LMFDB - Embedded newform 507.2.s.a.5.7

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			5.7
Character	$\chi$	$=$	507.5
Dual form			507.2.s.a.203.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.407325 + 2.22270i) q^{2} +(-1.46444 + 0.924888i) q^{3} +(-2.90444 - 1.10151i) q^{4} +(3.11001 + 0.188121i) q^{5} +(-1.45925 - 3.63174i) q^{6} +(1.33442 + 0.806684i) q^{7} +(1.29330 - 2.13939i) q^{8} +(1.28916 - 2.70888i) q^{9} +(-1.68492 + 6.83599i) q^{10} +(0.662987 + 3.61780i) q^{11} +(5.27215 - 1.07319i) q^{12} +(-0.793246 + 3.51721i) q^{13} +(-2.33656 + 2.63743i) q^{14} +(-4.72841 + 2.60092i) q^{15} +(-0.421785 - 0.373669i) q^{16} +(-1.84135 + 0.453853i) q^{17} +(5.49592 + 3.96882i) q^{18} +(-0.649110 + 0.649110i) q^{19} +(-8.82562 - 3.97209i) q^{20} +(-2.70027 + 0.0528481i) q^{21} -8.31133 q^{22} +2.86699 q^{23} +(0.0847278 + 4.32916i) q^{24} +(4.67322 + 0.567432i) q^{25} +(-7.49459 - 3.19579i) q^{26} +(0.617513 + 5.15933i) q^{27} +(-2.98717 - 3.81284i) q^{28} +(-3.34656 + 2.30996i) q^{29} +(-3.85506 - 11.5692i) q^{30} +(-0.107290 - 0.0840567i) q^{31} +(4.93815 - 3.86879i) q^{32} +(-4.31697 - 4.68486i) q^{33} +(-0.258749 - 4.27764i) q^{34} +(3.99830 + 2.75983i) q^{35} +(-6.72816 + 6.44777i) q^{36} +(5.54346 - 7.07570i) q^{37} +(-1.17838 - 1.70717i) q^{38} +(-2.09136 - 5.88440i) q^{39} +(4.42465 - 6.41021i) q^{40} +(0.0661792 + 0.212377i) q^{41} +(0.982420 - 6.02341i) q^{42} +(-7.19558 - 0.873702i) q^{43} +(2.05944 - 11.2380i) q^{44} +(4.51891 - 8.18214i) q^{45} +(-1.16779 + 6.37245i) q^{46} +(8.81729 + 3.96834i) q^{47} +(0.963279 + 0.157111i) q^{48} +(-2.12313 - 4.04528i) q^{49} +(-3.16475 + 10.1560i) q^{50} +(2.27679 - 2.36768i) q^{51} +(6.17817 - 9.34176i) q^{52} +(-0.861862 - 3.49671i) q^{53} +(-11.7192 - 0.728976i) q^{54} +(1.38131 + 11.3761i) q^{55} +(3.45162 - 1.81155i) q^{56} +(0.350228 - 1.55094i) q^{57} +(-3.77122 - 8.37930i) q^{58} +(-0.600912 + 9.93427i) q^{59} +(16.5983 - 2.34583i) q^{60} +(-11.7285 - 2.89082i) q^{61} +(0.230535 - 0.204236i) q^{62} +(3.90550 - 2.57484i) q^{63} +(6.06399 + 11.5540i) q^{64} +(-3.12866 + 10.7893i) q^{65} +(12.1714 - 7.68705i) q^{66} +(-8.03617 - 3.61678i) q^{67} +(5.84802 + 0.710079i) q^{68} +(-4.19853 + 2.65164i) q^{69} +(-7.76287 + 7.76287i) q^{70} +(-0.388510 - 1.24677i) q^{71} +(-4.12807 - 6.26143i) q^{72} +(11.1889 - 2.05044i) q^{73} +(13.4692 + 15.2035i) q^{74} +(-7.36846 + 3.49124i) q^{75} +(2.60030 - 1.17030i) q^{76} +(-2.03372 + 5.36249i) q^{77} +(13.9311 - 2.25161i) q^{78} +(2.60406 + 6.86634i) q^{79} +(-1.24146 - 1.24146i) q^{80} +(-5.67611 - 6.98439i) q^{81} +(-0.499005 + 0.0605902i) q^{82} +(-2.82964 - 0.881750i) q^{83} +(7.90098 + 2.82088i) q^{84} +(-5.81200 + 1.06509i) q^{85} +(4.87291 - 15.6377i) q^{86} +(2.76438 - 6.47799i) q^{87} +(8.59732 + 3.26053i) q^{88} +(5.66471 - 5.66471i) q^{89} +(16.3458 + 13.3770i) q^{90} +(-3.89580 + 4.05353i) q^{91} +(-8.32700 - 3.15801i) q^{92} +(0.234863 + 0.0238643i) q^{93} +(-12.4119 + 17.9818i) q^{94} +(-2.14085 + 1.89663i) q^{95} +(-3.65342 + 10.2328i) q^{96} +(14.7040 - 0.889431i) q^{97} +(9.85624 - 3.07133i) q^{98} +(10.6549 + 2.86798i) 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 $

$2$	−0.407325	+	2.22270i	−0.288022	+	1.57168i	0.447563	+	0.894252i	$0.352292\pi$
$2$	−0.407325	+	2.22270i	−0.288022	+	1.57168i	−0.735585	+	0.677433i	$0.763093\pi$
$3$	−1.46444	+	0.924888i	−0.845494	+	0.533984i
$3$	−1.46444	+	0.924888i	−0.845494	+	0.533984i
$4$	−2.90444	−	1.10151i	−1.45222	−	0.550755i
$5$	3.11001	+	0.188121i	1.39084	+	0.0841302i	0.738733	−	0.673998i	$-0.235424\pi$
$5$	3.11001	+	0.188121i	1.39084	+	0.0841302i	0.652105	+	0.758128i	$0.273886\pi$
$6$	−1.45925	−	3.63174i	−0.595734	−	1.48265i
$7$	1.33442	+	0.806684i	0.504363	+	0.304898i	0.746547	−	0.665332i	$-0.231710\pi$
$7$	1.33442	+	0.806684i	0.504363	+	0.304898i	−0.242184	+	0.970230i	$0.577864\pi$
$8$	1.29330	−	2.13939i	0.457252	−	0.756387i
$9$	1.28916	−	2.70888i	0.429721	−	0.902962i
$10$	−1.68492	+	6.83599i	−0.532818	+	2.16173i
$11$	0.662987	+	3.61780i	0.199898	+	1.09081i	0.918510	+	0.395397i	$0.129393\pi$
$11$	0.662987	+	3.61780i	0.199898	+	1.09081i	−0.718612	+	0.695411i	$0.755222\pi$
$12$	5.27215	−	1.07319i	1.52194	−	0.309803i
$13$	−0.793246	+	3.51721i	−0.220007	+	0.975498i
$13$	−0.793246	+	3.51721i	−0.220007	+	0.975498i
$14$	−2.33656	+	2.63743i	−0.624471	+	0.704882i
$15$	−4.72841	+	2.60092i	−1.22087	+	0.671554i
$16$	−0.421785	−	0.373669i	−0.105446	−	0.0934171i
$17$	−1.84135	+	0.453853i	−0.446594	+	0.110075i	−0.456198	−	0.889878i	$-0.650789\pi$
$17$	−1.84135	+	0.453853i	−0.446594	+	0.110075i	0.00960413	+	0.999954i	$0.496943\pi$
$18$	5.49592	+	3.96882i	1.29540	+	0.935459i
$19$	−0.649110	+	0.649110i	−0.148916	+	0.148916i	−0.777634	−	0.628718i	$-0.783580\pi$
$19$	−0.649110	+	0.649110i	−0.148916	+	0.148916i	0.628718	+	0.777634i	$0.283580\pi$
$20$	−8.82562	−	3.97209i	−1.97347	−	0.888186i
$21$	−2.70027	+	0.0528481i	−0.589247	+	0.0115324i
$22$	−8.31133			−1.77198
$23$	2.86699			0.597808			0.298904	−	0.954283i	$-0.403379\pi$
$23$	2.86699			0.597808			0.298904	+	0.954283i	$0.403379\pi$
$24$	0.0847278	+	4.32916i	0.0172950	+	0.883686i
$25$	4.67322	+	0.567432i	0.934645	+	0.113486i
$26$	−7.49459	−	3.19579i	−1.46981	−	0.626746i
$27$	0.617513	+	5.15933i	0.118840	+	0.992913i
$28$	−2.98717	−	3.81284i	−0.564522	−	0.720560i
$29$	−3.34656	+	2.30996i	−0.621441	+	0.428949i	−0.836741	−	0.547598i	$-0.815542\pi$
$29$	−3.34656	+	2.30996i	−0.621441	+	0.428949i	0.215301	+	0.976548i	$0.430927\pi$
$30$	−3.85506	−	11.5692i	−0.703834	−	2.11225i
$31$	−0.107290	−	0.0840567i	−0.0192699	−	0.0150970i	0.607038	−	0.794673i	$-0.292358\pi$
$31$	−0.107290	−	0.0840567i	−0.0192699	−	0.0150970i	−0.626308	+	0.779576i	$0.715435\pi$
$32$	4.93815	−	3.86879i	0.872950	−	0.683912i
$33$	−4.31697	−	4.68486i	−0.751487	−	0.815530i
$34$	−0.258749	−	4.27764i	−0.0443751	−	0.733609i
$35$	3.99830	+	2.75983i	0.675836	+	0.466496i
$36$	−6.72816	+	6.44777i	−1.12136	+	1.07463i
$37$	5.54346	−	7.07570i	0.911339	−	1.16324i	−0.0747803	−	0.997200i	$-0.523826\pi$
$37$	5.54346	−	7.07570i	0.911339	−	1.16324i	0.986119	−	0.166038i	$-0.0530975\pi$
$38$	−1.17838	−	1.70717i	−0.191158	−	0.276940i
$39$	−2.09136	−	5.88440i	−0.334886	−	0.942259i
$40$	4.42465	−	6.41021i	0.699598	−	1.01354i
$41$	0.0661792	+	0.212377i	0.0103355	+	0.0331677i	0.959745	−	0.280874i	$-0.0906244\pi$
$41$	0.0661792	+	0.212377i	0.0103355	+	0.0331677i	−0.949409	+	0.314042i	$0.898317\pi$
$42$	0.982420	−	6.02341i	0.151591	−	0.929432i
$43$	−7.19558	−	0.873702i	−1.09732	−	0.133238i	−0.448204	−	0.893931i	$-0.647936\pi$
$43$	−7.19558	−	0.873702i	−1.09732	−	0.133238i	−0.649112	+	0.760693i	$0.724859\pi$
$44$	2.05944	−	11.2380i	0.310472	−	1.69419i
$45$	4.51891	−	8.18214i	0.673639	−	1.21972i
$46$	−1.16779	+	6.37245i	−0.172182	+	0.939566i
$47$	8.81729	+	3.96834i	1.28613	+	0.578842i	0.934055	−	0.357128i	$-0.116244\pi$
$47$	8.81729	+	3.96834i	1.28613	+	0.578842i	0.352079	+	0.935970i	$0.385475\pi$
$48$	0.963279	+	0.157111i	0.139037	+	0.0226771i
$49$	−2.12313	−	4.04528i	−0.303304	−	0.577897i
$50$	−3.16475	+	10.1560i	−0.447563	+	1.43628i
$51$	2.27679	−	2.36768i	0.318814	−	0.331542i
$52$	6.17817	−	9.34176i	0.856759	−	1.29547i
$53$	−0.861862	−	3.49671i	−0.118386	−	0.480311i	−0.999966	−	0.00827561i	$-0.997366\pi$
$53$	−0.861862	−	3.49671i	−0.118386	−	0.480311i	0.881580	−	0.472035i	$-0.156480\pi$
