LMFDB - Embedded newform 507.2.s.a.5.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(5,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(52))

chi = DirichletCharacter(H, H._module([26, 3]))

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

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

chi := DirichletCharacter("507.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.s (of order $52$, 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:	$1392$
Relative dimension:	$58$ over $\Q(\zeta_{52})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label			5.20
Character	$\chi$	$=$	507.5
Dual form			507.2.s.a.203.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.205529 + 1.12154i) q^{2} +(0.653740 - 1.60394i) q^{3} +(0.654428 + 0.248192i) q^{4} +(-3.58890 - 0.217089i) q^{5} +(1.66452 + 1.06285i) q^{6} +(-1.80817 - 1.09308i) q^{7} +(-1.59261 + 2.63450i) q^{8} +(-2.14525 - 2.09712i) q^{9} +(0.981098 - 3.98047i) q^{10} +(1.03620 + 5.65434i) q^{11} +(0.825911 - 0.887411i) q^{12} +(2.04874 + 2.96693i) q^{13} +(1.59756 - 1.80327i) q^{14} +(-2.69441 + 5.61447i) q^{15} +(-1.57958 - 1.39939i) q^{16} +(-4.54606 + 1.12050i) q^{17} +(2.79291 - 1.97495i) q^{18} +(-2.39174 + 2.39174i) q^{19} +(-2.29480 - 1.03281i) q^{20} +(-2.93530 + 2.18560i) q^{21} -6.55452 q^{22} -1.16467 q^{23} +(3.18443 + 4.27674i) q^{24} +(7.86956 + 0.955538i) q^{25} +(-3.74860 + 1.68795i) q^{26} +(-4.76609 + 2.06987i) q^{27} +(-0.912024 - 1.16411i) q^{28} +(3.68914 - 2.54643i) q^{29} +(-5.74306 - 4.17582i) q^{30} +(2.84435 + 2.22841i) q^{31} +(-2.95254 + 2.31316i) q^{32} +(9.74663 + 2.03447i) q^{33} +(-0.322337 - 5.32887i) q^{34} +(6.25205 + 4.31548i) q^{35} +(-0.883422 - 1.90485i) q^{36} +(-3.98148 + 5.08199i) q^{37} +(-2.19086 - 3.17400i) q^{38} +(6.09812 - 1.34646i) q^{39} +(6.28766 - 9.10924i) q^{40} +(-3.02507 - 9.70781i) q^{41} +(-1.84795 - 3.74125i) q^{42} +(-5.12736 - 0.622574i) q^{43} +(-0.725246 + 3.95754i) q^{44} +(7.24382 + 7.99208i) q^{45} +(0.239373 - 1.30622i) q^{46} +(3.40765 + 1.53366i) q^{47} +(-3.27717 + 1.61872i) q^{48} +(-1.17841 - 2.24526i) q^{49} +(-2.68910 + 8.62962i) q^{50} +(-1.17472 + 8.02412i) q^{51} +(0.604389 + 2.45012i) q^{52} +(1.75692 + 7.12810i) q^{53} +(-1.34187 - 5.77077i) q^{54} +(-2.49132 - 20.5178i) q^{55} +(5.75942 - 3.02278i) q^{56} +(2.27263 + 5.39979i) q^{57} +(2.09769 + 4.66087i) q^{58} +(0.293499 - 4.85212i) q^{59} +(-3.15676 + 3.00554i) q^{60} +(-2.80038 - 0.690231i) q^{61} +(-3.08384 + 2.73204i) q^{62} +(1.58665 + 6.13686i) q^{63} +(-3.94888 - 7.52396i) q^{64} +(-6.70866 - 11.0928i) q^{65} +(-4.28496 + 10.5131i) q^{66} +(-1.39008 - 0.625623i) q^{67} +(-3.25317 - 0.395006i) q^{68} +(-0.761389 + 1.86805i) q^{69} +(-6.12495 + 6.12495i) q^{70} +(-0.979798 - 3.14428i) q^{71} +(8.94142 - 2.31176i) q^{72} +(4.88695 - 0.895566i) q^{73} +(-4.88133 - 5.50988i) q^{74} +(6.67728 - 11.9976i) q^{75} +(-2.15884 + 0.971613i) q^{76} +(4.30700 - 11.3566i) q^{77} +(0.256766 + 7.11601i) q^{78} +(-0.313705 - 0.827171i) q^{79} +(5.36518 + 5.36518i) q^{80} +(0.204168 + 8.99768i) q^{81} +(11.5094 - 1.39750i) q^{82} +(-17.0563 - 5.31495i) q^{83} +(-2.46339 + 0.701804i) q^{84} +(16.5586 - 3.03448i) q^{85} +(1.75206 - 5.62257i) q^{86} +(-1.67258 - 7.58186i) q^{87} +(-16.5466 - 6.27531i) q^{88} +(11.8116 - 11.8116i) q^{89} +(-10.4522 + 6.48161i) q^{90} +(-0.461399 - 7.60413i) q^{91} +(-0.762190 - 0.289061i) q^{92} +(5.43370 - 3.10537i) q^{93} +(-2.42043 + 3.50660i) q^{94} +(9.10296 - 8.06452i) q^{95} +(1.77998 + 6.24790i) q^{96} +(-9.84564 + 0.595552i) q^{97} +(2.76035 - 0.860158i) q^{98} +(9.63494 - 14.3030i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27}+ \cdots - 58 q^{99}+O(q^{100}) $ 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Character values

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

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{3}{52}\right)$

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 $

$2$	−0.205529	+	1.12154i	−0.145331	+	0.793047i	0.827488	+	0.561483i	$0.189769\pi$
$2$	−0.205529	+	1.12154i	−0.145331	+	0.793047i	−0.972820	+	0.231564i	$0.925616\pi$
$3$	0.653740	−	1.60394i	0.377437	−	0.926035i
$3$	0.653740	−	1.60394i	0.377437	−	0.926035i
$4$	0.654428	+	0.248192i	0.327214	+	0.124096i
$5$	−3.58890	−	0.217089i	−1.60501	−	0.0970850i	−0.766598	−	0.642127i	$-0.778052\pi$
$5$	−3.58890	−	0.217089i	−1.60501	−	0.0970850i	−0.838409	+	0.545042i	$0.816514\pi$
$6$	1.66452	+	1.06285i	0.679536	+	0.433907i
$7$	−1.80817	−	1.09308i	−0.683423	−	0.413144i	0.132595	−	0.991170i	$-0.457669\pi$
$7$	−1.80817	−	1.09308i	−0.683423	−	0.413144i	−0.816018	+	0.578027i	$0.803823\pi$
$8$	−1.59261	+	2.63450i	−0.563074	+	0.931438i
$9$	−2.14525	−	2.09712i	−0.715082	−	0.699040i
$10$	0.981098	−	3.98047i	0.310251	−	1.25874i
$11$	1.03620	+	5.65434i	0.312425	+	1.70485i	0.647010	+	0.762482i	$0.276019\pi$
$11$	1.03620	+	5.65434i	0.312425	+	1.70485i	−0.334585	+	0.942366i	$0.608596\pi$
$12$	0.825911	−	0.887411i	0.238420	−	0.256173i
$13$	2.04874	+	2.96693i	0.568219	+	0.822877i
$13$	2.04874	+	2.96693i	0.568219	+	0.822877i
$14$	1.59756	−	1.80327i	0.426965	−	0.481944i
$15$	−2.69441	+	5.61447i	−0.695693	+	1.44965i
$16$	−1.57958	−	1.39939i	−0.394896	−	0.349847i
$17$	−4.54606	+	1.12050i	−1.10258	+	0.271762i	−0.748289	−	0.663373i	$-0.769124\pi$
$17$	−4.54606	+	1.12050i	−1.10258	+	0.271762i	−0.354292	+	0.935135i	$0.615278\pi$
$18$	2.79291	−	1.97495i	0.658295	−	0.465501i
$19$	−2.39174	+	2.39174i	−0.548703	+	0.548703i	−0.926066	−	0.377362i	$-0.876831\pi$
$19$	−2.39174	+	2.39174i	−0.548703	+	0.548703i	0.377362	+	0.926066i	$0.376831\pi$
$20$	−2.29480	−	1.03281i	−0.513133	−	0.230943i
$21$	−2.93530	+	2.18560i	−0.640535	+	0.476938i
$22$	−6.55452			−1.39743
$23$	−1.16467			−0.242849			−0.121425	−	0.992601i	$-0.538746\pi$
$23$	−1.16467			−0.242849			−0.121425	+	0.992601i	$0.538746\pi$
$24$	3.18443	+	4.27674i	0.650019	+	0.872985i
$25$	7.86956	+	0.955538i	1.57391	+	0.191108i
$26$	−3.74860	+	1.68795i	−0.735160	+	0.331035i
$27$	−4.76609	+	2.06987i	−0.917235	+	0.398348i
$28$	−0.912024	−	1.16411i	−0.172356	−	0.219997i
$29$	3.68914	−	2.54643i	0.685056	−	0.472860i	−0.173998	−	0.984746i	$-0.555668\pi$
$29$	3.68914	−	2.54643i	0.685056	−	0.472860i	0.859053	+	0.511886i	$0.171053\pi$
$30$	−5.74306	−	4.17582i	−1.04853	−	0.762397i
$31$	2.84435	+	2.22841i	0.510861	+	0.400234i	0.838779	−	0.544472i	$-0.183270\pi$
$31$	2.84435	+	2.22841i	0.510861	+	0.400234i	−0.327918	+	0.944706i	$0.606347\pi$
$32$	−2.95254	+	2.31316i	−0.521940	+	0.408913i
$33$	9.74663	+	2.03447i	1.69667	+	0.354156i
$34$	−0.322337	−	5.32887i	−0.0552804	−	0.913894i
$35$	6.25205	+	4.31548i	1.05679	+	0.729449i
$36$	−0.883422	−	1.90485i	−0.147237	−	0.317475i
$37$	−3.98148	+	5.08199i	−0.654551	+	0.835473i	−0.994474	−	0.104980i	$-0.966522\pi$
$37$	−3.98148	+	5.08199i	−0.654551	+	0.835473i	0.339923	+	0.940453i	$0.389599\pi$
$38$	−2.19086	−	3.17400i	−0.355404	−	0.514891i
$39$	6.09812	−	1.34646i	0.976480	−	0.215607i
$40$	6.28766	−	9.10924i	0.994166	−	1.44030i
$41$	−3.02507	−	9.70781i	−0.472437	−	1.51610i	−0.816605	−	0.577197i	$-0.804147\pi$
$41$	−3.02507	−	9.70781i	−0.472437	−	1.51610i	0.344168	−	0.938908i	$-0.388161\pi$
$42$	−1.84795	−	3.74125i	−0.285144	−	0.577288i
$43$	−5.12736	−	0.622574i	−0.781915	−	0.0949417i	−0.280162	−	0.959953i	$-0.590388\pi$
$43$	−5.12736	−	0.622574i	−0.781915	−	0.0949417i	−0.501753	+	0.865011i	$0.667311\pi$
$44$	−0.725246	+	3.95754i	−0.109335	+	0.596621i
$45$	7.24382	+	7.99208i	1.07985	+	1.19139i
