LMFDB - Embedded newform 507.2.p.b.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

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

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.4
Character	$\chi$	$=$	507.25
Dual form			507.2.p.b.142.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50260 - 0.569861i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(0.436045 + 0.386302i) q^{4} +(2.17889 + 0.264565i) q^{5} +(0.384588 + 1.56033i) q^{6} +(0.728343 + 1.38774i) q^{7} +(1.05859 + 2.01697i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})$	\(q+(-1.50260 - 0.569861i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(0.436045 + 0.386302i) q^{4} +(2.17889 + 0.264565i) q^{5} +(0.384588 + 1.56033i) q^{6} +(0.728343 + 1.38774i) q^{7} +(1.05859 + 2.01697i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(-3.12324 - 1.63920i) q^{10} +(-2.56345 + 0.972190i) q^{11} +(0.0702187 - 0.578303i) q^{12} +(-2.87913 + 2.17040i) q^{13} +(-0.303589 - 2.50028i) q^{14} +(-1.02002 - 1.94348i) q^{15} +(-0.581678 - 4.79055i) q^{16} +(-5.96283 + 3.12953i) q^{17} +(1.06566 - 1.20288i) q^{18} -2.16929i q^{19} +(0.847893 + 0.957073i) q^{20} +(0.728343 - 1.38774i) q^{21} +4.40586 q^{22} -3.63673 q^{23} +(1.05859 - 2.01697i) q^{24} +(-0.177138 - 0.0436607i) q^{25} +(5.56300 - 1.62054i) q^{26} +(0.970942 - 0.239316i) q^{27} +(-0.218497 + 0.886479i) q^{28} +(-3.22000 + 8.49043i) q^{29} +(0.425165 + 3.50155i) q^{30} +(0.0241193 + 0.0978558i) q^{31} +(-0.765652 + 3.10637i) q^{32} +(2.25630 + 1.55741i) q^{33} +(10.7431 - 1.30445i) q^{34} +(1.21983 + 3.21643i) q^{35} +(-0.515823 + 0.270725i) q^{36} +(-0.494310 - 2.00550i) q^{37} +(-1.23619 + 3.25957i) q^{38} +(3.42173 + 1.13655i) q^{39} +(1.77292 + 4.67482i) q^{40} +(-6.54924 + 4.52061i) q^{41} +(-1.88523 + 1.67017i) q^{42} +(2.34919 + 0.579024i) q^{43} +(-1.49334 - 0.566350i) q^{44} +(-1.02002 + 1.94348i) q^{45} +(5.46455 + 2.07243i) q^{46} +(5.36826 + 6.05951i) q^{47} +(-3.61212 + 3.20005i) q^{48} +(2.58111 - 3.73938i) q^{49} +(0.241288 + 0.166549i) q^{50} +(5.96283 + 3.12953i) q^{51} +(-2.09386 - 0.165822i) q^{52} +(1.25539 - 0.658879i) q^{53} +(-1.59531 - 0.193706i) q^{54} +(-5.84269 + 1.44009i) q^{55} +(-2.02802 + 2.93809i) q^{56} +(-1.78529 + 1.23230i) q^{57} +(9.67674 - 10.9228i) q^{58} +(-5.98150 - 0.726285i) q^{59} +(0.305998 - 1.24148i) q^{60} +(5.27447 + 2.76825i) q^{61} +(0.0195226 - 0.160783i) q^{62} +(-1.55584 + 0.188913i) q^{63} +(-2.56199 + 3.71169i) q^{64} +(-6.84752 + 3.96734i) q^{65} +(-2.50281 - 3.62595i) q^{66} +(0.221583 + 0.250115i) q^{67} +(-3.80901 - 0.938836i) q^{68} +(2.06590 + 2.99297i) q^{69} -5.52815i q^{70} +(6.16364 - 4.25446i) q^{71} +(-2.26128 + 0.274569i) q^{72} +(-5.04927 + 1.91494i) q^{73} +(-0.400103 + 3.29515i) q^{74} +(0.0646940 + 0.170584i) q^{75} +(0.838001 - 0.945907i) q^{76} +(-3.21622 - 2.84932i) q^{77} +(-4.49382 - 3.65769i) q^{78} +(4.08292 - 3.61715i) q^{79} -10.5920i q^{80} +(-0.748511 - 0.663123i) q^{81} +(12.4170 - 3.06052i) q^{82} +(9.21499 + 6.36065i) q^{83} +(0.853679 - 0.323758i) q^{84} +(-13.8203 + 5.24135i) q^{85} +(-3.19993 - 2.20876i) q^{86} +(8.81666 - 2.17311i) q^{87} +(-4.67451 - 4.14126i) q^{88} -14.6305i q^{89} +(2.64020 - 2.33901i) q^{90} +(-5.10894 - 2.41469i) q^{91} +(-1.58578 - 1.40488i) q^{92} +(0.0668324 - 0.0754382i) q^{93} +(-4.61327 - 12.1642i) q^{94} +(0.573918 - 4.72664i) q^{95} +(2.99143 - 1.13450i) q^{96} +(-1.62820 + 0.197699i) q^{97} +(-6.00931 + 4.14792i) q^{98} -2.74161i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

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 $

$2$	−1.50260	−	0.569861i	−1.06250	−	0.402953i	−0.239442	−	0.970911i	$-0.576964\pi$
$2$	−1.50260	−	0.569861i	−1.06250	−	0.402953i	−0.823058	+	0.567958i	$0.807734\pi$
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$4$	0.436045	+	0.386302i	0.218023	+	0.193151i
$5$	2.17889	+	0.264565i	0.974430	+	0.118317i	0.592236	−	0.805765i	$-0.298245\pi$
$5$	2.17889	+	0.264565i	0.974430	+	0.118317i	0.382194	+	0.924082i	$0.375169\pi$
$6$	0.384588	+	1.56033i	0.157007	+	0.637004i
$7$	0.728343	+	1.38774i	0.275288	+	0.524517i	0.983370	−	0.181613i	$-0.0581317\pi$
$7$	0.728343	+	1.38774i	0.275288	+	0.524517i	−0.708082	+	0.706130i	$0.750439\pi$
$8$	1.05859	+	2.01697i	0.374267	+	0.713106i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	−3.12324	−	1.63920i	−0.987654	−	0.518361i
$11$	−2.56345	+	0.972190i	−0.772911	+	0.293126i	−0.709354	−	0.704852i	$-0.751013\pi$
$11$	−2.56345	+	0.972190i	−0.772911	+	0.293126i	−0.0635561	+	0.997978i	$0.520244\pi$
$12$	0.0702187	−	0.578303i	0.0202704	−	0.166942i
$13$	−2.87913	+	2.17040i	−0.798526	+	0.601960i
$13$	−2.87913	+	2.17040i	−0.798526	+	0.601960i
$14$	−0.303589	−	2.50028i	−0.0811374	−	0.668227i
$15$	−1.02002	−	1.94348i	−0.263368	−	0.501805i
$16$	−0.581678	−	4.79055i	−0.145420	−	1.19764i
$17$	−5.96283	+	3.12953i	−1.44620	+	0.759023i	−0.991313	−	0.131527i	$-0.958012\pi$
$17$	−5.96283	+	3.12953i	−1.44620	+	0.759023i	−0.454885	+	0.890550i	$0.650320\pi$
$18$	1.06566	−	1.20288i	0.251178	−	0.283522i
$19$		−	2.16929i		−	0.497668i	−0.968546	−	0.248834i	$-0.919953\pi$
$19$		−	2.16929i		−	0.497668i	0.968546	−	0.248834i	$-0.0800474\pi$
$20$	0.847893	+	0.957073i	0.189595	+	0.214008i
$21$	0.728343	−	1.38774i	0.158937	−	0.302830i
$22$	4.40586			0.939333
$23$	−3.63673			−0.758310			−0.379155	−	0.925333i	$-0.623785\pi$
$23$	−3.63673			−0.758310			−0.379155	+	0.925333i	$0.623785\pi$
$24$	1.05859	−	2.01697i	0.216083	−	0.411712i
$25$	−0.177138	−	0.0436607i	−0.0354277	−	0.00873213i
$26$	5.56300	−	1.62054i	1.09099	−	0.317814i
$27$	0.970942	−	0.239316i	0.186858	−	0.0460563i
$28$	−0.218497	+	0.886479i	−0.0412921	+	0.167529i
$29$	−3.22000	+	8.49043i	−0.597938	+	1.57663i	0.203834	+	0.979005i	$0.434660\pi$
$29$	−3.22000	+	8.49043i	−0.597938	+	1.57663i	−0.801773	+	0.597629i	$0.796110\pi$
$30$	0.425165	+	3.50155i	0.0776241	+	0.639292i
$31$	0.0241193	+	0.0978558i	0.00433195	+	0.0175754i	0.973068	−	0.230518i	$-0.0740421\pi$
$31$	0.0241193	+	0.0978558i	0.00433195	+	0.0175754i	−0.968736	+	0.248094i	$0.920196\pi$
$32$	−0.765652	+	3.10637i	−0.135349	+	0.549134i
$33$	2.25630	+	1.55741i	0.392772	+	0.271111i
$34$	10.7431	−	1.30445i	1.84243	−	0.223712i
$35$	1.21983	+	3.21643i	0.206189	+	0.543676i
$36$	−0.515823	+	0.270725i	−0.0859705	+	0.0451208i
$37$	−0.494310	−	2.00550i	−0.0812641	−	0.329702i	0.916213	−	0.400692i	$-0.131230\pi$
$37$	−0.494310	−	2.00550i	−0.0812641	−	0.329702i	−0.997477	+	0.0709903i	$0.977384\pi$
$38$	−1.23619	+	3.25957i	−0.200537	+	0.528772i
$39$	3.42173	+	1.13655i	0.547916	+	0.181993i
$40$	1.77292	+	4.67482i	0.280324	+	0.739154i
$41$	−6.54924	+	4.52061i	−1.02282	+	0.706001i	−0.956480	−	0.291796i	$-0.905747\pi$
$41$	−6.54924	+	4.52061i	−1.02282	+	0.706001i	−0.0663383	+	0.997797i	$0.521132\pi$
$42$	−1.88523	+	1.67017i	−0.290897	+	0.257712i
$43$	2.34919	+	0.579024i	0.358248	+	0.0883003i	0.414332	−	0.910126i	$-0.364015\pi$
$43$	2.34919	+	0.579024i	0.358248	+	0.0883003i	−0.0560837	+	0.998426i	$0.517861\pi$
$44$	−1.49334	−	0.566350i	−0.225130	−	0.0853804i
$45$	−1.02002	+	1.94348i	−0.152055	+	0.289717i
$46$	5.46455	+	2.07243i	0.805704	+	0.305563i
$47$	5.36826	+	6.05951i	0.783041	+	0.883871i	0.995641	−	0.0932686i	$-0.0297315\pi$
$47$	5.36826	+	6.05951i	0.783041	+	0.883871i	−0.212600	+	0.977139i	$0.568193\pi$
$48$	−3.61212	+	3.20005i	−0.521364	+	0.461888i
$49$	2.58111	−	3.73938i	0.368730	−	0.534198i
$50$	0.241288	+	0.166549i	0.0341232	+	0.0235536i
$51$	5.96283	+	3.12953i	0.834963	+	0.438222i
$52$	−2.09386	−	0.165822i	−0.290366	−	0.0229953i
$53$	1.25539	−	0.658879i	0.172441	−	0.0905039i	−0.376294	−	0.926500i	$-0.622802\pi$
$53$	1.25539	−	0.658879i	0.172441	−	0.0905039i	0.548735	+	0.835996i	$0.315110\pi$
$54$	−1.59531	−	0.193706i	−0.217095	−	0.0263601i
$55$	−5.84269	+	1.44009i	−0.787829	+	0.194182i
$56$	−2.02802	+	2.93809i	−0.271005	+	0.392619i
$57$	−1.78529	+	1.23230i	−0.236467	+	0.163221i
$58$	9.67674	−	10.9228i	1.27062	−	1.43423i
$59$	−5.98150	−	0.726285i	−0.778725	−	0.0945543i	−0.278484	−	0.960441i	$-0.589832\pi$
$59$	−5.98150	−	0.726285i	−0.778725	−	0.0945543i	−0.500240	+	0.865887i	$0.666755\pi$
$60$	0.305998	−	1.24148i	0.0395041	−	0.160275i
$61$	5.27447	+	2.76825i	0.675327	+	0.354439i	0.767269	−	0.641326i	$-0.221615\pi$
$61$	5.27447	+	2.76825i	0.675327	+	0.354439i	−0.0919423	+	0.995764i	$0.529308\pi$
$62$	0.0195226	−	0.160783i	0.00247937	−	0.0204194i
$63$	−1.55584	+	0.188913i	−0.196017	+	0.0238008i
$64$	−2.56199	+	3.71169i	−0.320249	+	0.463961i
$65$	−6.84752	+	3.96734i	−0.849330	+	0.492088i
$66$	−2.50281	−	3.62595i	−0.308075	−	0.446324i
$67$	0.221583	+	0.250115i	0.0270706	+	0.0305564i	0.761890	−	0.647706i	$-0.224272\pi$
$67$	0.221583	+	0.250115i	0.0270706	+	0.0305564i	−0.734819	+	0.678263i	$0.762733\pi$
$68$	−3.80901	−	0.938836i	−0.461910	−	0.113851i
$69$	2.06590	+	2.99297i	0.248705	+	0.360311i
$70$		−	5.52815i		−	0.660740i
$71$	6.16364	−	4.25446i	0.731490	−	0.504911i	−0.143140	−	0.989702i	$-0.545720\pi$
$71$	6.16364	−	4.25446i	0.731490	−	0.504911i	0.874630	+	0.484791i	$0.161104\pi$
$72$	−2.26128	+	0.274569i	−0.266494	+	0.0323582i
$73$	−5.04927	+	1.91494i	−0.590972	+	0.224126i	−0.631918	−	0.775035i	$-0.717732\pi$
$73$	−5.04927	+	1.91494i	−0.590972	+	0.224126i	0.0409459	+	0.999161i	$0.486963\pi$
