LMFDB - Embedded newform 630.2.t.c.311.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(311,630)]

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([5, 0, 1]))

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

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

chi := DirichletCharacter("630.311");

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.t (of order $6$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.11
Character	$\chi$	$=$	630.311
Dual form			630.2.t.c.551.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.336991 - 1.69895i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.557633 - 1.63983i) q^{6} +(0.104916 + 2.64367i) q^{7} +1.00000i q^{8} +(-2.77287 + 1.14506i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.336991 - 1.69895i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.557633 - 1.63983i) q^{6} +(0.104916 + 2.64367i) q^{7} +1.00000i q^{8} +(-2.77287 + 1.14506i) q^{9} +(0.866025 + 0.500000i) q^{10} +6.11380i q^{11} +(1.30284 - 1.14132i) q^{12} +(3.86893 + 2.23373i) q^{13} +(-1.23098 + 2.34194i) q^{14} +(-0.336991 - 1.69895i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.11723 - 1.93509i) q^{17} +(-2.97391 - 0.394783i) q^{18} +(-0.623812 + 0.360158i) q^{19} +(0.500000 + 0.866025i) q^{20} +(4.45611 - 1.06914i) q^{21} +(-3.05690 + 5.29471i) q^{22} -6.71710i q^{23} +(1.69895 - 0.336991i) q^{24} +1.00000 q^{25} +(2.23373 + 3.86893i) q^{26} +(2.87984 + 4.32510i) q^{27} +(-2.23703 + 1.41269i) q^{28} +(0.633929 - 0.365999i) q^{29} +(0.557633 - 1.63983i) q^{30} +(5.28276 - 3.05000i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(10.3871 - 2.06030i) q^{33} +(1.93509 - 1.11723i) q^{34} +(0.104916 + 2.64367i) q^{35} +(-2.37809 - 1.82885i) q^{36} +(-4.53567 - 7.85602i) q^{37} -0.720316 q^{38} +(2.49120 - 7.32587i) q^{39} +1.00000i q^{40} +(0.713952 - 1.23660i) q^{41} +(4.39368 + 1.30215i) q^{42} +(1.23875 + 2.14558i) q^{43} +(-5.29471 + 3.05690i) q^{44} +(-2.77287 + 1.14506i) q^{45} +(3.35855 - 5.81718i) q^{46} +(-4.18805 + 7.25392i) q^{47} +(1.63983 + 0.557633i) q^{48} +(-6.97799 + 0.554724i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-3.66413 - 1.24601i) q^{51} +4.46746i q^{52} +(0.193943 + 0.111973i) q^{53} +(0.331463 + 5.18557i) q^{54} +6.11380i q^{55} +(-2.64367 + 0.104916i) q^{56} +(0.822110 + 0.938456i) q^{57} +0.731999 q^{58} +(-4.88106 - 8.45424i) q^{59} +(1.30284 - 1.14132i) q^{60} +(-1.59270 - 0.919547i) q^{61} +6.10001 q^{62} +(-3.31809 - 7.21043i) q^{63} -1.00000 q^{64} +(3.86893 + 2.23373i) q^{65} +(10.0256 + 3.40926i) q^{66} +(6.54114 + 11.3296i) q^{67} +2.23445 q^{68} +(-11.4120 + 2.26360i) q^{69} +(-1.23098 + 2.34194i) q^{70} -7.83185i q^{71} +(-1.14506 - 2.77287i) q^{72} +(10.7713 + 6.21880i) q^{73} -9.07135i q^{74} +(-0.336991 - 1.69895i) q^{75} +(-0.623812 - 0.360158i) q^{76} +(-16.1629 + 0.641432i) q^{77} +(5.82038 - 5.09879i) q^{78} +(-7.49899 + 12.9886i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(6.37766 - 6.35023i) q^{81} +(1.23660 - 0.713952i) q^{82} +(1.95115 + 3.37949i) q^{83} +(3.15396 + 3.32454i) q^{84} +(1.11723 - 1.93509i) q^{85} +2.47750i q^{86} +(-0.835444 - 0.953677i) q^{87} -6.11380 q^{88} +(-5.83979 - 10.1148i) q^{89} +(-2.97391 - 0.394783i) q^{90} +(-5.49933 + 10.4625i) q^{91} +(5.81718 - 3.35855i) q^{92} +(-6.96205 - 7.94733i) q^{93} +(-7.25392 + 4.18805i) q^{94} +(-0.623812 + 0.360158i) q^{95} +(1.14132 + 1.30284i) q^{96} +(10.9748 - 6.33628i) q^{97} +(-6.32047 - 3.00859i) q^{98} +(-7.00069 - 16.9528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.336991	−	1.69895i	−0.194562	−	0.980890i
$3$	−0.336991	−	1.69895i	−0.194562	−	0.980890i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.557633	−	1.63983i	0.227653	−	0.669458i
$7$	0.104916	+	2.64367i	0.0396543	+	0.999213i
$7$	0.104916	+	2.64367i	0.0396543	+	0.999213i
$8$			1.00000i			0.353553i
$9$	−2.77287	+	1.14506i	−0.924291	+	0.381688i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$			6.11380i			1.84338i	0.387927	+	0.921690i	$0.373191\pi$
$11$			6.11380i			1.84338i	−0.387927	+	0.921690i	$0.626809\pi$
$12$	1.30284	−	1.14132i	0.376097	−	0.329470i
$13$	3.86893	+	2.23373i	1.07305	+	0.619525i	0.929013	−	0.370048i	$-0.120659\pi$
$13$	3.86893	+	2.23373i	1.07305	+	0.619525i	0.144036	+	0.989572i	$0.453992\pi$
$14$	−1.23098	+	2.34194i	−0.328992	+	0.625911i
$15$	−0.336991	−	1.69895i	−0.0870107	−	0.438667i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.11723	−	1.93509i	0.270967	−	0.469329i	−0.698142	−	0.715959i	$-0.745990\pi$
$17$	1.11723	−	1.93509i	0.270967	−	0.469329i	0.969110	+	0.246630i	$0.0793231\pi$
$18$	−2.97391	−	0.394783i	−0.700958	−	0.0930513i
$19$	−0.623812	+	0.360158i	−0.143112	+	0.0826259i	−0.569846	−	0.821751i	$-0.692997\pi$
$19$	−0.623812	+	0.360158i	−0.143112	+	0.0826259i	0.426734	+	0.904377i	$0.359664\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	4.45611	−	1.06914i	0.972404	−	0.233305i
$22$	−3.05690	+	5.29471i	−0.651733	+	1.12884i
$23$		−	6.71710i		−	1.40061i	−0.713842	−	0.700306i	$-0.753047\pi$
$23$		−	6.71710i		−	1.40061i	0.713842	−	0.700306i	$-0.246953\pi$
$24$	1.69895	−	0.336991i	0.346797	−	0.0687880i
$25$	1.00000			0.200000
$26$	2.23373	+	3.86893i	0.438070	+	0.758760i
$27$	2.87984	+	4.32510i	0.554226	+	0.832367i
$28$	−2.23703	+	1.41269i	−0.422759	+	0.266974i
$29$	0.633929	−	0.365999i	0.117718	−	0.0679644i	−0.439985	−	0.898005i	$-0.645016\pi$
$29$	0.633929	−	0.365999i	0.117718	−	0.0679644i	0.557703	+	0.830041i	$0.311683\pi$
$30$	0.557633	−	1.63983i	0.101809	−	0.299391i
$31$	5.28276	−	3.05000i	0.948812	−	0.547797i	0.0561004	−	0.998425i	$-0.482133\pi$
$31$	5.28276	−	3.05000i	0.948812	−	0.547797i	0.892712	+	0.450628i	$0.148800\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	10.3871	−	2.06030i	1.80815	−	0.358651i
$34$	1.93509	−	1.11723i	0.331866	−	0.191603i
$35$	0.104916	+	2.64367i	0.0177340	+	0.446862i
$36$	−2.37809	−	1.82885i	−0.396348	−	0.304808i
$37$	−4.53567	−	7.85602i	−0.745660	−	1.29152i	−0.949886	−	0.312597i	$-0.898801\pi$
$37$	−4.53567	−	7.85602i	−0.745660	−	1.29152i	0.204226	−	0.978924i	$-0.434532\pi$
$38$	−0.720316			−0.116851
$39$	2.49120	−	7.32587i	0.398912	−	1.17308i
$40$			1.00000i			0.158114i
$41$	0.713952	−	1.23660i	0.111501	−	0.193125i	−0.804875	−	0.593444i	$-0.797768\pi$
$41$	0.713952	−	1.23660i	0.111501	−	0.193125i	0.916375	+	0.400320i	$0.131101\pi$
$42$	4.39368	+	1.30215i	0.677959	+	0.200927i
$43$	1.23875	+	2.14558i	0.188907	+	0.327197i	0.944886	−	0.327399i	$-0.106172\pi$
$43$	1.23875	+	2.14558i	0.188907	+	0.327197i	−0.755979	+	0.654596i	$0.772839\pi$
$44$	−5.29471	+	3.05690i	−0.798207	+	0.460845i
$45$	−2.77287	+	1.14506i	−0.413356	+	0.170696i
$46$	3.35855	−	5.81718i	0.495191	−	0.857697i
$47$	−4.18805	+	7.25392i	−0.610890	+	1.05809i	0.380200	+	0.924904i	$0.375855\pi$
$47$	−4.18805	+	7.25392i	−0.610890	+	1.05809i	−0.991091	+	0.133189i	$0.957478\pi$
$48$	1.63983	+	0.557633i	0.236689	+	0.0804874i
$49$	−6.97799	+	0.554724i	−0.996855	+	0.0792463i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	−3.66413	−	1.24601i	−0.513080	−	0.174476i
$52$			4.46746i			0.619525i
$53$	0.193943	+	0.111973i	0.0266401	+	0.0153807i	0.513261	−	0.858233i	$-0.328437\pi$
$53$	0.193943	+	0.111973i	0.0266401	+	0.0153807i	−0.486621	+	0.873613i	$0.661771\pi$
$54$	0.331463	+	5.18557i	0.0451065	+	0.705667i
$55$			6.11380i			0.824385i
$56$	−2.64367	+	0.104916i	−0.353275	+	0.0140199i
$57$	0.822110	+	0.938456i	0.108891	+	0.124302i
$58$	0.731999			0.0961161
$59$	−4.88106	−	8.45424i	−0.635460	−	1.10065i	−0.986417	−	0.164258i	$-0.947477\pi$
$59$	−4.88106	−	8.45424i	−0.635460	−	1.10065i	0.350958	−	0.936391i	$-0.385856\pi$
$60$	1.30284	−	1.14132i	0.168196	−	0.147344i
$61$	−1.59270	−	0.919547i	−0.203925	−	0.117736i	0.394560	−	0.918870i	$-0.370897\pi$
$61$	−1.59270	−	0.919547i	−0.203925	−	0.117736i	−0.598485	+	0.801134i	$0.704230\pi$
$62$	6.10001			0.774702
$63$	−3.31809	−	7.21043i	−0.418040	−	0.908429i
$64$	−1.00000			−0.125000
$65$	3.86893	+	2.23373i	0.479882	+	0.277060i
$66$	10.0256	+	3.40926i	1.23407	+	0.419651i
$67$	6.54114	+	11.3296i	0.799127	+	1.38413i	0.920185	+	0.391484i	$0.128038\pi$
$67$	6.54114	+	11.3296i	0.799127	+	1.38413i	−0.121058	+	0.992645i	$0.538629\pi$
$68$	2.23445			0.270967
$69$	−11.4120	+	2.26360i	−1.37385	+	0.272506i
$70$	−1.23098	+	2.34194i	−0.147130	+	0.279916i
$71$		−	7.83185i		−	0.929470i	−0.885450	−	0.464735i	$-0.846150\pi$
$71$		−	7.83185i		−	0.929470i	0.885450	−	0.464735i	$-0.153850\pi$
$72$	−1.14506	−	2.77287i	−0.134947	−	0.326786i
$73$	10.7713	+	6.21880i	1.26068	+	0.727856i	0.973207	−	0.229932i	$-0.0738502\pi$
$73$	10.7713	+	6.21880i	1.26068	+	0.727856i	0.287477	+	0.957788i	$0.407184\pi$
$74$		−	9.07135i		−	1.05452i
$75$	−0.336991	−	1.69895i	−0.0389124	−	0.196178i
$76$	−0.623812	−	0.360158i	−0.0715561	−	0.0413130i
