LMFDB - Embedded newform 507.2.q.b.55.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

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

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			55.2
Character	$\chi$	$=$	507.55
Dual form			507.2.q.b.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.55963 + 1.91020i) q^{2} +(-0.996757 - 0.0804666i) q^{3} +(-0.816373 - 3.99886i) q^{4} +(-0.349402 - 2.87759i) q^{5} +(1.70828 - 1.77851i) q^{6} +(-1.82814 + 1.15605i) q^{7} +(4.54475 + 2.38527i) q^{8} +(0.987050 + 0.160411i) q^{9} +(6.04172 + 3.82055i) q^{10} +(4.50962 - 0.732885i) q^{11} +(0.491951 + 4.05158i) q^{12} +(-2.16339 + 2.88440i) q^{13} +(0.642945 - 5.29513i) q^{14} +(0.116720 + 2.89637i) q^{15} +(-4.13500 + 1.76176i) q^{16} +(-0.232197 + 0.146833i) q^{17} +(-1.84586 + 1.63529i) q^{18} +(-0.941341 + 1.63045i) q^{19} +(-11.2218 + 3.74640i) q^{20} +(1.91523 - 1.00519i) q^{21} +(-5.63340 + 9.75734i) q^{22} +(-4.32649 - 7.49370i) q^{23} +(-4.33808 - 2.74323i) q^{24} +(-3.30371 + 0.814293i) q^{25} +(-2.13569 - 8.63112i) q^{26} +(-0.970942 - 0.239316i) q^{27} +(6.11531 + 6.36671i) q^{28} +(-3.30777 + 4.05129i) q^{29} +(-5.71470 - 4.29432i) q^{30} +(-9.63694 - 2.37529i) q^{31} +(0.227772 - 0.786359i) q^{32} +(-4.55397 + 0.367635i) q^{33} +(0.0816623 - 0.672550i) q^{34} +(3.96538 + 4.85670i) q^{35} +(-0.164339 - 4.07803i) q^{36} +(2.39479 + 8.26776i) q^{37} +(-1.64635 - 4.34106i) q^{38} +(2.38847 - 2.70096i) q^{39} +(5.27587 - 13.9113i) q^{40} +(-0.524990 - 0.0423816i) q^{41} +(-1.06694 + 5.22622i) q^{42} +(-2.04689 + 7.06669i) q^{43} +(-6.61224 - 17.4350i) q^{44} +(0.116720 - 2.89637i) q^{45} +(21.0623 + 3.42295i) q^{46} +(-1.10858 - 0.982114i) q^{47} +(4.26335 - 1.42332i) q^{48} +(-0.995196 + 2.09733i) q^{49} +(3.59712 - 7.58077i) q^{50} +(0.243259 - 0.127672i) q^{51} +(13.3004 + 6.29635i) q^{52} +(-2.79316 - 1.46597i) q^{53} +(1.97146 - 1.48145i) q^{54} +(-3.68461 - 12.7208i) q^{55} +(-11.0659 + 0.893333i) q^{56} +(1.06949 - 1.54942i) q^{57} +(-2.57987 - 12.6370i) q^{58} +(-4.21005 - 1.79373i) q^{59} +(11.4869 - 2.83127i) q^{60} +(0.366050 - 9.08343i) q^{61} +(19.5674 - 14.7040i) q^{62} +(-1.98991 + 0.847820i) q^{63} +(-3.95966 - 5.73655i) q^{64} +(9.05599 + 5.21753i) q^{65} +(6.40027 - 9.27240i) q^{66} +(-1.53361 + 7.51213i) q^{67} +(0.776723 + 0.808654i) q^{68} +(3.70947 + 7.81754i) q^{69} -15.4618 q^{70} +(4.04628 + 8.52736i) q^{71} +(4.10327 + 3.08341i) q^{72} +(-4.50153 + 11.8696i) q^{73} +(-19.5281 - 8.32015i) q^{74} +(3.35852 - 0.545813i) q^{75} +(7.28843 + 2.43324i) q^{76} +(-7.39697 + 6.55314i) q^{77} +(1.43425 + 8.77499i) q^{78} +(-6.34308 - 5.61948i) q^{79} +(6.51439 + 11.2833i) q^{80} +(0.948536 + 0.316668i) q^{81} +(0.899750 - 0.936739i) q^{82} +(-4.70753 - 6.82003i) q^{83} +(-5.58317 - 6.83814i) q^{84} +(0.503654 + 0.616864i) q^{85} +(-10.3064 - 14.9314i) q^{86} +(3.62304 - 3.77198i) q^{87} +(22.2432 + 7.42589i) q^{88} +(7.31393 + 12.6681i) q^{89} +(5.35062 + 4.74024i) q^{90} +(0.620485 - 7.77405i) q^{91} +(-26.4342 + 23.4187i) q^{92} +(9.41456 + 3.14304i) q^{93} +(3.60501 - 0.585872i) q^{94} +(5.02067 + 2.13911i) q^{95} +(-0.290309 + 0.765481i) q^{96} +(1.04640 + 0.786320i) q^{97} +(-2.45419 - 5.17210i) q^{98} +4.56879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{28}{39}\right)$

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 $

$2$	−1.55963	+	1.91020i	−1.10283	+	1.35072i	−0.172069	+	0.985085i	$0.555045\pi$
$2$	−1.55963	+	1.91020i	−1.10283	+	1.35072i	−0.930759	+	0.365634i	$0.880852\pi$
$3$	−0.996757	−	0.0804666i	−0.575478	−	0.0464574i
$3$	−0.996757	−	0.0804666i	−0.575478	−	0.0464574i
$4$	−0.816373	−	3.99886i	−0.408187	−	1.99943i
$5$	−0.349402	−	2.87759i	−0.156257	−	1.28690i	−0.834069	−	0.551660i	$-0.813995\pi$
$5$	−0.349402	−	2.87759i	−0.156257	−	1.28690i	0.677811	−	0.735236i	$-0.262929\pi$
$6$	1.70828	−	1.77851i	0.697404	−	0.726075i
$7$	−1.82814	+	1.15605i	−0.690972	+	0.436944i	−0.833260	−	0.552881i	$-0.813528\pi$
$7$	−1.82814	+	1.15605i	−0.690972	+	0.436944i	0.142288	+	0.989825i	$0.454554\pi$
$8$	4.54475	+	2.38527i	1.60681	+	0.843320i
$9$	0.987050	+	0.160411i	0.329017	+	0.0534704i
$10$	6.04172	+	3.82055i	1.91056	+	1.20816i
$11$	4.50962	−	0.732885i	1.35970	−	0.220973i	0.563557	−	0.826077i	$-0.309433\pi$
$11$	4.50962	−	0.732885i	1.35970	−	0.220973i	0.796146	+	0.605104i	$0.206869\pi$
$12$	0.491951	+	4.05158i	0.142014	+	1.16959i
$13$	−2.16339	+	2.88440i	−0.600016	+	0.799988i
$13$	−2.16339	+	2.88440i	−0.600016	+	0.799988i
$14$	0.642945	−	5.29513i	0.171834	−	1.41518i
$15$	0.116720	+	2.89637i	0.0301369	+	0.747840i
$16$	−4.13500	+	1.76176i	−1.03375	+	0.440440i
$17$	−0.232197	+	0.146833i	−0.0563161	+	0.0356122i	−0.562327	−	0.826915i	$-0.690094\pi$
$17$	−0.232197	+	0.146833i	−0.0563161	+	0.0356122i	0.506011	+	0.862527i	$0.331119\pi$
$18$	−1.84586	+	1.63529i	−0.435072	+	0.385440i
$19$	−0.941341	+	1.63045i	−0.215959	+	0.374051i	−0.953569	−	0.301176i	$-0.902621\pi$
$19$	−0.941341	+	1.63045i	−0.215959	+	0.374051i	0.737610	+	0.675227i	$0.235954\pi$
$20$	−11.2218	+	3.74640i	−2.50928	+	0.837720i
$21$	1.91523	−	1.00519i	0.417938	−	0.219351i
$22$	−5.63340	+	9.75734i	−1.20105	+	2.08027i
$23$	−4.32649	−	7.49370i	−0.902136	−	1.56255i	−0.824716	−	0.565547i	$-0.808665\pi$
$23$	−4.32649	−	7.49370i	−0.902136	−	1.56255i	−0.0774199	−	0.996999i	$-0.524668\pi$
$24$	−4.33808	−	2.74323i	−0.885507	−	0.559960i
$25$	−3.30371	+	0.814293i	−0.660743	+	0.162859i
$26$	−2.13569	−	8.63112i	−0.418844	−	1.69270i
$27$	−0.970942	−	0.239316i	−0.186858	−	0.0460563i
$28$	6.11531	+	6.36671i	1.15568	+	1.20319i
$29$	−3.30777	+	4.05129i	−0.614238	+	0.752305i	−0.984262	−	0.176717i	$-0.943452\pi$
$29$	−3.30777	+	4.05129i	−0.614238	+	0.752305i	0.370024	+	0.929022i	$0.379350\pi$
$30$	−5.71470	−	4.29432i	−1.04336	−	0.784032i
$31$	−9.63694	−	2.37529i	−1.73085	−	0.426615i	−0.756925	−	0.653502i	$-0.773299\pi$
$31$	−9.63694	−	2.37529i	−1.73085	−	0.426615i	−0.973921	+	0.226886i	$0.927145\pi$
$32$	0.227772	−	0.786359i	0.0402647	−	0.139010i
$33$	−4.55397	+	0.367635i	−0.792745	+	0.0639970i
$34$	0.0816623	−	0.672550i	0.0140050	−	0.115341i
$35$	3.96538	+	4.85670i	0.670271	+	0.820933i
$36$	−0.164339	−	4.07803i	−0.0273898	−	0.679672i
$37$	2.39479	+	8.26776i	0.393701	+	1.35921i	0.875622	+	0.482997i	$0.160452\pi$
$37$	2.39479	+	8.26776i	0.393701	+	1.35921i	−0.481921	+	0.876215i	$0.660061\pi$
$38$	−1.64635	−	4.34106i	−0.267073	−	0.704213i
$39$	2.38847	−	2.70096i	0.382462	−	0.432500i
$40$	5.27587	−	13.9113i	0.834189	−	2.19957i
$41$	−0.524990	−	0.0423816i	−0.0819897	−	0.00661889i	0.0394037	−	0.999223i	$-0.487454\pi$
$41$	−0.524990	−	0.0423816i	−0.0819897	−	0.00661889i	−0.121393	+	0.992604i	$0.538736\pi$
$42$	−1.06694	+	5.22622i	−0.164633	+	0.806423i
$43$	−2.04689	+	7.06669i	−0.312148	+	1.07766i	0.639072	+	0.769147i	$0.279319\pi$
$43$	−2.04689	+	7.06669i	−0.312148	+	1.07766i	−0.951220	+	0.308513i	$0.900169\pi$
$44$	−6.61224	−	17.4350i	−0.996833	−	2.62843i
$45$	0.116720	−	2.89637i	0.0173996	−	0.431765i
$46$	21.0623	+	3.42295i	3.10546	+	0.504686i
$47$	−1.10858	−	0.982114i	−0.161703	−	0.143256i	0.578392	−	0.815759i	$-0.303681\pi$
$47$	−1.10858	−	0.982114i	−0.161703	−	0.143256i	−0.740094	+	0.672503i	$0.765219\pi$
$48$	4.26335	−	1.42332i	0.615362	−	0.205438i
$49$	−0.995196	+	2.09733i	−0.142171	+	0.299619i
$50$	3.59712	−	7.58077i	0.508710	−	1.07208i
