LMFDB - Embedded newform 507.2.t.a.4.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [507,2,Mod(4,507)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("507.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(78)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, minimal)

Newform invariants

comment:select newform

sage:traces = [336] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			4.13
Character	$\chi$	$=$	507.4
Dual form			507.2.t.a.127.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.45059 + 0.0987553i) q^{2} +(0.278217 - 0.960518i) q^{3} +(4.00211 + 0.323084i) q^{4} +(0.599077 + 0.227200i) q^{5} +(0.776653 - 2.32636i) q^{6} +(0.599988 + 1.40822i) q^{7} +(4.90623 + 0.595725i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(1.44565 + 0.615935i) q^{10} +(-0.646311 - 1.02206i) q^{11} +(1.42379 - 3.75421i) q^{12} +(-3.47529 + 0.960387i) q^{13} +(1.33125 + 3.51023i) q^{14} +(0.384903 - 0.512213i) q^{15} +(4.03805 + 0.656247i) q^{16} +(1.66784 - 0.710598i) q^{17} +(-2.01843 - 1.39322i) q^{18} +(0.359707 - 0.207677i) q^{19} +(2.32417 + 1.10283i) q^{20} +(1.51955 - 0.184507i) q^{21} +(-1.48291 - 2.56847i) q^{22} +(-1.08474 + 1.87883i) q^{23} +(1.93720 - 4.54679i) q^{24} +(-3.43528 - 3.04339i) q^{25} +(-8.61135 + 2.01031i) q^{26} +(-0.748511 + 0.663123i) q^{27} +(1.94624 + 5.82971i) q^{28} +(-0.0985853 + 2.44637i) q^{29} +(0.993822 - 1.21721i) q^{30} +(-1.96330 - 2.21611i) q^{31} +(0.146010 + 0.0298081i) q^{32} +(-1.16152 + 0.336439i) q^{33} +(4.15735 - 1.57668i) q^{34} +(0.0394906 + 0.979950i) q^{35} +(-3.20987 - 2.41206i) q^{36} +(1.27243 - 0.259769i) q^{37} +(0.902003 - 0.473407i) q^{38} +(-0.0444181 + 3.60528i) q^{39} +(2.80386 + 1.47158i) q^{40} +(0.265784 + 0.0769854i) q^{41} +(3.74201 - 0.302087i) q^{42} +(0.146299 - 0.716621i) q^{43} +(-2.25640 - 4.29921i) q^{44} +(-0.384903 - 0.512213i) q^{45} +(-2.84380 + 4.49711i) q^{46} +(3.15089 - 2.17490i) q^{47} +(1.75379 - 3.69604i) q^{48} +(3.22596 - 3.35858i) q^{49} +(-8.11791 - 7.79735i) q^{50} +(-0.218522 - 1.79969i) q^{51} +(-14.2188 + 2.72077i) q^{52} +(-1.26656 + 10.4310i) q^{53} +(-1.89978 + 1.55112i) q^{54} +(-0.154978 - 0.759134i) q^{55} +(2.10477 + 7.26650i) q^{56} +(-0.0994007 - 0.403284i) q^{57} +(-0.483184 + 5.98530i) q^{58} +(0.253632 + 1.56066i) q^{59} +(1.70591 - 1.92558i) q^{60} +(2.39841 - 1.80229i) q^{61} +(-4.59239 - 5.62466i) q^{62} +(0.245543 - 1.51089i) q^{63} +(-7.58943 - 1.87063i) q^{64} +(-2.30017 - 0.214240i) q^{65} +(-2.87964 + 0.709767i) q^{66} +(0.726188 + 8.99545i) q^{67} +(6.90445 - 2.30504i) q^{68} +(1.50285 + 1.56464i) q^{69} +2.40535i q^{70} +(-8.53010 + 8.19327i) q^{71} +(-3.82831 - 3.12571i) q^{72} +(1.85514 - 3.53468i) q^{73} +(3.14386 - 0.510928i) q^{74} +(-3.87899 + 2.45292i) q^{75} +(1.50668 - 0.714931i) q^{76} +(1.05151 - 1.52337i) q^{77} +(-0.464891 + 8.83066i) q^{78} +(3.39473 + 4.91812i) q^{79} +(2.27000 + 1.31059i) q^{80} +(0.428693 + 0.903450i) q^{81} +(0.643725 + 0.214907i) q^{82} +(3.10833 - 12.6110i) q^{83} +(6.14102 - 0.247475i) q^{84} +(1.16061 - 0.0467709i) q^{85} +(0.429289 - 1.74169i) q^{86} +(2.32235 + 0.775315i) q^{87} +(-2.56209 - 5.39949i) q^{88} +(-5.92905 - 3.42314i) q^{89} +(-0.892655 - 1.29323i) q^{90} +(-3.43757 - 4.31777i) q^{91} +(-4.94828 + 7.16882i) q^{92} +(-2.67484 + 1.26923i) q^{93} +(7.93631 - 5.01862i) q^{94} +(0.262676 - 0.0426890i) q^{95} +(0.0692537 - 0.131952i) q^{96} +(1.76546 + 1.44146i) q^{97} +(8.23719 - 7.91193i) q^{98} +1.20927i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31}+ \cdots + 104 q^{98}+O(q^{100}) $ 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{78}\right)$

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 $

$2$	2.45059	+	0.0987553i	1.73283	+	0.0698306i	0.886470	−	0.462786i	$-0.153150\pi$
$2$	2.45059	+	0.0987553i	1.73283	+	0.0698306i	0.846357	+	0.532616i	$0.178791\pi$
$3$	0.278217	−	0.960518i	0.160629	−	0.554555i
$3$	0.278217	−	0.960518i	0.160629	−	0.554555i
$4$	4.00211	+	0.323084i	2.00106	+	0.161542i
$5$	0.599077	+	0.227200i	0.267915	+	0.101607i	0.484904	−	0.874567i	$-0.338854\pi$
$5$	0.599077	+	0.227200i	0.267915	+	0.101607i	−0.216989	+	0.976174i	$0.569624\pi$
$6$	0.776653	−	2.32636i	0.317067	−	0.949732i
$7$	0.599988	+	1.40822i	0.226774	+	0.532258i	0.994033	−	0.109079i	$-0.0347902\pi$
$7$	0.599988	+	1.40822i	0.226774	+	0.532258i	−0.767259	+	0.641337i	$0.778380\pi$
$8$	4.90623	+	0.595725i	1.73462	+	0.210620i
$9$	−0.845190	−	0.534466i	−0.281730	−	0.178155i
$10$	1.44565	+	0.615935i	0.457155	+	0.194776i
$11$	−0.646311	−	1.02206i	−0.194870	−	0.308163i	0.733591	−	0.679591i	$-0.237843\pi$
$11$	−0.646311	−	1.02206i	−0.194870	−	0.308163i	−0.928462	+	0.371428i	$0.878868\pi$
$12$	1.42379	−	3.75421i	0.411012	−	1.08375i
$13$	−3.47529	+	0.960387i	−0.963873	+	0.266363i
$13$	−3.47529	+	0.960387i	−0.963873	+	0.266363i
$14$	1.33125	+	3.51023i	0.355792	+	0.938147i
$15$	0.384903	−	0.512213i	0.0993815	−	0.132253i
$16$	4.03805	+	0.656247i	1.00951	+	0.164062i
$17$	1.66784	−	0.710598i	0.404510	−	0.172345i	−0.180122	−	0.983644i	$-0.557649\pi$
$17$	1.66784	−	0.710598i	0.404510	−	0.172345i	0.584632	+	0.811299i	$0.301239\pi$
$18$	−2.01843	−	1.39322i	−0.475749	−	0.328386i
$19$	0.359707	−	0.207677i	0.0825224	−	0.0476443i	−0.458171	−	0.888864i	$-0.651495\pi$
$19$	0.359707	−	0.207677i	0.0825224	−	0.0476443i	0.540693	+	0.841220i	$0.318162\pi$
$20$	2.32417	+	1.10283i	0.519700	+	0.246601i
$21$	1.51955	−	0.184507i	0.331593	−	0.0402627i
$22$	−1.48291	−	2.56847i	−0.316157	−	0.547600i
$23$	−1.08474	+	1.87883i	−0.226184	+	0.391763i	−0.956674	−	0.291161i	$-0.905958\pi$
$23$	−1.08474	+	1.87883i	−0.226184	+	0.391763i	0.730490	+	0.682924i	$0.239292\pi$
$24$	1.93720	−	4.54679i	0.395430	−	0.928109i
$25$	−3.43528	−	3.04339i	−0.687056	−	0.608679i
$26$	−8.61135	+	2.01031i	−1.68883	+	0.394254i
$27$	−0.748511	+	0.663123i	−0.144051	+	0.127618i
$28$	1.94624	+	5.82971i	0.367806	+	1.10171i
$29$	−0.0985853	+	2.44637i	−0.0183068	+	0.454279i	0.963876	+	0.266351i	$0.0858181\pi$
$29$	−0.0985853	+	2.44637i	−0.0183068	+	0.454279i	−0.982183	+	0.187928i	$0.939823\pi$
$30$	0.993822	−	1.21721i	0.181446	−	0.222231i
$31$	−1.96330	−	2.21611i	−0.352620	−	0.398025i	0.545260	−	0.838267i	$-0.316431\pi$
$31$	−1.96330	−	2.21611i	−0.352620	−	0.398025i	−0.897879	+	0.440242i	$0.854893\pi$
$32$	0.146010	+	0.0298081i	0.0258111	+	0.00526938i
$33$	−1.16152	+	0.336439i	−0.202195	+	0.0585665i
$34$	4.15735	−	1.57668i	0.712980	−	0.270398i
$35$	0.0394906	+	0.979950i	0.00667514	+	0.165642i
$36$	−3.20987	−	2.41206i	−0.534978	−	0.402010i
$37$	1.27243	−	0.259769i	0.209187	−	0.0427058i	−0.0942893	−	0.995545i	$-0.530058\pi$
$37$	1.27243	−	0.259769i	0.209187	−	0.0427058i	0.303476	+	0.952839i	$0.401853\pi$
$38$	0.902003	−	0.473407i	0.146324	−	0.0767968i
$39$	−0.0444181	+	3.60528i	−0.00711258	+	0.577306i
$40$	2.80386	+	1.47158i	0.443329	+	0.232677i
$41$	0.265784	+	0.0769854i	0.0415085	+	0.0120231i	0.298907	−	0.954282i	$-0.403378\pi$
$41$	0.265784	+	0.0769854i	0.0415085	+	0.0120231i	−0.257398	+	0.966305i	$0.582865\pi$
$42$	3.74201	−	0.302087i	0.577405	−	0.0466130i
$43$	0.146299	−	0.716621i	0.0223104	−	0.109284i	−0.967111	−	0.254356i	$-0.918136\pi$
$43$	0.146299	−	0.716621i	0.0223104	−	0.109284i	0.989421	+	0.145073i	$0.0463416\pi$
$44$	−2.25640	−	4.29921i	−0.340165	−	0.648131i
$45$	−0.384903	−	0.512213i	−0.0573780	−	0.0763562i
$46$	−2.84380	+	4.49711i	−0.419295	+	0.663062i
$47$	3.15089	−	2.17490i	0.459604	−	0.317242i	−0.315667	−	0.948870i	$-0.602228\pi$
$47$	3.15089	−	2.17490i	0.459604	−	0.317242i	0.775272	+	0.631628i	$0.217613\pi$
$48$	1.75379	−	3.69604i	0.253138	−	0.533477i
$49$	3.22596	−	3.35858i	0.460852	−	0.479798i
$50$	−8.11791	−	7.79735i	−1.14805	−	1.10271i
$51$	−0.218522	−	1.79969i	−0.0305991	−	0.252007i
$52$	−14.2188	+	2.72077i	−1.97179	+	0.377302i
$53$	−1.26656	+	10.4310i	−0.173975	+	1.43281i	0.600204	+	0.799847i	$0.295086\pi$
$53$	−1.26656	+	10.4310i	−0.173975	+	1.43281i	−0.774179	+	0.632967i	$0.781837\pi$
$54$	−1.89978	+	1.55112i	−0.258527	+	0.211081i
$55$	−0.154978	−	0.759134i	−0.0208973	−	0.102362i
$56$	2.10477	+	7.26650i	0.281261	+	0.971027i
$57$	−0.0994007	−	0.403284i	−0.0131659	−	0.0534163i
$58$	−0.483184	+	5.98530i	−0.0634451	+	0.785909i
$59$	0.253632	+	1.56066i	0.0330200	+	0.203180i	0.998318	−	0.0579692i	$-0.0184625\pi$
$59$	0.253632	+	1.56066i	0.0330200	+	0.203180i	−0.965298	+	0.261150i	$0.915898\pi$
$60$	1.70591	−	1.92558i	0.220232	−	0.248591i
$61$	2.39841	−	1.80229i	0.307085	−	0.230760i	−0.436015	−	0.899939i	$-0.643611\pi$
$61$	2.39841	−	1.80229i	0.307085	−	0.230760i	0.743101	+	0.669180i	$0.233354\pi$
$62$	−4.59239	−	5.62466i	−0.583234	−	0.714332i
$63$	0.245543	−	1.51089i	0.0309356	−	0.190354i
$64$	−7.58943	−	1.87063i	−0.948679	−	0.233828i
$65$	−2.30017	−	0.214240i	−0.285300	−	0.0265732i
$66$	−2.87964	+	0.709767i	−0.354459	+	0.0873662i
$67$	0.726188	+	8.99545i	0.0887180	+	1.09897i	0.875979	+	0.482349i	$0.160216\pi$
$67$	0.726188	+	8.99545i	0.0887180	+	1.09897i	−0.787261	+	0.616620i	$0.788502\pi$
$68$	6.90445	−	2.30504i	0.837288	−	0.279528i
$69$	1.50285	+	1.56464i	0.180922	+	0.188360i
$70$			2.40535i			0.287495i
$71$	−8.53010	+	8.19327i	−1.01234	+	0.972362i	−0.999620	−	0.0275571i	$-0.991227\pi$
$71$	−8.53010	+	8.19327i	−1.01234	+	0.972362i	−0.0127159	+	0.999919i	$0.504048\pi$
$72$	−3.82831	−	3.12571i	−0.451170	−	0.368369i
$73$	1.85514	−	3.53468i	0.217128	−	0.413703i	−0.752392	−	0.658716i	$-0.771100\pi$