$77$	−16.1629	+	0.641432i	−1.84193	+	0.0730980i
$78$	5.82038	−	5.09879i	0.659028	−	0.577325i
$79$	−7.49899	+	12.9886i	−0.843702	+	1.46133i	0.0430414	+	0.999073i	$0.486295\pi$
$79$	−7.49899	+	12.9886i	−0.843702	+	1.46133i	−0.886744	+	0.462262i	$0.847038\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	6.37766	−	6.35023i	0.708629	−	0.705581i
$82$	1.23660	−	0.713952i	0.136560	−	0.0788428i
$83$	1.95115	+	3.37949i	0.214167	+	0.370947i	0.953014	−	0.302925i	$-0.0979631\pi$
$83$	1.95115	+	3.37949i	0.214167	+	0.370947i	−0.738848	+	0.673872i	$0.764630\pi$
$84$	3.15396	+	3.32454i	0.344125	+	0.362737i
$85$	1.11723	−	1.93509i	0.121180	−	0.209890i
$86$			2.47750i			0.267155i
$87$	−0.835444	−	0.953677i	−0.0895690	−	0.102245i
$88$	−6.11380			−0.651733
$89$	−5.83979	−	10.1148i	−0.619016	−	1.07217i	−0.989666	−	0.143395i	$-0.954198\pi$
$89$	−5.83979	−	10.1148i	−0.619016	−	1.07217i	0.370649	−	0.928773i	$-0.379135\pi$
$90$	−2.97391	−	0.394783i	−0.313478	−	0.0416138i
$91$	−5.49933	+	10.4625i	−0.576487	+	1.09677i
$92$	5.81718	−	3.35855i	0.606483	−	0.350153i
$93$	−6.96205	−	7.94733i	−0.721931	−	0.824100i
$94$	−7.25392	+	4.18805i	−0.748185	+	0.431965i
$95$	−0.623812	+	0.360158i	−0.0640017	+	0.0369514i
$96$	1.14132	+	1.30284i	0.116485	+	0.132971i
$97$	10.9748	−	6.33628i	1.11432	−	0.643351i	0.174373	−	0.984680i	$-0.444210\pi$
$97$	10.9748	−	6.33628i	1.11432	−	0.643351i	0.939944	+	0.341328i	$0.110877\pi$
$98$	−6.32047	−	3.00859i	−0.638464	−	0.303913i
$99$	−7.00069	−	16.9528i	−0.703595	−	1.70382i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	0.196980			0.0196002			0.00980010	−	0.999952i	$-0.496880\pi$
$101$	0.196980			0.0196002			0.00980010	+	0.999952i	$0.496880\pi$
$102$	−2.55022	−	2.91114i	−0.252510	−	0.288245i
$103$			6.81626i			0.671626i	0.941929	+	0.335813i	$0.109011\pi$
$103$			6.81626i			0.671626i	−0.941929	+	0.335813i	$0.890989\pi$
$104$	−2.23373	+	3.86893i	−0.219035	+	0.379380i
$105$	4.45611	−	1.06914i	0.434872	−	0.104337i
$106$	0.111973	+	0.193943i	0.0108758	+	0.0188374i
$107$	4.67098	−	2.69679i	0.451560	−	0.260709i	−0.256929	−	0.966430i	$-0.582711\pi$
$107$	4.67098	−	2.69679i	0.451560	−	0.260709i	0.708489	+	0.705722i	$0.249377\pi$
$108$	−2.30573	+	4.65657i	−0.221869	+	0.448078i
$109$	6.74410	−	11.6811i	0.645967	−	1.11885i	−0.338110	−	0.941107i	$-0.609788\pi$
$109$	6.74410	−	11.6811i	0.645967	−	1.11885i	0.984077	−	0.177742i	$-0.0568791\pi$
$110$	−3.05690	+	5.29471i	−0.291464	+	0.504830i
$111$	−11.8185	+	10.3533i	−1.12176	+	0.982692i
$112$	−2.34194	−	1.23098i	−0.221293	−	0.116316i
$113$	−16.3111	−	9.41722i	−1.53442	−	0.885897i	−0.999150	−	0.0412153i	$-0.986877\pi$
$113$	−16.3111	−	9.41722i	−1.53442	−	0.885897i	−0.535269	−	0.844682i	$-0.679790\pi$
$114$	0.242740	+	1.22378i	0.0227347	+	0.114618i
$115$		−	6.71710i		−	0.626373i
$116$	0.633929	+	0.365999i	0.0588589	+	0.0339822i
$117$	−13.2858	−	1.76368i	−1.22827	−	0.163052i
$118$		−	9.76212i		−	0.898676i
$119$	5.23297	+	2.75056i	0.479705	+	0.252143i
$120$	1.69895	−	0.336991i	0.155092	−	0.0307629i
$121$	−26.3785			−2.39805
$122$	−0.919547	−	1.59270i	−0.0832519	−	0.144196i
$123$	−2.34152	−	0.796246i	−0.211128	−	0.0717951i
$124$	5.28276	+	3.05000i	0.474406	+	0.273898i
$125$	1.00000			0.0894427
$126$	0.731668	−	7.90346i	0.0651821	−	0.704096i
$127$	12.6907			1.12612			0.563060	−	0.826416i	$-0.309624\pi$
$127$	12.6907			1.12612			0.563060	+	0.826416i	$0.309624\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	3.22778	−	2.82761i	0.284190	−	0.248957i
$130$	2.23373	+	3.86893i	0.195911	+	0.339328i
$131$	−8.69627			−0.759796			−0.379898	−	0.925028i	$-0.624041\pi$
$131$	−8.69627			−0.759796			−0.379898	+	0.925028i	$0.624041\pi$
$132$	6.97779	+	7.96530i	0.607339	+	0.693291i
$133$	−1.01759	−	1.61137i	−0.0882359	−	0.139723i
$134$			13.0823i			1.13014i
$135$	2.87984	+	4.32510i	0.247857	+	0.372246i
$136$	1.93509	+	1.11723i	0.165933	+	0.0958014i
$137$		−	20.4737i		−	1.74919i	−0.484855	−	0.874594i	$-0.661128\pi$
$137$		−	20.4737i		−	1.74919i	0.484855	−	0.874594i	$-0.338872\pi$
$138$	−11.0149	−	3.74568i	−0.937652	−	0.318853i
$139$	1.45863	+	0.842140i	0.123719	+	0.0714294i	0.560583	−	0.828099i	$-0.310577\pi$
$139$	1.45863	+	0.842140i	0.123719	+	0.0714294i	−0.436863	+	0.899528i	$0.643911\pi$
$140$	−2.23703	+	1.41269i	−0.189063	+	0.119394i
$141$	13.7354	+	4.67079i	1.15673	+	0.393352i
$142$	3.91593	−	6.78258i	0.328617	−	0.569182i
$143$	−13.6566	+	23.6539i	−1.14202	+	1.97804i
$144$	0.394783	−	2.97391i	0.0328986	−	0.247826i
$145$	0.633929	−	0.365999i	0.0526450	−	0.0303946i
$146$	6.21880	+	10.7713i	0.514672	+	0.891438i
$147$	3.29397	+	11.6683i	0.271682	+	0.962387i
$148$	4.53567	−	7.85602i	0.372830	−	0.645761i
$149$		−	5.72362i		−	0.468897i	−0.972129	−	0.234448i	$-0.924672\pi$
$149$		−	5.72362i		−	0.468897i	0.972129	−	0.234448i	$-0.0753284\pi$
$150$	0.557633	−	1.63983i	0.0455305	−	0.133892i
$151$	−6.98531			−0.568456			−0.284228	−	0.958757i	$-0.591737\pi$
$151$	−6.98531			−0.568456			−0.284228	+	0.958757i	$0.591737\pi$
$152$	−0.360158	−	0.623812i	−0.0292127	−	0.0505978i
$153$	−0.882125	+	6.64507i	−0.0713156	+	0.537222i
$154$	−14.3182	−	7.52594i	−1.15379	−	0.606457i
$155$	5.28276	−	3.05000i	0.424322	−	0.244982i
$156$	7.58999	−	1.50549i	0.607686	−	0.120536i
$157$	15.4710	−	8.93219i	1.23472	−	0.712867i	0.266711	−	0.963777i	$-0.414063\pi$
$157$	15.4710	−	8.93219i	1.23472	−	0.712867i	0.968010	+	0.250910i	$0.0807299\pi$
$158$	−12.9886	+	7.49899i	−1.03332	+	0.596588i
$159$	0.124880	−	0.367234i	0.00990362	−	0.0291236i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	17.7578	−	0.704728i	1.39951	−	0.0555404i
$162$	8.69833	−	2.31063i	0.683406	−	0.181540i
$163$	−4.05646	−	7.02600i	−0.317727	−	0.550319i	0.662287	−	0.749250i	$-0.269586\pi$
$163$	−4.05646	−	7.02600i	−0.317727	−	0.550319i	−0.980013	+	0.198932i	$0.936253\pi$
$164$	1.42790			0.111501
$165$	10.3871	−	2.06030i	0.808631	−	0.160394i
$166$			3.90230i			0.302877i
$167$	1.29948	−	2.25076i	0.100557	−	0.174169i	−0.811357	−	0.584550i	$-0.801271\pi$
$167$	1.29948	−	2.25076i	0.100557	−	0.174169i	0.911914	+	0.410381i	$0.134604\pi$
$168$	1.06914	+	4.45611i	0.0824859	+	0.343797i
$169$	3.47909	+	6.02595i	0.267622	+	0.463535i
$170$	1.93509	−	1.11723i	0.148415	−	0.0856874i
$171$	1.31735	−	1.71298i	0.100740	−	0.130995i
$172$	−1.23875	+	2.14558i	−0.0944537	+	0.163599i
$173$	7.08170	−	12.2659i	0.538412	−	0.932557i	−0.460578	−	0.887619i	$-0.652358\pi$
$173$	7.08170	−	12.2659i	0.538412	−	0.932557i	0.998990	−	0.0449373i	$-0.0143088\pi$
$174$	−0.246677	−	1.24363i	−0.0187005	−	0.0942794i
$175$	0.104916	+	2.64367i	0.00793087	+	0.199843i
$176$	−5.29471	−	3.05690i	−0.399103	−	0.230422i
$177$	−12.7185	+	11.1417i	−0.955979	+	0.837461i
$178$		−	11.6796i		−	0.875421i
$179$	−15.8658	−	9.16012i	−1.18587	−	0.684660i	−0.228501	−	0.973544i	$-0.573382\pi$
$179$	−15.8658	−	9.16012i	−1.18587	−	0.684660i	−0.957364	+	0.288884i	$0.906716\pi$
$180$	−2.37809	−	1.82885i	−0.177252	−	0.136314i
$181$			0.536166i			0.0398529i	0.999801	+	0.0199265i	$0.00634321\pi$
$181$			0.536166i			0.0398529i	−0.999801	+	0.0199265i	$0.993657\pi$
$182$	−9.99383	+	6.31115i	−0.740792	+	0.467814i
$183$	−1.02554	+	3.01580i	−0.0758101	+	0.222935i
$184$	6.71710			0.495191
$185$	−4.53567	−	7.85602i	−0.333469	−	0.577586i
$186$	−2.05565	−	10.3636i	−0.150727	−	0.759897i
$187$	11.8308	+	6.83050i	0.865152	+	0.499496i
$188$	−8.37611			−0.610890
$189$	−11.1320	+	8.06712i	−0.809734	+	0.586797i
$190$	−0.720316			−0.0522572
$191$	−4.04414	−	2.33488i	−0.292623	−	0.168946i	0.346501	−	0.938050i	$-0.387370\pi$
$191$	−4.04414	−	2.33488i	−0.292623	−	0.168946i	−0.639124	+	0.769103i	$0.720703\pi$
$192$	0.336991	+	1.69895i	0.0243202	+	0.122611i
$193$	9.89647	+	17.1412i	0.712363	+	1.23385i	0.963968	+	0.266019i	$0.0857085\pi$
$193$	9.89647	+	17.1412i	0.712363	+	1.23385i	−0.251604	+	0.967830i	$0.580958\pi$
$194$	12.6726			0.909836
$195$	2.49120	−	7.32587i	0.178399	−	0.524617i
$196$	−3.96940	−	5.76575i	−0.283528	−	0.411839i
$197$			16.1466i			1.15040i	0.818013	+	0.575199i	$0.195075\pi$
$197$			16.1466i			1.15040i	−0.818013	+	0.575199i	$0.804925\pi$
$198$	2.41363	−	18.1819i	0.171529	−	1.29213i
$199$	0.660045	+	0.381077i	0.0467894	+	0.0270139i	0.523212	−	0.852202i	$-0.324734\pi$
$199$	0.660045	+	0.381077i	0.0467894	+	0.0270139i	−0.476423	+	0.879216i	$0.658067\pi$
$200$			1.00000i			0.0707107i
$201$	17.0441	−	14.9311i	1.20220	−	1.05316i
$202$	0.170589	+	0.0984898i	0.0120026	+	0.00692972i
$203$	1.03409	+	1.63750i	0.0725789	+	0.114930i
$204$	−0.752991	−	3.79623i	−0.0527199	−	0.265789i
$205$	0.713952	−	1.23660i	0.0498646	−	0.0863679i
$206$	−3.40813	+	5.90305i	−0.237456	+	0.411285i
$207$	7.69151	+	18.6257i	0.534597	+	1.29457i
$208$	−3.86893	+	2.23373i	−0.268262	+	0.154881i
$209$	−2.20193	−	3.81386i	−0.152311	−	0.263810i
$210$	4.39368	+	1.30215i	0.303192	+	0.0898572i
