LMFDB - Embedded newform 630.2.j.h.421.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("630.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			421.1
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	630.421
Dual form			630.2.j.h.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.724745 - 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.72474 - 0.158919i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-1.94949 + 2.28024i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.724745 - 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.72474 - 0.158919i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-1.94949 + 2.28024i) q^{9} -1.00000 q^{10} +(0.275255 - 0.476756i) q^{11} +(-1.00000 + 1.41421i) q^{12} +(-2.22474 - 3.85337i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-1.00000 + 1.41421i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.00000 q^{17} +(1.00000 + 2.82843i) q^{18} -5.89898 q^{19} +(-0.500000 + 0.866025i) q^{20} +(1.72474 + 0.158919i) q^{21} +(-0.275255 - 0.476756i) q^{22} +(1.22474 + 2.12132i) q^{23} +(0.724745 + 1.57313i) q^{24} +(-0.500000 + 0.866025i) q^{25} -4.44949 q^{26} +(5.00000 + 1.41421i) q^{27} +1.00000 q^{28} +(-1.22474 + 2.12132i) q^{29} +(0.724745 + 1.57313i) q^{30} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.949490 - 0.0874863i) q^{33} +(-1.50000 + 2.59808i) q^{34} +1.00000 q^{35} +(2.94949 + 0.548188i) q^{36} -1.55051 q^{37} +(-2.94949 + 5.10867i) q^{38} +(-4.44949 + 6.29253i) q^{39} +(0.500000 + 0.866025i) q^{40} +(5.72474 + 9.91555i) q^{41} +(1.00000 - 1.41421i) q^{42} +(2.94949 - 5.10867i) q^{43} -0.550510 q^{44} +(2.94949 + 0.548188i) q^{45} +2.44949 q^{46} +(4.89898 - 8.48528i) q^{47} +(1.72474 + 0.158919i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} +(2.17423 + 4.71940i) q^{51} +(-2.22474 + 3.85337i) q^{52} -1.34847 q^{53} +(3.72474 - 3.62302i) q^{54} -0.550510 q^{55} +(0.500000 - 0.866025i) q^{56} +(4.27526 + 9.27987i) q^{57} +(1.22474 + 2.12132i) q^{58} +(-3.94949 - 6.84072i) q^{59} +(1.72474 + 0.158919i) q^{60} +(2.67423 - 4.63191i) q^{61} -2.00000 q^{62} +(-1.00000 - 2.82843i) q^{63} +1.00000 q^{64} +(-2.22474 + 3.85337i) q^{65} +(-0.550510 + 0.778539i) q^{66} +(-6.84847 - 11.8619i) q^{67} +(1.50000 + 2.59808i) q^{68} +(2.44949 - 3.46410i) q^{69} +(0.500000 - 0.866025i) q^{70} -8.44949 q^{71} +(1.94949 - 2.28024i) q^{72} -11.8990 q^{73} +(-0.775255 + 1.34278i) q^{74} +(1.72474 + 0.158919i) q^{75} +(2.94949 + 5.10867i) q^{76} +(0.275255 + 0.476756i) q^{77} +(3.22474 + 6.99964i) q^{78} +(-1.00000 + 1.73205i) q^{79} +1.00000 q^{80} +(-1.39898 - 8.89060i) q^{81} +11.4495 q^{82} +(3.55051 - 6.14966i) q^{83} +(-0.724745 - 1.57313i) q^{84} +(1.50000 + 2.59808i) q^{85} +(-2.94949 - 5.10867i) q^{86} +(4.22474 + 0.389270i) q^{87} +(-0.275255 + 0.476756i) q^{88} -10.8990 q^{89} +(1.94949 - 2.28024i) q^{90} +4.44949 q^{91} +(1.22474 - 2.12132i) q^{92} +(-2.00000 + 2.82843i) q^{93} +(-4.89898 - 8.48528i) q^{94} +(2.94949 + 5.10867i) q^{95} +(1.00000 - 1.41421i) q^{96} +(7.84847 - 13.5939i) q^{97} -1.00000 q^{98} +(0.550510 + 1.55708i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 2 * q^9	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 2 q^{9} - 4 q^{10} + 6 q^{11} - 4 q^{12} - 4 q^{13} + 2 q^{14} - 4 q^{15} - 2 q^{16} - 12 q^{17} + 4 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} - 6 q^{22} - 2 q^{24} - 2 q^{25} - 8 q^{26} + 20 q^{27} + 4 q^{28} - 2 q^{30} - 4 q^{31} + 2 q^{32} + 6 q^{33} - 6 q^{34} + 4 q^{35} + 2 q^{36} - 16 q^{37} - 2 q^{38} - 8 q^{39} + 2 q^{40} + 18 q^{41} + 4 q^{42} + 2 q^{43} - 12 q^{44} + 2 q^{45} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 6 q^{51} - 4 q^{52} + 24 q^{53} + 10 q^{54} - 12 q^{55} + 2 q^{56} + 22 q^{57} - 6 q^{59} + 2 q^{60} - 4 q^{61} - 8 q^{62} - 4 q^{63} + 4 q^{64} - 4 q^{65} - 12 q^{66} + 2 q^{67} + 6 q^{68} + 2 q^{70} - 24 q^{71} - 2 q^{72} - 28 q^{73} - 8 q^{74} + 2 q^{75} + 2 q^{76} + 6 q^{77} + 8 q^{78} - 4 q^{79} + 4 q^{80} + 14 q^{81} + 36 q^{82} + 24 q^{83} + 2 q^{84} + 6 q^{85} - 2 q^{86} + 12 q^{87} - 6 q^{88} - 24 q^{89} - 2 q^{90} + 8 q^{91} - 8 q^{93} + 2 q^{95} + 4 q^{96} + 2 q^{97} - 4 q^{98} + 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 2 * q^9 - 4 * q^10 + 6 * q^11 - 4 * q^12 - 4 * q^13 + 2 * q^14 - 4 * q^15 - 2 * q^16 - 12 * q^17 + 4 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 - 6 * q^22 - 2 * q^24 - 2 * q^25 - 8 * q^26 + 20 * q^27 + 4 * q^28 - 2 * q^30 - 4 * q^31 + 2 * q^32 + 6 * q^33 - 6 * q^34 + 4 * q^35 + 2 * q^36 - 16 * q^37 - 2 * q^38 - 8 * q^39 + 2 * q^40 + 18 * q^41 + 4 * q^42 + 2 * q^43 - 12 * q^44 + 2 * q^45 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 6 * q^51 - 4 * q^52 + 24 * q^53 + 10 * q^54 - 12 * q^55 + 2 * q^56 + 22 * q^57 - 6 * q^59 + 2 * q^60 - 4 * q^61 - 8 * q^62 - 4 * q^63 + 4 * q^64 - 4 * q^65 - 12 * q^66 + 2 * q^67 + 6 * q^68 + 2 * q^70 - 24 * q^71 - 2 * q^72 - 28 * q^73 - 8 * q^74 + 2 * q^75 + 2 * q^76 + 6 * q^77 + 8 * q^78 - 4 * q^79 + 4 * q^80 + 14 * q^81 + 36 * q^82 + 24 * q^83 + 2 * q^84 + 6 * q^85 - 2 * q^86 + 12 * q^87 - 6 * q^88 - 24 * q^89 - 2 * q^90 + 8 * q^91 - 8 * q^93 + 2 * q^95 + 4 * q^96 + 2 * q^97 - 4 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.724745	−	1.57313i	−0.418432	−	0.908248i
$3$	−0.724745	−	1.57313i	−0.418432	−	0.908248i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.72474	−	0.158919i	−0.704124	−	0.0648783i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−1.00000			−0.353553
$9$	−1.94949	+	2.28024i	−0.649830	+	0.760080i
$10$	−1.00000			−0.316228
$11$	0.275255	−	0.476756i	0.0829925	−	0.143747i	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	0.275255	−	0.476756i	0.0829925	−	0.143747i	0.904534	+	0.426401i	$0.140219\pi$
$12$	−1.00000	+	1.41421i	−0.288675	+	0.408248i
$13$	−2.22474	−	3.85337i	−0.617033	−	1.06873i	−0.990024	−	0.140898i	$-0.955001\pi$
$13$	−2.22474	−	3.85337i	−0.617033	−	1.06873i	0.372991	−	0.927835i	$-0.378332\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$	−1.00000	+	1.41421i	−0.258199	+	0.365148i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$	1.00000	+	2.82843i	0.235702	+	0.666667i
$19$	−5.89898			−1.35332			−0.676659	−	0.736296i	$-0.736573\pi$
$19$	−5.89898			−1.35332			−0.676659	+	0.736296i	$0.736573\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	1.72474	+	0.158919i	0.376370	+	0.0346789i
$22$	−0.275255	−	0.476756i	−0.0586846	−	0.101645i
$23$	1.22474	+	2.12132i	0.255377	+	0.442326i	0.964998	−	0.262258i	$-0.0844671\pi$
$23$	1.22474	+	2.12132i	0.255377	+	0.442326i	−0.709621	+	0.704584i	$0.751134\pi$
$24$	0.724745	+	1.57313i	0.147938	+	0.321114i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−4.44949			−0.872617
$27$	5.00000	+	1.41421i	0.962250	+	0.272166i
$28$	1.00000			0.188982
$29$	−1.22474	+	2.12132i	−0.227429	+	0.393919i	−0.957046	−	0.289938i	$-0.906365\pi$
$29$	−1.22474	+	2.12132i	−0.227429	+	0.393919i	0.729616	+	0.683857i	$0.239699\pi$
$30$	0.724745	+	1.57313i	0.132320	+	0.287213i
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.949490	−	0.0874863i	−0.165285	−	0.0152294i
$34$	−1.50000	+	2.59808i	−0.257248	+	0.445566i
$35$	1.00000			0.169031
$36$	2.94949	+	0.548188i	0.491582	+	0.0913647i
$37$	−1.55051			−0.254902			−0.127451	−	0.991845i	$-0.540680\pi$
$37$	−1.55051			−0.254902			−0.127451	+	0.991845i	$0.540680\pi$
$38$	−2.94949	+	5.10867i	−0.478470	+	0.828735i
$39$	−4.44949	+	6.29253i	−0.712489	+	1.00761i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	5.72474	+	9.91555i	0.894055	+	1.54855i	0.834970	+	0.550296i	$0.185485\pi$
$41$	5.72474	+	9.91555i	0.894055	+	1.54855i	0.0590851	+	0.998253i	$0.481182\pi$
$42$	1.00000	−	1.41421i	0.154303	−	0.218218i
$43$	2.94949	−	5.10867i	0.449793	−	0.779064i	−0.548579	−	0.836099i	$-0.684831\pi$
$43$	2.94949	−	5.10867i	0.449793	−	0.779064i	0.998372	+	0.0570343i	$0.0181644\pi$
$44$	−0.550510			−0.0829925
$45$	2.94949	+	0.548188i	0.439684	+	0.0817191i
$46$	2.44949			0.361158
$47$	4.89898	−	8.48528i	0.714590	−	1.23771i	−0.248528	−	0.968625i	$-0.579947\pi$
$47$	4.89898	−	8.48528i	0.714590	−	1.23771i	0.963118	−	0.269081i	$-0.0867199\pi$
$48$	1.72474	+	0.158919i	0.248945	+	0.0229379i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	2.17423	+	4.71940i	0.304454	+	0.660848i
$52$	−2.22474	+	3.85337i	−0.308517	+	0.534366i
$53$	−1.34847			−0.185226			−0.0926132	−	0.995702i	$-0.529522\pi$
$53$	−1.34847			−0.185226			−0.0926132	+	0.995702i	$0.529522\pi$
$54$	3.72474	−	3.62302i	0.506874	−	0.493031i
$55$	−0.550510			−0.0742308
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	4.27526	+	9.27987i	0.566271	+	1.22915i
$58$	1.22474	+	2.12132i	0.160817	+	0.278543i
$59$	−3.94949	−	6.84072i	−0.514180	−	0.890585i	−0.999865	−	0.0164515i	$-0.994763\pi$
$59$	−3.94949	−	6.84072i	−0.514180	−	0.890585i	0.485685	−	0.874134i	$-0.338570\pi$
$60$	1.72474	+	0.158919i	0.222664	+	0.0205163i
$61$	2.67423	−	4.63191i	0.342401	−	0.593055i	−0.642477	−	0.766305i	$-0.722093\pi$
