LMFDB - Embedded newform 507.2.p.a.64.4

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:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			64.4
Character	$\chi$	$=$	507.64
Dual form			507.2.p.a.103.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39250 - 0.169080i) q^{2} +(-0.748511 + 0.663123i) q^{3} +(-0.0314082 - 0.00774143i) q^{4} +(-1.23718 - 2.35725i) q^{5} +(1.15442 - 0.796842i) q^{6} +(-2.90606 - 1.10212i) q^{7} +(2.66558 + 1.01092i) q^{8} +(0.120537 - 0.992709i) q^{9} +O(q^{10})$	\(q+(-1.39250 - 0.169080i) q^{2} +(-0.748511 + 0.663123i) q^{3} +(-0.0314082 - 0.00774143i) q^{4} +(-1.23718 - 2.35725i) q^{5} +(1.15442 - 0.796842i) q^{6} +(-2.90606 - 1.10212i) q^{7} +(2.66558 + 1.01092i) q^{8} +(0.120537 - 0.992709i) q^{9} +(1.32421 + 3.49165i) q^{10} +(-0.705640 + 0.0856802i) q^{11} +(0.0286429 - 0.0150330i) q^{12} +(-3.02472 - 1.96242i) q^{13} +(3.86034 + 2.02606i) q^{14} +(2.48918 + 0.944023i) q^{15} +(-3.48361 - 1.82834i) q^{16} +(-0.207085 + 0.546038i) q^{17} +(-0.335695 + 1.36197i) q^{18} +0.343668i q^{19} +(0.0206091 + 0.0836145i) q^{20} +(2.90606 - 1.10212i) q^{21} +0.997093 q^{22} +7.47498 q^{23} +(-2.66558 + 1.01092i) q^{24} +(-1.18568 + 1.71775i) q^{25} +(3.88012 + 3.24410i) q^{26} +(0.568065 + 0.822984i) q^{27} +(0.0827421 + 0.0571127i) q^{28} +(-1.20770 + 9.94634i) q^{29} +(-3.30658 - 1.73543i) q^{30} +(1.13545 - 0.783748i) q^{31} +(-0.150582 - 0.103939i) q^{32} +(0.471363 - 0.532059i) q^{33} +(0.380691 - 0.725346i) q^{34} +(0.997337 + 8.21381i) q^{35} +(-0.0114708 + 0.0302461i) q^{36} +(-6.51051 + 4.49388i) q^{37} +(0.0581076 - 0.478559i) q^{38} +(3.56536 - 0.536865i) q^{39} +(-0.914807 - 7.53411i) q^{40} +(1.45933 + 1.64724i) q^{41} +(-4.23304 + 1.04335i) q^{42} +(-3.93255 + 5.69729i) q^{43} +(0.0228262 + 0.00277160i) q^{44} +(-2.48918 + 0.944023i) q^{45} +(-10.4089 - 1.26387i) q^{46} +(0.745302 + 3.02381i) q^{47} +(3.81993 - 0.941529i) q^{48} +(1.99091 + 1.76379i) q^{49} +(1.94150 - 2.19150i) q^{50} +(-0.207085 - 0.546038i) q^{51} +(0.0798090 + 0.0850518i) q^{52} +(-0.387364 + 1.02139i) q^{53} +(-0.651881 - 1.24206i) q^{54} +(1.07497 + 1.55737i) q^{55} +(-6.63216 - 5.87558i) q^{56} +(-0.227894 - 0.257240i) q^{57} +(3.36346 - 13.6461i) q^{58} +(1.98689 + 3.78571i) q^{59} +(-0.0708728 - 0.0489200i) q^{60} +(4.08507 + 10.7714i) q^{61} +(-1.71364 + 0.899388i) q^{62} +(-1.44437 + 2.75202i) q^{63} +(6.08178 + 5.38799i) q^{64} +(-0.883796 + 9.55787i) q^{65} +(-0.746335 + 0.661195i) q^{66} +(-3.02055 - 12.2549i) q^{67} +(0.0107313 - 0.0155470i) q^{68} +(-5.59511 + 4.95683i) q^{69} -11.6064i q^{70} +(5.94550 + 6.71108i) q^{71} +(1.32485 - 2.52429i) q^{72} +(-7.87817 + 0.956583i) q^{73} +(9.82573 - 5.15694i) q^{74} +(-0.251587 - 2.07200i) q^{75} +(0.00266049 - 0.0107940i) q^{76} +(2.14506 + 0.528710i) q^{77} +(-5.05554 + 0.144753i) q^{78} +(14.1517 - 3.48808i) q^{79} +10.4737i q^{80} +(-0.970942 - 0.239316i) q^{81} +(-1.75360 - 2.54053i) q^{82} +(7.69046 - 8.68074i) q^{83} +(-0.0998061 + 0.0121186i) q^{84} +(1.54335 - 0.187396i) q^{85} +(6.43939 - 7.26857i) q^{86} +(-5.69166 - 8.24580i) q^{87} +(-1.96755 - 0.484959i) q^{88} -14.5507i q^{89} +(3.62581 - 0.893683i) q^{90} +(6.62716 + 9.03651i) q^{91} +(-0.234776 - 0.0578671i) q^{92} +(-0.330179 + 1.33959i) q^{93} +(-0.526568 - 4.33668i) q^{94} +(0.810111 - 0.425179i) q^{95} +(0.181637 - 0.0220547i) q^{96} +(-2.26887 + 4.32297i) q^{97} +(-2.47412 - 2.79271i) q^{98} +0.710823i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9}+O(q^{10}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31} + 130 q^{32} + 13 q^{33} - 65 q^{34} - 35 q^{35} + 12 q^{36} + 61 q^{38} + 12 q^{40} - 63 q^{42} + 72 q^{43} - 39 q^{44} - 8 q^{48} - 68 q^{49} - 52 q^{50} - 4 q^{51} + 65 q^{52} - q^{53} + 53 q^{55} - 14 q^{56} - 13 q^{57} - 26 q^{58} - 104 q^{59} + 117 q^{60} + 12 q^{61} + 49 q^{62} - 32 q^{64} - 52 q^{65} - 46 q^{66} + 26 q^{67} - 84 q^{68} - 4 q^{69} - 39 q^{71} - 52 q^{73} + 29 q^{74} + 8 q^{75} - 130 q^{76} + 60 q^{77} + 65 q^{78} + 14 q^{79} - 14 q^{81} + 45 q^{82} + 78 q^{83} - 13 q^{85} - 13 q^{86} - 46 q^{87} - 26 q^{88} - 4 q^{90} - 208 q^{91} + 82 q^{92} - 39 q^{93} + 25 q^{94} - 66 q^{95} + 65 q^{96} + 26 q^{97} - 104 q^{98}+O(q^{100}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.39250	−	0.169080i	−0.984648	−	0.119558i	−0.387655	−	0.921804i	$-0.626715\pi$
$2$	−1.39250	−	0.169080i	−0.984648	−	0.119558i	−0.596993	+	0.802247i	$0.703638\pi$
$3$	−0.748511	+	0.663123i	−0.432153	+	0.382854i
$3$	−0.748511	+	0.663123i	−0.432153	+	0.382854i
$4$	−0.0314082	−	0.00774143i	−0.0157041	−	0.00387072i
$5$	−1.23718	−	2.35725i	−0.553283	−	1.05419i	−0.988120	−	0.153684i	$-0.950886\pi$
$5$	−1.23718	−	2.35725i	−0.553283	−	1.05419i	0.434837	−	0.900509i	$-0.356806\pi$
$6$	1.15442	−	0.796842i	0.471292	−	0.325309i
$7$	−2.90606	−	1.10212i	−1.09839	−	0.416563i	−0.262202	−	0.965013i	$-0.584449\pi$
$7$	−2.90606	−	1.10212i	−1.09839	−	0.416563i	−0.836183	+	0.548450i	$0.815218\pi$
$8$	2.66558	+	1.01092i	0.942424	+	0.357414i
$9$	0.120537	−	0.992709i	0.0401789	−	0.330903i
$10$	1.32421	+	3.49165i	0.418752	+	1.10416i
$11$	−0.705640	+	0.0856802i	−0.212759	+	0.0258336i	−0.226222	−	0.974076i	$-0.572637\pi$
$11$	−0.705640	+	0.0856802i	−0.212759	+	0.0258336i	0.0134633	+	0.999909i	$0.495714\pi$
$12$	0.0286429	−	0.0150330i	0.00826850	−	0.00433964i
$13$	−3.02472	−	1.96242i	−0.838905	−	0.544278i
$13$	−3.02472	−	1.96242i	−0.838905	−	0.544278i
$14$	3.86034	+	2.02606i	1.03172	+	0.541488i
$15$	2.48918	+	0.944023i	0.642705	+	0.243746i
$16$	−3.48361	−	1.82834i	−0.870903	−	0.457085i
$17$	−0.207085	+	0.546038i	−0.0502255	+	0.132434i	−0.957781	−	0.287498i	$-0.907177\pi$
$17$	−0.207085	+	0.546038i	−0.0502255	+	0.132434i	0.907556	+	0.419931i	$0.137946\pi$
$18$	−0.335695	+	1.36197i	−0.0791241	+	0.321019i
$19$			0.343668i			0.0788429i	0.999223	+	0.0394215i	$0.0125515\pi$
$19$			0.343668i			0.0788429i	−0.999223	+	0.0394215i	$0.987449\pi$
$20$	0.0206091	+	0.0836145i	0.00460834	+	0.0186968i
$21$	2.90606	−	1.10212i	0.634153	−	0.240503i
$22$	0.997093			0.212581
$23$	7.47498			1.55864			0.779321	−	0.626625i	$-0.215564\pi$
$23$	7.47498			1.55864			0.779321	+	0.626625i	$0.215564\pi$
$24$	−2.66558	+	1.01092i	−0.544109	+	0.206353i
$25$	−1.18568	+	1.71775i	−0.237135	+	0.343550i
$26$	3.88012	+	3.24410i	0.760954	+	0.636220i
$27$	0.568065	+	0.822984i	0.109324	+	0.158383i
$28$	0.0827421	+	0.0571127i	0.0156368	+	0.0107933i
$29$	−1.20770	+	9.94634i	−0.224265	+	1.84699i	0.252050	+	0.967714i	$0.418895\pi$
$29$	−1.20770	+	9.94634i	−0.224265	+	1.84699i	−0.476315	+	0.879275i	$0.658028\pi$
$30$	−3.30658	−	1.73543i	−0.603696	−	0.316844i
$31$	1.13545	−	0.783748i	0.203934	−	0.140765i	−0.461721	−	0.887025i	$-0.652768\pi$
$31$	1.13545	−	0.783748i	0.203934	−	0.140765i	0.665655	+	0.746260i	$0.268152\pi$
$32$	−0.150582	−	0.103939i	−0.0266194	−	0.0183741i
$33$	0.471363	−	0.532059i	0.0820537	−	0.0926195i
$34$	0.380691	−	0.725346i	0.0652879	−	0.124396i
$35$	0.997337	+	8.21381i	0.168581	+	1.38839i
$36$	−0.0114708	+	0.0302461i	−0.00191181	+	0.00504102i
$37$	−6.51051	+	4.49388i	−1.07032	+	0.738790i	−0.966722	−	0.255830i	$-0.917651\pi$
$37$	−6.51051	+	4.49388i	−1.07032	+	0.738790i	−0.103600	+	0.994619i	$0.533036\pi$
$38$	0.0581076	−	0.478559i	0.00942630	−	0.0776326i
$39$	3.56536	−	0.536865i	0.570914	−	0.0859671i
$40$	−0.914807	−	7.53411i	−0.144644	−	1.19125i
$41$	1.45933	+	1.64724i	0.227909	+	0.257256i	0.851330	−	0.524630i	$-0.175796\pi$
$41$	1.45933	+	1.64724i	0.227909	+	0.257256i	−0.623421	+	0.781886i	$0.714258\pi$
$42$	−4.23304	+	1.04335i	−0.653172	+	0.160992i
$43$	−3.93255	+	5.69729i	−0.599709	+	0.868828i	−0.998844	−	0.0480637i	$-0.984695\pi$
$43$	−3.93255	+	5.69729i	−0.599709	+	0.868828i	0.399135	+	0.916892i	$0.369310\pi$
$44$	0.0228262	+	0.00277160i	0.00344118	+	0.000417835i
$45$	−2.48918	+	0.944023i	−0.371066	+	0.140727i
$46$	−10.4089	−	1.26387i	−1.53471	−	0.186348i
$47$	0.745302	+	3.02381i	0.108714	+	0.441068i	0.999922	−	0.0125268i	$-0.00398750\pi$
$47$	0.745302	+	3.02381i	0.108714	+	0.441068i	−0.891208	+	0.453595i	$0.850141\pi$
$48$	3.81993	−	0.941529i	0.551360	−	0.135898i
$49$	1.99091	+	1.76379i	0.284416	+	0.251970i
$50$	1.94150	−	2.19150i	0.274569	−	0.309924i
$51$	−0.207085	−	0.546038i	−0.0289977	−	0.0764607i
$52$	0.0798090	+	0.0850518i	0.0110675	+	0.0117946i
$53$	−0.387364	+	1.02139i	−0.0532085	+	0.140299i	−0.958985	−	0.283456i	$-0.908519\pi$
$53$	−0.387364	+	1.02139i	−0.0532085	+	0.140299i	0.905777	+	0.423755i	$0.139288\pi$
$54$	−0.651881	−	1.24206i	−0.0887098	−	0.169022i
$55$	1.07497	+	1.55737i	0.144949	+	0.209995i
$56$	−6.63216	−	5.87558i	−0.886260	−	0.785158i
$57$	−0.227894	−	0.257240i	−0.0301853	−	0.0340722i
$58$	3.36346	−	13.6461i	0.441644	−	1.79182i
$59$	1.98689	+	3.78571i	0.258671	+	0.492857i	0.979809	−	0.199935i	$-0.0640730\pi$
$59$	1.98689	+	3.78571i	0.258671	+	0.492857i	−0.721138	+	0.692791i	$0.756381\pi$
$60$	−0.0708728	−	0.0489200i	−0.00914964	−	0.00631554i
$61$	4.08507	+	10.7714i	0.523039	+	1.37914i	0.892984	+	0.450088i	$0.148607\pi$
$61$	4.08507	+	10.7714i	0.523039	+	1.37914i	−0.369945	+	0.929054i	$0.620624\pi$
$62$	−1.71364	+	0.899388i	−0.217632	+	0.114222i
$63$	−1.44437	+	2.75202i	−0.181974	+	0.346722i
$64$	6.08178	+	5.38799i	0.760222	+	0.673498i
$65$	−0.883796	+	9.55787i	−0.109621	+	1.18551i
$66$	−0.746335	+	0.661195i	−0.0918674	+	0.0813874i
$67$	−3.02055	−	12.2549i	−0.369019	−	1.49717i	−0.802854	−	0.596176i	$-0.796686\pi$
$67$	−3.02055	−	12.2549i	−0.369019	−	1.49717i	0.433835	−	0.900992i	$-0.357160\pi$
