LMFDB - Embedded newform 930.2.z.b.349.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(109,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.z (of order $10$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 44 x^{13} + 63 x^{12} - 46 x^{11} + 110 x^{10} - 120 x^{9} - 79 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 44x^13 + 63x^12 - 46x^11 + 110x^10 - 120x^9 - 79x^8 + 120x^7 + 110x^6 + 46x^5 + 63x^4 + 44x^3 + 18x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.2
Root			$0.297049 + 0.582991i$ of defining polynomial
Character	$\chi$	$=$	930.349
Dual form			930.2.z.b.469.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.21127 + 0.332092i) q^{5} -1.00000 q^{6} +(-0.907165 + 1.24861i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.21127 + 0.332092i) q^{5} -1.00000 q^{6} +(-0.907165 + 1.24861i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-2.00042 - 0.999158i) q^{10} +(1.74861 + 1.27044i) q^{11} +(0.951057 + 0.309017i) q^{12} +(0.363271 - 0.118034i) q^{13} +(1.24861 - 0.907165i) q^{14} +(2.20566 - 0.367482i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.638760 - 0.879178i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(1.32328 - 4.07263i) q^{19} +(1.59376 + 1.56842i) q^{20} +(-0.476925 + 1.46782i) q^{21} +(-1.27044 - 1.74861i) q^{22} +(2.62866 + 3.61803i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(4.77943 + 1.46869i) q^{25} -0.381966 q^{26} +(0.587785 - 0.809017i) q^{27} +(-1.46782 + 0.476925i) q^{28} +(-1.31677 + 4.05259i) q^{29} +(-2.21127 - 0.332092i) q^{30} +(5.47414 + 1.01677i) q^{31} -1.00000i q^{32} +(2.05561 + 0.667908i) q^{33} +(0.335816 + 1.03354i) q^{34} +(-2.42064 + 2.45974i) q^{35} +1.00000 q^{36} -3.70476i q^{37} +(-2.51702 + 3.46439i) q^{38} +(0.309017 - 0.224514i) q^{39} +(-1.03108 - 1.98415i) q^{40} +(0.587210 - 1.80725i) q^{41} +(0.907165 - 1.24861i) q^{42} +(7.37483 + 2.39623i) q^{43} +(0.667908 + 2.05561i) q^{44} +(1.98415 - 1.03108i) q^{45} +(-1.38197 - 4.25325i) q^{46} +(-9.01470 + 2.92905i) q^{47} +(0.587785 + 0.809017i) q^{48} +(1.42705 + 4.39201i) q^{49} +(-4.09166 - 2.87373i) q^{50} +(-0.879178 - 0.638760i) q^{51} +(0.363271 + 0.118034i) q^{52} +(-3.47954 - 4.78918i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(3.44474 + 3.38998i) q^{55} +1.54336 q^{56} -4.28222i q^{57} +(2.50464 - 3.44734i) q^{58} +(1.08442 + 3.33751i) q^{59} +(2.00042 + 0.999158i) q^{60} -4.97335 q^{61} +(-4.89201 - 2.65861i) q^{62} +1.54336i q^{63} +(-0.309017 + 0.951057i) q^{64} +(0.842489 - 0.140366i) q^{65} +(-1.74861 - 1.27044i) q^{66} +2.20197i q^{67} -1.08672i q^{68} +(3.61803 + 2.62866i) q^{69} +(3.06227 - 1.59134i) q^{70} +(-4.31677 + 3.13631i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(3.86791 - 5.32373i) q^{73} +(-1.14483 + 3.52343i) q^{74} +(4.99936 - 0.0801180i) q^{75} +(3.46439 - 2.51702i) q^{76} +(-3.17255 + 1.03082i) q^{77} +(-0.363271 + 0.118034i) q^{78} +(4.01750 - 2.91888i) q^{79} +(0.367482 + 2.20566i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.11694 + 1.53734i) q^{82} +(1.57743 + 0.512538i) q^{83} +(-1.24861 + 0.907165i) q^{84} +(-1.12050 - 2.15623i) q^{85} +(-6.27340 - 4.55789i) q^{86} +4.26114i q^{87} -2.16140i q^{88} +(-0.341842 - 0.248363i) q^{89} +(-2.20566 + 0.367482i) q^{90} +(-0.182169 + 0.560659i) q^{91} +4.47214i q^{92} +(5.52041 - 0.724595i) q^{93} +9.47861 q^{94} +(4.27861 - 8.56624i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(8.18713 - 11.2686i) q^{97} -4.61803i q^{98} +2.16140 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 12 * q^5 - 16 * q^6 + 4 * q^9	$ 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9} + 4 q^{10} + 8 q^{11} + 4 q^{15} - 4 q^{16} + 8 q^{19} - 2 q^{20} - 4 q^{24} + 16 q^{25} - 24 q^{26} + 36 q^{29} - 12 q^{30} + 40 q^{31} + 8 q^{34} + 14 q^{35} + 16 q^{36} - 4 q^{39} + 6 q^{40} + 32 q^{41} + 12 q^{44} - 2 q^{45} - 40 q^{46} - 4 q^{49} - 8 q^{50} + 8 q^{51} - 4 q^{54} + 24 q^{55} - 4 q^{60} - 16 q^{61} + 4 q^{64} + 6 q^{65} - 8 q^{66} + 40 q^{69} + 18 q^{70} - 12 q^{71} - 12 q^{74} - 8 q^{75} + 32 q^{76} - 8 q^{79} - 8 q^{80} - 4 q^{81} - 40 q^{85} - 68 q^{86} + 20 q^{89} - 4 q^{90} - 56 q^{94} - 18 q^{95} + 4 q^{96} - 8 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 + 12 * q^5 - 16 * q^6 + 4 * q^9 + 4 * q^10 + 8 * q^11 + 4 * q^15 - 4 * q^16 + 8 * q^19 - 2 * q^20 - 4 * q^24 + 16 * q^25 - 24 * q^26 + 36 * q^29 - 12 * q^30 + 40 * q^31 + 8 * q^34 + 14 * q^35 + 16 * q^36 - 4 * q^39 + 6 * q^40 + 32 * q^41 + 12 * q^44 - 2 * q^45 - 40 * q^46 - 4 * q^49 - 8 * q^50 + 8 * q^51 - 4 * q^54 + 24 * q^55 - 4 * q^60 - 16 * q^61 + 4 * q^64 + 6 * q^65 - 8 * q^66 + 40 * q^69 + 18 * q^70 - 12 * q^71 - 12 * q^74 - 8 * q^75 + 32 * q^76 - 8 * q^79 - 8 * q^80 - 4 * q^81 - 40 * q^85 - 68 * q^86 + 20 * q^89 - 4 * q^90 - 56 * q^94 - 18 * q^95 + 4 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	2.21127	+	0.332092i	0.988910	+	0.148516i
$5$	2.21127	+	0.332092i	0.988910	+	0.148516i
$6$	−1.00000			−0.408248
$7$	−0.907165	+	1.24861i	−0.342876	+	0.471929i	−0.945279	−	0.326264i	$-0.894210\pi$
$7$	−0.907165	+	1.24861i	−0.342876	+	0.471929i	0.602402	+	0.798192i	$0.294210\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	−2.00042	−	0.999158i	−0.632589	−	0.315962i
$11$	1.74861	+	1.27044i	0.527225	+	0.383051i	0.819319	−	0.573339i	$-0.194352\pi$
$11$	1.74861	+	1.27044i	0.527225	+	0.383051i	−0.292094	+	0.956390i	$0.594352\pi$
$12$	0.951057	+	0.309017i	0.274546	+	0.0892055i
$13$	0.363271	−	0.118034i	0.100753	−	0.0327367i	−0.258207	−	0.966090i	$-0.583131\pi$
$13$	0.363271	−	0.118034i	0.100753	−	0.0327367i	0.358960	+	0.933353i	$0.383131\pi$
$14$	1.24861	−	0.907165i	0.333704	−	0.242450i
$15$	2.20566	−	0.367482i	0.569500	−	0.0948834i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.638760	−	0.879178i	−0.154922	−	0.213232i	0.724500	−	0.689275i	$-0.242071\pi$
$17$	−0.638760	−	0.879178i	−0.154922	−	0.213232i	−0.879422	+	0.476043i	$0.842071\pi$
$18$	−0.951057	+	0.309017i	−0.224166	+	0.0728360i
$19$	1.32328	−	4.07263i	0.303581	−	0.934326i	−0.676622	−	0.736330i	$-0.736557\pi$
$19$	1.32328	−	4.07263i	0.303581	−	0.934326i	0.980203	−	0.197995i	$-0.0634431\pi$
$20$	1.59376	+	1.56842i	0.356375	+	0.350709i
$21$	−0.476925	+	1.46782i	−0.104074	+	0.320306i
$22$	−1.27044	−	1.74861i	−0.270858	−	0.372804i
$23$	2.62866	+	3.61803i	0.548113	+	0.754412i	0.989755	−	0.142779i	$-0.0456039\pi$
$23$	2.62866	+	3.61803i	0.548113	+	0.754412i	−0.441642	+	0.897191i	$0.645604\pi$
$24$	−0.809017	−	0.587785i	−0.165140	−	0.119981i
$25$	4.77943	+	1.46869i	0.955886	+	0.293738i
$26$	−0.381966			−0.0749097
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	−1.46782	+	0.476925i	−0.277393	+	0.0901304i
$29$	−1.31677	+	4.05259i	−0.244517	+	0.752547i	0.751198	+	0.660077i	$0.229476\pi$
$29$	−1.31677	+	4.05259i	−0.244517	+	0.752547i	−0.995715	+	0.0924701i	$0.970524\pi$
$30$	−2.21127	−	0.332092i	−0.403721	−	0.0606314i
$31$	5.47414	+	1.01677i	0.983184	+	0.182617i
$31$	5.47414	+	1.01677i	0.983184	+	0.182617i
$32$		−	1.00000i		−	0.176777i
$33$	2.05561	+	0.667908i	0.357836	+	0.116268i
$34$	0.335816	+	1.03354i	0.0575920	+	0.177250i
$35$	−2.42064	+	2.45974i	−0.409163	+	0.415772i
$36$	1.00000			0.166667
$37$		−	3.70476i		−	0.609058i	−0.952503	−	0.304529i	$-0.901501\pi$
$37$		−	3.70476i		−	0.609058i	0.952503	−	0.304529i	$-0.0984991\pi$
$38$	−2.51702	+	3.46439i	−0.408315	+	0.561998i
$39$	0.309017	−	0.224514i	0.0494823	−	0.0359510i
$40$	−1.03108	−	1.98415i	−0.163029	−	0.313722i
$41$	0.587210	−	1.80725i	0.0917068	−	0.282245i	−0.894675	−	0.446718i	$-0.852593\pi$
$41$	0.587210	−	1.80725i	0.0917068	−	0.282245i	0.986381	+	0.164474i	$0.0525926\pi$
$42$	0.907165	−	1.24861i	0.139979	−	0.192664i
$43$	7.37483	+	2.39623i	1.12465	+	0.365421i	0.811541	−	0.584296i	$-0.198629\pi$
$43$	7.37483	+	2.39623i	1.12465	+	0.365421i	0.313110	+	0.949717i	$0.398629\pi$
$44$	0.667908	+	2.05561i	0.100691	+	0.309895i
$45$	1.98415	−	1.03108i	0.295780	−	0.153705i
$46$	−1.38197	−	4.25325i	−0.203760	−	0.627108i
$47$	−9.01470	+	2.92905i	−1.31493	+	0.427246i	−0.880750	−	0.473581i	$-0.842961\pi$
$47$	−9.01470	+	2.92905i	−1.31493	+	0.427246i	−0.434178	+	0.900827i	$0.642961\pi$
$48$	0.587785	+	0.809017i	0.0848395	+	0.116772i
$49$	1.42705	+	4.39201i	0.203864	+	0.627430i
$50$	−4.09166	−	2.87373i	−0.578648	−	0.406407i
$51$	−0.879178	−	0.638760i	−0.123110	−	0.0894443i
$52$	0.363271	+	0.118034i	0.0503767	+	0.0163684i
$53$	−3.47954	−	4.78918i	−0.477952	−	0.657844i	0.500158	−	0.865934i	$-0.333275\pi$
$53$	−3.47954	−	4.78918i	−0.477952	−	0.657844i	−0.978110	+	0.208090i	$0.933275\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$	3.44474	+	3.38998i	0.464488	+	0.457104i
$56$	1.54336			0.206240
$57$		−	4.28222i		−	0.567194i
$58$	2.50464	−	3.44734i	0.328875	−	0.452658i
$59$	1.08442	+	3.33751i	0.141180	+	0.434507i	0.996500	−	0.0835931i	$-0.0266396\pi$
$59$	1.08442	+	3.33751i	0.141180	+	0.434507i	−0.855320	+	0.518100i	$0.826640\pi$
$60$	2.00042	+	0.999158i	0.258253	+	0.128991i
$61$	−4.97335			−0.636772			−0.318386	−	0.947961i	$-0.603141\pi$
$61$	−4.97335			−0.636772			−0.318386	+	0.947961i	$0.603141\pi$
$62$	−4.89201	−	2.65861i	−0.621286	−	0.337644i
$63$			1.54336i			0.194445i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	0.842489	−	0.140366i	0.104498	−	0.0174102i