$46$	0.239373	−	1.30622i	0.0352936	−	0.192591i
$47$	3.40765	+	1.53366i	0.497057	+	0.223707i	0.643405	−	0.765526i	$-0.277521\pi$
$47$	3.40765	+	1.53366i	0.497057	+	0.223707i	−0.146348	+	0.989233i	$0.546752\pi$
$48$	−3.27717	+	1.61872i	−0.473019	+	0.233642i
$49$	−1.17841	−	2.24526i	−0.168344	−	0.320752i
$50$	−2.68910	+	8.62962i	−0.380296	+	1.22041i
$51$	−1.17472	+	8.02412i	−0.164494	+	1.12360i
$52$	0.604389	+	2.45012i	0.0838137	+	0.339771i
$53$	1.75692	+	7.12810i	0.241331	+	0.979120i	0.959152	+	0.282891i	$0.0912936\pi$
$53$	1.75692	+	7.12810i	0.241331	+	0.979120i	−0.717821	+	0.696228i	$0.754860\pi$
$54$	−1.34187	−	5.77077i	−0.182605	−	0.785302i
$55$	−2.49132	−	20.5178i	−0.335929	−	2.76662i
$56$	5.75942	−	3.02278i	0.769635	−	0.403936i
$57$	2.27263	+	5.39979i	0.301018	+	0.715220i
$58$	2.09769	+	4.66087i	0.275440	+	0.612002i
$59$	0.293499	−	4.85212i	0.0382103	−	0.631692i	−0.927782	−	0.373122i	$-0.878287\pi$
$59$	0.293499	−	4.85212i	0.0382103	−	0.631692i	0.965993	−	0.258570i	$-0.0832512\pi$
$60$	−3.15676	+	3.00554i	−0.407536	+	0.388013i
$61$	−2.80038	−	0.690231i	−0.358552	−	0.0883750i	0.0559250	−	0.998435i	$-0.482189\pi$
$61$	−2.80038	−	0.690231i	−0.358552	−	0.0883750i	−0.414477	+	0.910060i	$0.636035\pi$
$62$	−3.08384	+	2.73204i	−0.391648	+	0.346970i
$63$	1.58665	+	6.13686i	0.199900	+	0.773172i
$64$	−3.94888	−	7.52396i	−0.493610	−	0.940495i
$65$	−6.70866	−	11.0928i	−0.832107	−	1.37589i
$66$	−4.28496	+	10.5131i	−0.527442	+	1.29407i
$67$	−1.39008	−	0.625623i	−0.169825	−	0.0764320i	0.323717	−	0.946154i	$-0.395067\pi$
$67$	−1.39008	−	0.625623i	−0.169825	−	0.0764320i	−0.493542	+	0.869722i	$0.664298\pi$
$68$	−3.25317	−	0.395006i	−0.394505	−	0.0479016i
$69$	−0.761389	+	1.86805i	−0.0916604	+	0.224887i
$70$	−6.12495	+	6.12495i	−0.732071	+	0.732071i
$71$	−0.979798	−	3.14428i	−0.116281	−	0.373158i	0.878172	−	0.478345i	$-0.158763\pi$
$71$	−0.979798	−	3.14428i	−0.116281	−	0.373158i	−0.994452	+	0.105188i	$0.966456\pi$
$72$	8.94142	−	2.31176i	1.05376	−	0.272443i
$73$	4.88695	−	0.895566i	0.571974	−	0.104818i	0.113519	−	0.993536i	$-0.463788\pi$
$73$	4.88695	−	0.895566i	0.571974	−	0.104818i	0.458455	+	0.888718i	$0.348403\pi$
$74$	−4.88133	−	5.50988i	−0.567443	−	0.640510i
$75$	6.67728	−	11.9976i	0.771026	−	1.38537i
$76$	−2.15884	+	0.971613i	−0.247636	+	0.111452i
$77$	4.30700	−	11.3566i	0.490829	−	1.29421i
$78$	0.256766	+	7.11601i	0.0290730	+	0.805729i
$79$	−0.313705	−	0.827171i	−0.0352945	−	0.0930640i	0.916210	−	0.400698i	$-0.131232\pi$
$79$	−0.313705	−	0.827171i	−0.0352945	−	0.0930640i	−0.951505	+	0.307633i	$0.900463\pi$
$80$	5.36518	+	5.36518i	0.599846	+	0.599846i
$81$	0.204168	+	8.99768i	0.0226854	+	0.999743i
$82$	11.5094	−	1.39750i	1.27100	−	0.154328i
$83$	−17.0563	−	5.31495i	−1.87217	−	0.583392i	−0.994579	−	0.103983i	$-0.966841\pi$
$83$	−17.0563	−	5.31495i	−1.87217	−	0.583392i	−0.877591	−	0.479409i	$-0.840851\pi$
$84$	−2.46339	+	0.701804i	−0.268778	+	0.0765731i
$85$	16.5586	−	3.03448i	1.79603	−	0.329136i
$86$	1.75206	−	5.62257i	0.188930	−	0.606297i
$87$	−1.67258	−	7.58186i	−0.179319	−	0.812860i
$88$	−16.5466	−	6.27531i	−1.76388	−	0.668950i
$89$	11.8116	−	11.8116i	1.25202	−	1.25202i	0.297213	−	0.954811i	$-0.403943\pi$
$89$	11.8116	−	11.8116i	1.25202	−	1.25202i	0.954811	−	0.297213i	$-0.0960570\pi$
$90$	−10.4522	+	6.48161i	−1.10176	+	0.683222i
$91$	−0.461399	−	7.60413i	−0.0483677	−	0.797130i
$92$	−0.762190	−	0.289061i	−0.0794638	−	0.0301366i
$93$	5.43370	−	3.10537i	0.563448	−	0.322012i
$94$	−2.42043	+	3.50660i	−0.249648	+	0.361678i
$95$	9.10296	−	8.06452i	0.933944	−	0.827402i
$96$	1.77998	+	6.24790i	0.181669	+	0.637674i
$97$	−9.84564	+	0.595552i	−0.999674	+	0.0604691i	−0.552100	−	0.833778i	$-0.686173\pi$
$97$	−9.84564	+	0.595552i	−0.999674	+	0.0604691i	−0.447574	+	0.894247i	$0.647712\pi$
$98$	2.76035	−	0.860158i	0.278837	−	0.0868891i
$99$	9.63494	−	14.3030i	0.968348	−	1.43750i
$100$	4.91291	+	2.57849i	0.491291	+	0.257849i
$101$	−2.32591	+	19.1556i	−0.231437	+	1.90606i	0.162146	+	0.986767i	$0.448158\pi$
$101$	−2.32591	+	19.1556i	−0.231437	+	1.90606i	−0.393583	+	0.919289i	$0.628765\pi$
$102$	−8.75792	−	2.96669i	−0.867163	−	0.293746i
$103$	−4.10560	+	7.82256i	−0.404536	+	0.770780i	−0.999455	−	0.0330061i	$-0.989492\pi$
$103$	−4.10560	+	7.82256i	−0.404536	+	0.770780i	0.594919	+	0.803786i	$0.297184\pi$
$104$	−11.0792	+	0.672258i	−1.08641	+	0.0659204i
$105$	11.0090	−	7.20671i	1.07437	−	0.703303i
$106$	−8.35553	+	0.505416i	−0.811561	+	0.0490904i
$107$	10.3875	+	11.7251i	1.00420	+	1.13351i	0.991036	+	0.133594i	$0.0426517\pi$
$107$	10.3875	+	11.7251i	1.00420	+	1.13351i	0.0131634	+	0.999913i	$0.495810\pi$
$108$	−3.63279	+	0.171679i	−0.349566	+	0.0165199i
$109$	11.3289	+	14.4602i	1.08511	+	1.38504i	0.916820	+	0.399300i	$0.130747\pi$
$109$	11.3289	+	14.4602i	1.08511	+	1.38504i	0.168288	+	0.985738i	$0.446176\pi$
$110$	23.5236	+	1.42291i	2.24288	+	0.135669i
$111$	5.54834	+	9.70836i	0.526626	+	0.921476i
$112$	1.32651	+	4.25693i	0.125344	+	0.402242i
$113$	4.23781	+	8.07448i	0.398660	+	0.759583i	0.999199	−	0.0400123i	$-0.0127397\pi$
$113$	4.23781	+	8.07448i	0.398660	+	0.759583i	−0.600539	+	0.799595i	$0.705047\pi$
$114$	−6.52316	+	1.43903i	−0.610950	+	0.134777i
$115$	4.17987	+	0.252836i	0.389775	+	0.0235770i
$116$	3.04628	−	0.750840i	0.282840	−	0.0697138i
$117$	1.82694	−	10.6613i	0.168901	−	0.985633i
$118$	5.38151	+	1.32642i	0.495408	+	0.122107i
$119$	9.44483	+	2.94313i	0.865806	+	0.269796i
$120$	−10.5002	−	16.0401i	−0.958531	−	1.46425i
$121$	−20.6127	+	7.81736i	−1.87388	+	0.710669i
$122$	1.34968	−	2.99887i	0.122194	−	0.271505i
$123$	−17.5484	−	1.49435i	−1.58228	−	0.134741i
$124$	1.30835	+	2.16428i	0.117493	+	0.194358i
$125$	−10.3528	−	1.89723i	−0.925985	−	0.169693i
$126$	−7.20883	+	0.518187i	−0.642213	+	0.0461638i
$127$	5.01795	−	1.90306i	0.445271	−	0.168869i	−0.121770	−	0.992558i	$-0.538857\pi$
$127$	5.01795	−	1.90306i	0.445271	−	0.168869i	0.567042	+	0.823689i	$0.308088\pi$
$128$	2.08816	−	0.650696i	0.184569	−	0.0575140i
$129$	−4.35054	+	7.81698i	−0.383043	+	0.688246i
$130$	13.8198	−	5.24412i	1.21208	−	0.459940i
$131$	14.3010	−	9.87126i	1.24948	−	0.862456i	0.254957	−	0.966952i	$-0.417939\pi$
$131$	14.3010	−	9.87126i	1.24948	−	0.862456i	0.994525	+	0.104497i	$0.0333232\pi$
$132$	5.87353	+	3.75045i	0.511225	+	0.326435i
$133$	6.93903	−	1.71032i	0.601690	−	0.148303i
$134$	0.987361	−	1.43044i	0.0852950	−	0.123571i
$135$	17.5544	−	6.39392i	1.51084	−	0.550301i
$136$	4.28814	−	13.7611i	0.367705	−	1.18001i
$137$	−0.805640	−	1.02832i	−0.0688305	−	0.0878556i	0.751542	−	0.659686i	$-0.229311\pi$
$137$	−0.805640	−	1.02832i	−0.0688305	−	0.0878556i	−0.820372	+	0.571830i	$0.806234\pi$
$138$	−1.93860	−	1.23787i	−0.165025	−	0.105374i
$139$	10.0989	+	8.94688i	0.856581	+	0.758865i	0.972131	−	0.234437i	$-0.0753246\pi$
$139$	10.0989	+	8.94688i	0.856581	+	0.758865i	−0.115550	+	0.993302i	$0.536863\pi$
$140$	3.02045	+	4.37588i	0.255275	+	0.369829i
$141$	4.68762	−	4.46306i	0.394769	−	0.375857i
$142$	3.72781	−	0.452638i	0.312831	−	0.0379845i
$143$	−14.6531	+	14.6586i	−1.22535	+	1.22581i
$144$	0.453909	+	6.31461i	0.0378257	+	0.526218i
$145$	−13.7928	+	8.33802i	−1.14543	+	0.692435i
$146$			5.66496i			0.468835i
$147$	−4.37164	+	0.422272i	−0.360567	+	0.0348284i
$148$	−3.86690	+	2.33762i	−0.317857	+	0.192152i
$149$	0.878817	−	1.95265i	0.0719955	−	0.159967i	−0.872388	−	0.488815i	$-0.837429\pi$
$149$	0.878817	−	1.95265i	0.0719955	−	0.159967i	0.944383	+	0.328847i	$0.106660\pi$
