	0.259858i
$93$	−11.0687	+	0.633789i	−1.14777	+	0.0657209i
$94$	−6.29469			−0.649248
$95$	0.153889			0.0157887
$96$	1.72922	−	0.0990147i	0.176488	−	0.0101056i
$97$	−4.23213	+	7.33026i	−0.429707	+	0.744275i	−0.996847	−	0.0793465i	$-0.974717\pi$
$97$	−4.23213	+	7.33026i	−0.429707	+	0.744275i	0.567140	+	0.823622i	$0.308050\pi$
$98$	−3.04944	−	6.30087i	−0.308040	−	0.636484i
$99$	−1.27661	−	1.72182i	−0.128304	−	0.173049i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	5.82008	+	10.0807i	0.579120	+	1.00306i	0.995581	+	0.0939111i	$0.0299370\pi$
$101$	5.82008	+	10.0807i	0.579120	+	1.00306i	−0.416461	+	0.909154i	$0.636730\pi$
$102$	−2.51612	+	4.99778i	−0.249133	+	0.494854i
$103$	4.24519	−	7.35289i	0.418291	−	0.724501i	−0.577477	−	0.816407i	$-0.695963\pi$
$103$	4.24519	−	7.35289i	0.418291	−	0.724501i	0.995768	+	0.0919058i	$0.0292959\pi$
$104$	−0.823772	−	1.42682i	−0.0807775	−	0.139911i
$105$	2.37321	+	3.92019i	0.231602	+	0.382571i
$106$	−0.576945	+	0.999298i	−0.0560378	+	0.0970604i
$107$	1.76107	+	3.05026i	0.170249	+	0.294880i	0.938507	−	0.345261i	$-0.112210\pi$
$107$	1.76107	+	3.05026i	0.170249	+	0.294880i	−0.768258	+	0.640140i	$0.778876\pi$
$108$	5.11984	−	0.887250i	0.492657	−	0.0853756i
$109$	5.21434	−	9.03150i	0.499443	−	0.865061i	−0.500557	−	0.865704i	$-0.666871\pi$
$109$	5.21434	−	9.03150i	0.499443	−	0.865061i	1.00000		0.000642856i	$0.000204627\pi$
$110$	0.714483			0.0681233
$111$	8.93037	+	13.6070i	0.847633	+	1.29152i
$112$	1.40545	−	2.24159i	0.132802	−	0.211810i
$113$	−2.85715	−	4.94874i	−0.268779	−	0.465538i	0.699768	−	0.714370i	$-0.253287\pi$
$113$	−2.85715	−	4.94874i	−0.268779	−	0.465538i	−0.968547	+	0.248832i	$0.919953\pi$
$114$	−0.146250	−	0.222838i	−0.0136976	−	0.0208707i
$115$	−1.43903	−	2.49247i	−0.134190	−	0.232424i
$116$	−0.602632	+	1.04379i	−0.0559530	+	0.0969134i
$117$	−2.94376	−	3.97038i	−0.272150	−	0.367062i
$118$	1.24707			0.114802
$119$	4.00115	+	7.55276i	0.366785	+	0.692361i
$120$	−0.778860	+	1.54705i	−0.0710999	+	0.141226i
$121$	5.24476	−	9.08419i	0.476796	−	0.825835i
$122$	−9.20709			−0.833570
$123$	5.88149	+	8.96150i	0.530316	+	0.808031i
$124$	−6.40096			−0.574823
$125$	1.00000			0.0894427
$126$	3.42118	−	7.16209i	0.304783	−	0.638050i
$127$	9.02973			0.801259			0.400629	−	0.916240i	$-0.368792\pi$
$127$	9.02973			0.801259			0.400629	+	0.916240i	$0.368792\pi$
$128$	1.00000			0.0883883
$129$	7.48383	−	14.8652i	0.658914	−	1.30881i
$130$	1.64754			0.144499
$131$	−9.17401	+	15.8899i	−0.801537	+	1.38830i	0.117067	+	0.993124i	$0.462651\pi$
$131$	−9.17401	+	15.8899i	−0.801537	+	1.38830i	−0.918604	+	0.395179i	$0.870682\pi$
$132$	−0.679015	−	1.03460i	−0.0591007	−	0.0900504i
$133$	−0.406883	−	0.0148284i	−0.0352812	−	0.00128579i
$134$	−12.4936			−1.07928
$135$	−1.79154	+	4.87754i	−0.154191	+	0.419792i
$136$	−1.61526	+	2.79771i	−0.138507	+	0.239901i
$137$	8.94199	+	15.4880i	0.763966	+	1.32323i	0.940791	+	0.338986i	$0.110084\pi$
$137$	8.94199	+	15.4880i	0.763966	+	1.32323i	−0.176825	+	0.984242i	$0.556583\pi$
$138$	−2.24160	+	4.45251i	−0.190818	+	0.379023i
$139$	−0.436114	−	0.755372i	−0.0369907	−	0.0640698i	0.846937	−	0.531693i	$-0.178444\pi$
$139$	−0.436114	−	0.755372i	−0.0369907	−	0.0640698i	−0.883928	+	0.467623i	$0.845111\pi$
$140$	1.23855	+	2.33795i	0.104677	+	0.197593i
$141$	−10.8849	+	0.623267i	−0.916673	+	0.0524886i
$142$	−3.71448			−0.311712
$143$	−0.588571	+	1.01944i	−0.0492188	+	0.0852495i
$144$	2.98039	−	0.342436i	0.248366	−	0.0285364i
$145$	−0.602632	−	1.04379i	−0.0500459	−	0.0866820i
$146$	−1.45160	+	2.51424i	−0.120135	+	0.208080i
$147$	−5.89703	−	10.5936i	−0.486379	−	0.873748i
$148$	4.69842	+	8.13791i	0.386208	+	0.668932i
$149$	−0.571398	+	0.989690i	−0.0468107	+	0.0810786i	−0.888481	−	0.458913i	$-0.848239\pi$
$149$	−0.571398	+	0.989690i	−0.0468107	+	0.0810786i	0.841671	+	0.539991i	$0.181572\pi$
$150$	−0.950358	−	1.44804i	−0.0775964	−	0.118232i
$151$	0.158200	+	0.274011i	0.0128741	+	0.0222987i	0.872391	−	0.488809i	$-0.162569\pi$
$151$	0.158200	+	0.274011i	0.0128741	+	0.0222987i	−0.859517	+	0.511108i	$0.829235\pi$
$152$	−0.0769447	−	0.133272i	−0.00624104	−	0.0108098i
$153$	−3.85606	+	8.89138i	−0.311744	+	0.718826i
$154$	−1.88909	−	0.0688459i	−0.152227	−	0.00554776i
$155$	3.20048	−	5.54339i	0.257069	−	0.445256i
$156$	−1.56576	−	2.38571i	−0.125361	−	0.191010i
$157$	−13.7530			−1.09761			−0.548805	−	0.835950i	$-0.684917\pi$
$157$	−13.7530			−1.09761			−0.548805	+	0.835950i	$0.684917\pi$
$158$	−2.44228			−0.194297
$159$	−0.898718	+	1.78513i	−0.0712730	+	0.141570i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	3.56462	+	6.72874i	0.280931	+	0.530299i
$162$	8.76547	−	2.04119i	0.688681	−	0.160371i
$163$	2.04615	+	3.54404i	0.160267	+	0.277590i	0.934964	−	0.354742i	$-0.115431\pi$
$163$	2.04615	+	3.54404i	0.160267	+	0.277590i	−0.774698	+	0.632332i	$0.782098\pi$
$164$	3.09435	+	5.35958i	0.241628	+	0.418513i
$165$	1.23550	−	0.0707444i	0.0961833	−	0.00550744i
$166$	2.21659	−	3.83925i	0.172041	−	0.297984i
$167$	3.13912	+	5.43712i	0.242913	+	0.420737i	0.961543	−	0.274656i	$-0.0885638\pi$
$167$	3.13912	+	5.43712i	0.242913	+	0.420737i	−0.718630	+	0.695393i	$0.755230\pi$
$168$	2.20837	−	4.01536i	0.170380	−	0.309791i
$169$	5.14280	−	8.90759i	0.395600	−	0.685199i
$170$	−1.61526	−	2.79771i	−0.123884	−	0.214574i
$171$	−0.274963	−	0.370855i	−0.0210269	−	0.0283600i
$172$	4.80435	−	8.32137i	0.366328	−	0.634499i
$173$	−15.1441			−1.15139			−0.575694	−	0.817665i	$-0.695268\pi$
$173$	−15.1441			−1.15139			−0.575694	+	0.817665i	$0.695268\pi$
$174$	−0.938732	+	1.86461i	−0.0711651	+	0.141356i
$175$	−2.64400	−	0.0963576i	−0.199867	−	0.00728395i
$176$	−0.357242	−	0.618760i	−0.0269281	−	0.0466408i
$177$	2.15645	−	0.123478i	0.162089	−	0.00928118i
$178$	−5.52854	−	9.57571i	−0.414382	−	0.717730i
$179$	10.3341	−	17.8993i	0.772410	−	1.33785i	−0.163829	−	0.986489i	$-0.552384\pi$
$179$	10.3341	−	17.8993i	0.772410	−	1.33785i	0.936239	−	0.351365i	$-0.114282\pi$
$180$	−1.19364	+	2.75231i	−0.0889685	+	0.205145i
$181$	−24.3018			−1.80634			−0.903168	−	0.429288i	$-0.858765\pi$
$181$	−24.3018			−1.80634			−0.903168	+	0.429288i	$0.858765\pi$
$182$	−4.35610	−	0.158753i	−0.322896	−	0.0117676i
$183$	−15.9211	+	0.911637i	−1.17692	+	0.0673902i
$184$	−1.43903	+	2.49247i	−0.106087	+	0.183747i
$185$	−9.39685			−0.690870
$186$	−11.0687	+	0.633789i	−0.811593	+	0.0464717i
$187$	2.30815			0.168788
$188$	−6.29469			−0.459087
$189$	5.20681	−	12.7236i	0.378740	−	0.925503i
$190$	0.153889			0.0111643
$191$	17.5658			1.27102			0.635510	−	0.772093i	$-0.280790\pi$
$191$	17.5658			1.27102			0.635510	+	0.772093i	$0.280790\pi$
$192$	1.72922	−	0.0990147i	0.124796	−	0.00714577i
$193$	26.1637			1.88331			0.941653	−	0.336585i	$-0.109272\pi$
$193$	26.1637			1.88331			0.941653	+	0.336585i	$0.109272\pi$
$194$	−4.23213	+	7.33026i	−0.303849	+	0.526282i
$195$	2.84896	−	0.163131i	0.204019	−	0.0116821i
$196$	−3.04944	−	6.30087i	−0.217817	−	0.450062i
$197$	−19.1886			−1.36713			−0.683564	−	0.729890i	$-0.739571\pi$
$197$	−19.1886			−1.36713			−0.683564	+	0.729890i	$0.739571\pi$
$198$	−1.27661	−	1.72182i	−0.0907244	−	0.122364i
$199$	12.6145	−	21.8489i	0.894216	−	1.54883i	0.0594449	−	0.998232i	$-0.481067\pi$
$199$	12.6145	−	21.8489i	0.894216	−	1.54883i	0.834771	−	0.550597i	$-0.185600\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−21.6042	+	1.23705i	−1.52384	+	0.0872550i
$202$	5.82008	+	10.0807i	0.409499	+	0.709274i
$203$	1.49278	+	2.81784i	0.104773	+	0.197774i
$204$	−2.51612	+	4.99778i	−0.176163	+	0.349914i
$205$	−6.18871			−0.432238
$206$	4.24519	−	7.35289i	0.295776	−	0.512300i
$207$	−3.43536	+	7.92131i	−0.238774	+	0.550569i
$208$	−0.823772	−	1.42682i	−0.0571183	−	0.0989318i
$209$	−0.0549757	+	0.0952207i	−0.00380275	+	0.00658655i
$210$	2.37321	+	3.92019i	0.163767	+	0.270518i
$211$	−10.0339	−	17.3793i	−0.690763	−	1.19644i	−0.971588	−	0.236678i	$-0.923941\pi$
