LMFDB - Embedded newform 507.2.s.a.5.11

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			5.11
Character	$\chi$	$=$	507.5
Dual form			507.2.s.a.203.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.367556 + 2.00569i) q^{2} +(1.27896 + 1.16801i) q^{3} +(-2.01765 - 0.765194i) q^{4} +(1.15023 + 0.0695764i) q^{5} +(-2.81276 + 2.13589i) q^{6} +(-2.33236 - 1.40996i) q^{7} +(0.166545 - 0.275500i) q^{8} +(0.271498 + 2.98769i) q^{9} +(-0.562324 + 2.28144i) q^{10} +(0.882698 + 4.81672i) q^{11} +(-1.68675 - 3.33530i) q^{12} +(3.44336 - 1.06924i) q^{13} +(3.68521 - 4.15974i) q^{14} +(1.38984 + 1.43247i) q^{15} +(-2.73904 - 2.42658i) q^{16} +(-3.64273 + 0.897854i) q^{17} +(-6.09216 - 0.553602i) q^{18} +(-2.46391 + 2.46391i) q^{19} +(-2.26753 - 1.02053i) q^{20} +(-1.33615 - 4.52751i) q^{21} -9.98528 q^{22} -1.42206 q^{23} +(0.534792 - 0.157827i) q^{24} +(-3.64535 - 0.442625i) q^{25} +(0.878934 + 7.29931i) q^{26} +(-3.14242 + 4.13826i) q^{27} +(3.62699 + 4.62951i) q^{28} +(6.36070 - 4.39047i) q^{29} +(-3.38394 + 2.26108i) q^{30} +(6.30211 + 4.93739i) q^{31} +(6.38054 - 4.99883i) q^{32} +(-4.49705 + 7.19142i) q^{33} +(-0.461905 - 7.63620i) q^{34} +(-2.58466 - 1.78406i) q^{35} +(1.73837 - 6.23586i) q^{36} +(3.95841 - 5.05254i) q^{37} +(-4.03620 - 5.84745i) q^{38} +(5.65282 + 2.65436i) q^{39} +(0.210734 - 0.305301i) q^{40} +(2.47472 + 7.94166i) q^{41} +(9.57187 - 1.01579i) q^{42} +(5.96732 + 0.724564i) q^{43} +(1.90475 - 10.3939i) q^{44} +(0.104414 + 3.45543i) q^{45} +(0.522688 - 2.85221i) q^{46} +(-4.03414 - 1.81562i) q^{47} +(-0.668863 - 6.30273i) q^{48} +(0.198843 + 0.378864i) q^{49} +(2.22764 - 7.14873i) q^{50} +(-5.70763 - 3.10643i) q^{51} +(-7.76567 - 0.477486i) q^{52} +(-1.80602 - 7.32731i) q^{53} +(-7.14504 - 7.82375i) q^{54} +(0.680179 + 5.60178i) q^{55} +(-0.776886 + 0.407741i) q^{56} +(-6.02912 + 0.273377i) q^{57} +(6.46800 + 14.3713i) q^{58} +(0.278202 - 4.59922i) q^{59} +(-1.70810 - 3.95373i) q^{60} +(-0.958535 - 0.236258i) q^{61} +(-12.2192 + 10.8253i) q^{62} +(3.57929 - 7.35116i) q^{63} +(4.27975 + 8.15438i) q^{64} +(4.03506 - 0.990300i) q^{65} +(-12.7708 - 11.6629i) q^{66} +(12.4158 + 5.58789i) q^{67} +(8.03680 + 0.975844i) q^{68} +(-1.81877 - 1.66099i) q^{69} +(4.52827 - 4.52827i) q^{70} +(-3.79765 - 12.1871i) q^{71} +(0.868324 + 0.422788i) q^{72} +(9.71480 - 1.78030i) q^{73} +(8.67888 + 9.79643i) q^{74} +(-4.14528 - 4.82391i) q^{75} +(6.85667 - 3.08594i) q^{76} +(4.73262 - 12.4789i) q^{77} +(-7.40155 + 10.3622i) q^{78} +(5.39362 + 14.2218i) q^{79} +(-2.98170 - 2.98170i) q^{80} +(-8.85258 + 1.62231i) q^{81} +(-16.8381 + 2.04451i) q^{82} +(16.4482 + 5.12546i) q^{83} +(-0.768532 + 10.1573i) q^{84} +(-4.25247 + 0.779294i) q^{85} +(-3.64657 + 11.7023i) q^{86} +(13.2632 + 1.81411i) q^{87} +(1.47401 + 0.559020i) q^{88} +(-3.07950 + 3.07950i) q^{89} +(-6.96889 - 1.06064i) q^{90} +(-9.53873 - 2.36115i) q^{91} +(2.86923 + 1.08815i) q^{92} +(2.29325 + 13.6757i) q^{93} +(5.12434 - 7.42389i) q^{94} +(-3.00550 + 2.66264i) q^{95} +(13.9992 + 1.05921i) q^{96} +(-10.0469 + 0.607726i) q^{97} +(-0.832968 + 0.259563i) q^{98} +(-14.1512 + 3.94496i) 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 $

$2$	−0.367556	+	2.00569i	−0.259901	+	1.41823i	0.551710	+	0.834036i	$0.313976\pi$
$2$	−0.367556	+	2.00569i	−0.259901	+	1.41823i	−0.811611	+	0.584199i	$0.801409\pi$
$3$	1.27896	+	1.16801i	0.738410	+	0.674352i
$3$	1.27896	+	1.16801i	0.738410	+	0.674352i
$4$	−2.01765	−	0.765194i	−1.00883	−	0.382597i
$5$	1.15023	+	0.0695764i	0.514400	+	0.0311155i	0.315540	−	0.948912i	$-0.397814\pi$
$5$	1.15023	+	0.0695764i	0.514400	+	0.0311155i	0.198861	+	0.980028i	$0.436276\pi$
$6$	−2.81276	+	2.13589i	−1.14830	+	0.871974i
$7$	−2.33236	−	1.40996i	−0.881548	−	0.532914i	0.00266586	−	0.999996i	$-0.499151\pi$
$7$	−2.33236	−	1.40996i	−0.881548	−	0.532914i	−0.884214	+	0.467082i	$0.845305\pi$
$8$	0.166545	−	0.275500i	0.0588827	−	0.0974038i
$9$	0.271498	+	2.98769i	0.0904994	+	0.995897i
$10$	−0.562324	+	2.28144i	−0.177822	+	0.721454i
$11$	0.882698	+	4.81672i	0.266143	+	1.45230i	0.796560	+	0.604560i	$0.206651\pi$
$11$	0.882698	+	4.81672i	0.266143	+	1.45230i	−0.530416	+	0.847737i	$0.677964\pi$
$12$	−1.68675	−	3.33530i	−0.486922	−	0.962817i
$13$	3.44336	−	1.06924i	0.955016	−	0.296554i
$13$	3.44336	−	1.06924i	0.955016	−	0.296554i
$14$	3.68521	−	4.15974i	0.984913	−	1.11174i
$15$	1.38984	+	1.43247i	0.358856	+	0.369863i
$16$	−2.73904	−	2.42658i	−0.684760	−	0.606644i
$17$	−3.64273	+	0.897854i	−0.883493	+	0.217761i	−0.654859	−	0.755751i	$-0.727272\pi$
$17$	−3.64273	+	0.897854i	−0.883493	+	0.217761i	−0.228634	+	0.973512i	$0.573426\pi$
$18$	−6.09216	−	0.553602i	−1.43594	−	0.130485i
$19$	−2.46391	+	2.46391i	−0.565259	+	0.565259i	−0.930797	−	0.365538i	$-0.880885\pi$
$19$	−2.46391	+	2.46391i	−0.565259	+	0.565259i	0.365538	+	0.930797i	$0.380885\pi$
$20$	−2.26753	−	1.02053i	−0.507036	−	0.228198i
$21$	−1.33615	−	4.52751i	−0.291572	−	0.987983i
$22$	−9.98528			−2.12887
$23$	−1.42206			−0.296521			−0.148260	−	0.988948i	$-0.547367\pi$
$23$	−1.42206			−0.296521			−0.148260	+	0.988948i	$0.547367\pi$
