LMFDB - Embedded newform 330.2.j.a.287.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [330,2,Mod(23,330)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(330, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("330.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 330 = 2 \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	330.j (of order $4$, 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:	$2.63506326670$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 18 x^{18} - 52 x^{17} + 146 x^{16} - 348 x^{15} + 794 x^{14} - 1652 x^{13} + \cdots + 59049 $ x^20 - 4x^19 + 18x^18 - 52x^17 + 146x^16 - 348x^15 + 794x^14 - 1652x^13 + 3345x^12 - 6168x^11 + 11248x^10 - 18504x^9 + 30105x^8 - 44604x^7 + 64314x^6 - 84564x^5 + 106434x^4 - 113724x^3 + 118098x^2 - 78732*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			287.7
Root			$-1.12724 + 1.31504i$ of defining polynomial
Character	$\chi$	$=$	330.287
Dual form			330.2.j.a.23.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.31504 + 1.12724i) q^{3} -1.00000i q^{4} +(-0.674951 - 2.13177i) q^{5} +(-0.132792 + 1.72695i) q^{6} +(3.33351 + 3.33351i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.458652 - 2.96473i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.31504 + 1.12724i) q^{3} -1.00000i q^{4} +(-0.674951 - 2.13177i) q^{5} +(-0.132792 + 1.72695i) q^{6} +(3.33351 + 3.33351i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.458652 - 2.96473i) q^{9} +(-1.98465 - 1.03013i) q^{10} -1.00000i q^{11} +(1.12724 + 1.31504i) q^{12} +(3.42826 - 3.42826i) q^{13} +4.71430 q^{14} +(3.29061 + 2.04253i) q^{15} -1.00000 q^{16} +(4.25219 - 4.25219i) q^{17} +(-1.77207 - 2.42070i) q^{18} +1.14457i q^{19} +(-2.13177 + 0.674951i) q^{20} +(-8.14137 - 0.626022i) q^{21} +(-0.707107 - 0.707107i) q^{22} +(0.277597 + 0.277597i) q^{23} +(1.72695 + 0.132792i) q^{24} +(-4.08888 + 2.87768i) q^{25} -4.84829i q^{26} +(2.73883 + 4.41575i) q^{27} +(3.33351 - 3.33351i) q^{28} +3.53526 q^{29} +(3.77109 - 0.882526i) q^{30} -2.83680 q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.12724 + 1.31504i) q^{33} -6.01351i q^{34} +(4.85632 - 9.35624i) q^{35} +(-2.96473 - 0.458652i) q^{36} +(-3.05254 - 3.05254i) q^{37} +(0.809333 + 0.809333i) q^{38} +(-0.643815 + 8.37276i) q^{39} +(-1.03013 + 1.98465i) q^{40} +10.9476i q^{41} +(-6.19948 + 5.31416i) q^{42} +(2.91554 - 2.91554i) q^{43} -1.00000 q^{44} +(-6.62969 + 1.02331i) q^{45} +0.392582 q^{46} +(-4.60530 + 4.60530i) q^{47} +(1.31504 - 1.12724i) q^{48} +15.2246i q^{49} +(-0.856449 + 4.92610i) q^{50} +(-0.798547 + 10.3850i) q^{51} +(-3.42826 - 3.42826i) q^{52} +(-4.02811 - 4.02811i) q^{53} +(5.05905 + 1.18576i) q^{54} +(-2.13177 + 0.674951i) q^{55} -4.71430i q^{56} +(-1.29021 - 1.50515i) q^{57} +(2.49981 - 2.49981i) q^{58} -10.8278 q^{59} +(2.04253 - 3.29061i) q^{60} +0.449010 q^{61} +(-2.00592 + 2.00592i) q^{62} +(11.4119 - 8.35405i) q^{63} +1.00000i q^{64} +(-9.62216 - 4.99435i) q^{65} +(1.72695 + 0.132792i) q^{66} +(4.76352 + 4.76352i) q^{67} +(-4.25219 - 4.25219i) q^{68} +(-0.677970 - 0.0521318i) q^{69} +(-3.18192 - 10.0498i) q^{70} -3.85485i q^{71} +(-2.42070 + 1.77207i) q^{72} +(-5.71747 + 5.71747i) q^{73} -4.31694 q^{74} +(2.13320 - 8.39342i) q^{75} +1.14457 q^{76} +(3.33351 - 3.33351i) q^{77} +(5.46519 + 6.37568i) q^{78} -1.05639i q^{79} +(0.674951 + 2.13177i) q^{80} +(-8.57928 - 2.71956i) q^{81} +(7.74109 + 7.74109i) q^{82} +(-2.72084 - 2.72084i) q^{83} +(-0.626022 + 8.14137i) q^{84} +(-11.9347 - 6.19467i) q^{85} -4.12319i q^{86} +(-4.64901 + 3.98510i) q^{87} +(-0.707107 + 0.707107i) q^{88} -3.84257 q^{89} +(-3.96431 + 5.41149i) q^{90} +22.8563 q^{91} +(0.277597 - 0.277597i) q^{92} +(3.73050 - 3.19776i) q^{93} +6.51288i q^{94} +(2.43996 - 0.772529i) q^{95} +(0.132792 - 1.72695i) q^{96} +(4.30030 + 4.30030i) q^{97} +(10.7654 + 10.7654i) q^{98} +(-2.96473 - 0.458652i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{6} + 20 q^{9}+O(q^{10}) $ 20 * q + 4 * q^6 + 20 * q^9	$ 20 q + 4 q^{6} + 20 q^{9} - 4 q^{12} + 8 q^{13} - 8 q^{15} - 20 q^{16} + 8 q^{17} - 8 q^{18} - 12 q^{20} + 36 q^{23} + 12 q^{25} - 16 q^{29} + 32 q^{30} + 16 q^{31} - 4 q^{33} - 8 q^{35} - 4 q^{36} - 4 q^{37} + 32 q^{39} - 8 q^{40} - 16 q^{42} - 20 q^{44} + 20 q^{45} - 24 q^{46} + 12 q^{47} - 16 q^{50} - 16 q^{51} - 8 q^{52} + 20 q^{53} - 12 q^{54} - 12 q^{55} - 28 q^{57} - 8 q^{58} - 112 q^{59} + 24 q^{60} + 8 q^{61} + 16 q^{62} - 8 q^{63} - 56 q^{65} + 20 q^{67} - 8 q^{68} + 28 q^{69} - 8 q^{70} + 8 q^{72} - 8 q^{73} + 8 q^{74} + 8 q^{75} - 16 q^{76} + 36 q^{78} + 24 q^{82} + 16 q^{83} - 12 q^{84} - 72 q^{87} - 32 q^{89} + 40 q^{90} + 36 q^{92} - 76 q^{93} - 4 q^{96} - 44 q^{97} - 56 q^{98} - 4 q^{99}+O(q^{100}) $ 20 * q + 4 * q^6 + 20 * q^9 - 4 * q^12 + 8 * q^13 - 8 * q^15 - 20 * q^16 + 8 * q^17 - 8 * q^18 - 12 * q^20 + 36 * q^23 + 12 * q^25 - 16 * q^29 + 32 * q^30 + 16 * q^31 - 4 * q^33 - 8 * q^35 - 4 * q^36 - 4 * q^37 + 32 * q^39 - 8 * q^40 - 16 * q^42 - 20 * q^44 + 20 * q^45 - 24 * q^46 + 12 * q^47 - 16 * q^50 - 16 * q^51 - 8 * q^52 + 20 * q^53 - 12 * q^54 - 12 * q^55 - 28 * q^57 - 8 * q^58 - 112 * q^59 + 24 * q^60 + 8 * q^61 + 16 * q^62 - 8 * q^63 - 56 * q^65 + 20 * q^67 - 8 * q^68 + 28 * q^69 - 8 * q^70 + 8 * q^72 - 8 * q^73 + 8 * q^74 + 8 * q^75 - 16 * q^76 + 36 * q^78 + 24 * q^82 + 16 * q^83 - 12 * q^84 - 72 * q^87 - 32 * q^89 + 40 * q^90 + 36 * q^92 - 76 * q^93 - 4 * q^96 - 44 * q^97 - 56 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/330\mathbb{Z}\right)^\times$.

$n$	$67$	$211$	$221$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.31504	+	1.12724i	−0.759238	+	0.650813i
$3$	−1.31504	+	1.12724i	−0.759238	+	0.650813i
$4$		−	1.00000i		−	0.500000i
$5$	−0.674951	−	2.13177i	−0.301847	−	0.953356i
$5$	−0.674951	−	2.13177i	−0.301847	−	0.953356i
$6$	−0.132792	+	1.72695i	−0.0542122	+	0.705026i
$7$	3.33351	+	3.33351i	1.25995	+	1.25995i	0.951116	+	0.308833i	$0.0999385\pi$
$7$	3.33351	+	3.33351i	1.25995	+	1.25995i	0.308833	+	0.951116i	$0.400061\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.458652	−	2.96473i	0.152884	−	0.988244i
$10$	−1.98465	−	1.03013i	−0.627602	−	0.325755i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	1.12724	+	1.31504i	0.325407	+	0.379619i
$13$	3.42826	−	3.42826i	0.950827	−	0.950827i	−0.0480190	−	0.998846i	$-0.515291\pi$
$13$	3.42826	−	3.42826i	0.950827	−	0.950827i	0.998846	+	0.0480190i	$0.0152908\pi$
$14$	4.71430			1.25995
$15$	3.29061	+	2.04253i	0.849631	+	0.527378i
$16$	−1.00000			−0.250000
$17$	4.25219	−	4.25219i	1.03131	−	1.03131i	0.0318144	−	0.999494i	$-0.489871\pi$
$17$	4.25219	−	4.25219i	1.03131	−	1.03131i	0.999494	−	0.0318144i	$-0.0101285\pi$
$18$	−1.77207	−	2.42070i	−0.417680	−	0.570564i
$19$			1.14457i			0.262582i	0.991344	+	0.131291i	$0.0419123\pi$
$19$			1.14457i			0.262582i	−0.991344	+	0.131291i	$0.958088\pi$
$20$	−2.13177	+	0.674951i	−0.476678	+	0.150924i
$21$	−8.14137	−	0.626022i	−1.77659	−	0.136609i
$22$	−0.707107	−	0.707107i	−0.150756	−	0.150756i
$23$	0.277597	+	0.277597i	0.0578830	+	0.0578830i	0.735456	−	0.677573i	$-0.236968\pi$
$23$	0.277597	+	0.277597i	0.0578830	+	0.0578830i	−0.677573	+	0.735456i	$0.736968\pi$
$24$	1.72695	+	0.132792i	0.352513	+	0.0271061i
$25$	−4.08888	+	2.87768i	−0.817776	+	0.575536i
$26$		−	4.84829i		−	0.950827i
$27$	2.73883	+	4.41575i	0.527087	+	0.849811i
$28$	3.33351	−	3.33351i	0.629975	−	0.629975i
$29$	3.53526			0.656482			0.328241	−	0.944594i	$-0.393544\pi$
$29$	3.53526			0.656482			0.328241	+	0.944594i	$0.393544\pi$
$30$	3.77109	−	0.882526i	0.688504	−	0.161127i
$31$	−2.83680			−0.509504			−0.254752	−	0.967006i	$-0.581994\pi$
$31$	−2.83680			−0.509504			−0.254752	+	0.967006i	$0.581994\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	1.12724	+	1.31504i	0.196228	+	0.228919i
$34$		−	6.01351i		−	1.03131i
$35$	4.85632	−	9.35624i	0.820868	−	1.58149i
$36$	−2.96473	−	0.458652i	−0.494122	−	0.0764420i
$37$	−3.05254	−	3.05254i	−0.501835	−	0.501835i	0.410173	−	0.912008i	$-0.365468\pi$
$37$	−3.05254	−	3.05254i	−0.501835	−	0.501835i	−0.912008	+	0.410173i	$0.865468\pi$
$38$	0.809333	+	0.809333i	0.131291	+	0.131291i
$39$	−0.643815	+	8.37276i	−0.103093	+	1.34072i
$40$	−1.03013	+	1.98465i	−0.162877	+	0.313801i
$41$			10.9476i			1.70972i	0.518857	+	0.854861i	$0.326358\pi$
$41$			10.9476i			1.70972i	−0.518857	+	0.854861i	$0.673642\pi$
$42$	−6.19948	+	5.31416i	−0.956601	+	0.819992i
$43$	2.91554	−	2.91554i	0.444615	−	0.444615i	−0.448944	−	0.893560i	$-0.648200\pi$
$43$	2.91554	−	2.91554i	0.444615	−	0.444615i	0.893560	+	0.448944i	$0.148200\pi$
$44$	−1.00000			−0.150756
$45$	−6.62969	+	1.02331i	−0.988296	+	0.152546i
$46$	0.392582			0.0578830
$47$	−4.60530	+	4.60530i	−0.671752	+	0.671752i	−0.958120	−	0.286367i	$-0.907552\pi$
$47$	−4.60530	+	4.60530i	−0.671752	+	0.671752i	0.286367	+	0.958120i	$0.407552\pi$
$48$	1.31504	−	1.12724i	0.189809	−	0.162703i
$49$			15.2246i			2.17495i
$50$	−0.856449	+	4.92610i	−0.121120	+	0.696656i
$51$	−0.798547	+	10.3850i	−0.111819	+	1.45420i