$66$	−1.74861	−	1.27044i	−0.215239	−	0.156380i
$67$			2.20197i			0.269013i	0.990913	+	0.134507i	$0.0429450\pi$
$67$			2.20197i			0.269013i	−0.990913	+	0.134507i	$0.957055\pi$
$68$		−	1.08672i		−	0.131785i
$69$	3.61803	+	2.62866i	0.435560	+	0.316453i
$70$	3.06227	−	1.59134i	0.366011	−	0.190201i
$71$	−4.31677	+	3.13631i	−0.512306	+	0.372212i	−0.813698	−	0.581288i	$-0.802549\pi$
$71$	−4.31677	+	3.13631i	−0.512306	+	0.372212i	0.301392	+	0.953500i	$0.402549\pi$
$72$	−0.951057	−	0.309017i	−0.112083	−	0.0364180i
$73$	3.86791	−	5.32373i	0.452705	−	0.623095i	−0.520271	−	0.854001i	$-0.674169\pi$
$73$	3.86791	−	5.32373i	0.452705	−	0.623095i	0.972976	+	0.230906i	$0.0741690\pi$
$74$	−1.14483	+	3.52343i	−0.133084	+	0.409591i
$75$	4.99936	−	0.0801180i	0.577276	−	0.00925123i
$76$	3.46439	−	2.51702i	0.397392	−	0.288723i
$77$	−3.17255	+	1.03082i	−0.361546	+	0.117473i
$78$	−0.363271	+	0.118034i	−0.0411324	+	0.0133647i
$79$	4.01750	−	2.91888i	0.452004	−	0.328400i	−0.338383	−	0.941009i	$-0.609880\pi$
$79$	4.01750	−	2.91888i	0.452004	−	0.328400i	0.790386	+	0.612609i	$0.209880\pi$
$80$	0.367482	+	2.20566i	0.0410857	+	0.246601i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−1.11694	+	1.53734i	−0.123345	+	0.169770i
$83$	1.57743	+	0.512538i	0.173145	+	0.0562584i	0.394307	−	0.918979i	$-0.370985\pi$
$83$	1.57743	+	0.512538i	0.173145	+	0.0562584i	−0.221161	+	0.975237i	$0.570985\pi$
$84$	−1.24861	+	0.907165i	−0.136234	+	0.0989799i
$85$	−1.12050	−	2.15623i	−0.121536	−	0.233876i
$86$	−6.27340	−	4.55789i	−0.676479	−	0.491490i
$87$			4.26114i			0.456843i
$88$		−	2.16140i		−	0.230406i
$89$	−0.341842	−	0.248363i	−0.0362352	−	0.0263264i	0.569520	−	0.821977i	$-0.307129\pi$
$89$	−0.341842	−	0.248363i	−0.0362352	−	0.0263264i	−0.605755	+	0.795651i	$0.707129\pi$
$90$	−2.20566	+	0.367482i	−0.232497	+	0.0387360i
$91$	−0.182169	+	0.560659i	−0.0190965	+	0.0587730i
$92$			4.47214i			0.466252i
$93$	5.52041	−	0.724595i	0.572440	−	0.0751370i
$94$	9.47861			0.977644
$95$	4.27861	−	8.56624i	0.438976	−	0.878877i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	8.18713	−	11.2686i	0.831277	−	1.14415i	−0.156407	−	0.987693i	$-0.549991\pi$
$97$	8.18713	−	11.2686i	0.831277	−	1.14415i	0.987684	−	0.156462i	$-0.0500088\pi$
$98$		−	4.61803i		−	0.466492i
$99$	2.16140			0.217228
$100$	3.00337	+	3.99747i	0.300337	+	0.399747i
$101$	−0.627784	+	0.456112i	−0.0624668	+	0.0453848i	−0.618580	−	0.785721i	$-0.712292\pi$
$101$	−0.627784	+	0.456112i	−0.0624668	+	0.0453848i	0.556114	+	0.831106i	$0.312292\pi$
$102$	0.638760	+	0.879178i	0.0632467	+	0.0870516i
$103$	16.0896	+	5.22783i	1.58536	+	0.515114i	0.963430	−	0.267961i	$-0.0863500\pi$
$103$	16.0896	+	5.22783i	1.58536	+	0.515114i	0.621927	+	0.783075i	$0.286350\pi$
$104$	−0.309017	−	0.224514i	−0.0303016	−	0.0220154i
$105$	−1.54206	+	3.08737i	−0.150490	+	0.301297i
$106$	1.82930	+	5.63002i	0.177678	+	0.546836i
$107$	0.530255	+	0.729834i	0.0512617	+	0.0705557i	0.833878	−	0.551948i	$-0.186115\pi$
$107$	0.530255	+	0.729834i	0.0512617	+	0.0705557i	−0.782617	+	0.622504i	$0.786115\pi$
$108$	0.951057	−	0.309017i	0.0915155	−	0.0297352i
$109$	−4.32528	−	13.3118i	−0.414287	−	1.27504i	−0.912887	−	0.408211i	$-0.866153\pi$
$109$	−4.32528	−	13.3118i	−0.414287	−	1.27504i	0.498601	−	0.866832i	$-0.333847\pi$
$110$	−2.22858	−	4.28854i	−0.212487	−	0.408896i
$111$	−1.14483	−	3.52343i	−0.108663	−	0.334430i
$112$	−1.46782	−	0.476925i	−0.138696	−	0.0450652i
$113$	2.39446	−	3.29569i	0.225252	−	0.310033i	−0.681401	−	0.731911i	$-0.738629\pi$
$113$	2.39446	−	3.29569i	0.225252	−	0.310033i	0.906653	+	0.421878i	$0.138629\pi$
$114$	−1.32328	+	4.07263i	−0.123936	+	0.381437i
$115$	4.61115	+	8.87341i	0.429992	+	0.827449i
$116$	−3.44734	+	2.50464i	−0.320077	+	0.232550i
$117$	0.224514	−	0.309017i	0.0207563	−	0.0285686i
$118$		−	3.50926i		−	0.323054i
$119$	1.67721			0.153749
$120$	−1.59376	−	1.56842i	−0.145489	−	0.143176i
$121$	−1.95557	−	6.01864i	−0.177779	−	0.547149i
$122$	4.72994	+	1.53685i	0.428228	+	0.139140i
$123$		−	1.90025i		−	0.171340i
$124$	3.83103	+	4.04020i	0.344036	+	0.362821i
$125$	10.0809	+	4.83488i	0.901660	+	0.432445i
$126$	0.476925	−	1.46782i	0.0424879	−	0.130764i
$127$	−0.316103	+	0.102708i	−0.0280496	+	0.00911386i	−0.323008	−	0.946396i	$-0.604694\pi$
$127$	−0.316103	+	0.102708i	−0.0280496	+	0.00911386i	0.294959	+	0.955510i	$0.404694\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	7.75435			0.682733
$130$	−0.844630	−	0.126848i	−0.0740789	−	0.0111253i
$131$	0.571884	+	0.415498i	0.0499657	+	0.0363022i	0.612488	−	0.790480i	$-0.290169\pi$
$131$	0.571884	+	0.415498i	0.0499657	+	0.0363022i	−0.562522	+	0.826782i	$0.690169\pi$
$132$	1.27044	+	1.74861i	0.110577	+	0.152197i
$133$	3.88468	+	5.34680i	0.336844	+	0.463627i
$134$	0.680446	−	2.09420i	0.0587816	−	0.180911i
$135$	1.56842	−	1.59376i	0.134988	−	0.137169i
$136$	−0.335816	+	1.03354i	−0.0287960	+	0.0886250i
$137$	−18.0471	+	5.86385i	−1.54187	+	0.500983i	−0.951891	−	0.306438i	$-0.900863\pi$
$137$	−18.0471	+	5.86385i	−1.54187	+	0.500983i	−0.589976	+	0.807421i	$0.700863\pi$
$138$	−2.62866	−	3.61803i	−0.223766	−	0.307988i
$139$	−3.32758	−	10.2412i	−0.282242	−	0.868651i	−0.987212	−	0.159414i	$-0.949040\pi$
$139$	−3.32758	−	10.2412i	−0.282242	−	0.868651i	0.704970	−	0.709237i	$-0.250960\pi$
$140$	−3.40414	+	0.567157i	−0.287702	+	0.0479336i
$141$	−7.66836	+	5.57139i	−0.645792	+	0.469196i
$142$	5.07466	−	1.64886i	0.425856	−	0.138369i
$143$	0.785173	+	0.255118i	0.0656595	+	0.0213341i
$144$	0.809017	+	0.587785i	0.0674181	+	0.0489821i
$145$	−4.25756	+	8.52408i	−0.353571	+	0.707886i
$146$	−5.32373	+	3.86791i	−0.440595	+	0.320111i
$147$	2.71441	+	3.73607i	0.223881	+	0.308146i
$148$	2.17760	−	2.99721i	0.178998	−	0.246369i
$149$	−8.77543			−0.718911			−0.359456	−	0.933162i	$-0.617038\pi$
$149$	−8.77543			−0.718911			−0.359456	+	0.933162i	$0.617038\pi$
$150$	−4.77943	−	1.46869i	−0.390239	−	0.119918i
$151$	−14.6157	−	10.6189i	−1.18941	−	0.864156i	−0.196207	−	0.980563i	$-0.562862\pi$
$151$	−14.6157	−	10.6189i	−1.18941	−	0.864156i	−0.993202	+	0.116407i	$0.962862\pi$
$152$	−4.07263	+	1.32328i	−0.330334	+	0.107332i
$153$	−1.03354	−	0.335816i	−0.0835564	−	0.0271491i
$154$	3.33582			0.268808
$155$	11.7671	+	4.06627i	0.945159	+	0.326611i
$156$	0.381966			0.0305818
$157$	−6.68360	−	2.17163i	−0.533409	−	0.173315i	0.0299130	−	0.999553i	$-0.490477\pi$
$157$	−6.68360	−	2.17163i	−0.533409	−	0.173315i	−0.563322	+	0.826237i	$0.690477\pi$
$158$	−4.72285	+	1.53455i	−0.375730	+	0.122082i
$159$	−4.78918	−	3.47954i	−0.379807	−	0.275946i
$160$	0.332092	−	2.21127i	0.0262542	−	0.174816i
$161$	−6.90212			−0.543964
$162$	−0.587785	+	0.809017i	−0.0461808	+	0.0635624i
$163$	11.4835	+	15.8056i	0.899453	+	1.23799i	0.970642	+	0.240528i	$0.0773207\pi$
$163$	11.4835	+	15.8056i	0.899453	+	1.23799i	−0.0711888	+	0.997463i	$0.522679\pi$
$164$	1.53734	−	1.11694i	0.120046	−	0.0872184i
$165$	4.32370	+	2.15958i	0.336600	+	0.168123i
$166$	−1.34184	−	0.974905i	−0.104147	−	0.0756673i
$167$	4.67718	+	1.51971i	0.361931	+	0.117599i	0.484337	−	0.874882i	$-0.339061\pi$
$167$	4.67718	+	1.51971i	0.361931	+	0.117599i	−0.122406	+	0.992480i	$0.539061\pi$
$168$	1.46782	−	0.476925i	0.113245	−	0.0367956i
$169$	−10.3992	+	7.55545i	−0.799937	+	0.581189i
$170$	0.399351	+	2.39695i	0.0306288	+	0.183838i
$171$	−1.32328	−	4.07263i	−0.101194	−	0.311442i
$172$	4.55789	+	6.27340i	0.347536	+	0.478343i
$173$	−4.02967	+	1.30932i	−0.306370	+	0.0995456i	−0.458167	−	0.888866i	$-0.651494\pi$
$173$	−4.02967	+	1.30932i	−0.306370	+	0.0995456i	0.151797	+	0.988412i	$0.451494\pi$
$174$	1.31677	−	4.05259i	0.0998238	−	0.307226i
$175$	−6.16955	+	4.63528i	−0.466374	+	0.350394i
$176$	−0.667908	+	2.05561i	−0.0503455	+	0.154947i
$177$	2.06269	+	2.83905i	0.155042	+	0.213396i
$178$	0.248363	+	0.341842i	0.0186156	+	0.0256221i
$179$	−2.55841	−	1.85879i	−0.191225	−	0.138933i	0.488054	−	0.872814i	$-0.337707\pi$
$179$	−2.55841	−	1.85879i	−0.191225	−	0.138933i	−0.679278	+	0.733881i	$0.737707\pi$
$180$	2.21127	+	0.332092i	0.164818	+	0.0247527i
$181$	−20.7015			−1.53873			−0.769364	−	0.638811i	$-0.779427\pi$
$181$	−20.7015			−1.53873			−0.769364	+	0.638811i	$0.779427\pi$
$182$	0.346506	−	0.476925i	0.0256848	−	0.0353520i
$183$	−4.72994	+	1.53685i	−0.349647	+	0.113607i
$184$	1.38197	−	4.25325i	0.101880	−	0.313554i
$185$	1.23032	−	8.19222i	0.0904549	−	0.602304i
$186$	−5.47414	−	1.01677i	−0.401383	−	0.0745533i
$187$		−	2.34884i		−	0.171764i
$188$	−9.01470	−	2.92905i	−0.657464	−	0.213623i
$189$	0.476925	+	1.46782i	0.0346912	+	0.106769i
$190$	−6.71632	+	6.82481i	−0.487253	+	0.495124i
$191$	−20.7597			−1.50212			−0.751059	−	0.660236i	$-0.770456\pi$
$191$	−20.7597			−1.50212			−0.751059	+	0.660236i	$0.770456\pi$
$192$			1.00000i			0.0721688i
$193$	6.48891	−	8.93123i	0.467082	−	0.642884i	−0.508876	−	0.860840i	$-0.669939\pi$
$193$	6.48891	−	8.93123i	0.467082	−	0.642884i	0.975959	+	0.217956i	$0.0699389\pi$
$194$	−11.2686	+	8.18713i	−0.809039	+	0.587802i
$195$	0.757879	−	0.393839i	0.0542729	−	0.0282034i
$196$	−1.42705	+	4.39201i	−0.101932	+	0.313715i
$197$	2.27044	−	3.12500i	0.161762	−	0.222647i	−0.720440	−	0.693517i	$-0.756060\pi$
$197$	2.27044	−	3.12500i	0.161762	−	0.222647i	0.882202	+	0.470871i	$0.156060\pi$
$198$	−2.05561	−	0.667908i	−0.146086	−	0.0474662i
