LMFDB - Embedded newform 260.2.bg.c.23.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(23,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 10]))

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

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

chi := DirichletCharacter("260.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bg (of order $12$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.9
Character	$\chi$	$=$	260.23
Dual form			260.2.bg.c.147.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08563 + 0.906314i) q^{2} +(-0.274584 - 0.0735746i) q^{3} +(0.357191 - 1.96785i) q^{4} +(2.19604 - 0.421205i) q^{5} +(0.364779 - 0.168984i) q^{6} +(-0.487864 - 1.82073i) q^{7} +(1.39571 + 2.46008i) q^{8} +(-2.52809 - 1.45960i) q^{9} +O(q^{10})$	\(q+(-1.08563 + 0.906314i) q^{2} +(-0.274584 - 0.0735746i) q^{3} +(0.357191 - 1.96785i) q^{4} +(2.19604 - 0.421205i) q^{5} +(0.364779 - 0.168984i) q^{6} +(-0.487864 - 1.82073i) q^{7} +(1.39571 + 2.46008i) q^{8} +(-2.52809 - 1.45960i) q^{9} +(-2.00235 + 2.44757i) q^{10} +(-3.15071 - 5.45719i) q^{11} +(-0.242862 + 0.514059i) q^{12} +(2.71561 + 2.37180i) q^{13} +(2.17980 + 1.53449i) q^{14} +(-0.633987 - 0.0459166i) q^{15} +(-3.74483 - 1.40579i) q^{16} +(-1.27267 - 4.74965i) q^{17} +(4.06743 - 0.706663i) q^{18} +(1.94787 + 1.12460i) q^{19} +(-0.0444596 - 4.47191i) q^{20} +0.535839i q^{21} +(8.36644 + 3.06897i) q^{22} +(4.59956 + 1.23245i) q^{23} +(-0.202239 - 0.778188i) q^{24} +(4.64517 - 1.84996i) q^{25} +(-5.09775 - 0.113709i) q^{26} +(1.18981 + 1.18981i) q^{27} +(-3.75718 + 0.309691i) q^{28} +(1.82327 - 1.05266i) q^{29} +(0.729891 - 0.524743i) q^{30} -0.466728 q^{31} +(5.33959 - 1.86782i) q^{32} +(0.463624 + 1.73027i) q^{33} +(5.68632 + 4.00294i) q^{34} +(-1.83827 - 3.79291i) q^{35} +(-3.77527 + 4.45354i) q^{36} +(-0.0476908 + 0.177985i) q^{37} +(-3.13391 + 0.544477i) q^{38} +(-0.571159 - 0.851059i) q^{39} +(4.10122 + 4.81456i) q^{40} +(0.210988 - 0.121814i) q^{41} +(-0.485638 - 0.581724i) q^{42} +(2.18416 + 8.15138i) q^{43} +(-11.8643 + 4.25085i) q^{44} +(-6.16658 - 2.14048i) q^{45} +(-6.11041 + 2.83066i) q^{46} +(-4.45165 + 4.45165i) q^{47} +(0.924840 + 0.661533i) q^{48} +(2.98512 - 1.72346i) q^{49} +(-3.36630 + 6.21836i) q^{50} +1.39782i q^{51} +(5.63734 - 4.49672i) q^{52} +(-3.77074 - 3.77074i) q^{53} +(-2.37004 - 0.213355i) q^{54} +(-9.21767 - 10.6571i) q^{55} +(3.79824 - 3.74140i) q^{56} +(-0.452112 - 0.452112i) q^{57} +(-1.02535 + 2.79525i) q^{58} +(-9.74883 - 5.62849i) q^{59} +(-0.316811 + 1.23119i) q^{60} +(4.07008 - 7.04959i) q^{61} +(0.506694 - 0.423002i) q^{62} +(-1.42417 + 5.31507i) q^{63} +(-4.10400 + 6.86711i) q^{64} +(6.96260 + 4.06475i) q^{65} +(-2.07149 - 1.45825i) q^{66} +(8.55741 + 2.29295i) q^{67} +(-9.80117 + 0.807875i) q^{68} +(-1.17229 - 0.676821i) q^{69} +(5.43325 + 2.45166i) q^{70} +(-5.42763 + 9.40093i) q^{71} +(0.0622465 - 8.25648i) q^{72} +(-10.7151 + 10.7151i) q^{73} +(-0.109535 - 0.236449i) q^{74} +(-1.41160 + 0.166204i) q^{75} +(2.90881 - 3.43141i) q^{76} +(-8.39897 + 8.39897i) q^{77} +(1.39140 + 0.406288i) q^{78} +10.9673 q^{79} +(-8.81592 - 1.50984i) q^{80} +(4.13962 + 7.17004i) q^{81} +(-0.118653 + 0.323466i) q^{82} +(2.50039 + 2.50039i) q^{83} +(1.05445 + 0.191397i) q^{84} +(-4.79540 - 9.89437i) q^{85} +(-9.75890 - 6.86987i) q^{86} +(-0.578089 + 0.154898i) q^{87} +(9.02767 - 15.3676i) q^{88} +(4.10565 + 7.11119i) q^{89} +(8.63458 - 3.26508i) q^{90} +(2.99358 - 6.10153i) q^{91} +(4.06819 - 8.61100i) q^{92} +(0.128156 + 0.0343393i) q^{93} +(0.798261 - 8.86745i) q^{94} +(4.75129 + 1.64922i) q^{95} +(-1.60359 + 0.120014i) q^{96} +(-8.69112 + 2.32878i) q^{97} +(-1.67874 + 4.57649i) q^{98} +18.3950i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 6 q^{2} - 12 q^{6}+O(q^{10}) $ 144 * q - 6 * q^2 - 12 * q^6	$ 144 q - 6 q^{2} - 12 q^{6} + 12 q^{10} - 12 q^{12} + 4 q^{13} - 12 q^{16} - 24 q^{17} - 42 q^{20} - 12 q^{22} - 24 q^{25} - 36 q^{26} - 6 q^{28} - 36 q^{32} - 12 q^{33} - 76 q^{36} + 48 q^{37} - 16 q^{38} + 76 q^{40} - 72 q^{41} + 40 q^{42} - 120 q^{45} - 12 q^{46} - 40 q^{48} + 120 q^{50} - 10 q^{52} + 8 q^{53} - 20 q^{56} + 126 q^{58} + 16 q^{61} - 44 q^{62} + 32 q^{65} + 96 q^{66} - 64 q^{68} - 54 q^{72} - 12 q^{76} + 40 q^{77} - 100 q^{78} - 24 q^{80} - 32 q^{81} - 78 q^{82} - 24 q^{85} - 10 q^{88} - 8 q^{90} + 100 q^{92} - 48 q^{93} - 12 q^{97} - 162 q^{98}+O(q^{100}) $ 144 * q - 6 * q^2 - 12 * q^6 + 12 * q^10 - 12 * q^12 + 4 * q^13 - 12 * q^16 - 24 * q^17 - 42 * q^20 - 12 * q^22 - 24 * q^25 - 36 * q^26 - 6 * q^28 - 36 * q^32 - 12 * q^33 - 76 * q^36 + 48 * q^37 - 16 * q^38 + 76 * q^40 - 72 * q^41 + 40 * q^42 - 120 * q^45 - 12 * q^46 - 40 * q^48 + 120 * q^50 - 10 * q^52 + 8 * q^53 - 20 * q^56 + 126 * q^58 + 16 * q^61 - 44 * q^62 + 32 * q^65 + 96 * q^66 - 64 * q^68 - 54 * q^72 - 12 * q^76 + 40 * q^77 - 100 * q^78 - 24 * q^80 - 32 * q^81 - 78 * q^82 - 24 * q^85 - 10 * q^88 - 8 * q^90 + 100 * q^92 - 48 * q^93 - 12 * q^97 - 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.08563	+	0.906314i	−0.767657	+	0.640861i
$2$	−1.08563	+	0.906314i	−0.767657	+	0.640861i
$3$	−0.274584	−	0.0735746i	−0.158531	−	0.0424783i	0.178681	−	0.983907i	$-0.442817\pi$
$3$	−0.274584	−	0.0735746i	−0.158531	−	0.0424783i	−0.337212	+	0.941429i	$0.609484\pi$
$4$	0.357191	−	1.96785i	0.178596	−	0.983923i
$5$	2.19604	−	0.421205i	0.982098	−	0.188368i
$5$	2.19604	−	0.421205i	0.982098	−	0.188368i
$6$	0.364779	−	0.168984i	0.148920	−	0.0689876i
$7$	−0.487864	−	1.82073i	−0.184395	−	0.688173i	−0.994759	−	0.102246i	$-0.967397\pi$
$7$	−0.487864	−	1.82073i	−0.184395	−	0.688173i	0.810364	−	0.585927i	$-0.199270\pi$
$8$	1.39571	+	2.46008i	0.493457	+	0.869770i
$9$	−2.52809	−	1.45960i	−0.842698	−	0.486532i
$10$	−2.00235	+	2.44757i	−0.633197	+	0.773990i
$11$	−3.15071	−	5.45719i	−0.949975	−	1.64540i	−0.745470	−	0.666539i	$-0.767775\pi$
$11$	−3.15071	−	5.45719i	−0.949975	−	1.64540i	−0.204505	−	0.978866i	$-0.565558\pi$
$12$	−0.242862	+	0.514059i	−0.0701083	+	0.148396i
$13$	2.71561	+	2.37180i	0.753175	+	0.657820i
$13$	2.71561	+	2.37180i	0.753175	+	0.657820i
$14$	2.17980	+	1.53449i	0.582575	+	0.410109i
$15$	−0.633987	−	0.0459166i	−0.163695	−	0.0118556i
$16$	−3.74483	−	1.40579i	−0.936207	−	0.351448i
$17$	−1.27267	−	4.74965i	−0.308667	−	1.15196i	−0.929743	−	0.368210i	$-0.879971\pi$
$17$	−1.27267	−	4.74965i	−0.308667	−	1.15196i	0.621076	−	0.783750i	$-0.286696\pi$
$18$	4.06743	−	0.706663i	0.958702	−	0.166562i
$19$	1.94787	+	1.12460i	0.446872	+	0.258002i	0.706508	−	0.707705i	$-0.250269\pi$
$19$	1.94787	+	1.12460i	0.446872	+	0.258002i	−0.259636	+	0.965707i	$0.583603\pi$
$20$	−0.0444596	−	4.47191i	−0.00994146	−	0.999951i
$21$			0.535839i			0.116930i
$22$	8.36644	+	3.06897i	1.78373	+	0.654306i
$23$	4.59956	+	1.23245i	0.959074	+	0.256983i	0.704208	−	0.709993i	$-0.251302\pi$
$23$	4.59956	+	1.23245i	0.959074	+	0.256983i	0.254866	+	0.966977i	$0.417969\pi$
$24$	−0.202239	−	0.778188i	−0.0412819	−	0.158847i
$25$	4.64517	−	1.84996i	0.929035	−	0.369993i
$26$	−5.09775	−	0.113709i	−0.999751	−	0.0223002i
$27$	1.18981	+	1.18981i	0.228980	+	0.228980i
$28$	−3.75718	+	0.309691i	−0.710041	+	0.0585261i
$29$	1.82327	−	1.05266i	0.338572	−	0.195475i	−0.321068	−	0.947056i	$-0.604042\pi$
$29$	1.82327	−	1.05266i	0.338572	−	0.195475i	0.659640	+	0.751581i	$0.270709\pi$
$30$	0.729891	−	0.524743i	0.133259	−	0.0958045i
$31$	−0.466728			−0.0838267			−0.0419134	−	0.999121i	$-0.513345\pi$
$31$	−0.466728			−0.0838267			−0.0419134	+	0.999121i	$0.513345\pi$
$32$	5.33959	−	1.86782i	0.943916	−	0.330186i
$33$	0.463624	+	1.73027i	0.0807066	+	0.301201i
$34$	5.68632	+	4.00294i	0.975196	+	0.686498i
$35$	−1.83827	−	3.79291i	−0.310724	−	0.641119i
$36$	−3.77527	+	4.45354i	−0.629212	+	0.742257i
$37$	−0.0476908	+	0.177985i	−0.00784032	+	0.0292605i	−0.969735	−	0.244159i	$-0.921488\pi$
$37$	−0.0476908	+	0.177985i	−0.00784032	+	0.0292605i	0.961895	+	0.273420i	$0.0881547\pi$
$38$	−3.13391	+	0.544477i	−0.508388	+	0.0883258i
$39$	−0.571159	−	0.851059i	−0.0914587	−	0.136279i
$40$	4.10122	+	4.81456i	0.648460	+	0.761248i
$41$	0.210988	−	0.121814i	0.0329508	−	0.0190241i	−0.483434	−	0.875381i	$-0.660611\pi$
$41$	0.210988	−	0.121814i	0.0329508	−	0.0190241i	0.516385	+	0.856357i	$0.327277\pi$
$42$	−0.485638	−	0.581724i	−0.0749356	−	0.0897619i
$43$	2.18416	+	8.15138i	0.333081	+	1.24307i	0.905935	+	0.423417i	$0.139169\pi$
$43$	2.18416	+	8.15138i	0.333081	+	1.24307i	−0.572854	+	0.819657i	$0.694164\pi$
$44$	−11.8643	+	4.25085i	−1.78861	+	0.640840i
$45$	−6.16658	−	2.14048i	−0.919259	−	0.319084i
$46$	−6.11041	+	2.83066i	−0.900930	+	0.417358i
$47$	−4.45165	+	4.45165i	−0.649340	+	0.649340i	−0.952834	−	0.303493i	$-0.901847\pi$
$47$	−4.45165	+	4.45165i	−0.649340	+	0.649340i	0.303493	+	0.952834i	$0.401847\pi$
$48$	0.924840	+	0.661533i	0.133489	+	0.0954840i
$49$	2.98512	−	1.72346i	0.426445	−	0.246208i
$50$	−3.36630	+	6.21836i	−0.476067	+	0.879409i
$51$			1.39782i			0.195733i
$52$	5.63734	−	4.49672i	0.781758	−	0.623582i
$53$	−3.77074	−	3.77074i	−0.517951	−	0.517951i	0.399000	−	0.916951i	$-0.369357\pi$
$53$	−3.77074	−	3.77074i	−0.517951	−	0.517951i	−0.916951	+	0.399000i	$0.869357\pi$
$54$	−2.37004	−	0.213355i	−0.322522	−	0.0290339i
$55$	−9.21767	−	10.6571i	−1.24291	−	1.43700i
$56$	3.79824	−	3.74140i	0.507561	−	0.499965i
$57$	−0.452112	−	0.452112i	−0.0598837	−	0.0598837i
$58$	−1.02535	+	2.79525i	−0.134635	+	0.367035i
$59$	−9.74883	−	5.62849i	−1.26919	−	0.732767i	−0.294355	−	0.955696i	$-0.595105\pi$
$59$	−9.74883	−	5.62849i	−1.26919	−	0.732767i	−0.974835	+	0.222929i	$0.928438\pi$
$60$	−0.316811	+	1.23119i	−0.0409002	+	0.158946i
$61$	4.07008	−	7.04959i	0.521121	−	0.902607i	−0.478578	−	0.878045i	$-0.658848\pi$