$52$	−3.42826	−	3.42826i	−0.475414	−	0.475414i
$53$	−4.02811	−	4.02811i	−0.553303	−	0.553303i	0.374089	−	0.927393i	$-0.377955\pi$
$53$	−4.02811	−	4.02811i	−0.553303	−	0.553303i	−0.927393	+	0.374089i	$0.877955\pi$
$54$	5.05905	+	1.18576i	0.688449	+	0.161362i
$55$	−2.13177	+	0.674951i	−0.287448	+	0.0910104i
$56$		−	4.71430i		−	0.629975i
$57$	−1.29021	−	1.50515i	−0.170892	−	0.199362i
$58$	2.49981	−	2.49981i	0.328241	−	0.328241i
$59$	−10.8278			−1.40966			−0.704832	−	0.709375i	$-0.748977\pi$
$59$	−10.8278			−1.40966			−0.704832	+	0.709375i	$0.748977\pi$
$60$	2.04253	−	3.29061i	0.263689	−	0.424815i
$61$	0.449010			0.0574899			0.0287449	−	0.999587i	$-0.490849\pi$
$61$	0.449010			0.0574899			0.0287449	+	0.999587i	$0.490849\pi$
$62$	−2.00592	+	2.00592i	−0.254752	+	0.254752i
$63$	11.4119	−	8.35405i	1.43776	−	1.05251i
$64$			1.00000i			0.125000i
$65$	−9.62216	−	4.99435i	−1.19348	−	0.619473i
$66$	1.72695	+	0.132792i	0.212573	+	0.0163456i
$67$	4.76352	+	4.76352i	0.581956	+	0.581956i	0.935440	−	0.353484i	$-0.115003\pi$
$67$	4.76352	+	4.76352i	0.581956	+	0.581956i	−0.353484	+	0.935440i	$0.615003\pi$
$68$	−4.25219	−	4.25219i	−0.515654	−	0.515654i
$69$	−0.677970	−	0.0521318i	−0.0816180	−	0.00627593i
$70$	−3.18192	−	10.0498i	−0.380312	−	1.20118i
$71$		−	3.85485i		−	0.457487i	−0.973487	−	0.228743i	$-0.926538\pi$
$71$		−	3.85485i		−	0.457487i	0.973487	−	0.228743i	$-0.0734617\pi$
$72$	−2.42070	+	1.77207i	−0.285282	+	0.208840i
$73$	−5.71747	+	5.71747i	−0.669179	+	0.669179i	−0.957526	−	0.288347i	$-0.906894\pi$
$73$	−5.71747	+	5.71747i	−0.669179	+	0.669179i	0.288347	+	0.957526i	$0.406894\pi$
$74$	−4.31694			−0.501835
$75$	2.13320	−	8.39342i	0.246320	−	0.969188i
$76$	1.14457			0.131291
$77$	3.33351	−	3.33351i	0.379889	−	0.379889i
$78$	5.46519	+	6.37568i	0.618811	+	0.721904i
$79$		−	1.05639i		−	0.118854i	−0.998233	−	0.0594268i	$-0.981073\pi$
$79$		−	1.05639i		−	0.118854i	0.998233	−	0.0594268i	$-0.0189273\pi$
$80$	0.674951	+	2.13177i	0.0754618	+	0.238339i
$81$	−8.57928	−	2.71956i	−0.953253	−	0.302173i
$82$	7.74109	+	7.74109i	0.854861	+	0.854861i
$83$	−2.72084	−	2.72084i	−0.298651	−	0.298651i	0.541835	−	0.840485i	$-0.317730\pi$
$83$	−2.72084	−	2.72084i	−0.298651	−	0.298651i	−0.840485	+	0.541835i	$0.817730\pi$
$84$	−0.626022	+	8.14137i	−0.0683046	+	0.888297i
$85$	−11.9347	−	6.19467i	−1.29450	−	0.671907i
$86$		−	4.12319i		−	0.444615i
$87$	−4.64901	+	3.98510i	−0.498426	+	0.427247i
$88$	−0.707107	+	0.707107i	−0.0753778	+	0.0753778i
$89$	−3.84257			−0.407312			−0.203656	−	0.979042i	$-0.565282\pi$
$89$	−3.84257			−0.407312			−0.203656	+	0.979042i	$0.565282\pi$
$90$	−3.96431	+	5.41149i	−0.417875	+	0.570421i
$91$	22.8563			2.39599
$92$	0.277597	−	0.277597i	0.0289415	−	0.0289415i
$93$	3.73050	−	3.19776i	0.386835	−	0.331592i
$94$			6.51288i			0.671752i
$95$	2.43996	−	0.772529i	0.250335	−	0.0792598i
$96$	0.132792	−	1.72695i	0.0135530	−	0.176256i
$97$	4.30030	+	4.30030i	0.436629	+	0.436629i	0.890876	−	0.454247i	$-0.150092\pi$
$97$	4.30030	+	4.30030i	0.436629	+	0.436629i	−0.454247	+	0.890876i	$0.650092\pi$
$98$	10.7654	+	10.7654i	1.08747	+	1.08747i
$99$	−2.96473	−	0.458652i	−0.297967	−	0.0460962i
$100$	2.87768	+	4.08888i	0.287768	+	0.408888i
$101$			18.2655i			1.81749i	0.417357	+	0.908743i	$0.362957\pi$
$101$			18.2655i			1.81749i	−0.417357	+	0.908743i	$0.637043\pi$
$102$	6.77868	+	7.90799i	0.671189	+	0.783008i
$103$	1.95089	−	1.95089i	0.192227	−	0.192227i	−0.604430	−	0.796658i	$-0.706599\pi$
$103$	1.95089	−	1.95089i	0.192227	−	0.192227i	0.796658	+	0.604430i	$0.206599\pi$
$104$	−4.84829			−0.475414
$105$	4.16049	+	17.7781i	0.406023	+	1.73496i
$106$	−5.69661			−0.553303
$107$	3.28312	−	3.28312i	0.317392	−	0.317392i	−0.530373	−	0.847764i	$-0.677948\pi$
$107$	3.28312	−	3.28312i	0.317392	−	0.317392i	0.847764	+	0.530373i	$0.177948\pi$
$108$	4.41575	−	2.73883i	0.424906	−	0.263544i
$109$		−	15.8668i		−	1.51977i	−0.650060	−	0.759883i	$-0.725256\pi$
$109$		−	15.8668i		−	1.51977i	0.650060	−	0.759883i	$-0.274744\pi$
$110$	−1.03013	+	1.98465i	−0.0982187	+	0.189229i
$111$	7.45516	+	0.573257i	0.707612	+	0.0544111i
$112$	−3.33351	−	3.33351i	−0.314987	−	0.314987i
$113$	0.904071	+	0.904071i	0.0850478	+	0.0850478i	0.748351	−	0.663303i	$-0.230846\pi$
$113$	0.904071	+	0.904071i	0.0850478	+	0.0850478i	−0.663303	+	0.748351i	$0.730846\pi$
$114$	−1.97662	−	0.151990i	−0.185127	−	0.0142352i
$115$	0.404409	−	0.779137i	0.0377113	−	0.0726549i
$116$		−	3.53526i		−	0.328241i
$117$	−8.59149	−	11.7362i	−0.794283	−	1.08502i
$118$	−7.65643	+	7.65643i	−0.704832	+	0.704832i
$119$	28.3495			2.59879
$120$	−0.882526	−	3.77109i	−0.0805633	−	0.344252i
$121$	−1.00000			−0.0909091
$122$	0.317498	−	0.317498i	0.0287449	−	0.0287449i
$123$	−12.3405	−	14.3965i	−1.11271	−	1.29809i
$124$			2.83680i			0.254752i
$125$	8.89435	+	6.77426i	0.795534	+	0.605908i
$126$	2.16222	−	13.9766i	0.192626	−	1.24514i
$127$	12.4309	+	12.4309i	1.10306	+	1.10306i	0.994039	+	0.109021i	$0.0347716\pi$
$127$	12.4309	+	12.4309i	1.10306	+	1.10306i	0.109021	+	0.994039i	$0.465228\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−0.547528	+	7.12056i	−0.0482071	+	0.626930i
$130$	−10.3354	+	3.27236i	−0.906477	+	0.287005i
$131$			0.143590i			0.0125455i	0.999980	+	0.00627276i	$0.00199670\pi$
$131$			0.143590i			0.0125455i	−0.999980	+	0.00627276i	$0.998003\pi$
$132$	1.31504	−	1.12724i	0.114459	−	0.0981138i
$133$	−3.81544	+	3.81544i	−0.330841	+	0.330841i
$134$	6.73663			0.581956
$135$	7.56478	−	8.81896i	0.651073	−	0.759015i
$136$	−6.01351			−0.515654
$137$	13.1972	−	13.1972i	1.12751	−	1.12751i	0.136934	−	0.990580i	$-0.456275\pi$
$137$	13.1972	−	13.1972i	1.12751	−	1.12751i	0.990580	−	0.136934i	$-0.0437247\pi$
$138$	−0.516260	+	0.442534i	−0.0439470	+	0.0376710i
$139$		−	6.75125i		−	0.572634i	−0.958135	−	0.286317i	$-0.907569\pi$
$139$		−	6.75125i		−	0.572634i	0.958135	−	0.286317i	$-0.0924310\pi$
$140$	−9.35624	−	4.85632i	−0.790747	−	0.410434i
$141$	0.864860	−	11.2474i	0.0728343	−	0.947205i
$142$	−2.72579	−	2.72579i	−0.228743	−	0.228743i
$143$	−3.42826	−	3.42826i	−0.286685	−	0.286685i
$144$	−0.458652	+	2.96473i	−0.0382210	+	0.247061i
$145$	−2.38613	−	7.53636i	−0.198157	−	0.625861i
$146$			8.08572i			0.669179i
$147$	−17.1618	−	20.0210i	−1.41548	−	1.65130i
$148$	−3.05254	+	3.05254i	−0.250917	+	0.250917i
$149$	−22.2180			−1.82017			−0.910084	−	0.414425i	$-0.863983\pi$
$149$	−22.2180			−1.82017			−0.910084	+	0.414425i	$0.863983\pi$
$150$	−4.42665	−	7.44344i	−0.361434	−	0.607754i
$151$	−13.0150			−1.05915			−0.529573	−	0.848264i	$-0.677648\pi$
$151$	−13.0150			−1.05915			−0.529573	+	0.848264i	$0.677648\pi$
$152$	0.809333	−	0.809333i	0.0656456	−	0.0656456i
$153$	−10.6563	−	14.5569i	−0.861514	−	1.17685i
$154$		−	4.71430i		−	0.379889i
$155$	1.91470	+	6.04740i	0.153792	+	0.485739i
$156$	8.37276	+	0.643815i	0.670358	+	0.0515464i
$157$	6.79217	+	6.79217i	0.542074	+	0.542074i	0.924137	−	0.382062i	$-0.124786\pi$
$157$	6.79217	+	6.79217i	0.542074	+	0.542074i	−0.382062	+	0.924137i	$0.624786\pi$
$158$	−0.746983	−	0.746983i	−0.0594268	−	0.0594268i
$159$	9.83777	+	0.756465i	0.780186	+	0.0599916i
$160$	1.98465	+	1.03013i	0.156900	+	0.0814386i
$161$			1.85075i			0.145859i
$162$	−7.98948	+	4.14345i	−0.627713	+	0.325540i
$163$	1.78859	−	1.78859i	0.140093	−	0.140093i	−0.633582	−	0.773675i	$-0.718416\pi$
$163$	1.78859	−	1.78859i	0.140093	−	0.140093i	0.773675	+	0.633582i	$0.218416\pi$
$164$	10.9476			0.854861
$165$	2.04253	−	3.29061i	0.159010	−	0.256173i
$166$	−3.84784			−0.298651
$167$	−5.12540	+	5.12540i	−0.396615	+	0.396615i	−0.877037	−	0.480422i	$-0.840484\pi$
$167$	−5.12540	+	5.12540i	−0.396615	+	0.396615i	0.480422	+	0.877037i	$0.340484\pi$
$168$	5.31416	+	6.19948i	0.409996	+	0.478301i
$169$		−	10.5059i		−	0.808146i
$170$	−12.8194	+	4.05882i	−0.983204	+	0.311298i
$171$	3.39334	+	0.524959i	0.259495	+	0.0401446i
$172$	−2.91554	−	2.91554i	−0.222308	−	0.222308i
$173$	13.8077	+	13.8077i	1.04978	+	1.04978i	0.998694	+	0.0510894i	$0.0162693\pi$
$173$	13.8077	+	13.8077i	1.04978	+	1.04978i	0.0510894	+	0.998694i	$0.483731\pi$
$174$	−0.469455	+	6.10523i	−0.0355893	+	0.462836i
$175$	−23.2231	−	4.03756i	−1.75550	−	0.305211i
$176$			1.00000i			0.0753778i
$177$	14.2390	−	12.2056i	1.07027	−	0.917428i
$178$	−2.71711	+	2.71711i	−0.203656	+	0.203656i
$179$	−24.9262			−1.86307			−0.931534	−	0.363654i	$-0.881529\pi$
$179$	−24.9262			−1.86307			−0.931534	+	0.363654i	$0.881529\pi$
$180$	1.02331	+	6.62969i	0.0762730	+	0.494148i
$181$	13.2190			0.982560			0.491280	−	0.871002i	$-0.336529\pi$
$181$	13.2190			0.982560			0.491280	+	0.871002i	$0.336529\pi$
$182$	16.1618	−	16.1618i	1.19799	−	1.19799i
$183$	−0.590466	+	0.506143i	−0.0436485	+	0.0374152i
$184$		−	0.392582i		−	0.0289415i
$185$	−4.44700	+	8.56763i	−0.326950	+	0.629905i
$186$	0.376705	−	4.89902i	0.0276213	−	0.359213i
$187$	−4.25219	−	4.25219i	−0.310951	−	0.310951i
$188$	4.60530	+	4.60530i	0.335876	+	0.335876i
$189$	−5.59004	+	23.8499i	−0.406616	+	1.73482i
$190$	1.17905	−	2.27157i	0.0855374	−	0.164797i