$24$	0.534792	−	0.157827i	0.109164	−	0.0322163i
$25$	−3.64535	−	0.442625i	−0.729069	−	0.0885250i
$26$	0.878934	+	7.29931i	0.172373	+	1.43151i
$27$	−3.14242	+	4.13826i	−0.604759	+	0.796409i
$28$	3.62699	+	4.62951i	0.685437	+	0.874895i
$29$	6.36070	−	4.39047i	1.18115	−	0.815290i	0.194946	−	0.980814i	$-0.437547\pi$
$29$	6.36070	−	4.39047i	1.18115	−	0.815290i	0.986206	+	0.165524i	$0.0529315\pi$
$30$	−3.38394	+	2.26108i	−0.617819	+	0.412814i
$31$	6.30211	+	4.93739i	1.13189	+	0.886782i	0.994603	−	0.103749i	$-0.0330839\pi$
$31$	6.30211	+	4.93739i	1.13189	+	0.886782i	0.137290	+	0.990531i	$0.456161\pi$
$32$	6.38054	−	4.99883i	1.12793	−	0.883677i
$33$	−4.49705	+	7.19142i	−0.782836	+	1.25187i
$34$	−0.461905	−	7.63620i	−0.0792160	−	1.30960i
$35$	−2.58466	−	1.78406i	−0.436887	−	0.301561i
$36$	1.73837	−	6.23586i	0.289729	−	1.03931i
$37$	3.95841	−	5.05254i	0.650759	−	0.830632i	−0.343328	−	0.939215i	$-0.611554\pi$
$37$	3.95841	−	5.05254i	0.650759	−	0.830632i	0.994087	+	0.108583i	$0.0346313\pi$
$38$	−4.03620	−	5.84745i	−0.654758	−	0.948581i
$39$	5.65282	+	2.65436i	0.905175	+	0.425038i
$40$	0.210734	−	0.305301i	0.0333200	−	0.0482724i
$41$	2.47472	+	7.94166i	0.386487	+	1.24028i	0.919135	+	0.393943i	$0.128889\pi$
$41$	2.47472	+	7.94166i	0.386487	+	1.24028i	−0.532648	+	0.846337i	$0.678803\pi$
$42$	9.57187	−	1.01579i	1.47697	−	0.156740i
$43$	5.96732	+	0.724564i	0.910008	+	0.110495i	0.562134	−	0.827046i	$-0.309981\pi$
$43$	5.96732	+	0.724564i	0.910008	+	0.110495i	0.347874	+	0.937541i	$0.386904\pi$
$44$	1.90475	−	10.3939i	0.287152	−	1.56694i
$45$	0.104414	+	3.45543i	0.0155651	+	0.515105i
$46$	0.522688	−	2.85221i	0.0770661	−	0.420536i
$47$	−4.03414	−	1.81562i	−0.588440	−	0.264835i	0.0942438	−	0.995549i	$-0.469957\pi$
$47$	−4.03414	−	1.81562i	−0.588440	−	0.264835i	−0.682684	+	0.730714i	$0.739187\pi$
$48$	−0.668863	−	6.30273i	−0.0965420	−	0.909721i
$49$	0.198843	+	0.378864i	0.0284062	+	0.0541234i
$50$	2.22764	−	7.14873i	0.315035	−	1.01098i
$51$	−5.70763	−	3.10643i	−0.799228	−	0.434988i
$52$	−7.76567	−	0.477486i	−1.07691	−	0.0662153i
$53$	−1.80602	−	7.32731i	−0.248076	−	1.00648i	−0.954385	−	0.298579i	$-0.903487\pi$
$53$	−1.80602	−	7.32731i	−0.248076	−	1.00648i	0.706309	−	0.707904i	$-0.250359\pi$
$54$	−7.14504	−	7.82375i	−0.972317	−	1.06468i
$55$	0.680179	+	5.60178i	0.0917153	+	0.755343i
$56$	−0.776886	+	0.407741i	−0.103816	+	0.0544867i
$57$	−6.02912	+	0.273377i	−0.798576	+	0.0362096i
$58$	6.46800	+	14.3713i	0.849290	+	1.88705i
$59$	0.278202	−	4.59922i	0.0362188	−	0.598768i	−0.934111	−	0.356982i	$-0.883806\pi$
$59$	0.278202	−	4.59922i	0.0362188	−	0.598768i	0.970330	−	0.241785i	$-0.0777329\pi$
$60$	−1.70810	−	3.95373i	−0.220514	−	0.510424i
$61$	−0.958535	−	0.236258i	−0.122728	−	0.0302497i	0.177473	−	0.984126i	$-0.443208\pi$
$61$	−0.958535	−	0.236258i	−0.122728	−	0.0302497i	−0.300201	+	0.953876i	$0.597054\pi$
$62$	−12.2192	+	10.8253i	−1.55185	+	1.37481i
$63$	3.57929	−	7.35116i	0.450948	−	0.926159i
$64$	4.27975	+	8.15438i	0.534968	+	1.01930i
$65$	4.03506	−	0.990300i	0.500488	−	0.122832i
$66$	−12.7708	−	11.6629i	−1.57198	−	1.43561i
$67$	12.4158	+	5.58789i	1.51683	+	0.682669i	0.986295	−	0.164994i	$-0.0527604\pi$
$67$	12.4158	+	5.58789i	1.51683	+	0.682669i	0.530535	+	0.847663i	$0.321991\pi$
$68$	8.03680	+	0.975844i	0.974605	+	0.118338i
$69$	−1.81877	−	1.66099i	−0.218954	−	0.199959i
$70$	4.52827	−	4.52827i	0.541232	−	0.541232i
$71$	−3.79765	−	12.1871i	−0.450698	−	1.44634i	−0.848660	−	0.528938i	$-0.822590\pi$
$71$	−3.79765	−	12.1871i	−0.450698	−	1.44634i	0.397963	−	0.917402i	$-0.369717\pi$
$72$	0.868324	+	0.422788i	0.102333	+	0.0498260i
$73$	9.71480	−	1.78030i	1.13703	−	0.208369i	0.421419	−	0.906866i	$-0.361532\pi$
$73$	9.71480	−	1.78030i	1.13703	−	0.208369i	0.715612	+	0.698497i	$0.246148\pi$
$74$	8.67888	+	9.79643i	1.00890	+	1.13881i
$75$	−4.14528	−	4.82391i	−0.478655	−	0.557017i
$76$	6.85667	−	3.08594i	0.786514	−	0.353981i
$77$	4.73262	−	12.4789i	0.539332	−	1.42210i
$78$	−7.40155	+	10.3622i	−0.838061	+	1.17328i
$79$	5.39362	+	14.2218i	0.606830	+	1.60008i	0.787349	+	0.616507i	$0.211453\pi$
$79$	5.39362	+	14.2218i	0.606830	+	1.60008i	−0.180519	+	0.983571i	$0.557778\pi$
$80$	−2.98170	−	2.98170i	−0.333365	−	0.333365i
$81$	−8.85258	+	1.62231i	−0.983620	+	0.180256i
$82$	−16.8381	+	2.04451i	−1.85946	+	0.225779i
$83$	16.4482	+	5.12546i	1.80542	+	0.562593i	0.999564	−	0.0295147i	$-0.00939617\pi$
$83$	16.4482	+	5.12546i	1.80542	+	0.562593i	0.805859	+	0.592107i	$0.201704\pi$
$84$	−0.768532	+	10.1573i	−0.0838537	+	1.10826i
$85$	−4.25247	+	0.779294i	−0.461245	+	0.0845263i
$86$	−3.64657	+	11.7023i	−0.393220	+	1.26189i
$87$	13.2632	+	1.81411i	1.42197	+	0.194493i
$88$	1.47401	+	0.559020i	0.157131	+	0.0595917i
$89$	−3.07950	+	3.07950i	−0.326427	+	0.326427i	−0.851226	−	0.524799i	$-0.824140\pi$
$89$	−3.07950	+	3.07950i	−0.326427	+	0.326427i	0.524799	+	0.851226i	$0.324140\pi$
$90$	−6.96889	−	1.06064i	−0.734586	−	0.111802i
$91$	−9.53873	−	2.36115i	−0.999931	−	0.247515i
$92$	2.86923	+	1.08815i	0.299138	+	0.113448i
$93$	2.29325	+	13.6757i	0.237799	+	1.41810i
