LMFDB - Embedded newform 630.2.i.h.121.2

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} - 5 x^{11} + 14 x^{10} - 28 x^{9} + 36 x^{8} - 24 x^{7} + 33 x^{6} + 42 x^{5} + 114 x^{4} + \cdots + 79 $ x^12 - 5x^11 + 14x^10 - 28x^9 + 36x^8 - 24x^7 + 33x^6 + 42x^5 + 114x^4 + 104x^3 + 197x^2 + 166*x + 79
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			121.2
Root			$-0.659665 - 0.495491i$ of defining polynomial
Character	$\chi$	$=$	630.121
Dual form			630.2.i.h.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.13098 - 1.31183i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.13098 - 1.31183i) q^{6} +(0.0665372 + 2.64491i) q^{7} +1.00000 q^{8} +(-0.441782 + 2.96729i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.13098 - 1.31183i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.13098 - 1.31183i) q^{6} +(0.0665372 + 2.64491i) q^{7} +1.00000 q^{8} +(-0.441782 + 2.96729i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.71219 + 4.69765i) q^{11} +(-1.13098 - 1.31183i) q^{12} +(-2.92541 + 5.06696i) q^{13} +(0.0665372 + 2.64491i) q^{14} +(0.570587 - 1.63537i) q^{15} +1.00000 q^{16} +(-1.75409 - 3.03817i) q^{17} +(-0.441782 + 2.96729i) q^{18} +(2.62182 - 4.54112i) q^{19} +(0.500000 + 0.866025i) q^{20} +(3.39442 - 3.07862i) q^{21} +(-2.71219 + 4.69765i) q^{22} +(3.96948 + 6.87534i) q^{23} +(-1.13098 - 1.31183i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.92541 + 5.06696i) q^{26} +(4.39222 - 2.77640i) q^{27} +(0.0665372 + 2.64491i) q^{28} +(-4.29745 - 7.44340i) q^{29} +(0.570587 - 1.63537i) q^{30} +3.59197 q^{31} +1.00000 q^{32} +(9.22992 - 1.75501i) q^{33} +(-1.75409 - 3.03817i) q^{34} +(-2.25729 + 1.38008i) q^{35} +(-0.441782 + 2.96729i) q^{36} +(0.172034 - 0.297972i) q^{37} +(2.62182 - 4.54112i) q^{38} +(9.95555 - 1.89298i) q^{39} +(0.500000 + 0.866025i) q^{40} +(0.330137 - 0.571815i) q^{41} +(3.39442 - 3.07862i) q^{42} +(3.57361 + 6.18968i) q^{43} +(-2.71219 + 4.69765i) q^{44} +(-2.79064 + 1.10105i) q^{45} +(3.96948 + 6.87534i) q^{46} +1.94723 q^{47} +(-1.13098 - 1.31183i) q^{48} +(-6.99115 + 0.351971i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-2.00172 + 5.73716i) q^{51} +(-2.92541 + 5.06696i) q^{52} +(0.405384 + 0.702146i) q^{53} +(4.39222 - 2.77640i) q^{54} -5.42437 q^{55} +(0.0665372 + 2.64491i) q^{56} +(-8.92238 + 1.69653i) q^{57} +(-4.29745 - 7.44340i) q^{58} -0.0658445 q^{59} +(0.570587 - 1.63537i) q^{60} +4.23722 q^{61} +3.59197 q^{62} +(-7.87763 - 0.971040i) q^{63} +1.00000 q^{64} -5.85082 q^{65} +(9.22992 - 1.75501i) q^{66} +3.37378 q^{67} +(-1.75409 - 3.03817i) q^{68} +(4.52987 - 12.9831i) q^{69} +(-2.25729 + 1.38008i) q^{70} -5.85724 q^{71} +(-0.441782 + 2.96729i) q^{72} +(1.16225 + 2.01308i) q^{73} +(0.172034 - 0.297972i) q^{74} +(1.70156 - 0.323541i) q^{75} +(2.62182 - 4.54112i) q^{76} +(-12.6053 - 6.86094i) q^{77} +(9.95555 - 1.89298i) q^{78} +16.9663 q^{79} +(0.500000 + 0.866025i) q^{80} +(-8.60966 - 2.62179i) q^{81} +(0.330137 - 0.571815i) q^{82} +(-4.66838 - 8.08588i) q^{83} +(3.39442 - 3.07862i) q^{84} +(1.75409 - 3.03817i) q^{85} +(3.57361 + 6.18968i) q^{86} +(-4.90414 + 14.0558i) q^{87} +(-2.71219 + 4.69765i) q^{88} +(7.34444 - 12.7209i) q^{89} +(-2.79064 + 1.10105i) q^{90} +(-13.5963 - 7.40032i) q^{91} +(3.96948 + 6.87534i) q^{92} +(-4.06244 - 4.71205i) q^{93} +1.94723 q^{94} +5.24363 q^{95} +(-1.13098 - 1.31183i) q^{96} +(0.116278 + 0.201400i) q^{97} +(-6.99115 + 0.351971i) q^{98} +(-12.7411 - 10.1232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9	\( 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} + 2 q^{13} + 8 q^{14} + 7 q^{15} + 12 q^{16} + 7 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{20} + 17 q^{21} - 7 q^{22} - 9 q^{23} + 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 8 q^{28} - 9 q^{29} + 7 q^{30} - 18 q^{31} + 12 q^{32} + 3 q^{33} + 7 q^{34} + 4 q^{35} - 4 q^{36} - 12 q^{37} + 14 q^{38} - 14 q^{39} + 6 q^{40} + q^{41} + 17 q^{42} + 7 q^{43} - 7 q^{44} - 5 q^{45} - 9 q^{46} - 14 q^{47} + 2 q^{48} - 24 q^{49} - 6 q^{50} - 3 q^{51} + 2 q^{52} + 2 q^{53} + 11 q^{54} - 14 q^{55} + 8 q^{56} - 14 q^{57} - 9 q^{58} - 58 q^{59} + 7 q^{60} + 22 q^{61} - 18 q^{62} - 13 q^{63} + 12 q^{64} + 4 q^{65} + 3 q^{66} + 44 q^{67} + 7 q^{68} - 18 q^{69} + 4 q^{70} + 10 q^{71} - 4 q^{72} + 6 q^{73} - 12 q^{74} + 5 q^{75} + 14 q^{76} - 23 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} - 4 q^{81} + q^{82} - 26 q^{83} + 17 q^{84} - 7 q^{85} + 7 q^{86} - 12 q^{87} - 7 q^{88} + 2 q^{89} - 5 q^{90} - 4 q^{91} - 9 q^{92} - 26 q^{93} - 14 q^{94} + 28 q^{95} + 2 q^{96} + 6 q^{97} - 24 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 + 2 * q^13 + 8 * q^14 + 7 * q^15 + 12 * q^16 + 7 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^20 + 17 * q^21 - 7 * q^22 - 9 * q^23 + 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 8 * q^28 - 9 * q^29 + 7 * q^30 - 18 * q^31 + 12 * q^32 + 3 * q^33 + 7 * q^34 + 4 * q^35 - 4 * q^36 - 12 * q^37 + 14 * q^38 - 14 * q^39 + 6 * q^40 + q^41 + 17 * q^42 + 7 * q^43 - 7 * q^44 - 5 * q^45 - 9 * q^46 - 14 * q^47 + 2 * q^48 - 24 * q^49 - 6 * q^50 - 3 * q^51 + 2 * q^52 + 2 * q^53 + 11 * q^54 - 14 * q^55 + 8 * q^56 - 14 * q^57 - 9 * q^58 - 58 * q^59 + 7 * q^60 + 22 * q^61 - 18 * q^62 - 13 * q^63 + 12 * q^64 + 4 * q^65 + 3 * q^66 + 44 * q^67 + 7 * q^68 - 18 * q^69 + 4 * q^70 + 10 * q^71 - 4 * q^72 + 6 * q^73 - 12 * q^74 + 5 * q^75 + 14 * q^76 - 23 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 - 4 * q^81 + q^82 - 26 * q^83 + 17 * q^84 - 7 * q^85 + 7 * q^86 - 12 * q^87 - 7 * q^88 + 2 * q^89 - 5 * q^90 - 4 * q^91 - 9 * q^92 - 26 * q^93 - 14 * q^94 + 28 * q^95 + 2 * q^96 + 6 * q^97 - 24 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.13098	−	1.31183i	−0.652970	−	0.757384i
$3$	−1.13098	−	1.31183i	−0.652970	−	0.757384i
$4$	1.00000			0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.13098	−	1.31183i	−0.461719	−	0.535551i
$7$	0.0665372	+	2.64491i	0.0251487	+	0.999684i
$7$	0.0665372	+	2.64491i	0.0251487	+	0.999684i
$8$	1.00000			0.353553
$9$	−0.441782	+	2.96729i	−0.147261	+	0.989098i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−2.71219	+	4.69765i	−0.817755	+	1.41639i	0.0895773	+	0.995980i	$0.471448\pi$
$11$	−2.71219	+	4.69765i	−0.817755	+	1.41639i	−0.907333	+	0.420414i	$0.861885\pi$
$12$	−1.13098	−	1.31183i	−0.326485	−	0.378692i
$13$	−2.92541	+	5.06696i	−0.811363	+	1.40532i	0.100547	+	0.994932i	$0.467941\pi$
$13$	−2.92541	+	5.06696i	−0.811363	+	1.40532i	−0.911910	+	0.410390i	$0.865393\pi$
$14$	0.0665372	+	2.64491i	0.0177828	+	0.706883i
$15$	0.570587	−	1.63537i	0.147325	−	0.422250i
$16$	1.00000			0.250000
$17$	−1.75409	−	3.03817i	−0.425428	−	0.736864i	0.571032	−	0.820928i	$-0.306543\pi$
$17$	−1.75409	−	3.03817i	−0.425428	−	0.736864i	−0.996460	+	0.0840642i	$0.973210\pi$
$18$	−0.441782	+	2.96729i	−0.104129	+	0.699398i
$19$	2.62182	−	4.54112i	0.601486	−	1.04180i	−0.391110	−	0.920344i	$-0.627909\pi$
$19$	2.62182	−	4.54112i	0.601486	−	1.04180i	0.992596	−	0.121460i	$-0.0387577\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	3.39442	−	3.07862i	0.740723	−	0.671811i
$22$	−2.71219	+	4.69765i	−0.578240	+	1.00154i
$23$	3.96948	+	6.87534i	0.827694	+	1.43361i	0.899843	+	0.436214i	$0.143681\pi$
$23$	3.96948	+	6.87534i	0.827694	+	1.43361i	−0.0721486	+	0.997394i	$0.522986\pi$
$24$	−1.13098	−	1.31183i	−0.230860	−	0.267776i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.92541	+	5.06696i	−0.573720	+	0.993713i
$27$	4.39222	−	2.77640i	0.845283	−	0.534318i
$28$	0.0665372	+	2.64491i	0.0125744	+	0.499842i
$29$	−4.29745	−	7.44340i	−0.798016	−	1.38220i	−0.920906	−	0.389784i	$-0.872550\pi$
$29$	−4.29745	−	7.44340i	−0.798016	−	1.38220i	0.122890	−	0.992420i	$-0.460784\pi$
$30$	0.570587	−	1.63537i	0.104175	−	0.298576i
$31$	3.59197			0.645137			0.322569	−	0.946546i	$-0.395454\pi$
$31$	3.59197			0.645137			0.322569	+	0.946546i	$0.395454\pi$
$32$	1.00000			0.176777
$33$	9.22992	−	1.75501i	1.60672	−	0.305508i
$34$	−1.75409	−	3.03817i	−0.300823	−	0.521041i
$35$	−2.25729	+	1.38008i	−0.381552	+	0.233276i
$36$	−0.441782	+	2.96729i	−0.0736303	+	0.494549i
$37$	0.172034	−	0.297972i	0.0282823	−	0.0489863i	−0.851538	−	0.524293i	$-0.824330\pi$
$37$	0.172034	−	0.297972i	0.0282823	−	0.0489863i	0.879820	+	0.475307i	$0.157663\pi$
$38$	2.62182	−	4.54112i	0.425315	−	0.736667i
$39$	9.95555	−	1.89298i	1.59416	−	0.303120i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	0.330137	−	0.571815i	0.0515588	−	0.0893024i	−0.839094	−	0.543986i	$-0.816914\pi$
$41$	0.330137	−	0.571815i	0.0515588	−	0.0893024i	0.890653	+	0.454684i	$0.150248\pi$
$42$	3.39442	−	3.07862i	0.523770	−	0.475042i
$43$	3.57361	+	6.18968i	0.544971	+	0.943917i	0.998609	+	0.0527308i	$0.0167925\pi$
$43$	3.57361	+	6.18968i	0.544971	+	0.943917i	−0.453638	+	0.891186i	$0.649874\pi$
$44$	−2.71219	+	4.69765i	−0.408878	+	0.708197i
$45$	−2.79064	+	1.10105i	−0.416004	+	0.164135i
$46$	3.96948	+	6.87534i	0.585268	+	1.01371i
$47$	1.94723			0.284033			0.142016	−	0.989864i	$-0.454641\pi$
$47$	1.94723			0.284033			0.142016	+	0.989864i	$0.454641\pi$
$48$	−1.13098	−	1.31183i	−0.163242	−	0.189346i
$49$	−6.99115	+	0.351971i	−0.998735	+	0.0502815i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−2.00172	+	5.73716i	−0.280297	+	0.803362i
$52$	−2.92541	+	5.06696i	−0.405682	+	0.702661i