$74$	−0.400103	+	3.29515i	−0.0465111	+	0.383053i
$75$	0.0646940	+	0.170584i	0.00747022	+	0.0196973i
$76$	0.838001	−	0.945907i	0.0961253	−	0.108503i
$77$	−3.21622	−	2.84932i	−0.366523	−	0.324711i
$78$	−4.49382	−	3.65769i	−0.508825	−	0.414152i
$79$	4.08292	−	3.61715i	0.459364	−	0.406961i	−0.401450	−	0.915881i	$-0.631494\pi$
$79$	4.08292	−	3.61715i	0.459364	−	0.406961i	0.860814	+	0.508920i	$0.169955\pi$
$80$		−	10.5920i		−	1.18422i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	12.4170	−	3.06052i	1.37123	−	0.337978i
$83$	9.21499	+	6.36065i	1.01148	+	0.698172i	0.953886	−	0.300168i	$-0.0970428\pi$
$83$	9.21499	+	6.36065i	1.01148	+	0.698172i	0.0575905	+	0.998340i	$0.481658\pi$
$84$	0.853679	−	0.323758i	0.0931440	−	0.0353248i
$85$	−13.8203	+	5.24135i	−1.49902	+	0.568505i
$86$	−3.19993	−	2.20876i	−0.345058	−	0.238176i
$87$	8.81666	−	2.17311i	0.945245	−	0.232982i
$88$	−4.67451	−	4.14126i	−0.498305	−	0.441460i
$89$		−	14.6305i		−	1.55083i	−0.631453	−	0.775414i	$-0.717541\pi$
$89$		−	14.6305i		−	1.55083i	0.631453	−	0.775414i	$-0.282459\pi$
$90$	2.64020	−	2.33901i	0.278301	−	0.246553i
$91$	−5.10894	−	2.41469i	−0.535563	−	0.253128i
$92$	−1.58578	−	1.40488i	−0.165329	−	0.146469i
$93$	0.0668324	−	0.0754382i	0.00693020	−	0.00782258i
$94$	−4.61327	−	12.1642i	−0.475822	−	1.25464i
$95$	0.573918	−	4.72664i	0.0588827	−	0.484943i
$96$	2.99143	−	1.13450i	0.305312	−	0.115789i
$97$	−1.62820	+	0.197699i	−0.165319	+	0.0200733i	−0.202777	−	0.979225i	$-0.564997\pi$
$97$	−1.62820	+	0.197699i	−0.165319	+	0.0200733i	0.0374588	+	0.999298i	$0.488074\pi$
$98$	−6.00931	+	4.14792i	−0.607032	+	0.419004i
$99$		−	2.74161i		−	0.275543i
$100$	−0.0603741	−	0.0874670i	−0.00603741	−	0.00874670i
$101$	−2.26631	−	0.558595i	−0.225506	−	0.0555823i	0.124943	−	0.992164i	$-0.460125\pi$
$101$	−2.26631	−	0.558595i	−0.225506	−	0.0555823i	−0.350450	+	0.936582i	$0.613971\pi$
$102$	−7.17635	−	8.10042i	−0.710564	−	0.802061i
$103$	5.69669	+	8.25309i	0.561312	+	0.813201i	0.996183	−	0.0872922i	$-0.0278214\pi$
$103$	5.69669	+	8.25309i	0.561312	+	0.813201i	−0.434871	+	0.900493i	$0.643206\pi$
$104$	−7.42543	−	3.50955i	−0.728123	−	0.344140i
$105$	1.95413	−	2.83104i	0.190703	−	0.276282i
$106$	−2.26182	+	0.274634i	−0.219687	+	0.0266748i
$107$	−1.97945	+	16.3022i	−0.191361	+	1.57600i	0.508082	+	0.861309i	$0.330355\pi$
$107$	−1.97945	+	16.3022i	−0.191361	+	1.57600i	−0.699443	+	0.714688i	$0.746568\pi$
$108$	0.515823	+	0.270725i	0.0496351	+	0.0260505i
$109$	0.396108	−	1.60707i	0.0379403	−	0.153930i	−0.948916	−	0.315527i	$-0.897819\pi$
$109$	0.396108	−	1.60707i	0.0379403	−	0.153930i	0.986857	+	0.161598i	$0.0516647\pi$
$110$	9.59989	+	1.16564i	0.915314	+	0.111139i
$111$	−1.36969	+	1.54606i	−0.130005	+	0.146746i
$112$	6.22439	−	4.29638i	0.588149	−	0.405970i
$113$	5.36926	−	7.77871i	0.505097	−	0.731760i	−0.484631	−	0.874718i	$-0.661046\pi$
$113$	5.36926	−	7.77871i	0.505097	−	0.731760i	0.989729	+	0.142959i	$0.0456617\pi$
$114$	3.38481	−	0.834281i	0.317017	−	0.0781376i
$115$	−7.92404	−	0.962152i	−0.738920	−	0.0897212i
$116$	−4.68394	+	2.45832i	−0.434893	+	0.228249i
$117$	−1.00841	−	3.46166i	−0.0932271	−	0.320031i
$118$	8.57392	+	4.49994i	0.789293	+	0.414253i
$119$	−8.68597	−	5.99549i	−0.796241	−	0.549606i
$120$	2.84016	−	4.11469i	0.259270	−	0.375618i
$121$	−2.60747	+	2.31002i	−0.237043	+	0.210002i
$122$	−6.34790	−	7.16530i	−0.574712	−	0.648715i
$123$	7.44078	+	2.82192i	0.670913	+	0.254444i
$124$	−0.0272848	+	0.0519869i	−0.00245025	+	0.00466856i
$125$	−10.6357	−	4.03360i	−0.951288	−	0.360776i
$126$	2.44545	+	0.602750i	0.217858	+	0.0536972i
$127$	8.77382	−	7.77293i	0.778551	−	0.689736i	−0.177115	−	0.984190i	$-0.556676\pi$
$127$	8.77382	−	7.77293i	0.778551	−	0.689736i	0.955665	+	0.294455i	$0.0951380\pi$
$128$	11.2308	−	7.75206i	0.992672	−	0.685192i
$129$	−0.857966	−	2.26227i	−0.0755397	−	0.199182i
$130$	12.5499	−	2.05920i	1.10070	−	0.180604i
$131$	4.21690	−	11.1190i	0.368432	−	0.971475i	−0.614730	−	0.788738i	$-0.710735\pi$
$131$	4.21690	−	11.1190i	0.368432	−	0.971475i	0.983162	−	0.182737i	$-0.0584958\pi$
$132$	0.382218	+	1.55072i	0.0332678	+	0.134973i
$133$	3.01041	−	1.57998i	0.261036	−	0.137002i
$134$	−0.190419	−	0.502095i	−0.0164497	−	0.0433744i
$135$	2.17889	−	0.264565i	0.187529	−	0.0227702i
$136$	−12.6243	−	8.71395i	−1.08253	−	0.747215i
$137$	−3.78169	+	15.3429i	−0.323092	+	1.31083i	0.554803	+	0.831981i	$0.312793\pi$
$137$	−3.78169	+	15.3429i	−0.323092	+	1.31083i	−0.877895	+	0.478853i	$0.841053\pi$
$138$	−1.39864	−	5.67451i	−0.119060	−	0.483047i
$139$	−1.13022	−	9.30821i	−0.0958642	−	0.789512i	−0.958777	−	0.284160i	$-0.908285\pi$
$139$	−1.13022	−	9.30821i	−0.0958642	−	0.789512i	0.862913	−	0.505353i	$-0.168638\pi$
$140$	−0.710614	+	1.87373i	−0.0600578	+	0.158359i
$141$	1.93736	−	7.86019i	0.163155	−	0.661947i
$142$	−11.6859	+	2.88033i	−0.980663	+	0.241712i
$143$	5.27047	−	8.36277i	0.440739	−	0.699330i
$144$	4.68551	+	1.15487i	0.390459	+	0.0962395i
$145$	−9.26230	+	17.6478i	−0.769192	+	1.46557i
$146$	8.67828			0.718220
$147$	−4.54369			−0.374757
$148$	0.559186	−	1.06544i	0.0459648	−	0.0875786i
$149$	−12.1449	−	13.7088i	−0.994953	−	1.12307i	−0.992398	−	0.123073i	$-0.960725\pi$
$149$	−12.1449	−	13.7088i	−0.994953	−	1.12307i	−0.00255487	−	0.999997i	$-0.500813\pi$
$150$		−	0.293186i		−	0.0239386i
$151$	−13.2140	+	14.9155i	−1.07534	+	1.21381i	−0.0995658	+	0.995031i	$0.531745\pi$
$151$	−13.2140	+	14.9155i	−1.07534	+	1.21381i	−0.975775	+	0.218778i	$0.929793\pi$
$152$	4.37538	−	2.29638i	0.354890	−	0.186261i
$153$	−0.811717	−	6.68509i	−0.0656234	−	0.540457i
$154$	3.20898	+	6.11420i	0.258587	+	0.492696i
$155$	0.0266641	+	0.219598i	0.00214171	+	0.0176386i
$156$	1.05298	+	1.81741i	0.0843058	+	0.145509i
$157$	−1.75892	+	14.4860i	−0.140377	+	1.15611i	0.736858	+	0.676048i	$0.236309\pi$
$157$	−1.75892	+	14.4860i	−0.140377	+	1.15611i	−0.877235	+	0.480062i	$0.840614\pi$
$158$	−8.19627	+	3.10843i	−0.652060	+	0.247294i
$159$	−1.25539	−	0.658879i	−0.0995588	−	0.0522525i
$160$	−2.49011	+	6.56588i	−0.196860	+	0.519078i
$161$	−2.64879	−	5.04684i	−0.208754	−	0.397747i
$162$	0.746825	+	1.42296i	0.0586761	+	0.111798i
$163$	−4.70677	−	19.0961i	−0.368663	−	1.49572i	−0.803549	−	0.595239i	$-0.797058\pi$
$163$	−4.70677	−	19.0961i	−0.368663	−	1.49572i	0.434886	−	0.900485i	$-0.356789\pi$
$164$	−4.60209	−	0.558794i	−0.359363	−	0.0436345i
$165$	4.50420	+	3.99038i	0.350652	+	0.310650i
$166$	−10.2218	−	14.8088i	−0.793363	−	1.14938i
$167$	7.88718	+	2.99121i	0.610328	+	0.231467i	0.640351	−	0.768082i	$-0.278789\pi$
$167$	7.88718	+	2.99121i	0.610328	+	0.231467i	−0.0300230	+	0.999549i	$0.509558\pi$
$168$	3.57005			0.275435
$169$	3.57874	−	12.4977i	0.275288	−	0.961362i
$170$	23.7533			1.82179
$171$	2.02832	+	0.769240i	0.155109	+	0.0588252i
$172$	0.800676	+	1.15998i	0.0610510	+	0.0884476i
$173$	8.95807	+	7.93615i	0.681069	+	0.603375i	0.931057	−	0.364874i	$-0.118888\pi$
$173$	8.95807	+	7.93615i	0.681069	+	0.603375i	−0.249988	+	0.968249i	$0.580427\pi$
$174$	−14.4863	−	1.75895i	−1.09820	−	0.133346i
$175$	−0.0684277	−	0.277622i	−0.00517265	−	0.0209863i
$176$	6.14843	+	11.7149i	0.463455	+	0.883040i
$177$	2.80016	+	5.33525i	0.210473	+	0.401022i
$178$	−8.33735	+	21.9838i	−0.624911	+	1.64775i
$179$	−2.54460	−	1.33551i	−0.190192	−	0.0998205i	0.366939	−	0.930245i	$-0.380406\pi$
$179$	−2.54460	−	1.33551i	−0.190192	−	0.0998205i	−0.557131	+	0.830424i	$0.688098\pi$
$180$	−1.19555	+	0.453411i	−0.0891107	+	0.0337952i
$181$	−1.40868	+	11.6015i	−0.104707	+	0.862336i	0.841831	+	0.539742i	$0.181478\pi$
$181$	−1.40868	+	11.6015i	−0.104707	+	0.862336i	−0.946537	+	0.322594i	$0.895445\pi$
$182$	6.30066	+	6.53970i	0.467036	+	0.484755i
$183$	−0.718011	−	5.91335i	−0.0530769	−	0.437127i
$184$	−3.84979	−	7.33517i	−0.283810	−	0.540756i
$185$	−0.546464	−	4.50053i	−0.0401768	−	0.330886i
$186$	−0.143412	+	0.0752683i	−0.0105155	+	0.00551894i
$187$	12.2429	−	13.8194i	0.895292	−	1.01058i
$188$			4.71599i			0.343949i
$189$	1.03929	+	1.17311i	0.0755970	+	0.0853314i
$190$	−3.55590	+	6.77520i	−0.257972	+	0.491524i
$191$	21.9814			1.59052			0.795260	−	0.606268i	$-0.207334\pi$
$191$	21.9814			1.59052			0.795260	+	0.606268i	$0.207334\pi$
$192$	4.51004			0.325484
$193$	−6.50438	+	12.3931i	−0.468196	+	0.892073i	0.530810	+	0.847491i	$0.321888\pi$
$193$	−6.50438	+	12.3931i	−0.468196	+	0.892073i	−0.999006	+	0.0445817i	$0.985804\pi$
$194$	2.55919	+	0.630785i	0.183739	+	0.0452877i
$195$	7.15489	+	3.38169i	0.512372	+	0.242168i
$196$	2.57001	−	0.633451i	0.183572	−	0.0452465i
$197$	−4.98836	+	20.2386i	−0.355406	+	1.44194i	0.472630	+	0.881261i	$0.343305\pi$
$197$	−4.98836	+	20.2386i	−0.355406	+	1.44194i	−0.828035	+	0.560676i	$0.810541\pi$
$198$	−1.56234	+	4.11955i	−0.111031	+	0.292764i
$199$	2.36385	+	19.4680i	0.167569	+	1.38005i	0.797462	+	0.603370i	$0.206176\pi$
$199$	2.36385	+	19.4680i	0.167569	+	1.38005i	−0.629893	+	0.776682i	$0.716901\pi$
$200$	−0.0994540	−	0.403501i	−0.00703246	−	0.0285318i
$201$	0.0799675	−	0.324441i	0.00564047	−	0.0228843i
$202$	3.08704	+	2.13083i	0.217203	+	0.149924i
$203$	−14.1278	+	1.71542i	−0.991577	+	0.120399i
$204$	1.39112	+	3.66807i	0.0973976	+	0.256816i
$205$	−15.4661	+	8.11722i	−1.08020	+	0.566931i
$206$	−3.85674	−	15.6474i	−0.268712	−	1.09021i