$94$	5.12434	−	7.42389i	0.528535	−	0.765716i
$95$	−3.00550	+	2.66264i	−0.308358	+	0.273181i
$96$	13.9992	+	1.05921i	1.42878	+	0.108106i
$97$	−10.0469	+	0.607726i	−1.02011	+	0.0617052i	−0.561955	−	0.827168i	$-0.689951\pi$
$97$	−10.0469	+	0.607726i	−1.02011	+	0.0617052i	−0.458154	+	0.888873i	$0.651489\pi$
$98$	−0.832968	+	0.259563i	−0.0841425	+	0.0262199i
$99$	−14.1512	+	3.94496i	−1.42225	+	0.396483i
$100$	7.01634	+	3.68246i	0.701634	+	0.368246i
$101$	0.776773	−	6.39730i	0.0772918	−	0.636556i	−0.901657	−	0.432451i	$-0.857649\pi$
$101$	0.776773	−	6.39730i	0.0772918	−	0.636556i	0.978949	−	0.204104i	$-0.0654282\pi$
$102$	8.32841	−	10.3059i	0.824635	−	1.02044i
$103$	6.22483	−	11.8604i	0.613351	−	1.16864i	−0.358608	−	0.933488i	$-0.616748\pi$
$103$	6.22483	−	11.8604i	0.613351	−	1.16864i	0.971958	−	0.235153i	$-0.0755593\pi$
$104$	0.278900	−	1.12672i	0.0273484	−	0.110484i
$105$	−1.22188	−	5.30066i	−0.119243	−	0.517291i
$106$	15.3601	−	0.929115i	1.49190	−	0.0902436i
$107$	−4.23917	−	4.78503i	−0.409816	−	0.462586i	0.506971	−	0.861963i	$-0.330765\pi$
$107$	−4.23917	−	4.78503i	−0.409816	−	0.462586i	−0.916787	+	0.399377i	$0.869227\pi$
$108$	9.50688	−	5.94501i	0.914800	−	0.572058i
$109$	0.290173	+	0.370378i	0.0277935	+	0.0354758i	0.800880	−	0.598824i	$-0.204365\pi$
$109$	0.290173	+	0.370378i	0.0277935	+	0.0354758i	−0.773087	+	0.634300i	$0.781288\pi$
$110$	−11.4854	−	0.694740i	−1.09509	−	0.0662408i
$111$	10.9641	−	1.83855i	1.04067	−	0.174507i
$112$	2.96704	+	9.52158i	0.280359	+	0.899704i
$113$	2.14475	+	4.08648i	0.201761	+	0.384424i	0.965223	−	0.261430i	$-0.0841939\pi$
$113$	2.14475	+	4.08648i	0.201761	+	0.384424i	−0.763461	+	0.645854i	$0.776502\pi$
$114$	1.66773	−	12.1930i	0.156197	−	1.14198i
$115$	−1.63571	−	0.0989420i	−0.152530	−	0.00922639i
$116$	−16.1932	+	3.99127i	−1.50350	+	0.370580i
$117$	4.12942	+	9.99739i	0.381765	+	0.924259i
$118$	9.12234	+	2.24846i	0.839780	+	0.206987i
$119$	9.76210	+	3.04199i	0.894890	+	0.278859i
$120$	0.626117	−	0.144329i	0.0571564	−	0.0131754i
$121$	−12.1365	+	4.60277i	−1.10332	+	0.418434i
$122$	0.826174	−	1.83568i	0.0747983	−	0.166195i
$123$	−6.11087	+	13.0476i	−0.550999	+	1.17646i
$124$	−8.93741	−	14.7843i	−0.802603	−	1.32767i
$125$	−9.82951	−	1.80132i	−0.879178	−	0.161115i
$126$	13.4285	+	9.88090i	1.19631	+	0.880260i
$127$	−1.61687	+	0.613200i	−0.143474	+	0.0544127i	−0.425297	−	0.905054i	$-0.639830\pi$
$127$	−1.61687	+	0.613200i	−0.143474	+	0.0544127i	0.281822	+	0.959467i	$0.409061\pi$
$128$	−2.45115	+	0.763808i	−0.216653	+	0.0675117i
$129$	6.78569	+	7.89659i	0.597447	+	0.695256i
$130$	0.503121	+	8.45707i	0.0441266	+	0.741734i
$131$	−5.34854	+	3.69183i	−0.467304	+	0.322557i	−0.778342	−	0.627841i	$-0.783939\pi$
$131$	−5.34854	+	3.69183i	−0.467304	+	0.322557i	0.311037	+	0.950398i	$0.399324\pi$
$132$	14.5763	−	11.0687i	1.26871	−	0.963403i
$133$	9.22072	−	2.27270i	0.799538	−	0.197068i
$134$	−15.7711	+	22.8483i	−1.36241	+	1.97379i
$135$	−3.90244	+	4.54133i	−0.335869	+	0.390856i
$136$	−0.359322	+	1.15311i	−0.0308116	+	0.0988780i
$137$	10.7127	+	13.6737i	0.915246	+	1.16823i	0.985326	+	0.170684i	$0.0545977\pi$
$137$	10.7127	+	13.6737i	0.915246	+	1.16823i	−0.0700798	+	0.997541i	$0.522325\pi$
$138$	3.99992	−	3.03737i	0.340496	−	0.258559i
$139$	−0.189430	−	0.167821i	−0.0160673	−	0.0142344i	0.655051	−	0.755585i	$-0.272647\pi$
$139$	−0.189430	−	0.167821i	−0.0160673	−	0.0142344i	−0.671118	+	0.741350i	$0.734186\pi$
$140$	3.84978	+	5.57738i	0.325366	+	0.471374i
$141$	−3.03886	−	7.03404i	−0.255918	−	0.592373i
$142$	25.8393	−	3.13746i	2.16839	−	0.263290i
$143$	8.18968	+	15.6419i	0.684855	+	1.30804i
$144$	6.50621	−	8.84221i	0.542184	−	0.736851i
$145$	7.62176	−	4.60752i	0.632953	−	0.382633i
$146$			20.1392i			1.66673i
$147$	−0.188204	+	0.716804i	−0.0155228	+	0.0591210i
$148$	−11.8529	+	7.16531i	−0.974300	+	0.588985i
$149$	−2.95799	+	6.57238i	−0.242328	+	0.538430i	−0.992418	−	0.122905i	$-0.960779\pi$
$149$	−2.95799	+	6.57238i	−0.242328	+	0.538430i	0.750091	+	0.661335i	$0.230010\pi$
$150$	11.1989	−	6.54107i	0.914384	−	0.534076i
$151$	−18.4184	+	8.28943i	−1.49886	+	0.674584i	−0.983254	−	0.182239i	$-0.941665\pi$
$151$	−18.4184	+	8.28943i	−1.49886	+	0.674584i	−0.515610	+	0.856823i	$0.672435\pi$
$152$	0.268453	+	1.08916i	0.0217744	+	0.0883423i
$153$	−3.67150	−	10.6396i	−0.296823	−	0.860160i
$154$	23.2892	+	14.0788i	1.87670	+	1.13451i
$155$	6.90538	+	6.11764i	0.554654	+	0.491380i
$156$	−9.37431	−	9.68108i	−0.750546	−	0.775107i
$157$	4.25047	−	3.76559i	0.339224	−	0.300526i	−0.476261	−	0.879304i	$-0.658008\pi$
$157$	4.25047	−	3.76559i	0.339224	−	0.300526i	0.815486	+	0.578777i	$0.196470\pi$
$158$	−30.5070	+	5.59061i	−2.42700	+	0.444765i
$159$	6.24854	−	11.4808i	0.495542	−	0.910487i
$160$	7.68691	−	5.30589i	0.607704	−	0.419468i
$161$	3.31676	+	2.00505i	0.261397	+	0.158020i
$162$	−2.01746e−5	−	18.3518i	−1.58507e−6	−	1.44185i
$163$	−6.42505	+	8.20097i	−0.503249	+	0.642349i	−0.970307	−	0.241877i	$-0.922237\pi$
$163$	−6.42505	+	8.20097i	−0.503249	+	0.642349i	0.467058	+	0.884227i	$0.345314\pi$