$51$	0.243259	−	0.127672i	0.0340631	−	0.0178777i
$52$	13.3004	+	6.29635i	1.84444	+	0.873147i
$53$	−2.79316	−	1.46597i	−0.383671	−	0.201366i	0.261850	−	0.965109i	$-0.415667\pi$
$53$	−2.79316	−	1.46597i	−0.383671	−	0.201366i	−0.645521	+	0.763743i	$0.723360\pi$
$54$	1.97146	−	1.48145i	0.268281	−	0.201600i
$55$	−3.68461	−	12.7208i	−0.496833	−	1.71527i
$56$	−11.0659	+	0.893333i	−1.47874	+	0.119377i
$57$	1.06949	−	1.54942i	0.141657	−	0.205225i
$58$	−2.57987	−	12.6370i	−0.338754	−	1.65933i
$59$	−4.21005	−	1.79373i	−0.548101	−	0.233524i	0.100121	−	0.994975i	$-0.468077\pi$
$59$	−4.21005	−	1.79373i	−0.548101	−	0.233524i	−0.648222	+	0.761451i	$0.724487\pi$
$60$	11.4869	−	2.83127i	1.48295	−	0.365515i
$61$	0.366050	−	9.08343i	0.0468678	−	1.16301i	−0.789111	−	0.614251i	$-0.789458\pi$
$61$	0.366050	−	9.08343i	0.0468678	−	1.16301i	0.835978	−	0.548762i	$-0.184901\pi$
$62$	19.5674	−	14.7040i	2.48506	−	1.86740i
$63$	−1.98991	+	0.847820i	−0.250705	+	0.106815i
$64$	−3.95966	−	5.73655i	−0.494957	−	0.717069i
$65$	9.05599	+	5.21753i	1.12326	+	0.647155i
$66$	6.40027	−	9.27240i	0.787819	−	1.14135i
$67$	−1.53361	+	7.51213i	−0.187361	+	0.917753i	0.772011	+	0.635609i	$0.219251\pi$
$67$	−1.53361	+	7.51213i	−0.187361	+	0.917753i	−0.959372	+	0.282144i	$0.908954\pi$
$68$	0.776723	+	0.808654i	0.0941915	+	0.0980637i
$69$	3.70947	+	7.81754i	0.446568	+	0.941122i
$70$	−15.4618			−1.84804
$71$	4.04628	+	8.52736i	0.480206	+	1.01201i	0.988555	+	0.150861i	$0.0482046\pi$
$71$	4.04628	+	8.52736i	0.480206	+	1.01201i	−0.508349	+	0.861151i	$0.669744\pi$
$72$	4.10327	+	3.08341i	0.483575	+	0.363383i
$73$	−4.50153	+	11.8696i	−0.526864	+	1.38923i	0.362482	+	0.931991i	$0.381929\pi$
$73$	−4.50153	+	11.8696i	−0.526864	+	1.38923i	−0.889346	+	0.457235i	$0.848840\pi$
$74$	−19.5281	−	8.32015i	−2.27010	−	0.967198i
$75$	3.35852	−	0.545813i	0.387809	−	0.0630251i
$76$	7.28843	+	2.43324i	0.836041	+	0.279111i
$77$	−7.39697	+	6.55314i	−0.842963	+	0.746800i
$78$	1.43425	+	8.77499i	0.162397	+	0.993571i
$79$	−6.34308	−	5.61948i	−0.713652	−	0.632241i	0.226097	−	0.974105i	$-0.427403\pi$
$79$	−6.34308	−	5.61948i	−0.713652	−	0.632241i	−0.939749	+	0.341864i	$0.888942\pi$
$80$	6.51439	+	11.2833i	0.728331	+	1.26151i
$81$	0.948536	+	0.316668i	0.105393	+	0.0351853i
$82$	0.899750	−	0.936739i	0.0993607	−	0.103445i
$83$	−4.70753	−	6.82003i	−0.516718	−	0.748596i	0.474582	−	0.880211i	$-0.342599\pi$
$83$	−4.70753	−	6.82003i	−0.516718	−	0.748596i	−0.991301	+	0.131615i	$0.957984\pi$
$84$	−5.58317	−	6.83814i	−0.609174	−	0.746102i
$85$	0.503654	+	0.616864i	0.0546289	+	0.0669083i
$86$	−10.3064	−	14.9314i	−1.11137	−	1.61010i
$87$	3.62304	−	3.77198i	0.388431	−	0.404399i
$88$	22.2432	+	7.42589i	2.37114	+	0.791602i
$89$	7.31393	+	12.6681i	0.775275	+	1.34282i	0.934640	+	0.355596i	$0.115722\pi$
$89$	7.31393	+	12.6681i	0.775275	+	1.34282i	−0.159365	+	0.987220i	$0.550945\pi$
$90$	5.35062	+	4.74024i	0.564005	+	0.499665i
$91$	0.620485	−	7.77405i	0.0650445	−	0.814942i
$92$	−26.4342	+	23.4187i	−2.75596	+	2.44157i
$93$	9.41456	+	3.14304i	0.976245	+	0.325918i
$94$	3.60501	−	0.585872i	0.371829	−	0.0604280i
$95$	5.02067	+	2.13911i	0.515110	+	0.219468i
$96$	−0.290309	+	0.765481i	−0.0296295	+	0.0781265i
$97$	1.04640	+	0.786320i	0.106246	+	0.0798387i	0.652538	−	0.757756i	$-0.273704\pi$
$97$	1.04640	+	0.786320i	0.106246	+	0.0798387i	−0.546291	+	0.837595i	$0.683961\pi$
$98$	−2.45419	−	5.17210i	−0.247911	−	0.522461i
$99$	4.56879			0.459181
$100$	5.95331	+	12.5463i	0.595331	+	1.25463i
$101$	4.22391	+	4.39756i	0.420295	+	0.437573i	0.897363	−	0.441293i	$-0.145480\pi$
$101$	4.22391	+	4.39756i	0.420295	+	0.437573i	−0.477068	+	0.878866i	$0.658301\pi$
$102$	−0.135515	+	0.663798i	−0.0134180	+	0.0657258i
$103$	−4.88771	+	7.08107i	−0.481601	+	0.697719i	−0.986186	−	0.165643i	$-0.947030\pi$
$103$	−4.88771	+	7.08107i	−0.481601	+	0.697719i	0.504585	+	0.863362i	$0.331645\pi$
$104$	−16.7121	+	7.94860i	−1.63876	+	0.779424i
$105$	−3.56172	−	5.16004i	−0.347588	−	0.503568i
$106$	7.15661	−	3.04915i	0.695111	−	0.296159i
$107$	−5.64926	+	4.24514i	−0.546134	+	0.410393i	−0.837678	−	0.546164i	$-0.816087\pi$
$107$	−5.64926	+	4.24514i	−0.546134	+	0.410393i	0.291544	+	0.956557i	$0.405831\pi$
$108$	−0.164339	+	4.07803i	−0.0158135	+	0.392409i
$109$	4.83664	−	1.19212i	0.463266	−	0.114185i	−0.000772746	−	1.00000i	$-0.500246\pi$
$109$	4.83664	−	1.19212i	0.463266	−	0.114185i	0.464039	+	0.885815i	$0.346400\pi$
$110$	30.0459	+	12.8014i	2.86477	+	1.22056i
$111$	−1.72174	−	8.43365i	−0.163421	−	0.800487i
$112$	5.52268	−	8.00099i	0.521844	−	0.756022i
$113$	−14.5645	+	1.17577i	−1.37012	+	0.110607i	−0.743508	−	0.668727i	$-0.766840\pi$
$113$	−14.5645	+	1.17577i	−1.37012	+	0.110607i	−0.626609	+	0.779334i	$0.715557\pi$
$114$	1.29170	+	4.45946i	0.120979	+	0.417667i
$115$	−20.0521	+	15.0682i	−1.86987	+	1.40511i
$116$	18.9009	+	9.91996i	1.75490	+	0.921045i
$117$	−2.59806	+	2.50001i	−0.240191	+	0.231126i
$118$	9.99253	−	5.24449i	0.919887	−	0.482794i
$119$	0.254744	−	0.536861i	0.0233523	−	0.0492140i
$120$	−6.37816	+	13.4417i	−0.582244	+	1.22705i
$121$	9.36569	−	3.12673i	0.851426	−	0.284248i
$122$	16.7803	+	14.8660i	1.51922	+	1.34591i
$123$	0.519877	+	0.0844883i	0.0468758	+	0.00761805i
$124$	−1.63112	+	40.4759i	−0.146479	+	3.63485i
$125$	−1.64198	−	4.32955i	−0.146863	−	0.387247i
$126$	1.48402	−	5.12342i	0.132207	−	0.456431i
$127$	2.45696	−	12.0350i	0.218020	−	1.06793i	−0.712495	−	0.701677i	$-0.752435\pi$
$127$	2.45696	−	12.0350i	0.218020	−	1.06793i	0.930515	−	0.366254i	$-0.119360\pi$
$128$	18.7657	+	1.51492i	1.65867	+	0.133901i
$129$	2.60889	−	6.87907i	0.229700	−	0.605668i
$130$	−24.0906	+	9.16137i	−2.11288	+	0.803506i
$131$	2.36666	+	6.24038i	0.206776	+	0.545225i	0.997781	−	0.0665861i	$-0.0212107\pi$
$131$	2.36666	+	6.24038i	0.206776	+	0.545225i	−0.791004	+	0.611811i	$0.790441\pi$
$132$	5.18786	+	17.9106i	0.451545	+	1.55892i
$133$	−0.163972	−	4.06892i	−0.0142182	−	0.352820i
$134$	−11.9578	−	14.6457i	−1.03300	−	1.26520i
$135$	−0.349402	+	2.87759i	−0.0300718	+	0.247663i
$136$	−1.40551	+	0.113465i	−0.120522	+	0.00972953i
$137$	−3.12169	+	10.7773i	−0.266704	+	0.920768i	0.709644	+	0.704561i	$0.248856\pi$
$137$	−3.12169	+	10.7773i	−0.266704	+	0.920768i	−0.976347	+	0.216207i	$0.930631\pi$
$138$	−20.7185	−	5.10666i	−1.76368	−	0.434708i
$139$	−12.8986	−	9.69264i	−1.09404	−	0.822119i	−0.108932	−	0.994049i	$-0.534743\pi$
$139$	−12.8986	−	9.69264i	−1.09404	−	0.822119i	−0.985109	+	0.171930i	$0.945000\pi$
$140$	16.1841	−	19.8219i	1.36780	−	1.67525i
$141$	1.02596	+	1.06813i	0.0864010	+	0.0899530i
$142$	−22.5997	−	5.57033i	−1.89653	−	0.467452i
$143$	−7.64214	+	14.5931i	−0.639068	+	1.22033i
$144$	−4.36406	+	1.07564i	−0.363672	+	0.0896370i
$145$	12.8137	+	8.10287i	1.06412	+	0.672907i
$146$	−15.6525	−	27.1110i	−1.29541	−	2.24372i
$147$	1.16073	−	2.01045i	0.0957357	−	0.165819i
$148$	31.1066	−	16.3260i	2.55695	−	1.34199i
$149$	4.44315	−	1.48334i	0.363997	−	0.121520i	−0.128786	−	0.991672i	$-0.541108\pi$
$149$	4.44315	−	1.48334i	0.363997	−	0.121520i	0.492783	+	0.870152i	$0.335980\pi$
$150$	−4.19545	+	7.26674i	−0.342557	+	0.593327i
$151$	−2.42334	+	2.14689i	−0.197208	+	0.174711i	−0.755948	−	0.654632i	$-0.772824\pi$
$151$	−2.42334	+	2.14689i	−0.197208	+	0.174711i	0.558739	+	0.829343i	$0.311285\pi$
$152$	−8.16723	+	5.16464i	−0.662450	+	0.418908i
$153$	−0.252744	+	0.107684i	−0.0204331	+	0.00870575i