$207$	1.28960	−	3.40040i	0.0896335	−	0.236344i
$208$	12.0721	+	12.5301i	0.837051	+	0.868808i
$209$	2.10896	+	5.56087i	0.145880	+	0.384653i
$210$	−4.54958	+	3.14035i	−0.313951	+	0.216704i
$211$	0.244600	−	0.216697i	0.0168390	−	0.0149180i	−0.654661	−	0.755922i	$-0.727189\pi$
$211$	0.244600	−	0.216697i	0.0168390	−	0.0149180i	0.671500	+	0.741004i	$0.265650\pi$
$212$	0.801932	+	0.197659i	0.0550769	+	0.0135752i
$213$	−7.00270	−	2.65577i	−0.479817	−	0.181971i
$214$	12.2643	−	23.3677i	0.838373	−	1.59739i
$215$	4.96544	+	1.88314i	0.338640	+	0.128429i
$216$	1.51052	+	1.70502i	0.102778	+	0.116012i
$217$	−0.118231	+	0.104744i	−0.00802608	+	0.00711048i
$218$	−1.51100	+	2.18906i	−0.102338	+	0.148262i
$219$	4.44427	+	3.06766i	0.300316	+	0.207293i
$220$	−3.10399	−	1.62910i	−0.209271	−	0.109834i
$221$	10.3754	−	21.9520i	0.697925	−	1.47665i
$222$	2.93914	−	1.54258i	0.197262	−	0.103531i
$223$	10.6024	+	1.28736i	0.709986	+	0.0862079i	0.467559	−	0.883962i	$-0.345133\pi$
$223$	10.6024	+	1.28736i	0.709986	+	0.0862079i	0.242427	+	0.970170i	$0.422057\pi$
$224$	−4.86850	+	1.19998i	−0.325290	+	0.0801768i
$225$	0.103638	−	0.150145i	0.00690917	−	0.0100097i
$226$	−12.5006	+	8.62856i	−0.831530	+	0.573964i
$227$	7.53242	−	8.50234i	0.499944	−	0.564320i	−0.443320	−	0.896363i	$-0.646199\pi$
$227$	7.53242	−	8.50234i	0.499944	−	0.564320i	0.943264	+	0.332043i	$0.107738\pi$
$228$	−1.25450	−	0.152324i	−0.0830816	−	0.0100879i
$229$	2.63752	−	10.7008i	0.174292	−	0.707130i	−0.817133	−	0.576450i	$-0.804438\pi$
$229$	2.63752	−	10.7008i	0.174292	−	0.707130i	0.991425	−	0.130681i	$-0.0417162\pi$
$230$	11.3584	+	5.96133i	0.748949	+	0.393079i
$231$	−0.517926	+	4.26550i	−0.0340770	+	0.280649i
$232$	−20.5336	+	2.49323i	−1.34810	+	0.163688i
$233$	−10.1267	+	14.6711i	−0.663422	+	0.961133i	0.336389	+	0.941723i	$0.390794\pi$
$233$	−10.1267	+	14.6711i	−0.663422	+	0.961133i	−0.999812	+	0.0194100i	$0.993821\pi$
$234$	−0.457438	+	5.77615i	−0.0299037	+	0.377599i
$235$	10.0937	+	14.6233i	0.658441	+	0.953917i
$236$	−2.32764	−	2.62736i	−0.151516	−	0.171027i
$237$	−5.29622	−	1.30540i	−0.344026	−	0.0847949i
$238$	9.63494	+	13.9586i	0.624541	+	0.904803i
$239$		−	22.8111i		−	1.47553i	−0.675059	−	0.737764i	$-0.735882\pi$
$239$		−	22.8111i		−	1.47553i	0.675059	−	0.737764i	$-0.264118\pi$
$240$	−8.71703	+	6.01693i	−0.562682	+	0.388391i
$241$	−5.74691	+	0.697802i	−0.370191	+	0.0449494i	−0.303519	−	0.952826i	$-0.598161\pi$
$241$	−5.74691	+	0.697802i	−0.370191	+	0.0449494i	−0.0666728	+	0.997775i	$0.521238\pi$
$242$	5.23438	−	1.98514i	0.336479	−	0.127610i
$243$	−0.120537	+	0.992709i	−0.00773243	+	0.0636823i
$244$	1.23052	+	3.24462i	0.0787762	+	0.207716i
$245$	6.61327	−	7.46483i	0.422506	−	0.476911i
$246$	−9.57242	−	8.48042i	−0.610315	−	0.540692i
$247$	4.70822	+	6.24565i	0.299577	+	0.397401i
$248$	−0.171840	+	0.152237i	−0.0109118	+	0.00966704i
$249$		−	11.1971i		−	0.709584i
$250$	13.6827	+	12.1218i	0.865367	+	0.766648i
$251$	−24.6912	+	6.08584i	−1.55850	+	0.384135i	−0.922014	−	0.387157i	$-0.873457\pi$
$251$	−24.6912	+	6.08584i	−1.55850	+	0.384135i	−0.636482	+	0.771291i	$0.719611\pi$
$252$	−0.751392	−	0.518648i	−0.0473332	−	0.0326718i
$253$	9.32259	−	3.53559i	0.586106	−	0.222281i
$254$	−17.6130	+	6.67974i	−1.10514	+	0.419124i
$255$	12.1644	+	8.39647i	0.761763	+	0.525807i
$256$	−12.5350	+	3.08961i	−0.783441	+	0.193101i
$257$	−3.06726	−	2.71735i	−0.191330	−	0.169504i	0.562019	−	0.827124i	$-0.310025\pi$
$257$	−3.06726	−	2.71735i	−0.191330	−	0.169504i	−0.753350	+	0.657620i	$0.771563\pi$
$258$			3.88821i			0.242069i
$259$	2.42308	−	2.14666i	0.150563	−	0.133387i
$260$	−4.51842	−	0.915270i	−0.280221	−	0.0567626i
$261$	−6.79687	−	6.02150i	−0.420716	−	0.372721i
$262$	−12.6726	+	14.3044i	−0.782917	+	0.883731i
$263$	−3.08205	−	8.12669i	−0.190047	−	0.501113i	0.805796	−	0.592193i	$-0.201738\pi$
$263$	−3.08205	−	8.12669i	−0.190047	−	0.501113i	−0.995844	+	0.0910794i	$0.970968\pi$
$264$	−0.752762	+	6.19955i	−0.0463293	+	0.381556i
$265$	2.90967	−	1.10349i	0.178740	−	0.0677870i
$266$	−5.42382	+	0.658570i	−0.332555	+	0.0403795i
$267$	−12.0407	+	8.31106i	−0.736876	+	0.508629i
$268$			0.194660i			0.0118907i
$269$	12.8888	+	18.6727i	0.785847	+	1.13850i	0.987280	+	0.158994i	$0.0508249\pi$
$269$	12.8888	+	18.6727i	0.785847	+	1.13850i	−0.201433	+	0.979502i	$0.564560\pi$
$270$	−3.42477	−	0.844130i	−0.208425	−	0.0513721i
$271$	5.79159	+	6.53736i	0.351814	+	0.397116i	0.897602	−	0.440807i	$-0.145308\pi$
$271$	5.79159	+	6.53736i	0.351814	+	0.397116i	−0.545787	+	0.837924i	$0.683769\pi$
$272$	18.4606	+	26.7448i	1.11934	+	1.62164i
$273$	0.914960	+	5.57628i	0.0553759	+	0.337492i
$274$	14.4257	−	20.8992i	0.871489	−	1.26257i
$275$	0.496532	−	0.0602899i	0.0299420	−	0.00363562i
$276$	−0.255366	+	2.10313i	−0.0153712	+	0.126594i
$277$	20.9238	+	10.9817i	1.25719	+	0.659824i	0.955895	−	0.293708i	$-0.0948893\pi$
$277$	20.9238	+	10.9817i	1.25719	+	0.659824i	0.301294	+	0.953531i	$0.402582\pi$
$278$	−3.60612	+	14.6306i	−0.216281	+	0.877485i
$279$	−0.100050	−	0.0121482i	−0.00598981	−	0.000727295i
$280$	−5.19614	+	5.86523i	−0.310529	+	0.350515i
$281$	−14.1621	+	9.77541i	−0.844841	+	0.583152i	−0.909946	−	0.414727i	$-0.863877\pi$
$281$	−14.1621	+	9.77541i	−0.844841	+	0.583152i	0.0651048	+	0.997878i	$0.479262\pi$
$282$	−7.39030	+	10.7067i	−0.440086	+	0.637574i
$283$	−27.7850	+	6.84838i	−1.65165	+	0.407094i	−0.951682	−	0.307085i	$-0.900647\pi$
$283$	−27.7850	+	6.84838i	−1.65165	+	0.407094i	−0.699963	+	0.714179i	$0.746800\pi$
$284$	4.33113	+	0.525895i	0.257006	+	0.0312061i
$285$	−4.21597	+	2.21271i	−0.249732	+	0.131070i
$286$	−12.6850	+	9.56247i	−0.750082	+	0.565441i
$287$	−11.0435	−	5.79609i	−0.651879	−	0.342133i
$288$	−2.63300	−	1.81743i	−0.155151	−	0.107093i
$289$	16.1042	−	23.3310i	0.947307	−	1.37241i
$290$	23.9743	−	21.2394i	1.40782	−	1.24722i
$291$	1.08763	+	1.22768i	0.0637578	+	0.0719676i
$292$	−2.94145	−	1.11555i	−0.172136	−	0.0652824i
$293$	6.35851	−	12.1151i	0.371468	−	0.707773i	−0.625929	−	0.779880i	$-0.715280\pi$
$293$	6.35851	−	12.1151i	0.371468	−	0.707773i	0.997397	+	0.0721069i	$0.0229723\pi$
$294$	6.82735	+	2.58927i	0.398179	+	0.151009i
$295$	−12.8409	−	3.16499i	−0.747625	−	0.184273i
$296$	3.52175	−	3.12000i	0.204698	−	0.181346i
$297$	−2.25630	+	1.55741i	−0.130924	+	0.0903704i
$298$	10.4369	+	27.5198i	0.604592	+	1.59418i
$299$	10.4706	−	7.89315i	0.605531	−	0.456473i
$300$	−0.0376875	+	0.0993738i	−0.00217589	+	0.00573735i
$301$	0.907482	+	3.68180i	0.0523064	+	0.212215i
$302$	28.3552	−	14.8819i	1.63166	−	0.856359i
$303$	0.827696	+	2.18245i	0.0475499	+	0.125379i
$304$	−10.3921	+	1.26183i	−0.596026	+	0.0723707i
$305$	10.7601	+	7.42717i	0.616122	+	0.425278i
$306$	−2.58989	+	10.5076i	−0.148054	+	0.600678i
$307$	−5.22660	−	21.2052i	−0.298298	−	1.21024i	−0.908462	−	0.417967i	$-0.862743\pi$
$307$	−5.22660	−	21.2052i	−0.298298	−	1.21024i	0.610164	−	0.792275i	$-0.291104\pi$
$308$	−0.301718	−	2.48487i	−0.0171920	−	0.141589i
$309$	3.55607	−	9.37657i	0.202297	−	0.533415i
$310$	0.0850751	−	0.345163i	0.00483194	−	0.0196040i
$311$	−6.47375	+	1.59564i	−0.367093	+	0.0904802i	−0.418547	−	0.908195i	$-0.637460\pi$
$311$	−6.47375	+	1.59564i	−0.367093	+	0.0904802i	0.0514544	+	0.998675i	$0.483614\pi$
$312$	1.32982	+	8.10466i	0.0752862	+	0.458836i
$313$	18.6019	+	4.58497i	1.05144	+	0.259158i	0.726922	−	0.686720i	$-0.240950\pi$
$313$	18.6019	+	4.58497i	1.05144	+	0.259158i	0.324522	+	0.945878i	$0.394796\pi$
$314$	10.8980	−	20.7644i	0.615008	−	1.17180i
$315$	−3.43997			−0.193821
$316$	3.17765			0.178757
$317$	−11.9429	+	22.7553i	−0.670781	+	1.27807i	0.277528	+	0.960718i	$0.410485\pi$
$317$	−11.9429	+	22.7553i	−0.670781	+	1.27807i	−0.948309	+	0.317349i	$0.897207\pi$
$318$	1.51088	+	1.70543i	0.0847258	+	0.0956357i
$319$		−	24.8953i		−	1.39387i
$320$	−6.56429	+	7.40955i	−0.366955	+	0.414206i
$321$	14.5409	−	7.63167i	0.811596	−	0.425958i
$322$	1.10407	+	9.09283i	0.0615274	+	0.506723i
$323$	6.78885	+	12.9351i	0.377742	+	0.719727i
$324$	−0.0702187	−	0.578303i	−0.00390104	−	0.0321279i
$325$	0.604765	−	0.258756i	0.0335463	−	0.0143532i
$326$	−3.80974	+	31.3761i	−0.211002	+	1.73776i
$327$	−1.54761	+	0.586931i	−0.0855830	+	0.0324574i
$328$	−16.0509	−	8.42414i	−0.886261	−	0.465145i
$329$	−4.49910	+	11.8632i	−0.248044	+	0.654037i
$330$	−4.49406	−	8.56271i	−0.247390	−	0.471362i
$331$	3.40978	+	6.49679i	0.187418	+	0.357096i	0.960977	−	0.276629i	$-0.0892174\pi$
$331$	3.40978	+	6.49679i	0.187418	+	0.357096i	−0.773558	+	0.633725i	$0.781525\pi$
$332$	1.56102	+	6.33330i	0.0856721	+	0.347585i
$333$	2.05046	+	0.248970i	0.112364	+	0.0136435i
$334$	−10.1467	−	8.98919i	−0.555203	−	0.491867i
$335$	0.416633	+	0.603597i	0.0227631	+	0.0329780i
$336$	−7.07171	−	2.68195i	−0.385793	−	0.146312i
$337$	−15.9993			−0.871538			−0.435769	−	0.900059i	$-0.643523\pi$
$337$	−15.9993			−0.871538			−0.435769	+	0.900059i	$0.643523\pi$
$338$	−12.4994	+	16.7397i	−0.679877	+	0.910518i
$339$	−9.45184			−0.513353
$340$	−8.05103	−	3.05335i	−0.436628	−	0.165591i
$341$	−0.156963	−	0.227400i	−0.00850003	−	0.0123144i
$342$	−2.60939	−	2.31172i	−0.141100	−	0.125003i
$343$	17.9601	+	2.18075i	0.969753	+	0.117749i
$344$	1.31895	+	5.35119i	0.0711130	+	0.288517i
$345$	3.70953	+	7.06792i	0.199714	+	0.380524i
$346$	−8.93789	−	17.0297i	−0.480504	−	0.915524i