$68$	0.0107313	−	0.0155470i	0.00130136	−	0.00188535i
$69$	−5.59511	+	4.95683i	−0.673571	+	0.596732i
$70$		−	11.6064i		−	1.38723i
$71$	5.94550	+	6.71108i	0.705601	+	0.796458i	0.986584	−	0.163254i	$-0.0521991\pi$
$71$	5.94550	+	6.71108i	0.705601	+	0.796458i	−0.280983	+	0.959713i	$0.590661\pi$
$72$	1.32485	−	2.52429i	0.156135	−	0.297490i
$73$	−7.87817	+	0.956583i	−0.922070	+	0.111960i	−0.567784	−	0.823178i	$-0.692199\pi$
$73$	−7.87817	+	0.956583i	−0.922070	+	0.111960i	−0.354286	+	0.935137i	$0.615276\pi$
$74$	9.82573	−	5.15694i	1.14222	−	0.599482i
$75$	−0.251587	−	2.07200i	−0.0290507	−	0.239254i
$76$	0.00266049	−	0.0107940i	0.000305179	−	0.00123816i
$77$	2.14506	+	0.528710i	0.244452	+	0.0602521i
$78$	−5.05554	+	0.144753i	−0.572428	+	0.0163901i
$79$	14.1517	−	3.48808i	1.59219	−	0.392439i	0.659092	−	0.752063i	$-0.270941\pi$
$79$	14.1517	−	3.48808i	1.59219	−	0.392439i	0.933098	+	0.359623i	$0.117095\pi$
$80$			10.4737i			1.17100i
$81$	−0.970942	−	0.239316i	−0.107882	−	0.0265906i
$82$	−1.75360	−	2.54053i	−0.193653	−	0.280555i
$83$	7.69046	−	8.68074i	0.844138	−	0.952835i	−0.155248	−	0.987876i	$-0.549618\pi$
$83$	7.69046	−	8.68074i	0.844138	−	0.952835i	0.999386	+	0.0350408i	$0.0111561\pi$
$84$	−0.0998061	+	0.0121186i	−0.0108897	+	0.00132225i
$85$	1.54335	−	0.187396i	0.167400	−	0.0203260i
$86$	6.43939	−	7.26857i	0.694377	−	0.783790i
$87$	−5.69166	−	8.24580i	−0.610210	−	0.884042i
$88$	−1.96755	−	0.484959i	−0.209742	−	0.0516968i
$89$		−	14.5507i		−	1.54237i	−0.636612	−	0.771184i	$-0.719665\pi$
$89$		−	14.5507i		−	1.54237i	0.636612	−	0.771184i	$-0.280335\pi$
$90$	3.62581	−	0.893683i	0.382194	−	0.0942024i
$91$	6.62716	+	9.03651i	0.694716	+	0.947283i
$92$	−0.234776	−	0.0578671i	−0.0244771	−	0.00603306i
$93$	−0.330179	+	1.33959i	−0.0342380	+	0.138909i
$94$	−0.526568	−	4.33668i	−0.0543114	−	0.447294i
$95$	0.810111	−	0.425179i	0.0831157	−	0.0436225i
$96$	0.181637	−	0.0220547i	0.0185382	−	0.00225095i
$97$	−2.26887	+	4.32297i	−0.230369	+	0.438931i	−0.973011	−	0.230757i	$-0.925880\pi$
$97$	−2.26887	+	4.32297i	−0.230369	+	0.438931i	0.742643	+	0.669688i	$0.233572\pi$
$98$	−2.47412	−	2.79271i	−0.249924	−	0.282106i
$99$			0.710823i			0.0714404i
$100$	0.0505379	−	0.0447726i	0.00505379	−	0.00447726i
$101$	−3.23080	+	4.68063i	−0.321477	+	0.465740i	−0.950089	−	0.311979i	$-0.899008\pi$
$101$	−3.23080	+	4.68063i	−0.321477	+	0.465740i	0.628612	+	0.777719i	$0.283623\pi$
$102$	0.196042	+	0.795374i	0.0194111	+	0.0787537i
$103$	5.09840	−	4.51678i	0.502360	−	0.445052i	−0.373491	−	0.927634i	$-0.621839\pi$
$103$	5.09840	−	4.51678i	0.502360	−	0.445052i	0.875851	+	0.482582i	$0.160301\pi$
$104$	−6.07876	−	8.28873i	−0.596072	−	0.812777i
$105$	−6.19328	−	5.48677i	−0.604402	−	0.535454i
$106$	0.712103	−	1.35680i	0.0691655	−	0.131784i
$107$	−4.44751	+	2.33423i	−0.429957	+	0.225659i	−0.665797	−	0.746133i	$-0.731908\pi$
$107$	−4.44751	+	2.33423i	−0.429957	+	0.225659i	0.235840	+	0.971792i	$0.424216\pi$
$108$	−0.0114708	−	0.0302461i	−0.00110378	−	0.00291043i
$109$	4.91641	+	3.39355i	0.470907	+	0.325044i	0.779773	−	0.626062i	$-0.215334\pi$
$109$	4.91641	+	3.39355i	0.470907	+	0.325044i	−0.308867	+	0.951105i	$0.599950\pi$
$110$	−1.23358	−	2.35039i	−0.117617	−	0.224101i
$111$	1.89319	−	7.68099i	0.179694	−	0.729047i
$112$	8.10851	+	9.15262i	0.766183	+	0.864841i
$113$	3.62961	+	3.21555i	0.341445	+	0.302494i	0.816366	−	0.577534i	$-0.195985\pi$
$113$	3.62961	+	3.21555i	0.341445	+	0.302494i	−0.474921	+	0.880028i	$0.657524\pi$
$114$	0.273849	+	0.396739i	0.0256483	+	0.0371580i
$115$	−9.24789	−	17.6204i	−0.862370	−	1.64311i
$116$	0.114931	−	0.303048i	0.0106711	−	0.0281373i
$117$	−2.31270	+	2.76612i	−0.213809	+	0.255728i
$118$	−2.12666	−	5.60755i	−0.195775	−	0.516217i
$119$	1.20360	−	1.35858i	0.110334	−	0.124541i
$120$	5.68078	+	5.03274i	0.518582	+	0.459424i
$121$	−10.1898	+	2.51155i	−0.926343	+	0.228323i
$122$	−3.86723	−	15.6900i	−0.350122	−	1.42050i
$123$	−2.18465	−	0.265264i	−0.196983	−	0.0239181i
$124$	−0.0417299	+	0.0158261i	−0.00374746	+	0.00142122i
$125$	−7.69781	−	0.934684i	−0.688513	−	0.0836006i
$126$	2.47660	−	3.58798i	0.220633	−	0.319643i
$127$	−21.2636	+	5.24100i	−1.88684	+	0.465064i	−0.886842	+	0.462073i	$0.847106\pi$
$127$	−21.2636	+	5.24100i	−1.88684	+	0.465064i	−0.999996	+	0.00299087i	$0.999048\pi$
$128$	−7.31523	−	8.25718i	−0.646581	−	0.729839i
$129$	−0.834442	−	6.87225i	−0.0734685	−	0.605068i
$130$	2.84674	−	13.1599i	0.249675	−	1.15420i
$131$	1.09902	−	9.05125i	0.0960219	−	0.790812i	−0.862552	−	0.505968i	$-0.831135\pi$
$131$	1.09902	−	9.05125i	0.0960219	−	0.790812i	0.958574	−	0.284843i	$-0.0919416\pi$
$132$	−0.0189236	+	0.0130620i	−0.00164709	+	0.00113690i
$133$	0.378764	−	0.998719i	0.0328430	−	0.0866000i
$134$	2.13407	+	17.5756i	0.184355	+	1.51830i
$135$	1.23718	−	2.35725i	0.106479	−	0.202879i
$136$	−1.10400	+	1.24616i	−0.0946674	+	0.106857i
$137$	−9.72171	−	6.71041i	−0.830582	−	0.573309i	0.0751444	−	0.997173i	$-0.476058\pi$
$137$	−9.72171	−	6.71041i	−0.830582	−	0.573309i	−0.905726	+	0.423864i	$0.860674\pi$
$138$	8.62930	−	5.95638i	0.734575	−	0.507040i
$139$	6.04767	+	3.17406i	0.512957	+	0.269220i	0.701279	−	0.712887i	$-0.252613\pi$
$139$	6.04767	+	3.17406i	0.512957	+	0.269220i	−0.188323	+	0.982107i	$0.560305\pi$
$140$	0.0322621	−	0.265702i	0.00272664	−	0.0224559i
$141$	−2.56302	−	1.76913i	−0.215846	−	0.148987i
$142$	−7.14441	−	10.3505i	−0.599545	−	0.868591i
$143$	2.30250	+	1.12560i	0.192545	+	0.0941278i
$144$	−2.23491	+	3.23783i	−0.186243	+	0.269819i
$145$	24.9401	−	9.45854i	2.07116	−	0.785489i
$146$	11.1321			0.921300
$147$	−2.65983			−0.219379
$148$	0.239273	−	0.0907442i	0.0196681	−	0.00745912i
$149$	1.48588	+	6.02847i	0.121728	+	0.493871i	0.999880	+	0.0154891i	$0.00493053\pi$
$149$	1.48588	+	6.02847i	0.121728	+	0.493871i	−0.878152	+	0.478382i	$0.841223\pi$
$150$			2.92781i			0.239055i
$151$	−2.60420	+	10.5657i	−0.211927	+	0.859822i	0.764614	+	0.644489i	$0.222930\pi$
$151$	−2.60420	+	10.5657i	−0.211927	+	0.859822i	−0.976541	+	0.215333i	$0.930916\pi$
$152$	−0.347421	+	0.916075i	−0.0281796	+	0.0743035i
$153$	0.517096	+	0.271393i	0.0418047	+	0.0219408i
$154$	−2.89761	−	1.09892i	−0.233496	−	0.0885533i
$155$	−3.25225	−	1.70691i	−0.261227	−	0.137102i
$156$	−0.116138	−	0.0107390i	−0.00929846	−	0.000859809i
$157$	5.39421	−	2.83110i	0.430504	−	0.225946i	−0.235530	−	0.971867i	$-0.575683\pi$
$157$	5.39421	−	2.83110i	0.430504	−	0.225946i	0.666035	+	0.745921i	$0.267990\pi$
$158$	−20.2960	+	2.46438i	−1.61467	+	0.196056i
$159$	−0.387364	−	1.02139i	−0.0307199	−	0.0810018i
$160$	−0.0587137	+	0.483551i	−0.00464173	+	0.0382281i
$161$	−21.7227	−	8.23834i	−1.71199	−	0.649272i
$162$	1.31158	+	0.497415i	0.103047	+	0.0390806i
$163$	−0.134954	+	0.0931520i	−0.0105704	+	0.00729623i	−0.573338	−	0.819319i	$-0.694352\pi$
$163$	−0.134954	+	0.0931520i	−0.0105704	+	0.00729623i	0.562768	+	0.826615i	$0.309737\pi$
$164$	−0.0330829	−	0.0630342i	−0.00258334	−	0.00492215i
$165$	−1.83735	−	0.452867i	−0.143038	−	0.0352556i
$166$	−12.1767	+	10.7876i	−0.945098	+	0.837283i
$167$	5.87210	+	0.713003i	0.454397	+	0.0551738i	0.344536	−	0.938773i	$-0.388036\pi$
$167$	5.87210	+	0.713003i	0.454397	+	0.0551738i	0.109861	+	0.993947i	$0.464959\pi$
$168$	8.86047			0.683600
$169$	5.29781	+	11.8715i	0.407524	+	0.913195i
$170$	−2.18080			−0.167260
$171$	0.341163	+	0.0414247i	0.0260894	+	0.00316782i
$172$	0.167620	−	0.148498i	0.0127809	−	0.0113229i
$173$	5.14848	+	1.26899i	0.391432	+	0.0964793i	0.430119	−	0.902772i	$-0.358472\pi$
$173$	5.14848	+	1.26899i	0.391432	+	0.0964793i	−0.0386874	+	0.999251i	$0.512318\pi$
$174$	6.53145	+	12.4446i	0.495148	+	0.943426i
$175$	5.33881	−	3.68512i	0.403576	−	0.278569i
$176$	2.61483	+	0.991674i	0.197100	+	0.0747502i
$177$	−3.99760	−	1.51609i	−0.300478	−	0.113956i
$178$	−2.46023	+	20.2618i	−0.184402	+	1.51869i
$179$	5.13789	+	13.5475i	0.384024	+	1.01259i	0.978092	+	0.208173i	$0.0667516\pi$
$179$	5.13789	+	13.5475i	0.384024	+	1.01259i	−0.594068	+	0.804415i	$0.702479\pi$
$180$	0.0854890	−	0.0103802i	0.00637197	−	0.000773698i
$181$	−6.62066	+	3.47479i	−0.492110	+	0.258279i	−0.692475	−	0.721442i	$-0.743480\pi$
$181$	−6.62066	+	3.47479i	−0.492110	+	0.258279i	0.200365	+	0.979721i	$0.435787\pi$
$182$	−7.70045	−	13.7039i	−0.570795	−	1.01580i
$183$	−10.2005	−	5.35364i	−0.754043	−	0.395752i
$184$	19.9252	+	7.55661i	1.46890	+	0.557081i
$185$	18.6478	+	9.78715i	1.37102	+	0.719565i
$186$	0.686274	−	1.80955i	0.0503200	−	0.132683i
$187$	0.0993428	−	0.403050i	0.00726467	−	0.0294739i
$188$		−	0.100742i		−	0.00734738i
$189$	−0.743799	−	3.01771i	−0.0541034	−	0.219506i
$190$	−1.19997	+	0.455089i	−0.0870551	+	0.0330156i
$191$	−11.3608			−0.822041			−0.411021	−	0.911626i	$-0.634828\pi$
$191$	−11.3608			−0.822041			−0.411021	+	0.911626i	$0.634828\pi$
$192$	−8.12517			−0.586384
$193$	−11.4570	+	4.34506i	−0.824692	+	0.312765i	−0.730606	−	0.682799i	$-0.760762\pi$
$193$	−11.4570	+	4.34506i	−0.824692	+	0.312765i	−0.0940865	+	0.995564i	$0.529993\pi$
$194$	3.89034	−	5.63613i	0.279310	−	0.404650i
$195$	−5.67651	−	7.74023i	−0.406503	−	0.554289i
$196$	−0.0488767	−	0.0708101i	−0.00349119	−	0.00505786i
$197$	20.7430	+	14.3178i	1.47788	+	1.02010i	0.989027	+	0.147735i	$0.0471981\pi$
$197$	20.7430	+	14.3178i	1.47788	+	1.02010i	0.488848	+	0.872369i	$0.337417\pi$
$198$	0.120186	−	0.989823i	0.00854126	−	0.0703436i
$199$	−8.86874	−	4.65468i	−0.628689	−	0.329961i	0.120108	−	0.992761i	$-0.461676\pi$
$199$	−8.86874	−	4.65468i	−0.628689	−	0.329961i	−0.748797	+	0.662800i	$0.769368\pi$
$200$	−4.89702	+	3.38017i	−0.346272	+	0.239014i