$53$	0.405384	+	0.702146i	0.0556838	+	0.0964472i	0.892524	−	0.451001i	$-0.148933\pi$
$53$	0.405384	+	0.702146i	0.0556838	+	0.0964472i	−0.836840	+	0.547448i	$0.815599\pi$
$54$	4.39222	−	2.77640i	0.597706	−	0.377820i
$55$	−5.42437			−0.731423
$56$	0.0665372	+	2.64491i	0.00889141	+	0.353442i
$57$	−8.92238	+	1.69653i	−1.18180	+	0.224711i
$58$	−4.29745	−	7.44340i	−0.564282	−	0.977366i
$59$	−0.0658445			−0.00857222			−0.00428611	−	0.999991i	$-0.501364\pi$
$59$	−0.0658445			−0.00857222			−0.00428611	+	0.999991i	$0.501364\pi$
$60$	0.570587	−	1.63537i	0.0736625	−	0.211125i
$61$	4.23722			0.542520			0.271260	−	0.962506i	$-0.412560\pi$
$61$	4.23722			0.542520			0.271260	+	0.962506i	$0.412560\pi$
$62$	3.59197			0.456181
$63$	−7.87763	−	0.971040i	−0.992488	−	0.122340i
$64$	1.00000			0.125000
$65$	−5.85082			−0.725705
$66$	9.22992	−	1.75501i	1.13612	−	0.216027i
$67$	3.37378			0.412173			0.206087	−	0.978534i	$-0.433927\pi$
$67$	3.37378			0.412173			0.206087	+	0.978534i	$0.433927\pi$
$68$	−1.75409	−	3.03817i	−0.212714	−	0.368432i
$69$	4.52987	−	12.9831i	0.545332	−	1.56299i
$70$	−2.25729	+	1.38008i	−0.269798	+	0.164951i
$71$	−5.85724			−0.695126			−0.347563	−	0.937657i	$-0.612991\pi$
$71$	−5.85724			−0.695126			−0.347563	+	0.937657i	$0.612991\pi$
$72$	−0.441782	+	2.96729i	−0.0520645	+	0.349699i
$73$	1.16225	+	2.01308i	0.136031	+	0.235613i	0.925991	−	0.377546i	$-0.123232\pi$
$73$	1.16225	+	2.01308i	0.136031	+	0.235613i	−0.789960	+	0.613159i	$0.789899\pi$
$74$	0.172034	−	0.297972i	0.0199986	−	0.0346386i
$75$	1.70156	−	0.323541i	0.196480	−	0.0373593i
$76$	2.62182	−	4.54112i	0.300743	−	0.520902i
$77$	−12.6053	−	6.86094i	−1.43651	−	0.781876i
$78$	9.95555	−	1.89298i	1.12724	−	0.214338i
$79$	16.9663			1.90885			0.954427	−	0.298446i	$-0.0964682\pi$
$79$	16.9663			1.90885			0.954427	+	0.298446i	$0.0964682\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−8.60966	−	2.62179i	−0.956629	−	0.291310i
$82$	0.330137	−	0.571815i	0.0364576	−	0.0631464i
$83$	−4.66838	−	8.08588i	−0.512422	−	0.887540i	−0.999896	−	0.0144032i	$-0.995415\pi$
$83$	−4.66838	−	8.08588i	−0.512422	−	0.887540i	0.487475	−	0.873137i	$-0.337918\pi$
$84$	3.39442	−	3.07862i	0.370361	−	0.335905i
$85$	1.75409	−	3.03817i	0.190257	−	0.329535i
$86$	3.57361	+	6.18968i	0.385352	+	0.667450i
$87$	−4.90414	+	14.0558i	−0.525779	+	1.50694i
$88$	−2.71219	+	4.69765i	−0.289120	+	0.500771i
$89$	7.34444	−	12.7209i	0.778509	−	1.34842i	−0.154292	−	0.988025i	$-0.549309\pi$
$89$	7.34444	−	12.7209i	0.778509	−	1.34842i	0.932801	−	0.360392i	$-0.117357\pi$
$90$	−2.79064	+	1.10105i	−0.294160	+	0.116061i
$91$	−13.5963	−	7.40032i	−1.42528	−	0.775764i
$92$	3.96948	+	6.87534i	0.413847	+	0.716804i
$93$	−4.06244	−	4.71205i	−0.421255	−	0.488616i
$94$	1.94723			0.200842
$95$	5.24363			0.537985
$96$	−1.13098	−	1.31183i	−0.115430	−	0.133888i
$97$	0.116278	+	0.201400i	0.0118063	+	0.0204490i	0.871868	−	0.489741i	$-0.162909\pi$
$97$	0.116278	+	0.201400i	0.0118063	+	0.0204490i	−0.860062	+	0.510190i	$0.829575\pi$
$98$	−6.99115	+	0.351971i	−0.706212	+	0.0355544i
$99$	−12.7411	−	10.1232i	−1.28053	−	1.01742i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	0.340309	−	0.589432i	0.0338620	−	0.0586507i	−0.848598	−	0.529039i	$-0.822553\pi$
$101$	0.340309	−	0.589432i	0.0338620	−	0.0586507i	0.882460	+	0.470388i	$0.155886\pi$
$102$	−2.00172	+	5.73716i	−0.198200	+	0.568063i
$103$	0.731446	+	1.26690i	0.0720715	+	0.124831i	0.899809	−	0.436284i	$-0.143706\pi$
$103$	0.731446	+	1.26690i	0.0720715	+	0.124831i	−0.827738	+	0.561115i	$0.810372\pi$
$104$	−2.92541	+	5.06696i	−0.286860	+	0.496856i
$105$	4.36338	+	1.40034i	0.425822	+	0.136659i
$106$	0.405384	+	0.702146i	0.0393744	+	0.0681984i
$107$	−0.166813	+	0.288928i	−0.0161264	+	0.0279317i	−0.873976	−	0.485969i	$-0.838467\pi$
$107$	−0.166813	+	0.288928i	−0.0161264	+	0.0279317i	0.857850	+	0.513901i	$0.171800\pi$
$108$	4.39222	−	2.77640i	0.422642	−	0.267159i
$109$	2.25839	+	3.91165i	0.216315	+	0.374669i	0.953679	−	0.300828i	$-0.0972629\pi$
$109$	2.25839	+	3.91165i	0.216315	+	0.374669i	−0.737364	+	0.675496i	$0.763930\pi$
$110$	−5.42437			−0.517194
$111$	−0.585455	+	0.111320i	−0.0555689	+	0.0105661i
$112$	0.0665372	+	2.64491i	0.00628718	+	0.249921i
$113$	−5.46779	+	9.47049i	−0.514366	+	0.890908i	0.485495	+	0.874240i	$0.338639\pi$
$113$	−5.46779	+	9.47049i	−0.514366	+	0.890908i	−0.999861	+	0.0166688i	$0.994694\pi$
$114$	−8.92238	+	1.69653i	−0.835657	+	0.158895i
$115$	−3.96948	+	6.87534i	−0.370156	+	0.641129i
$116$	−4.29745	−	7.44340i	−0.399008	−	0.691102i
$117$	−13.7428	−	10.9190i	−1.27052	−	1.00947i
$118$	−0.0658445			−0.00606147
$119$	7.91898	−	4.84156i	0.725932	−	0.443825i
$120$	0.570587	−	1.63537i	0.0520873	−	0.149288i
$121$	−9.21192	−	15.9555i	−0.837447	−	1.45050i
$122$	4.23722			0.383619
$123$	−1.12350	+	0.213626i	−0.101303	+	0.0192620i
$124$	3.59197			0.322569
$125$	−1.00000			−0.0894427
$126$	−7.87763	−	0.971040i	−0.701795	−	0.0865071i
$127$	20.4817			1.81745			0.908727	−	0.417392i	$-0.137056\pi$
$127$	20.4817			1.81745			0.908727	+	0.417392i	$0.137056\pi$
$128$	1.00000			0.0883883
$129$	4.07811	−	11.6883i	0.359058	−	1.02910i
$130$	−5.85082			−0.513151
$131$	−1.02889	−	1.78210i	−0.0898949	−	0.155703i	0.817572	−	0.575827i	$-0.195320\pi$
$131$	−1.02889	−	1.78210i	−0.0898949	−	0.155703i	−0.907467	+	0.420124i	$0.861986\pi$
$132$	9.22992	−	1.75501i	0.803362	−	0.152754i
$133$	12.1853	+	6.63233i	1.05660	+	0.575096i
$134$	3.37378			0.291450
$135$	4.60054	+	2.41558i	0.395952	+	0.207900i
$136$	−1.75409	−	3.03817i	−0.150412	−	0.260521i
$137$	−11.0372	+	19.1170i	−0.942970	+	1.63327i	−0.183204	+	0.983075i	$0.558647\pi$
$137$	−11.0372	+	19.1170i	−0.942970	+	1.63327i	−0.759766	+	0.650197i	$0.774687\pi$
$138$	4.52987	−	12.9831i	0.385608	−	1.10520i
$139$	−0.331564	+	0.574286i	−0.0281229	+	0.0487103i	−0.879744	−	0.475447i	$-0.842286\pi$
$139$	−0.331564	+	0.574286i	−0.0281229	+	0.0487103i	0.851621	+	0.524157i	$0.175620\pi$
$140$	−2.25729	+	1.38008i	−0.190776	+	0.116638i
$141$	−2.20227	−	2.55443i	−0.185465	−	0.215122i
$142$	−5.85724			−0.491529
$143$	−15.8685	−	27.4851i	−1.32699	−	2.29842i
$144$	−0.441782	+	2.96729i	−0.0368152	+	0.247274i
$145$	4.29745	−	7.44340i	0.356884	−	0.618141i
$146$	1.16225	+	2.01308i	0.0961888	+	0.166604i
$147$	8.36855	+	8.77311i	0.690226	+	0.723594i
$148$	0.172034	−	0.297972i	0.0141411	−	0.0244932i
$149$	−2.79809	−	4.84644i	−0.229229	−	0.397036i	0.728351	−	0.685204i	$-0.240287\pi$
$149$	−2.79809	−	4.84644i	−0.229229	−	0.397036i	−0.957580	+	0.288168i	$0.906954\pi$
$150$	1.70156	−	0.323541i	0.138932	−	0.0264170i
$151$	−7.61538	+	13.1902i	−0.619731	+	1.07341i	0.369803	+	0.929110i	$0.379425\pi$
$151$	−7.61538	+	13.1902i	−0.619731	+	1.07341i	−0.989535	+	0.144296i	$0.953908\pi$
$152$	2.62182	−	4.54112i	0.212657	−	0.368333i
$153$	9.79006	−	3.86268i	0.791479	−	0.312279i
$154$	−12.6053	−	6.86094i	−1.01577	−	0.552870i
$155$	1.79599	+	3.11074i	0.144257	+	0.249861i
$156$	9.95555	−	1.89298i	0.797082	−	0.151560i
$157$	−9.45814			−0.754842			−0.377421	−	0.926042i	$-0.623189\pi$
$157$	−9.45814			−0.754842			−0.377421	+	0.926042i	$0.623189\pi$
$158$	16.9663			1.34976
$159$	0.462614	−	1.32590i	0.0366877	−	0.105151i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−17.9206	+	10.9564i	−1.41234	+	0.863486i
$162$	−8.60966	−	2.62179i	−0.676439	−	0.205987i
$163$	−4.67319	+	8.09421i	−0.366033	+	0.633987i	−0.988941	−	0.148307i	$-0.952617\pi$
$163$	−4.67319	+	8.09421i	−0.366033	+	0.633987i	0.622909	+	0.782295i	$0.285951\pi$
$164$	0.330137	−	0.571815i	0.0257794	−	0.0446512i
$165$	6.13484	+	7.11584i	0.477597	+	0.553968i
$166$	−4.66838	−	8.08588i	−0.362337	−	0.627586i
$167$	1.09675	−	1.89963i	0.0848693	−	0.146998i	−0.820466	−	0.571695i	$-0.806286\pi$
$167$	1.09675	−	1.89963i	0.0848693	−	0.146998i	0.905335	+	0.424697i	$0.139619\pi$
$168$	3.39442	−	3.07862i	0.261885	−	0.237521i
$169$	−10.6161	−	18.3876i	−0.816620	−	1.41443i
$170$	1.75409	−	3.03817i	0.134532	−	0.233017i
$171$	12.3166	+	9.78588i	0.941871	+	0.748345i
$172$	3.57361	+	6.18968i	0.272485	+	0.471958i
$173$	−19.7016			−1.49788			−0.748941	−	0.662637i	$-0.769437\pi$
$173$	−19.7016			−1.49788			−0.748941	+	0.662637i	$0.769437\pi$
$174$	−4.90414	+	14.0558i	−0.371782	+	1.06557i
$175$	−2.32383	−	1.26483i	−0.175665	−	0.0956125i
$176$	−2.71219	+	4.69765i	−0.204439	+	0.354098i
$177$	0.0744686	+	0.0863766i	0.00559740	+	0.00649246i
$178$	7.34444	−	12.7209i	0.550489	−	0.953475i
$179$	−3.78831	−	6.56155i	−0.283152	−	0.490433i	0.689008	−	0.724754i	$-0.258047\pi$
$179$	−3.78831	−	6.56155i	−0.283152	−	0.490433i	−0.972159	+	0.234321i	$0.924713\pi$
$180$	−2.79064	+	1.10105i	−0.208002	+	0.0820676i
$181$	19.5571			1.45367			0.726835	−	0.686812i	$-0.240991\pi$
$181$	19.5571			1.45367			0.726835	+	0.686812i	$0.240991\pi$
$182$	−13.5963	−	7.40032i	−1.00783	−	0.548548i
$183$	−4.79219	−	5.55850i	−0.354249	−	0.410896i
$184$	3.96948	+	6.87534i	0.292634	+	0.506857i
$185$	0.344069			0.0252964
$186$	−4.06244	−	4.71205i	−0.297872	−	0.345504i
$187$	19.0296			1.39159
$188$	1.94723			0.142016
$189$	7.63558	+	11.4323i	0.555407	+	0.831579i
$190$	5.24363			0.380413
$191$	6.50176			0.470451			0.235225	−	0.971941i	$-0.424417\pi$
$191$	6.50176			0.470451			0.235225	+	0.971941i	$0.424417\pi$
$192$	−1.13098	−	1.31183i	−0.0816212	−	0.0946730i
$193$	16.9492			1.22003			0.610015	−	0.792390i	$-0.291164\pi$