$199$	1.22394	+	3.76689i	0.0867626	+	0.267028i	0.985020	−	0.172443i	$-0.0551660\pi$
$199$	1.22394	+	3.76689i	0.0867626	+	0.267028i	−0.898257	+	0.439471i	$0.855166\pi$
$200$	−1.62108	−	4.72991i	−0.114628	−	0.334455i
$201$	0.680446	+	2.09420i	0.0479950	+	0.147713i
$202$	0.738004	−	0.239792i	0.0519258	−	0.0168717i
$203$	−3.86556	−	5.32049i	−0.271309	−	0.373425i
$204$	−0.335816	−	1.03354i	−0.0235118	−	0.0723620i
$205$	1.89865	−	3.80130i	0.132608	−	0.265495i
$206$	−13.6866	−	9.94393i	−0.953594	−	0.692826i
$207$	4.25325	+	1.38197i	0.295622	+	0.0960533i
$208$	0.224514	+	0.309017i	0.0155672	+	0.0214265i
$209$	7.48791	−	5.44029i	0.517950	−	0.376312i
$210$	2.42064	−	2.45974i	0.167040	−	0.169738i
$211$	−21.2293			−1.46148			−0.730741	−	0.682654i	$-0.760825\pi$
$211$	−21.2293			−1.46148			−0.730741	+	0.682654i	$0.760825\pi$
$212$		−	5.91975i		−	0.406570i
$213$	−3.13631	+	4.31677i	−0.214897	+	0.295780i
$214$	−0.278772	−	0.857971i	−0.0190564	−	0.0586497i
$215$	15.5120	+	7.74783i	1.05791	+	0.528397i
$216$	−1.00000			−0.0680414
$217$	−6.23549	+	5.91266i	−0.423293	+	0.401378i
$218$			13.9969i			0.947990i
$219$	2.03348	−	6.25842i	0.137410	−	0.422905i
$220$	0.794274	+	4.76731i	0.0535499	+	0.321412i
$221$	−0.335816	−	0.243985i	−0.0225894	−	0.0164122i
$222$			3.70476i			0.248647i
$223$		−	15.4742i		−	1.03623i	−0.855311	−	0.518114i	$-0.826634\pi$
$223$		−	15.4742i		−	1.03623i	0.855311	−	0.518114i	$-0.173366\pi$
$224$	1.24861	+	0.907165i	0.0834260	+	0.0606125i
$225$	4.72991	−	1.62108i	0.315328	−	0.108072i
$226$	−3.29569	+	2.39446i	−0.219226	+	0.159277i
$227$	1.40592	+	0.456810i	0.0933140	+	0.0303195i	0.355302	−	0.934752i	$-0.384378\pi$
$227$	1.40592	+	0.456810i	0.0933140	+	0.0303195i	−0.261988	+	0.965071i	$0.584378\pi$
$228$	2.51702	−	3.46439i	0.166694	−	0.229435i
$229$	−4.18554	+	12.8818i	−0.276588	+	0.851250i	0.712207	+	0.701970i	$0.247696\pi$
$229$	−4.18554	+	12.8818i	−0.276588	+	0.851250i	−0.988795	+	0.149281i	$0.952304\pi$
$230$	−1.64343	−	9.86403i	−0.108364	−	0.650415i
$231$	−2.69873	+	1.96074i	−0.177564	+	0.129007i
$232$	4.05259	−	1.31677i	0.266065	−	0.0864499i
$233$	−14.9173	+	4.84693i	−0.977266	+	0.317533i	−0.753746	−	0.657166i	$-0.771755\pi$
$233$	−14.9173	+	4.84693i	−0.977266	+	0.317533i	−0.223521	+	0.974699i	$0.571755\pi$
$234$	−0.309017	+	0.224514i	−0.0202011	+	0.0146769i
$235$	−20.9066	+	3.48322i	−1.36380	+	0.227220i
$236$	−1.08442	+	3.33751i	−0.0705899	+	0.217253i
$237$	2.91888	−	4.01750i	0.189602	−	0.260965i
$238$	−1.59512	−	0.518286i	−0.103396	−	0.0335955i
$239$	6.30172	−	4.57847i	0.407624	−	0.296156i	−0.365015	−	0.931002i	$-0.618936\pi$
$239$	6.30172	−	4.57847i	0.407624	−	0.296156i	0.772639	+	0.634845i	$0.218936\pi$
$240$	1.03108	+	1.98415i	0.0665562	+	0.128077i
$241$	−10.6586	−	7.74393i	−0.686581	−	0.498831i	0.188953	−	0.981986i	$-0.439491\pi$
$241$	−10.6586	−	7.74393i	−0.686581	−	0.498831i	−0.875535	+	0.483156i	$0.839491\pi$
$242$			6.32837i			0.406803i
$243$		−	1.00000i		−	0.0641500i
$244$	−4.02352	−	2.92326i	−0.257580	−	0.187143i
$245$	1.69704	+	10.1858i	0.108420	+	0.650749i
$246$	−0.587210	+	1.80725i	−0.0374391	+	0.115226i
$247$		−	1.63566i		−	0.104075i
$248$	−2.39503	−	5.02631i	−0.152085	−	0.319171i
$249$	1.65861			0.105110
$250$	−8.09342	−	7.71340i	−0.511873	−	0.487839i
$251$	0.590934	+	1.81871i	0.0372994	+	0.114796i	0.967973	−	0.251056i	$-0.0807778\pi$
$251$	0.590934	+	1.81871i	0.0372994	+	0.114796i	−0.930673	+	0.365852i	$0.880778\pi$
$252$	−0.907165	+	1.24861i	−0.0571460	+	0.0786548i
$253$			9.66606i			0.607700i
$254$	0.332370			0.0208548
$255$	−1.73197	−	1.70444i	−0.108460	−	0.106736i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−11.1510	−	15.3480i	−0.695580	−	0.957384i	−0.999988	−	0.00484260i	$-0.998459\pi$
$257$	−11.1510	−	15.3480i	−0.695580	−	0.957384i	0.304408	−	0.952542i	$-0.401541\pi$
$258$	−7.37483	−	2.39623i	−0.459137	−	0.149183i
$259$	4.62578	+	3.36083i	0.287432	+	0.208832i
$260$	0.764093	+	0.381644i	0.0473870	+	0.0236686i
$261$	1.31677	+	4.05259i	0.0815058	+	0.250849i
$262$	−0.415498	−	0.571884i	−0.0256696	−	0.0353311i
$263$	−17.5103	+	5.68943i	−1.07973	+	0.350825i	−0.794270	−	0.607565i	$-0.792146\pi$
$263$	−17.5103	+	5.68943i	−1.07973	+	0.350825i	−0.285460	+	0.958391i	$0.592146\pi$
$264$	−0.667908	−	2.05561i	−0.0411069	−	0.126514i
$265$	−6.10376	−	11.7457i	−0.374951	−	0.721532i
$266$	−2.04230	−	6.28554i	−0.125221	−	0.385391i
$267$	−0.401859	−	0.130572i	−0.0245934	−	0.00799088i
$268$	−1.29429	+	1.78143i	−0.0790611	+	0.108818i
$269$	−9.02322	+	27.7706i	−0.550156	+	1.69321i	0.158249	+	0.987399i	$0.449415\pi$
$269$	−9.02322	+	27.7706i	−0.550156	+	1.69321i	−0.708405	+	0.705806i	$0.750585\pi$
$270$	−1.98415	+	1.03108i	−0.120752	+	0.0627498i
$271$	−8.12751	+	5.90498i	−0.493711	+	0.358702i	−0.806610	−	0.591085i	$-0.798700\pi$
$271$	−8.12751	+	5.90498i	−0.493711	+	0.358702i	0.312899	+	0.949786i	$0.398700\pi$
$272$	0.638760	−	0.879178i	0.0387305	−	0.0533080i
$273$			0.589512i			0.0356789i
$274$	18.9758			1.14637
$275$	6.49146	+	8.64012i	0.391450	+	0.521019i
$276$	1.38197	+	4.25325i	0.0831846	+	0.256016i
$277$	−7.30801	−	2.37452i	−0.439096	−	0.142671i	0.0811225	−	0.996704i	$-0.474149\pi$
$277$	−7.30801	−	2.37452i	−0.439096	−	0.142671i	−0.520219	+	0.854033i	$0.674149\pi$
$278$			10.7683i			0.645838i
$279$	5.02631	−	2.39503i	0.300917	−	0.143387i
$280$	3.41279	+	0.512538i	0.203953	+	0.0306300i
$281$	4.63726	−	14.2720i	0.276636	−	0.851397i	−0.712147	−	0.702031i	$-0.752277\pi$
$281$	4.63726	−	14.2720i	0.276636	−	0.851397i	0.988782	−	0.149366i	$-0.0477232\pi$
$282$	9.01470	−	2.92905i	0.536817	−	0.174423i
$283$	2.11242	−	2.90749i	0.125570	−	0.172832i	−0.741603	−	0.670839i	$-0.765934\pi$
$283$	2.11242	−	2.90749i	0.125570	−	0.172832i	0.867173	+	0.498006i	$0.165934\pi$
$284$	−5.33582			−0.316622
$285$	1.42209	−	9.46914i	0.0842373	−	0.560903i
$286$	−0.667908	−	0.485264i	−0.0394942	−	0.0286942i
$287$	1.72384	+	2.37267i	0.101755	+	0.140054i
$288$	−0.587785	−	0.809017i	−0.0346356	−	0.0476718i
$289$	4.88835	−	15.0448i	0.287550	−	0.884988i
$290$	6.68326	−	6.79123i	0.392455	−	0.398794i
$291$	4.30423	−	13.2471i	0.252318	−	0.776556i
$292$	6.25842	−	2.03348i	0.366246	−	0.119001i
$293$	2.60793	+	3.58951i	0.152357	+	0.209702i	0.878372	−	0.477977i	$-0.158630\pi$
$293$	2.60793	+	3.58951i	0.152357	+	0.209702i	−0.726015	+	0.687679i	$0.758630\pi$
$294$	−1.42705	−	4.39201i	−0.0832273	−	0.256147i
$295$	1.28959	+	7.74026i	0.0750829	+	0.450655i
$296$	−2.99721	+	2.17760i	−0.174209	+	0.126571i
$297$	2.05561	−	0.667908i	0.119279	−	0.0387560i
$298$	8.34593	+	2.71176i	0.483467	+	0.157088i
$299$	1.38197	+	1.00406i	0.0799212	+	0.0580661i
$300$	4.09166	+	2.87373i	0.236232	+	0.165915i
$301$	−9.68213	+	7.03448i	−0.558069	+	0.405461i
$302$	10.6189	+	14.6157i	0.611050	+	0.841039i
$303$	−0.456112	+	0.627784i	−0.0262029	+	0.0360653i
$304$	4.28222			0.245602
$305$	−10.9974	−	1.65161i	−0.629710	−	0.0945709i
$306$	0.879178	+	0.638760i	0.0502593	+	0.0365155i
$307$	−22.9191	+	7.44685i	−1.30806	+	0.425014i	−0.878378	−	0.477966i	$-0.841374\pi$
$307$	−22.9191	+	7.44685i	−1.30806	+	0.425014i	−0.429681	+	0.902981i	$0.641374\pi$
$308$	−3.17255	−	1.03082i	−0.180773	−	0.0587366i
$309$	16.9176			0.962410
$310$	−9.93466	−	7.50350i	−0.564251	−	0.426170i
$311$	32.7345			1.85620			0.928102	−	0.372325i	$-0.121439\pi$
$311$	32.7345			1.85620			0.928102	+	0.372325i	$0.121439\pi$
$312$	−0.363271	−	0.118034i	−0.0205662	−	0.00668236i
$313$	11.8328	−	3.84472i	0.668832	−	0.217317i	0.0451324	−	0.998981i	$-0.485629\pi$
$313$	11.8328	−	3.84472i	0.668832	−	0.217317i	0.623699	+	0.781664i	$0.285629\pi$
$314$	5.68541	+	4.13069i	0.320846	+	0.233108i
$315$	−0.512538	+	3.41279i	−0.0288782	+	0.192289i
$316$	4.96590			0.279354
$317$	0.284396	−	0.391438i	0.0159733	−	0.0219853i	−0.800956	−	0.598724i	$-0.795675\pi$
$317$	0.284396	−	0.391438i	0.0159733	−	0.0219853i	0.816929	+	0.576738i	$0.195675\pi$
$318$	3.47954	+	4.78918i	0.195123	+	0.268564i
$319$	−7.45106	+	5.41351i	−0.417179	+	0.303099i
$320$	−0.999158	+	2.00042i	−0.0558546	+	0.111827i
$321$	0.729834	+	0.530255i	0.0407354	+	0.0295960i
$322$	6.56431	+	2.13287i	0.365815	+	0.118860i
$323$	−4.42583	+	1.43804i	−0.246260	+	0.0800146i
$324$	0.809017	−	0.587785i	0.0449454	−	0.0326547i
$325$	1.90958	−	0.0306024i	0.105925	−	0.00169751i
$326$	−6.03721	−	18.5806i	−0.334370	−	1.02909i
$327$	−8.22717	−	11.3237i	−0.454964	−	0.626204i
$328$	−1.80725	+	0.587210i	−0.0997885	+	0.0324233i
$329$	4.52059	−	13.9129i	0.249228	−	0.767045i
$330$	−3.44474	−	3.38998i	−0.189627	−	0.186612i
$331$	−9.00648	+	27.7191i	−0.495041	+	1.52358i	0.321853	+	0.946790i	$0.395694\pi$
$331$	−9.00648	+	27.7191i	−0.495041	+	1.52358i	−0.816893	+	0.576789i	$0.804306\pi$
$332$	0.974905	+	1.34184i	0.0535049	+	0.0736431i
$333$	−2.17760	−	2.99721i	−0.119332	−	0.164246i
$334$	−3.97865	−	2.89066i	−0.217702	−	0.158170i
$335$	−0.731256	+	4.86915i	−0.0399528	+	0.266030i
$336$	−1.54336			−0.0841973
$337$	−9.72394	+	13.3839i	−0.529697	+	0.729065i	−0.987084	−	0.160202i	$-0.948785\pi$
$337$	−9.72394	+	13.3839i	−0.529697	+	0.729065i	0.457387	+	0.889268i	$0.348785\pi$
$338$	12.2250	−	3.97214i	0.664951	−	0.216056i
$339$	1.25884	−	3.87432i	0.0683709	−	0.210424i
$340$	0.360892	−	2.40304i	0.0195721	−	0.130323i