$201$	10.3874	+	7.16989i	0.732670	+	0.505725i
$202$	5.29031	−	5.97152i	0.372225	−	0.420155i
$203$	14.4717	−	27.5736i	1.01572	−	1.93529i
$204$	0.00227705	+	0.0187532i	0.000159426	+	0.00131299i
$205$	2.07750	−	5.47793i	0.145099	−	0.382595i
$206$	−7.86323	+	5.42760i	−0.547857	+	0.378159i
$207$	0.901010	−	7.42048i	0.0626245	−	0.515759i
$208$	6.94896	+	12.3665i	0.481824	+	0.857464i
$209$	−0.0294456	−	0.242506i	−0.00203679	−	0.0167745i
$210$	7.69645	+	8.68750i	0.531106	+	0.599495i
$211$	−16.6857	+	4.11267i	−1.14869	+	0.283128i	−0.767302	−	0.641286i	$-0.778401\pi$
$211$	−16.6857	+	4.11267i	−1.14869	+	0.283128i	−0.381392	+	0.924414i	$0.624555\pi$
$212$	0.0200735	−	0.0290814i	0.00137865	−	0.00199732i
$213$	−8.90054	−	1.08072i	−0.609855	−	0.0740498i
$214$	6.58785	−	2.49844i	0.450336	−	0.170790i
$215$	18.2952	+	2.22144i	1.24772	+	0.151501i
$216$	0.682250	+	2.76800i	0.0464212	+	0.188338i
$217$	−4.16348	+	1.02621i	−0.282635	+	0.0696634i
$218$	−6.27233	−	5.55680i	−0.424816	−	0.376354i
$219$	5.26256	−	5.94020i	0.355611	−	0.401402i
$220$	−0.0217067	−	0.0572359i	−0.00146347	−	0.00385885i
$221$	1.69793	−	1.24522i	0.114215	−	0.0837627i
$222$	−3.93498	+	10.3757i	−0.264099	+	0.696371i
$223$	0.157648	+	0.300372i	0.0105569	+	0.0201144i	0.890677	−	0.454636i	$-0.150231\pi$
$223$	0.157648	+	0.300372i	0.0105569	+	0.0201144i	−0.880120	+	0.474750i	$0.842538\pi$
$224$	0.323046	+	0.468014i	0.0215844	+	0.0312705i
$225$	1.56231	+	1.38408i	0.104154	+	0.0922723i
$226$	−4.51055	−	5.09136i	−0.300038	−	0.338672i
$227$	−1.35812	+	5.51009i	−0.0901413	+	0.365718i	−0.998638	−	0.0521744i	$-0.983385\pi$
$227$	−1.35812	+	5.51009i	−0.0901413	+	0.365718i	0.908497	+	0.417892i	$0.137231\pi$
$228$	0.00516636	+	0.00984367i	0.000342150	+	0.000651913i
$229$	20.8565	+	14.3962i	1.37824	+	0.951330i	0.999668	+	0.0257575i	$0.00819976\pi$
$229$	20.8565	+	14.3962i	1.37824	+	0.951330i	0.378571	+	0.925572i	$0.376416\pi$
$230$	9.89845	+	26.1001i	0.652684	+	1.72099i
$231$	−1.95620	+	1.02669i	−0.128708	+	0.0675514i
$232$	−13.2742	+	25.2919i	−0.871493	+	1.66049i
$233$	−21.2308	−	18.8088i	−1.39087	−	1.23221i	−0.940689	−	0.339270i	$-0.889820\pi$
$233$	−21.2308	−	18.8088i	−1.39087	−	1.23221i	−0.450184	−	0.892936i	$-0.648642\pi$
$234$	3.68814	−	3.46079i	0.241101	−	0.226239i
$235$	6.20579	−	5.49785i	0.404821	−	0.358640i
$236$	−0.0330980	−	0.134284i	−0.00215449	−	0.00874112i
$237$	−8.27967	+	11.9952i	−0.537822	+	0.779170i
$238$	−1.90573	+	1.68833i	−0.123530	+	0.109438i
$239$			15.0955i			0.976449i	0.872718	+	0.488225i	$0.162355\pi$
$239$			15.0955i			0.976449i	−0.872718	+	0.488225i	$0.837645\pi$
$240$	−6.94536	−	7.83969i	−0.448321	−	0.506050i
$241$	5.46207	−	10.4071i	0.351843	−	0.670381i	−0.643639	−	0.765329i	$-0.722576\pi$
$241$	5.46207	−	10.4071i	0.351843	−	0.670381i	0.995482	+	0.0949482i	$0.0302686\pi$
$242$	14.6139	−	1.77445i	0.939420	−	0.114066i
$243$	0.885456	−	0.464723i	0.0568020	−	0.0298120i
$244$	−0.0449184	−	0.369936i	−0.00287560	−	0.0236827i
$245$	1.69458	−	6.87519i	0.108263	−	0.439240i
$246$	2.99727	+	0.738762i	0.191099	+	0.0471017i
$247$	0.674422	−	1.03950i	0.0429124	−	0.0661418i
$248$	3.81895	−	0.941286i	0.242504	−	0.0597717i
$249$			11.5973i			0.734952i
$250$	10.5612	+	2.60310i	0.667948	+	0.164634i
$251$	10.5139	+	15.2320i	0.663629	+	0.961433i	0.999807	+	0.0196343i	$0.00625021\pi$
$251$	10.5139	+	15.2320i	0.663629	+	0.961433i	−0.336178	+	0.941798i	$0.609134\pi$
$252$	0.0666698	−	0.0752546i	0.00419980	−	0.00474059i
$253$	−5.27465	+	0.640458i	−0.331614	+	0.0402653i
$254$	30.4957	−	3.70285i	1.91347	−	0.232338i
$255$	−1.03095	+	1.16370i	−0.0645603	+	0.0728735i
$256$	−0.440905	−	0.638761i	−0.0275566	−	0.0399226i
$257$	−26.4977	−	6.53110i	−1.65288	−	0.407399i	−0.700829	−	0.713329i	$-0.747186\pi$
$257$	−26.4977	−	6.53110i	−1.65288	−	0.407399i	−0.952054	+	0.305930i	$0.901033\pi$
$258$			9.71071i			0.604562i
$259$	23.8727	−	5.88409i	1.48338	−	0.365620i
$260$	0.101750	−	0.293354i	0.00631027	−	0.0181930i
$261$	9.72825	+	2.39780i	0.602163	+	0.148420i
$262$	−3.06078	+	12.4181i	−0.189096	+	0.767191i
$263$	3.19843	+	26.3415i	0.197224	+	1.62428i	0.669485	+	0.742826i	$0.266515\pi$
$263$	3.19843	+	26.3415i	0.197224	+	1.62428i	−0.472261	+	0.881459i	$0.656562\pi$
$264$	1.79432	−	0.941733i	0.110433	−	0.0579597i
$265$	2.88692	−	0.350535i	0.177342	−	0.0215332i
$266$	−0.696294	+	1.32668i	−0.0426925	+	0.0813438i
$267$	9.64888	+	10.8913i	0.590502	+	0.666539i
$268$			0.408287i			0.0249401i
$269$	−17.7881	+	15.7589i	−1.08456	+	0.960836i	−0.999369	−	0.0355282i	$-0.988689\pi$
$269$	−17.7881	+	15.7589i	−1.08456	+	0.960836i	−0.0851915	+	0.996365i	$0.527150\pi$
$270$	−2.12134	+	3.07329i	−0.129101	+	0.187034i
$271$	−4.25411	−	17.2596i	−0.258419	−	1.04845i	−0.946472	−	0.322786i	$-0.895381\pi$
$271$	−4.25411	−	17.2596i	−0.258419	−	1.04845i	0.688054	−	0.725660i	$-0.258465\pi$
$272$	1.71975	−	1.52356i	0.104275	−	0.0923796i
$273$	−10.9528	−	2.36930i	−0.662895	−	0.143396i
$274$	12.4029	+	10.9880i	0.749287	+	0.663810i
$275$	0.689484	−	1.31370i	0.0415775	−	0.0792192i
$276$	0.214105	−	0.112371i	0.0128876	−	0.00676395i
$277$	4.21156	+	11.1050i	0.253048	+	0.667233i	0.999997	+	0.00235163i	$0.000748547\pi$
$277$	4.21156	+	11.1050i	0.253048	+	0.667233i	−0.746949	+	0.664881i	$0.768482\pi$
$278$	−7.88472	−	5.44243i	−0.472894	−	0.326415i
$279$	−0.641169	−	1.22165i	−0.0383858	−	0.0731380i
$280$	−5.64503	+	22.9028i	−0.337355	+	1.36870i
$281$	−6.66810	−	7.52673i	−0.397786	−	0.449007i	0.515156	−	0.857096i	$-0.327734\pi$
$281$	−6.66810	−	7.52673i	−0.397786	−	0.449007i	−0.912942	+	0.408089i	$0.866195\pi$
$282$	3.26989	+	2.89687i	0.194719	+	0.172506i
$283$	8.59772	+	12.4560i	0.511082	+	0.740430i	0.990553	−	0.137128i	$-0.0437871\pi$
$283$	8.59772	+	12.4560i	0.511082	+	0.740430i	−0.479472	+	0.877557i	$0.659172\pi$
$284$	−0.134784	−	0.256810i	−0.00799797	−	0.0152389i
$285$	−0.324431	+	0.855454i	−0.0192176	+	0.0506727i
$286$	−3.01592	−	1.95672i	−0.178335	−	0.115703i
$287$	−2.42543	−	6.39533i	−0.143169	−	0.377504i
$288$	−0.121332	+	0.136956i	−0.00714957	+	0.00807020i
$289$	12.4694	+	11.0469i	0.733495	+	0.649820i
$290$	−36.3284	+	8.95416i	−2.13328	+	0.525806i
$291$	−1.16839	−	4.74033i	−0.0684920	−	0.277883i
$292$	0.254845	+	0.0309437i	0.0149137	+	0.00181085i
$293$	−25.8956	+	9.82091i	−1.51284	+	0.573744i	−0.964864	−	0.262751i	$-0.915370\pi$
$293$	−25.8956	+	9.82091i	−1.51284	+	0.573744i	−0.547975	+	0.836495i	$0.684601\pi$
$294$	3.70382	+	0.449725i	0.216011	+	0.0262285i
$295$	6.46570	−	9.36719i	0.376448	−	0.545379i
$296$	−21.8972	+	5.39718i	−1.27275	+	0.313705i
$297$	−0.471363	−	0.532059i	−0.0273512	−	0.0308732i
$298$	−1.04980	−	8.64589i	−0.0608134	−	0.500843i
$299$	−22.6097	−	14.6691i	−1.30755	−	0.848334i
$300$	−0.00813838	+	0.0670256i	−0.000469870	+	0.00386973i
$301$	17.7073	−	12.2225i	1.02063	−	0.704492i
$302$	5.41281	−	14.2724i	0.311472	−	0.821285i
$303$	−0.685539	−	5.64592i	−0.0393832	−	0.324350i
$304$	0.628343	−	1.19721i	0.0360379	−	0.0686646i
$305$	20.3370	−	22.9557i	1.16449	−	1.31444i
$306$	−0.674170	−	0.465346i	−0.0385397	−	0.0266021i
$307$	−13.3050	+	9.18379i	−0.759358	+	0.524147i	−0.883678	−	0.468095i	$-0.844940\pi$
$307$	−13.3050	+	9.18379i	−0.759358	+	0.524147i	0.124320	+	0.992242i	$0.460325\pi$
$308$	−0.0632796	−	0.0332117i	−0.00360569	−	0.00189241i
$309$	−0.821022	+	6.76172i	−0.0467063	+	0.384661i
$310$	4.24016	+	2.92677i	0.240825	+	0.166229i
$311$	2.19959	+	3.18665i	0.124727	+	0.180698i	0.880373	−	0.474282i	$-0.157292\pi$
$311$	2.19959	+	3.18665i	0.124727	+	0.180698i	−0.755646	+	0.654980i	$0.772677\pi$
$312$	10.0465	+	2.17324i	0.568769	+	0.123035i
$313$	4.40872	−	6.38714i	0.249196	−	0.361022i	−0.678346	−	0.734743i	$-0.737303\pi$
$313$	4.40872	−	6.38714i	0.249196	−	0.361022i	0.927541	+	0.373721i	$0.121918\pi$
$314$	−7.99013	+	3.03026i	−0.450909	+	0.171007i
$315$	8.27414			0.466195
$316$	−0.471482			−0.0265229
$317$	−17.6794	+	6.70493i	−0.992976	+	0.376586i	−0.796972	−	0.604017i	$-0.793566\pi$
$317$	−17.6794	+	6.70493i	−0.992976	+	0.376586i	−0.196005	+	0.980603i	$0.562797\pi$
$318$	0.366707	+	1.48779i	0.0205639	+	0.0834311i
$319$		−	7.12201i		−	0.398756i
$320$	5.17657	−	21.0022i	0.289379	−	1.17406i
$321$	1.78113	−	4.69645i	0.0994128	−	0.262130i
$322$	28.8560	+	15.1448i	1.60808	+	0.843986i
$323$	−0.187656	−	0.0711686i	−0.0104415	−	0.00395993i
$324$	0.0286429	+	0.0150330i	0.00159127	+	0.000835165i
$325$	6.95728	−	2.86891i	0.385921	−	0.159138i
$326$	0.203674	−	0.106896i	0.0112805	−	0.00592044i
$327$	−5.93033	+	0.720072i	−0.327948	+	0.0398201i
$328$	2.22472	+	5.86611i	0.122840	+	0.323902i
$329$	1.16672	−	9.60877i	0.0643231	−	0.529749i
$330$	2.48195	+	0.941279i	0.136627	+	0.0518157i
$331$	−9.89709	−	3.75347i	−0.543994	−	0.206310i	0.0672726	−	0.997735i	$-0.478570\pi$
$331$	−9.89709	−	3.75347i	−0.543994	−	0.206310i	−0.611266	+	0.791425i	$0.709339\pi$
$332$	−0.308745	+	0.213111i	−0.0169446	+	0.0116960i
$333$	3.67636	+	7.00472i	0.201463	+	0.383856i
$334$	−8.05637	−	1.98572i	−0.440825	−	0.108654i
$335$	−25.1508	+	22.2816i	−1.37413	+	1.21738i
$336$	−12.1386	−	1.47390i	−0.662216	−	0.0804076i
$337$	−11.5917			−0.631440			−0.315720	−	0.948852i	$-0.602246\pi$
$337$	−11.5917			−0.631440			−0.315720	+	0.948852i	$0.602246\pi$
$338$	−5.36997	−	17.4269i	−0.292088	−	0.947898i
$339$	−4.84911			−0.263367
$340$	−0.0499245	−	0.00606194i	−0.00270754	−	0.000328755i
$341$	−0.734071	+	0.650330i	−0.0397522	+	0.0352173i
$342$	−0.468066	−	0.115368i	−0.0253101	−	0.00623838i
$343$	6.26882	+	11.9442i	0.338485	+	0.644928i
$344$	−16.2420	+	11.2111i	−0.875712	+	0.604460i