$193$	16.9492			1.22003			0.610015	+	0.792390i	$0.291164\pi$
$194$	0.116278	+	0.201400i	0.00834829	+	0.0144597i
$195$	6.61715	+	7.67527i	0.473864	+	0.549637i
$196$	−6.99115	+	0.351971i	−0.499368	+	0.0251408i
$197$	3.20284			0.228193			0.114097	−	0.993470i	$-0.463603\pi$
$197$	3.20284			0.228193			0.114097	+	0.993470i	$0.463603\pi$
$198$	−12.7411	−	10.1232i	−0.905470	−	0.719424i
$199$	8.41802	+	14.5804i	0.596737	+	1.03358i	0.993299	+	0.115571i	$0.0368699\pi$
$199$	8.41802	+	14.5804i	0.596737	+	1.03358i	−0.396562	+	0.918008i	$0.629797\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−3.81567	−	4.42582i	−0.269137	−	0.312173i
$202$	0.340309	−	0.589432i	0.0239440	−	0.0414723i
$203$	19.4012	−	11.8616i	1.36170	−	0.832524i
$204$	−2.00172	+	5.73716i	−0.140148	+	0.401681i
$205$	0.660275			0.0461156
$206$	0.731446	+	1.26690i	0.0509622	+	0.0882692i
$207$	−22.1548	+	8.74121i	−1.53987	+	0.607556i
$208$	−2.92541	+	5.06696i	−0.202841	+	0.351330i
$209$	14.2217	+	24.6327i	0.983736	+	1.70388i
$210$	4.36338	+	1.40034i	0.301101	+	0.0966328i
$211$	9.13664	−	15.8251i	0.628992	−	1.08945i	−0.358762	−	0.933429i	$-0.616801\pi$
$211$	9.13664	−	15.8251i	0.628992	−	1.08945i	0.987754	−	0.156017i	$-0.0498655\pi$
$212$	0.405384	+	0.702146i	0.0278419	+	0.0482236i
$213$	6.62440	+	7.68369i	0.453897	+	0.526477i
$214$	−0.166813	+	0.288928i	−0.0114031	+	0.0197507i
$215$	−3.57361	+	6.18968i	−0.243718	+	0.422132i
$216$	4.39222	−	2.77640i	0.298853	−	0.188910i
$217$	0.239000	+	9.50046i	0.0162244	+	0.644933i
$218$	2.25839	+	3.91165i	0.152958	+	0.264931i
$219$	1.32633	−	3.80142i	0.0896253	−	0.256876i
$220$	−5.42437			−0.365711
$221$	20.5257			1.38071
$222$	−0.585455	+	0.111320i	−0.0392932	+	0.00747133i
$223$	8.05899	+	13.9586i	0.539670	+	0.934735i	0.998922	+	0.0464292i	$0.0147842\pi$
$223$	8.05899	+	13.9586i	0.539670	+	0.934735i	−0.459252	+	0.888306i	$0.651882\pi$
$224$	0.0665372	+	2.64491i	0.00444571	+	0.176721i
$225$	−2.34886	−	1.86624i	−0.156591	−	0.124416i
$226$	−5.46779	+	9.47049i	−0.363712	+	0.629967i
$227$	−7.18394	+	12.4429i	−0.476815	+	0.825867i	−0.999647	−	0.0265685i	$-0.991542\pi$
$227$	−7.18394	+	12.4429i	−0.476815	+	0.825867i	0.522832	+	0.852435i	$0.324875\pi$
$228$	−8.92238	+	1.69653i	−0.590899	+	0.112356i
$229$	3.50773	+	6.07557i	0.231797	+	0.401485i	0.958337	−	0.285640i	$-0.0922060\pi$
$229$	3.50773	+	6.07557i	0.231797	+	0.401485i	−0.726540	+	0.687125i	$0.758873\pi$
$230$	−3.96948	+	6.87534i	−0.261740	+	0.453347i
$231$	5.25598	+	24.2956i	0.345818	+	1.59853i
$232$	−4.29745	−	7.44340i	−0.282141	−	0.488683i
$233$	11.7792	−	20.4022i	0.771683	−	1.33659i	−0.164956	−	0.986301i	$-0.552748\pi$
$233$	11.7792	−	20.4022i	0.771683	−	1.33659i	0.936640	−	0.350294i	$-0.113918\pi$
$234$	−13.7428	−	10.9190i	−0.898393	−	0.713800i
$235$	0.973616	+	1.68635i	0.0635117	+	0.110005i
$236$	−0.0658445			−0.00428611
$237$	−19.1884	−	22.2568i	−1.24642	−	1.44573i
$238$	7.91898	−	4.84156i	0.513311	−	0.313832i
$239$	10.8073	−	18.7188i	0.699067	−	1.21082i	−0.269723	−	0.962938i	$-0.586932\pi$
$239$	10.8073	−	18.7188i	0.699067	−	1.21082i	0.968790	−	0.247882i	$-0.0797345\pi$
$240$	0.570587	−	1.63537i	0.0368312	−	0.105563i
$241$	5.90758	−	10.2322i	0.380541	−	0.659116i	−0.610599	−	0.791940i	$-0.709071\pi$
$241$	5.90758	−	10.2322i	0.380541	−	0.659116i	0.991140	+	0.132824i	$0.0424046\pi$
$242$	−9.21192	−	15.9555i	−0.592165	−	1.02566i
$243$	6.29799	+	14.2596i	0.404016	+	0.914752i
$244$	4.23722			0.271260
$245$	−3.80039	−	5.87852i	−0.242798	−	0.375565i
$246$	−1.12350	+	0.213626i	−0.0716317	+	0.0136203i
$247$	15.3398	+	26.5693i	0.976047	+	1.69056i
$248$	3.59197			0.228090
$249$	−5.32744	+	15.2691i	−0.337613	+	0.967637i
$250$	−1.00000			−0.0632456
$251$	9.66854			0.610273			0.305136	−	0.952309i	$-0.401298\pi$
$251$	9.66854			0.610273			0.305136	+	0.952309i	$0.401298\pi$
$252$	−7.87763	−	0.971040i	−0.496244	−	0.0611698i
$253$	−43.0639			−2.70740
$254$	20.4817			1.28513
$255$	−5.96938	+	1.13504i	−0.373817	+	0.0710789i
$256$	1.00000			0.0625000
$257$	−4.25549	−	7.37073i	−0.265450	−	0.459773i	0.702231	−	0.711949i	$-0.252187\pi$
$257$	−4.25549	−	7.37073i	−0.265450	−	0.459773i	−0.967681	+	0.252176i	$0.918854\pi$
$258$	4.07811	−	11.6883i	0.253892	−	0.727684i
$259$	0.799558	+	0.435190i	0.0496821	+	0.0270414i
$260$	−5.85082			−0.362853
$261$	23.9853	−	9.46343i	1.48465	−	0.585772i
$262$	−1.02889	−	1.78210i	−0.0635653	−	0.110098i
$263$	−0.206896	+	0.358354i	−0.0127577	+	0.0220971i	−0.872334	−	0.488911i	$-0.837394\pi$
$263$	−0.206896	+	0.358354i	−0.0127577	+	0.0220971i	0.859576	+	0.511008i	$0.170728\pi$
$264$	9.22992	−	1.75501i	0.568062	−	0.108013i
$265$	−0.405384	+	0.702146i	−0.0249025	+	0.0431325i
$266$	12.1853	+	6.63233i	0.747130	+	0.406654i
$267$	−24.9941	+	4.75246i	−1.52961	+	0.290846i
$268$	3.37378			0.206087
$269$	−3.59412	−	6.22519i	−0.219137	−	0.379557i	0.735407	−	0.677625i	$-0.236991\pi$
$269$	−3.59412	−	6.22519i	−0.219137	−	0.379557i	−0.954544	+	0.298069i	$0.903658\pi$
$270$	4.60054	+	2.41558i	0.279980	+	0.147007i
$271$	2.19833	−	3.80762i	0.133539	−	0.231296i	−0.791499	−	0.611170i	$-0.790699\pi$
$271$	2.19833	−	3.80762i	0.133539	−	0.231296i	0.925038	+	0.379874i	$0.124033\pi$
$272$	−1.75409	−	3.03817i	−0.106357	−	0.184216i
$273$	5.66919	+	26.2056i	0.343115	+	1.58604i
$274$	−11.0372	+	19.1170i	−0.666780	+	1.15490i
$275$	−2.71219	−	4.69765i	−0.163551	−	0.283279i
$276$	4.52987	−	12.9831i	0.272666	−	0.781493i
$277$	6.51686	−	11.2875i	0.391560	−	0.678202i	−0.601096	−	0.799177i	$-0.705269\pi$
$277$	6.51686	−	11.2875i	0.391560	−	0.678202i	0.992655	+	0.120976i	$0.0386023\pi$
$278$	−0.331564	+	0.574286i	−0.0198859	+	0.0344434i
$279$	−1.58687	+	10.6584i	−0.0950033	+	0.638104i
$280$	−2.25729	+	1.38008i	−0.134899	+	0.0824756i
$281$	2.56584	+	4.44417i	0.153065	+	0.265117i	0.932353	−	0.361549i	$-0.117752\pi$
$281$	2.56584	+	4.44417i	0.153065	+	0.265117i	−0.779288	+	0.626667i	$0.784419\pi$
$282$	−2.20227	−	2.55443i	−0.131144	−	0.152114i
$283$	−10.1635			−0.604160			−0.302080	−	0.953283i	$-0.597681\pi$
$283$	−10.1635			−0.604160			−0.302080	+	0.953283i	$0.597681\pi$
$284$	−5.85724			−0.347563
$285$	−5.93043	−	6.87874i	−0.351288	−	0.407461i
$286$	−15.8685	−	27.4851i	−0.938326	−	1.62523i
$287$	1.53437	+	0.835138i	0.0905708	+	0.0492966i
$288$	−0.441782	+	2.96729i	−0.0260322	+	0.174849i
$289$	2.34636	−	4.06402i	0.138021	−	0.239060i
$290$	4.29745	−	7.44340i	0.252355	−	0.437091i
$291$	0.132694	−	0.380315i	0.00777864	−	0.0222945i
$292$	1.16225	+	2.01308i	0.0680157	+	0.117807i
$293$	7.75877	−	13.4386i	0.453272	−	0.785091i	−0.545315	−	0.838231i	$-0.683590\pi$
$293$	7.75877	−	13.4386i	0.453272	−	0.785091i	0.998587	+	0.0531407i	$0.0169232\pi$
$294$	8.36855	+	8.77311i	0.488064	+	0.511658i
$295$	−0.0329222	−	0.0570230i	−0.00191681	−	0.00332001i
$296$	0.172034	−	0.297972i	0.00999929	−	0.0173193i
$297$	1.13001	+	28.1632i	0.0655700	+	1.63420i
$298$	−2.79809	−	4.84644i	−0.162089	−	0.280747i
$299$	−46.4495			−2.68624
$300$	1.70156	−	0.323541i	0.0982399	−	0.0186797i
$301$	−16.1334	+	9.86374i	−0.929913	+	0.568537i
$302$	−7.61538	+	13.1902i	−0.438216	+	0.759013i
$303$	−1.15811	+	0.220208i	−0.0665320	+	0.0126506i
$304$	2.62182	−	4.54112i	0.150371	−	0.260451i
$305$	2.11861	+	3.66954i	0.121311	+	0.210117i
$306$	9.79006	−	3.86268i	0.559660	−	0.220815i
$307$	−28.3895			−1.62027			−0.810137	−	0.586241i	$-0.800607\pi$
$307$	−28.3895			−1.62027			−0.810137	+	0.586241i	$0.800607\pi$
$308$	−12.6053	−	6.86094i	−0.718256	−	0.390938i
$309$	0.834707	−	2.39237i	0.0474848	−	0.136097i
$310$	1.79599	+	3.11074i	0.102005	+	0.176678i
$311$	−20.6637			−1.17173			−0.585866	−	0.810408i	$-0.699245\pi$
$311$	−20.6637			−1.17173			−0.585866	+	0.810408i	$0.699245\pi$
$312$	9.95555	−	1.89298i	0.563622	−	0.107169i
$313$	22.1157			1.25005			0.625027	−	0.780603i	$-0.285088\pi$
$313$	22.1157			1.25005			0.625027	+	0.780603i	$0.285088\pi$
$314$	−9.45814			−0.533754
$315$	−3.09787	−	7.30775i	−0.174545	−	0.411745i
$316$	16.9663			0.954427
$317$	31.0936			1.74639			0.873196	−	0.487369i	$-0.162043\pi$
$317$	31.0936			1.74639			0.873196	+	0.487369i	$0.162043\pi$
$318$	0.462614	−	1.32590i	0.0259421	−	0.0743531i
$319$	46.6219			2.61033
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	0.567685	−	0.107941i	0.0316851	−	0.00602471i
$322$	−17.9206	+	10.9564i	−0.998675	+	0.610577i
$323$	−18.3956			−1.02356
$324$	−8.60966	−	2.62179i	−0.478314	−	0.145655i
$325$	−2.92541	−	5.06696i	−0.162273	−	0.281064i
$326$	−4.67319	+	8.09421i	−0.258824	+	0.448297i
$327$	2.57722	−	7.38662i	0.142521	−	0.408481i
$328$	0.330137	−	0.571815i	0.0182288	−	0.0315732i
$329$	0.129563	+	5.15026i	0.00714306	+	0.283943i
$330$	6.13484	+	7.11584i	0.337712	+	0.391714i
$331$	−27.1281			−1.49109			−0.745547	−	0.666453i	$-0.767812\pi$
$331$	−27.1281			−1.49109			−0.745547	+	0.666453i	$0.767812\pi$
$332$	−4.66838	−	8.08588i	−0.256211	−	0.443770i
$333$	0.808169	+	0.642115i	0.0442874	+	0.0351877i
$334$	1.09675	−	1.89963i	0.0600116	−	0.103943i
$335$	1.68689	+	2.92178i	0.0921647	+	0.159634i
$336$	3.39442	−	3.07862i	0.185181	−	0.167953i
$337$	4.40226	−	7.62494i	0.239806	−	0.415357i	−0.720852	−	0.693089i	$-0.756249\pi$
$337$	4.40226	−	7.62494i	0.239806	−	0.415357i	0.960659	+	0.277732i	$0.0895827\pi$
$338$	−10.6161	−	18.3876i	−0.577437	−	1.00015i
$339$	18.6076	−	3.53811i	1.01063	−	0.192164i
$340$	1.75409	−	3.03817i	0.0951287	−	0.164768i