$341$	8.28037	+	8.73248i	0.448407	+	0.472890i
$342$			4.28222i			0.231556i
$343$	−17.0532	−	5.54093i	−0.920788	−	0.299182i
$344$	−2.39623	−	7.37483i	−0.129196	−	0.397624i
$345$	7.12749	+	7.01419i	0.383731	+	0.377631i
$346$	4.23704			0.227785
$347$		−	16.8460i		−	0.904340i	−0.891932	−	0.452170i	$-0.850650\pi$
$347$		−	16.8460i		−	0.904340i	0.891932	−	0.452170i	$-0.149350\pi$
$348$	−2.50464	+	3.44734i	−0.134263	+	0.184797i
$349$	−1.27971	+	0.929762i	−0.0685012	+	0.0497690i	−0.621509	−	0.783407i	$-0.713480\pi$
$349$	−1.27971	+	0.929762i	−0.0685012	+	0.0497690i	0.553008	+	0.833176i	$0.313480\pi$
$350$	7.29997	−	2.50192i	0.390200	−	0.133733i
$351$	0.118034	−	0.363271i	0.00630019	−	0.0193900i
$352$	1.27044	−	1.74861i	0.0677145	−	0.0932010i
$353$	−3.82933	−	1.24422i	−0.203814	−	0.0662233i	0.205331	−	0.978693i	$-0.434173\pi$
$353$	−3.82933	−	1.24422i	−0.203814	−	0.0662233i	−0.409145	+	0.912469i	$0.634173\pi$
$354$	−1.08442	−	3.33751i	−0.0576364	−	0.177387i
$355$	−10.5871	+	5.50167i	−0.561904	+	0.291999i
$356$	−0.130572	−	0.401859i	−0.00692030	−	0.0212985i
$357$	1.59512	−	0.518286i	0.0844227	−	0.0274306i
$358$	1.85879	+	2.55841i	0.0982403	+	0.135216i
$359$	−3.33697	−	10.2701i	−0.176119	−	0.542038i	0.823564	−	0.567223i	$-0.191982\pi$
$359$	−3.33697	−	10.2701i	−0.176119	−	0.542038i	−0.999683	+	0.0251856i	$0.991982\pi$
$360$	−2.00042	−	0.999158i	−0.105431	−	0.0526603i
$361$	0.536063	+	0.389473i	0.0282138	+	0.0204986i
$362$	19.6883	+	6.39711i	1.03479	+	0.336224i
$363$	−3.71972	−	5.11976i	−0.195235	−	0.268718i
$364$	−0.476925	+	0.346506i	−0.0249977	+	0.0181619i
$365$	10.3210	−	10.4877i	0.540224	−	0.548951i
$366$	4.97335			0.259961
$367$			5.82229i			0.303921i	0.988387	+	0.151961i	$0.0485587\pi$
$367$			5.82229i			0.303921i	−0.988387	+	0.151961i	$0.951441\pi$
$368$	−2.62866	+	3.61803i	−0.137028	+	0.188603i
$369$	−0.587210	−	1.80725i	−0.0305689	−	0.0940815i
$370$	−3.70164	+	7.41107i	−0.192439	+	0.385283i
$371$	9.13632			0.474334
$372$	4.89201	+	2.65861i	0.253639	+	0.137842i
$373$		−	13.3684i		−	0.692189i	−0.938200	−	0.346094i	$-0.887508\pi$
$373$		−	13.3684i		−	0.692189i	0.938200	−	0.346094i	$-0.112492\pi$
$374$	−0.725832	+	2.23388i	−0.0375319	+	0.115511i
$375$	11.0815	+	1.48308i	0.572248	+	0.0765861i
$376$	7.66836	+	5.57139i	0.395465	+	0.287322i
$377$			1.62761i			0.0838263i
$378$		−	1.54336i		−	0.0793820i
$379$	16.0037	+	11.6274i	0.822057	+	0.597260i	0.917301	−	0.398194i	$-0.130363\pi$
$379$	16.0037	+	11.6274i	0.822057	+	0.597260i	−0.0952438	+	0.995454i	$0.530363\pi$
$380$	8.49658	−	4.41533i	0.435865	−	0.226501i
$381$	−0.268893	+	0.195362i	−0.0137758	+	0.0100087i
$382$	19.7436	+	6.41509i	1.01017	+	0.328225i
$383$	0.198993	−	0.273890i	0.0101681	−	0.0139951i	−0.803903	−	0.594761i	$-0.797247\pi$
$383$	0.198993	−	0.273890i	0.0101681	−	0.0139951i	0.814071	+	0.580766i	$0.197247\pi$
$384$	0.309017	−	0.951057i	0.0157695	−	0.0485334i
$385$	−7.35769	+	1.22585i	−0.374983	+	0.0624752i
$386$	−8.93123	+	6.48891i	−0.454587	+	0.330277i
$387$	7.37483	−	2.39623i	0.374884	−	0.121807i
$388$	13.2471	−	4.30423i	0.672517	−	0.218514i
$389$	−4.37570	+	3.17913i	−0.221857	+	0.161188i	−0.693162	−	0.720782i	$-0.743783\pi$
$389$	−4.37570	+	3.17913i	−0.221857	+	0.161188i	0.471305	+	0.881970i	$0.343783\pi$
$390$	−0.842489	+	0.140366i	−0.0426611	+	0.00710769i
$391$	1.50182	−	4.62211i	0.0759501	−	0.233750i
$392$	2.71441	−	3.73607i	0.137099	−	0.188700i
$393$	0.672290	+	0.218440i	0.0339125	+	0.0110189i
$394$	−3.12500	+	2.27044i	−0.157435	+	0.114383i
$395$	9.85311	−	5.12026i	0.495764	−	0.257628i
$396$	1.74861	+	1.27044i	0.0878708	+	0.0638418i
$397$		−	13.5456i		−	0.679833i	−0.940456	−	0.339917i	$-0.889601\pi$
$397$		−	13.5456i		−	0.679833i	0.940456	−	0.339917i	$-0.110399\pi$
$398$		−	3.96074i		−	0.198534i
$399$	5.34680	+	3.88468i	0.267675	+	0.194477i
$400$	0.0801180	+	4.99936i	0.00400590	+	0.249968i
$401$	9.56816	−	29.4478i	0.477811	−	1.47055i	−0.364318	−	0.931275i	$-0.618698\pi$
$401$	9.56816	−	29.4478i	0.477811	−	1.47055i	0.842129	−	0.539277i	$-0.181302\pi$
$402$		−	2.20197i		−	0.109824i
$403$	2.10861	−	0.276771i	0.105037	−	0.0137869i
$404$	−0.775984			−0.0386066
$405$	0.999158	−	2.00042i	0.0496486	−	0.0994017i
$406$	2.03225	+	6.25461i	0.100859	+	0.310411i
$407$	4.70666	−	6.47816i	0.233300	−	0.321111i
$408$			1.08672i			0.0538008i
$409$	−5.96474			−0.294938			−0.147469	−	0.989067i	$-0.547113\pi$
$409$	−5.96474			−0.294938			−0.147469	+	0.989067i	$0.547113\pi$
$410$	−2.98039	+	3.02854i	−0.147191	+	0.149569i
$411$	−15.3518	+	11.1537i	−0.757247	+	0.550172i
$412$	9.94393	+	13.6866i	0.489902	+	0.674293i
$413$	−5.15098	−	1.67366i	−0.253463	−	0.0823552i
$414$	−3.61803	−	2.62866i	−0.177817	−	0.129191i
$415$	3.31791	+	1.65721i	0.162870	+	0.0813493i
$416$	−0.118034	−	0.363271i	−0.00578709	−	0.0178108i
$417$	−6.32944	−	8.71172i	−0.309954	−	0.426615i
$418$	−8.80257	+	2.86013i	−0.430548	+	0.139893i
$419$	−7.19594	−	22.1468i	−0.351545	−	1.08194i	−0.957986	−	0.286815i	$-0.907403\pi$
$419$	−7.19594	−	22.1468i	−0.351545	−	1.08194i	0.606441	−	0.795128i	$-0.292597\pi$
$420$	−3.06227	+	1.59134i	−0.149423	+	0.0776492i
$421$	−9.05571	−	27.8706i	−0.441349	−	1.35833i	−0.886439	−	0.462845i	$-0.846828\pi$
$421$	−9.05571	−	27.8706i	−0.441349	−	1.35833i	0.445090	−	0.895486i	$-0.353172\pi$
$422$	20.1902	+	6.56020i	0.982845	+	0.319346i
$423$	−5.57139	+	7.66836i	−0.270890	+	0.372848i
$424$	−1.82930	+	5.63002i	−0.0888389	+	0.273418i
$425$	−1.76167	−	5.14011i	−0.0854535	−	0.249332i
$426$	4.31677	−	3.13631i	0.209148	−	0.151955i
$427$	4.51165	−	6.20976i	0.218334	−	0.300511i
$428$			0.902124i			0.0436058i
$429$	0.825580			0.0398594
$430$	−12.3585	−	12.1621i	−0.595982	−	0.586508i
$431$	4.88405	+	15.0316i	0.235256	+	0.724044i	0.997087	+	0.0762685i	$0.0243006\pi$
$431$	4.88405	+	15.0316i	0.235256	+	0.724044i	−0.761831	+	0.647776i	$0.775699\pi$
$432$	0.951057	+	0.309017i	0.0457577	+	0.0148676i
$433$			21.4746i			1.03200i	0.856587	+	0.516002i	$0.172580\pi$
$433$			21.4746i			1.03200i	−0.856587	+	0.516002i	$0.827420\pi$
$434$	7.75742	−	3.69640i	0.372368	−	0.177433i
$435$	−1.41509	+	9.42254i	−0.0678484	+	0.451776i
$436$	4.32528	−	13.3118i	0.207143	−	0.637522i
$437$	18.2134	−	5.91788i	0.871263	−	0.283091i
$438$	−3.86791	+	5.32373i	−0.184816	+	0.254378i
$439$	32.1050			1.53229			0.766144	−	0.642669i	$-0.222173\pi$
$439$	32.1050			1.53229			0.766144	+	0.642669i	$0.222173\pi$
$440$	0.717782	−	4.77943i	0.0342189	−	0.227850i
$441$	3.73607	+	2.71441i	0.177908	+	0.129258i
$442$	0.243985	+	0.335816i	0.0116052	+	0.0159731i
$443$	−4.30918	−	5.93108i	−0.204735	−	0.281794i	0.694286	−	0.719699i	$-0.255720\pi$
$443$	−4.30918	−	5.93108i	−0.204735	−	0.281794i	−0.899021	+	0.437906i	$0.855720\pi$
$444$	1.14483	−	3.52343i	0.0543314	−	0.167215i
$445$	−0.673426	−	0.662720i	−0.0319234	−	0.0314159i
$446$	−4.78179	+	14.7168i	−0.226424	+	0.696862i
$447$	−8.34593	+	2.71176i	−0.394749	+	0.128262i
$448$	−0.907165	−	1.24861i	−0.0428595	−	0.0589911i
$449$	4.42971	+	13.6332i	0.209051	+	0.643393i	0.999523	+	0.0308941i	$0.00983547\pi$
$449$	4.42971	+	13.6332i	0.209051	+	0.643393i	−0.790472	+	0.612499i	$0.790165\pi$
$450$	−4.99936	+	0.0801180i	−0.235672	+	0.00377680i
$451$	3.32279	−	2.41415i	0.156464	−	0.113678i
$452$	3.87432	−	1.25884i	0.182233	−	0.0592110i
$453$	−17.1818	−	5.58270i	−0.807270	−	0.262298i
$454$	−1.19594	−	0.868904i	−0.0561284	−	0.0407797i
$455$	−0.589016	+	1.17927i	−0.0276135	+	0.0552851i
$456$	−3.46439	+	2.51702i	−0.162235	+	0.117870i
$457$	−16.6365	−	22.8981i	−0.778221	−	1.07113i	−0.995476	−	0.0950141i	$-0.969710\pi$
$457$	−16.6365	−	22.8981i	−0.778221	−	1.07113i	0.217255	−	0.976115i	$-0.430290\pi$
$458$	7.96136	−	10.9579i	0.372010	−	0.512028i
$459$	−1.08672			−0.0507239
$460$	−1.48516	+	9.88910i	−0.0692460	+	0.461082i
$461$	−4.14049	−	3.00824i	−0.192842	−	0.140108i	0.487175	−	0.873305i	$-0.338027\pi$
$461$	−4.14049	−	3.00824i	−0.192842	−	0.140108i	−0.680017	+	0.733197i	$0.738027\pi$
$462$	3.17255	−	1.03082i	0.147600	−	0.0479583i
$463$	28.8048	+	9.35925i	1.33867	+	0.434961i	0.888867	−	0.458165i	$-0.151493\pi$
$463$	28.8048	+	9.35925i	1.33867	+	0.434961i	0.449806	+	0.893126i	$0.351493\pi$
$464$	−4.26114			−0.197819
$465$	12.4478	+	0.231010i	0.577251	+	0.0107128i
$466$	15.6850			0.726594
$467$	1.96730	+	0.639214i	0.0910357	+	0.0295793i	0.354181	−	0.935177i	$-0.384760\pi$
$467$	1.96730	+	0.639214i	0.0910357	+	0.0295793i	−0.263145	+	0.964756i	$0.584760\pi$
$468$	0.363271	−	0.118034i	0.0167922	−	0.00545612i
$469$	−2.74939	−	1.99755i	−0.126955	−	0.0922383i
$470$	20.9598	+	3.14777i	0.966802	+	0.145196i
$471$	−7.02755			−0.323812
$472$	2.06269	−	2.83905i	0.0949432	−	0.130678i
$473$	9.85142	+	13.5593i	0.452969	+	0.623458i
$474$	−4.01750	+	2.91888i	−0.184530	+	0.134069i
$475$	12.3059	−	17.5214i	0.564636	−	0.803936i
$476$	1.35689	+	0.985838i	0.0621929	+	0.0451858i
$477$	−5.63002	−	1.82930i	−0.257781	−	0.0837581i
$478$	−7.40811	+	2.40704i	−0.338839	+	0.110096i
$479$	−24.3612	+	17.6995i	−1.11309	+	0.808710i	−0.983148	−	0.182812i	$-0.941480\pi$
$479$	−24.3612	+	17.6995i	−1.11309	+	0.808710i	−0.129945	+	0.991521i	$0.541480\pi$
$480$	−0.367482	−	2.20566i	−0.0167732	−	0.100674i
$481$	−0.437287	−	1.34583i	−0.0199386	−	0.0613647i
$482$	7.74393	+	10.6586i	0.352726	+	0.485486i