$54$	−11.7192	−	0.728976i	−1.59478	−	0.0992011i
$55$	1.38131	+	11.3761i	0.186256	+	1.53396i
$56$	3.45162	−	1.81155i	0.461242	−	0.242078i
$57$	0.350228	−	1.55094i	0.0463888	−	0.205426i
$58$	−3.77122	−	8.37930i	−0.495185	−	1.10026i
$59$	−0.600912	+	9.93427i	−0.0782321	+	1.29333i	0.721264	+	0.692660i	$0.243561\pi$
$59$	−0.600912	+	9.93427i	−0.0782321	+	1.29333i	−0.799496	+	0.600671i	$0.794900\pi$
$60$	16.5983	−	2.34583i	2.14283	−	0.302845i
$61$	−11.7285	−	2.89082i	−1.50168	−	0.370132i	−0.599111	−	0.800666i	$-0.704479\pi$
$61$	−11.7285	−	2.89082i	−1.50168	−	0.370132i	−0.902574	+	0.430534i	$0.858325\pi$
$62$	0.230535	−	0.204236i	0.0292779	−	0.0259380i
$63$	3.90550	−	2.57484i	0.492047	−	0.324399i
$64$	6.06399	+	11.5540i	0.757998	+	1.44425i
$65$	−3.12866	+	10.7893i	−0.388063	+	1.33825i
$66$	12.1714	−	7.68705i	1.49820	−	0.946211i
$67$	−8.03617	−	3.61678i	−0.981774	−	0.441861i	−0.145013	−	0.989430i	$-0.546323\pi$
$67$	−8.03617	−	3.61678i	−0.981774	−	0.441861i	−0.836760	+	0.547569i	$0.815553\pi$
$68$	5.84802	+	0.710079i	0.709177	+	0.0861097i
$69$	−4.19853	+	2.65164i	−0.505443	+	0.319220i
$70$	−7.76287	+	7.76287i	−0.927841	+	0.927841i
$71$	−0.388510	−	1.24677i	−0.0461076	−	0.147965i	0.928796	−	0.370591i	$-0.120845\pi$
$71$	−0.388510	−	1.24677i	−0.0461076	−	0.147965i	−0.974904	+	0.222626i	$0.928537\pi$
$72$	−4.12807	−	6.26143i	−0.486498	−	0.737916i
$73$	11.1889	−	2.05044i	1.30956	−	0.239986i	0.520268	−	0.854003i	$-0.325832\pi$
$73$	11.1889	−	2.05044i	1.30956	−	0.239986i	0.789293	+	0.614017i	$0.210447\pi$
$74$	13.4692	+	15.2035i	1.56576	+	1.76738i
$75$	−7.36846	+	3.49124i	−0.850837	+	0.403133i
$76$	2.60030	−	1.17030i	0.298275	−	0.134243i
$77$	−2.03372	+	5.36249i	−0.231764	+	0.611112i
$78$	13.9311	−	2.25161i	1.57739	−	0.254945i
$79$	2.60406	+	6.86634i	0.292979	+	0.772523i	0.997993	+	0.0633290i	$0.0201718\pi$
$79$	2.60406	+	6.86634i	0.292979	+	0.772523i	−0.705013	+	0.709194i	$0.749059\pi$
$80$	−1.24146	−	1.24146i	−0.138799	−	0.138799i
$81$	−5.67611	−	6.98439i	−0.630679	−	0.776044i
$82$	−0.499005	+	0.0605902i	−0.0551059	+	0.00669107i
$83$	−2.82964	−	0.881750i	−0.310593	−	0.0967846i	0.138244	−	0.990398i	$-0.455854\pi$
$83$	−2.82964	−	0.881750i	−0.310593	−	0.0967846i	−0.448837	+	0.893613i	$0.648162\pi$
$84$	7.90098	+	2.82088i	0.862068	+	0.307783i
$85$	−5.81200	+	1.06509i	−0.630400	+	0.115525i
$86$	4.87291	−	15.6377i	0.525460	−	1.68626i
$87$	2.76438	−	6.47799i	0.296372	−	0.694514i
$88$	8.59732	+	3.26053i	0.916477	+	0.347574i
$89$	5.66471	−	5.66471i	0.600458	−	0.600458i	−0.339976	−	0.940434i	$-0.610419\pi$
$89$	5.66471	−	5.66471i	0.600458	−	0.600458i	0.940434	+	0.339976i	$0.110419\pi$
$90$	16.3458	+	13.3770i	1.72299	+	1.41006i
$91$	−3.89580	+	4.05353i	−0.408391	+	0.424926i
$92$	−8.32700	−	3.15801i	−0.868149	−	0.329246i
$93$	0.234863	+	0.0238643i	0.0243542	+	0.00247461i
$94$	−12.4119	+	17.9818i	−1.28019	+	1.85468i
$95$	−2.14085	+	1.89663i	−0.219646	+	0.194590i
$96$	−3.65342	+	10.2328i	−0.372875	+	1.04439i
$97$	14.7040	−	0.889431i	1.49297	−	0.0903080i	0.706401	−	0.707812i	$-0.250317\pi$
$97$	14.7040	−	0.889431i	1.49297	−	0.0903080i	0.786568	+	0.617504i	$0.211856\pi$
$98$	9.85624	−	3.07133i	0.995631	−	0.310251i
$99$	10.6549	+	2.86798i	1.07086	+	0.288243i
$100$	−12.9481	−	6.79567i	−1.29481	−	0.679567i
$101$	1.34172	−	11.0501i	0.133507	−	1.09953i	−0.759825	−	0.650128i	$-0.774715\pi$
$101$	1.34172	−	11.0501i	0.133507	−	1.09953i	0.893332	−	0.449398i	$-0.148362\pi$
$102$	4.33526	+	6.02502i	0.429254	+	0.596566i
$103$	−7.90080	+	15.0537i	−0.778489	+	1.48329i	0.0944874	+	0.995526i	$0.469879\pi$
$103$	−7.90080	+	15.0537i	−0.778489	+	1.48329i	−0.872977	+	0.487762i	$0.837814\pi$
$104$	6.49876	+	6.24588i	0.637256	+	0.612459i
$105$	−8.40780	−	0.343619i	−0.820517	−	0.0335338i
$106$	8.12320	−	0.491363i	0.788995	−	0.0477254i
$107$	9.49472	+	10.7173i	0.917889	+	1.03608i	0.999224	+	0.0393959i	$0.0125434\pi$
$107$	9.49472	+	10.7173i	0.917889	+	1.03608i	−0.0813344	+	0.996687i	$0.525918\pi$
$108$	3.88952	−	15.6652i	0.374269	−	1.50738i
$109$	−3.22764	−	4.11978i	−0.309152	−	0.394603i	0.607480	−	0.794335i	$-0.292180\pi$
$109$	−3.22764	−	4.11978i	−0.309152	−	0.394603i	−0.916632	+	0.399731i	$0.869103\pi$
$110$	−25.8483	−	1.56354i	−2.46454	−	0.149077i
$111$	−1.57382	+	15.4890i	−0.149381	+	1.47015i
$112$	−0.261405	−	0.838877i	−0.0247004	−	0.0792665i
$113$	1.14374	+	2.17922i	0.107594	+	0.205004i	0.933300	−	0.359097i	$-0.116915\pi$
$113$	1.14374	+	2.17922i	0.107594	+	0.205004i	−0.825706	+	0.564101i	$0.809223\pi$
$114$	3.30461	+	1.41019i	0.309505	+	0.132076i
$115$	8.91636	+	0.539340i	0.831454	+	0.0502937i
$116$	12.2643	−	3.02289i	1.13871	−	0.280668i
$117$	8.50509	+	6.68307i	0.786296	+	0.617850i
$118$	−21.8361	−	5.38212i	−2.01018	−	0.495464i
$119$	−2.82325	−	0.879761i	−0.258807	−	0.0806475i
$120$	−0.550901	+	13.4797i	−0.0502902	+	1.23052i
$121$	−2.36376	+	0.896457i	−0.214887	+	0.0814960i
$122$	11.2027	−	24.8915i	1.01425	−	2.25357i
$123$	−0.293340	−	0.249804i	−0.0264496	−	0.0225241i
$124$	0.219030	+	0.362319i	0.0196694	+	0.0325372i
$125$	−0.896272	−	0.164248i	−0.0801650	−	0.0146908i
$126$	4.13228	+	9.72954i	0.368133	+	0.866777i
$127$	20.0320	−	7.59713i	1.77755	−	0.674136i	0.778640	−	0.627472i	$-0.215910\pi$
$127$	20.0320	−	7.59713i	1.77755	−	0.674136i	0.998911	−	0.0466643i	$-0.0148591\pi$
$128$	−16.1727	+	5.03962i	−1.42948	+	0.445443i
$129$	11.3456	−	5.37563i	0.998922	−	0.473297i
$130$	−22.7070	−	11.3488i	−1.99154	−	0.995358i
$131$	−12.2647	+	8.46570i	−1.07157	+	0.739652i	−0.966977	−	0.254863i	$-0.917970\pi$
$131$	−12.2647	+	8.46570i	−1.07157	+	0.739652i	−0.104593	+	0.994515i	$0.533354\pi$
$132$	7.37796	+	18.3621i	0.642169	+	1.59821i
$133$	−1.38981	+	0.342558i	−0.120512	+	0.0297035i
$134$	11.3123	−	16.3888i	0.977238	−	1.41577i
$135$	0.949894	+	16.1617i	0.0817539	+	1.39098i
$136$	−1.41046	+	4.52633i	−0.120946	+	0.388130i
$137$	8.09612	+	10.3339i	0.691699	+	0.882888i	0.997605	−	0.0691738i	$-0.0220363\pi$
$137$	8.09612	+	10.3339i	0.691699	+	0.882888i	−0.305906	+	0.952062i	$0.598959\pi$
$138$	−4.18364	−	10.4121i	−0.356135	−	0.886340i
$139$	−2.84374	−	2.51933i	−0.241203	−	0.213687i	0.533857	−	0.845575i	$-0.320742\pi$
$139$	−2.84374	−	2.51933i	−0.241203	−	0.213687i	−0.775060	+	0.631888i	$0.782280\pi$
$140$	−8.57285	−	12.4199i	−0.724538	−	1.04968i
$141$	−16.5827	+	2.34361i	−1.39651	+	0.197368i
$142$	2.92945	−	0.355699i	0.245834	−	0.0298496i
$143$	−13.2505	−	0.537943i	−1.10806	−	0.0449850i
$144$	−1.55597	+	0.660846i	−0.129665	+	0.0550705i
$145$	−10.8424	+	6.55445i	−0.900411	+	0.544317i
$146$			25.7047i			2.12734i
$147$	6.85062	+	3.96041i	0.565030	+	0.326649i
$148$	−23.8946	+	14.4448i	−1.96412	+	1.18735i
$149$	−7.83344	+	17.4052i	−0.641741	+	1.42589i	0.247699	+	0.968837i	$0.420325\pi$
$149$	−7.83344	+	17.4052i	−0.641741	+	1.42589i	−0.889440	+	0.457052i	$0.848905\pi$
$150$	−4.75861	−	17.7999i	−0.388539	−	1.45336i
$151$	2.13287	−	0.959925i	0.173570	−	0.0781176i	−0.321765	−	0.946820i	$-0.604276\pi$
$151$	2.13287	−	0.959925i	0.173570	−	0.0781176i	0.495335	+	0.868702i	$0.335045\pi$
$152$	0.549200	+	2.22819i	0.0445460	+	0.180730i
$153$	−1.14437	+	5.57310i	−0.0925169	+	0.450559i
$154$	−11.0908	−	6.70462i	−0.893722	−	0.540274i
$155$	−0.317861	−	0.281601i	−0.0255312	−	0.0226187i
$156$	−0.407477	+	19.3946i	−0.0326243	+	1.55281i
$157$	15.3714	−	13.6179i	1.22677	−	1.08683i	0.233343	−	0.972395i	$-0.425034\pi$