$341$	−9.74210	+	16.8738i	−0.527564	+	0.913768i
$342$	12.3166	+	9.78588i	0.666003	+	0.529160i
$343$	−1.39610	−	18.4676i	−0.0753825	−	0.997155i
$344$	3.57361	+	6.18968i	0.192676	+	0.333725i
$345$	13.5087	−	2.56858i	0.727282	−	0.138288i
$346$	−19.7016			−1.05916
$347$	19.2968			1.03591			0.517953	−	0.855409i	$-0.326694\pi$
$347$	19.2968			1.03591			0.517953	+	0.855409i	$0.326694\pi$
$348$	−4.90414	+	14.0558i	−0.262889	+	0.753471i
$349$	8.28885	+	14.3567i	0.443692	+	0.768497i	0.997960	−	0.0638410i	$-0.0203350\pi$
$349$	8.28885	+	14.3567i	0.443692	+	0.768497i	−0.554268	+	0.832338i	$0.687002\pi$
$350$	−2.32383	−	1.26483i	−0.124214	−	0.0676082i
$351$	1.21885	+	30.3773i	0.0650574	+	1.62142i
$352$	−2.71219	+	4.69765i	−0.144560	+	0.250385i
$353$	−13.4978	+	23.3789i	−0.718416	+	1.24433i	0.243211	+	0.969973i	$0.421799\pi$
$353$	−13.4978	+	23.3789i	−0.718416	+	1.24433i	−0.961627	+	0.274360i	$0.911534\pi$
$354$	0.0744686	+	0.0863766i	0.00395796	+	0.00459086i
$355$	−2.92862	−	5.07252i	−0.155435	−	0.269221i
$356$	7.34444	−	12.7209i	0.389255	−	0.674209i
$357$	−15.3075	−	4.91264i	−0.810157	−	0.260005i
$358$	−3.78831	−	6.56155i	−0.200219	−	0.346789i
$359$	−5.87285	+	10.1721i	−0.309957	+	0.536862i	−0.978353	−	0.206944i	$-0.933648\pi$
$359$	−5.87285	+	10.1721i	−0.309957	+	0.536862i	0.668395	+	0.743806i	$0.266981\pi$
$360$	−2.79064	+	1.10105i	−0.147080	+	0.0580305i
$361$	−4.24784	−	7.35747i	−0.223570	−	0.387235i
$362$	19.5571			1.02790
$363$	−10.5124	+	30.1298i	−0.551758	+	1.58140i
$364$	−13.5963	−	7.40032i	−0.712641	−	0.387882i
$365$	−1.16225	+	2.01308i	−0.0608351	+	0.105370i
$366$	−4.79219	−	5.55850i	−0.250492	−	0.290547i
$367$	5.62339	−	9.73999i	0.293538	−	0.508423i	−0.681105	−	0.732185i	$-0.738500\pi$
$367$	5.62339	−	9.73999i	0.293538	−	0.508423i	0.974644	+	0.223762i	$0.0718338\pi$
$368$	3.96948	+	6.87534i	0.206924	+	0.358402i
$369$	1.55089	+	1.23223i	0.0807363	+	0.0641474i
$370$	0.344069			0.0178873
$371$	−1.83014	+	1.11893i	−0.0950163	+	0.0580917i
$372$	−4.06244	−	4.71205i	−0.210628	−	0.244308i
$373$	−17.5298	−	30.3626i	−0.907661	−	1.57212i	−0.817305	−	0.576206i	$-0.804533\pi$
$373$	−17.5298	−	30.3626i	−0.907661	−	1.57212i	−0.0903564	−	0.995909i	$-0.528801\pi$
$374$	19.0296			0.983999
$375$	1.13098	+	1.31183i	0.0584034	+	0.0677425i
$376$	1.94723			0.100421
$377$	50.2872			2.58992
$378$	7.63558	+	11.4323i	0.392732	+	0.588015i
$379$	−2.86903			−0.147372			−0.0736860	−	0.997281i	$-0.523476\pi$
$379$	−2.86903			−0.147372			−0.0736860	+	0.997281i	$0.523476\pi$
$380$	5.24363			0.268993
$381$	−23.1643	−	26.8684i	−1.18674	−	1.37651i
$382$	6.50176			0.332659
$383$	11.6637	+	20.2021i	0.595986	+	1.03228i	0.993407	+	0.114642i	$0.0365720\pi$
$383$	11.6637	+	20.2021i	0.595986	+	1.03228i	−0.397421	+	0.917636i	$0.630095\pi$
$384$	−1.13098	−	1.31183i	−0.0577149	−	0.0669439i
$385$	−0.360923	−	14.3470i	−0.0183943	−	0.731191i
$386$	16.9492			0.862691
$387$	−19.9453	+	7.86947i	−1.01388	+	0.400027i
$388$	0.116278	+	0.201400i	0.00590313	+	0.0102245i
$389$	11.4813	−	19.8863i	0.582127	−	1.00827i	−0.413100	−	0.910686i	$-0.635554\pi$
$389$	11.4813	−	19.8863i	0.582127	−	1.00827i	0.995227	−	0.0975879i	$-0.0311127\pi$
$390$	6.61715	+	7.67527i	0.335072	+	0.388652i
$391$	13.9256	−	24.1199i	0.704249	−	1.21980i
$392$	−6.99115	+	0.351971i	−0.353106	+	0.0177772i
$393$	−1.17415	+	3.36524i	−0.0592279	+	0.169754i
$394$	3.20284			0.161357
$395$	8.48313	+	14.6932i	0.426833	+	0.739296i
$396$	−12.7411	−	10.1232i	−0.640264	−	0.508709i
$397$	−16.3423	+	28.3057i	−0.820197	+	1.42062i	0.0853377	+	0.996352i	$0.472803\pi$
$397$	−16.3423	+	28.3057i	−0.820197	+	1.42062i	−0.905535	+	0.424271i	$0.860530\pi$
$398$	8.41802	+	14.5804i	0.421957	+	0.730851i
$399$	−5.08085	−	23.4860i	−0.254361	−	1.17577i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	15.2284	+	26.3763i	0.760468	+	1.31717i	0.942610	+	0.333897i	$0.108364\pi$
$401$	15.2284	+	26.3763i	0.760468	+	1.31717i	−0.182142	+	0.983272i	$0.558303\pi$
$402$	−3.81567	−	4.42582i	−0.190308	−	0.220740i
$403$	−10.5080	+	18.2004i	−0.523440	+	0.906625i
$404$	0.340309	−	0.589432i	0.0169310	−	0.0293253i
$405$	−2.03429	−	8.76708i	−0.101085	−	0.435640i
$406$	19.4012	−	11.8616i	0.962866	−	0.588684i
$407$	0.933178	+	1.61631i	0.0462559	+	0.0801176i
$408$	−2.00172	+	5.73716i	−0.0990998	+	0.284032i
$409$	−13.3108			−0.658178			−0.329089	−	0.944299i	$-0.606742\pi$
$409$	−13.3108			−0.658178			−0.329089	+	0.944299i	$0.606742\pi$
$410$	0.660275			0.0326086
$411$	37.5609	−	7.14196i	1.85274	−	0.352287i
$412$	0.731446	+	1.26690i	0.0360357	+	0.0624157i
$413$	−0.00438111	−	0.174153i	−0.000215580	−	0.00856951i
$414$	−22.1548	+	8.74121i	−1.08885	+	0.429607i
$415$	4.66838	−	8.08588i	0.229162	−	0.396920i
$416$	−2.92541	+	5.06696i	−0.143430	+	0.248428i
$417$	1.12836	−	0.214549i	0.0552558	−	0.0105065i
$418$	14.2217	+	24.6327i	0.695607	+	1.20483i
$419$	−11.5272	+	19.9658i	−0.563143	+	0.975392i	0.434077	+	0.900876i	$0.357075\pi$
$419$	−11.5272	+	19.9658i	−0.563143	+	0.975392i	−0.997220	+	0.0745163i	$0.976259\pi$
$420$	4.36338	+	1.40034i	0.212911	+	0.0683297i
$421$	−16.8883	−	29.2515i	−0.823087	−	1.42563i	−0.903373	−	0.428857i	$-0.858917\pi$
$421$	−16.8883	−	29.2515i	−0.823087	−	1.42563i	0.0802855	−	0.996772i	$-0.474417\pi$
$422$	9.13664	−	15.8251i	0.444765	−	0.770355i
$423$	−0.860252	+	5.77801i	−0.0418269	+	0.280936i
$424$	0.405384	+	0.702146i	0.0196872	+	0.0340992i
$425$	3.50817			0.170171
$426$	6.62440	+	7.68369i	0.320953	+	0.372276i
$427$	0.281933	+	11.2071i	0.0136437	+	0.542348i
$428$	−0.166813	+	0.288928i	−0.00806319	+	0.0139659i
$429$	−18.1088	+	51.9018i	−0.874299	+	2.50584i
$430$	−3.57361	+	6.18968i	−0.172335	+	0.298493i
$431$	7.80158	+	13.5127i	0.375789	+	0.650886i	0.990445	−	0.137910i	$-0.0440384\pi$
$431$	7.80158	+	13.5127i	0.375789	+	0.650886i	−0.614656	+	0.788795i	$0.710705\pi$
$432$	4.39222	−	2.77640i	0.211321	−	0.133580i
$433$	−14.4129			−0.692642			−0.346321	−	0.938116i	$-0.612569\pi$
$433$	−14.4129			−0.692642			−0.346321	+	0.938116i	$0.612569\pi$
$434$	0.239000	+	9.50046i	0.0114724	+	0.456037i
$435$	−14.6248	+	2.78080i	−0.701204	+	0.133329i
$436$	2.25839	+	3.91165i	0.108157	+	0.187334i
$437$	41.6290			1.99139
$438$	1.32633	−	3.80142i	0.0633747	−	0.181639i
$439$	−3.60584			−0.172098			−0.0860488	−	0.996291i	$-0.527424\pi$
$439$	−3.60584			−0.172098			−0.0860488	+	0.996291i	$0.527424\pi$
$440$	−5.42437			−0.258597
$441$	2.04416	−	20.9003i	0.0973410	−	0.995251i
$442$	20.5257			0.976308
$443$	−0.266687			−0.0126707			−0.00633533	−	0.999980i	$-0.502017\pi$
$443$	−0.266687			−0.0126707			−0.00633533	+	0.999980i	$0.502017\pi$
$444$	−0.585455	+	0.111320i	−0.0277845	+	0.00528303i
$445$	14.6889			0.696320
$446$	8.05899	+	13.9586i	0.381604	+	0.660958i
$447$	−3.19311	+	9.15183i	−0.151029	+	0.432867i
$448$	0.0665372	+	2.64491i	0.00314359	+	0.124960i
$449$	33.6153			1.58640			0.793202	−	0.608958i	$-0.208412\pi$
$449$	33.6153			1.58640			0.793202	+	0.608958i	$0.208412\pi$
$450$	−2.34886	−	1.86624i	−0.110726	−	0.0879754i
$451$	1.79079	+	3.10174i	0.0843249	+	0.146055i
$452$	−5.46779	+	9.47049i	−0.257183	+	0.445454i
$453$	25.9161	−	4.92778i	1.21765	−	0.231527i
$454$	−7.18394	+	12.4429i	−0.337159	+	0.583976i
$455$	−0.389298	−	15.4749i	−0.0182505	−	0.725476i
$456$	−8.92238	+	1.69653i	−0.417829	+	0.0794473i
$457$	−8.86739			−0.414799			−0.207399	−	0.978256i	$-0.566500\pi$
$457$	−8.86739			−0.414799			−0.207399	+	0.978256i	$0.566500\pi$
$458$	3.50773	+	6.07557i	0.163906	+	0.283893i
$459$	−16.1395	−	8.47426i	−0.753327	−	0.395544i
$460$	−3.96948	+	6.87534i	−0.185078	+	0.320565i
$461$	14.1466	+	24.5027i	0.658874	+	1.14120i	0.980908	+	0.194475i	$0.0623002\pi$
$461$	14.1466	+	24.5027i	0.658874	+	1.14120i	−0.322034	+	0.946728i	$0.604366\pi$
$462$	5.25598	+	24.2956i	0.244530	+	1.13033i
$463$	10.6916	−	18.5184i	0.496880	−	0.860622i	−0.503113	−	0.864221i	$-0.667812\pi$
$463$	10.6916	−	18.5184i	0.496880	−	0.860622i	0.999994	+	0.00359858i	$0.00114547\pi$
$464$	−4.29745	−	7.44340i	−0.199504	−	0.345551i
$465$	2.04953	−	5.87420i	0.0950448	−	0.272409i
$466$	11.7792	−	20.4022i	0.545663	−	0.945115i
$467$	6.52517	−	11.3019i	0.301949	−	0.522991i	−0.674628	−	0.738158i	$-0.735696\pi$
$467$	6.52517	−	11.3019i	0.301949	−	0.522991i	0.976577	+	0.215167i	$0.0690294\pi$
$468$	−13.7428	−	10.9190i	−0.635259	−	0.504733i
$469$	0.224482	+	8.92337i	0.0103656	+	0.412043i
$470$	0.973616	+	1.68635i	0.0449095	+	0.0777856i
$471$	10.6969	+	12.4074i	0.492889	+	0.571705i
$472$	−0.0658445			−0.00303074
$473$	−38.7692			−1.78261
$474$	−19.1884	−	22.2568i	−0.881355	−	1.02229i
$475$	2.62182	+	4.54112i	0.120297	+	0.208361i
$476$	7.91898	−	4.84156i	0.362966	−	0.221913i
$477$	−2.26256	+	0.892698i	−0.103596	+	0.0408738i
$478$	10.8073	−	18.7188i	0.494315	−	0.856179i
$479$	20.0416	−	34.7131i	0.915726	−	1.58608i	0.109891	−	0.993944i	$-0.464950\pi$
$479$	20.0416	−	34.7131i	0.915726	−	1.58608i	0.805835	−	0.592140i	$-0.201717\pi$
$480$	0.570587	−	1.63537i	0.0260436	−	0.0746440i
$481$	1.00654	+	1.74338i	0.0458944	+	0.0794914i
$482$	5.90758	−	10.2322i	0.269083	−	0.466065i
$483$	34.6407	+	11.1173i	1.57621	+	0.505853i
$484$	−9.21192	−	15.9555i	−0.418724	−	0.725251i
$485$	−0.116278	+	0.201400i	−0.00527992	+	0.00914509i
$486$	6.29799	+	14.2596i	0.285682	+	0.646827i
$487$	−14.2575	−	24.6947i	−0.646068	−	1.11902i	−0.984054	−	0.177871i	$-0.943079\pi$