$150$	12.0834	+	9.95468i	0.986607	+	0.812796i
$151$	−7.21987	+	3.24940i	−0.587545	+	0.264432i	−0.682305	−	0.731068i	$-0.739022\pi$
$151$	−7.21987	+	3.24940i	−0.587545	+	0.264432i	0.0947601	+	0.995500i	$0.469792\pi$
$152$	−2.49193	−	10.1102i	−0.202123	−	0.820044i
$153$	12.1022	+	7.12988i	0.978409	+	0.576417i
$154$	11.8517	+	7.16459i	0.955035	+	0.577339i
$155$	−9.72435	−	8.61502i	−0.781078	−	0.691975i
$156$	4.32496	+	0.632340i	0.346274	+	0.0506277i
$157$	−0.502197	+	0.444908i	−0.0400797	+	0.0355075i	−0.682925	−	0.730489i	$-0.739292\pi$
$157$	−0.502197	+	0.444908i	−0.0400797	+	0.0355075i	0.642845	+	0.765996i	$0.277754\pi$
$158$	0.992179	−	0.181824i	0.0789335	−	0.0144651i
$159$	12.5816	+	1.84193i	0.997787	+	0.146075i
$160$	11.0985	−	7.66076i	0.877416	−	0.605636i
$161$	2.10591	+	1.27307i	0.165969	+	0.100332i
$162$	−10.1332	−	1.62031i	−0.796140	−	0.127303i
$163$	7.35852	−	9.39246i	0.576364	−	0.735674i	−0.407773	−	0.913083i	$-0.633695\pi$
$163$	7.35852	−	9.39246i	0.576364	−	0.735674i	0.984137	+	0.177409i	$0.0567715\pi$
$164$	0.429705	−	7.10386i	0.0335543	−	0.554719i
$165$	−34.5380	−	9.41742i	−2.68878	−	0.733145i
$166$	9.46649	−	18.0369i	0.734742	−	1.39993i
$167$	21.8714	+	4.00808i	1.69246	+	0.310154i	0.938114	−	0.346326i	$-0.112571\pi$
$167$	21.8714	+	4.00808i	1.69246	+	0.310154i	0.754343	+	0.656480i	$0.227955\pi$
$168$	−1.08319	−	11.2139i	−0.0835697	−	0.865170i
$169$	−4.60530	+	12.1569i	−0.354254	+	0.935149i
$170$			19.1948i			1.47217i
$171$	10.1467	−	0.115105i	0.775934	−	0.00880231i
$172$	−3.20097	−	1.68000i	−0.244072	−	0.128099i
$173$	−0.314699	+	0.829794i	−0.0239262	+	0.0630881i	−0.946447	−	0.322859i	$-0.895356\pi$
$173$	−0.314699	+	0.829794i	−0.0239262	+	0.0630881i	0.922521	+	0.385947i	$0.126125\pi$
$174$	8.84710	−	0.317565i	0.670697	−	0.0240746i
$175$	−13.1850	−	10.3298i	−0.996694	−	0.780860i
$176$	6.27586	−	10.3815i	0.473061	−	0.782538i
$177$	−7.59063	−	3.64278i	−0.570547	−	0.273808i
$178$	10.8195	+	15.6747i	0.810955	+	1.17487i
$179$	9.31329	+	2.29552i	0.696108	+	0.171575i	0.571465	−	0.820627i	$-0.306375\pi$
$179$	9.31329	+	2.29552i	0.696108	+	0.171575i	0.124643	+	0.992202i	$0.460221\pi$
$180$	2.75700	+	7.02810i	0.205494	+	0.523844i
$181$	−9.73858	−	10.9926i	−0.723863	−	0.817072i	0.265258	−	0.964178i	$-0.414543\pi$
$181$	−9.73858	−	10.9926i	−0.723863	−	0.817072i	−0.989121	+	0.147105i	$0.953004\pi$
$182$	8.62315	+	1.04540i	0.639190	+	0.0774899i
$183$	−2.93781	+	4.04041i	−0.217169	+	0.298675i
$184$	1.85486	−	3.06831i	0.136742	−	0.226199i
$185$	15.3924	−	17.3744i	1.13167	−	1.27739i
$186$	2.36600	+	6.73234i	0.173484	+	0.493639i
$187$	−11.0463	−	24.5439i	−0.807787	−	1.79483i
$188$	1.84942	+	1.84942i	0.134883	+	0.134883i
$189$	10.8804	+	1.46702i	0.791434	+	0.106710i
$190$	7.17373	+	11.8668i	0.520437	+	0.860908i
$191$			6.81935i			0.493431i	0.969088	+	0.246715i	$0.0793513\pi$
$191$			6.81935i			0.493431i	−0.969088	+	0.246715i	$0.920649\pi$
$192$	−14.6495	+	1.41505i	−1.05724	+	0.102122i
$193$	2.27002	+	3.75508i	0.163400	+	0.270297i	0.926742	−	0.375698i	$-0.122597\pi$
$193$	2.27002	+	3.75508i	0.163400	+	0.270297i	−0.763342	+	0.645994i	$0.776443\pi$
$194$	1.35564	−	11.1647i	0.0973289	−	0.801576i
$195$	−22.1779	+	3.50849i	−1.58819	+	0.251248i
$196$	−0.213926	−	1.76184i	−0.0152804	−	0.125845i
$197$	−17.0631	+	13.3681i	−1.21570	+	0.952439i	−0.999713	−	0.0239577i	$-0.992373\pi$
$197$	−17.0631	+	13.3681i	−1.21570	+	0.952439i	−0.215985	+	0.976397i	$0.569296\pi$
$198$	14.0611	+	13.7456i	0.999277	+	0.976859i
$199$	0.820320	−	0.925950i	0.0581510	−	0.0656389i	−0.718715	−	0.695304i	$-0.755270\pi$
$199$	0.820320	−	0.925950i	0.0581510	−	0.0656389i	0.776866	+	0.629665i	$0.216808\pi$
$200$	−15.0505	+	19.2106i	−1.06423	+	1.35839i
$201$	−1.91221	+	1.82061i	−0.134877	+	0.128416i
$202$	−21.0057	−	6.54564i	−1.47796	−	0.460550i
$203$	−9.45402	+	0.571863i	−0.663542	+	0.0401369i
$204$	−2.76030	+	4.95966i	−0.193259	+	0.347246i
$205$	8.74925	+	35.4971i	0.611074	+	2.47923i
$206$	−7.92947	−	6.21235i	−0.552473	−	0.432835i
$207$	2.49849	+	2.44244i	0.173657	+	0.169762i
$208$	0.915721	−	7.55350i	0.0634938	−	0.523741i
$209$	−16.0020	−	11.0454i	−1.10688	−	0.764027i
$210$	5.81992	+	13.8282i	0.401613	+	0.954235i
$211$	0.878588	+	2.31665i	0.0604845	+	0.159485i	0.961852	−	0.273571i	$-0.0882047\pi$
$211$	0.878588	+	2.31665i	0.0604845	+	0.159485i	−0.901367	+	0.433055i	$0.857436\pi$
$212$	−0.619359	+	5.10088i	−0.0425378	+	0.350330i
$213$	−5.68377	−	0.484007i	−0.389446	−	0.0331636i
$214$	−15.2851	+	9.24014i	−1.04487	+	0.631643i
$215$	18.2665	+	3.34745i	1.24576	+	0.228294i
$216$	2.13745	−	15.8528i	0.145435	−	1.07865i
$217$	−2.70725	−	7.13843i	−0.183780	−	0.484588i
$218$	−18.5461	+	9.73374i	−1.25610	+	0.659252i
$219$	1.75836	−	8.42384i	0.118819	−	0.569230i
$220$	3.46197	−	14.0458i	0.233406	−	0.946966i
$221$	−12.6382	−	11.1922i	−0.850135	−	0.752869i
$222$	−12.0286	+	4.22732i	−0.807309	+	0.283719i
$223$	−0.442327	+	7.31254i	−0.0296204	+	0.489684i	0.952871	+	0.303376i	$0.0981138\pi$
$223$	−0.442327	+	7.31254i	−0.0296204	+	0.489684i	−0.982491	+	0.186308i	$0.940348\pi$
$224$	7.86714	−	0.955244i	0.525646	−	0.0638249i
$225$	−14.8783	−	18.5533i	−0.991885	−	1.23689i
$226$	−9.92682	+	3.09332i	−0.660323	+	0.205765i
$227$	−10.7552	+	4.84052i	−0.713847	+	0.321277i	−0.734593	−	0.678508i	$-0.762627\pi$
$227$	−10.7552	+	4.84052i	−0.713847	+	0.321277i	0.0207456	+	0.999785i	$0.493396\pi$
$228$	0.147091	+	4.09783i	0.00974133	+	0.271385i
$229$	−3.05981	+	2.39721i	−0.202198	+	0.158412i	−0.712710	−	0.701458i	$-0.752533\pi$
$229$	−3.05981	+	2.39721i	−0.202198	+	0.158412i	0.510512	+	0.859870i	$0.329456\pi$
$230$	−1.14265	+	4.63592i	−0.0753442	+	0.305683i
$231$	−15.3997	−	14.3325i	−1.01323	−	0.943007i
$232$	0.833205	+	13.7745i	0.0547026	+	0.904341i
$233$	−1.39673	+	0.733061i	−0.0915029	+	0.0480245i	−0.509854	−	0.860261i	$-0.670301\pi$
$233$	−1.39673	+	0.733061i	−0.0915029	+	0.0480245i	0.418351	+	0.908285i	$0.362608\pi$
$234$	11.5815	+	4.24018i	0.757107	+	0.277189i
$235$	−11.8968	−	6.24392i	−0.776062	−	0.407309i
$236$	1.39633	−	3.10252i	0.0908934	−	0.201957i
$237$	−1.53181	−	0.0375918i	−0.0995020	−	0.00244185i
$238$	−5.24202	+	9.98783i	−0.339790	+	0.647415i
$239$	5.12966	+	5.12966i	0.331810	+	0.331810i	0.853274	−	0.521464i	$-0.174614\pi$
$239$	5.12966	+	5.12966i	0.331810	+	0.331810i	−0.521464	+	0.853274i	$0.674614\pi$
$240$	12.1129	−	5.09799i	0.781882	−	0.329074i
$241$	0.880878	+	14.5626i	0.0567423	+	0.938062i	0.909486	+	0.415734i	$0.136475\pi$
$241$	0.880878	+	14.5626i	0.0567423	+	0.938062i	−0.852744	+	0.522329i	$0.825063\pi$
$242$	−4.53095	−	24.7246i	−0.291260	−	1.58936i
$243$	14.5652	+	5.55468i	0.934359	+	0.356333i
$244$	−1.66134	−	1.14674i	−0.106356	−	0.0734124i
$245$	3.74176	+	8.31386i	0.239053	+	0.531153i
$246$	5.28267	−	19.3740i	0.336811	−	1.23524i
$247$	−11.9962	−	2.19606i	−0.763299	−	0.139732i
$248$	−10.4007	+	3.94446i	−0.660445	+	0.250474i
$249$	−19.6752	+	23.8827i	−1.24687	+	1.51350i
$250$	4.25562	−	11.2211i	0.269149	−	0.709688i
$251$	−1.61856	−	13.3300i	−0.102163	−	0.841385i	−0.950241	−	0.311514i	$-0.899164\pi$
$251$	−1.61856	−	13.3300i	−0.102163	−	0.841385i	0.848079	−	0.529870i	$-0.177759\pi$
$252$	−0.484768	+	4.40993i	−0.0305375	+	0.277800i
$253$	−1.20682	−	6.58541i	−0.0758722	−	0.414021i
$254$	1.10301	+	6.01896i	0.0692093	+	0.377663i
$255$	5.95792	−	28.5428i	0.373099	−	1.78742i
$256$	−1.74786	−	14.3949i	−0.109241	−	0.899684i
$257$	0.779133	−	2.05441i	0.0486010	−	0.128150i	−0.908518	−	0.417846i	$-0.862785\pi$