$61$	2.67423	−	4.63191i	0.342401	−	0.593055i	0.984878	+	0.173249i	$0.0554267\pi$
$62$	−2.00000			−0.254000
$63$	−1.00000	−	2.82843i	−0.125988	−	0.356348i
$64$	1.00000			0.125000
$65$	−2.22474	+	3.85337i	−0.275946	+	0.477952i
$66$	−0.550510	+	0.778539i	−0.0677631	+	0.0958315i
$67$	−6.84847	−	11.8619i	−0.836674	−	1.44916i	−0.892660	−	0.450730i	$-0.851164\pi$
$67$	−6.84847	−	11.8619i	−0.836674	−	1.44916i	0.0559867	−	0.998432i	$-0.482170\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	2.44949	−	3.46410i	0.294884	−	0.417029i
$70$	0.500000	−	0.866025i	0.0597614	−	0.103510i
$71$	−8.44949			−1.00277			−0.501385	−	0.865224i	$-0.667176\pi$
$71$	−8.44949			−1.00277			−0.501385	+	0.865224i	$0.667176\pi$
$72$	1.94949	−	2.28024i	0.229750	−	0.268729i
$73$	−11.8990			−1.39267			−0.696335	−	0.717717i	$-0.745187\pi$
$73$	−11.8990			−1.39267			−0.696335	+	0.717717i	$0.745187\pi$
$74$	−0.775255	+	1.34278i	−0.0901216	+	0.156095i
$75$	1.72474	+	0.158919i	0.199156	+	0.0183503i
$76$	2.94949	+	5.10867i	0.338330	+	0.586004i
$77$	0.275255	+	0.476756i	0.0313682	+	0.0543314i
$78$	3.22474	+	6.99964i	0.365130	+	0.792553i
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	−0.916781	−	0.399390i	$-0.869222\pi$
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	0.804272	+	0.594261i	$0.202555\pi$
$80$	1.00000			0.111803
$81$	−1.39898	−	8.89060i	−0.155442	−	0.987845i
$82$	11.4495			1.26438
$83$	3.55051	−	6.14966i	0.389719	−	0.675013i	−0.602692	−	0.797974i	$-0.705905\pi$
$83$	3.55051	−	6.14966i	0.389719	−	0.675013i	0.992412	+	0.122960i	$0.0392388\pi$
$84$	−0.724745	−	1.57313i	−0.0790761	−	0.171643i
$85$	1.50000	+	2.59808i	0.162698	+	0.281801i
$86$	−2.94949	−	5.10867i	−0.318052	−	0.550882i
$87$	4.22474	+	0.389270i	0.452940	+	0.0417341i
$88$	−0.275255	+	0.476756i	−0.0293423	+	0.0508223i
$89$	−10.8990			−1.15529			−0.577645	−	0.816288i	$-0.696028\pi$
$89$	−10.8990			−1.15529			−0.577645	+	0.816288i	$0.696028\pi$
$90$	1.94949	−	2.28024i	0.205494	−	0.240358i
$91$	4.44949			0.466433
$92$	1.22474	−	2.12132i	0.127688	−	0.221163i
$93$	−2.00000	+	2.82843i	−0.207390	+	0.293294i
$94$	−4.89898	−	8.48528i	−0.505291	−	0.875190i
$95$	2.94949	+	5.10867i	0.302611	+	0.524138i
$96$	1.00000	−	1.41421i	0.102062	−	0.144338i
$97$	7.84847	−	13.5939i	0.796891	−	1.38026i	−0.124740	−	0.992189i	$-0.539810\pi$
$97$	7.84847	−	13.5939i	0.796891	−	1.38026i	0.921631	−	0.388067i	$-0.126857\pi$
$98$	−1.00000			−0.101015
$99$	0.550510	+	1.55708i	0.0553284	+	0.156492i
$100$	1.00000			0.100000
$101$	−2.44949	+	4.24264i	−0.243733	+	0.422159i	−0.961775	−	0.273842i	$-0.911706\pi$
$101$	−2.44949	+	4.24264i	−0.243733	+	0.422159i	0.718041	+	0.696000i	$0.245039\pi$
$102$	5.17423	+	0.476756i	0.512326	+	0.0472059i
$103$	−10.1237	−	17.5348i	−0.997520	−	1.72776i	−0.559712	−	0.828687i	$-0.689088\pi$
$103$	−10.1237	−	17.5348i	−0.997520	−	1.72776i	−0.437809	−	0.899068i	$-0.644245\pi$
$104$	2.22474	+	3.85337i	0.218154	+	0.377854i
$105$	−0.724745	−	1.57313i	−0.0707279	−	0.153522i
$106$	−0.674235	+	1.16781i	−0.0654875	+	0.113428i
$107$	6.79796			0.657183			0.328592	−	0.944472i	$-0.393426\pi$
$107$	6.79796			0.657183			0.328592	+	0.944472i	$0.393426\pi$
$108$	−1.27526	−	5.03723i	−0.122711	−	0.484708i
$109$	−12.4495			−1.19244			−0.596222	−	0.802819i	$-0.703332\pi$
$109$	−12.4495			−1.19244			−0.596222	+	0.802819i	$0.703332\pi$
$110$	−0.275255	+	0.476756i	−0.0262445	+	0.0454569i
$111$	1.12372	+	2.43916i	0.106659	+	0.231515i
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	8.44949	+	14.6349i	0.794861	+	1.37674i	0.922927	+	0.384974i	$0.125790\pi$
$113$	8.44949	+	14.6349i	0.794861	+	1.37674i	−0.128066	+	0.991766i	$0.540877\pi$
$114$	10.1742	+	0.937458i	0.952904	+	0.0878010i
$115$	1.22474	−	2.12132i	0.114208	−	0.197814i
$116$	2.44949			0.227429
$117$	13.1237	+	2.43916i	1.21329	+	0.225500i
$118$	−7.89898			−0.727160
$119$	1.50000	−	2.59808i	0.137505	−	0.238165i
$120$	1.00000	−	1.41421i	0.0912871	−	0.129099i
$121$	5.34847	+	9.26382i	0.486224	+	0.842165i
$122$	−2.67423	−	4.63191i	−0.242114	−	0.419353i
$123$	11.4495	−	16.1920i	1.03237	−	1.45999i
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$	1.00000			0.0894427
$126$	−2.94949	−	0.548188i	−0.262761	−	0.0488365i
$127$	13.1464			1.16656			0.583278	−	0.812272i	$-0.301770\pi$
$127$	13.1464			1.16656			0.583278	+	0.812272i	$0.301770\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−10.1742	−	0.937458i	−0.895791	−	0.0825385i
$130$	2.22474	+	3.85337i	0.195123	+	0.337963i
$131$	−4.34847	−	7.53177i	−0.379928	−	0.658054i	0.611124	−	0.791535i	$-0.290718\pi$
$131$	−4.34847	−	7.53177i	−0.379928	−	0.658054i	−0.991051	+	0.133481i	$0.957384\pi$
$132$	0.398979	+	0.866025i	0.0347267	+	0.0753778i
$133$	2.94949	−	5.10867i	0.255753	−	0.442978i
$134$	−13.6969			−1.18324
$135$	−1.27526	−	5.03723i	−0.109756	−	0.433536i
$136$	3.00000			0.257248
$137$	−1.62372	+	2.81237i	−0.138724	+	0.240277i	−0.927014	−	0.375027i	$-0.877633\pi$
$137$	−1.62372	+	2.81237i	−0.138724	+	0.240277i	0.788290	+	0.615304i	$0.210967\pi$
$138$	−1.77526	−	3.85337i	−0.151120	−	0.328021i
$139$	−4.39898	−	7.61926i	−0.373117	−	0.646257i	0.616927	−	0.787021i	$-0.288378\pi$
$139$	−4.39898	−	7.61926i	−0.373117	−	0.646257i	−0.990043	+	0.140764i	$0.955044\pi$
$140$	−0.500000	−	0.866025i	−0.0422577	−	0.0731925i
$141$	−16.8990	−	1.55708i	−1.42315	−	0.131130i
$142$	−4.22474	+	7.31747i	−0.354533	+	0.614069i
$143$	−2.44949			−0.204837
$144$	−1.00000	−	2.82843i	−0.0833333	−	0.235702i
$145$	2.44949			0.203419
$146$	−5.94949	+	10.3048i	−0.492383	+	0.852833i
$147$	−1.00000	+	1.41421i	−0.0824786	+	0.116642i
$148$	0.775255	+	1.34278i	0.0637256	+	0.110376i
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$	1.00000	−	1.41421i	0.0816497	−	0.115470i
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	0.994540	+	0.104357i	$0.0332784\pi$
$152$	5.89898			0.478470
$153$	5.84847	−	6.84072i	0.472821	−	0.553039i
$154$	0.550510			0.0443614
$155$	−1.00000	+	1.73205i	−0.0803219	+	0.139122i
$156$	7.67423	+	0.707107i	0.614431	+	0.0566139i
$157$	−4.67423	−	8.09601i	−0.373045	−	0.646132i	0.616988	−	0.786973i	$-0.288353\pi$
$157$	−4.67423	−	8.09601i	−0.373045	−	0.646132i	−0.990032	+	0.140841i	$0.955019\pi$
$158$	1.00000	+	1.73205i	0.0795557	+	0.137795i
$159$	0.977296	+	2.12132i	0.0775046	+	0.168232i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−2.44949			−0.193047
$162$	−8.39898	−	3.23375i	−0.659886	−	0.254067i
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$	5.72474	−	9.91555i	0.447027	−	0.774274i
$165$	0.398979	+	0.866025i	0.0310605	+	0.0674200i
$166$	−3.55051	−	6.14966i	−0.275573	−	0.477307i
$167$	12.6742	+	21.9524i	0.980762	+	1.69873i	0.659437	+	0.751760i	$0.270795\pi$
$167$	12.6742	+	21.9524i	0.980762	+	1.69873i	0.321325	+	0.946969i	$0.395872\pi$
$168$	−1.72474	−	0.158919i	−0.133067	−	0.0122608i
$169$	−3.39898	+	5.88721i	−0.261460	+	0.452862i
$170$	3.00000			0.230089
$171$	11.5000	−	13.4511i	0.879427	−	1.02863i
$172$	−5.89898			−0.449793
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$	2.44949	−	3.46410i	0.185695	−	0.262613i
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	0.275255	+	0.476756i	0.0207481	+	0.0359368i
$177$	−7.89898	+	11.1708i	−0.593724	+	0.839652i
$178$	−5.44949	+	9.43879i	−0.408457	+	0.707467i
$179$	6.00000			0.448461			0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000			0.448461			0.224231	+	0.974536i	$0.428013\pi$
$180$	−1.00000	−	2.82843i	−0.0745356	−	0.210819i
$181$	17.7980			1.32291			0.661456	−	0.749984i	$-0.269939\pi$
$181$	17.7980			1.32291			0.661456	+	0.749984i	$0.269939\pi$
$182$	2.22474	−	3.85337i	0.164909	−	0.285631i
$183$	−9.22474	−	0.849971i	−0.681913	−	0.0628317i
$184$	−1.22474	−	2.12132i	−0.0902894	−	0.156386i
$185$	0.775255	+	1.34278i	0.0569979	+	0.0987232i
$186$	1.44949	+	3.14626i	0.106282	+	0.230695i
$187$	−0.825765	+	1.43027i	−0.0603859	+	0.104592i
$188$	−9.79796			−0.714590
$189$	−3.72474	+	3.62302i	−0.270935	+	0.263536i
$190$	5.89898			0.427957
$191$	−3.55051	+	6.14966i	−0.256906	+	0.444974i	−0.965411	−	0.260731i	$-0.916036\pi$
$191$	−3.55051	+	6.14966i	−0.256906	+	0.444974i	0.708506	+	0.705705i	$0.249370\pi$
$192$	−0.724745	−	1.57313i	−0.0523040	−	0.113531i
$193$	−0.724745	−	1.25529i	−0.0521683	−	0.0903581i	0.838762	−	0.544498i	$-0.183280\pi$
$193$	−0.724745	−	1.25529i	−0.0521683	−	0.0903581i	−0.890930	+	0.454140i	$0.849947\pi$
$194$	−7.84847	−	13.5939i	−0.563487	−	0.975989i
$195$	7.67423	+	0.707107i	0.549563	+	0.0506370i
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	7.34847			0.523557			0.261778	−	0.965128i	$-0.415691\pi$
$197$	7.34847			0.523557			0.261778	+	0.965128i	$0.415691\pi$
$198$	1.62372	+	0.301783i	0.115393	+	0.0214468i
$199$	6.65153			0.471515			0.235757	−	0.971812i	$-0.424243\pi$
$199$	6.65153			0.471515			0.235757	+	0.971812i	$0.424243\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−13.6969	+	19.3704i	−0.966108	+	1.36628i
$202$	2.44949	+	4.24264i	0.172345	+	0.298511i
$203$	−1.22474	−	2.12132i	−0.0859602	−	0.148888i