$487$	−14.2575	−	24.6947i	−0.646068	−	1.11902i	0.337986	−	0.941151i	$-0.390254\pi$
$488$	4.23722			0.191810
$489$	15.9035	−	3.02394i	0.719180	−	0.136747i
$490$	−3.80039	−	5.87852i	−0.171684	−	0.265565i
$491$	−6.92505	+	11.9945i	−0.312523	+	0.541306i	−0.978908	−	0.204302i	$-0.934507\pi$
$491$	−6.92505	+	11.9945i	−0.312523	+	0.541306i	0.666385	+	0.745608i	$0.267841\pi$
$492$	−1.12350	+	0.213626i	−0.0506513	+	0.00963101i
$493$	−15.0762	+	26.1127i	−0.678997	+	1.17606i
$494$	15.3398	+	26.5693i	0.690169	+	1.19541i
$495$	2.39639	−	16.0957i	0.107710	−	0.723448i
$496$	3.59197			0.161284
$497$	−0.389724	−	15.4919i	−0.0174815	−	0.694906i
$498$	−5.32744	+	15.2691i	−0.238728	+	0.684223i
$499$	−17.8754	−	30.9611i	−0.800212	−	1.38601i	−0.919476	−	0.393145i	$-0.871387\pi$
$499$	−17.8754	−	30.9611i	−0.800212	−	1.38601i	0.119264	−	0.992863i	$-0.461946\pi$
$500$	−1.00000			−0.0447214
$501$	−3.73239	+	0.709689i	−0.166751	+	0.0317066i
$502$	9.66854			0.431528
$503$	7.63564			0.340457			0.170228	−	0.985405i	$-0.445549\pi$
$503$	7.63564			0.340457			0.170228	+	0.985405i	$0.445549\pi$
$504$	−7.87763	−	0.971040i	−0.350898	−	0.0432536i
$505$	0.680618			0.0302871
$506$	−43.0639			−1.91442
$507$	−12.1148	+	34.7223i	−0.538036	+	1.54207i
$508$	20.4817			0.908727
$509$	−21.2215	−	36.7567i	−0.940627	−	1.62921i	−0.764279	−	0.644885i	$-0.776905\pi$
$509$	−21.2215	−	36.7567i	−0.940627	−	1.62921i	−0.176348	−	0.984328i	$-0.556428\pi$
$510$	−5.96938	+	1.13504i	−0.264329	+	0.0502603i
$511$	−5.24710	+	3.20801i	−0.232118	+	0.141914i
$512$	1.00000			0.0441942
$513$	−1.09236	−	27.2248i	−0.0482289	−	1.20200i
$514$	−4.25549	−	7.37073i	−0.187702	−	0.325109i
$515$	−0.731446	+	1.26690i	−0.0322313	+	0.0558263i
$516$	4.07811	−	11.6883i	0.179529	−	0.514551i
$517$	−5.28126	+	9.14740i	−0.232269	+	0.402302i
$518$	0.799558	+	0.435190i	0.0351305	+	0.0191211i
$519$	22.2820	+	25.8450i	0.978072	+	1.13447i
$520$	−5.85082			−0.256576
$521$	−7.08115	−	12.2649i	−0.310231	−	0.537336i	0.668181	−	0.743999i	$-0.267073\pi$
$521$	−7.08115	−	12.2649i	−0.310231	−	0.537336i	−0.978412	+	0.206663i	$0.933740\pi$
$522$	23.9853	−	9.46343i	1.04981	−	0.414203i
$523$	−0.100561	+	0.174177i	−0.00439723	+	0.00761623i	−0.868216	−	0.496187i	$-0.834733\pi$
$523$	−0.100561	+	0.174177i	−0.00439723	+	0.00761623i	0.863818	+	0.503803i	$0.168066\pi$
$524$	−1.02889	−	1.78210i	−0.0449475	−	0.0778513i
$525$	0.968956	+	4.47896i	0.0422887	+	0.195478i
$526$	−0.206896	+	0.358354i	−0.00902109	+	0.0156250i
$527$	−6.30063	−	10.9130i	−0.274460	−	0.475378i
$528$	9.22992	−	1.75501i	0.401681	−	0.0763769i
$529$	−20.0136	+	34.6645i	−0.870155	+	1.50715i
$530$	−0.405384	+	0.702146i	−0.0176088	+	0.0304993i
$531$	0.0290889	−	0.195380i	0.00126235	−	0.00847876i
$532$	12.1853	+	6.63233i	0.528301	+	0.287548i
$533$	1.93157	+	3.34559i	0.0836658	+	0.144913i
$534$	−24.9941	+	4.75246i	−1.08160	+	0.205659i
$535$	−0.333625			−0.0144239
$536$	3.37378			0.145725
$537$	−4.32313	+	12.3906i	−0.186557	+	0.534693i
$538$	−3.59412	−	6.22519i	−0.154953	−	0.268387i
$539$	17.3079	−	33.7965i	0.745502	−	1.45572i
$540$	4.60054	+	2.41558i	0.197976	+	0.103950i
$541$	0.135983	−	0.235529i	0.00584636	−	0.0101262i	−0.863087	−	0.505055i	$-0.831472\pi$
$541$	0.135983	−	0.235529i	0.00584636	−	0.0101262i	0.868934	+	0.494928i	$0.164806\pi$
$542$	2.19833	−	3.80762i	0.0944264	−	0.163551i
$543$	−22.1187	−	25.6556i	−0.949203	−	1.10099i
$544$	−1.75409	−	3.03817i	−0.0752058	−	0.130260i
$545$	−2.25839	+	3.91165i	−0.0967390	+	0.167557i
$546$	5.66919	+	26.2056i	0.242619	+	1.12150i
$547$	2.29429	+	3.97382i	0.0980967	+	0.169908i	0.910897	−	0.412634i	$-0.135391\pi$
$547$	2.29429	+	3.97382i	0.0980967	+	0.169908i	−0.812800	+	0.582543i	$0.802058\pi$
$548$	−11.0372	+	19.1170i	−0.471485	+	0.816636i
$549$	−1.87193	+	12.5731i	−0.0798918	+	0.536605i
$550$	−2.71219	−	4.69765i	−0.115648	−	0.200308i
$551$	−45.0685			−1.91998
$552$	4.52987	−	12.9831i	0.192804	−	0.552599i
$553$	1.12889	+	44.8743i	0.0480052	+	1.90825i
$554$	6.51686	−	11.2875i	0.276875	−	0.479561i
$555$	−0.389134	−	0.451359i	−0.0165178	−	0.0191591i
$556$	−0.331564	+	0.574286i	−0.0140615	+	0.0243552i
$557$	0.0264236	+	0.0457671i	0.00111960	+	0.00193921i	0.866585	−	0.499030i	$-0.166310\pi$
$557$	0.0264236	+	0.0457671i	0.00111960	+	0.00193921i	−0.865465	+	0.500969i	$0.832977\pi$
$558$	−1.58687	+	10.6584i	−0.0671775	+	0.451207i
$559$	−41.8171			−1.76868
$560$	−2.25729	+	1.38008i	−0.0953881	+	0.0583190i
$561$	−21.5221	−	24.9636i	−0.908663	−	1.05396i
$562$	2.56584	+	4.44417i	0.108234	+	0.187466i
$563$	29.6089			1.24787			0.623934	−	0.781477i	$-0.285533\pi$
$563$	29.6089			1.24787			0.623934	+	0.781477i	$0.285533\pi$
$564$	−2.20227	−	2.55443i	−0.0927325	−	0.107561i
$565$	−10.9356			−0.460063
$566$	−10.1635			−0.427205
$567$	6.36155	−	22.9463i	0.267160	−	0.963652i
$568$	−5.85724			−0.245764
$569$	18.3091			0.767559			0.383779	−	0.923425i	$-0.374622\pi$
$569$	18.3091			0.767559			0.383779	+	0.923425i	$0.374622\pi$
$570$	−5.93043	−	6.87874i	−0.248398	−	0.288119i
$571$	−35.8198			−1.49901			−0.749506	−	0.661997i	$-0.769709\pi$
$571$	−35.8198			−1.49901			−0.749506	+	0.661997i	$0.769709\pi$
$572$	−15.8685	−	27.4851i	−0.663496	−	1.14921i
$573$	−7.35334	−	8.52919i	−0.307190	−	0.356312i
$574$	1.53437	+	0.835138i	0.0640433	+	0.0348580i
$575$	−7.93896			−0.331078
$576$	−0.441782	+	2.96729i	−0.0184076	+	0.123637i
$577$	−11.4602	−	19.8496i	−0.477094	−	0.826351i	0.522562	−	0.852602i	$-0.324976\pi$
$577$	−11.4602	−	19.8496i	−0.477094	−	0.826351i	−0.999655	+	0.0262509i	$0.991643\pi$
$578$	2.34636	−	4.06402i	0.0975958	−	0.169041i
$579$	−19.1691	−	22.2344i	−0.796642	−	0.924030i
$580$	4.29745	−	7.44340i	0.178442	−	0.309070i
$581$	21.0758	−	12.8855i	0.874373	−	0.534580i
$582$	0.132694	−	0.380315i	0.00550033	−	0.0157646i
$583$	−4.39791			−0.182143
$584$	1.16225	+	2.01308i	0.0480944	+	0.0833019i
$585$	2.58479	−	17.3611i	0.106868	−	0.717793i
$586$	7.75877	−	13.4386i	0.320512	−	0.555143i
$587$	−11.1593	−	19.3286i	−0.460596	−	0.797775i	0.538395	−	0.842693i	$-0.319031\pi$
$587$	−11.1593	−	19.3286i	−0.460596	−	0.797775i	−0.998991	+	0.0449176i	$0.985697\pi$
$588$	8.36855	+	8.77311i	0.345113	+	0.361797i
$589$	9.41749	−	16.3116i	0.388041	−	0.672106i
$590$	−0.0329222	−	0.0570230i	−0.00135539	−	0.00234760i
$591$	−3.62234	−	4.20158i	−0.149003	−	0.172830i
$592$	0.172034	−	0.297972i	0.00707057	−	0.0122466i
$593$	−2.77642	+	4.80891i	−0.114014	+	0.197478i	−0.917385	−	0.398001i	$-0.869704\pi$
$593$	−2.77642	+	4.80891i	−0.114014	+	0.197478i	0.803371	+	0.595479i	$0.203038\pi$
$594$	1.13001	+	28.1632i	0.0463650	+	1.15555i
$595$	8.15240	+	4.43726i	0.334216	+	0.181910i
$596$	−2.79809	−	4.84644i	−0.114614	−	0.198518i
$597$	9.60643	−	27.5331i	0.393165	−	1.12686i
$598$	−46.4495			−1.89946
$599$	5.58050			0.228013			0.114006	−	0.993480i	$-0.463632\pi$
$599$	5.58050			0.228013			0.114006	+	0.993480i	$0.463632\pi$
$600$	1.70156	−	0.323541i	0.0694661	−	0.0132085i
$601$	3.46433	+	6.00040i	0.141313	+	0.244761i	0.927991	−	0.372602i	$-0.121534\pi$
$601$	3.46433	+	6.00040i	0.141313	+	0.244761i	−0.786678	+	0.617363i	$0.788201\pi$
$602$	−16.1334	+	9.86374i	−0.657548	+	0.402016i
$603$	−1.49048	+	10.0110i	−0.0606969	+	0.407680i
$604$	−7.61538	+	13.1902i	−0.309866	+	0.536703i
$605$	9.21192	−	15.9555i	0.374518	−	0.648684i
$606$	−1.15811	+	0.220208i	−0.0470452	+	0.00894533i
$607$	14.7475	+	25.5434i	0.598582	+	1.03677i	0.993031	+	0.117856i	$0.0376021\pi$
$607$	14.7475	+	25.5434i	0.598582	+	1.03677i	−0.394449	+	0.918918i	$0.629065\pi$
$608$	2.62182	−	4.54112i	0.106329	−	0.184167i
$609$	−37.5028	−	12.0358i	−1.51969	−	0.487715i
$610$	2.11861	+	3.66954i	0.0857799	+	0.148575i
$611$	−5.69645	+	9.86654i	−0.230454	+	0.399158i
$612$	9.79006	−	3.86268i	0.395740	−	0.156140i
$613$	4.42149	+	7.65824i	0.178582	+	0.309313i	0.941395	−	0.337306i	$-0.109516\pi$
$613$	4.42149	+	7.65824i	0.178582	+	0.309313i	−0.762813	+	0.646619i	$0.776182\pi$
$614$	−28.3895			−1.14571
$615$	−0.746755	−	0.866166i	−0.0301121	−	0.0349272i
$616$	−12.6053	−	6.86094i	−0.507883	−	0.276435i
$617$	0.331920	−	0.574902i	0.0133626	−	0.0231447i	−0.859267	−	0.511528i	$-0.829080\pi$
$617$	0.331920	−	0.574902i	0.0133626	−	0.0231447i	0.872629	+	0.488383i	$0.162413\pi$
$618$	0.834707	−	2.39237i	0.0335768	−	0.0962351i
$619$	−0.111813	+	0.193666i	−0.00449415	+	0.00778410i	−0.868264	−	0.496103i	$-0.834764\pi$
$619$	−0.111813	+	0.193666i	−0.00449415	+	0.00778410i	0.863770	+	0.503887i	$0.168097\pi$
$620$	1.79599	+	3.11074i	0.0721285	+	0.124930i
$621$	36.5235	+	19.1772i	1.46564	+	0.769553i
$622$	−20.6637			−0.828540
$623$	34.1345	+	18.5790i	1.36757	+	0.744352i
$624$	9.95555	−	1.89298i	0.398541	−	0.0757799i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	22.1157			0.883922
$627$	16.2295	−	46.5155i	0.648142	−	1.85765i
$628$	−9.45814			−0.377421
$629$	−1.20705			−0.0481283
$630$	−3.09787	−	7.30775i	−0.123422	−	0.291148i
$631$	43.3179			1.72446			0.862229	−	0.506519i	$-0.169068\pi$
$631$	43.3179			1.72446			0.862229	+	0.506519i	$0.169068\pi$
$632$	16.9663			0.674881
$633$	−31.0932	+	5.91216i	−1.23584	+	0.234987i
$634$	31.0936			1.23489
$635$	10.2408	+	17.7376i	0.406395	+	0.703897i
$636$	0.462614	−	1.32590i	0.0183438	−	0.0525755i
$637$	18.6686	−	36.4535i	0.739675	−	1.44434i
$638$	46.6219			1.84578