$345$	18.6066	+	7.05656i	1.00175	+	0.379912i
$346$	−6.95471	−	2.63757i	−0.373888	−	0.141797i
$347$	1.95975	−	16.1400i	0.105205	−	0.866439i	−0.840590	−	0.541672i	$-0.817791\pi$
$347$	1.95975	−	16.1400i	0.105205	−	0.866439i	0.945794	−	0.324766i	$-0.105286\pi$
$348$	0.114931	+	0.303048i	0.00616094	+	0.0162451i
$349$	−13.5025	+	1.63950i	−0.722772	+	0.0877604i	−0.473652	−	0.880712i	$-0.657064\pi$
$349$	−13.5025	+	1.63950i	−0.722772	+	0.0877604i	−0.249120	+	0.968473i	$0.580141\pi$
$350$	−8.05739	+	4.22884i	−0.430686	+	0.226041i
$351$	−0.103194	−	3.60407i	−0.00550808	−	0.192371i
$352$	0.115162	+	0.0604419i	0.00613818	+	0.00322156i
$353$	1.18893	+	0.450900i	0.0632801	+	0.0239990i	0.386042	−	0.922481i	$-0.373842\pi$
$353$	1.18893	+	0.450900i	0.0632801	+	0.0239990i	−0.322762	+	0.946480i	$0.604611\pi$
$354$	5.31032	+	2.78707i	0.282240	+	0.148131i
$355$	8.46403	−	22.3178i	0.449224	−	1.18451i
$356$	−0.112643	+	0.457011i	−0.00597007	+	0.0242215i
$357$			1.81505i			0.0960626i
$358$	−4.86391	−	19.7336i	−0.257065	−	1.04296i
$359$	15.4021	−	5.84123i	0.812890	−	0.308288i	0.0870954	−	0.996200i	$-0.472242\pi$
$359$	15.4021	−	5.84123i	0.812890	−	0.308288i	0.725795	+	0.687911i	$0.241472\pi$
$360$	−7.58945			−0.399999
$361$	18.8819			0.993784
$362$	9.80681	−	3.71923i	0.515435	−	0.195479i
$363$	5.96169	−	8.63699i	0.312907	−	0.453325i
$364$	−0.138192	−	0.335124i	−0.00724323	−	0.0175653i
$365$	12.0016	+	17.3873i	0.628192	+	0.910094i
$366$	13.2990	+	9.17966i	0.695151	+	0.479828i
$367$	−0.311553	+	2.56587i	−0.0162629	+	0.133937i	−0.998579	−	0.0532935i	$-0.983028\pi$
$367$	−0.311553	+	2.56587i	−0.0162629	+	0.133937i	0.982316	+	0.187231i	$0.0599512\pi$
$368$	−26.0399	−	13.6668i	−1.35743	−	0.712432i
$369$	1.81113	−	1.25014i	0.0942838	−	0.0650794i
$370$	−24.3124	−	16.7816i	−1.26394	−	0.872435i
$371$	2.25140	−	2.54131i	0.116887	−	0.131938i
$372$	0.0207407	−	0.0395181i	0.00107535	−	0.00204892i
$373$	0.627350	+	5.16669i	0.0324829	+	0.267521i	0.999897	+	0.0143231i	$0.00455933\pi$
$373$	0.627350	+	5.16669i	0.0324829	+	0.267521i	−0.967414	+	0.253198i	$0.918518\pi$
$374$	−0.206483	+	0.544451i	−0.0106770	+	0.0281529i
$375$	6.38171	−	4.40497i	0.329550	−	0.227472i
$376$	−1.07017	+	8.81364i	−0.0551898	+	0.454529i
$377$	23.1719	−	27.7148i	1.19341	−	1.42739i
$378$	0.525506	+	4.32793i	0.0270291	+	0.222605i
$379$	−14.1925	−	16.0200i	−0.729018	−	0.822892i	0.260775	−	0.965400i	$-0.416022\pi$
$379$	−14.1925	−	16.0200i	−0.729018	−	0.822892i	−0.989794	+	0.142508i	$0.954483\pi$
$380$	−0.0287357	+	0.00708270i	−0.00147411	+	0.000363335i
$381$	12.4406	−	18.0233i	0.637351	−	0.923362i
$382$	15.8200	+	1.92090i	0.809421	+	0.0982815i
$383$	14.5109	−	5.50326i	0.741473	−	0.281204i	0.0451973	−	0.998978i	$-0.485608\pi$
$383$	14.5109	−	5.50326i	0.741473	−	0.281204i	0.696276	+	0.717774i	$0.254839\pi$
$384$	10.9511	+	1.32970i	0.558843	+	0.0678559i
$385$	−1.40752	−	5.71054i	−0.0717340	−	0.291036i
$386$	16.6886	−	4.11336i	0.849425	−	0.209365i
$387$	5.18173	+	4.59061i	0.263402	+	0.233354i
$388$	0.104727	−	0.118213i	0.00531672	−	0.00600133i
$389$	11.8003	+	31.1148i	0.598299	+	1.57758i	0.801208	+	0.598387i	$0.204191\pi$
$389$	11.8003	+	31.1148i	0.598299	+	1.57758i	−0.202909	+	0.979198i	$0.565039\pi$
$390$	6.59583	+	11.7381i	0.333993	+	0.594381i
$391$	−1.54796	+	4.08163i	−0.0782835	+	0.206417i
$392$	3.52387	+	6.71418i	0.177982	+	0.339117i
$393$	5.17946	+	7.50375i	0.261269	+	0.378514i
$394$	−26.4638	−	23.4449i	−1.33323	−	1.18113i
$395$	−25.7304	−	29.0436i	−1.29464	−	1.46134i
$396$	0.00550279	−	0.0223257i	0.000276526	−	0.00112191i
$397$	−13.2055	−	25.1610i	−0.662764	−	1.26279i	−0.952165	−	0.305584i	$-0.901148\pi$
$397$	−13.2055	−	25.1610i	−0.662764	−	1.26279i	0.289401	−	0.957208i	$-0.406544\pi$
$398$	11.5627	+	7.98118i	0.579587	+	0.400060i
$399$	0.378764	+	0.998719i	0.0189619	+	0.0499985i
$400$	7.27107	−	3.81615i	0.363554	−	0.190808i
$401$	−9.16904	+	17.4702i	−0.457880	+	0.872418i	0.541614	+	0.840627i	$0.317813\pi$
$401$	−9.16904	+	17.4702i	−0.457880	+	0.872418i	−0.999495	+	0.0317907i	$0.989879\pi$
$402$	−13.2522	−	11.7404i	−0.660958	−	0.585558i
$403$	−4.97247	+	0.142374i	−0.247696	+	0.00709218i
$404$	0.137709	−	0.121999i	0.00685126	−	0.00606969i
$405$	0.637102	+	2.58483i	0.0316579	+	0.128441i
$406$	−24.8141	+	35.9494i	−1.23150	+	1.78414i
$407$	4.20904	−	3.72889i	0.208634	−	0.184834i
$408$		−	1.66485i		−	0.0824226i
$409$	4.85950	+	5.48524i	0.240287	+	0.271227i	0.856266	−	0.516534i	$-0.172778\pi$
$409$	4.85950	+	5.48524i	0.240287	+	0.271227i	−0.615980	+	0.787762i	$0.711240\pi$
$410$	−3.81914	+	7.27676i	−0.188614	+	0.359374i
$411$	11.7266	−	1.42387i	0.578432	−	0.0702344i
$412$	−0.195098	+	0.102395i	−0.00961179	+	0.00504466i
$413$	−1.60171	−	13.1913i	−0.0788150	−	0.649100i
$414$	−2.50932	+	10.1807i	−0.123326	+	0.500354i
$415$	−29.9771	−	7.38869i	−1.47152	−	0.362697i
$416$	0.251496	+	0.609893i	0.0123306	+	0.0299025i
$417$	−6.63154	+	1.63453i	−0.324748	+	0.0800431i
$418$			0.342669i			0.0167605i
$419$	−3.16160	−	0.779264i	−0.154454	−	0.0380695i	0.161330	−	0.986900i	$-0.448422\pi$
$419$	−3.16160	−	0.779264i	−0.154454	−	0.0380695i	−0.315785	+	0.948831i	$0.602268\pi$
$420$	0.152045	+	0.220275i	0.00741901	+	0.0107483i
$421$	5.19567	−	5.86470i	0.253222	−	0.285828i	−0.608130	−	0.793838i	$-0.708080\pi$
$421$	5.19567	−	5.86470i	0.253222	−	0.285828i	0.861352	+	0.508009i	$0.169618\pi$
$422$	23.9303	−	2.90567i	1.16491	−	0.141446i
$423$	3.09160	−	0.375388i	0.150319	−	0.0182520i
$424$	−2.06510	+	2.33101i	−0.100290	+	0.113204i
$425$	−0.692421	−	1.00315i	−0.0335874	−	0.0486597i
$426$	12.2113	+	3.00981i	0.591639	+	0.145826i
$427$		−	35.8046i		−	1.73271i
$428$	0.157759	−	0.0388841i	0.00762556	−	0.00187953i
$429$	−2.46986	+	0.684314i	−0.119246	+	0.0330390i
$430$	−25.1005	−	6.18672i	−1.21045	−	0.298350i
$431$	4.62732	−	18.7738i	0.222890	−	0.904301i	−0.747792	−	0.663933i	$-0.768886\pi$
$431$	4.62732	−	18.7738i	0.222890	−	0.904301i	0.970682	−	0.240367i	$-0.0772680\pi$
$432$	−0.474222	−	3.90557i	−0.0228160	−	0.187907i
$433$	−11.1703	+	5.86264i	−0.536812	+	0.281741i	−0.711264	−	0.702925i	$-0.751877\pi$
$433$	−11.1703	+	5.86264i	−0.536812	+	0.281741i	0.174452	+	0.984666i	$0.444185\pi$
$434$	5.97117	−	0.725031i	0.286625	−	0.0348026i
$435$	−12.3958	+	23.6182i	−0.594332	+	1.13241i
$436$	−0.128145	−	0.144646i	−0.00613702	−	0.00692727i
$437$			2.56892i			0.122888i
$438$	−8.33250	+	7.38195i	−0.398142	+	0.352723i
$439$	8.01132	−	11.6064i	0.382360	−	0.553943i	−0.583797	−	0.811900i	$-0.698434\pi$
$439$	8.01132	−	11.6064i	0.382360	−	0.553943i	0.966157	+	0.257956i	$0.0830490\pi$
$440$	1.29105	+	5.23799i	0.0615484	+	0.249711i
$441$	1.99091	−	1.76379i	0.0948052	−	0.0839901i
$442$	−2.57491	+	1.44689i	−0.122476	+	0.0688215i
$443$	15.0301	+	13.3155i	0.714103	+	0.632640i	0.939866	−	0.341542i	$-0.110949\pi$
$443$	15.0301	+	13.3155i	0.714103	+	0.632640i	−0.225764	+	0.974182i	$0.572488\pi$
$444$	−0.118924	+	0.226590i	−0.00564387	+	0.0107535i
$445$	−34.2995	+	18.0018i	−1.62595	+	0.853366i
$446$	−0.168738	−	0.444925i	−0.00798996	−	0.0210678i
$447$	−5.10981	−	3.52705i	−0.241686	−	0.166824i
$448$	−11.7358	−	22.3606i	−0.554463	−	1.05644i
$449$	3.97201	−	16.1151i	0.187451	−	0.760517i	−0.799657	−	0.600457i	$-0.794985\pi$
$449$	3.97201	−	16.1151i	0.187451	−	0.760517i	0.987107	−	0.160059i	$-0.0511686\pi$
$450$	−1.94150	−	2.19150i	−0.0915230	−	0.103308i
$451$	−1.17090	−	1.03732i	−0.0551354	−	0.0488457i
$452$	−0.0891066	−	0.129093i	−0.00419122	−	0.00607203i
$453$	−5.05706	−	9.63542i	−0.237601	−	0.452712i
$454$	2.82283	−	7.44319i	0.132482	−	0.349326i
$455$	13.1023	−	26.8016i	0.614245	−	1.25648i
$456$	−0.347421	−	0.916075i	−0.0162695	−	0.0428991i
$457$	−5.83158	+	6.58250i	−0.272790	+	0.307916i	−0.868901	−	0.494986i	$-0.835173\pi$
$457$	−5.83158	+	6.58250i	−0.272790	+	0.307916i	0.596111	+	0.802902i	$0.296712\pi$
$458$	−26.6087	−	23.5732i	−1.24334	−	1.10150i
$459$	−0.567018	+	0.139757i	−0.0264662	+	0.00652332i
$460$	0.154053	+	0.625017i	0.00718275	+	0.0291416i
$461$	12.6665	+	1.53799i	0.589938	+	0.0716314i	0.410062	−	0.912058i	$-0.365507\pi$
$461$	12.6665	+	1.53799i	0.589938	+	0.0716314i	0.179876	+	0.983689i	$0.442430\pi$
$462$	2.89761	−	1.09892i	0.134809	−	0.0511263i
$463$	−2.14484	−	0.260430i	−0.0996790	−	0.0121032i	0.0705452	−	0.997509i	$-0.477526\pi$
$463$	−2.14484	−	0.260430i	−0.0996790	−	0.0121032i	−0.170224	+	0.985405i	$0.554449\pi$
$464$	22.3925	−	32.4411i	1.03954	−	1.50604i
$465$	3.56623	−	0.878997i	0.165380	−	0.0407625i
$466$	26.3837	+	29.7810i	1.22220	+	1.37958i
$467$	−0.552658	−	4.55155i	−0.0255739	−	0.210620i	0.974320	−	0.225167i	$-0.0722927\pi$
$467$	−0.552658	−	4.55155i	−0.0255739	−	0.210620i	−0.999894	+	0.0145463i	$0.995370\pi$
$468$	0.0940516	−	0.0689753i	0.00434754	−	0.00318838i
$469$	−4.72845	+	38.9423i	−0.218340	+	1.79819i
$470$	−9.57116	+	6.60650i	−0.441485	+	0.304735i
$471$	−2.16026	+	5.69613i	−0.0995393	+	0.262464i
$472$	1.46917	+	12.0997i	0.0676239	+	0.556933i
$473$	2.28682	−	4.35718i	0.105148	−	0.200343i
$474$	13.5576	−	15.3034i	0.622722	−	0.702907i
$475$	−0.590336	−	0.407480i	−0.0270865	−	0.0186965i
$476$	−0.0483204	+	0.0333531i	−0.00221476	+	0.00152874i
$477$	0.967256	+	0.507655i	0.0442876	+	0.0232439i
$478$	2.55236	−	21.0206i	0.116742	−	0.961459i
$479$	27.5370	+	19.0075i	1.25820	+	0.868473i	0.995346	−	0.0963630i	$-0.0307210\pi$
$479$	27.5370	+	19.0075i	1.25820	+	0.868473i	0.262854	+	0.964836i	$0.415336\pi$
$480$	−0.276706	−	0.400878i	−0.0126298	−	0.0182975i
$481$	28.5113	−	0.816352i	1.30000	−	0.0372224i
$482$	−9.36559	+	13.5684i	−0.426591	+	0.618024i