$211$	−10.0339	−	17.3793i	−0.690763	−	1.19644i	0.280825	−	0.959759i	$-0.409392\pi$
$212$	−0.576945	+	0.999298i	−0.0396247	+	0.0686320i
$213$	−6.42315	+	0.367789i	−0.440107	+	0.0252005i
$214$	1.76107	+	3.05026i	0.120384	+	0.208511i
$215$	4.80435	+	8.32137i	0.327654	+	0.567513i
$216$	5.11984	−	0.887250i	0.348361	−	0.0603697i
$217$	−8.99620	+	14.3483i	−0.610702	+	0.974027i
$218$	5.21434	−	9.03150i	0.353160	−	0.611690i
$219$	−2.26118	+	4.49140i	−0.152796	+	0.303500i
$220$	0.714483			0.0481704
$221$	5.32241			0.358024
$222$	8.93037	+	13.6070i	0.599367	+	0.913243i
$223$	−2.32770	+	4.03170i	−0.155875	+	0.269983i	−0.933377	−	0.358897i	$-0.883153\pi$
$223$	−2.32770	+	4.03170i	−0.155875	+	0.269983i	0.777503	+	0.628880i	$0.216486\pi$
$224$	1.40545	−	2.24159i	0.0939053	−	0.149772i
$225$	−1.78675	−	2.40988i	−0.119117	−	0.160658i
$226$	−2.85715	−	4.94874i	−0.190055	−	0.329185i
$227$	8.25676	+	14.3011i	0.548020	+	0.949199i	0.998410	+	0.0563672i	$0.0179518\pi$
$227$	8.25676	+	14.3011i	0.548020	+	0.949199i	−0.450390	+	0.892832i	$0.648715\pi$
$228$	−0.146250	−	0.222838i	−0.00968565	−	0.0147578i
$229$	2.67044	−	4.62535i	0.176468	−	0.305651i	−0.764200	−	0.644979i	$-0.776866\pi$
$229$	2.67044	−	4.62535i	0.176468	−	0.305651i	0.940668	+	0.339327i	$0.110199\pi$
$230$	−1.43903	−	2.49247i	−0.0948867	−	0.164349i
$231$	−3.27347	+	0.0679983i	−0.215378	+	0.00447396i
$232$	−0.602632	+	1.04379i	−0.0395647	+	0.0685281i
$233$	−0.625333	−	1.08311i	−0.0409669	−	0.0709568i	0.844815	−	0.535059i	$-0.179710\pi$
$233$	−0.625333	−	1.08311i	−0.0409669	−	0.0709568i	−0.885782	+	0.464102i	$0.846377\pi$
$234$	−2.94376	−	3.97038i	−0.192439	−	0.259552i
$235$	3.14735	−	5.45136i	0.205310	−	0.355608i
$236$	1.24707			0.0811772
$237$	−4.22324	+	0.241822i	−0.274329	+	0.0157080i
$238$	4.00115	+	7.55276i	0.259356	+	0.489573i
$239$	0.665842	+	1.15327i	0.0430698	+	0.0745990i	0.886757	−	0.462237i	$-0.152953\pi$
$239$	0.665842	+	1.15327i	0.0430698	+	0.0745990i	−0.843687	+	0.536836i	$0.819620\pi$
$240$	−0.778860	+	1.54705i	−0.0502752	+	0.0998619i
$241$	8.51454	+	14.7476i	0.548470	+	0.949978i	0.998380	+	0.0569036i	$0.0181228\pi$
$241$	8.51454	+	14.7476i	0.548470	+	0.949978i	−0.449910	+	0.893074i	$0.648544\pi$
$242$	5.24476	−	9.08419i	0.337146	−	0.583954i
$243$	14.9553	−	4.39757i	0.959384	−	0.282104i
$244$	−9.20709			−0.589423
$245$	6.98143	+	0.509538i	0.446027	+	0.0325532i
$246$	5.88149	+	8.96150i	0.374990	+	0.571364i
$247$	−0.126770	+	0.219572i	−0.00806617	+	0.0139710i
$248$	−6.40096			−0.406461
$249$	3.45283	−	6.85838i	0.218814	−	0.434632i
$250$	1.00000			0.0632456
$251$	19.1121			1.20635			0.603174	−	0.797610i	$-0.293903\pi$
$251$	19.1121			1.20635			0.603174	+	0.797610i	$0.293903\pi$
$252$	3.42118	−	7.16209i	0.215514	−	0.451169i
$253$	2.05632			0.129280
$254$	9.02973			0.566575
$255$	−3.07014	−	4.67791i	−0.192260	−	0.292942i
$256$	1.00000			0.0625000
$257$	−15.5139	+	26.8709i	−0.967733	+	1.67616i	−0.265648	+	0.964070i	$0.585586\pi$
$257$	−15.5139	+	26.8709i	−0.967733	+	1.67616i	−0.702085	+	0.712093i	$0.747747\pi$
$258$	7.48383	−	14.8652i	0.465923	−	0.925465i
$259$	24.8452	+	0.905458i	1.54381	+	0.0562624i
$260$	1.64754			0.102176
$261$	−1.43865	+	3.31726i	−0.0890501	+	0.205334i
$262$	−9.17401	+	15.8899i	−0.566772	+	0.981679i
$263$	10.4507	+	18.1011i	0.644417	+	1.11616i	0.984436	+	0.175745i	$0.0562333\pi$
$263$	10.4507	+	18.1011i	0.644417	+	1.11616i	−0.340019	+	0.940419i	$0.610433\pi$
$264$	−0.679015	−	1.03460i	−0.0417905	−	0.0636752i
$265$	−0.576945	−	0.999298i	−0.0354414	−	0.0613864i
$266$	−0.406883	−	0.0148284i	−0.0249476	−	0.000909188i
$267$	−10.5082	−	16.0111i	−0.643091	−	0.979863i
$268$	−12.4936			−0.763170
$269$	10.4350	−	18.0740i	0.636234	−	1.10199i	−0.350018	−	0.936743i	$-0.613825\pi$
$269$	10.4350	−	18.0740i	0.636234	−	1.10199i	0.986252	−	0.165247i	$-0.0528421\pi$
$270$	−1.79154	+	4.87754i	−0.109030	+	0.296838i
$271$	−6.19759	−	10.7345i	−0.376477	−	0.652077i	0.614070	−	0.789251i	$-0.289531\pi$
$271$	−6.19759	−	10.7345i	−0.376477	−	0.652077i	−0.990547	+	0.137175i	$0.956198\pi$
$272$	−1.61526	+	2.79771i	−0.0979393	+	0.169636i
$273$	−7.54837	+	0.156799i	−0.456848	+	0.00948990i
$274$	8.94199	+	15.4880i	0.540206	+	0.935664i
$275$	−0.357242	+	0.618760i	−0.0215425	+	0.0373127i
$276$	−2.24160	+	4.45251i	−0.134929	+	0.268010i
$277$	5.24812	+	9.09000i	0.315329	+	0.546165i	0.979507	−	0.201409i	$-0.0645519\pi$
$277$	5.24812	+	9.09000i	0.315329	+	0.546165i	−0.664179	+	0.747574i	$0.731219\pi$
$278$	−0.436114	−	0.755372i	−0.0261564	−	0.0453042i
$279$	−19.0774	+	2.19192i	−1.14213	+	0.131227i
$280$	1.23855	+	2.33795i	0.0740175	+	0.139719i
$281$	15.8173	−	27.3964i	0.943582	−	1.63433i	0.185017	−	0.982735i	$-0.440766\pi$
$281$	15.8173	−	27.3964i	0.943582	−	1.63433i	0.758565	−	0.651597i	$-0.225901\pi$
$282$	−10.8849	+	0.623267i	−0.648186	+	0.0371150i
$283$	12.8565			0.764241			0.382120	−	0.924113i	$-0.375194\pi$
$283$	12.8565			0.764241			0.382120	+	0.924113i	$0.375194\pi$
$284$	−3.71448			−0.220414
$285$	0.266108	−	0.0152373i	0.0157629	−	0.000902581i
$286$	−0.588571	+	1.01944i	−0.0348029	+	0.0602805i
$287$	16.3629	+	0.596329i	0.965873	+	0.0352002i
$288$	2.98039	−	0.342436i	0.175621	−	0.0201782i
$289$	3.28190	+	5.68441i	0.193053	+	0.334377i
$290$	−0.602632	−	1.04379i	−0.0353878	−	0.0612934i
$291$	−6.59247	+	13.0947i	−0.386457	+	0.767623i
$292$	−1.45160	+	2.51424i	−0.0849482	+	0.147135i
$293$	−14.3055	−	24.7778i	−0.835735	−	1.44754i	−0.893430	−	0.449202i	$-0.851708\pi$
$293$	−14.3055	−	24.7778i	−0.835735	−	1.44754i	0.0576951	−	0.998334i	$-0.481625\pi$
$294$	−5.89703	−	10.5936i	−0.343922	−	0.617833i
$295$	−0.623534	+	1.07999i	−0.0363035	+	0.0628796i
$296$	4.69842	+	8.13791i	0.273090	+	0.473006i
$297$	−2.37802	−	2.85099i	−0.137986	−	0.165431i
$298$	−0.571398	+	0.989690i	−0.0331002	+	0.0573312i
$299$	4.74173			0.274221
$300$	−0.950358	−	1.44804i	−0.0548690	−	0.0836026i
$301$	−11.9008	−	22.4646i	−0.685954	−	1.29484i
$302$	0.158200	+	0.274011i	0.00910340	+	0.0157675i
$303$	11.0623	+	16.8554i	0.635514	+	0.968318i
$304$	−0.0769447	−	0.133272i	−0.00441308	−	0.00764368i
$305$	4.60354	−	7.97357i	0.263598	−	0.456565i
$306$	−3.85606	+	8.89138i	−0.220436	+	0.508286i
$307$	34.6549			1.97786			0.988930	−	0.148382i	$-0.0474067\pi$
$307$	34.6549			1.97786			0.988930	+	0.148382i	$0.0474067\pi$
$308$	−1.88909	−	0.0688459i	−0.107641	−	0.00392286i
$309$	6.61282	−	13.1351i	0.376190	−	0.747229i
$310$	3.20048	−	5.54339i	0.181775	−	0.314843i
$311$	17.6573			1.00125			0.500626	−	0.865664i	$-0.333103\pi$
$311$	17.6573			1.00125			0.500626	+	0.865664i	$0.333103\pi$
$312$	−1.56576	−	2.38571i	−0.0886436	−	0.135064i
$313$	1.25714			0.0710578			0.0355289	−	0.999369i	$-0.488688\pi$
$313$	1.25714			0.0710578			0.0355289	+	0.999369i	$0.488688\pi$
$314$	−13.7530			−0.776127
$315$	4.49196	+	6.54387i	0.253093	+	0.368705i
$316$	−2.44228			−0.137389
$317$	−4.91403			−0.275999			−0.138000	−	0.990432i	$-0.544067\pi$
$317$	−4.91403			−0.275999			−0.138000	+	0.990432i	$0.544067\pi$
$318$	−0.898718	+	1.78513i	−0.0503976	+	0.100105i
$319$	0.861141			0.0482146
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	3.34729	+	5.10019i	0.186828	+	0.284665i
$322$	3.56462	+	6.72874i	0.198648	+	0.374978i
$323$	0.497142			0.0276617
$324$	8.76547	−	2.04119i	0.486971	−	0.113399i
$325$	−0.823772	+	1.42682i	−0.0456947	+	0.0791455i
$326$	2.04615	+	3.54404i	0.113326	+	0.196286i
$327$	8.12248	−	16.1337i	0.449174	−	0.892198i
$328$	3.09435	+	5.35958i	0.170857	+	0.295933i
$329$	−8.84685	+	14.1101i	−0.487743	+	0.777915i
$330$	1.23550	−	0.0707444i	0.0680119	−	0.00389435i
$331$	30.0766			1.65316			0.826579	−	0.562821i	$-0.190284\pi$
$331$	30.0766			1.65316			0.826579	+	0.562821i	$0.190284\pi$
$332$	2.21659	−	3.83925i	0.121651	−	0.210706i
$333$	16.7899	+	22.6452i	0.920079	+	1.24095i
$334$	3.13912	+	5.43712i	0.171765	+	0.297506i