$73$	1.85514	−	3.53468i	0.217128	−	0.413703i	0.969520	+	0.245013i	$0.0787922\pi$
$74$	3.14386	−	0.510928i	0.365467	−	0.0593941i
$75$	−3.87899	+	2.45292i	−0.447907	+	0.283239i
$76$	1.50668	−	0.714931i	0.172829	−	0.0820082i
$77$	1.05151	−	1.52337i	0.119831	−	0.173605i
$78$	−0.464891	+	8.83066i	−0.0526385	+	0.999876i
$79$	3.39473	+	4.91812i	0.381937	+	0.553331i	0.966055	−	0.258338i	$-0.0831747\pi$
$79$	3.39473	+	4.91812i	0.381937	+	0.553331i	−0.584118	+	0.811669i	$0.698559\pi$
$80$	2.27000	+	1.31059i	0.253794	+	0.146528i
$81$	0.428693	+	0.903450i	0.0476325	+	0.100383i
$82$	0.643725	+	0.214907i	0.0710875	+	0.0237325i
$83$	3.10833	−	12.6110i	0.341184	−	1.38424i	−0.510363	−	0.859959i	$-0.670489\pi$
$83$	3.10833	−	12.6110i	0.341184	−	1.38424i	0.851547	−	0.524279i	$-0.175665\pi$
$84$	6.14102	−	0.247475i	0.670041	−	0.0270017i
$85$	1.16061	−	0.0467709i	0.125886	−	0.00507302i
$86$	0.429289	−	1.74169i	0.0462914	−	0.187812i
$87$	2.32235	+	0.775315i	0.248982	+	0.0831225i
$88$	−2.56209	−	5.39949i	−0.273120	−	0.575587i
$89$	−5.92905	−	3.42314i	−0.628478	−	0.362852i	0.151684	−	0.988429i	$-0.451530\pi$
$89$	−5.92905	−	3.42314i	−0.628478	−	0.362852i	−0.780163	+	0.625577i	$0.784864\pi$
$90$	−0.892655	−	1.29323i	−0.0940941	−	0.136319i
$91$	−3.43757	−	4.31777i	−0.360355	−	0.452625i
$92$	−4.94828	+	7.16882i	−0.515894	+	0.747401i
$93$	−2.67484	+	1.26923i	−0.277368	+	0.131613i
$94$	7.93631	−	5.01862i	0.818568	−	0.517631i
$95$	0.262676	−	0.0426890i	0.0269500	−	0.00437980i
$96$	0.0692537	−	0.131952i	0.00706817	−	0.0134673i
$97$	1.76546	+	1.44146i	0.179256	+	0.146358i	0.717825	−	0.696223i	$-0.245138\pi$
$97$	1.76546	+	1.44146i	0.179256	+	0.146358i	−0.538570	+	0.842581i	$0.681035\pi$
$98$	8.23719	−	7.91193i	0.832082	−	0.799225i
$99$			1.20927i			0.121536i
$100$	−12.7651	−	13.2899i	−1.27651	−	1.32899i
$101$	4.90745	−	1.63835i	0.488310	−	0.163022i	−0.0618428	−	0.998086i	$-0.519698\pi$
$101$	4.90745	−	1.63835i	0.488310	−	0.163022i	0.550153	+	0.835064i	$0.314570\pi$
$102$	−0.357778	−	4.43187i	−0.0354253	−	0.438821i
$103$	−9.92673	+	2.44672i	−0.978109	+	0.241082i	−0.695796	−	0.718240i	$-0.744948\pi$
$103$	−9.92673	+	2.44672i	−0.978109	+	0.241082i	−0.282314	+	0.959322i	$0.591102\pi$
$104$	−17.6227	+	2.64157i	−1.72805	+	0.259027i
$105$	0.952247	+	0.234708i	0.0929298	+	0.0229051i
$106$	−4.13393	+	25.4371i	−0.401523	+	2.47067i
$107$	4.41363	+	5.40572i	0.426682	+	0.522590i	0.942544	−	0.334081i	$-0.108426\pi$
$107$	4.41363	+	5.40572i	0.426682	+	0.522590i	−0.515863	+	0.856671i	$0.672528\pi$
$108$	−3.20987	+	2.41206i	−0.308870	+	0.232101i
$109$	6.39735	−	7.22112i	0.612755	−	0.691657i	−0.357453	−	0.933931i	$-0.616355\pi$
$109$	6.39735	−	7.22112i	0.612755	−	0.691657i	0.970208	+	0.242274i	$0.0778932\pi$
$110$	−0.304819	−	1.87563i	−0.0290634	−	0.178834i
$111$	0.104500	−	1.29447i	0.00991872	−	0.122865i
$112$	1.49864	+	6.08021i	0.141608	+	0.574526i
$113$	3.19287	+	11.0231i	0.300360	+	1.03696i	0.958742	+	0.284279i	$0.0917542\pi$
$113$	3.19287	+	11.0231i	0.300360	+	1.03696i	−0.658381	+	0.752684i	$0.728759\pi$
$114$	−0.203764	−	0.998100i	−0.0190842	−	0.0934806i
$115$	−1.07671	+	0.879108i	−0.100404	+	0.0819773i
$116$	−1.18493	+	9.75879i	−0.110018	+	0.906081i
$117$	3.45058	+	1.04572i	0.319006	+	0.0966764i
$118$	0.467423	+	3.84958i	0.0430298	+	0.354382i
$119$	2.00136	+	1.92233i	0.183465	+	0.176220i
$120$	2.19356	−	2.28374i	0.200244	−	0.208476i
$121$	4.08873	−	8.61682i	0.371703	−	0.783347i
$122$	6.05551	−	4.17982i	0.548240	−	0.378423i
$123$	0.147892	−	0.233872i	0.0133349	−	0.0210875i
$124$	−7.14137	−	9.50344i	−0.641314	−	0.853434i
$125$	−2.85531	−	5.44033i	−0.255386	−	0.486598i
$126$	0.750934	−	3.67832i	0.0668985	−	0.327691i
$127$	1.77715	−	0.143466i	0.157696	−	0.0127306i	−0.00136629	−	0.999999i	$-0.500435\pi$
$127$	1.77715	−	0.143466i	0.157696	−	0.0127306i	0.159063	+	0.987269i	$0.449153\pi$
$128$	−18.7001	−	5.41655i	−1.65287	−	0.478760i
$129$	−0.647624	−	0.339900i	−0.0570201	−	0.0299265i
$130$	−5.61560	−	0.752168i	−0.492521	−	0.0659695i
$131$	−13.8553	+	7.27183i	−1.21054	+	0.635343i	−0.944466	−	0.328609i	$-0.893420\pi$
$131$	−13.8553	+	7.27183i	−1.21054	+	0.635343i	−0.266078	+	0.963951i	$0.585728\pi$
$132$	−4.75724	+	0.971198i	−0.414065	+	0.0845319i
$133$	0.508275	+	0.381944i	0.0440730	+	0.0331187i
$134$	0.891239	+	22.1159i	0.0769913	+	1.91052i
$135$	−0.599077	+	0.227200i	−0.0515603	+	0.0195542i
$136$	8.60611	−	2.49279i	0.737968	−	0.213755i
$137$	7.67830	+	1.56754i	0.656002	+	0.133924i	0.516485	−	0.856296i	$-0.327240\pi$
$137$	7.67830	+	1.56754i	0.656002	+	0.133924i	0.139516	+	0.990220i	$0.455445\pi$
$138$	3.52836	+	3.98269i	0.300354	+	0.339029i
$139$	12.9247	−	15.8299i	1.09626	−	1.34268i	0.161715	−	0.986838i	$-0.448297\pi$
$139$	12.9247	−	15.8299i	1.09626	−	1.34268i	0.934547	−	0.355840i	$-0.115805\pi$
$140$	−0.158560	+	3.93463i	−0.0134008	+	0.332537i
$141$	−1.21240	−	3.63158i	−0.102103	−	0.305834i
$142$	−21.7129	+	19.2359i	−1.82210	+	1.61424i
$143$	3.22769	+	2.93125i	0.269913	+	0.245123i
$144$	−3.06218	−	2.71285i	−0.255181	−	0.226071i
$145$	−0.614874	+	1.44316i	−0.0510625	+	0.119848i
$146$	4.89526	−	8.47884i	0.405135	−	0.701714i
$147$	−2.32846	−	4.03301i	−0.192048	−	0.332637i
$148$	5.17635	−	0.628523i	0.425493	−	0.0516642i
$149$	12.7816	+	6.06494i	1.04711	+	0.496860i	0.872926	−	0.487854i	$-0.162220\pi$
$149$	12.7816	+	6.06494i	1.04711	+	0.496860i	0.174184	+	0.984713i	$0.444271\pi$
$150$	−9.74804	+	5.62804i	−0.795924	+	0.459527i
$151$	−2.35046	−	1.62241i	−0.191278	−	0.132030i	0.468577	−	0.883423i	$-0.344767\pi$
$151$	−2.35046	−	1.62241i	−0.191278	−	0.132030i	−0.659855	+	0.751393i	$0.729382\pi$
$152$	1.88852	−	0.804625i	0.153180	−	0.0652637i
$153$	−1.78943	−	0.290811i	−0.144667	−	0.0235106i
$154$	2.72726	−	3.62932i	0.219769	−	0.292459i
$155$	−0.672669	−	1.77368i	−0.0540300	−	0.142466i
$156$	−1.34257	+	14.4144i	−0.107492	+	1.15407i
$157$	4.95660	−	13.0695i	0.395580	−	1.04306i	−0.578266	−	0.815849i	$-0.696270\pi$
$157$	4.95660	−	13.0695i	0.395580	−	1.04306i	0.973846	−	0.227210i	$-0.0729605\pi$
$158$	7.83340	+	12.3875i	0.623192	+	0.985499i
$159$	9.66682	+	4.11865i	0.766629	+	0.326630i
$160$	0.0806986	+	0.0510307i	0.00637979	+	0.00403433i
$161$	−3.29664	−	0.400284i	−0.259812	−	0.0315468i
$162$	0.961328	+	2.25632i	0.0755291	+	0.177273i
$163$	6.45593	−	19.3379i	0.505667	−	1.51466i	−0.318283	−	0.947996i	$-0.603106\pi$
$163$	6.45593	−	19.3379i	0.505667	−	1.51466i	0.823950	−	0.566662i	$-0.191766\pi$
$164$	1.03883	+	0.393975i	0.0811187	+	0.0307643i
$165$	−0.772279	−	0.0623448i	−0.0601219	−	0.00485354i
$166$	8.86265	−	30.5974i	0.687875	−	2.37482i
$167$	−19.5374	−	0.787329i	−1.51185	−	0.0609254i	−0.729592	−	0.683883i	$-0.760290\pi$
$167$	−19.5374	−	0.787329i	−1.51185	−	0.0609254i	−0.782256	+	0.622958i	$0.785931\pi$
$168$	7.56519			0.583667
$169$	11.1553	−	6.67525i	0.858101	−	0.513481i
$170$	2.84879			0.218492
$171$	−0.415017	−	0.0167246i	−0.0317371	−	0.00127896i
$172$	0.817035	−	2.82073i	0.0622983	−	0.215079i
$173$	22.1082	+	1.78476i	1.68086	+	0.135693i	0.883693	−	0.468067i	$-0.155050\pi$
$173$	22.1082	+	1.78476i	1.68086	+	0.135693i	0.797166	+	0.603760i	$0.206332\pi$
$174$	5.61456	+	2.12932i	0.425639	+	0.161424i
$175$	2.22465	−	6.66364i	0.168168	−	0.503724i
$176$	−1.93911	−	4.55127i	−0.146166	−	0.343065i
$177$	1.56960	+	0.190585i	0.117979	+	0.0143252i
$178$	−14.1916	−	8.97423i	−1.06371	−	0.672647i
$179$	5.99907	+	2.55597i	0.448392	+	0.191042i	0.604345	−	0.796722i	$-0.293435\pi$
$179$	5.99907	+	2.55597i	0.448392	+	0.191042i	−0.155953	+	0.987764i	$0.549845\pi$
$180$	−1.37494	−	2.17429i	−0.102482	−	0.162062i
$181$	3.41450	−	9.00329i	0.253797	−	0.669209i	−0.746196	−	0.665726i	$-0.768122\pi$
$181$	3.41450	−	9.00329i	0.253797	−	0.669209i	0.999994	−	0.00348314i	$-0.00110872\pi$
$182$	−7.99767	−	10.9205i	−0.592827	−	0.809484i
$183$	−1.06385	−	2.80515i	−0.0786422	−	0.207363i
$184$	−6.44126	+	8.57176i	−0.474856	+	0.631918i
$185$	0.821304	+	0.133475i	0.0603835	+	0.00981327i
$186$	−6.68027	+	2.84620i	−0.489821	+	0.208693i
$187$	−1.80422	−	1.24536i	−0.131937	−	0.0910697i
$188$	13.3129	−	7.68620i	0.970942	−	0.560574i
$189$	−1.38292	−	0.656204i	−0.100593	−	0.0477319i
$190$	0.647927	−	0.0786725i	0.0470055	−	0.00570751i
$191$	8.11974	+	14.0638i	0.587524	+	1.01762i	0.994556	+	0.104207i	$0.0332306\pi$
$191$	8.11974	+	14.0638i	0.587524	+	1.01762i	−0.407032	+	0.913414i	$0.633436\pi$
$192$	−3.90828	+	6.76935i	−0.282056	+	0.488536i
$193$	1.54656	−	3.62991i	0.111324	−	0.261287i	−0.854994	−	0.518638i	$-0.826439\pi$
$193$	1.54656	−	3.62991i	0.111324	−	0.261287i	0.966318	+	0.257351i	$0.0828496\pi$
$194$	4.18407	+	3.70676i	0.300399	+	0.266130i
$195$	−0.845728	+	2.14975i	−0.0605638	+	0.153946i
$196$	13.9958	−	12.3992i	0.999699	−	0.885656i
$197$	0.604252	+	1.80996i	0.0430512	+	0.128954i	0.967868	−	0.251459i	$-0.0809102\pi$
$197$	0.604252	+	1.80996i	0.0430512	+	0.128954i	−0.924817	+	0.380413i	$0.875782\pi$
$198$	−0.119421	+	2.96341i	−0.00848691	+	0.210601i
$199$	10.7048	−	13.1109i	0.758840	−	0.929410i	−0.240308	−	0.970697i	$-0.577248\pi$
$199$	10.7048	−	13.1109i	0.758840	−	0.929410i	0.999147	+	0.0412869i	$0.0131458\pi$
$200$	−15.0413	−	16.9781i	−1.06358	−	1.20053i
$201$	8.84233	+	1.80517i	0.623690	+	0.127327i
$202$	12.1879	−	3.53028i	0.857540	−	0.248390i
$203$	−3.50418	+	1.32896i	−0.245945	+	0.0932747i
$204$	−0.293098	−	7.27315i	−0.0205210	−	0.509223i
$205$	0.141734	+	0.106506i	0.00989914	+	0.00743872i