$347$	−4.80762	+	12.6767i	−0.258087	+	0.680519i	0.741864	+	0.670551i	$0.233942\pi$
$347$	−4.80762	+	12.6767i	−0.258087	+	0.680519i	−0.999950	+	0.00996796i	$0.996827\pi$
$348$	4.68394	+	2.45832i	0.251086	+	0.131780i
$349$	0.768123	−	0.291311i	0.0411167	−	0.0155935i	−0.333961	−	0.942587i	$-0.608385\pi$
$349$	0.768123	−	0.291311i	0.0411167	−	0.0155935i	0.375078	+	0.926993i	$0.377616\pi$
$350$	−0.0553866	+	0.456150i	−0.00296054	+	0.0243822i
$351$	−2.27605	+	2.79635i	−0.121487	+	0.149258i
$352$	−1.05727	−	8.70740i	−0.0563526	−	0.464106i
$353$	−12.1259	−	23.1040i	−0.645398	−	1.22970i	−0.959873	−	0.280437i	$-0.909521\pi$
$353$	−12.1259	−	23.1040i	−0.645398	−	1.22970i	0.314475	−	0.949266i	$-0.398172\pi$
$354$	−1.16716	−	9.61246i	−0.0620340	−	0.510896i
$355$	14.5555	−	7.63931i	0.772525	−	0.405453i
$356$	5.65179	−	6.37955i	0.299544	−	0.338116i
$357$			10.5542i			0.558589i
$358$	3.06246	+	3.45680i	0.161856	+	0.182698i
$359$	15.2096	−	28.9795i	0.802733	−	1.52948i	−0.0449584	−	0.998989i	$-0.514316\pi$
$359$	15.2096	−	28.9795i	0.802733	−	1.52948i	0.847691	−	0.530490i	$-0.177992\pi$
$360$	−4.99972			−0.263508
$361$	14.2942			0.752326
$362$	8.72796	−	16.6297i	0.458731	−	0.874039i
$363$	3.38232	+	0.833668i	0.177526	+	0.0437562i
$364$	−1.29493	−	3.02651i	−0.0678728	−	0.158632i
$365$	−11.5084	+	2.83657i	−0.602379	+	0.148473i
$366$	−2.29091	+	9.29457i	−0.119748	+	0.485835i
$367$	4.37394	−	11.5331i	0.228318	−	0.602025i	−0.771079	−	0.636739i	$-0.780283\pi$
$367$	4.37394	−	11.5331i	0.228318	−	0.602025i	0.999397	+	0.0347141i	$0.0110521\pi$
$368$	2.11541	+	17.4219i	0.110273	+	0.908181i
$369$	−1.90445	−	7.72667i	−0.0991419	−	0.402235i
$370$	−1.74356	+	7.07391i	−0.0906435	+	0.367755i
$371$	1.82871	+	1.26227i	0.0949417	+	0.0655335i
$372$	0.0582839	−	0.00707695i	0.00302188	−	0.000366923i
$373$	−8.41323	−	22.1839i	−0.435621	−	1.14864i	−0.955654	−	0.294492i	$-0.904850\pi$
$373$	−8.41323	−	22.1839i	−0.435621	−	1.14864i	0.520033	−	0.854146i	$-0.325920\pi$
$374$	−26.2714	+	13.7883i	−1.35846	+	0.712975i
$375$	2.72219	+	11.0444i	0.140573	+	0.570329i
$376$	−6.53908	+	17.2421i	−0.337227	+	0.889195i
$377$	−9.15684	−	31.4337i	−0.471601	−	1.61892i
$378$	−0.893122	−	2.35497i	−0.0459372	−	0.121127i
$379$	8.48058	−	5.85372i	0.435618	−	0.300686i	−0.330000	−	0.943981i	$-0.607049\pi$
$379$	8.48058	−	5.85372i	0.435618	−	0.300686i	0.765618	+	0.643295i	$0.222433\pi$
$380$	2.07617	−	1.83932i	0.106505	−	0.0943552i
$381$	−11.3811	−	2.80519i	−0.583071	−	0.143714i
$382$	−33.0293	−	12.5264i	−1.68993	−	0.640905i
$383$	7.95965	−	15.1658i	0.406719	−	0.774938i	−0.592819	−	0.805336i	$-0.701985\pi$
$383$	7.95965	−	15.1658i	0.406719	−	0.774938i	0.999538	+	0.0303974i	$0.00967728\pi$
$384$	−12.7596	−	4.83910i	−0.651138	−	0.246944i
$385$	−6.25397	−	7.05927i	−0.318732	−	0.359774i
$386$	16.8358	−	14.9152i	0.856921	−	0.759166i
$387$	−1.37443	+	1.99121i	−0.0698663	+	0.101219i
$388$	−0.786340	−	0.542772i	−0.0399204	−	0.0275551i
$389$	21.3537	+	11.2073i	1.08267	+	0.568231i	0.909095	−	0.416589i	$-0.136775\pi$
$389$	21.3537	+	11.2073i	1.08267	+	0.568231i	0.173579	+	0.984820i	$0.444467\pi$
$390$	−8.82385	−	9.15862i	−0.446813	−	0.463765i
$391$	21.6852	−	11.3813i	1.09667	−	0.575575i
$392$	10.2745	+	1.24756i	0.518943	+	0.0630111i
$393$	−11.5463	+	2.84590i	−0.582432	+	0.143557i
$394$	19.0287	−	27.5678i	0.958651	−	1.38885i
$395$	9.85320	−	6.80118i	0.495769	−	0.342204i
$396$	1.05909	−	1.19547i	0.0532214	−	0.0600745i
$397$	−31.8508	−	3.86739i	−1.59855	−	0.194099i	−0.727785	−	0.685805i	$-0.759450\pi$
$397$	−31.8508	−	3.86739i	−1.59855	−	0.194099i	−0.870761	+	0.491707i	$0.836373\pi$
$398$	7.54216	−	30.5997i	0.378054	−	1.53383i
$399$	−3.01041	−	1.57998i	−0.150709	−	0.0790982i
$400$	−0.106121	+	0.873986i	−0.00530606	+	0.0436993i
$401$	10.5727	−	1.28375i	0.527974	−	0.0641076i	0.147790	−	0.989019i	$-0.452784\pi$
$401$	10.5727	−	1.28375i	0.527974	−	0.0641076i	0.380183	+	0.924911i	$0.375861\pi$
$402$	−0.305045	+	0.441935i	−0.0152143	+	0.0220417i
$403$	−0.281829	−	0.229391i	−0.0140389	−	0.0114268i
$404$	−0.772427	−	1.11905i	−0.0384297	−	0.0556750i
$405$	−1.45548	−	1.64290i	−0.0723236	−	0.0816365i
$406$	22.2060	+	5.47328i	1.10206	+	0.271635i
$407$	3.21686	+	4.66043i	0.159454	+	0.231009i
$408$			15.3397i			0.759429i
$409$	15.6808	−	10.8237i	0.775365	−	0.535196i	−0.113405	−	0.993549i	$-0.536176\pi$
$409$	15.6808	−	10.8237i	0.775365	−	0.535196i	0.888770	+	0.458353i	$0.151560\pi$
$410$	27.8650	−	3.38342i	1.37615	−	0.167095i
$411$	14.7752	−	5.60350i	0.728808	−	0.276400i
$412$	−0.704170	+	5.79936i	−0.0346920	+	0.285714i
$413$	−3.34869	−	8.82976i	−0.164778	−	0.434484i
$414$	−3.87551	+	4.37455i	−0.190471	+	0.214997i
$415$	18.3957	+	16.2971i	0.903007	+	0.799995i
$416$	−4.53765	−	10.6054i	−0.222477	−	0.519973i
$417$	−7.01847	+	6.21782i	−0.343696	+	0.304488i
$418$		−	9.55758i		−	0.467476i
$419$	−29.1625	−	25.8358i	−1.42468	−	1.26216i	−0.915984	−	0.401215i	$-0.868588\pi$
$419$	−29.1625	−	25.8358i	−1.42468	−	1.26216i	−0.508700	−	0.860944i	$-0.669874\pi$
$420$	1.94573	−	0.479579i	0.0949418	−	0.0234010i
$421$	−2.96673	−	2.04779i	−0.144590	−	0.0998031i	0.493574	−	0.869704i	$-0.335690\pi$
$421$	−2.96673	−	2.04779i	−0.144590	−	0.0998031i	−0.638164	+	0.769901i	$0.720306\pi$
$422$	−0.491023	+	0.186220i	−0.0239026	+	0.00906507i
$423$	−7.56935	+	2.87068i	−0.368035	+	0.139577i
$424$	2.65787	+	1.83460i	0.129078	+	0.0890960i
$425$	1.19288	−	0.294019i	0.0578633	−	0.0142620i
$426$	9.00884	+	7.98113i	0.436480	+	0.386687i
$427$			9.33584i			0.451793i
$428$	−7.16072	+	6.34385i	−0.346127	+	0.306641i
$429$	−9.87640	+	0.413085i	−0.476837	+	0.0199439i
$430$	−6.38795	−	5.65923i	−0.308054	−	0.272912i
$431$	0.179546	−	0.202665i	0.00864842	−	0.00976205i	−0.744171	−	0.667990i	$-0.767155\pi$
$431$	0.179546	−	0.202665i	0.00864842	−	0.00976205i	0.752819	+	0.658228i	$0.228694\pi$
$432$	−1.71123	−	4.51214i	−0.0823316	−	0.217091i
$433$	−1.63205	+	13.4411i	−0.0784312	+	0.645939i	0.899486	+	0.436949i	$0.143941\pi$
$433$	−1.63205	+	13.4411i	−0.0784312	+	0.645939i	−0.977918	+	0.208991i	$0.932982\pi$
$434$	0.237344	−	0.0900128i	0.0113929	−	0.00432075i
$435$	19.7855	−	2.40239i	0.948640	−	0.115186i
$436$	0.793537	−	0.547739i	0.0380035	−	0.0262319i
$437$			7.88911i			0.377387i
$438$	−4.92983	−	7.14209i	−0.235556	−	0.341262i
$439$	3.44309	+	0.848644i	0.164329	+	0.0405036i	0.320622	−	0.947207i	$-0.396108\pi$
$439$	3.44309	+	0.848644i	0.164329	+	0.0405036i	−0.156292	+	0.987711i	$0.549954\pi$
$440$	−9.08962	−	10.2601i	−0.433331	−	0.489129i
$441$	2.58111	+	3.73938i	0.122910	+	0.178066i
$442$	−28.0997	+	27.0726i	−1.33657	+	1.28771i
$443$	−0.399366	+	0.578582i	−0.0189745	+	0.0274892i	−0.832356	−	0.554241i	$-0.813009\pi$
$443$	−0.399366	+	0.578582i	−0.0189745	+	0.0274892i	0.813382	+	0.581730i	$0.197624\pi$
$444$	−1.19449	+	0.145038i	−0.0566882	+	0.00688319i
$445$	3.87072	−	31.8782i	0.183490	−	1.51117i
$446$	−15.1975	−	7.97625i	−0.719622	−	0.377687i
$447$	−4.38301	+	17.7826i	−0.207309	+	0.841087i
$448$	−7.01687	−	0.852003i	−0.331516	−	0.0402533i
$449$	4.00535	−	4.52110i	0.189024	−	0.213364i	−0.646357	−	0.763035i	$-0.723708\pi$
$449$	4.00535	−	4.52110i	0.189024	−	0.213364i	0.835381	+	0.549671i	$0.185247\pi$
$450$	−0.241288	+	0.166549i	−0.0113744	+	0.00785119i
$451$	12.3938	−	17.9555i	0.583600	−	0.845491i
$452$	5.34617	−	1.31771i	0.251463	−	0.0619800i
$453$	19.7817	+	2.40193i	0.929423	+	0.112852i
$454$	−16.1634	+	8.48319i	−0.758585	+	0.398136i
$455$	−10.4930	−	6.61300i	−0.491919	−	0.310022i
$456$	−4.37538	−	2.29638i	−0.204896	−	0.107538i
$457$	21.9134	+	15.1257i	1.02506	+	0.707551i	0.956987	−	0.290130i	$-0.0936984\pi$
$457$	21.9134	+	15.1257i	1.02506	+	0.707551i	0.0680766	+	0.997680i	$0.478314\pi$
$458$	−10.0611	+	14.5760i	−0.470125	+	0.681094i
$459$	−5.04061	+	4.46559i	−0.235276	+	0.208436i
$460$	−3.08356	−	3.48062i	−0.143772	−	0.162285i
$461$	−36.9921	−	14.0293i	−1.72289	−	0.653408i	−0.723573	−	0.690248i	$-0.757501\pi$
$461$	−36.9921	−	14.0293i	−1.72289	−	0.653408i	−0.999321	+	0.0368403i	$0.988271\pi$
$462$	3.20898	−	6.11420i	0.149295	−	0.284458i
$463$	−25.5171	−	9.67735i	−1.18588	−	0.449744i	−0.318755	−	0.947837i	$-0.603265\pi$
$463$	−25.5171	−	9.67735i	−1.18588	−	0.449744i	−0.867124	+	0.498093i	$0.834034\pi$
$464$	42.5469	+	10.4869i	1.97519	+	0.486840i
$465$	0.165579	−	0.146690i	0.00767854	−	0.00680259i
$466$	23.5769	−	16.2739i	1.09218	−	0.753875i
$467$	−5.65460	−	14.9100i	−0.261664	−	0.689950i	−0.999882	−	0.0153881i	$-0.995102\pi$
$467$	−5.65460	−	14.9100i	−0.261664	−	0.689950i	0.738218	−	0.674562i	$-0.235668\pi$
$468$	0.897539	−	1.89899i	0.0414887	−	0.0877809i
$469$	−0.185707	+	0.489669i	−0.00857516	+	0.0226108i
$470$	−6.83359	−	27.7250i	−0.315210	−	1.27886i
$471$	12.9209	−	6.78143i	0.595365	−	0.312472i
$472$	−4.86704	−	12.8333i	−0.224024	−	0.590702i
$473$	−6.58497	+	0.799560i	−0.302777	+	0.0367638i
$474$	7.21420	+	4.97960i	0.331359	+	0.228721i
$475$	−0.0947125	+	0.384264i	−0.00434571	+	0.0176312i
$476$	−1.47140	−	5.96971i	−0.0674416	−	0.273621i
$477$	0.170895	+	1.40745i	0.00782476	+	0.0644427i
$478$	−12.9992	+	34.2760i	−0.594568	+	1.56775i
$479$	−1.27161	+	5.15914i	−0.0581015	+	0.235727i	−0.992812	−	0.119682i	$-0.961812\pi$
$479$	−1.27161	+	5.15914i	−0.0581015	+	0.235727i	0.934711	+	0.355409i	$0.115659\pi$