$61$	4.07008	−	7.04959i	0.521121	−	0.902607i	0.999698	−	0.0245621i	$-0.00781916\pi$
$62$	0.506694	−	0.423002i	0.0643502	−	0.0537212i
$63$	−1.42417	+	5.31507i	−0.179428	+	0.669636i
$64$	−4.10400	+	6.86711i	−0.513001	+	0.858388i
$65$	6.96260	+	4.06475i	0.863605	+	0.504170i
$66$	−2.07149	−	1.45825i	−0.254983	−	0.179498i
$67$	8.55741	+	2.29295i	1.04545	+	0.280129i	0.740372	−	0.672197i	$-0.234649\pi$
$67$	8.55741	+	2.29295i	1.04545	+	0.280129i	0.305082	+	0.952326i	$0.401316\pi$
$68$	−9.80117	+	0.807875i	−1.18857	+	0.0979692i
$69$	−1.17229	−	0.676821i	−0.141127	−	0.0814796i
$70$	5.43325	+	2.45166i	0.649398	+	0.293029i
$71$	−5.42763	+	9.40093i	−0.644141	+	1.11568i	0.340358	+	0.940296i	$0.389452\pi$
$71$	−5.42763	+	9.40093i	−0.644141	+	1.11568i	−0.984499	+	0.175389i	$0.943882\pi$
$72$	0.0622465	−	8.25648i	0.00733582	−	0.973036i
$73$	−10.7151	+	10.7151i	−1.25411	+	1.25411i	−0.300248	+	0.953861i	$0.597069\pi$
$73$	−10.7151	+	10.7151i	−1.25411	+	1.25411i	−0.953861	+	0.300248i	$0.902931\pi$
$74$	−0.109535	−	0.236449i	−0.0127332	−	0.0274866i
$75$	−1.41160	+	0.166204i	−0.162998	+	0.0191915i
$76$	2.90881	−	3.43141i	0.333663	−	0.393610i
$77$	−8.39897	+	8.39897i	−0.957152	+	0.957152i
$78$	1.39140	+	0.406288i	0.157544	+	0.0460030i
$79$	10.9673			1.23392			0.616960	−	0.786994i	$-0.288364\pi$
$79$	10.9673			1.23392			0.616960	+	0.786994i	$0.288364\pi$
$80$	−8.81592	−	1.50984i	−0.985649	−	0.168805i
$81$	4.13962	+	7.17004i	0.459958	+	0.796671i
$82$	−0.118653	+	0.323466i	−0.0131031	+	0.0357209i
$83$	2.50039	+	2.50039i	0.274453	+	0.274453i	0.830890	−	0.556437i	$-0.187832\pi$
$83$	2.50039	+	2.50039i	0.274453	+	0.274453i	−0.556437	+	0.830890i	$0.687832\pi$
$84$	1.05445	+	0.191397i	0.115050	+	0.0208831i
$85$	−4.79540	−	9.89437i	−0.520134	−	1.07320i
$86$	−9.75890	−	6.86987i	−1.05233	−	0.740797i
$87$	−0.578089	+	0.154898i	−0.0619776	+	0.0166069i
$88$	9.02767	−	15.3676i	0.962352	−	1.63820i
$89$	4.10565	+	7.11119i	0.435198	+	0.753784i	0.997312	−	0.0732754i	$-0.0233452\pi$
$89$	4.10565	+	7.11119i	0.435198	+	0.753784i	−0.562114	+	0.827060i	$0.690012\pi$
$90$	8.63458	−	3.26508i	0.910165	−	0.344169i
$91$	2.99358	−	6.10153i	0.313812	−	0.639614i
$92$	4.06819	−	8.61100i	0.424138	−	0.897758i
$93$	0.128156	+	0.0343393i	0.0132891	+	0.00356082i
$94$	0.798261	−	8.86745i	0.0823343	−	0.914608i
$95$	4.75129	+	1.64922i	0.487472	+	0.169207i
$96$	−1.60359	+	0.120014i	−0.163666	+	0.0122489i
$97$	−8.69112	+	2.32878i	−0.882450	+	0.236452i	−0.671464	−	0.741037i	$-0.734334\pi$
$97$	−8.69112	+	2.32878i	−0.882450	+	0.236452i	−0.210986	+	0.977489i	$0.567667\pi$
$98$	−1.67874	+	4.57649i	−0.169579	+	0.462295i
$99$			18.3950i			1.84877i
$100$	−1.98123	−	9.80177i	−0.198123	−	0.980177i
$101$	1.48442	+	2.57109i	0.147705	+	0.255833i	0.930379	−	0.366599i	$-0.119478\pi$
$101$	1.48442	+	2.57109i	0.147705	+	0.255833i	−0.782674	+	0.622432i	$0.786145\pi$
$102$	−1.26686	−	1.51751i	−0.125438	−	0.150256i
$103$	8.36550	−	8.36550i	0.824277	−	0.824277i	−0.162441	−	0.986718i	$-0.551937\pi$
$103$	8.36550	−	8.36550i	0.824277	−	0.824277i	0.986718	+	0.162441i	$0.0519367\pi$
$104$	−2.04463	+	9.99097i	−0.200493	+	0.979695i
$105$	0.225698	+	1.17672i	0.0220259	+	0.114836i
$106$	7.51111	+	0.676161i	0.729543	+	0.0656746i
$107$	1.40619	−	5.24796i	0.135941	−	0.507339i	−0.864051	−	0.503404i	$-0.832081\pi$
$107$	1.40619	−	5.24796i	0.135941	−	0.507339i	0.999992	−	0.00393512i	$-0.00125259\pi$
$108$	2.76636	−	1.91638i	0.266193	−	0.184404i
$109$	0.423449			0.0405591			0.0202795	−	0.999794i	$-0.493544\pi$
$109$	0.423449			0.0405591			0.0202795	+	0.999794i	$0.493544\pi$
$110$	19.6657	+	3.21559i	1.87505	+	0.306594i
$111$	0.0261903	−	0.0453629i	0.00248587	−	0.00430566i
$112$	−0.732609	+	7.50418i	−0.0692250	+	0.709078i
$113$	5.27493	−	1.41341i	0.496224	−	0.132963i	−0.00202326	−	0.999998i	$-0.500644\pi$
$113$	5.27493	−	1.41341i	0.496224	−	0.132963i	0.498247	+	0.867035i	$0.333977\pi$
$114$	0.900582	+	0.0810717i	0.0843472	+	0.00759306i
$115$	10.6199	+	0.769148i	0.990312	+	0.0717235i
$116$	−1.42022	−	3.96391i	−0.131864	−	0.368039i
$117$	−3.40345	−	9.95983i	−0.314649	−	0.920787i
$118$	15.6848	−	2.72503i	1.44390	−	0.250860i
$119$	−8.02697	+	4.63437i	−0.735831	+	0.424832i
$120$	−0.771902	−	1.62375i	−0.0704647	−	0.148227i
$121$	−14.3539	+	24.8618i	−1.30490	+	2.26016i
$122$	1.97053	+	11.3420i	0.178403	+	1.02686i
$123$	−0.0668963	+	0.0179248i	−0.00603184	+	0.00161623i
$124$	−0.166711	+	0.918447i	−0.0149711	+	0.0824790i
$125$	9.42177	−	6.01916i	0.842709	−	0.538370i
$126$	−3.27100	−	7.06095i	−0.291404	−	0.629040i
$127$	−2.10175	+	7.84383i	−0.186500	+	0.696027i	0.807805	+	0.589450i	$0.200656\pi$
$127$	−2.10175	+	7.84383i	−0.186500	+	0.696027i	−0.994304	+	0.106577i	$0.966011\pi$
$128$	−1.76832	−	11.1747i	−0.156299	−	0.987710i
$129$		−	2.39894i		−	0.211215i
$130$	−11.2428	+	1.89749i	−0.986055	+	0.166421i
$131$			0.411706i			0.0359709i	0.999838	+	0.0179855i	$0.00572526\pi$
$131$			0.411706i			0.0359709i	−0.999838	+	0.0179855i	$0.994275\pi$
$132$	3.57050	−	0.294304i	0.310773	−	0.0256159i
$133$	1.09731	−	4.09521i	0.0951487	−	0.355100i
$134$	−11.3683	+	5.26640i	−0.982074	+	0.454947i
$135$	3.11403	+	2.11172i	0.268013	+	0.181748i
$136$	9.90827	−	9.75999i	0.849627	−	0.836912i
$137$	−1.70937	+	0.458023i	−0.146041	+	0.0391316i	−0.331099	−	0.943596i	$-0.607419\pi$
$137$	−1.70937	+	0.458023i	−0.146041	+	0.0391316i	0.185058	+	0.982728i	$0.440753\pi$
$138$	1.88608	−	0.327683i	0.160554	−	0.0278942i
$139$	7.59597	−	13.1566i	0.644281	−	1.11593i	−0.340185	−	0.940358i	$-0.610490\pi$
$139$	7.59597	−	13.1566i	0.644281	−	1.11593i	0.984467	−	0.175570i	$-0.0561768\pi$
$140$	−8.12048	+	2.26264i	−0.686306	+	0.191228i
$141$	1.54988	−	0.894825i	0.130524	−	0.0753578i
$142$	−2.62779	−	15.1251i	−0.220519	−	1.26927i
$143$	4.38728	−	22.2925i	0.366883	−	1.86419i
$144$	7.41539	+	9.01991i	0.617949	+	0.751659i
$145$	3.56058	−	3.07966i	0.295690	−	0.255751i
$146$	1.92141	−	21.3439i	0.159017	−	1.76643i
$147$	−0.946468	+	0.253605i	−0.0780633	+	0.0209170i
$148$	0.333211	+	0.157423i	0.0273898	+	0.0129401i
$149$	5.16977	−	8.95430i	0.423524	−	0.733565i	−0.572757	−	0.819725i	$-0.694126\pi$
$149$	5.16977	−	8.95430i	0.423524	−	0.733565i	0.996281	+	0.0861600i	$0.0274596\pi$
$150$	1.38185	−	1.45979i	0.112827	−	0.119191i
$151$	21.0962			1.71679			0.858394	−	0.512992i	$-0.171463\pi$
$151$	21.0962			1.71679			0.858394	+	0.512992i	$0.171463\pi$
$152$	−0.0479603	+	6.36154i	−0.00389010	+	0.515989i
$153$	−3.71515	+	13.8651i	−0.300352	+	1.12093i
$154$	1.50609	−	16.7303i	0.121364	−	1.34817i
$155$	−1.02495	+	0.196588i	−0.0823261	+	0.0157903i
$156$	−1.87877	+	0.819962i	−0.150422	+	0.0656495i
$157$	−4.88792	+	4.88792i	−0.390098	+	0.390098i	−0.874722	−	0.484624i	$-0.838956\pi$
$157$	−4.88792	+	4.88792i	−0.390098	+	0.390098i	0.484624	+	0.874722i	$0.338956\pi$
$158$	−11.9065	+	9.93983i	−0.947228	+	0.790771i
$159$	0.757955	+	1.31282i	0.0601097	+	0.104113i
$160$	10.9392	−	6.35086i	0.864822	−	0.502079i
$161$		−	8.97584i		−	0.707395i
$162$	−10.9924	−	4.03222i	−0.863645	−	0.316801i
$163$	−8.44752	+	2.26351i	−0.661661	+	0.177292i	−0.573996	−	0.818858i	$-0.694607\pi$
$163$	−8.44752	+	2.26351i	−0.661661	+	0.177292i	−0.0876655	+	0.996150i	$0.527941\pi$
$164$	−0.164348	−	0.458702i	−0.0128334	−	0.0358186i
$165$	1.74693	+	3.60446i	0.135999	+	0.280607i
$166$	−4.98064	−	0.448364i	−0.386573	−	0.0347998i
$167$	4.33292	+	1.16100i	0.335291	+	0.0898410i	0.422537	−	0.906346i	$-0.361140\pi$
$167$	4.33292	+	1.16100i	0.335291	+	0.0898410i	−0.0872454	+	0.996187i	$0.527806\pi$
$168$	−1.31821	+	0.747874i	−0.101702	+	0.0576998i
$169$	1.74909	+	12.8818i	0.134546	+	0.990907i
$170$	14.1734	+	6.39551i	1.08705	+	0.490513i
$171$	−3.28293	−	5.68620i	−0.251052	−	0.434835i
$172$	16.8208	−	1.38648i	1.28258	−	0.105718i
$173$	−5.28855	+	1.41706i	−0.402081	+	0.107737i	−0.454192	−	0.890904i	$-0.650072\pi$
$173$	−5.28855	+	1.41706i	−0.402081	+	0.107737i	0.0521104	+	0.998641i	$0.483405\pi$
$174$	0.487205	−	0.692092i	0.0369349	−	0.0524674i
$175$	−5.63451	−	7.55510i	−0.425929	−	0.571112i
$176$	4.12719	+	24.8655i	0.311098	+	1.87431i
$177$	2.26276	+	2.26276i	0.170079	+	0.170079i
$178$	−10.9022	−	3.99912i	−0.817153	−	0.299747i
$179$	−10.9690	−	18.9988i	−0.819861	−	1.42004i	−0.905785	−	0.423739i	$-0.860718\pi$
$179$	−10.9690	−	18.9988i	−0.819861	−	1.42004i	0.0859238	−	0.996302i	$-0.472616\pi$
$180$	−6.41479	+	11.3703i	−0.478130	+	0.847493i
$181$	1.09140			0.0811234			0.0405617	−	0.999177i	$-0.487085\pi$
$181$	1.09140			0.0811234			0.0405617	+	0.999177i	$0.487085\pi$
$182$	2.27998	+	9.33713i	0.169003	+	0.692114i
$183$	−1.63625	+	1.63625i	−0.120955	+	0.120955i
$184$	3.38771	+	13.0354i	0.249745	+	0.960984i
$185$	−0.0297630	+	0.410949i	−0.00218822	+	0.0302135i
$186$	−0.170252	+	0.0788697i	−0.0124835	+	0.00578300i
$187$	−21.9100	+	21.9100i	−1.60222	+	1.60222i
$188$	7.17007	+	10.3503i	0.522931	+	0.754870i
$189$	1.58587	−	2.74680i	0.115355	−	0.199800i
$190$	−6.65286	+	2.51571i	−0.482649	+	0.182509i
$191$	3.94053	+	2.27506i	0.285126	+	0.164618i	0.635742	−	0.771902i	$-0.280694\pi$
$191$	3.94053	+	2.27506i	0.285126	+	0.164618i	−0.350615	+	0.936520i	$0.614028\pi$
$192$	1.63214	−	1.58365i	0.117789	−	0.114290i
$193$	1.07780	+	0.288795i	0.0775816	+	0.0207879i	0.297401	−	0.954753i	$-0.403880\pi$
$193$	1.07780	+	0.288795i	0.0775816	+	0.0207879i	−0.219819	+	0.975541i	$0.570547\pi$
$194$	7.32475	−	10.4051i	0.525887	−	0.747041i
$195$	−1.61276	−	1.62838i	−0.115492	−	0.116611i
$196$	−2.32524	−	6.48985i	−0.166089	−	0.463561i
$197$	2.61816	−	9.77112i	0.186536	−	0.696164i	−0.807760	−	0.589512i	$-0.799320\pi$
$197$	2.61816	−	9.77112i	0.186536	−	0.696164i	0.994296	−	0.106652i	$-0.0340131\pi$