$164$	1.08379	−	17.9172i	0.0846296	−	1.39909i
$165$	−5.67302	+	7.95893i	−0.441644	+	0.619602i
$166$	−16.3257	+	31.1060i	−1.26712	+	2.41430i
$167$	1.66277	+	0.304715i	0.128669	+	0.0235795i	0.244204	−	0.969724i	$-0.421473\pi$
$167$	1.66277	+	0.304715i	0.128669	+	0.0235795i	−0.115534	+	0.993303i	$0.536858\pi$
$168$	−1.46986	−	0.385925i	−0.113402	−	0.0297748i
$169$	10.7135	−	7.36356i	0.824112	−	0.566427i
$170$		−	8.81555i		−	0.676122i
$171$	−8.03033	−	6.69244i	−0.614095	−	0.511784i
$172$	−11.4855	−	6.02808i	−0.875764	−	0.459637i
$173$	2.82688	−	7.45388i	0.214924	−	0.566708i	−0.783586	−	0.621284i	$-0.786611\pi$
$173$	2.82688	−	7.45388i	0.214924	−	0.566708i	0.998510	+	0.0545760i	$0.0173807\pi$
$174$	−8.51351	+	25.9351i	−0.645408	+	1.96613i
$175$	7.87817	+	6.17215i	0.595533	+	0.466571i
$176$	9.27041	−	15.3351i	0.698783	−	1.15593i
$177$	5.72775	−	5.55730i	0.430524	−	0.417712i
$178$	−5.04463	−	7.30841i	−0.378111	−	0.547789i
$179$	−9.19596	−	2.26660i	−0.687338	−	0.169414i	−0.119846	−	0.992792i	$-0.538240\pi$
$179$	−9.19596	−	2.26660i	−0.687338	−	0.169414i	−0.567492	+	0.823379i	$0.692086\pi$
$180$	2.43341	−	7.05175i	0.181375	−	0.525607i
$181$	−7.98853	−	9.01719i	−0.593783	−	0.670242i	0.372408	−	0.928069i	$-0.378532\pi$
$181$	−7.98853	−	9.01719i	−0.593783	−	0.670242i	−0.966191	+	0.257827i	$0.916994\pi$
$182$	8.24174	−	18.2639i	0.610918	−	1.35381i
$183$	−0.949980	−	1.42175i	−0.0702246	−	0.105098i
$184$	−0.236838	+	0.391778i	−0.0174599	+	0.0288823i
$185$	4.90464	−	5.53619i	0.360596	−	0.407029i
$186$	−28.2721	−	0.427040i	−2.07301	−	0.0313121i
$187$	−7.54015	−	16.7535i	−0.551390	−	1.22514i
$188$	6.75019	+	6.75019i	0.492308	+	0.492308i
$189$	13.1640	−	5.22122i	0.957542	−	0.379788i
$190$	−4.23573	−	7.00676i	−0.307292	−	0.508324i
$191$		−	1.77614i		−	0.128517i	−0.997933	−	0.0642585i	$-0.979532\pi$
$191$		−	1.77614i		−	0.128517i	0.997933	−	0.0642585i	$-0.0204682\pi$
$192$	−4.05076	+	15.4279i	−0.292339	+	1.11342i
$193$	−5.90722	−	9.77173i	−0.425211	−	0.703385i	0.567570	−	0.823325i	$-0.307884\pi$
$193$	−5.90722	−	9.77173i	−0.425211	−	0.703385i	−0.992781	+	0.119940i	$0.961730\pi$
$194$	2.47389	−	20.3743i	0.177615	−	1.46279i
$195$	6.31738	+	3.44644i	0.452397	+	0.246805i
$196$	−0.111292	−	0.916569i	−0.00794940	−	0.0654692i
$197$	2.65562	−	2.08054i	0.189205	−	0.148233i	−0.517647	−	0.855595i	$-0.673192\pi$
$197$	2.65562	−	2.08054i	0.189205	−	0.148233i	0.706852	+	0.707362i	$0.250115\pi$
$198$	−2.71099	−	29.8329i	−0.192661	−	2.12013i
$199$	5.83801	−	6.58975i	0.413846	−	0.467135i	−0.504213	−	0.863579i	$-0.668217\pi$
$199$	5.83801	−	6.58975i	0.413846	−	0.467135i	0.918059	+	0.396444i	$0.129756\pi$
$200$	−0.729058	+	0.930574i	−0.0515522	+	0.0658015i
$201$	9.35262	+	21.6485i	0.659683	+	1.52697i
$202$	12.5455	+	3.90933i	0.882697	+	0.275060i
$203$	−21.0258	+	1.27183i	−1.47572	+	0.0892647i
$204$	9.13898	+	10.6351i	0.639857	+	0.744609i
$205$	2.29396	+	9.30696i	0.160217	+	0.650026i
$206$	21.5003	+	16.8444i	1.49800	+	1.17361i
$207$	−0.386088	−	4.24868i	−0.0268350	−	0.295304i
$208$	−12.0261	−	5.42689i	−0.833859	−	0.376287i
$209$	−14.0428	−	9.69307i	−0.971364	−	0.670484i
$210$	11.0806	−	0.502424i	0.764632	−	0.0346705i
$211$	−6.05803	−	15.9737i	−0.417052	−	1.09968i	−0.964789	−	0.263025i	$-0.915280\pi$
$211$	−6.05803	−	15.9737i	−0.417052	−	1.09968i	0.547737	−	0.836650i	$-0.315489\pi$
$212$	−1.96290	+	16.1659i	−0.134812	+	1.11028i
$213$	9.37759	−	20.0225i	0.642542	−	1.37192i
$214$	11.1554	−	6.74367i	0.762567	−	0.460988i
$215$	6.81341	+	1.24860i	0.464670	+	0.0851540i
$216$	0.616734	+	1.55494i	0.0419634	+	0.105800i
$217$	−7.73726	−	20.4015i	−0.525240	−	1.38494i
$218$	−0.849517	+	0.445861i	−0.0575365	+	0.0301975i
$219$	14.5043	+	9.07005i	0.980109	+	0.612897i
$220$	2.91408	−	11.8229i	0.196467	−	0.797100i
$221$	−11.5832	+	6.98659i	−0.779172	+	0.469969i
$222$	−0.342367	+	22.6663i	−0.0229782	+	1.52126i
$223$	−0.844470	+	13.9607i	−0.0565499	+	0.934881i	0.853685	+	0.520789i	$0.174362\pi$
$223$	−0.844470	+	13.9607i	−0.0565499	+	0.934881i	−0.910235	+	0.414092i	$0.864099\pi$
$224$	−21.9298	+	2.66276i	−1.46525	+	0.177913i
$225$	0.332721	−	11.0113i	0.0221814	−	0.734089i
$226$	−8.98452	+	2.79969i	−0.597642	+	0.186233i
$227$	8.91270	−	4.01128i	0.591556	−	0.266238i	−0.0924460	−	0.995718i	$-0.529469\pi$
$227$	8.91270	−	4.01128i	0.591556	−	0.266238i	0.684002	+	0.729480i	$0.260238\pi$
$228$	12.3738	+	4.06187i	0.819478	+	0.269004i
$229$	−10.8960	+	8.53648i	−0.720028	+	0.564106i	−0.908456	−	0.417981i	$-0.862738\pi$
$229$	−10.8960	+	8.53648i	−0.720028	+	0.564106i	0.188427	+	0.982087i	$0.439661\pi$
$230$	0.799660	−	3.24435i	0.0527280	−	0.213926i
$231$	20.6283	−	10.4323i	1.35724	−	0.686395i
$232$	−0.150229	−	2.48358i	−0.00986302	−	0.163055i
$233$	18.4739	−	9.69583i	1.21026	−	0.635195i	0.265869	−	0.964009i	$-0.414341\pi$
$233$	18.4739	−	9.69583i	1.21026	−	0.635195i	0.944395	+	0.328814i	$0.106649\pi$
$234$	−21.5694	+	4.60773i	−1.41004	+	0.301217i
$235$	−4.51389	−	2.36907i	−0.294453	−	0.154541i
$236$	−4.08061	+	9.06674i	−0.265625	+	0.590195i
$237$	−9.71299	+	24.4890i	−0.630927	+	1.59073i