$204$	3.00000	−	4.24264i	0.210042	−	0.297044i
$205$	5.72474	−	9.91555i	0.399834	−	0.692532i
$206$	−20.2474			−1.41071
$207$	−7.22474	−	1.34278i	−0.502154	−	0.0933298i
$208$	4.44949			0.308517
$209$	−1.62372	+	2.81237i	−0.112315	+	0.194536i
$210$	−1.72474	−	0.158919i	−0.119019	−	0.0109664i
$211$	3.34847	+	5.79972i	0.230518	+	0.399269i	0.957961	−	0.286899i	$-0.0926246\pi$
$211$	3.34847	+	5.79972i	0.230518	+	0.399269i	−0.727443	+	0.686169i	$0.759291\pi$
$212$	0.674235	+	1.16781i	0.0463066	+	0.0802054i
$213$	6.12372	+	13.2922i	0.419591	+	0.910764i
$214$	3.39898	−	5.88721i	0.232349	−	0.402441i
$215$	−5.89898			−0.402307
$216$	−5.00000	−	1.41421i	−0.340207	−	0.0962250i
$217$	2.00000			0.135769
$218$	−6.22474	+	10.7816i	−0.421593	+	0.730220i
$219$	8.62372	+	18.7187i	0.582737	+	1.26489i
$220$	0.275255	+	0.476756i	0.0185577	+	0.0321429i
$221$	6.67423	+	11.5601i	0.448958	+	0.777617i
$222$	2.67423	+	0.246405i	0.179483	+	0.0165376i
$223$	−3.32577	+	5.76039i	−0.222710	+	0.385745i	−0.955630	−	0.294570i	$-0.904824\pi$
$223$	−3.32577	+	5.76039i	−0.222710	+	0.385745i	0.732920	+	0.680315i	$0.238157\pi$
$224$	−1.00000			−0.0668153
$225$	−1.00000	−	2.82843i	−0.0666667	−	0.188562i
$226$	16.8990			1.12410
$227$	12.5227	−	21.6900i	0.831161	−	1.43961i	−0.0659571	−	0.997822i	$-0.521010\pi$
$227$	12.5227	−	21.6900i	0.831161	−	1.43961i	0.897118	−	0.441791i	$-0.145657\pi$
$228$	5.89898	−	8.34242i	0.390669	−	0.552490i
$229$	−0.325765	−	0.564242i	−0.0215272	−	0.0372862i	0.855061	−	0.518527i	$-0.173520\pi$
$229$	−0.325765	−	0.564242i	−0.0215272	−	0.0372862i	−0.876588	+	0.481241i	$0.840186\pi$
$230$	−1.22474	−	2.12132i	−0.0807573	−	0.139876i
$231$	0.550510	−	0.778539i	0.0362209	−	0.0512241i
$232$	1.22474	−	2.12132i	0.0804084	−	0.139272i
$233$	−18.5505			−1.21528			−0.607642	−	0.794211i	$-0.707885\pi$
$233$	−18.5505			−1.21528			−0.607642	+	0.794211i	$0.707885\pi$
$234$	8.67423	−	10.1459i	0.567052	−	0.663258i
$235$	−9.79796			−0.639148
$236$	−3.94949	+	6.84072i	−0.257090	+	0.445293i
$237$	3.44949	+	0.317837i	0.224068	+	0.0206457i
$238$	−1.50000	−	2.59808i	−0.0972306	−	0.168408i
$239$	−6.55051	−	11.3458i	−0.423717	−	0.733900i	0.572582	−	0.819847i	$-0.305942\pi$
$239$	−6.55051	−	11.3458i	−0.423717	−	0.733900i	−0.996300	+	0.0859473i	$0.972608\pi$
$240$	−0.724745	−	1.57313i	−0.0467821	−	0.101545i
$241$	−6.17423	+	10.6941i	−0.397717	+	0.688867i	−0.993444	−	0.114321i	$-0.963531\pi$
$241$	−6.17423	+	10.6941i	−0.397717	+	0.688867i	0.595726	+	0.803187i	$0.296864\pi$
$242$	10.6969			0.687625
$243$	−12.9722	+	8.64420i	−0.832167	+	0.554526i
$244$	−5.34847			−0.342401
$245$	−0.500000	+	0.866025i	−0.0319438	+	0.0553283i
$246$	−8.29796	−	18.0116i	−0.529059	−	1.14838i
$247$	13.1237	+	22.7310i	0.835043	+	1.44634i
$248$	1.00000	+	1.73205i	0.0635001	+	0.109985i
$249$	−12.2474	−	1.12848i	−0.776151	−	0.0715148i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−13.8990			−0.877296			−0.438648	−	0.898659i	$-0.644542\pi$
$251$	−13.8990			−0.877296			−0.438648	+	0.898659i	$0.644542\pi$
$252$	−1.94949	+	2.28024i	−0.122806	+	0.143642i
$253$	1.34847			0.0847775
$254$	6.57321	−	11.3851i	0.412440	−	0.714367i
$255$	3.00000	−	4.24264i	0.187867	−	0.265684i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.84847	+	4.93369i	0.177683	+	0.307755i	0.941086	−	0.338166i	$-0.109807\pi$
$257$	2.84847	+	4.93369i	0.177683	+	0.307755i	−0.763404	+	0.645922i	$0.776473\pi$
$258$	−5.89898	+	8.34242i	−0.367254	+	0.519376i
$259$	0.775255	−	1.34278i	0.0481720	−	0.0834364i
$260$	4.44949			0.275946
$261$	−2.44949	−	6.92820i	−0.151620	−	0.428845i
$262$	−8.69694			−0.537299
$263$	0.674235	−	1.16781i	0.0415751	−	0.0720102i	−0.844489	−	0.535573i	$-0.820096\pi$
$263$	0.674235	−	1.16781i	0.0415751	−	0.0720102i	0.886064	+	0.463563i	$0.153429\pi$
$264$	0.949490	+	0.0874863i	0.0584371	+	0.00538441i
$265$	0.674235	+	1.16781i	0.0414179	+	0.0717379i
$266$	−2.94949	−	5.10867i	−0.180845	−	0.313232i
$267$	7.89898	+	17.1455i	0.483410	+	1.04929i
$268$	−6.84847	+	11.8619i	−0.418337	+	0.724581i
$269$	23.1464			1.41126			0.705631	−	0.708579i	$-0.250664\pi$
$269$	23.1464			1.41126			0.705631	+	0.708579i	$0.250664\pi$
$270$	−5.00000	−	1.41421i	−0.304290	−	0.0860663i
$271$	21.3485			1.29683			0.648414	−	0.761288i	$-0.275433\pi$
$271$	21.3485			1.29683			0.648414	+	0.761288i	$0.275433\pi$
$272$	1.50000	−	2.59808i	0.0909509	−	0.157532i
$273$	−3.22474	−	6.99964i	−0.195170	−	0.423637i
$274$	1.62372	+	2.81237i	0.0980928	+	0.169902i
$275$	0.275255	+	0.476756i	0.0165985	+	0.0287495i
$276$	−4.22474	−	0.389270i	−0.254300	−	0.0234313i
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	−0.894503	−	0.447062i	$-0.852470\pi$
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	0.834419	+	0.551131i	$0.185804\pi$
$278$	−8.79796			−0.527667
$279$	5.89898	+	1.09638i	0.353163	+	0.0656383i
$280$	−1.00000			−0.0597614
$281$	12.0000	−	20.7846i	0.715860	−	1.23991i	−0.246767	−	0.969075i	$-0.579368\pi$
$281$	12.0000	−	20.7846i	0.715860	−	1.23991i	0.962627	−	0.270831i	$-0.0872985\pi$
$282$	−9.79796	+	13.8564i	−0.583460	+	0.825137i
$283$	8.00000	+	13.8564i	0.475551	+	0.823678i	0.999608	−	0.0280052i	$-0.00891551\pi$
$283$	8.00000	+	13.8564i	0.475551	+	0.823678i	−0.524057	+	0.851683i	$0.675582\pi$
$284$	4.22474	+	7.31747i	0.250692	+	0.434212i
$285$	5.89898	−	8.34242i	0.349425	−	0.494162i
$286$	−1.22474	+	2.12132i	−0.0724207	+	0.125436i
$287$	−11.4495			−0.675842
$288$	−2.94949	−	0.548188i	−0.173800	−	0.0323023i
$289$	−8.00000			−0.470588
$290$	1.22474	−	2.12132i	0.0719195	−	0.124568i
$291$	−27.0732	−	2.49454i	−1.58706	−	0.146232i
$292$	5.94949	+	10.3048i	0.348168	+	0.603044i
$293$	14.5732	+	25.2415i	0.851376	+	1.47463i	0.879967	+	0.475036i	$0.157565\pi$
$293$	14.5732	+	25.2415i	0.851376	+	1.47463i	−0.0285903	+	0.999591i	$0.509102\pi$
$294$	0.724745	+	1.57313i	0.0422680	+	0.0917469i
$295$	−3.94949	+	6.84072i	−0.229948	+	0.398282i
$296$	1.55051			0.0901216
$297$	2.05051	−	1.99451i	0.118983	−	0.115733i
$298$		0			0
$299$	5.44949	−	9.43879i	0.315152	−	0.545859i
$300$	−0.724745	−	1.57313i	−0.0418432	−	0.0908248i
$301$	2.94949	+	5.10867i	0.170006	+	0.294459i
$302$	−5.00000	−	8.66025i	−0.287718	−	0.498342i
$303$	8.44949	+	0.778539i	0.485411	+	0.0447259i
$304$	2.94949	−	5.10867i	0.169165	−	0.293002i
$305$	−5.34847			−0.306252
$306$	−3.00000	−	8.48528i	−0.171499	−	0.485071i
$307$	−27.4495			−1.56663			−0.783313	−	0.621628i	$-0.786472\pi$
$307$	−27.4495			−1.56663			−0.783313	+	0.621628i	$0.786472\pi$
$308$	0.275255	−	0.476756i	0.0156841	−	0.0271657i
$309$	−20.2474	+	28.6342i	−1.15184	+	1.62894i
$310$	1.00000	+	1.73205i	0.0567962	+	0.0983739i
$311$	0.550510	+	0.953512i	0.0312166	+	0.0540687i	0.881212	−	0.472722i	$-0.156729\pi$
$311$	0.550510	+	0.953512i	0.0312166	+	0.0540687i	−0.849995	+	0.526791i	$0.823395\pi$
$312$	4.44949	−	6.29253i	0.251903	−	0.356244i
$313$	4.60102	−	7.96920i	0.260065	−	0.450446i	−0.706194	−	0.708018i	$-0.749589\pi$
$313$	4.60102	−	7.96920i	0.260065	−	0.450446i	0.966259	+	0.257573i	$0.0829227\pi$
$314$	−9.34847			−0.527565
$315$	−1.94949	+	2.28024i	−0.109841	+	0.128477i
$316$	2.00000			0.112509
$317$	−0.123724	+	0.214297i	−0.00694905	+	0.0120361i	−0.869479	−	0.493970i	$-0.835545\pi$
$317$	−0.123724	+	0.214297i	−0.00694905	+	0.0120361i	0.862530	+	0.506006i	$0.168879\pi$
$318$	2.32577	+	0.214297i	0.130422	+	0.0120172i
$319$	0.674235	+	1.16781i	0.0377499	+	0.0653847i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−4.92679	−	10.6941i	−0.274986	−	0.596886i
$322$	−1.22474	+	2.12132i	−0.0682524	+	0.118217i
$323$	17.6969			0.984684
$324$	−7.00000	+	5.65685i	−0.388889	+	0.314270i
$325$	4.44949			0.246813
$326$	1.00000	−	1.73205i	0.0553849	−	0.0959294i
$327$	9.02270	+	19.5847i	0.498957	+	1.08304i
$328$	−5.72474	−	9.91555i	−0.316096	−	0.547495i
$329$	4.89898	+	8.48528i	0.270089	+	0.467809i
$330$	0.949490	+	0.0874863i	0.0522677	+	0.00481596i
$331$	−5.34847	+	9.26382i	−0.293978	+	0.509186i	−0.974747	−	0.223313i	$-0.928313\pi$
$331$	−5.34847	+	9.26382i	−0.293978	+	0.509186i	0.680768	+	0.732499i	$0.261646\pi$
$332$	−7.10102			−0.389719
$333$	3.02270	−	3.53553i	0.165643	−	0.193746i
$334$	25.3485			1.38701
$335$	−6.84847	+	11.8619i	−0.374172	+	0.648085i
$336$	−1.00000	+	1.41421i	−0.0545545	+	0.0771517i
$337$	−9.72474	−	16.8438i	−0.529741	−	0.917538i	−0.999398	−	0.0346890i	$-0.988956\pi$
$337$	−9.72474	−	16.8438i	−0.529741	−	0.917538i	0.469658	−	0.882849i	$-0.344377\pi$
$338$	3.39898	+	5.88721i	0.184880	+	0.320222i
$339$	16.8990	−	23.8988i	0.917827	−	1.29800i
$340$	1.50000	−	2.59808i	0.0813489	−	0.140900i
$341$	−1.10102			−0.0596236
$342$	−5.89898	−	16.6848i	−0.318980	−	0.902212i
$343$	1.00000			0.0539949
$344$	−2.94949	+	5.10867i	−0.159026	+	0.275441i
$345$	−4.22474	−	0.389270i	−0.227453	−	0.0209576i
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	−9.94949	−	17.2330i	−0.534117	−	0.925117i	−0.999206	−	0.0398531i	$-0.987311\pi$
$347$	−9.94949	−	17.2330i	−0.534117	−	0.925117i	0.465089	−	0.885264i	$-0.346022\pi$