$198$	−16.6717	−	19.9702i	−1.18480	−	1.41922i
$199$	−7.14207	+	12.3704i	−0.506288	+	0.876917i	0.493685	+	0.869641i	$0.335649\pi$
$199$	−7.14207	+	12.3704i	−0.506288	+	0.876917i	−0.999974	+	0.00727615i	$0.997684\pi$
$200$	11.0344	+	8.84550i	0.780247	+	0.625471i
$201$	−2.18103	−	1.25922i	−0.153838	−	0.0888182i
$202$	−3.94174	−	1.44591i	−0.277340	−	0.101734i
$203$	−2.80613	−	2.80613i	−0.196951	−	0.196951i
$204$	2.75068	+	0.499287i	0.192586	+	0.0349571i
$205$	0.412029	−	0.356377i	0.0287773	−	0.0248905i
$206$	−1.50008	+	16.6636i	−0.104516	+	1.16101i
$207$	−9.82923	−	9.82923i	−0.683179	−	0.683179i
$208$	−6.83523	−	12.6996i	−0.473938	−	0.880558i
$209$		−	14.1732i		−	0.980381i
$210$	−1.31151	−	1.07293i	−0.0905024	−	0.0740395i
$211$	3.29929	−	1.90485i	0.227133	−	0.131135i	−0.382116	−	0.924114i	$-0.624804\pi$
$211$	3.29929	−	1.90485i	0.227133	−	0.131135i	0.609249	+	0.792979i	$0.291471\pi$
$212$	−8.76711	+	6.07336i	−0.602128	+	0.417120i
$213$	2.18201	−	2.18201i	0.149509	−	0.149509i
$214$	3.22970	+	6.97179i	0.220777	+	0.476582i
$215$	8.22989	+	16.9808i	0.561274	+	1.15808i
$216$	−1.26641	+	4.58767i	−0.0861681	+	0.312151i
$217$	0.227700	+	0.849787i	0.0154573	+	0.0576873i
$218$	−0.459709	+	0.383778i	−0.0311355	+	0.0259927i
$219$	3.73056	−	2.15384i	0.252088	−	0.145543i
$220$	−24.2640	+	14.3323i	−1.63588	+	0.966286i
$221$	7.80918	−	15.9167i	0.525302	−	1.07068i
$222$	0.0126800	+	0.0729840i	0.000851027	+	0.00489836i
$223$	−6.60183	+	24.6384i	−0.442091	+	1.64991i	0.281412	+	0.959587i	$0.409197\pi$
$223$	−6.60183	+	24.6384i	−0.442091	+	1.64991i	−0.723504	+	0.690321i	$0.757469\pi$
$224$	−6.00579	−	8.81074i	−0.401279	−	0.588693i
$225$	−14.4436	−	2.10319i	−0.962909	−	0.140213i
$226$	−4.44563	+	6.31518i	−0.295719	+	0.420080i
$227$	1.60399	+	5.98619i	0.106461	+	0.397317i	0.998507	−	0.0546274i	$-0.0173971\pi$
$227$	1.60399	+	5.98619i	0.106461	+	0.397317i	−0.892046	+	0.451945i	$0.850730\pi$
$228$	−1.05118	+	0.728196i	−0.0696159	+	0.0482259i
$229$	−11.7548			−0.776780			−0.388390	−	0.921495i	$-0.626969\pi$
$229$	−11.7548			−0.776780			−0.388390	+	0.921495i	$0.626969\pi$
$230$	−12.2264	+	8.78996i	−0.806185	+	0.579593i
$231$	2.92418	−	1.68827i	0.192397	−	0.111080i
$232$	5.13438	+	3.01617i	0.337089	+	0.198021i
$233$	19.5093	+	19.5093i	1.27810	+	1.27810i	0.941731	+	0.336367i	$0.109198\pi$
$233$	19.5093	+	19.5093i	1.27810	+	1.27810i	0.336367	+	0.941731i	$0.390802\pi$
$234$	12.7216	+	7.72812i	0.831638	+	0.505203i
$235$	−7.90095	+	11.6511i	−0.515401	+	0.760032i
$236$	−14.5582	+	17.1737i	−0.947658	+	1.11792i
$237$	−3.01145	−	0.806916i	−0.195615	−	0.0524148i
$238$	4.51414	−	12.3062i	0.292608	−	0.797691i
$239$		−	20.4405i		−	1.32219i	−0.750304	−	0.661093i	$-0.770093\pi$
$239$		−	20.4405i		−	1.32219i	0.750304	−	0.661093i	$-0.229907\pi$
$240$	2.30962	+	1.06320i	0.149086	+	0.0686296i
$241$	14.4513	+	8.34345i	0.930888	+	0.537449i	0.887092	−	0.461592i	$-0.152722\pi$
$241$	14.4513	+	8.34345i	0.930888	+	0.537449i	0.0437959	+	0.999040i	$0.486055\pi$
$242$	−6.94946	−	39.9999i	−0.446728	−	2.57129i
$243$	−1.91565	−	7.14929i	−0.122889	−	0.458627i
$244$	−12.4187	−	10.5273i	−0.795026	−	0.673944i
$245$	5.82950	−	5.04212i	0.372433	−	0.322129i
$246$	0.0563792	−	0.0800888i	0.00359461	−	0.00510627i
$247$	2.62232	+	7.67395i	0.166854	+	0.488282i
$248$	−0.651415	−	1.14819i	−0.0413649	−	0.0729100i
$249$	−0.502602	−	0.870532i	−0.0318511	−	0.0551678i
$250$	−4.77332	+	15.0737i	−0.301891	+	0.953342i
$251$	15.2658	+	8.81371i	0.963569	+	0.556317i	0.897270	−	0.441483i	$-0.145547\pi$
$251$	15.2658	+	8.81371i	0.963569	+	0.556317i	0.0662993	+	0.997800i	$0.478881\pi$
$252$	9.95054	+	4.70104i	0.626825	+	0.296138i
$253$	−7.76617	−	28.9837i	−0.488255	−	1.82219i
$254$	−4.82725	−	10.4203i	−0.302888	−	0.653831i
$255$	0.588766	+	3.06966i	0.0368700	+	0.192229i
$256$	12.0475	+	10.5289i	0.752968	+	0.658057i
$257$	1.74193	+	0.466749i	0.108659	+	0.0291150i	0.312739	−	0.949839i	$-0.398754\pi$
$257$	1.74193	+	0.466749i	0.108659	+	0.0291150i	−0.204080	+	0.978954i	$0.565420\pi$
$258$	2.17419	+	2.60436i	0.135359	+	0.162141i
$259$	0.347329			0.0215820
$260$	10.4858	−	12.2494i	0.650300	−	0.759678i
$261$	−6.14585			−0.380418
$262$	−0.373135	−	0.446961i	−0.0230524	−	0.0276134i
$263$	−5.55336	−	1.48802i	−0.342435	−	0.0917551i	0.0835032	−	0.996508i	$-0.473389\pi$
$263$	−5.55336	−	1.48802i	−0.342435	−	0.0917551i	−0.425938	+	0.904752i	$0.640056\pi$
$264$	−3.60952	+	3.55550i	−0.222151	+	0.218826i
$265$	−9.86895	−	6.69244i	−0.606245	−	0.411113i
$266$	2.52027	+	5.44039i	0.154528	+	0.333572i
$267$	−0.604142	−	2.25469i	−0.0369729	−	0.137985i
$268$	7.56880	−	16.0206i	0.462338	−	0.978616i
$269$	16.9489	+	9.78545i	1.03339	+	0.596629i	0.917955	−	0.396685i	$-0.129840\pi$
$269$	16.9489	+	9.78545i	1.03339	+	0.596629i	0.115438	+	0.993315i	$0.463173\pi$
$270$	−5.29457	+	0.529738i	−0.322217	+	0.0322388i
$271$	−11.5709	−	20.0413i	−0.702880	−	1.21742i	−0.967451	−	0.253058i	$-0.918564\pi$
$271$	−11.5709	−	20.0413i	−0.702880	−	1.21742i	0.264571	−	0.964366i	$-0.414770\pi$
$272$	−1.91112	+	19.5757i	−0.115879	+	1.18695i
$273$	−1.27091	+	1.45513i	−0.0769187	+	0.0880685i
$274$	1.44063	−	2.04647i	0.0870316	−	0.123632i
$275$	−24.7312	−	19.5209i	−1.49135	−	1.17715i
$276$	−1.75061	+	2.06513i	−0.105374	+	0.124306i
$277$	−1.03296	−	3.85506i	−0.0620646	−	0.231628i	0.927925	−	0.372766i	$-0.121591\pi$
$277$	−1.03296	−	3.85506i	−0.0620646	−	0.231628i	−0.989990	+	0.141138i	$0.954924\pi$
$278$	3.67759	+	21.1675i	0.220567	+	1.26955i
$279$	1.17993	+	0.681233i	0.0706406	+	0.0407844i
$280$	6.76519	−	9.81609i	0.404297	−	0.586624i
$281$			17.4146i			1.03887i	0.854510	+	0.519435i	$0.173858\pi$
$281$			17.4146i			1.03887i	−0.854510	+	0.519435i	$0.826142\pi$
$282$	−0.871609	+	2.37613i	−0.0519035	+	0.141496i
$283$	17.8397	+	4.78012i	1.06046	+	0.284149i	0.746567	−	0.665310i	$-0.231701\pi$
$283$	17.8397	+	4.78012i	1.06046	+	0.284149i	0.313891	+	0.949459i	$0.398367\pi$
$284$	16.5609	+	14.0387i	0.982707	+	0.833041i
$285$	−1.18329	−	0.802424i	−0.0700919	−	0.0475315i
$286$	15.4410	+	28.1777i	0.913046	+	1.66618i
$287$	−0.324724	−	0.324724i	−0.0191679	−	0.0191679i
$288$	−16.2252	−	3.07163i	−0.956082	−	0.180998i
$289$	−6.21711	+	3.58945i	−0.365712	+	0.211144i
$290$	−1.07434	+	6.57037i	−0.0630873	+	0.385825i
$291$	2.55778			0.149940
$292$	17.2583	+	24.9130i	1.00997	+	1.45792i
$293$	−3.22969	−	12.0534i	−0.188680	−	0.704164i	−0.993813	−	0.111069i	$-0.964572\pi$
$293$	−3.22969	−	12.0534i	−0.188680	−	0.704164i	0.805132	−	0.593095i	$-0.202094\pi$
$294$	0.797669	−	1.13312i	0.0465210	−	0.0660848i
$295$	−23.7796	−	8.25413i	−1.38450	−	0.480574i
$296$	−0.504419	+	0.131091i	−0.0293188	+	0.00761951i
$297$	2.74428	−	10.2418i	0.159239	−	0.594289i
$298$	2.50294	+	14.4065i	0.144992	+	0.834546i
$299$	9.56748	+	14.2561i	0.553302	+	0.824451i
$300$	−0.177148	+	2.83718i	−0.0102277	+	0.163805i
$301$	13.7759	−	7.95354i	0.794032	−	0.458434i
$302$	−22.9027	+	19.1198i	−1.31790	+	1.10022i
$303$	−0.218431	−	0.815195i	−0.0125485	−	0.0468318i
$304$	−5.71348	−	6.94975i	−0.327691	−	0.398596i
$305$	5.96874	−	17.1955i	0.341769	−	0.984612i
$306$	−8.53288	−	18.4195i	−0.487792	−	1.05297i
$307$	14.8252	−	14.8252i	0.846116	−	0.846116i	−0.143530	−	0.989646i	$-0.545845\pi$
$307$	14.8252	−	14.8252i	0.846116	−	0.846116i	0.989646	+	0.143530i	$0.0458453\pi$
$308$	13.5278	+	19.5279i	0.770820	+	1.11271i
$309$	−2.91252	+	1.68154i	−0.165688	+	0.0956597i
$310$	0.934550	−	1.14235i	0.0530789	−	0.0648811i
$311$			9.79374i			0.555352i	0.960675	+	0.277676i	$0.0895642\pi$
$311$			9.79374i			0.555352i	−0.960675	+	0.277676i	$0.910436\pi$
$312$	1.29651	−	2.59293i	0.0734001	−	0.146796i
$313$	−0.235408	−	0.235408i	−0.0133060	−	0.0133060i	0.700422	−	0.713728i	$-0.252995\pi$
$313$	−0.235408	−	0.235408i	−0.0133060	−	0.0133060i	−0.713728	+	0.700422i	$0.752995\pi$
$314$	0.876490	−	9.73646i	0.0494632	−	0.549460i
$315$	−0.888798	+	12.2720i	−0.0500781	+	0.691447i
$316$	3.91743	−	21.5820i	0.220373	−	1.21408i
$317$	0.751406	+	0.751406i	0.0422031	+	0.0422031i	0.727893	−	0.685690i	$-0.240500\pi$
$317$	0.751406	+	0.751406i	0.0422031	+	0.0422031i	−0.685690	+	0.727893i	$0.740500\pi$
$318$	−2.01268	−	0.738290i	−0.112866	−	0.0414012i
$319$	−11.4892	−	6.63327i	−0.643269	−	0.371392i
$320$	−6.12010	+	16.8091i	−0.342124	+	0.939655i
$321$	−0.772232	+	1.33755i	−0.0431018	+	0.0746545i
$322$	8.13492	+	9.74445i	0.453342	+	0.543037i
$323$	2.86249	−	10.6830i	0.159273	−	0.594416i
$324$	15.5882	−	5.58506i	0.866009	−	0.310281i
$325$	17.0022	+	5.99366i	0.943114	+	0.332468i
$326$	7.11945	−	10.1134i	0.394310	−	0.560132i
$327$	−0.116272	−	0.0311551i	−0.00642987	−	0.00172288i
$328$	0.594149	+	0.349031i	0.0328064	+	0.0192720i
$329$	10.2771	+	5.93348i	0.566594	+	0.327123i
$330$	−5.16330	−	2.32984i	−0.284230	−	0.128254i
$331$	−4.29662	+	7.44196i	−0.236163	+	0.409047i	−0.959610	−	0.281333i	$-0.909223\pi$
$331$	−4.29662	+	7.44196i	−0.236163	+	0.409047i	0.723447	+	0.690380i	$0.242557\pi$
$332$	5.81350	−	4.02726i	0.319057	−	0.221025i
$333$	0.380352	−	0.380352i	0.0208432	−	0.0208432i
$334$	−5.75618	+	2.66656i	−0.314964	+	0.145908i
$335$	19.7582	+	1.43099i	1.07951	+	0.0781833i
$336$	0.753279	−	2.00663i	0.0410947	−	0.109470i
$337$	20.4609	−	20.4609i	1.11458	−	1.11458i	0.122054	−	0.992523i	$-0.461052\pi$
$337$	20.4609	−	20.4609i	1.11458	−	1.11458i	0.992523	−	0.122054i	$-0.0389482\pi$
$338$	−13.5738	−	12.3997i	−0.738318	−	0.674452i
$339$	−1.55240			−0.0843149
$340$	−21.1835	+	5.90242i	−1.14883	+	0.320104i
$341$	1.47052	+	2.54702i	0.0796333	+	0.137929i
$342$	8.71754	+	3.19776i	0.471391	+	0.172915i
$343$	−13.9244	−	13.9244i	−0.751846	−	0.751846i
$344$	−17.0046	+	16.7501i	−0.916828	+	0.903107i