$157$	15.3714	−	13.6179i	1.22677	−	1.08683i	0.993431	−	0.114432i	$-0.0365048\pi$
$158$	−16.3225	+	2.99121i	−1.29855	+	0.237968i
$159$	4.49621	+	4.32360i	0.356573	+	0.342884i
$160$	16.0855	−	11.1030i	1.27167	−	0.877770i
$161$	3.82576	+	2.31275i	0.301512	+	0.182271i
$162$	17.8362	−	9.77137i	1.40135	−	0.767711i
$163$	12.5934	−	16.0743i	0.986395	−	1.25904i	0.0205851	−	0.999788i	$-0.493447\pi$
$163$	12.5934	−	16.0743i	0.986395	−	1.25904i	0.965810	−	0.259252i	$-0.0834760\pi$
$164$	0.0417211	−	0.689732i	0.00325787	−	0.0538591i
$165$	−12.5445	−	15.3821i	−0.976587	−	1.19749i
$166$	3.11244	−	5.93027i	0.241573	−	0.460278i
$167$	10.7746	+	1.97451i	0.833760	+	0.152792i	0.580145	−	0.814513i	$-0.302996\pi$
$167$	10.7746	+	1.97451i	0.833760	+	0.152792i	0.253615	+	0.967305i	$0.418380\pi$
$168$	−3.37920	+	5.84526i	−0.260711	+	0.450972i
$169$	−11.7415	−	5.58002i	−0.903194	−	0.429233i
$170$		−	13.3522i		−	1.02406i
$171$	0.921555	+	2.59517i	0.0704731	+	0.198458i
$172$	19.9368	+	10.4636i	1.52016	+	0.797843i
$173$	−0.129882	+	0.342471i	−0.00987475	+	0.0260376i	−0.939863	−	0.341552i	$-0.889048\pi$
$173$	−0.129882	+	0.342471i	−0.00987475	+	0.0260376i	0.929988	+	0.367589i	$0.119817\pi$
$174$	13.2726	+	8.78302i	1.00620	+	0.665839i
$175$	5.77830	+	4.52701i	0.436798	+	0.342210i
$176$	1.07222	−	1.77367i	0.0808217	−	0.133695i
$177$	−8.30809	−	15.1039i	−0.624474	−	1.13528i
$178$	10.2836	+	14.8983i	0.770786	+	1.11668i
$179$	20.2718	+	4.99656i	1.51519	+	0.373460i	0.907273	−	0.420543i	$-0.138160\pi$
$179$	20.2718	+	4.99656i	1.51519	+	0.373460i	0.607914	+	0.794003i	$0.292006\pi$
$180$	−22.1376	+	18.7869i	−1.65004	+	1.40029i
$181$	5.80356	+	6.55087i	0.431375	+	0.486922i	0.923498	−	0.383604i	$-0.125317\pi$
$181$	5.80356	+	6.55087i	0.431375	+	0.486922i	−0.492122	+	0.870526i	$0.663779\pi$
$182$	−7.42292	−	10.3103i	−0.550224	−	0.764250i
$183$	19.8494	−	6.61415i	1.46731	−	0.488932i
$184$	3.70788	−	6.13359i	0.273349	−	0.452174i
$185$	18.5713	−	20.9627i	1.36539	−	1.54121i
$186$	−0.148709	+	0.512310i	−0.0109038	+	0.0375644i
$187$	−2.86274	−	6.36075i	−0.209344	−	0.465144i
$188$	−21.2381	−	21.2381i	−1.54895	−	1.54895i
$189$	−3.33793	+	7.38285i	−0.242799	+	0.537023i
$190$	−3.34361	−	5.53100i	−0.242571	−	0.401261i
$191$		−	4.08514i		−	0.295590i	−0.989018	−	0.147795i	$-0.952782\pi$
$191$		−	4.08514i		−	0.295590i	0.989018	−	0.147795i	$-0.0472176\pi$
$192$	−19.5665	−	11.3116i	−1.41209	−	0.816342i
$193$	−1.76503	−	2.91971i	−0.127050	−	0.210166i	0.785780	−	0.618506i	$-0.212262\pi$
$193$	−1.76503	−	2.91971i	−0.127050	−	0.210166i	−0.912830	+	0.408340i	$0.866108\pi$
$194$	−4.01238	+	33.0449i	−0.288072	+	2.37249i
$195$	−5.39718	−	18.6940i	−0.386500	−	1.33870i
$196$	1.71058	+	14.0879i	0.122185	+	1.00628i
$197$	−4.69982	+	3.68208i	−0.334849	+	0.262337i	−0.770033	−	0.638004i	$-0.779760\pi$
$197$	−4.69982	+	3.68208i	−0.334849	+	0.262337i	0.435184	+	0.900341i	$0.356683\pi$
$198$	−10.7147	+	22.5144i	−0.761458	+	1.60003i
$199$	16.9331	−	19.1136i	1.20036	−	1.35493i	0.281883	−	0.959449i	$-0.409041\pi$
$199$	16.9331	−	19.1136i	1.20036	−	1.35493i	0.918476	−	0.395477i	$-0.129421\pi$
$200$	7.25785	−	9.26396i	0.513208	−	0.655061i
$201$	15.1136	−	2.13599i	1.06603	−	0.150661i
$202$	24.0145	+	7.48323i	1.68966	+	0.526518i
$203$	−6.32912	+	0.382841i	−0.444217	+	0.0268702i
$204$	−9.22082	+	4.36890i	−0.645586	+	0.305884i
$205$	0.165866	+	0.672943i	0.0115845	+	0.0470004i
$206$	−30.2417	−	23.6929i	−2.10704	−	1.65076i
$207$	3.69602	−	7.76634i	0.256891	−	0.539798i
$208$	1.64885	−	1.18709i	0.114327	−	0.0823101i
$209$	−2.77870	−	1.91800i	−0.192207	−	0.132671i
$210$	4.18846	−	18.5480i	0.289032	−	1.27994i
$211$	−1.04992	−	2.76841i	−0.0722795	−	0.190585i	0.894008	−	0.448051i	$-0.147882\pi$
$211$	−1.04992	−	2.76841i	−0.0722795	−	0.190585i	−0.966287	+	0.257466i	$0.917113\pi$
$212$	−1.34843	+	11.1053i	−0.0926108	+	0.762719i
$213$	1.72207	+	1.46649i	0.117994	+	0.100482i
$214$	−27.6888	+	16.7385i	−1.89277	+	1.14422i
$215$	−22.2140	−	4.07086i	−1.51498	−	0.277630i
$216$	11.8364	+	5.35148i	0.805367	+	0.364122i
$217$	−0.0753632	−	0.198716i	−0.00511599	−	0.0134897i
$218$	10.4717	−	5.49598i	0.709235	−	0.372235i
$219$	−14.4890	+	13.3512i	−0.979078	+	0.902192i
$220$	8.51896	−	34.5628i	0.574348	−	2.33022i
$221$	−0.135650	−	6.83644i	−0.00912478	−	0.459869i
$222$	−33.7863	−	9.80719i	−2.26759	−	0.658216i
$223$	−0.0818755	+	1.35356i	−0.00548279	+	0.0906414i	−0.999888	−	0.0149956i	$-0.995227\pi$
$223$	−0.0818755	+	1.35356i	−0.00548279	+	0.0906414i	0.994405	+	0.105637i	$0.0336881\pi$
$224$	9.71045	−	1.17906i	0.648807	−	0.0787794i
$225$	7.56166	−	11.9277i	0.504111	−	0.795181i
$226$	−5.30962	+	1.65455i	−0.353191	+	0.110059i
$227$	−6.77896	+	3.05096i	−0.449935	+	0.202499i	−0.622695	−	0.782465i	$-0.713962\pi$
$227$	−6.77896	+	3.05096i	−0.449935	+	0.202499i	0.172760	+	0.984964i	$0.444732\pi$
$228$	−2.72559	+	4.11882i	−0.180506	+	0.272776i
$229$	11.6130	−	9.09818i	0.767407	−	0.601225i	−0.154789	−	0.987948i	$-0.549470\pi$
$229$	11.6130	−	9.09818i	0.767407	−	0.601225i	0.922196	+	0.386723i	$0.126393\pi$
$230$	−4.83064	+	19.5987i	−0.318523	+	1.29230i
$231$	−1.98144	−	9.73400i	−0.130369	−	0.640450i
$232$	0.613784	+	10.1471i	0.0402969	+	0.666187i
$233$	19.5455	−	10.2583i	1.28047	−	0.672041i	0.319207	−	0.947685i	$-0.396583\pi$
$233$	19.5455	−	10.2583i	1.28047	−	0.672041i	0.961260	+	0.275644i	$0.0888911\pi$
$234$	−18.3188	+	16.1821i	−1.19754	+	1.05786i
$235$	26.6753	+	14.0003i	1.74011	+	0.913278i
$236$	12.6880	−	28.1916i	0.825919	−	1.83512i
$237$	−10.1641	−	7.64687i	−0.660228	−	0.496717i
$238$	3.10542	−	5.91689i	0.201295	−	0.383535i
$239$	2.59827	+	2.59827i	0.168068	+	0.168068i	0.786130	−	0.618061i	$-0.212082\pi$
$239$	2.59827	+	2.59827i	0.168068	+	0.168068i	−0.618061	+	0.786130i	$0.712082\pi$
$240$	2.96625	+	0.669830i	0.191471	+	0.0432374i
$241$	1.64293	+	27.1609i	0.105831	+	1.74959i	0.533634	+	0.845716i	$0.320826\pi$
$241$	1.64293	+	27.1609i	0.105831	+	1.74959i	−0.427803	+	0.903872i	$0.640712\pi$
$242$	−1.02973	−	5.61908i	−0.0661938	−	0.361208i
$243$	14.7721	+	4.97845i	0.947631	+	0.319368i
$244$	30.8806	+	21.3153i	1.97693	+	1.36457i
$245$	−5.84194	−	12.9803i	−0.373228	−	0.829279i
$246$	0.674724	−	0.550255i	0.0430188	−	0.0350830i
$247$	−1.76815	−	2.79796i	−0.112505	−	0.178030i
$248$	−0.318589	+	0.120825i	−0.0202304	+	0.00767238i
$249$	4.95935	−	1.32583i	0.314286	−	0.0840209i
$250$	0.730147	−	1.92524i	0.0461786	−	0.121763i
$251$	1.07486	+	8.85224i	0.0678443	+	0.558748i	0.986509	+	0.163709i	$0.0523459\pi$
$251$	1.07486	+	8.85224i	0.0678443	+	0.558748i	−0.918664	+	0.395039i	$0.870731\pi$
$252$	−14.1795	+	3.17652i	−0.893225	+	0.200102i
$253$	1.90077	+	10.3722i	0.119501	+	0.652094i
$254$	8.72660	+	47.6195i	0.547556	+	2.98791i
$255$	7.52624	−	6.93521i	0.471311	−	0.434300i
$256$	−1.46834	−	12.0929i	−0.0917712	−	0.755804i
$257$	3.28347	−	8.65780i	0.204817	−	0.540059i	−0.792767	−	0.609525i	$-0.791360\pi$
$257$	3.28347	−	8.65780i	0.204817	−	0.540059i	0.997584	+	0.0694659i	$0.0221295\pi$
$258$	7.32706	+	27.4074i	0.456163	+	1.70631i
$259$	13.1052	−	4.97013i	0.814315	−	0.308829i
$260$	20.9716	−	27.8907i	1.30060	−	1.72971i
$261$	1.94316	+	12.0434i	0.120279	+	0.745466i
$262$	−13.8210	−	30.7090i	−0.853864	−	1.89721i
$263$	−24.3489	−	16.8068i	−1.50142	−	1.03635i	−0.983498	−	0.180921i	$-0.942092\pi$