$154$	−0.981281	−	24.3502i	−0.0790739	−	1.96220i
$155$	−3.46794	+	28.5611i	−0.278552	+	2.29408i
$156$	−12.7507	−	7.34617i	−1.02087	−	0.588165i
$157$	−2.12668	−	17.5148i	−0.169728	−	1.39783i	−0.789836	−	0.613318i	$-0.789835\pi$
$157$	−2.12668	−	17.5148i	−0.169728	−	1.39783i	0.620109	−	0.784516i	$-0.287089\pi$
$158$	20.6272	−	3.35225i	1.64102	−	0.266691i
$159$	2.66615	+	1.68597i	0.211439	+	0.133706i
$160$	−2.34240	−	0.380677i	−0.185183	−	0.0300952i
$161$	16.5725	+	8.69791i	1.30610	+	0.685492i
$162$	−2.08427	+	1.31801i	−0.163756	+	0.103553i
$163$	8.07502	−	8.40699i	0.632485	−	0.658486i	−0.325421	−	0.945569i	$-0.605506\pi$
$163$	8.07502	−	8.40699i	0.632485	−	0.658486i	0.957906	+	0.287083i	$0.0926855\pi$
$164$	0.259110	+	2.13396i	0.0202331	+	0.166634i
$165$	2.64907	+	12.9760i	0.206230	+	1.01018i
$166$	20.3697	+	1.64441i	1.58099	+	0.127631i
$167$	2.30124	−	2.81850i	0.178075	−	0.218102i	−0.677853	−	0.735198i	$-0.737089\pi$
$167$	2.30124	−	2.81850i	0.178075	−	0.218102i	0.855928	+	0.517095i	$0.172987\pi$
$168$	11.1019			0.856531
$169$	−3.63949	−	12.4801i	−0.279961	−	0.960011i
$170$	−1.96385			−0.150621
$171$	−1.19069	+	1.45834i	−0.0910547	+	0.111522i
$172$	29.9297	+	2.41618i	2.28212	+	0.184232i
$173$	−2.04821	−	10.0328i	−0.155722	−	0.762778i	−0.980376	−	0.197139i	$-0.936835\pi$
$173$	−2.04821	−	10.0328i	−0.155722	−	0.762778i	0.824653	−	0.565638i	$-0.191370\pi$
$174$	1.55465	+	12.8037i	0.117857	+	0.970643i
$175$	5.09829	−	5.30788i	0.385395	−	0.401238i
$176$	−17.3561	+	10.9754i	−1.30827	+	0.827298i
$177$	4.05206	+	2.12668i	0.304571	+	0.159851i
$178$	−35.6057	−	5.78649i	−2.66876	−	0.433716i
$179$	−21.6508	−	13.6911i	−1.61826	−	1.02332i	−0.963582	−	0.267412i	$-0.913831\pi$
$179$	−21.6508	−	13.6911i	−1.61826	−	1.02332i	−0.654674	−	0.755911i	$-0.727194\pi$
$180$	−11.6775	+	1.89777i	−0.870387	+	0.141452i
$181$	−0.221761	−	1.82637i	−0.0164834	−	0.135753i	0.982144	−	0.188131i	$-0.0602429\pi$
$181$	−0.221761	−	1.82637i	−0.0164834	−	0.135753i	−0.998627	+	0.0523782i	$0.983320\pi$
$182$	13.8823	+	13.3099i	1.02903	+	0.986598i
$183$	−1.09577	+	9.02452i	−0.0810020	+	0.667111i
$184$	−1.78833	−	44.3769i	−0.131837	−	3.27151i
$185$	22.9545	−	9.77998i	1.68765	−	0.719039i
$186$	−20.6871	+	13.0817i	−1.51685	+	0.959200i
$187$	−0.939511	+	0.832334i	−0.0687038	+	0.0608663i
$188$	−3.02232	+	5.23482i	−0.220426	+	0.381788i
$189$	2.05168	−	0.684950i	0.149237	−	0.0498228i
$190$	−11.9165	+	6.25429i	−0.864517	+	0.453734i
$191$	11.4957	−	19.9112i	0.831803	−	1.44072i	−0.0648048	−	0.997898i	$-0.520642\pi$
$191$	11.4957	−	19.9112i	0.831803	−	1.44072i	0.896607	−	0.442826i	$-0.146024\pi$
$192$	3.48522	+	6.03657i	0.251524	+	0.435652i
$193$	17.1180	+	10.8248i	1.23218	+	0.779186i	0.981976	−	0.189006i	$-0.0605267\pi$
$193$	17.1180	+	10.8248i	1.23218	+	0.779186i	0.250208	+	0.968192i	$0.419501\pi$
$194$	−3.13404	+	0.772471i	−0.225011	+	0.0554602i
$195$	−8.60679	−	5.92931i	−0.616345	−	0.424607i
$196$	9.19939	+	2.26744i	0.657099	+	0.161960i
$197$	7.51329	+	7.82216i	0.535300	+	0.557306i	0.932846	−	0.360276i	$-0.117318\pi$
$197$	7.51329	+	7.82216i	0.535300	+	0.557306i	−0.397546	+	0.917582i	$0.630138\pi$
$198$	−7.12564	+	8.72732i	−0.506397	+	0.620224i
$199$	16.4288	+	12.3454i	1.16460	+	0.875143i	0.993911	−	0.110181i	$-0.0351432\pi$
$199$	16.4288	+	12.3454i	1.16460	+	0.875143i	0.170692	+	0.985324i	$0.445400\pi$
$200$	−16.9569	−	4.17949i	−1.19903	−	0.295535i
$201$	2.13312	−	7.36437i	0.150458	−	0.519442i
$202$	−14.9880	+	1.20996i	−1.05455	+	0.0851322i
$203$	1.36360	−	11.2302i	0.0957059	−	0.788209i
$204$	−0.709135	−	0.868532i	−0.0496494	−	0.0608094i
$205$	0.0614760	+	1.52551i	0.00429367	+	0.106546i
$206$	−5.90326	−	20.3804i	−0.411300	−	1.41997i
$207$	−3.06839	−	8.09068i	−0.213268	−	0.562341i
$208$	3.86401	−	15.7384i	0.267921	−	1.09126i
$209$	−3.05016	+	8.04262i	−0.210984	+	0.556319i
$210$	15.4117	+	1.24416i	1.06351	+	0.0858553i
$211$	−2.57955	+	12.6355i	−0.177584	+	0.869863i	0.789174	+	0.614169i	$0.210509\pi$
$211$	−2.57955	+	12.6355i	−0.177584	+	0.869863i	−0.966758	+	0.255693i	$0.917696\pi$
$212$	−3.58193	+	12.3663i	−0.246008	+	0.849318i
$213$	−3.34700	−	8.82530i	−0.229332	−	0.604700i
$214$	0.701684	−	17.4121i	0.0479661	−	1.19027i
$215$	21.0502	+	3.42099i	1.43561	+	0.233310i
$216$	−3.84186	−	3.40359i	−0.261405	−	0.231585i
$217$	20.3636	−	6.79838i	1.38237	−	0.461504i
$218$	−5.26619	+	11.0983i	−0.356671	+	0.751668i
$219$	5.44203	−	11.4688i	0.367738	−	0.774992i
$220$	−47.8605	+	25.1191i	−3.22676	+	1.69353i
$221$	0.0788096	−	0.987405i	0.00530131	−	0.0664201i
$222$	18.7953	+	9.86453i	1.26146	+	0.662064i
$223$	−19.4356	+	14.6049i	−1.30150	+	0.978017i	−0.301808	+	0.953369i	$0.597590\pi$
$223$	−19.4356	+	14.6049i	−1.30150	+	0.978017i	−0.999696	+	0.0246486i	$0.992153\pi$
$224$	0.492668	+	1.70089i	0.0329178	+	0.113645i
$225$	−3.39155	+	0.273795i	−0.226104	+	0.0182530i
$226$	20.4694	−	29.6550i	1.36160	−	1.97262i
$227$	−3.19743	−	15.6620i	−0.212221	−	1.03953i	−0.936674	−	0.350203i	$-0.886113\pi$
$227$	−3.19743	−	15.6620i	−0.212221	−	1.03953i	0.724453	−	0.689324i	$-0.242092\pi$
$228$	−7.06900	−	3.01182i	−0.468156	−	0.199463i
$229$	8.75603	−	2.15817i	0.578615	−	0.142616i	0.0608624	−	0.998146i	$-0.480615\pi$
$229$	8.75603	−	2.15817i	0.578615	−	0.142616i	0.517753	+	0.855530i	$0.326769\pi$
$230$	2.49063	−	61.8045i	0.164228	−	4.07527i
$231$	7.90029	−	5.93669i	0.519801	−	0.390605i
$232$	−24.6964	+	10.5222i	−1.62140	+	0.690813i
$233$	−1.62530	−	2.35466i	−0.106477	−	0.154259i	0.766123	−	0.642694i	$-0.222183\pi$
$233$	−1.62530	−	2.35466i	−0.106477	−	0.154259i	−0.872600	+	0.488435i	$0.837568\pi$
$234$	−0.723506	−	8.86194i	−0.0472971	−	0.579323i
$235$	−2.43878	+	3.53318i	−0.159088	+	0.230479i
$236$	−3.73592	+	18.2997i	−0.243188	+	1.19121i
$237$	5.87033	+	6.11166i	0.381319	+	0.396995i
$238$	0.628208	+	1.32392i	0.0407207	+	0.0858170i
$239$	4.03838			0.261221			0.130611	−	0.991434i	$-0.458306\pi$
$239$	4.03838			0.261221			0.130611	+	0.991434i	$0.458306\pi$
$240$	−5.58534	−	11.7709i	−0.360532	−	0.759806i
$241$	10.7656	+	8.08984i	0.693474	+	0.521112i	0.888034	−	0.459779i	$-0.152071\pi$
$241$	10.7656	+	8.08984i	0.693474	+	0.521112i	−0.194559	+	0.980891i	$0.562328\pi$
$242$	−8.63436	+	22.7669i	−0.555038	+	1.46351i
$243$	−0.919979	−	0.391967i	−0.0590167	−	0.0251447i
$244$	−36.6222	+	5.95168i	−2.34450	+	0.381018i
$245$	6.38298	+	2.13095i	0.407793	+	0.136141i
$246$	−0.972208	+	0.861301i	−0.0619857	+	0.0549146i
$247$	−2.66638	−	6.24250i	−0.169658	−	0.397201i
$248$	−38.1318	−	33.7818i	−2.42137	−	2.14515i
$249$	4.14348	+	7.17672i	0.262582	+	0.454806i
$250$	10.8312	+	3.61599i	0.685026	+	0.228695i
$251$	−9.51755	+	9.90882i	−0.600742	+	0.625439i	−0.950248	−	0.311495i	$-0.899170\pi$
$251$	−9.51755	+	9.90882i	−0.600742	+	0.625439i	0.349505	+	0.936934i	$0.386350\pi$
$252$	5.01482	+	7.26522i	0.315904	+	0.457666i
$253$	−25.0029	−	30.6230i	−1.57192	−	1.92525i
$254$	19.1573	+	23.4634i	1.20204	+	1.47223i
$255$	−0.452384	−	0.655391i	−0.0283294	−	0.0410422i
$256$	−22.5042	+	23.4294i	−1.40651	+	1.46433i
$257$	−7.30541	−	2.43891i	−0.455699	−	0.152135i	0.0795465	−	0.996831i	$-0.474653\pi$
$257$	−7.30541	−	2.43891i	−0.455699	−	0.152135i	−0.535246	+	0.844696i	$0.679781\pi$
$258$	9.07152	+	15.7123i	0.564768	+	0.978208i
$259$	−13.9359	−	12.3461i	−0.865935	−	0.767152i
$260$	13.4711	−	40.4731i	0.835442	−	2.51004i
$261$	−3.91481	+	3.46822i	−0.242321	+	0.214677i