$335$	6.24681	−	10.8198i	0.341300	−	0.591149i
$336$	2.20837	−	4.01536i	0.120477	−	0.219056i
$337$	8.27039	+	14.3247i	0.450517	+	0.780318i	0.998418	−	0.0562251i	$-0.0179065\pi$
$337$	8.27039	+	14.3247i	0.450517	+	0.780318i	−0.547901	+	0.836543i	$0.684573\pi$
$338$	5.14280	−	8.90759i	0.279731	−	0.484509i
$339$	−5.43064	−	8.27455i	−0.294952	−	0.449412i
$340$	−1.61526	−	2.79771i	−0.0875996	−	0.151727i
$341$	2.28669	+	3.96066i	0.123831	+	0.214482i
$342$	−0.274963	−	0.370855i	−0.0148683	−	0.0200535i
$343$	−18.4098	−	2.01993i	−0.994035	−	0.109066i
$344$	4.80435	−	8.32137i	0.259033	−	0.448658i
$345$	−2.73519	−	4.16754i	−0.147257	−	0.224373i
$346$	−15.1441			−0.814154
$347$	5.80220			0.311478			0.155739	−	0.987798i	$-0.450224\pi$
$347$	5.80220			0.311478			0.155739	+	0.987798i	$0.450224\pi$
$348$	−0.938732	+	1.86461i	−0.0503213	+	0.0999535i
$349$	−12.5953	+	21.8157i	−0.674211	+	1.16777i	0.302487	+	0.953153i	$0.402183\pi$
$349$	−12.5953	+	21.8157i	−0.674211	+	1.16777i	−0.976699	+	0.214615i	$0.931150\pi$
$350$	−2.64400	−	0.0963576i	−0.141328	−	0.00515053i
$351$	−5.48353	−	6.57418i	−0.292689	−	0.350904i
$352$	−0.357242	−	0.618760i	−0.0190410	−	0.0329800i
$353$	−1.97987	−	3.42924i	−0.105378	−	0.182520i	0.808515	−	0.588476i	$-0.200272\pi$
$353$	−1.97987	−	3.42924i	−0.105378	−	0.182520i	−0.913893	+	0.405956i	$0.866939\pi$
$354$	2.15645	−	0.123478i	0.114614	−	0.00656278i
$355$	1.85724	−	3.21684i	0.0985721	−	0.170732i
$356$	−5.52854	−	9.57571i	−0.293012	−	0.507512i
$357$	7.66670	+	12.6642i	0.405765	+	0.670261i
$358$	10.3341	−	17.8993i	0.546176	−	0.946005i
$359$	−6.99027	−	12.1075i	−0.368932	−	0.639010i	0.620467	−	0.784233i	$-0.286943\pi$
$359$	−6.99027	−	12.1075i	−0.368932	−	0.639010i	−0.989399	+	0.145223i	$0.953610\pi$
$360$	−1.19364	+	2.75231i	−0.0629102	+	0.145060i
$361$	9.48816	−	16.4340i	0.499377	−	0.864946i
$362$	−24.3018			−1.27727
$363$	8.16986	−	16.2278i	0.428807	−	0.851741i
$364$	−4.35610	−	0.158753i	−0.228322	−	0.00832094i
$365$	−1.45160	−	2.51424i	−0.0759800	−	0.131601i
$366$	−15.9211	+	0.911637i	−0.832207	+	0.0476520i
$367$	−3.52613	−	6.10743i	−0.184062	−	0.318805i	0.759198	−	0.650860i	$-0.225591\pi$
$367$	−3.52613	−	6.10743i	−0.184062	−	0.318805i	−0.943260	+	0.332055i	$0.892258\pi$
$368$	−1.43903	+	2.49247i	−0.0750145	+	0.129929i
$369$	11.0577	+	14.9140i	0.575641	+	0.776393i
$370$	−9.39685			−0.488519
$371$	1.42915	+	2.69773i	0.0741978	+	0.140059i
$372$	−11.0687	+	0.633789i	−0.573883	+	0.0328604i
$373$	−14.5747	+	25.2441i	−0.754649	+	1.30709i	0.190899	+	0.981610i	$0.438860\pi$
$373$	−14.5747	+	25.2441i	−0.754649	+	1.30709i	−0.945548	+	0.325481i	$0.894474\pi$
$374$	2.30815			0.119351
$375$	1.72922	−	0.0990147i	0.0892965	−	0.00511310i
$376$	−6.29469			−0.324624
$377$	1.98573			0.102270
$378$	5.20681	−	12.7236i	0.267810	−	0.654430i
$379$	31.6713			1.62684			0.813422	−	0.581673i	$-0.197602\pi$
$379$	31.6713			1.62684			0.813422	+	0.581673i	$0.197602\pi$
$380$	0.153889			0.00789436
$381$	15.6144	−	0.894076i	0.799948	−	0.0458049i
$382$	17.5658			0.898747
$383$	−2.29736	+	3.97914i	−0.117389	+	0.203325i	−0.918732	−	0.394881i	$-0.870786\pi$
$383$	−2.29736	+	3.97914i	−0.117389	+	0.203325i	0.801343	+	0.598205i	$0.204119\pi$
$384$	1.72922	−	0.0990147i	0.0882438	−	0.00505282i
$385$	1.00417	−	1.60158i	0.0511771	−	0.0816239i
$386$	26.1637			1.33170
$387$	11.4693	−	26.4461i	0.583017	−	1.34433i
$388$	−4.23213	+	7.33026i	−0.214854	+	0.372138i
$389$	−17.0012	−	29.4470i	−0.861997	−	1.49302i	−0.869999	−	0.493054i	$-0.835880\pi$
$389$	−17.0012	−	29.4470i	−0.861997	−	1.49302i	0.00800198	−	0.999968i	$-0.497453\pi$
$390$	2.84896	−	0.163131i	0.144263	−	0.00826047i
$391$	−4.64880	−	8.05195i	−0.235100	−	0.407205i
$392$	−3.04944	−	6.30087i	−0.154020	−	0.318242i
$393$	−14.2905	+	28.3854i	−0.720863	+	1.43185i
$394$	−19.1886			−0.966706
$395$	1.22114	−	2.11508i	0.0614422	−	0.106421i
$396$	−1.27661	−	1.72182i	−0.0641519	−	0.0865245i
$397$	3.56605	+	6.17658i	0.178975	+	0.309994i	0.941530	−	0.336930i	$-0.109389\pi$
$397$	3.56605	+	6.17658i	0.178975	+	0.309994i	−0.762555	+	0.646924i	$0.776055\pi$
$398$	12.6145	−	21.8489i	0.632306	−	1.09519i
$399$	−0.705058	+	0.0146459i	−0.0352970	+	0.000733210i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	5.20071	−	9.00790i	0.259711	−	0.449833i	−0.706453	−	0.707760i	$-0.749706\pi$
$401$	5.20071	−	9.00790i	0.259711	−	0.449833i	0.966165	+	0.257927i	$0.0830393\pi$
$402$	−21.6042	+	1.23705i	−1.07752	+	0.0616986i
$403$	5.27293	+	9.13298i	0.262663	+	0.454946i
$404$	5.82008	+	10.0807i	0.289560	+	0.501532i
$405$	−2.61502	+	8.61172i	−0.129941	+	0.427920i
$406$	1.49278	+	2.81784i	0.0740854	+	0.139847i
$407$	3.35694	−	5.81440i	0.166398	−	0.288209i
$408$	−2.51612	+	4.99778i	−0.124566	+	0.247427i
$409$	8.13727			0.402362			0.201181	−	0.979554i	$-0.435522\pi$
$409$	8.13727			0.402362			0.201181	+	0.979554i	$0.435522\pi$
$410$	−6.18871			−0.305639
$411$	16.9962	+	25.8967i	0.838361	+	1.27739i
$412$	4.24519	−	7.35289i	0.209146	−	0.362251i
$413$	1.75269	−	2.79541i	0.0862440	−	0.137553i
$414$	−3.43536	+	7.92131i	−0.168839	+	0.389311i
$415$	2.21659	+	3.83925i	0.108808	+	0.188462i
$416$	−0.823772	−	1.42682i	−0.0403888	−	0.0699554i
$417$	−0.828929	−	1.26302i	−0.0405928	−	0.0618504i
$418$	−0.0549757	+	0.0952207i	−0.00268895	+	0.00465740i
$419$	−6.88164	−	11.9194i	−0.336190	−	0.582298i	0.647523	−	0.762046i	$-0.275805\pi$
$419$	−6.88164	−	11.9194i	−0.336190	−	0.582298i	−0.983713	+	0.179748i	$0.942472\pi$
$420$	2.37321	+	3.92019i	0.115801	+	0.191285i
$421$	−8.52205	+	14.7606i	−0.415339	+	0.719389i	−0.995464	−	0.0951387i	$-0.969671\pi$
$421$	−8.52205	+	14.7606i	−0.415339	+	0.719389i	0.580125	+	0.814528i	$0.303004\pi$
$422$	−10.0339	−	17.3793i	−0.488443	−	0.846009i
$423$	−18.7606	+	2.15553i	−0.912174	+	0.104805i
$424$	−0.576945	+	0.999298i	−0.0280189	+	0.0485302i
$425$	3.23051			0.156703
$426$	−6.42315	+	0.367789i	−0.311203	+	0.0178194i
$427$	−12.9401	+	20.6385i	−0.626214	+	0.998767i
$428$	1.76107	+	3.05026i	0.0851244	+	0.147440i
$429$	−0.916829	+	1.82110i	−0.0442649	+	0.0879237i
$430$	4.80435	+	8.32137i	0.231686	+	0.401292i
$431$	−3.94159	+	6.82703i	−0.189860	+	0.328847i	−0.945203	−	0.326482i	$-0.894137\pi$
$431$	−3.94159	+	6.82703i	−0.189860	+	0.328847i	0.755344	+	0.655329i	$0.227470\pi$
$432$	5.11984	−	0.887250i	0.246329	−	0.0426878i
$433$	15.3356			0.736983			0.368491	−	0.929631i	$-0.379874\pi$
$433$	15.3356			0.736983			0.368491	+	0.929631i	$0.379874\pi$
$434$	−8.99620	+	14.3483i	−0.431831	+	0.688741i
$435$	−1.14543	−	1.74527i	−0.0549193	−	0.0836793i
$436$	5.21434	−	9.03150i	0.249722	−	0.432530i
$437$	0.442902			0.0211869
$438$	−2.26118	+	4.49140i	−0.108043	+	0.214607i
$439$	11.4596			0.546937			0.273469	−	0.961881i	$-0.411829\pi$
$439$	11.4596			0.546937			0.273469	+	0.961881i	$0.411829\pi$
$440$	0.714483			0.0340616
$441$	−11.2462	−	17.7348i	−0.535532	−	0.844515i
$442$	5.32241			0.253161
$443$	−29.9668			−1.42377			−0.711883	−	0.702298i	$-0.752157\pi$
$443$	−29.9668			−1.42377			−0.711883	+	0.702298i	$0.752157\pi$
$444$	8.93037	+	13.6070i	0.423817	+	0.645760i
$445$	11.0571			0.524156
$446$	−2.32770	+	4.03170i	−0.110220	+	0.190907i
$447$	−0.890077	+	1.76797i	−0.0420992	+	0.0836220i
$448$	1.40545	−	2.24159i	0.0664011	−	0.105905i
$449$	3.37658			0.159351			0.0796754	−	0.996821i	$-0.474612\pi$
$449$	3.37658			0.159351			0.0796754	+	0.996821i	$0.474612\pi$
$450$	−1.78675	−	2.40988i	−0.0842284	−	0.113603i
$451$	2.21086	−	3.82933i	0.104106	−	0.180316i
$452$	−2.85715	−	4.94874i	−0.134389	−	0.232769i
$453$	0.300694	+	0.458160i	0.0141278	+	0.0215262i
$454$	8.25676	+	14.3011i	0.387509	+	0.671185i
$455$	2.31553	−	3.69312i	0.108554	−	0.173136i
$456$	−0.146250	−	0.222838i	−0.00684879	−	0.0104353i
$457$	−25.0722			−1.17283			−0.586415	−	0.810011i	$-0.699461\pi$
$457$	−25.0722			−1.17283			−0.586415	+	0.810011i	$0.699461\pi$