$345$	−2.85947	−	0.992552i	−0.153949	−	0.0534372i
$346$	4.45712	−	6.33150i	0.239616	−	0.340383i
$347$	4.85812	−	1.30173i	0.260797	−	0.0698805i	−0.126051	−	0.992024i	$-0.540230\pi$
$347$	4.85812	−	1.30173i	0.260797	−	0.0698805i	0.386848	+	0.922143i	$0.373564\pi$
$348$	0.0983279	+	1.19292i	0.00527093	+	0.0639471i
$349$	−5.07385	−	8.78817i	−0.271597	−	0.470420i	0.697674	−	0.716416i	$-0.254218\pi$
$349$	−5.07385	−	8.78817i	−0.271597	−	0.470420i	−0.969271	+	0.245996i	$0.920885\pi$
$350$	12.9643	+	3.09542i	0.692970	+	0.165457i
$351$	0.409067	+	6.05307i	0.0218344	+	0.323089i
$352$	−27.0165	−	23.2542i	−1.43999	−	1.23945i
$353$	8.39388	+	2.24913i	0.446761	+	0.119709i	0.475183	−	0.879887i	$-0.342382\pi$
$353$	8.39388	+	2.24913i	0.446761	+	0.119709i	−0.0284225	+	0.999596i	$0.509048\pi$
$354$	−4.50729	−	0.405753i	−0.239560	−	0.0215655i
$355$	−7.95957	+	22.9309i	−0.422450	+	1.21705i
$356$	15.4602	−	5.53922i	0.819390	−	0.293578i
$357$	2.54505	−	0.681944i	0.134698	−	0.0360923i
$358$	29.1272	+	10.6844i	1.53942	+	0.564688i
$359$		−	12.6968i		−	0.670113i	−0.942198	−	0.335056i	$-0.891245\pi$
$359$		−	12.6968i		−	0.670113i	0.942198	−	0.335056i	$-0.108755\pi$
$360$	−3.34097	−	18.1578i	−0.176085	−	0.956999i
$361$	−6.97053	−	12.0733i	−0.366870	−	0.635438i
$362$	−1.18486	+	0.989155i	−0.0622750	+	0.0519888i
$363$	5.77056	−	5.77056i	0.302876	−	0.302876i
$364$	−10.9376	−	8.07030i	−0.573285	−	0.422999i
$365$	−19.0175	+	28.0441i	−0.995424	+	1.46789i
$366$	0.293409	−	3.25932i	0.0153367	−	0.170367i
$367$	2.17691	−	8.12436i	0.113634	−	0.424088i	−0.885547	−	0.464550i	$-0.846216\pi$
$367$	2.17691	−	8.12436i	0.113634	−	0.424088i	0.999181	+	0.0404617i	$0.0128829\pi$
$368$	−15.4920	−	11.0813i	−0.807576	−	0.577654i
$369$	−0.711196			−0.0370234
$370$	−0.340137	−	0.473113i	−0.0176829	−	0.0245960i
$371$	−5.02591	+	8.70513i	−0.260932	+	0.451948i
$372$	0.113351	−	0.239925i	0.00587695	−	0.0124395i
$373$	8.41357	−	2.25441i	0.435638	−	0.116729i	−0.0343334	−	0.999410i	$-0.510931\pi$
$373$	8.41357	−	2.25441i	0.435638	−	0.116729i	0.469972	+	0.882682i	$0.344264\pi$
$374$	3.92885	−	43.6434i	0.203156	−	2.25675i
$375$	−3.02992	+	0.959562i	−0.156465	+	0.0495516i
$376$	−17.1646	−	4.73823i	−0.885199	−	0.244355i
$377$	7.44799	+	1.46580i	0.383591	+	0.0754928i
$378$	0.767797	+	4.41931i	0.0394912	+	0.227305i
$379$	16.5356	−	9.54686i	0.849379	−	0.490389i	−0.0110623	−	0.999939i	$-0.503521\pi$
$379$	16.5356	−	9.54686i	0.849379	−	0.490389i	0.860441	+	0.509550i	$0.170188\pi$
$380$	4.94253	−	8.76071i	0.253546	−	0.449415i
$381$	1.15421	−	1.99915i	0.0591321	−	0.102420i
$382$	−6.33988	+	1.10147i	−0.324376	+	0.0563562i
$383$	−21.2064	+	5.68225i	−1.08360	+	0.290349i	−0.756069	−	0.654491i	$-0.772883\pi$
$383$	−21.2064	+	5.68225i	−1.08360	+	0.290349i	−0.327530	+	0.944841i	$0.606216\pi$
$384$	−0.336620	+	3.19849i	−0.0171780	+	0.163222i
$385$	−14.9068	+	21.9822i	−0.759720	+	1.12031i
$386$	−1.43183	+	0.663298i	−0.0728782	+	0.0337610i
$387$	6.37597	−	23.7954i	0.324109	−	1.20959i
$388$	1.47828	+	17.9346i	0.0750485	+	0.910492i
$389$		−	16.4637i		−	0.834745i	−0.908735	−	0.417373i	$-0.862951\pi$
$389$		−	16.4637i		−	0.834745i	0.908735	−	0.417373i	$-0.137049\pi$
$390$	3.22669	+	0.306161i	0.163390	+	0.0155031i
$391$		−	23.4148i		−	1.18414i
$392$	8.40619	+	4.93819i	0.424577	+	0.249416i
$393$	0.0302911	−	0.113048i	0.00152798	−	0.00570251i
$394$	6.01334	+	12.9807i	0.302948	+	0.653959i
$395$	24.0847	−	4.61949i	1.21183	−	0.232432i
$396$	36.1986	+	6.57055i	1.81905	+	0.330182i
$397$	−27.2427	+	7.29966i	−1.36727	+	0.366359i	−0.866481	−	0.499209i	$-0.833624\pi$
$397$	−27.2427	+	7.29966i	−1.36727	+	0.366359i	−0.500790	+	0.865569i	$0.666957\pi$
$398$	−3.45783	−	19.9027i	−0.173326	−	0.997632i
$399$	−0.602606	+	1.04375i	−0.0301681	+	0.0522526i
$400$	−19.9960	+	0.397639i	−0.999802	+	0.0198819i
$401$	−3.73704	+	2.15758i	−0.186619	+	0.107744i	−0.590399	−	0.807112i	$-0.701030\pi$
$401$	−3.73704	+	2.15758i	−0.186619	+	0.107744i	0.403780	+	0.914856i	$0.367696\pi$
$402$	3.50903	−	0.609649i	0.175015	−	0.0304065i
$403$	−1.26745	−	1.10699i	−0.0631362	−	0.0551429i
$404$	5.58973	−	2.00274i	0.278099	−	0.0996398i
$405$	12.1108	+	14.0020i	0.601792	+	0.695767i
$406$	5.58965	+	0.503188i	0.277410	+	0.0249728i
$407$	1.12156	−	0.300520i	0.0555934	−	0.0148962i
$408$	−3.43874	+	1.95094i	−0.170243	+	0.0965859i
$409$	−13.4186	+	23.2417i	−0.663506	+	1.14923i	0.316182	+	0.948699i	$0.397599\pi$
$409$	−13.4186	+	23.2417i	−0.663506	+	1.14923i	−0.979688	+	0.200528i	$0.935734\pi$
$410$	−0.124322	+	0.760322i	−0.00613983	+	0.0375496i
$411$	0.503064			0.0248143
$412$	−13.4739	−	19.4501i	−0.663813	−	0.958237i
$413$	−5.49188	+	20.4960i	−0.270238	+	1.00854i
$414$	19.5793	+	1.76256i	0.962270	+	0.0866249i
$415$	6.54413	+	4.43778i	0.321239	+	0.217842i
$416$	18.9304	+	7.59221i	0.928137	+	0.372239i
$417$	−3.05372	+	3.05372i	−0.149541	+	0.149541i
$418$	12.8454	+	15.3869i	0.628287	+	0.752596i
$419$	11.6840	+	20.2373i	0.570802	+	0.988658i	0.996484	+	0.0837852i	$0.0267010\pi$
$419$	11.6840	+	20.2373i	0.570802	+	0.988658i	−0.425682	+	0.904873i	$0.639966\pi$
$420$	2.39623	−	0.0238232i	0.116924	−	0.00116245i
$421$			13.4883i			0.657378i	0.944438	+	0.328689i	$0.106607\pi$
$421$			13.4883i			0.657378i	−0.944438	+	0.328689i	$0.893393\pi$
$422$	−1.85543	+	5.05816i	−0.0903208	+	0.246227i
$423$	17.7518	−	4.75658i	0.863122	−	0.231273i
$424$	4.01348	−	14.5392i	0.194912	−	0.706085i
$425$	−14.6984	−	19.7086i	−0.712979	−	0.956007i
$426$	−0.391273	+	4.34644i	−0.0189572	+	0.210586i
$427$	−14.8211	−	3.97130i	−0.717242	−	0.192184i
$428$	−9.82489	−	4.64168i	−0.474904	−	0.224364i
$429$	−2.84484	+	5.79837i	−0.137350	+	0.279948i
$430$	−24.3245	−	10.9760i	−1.17303	−	0.529310i
$431$	−8.53621	−	14.7851i	−0.411175	−	0.712176i	0.583844	−	0.811866i	$-0.301548\pi$
$431$	−8.53621	−	14.7851i	−0.411175	−	0.712176i	−0.995018	+	0.0996905i	$0.968215\pi$
$432$	−2.78302	−	6.12828i	−0.133898	−	0.294847i
$433$	−8.48688	+	2.27405i	−0.407853	+	0.109284i	−0.456912	−	0.889512i	$-0.651045\pi$
$433$	−8.48688	+	2.27405i	−0.407853	+	0.109284i	0.0490586	+	0.998796i	$0.484378\pi$
$434$	−1.01737	−	0.716188i	−0.0488354	−	0.0343781i
$435$	−1.20426	+	0.583657i	−0.0577399	+	0.0279842i
$436$	0.151252	−	0.833282i	0.00724367	−	0.0399070i
$437$	7.57333	+	7.57333i	0.362281	+	0.362281i
$438$	−2.09796	+	5.71933i	−0.100244	+	0.273280i
$439$	6.19098	+	10.7231i	0.295479	+	0.511785i	0.975096	−	0.221782i	$-0.0711873\pi$
$439$	6.19098	+	10.7231i	0.295479	+	0.511785i	−0.679617	+	0.733567i	$0.737854\pi$
$440$	13.3522	−	37.5504i	0.636540	−	1.79015i
$441$	−10.0622			−0.479152
$442$	5.94766	+	24.3573i	0.282901	+	1.15856i
$443$	−13.7497	+	13.7497i	−0.653266	+	0.653266i	−0.953778	−	0.300512i	$-0.902842\pi$
$443$	−13.7497	+	13.7497i	−0.653266	+	0.653266i	0.300512	+	0.953778i	$0.402842\pi$
$444$	−0.0799122	−	0.0677416i	−0.00379247	−	0.00321488i
$445$	12.0114	+	13.8871i	0.569396	+	0.658313i
$446$	−15.1629	−	32.7315i	−0.717986	−	1.54988i
$447$	−2.07834	+	2.07834i	−0.0983023	+	0.0983023i
$448$	14.5054	+	4.12209i	0.685315	+	0.194750i
$449$	4.90708	−	8.49931i	0.231579	−	0.401107i	−0.726694	−	0.686962i	$-0.758944\pi$
$449$	4.90708	−	8.49931i	0.231579	−	0.401107i	0.958273	+	0.285854i	$0.0922774\pi$
$450$	17.5866	−	10.8072i	0.829041	−	0.509455i
$451$	−1.32952	−	0.767600i	−0.0626048	−	0.0361449i
$452$	−0.897220	−	10.8851i	−0.0422017	−	0.511992i
$453$	−5.79269	−	1.55215i	−0.272164	−	0.0729262i
$454$	−7.16671	−	5.04507i	−0.336350	−	0.236777i
$455$	4.00402	−	14.6601i	0.187711	−	0.687276i
$456$	0.481217	−	1.74325i	0.0225350	−	0.0816351i
$457$	−6.68536	+	24.9501i	−0.312728	+	1.16712i	0.613358	+	0.789805i	$0.289818\pi$
$457$	−6.68536	+	24.9501i	−0.312728	+	1.16712i	−0.926086	+	0.377312i	$0.876849\pi$
$458$	12.7614	−	10.6535i	0.596301	−	0.497807i
$459$	4.13697	−	7.16544i	0.193097	−	0.334454i
$460$	5.30691	−	20.6236i	0.247436	−	0.961581i
$461$	−27.1456	−	15.6725i	−1.26430	−	0.729941i	−0.290393	−	0.956908i	$-0.593786\pi$
$461$	−27.1456	−	15.6725i	−1.26430	−	0.729941i	−0.973903	+	0.226966i	$0.927119\pi$
$462$	−1.64447	+	4.48306i	−0.0765077	+	0.208571i
$463$	1.93134	+	1.93134i	0.0897570	+	0.0897570i	0.750560	−	0.660803i	$-0.229784\pi$
$463$	1.93134	+	1.93134i	0.0897570	+	0.0897570i	−0.660803	+	0.750560i	$0.729784\pi$
$464$	−8.30764	+	1.37891i	−0.385673	+	0.0640141i
$465$	0.295899	+	0.0214305i	0.0137220	+	0.000993817i
$466$	−38.8615	−	3.49837i	−1.80022	−	0.162059i
$467$	7.72171	+	7.72171i	0.357318	+	0.357318i	0.862823	−	0.505505i	$-0.168694\pi$
$467$	7.72171	+	7.72171i	0.357318	+	0.357318i	−0.505505	+	0.862823i	$0.668694\pi$
$468$	−20.8151	+	3.13989i	−0.962178	+	0.145141i
$469$		−	16.6994i		−	0.771108i
$470$	−1.98200	−	19.8095i	−0.0914228	−	0.913744i
$471$	1.70177	−	0.982517i	0.0784134	−	0.0452720i
$472$	0.240035	−	31.8386i	0.0110485	−	1.46549i
$473$	37.6020	−	37.6020i	1.72894	−	1.72894i
$474$	4.00065	−	1.85331i	0.183756	−	0.0851252i
$475$	11.1287	+	1.62049i	0.510618	+	0.0743532i
$476$	6.25257	+	17.4512i	0.286586	+	0.799874i
$477$	4.02903	+	15.0365i	0.184477	+	0.688476i
$478$	18.5255	+	22.1908i	0.847337	+	1.01499i
$479$	10.4335	−	6.02378i	0.476718	−	0.275234i	−0.242329	−	0.970194i	$-0.577911\pi$
$479$	10.4335	−	6.02378i	0.476718	−	0.275234i	0.719048	+	0.694960i	$0.244578\pi$
$480$	−3.47100	+	0.938995i	−0.158429	+	0.0428591i
$481$	−0.551654	+	0.370224i	−0.0251533	+	0.0168807i
$482$	−23.2505	+	4.03948i	−1.05903	+	0.183993i
$483$	−0.660393	+	2.46462i	−0.0300489	+	0.112144i
$484$	43.7970	+	37.1267i	1.99077	+	1.68758i
$485$	−18.1052	+	8.77483i	−0.822113	+	0.398445i
$486$	8.55919	+	6.02532i	0.388253	+	0.273314i
$487$	6.25526	+	23.3449i	0.283453	+	1.05786i	0.949962	+	0.312364i	$0.101121\pi$