$211$	5.84214	−	10.1189i	0.402189	−	0.696613i	−0.591800	−	0.806085i	$-0.701583\pi$
$211$	5.84214	−	10.1189i	0.402189	−	0.696613i	0.993990	+	0.109472i	$0.0349160\pi$
$212$			0.223946i			0.0153807i
$213$	−13.3059	+	2.63926i	−0.911708	+	0.180839i
$214$	5.39358			0.368698
$215$	1.23875	+	2.14558i	0.0844819	+	0.146327i
$216$	−4.32510	+	2.87984i	−0.294286	+	0.195948i
$217$	8.61745	+	13.6459i	0.584991	+	0.926343i
$218$	11.6811	−	6.74410i	0.791145	−	0.456768i
$219$	6.93562	−	20.3956i	0.468666	−	1.37821i
$220$	−5.29471	+	3.05690i	−0.356969	+	0.206096i
$221$	8.64495	−	4.99116i	0.581522	−	0.335742i
$222$	−15.4118	+	3.05696i	−1.03437	+	0.205170i
$223$	−6.37774	+	3.68219i	−0.427085	+	0.246577i	−0.698104	−	0.715996i	$-0.745973\pi$
$223$	−6.37774	+	3.68219i	−0.427085	+	0.246577i	0.271019	+	0.962574i	$0.412639\pi$
$224$	−1.41269	−	2.23703i	−0.0943896	−	0.149468i
$225$	−2.77287	+	1.14506i	−0.184858	+	0.0763375i
$226$	−9.41722	−	16.3111i	−0.626424	−	1.08500i
$227$	13.8820			0.921381			0.460690	−	0.887561i	$-0.347602\pi$
$227$	13.8820			0.921381			0.460690	+	0.887561i	$0.347602\pi$
$228$	−0.401672	+	1.18120i	−0.0266014	+	0.0782266i
$229$		−	16.4020i		−	1.08388i	−0.840418	−	0.541939i	$-0.817690\pi$
$229$		−	16.4020i		−	1.08388i	0.840418	−	0.541939i	$-0.182310\pi$
$230$	3.35855	−	5.81718i	0.221456	−	0.383574i
$231$	6.53651	+	27.2438i	0.430070	+	1.79251i
$232$	0.365999	+	0.633929i	0.0240290	+	0.0416195i
$233$	−11.5552	+	6.67137i	−0.757003	+	0.437056i	−0.828219	−	0.560405i	$-0.810646\pi$
$233$	−11.5552	+	6.67137i	−0.757003	+	0.437056i	0.0712156	+	0.997461i	$0.477312\pi$
$234$	−10.6240	−	8.17030i	−0.694514	−	0.534109i
$235$	−4.18805	+	7.25392i	−0.273198	+	0.473194i
$236$	4.88106	−	8.45424i	0.317730	−	0.550324i
$237$	24.5941	+	8.36337i	1.59756	+	0.543259i
$238$	3.15660	+	4.99854i	0.204612	+	0.324007i
$239$	−5.40343	−	3.11967i	−0.349519	−	0.201795i	0.314954	−	0.949107i	$-0.398011\pi$
$239$	−5.40343	−	3.11967i	−0.349519	−	0.201795i	−0.664473	+	0.747312i	$0.731344\pi$
$240$	1.63983	+	0.557633i	0.105851	+	0.0359951i
$241$		−	2.52754i		−	0.162813i	−0.996681	−	0.0814066i	$-0.974059\pi$
$241$		−	2.52754i		−	0.162813i	0.996681	−	0.0814066i	$-0.0259412\pi$
$242$	−22.8445	−	13.1893i	−1.46850	−	0.847839i
$243$	−12.9380	−	8.69537i	−0.829970	−	0.557808i
$244$		−	1.83909i		−	0.117736i
$245$	−6.97799	+	0.554724i	−0.445807	+	0.0354400i
$246$	−1.62969	−	1.86033i	−0.103905	−	0.118610i
$247$	−3.21798			−0.204755
$248$	3.05000	+	5.28276i	0.193675	+	0.335456i
$249$	5.08407	−	4.45377i	0.322190	−	0.282246i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	22.8300			1.44102			0.720508	−	0.693447i	$-0.243909\pi$
$251$	22.8300			1.44102			0.720508	+	0.693447i	$0.243909\pi$
$252$	4.58537	−	6.47876i	0.288851	−	0.408124i
$253$	41.0670			2.58186
$254$	10.9905	+	6.34536i	0.689604	+	0.398143i
$255$	−3.66413	−	1.24601i	−0.229457	−	0.0780279i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	17.7320			1.10609			0.553045	−	0.833151i	$-0.313466\pi$
$257$	17.7320			1.10609			0.553045	+	0.833151i	$0.313466\pi$
$258$	4.20915	−	0.834894i	0.262050	−	0.0519782i
$259$	20.2929	−	12.8150i	1.26094	−	0.796288i
$260$			4.46746i			0.277060i
$261$	−1.33871	+	1.74076i	−0.0828643	+	0.107750i
$262$	−7.53119	−	4.34813i	−0.465278	−	0.268629i
$263$		−	7.48303i		−	0.461424i	−0.973022	−	0.230712i	$-0.925895\pi$
$263$		−	7.48303i		−	0.461424i	0.973022	−	0.230712i	$-0.0741054\pi$
$264$	2.06030	+	10.3871i	0.126802	+	0.639279i
$265$	0.193943	+	0.111973i	0.0119138	+	0.00687846i
$266$	−0.0755723	−	1.90428i	−0.00463364	−	0.116759i
$267$	−15.2166	+	13.3301i	−0.931242	+	0.815790i
$268$	−6.54114	+	11.3296i	−0.399564	+	0.692065i
$269$	−3.58549	+	6.21025i	−0.218611	+	0.378646i	−0.954384	−	0.298583i	$-0.903486\pi$
$269$	−3.58549	+	6.21025i	−0.218611	+	0.378646i	0.735772	+	0.677229i	$0.236819\pi$
$270$	0.331463	+	5.18557i	0.0201722	+	0.315584i
$271$	−16.4457	+	9.49493i	−0.999005	+	0.576776i	−0.907954	−	0.419070i	$-0.862356\pi$
$271$	−16.4457	+	9.49493i	−0.999005	+	0.576776i	−0.0910514	+	0.995846i	$0.529023\pi$
$272$	1.11723	+	1.93509i	0.0677419	+	0.117332i
$273$	19.6286	+	5.81732i	1.18797	+	0.352080i
$274$	10.2369	−	17.7308i	0.618432	−	1.07116i
$275$			6.11380i			0.368676i
$276$	−7.66636	−	8.75131i	−0.461460	−	0.526767i
$277$	−8.61527			−0.517641			−0.258821	−	0.965925i	$-0.583334\pi$
$277$	−8.61527			−0.517641			−0.258821	+	0.965925i	$0.583334\pi$
$278$	0.842140	+	1.45863i	0.0505082	+	0.0874828i
$279$	−11.1560	+	14.5064i	−0.667892	+	0.868474i
$280$	−2.64367	+	0.104916i	−0.157990	+	0.00626990i
$281$	−19.0254	+	10.9843i	−1.13496	+	0.655268i	−0.945177	−	0.326558i	$-0.894111\pi$
$281$	−19.0254	+	10.9843i	−1.13496	+	0.655268i	−0.189781	+	0.981827i	$0.560778\pi$
$282$	9.55981	+	10.9127i	0.569278	+	0.649843i
$283$	−13.9204	+	8.03697i	−0.827485	+	0.477749i	−0.852991	−	0.521926i	$-0.825214\pi$
$283$	−13.9204	+	8.03697i	−0.827485	+	0.477749i	0.0255060	+	0.999675i	$0.491880\pi$
$284$	6.78258	−	3.91593i	0.402472	−	0.232368i
$285$	0.822110	+	0.938456i	0.0486976	+	0.0555894i
$286$	−23.6539	+	13.6566i	−1.39868	+	0.807530i
$287$	3.34407	+	1.75771i	0.197394	+	0.103755i
$288$	1.82885	−	2.37809i	0.107766	−	0.140130i
$289$	6.00361	+	10.3986i	0.353153	+	0.611680i
$290$	0.731999			0.0429844
$291$	−14.4634	−	16.5103i	−0.847861	−	0.967851i
$292$			12.4376i			0.727856i
$293$	−10.0760	+	17.4522i	−0.588649	+	1.01957i	0.405761	+	0.913979i	$0.367007\pi$
$293$	−10.0760	+	17.4522i	−0.588649	+	1.01957i	−0.994410	+	0.105591i	$0.966327\pi$
$294$	−2.98150	+	11.7520i	−0.173885	+	0.685393i
$295$	−4.88106	−	8.45424i	−0.284186	−	0.492225i
$296$	7.85602	−	4.53567i	0.456622	−	0.263631i
$297$	−26.4428	+	17.6068i	−1.53437	+	1.02165i
$298$	2.86181	−	4.95680i	0.165780	−	0.287140i
$299$	15.0042	−	25.9880i	0.867714	−	1.50293i
$300$	1.30284	−	1.14132i	0.0752195	−	0.0658941i
$301$	−5.54223	+	3.49995i	−0.319449	+	0.201734i
$302$	−6.04945	−	3.49265i	−0.348107	−	0.200980i
$303$	−0.0663804	−	0.334659i	−0.00381345	−	0.0192256i
$304$		−	0.720316i		−	0.0413130i
$305$	−1.59270	−	0.919547i	−0.0911979	−	0.0526531i
$306$	−4.08648	+	5.31374i	−0.233608	+	0.303766i
$307$		−	9.18411i		−	0.524165i	−0.965046	−	0.262082i	$-0.915591\pi$
$307$		−	9.18411i		−	0.524165i	0.965046	−	0.262082i	$-0.0844092\pi$
$308$	−8.63693	−	13.6767i	−0.492135	−	0.779305i
$309$	11.5805	−	2.29702i	0.658791	−	0.130673i
$310$	6.10001			0.346457
$311$	4.44185	+	7.69351i	0.251874	+	0.436259i	0.964042	−	0.265751i	$-0.0856197\pi$
$311$	4.44185	+	7.69351i	0.251874	+	0.436259i	−0.712168	+	0.702009i	$0.752286\pi$
$312$	7.32587	+	2.49120i	0.414746	+	0.141037i
$313$	−20.3812	−	11.7671i	−1.15202	−	0.665116i	−0.202638	−	0.979254i	$-0.564951\pi$
$313$	−20.3812	−	11.7671i	−1.15202	−	0.665116i	−0.949377	+	0.314138i	$0.898285\pi$
$314$	17.8644			1.00815
$315$	−3.31809	−	7.21043i	−0.186953	−	0.406262i
$316$	−14.9980			−0.843702
$317$	9.40027	+	5.42725i	0.527972	+	0.304825i	0.740190	−	0.672398i	$-0.234735\pi$
$317$	9.40027	+	5.42725i	0.527972	+	0.304825i	−0.212218	+	0.977222i	$0.568069\pi$
$318$	0.291766	−	0.255594i	0.0163614	−	0.0143330i
$319$	2.23765	+	3.87572i	0.125284	+	0.216999i
$320$	−1.00000			−0.0559017
$321$	−6.15579	−	7.02697i	−0.343583	−	0.392207i
$322$	15.7311	+	8.26859i	0.876659	+	0.460791i
$323$			1.60951i			0.0895557i
$324$	8.68829	+	2.34810i	0.482683	+	0.130450i
$325$	3.86893	+	2.23373i	0.214610	+	0.123905i
$326$		−	8.11292i		−	0.449333i
$327$	−22.1184	−	7.52146i	−1.22315	−	0.415938i
$328$	1.23660	+	0.713952i	0.0682798	+	0.0394214i
$329$	−19.6164	−	10.3108i	−1.08149	−	0.568452i
$330$	10.0256	+	3.40926i	0.551891	+	0.187673i
$331$	−2.43508	+	4.21769i	−0.133844	+	0.231825i	−0.925155	−	0.379589i	$-0.876066\pi$
$331$	−2.43508	+	4.21769i	−0.133844	+	0.231825i	0.791311	+	0.611414i	$0.209399\pi$
$332$	−1.95115	+	3.37949i	−0.107083	+	0.185474i
$333$	21.5725	+	16.5901i	1.18217	+	0.909133i
$334$	2.25076	−	1.29948i	0.123156	−	0.0711043i
$335$	6.54114	+	11.3296i	0.357381	+	0.619001i
$336$	−1.30215	+	4.39368i	−0.0710383	+	0.239695i
$337$	−10.6309	+	18.4133i	−0.579103	+	1.00304i	0.416480	+	0.909145i	$0.363264\pi$
$337$	−10.6309	+	18.4133i	−0.579103	+	1.00304i	−0.995583	+	0.0938903i	$0.970070\pi$
$338$			6.95817i			0.378475i
$339$	−10.5027	+	30.8853i	−0.570428	+	1.67746i
$340$	2.23445			0.121180
$341$	18.6471	+	32.2978i	1.00980	+	1.74902i
$342$	1.99735	−	0.824807i	0.108004	−	0.0446005i
$343$	−2.19861	−	18.3893i	−0.118714	−	0.992929i
$344$	−2.14558	+	1.23875i	−0.115682	+	0.0667888i
$345$	−11.4120	+	2.26360i	−0.614403	+	0.121868i
$346$	12.2659	−	7.08170i	0.659417	−	0.380715i
$347$	0.561393	−	0.324120i	0.0301371	−	0.0173997i	−0.484856	−	0.874594i	$-0.661128\pi$
$347$	0.561393	−	0.324120i	0.0301371	−	0.0173997i	0.514993	+	0.857194i	$0.327795\pi$
$348$	0.408187	−	1.20035i	0.0218811	−	0.0643457i