$238$	−9.68940	+	18.4616i	−0.628070	+	1.19669i
$239$	19.0670	+	19.0670i	1.23334	+	1.23334i	0.962672	+	0.270671i	$0.0872457\pi$
$239$	19.0670	+	19.0670i	1.23334	+	1.23334i	0.270671	+	0.962672i	$0.412754\pi$
$240$	−0.330828	−	7.29616i	−0.0213548	−	0.470965i
$241$	−1.48527	−	24.5545i	−0.0956750	−	1.58170i	−0.656865	−	0.754008i	$-0.728118\pi$
$241$	−1.48527	−	24.5545i	−0.0956750	−	1.58170i	0.561190	−	0.827687i	$-0.310344\pi$
$242$	−4.77087	−	26.0338i	−0.306683	−	1.67352i
$243$	−13.2170	−	8.26504i	−0.847871	−	0.530203i
$244$	1.75321	+	1.21015i	0.112238	+	0.0774720i
$245$	0.202356	+	0.449617i	0.0129281	+	0.0287250i
$246$	−23.9233	−	17.0522i	−1.52530	−	1.08721i
$247$	−5.84961	+	11.1186i	−0.372202	+	0.707461i
$248$	2.40984	−	0.913931i	0.153025	−	0.0580346i
$249$	15.0500	+	25.7670i	0.953758	+	1.63291i
$250$	7.22579	−	19.0528i	0.456999	−	1.20501i
$251$	−1.49787	−	12.3361i	−0.0945450	−	0.778648i	−0.960453	−	0.278444i	$-0.910181\pi$
$251$	−1.49787	−	12.3361i	−0.0945450	−	0.778648i	0.865908	−	0.500204i	$-0.166742\pi$
$252$	−12.8468	+	12.0932i	−0.809274	+	0.761802i
$253$	−1.25525	−	6.84969i	−0.0789170	−	0.430636i
$254$	−0.635595	−	3.46833i	−0.0398808	−	0.217622i
$255$	−6.34898	−	3.97024i	−0.397588	−	0.248626i
$256$	1.58908	+	13.0872i	0.0993172	+	0.817951i
$257$	1.53623	−	4.05071i	0.0958275	−	0.252676i	−0.878528	−	0.477691i	$-0.841474\pi$
$257$	1.53623	−	4.05071i	0.0958275	−	0.252676i	0.974355	+	0.225015i	$0.0722431\pi$
$258$	−18.3322	+	10.7075i	−1.14131	+	0.666622i
$259$	−16.3563	+	6.20313i	−1.01633	+	0.385444i
$260$	−8.89912	−	1.08953i	−0.551900	−	0.0675696i
$261$	14.8443	+	17.8118i	0.918838	+	1.10252i
$262$	−5.43877	−	12.0845i	−0.336008	−	0.746580i
$263$	−5.28997	−	3.65140i	−0.326194	−	0.225155i	0.393701	−	0.919239i	$-0.371195\pi$
$263$	−5.28997	−	3.65140i	−0.326194	−	0.225155i	−0.719895	+	0.694083i	$0.755810\pi$
$264$	1.23227	+	2.43663i	0.0758410	+	0.149964i
$265$	−1.56754	−	8.55377i	−0.0962930	−	0.525454i
$266$	1.16920	+	19.3292i	0.0716884	+	1.18515i
$267$	−7.53547	+	0.341679i	−0.461163	+	0.0209104i
$268$	−20.7749	−	20.7749i	−1.26903	−	1.26903i
$269$	−8.29974	+	15.8138i	−0.506044	+	0.964186i	0.489688	+	0.871898i	$0.337111\pi$
$269$	−8.29974	+	15.8138i	−0.506044	+	0.964186i	−0.995732	+	0.0922888i	$0.970582\pi$
$270$	−7.67412	−	9.49627i	−0.467032	−	0.577925i
$271$	−7.49493	+	16.6530i	−0.455284	+	1.01160i	0.531125	+	0.847294i	$0.321769\pi$
$271$	−7.49493	+	16.6530i	−0.455284	+	1.01160i	−0.986409	+	0.164307i	$0.947461\pi$
$272$	12.1563	+	6.38012i	0.737084	+	0.386852i
$273$	−9.44185	−	14.1612i	−0.571446	−	0.857073i
$274$	−31.3627	+	16.4604i	−1.89469	+	0.994411i
$275$	−1.08573	−	17.9493i	−0.0654723	−	1.08239i
$276$	2.39866	+	4.74300i	0.144383	+	0.285495i
$277$	2.57991	−	10.4671i	0.155012	−	0.628908i	−0.841105	−	0.540871i	$-0.818095\pi$
$277$	2.57991	−	10.4671i	0.155012	−	0.628908i	0.996117	−	0.0880368i	$-0.0280593\pi$
$278$	0.406222	−	0.318255i	0.0243636	−	0.0190876i
$279$	−13.0404	+	20.1693i	−0.780707	+	1.20750i
$280$	−0.921970	+	0.414945i	−0.0550983	+	0.0247977i
$281$	−6.25721	+	1.94982i	−0.373274	+	0.116317i	−0.478400	−	0.878142i	$-0.658783\pi$
$281$	−6.25721	+	1.94982i	−0.373274	+	0.116317i	0.105126	+	0.994459i	$0.466475\pi$
$282$	15.2250	−	3.50960i	0.906637	−	0.208994i
$283$	0.426154	−	0.0517444i	0.0253322	−	0.00307589i	−0.107861	−	0.994166i	$-0.534400\pi$
$283$	0.426154	−	0.0517444i	0.0253322	−	0.00307589i	0.133193	+	0.991090i	$0.457477\pi$
$284$	−1.66315	+	27.4952i	−0.0986900	+	1.63154i
$285$	−6.95392	−	0.105037i	−0.411915	−	0.00622184i
$286$	−34.3829	+	10.6767i	−2.03310	+	0.631324i
$287$	5.42548	−	22.0121i	0.320256	−	1.29933i
$288$	16.6673	+	17.7059i	0.982128	+	1.04333i
$289$	−2.58938	+	1.35901i	−0.152316	+	0.0799417i
$290$	6.43981	+	16.9804i	0.378159	+	0.997123i
$291$	−13.5595	−	10.9576i	−0.794870	−	0.642348i
$292$	−20.9634	−	3.84168i	−1.22679	−	0.224817i
$293$	27.8251	−	16.8209i	1.62556	−	0.982685i	0.650850	−	0.759206i	$-0.274413\pi$
$293$	27.8251	−	16.8209i	1.62556	−	0.982685i	0.974709	−	0.223478i	$-0.0717411\pi$
$294$	−1.36851	−	0.640944i	−0.0798131	−	0.0373806i
$295$	0.639994	−	5.27082i	0.0372619	−	0.306879i
$296$	−0.732718	−	1.93202i	−0.0425883	−	0.112296i
$297$	−22.7067	−	11.4833i	−1.31757	−	0.666331i
$298$	−12.0949	−	8.34852i	−0.700640	−	0.483617i
$299$	−4.89668	+	1.52053i	−0.283182	+	0.0879344i
$300$	4.67249	+	12.9049i	0.269767	+	0.745065i
$301$	−12.8963	−	10.1036i	−0.743331	−	0.582363i
$302$	−9.85623	−	39.9883i	−0.567162	−	2.30107i
$303$	8.46559	−	7.27464i	0.486335	−	0.417917i
$304$	12.7276	−	0.769878i	0.729978	−	0.0441555i
$305$	−1.08610	−	0.338443i	−0.0621900	−	0.0193792i
$306$	22.6892	−	3.45324i	1.29705	−	0.197409i
$307$	6.13238	−	7.82740i	0.349993	−	0.446733i	−0.579831	−	0.814737i	$-0.696882\pi$
$307$	6.13238	−	7.82740i	0.349993	−	0.446733i	0.929825	+	0.368003i	$0.119958\pi$
$308$	−19.0975	+	21.5567i	−1.08818	+	1.22831i
$309$	21.8144	−	7.89838i	1.24098	−	0.449323i
$310$	−14.8082	+	11.6015i	−0.841048	+	0.658919i
$311$	0.186438	+	1.53546i	0.0105719	+	0.0870677i	0.997040	−	0.0768869i	$-0.0244980\pi$