$263$	−24.3489	−	16.8068i	−1.50142	−	1.03635i	−0.517918	−	0.855431i	$-0.673293\pi$
$264$	−15.6059	+	3.17671i	−0.960475	+	0.195513i
$265$	−2.02260	−	11.0369i	−0.124247	−	0.677994i
$266$	−0.195298	−	3.22866i	−0.0119745	−	0.197962i
$267$	−3.05640	+	13.5349i	−0.187049	+	0.828320i
$268$	19.3567	+	19.3567i	1.18240	+	1.18240i
$269$	11.9440	−	22.7574i	0.728240	−	1.38755i	−0.186072	−	0.982536i	$-0.559576\pi$
$269$	11.9440	−	22.7574i	0.728240	−	1.38755i	0.914312	−	0.405010i	$-0.132732\pi$
$270$	−36.3096	−	4.47174i	−2.20973	−	0.272141i
$271$	6.16370	−	13.6952i	0.374418	−	0.831923i	−0.624294	−	0.781189i	$-0.714613\pi$
$271$	6.16370	−	13.6952i	0.374418	−	0.831923i	0.998712	−	0.0507334i	$-0.0161559\pi$
$272$	0.946245	+	0.496627i	0.0573745	+	0.0301125i
$273$	1.95610	−	9.53933i	0.118388	−	0.577347i
$274$	−26.2670	+	13.7860i	−1.58685	+	0.832841i
$275$	1.04543	+	17.2830i	0.0630417	+	1.04220i
$276$	15.1152	−	3.07682i	0.909827	−	0.185203i
$277$	−2.97394	+	12.0658i	−0.178687	+	0.724962i	0.811398	+	0.584494i	$0.198707\pi$
$277$	−2.97394	+	12.0658i	−0.178687	+	0.724962i	−0.990085	+	0.140468i	$0.955139\pi$
$278$	6.75804	−	5.29458i	0.405320	−	0.317548i
$279$	−0.366015	+	0.182275i	−0.0219127	+	0.0109125i
$280$	11.0754	−	4.98461i	0.661879	−	0.297888i
$281$	−15.8277	+	4.93211i	−0.944201	+	0.294225i	−0.730685	−	0.682715i	$-0.760799\pi$
$281$	−15.8277	+	4.93211i	−0.944201	+	0.294225i	−0.213516	+	0.976940i	$0.568491\pi$
$282$	1.54538	−	37.8129i	0.0920258	−	2.25172i
$283$	−10.0734	+	1.22314i	−0.598804	+	0.0727080i	−0.414326	−	0.910129i	$-0.635983\pi$
$283$	−10.0734	+	1.22314i	−0.598804	+	0.0727080i	−0.184478	+	0.982837i	$0.559059\pi$
$284$	−0.244927	+	4.04912i	−0.0145337	+	0.240271i
$285$	1.38098	−	4.75754i	0.0818019	−	0.281812i
$286$	6.59293	−	29.2327i	0.389848	−	1.72857i
$287$	−0.0830101	+	0.336785i	−0.00489993	+	0.0198798i
$288$	−4.11403	−	18.3644i	−0.242422	−	1.08213i
$289$	−11.8682	+	6.22889i	−0.698127	+	0.366405i
$290$	−10.1522	−	26.7691i	−0.596157	−	1.57194i
$291$	−20.7106	+	14.9021i	−1.21407	+	0.873577i
$292$	−34.7561	−	6.36929i	−2.03395	−	0.372734i
$293$	−26.2485	+	15.8678i	−1.53346	+	0.927006i	−0.536938	+	0.843622i	$0.680419\pi$
$293$	−26.2485	+	15.8678i	−1.53346	+	0.927006i	−0.996517	+	0.0833840i	$0.973427\pi$
$294$	−11.5932	+	13.6137i	−0.676131	+	0.793967i
$295$	−3.73769	+	30.7826i	−0.217617	+	1.79223i
$296$	−7.96828	−	21.0106i	−0.463147	−	1.22122i
$297$	−18.2560	+	5.65461i	−1.05932	+	0.328114i
$298$	−35.4957	−	24.5009i	−2.05621	−	1.41930i
$299$	−2.27423	+	10.0838i	−0.131522	+	0.583161i
$300$	25.2469	−	2.02367i	1.45763	−	0.116837i
$301$	−8.89712	−	6.97045i	−0.512821	−	0.401770i
$302$	1.26485	+	5.13172i	0.0727842	+	0.295297i
$303$	8.25523	+	17.4231i	0.474251	+	1.00093i
$304$	0.516337	−	0.0312326i	0.0296139	−	0.00179131i
$305$	−35.9320	−	11.1969i	−2.05746	−	0.641131i
$306$	−11.9212	−	4.81365i	−0.681489	−	0.275178i
$307$	10.5999	−	13.5298i	0.604969	−	0.772185i	−0.383511	−	0.923536i	$-0.625285\pi$
$307$	10.5999	−	13.5298i	0.604969	−	0.772185i	0.988480	+	0.151351i	$0.0483623\pi$
$308$	11.8137	−	13.3349i	0.673145	−	0.759824i
$309$	−2.35276	−	29.3526i	−0.133844	−	1.66981i
$310$	0.755386	−	0.591807i	0.0429030	−	0.0336124i
$311$	−3.62992	−	29.8951i	−0.205834	−	1.69520i	−0.619685	−	0.784851i	$-0.712739\pi$
$311$	−3.62992	−	29.8951i	−0.205834	−	1.69520i	0.413851	−	0.910345i	$-0.364184\pi$
$312$	−15.2938	−	3.13608i	−0.865840	−	0.177546i
$313$	−0.260561	+	2.14591i	−0.0147278	+	0.121294i	−0.998218	−	0.0596644i	$-0.980997\pi$
$313$	−0.260561	+	2.14591i	−0.0147278	+	0.121294i	0.983491	+	0.180959i	$0.0579200\pi$
$314$	24.0073	+	39.7130i	1.35481	+	2.24113i
$315$	12.6305	−	7.27307i	0.711649	−	0.409791i
$316$		−	22.8113i		−	1.28323i
$317$	−12.9066	−	21.3501i	−0.724906	−	1.19914i	−0.973090	−	0.230427i	$-0.925988\pi$
$317$	−12.9066	−	21.3501i	−0.724906	−	1.19914i	0.248184	−	0.968713i	$-0.420166\pi$
$318$	−11.4415	+	8.23262i	−0.641606	+	0.461662i
$319$	−10.5757	−	10.5757i	−0.592126	−	0.592126i
$320$	16.6855	+	37.0737i	0.932749	+	2.07248i
$321$	−23.8168	−	6.91331i	−1.32932	−	0.385864i
$322$	−6.69888	+	7.56147i	−0.373314	+	0.421384i
$323$	0.900640	−	1.48984i	0.0501129	−	0.0828969i
$324$	8.79256	+	26.5381i	0.488476	+	1.47434i
$325$	−5.70279	+	15.9866i	−0.316334	+	0.886776i
$326$	30.5988	+	34.5389i	1.69471	+	1.91293i
$327$	8.53702	+	3.04796i	0.472098	+	0.168553i
$328$	0.539945	+	0.133085i	0.0298135	+	0.00734836i
$329$	8.56476	+	12.4082i	0.472191	+	0.684086i
$330$	39.2994	−	21.6171i	2.16336	−	1.18998i
$331$	−6.43923	+	10.6518i	−0.353932	+	0.585475i	−0.981122	−	0.193391i	$-0.938051\pi$
$331$	−6.43923	+	10.6518i	−0.353932	+	0.585475i	0.627190	+	0.778867i	$0.284205\pi$
$332$	7.24725	+	5.67786i	0.397745	+	0.311613i
$333$	−12.0208	−	24.1383i	−0.658738	−	1.32277i
$334$	−8.77748	+	23.1443i	−0.480282	+	1.26640i
$335$	−24.3122	−	12.7600i	−1.32831	−	0.697153i
$336$	1.15868	+	0.986715i	0.0632111	+	0.0538297i
$337$			16.6780i			0.908510i	0.890872	+	0.454255i	$0.150095\pi$
$337$			16.6780i			0.908510i	−0.890872	+	0.454255i	$0.849905\pi$
$338$	17.1853	−	23.8250i	0.934758	−	1.29591i
$339$	−3.69048	−	2.13350i	−0.200439	−	0.115876i
$340$	18.0538	+	3.30849i	0.979106	+	0.179428i
$341$	0.232968	−	0.443884i	0.0126159	−	0.0240377i
$342$	−6.14366	+	0.991261i	−0.332211	+	0.0536012i
$343$	1.08916	−	18.0060i	0.0588092	−	0.972231i
$344$	−11.1753	+	14.2642i	−0.602529	+	0.769072i
$345$	−13.5563	+	7.45680i	−0.729846	+	0.401461i
$346$	−0.708305	−	0.428185i	−0.0380787	−	0.0230194i
$347$	−0.549526	+	0.379310i	−0.0295001	+	0.0203624i	−0.582724	−	0.812670i	$-0.698013\pi$
$347$	−0.549526	+	0.379310i	−0.0295001	+	0.0203624i	0.553223	+	0.833033i	$0.313398\pi$
$348$	−15.1645	+	15.7700i	−0.812904	+	0.845359i
$349$	28.8942	−	5.29506i	1.54667	−	0.283438i	0.661947	−	0.749551i	$-0.269730\pi$
$349$	28.8942	−	5.29506i	1.54667	−	0.283438i	0.884725	+	0.466113i	$0.154346\pi$
$350$	−12.4158	+	10.9995i	−0.663653	+	0.587945i
$351$	−18.6363	−	1.92069i	−0.994731	−	0.102519i
$352$	17.2705	+	15.3003i	0.920518	+	0.815508i
$353$	18.6962	+	11.3022i	0.995098	+	0.601557i	0.918465	−	0.395502i	$-0.129429\pi$
$353$	18.6962	+	11.3022i	0.995098	+	0.601557i	0.0766325	+	0.997059i	$0.475583\pi$
$354$	36.9555	−	12.3142i	1.96416	−	0.654491i
$355$	−0.973725	−	3.95056i	−0.0516799	−	0.209674i
$356$	−22.6926	+	10.2131i	−1.20270	+	0.541293i
$357$	4.94816	−	1.32284i	0.261884	−	0.0700119i
$358$	−19.3630	+	43.0229i	−1.02337	+	2.27383i
$359$	−9.64280	+	5.82927i	−0.508927	+	0.307657i	−0.748402	−	0.663245i	$-0.769179\pi$
$359$	−9.64280	+	5.82927i	−0.508927	+	0.307657i	0.239475	+	0.970903i	$0.423025\pi$
$360$	−11.6604	−	20.2497i	−0.614558	−	1.06725i
$361$			18.1573i			0.955648i
$362$	−16.9245	+	10.2312i	−0.889534	+	0.537742i
$363$	2.63246	−	3.49902i	0.138168	−	0.183651i
$364$	15.7801	−	7.48199i	0.827103	−	0.392163i
$365$	35.1833	−	4.27203i	1.84158	−	0.223608i
$366$	6.61610	+	46.8134i	0.345829	+	2.44697i
$367$	−4.94045	−	7.15747i	−0.257889	−	0.373617i	0.672557	−	0.740045i	$-0.265196\pi$
$367$	−4.94045	−	7.15747i	−0.257889	−	0.373617i	−0.930446	+	0.366428i	$0.880581\pi$
$368$	−1.20925	−	1.07130i	−0.0630366	−	0.0558455i
$369$	0.660620	+	0.0945164i	0.0343905	+	0.00492032i
$370$	39.0291	+	49.8170i	2.02903	+	2.58986i
$371$	1.67066	−	5.36133i	0.0867363	−	0.278346i
$372$	−0.655860	−	0.328017i	−0.0340048	−	0.0170069i
$373$	2.55292	−	3.69854i	0.132185	−	0.191503i	−0.751302	−	0.659958i	$-0.770574\pi$