$206$	−24.5679	+	5.01558i	−1.71173	+	0.349452i
$207$	1.92098	−	1.00821i	0.133517	−	0.0700754i
$208$	−14.6637	+	1.59744i	−1.01674	+	0.110763i
$209$	−0.444741	−	0.233418i	−0.0307634	−	0.0161459i
$210$	2.31039	+	0.669211i	0.159432	+	0.0461800i
$211$	−10.6253	+	0.857763i	−0.731476	+	0.0590508i	−0.440592	−	0.897708i	$-0.645231\pi$
$211$	−10.6253	+	0.857763i	−0.731476	+	0.0590508i	−0.290884	+	0.956758i	$0.593949\pi$
$212$	−8.43901	+	41.3370i	−0.579594	+	2.83904i
$213$	5.49656	+	10.4728i	0.376618	+	0.717586i
$214$	10.2821	+	13.6831i	0.702873	+	0.935354i
$215$	0.250461	−	0.396072i	0.0170813	−	0.0270119i
$216$	−4.06741	+	2.80753i	−0.276752	+	0.191028i
$217$	1.94282	−	4.09441i	0.131887	−	0.277946i
$218$	16.3904	−	17.0642i	1.11010	−	1.15573i
$219$	−2.87899	−	2.76531i	−0.194544	−	0.186862i
$220$	−0.374977	−	3.08821i	−0.0252809	−	0.208207i
$221$	−5.11377	+	4.07131i	−0.343989	+	0.273866i
$222$	0.383923	−	3.16189i	0.0257672	−	0.212212i
$223$	−16.7760	+	13.6972i	−1.12340	+	0.917231i	−0.997201	−	0.0747728i	$-0.976177\pi$
$223$	−16.7760	+	13.6972i	−1.12340	+	0.917231i	−0.126204	+	0.992004i	$0.540279\pi$
$224$	0.0456276	+	0.223499i	0.00304862	+	0.0149331i
$225$	1.27688	+	4.40829i	0.0851250	+	0.293886i
$226$	6.73583	+	27.3283i	0.448060	+	1.81785i
$227$	−0.0704928	+	0.873211i	−0.00467877	+	0.0579570i	−0.998675	−	0.0514540i	$-0.983614\pi$
$227$	−0.0704928	+	0.873211i	−0.00467877	+	0.0579570i	0.993997	+	0.109411i	$0.0348965\pi$
$228$	−0.267518	−	1.64610i	−0.0177168	−	0.109016i
$229$	0.518915	−	0.585734i	0.0342909	−	0.0387064i	−0.731115	−	0.682254i	$-0.761000\pi$
$229$	0.518915	−	0.585734i	0.0342909	−	0.0387064i	0.765406	+	0.643548i	$0.222538\pi$
$230$	−2.72539	+	2.04800i	−0.179707	+	0.135041i
$231$	−1.17068	−	1.43382i	−0.0770251	−	0.0943386i
$232$	−1.94104	+	11.9437i	−0.127436	+	0.784144i
$233$	11.4349	+	2.81845i	0.749125	+	0.184643i	0.595354	−	0.803464i	$-0.297012\pi$
$233$	11.4349	+	2.81845i	0.749125	+	0.184643i	0.153771	+	0.988106i	$0.450858\pi$
$234$	8.35267	+	2.90338i	0.546031	+	0.189800i
$235$	2.38176	−	0.587051i	0.155369	−	0.0382950i
$236$	0.510839	+	6.32787i	0.0332528	+	0.411909i
$237$	5.66841	−	1.89239i	0.368203	−	0.122924i
$238$	4.71467	+	4.90849i	0.305607	+	0.318170i
$239$			20.3211i			1.31446i	0.753689	+	0.657231i	$0.228272\pi$
$239$			20.3211i			1.31446i	−0.753689	+	0.657231i	$0.771728\pi$
$240$	1.89040	−	1.81575i	0.122025	−	0.117206i
$241$	−17.0109	−	13.8890i	−1.09577	−	0.894668i	−0.100806	−	0.994906i	$-0.532142\pi$
$241$	−17.0109	−	13.8890i	−1.09577	−	0.894668i	−0.994964	+	0.100238i	$0.968040\pi$
$242$	10.8707	−	20.7125i	0.698798	−	1.33145i
$243$	0.987050	−	0.160411i	0.0633193	−	0.0102904i
$244$	10.1810	−	6.43808i	0.651773	−	0.412156i
$245$	2.69567	−	1.27911i	0.172220	−	0.0817194i
$246$	0.385518	−	0.558519i	0.0245797	−	0.0356099i
$247$	−1.05064	+	1.06720i	−0.0668504	+	0.0679040i
$248$	−8.31223	−	12.0423i	−0.527827	−	0.764690i
$249$	−11.2483	−	6.49421i	−0.712833	−	0.411554i
$250$	−6.45992	−	13.6140i	−0.408561	−	0.861024i
$251$	0.293460	+	0.0979715i	0.0185231	+	0.00618391i	0.325914	−	0.945399i	$-0.394328\pi$
$251$	0.293460	+	0.0979715i	0.0185231	+	0.00618391i	−0.307391	+	0.951583i	$0.599456\pi$
$252$	1.47084	−	5.96742i	0.0926540	−	0.375912i
$253$	2.62135	−	0.105637i	0.164803	−	0.00664134i
$254$	4.36922	−	0.176074i	0.274149	−	0.0110478i
$255$	0.277977	−	1.12780i	0.0174076	−	0.0706255i
$256$	−30.4628	−	10.1700i	−1.90392	−	0.635623i
$257$	3.50307	+	7.38256i	0.218515	+	0.460511i	0.982874	−	0.184280i	$-0.0589954\pi$
$257$	3.50307	+	7.38256i	0.218515	+	0.460511i	−0.764358	+	0.644792i	$0.776944\pi$
$258$	−1.55349	−	0.896910i	−0.0967163	−	0.0558392i
$259$	1.12926	+	1.63601i	0.0701686	+	0.101657i
$260$	−9.13631	−	1.60056i	−0.566610	−	0.0992626i
$261$	1.39082	−	2.01496i	0.0860898	−	0.124723i
$262$	−34.6718	+	16.4520i	−2.14203	+	1.01641i
$263$	−22.7029	+	14.3565i	−1.39992	+	0.885257i	−0.999517	−	0.0310814i	$-0.990105\pi$
$263$	−22.7029	+	14.3565i	−1.39992	+	0.885257i	−0.400405	+	0.916338i	$0.631131\pi$
$264$	−5.89912	+	0.958701i	−0.363066	+	0.0590040i
$265$	−3.12869	+	5.96123i	−0.192194	+	0.366195i
$266$	1.20785	+	0.986182i	0.0740583	+	0.0604667i
$267$	−4.93755	+	4.74259i	−0.302173	+	0.290241i
$268$			36.2354i			2.21343i
$269$	−1.82594	−	1.90101i	−0.111330	−	0.115907i	0.663205	−	0.748437i	$-0.269196\pi$
$269$	−1.82594	−	1.90101i	−0.111330	−	0.115907i	−0.774535	+	0.632531i	$0.782016\pi$
$270$	−1.49053	+	0.497611i	−0.0907106	+	0.0302836i
$271$	−0.109409	−	1.35527i	−0.00664612	−	0.0823270i	0.992584	−	0.121561i	$-0.0387901\pi$
$271$	−0.109409	−	1.35527i	−0.00664612	−	0.0823270i	−0.999230	+	0.0392344i	$0.987508\pi$
$272$	7.20113	−	1.77492i	0.436633	−	0.107620i
$273$	−5.10368	+	2.10057i	−0.308889	+	0.127132i
$274$	18.6616	+	4.59966i	1.12739	+	0.277876i
$275$	−0.890268	+	5.47804i	−0.0536852	+	0.330338i
$276$	5.50908	+	6.74740i	0.331608	+	0.406146i
$277$	−2.82663	+	2.12408i	−0.169836	+	0.127623i	−0.682262	−	0.731108i	$-0.739003\pi$
$277$	−2.82663	+	2.12408i	−0.169836	+	0.127623i	0.512426	+	0.858732i	$0.328747\pi$
$278$	33.2365	−	37.5162i	1.99339	−	2.25008i
$279$	0.474929	+	2.92235i	0.0284332	+	0.174957i
$280$	−0.390030	+	4.83139i	−0.0233088	+	0.288731i
$281$	−5.78959	−	23.4893i	−0.345378	−	1.40125i	−0.844887	−	0.534945i	$-0.820332\pi$
$281$	−5.78959	−	23.4893i	−0.345378	−	1.40125i	0.499509	−	0.866309i	$-0.333514\pi$
$282$	−2.61245	−	9.01924i	−0.155569	−	0.537088i
$283$	1.41398	+	6.92614i	0.0840525	+	0.411716i	0.999947	+	0.0102973i	$0.00327778\pi$
$283$	1.41398	+	6.92614i	0.0840525	+	0.411716i	−0.915894	+	0.401419i	$0.868517\pi$
$284$	−36.7855	+	30.0344i	−2.18282	+	1.78222i
$285$	0.0320775	−	0.264182i	0.00190011	−	0.0156488i
$286$	7.62027	+	7.50203i	0.450596	+	0.443604i
$287$	0.0510548	+	0.420474i	0.00301367	+	0.0248198i
$288$	−0.107475	−	0.103231i	−0.00633300	−	0.00608293i
$289$	−9.49959	+	9.89012i	−0.558799	+	0.581772i
$290$	−1.64932	+	3.47588i	−0.0968516	+	0.204110i
$291$	1.87573	−	1.29472i	0.109957	−	0.0758979i
$292$	8.56649	−	13.5468i	0.501316	−	0.792768i
$293$	−7.24810	−	9.64547i	−0.423439	−	0.563494i	0.536430	−	0.843945i	$-0.319773\pi$
$293$	−7.24810	−	9.64547i	−0.423439	−	0.563494i	−0.959869	+	0.280450i	$0.909516\pi$
$294$	−5.30782	−	10.1132i	−0.309558	−	0.589814i
$295$	−0.202636	+	0.992578i	−0.0117979	+	0.0577901i
$296$	6.39761	−	0.516468i	0.371853	−	0.0300191i
$297$	1.16152	+	0.336439i	0.0673983	+	0.0195222i
$298$	30.7235	+	16.1249i	1.77976	+	0.934092i
$299$	1.96539	−	7.57125i	0.113662	−	0.437856i
$300$	−16.3167	+	8.56364i	−0.942043	+	0.494422i
$301$	1.09694	−	0.223942i	0.0632265	−	0.0129078i
$302$	−5.59979	−	4.20797i	−0.322232	−	0.242142i
$303$	−0.208324	−	5.16951i	−0.0119679	−	0.296981i
$304$	1.58880	−	0.602553i	0.0911240	−	0.0345588i
$305$	1.84631	−	0.534791i	0.105720	−	0.0306220i
$306$	−4.35643	−	0.889372i	−0.249041	−	0.0508420i
$307$	1.25644	+	1.41823i	0.0717090	+	0.0809427i	0.783270	−	0.621681i	$-0.213550\pi$
$307$	1.25644	+	1.41823i	0.0717090	+	0.0809427i	−0.711561	+	0.702624i	$0.752012\pi$
$308$	4.70044	−	5.75699i	0.267832	−	0.328035i
$309$	−0.411671	+	10.2155i	−0.0234192	+	0.581141i
$310$	−1.47327	−	4.41299i	−0.0836763	−	0.250641i
$311$	0.585775	−	0.518951i	0.0332162	−	0.0294270i	−0.646351	−	0.763040i	$-0.723706\pi$
$311$	0.585775	−	0.518951i	0.0332162	−	0.0294270i	0.679568	+	0.733613i	$0.262167\pi$
$312$	−2.36568	+	17.6619i	−0.133930	+	0.999907i
$313$	17.2740	+	15.3035i	0.976386	+	0.865002i	0.990860	−	0.134893i	$-0.0430691\pi$
$313$	17.2740	+	15.3035i	0.976386	+	0.865002i	−0.0144745	+	0.999895i	$0.504608\pi$
$314$	13.4373	−	31.5384i	0.758309	−	1.77982i
$315$	0.490373	−	0.849351i	0.0276294	−	0.0478555i
$316$	11.9971	+	20.7796i	0.674892	+	1.16895i
$317$	7.51997	−	0.913089i	0.422363	−	0.0512842i	0.0934041	−	0.995628i	$-0.470225\pi$
$317$	7.51997	−	0.913089i	0.422363	−	0.0512842i	0.328959	+	0.944344i	$0.393302\pi$
$318$	23.2827	+	11.0478i	1.30563	+	0.619528i
$319$	2.56405	−	1.48036i	0.143559	−	0.0828840i
$320$	−4.12164	−	2.84497i	−0.230407	−	0.159038i
$321$	6.42024	−	2.73541i	0.358343	−	0.152676i
$322$	−8.03917	−	1.30649i	−0.448006	−	0.0728080i
$323$	0.452357	−	0.601978i	0.0251698	−	0.0334950i
$324$	1.42379	+	3.75421i	0.0790992	+	0.208567i
$325$	14.8614	+	7.27748i	0.824364	+	0.403682i
$326$	17.7305	−	46.7516i	0.982003	−	2.58933i
$327$	−5.15616	−	8.15381i	−0.285136	−	0.450907i
$328$	1.25814	+	0.536043i	0.0694691	+	0.0295980i
$329$	4.95324	+	3.13224i	0.273081	+	0.172686i
$330$	−1.88638	−	0.229048i	−0.103842	−	0.0126087i
$331$	−1.30174	−	3.05530i	−0.0715501	−	0.167934i	0.880364	−	0.474298i	$-0.157298\pi$
$331$	−1.30174	−	3.05530i	−0.0715501	−	0.167934i	−0.951915	+	0.306363i	$0.900888\pi$
$332$	16.5143	−	49.4664i	0.906341	−	2.71482i
$333$	−1.21429	−	0.460518i	−0.0665425	−	0.0252362i
$334$	−47.8003	−	3.85884i	−2.61552	−	0.211146i
$335$	−1.60872	+	5.55395i	−0.0878939	+	0.303445i
$336$	6.25710	+	0.252153i	0.341353	+	0.0137561i
$337$	−13.0936			−0.713253			−0.356626	−	0.934247i	$-0.616073\pi$
$337$	−13.0936			−0.713253			−0.356626	+	0.934247i	$0.616073\pi$
$338$	27.9963	−	15.2566i	1.52280	−	0.829852i
$339$	11.4762			0.623300
$340$	4.66000	+	0.187792i	0.252724	+	0.0101844i
$341$	−0.996092	+	3.43891i	−0.0539414	+	0.186227i
$342$	−1.01538	−	0.0819703i	−0.0549057	−	0.00443244i
$343$	16.6839	+	6.32735i	0.900843	+	0.341645i
$344$	1.14469	−	3.42876i	0.0617174	−	0.184866i
$345$	0.544839	+	1.27878i	0.0293332	+	0.0688475i