$191$		−	16.1440i		−	1.16814i	−0.811704	−	0.584069i	$-0.801460\pi$
$191$		−	16.1440i		−	1.16814i	0.811704	−	0.584069i	$-0.198540\pi$
$192$	−1.12724	−	1.31504i	−0.0813517	−	0.0949047i
$193$	3.84880	−	3.84880i	0.277043	−	0.277043i	−0.554885	−	0.831927i	$-0.687238\pi$
$193$	3.84880	−	3.84880i	0.277043	−	0.277043i	0.831927	+	0.554885i	$0.187238\pi$
$194$	6.08154			0.436629
$195$	18.2833	−	4.27874i	1.30930	−	0.306407i
$196$	15.2246			1.08747
$197$	−1.60411	+	1.60411i	−0.114288	+	0.114288i	−0.761938	−	0.647650i	$-0.775752\pi$
$197$	−1.60411	+	1.60411i	−0.114288	+	0.114288i	0.647650	+	0.761938i	$0.275752\pi$
$198$	−2.42070	+	1.77207i	−0.172032	+	0.125935i
$199$			20.7297i			1.46949i	0.678345	+	0.734744i	$0.262698\pi$
$199$			20.7297i			1.46949i	−0.678345	+	0.734744i	$0.737302\pi$
$200$	4.92610	+	0.856449i	0.348328	+	0.0605601i
$201$	−11.6338	−	0.894572i	−0.820588	−	0.0630982i
$202$	12.9157	+	12.9157i	0.908743	+	0.908743i
$203$	11.7848	+	11.7848i	0.827134	+	0.827134i
$204$	10.3850	+	0.798547i	0.727099	+	0.0559095i
$205$	23.3377	−	7.38907i	1.62997	−	0.516075i
$206$		−	2.75898i		−	0.192227i
$207$	0.950322	−	0.695681i	0.0660519	−	0.0483532i
$208$	−3.42826	+	3.42826i	−0.237707	+	0.237707i
$209$	1.14457			0.0791716
$210$	15.5129	+	9.62908i	1.07049	+	0.664469i
$211$	−14.8071			−1.01936			−0.509680	−	0.860364i	$-0.670236\pi$
$211$	−14.8071			−1.01936			−0.509680	+	0.860364i	$0.670236\pi$
$212$	−4.02811	+	4.02811i	−0.276652	+	0.276652i
$213$	4.34535	+	5.06928i	0.297739	+	0.347341i
$214$		−	4.64304i		−	0.317392i
$215$	−8.18310	−	4.24741i	−0.558083	−	0.289671i
$216$	1.18576	−	5.05905i	0.0806810	−	0.344225i
$217$	−9.45650	−	9.45650i	−0.641949	−	0.641949i
$218$	−11.2195	−	11.2195i	−0.759883	−	0.759883i
$219$	1.07372	−	13.9637i	0.0725553	−	0.943576i
$220$	0.674951	+	2.13177i	0.0455052	+	0.143724i
$221$		−	29.1552i		−	1.96119i
$222$	5.67695	−	4.86624i	0.381012	−	0.326601i
$223$	−13.0398	+	13.0398i	−0.873209	+	0.873209i	−0.992821	−	0.119611i	$-0.961835\pi$
$223$	−13.0398	+	13.0398i	−0.873209	+	0.873209i	0.119611	+	0.992821i	$0.461835\pi$
$224$	−4.71430			−0.314987
$225$	6.65618	+	13.4423i	0.443745	+	0.896153i
$226$	1.27855			0.0850478
$227$	−3.05955	+	3.05955i	−0.203069	+	0.203069i	−0.801314	−	0.598244i	$-0.795865\pi$
$227$	−3.05955	+	3.05955i	−0.203069	+	0.203069i	0.598244	+	0.801314i	$0.295865\pi$
$228$	−1.50515	+	1.29021i	−0.0996812	+	0.0854461i
$229$		−	12.8717i		−	0.850585i	−0.905056	−	0.425292i	$-0.860171\pi$
$229$		−	12.8717i		−	0.850585i	0.905056	−	0.425292i	$-0.139829\pi$
$230$	−0.264973	−	0.836893i	−0.0174718	−	0.0551831i
$231$	−0.626022	+	8.14137i	−0.0411892	+	0.535663i
$232$	−2.49981	−	2.49981i	−0.164120	−	0.164120i
$233$	−4.88936	−	4.88936i	−0.320313	−	0.320313i	0.528574	−	0.848887i	$-0.322727\pi$
$233$	−4.88936	−	4.88936i	−0.320313	−	0.320313i	−0.848887	+	0.528574i	$0.822727\pi$
$234$	−14.3739	−	2.22368i	−0.939650	−	0.145366i
$235$	12.9258	+	6.70909i	0.843186	+	0.437653i
$236$			10.8278i			0.704832i
$237$	1.19081	+	1.38920i	0.0773515	+	0.0902381i
$238$	20.0461	−	20.0461i	1.29940	−	1.29940i
$239$	−1.74225			−0.112697			−0.0563485	−	0.998411i	$-0.517946\pi$
$239$	−1.74225			−0.112697			−0.0563485	+	0.998411i	$0.517946\pi$
$240$	−3.29061	−	2.04253i	−0.212408	−	0.131844i
$241$	−18.0387			−1.16197			−0.580987	−	0.813913i	$-0.697333\pi$
$241$	−18.0387			−1.16197			−0.580987	+	0.813913i	$0.697333\pi$
$242$	−0.707107	+	0.707107i	−0.0454545	+	0.0454545i
$243$	14.3477	−	6.09459i	0.920404	−	0.390968i
$244$		−	0.449010i		−	0.0287449i
$245$	32.4554	−	10.2759i	2.07350	−	0.656501i
$246$	−18.9059	−	1.45375i	−1.20540	−	0.0926878i
$247$	3.92388	+	3.92388i	0.249671	+	0.249671i
$248$	2.00592	+	2.00592i	0.127376	+	0.127376i
$249$	6.64505	+	0.510964i	0.421113	+	0.0323810i
$250$	11.0794	−	1.49913i	0.700721	−	0.0948130i
$251$			21.0504i			1.32869i	0.747426	+	0.664345i	$0.231289\pi$
$251$			21.0504i			1.32869i	−0.747426	+	0.664345i	$0.768711\pi$
$252$	−8.35405	−	11.4119i	−0.526256	−	0.718882i
$253$	0.277597	−	0.277597i	0.0174524	−	0.0174524i
$254$	17.5799			1.10306
$255$	22.6775	−	5.30708i	1.42012	−	0.332342i
$256$	1.00000			0.0625000
$257$	−8.61243	+	8.61243i	−0.537228	+	0.537228i	−0.922714	−	0.385485i	$-0.874034\pi$
$257$	−8.61243	+	8.61243i	−0.537228	+	0.537228i	0.385485	+	0.922714i	$0.374034\pi$
$258$	4.64783	+	5.42216i	0.289362	+	0.337569i
$259$		−	20.3514i		−	1.26457i
$260$	−4.99435	+	9.62216i	−0.309736	+	0.596741i
$261$	1.62145	−	10.4811i	0.100366	−	0.648764i
$262$	0.101534	+	0.101534i	0.00627276	+	0.00627276i
$263$	10.8893	+	10.8893i	0.671462	+	0.671462i	0.958053	−	0.286591i	$-0.0925222\pi$
$263$	10.8893	+	10.8893i	0.671462	+	0.671462i	−0.286591	+	0.958053i	$0.592522\pi$
$264$	0.132792	−	1.72695i	0.00817280	−	0.106287i
$265$	−5.86822	+	11.3058i	−0.360482	+	0.694508i
$266$			5.39585i			0.330841i
$267$	5.05313	−	4.33151i	0.309247	−	0.265084i
$268$	4.76352	−	4.76352i	0.290978	−	0.290978i
$269$	−12.3295			−0.751745			−0.375872	−	0.926671i	$-0.622657\pi$
$269$	−12.3295			−0.751745			−0.375872	+	0.926671i	$0.622657\pi$
$270$	−0.886835	−	11.5851i	−0.0539711	−	0.705044i
$271$	14.6622			0.890664			0.445332	−	0.895366i	$-0.353086\pi$
$271$	14.6622			0.890664			0.445332	+	0.895366i	$0.353086\pi$
$272$	−4.25219	+	4.25219i	−0.257827	+	0.257827i
$273$	−30.0569	+	25.7646i	−1.81913	+	1.55934i
$274$		−	18.6637i		−	1.12751i
$275$	2.87768	+	4.08888i	0.173531	+	0.246569i
$276$	−0.0521318	+	0.677970i	−0.00313796	+	0.0408090i
$277$	19.4307	+	19.4307i	1.16748	+	1.16748i	0.982799	+	0.184679i	$0.0591245\pi$
$277$	19.4307	+	19.4307i	1.16748	+	1.16748i	0.184679	+	0.982799i	$0.440876\pi$
$278$	−4.77386	−	4.77386i	−0.286317	−	0.286317i
$279$	−1.30110	+	8.41035i	−0.0778950	+	0.503514i
$280$	−10.0498	+	3.18192i	−0.600590	+	0.190156i
$281$			27.8635i			1.66220i	0.556126	+	0.831098i	$0.312287\pi$
$281$			27.8635i			1.66220i	−0.556126	+	0.831098i	$0.687713\pi$
$282$	−7.34159	−	8.56469i	−0.437185	−	0.510020i
$283$	4.61843	−	4.61843i	0.274537	−	0.274537i	−0.556386	−	0.830924i	$-0.687813\pi$
$283$	4.61843	−	4.61843i	0.274537	−	0.274537i	0.830924	+	0.556386i	$0.187813\pi$
$284$	−3.85485			−0.228743
$285$	−2.33781	+	3.76633i	−0.138480	+	0.223098i
$286$	−4.84829			−0.286685
$287$	−36.4938	+	36.4938i	−2.15416	+	2.15416i
$288$	1.77207	+	2.42070i	0.104420	+	0.142641i
$289$		−	19.1623i		−	1.12719i
$290$	−7.01626	−	3.64177i	−0.412009	−	0.213852i
$291$	−10.5025	−	0.807581i	−0.615669	−	0.0473412i
$292$	5.71747	+	5.71747i	0.334589	+	0.334589i
$293$	−1.33505	−	1.33505i	−0.0779942	−	0.0779942i	0.667034	−	0.745028i	$-0.267564\pi$
$293$	−1.33505	−	1.33505i	−0.0779942	−	0.0779942i	−0.745028	+	0.667034i	$0.767564\pi$
$294$	−26.2922	−	2.02171i	−1.53339	−	0.117909i
$295$	7.30825	+	23.0824i	0.425503	+	1.34391i
$296$			4.31694i			0.250917i
$297$	4.41575	−	2.73883i	0.256228	−	0.158923i
$298$	−15.7105	+	15.7105i	−0.910084	+	0.910084i
$299$	1.90335			0.110073
$300$	−8.39342	−	2.13320i	−0.484594	−	0.123160i
$301$	19.4380			1.12039
$302$	−9.20300	+	9.20300i	−0.529573	+	0.529573i
$303$	−20.5896	−	24.0198i	−1.18284	−	1.37990i
$304$		−	1.14457i		−	0.0656456i
$305$	−0.303060	−	0.957187i	−0.0173532	−	0.0548083i
$306$	−17.8284	−	2.75811i	−1.01918	−	0.157670i
$307$	−5.80877	−	5.80877i	−0.331524	−	0.331524i	0.521641	−	0.853165i	$-0.325320\pi$
$307$	−5.80877	−	5.80877i	−0.331524	−	0.331524i	−0.853165	+	0.521641i	$0.825320\pi$
$308$	−3.33351	−	3.33351i	−0.189945	−	0.189945i
$309$	−0.366371	+	4.76463i	−0.0208421	+	0.271050i
$310$	5.63005	+	2.92226i	0.319766	+	0.165973i
$311$			9.85109i			0.558604i	0.960203	+	0.279302i	$0.0901031\pi$
$311$			9.85109i			0.558604i	−0.960203	+	0.279302i	$0.909897\pi$
$312$	6.37568	−	5.46519i	0.360952	−	0.309406i
$313$	14.0537	−	14.0537i	0.794363	−	0.794363i	−0.187837	−	0.982200i	$-0.560148\pi$
$313$	14.0537	−	14.0537i	0.794363	−	0.794363i	0.982200	+	0.187837i	$0.0601476\pi$
$314$	9.60558			0.542074
$315$	−25.5114	−	18.6890i	−1.43740	−	1.05300i
$316$	−1.05639			−0.0594268
$317$	3.63115	−	3.63115i	0.203946	−	0.203946i	−0.597742	−	0.801688i	$-0.703935\pi$
$317$	3.63115	−	3.63115i	0.203946	−	0.203946i	0.801688	+	0.597742i	$0.203935\pi$
$318$	7.49125	−	6.42145i	0.420089	−	0.360097i
$319$		−	3.53526i		−	0.197937i
$320$	2.13177	−	0.674951i	0.119170	−	0.0377309i
$321$	−0.616559	+	8.01831i	−0.0344130	+	0.447538i
$322$	1.30868	+	1.30868i	0.0729296	+	0.0729296i
$323$	4.86693	+	4.86693i	0.270803	+	0.270803i
$324$	−2.71956	+	8.57928i	−0.151087	+	0.476627i
$325$	−4.15231	+	23.8832i	−0.230329	+	1.32480i
$326$		−	2.52944i		−	0.140093i
$327$	17.8857	+	20.8655i	0.989084	+	1.15386i
$328$	7.74109	−	7.74109i	0.427430	−	0.427430i
$329$	−30.7037			−1.69275
$330$	−0.882526	−	3.77109i	−0.0485815	−	0.207592i
$331$	−11.2947			−0.620811			−0.310405	−	0.950604i	$-0.600465\pi$
$331$	−11.2947			−0.620811			−0.310405	+	0.950604i	$0.600465\pi$
$332$	−2.72084	+	2.72084i	−0.149325	+	0.149325i
$333$	−10.4500	+	7.64991i	−0.572658	+	0.419213i
$334$			7.24841i			0.396615i
$335$	6.93958	−	13.3699i	0.379150	−	0.730473i