$487$	6.25526	+	23.3449i	0.283453	+	1.05786i	−0.666510	+	0.745496i	$0.732212\pi$
$488$	23.0232	+	0.173574i	1.04221	+	0.00785735i
$489$	2.48609			0.112425
$490$	−1.75894	+	10.7572i	−0.0794610	+	0.485963i
$491$	−35.2136	+	20.3306i	−1.58917	+	0.917507i	−0.595724	+	0.803189i	$0.703135\pi$
$491$	−35.2136	+	20.3306i	−1.58917	+	0.917507i	−0.993444	+	0.114317i	$0.963532\pi$
$492$	0.0113785	+	0.138044i	0.000512982	+	0.00622351i
$493$	−7.32019	−	7.32019i	−0.329685	−	0.329685i
$494$	−9.80188	−	5.95444i	−0.441008	−	0.267903i
$495$	7.74808	+	40.3962i	0.348250	+	1.81568i
$496$	1.74781	+	0.656123i	0.0784792	+	0.0294608i
$497$	19.7645	+	5.29589i	0.886561	+	0.237553i
$498$	1.33462	+	0.489562i	0.0598056	+	0.0219378i
$499$			3.22798i			0.144504i	0.997386	+	0.0722521i	$0.0230186\pi$
$499$			3.22798i			0.144504i	−0.997386	+	0.0722521i	$0.976981\pi$
$500$	−8.47940	−	20.6906i	−0.379210	−	0.925311i
$501$	−1.10433	−	0.637585i	−0.0493378	−	0.0284852i
$502$	−24.5610	+	4.26716i	−1.09621	+	0.190453i
$503$	8.10577	+	30.2511i	0.361418	+	1.34883i	0.872212	+	0.489128i	$0.162685\pi$
$503$	8.10577	+	30.2511i	0.361418	+	1.34883i	−0.510793	+	0.859704i	$0.670648\pi$
$504$	−15.0632	+	3.91471i	−0.670970	+	0.174375i
$505$	4.34280	+	5.02097i	0.193252	+	0.223430i
$506$	34.6996	+	24.4271i	1.54258	+	1.08592i
$507$	0.467500	−	3.66582i	0.0207624	−	0.162805i
$508$	14.6847	+	6.93766i	0.651529	+	0.307809i
$509$	−1.17487	−	2.03493i	−0.0520750	−	0.0901966i	0.838813	−	0.544420i	$-0.183250\pi$
$509$	−1.17487	−	2.03493i	−0.0520750	−	0.0901966i	−0.890888	+	0.454223i	$0.849917\pi$
$510$	−3.42125	−	2.79891i	−0.151496	−	0.123938i
$511$	24.7369	+	14.2819i	1.09430	+	0.631792i
$512$	−22.6216	−	0.511718i	−0.999744	−	0.0226150i
$513$	0.979534	+	3.65567i	0.0432475	+	0.161402i
$514$	−2.31412	+	1.07202i	−0.102071	+	0.0472848i
$515$	14.8474	−	21.8946i	0.654254	−	0.964789i
$516$	−4.72074	−	0.856880i	−0.207819	−	0.0377220i
$517$	38.3194	+	10.2677i	1.68528	+	0.451571i
$518$	−0.377072	+	0.314789i	−0.0165676	+	0.0138310i
$519$	1.55641			0.0683189
$520$	−0.281853	+	22.8018i	−0.0123601	+	0.999924i
$521$	−28.7541			−1.25974			−0.629870	−	0.776701i	$-0.716892\pi$
$521$	−28.7541			−1.25974			−0.629870	+	0.776701i	$0.716892\pi$
$522$	6.67212	−	5.57006i	0.292031	−	0.243795i
$523$	−3.44372	−	0.922741i	−0.150583	−	0.0403487i	0.182740	−	0.983161i	$-0.441503\pi$
$523$	−3.44372	−	0.922741i	−0.150583	−	0.0403487i	−0.333323	+	0.942813i	$0.608170\pi$
$524$	0.810174	+	0.147058i	0.0353926	+	0.00642425i
$525$	0.991282	+	2.48907i	0.0432631	+	0.108632i
$526$	7.37751	−	3.41764i	0.321675	−	0.149016i
$527$	0.593988	+	2.21679i	0.0258745	+	0.0965651i
$528$	0.696208	−	7.13132i	0.0302986	−	0.310351i
$529$	−0.281593	−	0.162578i	−0.0122432	−	0.00706859i
$530$	16.7795	−	1.67884i	0.728854	−	0.0729240i
$531$	16.4306	+	28.4587i	0.713029	+	1.23500i
$532$	−7.66679	−	3.62210i	−0.332397	−	0.157038i
$533$	0.861880	+	0.169623i	0.0373322	+	0.00734717i
$534$	2.69933	+	1.90022i	0.116811	+	0.0822305i
$535$	0.877576	−	12.1170i	0.0379409	−	0.523864i
$536$	6.30279	+	24.2522i	0.272239	+	1.04754i
$537$	1.61408	+	6.02382i	0.0696526	+	0.259947i
$538$	−27.2689	+	4.73762i	−1.17565	+	0.204254i
$539$	−18.8105	−	10.8602i	−0.810224	−	0.467783i
$540$	5.26785	−	5.37364i	0.226692	−	0.231245i
$541$		−	22.0179i		−	0.946625i	−0.880894	−	0.473313i	$-0.843058\pi$
$541$		−	22.0179i		−	0.946625i	0.880894	−	0.473313i	$-0.156942\pi$
$542$	30.7254	+	11.2707i	1.31977	+	0.484117i
$543$	−0.299682	−	0.0802996i	−0.0128606	−	0.00344599i
$544$	−15.6670	−	22.9841i	−0.671717	−	0.985436i
$545$	0.929910	−	0.178359i	0.0398330	−	0.00764004i
$546$	0.0609297	−	2.73157i	0.00260755	−	0.116901i
$547$	−24.8183	−	24.8183i	−1.06115	−	1.06115i	−0.998004	−	0.0631505i	$-0.979885\pi$
$547$	−24.8183	−	24.8183i	−1.06115	−	1.06115i	−0.0631505	−	0.998004i	$-0.520115\pi$
$548$	0.290748	+	3.52737i	0.0124202	+	0.150682i
$549$	−20.5791	+	11.8813i	−0.878294	+	0.507083i
$550$	44.5410	−	1.22172i	1.89924	−	0.0520943i
$551$	4.73531			0.201731
$552$	0.0288640	−	3.82857i	0.00122853	−	0.162955i
$553$	−5.35056	−	19.9686i	−0.227529	−	0.849150i
$554$	4.61531	+	3.24899i	0.196086	+	0.138036i
$555$	0.0384078	−	0.110650i	0.00163032	−	0.00469684i
$556$	−23.1769	−	19.6471i	−0.982921	−	0.833223i
$557$	−8.03784	+	29.9976i	−0.340574	+	1.27104i	0.557124	+	0.830429i	$0.311905\pi$
$557$	−8.03784	+	29.9976i	−0.340574	+	1.27104i	−0.897698	+	0.440611i	$0.854762\pi$
$558$	−1.89838	+	0.329819i	−0.0803649	+	0.0139623i
$559$	−13.4022	+	27.3164i	−0.566851	+	1.15536i
$560$	1.55196	+	16.7880i	0.0655821	+	0.709424i
$561$	7.62814	−	4.40411i	0.322060	−	0.185942i
$562$	−15.7831	−	18.9059i	−0.665771	−	0.797497i
$563$	−9.54947	−	35.6391i	−0.402462	−	1.50201i	−0.808688	−	0.588237i	$-0.799822\pi$
$563$	−9.54947	−	35.6391i	−0.402462	−	1.50201i	0.406226	−	0.913773i	$-0.366845\pi$
$564$	−1.20727	−	3.36955i	−0.0508353	−	0.141884i
$565$	10.9886	−	5.32573i	0.462294	−	0.224055i
$566$	−23.6996	+	10.9789i	−0.996168	+	0.461476i
$567$	11.0352	−	11.0352i	0.463433	−	0.463433i
$568$	−30.7024	−	0.231469i	−1.28825	−	0.00971222i
$569$	−19.8062	+	11.4351i	−0.830321	+	0.479386i	−0.853963	−	0.520334i	$-0.825807\pi$
$569$	−19.8062	+	11.4351i	−0.830321	+	0.479386i	0.0236415	+	0.999720i	$0.492474\pi$
$570$	2.01186	−	0.201293i	0.0842676	−	0.00843122i
$571$		−	5.34830i		−	0.223819i	−0.993718	−	0.111910i	$-0.964303\pi$
$571$		−	5.34830i		−	0.223819i	0.993718	−	0.111910i	$-0.0356967\pi$
$572$	−42.3010	−	16.5962i	−1.76870	−	0.693920i
$573$	−0.914619	−	0.914619i	−0.0382087	−	0.0382087i
$574$	0.646833	+	0.0582288i	0.0269983	+	0.00243042i
$575$	23.6457	−	2.78408i	0.986095	−	0.116104i
$576$	20.3985	−	11.3705i	0.849938	−	0.473771i
$577$	−10.6756	−	10.6756i	−0.444429	−	0.444429i	0.449068	−	0.893498i	$-0.351756\pi$
$577$	−10.6756	−	10.6756i	−0.444429	−	0.444429i	−0.893498	+	0.449068i	$0.851756\pi$
$578$	3.49632	−	9.53147i	0.145428	−	0.396457i
$579$	−0.274698	−	0.158597i	−0.0114161	−	0.00659107i
$580$	−4.78848	−	8.10669i	−0.198831	−	0.336612i
$581$	3.33270	−	5.77240i	0.138264	−	0.239479i
$582$	−2.77681	+	2.31815i	−0.115102	+	0.0960906i
$583$	−8.69714	+	32.4582i	−0.360199	+	1.34428i
$584$	−41.3152	−	11.4049i	−1.70964	−	0.471938i
$585$	−11.6692	−	20.4386i	−0.482463	−	0.845034i
$586$	14.4304	+	10.1584i	0.596113	+	0.419639i
$587$	18.0361	+	4.83275i	0.744429	+	0.199469i	0.611046	−	0.791595i	$-0.290749\pi$
$587$	18.0361	+	4.83275i	0.744429	+	0.199469i	0.133383	+	0.991065i	$0.457416\pi$
$588$	0.160986	+	1.95309i	0.00663895	+	0.0805440i
$589$	−0.909125	−	0.524883i	−0.0374598	−	0.0216274i
$590$	33.2967	−	12.5908i	1.37080	−	0.518355i
$591$	−1.43781	+	2.49036i	−0.0591437	+	0.102440i
$592$	0.428804	−	0.599478i	0.0176237	−	0.0246384i
$593$	−2.67173	+	2.67173i	−0.109715	+	0.109715i	−0.759833	−	0.650118i	$-0.774719\pi$
$593$	−2.67173	+	2.67173i	−0.109715	+	0.109715i	0.650118	+	0.759833i	$0.274719\pi$
$594$	6.30300	+	13.6060i	0.258615	+	0.558261i
$595$	−15.6755	+	13.5583i	−0.642634	+	0.555835i
$596$	−15.7741	−	13.3717i	−0.646132	−	0.547726i
$597$	2.87125	−	2.87125i	0.117512	−	0.117512i
$598$	−23.3073	−	6.80572i	−0.953105	−	0.278307i
$599$	−21.3746			−0.873342			−0.436671	−	0.899621i	$-0.643843\pi$
$599$	−21.3746			−0.873342			−0.436671	+	0.899621i	$0.643843\pi$
$600$	−2.37906	−	3.24068i	−0.0971245	−	0.132300i
$601$	−15.4360	−	26.7359i	−0.629648	−	1.09058i	−0.987622	−	0.156850i	$-0.949866\pi$
$601$	−15.4360	−	26.7359i	−0.629648	−	1.09058i	0.357975	−	0.933731i	$-0.383467\pi$
$602$	−7.74719	+	21.1199i	−0.315752	+	0.860784i
$603$	−18.2871	−	18.2871i	−0.744710	−	0.744710i
$604$	7.53539	−	41.5141i	0.306611	−	1.68919i
$605$	−21.0499	+	60.6433i	−0.855802	+	2.46550i
$606$	0.975958	+	0.687035i	0.0396456	+	0.0279089i
$607$	16.4930	−	4.41929i	0.669430	−	0.179373i	0.0919320	−	0.995765i	$-0.470696\pi$
$607$	16.4930	−	4.41929i	0.669430	−	0.179373i	0.577498	+	0.816392i	$0.304029\pi$
$608$	12.5014	+	2.36666i	0.506998	+	0.0959809i
$609$	0.564058	+	0.976977i	0.0228568	+	0.0395891i
$610$	9.10467	+	24.0775i	0.368637	+	0.974871i
$611$	−22.6474	+	1.53051i	−0.916216	+	0.0619179i
$612$	25.9574	+	12.2634i	1.04927	+	0.495717i
$613$	−45.8255	−	12.2789i	−1.85087	−	0.495940i	−0.851287	−	0.524701i	$-0.824177\pi$
$613$	−45.8255	−	12.2789i	−1.85087	−	0.495940i	−0.999586	+	0.0287607i	$0.990844\pi$
$614$	−2.65841	+	29.5309i	−0.107285	+	1.19177i
$615$	−0.139357	+	0.0675406i	−0.00561941	+	0.00272350i
$616$	−32.3847	−	8.93966i	−1.30482	−	0.360189i
$617$	2.27909	−	0.610680i	0.0917526	−	0.0245850i	−0.212651	−	0.977128i	$-0.568210\pi$
$617$	2.27909	−	0.610680i	0.0917526	−	0.0245850i	0.304403	+	0.952543i	$0.401543\pi$
$618$	1.63792	−	4.46520i	0.0658867	−	0.179617i
$619$			30.0916i			1.20948i	0.796422	+	0.604742i	$0.206724\pi$
$619$			30.0916i			1.20948i	−0.796422	+	0.604742i	$0.793276\pi$
$620$	0.0207505	+	2.08717i	0.000833360	+	0.0838226i
$621$	4.00623	+	6.93900i	0.160765	+	0.278452i
$622$	−8.87620	−	10.6324i	−0.355903	−	0.426320i
$623$	10.9446	−	10.9446i	0.438485	−	0.438485i
$624$	0.942479	+	3.99000i	0.0377294	+	0.159728i
$625$	18.1553	−	17.1868i	0.726211	−	0.687472i
$626$	0.468919	+	0.0422128i	0.0187418	+	0.00168716i
$627$	−1.04279	+	3.89173i	−0.0416449	+	0.155421i
$628$	7.87274	+	11.3646i	0.314157	+	0.453496i
$629$	0.906060			0.0361270
$630$	−10.1573	−	14.1284i	−0.404678	−	0.562888i
$631$	−6.10705	+	10.5777i	−0.243118	+	0.421092i	−0.961601	−	0.274452i	$-0.911503\pi$
$631$	−6.10705	+	10.5777i	−0.243118	+	0.421092i	0.718483	+	0.695545i	$0.244837\pi$
$632$	15.3072	+	26.9805i	0.608886	+	1.07323i
$633$	−1.04608	+	0.280297i	−0.0415780	+	0.0111408i
$634$	−1.49676	−	0.134740i	−0.0594439	−	0.00535122i
$635$	−1.31166	+	18.1106i	−0.0520518	+	0.718698i