$346$	54.0019	+	6.55702i	2.90316	+	0.352508i
$347$	−5.68035	−	3.59204i	−0.304937	−	0.192831i	0.373229	−	0.927739i	$-0.378251\pi$
$347$	−5.68035	−	3.59204i	−0.304937	−	0.192831i	−0.678166	+	0.734909i	$0.737225\pi$
$348$	9.04383	+	3.85321i	0.484800	+	0.206554i
$349$	16.8238	+	26.6047i	0.900557	+	1.42412i	0.905602	+	0.424129i	$0.139420\pi$
$349$	16.8238	+	26.6047i	0.900557	+	1.42412i	−0.00504492	+	0.999987i	$0.501606\pi$
$350$	6.10977	−	16.1101i	0.326581	−	0.861123i
$351$	1.96444	−	3.02341i	0.104854	−	0.161377i
$352$	−0.0639021	−	0.168496i	−0.00340599	−	0.00898087i
$353$	20.2724	−	26.9777i	1.07899	−	1.43588i	0.187827	−	0.982202i	$-0.439856\pi$
$353$	20.2724	−	26.9777i	1.07899	−	1.43588i	0.891166	−	0.453677i	$-0.149888\pi$
$354$	3.82763	+	0.622051i	0.203436	+	0.0330616i
$355$	−6.97169	+	2.97036i	−0.370019	+	0.157650i
$356$	−22.6228	−	15.6154i	−1.19900	−	0.827613i
$357$	2.40325	−	1.38752i	0.127194	−	0.0734352i
$358$	14.4488	+	6.85606i	0.763645	+	0.362354i
$359$	−9.89525	+	1.20150i	−0.522251	+	0.0634128i	−0.377418	−	0.926043i	$-0.623188\pi$
$359$	−9.89525	+	1.20150i	−0.522251	+	0.0634128i	−0.144834	+	0.989456i	$0.546265\pi$
$360$	−1.58329	−	2.74233i	−0.0834465	−	0.144534i
$361$	−9.41374	+	16.3051i	−0.495460	+	0.858162i
$362$	9.25664	−	21.7261i	0.486518	−	1.14190i
$363$	−7.13905	−	6.32465i	−0.374703	−	0.331958i
$364$	−12.3625	−	18.3908i	−0.647974	−	0.963940i
$365$	1.91445	−	1.69606i	0.100207	−	0.0887756i
$366$	−2.33004	−	6.97932i	−0.121793	−	0.364815i
$367$	0.605866	−	15.0344i	0.0316259	−	0.784790i	−0.903102	−	0.429426i	$-0.858716\pi$
$367$	0.605866	−	15.0344i	0.0316259	−	0.784790i	0.934728	−	0.355364i	$-0.115643\pi$
$368$	−5.61321	+	6.87494i	−0.292609	+	0.358381i
$369$	−0.183492	−	0.207120i	−0.00955222	−	0.0107822i
$370$	1.99950	+	0.408200i	0.103949	+	0.0212213i
$371$	−15.4491	+	4.47490i	−0.802080	+	0.232325i
$372$	−11.1151	+	4.21539i	−0.576290	+	0.218558i
$373$	0.521285	+	12.9355i	0.0269911	+	0.669777i	0.954893	+	0.296952i	$0.0959700\pi$
$373$	0.521285	+	12.9355i	0.0269911	+	0.669777i	−0.927901	+	0.372826i	$0.878389\pi$
$374$	−4.29840	−	3.23004i	−0.222265	−	0.167021i
$375$	−6.01994	+	1.22898i	−0.310868	+	0.0634642i
$376$	16.7546	−	8.79351i	0.864055	−	0.453491i
$377$	−2.00685	−	8.59652i	−0.103358	−	0.442744i
$378$	−3.32417	−	1.74466i	−0.170977	−	0.0897355i
$379$	−22.8466	−	6.61760i	−1.17355	−	0.339924i	−0.366508	−	0.930415i	$-0.619447\pi$
$379$	−22.8466	−	6.61760i	−1.17355	−	0.339924i	−0.807044	+	0.590491i	$0.798934\pi$
$380$	1.06505	−	0.0859799i	0.0546360	−	0.00441067i
$381$	0.356631	−	1.74690i	0.0182708	−	0.0894962i
$382$	18.5093	+	35.2665i	0.947017	+	1.80439i
$383$	14.3299	+	19.0697i	0.732226	+	0.974416i	0.999940	+	0.0109175i	$0.00347522\pi$
$383$	14.3299	+	19.0697i	0.732226	+	0.974416i	−0.267714	+	0.963498i	$0.586268\pi$
$384$	−10.4054	+	16.4548i	−0.530998	+	0.839706i
$385$	0.976044	−	0.673715i	0.0497438	−	0.0343357i
$386$	4.14846	−	8.74269i	0.211151	−	0.444991i
$387$	−0.506660	+	0.527489i	−0.0257550	+	0.0268138i
$388$	6.59987	+	6.33926i	0.335058	+	0.321827i
$389$	−4.35870	−	35.8971i	−0.220995	−	1.82006i	−0.507134	−	0.861867i	$-0.669295\pi$
$389$	−4.35870	−	35.8971i	−0.220995	−	1.82006i	0.286139	−	0.958188i	$-0.407628\pi$
$390$	−2.28483	+	5.18462i	−0.115697	+	0.262533i
$391$	−0.474079	+	3.90439i	−0.0239752	+	0.197454i
$392$	17.8281	−	14.5562i	0.900456	−	0.735200i
$393$	3.12993	+	15.3314i	0.157884	+	0.773368i
$394$	1.30203	+	4.49513i	0.0655953	+	0.226461i
$395$	0.916309	+	3.71761i	0.0461045	+	0.187053i
$396$	−0.390695	+	4.83962i	−0.0196331	+	0.243200i
$397$	−3.15055	−	19.3861i	−0.158122	−	0.972961i	−0.937900	−	0.346905i	$-0.887232\pi$
$397$	−3.15055	−	19.3861i	−0.158122	−	0.972961i	0.779779	−	0.626055i	$-0.215332\pi$
$398$	27.5277	−	31.0724i	1.37984	−	1.55752i
$399$	0.508275	−	0.381944i	0.0254456	−	0.0191211i
$400$	−11.8746	−	14.5438i	−0.593731	−	0.727188i
$401$	−5.02705	+	30.9327i	−0.251039	+	1.54470i	0.489086	+	0.872236i	$0.337330\pi$
$401$	−5.02705	+	30.9327i	−0.251039	+	1.54470i	−0.740125	+	0.672469i	$0.765234\pi$
$402$	21.4906	+	5.29697i	1.07186	+	0.264189i
$403$	8.95137	+	5.81610i	0.445900	+	0.289721i
$404$	20.1695	−	4.97134i	1.00347	−	0.247333i
$405$	0.0515559	+	0.638635i	0.00256183	+	0.0317340i
$406$	−8.71855	+	2.91068i	−0.432694	+	0.144455i
$407$	−1.08789	−	1.13261i	−0.0539246	−	0.0561415i
$408$		−	8.95987i		−	0.443579i
$409$	−10.7397	+	10.3156i	−0.531043	+	0.510073i	−0.909589	−	0.415509i	$-0.863604\pi$
$409$	−10.7397	+	10.3156i	−0.531043	+	0.510073i	0.378546	+	0.925582i	$0.376424\pi$
$410$	0.336814	+	0.275000i	0.0166340	+	0.0135813i
$411$	3.64189	−	6.93903i	0.179641	−	0.342277i
$412$	−40.5184	+	6.58488i	−1.99620	+	0.324414i
$413$	−2.04558	+	1.29355i	−0.100656	+	0.0636512i
$414$	4.80710	−	2.28100i	0.236256	−	0.112105i
$415$	4.72735	−	6.84875i	0.232056	−	0.336192i
$416$	−0.536054	+	0.0366340i	−0.0262822	+	0.00179613i
$417$	−11.6090	−	16.8186i	−0.568497	−	0.823611i
$418$	−1.06683	−	0.615932i	−0.0521801	−	0.0301262i
$419$	1.14483	+	2.41267i	0.0559284	+	0.117867i	0.929490	−	0.368846i	$-0.120247\pi$
$419$	1.14483	+	2.41267i	0.0559284	+	0.117867i	−0.873562	+	0.486713i	$0.838196\pi$
$420$	3.73517	+	1.24698i	0.182258	+	0.0608465i
$421$	2.13692	−	8.66981i	0.104147	−	0.422541i	−0.895604	−	0.444852i	$-0.853256\pi$
$421$	2.13692	−	8.66981i	0.104147	−	0.422541i	0.999751	+	0.0223112i	$0.00710247\pi$
$422$	−26.1229	+	1.05272i	−1.27164	+	0.0512455i
$423$	−3.82551	+	0.154163i	−0.186003	+	0.00749565i
$424$	−12.4281	+	50.4226i	−0.603560	+	2.44874i
$425$	−7.89212	−	2.63478i	−0.382824	−	0.127805i
$426$	12.4356	+	26.2074i	0.602505	+	1.26975i
$427$	3.97704	+	2.29615i	0.192463	+	0.111118i
$428$	15.9173	+	23.0603i	0.769394	+	1.11466i
$429$	3.71352	−	2.28473i	0.179290	−	0.110308i
$430$	0.652890	−	0.945874i	0.0314851	−	0.0456141i
$431$	−26.3806	+	12.5177i	−1.27071	+	0.602958i	−0.940128	−	0.340820i	$-0.889295\pi$
$431$	−26.3806	+	12.5177i	−1.27071	+	0.602958i	−0.330579	+	0.943778i	$0.607244\pi$
$432$	−3.45770	+	2.18651i	−0.166358	+	0.105199i
$433$	17.7604	−	2.88634i	0.853508	−	0.138709i	0.282111	−	0.959382i	$-0.408965\pi$
$433$	17.7604	−	2.88634i	0.853508	−	0.138709i	0.571398	+	0.820673i	$0.306401\pi$
$434$	5.16539	−	9.84184i	0.247947	−	0.472423i
$435$	1.21512	+	0.992111i	0.0582603	+	0.0475681i
$436$	27.9359	−	26.8328i	1.33789	−	1.28506i
$437$			0.901103i			0.0431056i
$438$	−6.78213	−	7.06095i	−0.324063	−	0.337385i
$439$	−25.3976	+	8.47896i	−1.21216	+	0.404679i	−0.849673	−	0.527310i	$-0.823201\pi$
$439$	−25.3976	+	8.47896i	−1.21216	+	0.404679i	−0.362488	+	0.931988i	$0.618073\pi$
$440$	−0.308125	−	3.81681i	−0.0146893	−	0.181959i
$441$	−4.52160	+	1.11447i	−0.215314	+	0.0530702i
$442$	−12.9338	+	9.47208i	−0.615198	+	0.450541i
$443$	27.2411	+	6.71432i	1.29426	+	0.319007i	0.825542	−	0.564340i	$-0.190869\pi$
$443$	27.2411	+	6.71432i	1.29426	+	0.319007i	0.468719	+	0.883347i	$0.344716\pi$
$444$	0.836444	−	5.14684i	0.0396959	−	0.244258i
$445$	−2.77422	−	3.39780i	−0.131511	−	0.161071i
$446$	−42.4638	+	31.9094i	−2.01072	+	1.51096i
$447$	9.38155	−	10.5896i	0.443732	−	0.500870i
$448$	−1.91931	−	11.8100i	−0.0906787	−	0.557968i
$449$	−0.407765	+	5.05108i	−0.0192436	+	0.238375i	0.979984	+	0.199077i	$0.0637943\pi$
$449$	−0.407765	+	5.05108i	−0.0192436	+	0.238375i	−0.999228	+	0.0392984i	$0.987488\pi$
$450$	2.69375	+	10.9290i	0.126985	+	0.515198i
$451$	−0.0930958	−	0.321404i	−0.00438371	−	0.0151343i
$452$	9.21686	+	45.1471i	0.433524	+	2.12354i
$453$	−2.21229	+	1.80628i	−0.103943	+	0.0848664i
$454$	−0.258983	+	2.13292i	−0.0121547	+	0.100103i
$455$	−1.07837	−	3.36769i	−0.0505549	−	0.157880i
$456$	−0.247436	−	2.03782i	−0.0115873	−	0.0954298i
$457$	−16.1980	−	15.5584i	−0.757712	−	0.727792i	0.210590	−	0.977574i	$-0.432461\pi$
$457$	−16.1980	−	15.5584i	−0.757712	−	0.727792i	−0.968302	+	0.249782i	$0.919641\pi$
$458$	1.32949	−	1.38415i	0.0621230	−	0.0646769i
$459$	−0.777179	+	1.63787i	−0.0362756	+	0.0764492i
$460$	−4.59315	+	3.17042i	−0.214157	+	0.147822i
$461$	−15.1003	+	23.8792i	−0.703291	+	1.11217i	0.284843	+	0.958574i	$0.408058\pi$
$461$	−15.1003	+	23.8792i	−0.703291	+	1.11217i	−0.988134	+	0.153592i	$0.950916\pi$
$462$	−2.72726	−	3.62932i	−0.126883	−	0.168851i
$463$	4.91217	+	9.35936i	0.228288	+	0.434966i	0.972476	−	0.233004i	$-0.0748556\pi$
$463$	4.91217	+	9.35936i	0.228288	+	0.434966i	−0.744188	+	0.667970i	$0.767163\pi$
$464$	−2.00351	+	9.81386i	−0.0930108	+	0.455597i
$465$	−1.89080	+	0.152641i	−0.0876838	+	0.00707857i
$466$	27.7439	+	8.03611i	1.28521	+	0.372266i
$467$	−6.07986	−	3.19096i	−0.281342	−	0.147660i	0.318150	−	0.948040i	$-0.396938\pi$
$467$	−6.07986	−	3.19096i	−0.281342	−	0.147660i	−0.599492	+	0.800381i	$0.704631\pi$
$468$	13.4717	+	5.29990i	0.622732	+	0.244988i
$469$	−12.2319	+	6.41979i	−0.564816	+	0.296439i
$470$	5.89469	−	1.20341i	0.271902	−	0.0555091i
$471$	−11.1745	−	8.39707i	−0.514892	−	0.386916i
$472$	0.314654	+	7.80805i	0.0144831	+	0.359394i
$473$	−0.826984	+	0.313634i	−0.0380248	+	0.0144209i
$474$	14.0778	−	4.07769i	0.646616	−	0.187295i
$475$	−1.86774	−	0.381301i	−0.0856976	−	0.0174953i
$476$	7.38860	+	8.34001i	0.338656	+	0.382264i
$477$	6.64552	−	8.13928i	0.304277	−	0.372672i
$478$	−2.00681	+	49.7986i	−0.0917896	+	2.27773i
$479$	0.278603	+	0.834517i	0.0127297	+	0.0381300i	0.954710	−	0.297539i	$-0.0961658\pi$
$479$	0.278603	+	0.834517i	0.0127297	+	0.0381300i	−0.941980	+	0.335669i	$0.891038\pi$