$483$	21.7227	−	8.23834i	0.988418	−	0.374857i
$484$	0.339486			0.0154312
$485$	12.9973			0.590177
$486$	−1.31158	+	0.497415i	−0.0594943	+	0.0225632i
$487$	−1.76177	−	7.14777i	−0.0798332	−	0.323896i	0.917424	−	0.397911i	$-0.130265\pi$
$487$	−1.76177	−	7.14777i	−0.0798332	−	0.323896i	−0.997257	+	0.0740151i	$0.976419\pi$
$488$			32.8418i			1.48668i
$489$	0.0392433	−	0.159216i	0.00177464	−	0.00720001i
$490$	−3.52217	+	9.28720i	−0.159115	+	0.419553i
$491$	1.65392	+	0.868043i	0.0746402	+	0.0391742i	0.501630	−	0.865082i	$-0.332734\pi$
$491$	1.65392	+	0.868043i	0.0746402	+	0.0391742i	−0.426990	+	0.904256i	$0.640426\pi$
$492$	0.0665623	+	0.0252438i	0.00300086	+	0.00113808i
$493$	−5.18099	−	2.71919i	−0.233340	−	0.122466i
$494$	−1.11489	+	1.33347i	−0.0501614	+	0.0599958i
$495$	1.67558	−	0.879415i	0.0753119	−	0.0395268i
$496$	−5.38844	+	0.654275i	−0.241948	+	0.0293778i
$497$	−9.88152	−	26.0554i	−0.443247	−	1.16875i
$498$	1.96088	−	16.1493i	0.0878693	−	0.723669i
$499$	−38.7110	−	14.6811i	−1.73294	−	0.657218i	−0.733201	−	0.680012i	$-0.761975\pi$
$499$	−38.7110	−	14.6811i	−1.73294	−	0.657218i	−0.999740	+	0.0227936i	$0.992744\pi$
$500$	0.234539	+	0.0889489i	0.0104889	+	0.00397791i
$501$	−4.86814	+	3.36024i	−0.217493	+	0.150124i
$502$	−12.0652	−	22.9882i	−0.538494	−	1.02602i
$503$	5.23945	+	1.29141i	0.233616	+	0.0575811i	0.354385	−	0.935099i	$-0.384690\pi$
$503$	5.23945	+	1.29141i	0.233616	+	0.0575811i	−0.120770	+	0.992681i	$0.538536\pi$
$504$	−6.63216	+	5.87558i	−0.295420	+	0.261719i
$505$	15.0305	+	1.82503i	0.668847	+	0.0812128i
$506$	7.45325			0.331337
$507$	−11.8377	−	5.37287i	−0.525733	−	0.238618i
$508$	0.708424			0.0314312
$509$	−18.8890	−	2.29354i	−0.837241	−	0.101659i	−0.309325	−	0.950956i	$-0.600103\pi$
$509$	−18.8890	−	2.29354i	−0.837241	−	0.101659i	−0.527916	+	0.849297i	$0.677026\pi$
$510$	1.63235	−	1.44614i	0.0722818	−	0.0640361i
$511$	23.9487	+	5.90281i	1.05943	+	0.261125i
$512$	10.7591	+	20.4998i	0.475491	+	0.905972i
$513$	−0.282834	+	0.195226i	−0.0124874	+	0.00861944i
$514$	35.7939	+	13.5748i	1.57880	+	0.598760i
$515$	−16.9548	−	6.43011i	−0.747118	−	0.283344i
$516$	−0.0269927	+	0.222305i	−0.00118829	+	0.00978643i
$517$	−0.784996	−	2.06986i	−0.0345241	−	0.0910325i
$518$	−34.2377	+	4.15721i	−1.50432	+	0.182657i
$519$	−4.69519	+	2.46422i	−0.206096	+	0.108167i
$520$	−12.0181	+	24.5838i	−0.527027	+	1.07807i
$521$	34.6950	+	18.2093i	1.52002	+	0.797766i	0.998461	−	0.0554521i	$-0.0176600\pi$
$521$	34.6950	+	18.2093i	1.52002	+	0.797766i	0.521555	+	0.853218i	$0.325352\pi$
$522$	−13.1412	−	4.98380i	−0.575174	−	0.218135i
$523$	−31.2172	−	16.3841i	−1.36503	−	0.716425i	−0.386457	−	0.922307i	$-0.626301\pi$
$523$	−31.2172	−	16.3841i	−1.36503	−	0.716425i	−0.978577	+	0.205882i	$0.933994\pi$
$524$	−0.104588	+	0.275776i	−0.00456895	+	0.0120473i
$525$	−1.55247	+	6.29864i	−0.0677555	+	0.274895i
$526$		−	37.2214i		−	1.62293i
$527$	0.192821	+	0.782304i	0.00839940	+	0.0340777i
$528$	−2.61483	+	0.991674i	−0.113796	+	0.0431571i
$529$	32.8754			1.42936
$530$	−4.07931			−0.177194
$531$	3.99760	−	1.51609i	0.173481	−	0.0657926i
$532$	−0.0196278	+	0.0284358i	−0.000850975	+	0.00123285i
$533$	−1.18147	−	7.84625i	−0.0511753	−	0.339859i
$534$	−11.5946	−	16.7976i	−0.501746	−	0.726905i
$535$	11.0047	+	7.59602i	0.475776	+	0.328405i
$536$	4.33717	−	35.7198i	0.187337	−	1.54286i
$537$	−12.8294	−	6.73340i	−0.553630	−	0.290568i
$538$	27.4345	−	18.9367i	1.18279	−	0.816418i
$539$	−1.55599	−	1.07402i	−0.0670212	−	0.0462614i
$540$	−0.0571061	+	0.0644594i	−0.00245745	+	0.00277389i
$541$	−9.24735	+	17.6194i	−0.397575	+	0.757515i	−0.999147	−	0.0413032i	$-0.986849\pi$
$541$	−9.24735	+	17.6194i	−0.397575	+	0.757515i	0.601572	+	0.798819i	$0.294541\pi$
$542$	3.00560	+	24.7533i	0.129101	+	1.06325i
$543$	2.65142	−	6.99123i	0.113784	−	0.300022i
$544$	0.0879382	−	0.0606994i	0.00377032	−	0.00260246i
$545$	1.91697	−	15.7876i	0.0821138	−	0.676268i
$546$	14.8512	+	5.15116i	0.635574	+	0.220449i
$547$	−5.32437	−	43.8501i	−0.227654	−	1.87490i	−0.440417	−	0.897793i	$-0.645170\pi$
$547$	−5.32437	−	43.8501i	−0.227654	−	1.87490i	0.212764	−	0.977104i	$-0.431754\pi$
$548$	0.253393	+	0.286022i	0.0108244	+	0.0122183i
$549$	11.1853	−	2.75693i	0.477377	−	0.117663i
$550$	−1.18223	+	1.71276i	−0.0504105	+	0.0730322i
$551$	−3.41824	−	0.415050i	−0.145622	−	0.0176817i
$552$	−19.9252	+	7.55661i	−0.848071	+	0.321631i
$553$	−44.9699	−	5.46033i	−1.91231	−	0.232197i
$554$	−3.98697	−	16.1758i	−0.169390	−	0.687243i
$555$	−20.4482	+	5.04003i	−0.867978	+	0.213937i
$556$	−0.165375	−	0.146509i	−0.00701345	−	0.00621338i
$557$	10.9395	−	12.3481i	0.463522	−	0.523208i	−0.469546	−	0.882908i	$-0.655583\pi$
$557$	10.9395	−	12.3481i	0.463522	−	0.523208i	0.933068	+	0.359700i	$0.117121\pi$
$558$	0.686274	+	1.80955i	0.0290523	+	0.0766046i
$559$	23.0753	−	9.51535i	0.975983	−	0.402456i
$560$	11.5433	−	30.4372i	0.487794	−	1.28621i
$561$	0.192912	+	0.367563i	0.00814476	+	0.0155185i
$562$	8.01273	+	11.6084i	0.337997	+	0.489673i
$563$	11.6211	+	10.2954i	0.489771	+	0.433900i	0.871515	−	0.490369i	$-0.163138\pi$
$563$	11.6211	+	10.2954i	0.489771	+	0.433900i	−0.381744	+	0.924268i	$0.624676\pi$
$564$	0.0668045	+	0.0754066i	0.00281298	+	0.00317519i
$565$	3.08938	−	12.5341i	0.129971	−	0.527313i
$566$	−9.86630	−	18.7987i	−0.414711	−	0.790166i
$567$	2.55786	+	1.76556i	0.107420	+	0.0741466i
$568$	9.06382	+	23.8993i	0.380309	+	1.00279i
$569$	−21.9993	+	11.5461i	−0.922258	+	0.484038i	−0.857859	−	0.513886i	$-0.828205\pi$
$569$	−21.9993	+	11.5461i	−0.922258	+	0.484038i	−0.0643994	+	0.997924i	$0.520513\pi$
$570$	0.596412	−	1.13637i	0.0249809	−	0.0475972i
$571$	−11.0029	−	9.74769i	−0.460455	−	0.407928i	0.400748	−	0.916188i	$-0.368750\pi$
$571$	−11.0029	−	9.74769i	−0.460455	−	0.407928i	−0.861203	+	0.508260i	$0.830289\pi$
$572$	−0.0636037	−	0.0531779i	−0.00265940	−	0.00222348i
$573$	8.50371	−	7.53363i	0.355247	−	0.314722i
$574$	2.29609	+	9.31561i	0.0958370	+	0.388826i
$575$	−8.86292	+	12.8402i	−0.369609	+	0.535471i
$576$	6.08178	−	5.38799i	0.253407	−	0.224499i
$577$			30.8718i			1.28521i	0.766197	+	0.642605i	$0.222147\pi$
$577$			30.8718i			1.28521i	−0.766197	+	0.642605i	$0.777853\pi$
$578$	−15.4959	−	17.4912i	−0.644543	−	0.727539i
$579$	5.69437	−	10.8497i	0.236650	−	0.450899i
$580$	−0.856548	+	0.104004i	−0.0355662	+	0.00431852i
$581$	−31.9161	+	16.7509i	−1.32410	+	0.694944i
$582$	0.825484	+	6.79847i	0.0342174	+	0.281806i
$583$	0.185826	−	0.753926i	0.00769613	−	0.0312244i
$584$	−21.9669	−	5.41435i	−0.908997	−	0.224048i
$585$	9.38165	+	2.02943i	0.387883	+	0.0839064i
$586$	37.7202	−	9.29721i	1.55821	−	0.384064i
$587$			21.8022i			0.899873i	0.893061	+	0.449936i	$0.148553\pi$
$587$			21.8022i			0.899873i	−0.893061	+	0.449936i	$0.851447\pi$
$588$	0.0835405	+	0.0205909i	0.00344515	+	0.000849154i
$589$	0.269349	+	0.390220i	0.0110983	+	0.0160787i
$590$	−10.5873	+	11.9506i	−0.435873	+	0.491999i
$591$	−25.0208	+	3.03808i	−1.02922	+	0.124970i
$592$	30.8964	−	3.75151i	1.26984	−	0.154186i
$593$	−26.4251	+	29.8278i	−1.08515	+	1.22488i	−0.112243	+	0.993681i	$0.535804\pi$
$593$	−26.4251	+	29.8278i	−1.08515	+	1.22488i	−0.972906	+	0.231200i	$0.925735\pi$
$594$	0.566413	+	0.820591i	0.0232402	+	0.0336693i
$595$	−4.69159	−	1.15637i	−0.192336	−	0.0474067i
$596$		−	0.200846i		−	0.00822699i
$597$	9.72497	−	2.39699i	0.398017	−	0.0981023i
$598$	29.0038	+	24.2496i	1.18605	+	0.991638i
$599$	−1.09549	−	0.270014i	−0.0447605	−	0.0110325i	0.216872	−	0.976200i	$-0.430415\pi$
$599$	−1.09549	−	0.270014i	−0.0447605	−	0.0110325i	−0.261632	+	0.965168i	$0.584261\pi$
$600$	1.42401	−	5.77742i	0.0581348	−	0.235862i
$601$	−3.44920	−	28.4067i	−0.140696	−	1.15874i	−0.876452	−	0.481489i	$-0.840096\pi$
$601$	−3.44920	−	28.4067i	−0.140696	−	1.15874i	0.735756	−	0.677246i	$-0.236827\pi$
$602$	−26.7241	+	14.0259i	−1.08919	+	0.571652i
$603$	−12.5296	+	1.52137i	−0.510244	+	0.0619549i
$604$	0.163587	−	0.311689i	0.00665626	−	0.0126824i
$605$	18.5269	+	20.9126i	0.753226	+	0.850217i
$606$			7.97787i			0.324079i
$607$	32.7453	−	29.0098i	1.32909	−	1.17747i	0.359385	−	0.933189i	$-0.382986\pi$
$607$	32.7453	−	29.0098i	1.32909	−	1.17747i	0.969704	−	0.244282i	$-0.0785521\pi$
$608$	0.0357207	−	0.0517504i	0.00144867	−	0.00209875i
$609$	7.45242	+	30.2357i	0.301987	+	1.22521i
$610$	−32.2007	+	28.5273i	−1.30377	+	1.15504i
$611$	3.67966	−	10.6088i	0.148863	−	0.429185i
$612$	−0.0141401	−	0.0125270i	−0.000571579	−	0.000506375i
$613$	−15.7338	+	29.9783i	−0.635484	+	1.21081i	0.328412	+	0.944535i	$0.393487\pi$
$613$	−15.7338	+	29.9783i	−0.635484	+	1.21081i	−0.963896	+	0.266279i	$0.914206\pi$
$614$	20.0801	−	10.5388i	0.810366	−	0.425313i
$615$	2.07750	+	5.47793i	0.0837730	+	0.220891i
$616$	5.18334	+	3.57780i	0.208843	+	0.144154i
$617$	5.04336	+	9.60933i	0.203038	+	0.386857i	0.965590	−	0.260071i	$-0.0837459\pi$
$617$	5.04336	+	9.60933i	0.203038	+	0.386857i	−0.762551	+	0.646928i	$0.776054\pi$
$618$	2.28655	−	9.27690i	0.0919785	−	0.373172i
$619$	30.9880	+	34.9782i	1.24551	+	1.40589i	0.879923	+	0.475116i	$0.157594\pi$
$619$	30.9880	+	34.9782i	1.24551	+	1.40589i	0.365589	+	0.930776i	$0.380868\pi$
$620$	0.0889334	+	0.0787881i	0.00357165	+	0.00316421i
$621$	4.24627	+	6.15179i	0.170397	+	0.246863i
$622$	−2.52413	−	4.80933i	−0.101208	−	0.192836i
$623$	−16.0366	+	42.2850i	−0.642493	+	1.69411i
$624$	−13.4019	−	4.64846i	−0.536505	−	0.186087i
$625$	11.0210	+	29.0599i	0.440839	+	1.16240i
$626$	−7.21910	+	8.14868i	−0.288533	+	0.325687i
$627$	0.182852	+	0.161993i	0.00730240	+	0.00646936i
$628$	−0.191339	+	0.0471609i	−0.00763527	+	0.00188192i