$257$	0.779133	−	2.05441i	0.0486010	−	0.128150i	0.957119	+	0.289696i	$0.0935542\pi$
$258$	−7.87287	−	6.48591i	−0.490144	−	0.403795i
$259$	12.7542	−	4.83702i	0.792506	−	0.300558i
$260$	−1.63720	−	8.92446i	−0.101535	−	0.553472i
$261$	−13.2543	−	2.27385i	−0.820419	−	0.140748i
$262$	8.13171	+	18.0679i	0.502379	+	1.11624i
$263$	−6.81544	−	4.70436i	−0.420258	−	0.290083i	0.339107	−	0.940748i	$-0.389875\pi$
$263$	−6.81544	−	4.70436i	−0.420258	−	0.290083i	−0.759365	+	0.650665i	$0.774490\pi$
$264$	−20.8824	+	22.4374i	−1.28522	+	1.38093i
$265$	−4.75798	−	25.9635i	−0.292281	−	1.59492i
$266$	0.492010	+	8.13390i	0.0301671	+	0.498721i
$267$	−11.2233	−	26.6668i	−0.686858	−	1.63198i
$268$	−0.754431	−	0.754431i	−0.0460842	−	0.0460842i
$269$	4.22304	−	8.04633i	0.257483	−	0.490593i	−0.722059	−	0.691831i	$-0.756804\pi$
$269$	4.22304	−	8.04633i	0.257483	−	0.490593i	0.979542	+	0.201238i	$0.0644965\pi$
$270$	3.56308	+	21.0020i	0.216842	+	1.27814i
$271$	−3.51244	+	7.80433i	−0.213366	+	0.474079i	−0.987236	−	0.159265i	$-0.949088\pi$
$271$	−3.51244	+	7.80433i	−0.213366	+	0.474079i	0.773870	+	0.633344i	$0.218318\pi$
$272$	8.74890	+	4.59178i	0.530480	+	0.278417i
$273$	−12.4982	−	4.23107i	−0.756426	−	0.256076i
$274$	1.31889	−	0.692205i	0.0796768	−	0.0418176i
$275$	2.75148	+	45.4873i	0.165920	+	2.74299i
$276$	−0.961910	+	1.03354i	−0.0579002	+	0.0622116i
$277$	1.93380	−	7.84574i	0.116191	−	0.471405i	−0.883803	−	0.467859i	$-0.845025\pi$
$277$	1.93380	−	7.84574i	0.116191	−	0.471405i	0.999994	−	0.00354521i	$-0.00112848\pi$
$278$	−12.1099	+	9.48750i	−0.726303	+	0.569022i
$279$	−1.42860	−	10.7454i	−0.0855279	−	0.643312i
$280$	−21.3262	+	9.59816i	−1.27449	+	0.573600i
$281$	−11.9584	+	3.72638i	−0.713377	+	0.222297i	−0.632649	−	0.774439i	$-0.718032\pi$
$281$	−11.9584	+	3.72638i	−0.713377	+	0.222297i	−0.0807284	+	0.996736i	$0.525725\pi$
$282$	4.04204	+	6.17463i	0.240700	+	0.367694i
$283$	23.6233	−	2.86839i	1.40426	−	0.170508i	0.616920	−	0.787026i	$-0.288380\pi$
$283$	23.6233	−	2.86839i	1.40426	−	0.170508i	0.787341	+	0.616517i	$0.211457\pi$
$284$	0.139178	−	2.30089i	0.00825869	−	0.136532i
$285$	−6.98403	−	19.8727i	−0.413698	−	1.17716i
$286$	−13.4285	−	19.4468i	−0.794046	−	1.14991i
$287$	−5.14152	+	20.8600i	−0.303494	+	1.23133i
$288$	11.1849	+	1.22952i	0.659077	+	0.0724499i
$289$	4.35837	−	2.28745i	0.256375	−	0.134556i
$290$	−6.51658	−	17.1828i	−0.382667	−	1.00901i
$291$	−5.48127	+	16.1812i	−0.321318	+	0.948556i
$292$	3.42043	+	0.626817i	0.200165	+	0.0366817i
$293$	−1.58999	+	0.961185i	−0.0928884	+	0.0561530i	−0.563020	−	0.826444i	$-0.690360\pi$
$293$	−1.58999	+	0.961185i	−0.0928884	+	0.0561530i	0.470131	+	0.882597i	$0.344207\pi$
$294$	0.424907	−	4.98975i	0.0247811	−	0.291008i
$295$	−2.10668	+	17.3501i	−0.122656	+	1.01016i
$296$	−7.04755	−	18.5829i	−0.409631	−	1.08011i
$297$	−16.6424	−	24.8043i	−0.965689	−	1.43929i
$298$	2.00935	+	1.38695i	0.116399	+	0.0803441i
$299$	−2.38610	−	3.45547i	−0.137992	−	0.199835i
$300$	7.34752	−	6.19435i	0.424209	−	0.357631i
$301$	8.59061	+	6.73031i	0.495154	+	0.387929i
$302$	−2.16043	−	8.76520i	−0.124319	−	0.504381i
$303$	29.2039	+	16.2534i	1.67772	+	0.933735i
$304$	7.12494	−	0.430979i	0.408643	−	0.0247184i
$305$	9.90045	+	3.08510i	0.566898	+	0.176653i
$306$	−10.4838	+	12.1077i	−0.599319	+	0.692153i
$307$	−2.73970	+	3.49696i	−0.156363	+	0.199582i	−0.859014	−	0.511952i	$-0.828922\pi$
$307$	−2.73970	+	3.49696i	−0.156363	+	0.199582i	0.702651	+	0.711534i	$0.251999\pi$
$308$	5.63725	−	6.36314i	0.321212	−	0.362574i
$309$	9.86292	+	11.6991i	0.561082	+	0.665536i
$310$	11.6607	−	9.13558i	0.662284	−	0.518866i
$311$	−2.05349	−	16.9120i	−0.116443	−	0.958990i	−0.927448	−	0.373952i	$-0.878003\pi$
$311$	−2.05349	−	16.9120i	−0.116443	−	0.958990i	0.811006	−	0.585038i	$-0.198921\pi$
$312$	−6.16468	+	18.2099i	−0.349006	+	1.03093i
$313$	1.84968	−	15.2335i	0.104550	−	0.861048i	−0.842219	−	0.539135i	$-0.818751\pi$
$313$	1.84968	−	15.2335i	0.104550	−	0.861048i	0.946769	−	0.321913i	$-0.104326\pi$
$314$	−0.395765	−	0.654675i	−0.0223343	−	0.0369454i
$315$	−4.36211	−	22.3691i	−0.245777	−	1.26035i
$316$		−	0.619183i		−	0.0348318i
$317$	−2.63730	−	4.36263i	−0.148126	−	0.245030i	0.772903	−	0.634524i	$-0.218804\pi$
$317$	−2.63730	−	4.36263i	−0.148126	−	0.245030i	−0.921029	+	0.389494i	$0.872650\pi$
$318$	−4.65169	+	13.7322i	−0.260854	+	0.770062i
$319$	18.2210	+	18.2210i	1.02018	+	1.02018i
$320$	12.5388	+	27.8600i	0.700939	+	1.55742i
$321$	25.5971	−	8.99580i	1.42869	−	0.502096i
$322$	−1.86062	+	2.10020i	−0.103688	+	0.117040i
$323$	8.19305	−	13.5530i	0.455874	−	0.754107i
$324$	−2.09954	+	5.93901i	−0.116641	+	0.329945i
$325$	13.2877	+	25.3061i	0.737069	+	1.40373i
$326$	9.02160	+	10.1833i	0.499660	+	0.564000i
$327$	30.5995	−	8.71758i	1.69215	−	0.482083i
$328$	30.3930	+	7.49121i	1.67817	+	0.413633i
$329$	−4.48520	−	6.49794i	−0.247277	−	0.358243i
$330$	17.6606	−	36.8002i	0.972182	−	2.02578i
$331$	−13.4213	+	22.2015i	−0.737701	+	1.22031i	0.231211	+	0.972904i	$0.425731\pi$
$331$	−13.4213	+	22.2015i	−0.737701	+	1.22031i	−0.968913	+	0.247404i	$0.920423\pi$
$332$	−9.84299	−	7.71149i	−0.540204	−	0.423223i
$333$	19.1988	−	2.55247i	1.05209	−	0.139874i
$334$	−8.99042	+	23.7058i	−0.491934	+	1.29712i
$335$	4.85304	+	2.54707i	0.265150	+	0.139161i
$336$	7.69506	+	0.655280i	0.419800	+	0.0357485i
$337$		−	3.05780i		−	0.166569i	−0.996526	−	0.0832844i	$-0.973459\pi$
$337$		−	3.05780i		−	0.166569i	0.996526	−	0.0832844i	$-0.0265410\pi$
$338$	−12.6879	−	7.66362i	−0.690133	−	0.416846i
$339$	15.7214	−	1.51858i	0.853870	−	0.0824782i
$340$	11.5896	+	2.12387i	0.628533	+	0.115183i
$341$	−9.65287	+	18.3920i	−0.522732	+	0.995983i
$342$	−1.95634	+	11.4035i	−0.105787	+	0.616631i
$343$	−1.21650	+	20.1111i	−0.0656847	+	1.08590i
$344$	9.80608	−	12.5165i	0.528708	−	0.674846i
$345$	3.13808	−	6.53897i	0.168949	−	0.352047i
$346$	−0.865965	−	0.523494i	−0.0465546	−	0.0281432i
$347$	−27.0627	+	18.6801i	−1.45280	+	1.00280i	−0.459388	+	0.888236i	$0.651931\pi$
$347$	−27.0627	+	18.6801i	−1.45280	+	1.00280i	−0.993416	+	0.114563i	$0.963453\pi$
$348$	0.787173	−	5.37690i	0.0421969	−	0.288232i
$349$	2.04947	−	0.375580i	0.109706	−	0.0201043i	−0.125122	−	0.992141i	$-0.539932\pi$
$349$	2.04947	−	0.375580i	0.109706	−	0.0201043i	0.234827	+	0.972037i	$0.424548\pi$
$350$	14.2952	−	12.6644i	0.764109	−	0.676941i
$351$	−15.9057	−	9.89999i	−0.848981	−	0.528423i
$352$	−16.1388	−	14.2977i	−0.860202	−	0.762073i
$353$	−20.5736	−	12.4371i	−1.09502	−	0.661963i	−0.149905	−	0.988700i	$-0.547897\pi$
$353$	−20.5736	−	12.4371i	−1.09502	−	0.661963i	−0.945115	+	0.326738i	$0.894051\pi$
$354$	5.64561	−	7.76448i	0.300061	−	0.412677i
$355$	2.83381	+	11.4972i	0.150403	+	0.610210i
$356$	10.6614	−	4.79829i	0.565051	−	0.254309i
$357$	10.8951	−	13.2249i	0.576628	−	0.699936i
$358$	−4.48866	+	9.97340i	−0.237233	+	0.527111i
$359$	−27.1686	+	16.4240i	−1.43391	+	0.866826i	−0.999427	−	0.0338559i	$-0.989221\pi$
$359$	−27.1686	+	16.4240i	−1.43391	+	0.866826i	−0.434479	+	0.900682i	$0.643067\pi$
$360$	−32.5918	+	6.35560i	−1.71774	+	0.334970i
$361$			7.55913i			0.397849i
$362$	14.3302	−	8.66288i	0.753177	−	0.455311i
$363$	−0.936769	+	38.1720i	−0.0491676	+	2.00351i
$364$	1.58533	−	5.09088i	0.0830940	−	0.266834i
$365$	−17.7332	+	2.15320i	−0.928198	+	0.112704i
$366$	−3.92766	−	4.12529i	−0.205302	−	0.215632i
$367$	5.76298	+	8.34912i	0.300825	+	0.435820i	0.944023	−	0.329880i	$-0.107008\pi$
$367$	5.76298	+	8.34912i	0.300825	+	0.435820i	−0.643198	+	0.765700i	$0.722393\pi$
$368$	1.83969	+	1.62982i	0.0959002	+	0.0849602i