$458$	2.67044	−	4.62535i	0.124782	−	0.216128i
$459$	−5.78759	+	15.7569i	−0.270142	+	0.735471i
$460$	−1.43903	−	2.49247i	−0.0670950	−	0.116212i
$461$	18.4429	−	31.9440i	0.858970	−	1.48778i	−0.0139415	−	0.999903i	$-0.504438\pi$
$461$	18.4429	−	31.9440i	0.858970	−	1.48778i	0.872912	−	0.487878i	$-0.162229\pi$
$462$	−3.27347	+	0.0679983i	−0.152295	+	0.00316357i
$463$	14.7697	+	25.5818i	0.686405	+	1.18889i	0.972993	+	0.230835i	$0.0741456\pi$
$463$	14.7697	+	25.5818i	0.686405	+	1.18889i	−0.286588	+	0.958054i	$0.592521\pi$
$464$	−0.602632	+	1.04379i	−0.0279765	+	0.0484567i
$465$	4.98545	−	9.90263i	0.231195	−	0.459223i
$466$	−0.625333	−	1.08311i	−0.0289680	−	0.0501740i
$467$	−17.8292	−	30.8810i	−0.825035	−	1.42900i	−0.901893	−	0.431960i	$-0.857822\pi$
$467$	−17.8292	−	30.8810i	−0.825035	−	1.42900i	0.0768575	−	0.997042i	$-0.475511\pi$
$468$	−2.94376	−	3.97038i	−0.136075	−	0.183531i
$469$	−17.5591	+	28.0056i	−0.810805	+	1.29318i
$470$	3.14735	−	5.45136i	0.145176	−	0.251453i
$471$	−23.7820	+	1.36175i	−1.09582	+	0.0627462i
$472$	1.24707			0.0574009
$473$	−6.86525			−0.315665
$474$	−4.22324	+	0.241822i	−0.193980	+	0.0111072i
$475$	−0.0769447	+	0.133272i	−0.00353047	+	0.00611495i
$476$	4.00115	+	7.55276i	0.183392	+	0.346180i
$477$	−1.37733	+	3.17587i	−0.0630634	+	0.145413i
$478$	0.665842	+	1.15327i	0.0304549	+	0.0527495i
$479$	7.13005	+	12.3496i	0.325780	+	0.564268i	0.981670	−	0.190589i	$-0.0610397\pi$
$479$	7.13005	+	12.3496i	0.325780	+	0.564268i	−0.655890	+	0.754857i	$0.727706\pi$
$480$	−0.778860	+	1.54705i	−0.0355499	+	0.0706130i
$481$	7.74086	−	13.4076i	0.352953	−	0.611332i
$482$	8.51454	+	14.7476i	0.387827	+	0.671736i
$483$	6.83024	+	11.2825i	0.310787	+	0.513372i
$484$	5.24476	−	9.08419i	0.238398	−	0.412918i
$485$	−4.23213	−	7.33026i	−0.192171	−	0.332850i
$486$	14.9553	−	4.39757i	0.678387	−	0.199478i
$487$	20.1589	−	34.9163i	0.913488	−	1.58221i	0.104387	−	0.994537i	$-0.466712\pi$
$487$	20.1589	−	34.9163i	0.913488	−	1.58221i	0.809101	−	0.587670i	$-0.199955\pi$
$488$	−9.20709			−0.416785
$489$	3.88915	+	5.92581i	0.175874	+	0.267974i
$490$	6.98143	+	0.509538i	0.315389	+	0.0230186i
$491$	−5.36192	−	9.28713i	−0.241980	−	0.419122i	0.719298	−	0.694702i	$-0.244464\pi$
$491$	−5.36192	−	9.28713i	−0.241980	−	0.419122i	−0.961278	+	0.275580i	$0.911130\pi$
$492$	5.88149	+	8.96150i	0.265158	+	0.404015i
$493$	−1.94681	−	3.37197i	−0.0876799	−	0.151866i
$494$	−0.126770	+	0.219572i	−0.00570364	+	0.00987900i
$495$	2.12944	−	0.244665i	0.0957112	−	0.0109969i
$496$	−6.40096			−0.287411
$497$	−5.22051	+	8.32634i	−0.234172	+	0.373488i
$498$	3.45283	−	6.85838i	0.154725	−	0.307332i
$499$	−13.2928	+	23.0237i	−0.595066	+	1.03068i	0.398472	+	0.917181i	$0.369541\pi$
$499$	−13.2928	+	23.0237i	−0.595066	+	1.03068i	−0.993538	+	0.113504i	$0.963793\pi$
$500$	1.00000			0.0447214
$501$	5.96659	+	9.09115i	0.266567	+	0.406163i
$502$	19.1121			0.853016
$503$	14.8056			0.660147			0.330074	−	0.943955i	$-0.392926\pi$
$503$	14.8056			0.660147			0.330074	+	0.943955i	$0.392926\pi$
$504$	3.42118	−	7.16209i	0.152391	−	0.319025i
$505$	−11.6402			−0.517980
$506$	2.05632			0.0914147
$507$	8.01104	−	15.9124i	0.355783	−	0.706694i
$508$	9.02973			0.400629
$509$	−19.2566	+	33.3534i	−0.853535	+	1.47837i	0.0244632	+	0.999701i	$0.492212\pi$
$509$	−19.2566	+	33.3534i	−0.853535	+	1.47837i	−0.877998	+	0.478665i	$0.841121\pi$
$510$	−3.07014	−	4.67791i	−0.135948	−	0.207141i
$511$	3.59575	+	6.78751i	0.159067	+	0.300262i
$512$	1.00000			0.0441942
$513$	−0.512191	−	0.614063i	−0.0226138	−	0.0271116i
$514$	−15.5139	+	26.8709i	−0.684291	+	1.18523i
$515$	4.24519	+	7.35289i	0.187065	+	0.324007i
$516$	7.48383	−	14.8652i	0.329457	−	0.654403i
$517$	2.24872	+	3.89491i	0.0988988	+	0.171298i
$518$	24.8452	+	0.905458i	1.09164	+	0.0397835i
$519$	−26.1875	+	1.49949i	−1.14951	+	0.0658205i
$520$	1.64754			0.0722496
$521$	17.8768	−	30.9636i	0.783199	−	1.35654i	−0.146870	−	0.989156i	$-0.546920\pi$
$521$	17.8768	−	30.9636i	0.783199	−	1.35654i	0.930069	−	0.367384i	$-0.119747\pi$
$522$	−1.43865	+	3.31726i	−0.0629679	+	0.145193i
$523$	−12.2253	−	21.1749i	−0.534576	−	0.925912i	−0.999184	−	0.0403960i	$-0.987138\pi$
$523$	−12.2253	−	21.1749i	−0.534576	−	0.925912i	0.464608	−	0.885517i	$-0.346195\pi$
$524$	−9.17401	+	15.8899i	−0.400769	+	0.694152i
$525$	−4.58159	+	0.0951713i	−0.199957	+	0.00415362i
$526$	10.4507	+	18.1011i	0.455672	+	0.789247i
$527$	10.3392	−	17.9080i	0.450382	−	0.780084i
$528$	−0.679015	−	1.03460i	−0.0295503	−	0.0450252i
$529$	7.35840	+	12.7451i	0.319930	+	0.554135i
$530$	−0.576945	−	0.999298i	−0.0250609	−	0.0434067i
$531$	3.71675	−	0.427041i	0.161293	−	0.0185320i
$532$	−0.406883	−	0.0148284i	−0.0176406	−	0.000642893i
$533$	5.09809	−	8.83014i	0.220823	−	0.382476i
$534$	−10.5082	−	16.0111i	−0.454734	−	0.692868i
$535$	−3.52213			−0.152275
$536$	−12.4936			−0.539642
$537$	16.0977	−	31.9750i	0.694667	−	1.37982i
$538$	10.4350	−	18.0740i	0.449885	−	0.779224i
$539$	−2.80934	+	4.13780i	−0.121007	+	0.178228i
$540$	−1.79154	+	4.87754i	−0.0770956	+	0.209896i
$541$	0.930823	+	1.61223i	0.0400192	+	0.0693153i	0.885341	−	0.464942i	$-0.153925\pi$
$541$	0.930823	+	1.61223i	0.0400192	+	0.0693153i	−0.845322	+	0.534257i	$0.820591\pi$
$542$	−6.19759	−	10.7345i	−0.266209	−	0.461088i
$543$	−42.0230	+	2.40623i	−1.80338	+	0.103261i
$544$	−1.61526	+	2.79771i	−0.0692535	+	0.119951i
$545$	5.21434	+	9.03150i	0.223358	+	0.386867i
$546$	−7.54837	+	0.156799i	−0.323040	+	0.00671037i
$547$	−12.3911	+	21.4620i	−0.529805	+	0.917649i	0.469591	+	0.882884i	$0.344402\pi$
$547$	−12.3911	+	21.4620i	−0.529805	+	0.917649i	−0.999396	+	0.0347649i	$0.988932\pi$
$548$	8.94199	+	15.4880i	0.381983	+	0.661614i
$549$	−27.4407	+	3.15284i	−1.17114	+	0.134560i
$550$	−0.357242	+	0.618760i	−0.0152328	+	0.0263840i
$551$	0.185477			0.00790160
$552$	−2.24160	+	4.45251i	−0.0954089	+	0.189511i
$553$	−3.43249	+	5.47459i	−0.145964	+	0.232803i
$554$	5.24812	+	9.09000i	0.222971	+	0.386197i
$555$	−16.2492	+	0.930426i	−0.689740	+	0.0394944i
$556$	−0.436114	−	0.755372i	−0.0184954	−	0.0320349i
$557$	0.357368	−	0.618980i	0.0151422	−	0.0262270i	−0.858355	−	0.513056i	$-0.828513\pi$
$557$	0.357368	−	0.618980i	0.0151422	−	0.0262270i	0.873497	+	0.486829i	$0.161847\pi$
$558$	−19.0774	+	2.19192i	−0.807609	+	0.0927913i
$559$	−15.8308			−0.669570
$560$	1.23855	+	2.33795i	0.0523383	+	0.0987963i
$561$	3.99129	−	0.228540i	0.168512	−	0.00964899i
$562$	15.8173	−	27.3964i	0.667213	−	1.15565i
$563$	19.3941			0.817362			0.408681	−	0.912677i	$-0.365989\pi$
$563$	19.3941			0.817362			0.408681	+	0.912677i	$0.365989\pi$
$564$	−10.8849	+	0.623267i	−0.458337	+	0.0262443i
$565$	5.71431			0.240403
$566$	12.8565			0.540400
$567$	7.74390	−	22.5174i	0.325213	−	0.945641i
$568$	−3.71448			−0.155856
$569$	−25.2785			−1.05973			−0.529864	−	0.848082i	$-0.677757\pi$
$569$	−25.2785			−1.05973			−0.529864	+	0.848082i	$0.677757\pi$
$570$	0.266108	−	0.0152373i	0.0111461	−	0.000638221i
$571$	−31.3342			−1.31129			−0.655647	−	0.755067i	$-0.727604\pi$
$571$	−31.3342			−1.31129			−0.655647	+	0.755067i	$0.727604\pi$
$572$	−0.588571	+	1.01944i	−0.0246094	+	0.0426247i
$573$	30.3752	−	1.73928i	1.26894	−	0.0726593i
$574$	16.3629	+	0.596329i	0.682975	+	0.0248903i
$575$	2.87806			0.120023
$576$	2.98039	−	0.342436i	0.124183	−	0.0142682i
$577$	−2.14572	+	3.71650i	−0.0893277	+	0.154720i	−0.907227	−	0.420641i	$-0.861805\pi$
$577$	−2.14572	+	3.71650i	−0.0893277	+	0.154720i	0.817899	+	0.575361i	$0.195139\pi$
$578$	3.28190	+	5.68441i	0.136509	+	0.236440i
$579$	45.2428	−	2.59059i	1.88023	−	0.107661i
$580$	−0.602632	−	1.04379i	−0.0250229	−	0.0433410i
$581$	−5.49073	−	10.3646i	−0.227794	−	0.429994i
$582$	−6.59247	+	13.0947i	−0.273267	+	0.542791i
$583$	0.824434			0.0341446
$584$	−1.45160	+	2.51424i	−0.0600675	+	0.104040i
$585$	4.91033	−	0.564179i	0.203017	−	0.0233259i