$480$	6.81815	−	1.68052i	0.311205	−	0.0767051i
$481$	5.77591	+	4.70123i	0.263359	+	0.214358i
$482$	9.03297	+	2.22643i	0.411440	+	0.101411i
$483$	−2.64879	+	5.04684i	−0.120524	+	0.229639i
$484$	−2.02934			−0.0922429
$485$	−3.59997			−0.163466
$486$	0.746825	−	1.42296i	0.0338767	−	0.0645466i
$487$	21.2216	+	23.9542i	0.961643	+	1.08547i	0.996289	+	0.0860704i	$0.0274310\pi$
$487$	21.2216	+	23.9542i	0.961643	+	1.08547i	−0.0346465	+	0.999400i	$0.511031\pi$
$488$			13.5689i			0.614234i
$489$	−13.0421	+	14.7214i	−0.589782	+	0.665726i
$490$	−14.1910	+	7.44802i	−0.641085	+	0.336467i
$491$	2.94561	+	24.2593i	0.132934	+	1.09481i	0.894609	+	0.446849i	$0.147454\pi$
$491$	2.94561	+	24.2593i	0.132934	+	1.09481i	−0.761676	+	0.647959i	$0.775623\pi$
$492$	2.15440	+	4.10487i	0.0971280	+	0.185062i
$493$	−7.37081	−	60.7041i	−0.331965	−	2.73397i
$494$	−3.51541	−	12.0677i	−0.158166	−	0.542954i
$495$	0.725336	−	5.97368i	0.0326014	−	0.268497i
$496$	0.454754	−	0.172465i	0.0204190	−	0.00774392i
$497$	10.3933	+	5.45484i	0.466205	+	0.244683i
$498$	−6.38077	+	16.8247i	−0.285929	+	0.753933i
$499$	1.24360	+	2.36949i	0.0556714	+	0.106073i	0.911702	−	0.410852i	$-0.134769\pi$
$499$	1.24360	+	2.36949i	0.0556714	+	0.106073i	−0.856031	+	0.516925i	$0.827077\pi$
$500$	−3.07947	−	5.86744i	−0.137718	−	0.262400i
$501$	−2.01871	−	8.19022i	−0.0901892	−	0.365912i
$502$	40.5691	+	4.92598i	1.81069	+	0.219857i
$503$	−4.40592	−	3.90330i	−0.196450	−	0.174040i	0.559163	−	0.829058i	$-0.311123\pi$
$503$	−4.40592	−	3.90330i	−0.196450	−	0.174040i	−0.755613	+	0.655018i	$0.772661\pi$
$504$	−2.02802	−	2.93809i	−0.0903351	−	0.130873i
$505$	−4.79025	−	1.81670i	−0.213164	−	0.0808423i
$506$	−16.0229			−0.712306
$507$	−12.3184	+	4.15426i	−0.547078	+	0.184497i
$508$	6.82848			0.302965
$509$	12.9453	+	4.90952i	0.573792	+	0.217611i	0.624396	−	0.781108i	$-0.285345\pi$
$509$	12.9453	+	4.90952i	0.573792	+	0.217611i	−0.0506034	+	0.998719i	$0.516114\pi$
$510$	−13.4934	−	19.5485i	−0.597497	−	0.865624i
$511$	−6.33504	−	5.61235i	−0.280245	−	0.248276i
$512$	−6.49807	−	0.789009i	−0.287177	−	0.0348696i
$513$	−0.519144	−	2.10625i	−0.0229208	−	0.0929933i
$514$	3.06035	+	5.83101i	0.134986	+	0.257195i
$515$	10.2290	+	19.4897i	0.450743	+	0.858820i
$516$	0.499808	−	1.31789i	0.0220028	−	0.0580167i
$517$	−19.6523	−	10.3143i	−0.864307	−	0.453623i
$518$	−4.86423	+	1.84476i	−0.213722	+	0.0810540i
$519$	1.44257	−	11.8806i	0.0633216	−	0.521500i
$520$	−15.2507	−	9.61144i	−0.668787	−	0.421490i
$521$	1.59819	+	13.1623i	0.0700181	+	0.576651i	0.984925	+	0.172985i	$0.0553411\pi$
$521$	1.59819	+	13.1623i	0.0700181	+	0.576651i	−0.914906	+	0.403666i	$0.867736\pi$
$522$	6.78156	+	12.9212i	0.296821	+	0.565545i
$523$	3.04998	+	25.1189i	0.133366	+	1.09837i	0.893645	+	0.448774i	$0.148139\pi$
$523$	3.04998	+	25.1189i	0.133366	+	1.09837i	−0.760279	+	0.649597i	$0.774938\pi$
$524$	6.13407	−	3.21941i	0.267968	−	0.140640i
$525$	−0.189607	+	0.214022i	−0.00827514	+	0.00934070i
$526$			13.9675i			0.609012i
$527$	−0.450062	−	0.508015i	−0.0196050	−	0.0221295i
$528$	6.14843	−	11.7149i	0.267576	−	0.509824i
$529$	−9.77420			−0.424965
$530$	−5.00091			−0.217226
$531$	2.80016	−	5.33525i	0.121516	−	0.231530i
$532$	1.92303	+	0.473984i	0.0833738	+	0.0205498i
$533$	9.04455	−	27.2299i	0.391763	−	1.17946i
$534$	22.8284	−	5.62671i	0.987884	−	0.243491i
$535$	−8.62601	+	34.9971i	−0.372935	+	1.51306i
$536$	−0.269910	+	0.711694i	−0.0116583	+	0.0307405i
$537$	0.346395	+	2.85282i	0.0149480	+	0.123108i
$538$	−8.72593	−	35.4025i	−0.376202	−	1.52631i
$539$	−2.98117	+	12.0951i	−0.128408	+	0.520971i
$540$	1.05230	+	0.726348i	0.0452837	+	0.0312571i
$541$	−26.5499	+	3.22374i	−1.14147	+	0.138599i	−0.669358	−	0.742940i	$-0.733431\pi$
$541$	−26.5499	+	3.22374i	−1.14147	+	0.138599i	−0.472111	+	0.881539i	$0.656508\pi$
$542$	−4.97707	−	13.1234i	−0.213783	−	0.563700i
$543$	10.3481	−	5.43110i	0.444080	−	0.233071i
$544$	−5.15604	−	20.9189i	−0.221063	−	0.896890i
$545$	1.28825	−	3.39684i	0.0551826	−	0.145505i
$546$	1.80289	−	8.90032i	0.0771564	−	0.380899i
$547$	1.01075	+	2.66514i	0.0432167	+	0.113953i	0.954887	−	0.296969i	$-0.0959759\pi$
$547$	1.01075	+	2.66514i	0.0432167	+	0.113953i	−0.911670	+	0.410922i	$0.865207\pi$
$548$	−7.57600	+	5.22933i	−0.323631	+	0.223386i
$549$	−4.45872	+	3.95008i	−0.190293	+	0.168585i
$550$	−0.780447	−	0.192363i	−0.0332784	−	0.00820238i
$551$	18.4182	+	6.98510i	0.784641	+	0.297575i
$552$	−3.84979	+	7.33517i	−0.163858	+	0.312205i
$553$	7.99343	+	3.03151i	0.339915	+	0.128913i
$554$	−25.1821	−	28.4247i	−1.06988	−	1.20765i
$555$	−3.39344	+	3.00633i	−0.144044	+	0.127611i
$556$	3.10296	−	4.49541i	0.131595	−	0.190648i
$557$	23.3178	+	16.0951i	0.988008	+	0.681973i	0.948345	−	0.317240i	$-0.102756\pi$
$557$	23.3178	+	16.0951i	0.988008	+	0.681973i	0.0396632	+	0.999213i	$0.487371\pi$
$558$	0.143412	+	0.0752683i	0.00607110	+	0.00318636i
$559$	−8.02033	+	3.43160i	−0.339224	+	0.145141i
$560$	14.6989	−	7.71460i	0.621143	−	0.326001i
$561$	−18.3279	−	2.22541i	−0.773806	−	0.0939571i
$562$	26.8506	−	6.61809i	1.13263	−	0.279167i
$563$	−1.61779	+	2.34378i	−0.0681819	+	0.0987785i	−0.855591	−	0.517652i	$-0.826806\pi$
$563$	−1.61779	+	2.34378i	−0.0681819	+	0.0987785i	0.787410	+	0.616430i	$0.211422\pi$
$564$	3.88119	−	2.67899i	0.163427	−	0.112806i
$565$	13.7570	−	15.5284i	0.578761	−	0.653287i
$566$	45.6524	+	5.54320i	1.91891	+	0.232998i
$567$	0.375070	−	1.52172i	0.0157515	−	0.0639063i
$568$	15.1059	+	7.92816i	0.633828	+	0.332658i
$569$	−2.13513	+	17.5844i	−0.0895093	+	0.737175i	0.876991	+	0.480508i	$0.159548\pi$
$569$	−2.13513	+	17.5844i	−0.0895093	+	0.737175i	−0.966500	+	0.256667i	$0.917375\pi$
$570$	7.59586	−	0.922304i	0.318155	−	0.0386311i
$571$	−11.2877	+	16.3531i	−0.472376	+	0.684355i	−0.984665	−	0.174459i	$-0.944183\pi$
$571$	−11.2877	+	16.3531i	−0.472376	+	0.684355i	0.512288	+	0.858813i	$0.328798\pi$
$572$	5.52872	−	1.61055i	0.231168	−	0.0673406i
$573$	−12.4869	−	18.0904i	−0.521647	−	0.755736i
$574$	13.2910	+	15.0025i	0.554758	+	0.626192i
$575$	0.644204	+	0.158782i	0.0268652	+	0.00662167i
$576$	−2.56199	−	3.71169i	−0.106750	−	0.154654i
$577$			15.1156i			0.629270i	0.949213	+	0.314635i	$0.101882\pi$
$577$			15.1156i			0.629270i	−0.949213	+	0.314635i	$0.898118\pi$
$578$	−37.4936	+	25.8800i	−1.55953	+	1.07647i
$579$	13.8942	−	1.68706i	0.577424	−	0.0701119i
$580$	−10.8562	+	4.11721i	−0.450778	+	0.170958i
$581$	−2.11526	+	17.4208i	−0.0877559	+	0.722735i
$582$	−0.934663	−	2.46450i	−0.0387430	−	0.102157i
$583$	−2.57758	+	2.90948i	−0.106752	+	0.120498i
$584$	−9.20745	−	8.15709i	−0.381007	−	0.337543i
$585$	−1.28137	−	7.80938i	−0.0529781	−	0.322878i
$586$	−16.4582	+	14.5807i	−0.679884	+	0.602324i
$587$			27.6863i			1.14274i	0.820694	+	0.571368i	$0.193587\pi$
$587$			27.6863i			1.14274i	−0.820694	+	0.571368i	$0.806413\pi$
$588$	−1.98125	−	1.75524i	−0.0817055	−	0.0723848i
$589$	0.212277	−	0.0523216i	0.00874673	−	0.00215588i
$590$	17.4911	+	12.0732i	0.720098	+	0.497047i
$591$	19.4897	−	7.39147i	0.801700	−	0.304045i
$592$	−9.31990	+	3.53457i	−0.383046	+	0.145270i
$593$	26.3216	+	18.1685i	1.08090	+	0.746089i	0.968859	−	0.247615i	$-0.0796467\pi$
$593$	26.3216	+	18.1685i	1.08090	+	0.746089i	0.112038	+	0.993704i	$0.464262\pi$
$594$	4.27783	−	1.05439i	0.175522	−	0.0432622i
$595$	−17.3396	−	15.3615i	−0.710853	−	0.629761i
$596$		−	10.6693i		−	0.437031i
$597$	14.6791	−	13.0045i	0.600774	−	0.532239i
$598$	−20.2311	+	5.89346i	−0.827313	+	0.241002i
$599$	−26.7766	−	23.7220i	−1.09406	−	0.969256i	−0.0944088	−	0.995534i	$-0.530096\pi$
$599$	−26.7766	−	23.7220i	−1.09406	−	0.969256i	−0.999655	+	0.0262779i	$0.991635\pi$
$600$	−0.275578	+	0.311064i	−0.0112504	+	0.0126991i
$601$	5.95104	+	15.6916i	0.242748	+	0.640074i	0.999914	−	0.0131493i	$-0.00418569\pi$
$601$	5.95104	+	15.6916i	0.242748	+	0.640074i	−0.757166	+	0.653223i	$0.773416\pi$
$602$	0.734532	−	6.04941i	0.0299373	−	0.246556i
$603$	−0.312436	+	0.118491i	−0.0127234	+	0.00482534i
$604$	−11.5238	+	1.39924i	−0.468897	+	0.0569344i
$605$	−6.29255	+	4.34344i	−0.255829	+	0.176586i
$606$		−	3.75103i		−	0.152375i
$607$	19.7524	+	28.6163i	0.801727	+	1.16150i	0.983985	+	0.178251i	$0.0570439\pi$
$607$	19.7524	+	28.6163i	0.801727	+	1.16150i	−0.182258	+	0.983251i	$0.558341\pi$
$608$	6.73861	+	1.66092i	0.273287	+	0.0673591i
$609$	9.43727	+	10.6525i	0.382417	+	0.431660i
$610$	−11.9357	−	17.2918i	−0.483262	−	0.700126i
$611$	−28.6075	−	5.79484i	−1.15733	−	0.234434i
$612$	2.22852	−	3.22857i	0.0900826	−	0.130507i
$613$	13.6040	−	1.65183i	0.549461	−	0.0667166i	0.158902	−	0.987294i	$-0.449205\pi$
$613$	13.6040	−	1.65183i	0.549461	−	0.0667166i	0.390559	+	0.920578i	$0.372282\pi$
$614$	−4.23050	+	34.8413i	−0.170729	+	1.40608i
$615$	15.4661	+	8.11722i	0.623652	+	0.327318i
$616$	2.34235	−	9.50328i	0.0943759	−	0.382898i
$617$	−20.8474	−	2.53134i	−0.839286	−	0.101908i	−0.310406	−	0.950604i	$-0.600465\pi$
$617$	−20.8474	−	2.53134i	−0.839286	−	0.101908i	−0.528880	+	0.848696i	$0.677388\pi$
$618$	−10.6867	+	12.0628i	−0.429882	+	0.485236i
$619$	11.9721	−	8.26375i	0.481200	−	0.332148i	−0.302647	−	0.953103i	$-0.597870\pi$
$619$	11.9721	−	8.26375i	0.481200	−	0.332148i	0.783847	+	0.620955i	$0.213255\pi$
$620$	−0.0732046	+	0.106055i	−0.00293997	+	0.00425928i
$621$	−3.53105	+	0.870326i	−0.141696	+	0.0349250i