$348$	−1.77526	−	3.85337i	−0.0951637	−	0.206562i
$349$	−15.0227	+	26.0201i	−0.804147	+	1.39282i	0.112719	+	0.993627i	$0.464044\pi$
$349$	−15.0227	+	26.0201i	−0.804147	+	1.39282i	−0.916865	+	0.399196i	$0.869289\pi$
$350$	−1.00000			−0.0534522
$351$	−5.67423	−	22.4131i	−0.302868	−	1.19632i
$352$	0.550510			0.0293423
$353$	−5.84847	+	10.1298i	−0.311283	+	0.539157i	−0.978640	−	0.205580i	$-0.934092\pi$
$353$	−5.84847	+	10.1298i	−0.311283	+	0.539157i	0.667358	+	0.744737i	$0.267425\pi$
$354$	5.72474	+	12.4261i	0.304267	+	0.660442i
$355$	4.22474	+	7.31747i	0.224226	+	0.388371i
$356$	5.44949	+	9.43879i	0.288822	+	0.500255i
$357$	−5.17423	−	0.476756i	−0.273850	−	0.0252326i
$358$	3.00000	−	5.19615i	0.158555	−	0.274625i
$359$	22.0454			1.16351			0.581756	−	0.813363i	$-0.302366\pi$
$359$	22.0454			1.16351			0.581756	+	0.813363i	$0.302366\pi$
$360$	−2.94949	−	0.548188i	−0.155452	−	0.0288921i
$361$	15.7980			0.831472
$362$	8.89898	−	15.4135i	0.467720	−	0.810115i
$363$	10.6969	−	15.1278i	0.561444	−	0.794001i
$364$	−2.22474	−	3.85337i	−0.116608	−	0.201972i
$365$	5.94949	+	10.3048i	0.311411	+	0.539379i
$366$	−5.34847	+	7.56388i	−0.279569	+	0.395370i
$367$	−7.67423	+	13.2922i	−0.400592	+	0.693845i	−0.993797	−	0.111206i	$-0.964529\pi$
$367$	−7.67423	+	13.2922i	−0.400592	+	0.693845i	0.593206	+	0.805051i	$0.297862\pi$
$368$	−2.44949			−0.127688
$369$	−33.7702	−	6.27647i	−1.75800	−	0.326740i
$370$	1.55051			0.0806072
$371$	0.674235	−	1.16781i	0.0350045	−	0.0606296i
$372$	3.44949	+	0.317837i	0.178848	+	0.0164791i
$373$	13.4495	+	23.2952i	0.696388	+	1.20618i	0.969710	+	0.244257i	$0.0785441\pi$
$373$	13.4495	+	23.2952i	0.696388	+	1.20618i	−0.273322	+	0.961923i	$0.588123\pi$
$374$	0.825765	+	1.43027i	0.0426993	+	0.0739574i
$375$	−0.724745	−	1.57313i	−0.0374257	−	0.0812362i
$376$	−4.89898	+	8.48528i	−0.252646	+	0.437595i
$377$	10.8990			0.561326
$378$	1.27526	+	5.03723i	0.0655920	+	0.259087i
$379$	2.55051			0.131011			0.0655055	−	0.997852i	$-0.479134\pi$
$379$	2.55051			0.131011			0.0655055	+	0.997852i	$0.479134\pi$
$380$	2.94949	−	5.10867i	0.151306	−	0.262069i
$381$	−9.52781	−	20.6811i	−0.488124	−	1.05952i
$382$	3.55051	+	6.14966i	0.181660	+	0.314644i
$383$	−13.3485	−	23.1202i	−0.682075	−	1.18139i	−0.974347	−	0.225053i	$-0.927744\pi$
$383$	−13.3485	−	23.1202i	−0.682075	−	1.18139i	0.292272	−	0.956335i	$-0.405589\pi$
$384$	−1.72474	−	0.158919i	−0.0880155	−	0.00810978i
$385$	0.275255	−	0.476756i	0.0140283	−	0.0242977i
$386$	−1.44949			−0.0737771
$387$	5.89898	+	16.6848i	0.299862	+	0.848138i
$388$	−15.6969			−0.796891
$389$	−15.7980	+	27.3629i	−0.800988	+	1.38735i	0.117978	+	0.993016i	$0.462359\pi$
$389$	−15.7980	+	27.3629i	−0.800988	+	1.38735i	−0.918966	+	0.394336i	$0.870975\pi$
$390$	4.44949	−	6.29253i	0.225309	−	0.318635i
$391$	−3.67423	−	6.36396i	−0.185814	−	0.321839i
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$	−8.69694	+	12.2993i	−0.438703	+	0.620419i
$394$	3.67423	−	6.36396i	0.185105	−	0.320612i
$395$	2.00000			0.100631
$396$	1.07321	−	1.25529i	0.0539310	−	0.0630809i
$397$	−32.0454			−1.60831			−0.804156	−	0.594418i	$-0.797383\pi$
$397$	−32.0454			−1.60831			−0.804156	+	0.594418i	$0.797383\pi$
$398$	3.32577	−	5.76039i	0.166706	−	0.288742i
$399$	−10.1742	−	0.937458i	−0.509349	−	0.0469316i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−4.50000	−	7.79423i	−0.224719	−	0.389225i	0.731516	−	0.681824i	$-0.238813\pi$
$401$	−4.50000	−	7.79423i	−0.224719	−	0.389225i	−0.956235	+	0.292599i	$0.905480\pi$
$402$	9.92679	+	21.5471i	0.495103	+	1.07467i
$403$	−4.44949	+	7.70674i	−0.221645	+	0.383900i
$404$	4.89898			0.243733
$405$	−7.00000	+	5.65685i	−0.347833	+	0.281091i
$406$	−2.44949			−0.121566
$407$	−0.426786	+	0.739215i	−0.0211550	+	0.0366415i
$408$	−2.17423	−	4.71940i	−0.107641	−	0.233645i
$409$	0.376276	+	0.651729i	0.0186056	+	0.0322259i	0.875178	−	0.483800i	$-0.160744\pi$
$409$	0.376276	+	0.651729i	0.0186056	+	0.0322259i	−0.856573	+	0.516026i	$0.827411\pi$
$410$	−5.72474	−	9.91555i	−0.282725	−	0.489694i
$411$	5.60102	+	0.516080i	0.276278	+	0.0254564i
$412$	−10.1237	+	17.5348i	−0.498760	+	0.863878i
$413$	7.89898			0.388683
$414$	−4.77526	+	5.58542i	−0.234691	+	0.274509i
$415$	−7.10102			−0.348575
$416$	2.22474	−	3.85337i	0.109077	−	0.188927i
$417$	−8.79796	+	12.4422i	−0.430838	+	0.609297i
$418$	1.62372	+	2.81237i	0.0794190	+	0.137558i
$419$	6.79796	+	11.7744i	0.332102	+	0.575218i	0.982924	−	0.184013i	$-0.0589088\pi$
$419$	6.79796	+	11.7744i	0.332102	+	0.575218i	−0.650822	+	0.759231i	$0.725576\pi$
$420$	−1.00000	+	1.41421i	−0.0487950	+	0.0690066i
$421$	9.22474	−	15.9777i	0.449587	−	0.778707i	−0.548772	−	0.835972i	$-0.684905\pi$
$421$	9.22474	−	15.9777i	0.449587	−	0.778707i	0.998359	+	0.0572650i	$0.0182380\pi$
$422$	6.69694			0.326002
$423$	9.79796	+	27.7128i	0.476393	+	1.34744i
$424$	1.34847			0.0654875
$425$	1.50000	−	2.59808i	0.0727607	−	0.126025i
$426$	14.5732	+	1.34278i	0.706075	+	0.0650580i
$427$	2.67423	+	4.63191i	0.129415	+	0.224154i
$428$	−3.39898	−	5.88721i	−0.164296	−	0.284569i
$429$	1.77526	+	3.85337i	0.0857101	+	0.186043i
$430$	−2.94949	+	5.10867i	−0.142237	+	0.246362i
$431$	−12.4949			−0.601858			−0.300929	−	0.953647i	$-0.597297\pi$
$431$	−12.4949			−0.601858			−0.300929	+	0.953647i	$0.597297\pi$
$432$	−3.72474	+	3.62302i	−0.179207	+	0.174313i
$433$	−32.5959			−1.56646			−0.783230	−	0.621732i	$-0.786429\pi$
$433$	−32.5959			−1.56646			−0.783230	+	0.621732i	$0.786429\pi$
$434$	1.00000	−	1.73205i	0.0480015	−	0.0831411i
$435$	−1.77526	−	3.85337i	−0.0851170	−	0.184755i
$436$	6.22474	+	10.7816i	0.298111	+	0.516344i
$437$	−7.22474	−	12.5136i	−0.345606	−	0.598608i
$438$	20.5227	+	1.89097i	0.980613	+	0.0903540i
$439$	−13.6742	+	23.6845i	−0.652636	+	1.13040i	0.329845	+	0.944035i	$0.393003\pi$
$439$	−13.6742	+	23.6845i	−0.652636	+	1.13040i	−0.982481	+	0.186363i	$0.940330\pi$
$440$	0.550510			0.0262445
$441$	2.94949	+	0.548188i	0.140452	+	0.0261042i
$442$	13.3485			0.634922
$443$	17.8485	−	30.9145i	0.848006	−	1.46879i	−0.0349782	−	0.999388i	$-0.511136\pi$
$443$	17.8485	−	30.9145i	0.848006	−	1.46879i	0.882985	−	0.469402i	$-0.155530\pi$
$444$	1.55051	−	2.19275i	0.0735840	−	0.104063i
$445$	5.44949	+	9.43879i	0.258331	+	0.447442i
$446$	3.32577	+	5.76039i	0.157480	+	0.272763i
$447$		0			0
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	−6.30306			−0.297460			−0.148730	−	0.988878i	$-0.547519\pi$
$449$	−6.30306			−0.297460			−0.148730	+	0.988878i	$0.547519\pi$
$450$	−2.94949	−	0.548188i	−0.139040	−	0.0258418i
$451$	6.30306			0.296800
$452$	8.44949	−	14.6349i	0.397431	−	0.688370i
$453$	−17.2474	−	1.58919i	−0.810356	−	0.0746665i
$454$	−12.5227	−	21.6900i	−0.587720	−	1.01796i
$455$	−2.22474	−	3.85337i	−0.104298	−	0.180649i
$456$	−4.27526	−	9.27987i	−0.200207	−	0.434570i
$457$	16.7247	−	28.9681i	0.782351	−	1.35507i	−0.148219	−	0.988955i	$-0.547354\pi$
$457$	16.7247	−	28.9681i	0.782351	−	1.35507i	0.930569	−	0.366116i	$-0.119313\pi$
$458$	−0.651531			−0.0304440
$459$	−15.0000	−	4.24264i	−0.700140	−	0.198030i
$460$	−2.44949			−0.114208
$461$	−3.67423	+	6.36396i	−0.171126	+	0.296399i	−0.938814	−	0.344425i	$-0.888074\pi$
$461$	−3.67423	+	6.36396i	−0.171126	+	0.296399i	0.767688	+	0.640824i	$0.221407\pi$
$462$	−0.398979	−	0.866025i	−0.0185622	−	0.0402911i
$463$	14.0000	+	24.2487i	0.650635	+	1.12693i	0.982969	+	0.183771i	$0.0588306\pi$
$463$	14.0000	+	24.2487i	0.650635	+	1.12693i	−0.332334	+	0.943162i	$0.607836\pi$
$464$	−1.22474	−	2.12132i	−0.0568574	−	0.0984798i
$465$	3.44949	+	0.317837i	0.159966	+	0.0147393i
$466$	−9.27526	+	16.0652i	−0.429668	+	0.744207i
$467$	23.9444			1.10801			0.554007	−	0.832512i	$-0.313098\pi$
$467$	23.9444			1.10801			0.554007	+	0.832512i	$0.313098\pi$
$468$	−4.44949	−	12.5851i	−0.205678	−	0.581744i
$469$	13.6969			0.632466
$470$	−4.89898	+	8.48528i	−0.225973	+	0.391397i
$471$	−9.34847	+	13.2207i	−0.430755	+	0.609179i
$472$	3.94949	+	6.84072i	0.181790	+	0.314870i
$473$	−1.62372	−	2.81237i	−0.0746589	−	0.129313i
$474$	2.00000	−	2.82843i	0.0918630	−	0.129914i
$475$	2.94949	−	5.10867i	0.135332	−	0.234402i
$476$	−3.00000			−0.137505
$477$	2.62883	−	3.07483i	0.120366	−	0.140787i
$478$	−13.1010			−0.599227
$479$	13.4722	−	23.3345i	0.615560	−	1.06618i	−0.374726	−	0.927136i	$-0.622263\pi$
$479$	13.4722	−	23.3345i	0.615560	−	1.06618i	0.990286	−	0.139046i	$-0.0444036\pi$
$480$	−1.72474	−	0.158919i	−0.0787235	−	0.00725361i
$481$	3.44949	+	5.97469i	0.157283	+	0.272422i
$482$	6.17423	+	10.6941i	0.281229	+	0.487102i
$483$	1.77526	+	3.85337i	0.0807769	+	0.175334i
$484$	5.34847	−	9.26382i	0.243112	−	0.421083i
$485$	−15.6969			−0.712761
$486$	1.00000	+	15.5563i	0.0453609	+	0.705650i
$487$	−22.4949			−1.01934			−0.509671	−	0.860370i	$-0.670233\pi$
$487$	−22.4949			−1.01934			−0.509671	+	0.860370i	$0.670233\pi$
$488$	−2.67423	+	4.63191i	−0.121057	+	0.209677i
$489$	−1.44949	−	3.14626i	−0.0655482	−	0.142279i
$490$	0.500000	+	0.866025i	0.0225877	+	0.0391230i
$491$	−5.17423	−	8.96204i	−0.233510	−	0.404451i	0.725329	−	0.688403i	$-0.241688\pi$