$369$	−13.8689	+	27.1696i	−0.721987	+	1.41439i
$370$	16.3225	+	20.8341i	0.848565	+	1.08311i
$371$	4.61475	−	14.8092i	0.239586	−	0.768858i
$372$	4.32670	−	0.683642i	0.224329	−	0.0354452i
$373$	2.70427	−	3.91781i	0.140022	−	0.202857i	−0.746699	−	0.665162i	$-0.768362\pi$
$373$	2.70427	−	3.91781i	0.140022	−	0.202857i	0.886721	+	0.462306i	$0.152978\pi$
$374$	29.7972	−	7.34436i	1.54078	−	0.379768i
$375$	−9.81110	+	15.3650i	−0.506643	+	0.793446i
$376$	−9.46750	+	6.53495i	−0.488249	+	0.337014i
$377$	15.1132	+	5.72842i	0.778367	+	0.295029i
$378$	−3.88156	+	11.9013i	−0.199646	+	0.612136i
$379$	−4.53084	+	1.41187i	−0.232734	+	0.0725228i	−0.411652	−	0.911341i	$-0.635048\pi$
$379$	−4.53084	+	1.41187i	−0.232734	+	0.0725228i	0.178918	+	0.983864i	$0.442740\pi$
$380$	7.95878	−	3.01837i	0.408277	−	0.154839i
$381$	0.228047	−	9.29260i	0.0116832	−	0.476074i
$382$	−7.64815	−	1.40158i	−0.391314	−	0.0717109i
$383$	5.29084	+	8.75213i	0.270350	+	0.447213i	0.961227	−	0.275759i	$-0.0889293\pi$
$383$	5.29084	+	8.75213i	0.270350	+	0.447213i	−0.690877	+	0.722972i	$0.742775\pi$
$384$	0.321435	−	3.77467i	0.0164032	−	0.192625i
$385$	−17.9228	+	39.8229i	−0.913432	+	2.02956i
$386$	−4.67802	+	1.77414i	−0.238105	+	0.0903013i
$387$	9.69384	+	12.0883i	0.492766	+	0.614481i
$388$	−6.59108	−	2.05386i	−0.334611	−	0.104269i
$389$	23.0308	+	5.67657i	1.16771	+	0.287814i	0.775067	−	0.631879i	$-0.217716\pi$
$389$	23.0308	+	5.67657i	1.16771	+	0.287814i	0.392639	+	0.919693i	$0.371562\pi$
$390$	0.623295	−	25.5944i	0.0315618	−	1.29602i
$391$	5.29464	−	1.30501i	0.267761	−	0.0659972i
$392$	7.79190	+	0.471323i	0.393550	+	0.0238054i
$393$	−6.48377	−	29.3912i	−0.327063	−	1.48259i
$394$	−11.4859	−	21.8845i	−0.578650	−	1.10252i
$395$	0.946286	+	3.03674i	0.0476128	+	0.152795i
$396$	9.85526	−	6.96897i	0.495246	−	0.350204i
$397$	−28.6356	−	1.73214i	−1.43718	−	0.0869334i	−0.676683	−	0.736274i	$-0.736583\pi$
$397$	−28.6356	−	1.73214i	−1.43718	−	0.0869334i	−0.760497	+	0.649341i	$0.775045\pi$
$398$	0.869888	+	1.11033i	0.0436035	+	0.0556558i
$399$	1.79308	−	12.2479i	0.0897662	−	0.613161i
$400$	−11.0935	−	12.5219i	−0.554673	−	0.626096i
$401$	−18.5942	+	1.12474i	−0.928550	+	0.0561670i	−0.517725	−	0.855547i	$-0.673221\pi$
$401$	−18.5942	+	1.12474i	−0.928550	+	0.0561670i	−0.410825	+	0.911714i	$0.634759\pi$
$402$	−1.64886	−	2.51880i	−0.0822377	−	0.125627i
$403$	−0.784171	+	13.0044i	−0.0390623	+	0.647796i
$404$	−6.27642	+	11.9587i	−0.312263	+	0.594968i
$405$	1.22056	−	32.3362i	0.0606499	−	1.60680i
$406$	1.30171	−	10.7206i	0.0646029	−	0.532053i
$407$	−32.8609	−	17.2467i	−1.62885	−	0.854888i
$408$	−19.2687	−	15.8741i	−0.953943	−	0.785887i
$409$	16.6684	−	5.19410i	0.824202	−	0.256832i	0.143740	−	0.989615i	$-0.454087\pi$
$409$	16.6684	−	5.19410i	0.824202	−	0.256832i	0.680461	+	0.732784i	$0.261779\pi$
$410$	−41.6096	+	2.51691i	−2.05495	+	0.124302i
$411$	−2.17605	+	0.619941i	−0.107337	+	0.0305795i
$412$	−4.62832	+	4.10033i	−0.228021	+	0.202009i
$413$	−5.83443	+	8.45263i	−0.287093	+	0.415927i
$414$	−3.25281	+	2.30016i	−0.159867	+	0.113047i
$415$	60.0596	+	22.7776i	2.94821	+	1.11811i
$416$	−12.9120	−	4.02087i	−0.633062	−	0.197140i
$417$	20.9524	−	10.3492i	1.02604	−	0.506801i
$418$	15.6767	−	15.6767i	0.766774	−	0.766774i
$419$	23.1230	+	8.76941i	1.12963	+	0.428414i	0.847412	−	0.530935i	$-0.178159\pi$
$419$	23.1230	+	8.76941i	1.12963	+	0.428414i	0.282222	+	0.959349i	$0.408929\pi$
$420$	8.99324	−	1.98393i	0.438825	−	0.0968060i
$421$	7.97183	−	25.5825i	0.388523	−	1.24682i	−0.528825	−	0.848731i	$-0.677367\pi$
$421$	7.97183	−	25.5825i	0.388523	−	1.24682i	0.917349	−	0.398085i	$-0.130325\pi$
$422$	−2.77878	+	0.509231i	−0.135269	+	0.0247890i
$423$	−4.09399	−	10.4363i	−0.199056	−	0.507432i
$424$	−21.5771	−	6.72369i	−1.04788	−	0.326531i
$425$	−36.8462	+	4.47394i	−1.78730	+	0.217018i
$426$	1.71101	−	6.27509i	0.0828989	−	0.304029i
$427$	4.30908	+	4.30908i	0.208531	+	0.208531i
$428$	3.88782	+	10.2513i	0.187925	+	0.495517i
$429$	13.9322	+	33.0856i	0.672653	+	1.59739i
$430$	−7.50859	+	19.7985i	−0.362096	+	0.954769i
$431$	33.9196	−	15.2660i	1.63385	−	0.735335i	0.634553	−	0.772880i	$-0.281184\pi$
$431$	33.9196	−	15.2660i	1.63385	−	0.735335i	0.999295	+	0.0375447i	$0.0119537\pi$
$432$	10.4250	+	3.40007i	0.501573	+	0.163586i
$433$	−16.4153	−	18.5291i	−0.788870	−	0.890451i	0.207265	−	0.978285i	$-0.433544\pi$
$433$	−16.4153	−	18.5291i	−0.788870	−	0.890451i	−0.996135	+	0.0878343i	$0.972005\pi$
$434$	8.56243	−	1.56912i	0.411010	−	0.0753204i
$435$	4.35679	+	27.5737i	0.208892	+	1.32206i
$436$	3.82502	+	12.2749i	0.183185	+	0.587862i
$437$	2.78558	−	2.78558i	0.133252	−	0.133252i
$438$	9.08625	+	3.70341i	0.434158	+	0.176956i
$439$	19.7548	+	2.39867i	0.942846	+	0.114482i	0.577501	−	0.816390i	$-0.304028\pi$
$439$	19.7548	+	2.39867i	0.942846	+	0.114482i	0.365345	+	0.930872i	$0.380951\pi$
$440$	58.0220	+	26.1136i	2.76609	+	1.24492i
$441$	−2.18062	+	7.28791i	−0.103839	+	0.347043i
$442$	15.1500	−	11.8738i	0.720611	−	0.564781i
$443$	−1.25061	−	2.38283i	−0.0594181	−	0.113212i	0.853936	−	0.520378i	$-0.174209\pi$
$443$	−1.25061	−	2.38283i	−0.0594181	−	0.113212i	−0.913354	+	0.407167i	$0.866517\pi$
$444$	1.22146	+	7.73048i	0.0579678	+	0.366872i
$445$	−44.9548	+	39.8264i	−2.13106	+	1.88795i
$446$	−8.11038	−	1.99903i	−0.384037	−	0.0946567i
$447$	−2.55742	−	2.68610i	−0.120962	−	0.127048i
$448$	−1.08402	+	17.9210i	−0.0512152	+	0.846688i
$449$	0.440964	+	0.979781i	0.0208104	+	0.0462387i	0.922012	−	0.387162i	$-0.126544\pi$
$449$	0.440964	+	0.979781i	0.0208104	+	0.0462387i	−0.901202	+	0.433400i	$0.857314\pi$
$450$	23.8661	−	12.8733i	1.12506	−	0.606853i
$451$	51.7567	−	27.1640i	2.43713	−	1.27910i
$452$	0.769325	+	6.33596i	0.0361860	+	0.298018i
$453$	0.491921	+	13.7045i	0.0231125	+	0.643894i
$454$	−3.21832	−	13.0572i	−0.151043	−	0.612806i
$455$	0.00514415	+	27.3907i	0.000241162	+	1.28409i
$456$	−17.8452	−	2.61252i	−0.835678	−	0.122342i
$457$	8.22446	−	26.3932i	0.384724	−	1.23462i	−0.535936	−	0.844258i	$-0.680041\pi$
$457$	8.22446	−	26.3932i	0.384724	−	1.23462i	0.920660	−	0.390365i	$-0.127651\pi$
$458$	−2.05968	−	3.92439i	−0.0962424	−	0.183375i
$459$	19.3476	−	14.7502i	0.903070	−	0.688480i
$460$	2.67268	+	1.20287i	0.124614	+	0.0560843i
$461$	−7.60790	+	41.5150i	−0.354335	+	1.93354i	0.00410440	+	0.999992i	$0.498694\pi$
$461$	−7.60790	+	41.5150i	−0.354335	+	1.93354i	−0.358440	+	0.933553i	$0.616691\pi$
$462$	19.2395	−	14.3256i	0.895102	−	0.666487i
$463$	1.78393	−	9.73460i	0.0829063	−	0.452405i	−0.915804	−	0.401626i	$-0.868445\pi$
$463$	1.78393	−	9.73460i	0.0829063	−	0.452405i	0.998710	−	0.0507788i	$-0.0161704\pi$
$464$	−9.39074	−	1.14024i	−0.435954	−	0.0529344i
$465$	−20.1752	+	9.96528i	−0.935601	+	0.462129i
$466$	−0.535086	−	1.71715i	−0.0247874	−	0.0795456i
$467$	16.8967	−	24.4790i	0.781884	−	1.13275i	−0.206150	−	0.978520i	$-0.566094\pi$
$467$	16.8967	−	24.4790i	0.781884	−	1.13275i	0.988034	−	0.154234i	$-0.0492910\pi$
$468$	3.84164	−	6.52359i	0.177580	−	0.301553i
$469$	1.82964	+	2.65069i	0.0844849	+	0.122398i
$470$	9.44794	−	12.0594i	0.435801	−	0.556259i
$471$	0.385299	+	1.09635i	0.0177536	+	0.0505171i
$472$	12.3155	+	8.50077i	0.566866	+	0.391280i
$473$	−1.79271	−	29.6370i	−0.0824287	−	1.36271i
$474$	0.356993	−	1.71026i	0.0163972	−	0.0785549i
$475$	−21.1074	+	16.5366i	−0.968473	+	0.758750i
$476$	5.45051	+	4.27020i	0.249824	+	0.195724i
$477$	11.1795	−	18.9760i	0.511872	−	0.868851i
$478$	−6.80740	+	4.69881i	−0.311363	+	0.214918i