$373$	2.55292	−	3.69854i	0.132185	−	0.191503i	0.883487	+	0.468455i	$0.155189\pi$
$374$	15.3041	−	3.77212i	0.791356	−	0.195052i
$375$	1.46445	−	0.588420i	0.0756237	−	0.0303859i
$376$	19.8932	−	13.7313i	1.02592	−	0.708139i
$377$	−5.46998	−	13.6029i	−0.281718	−	0.700586i
$378$	−15.0502	−	10.4264i	−0.774100	−	0.536277i
$379$	−24.1238	+	7.51729i	−1.23916	+	0.386137i	−0.845925	−	0.533301i	$-0.820951\pi$
$379$	−24.1238	+	7.51729i	−1.23916	+	0.386137i	−0.393233	+	0.919439i	$0.628643\pi$
$380$	8.30712	−	3.15048i	0.426146	−	0.161616i
$381$	−22.3091	+	29.6529i	−1.14293	+	1.51916i
$382$	9.08003	+	1.66398i	0.464575	+	0.0851365i
$383$	13.2197	+	21.8680i	0.675493	+	1.11740i	0.985986	+	0.166827i	$0.0533521\pi$
$383$	13.2197	+	21.8680i	0.675493	+	1.11740i	−0.310493	+	0.950576i	$0.600494\pi$
$384$	19.0228	−	22.3381i	0.970756	−	1.13994i
$385$	−7.33369	+	16.2948i	−0.373759	+	0.830459i
$386$	7.20858	−	2.73386i	0.366907	−	0.139150i
$387$	−11.6430	+	18.3657i	−0.591849	+	0.933579i
$388$	−43.6867	−	13.6133i	−2.21786	−	0.691113i
$389$	29.6859	+	7.31692i	1.50514	+	0.370983i	0.903780	−	0.427998i	$-0.140781\pi$
$389$	29.6859	+	7.31692i	1.50514	+	0.370983i	0.601356	+	0.798981i	$0.294627\pi$
$390$	43.7495	−	4.38180i	2.21534	−	0.221881i
$391$	−5.27913	+	1.30119i	−0.266977	+	0.0658040i
$392$	−11.4003	−	0.689589i	−0.575800	−	0.0348295i
$393$	10.1311	−	23.7410i	0.511044	−	1.19757i
$394$	−6.26979	−	11.9461i	−0.315868	−	0.601835i
$395$	6.80694	+	21.8442i	0.342494	+	1.09910i
$396$	−27.7874	−	20.0664i	−1.39637	−	1.00837i
$397$	1.91817	+	0.116028i	0.0962702	+	0.00582328i	0.108443	−	0.994103i	$-0.465413\pi$
$397$	1.91817	+	0.116028i	0.0962702	+	0.00582328i	−0.0121731	+	0.999926i	$0.503875\pi$
$398$	35.5864	+	45.4227i	1.78379	+	2.27683i
$399$	1.71847	−	1.78708i	0.0860309	−	0.0894657i
$400$	−1.75906	−	1.98557i	−0.0879531	−	0.0992785i
$401$	−0.948024	+	0.0573449i	−0.0473420	+	0.00286367i	−0.0840325	−	0.996463i	$-0.526780\pi$
$401$	−0.948024	+	0.0573449i	−0.0473420	+	0.00286367i	0.0366905	+	0.999327i	$0.488318\pi$
$402$	−1.40847	+	34.4630i	−0.0702481	+	1.71886i
$403$	0.380753	−	0.310685i	0.0189666	−	0.0154763i
$404$	−16.0687	+	30.6164i	−0.799450	+	1.52322i
$405$	−16.3389	−	22.7893i	−0.811884	−	1.13241i
$406$	1.72707	−	14.2237i	0.0857129	−	0.705909i
$407$	29.2737	+	15.3640i	1.45104	+	0.761567i
$408$	−2.12081	−	7.93306i	−0.104996	−	0.392745i
$409$	1.78172	−	0.555206i	0.0881003	−	0.0274532i	−0.253136	−	0.967431i	$-0.581462\pi$
$409$	1.78172	−	0.555206i	0.0881003	−	0.0274532i	0.341236	+	0.939978i	$0.389154\pi$
$410$	−1.56331	+	0.0945628i	−0.0772064	+	0.00467012i
$411$	−21.4140	−	7.64541i	−1.05628	−	0.377121i
$412$	39.5292	−	35.0199i	1.94747	−	1.72530i
$413$	−8.81569	+	12.7717i	−0.433792	+	0.628456i
$414$	15.7567	+	11.3785i	0.774402	+	0.559225i
$415$	−8.63432	−	3.27456i	−0.423842	−	0.160742i
$416$	9.69019	+	20.4374i	0.475100	+	1.00203i
$417$	6.49458	+	1.05927i	0.318041	+	0.0518726i
$418$	5.39497	−	5.39497i	0.263877	−	0.263877i
$419$	5.65326	+	2.14400i	0.276180	+	0.104741i	0.488806	−	0.872392i	$-0.337432\pi$
$419$	5.65326	+	2.14400i	0.276180	+	0.104741i	−0.212626	+	0.977134i	$0.568202\pi$
$420$	24.0415	+	10.2593i	1.17310	+	0.500602i
$421$	−5.18124	+	16.6272i	−0.252518	+	0.810360i	0.738218	+	0.674562i	$0.235667\pi$
$421$	−5.18124	+	16.6272i	−0.252518	+	0.810360i	−0.990737	+	0.135798i	$0.956640\pi$
$422$	6.58100	−	1.20601i	0.320358	−	0.0587078i
$423$	22.1167	−	18.7692i	1.07535	−	0.912589i
$424$	−8.59547	−	2.67846i	−0.417433	−	0.130077i
$425$	−8.86258	+	1.07611i	−0.429898	+	0.0521991i
$426$	−3.96101	+	3.23031i	−0.191912	+	0.156509i
$427$	−13.3188	−	13.3188i	−0.644542	−	0.644542i
$428$	−15.7716	−	41.5864i	−0.762350	−	2.01015i
$429$	19.9021	−	11.4674i	0.960880	−	0.553653i
$430$	18.0966	−	47.7168i	0.872695	−	2.30111i
$431$	23.9882	−	10.7962i	1.15547	−	0.520035i	0.260199	−	0.965555i	$-0.416212\pi$
$431$	23.9882	−	10.7962i	1.15547	−	0.520035i	0.895272	+	0.445520i	$0.146981\pi$
$432$	1.66742	−	2.40687i	0.0802239	−	0.115801i
$433$	10.3692	+	11.7044i	0.498311	+	0.562476i	0.942822	−	0.333297i	$-0.108161\pi$
$433$	10.3692	+	11.7044i	0.498311	+	0.562476i	−0.444511	+	0.895773i	$0.646623\pi$
$434$	0.472384	−	0.0865676i	0.0226752	−	0.00415538i
$435$	9.81588	−	19.6266i	0.470635	−	0.941023i
$436$	4.83652	+	15.5209i	0.231627	+	0.743318i
$437$	−1.86099	+	1.86099i	−0.0890232	+	0.0890232i
$438$	−23.7740	−	37.6430i	−1.13597	−	1.79865i
$439$	−19.6752	−	2.38901i	−0.939048	−	0.114021i	−0.363322	−	0.931664i	$-0.618357\pi$
$439$	−19.6752	−	2.38901i	−0.939048	−	0.114021i	−0.575726	+	0.817643i	$0.695281\pi$
$440$	26.1244	+	11.7576i	1.24543	+	0.560523i
$441$	−13.6953	+	0.536277i	−0.652155	+	0.0255370i
$442$	15.2506	+	2.48314i	0.725397	+	0.118111i
$443$	−7.46473	−	14.2229i	−0.354660	−	0.675748i	0.641128	−	0.767434i	$-0.278467\pi$
$443$	−7.46473	−	14.2229i	−0.354660	−	0.675748i	−0.995788	+	0.0916857i	$0.970774\pi$
$444$	21.6324	−	43.2534i	1.02663	−	2.05271i
$445$	18.6830	−	16.5517i	0.885657	−	0.784624i
$446$	−2.97521	−	0.733325i	−0.140880	−	0.0347239i
$447$	−4.62626	−	32.7339i	−0.218815	−	1.54826i
$448$	−1.22850	+	20.3096i	−0.0580412	+	0.959536i
$449$	5.48851	+	12.1950i	0.259019	+	0.575516i	0.994817	−	0.101685i	$-0.0324234\pi$
$449$	5.48851	+	12.1950i	0.259019	+	0.575516i	−0.735798	+	0.677201i	$0.763193\pi$
$450$	23.4316	+	21.6657i	1.10458	+	1.02133i
$451$	−0.724461	+	0.380226i	−0.0341135	+	0.0179042i
$452$	−0.921503	−	7.58926i	−0.0433439	−	0.356969i
$453$	−2.23563	+	3.37841i	−0.105039	+	0.158732i
$454$	−4.02013	−	16.3103i	−0.188674	−	0.765481i
$455$	−12.8785	+	11.8736i	−0.603755	+	0.556645i
$456$	−2.86510	−	2.75510i	−0.134171	−	0.129020i
$457$	1.45844	−	4.68030i	0.0682230	−	0.218935i	−0.914313	−	0.405009i	$-0.867269\pi$
$457$	1.45844	−	4.68030i	0.0682230	−	0.218935i	0.982536	+	0.186073i	$0.0595762\pi$
$458$	15.4923	+	29.5181i	0.723906	+	1.37929i
$459$	−3.47863	−	9.21988i	−0.162369	−	0.430347i
$460$	−25.3029	−	11.3879i	−1.17976	−	0.530965i
$461$	4.55551	−	24.8586i	0.212171	−	1.15778i	−0.689146	−	0.724622i	$-0.742014\pi$
$461$	4.55551	−	24.8586i	0.212171	−	1.15778i	0.901318	−	0.433159i	$-0.142601\pi$
$462$	22.4428	−	0.439238i	1.04413	−	0.0204352i
$463$	−0.598007	+	3.26322i	−0.0277918	+	0.151655i	−0.994589	−	0.103891i	$-0.966871\pi$
$463$	−0.598007	+	3.26322i	−0.0277918	+	0.151655i	0.966797	+	0.255546i	$0.0822552\pi$
$464$	2.27469	+	0.276197i	0.105600	+	0.0128221i
$465$	0.725938	+	0.118401i	0.0336646	+	0.00549070i
$466$	14.8397	+	47.6221i	0.687434	+	2.20605i
$467$	−10.9259	+	15.8289i	−0.505591	+	0.732475i	−0.989798	−	0.142479i	$-0.954493\pi$
$467$	−10.9259	+	15.8289i	−0.505591	+	0.732475i	0.484207	+	0.874953i	$0.339108\pi$
$468$	−17.3411	−	28.7790i	−0.801591	−	1.33031i
$469$	−7.80601	−	11.3090i	−0.360448	−	0.522199i
$470$	−41.9839	+	53.5885i	−1.93657	+	2.47186i
$471$	−9.91549	+	34.1594i	−0.456882	+	1.57398i
$472$	20.4761	+	14.1336i	0.942487	+	0.650552i
$473$	−1.60970	−	26.6114i	−0.0740139	−	1.22360i
$474$	21.1368	−	19.4769i	0.970843	−	0.894604i
$475$	−3.40176	+	2.66511i	−0.156083	+	0.122284i
$476$	7.23090	+	5.66505i	0.331428	+	0.259657i
$477$	−10.5833	−	2.17315i	−0.484575	−	0.0995017i
$478$	−6.83352	+	4.71684i	−0.312558	+	0.215743i
$479$	−23.9823	−	30.6112i	−1.09578	−	1.39866i	−0.909270	−	0.416208i	$-0.863359\pi$
$479$	−23.9823	−	30.6112i	−1.09578	−	1.39866i	−0.186511	−	0.982453i	$-0.559718\pi$