$483$	−6.56431	+	2.13287i	−0.298686	+	0.0970491i
$484$	1.95557	−	6.01864i	0.0888897	−	0.273574i
$485$	21.8462	−	22.1991i	0.991983	−	1.00801i
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	25.0188	+	34.4354i	1.13371	+	1.56042i	0.780823	+	0.624752i	$0.214800\pi$
$487$	25.0188	+	34.4354i	1.13371	+	1.56042i	0.352887	+	0.935666i	$0.385200\pi$
$488$	2.92326	+	4.02352i	0.132330	+	0.182136i
$489$	15.8056	+	11.4835i	0.714755	+	0.519300i
$490$	1.53361	−	10.2117i	0.0692815	−	0.461318i
$491$	9.09452			0.410430			0.205215	−	0.978717i	$-0.434211\pi$
$491$	9.09452			0.410430			0.205215	+	0.978717i	$0.434211\pi$
$492$	1.11694	−	1.53734i	0.0503555	−	0.0693085i
$493$	4.40404	−	1.43096i	0.198348	−	0.0644472i
$494$	−0.505447	+	1.55561i	−0.0227411	+	0.0699901i
$495$	4.77943	+	0.717782i	0.214819	+	0.0322619i
$496$	0.724595	+	5.52041i	0.0325353	+	0.247874i
$497$		−	8.23510i		−	0.369395i
$498$	−1.57743	−	0.512538i	−0.0706863	−	0.0229674i
$499$	3.73432	+	11.4931i	0.167171	+	0.514500i	0.999190	−	0.0402477i	$-0.0128147\pi$
$499$	3.73432	+	11.4931i	0.167171	+	0.514500i	−0.832018	+	0.554748i	$0.812815\pi$
$500$	5.31372	+	9.83689i	0.237637	+	0.439919i
$501$	4.91788			0.219715
$502$		−	1.91230i		−	0.0853503i
$503$	−9.18621	+	12.6437i	−0.409593	+	0.563756i	−0.963119	−	0.269076i	$-0.913282\pi$
$503$	−9.18621	+	12.6437i	−0.409593	+	0.563756i	0.553526	+	0.832832i	$0.313282\pi$
$504$	1.24861	−	0.907165i	0.0556173	−	0.0404084i
$505$	−1.53967	+	0.800104i	−0.0685145	+	0.0356042i
$506$	2.98698	−	9.19297i	0.132787	−	0.408677i
$507$	−7.55545	+	10.3992i	−0.335549	+	0.461844i
$508$	−0.316103	−	0.102708i	−0.0140248	−	0.00455693i
$509$	6.59412	+	20.2946i	0.292279	+	0.899542i	0.984122	+	0.177494i	$0.0567991\pi$
$509$	6.59412	+	20.2946i	0.292279	+	0.899542i	−0.691843	+	0.722048i	$0.743201\pi$
$510$	1.12050	+	2.15623i	0.0496167	+	0.0954793i
$511$	3.13840	+	9.65900i	0.138835	+	0.427289i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−2.51702	−	3.46439i	−0.111129	−	0.152956i
$514$	5.86243	+	18.0427i	0.258581	+	0.795830i
$515$	33.8424	+	16.9034i	1.49127	+	0.744852i
$516$	6.27340	+	4.55789i	0.276171	+	0.200650i
$517$	−19.4843	−	6.33084i	−0.856920	−	0.278430i
$518$	−3.36083	−	4.62578i	−0.147666	−	0.203245i
$519$	−3.42784	+	2.49047i	−0.150465	+	0.109319i
$520$	−0.608761	−	0.599083i	−0.0266959	−	0.0262715i
$521$	21.3473			0.935243			0.467621	−	0.883929i	$-0.345111\pi$
$521$	21.3473			0.935243			0.467621	+	0.883929i	$0.345111\pi$
$522$		−	4.26114i		−	0.186505i
$523$	9.91781	−	13.6507i	0.433676	−	0.596903i	−0.535116	−	0.844778i	$-0.679732\pi$
$523$	9.91781	−	13.6507i	0.433676	−	0.596903i	0.968792	+	0.247875i	$0.0797323\pi$
$524$	0.218440	+	0.672290i	0.00954261	+	0.0293691i
$525$	−4.43521	+	6.31491i	−0.193568	+	0.275605i
$526$	18.4114			0.802775
$527$	−2.60274	−	5.46221i	−0.113377	−	0.237938i
$528$			2.16140i			0.0940627i
$529$	0.927051	−	2.85317i	0.0403066	−	0.124051i
$530$	2.17540	+	13.0570i	0.0944934	+	0.567159i
$531$	2.83905	+	2.06269i	0.123204	+	0.0895133i
$532$			6.60901i			0.286537i
$533$		−	0.725832i		−	0.0314393i
$534$	0.341842	+	0.248363i	0.0147930	+	0.0107477i
$535$	0.930166	+	1.78995i	0.0402146	+	0.0773864i
$536$	1.78143	−	1.29429i	0.0769461	−	0.0559046i
$537$	−3.00759	−	0.977226i	−0.129787	−	0.0421704i
$538$	17.1632	−	23.6231i	0.739958	−	1.01846i
$539$	−3.08442	+	9.49288i	−0.132855	+	0.408887i
$540$	2.20566	−	0.367482i	0.0949167	−	0.0158139i
$541$	13.4650	−	9.78290i	0.578906	−	0.420600i	−0.259424	−	0.965764i	$-0.583533\pi$
$541$	13.4650	−	9.78290i	0.578906	−	0.420600i	0.838330	+	0.545164i	$0.183533\pi$
$542$	9.55446	−	3.10443i	0.410399	−	0.133347i
$543$	−19.6883	+	6.39711i	−0.844904	+	0.274526i
$544$	−0.879178	+	0.638760i	−0.0376944	+	0.0273866i
$545$	−5.14361	−	30.8725i	−0.220328	−	1.32243i
$546$	0.182169	−	0.560659i	0.00779612	−	0.0239940i
$547$	16.5742	−	22.8124i	0.708662	−	0.975389i	−0.291163	−	0.956673i	$-0.594042\pi$
$547$	16.5742	−	22.8124i	0.708662	−	0.975389i	0.999825	−	0.0187156i	$-0.00595770\pi$
$548$	−18.0471	−	5.86385i	−0.770933	−	0.250491i
$549$	−4.02352	+	2.92326i	−0.171720	+	0.124762i
$550$	−3.50380	−	10.2232i	−0.149403	−	0.435919i
$551$	14.7623	+	10.7254i	0.628893	+	0.456918i
$552$		−	4.47214i		−	0.190347i
$553$			7.66418i			0.325914i
$554$	6.21657	+	4.51660i	0.264117	+	0.191892i
$555$	−1.36143	−	8.17145i	−0.0577895	−	0.346859i
$556$	3.32758	−	10.2412i	0.141121	−	0.434325i
$557$			26.1159i			1.10657i	0.832993	+	0.553283i	$0.186625\pi$
$557$			26.1159i			1.10657i	−0.832993	+	0.553283i	$0.813375\pi$
$558$	−5.52041	+	0.724595i	−0.233698	+	0.0306745i
$559$	2.96190			0.125275
$560$	−3.08737	−	1.54206i	−0.130465	−	0.0651640i
$561$	−0.725832	−	2.23388i	−0.0306446	−	0.0943145i
$562$	−8.82059	+	12.1405i	−0.372074	+	0.512116i
$563$		−	0.639524i		−	0.0269527i	−0.999909	−	0.0134764i	$-0.995710\pi$
$563$		−	0.639524i		−	0.0269527i	0.999909	−	0.0134764i	$-0.00428979\pi$
$564$	−9.47861			−0.399122
$565$	6.38927	−	6.49248i	0.268799	−	0.273141i
$566$	−2.90749	+	2.11242i	−0.122211	+	0.0887915i
$567$	0.907165	+	1.24861i	0.0380974	+	0.0524365i
$568$	5.07466	+	1.64886i	0.212928	+	0.0691845i
$569$	8.67741	+	6.30451i	0.363776	+	0.264299i	0.754625	−	0.656156i	$-0.227819\pi$
$569$	8.67741	+	6.30451i	0.363776	+	0.264299i	−0.390849	+	0.920455i	$0.627819\pi$
$570$	−4.27861	+	8.56624i	−0.179211	+	0.358800i
$571$	3.86828	+	11.9054i	0.161883	+	0.498223i	0.998793	−	0.0491164i	$-0.0156405\pi$
$571$	3.86828	+	11.9054i	0.161883	+	0.498223i	−0.836910	+	0.547340i	$0.815641\pi$
$572$	0.485264	+	0.667908i	0.0202899	+	0.0279266i
$573$	−19.7436	+	6.41509i	−0.824802	+	0.267994i
$574$	−0.906278	−	2.78924i	−0.0378273	−	0.116420i
$575$	7.24971	+	21.1528i	0.302334	+	0.882134i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−32.0347	−	10.4087i	−1.33362	−	0.433321i	−0.446471	−	0.894798i	$-0.647320\pi$
$577$	−32.0347	−	10.4087i	−1.33362	−	0.433321i	−0.887152	+	0.461477i	$0.847320\pi$
$578$	−9.29819	+	12.7979i	−0.386754	+	0.532321i
$579$	3.41142	−	10.4993i	0.141774	−	0.436335i
$580$	−8.45476	+	4.39360i	−0.351065	+	0.182434i
$581$	−2.07095	+	1.50463i	−0.0859174	+	0.0624226i
$582$	−8.18713	+	11.2686i	−0.339367	+	0.467099i
$583$		−	12.7949i		−	0.529912i
$584$	−6.58049			−0.272303
$585$	0.599083	−	0.608761i	0.0247690	−	0.0251692i
$586$	−1.37107	−	4.21972i	−0.0566384	−	0.174315i
$587$	25.8363	+	8.39473i	1.06638	+	0.346488i	0.789077	−	0.614295i	$-0.210559\pi$
$587$	25.8363	+	8.39473i	1.06638	+	0.346488i	0.277303	+	0.960783i	$0.410559\pi$
$588$			4.61803i			0.190445i
$589$	11.3847	−	20.9487i	0.469100	−	0.863175i
$590$	1.16540	−	7.75993i	0.0479787	−	0.319471i
$591$	1.19364	−	3.67365i	0.0490999	−	0.151114i
$592$	3.52343	−	1.14483i	0.144812	−	0.0470524i
$593$	23.2183	−	31.9572i	0.953461	−	1.31233i	0.00348754	−	0.999994i	$-0.498890\pi$
$593$	23.2183	−	31.9572i	0.953461	−	1.31233i	0.949973	−	0.312332i	$-0.101110\pi$
$594$	−2.16140			−0.0886831
$595$	3.70876	+	0.556987i	0.152044	+	0.0228343i
$596$	−7.09947	−	5.15807i	−0.290806	−	0.211283i
$597$	2.32807	+	3.20431i	0.0952814	+	0.131144i
$598$	−1.00406	−	1.38197i	−0.0410589	−	0.0565128i
$599$	10.7618	−	33.1214i	0.439715	−	1.35330i	−0.448461	−	0.893802i	$-0.648028\pi$
$599$	10.7618	−	33.1214i	0.439715	−	1.35330i	0.888177	−	0.459502i	$-0.151972\pi$
$600$	−3.00337	−	3.99747i	−0.122612	−	0.163196i
$601$	0.651067	−	2.00378i	0.0265576	−	0.0817358i	−0.936899	−	0.349599i	$-0.886318\pi$
$601$	0.651067	−	2.00378i	0.0265576	−	0.0817358i	0.963457	+	0.267864i	$0.0863177\pi$
$602$	11.3820	−	3.69825i	0.463897	−	0.150729i
$603$	1.29429	+	1.78143i	0.0527074	+	0.0725455i
$604$	−5.58270	−	17.1818i	−0.227157	−	0.699117i
$605$	−2.32556	−	13.9583i	−0.0945475	−	0.567484i
$606$	0.627784	−	0.456112i	0.0255020	−	0.0185283i
$607$	−35.3225	+	11.4770i	−1.43370	+	0.465836i	−0.919926	−	0.392093i	$-0.871751\pi$
$607$	−35.3225	+	11.4770i	−1.43370	+	0.465836i	−0.513769	+	0.857928i	$0.671751\pi$
$608$	−4.07263	−	1.32328i	−0.165167	−	0.0536660i
$609$	−5.32049	−	3.86556i	−0.215597	−	0.156640i
$610$	9.94879	+	4.96916i	0.402815	+	0.201196i
$611$	−2.92905	+	2.12808i	−0.118497	+	0.0860929i
$612$	−0.638760	−	0.879178i	−0.0258204	−	0.0355387i
$613$	1.97399	−	2.71696i	0.0797286	−	0.109737i	−0.767290	−	0.641300i	$-0.778395\pi$
$613$	1.97399	−	2.71696i	0.0797286	−	0.109737i	0.847019	+	0.531563i	$0.178395\pi$
$614$	24.0985			0.972537
$615$	0.631058	−	4.20197i	0.0254467	−	0.169440i
$616$	2.69873	+	1.96074i	0.108735	+	0.0790006i
$617$	0.838896	−	0.272574i	0.0337727	−	0.0109734i	−0.292082	−	0.956393i	$-0.594348\pi$
$617$	0.838896	−	0.272574i	0.0337727	−	0.0109734i	0.325855	+	0.945420i	$0.394348\pi$
$618$	−16.0896	−	5.22783i	−0.647219	−	0.210294i
$619$	7.56844			0.304201			0.152101	−	0.988365i	$-0.451396\pi$
$619$	7.56844			0.304201			0.152101	+	0.988365i	$0.451396\pi$
$620$	7.12972	+	10.2062i	0.286336	+	0.409892i
$621$	4.47214			0.179461
$622$	−31.1324	−	10.1155i	−1.24829	−	0.405596i
$623$	0.620214	−	0.201520i	0.0248484	−	0.00807372i
$624$	0.309017	+	0.224514i	0.0123706	+	0.00898775i
$625$	20.6859	+	14.0390i	0.827436	+	0.561560i
$626$	−12.4418			−0.497274
$627$	5.44029	−	7.48791i	0.217264	−	0.299038i
$628$	−4.13069	−	5.68541i	−0.164832	−	0.226872i
$629$	−3.25714	+	2.36645i	−0.129871	+	0.0943566i
$630$	1.54206	−	3.08737i	0.0614372	−	0.123004i