$479$	−3.82760	−	4.88557i	−0.174888	−	0.223227i	0.691787	−	0.722102i	$-0.256824\pi$
$479$	−3.82760	−	4.88557i	−0.174888	−	0.223227i	−0.866674	+	0.498874i	$0.833747\pi$
$480$	−5.03185	−	22.8095i	−0.229671	−	1.04111i
$481$	−23.2349	−	1.40107i	−1.05942	−	0.0638835i
$482$	−16.5136	−	2.00511i	−0.752174	−	0.0913304i
$483$	3.41864	−	2.54550i	0.155554	−	0.115824i
$484$	−15.4297			−0.701351
$485$	35.4644			1.61035
$486$	−9.22336	+	15.1938i	−0.418380	+	0.689204i
$487$	19.1230	+	8.60656i	0.866546	+	0.390001i	0.794401	−	0.607394i	$-0.207785\pi$
$487$	19.1230	+	8.60656i	0.866546	+	0.390001i	0.0721448	+	0.997394i	$0.477016\pi$
$488$	6.27833	−	6.27833i	0.284207	−	0.284207i
$489$	−10.2544	−	17.9429i	−0.463719	−	0.811404i
$490$	−10.0933	+	2.48779i	−0.455971	+	0.112387i
$491$	0.0271413	+	0.0240451i	0.00122487	+	0.00108514i	0.663735	−	0.747968i	$-0.268970\pi$
$491$	0.0271413	+	0.0240451i	0.00122487	+	0.00108514i	−0.662510	+	0.749053i	$0.730509\pi$
$492$	−11.1133	−	5.33330i	−0.501024	−	0.240444i
$493$	−13.9178	+	15.7099i	−0.626824	+	0.707538i
$494$	4.92853	−	13.0028i	0.221745	−	0.585025i
$495$	−37.6839	+	49.2404i	−1.69376	+	2.21319i
$496$	−1.37448	−	7.50031i	−0.0617161	−	0.336774i
$497$	−1.66530	+	6.75638i	−0.0746989	+	0.303065i
$498$	−22.7415	−	26.9751i	−1.01907	−	1.20878i
$499$	14.0079	−	23.1719i	0.627080	−	1.03732i	−0.367162	−	0.930157i	$-0.619671\pi$
$499$	14.0079	−	23.1719i	0.627080	−	1.03732i	0.994242	−	0.107159i	$-0.0341755\pi$
$500$	−6.30431	−	3.81109i	−0.281937	−	0.170437i
$501$	20.7269	−	32.4601i	0.926010	−	1.45021i
$502$	15.2828	+	0.924439i	0.682105	+	0.0412597i
$503$	1.14867	+	0.435632i	0.0512165	+	0.0194239i	0.380080	−	0.924954i	$-0.375896\pi$
$503$	1.14867	+	0.435632i	0.0512165	+	0.0194239i	−0.328864	+	0.944377i	$0.606666\pi$
$504$	−18.6945	−	5.59360i	−0.832720	−	0.249159i
$505$	12.5060	−	68.2428i	0.556508	−	3.03676i
$506$	7.63382			0.339365
$507$	16.4883	+	15.3341i	0.732273	+	0.681012i
$508$	3.75622			0.166655
$509$	−4.38130	+	23.9080i	−0.194198	+	1.05970i	0.731614	+	0.681719i	$0.238767\pi$
$509$	−4.38130	+	23.9080i	−0.194198	+	1.05970i	−0.925812	+	0.377984i	$0.876617\pi$
$510$	30.7873	+	12.5484i	1.36328	+	0.555653i
$511$	−9.81534	−	3.72247i	−0.434205	−	0.164672i
$512$	20.8701	+	1.26241i	0.922338	+	0.0557911i
$513$	6.44866	−	16.3499i	0.284715	−	0.721864i
$514$	2.14396	+	1.29607i	0.0945659	+	0.0571671i
$515$	16.4328	−	27.1831i	0.724115	−	1.19783i
$516$	−4.78723	+	4.03588i	−0.210746	+	0.177670i
$517$	−5.14084	+	20.8572i	−0.226094	+	0.917299i
$518$	2.80354	+	15.2984i	0.123181	+	0.672175i
$519$	1.12521	+	1.04723i	0.0493912	+	0.0459683i
$520$	39.9082	−	0.00749504i	1.75009	−	0.000328679i
$521$	−5.25754	+	5.93453i	−0.230337	+	0.259997i	−0.852304	−	0.523047i	$-0.824795\pi$
$521$	−5.25754	+	5.93453i	−0.230337	+	0.259997i	0.621967	+	0.783043i	$0.286334\pi$
$522$	5.27435	−	14.3978i	0.230852	−	0.630176i
$523$	6.68252	+	5.92019i	0.292206	+	0.258872i	0.796471	−	0.604677i	$-0.206698\pi$
$523$	6.68252	+	5.92019i	0.292206	+	0.258872i	−0.504265	+	0.863549i	$0.668236\pi$
$524$	11.8089	−	2.91064i	0.515876	−	0.127152i
$525$	−25.1880	+	14.3950i	−1.09929	+	0.628248i
$526$	6.67689	−	6.67689i	0.291126	−	0.291126i
$527$	−15.4275	−	6.94337i	−0.672034	−	0.302458i
$528$	−12.5486	−	16.8529i	−0.546107	−	0.733430i
$529$	−21.6436			−0.941024
$530$	30.0969			1.30733
$531$	−10.8051	+	9.79349i	−0.468902	+	0.425001i
$532$	4.96558	+	0.602931i	0.215285	+	0.0261404i
$533$	22.6047	−	28.8640i	0.979120	−	1.25024i
$534$	32.2145	−	7.10661i	1.39406	−	0.307533i
$535$	−34.7344	−	44.3352i	−1.50170	−	1.91678i
$536$	3.86206	−	2.66579i	0.166816	−	0.115144i
$537$	9.77035	−	13.4373i	0.421622	−	0.579861i
$538$	8.15630	+	6.39005i	0.351643	+	0.275495i
$539$	11.4744	−	8.98964i	0.494239	−	0.387211i
$540$	13.0750	+	0.172497i	0.562659	+	0.00742310i
$541$	−0.773058	−	12.7802i	−0.0332364	−	0.549463i	−0.976242	−	0.216685i	$-0.930476\pi$
$541$	−0.773058	−	12.7802i	−0.0332364	−	0.549463i	0.943005	−	0.332778i	$-0.107986\pi$
$542$	−8.03093	−	5.54335i	−0.344958	−	0.238107i
$543$	−23.9980	+	8.43380i	−1.02985	+	0.361929i
$544$	10.8305	−	13.8241i	0.464354	−	0.592704i
$545$	−37.5191	−	54.3557i	−1.60714	−	2.32834i
$546$	7.31405	−	13.1476i	0.313013	−	0.562665i
$547$	−12.3244	+	17.8549i	−0.526952	+	0.763421i	−0.992584	−	0.121557i	$-0.961211\pi$
$547$	−12.3244	+	17.8549i	−0.526952	+	0.763421i	0.465633	+	0.884978i	$0.345827\pi$
$548$	−0.272012	−	0.872917i	−0.0116198	−	0.0372892i
$549$	4.56000	+	7.35345i	0.194616	+	0.313837i
$550$	−51.5812	−	6.26310i	−2.19943	−	0.267059i
$551$	−2.73307	+	14.9139i	−0.116433	+	0.635352i
$552$	−3.70879	−	4.98097i	−0.157857	−	0.212004i
$553$	−0.336930	+	1.83857i	−0.0143277	+	0.0781838i
$554$	8.40183	+	3.78136i	0.356960	+	0.160655i
$555$	−17.8049	−	36.0468i	−0.755776	−	1.53010i
$556$	4.38849	+	8.36157i	0.186114	+	0.354610i
$557$	9.33042	−	29.9424i	0.395343	−	1.26870i	−0.515836	−	0.856687i	$-0.672519\pi$
$557$	9.33042	−	29.9424i	0.395343	−	1.26870i	0.911179	−	0.412012i	$-0.135174\pi$
$558$	12.3450	+	0.606277i	0.522607	+	0.0256657i
$559$	−8.65752	−	16.4880i	−0.366174	−	0.697368i
$560$	−3.83660	−	15.5657i	−0.162126	−	0.657771i
$561$	−46.5884	+	1.67228i	−1.96696	+	0.0706038i
$562$	−1.72148	−	14.1777i	−0.0726162	−	0.598048i
$563$	21.8211	−	11.4526i	0.919648	−	0.482669i	0.0626776	−	0.998034i	$-0.480036\pi$
$563$	21.8211	−	11.4526i	0.919648	−	0.482669i	0.856971	+	0.515365i	$0.172344\pi$
$564$	4.17541	−	1.75732i	0.175816	−	0.0739966i
$565$	−13.4562	−	29.8985i	−0.566108	−	1.25784i
$566$	−1.63828	+	27.0840i	−0.0688620	+	1.13843i
$567$	9.46598	−	16.4925i	0.397534	−	0.692620i
$568$	9.84406	+	2.42634i	0.413048	+	0.101807i
$569$	−23.4698	+	20.7924i	−0.983904	+	0.871663i	−0.991735	−	0.128306i	$-0.959046\pi$
$569$	−23.4698	+	20.7924i	−0.983904	+	0.871663i	0.00783040	+	0.999969i	$0.497507\pi$
$570$	23.7234	−	3.74843i	0.993664	−	0.157004i
$571$	3.84360	+	7.32337i	0.160850	+	0.306473i	0.952520	−	0.304474i	$-0.0984808\pi$
$571$	3.84360	+	7.32337i	0.160850	+	0.306473i	−0.791671	+	0.610948i	$0.790789\pi$
$572$	−13.2276	+	5.95623i	−0.553072	+	0.249042i
$573$	10.9378	+	4.45808i	0.456934	+	0.186239i
$574$	−22.3385	−	10.0537i	−0.932392	−	0.419635i
$575$	−9.16541	−	1.11288i	−0.382224	−	0.0464104i
$576$	−7.30733	+	24.4220i	−0.304472	+	1.01758i
$577$	−25.8598	+	25.8598i	−1.07656	+	1.07656i	−0.0797405	+	0.996816i	$0.525409\pi$
$577$	−25.8598	+	25.8598i	−1.07656	+	1.07656i	−0.996816	+	0.0797405i	$0.974591\pi$
$578$	1.66969	+	5.35822i	0.0694499	+	0.222873i
$579$	7.50693	−	1.18614i	0.311977	−	0.0492941i
$580$	−11.0958	+	2.03338i	−0.460728	+	0.0844316i
$581$	25.0310	+	28.2541i	1.03846	+	1.17218i
$582$	−17.0212	−	9.47315i	−0.705552	−	0.392675i
$583$	−38.4842	+	17.3203i	−1.59385	+	0.717334i
$584$	−5.42364	+	14.3010i	−0.224432	+	0.591778i
$585$	−8.87115	+	37.8656i	−0.366777	+	1.56555i
$586$	−0.751214	−	1.98079i	−0.0310324	−	0.0818257i
$587$	−14.2676	−	14.2676i	−0.588887	−	0.588887i	0.348443	−	0.937330i	$-0.386711\pi$
$587$	−14.2676	−	14.2676i	−0.588887	−	0.588887i	−0.937330	+	0.348443i	$0.886711\pi$
$588$	−2.96573	−	0.808660i	−0.122305	−	0.0333486i
$589$	−12.1327	+	1.47318i	−0.499921	+	0.0607014i
$590$	−19.0258	−	5.92867i	−0.783279	−	0.244079i
$591$	10.2868	+	36.1075i	0.423142	+	1.48527i
$592$	13.4008	−	2.45578i	0.550768	−	0.100932i
$593$	0.0381036	−	0.122279i	0.00156473	−	0.00502139i	−0.953935	−	0.300013i	$-0.903009\pi$
$593$	0.0381036	−	0.122279i	0.00156473	−	0.00502139i	0.955500	+	0.294991i	$0.0953168\pi$
$594$	31.2395	−	13.5670i	1.28177	−	0.556662i