$639$	2.58762	−	17.3801i	0.102365	−	0.687548i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−17.0097	+	29.4617i	−0.671843	+	1.16367i	0.305538	+	0.952180i	$0.401164\pi$
$641$	−17.0097	+	29.4617i	−0.671843	+	1.16367i	−0.977381	+	0.211486i	$0.932170\pi$
$642$	0.567685	−	0.107941i	0.0224047	−	0.00426011i
$643$	20.9518	−	36.2896i	0.826259	−	1.43112i	−0.0746939	−	0.997207i	$-0.523798\pi$
$643$	20.9518	−	36.2896i	0.826259	−	1.43112i	0.900953	−	0.433916i	$-0.142869\pi$
$644$	−17.9206	+	10.9564i	−0.706170	+	0.431743i
$645$	12.1615	−	2.31242i	0.478857	−	0.0910515i
$646$	−18.3956			−0.723764
$647$	−20.9082	−	36.2141i	−0.821987	−	1.42372i	−0.904201	−	0.427108i	$-0.859532\pi$
$647$	−20.9082	−	36.2141i	−0.821987	−	1.42372i	0.0822137	−	0.996615i	$-0.473801\pi$
$648$	−8.60966	−	2.62179i	−0.338219	−	0.102994i
$649$	0.178583	−	0.309314i	0.00700998	−	0.0121416i
$650$	−2.92541	−	5.06696i	−0.114744	−	0.198743i
$651$	12.1927	−	11.0583i	0.477868	−	0.433410i
$652$	−4.67319	+	8.09421i	−0.183016	+	0.316994i
$653$	−18.8386	−	32.6295i	−0.737213	−	1.27689i	−0.953745	−	0.300615i	$-0.902808\pi$
$653$	−18.8386	−	32.6295i	−0.737213	−	1.27689i	0.216532	−	0.976275i	$-0.430525\pi$
$654$	2.57722	−	7.38662i	0.100777	−	0.288840i
$655$	1.02889	−	1.78210i	0.0402022	−	0.0696323i
$656$	0.330137	−	0.571815i	0.0128897	−	0.0223256i
$657$	−6.48687	+	2.55940i	−0.253077	+	0.0998518i
$658$	0.129563	+	5.15026i	0.00505091	+	0.200778i
$659$	6.82604	+	11.8231i	0.265905	+	0.460561i	0.967800	−	0.251719i	$-0.0809960\pi$
$659$	6.82604	+	11.8231i	0.265905	+	0.460561i	−0.701895	+	0.712280i	$0.747663\pi$
$660$	6.13484	+	7.11584i	0.238798	+	0.276984i
$661$	−18.8203			−0.732026			−0.366013	−	0.930610i	$-0.619277\pi$
$661$	−18.8203			−0.732026			−0.366013	+	0.930610i	$0.619277\pi$
$662$	−27.1281			−1.05436
$663$	−23.2141	−	26.9262i	−0.901561	−	1.04573i
$664$	−4.66838	−	8.08588i	−0.181168	−	0.313793i
$665$	0.348897	+	13.8690i	0.0135296	+	0.537815i
$666$	0.808169	+	0.642115i	0.0313159	+	0.0248814i
$667$	34.1173	−	59.0929i	1.32103	−	2.28808i
$668$	1.09675	−	1.89963i	0.0424346	−	0.0734989i
$669$	9.19671	−	26.3588i	0.355565	−	1.01909i
$670$	1.68689	+	2.92178i	0.0651703	+	0.112878i
$671$	−11.4921	+	19.9049i	−0.443648	+	0.768422i
$672$	3.39442	−	3.07862i	0.130943	−	0.118760i
$673$	−3.45927	−	5.99164i	−0.133345	−	0.230961i	0.791619	−	0.611015i	$-0.209239\pi$
$673$	−3.45927	−	5.99164i	−0.133345	−	0.230961i	−0.924964	+	0.380055i	$0.875905\pi$
$674$	4.40226	−	7.62494i	0.169569	−	0.293702i
$675$	0.208321	+	5.19197i	0.00801829	+	0.199839i
$676$	−10.6161	−	18.3876i	−0.408310	−	0.707214i
$677$	−30.7836			−1.18311			−0.591555	−	0.806264i	$-0.701486\pi$
$677$	−30.7836			−1.18311			−0.591555	+	0.806264i	$0.701486\pi$
$678$	18.6076	−	3.53811i	0.714620	−	0.135880i
$679$	−0.524948	+	0.320946i	−0.0201457	+	0.0123168i
$680$	1.75409	−	3.03817i	0.0672661	−	0.116508i
$681$	24.4479	−	4.64860i	0.936844	−	0.178135i
$682$	−9.74210	+	16.8738i	−0.373044	+	0.646132i
$683$	0.631559	+	1.09389i	0.0241659	+	0.0418566i	0.877855	−	0.478926i	$-0.158974\pi$
$683$	0.631559	+	1.09389i	0.0241659	+	0.0418566i	−0.853690	+	0.520782i	$0.825640\pi$
$684$	12.3166	+	9.78588i	0.470935	+	0.374173i
$685$	−22.0744			−0.843418
$686$	−1.39610	−	18.4676i	−0.0533035	−	0.705095i
$687$	4.00293	−	11.4729i	0.152721	−	0.437717i
$688$	3.57361	+	6.18968i	0.136243	+	0.235979i
$689$	−4.74366			−0.180719
$690$	13.5087	−	2.56858i	0.514266	−	0.0977842i
$691$	−32.9767			−1.25449			−0.627246	−	0.778821i	$-0.715818\pi$
$691$	−32.9767			−1.25449			−0.627246	+	0.778821i	$0.715818\pi$
$692$	−19.7016			−0.748941
$693$	25.9272	−	34.3727i	0.984893	−	1.30571i
$694$	19.2968			0.732496
$695$	−0.663129			−0.0251539
$696$	−4.90414	+	14.0558i	−0.185891	+	0.532785i
$697$	−2.31636			−0.0877383
$698$	8.28885	+	14.3567i	0.313738	+	0.543410i
$699$	−40.0863	+	7.62214i	−1.51620	+	0.288296i
$700$	−2.32383	−	1.26483i	−0.0878326	−	0.0478062i
$701$	7.02372			0.265282			0.132641	−	0.991164i	$-0.457654\pi$
$701$	7.02372			0.265282			0.132641	+	0.991164i	$0.457654\pi$
$702$	1.21885	+	30.3773i	0.0460026	+	1.14652i
$703$	−0.902085	−	1.56246i	−0.0340228	−	0.0589292i
$704$	−2.71219	+	4.69765i	−0.102219	+	0.177049i
$705$	1.11107	−	3.18444i	0.0418451	−	0.119933i
$706$	−13.4978	+	23.3789i	−0.507997	+	0.879876i
$707$	1.58164	+	0.860869i	0.0594837	+	0.0323763i
$708$	0.0744686	+	0.0863766i	0.00279870	+	0.00324623i
$709$	−21.4818			−0.806768			−0.403384	−	0.915031i	$-0.632166\pi$
$709$	−21.4818			−0.806768			−0.403384	+	0.915031i	$0.632166\pi$
$710$	−2.92862	−	5.07252i	−0.109909	−	0.190368i
$711$	−7.49539	+	50.3439i	−0.281099	+	1.88804i
$712$	7.34444	−	12.7209i	0.275245	−	0.476738i
$713$	14.2583	+	24.6960i	0.533976	+	0.924874i
$714$	−15.3075	−	4.91264i	−0.572868	−	0.183851i
$715$	15.8685	−	27.4851i	0.593449	−	1.02788i
$716$	−3.78831	−	6.56155i	−0.141576	−	0.245217i
$717$	−36.7787	+	6.99322i	−1.37353	+	0.261167i
$718$	−5.87285	+	10.1721i	−0.219173	+	0.379619i
$719$	−18.1005	+	31.3510i	−0.675035	+	1.16919i	0.301424	+	0.953490i	$0.402538\pi$
$719$	−18.1005	+	31.3510i	−0.675035	+	1.16919i	−0.976459	+	0.215704i	$0.930795\pi$
$720$	−2.79064	+	1.10105i	−0.104001	+	0.0410338i
$721$	−3.30218	+	2.01891i	−0.122979	+	0.0751880i
$722$	−4.24784	−	7.35747i	−0.158088	−	0.273817i
$723$	−20.1042	+	3.82269i	−0.747685	+	0.142167i
$724$	19.5571			0.726835
$725$	8.59489			0.319206
$726$	−10.5124	+	30.1298i	−0.390152	+	1.11822i
$727$	−13.4185	−	23.2415i	−0.497664	−	0.861979i	0.502332	−	0.864675i	$-0.332475\pi$
$727$	−13.4185	−	23.2415i	−0.497664	−	0.861979i	−0.999996	+	0.00269527i	$0.999142\pi$
$728$	−13.5963	−	7.40032i	−0.503913	−	0.274274i
$729$	11.5832	−	24.3891i	0.429008	−	0.903301i
$730$	−1.16225	+	2.01308i	−0.0430169	+	0.0745075i
$731$	12.5368	−	21.7145i	0.463692	−	0.803138i
$732$	−4.79219	−	5.55850i	−0.177125	−	0.205448i
$733$	−5.59820	−	9.69636i	−0.206774	−	0.358143i	0.743922	−	0.668266i	$-0.232963\pi$
$733$	−5.59820	−	9.69636i	−0.206774	−	0.358143i	−0.950697	+	0.310123i	$0.899630\pi$
$734$	5.62339	−	9.73999i	0.207563	−	0.359510i
$735$	−3.41346	+	11.6339i	−0.125907	+	0.429124i
$736$	3.96948	+	6.87534i	0.146317	+	0.253429i
$737$	−9.15033	+	15.8488i	−0.337057	+	0.583799i
$738$	1.55089	+	1.23223i	0.0570892	+	0.0453591i
$739$	25.0873	+	43.4524i	0.922850	+	1.59842i	0.794983	+	0.606631i	$0.207480\pi$
$739$	25.0873	+	43.4524i	0.922850	+	1.59842i	0.127867	+	0.991791i	$0.459187\pi$
$740$	0.344069			0.0126482
$741$	17.5054	−	50.1724i	0.643076	−	1.84313i
$742$	−1.83014	+	1.11893i	−0.0671867	+	0.0410770i
$743$	−10.9343	+	18.9387i	−0.401139	+	0.694794i	−0.993864	−	0.110612i	$-0.964719\pi$
$743$	−10.9343	+	18.9387i	−0.401139	+	0.694794i	0.592724	+	0.805405i	$0.298052\pi$
$744$	−4.06244	−	4.71205i	−0.148936	−	0.172752i
$745$	2.79809	−	4.84644i	0.102514	−	0.177560i
$746$	−17.5298	−	30.3626i	−0.641813	−	1.11165i
$747$	26.0556	−	10.2803i	0.953324	−	0.376135i
$748$	19.0296			0.695793
$749$	−0.775289	−	0.421981i	−0.0283284	−	0.0154188i
$750$	1.13098	+	1.31183i	0.0412974	+	0.0479012i
$751$	16.1937	+	28.0482i	0.590915	+	1.02349i	0.994109	+	0.108381i	$0.0345665\pi$
$751$	16.1937	+	28.0482i	0.590915	+	1.02349i	−0.403194	+	0.915114i	$0.632100\pi$
$752$	1.94723			0.0710082
$753$	−10.9349	−	12.6835i	−0.398490	−	0.462211i
$754$	50.2872			1.83135
$755$	−15.2308			−0.554304
$756$	7.63558	+	11.4323i	0.277704	+	0.415789i
$757$	−5.06108			−0.183948			−0.0919740	−	0.995761i	$-0.529318\pi$
$757$	−5.06108			−0.183948			−0.0919740	+	0.995761i	$0.529318\pi$
$758$	−2.86903			−0.104208
$759$	48.7043	+	56.4924i	1.76785	+	2.05054i
$760$	5.24363			0.190207
$761$	4.64329	+	8.04242i	0.168319	+	0.291538i	0.937829	−	0.347097i	$-0.112833\pi$
$761$	4.64329	+	8.04242i	0.168319	+	0.291538i	−0.769510	+	0.638635i	$0.779499\pi$
$762$	−23.1643	−	26.8684i	−0.839154	−	0.973339i
$763$	−10.1957	+	6.23353i	−0.369110	+	0.225669i
$764$	6.50176			0.235225
$765$	8.24021	+	6.54710i	0.297925	+	0.236711i
$766$	11.6637	+	20.2021i	0.421426	+	0.729931i
$767$	0.192622	−	0.333631i	0.00695518	−	0.0120467i
$768$	−1.13098	−	1.31183i	−0.0408106	−	0.0473365i
$769$	−24.5112	+	42.4546i	−0.883896	+	1.53095i	−0.0369227	+	0.999318i	$0.511756\pi$
$769$	−24.5112	+	42.4546i	−0.883896	+	1.53095i	−0.846974	+	0.531635i	$0.821578\pi$
$770$	−0.360923	−	14.3470i	−0.0130068	−	0.517030i
$771$	−4.85626	+	13.9186i	−0.174894	+	0.501266i
$772$	16.9492			0.610015
$773$	−2.54319	−	4.40493i	−0.0914721	−	0.158434i	0.816659	−	0.577121i	$-0.195824\pi$
$773$	−2.54319	−	4.40493i	−0.0914721	−	0.158434i	−0.908131	+	0.418687i	$0.862491\pi$
$774$	−19.9453	+	7.86947i	−0.716920	+	0.282862i
$775$	−1.79599	+	3.11074i	−0.0645137	+	0.111741i
$776$	0.116278	+	0.201400i	0.00417414	+	0.00722983i
$777$	−0.333387	−	1.54107i	−0.0119602	−	0.0552856i
$778$	11.4813	−	19.8863i	0.411626	−	0.712957i
$779$	−1.73112	−	2.99839i	−0.0620238	−	0.107428i
$780$	6.61715	+	7.67527i	0.236932	+	0.274819i
$781$	15.8859	−	27.5152i	0.568443	−	0.984572i
$782$	13.9256	−	24.1199i	0.497979	−	0.862526i
$783$	−39.5412	−	20.7616i	−1.41309	−	0.741960i
$784$	−6.99115	+	0.351971i	−0.249684	+	0.0125704i
$785$	−4.72907	−	8.19099i	−0.168788	−	0.292349i
$786$	−1.17415	+	3.36524i	−0.0418805	+	0.120034i
$787$	50.2789			1.79225			0.896125	−	0.443802i	$-0.146371\pi$
$787$	50.2789			1.79225			0.896125	+	0.443802i	$0.146371\pi$
$788$	3.20284			0.114097
$789$	0.704093	−	0.133879i	0.0250664	−	0.00476621i