$311$	0.186438	+	1.53546i	0.0105719	+	0.0870677i	−0.986468	+	0.163955i	$0.947575\pi$
$312$	1.67273	−	1.11528i	0.0946995	−	0.0631401i
$313$	0.384518	−	3.16679i	0.0217342	−	0.178997i	−0.977799	−	0.209545i	$-0.932802\pi$
$313$	0.384518	−	3.16679i	0.0217342	−	0.178997i	0.999533	+	0.0305471i	$0.00972497\pi$
$314$	5.99030	+	9.90917i	0.338052	+	0.559207i
$315$	4.62849	−	8.20652i	0.260786	−	0.462385i
$316$		−	32.8218i		−	1.84637i
$317$	−13.3992	−	22.1651i	−0.752576	−	1.24491i	−0.963578	−	0.267428i	$-0.913826\pi$
$317$	−13.3992	−	22.1651i	−0.752576	−	1.24491i	0.211002	−	0.977486i	$-0.432327\pi$
$318$	20.7302	+	16.7525i	1.16249	+	0.939431i
$319$	26.7623	+	26.7623i	1.49840	+	1.49840i
$320$	4.35536	+	9.67721i	0.243472	+	0.540973i
$321$	0.167228	−	11.0713i	0.00933376	−	0.617938i
$322$	−5.24060	+	5.91541i	−0.292047	+	0.329653i
$323$	6.76313	−	11.1876i	0.376311	−	0.622494i
$324$	19.1028	+	3.50069i	1.06127	+	0.194483i
$325$	−13.0255	+	2.37363i	−0.722525	+	0.131665i
$326$	−14.0870	−	15.9009i	−0.780207	−	0.880672i
$327$	−0.0614854	+	0.812625i	−0.00340015	+	0.0449383i
$328$	2.60008	+	0.640862i	0.143565	+	0.0353857i
$329$	6.84911	+	9.92265i	0.377604	+	0.547054i
$330$	−13.8780	−	14.3036i	−0.763957	−	0.787390i
$331$	13.4914	−	22.3175i	0.741554	−	1.22668i	−0.226027	−	0.974121i	$-0.572574\pi$
$331$	13.4914	−	22.3175i	0.741554	−	1.22668i	0.967581	−	0.252560i	$-0.0812724\pi$
$332$	−29.2647	−	22.9275i	−1.60611	−	1.25831i
$333$	16.1701	+	10.4548i	0.886117	+	0.572917i
$334$	−1.22232	+	3.22301i	−0.0668826	+	0.176355i
$335$	13.8923	+	7.29123i	0.759016	+	0.398362i
$336$	−7.32657	+	15.6433i	−0.399697	+	0.853412i
$337$		−	9.56817i		−	0.521212i	−0.965445	−	0.260606i	$-0.916078\pi$
$337$		−	9.56817i		−	0.521212i	0.965445	−	0.260606i	$-0.0839223\pi$
$338$	10.8312	+	24.1944i	0.589139	+	1.31600i
$339$	−2.03000	+	7.73156i	−0.110254	+	0.419921i
$340$	9.17631	+	1.68162i	0.497655	+	0.0911987i
$341$	−18.2192	+	34.7138i	−0.986625	+	1.87986i
$342$	16.3745	−	13.6465i	0.885434	−	0.737918i
$343$	−1.08148	+	17.8791i	−0.0583947	+	0.965379i
$344$	1.19345	−	1.52332i	0.0643463	−	0.0821320i
$345$	−1.97644	−	2.03707i	−0.106408	−	0.109672i
$346$	13.9111	+	8.40956i	0.747866	+	0.452101i
$347$	0.345550	−	0.238516i	0.0185501	−	0.0128042i	−0.558754	−	0.829334i	$-0.688720\pi$
$347$	0.345550	−	0.238516i	0.0185501	−	0.0128042i	0.577304	+	0.816529i	$0.304105\pi$
$348$	−25.3724	−	13.8092i	−1.36010	−	0.740250i
$349$	19.5360	−	3.58010i	1.04574	−	0.191638i	0.370190	−	0.928956i	$-0.379293\pi$
$349$	19.5360	−	3.58010i	1.04574	−	0.191638i	0.675546	+	0.737318i	$0.263908\pi$
$350$	−15.2751	+	13.5325i	−0.816487	+	0.723344i
$351$	−6.39569	+	17.6095i	−0.341376	+	0.939927i
$352$	29.7101	+	26.3208i	1.58355	+	1.40290i
$353$	−22.6455	−	13.6897i	−1.20530	−	0.728629i	−0.235345	−	0.971912i	$-0.575622\pi$
$353$	−22.6455	−	13.6897i	−1.20530	−	0.728629i	−0.969955	+	0.243283i	$0.921776\pi$
$354$	9.04093	+	13.5307i	0.480520	+	0.719148i
$355$	−3.52025	−	14.2822i	−0.186835	−	0.758021i
$356$	8.56978	−	3.85695i	0.454198	−	0.204418i
$357$	8.93229	+	15.2928i	0.472747	+	0.809383i
$358$	7.92612	−	17.6111i	0.418908	−	0.930776i
$359$	−12.5959	+	7.61446i	−0.664784	+	0.401876i	−0.809112	−	0.587654i	$-0.800052\pi$
$359$	−12.5959	+	7.61446i	−0.664784	+	0.401876i	0.144328	+	0.989530i	$0.453898\pi$
$360$	0.969360	+	0.546720i	0.0510898	+	0.0288147i
$361$			6.85833i			0.360965i
$362$	21.0219	−	12.7082i	1.10489	−	0.667927i
$363$	−20.8982	−	8.28880i	−1.09687	−	0.435049i
$364$	17.4391	+	12.0630i	0.914057	+	0.632270i
$365$	11.2982	−	1.37185i	0.591373	−	0.0718057i
$366$	3.20075	−	1.38279i	0.167306	−	0.0722797i
$367$	−7.42047	−	10.7504i	−0.387346	−	0.561167i	0.580004	−	0.814614i	$-0.303051\pi$
$367$	−7.42047	−	10.7504i	−0.387346	−	0.561167i	−0.967349	+	0.253447i	$0.918436\pi$
$368$	3.89509	+	3.45075i	0.203045	+	0.179883i
$369$	−23.0553	+	9.54985i	−1.20021	+	0.497145i
$370$	9.30114	+	11.8720i	0.483543	+	0.617197i
$371$	−6.11892	+	19.6363i	−0.317678	+	1.01947i
$372$	5.83758	−	29.3476i	0.302665	−	1.52160i
$373$	−7.10819	+	10.2980i	−0.368048	+	0.533210i	−0.962628	−	0.270827i	$-0.912703\pi$
$373$	−7.10819	+	10.2980i	−0.368048	+	0.533210i	0.594580	+	0.804036i	$0.297318\pi$
$374$	36.3737	−	8.96532i	1.88084	−	0.463586i
$375$	−10.4676	−	13.7848i	−0.540546	−	0.711845i
$376$	−1.17207	+	0.809022i	−0.0604449	+	0.0417221i
$377$	17.2077	−	21.9191i	0.886242	−	1.12889i
$378$	5.63362	+	28.3220i	0.289762	+	1.45673i
$379$	15.8281	−	4.93225i	0.813037	−	0.253353i	0.137332	−	0.990525i	$-0.456147\pi$
$379$	15.8281	−	4.93225i	0.813037	−	0.253353i	0.675705	+	0.737172i	$0.263839\pi$
$380$	8.10149	−	3.07249i	0.415597	−	0.157615i
$381$	−2.78415	−	1.10427i	−0.142636	−	0.0565733i
$382$	3.56238	+	0.652831i	0.182267	+	0.0334017i
$383$	−19.2117	−	31.7800i	−0.981671	−	1.62388i	−0.761231	−	0.648481i	$-0.775405\pi$
$383$	−19.2117	−	31.7800i	−0.981671	−	1.62388i	−0.220440	−	0.975401i	$-0.570749\pi$
$384$	−4.02707	−	1.88608i	−0.205505	−	0.0962488i
$385$	6.31186	−	14.0244i	0.321682	−	0.714748i
$386$	21.7703	−	8.25638i	1.10808	−	0.420238i
$387$	−0.544655	+	18.0252i	−0.0276864	+	0.916274i