$480$	−13.2872	+	31.1370i	−0.606474	+	1.42120i
$481$	20.4894	+	25.1103i	0.934236	+	1.14493i
$482$	−61.0397	−	7.41156i	−2.78028	−	0.337587i
$483$	−7.74163	+	0.151515i	−0.352257	+	0.00689416i
$484$	7.85286			0.356948
$485$	45.8970			2.08408
$486$	−17.0826	+	30.8061i	−0.774884	+	1.39739i
$487$	−16.4479	−	7.40260i	−0.745325	−	0.335444i	0.00191450	−	0.999998i	$-0.499391\pi$
$487$	−16.4479	−	7.40260i	−0.745325	−	0.335444i	−0.747240	+	0.664554i	$0.768621\pi$
$488$	−21.3531	+	21.3531i	−0.966611	+	0.966611i
$489$	−3.57536	+	35.1874i	−0.161684	+	1.59123i
$490$	31.2308	−	7.69770i	1.41086	−	0.347747i
$491$	−14.8378	−	13.1451i	−0.669621	−	0.593232i	0.258275	−	0.966071i	$-0.416846\pi$
$491$	−14.8378	−	13.1451i	−0.669621	−	0.593232i	−0.927896	+	0.372839i	$0.878384\pi$
$492$	0.576827	+	1.04866i	0.0260054	+	0.0472772i
$493$	5.11381	−	5.77230i	0.230315	−	0.259971i
$494$	6.93923	−	2.79039i	0.312211	−	0.125546i
$495$	32.5973	+	10.9239i	1.46514	+	0.490991i
$496$	0.0138441	+	0.0755449i	0.000621619	+	0.00339207i
$497$	0.487316	−	1.97712i	0.0218591	−	0.0886860i
$498$	0.926848	+	11.5632i	0.0415331	+	0.518158i
$499$	14.0611	−	23.2598i	0.629460	−	1.04125i	−0.364468	−	0.931216i	$-0.618749\pi$
$499$	14.0611	−	23.2598i	0.629460	−	1.04125i	0.993927	−	0.110037i	$-0.0350971\pi$
$500$	2.42225	+	1.46430i	0.108326	+	0.0654855i
$501$	−17.6049	+	7.07371i	−0.786528	+	0.316030i
$502$	−20.1137	−	1.21665i	−0.897717	−	0.0543019i
$503$	−24.3827	−	9.24712i	−1.08717	−	0.412309i	−0.255063	−	0.966925i	$-0.582096\pi$
$503$	−24.3827	−	9.24712i	−1.08717	−	0.412309i	−0.832107	+	0.554616i	$0.812865\pi$
$504$	−0.457576	−	11.6854i	−0.0203820	−	0.520510i
$505$	6.25153	−	34.1135i	0.278189	−	1.51803i
$506$	−23.8285			−1.05931
$507$	22.3556	−	2.68799i	0.992849	−	0.119378i
$508$	−66.5500			−2.95268
$509$	−0.609520	+	3.32604i	−0.0270165	+	0.147424i	−0.994362	−	0.106036i	$-0.966184\pi$
$509$	−0.609520	+	3.32604i	−0.0270165	+	0.147424i	0.967346	+	0.253460i	$0.0815687\pi$
$510$	12.3493	+	19.5534i	0.546834	+	0.865840i
$511$	16.5847	+	6.28976i	0.733665	+	0.278243i
$512$	−6.34074	−	0.383544i	−0.280224	−	0.0169504i
$513$	−3.74981	−	2.94814i	−0.165558	−	0.130163i
$514$	17.9062	+	10.8247i	0.789811	+	0.477457i
$515$	−27.4035	+	45.3309i	−1.20754	+	1.99752i
$516$	−38.8738	+	3.11594i	−1.71133	+	0.137172i
$517$	−8.51092	+	34.5302i	−0.374310	+	1.51864i
$518$	5.70905	+	31.1533i	0.250841	+	1.36880i
$519$	−0.126543	−	0.621654i	−0.00555461	−	0.0272876i
$520$	19.0362	+	20.6473i	0.834793	+	0.905444i
$521$	17.0569	−	19.2533i	0.747277	−	0.843502i	−0.244742	−	0.969588i	$-0.578703\pi$
$521$	17.0569	−	19.2533i	0.747277	−	0.843502i	0.992019	+	0.126087i	$0.0402418\pi$
$522$	−27.5603	−	0.586499i	−1.20628	−	0.0256704i
$523$	−11.2863	−	9.99879i	−0.493516	−	0.437217i	0.379295	−	0.925276i	$-0.376167\pi$
$523$	−11.2863	−	9.99879i	−0.493516	−	0.437217i	−0.872811	+	0.488059i	$0.837705\pi$
$524$	44.9471	−	11.0785i	1.96352	−	0.483965i
$525$	−12.6489	−	1.28525i	−0.552045	−	0.0560928i
$526$	47.2743	−	47.2743i	2.06126	−	2.06126i
$527$	0.235709	+	0.106084i	0.0102676	+	0.00462109i
$528$	0.0702441	+	3.58912i	0.00305698	+	0.156196i
$529$	−14.7804			−0.642625
$530$	25.3557			1.10138
$531$	26.1361	+	14.4347i	1.13421	+	0.626413i
$532$	4.41396	+	0.535951i	0.191369	+	0.0232364i
$533$	−0.799469	+	0.0642993i	−0.0346289	+	0.00278511i
$534$	−28.8390	−	12.3065i	−1.24798	−	0.532556i
$535$	27.5125	+	35.1171i	1.18947	+	1.51825i
$536$	−18.1309	+	12.5149i	−0.783136	+	0.540559i
$537$	−34.3081	+	11.4320i	−1.48050	+	0.493328i
$538$	45.7178	+	35.8176i	1.97104	+	1.54421i
$539$	13.2274	−	10.3630i	0.569745	−	0.446367i
$540$	15.0434	−	47.9871i	0.647364	−	2.06504i
$541$	−2.71704	−	44.9180i	−0.116814	−	1.93117i	−0.311382	−	0.950285i	$-0.600792\pi$
$541$	−2.71704	−	44.9180i	−0.116814	−	1.93117i	0.194568	−	0.980889i	$-0.437670\pi$
$542$	27.9296	+	19.2784i	1.19968	+	0.828079i
$543$	−14.5578	−	4.22570i	−0.624734	−	0.181342i
$544$	−7.33701	+	9.36500i	−0.314572	+	0.401521i
$545$	−9.26298	−	13.4197i	−0.396782	−	0.574838i
$546$	20.4063	+	8.23342i	0.873308	+	0.352358i
$547$	11.5798	−	16.7762i	0.495116	−	0.717299i	−0.493167	−	0.869935i	$-0.664161\pi$
$547$	11.5798	−	16.7762i	0.495116	−	0.717299i	0.988283	+	0.152636i	$0.0487761\pi$
$548$	−12.1318	−	38.9323i	−0.518244	−	1.66310i
$549$	−22.9509	+	28.0445i	−0.979521	+	1.19691i
$550$	−38.8407	−	4.71612i	−1.65617	−	0.201096i
$551$	0.672865	−	3.67171i	0.0286650	−	0.156420i
$552$	0.242914	+	12.4116i	0.0103391	+	0.528275i
$553$	−2.06406	+	11.2632i	−0.0877728	+	0.478961i
$554$	−25.6072	−	11.5249i	−1.08795	−	0.489645i
$555$	−7.80842	+	47.8749i	−0.331449	+	2.03218i
$556$	5.48440	+	10.4497i	0.232590	+	0.443164i
$557$	−1.12565	+	3.61234i	−0.0476954	+	0.153060i	−0.975496	−	0.220016i	$-0.929389\pi$
$557$	−1.12565	+	3.61234i	−0.0476954	+	0.153060i	0.927801	+	0.373076i	$0.121697\pi$
$558$	−0.256055	−	0.887786i	−0.0108397	−	0.0375830i
$559$	8.78086	−	24.6153i	0.371391	−	1.04112i
$560$	−0.655161	−	2.65809i	−0.0276856	−	0.112325i
$561$	10.0753	+	6.66722i	0.425379	+	0.281490i
$562$	−4.51558	−	37.1891i	−0.190478	−	1.56873i
$563$	−6.53535	+	3.43002i	−0.275432	+	0.144558i	−0.596784	−	0.802402i	$-0.703555\pi$
$563$	−6.53535	+	3.43002i	−0.275432	+	0.144558i	0.321352	+	0.946960i	$0.395863\pi$
$564$	50.7449	+	11.4591i	2.13674	+	0.482514i
$565$	3.14709	+	6.99256i	0.132399	+	0.294179i
$566$	1.38450	−	22.8884i	0.0581947	−	0.962073i
$567$	−1.94011	−	13.8989i	−0.0814770	−	0.583701i
$568$	−3.16979	−	0.781282i	−0.133001	−	0.0327819i
$569$	−1.45979	+	1.29326i	−0.0611977	+	0.0542164i	−0.693167	−	0.720777i	$-0.743785\pi$
$569$	−1.45979	+	1.29326i	−0.0611977	+	0.0542164i	0.631970	+	0.774993i	$0.282247\pi$
$570$	10.0121	+	5.00735i	0.419359	+	0.209735i
$571$	−2.67885	−	5.10413i	−0.112107	−	0.213601i	0.822938	−	0.568131i	$-0.192333\pi$
$571$	−2.67885	−	5.10413i	−0.112107	−	0.213601i	−0.935045	+	0.354530i	$0.884641\pi$
$572$	37.8927	+	16.1579i	1.58437	+	0.675598i
$573$	3.77830	+	5.98244i	0.157841	+	0.249920i
$574$	−0.714760	−	0.321687i	−0.0298335	−	0.0134270i
$575$	13.3981	+	1.62682i	0.558738	+	0.0678431i
$576$	39.1158	−	1.53169i	1.62983	−	0.0638205i
$577$	−1.35461	+	1.35461i	−0.0563932	+	0.0563932i	−0.734741	−	0.678348i	$-0.762696\pi$
$577$	−1.35461	+	1.35461i	−0.0563932	+	0.0563932i	0.678348	+	0.734741i	$0.262696\pi$
$578$	−9.01075	−	28.9165i	−0.374798	−	1.20277i
$579$	5.28519	+	2.64329i	0.219645	+	0.109851i
$580$	38.7109	−	7.09403i	1.60738	−	0.294563i
$581$	−3.06463	−	3.45925i	−0.127142	−	0.143514i
$582$	−24.6870	−	52.1033i	−1.02331	−	2.15975i
$583$	12.0790	−	5.43632i	0.500262	−	0.225149i
$584$	10.0840	−	26.5892i	0.417277	−	1.10027i
$585$	25.1937	+	22.3844i	1.04163	+	0.925481i
$586$	−24.5776	−	64.8059i	−1.01529	−	2.67711i
$587$	1.06389	+	1.06389i	0.0439115	+	0.0439115i	0.728722	−	0.684810i	$-0.240115\pi$
$587$	1.06389	+	1.06389i	0.0439115	+	0.0439115i	−0.684810	+	0.728722i	$0.740115\pi$
$588$	−15.5348	−	19.0488i	−0.640645	−	0.785560i
$589$	0.124205	−	0.0150813i	0.00511779	−	0.000621412i
$590$	−66.8980	−	20.8463i	−2.75415	−	0.858227i
$591$	3.47710	−	9.73899i	0.143029	−	0.400608i
$592$	−4.98211	+	0.913006i	−0.204764	+	0.0375243i
$593$	4.99203	−	16.0200i	0.204998	−	0.657863i	−0.793769	−	0.608220i	$-0.791884\pi$
$593$	4.99203	−	16.0200i	0.204998	−	0.657863i	0.998767	−	0.0496429i	$-0.0158083\pi$
$594$	−5.13236	−	42.8809i	−0.210583	−	1.75942i