$586$	−14.3055	−	24.7778i	−0.590954	−	1.02356i
$587$	−8.63045	+	14.9484i	−0.356217	+	0.616985i	−0.987325	−	0.158709i	$-0.949267\pi$
$587$	−8.63045	+	14.9484i	−0.356217	+	0.616985i	0.631109	+	0.775694i	$0.282600\pi$
$588$	−5.89703	−	10.5936i	−0.243189	−	0.436874i
$589$	0.492520	+	0.853069i	0.0202939	+	0.0351501i
$590$	−0.623534	+	1.07999i	−0.0256705	+	0.0444626i
$591$	−33.1812	+	1.89995i	−1.36489	+	0.0781535i
$592$	4.69842	+	8.13791i	0.193104	+	0.334466i
$593$	−3.11040	−	5.38737i	−0.127729	−	0.221233i	0.795067	−	0.606521i	$-0.207435\pi$
$593$	−3.11040	−	5.38737i	−0.127729	−	0.221233i	−0.922796	+	0.385288i	$0.874102\pi$
$594$	−2.37802	−	2.85099i	−0.0975712	−	0.116978i
$595$	−8.54146	−	0.311284i	−0.350166	−	0.0127614i
$596$	−0.571398	+	0.989690i	−0.0234054	+	0.0405393i
$597$	19.6498	−	39.0306i	0.804213	−	1.59741i
$598$	4.74173			0.193904
$599$	−33.9612			−1.38762			−0.693808	−	0.720160i	$-0.744069\pi$
$599$	−33.9612			−1.38762			−0.693808	+	0.720160i	$0.744069\pi$
$600$	−0.950358	−	1.44804i	−0.0387982	−	0.0591160i
$601$	−19.1838	+	33.2273i	−0.782522	+	1.35537i	0.147946	+	0.988995i	$0.452734\pi$
$601$	−19.1838	+	33.2273i	−0.782522	+	1.35537i	−0.930468	+	0.366373i	$0.880599\pi$
$602$	−11.9008	−	22.4646i	−0.485042	−	0.915589i
$603$	−37.2359	+	4.27827i	−1.51636	+	0.174225i
$604$	0.158200	+	0.274011i	0.00643707	+	0.0111493i
$605$	5.24476	+	9.08419i	0.213230	+	0.369325i
$606$	11.0623	+	16.8554i	0.449376	+	0.684704i
$607$	3.83103	−	6.63554i	0.155497	−	0.269328i	−0.777743	−	0.628582i	$-0.783636\pi$
$607$	3.83103	−	6.63554i	0.155497	−	0.269328i	0.933240	+	0.359254i	$0.116969\pi$
$608$	−0.0769447	−	0.133272i	−0.00312052	−	0.00540490i
$609$	2.86035	+	4.72486i	0.115907	+	0.191461i
$610$	4.60354	−	7.97357i	0.186392	−	0.322840i
$611$	5.18539	+	8.98136i	0.209778	+	0.363347i
$612$	−3.85606	+	8.89138i	−0.155872	+	0.359413i
$613$	−20.9889	+	36.3539i	−0.847735	+	1.46832i	0.0354902	+	0.999370i	$0.488701\pi$
$613$	−20.9889	+	36.3539i	−0.847735	+	1.46832i	−0.883225	+	0.468950i	$0.844633\pi$
$614$	34.6549			1.39856
$615$	−10.7016	+	0.612773i	−0.431531	+	0.0247094i
$616$	−1.88909	−	0.0688459i	−0.0761136	−	0.00277388i
$617$	−17.4083	−	30.1520i	−0.700832	−	1.21388i	−0.968175	−	0.250274i	$-0.919479\pi$
$617$	−17.4083	−	30.1520i	−0.700832	−	1.21388i	0.267343	−	0.963601i	$-0.413854\pi$
$618$	6.61282	−	13.1351i	0.266007	−	0.528371i
$619$	1.32726	+	2.29888i	0.0533471	+	0.0923998i	0.891466	−	0.453088i	$-0.149678\pi$
$619$	1.32726	+	2.29888i	0.0533471	+	0.0923998i	−0.838119	+	0.545488i	$0.816344\pi$
$620$	3.20048	−	5.54339i	0.128534	−	0.222628i
$621$	−5.15615	+	14.0378i	−0.206909	+	0.563319i
$622$	17.6573			0.707992
$623$	−29.2349	−	1.06543i	−1.17127	−	0.0426857i
$624$	−1.56576	−	2.38571i	−0.0626805	−	0.0955048i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	1.25714			0.0502455
$627$	−0.0856367	+	0.170101i	−0.00342000	+	0.00679317i
$628$	−13.7530			−0.548805
$629$	−30.3566			−1.21040
$630$	4.49196	+	6.54387i	0.178964	+	0.260714i
$631$	−1.91702			−0.0763152			−0.0381576	−	0.999272i	$-0.512149\pi$
$631$	−1.91702			−0.0763152			−0.0381576	+	0.999272i	$0.512149\pi$
$632$	−2.44228			−0.0971487
$633$	−19.0716	−	29.0590i	−0.758029	−	1.15499i
$634$	−4.91403			−0.195161
$635$	−4.51486	+	7.81997i	−0.179167	+	0.310326i
$636$	−0.898718	+	1.78513i	−0.0356365	+	0.0707850i
$637$	−6.47813	+	9.54147i	−0.256673	+	0.378047i
$638$	0.861141			0.0340929
$639$	−11.0706	+	1.27197i	−0.437947	+	0.0503185i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−9.24750	−	16.0171i	−0.365254	−	0.632639i	0.623563	−	0.781773i	$-0.285685\pi$
$641$	−9.24750	−	16.0171i	−0.365254	−	0.632639i	−0.988817	+	0.149134i	$0.952351\pi$
$642$	3.34729	+	5.10019i	0.132107	+	0.201288i
$643$	−1.74128	−	3.01599i	−0.0686694	−	0.118939i	0.829646	−	0.558289i	$-0.188542\pi$
$643$	−1.74128	−	3.01599i	−0.0686694	−	0.118939i	−0.898316	+	0.439350i	$0.855209\pi$
$644$	3.56462	+	6.72874i	0.140466	+	0.265150i
$645$	9.13171	+	13.9138i	0.359561	+	0.547854i
$646$	0.497142			0.0195598
$647$	−10.5425	+	18.2602i	−0.414469	+	0.717881i	−0.995373	−	0.0960910i	$-0.969366\pi$
$647$	−10.5425	+	18.2602i	−0.414469	+	0.717881i	0.580904	+	0.813972i	$0.302699\pi$
$648$	8.76547	−	2.04119i	0.344340	−	0.0801855i
$649$	−0.445504	−	0.771636i	−0.0174876	−	0.0302894i
$650$	−0.823772	+	1.42682i	−0.0323110	+	0.0559643i
$651$	−14.1357	+	25.7021i	−0.554022	+	1.00735i
$652$	2.04615	+	3.54404i	0.0801334	+	0.138795i
$653$	2.86772	−	4.96703i	0.112222	−	0.194375i	−0.804444	−	0.594029i	$-0.797536\pi$
$653$	2.86772	−	4.96703i	0.112222	−	0.194375i	0.916666	+	0.399654i	$0.130870\pi$
$654$	8.12248	−	16.1337i	0.317614	−	0.630879i
$655$	−9.17401	−	15.8899i	−0.358458	−	0.620868i
$656$	3.09435	+	5.35958i	0.120814	+	0.209256i
$657$	−3.46536	+	7.99049i	−0.135197	+	0.311739i
$658$	−8.84685	+	14.1101i	−0.344886	+	0.550069i
$659$	−5.52636	+	9.57194i	−0.215276	+	0.372870i	−0.953358	−	0.301842i	$-0.902399\pi$
$659$	−5.52636	+	9.57194i	−0.215276	+	0.372870i	0.738082	+	0.674711i	$0.235732\pi$
$660$	1.23550	−	0.0707444i	0.0480917	−	0.00275372i
$661$	2.36825			0.0921144			0.0460572	−	0.998939i	$-0.485334\pi$
$661$	2.36825			0.0921144			0.0460572	+	0.998939i	$0.485334\pi$
$662$	30.0766			1.16896
$663$	9.20361	−	0.526997i	0.357439	−	0.0204669i
$664$	2.21659	−	3.83925i	0.0860205	−	0.148992i
$665$	0.216283	−	0.344957i	0.00838711	−	0.0133769i
$666$	16.7899	+	22.6452i	0.650594	+	0.877486i
$667$	−1.73441	−	3.00408i	−0.0671566	−	0.116319i
$668$	3.13912	+	5.43712i	0.121456	+	0.210369i
$669$	−3.62591	+	7.20217i	−0.140186	+	0.278452i
$670$	6.24681	−	10.8198i	0.241335	−	0.418005i
$671$	3.28915	+	5.69698i	0.126976	+	0.219929i
$672$	2.20837	−	4.01536i	0.0851898	−	0.154896i
$673$	0.952561	−	1.64988i	0.0367185	−	0.0635984i	−0.847082	−	0.531462i	$-0.821643\pi$
$673$	0.952561	−	1.64988i	0.0367185	−	0.0635984i	0.883801	+	0.467864i	$0.154976\pi$
$674$	8.27039	+	14.3247i	0.318563	+	0.551768i
$675$	−3.32830	−	3.99029i	−0.128106	−	0.153586i
$676$	5.14280	−	8.90759i	0.197800	−	0.342600i
$677$	−9.45575			−0.363414			−0.181707	−	0.983353i	$-0.558162\pi$
$677$	−9.45575			−0.363414			−0.181707	+	0.983353i	$0.558162\pi$
$678$	−5.43064	−	8.27455i	−0.208563	−	0.317782i
$679$	10.4834	+	19.7890i	0.402316	+	0.759431i
$680$	−1.61526	−	2.79771i	−0.0619422	−	0.107287i
$681$	15.6938	+	23.9122i	0.601386	+	0.916319i
$682$	2.28669	+	3.96066i	0.0875618	+	0.151661i
$683$	−0.925204	+	1.60250i	−0.0354019	+	0.0613179i	−0.883184	−	0.469028i	$-0.844604\pi$
$683$	−0.925204	+	1.60250i	−0.0354019	+	0.0613179i	0.847782	+	0.530346i	$0.177938\pi$
$684$	−0.274963	−	0.370855i	−0.0105135	−	0.0141800i
$685$	−17.8840			−0.683312
$686$	−18.4098	−	2.01993i	−0.702889	−	0.0771213i
$687$	4.15980	−	8.26265i	0.158706	−	0.315240i
$688$	4.80435	−	8.32137i	0.183164	−	0.317249i
$689$	1.90108			0.0724255
$690$	−2.73519	−	4.16754i	−0.104127	−	0.158656i
$691$	−23.3344			−0.887682			−0.443841	−	0.896106i	$-0.646384\pi$
$691$	−23.3344			−0.887682			−0.443841	+	0.896106i	$0.646384\pi$
$692$	−15.1441			−0.575694
$693$	−5.65381	+	0.441705i	−0.214770	+	0.0167790i
$694$	5.80220			0.220248
$695$	0.872228			0.0330855
$696$	−0.938732	+	1.86461i	−0.0355825	+	0.0706778i
$697$	−19.9927			−0.757277
$698$	−12.5953	+	21.8157i	−0.476739	+	0.825737i
$699$	−1.18858	−	1.81101i	−0.0449563	−	0.0684988i
$700$	−2.64400	−	0.0963576i	−0.0999337	−	0.00364197i
$701$	−43.6091			−1.64709			−0.823546	−	0.567249i	$-0.808008\pi$
$701$	−43.6091			−1.64709			−0.823546	+	0.567249i	$0.808008\pi$
$702$	−5.48353	−	6.57418i	−0.206962	−	0.248126i
$703$	0.723038	−	1.25234i	0.0272699	−	0.0472328i
$704$	−0.357242	−	0.618760i	−0.0134640	−	0.0233204i
$705$	4.90268	−	9.73823i	0.184646	−	0.366763i
$706$	−1.97987	−	3.42924i	−0.0745134	−	0.129061i
$707$	30.7765	+	1.12162i	1.15747	+	0.0421828i
$708$	2.15645	−	0.123478i	0.0810444	−	0.00464059i