$790$	8.48313	+	14.6932i	0.301816	+	0.522761i
$791$	−25.4124	−	13.8317i	−0.903562	−	0.491798i
$792$	−12.7411	−	10.1232i	−0.452735	−	0.359712i
$793$	−12.3956	+	21.4698i	−0.440181	+	0.762415i
$794$	−16.3423	+	28.3057i	−0.579967	+	1.00453i
$795$	1.37957	−	0.262317i	0.0489285	−	0.00930342i
$796$	8.41802	+	14.5804i	0.298369	+	0.516790i
$797$	−8.23362	+	14.2610i	−0.291650	+	0.505152i	−0.974200	−	0.225687i	$-0.927537\pi$
$797$	−8.23362	+	14.2610i	−0.291650	+	0.505152i	0.682550	+	0.730839i	$0.260871\pi$
$798$	−5.08085	−	23.4860i	−0.179860	−	0.831397i
$799$	−3.41561	−	5.91601i	−0.120836	−	0.209294i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	34.5021	+	27.4130i	1.21907	+	0.968591i
$802$	15.2284	+	26.3763i	0.537732	+	0.931379i
$803$	−12.6090			−0.444962
$804$	−3.81567	−	4.42582i	−0.134568	−	0.156087i
$805$	−18.4488	−	10.0415i	−0.650235	−	0.353915i
$806$	−10.5080	+	18.2004i	−0.370128	+	0.641081i
$807$	−4.10151	+	11.7554i	−0.144380	+	0.413810i
$808$	0.340309	−	0.589432i	0.0119720	−	0.0207362i
$809$	−5.57600	−	9.65791i	−0.196042	−	0.339554i	0.751200	−	0.660075i	$-0.229475\pi$
$809$	−5.57600	−	9.65791i	−0.196042	−	0.339554i	−0.947242	+	0.320521i	$0.896142\pi$
$810$	−2.03429	−	8.76708i	−0.0714777	−	0.308044i
$811$	18.1639			0.637821			0.318911	−	0.947785i	$-0.396683\pi$
$811$	18.1639			0.637821			0.318911	+	0.947785i	$0.396683\pi$
$812$	19.4012	−	11.8616i	0.680849	−	0.416262i
$813$	−7.48120	+	1.42250i	−0.262377	+	0.0498893i
$814$	0.933178	+	1.61631i	0.0327079	+	0.0566517i
$815$	−9.34638			−0.327390
$816$	−2.00172	+	5.73716i	−0.0700742	+	0.200841i
$817$	37.4774			1.31117
$818$	−13.3108			−0.465402
$819$	27.9655	−	37.0750i	0.977195	−	1.29550i
$820$	0.660275			0.0230578
$821$	7.19761			0.251198			0.125599	−	0.992081i	$-0.459915\pi$
$821$	7.19761			0.251198			0.125599	+	0.992081i	$0.459915\pi$
$822$	37.5609	−	7.14196i	1.31009	−	0.249105i
$823$	−28.0672			−0.978361			−0.489181	−	0.872183i	$-0.662704\pi$
$823$	−28.0672			−0.978361			−0.489181	+	0.872183i	$0.662704\pi$
$824$	0.731446	+	1.26690i	0.0254811	+	0.0441346i
$825$	−3.09508	+	8.87085i	−0.107757	+	0.308843i
$826$	−0.00438111	−	0.174153i	−0.000152438	−	0.00605956i
$827$	29.0730			1.01097			0.505483	−	0.862836i	$-0.331314\pi$
$827$	29.0730			1.01097			0.505483	+	0.862836i	$0.331314\pi$
$828$	−22.1548	+	8.74121i	−0.769933	+	0.303778i
$829$	−9.93586	−	17.2094i	−0.345087	−	0.597708i	0.640283	−	0.768139i	$-0.278817\pi$
$829$	−9.93586	−	17.2094i	−0.345087	−	0.597708i	−0.985370	+	0.170431i	$0.945484\pi$
$830$	4.66838	−	8.08588i	0.162042	−	0.280665i
$831$	−22.1777	+	4.21694i	−0.769336	+	0.146284i
$832$	−2.92541	+	5.06696i	−0.101420	+	0.175665i
$833$	13.3324	+	20.6229i	0.461941	+	0.714540i
$834$	1.12836	−	0.214549i	0.0390718	−	0.00742924i
$835$	2.19351			0.0759094
$836$	14.2217	+	24.6327i	0.491868	+	0.851941i
$837$	15.7767	−	9.97274i	0.545324	−	0.344708i
$838$	−11.5272	+	19.9658i	−0.398202	+	0.689706i
$839$	−9.70999	−	16.8182i	−0.335226	−	0.580629i	0.648302	−	0.761383i	$-0.275479\pi$
$839$	−9.70999	−	16.8182i	−0.335226	−	0.580629i	−0.983528	+	0.180755i	$0.942146\pi$
$840$	4.36338	+	1.40034i	0.150551	+	0.0483164i
$841$	−22.4361	+	38.8605i	−0.773659	+	1.34002i
$842$	−16.8883	−	29.2515i	−0.582010	−	1.00807i
$843$	2.92808	−	8.39220i	0.100848	−	0.289043i
$844$	9.13664	−	15.8251i	0.314496	−	0.544723i
$845$	10.6161	−	18.3876i	0.365204	−	0.632551i
$846$	−0.860252	+	5.77801i	−0.0295761	+	0.198652i
$847$	41.5880	−	25.4264i	1.42898	−	0.873661i
$848$	0.405384	+	0.702146i	0.0139209	+	0.0241118i
$849$	11.4947	+	13.3328i	0.394498	+	0.457581i
$850$	3.50817			0.120329
$851$	2.73155			0.0936363
$852$	6.62440	+	7.68369i	0.226948	+	0.263239i
$853$	−4.27638	−	7.40691i	−0.146420	−	0.253608i	0.783482	−	0.621415i	$-0.213442\pi$
$853$	−4.27638	−	7.40691i	−0.146420	−	0.253608i	−0.929902	+	0.367807i	$0.880109\pi$
$854$	0.281933	+	11.2071i	0.00964754	+	0.383498i
$855$	−2.31654	+	15.5594i	−0.0792241	+	0.532120i
$856$	−0.166813	+	0.288928i	−0.00570154	+	0.00987535i
$857$	−0.922028	+	1.59700i	−0.0314959	+	0.0545525i	−0.881344	−	0.472476i	$-0.843360\pi$
$857$	−0.922028	+	1.59700i	−0.0314959	+	0.0545525i	0.849848	+	0.527028i	$0.176694\pi$
$858$	−18.1088	+	51.9018i	−0.618223	+	1.77190i
$859$	−1.48456	−	2.57133i	−0.0506525	−	0.0877326i	0.839587	−	0.543224i	$-0.182797\pi$
$859$	−1.48456	−	2.57133i	−0.0506525	−	0.0877326i	−0.890240	+	0.455492i	$0.849463\pi$
$860$	−3.57361	+	6.18968i	−0.121859	+	0.211066i
$861$	−0.639777	−	2.95735i	−0.0218035	−	0.100786i
$862$	7.80158	+	13.5127i	0.265723	+	0.460246i
$863$	−13.6213	+	23.5928i	−0.463675	+	0.803109i	−0.999141	−	0.0414480i	$-0.986803\pi$
$863$	−13.6213	+	23.5928i	−0.463675	+	0.803109i	0.535465	+	0.844557i	$0.320136\pi$
$864$	4.39222	−	2.77640i	0.149426	−	0.0944550i
$865$	−9.85078	−	17.0621i	−0.334937	−	0.580127i
$866$	−14.4129			−0.489772
$867$	−7.98497	+	1.51829i	−0.271184	+	0.0515638i
$868$	0.239000	+	9.50046i	0.00811218	+	0.322467i
$869$	−46.0157	+	79.7015i	−1.56097	+	2.70369i
$870$	−14.6248	+	2.78080i	−0.495826	+	0.0942780i
$871$	−9.86970	+	17.0948i	−0.334422	+	0.579236i
$872$	2.25839	+	3.91165i	0.0764789	+	0.132465i
$873$	−0.648982	+	0.256057i	−0.0219647	+	0.00866621i
$874$	41.6290			1.40812
$875$	−0.0665372	−	2.64491i	−0.00224937	−	0.0894144i
$876$	1.32633	−	3.80142i	0.0448127	−	0.128438i
$877$	19.4153	+	33.6284i	0.655609	+	1.13555i	0.981741	+	0.190224i	$0.0609215\pi$
$877$	19.4153	+	33.6284i	0.655609	+	1.13555i	−0.326131	+	0.945325i	$0.605745\pi$
$878$	−3.60584			−0.121691
$879$	−26.4041	+	5.02057i	−0.890588	+	0.169339i
$880$	−5.42437			−0.182856
$881$	−52.7479			−1.77712			−0.888560	−	0.458760i	$-0.848294\pi$
$881$	−52.7479			−1.77712			−0.888560	+	0.458760i	$0.848294\pi$
$882$	2.04416	−	20.9003i	0.0688305	−	0.703749i
$883$	30.3297			1.02068			0.510338	−	0.859974i	$-0.329520\pi$
$883$	30.3297			1.02068			0.510338	+	0.859974i	$0.329520\pi$
$884$	20.5257			0.690354
$885$	−0.0375700	+	0.107680i	−0.00126290	+	0.00361962i
$886$	−0.266687			−0.00895951
$887$	22.8255	+	39.5350i	0.766406	+	1.32745i	0.939500	+	0.342549i	$0.111290\pi$
$887$	22.8255	+	39.5350i	0.766406	+	1.32745i	−0.173094	+	0.984905i	$0.555377\pi$
$888$	−0.585455	+	0.111320i	−0.0196466	+	0.00373567i
$889$	1.36279	+	54.1722i	0.0457066	+	1.81688i
$890$	14.6889			0.492373
$891$	35.6673	−	33.3343i	1.19490	−	1.11674i
$892$	8.05899	+	13.9586i	0.269835	+	0.467368i
$893$	5.10528	−	8.84261i	0.170842	−	0.295907i
$894$	−3.19311	+	9.15183i	−0.106794	+	0.306083i
$895$	3.78831	−	6.56155i	0.126629	−	0.219328i
$896$	0.0665372	+	2.64491i	0.00222285	+	0.0883604i
$897$	52.5333	+	60.9337i	1.75404	+	2.03452i
$898$	33.6153			1.12176
$899$	−15.4363	−	26.7365i	−0.514830	−	0.891711i
$900$	−2.34886	−	1.86624i	−0.0782953	−	0.0622080i
$901$	1.42216	−	2.46325i	0.0473789	−	0.0820627i
$902$	1.79079	+	3.10174i	0.0596267	+	0.103277i
$903$	31.1860	+	10.0086i	1.03781	+	0.333064i
$904$	−5.46779	+	9.47049i	−0.181856	+	0.314984i
$905$	9.77856	+	16.9370i	0.325050	+	0.563004i
$906$	25.9161	−	4.92778i	0.861006	−	0.163715i
$907$	20.8464	−	36.1071i	0.692195	−	1.19892i	−0.278922	−	0.960314i	$-0.589977\pi$
$907$	20.8464	−	36.1071i	0.692195	−	1.19892i	0.971117	−	0.238603i	$-0.0766894\pi$
$908$	−7.18394	+	12.4429i	−0.238407	+	0.412933i
$909$	1.59868	+	1.27020i	0.0530247	+	0.0421298i
$910$	−0.389298	−	15.4749i	−0.0129051	−	0.512989i
$911$	−23.5950	−	40.8677i	−0.781737	−	1.35401i	−0.930929	−	0.365200i	$-0.881001\pi$
$911$	−23.5950	−	40.8677i	−0.781737	−	1.35401i	0.149192	−	0.988808i	$-0.452333\pi$
$912$	−8.92238	+	1.69653i	−0.295449	+	0.0561778i
$913$	50.6461			1.67614
$914$	−8.86739			−0.293307
$915$	2.41770	−	6.92941i	0.0799267	−	0.229079i
$916$	3.50773	+	6.07557i	0.115899	+	0.200742i
$917$	4.64504	−	2.83991i	0.153393	−	0.0937822i
$918$	−16.1395	−	8.47426i	−0.532683	−	0.279692i
$919$	−15.1278	+	26.2022i	−0.499021	+	0.864330i	−0.999999	−	0.00112980i	$-0.999640\pi$
$919$	−15.1278	+	26.2022i	−0.499021	+	0.864330i	0.500978	+	0.865460i	$0.332974\pi$
$920$	−3.96948	+	6.87534i	−0.130870	+	0.226673i
$921$	32.1079	+	37.2421i	1.05799	+	1.22717i
$922$	14.1466	+	24.5027i	0.465894	+	0.806952i
$923$	17.1348	−	29.6784i	0.564000	−	0.976876i
$924$	5.25598	+	24.2956i	0.172909	+	0.799266i
$925$	0.172034	+	0.297972i	0.00565645	+	0.00979726i
$926$	10.6916	−	18.5184i	0.351347	−	0.608552i
$927$	−4.08241	+	1.61072i	−0.134084	+	0.0529030i
$928$	−4.29745	−	7.44340i	−0.141071	−	0.244341i
$929$	31.8189			1.04395			0.521973	−	0.852962i	$-0.325196\pi$
$929$	31.8189			1.04395			0.521973	+	0.852962i	$0.325196\pi$
$930$	2.04953	−	5.87420i	0.0672068	−	0.192622i
$931$	−16.7312	+	32.6704i	−0.548342	+	1.07073i
$932$	11.7792	−	20.4022i	0.385842	−	0.668297i
$933$	23.3702	+	27.1072i	0.765106	+	0.887451i
$934$	6.52517	−	11.3019i	0.213510	−	0.369810i
$935$	9.51482	+	16.4802i	0.311168	+	0.538959i
$936$	−13.7428	−	10.9190i	−0.449196	−	0.356900i
$937$	4.61335			0.150711			0.0753557	−	0.997157i	$-0.475991\pi$
$937$	4.61335			0.150711			0.0753557	+	0.997157i	$0.475991\pi$
$938$	0.224482	+	8.92337i	0.00732960	+	0.291358i
$939$	−25.0124	−	29.0120i	−0.816248	−	0.946771i
$940$	0.973616	+	1.68635i	0.0317558	+	0.0550027i
$941$	−31.0380			−1.01181			−0.505904	−	0.862590i	$-0.668841\pi$
$941$	−31.0380			−1.01181			−0.505904	+	0.862590i	$0.668841\pi$
$942$	10.6969	+	12.4074i	0.348525	+	0.404256i
$943$	5.24190			0.170700