$349$	11.4424	−	6.60629i	0.612500	−	0.353627i	−0.161444	−	0.986882i	$-0.551615\pi$
$349$	11.4424	−	6.60629i	0.612500	−	0.353627i	0.773943	+	0.633255i	$0.218282\pi$
$350$	−1.23098	+	2.34194i	−0.0657984	+	0.125182i
$351$	1.48080	+	23.1663i	0.0790392	+	1.23653i
$352$	−3.05690	−	5.29471i	−0.162933	−	0.282209i
$353$	−15.9257			−0.847639			−0.423819	−	0.905747i	$-0.639311\pi$
$353$	−15.9257			−0.847639			−0.423819	+	0.905747i	$0.639311\pi$
$354$	−16.5854	+	3.28975i	−0.881503	+	0.174848i
$355$		−	7.83185i		−	0.415672i
$356$	5.83979	−	10.1148i	0.309508	−	0.536084i
$357$	2.90960	−	9.81747i	0.153993	−	0.519596i
$358$	−9.16012	−	15.8658i	−0.484128	−	0.838533i
$359$	−13.0760	+	7.54942i	−0.690123	+	0.398443i	−0.803658	−	0.595091i	$-0.797116\pi$
$359$	−13.0760	+	7.54942i	−0.690123	+	0.398443i	0.113535	+	0.993534i	$0.463783\pi$
$360$	−1.14506	−	2.77287i	−0.0603501	−	0.146143i
$361$	−9.24057	+	16.0051i	−0.486346	+	0.842376i
$362$	−0.268083	+	0.464334i	−0.0140901	+	0.0244048i
$363$	8.88933	+	44.8159i	0.466569	+	2.35222i
$364$	−11.8105	+	0.468706i	−0.619038	+	0.0245668i
$365$	10.7713	+	6.21880i	0.563795	+	0.325507i
$366$	−2.39605	+	2.09899i	−0.125243	+	0.109716i
$367$		−	12.7708i		−	0.666630i	−0.942816	−	0.333315i	$-0.891833\pi$
$367$		−	12.7708i		−	0.666630i	0.942816	−	0.333315i	$-0.108167\pi$
$368$	5.81718	+	3.35855i	0.303242	+	0.175077i
$369$	−0.563713	+	4.24646i	−0.0293457	+	0.221062i
$370$		−	9.07135i		−	0.471597i
$371$	−0.275672	+	0.524470i	−0.0143122	+	0.0272291i
$372$	3.40157	−	10.0030i	0.176363	−	0.518630i
$373$	8.30398			0.429964			0.214982	−	0.976618i	$-0.431031\pi$
$373$	8.30398			0.429964			0.214982	+	0.976618i	$0.431031\pi$
$374$	6.83050	+	11.8308i	0.353197	+	0.611755i
$375$	−0.336991	−	1.69895i	−0.0174021	−	0.0877335i
$376$	−7.25392	−	4.18805i	−0.374092	−	0.215982i
$377$	3.27017			0.168422
$378$	−13.6742	+	1.42033i	−0.703323	+	0.0730537i
$379$	−7.54965			−0.387800			−0.193900	−	0.981021i	$-0.562114\pi$
$379$	−7.54965			−0.387800			−0.193900	+	0.981021i	$0.562114\pi$
$380$	−0.623812	−	0.360158i	−0.0320009	−	0.0184757i
$381$	−4.27666	−	21.5609i	−0.219100	−	1.10460i
$382$	−2.33488	−	4.04414i	−0.119463	−	0.206916i
$383$	10.8396			0.553880			0.276940	−	0.960887i	$-0.410680\pi$
$383$	10.8396			0.553880			0.276940	+	0.960887i	$0.410680\pi$
$384$	−0.557633	+	1.63983i	−0.0284566	+	0.0836823i
$385$	−16.1629	+	0.641432i	−0.823736	+	0.0326904i
$386$			19.7929i			1.00743i
$387$	−5.89171	−	4.53096i	−0.299493	−	0.230322i
$388$	10.9748	+	6.33628i	0.557159	+	0.321676i
$389$			18.8709i			0.956790i	0.878145	+	0.478395i	$0.158781\pi$
$389$			18.8709i			0.956790i	−0.878145	+	0.478395i	$0.841219\pi$
$390$	5.82038	−	5.09879i	0.294726	−	0.258187i
$391$	−12.9982	−	7.50453i	−0.657349	−	0.379520i
$392$	−0.554724	−	6.97799i	−0.0280178	−	0.352441i
$393$	2.93056	+	14.7745i	0.147827	+	0.745277i
$394$	−8.07331	+	13.9834i	−0.406727	+	0.704472i
$395$	−7.49899	+	12.9886i	−0.377315	+	0.653529i
$396$	11.1812	−	14.5392i	0.561877	−	0.730621i
$397$	20.8331	−	12.0280i	1.04558	−	0.603667i	0.124173	−	0.992261i	$-0.460372\pi$
$397$	20.8331	−	12.0280i	1.04558	−	0.603667i	0.921409	+	0.388593i	$0.127039\pi$
$398$	0.381077	+	0.660045i	0.0191017	+	0.0330851i
$399$	−2.39472	+	2.27185i	−0.119886	+	0.113735i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	19.4786i		−	0.972715i	−0.873760	−	0.486357i	$-0.838325\pi$
$401$		−	19.4786i		−	0.972715i	0.873760	−	0.486357i	$-0.161675\pi$
$402$	22.2262	−	4.40861i	1.10854	−	0.219882i
$403$	27.2515			1.35750
$404$	0.0984898	+	0.170589i	0.00490005	+	0.00848714i
$405$	6.37766	−	6.35023i	0.316909	−	0.315546i
$406$	0.0767980	+	1.93516i	0.00381142	+	0.0960405i
$407$	48.0301	−	27.7302i	2.38076	−	1.37454i
$408$	1.24601	−	3.66413i	0.0616865	−	0.181401i
$409$	24.8052	−	14.3213i	1.22654	−	0.708142i	0.260234	−	0.965546i	$-0.416200\pi$
$409$	24.8052	−	14.3213i	1.22654	−	0.708142i	0.966304	+	0.257404i	$0.0828670\pi$
$410$	1.23660	−	0.713952i	0.0610714	−	0.0352596i
$411$	−34.7839	+	6.89946i	−1.71576	+	0.340325i
$412$	−5.90305	+	3.40813i	−0.290823	+	0.167907i
$413$	21.8381	−	13.7909i	1.07458	−	0.678606i
$414$	−2.65180	+	19.9761i	−0.130329	+	0.981770i
$415$	1.95115	+	3.37949i	0.0957782	+	0.165893i
$416$	−4.46746			−0.219035
$417$	0.939211	−	2.76194i	0.0459933	−	0.135253i
$418$		−	4.40387i		−	0.215400i
$419$	13.3187	−	23.0686i	0.650659	−	1.12697i	−0.332304	−	0.943172i	$-0.607826\pi$
$419$	13.3187	−	23.0686i	0.650659	−	1.12697i	0.982963	−	0.183802i	$-0.0588405\pi$
$420$	3.15396	+	3.32454i	0.153897	+	0.162221i
$421$	−6.85328	−	11.8702i	−0.334008	−	0.578520i	0.649285	−	0.760545i	$-0.275068\pi$
$421$	−6.85328	−	11.8702i	−0.334008	−	0.578520i	−0.983294	+	0.182025i	$0.941735\pi$
$422$	10.1189	−	5.84214i	0.492579	−	0.284391i
$423$	3.30675	−	24.9098i	0.160780	−	1.21116i
$424$	−0.111973	+	0.193943i	−0.00543790	+	0.00941871i
$425$	1.11723	−	1.93509i	0.0541935	−	0.0938659i
$426$	−12.8429	−	4.36730i	−0.622241	−	0.211596i
$427$	2.26388	−	4.30705i	0.109557	−	0.208433i
$428$	4.67098	+	2.69679i	0.225780	+	0.130354i
$429$	44.7889	+	15.2307i	2.16243	+	0.735346i
$430$			2.47750i			0.119475i
$431$	22.9075	+	13.2257i	1.10342	+	0.637058i	0.937116	−	0.349018i	$-0.113485\pi$
$431$	22.9075	+	13.2257i	1.10342	+	0.637058i	0.166300	+	0.986075i	$0.446818\pi$
$432$	−5.18557	+	0.331463i	−0.249491	+	0.0159475i
$433$			6.34697i			0.305016i	0.988302	+	0.152508i	$0.0487350\pi$
$433$			6.34697i			0.305016i	−0.988302	+	0.152508i	$0.951265\pi$
$434$	0.639986	+	16.1264i	0.0307203	+	0.774093i
$435$	−0.835444	−	0.953677i	−0.0400565	−	0.0457253i
$436$	13.4882			0.645967
$437$	2.41922	+	4.19021i	0.115727	+	0.200445i
$438$	16.2042	−	14.1953i	0.774267	−	0.678277i
$439$	13.6963	+	7.90756i	0.653689	+	0.377407i	0.789868	−	0.613277i	$-0.210149\pi$
$439$	13.6963	+	7.90756i	0.653689	+	0.377407i	−0.136179	+	0.990684i	$0.543482\pi$
$440$	−6.11380			−0.291464
$441$	18.7139	−	9.52841i	0.891137	−	0.453734i
$442$	9.98233			0.474811
$443$	−1.98778	−	1.14765i	−0.0944423	−	0.0545263i	0.452035	−	0.892000i	$-0.350698\pi$
$443$	−1.98778	−	1.14765i	−0.0944423	−	0.0545263i	−0.546477	+	0.837474i	$0.684032\pi$
$444$	−14.8755	−	5.05848i	−0.705959	−	0.240065i
$445$	−5.83979	−	10.1148i	−0.276833	−	0.479488i
$446$	−7.36437			−0.348713
$447$	−9.72415	+	1.92881i	−0.459936	+	0.0912295i
$448$	−0.104916	−	2.64367i	−0.00495679	−	0.124902i
$449$		−	1.43524i		−	0.0677333i	−0.999426	−	0.0338666i	$-0.989218\pi$
$449$		−	1.43524i		−	0.0677333i	0.999426	−	0.0338666i	$-0.0107821\pi$
$450$	−2.97391	−	0.394783i	−0.140192	−	0.0186103i
$451$	7.56033	+	4.36496i	0.356002	+	0.205538i
$452$		−	18.8344i		−	0.885897i
$453$	2.35399	+	11.8677i	0.110600	+	0.557593i
$454$	12.0222	+	6.94100i	0.564228	+	0.325757i
$455$	−5.49933	+	10.4625i	−0.257813	+	0.490491i
$456$	−0.938456	+	0.822110i	−0.0439472	+	0.0384988i
$457$	17.4266	−	30.1838i	0.815184	−	1.41194i	−0.0940122	−	0.995571i	$-0.529969\pi$
$457$	17.4266	−	30.1838i	0.815184	−	1.41194i	0.909196	−	0.416369i	$-0.136697\pi$
$458$	8.20102	−	14.2046i	0.383209	−	0.663737i
$459$	11.5869	−	0.740640i	0.540831	−	0.0345701i
$460$	5.81718	−	3.35855i	0.271228	−	0.156593i
$461$	8.41259	+	14.5710i	0.391813	+	0.678641i	0.992689	−	0.120702i	$-0.0385145\pi$
$461$	8.41259	+	14.5710i	0.391813	+	0.678641i	−0.600875	+	0.799343i	$0.705181\pi$
$462$	−7.96111	+	26.8621i	−0.370384	+	1.24974i
$463$	−3.64092	+	6.30627i	−0.169208	+	0.293077i	−0.938142	−	0.346252i	$-0.887454\pi$
$463$	−3.64092	+	6.30627i	−0.169208	+	0.293077i	0.768934	+	0.639329i	$0.220788\pi$
$464$			0.731999i			0.0339822i
$465$	−6.96205	−	7.94733i	−0.322858	−	0.368549i
$466$	−13.3427			−0.618091
$467$	−15.5681	−	26.9647i	−0.720404	−	1.24778i	−0.960838	−	0.277111i	$-0.910623\pi$
$467$	−15.5681	−	26.9647i	−0.720404	−	1.24778i	0.240434	−	0.970666i	$-0.422710\pi$
$468$	−5.11552	−	12.3877i	−0.236465	−	0.572621i
$469$	−29.2654	+	18.4813i	−1.35135	+	0.853386i
$470$	−7.25392	+	4.18805i	−0.334598	+	0.193180i
$471$	−20.3890	−	23.2744i	−0.939473	−	1.07243i
$472$	8.45424	−	4.88106i	0.389138	−	0.224669i
$473$	−13.1176	+	7.57346i	−0.603149	+	0.348228i
$474$	17.1175	+	19.5400i	0.786232	+	0.897500i
$475$	−0.623812	+	0.360158i	−0.0286225	+	0.0165252i
$476$	0.234429	+	5.90716i	0.0107450	+	0.270754i
$477$	−0.665996	−	0.0884103i	−0.0304939	−	0.00404803i
$478$	−3.11967	−	5.40343i	−0.142690	−	0.247147i
$479$	−31.0310			−1.41784			−0.708922	−	0.705287i	$-0.750818\pi$
$479$	−31.0310			−1.41784			−0.708922	+	0.705287i	$0.750818\pi$
$480$	1.14132	+	1.30284i	0.0520938	+	0.0594662i
$481$		−	40.5259i		−	1.84782i
$482$	1.26377	−	2.18891i	0.0575632	−	0.0997023i
$483$	−7.18152	−	29.9322i	−0.326771	−	1.36196i
$484$	−13.1893	−	22.8445i	−0.599512	−	1.03839i
$485$	10.9748	−	6.33628i	0.498338	−	0.287715i
$486$	−6.85691	−	13.9994i	−0.311036	−	0.635025i
$487$	−21.4771	+	37.1994i	−0.973221	+	1.68567i	−0.287535	+	0.957770i	$0.592836\pi$