$629$	−1.10560	−	4.48560i	−0.0440832	−	0.178853i
$630$	−11.5218	−	1.39899i	−0.459038	−	0.0557373i
$631$	−4.63097	+	1.75629i	−0.184356	+	0.0699170i	−0.445055	−	0.895503i	$-0.646816\pi$
$631$	−4.63097	+	1.75629i	−0.184356	+	0.0699170i	0.260700	+	0.965420i	$0.416047\pi$
$632$	41.2486	+	5.00849i	1.64078	+	0.199227i
$633$	9.76225	−	14.1431i	0.388015	−	0.562136i
$634$	25.7523	−	6.34738i	1.02276	−	0.252087i
$635$	38.6612	+	43.6394i	1.53422	+	1.73178i
$636$	0.00425935	+	0.0350789i	0.000168894	+	0.00139097i
$637$	−2.56063	−	9.24197i	−0.101456	−	0.366180i
$638$	−1.20419	+	9.91742i	−0.0476745	+	0.392635i
$639$	7.37880	−	5.09322i	0.291901	−	0.201485i
$640$	−10.4140	+	27.4594i	−0.411649	+	1.08543i
$641$	0.992303	+	8.17235i	0.0391936	+	0.322789i	0.999098	+	0.0424613i	$0.0135199\pi$
$641$	0.992303	+	8.17235i	0.0391936	+	0.322789i	−0.959904	+	0.280327i	$0.909557\pi$
$642$	−3.27430	+	6.23866i	−0.129226	+	0.246220i
$643$	6.02464	−	6.80042i	0.237589	−	0.268182i	−0.617608	−	0.786486i	$-0.711898\pi$
$643$	6.02464	−	6.80042i	0.237589	−	0.268182i	0.855196	+	0.518304i	$0.173436\pi$
$644$	0.618495	+	0.426917i	0.0243721	+	0.0168229i
$645$	−15.1672	+	10.4692i	−0.597209	+	0.412224i
$646$	0.249278	+	0.130831i	0.00980773	+	0.00514749i
$647$	3.31917	−	27.3358i	0.130490	−	1.07468i	−0.769462	−	0.638693i	$-0.779475\pi$
$647$	3.31917	−	27.3358i	0.130490	−	1.07468i	0.899952	−	0.435990i	$-0.143602\pi$
$648$	−2.34619	−	1.61946i	−0.0921671	−	0.0636184i
$649$	−1.72639	−	2.50111i	−0.0677668	−	0.0981771i
$650$	−10.1731	+	2.81862i	−0.399022	+	0.110555i
$651$	2.43591	−	3.52902i	0.0954708	−	0.138313i
$652$	0.00495980	−	0.00188100i	0.000194241	−	7.36658e-5i
$653$	32.5622			1.27426			0.637128	−	0.770758i	$-0.280122\pi$
$653$	32.5622			1.27426			0.637128	+	0.770758i	$0.280122\pi$
$654$	8.37975			0.327674
$655$	−22.6957	+	8.60735i	−0.886795	+	0.336317i
$656$	−2.07202	−	8.40650i	−0.0808986	−	0.328219i
$657$			7.93603i			0.309614i
$658$	−3.24931	+	13.1830i	−0.126671	+	0.513926i
$659$	−6.69219	+	17.6459i	−0.260691	+	0.687385i	0.739212	+	0.673472i	$0.235198\pi$
$659$	−6.69219	+	17.6459i	−0.260691	+	0.687385i	−0.999903	+	0.0139128i	$0.995571\pi$
$660$	0.0542022	+	0.0284475i	0.00210982	+	0.00110732i
$661$	−42.8360	−	16.2456i	−1.66613	−	0.631879i	−0.672046	−	0.740509i	$-0.734584\pi$
$661$	−42.8360	−	16.2456i	−1.66613	−	0.631879i	−0.994082	+	0.108630i	$0.965354\pi$
$662$	13.1471	+	6.90013i	0.510976	+	0.268181i
$663$	−0.445184	+	2.05800i	−0.0172895	+	0.0799260i
$664$	29.2751	−	15.3647i	1.13609	−	0.596267i
$665$	−2.82283	+	0.342753i	−0.109465	+	0.0132914i
$666$	−3.93498	−	10.3757i	−0.152477	−	0.402050i
$667$	−9.02757	+	74.3487i	−0.349549	+	2.87879i
$668$	−0.178913	−	0.0678527i	−0.00692234	−	0.00262530i
$669$	−0.317185	−	0.120292i	−0.0122631	−	0.00465077i
$670$	38.7899	−	26.7747i	1.49858	−	1.03440i
$671$	−3.80549	−	7.25075i	−0.146909	−	0.279912i
$672$	−0.552154	−	0.136094i	−0.0212998	−	0.00524993i
$673$	−0.526306	+	0.466267i	−0.0202876	+	0.0179733i	−0.673206	−	0.739455i	$-0.735083\pi$
$673$	−0.526306	+	0.466267i	−0.0202876	+	0.0179733i	0.652918	+	0.757429i	$0.273545\pi$
$674$	16.1415	+	1.95993i	0.621746	+	0.0754937i
$675$	−2.08722			−0.0803372
$676$	−0.0744922	−	0.413876i	−0.00286508	−	0.0159183i
$677$	−31.7978			−1.22209			−0.611043	−	0.791597i	$-0.709250\pi$
$677$	−31.7978			−1.22209			−0.611043	+	0.791597i	$0.709250\pi$
$678$	6.75239	+	0.819889i	0.259324	+	0.0314877i
$679$	11.3579	−	10.0622i	0.435876	−	0.386153i
$680$	4.30336	+	1.06068i	0.165026	+	0.0406753i
$681$	−2.63730	−	5.02496i	−0.101062	−	0.192557i
$682$	1.13215	−	0.781469i	0.0433524	−	0.0299240i
$683$	−10.2816	−	3.89929i	−0.393414	−	0.149202i	0.149962	−	0.988692i	$-0.452085\pi$
$683$	−10.2816	−	3.89929i	−0.393414	−	0.149202i	−0.543376	+	0.839490i	$0.682854\pi$
$684$	−0.0103946	−	0.00394216i	−0.000397449	−	0.000150732i
$685$	−3.79061	+	31.2184i	−0.144832	+	1.19280i
$686$	−6.70981	−	17.6923i	−0.256182	−	0.675496i
$687$	−25.1578	+	3.05471i	−0.959830	+	0.116545i
$688$	24.1161	−	12.6571i	0.919417	−	0.482547i
$689$	3.17607	−	2.32926i	0.120999	−	0.0887376i
$690$	−24.7166	−	12.9723i	−0.940946	−	0.493847i
$691$	−18.6209	−	7.06199i	−0.708374	−	0.268651i	−0.0260081	−	0.999662i	$-0.508280\pi$
$691$	−18.6209	−	7.06199i	−0.708374	−	0.268651i	−0.682366	+	0.731011i	$0.739049\pi$
$692$	−0.151881	−	0.0797133i	−0.00577365	−	0.00303024i
$693$	0.783413	−	2.06569i	0.0297594	−	0.0784691i
$694$	−5.45790	+	22.1436i	−0.207179	+	0.840559i
$695$		−	18.1827i		−	0.689710i
$696$	−6.83573	−	27.7336i	−0.259108	−	1.05124i
$697$	−1.20166	+	0.455730i	−0.0455162	+	0.0172620i
$698$	19.0795			0.722168
$699$	28.3640			1.07282
$700$	−0.196211	+	0.0744129i	−0.00741607	+	0.00281254i
$701$	−6.45002	+	9.34446i	−0.243614	+	0.352935i	−0.925649	−	0.378384i	$-0.876480\pi$
$701$	−6.45002	+	9.34446i	−0.243614	+	0.352935i	0.682035	+	0.731320i	$0.261095\pi$
$702$	−0.465681	+	5.03613i	−0.0175760	+	0.190077i
$703$	−1.54441	−	2.23746i	−0.0582483	−	0.0843873i
$704$	−4.75319	−	3.28089i	−0.179143	−	0.123653i
$705$	−0.999352	+	8.23041i	−0.0376378	+	0.309975i
$706$	−1.57934	−	0.828903i	−0.0594394	−	0.0311962i
$707$	14.5475	−	10.0414i	0.547116	−	0.377647i
$708$	0.113821	+	0.0785648i	0.00427765	+	0.00295265i
$709$	25.1260	−	28.3614i	0.943628	−	1.06514i	−0.0541519	−	0.998533i	$-0.517246\pi$
$709$	25.1260	−	28.3614i	0.943628	−	1.06514i	0.997780	−	0.0666028i	$-0.0212160\pi$
$710$	−15.5597	+	29.6465i	−0.583944	+	1.11261i
$711$	−1.75685	−	14.4689i	−0.0658870	−	0.542628i
$712$	14.7096	−	38.7859i	0.551264	−	1.45356i
$713$	8.48750	−	5.85850i	0.317859	−	0.219403i
$714$	0.306889	−	2.52746i	0.0114850	−	0.0945879i
$715$	−0.195278	−	6.82014i	−0.00730298	−	0.255059i
$716$	−0.0564949	−	0.465278i	−0.00211131	−	0.0173882i
$717$	−10.0102	−	11.2992i	−0.373837	−	0.421975i
$718$	−22.4351	+	5.52974i	−0.837269	+	0.206368i
$719$	−14.9624	+	21.6768i	−0.558003	+	0.808406i	−0.995885	−	0.0906258i	$-0.971113\pi$
$719$	−14.9624	+	21.6768i	−0.558003	+	0.808406i	0.437882	+	0.899032i	$0.355729\pi$
$720$	10.3973	+	1.26247i	0.387486	+	0.0470494i
$721$	−19.7943	+	7.50697i	−0.737177	+	0.279574i
$722$	−26.2931	−	3.19256i	−0.978527	−	0.118815i
$723$	2.81277	+	11.4119i	0.104608	+	0.424412i
$724$	0.234843	−	0.0578837i	0.00872788	−	0.00215123i
$725$	−15.6534	−	13.8677i	−0.581352	−	0.515033i
$726$	−9.76201	+	11.0190i	−0.362302	+	0.408955i
$727$	−14.0903	−	37.1532i	−0.522582	−	1.37793i	−0.893414	−	0.449234i	$-0.851697\pi$
$727$	−14.0903	−	37.1532i	−0.522582	−	1.37793i	0.370832	−	0.928700i	$-0.379072\pi$
$728$	8.53004	+	30.7870i	0.316144	+	1.14104i
$729$	−0.354605	+	0.935016i	−0.0131335	+	0.0346302i
$730$	−13.7724	−	26.2411i	−0.509740	−	0.971227i
$731$	−2.29656	−	3.32715i	−0.0849415	−	0.123059i
$732$	0.278935	+	0.247115i	0.0103097	+	0.00913362i
$733$	−0.632271	−	0.713687i	−0.0233535	−	0.0263606i	0.736718	−	0.676200i	$-0.236375\pi$
$733$	−0.632271	−	0.713687i	−0.0233535	−	0.0263606i	−0.760071	+	0.649840i	$0.774836\pi$
$734$	0.867676	−	3.52030i	0.0320265	−	0.129937i
$735$	3.29068	+	6.26987i	0.121379	+	0.231268i
$736$	−1.12560	−	0.776945i	−0.0414902	−	0.0286386i
$737$	3.18142	+	8.38872i	0.117189	+	0.309002i
$738$	−2.73338	+	1.43459i	−0.100617	+	0.0528080i
$739$	−6.35159	+	12.1020i	−0.233647	+	0.445178i	−0.973846	−	0.227211i	$-0.927039\pi$
$739$	−6.35159	+	12.1020i	−0.233647	+	0.445178i	0.740198	+	0.672389i	$0.234732\pi$
$740$	−0.509929	−	0.451758i	−0.0187454	−	0.0166070i
$741$	0.184503	+	1.22530i	0.00677790	+	0.0450126i
$742$	−3.56477	+	3.15811i	−0.130867	+	0.115938i
$743$	−2.80643	−	11.3861i	−0.102958	−	0.417716i	0.896733	−	0.442571i	$-0.145934\pi$
$743$	−2.80643	−	11.3861i	−0.102958	−	0.417716i	−0.999691	+	0.0248552i	$0.992088\pi$
$744$	−2.23434	+	3.23699i	−0.0819147	+	0.118674i
$745$	12.3723	−	10.9609i	0.453285	−	0.401576i
$746$		−	7.30070i		−	0.267298i
$747$	−7.69046	−	8.68074i	−0.281379	−	0.317612i
$748$	−0.00624036	+	0.0118900i	−0.000228170	+	0.000434742i
$749$	15.4973	−	1.88172i	0.566260	−	0.0687564i
$750$	−9.63134	+	5.05492i	−0.351687	+	0.184579i
$751$	−1.52474	−	12.5574i	−0.0556386	−	0.458225i	−0.993727	−	0.111830i	$-0.964329\pi$
$751$	−1.52474	−	12.5574i	−0.0556386	−	0.458225i	0.938089	−	0.346395i	$-0.112594\pi$
$752$	2.93221	−	11.8964i	0.106927	−	0.433819i
$753$	−17.9704	−	4.42931i	−0.654878	−	0.161413i
$754$	−36.9529	+	34.6751i	−1.34575	+	1.26279i
$755$	28.1278	−	6.93287i	1.02367	−	0.252313i
$756$			0.100539i			0.00365657i
$757$	9.02290	+	2.22395i	0.327943	+	0.0808307i	0.399850	−	0.916581i	$-0.369062\pi$
$757$	9.02290	+	2.22395i	0.327943	+	0.0808307i	−0.0719069	+	0.997411i	$0.522908\pi$
$758$	17.0544	+	24.7075i	0.619443	+	0.897419i
$759$	3.52343	−	3.97713i	0.127892	−	0.144361i
$760$	2.58924	−	0.314390i	0.0939215	−	0.0114041i
$761$	11.0356	−	1.33997i	0.400041	−	0.0485738i	0.0819561	−	0.996636i	$-0.473883\pi$
$761$	11.0356	−	1.33997i	0.400041	−	0.0485738i	0.318085	+	0.948062i	$0.396960\pi$
$762$	−20.3709	+	22.9940i	−0.737961	+	0.832986i
$763$	−10.5473	−	15.2803i	−0.381836	−	0.553185i
$764$	0.356824	+	0.0879492i	0.0129094	+	0.00318189i
$765$		−	1.55468i		−	0.0562097i
$766$	−21.1370	+	5.20980i	−0.763710	+	0.188238i
$767$	1.41936	−	15.3498i	0.0512503	−	0.554249i
$768$	0.753599	+	0.185746i	0.0271932	+	0.00670251i
$769$	1.34453	−	5.45498i	0.0484850	−	0.196712i	−0.941705	−	0.336440i	$-0.890777\pi$
$769$	1.34453	−	5.45498i	0.0484850	−	0.196712i	0.990190	+	0.139729i	$0.0446231\pi$
$770$	0.994437	+	8.18993i	0.0358370	+	0.295145i
$771$	24.1648	−	12.6826i	0.870272	−	0.456754i
$772$	0.393481	−	0.0477772i	0.0141617	−	0.00171954i