$631$	25.6058	+	18.6037i	1.01935	+	0.740601i	0.966150	−	0.257983i	$-0.0830578\pi$
$631$	25.6058	+	18.6037i	1.01935	+	0.740601i	0.0532005	+	0.998584i	$0.483058\pi$
$632$	−4.72285	−	1.53455i	−0.187865	−	0.0610410i
$633$	−20.1902	+	6.56020i	−0.802490	+	0.260745i
$634$	−0.391438	+	0.284396i	−0.0155460	+	0.0112948i
$635$	−0.733097	+	0.122140i	−0.0290921	+	0.00484698i
$636$	−1.82930	−	5.63002i	−0.0725366	−	0.223245i
$637$	1.03681	+	1.42705i	0.0410800	+	0.0565418i
$638$	8.75925	−	2.84605i	0.346782	−	0.112676i
$639$	−1.64886	+	5.07466i	−0.0652278	+	0.200751i
$640$	1.56842	−	1.59376i	0.0619972	−	0.0629987i
$641$	−2.80980	+	8.64769i	−0.110981	+	0.341563i	−0.991088	−	0.133212i	$-0.957471\pi$
$641$	−2.80980	+	8.64769i	−0.110981	+	0.341563i	0.880107	+	0.474776i	$0.157471\pi$
$642$	−0.530255	−	0.729834i	−0.0209275	−	0.0288042i
$643$	−18.5094	−	25.4759i	−0.729938	−	1.00467i	−0.999135	−	0.0415878i	$-0.986758\pi$
$643$	−18.5094	−	25.4759i	−0.729938	−	1.00467i	0.269197	−	0.963085i	$-0.413242\pi$
$644$	−5.58394	−	4.05697i	−0.220038	−	0.159867i
$645$	17.1470	+	2.57516i	0.675161	+	0.101397i
$646$	4.65359			0.183093
$647$	−14.0749	+	19.3724i	−0.553340	+	0.761607i	−0.990461	−	0.137796i	$-0.955998\pi$
$647$	−14.0749	+	19.3724i	−0.553340	+	0.761607i	0.437121	+	0.899403i	$0.355998\pi$
$648$	−0.951057	+	0.309017i	−0.0373610	+	0.0121393i
$649$	−2.34387	+	7.21368i	−0.0920048	+	0.283162i
$650$	−1.82558	−	0.560990i	−0.0716051	−	0.0220038i
$651$	−4.10319	+	7.55015i	−0.160817	+	0.295914i
$652$			19.5368i			0.765121i
$653$	−31.9211	−	10.3718i	−1.24917	−	0.405879i	−0.391546	−	0.920159i	$-0.628059\pi$
$653$	−31.9211	−	10.3718i	−1.24917	−	0.405879i	−0.857623	+	0.514279i	$0.828059\pi$
$654$	4.32528	+	13.3118i	0.169132	+	0.520534i
$655$	1.12661	+	1.10870i	0.0440202	+	0.0433204i
$656$	1.90025			0.0741924
$657$		−	6.58049i		−	0.256729i
$658$	−8.59867	+	11.8351i	−0.335211	+	0.461378i
$659$	−32.1516	+	23.3595i	−1.25245	+	0.909957i	−0.998361	−	0.0572244i	$-0.981775\pi$
$659$	−32.1516	+	23.3595i	−1.25245	+	0.909957i	−0.254087	+	0.967181i	$0.581775\pi$
$660$	2.22858	+	4.28854i	0.0867474	+	0.166931i
$661$	2.04838	−	6.30427i	0.0796727	−	0.245208i	−0.903284	−	0.429042i	$-0.858851\pi$
$661$	2.04838	−	6.30427i	0.0796727	−	0.245208i	0.982957	+	0.183835i	$0.0588511\pi$
$662$	17.1313	−	23.5793i	0.665828	−	0.916434i
$663$	−0.394776	−	0.128270i	−0.0153318	−	0.00498161i
$664$	−0.512538	−	1.57743i	−0.0198903	−	0.0612162i
$665$	6.81445	+	13.1133i	0.264253	+	0.508512i
$666$	1.14483	+	3.52343i	0.0443614	+	0.136530i
$667$	−18.1237	+	5.88876i	−0.701754	+	0.228014i
$668$	2.89066	+	3.97865i	0.111843	+	0.153939i
$669$	−4.78179	−	14.7168i	−0.184875	−	0.568986i
$670$	2.20012	−	4.40487i	0.0849979	−	0.170175i
$671$	−8.69643	−	6.31833i	−0.335722	−	0.243916i
$672$	1.46782	+	0.476925i	0.0566226	+	0.0183978i
$673$	10.3303	+	14.2184i	0.398203	+	0.548079i	0.960292	−	0.278998i	$-0.0900021\pi$
$673$	10.3303	+	14.2184i	0.398203	+	0.548079i	−0.562089	+	0.827077i	$0.690002\pi$
$674$	13.3839	−	9.72394i	0.515527	−	0.374552i
$675$	3.99747	−	3.00337i	0.153863	−	0.115600i
$676$	−12.8541			−0.494389
$677$		−	48.5416i		−	1.86560i	−0.360389	−	0.932802i	$-0.617356\pi$
$677$		−	48.5416i		−	1.86560i	0.360389	−	0.932802i	$-0.382644\pi$
$678$	−2.39446	+	3.29569i	−0.0919587	+	0.126570i
$679$	6.64298	+	20.4450i	0.254934	+	0.784607i
$680$	−1.08581	+	2.17390i	−0.0416389	+	0.0833654i
$681$	1.47827			0.0566474
$682$	−5.17661	−	10.8639i	−0.198223	−	0.415998i
$683$		−	36.3529i		−	1.39101i	−0.718523	−	0.695503i	$-0.755182\pi$
$683$		−	36.3529i		−	1.39101i	0.718523	−	0.695503i	$-0.244818\pi$
$684$	1.32328	−	4.07263i	0.0505968	−	0.155721i
$685$	−41.8543	+	6.97327i	−1.59917	+	0.266435i
$686$	14.5063	+	10.5395i	0.553855	+	0.402399i
$687$			13.5447i			0.516762i
$688$			7.75435i			0.295632i
$689$	−1.82930	−	1.32907i	−0.0696909	−	0.0506334i
$690$	−4.61115	−	8.87341i	−0.175543	−	0.337805i
$691$	10.4505	−	7.59271i	0.397554	−	0.288840i	−0.370990	−	0.928637i	$-0.620982\pi$
$691$	10.4505	−	7.59271i	0.397554	−	0.288840i	0.768544	+	0.639797i	$0.220982\pi$
$692$	−4.02967	−	1.30932i	−0.153185	−	0.0497728i
$693$	−1.96074	+	2.69873i	−0.0744825	+	0.102516i
$694$	−5.20569	+	16.0215i	−0.197605	+	0.608167i
$695$	−3.95715	−	23.7512i	−0.150103	−	0.900935i
$696$	3.44734	−	2.50464i	0.130671	−	0.0949380i
$697$	−1.96398	+	0.638135i	−0.0743910	+	0.0241711i
$698$	1.50439	−	0.488805i	0.0569419	−	0.0185015i
$699$	−12.6894	+	9.21941i	−0.479958	+	0.348710i
$700$	−7.71582	+	0.123651i	−0.291631	+	0.00467357i
$701$	−5.56088	+	17.1146i	−0.210032	+	0.646411i	0.789437	+	0.613831i	$0.210372\pi$
$701$	−5.56088	+	17.1146i	−0.210032	+	0.646411i	−0.999469	+	0.0325800i	$0.989628\pi$
$702$	−0.224514	+	0.309017i	−0.00847373	+	0.0116631i
$703$	−15.0881	−	4.90242i	−0.569059	−	0.184898i
$704$	−1.74861	+	1.27044i	−0.0659031	+	0.0478814i
$705$	−18.8070	+	9.77324i	−0.708313	+	0.368082i
$706$	3.25742	+	2.36665i	0.122595	+	0.0890702i
$707$		−	1.19762i		−	0.0450413i
$708$			3.50926i			0.131886i
$709$	−40.0514	−	29.0990i	−1.50416	−	1.09284i	−0.968687	−	0.248286i	$-0.920133\pi$
$709$	−40.0514	−	29.0990i	−1.50416	−	1.09284i	−0.535475	−	0.844551i	$-0.679867\pi$
$710$	11.7690	−	1.96082i	0.441684	−	0.0735881i
$711$	1.53455	−	4.72285i	0.0575500	−	0.177121i
$712$			0.422540i			0.0158354i
$713$	10.7109	+	22.4784i	0.401127	+	0.841821i
$714$	−1.67721			−0.0627679
$715$	1.65151	+	0.824885i	0.0617629	+	0.0308489i
$716$	−0.977226	−	3.00759i	−0.0365206	−	0.112399i
$717$	4.57847	−	6.30172i	0.170986	−	0.235342i
$718$			10.7987i			0.403003i
$719$	−42.9610			−1.60217			−0.801087	−	0.598548i	$-0.795745\pi$
$719$	−42.9610			−1.60217			−0.801087	+	0.598548i	$0.795745\pi$
$720$	1.59376	+	1.56842i	0.0593958	+	0.0584516i
$721$	−21.1234	+	15.3471i	−0.786678	+	0.571555i
$722$	−0.389473	−	0.536063i	−0.0144947	−	0.0199502i
$723$	−12.5299	−	4.07123i	−0.465994	−	0.151411i
$724$	−16.7478	−	12.1680i	−0.622429	−	0.452221i
$725$	−12.2454	+	17.4351i	−0.454782	+	0.647525i
$726$	1.95557	+	6.01864i	0.0725781	+	0.223373i
$727$	2.54743	+	3.50623i	0.0944789	+	0.130039i	0.853639	−	0.520864i	$-0.174390\pi$
$727$	2.54743	+	3.50623i	0.0944789	+	0.130039i	−0.759161	+	0.650903i	$0.774390\pi$
$728$	0.560659	−	0.182169i	0.0207794	−	0.00675164i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	−13.0567	+	6.78504i	−0.483250	+	0.251125i
$731$	−2.60404	−	8.01440i	−0.0963138	−	0.296423i
$732$	−4.72994	−	1.53685i	−0.174824	−	0.0568036i
$733$	−7.20897	+	9.92230i	−0.266269	+	0.366488i	−0.921126	−	0.389265i	$-0.872729\pi$
$733$	−7.20897	+	9.92230i	−0.266269	+	0.366488i	0.654856	+	0.755753i	$0.272729\pi$
$734$	1.79919	−	5.53733i	0.0664092	−	0.204387i
$735$	4.76158	+	9.16289i	0.175634	+	0.337978i
$736$	3.61803	−	2.62866i	0.133363	−	0.0968935i
$737$	−2.79746	+	3.85038i	−0.103046	+	0.141830i
$738$			1.90025i			0.0699492i
$739$	41.9260			1.54227			0.771136	−	0.636671i	$-0.219689\pi$
$739$	41.9260			1.54227			0.771136	+	0.636671i	$0.219689\pi$
$740$	5.81062	−	5.90448i	0.213602	−	0.217053i
$741$	−0.505447	−	1.55561i	−0.0185681	−	0.0571466i
$742$	−8.68916	−	2.82328i	−0.318989	−	0.103646i
$743$			33.8788i			1.24289i	0.783456	+	0.621447i	$0.213455\pi$
$743$			33.8788i			1.24289i	−0.783456	+	0.621447i	$0.786545\pi$
$744$	−3.83103	−	4.04020i	−0.140452	−	0.148121i
$745$	−19.4048	−	2.91425i	−0.710938	−	0.106770i
$746$	−4.13106	+	12.7141i	−0.151249	+	0.465496i
$747$	1.57743	−	0.512538i	0.0577151	−	0.0187528i
$748$	1.38061	−	1.90025i	0.0504802	−	0.0694801i
$749$	−1.39230			−0.0508737
$750$	−10.0809	−	4.83488i	−0.368101	−	0.176545i
$751$	−28.7838	−	20.9126i	−1.05033	−	0.763113i	−0.0780588	−	0.996949i	$-0.524872\pi$
$751$	−28.7838	−	20.9126i	−1.05033	−	0.763113i	−0.972276	+	0.233836i	$0.924872\pi$
$752$	−5.57139	−	7.66836i	−0.203168	−	0.279636i
$753$	1.12402	+	1.54709i	0.0409617	+	0.0563790i
$754$	0.502960	−	1.54795i	0.0183167	−	0.0563731i
$755$	−28.7928	−	28.3351i	−1.04788	−	1.03122i
$756$	−0.476925	+	1.46782i	−0.0173456	+	0.0533843i
$757$	−38.4509	+	12.4935i	−1.39752	+	0.454082i	−0.908389	−	0.418127i	$-0.862687\pi$
$757$	−38.4509	+	12.4935i	−1.39752	+	0.454082i	−0.489133	+	0.872209i	$0.662687\pi$
$758$	−11.6274	−	16.0037i	−0.422326	−	0.581282i
$759$	2.98698	+	9.19297i	0.108420	+	0.333684i
$760$	−9.44514	+	1.57364i	−0.342611	+	0.0570818i
$761$	13.1439	−	9.54963i	0.476467	−	0.346174i	−0.323489	−	0.946232i	$-0.604856\pi$
$761$	13.1439	−	9.54963i	0.476467	−	0.346174i	0.799956	+	0.600058i	$0.204856\pi$
$762$	0.316103	−	0.102708i	0.0114512	−	0.00372072i
$763$	20.5450	+	6.67547i	0.743779	+	0.241668i
$764$	−16.7949	−	12.2022i	−0.607619	−	0.441461i
$765$	−2.17390	−	1.08581i	−0.0785977	−	0.0392575i
$766$	−0.273890	+	0.198993i	−0.00989606	+	0.00718991i
$767$	0.787879	+	1.08442i	0.0284487	+	0.0391562i
$768$	−0.587785	+	0.809017i	−0.0212099	+	0.0291929i
$769$	−11.0518			−0.398537			−0.199268	−	0.979945i	$-0.563857\pi$
$769$	−11.0518			−0.398537			−0.199268	+	0.979945i	$0.563857\pi$
$770$	7.37639	+	1.10780i	0.265827	+	0.0399223i
$771$	−15.3480	−	11.1510i	−0.552746	−	0.401594i
$772$	10.4993	−	3.41142i	0.377878	−	0.122780i
$773$	24.6045	+	7.99449i	0.884963	+	0.287542i	0.716016	−	0.698083i	$-0.245964\pi$
$773$	24.6045	+	7.99449i	0.884963	+	0.287542i	0.168946	+	0.985625i	$0.445964\pi$
$774$	−7.75435			−0.278724