$480$	0.0714677	−	0.0633148i	0.00326204	−	0.00288991i
$481$	−4.17260	+	2.12480i	−0.190254	+	0.0968826i
$482$	−40.3151	−	35.7161i	−1.83630	−	1.62682i
$483$	−1.30166	+	3.05512i	−0.0592277	+	0.139013i
$484$	19.1475	−	33.1645i	0.870342	−	1.50748i
$485$	0.730149	+	1.26465i	0.0331543	+	0.0574250i
$486$	2.43469	−	0.295625i	0.110440	−	0.0134098i
$487$	−24.5974	−	11.6716i	−1.11462	−	0.528892i	−0.219898	−	0.975523i	$-0.570573\pi$
$487$	−24.5974	−	11.6716i	−1.11462	−	0.528892i	−0.894718	+	0.446631i	$0.852624\pi$
$488$	12.8408	−	7.41367i	0.581278	−	0.335601i
$489$	−16.7782	−	11.5812i	−0.758737	−	0.523718i
$490$	6.73229	−	2.86836i	0.304134	−	0.129579i
$491$	−19.3099	−	3.13816i	−0.871442	−	0.141623i	−0.291785	−	0.956484i	$-0.594249\pi$
$491$	−19.3099	−	3.13816i	−0.871442	−	0.141623i	−0.579657	+	0.814861i	$0.696813\pi$
$492$	0.667440	−	0.888201i	0.0300905	−	0.0400432i
$493$	1.57396	+	4.15020i	0.0708877	+	0.186915i
$494$	−2.68007	+	2.51150i	−0.120582	+	0.112998i
$495$	−0.274745	+	0.724443i	−0.0123489	+	0.0325613i
$496$	−6.47360	−	10.2372i	−0.290673	−	0.459663i
$497$	−16.6559	−	7.09642i	−0.747119	−	0.318318i
$498$	−26.9236	−	17.0255i	−1.20648	−	0.762930i
$499$	−35.3293	−	4.28975i	−1.58156	−	0.192036i	−0.717911	−	0.696135i	$-0.754902\pi$
$499$	−35.3293	−	4.28975i	−1.58156	−	0.192036i	−0.863646	+	0.504099i	$0.831825\pi$
$500$	−9.66958	−	22.6953i	−0.432437	−	1.01497i
$501$	−6.19188	+	18.5470i	−0.276633	+	0.828617i
$502$	0.709475	+	0.269069i	0.0316654	+	0.0120091i
$503$	−14.7518	−	1.19089i	−0.657749	−	0.0530990i	−0.252914	−	0.967489i	$-0.581389\pi$
$503$	−14.7518	−	1.19089i	−0.657749	−	0.0530990i	−0.404835	+	0.914390i	$0.632671\pi$
$504$	2.10477	−	7.26650i	0.0937538	−	0.323676i
$505$	3.31217	+	0.133476i	0.147390	+	0.00593960i
$506$	6.43429			0.286039
$507$	−3.30810	−	12.5721i	−0.146918	−	0.558344i
$508$	7.15869			0.317616
$509$	−1.08774	−	0.0438345i	−0.0482133	−	0.00194293i	0.0161476	−	0.999870i	$-0.494860\pi$
$509$	−1.08774	−	0.0438345i	−0.0482133	−	0.00194293i	−0.0643609	+	0.997927i	$0.520501\pi$
$510$	0.792584	−	2.73632i	0.0350962	−	0.121166i
$511$	6.09068	+	0.491691i	0.269436	+	0.0217511i
$512$	−37.2401	−	14.1233i	−1.64579	−	0.624167i
$513$	−0.131529	+	0.393978i	−0.00580716	+	0.0173946i
$514$	7.85551	+	18.4376i	0.346492	+	0.813246i
$515$	−6.50276	−	0.789578i	−0.286546	−	0.0347930i
$516$	−2.48205	−	1.56955i	−0.109266	−	0.0690957i
$517$	−4.25933	−	1.81473i	−0.187325	−	0.0798119i
$518$	2.60578	+	4.12071i	0.114491	+	0.181054i
$519$	7.86520	−	20.7388i	0.345244	−	0.910333i
$520$	−11.1575	−	2.42138i	−0.489290	−	0.106184i
$521$	1.25504	+	3.30927i	0.0549844	+	0.144982i	0.959694	−	0.281047i	$-0.0906816\pi$
$521$	1.25504	+	3.30927i	0.0549844	+	0.144982i	−0.904710	+	0.426028i	$0.859912\pi$
$522$	3.60732	−	4.80047i	0.157888	−	0.210111i
$523$	−38.1292	−	6.19660i	−1.66727	−	0.270958i	−0.747747	−	0.663984i	$-0.768864\pi$
$523$	−38.1292	−	6.19660i	−1.66727	−	0.270958i	−0.919527	+	0.393026i	$0.871428\pi$
$524$	−57.7999	+	24.6263i	−2.52500	+	1.07580i
$525$	−5.78161	−	3.99076i	−0.252330	−	0.174171i
$526$	−57.0533	+	32.9397i	−2.48764	+	1.43624i
$527$	−4.84923	−	2.30099i	−0.211236	−	0.100233i
$528$	−4.91107	+	0.596312i	−0.213727	+	0.0259511i
$529$	9.14667	+	15.8425i	0.397681	+	0.688804i
$530$	−8.25584	+	14.2995i	−0.358611	+	0.621132i
$531$	0.619751	−	1.45461i	0.0268949	−	0.0631247i
$532$	1.91077	+	1.69280i	0.0828426	+	0.0733921i
$533$	−0.997614	−	0.0122909i	−0.0432115	−	0.000532378i
$534$	−12.5683	+	11.1345i	−0.543882	+	0.481837i
$535$	1.41593	+	4.24121i	0.0612158	+	0.183364i
$536$	−1.79596	+	44.5664i	−0.0775738	+	1.92497i
$537$	4.12410	−	5.05110i	0.177968	−	0.217971i
$538$	−4.28690	−	4.83891i	−0.184821	−	0.208620i
$539$	−5.51765	−	1.12644i	−0.237662	−	0.0485191i
$540$	−2.47098	+	0.715727i	−0.106334	+	0.0308000i
$541$	−4.59084	+	1.74107i	−0.197375	+	0.0748546i	−0.451312	−	0.892366i	$-0.649044\pi$
$541$	−4.59084	+	1.74107i	−0.197375	+	0.0748546i	0.253936	+	0.967221i	$0.418275\pi$
$542$	−0.134276	−	3.33202i	−0.00576764	−	0.143123i
$543$	−7.69785	−	5.78456i	−0.330346	−	0.248239i
$544$	0.264702	−	0.0540393i	0.0113490	−	0.00231691i
$545$	5.47314	−	2.87252i	0.234443	−	0.123045i
$546$	−12.7145	+	4.64362i	−0.544129	+	0.198729i
$547$	−6.09548	−	3.19916i	−0.260624	−	0.136786i	0.329351	−	0.944208i	$-0.393170\pi$
$547$	−6.09548	−	3.19916i	−0.260624	−	0.136786i	−0.589975	+	0.807422i	$0.700862\pi$
$548$	30.2230	+	8.75420i	1.29106	+	0.373961i
$549$	−2.99038	+	0.241408i	−0.127626	+	0.0103031i
$550$	−2.72267	+	13.3365i	−0.116095	+	0.568670i
$551$	0.472592	+	0.900449i	0.0201331	+	0.0383604i
$552$	6.44126	+	8.57176i	0.274158	+	0.364838i
$553$	−4.88901	+	7.73135i	−0.207902	+	0.328770i
$554$	−7.13667	+	4.92609i	−0.303208	+	0.209290i
$555$	0.356706	−	0.751743i	0.0151413	−	0.0319097i
$556$	56.8407	−	59.1774i	2.41058	−	2.50968i
$557$	−11.0047	−	10.5702i	−0.466284	−	0.447872i	0.422388	−	0.906415i	$-0.361192\pi$
$557$	−11.0047	−	10.5702i	−0.466284	−	0.447872i	−0.888672	+	0.458543i	$0.848372\pi$
$558$	0.875256	+	7.20838i	0.0370525	+	0.305155i
$559$	0.179801	+	2.63097i	0.00760476	+	0.111278i
$560$	−0.483624	+	3.98300i	−0.0204368	+	0.168313i
$561$	−1.69816	+	1.38650i	−0.0716962	+	0.0585381i
$562$	−11.8682	−	58.1343i	−0.500630	−	2.45225i
$563$	−9.73972	−	33.6254i	−0.410480	−	1.41714i	−0.853717	−	0.520738i	$-0.825657\pi$
$563$	−9.73972	−	33.6254i	−0.410480	−	1.41714i	0.443236	−	0.896405i	$-0.353830\pi$
$564$	−3.67886	−	14.9257i	−0.154908	−	0.628486i
$565$	−0.591665	+	7.32908i	−0.0248915	+	0.308337i
$566$	2.78109	+	17.1128i	0.116898	+	0.719303i
$567$	−1.01505	+	1.14575i	−0.0426281	+	0.0481171i
$568$	−46.7316	+	35.1165i	−1.96081	+	1.47346i
$569$	17.4027	+	21.3144i	0.729559	+	0.893548i	0.997556	−	0.0698722i	$-0.0222592\pi$
$569$	17.4027	+	21.3144i	0.729559	+	0.893548i	−0.267997	+	0.963420i	$0.586362\pi$
$570$	0.104698	−	0.644233i	0.00438532	−	0.0269840i
$571$	19.5362	+	4.81524i	0.817565	+	0.201512i	0.625854	−	0.779940i	$-0.284750\pi$
$571$	19.5362	+	4.81524i	0.817565	+	0.201512i	0.191710	+	0.981452i	$0.438597\pi$
$572$	11.9706	+	12.7740i	0.500514	+	0.534108i
$573$	15.7676	−	3.88636i	0.658701	−	0.162355i
$574$	0.0835902	+	1.03545i	0.00348899	+	0.0432188i
$575$	9.44440	−	3.15300i	0.393859	−	0.131489i
$576$	5.41473	+	5.63733i	0.225614	+	0.234889i
$577$			41.9558i			1.74664i	0.487144	+	0.873322i	$0.338039\pi$
$577$			41.9558i			1.74664i	−0.487144	+	0.873322i	$0.661961\pi$
$578$	−24.2563	+	23.2985i	−1.00893	+	0.969089i
$579$	−3.05632	−	2.49541i	−0.127016	−	0.103706i
$580$	−2.92706	+	5.57705i	−0.121540	+	0.231574i
$581$	19.6241	−	3.18922i	0.814144	−	0.132311i
$582$	4.72449	−	2.98759i	0.195837	−	0.123840i
$583$	11.4797	−	5.44720i	0.475442	−	0.225600i
$584$	11.2075	−	16.2368i	0.463768	−	0.671884i
$585$	1.82957	+	1.41043i	0.0756435	+	0.0583143i
$586$	−16.8096	−	24.3529i	−0.694397	−	1.00601i
$587$	−29.5348	−	17.0519i	−1.21903	−	0.703807i	−0.254320	−	0.967120i	$-0.581852\pi$
$587$	−29.5348	−	17.0519i	−1.21903	−	0.703807i	−0.964711	+	0.263313i	$0.915185\pi$
$588$	−8.01577	−	16.8929i	−0.330565	−	0.696650i
$589$	−1.16645	−	0.389418i	−0.0480627	−	0.0160457i
$590$	−0.594601	+	2.41239i	−0.0244793	+	0.0993165i
$591$	1.90661	−	0.0768337i	0.0784274	−	0.00316052i
$592$	5.30862	−	0.213930i	0.218183	−	0.00879247i
$593$	−6.73103	+	27.3089i	−0.276410	+	1.12144i	0.654461	+	0.756095i	$0.272895\pi$
$593$	−6.73103	+	27.3089i	−0.276410	+	1.12144i	−0.930872	+	0.365346i	$0.880951\pi$
$594$	2.81319	+	0.939180i	0.115426	+	0.0385350i
$595$	0.762215	+	1.60633i	0.0312478	+	0.0658533i
$596$	49.1939	+	28.4021i	2.01506	+	1.16340i
$597$	−9.61505	−	13.9298i	−0.393518	−	0.570109i
$598$	5.56407	−	18.3599i	0.227532	−	0.750792i
$599$	−15.6899	+	22.7308i	−0.641073	+	0.928754i	−0.999989	−	0.00461534i	$-0.998531\pi$
$599$	−15.6899	+	22.7308i	−0.641073	+	0.928754i	0.358917	+	0.933370i	$0.383146\pi$
$600$	−20.4925	+	9.72381i	−0.836603	+	0.396973i
$601$	28.8169	−	18.2227i	1.17547	−	0.743320i	0.203646	−	0.979045i	$-0.434721\pi$
$601$	28.8169	−	18.2227i	1.17547	−	0.743320i	0.971820	+	0.235725i	$0.0757463\pi$
$602$	2.71026	−	0.440460i	0.110462	−	0.0179518i
$603$	4.19399	−	7.99099i	0.170793	−	0.325418i
$604$	−8.88264	−	7.25245i	−0.361430	−	0.295098i
$605$	4.40720	−	4.23317i	0.179178	−	0.172103i
$606$		−	12.6889i		−	0.515452i
$607$	10.5836	+	11.0187i	0.429576	+	0.447236i	0.900447	−	0.434966i	$-0.143240\pi$
$607$	10.5836	+	11.0187i	0.429576	+	0.447236i	−0.470871	+	0.882202i	$0.656060\pi$
$608$	0.0587112	−	0.0196007i	0.00238105	−	0.000794912i
$609$	0.301566	+	3.73557i	0.0122201	+	0.151373i
$610$	4.57737	−	1.12822i	0.185332	−	0.0456803i
$611$	−8.86151	+	10.5845i	−0.358498	+	0.428203i
$612$	−7.06754	−	1.74199i	−0.285688	−	0.0704159i
$613$	−6.88862	+	42.3874i	−0.278229	+	1.71201i	0.352337	+	0.935873i	$0.385387\pi$
$613$	−6.88862	+	42.3874i	−0.278229	+	1.71201i	−0.630566	+	0.776136i	$0.717177\pi$
$614$	2.93897	+	3.59958i	0.118607	+	0.145267i
$615$	0.141734	−	0.106506i	0.00571527	−	0.00429475i
$616$	6.06646	−	6.84762i	0.244425	−	0.275898i
$617$	−0.459888	−	2.82980i	−0.0185144	−	0.113924i	0.976148	−	0.217106i	$-0.0696617\pi$
$617$	−0.459888	−	2.82980i	−0.0185144	−	0.113924i	−0.994662	+	0.103182i	$0.967098\pi$
$618$	−2.01767	+	24.9934i	−0.0811627	+	1.00538i
$619$	−4.54642	−	18.4455i	−0.182736	−	0.741388i	−0.988761	−	0.149507i	$-0.952231\pi$
$619$	−4.54642	−	18.4455i	−0.182736	−	0.741388i	0.806025	−	0.591882i	$-0.201615\pi$
$620$	−2.11905	−	7.31580i	−0.0851030	−	0.293810i