$336$	8.14137	+	0.626022i	0.444148	+	0.0341523i
$337$	−11.7847	−	11.7847i	−0.641954	−	0.641954i	0.309081	−	0.951036i	$-0.399978\pi$
$337$	−11.7847	−	11.7847i	−0.641954	−	0.641954i	−0.951036	+	0.309081i	$0.899978\pi$
$338$	−7.42879	−	7.42879i	−0.404073	−	0.404073i
$339$	−2.20799	−	0.169781i	−0.119922	−	0.00922126i
$340$	−6.19467	+	11.9347i	−0.335953	+	0.647251i
$341$			2.83680i			0.153621i
$342$	2.77066	−	2.02825i	0.149820	−	0.109675i
$343$	−27.4169	+	27.4169i	−1.48037	+	1.48037i
$344$	−4.12319			−0.222308
$345$	0.346464	+	1.48046i	0.0186530	+	0.0797054i
$346$	19.5271			1.04978
$347$	14.6606	−	14.6606i	0.787022	−	0.787022i	−0.193983	−	0.981005i	$-0.562141\pi$
$347$	14.6606	−	14.6606i	0.787022	−	0.787022i	0.981005	+	0.193983i	$0.0621407\pi$
$348$	3.98510	+	4.64901i	0.213624	+	0.249213i
$349$		−	10.3131i		−	0.552049i	−0.961151	−	0.276025i	$-0.910983\pi$
$349$		−	10.3131i		−	0.552049i	0.961151	−	0.276025i	$-0.0890171\pi$
$350$	−19.2762	+	13.5662i	−1.03036	+	0.725146i
$351$	24.5277	+	5.74892i	1.30919	+	0.306855i
$352$	0.707107	+	0.707107i	0.0376889	+	0.0376889i
$353$	−10.4743	−	10.4743i	−0.557488	−	0.557488i	0.371103	−	0.928592i	$-0.378980\pi$
$353$	−10.4743	−	10.4743i	−0.557488	−	0.557488i	−0.928592	+	0.371103i	$0.878980\pi$
$354$	1.43785	−	18.6991i	0.0764209	−	0.993848i
$355$	−8.21766	+	2.60184i	−0.436148	+	0.138091i
$356$			3.84257i			0.203656i
$357$	−37.2807	+	31.9567i	−1.97310	+	1.69133i
$358$	−17.6255	+	17.6255i	−0.931534	+	0.931534i
$359$	2.08196			0.109882			0.0549408	−	0.998490i	$-0.482503\pi$
$359$	2.08196			0.109882			0.0549408	+	0.998490i	$0.482503\pi$
$360$	5.41149	+	3.96431i	0.285211	+	0.208938i
$361$	17.6900			0.931050
$362$	9.34724	−	9.34724i	0.491280	−	0.491280i
$363$	1.31504	−	1.12724i	0.0690216	−	0.0591649i
$364$		−	22.8563i		−	1.19799i
$365$	16.0473	+	8.32931i	0.839956	+	0.435976i
$366$	−0.0596251	+	0.775420i	−0.00311665	+	0.0405318i
$367$	−19.9230	−	19.9230i	−1.03997	−	1.03997i	−0.999167	−	0.0408055i	$-0.987008\pi$
$367$	−19.9230	−	19.9230i	−1.03997	−	1.03997i	−0.0408055	−	0.999167i	$-0.512992\pi$
$368$	−0.277597	−	0.277597i	−0.0144707	−	0.0144707i
$369$	32.4566	+	5.02112i	1.68962	+	0.261389i
$370$	2.91373	+	9.20273i	0.151477	+	0.478427i
$371$		−	26.8555i		−	1.39427i
$372$	−3.19776	−	3.73050i	−0.165796	−	0.193417i
$373$	−15.0976	+	15.0976i	−0.781726	+	0.781726i	−0.980122	−	0.198396i	$-0.936427\pi$
$373$	−15.0976	+	15.0976i	−0.781726	+	0.781726i	0.198396	+	0.980122i	$0.436427\pi$
$374$	−6.01351			−0.310951
$375$	−19.3326	+	1.11766i	−0.998333	+	0.0577160i
$376$	6.51288			0.335876
$377$	12.1198	−	12.1198i	0.624201	−	0.624201i
$378$	12.9116	+	20.8172i	0.664103	+	1.07072i
$379$		−	16.9640i		−	0.871384i	−0.900096	−	0.435692i	$-0.856504\pi$
$379$		−	16.9640i		−	0.871384i	0.900096	−	0.435692i	$-0.143496\pi$
$380$	−0.772529	−	2.43996i	−0.0396299	−	0.125167i
$381$	−30.3596	−	2.33447i	−1.55537	−	0.119599i
$382$	−11.4155	−	11.4155i	−0.584069	−	0.584069i
$383$	6.62488	+	6.62488i	0.338516	+	0.338516i	0.855808	−	0.517293i	$-0.173060\pi$
$383$	6.62488	+	6.62488i	0.338516	+	0.338516i	−0.517293	+	0.855808i	$0.673060\pi$
$384$	−1.72695	−	0.132792i	−0.0881282	−	0.00677652i
$385$	−9.35624	−	4.85632i	−0.476838	−	0.247501i
$386$		−	5.44303i		−	0.277043i
$387$	−7.30657	−	9.98100i	−0.371414	−	0.507363i
$388$	4.30030	−	4.30030i	0.218315	−	0.218315i
$389$	5.38854			0.273210			0.136605	−	0.990626i	$-0.456381\pi$
$389$	5.38854			0.273210			0.136605	+	0.990626i	$0.456381\pi$
$390$	9.90275	−	15.9538i	0.501445	−	0.807852i
$391$	2.36079			0.119390
$392$	10.7654	−	10.7654i	0.543736	−	0.543736i
$393$	−0.161861	−	0.188827i	−0.00816480	−	0.00952504i
$394$			2.26856i			0.114288i
$395$	−2.25199	+	0.713014i	−0.113310	+	0.0358756i
$396$	−0.458652	+	2.96473i	−0.0230481	+	0.148983i
$397$	−12.8557	−	12.8557i	−0.645208	−	0.645208i	0.306623	−	0.951831i	$-0.400801\pi$
$397$	−12.8557	−	12.8557i	−0.645208	−	0.645208i	−0.951831	+	0.306623i	$0.900801\pi$
$398$	14.6581	+	14.6581i	0.734744	+	0.734744i
$399$	0.716526	−	9.31837i	0.0358712	−	0.466502i
$400$	4.08888	−	2.87768i	0.204444	−	0.143884i
$401$		−	5.55956i		−	0.277631i	−0.990318	−	0.138816i	$-0.955670\pi$
$401$		−	5.55956i		−	0.277631i	0.990318	−	0.138816i	$-0.0443295\pi$
$402$	−8.85893	+	7.59381i	−0.441843	+	0.378745i
$403$	−9.72527	+	9.72527i	−0.484450	+	0.484450i
$404$	18.2655			0.908743
$405$	−0.00688291	+	20.1246i	−0.000342015	+	1.00000i
$406$	16.6663			0.827134
$407$	−3.05254	+	3.05254i	−0.151309	+	0.151309i
$408$	7.90799	−	6.77868i	0.391504	−	0.335595i
$409$		−	7.15226i		−	0.353657i	−0.984242	−	0.176828i	$-0.943416\pi$
$409$		−	7.15226i		−	0.353657i	0.984242	−	0.176828i	$-0.0565837\pi$
$410$	11.2774	−	21.7271i	0.556950	−	1.07302i
$411$	−2.47839	+	32.2313i	−0.122250	+	1.58985i
$412$	−1.95089	−	1.95089i	−0.0961137	−	0.0961137i
$413$	−36.0947	−	36.0947i	−1.77610	−	1.77610i
$414$	0.180058	−	1.16390i	0.00884938	−	0.0572025i
$415$	−3.96377	+	7.63663i	−0.194574	+	0.374867i
$416$			4.84829i			0.237707i
$417$	7.61029	+	8.87815i	0.372678	+	0.434765i
$418$	0.809333	−	0.809333i	0.0395858	−	0.0395858i
$419$	16.8052			0.820990			0.410495	−	0.911863i	$-0.365356\pi$
$419$	16.8052			0.820990			0.410495	+	0.911863i	$0.365356\pi$
$420$	17.7781	−	4.16049i	0.867481	−	0.203011i
$421$	36.1798			1.76329			0.881647	−	0.471909i	$-0.156435\pi$
$421$	36.1798			1.76329			0.881647	+	0.471909i	$0.156435\pi$
$422$	−10.4702	+	10.4702i	−0.509680	+	0.509680i
$423$	11.5413	+	15.7657i	0.561155	+	0.766556i
$424$			5.69661i			0.276652i
$425$	−5.15027	+	29.6232i	−0.249825	+	1.43693i
$426$	6.65715	+	0.511894i	0.322540	+	0.0248014i
$427$	1.49678	+	1.49678i	0.0724343	+	0.0724343i
$428$	−3.28312	−	3.28312i	−0.158696	−	0.158696i
$429$	8.37276	+	0.643815i	0.404241	+	0.0310837i
$430$	−8.78970	+	2.78295i	−0.423877	+	0.134206i
$431$		−	0.882142i		−	0.0424913i	−0.999774	−	0.0212456i	$-0.993237\pi$
$431$		−	0.882142i		−	0.0424913i	0.999774	−	0.0212456i	$-0.00676321\pi$
$432$	−2.73883	−	4.41575i	−0.131772	−	0.212453i
$433$	−1.55335	+	1.55335i	−0.0746491	+	0.0746491i	−0.743446	−	0.668796i	$-0.766810\pi$
$433$	−1.55335	+	1.55335i	−0.0746491	+	0.0746491i	0.668796	+	0.743446i	$0.266810\pi$
$434$	−13.3735			−0.641949
$435$	11.6332	+	7.22086i	0.557767	+	0.346214i
$436$	−15.8668			−0.759883
$437$	−0.317729	+	0.317729i	−0.0151991	+	0.0151991i
$438$	−9.11456	−	10.6330i	−0.435511	−	0.508066i
$439$			9.54662i			0.455635i	0.973704	+	0.227818i	$0.0731590\pi$
$439$			9.54662i			0.455635i	−0.973704	+	0.227818i	$0.926841\pi$
$440$	1.98465	+	1.03013i	0.0946145	+	0.0491093i
$441$	45.1369	+	6.98280i	2.14938	+	0.332514i
$442$	−20.6159	−	20.6159i	−0.980596	−	0.980596i
$443$	16.1767	+	16.1767i	0.768580	+	0.768580i	0.977856	−	0.209277i	$-0.0671109\pi$
$443$	16.1767	+	16.1767i	0.768580	+	0.768580i	−0.209277	+	0.977856i	$0.567111\pi$
$444$	0.573257	−	7.45516i	0.0272056	−	0.353806i
$445$	2.59355	+	8.19148i	0.122946	+	0.388314i
$446$			18.4411i			0.873209i
$447$	29.2175	−	25.0450i	1.38194	−	1.18459i
$448$	−3.33351	+	3.33351i	−0.157494	+	0.157494i
$449$	33.9748			1.60337			0.801686	−	0.597746i	$-0.203937\pi$
$449$	33.9748			1.60337			0.801686	+	0.597746i	$0.203937\pi$
$450$	14.2118	+	4.79851i	0.669949	+	0.226204i
$451$	10.9476			0.515500
$452$	0.904071	−	0.904071i	0.0425239	−	0.0425239i
$453$	17.1152	−	14.6711i	0.804144	−	0.689307i
$454$			4.32685i			0.203069i
$455$	−15.4269	−	48.7243i	−0.723223	−	2.28423i
$456$	−0.151990	+	1.97662i	−0.00711758	+	0.0925636i
$457$	−20.9397	−	20.9397i	−0.979518	−	0.979518i	0.0202767	−	0.999794i	$-0.493545\pi$
$457$	−20.9397	−	20.9397i	−0.979518	−	0.979518i	−0.999794	+	0.0202767i	$0.993545\pi$
$458$	−9.10166	−	9.10166i	−0.425292	−	0.425292i
$459$	30.4226	+	7.13060i	1.42001	+	0.332828i
$460$	−0.779137	−	0.404409i	−0.0363275	−	0.0188556i
$461$		−	28.7843i		−	1.34062i	−0.742081	−	0.670310i	$-0.766161\pi$
$461$		−	28.7843i		−	1.34062i	0.742081	−	0.670310i	$-0.233839\pi$
$462$	5.31416	+	6.19948i	0.247237	+	0.288426i
$463$	−5.27100	+	5.27100i	−0.244964	+	0.244964i	−0.818900	−	0.573936i	$-0.805416\pi$
$463$	−5.27100	+	5.27100i	−0.244964	+	0.244964i	0.573936	+	0.818900i	$0.305416\pi$
$464$	−3.53526			−0.164120
$465$	−9.33479	−	5.79423i	−0.432890	−	0.268701i
$466$	−6.91460			−0.320313
$467$	4.21375	−	4.21375i	0.194989	−	0.194989i	−0.602859	−	0.797848i	$-0.705972\pi$
$467$	4.21375	−	4.21375i	0.194989	−	0.194989i	0.797848	+	0.602859i	$0.205972\pi$
$468$	−11.7362	+	8.59149i	−0.542508	+	0.397142i
$469$			31.7585i			1.46647i
$470$	13.8840	−	4.39588i	0.640419	−	0.202767i
$471$	−16.5884	−	1.27555i	−0.764352	−	0.0587741i
$472$	7.65643	+	7.65643i	0.352416	+	0.352416i
$473$	−2.91554	−	2.91554i	−0.134057	−	0.134057i
$474$	1.82434	+	0.140281i	0.0837948	+	0.00644332i
$475$	−3.29371	−	4.68001i	−0.151126	−	0.214734i
$476$		−	28.3495i		−	1.29940i
$477$	−13.7898	+	10.0948i	−0.631390	+	0.462207i
$478$	−1.23196	+	1.23196i	−0.0563485	+	0.0563485i
$479$	41.5438			1.89819			0.949093	−	0.314997i	$-0.102004\pi$
$479$	41.5438			1.89819			0.949093	+	0.314997i	$0.102004\pi$