$775$	24.6699	+	12.8994i	0.886170	+	0.463360i
$776$	−13.9288			−0.500014
$777$	5.43793	+	1.76689i	0.195085	+	0.0633869i
$778$	5.14394	−	1.67137i	0.184419	−	0.0599214i
$779$	−6.58321	−	4.78298i	−0.235868	−	0.171368i
$780$	0.844630	+	0.126848i	0.0302426	+	0.00454188i
$781$	−11.5328			−0.412676
$782$	−2.85662	+	3.93180i	−0.102153	+	0.140601i
$783$	2.50464	+	3.44734i	0.0895084	+	0.123198i
$784$	−3.73607	+	2.71441i	−0.133431	+	0.0969433i
$785$	−14.0581	−	7.02163i	−0.501754	−	0.250613i
$786$	−0.571884	−	0.415498i	−0.0203984	−	0.0148203i
$787$	−27.1539	−	8.82285i	−0.967933	−	0.314501i	−0.217952	−	0.975960i	$-0.569938\pi$
$787$	−27.1539	−	8.82285i	−0.967933	−	0.314501i	−0.749981	+	0.661459i	$0.769938\pi$
$788$	3.67365	−	1.19364i	0.130868	−	0.0425217i
$789$	−14.8951	+	10.8219i	−0.530281	+	0.385271i
$790$	−10.9531	+	1.82488i	−0.389694	+	0.0649263i
$791$	1.94285	+	5.97948i	0.0690798	+	0.212606i
$792$	−1.27044	−	1.74861i	−0.0451430	−	0.0621340i
$793$	−1.80668	+	0.587024i	−0.0641569	+	0.0208458i
$794$	−4.18581	+	12.8826i	−0.148549	+	0.457187i
$795$	−9.43464	−	9.28466i	−0.334612	−	0.329293i
$796$	−1.22394	+	3.76689i	−0.0433813	+	0.133514i
$797$	3.38685	+	4.66160i	0.119969	+	0.165122i	0.864777	−	0.502155i	$-0.167459\pi$
$797$	3.38685	+	4.66160i	0.119969	+	0.165122i	−0.744809	+	0.667278i	$0.767459\pi$
$798$	−3.88468	−	5.34680i	−0.137516	−	0.189275i
$799$	8.33339	+	6.05456i	0.294814	+	0.214195i
$800$	1.46869	−	4.77943i	0.0519260	−	0.168978i
$801$	−0.422540			−0.0149297
$802$	−18.1997	+	25.0498i	−0.642655	+	0.884538i
$803$	13.5269	−	4.39516i	0.477355	−	0.155102i
$804$	−0.680446	+	2.09420i	−0.0239975	+	0.0738567i
$805$	−15.2625	−	2.29214i	−0.537931	−	0.0807873i
$806$	−2.09093	−	0.388372i	−0.0736500	−	0.0136798i
$807$			29.1998i			1.02788i
$808$	0.738004	+	0.239792i	0.0259629	+	0.00843586i
$809$	−4.93207	−	15.1793i	−0.173402	−	0.533677i	0.826155	−	0.563444i	$-0.190524\pi$
$809$	−4.93207	−	15.1793i	−0.173402	−	0.533677i	−0.999557	+	0.0297661i	$0.990524\pi$
$810$	−1.56842	+	1.59376i	−0.0551087	+	0.0559989i
$811$	45.9838			1.61471			0.807354	−	0.590067i	$-0.200899\pi$
$811$	45.9838			1.61471			0.807354	+	0.590067i	$0.200899\pi$
$812$		−	6.57649i		−	0.230789i
$813$	−5.90498	+	8.12751i	−0.207097	+	0.285044i
$814$	−6.47816	+	4.70666i	−0.227059	+	0.164968i
$815$	20.1441	+	38.7640i	0.705617	+	1.35785i
$816$	0.335816	−	1.03354i	0.0117559	−	0.0361810i
$817$	19.5179	−	26.8641i	0.682845	−	0.939855i
$818$	5.67281	+	1.84321i	0.198345	+	0.0644462i
$819$	0.182169	+	0.560659i	0.00636551	+	0.0195910i
$820$	3.77039	−	1.95932i	0.131668	−	0.0684224i
$821$	−4.51697	−	13.9018i	−0.157643	−	0.485176i	0.840776	−	0.541383i	$-0.182099\pi$
$821$	−4.51697	−	13.9018i	−0.157643	−	0.485176i	−0.998419	+	0.0562072i	$0.982099\pi$
$822$	18.0471	−	5.86385i	0.629464	−	0.204525i
$823$	7.74274	+	10.6570i	0.269895	+	0.371478i	0.922354	−	0.386345i	$-0.126263\pi$
$823$	7.74274	+	10.6570i	0.269895	+	0.371478i	−0.652459	+	0.757824i	$0.726263\pi$
$824$	−5.22783	−	16.0896i	−0.182120	−	0.560508i
$825$	8.84369	+	6.21127i	0.307898	+	0.216249i
$826$	4.38169	+	3.18348i	0.152458	+	0.110768i
$827$	19.7216	+	6.40792i	0.685786	+	0.222825i	0.631127	−	0.775680i	$-0.282593\pi$
$827$	19.7216	+	6.40792i	0.685786	+	0.222825i	0.0546590	+	0.998505i	$0.482593\pi$
$828$	2.62866	+	3.61803i	0.0913521	+	0.125735i
$829$	13.8841	−	10.0874i	0.482215	−	0.350350i	−0.319968	−	0.947428i	$-0.603672\pi$
$829$	13.8841	−	10.0874i	0.482215	−	0.350350i	0.802183	+	0.597079i	$0.203672\pi$
$830$	−2.64342	−	2.60139i	−0.0917543	−	0.0902957i
$831$	−7.68410			−0.266558
$832$			0.381966i			0.0132423i
$833$	2.94982	−	4.06007i	0.102205	−	0.140673i
$834$	3.32758	+	10.2412i	0.115225	+	0.354625i
$835$	9.83783	+	4.91374i	0.340452	+	0.170047i
$836$	9.25557			0.320111
$837$	4.04020	−	3.83103i	0.139650	−	0.132420i
$838$			23.2866i			0.804421i
$839$	8.25219	−	25.3976i	0.284897	−	0.876823i	−0.701532	−	0.712638i	$-0.747500\pi$
$839$	8.25219	−	25.3976i	0.284897	−	0.876823i	0.986429	−	0.164186i	$-0.0524996\pi$
$840$	3.40414	−	0.567157i	0.117454	−	0.0195688i
$841$	8.77189	+	6.37315i	0.302479	+	0.219764i
$842$			29.3049i			1.00991i
$843$		−	15.0065i		−	0.516850i
$844$	−17.1748	−	12.4782i	−0.591182	−	0.429519i
$845$	−25.5045	+	13.2537i	−0.877382	+	0.455940i
$846$	7.66836	−	5.57139i	0.263644	−	0.191548i
$847$	9.28893	+	3.01816i	0.319172	+	0.103705i
$848$	3.47954	−	4.78918i	0.119488	−	0.164461i
$849$	1.11056	−	3.41796i	0.0381144	−	0.117304i
$850$	0.0870662	+	5.43292i	0.00298634	+	0.186348i
$851$	13.4039	−	9.73853i	0.459481	−	0.333833i
$852$	−5.07466	+	1.64886i	−0.173855	+	0.0564889i
$853$	42.8187	−	13.9126i	1.46609	−	0.476360i	0.536162	−	0.844115i	$-0.319873\pi$
$853$	42.8187	−	13.9126i	1.46609	−	0.476360i	0.929923	+	0.367755i	$0.119873\pi$
$854$	−6.20976	+	4.51165i	−0.212493	+	0.154386i
$855$	−1.57364	−	9.44514i	−0.0538173	−	0.323017i
$856$	0.278772	−	0.857971i	0.00952822	−	0.0293249i
$857$	26.3941	−	36.3283i	0.901604	−	1.24095i	−0.0683494	−	0.997661i	$-0.521773\pi$
$857$	26.3941	−	36.3283i	0.901604	−	1.24095i	0.969954	−	0.243290i	$-0.0782267\pi$
$858$	−0.785173	−	0.255118i	−0.0268054	−	0.00870959i
$859$	−32.0553	+	23.2896i	−1.09371	+	0.794630i	−0.980023	−	0.198887i	$-0.936267\pi$
$859$	−32.0553	+	23.2896i	−1.09371	+	0.794630i	−0.113691	+	0.993516i	$0.536267\pi$
$860$	7.99539	+	15.3858i	0.272641	+	0.524652i
$861$	2.37267	+	1.72384i	0.0808602	+	0.0587484i
$862$		−	15.8051i		−	0.538324i
$863$		−	12.1695i		−	0.414256i	−0.978314	−	0.207128i	$-0.933588\pi$
$863$		−	12.1695i		−	0.414256i	0.978314	−	0.207128i	$-0.0664116\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	−9.34549	+	1.55704i	−0.317756	+	0.0529408i
$866$	6.63602	−	20.4236i	0.225501	−	0.694021i
$867$		−	15.8190i		−	0.537242i
$868$	−8.52000	+	1.11831i	−0.289187	+	0.0379580i
$869$	10.7333			0.364102
$870$	4.25756	−	8.52408i	0.144345	−	0.288993i
$871$	0.259907	+	0.799912i	0.00880662	+	0.0271040i
$872$	−8.22717	+	11.3237i	−0.278607	+	0.383470i
$873$		−	13.9288i		−	0.471418i
$874$	−19.1507			−0.647781
$875$	−15.1819	+	8.20100i	−0.513241	+	0.277244i
$876$	5.32373	−	3.86791i	0.179872	−	0.130685i
$877$	10.1133	+	13.9198i	0.341502	+	0.470037i	0.944879	−	0.327419i	$-0.106179\pi$
$877$	10.1133	+	13.9198i	0.341502	+	0.470037i	−0.603378	+	0.797456i	$0.706179\pi$
$878$	−30.5337	−	9.92099i	−1.03046	−	0.334817i
$879$	3.58951	+	2.60793i	0.121071	+	0.0879634i
$880$	−2.15958	+	4.32370i	−0.0727993	+	0.145752i
$881$	2.53060	+	7.78839i	0.0852582	+	0.262398i	0.984593	−	0.174864i	$-0.0559485\pi$
$881$	2.53060	+	7.78839i	0.0852582	+	0.262398i	−0.899334	+	0.437261i	$0.855948\pi$
$882$	−2.71441	−	3.73607i	−0.0913990	−	0.125800i
$883$	−9.26933	+	3.01179i	−0.311938	+	0.101355i	−0.460802	−	0.887503i	$-0.652438\pi$
$883$	−9.26933	+	3.01179i	−0.311938	+	0.101355i	0.148864	+	0.988858i	$0.452438\pi$
$884$	−0.128270	−	0.394776i	−0.00431420	−	0.0132777i
$885$	3.61835	+	6.96292i	0.121629	+	0.234056i
$886$	2.26547	+	6.97240i	0.0761099	+	0.234242i
$887$	16.5248	+	5.36922i	0.554847	+	0.180281i	0.573001	−	0.819554i	$-0.305779\pi$
$887$	16.5248	+	5.36922i	0.554847	+	0.180281i	−0.0181542	+	0.999835i	$0.505779\pi$
$888$	−2.17760	+	2.99721i	−0.0730755	+	0.100580i
$889$	0.158516	−	0.487861i	0.00531644	−	0.0163623i
$890$	0.435674	+	0.838384i	0.0146038	+	0.0281027i
$891$	1.74861	−	1.27044i	0.0585805	−	0.0425612i
$892$	9.09550	−	12.5189i	0.304540	−	0.419163i
$893$			40.5895i			1.35828i
$894$	8.77543			0.293494
$895$	−5.04004	−	4.95992i	−0.168470	−	0.165792i
$896$	0.476925	+	1.46782i	0.0159329	+	0.0490366i
$897$	1.62460	+	0.527864i	0.0542438	+	0.0176249i
$898$		−	14.3348i		−	0.478360i
$899$	−11.3287	+	20.8456i	−0.377834	+	0.695239i
$900$	4.77943	+	1.46869i	0.159314	+	0.0489563i
$901$	−1.98795	+	6.11828i	−0.0662282	+	0.203829i
$902$	−3.90618	+	1.26919i	−0.130061	+	0.0422595i
$903$	−7.03448	+	9.68213i	−0.234093	+	0.322201i
$904$	−4.07370			−0.135489
$905$	−45.7765	−	6.87479i	−1.52166	−	0.228526i
$906$	14.6157	+	10.6189i	0.485574	+	0.352790i
$907$	−15.7307	−	21.6514i	−0.522329	−	0.718925i	0.463608	−	0.886040i	$-0.346555\pi$
$907$	−15.7307	−	21.6514i	−0.522329	−	0.718925i	−0.985937	+	0.167116i	$0.946555\pi$
$908$	0.868904	+	1.19594i	0.0288356	+	0.0396888i
$909$	−0.239792	+	0.738004i	−0.00795340	+	0.0244781i
$910$	0.924602	−	0.939538i	0.0306503	−	0.0311454i
$911$	−5.50126	+	16.9311i	−0.182265	+	0.560954i	−0.999891	−	0.0147966i	$-0.995290\pi$
$911$	−5.50126	+	16.9311i	−0.182265	+	0.560954i	0.817626	+	0.575750i	$0.195290\pi$
$912$	4.07263	−	1.32328i	0.134858	−	0.0438181i
$913$	2.10716	+	2.90025i	0.0697367	+	0.0959843i
$914$	8.74630	+	26.9184i	0.289302	+	0.890380i
$915$	−10.9695	+	1.82762i	−0.362642	+	0.0604191i
$916$	−10.9579	+	7.96136i	−0.362058	+	0.263051i
$917$	−1.03759	+	0.337132i	−0.0342641	+	0.0111331i
$918$	1.03354	+	0.335816i	0.0341118	+	0.0110836i
$919$	−23.7431	−	17.2504i	−0.783212	−	0.569037i	0.122729	−	0.992440i	$-0.460835\pi$
$919$	−23.7431	−	17.2504i	−0.783212	−	0.569037i	−0.905941	+	0.423404i	$0.860835\pi$
$920$	4.46837	−	8.94615i	0.147318	−	0.294946i
$921$	−19.4961	+	14.1648i	−0.642419	+	0.466745i
$922$	3.00824	+	4.14049i	0.0990713	+	0.136360i
$923$	−1.19797	+	1.64886i	−0.0394315	+	0.0542728i
$924$	−3.33582			−0.109740
$925$	5.44114	−	17.7066i	0.178904	−	0.582190i