$621$	−0.433952	−	2.12564i	−0.0174139	−	0.0852990i
$622$	1.48674	−	1.21389i	0.0596129	−	0.0486724i
$623$	1.26319	−	10.4033i	0.0506085	−	0.416798i
$624$	−2.54531	+	14.5291i	−0.101894	+	0.581631i
$625$	2.29150	+	18.8722i	0.0916601	+	0.754889i
$626$	40.8202	+	39.2084i	1.63150	+	1.56708i
$627$	−0.347937	+	0.362241i	−0.0138953	+	0.0144665i
$628$	24.0594	−	50.7042i	0.960076	−	2.02332i
$629$	1.93762	−	1.33744i	0.0772579	−	0.0533273i
$630$	1.28558	−	2.03298i	0.0512187	−	0.0809959i
$631$	−24.8458	−	33.0638i	−0.989096	−	1.31625i	−0.948400	−	0.317076i	$-0.897299\pi$
$631$	−24.8458	−	33.0638i	−0.989096	−	1.31625i	−0.0406959	−	0.999172i	$-0.512957\pi$
$632$	13.7255	+	26.1518i	0.545971	+	1.04026i
$633$	−2.13225	+	10.4444i	−0.0847492	+	0.415129i
$634$	18.5185	−	1.49497i	0.735464	−	0.0593728i
$635$	1.09724	+	0.317820i	0.0435427	+	0.0126123i
$636$	37.3571	+	19.6065i	1.48130	+	0.777448i
$637$	−7.98563	+	14.7702i	−0.316402	+	0.585218i
$638$	6.42963	−	3.37453i	0.254551	−	0.133599i
$639$	11.5886	−	2.36582i	0.458437	−	0.0935906i
$640$	−9.97216	−	7.49359i	−0.394184	−	0.296210i
$641$	−0.414130	−	10.2765i	−0.0163572	−	0.405899i	−0.986540	−	0.163523i	$-0.947714\pi$
$641$	−0.414130	−	10.2765i	−0.0163572	−	0.405899i	0.970182	−	0.242376i	$-0.0779267\pi$
$642$	16.0035	−	6.06932i	0.631607	−	0.239537i
$643$	−16.0215	+	4.64067i	−0.631825	+	0.183010i	−0.578651	−	0.815575i	$-0.696421\pi$
$643$	−16.0215	+	4.64067i	−0.631825	+	0.183010i	−0.0531734	+	0.998585i	$0.516934\pi$
$644$	−13.0642	−	2.66707i	−0.514801	−	0.105097i
$645$	−0.310751	−	0.350766i	−0.0122358	−	0.0138114i
$646$	1.16799	−	1.43053i	0.0459539	−	0.0562834i
$647$	−1.66730	+	41.3736i	−0.0655483	+	1.62656i	0.547701	+	0.836674i	$0.315503\pi$
$647$	−1.66730	+	41.3736i	−0.0655483	+	1.62656i	−0.613249	+	0.789890i	$0.710138\pi$
$648$	1.56506	+	4.68792i	0.0614813	+	0.184159i
$649$	1.43116	−	1.26790i	0.0561780	−	0.0497693i
$650$	35.7006	+	19.3018i	1.40029	+	0.757077i
$651$	−3.39222	−	3.00525i	−0.132952	−	0.117785i
$652$	32.0851	−	75.3065i	1.25655	−	2.94923i
$653$	9.77606	−	16.9326i	0.382567	−	0.662625i	−0.608861	−	0.793277i	$-0.708373\pi$
$653$	9.77606	−	16.9326i	0.382567	−	0.662625i	0.991428	+	0.130651i	$0.0417068\pi$
$654$	−11.8304	−	20.4908i	−0.462605	−	0.801255i
$655$	−9.95255	+	1.20846i	−0.388878	+	0.0472184i
$656$	1.02273	+	0.485291i	0.0399309	+	0.0189474i
$657$	−3.45711	+	1.99597i	−0.134875	+	0.0778701i
$658$	11.8290	+	8.16499i	0.461143	+	0.318304i
$659$	29.3399	−	12.5005i	1.14292	−	0.486952i	0.264283	−	0.964445i	$-0.414865\pi$
$659$	29.3399	−	12.5005i	1.14292	−	0.486952i	0.878635	+	0.477493i	$0.158454\pi$
$660$	−3.07061	−	0.499022i	−0.119523	−	0.0194244i
$661$	−2.04748	+	2.72470i	−0.0796377	+	0.105979i	−0.837504	−	0.546432i	$-0.815986\pi$
$661$	−2.04748	+	2.72470i	−0.0796377	+	0.105979i	0.757866	+	0.652410i	$0.226242\pi$
$662$	−2.88830	−	7.61583i	−0.112257	−	0.295998i
$663$	2.48782	+	6.04457i	0.0966190	+	0.234752i
$664$	22.7629	−	60.0208i	0.883372	−	2.32926i
$665$	0.217718	+	0.344294i	0.00844274	+	0.0133511i
$666$	−2.93024	−	1.24846i	−0.113544	−	0.0483767i
$667$	−4.48936	−	2.83890i	−0.173829	−	0.109923i
$668$	−77.9364	−	9.46319i	−3.01545	−	0.366142i
$669$	8.48902	+	19.9245i	0.328204	+	0.770324i
$670$	−4.49080	+	13.4516i	−0.173495	+	0.519680i
$671$	−3.39217	−	1.28648i	−0.130953	−	0.0496640i
$672$	0.227369	+	0.0183551i	0.00877095	+	0.000708064i
$673$	12.1526	−	41.9558i	0.468450	−	1.61728i	−0.284138	−	0.958783i	$-0.591707\pi$
$673$	12.1526	−	41.9558i	0.468450	−	1.61728i	0.752587	−	0.658492i	$-0.228806\pi$
$674$	−32.0870	−	1.29306i	−1.23594	−	0.0498068i
$675$	4.58949			0.176649
$676$	46.8015	−	23.1110i	1.80006	−	0.888885i
$677$	15.7402			0.604945			0.302472	−	0.953158i	$-0.402188\pi$
$677$	15.7402			0.604945			0.302472	+	0.953158i	$0.402188\pi$
$678$	28.1234	+	1.13333i	1.08007	+	0.0435254i
$679$	−0.970635	+	3.35102i	−0.0372495	+	0.128600i
$680$	5.72208	+	0.461934i	0.219432	+	0.0177144i
$681$	0.819122	+	0.310652i	0.0313888	+	0.0119042i
$682$	−2.78062	+	8.32898i	−0.106476	+	0.318933i
$683$	1.60241	+	3.76099i	0.0613144	+	0.143910i	0.947818	−	0.318811i	$-0.103283\pi$
$683$	1.60241	+	3.76099i	0.0613144	+	0.143910i	−0.886504	+	0.462721i	$0.846873\pi$
$684$	−1.65554	−	0.201019i	−0.0633012	−	0.00768616i
$685$	4.24375	+	2.68358i	0.162145	+	0.102534i
$686$	40.2604	+	17.1533i	1.53715	+	0.654918i
$687$	−0.418237	−	0.661389i	−0.0159567	−	0.0252335i
$688$	1.06104	−	2.79774i	0.0404519	−	0.106663i
$689$	−5.61618	−	37.4673i	−0.213959	−	1.42739i
$690$	1.20889	+	3.18758i	0.0460216	+	0.121349i
$691$	4.42892	−	5.89382i	0.168484	−	0.224212i	−0.707301	−	0.706912i	$-0.750088\pi$
$691$	4.42892	−	5.89382i	0.168484	−	0.224212i	0.875785	+	0.482701i	$0.160344\pi$
$692$	87.9031	+	14.2856i	3.34157	+	0.543058i
$693$	−1.70292	+	0.725545i	−0.0646884	+	0.0275612i
$694$	−13.5655	−	9.36356i	−0.514938	−	0.355436i
$695$	11.3395	−	6.54684i	0.430130	−	0.248336i
$696$	10.9321	+	5.18736i	0.414381	+	0.196626i
$697$	0.497990	−	0.0604670i	0.0188627	−	0.00229035i
$698$	38.6008	+	66.8586i	1.46106	+	2.53063i
$699$	5.88856	−	10.1993i	0.222726	−	0.385772i
$700$	11.0562	−	25.9499i	0.417886	−	0.980814i
$701$	−6.71017	−	5.94470i	−0.253440	−	0.224528i	0.526831	−	0.849970i	$-0.323380\pi$
$701$	−6.71017	−	5.94470i	−0.253440	−	0.224528i	−0.780271	+	0.625442i	$0.784919\pi$
$702$	5.11261	−	7.21512i	0.192963	−	0.272317i
$703$	0.403755	−	0.357696i	0.0152279	−	0.0134908i
$704$	2.99324	+	8.96586i	0.112812	+	0.337914i
$705$	0.0987740	−	2.45105i	0.00372005	−	0.0923120i
$706$	52.3436	−	64.1093i	1.96998	−	2.41278i
$707$	5.25157	+	5.92780i	0.197506	+	0.222938i
$708$	6.22016	+	1.26985i	0.233768	+	0.0477241i
$709$	−1.49999	+	0.434476i	−0.0563331	+	0.0163171i	−0.306264	−	0.951946i	$-0.599079\pi$
$709$	−1.49999	+	0.434476i	−0.0563331	+	0.0163171i	0.249931	+	0.968264i	$0.419592\pi$
$710$	−17.3781	+	6.59063i	−0.652187	+	0.247342i
$711$	−0.240628	−	5.97111i	−0.00902424	−	0.223934i
$712$	−27.0501	−	20.3268i	−1.01374	−	0.761779i
$713$	6.29336	−	1.28480i	0.235688	−	0.0481161i
$714$	6.02640	−	3.16290i	0.225532	−	0.118369i
$715$	1.26766	+	2.48937i	0.0474077	+	0.0930973i
$716$	23.1832	+	12.1675i	0.866396	+	0.454720i
$717$	19.5188	+	5.65368i	0.728942	+	0.211141i
$718$	−24.3678	+	1.96718i	−0.909400	+	0.0734143i
$719$	−0.451644	+	2.21230i	−0.0168435	+	0.0825049i	−0.987344	−	0.158596i	$-0.949303\pi$
$719$	−0.451644	+	2.21230i	−0.0168435	+	0.0825049i	0.970500	+	0.241101i	$0.0775084\pi$
$720$	−1.21812	−	2.32093i	−0.0453966	−	0.0864960i
$721$	−9.40144	−	12.5110i	−0.350128	−	0.465935i
$722$	−24.6794	+	39.0274i	−0.918473	+	1.45245i
$723$	−18.0734	+	12.4751i	−0.672156	+	0.463955i
$724$	16.5740	−	34.9290i	0.615968	−	1.29813i
$725$	7.78393	−	8.10393i	0.289088	−	0.300972i
$726$	−16.8703	−	16.2041i	−0.626115	−	0.601392i
$727$	−0.0176277	−	0.145177i	−0.000653776	−	0.00538433i	0.992378	−	0.123228i	$-0.0393248\pi$
$727$	−0.0176277	−	0.145177i	−0.000653776	−	0.00538433i	−0.993032	+	0.117844i	$0.962402\pi$
$728$	−14.2933	−	23.2318i	−0.529746	−	0.861028i
$729$	0.120537	−	0.992709i	0.00446432	−	0.0367670i
$730$	4.85903	−	3.96727i	0.179841	−	0.146835i
$731$	−0.265227	−	1.29917i	−0.00980976	−	0.0480514i
$732$	−3.35136	−	11.5702i	−0.123870	−	0.427648i
$733$	−1.85726	−	7.53519i	−0.0685994	−	0.278319i	0.926618	−	0.376004i	$-0.122702\pi$
$733$	−1.85726	−	7.53519i	−0.0685994	−	0.278319i	−0.995217	+	0.0976856i	$0.968856\pi$
$734$	2.96946	−	36.7833i	0.109605	−	1.35770i
$735$	−0.478627	−	2.94511i	−0.0176544	−	0.108632i
$736$	−0.214387	+	0.241993i	−0.00790241	+	0.00891998i
$737$	8.72454	−	6.55607i	0.321373	−	0.241496i
$738$	−0.429210	−	0.525686i	−0.0157994	−	0.0193508i
$739$	−7.99380	+	49.1878i	−0.294057	+	1.80940i	0.247666	+	0.968846i	$0.420337\pi$
$739$	−7.99380	+	49.1878i	−0.294057	+	1.80940i	−0.541722	+	0.840558i	$0.682228\pi$
$740$	3.24383	+	0.799532i	0.119246	+	0.0293914i
$741$	0.732755	+	1.30607i	0.0269184	+	0.0479796i
$742$	−38.3014	+	9.44045i	−1.40609	+	0.346570i
$743$	1.76416	+	21.8531i	0.0647209	+	0.801712i	0.944961	+	0.327184i	$0.106100\pi$
$743$	1.76416	+	21.8531i	0.0647209	+	0.801712i	−0.880240	+	0.474529i	$0.842618\pi$
$744$	−13.8795	+	4.63366i	−0.508847	+	0.169878i
$745$	6.27920	+	6.53734i	0.230052	+	0.239510i
$746$			31.7512i			1.16249i
$747$	−9.36729	+	8.99740i	−0.342731	+	0.329198i
$748$	−6.81832	−	5.56699i	−0.249302	−	0.203549i
$749$	−4.96433	+	9.45874i	−0.181393	+	0.345615i
$750$	−14.8737	+	2.41722i	−0.543112	+	0.0882644i
$751$	37.8389	−	23.9279i	1.38076	−	0.873141i	0.382063	−	0.924136i	$-0.375214\pi$
$751$	37.8389	−	23.9279i	1.38076	−	0.873141i	0.998699	+	0.0509956i	$0.0162394\pi$
$752$	14.1507	−	6.71460i	0.516024	−	0.244856i
$753$	0.175749	−	0.254617i	0.00640466	−	0.00927875i
$754$	−4.06900	−	21.2647i	−0.148184	−	0.774416i
$755$	−1.03950	−	1.50597i	−0.0378311	−	0.0548079i
$756$	−5.32260	−	3.07300i	−0.193581	−	0.111764i
$757$	−1.93259	−	4.07286i	−0.0702413	−	0.148030i	0.865293	−	0.501267i	$-0.167132\pi$
$757$	−1.93259	−	4.07286i	−0.0702413	−	0.148030i	−0.935534	+	0.353236i	$0.885081\pi$
$758$	−55.3341	−	18.4732i	−2.00983	−	0.670979i
$759$	0.627840	−	2.54725i	0.0227892	−	0.0924593i
$760$	1.31418	−	0.0529597i	0.0476704	−	0.00192105i
$761$	−44.6243	+	1.79830i	−1.61763	+	0.0651883i	−0.832457	−	0.554089i	$-0.813067\pi$
$761$	−44.6243	+	1.79830i	−1.61763	+	0.0651883i	−0.785172	+	0.619277i	$0.787426\pi$
$762$	1.04647	−	4.24570i	0.0379097	−	0.153806i
$763$	14.0073	+	4.67631i	0.507097	+	0.169294i