$262$	−15.6115	−	5.21190i	−0.964484	−	0.321992i
$263$	14.4701	−	2.35163i	0.892267	−	0.145007i	0.303043	−	0.952977i	$-0.401998\pi$
$263$	14.4701	−	2.35163i	0.892267	−	0.145007i	0.589224	+	0.807970i	$0.299433\pi$
$264$	−21.5736	−	9.19164i	−1.32776	−	0.565707i
$265$	−3.24251	+	8.54979i	−0.199186	+	0.525209i
$266$	8.02822	+	6.03281i	0.492242	+	0.369895i
$267$	−6.27086	−	13.2155i	−0.383770	−	0.808778i
$268$	31.2920			1.91146
$269$	−10.4124	−	21.9437i	−0.634857	−	1.33793i	−0.924641	−	0.380840i	$-0.875635\pi$
$269$	−10.4124	−	21.9437i	−0.634857	−	1.33793i	0.289784	−	0.957092i	$-0.406416\pi$
$270$	−4.95184	−	5.15541i	−0.301359	−	0.313748i
$271$	−1.96377	+	9.61920i	−0.119291	+	0.584325i	0.875572	+	0.483088i	$0.160485\pi$
$271$	−1.96377	+	9.61920i	−0.119291	+	0.584325i	−0.994862	+	0.101236i	$0.967720\pi$
$272$	0.701452	−	1.01623i	0.0425318	−	0.0616179i
$273$	−1.24402	+	7.69892i	−0.0752918	+	0.465960i
$274$	−15.7182	−	22.7717i	−0.949571	−	1.37569i
$275$	−14.3017	+	6.09340i	−0.862427	+	0.367446i
$276$	28.2330	−	21.2157i	1.69942	−	1.27703i
$277$	0.509422	−	12.6412i	0.0306082	−	0.759534i	−0.908901	−	0.417011i	$-0.863078\pi$
$277$	0.509422	−	12.6412i	0.0306082	−	0.759534i	0.939509	−	0.342523i	$-0.111281\pi$
$278$	38.6320	−	9.52192i	2.31699	−	0.571087i
$279$	−9.13112	−	3.89041i	−0.546666	−	0.232913i
$280$	6.43710	+	31.5310i	0.384690	+	1.88434i
$281$	−7.82896	+	11.3422i	−0.467037	+	0.676619i	−0.983751	−	0.179539i	$-0.942540\pi$
$281$	−7.82896	+	11.3422i	−0.467037	+	0.676619i	0.516714	+	0.856158i	$0.327155\pi$
$282$	−3.64047	+	0.293889i	−0.216787	+	0.0175008i
$283$	6.03738	+	20.8435i	0.358885	+	1.23901i	0.913476	+	0.406892i	$0.133387\pi$
$283$	6.03738	+	20.8435i	0.358885	+	1.23901i	−0.554591	+	0.832123i	$0.687125\pi$
$284$	30.7965	−	23.1420i	1.82743	−	1.37323i
$285$	−4.83226	−	2.53617i	−0.286239	−	0.150230i
$286$	−15.9568	−	37.3579i	−0.943545	−	2.20902i
$287$	1.00875	−	0.529433i	0.0595446	−	0.0312514i
$288$	0.350963	−	0.739638i	0.0206807	−	0.0435836i
$289$	−7.25542	+	15.2905i	−0.426789	+	0.899439i
$290$	−35.4628	+	11.8392i	−2.08245	+	0.695223i
$291$	−0.979737	−	0.867971i	−0.0574332	−	0.0508814i
$292$	51.1396	+	8.31099i	2.99272	+	0.486364i
$293$	0.617380	−	15.3201i	0.0360677	−	0.895011i	−0.875340	−	0.483507i	$-0.839363\pi$
$293$	0.617380	−	15.3201i	0.0360677	−	0.895011i	0.911408	−	0.411504i	$-0.134996\pi$
$294$	2.03005	+	5.35281i	0.118395	+	0.312182i
$295$	−3.69062	+	12.7415i	−0.214876	+	0.741839i
$296$	−8.83713	+	43.2871i	−0.513648	+	2.51601i
$297$	−4.55397	−	0.367635i	−0.264248	−	0.0213323i
$298$	−4.09620	+	10.8008i	−0.237287	+	0.625673i
$299$	30.9747	+	3.73249i	1.79131	+	0.215855i
$300$	−4.92444	−	12.9847i	−0.284313	−	0.749671i
$301$	−4.42741	−	15.2852i	−0.255192	−	0.881024i
$302$	−0.321480	−	7.97743i	−0.0184991	−	0.459050i
$303$	−3.85636	−	4.72318i	−0.221542	−	0.271340i
$304$	1.01999	−	8.40033i	0.0585002	−	0.481792i
$305$	−26.2662	+	2.12043i	−1.50400	+	0.121415i
$306$	0.188489	−	0.650741i	0.0107752	−	0.0372004i
$307$	−17.7151	−	4.36637i	−1.01105	−	0.249202i	−0.301206	−	0.953559i	$-0.597389\pi$
$307$	−17.7151	−	4.36637i	−1.01105	−	0.249202i	−0.709846	+	0.704357i	$0.751235\pi$
$308$	32.2438	+	24.2296i	1.83726	+	1.38061i
$309$	5.44165	−	6.66482i	0.309565	−	0.379148i
$310$	−49.1488	−	51.1693i	−2.79146	−	2.90622i
$311$	−7.76364	−	1.91356i	−0.440235	−	0.108508i	0.0129670	−	0.999916i	$-0.495872\pi$
$311$	−7.76364	−	1.91356i	−0.440235	−	0.108508i	−0.453202	+	0.891408i	$0.649719\pi$
$312$	17.2975	−	6.57805i	0.979280	−	0.372409i
$313$	28.7726	−	7.09180i	1.62632	−	0.400852i	0.682389	−	0.730989i	$-0.260941\pi$
$313$	28.7726	−	7.09180i	1.62632	−	0.400852i	0.943933	+	0.330136i	$0.107095\pi$
$314$	36.7737	+	23.2543i	2.07526	+	1.31232i
$315$	3.13496	+	5.42990i	0.176635	+	0.305940i
$316$	−17.2932	+	29.9527i	−0.972818	+	1.68497i
$317$	−20.6228	+	10.8237i	−1.15829	+	0.607919i	−0.930681	−	0.365832i	$-0.880784\pi$
$317$	−20.6228	+	10.8237i	−1.15829	+	0.607919i	−0.227613	+	0.973752i	$0.573092\pi$
$318$	−7.37876	+	2.46339i	−0.413780	+	0.138140i
$319$	−11.9477	+	20.6940i	−0.668942	+	1.15864i
$320$	−15.1239	+	13.3986i	−0.845453	+	0.749006i
$321$	5.97253	−	3.77680i	0.333354	−	0.210800i
$322$	−42.4618	+	18.0913i	−2.36630	+	1.00819i
$323$	−0.0208266	−	0.516806i	−0.00115882	−	0.0287559i
$324$	0.491951	−	4.05158i	0.0273306	−	0.225088i
$325$	4.79848	−	11.2909i	0.266172	−	0.626304i
$326$	3.46499	+	28.5368i	0.191908	+	1.58051i
$327$	−4.91688	+	0.799071i	−0.271904	+	0.0441887i
$328$	−2.28486	−	1.44486i	−0.126160	−	0.0797788i
$329$	3.16200	+	0.513875i	0.174327	+	0.0283309i
$330$	−28.9184	−	15.1775i	−1.59191	−	0.835497i
$331$	11.7646	−	7.43949i	0.646642	−	0.408911i	−0.170492	−	0.985359i	$-0.554536\pi$
$331$	11.7646	−	7.43949i	0.646642	−	0.408911i	0.817134	+	0.576448i	$0.195561\pi$
$332$	−23.4293	+	24.3924i	−1.28585	+	1.33871i
$333$	1.03753	+	8.54485i	0.0568564	+	0.468255i
$334$	1.79483	+	8.79166i	0.0982088	+	0.481058i
$335$	22.1527	+	1.78835i	1.21033	+	0.0977079i
$336$	−6.14859	+	7.53065i	−0.335433	+	0.410831i
$337$	30.5890			1.66629			0.833145	−	0.553054i	$-0.186538\pi$
$337$	30.5890			1.66629			0.833145	+	0.553054i	$0.186538\pi$
$338$	29.5159	+	12.5123i	1.60545	+	0.680579i
$339$	14.6119			0.793611
$340$	2.05558	−	2.51763i	0.111480	−	0.136538i
$341$	−45.1998	−	3.64891i	−2.44771	−	0.197599i
$342$	−0.928673	−	4.54894i	−0.0502169	−	0.245978i
$343$	−2.43029	−	20.0153i	−0.131223	−	1.08072i
$344$	−26.1586	+	27.2340i	−1.41038	+	1.46836i
$345$	21.1996	−	13.4058i	1.14135	−	0.721743i
$346$	22.3591	+	11.7350i	1.20203	+	0.630876i
$347$	−5.55033	−	0.902016i	−0.297957	−	0.0484228i	0.00959493	−	0.999954i	$-0.496946\pi$
$347$	−5.55033	−	0.902016i	−0.297957	−	0.0484228i	−0.307552	+	0.951531i	$0.599510\pi$
$348$	−18.0414	−	11.4087i	−0.967120	−	0.611570i
$349$	−27.1046	+	4.40493i	−1.45088	+	0.235790i	−0.834215	−	0.551439i	$-0.814079\pi$
$349$	−27.1046	+	4.40493i	−1.45088	+	0.235790i	−0.616661	+	0.787229i	$0.711515\pi$
$350$	2.18768	+	18.0171i	0.116936	+	0.963056i
$351$	2.79081	−	2.28285i	0.148962	−	0.121849i
$352$	0.450853	−	3.71311i	0.0240306	−	0.197910i
$353$	−1.33232	−	33.0612i	−0.0709122	−	1.75967i	−0.509028	−	0.860750i	$-0.669995\pi$
$353$	−1.33232	−	33.0612i	−0.0709122	−	1.75967i	0.438116	−	0.898918i	$-0.355646\pi$
$354$	−10.3821	+	4.42341i	−0.551804	+	0.235102i
$355$	23.1244	−	14.6230i	1.22732	−	0.776109i
$356$	44.6871	−	39.5893i	2.36841	−	2.09823i
$357$	−0.297117	+	0.514622i	−0.0157251	+	0.0272367i
$358$	59.9202	−	20.0043i	3.16688	−	1.05726i
$359$	−0.714596	+	0.375049i	−0.0377149	+	0.0197943i	−0.483475	−	0.875358i	$-0.660626\pi$
$359$	−0.714596	+	0.375049i	−0.0377149	+	0.0197943i	0.445760	+	0.895152i	$0.352933\pi$
$360$	7.43909	−	12.8849i	0.392074	−	0.679093i
$361$	7.72775	+	13.3849i	0.406724	+	0.704466i
$362$	3.83460	+	2.42485i	0.201542	+	0.127447i
$363$	−9.58692	+	2.36296i	−0.503183	+	0.124023i
$364$	−31.5939	+	3.86530i	−1.65597	+	0.202597i
$365$	35.7285	+	8.80629i	1.87012	+	0.460942i
$366$	−15.5297	−	16.1681i	−0.811749	−	0.845120i
$367$	−7.75429	+	9.49729i	−0.404771	+	0.495754i	−0.936259	−	0.351312i	$-0.885736\pi$
$367$	−7.75429	+	9.49729i	−0.404771	+	0.495754i	0.531488	+	0.847066i	$0.321633\pi$
$368$	31.0921	+	23.3642i	1.62079	+	1.21794i
$369$	−0.511393	−	0.126047i	−0.0266221	−	0.00656175i
$370$	−17.1188	+	59.1009i	−0.889964	+	3.07251i
$371$	6.80102	−	0.549035i	0.353091	−	0.0285045i