$487$	−21.4771	+	37.1994i	−0.973221	+	1.68567i	−0.685686	+	0.727898i	$0.740498\pi$
$488$	0.919547	−	1.59270i	0.0416259	−	0.0720982i
$489$	−10.5698	+	9.25943i	−0.477985	+	0.418726i
$490$	−6.32047	−	3.00859i	−0.285530	−	0.135914i
$491$	28.8133	+	16.6354i	1.30033	+	0.750744i	0.980460	−	0.196719i	$-0.0630286\pi$
$491$	28.8133	+	16.6354i	1.30033	+	0.750744i	0.319867	+	0.947463i	$0.396362\pi$
$492$	−0.481191	−	2.42594i	−0.0216938	−	0.109370i
$493$		−	1.63562i		−	0.0736645i
$494$	−2.78685	−	1.60899i	−0.125386	−	0.0723919i
$495$	−7.00069	−	16.9528i	−0.314657	−	0.761972i
$496$			6.10001i			0.273898i
$497$	20.7048	−	0.821683i	0.928739	−	0.0368575i
$498$	6.62982	−	1.31504i	0.297089	−	0.0589284i
$499$	−34.3513			−1.53778			−0.768888	−	0.639384i	$-0.779190\pi$
$499$	−34.3513			−1.53778			−0.768888	+	0.639384i	$0.779190\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−4.26185	−	1.44927i	−0.190406	−	0.0647484i
$502$	19.7713	+	11.4150i	0.882438	+	0.509476i
$503$	29.6702			1.32293			0.661465	−	0.749976i	$-0.269935\pi$
$503$	29.6702			1.32293			0.661465	+	0.749976i	$0.269935\pi$
$504$	7.21043	−	3.31809i	0.321178	−	0.147799i
$505$	0.196980			0.00876548
$506$	35.5651	+	20.5335i	1.58106	+	0.912826i
$507$	9.06539	−	7.94149i	0.402608	−	0.352694i
$508$	6.34536	+	10.9905i	0.281530	+	0.487624i
$509$	33.5110			1.48535			0.742674	−	0.669653i	$-0.233557\pi$
$509$	33.5110			1.48535			0.742674	+	0.669653i	$0.233557\pi$
$510$	−2.55022	−	2.91114i	−0.112926	−	0.128907i
$511$	−15.3104	+	29.1282i	−0.677292	+	1.28855i
$512$		−	1.00000i		−	0.0441942i
$513$	−3.35420	−	1.66085i	−0.148092	−	0.0733285i
$514$	15.3563	+	8.86599i	0.677339	+	0.391062i
$515$			6.81626i			0.300360i
$516$	4.06268	+	1.38153i	0.178849	+	0.0608186i
$517$	−44.3490	−	25.6049i	−1.95047	−	1.12610i
$518$	23.9817	−	0.951725i	1.05369	−	0.0418164i
$519$	−23.2256	−	7.89798i	−1.01949	−	0.346683i
$520$	−2.23373	+	3.86893i	−0.0979555	+	0.169664i
$521$	−9.49346	+	16.4432i	−0.415916	+	0.720388i	−0.995524	−	0.0945075i	$-0.969872\pi$
$521$	−9.49346	+	16.4432i	−0.415916	+	0.720388i	0.579608	+	0.814895i	$0.303206\pi$
$522$	−2.02974	+	0.838185i	−0.0888393	+	0.0366863i
$523$	−24.1869	+	13.9643i	−1.05762	+	0.610617i	−0.924773	−	0.380519i	$-0.875745\pi$
$523$	−24.1869	+	13.9643i	−1.05762	+	0.610617i	−0.132847	+	0.991137i	$0.542412\pi$
$524$	−4.34813	−	7.53119i	−0.189949	−	0.329001i
$525$	4.45611	−	1.06914i	0.194481	−	0.0466611i
$526$	3.74152	−	6.48050i	0.163138	−	0.282563i
$527$		−	13.6302i		−	0.593740i
$528$	−3.40926	+	10.0256i	−0.148369	+	0.436308i
$529$	−22.1195			−0.961716
$530$	0.111973	+	0.193943i	0.00486380	+	0.00842435i
$531$	23.2152	+	17.8534i	1.00745	+	0.774773i
$532$	0.886691	−	1.68694i	0.0384429	−	0.0731381i
$533$	5.52446	−	3.18955i	0.239291	−	0.138155i
$534$	−19.8430	+	3.93591i	−0.858692	+	0.170324i
$535$	4.67098	−	2.69679i	0.201944	−	0.116592i
$536$	−11.3296	+	6.54114i	−0.489364	+	0.282534i
$537$	−10.2160	+	30.0421i	−0.440852	+	1.29641i
$538$	−6.21025	+	3.58549i	−0.267743	+	0.154581i
$539$	−3.39147	−	42.6620i	−0.146081	−	1.83758i
$540$	−2.30573	+	4.65657i	−0.0992228	+	0.200387i
$541$	−4.46304	−	7.73021i	−0.191881	−	0.332348i	0.753993	−	0.656883i	$-0.228125\pi$
$541$	−4.46304	−	7.73021i	−0.191881	−	0.332348i	−0.945874	+	0.324535i	$0.894792\pi$
$542$	−18.9899			−0.815684
$543$	0.910920	−	0.180683i	0.0390913	−	0.00775386i
$544$			2.23445i			0.0958014i
$545$	6.74410	−	11.6811i	0.288885	−	0.500364i
$546$	14.0902	+	14.8522i	0.603004	+	0.635617i
$547$	7.61080	+	13.1823i	0.325414	+	0.563634i	0.981596	−	0.190969i	$-0.0611629\pi$
$547$	7.61080	+	13.1823i	0.325414	+	0.563634i	−0.656182	+	0.754603i	$0.727830\pi$
$548$	17.7308	−	10.2369i	0.757421	−	0.437297i
$549$	5.46930	+	0.726044i	0.233424	+	0.0309868i
$550$	−3.05690	+	5.29471i	−0.130347	+	0.225767i
$551$	−0.263635	+	0.456629i	−0.0112312	+	0.0194531i
$552$	−2.26360	−	11.4120i	−0.0963454	−	0.485728i
$553$	−35.1244	−	18.4621i	−1.49364	−	0.785090i
$554$	−7.46104	−	4.30763i	−0.316989	−	0.183014i
$555$	−11.8185	+	10.3533i	−0.501668	+	0.439473i
$556$			1.68428i			0.0714294i
$557$	−26.7294	−	15.4322i	−1.13256	−	0.653884i	−0.187983	−	0.982172i	$-0.560195\pi$
$557$	−26.7294	−	15.4322i	−1.13256	−	0.653884i	−0.944578	+	0.328288i	$0.893528\pi$
$558$	−16.9146	+	6.98489i	−0.716050	+	0.295694i
$559$			11.0681i			0.468131i
$560$	−2.34194	−	1.23098i	−0.0989652	−	0.0520182i
$561$	7.61783	−	22.4017i	0.321625	−	0.945802i
$562$	−21.9686			−0.926689
$563$	11.1561	+	19.3230i	0.470174	+	0.814366i	0.999418	−	0.0341041i	$-0.0108578\pi$
$563$	11.1561	+	19.3230i	0.470174	+	0.814366i	−0.529244	+	0.848470i	$0.677524\pi$
$564$	2.82267	+	14.2306i	0.118856	+	0.599216i
$565$	−16.3111	−	9.41722i	−0.686213	−	0.396185i
$566$	−16.0739			−0.675638
$567$	17.4570	+	16.1942i	0.733126	+	0.680092i
$568$	7.83185			0.328617
$569$	33.2913	+	19.2208i	1.39564	+	0.805776i	0.993933	−	0.109990i	$-0.0350819\pi$
$569$	33.2913	+	19.2208i	1.39564	+	0.805776i	0.401712	+	0.915766i	$0.368415\pi$
$570$	0.242740	+	1.22378i	0.0101673	+	0.0512586i
$571$	−0.734675	−	1.27250i	−0.0307452	−	0.0532523i	0.850243	−	0.526390i	$-0.176455\pi$
$571$	−0.734675	−	1.27250i	−0.0307452	−	0.0532523i	−0.880989	+	0.473137i	$0.843121\pi$
$572$	−27.3131			−1.14202
$573$	−2.60402	+	7.65763i	−0.108784	+	0.319902i
$574$	2.01719	+	3.19426i	0.0841959	+	0.133326i
$575$		−	6.71710i		−	0.280123i
$576$	2.77287	−	1.14506i	0.115536	−	0.0477110i
$577$	−19.6517	−	11.3459i	−0.818112	−	0.472337i	0.0316532	−	0.999499i	$-0.489923\pi$
$577$	−19.6517	−	11.3459i	−0.818112	−	0.472337i	−0.849765	+	0.527162i	$0.823256\pi$
$578$			12.0072i			0.499434i
$579$	25.7870	−	22.5900i	1.07167	−	0.938810i
$580$	0.633929	+	0.365999i	0.0263225	+	0.0151973i
$581$	−8.72956	+	5.51276i	−0.362163	+	0.228708i
$582$	−4.27054	−	21.5301i	−0.177019	−	0.892449i
$583$	−0.684581	+	1.18573i	−0.0283525	+	0.0491079i
$584$	−6.21880	+	10.7713i	−0.257336	+	0.445719i
$585$	−13.2858	−	1.76368i	−0.549301	−	0.0729191i
$586$	−17.4522	+	10.0760i	−0.720945	+	0.416238i
$587$	−21.7046	−	37.5934i	−0.895843	−	1.55165i	−0.832758	−	0.553638i	$-0.813239\pi$
$587$	−21.7046	−	37.5934i	−0.895843	−	1.55165i	−0.0630853	−	0.998008i	$-0.520094\pi$
$588$	−8.45808	+	8.68682i	−0.348805	+	0.358238i
$589$	−2.19697	+	3.80526i	−0.0905244	+	0.156793i
$590$		−	9.76212i		−	0.401900i
$591$	27.4323	−	5.44126i	1.12841	−	0.223824i
$592$	9.07135			0.372830
$593$	4.44261	+	7.69482i	0.182436	+	0.315988i	0.942710	−	0.333615i	$-0.108268\pi$
$593$	4.44261	+	7.69482i	0.182436	+	0.315988i	−0.760274	+	0.649603i	$0.774935\pi$
$594$	−31.7035	+	2.02650i	−1.30081	+	0.0831484i
$595$	5.23297	+	2.75056i	0.214531	+	0.112762i
$596$	4.95680	−	2.86181i	0.203038	−	0.117224i
$597$	0.425003	−	1.24980i	0.0173942	−	0.0511511i
$598$	25.9880	−	15.0042i	1.06273	−	0.613567i
$599$	−31.1268	+	17.9711i	−1.27181	+	0.734278i	−0.975328	−	0.220761i	$-0.929146\pi$
$599$	−31.1268	+	17.9711i	−1.27181	+	0.734278i	−0.296479	+	0.955039i	$0.595813\pi$
$600$	1.69895	−	0.336991i	0.0693594	−	0.0137576i
$601$	18.2810	−	10.5545i	0.745696	−	0.430528i	−0.0784408	−	0.996919i	$-0.524994\pi$
$601$	18.2810	−	10.5545i	0.745696	−	0.430528i	0.824137	+	0.566391i	$0.191661\pi$
$602$	−6.54968	+	0.259928i	−0.266945	+	0.0105939i
$603$	−31.1108	−	23.9255i	−1.26693	−	0.974322i
$604$	−3.49265	−	6.04945i	−0.142114	−	0.246149i
$605$	−26.3785			−1.07244
$606$	0.109842	−	0.323013i	0.00446204	−	0.0131215i
$607$		−	32.5181i		−	1.31987i	−0.751323	−	0.659935i	$-0.770584\pi$
$607$		−	32.5181i		−	1.31987i	0.751323	−	0.659935i	$-0.229416\pi$
$608$	0.360158	−	0.623812i	0.0146063	−	0.0252989i
$609$	2.43356	−	2.30869i	0.0986127	−	0.0935530i
$610$	−0.919547	−	1.59270i	−0.0372314	−	0.0644866i
$611$	−32.4066	+	18.7099i	−1.31103	+	0.756923i
$612$	−6.19586	+	2.55859i	−0.250453	+	0.103425i
$613$	−15.2816	+	26.4686i	−0.617219	+	1.06905i	0.372772	+	0.927923i	$0.378407\pi$
$613$	−15.2816	+	26.4686i	−0.617219	+	1.06905i	−0.989991	+	0.141132i	$0.954926\pi$
$614$	4.59205	−	7.95367i	0.185320	−	0.320984i
$615$	−2.34152	−	0.796246i	−0.0944192	−	0.0321077i
$616$	−0.641432	−	16.1629i	−0.0258441	−	0.651221i
$617$	12.0852	+	6.97739i	0.486531	+	0.280899i	0.723134	−	0.690707i	$-0.242701\pi$
$617$	12.0852	+	6.97739i	0.486531	+	0.280899i	−0.236603	+	0.971606i	$0.576034\pi$
$618$	11.1775	+	3.80097i	0.449626	+	0.152898i
$619$		−	6.29052i		−	0.252837i	−0.991977	−	0.126419i	$-0.959652\pi$
$619$		−	6.29052i		−	0.252837i	0.991977	−	0.126419i	$-0.0403483\pi$
$620$	5.28276	+	3.05000i	0.212161	+	0.122491i
$621$	29.0522	−	19.3442i	1.16582	−	0.776255i
$622$			8.88370i			0.356204i
$623$	26.1275	−	16.4997i	1.04678	−	0.661046i
$624$	5.09879	+	5.82038i	0.204115	+	0.233002i
$625$	1.00000			0.0400000
$626$	−11.7671	−	20.3812i	−0.470308	−	0.814598i
$627$	−5.73753	+	5.02622i	−0.229135	+	0.200728i
$628$	15.4710	+	8.93219i	0.617361	+	0.356433i