$636$	2.85415	−	1.02261i	0.113175	−	0.0405492i
$637$	12.1941	+	2.39987i	0.483148	+	0.0950862i
$638$	18.4848	−	3.21150i	0.731821	−	0.127144i
$639$	27.4431	−	15.8443i	1.08563	−	0.626790i
$640$	−8.59011	−	23.7952i	−0.339554	−	0.940587i
$641$	−10.4256	+	18.0577i	−0.411787	+	0.713236i	−0.995085	−	0.0990221i	$-0.968429\pi$
$641$	−10.4256	+	18.0577i	−0.411787	+	0.713236i	0.583298	+	0.812258i	$0.301762\pi$
$642$	−0.373876	−	2.15197i	−0.0147557	−	0.0849313i
$643$	−20.8135	+	5.57696i	−0.820805	+	0.219934i	−0.644698	−	0.764437i	$-0.723017\pi$
$643$	−20.8135	+	5.57696i	−0.820805	+	0.219934i	−0.176107	+	0.984371i	$0.556350\pi$
$644$	−17.6631	−	3.20609i	−0.696022	−	0.126338i
$645$	−1.01044	−	5.26816i	−0.0397862	−	0.207434i
$646$	6.57450	+	14.1921i	0.258670	+	0.558379i
$647$	4.63727	−	17.3065i	0.182310	−	0.680389i	−0.812881	−	0.582430i	$-0.802102\pi$
$647$	4.63727	−	17.3065i	0.182310	−	0.680389i	0.995190	−	0.0979590i	$-0.0312314\pi$
$648$	−11.8612	+	20.1911i	−0.465951	+	0.793180i
$649$			70.9350i			2.78444i
$650$	−23.8903	+	8.90245i	−0.937055	+	0.349183i
$651$		−	0.250091i		−	0.00980183i
$652$	1.43685	+	17.4319i	0.0562714	+	0.682687i
$653$	−11.9979	+	44.7770i	−0.469516	+	1.75226i	0.171950	+	0.985106i	$0.444993\pi$
$653$	−11.9979	+	44.7770i	−0.469516	+	1.75226i	−0.641466	+	0.767152i	$0.721673\pi$
$654$	0.154465	−	0.0715563i	0.00604007	−	0.00279807i
$655$	0.173413	+	0.904123i	0.00677579	+	0.0353270i
$656$	−0.961359	+	0.159567i	−0.0375347	+	0.00623004i
$657$	42.7285	−	11.4491i	1.66700	−	0.446671i
$658$	−16.5347	+	2.87269i	−0.644590	+	0.111989i
$659$	−22.4349	+	38.8583i	−0.873938	+	1.51370i	−0.0160481	+	0.999871i	$0.505108\pi$
$659$	−22.4349	+	38.8583i	−0.873938	+	1.51370i	−0.857890	+	0.513834i	$0.828225\pi$
$660$	7.71700	−	2.15022i	0.300384	−	0.0836970i
$661$	41.5106	−	23.9662i	1.61458	−	0.932177i	0.626286	−	0.779593i	$-0.284574\pi$
$661$	41.5106	−	23.9662i	1.61458	−	0.932177i	0.988291	−	0.152584i	$-0.0487593\pi$
$662$	−2.08021	−	11.9733i	−0.0808495	−	0.465356i
$663$	−3.31534	+	3.79592i	−0.128757	+	0.147421i
$664$	−2.66135	+	9.64098i	−0.103281	+	0.374142i
$665$	0.684810	−	9.45543i	0.0265558	−	0.366666i
$666$	−0.0682039	+	0.757641i	−0.00264285	+	0.0293580i
$667$	9.68356	−	2.59470i	0.374949	−	0.100467i
$668$	3.83235	−	8.11181i	0.148278	−	0.313855i
$669$	3.62552	−	6.27958i	0.140171	−	0.242783i
$670$	−22.7471	+	16.3536i	−0.878795	+	0.631795i
$671$	−51.2946			−1.98021
$672$	1.00085	+	2.86116i	0.0386086	+	0.110372i
$673$	4.08690	−	15.2525i	0.157538	−	0.587941i	−0.841336	−	0.540512i	$-0.818231\pi$
$673$	4.08690	−	15.2525i	0.157538	−	0.587941i	0.998875	−	0.0474289i	$-0.0151028\pi$
$674$	−3.66901	+	40.7570i	−0.141325	+	1.56990i
$675$	7.72800	+	3.32578i	0.297451	+	0.128009i
$676$	25.9741	+	1.15932i	0.999005	+	0.0445893i
$677$	13.2971	−	13.2971i	0.511050	−	0.511050i	−0.403798	−	0.914848i	$-0.632310\pi$
$677$	13.2971	−	13.2971i	0.511050	−	0.511050i	0.914848	+	0.403798i	$0.132310\pi$
$678$	1.68534	−	1.40696i	0.0647250	−	0.0540341i
$679$	8.48018	+	14.6881i	0.325439	+	0.563678i
$680$	17.6480	−	25.6067i	0.676770	−	0.981973i
$681$		−	1.76172i		−	0.0675094i
$682$	−3.90485	−	1.43237i	−0.149524	−	0.0548483i
$683$	21.0811	−	5.64867i	0.806647	−	0.216140i	0.168147	−	0.985762i	$-0.446222\pi$
$683$	21.0811	−	5.64867i	0.806647	−	0.216140i	0.638500	+	0.769622i	$0.279555\pi$
$684$	−12.3622	+	4.42924i	−0.472681	+	0.169356i
$685$	−3.56091	+	1.72583i	−0.136056	+	0.0659406i
$686$	27.7366	+	2.49689i	1.05899	+	0.0953317i
$687$	3.22768	+	0.864855i	0.123144	+	0.0329963i
$688$	3.27987	−	33.5960i	0.125044	−	1.28084i
$689$	−1.29641	−	19.1833i	−0.0493893	−	0.730826i
$690$	4.00389	−	1.51403i	0.152426	−	0.0576382i
$691$	−12.5467	−	21.7315i	−0.477297	−	0.826703i	0.522364	−	0.852723i	$-0.325050\pi$
$691$	−12.5467	−	21.7315i	−0.477297	−	0.826703i	−0.999661	+	0.0260191i	$0.991717\pi$
$692$	0.899537	+	10.9132i	0.0341953	+	0.414858i
$693$	33.4925	−	8.97429i	1.27227	−	0.340905i
$694$	−4.09435	+	5.81618i	−0.155419	+	0.220779i
$695$	11.1394	−	32.0919i	0.422542	−	1.21731i
$696$	−1.18791	−	1.20595i	−0.0450274	−	0.0457115i
$697$	−0.847091	−	0.847091i	−0.0320859	−	0.0320859i
$698$	13.4732	+	4.94221i	0.509967	+	0.187065i
$699$	−3.92156	−	6.79234i	−0.148327	−	0.256910i
$700$	−16.8799	+	8.38922i	−0.637999	+	0.317083i
$701$	−9.01667			−0.340555			−0.170277	−	0.985396i	$-0.554466\pi$
$701$	−9.01667			−0.340555			−0.170277	+	0.985396i	$0.554466\pi$
$702$	−5.93008	−	6.20066i	−0.223816	−	0.234029i
$703$	−0.293058	+	0.293058i	−0.0110529	+	0.0110529i
$704$	50.4056	+	0.760070i	1.89973	+	0.0286462i
$705$	3.02670	−	2.61789i	0.113992	−	0.0985953i
$706$	−11.1511	+	5.16576i	−0.419676	+	0.194416i
$707$	3.95708	−	3.95708i	0.148821	−	0.148821i
$708$	5.26100	−	3.64452i	0.197720	−	0.136970i
$709$	18.0836	−	31.3217i	0.679143	−	1.17631i	−0.296097	−	0.955158i	$-0.595685\pi$
$709$	18.0836	−	31.3217i	0.679143	−	1.17631i	0.975239	−	0.221152i	$-0.0709817\pi$
$710$	−12.1415	−	32.1084i	−0.455661	−	1.20501i
$711$	−27.7264	−	16.0078i	−1.03982	−	0.600341i
$712$	−11.7638	+	20.0254i	−0.440868	+	0.750482i
$713$	−2.14674	−	0.575217i	−0.0803960	−	0.0215420i
$714$	−2.14493	+	3.04695i	−0.0802720	+	0.114029i
$715$	0.244945	−	50.8031i	0.00916043	−	1.89993i
$716$	−41.3048	+	14.7991i	−1.54363	+	0.553066i
$717$	−1.50390	+	5.61263i	−0.0561642	+	0.209608i
$718$	11.5073	+	13.7841i	0.429449	+	0.514417i
$719$	−0.271229	+	0.469782i	−0.0101151	+	0.0175199i	−0.871039	−	0.491214i	$-0.836553\pi$
$719$	−0.271229	+	0.469782i	−0.0101151	+	0.0175199i	0.860924	+	0.508734i	$0.169886\pi$
$720$	20.0837	+	16.6847i	0.748475	+	0.621801i
$721$	−19.3126	−	11.1501i	−0.719238	−	0.415252i
$722$	18.5096	+	6.78968i	0.688858	+	0.252686i
$723$	−3.35422	−	3.35422i	−0.124745	−	0.124745i
$724$	0.389840	−	2.14771i	0.0144883	−	0.0798192i
$725$	6.52200	−	8.26277i	0.242221	−	0.306872i
$726$	−1.03476	+	11.4946i	−0.0384037	+	0.426606i
$727$	−24.5974	−	24.5974i	−0.912267	−	0.912267i	0.0841836	−	0.996450i	$-0.473172\pi$
$727$	−24.5974	−	24.5974i	−0.912267	−	0.912267i	−0.996450	+	0.0841836i	$0.973172\pi$
$728$	19.1884	−	1.15150i	0.711170	−	0.0426775i
$729$		−	22.7337i		−	0.841989i
$730$	−4.77066	−	47.6814i	−0.176570	−	1.76477i
$731$	35.9366	−	20.7480i	1.32916	−	0.767392i
$732$	2.63543	+	3.80434i	0.0974084	+	0.140612i
$733$	−10.0930	+	10.0930i	−0.372792	+	0.372792i	−0.868493	−	0.495701i	$-0.834911\pi$
$733$	−10.0930	+	10.0930i	−0.372792	+	0.372792i	0.495701	+	0.868493i	$0.334911\pi$
$734$	4.99989	+	10.7930i	0.184549	+	0.398378i
$735$	−1.97166	+	0.955583i	−0.0727258	+	0.0352472i
$736$	26.8617	−	2.01035i	0.990137	−	0.0741026i
$737$	−14.4488	−	53.9238i	−0.532230	−	1.98631i
$738$	0.772097	−	0.644567i	0.0284213	−	0.0237268i
$739$	7.40502	−	4.27529i	0.272398	−	0.157269i	−0.357579	−	0.933883i	$-0.616398\pi$
$739$	7.40502	−	4.27529i	0.272398	−	0.157269i	0.629977	+	0.776614i	$0.283064\pi$
$740$	0.798052	+	0.205356i	0.0293370	+	0.00754904i
$741$	−0.155440	−	2.30008i	−0.00571021	−	0.0844956i
$742$	−2.43329	−	14.0056i	−0.0893290	−	0.514162i
$743$	4.46180	−	16.6517i	0.163688	−	0.610890i	−0.834516	−	0.550983i	$-0.814253\pi$
$743$	4.46180	−	16.6517i	0.163688	−	0.610890i	0.998204	−	0.0599072i	$-0.0190805\pi$
$744$	0.0943907	+	0.363202i	0.00346053	+	0.0133156i
$745$	7.58142	−	21.8415i	0.277762	−	0.800211i
$746$	−7.09084	+	10.0728i	−0.259614	+	0.368791i
$747$	−2.67166	−	9.97078i	−0.0977510	−	0.364812i
$748$	35.2894	+	50.9415i	1.29031	+	1.86260i
$749$	−10.2412			−0.374204
$750$	2.41972	−	3.78779i	0.0883556	−	0.138311i
$751$	−19.8808	+	11.4782i	−0.725459	+	0.418844i	−0.816759	−	0.576979i	$-0.804231\pi$
$751$	−19.8808	+	11.4782i	−0.725459	+	0.418844i	0.0912996	+	0.995823i	$0.470898\pi$
$752$	22.9288	−	10.4126i	0.836127	−	0.379708i
$753$	−3.54328	−	3.54328i	−0.129124	−	0.129124i
$754$	−9.41425	+	5.15889i	−0.342847	+	0.187876i
$755$	46.3281	−	8.88583i	1.68605	−	0.323388i
$756$	−4.83882	−	4.10187i	−0.175986	−	0.149184i
$757$	−5.34108	−	1.43114i	−0.194125	−	0.0520156i	0.160447	−	0.987045i	$-0.448707\pi$
$757$	−5.34108	−	1.43114i	−0.194125	−	0.0520156i	−0.354571	+	0.935029i	$0.615373\pi$
$758$	−9.29917	+	25.3508i	−0.337761	+	0.920784i
$759$			8.52986i			0.309614i
$760$	2.57419	+	13.9904i	0.0933755	+	0.507485i
$761$	4.86978	+	2.81157i	0.176529	+	0.101919i	0.585661	−	0.810556i	$-0.300835\pi$
$761$	4.86978	+	2.81157i	0.176529	+	0.101919i	−0.409132	+	0.912475i	$0.634168\pi$
$762$	0.558812	+	3.21642i	0.0202436	+	0.116519i
$763$	−0.206586	−	0.770988i	−0.00747890	−	0.0279116i
$764$	5.88449	−	6.94171i	0.212894	−	0.251142i
$765$	−2.31856	+	32.0132i	−0.0838278	+	1.15744i
$766$	17.8725	−	25.3885i	0.645759	−	0.917325i
$767$	−13.1244	−	38.4071i	−0.473893	−	1.38680i
$768$	−2.53339	−	3.77746i	−0.0914157	−	0.136307i
$769$	17.7196	+	30.6912i	0.638984	+	1.10675i	0.985656	+	0.168766i	$0.0539783\pi$
$769$	17.7196	+	30.6912i	0.638984	+	1.10675i	−0.346672	+	0.937986i	$0.612688\pi$
$770$	−3.73945	−	37.3748i	−0.134761	−	1.34689i
$771$	−0.443966	−	0.256324i	−0.0159890	−	0.00923128i
$772$	0.953284	−	2.01778i	0.0343094	−	0.0726216i
$773$	4.25688	+	15.8869i	0.153109	+	0.571411i	0.999260	+	0.0384675i	$0.0122476\pi$
$773$	4.25688	+	15.8869i	0.153109	+	0.571411i	−0.846151	+	0.532944i	$0.821086\pi$
$774$	14.6442	+	31.6117i	0.526374	+	1.13626i
$775$	−2.16803	+	0.863429i	−0.0778779	+	0.0310153i
$776$	−17.8593	−	18.1306i	−0.641110	−	0.650850i
$777$	−0.0953711	−	0.0255546i	−0.00342142	−	0.000916766i
$778$	14.9213	+	17.8736i	0.534955	+	0.640798i
$779$	0.547969			0.0196330
$780$	−3.78047	+	2.59201i	−0.135363	+	0.0928089i
$781$	68.4035			2.44767
$782$	21.2212	+	25.4198i	0.758867	+	0.909012i
$783$	3.42182	+	0.916873i	0.122286	+	0.0327664i