$372$	4.88279	−	40.2134i	0.253161	−	2.08497i
$373$	10.6323	+	13.0222i	0.550521	+	0.674266i	0.972652	−	0.232269i	$-0.0746150\pi$
$373$	10.6323	+	13.0222i	0.550521	+	0.674266i	−0.422130	+	0.906535i	$0.638718\pi$
$374$	−0.124635	−	3.09280i	−0.00644474	−	0.159925i
$375$	1.28827	+	4.44763i	0.0665261	+	0.229675i
$376$	−2.69560	−	7.10772i	−0.139015	−	0.366552i
$377$	−4.52951	−	18.3054i	−0.233282	−	0.942778i
$378$	−1.89147	+	4.98739i	−0.0972867	+	0.256524i
$379$	13.9183	+	1.12360i	0.714933	+	0.0577154i	0.432581	−	0.901595i	$-0.357603\pi$
$379$	13.9183	+	1.12360i	0.714933	+	0.0577154i	0.282353	+	0.959311i	$0.408885\pi$
$380$	4.45525	−	21.8233i	0.228550	−	1.11951i
$381$	−3.41740	+	11.7982i	−0.175079	+	0.604442i
$382$	20.1053	+	53.0134i	1.02868	+	2.71240i
$383$	0.842022	−	20.8946i	0.0430253	−	1.06766i	−0.823119	−	0.567868i	$-0.807768\pi$
$383$	0.842022	−	20.8946i	0.0430253	−	1.06766i	0.866145	−	0.499793i	$-0.166591\pi$
$384$	−18.5829	−	3.02002i	−0.948305	−	0.154115i
$385$	21.4418	+	18.9957i	1.09277	+	0.968113i
$386$	−47.3755	+	15.8163i	−2.41135	+	0.805026i
$387$	−3.15396	+	6.64683i	−0.160325	+	0.337878i
$388$	2.29013	−	4.82635i	0.116264	−	0.245021i
$389$	10.2894	−	5.40031i	0.521695	−	0.273807i	−0.183253	−	0.983066i	$-0.558663\pi$
$389$	10.2894	−	5.40031i	0.521695	−	0.273807i	0.704948	+	0.709259i	$0.250970\pi$
$390$	24.7497	−	7.19318i	1.25325	−	0.364241i
$391$	2.10492	+	1.10475i	0.106450	+	0.0558695i
$392$	−9.52562	+	7.15804i	−0.481116	+	0.361535i
$393$	−1.85685	−	6.41058i	−0.0936656	−	0.323371i
$394$	−26.6599	+	2.15221i	−1.34311	+	0.108427i
$395$	−13.9543	+	20.2162i	−0.702115	+	1.01719i
$396$	−3.72984	−	18.2699i	−0.187431	−	0.918099i
$397$	6.48174	+	2.76161i	0.325309	+	0.138601i	0.548446	−	0.836186i	$-0.315220\pi$
$397$	6.48174	+	2.76161i	0.325309	+	0.138601i	−0.223137	+	0.974787i	$0.571630\pi$
$398$	−49.2051	+	12.1280i	−2.46643	+	0.607920i
$399$	−0.163972	+	4.06892i	−0.00820887	+	0.203701i
$400$	12.2263	−	9.18745i	0.611314	−	0.459372i
$401$	−8.17565	+	3.48332i	−0.408272	+	0.173949i	−0.586332	−	0.810071i	$-0.699428\pi$
$401$	−8.17565	+	3.48332i	−0.408272	+	0.173949i	0.178059	+	0.984020i	$0.443018\pi$
$402$	10.7406	+	15.5604i	0.535691	+	0.776083i
$403$	27.6998	−	22.6581i	1.37982	−	1.12868i
$404$	14.1369	−	20.4809i	0.703339	−	1.01896i
$405$	0.579819	−	2.84014i	0.0288114	−	0.141128i
$406$	19.3254	+	20.1198i	0.959102	+	0.998530i
$407$	16.8589	+	35.5294i	0.835665	+	1.76113i
$408$	1.41009			0.0698097
$409$	−4.95339	−	10.4390i	−0.244929	−	0.516177i	0.743337	−	0.668917i	$-0.233242\pi$
$409$	−4.95339	−	10.4390i	−0.244929	−	0.516177i	−0.988266	+	0.152739i	$0.951190\pi$
$410$	−3.00992	−	2.26181i	−0.148649	−	0.111703i
$411$	3.97878	−	10.4912i	0.196259	−	0.517492i
$412$	32.3064	+	13.7645i	1.59162	+	0.678127i
$413$	9.77019	−	1.58781i	0.480760	−	0.0781310i
$414$	20.2404	+	6.75725i	0.994763	+	0.332101i
$415$	−17.9804	+	15.9293i	−0.882624	+	0.781937i
$416$	1.77541	+	2.35818i	0.0870467	+	0.115619i
$417$	12.0768	+	10.6991i	0.591403	+	0.523938i
$418$	−10.6059	−	18.3700i	−0.518752	−	0.898505i
$419$	−9.48559	−	3.16676i	−0.463401	−	0.154706i	0.0753744	−	0.997155i	$-0.475985\pi$
$419$	−9.48559	−	3.16676i	−0.463401	−	0.154706i	−0.538776	+	0.842449i	$0.681113\pi$
$420$	−17.7266	+	18.4553i	−0.864968	+	0.900527i
$421$	−3.47920	−	5.04048i	−0.169566	−	0.245658i	0.728983	−	0.684531i	$-0.239993\pi$
$421$	−3.47920	−	5.04048i	−0.169566	−	0.245658i	−0.898549	+	0.438873i	$0.855378\pi$
$422$	−20.1132	−	24.6342i	−0.979096	−	1.19917i
$423$	−0.936679	−	1.14722i	−0.0455429	−	0.0557799i
$424$	−9.19751	−	13.3249i	−0.446671	−	0.647114i
$425$	0.647549	−	0.674170i	0.0314107	−	0.0327020i
$426$	22.0782	+	7.37080i	1.06969	+	0.357116i
$427$	9.83166	+	17.0289i	0.475787	+	0.824088i
$428$	21.5876	+	19.1250i	1.04348	+	0.924440i
$429$	8.79162	−	13.9308i	0.424463	−	0.672586i
$430$	−39.3654	+	34.8747i	−1.89837	+	1.68181i
$431$	−12.9436	−	4.32120i	−0.623470	−	0.208145i	−0.0126571	−	0.999920i	$-0.504029\pi$
$431$	−12.9436	−	4.32120i	−0.623470	−	0.208145i	−0.610813	+	0.791775i	$0.709157\pi$
$432$	4.43646	−	0.720995i	0.213449	−	0.0346889i
$433$	−33.0411	−	14.0775i	−1.58785	−	0.676521i	−0.595893	−	0.803064i	$-0.703202\pi$
$433$	−33.0411	−	14.0775i	−1.58785	−	0.676521i	−0.991961	+	0.126542i	$0.959612\pi$
$434$	−18.7735	+	49.5017i	−0.901157	+	2.37616i
$435$	−12.1201	−	9.10767i	−0.581115	−	0.436679i
$436$	−8.71564	−	18.3678i	−0.417404	−	0.879659i
$437$	16.2908			0.779296
$438$	13.4203	+	28.2826i	0.641245	+	1.35139i
$439$	5.03128	+	5.23812i	0.240130	+	0.250002i	0.830352	−	0.557239i	$-0.188139\pi$
$439$	5.03128	+	5.23812i	0.240130	+	0.250002i	−0.590222	+	0.807241i	$0.700960\pi$
$440$	13.5968	−	66.6015i	0.648202	−	3.17510i
$441$	−1.31874	+	1.91053i	−0.0627973	+	0.0909777i
$442$	1.76323	+	1.69053i	0.0838684	+	0.0804105i
$443$	5.05329	+	7.32096i	0.240089	+	0.347829i	0.924443	−	0.381321i	$-0.124531\pi$
$443$	5.05329	+	7.32096i	0.240089	+	0.347829i	−0.684353	+	0.729150i	$0.739915\pi$
$444$	−32.3194	+	13.7700i	−1.53381	+	0.653496i
$445$	33.8981	−	25.4727i	1.60692	−	1.20752i
$446$	2.41406	−	59.9043i	0.114309	−	2.83655i
$447$	−4.54810	+	1.12101i	−0.215118	+	0.0530218i
$448$	13.8705	+	5.90967i	0.655320	+	0.279206i
$449$	1.51994	+	7.44518i	0.0717306	+	0.351360i	0.999777	−	0.0211042i	$-0.00671816\pi$
$449$	1.51994	+	7.44518i	0.0717306	+	0.351360i	−0.928047	+	0.372464i	$0.878513\pi$
$450$	4.76658	−	6.90558i	0.224699	−	0.325532i
$451$	−2.39857	+	0.193632i	−0.112944	+	0.00911780i
$452$	16.5918	+	57.2817i	0.780415	+	2.69430i
$453$	2.58823	−	1.94493i	0.121606	−	0.0913808i
$454$	34.9045	+	18.3193i	1.63815	+	0.859768i
$455$	−22.5873	+	0.930772i	−1.05891	+	0.0436353i
$456$	8.55632	−	4.49071i	0.400687	−	0.210297i
$457$	8.60916	−	18.1434i	0.402720	−	0.848714i	−0.596227	−	0.802816i	$-0.703334\pi$
$457$	8.60916	−	18.1434i	0.402720	−	0.848714i	0.998946	−	0.0458974i	$-0.0146147\pi$
$458$	−9.53366	+	20.0918i	−0.445479	+	0.938827i
$459$	0.260589	−	0.0869975i	0.0121633	−	0.00406070i
$460$	76.6255	+	67.8843i	3.57268	+	3.16512i
$461$	4.73217	+	0.769053i	0.220399	+	0.0358184i	0.269608	−	0.962970i	$-0.413106\pi$
$461$	4.73217	+	0.769053i	0.220399	+	0.0358184i	−0.0492088	+	0.998789i	$0.515670\pi$
$462$	−0.981281	+	24.3502i	−0.0456533	+	1.13288i
$463$	6.13193	+	16.1686i	0.284975	+	0.751417i	0.998699	+	0.0509900i	$0.0162377\pi$
$463$	6.13193	+	16.1686i	0.284975	+	0.751417i	−0.713724	+	0.700427i	$0.752993\pi$
$464$	6.54025	−	22.5796i	0.303624	−	1.04823i
$465$	5.75491	−	28.1894i	0.266878	−	1.30725i
$466$	7.03276	+	0.567743i	0.325786	+	0.0263002i
$467$	−3.29505	+	8.68833i	−0.152477	+	0.402048i	−0.989389	−	0.145289i	$-0.953589\pi$
$467$	−3.29505	+	8.68833i	−0.152477	+	0.402048i	0.836913	+	0.547336i	$0.184358\pi$
$468$	12.1182	+	8.34835i	0.560164	+	0.385903i
$469$	−5.88071	−	15.5061i	−0.271546	−	0.716007i
$470$	−2.94550	−	10.1690i	−0.135866	−	0.469062i
$471$	0.710430	+	17.6291i	0.0327349	+	0.812308i
$472$	−14.8551	−	18.1942i	−0.683760	−	0.837454i
$473$	−4.05164	+	33.3683i	−0.186295	+	1.53427i
$474$	−20.8301	+	1.68158i	−0.956758	+	0.0772375i
$475$	1.78226	−	6.15307i	0.0817757	−	0.282322i
$476$	−2.35480	−	0.580406i	−0.107932	−	0.0266028i
$477$	−2.52184	−	1.89504i	−0.115467	−	0.0867678i
$478$	−6.29840	+	7.71413i	−0.288082	+	0.352836i
$479$	−18.3863	−	19.1422i	−0.840093	−	0.874629i	0.153442	−	0.988158i	$-0.450964\pi$