$622$	10.6367	+	1.29154i	0.426495	+	0.0517858i
$623$	20.3033	−	10.6560i	0.813436	−	0.426924i
$624$	3.45434	−	17.0531i	0.138284	−	0.682670i
$625$	−21.2992	−	11.1787i	−0.851969	−	0.447148i
$626$	−25.3385	−	17.4899i	−1.01273	−	0.699037i
$627$	3.37848	−	4.89457i	0.134923	−	0.195470i
$628$	−6.36295	+	5.63708i	−0.253909	+	0.224944i
$629$	9.22375	+	10.4115i	0.367775	+	0.415132i
$630$	5.16891	+	1.96031i	0.205934	+	0.0781006i
$631$	−11.9581	+	22.7843i	−0.476045	+	0.907029i	0.522475	+	0.852654i	$0.325009\pi$
$631$	−11.9581	+	22.7843i	−0.476045	+	0.907029i	−0.998521	+	0.0543741i	$0.982684\pi$
$632$	11.6178	+	4.40605i	0.462131	+	0.175263i
$633$	−0.317286	−	0.0782041i	−0.0126110	−	0.00310833i
$634$	30.9128	−	27.3864i	1.22770	−	1.08765i
$635$	21.1736	−	14.6151i	0.840250	−	0.579983i
$636$	−0.292880	−	0.772260i	−0.0116134	−	0.0306221i
$637$	0.684608	+	16.3682i	0.0271251	+	0.648531i
$638$	−14.1869	+	37.4077i	−0.561663	+	1.48098i
$639$	1.79233	+	7.27176i	0.0709034	+	0.287666i
$640$	26.5216	−	13.9196i	1.04836	−	0.550221i
$641$	7.40865	+	19.5350i	0.292624	+	0.771587i	0.998027	+	0.0627803i	$0.0199967\pi$
$641$	7.40865	+	19.5350i	0.292624	+	0.771587i	−0.705403	+	0.708806i	$0.749234\pi$
$642$	−26.1982	+	3.18104i	−1.03396	+	0.125546i
$643$	27.5723	+	19.0318i	1.08735	+	0.750541i	0.970135	−	0.242566i	$-0.0779891\pi$
$643$	27.5723	+	19.0318i	1.08735	+	0.750541i	0.117211	+	0.993107i	$0.462604\pi$
$644$	0.794616	−	3.22388i	0.0313123	−	0.127039i
$645$	−1.27090	−	5.15623i	−0.0500415	−	0.203026i
$646$	−2.82973	−	23.3050i	−0.111334	−	0.916921i
$647$	−5.35649	+	14.1239i	−0.210585	+	0.555268i	−0.998139	−	0.0609782i	$-0.980578\pi$
$647$	−5.35649	+	14.1239i	−0.210585	+	0.555268i	0.787554	+	0.616246i	$0.211347\pi$
$648$	0.545134	−	2.21169i	0.0214149	−	0.0868836i
$649$	16.0394	−	3.95335i	0.629601	−	0.155183i
$650$	−1.05617	+	0.0441750i	−0.0414266	+	0.00173269i
$651$	0.153366	+	0.0378013i	0.00601088	+	0.00148155i
$652$	5.32451	−	10.1450i	0.208524	−	0.397309i
$653$	7.10013			0.277850			0.138925	−	0.990303i	$-0.455635\pi$
$653$	7.10013			0.277850			0.138925	+	0.990303i	$0.455635\pi$
$654$	2.65991			0.104011
$655$	12.1299	−	23.1115i	0.473953	−	0.903042i
$656$	25.4658	+	28.7449i	0.994271	+	1.12230i
$657$		−	5.40019i		−	0.210682i
$658$	13.5207	−	15.2617i	0.527092	−	0.594964i
$659$	−15.5286	+	8.15002i	−0.604907	+	0.317480i	−0.739225	−	0.673459i	$-0.764808\pi$
$659$	−15.5286	+	8.15002i	−0.604907	+	0.317480i	0.134318	+	0.990938i	$0.457116\pi$
$660$	0.422545	+	3.47997i	0.0164475	+	0.135458i
$661$	21.2231	+	40.4372i	0.825482	+	1.57283i	0.819666	+	0.572842i	$0.194159\pi$
$661$	21.2231	+	40.4372i	0.825482	+	1.57283i	0.00581659	+	0.999983i	$0.498149\pi$
$662$	−1.42127	−	11.7052i	−0.0552391	−	0.454935i
$663$	−23.9601	+	3.93139i	−0.930532	+	0.152682i
$664$	−3.07436	+	25.3196i	−0.119308	+	0.982593i
$665$	6.97736	−	2.64616i	0.270571	−	0.102614i
$666$	−2.93914	−	1.54258i	−0.113889	−	0.0597737i
$667$	11.7103	−	30.8774i	0.453423	−	1.19558i
$668$	2.28365	+	4.35114i	0.0883572	+	0.168351i
$669$	−4.96335	−	9.45687i	−0.191894	−	0.365624i
$670$	−0.282066	−	1.14439i	−0.0108972	−	0.0442116i
$671$	−16.2121	−	1.96851i	−0.625862	−	0.0759934i
$672$	3.75318	+	3.32503i	0.144782	+	0.128266i
$673$	−6.65701	−	9.64434i	−0.256609	−	0.371762i	0.673413	−	0.739267i	$-0.264828\pi$
$673$	−6.65701	−	9.64434i	−0.256609	−	0.371762i	−0.930022	+	0.367505i	$0.880212\pi$
$674$	24.0406	+	9.11738i	0.926008	+	0.351188i
$675$	−0.182440			−0.00702211
$676$	6.38839	−	4.06709i	0.245707	−	0.156426i
$677$	−26.3324			−1.01204			−0.506018	−	0.862523i	$-0.668883\pi$
$677$	−26.3324			−1.01204			−0.506018	+	0.862523i	$0.668883\pi$
$678$	14.2023	+	5.38624i	0.545438	+	0.206857i
$679$	−1.46024	−	2.11553i	−0.0560390	−	0.0811865i
$680$	−25.2016	−	22.3267i	−0.966439	−	0.856190i
$681$	−11.2762	−	1.36918i	−0.432105	−	0.0524670i
$682$	0.106266	+	0.431139i	0.00406914	+	0.0165092i
$683$	5.54668	+	10.5683i	0.212238	+	0.404385i	0.968181	−	0.250252i	$-0.0805135\pi$
$683$	5.54668	+	10.5683i	0.212238	+	0.404385i	−0.755943	+	0.654638i	$0.772821\pi$
$684$	0.587279	+	1.11897i	0.0224552	+	0.0427848i
$685$	−12.2991	+	32.4301i	−0.469924	+	1.23909i
$686$	−25.7441	−	13.5115i	−0.982914	−	0.515873i
$687$	−10.3049	+	3.90813i	−0.393156	+	0.149104i
$688$	1.40737	−	11.5907i	0.0536555	−	0.441892i
$689$	−2.18439	+	4.62169i	−0.0832187	+	0.176072i
$690$	−1.54621	−	12.7342i	−0.0588632	−	0.484782i
$691$	18.7885	+	35.7986i	0.714750	+	1.36184i	0.923395	+	0.383851i	$0.125402\pi$
$691$	18.7885	+	35.7986i	0.714750	+	1.36184i	−0.208646	+	0.977991i	$0.566905\pi$
$692$	0.840367	+	6.92104i	0.0319460	+	0.263099i
$693$	3.80465	−	1.99684i	0.144527	−	0.0758535i
$694$	14.4479	−	16.3083i	0.548434	−	0.619054i
$695$		−	20.5806i		−	0.780667i
$696$	13.7163	+	15.4825i	0.519915	+	0.586862i
$697$	24.9046	−	47.4517i	0.943327	−	1.79736i
$698$	−1.32019			−0.0499699
$699$	17.8267			0.674266
$700$	0.0774085	−	0.147490i	0.00292577	−	0.00557458i
$701$	−0.213229	−	0.0525562i	−0.00805355	−	0.00198502i	0.235287	−	0.971926i	$-0.424397\pi$
$701$	−0.213229	−	0.0525562i	−0.00805355	−	0.00198502i	−0.243340	+	0.969941i	$0.578243\pi$
$702$	5.01353	−	2.90476i	0.189224	−	0.109633i
$703$	−4.35050	+	1.07230i	−0.164082	+	0.0404426i
$704$	2.95909	−	12.0055i	0.111525	−	0.452474i
$705$	6.30083	−	16.6139i	0.237303	−	0.625717i
$706$	5.05433	+	41.6262i	0.190222	+	1.56662i
$707$	−0.875465	−	3.55190i	−0.0329252	−	0.133583i
$708$	−0.840026	+	3.40812i	−0.0315701	+	0.128085i
$709$	−32.9972	−	22.7763i	−1.23923	−	0.855382i	−0.245748	−	0.969334i	$-0.579034\pi$
$709$	−32.9972	−	22.7763i	−1.23923	−	0.855382i	−0.993486	+	0.113952i	$0.963649\pi$
$710$	−26.2244	+	3.18422i	−0.984186	+	0.119502i
$711$	1.93427	+	5.10025i	0.0725408	+	0.191274i
$712$	29.5092	−	15.4876i	1.10590	−	0.580424i
$713$	−0.0877153	−	0.355875i	−0.00328496	−	0.0133276i
$714$	6.01445	−	15.8588i	0.225085	−	0.593501i
$715$	13.6963	−	16.8272i	0.512212	−	0.629301i
$716$	−0.593650	−	1.56533i	−0.0221857	−	0.0584990i
$717$	−18.7732	+	12.9582i	−0.701097	+	0.483932i
$718$	−39.3683	+	34.8772i	−1.46921	+	1.30161i
$719$	−48.4296	−	11.9368i	−1.80612	−	0.445168i	−0.815148	−	0.579252i	$-0.803345\pi$
$719$	−48.4296	−	11.9368i	−1.80612	−	0.445168i	−0.990970	+	0.134084i	$0.957191\pi$
$720$	9.90367	+	3.75597i	0.369088	+	0.139977i
$721$	−7.30400	+	13.9166i	−0.272015	+	0.518282i
$722$	−21.4785	−	8.14571i	−0.799346	−	0.303152i
$723$	3.83890	+	4.33322i	0.142770	+	0.161154i
$724$	−5.09595	+	4.51462i	−0.189390	+	0.167785i
$725$	0.941083	−	1.36339i	0.0349509	−	0.0506352i
$726$	−4.60721	−	3.18012i	−0.170989	−	0.118026i
$727$	14.9487	+	7.84566i	0.554415	+	0.290980i	0.718570	−	0.695455i	$-0.244797\pi$
$727$	14.9487	+	7.84566i	0.554415	+	0.290980i	−0.164154	+	0.986435i	$0.552489\pi$
$728$	−0.537907	−	12.8607i	−0.0199361	−	0.476651i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	18.9090	+	2.29597i	0.699855	+	0.0849777i
$731$	−15.8199	+	3.89925i	−0.585120	+	0.144219i
$732$	1.97126	−	2.85586i	0.0728597	−	0.105556i
$733$	−36.4092	+	25.1315i	−1.34480	+	0.928252i	−0.999946	−	0.0104028i	$-0.996689\pi$
$733$	−36.4092	+	25.1315i	−1.34480	+	0.928252i	−0.344859	+	0.938655i	$0.612073\pi$
$734$	−13.1446	+	14.8372i	−0.485175	+	0.547650i
$735$	−9.90020	−	1.20210i	−0.365174	−	0.0443402i
$736$	2.78447	−	11.2970i	0.102637	−	0.416414i
$737$	−0.811177	−	0.425739i	−0.0298801	−	0.0156823i
$738$	−1.54150	+	12.6954i	−0.0567433	+	0.467323i
$739$	−26.2707	+	3.18984i	−0.966383	+	0.117340i	−0.588486	−	0.808508i	$-0.700276\pi$
$739$	−26.2707	+	3.18984i	−0.966383	+	0.117340i	−0.377897	+	0.925848i	$0.623353\pi$
$740$	1.50028	−	2.17354i	0.0551515	−	0.0799008i
$741$	2.46550	−	7.42272i	0.0905724	−	0.272680i
$742$	−2.02850	−	2.93879i	−0.0744686	−	0.107886i
$743$	−2.81035	−	3.17223i	−0.103102	−	0.116378i	0.694695	−	0.719305i	$-0.255539\pi$
$743$	−2.81035	−	3.17223i	−0.103102	−	0.116378i	−0.797796	+	0.602927i	$0.794001\pi$
$744$	0.222904	+	0.0549410i	0.00817207	+	0.00201423i
$745$	−22.8356	−	33.0831i	−0.836633	−	1.21207i
$746$			38.1279i			1.39596i
$747$	−9.21499	+	6.36065i	−0.337159	+	0.232724i
$748$	10.6769	−	1.29642i	0.390388	−	0.0474017i
$749$	−24.0650	+	9.12666i	−0.879317	+	0.333481i
$750$	2.20339	−	18.1466i	0.0804564	−	0.662618i
$751$	12.8197	+	33.8028i	0.467798	+	1.23348i	0.936669	+	0.350216i	$0.113892\pi$
$751$	12.8197	+	33.8028i	0.467798	+	1.23348i	−0.468871	+	0.883267i	$0.655339\pi$
$752$	25.9058	−	29.2416i	0.944687	−	1.06633i
$753$	19.0348	+	16.8633i	0.693665	+	0.614534i
$754$	−4.15378	+	52.4504i	−0.151272	+	1.91013i
$755$	−32.7380	+	29.0033i	−1.19146	+	1.05554i
$756$			0.913009i			0.0332058i
$757$	19.2231	+	17.0302i	0.698677	+	0.618974i	0.935811	−	0.352503i	$-0.114670\pi$
$757$	19.2231	+	17.0302i	0.698677	+	0.618974i	−0.237134	+	0.971477i	$0.576208\pi$
$758$	−16.0787	+	3.96305i	−0.584006	+	0.143945i
$759$	−8.20557	−	5.66390i	−0.297843	−	0.205586i
$760$	10.1410	−	3.84598i	0.367853	−	0.139508i
$761$	35.2316	−	13.3616i	1.27714	−	0.484357i	0.379546	−	0.925173i	$-0.376080\pi$
$761$	35.2316	−	13.3616i	1.27714	−	0.484357i	0.897597	+	0.440816i	$0.145311\pi$
$762$	15.5027	+	10.7007i	0.561602	+	0.387646i
$763$	2.51870	−	0.620805i	0.0911832	−	0.0224747i
$764$	9.58490	+	8.49148i	0.346769	+	0.307211i
$765$		−	14.7808i		−	0.534402i
$766$	−20.6026	+	18.2523i	−0.744402	+	0.659483i