$491$	−5.17423	−	8.96204i	−0.233510	−	0.404451i	−0.958839	+	0.283952i	$0.908354\pi$
$492$	−19.7474	−	1.81954i	−0.890284	−	0.0820311i
$493$	3.67423	−	6.36396i	0.165479	−	0.286618i
$494$	26.2474			1.18093
$495$	1.07321	−	1.25529i	0.0482374	−	0.0564213i
$496$	2.00000			0.0898027
$497$	4.22474	−	7.31747i	0.189506	−	0.328234i
$498$	−7.10102	+	10.0424i	−0.318204	+	0.450009i
$499$	18.6237	+	32.2572i	0.833712	+	1.44403i	0.895074	+	0.445917i	$0.147122\pi$
$499$	18.6237	+	32.2572i	0.833712	+	1.44403i	−0.0613621	+	0.998116i	$0.519544\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	25.3485	−	35.8481i	1.13249	−	1.60158i
$502$	−6.94949	+	12.0369i	−0.310171	+	0.537232i
$503$	23.3939			1.04308			0.521541	−	0.853226i	$-0.325357\pi$
$503$	23.3939			1.04308			0.521541	+	0.853226i	$0.325357\pi$
$504$	1.00000	+	2.82843i	0.0445435	+	0.125988i
$505$	4.89898			0.218002
$506$	0.674235	−	1.16781i	0.0299734	−	0.0519154i
$507$	11.7247	+	1.08032i	0.520714	+	0.0479788i
$508$	−6.57321	−	11.3851i	−0.291639	−	0.505134i
$509$	−5.87628	−	10.1780i	−0.260461	−	0.451132i	0.705903	−	0.708308i	$-0.250541\pi$
$509$	−5.87628	−	10.1780i	−0.260461	−	0.451132i	−0.966365	+	0.257176i	$0.917208\pi$
$510$	−2.17423	−	4.71940i	−0.0962767	−	0.208978i
$511$	5.94949	−	10.3048i	0.263190	−	0.455858i
$512$	−1.00000			−0.0441942
$513$	−29.4949	−	8.34242i	−1.30223	−	0.368327i
$514$	5.69694			0.251281
$515$	−10.1237	+	17.5348i	−0.446105	+	0.772676i
$516$	4.27526	+	9.27987i	0.188208	+	0.408524i
$517$	−2.69694	−	4.67123i	−0.118611	−	0.205441i
$518$	−0.775255	−	1.34278i	−0.0340628	−	0.0589984i
$519$	−10.3485	−	0.953512i	−0.454247	−	0.0418545i
$520$	2.22474	−	3.85337i	0.0975615	−	0.168982i
$521$	1.65153			0.0723549			0.0361774	−	0.999345i	$-0.488482\pi$
$521$	1.65153			0.0723549			0.0361774	+	0.999345i	$0.488482\pi$
$522$	−7.22474	−	1.34278i	−0.316218	−	0.0587719i
$523$	−29.5959			−1.29414			−0.647070	−	0.762431i	$-0.724006\pi$
$523$	−29.5959			−1.29414			−0.647070	+	0.762431i	$0.724006\pi$
$524$	−4.34847	+	7.53177i	−0.189964	+	0.329027i
$525$	−1.00000	+	1.41421i	−0.0436436	+	0.0617213i
$526$	−0.674235	−	1.16781i	−0.0293980	−	0.0509189i
$527$	3.00000	+	5.19615i	0.130682	+	0.226348i
$528$	0.550510	−	0.778539i	0.0239579	−	0.0338816i
$529$	8.50000	−	14.7224i	0.369565	−	0.640106i
$530$	1.34847			0.0585738
$531$	23.2980	+	4.33013i	1.01105	+	0.187912i
$532$	−5.89898			−0.255753
$533$	25.4722	−	44.1191i	1.10332	−	1.91101i
$534$	18.7980	+	1.73205i	0.813467	+	0.0749532i
$535$	−3.39898	−	5.88721i	−0.146951	−	0.254526i
$536$	6.84847	+	11.8619i	0.295809	+	0.512356i
$537$	−4.34847	−	9.43879i	−0.187650	−	0.407314i
$538$	11.5732	−	20.0454i	0.498957	−	0.864218i
$539$	−0.550510			−0.0237122
$540$	−3.72474	+	3.62302i	−0.160287	+	0.155910i
$541$	10.6969			0.459897			0.229949	−	0.973203i	$-0.426144\pi$
$541$	10.6969			0.459897			0.229949	+	0.973203i	$0.426144\pi$
$542$	10.6742	−	18.4883i	0.458498	−	0.794141i
$543$	−12.8990	−	27.9985i	−0.553548	−	1.20153i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	6.22474	+	10.7816i	0.266639	+	0.461832i
$546$	−7.67423	−	0.707107i	−0.328427	−	0.0302614i
$547$	7.84847	−	13.5939i	0.335576	−	0.581235i	−0.648019	−	0.761624i	$-0.724402\pi$
$547$	7.84847	−	13.5939i	0.335576	−	0.581235i	0.983595	+	0.180389i	$0.0577356\pi$
$548$	3.24745			0.138724
$549$	5.34847	+	15.1278i	0.228267	+	0.645637i
$550$	0.550510			0.0234738
$551$	7.22474	−	12.5136i	0.307784	−	0.533098i
$552$	−2.44949	+	3.46410i	−0.104257	+	0.147442i
$553$	−1.00000	−	1.73205i	−0.0425243	−	0.0736543i
$554$	1.00000	+	1.73205i	0.0424859	+	0.0735878i
$555$	1.55051	−	2.19275i	0.0658155	−	0.0930772i
$556$	−4.39898	+	7.61926i	−0.186558	+	0.323128i
$557$	−7.59592			−0.321849			−0.160925	−	0.986967i	$-0.551448\pi$
$557$	−7.59592			−0.321849			−0.160925	+	0.986967i	$0.551448\pi$
$558$	3.89898	−	4.56048i	0.165057	−	0.193060i
$559$	−26.2474			−1.11015
$560$	−0.500000	+	0.866025i	−0.0211289	+	0.0365963i
$561$	2.84847	+	0.262459i	0.120262	+	0.0110810i
$562$	−12.0000	−	20.7846i	−0.506189	−	0.876746i
$563$	17.9722	+	31.1288i	0.757438	+	1.31192i	0.944153	+	0.329506i	$0.106882\pi$
$563$	17.9722	+	31.1288i	0.757438	+	1.31192i	−0.186716	+	0.982414i	$0.559784\pi$
$564$	7.10102	+	15.4135i	0.299007	+	0.649025i
$565$	8.44949	−	14.6349i	0.355473	−	0.615697i
$566$	16.0000			0.672530
$567$	8.39898	+	3.23375i	0.352724	+	0.135805i
$568$	8.44949			0.354533
$569$	15.6464	−	27.1004i	0.655932	−	1.13611i	−0.325727	−	0.945464i	$-0.605609\pi$
$569$	15.6464	−	27.1004i	0.655932	−	1.13611i	0.981659	−	0.190644i	$-0.0610577\pi$
$570$	−4.27526	−	9.27987i	−0.179071	−	0.388691i
$571$	−12.1742	−	21.0864i	−0.509476	−	0.882438i	−0.999940	−	0.0109766i	$-0.996506\pi$
$571$	−12.1742	−	21.0864i	−0.509476	−	0.882438i	0.490464	−	0.871462i	$-0.336827\pi$
$572$	1.22474	+	2.12132i	0.0512092	+	0.0886969i
$573$	12.2474	+	1.12848i	0.511645	+	0.0471431i
$574$	−5.72474	+	9.91555i	−0.238946	+	0.413867i
$575$	−2.44949			−0.102151
$576$	−1.94949	+	2.28024i	−0.0812287	+	0.0950100i
$577$	−29.8990			−1.24471			−0.622355	−	0.782735i	$-0.713824\pi$
$577$	−29.8990			−1.24471			−0.622355	+	0.782735i	$0.713824\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	−1.44949	+	2.04989i	−0.0602387	+	0.0851904i
$580$	−1.22474	−	2.12132i	−0.0508548	−	0.0880830i
$581$	3.55051	+	6.14966i	0.147300	+	0.255131i
$582$	−15.6969	+	22.1988i	−0.650659	+	0.920171i
$583$	−0.371173	+	0.642891i	−0.0153724	+	0.0266258i
$584$	11.8990			0.492383
$585$	−4.44949	−	12.5851i	−0.183964	−	0.520328i
$586$	29.1464			1.20403
$587$	7.37628	−	12.7761i	0.304451	−	0.527325i	−0.672688	−	0.739927i	$-0.734860\pi$
$587$	7.37628	−	12.7761i	0.304451	−	0.527325i	0.977139	+	0.212601i	$0.0681935\pi$
$588$	1.72474	+	0.158919i	0.0711273	+	0.00655369i
$589$	5.89898	+	10.2173i	0.243063	+	0.420998i
$590$	3.94949	+	6.84072i	0.162598	+	0.281628i
$591$	−5.32577	−	11.5601i	−0.219073	−	0.475520i
$592$	0.775255	−	1.34278i	0.0318628	−	0.0551880i
$593$	−2.20204			−0.0904270			−0.0452135	−	0.998977i	$-0.514397\pi$
$593$	−2.20204			−0.0904270			−0.0452135	+	0.998977i	$0.514397\pi$
$594$	−0.702041	−	2.77305i	−0.0288051	−	0.113780i
$595$	−3.00000			−0.122988
$596$		0			0
$597$	−4.82066	−	10.4637i	−0.197297	−	0.428252i
$598$	−5.44949	−	9.43879i	−0.222846	−	0.385981i
$599$	3.79796	+	6.57826i	0.155180	+	0.268780i	0.933125	−	0.359553i	$-0.117071\pi$
$599$	3.79796	+	6.57826i	0.155180	+	0.268780i	−0.777944	+	0.628333i	$0.783737\pi$
$600$	−1.72474	−	0.158919i	−0.0704124	−	0.00648783i
$601$	−7.27526	+	12.6011i	−0.296764	+	0.514010i	−0.975394	−	0.220470i	$-0.929241\pi$
$601$	−7.27526	+	12.6011i	−0.296764	+	0.514010i	0.678630	+	0.734480i	$0.262574\pi$
$602$	5.89898			0.240424
$603$	40.3990	+	7.50850i	1.64517	+	0.305770i
$604$	−10.0000			−0.406894
$605$	5.34847	−	9.26382i	0.217446	−	0.376628i
$606$	4.89898	−	6.92820i	0.199007	−	0.281439i
$607$	−1.79796	−	3.11416i	−0.0729769	−	0.126400i	0.827228	−	0.561867i	$-0.189917\pi$
$607$	−1.79796	−	3.11416i	−0.0729769	−	0.126400i	−0.900205	+	0.435467i	$0.856583\pi$
$608$	−2.94949	−	5.10867i	−0.119618	−	0.207184i
$609$	−2.44949	+	3.46410i	−0.0992583	+	0.140372i
$610$	−2.67423	+	4.63191i	−0.108277	+	0.187541i
$611$	−43.5959			−1.76370
$612$	−8.84847	−	1.64456i	−0.357678	−	0.0664776i
$613$	31.3939			1.26799			0.633993	−	0.773338i	$-0.281415\pi$
$613$	31.3939			1.26799			0.633993	+	0.773338i	$0.281415\pi$
$614$	−13.7247	+	23.7720i	−0.553886	+	0.959358i
$615$	−19.7474	−	1.81954i	−0.796294	−	0.0733708i
$616$	−0.275255	−	0.476756i	−0.0110903	−	0.0192090i
$617$	−15.5227	−	26.8861i	−0.624921	−	1.08239i	−0.988556	−	0.150853i	$-0.951798\pi$
$617$	−15.5227	−	26.8861i	−0.624921	−	1.08239i	0.363636	−	0.931541i	$-0.381535\pi$
$618$	14.6742	+	31.8519i	0.590284	+	1.28127i
$619$	14.6464	−	25.3684i	0.588690	−	1.01964i	−0.405715	−	0.914000i	$-0.632977\pi$
$619$	14.6464	−	25.3684i	0.588690	−	1.01964i	0.994404	−	0.105641i	$-0.0336893\pi$
$620$	2.00000			0.0803219
$621$	3.12372	+	12.3387i	0.125351	+	0.495133i
$622$	1.10102			0.0441469
$623$	5.44949	−	9.43879i	0.218329	−	0.378157i
$624$	−3.22474	−	6.99964i	−0.129093	−	0.280210i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−4.60102	−	7.96920i	−0.183894	−	0.318513i
$627$	5.60102	+	0.516080i	0.223683	+	0.0206103i
$628$	−4.67423	+	8.09601i	−0.186522	+	0.323066i
$629$	4.65153			0.185469
$630$	1.00000	+	2.82843i	0.0398410	+	0.112687i
$631$	18.6515			0.742506			0.371253	−	0.928532i	$-0.378928\pi$
$631$	18.6515			0.742506			0.371253	+	0.928532i	$0.378928\pi$
$632$	1.00000	−	1.73205i	0.0397779	−	0.0688973i
$633$	6.69694	−	9.47090i	0.266179	−	0.376435i
$634$	0.123724	+	0.214297i	0.00491372	+	0.00851082i
$635$	−6.57321	−	11.3851i	−0.260850	−	0.451806i
$636$	1.34847	−	1.90702i	0.0534703	−	0.0756184i
$637$	−2.22474	+	3.85337i	−0.0881476	+	0.152676i
$638$	1.34847			0.0533864
$639$	16.4722	−	19.2669i	0.651630	−	0.762185i
$640$	−1.00000			−0.0395285
$641$	−9.94949	+	17.2330i	−0.392981	+	0.680663i	−0.992841	−	0.119442i	$-0.961890\pi$
$641$	−9.94949	+	17.2330i	−0.392981	+	0.680663i	0.599860	+	0.800105i	$0.295223\pi$