$479$	−18.3863	−	19.1422i	−0.840093	−	0.874629i	−0.993535	+	0.113528i	$0.963785\pi$
$480$	2.30417	+	0.567927i	0.105171	+	0.0259222i
$481$	−29.0284	−	10.9789i	−1.32358	−	0.500594i
$482$	−32.2437	+	7.94735i	−1.46866	+	0.361992i
$483$	−15.8189	−	10.0032i	−0.719783	−	0.455163i
$484$	−20.1492	−	34.8995i	−0.915875	−	1.58634i
$485$	1.89709	−	3.28586i	0.0861424	−	0.149203i
$486$	2.18357	−	1.14602i	0.0990487	−	0.0519847i
$487$	−18.5787	+	6.20249i	−0.841883	+	0.281062i	−0.704719	−	0.709487i	$-0.748927\pi$
$487$	−18.5787	+	6.20249i	−0.841883	+	0.281062i	−0.137164	+	0.990548i	$0.543799\pi$
$488$	23.3300	−	40.4088i	1.05610	−	1.82922i
$489$	−8.72532	+	7.72996i	−0.394573	+	0.349561i
$490$	−14.0257	+	8.86929i	−0.633615	+	0.400674i
$491$	−15.2760	+	6.50849i	−0.689395	+	0.293724i	−0.708111	−	0.706101i	$-0.750452\pi$
$491$	−15.2760	+	6.50849i	−0.689395	+	0.293724i	0.0187160	+	0.999825i	$0.494042\pi$
$492$	−0.0865570	−	2.14789i	−0.00390229	−	0.0968344i
$493$	0.173195	−	1.42639i	0.00780030	−	0.0642412i
$494$	16.0830	+	4.64269i	0.723610	+	0.208885i
$495$	−1.59635	−	13.1471i	−0.0717504	−	0.590918i
$496$	44.0335	−	7.15613i	1.97716	−	0.321320i
$497$	−17.2552	−	10.9115i	−0.774001	−	0.489449i
$498$	−20.1713	−	3.27816i	−0.903898	−	0.146898i
$499$	−21.3644	−	11.2129i	−0.956402	−	0.501958i	−0.0870779	−	0.996202i	$-0.527753\pi$
$499$	−21.3644	−	11.2129i	−0.956402	−	0.501958i	−0.869324	+	0.494243i	$0.835445\pi$
$500$	−15.9728	+	10.1006i	−0.714325	+	0.451712i
$501$	−2.52057	+	2.62419i	−0.112611	+	0.117240i
$502$	−4.08398	−	33.6346i	−0.182277	−	1.50119i
$503$	0.939103	+	4.60003i	0.0418726	+	0.205105i	0.995345	−	0.0963743i	$-0.0307246\pi$
$503$	0.939103	+	4.60003i	0.0418726	+	0.205105i	−0.953473	+	0.301480i	$0.902519\pi$
$504$	−11.0659	−	0.893333i	−0.492915	−	0.0397922i
$505$	11.1785	−	13.6912i	0.497437	−	0.609250i
$506$	97.4915			4.33403
$507$	2.62345	+	12.7325i	0.116512	+	0.565472i
$508$	−50.1320			−2.22425
$509$	−20.0723	+	24.5841i	−0.889687	+	1.08967i	0.105764	+	0.994391i	$0.466271\pi$
$509$	−20.0723	+	24.5841i	−0.889687	+	1.08967i	−0.995451	+	0.0952776i	$0.969626\pi$
$510$	1.95748	+	0.158025i	0.0866789	+	0.00699744i
$511$	−5.49232	−	26.9032i	−0.242966	−	1.19013i
$512$	−5.11793	−	42.1500i	−0.226183	−	1.86278i
$513$	1.30418	−	1.35780i	0.0575810	−	0.0599481i
$514$	16.0526	−	10.1510i	0.708049	−	0.447743i
$515$	22.0842	+	11.5907i	0.973145	+	0.510746i
$516$	−29.6383	−	4.81669i	−1.30475	−	0.212043i
$517$	−5.71904	−	3.61650i	−0.251523	−	0.159054i
$518$	45.3186	−	7.36499i	1.99118	−	0.323599i
$519$	1.23426	+	10.1651i	0.0541780	+	0.446196i
$520$	28.7120	+	45.3133i	1.25911	+	1.98712i
$521$	0.339231	−	2.79382i	0.0148620	−	0.122399i	−0.983390	−	0.181507i	$-0.941902\pi$
$521$	0.339231	−	2.79382i	0.0148620	−	0.122399i	0.998252	+	0.0591077i	$0.0188255\pi$
$522$	−0.519338	−	12.8872i	−0.0227308	−	0.564059i
$523$	−4.83380	+	2.05949i	−0.211367	+	0.0900551i	−0.495055	−	0.868861i	$-0.664852\pi$
$523$	−4.83380	+	2.05949i	−0.211367	+	0.0900551i	0.283688	+	0.958917i	$0.408442\pi$
$524$	23.0223	−	14.5584i	1.00574	−	0.635988i
$525$	−5.50887	+	4.88043i	−0.240427	+	0.212999i
$526$	−18.0760	+	31.3086i	−0.788152	+	1.36512i
$527$	2.58644	−	0.863482i	0.112667	−	0.0376138i
$528$	18.1830	−	9.54317i	0.791313	−	0.415313i
$529$	−25.9371	+	44.9243i	−1.12770	+	1.95323i
$530$	−11.2747	−	19.5284i	−0.489743	−	0.848259i
$531$	−3.86779	−	2.44584i	−0.167848	−	0.106141i
$532$	−16.1372	+	3.97746i	−0.699636	+	0.172445i
$533$	1.25800	−	1.42259i	0.0544902	−	0.0616193i
$534$	35.0246	+	8.63280i	1.51566	+	0.373578i
$535$	14.1896	+	14.7730i	0.613471	+	0.638691i
$536$	−24.8883	+	30.4827i	−1.07501	+	1.31665i
$537$	20.4789	+	15.3889i	0.883730	+	0.664080i
$538$	58.1566	+	14.3343i	2.50731	+	0.617996i
$539$	−2.95086	+	10.1875i	−0.127102	+	0.438808i
$540$	11.7923	−	0.951974i	0.507460	−	0.0409664i
$541$	−0.326046	+	2.68523i	−0.0140178	+	0.115447i	−0.998038	−	0.0626092i	$-0.980058\pi$
$541$	−0.326046	+	2.68523i	−0.0140178	+	0.115447i	0.984020	+	0.178056i	$0.0569809\pi$
$542$	−15.3119	−	18.7536i	−0.657701	−	0.805538i
$543$	0.0740805	+	1.83829i	0.00317910	+	0.0788885i
$544$	0.0625752	+	0.216035i	0.00268289	+	0.00926241i
$545$	−5.12037	−	13.5013i	−0.219333	−	0.578333i
$546$	−12.7663	−	14.3838i	−0.546347	−	0.615571i
$547$	14.6511	−	38.6319i	0.626437	−	1.65178i	−0.125144	−	0.992139i	$-0.539939\pi$
$547$	14.6511	−	38.6319i	0.626437	−	1.65178i	0.751581	−	0.659641i	$-0.229291\pi$
$548$	45.6454	+	3.68488i	1.94988	+	0.157410i
$549$	1.81839	−	8.90708i	0.0776071	−	0.380145i
$550$	10.6658	−	36.8227i	0.454792	−	1.57013i
$551$	−3.49168	−	9.20681i	−0.148751	−	0.392223i
$552$	−1.78833	+	44.3769i	−0.0761162	+	1.88880i
$553$	18.0924	+	2.94030i	0.769367	+	0.125034i
$554$	23.3527	+	20.6887i	0.992162	+	0.878979i
$555$	−23.6670	+	7.90120i	−1.00461	+	0.335387i
$556$	−28.2295	+	59.4923i	−1.19720	+	2.52304i
$557$	−2.93985	+	6.19561i	−0.124566	+	0.262516i	−0.956147	−	0.292886i	$-0.905384\pi$
$557$	−2.93985	+	6.19561i	−0.124566	+	0.262516i	0.831582	+	0.555402i	$0.187436\pi$
$558$	21.6727	−	11.3747i	0.917478	−	0.481530i
$559$	−15.9549	−	21.1921i	−0.674821	−	0.896329i
$560$	−24.9532	−	13.0964i	−1.05446	−	0.553425i
$561$	1.00344	−	0.754036i	0.0423652	−	0.0318354i
$562$	−9.45562	−	32.6446i	−0.398861	−	1.37703i
$563$	25.9878	−	2.09795i	1.09525	−	0.0884181i	0.480393	−	0.877053i	$-0.340494\pi$
$563$	25.9878	−	2.09795i	1.09525	−	0.0884181i	0.614861	+	0.788635i	$0.289212\pi$
$564$	3.43375	−	4.97465i	0.144587	−	0.209470i
$565$	8.47227	+	41.4999i	0.356431	+	1.74591i
$566$	−49.2314	−	20.9755i	−2.06935	−	0.881667i
$567$	−2.10014	+	0.517638i	−0.0881975	+	0.0217387i
$568$	−1.95070	+	48.4062i	−0.0818497	+	2.03108i
$569$	24.7155	−	18.5725i	1.03613	−	0.778601i	0.0605317	−	0.998166i	$-0.480720\pi$
$569$	24.7155	−	18.5725i	1.03613	−	0.778601i	0.975598	+	0.219565i	$0.0704640\pi$
$570$	12.3812	−	5.27512i	0.518590	−	0.220951i
$571$	−7.05167	−	10.2161i	−0.295103	−	0.427531i	0.647185	−	0.762333i	$-0.275946\pi$
$571$	−7.05167	−	10.2161i	−0.295103	−	0.427531i	−0.942289	+	0.334802i	$0.891331\pi$
$572$	64.5945	+	18.6465i	2.70083	+	0.779649i
$573$	−13.0606	+	18.9216i	−0.545616	+	0.790462i
$574$	−0.561955	+	2.75264i	−0.0234556	+	0.114893i
$575$	20.3956	+	21.2340i	0.850554	+	0.885520i
$576$	−2.98817	−	6.29744i	−0.124507	−	0.262393i
$577$	3.72419			0.155040			0.0775200	−	0.996991i	$-0.475300\pi$
$577$	3.72419			0.155040			0.0775200	+	0.996991i	$0.475300\pi$
$578$	−17.8921	−	37.7069i	−0.744215	−	1.56840i
$579$	−16.1915	−	12.1671i	−0.672896	−	0.505648i
$580$	21.9415	−	57.8550i	0.911072	−	2.40230i
$581$	16.4903	+	7.02585i	0.684132	+	0.291481i
$582$	3.18603	−	0.517781i	0.132065	−	0.0214627i
$583$	−13.6705	−	4.56389i	−0.566175	−	0.189017i
$584$	−48.7704	+	43.2068i	−2.01813	+	1.78791i
$585$	8.10177	+	6.60265i	0.334967	+	0.272986i
$586$	28.3017	+	25.0731i	1.16913	+	1.03576i
$587$	−19.8736	−	34.4221i	−0.820272	−	1.42075i	−0.905480	−	0.424389i	$-0.860489\pi$
$587$	−19.8736	−	34.4221i	−0.820272	−	1.42075i	0.0852084	−	0.996363i	$-0.472844\pi$
$588$	−8.98710	−	3.00034i	−0.370622	−	0.123732i
$589$	12.9445	−	13.4766i	0.533367	−	0.555294i
$590$	−18.5829	−	26.9219i	−0.765045	−	1.10836i
$591$	−6.85950	−	8.40137i	−0.282162	−	0.345586i
$592$	−24.4682	−	29.9682i	−1.00564	−	1.23168i
$593$	−5.30187	−	7.68108i	−0.217722	−	0.315424i	0.698870	−	0.715248i	$-0.253686\pi$
$593$	−5.30187	−	7.68108i	−0.217722	−	0.315424i	−0.916592	+	0.399824i	$0.869071\pi$