$388$	20.7362	+	6.46166i	1.05272	+	0.328041i
$389$	1.24234	+	0.306209i	0.0629891	+	0.0155254i	0.270684	−	0.962668i	$-0.412750\pi$
$389$	1.24234	+	0.306209i	0.0629891	+	0.0155254i	−0.207695	+	0.978194i	$0.566596\pi$
$390$	−9.23448	+	11.4039i	−0.467606	+	0.577461i
$391$	5.18020	−	1.27680i	0.261974	−	0.0645708i
$392$	0.137493	+	0.00831681i	0.00694446	+	0.000420062i
$393$	−11.1527	−	1.52544i	−0.562579	−	0.0769482i
$394$	3.19683	+	6.09105i	0.161054	+	0.306863i
$395$	5.21443	+	16.7337i	0.262366	+	0.841963i
$396$	31.5709	+	2.86889i	1.58650	+	0.144167i
$397$	−18.0253	−	1.09033i	−0.904664	−	0.0547221i	−0.398509	−	0.917165i	$-0.630472\pi$
$397$	−18.0253	−	1.09033i	−0.904664	−	0.0547221i	−0.506155	+	0.862442i	$0.668934\pi$
$398$	11.0712	+	14.1313i	0.554949	+	0.708339i
$399$	14.4475	+	7.86320i	0.723280	+	0.393652i
$400$	8.91068	+	10.0581i	0.445534	+	0.502904i
$401$	−5.31327	+	0.321394i	−0.265332	+	0.0160496i	−0.192509	−	0.981295i	$-0.561662\pi$
$401$	−5.31327	+	0.321394i	−0.265332	+	0.0160496i	−0.0728232	+	0.997345i	$0.523201\pi$
$402$	−46.8577	+	10.8014i	−2.33705	+	0.538725i
$403$	26.9797	+	10.2627i	1.34395	+	0.511224i
$404$	−6.46244	+	12.3131i	−0.321518	+	0.612602i
$405$	−10.2954	+	1.25010i	−0.511583	+	0.0621180i
$406$	5.17727	−	42.6387i	0.256944	−	2.11612i
$407$	27.8308	+	14.6067i	1.37952	+	0.724028i
$408$	−1.80640	+	1.05509i	−0.0894301	+	0.0522346i
$409$	−1.90329	+	0.593090i	−0.0941118	+	0.0293264i	−0.344197	−	0.938897i	$-0.611849\pi$
$409$	−1.90329	+	0.593090i	−0.0941118	+	0.0293264i	0.250086	+	0.968224i	$0.419541\pi$
$410$	−19.5100	+	1.18014i	−0.963530	+	0.0582828i
$411$	−2.26994	+	30.0007i	−0.111968	+	1.47983i
$412$	−21.6351	+	19.1670i	−1.06588	+	0.944290i
$413$	−7.13358	+	10.3348i	−0.351020	+	0.508541i
$414$	8.66344	+	0.787257i	0.425785	+	0.0386916i
$415$	18.5627	+	7.03989i	0.911205	+	0.345575i
$416$	16.6255	−	24.0351i	0.815134	−	1.17842i
$417$	−0.0462582	−	0.435893i	−0.00226527	−	0.0213458i
$418$	24.6028	−	24.6028i	1.20336	−	1.20336i
$419$	12.7229	+	4.82516i	0.621555	+	0.235725i	0.645222	−	0.763995i	$-0.276765\pi$
$419$	12.7229	+	4.82516i	0.621555	+	0.235725i	−0.0236669	+	0.999720i	$0.507534\pi$
$420$	−1.59070	+	11.6299i	−0.0776184	+	0.567479i
$421$	8.09361	−	25.9733i	0.394458	−	1.26586i	−0.517537	−	0.855661i	$-0.673151\pi$
$421$	8.09361	−	25.9733i	0.394458	−	1.26586i	0.911995	−	0.410200i	$-0.134541\pi$
$422$	34.2649	−	6.27928i	1.66799	−	0.305671i
$423$	4.32925	−	12.5457i	0.210495	−	0.609993i
$424$	−2.31945	−	0.722771i	−0.112643	−	0.0351009i
$425$	13.6764	−	1.66062i	0.663405	−	0.0805519i
$426$	36.7121	+	26.1679i	1.77871	+	1.26784i
$427$	1.90253	+	1.90253i	0.0920700	+	0.0920700i
$428$	4.89168	+	12.8983i	0.236448	+	0.623463i
$429$	−7.79561	+	29.5711i	−0.376376	+	1.42770i
$430$	−5.00861	+	13.2066i	−0.241537	+	0.636880i
$431$	−21.8955	+	9.85437i	−1.05467	+	0.474668i	−0.862165	−	0.506628i	$-0.830892\pi$
$431$	−21.8955	+	9.85437i	−1.05467	+	0.474668i	−0.192505	+	0.981296i	$0.561661\pi$
$432$	18.6490	−	3.70954i	0.897251	−	0.178475i
$433$	3.47346	+	3.92072i	0.166924	+	0.188418i	0.826020	−	0.563640i	$-0.190600\pi$
$433$	3.47346	+	3.92072i	0.166924	+	0.188418i	−0.659097	+	0.752058i	$0.729061\pi$
$434$	43.7629	−	8.01984i	2.10068	−	0.384965i
$435$	15.1296	+	3.00946i	0.725409	+	0.144293i
$436$	−0.302056	−	0.969332i	−0.0144659	−	0.0464226i
$437$	3.50383	−	3.50383i	0.167611	−	0.167611i
$438$	−23.5228	+	25.7573i	−1.12396	+	1.23073i
$439$	7.80393	+	0.947569i	0.372461	+	0.0452250i	0.304627	−	0.952472i	$-0.401468\pi$
$439$	7.80393	+	0.947569i	0.372461	+	0.0452250i	0.0678340	+	0.997697i	$0.478391\pi$
$440$	1.65657	+	0.745561i	0.0789738	+	0.0355432i
$441$	−1.07794	+	0.696942i	−0.0513306	+	0.0331877i
$442$	−9.75543	−	25.8003i	−0.464019	−	1.22719i
$443$	−11.8889	−	22.6524i	−0.564859	−	1.07625i	−0.985604	−	0.169070i	$-0.945924\pi$
$443$	−11.8889	−	22.6524i	−0.564859	−	1.07625i	0.420745	−	0.907179i	$-0.361769\pi$
$444$	−23.5286	−	4.68011i	−1.11662	−	0.222108i
$445$	−3.75641	+	3.32789i	−0.178071	+	0.157757i
$446$	−27.6905	−	6.82510i	−1.31118	−	0.323178i
$447$	−11.4598	+	4.95087i	−0.542029	+	0.234168i
$448$	1.51544	−	25.0532i	0.0715977	−	1.18365i
$449$	−8.53002	−	18.9529i	−0.402557	−	0.894444i	−0.995982	−	0.0895549i	$-0.971456\pi$
$449$	−8.53002	−	18.9529i	−0.402557	−	0.894444i	0.593425	−	0.804889i	$-0.297775\pi$
$450$	21.9630	+	4.71462i	1.03535	+	0.222249i
$451$	−36.0684	+	18.9301i	−1.69839	+	0.891386i
$452$	−1.20041	−	9.88625i	−0.0564624	−	0.465010i
$453$	−33.2386	−	10.9110i	−1.56168	−	0.512642i
$454$	4.76946	+	19.3504i	0.223842	+	0.908162i
$455$	−10.8075	−	3.37954i	−0.506663	−	0.158435i
$456$	−0.928806	+	1.70655i	−0.0434953	+	0.0799165i
$457$	−4.51215	+	14.4800i	−0.211069	+	0.677345i	0.787098	+	0.616828i	$0.211583\pi$
$457$	−4.51215	+	14.4800i	−0.211069	+	0.677345i	−0.998167	+	0.0605172i	$0.980725\pi$
$458$	−13.1166	−	24.9916i	−0.612899	−	1.16778i
$459$	7.73145	−	17.8960i	0.360873	−	0.835315i
$460$	3.22457	+	1.45126i	0.150347	+	0.0676655i
$461$	2.88903	−	15.7649i	0.134556	−	0.734246i	−0.845262	−	0.534352i	$-0.820556\pi$