$480$	−3.77109	+	0.882526i	−0.172126	+	0.0402816i
$481$	−20.9298			−0.954316
$482$	−12.7553	+	12.7553i	−0.580987	+	0.580987i
$483$	−2.08624	−	2.43380i	−0.0949272	−	0.110742i
$484$			1.00000i			0.0454545i
$485$	6.26475	−	12.0697i	0.284468	−	0.548058i
$486$	5.83581	−	14.4549i	0.264718	−	0.655686i
$487$	24.8749	+	24.8749i	1.12719	+	1.12719i	0.990632	+	0.136555i	$0.0436031\pi$
$487$	24.8749	+	24.8749i	1.12719	+	1.12719i	0.136555	+	0.990632i	$0.456397\pi$
$488$	−0.317498	−	0.317498i	−0.0143725	−	0.0143725i
$489$	−0.335890	+	4.36823i	−0.0151895	+	0.197538i
$490$	15.6833	−	30.2156i	0.708498	−	1.36500i
$491$		−	20.8884i		−	0.942679i	−0.881952	−	0.471340i	$-0.843771\pi$
$491$		−	20.8884i		−	0.942679i	0.881952	−	0.471340i	$-0.156229\pi$
$492$	−14.3965	+	12.3405i	−0.649043	+	0.556355i
$493$	15.0326	−	15.0326i	0.677035	−	0.677035i
$494$	5.54920			0.249671
$495$	1.02331	+	6.62969i	0.0459943	+	0.297983i
$496$	2.83680			0.127376
$497$	12.8502	−	12.8502i	0.576410	−	0.576410i
$498$	5.06006	−	4.33745i	0.226747	−	0.194366i
$499$			28.3321i			1.26832i	0.773202	+	0.634160i	$0.218654\pi$
$499$			28.3321i			1.26832i	−0.773202	+	0.634160i	$0.781346\pi$
$500$	6.77426	−	8.89435i	0.302954	−	0.397767i
$501$	0.962533	−	12.5177i	0.0430028	−	0.559248i
$502$	14.8849	+	14.8849i	0.664345	+	0.664345i
$503$	−9.14965	−	9.14965i	−0.407963	−	0.407963i	0.473065	−	0.881028i	$-0.343148\pi$
$503$	−9.14965	−	9.14965i	−0.407963	−	0.407963i	−0.881028	+	0.473065i	$0.843148\pi$
$504$	−13.9766	−	2.16222i	−0.622569	−	0.0963130i
$505$	38.9378	−	12.3283i	1.73271	−	0.548603i
$506$		−	0.392582i		−	0.0174524i
$507$	11.8427	+	13.8157i	0.525952	+	0.613575i
$508$	12.4309	−	12.4309i	0.551530	−	0.551530i
$509$	−17.5615			−0.778401			−0.389200	−	0.921153i	$-0.627249\pi$
$509$	−17.5615			−0.778401			−0.389200	+	0.921153i	$0.627249\pi$
$510$	12.2827	−	19.7881i	0.543889	−	0.876231i
$511$	−38.1185			−1.68626
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−5.05413	+	3.13478i	−0.223145	+	0.138404i
$514$			12.1798i			0.537228i
$515$	−5.47562	−	2.84210i	−0.241284	−	0.125238i
$516$	7.12056	+	0.547528i	0.313465	+	0.0241036i
$517$	4.60530	+	4.60530i	0.202541	+	0.202541i
$518$	−14.3906	−	14.3906i	−0.632286	−	0.632286i
$519$	−33.7224	−	2.59305i	−1.48025	−	0.113822i
$520$	3.27236	+	10.3354i	0.143502	+	0.453239i
$521$		−	12.6663i		−	0.554922i	−0.960737	−	0.277461i	$-0.910507\pi$
$521$		−	12.6663i		−	0.554922i	0.960737	−	0.277461i	$-0.0894929\pi$
$522$	−6.26472	−	8.55780i	−0.274199	−	0.374565i
$523$	−5.67775	+	5.67775i	−0.248271	+	0.248271i	−0.820261	−	0.571990i	$-0.806172\pi$
$523$	−5.67775	+	5.67775i	−0.248271	+	0.248271i	0.571990	+	0.820261i	$0.306172\pi$
$524$	0.143590			0.00627276
$525$	35.0906	−	20.8685i	1.53148	−	0.910777i
$526$	15.3998			0.671462
$527$	−12.0626	+	12.0626i	−0.525456	+	0.525456i
$528$	−1.12724	−	1.31504i	−0.0490569	−	0.0572297i
$529$		−	22.8459i		−	0.993299i
$530$	3.84493	+	12.1438i	0.167013	+	0.527495i
$531$	−4.96620	+	32.1016i	−0.215515	+	1.39309i
$532$	3.81544	+	3.81544i	0.165420	+	0.165420i
$533$	37.5311	+	37.5311i	1.62565	+	1.62565i
$534$	0.510264	−	6.63595i	0.0220813	−	0.287165i
$535$	−9.21481	−	4.78292i	−0.398391	−	0.206783i
$536$		−	6.73663i		−	0.290978i
$537$	32.7789	−	28.0978i	1.41451	−	1.21251i
$538$	−8.71830	+	8.71830i	−0.375872	+	0.375872i
$539$	15.2246			0.655771
$540$	−8.81896	−	7.56478i	−0.379508	−	0.325536i
$541$	−21.5294			−0.925620			−0.462810	−	0.886457i	$-0.653159\pi$
$541$	−21.5294			−0.925620			−0.462810	+	0.886457i	$0.653159\pi$
$542$	10.3677	−	10.3677i	0.445332	−	0.445332i
$543$	−17.3835	+	14.9010i	−0.745997	+	0.639463i
$544$			6.01351i			0.257827i
$545$	−33.8244	+	10.7093i	−1.44888	+	0.458737i
$546$	−3.03514	+	39.4717i	−0.129892	+	1.68923i
$547$	−24.2212	−	24.2212i	−1.03563	−	1.03563i	−0.999342	−	0.0362836i	$-0.988448\pi$
$547$	−24.2212	−	24.2212i	−1.03563	−	1.03563i	−0.0362836	−	0.999342i	$-0.511552\pi$
$548$	−13.1972	−	13.1972i	−0.563757	−	0.563757i
$549$	0.205939	−	1.33120i	0.00878928	−	0.0568140i
$550$	4.92610	+	0.856449i	0.210050	+	0.0365191i
$551$			4.04636i			0.172381i
$552$	0.442534	+	0.516260i	0.0188355	+	0.0219735i
$553$	3.52150	−	3.52150i	0.149750	−	0.149750i
$554$	27.4792			1.16748
$555$	−3.80982	−	16.2796i	−0.161718	−	0.691031i
$556$	−6.75125			−0.286317
$557$	4.99447	−	4.99447i	0.211623	−	0.211623i	−0.593334	−	0.804957i	$-0.702189\pi$
$557$	4.99447	−	4.99447i	0.211623	−	0.211623i	0.804957	+	0.593334i	$0.202189\pi$
$558$	5.02700	+	6.86703i	0.212810	+	0.290705i
$559$		−	19.9904i		−	0.845505i
$560$	−4.85632	+	9.35624i	−0.205217	+	0.395373i
$561$	10.3850	+	0.798547i	0.438457	+	0.0337147i
$562$	19.7025	+	19.7025i	0.831098	+	0.831098i
$563$	−13.8899	−	13.8899i	−0.585392	−	0.585392i	0.350988	−	0.936380i	$-0.385846\pi$
$563$	−13.8899	−	13.8899i	−0.585392	−	0.585392i	−0.936380	+	0.350988i	$0.885846\pi$
$564$	−11.2474	−	0.864860i	−0.473603	−	0.0364172i
$565$	1.31707	−	2.53747i	0.0554094	−	0.106752i
$566$		−	6.53145i		−	0.274537i
$567$	−19.5334	−	37.6648i	−0.820328	−	1.58177i
$568$	−2.72579	+	2.72579i	−0.114372	+	0.114372i
$569$	−27.0215			−1.13280			−0.566400	−	0.824130i	$-0.691664\pi$
$569$	−27.0215			−1.13280			−0.566400	+	0.824130i	$0.691664\pi$
$570$	1.01011	+	4.31628i	0.0423090	+	0.180789i
$571$	5.67422			0.237459			0.118729	−	0.992927i	$-0.462118\pi$
$571$	5.67422			0.237459			0.118729	+	0.992927i	$0.462118\pi$
$572$	−3.42826	+	3.42826i	−0.143343	+	0.143343i
$573$	18.1982	+	21.2300i	0.760240	+	0.886895i
$574$			51.6101i			2.15416i
$575$	−1.93390	−	0.336226i	−0.0806491	−	0.0140216i
$576$	2.96473	+	0.458652i	0.123531	+	0.0191105i
$577$	−16.8036	−	16.8036i	−0.699545	−	0.699545i	0.264768	−	0.964312i	$-0.414705\pi$
$577$	−16.8036	−	16.8036i	−0.699545	−	0.699545i	−0.964312	+	0.264768i	$0.914705\pi$
$578$	−13.5498	−	13.5498i	−0.563597	−	0.563597i
$579$	−0.722792	+	9.39985i	−0.0300382	+	0.390645i
$580$	−7.53636	+	2.38613i	−0.312930	+	0.0990786i
$581$		−	18.1399i		−	0.752570i
$582$	−7.99746	+	6.85536i	−0.331505	+	0.284164i
$583$	−4.02811	+	4.02811i	−0.166827	+	0.166827i
$584$	8.08572			0.334589
$585$	−19.2201	+	26.2365i	−0.794654	+	1.08474i
$586$	−1.88804			−0.0779942
$587$	−19.6723	+	19.6723i	−0.811964	+	0.811964i	−0.984928	−	0.172964i	$-0.944665\pi$
$587$	−19.6723	+	19.6723i	−0.811964	+	0.811964i	0.172964	+	0.984928i	$0.444665\pi$
$588$	−20.0210	+	17.1618i	−0.825650	+	0.707742i
$589$		−	3.24691i		−	0.133787i
$590$	21.4895	+	11.1540i	0.884707	+	0.459204i
$591$	0.301247	−	3.91769i	0.0123916	−	0.161152i
$592$	3.05254	+	3.05254i	0.125459	+	0.125459i
$593$	32.6870	+	32.6870i	1.34229	+	1.34229i	0.893772	+	0.448521i	$0.148049\pi$
$593$	32.6870	+	32.6870i	1.34229	+	1.34229i	0.448521	+	0.893772i	$0.351951\pi$
$594$	1.18576	−	5.05905i	0.0486525	−	0.207575i
$595$	−19.1345	−	60.4346i	−0.784438	−	2.47758i
$596$			22.2180i			0.910084i
$597$	−23.3673	−	27.2603i	−0.956362	−	1.11569i
$598$	1.34587	−	1.34587i	0.0550367	−	0.0550367i
$599$	−11.3829			−0.465093			−0.232547	−	0.972585i	$-0.574706\pi$
$599$	−11.3829			−0.465093			−0.232547	+	0.972585i	$0.574706\pi$
$600$	−7.44344	+	4.42665i	−0.303877	+	0.180717i
$601$	30.3637			1.23856			0.619281	−	0.785170i	$-0.287424\pi$
$601$	30.3637			1.23856			0.619281	+	0.785170i	$0.287424\pi$
$602$	13.7447	−	13.7447i	0.560193	−	0.560193i
$603$	16.3073	−	11.9378i	0.664087	−	0.486143i
$604$			13.0150i			0.529573i
$605$	0.674951	+	2.13177i	0.0274407	+	0.0866688i
$606$	−31.5437	−	2.42552i	−1.28137	−	0.0985299i
$607$	−12.0786	−	12.0786i	−0.490257	−	0.490257i	0.418130	−	0.908387i	$-0.362686\pi$
$607$	−12.0786	−	12.0786i	−0.490257	−	0.490257i	−0.908387	+	0.418130i	$0.862686\pi$
$608$	−0.809333	−	0.809333i	−0.0328228	−	0.0328228i
$609$	−28.7819	−	2.21315i	−1.16630	−	0.0896815i
$610$	−0.891129	−	0.462537i	−0.0360808	−	0.0187276i
$611$			31.5763i			1.27744i
$612$	−14.5569	+	10.6563i	−0.588427	+	0.430757i
$613$	−5.41272	+	5.41272i	−0.218618	+	0.218618i	−0.807916	−	0.589298i	$-0.799404\pi$
$613$	−5.41272	+	5.41272i	−0.218618	+	0.218618i	0.589298	+	0.807916i	$0.299404\pi$
$614$	−8.21484			−0.331524
$615$	−22.3607	+	36.0241i	−0.901669	+	1.45263i
$616$	−4.71430			−0.189945
$617$	−0.750282	+	0.750282i	−0.0302052	+	0.0302052i	−0.722048	−	0.691843i	$-0.756799\pi$
$617$	−0.750282	+	0.750282i	−0.0302052	+	0.0302052i	0.691843	+	0.722048i	$0.256799\pi$
$618$	3.11004	+	3.62817i	0.125104	+	0.145946i
$619$		−	26.9807i		−	1.08445i	−0.840234	−	0.542224i	$-0.817583\pi$
$619$		−	26.9807i		−	1.08445i	0.840234	−	0.542224i	$-0.182417\pi$
$620$	6.04740	−	1.91470i	0.242869	−	0.0768962i
$621$	−0.465509	+	1.98609i	−0.0186802	+	0.0796990i
$622$	6.96577	+	6.96577i	0.279302	+	0.279302i
$623$	−12.8093	−	12.8093i	−0.513193	−	0.513193i
$624$	0.643815	−	8.37276i	0.0257732	−	0.335179i
$625$	8.43792	−	23.5330i	0.337517	−	0.941320i
$626$		−	19.8750i		−	0.794363i
$627$	−1.50515	+	1.29021i	−0.0601100	+	0.0515259i
$628$	6.79217	−	6.79217i	0.271037	−	0.271037i
$629$	−25.9600			−1.03509
$630$	−31.2544	+	4.82419i	−1.24520	+	0.192200i