$594$	7.80479	−	8.12565i	0.320234	−	0.333399i
$595$	−1.63387	−	0.545467i	−0.0669822	−	0.0223620i
$596$	−9.55894	−	16.5566i	−0.391550	−	0.678184i
$597$	−15.3821	−	13.6273i	−0.629547	−	0.557730i
$598$	−55.4390	+	53.3467i	−2.26707	+	2.18151i
$599$	−9.28469	+	8.22552i	−0.379362	+	0.336086i	−0.831159	−	0.556036i	$-0.812322\pi$
$599$	−9.28469	+	8.22552i	−0.379362	+	0.336086i	0.451796	+	0.892121i	$0.350783\pi$
$600$	16.5656	+	5.53040i	0.676287	+	0.225778i
$601$	30.9131	−	5.02387i	1.26097	−	0.204928i	0.507064	−	0.861909i	$-0.330731\pi$
$601$	30.9131	−	5.02387i	1.26097	−	0.204928i	0.753907	+	0.656981i	$0.228167\pi$
$602$	36.1030	+	15.3820i	1.47145	+	0.626925i
$603$	−2.71878	+	7.16884i	−0.110717	+	0.291938i
$604$	10.5635	+	7.93793i	0.429821	+	0.322990i
$605$	−12.2698	−	25.8581i	−0.498839	−	1.05128i
$606$	15.0368			0.610826
$607$	−16.9481	−	35.7173i	−0.687901	−	1.44972i	−0.883209	−	0.468980i	$-0.844622\pi$
$607$	−16.9481	−	35.7173i	−0.687901	−	1.44972i	0.195307	−	0.980742i	$-0.437430\pi$
$608$	1.06771	+	1.11160i	0.0433013	+	0.0450814i
$609$	−2.26284	+	11.0841i	−0.0916948	+	0.449151i
$610$	36.9153	−	53.4810i	1.49466	−	2.16538i
$611$	5.23109	−	1.07288i	0.211627	−	0.0434041i
$612$	0.636947	+	0.922778i	0.0257471	+	0.0373011i
$613$	−17.2074	+	7.33139i	−0.695000	+	0.296112i	−0.710429	−	0.703769i	$-0.751499\pi$
$613$	−17.2074	+	7.33139i	−0.695000	+	0.296112i	0.0154285	+	0.999881i	$0.495089\pi$
$614$	35.9697	−	27.0295i	1.45162	−	1.09082i
$615$	0.0614760	−	1.52551i	0.00247895	−	0.0615146i
$616$	−49.2484	+	12.1386i	−1.98427	+	0.489080i
$617$	24.4312	+	10.4092i	0.983565	+	0.419058i	0.823046	−	0.567975i	$-0.192273\pi$
$617$	24.4312	+	10.4092i	0.983565	+	0.419058i	0.160519	+	0.987033i	$0.448683\pi$
$618$	4.24418	+	20.7893i	0.170726	+	0.836270i
$619$	14.6674	−	21.2495i	0.589534	−	0.854088i	−0.408750	−	0.912647i	$-0.634035\pi$
$619$	14.6674	−	21.2495i	0.589534	−	0.854088i	0.998284	+	0.0585585i	$0.0186504\pi$
$620$	117.043	−	9.44868i	4.70056	−	0.379468i
$621$	2.40741	+	8.31135i	0.0966061	+	0.333523i
$622$	15.7637	−	11.8457i	0.632068	−	0.474968i
$623$	−28.0158	−	14.7038i	−1.12243	−	0.589096i
$624$	−5.11789	+	15.3764i	−0.204879	+	0.615548i
$625$	−26.9492	+	14.1440i	−1.07797	+	0.565760i
$626$	−31.3279	+	66.0221i	−1.25211	+	2.63878i
$627$	3.68743	−	7.77110i	0.147262	−	0.310348i
$628$	−68.3031	+	22.8029i	−2.72559	+	0.909936i
$629$	−1.77004	−	1.56812i	−0.0705761	−	0.0625250i
$630$	−15.2616	−	2.48025i	−0.608037	−	0.0988156i
$631$	−0.253469	+	6.28976i	−0.0100904	+	0.250391i	0.986269	+	0.165144i	$0.0528090\pi$
$631$	−0.253469	+	6.28976i	−0.0100904	+	0.250391i	−0.996360	+	0.0852470i	$0.972832\pi$
$632$	−15.4237	−	40.6691i	−0.613524	−	1.61773i
$633$	3.58792	−	12.3869i	0.142607	−	0.492337i
$634$	11.4886	−	56.2748i	0.456270	−	2.23496i
$635$	−35.4901	−	2.86506i	−1.40838	−	0.113696i
$636$	4.56538	−	12.0379i	0.181029	−	0.477335i
$637$	−3.89654	−	7.40789i	−0.154386	−	0.293511i
$638$	−20.8958	−	55.0976i	−0.827271	−	2.18133i
$639$	2.62600	+	9.06601i	0.103883	+	0.358646i
$640$	−2.19745	−	54.5291i	−0.0868618	−	2.15545i
$641$	15.5596	+	19.0570i	0.614567	+	0.752708i	0.984314	−	0.176425i	$-0.0564532\pi$
$641$	15.5596	+	19.0570i	0.614567	+	0.752708i	−0.369747	+	0.929132i	$0.620556\pi$
$642$	−2.10050	+	17.2992i	−0.0829001	+	0.682744i
$643$	−41.1695	+	3.32355i	−1.62357	+	0.131068i	−0.858476	−	0.512854i	$-0.828588\pi$
$643$	−41.1695	+	3.32355i	−1.62357	+	0.131068i	−0.765091	+	0.643922i	$0.777306\pi$
$644$	21.2524	−	73.3718i	0.837462	−	2.89125i
$645$	−20.7067	−	5.10374i	−0.815324	−	0.200959i
$646$	1.01969	+	0.766245i	0.0401191	+	0.0301475i
$647$	14.6194	−	17.9055i	0.574747	−	0.703938i	−0.402649	−	0.915355i	$-0.631910\pi$
$647$	14.6194	−	17.9055i	0.574747	−	0.703938i	0.977396	+	0.211417i	$0.0678078\pi$
$648$	3.55552	+	3.70169i	0.139674	+	0.145416i
$649$	−20.3003	−	5.00358i	−0.796858	−	0.196408i
$650$	14.0840	+	26.7757i	0.552419	+	1.05023i
$651$	−20.8446	+	5.13774i	−0.816965	+	0.201364i
$652$	−40.2106	−	25.4277i	−1.57477	−	0.995824i
$653$	−11.5230	−	19.9585i	−0.450931	−	0.781036i	0.547513	−	0.836797i	$-0.315575\pi$
$653$	−11.5230	−	19.9585i	−0.450931	−	0.781036i	−0.998444	+	0.0557613i	$0.982241\pi$
$654$	6.14215	−	10.6385i	0.240177	−	0.415999i
$655$	17.1303	−	8.99068i	0.669337	−	0.351295i
$656$	2.24550	−	0.749658i	0.0876720	−	0.0292692i
$657$	−6.34724	+	10.9937i	−0.247630	+	0.428907i
$658$	−5.91317	+	5.23861i	−0.230519	+	0.204222i
$659$	−28.4701	+	18.0034i	−1.10904	+	0.701312i	−0.957872	−	0.287196i	$-0.907277\pi$
$659$	−28.4701	+	18.0034i	−1.10904	+	0.701312i	−0.151165	+	0.988509i	$0.548302\pi$
$660$	49.7266	−	21.1865i	1.93560	−	0.824684i
$661$	0.660475	+	16.3895i	0.0256895	+	0.637478i	0.959832	+	0.280577i	$0.0905257\pi$
$661$	0.660475	+	16.3895i	0.0256895	+	0.637478i	−0.934142	+	0.356901i	$0.883833\pi$
$662$	−4.13754	+	34.0757i	−0.160810	+	1.32439i
$663$	−0.158007	+	0.977862i	−0.00613649	+	0.0379770i
$664$	−5.12693	−	42.2241i	−0.198964	−	1.63861i
$665$	−11.6514	+	1.89354i	−0.451822	+	0.0734282i
$666$	−17.9406	−	11.3449i	−0.695184	−	0.439607i
$667$	44.6702	+	7.25961i	1.72964	+	0.281093i
$668$	−13.1495	−	6.90137i	−0.508768	−	0.267022i
$669$	20.5478	−	12.9936i	0.794423	−	0.502363i
$670$	−37.9662	+	39.5270i	−1.46676	+	1.52706i
$671$	−5.00636	−	41.2311i	−0.193268	−	1.59171i
$672$	−0.354206	−	1.73501i	−0.0136638	−	0.0669297i
$673$	−31.2967	−	2.52653i	−1.20640	−	0.0973907i	−0.539141	−	0.842216i	$-0.681251\pi$
$673$	−31.2967	−	2.52653i	−1.20640	−	0.0973907i	−0.667260	+	0.744825i	$0.732533\pi$
$674$	−47.7077	+	58.4313i	−1.83763	+	2.25069i
$675$	3.40259			0.130966
$676$	−46.9352	+	24.7423i	−1.80520	+	0.951625i
$677$	22.9254			0.881094			0.440547	−	0.897729i	$-0.354784\pi$
$677$	22.9254			0.881094			0.440547	+	0.897729i	$0.354784\pi$
$678$	−22.7893	+	27.9118i	−0.875216	+	1.07194i
$679$	−2.82199	−	0.227815i	−0.108298	−	0.00874272i
$680$	0.817595	+	4.00484i	0.0313533	+	0.153579i
$681$	1.92679	+	15.8685i	0.0738348	+	0.608084i
$682$	77.4653	−	80.6500i	2.96630	−	3.08825i
$683$	24.8475	−	15.7126i	0.950764	−	0.601227i	0.0334711	−	0.999440i	$-0.489344\pi$
$683$	24.8475	−	15.7126i	0.950764	−	0.601227i	0.917293	+	0.398213i	$0.130369\pi$
$684$	6.80373	+	3.57087i	0.260147	+	0.136536i
$685$	32.1034	+	5.21731i	1.22661	+	0.199343i
$686$	42.0236	+	26.5741i	1.60447	+	1.01460i
$687$	−8.90130	+	1.44660i	−0.339606	+	0.0551913i
$688$	−3.98591	−	32.8269i	−0.151961	−	1.25151i
$689$	10.2711	−	4.88514i	0.391299	−	0.186109i
$690$	−7.45575	+	61.4036i	−0.283836	+	2.33760i
$691$	−0.853914	−	21.1897i	−0.0324844	−	0.806092i	−0.930536	−	0.366201i	$-0.880658\pi$
$691$	−0.853914	−	21.1897i	−0.0324844	−	0.806092i	0.898051	−	0.439891i	$-0.144983\pi$
$692$	−38.4476	+	16.3810i	−1.46156	+	0.622711i
$693$	−8.35238	+	5.28173i	−0.317281	+	0.200636i
$694$	10.3795	−	9.19545i	0.394001	−	0.349055i
$695$	−23.3846	+	40.5034i	−0.887029	+	1.53638i
$696$	25.4630	−	8.50080i	0.965173	−	0.322222i
$697$	0.128124	−	0.0672448i	0.00485305	−	0.00254708i
$698$	33.8590	−	58.6454i	1.28158	−	2.21976i
$699$	1.43056	+	2.47781i	0.0541088	+	0.0937192i
$700$	−25.3876	−	16.0541i	−0.959561	−	0.606789i
$701$	−32.8998	+	8.10907i	−1.24261	+	0.306275i	−0.805209	−	0.592992i	$-0.797947\pi$
$701$	−32.8998	+	8.10907i	−1.24261	+	0.306275i	−0.437400	+	0.899267i	$0.644101\pi$
$702$	0.00807001	+	8.89142i	0.000304583	+	0.335585i