$773$	7.01998	−	13.3754i	0.252491	−	0.481081i	−0.725912	−	0.687787i	$-0.758582\pi$
$773$	7.01998	−	13.3754i	0.252491	−	0.481081i	0.978403	+	0.206706i	$0.0662744\pi$
$774$	−6.43939	−	7.26857i	−0.231459	−	0.261263i
$775$			2.87970i			0.103442i
$776$	−10.4180	+	9.22957i	−0.373986	+	0.331322i
$777$	−13.9671	+	20.2348i	−0.501067	+	0.725921i
$778$	−11.1710	−	45.3227i	−0.400501	−	1.62490i
$779$	−0.566105	+	0.501525i	−0.0202828	+	0.0179690i
$780$	0.118369	+	0.287051i	0.00423827	+	0.0102781i
$781$	−4.77039	−	4.22619i	−0.170698	−	0.151225i
$782$	2.84566	−	5.42195i	0.101760	−	0.193888i
$783$	−8.87173	+	4.65624i	−0.317050	+	0.166401i
$784$	−3.71074	−	9.78443i	−0.132527	−	0.349444i
$785$	−13.3472	−	9.21290i	−0.476382	−	0.328822i
$786$	−5.94368	−	11.3247i	−0.212004	−	0.403940i
$787$	−7.64808	+	31.0295i	−0.272625	+	1.10608i	0.661732	+	0.749741i	$0.269822\pi$
$787$	−7.64808	+	31.0295i	−0.272625	+	1.10608i	−0.934356	+	0.356340i	$0.884024\pi$
$788$	−0.540659	−	0.610278i	−0.0192602	−	0.0217403i
$789$	−19.8617	−	17.5959i	−0.707095	−	0.626431i
$790$	30.9190	+	44.7939i	1.10005	+	1.59369i
$791$	−7.00391	−	13.3448i	−0.249031	−	0.474488i
$792$	−0.718585	+	1.89475i	−0.0255338	+	0.0673271i
$793$	8.78192	−	40.5972i	0.311855	−	1.44165i
$794$	14.1345	+	37.2695i	0.501613	+	1.32264i
$795$	−1.92844	+	2.17676i	−0.0683947	+	0.0772017i
$796$	0.242518	+	0.214852i	0.00859581	+	0.00761522i
$797$	47.1888	−	11.6310i	1.67151	−	0.411991i	0.713947	−	0.700200i	$-0.246906\pi$
$797$	47.1888	−	11.6310i	1.67151	−	0.411991i	0.957568	+	0.288209i	$0.0930597\pi$
$798$	−0.358566	−	1.45476i	−0.0126931	−	0.0514980i
$799$	−1.80546	−	0.219222i	−0.0638725	−	0.00775552i
$800$	0.357084	−	0.135424i	0.0126248	−	0.00478796i
$801$	−14.4446	−	1.75389i	−0.510374	−	0.0619706i
$802$	15.7218	−	22.7769i	0.555155	−	0.804281i
$803$	5.47719	−	1.35001i	0.193286	−	0.0476407i
$804$	−0.270744	−	0.305607i	−0.00954841	−	0.0107779i
$805$	7.45508	+	61.3981i	0.262757	+	2.16400i
$806$	6.94825	+	0.642491i	0.244742	+	0.0226308i
$807$	2.86451	−	23.5914i	0.100836	−	0.830456i
$808$	−13.3437	+	9.21049i	−0.469430	+	0.324024i
$809$	18.2934	−	48.2358i	0.643163	−	1.69588i	−0.0724399	−	0.997373i	$-0.523079\pi$
$809$	18.2934	−	48.2358i	0.643163	−	1.69588i	0.715603	−	0.698508i	$-0.246152\pi$
$810$	−0.450123	−	3.70710i	−0.0158157	−	0.130254i
$811$	−18.2310	+	34.7364i	−0.640179	+	1.21976i	0.321845	+	0.946792i	$0.395697\pi$
$811$	−18.2310	+	34.7364i	−0.640179	+	1.21976i	−0.962024	+	0.272966i	$0.911995\pi$
$812$	−0.667990	+	0.754005i	−0.0234419	+	0.0264604i
$813$	14.6295	+	10.0980i	0.513078	+	0.354152i
$814$	−6.49158	+	4.48082i	−0.227530	+	0.157053i
$815$	0.386544	+	0.202874i	0.0135401	+	0.00710637i
$816$	−0.276940	+	2.28081i	−0.00969484	+	0.0798442i
$817$	−1.95798	−	1.35149i	−0.0685010	−	0.0472828i
$818$	−5.83941	−	8.45985i	−0.204170	−	0.295792i
$819$	9.76944	−	5.48961i	0.341372	−	0.191823i
$820$	−0.107658	+	0.155969i	−0.00375957	+	0.00544668i
$821$	10.3784	−	3.93600i	0.362208	−	0.137367i	−0.166786	−	0.985993i	$-0.553339\pi$
$821$	10.3784	−	3.93600i	0.362208	−	0.137367i	0.528994	+	0.848626i	$0.322570\pi$
$822$	−16.5701			−0.577949
$823$	51.4688			1.79409			0.897045	−	0.441938i	$-0.145709\pi$
$823$	51.4688			1.79409			0.897045	+	0.441938i	$0.145709\pi$
$824$	18.1563	−	6.88577i	0.632504	−	0.239877i
$825$	0.355060	+	1.44053i	0.0123616	+	0.0501529i
$826$			18.6397i			0.648558i
$827$	−9.52502	+	38.6445i	−0.331217	+	1.34380i	0.535303	+	0.844660i	$0.320197\pi$
$827$	−9.52502	+	38.6445i	−0.331217	+	1.34380i	−0.866521	+	0.499141i	$0.833649\pi$
$828$	−0.0857443	+	0.226089i	−0.00297982	+	0.00785714i
$829$	−46.6716	−	24.4951i	−1.62097	−	0.850752i	−0.997630	−	0.0688017i	$-0.978082\pi$
$829$	−46.6716	−	24.4951i	−1.62097	−	0.850752i	−0.623341	−	0.781950i	$-0.714225\pi$
$830$	40.4939	+	15.3573i	1.40556	+	0.533060i
$831$	−10.5163	−	5.51941i	−0.364808	−	0.191466i
$832$	−7.82216	−	28.2321i	−0.271185	−	0.978773i
$833$	−1.37539	+	0.721858i	−0.0476543	+	0.0250109i
$834$	9.51080	−	1.15482i	0.329332	−	0.0399881i
$835$	−5.58412	−	14.7241i	−0.193246	−	0.509549i
$836$	−0.000952512		0.00784464i	−3.29433e−5		0.000271313i
$837$	1.29002	+	0.489241i	0.0445897	+	0.0169107i
$838$	4.27078	+	1.61969i	0.147532	+	0.0559513i
$839$	−35.4948	+	24.5003i	−1.22542	+	0.845844i	−0.991964	−	0.126524i	$-0.959618\pi$
$839$	−35.4948	+	24.5003i	−1.22542	+	0.845844i	−0.233453	+	0.972368i	$0.575002\pi$
$840$	−10.9620	−	20.8863i	−0.378224	−	0.720647i
$841$	−69.3138	−	17.0843i	−2.39013	−	0.589115i
$842$	−8.22660	+	7.28813i	−0.283507	+	0.251166i
$843$	9.98229	+	1.21207i	0.343808	+	0.0417459i
$844$	0.555907			0.0191351
$845$	21.4298	−	27.1754i	0.737207	−	0.934864i
$846$	−4.36853			−0.150193
$847$	32.3801	+	3.93165i	1.11259	+	0.135093i
$848$	3.21688	−	2.84991i	0.110468	−	0.0978662i
$849$	−14.6953	−	3.62207i	−0.504342	−	0.124309i
$850$	0.794586	+	1.51396i	0.0272541	+	0.0519283i
$851$	−48.6660	+	33.5917i	−1.66825	+	1.15151i
$852$	0.271184	+	0.102846i	0.00929060	+	0.00352346i
$853$	28.8591	+	10.9448i	0.988117	+	0.374744i	0.795118	−	0.606455i	$-0.207409\pi$
$853$	28.8591	+	10.9448i	0.988117	+	0.374744i	0.193000	+	0.981199i	$0.438178\pi$
$854$	−6.05386	+	49.8580i	−0.207159	+	1.70611i
$855$	−0.324431	−	0.855454i	−0.0110953	−	0.0292559i
$856$	−14.2149	+	1.72600i	−0.485856	+	0.0589936i
$857$	25.6054	−	13.4387i	0.874664	−	0.459059i	0.0332479	−	0.999447i	$-0.489415\pi$
$857$	25.6054	−	13.4387i	0.874664	−	0.459059i	0.841416	+	0.540388i	$0.181723\pi$
$858$	3.55499	−	0.535304i	0.121365	−	0.0182750i
$859$	33.9702	+	17.8290i	1.15905	+	0.608316i	0.930887	−	0.365307i	$-0.119036\pi$
$859$	33.9702	+	17.8290i	1.15905	+	0.608316i	0.228162	+	0.973623i	$0.426728\pi$
$860$	−0.557422	−	0.211402i	−0.0190079	−	0.00720876i
$861$	6.05635	+	3.17862i	0.206400	+	0.108327i
$862$	−9.61783	+	25.3601i	−0.327585	+	0.863770i
$863$	−6.64356	+	26.9540i	−0.226150	+	0.917525i	0.742650	+	0.669680i	$0.233569\pi$
$863$	−6.64356	+	26.9540i	−0.226150	+	0.917525i	−0.968800	+	0.247845i	$0.920278\pi$
$864$		−	0.182971i		−	0.00622480i
$865$	−3.37828	−	13.7062i	−0.114865	−	0.466025i
$866$	16.5460	−	6.27506i	0.562255	−	0.213235i
$867$	−16.6590			−0.565768
$868$	0.138712			0.00470819
$869$	−9.68714	+	3.67385i	−0.328614	+	0.124627i
$870$	21.2545	−	30.7925i	0.720596	−	1.04396i
$871$	−14.9129	+	42.9950i	−0.505303	+	1.45683i
$872$	9.67447	+	14.0159i	0.327619	+	0.474638i
$873$	4.01797	+	2.77340i	0.135988	+	0.0938655i
$874$	0.434353	−	3.57722i	0.0146922	−	0.121001i
$875$	21.3401	+	11.2002i	0.721428	+	0.378635i
$876$	−0.211273	+	0.145832i	−0.00713827	+	0.00492719i
$877$	10.2336	+	7.06375i	0.345565	+	0.238526i	0.728187	−	0.685379i	$-0.240363\pi$
$877$	10.2336	+	7.06375i	0.345565	+	0.238526i	−0.382622	+	0.923905i	$0.624979\pi$
$878$	−13.1182	+	14.8074i	−0.442718	+	0.499725i
$879$	12.8707	−	24.5230i	0.434117	−	0.827141i
$880$	−0.897390	−	7.39067i	−0.0302510	−	0.249140i
$881$	−8.70416	+	22.9510i	−0.293250	+	0.773238i	0.704716	+	0.709490i	$0.251075\pi$
$881$	−8.70416	+	22.9510i	−0.293250	+	0.773238i	−0.997966	+	0.0637480i	$0.979695\pi$
$882$	−3.07057	+	2.11946i	−0.103391	+	0.0713660i
$883$	−0.741799	+	6.10927i	−0.0249635	+	0.205593i	−0.999854	−	0.0170921i	$-0.994559\pi$
$883$	−0.741799	+	6.10927i	−0.0249635	+	0.205593i	0.974890	+	0.222685i	$0.0714822\pi$
$884$	−0.0629688	+	0.0259658i	−0.00211787	+	0.000873325i
$885$	1.37195	+	11.2990i	0.0461175	+	0.379812i
$886$	−18.6781	−	21.0832i	−0.627503	−	0.708304i
$887$	1.79670	−	0.442848i	0.0603274	−	0.0148694i	−0.209036	−	0.977908i	$-0.567033\pi$
$887$	1.79670	−	0.442848i	0.0603274	−	0.0148694i	0.269364	+	0.963038i	$0.413187\pi$
$888$	12.8113	−	18.5604i	0.429920	−	0.622846i
$889$	67.5694	+	8.20440i	2.26620	+	0.275167i
$890$	50.8059	−	19.2681i	1.70302	−	0.645870i
$891$	0.705640	+	0.0856802i	0.0236398	+	0.00287040i
$892$	−0.00262612	−	0.0106546i	−8.79290e−5	−	0.000356742i
$893$	−1.03919	+	0.256137i	−0.0347751	+	0.00857129i
$894$	6.51908	+	5.77540i	0.218030	+	0.193158i
$895$	25.5783	−	28.8719i	0.854988	−	0.965082i
$896$	12.1580	+	32.0581i	0.406171	+	1.07099i
$897$	26.6510	−	4.01305i	0.889851	−	0.133992i
$898$	−8.25577	+	21.7687i	−0.275499	+	0.726430i
$899$	6.42413	+	12.2402i	0.214257	+	0.408232i
$900$	−0.0383545	−	0.0555661i	−0.00127848	−	0.00185220i
$901$	−0.477503	−	0.423031i	−0.0159079	−	0.0140932i
$902$	1.45509	+	1.64245i	0.0484491	+	0.0546877i
$903$	−5.14912	+	20.8908i	−0.171352	+	0.695202i
$904$	6.42434	+	12.2406i	0.213670	+	0.407115i
$905$	16.3819	+	11.3076i	0.544552	+	0.375877i
$906$	5.41281	+	14.2724i	0.179829	+	0.474169i
$907$	1.02596	−	0.538464i	0.0340663	−	0.0178794i	−0.447604	−	0.894232i	$-0.647723\pi$
$907$	1.02596	−	0.538464i	0.0340663	−	0.0178794i	0.481670	+	0.876352i	$0.340030\pi$
$908$	0.0853121	−	0.162549i	0.00283118	−	0.00539436i
$909$	4.25707	+	3.77144i	0.141198	+	0.125091i
$910$	−22.7766	+	35.1060i	−0.755037	+	1.16375i
$911$	−4.52539	+	4.00915i	−0.149933	+	0.132829i	−0.734755	−	0.678333i	$-0.762703\pi$
$911$	−4.52539	+	4.00915i	−0.149933	+	0.132829i	0.584822	+	0.811162i	$0.301164\pi$
$912$	0.323574	+	1.31279i	0.0107146	+	0.0434709i
$913$	−4.68293	+	6.78440i	−0.154982	+	0.224531i
$914$	9.23346	−	8.18014i	0.305416	−	0.270575i
$915$			30.6685i			1.01387i
$916$	−0.543620	−	0.613620i	−0.0179617	−	0.0202746i
$917$	−13.1694	+	25.0922i	−0.434892	+	0.828617i
$918$	0.813205	−	0.0987409i	0.0268398	−	0.00325894i
$919$	25.4668	−	13.3660i	0.840073	−	0.440904i	0.0109296	−	0.999940i	$-0.496521\pi$
$919$	25.4668	−	13.3660i	0.840073	−	0.440904i	0.829143	+	0.559036i	$0.188829\pi$