$595$	−33.2577	−	12.6130i	−1.36343	−	0.517082i
$596$	1.05976	−	1.05976i	0.0434093	−	0.0434093i
$597$	−0.948892	−	1.92108i	−0.0388356	−	0.0786244i
$598$	4.36586	−	1.96590i	0.178533	−	0.0803916i
$599$	12.8747	+	4.88274i	0.526047	+	0.199503i	0.603309	−	0.797508i	$-0.293849\pi$
$599$	12.8747	+	4.88274i	0.526047	+	0.199503i	−0.0772621	+	0.997011i	$0.524618\pi$
$600$	20.9735	+	36.6989i	0.856239	+	1.49823i
$601$	−17.8064	+	25.7970i	−0.726337	+	1.05228i	0.269665	+	0.962954i	$0.413087\pi$
$601$	−17.8064	+	25.7970i	−0.726337	+	1.05228i	−0.996002	+	0.0893272i	$0.971528\pi$
$602$	−9.31392	+	8.25141i	−0.379607	+	0.336302i
$603$	1.67005	+	4.25728i	0.0680098	+	0.173370i
$604$	−5.53136	+	0.334586i	−0.225068	+	0.0136141i
$605$	75.6740	−	23.5810i	3.07659	−	0.958703i
$606$	−24.2311	+	29.4127i	−0.984321	+	1.19481i
$607$	−0.813439	−	0.426925i	−0.0330165	−	0.0173284i	0.448134	−	0.893966i	$-0.352089\pi$
$607$	−0.813439	−	0.426925i	−0.0330165	−	0.0173284i	−0.481151	+	0.876638i	$0.659781\pi$
$608$	1.52921	−	12.5942i	0.0620178	−	0.510762i
$609$	−5.26324	+	15.5375i	−0.213277	+	0.629612i
$610$	−5.49489	+	10.4696i	−0.222482	+	0.423903i
$611$	2.43115	+	13.2523i	0.0983539	+	0.536132i
$612$	6.15048	+	7.66968i	0.248618	+	0.310028i
$613$	48.4001	−	2.92767i	1.95486	−	0.118247i	0.965185	−	0.261566i	$-0.0842390\pi$
$613$	48.4001	−	2.92767i	1.95486	−	0.118247i	0.989677	+	0.143319i	$0.0457775\pi$
$614$	−3.35889	−	3.79140i	−0.135554	−	0.153008i
$615$	62.6550	+	9.17262i	2.52649	+	0.369876i
$616$	23.0597	+	29.4335i	0.929102	+	1.18591i
$617$	−12.3940	−	0.749697i	−0.498962	−	0.0301817i	−0.191019	−	0.981586i	$-0.561179\pi$
$617$	−12.3940	−	0.749697i	−0.498962	−	0.0301817i	−0.307943	+	0.951405i	$0.599641\pi$
$618$	−15.1480	+	8.65714i	−0.609344	+	0.348241i
$619$	−11.9147	−	38.2357i	−0.478893	−	1.53682i	−0.806047	−	0.591852i	$-0.798397\pi$
$619$	−11.9147	−	38.2357i	−0.478893	−	1.53682i	0.327154	−	0.944971i	$-0.393911\pi$
$620$	−4.22571	−	8.05142i	−0.169709	−	0.323353i
$621$	5.55090	−	2.41071i	0.222750	−	0.0967385i
$622$	19.3895	+	1.17285i	0.777447	+	0.0470269i
$623$	−34.2682	+	8.44636i	−1.37293	+	0.338396i
$624$	−11.5167	−	6.40679i	−0.461037	−	0.256477i
$625$	−1.74161	−	0.429268i	−0.0696644	−	0.0171707i
$626$	16.7048	+	5.20542i	0.667657	+	0.208050i
$627$	−28.1774	+	18.4455i	−1.12530	+	0.736642i
$628$	−0.439075	+	0.166519i	−0.0175210	+	0.00664484i
$629$	12.4057	−	27.5643i	0.494646	−	1.09906i
$630$	25.9843	−	0.294769i	1.03524	−	0.0117439i
$631$	6.49745	+	10.7481i	0.258659	+	0.427875i	0.957938	−	0.286974i	$-0.0926493\pi$
$631$	6.49745	+	10.7481i	0.258659	+	0.427875i	−0.699279	+	0.714849i	$0.746495\pi$
$632$	2.67879	+	0.490907i	0.106557	+	0.0195272i
$633$	4.29013	+	0.105283i	0.170517	+	0.00418462i
$634$	5.43490	−	2.06119i	0.215847	−	0.0818601i
$635$	−18.4221	+	5.74055i	−0.731058	+	0.227807i
$636$	7.77661	+	4.32807i	0.308363	+	0.171619i
$637$	4.24728	−	8.09621i	0.168283	−	0.320784i
$638$	−24.1805	+	16.6906i	−0.957317	+	0.660788i
$639$	−4.49203	+	8.80002i	−0.177702	+	0.348123i
$640$	−7.63546	+	1.88197i	−0.301818	+	0.0743915i
$641$	−16.2241	+	23.5047i	−0.640814	+	0.928379i	−0.999988	−	0.00489149i	$-0.998443\pi$
$641$	−16.2241	+	23.5047i	−0.640814	+	0.928379i	0.359174	+	0.933271i	$0.383058\pi$
$642$	4.82817	+	30.5570i	0.190553	+	1.20599i
$643$	−0.593642	+	1.90507i	−0.0234110	+	0.0751284i	−0.965687	−	0.259708i	$-0.916374\pi$
$643$	−0.593642	+	1.90507i	−0.0234110	+	0.0751284i	0.942276	+	0.334837i	$0.108681\pi$
$644$	1.06220	+	1.35580i	0.0418566	+	0.0534260i
$645$	17.3106	−	27.1099i	0.681606	−	1.06745i
$646$	13.5162	+	11.9743i	0.531789	+	0.471124i
$647$	0.279251	+	0.404565i	0.0109785	+	0.0159051i	0.828435	−	0.560086i	$-0.189232\pi$
$647$	0.279251	+	0.404565i	0.0109785	+	0.0159051i	−0.817456	+	0.575991i	$0.804616\pi$
$648$	−24.0296	−	13.7919i	−0.943971	−	0.541799i
$649$	27.7396	−	3.36820i	1.08888	−	0.132214i
$650$	−31.1127	+	9.70152i	−1.22034	+	0.380525i
$651$	−13.2194	−	0.324415i	−0.518111	−	0.0127148i
$652$	7.14676	−	4.32037i	0.279889	−	0.169199i
$653$			20.0628i			0.785119i	0.919727	+	0.392559i	$0.128410\pi$
$653$			20.0628i			0.785119i	−0.919727	+	0.392559i	$0.871590\pi$
$654$	3.48801	+	36.1102i	0.136392	+	1.41202i
$655$	−53.4678	+	32.3224i	−2.08916	+	1.26294i
$656$	−8.80664	+	19.5675i	−0.343841	+	0.763984i
$657$	−12.3618	−	8.32731i	−0.482280	−	0.324879i
$658$	8.20952	−	3.69481i	0.320040	−	0.144039i
$659$	0.605186	+	2.45533i	0.0235747	+	0.0956463i	0.981551	−	0.191202i	$-0.0612386\pi$
$659$	0.605186	+	2.45533i	0.0235747	+	0.0956463i	−0.957976	+	0.286848i	$0.907392\pi$
$660$	−20.2654	−	14.7351i	−0.788828	−	0.573563i
$661$	37.8030	+	22.8527i	1.47037	+	0.888868i	0.999979	+	0.00640732i	$0.00203953\pi$
$661$	37.8030	+	22.8527i	1.47037	+	0.888868i	0.470387	+	0.882460i	$0.344114\pi$
$662$	−22.1414	−	19.6156i	−0.860550	−	0.762380i
$663$	−26.2137	+	12.9541i	−1.01806	+	0.503094i
$664$	41.1663	−	36.4702i	1.59756	−	1.41532i
$665$	−25.2748	+	4.63178i	−0.980115	+	0.179613i
$666$	−1.08323	+	22.0568i	−0.0419743	+	0.854683i
$667$	−4.29661	+	2.96574i	−0.166365	+	0.114834i
$668$	13.3185	+	8.05130i	0.515307	+	0.311514i
$669$	11.4397	+	5.48997i	0.442285	+	0.212254i
$670$	−3.85408	+	4.91937i	−0.148896	+	0.190052i
$671$	1.00106	−	16.5495i	0.0386455	−	0.638887i
$672$	3.61092	−	13.2429i	0.139294	−	0.510856i
$673$	−6.00134	+	11.4346i	−0.231335	+	0.440771i	−0.973258	−	0.229713i	$-0.926221\pi$
$673$	−6.00134	+	11.4346i	−0.231335	+	0.440771i	0.741924	+	0.670484i	$0.233914\pi$
$674$	3.42944	+	0.628467i	0.132097	+	0.0242077i
$675$	−39.4849	+	11.7348i	−1.51977	+	0.451674i
$676$	−6.03109	+	6.81285i	−0.231965	+	0.262033i
$677$			25.1286i			0.965772i	0.875683	+	0.482886i	$0.160411\pi$
$677$			25.1286i			0.965772i	−0.875683	+	0.482886i	$0.839589\pi$
$678$	−1.52806	+	17.9443i	−0.0586848	+	0.689145i
$679$	18.4536	+	9.68517i	0.708183	+	0.371683i
$680$	−18.3771	+	48.4565i	−0.704731	+	1.85822i
$681$	0.732798	+	20.4151i	0.0280809	+	0.782309i
$682$	−18.6434	−	14.6061i	−0.713892	−	0.559298i
$683$	−3.17247	+	5.24790i	−0.121391	+	0.200805i	−0.910567	−	0.413362i	$-0.864354\pi$
$683$	−3.17247	+	5.24790i	−0.121391	+	0.200805i	0.789176	+	0.614168i	$0.210508\pi$
$684$	6.66883	+	2.44299i	0.254989	+	0.0934101i
$685$	2.66813	+	3.86545i	0.101944	+	0.147691i
$686$	−22.3053	−	5.49777i	−0.851622	−	0.209906i
$687$	1.84466	+	6.47490i	0.0703780	+	0.247033i
$688$	7.22787	+	8.15858i	0.275560	+	0.311043i
$689$	−17.5491	+	19.8163i	−0.668566	+	0.754941i
$690$	6.68874	+	4.86343i	0.254636	+	0.185148i
$691$	16.9454	−	28.0311i	0.644634	−	1.06635i	−0.347074	−	0.937838i	$-0.612825\pi$
$691$	16.9454	−	28.0311i	0.644634	−	1.06635i	0.991707	−	0.128517i	$-0.0410216\pi$
$692$	−0.411897	+	0.464935i	−0.0156580	+	0.0176742i
$693$	−33.0558	+	15.3305i	−1.25569	+	0.582357i
$694$	−15.3882	−	34.1912i	−0.584128	−	1.29788i
$695$	−34.3019	−	34.3019i	−1.30114	−	1.30114i
$696$	22.6382	+	7.66855i	0.858099	+	0.290676i
$697$	24.6298	+	40.7427i	0.932920	+	1.54324i
$698$			2.37575i			0.0899236i
$699$	0.262686	+	2.71951i	0.00993571	+	0.102861i
$700$	−6.06488	−	10.0325i	−0.229231	−	0.379194i
$701$	−1.11765	+	9.20466i	−0.0422130	+	0.347655i	0.956265	+	0.292502i	$0.0944878\pi$
$701$	−1.11765	+	9.20466i	−0.0422130	+	0.347655i	−0.998478	+	0.0551533i	$0.982435\pi$
$702$	14.3723	−	15.8041i	0.542447	−	0.596486i
$703$	−2.63212	−	21.6775i	−0.0992724	−	0.817582i
$704$	38.4512	−	30.1246i	1.44918	−	1.13536i
$705$	−17.7923	+	14.9998i	−0.670097	+	0.564927i
$706$	18.1772	−	20.5178i	0.684108	−	0.772198i