$642$	−11.7247	−	1.08032i	−0.462739	−	0.0426369i
$643$	1.47730	+	2.55875i	0.0582589	+	0.100907i	0.893684	−	0.448697i	$-0.148112\pi$
$643$	1.47730	+	2.55875i	0.0582589	+	0.100907i	−0.835425	+	0.549604i	$0.814778\pi$
$644$	1.22474	+	2.12132i	0.0482617	+	0.0835917i
$645$	4.27526	+	9.27987i	0.168338	+	0.365395i
$646$	8.84847	−	15.3260i	0.348138	−	0.602993i
$647$	−44.9444			−1.76695			−0.883473	−	0.468482i	$-0.844801\pi$
$647$	−44.9444			−1.76695			−0.883473	+	0.468482i	$0.844801\pi$
$648$	1.39898	+	8.89060i	0.0549571	+	0.349256i
$649$	−4.34847			−0.170692
$650$	2.22474	−	3.85337i	0.0872617	−	0.151142i
$651$	−1.44949	−	3.14626i	−0.0568100	−	0.123312i
$652$	−1.00000	−	1.73205i	−0.0391630	−	0.0678323i
$653$	−16.5959	−	28.7450i	−0.649448	−	1.12488i	−0.983255	−	0.182236i	$-0.941666\pi$
$653$	−16.5959	−	28.7450i	−0.649448	−	1.12488i	0.333806	−	0.942642i	$-0.391667\pi$
$654$	21.4722	+	1.97846i	0.839629	+	0.0773637i
$655$	−4.34847	+	7.53177i	−0.169909	+	0.294291i
$656$	−11.4495			−0.447027
$657$	23.1969	−	27.1325i	0.904999	−	1.05854i
$658$	9.79796			0.381964
$659$	6.24745	−	10.8209i	0.243366	−	0.421522i	−0.718305	−	0.695728i	$-0.755082\pi$
$659$	6.24745	−	10.8209i	0.243366	−	0.421522i	0.961671	+	0.274206i	$0.0884150\pi$
$660$	0.550510	−	0.778539i	0.0214286	−	0.0303046i
$661$	13.1464	+	22.7703i	0.511337	+	0.885661i	0.999914	+	0.0131405i	$0.00418286\pi$
$661$	13.1464	+	22.7703i	0.511337	+	0.885661i	−0.488577	+	0.872521i	$0.662484\pi$
$662$	5.34847	+	9.26382i	0.207874	+	0.360049i
$663$	13.3485	−	18.8776i	0.518412	−	0.733145i
$664$	−3.55051	+	6.14966i	−0.137787	+	0.238653i
$665$	−5.89898			−0.228753
$666$	−1.55051	−	4.38551i	−0.0600811	−	0.169935i
$667$	−6.00000			−0.232321
$668$	12.6742	−	21.9524i	0.490381	−	0.849365i
$669$	11.4722	+	1.05705i	0.443541	+	0.0408680i
$670$	6.84847	+	11.8619i	0.264579	+	0.458265i
$671$	−1.47219	−	2.54991i	−0.0568334	−	0.0984383i
$672$	0.724745	+	1.57313i	0.0279576	+	0.0606849i
$673$	19.6969	−	34.1161i	0.759261	−	1.31508i	−0.183967	−	0.982932i	$-0.558894\pi$
$673$	19.6969	−	34.1161i	0.759261	−	1.31508i	0.943228	−	0.332146i	$-0.107773\pi$
$674$	−19.4495			−0.749166
$675$	−3.72474	+	3.62302i	−0.143365	+	0.139450i
$676$	6.79796			0.261460
$677$	−6.42679	+	11.1315i	−0.247001	+	0.427819i	−0.962692	−	0.270598i	$-0.912779\pi$
$677$	−6.42679	+	11.1315i	−0.247001	+	0.427819i	0.715691	+	0.698417i	$0.246112\pi$
$678$	−12.2474	−	26.5843i	−0.470360	−	1.02096i
$679$	7.84847	+	13.5939i	0.301197	+	0.521688i
$680$	−1.50000	−	2.59808i	−0.0575224	−	0.0996317i
$681$	−43.1969	−	3.98018i	−1.65531	−	0.152521i
$682$	−0.550510	+	0.953512i	−0.0210801	+	0.0365119i
$683$	18.7980			0.719284			0.359642	−	0.933090i	$-0.382899\pi$
$683$	18.7980			0.719284			0.359642	+	0.933090i	$0.382899\pi$
$684$	−17.3990	−	3.23375i	−0.665267	−	0.123646i
$685$	3.24745			0.124079
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	−0.651531	+	0.921404i	−0.0248574	+	0.0351537i
$688$	2.94949	+	5.10867i	0.112448	+	0.194766i
$689$	3.00000	+	5.19615i	0.114291	+	0.197958i
$690$	−2.44949	+	3.46410i	−0.0932505	+	0.131876i
$691$	−1.79796	+	3.11416i	−0.0683976	+	0.118468i	−0.898196	−	0.439595i	$-0.855122\pi$
$691$	−1.79796	+	3.11416i	−0.0683976	+	0.118468i	0.829799	+	0.558063i	$0.188455\pi$
$692$	−6.00000			−0.228086
$693$	−1.62372	−	0.301783i	−0.0616802	−	0.0114638i
$694$	−19.8990			−0.755355
$695$	−4.39898	+	7.61926i	−0.166863	+	0.289015i
$696$	−4.22474	−	0.389270i	−0.160139	−	0.0147552i
$697$	−17.1742	−	29.7466i	−0.650521	−	1.12673i
$698$	15.0227	+	26.0201i	0.568618	+	0.984875i
$699$	13.4444	+	29.1824i	0.508513	+	1.10378i
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	31.8434			1.20271			0.601354	−	0.798983i	$-0.294628\pi$
$701$	31.8434			1.20271			0.601354	+	0.798983i	$0.294628\pi$
$702$	−22.2474	−	6.29253i	−0.839676	−	0.237496i
$703$	9.14643			0.344964
$704$	0.275255	−	0.476756i	0.0103741	−	0.0179684i
$705$	7.10102	+	15.4135i	0.267440	+	0.580505i
$706$	5.84847	+	10.1298i	0.220110	+	0.381242i
$707$	−2.44949	−	4.24264i	−0.0921225	−	0.159561i
$708$	13.6237	+	1.25529i	0.512011	+	0.0471769i
$709$	11.6742	−	20.2204i	0.438435	−	0.759392i	−0.559134	−	0.829077i	$-0.688866\pi$
$709$	11.6742	−	20.2204i	0.438435	−	0.759392i	0.997569	+	0.0696855i	$0.0221996\pi$
$710$	8.44949			0.317104
$711$	−2.00000	−	5.65685i	−0.0750059	−	0.212149i
$712$	10.8990			0.408457
$713$	2.44949	−	4.24264i	0.0917341	−	0.158888i
$714$	−3.00000	+	4.24264i	−0.112272	+	0.158777i
$715$	1.22474	+	2.12132i	0.0458029	+	0.0793329i
$716$	−3.00000	−	5.19615i	−0.112115	−	0.194189i
$717$	−13.1010	+	18.5276i	−0.489267	+	0.691927i
$718$	11.0227	−	19.0919i	0.411364	−	0.712503i
$719$	44.4495			1.65769			0.828843	−	0.559481i	$-0.189000\pi$
$719$	44.4495			1.65769			0.828843	+	0.559481i	$0.189000\pi$
$720$	−1.94949	+	2.28024i	−0.0726532	+	0.0849795i
$721$	20.2474			0.754054
$722$	7.89898	−	13.6814i	0.293970	−	0.509170i
$723$	21.2980	+	1.96240i	0.792080	+	0.0729825i
$724$	−8.89898	−	15.4135i	−0.330728	−	0.572838i
$725$	−1.22474	−	2.12132i	−0.0454859	−	0.0787839i
$726$	−7.75255	−	16.8277i	−0.287724	−	0.624534i
$727$	8.12372	−	14.0707i	0.301292	−	0.521854i	−0.675137	−	0.737693i	$-0.735915\pi$
$727$	8.12372	−	14.0707i	0.301292	−	0.521854i	0.976429	+	0.215839i	$0.0692487\pi$
$728$	−4.44949			−0.164909
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$	11.8990			0.440401
$731$	−8.84847	+	15.3260i	−0.327272	+	0.566853i
$732$	3.87628	+	8.41385i	0.143271	+	0.310985i
$733$	23.1237	+	40.0515i	0.854094	+	1.47933i	0.877483	+	0.479608i	$0.159221\pi$
$733$	23.1237	+	40.0515i	0.854094	+	1.47933i	−0.0233885	+	0.999726i	$0.507445\pi$
$734$	7.67423	+	13.2922i	0.283261	+	0.490623i
$735$	1.72474	+	0.158919i	0.0636182	+	0.00586180i
$736$	−1.22474	+	2.12132i	−0.0451447	+	0.0781929i
$737$	−7.54031			−0.277751
$738$	−22.3207	+	26.1076i	−0.821635	+	0.961033i
$739$	−13.2474			−0.487315			−0.243658	−	0.969861i	$-0.578347\pi$
$739$	−13.2474			−0.487315			−0.243658	+	0.969861i	$0.578347\pi$
$740$	0.775255	−	1.34278i	0.0284989	−	0.0493616i
$741$	26.2474	−	37.1195i	0.964224	−	1.36362i
$742$	−0.674235	−	1.16781i	−0.0247519	−	0.0428716i
$743$	−12.7980	−	22.1667i	−0.469512	−	0.813218i	0.529881	−	0.848072i	$-0.322237\pi$
$743$	−12.7980	−	22.1667i	−0.469512	−	0.813218i	−0.999392	+	0.0348542i	$0.988903\pi$
$744$	2.00000	−	2.82843i	0.0733236	−	0.103695i
$745$		0			0
$746$	26.8990			0.984842
$747$	7.10102	+	20.0847i	0.259813	+	0.734861i
$748$	1.65153			0.0603859
$749$	−3.39898	+	5.88721i	−0.124196	+	0.215114i
$750$	−1.72474	−	0.158919i	−0.0629788	−	0.00580289i
$751$	4.57321	+	7.92104i	0.166879	+	0.289043i	0.937321	−	0.348467i	$-0.113298\pi$
$751$	4.57321	+	7.92104i	0.166879	+	0.289043i	−0.770442	+	0.637510i	$0.779964\pi$
$752$	4.89898	+	8.48528i	0.178647	+	0.309426i
$753$	10.0732	+	21.8649i	0.367088	+	0.796802i
$754$	5.44949	−	9.43879i	0.198459	−	0.343741i
$755$	−10.0000			−0.363937
$756$	5.00000	+	1.41421i	0.181848	+	0.0514344i
$757$	33.3485			1.21207			0.606035	−	0.795438i	$-0.292759\pi$
$757$	33.3485			1.21207			0.606035	+	0.795438i	$0.292759\pi$
$758$	1.27526	−	2.20881i	0.0463194	−	0.0802275i
$759$	−0.977296	−	2.12132i	−0.0354736	−	0.0769991i
$760$	−2.94949	−	5.10867i	−0.106989	−	0.185311i
$761$	18.7980	+	32.5590i	0.681425	+	1.18026i	0.974546	+	0.224188i	$0.0719730\pi$
$761$	18.7980	+	32.5590i	0.681425	+	1.18026i	−0.293120	+	0.956076i	$0.594694\pi$
$762$	−22.6742	−	2.08921i	−0.821401	−	0.0756842i
$763$	6.22474	−	10.7816i	0.225351	−	0.390319i
$764$	7.10102			0.256906
$765$	−8.84847	−	1.64456i	−0.319917	−	0.0594594i
$766$	−26.6969			−0.964600
$767$	−17.5732	+	30.4377i	−0.634532	+	1.09904i
$768$	−1.00000	+	1.41421i	−0.0360844	+	0.0510310i
$769$	11.5505	+	20.0061i	0.416522	+	0.721437i	0.995587	−	0.0938441i	$-0.0299155\pi$
$769$	11.5505	+	20.0061i	0.416522	+	0.721437i	−0.579065	+	0.815281i	$0.696582\pi$
$770$	−0.275255	−	0.476756i	−0.00991951	−	0.0171811i
$771$	5.69694	−	8.05669i	0.205170	−	0.290155i
$772$	−0.724745	+	1.25529i	−0.0260841	+	0.0451791i
$773$	−36.2474			−1.30373			−0.651865	−	0.758335i	$-0.726013\pi$
$773$	−36.2474			−1.30373			−0.651865	+	0.758335i	$0.726013\pi$
$774$	17.3990	+	3.23375i	0.625393	+	0.116235i
$775$	2.00000			0.0718421
$776$	−7.84847	+	13.5939i	−0.281744	+	0.487994i
$777$	−2.67423	−	0.246405i	−0.0959376	−	0.00883973i
$778$	15.7980	+	27.3629i	0.566384	+	0.981006i
$779$	−33.7702	−	58.4916i	−1.20994	−	2.09568i
$780$	−3.22474	−	6.99964i	−0.115464	−	0.250627i
$781$	−2.32577	+	4.02834i	−0.0832224	+	0.144145i
$782$	−7.34847			−0.262781
$783$	−9.12372	+	8.87455i	−0.326055	+	0.317151i
$784$	1.00000			0.0357143
$785$	−4.67423	+	8.09601i	−0.166831	+	0.288959i
$786$	6.30306	+	13.6814i	0.224823	+	0.488001i
$787$	−18.6969	−	32.3840i	−0.666474	−	1.15437i	−0.978883	−	0.204419i	$-0.934469\pi$
$787$	−18.6969	−	32.3840i	−0.666474	−	1.15437i	0.312410	−	0.949948i	$-0.398864\pi$
$788$	−3.67423	−	6.36396i	−0.130889	−	0.226707i
$789$	−2.32577	−	0.214297i	−0.0827994	−	0.00762917i