$944$	−0.0658445			−0.00214305
$945$	−6.08288	+	12.3288i	−0.197876	+	0.401055i
$946$	−38.7692			−1.26050
$947$	50.2359			1.63245			0.816223	−	0.577736i	$-0.196064\pi$
$947$	50.2359			1.63245			0.816223	+	0.577736i	$0.196064\pi$
$948$	−19.1884	−	22.2568i	−0.623212	−	0.722867i
$949$	−13.6003			−0.441484
$950$	2.62182	+	4.54112i	0.0850629	+	0.147333i
$951$	−35.1662	−	40.7895i	−1.14034	−	1.32269i
$952$	7.91898	−	4.84156i	0.256656	−	0.156916i
$953$	−5.05700			−0.163812			−0.0819062	−	0.996640i	$-0.526101\pi$
$953$	−5.05700			−0.163812			−0.0819062	+	0.996640i	$0.526101\pi$
$954$	−2.26256	+	0.892698i	−0.0732532	+	0.0289022i
$955$	3.25088	+	5.63069i	0.105196	+	0.182205i
$956$	10.8073	−	18.7188i	0.349534	−	0.605410i
$957$	−52.7283	−	61.1599i	−1.70446	−	1.97702i
$958$	20.0416	−	34.7131i	0.647516	−	1.12153i
$959$	−51.2971	−	27.9204i	−1.65647	−	0.901597i
$960$	0.570587	−	1.63537i	0.0184156	−	0.0527813i
$961$	−18.0977			−0.583798
$962$	1.00654	+	1.74338i	0.0324522	+	0.0562089i
$963$	−0.783639	−	0.622625i	−0.0252524	−	0.0200638i
$964$	5.90758	−	10.2322i	0.190270	−	0.329558i
$965$	8.47459	+	14.6784i	0.272807	+	0.472515i
$966$	34.6407	+	11.1173i	1.11455	+	0.357692i
$967$	9.51252	−	16.4762i	0.305902	−	0.529838i	−0.671560	−	0.740950i	$-0.734375\pi$
$967$	9.51252	−	16.4762i	0.305902	−	0.529838i	0.977462	+	0.211113i	$0.0677087\pi$
$968$	−9.21192	−	15.9555i	−0.296082	−	0.512830i
$969$	20.8050	+	24.1318i	0.668352	+	0.775225i
$970$	−0.116278	+	0.201400i	−0.00373347	+	0.00646655i
$971$	−26.9424	+	46.6656i	−0.864623	+	1.49757i	0.00279886	+	0.999996i	$0.499109\pi$
$971$	−26.9424	+	46.6656i	−0.864623	+	1.49757i	−0.867421	+	0.497574i	$0.834224\pi$
$972$	6.29799	+	14.2596i	0.202008	+	0.457376i
$973$	−1.54100	−	0.838748i	−0.0494022	−	0.0268890i
$974$	−14.2575	−	24.6947i	−0.456839	−	0.791268i
$975$	−3.33840	+	9.56825i	−0.106915	+	0.306429i
$976$	4.23722			0.135630
$977$	−33.1514			−1.06061			−0.530304	−	0.847808i	$-0.677922\pi$
$977$	−33.1514			−1.06061			−0.530304	+	0.847808i	$0.677922\pi$
$978$	15.9035	−	3.02394i	0.508537	−	0.0966949i
$979$	39.8390	+	69.0032i	1.27326	+	2.20535i
$980$	−3.80039	−	5.87852i	−0.121399	−	0.187783i
$981$	−12.6047	+	4.97322i	−0.402438	+	0.158783i
$982$	−6.92505	+	11.9945i	−0.220987	+	0.382761i
$983$	6.95122	−	12.0399i	0.221709	−	0.384012i	−0.733618	−	0.679562i	$-0.762170\pi$
$983$	6.95122	−	12.0399i	0.221709	−	0.384012i	0.955327	+	0.295550i	$0.0955030\pi$
$984$	−1.12350	+	0.213626i	−0.0358159	+	0.00681015i
$985$	1.60142	+	2.77374i	0.0510255	+	0.0883788i
$986$	−15.0762	+	26.1127i	−0.480124	+	0.831599i
$987$	6.60972	−	5.99479i	0.210390	−	0.190816i
$988$	15.3398	+	26.5693i	0.488023	+	0.845281i
$989$	−28.3708	+	49.1396i	−0.902138	+	1.56255i
$990$	2.39639	−	16.0957i	0.0761623	−	0.511555i
$991$	−0.921295	−	1.59573i	−0.0292659	−	0.0506900i	0.851022	−	0.525131i	$-0.175984\pi$
$991$	−0.921295	−	1.59573i	−0.0292659	−	0.0506900i	−0.880287	+	0.474441i	$0.842650\pi$
$992$	3.59197			0.114045
$993$	30.6812	+	35.5874i	0.973640	+	1.12933i
$994$	−0.389724	−	15.4919i	−0.0123613	−	0.491373i
$995$	−8.41802	+	14.5804i	−0.266869	+	0.462231i
$996$	−5.32744	+	15.2691i	−0.168806	+	0.483819i
$997$	−17.2937	+	29.9535i	−0.547696	+	0.948637i	0.450736	+	0.892657i	$0.351162\pi$
$997$	−17.2937	+	29.9535i	−0.547696	+	0.948637i	−0.998432	+	0.0559800i	$0.982172\pi$
$998$	−17.8754	−	30.9611i	−0.565835	−	0.980056i
$999$	−0.0716768	−	1.78640i	−0.00226775	−	0.0565191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.h.121.2	✓	12
3.2	odd	2		1890.2.i.f.1171.4		12
7.4	even	3		630.2.l.f.571.4	yes	12
9.2	odd	6		1890.2.l.h.1801.5		12
9.7	even	3		630.2.l.f.331.4	yes	12
21.11	odd	6		1890.2.l.h.361.5		12
63.11	odd	6		1890.2.i.f.991.4		12
63.25	even	3	inner	630.2.i.h.151.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.h.121.2	✓	12	1.1	even	1	trivial
630.2.i.h.151.2	yes	12	63.25	even	3	inner
630.2.l.f.331.4	yes	12	9.7	even	3
630.2.l.f.571.4	yes	12	7.4	even	3
1890.2.i.f.991.4		12	63.11	odd	6
1890.2.i.f.1171.4		12	3.2	odd	2
1890.2.l.h.361.5		12	21.11	odd	6
1890.2.l.h.1801.5		12	9.2	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.13098 - 1.31183i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.13098 - 1.31183i) q^{6} +(0.0665372 + 2.64491i) q^{7} +1.00000 q^{8} +(-0.441782 + 2.96729i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.13098 - 1.31183i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.13098 - 1.31183i) q^{6} +(0.0665372 + 2.64491i) q^{7} +1.00000 q^{8} +(-0.441782 + 2.96729i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.71219 + 4.69765i) q^{11} +(-1.13098 - 1.31183i) q^{12} +(-2.92541 + 5.06696i) q^{13} +(0.0665372 + 2.64491i) q^{14} +(0.570587 - 1.63537i) q^{15} +1.00000 q^{16} +(-1.75409 - 3.03817i) q^{17} +(-0.441782 + 2.96729i) q^{18} +(2.62182 - 4.54112i) q^{19} +(0.500000 + 0.866025i) q^{20} +(3.39442 - 3.07862i) q^{21} +(-2.71219 + 4.69765i) q^{22} +(3.96948 + 6.87534i) q^{23} +(-1.13098 - 1.31183i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.92541 + 5.06696i) q^{26} +(4.39222 - 2.77640i) q^{27} +(0.0665372 + 2.64491i) q^{28} +(-4.29745 - 7.44340i) q^{29} +(0.570587 - 1.63537i) q^{30} +3.59197 q^{31} +1.00000 q^{32} +(9.22992 - 1.75501i) q^{33} +(-1.75409 - 3.03817i) q^{34} +(-2.25729 + 1.38008i) q^{35} +(-0.441782 + 2.96729i) q^{36} +(0.172034 - 0.297972i) q^{37} +(2.62182 - 4.54112i) q^{38} +(9.95555 - 1.89298i) q^{39} +(0.500000 + 0.866025i) q^{40} +(0.330137 - 0.571815i) q^{41} +(3.39442 - 3.07862i) q^{42} +(3.57361 + 6.18968i) q^{43} +(-2.71219 + 4.69765i) q^{44} +(-2.79064 + 1.10105i) q^{45} +(3.96948 + 6.87534i) q^{46} +1.94723 q^{47} +(-1.13098 - 1.31183i) q^{48} +(-6.99115 + 0.351971i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-2.00172 + 5.73716i) q^{51} +(-2.92541 + 5.06696i) q^{52} +(0.405384 + 0.702146i) q^{53} +(4.39222 - 2.77640i) q^{54} -5.42437 q^{55} +(0.0665372 + 2.64491i) q^{56} +(-8.92238 + 1.69653i) q^{57} +(-4.29745 - 7.44340i) q^{58} -0.0658445 q^{59} +(0.570587 - 1.63537i) q^{60} +4.23722 q^{61} +3.59197 q^{62} +(-7.87763 - 0.971040i) q^{63} +1.00000 q^{64} -5.85082 q^{65} +(9.22992 - 1.75501i) q^{66} +3.37378 q^{67} +(-1.75409 - 3.03817i) q^{68} +(4.52987 - 12.9831i) q^{69} +(-2.25729 + 1.38008i) q^{70} -5.85724 q^{71} +(-0.441782 + 2.96729i) q^{72} +(1.16225 + 2.01308i) q^{73} +(0.172034 - 0.297972i) q^{74} +(1.70156 - 0.323541i) q^{75} +(2.62182 - 4.54112i) q^{76} +(-12.6053 - 6.86094i) q^{77} +(9.95555 - 1.89298i) q^{78} +16.9663 q^{79} +(0.500000 + 0.866025i) q^{80} +(-8.60966 - 2.62179i) q^{81} +(0.330137 - 0.571815i) q^{82} +(-4.66838 - 8.08588i) q^{83} +(3.39442 - 3.07862i) q^{84} +(1.75409 - 3.03817i) q^{85} +(3.57361 + 6.18968i) q^{86} +(-4.90414 + 14.0558i) q^{87} +(-2.71219 + 4.69765i) q^{88} +(7.34444 - 12.7209i) q^{89} +(-2.79064 + 1.10105i) q^{90} +(-13.5963 - 7.40032i) q^{91} +(3.96948 + 6.87534i) q^{92} +(-4.06244 - 4.71205i) q^{93} +1.94723 q^{94} +5.24363 q^{95} +(-1.13098 - 1.31183i) q^{96} +(0.116278 + 0.201400i) q^{97} +(-6.99115 + 0.351971i) q^{98} +(-12.7411 - 10.1232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9	\( 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} + 2 q^{13} + 8 q^{14} + 7 q^{15} + 12 q^{16} + 7 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{20} + 17 q^{21} - 7 q^{22} - 9 q^{23} + 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 8 q^{28} - 9 q^{29} + 7 q^{30} - 18 q^{31} + 12 q^{32} + 3 q^{33} + 7 q^{34} + 4 q^{35} - 4 q^{36} - 12 q^{37} + 14 q^{38} - 14 q^{39} + 6 q^{40} + q^{41} + 17 q^{42} + 7 q^{43} - 7 q^{44} - 5 q^{45} - 9 q^{46} - 14 q^{47} + 2 q^{48} - 24 q^{49} - 6 q^{50} - 3 q^{51} + 2 q^{52} + 2 q^{53} + 11 q^{54} - 14 q^{55} + 8 q^{56} - 14 q^{57} - 9 q^{58} - 58 q^{59} + 7 q^{60} + 22 q^{61} - 18 q^{62} - 13 q^{63} + 12 q^{64} + 4 q^{65} + 3 q^{66} + 44 q^{67} + 7 q^{68} - 18 q^{69} + 4 q^{70} + 10 q^{71} - 4 q^{72} + 6 q^{73} - 12 q^{74} + 5 q^{75} + 14 q^{76} - 23 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} - 4 q^{81} + q^{82} - 26 q^{83} + 17 q^{84} - 7 q^{85} + 7 q^{86} - 12 q^{87} - 7 q^{88} + 2 q^{89} - 5 q^{90} - 4 q^{91} - 9 q^{92} - 26 q^{93} - 14 q^{94} + 28 q^{95} + 2 q^{96} + 6 q^{97} - 24 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 + 2 * q^13 + 8 * q^14 + 7 * q^15 + 12 * q^16 + 7 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^20 + 17 * q^21 - 7 * q^22 - 9 * q^23 + 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 8 * q^28 - 9 * q^29 + 7 * q^30 - 18 * q^31 + 12 * q^32 + 3 * q^33 + 7 * q^34 + 4 * q^35 - 4 * q^36 - 12 * q^37 + 14 * q^38 - 14 * q^39 + 6 * q^40 + q^41 + 17 * q^42 + 7 * q^43 - 7 * q^44 - 5 * q^45 - 9 * q^46 - 14 * q^47 + 2 * q^48 - 24 * q^49 - 6 * q^50 - 3 * q^51 + 2 * q^52 + 2 * q^53 + 11 * q^54 - 14 * q^55 + 8 * q^56 - 14 * q^57 - 9 * q^58 - 58 * q^59 + 7 * q^60 + 22 * q^61 - 18 * q^62 - 13 * q^63 + 12 * q^64 + 4 * q^65 + 3 * q^66 + 44 * q^67 + 7 * q^68 - 18 * q^69 + 4 * q^70 + 10 * q^71 - 4 * q^72 + 6 * q^73 - 12 * q^74 + 5 * q^75 + 14 * q^76 - 23 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 - 4 * q^81 + q^82 - 26 * q^83 + 17 * q^84 - 7 * q^85 + 7 * q^86 - 12 * q^87 - 7 * q^88 + 2 * q^89 - 5 * q^90 - 4 * q^91 - 9 * q^92 - 26 * q^93 - 14 * q^94 + 28 * q^95 + 2 * q^96 + 6 * q^97 - 24 * q^98 - 27 * q^99

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