$707$	25.1442	−	32.0942i	0.945644	−	1.20703i
$708$	−4.06342	−	4.26787i	−0.152713	−	0.160397i
$709$	−2.95379	−	0.920438i	−0.110932	−	0.0345678i	0.241535	−	0.970392i	$-0.422349\pi$
$709$	−2.95379	−	0.920438i	−0.110932	−	0.0345678i	−0.352467	+	0.935824i	$0.614657\pi$
$710$	−13.4770	+	0.815209i	−0.505783	+	0.0305942i
$711$	−1.06170	+	2.43236i	−0.0398170	+	0.0912207i
$712$	12.3064	+	49.9289i	0.461200	+	1.87116i
$713$	−3.31272	−	2.59535i	−0.124062	−	0.0971966i
$714$	12.5930	+	14.9373i	0.471280	+	0.559016i
$715$	55.7708	−	49.4273i	2.08571	−	1.84848i
$716$	5.52515	+	3.81374i	0.206485	+	0.142526i
$717$	11.5811	−	4.87420i	0.432505	−	0.182030i
$718$	−12.8362	−	33.8463i	−0.479042	−	1.26313i
$719$	4.80819	−	39.5990i	0.179315	−	1.47679i	−0.573849	−	0.818961i	$-0.694550\pi$
$719$	4.80819	−	39.5990i	0.179315	−	1.47679i	0.753164	−	0.657833i	$-0.228527\pi$
$720$	−0.258205	−	22.7611i	−0.00962273	−	0.848255i
$721$	15.9743	−	9.65677i	0.594912	−	0.359637i
$722$	−8.47785	−	1.55362i	−0.315513	−	0.0578199i
$723$	23.9335	+	8.10731i	0.890095	+	0.301514i
$724$	−3.64493	−	9.61090i	−0.135463	−	0.357186i
$725$	31.4651	−	16.5142i	1.16858	−	0.613321i
$726$	−42.6188	−	8.89609i	−1.58173	−	0.330165i
$727$	−5.72430	+	23.2244i	−0.212303	+	0.861345i	0.764049	+	0.645158i	$0.223208\pi$
$727$	−5.72430	+	23.2244i	−0.212303	+	0.861345i	−0.976352	+	0.216187i	$0.930638\pi$
$728$	20.7679	+	10.8949i	0.769711	+	0.403791i
$729$	18.4312	−	19.7304i	0.682638	−	0.730756i
$730$	1.22980	−	20.3310i	0.0455169	−	0.752484i
$731$	24.0069	−	2.91496i	0.887927	−	0.107814i
$732$	−2.92538	+	1.91502i	−0.108125	+	0.0707810i
$733$	−35.1950	+	10.9672i	−1.29996	+	0.405083i	−0.867889	−	0.496758i	$-0.834524\pi$
$733$	−35.1950	+	10.9672i	−1.29996	+	0.405083i	−0.432068	+	0.901841i	$0.642216\pi$
$734$	−10.5483	+	4.74741i	−0.389345	+	0.175230i
$735$	15.7811	−	0.566459i	0.582094	−	0.0208942i
$736$	3.43872	−	2.69406i	0.126753	−	0.0993044i
$737$	2.09709	−	8.50824i	0.0772474	−	0.313405i
$738$	−27.6212	−	21.1387i	−1.01675	−	0.778125i
$739$	2.14666	+	35.4886i	0.0789663	+	1.30547i	0.794660	+	0.607055i	$0.207649\pi$
$739$	2.14666	+	35.4886i	0.0789663	+	1.30547i	−0.715694	+	0.698414i	$0.753889\pi$
$740$	14.3854	−	7.55005i	0.528818	−	0.277545i
$741$	−11.3647	+	17.8055i	−0.417494	+	0.654102i
$742$	15.6607	+	8.21935i	0.574921	+	0.301742i
$743$	−8.10871	+	18.0168i	−0.297480	+	0.660973i	−0.998646	−	0.0520252i	$-0.983432\pi$
$743$	−8.10871	+	18.0168i	−0.297480	+	0.660973i	0.701166	+	0.712998i	$0.252663\pi$
$744$	−0.472673	+	19.2608i	−0.0173290	+	0.706133i
$745$	−3.57789	+	6.81710i	−0.131084	+	0.249759i
$746$	3.83816	+	3.83816i	0.140525	+	0.140525i
$747$	25.4438	+	47.1710i	0.930942	+	1.72590i
$748$	−1.13742	−	18.8038i	−0.0415883	−	0.687536i
$749$	−5.96597	−	32.5553i	−0.217992	−	1.18954i
$750$	−15.2160	−	14.1615i	−0.555609	−	0.517104i
$751$	23.7633	+	16.4026i	0.867135	+	0.598540i	0.916408	−	0.400245i	$-0.131075\pi$
$751$	23.7633	+	16.4026i	0.867135	+	0.598540i	−0.0492732	+	0.998785i	$0.515690\pi$
$752$	−3.23649	−	7.19117i	−0.118022	−	0.262235i
$753$	−22.4387	−	6.11831i	−0.817712	−	0.222964i
$754$	−9.53083	+	15.7726i	−0.347093	+	0.574405i
$755$	26.6168	−	10.0944i	0.968686	−	0.367374i
$756$	6.75636	+	3.66049i	0.245726	+	0.133131i
$757$	7.87503	−	20.7647i	0.286223	−	0.754708i	−0.712376	−	0.701798i	$-0.752381\pi$
$757$	7.87503	−	20.7647i	0.286223	−	0.754708i	0.998599	−	0.0529100i	$-0.0168497\pi$
$758$	−0.652241	−	5.37169i	−0.0236905	−	0.195109i
$759$	−11.3516	−	2.36948i	−0.412035	−	0.0860067i
$760$	6.74851	+	36.8254i	0.244794	+	1.33580i
$761$	−5.04218	−	27.5143i	−0.182779	−	0.997391i	−0.939216	−	0.343326i	$-0.888447\pi$
$761$	−5.04218	−	27.5143i	−0.182779	−	0.997391i	0.756438	−	0.654066i	$-0.226938\pi$
$762$	10.3751	+	2.16567i	0.375851	+	0.0784538i
$763$	−4.67837	−	38.5298i	−0.169368	−	1.39487i
$764$	−1.69251	+	4.46277i	−0.0612328	+	0.161458i
$765$	−41.8860	−	28.2157i	−1.51439	−	1.02014i
$766$	−10.9033	+	4.13506i	−0.393951	+	0.149406i
$767$	14.9972	−	9.06996i	0.541517	−	0.327497i
$768$	−24.2313	−	6.60709i	−0.874371	−	0.238413i
$769$	−8.59827	−	19.1046i	−0.310061	−	0.688928i	0.689307	−	0.724470i	$-0.257915\pi$
$769$	−8.59827	−	19.1046i	−0.310061	−	0.688928i	−0.999368

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.s (of order \(52\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.205529 + 1.12154i) q^{2} +(0.653740 - 1.60394i) q^{3} +(0.654428 + 0.248192i) q^{4} +(-3.58890 - 0.217089i) q^{5} +(1.66452 + 1.06285i) q^{6} +(-1.80817 - 1.09308i) q^{7} +(-1.59261 + 2.63450i) q^{8} +(-2.14525 - 2.09712i) q^{9} +(0.981098 - 3.98047i) q^{10} +(1.03620 + 5.65434i) q^{11} +(0.825911 - 0.887411i) q^{12} +(2.04874 + 2.96693i) q^{13} +(1.59756 - 1.80327i) q^{14} +(-2.69441 + 5.61447i) q^{15} +(-1.57958 - 1.39939i) q^{16} +(-4.54606 + 1.12050i) q^{17} +(2.79291 - 1.97495i) q^{18} +(-2.39174 + 2.39174i) q^{19} +(-2.29480 - 1.03281i) q^{20} +(-2.93530 + 2.18560i) q^{21} -6.55452 q^{22} -1.16467 q^{23} +(3.18443 + 4.27674i) q^{24} +(7.86956 + 0.955538i) q^{25} +(-3.74860 + 1.68795i) q^{26} +(-4.76609 + 2.06987i) q^{27} +(-0.912024 - 1.16411i) q^{28} +(3.68914 - 2.54643i) q^{29} +(-5.74306 - 4.17582i) q^{30} +(2.84435 + 2.22841i) q^{31} +(-2.95254 + 2.31316i) q^{32} +(9.74663 + 2.03447i) q^{33} +(-0.322337 - 5.32887i) q^{34} +(6.25205 + 4.31548i) q^{35} +(-0.883422 - 1.90485i) q^{36} +(-3.98148 + 5.08199i) q^{37} +(-2.19086 - 3.17400i) q^{38} +(6.09812 - 1.34646i) q^{39} +(6.28766 - 9.10924i) q^{40} +(-3.02507 - 9.70781i) q^{41} +(-1.84795 - 3.74125i) q^{42} +(-5.12736 - 0.622574i) q^{43} +(-0.725246 + 3.95754i) q^{44} +(7.24382 + 7.99208i) q^{45} +(0.239373 - 1.30622i) q^{46} +(3.40765 + 1.53366i) q^{47} +(-3.27717 + 1.61872i) q^{48} +(-1.17841 - 2.24526i) q^{49} +(-2.68910 + 8.62962i) q^{50} +(-1.17472 + 8.02412i) q^{51} +(0.604389 + 2.45012i) q^{52} +(1.75692 + 7.12810i) q^{53} +(-1.34187 - 5.77077i) q^{54} +(-2.49132 - 20.5178i) q^{55} +(5.75942 - 3.02278i) q^{56} +(2.27263 + 5.39979i) q^{57} +(2.09769 + 4.66087i) q^{58} +(0.293499 - 4.85212i) q^{59} +(-3.15676 + 3.00554i) q^{60} +(-2.80038 - 0.690231i) q^{61} +(-3.08384 + 2.73204i) q^{62} +(1.58665 + 6.13686i) q^{63} +(-3.94888 - 7.52396i) q^{64} +(-6.70866 - 11.0928i) q^{65} +(-4.28496 + 10.5131i) q^{66} +(-1.39008 - 0.625623i) q^{67} +(-3.25317 - 0.395006i) q^{68} +(-0.761389 + 1.86805i) q^{69} +(-6.12495 + 6.12495i) q^{70} +(-0.979798 - 3.14428i) q^{71} +(8.94142 - 2.31176i) q^{72} +(4.88695 - 0.895566i) q^{73} +(-4.88133 - 5.50988i) q^{74} +(6.67728 - 11.9976i) q^{75} +(-2.15884 + 0.971613i) q^{76} +(4.30700 - 11.3566i) q^{77} +(0.256766 + 7.11601i) q^{78} +(-0.313705 - 0.827171i) q^{79} +(5.36518 + 5.36518i) q^{80} +(0.204168 + 8.99768i) q^{81} +(11.5094 - 1.39750i) q^{82} +(-17.0563 - 5.31495i) q^{83} +(-2.46339 + 0.701804i) q^{84} +(16.5586 - 3.03448i) q^{85} +(1.75206 - 5.62257i) q^{86} +(-1.67258 - 7.58186i) q^{87} +(-16.5466 - 6.27531i) q^{88} +(11.8116 - 11.8116i) q^{89} +(-10.4522 + 6.48161i) q^{90} +(-0.461399 - 7.60413i) q^{91} +(-0.762190 - 0.289061i) q^{92} +(5.43370 - 3.10537i) q^{93} +(-2.42043 + 3.50660i) q^{94} +(9.10296 - 8.06452i) q^{95} +(1.77998 + 6.24790i) q^{96} +(-9.84564 + 0.595552i) q^{97} +(2.76035 - 0.860158i) q^{98} +(9.63494 - 14.3030i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27}+ \cdots - 58 q^{99}+O(q^{100}) \) 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Introduction

L-functions

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