$629$	−20.2695			−0.808198
$630$	0.731668	−	7.90346i	0.0291503	−	0.314881i
$631$	−31.2195			−1.24283			−0.621415	−	0.783481i	$-0.713442\pi$
$631$	−31.2195			−1.24283			−0.621415	+	0.783481i	$0.713442\pi$
$632$	−12.9886	−	7.49899i	−0.516660	−	0.298294i
$633$	−19.1602	−	6.51554i	−0.761551	−	0.258969i
$634$	5.42725	+	9.40027i	0.215544	+	0.373332i
$635$	12.6907			0.503616
$636$	0.380474	−	0.0754679i	0.0150868	−	0.00299250i
$637$	−28.2364	−	13.4407i	−1.11877	−	0.532541i
$638$			4.47529i			0.177179i
$639$	8.96797	+	21.7167i	0.354767	+	0.859101i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$			19.1446i			0.756167i	0.925771	+	0.378084i	$0.123417\pi$
$641$			19.1446i			0.756167i	−0.925771	+	0.378084i	$0.876583\pi$
$642$	−1.81759	−	9.16343i	−0.0717345	−	0.361652i
$643$	18.7635	+	10.8331i	0.739961	+	0.427217i	0.822055	−	0.569408i	$-0.192827\pi$
$643$	18.7635	+	10.8331i	0.739961	+	0.427217i	−0.0820940	+	0.996625i	$0.526161\pi$
$644$	9.48922	+	15.0263i	0.373927	+	0.592121i
$645$	3.22778	−	2.82761i	0.127094	−	0.111337i
$646$	−0.804757	+	1.39388i	−0.0316627	+	0.0548414i
$647$	−9.80085	+	16.9756i	−0.385311	+	0.667379i	−0.991812	−	0.127704i	$-0.959239\pi$
$647$	−9.80085	+	16.9756i	−0.385311	+	0.667379i	0.606501	+	0.795083i	$0.292573\pi$
$648$	6.35023	+	6.37766i	0.249461	+	0.250538i
$649$	51.6876	−	29.8418i	2.02891	−	1.17139i
$650$	2.23373	+	3.86893i	0.0876140	+	0.151752i
$651$	20.2797	−	19.2392i	0.794824	−	0.754043i
$652$	4.05646	−	7.02600i	0.158863	−	0.275159i
$653$		−	10.1644i		−	0.397763i	−0.980024	−	0.198881i	$-0.936269\pi$
$653$		−	10.1644i		−	0.397763i	0.980024	−	0.198881i	$-0.0637308\pi$
$654$	−15.3943	−	17.5730i	−0.601966	−	0.687157i
$655$	−8.69627			−0.339791
$656$	0.713952	+	1.23660i	0.0278751	+	0.0482811i
$657$	−36.9883	−	4.91016i	−1.44305	−	0.191564i
$658$	−11.8329	−	18.7376i	−0.461294	−	0.730467i
$659$	−6.03415	+	3.48382i	−0.235057	+	0.135710i	−0.612903	−	0.790158i	$-0.709998\pi$
$659$	−6.03415	+	3.48382i	−0.235057	+	0.135710i	0.377846	+	0.925869i	$0.376665\pi$
$660$	6.97779	+	7.96530i	0.271610	+	0.310049i
$661$	32.7721	−	18.9210i	1.27469	−	0.735941i	0.298821	−	0.954309i	$-0.403407\pi$
$661$	32.7721	−	18.9210i	1.27469	−	0.735941i	0.975866	+	0.218368i	$0.0700733\pi$
$662$	−4.21769	+	2.43508i	−0.163925	+	0.0946422i
$663$	−11.3930	−	13.0054i	−0.442468	−	0.505087i
$664$	−3.37949	+	1.95115i	−0.131150	+	0.0757193i
$665$	−1.01759	−	1.61137i	−0.0394603	−	0.0624861i
$666$	10.3873	+	25.1537i	0.402498	+	0.974686i
$667$	−2.45846	−	4.25817i	−0.0951918	−	0.164877i
$668$	2.59896			0.100557
$669$	8.40510	+	9.59460i	0.324960	+	0.370949i
$670$			13.0823i			0.505413i
$671$	5.62193	−	9.73746i	0.217032	−	0.375911i
$672$	−3.32454	+	3.15396i	−0.128247	+	0.121667i
$673$	−14.5047	−	25.1229i	−0.559115	−	0.968415i	−0.997571	−	0.0696623i	$-0.977808\pi$
$673$	−14.5047	−	25.1229i	−0.559115	−	0.968415i	0.438456	−	0.898753i	$-0.355526\pi$
$674$	−18.4133	+	10.6309i	−0.709253	+	0.409487i
$675$	2.87984	+	4.32510i	0.110845	+	0.166473i
$676$	−3.47909	+	6.02595i	−0.133811	+	0.231767i
$677$	−20.8785	+	36.1626i	−0.802426	+	1.38984i	0.115589	+	0.993297i	$0.463124\pi$
$677$	−20.8785	+	36.1626i	−0.802426	+	1.38984i	−0.918015	+	0.396545i	$0.870209\pi$
$678$	−24.5382	+	21.4961i	−0.942386	+	0.825552i
$679$	17.9024	+	28.3488i	0.687033	+	1.08793i
$680$	1.93509	+	1.11723i	0.0742075	+	0.0428437i
$681$	−4.67811	−	23.5848i	−0.179266	−	0.903773i
$682$			37.2942i			1.42807i
$683$	−11.7954	−	6.81007i	−0.451338	−	0.260580i	0.257057	−	0.966396i	$-0.417247\pi$
$683$	−11.7954	−	6.81007i	−0.451338	−	0.260580i	−0.708395	+	0.705816i	$0.750580\pi$
$684$	2.14216	+	0.284369i	0.0819074	+	0.0108731i
$685$		−	20.4737i		−	0.782261i
$686$	7.29060	−	17.0249i	0.278356	−	0.650014i
$687$	−27.8663	+	5.52734i	−1.06317	+	0.210881i
$688$	−2.47750			−0.0944537
$689$	0.500235	+	0.866433i	0.0190574	+	0.0330085i
$690$	−11.0149	−	3.74568i	−0.419331	−	0.142596i
$691$	−3.99544	−	2.30677i	−0.151994	−	0.0877537i	0.422074	−	0.906561i	$-0.361302\pi$
$691$	−3.99544	−	2.30677i	−0.151994	−	0.0877537i	−0.574068	+	0.818808i	$0.694636\pi$
$692$	14.1634			0.538412
$693$	44.0831	−	20.2861i	1.67458	−	0.770606i
$694$	0.648240			0.0246069
$695$	1.45863	+	0.842140i	0.0553290	+	0.0319442i
$696$	0.953677	−	0.835444i	0.0361490	−	0.0316674i
$697$	−1.59529	−	2.76313i	−0.0604260	−	0.104661i
$698$	13.2126			0.500104
$699$	15.2283	+	17.3835i	0.575988	+	0.657503i
$700$	−2.23703	+	1.41269i	−0.0845517	+	0.0533948i
$701$		−	13.6110i		−	0.514081i	−0.966401	−	0.257040i	$-0.917253\pi$
$701$		−	13.6110i		−	0.514081i	0.966401	−	0.257040i	$-0.0827474\pi$
$702$	−10.3007	+	20.8030i	−0.388777	+	0.785159i
$703$	5.65881	+	3.26712i	0.213426	+	0.123222i
$704$		−	6.11380i		−	0.230422i
$705$	13.7354	+	4.67079i	0.517305	+	0.175912i
$706$	−13.7921	−	7.96285i	−0.519071	−	0.299686i
$707$	0.0206662	+	0.520749i	0.000777233	+	0.0195848i
$708$	−16.0082	−	5.44368i	−0.601626	−	0.204586i
$709$	−5.71967	+	9.90676i	−0.214807	+	0.372056i	−0.953213	−	0.302300i	$-0.902246\pi$
$709$	−5.71967	+	9.90676i	−0.214807	+	0.372056i	0.738406	+	0.674356i	$0.235579\pi$
$710$	3.91593	−	6.78258i	0.146962	−	0.254546i
$711$	5.92095	−	44.6026i	0.222053	−	1.67273i
$712$	10.1148	−	5.83979i	0.379069	−	0.218855i
$713$	−20.4872	−	35.4849i	−0.767251	−	1.32892i
$714$	7.42853	−	7.04738i	0.278006	−	0.263741i
$715$	−13.6566	+	23.6539i	−0.510727	+	0.884605i
$716$		−	18.3202i		−	0.684660i
$717$	−3.47926	+	10.2315i	−0.129936	+	0.382101i
$718$	−15.0988			−0.563483
$719$	15.0806	+	26.1204i	0.562412	+	0.974126i	0.997285	+	0.0736344i	$0.0234598\pi$
$719$	15.0806	+	26.1204i	0.562412	+	0.974126i	−0.434873	+	0.900492i	$0.643207\pi$
$720$	0.394783	−	2.97391i	0.0147127	−	0.110831i
$721$	−18.0199	+	0.715131i	−0.671098	+	0.0266329i
$722$	−16.0051	+	9.24057i	−0.595650	+	0.343898i
$723$	−4.29417	+	0.851759i	−0.159702	+	0.0316772i
$724$	−0.464334	+	0.268083i	−0.0172568	+	0.00996323i
$725$	0.633929	−	0.365999i	0.0235435	−	0.0135929i
$726$	−14.7096	+	43.2564i	−0.545923	+	1.60539i
$727$	33.9927	−	19.6257i	1.26072	−	0.727878i	0.287507	−	0.957778i	$-0.407173\pi$
$727$	33.9927	−	19.6257i	1.26072	−	0.727878i	0.973214	+	0.229901i	$0.0738401\pi$
$728$	−10.4625	−	5.49933i	−0.387767	−	0.203819i
$729$	−10.4130	+	24.9112i	−0.385668	+	0.922638i
$730$	6.21880	+	10.7713i	0.230168	+	0.398663i
$731$	5.53585			0.204751
$732$	−3.12453	+	0.619758i	−0.115486	+	0.0229069i
$733$			45.6277i			1.68530i	0.538463	+	0.842649i	$0.319005\pi$
$733$			45.6277i			1.68530i	−0.538463	+	0.842649i	$0.680995\pi$
$734$	6.38539	−	11.0598i	0.235689	−	0.408226i
$735$	3.29397	+	11.6683i	0.121500	+	0.430393i
$736$	3.35855	+	5.81718i	0.123798	+	0.214424i
$737$	−69.2668	+	39.9912i	−2.55148	+	1.47310i
$738$	−2.61142	+	3.39568i	−0.0961276	+	0.124997i
$739$	−0.454714	+	0.787588i	−0.0167269	+	0.0289719i	−0.874268	−	0.485444i	$-0.838658\pi$
$739$	−0.454714	+	0.787588i	−0.0167269	+	0.0289719i	0.857541	+	0.514416i	$0.171991\pi$
$740$	4.53567	−	7.85602i	0.166735	−	0.288793i
$741$	1.08443	+	5.46719i	0.0398376	+	0.200842i
$742$	−0.500974	+	0.316368i	−0.0183913	+	0.0116142i
$743$	−14.2357	−	8.21897i	−0.522256	−	0.301525i	0.215601	−	0.976482i	$-0.430829\pi$
$743$	−14.2357	−	8.21897i	−0.522256	−	0.301525i	−0.737857	+	0.674957i	$0.764162\pi$
$744$	7.94733	−	6.96205i	0.291363	−	0.255241i
$745$		−	5.72362i		−	0.209697i
$746$	7.19146	+	4.15199i	0.263298	+	0.152015i
$747$	−9.28003	−	7.13672i	−0.339538	−	0.261119i
$748$			13.6610i			0.499496i
$749$	7.61948	+	12.0656i	0.278410	+	0.440867i
$750$	0.557633	−	1.63983i	0.0203619	−	0.0598782i
$751$	4.45127			0.162429			0.0812146	−	0.996697i	$-0.474120\pi$
$751$	4.45127			0.162429			0.0812146	+	0.996697i	$0.474120\pi$
$752$	−4.18805	−	7.25392i	−0.152723	−	0.264523i
$753$	−7.69350	−	38.7870i	−0.280367	−	1.41348i
$754$	2.83205	+	1.63509i	0.103137	+	0.0595463i
$755$	−6.98531			−0.254221
$756$	−12.5523	−	5.60704i	−0.456524	−	0.203926i
$757$	24.4655			0.889213			0.444606	−	0.895726i	$-0.353344\pi$
$757$	24.4655			0.889213			0.444606	+	0.895726i	$0.353344\pi$
$758$	−6.53819	−	3.77483i	−0.237478	−	0.137108i
$759$	−13.8392	−	69.7709i	−0.502332	−	2.53252i
$760$	−0.360158	−	0.623812i	−0.0130643	−	0.0226280i
$761$	−20.0231			−0.725836			−0.362918	−	0.931821i	$-0.618220\pi$
$761$	−20.0231			−0.725836			−0.362918	+	0.931821i	$0.618220\pi$
$762$	7.07676	−	20.8106i	0.256364	−	0.753890i
$763$	31.5886	+	16.6036i	1.14358	+	0.601092i
$764$		−	4.66977i		−	0.168946i
$765$	−0.882125	+	6.64507i	−0.0318933	+	0.240253i
$766$	9.38741	+	5.41982i	0.339181	+	0.195826i
$767$		−	43.6119i		−	1.57473i
$768$	−1.30284	+	1.14132i	−0.0470122	+	0.0411838i
$769$	−26.6527	−	15.3880i	−0.961122	−	0.554904i	−0.0646039	−	0.997911i	$-0.520578\pi$
$769$	−26.6527	−	15.3880i	−0.961122	−	0.554904i	−0.896518	+	0.443007i	$0.853912\pi$
$770$	−14.3182	−	7.52594i	−0.515991	−	0.271216i