$926$	−24.5028	−	17.8023i	−0.805213	−	0.585021i
$927$	16.0896	−	5.22783i	0.528452	−	0.171705i
$928$	4.05259	+	1.31677i	0.133033	+	0.0432250i
$929$	8.79320			0.288495			0.144248	−	0.989542i	$-0.453924\pi$
$929$	8.79320			0.288495			0.144248	+	0.989542i	$0.453924\pi$
$930$	−11.7671	−	4.06627i	−0.385860	−	0.133338i
$931$	19.7754			0.648113
$932$	−14.9173	−	4.84693i	−0.488633	−	0.158767i
$933$	31.1324	−	10.1155i	1.01923	−	0.331167i
$934$	−1.67348	−	1.21586i	−0.0547581	−	0.0397841i
$935$	0.780031	−	5.19392i	0.0255097	−	0.169859i
$936$	−0.381966			−0.0124849
$937$	−3.17240	+	4.36643i	−0.103638	+	0.142645i	−0.857686	−	0.514174i	$-0.828099\pi$
$937$	−3.17240	+	4.36643i	−0.103638	+	0.142645i	0.754048	+	0.656819i	$0.228099\pi$
$938$	1.99755	+	2.74939i	0.0652223	+	0.0897709i
$939$	10.0656	−	7.31310i	0.328479	−	0.238654i
$940$	−18.9612	−	9.47063i	−0.618447	−	0.308898i
$941$	47.5574	+	34.5524i	1.55033	+	1.12638i	0.943419	+	0.331604i	$0.107590\pi$
$941$	47.5574	+	34.5524i	1.55033	+	1.12638i	0.606907	+	0.794773i	$0.292410\pi$
$942$	6.68360	+	2.17163i	0.217763	+	0.0707556i
$943$	8.08225	−	2.62608i	0.263194	−	0.0855170i
$944$	−2.83905	+	2.06269i	−0.0924033	+	0.0671350i
$945$	0.567157	+	3.40414i	0.0184496	+	0.110737i
$946$	−5.17920	−	15.9399i	−0.168390	−	0.518252i
$947$	−4.66622	−	6.42251i	−0.151632	−	0.208703i	0.726443	−	0.687227i	$-0.241172\pi$
$947$	−4.66622	−	6.42251i	−0.151632	−	0.208703i	−0.878075	+	0.478523i	$0.841172\pi$
$948$	4.72285	−	1.53455i	0.153391	−	0.0498398i
$949$	0.776721	−	2.39050i	0.0252134	−	0.0775990i
$950$	−17.1181	+	12.8611i	−0.555383	+	0.417268i
$951$	0.149516	−	0.460163i	0.00484839	−	0.0149218i
$952$	−0.985838	−	1.35689i	−0.0319512	−	0.0439771i
$953$	29.4647	+	40.5546i	0.954454	+	1.31369i	0.949520	+	0.313706i	$0.101571\pi$
$953$	29.4647	+	40.5546i	0.954454	+	1.31369i	0.00493387	+	0.999988i	$0.498429\pi$
$954$	4.78918	+	3.47954i	0.155055	+	0.112654i
$955$	−45.9052	−	6.89412i	−1.48546	−	0.223088i
$956$	7.78935			0.251926
$957$	−5.41351	+	7.45106i	−0.174994	+	0.240859i
$958$	28.6384	−	9.30516i	0.925263	−	0.300636i
$959$	9.05005	−	27.8532i	0.292241	−	0.899426i
$960$	−0.332092	+	2.21127i	−0.0107182	+	0.0713684i
$961$	28.9324	+	11.1319i	0.933302	+	0.359093i
$962$			1.41509i			0.0456244i
$963$	0.857971	+	0.278772i	0.0276477	+	0.00898329i
$964$	−4.07123	−	12.5299i	−0.131125	−	0.403562i
$965$	17.3147	−	17.5944i	0.557381	−	0.566385i
$966$	6.90212			0.222072
$967$			43.3024i			1.39251i	0.717794	+	0.696256i	$0.245152\pi$
$967$			43.3024i			1.39251i	−0.717794	+	0.696256i	$0.754848\pi$
$968$	−3.71972	+	5.11976i	−0.119556	+	0.164555i
$969$	−3.76483	+	2.73531i	−0.120944	+	0.0878708i
$970$	−27.6368	+	14.3617i	−0.887365	+	0.461127i
$971$	6.81223	−	20.9659i	0.218615	−	0.672828i	−0.780262	−	0.625453i	$-0.784914\pi$
$971$	6.81223	−	20.9659i	0.218615	−	0.672828i	0.998877	−	0.0473751i	$-0.0150856\pi$
$972$	0.587785	−	0.809017i	0.0188532	−	0.0259492i
$973$	15.8059	+	5.13566i	0.506715	+	0.164642i
$974$	−13.1532	−	40.4813i	−0.421454	−	1.29710i
$975$	1.80667	−	0.619199i	0.0578596	−	0.0198302i
$976$	−1.53685	−	4.72994i	−0.0491934	−	0.151402i
$977$	−9.52121	+	3.09363i	−0.304611	+	0.0989740i	−0.457334	−	0.889295i	$-0.651196\pi$
$977$	−9.52121	+	3.09363i	−0.304611	+	0.0989740i	0.152723	+	0.988269i	$0.451196\pi$
$978$	−11.4835	−	15.8056i	−0.367200	−	0.505408i
$979$	−0.282218	−	0.868577i	−0.00901972	−	0.0277598i
$980$	−4.61415	+	9.23801i	−0.147394	+	0.295097i
$981$	−11.3237	−	8.22717i	−0.361539	−	0.262673i
$982$	−8.64940	−	2.81036i	−0.276013	−	0.0896822i
$983$	0.266884	+	0.367334i	0.00851228	+	0.0117161i	0.813252	−	0.581912i	$-0.197695\pi$
$983$	0.266884	+	0.367334i	0.00851228	+	0.0117161i	−0.804740	+	0.593628i	$0.797695\pi$
$984$	−1.53734	+	1.11694i	−0.0490085	+	0.0356067i
$985$	6.05835	−	6.15621i	0.193035	−	0.196153i
$986$	−4.63069			−0.147471
$987$		−	14.6289i		−	0.465644i
$988$	0.961418	−	1.32328i	0.0305868	−	0.0420991i
$989$	10.7163	+	32.9812i	0.340757	+	1.04874i
$990$	−4.32370	−	2.15958i	−0.137416	−	0.0686358i
$991$	41.3457			1.31339			0.656695	−	0.754156i	$-0.271954\pi$
$991$	41.3457			1.31339			0.656695	+	0.754156i	$0.271954\pi$
$992$	1.01677	−	5.47414i	0.0322825	−	0.173804i
$993$			29.1456i			0.924907i
$994$	−2.54478	+	7.83204i	−0.0807157	+	0.248417i
$995$	1.45550	+	8.73607i	0.0461425	+	0.276952i
$996$	1.34184	+	0.974905i	0.0425179	+	0.0308911i
$997$			4.24883i			0.134562i	0.997734	+	0.0672810i	$0.0214324\pi$
$997$			4.24883i			0.134562i	−0.997734	+	0.0672810i	$0.978568\pi$
$998$		−	12.0845i		−	0.382529i
$999$	−2.99721	−	2.17760i	−0.0948276	−	0.0688963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.b.349.2	✓	16
5.4	even	2	inner	930.2.z.b.349.4	yes	16
31.4	even	5	inner	930.2.z.b.469.4	yes	16
155.4	even	10	inner	930.2.z.b.469.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.b.349.2	✓	16	1.1	even	1	trivial
930.2.z.b.349.4	yes	16	5.4	even	2	inner
930.2.z.b.469.2	yes	16	155.4	even	10	inner
930.2.z.b.469.4	yes	16	31.4	even	5	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.21127 + 0.332092i) q^{5} -1.00000 q^{6} +(-0.907165 + 1.24861i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.21127 + 0.332092i) q^{5} -1.00000 q^{6} +(-0.907165 + 1.24861i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-2.00042 - 0.999158i) q^{10} +(1.74861 + 1.27044i) q^{11} +(0.951057 + 0.309017i) q^{12} +(0.363271 - 0.118034i) q^{13} +(1.24861 - 0.907165i) q^{14} +(2.20566 - 0.367482i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.638760 - 0.879178i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(1.32328 - 4.07263i) q^{19} +(1.59376 + 1.56842i) q^{20} +(-0.476925 + 1.46782i) q^{21} +(-1.27044 - 1.74861i) q^{22} +(2.62866 + 3.61803i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(4.77943 + 1.46869i) q^{25} -0.381966 q^{26} +(0.587785 - 0.809017i) q^{27} +(-1.46782 + 0.476925i) q^{28} +(-1.31677 + 4.05259i) q^{29} +(-2.21127 - 0.332092i) q^{30} +(5.47414 + 1.01677i) q^{31} -1.00000i q^{32} +(2.05561 + 0.667908i) q^{33} +(0.335816 + 1.03354i) q^{34} +(-2.42064 + 2.45974i) q^{35} +1.00000 q^{36} -3.70476i q^{37} +(-2.51702 + 3.46439i) q^{38} +(0.309017 - 0.224514i) q^{39} +(-1.03108 - 1.98415i) q^{40} +(0.587210 - 1.80725i) q^{41} +(0.907165 - 1.24861i) q^{42} +(7.37483 + 2.39623i) q^{43} +(0.667908 + 2.05561i) q^{44} +(1.98415 - 1.03108i) q^{45} +(-1.38197 - 4.25325i) q^{46} +(-9.01470 + 2.92905i) q^{47} +(0.587785 + 0.809017i) q^{48} +(1.42705 + 4.39201i) q^{49} +(-4.09166 - 2.87373i) q^{50} +(-0.879178 - 0.638760i) q^{51} +(0.363271 + 0.118034i) q^{52} +(-3.47954 - 4.78918i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(3.44474 + 3.38998i) q^{55} +1.54336 q^{56} -4.28222i q^{57} +(2.50464 - 3.44734i) q^{58} +(1.08442 + 3.33751i) q^{59} +(2.00042 + 0.999158i) q^{60} -4.97335 q^{61} +(-4.89201 - 2.65861i) q^{62} +1.54336i q^{63} +(-0.309017 + 0.951057i) q^{64} +(0.842489 - 0.140366i) q^{65} +(-1.74861 - 1.27044i) q^{66} +2.20197i q^{67} -1.08672i q^{68} +(3.61803 + 2.62866i) q^{69} +(3.06227 - 1.59134i) q^{70} +(-4.31677 + 3.13631i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(3.86791 - 5.32373i) q^{73} +(-1.14483 + 3.52343i) q^{74} +(4.99936 - 0.0801180i) q^{75} +(3.46439 - 2.51702i) q^{76} +(-3.17255 + 1.03082i) q^{77} +(-0.363271 + 0.118034i) q^{78} +(4.01750 - 2.91888i) q^{79} +(0.367482 + 2.20566i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.11694 + 1.53734i) q^{82} +(1.57743 + 0.512538i) q^{83} +(-1.24861 + 0.907165i) q^{84} +(-1.12050 - 2.15623i) q^{85} +(-6.27340 - 4.55789i) q^{86} +4.26114i q^{87} -2.16140i q^{88} +(-0.341842 - 0.248363i) q^{89} +(-2.20566 + 0.367482i) q^{90} +(-0.182169 + 0.560659i) q^{91} +4.47214i q^{92} +(5.52041 - 0.724595i) q^{93} +9.47861 q^{94} +(4.27861 - 8.56624i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(8.18713 - 11.2686i) q^{97} -4.61803i q^{98} +2.16140 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 12 * q^5 - 16 * q^6 + 4 * q^9	\( 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9} + 4 q^{10} + 8 q^{11} + 4 q^{15} - 4 q^{16} + 8 q^{19} - 2 q^{20} - 4 q^{24} + 16 q^{25} - 24 q^{26} + 36 q^{29} - 12 q^{30} + 40 q^{31} + 8 q^{34} + 14 q^{35} + 16 q^{36} - 4 q^{39} + 6 q^{40} + 32 q^{41} + 12 q^{44} - 2 q^{45} - 40 q^{46} - 4 q^{49} - 8 q^{50} + 8 q^{51} - 4 q^{54} + 24 q^{55} - 4 q^{60} - 16 q^{61} + 4 q^{64} + 6 q^{65} - 8 q^{66} + 40 q^{69} + 18 q^{70} - 12 q^{71} - 12 q^{74} - 8 q^{75} + 32 q^{76} - 8 q^{79} - 8 q^{80} - 4 q^{81} - 40 q^{85} - 68 q^{86} + 20 q^{89} - 4 q^{90} - 56 q^{94} - 18 q^{95} + 4 q^{96} - 8 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 + 12 * q^5 - 16 * q^6 + 4 * q^9 + 4 * q^10 + 8 * q^11 + 4 * q^15 - 4 * q^16 + 8 * q^19 - 2 * q^20 - 4 * q^24 + 16 * q^25 - 24 * q^26 + 36 * q^29 - 12 * q^30 + 40 * q^31 + 8 * q^34 + 14 * q^35 + 16 * q^36 - 4 * q^39 + 6 * q^40 + 32 * q^41 + 12 * q^44 - 2 * q^45 - 40 * q^46 - 4 * q^49 - 8 * q^50 + 8 * q^51 - 4 * q^54 + 24 * q^55 - 4 * q^60 - 16 * q^61 + 4 * q^64 + 6 * q^65 - 8 * q^66 + 40 * q^69 + 18 * q^70 - 12 * q^71 - 12 * q^74 - 8 * q^75 + 32 * q^76 - 8 * q^79 - 8 * q^80 - 4 * q^81 - 40 * q^85 - 68 * q^86 + 20 * q^89 - 4 * q^90 - 56 * q^94 - 18 * q^95 + 4 * q^96 - 8 * q^99

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