$790$	1.00000	−	1.73205i	0.0355784	−	0.0616236i
$791$	−16.8990			−0.600859
$792$	−0.550510	−	1.55708i	−0.0195615	−	0.0553284i
$793$	−23.7980			−0.845090
$794$	−16.0227	+	27.7521i	−0.568624	+	0.984886i
$795$	1.34847	−	1.90702i	0.0478253	−	0.0676352i
$796$	−3.32577	−	5.76039i	−0.117879	−	0.204172i
$797$	10.8990	+	18.8776i	0.386062	+	0.668678i	0.991916	−	0.126897i	$-0.0405019\pi$
$797$	10.8990	+	18.8776i	0.386062	+	0.668678i	−0.605854	+	0.795576i	$0.707169\pi$
$798$	−5.89898	+	8.34242i	−0.208822	+	0.295318i
$799$	−14.6969	+	25.4558i	−0.519940	+	0.900563i
$800$	−1.00000			−0.0353553
$801$	21.2474	−	24.8523i	0.750742	−	0.878112i
$802$	−9.00000			−0.317801
$803$	−3.27526	+	5.67291i	−0.115581	+	0.200193i
$804$	23.6237	+	2.17670i	0.833145	+	0.0767662i
$805$	1.22474	+	2.12132i	0.0431666	+	0.0747667i
$806$	4.44949	+	7.70674i	0.156727	+	0.271458i
$807$	−16.7753	−	36.4124i	−0.590517	−	1.28178i
$808$	2.44949	−	4.24264i	0.0861727	−	0.149256i
$809$	17.2020			0.604792			0.302396	−	0.953182i	$-0.402214\pi$
$809$	17.2020			0.604792			0.302396	+	0.953182i	$0.402214\pi$
$810$	1.39898	+	8.89060i	0.0491551	+	0.312384i
$811$	−33.6969			−1.18326			−0.591630	−	0.806210i	$-0.701515\pi$
$811$	−33.6969			−1.18326			−0.591630	+	0.806210i	$0.701515\pi$
$812$	−1.22474	+	2.12132i	−0.0429801	+	0.0744438i
$813$	−15.4722	−	33.5840i	−0.542634	−	1.17784i
$814$	0.426786	+	0.739215i	0.0149588	+	0.0259095i
$815$	−1.00000	−	1.73205i	−0.0350285	−	0.0606711i
$816$	−5.17423	−	0.476756i	−0.181134	−	0.0166898i
$817$	−17.3990	+	30.1359i	−0.608713	+	1.05432i
$818$	0.752551			0.0263123
$819$	−8.67423	+	10.1459i	−0.303102	+	0.354526i
$820$	−11.4495			−0.399834
$821$	−7.77526	+	13.4671i	−0.271358	+	0.470006i	−0.969210	−	0.246236i	$-0.920806\pi$
$821$	−7.77526	+	13.4671i	−0.271358	+	0.470006i	0.697852	+	0.716242i	$0.254139\pi$
$822$	3.24745	−	4.59259i	0.113268	−	0.160185i
$823$	22.0227	+	38.1444i	0.767663	+	1.32963i	0.938827	+	0.344389i	$0.111914\pi$
$823$	22.0227	+	38.1444i	0.767663	+	1.32963i	−0.171164	+	0.985243i	$0.554753\pi$
$824$	10.1237	+	17.5348i	0.352677	+	0.610854i
$825$	0.550510	−	0.778539i	0.0191663	−	0.0271053i
$826$	3.94949	−	6.84072i	0.137420	−	0.238019i
$827$	−20.6969			−0.719703			−0.359852	−	0.933010i	$-0.617173\pi$
$827$	−20.6969			−0.719703			−0.359852	+	0.933010i	$0.617173\pi$
$828$	2.44949	+	6.92820i	0.0851257	+	0.240772i
$829$	40.0908			1.39241			0.696206	−	0.717842i	$-0.254870\pi$
$829$	40.0908			1.39241			0.696206	+	0.717842i	$0.254870\pi$
$830$	−3.55051	+	6.14966i	−0.123240	+	0.213458i
$831$	3.44949	+	0.317837i	0.119661	+	0.0110257i
$832$	−2.22474	−	3.85337i	−0.0771292	−	0.133592i
$833$	1.50000	+	2.59808i	0.0519719	+	0.0900180i
$834$	6.37628	+	13.8404i	0.220792	+	0.479252i
$835$	12.6742	−	21.9524i	0.438610	−	0.759695i
$836$	3.24745			0.112315
$837$	−2.55051	−	10.0745i	−0.0881585	−	0.348225i
$838$	13.5959			0.469663
$839$	−8.32577	+	14.4206i	−0.287437	+	0.497856i	−0.973197	−	0.229972i	$-0.926137\pi$
$839$	−8.32577	+	14.4206i	−0.287437	+	0.497856i	0.685760	+	0.727828i	$0.259470\pi$
$840$	0.724745	+	1.57313i	0.0250061	+	0.0542782i
$841$	11.5000	+	19.9186i	0.396552	+	0.686848i
$842$	−9.22474	−	15.9777i	−0.317906	−	0.550629i
$843$	−41.3939	−	3.81405i	−1.42568	−	0.131363i
$844$	3.34847	−	5.79972i	0.115259	−	0.199635i
$845$	6.79796			0.233857
$846$	28.8990	+	5.37113i	0.993567	+	0.184663i
$847$	−10.6969			−0.367551
$848$	0.674235	−	1.16781i	0.0231533	−	0.0401027i
$849$	16.0000	−	22.6274i	0.549119	−	0.776571i
$850$	−1.50000	−	2.59808i	−0.0514496	−	0.0891133i
$851$	−1.89898	−	3.28913i	−0.0650962	−	0.112750i
$852$	8.44949	−	11.9494i	0.289475	−	0.409379i
$853$	27.3485	−	47.3689i	0.936394	−	1.62188i	0.164264	−	0.986416i	$-0.447475\pi$
$853$	27.3485	−	47.3689i	0.936394	−	1.62188i	0.772130	−	0.635465i	$-0.219192\pi$
$854$	5.34847			0.183021
$855$	−17.3990	−	3.23375i	−0.595033	−	0.110592i
$856$	−6.79796			−0.232349
$857$	−28.0454	+	48.5761i	−0.958013	+	1.65933i	−0.230695	+	0.973026i	$0.574100\pi$
$857$	−28.0454	+	48.5761i	−0.958013	+	1.65933i	−0.727318	+	0.686301i	$0.759233\pi$
$858$	4.22474	+	0.389270i	0.144230	+	0.0132894i
$859$	−26.1969	−	45.3744i	−0.893828	−	1.54816i	−0.835248	−	0.549873i	$-0.814676\pi$
$859$	−26.1969	−	45.3744i	−0.893828	−	1.54816i	−0.0585796	−	0.998283i	$-0.518657\pi$
$860$	2.94949	+	5.10867i	0.100577	+	0.174204i
$861$	8.29796	+	18.0116i	0.282794	+	0.613832i
$862$	−6.24745	+	10.8209i	−0.212789	+	0.368561i
$863$	−34.8990			−1.18798			−0.593988	−	0.804474i	$-0.702447\pi$
$863$	−34.8990			−1.18798			−0.593988	+	0.804474i	$0.702447\pi$
$864$	1.27526	+	5.03723i	0.0433851	+	0.171370i
$865$	−6.00000			−0.204006
$866$	−16.2980	+	28.2289i	−0.553827	+	0.959257i
$867$	5.79796	+	12.5851i	0.196909	+	0.427411i
$868$	−1.00000	−	1.73205i	−0.0339422	−	0.0587896i
$869$	0.550510	+	0.953512i	0.0186748	+	0.0323457i
$870$	−4.22474	−	0.389270i	−0.143232	−	0.0131975i
$871$	−30.4722	+	52.7794i	−1.03251	+	1.78836i
$872$	12.4495			0.421593
$873$	15.6969	+	44.3976i	0.531261	+	1.50263i
$874$	−14.4495			−0.488761
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$	11.8990	−	16.8277i	0.402029	−	0.568555i
$877$	−18.0227	−	31.2162i	−0.608583	−	1.05410i	−0.991474	−	0.130304i	$-0.958405\pi$
$877$	−18.0227	−	31.2162i	−0.608583	−	1.05410i	0.382891	−	0.923794i	$-0.374929\pi$
$878$	13.6742	+	23.6845i	0.461483	+	0.799312i
$879$	29.1464	−	41.2193i	0.983085	−	1.39029i
$880$	0.275255	−	0.476756i	0.00927885	−	0.0160714i
$881$	−46.2929			−1.55965			−0.779823	−	0.626000i	$-0.784691\pi$
$881$	−46.2929			−1.55965			−0.779823	+	0.626000i	$0.784691\pi$
$882$	1.94949	−	2.28024i	0.0656427	−	0.0767796i
$883$	−44.5959			−1.50077			−0.750386	−	0.661000i	$-0.770132\pi$
$883$	−44.5959			−1.50077			−0.750386	+	0.661000i	$0.770132\pi$
$884$	6.67423	−	11.5601i	0.224479	−	0.388809i
$885$	13.6237	+	1.25529i	0.457956	+	0.0421963i
$886$	−17.8485	−	30.9145i	−0.599631	−	1.03859i
$887$	−27.0000	−	46.7654i	−0.906571	−	1.57023i	−0.818794	−	0.574087i	$-0.805357\pi$
$887$	−27.0000	−	46.7654i	−0.906571	−	1.57023i	−0.0877772	−	0.996140i	$-0.527976\pi$
$888$	−1.12372	−	2.43916i	−0.0377097	−	0.0818528i
$889$	−6.57321	+	11.3851i	−0.220459	+	0.381845i
$890$	10.8990			0.365335
$891$	−4.62372	−	1.78021i	−0.154901	−	0.0596394i
$892$	6.65153			0.222710
$893$	−28.8990	+	50.0545i	−0.967067	+	1.67501i
$894$		0			0
$895$	−3.00000	−	5.19615i	−0.100279	−	0.173688i
$896$	0.500000	+	0.866025i	0.0167038	+	0.0289319i
$897$	−18.7980	−	1.73205i	−0.627646	−	0.0578315i
$898$	−3.15153	+	5.45861i	−0.105168	+	0.182156i
$899$	4.89898			0.163390
$900$	−1.94949	+	2.28024i	−0.0649830	+	0.0760080i
$901$	4.04541			0.134772
$902$	3.15153	−	5.45861i	0.104934	−	0.181752i
$903$	5.89898	−	8.34242i	0.196306	−	0.277618i
$904$	−8.44949	−	14.6349i	−0.281026	−	0.486751i
$905$	−8.89898	−	15.4135i	−0.295812	−	0.512362i
$906$	−10.0000	+	14.1421i	−0.332228	+	0.469841i
$907$	−10.1515	+	17.5830i	−0.337076	+	0.583833i	−0.983881	−	0.178822i	$-0.942771\pi$
$907$	−10.1515	+	17.5830i	−0.337076	+	0.583833i	0.646805	+	0.762655i	$0.276105\pi$
$908$	−25.0454			−0.831161
$909$	−4.89898	−	13.8564i	−0.162489	−	0.459588i
$910$	−4.44949			−0.147499
$911$	−16.4722	+	28.5307i	−0.545748	+	0.945263i	0.452811	+	0.891606i	$0.350421\pi$
$911$	−16.4722	+	28.5307i	−0.545748	+	0.945263i	−0.998559	+	0.0536571i	$0.982912\pi$
$912$	−10.1742	−	0.937458i	−0.336903	−	0.0310423i
$913$	−1.95459	−	3.38545i	−0.0646876	−	0.112042i
$914$	−16.7247	−	28.9681i	−0.553205	−	0.958180i
$915$	3.87628	+	8.41385i	0.128146	+	0.278153i
$916$	−0.325765	+	0.564242i	−0.0107636	+	0.0186431i
$917$	8.69694			0.287198
$918$	−11.1742	+	10.8691i	−0.368805	+	0.358732i
$919$	47.5505			1.56855			0.784273	−	0.620415i	$-0.213036\pi$
$919$	47.5505			1.56855			0.784273	+	0.620415i	$0.213036\pi$
$920$	−1.22474	+	2.12132i	−0.0403786	+	0.0699379i
$921$	19.8939	+	43.1817i	0.655526	+	1.42288i
$922$	3.67423	+	6.36396i	0.121004	+	0.209586i
$923$	18.7980	+	32.5590i	0.618742	+	1.07169i
$924$	−0.949490	−	0.0874863i	−0.0312359	−	0.00287809i
$925$	0.775255	−	1.34278i	0.0254902	−	0.0441504i
$926$	28.0000			0.920137
$927$	59.7196	+	11.0994i	1.96145	+	0.364553i
$928$	−2.44949			−0.0804084
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	−0.679770	−	0.733426i	$-0.737920\pi$
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	0.975050	+	0.221985i	$0.0712536\pi$
$930$	2.00000	−	2.82843i	0.0655826	−	0.0927478i
$931$	2.94949	+	5.10867i	0.0966656	+	0.167430i
$932$	9.27526	+	16.0652i	0.303821	+	0.526234i
$933$	1.10102	−	1.55708i	0.0360458	−	0.0509764i
$934$	11.9722	−	20.7364i	0.391742	−	0.678517i
$935$	1.65153			0.0540108
$936$	−13.1237	−	2.43916i	−0.428962	−	0.0797264i
$937$	−45.3939			−1.48295			−0.741477	−	0.670979i	$-0.765874\pi$
$937$	−45.3939			−1.48295			−0.741477	+	0.670979i	$0.765874\pi$
$938$	6.84847	−	11.8619i	0.223610	−	0.387305i
$939$	−15.8712	−	1.46238i	−0.517936	−	0.0477228i
$940$	4.89898	+	8.48528i	0.159787	+	0.276759i
$941$	29.1464	+	50.4831i	0.950146	+	1.64570i	0.745103	+	0.666949i	$0.232400\pi$