$709$	−6.20185			−0.232915			−0.116458	−	0.993196i	$-0.537154\pi$
$709$	−6.20185			−0.232915			−0.116458	+	0.993196i	$0.537154\pi$
$710$	1.85724	−	3.21684i	0.0697010	−	0.120726i
$711$	−7.27895	+	0.836325i	−0.272982	+	0.0313646i
$712$	−5.52854	−	9.57571i	−0.207191	−	0.358865i
$713$	9.21116	−	15.9542i	0.344961	−	0.597489i
$714$	7.66670	+	12.6642i	0.286919	+	0.473946i
$715$	−0.588571	−	1.01944i	−0.0220113	−	0.0381247i
$716$	10.3341	−	17.8993i	0.386205	−	0.668927i
$717$	1.26558	+	1.92833i	0.0472639	+	0.0720149i
$718$	−6.99027	−	12.1075i	−0.260875	−	0.451848i
$719$	−8.23612	−	14.2654i	−0.307155	−	0.532009i	0.670583	−	0.741834i	$-0.266044\pi$
$719$	−8.23612	−	14.2654i	−0.307155	−	0.532009i	−0.977739	+	0.209825i	$0.932710\pi$
$720$	−1.19364	+	2.75231i	−0.0444842	+	0.102573i
$721$	−10.5158	−	19.8501i	−0.391627	−	0.739255i
$722$	9.48816	−	16.4340i	0.353113	−	0.611609i
$723$	16.1837	+	24.6588i	0.601879	+	0.917070i
$724$	−24.3018			−0.903168
$725$	1.20526			0.0447624
$726$	8.16986	−	16.2278i	0.303212	−	0.602272i
$727$	10.1772	−	17.6274i	0.377450	−	0.653763i	−0.613240	−	0.789896i	$-0.710134\pi$
$727$	10.1772	−	17.6274i	0.377450	−	0.653763i	0.990690	+	0.136134i	$0.0434677\pi$
$728$	−4.35610	−	0.158753i	−0.161448	−	0.00588379i
$729$	25.4256	−	9.08516i	0.941688	−	0.336487i
$730$	−1.45160	−	2.51424i	−0.0537260	−	0.0930561i
$731$	15.5205	+	26.8823i	0.574047	+	0.994278i
$732$	−15.9211	+	0.911637i	−0.588459	+	0.0336951i
$733$	20.0756	−	34.7719i	0.741509	−	1.28433i	−0.210299	−	0.977637i	$-0.567444\pi$
$733$	20.0756	−	34.7719i	0.741509	−	1.28433i	0.951808	−	0.306694i	$-0.0992228\pi$
$734$	−3.52613	−	6.10743i	−0.130152	−	0.225429i
$735$	12.1229	+	0.189838i	0.447159	+	0.00700229i
$736$	−1.43903	+	2.49247i	−0.0530433	+	0.0918737i
$737$	4.46324	+	7.73056i	0.164406	+	0.284759i
$738$	11.0577	+	14.9140i	0.407040	+	0.548993i
$739$	−2.20683	+	3.82234i	−0.0811795	+	0.140607i	−0.903757	−	0.428046i	$-0.859202\pi$
$739$	−2.20683	+	3.82234i	−0.0811795	+	0.140607i	0.822577	+	0.568653i	$0.192535\pi$
$740$	−9.39685			−0.345435
$741$	−0.197472	+	0.392240i	−0.00725431	+	0.0144093i
$742$	1.42915	+	2.69773i	0.0524657	+	0.0990369i
$743$	20.4036	+	35.3401i	0.748536	+	1.29650i	0.948524	+	0.316705i	$0.102576\pi$
$743$	20.4036	+	35.3401i	0.748536	+	1.29650i	−0.199988	+	0.979798i	$0.564090\pi$
$744$	−11.0687	+	0.633789i	−0.405796	+	0.0232358i
$745$	−0.571398	−	0.989690i	−0.0209344	−	0.0362594i
$746$	−14.5747	+	25.2441i	−0.533618	+	0.924253i
$747$	5.29162	−	12.2015i	0.193610	−	0.446430i
$748$	2.30815			0.0843942
$749$	9.31251	+	0.339384i	0.340272	+	0.0124008i
$750$	1.72922	−	0.0990147i	0.0631421	−	0.00361551i
$751$	−11.2580	+	19.4995i	−0.410811	+	0.711546i	−0.994979	−	0.100087i	$-0.968088\pi$
$751$	−11.2580	+	19.4995i	−0.410811	+	0.711546i	0.584168	+	0.811633i	$0.301421\pi$
$752$	−6.29469			−0.229544
$753$	33.0491	−	1.89238i	1.20437	−	0.0689623i
$754$	1.98573			0.0723159
$755$	−0.316400			−0.0115150
$756$	5.20681	−	12.7236i	0.189370	−	0.462752i
$757$	8.79446			0.319640			0.159820	−	0.987146i	$-0.448909\pi$
$757$	8.79446			0.319640			0.159820	+	0.987146i	$0.448909\pi$
$758$	31.6713			1.15035
$759$	3.55583	−	0.203606i	0.129068	−	0.00739044i
$760$	0.153889			0.00558216
$761$	−13.8254	+	23.9462i	−0.501169	+	0.868050i	0.498830	+	0.866700i	$0.333763\pi$
$761$	−13.8254	+	23.9462i	−0.501169	+	0.868050i	−0.999999	+	0.00135035i	$0.999570\pi$
$762$	15.6144	−	0.894076i	0.565649	−	0.0323890i
$763$	−12.9164	−	24.3817i	−0.467607	−	0.882677i
$764$	17.5658			0.635510
$765$	−5.77213	−	7.78514i	−0.208692	−	0.281472i
$766$	−2.29736	+	3.97914i	−0.0830069	+	0.143772i
$767$	−1.02730	−	1.77933i	−0.0370936	−	0.0642480i
$768$	1.72922	−	0.0990147i	0.0623978	−	0.00357289i
$769$	−1.97706	−	3.42437i	−0.0712947	−	0.123486i	0.828174	−	0.560471i	$-0.189380\pi$
$769$	−1.97706	−	3.42437i	−0.0712947	−	0.123486i	−0.899469	+	0.436985i	$0.856046\pi$
$770$	1.00417	−	1.60158i	0.0361877	−	0.0577168i
$771$	−24.1664	+	48.0018i	−0.870331	+	1.72874i
$772$	26.1637			0.941653
$773$	−13.4193	+	23.2429i	−0.482658	+	0.835989i	−0.999802	−	0.0199099i	$-0.993662\pi$
$773$	−13.4193	+	23.2429i	−0.482658	+	0.835989i	0.517143	+	0.855899i	$0.326995\pi$
$774$	11.4693	−	26.4461i	0.412256	−	0.950587i
$775$	3.20048	+	5.54339i	0.114965	+	0.199124i
$776$	−4.23213	+	7.33026i	−0.151925	+	0.263141i
$777$	43.0525	−	0.894310i	1.54450	−	0.0320832i
$778$	−17.0012	−	29.4470i	−0.609524	−	1.05573i
$779$	0.476188	−	0.824783i	0.0170612	−	0.0295509i
$780$	2.84896	−	0.163131i	0.102009	−	0.00584103i
$781$	1.32697	+	2.29838i	0.0474826	+	0.0822423i
$782$	−4.64880	−	8.05195i	−0.166241	−	0.287937i
$783$	−2.15928	+	5.87872i	−0.0771664	+	0.210088i
$784$	−3.04944	−	6.30087i	−0.108909	−	0.225031i
$785$	6.87651	−	11.9105i	0.245433	−	0.425103i
$786$	−14.2905	+	28.3854i	−0.509727	+	1.01247i
$787$	2.52940			0.0901635			0.0450817	−	0.998983i	$-0.485645\pi$
$787$	2.52940			0.0901635			0.0450817	+	0.998983i	$0.485645\pi$
$788$	−19.1886			−0.683564
$789$	19.8638	+	30.2660i	0.707170	+	1.07750i
$790$	1.22114	−	2.11508i	0.0434462	−	0.0752511i
$791$	−15.1086	−	0.550617i	−0.537200	−	0.0195777i
$792$	−1.27661	−	1.72182i	−0.0453622	−	0.0611821i
$793$	7.58454	+	13.1368i	0.269335	+	0.466502i
$794$	3.56605	+	6.17658i	0.126554	+	0.219199i
$795$	−1.09661	−	1.67088i	−0.0388927	−	0.0592599i
$796$	12.6145	−	21.8489i	0.447108	−	0.774414i
$797$	−16.6824	−	28.8948i	−0.590922	−	1.02351i	−0.994109	−	0.108389i	$-0.965431\pi$
$797$	−16.6824	−	28.8948i	−0.590922	−	1.02351i	0.403187	−	0.915118i	$-0.367902\pi$
$798$	−0.705058	+	0.0146459i	−0.0249588	+	0.000518458i
$799$	10.1675	−	17.6107i	0.359702	−	0.623021i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−19.7563	−	26.6462i	−0.698054	−	0.941497i
$802$	5.20071	−	9.00790i	0.183644	−	0.318080i
$803$	2.07428			0.0731998
$804$	−21.6042	+	1.23705i	−0.761921	+	0.0436275i
$805$	−7.60957	−	0.277323i	−0.268202	−	0.00977434i
$806$	5.27293	+	9.13298i	0.185731	+	0.321696i
$807$	16.2548	−	32.2871i	0.572197	−	1.13656i
$808$	5.82008	+	10.0807i	0.204750	+	0.354637i
$809$	−3.78183	+	6.55033i	−0.132962	+	0.230297i	−0.924817	−	0.380412i	$-0.875782\pi$
$809$	−3.78183	+	6.55033i	−0.132962	+	0.230297i	0.791855	+	0.610709i	$0.209116\pi$
$810$	−2.61502	+	8.61172i	−0.0918823	+	0.302585i
$811$	47.1553			1.65585			0.827923	−	0.560843i	$-0.189523\pi$
$811$	47.1553			1.65585			0.827923	+	0.560843i	$0.189523\pi$
$812$	1.49278	+	2.81784i	0.0523863	+	0.0988869i
$813$	−11.7799	−	17.9487i	−0.413138	−	0.629489i
$814$	3.35694	−	5.81440i	0.117661	−	0.203795i
$815$	−4.09230			−0.143347
$816$	−2.51612	+	4.99778i	−0.0880817	+	0.174957i
$817$	−1.47868			−0.0517324
$818$	8.13727			0.284513
$819$	−13.0373	+	1.01854i	−0.455558	+	0.0355906i
$820$	−6.18871			−0.216119
$821$	−8.88841			−0.310208			−0.155104	−	0.987898i	$-0.549571\pi$
$821$	−8.88841			−0.310208			−0.155104	+	0.987898i	$0.549571\pi$
$822$	16.9962	+	25.8967i	0.592811	+	0.903252i
$823$	−36.1929			−1.26161			−0.630803	−	0.775943i	$-0.717275\pi$
$823$	−36.1929			−1.26161			−0.630803	+	0.775943i	$0.717275\pi$
$824$	4.24519	−	7.35289i	0.147888	−	0.256150i
$825$	−0.556482	+	1.10534i	−0.0193742	+	0.0384831i
$826$	1.75269	−	2.79541i	0.0609837	−	0.0972648i
$827$	−37.6461			−1.30908			−0.654542	−	0.756026i	$-0.727138\pi$
$827$	−37.6461			−1.30908			−0.654542	+	0.756026i	$0.727138\pi$
$828$	−3.43536	+	7.92131i	−0.119387	+	0.275285i
$829$	5.59846	−	9.69681i	0.194442	−	0.336784i	−0.752275	−	0.658849i	$-0.771044\pi$
$829$	5.59846	−	9.69681i	0.194442	−	0.336784i	0.946718	+	0.322065i	$0.104377\pi$
$830$	2.21659	+	3.83925i	0.0769391	+	0.133262i
$831$	9.97518	+	15.1990i	0.346035	+	0.527246i
$832$	−0.823772	−	1.42682i	−0.0285592	−	0.0494659i
$833$	22.5536	+	1.64607i	0.781436	+	0.0570329i
$834$	−0.828929	−	1.26302i	−0.0287035	−	0.0437348i
$835$	−6.27825			−0.217268
$836$	−0.0549757	+	0.0952207i	−0.00190137	+	0.00329328i