$767$	18.7978	−	10.8912i	0.678750	−	0.393257i
$768$	9.66342	+	8.56104i	0.348699	+	0.308920i
$769$	0.247952	−	0.279880i	0.00894137	−	0.0100927i	−0.744023	−	0.668154i	$-0.767085\pi$
$769$	0.247952	−	0.279880i	0.00894137	−	0.0100927i	0.752964	+	0.658061i	$0.228623\pi$
$770$	5.37441	+	14.1712i	0.193680	+	0.510693i
$771$	−0.493937	+	4.06794i	−0.0177887	+	0.146503i
$772$	−7.62368	+	2.89128i	−0.274382	+	0.104059i
$773$	13.5876	−	1.64983i	0.488710	−	0.0593402i	0.127527	−	0.991835i	$-0.459296\pi$
$773$	13.5876	−	1.64983i	0.488710	−	0.0593402i	0.361183	+	0.932495i	$0.382373\pi$
$774$	3.19993	−	2.20876i	0.115019	−	0.0793921i
$775$		−	0.0183871i		−	0.000660483i
$776$	−2.12234	−	3.07474i	−0.0761877	−	0.110377i
$777$	−3.14314	−	0.774714i	−0.112759	−	0.0277927i
$778$	−25.6994	−	29.0087i	−0.921370	−	1.04001i
$779$	9.80650	+	14.2072i	0.351354	+	0.509025i
$780$	1.81350	+	4.23852i	0.0649338	+	0.151763i
$781$	−11.6641	+	16.8983i	−0.417374	+	0.604670i
$782$	−39.0699	+	4.74395i	−1.39714	+	0.169643i
$783$	−1.09454	+	9.01431i	−0.0391155	+	0.322145i
$784$	−19.4151	−	10.1898i	−0.693396	−	0.363922i
$785$	−7.66499	+	31.0981i	−0.273575	+	1.10994i
$786$	18.9712	+	2.30352i	0.676680	+	0.0821638i
$787$	13.2500	−	14.9562i	0.472312	−	0.533130i	−0.463281	−	0.886212i	$-0.653328\pi$
$787$	13.2500	−	14.9562i	0.472312	−	0.533130i	0.935592	+	0.353082i	$0.114866\pi$
$788$	−9.99335	+	6.89791i	−0.355998	+	0.245728i
$789$	−4.93733	+	7.15296i	−0.175774	+	0.254652i
$790$	−18.6812	+	4.60449i	−0.664646	+	0.163820i
$791$	14.7055	+	1.78557i	0.522867	+	0.0634876i
$792$	5.52975	−	2.90224i	0.196491	−	0.103126i
$793$	−21.1941	+	3.47754i	−0.752624	+	0.123491i
$794$	45.6552	+	23.9617i	1.62024	+	0.850368i
$795$	−2.56104	−	1.76776i	−0.0908306	−	0.0626959i
$796$	−6.48980	+	9.40210i	−0.230025	+	0.333249i
$797$	21.7441	−	19.2636i	0.770214	−	0.682350i	−0.183515	−	0.983017i	$-0.558748\pi$
$797$	21.7441	−	19.2636i	0.770214	−	0.682350i	0.953729	+	0.300667i	$0.0972091\pi$
$798$	3.62307	+	4.08960i	0.128255	+	0.144770i
$799$	−50.9734	−	19.3317i	−1.80331	−	0.683906i
$800$	0.271252	−	0.516828i	0.00959022	−	0.0182726i
$801$	13.6797	+	5.18804i	0.483350	+	0.183310i
$802$	−16.6181	−	4.09598i	−0.586804	−	0.144634i
$803$	11.0819	−	9.81770i	0.391071	−	0.346459i
$804$	0.160202	−	0.110579i	0.00564988	−	0.00389983i
$805$	−4.43620	−	11.6973i	−0.156355	−	0.412275i
$806$	0.292755	+	0.505286i	0.0103118	+	0.0177979i
$807$	8.04565	−	21.2146i	0.283220	−	0.746790i
$808$	−1.27242	−	5.16239i	−0.0447634	−	0.181612i
$809$	47.3213	−	24.8361i	1.66373	−	0.873192i	0.672642	−	0.739968i	$-0.265159\pi$
$809$	47.3213	−	24.8361i	1.66373	−	0.873192i	0.991086	−	0.133224i	$-0.0425331\pi$
$810$	1.25079	+	3.29805i	0.0439481	+	0.115882i
$811$	−2.67315	+	0.324579i	−0.0938670	+	0.0113975i	−0.167335	−	0.985900i	$-0.553516\pi$
$811$	−2.67315	+	0.324579i	−0.0938670	+	0.0113975i	0.0734684	+	0.997298i	$0.476593\pi$
$812$	−6.82303	−	4.70960i	−0.239441	−	0.165274i
$813$	2.09014	−	8.48003i	0.0733044	−	0.297408i
$814$	−2.17786	−	8.83594i	−0.0763341	−	0.309699i
$815$	−5.20337	−	42.8536i	−0.182266	−	1.50110i
$816$	11.5237	−	30.3856i	0.403412	−	1.06371i
$817$	1.25607	−	5.09607i	0.0439443	−	0.178289i
$818$	−29.7300	+	7.32778i	−1.03948	+	0.256210i
$819$	4.06943	−	3.92069i	0.142197	−	0.137000i
$820$	−9.87961	−	2.43510i	−0.345011	−	0.0850375i
$821$	11.0988	−	21.1470i	0.387351	−	0.738035i	−0.611221	−	0.791460i	$-0.709321\pi$
$821$	11.0988	−	21.1470i	0.387351	−	0.738035i	0.998572	+	0.0534247i	$0.0170137\pi$
$822$	−25.3945			−0.885734
$823$	38.4389			1.33990			0.669948	−	0.742408i	$-0.266316\pi$
$823$	38.4389			1.33990			0.669948	+	0.742408i	$0.266316\pi$
$824$	−10.6158	+	20.2267i	−0.369818	+	0.704629i
$825$	−0.331680	−	0.374390i	−0.0115476	−	0.0130346i
$826$			15.1759i			0.528037i
$827$	8.96596	−	10.1205i	0.311777	−	0.351923i	−0.571646	−	0.820501i	$-0.693695\pi$
$827$	8.96596	−	10.1205i	0.311777	−	0.351923i	0.883423	+	0.468577i	$0.155233\pi$
$828$	1.87591	−	0.984552i	0.0651923	−	0.0342156i
$829$	2.86344	+	23.5826i	0.0994514	+	0.819056i	0.954025	+	0.299726i	$0.0968953\pi$
$829$	2.86344	+	23.5826i	0.0994514	+	0.819056i	−0.854574	+	0.519330i	$0.826182\pi$
$830$	−18.3542	−	34.9710i	−0.637084	−	1.21386i
$831$	−2.84835	−	23.4582i	−0.0988080	−	0.813757i
$832$	−0.679537	−	16.2470i	−0.0235587	−	0.563262i
$833$	−3.68819	+	30.3750i	−0.127788	+	1.05243i
$834$	14.0893	−	5.34335i	0.487871	−	0.185025i
$835$	16.3939	+	8.60420i	0.567335	+	0.297761i
$836$	−1.22857	+	3.23949i	−0.0424911	+	0.112040i
$837$	0.0468369	+	0.0892402i	0.00161892	+	0.00308459i
$838$	29.0969	+	55.4394i	1.00513	+	1.91512i
$839$	−6.45180	−	26.1760i	−0.222741	−	0.903696i	−0.970767	−	0.240026i	$-0.922844\pi$
$839$	−6.45180	−	26.1760i	−0.222741	−	0.903696i	0.748025	−	0.663670i	$-0.231002\pi$
$840$	7.77874	+	0.944510i	0.268392	+	0.0325887i
$841$	−40.0123	−	35.4478i	−1.37973	−	1.22234i
$842$	3.29086	+	4.76764i	0.113411	+	0.164304i
$843$	16.0900	+	6.10213i	0.554169	+	0.210169i
$844$	0.190367			0.00655270
$845$	11.1041	−	26.2843i	0.381994	−	0.904208i
$846$	13.0096			0.447279
$847$	−5.10485	−	1.93601i	−0.175405	−	0.0665222i
$848$	−3.88662	−	5.63075i	−0.133467	−	0.193361i
$849$	21.4198	+	18.9763i	0.735125	+	0.651264i
$850$	−1.95998	−	0.237984i	−0.0672266	−	0.00816279i
$851$	1.79767	+	7.29345i	0.0616234	+	0.250016i
$852$	−2.02756	−	3.86320i	−0.0694631	−	0.132351i
$853$	−8.17519	−	15.5765i	−0.279913	−	0.533330i	0.704390	−	0.709813i	$-0.251220\pi$
$853$	−8.17519	−	15.5765i	−0.279913	−	0.533330i	−0.984304	+	0.176482i	$0.943528\pi$
$854$	5.32013	−	14.0280i	0.182051	−	0.480030i
$855$	4.21597	+	2.21271i	0.144183	+	0.0756731i
$856$	−34.9765	+	13.2648i	−1.19547	+	0.453383i
$857$	−4.08838	+	33.6708i	−0.139656	+	1.15017i	0.739336	+	0.673337i	$0.235140\pi$
$857$	−4.08838	+	33.6708i	−0.139656	+	1.15017i	−0.878992	+	0.476837i	$0.841783\pi$
$858$	15.0757	+	5.00747i	0.514675	+	0.170952i
$859$	−1.82949	−	15.0672i	−0.0624214	−	0.514087i	−0.990064	−	0.140618i	$-0.955091\pi$
$859$	−1.82949	−	15.0672i	−0.0624214	−	0.514087i	0.927643	−	0.373469i	$-0.121832\pi$
$860$	1.43769	+	2.73930i	0.0490250	+	0.0934093i
$861$	1.50335	+	12.3812i	0.0512340	+	0.421950i
$862$	−0.385277	+	0.202209i	−0.0131226	+	0.00688726i
$863$	−36.0527	+	40.6951i	−1.22725	+	1.38528i	−0.329861	+	0.944029i	$0.607002\pi$
$863$	−36.0527	+	40.6951i	−1.22725	+	1.38528i	−0.897386	+	0.441246i	$0.854537\pi$
$864$			3.19934i			0.108844i
$865$	17.4190	+	19.6620i	0.592264	+	0.668528i
$866$	10.1119	−	19.2666i	0.343616	−	0.654706i
$867$	−28.3493			−0.962792
$868$	−0.0920171			−0.00312326
$869$	−6.94982	+	13.2418i	−0.235756	+	0.449196i
$870$	−31.0987	−	7.66514i	−1.05434	−	0.259872i
$871$	−1.18081	−	0.239191i	−0.0400104	−	0.00810467i
$872$	3.66073	−	0.902289i	0.123968	−	0.0305554i
$873$	0.392516	−	1.59250i	0.0132846	−	0.0538979i
$874$	4.49570	−	11.8542i	0.152069	−	0.400974i
$875$	−2.14886	−	17.6975i	−0.0726448	−	0.598284i
$876$	0.752860	+	3.05447i	0.0254368	+	0.103201i
$877$	7.80274	−	31.6569i	0.263480	−	1.06898i	−0.678846	−	0.734281i	$-0.737519\pi$
$877$	7.80274	−	31.6569i	0.263480	−	1.06898i	0.942325	−	0.334698i	$-0.108634\pi$
$878$	−4.68997	−	3.23725i	−0.158279	−	0.109252i
$879$	−13.5826	+	1.64923i	−0.458130	+	0.0556270i
$880$	10.2974	+	27.1521i	0.347126	+	0.915296i
$881$	−9.58160	+	5.02881i	−0.322812	+	0.169425i	−0.618343	−	0.785908i	$-0.712196\pi$
$881$	−9.58160	+	5.02881i	−0.322812	+	0.169425i	0.295531	+	0.955333i	$0.404503\pi$
$882$	−1.74745	−	7.08967i	−0.0588396	−	0.238722i
$883$	11.2834	−	29.7518i	0.379715	−	1.00123i	−0.599852	−	0.800111i	$-0.704774\pi$
$883$	11.2834	−	29.7518i	0.379715	−	1.00123i	0.979567	−	0.201116i	$-0.0644568\pi$
$884$	13.0043	−	5.56404i	0.437381	−	0.187139i
$885$	4.68971	+	12.3658i	0.157643	+	0.415670i
$886$	0.929799	−	0.641794i	0.0312372	−	0.0215615i
$887$	15.4235	−	13.6640i	0.517871	−	0.458793i	−0.363245	−	0.931693i	$-0.618331\pi$
$887$	15.4235	−	13.6640i	0.517871	−	0.458793i	0.881116	+	0.472900i	$0.156793\pi$
$888$	−4.56829	−	1.12598i	−0.153302	−	0.0377855i
$889$	17.1772	+	6.51444i	0.576104	+	0.218487i
$890$	−23.9823	+	45.6945i	−0.803889	+	1.53168i
$891$	2.56345	+	0.972190i	0.0858789	+	0.0325696i
$892$	4.12580	+	4.65706i	0.138142	+	0.155930i
$893$	13.1448	−	11.6453i	0.439875	−	0.389695i
$894$	16.7195	−	24.2224i	0.559184	−	0.810119i
$895$	−5.19107	−	3.58314i	−0.173518	−	0.119771i
$896$	18.9377	+	9.93929i	0.632666	+	0.332048i
$897$	−12.4439	−	4.13332i	−0.415490	−	0.138007i
$898$	−8.59484	+	4.51092i	−0.286814	+	0.150531i
$899$	−0.908502	−	0.110312i	−0.0303002	−	0.00367912i
$900$	0.103192	−	0.0254345i	0.00343973	−	0.000847818i
$901$	−5.42368	+	7.85756i	−0.180689	+	0.261773i
$902$	−28.8550	+	19.9172i	−0.960767	+	0.663170i
$903$	2.51455	−	2.83834i	0.0836791	−	0.0944542i
$904$	21.3732	+	2.59518i	0.710863	+	0.0863144i
$905$	−6.13873	+	24.9058i	−0.204058	+	0.827897i
$906$	−28.3552	−	14.8819i	−0.942037	−	0.494419i
$907$	−2.62361	+	21.6074i	−0.0871156	+	0.717462i	0.882068	+	0.471122i	$0.156151\pi$
$907$	−2.62361	+	21.6074i	−0.0871156	+	0.717462i	−0.969184	+	0.246340i	$0.920772\pi$
$908$	6.56895	−	0.797615i	0.217998	−	0.0264698i
$909$	1.32594	−	1.92096i	0.0439786	−	0.0637141i
$910$	11.9983	+	15.9162i	0.397739	+	0.527618i
$911$	4.84528	+	7.01960i	0.160531	+	0.232570i	0.894993	−	0.446081i	$-0.147181\pi$