$771$	−5.97552	−	30.1258i	−0.215203	−	1.08495i
$772$	−9.89647	+	17.1412i	−0.356182	+	0.616925i
$773$	7.03900	−	12.1919i	0.253175	−	0.438512i	−0.711223	−	0.702966i	$-0.751858\pi$
$773$	7.03900	−	12.1919i	0.253175	−	0.438512i	0.964398	+	0.264454i	$0.0851918\pi$
$774$	−2.83689	−	6.86979i	−0.101970	−	0.246929i
$775$	5.28276	−	3.05000i	0.189762	−	0.109559i
$776$	6.33628	+	10.9748i	0.227459	+	0.393971i
$777$	−28.6107	−	30.1580i	−1.02640	−	1.08191i
$778$	−9.43543	+	16.3426i	−0.338276	+	0.585912i
$779$			1.02854i			0.0368513i
$780$	7.58999	−	1.50549i	0.271765	−	0.0539053i
$781$	47.8824			1.71337
$782$	−7.50453	−	12.9982i	−0.268361	−	0.464816i
$783$	3.40860	+	1.68779i	0.121813	+	0.0603167i
$784$	3.00859	−	6.32047i	0.107450	−	0.225731i
$785$	15.4710	−	8.93219i	0.552184	−	0.318804i
$786$	−4.84933	+	14.2604i	−0.172970	+	0.508652i
$787$	38.2737	−	22.0973i	1.36431	−	0.787685i	0.374116	−	0.927382i	$-0.377946\pi$
$787$	38.2737	−	22.0973i	1.36431	−	0.787685i	0.990194	+	0.139697i	$0.0446130\pi$
$788$	−13.9834	+	8.07331i	−0.498137	+	0.287600i
$789$	−12.7133	+	2.52171i	−0.452606	+	0.0897754i
$790$	−12.9886	+	7.49899i	−0.462115	+	0.266802i
$791$	23.1847	−	44.1092i	0.824354	−	1.56834i
$792$	16.9528	−	7.00069i	0.602391	−	0.248759i
$793$	−4.10804	−	7.11533i	−0.145881	−	0.252673i
$794$	24.0560			0.853715
$795$	0.124880	−	0.367234i	0.00442903	−	0.0130244i
$796$			0.762155i			0.0270139i
$797$	−18.7299	+	32.4411i	−0.663446	+	1.14912i	0.316259	+	0.948673i	$0.397573\pi$
$797$	−18.7299	+	32.4411i	−0.663446	+	1.14912i	−0.979704	+	0.200449i	$0.935760\pi$
$798$	−3.20981	+	0.770118i	−0.113626	+	0.0272619i
$799$	9.35801	+	16.2086i	0.331063	+	0.573417i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	27.7751	+	21.3602i	0.981385	+	0.754725i
$802$	9.73930	−	16.8690i	0.343907	−	0.595664i
$803$	−38.0205	+	65.8535i	−1.34172	+	2.32392i
$804$	21.4527	+	7.29511i	0.756579	+	0.257279i
$805$	17.7578	−	0.704728i	0.625880	−	0.0248384i
$806$	23.6005	+	13.6258i	0.831293	+	0.479947i
$807$	11.7592	+	3.99878i	0.413943	+	0.140764i
$808$			0.196980i			0.00692972i
$809$	11.6506	+	6.72649i	0.409614	+	0.236491i	0.690624	−	0.723214i	$-0.257336\pi$
$809$	11.6506	+	6.72649i	0.409614	+	0.236491i	−0.281010	+	0.959705i	$0.590669\pi$
$810$	8.69833	−	2.31063i	0.305628	−	0.0811873i
$811$			7.87677i			0.276591i	0.990391	+	0.138295i	$0.0441623\pi$
$811$			7.87677i			0.276591i	−0.990391	+	0.138295i	$0.955838\pi$
$812$	−0.901073	+	1.71430i	−0.0316214	+	0.0601601i
$813$	21.6735	+	24.7407i	0.760122	+	0.867696i
$814$	55.4604			1.94389
$815$	−4.05646	−	7.02600i	−0.142092	−	0.246110i
$816$	2.91114	−	2.55022i	0.101910	−	0.0892757i
$817$	−1.54549	−	0.892290i	−0.0540699	−	0.0312173i
$818$	28.6426			1.00146
$819$	3.26869	−	35.3084i	0.114217	−	1.23377i
$820$	1.42790			0.0498646
$821$	20.0805	+	11.5935i	0.700814	+	0.404615i	0.807650	−	0.589662i	$-0.200739\pi$
$821$	20.0805	+	11.5935i	0.700814	+	0.404615i	−0.106837	+	0.994277i	$0.534072\pi$
$822$	−33.5735	−	11.4168i	−1.17101	−	0.398208i
$823$	−7.46576	−	12.9311i	−0.260240	−	0.450749i	0.706066	−	0.708146i	$-0.250468\pi$
$823$	−7.46576	−	12.9311i	−0.260240	−	0.450749i	−0.966306	+	0.257398i	$0.917135\pi$
$824$	−6.81626			−0.237456
$825$	10.3871	−	2.06030i	0.361631	−	0.0717303i
$826$	25.8078	−	1.02420i	0.897969	−	0.0356364i
$827$			20.3605i			0.708004i	0.935245	+	0.354002i	$0.115179\pi$
$827$			20.3605i			0.708004i	−0.935245	+	0.354002i	$0.884821\pi$
$828$	−12.2846	+	15.9739i	−0.426918	+	0.555131i
$829$	−26.4740	−	15.2848i	−0.919482	−	0.530863i	−0.0360120	−	0.999351i	$-0.511465\pi$
$829$	−26.4740	−	15.2848i	−0.919482	−	0.530863i	−0.883470	+	0.468488i	$0.844799\pi$
$830$			3.90230i			0.135451i
$831$	2.90327	+	14.6369i	0.100713	+	0.507749i
$832$	−3.86893	−	2.23373i	−0.134131	−	0.0774406i
$833$	−6.72255	+	14.1228i	−0.232923	+	0.489326i
$834$	2.19435	−	1.92230i	0.0759841	−	0.0665638i
$835$	1.29948	−	2.25076i	0.0449703	−	0.0778909i
$836$	2.20193	−	3.81386i	0.0761555	−	0.131905i
$837$	28.4051	+	14.0650i	0.981824	+	0.486156i
$838$	23.0686	−	13.3187i	0.796891	−	0.460085i
$839$	−7.60897	−	13.1791i	−0.262691	−	0.454994i	0.704265	−	0.709937i	$-0.251277\pi$
$839$	−7.60897	−	13.1791i	−0.262691	−	0.454994i	−0.966956	+	0.254943i	$0.917943\pi$
$840$	1.06914	+	4.45611i	0.0368888	+	0.153750i
$841$	−14.2321	+	24.6507i	−0.490762	+	0.850024i
$842$		−	13.7066i		−	0.472359i
$843$	25.0732	+	28.6216i	0.863566	+	0.985779i
$844$	11.6843			0.402189
$845$	3.47909	+	6.02595i	0.119684	+	0.207299i
$846$	15.3186	−	19.9191i	0.526665	−	0.684834i
$847$	−2.76752	−	69.7362i	−0.0950931	−	2.39616i
$848$	−0.193943	+	0.111973i	−0.00666004	+	0.00384517i
$849$	18.3455	+	20.9418i	0.629616	+	0.718720i
$850$	1.93509	−	1.11723i	0.0663732	−	0.0383206i
$851$	−52.7697	+	30.4666i	−1.80892	+	1.04438i
$852$	−8.93864	−	10.2037i	−0.306233	−	0.349571i
$853$	2.19189	−	1.26549i	0.0750488	−	0.0433294i	−0.462006	−	0.886877i	$-0.652870\pi$
$853$	2.19189	−	1.26549i	0.0750488	−	0.0433294i	0.537055	+	0.843547i	$0.319537\pi$
$854$	4.11410	−	2.59808i	0.140782	−	0.0889044i
$855$	1.31735	−	1.71298i	0.0450524	−	0.0585826i
$856$	2.69679	+	4.67098i	0.0921744	+	0.159651i
$857$	−1.76354			−0.0602412			−0.0301206	−	0.999546i	$-0.509589\pi$
$857$	−1.76354			−0.0602412			−0.0301206	+	0.999546i	$0.509589\pi$
$858$	31.1730	+	35.5846i	1.06423	+	1.21484i
$859$			30.7125i			1.04790i	0.851749	+	0.523949i	$0.175542\pi$
$859$			30.7125i			1.04790i	−0.851749	+	0.523949i	$0.824458\pi$
$860$	−1.23875	+	2.14558i	−0.0422410	+	0.0731635i
$861$	1.85935	−	6.27375i	0.0633665	−	0.213809i
$862$	13.2257	+	22.9075i	0.450468	+	0.780233i
$863$	36.6863	−	21.1809i	1.24882	−	0.721005i	0.277943	−	0.960598i	$-0.410347\pi$
$863$	36.6863	−	21.1809i	1.24882	−	0.721005i	0.970873	+	0.239593i	$0.0770140\pi$
$864$	−4.65657	−	2.30573i	−0.158420	−	0.0784425i
$865$	7.08170	−	12.2659i	0.240785	−	0.417052i
$866$	−3.17349	+	5.49664i	−0.107839	+	0.186783i
$867$	15.6435	−	13.7041i	0.531280	−	0.465414i
$868$	−7.50896	+	14.2859i	−0.254871	+	0.484894i
$869$	−79.4099	−	45.8473i	−2.69380	−	1.55526i
$870$	−0.246677	−	1.24363i	−0.00836313	−	0.0421630i
$871$			58.4445i			1.98032i
$872$	11.6811	+	6.74410i	0.395573	+	0.228384i
$873$	−23.1762	+	30.1365i	−0.784394	+	1.01997i
$874$			4.83844i			0.163663i
$875$	0.104916	+	2.64367i	0.00354679	+	0.0893724i
$876$	21.1309	−	4.19136i	0.713947	−	0.141613i
$877$	28.7641			0.971296			0.485648	−	0.874154i	$-0.338584\pi$
$877$	28.7641			0.971296			0.485648	+	0.874154i	$0.338584\pi$
$878$	7.90756	+	13.6963i	0.266867	+	0.462228i
$879$	33.0460	+	11.2375i	1.11461	+	0.379031i
$880$	−5.29471	−	3.05690i	−0.178484	−	0.103048i
$881$	0.505687			0.0170370			0.00851852	−	0.999964i	$-0.497288\pi$
$881$	0.505687			0.0170370			0.00851852	+	0.999964i	$0.497288\pi$
$882$	20.9709	+	1.10509i	0.706127	+	0.0372104i
$883$	30.2642			1.01847			0.509235	−	0.860627i	$-0.329928\pi$
$883$	30.2642			1.01847			0.509235	+	0.860627i	$0.329928\pi$
$884$	8.64495	+	4.99116i	0.290761	+	0.167871i
$885$	−12.7185	+	11.1417i	−0.427527	+	0.374524i
$886$	−1.14765	−	1.98778i	−0.0385559	−	0.0667808i
$887$	41.9418			1.40827			0.704134	−	0.710068i	$-0.251336\pi$
$887$	41.9418			1.40827			0.704134	+	0.710068i	$0.251336\pi$
$888$	−10.3533	−	11.8185i	−0.347434	−	0.396603i
$889$	1.33145	+	33.5501i	0.0446555	+	1.12523i
$890$		−	11.6796i		−	0.391500i
$891$	38.8240	+	38.9917i	1.30065	+	1.30627i
$892$	−6.37774	−	3.68219i	−0.213542	−	0.123289i
$893$		−	6.03344i		−	0.201901i
$894$	−9.38576	−	3.19168i	−0.313907	−	0.106746i
$895$	−15.8658	−	9.16012i	−0.530335	−	0.306189i
$896$	1.23098	−	2.34194i	0.0411240	−	0.0782388i
$897$	−49.2087	−	16.7337i	−1.64303	−	0.558721i
$898$	0.717621	−	1.24296i	0.0239473	−	0.0414780i
$899$	2.23260	−	3.86698i	0.0744613	−	0.128971i
$900$	−2.37809	−	1.82885i	−0.0792697	−	0.0609616i
$901$	0.433357	−	0.250199i	0.0144372	−	0.00833533i
$902$	4.36496	+	7.56033i	0.145337	+	0.251731i
$903$	7.81392	+	8.23653i	0.260031	+	0.274095i
$904$	9.41722	−	16.3111i	0.313212	−	0.542499i
$905$			0.536166i			0.0178228i
$906$	−3.89524	+	11.4547i	−0.129411	+	0.380558i
$907$	56.4502			1.87440			0.937199	−	0.348795i	$-0.113409\pi$
$907$	56.4502			1.87440			0.937199	+	0.348795i	$0.113409\pi$
$908$	6.94100	+	12.0222i	0.230345	+	0.398970i
$909$	−0.546200	+	0.225554i	−0.0181163	+	0.00748116i
$910$	−9.99383	+	6.31115i	−0.331292	+	0.209213i
$911$	−7.58916	+	4.38160i	−0.251440	+	0.145169i	−0.620424	−	0.784267i	$-0.713039\pi$
$911$	−7.58916	+	4.38160i	−0.251440	+	0.145169i	0.368983	+	0.929436i	$0.379706\pi$
$912$	−1.22378	+	0.242740i	−0.0405235	+	0.00803792i
$913$	−20.6615	+	11.9289i	−0.683797	+	0.394790i
$914$	30.1838	−	17.4266i	0.998392	−	0.576422i
$915$	−1.02554	+	3.01580i	−0.0339033	+	0.0996994i
$916$	14.2046	−	8.20102i	0.469333	−	0.270969i
$917$	−0.912373	−	22.9901i	−0.0301292	−	0.759199i