$764$	27.9523	+	58.9083i	1.01128	+	2.13123i
$765$	−1.00593	−	0.580776i	−0.0363696	−	0.0209980i
$766$	33.2336	+	48.1471i	1.20078	+	1.73963i
$767$	−2.38028	−	5.18016i	−0.0859469	−	0.187045i
$768$	−18.2437	+	26.4306i	−0.658313	+	0.953731i
$769$	−37.5100	+	17.7987i	−1.35265	+	0.641839i	−0.960556	−	0.278087i	$-0.910299\pi$
$769$	−37.5100	+	17.7987i	−1.35265	+	0.641839i	−0.392091	+	0.919926i	$0.628248\pi$
$770$	2.45842	−	1.55461i	0.0885951	−	0.0560242i
$771$	8.06569	−	1.31080i	0.290479	−	0.0472074i
$772$	7.36228	−	14.0277i	0.264974	−	0.504866i
$773$	18.3792	+	15.0061i	0.661052	+	0.539732i	0.902505	−	0.430680i	$-0.141726\pi$
$773$	18.3792	+	15.0061i	0.661052	+	0.539732i	−0.241452	+	0.970413i	$0.577624\pi$
$774$	−1.29371	+	1.24262i	−0.0465013	+	0.0446651i
$775$			13.5881i			0.488098i
$776$	7.80306	+	8.12385i	0.280114	+	0.291629i
$777$	1.88560	−	0.629505i	0.0676454	−	0.0225834i
$778$	−7.13634	−	88.3994i	−0.255850	−	3.16927i
$779$	0.111593	−	0.0275051i	0.00399822	−	0.000985472i
$780$	−4.07925	+	8.33028i	−0.146060	+	0.298272i
$781$	13.8871	+	3.42286i	0.496920	+	0.122480i
$782$	−1.54735	+	9.52124i	−0.0553332	+	0.340479i
$783$	−1.54845	−	1.89651i	−0.0553371	−	0.0677756i
$784$	15.2307	−	11.4451i	0.543952	−	0.408754i
$785$	5.93877	−	6.70349i	0.211964	−	0.239258i
$786$	6.15612	+	37.8801i	0.219581	+	1.35114i
$787$	−0.492204	+	6.09704i	−0.0175452	+	0.217336i	0.982043	+	0.188655i	$0.0604128\pi$
$787$	−0.492204	+	6.09704i	−0.0175452	+	0.217336i	−0.999589	+	0.0286811i	$0.990869\pi$
$788$	1.83352	+	7.43887i	0.0653164	+	0.264999i
$789$	7.47329	+	25.8008i	0.266056	+	0.918532i
$790$	1.87836	+	9.20082i	0.0668291	+	0.327351i
$791$	−13.6073	+	11.1100i	−0.483818	+	0.395025i
$792$	−0.720390	+	5.93294i	−0.0255979	+	0.210818i
$793$	−6.60429	+	8.56689i	−0.234525	+	0.304219i
$794$	−5.80622	−	47.8185i	−0.206055	−	1.69701i
$795$	4.85541	+	4.66369i	0.172204	+	0.165404i
$796$	47.0776	−	49.0129i	1.66862	−	1.73722i
$797$	21.1168	−	44.5027i	0.747995	−	1.57637i	−0.0675803	−	0.997714i	$-0.521528\pi$
$797$	21.1168	−	44.5027i	0.747995	−	1.57637i	0.815575	−	0.578651i	$-0.196421\pi$
$798$	1.28329	−	0.885792i	0.0454280	−	0.0313567i
$799$	3.70968	−	5.86640i	0.131239	−	0.207538i
$800$	−0.410867	−	0.546764i	−0.0145263	−	0.0193310i
$801$	3.18163	+	6.06208i	0.112417	+	0.214193i
$802$	−15.3740	+	75.3068i	−0.542875	+	2.65918i
$803$	−4.81166	+	0.388437i	−0.169800	+	0.0137076i
$804$	34.8048	+	10.0813i	1.22747	+	0.355541i
$805$	−1.88399	−	0.988796i	−0.0664021	−	0.0348505i
$806$	21.3618	+	15.1369i	0.752436	+	0.533173i
$807$	−2.33396	+	1.22496i	−0.0821593	+	0.0431206i
$808$	25.0531	−	5.11463i	0.881365	−	0.179932i
$809$	−2.95558	−	2.22097i	−0.103913	−	0.0780853i	0.547516	−	0.836795i	$-0.315574\pi$
$809$	−2.95558	−	2.22097i	−0.103913	−	0.0780853i	−0.651429	+	0.758710i	$0.725830\pi$
$810$	0.0632738	+	1.57012i	0.00222321	+	0.0551685i
$811$	5.11030	−	1.93808i	0.179447	−	0.0680552i	−0.263245	−	0.964729i	$-0.584793\pi$
$811$	5.11030	−	1.93808i	0.179447	−	0.0680552i	0.442692	+	0.896674i	$0.354024\pi$
$812$	−14.4535	+	4.18651i	−0.507218	+	0.146918i
$813$	−1.33220	−	0.271971i	−0.0467224	−	0.00953845i
$814$	−2.55411	−	2.88300i	−0.0895216	−	0.101049i
$815$	8.26115	−	10.1181i	0.289376	−	0.354421i
$816$	0.298638	−	7.41063i	0.0104544	−	0.259424i
$817$	−0.0962008	−	0.288156i	−0.00336564	−	0.0100813i
$818$	−27.3372	+	24.2187i	−0.955824	+	0.846786i
$819$	0.597703	+	5.48660i	0.0208854	+	0.191717i
$820$	0.532825	+	0.472042i	0.0186071	+	0.0164844i
$821$	18.2673	−	42.8750i	0.637535	−	1.49635i	−0.216581	−	0.976265i	$-0.569490\pi$
$821$	18.2673	−	42.8750i	0.637535	−	1.49635i	0.854115	−	0.520084i	$-0.174099\pi$
$822$	9.61003	−	16.6451i	0.335188	−	0.580563i
$823$	−22.9784	−	39.7998i	−0.800977	−	1.38733i	−0.918974	−	0.394318i	$-0.870981\pi$
$823$	−22.9784	−	39.7998i	−0.800977	−	1.38733i	0.117997	−	0.993014i	$-0.462353\pi$
$824$	−50.1604	+	6.09058i	−1.74742	+	0.212175i
$825$	5.01407	+	2.37921i	0.174568	+	0.0828333i
$826$	−5.14061	+	2.96793i	−0.178865	+	0.103268i
$827$	11.7911	+	8.13879i	0.410016	+	0.283014i	0.755166	−	0.655534i	$-0.227556\pi$
$827$	11.7911	+	8.13879i	0.410016	+	0.283014i	−0.345150	+	0.938548i	$0.612172\pi$
$828$	8.01372	−	3.41433i	0.278496	−	0.118656i
$829$	14.5244	+	2.36045i	0.504455	+	0.0819819i	0.407313	−	0.913289i	$-0.366466\pi$
$829$	14.5244	+	2.36045i	0.504455	+	0.0819819i	0.0971418	+	0.995271i	$0.469030\pi$
$830$	12.2611	−	16.3166i	0.425590	−	0.566358i
$831$	1.25380	+	3.30599i	0.0434937	+	0.114683i
$832$	28.1720	−	0.787815i	0.976689	−	0.0273126i
$833$	2.99377	−	7.89393i	0.103728	−	0.273509i
$834$	−26.7881	−	42.3619i	−0.927595	−	1.46687i
$835$	−11.5255	−	4.91056i	−0.398856	−	0.169937i
$836$	−1.70449	−	1.07785i	−0.0589510	−	0.0372784i
$837$	2.93911	+	0.356872i	0.101590	+	0.0123353i
$838$	2.56723	+	6.02552i	0.0886836	+	0.208148i
$839$	5.32147	−	15.9397i	0.183717	−	0.550301i	−0.815893	−	0.578203i	$-0.803754\pi$
$839$	5.32147	−	15.9397i	0.183717	−	0.550301i	0.999611	+	0.0279018i	$0.00888256\pi$
$840$	4.53212	+	1.71881i	0.156373	+	0.0593045i
$841$	22.9310	+	1.85118i	0.790723	+	0.0638338i
$842$	6.09289	−	21.0351i	0.209975	−	0.724917i
$843$	−24.1727	−	0.974125i	−0.832551	−	0.0335506i
$844$	−42.8008			−1.47326
$845$	8.19950	−	1.46450i	0.282071	−	0.0503804i
$846$	−9.38997			−0.322834
$847$	14.5876	+	0.587860i	0.501235	+	0.0201991i
$848$	−11.9598	+	41.2899i	−0.410700	+	1.41790i
$849$	7.04608	+	0.568818i	0.241821	+	0.0195218i
$850$	−19.0801	−	7.23614i	−0.654443	−	0.248197i
$851$	−0.892200	+	2.67246i	−0.0305842	+	0.0916109i
$852$	18.6143	+	43.6893i	0.637714	+	1.49677i
$853$	57.1833	+	6.94331i	1.95792	+	0.237734i	0.998952	−	0.0457793i	$-0.0145771\pi$
$853$	57.1833	+	6.94331i	1.95792	+	0.237734i	0.958968	+	0.283514i	$0.0915002\pi$
$854$	9.51934	+	6.01967i	0.325745	+	0.205989i
$855$	−0.244827	−	0.104311i	−0.00837291	−	0.00356736i
$856$	18.4340	+	29.1510i	0.630061	+	0.996361i
$857$	−2.45010	+	6.46037i	−0.0836937	+	0.220682i	−0.970330	−	0.241786i	$-0.922267\pi$
$857$	−2.45010	+	6.46037i	−0.0836937	+	0.220682i	0.886636	+	0.462468i	$0.153036\pi$
$858$	9.32593	−	5.23221i	0.318382	−	0.178625i
$859$	19.6584	+	51.8351i	0.670738	+	1.76859i	0.639142	+	0.769089i	$0.279290\pi$
$859$	19.6584	+	51.8351i	0.670738	+	1.76859i	0.0315961	+	0.999501i	$0.489941\pi$
$860$	1.13034	−	1.50420i	0.0385441	−	0.0512929i
$861$	0.418077	+	0.0679441i	0.0142480	+	0.00231553i
$862$	−65.8841	+	28.0706i	−2.24402	+	0.956088i
$863$	5.16835	+	3.56746i	0.175933	+	0.121438i	0.652777	−	0.757550i	$-0.273604\pi$
$863$	5.16835	+	3.56746i	0.175933	+	0.121438i	−0.476844	+	0.878988i	$0.658219\pi$
$864$	−0.129056	+	0.0745107i	−0.00439058	+	0.00253491i
$865$	12.8390	+	6.09220i	0.436540	+	0.207141i
$866$	43.8084	−	5.31930i	1.48867	−	0.180757i
$867$	6.85669	+	11.8761i	0.232865	+	0.403335i
$868$	9.09822	−	15.7586i	0.308814	−	0.534881i
$869$	2.83256	−	6.64825i	0.0960879	−	0.225527i
$870$	2.87977	+	2.55125i	0.0976334	+	0.0864956i
$871$	−11.1628	−	30.5644i	−0.378238	−	1.03564i
$872$	35.6887	−	31.6174i	1.20857	−	1.07070i
$873$	−0.721743	−	2.16188i	−0.0244273	−	0.0731687i
$874$	−0.0889887	+	2.20823i	−0.00301009	+	0.0746946i
$875$	5.94805	−	7.28504i	0.201081	−	0.246279i
$876$	−10.6286	−	11.9972i	−0.359108	−	0.405349i
$877$	2.54721	+	0.520017i	0.0860133	+	0.0175597i	0.242840	−	0.970066i	$-0.421921\pi$
$877$	2.54721	+	0.520017i	0.0860133	+	0.0175597i	−0.156826	+	0.987626i	$0.550126\pi$
$878$	−63.0764	+	18.2703i	−2.12872	+	0.616593i
$879$	−11.2812	+	4.27839i	−0.380505	+	0.144307i
$880$	−0.127631	−	3.16712i	−0.00430243	−	0.106764i
$881$	−26.7137	−	20.0740i	−0.900008	−	0.676312i	0.0465260	−	0.998917i	$-0.485185\pi$
$881$	−26.7137	−	20.0740i	−0.900008	−	0.676312i	−0.946534	+	0.322605i	$0.895441\pi$
$882$	−11.1906	+	2.28459i	−0.376809	+	0.0769260i
$883$	25.3403	−	13.2996i	0.852768	−	0.447567i	0.0190897	−	0.999818i	$-0.493923\pi$
$883$	25.3403	−	13.2996i	0.852768	−	0.447567i	0.833678	+	0.552251i	$0.186231\pi$
$884$	−21.7813	+	14.6416i	−0.732583	+	0.492452i
$885$	0.897013	+	0.470789i	0.0301527	+	0.0158254i
$886$	66.0935	+	19.1442i	2.22046	+	0.643163i
$887$	33.2597	−	2.68500i	1.11675	−	0.0901534i	0.491720	−	0.870754i	$-0.336369\pi$
$887$	33.2597	−	2.68500i	1.11675	−	0.0901534i	0.625031	+	0.780600i	$0.285086\pi$
$888$	1.28385	−	6.28871i	0.0430831	−	0.211035i
$889$	1.26830	+	2.41654i	0.0425374	+	0.0810482i
$890$	−6.46292	−	8.60058i	−0.216637	−	0.288292i
$891$	0.646311	−	1.02206i	0.0216522	−	0.0342403i
$892$	−71.5648	+	49.3976i	−2.39617	+	1.65396i
$893$	0.681720	−	1.43669i	0.0228129	−	0.0480771i
$894$	24.0361	−	25.0242i	0.803887	−	0.836935i
$895$	3.01319	+	2.89421i	0.100720	+	0.0967427i
$896$	−3.59212	−	29.5838i	−0.120004	−	0.988325i
$897$	−6.72551	−	3.99425i	−0.224558	−	0.133364i
$898$	−1.49809	+	12.3379i	−0.0499918	+	0.411719i
$899$	5.61497	−	4.58448i	0.187270	−	0.152901i
$900$	3.68595	+	18.0550i	0.122865	+	0.601833i
$901$	5.29987	+	18.2973i	0.176564	+	0.609571i
$902$	−0.196399	−	0.796822i	−0.00653937	−	0.0265313i
$903$	0.0900876	−	1.11593i	0.00299793	−	0.0371360i
$904$	9.09826	+	55.9838i	0.302604	+	1.86199i
$905$	4.09109	−	4.61788i	0.135992	−	0.153504i
$906$	−5.59979	+	4.20797i	−0.186041	+	0.139800i
$907$	12.9841	+	15.9026i	0.431128	+	0.528036i	0.943786	−	0.330557i	$-0.107236\pi$
$907$	12.9841	+	15.9026i	0.431128	+	0.528036i	−0.512658	+	0.858593i	$0.671339\pi$
$908$	−0.564241	+	3.47191i	−0.0187250	+	0.115219i