$941$	29.1464	+	50.4831i	0.950146	+	1.64570i	0.205043	+	0.978753i	$0.434267\pi$
$942$	6.77526	+	14.7064i	0.220750	+	0.479160i
$943$	−14.0227	+	24.2880i	−0.456642	+	0.790927i
$944$	7.89898			0.257090
$945$	5.00000	+	1.41421i	0.162650	+	0.0460044i
$946$	−3.24745			−0.105584
$947$	−29.2980	+	50.7456i	−0.952056	+	1.64901i	−0.211089	+	0.977467i	$0.567701\pi$
$947$	−29.2980	+	50.7456i	−0.952056	+	1.64901i	−0.740966	+	0.671542i	$0.765632\pi$
$948$	−1.44949	−	3.14626i	−0.0470772	−	0.102186i
$949$	26.4722	+	45.8512i	0.859324	+	1.48839i
$950$	−2.94949	−	5.10867i	−0.0956941	−	0.165747i
$951$	0.426786	+	0.0393242i	0.0138395	+	0.00127517i
$952$	−1.50000	+	2.59808i	−0.0486153	+	0.0842041i
$953$	−22.8434			−0.739969			−0.369985	−	0.929038i	$-0.620637\pi$
$953$	−22.8434			−0.739969			−0.369985	+	0.929038i	$0.620637\pi$
$954$	−1.34847	−	3.81405i	−0.0436583	−	0.123484i
$955$	7.10102			0.229784
$956$	−6.55051	+	11.3458i	−0.211859	+	0.366950i
$957$	1.34847	−	1.90702i	0.0435898	−	0.0616453i
$958$	−13.4722	−	23.3345i	−0.435267	−	0.753904i
$959$	−1.62372	−	2.81237i	−0.0524328	−	0.0908163i
$960$	−1.00000	+	1.41421i	−0.0322749	+	0.0456435i
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	6.89898			0.222432
$963$	−13.2526	+	15.5010i	−0.427057	+	0.499512i
$964$	12.3485			0.397717
$965$	−0.724745	+	1.25529i	−0.0233304	+	0.0404094i
$966$	4.22474	+	0.389270i	0.135929	+	0.0125245i
$967$	−14.1010	−	24.4237i	−0.453458	−	0.785413i	0.545140	−	0.838345i	$-0.316477\pi$
$967$	−14.1010	−	24.4237i	−0.453458	−	0.785413i	−0.998598	+	0.0529324i	$0.983143\pi$
$968$	−5.34847	−	9.26382i	−0.171906	−	0.297750i
$969$	−12.8258	−	27.8396i	−0.412023	−	0.894338i
$970$	−7.84847	+	13.5939i	−0.251999	+	0.436475i
$971$	−45.7980			−1.46973			−0.734863	−	0.678215i	$-0.762754\pi$
$971$	−45.7980			−1.46973			−0.734863	+	0.678215i	$0.762754\pi$
$972$	13.9722	+	6.91215i	0.448158	+	0.221707i
$973$	8.79796			0.282050
$974$	−11.2474	+	19.4812i	−0.360392	+	0.624216i
$975$	−3.22474	−	6.99964i	−0.103274	−	0.224168i
$976$	2.67423	+	4.63191i	0.0856002	+	0.148264i
$977$	−14.9722	−	25.9326i	−0.479003	−	0.829657i	0.520707	−	0.853735i	$-0.325668\pi$
$977$	−14.9722	−	25.9326i	−0.479003	−	0.829657i	−0.999710	+	0.0240780i	$0.992335\pi$
$978$	−3.44949	−	0.317837i	−0.110303	−	0.0101633i
$979$	−3.00000	+	5.19615i	−0.0958804	+	0.166070i
$980$	1.00000			0.0319438
$981$	24.2702	−	28.3878i	0.774886	−	0.906353i
$982$	−10.3485			−0.330233
$983$	−18.4949	+	32.0341i	−0.589896	+	1.02173i	0.404350	+	0.914604i	$0.367498\pi$
$983$	−18.4949	+	32.0341i	−0.589896	+	1.02173i	−0.994246	+	0.107125i	$0.965836\pi$
$984$	−11.4495	+	16.1920i	−0.364996	+	0.516183i
$985$	−3.67423	−	6.36396i	−0.117071	−	0.202773i
$986$	−3.67423	−	6.36396i	−0.117011	−	0.202670i
$987$	9.79796	−	13.8564i	0.311872	−	0.441054i
$988$	13.1237	−	22.7310i	0.417521	−	0.723168i
$989$	14.4495			0.459467
$990$	−0.550510	−	1.55708i	−0.0174964	−	0.0494872i
$991$	3.10102			0.0985072			0.0492536	−	0.998786i	$-0.484316\pi$
$991$	3.10102			0.0985072			0.0492536	+	0.998786i	$0.484316\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$	18.4495	+	1.69994i	0.585477	+	0.0539461i
$994$	−4.22474	−	7.31747i	−0.134001	−	0.232096i
$995$	−3.32577	−	5.76039i	−0.105434	−	0.182617i
$996$	5.14643	+	11.1708i	0.163071	+	0.353962i
$997$	−21.6969	+	37.5802i	−0.687149	+	1.19018i	0.285607	+	0.958347i	$0.407805\pi$
$997$	−21.6969	+	37.5802i	−0.687149	+	1.19018i	−0.972756	+	0.231830i	$0.925529\pi$
$998$	37.2474			1.17905
$999$	−7.75255	−	2.19275i	−0.245280	−	0.0693756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.j.h.421.1	yes	4
3.2	odd	2		1890.2.j.g.1261.2		4
9.2	odd	6		5670.2.a.bi.1.1		2
9.4	even	3	inner	630.2.j.h.211.1	✓	4
9.5	odd	6		1890.2.j.g.631.2		4
9.7	even	3		5670.2.a.ba.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.h.211.1	✓	4	9.4	even	3	inner
630.2.j.h.421.1	yes	4	1.1	even	1	trivial
1890.2.j.g.631.2		4	9.5	odd	6
1890.2.j.g.1261.2		4	3.2	odd	2
5670.2.a.ba.1.2		2	9.7	even	3
5670.2.a.bi.1.1		2	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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.724745 - 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.72474 - 0.158919i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-1.94949 + 2.28024i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.724745 - 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.72474 - 0.158919i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-1.94949 + 2.28024i) q^{9} -1.00000 q^{10} +(0.275255 - 0.476756i) q^{11} +(-1.00000 + 1.41421i) q^{12} +(-2.22474 - 3.85337i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-1.00000 + 1.41421i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.00000 q^{17} +(1.00000 + 2.82843i) q^{18} -5.89898 q^{19} +(-0.500000 + 0.866025i) q^{20} +(1.72474 + 0.158919i) q^{21} +(-0.275255 - 0.476756i) q^{22} +(1.22474 + 2.12132i) q^{23} +(0.724745 + 1.57313i) q^{24} +(-0.500000 + 0.866025i) q^{25} -4.44949 q^{26} +(5.00000 + 1.41421i) q^{27} +1.00000 q^{28} +(-1.22474 + 2.12132i) q^{29} +(0.724745 + 1.57313i) q^{30} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.949490 - 0.0874863i) q^{33} +(-1.50000 + 2.59808i) q^{34} +1.00000 q^{35} +(2.94949 + 0.548188i) q^{36} -1.55051 q^{37} +(-2.94949 + 5.10867i) q^{38} +(-4.44949 + 6.29253i) q^{39} +(0.500000 + 0.866025i) q^{40} +(5.72474 + 9.91555i) q^{41} +(1.00000 - 1.41421i) q^{42} +(2.94949 - 5.10867i) q^{43} -0.550510 q^{44} +(2.94949 + 0.548188i) q^{45} +2.44949 q^{46} +(4.89898 - 8.48528i) q^{47} +(1.72474 + 0.158919i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} +(2.17423 + 4.71940i) q^{51} +(-2.22474 + 3.85337i) q^{52} -1.34847 q^{53} +(3.72474 - 3.62302i) q^{54} -0.550510 q^{55} +(0.500000 - 0.866025i) q^{56} +(4.27526 + 9.27987i) q^{57} +(1.22474 + 2.12132i) q^{58} +(-3.94949 - 6.84072i) q^{59} +(1.72474 + 0.158919i) q^{60} +(2.67423 - 4.63191i) q^{61} -2.00000 q^{62} +(-1.00000 - 2.82843i) q^{63} +1.00000 q^{64} +(-2.22474 + 3.85337i) q^{65} +(-0.550510 + 0.778539i) q^{66} +(-6.84847 - 11.8619i) q^{67} +(1.50000 + 2.59808i) q^{68} +(2.44949 - 3.46410i) q^{69} +(0.500000 - 0.866025i) q^{70} -8.44949 q^{71} +(1.94949 - 2.28024i) q^{72} -11.8990 q^{73} +(-0.775255 + 1.34278i) q^{74} +(1.72474 + 0.158919i) q^{75} +(2.94949 + 5.10867i) q^{76} +(0.275255 + 0.476756i) q^{77} +(3.22474 + 6.99964i) q^{78} +(-1.00000 + 1.73205i) q^{79} +1.00000 q^{80} +(-1.39898 - 8.89060i) q^{81} +11.4495 q^{82} +(3.55051 - 6.14966i) q^{83} +(-0.724745 - 1.57313i) q^{84} +(1.50000 + 2.59808i) q^{85} +(-2.94949 - 5.10867i) q^{86} +(4.22474 + 0.389270i) q^{87} +(-0.275255 + 0.476756i) q^{88} -10.8990 q^{89} +(1.94949 - 2.28024i) q^{90} +4.44949 q^{91} +(1.22474 - 2.12132i) q^{92} +(-2.00000 + 2.82843i) q^{93} +(-4.89898 - 8.48528i) q^{94} +(2.94949 + 5.10867i) q^{95} +(1.00000 - 1.41421i) q^{96} +(7.84847 - 13.5939i) q^{97} -1.00000 q^{98} +(0.550510 + 1.55708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 2 q^{9} - 4 q^{10} + 6 q^{11} - 4 q^{12} - 4 q^{13} + 2 q^{14} - 4 q^{15} - 2 q^{16} - 12 q^{17} + 4 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} - 6 q^{22} - 2 q^{24} - 2 q^{25} - 8 q^{26} + 20 q^{27} + 4 q^{28} - 2 q^{30} - 4 q^{31} + 2 q^{32} + 6 q^{33} - 6 q^{34} + 4 q^{35} + 2 q^{36} - 16 q^{37} - 2 q^{38} - 8 q^{39} + 2 q^{40} + 18 q^{41} + 4 q^{42} + 2 q^{43} - 12 q^{44} + 2 q^{45} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 6 q^{51} - 4 q^{52} + 24 q^{53} + 10 q^{54} - 12 q^{55} + 2 q^{56} + 22 q^{57} - 6 q^{59} + 2 q^{60} - 4 q^{61} - 8 q^{62} - 4 q^{63} + 4 q^{64} - 4 q^{65} - 12 q^{66} + 2 q^{67} + 6 q^{68} + 2 q^{70} - 24 q^{71} - 2 q^{72} - 28 q^{73} - 8 q^{74} + 2 q^{75} + 2 q^{76} + 6 q^{77} + 8 q^{78} - 4 q^{79} + 4 q^{80} + 14 q^{81} + 36 q^{82} + 24 q^{83} + 2 q^{84} + 6 q^{85} - 2 q^{86} + 12 q^{87} - 6 q^{88} - 24 q^{89} - 2 q^{90} + 8 q^{91} - 8 q^{93} + 2 q^{95} + 4 q^{96} + 2 q^{97} - 4 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 2 * q^9 - 4 * q^10 + 6 * q^11 - 4 * q^12 - 4 * q^13 + 2 * q^14 - 4 * q^15 - 2 * q^16 - 12 * q^17 + 4 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 - 6 * q^22 - 2 * q^24 - 2 * q^25 - 8 * q^26 + 20 * q^27 + 4 * q^28 - 2 * q^30 - 4 * q^31 + 2 * q^32 + 6 * q^33 - 6 * q^34 + 4 * q^35 + 2 * q^36 - 16 * q^37 - 2 * q^38 - 8 * q^39 + 2 * q^40 + 18 * q^41 + 4 * q^42 + 2 * q^43 - 12 * q^44 + 2 * q^45 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 6 * q^51 - 4 * q^52 + 24 * q^53 + 10 * q^54 - 12 * q^55 + 2 * q^56 + 22 * q^57 - 6 * q^59 + 2 * q^60 - 4 * q^61 - 8 * q^62 - 4 * q^63 + 4 * q^64 - 4 * q^65 - 12 * q^66 + 2 * q^67 + 6 * q^68 + 2 * q^70 - 24 * q^71 - 2 * q^72 - 28 * q^73 - 8 * q^74 + 2 * q^75 + 2 * q^76 + 6 * q^77 + 8 * q^78 - 4 * q^79 + 4 * q^80 + 14 * q^81 + 36 * q^82 + 24 * q^83 + 2 * q^84 + 6 * q^85 - 2 * q^86 + 12 * q^87 - 6 * q^88 - 24 * q^89 - 2 * q^90 + 8 * q^91 - 8 * q^93 + 2 * q^95 + 4 * q^96 + 2 * q^97 - 4 * q^98 + 12 * q^99

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