$631$	31.5743			1.25695			0.628476	−	0.777829i	$-0.283679\pi$
$631$	31.5743			1.25695			0.628476	+	0.777829i	$0.283679\pi$
$632$	−0.746983	+	0.746983i	−0.0297134	+	0.0297134i
$633$	19.4719	−	16.6911i	0.773937	−	0.663414i
$634$		−	5.13523i		−	0.203946i
$635$	18.1095	−	34.8899i	0.718654	−	1.38457i
$636$	0.756465	−	9.83777i	0.0299958	−	0.390093i
$637$	52.1939	+	52.1939i	2.06800	+	2.06800i
$638$	−2.49981	−	2.49981i	−0.0989683	−	0.0989683i
$639$	−11.4286	−	1.76803i	−0.452109	−	0.0699424i
$640$	1.03013	−	1.98465i	0.0407193	−	0.0784502i
$641$		−	42.7929i		−	1.69022i	−0.534594	−	0.845109i	$-0.679535\pi$
$641$		−	42.7929i		−	1.69022i	0.534594	−	0.845109i	$-0.320465\pi$
$642$	5.23383	+	6.10577i	0.206563	+	0.240976i
$643$	−16.0597	+	16.0597i	−0.633333	+	0.633333i	−0.948903	−	0.315569i	$-0.897805\pi$
$643$	−16.0597	+	16.0597i	−0.633333	+	0.633333i	0.315569	+	0.948903i	$0.397805\pi$
$644$	1.85075			0.0729296
$645$	15.5489	−	3.63883i	0.612239	−	0.143279i
$646$	6.88288			0.270803
$647$	22.2175	−	22.2175i	0.873459	−	0.873459i	−0.119389	−	0.992848i	$-0.538093\pi$
$647$	22.2175	−	22.2175i	0.873459	−	0.873459i	0.992848	+	0.119389i	$0.0380934\pi$
$648$	4.14345	+	7.98948i	0.162770	+	0.313857i
$649$			10.8278i			0.425029i
$650$	13.9518	+	19.8241i	0.547235	+	0.777564i
$651$	23.0954	+	1.77590i	0.905181	+	0.0696030i
$652$	−1.78859	−	1.78859i	−0.0700464	−	0.0700464i
$653$	8.94052	+	8.94052i	0.349870	+	0.349870i	0.860061	−	0.510191i	$-0.170425\pi$
$653$	8.94052	+	8.94052i	0.349870	+	0.349870i	−0.510191	+	0.860061i	$0.670425\pi$
$654$	27.4012	+	2.10699i	1.07147	+	0.0823898i
$655$	0.306101	−	0.0969163i	0.0119604	−	0.00378683i
$656$		−	10.9476i		−	0.427430i
$657$	14.3284	+	19.5731i	0.559005	+	0.763619i
$658$	−21.7108	+	21.7108i	−0.846374	+	0.846374i
$659$	4.99296			0.194498			0.0972491	−	0.995260i	$-0.468996\pi$
$659$	4.99296			0.194498			0.0972491	+	0.995260i	$0.468996\pi$
$660$	−3.29061	−	2.04253i	−0.128087	−	0.0795052i
$661$	−26.6139			−1.03516			−0.517580	−	0.855635i	$-0.673167\pi$
$661$	−26.6139			−1.03516			−0.517580	+	0.855635i	$0.673167\pi$
$662$	−7.98653	+	7.98653i	−0.310405	+	0.310405i
$663$	32.8650	+	38.3402i	1.27637	+	1.48901i
$664$			3.84784i			0.149325i
$665$	10.7089	+	5.55840i	0.415272	+	0.215546i
$666$	−1.97997	+	12.7986i	−0.0767225	+	0.495935i
$667$	0.981378	+	0.981378i	0.0379991	+	0.0379991i
$668$	5.12540	+	5.12540i	0.198308	+	0.198308i
$669$	2.44883	−	31.8468i	0.0946772	−	1.23127i
$670$	−4.54690	−	14.3609i	−0.175662	−	0.554812i
$671$		−	0.449010i		−	0.0173339i
$672$	6.19948	−	5.31416i	0.239150	−	0.204998i
$673$	23.9170	−	23.9170i	0.921931	−	0.921931i	−0.0752345	−	0.997166i	$-0.523971\pi$
$673$	23.9170	−	23.9170i	0.921931	−	0.921931i	0.997166	+	0.0752345i	$0.0239705\pi$
$674$	−16.6661			−0.641954
$675$	−23.9058	−	10.1740i	−0.920136	−	0.391598i
$676$	−10.5059			−0.404073
$677$	−12.8794	+	12.8794i	−0.494994	+	0.494994i	−0.909875	−	0.414882i	$-0.863823\pi$
$677$	−12.8794	+	12.8794i	−0.494994	+	0.494994i	0.414882	+	0.909875i	$0.363823\pi$
$678$	−1.68134	+	1.44123i	−0.0645715	+	0.0553502i
$679$			28.6702i			1.10026i
$680$	4.05882	+	12.8194i	0.155649	+	0.491602i
$681$	0.574573	−	7.47227i	0.0220177	−	0.286338i
$682$	2.00592	+	2.00592i	0.0768106	+	0.0768106i
$683$	−21.1489	−	21.1489i	−0.809239	−	0.809239i	0.175280	−	0.984519i	$-0.443917\pi$
$683$	−21.1489	−	21.1489i	−0.809239	−	0.809239i	−0.984519	+	0.175280i	$0.943917\pi$
$684$	0.524959	−	3.39334i	0.0200723	−	0.129748i
$685$	−37.0409	−	19.2259i	−1.41526	−	0.734585i
$686$			38.7733i			1.48037i
$687$	14.5095	+	16.9268i	0.553572	+	0.645796i
$688$	−2.91554	+	2.91554i	−0.111154	+	0.111154i
$689$	−27.6188			−1.05219
$690$	1.29183	+	0.801858i	0.0491792	+	0.0305262i
$691$	−17.1200			−0.651276			−0.325638	−	0.945495i	$-0.605579\pi$
$691$	−17.1200			−0.651276			−0.325638	+	0.945495i	$0.605579\pi$
$692$	13.8077	−	13.8077i	0.524892	−	0.524892i
$693$	−8.35405	−	11.4119i	−0.317344	−	0.433502i
$694$		−	20.7332i		−	0.787022i
$695$	−14.3921	+	4.55676i	−0.545924	+	0.172848i
$696$	6.10523	+	0.469455i	0.231418	+	0.0177947i
$697$	46.5511	+	46.5511i	1.76325	+	1.76325i
$698$	−7.29248	−	7.29248i	−0.276025	−	0.276025i
$699$	11.9412	+	0.918205i	0.451657	+	0.0347297i
$700$	−4.03756	+	23.2231i	−0.152605	+	0.877752i
$701$			23.2836i			0.879411i	0.898142	+	0.439706i	$0.144917\pi$
$701$			23.2836i			0.879411i	−0.898142	+	0.439706i	$0.855083\pi$
$702$	21.4088	−	13.2786i	0.808024	−	0.501169i
$703$	3.49385	−	3.49385i	0.131773	−	0.131773i
$704$	1.00000			0.0376889
$705$	−24.5607	+	5.74779i	−0.925009	+	0.216474i
$706$	−14.8128			−0.557488
$707$	−60.8883	+	60.8883i	−2.28994	+	2.28994i
$708$	−12.2056	−	14.2390i	−0.458714	−	0.535135i
$709$			2.07946i			0.0780957i	0.999237	+	0.0390479i	$0.0124325\pi$
$709$			2.07946i			0.0780957i	−0.999237	+	0.0390479i	$0.987568\pi$
$710$	−3.97098	+	7.65054i	−0.149028	+	0.287120i
$711$	−3.13193	−	0.484517i	−0.117456	−	0.0181708i
$712$	2.71711	+	2.71711i	0.101828	+	0.101828i
$713$	−0.787487	−	0.787487i	−0.0294916	−	0.0294916i
$714$	−3.76459	+	48.9582i	−0.140886	+	1.83222i
$715$	−4.99435	+	9.62216i	−0.186778	+	0.359848i
$716$			24.9262i			0.931534i
$717$	2.29113	−	1.96394i	0.0855638	−	0.0733447i
$718$	1.47217	−	1.47217i	0.0549408	−	0.0549408i
$719$	42.1133			1.57056			0.785280	−	0.619141i	$-0.212519\pi$
$719$	42.1133			1.57056			0.785280	+	0.619141i	$0.212519\pi$
$720$	6.62969	−	1.02331i	0.247074	−	0.0381365i
$721$	13.0067			0.484394
$722$	12.5087	−	12.5087i	0.465525	−	0.465525i
$723$	23.7216	−	20.3340i	0.882214	−	0.756228i
$724$		−	13.2190i		−	0.491280i
$725$	−14.4553	+	10.1734i	−0.536855	+	0.377829i
$726$	0.132792	−	1.72695i	0.00492838	−	0.0640932i
$727$	−18.7383	−	18.7383i	−0.694967	−	0.694967i	0.268354	−	0.963320i	$-0.413520\pi$
$727$	−18.7383	−	18.7383i	−0.694967	−	0.694967i	−0.963320	+	0.268354i	$0.913520\pi$
$728$	−16.1618	−	16.1618i	−0.598997	−	0.598997i
$729$	−11.9977	+	24.1879i	−0.444358	+	0.895849i
$730$	17.2369	−	5.45746i	0.637966	−	0.201990i
$731$		−	24.7949i		−	0.917071i
$732$	0.506143	+	0.590466i	0.0187076	+	0.0218242i
$733$	13.3545	−	13.3545i	0.493259	−	0.493259i	−0.416073	−	0.909331i	$-0.636594\pi$
$733$	13.3545	−	13.3545i	0.493259	−	0.493259i	0.909331	+	0.416073i	$0.136594\pi$
$734$	−28.1754			−1.03997
$735$	−31.0967	+	50.0982i	−1.14702	+	1.84790i
$736$	−0.392582			−0.0144707
$737$	4.76352	−	4.76352i	0.175466	−	0.175466i
$738$	26.5007	−	19.3998i	0.975506	−	0.714117i
$739$		−	30.4955i		−	1.12180i	−0.827885	−	0.560898i	$-0.810456\pi$
$739$		−	30.4955i		−	1.12180i	0.827885	−	0.560898i	$-0.189544\pi$
$740$	8.56763	+	4.44700i	0.314952	+	0.163475i
$741$	−9.58322	−	0.736891i	−0.352048	−	0.0270704i
$742$	−18.9897	−	18.9897i	−0.697134	−	0.697134i
$743$	−3.29428	−	3.29428i	−0.120855	−	0.120855i	0.644092	−	0.764948i	$-0.277235\pi$
$743$	−3.29428	−	3.29428i	−0.120855	−	0.120855i	−0.764948	+	0.644092i	$0.777235\pi$
$744$	−4.89902	−	0.376705i	−0.179607	−	0.0138107i
$745$	14.9960	+	47.3636i	0.549412	+	1.73527i
$746$			21.3513i			0.781726i
$747$	−9.31447	+	6.81864i	−0.340799	+	0.249481i
$748$	−4.25219	+	4.25219i	−0.155476	+	0.155476i
$749$	21.8887			0.799795
$750$	−12.8799	+	14.4605i	−0.470309	+	0.528024i
$751$	−49.5654			−1.80867			−0.904333	−	0.426828i	$-0.859631\pi$
$751$	−49.5654			−1.80867			−0.904333	+	0.426828i	$0.859631\pi$
$752$	4.60530	−	4.60530i	0.167938	−	0.167938i
$753$	−23.7289	−	27.6821i	−0.864729	−	1.00879i
$754$		−	17.1400i		−	0.624201i
$755$	8.78450	+	27.7450i	0.319701	+	1.00974i
$756$	23.8499	+	5.59004i	0.867411	+	0.203308i
$757$	−13.1734	−	13.1734i	−0.478794	−	0.478794i	0.425952	−	0.904746i	$-0.359939\pi$
$757$	−13.1734	−	13.1734i	−0.478794	−	0.478794i	−0.904746	+	0.425952i	$0.859939\pi$
$758$	−11.9954	−	11.9954i	−0.435692	−	0.435692i
$759$	−0.0521318	+	0.677970i	−0.00189226	+	0.0246087i
$760$	−2.27157	−	1.17905i	−0.0823986	−	0.0427687i
$761$		−	27.7298i		−	1.00520i	−0.864518	−	0.502602i	$-0.832376\pi$
$761$		−	27.7298i		−	1.00520i	0.864518	−	0.502602i	$-0.167624\pi$
$762$	−23.1182	+	19.8168i	−0.837485	+	0.717886i
$763$	52.8922	−	52.8922i	1.91483	−	1.91483i
$764$	−16.1440			−0.584069
$765$	−23.8394	+	32.5420i	−0.861916	+	1.17656i
$766$	9.36900			0.338516
$767$	−37.1206	+	37.1206i	−1.34035	+	1.34035i
$768$	−1.31504	+	1.12724i	−0.0474524	+	0.0406758i
$769$		−	22.6443i		−	0.816575i	−0.912853	−	0.408287i	$-0.866126\pi$
$769$		−	22.6443i		−	0.816575i	0.912853	−	0.408287i	$-0.133874\pi$
$770$	−10.0498	+	3.18192i	−0.362170	+	0.114668i
$771$	1.61738	−	21.0340i	0.0582487	−	0.757520i
$772$	−3.84880	−	3.84880i	−0.138521	−	0.138521i
$773$	20.2870	+	20.2870i	0.729674	+	0.729674i	0.970555	−	0.240881i	$-0.0774364\pi$
$773$	20.2870	+	20.2870i	0.729674	+	0.729674i	−0.240881	+	0.970555i	$0.577436\pi$
$774$	−12.2242	−	1.89111i	−0.439388	−	0.0679745i
$775$	11.5993	−	8.16340i	0.416660	−	0.293238i
$776$		−	6.08154i		−	0.218315i
$777$	22.9409	+	26.7628i	0.823001	+	0.960111i
$778$	3.81027	−	3.81027i	0.136605	−	0.136605i
$779$	−12.5302			−0.448943
$780$	−4.27874	−	18.2833i	−0.153204	−	0.654649i