$595$	−8.61484	−	3.26718i	−0.353174	−	0.133941i
$596$	41.9238	−	41.9238i	1.71726	−	1.71726i
$597$	−7.11965	+	43.6519i	−0.291388	+	1.78655i
$598$	−21.4869	−	9.16229i	−0.878664	−	0.374674i
$599$	3.23463	+	1.22673i	0.132164	+	0.0501230i	0.419800	−	0.907617i	$-0.362100\pi$
$599$	3.23463	+	1.22673i	0.132164	+	0.0501230i	−0.287636	+	0.957740i	$0.592869\pi$
$600$	−2.06055	+	20.2792i	−0.0841217	+	0.827895i
$601$	12.6218	−	18.2859i	0.514856	−	0.745897i	−0.476201	−	0.879336i	$-0.657987\pi$
$601$	12.6218	−	18.2859i	0.514856	−	0.745897i	0.991057	+	0.133439i	$0.0426020\pi$
$602$	19.1172	−	16.9364i	0.779160	−	0.690275i
$603$	−20.1574	+	17.1064i	−0.820872	+	0.696627i
$604$	−7.25215	+	0.438674i	−0.295086	+	0.0178494i
$605$	−7.51996	+	2.34332i	−0.305730	+	0.0952693i
$606$	−42.0889	+	11.2520i	−1.70975	+	0.457082i
$607$	24.2893	+	12.7480i	0.985874	+	0.517427i	0.878988	−	0.476845i	$-0.158220\pi$
$607$	24.2893	+	12.7480i	0.985874	+	0.517427i	0.106886	+	0.994271i	$0.465912\pi$
$608$	−0.694130	+	5.71667i	−0.0281507	+	0.231842i
$609$	8.91453	−	6.41438i	0.361235	−	0.259924i
$610$	39.5233	−	75.3053i	1.60025	−	3.04902i
$611$	−20.9518	+	27.8644i	−0.847618	+	1.12727i
$612$	9.46258	−	14.9262i	0.382502	−	0.603356i
$613$	−33.6656	+	2.03639i	−1.35974	+	0.0822490i	−0.724077	−	0.689719i	$-0.757734\pi$
$613$	−33.6656	+	2.03639i	−1.35974	+	0.0822490i	−0.635662	+	0.771968i	$0.719273\pi$
$614$	25.7550	+	29.0714i	1.03939	+	1.17323i
$615$	−0.865297	−	0.832077i	−0.0348921	−	0.0335526i
$616$	8.84220	+	11.2862i	0.356262	+	0.454735i
$617$	−7.68311	−	0.464743i	−0.309311	−	0.0187098i	−0.0950059	−	0.995477i	$-0.530287\pi$
$617$	−7.68311	−	0.464743i	−0.309311	−	0.0187098i	−0.214305	+	0.976767i	$0.568749\pi$
$618$	66.2004	+	6.72656i	2.66297	+	0.270582i
$619$	2.43445	+	7.81244i	0.0978489	+	0.314008i	0.990647	−	0.136449i	$-0.0435688\pi$
$619$	2.43445	+	7.81244i	0.0978489	+	0.314008i	−0.892798	+	0.450457i	$0.851261\pi$
$620$	0.613024	+	1.16802i	0.0246196	+	0.0469088i
$621$	1.77040	+	14.7917i	0.0710438	+	0.593572i
$622$	67.9263	+	4.10879i	2.72360	+	0.164747i
$623$	12.1287	−	2.98947i	0.485928	−	0.119770i
$624$	−1.31671	+	3.26343i	−0.0527106	+	0.130642i
$625$	−25.6103	−	6.31237i	−1.02441	−	0.252495i
$626$	−4.66359	−	1.45323i	−0.186394	−	0.0580828i
$627$	5.84318	+	0.238805i	0.233354	+	0.00953696i
$628$	−59.6457	+	22.6206i	−2.38012	+	0.902661i
$629$	−6.99614	+	15.5448i	−0.278954	+	0.619811i
$630$	11.0211	+	31.0363i	0.439092	+	1.23652i
$631$	−10.2917	−	17.0245i	−0.409706	−	0.677736i	0.580978	−	0.813919i	$-0.302670\pi$
$631$	−10.2917	−	17.0245i	−0.409706	−	0.677736i	−0.990684	+	0.136183i	$0.956516\pi$
$632$	18.0576	+	3.30917i	0.718292	+	0.131632i
$633$	4.09802	+	3.08311i	0.162882	+	0.122543i
$634$	52.7120	−	19.9910i	2.09346	−	0.793944i
$635$	63.7288	−	19.8587i	2.52900	−	0.788068i
$636$	−8.29651	−	17.5103i	−0.328978	−	0.694327i
$637$	15.9123	−	4.25858i	0.630467	−	0.168731i
$638$	27.8144	−	19.1989i	1.10118	−	0.760091i
$639$	−3.87821	−	0.554865i	−0.153420	−	0.0219501i
$640$	−51.2453	+	12.6308i	−2.02565	+	0.499277i
$641$	−0.335075	+	0.485440i	−0.0132347	+	0.0191737i	−0.829545	−	0.558439i	$-0.811400\pi$
$641$	−0.335075	+	0.485440i	−0.0132347	+	0.0191737i	0.816311	+	0.577613i	$0.196016\pi$
$642$	25.0674	−	50.1215i	0.989330	−	1.97814i
$643$	−10.2664	+	32.9460i	−0.404866	+	1.29926i	0.497189	+	0.867642i	$0.334366\pi$
$643$	−10.2664	+	32.9460i	−0.404866	+	1.29926i	−0.902056	+	0.431620i	$0.857942\pi$
$644$	−8.56418	−	10.9314i	−0.337476	−	0.430756i
$645$	36.2961	−	14.5839i	1.42916	−	0.574241i
$646$	2.94461	+	2.60870i	0.115854	+	0.102638i
$647$	19.9583	+	28.9146i	0.784642	+	1.13675i	0.987512	+	0.157544i	$0.0503577\pi$
$647$	19.9583	+	28.9146i	0.784642	+	1.13675i	−0.202870	+	0.979206i	$0.565027\pi$
$648$	−22.2832	+	3.11045i	−0.875369	+	0.122190i
$649$	−36.3386	+	4.41231i	−1.42642	+	0.173198i
$650$	−33.2105	−	19.1873i	−1.30262	−	0.752588i
$651$	0.294155	+	0.221306i	0.0115289	+	0.00867365i
$652$	−54.2830	+	32.8152i	−2.12589	+	1.28514i
$653$		−	15.2297i		−	0.595986i	−0.954568	−	0.297993i	$-0.903683\pi$
$653$		−	15.2297i		−	0.595986i	0.954568	−	0.297993i	$-0.0963172\pi$
$654$	−10.2520	+	17.7337i	−0.400886	+	0.693443i
$655$	−39.7359	+	24.0212i	−1.55261	+	0.938585i
$656$	0.0514451	−	0.114306i	0.00200859	−	0.00446291i
$657$	8.86991	−	32.9528i	0.346048	−	1.28561i
$658$	−31.0683	+	13.9827i	−1.21117	+	0.545103i
$659$	−9.15824	−	37.1565i	−0.356754	−	1.44741i	−0.825663	−	0.564163i	$-0.809199\pi$
$659$	−9.15824	−	37.1565i	−0.356754	−	1.44741i	0.468909	−	0.883247i	$-0.344647\pi$
$660$	19.4912	+	58.4942i	0.758695	+	2.27688i
$661$	13.7605	+	8.31851i	0.535221	+	0.323553i	0.759003	−	0.651087i	$-0.225687\pi$
$661$	13.7605	+	8.31851i	0.535221	+	0.323553i	−0.223782	+	0.974639i	$0.571840\pi$
$662$	−21.0528	−	18.6512i	−0.818242	−	0.724899i
$663$	6.52159	+	9.88609i	0.253278	+	0.383944i
$664$	−5.54598	+	4.91331i	−0.215226	+	0.190673i
$665$	−4.38677	+	0.803905i	−0.170112	+	0.0311741i
$666$	58.5486	−	16.8866i	2.26871	−	0.654341i
$667$	−9.59454	+	6.62263i	−0.371502	+	0.256429i
$668$	−29.1191	−	17.6031i	−1.12665	−	0.681085i
$669$	−1.13199	−	2.05794i	−0.0437654	−	0.0795645i
$670$	38.2646	−	48.8411i	1.47829	−	1.88690i
$671$	2.68257	−	44.3481i	0.103559	−	1.71204i
$672$	−13.1299	+	10.7077i	−0.506496	+	0.413060i
$673$	10.5690	−	20.1376i	0.407406	−	0.776247i	−0.592157	−	0.805823i	$-0.701723\pi$
$673$	10.5690	−	20.1376i	0.407406	−	0.776247i	0.999563	+	0.0295761i	$0.00941575\pi$
$674$	−37.0702	−	6.79337i	−1.42789	−	0.261671i
$675$	−0.0417914	+	24.4611i	−0.00160855	+	0.941508i
$676$	27.9561	+	29.1402i	1.07524	+	1.12078i
$677$			47.4431i			1.82339i	0.410873	+	0.911693i	$0.365224\pi$
$677$			47.4431i			1.82339i	−0.410873	+	0.911693i	$0.634776\pi$
$678$	6.24535	−	7.33379i	0.239851	−	0.281652i
$679$	20.3388	+	10.6746i	0.780533	+	0.409655i
$680$	−5.23805	+	13.8116i	−0.200870	+	0.529651i
$681$	7.10558	−	10.7377i	0.272286	−	0.411471i
$682$	0.891727	+	0.698623i	0.0341460	+	0.0267517i
$683$	3.22909	−	5.34156i	0.123558	−	0.204389i	−0.787879	−	0.615830i	$-0.788821\pi$
$683$	3.22909	−	5.34156i	0.123558	−	0.204389i	0.911436	+	0.411441i	$0.134974\pi$
$684$	0.182005	−	8.55263i	0.00695914	−	0.327018i
$685$	23.2350	+	33.6617i	0.887763	+	1.28615i
$686$	39.5782	+	9.75515i	1.51110	+	0.372453i
$687$	−8.59169	+	24.0644i	−0.327793	+	0.918116i
$688$	2.70851	+	3.05728i	0.103261	+	0.116558i
$689$	12.9823	−	0.257598i	0.494588	−	0.00981368i
$690$	−11.0524	−	33.1689i	−0.420758	−	1.26272i
$691$	5.79316	−	9.58305i	0.220382	−	0.364556i	−0.725953	−	0.687745i	$-0.758601\pi$
$691$	5.79316	−	9.58305i	0.220382	−	0.364556i	0.946335	+	0.323188i	$0.104755\pi$
$692$	0.754470	−	0.851620i	0.0286806	−	0.0323737i
$693$	11.9046	+	12.4222i	0.452217	+	0.471882i
$694$	−0.619257	−	1.37593i	−0.0235067	−	0.0522297i
$695$	−8.37011	−	8.37011i	−0.317496	−	0.317496i
$696$	−10.2837	−	14.2921i	−0.389805	−	0.541740i
$697$	−0.218247	−	0.361025i	−0.00826669	−	0.0136748i
$698$			66.3799i			2.51252i
$699$	−19.1354	+	33.1000i	−0.723768	+	1.25196i
$700$	−11.7962	−	19.5133i	−0.445854	−	0.737533i
$701$	−4.57269	+	37.6595i	−0.172708	+	1.42238i	0.606236	+	0.795285i	$0.292679\pi$
$701$	−4.57269	+	37.6595i	−0.172708	+	1.42238i	−0.778944	+	0.627093i	$0.784245\pi$
$702$	11.8601	−	40.6405i	0.447632	−	1.53388i
$703$	0.994594	+	8.19122i	0.0375118	+	0.308938i
$704$	−37.7796	+	29.5984i	−1.42387	+	1.11553i