$837$	−32.7719	+	5.67925i	−1.13276	+	0.196303i
$838$	−6.88164	−	11.9194i	−0.237722	−	0.411747i
$839$	−12.3118	+	21.3247i	−0.425052	+	0.736212i	−0.996425	−	0.0844785i	$-0.973078\pi$
$839$	−12.3118	+	21.3247i	−0.425052	+	0.736212i	0.571373	+	0.820690i	$0.306411\pi$
$840$	2.37321	+	3.92019i	0.0818837	+	0.135259i
$841$	13.7737	+	23.8567i	0.474954	+	0.822645i
$842$	−8.52205	+	14.7606i	−0.293689	+	0.508685i
$843$	24.6390	−	48.9405i	0.848611	−	1.68560i
$844$	−10.0339	−	17.3793i	−0.345382	−	0.598218i
$845$	5.14280	+	8.90759i	0.176918	+	0.306430i
$846$	−18.7606	+	2.15553i	−0.645004	+	0.0741086i
$847$	−12.9918	−	24.5239i	−0.446403	−	0.842652i
$848$	−0.576945	+	0.999298i	−0.0198124	+	0.0343160i
$849$	22.2317	−	1.27298i	0.762991	−	0.0436887i
$850$	3.23051			0.110806
$851$	−27.0447			−0.927079
$852$	−6.42315	+	0.367789i	−0.220054	+	0.0126002i
$853$	25.6906	−	44.4975i	0.879630	−	1.52356i	0.0278834	−	0.999611i	$-0.491123\pi$
$853$	25.6906	−	44.4975i	0.879630	−	1.52356i	0.851747	−	0.523953i	$-0.175543\pi$
$854$	−12.9401	+	20.6385i	−0.442800	+	0.706235i
$855$	0.458651	−	0.0526973i	0.0156855	−	0.00180221i
$856$	1.76107	+	3.05026i	0.0601920	+	0.104256i
$857$	9.80966	+	16.9908i	0.335092	+	0.580396i	0.983502	−	0.180895i	$-0.0578993\pi$
$857$	9.80966	+	16.9908i	0.335092	+	0.580396i	−0.648411	+	0.761291i	$0.724566\pi$
$858$	−0.916829	+	1.82110i	−0.0313000	+	0.0621714i
$859$	4.82699	−	8.36059i	0.164695	−	0.285260i	−0.771852	−	0.635802i	$-0.780669\pi$
$859$	4.82699	−	8.36059i	0.164695	−	0.285260i	0.936547	+	0.350542i	$0.114003\pi$
$860$	4.80435	+	8.32137i	0.163827	+	0.283757i
$861$	28.3541	−	0.588987i	0.966306	−	0.0200726i
$862$	−3.94159	+	6.82703i	−0.134251	+	0.232530i
$863$	18.1910	+	31.5077i	0.619227	+	1.07253i	0.989627	+	0.143661i	$0.0458874\pi$
$863$	18.1910	+	31.5077i	0.619227	+	1.07253i	−0.370400	+	0.928872i	$0.620779\pi$
$864$	5.11984	−	0.887250i	0.174181	−	0.0301848i
$865$	7.57207	−	13.1152i	0.257458	−	0.445931i
$866$	15.3356			0.521125
$867$	6.23796	+	9.50463i	0.211852	+	0.322794i
$868$	−8.99620	+	14.3483i	−0.305351	+	0.487013i
$869$	0.872484	+	1.51119i	0.0295970	+	0.0512635i
$870$	−1.14543	−	1.74527i	−0.0388338	−	0.0591702i
$871$	10.2919	+	17.8261i	0.348728	+	0.604014i
$872$	5.21434	−	9.03150i	0.176580	−	0.305845i
$873$	−10.1033	+	23.2963i	−0.341943	+	0.788460i
$874$	0.442902			0.0149814
$875$	1.40545	−	2.24159i	0.0475128	−	0.0757795i
$876$	−2.26118	+	4.49140i	−0.0763982	+	0.151750i
$877$	−16.3082	+	28.2467i	−0.550690	+	0.953823i	0.447535	+	0.894267i	$0.352302\pi$
$877$	−16.3082	+	28.2467i	−0.550690	+	0.953823i	−0.998225	+	0.0595569i	$0.981031\pi$
$878$	11.4596			0.386743
$879$	−27.1907	−	41.4298i	−0.917119	−	1.39739i
$880$	0.714483			0.0240852
$881$	38.3849			1.29322			0.646611	−	0.762820i	$-0.276186\pi$
$881$	38.3849			1.29322			0.646611	+	0.762820i	$0.276186\pi$
$882$	−11.2462	−	17.7348i	−0.378679	−	0.597162i
$883$	−14.2675			−0.480139			−0.240070	−	0.970756i	$-0.577170\pi$
$883$	−14.2675			−0.480139			−0.240070	+	0.970756i	$0.577170\pi$
$884$	5.32241			0.179012
$885$	−0.971291	+	1.92928i	−0.0326496	+	0.0648521i
$886$	−29.9668			−1.00675
$887$	16.4739	−	28.5337i	0.553141	−	0.958068i	−0.444905	−	0.895578i	$-0.646762\pi$
$887$	16.4739	−	28.5337i	0.553141	−	0.958068i	0.998046	−	0.0624901i	$-0.0199042\pi$
$888$	8.93037	+	13.6070i	0.299684	+	0.456621i
$889$	12.6908	−	20.2409i	0.425636	−	0.678859i
$890$	11.0571			0.370634
$891$	−4.39440	−	4.69453i	−0.147218	−	0.157273i
$892$	−2.32770	+	4.03170i	−0.0779373	+	0.134991i
$893$	0.484343	+	0.838907i	0.0162079	+	0.0280730i
$894$	−0.890077	+	1.76797i	−0.0297686	+	0.0591296i
$895$	10.3341	+	17.8993i	0.345432	+	0.598306i
$896$	1.40545	−	2.24159i	0.0469527	−	0.0748862i
$897$	8.19948	−	0.469501i	0.273773	−	0.0156762i
$898$	3.37658			0.112678
$899$	3.85742	−	6.68125i	0.128652	−	0.222832i
$900$	−1.78675	−	2.40988i	−0.0595585	−	0.0803292i
$901$	−1.86383	−	3.22824i	−0.0620931	−	0.107548i
$902$	2.21086	−	3.82933i	0.0736137	−	0.127503i
$903$	−22.8035	−	37.6679i	−0.758853	−	1.25351i
$904$	−2.85715	−	4.94874i	−0.0950276	−	0.164593i
$905$	12.1509	−	21.0459i	0.403909	−	0.699591i
$906$	0.300694	+	0.458160i	0.00998988	+	0.0152214i
$907$	−22.6310	−	39.1980i	−0.751450	−	1.30155i	−0.947120	−	0.320880i	$-0.896021\pi$
$907$	−22.6310	−	39.1980i	−0.751450	−	1.30155i	0.195670	−	0.980670i	$-0.437312\pi$
$908$	8.25676	+	14.3011i	0.274010	+	0.474600i
$909$	20.7981	+	28.0514i	0.689830	+	0.930405i
$910$	2.31553	−	3.69312i	0.0767592	−	0.122426i
$911$	2.92689	−	5.06952i	0.0969722	−	0.167961i	−0.813458	−	0.581624i	$-0.802418\pi$
$911$	2.92689	−	5.06952i	0.0969722	−	0.167961i	0.910430	+	0.413663i	$0.135751\pi$
$912$	−0.146250	−	0.222838i	−0.00484283	−	0.00737890i
$913$	−3.16744			−0.104827
$914$	−25.0722			−0.829316
$915$	7.17103	−	14.2439i	0.237067	−	0.470888i
$916$	2.67044	−	4.62535i	0.0882340	−	0.152826i
$917$	22.7249	+	42.8967i	0.750444	+	1.41657i
$918$	−5.78759	+	15.7569i	−0.191019	+	0.520057i
$919$	0.192401	+	0.333248i	0.00634671	+	0.0109928i	0.869181	−	0.494494i	$-0.164646\pi$
$919$	0.192401	+	0.333248i	0.00634671	+	0.0109928i	−0.862835	+	0.505486i	$0.831313\pi$
$920$	−1.43903	−	2.49247i	−0.0474434	−	0.0821743i
$921$	59.9259	−	3.43135i	1.97463	−	0.113067i
$922$	18.4429	−	31.9440i	0.607384	−	1.05202i
$923$	3.05989	+	5.29988i	0.100717	+	0.174448i
$924$	−3.27347	+	0.0679983i	−0.107689	+	0.00223698i
$925$	4.69842	−	8.13791i	0.154483	−	0.267573i
$926$	14.7697	+	25.5818i	0.485362	+	0.840671i
$927$	10.1344	−	23.3682i	0.332859	−	0.767512i
$928$	−0.602632	+	1.04379i	−0.0197824	+	0.0342641i
$929$	16.6050			0.544792			0.272396	−	0.962185i	$-0.412184\pi$
$929$	16.6050			0.544792			0.272396	+	0.962185i	$0.412184\pi$
$930$	4.98545	−	9.90263i	0.163479	−	0.324720i
$931$	−0.605091	+	0.891224i	−0.0198311	+	0.0292087i
$932$	−0.625333	−	1.08311i	−0.0204835	−	0.0354784i
$933$	30.5333	−	1.74833i	0.999614	−	0.0572377i
$934$	−17.8292	−	30.8810i	−0.583388	−	1.01046i
$935$	−1.15407	+	1.99891i	−0.0377422	+	0.0653714i
$936$	−2.94376	−	3.97038i	−0.0962197	−	0.129776i
$937$	19.5361			0.638218			0.319109	−	0.947718i	$-0.396616\pi$
$937$	19.5361			0.638218			0.319109	+	0.947718i	$0.396616\pi$
$938$	−17.5591	+	28.0056i	−0.573325	+	0.914414i
$939$	2.17387	−	0.124476i	0.0709416	−	0.00406211i
$940$	3.14735	−	5.45136i	0.102655	−	0.177804i
$941$	16.4586			0.536536			0.268268	−	0.963344i	$-0.413549\pi$
$941$	16.4586			0.536536			0.268268	+	0.963344i	$0.413549\pi$
$942$	−23.7820	+	1.36175i	−0.774858	+	0.0443682i
$943$	−17.8115			−0.580021
$944$	1.24707			0.0405886
$945$	8.41552	+	10.8710i	0.273757	+	0.353634i
$946$	−6.86525			−0.223209
$947$	−16.7012			−0.542715			−0.271357	−	0.962479i	$-0.587473\pi$
$947$	−16.7012			−0.542715			−0.271357	+	0.962479i	$0.587473\pi$
$948$	−4.22324	+	0.241822i	−0.137164	+	0.00785401i
$949$	4.78314			0.155267
$950$	−0.0769447	+	0.133272i	−0.00249642	+	0.00432392i
$951$	−8.49743	+	0.486562i	−0.275548	+	0.0157778i
$952$	4.00115	+	7.55276i	0.129678	+	0.244786i
$953$	−42.5993			−1.37993			−0.689963	−	0.723845i	$-0.742373\pi$
$953$	−42.5993			−1.37993			−0.689963	+	0.723845i	$0.742373\pi$
$954$	−1.37733	+	3.17587i	−0.0445926	+	0.102822i
$955$	−8.78292	+	15.2125i	−0.284209	+	0.492264i
$956$	0.665842	+	1.15327i	0.0215349	+	0.0372995i
$957$	1.48910	−	0.0852656i	0.0481358	−	0.00275625i
$958$	7.13005	+	12.3496i	0.230361	+	0.398998i
$959$	47.2852	+	1.72326i	1.52692	+	0.0556469i
$960$	−0.778860	+	1.54705i	−0.0251376	+	0.0499310i
$961$	9.97224			0.321685
$962$	7.74086	−	13.4076i	0.249575	−	0.432277i
$963$	6.29319	+	8.48791i	0.202795	+	0.273519i
$964$	8.51454	+	14.7476i	0.274235	+	0.474989i
$965$	−13.0819	+	22.6585i	−0.421120	+	0.729401i
$966$	6.83024	+	11.2825i	0.219760	+	0.363009i
$967$	6.13289	+	10.6225i	0.197221	+	0.341596i	0.947626	−	0.319382i	$-0.103475\pi$
$967$	6.13289	+	10.6225i	0.197221	+	0.341596i	−0.750406	+	0.660978i	$0.770142\pi$