$703$	−15.7345	−	3.87821i	−0.593438	−	0.146269i
$704$	−22.0608	−	22.9677i	−0.831448	−	0.865629i
$705$	2.71517	−	3.32548i	0.102259	−	0.125245i
$706$	65.2315	+	49.0183i	2.45502	+	1.84483i
$707$	−12.8057	−	3.15631i	−0.481607	−	0.118705i
$708$	5.19632	−	17.9398i	0.195290	−	0.674219i
$709$	−23.6443	+	1.90876i	−0.887980	+	0.0716852i	−0.516033	−	0.856569i	$-0.672592\pi$
$709$	−23.6443	+	1.90876i	−0.887980	+	0.0716852i	−0.371947	+	0.928254i	$0.621310\pi$
$710$	−8.13272	+	66.9790i	−0.305216	+	2.51368i
$711$	−5.35951	−	6.56421i	−0.200997	−	0.246177i
$712$	3.02316	+	75.0190i	0.113298	+	2.81146i
$713$	23.8944	+	82.4931i	0.894853	+	3.08939i
$714$	−0.519639	−	1.37018i	−0.0194470	−	0.0512776i
$715$	44.6630	+	16.8921i	1.67030	+	0.631728i
$716$	−37.0738	+	97.7556i	−1.38551	+	3.65330i
$717$	−4.02529	−	0.324955i	−0.150327	−	0.0121357i
$718$	0.398088	−	1.94996i	0.0148565	−	0.0727720i
$719$	−7.18341	+	24.8000i	−0.267896	+	0.924884i	0.707921	+	0.706292i	$0.249633\pi$
$719$	−7.18341	+	24.8000i	−0.267896	+	0.924884i	−0.975816	+	0.218592i	$0.929854\pi$
$720$	4.62007	+	12.1821i	0.172180	+	0.454001i
$721$	0.749377	−	18.5956i	0.0279083	−	0.692537i
$722$	−37.6203	−	6.11389i	−1.40008	−	0.227536i
$723$	−10.0797	−	8.92987i	−0.374870	−	0.332106i
$724$	−7.12234	+	2.37779i	−0.264700	+	0.0883698i
$725$	7.62900	−	16.0778i	0.283334	−	0.597114i
$726$	10.4383	−	21.9983i	0.387403	−	0.816435i
$727$	−29.7948	+	15.6375i	−1.10503	+	0.579963i	−0.915664	−	0.401944i	$-0.868335\pi$
$727$	−29.7948	+	15.6375i	−1.10503	+	0.579963i	−0.189363	+	0.981907i	$0.560642\pi$
$728$	21.3632	−	33.8511i	0.791771	−	1.25461i
$729$	0.885456	+	0.464723i	0.0327947	+	0.0172120i
$730$	−72.5452	+	54.5142i	−2.68502	+	2.01766i
$731$	−0.562338	−	1.94142i	−0.0207988	−	0.0718059i
$732$	36.9823	−	2.98552i	1.36691	−	0.110348i
$733$	−13.6979	+	19.8448i	−0.505942	+	0.732984i	−0.989847	−	0.142137i	$-0.954603\pi$
$733$	−13.6979	+	19.8448i	−0.505942	+	0.732984i	0.483905	+	0.875121i	$0.339218\pi$
$734$	−6.04790	−	29.6246i	−0.223232	−	1.09346i
$735$	−6.19081	−	2.63766i	−0.228351	−	0.0972914i
$736$	−6.87819	+	1.69532i	−0.253533	+	0.0624904i
$737$	−1.41049	+	35.0009i	−0.0519559	+	1.28927i
$738$	1.03836	−	0.780278i	0.0382226	−	0.0287224i
$739$	30.9188	−	13.1733i	1.13737	−	0.484586i	0.260572	−	0.965454i	$-0.416089\pi$
$739$	30.9188	−	13.1733i	1.13737	−	0.484586i	0.876793	+	0.480868i	$0.159678\pi$
$740$	−57.8482	−	83.8076i	−2.12654	−	3.08083i
$741$	2.15542	+	6.43682i	0.0791813	+	0.236462i
$742$	−9.55833	+	13.8476i	−0.350897	+	0.508362i
$743$	−10.1667	+	49.7998i	−0.372980	+	1.82698i	0.167810	+	0.985819i	$0.446330\pi$
$743$	−10.1667	+	49.7998i	−0.372980	+	1.82698i	−0.540790	+	0.841157i	$0.681875\pi$
$744$	35.2898	+	36.7406i	1.29379	+	1.34698i
$745$	−5.82089	−	12.2673i	−0.213261	−	0.449438i
$746$	−41.4577			−1.51787
$747$	−3.55256	−	7.48686i	−0.129981	−	0.273930i
$748$	4.09538	+	3.07748i	0.149742	+	0.112524i
$749$	5.42005	−	14.2915i	0.198044	−	0.522200i
$750$	−10.5051	−	4.47582i	−0.383593	−	0.163434i
$751$	43.6879	−	7.09997i	1.59419	−	0.259082i	0.702487	−	0.711697i	$-0.252073\pi$
$751$	43.6879	−	7.09997i	1.59419	−	0.259082i	0.891706	+	0.452615i	$0.149509\pi$
$752$	6.31421	+	2.10799i	0.230256	+	0.0768706i
$753$	10.2840	−	9.11084i	0.374770	−	0.332017i
$754$	42.0315	+	19.8975i	1.53070	+	0.724624i
$755$	7.02458	+	6.22324i	0.255651	+	0.226487i
$756$	−4.41395	−	7.64519i	−0.160534	−	0.278053i
$757$	48.7255	+	16.2670i	1.77096	+	0.591233i	0.999011	−	0.0444537i	$-0.0141547\pi$
$757$	48.7255	+	16.2670i	1.77096	+	0.591233i	0.771947	+	0.635687i	$0.219283\pi$
$758$	−23.8537	+	24.8343i	−0.866406	+	0.902024i
$759$	22.4577	+	32.5356i	0.815162	+	1.18097i
$760$	17.7154	+	21.6974i	0.642603	+	0.787046i
$761$	12.0980	+	14.8174i	0.438554	+	0.537131i	0.945834	−	0.324650i	$-0.105247\pi$
$761$	12.0980	+	14.8174i	0.438554	+	0.537131i	−0.507280	+	0.861781i	$0.669349\pi$
$762$	−17.2072	−	24.9289i	−0.623350	−	0.903078i
$763$	−7.46390	+	7.77074i	−0.270211	+	0.281320i
$764$	−89.0069	−	29.7149i	−3.22016	−	1.07505i
$765$	0.398180	+	0.689668i	0.0143962	+	0.0249350i
$766$	38.5996	+	34.1963i	1.39466	+	1.23556i
$767$	14.2818	−	8.26290i	0.515686	−	0.298356i
$768$	24.3165	−	21.5425i	0.877446	−	0.777350i
$769$	26.4905	+	8.84383i	0.955272	+	0.318917i	0.751226	&mi

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.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.55963 + 1.91020i) q^{2} +(-0.996757 - 0.0804666i) q^{3} +(-0.816373 - 3.99886i) q^{4} +(-0.349402 - 2.87759i) q^{5} +(1.70828 - 1.77851i) q^{6} +(-1.82814 + 1.15605i) q^{7} +(4.54475 + 2.38527i) q^{8} +(0.987050 + 0.160411i) q^{9} +(6.04172 + 3.82055i) q^{10} +(4.50962 - 0.732885i) q^{11} +(0.491951 + 4.05158i) q^{12} +(-2.16339 + 2.88440i) q^{13} +(0.642945 - 5.29513i) q^{14} +(0.116720 + 2.89637i) q^{15} +(-4.13500 + 1.76176i) q^{16} +(-0.232197 + 0.146833i) q^{17} +(-1.84586 + 1.63529i) q^{18} +(-0.941341 + 1.63045i) q^{19} +(-11.2218 + 3.74640i) q^{20} +(1.91523 - 1.00519i) q^{21} +(-5.63340 + 9.75734i) q^{22} +(-4.32649 - 7.49370i) q^{23} +(-4.33808 - 2.74323i) q^{24} +(-3.30371 + 0.814293i) q^{25} +(-2.13569 - 8.63112i) q^{26} +(-0.970942 - 0.239316i) q^{27} +(6.11531 + 6.36671i) q^{28} +(-3.30777 + 4.05129i) q^{29} +(-5.71470 - 4.29432i) q^{30} +(-9.63694 - 2.37529i) q^{31} +(0.227772 - 0.786359i) q^{32} +(-4.55397 + 0.367635i) q^{33} +(0.0816623 - 0.672550i) q^{34} +(3.96538 + 4.85670i) q^{35} +(-0.164339 - 4.07803i) q^{36} +(2.39479 + 8.26776i) q^{37} +(-1.64635 - 4.34106i) q^{38} +(2.38847 - 2.70096i) q^{39} +(5.27587 - 13.9113i) q^{40} +(-0.524990 - 0.0423816i) q^{41} +(-1.06694 + 5.22622i) q^{42} +(-2.04689 + 7.06669i) q^{43} +(-6.61224 - 17.4350i) q^{44} +(0.116720 - 2.89637i) q^{45} +(21.0623 + 3.42295i) q^{46} +(-1.10858 - 0.982114i) q^{47} +(4.26335 - 1.42332i) q^{48} +(-0.995196 + 2.09733i) q^{49} +(3.59712 - 7.58077i) q^{50} +(0.243259 - 0.127672i) q^{51} +(13.3004 + 6.29635i) q^{52} +(-2.79316 - 1.46597i) q^{53} +(1.97146 - 1.48145i) q^{54} +(-3.68461 - 12.7208i) q^{55} +(-11.0659 + 0.893333i) q^{56} +(1.06949 - 1.54942i) q^{57} +(-2.57987 - 12.6370i) q^{58} +(-4.21005 - 1.79373i) q^{59} +(11.4869 - 2.83127i) q^{60} +(0.366050 - 9.08343i) q^{61} +(19.5674 - 14.7040i) q^{62} +(-1.98991 + 0.847820i) q^{63} +(-3.95966 - 5.73655i) q^{64} +(9.05599 + 5.21753i) q^{65} +(6.40027 - 9.27240i) q^{66} +(-1.53361 + 7.51213i) q^{67} +(0.776723 + 0.808654i) q^{68} +(3.70947 + 7.81754i) q^{69} -15.4618 q^{70} +(4.04628 + 8.52736i) q^{71} +(4.10327 + 3.08341i) q^{72} +(-4.50153 + 11.8696i) q^{73} +(-19.5281 - 8.32015i) q^{74} +(3.35852 - 0.545813i) q^{75} +(7.28843 + 2.43324i) q^{76} +(-7.39697 + 6.55314i) q^{77} +(1.43425 + 8.77499i) q^{78} +(-6.34308 - 5.61948i) q^{79} +(6.51439 + 11.2833i) q^{80} +(0.948536 + 0.316668i) q^{81} +(0.899750 - 0.936739i) q^{82} +(-4.70753 - 6.82003i) q^{83} +(-5.58317 - 6.83814i) q^{84} +(0.503654 + 0.616864i) q^{85} +(-10.3064 - 14.9314i) q^{86} +(3.62304 - 3.77198i) q^{87} +(22.2432 + 7.42589i) q^{88} +(7.31393 + 12.6681i) q^{89} +(5.35062 + 4.74024i) q^{90} +(0.620485 - 7.77405i) q^{91} +(-26.4342 + 23.4187i) q^{92} +(9.41456 + 3.14304i) q^{93} +(3.60501 - 0.585872i) q^{94} +(5.02067 + 2.13911i) q^{95} +(-0.290309 + 0.765481i) q^{96} +(1.04640 + 0.786320i) q^{97} +(-2.45419 - 5.17210i) q^{98} +4.56879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more