$781$	−3.85485			−0.137937
$782$	1.66933	−	1.66933i	0.0596952	−	0.0596952i
$783$	9.68247	+	15.6108i	0.346023	+	0.557885i
$784$		−	15.2246i		−	0.543736i
$785$	9.89496	−	19.0637i	0.353166	−	0.680414i
$786$	−0.247973	−	0.0190677i	−0.00884492	−	0.000680121i
$787$	−0.625655	−	0.625655i	−0.0223022	−	0.0223022i	0.695868	−	0.718170i	$-0.255020\pi$
$787$	−0.625655	−	0.625655i	−0.0223022	−	0.0223022i	−0.718170	+	0.695868i	$0.755020\pi$
$788$	1.60411	+	1.60411i	0.0571441	+	0.0571441i
$789$	−26.5947	−	2.04497i	−0.946795	−	0.0728028i
$790$	−1.08822	+	2.09657i	−0.0387171	+	0.0745927i
$791$			6.02746i			0.214312i
$792$	1.77207	+	2.42070i	0.0629676	+	0.0860158i
$793$	1.53932	−	1.53932i	0.0546630	−	0.0546630i
$794$	−18.1807			−0.645208
$795$	−5.02740	−	21.4824i	−0.178304	−	0.761903i
$796$	20.7297			0.734744
$797$	0.836208	−	0.836208i	0.0296200	−	0.0296200i	−0.692142	−	0.721762i	$-0.743333\pi$
$797$	0.836208	−	0.836208i	0.0296200	−	0.0296200i	0.721762	+	0.692142i	$0.243333\pi$
$798$	−6.08242	−	7.09574i	−0.215315	−	0.251187i
$799$			39.1653i			1.38557i
$800$	0.856449	−	4.92610i	0.0302801	−	0.174164i
$801$	−1.76240	+	11.3922i	−0.0622715	+	0.402524i
$802$	−3.93120	−	3.93120i	−0.138816	−	0.138816i
$803$	5.71747	+	5.71747i	0.201765	+	0.201765i
$804$	−0.894572	+	11.6338i	−0.0315491	+	0.410294i
$805$	3.94537	−	1.24916i	0.139056	−	0.0440272i
$806$			13.7536i			0.484450i
$807$	16.2138	−	13.8984i	0.570753	−	0.489246i
$808$	12.9157	−	12.9157i	0.454371	−	0.454371i
$809$	−8.68490			−0.305345			−0.152672	−	0.988277i	$-0.548788\pi$
$809$	−8.68490			−0.305345			−0.152672	+	0.988277i	$0.548788\pi$
$810$	14.2254	+	14.2351i	0.499829	+	0.500171i
$811$	−12.5238			−0.439771			−0.219886	−	0.975526i	$-0.570568\pi$
$811$	−12.5238			−0.439771			−0.219886	+	0.975526i	$0.570568\pi$
$812$	11.7848	−	11.7848i	0.413567	−	0.413567i
$813$	−19.2813	+	16.5278i	−0.676226	+	0.579656i
$814$			4.31694i			0.151309i
$815$	−5.02006	−	2.60565i	−0.175845	−	0.0912718i
$816$	0.798547	−	10.3850i	0.0279547	−	0.363549i
$817$	3.33704	+	3.33704i	0.116748	+	0.116748i
$818$	−5.05741	−	5.05741i	−0.176828	−	0.176828i
$819$	10.4831	−	67.7628i	0.366308	−	2.36782i
$820$	−7.38907	−	23.3377i	−0.258037	−	0.814987i
$821$			14.3602i			0.501175i	0.968094	+	0.250587i	$0.0806237\pi$
$821$			14.3602i			0.501175i	−0.968094	+	0.250587i	$0.919376\pi$
$822$	21.0385	+	24.5434i	0.733801	+	0.856051i
$823$	6.94613	−	6.94613i	0.242127	−	0.242127i	−0.575603	−	0.817729i	$-0.695233\pi$
$823$	6.94613	−	6.94613i	0.242127	−	0.242127i	0.817729	+	0.575603i	$0.195233\pi$
$824$	−2.75898			−0.0961137
$825$	−8.39342	−	2.13320i	−0.292221	−	0.0742683i
$826$	−51.0456			−1.77610
$827$	18.5671	−	18.5671i	0.645640	−	0.645640i	−0.306296	−	0.951936i	$-0.599090\pi$
$827$	18.5671	−	18.5671i	0.645640	−	0.645640i	0.951936	+	0.306296i	$0.0990898\pi$
$828$	−0.695681	−	0.950322i	−0.0241766	−	0.0330260i
$829$			28.0636i			0.974691i	0.873209	+	0.487345i	$0.162035\pi$
$829$			28.0636i			0.974691i	−0.873209	+	0.487345i	$0.837965\pi$
$830$	2.59711	+	8.20272i	0.0901469	+	0.284721i
$831$	−47.4552	−	3.64902i	−1.64620	−	0.126583i
$832$	3.42826	+	3.42826i	0.118853	+	0.118853i
$833$	64.7380	+	64.7380i	2.24304	+	2.24304i
$834$	11.6591	+	0.896514i	0.403721	+	0.0310437i
$835$	14.3856	+	7.46678i	0.497833	+	0.258399i
$836$		−	1.14457i		−	0.0395858i
$837$	−7.76950	−	12.5266i	−0.268553	−	0.432982i
$838$	11.8831	−	11.8831i	0.410495	−	0.410495i
$839$	10.2487			0.353825			0.176912	−	0.984227i	$-0.443389\pi$
$839$	10.2487			0.353825			0.176912	+	0.984227i	$0.443389\pi$
$840$	9.62908	−	15.5129i	0.332235	−	0.535246i
$841$	−16.5019			−0.569032
$842$	25.5830	−	25.5830i	0.881647	−	0.881647i
$843$	−31.4089	−	36.6416i	−1.08178	−	1.26200i
$844$			14.8071i			0.509680i
$845$	−22.3961	+	7.09096i	−0.770451	+	0.243937i
$846$	19.3090	+	2.98714i	0.663855	+	0.102700i
$847$	−3.33351	−	3.33351i	−0.114541	−	0.114541i
$848$	4.02811	+	4.02811i	0.138326	+	0.138326i
$849$	−0.867326	+	11.2795i	−0.0297666	+	0.387112i
$850$	17.3050	+	24.5885i	0.593555	+	0.843380i
$851$		−	1.69475i		−	0.0580954i
$852$	5.06928	−	4.34535i	0.173671	−	0.148869i
$853$	2.87511	−	2.87511i	0.0984419	−	0.0984419i	−0.656171	−	0.754613i	$-0.727825\pi$
$853$	2.87511	−	2.87511i	0.0984419	−	0.0984419i	0.754613	+	0.656171i	$0.227825\pi$
$854$	2.11677			0.0724343
$855$	−1.17125	−	7.58815i	−0.0400559	−	0.259509i
$856$	−4.64304			−0.158696
$857$	33.0535	−	33.0535i	1.12909	−	1.12909i	0.138762	−	0.990326i	$-0.455688\pi$
$857$	33.0535	−	33.0535i	1.12909	−	1.12909i	0.990326	−	0.138762i	$-0.0443122\pi$
$858$	6.37568	−	5.46519i	0.217662	−	0.186579i
$859$			34.8056i			1.18755i	0.804630	+	0.593777i	$0.202364\pi$
$859$			34.8056i			1.18755i	−0.804630	+	0.593777i	$0.797636\pi$
$860$	−4.24741	+	8.18310i	−0.144835	+	0.279041i
$861$	6.85342	−	89.1282i	0.233564	−	3.03748i
$862$	−0.623769	−	0.623769i	−0.0212456	−	0.0212456i
$863$	−27.7876	−	27.7876i	−0.945900	−	0.945900i	0.0527095	−	0.998610i	$-0.483214\pi$
$863$	−27.7876	−	27.7876i	−0.945900	−	0.945900i	−0.998610	+	0.0527095i	$0.983214\pi$
$864$	−5.05905	−	1.18576i	−0.172112	−	0.0403405i
$865$	20.1154	−	38.7545i	0.683943	−	1.31769i
$866$			2.19676i			0.0746491i
$867$	21.6005	+	25.1991i	0.733592	+	0.855808i
$868$	−9.45650	+	9.45650i	−0.320975	+	0.320975i
$869$	−1.05639			−0.0358357
$870$	13.3318	−	3.11996i	0.451991	−	0.105777i
$871$	32.6611			1.10668
$872$	−11.2195	+	11.2195i	−0.379941	+	0.379941i
$873$	14.7216	−	10.7769i	0.498250	−	0.364743i
$874$			0.449337i			0.0151991i
$875$	7.06733	+	52.2315i	0.238919	+	1.76575i
$876$	−13.9637	−	1.07372i	−0.471788	−	0.0362777i
$877$	12.2027	+	12.2027i	0.412055	+	0.412055i	0.882454	−	0.470399i	$-0.155890\pi$
$877$	12.2027	+	12.2027i	0.412055	+	0.412055i	−0.470399	+	0.882454i	$0.655890\pi$
$878$	6.75048	+	6.75048i	0.227818	+	0.227818i
$879$	3.26055	+	0.250717i	0.109976	+	0.00845647i
$880$	2.13177	−	0.674951i	0.0718619	−	0.0227526i
$881$			24.7010i			0.832198i	0.909319	+	0.416099i	$0.136603\pi$
$881$			24.7010i			0.832198i	−0.909319	+	0.416099i	$0.863397\pi$
$882$	36.8542	−	26.9790i	1.24095	−	0.908431i
$883$	25.5716	−	25.5716i	0.860554	−	0.860554i	−0.130848	−	0.991402i	$-0.541770\pi$
$883$	25.5716	−	25.5716i	0.860554	−	0.860554i	0.991402	+	0.130848i	$0.0417700\pi$
$884$	−29.1552			−0.980596
$885$	−35.6301	−	22.1161i	−1.19769	−	0.743425i
$886$	22.8774			0.768580
$887$	−5.57017	+	5.57017i	−0.187028	+	0.187028i	−0.794410	−	0.607382i	$-0.792220\pi$
$887$	−5.57017	+	5.57017i	−0.187028	+	0.187028i	0.607382	+	0.794410i	$0.292220\pi$
$888$	−4.86624	−	5.67695i	−0.163300	−	0.190506i
$889$			82.8769i			2.77960i
$890$	7.62617	+	3.95834i	0.255630	+	0.132684i
$891$	−2.71956	+	8.57928i	−0.0911087	+	0.287417i
$892$	13.0398	+	13.0398i	0.436605	+	0.436605i
$893$	−5.27109	−	5.27109i	−0.176390	−	0.176390i
$894$	2.95037	−	38.3694i	0.0986753	−	1.28326i
$895$	16.8239	+	53.1368i	0.562362	+	1.77617i
$896$			4.71430i			0.157494i
$897$	−2.50298	+	2.14553i	−0.0835719	+	0.0716373i
$898$	24.0238	−	24.0238i	0.801686	−	0.801686i
$899$	−10.0288			−0.334480
$900$	13.4423	−	6.65618i	0.448077	−	0.221873i
$901$	−34.2566			−1.14125
$902$	7.74109	−	7.74109i	0.257750	−	0.257750i
$903$	−25.5617	+	21.9113i	−0.850639	+	0.729162i
$904$		−	1.27855i		−	0.0425239i
$905$	−8.92218	−	28.1799i	−0.296583	−	0.936730i
$906$	1.72829	−	22.4763i	0.0574187	−	0.746726i
$907$	−9.83158	−	9.83158i	−0.326452	−	0.326452i	0.524784	−	0.851236i	$-0.324146\pi$
$907$	−9.83158	−	9.83158i	−0.326452	−	0.326452i	−0.851236	+	0.524784i	$0.824146\pi$
$908$	3.05955	+	3.05955i	0.101535	+	0.101535i
$909$	54.1523	+	8.37751i	1.79612	+	0.277864i
$910$	−45.3617	−	23.5449i	−1.50373	−	0.780504i
$911$			19.4131i			0.643183i	0.946878	+	0.321592i	$0.104218\pi$
$911$			19.4131i			0.643183i	−0.946878	+	0.321592i	$0.895782\pi$
$912$	1.29021	+	1.50515i	0.0427230	+	0.0498406i
$913$	−2.72084	+	2.72084i	−0.0900466	+	0.0900466i
$914$	−29.6132			−0.979518
$915$	1.47752	+	0.917115i	0.0488452	+	0.0303189i
$916$	−12.8717			−0.425292
$917$	−0.478660	+	0.478660i	−0.0158067	+	0.0158067i
$918$	26.5541	−	16.4700i	0.876417	−	0.543589i
$919$			14.9841i			0.494279i	0.968980	+	0.247140i	$0.0794906\pi$
$919$			14.9841i			0.494279i	−0.968980	+	0.247140i	$0.920509\pi$
$920$	−0.836893	+	0.264973i	−0.0275916	+	0.00873591i
$921$	14.1866	+	1.09087i	0.467466	+	0.0359453i
$922$	−20.3536	−	20.3536i	−0.670310	−	0.670310i
$923$	−13.2154	−	13.2154i	−0.434991	−	0.434991i
$924$	8.14137	+	0.626022i	0.267831	+	0.0205946i
$925$	21.2657	+	3.69724i	0.699212	+	0.121565i
$926$			7.45433i			0.244964i
$927$	−4.88910	−	6.67866i	−0.160579	−	0.219356i
$928$	−2.49981	+	2.49981i	−0.0820602	+	0.0820602i
$929$	−10.8073			−0.354576			−0.177288	−	0.984159i	$-0.556732\pi$
$929$	−10.8073			−0.354576			−0.177288	+	0.984159i	$0.556732\pi$
$930$	−10.6978	+	2.50355i	−0.350796	+	0.0820946i
$931$	−17.4256			−0.571102
$932$	−4.88936	+	4.88936i	−0.160156	+	0.160156i
$933$	−11.1046	−	12.9546i	−0.363547	−	0.424113i
$934$		−	5.95914i		−	0.194989i
$935$	−6.19467	+	11.9347i	−0.202587	+	0.390307i