$705$	−52.0131	+	4.16912i	−1.95893	+	0.157018i
$706$	−32.7369	+	36.9523i	−1.23207	+	1.39072i
$707$	10.7044	−	13.6631i	0.402579	−	0.513854i
$708$	7.49325	+	53.0198i	0.281614	+	1.99261i
$709$	−15.0981	−	4.70475i	−0.567020	−	0.176691i	0.000572947	−	1.00000i	$-0.499818\pi$
$709$	−15.0981	−	4.70475i	−0.567020	−	0.176691i	−0.567593	+	0.823309i	$0.692125\pi$
$710$	9.17752	−	0.555138i	0.344426	−	0.0208339i
$711$	21.9572	+	1.79774i	0.823458	+	0.0674205i
$712$	−4.79281	−	19.4452i	−0.179618	−	0.728740i
$713$	−0.307600	−	0.240989i	−0.0115197	−	0.00902513i
$714$	0.924757	+	11.5371i	0.0346082	+	0.431765i
$715$	−41.1079	−	4.16570i	−1.53735	−	0.155788i
$716$	−53.3746	−	36.8418i	−1.99470	−	1.37684i
$717$	−6.20812	−	1.40190i	−0.231847	−	0.0523549i
$718$	−9.02897	−	23.8074i	−0.336958	−	0.888485i
$719$	4.73125	−	38.9653i	0.176446	−	1.45316i	−0.588202	−	0.808714i	$-0.700164\pi$
$719$	4.73125	−	38.9653i	0.176446	−	1.45316i	0.764648	−	0.644448i	$-0.222913\pi$
$720$	−4.96341	+	1.76253i	−0.184976	+	0.0656854i
$721$	−22.6866	+	13.7145i	−0.844893	+	0.510756i
$722$	−40.3582	−	7.39592i	−1.50198	−	0.275248i
$723$	−27.5268	−	38.2560i	−1.02373	−	1.42275i
$724$	−9.64026	−	25.4193i	−0.358278	−	0.944700i
$725$	−16.9500	+	8.89603i	−0.629506	+	0.330390i
$726$	6.70500	+	7.27641i	0.248846	+	0.270053i
$727$	−3.94024	+	15.9862i	−0.146135	+	0.592895i	0.851512	+	0.524336i	$0.175686\pi$
$727$	−3.94024	+	15.9862i	−0.146135	+	0.592895i	−0.997647	+	0.0685590i	$0.978160\pi$
$728$	3.63362	+	13.5771i	0.134671	+	0.503200i
$729$	−26.2374	+	6.37191i	−0.971754	+	0.235997i
$730$	−4.83560	+	79.9420i	−0.178973	+	2.95878i
$731$	13.6461	−	1.65694i	0.504721	−	0.0612842i
$732$	−64.9370	−	2.65391i	−2.40014	−	0.0980915i
$733$	−0.663573	+	0.206778i	−0.0245096	+	0.00763751i	−0.309733	−	0.950823i	$-0.600240\pi$
$733$	−0.663573	+	0.206778i	−0.0245096	+	0.00763751i	0.285224	+	0.958461i	$0.407932\pi$
$734$	17.9213	−	8.06571i	0.661486	−	0.297711i
$735$	20.5605	+	13.6057i	0.758384	+	0.501853i
$736$	14.1576	−	11.0918i	0.521856	−	0.408848i
$737$	7.75694	−	31.4711i	0.285731	−	1.15925i
$738$	−0.479168	+	1.42986i	−0.0176384	+	0.0526338i
$739$	2.54878	+	42.1364i	0.0937584	+	1.55001i	0.675942	+	0.736954i	$0.263737\pi$
$739$	2.54878	+	42.1364i	0.0937584	+	1.55001i	−0.582184	+	0.813057i	$0.697802\pi$
$740$	−77.0298	+	40.4284i	−2.83167	+	1.48618i
$741$	5.17715	+	2.46210i	0.190187	+	0.0904474i
$742$	11.2361	+	5.89717i	0.412491	+	0.216492i
$743$	−2.58604	+	5.74594i	−0.0948726	+	0.210798i	−0.953225	−	0.302263i	$-0.902258\pi$
$743$	−2.58604	+	5.74594i	−0.0948726	+	0.210798i	0.858352	+	0.513061i	$0.171489\pi$
$744$	0.354805	−	0.471600i	0.0130078	−	0.0172897i
$745$	−27.6364	+	52.6567i	−1.01252	+	1.92919i
$746$	7.18087	+	7.18087i	0.262910	+	0.262910i
$747$	−6.03642	+	6.52844i	−0.220861	+	0.238863i
$748$	1.30824	+	21.6278i	0.0478339	+	0.790789i
$749$	4.02444	+	21.9606i	0.147050	+	0.802424i
$750$	0.711375	+	3.49470i	0.0259758	+	0.127608i
$751$	−28.0965	−	19.3936i	−1.02526	−	0.707683i	−0.0682253	−	0.997670i	$-0.521734\pi$
$751$	−28.0965	−	19.3936i	−1.02526	−	0.707683i	−0.957031	+	0.289987i	$0.906349\pi$
$752$	−2.23615	−	4.96853i	−0.0815441	−	0.181184i
$753$	−9.76139	−	11.9694i	−0.355725	−	0.436191i
$754$	32.4632	−	6.61731i	1.18224	−	0.240988i
$755$	6.81381	−	2.58414i	0.247980	−	0.0940464i
$756$	17.8271	−	17.7663i	0.648365	−	0.646153i
$757$	−0.0342457	+	0.0902985i	−0.00124468	+	0.00328195i	−0.935637	−	0.352963i	$-0.885174\pi$
$757$	−0.0342457	+	0.0902985i	−0.00124468	+	0.00328195i	0.934392	+	0.356245i	$0.115943\pi$
$758$	−6.88244	−	56.6820i	−0.249981	−	2.05878i
$759$	−12.3767	−	13.4314i	−0.449245	−	0.487530i
$760$	1.28885	+	7.03302i	0.0467514	+	0.255114i
$761$	−1.31160	−	7.15719i	−0.0475456	−	0.259448i	0.951255	−	0.308404i	$-0.0997950\pi$
$761$	−1.31160	−	7.15719i	−0.0475456	−	0.259448i	−0.998801	+	0.0489566i	$0.984410\pi$
$762$	−56.8223	−	61.6648i	−2.05846	−	2.23388i
$763$	−0.983664	−	8.10120i	−0.0356110	−	0.293283i
$764$	−4.49982	+	11.8650i	−0.162798	+	0.429262i
$765$	−4.60742	+	17.1171i	−0.166582	+	0.618871i
$766$	−53.9907	+	20.4760i	−1.95076	+	0.739826i
$767$	−34.4642	−	9.99385i	−1.24443	−	0.360857i
$768$	13.3348	+	16.3512i	0.481179	+	0.590023i
$769$	−2.55437	−	5.67558i	−0.0921131	−	0.204667i	0.860083	−

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+(-0.407325 + 2.22270i) q^{2} +(-1.46444 + 0.924888i) q^{3} +(-2.90444 - 1.10151i) q^{4} +(3.11001 + 0.188121i) q^{5} +(-1.45925 - 3.63174i) q^{6} +(1.33442 + 0.806684i) q^{7} +(1.29330 - 2.13939i) q^{8} +(1.28916 - 2.70888i) q^{9} +(-1.68492 + 6.83599i) q^{10} +(0.662987 + 3.61780i) q^{11} +(5.27215 - 1.07319i) q^{12} +(-0.793246 + 3.51721i) q^{13} +(-2.33656 + 2.63743i) q^{14} +(-4.72841 + 2.60092i) q^{15} +(-0.421785 - 0.373669i) q^{16} +(-1.84135 + 0.453853i) q^{17} +(5.49592 + 3.96882i) q^{18} +(-0.649110 + 0.649110i) q^{19} +(-8.82562 - 3.97209i) q^{20} +(-2.70027 + 0.0528481i) q^{21} -8.31133 q^{22} +2.86699 q^{23} +(0.0847278 + 4.32916i) q^{24} +(4.67322 + 0.567432i) q^{25} +(-7.49459 - 3.19579i) q^{26} +(0.617513 + 5.15933i) q^{27} +(-2.98717 - 3.81284i) q^{28} +(-3.34656 + 2.30996i) q^{29} +(-3.85506 - 11.5692i) q^{30} +(-0.107290 - 0.0840567i) q^{31} +(4.93815 - 3.86879i) q^{32} +(-4.31697 - 4.68486i) q^{33} +(-0.258749 - 4.27764i) q^{34} +(3.99830 + 2.75983i) q^{35} +(-6.72816 + 6.44777i) q^{36} +(5.54346 - 7.07570i) q^{37} +(-1.17838 - 1.70717i) q^{38} +(-2.09136 - 5.88440i) q^{39} +(4.42465 - 6.41021i) q^{40} +(0.0661792 + 0.212377i) q^{41} +(0.982420 - 6.02341i) q^{42} +(-7.19558 - 0.873702i) q^{43} +(2.05944 - 11.2380i) q^{44} +(4.51891 - 8.18214i) q^{45} +(-1.16779 + 6.37245i) q^{46} +(8.81729 + 3.96834i) q^{47} +(0.963279 + 0.157111i) q^{48} +(-2.12313 - 4.04528i) q^{49} +(-3.16475 + 10.1560i) q^{50} +(2.27679 - 2.36768i) q^{51} +(6.17817 - 9.34176i) q^{52} +(-0.861862 - 3.49671i) q^{53} +(-11.7192 - 0.728976i) q^{54} +(1.38131 + 11.3761i) q^{55} +(3.45162 - 1.81155i) q^{56} +(0.350228 - 1.55094i) q^{57} +(-3.77122 - 8.37930i) q^{58} +(-0.600912 + 9.93427i) q^{59} +(16.5983 - 2.34583i) q^{60} +(-11.7285 - 2.89082i) q^{61} +(0.230535 - 0.204236i) q^{62} +(3.90550 - 2.57484i) q^{63} +(6.06399 + 11.5540i) q^{64} +(-3.12866 + 10.7893i) q^{65} +(12.1714 - 7.68705i) q^{66} +(-8.03617 - 3.61678i) q^{67} +(5.84802 + 0.710079i) q^{68} +(-4.19853 + 2.65164i) q^{69} +(-7.76287 + 7.76287i) q^{70} +(-0.388510 - 1.24677i) q^{71} +(-4.12807 - 6.26143i) q^{72} +(11.1889 - 2.05044i) q^{73} +(13.4692 + 15.2035i) q^{74} +(-7.36846 + 3.49124i) q^{75} +(2.60030 - 1.17030i) q^{76} +(-2.03372 + 5.36249i) q^{77} +(13.9311 - 2.25161i) q^{78} +(2.60406 + 6.86634i) q^{79} +(-1.24146 - 1.24146i) q^{80} +(-5.67611 - 6.98439i) q^{81} +(-0.499005 + 0.0605902i) q^{82} +(-2.82964 - 0.881750i) q^{83} +(7.90098 + 2.82088i) q^{84} +(-5.81200 + 1.06509i) q^{85} +(4.87291 - 15.6377i) q^{86} +(2.76438 - 6.47799i) q^{87} +(8.59732 + 3.26053i) q^{88} +(5.66471 - 5.66471i) q^{89} +(16.3458 + 13.3770i) q^{90} +(-3.89580 + 4.05353i) q^{91} +(-8.32700 - 3.15801i) q^{92} +(0.234863 + 0.0238643i) q^{93} +(-12.4119 + 17.9818i) q^{94} +(-2.14085 + 1.89663i) q^{95} +(-3.65342 + 10.2328i) q^{96} +(14.7040 - 0.889431i) q^{97} +(9.85624 - 3.07133i) q^{98} +(10.6549 + 2.86798i) 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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