$920$	−6.83817	−	56.3174i	−0.225448	−	1.85673i
$921$	3.86897	−	15.6970i	0.127487	−	0.517235i
$922$	−17.3781	−	4.28331i	−0.572317	−	0.141063i
$923$	−4.81348	−	31.9667i	−0.158438	−	1.05220i
$924$	0.0693888	−	0.0171028i	0.00228273	−	0.000562641i
$925$		−	16.5117i		−	0.542902i
$926$	2.94266	+	0.725300i	0.0967017	+	0.0238348i
$927$	−3.86931	−	5.60566i	−0.127085	−	0.184114i
$928$	1.21568	−	1.37221i	0.0399065	−	0.0450451i
$929$	24.2678	−	2.94664i	0.796199	−	0.0966761i	0.287680	−	0.957727i	$-0.407116\pi$
$929$	24.2678	−	2.94664i	0.796199	−	0.0966761i	0.508519	+	0.861051i	$0.330193\pi$
$930$	−5.11461	+	0.621026i	−0.167715	+	0.0203642i
$931$	−0.606160	+	0.684213i	−0.0198661	+	0.0224242i
$932$	0.521213	+	0.755108i	0.0170729	+	0.0247344i
$933$	−3.75955	−	0.926647i	−0.123082	−	0.0303371i
$934$			6.43148i			0.210445i
$935$	−1.07299	+	0.264469i	−0.0350906	+	0.00864906i
$936$	−8.96101	+	5.03535i	−0.292900	+	0.164585i
$937$	−21.6983	−	5.34816i	−0.708854	−	0.174717i	−0.131626	−	0.991300i	$-0.542020\pi$
$937$	−21.6983	−	5.34816i	−0.708854	−	0.174717i	−0.577229	+	0.816583i	$0.695866\pi$
$938$	13.1688	−	53.4278i	0.429975	−	1.74448i
$939$	0.935479	+	7.70436i	0.0305282	+	0.251422i
$940$	−0.237474	+	0.124636i	−0.00774556	+	0.00406518i
$941$	−0.257498	+	0.0312659i	−0.00839418	+	0.00101924i	−0.124733	−	0.992190i	$-0.539807\pi$
$941$	−0.257498	+	0.0312659i	−0.00839418	+	0.00101924i	0.116339	+	0.993210i	$0.462884\pi$
$942$	3.97127	−	7.56661i	0.129391	−	0.246534i
$943$	10.9085	+	12.3131i	0.355228	+	0.400970i
$944$		−	16.8206i		−	0.547465i
$945$	−6.19328	+	5.48677i	−0.201467	+	0.178485i
$946$	−3.92112	+	5.68072i	−0.127487	+	0.184696i
$947$	−7.49107	−	30.3924i	−0.243427	−	0.987622i	−0.957703	−	0.287758i	$-0.907090\pi$
$947$	−7.49107	−	30.3924i	−0.243427	−	0.987622i	0.714276	−	0.699864i	$-0.246756\pi$
$948$	0.352910	−	0.312651i	0.0114620	−	0.0101544i
$949$	25.7064	+	12.5669i	0.834466	+	0.407938i
$950$	0.753148	+	0.667231i	0.0244354	+	0.0216478i
$951$	8.78706	−	16.7424i	0.284940	−	0.542908i
$952$	4.58171	−	2.40467i	0.148494	−	0.0779358i
$953$	13.1469	+	34.6656i	0.425870	+	1.12293i	0.960607	+	0.277909i	$0.0896415\pi$
$953$	13.1469	+	34.6656i	0.425870	+	1.12293i	−0.534737	+	0.845019i	$0.679589\pi$
$954$	−1.26107	−	0.870455i	−0.0408287	−	0.0281820i
$955$	14.0554	+	26.7803i	0.454821	+	0.866590i
$956$	0.116861	−	0.474124i	0.00377956	−	0.0153343i
$957$	4.72277	+	5.33090i	0.152665	+	0.172324i
$958$	−35.1316	−	31.1239i	−1.13505	−	1.00557i
$959$	20.8561	+	30.2153i	0.673480	+	0.975704i
$960$	10.0523	+	19.1530i	0.324436	+	0.618162i
$961$	−10.3178	+	27.2057i	−0.332831	+	0.877603i
$962$	−39.8401	−	3.68394i	−1.28450	−	0.118775i
$963$	1.78113	+	4.69645i	0.0573960	+	0.151341i
$964$	−0.252120	+	0.284585i	−0.00812024	+	0.00916585i
$965$	24.4167	+	21.6313i	0.786002	+	0.696337i
$966$	−31.6419	+	7.79902i	−1.01806	+	0.250929i
$967$	9.19402	+	37.3016i	0.295660	+	1.19954i	0.911377	+	0.411572i	$0.135020\pi$
$967$	9.19402	+	37.3016i	0.295660	+	1.19954i	−0.615717	+	0.787967i	$0.711134\pi$
$968$	−29.7006	−	3.60631i	−0.954614	−	0.115911i
$969$	0.187656	−	0.0711686i	0.00602838	−	0.00228626i
$970$	−18.0988	−	2.19759i	−0.581117	−	0.0705604i
$971$	17.1846	−	24.8962i	0.551479	−	0.798956i	−0.443788	−	0.896132i	$-0.646366\pi$
$971$	17.1846	−	24.8962i	0.551479	−	0.798956i	0.995267	+	0.0971762i	$0.0309810\pi$
$972$	−0.0314082	+	0.00774143i	−0.00100742	+	0.000248307i
$973$	−14.0767	−	15.8893i	−0.451277	−	0.509386i
$974$	1.24472	+	10.2512i	0.0398833	+	0.328468i
$975$	−3.30516	+	6.76094i	−0.105850	+	0.216523i
$976$	5.46307	−	44.9924i	0.174868	−	1.44017i
$977$	−36.6098	+	25.2699i	−1.17125	+	0.808456i	−0.984746	−	0.173998i	$-0.944331\pi$
$977$	−36.6098	+	25.2699i	−1.17125	+	0.808456i	−0.186505	+	0.982454i	$0.559716\pi$
$978$	−0.0815668	+	0.215074i	−0.00260822	+	0.00687731i
$979$	1.24670	+	10.2675i	0.0398449	+	0.328152i
$980$	−0.106448	+	0.202819i	−0.00340035	+	0.00647882i
$981$	3.96142	−	4.47152i	0.126478	−	0.142765i
$982$	−2.15631	−	1.48840i	−0.0688108	−	0.0474966i
$983$	−28.3815	+	19.5904i	−0.905230	+	0.624835i	−0.927054	−	0.374927i	$-0.877668\pi$
$983$	−28.3815	+	19.5904i	−0.905230	+	0.624835i	0.0218245	+	0.999762i	$0.493053\pi$
$984$	−5.55518	−	2.91559i	−0.177093	−	0.0929455i
$985$	8.08792	−	66.6100i	0.257703	−	2.12237i
$986$	6.75477	+	4.66248i	0.215116	+	0.148484i
$987$	5.49849	+	7.96595i	0.175019	+	0.253559i
$988$	−0.0292296	+	0.0274278i	−0.000929918	+	0.000872596i
$989$	−29.3958	+	42.5871i	−0.934731	+	1.35419i
$990$	−2.48195	+	0.941279i	−0.0788815	+	0.0299158i
$991$	26.4281			0.839515			0.419757	−	0.907636i	$-0.362115\pi$
$991$	26.4281			0.839515			0.419757	+	0.907636i	$0.362115\pi$
$992$	−0.252442			−0.00801503
$993$	9.89709	−	3.75347i	0.314075	−	0.119113i
$994$	9.35458	+	37.9530i	0.296709	+	1.20380i
$995$			26.6645i			0.845321i
$996$	0.0897801	−	0.364252i	0.00284479	−	0.0115418i
$997$	10.3451	−	27.2779i	0.327633	−	0.863899i	−0.665445	−	0.746447i	$-0.731758\pi$
$997$	10.3451	−	27.2779i	0.327633	−	0.863899i	0.993079	−	0.117452i	$-0.0374725\pi$
$998$	51.4229	+	26.9888i	1.62776	+	0.854315i
$999$	−7.39678	−	2.80523i	−0.234024	−	0.0887535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.a.64.4	✓	168
169.103	even	26	inner	507.2.p.a.103.4	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.a.64.4	✓	168	1.1	even	1	trivial
507.2.p.a.103.4	yes	168	169.103	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)

\(f(q)\)	\(=\)	\(q+(-1.39250 - 0.169080i) q^{2} +(-0.748511 + 0.663123i) q^{3} +(-0.0314082 - 0.00774143i) q^{4} +(-1.23718 - 2.35725i) q^{5} +(1.15442 - 0.796842i) q^{6} +(-2.90606 - 1.10212i) q^{7} +(2.66558 + 1.01092i) q^{8} +(0.120537 - 0.992709i) q^{9} +O(q^{10})\)	\(q+(-1.39250 - 0.169080i) q^{2} +(-0.748511 + 0.663123i) q^{3} +(-0.0314082 - 0.00774143i) q^{4} +(-1.23718 - 2.35725i) q^{5} +(1.15442 - 0.796842i) q^{6} +(-2.90606 - 1.10212i) q^{7} +(2.66558 + 1.01092i) q^{8} +(0.120537 - 0.992709i) q^{9} +(1.32421 + 3.49165i) q^{10} +(-0.705640 + 0.0856802i) q^{11} +(0.0286429 - 0.0150330i) q^{12} +(-3.02472 - 1.96242i) q^{13} +(3.86034 + 2.02606i) q^{14} +(2.48918 + 0.944023i) q^{15} +(-3.48361 - 1.82834i) q^{16} +(-0.207085 + 0.546038i) q^{17} +(-0.335695 + 1.36197i) q^{18} +0.343668i q^{19} +(0.0206091 + 0.0836145i) q^{20} +(2.90606 - 1.10212i) q^{21} +0.997093 q^{22} +7.47498 q^{23} +(-2.66558 + 1.01092i) q^{24} +(-1.18568 + 1.71775i) q^{25} +(3.88012 + 3.24410i) q^{26} +(0.568065 + 0.822984i) q^{27} +(0.0827421 + 0.0571127i) q^{28} +(-1.20770 + 9.94634i) q^{29} +(-3.30658 - 1.73543i) q^{30} +(1.13545 - 0.783748i) q^{31} +(-0.150582 - 0.103939i) q^{32} +(0.471363 - 0.532059i) q^{33} +(0.380691 - 0.725346i) q^{34} +(0.997337 + 8.21381i) q^{35} +(-0.0114708 + 0.0302461i) q^{36} +(-6.51051 + 4.49388i) q^{37} +(0.0581076 - 0.478559i) q^{38} +(3.56536 - 0.536865i) q^{39} +(-0.914807 - 7.53411i) q^{40} +(1.45933 + 1.64724i) q^{41} +(-4.23304 + 1.04335i) q^{42} +(-3.93255 + 5.69729i) q^{43} +(0.0228262 + 0.00277160i) q^{44} +(-2.48918 + 0.944023i) q^{45} +(-10.4089 - 1.26387i) q^{46} +(0.745302 + 3.02381i) q^{47} +(3.81993 - 0.941529i) q^{48} +(1.99091 + 1.76379i) q^{49} +(1.94150 - 2.19150i) q^{50} +(-0.207085 - 0.546038i) q^{51} +(0.0798090 + 0.0850518i) q^{52} +(-0.387364 + 1.02139i) q^{53} +(-0.651881 - 1.24206i) q^{54} +(1.07497 + 1.55737i) q^{55} +(-6.63216 - 5.87558i) q^{56} +(-0.227894 - 0.257240i) q^{57} +(3.36346 - 13.6461i) q^{58} +(1.98689 + 3.78571i) q^{59} +(-0.0708728 - 0.0489200i) q^{60} +(4.08507 + 10.7714i) q^{61} +(-1.71364 + 0.899388i) q^{62} +(-1.44437 + 2.75202i) q^{63} +(6.08178 + 5.38799i) q^{64} +(-0.883796 + 9.55787i) q^{65} +(-0.746335 + 0.661195i) q^{66} +(-3.02055 - 12.2549i) q^{67} +(0.0107313 - 0.0155470i) q^{68} +(-5.59511 + 4.95683i) q^{69} -11.6064i q^{70} +(5.94550 + 6.71108i) q^{71} +(1.32485 - 2.52429i) q^{72} +(-7.87817 + 0.956583i) q^{73} +(9.82573 - 5.15694i) q^{74} +(-0.251587 - 2.07200i) q^{75} +(0.00266049 - 0.0107940i) q^{76} +(2.14506 + 0.528710i) q^{77} +(-5.05554 + 0.144753i) q^{78} +(14.1517 - 3.48808i) q^{79} +10.4737i q^{80} +(-0.970942 - 0.239316i) q^{81} +(-1.75360 - 2.54053i) q^{82} +(7.69046 - 8.68074i) q^{83} +(-0.0998061 + 0.0121186i) q^{84} +(1.54335 - 0.187396i) q^{85} +(6.43939 - 7.26857i) q^{86} +(-5.69166 - 8.24580i) q^{87} +(-1.96755 - 0.484959i) q^{88} -14.5507i q^{89} +(3.62581 - 0.893683i) q^{90} +(6.62716 + 9.03651i) q^{91} +(-0.234776 - 0.0578671i) q^{92} +(-0.330179 + 1.33959i) q^{93} +(-0.526568 - 4.33668i) q^{94} +(0.810111 - 0.425179i) q^{95} +(0.181637 - 0.0220547i) q^{96} +(-2.26887 + 4.32297i) q^{97} +(-2.47412 - 2.79271i) q^{98} +0.710823i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9}+O(q^{10}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31} + 130 q^{32} + 13 q^{33} - 65 q^{34} - 35 q^{35} + 12 q^{36} + 61 q^{38} + 12 q^{40} - 63 q^{42} + 72 q^{43} - 39 q^{44} - 8 q^{48} - 68 q^{49} - 52 q^{50} - 4 q^{51} + 65 q^{52} - q^{53} + 53 q^{55} - 14 q^{56} - 13 q^{57} - 26 q^{58} - 104 q^{59} + 117 q^{60} + 12 q^{61} + 49 q^{62} - 32 q^{64} - 52 q^{65} - 46 q^{66} + 26 q^{67} - 84 q^{68} - 4 q^{69} - 39 q^{71} - 52 q^{73} + 29 q^{74} + 8 q^{75} - 130 q^{76} + 60 q^{77} + 65 q^{78} + 14 q^{79} - 14 q^{81} + 45 q^{82} + 78 q^{83} - 13 q^{85} - 13 q^{86} - 46 q^{87} - 26 q^{88} - 4 q^{90} - 208 q^{91} + 82 q^{92} - 39 q^{93} + 25 q^{94} - 66 q^{95} + 65 q^{96} + 26 q^{97} - 104 q^{98}+O(q^{100}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

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