$936$	−2.22368	+	14.3739i	−0.0726831	+	0.469825i
$937$	−5.05776	−	5.05776i	−0.165230	−	0.165230i	0.619649	−	0.784879i	$-0.287275\pi$
$937$	−5.05776	−	5.05776i	−0.165230	−	0.165230i	−0.784879	+	0.619649i	$0.787275\pi$
$938$	22.4566	+	22.4566i	0.733235	+	0.733235i
$939$	−2.63924	+	34.3231i	−0.0861284	+	1.12009i
$940$	6.70909	−	12.9258i	0.218826	−	0.421593i
$941$			9.31955i			0.303809i	0.988395	+	0.151904i	$0.0485406\pi$
$941$			9.31955i			0.303809i	−0.988395	+	0.151904i	$0.951459\pi$
$942$	−12.6317	+	10.8278i	−0.411563	+	0.352789i
$943$	−3.03901	+	3.03901i	−0.0989638	+	0.0989638i
$944$	10.8278			0.352416
$945$	54.6154	−	4.18081i	1.77664	−	0.136002i
$946$	−4.12319			−0.134057
$947$	30.5880	−	30.5880i	0.993978	−	0.993978i	−0.00600404	−	0.999982i	$-0.501911\pi$
$947$	30.5880	−	30.5880i	0.993978	−	0.993978i	0.999982	+	0.00600404i	$0.00191116\pi$
$948$	1.38920	−	1.19081i	0.0451191	−	0.0386758i
$949$			39.2019i			1.27255i
$950$	−5.63827	−	0.980266i	−0.182930	−	0.0318040i
$951$	−0.681918	+	8.86829i	−0.0221127	+	0.287574i
$952$	−20.0461	−	20.0461i	−0.649698	−	0.649698i
$953$	23.2004	+	23.2004i	0.751535	+	0.751535i	0.974766	−	0.223231i	$-0.0716603\pi$
$953$	23.2004	+	23.2004i	0.751535	+	0.751535i	−0.223231	+	0.974766i	$0.571660\pi$
$954$	−2.61276	+	16.8889i	−0.0845912	+	0.546799i
$955$	−34.4153	+	10.8964i	−1.11365	+	0.352599i
$956$			1.74225i			0.0563485i
$957$	3.98510	+	4.64901i	0.128820	+	0.150281i
$958$	29.3759	−	29.3759i	0.949093	−	0.949093i
$959$	87.9861			2.84122
$960$	−2.04253	+	3.29061i	−0.0659222	+	0.106204i
$961$	−22.9526			−0.740406
$962$	−14.7996	+	14.7996i	−0.477158	+	0.477158i
$963$	−8.22777	−	11.2394i	−0.265136	−	0.362184i
$964$			18.0387i			0.580987i
$965$	−10.8025	−	5.60701i	−0.347745	−	0.180496i
$966$	−3.19615	−	0.245765i	−0.102835	−	0.00790735i
$967$	28.8696	+	28.8696i	0.928385	+	0.928385i	0.997602	−	0.0692164i	$-0.0220499\pi$
$967$	28.8696	+	28.8696i	0.928385	+	0.928385i	−0.0692164	+	0.997602i	$0.522050\pi$
$968$	0.707107	+	0.707107i	0.0227273	+	0.0227273i
$969$	−11.8864	−	0.913993i	−0.381847	−	0.0293617i
$970$	−4.10474	−	12.9644i	−0.131795	−	0.416263i
$971$			25.5535i			0.820052i	0.912074	+	0.410026i	$0.134480\pi$
$971$			25.5535i			0.820052i	−0.912074	+	0.410026i	$0.865520\pi$
$972$	−6.09459	−	14.3477i	−0.195484	−	0.460202i
$973$	22.5054	−	22.5054i	0.721489	−	0.721489i
$974$	35.1784			1.12719
$975$	−21.4617	−	36.0879i	−0.687323	−	1.15574i
$976$	−0.449010			−0.0143725
$977$	−10.3333	+	10.3333i	−0.330591	+	0.330591i	−0.852811	−	0.522220i	$-0.825104\pi$
$977$	−10.3333	+	10.3333i	−0.330591	+	0.330591i	0.522220	+	0.852811i	$0.325104\pi$
$978$	2.85129	+	3.32631i	0.0911743	+	0.106364i
$979$			3.84257i			0.122809i
$980$	−10.2759	−	32.4554i	−0.328251	−	1.03675i
$981$	−47.0409	−	7.27734i	−1.50190	−	0.232348i
$982$	−14.7703	−	14.7703i	−0.471340	−	0.471340i
$983$	−6.54967	−	6.54967i	−0.208902	−	0.208902i	0.594899	−	0.803801i	$-0.297192\pi$
$983$	−6.54967	−	6.54967i	−0.208902	−	0.208902i	−0.803801	+	0.594899i	$0.797192\pi$
$984$	−1.45375	+	18.9059i	−0.0463439	+	0.602699i
$985$	4.50230	+	2.33690i	0.143455	+	0.0744598i
$986$		−	21.2593i		−	0.677035i
$987$	40.3765	−	34.6105i	1.28520	−	1.10166i
$988$	3.92388	−	3.92388i	0.124835	−	0.124835i
$989$	1.61869			0.0514713
$990$	5.41149	+	3.96431i	0.171988	+	0.125994i
$991$	17.4736			0.555068			0.277534	−	0.960716i	$-0.410483\pi$
$991$	17.4736			0.555068			0.277534	+	0.960716i	$0.410483\pi$
$992$	2.00592	−	2.00592i	0.0636880	−	0.0636880i
$993$	14.8529	−	12.7318i	0.471343	−	0.404032i
$994$		−	18.1729i		−	0.576410i
$995$	44.1909	−	13.9915i	1.40094	−	0.443561i
$996$	0.510964	−	6.64505i	0.0161905	−	0.210556i
$997$	−16.1235	−	16.1235i	−0.510638	−	0.510638i	0.404084	−	0.914722i	$-0.367590\pi$
$997$	−16.1235	−	16.1235i	−0.510638	−	0.510638i	−0.914722	+	0.404084i	$0.867590\pi$
$998$	20.0338	+	20.0338i	0.634160	+	0.634160i
$999$	5.11888	−	21.8396i	0.161954	−	0.690975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	330.2.j.a.287.7	yes	20
3.2	odd	2		330.2.j.b.287.2	yes	20
5.3	odd	4		330.2.j.b.23.2	yes	20
15.8	even	4	inner	330.2.j.a.23.7	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.j.a.23.7	✓	20	15.8	even	4	inner
330.2.j.a.287.7	yes	20	1.1	even	1	trivial
330.2.j.b.23.2	yes	20	5.3	odd	4
330.2.j.b.287.2	yes	20	3.2	odd	2

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:	\( N \)	\(=\)	\( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	330.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.31504 + 1.12724i) q^{3} -1.00000i q^{4} +(-0.674951 - 2.13177i) q^{5} +(-0.132792 + 1.72695i) q^{6} +(3.33351 + 3.33351i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.458652 - 2.96473i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.31504 + 1.12724i) q^{3} -1.00000i q^{4} +(-0.674951 - 2.13177i) q^{5} +(-0.132792 + 1.72695i) q^{6} +(3.33351 + 3.33351i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.458652 - 2.96473i) q^{9} +(-1.98465 - 1.03013i) q^{10} -1.00000i q^{11} +(1.12724 + 1.31504i) q^{12} +(3.42826 - 3.42826i) q^{13} +4.71430 q^{14} +(3.29061 + 2.04253i) q^{15} -1.00000 q^{16} +(4.25219 - 4.25219i) q^{17} +(-1.77207 - 2.42070i) q^{18} +1.14457i q^{19} +(-2.13177 + 0.674951i) q^{20} +(-8.14137 - 0.626022i) q^{21} +(-0.707107 - 0.707107i) q^{22} +(0.277597 + 0.277597i) q^{23} +(1.72695 + 0.132792i) q^{24} +(-4.08888 + 2.87768i) q^{25} -4.84829i q^{26} +(2.73883 + 4.41575i) q^{27} +(3.33351 - 3.33351i) q^{28} +3.53526 q^{29} +(3.77109 - 0.882526i) q^{30} -2.83680 q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.12724 + 1.31504i) q^{33} -6.01351i q^{34} +(4.85632 - 9.35624i) q^{35} +(-2.96473 - 0.458652i) q^{36} +(-3.05254 - 3.05254i) q^{37} +(0.809333 + 0.809333i) q^{38} +(-0.643815 + 8.37276i) q^{39} +(-1.03013 + 1.98465i) q^{40} +10.9476i q^{41} +(-6.19948 + 5.31416i) q^{42} +(2.91554 - 2.91554i) q^{43} -1.00000 q^{44} +(-6.62969 + 1.02331i) q^{45} +0.392582 q^{46} +(-4.60530 + 4.60530i) q^{47} +(1.31504 - 1.12724i) q^{48} +15.2246i q^{49} +(-0.856449 + 4.92610i) q^{50} +(-0.798547 + 10.3850i) q^{51} +(-3.42826 - 3.42826i) q^{52} +(-4.02811 - 4.02811i) q^{53} +(5.05905 + 1.18576i) q^{54} +(-2.13177 + 0.674951i) q^{55} -4.71430i q^{56} +(-1.29021 - 1.50515i) q^{57} +(2.49981 - 2.49981i) q^{58} -10.8278 q^{59} +(2.04253 - 3.29061i) q^{60} +0.449010 q^{61} +(-2.00592 + 2.00592i) q^{62} +(11.4119 - 8.35405i) q^{63} +1.00000i q^{64} +(-9.62216 - 4.99435i) q^{65} +(1.72695 + 0.132792i) q^{66} +(4.76352 + 4.76352i) q^{67} +(-4.25219 - 4.25219i) q^{68} +(-0.677970 - 0.0521318i) q^{69} +(-3.18192 - 10.0498i) q^{70} -3.85485i q^{71} +(-2.42070 + 1.77207i) q^{72} +(-5.71747 + 5.71747i) q^{73} -4.31694 q^{74} +(2.13320 - 8.39342i) q^{75} +1.14457 q^{76} +(3.33351 - 3.33351i) q^{77} +(5.46519 + 6.37568i) q^{78} -1.05639i q^{79} +(0.674951 + 2.13177i) q^{80} +(-8.57928 - 2.71956i) q^{81} +(7.74109 + 7.74109i) q^{82} +(-2.72084 - 2.72084i) q^{83} +(-0.626022 + 8.14137i) q^{84} +(-11.9347 - 6.19467i) q^{85} -4.12319i q^{86} +(-4.64901 + 3.98510i) q^{87} +(-0.707107 + 0.707107i) q^{88} -3.84257 q^{89} +(-3.96431 + 5.41149i) q^{90} +22.8563 q^{91} +(0.277597 - 0.277597i) q^{92} +(3.73050 - 3.19776i) q^{93} +6.51288i q^{94} +(2.43996 - 0.772529i) q^{95} +(0.132792 - 1.72695i) q^{96} +(4.30030 + 4.30030i) q^{97} +(10.7654 + 10.7654i) q^{98} +(-2.96473 - 0.458652i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{6} + 20 q^{9}+O(q^{10}) \) 20 * q + 4 * q^6 + 20 * q^9	\( 20 q + 4 q^{6} + 20 q^{9} - 4 q^{12} + 8 q^{13} - 8 q^{15} - 20 q^{16} + 8 q^{17} - 8 q^{18} - 12 q^{20} + 36 q^{23} + 12 q^{25} - 16 q^{29} + 32 q^{30} + 16 q^{31} - 4 q^{33} - 8 q^{35} - 4 q^{36} - 4 q^{37} + 32 q^{39} - 8 q^{40} - 16 q^{42} - 20 q^{44} + 20 q^{45} - 24 q^{46} + 12 q^{47} - 16 q^{50} - 16 q^{51} - 8 q^{52} + 20 q^{53} - 12 q^{54} - 12 q^{55} - 28 q^{57} - 8 q^{58} - 112 q^{59} + 24 q^{60} + 8 q^{61} + 16 q^{62} - 8 q^{63} - 56 q^{65} + 20 q^{67} - 8 q^{68} + 28 q^{69} - 8 q^{70} + 8 q^{72} - 8 q^{73} + 8 q^{74} + 8 q^{75} - 16 q^{76} + 36 q^{78} + 24 q^{82} + 16 q^{83} - 12 q^{84} - 72 q^{87} - 32 q^{89} + 40 q^{90} + 36 q^{92} - 76 q^{93} - 4 q^{96} - 44 q^{97} - 56 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 4 * q^6 + 20 * q^9 - 4 * q^12 + 8 * q^13 - 8 * q^15 - 20 * q^16 + 8 * q^17 - 8 * q^18 - 12 * q^20 + 36 * q^23 + 12 * q^25 - 16 * q^29 + 32 * q^30 + 16 * q^31 - 4 * q^33 - 8 * q^35 - 4 * q^36 - 4 * q^37 + 32 * q^39 - 8 * q^40 - 16 * q^42 - 20 * q^44 + 20 * q^45 - 24 * q^46 + 12 * q^47 - 16 * q^50 - 16 * q^51 - 8 * q^52 + 20 * q^53 - 12 * q^54 - 12 * q^55 - 28 * q^57 - 8 * q^58 - 112 * q^59 + 24 * q^60 + 8 * q^61 + 16 * q^62 - 8 * q^63 - 56 * q^65 + 20 * q^67 - 8 * q^68 + 28 * q^69 - 8 * q^70 + 8 * q^72 - 8 * q^73 + 8 * q^74 + 8 * q^75 - 16 * q^76 + 36 * q^78 + 24 * q^82 + 16 * q^83 - 12 * q^84 - 72 * q^87 - 32 * q^89 + 40 * q^90 + 36 * q^92 - 76 * q^93 - 4 * q^96 - 44 * q^97 - 56 * q^98 - 4 * q^99

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