$784$	−13.6016	+	2.25760i	−0.485770	+	0.0806284i
$785$	−8.67524	+	12.7929i	−0.309633	+	0.456597i
$786$	0.0695719	+	0.150182i	0.00248155	+	0.00535680i
$787$	3.26213	+	12.1744i	0.116282	+	0.433972i	0.999380	−	0.0352180i	$-0.0112125\pi$
$787$	3.26213	+	12.1744i	0.116282	+	0.433972i	−0.883097	+	0.469190i	$0.844546\pi$
$788$	−18.2929	−	8.64230i	−0.651657	−	0.307869i
$789$	1.41538	+	0.817172i	0.0503890	+	0.0290921i
$790$	−21.9604	+	26.8433i	−0.781315	+	0.955042i
$791$	−5.14690	−	8.91469i	−0.183003	−	0.316970i
$792$	−45.2533	+	25.6741i	−1.60801	+	0.912289i
$793$	27.7730	−	9.49051i	0.986248	−	0.337018i
$794$	22.9597	−	32.6152i	0.814811	−	1.15747i
$795$	2.21746	+	2.56374i	0.0786453	+	0.0909265i
$796$	21.7920	+	18.4731i	0.772397	+	0.654762i
$797$	−1.43277	−	5.34717i	−0.0507513	−	0.189406i	0.935896	−	0.352275i	$-0.114592\pi$
$797$	−1.43277	−	5.34717i	−0.0507513	−	0.189406i	−0.986648	+	0.162869i	$0.947925\pi$
$798$	−0.291752	−	1.67927i	−0.0103279	−	0.0594456i
$799$	26.8093	+	15.4783i	0.948444	+	0.547585i
$800$	21.3480	−	18.5544i	0.754764	−	0.655996i
$801$		−	23.9703i		−	0.846950i
$802$	2.10160	−	5.72927i	0.0742102	−	0.202308i
$803$	92.2346	+	24.7142i	3.25489	+	0.872145i
$804$	−3.25698	+	3.84214i	−0.114865	+	0.135502i
$805$	−3.78066	−	19.7113i	−0.133251	−	0.694732i
$806$	2.37926	+	0.0530711i	0.0838059	+	0.00186935i
$807$	−3.93394	−	3.93394i	−0.138481	−	0.138481i
$808$	−4.25328	+	7.24028i	−0.149630	+	0.254712i
$809$	16.6728	−	9.62607i	0.586186	−	0.338435i	−0.177402	−	0.984138i	$-0.556769\pi$
$809$	16.6728	−	9.62607i	0.586186	−	0.338435i	0.763588	+	0.645704i	$0.223436\pi$
$810$	−25.8381	−	4.22486i	−0.907860	−	0.148446i
$811$	−31.9905			−1.12334			−0.561670	−	0.827362i	$-0.689841\pi$
$811$	−31.9905			−1.12334			−0.561670	+	0.827362i	$0.689841\pi$
$812$	−6.52434	+	4.51970i	−0.228960	+	0.158610i
$813$	1.70264	+	6.35435i	0.0597143	+	0.222857i
$814$	−0.945231	+	1.34273i	−0.0331303	+	0.0470628i
$815$	−17.5977	+	8.52888i	−0.616420	+	0.298754i
$816$	1.96504	−	5.23458i	0.0687902	−	0.183247i
$817$	−4.91262	+	18.3341i	−0.171871	+	0.641431i
$818$	−6.49660	−	37.3933i	−0.227148	−	1.30743i
$819$	−16.4738	+	11.0558i	−0.575641	+	0.386322i
$820$	−0.554122	−	0.938104i	−0.0193508	−	0.0327600i
$821$	43.7792	−	25.2759i	1.52791	−	0.882136i	0.528456	−	0.848961i	$-0.322771\pi$
$821$	43.7792	−	25.2759i	1.52791	−	0.882136i	0.999450	−	0.0331756i	$-0.0105620\pi$
$822$	−0.546142	+	0.455933i	−0.0190489	+	0.0159025i
$823$	−12.3623	−	46.1367i	−0.430923	−	1.60823i	−0.750639	−	0.660713i	$-0.770254\pi$
$823$	−12.3623	−	46.1367i	−0.430923	−	1.60823i	0.319716	−	0.947513i	$-0.396412\pi$
$824$	32.2556	+	8.90403i	1.12368	+	0.310187i
$825$	5.35455	+	7.17971i	0.186421	+	0.249966i
$826$	−12.6136	−	27.2284i	−0.438884	−	0.947398i
$827$	−28.1563	+	28.1563i	−0.979090	+	0.979090i	−0.999786	−	0.0206962i	$-0.993412\pi$
$827$	−28.1563	+	28.1563i	−0.979090	+	0.979090i	0.0206962	+	0.999786i	$0.493412\pi$
$828$	−22.8533	+	15.8315i	−0.794208	+	0.550182i
$829$	−22.6037	+	13.0502i	−0.785058	+	0.453253i	−0.838220	−	0.545333i	$-0.816403\pi$
$829$	−22.6037	+	13.0502i	−0.785058	+	0.453253i	0.0531621	+	0.998586i	$0.483070\pi$
$830$	−11.1265	+	1.11324i	−0.386208	+	0.0386412i
$831$			1.13454i			0.0393567i
$832$	−27.4323	+	8.91450i	−0.951044	+	0.309055i
$833$	−11.9849	−	11.9849i	−0.415252	−	0.415252i
$834$	0.547587	−	6.08285i	0.0189614	−	0.210632i
$835$	10.0043	+	0.724561i	0.346212	+	0.0250745i
$836$	−27.8907	−	5.06254i	−0.964619	−	0.175092i
$837$	−0.555319	−	0.555319i	−0.0191946	−	0.0191946i
$838$	−31.0259	−	11.3809i	−1.07177	−	0.393146i
$839$	−25.6440	−	14.8056i	−0.885330	−	0.511146i	−0.0129182	−	0.999917i	$-0.504112\pi$
$839$	−25.6440	−	14.8056i	−0.885330	−	0.511146i	−0.872412	+	0.488771i	$0.837445\pi$
$840$	−2.57983	+	2.19760i	−0.0890125	+	0.0758243i
$841$	−12.2838	+	21.2762i	−0.423579	+	0.733661i
$842$	−12.2246	−	14.6433i	−0.421288	−	0.504641i
$843$	1.28128	−	4.78178i	0.0441295	−	0.164693i
$844$	−2.56997	−	7.17289i	−0.0884619	−	0.246901i
$845$	9.26695	+	27.5522i	0.318793	+	0.947824i
$846$	−14.9610	+	21.2526i	−0.514369	+	0.730680i
$847$	52.2695	+	14.0056i	1.79600	+	0.481237i
$848$	8.81990	+	19.4217i	0.302876	+	0.666943i
$849$	−4.54679	−	2.62509i	−0.156045	−	0.0900929i
$850$	33.8192	+	8.07486i	1.15999	+	0.276965i
$851$	−0.438713	+	0.759874i	−0.0150389	+	0.0260481i
$852$	−3.51446	−	5.07325i	−0.120403	−	0.173807i
$853$	6.14594	−	6.14594i	0.210433	−	0.210433i	−0.594019	−	0.804451i	$-0.702459\pi$
$853$	6.14594	−	6.14594i	0.210433	−	0.210433i	0.804451	+	0.594019i	$0.202459\pi$
$854$	19.6895	−	9.12118i	0.673760	−	0.312120i
$855$	−9.60450	−	11.1043i	−0.328467	−	0.379760i
$856$	14.8730	−	3.86528i	0.508350	−	0.132112i
$857$	4.25016	−	4.25016i	0.145183	−	0.145183i	−0.630779	−	0.775962i	$-0.717265\pi$
$857$	4.25016	−	4.25016i	0.145183	−	0.145183i	0.775962	+	0.630779i	$0.217265\pi$
$858$	−2.16669	−	8.87320i	−0.0739697	−	0.302926i
$859$	−8.13036			−0.277404			−0.138702	−	0.990334i	$-0.544293\pi$
$859$	−8.13036			−0.277404			−0.138702	+	0.990334i	$0.544293\pi$
$860$	36.3552	−	10.1298i	1.23970	−	0.345422i
$861$	0.0652726	+	0.113056i	0.00222449	+	0.00385292i
$862$	22.6672	+	8.31474i	0.772047	+	0.283201i
$863$	7.04244	+	7.04244i	0.239727	+	0.239727i	0.816737	−	0.577010i	$-0.195781\pi$
$863$	7.04244	+	7.04244i	0.239727	+	0.239727i	−0.577010	+	0.816737i	$0.695781\pi$
$864$	8.57547	+	4.13077i	0.291743	+	0.140532i
$865$	−11.0170	+	5.33949i	−0.374589	+	0.181548i
$866$	7.15262	−	10.1606i	0.243056	−	0.345270i
$867$	1.97121	−	0.528184i	0.0669458	−	0.0179381i
$868$	1.75358	−	0.144541i	0.0595204	−	0.00490605i
$869$	−34.5548	−	59.8508i	−1.17219	−	2.03030i
$870$	0.778408	−	1.72507i	0.0263905	−	0.0584855i
$871$	17.8002	+	26.5233i	0.603136	+	0.898706i
$872$	0.591011	+	1.04172i	0.0200141	+	0.0352771i
$873$	25.3710	+	6.79815i	0.858680	+	0.230083i
$874$	−15.0856	−	1.35803i	−0.510280	−	0.0459361i
$875$	−15.5558	−	14.2180i	−0.525883	−	0.480656i
$876$	−2.90590	−	8.11049i	−0.0981812	−	0.274028i
$877$	13.7419	−	3.68213i	0.464030	−	0.124337i	−0.0192266	−	0.999815i	$-0.506120\pi$
$877$	13.7419	−	3.68213i	0.464030	−	0.124337i	0.483257	+	0.875479i	$0.339454\pi$
$878$	−16.4396	−	6.03035i	−0.554810	−	0.203515i
$879$			3.54728i			0.119647i
$880$	19.5369	+	52.8672i	0.658589	+	1.78215i
$881$	−12.3044	−	21.3119i	−0.414546	−	0.718015i	0.580835	−	0.814022i	$-0.302726\pi$
$881$	−12.3044	−	21.3119i	−0.414546	−	0.718015i	−0.995381	+	0.0960067i	$0.969393\pi$
$882$	10.9238	−	9.11951i	0.367825	−	0.307070i
$883$	−15.4583	+	15.4583i	−0.520212	+	0.520212i	−0.917635	−	0.397423i	$-0.869904\pi$
$883$	−15.4583	+	15.4583i	−0.520212	+	0.520212i	0.397423	+	0.917635i	$0.369904\pi$
$884$	−28.5323	−	21.0526i	−0.959645	−	0.708075i
$885$	5.92219	+	4.01602i	0.199072	+	0.134997i
$886$	2.46556	−	27.3886i	0.0828321	−	0.920137i
$887$	−10.6021	+	39.5677i	−0.355985	+	1.32855i	0.523255	+	0.852176i	$0.324717\pi$
$887$	−10.6021	+	39.5677i	−0.355985	+	1.32855i	−0.879240	+	0.476378i	$0.841949\pi$
$888$	0.148150	+	0.00111692i	0.00497160	+	3.74815e-5i
$889$	15.3069			0.513377
$890$	−25.6261	−	4.19018i	−0.858988	−	0.140455i
$891$	26.0855	−	45.1814i	0.873897	−	1.51363i
$892$	46.1264	+	21.7920i	1.54443	+	0.729650i
$893$	−13.6776	+	3.66490i	−0.457703	+	0.122641i
$894$	0.372684	−	4.13995i	0.0124644	−	0.138461i
$895$	−32.0907	−	37.1020i	−1.07267	−	1.24018i
$896$	−19.4834	+	8.67135i	−0.650894	+	0.289690i
$897$	−1.57819	−	4.61842i	−0.0526943	−	0.154205i
$898$	2.37576	+	13.6745i	0.0792802	+	0.456323i
$899$	−0.850968	+	0.491307i	−0.0283814	+	0.0163860i
$900$	−9.29790	+	27.6716i	−0.309930	+	0.922386i
$901$	−13.1108	+	22.7086i	−0.436785	+	0.756533i
$902$	2.13906	−	0.371634i	0.0712229	−	0.0123740i
$903$	−4.36783	+	1.17036i	−0.145352	+	0.0389470i
$904$	10.8394	+	11.0040i	0.360512	+	0.365989i
$905$	2.39677	−	0.459704i	0.0796712	−	0.0152811i
$906$	7.69546	−	3.56493i	0.255664	−	0.118437i
$907$	5.49734	−	20.5163i	0.182536	−	0.681234i	−0.812609	−	0.582810i	$-0.801953\pi$
$907$	5.49734	−	20.5163i	0.182536	−	0.681234i	0.995145	−	0.0984239i	$-0.0313801\pi$
$908$	12.3528	−	1.01820i	0.409943	−	0.0337901i
$909$		−	8.66660i		−	0.287453i
$910$	8.93976	+	19.5444i	0.296350	+	0.647889i
$911$			26.1821i			0.867452i	0.901045	+	0.433726i	$0.142801\pi$
$911$			26.1821i			0.867452i	−0.901045	+	0.433726i	$0.857199\pi$
$912$	1.05751	+	2.32866i	0.0350175	+	0.0771096i
$913$	5.76710	−	21.5231i	0.190863	−	0.712311i
$914$	−15.3548	−	33.1456i	−0.507891	−	1.09636i
$915$	−2.90407	+	4.28246i	−0.0960057	+	0.141574i
$916$	−4.19871	+	23.1316i	−0.138729	+	0.764291i
$917$	0.749608	−	0.200857i	0.0247542	−	0.00663287i
$918$	2.00291	+	11.5284i	0.0661059	+	0.380494i
$919$	24.4173	−	42.2920i	0.805452	−	1.39508i	−0.110534	−	0.993872i	$-0.535256\pi$
$919$	24.4173	−	42.2920i	0.805452	−	1.39508i	0.915986	−	0.401211i	$-0.131411\pi$
$920$	12.9301	+	27.1994i	0.426294	+	0.896737i
$921$	−5.16151	+	2.98000i	−0.170077	+	0.0981942i
$922$	43.6743	−	7.58784i	1.43834	−	0.249892i
$923$	−37.0365	+	12.6560i	−1.21907	+	0.416577i
$924$	−2.27777	−	6.35736i	−0.0749332	−	0.209142i
$925$	0.107733	+	0.914996i	0.00354223	+	0.0300849i
$926$	−3.84712	−	0.346324i	−0.126424	−	0.0113809i
$927$	−33.3590	+	8.93852i	−1.09565	+	0.293580i
$928$	7.76932	−	9.02631i	0.255040	−	0.296303i
$929$	−7.16013	+	12.4017i	−0.234916	+	0.406887i	−0.959248	−	0.282565i	$-0.908815\pi$
$929$	−7.16013	+	12.4017i	−0.234916	+	0.406887i	0.724332	+	0.689451i	$0.242148\pi$
$930$	−0.340660	+	0.244912i	−0.0111707	+	0.00803098i
$931$	7.75282			0.254089
$932$	45.3599	−	31.4228i	1.48581	−	1.02929i
$933$	0.720570	−	2.68920i	0.0235904	−	0.0880406i
$934$	−15.3812	−	1.38464i	−0.503289	−	0.0453068i
$935$	−38.8866	+	57.3437i	−1.27173	+	1.87534i