$909$	−5.02337	−	1.23815i	−0.166615	−	0.0410668i
$910$	−2.31007	−	8.35931i	−0.0765781	−	0.277108i
$911$	40.9620	−	10.0962i	1.35713	−	0.334503i	0.507397	−	0.861712i	$-0.330608\pi$
$911$	40.9620	−	10.0962i	1.35713	−	0.334503i	0.849736	+	0.527209i	$0.176762\pi$
$912$	−0.136731	−	1.69371i	−0.00452761	−	0.0560845i
$913$	−14.8982	+	4.97374i	−0.493057	+	0.164607i
$914$	−38.1582	−	39.7269i	−1.26216	−	1.31405i
$915$		−	1.92221i		−	0.0635461i
$916$	2.26600	−	2.17652i	0.0748707	−	0.0719142i
$917$	−18.5534	−	15.1484i	−0.612686	−	0.500243i
$918$	−2.06629	+	3.93699i	−0.0681979	+	0.129940i
$919$	24.6397	−	4.00433i	0.812787	−	0.132091i	0.260210	−	0.965552i	$-0.416208\pi$
$919$	24.6397	−	4.00433i	0.812787	−	0.132091i	0.552578	+	0.833461i	$0.313644\pi$
$920$	−5.80631	+	3.67169i	−0.191428	+	0.121052i
$921$	1.71180	−	0.812260i	0.0564058	−	0.0267649i
$922$	−39.3628	+	57.0269i	−1.29635	+	1.87808i
$923$	21.7759	−	36.6662i	0.716761	−	1.20688i
$924$	−4.22195	−	6.11655i	−0.138892	−	0.201220i
$925$	−5.16175	−	2.98014i	−0.169717	−	0.0979862i
$926$	11.1134	+	23.4210i	0.365210	+	0.769663i
$927$	9.69766	+	3.23755i	0.318513	+	0.106335i
$928$	−0.0873160	+	0.354255i	−0.00286629	+	0.0116290i
$929$	−2.29323	+	0.0924140i	−0.0752384	+	0.00303200i	−0.0778566	−	0.996965i	$-0.524808\pi$
$929$	−2.29323	+	0.0924140i	−0.0752384	+	0.00303200i	0.00261819	+	0.999997i	$0.499167\pi$
$930$	−4.64865	+	0.187334i	−0.152435	+	0.00614293i
$931$	0.462901	−	1.87806i	0.0151710	−	0.0615511i
$932$	44.8532	+	14.9742i	1.46921	+	0.490496i
$933$	−0.335489	−	0.707028i	−0.0109834	−	0.0231471i
$934$	−14.5841	−	8.42014i	−0.477207	−	0.275515i
$935$	−0.797918	−	1.15598i	−0.0260947	−	0.0378047i
$936$	16.3064	+	7.18612i	0.532991	+	0.234886i
$937$	−7.24966	+	10.5029i	−0.236836	+	0.343116i	−0.923322	−	0.384027i	$-0.874537\pi$
$937$	−7.24966	+	10.5029i	−0.236836	+	0.343116i	0.686486	+	0.727143i	$0.259152\pi$
$938$	−30.6093	+	14.5243i	−0.999430	+	0.474235i
$939$	19.5052	−	12.3343i	0.636527	−	0.402516i
$940$	9.72174	−	1.57994i	0.317088	−	0.0515319i
$941$	−14.1519	+	26.9641i	−0.461337	+	0.879005i	0.538012	+	0.842937i	$0.319176\pi$
$941$	−14.1519	+	26.9641i	−0.461337	+	0.879005i	−0.999349	+	0.0360677i	$0.988517\pi$
$942$	−26.5548	−	21.6813i	−0.865201	−	0.706415i
$943$	−0.432949	+	0.415854i	−0.0140988	+	0.0135421i
$944$			6.46846i			0.210530i
$945$	−0.679386	−	0.707316i	−0.0221004	−	0.0230090i
$946$	−2.05757	+	0.686918i	−0.0668974	+	0.0223336i
$947$	−2.91003	−	36.0471i	−0.0945631	−	1.17137i	−0.853815	−	0.520577i	$-0.825717\pi$
$947$	−2.91003	−	36.0471i	−0.0945631	−	1.17137i	0.759251	−	0.650797i	$-0.225565\pi$
$948$	23.2970	−	5.74220i	0.756653	−	0.186498i
$949$	−3.05251	+	14.0657i	−0.0990885	+	0.456592i
$950$	−4.53940	−	1.11886i	−0.147277	−	0.0363006i
$951$	1.21515	−	7.47710i	0.0394039	−	0.242462i
$952$	8.67397	+	10.6237i	0.281125	+	0.344315i
$953$	5.22853	−	3.92899i	0.169369	−	0.127272i	−0.512678	−	0.858581i	$-0.671347\pi$
$953$	5.22853	−	3.92899i	0.169369	−	0.127272i	0.682047	+	0.731309i	$0.261090\pi$
$954$	17.0892	−	19.2897i	0.553284	−	0.624528i
$955$	1.66905	+	10.2701i	0.0540093	+	0.332333i
$956$	−6.56542	+	81.3273i	−0.212341	+	2.63031i
$957$	−0.708545	−	2.87468i	−0.0229040	−	0.0929252i
$958$	0.600327	+	2.07257i	0.0193957	+	0.0669617i
$959$	2.39945	+	11.7533i	0.0774822	+	0.379533i
$960$	−3.87936	+	3.16740i	−0.125206	+	0.102227i
$961$	2.68005	−	22.0722i	0.0864532	−	0.712006i
$962$	−10.4352	+	4.79495i	−0.336443	+	0.154595i
$963$	−0.841186	−	6.92779i	−0.0271068	−	0.223245i
$964$	−63.5923	−	61.0813i	−2.04817	−	1.96729i
$965$	1.75122	−	1.82322i	0.0563739	−	0.0586914i
$966$	−3.49155	+	7.35828i	−0.112339	+	0.236749i
$967$	10.1389	−	6.99836i	0.326044	−	0.225052i	−0.393786	−	0.919202i	$-0.628835\pi$
$967$	10.1389	−	6.99836i	0.326044	−	0.225052i	0.719830	+	0.694150i	$0.244220\pi$
$968$	25.1935	−	39.8404i	0.809750	−	1.28052i
$969$	−0.452357	−	0.601978i	−0.0145318	−	0.0193383i
$970$	1.66440	+	3.17125i	0.0534407	+	0.101823i
$971$	−7.96916	+	39.0355i	−0.255743	+	1.25271i	0.625567	+	0.780171i	$0.284868\pi$
$971$	−7.96916	+	39.0355i	−0.255743	+	1.25271i	−0.881309	+	0.472540i	$0.843337\pi$
$972$	4.00211	−	0.323084i	0.128368	−	0.0103629i
$973$	30.0468	+	8.70315i	0.963255	+	0.279010i
$974$	−59.1256	−	31.0315i	−1.89451	−	0.994313i
$975$	11.1249	−	12.2500i	0.356281	−	0.392313i
$976$	10.8677	−	5.70379i	0.347865	−	0.182574i
$977$	7.39106	−	1.50890i	0.236461	−	0.0482739i	−0.0803335	−	0.996768i	$-0.525599\pi$
$977$	7.39106	−	1.50890i	0.236461	−	0.0482739i	0.316795	+	0.948494i	$0.397393\pi$
$978$	−39.9728	−	30.0376i	−1.27819	−	0.960497i
$979$	0.333361	+	8.27226i	0.0106543	+	0.264383i
$980$	11.2016	−	4.24822i	0.357823	−	0.135704i
$981$	−9.26642	+	2.68405i	−0.295854	+	0.0856951i
$982$	−47.0106	−	9.59728i	−1.50017	−	0.306262i
$983$	26.0986	+	29.4592i	0.832416	+	0.939603i	0.998921	−	0.0464373i	$-0.0147868\pi$
$983$	26.0986	+	29.4592i	0.832416	+	0.939603i	−0.166505	+	0.986041i	$0.553248\pi$
$984$	0.864915	−	1.05933i	0.0275725	−	0.0337701i
$985$	−0.0492283	+	1.22159i	−0.00156854	+	0.0389230i
$986$	3.44728	+	10.3259i	0.109784	+	0.328842i
$987$	4.38665	−	3.88623i	0.139629	−	0.123700i
$988$	−4.54956	+	3.93159i	−0.144741	+	0.125081i
$989$	1.18771	+	1.05222i	0.0377670	+	0.0334586i
$990$	−0.744829	+	1.74818i	−0.0236722	+	0.0555608i
$991$	−21.3898	+	37.0481i	−0.679468	+	1.17687i	0.295673	+	0.955289i	$0.404456\pi$
$991$	−21.3898	+	37.0481i	−0.679468	+	1.17687i	−0.975141	+	0.221584i	$0.928877\pi$
$992$	−0.220603	−	0.382096i	−0.00700416	−	0.0121316i
$993$	−3.29684	+	0.400308i	−0.104622	+	0.0127034i
$994$	−40.1159	−	19.0352i	−1.27240	−	0.603761i
$995$	9.39177	−	5.42234i	0.297739	−	0.171900i
$996$	−42.9188	−	29.6247i	−1.35994	−	0.938695i
$997$	37.4740	−	15.9662i	1.18681	−	0.505655i	0.293881	−	0.955842i	$-0.405053\pi$
$997$	37.4740	−	15.9662i	1.18681	−	0.505655i	0.892934	+	0.450188i	$0.148643\pi$
$998$	−86.1539	−	14.0014i	−2.72716	−	0.443206i
$999$	−0.780171	+	1.03822i	−0.0246835	+	0.0328478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.a.4.13	✓	336
169.127	even	78	inner	507.2.t.a.127.13	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.a.4.13	✓	336	1.1	even	1	trivial
507.2.t.a.127.13	yes	336	169.127	even	78	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(2.45059 + 0.0987553i) q^{2} +(0.278217 - 0.960518i) q^{3} +(4.00211 + 0.323084i) q^{4} +(0.599077 + 0.227200i) q^{5} +(0.776653 - 2.32636i) q^{6} +(0.599988 + 1.40822i) q^{7} +(4.90623 + 0.595725i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(1.44565 + 0.615935i) q^{10} +(-0.646311 - 1.02206i) q^{11} +(1.42379 - 3.75421i) q^{12} +(-3.47529 + 0.960387i) q^{13} +(1.33125 + 3.51023i) q^{14} +(0.384903 - 0.512213i) q^{15} +(4.03805 + 0.656247i) q^{16} +(1.66784 - 0.710598i) q^{17} +(-2.01843 - 1.39322i) q^{18} +(0.359707 - 0.207677i) q^{19} +(2.32417 + 1.10283i) q^{20} +(1.51955 - 0.184507i) q^{21} +(-1.48291 - 2.56847i) q^{22} +(-1.08474 + 1.87883i) q^{23} +(1.93720 - 4.54679i) q^{24} +(-3.43528 - 3.04339i) q^{25} +(-8.61135 + 2.01031i) q^{26} +(-0.748511 + 0.663123i) q^{27} +(1.94624 + 5.82971i) q^{28} +(-0.0985853 + 2.44637i) q^{29} +(0.993822 - 1.21721i) q^{30} +(-1.96330 - 2.21611i) q^{31} +(0.146010 + 0.0298081i) q^{32} +(-1.16152 + 0.336439i) q^{33} +(4.15735 - 1.57668i) q^{34} +(0.0394906 + 0.979950i) q^{35} +(-3.20987 - 2.41206i) q^{36} +(1.27243 - 0.259769i) q^{37} +(0.902003 - 0.473407i) q^{38} +(-0.0444181 + 3.60528i) q^{39} +(2.80386 + 1.47158i) q^{40} +(0.265784 + 0.0769854i) q^{41} +(3.74201 - 0.302087i) q^{42} +(0.146299 - 0.716621i) q^{43} +(-2.25640 - 4.29921i) q^{44} +(-0.384903 - 0.512213i) q^{45} +(-2.84380 + 4.49711i) q^{46} +(3.15089 - 2.17490i) q^{47} +(1.75379 - 3.69604i) q^{48} +(3.22596 - 3.35858i) q^{49} +(-8.11791 - 7.79735i) q^{50} +(-0.218522 - 1.79969i) q^{51} +(-14.2188 + 2.72077i) q^{52} +(-1.26656 + 10.4310i) q^{53} +(-1.89978 + 1.55112i) q^{54} +(-0.154978 - 0.759134i) q^{55} +(2.10477 + 7.26650i) q^{56} +(-0.0994007 - 0.403284i) q^{57} +(-0.483184 + 5.98530i) q^{58} +(0.253632 + 1.56066i) q^{59} +(1.70591 - 1.92558i) q^{60} +(2.39841 - 1.80229i) q^{61} +(-4.59239 - 5.62466i) q^{62} +(0.245543 - 1.51089i) q^{63} +(-7.58943 - 1.87063i) q^{64} +(-2.30017 - 0.214240i) q^{65} +(-2.87964 + 0.709767i) q^{66} +(0.726188 + 8.99545i) q^{67} +(6.90445 - 2.30504i) q^{68} +(1.50285 + 1.56464i) q^{69} +2.40535i q^{70} +(-8.53010 + 8.19327i) q^{71} +(-3.82831 - 3.12571i) q^{72} +(1.85514 - 3.53468i) q^{73} +(3.14386 - 0.510928i) q^{74} +(-3.87899 + 2.45292i) q^{75} +(1.50668 - 0.714931i) q^{76} +(1.05151 - 1.52337i) q^{77} +(-0.464891 + 8.83066i) q^{78} +(3.39473 + 4.91812i) q^{79} +(2.27000 + 1.31059i) q^{80} +(0.428693 + 0.903450i) q^{81} +(0.643725 + 0.214907i) q^{82} +(3.10833 - 12.6110i) q^{83} +(6.14102 - 0.247475i) q^{84} +(1.16061 - 0.0467709i) q^{85} +(0.429289 - 1.74169i) q^{86} +(2.32235 + 0.775315i) q^{87} +(-2.56209 - 5.39949i) q^{88} +(-5.92905 - 3.42314i) q^{89} +(-0.892655 - 1.29323i) q^{90} +(-3.43757 - 4.31777i) q^{91} +(-4.94828 + 7.16882i) q^{92} +(-2.67484 + 1.26923i) q^{93} +(7.93631 - 5.01862i) q^{94} +(0.262676 - 0.0426890i) q^{95} +(0.0692537 - 0.131952i) q^{96} +(1.76546 + 1.44146i) q^{97} +(8.23719 - 7.91193i) q^{98} +1.20927i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31}+ \cdots + 104 q^{98}+O(q^{100}) \) 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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