$918$	10.4049	+	5.15205i	0.343412	+	0.170043i
$919$	−1.64091	−	2.84214i	−0.0541287	−	0.0937536i	0.837691	−	0.546144i	$-0.183905\pi$
$919$	−1.64091	−	2.84214i	−0.0541287	−	0.0937536i	−0.891820	+	0.452390i	$0.850571\pi$
$920$	6.71710			0.221456
$921$	−15.6034	+	3.09496i	−0.514148	+	0.101982i
$922$			16.8252i			0.554108i
$923$	17.4942	−	30.3009i	0.575830	−	0.997366i
$924$	−20.3256	+	19.2827i	−0.668662	+	0.634353i
$925$	−4.53567	−	7.85602i	−0.149132	−	0.258304i
$926$	−6.30627	+	3.64092i	−0.207237	+	0.119648i
$927$	−7.80505	−	18.9006i	−0.256351	−	0.620778i
$928$	−0.365999	+	0.633929i	−0.0120145	+	0.0208098i
$929$	−30.0905	+	52.1182i	−0.987236	+	1.70994i	−0.355690	+	0.934604i	$0.615754\pi$
$929$	−30.0905	+	52.1182i	−0.987236	+	1.70994i	−0.631546	+	0.775339i	$0.717579\pi$
$930$	−2.05565	−	10.3636i	−0.0674074	−	0.339836i
$931$	4.15316	−	2.85922i	0.136114	−	0.0937072i
$932$	−11.5552	−	6.67137i	−0.378502	−	0.218528i
$933$	11.5740	−	10.1391i	0.378917	−	0.331940i
$934$		−	31.1361i		−	1.01881i
$935$	11.8308	+	6.83050i	0.386908	+	0.223381i
$936$	1.76368	−	13.2858i	0.0576476	−	0.434261i
$937$		−	6.30376i		−	0.205935i	−0.994685	−	0.102967i	$-0.967166\pi$
$937$		−	6.30376i		−	0.205935i	0.994685	−	0.102967i	$-0.0328337\pi$
$938$	−34.5852	+	1.37253i	−1.12925	+	0.0448148i
$939$	−13.1235	+	38.5921i	−0.428268	+	1.25941i
$940$	−8.37611			−0.273198
$941$	12.9299	+	22.3953i	0.421503	+	0.730065i	0.996087	−	0.0883810i	$-0.0281693\pi$
$941$	12.9299	+	22.3953i	0.421503	+	0.730065i	−0.574584	+	0.818446i	$0.694836\pi$
$942$	−6.02014	−	30.3507i	−0.196147	−	0.988880i
$943$	−8.30637	−	4.79569i	−0.270493	−	0.156169i
$944$	9.76212			0.317730
$945$	−11.1320	+	8.06712i	−0.362124	+	0.262423i
$946$	−15.1469			−0.492469
$947$	−32.6775	−	18.8663i	−1.06187	−	0.613074i	−0.135924	−	0.990719i	$-0.543400\pi$
$947$	−32.6775	−	18.8663i	−1.06187	−	0.613074i	−0.925950	+	0.377646i	$0.876734\pi$
$948$	5.05418	+	25.4808i	0.164152	+	0.827579i
$949$	27.7822	+	48.1203i	0.901850	+	1.56205i
$950$	−0.720316			−0.0233701
$951$	6.05283	−	17.7995i	0.196276	−	0.577190i
$952$	−2.75056	+	5.23297i	−0.0891461	+	0.169601i
$953$			19.5292i			0.632613i	0.948657	+	0.316306i	$0.102443\pi$
$953$			19.5292i			0.632613i	−0.948657	+	0.316306i	$0.897557\pi$
$954$	−0.532565	−	0.409564i	−0.0172424	−	0.0132601i
$955$	−4.04414	−	2.33488i	−0.130865	−	0.0755550i
$956$		−	6.23934i		−	0.201795i
$957$	5.83059	−	5.10774i	0.188476	−	0.165110i
$958$	−26.8737	−	15.5155i	−0.868249	−	0.501284i
$959$	54.1258	−	2.14801i	1.74781	−	0.0693629i
$960$	0.336991	+	1.69895i	0.0108763	+	0.0548334i
$961$	3.10505	−	5.37811i	0.100163	−	0.173487i
$962$	20.2629	−	35.0964i	0.653303	−	1.13155i
$963$	−9.86404	+	12.8264i	−0.317864	+	0.413326i
$964$	2.18891	−	1.26377i	0.0705002	−	0.0407033i
$965$	9.89647	+	17.1412i	0.318579	+	0.551794i
$966$	8.74670	−	29.5128i	0.281421	−	0.949558i
$967$	−17.7544	+	30.7515i	−0.570943	+	0.988902i	0.425527	+	0.904946i	$0.360089\pi$
$967$	−17.7544	+	30.7515i	−0.570943	+	0.988902i	−0.996469	+	0.0839557i	$0.973245\pi$
$968$		−	26.3785i		−	0.847839i
$969$	2.73449	−	0.542391i	0.0878443	−	0.0174241i
$970$	12.6726			0.406891
$971$	−16.8585	−	29.1998i	−0.541016	−	0.937067i	−0.998846	−	0.0480271i	$-0.984707\pi$
$971$	−16.8585	−	29.1998i	−0.541016	−	0.937067i	0.457830	−	0.889040i	$-0.348627\pi$
$972$	1.06143	−	15.5523i	0.0340455	−	0.498840i
$973$	−2.07331	+	3.94449i	−0.0664672	+	0.126455i
$974$	−37.1994	+	21.4771i	−1.19195	+	0.688171i
$975$	2.49120	−	7.32587i	0.0797823	−	0.234616i
$976$	1.59270	−	0.919547i	0.0509812	−	0.0294340i
$977$	−7.04757	+	4.06891i	−0.225472	+	0.130176i	−0.608481	−	0.793568i	$-0.708221\pi$
$977$	−7.04757	+	4.06891i	−0.225472	+	0.130176i	0.383010	+	0.923744i	$0.374888\pi$
$978$	−13.7835	+	2.73398i	−0.440747	+	0.0874231i
$979$	61.8399	−	35.7033i	1.97641	−	1.14108i
$980$	−3.96940	−	5.76575i	−0.126798	−	0.184180i
$981$	−5.32491	+	40.1127i	−0.170011	+	1.28070i
$982$	16.6354	+	28.8133i	0.530856	+	0.919470i
$983$	44.5437			1.42072			0.710362	−	0.703836i	$-0.248531\pi$
$983$	44.5437			1.42072			0.710362	+	0.703836i	$0.248531\pi$
$984$	0.796246	−	2.34152i	0.0253834	−	0.0746449i
$985$			16.1466i			0.514474i
$986$	0.817809	−	1.41649i	0.0260443	−	0.0451101i
$987$	−10.9070	+	36.8019i	−0.347173	+	1.17142i
$988$	−1.60899	−	2.78685i	−0.0511888	−	0.0886616i
$989$	14.4120	−	8.32080i	0.458276	−	0.264586i
$990$	2.41363	−	18.1819i	0.0767101	−	0.577859i
$991$	−30.3539	+	52.5745i	−0.964223	+	1.67008i	−0.252535	+	0.967588i	$0.581264\pi$
$991$	−30.3539	+	52.5745i	−0.964223	+	1.67008i	−0.711688	+	0.702496i	$0.752069\pi$
$992$	−3.05000	+	5.28276i	−0.0968377	+	0.167728i
$993$	7.98625	+	2.71576i	0.253436	+	0.0861822i
$994$	18.3418	+	9.64082i	0.581765	+	0.305788i
$995$	0.660045	+	0.381077i	0.0209248	+	0.0120810i
$996$	6.39911	+	2.17605i	0.202764	+	0.0689509i
$997$		−	17.7082i		−	0.560825i	−0.959880	−	0.280412i	$-0.909529\pi$
$997$		−	17.7082i		−	0.560825i	0.959880	−	0.280412i	$-0.0904712\pi$
$998$	−29.7491	−	17.1757i	−0.941692	−	0.543686i
$999$	20.9161	−	42.2413i	0.661755	−	1.33646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.c.311.11	✓	32
3.2	odd	2		1890.2.t.c.1151.1		32
7.5	odd	6		630.2.bk.c.131.1	yes	32
9.2	odd	6		630.2.bk.c.101.9	yes	32
9.7	even	3		1890.2.bk.c.521.1		32
21.5	even	6		1890.2.bk.c.341.1		32
63.47	even	6	inner	630.2.t.c.551.11	yes	32
63.61	odd	6		1890.2.t.c.1601.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.11	✓	32	1.1	even	1	trivial
630.2.t.c.551.11	yes	32	63.47	even	6	inner
630.2.bk.c.101.9	yes	32	9.2	odd	6
630.2.bk.c.131.1	yes	32	7.5	odd	6
1890.2.t.c.1151.1		32	3.2	odd	2
1890.2.t.c.1601.1		32	63.61	odd	6
1890.2.bk.c.341.1		32	21.5	even	6
1890.2.bk.c.521.1		32	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.336991 - 1.69895i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.557633 - 1.63983i) q^{6} +(0.104916 + 2.64367i) q^{7} +1.00000i q^{8} +(-2.77287 + 1.14506i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.336991 - 1.69895i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.557633 - 1.63983i) q^{6} +(0.104916 + 2.64367i) q^{7} +1.00000i q^{8} +(-2.77287 + 1.14506i) q^{9} +(0.866025 + 0.500000i) q^{10} +6.11380i q^{11} +(1.30284 - 1.14132i) q^{12} +(3.86893 + 2.23373i) q^{13} +(-1.23098 + 2.34194i) q^{14} +(-0.336991 - 1.69895i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.11723 - 1.93509i) q^{17} +(-2.97391 - 0.394783i) q^{18} +(-0.623812 + 0.360158i) q^{19} +(0.500000 + 0.866025i) q^{20} +(4.45611 - 1.06914i) q^{21} +(-3.05690 + 5.29471i) q^{22} -6.71710i q^{23} +(1.69895 - 0.336991i) q^{24} +1.00000 q^{25} +(2.23373 + 3.86893i) q^{26} +(2.87984 + 4.32510i) q^{27} +(-2.23703 + 1.41269i) q^{28} +(0.633929 - 0.365999i) q^{29} +(0.557633 - 1.63983i) q^{30} +(5.28276 - 3.05000i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(10.3871 - 2.06030i) q^{33} +(1.93509 - 1.11723i) q^{34} +(0.104916 + 2.64367i) q^{35} +(-2.37809 - 1.82885i) q^{36} +(-4.53567 - 7.85602i) q^{37} -0.720316 q^{38} +(2.49120 - 7.32587i) q^{39} +1.00000i q^{40} +(0.713952 - 1.23660i) q^{41} +(4.39368 + 1.30215i) q^{42} +(1.23875 + 2.14558i) q^{43} +(-5.29471 + 3.05690i) q^{44} +(-2.77287 + 1.14506i) q^{45} +(3.35855 - 5.81718i) q^{46} +(-4.18805 + 7.25392i) q^{47} +(1.63983 + 0.557633i) q^{48} +(-6.97799 + 0.554724i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-3.66413 - 1.24601i) q^{51} +4.46746i q^{52} +(0.193943 + 0.111973i) q^{53} +(0.331463 + 5.18557i) q^{54} +6.11380i q^{55} +(-2.64367 + 0.104916i) q^{56} +(0.822110 + 0.938456i) q^{57} +0.731999 q^{58} +(-4.88106 - 8.45424i) q^{59} +(1.30284 - 1.14132i) q^{60} +(-1.59270 - 0.919547i) q^{61} +6.10001 q^{62} +(-3.31809 - 7.21043i) q^{63} -1.00000 q^{64} +(3.86893 + 2.23373i) q^{65} +(10.0256 + 3.40926i) q^{66} +(6.54114 + 11.3296i) q^{67} +2.23445 q^{68} +(-11.4120 + 2.26360i) q^{69} +(-1.23098 + 2.34194i) q^{70} -7.83185i q^{71} +(-1.14506 - 2.77287i) q^{72} +(10.7713 + 6.21880i) q^{73} -9.07135i q^{74} +(-0.336991 - 1.69895i) q^{75} +(-0.623812 - 0.360158i) q^{76} +(-16.1629 + 0.641432i) q^{77} +(5.82038 - 5.09879i) q^{78} +(-7.49899 + 12.9886i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(6.37766 - 6.35023i) q^{81} +(1.23660 - 0.713952i) q^{82} +(1.95115 + 3.37949i) q^{83} +(3.15396 + 3.32454i) q^{84} +(1.11723 - 1.93509i) q^{85} +2.47750i q^{86} +(-0.835444 - 0.953677i) q^{87} -6.11380 q^{88} +(-5.83979 - 10.1148i) q^{89} +(-2.97391 - 0.394783i) q^{90} +(-5.49933 + 10.4625i) q^{91} +(5.81718 - 3.35855i) q^{92} +(-6.96205 - 7.94733i) q^{93} +(-7.25392 + 4.18805i) q^{94} +(-0.623812 + 0.360158i) q^{95} +(1.14132 + 1.30284i) q^{96} +(10.9748 - 6.33628i) q^{97} +(-6.32047 - 3.00859i) q^{98} +(-7.00069 - 16.9528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * q^99

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