$936$	19.7518	−	22.2738i	0.645608	−	0.728041i
$937$	−22.2266	+	22.2266i	−0.726110	+	0.726110i	−0.969843	−	0.243732i	$-0.921628\pi$
$937$	−22.2266	+	22.2266i	−0.726110	+	0.726110i	0.243732	+	0.969843i	$0.421628\pi$
$938$	15.1349	+	18.1294i	0.494172	+	0.591946i
$939$	0.0473192	+	0.0819592i	0.00154420	+	0.00267464i
$940$	20.1053	+	19.7095i	0.655764	+	0.642853i
$941$			54.7980i			1.78636i	0.449696	+	0.893182i	$0.351532\pi$
$941$			54.7980i			1.78636i	−0.449696	+	0.893182i	$0.648468\pi$
$942$	−0.957026	+	2.60899i	−0.0311816	+	0.0850055i
$943$	1.12058	−	0.300258i	0.0364911	−	0.00977776i
$944$	28.5952	+	34.7826i	0.930695	+	1.13208i
$945$	2.32566	−	6.70006i	0.0756537	−	0.217953i
$946$	−6.74271	+	74.9011i	−0.219224	+	2.43525i
$947$	−24.9758	−	6.69226i	−0.811606	−	0.217469i	−0.170933	−	0.985283i	$-0.554678\pi$
$947$	−24.9758	−	6.69226i	−0.811606	−	0.217469i	−0.640673	+	0.767814i	$0.721345\pi$
$948$	−2.66355	+	5.63785i	−0.0865081	+	0.183109i
$949$	−54.5122	+	3.68394i	−1.76954	+	0.119586i
$950$	−13.5503	+	8.32681i	−0.439630	+	0.270157i
$951$	−0.151040	−	0.261608i	−0.00489780	−	0.00848323i
$952$	−22.6042	−	13.2788i	−0.732608	−	0.430368i
$953$	40.4013	−	10.8255i	1.30873	−	0.350672i	0.463984	−	0.885844i	$-0.346420\pi$
$953$	40.4013	−	10.8255i	1.30873	−	0.350672i	0.844744	+	0.535171i	$0.179753\pi$
$954$	−18.0019	−	12.6726i	−0.582832	−	0.410290i
$955$	9.61182	+	3.33636i	0.311031	+	0.107962i
$956$	−40.2237	−	7.30117i	−1.30093	−	0.236137i
$957$	2.66670	+	2.66670i	0.0862022	+	0.0862022i
$958$	−5.86749	+	15.9956i	−0.189570	+	0.516795i
$959$	1.66788	+	2.88885i	0.0538586	+	0.0932858i
$960$	2.91720	−	4.16522i	0.0941522	−	0.134432i
$961$	−30.7822			−0.992973
$962$	0.263354	−	0.901898i	0.00849089	−	0.0290784i
$963$	−11.2149	+	11.2149i	−0.361394	+	0.361394i
$964$	21.5805	−	25.4577i	0.695060	−	0.819936i
$965$	2.48853	+	0.180232i	0.0801085	+	0.00580187i
$966$	−1.51678	−	3.27419i	−0.0488015	−	0.105345i
$967$	12.8865	−	12.8865i	0.414401	−	0.414401i	−0.468867	−	0.883269i	$-0.655338\pi$
$967$	12.8865	−	12.8865i	0.414401	−	0.414401i	0.883269	+	0.468867i	$0.155338\pi$
$968$	−81.1959	−	0.612145i	−2.60973	−	0.0196751i
$969$	−1.57199	+	2.72276i	−0.0504995	+	0.0874677i
$970$	11.7028	−	25.9352i	0.375753	−	0.832728i
$971$	16.2472	+	9.38032i	0.521397	+	0.301029i	0.737506	−	0.675340i	$-0.236003\pi$
$971$	16.2472	+	9.38032i	0.521397	+	0.301029i	−0.216109	+	0.976369i	$0.569337\pi$
$972$	−14.7530	+	1.21603i	−0.473201	+	0.0390043i
$973$	−27.6605	−	7.41160i	−0.886754	−	0.237605i
$974$	−27.9487	−	19.6748i	−0.895536	−	0.630421i
$975$	−4.22756	−	2.89670i	−0.135390	−	0.0927685i
$976$	−25.1520	+	20.6778i	−0.805097	+	0.661880i
$977$	1.33886	−	4.99669i	0.0428339	−	0.159858i	−0.941196	−	0.337860i	$-0.890297\pi$
$977$	1.33886	−	4.99669i	0.0428339	−	0.159858i	0.984030	+	0.178002i	$0.0569635\pi$
$978$	−2.69898	+	2.25318i	−0.0863038	+	0.0720487i
$979$	25.8714	−	44.8106i	0.826853	−	1.43215i
$980$	−7.83987	−	13.2726i	−0.250435	−	0.423976i
$981$	−1.07052	−	0.618064i	−0.0341790	−	0.0197333i
$982$	19.8031	−	53.9861i	0.631943	−	1.72277i
$983$	35.4602	+	35.4602i	1.13100	+	1.13100i	0.990011	+	0.140993i	$0.0450295\pi$
$983$	35.4602	+	35.4602i	1.13100	+	1.13100i	0.140993	+	0.990011i	$0.454970\pi$
$984$	−0.137464	−	0.139553i	−0.00438220	−	0.00444877i
$985$	1.63395	−	22.5605i	0.0520620	−	0.718839i
$986$	14.5814	+	1.31264i	0.464367	+	0.0418030i
$987$	−2.38537	−	2.38537i	−0.0759272	−	0.0759272i
$988$	16.0378	−	2.41925i	0.510231	−	0.0769667i
$989$			40.1846i			1.27780i
$990$	−45.0232	−	36.8332i	−1.43093	−	1.17064i
$991$	−4.96318	+	2.86549i	−0.157661	+	0.0910254i	−0.576755	−	0.816917i	$-0.695681\pi$
$991$	−4.96318	+	2.86549i	−0.157661	+	0.0910254i	0.419094	+	0.907943i	$0.362348\pi$
$992$	−2.49214	+	0.871761i	−0.0791254	+	0.0276784i
$993$	1.72732	−	1.72732i	0.0548149	−	0.0548149i
$994$	−26.2567	+	12.1635i	−0.832813	+	0.385802i
$995$	−10.4738	+	30.1742i	−0.332041	+	0.956587i
$996$	−1.89260	+	0.678097i	−0.0599693	+	0.0214863i
$997$	11.2182	+	41.8669i	0.355284	+	1.32594i	0.880127	+	0.474738i	$0.157457\pi$
$997$	11.2182	+	41.8669i	0.355284	+	1.32594i	−0.524843	+	0.851199i	$0.675876\pi$
$998$	−2.92556	−	3.50439i	−0.0926070	−	0.110930i
$999$	−0.268512	+	0.155025i	−0.00849533	+	0.00490478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bg.c.23.9	✓	144
4.3	odd	2	inner	260.2.bg.c.23.22	yes	144
5.2	odd	4	inner	260.2.bg.c.127.12	yes	144
13.4	even	6	inner	260.2.bg.c.43.4	yes	144
20.7	even	4	inner	260.2.bg.c.127.4	yes	144
52.43	odd	6	inner	260.2.bg.c.43.12	yes	144
65.17	odd	12	inner	260.2.bg.c.147.22	yes	144
260.147	even	12	inner	260.2.bg.c.147.9	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bg.c.23.9	✓	144	1.1	even	1	trivial
260.2.bg.c.23.22	yes	144	4.3	odd	2	inner
260.2.bg.c.43.4	yes	144	13.4	even	6	inner
260.2.bg.c.43.12	yes	144	52.43	odd	6	inner
260.2.bg.c.127.4	yes	144	20.7	even	4	inner
260.2.bg.c.127.12	yes	144	5.2	odd	4	inner
260.2.bg.c.147.9	yes	144	260.147	even	12	inner
260.2.bg.c.147.22	yes	144	65.17	odd	12	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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08563 + 0.906314i) q^{2} +(-0.274584 - 0.0735746i) q^{3} +(0.357191 - 1.96785i) q^{4} +(2.19604 - 0.421205i) q^{5} +(0.364779 - 0.168984i) q^{6} +(-0.487864 - 1.82073i) q^{7} +(1.39571 + 2.46008i) q^{8} +(-2.52809 - 1.45960i) q^{9} +O(q^{10})\)	\(q+(-1.08563 + 0.906314i) q^{2} +(-0.274584 - 0.0735746i) q^{3} +(0.357191 - 1.96785i) q^{4} +(2.19604 - 0.421205i) q^{5} +(0.364779 - 0.168984i) q^{6} +(-0.487864 - 1.82073i) q^{7} +(1.39571 + 2.46008i) q^{8} +(-2.52809 - 1.45960i) q^{9} +(-2.00235 + 2.44757i) q^{10} +(-3.15071 - 5.45719i) q^{11} +(-0.242862 + 0.514059i) q^{12} +(2.71561 + 2.37180i) q^{13} +(2.17980 + 1.53449i) q^{14} +(-0.633987 - 0.0459166i) q^{15} +(-3.74483 - 1.40579i) q^{16} +(-1.27267 - 4.74965i) q^{17} +(4.06743 - 0.706663i) q^{18} +(1.94787 + 1.12460i) q^{19} +(-0.0444596 - 4.47191i) q^{20} +0.535839i q^{21} +(8.36644 + 3.06897i) q^{22} +(4.59956 + 1.23245i) q^{23} +(-0.202239 - 0.778188i) q^{24} +(4.64517 - 1.84996i) q^{25} +(-5.09775 - 0.113709i) q^{26} +(1.18981 + 1.18981i) q^{27} +(-3.75718 + 0.309691i) q^{28} +(1.82327 - 1.05266i) q^{29} +(0.729891 - 0.524743i) q^{30} -0.466728 q^{31} +(5.33959 - 1.86782i) q^{32} +(0.463624 + 1.73027i) q^{33} +(5.68632 + 4.00294i) q^{34} +(-1.83827 - 3.79291i) q^{35} +(-3.77527 + 4.45354i) q^{36} +(-0.0476908 + 0.177985i) q^{37} +(-3.13391 + 0.544477i) q^{38} +(-0.571159 - 0.851059i) q^{39} +(4.10122 + 4.81456i) q^{40} +(0.210988 - 0.121814i) q^{41} +(-0.485638 - 0.581724i) q^{42} +(2.18416 + 8.15138i) q^{43} +(-11.8643 + 4.25085i) q^{44} +(-6.16658 - 2.14048i) q^{45} +(-6.11041 + 2.83066i) q^{46} +(-4.45165 + 4.45165i) q^{47} +(0.924840 + 0.661533i) q^{48} +(2.98512 - 1.72346i) q^{49} +(-3.36630 + 6.21836i) q^{50} +1.39782i q^{51} +(5.63734 - 4.49672i) q^{52} +(-3.77074 - 3.77074i) q^{53} +(-2.37004 - 0.213355i) q^{54} +(-9.21767 - 10.6571i) q^{55} +(3.79824 - 3.74140i) q^{56} +(-0.452112 - 0.452112i) q^{57} +(-1.02535 + 2.79525i) q^{58} +(-9.74883 - 5.62849i) q^{59} +(-0.316811 + 1.23119i) q^{60} +(4.07008 - 7.04959i) q^{61} +(0.506694 - 0.423002i) q^{62} +(-1.42417 + 5.31507i) q^{63} +(-4.10400 + 6.86711i) q^{64} +(6.96260 + 4.06475i) q^{65} +(-2.07149 - 1.45825i) q^{66} +(8.55741 + 2.29295i) q^{67} +(-9.80117 + 0.807875i) q^{68} +(-1.17229 - 0.676821i) q^{69} +(5.43325 + 2.45166i) q^{70} +(-5.42763 + 9.40093i) q^{71} +(0.0622465 - 8.25648i) q^{72} +(-10.7151 + 10.7151i) q^{73} +(-0.109535 - 0.236449i) q^{74} +(-1.41160 + 0.166204i) q^{75} +(2.90881 - 3.43141i) q^{76} +(-8.39897 + 8.39897i) q^{77} +(1.39140 + 0.406288i) q^{78} +10.9673 q^{79} +(-8.81592 - 1.50984i) q^{80} +(4.13962 + 7.17004i) q^{81} +(-0.118653 + 0.323466i) q^{82} +(2.50039 + 2.50039i) q^{83} +(1.05445 + 0.191397i) q^{84} +(-4.79540 - 9.89437i) q^{85} +(-9.75890 - 6.86987i) q^{86} +(-0.578089 + 0.154898i) q^{87} +(9.02767 - 15.3676i) q^{88} +(4.10565 + 7.11119i) q^{89} +(8.63458 - 3.26508i) q^{90} +(2.99358 - 6.10153i) q^{91} +(4.06819 - 8.61100i) q^{92} +(0.128156 + 0.0343393i) q^{93} +(0.798261 - 8.86745i) q^{94} +(4.75129 + 1.64922i) q^{95} +(-1.60359 + 0.120014i) q^{96} +(-8.69112 + 2.32878i) q^{97} +(-1.67874 + 4.57649i) q^{98} +18.3950i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 6 q^{2} - 12 q^{6}+O(q^{10}) \) 144 * q - 6 * q^2 - 12 * q^6	\( 144 q - 6 q^{2} - 12 q^{6} + 12 q^{10} - 12 q^{12} + 4 q^{13} - 12 q^{16} - 24 q^{17} - 42 q^{20} - 12 q^{22} - 24 q^{25} - 36 q^{26} - 6 q^{28} - 36 q^{32} - 12 q^{33} - 76 q^{36} + 48 q^{37} - 16 q^{38} + 76 q^{40} - 72 q^{41} + 40 q^{42} - 120 q^{45} - 12 q^{46} - 40 q^{48} + 120 q^{50} - 10 q^{52} + 8 q^{53} - 20 q^{56} + 126 q^{58} + 16 q^{61} - 44 q^{62} + 32 q^{65} + 96 q^{66} - 64 q^{68} - 54 q^{72} - 12 q^{76} + 40 q^{77} - 100 q^{78} - 24 q^{80} - 32 q^{81} - 78 q^{82} - 24 q^{85} - 10 q^{88} - 8 q^{90} + 100 q^{92} - 48 q^{93} - 12 q^{97} - 162 q^{98}+O(q^{100}) \) 144 * q - 6 * q^2 - 12 * q^6 + 12 * q^10 - 12 * q^12 + 4 * q^13 - 12 * q^16 - 24 * q^17 - 42 * q^20 - 12 * q^22 - 24 * q^25 - 36 * q^26 - 6 * q^28 - 36 * q^32 - 12 * q^33 - 76 * q^36 + 48 * q^37 - 16 * q^38 + 76 * q^40 - 72 * q^41 + 40 * q^42 - 120 * q^45 - 12 * q^46 - 40 * q^48 + 120 * q^50 - 10 * q^52 + 8 * q^53 - 20 * q^56 + 126 * q^58 + 16 * q^61 - 44 * q^62 + 32 * q^65 + 96 * q^66 - 64 * q^68 - 54 * q^72 - 12 * q^76 + 40 * q^77 - 100 * q^78 - 24 * q^80 - 32 * q^81 - 78 * q^82 - 24 * q^85 - 10 * q^88 - 8 * q^90 + 100 * q^92 - 48 * q^93 - 12 * q^97 - 162 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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