$911$	4.84528	+	7.01960i	0.160531	+	0.232570i	−0.734462	+	0.678650i	$0.762565\pi$
$912$	6.94184	+	7.83571i	0.229867	+	0.259466i
$913$	−29.8060	−	7.34651i	−0.986434	−	0.243134i
$914$	−24.3075	−	35.2155i	−0.804020	−	1.16482i
$915$		−	13.0745i		−	0.432230i
$916$	5.28383	−	3.64716i	0.174583	−	0.120506i
$917$	18.5017	−	2.24651i	0.610980	−	0.0741864i
$918$	10.1188	−	3.83755i	0.333970	−	0.126658i
$919$	−2.86307	+	23.5795i	−0.0944439	+	0.777815i	0.866135	+	0.499809i	$0.166597\pi$
$919$	−2.86307	+	23.5795i	−0.0944439	+	0.777815i	−0.960579	+	0.278006i	$0.910326\pi$
$920$	−6.44765	−	17.0010i	−0.212573	−	0.560508i
$921$	−14.4825	+	16.3473i	−0.477213	+	0.538662i
$922$	47.5896	+	42.1607i	1.56728	+	1.38849i
$923$	−8.51205	+	25.6267i	−0.280178	+	0.843513i
$924$	−1.87361	+	1.65988i	−0.0616373	+	0.0546059i
$925$			0.376832i			0.0123902i
$926$	32.8272	+	29.0824i	1.07877	+	0.955706i
$927$	−9.73684	+	2.39992i	−0.319800	+	0.0788236i
$928$	−23.9090	−	16.5032i	−0.784853	−	0.541745i
$929$	3.89077	−	1.47557i	0.127652	−	0.0484120i	−0.289952	−	0.957041i	$-0.593639\pi$
$929$	3.89077	−	1.47557i	0.127652	−	0.0484120i	0.417604	+	0.908629i	$0.362870\pi$
$930$	−0.332392	+	0.126060i	−0.0108996	+	0.00413366i
$931$	−8.11179	−	5.59917i	−0.265853	−	0.183505i
$932$	−10.0832	+	2.48528i	−0.330285	+	0.0814079i
$933$	4.99069	+	4.42137i	0.163388	+	0.144749i
$934$			25.6260i			0.838510i
$935$	30.3322	−	26.8719i	0.991967	−	0.878806i
$936$	5.91458	−	5.69839i	0.193324	−	0.186258i
$937$	−1.26530	−	1.12096i	−0.0413355	−	0.0366200i	0.642202	−	0.766535i	$-0.278021\pi$
$937$	−1.26530	−	1.12096i	−0.0413355	−	0.0366200i	−0.683538	+	0.729915i	$0.739559\pi$
$938$	0.558087	−	0.629950i	0.0182222	−	0.0205686i
$939$	−6.79375	−	17.9137i	−0.221706	−	0.584590i
$940$	−1.24769	+	10.2756i	−0.0406951	+	0.335154i
$941$	28.8339	−	10.9352i	0.939957	−	0.356479i	0.163424	−	0.986556i	$-0.447746\pi$
$941$	28.8339	−	10.9352i	0.939957	−	0.356479i	0.776532	+	0.630077i	$0.216977\pi$
$942$	−23.2795	+	2.82664i	−0.758487	+	0.0920969i
$943$	23.8178	−	16.4402i	0.775614	−	0.535368i
$944$			29.0771i			0.946380i
$945$	1.95413	+	2.83104i	0.0635678	+	0.0920939i
$946$	10.3502	+	2.55110i	0.336514	+	0.0829434i
$947$	−33.3236	−	37.6146i	−1.08287	−	1.22231i	−0.973591	−	0.228298i	$-0.926684\pi$
$947$	−33.3236	−	37.6146i	−1.08287	−	1.22231i	−0.109280	−	0.994011i	$-0.534854\pi$
$948$	−1.80511	−	2.61515i	−0.0586273	−	0.0849363i
$949$	10.3813	−	16.4723i	0.336992	−	0.534712i
$950$	0.361292	−	0.523422i	0.0117219	−	0.0169820i
$951$	25.5116	−	3.09767i	0.827271	−	0.100449i
$952$	2.89786	−	23.8661i	0.0939203	−	0.773504i
$953$	−19.1559	−	10.0538i	−0.620520	−	0.325674i	0.125001	−	0.992157i	$-0.460107\pi$
$953$	−19.1559	−	10.0538i	−0.620520	−	0.325674i	−0.745520	+	0.666483i	$0.767799\pi$
$954$	0.545264	−	2.21222i	0.0176536	−	0.0716233i
$955$	47.8951	+	5.81552i	1.54985	+	0.188186i
$956$	8.81199	−	9.94668i	0.285000	−	0.321698i
$957$	−20.4884	+	14.1421i	−0.662297	+	0.457150i
$958$	4.85072	−	7.02748i	0.156720	−	0.227048i
$959$	−24.0464	+	5.92690i	−0.776498	+	0.191390i
$960$	9.82688	+	1.19320i	0.317161	+	0.0385103i
$961$	27.4401	−	14.4017i	0.885166	−	0.464571i
$962$	−5.99983	−	10.3555i	−0.193442	−	0.333876i
$963$	−14.5409	−	7.63167i	−0.468575	−	0.245927i
$964$	−2.77548	−	1.91577i	−0.0893921	−	0.0617029i
$965$	−17.4511	+	25.2823i	−0.561771	+	0.813866i
$966$	6.85607	−	6.07395i	0.220590	−	0.195426i
$967$	6.00322	+	6.77624i	0.193051	+	0.217909i	0.837064	−	0.547105i	$-0.184270\pi$
$967$	6.00322	+	6.77624i	0.193051	+	0.217909i	−0.644013	+	0.765014i	$0.722732\pi$
$968$	−7.41947	−	2.81384i	−0.238471	−	0.0904401i
$969$	6.78885	−	12.9351i	0.218089	−	0.415535i
$970$	5.40932	+	2.05149i	0.173683	+	0.0658692i
$971$	−27.7493	−	6.83959i	−0.890517	−	0.219493i	−0.232591	−	0.972575i	$-0.574720\pi$
$971$	−27.7493	−	6.83959i	−0.890517	−	0.219493i	−0.657927	+	0.753082i	$0.728566\pi$
$972$	−0.436045	+	0.386302i	−0.0139862	+	0.0123907i
$973$	12.0942	−	8.34803i	0.387723	−	0.267626i
$974$	−18.2370	−	48.0870i	−0.584351	−	1.54081i
$975$	−0.556498	−	0.350721i	−0.0178222	−	0.0112321i
$976$	10.1934	−	26.8778i	0.326283	−	0.860339i
$977$	−1.39181	−	5.64680i	−0.0445280	−	0.180657i	0.944467	−	0.328606i	$-0.106579\pi$
$977$	−1.39181	−	5.64680i	−0.0445280	−	0.180657i	−0.988995	+	0.147949i	$0.952733\pi$
$978$	27.9862	−	14.6883i	0.894899	−	0.469679i
$979$	14.2236	+	37.5046i	0.454589	+	1.19865i
$980$	5.76737	−	0.700285i	0.184232	−	0.0223698i
$981$	1.36218	+	0.940243i	0.0434910	+	0.0300197i
$982$	9.39836	−	38.1307i	0.299914	−	1.21680i
$983$	9.66344	+	39.2061i	0.308216	+	1.25048i	0.896942	+	0.442148i	$0.145784\pi$
$983$	9.66344	+	39.2061i	0.308216	+	1.25048i	−0.588726	+	0.808333i	$0.700370\pi$
$984$	2.18500	+	17.9951i	0.0696551	+	0.573661i
$985$	−16.2235	+	42.7779i	−0.516924	+	1.36302i
$986$	−23.5175	+	95.4143i	−0.748950	+	3.03861i
$987$	12.3190	−	3.03635i	0.392117	−	0.0966482i
$988$	−0.359715	+	4.54218i	−0.0114441	+	0.144506i
$989$	−8.54338	−	2.10575i	−0.271664	−	0.0669590i
$990$	−4.49406	+	8.56271i	−0.142831	+	0.272141i
$991$	−21.0996			−0.670251			−0.335126	−	0.942173i	$-0.608779\pi$
$991$	−21.0996			−0.670251			−0.335126	+	0.942173i	$0.608779\pi$
$992$	−0.322443			−0.0102376
$993$	3.40978	−	6.49679i	0.108206	−	0.206169i
$994$	−12.5085	−	14.1192i	−0.396746	−	0.447834i
$995$			43.0441i			1.36459i
$996$	4.32545	−	4.88242i	0.137057	−	0.154705i
$997$	−16.4600	+	8.63885i	−0.521292	+	0.273595i	−0.704779	−	0.709427i	$-0.748954\pi$
$997$	−16.4600	+	8.63885i	−0.521292	+	0.273595i	0.183487	+	0.983022i	$0.441262\pi$
$998$	−0.518360	−	4.26908i	−0.0164084	−	0.135135i
$999$	−0.959893	−	1.82892i	−0.0303697	−	0.0578646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.b.25.4	✓	192
169.142	even	26	inner	507.2.p.b.142.4	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.b.25.4	✓	192	1.1	even	1	trivial
507.2.p.b.142.4	yes	192	169.142	even	26	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50260 - 0.569861i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(0.436045 + 0.386302i) q^{4} +(2.17889 + 0.264565i) q^{5} +(0.384588 + 1.56033i) q^{6} +(0.728343 + 1.38774i) q^{7} +(1.05859 + 2.01697i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})\)	\(q+(-1.50260 - 0.569861i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(0.436045 + 0.386302i) q^{4} +(2.17889 + 0.264565i) q^{5} +(0.384588 + 1.56033i) q^{6} +(0.728343 + 1.38774i) q^{7} +(1.05859 + 2.01697i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(-3.12324 - 1.63920i) q^{10} +(-2.56345 + 0.972190i) q^{11} +(0.0702187 - 0.578303i) q^{12} +(-2.87913 + 2.17040i) q^{13} +(-0.303589 - 2.50028i) q^{14} +(-1.02002 - 1.94348i) q^{15} +(-0.581678 - 4.79055i) q^{16} +(-5.96283 + 3.12953i) q^{17} +(1.06566 - 1.20288i) q^{18} -2.16929i q^{19} +(0.847893 + 0.957073i) q^{20} +(0.728343 - 1.38774i) q^{21} +4.40586 q^{22} -3.63673 q^{23} +(1.05859 - 2.01697i) q^{24} +(-0.177138 - 0.0436607i) q^{25} +(5.56300 - 1.62054i) q^{26} +(0.970942 - 0.239316i) q^{27} +(-0.218497 + 0.886479i) q^{28} +(-3.22000 + 8.49043i) q^{29} +(0.425165 + 3.50155i) q^{30} +(0.0241193 + 0.0978558i) q^{31} +(-0.765652 + 3.10637i) q^{32} +(2.25630 + 1.55741i) q^{33} +(10.7431 - 1.30445i) q^{34} +(1.21983 + 3.21643i) q^{35} +(-0.515823 + 0.270725i) q^{36} +(-0.494310 - 2.00550i) q^{37} +(-1.23619 + 3.25957i) q^{38} +(3.42173 + 1.13655i) q^{39} +(1.77292 + 4.67482i) q^{40} +(-6.54924 + 4.52061i) q^{41} +(-1.88523 + 1.67017i) q^{42} +(2.34919 + 0.579024i) q^{43} +(-1.49334 - 0.566350i) q^{44} +(-1.02002 + 1.94348i) q^{45} +(5.46455 + 2.07243i) q^{46} +(5.36826 + 6.05951i) q^{47} +(-3.61212 + 3.20005i) q^{48} +(2.58111 - 3.73938i) q^{49} +(0.241288 + 0.166549i) q^{50} +(5.96283 + 3.12953i) q^{51} +(-2.09386 - 0.165822i) q^{52} +(1.25539 - 0.658879i) q^{53} +(-1.59531 - 0.193706i) q^{54} +(-5.84269 + 1.44009i) q^{55} +(-2.02802 + 2.93809i) q^{56} +(-1.78529 + 1.23230i) q^{57} +(9.67674 - 10.9228i) q^{58} +(-5.98150 - 0.726285i) q^{59} +(0.305998 - 1.24148i) q^{60} +(5.27447 + 2.76825i) q^{61} +(0.0195226 - 0.160783i) q^{62} +(-1.55584 + 0.188913i) q^{63} +(-2.56199 + 3.71169i) q^{64} +(-6.84752 + 3.96734i) q^{65} +(-2.50281 - 3.62595i) q^{66} +(0.221583 + 0.250115i) q^{67} +(-3.80901 - 0.938836i) q^{68} +(2.06590 + 2.99297i) q^{69} -5.52815i q^{70} +(6.16364 - 4.25446i) q^{71} +(-2.26128 + 0.274569i) q^{72} +(-5.04927 + 1.91494i) q^{73} +(-0.400103 + 3.29515i) q^{74} +(0.0646940 + 0.170584i) q^{75} +(0.838001 - 0.945907i) q^{76} +(-3.21622 - 2.84932i) q^{77} +(-4.49382 - 3.65769i) q^{78} +(4.08292 - 3.61715i) q^{79} -10.5920i q^{80} +(-0.748511 - 0.663123i) q^{81} +(12.4170 - 3.06052i) q^{82} +(9.21499 + 6.36065i) q^{83} +(0.853679 - 0.323758i) q^{84} +(-13.8203 + 5.24135i) q^{85} +(-3.19993 - 2.20876i) q^{86} +(8.81666 - 2.17311i) q^{87} +(-4.67451 - 4.14126i) q^{88} -14.6305i q^{89} +(2.64020 - 2.33901i) q^{90} +(-5.10894 - 2.41469i) q^{91} +(-1.58578 - 1.40488i) q^{92} +(0.0668324 - 0.0754382i) q^{93} +(-4.61327 - 12.1642i) q^{94} +(0.573918 - 4.72664i) q^{95} +(2.99143 - 1.13450i) q^{96} +(-1.62820 + 0.197699i) q^{97} +(-6.00931 + 4.14792i) q^{98} -2.74161i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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