$968$	5.24476	−	9.08419i	0.168573	−	0.291977i
$969$	0.859666	−	0.0492244i	0.0276165	−	0.00158131i
$970$	−4.23213	−	7.33026i	−0.135885	−	0.235360i
$971$	−12.7923	−	22.1570i	−0.410525	−	0.711050i	0.584422	−	0.811450i	$-0.301321\pi$
$971$	−12.7923	−	22.1570i	−0.410525	−	0.711050i	−0.994947	+	0.100399i	$0.967988\pi$
$972$	14.9553	−	4.39757i	0.479692	−	0.141052i
$973$	−2.30617	−	0.0840458i	−0.0739323	−	0.00269438i
$974$	20.1589	−	34.9163i	0.645933	−	1.11879i
$975$	−1.28321	+	2.54884i	−0.0410955	+	0.0816282i
$976$	−9.20709			−0.294712
$977$	18.7484			0.599813			0.299907	−	0.953969i	$-0.403044\pi$
$977$	18.7484			0.599813			0.299907	+	0.953969i	$0.403044\pi$
$978$	3.88915	+	5.92581i	0.124361	+	0.189487i
$979$	−3.95005	+	6.84168i	−0.126244	+	0.218661i
$980$	6.98143	+	0.509538i	0.223014	+	0.0162766i
$981$	12.4481	−	28.7030i	0.397436	−	0.916416i
$982$	−5.36192	−	9.28713i	−0.171106	−	0.296364i
$983$	21.3371	+	36.9570i	0.680548	+	1.17874i	0.974814	+	0.223021i	$0.0715917\pi$
$983$	21.3371	+	36.9570i	0.680548	+	1.17874i	−0.294265	+	0.955724i	$0.595075\pi$
$984$	5.88149	+	8.96150i	0.187495	+	0.285682i
$985$	9.59428	−	16.6178i	0.305699	−	0.529487i
$986$	−1.94681	−	3.37197i	−0.0619991	−	0.107386i
$987$	−13.9010	+	25.2754i	−0.442474	+	0.804526i
$988$	−0.126770	+	0.219572i	−0.00403309	+	0.00698551i
$989$	13.8272	+	23.9494i	0.439679	+	0.761546i
$990$	2.12944	−	0.244665i	0.0676780	−	0.00777596i
$991$	10.5017	−	18.1894i	0.333597	−	0.577807i	−0.649617	−	0.760261i	$-0.725071\pi$
$991$	10.5017	−	18.1894i	0.333597	−	0.577807i	0.983214	+	0.182454i	$0.0584042\pi$
$992$	−6.40096			−0.203231
$993$	52.0089	−	2.97802i	1.65045	−	0.0945047i
$994$	−5.22051	+	8.32634i	−0.165584	+	0.264096i
$995$	12.6145	+	21.8489i	0.399906	+	0.692657i
$996$	3.45283	−	6.85838i	0.109407	−	0.217316i
$997$	3.72215	+	6.44696i	0.117882	+	0.204177i	0.918928	−	0.394425i	$-0.129056\pi$
$997$	3.72215	+	6.44696i	0.117882	+	0.204177i	−0.801046	+	0.598602i	$0.795723\pi$
$998$	−13.2928	+	23.0237i	−0.420775	+	0.728804i
$999$	31.2755	+	37.4961i	0.989514	+	1.18633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.g.151.6	yes	12
3.2	odd	2		1890.2.i.g.991.3		12
7.2	even	3		630.2.l.g.331.2	yes	12
9.4	even	3		630.2.l.g.571.2	yes	12
9.5	odd	6		1890.2.l.g.361.4		12
21.2	odd	6		1890.2.l.g.1801.4		12
63.23	odd	6		1890.2.i.g.1171.3		12
63.58	even	3	inner	630.2.i.g.121.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.g.121.6	✓	12	63.58	even	3	inner
630.2.i.g.151.6	yes	12	1.1	even	1	trivial
630.2.l.g.331.2	yes	12	7.2	even	3
630.2.l.g.571.2	yes	12	9.4	even	3
1890.2.i.g.991.3		12	3.2	odd	2
1890.2.i.g.1171.3		12	63.23	odd	6
1890.2.l.g.361.4		12	9.5	odd	6
1890.2.l.g.1801.4		12	21.2	odd	6

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.72922 - 0.0990147i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.72922 - 0.0990147i) q^{6} +(1.40545 - 2.24159i) q^{7} +1.00000 q^{8} +(2.98039 - 0.342436i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.72922 - 0.0990147i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.72922 - 0.0990147i) q^{6} +(1.40545 - 2.24159i) q^{7} +1.00000 q^{8} +(2.98039 - 0.342436i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.357242 - 0.618760i) q^{11} +(1.72922 - 0.0990147i) q^{12} +(-0.823772 - 1.42682i) q^{13} +(1.40545 - 2.24159i) q^{14} +(-0.778860 + 1.54705i) q^{15} +1.00000 q^{16} +(-1.61526 + 2.79771i) q^{17} +(2.98039 - 0.342436i) q^{18} +(-0.0769447 - 0.133272i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(2.20837 - 4.01536i) q^{21} +(-0.357242 - 0.618760i) q^{22} +(-1.43903 + 2.49247i) q^{23} +(1.72922 - 0.0990147i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.823772 - 1.42682i) q^{26} +(5.11984 - 0.887250i) q^{27} +(1.40545 - 2.24159i) q^{28} +(-0.602632 + 1.04379i) q^{29} +(-0.778860 + 1.54705i) q^{30} -6.40096 q^{31} +1.00000 q^{32} +(-0.679015 - 1.03460i) q^{33} +(-1.61526 + 2.79771i) q^{34} +(1.23855 + 2.33795i) q^{35} +(2.98039 - 0.342436i) q^{36} +(4.69842 + 8.13791i) q^{37} +(-0.0769447 - 0.133272i) q^{38} +(-1.56576 - 2.38571i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(3.09435 + 5.35958i) q^{41} +(2.20837 - 4.01536i) q^{42} +(4.80435 - 8.32137i) q^{43} +(-0.357242 - 0.618760i) q^{44} +(-1.19364 + 2.75231i) q^{45} +(-1.43903 + 2.49247i) q^{46} -6.29469 q^{47} +(1.72922 - 0.0990147i) q^{48} +(-3.04944 - 6.30087i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-2.51612 + 4.99778i) q^{51} +(-0.823772 - 1.42682i) q^{52} +(-0.576945 + 0.999298i) q^{53} +(5.11984 - 0.887250i) q^{54} +0.714483 q^{55} +(1.40545 - 2.24159i) q^{56} +(-0.146250 - 0.222838i) q^{57} +(-0.602632 + 1.04379i) q^{58} +1.24707 q^{59} +(-0.778860 + 1.54705i) q^{60} -9.20709 q^{61} -6.40096 q^{62} +(3.42118 - 7.16209i) q^{63} +1.00000 q^{64} +1.64754 q^{65} +(-0.679015 - 1.03460i) q^{66} -12.4936 q^{67} +(-1.61526 + 2.79771i) q^{68} +(-2.24160 + 4.45251i) q^{69} +(1.23855 + 2.33795i) q^{70} -3.71448 q^{71} +(2.98039 - 0.342436i) q^{72} +(-1.45160 + 2.51424i) q^{73} +(4.69842 + 8.13791i) q^{74} +(-0.950358 - 1.44804i) q^{75} +(-0.0769447 - 0.133272i) q^{76} +(-1.88909 - 0.0688459i) q^{77} +(-1.56576 - 2.38571i) q^{78} -2.44228 q^{79} +(-0.500000 + 0.866025i) q^{80} +(8.76547 - 2.04119i) q^{81} +(3.09435 + 5.35958i) q^{82} +(2.21659 - 3.83925i) q^{83} +(2.20837 - 4.01536i) q^{84} +(-1.61526 - 2.79771i) q^{85} +(4.80435 - 8.32137i) q^{86} +(-0.938732 + 1.86461i) q^{87} +(-0.357242 - 0.618760i) q^{88} +(-5.52854 - 9.57571i) q^{89} +(-1.19364 + 2.75231i) q^{90} +(-4.35610 - 0.158753i) q^{91} +(-1.43903 + 2.49247i) q^{92} +(-11.0687 + 0.633789i) q^{93} -6.29469 q^{94} +0.153889 q^{95} +(1.72922 - 0.0990147i) q^{96} +(-4.23213 + 7.33026i) q^{97} +(-3.04944 - 6.30087i) q^{98} +(-1.27661 - 1.72182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9} - 6 q^{10} + 3 q^{11} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} + 8 q^{19} - 6 q^{20} + 5 q^{21} + 3 q^{22} + 11 q^{23} - 6 q^{25} - 2 q^{26} - 27 q^{27} + 4 q^{28} + 13 q^{29} + 3 q^{30} - 42 q^{31} + 12 q^{32} + 17 q^{33} + q^{34} + 4 q^{35} + 4 q^{36} + 18 q^{37} + 8 q^{38} - 24 q^{39} - 6 q^{40} + 5 q^{41} + 5 q^{42} - 11 q^{43} + 3 q^{44} + q^{45} + 11 q^{46} + 46 q^{47} - 6 q^{50} - 27 q^{51} - 2 q^{52} + 2 q^{53} - 27 q^{54} - 6 q^{55} + 4 q^{56} - 44 q^{57} + 13 q^{58} - 2 q^{59} + 3 q^{60} + 2 q^{61} - 42 q^{62} + 9 q^{63} + 12 q^{64} + 4 q^{65} + 17 q^{66} - 4 q^{67} + q^{68} - 24 q^{69} + 4 q^{70} - 30 q^{71} + 4 q^{72} + 22 q^{73} + 18 q^{74} - 3 q^{75} + 8 q^{76} - 31 q^{77} - 24 q^{78} - 54 q^{79} - 6 q^{80} + 52 q^{81} + 5 q^{82} + 6 q^{83} + 5 q^{84} + q^{85} - 11 q^{86} - 28 q^{87} + 3 q^{88} - 18 q^{89} + q^{90} + 14 q^{91} + 11 q^{92} - 38 q^{93} + 46 q^{94} - 16 q^{95} - 4 q^{97} + 63 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9 - 6 * q^10 + 3 * q^11 - 2 * q^13 + 4 * q^14 + 3 * q^15 + 12 * q^16 + q^17 + 4 * q^18 + 8 * q^19 - 6 * q^20 + 5 * q^21 + 3 * q^22 + 11 * q^23 - 6 * q^25 - 2 * q^26 - 27 * q^27 + 4 * q^28 + 13 * q^29 + 3 * q^30 - 42 * q^31 + 12 * q^32 + 17 * q^33 + q^34 + 4 * q^35 + 4 * q^36 + 18 * q^37 + 8 * q^38 - 24 * q^39 - 6 * q^40 + 5 * q^41 + 5 * q^42 - 11 * q^43 + 3 * q^44 + q^45 + 11 * q^46 + 46 * q^47 - 6 * q^50 - 27 * q^51 - 2 * q^52 + 2 * q^53 - 27 * q^54 - 6 * q^55 + 4 * q^56 - 44 * q^57 + 13 * q^58 - 2 * q^59 + 3 * q^60 + 2 * q^61 - 42 * q^62 + 9 * q^63 + 12 * q^64 + 4 * q^65 + 17 * q^66 - 4 * q^67 + q^68 - 24 * q^69 + 4 * q^70 - 30 * q^71 + 4 * q^72 + 22 * q^73 + 18 * q^74 - 3 * q^75 + 8 * q^76 - 31 * q^77 - 24 * q^78 - 54 * q^79 - 6 * q^80 + 52 * q^81 + 5 * q^82 + 6 * q^83 + 5 * q^84 + q^85 - 11 * q^86 - 28 * q^87 + 3 * q^88 - 18 * q^89 + q^90 + 14 * q^91 + 11 * q^92 - 38 * q^93 + 46 * q^94 - 16 * q^95 - 4 * q^97 + 63 * q^99

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