$461$	2.88903	−	15.7649i	0.134556	−	0.734246i	0.979818	−	0.199894i	$-0.0640597\pi$
$462$	13.3419	+	45.2084i	0.620720	+	2.10329i
$463$	−2.18499	+	11.9231i	−0.101545	+	0.554114i	0.893022	+	0.450013i	$0.148581\pi$
$463$	−2.18499	+	11.9231i	−0.101545	+	0.554114i	−0.994567	+	0.104100i	$0.966804\pi$
$464$	−28.0760	−	3.40905i	−1.30340	−	0.158261i
$465$	1.68627	+	15.8898i	0.0781988	+	0.736872i
$466$	12.6566	+	40.6166i	0.586307	+	1.88153i
$467$	−10.8998	+	15.7910i	−0.504381	+	0.730722i	−0.989628	−	0.143655i	$-0.954114\pi$
$467$	−10.8998	+	15.7910i	−0.504381	+	0.730722i	0.485247	+	0.874377i	$0.338730\pi$
$468$	−0.681789	−	23.3311i	−0.0315157	−	1.07848i
$469$	−21.0793	−	30.5387i	−0.973354	−	1.41015i
$470$	6.41072	−	8.18268i	0.295704	−	0.377439i
$471$	9.83444	+	0.148546i	0.453147	+	0.00684465i
$472$	−1.22075	−	0.842623i	−0.0561896	−	0.0387849i
$473$	1.77731	+	29.3825i	0.0817210	+	1.35101i
$474$	−45.5472	−	28.4823i	−2.09205	−	1.30824i
$475$	10.0724	−	7.89121i	0.462152	−	0.362073i
$476$	−17.3688	−	13.6076i	−0.796097	−	0.623702i
$477$	21.4014	−	7.38517i	0.979902	−	0.338144i
$478$	−45.2507	+	31.2343i	−2.06972	+	1.42862i
$479$	11.3498	+	14.4869i	0.518584	+	0.661924i	0.973520	−	0.228600i	$-0.0734148\pi$
$479$	11.3498	+	14.4869i	0.518584	+	0.661924i	−0.454936	+	0.890524i	$0.650338\pi$
$480$	16.0286	+	2.19236i	0.731603	+	0.100067i
$481$	8.22786	−	21.6302i	0.375158	−	0.986252i
$482$	49.7946	+	6.04616i	2.26808	+	0.275395i
$483$	1.90009	+	6.43840i	0.0864573	+	0.292957i
$484$	28.0092			1.27315
$485$	−11.5986			−0.526664
$486$	21.4351	−	23.4713i	0.972315	−	1.06468i
$487$	−16.8327	−	7.57578i	−0.762762	−	0.343291i	−0.00858579	−	0.999963i	$-0.502733\pi$
$487$	−16.8327	−	7.57578i	−0.762762	−	0.343291i	−0.754177	+	0.656672i	$0.771964\pi$
$488$	−0.224728	+	0.224728i	−0.0101730	+	0.0101730i
$489$	−17.7962	+	2.98421i	−0.804773	+	0.134951i
$490$	−0.976168	+	0.240604i	−0.0440988	+	0.0108694i
$491$	10.4749	+	9.27993i	0.472725	+	0.418797i	0.865555	−	0.500813i	$-0.166966\pi$
$491$	10.4749	+	9.27993i	0.472725	+	0.418797i	−0.392831	+	0.919611i	$0.628504\pi$
$492$	22.3136	−	21.6495i	1.00597	−	0.976036i
$493$	−19.2283	+	21.7043i	−0.866001	+	0.977513i
$494$	−20.1504	−	15.8192i	−0.906610	−	0.711739i
$495$	−16.5517	+	3.55304i	−0.743944	+	0.159697i
$496$	−5.28078	−	28.8163i	−0.237114	−	1.29389i
$497$	−8.32581	+	33.7791i	−0.373464	+	1.51520i
$498$	−57.2122	+	20.7149i	−2.56374	+	0.928256i
$499$	−13.5273	+	22.3770i	−0.605567	+	1.00173i	0.391115	+	0.920342i	$0.372089\pi$
$499$	−13.5273	+	22.3770i	−0.605567	+	1.00173i	−0.996682	+	0.0813888i	$0.974064\pi$
$500$	18.4542	+	11.1559i	0.825295	+	0.498908i
$501$	1.77072	+	2.33186i	0.0791099	+	0.104180i
$502$	25.2929	+	1.52994i	1.12888	+	0.0682845i
$503$	6.66473	+	2.52760i	0.297165	+	0.112700i	0.498682	−	0.866785i	$-0.333818\pi$
$503$	6.66473	+	2.52760i	0.297165	+	0.112700i	−0.201516	+	0.979485i	$0.564587\pi$
$504$	−1.42913	−	2.21039i	−0.0636584	−	0.0984588i
$505$	1.33857	−	7.30435i	0.0595657	−	0.325039i
$506$	14.1997			0.631254
$507$	22.3028	+	3.09571i	0.990504	+	0.137485i
$508$	3.73151			0.165559
$509$	4.20955	−	22.9707i	0.186585	−	1.01816i	−0.748340	−	0.663315i	$-0.769149\pi$
$509$	4.20955	−	22.9707i	0.186585	−	1.01816i	0.934925	−	0.354845i	$-0.115466\pi$
$510$	10.2967	−	11.2748i	0.455944	−	0.499256i
$511$	−25.1685	−	9.54517i	−1.11339	−	0.422253i
$512$	−31.9584	−	1.93312i	−1.41237	−	0.0854328i
$513$	−2.45366	−	17.9389i	−0.108332	−	0.792022i
$514$	7.55980	+	4.57006i	0.333449	+	0.201577i
$515$	7.98521	−	13.2092i	0.351871	−	0.582065i
$516$	−7.64873	−	21.1249i	−0.336717	−	0.929974i
$517$	5.18442	−	21.0340i	0.228010	−	0.925074i
$518$	−6.42968	−	35.0856i	−0.282504	−	1.54157i
$519$	12.3217	−	6.23141i	0.540862	−	0.273528i
$520$	0.399194	−	1.27659i	0.0175058	−	0.0559821i
$521$	−19.2632	+	21.7437i	−0.843937	+	0.952608i	−0.999379	−	0.0352371i	$-0.988781\pi$
$521$	−19.2632	+	21.7437i	−0.843937	+	0.952608i	0.155442	+	0.987845i	$0.450320\pi$
$522$	−41.1810	+	23.2262i	−1.80244	+	1.01658i
$523$	29.9005	+	26.4896i	1.30746	+	1.15831i	0.976704	+	0.214590i	$0.0688416\pi$
$523$	29.9005	+	26.4896i	1.30746	+	1.15831i	0.330754	+	0.943717i	$0.392697\pi$
$524$	13.6165	−	3.35616i	0.594838	−	0.146614i
$525$	2.86675	+	17.0957i	0.125115	+	0.746120i
$526$	9.26794	−	9.26794i	0.404101	−	0.404101i
$527$	−27.3900	−	12.3272i	−1.19313	−	0.536983i
$528$	29.7681	−	8.78514i	1.29549	−	0.382324i
$529$	−20.9777			−0.912075
$530$	17.7324			0.770244
$531$	13.8166	−	0.417500i	0.599588	−	0.0181180i
$532$	−20.3432	−	2.47012i	−0.881992	−	0.107093i
$533$	17.0129	+	24.6999i	0.736911	+	1.06987i
$534$	2.08441	−	15.2394i	0.0902010	−	0.659473i
$535$	−4.54311	−	5.79885i	−0.196416	−	0.250706i
$536$	3.60725	−	2.48991i	0.155810	−	0.107548i
$537$	−9.11389	−	13.6399i	−0.393293	−	0.588605i
$538$	−28.6670	−	22.4591i	−1.23592	−	0.968283i
$539$	−1.64936	+	1.29219i	−0.0710432	+	0.0556588i
$540$	11.3488	−	6.17670i	0.488373	−	0.265803i
$541$	1.44772	+	23.9337i	0.0622424	+	1.02899i	0.886486	+	0.462755i	$0.153139\pi$
$541$	1.44772	+	23.9337i	0.0622424	+	1.02899i	−0.824244	+	0.566235i	$0.808400\pi$
$542$	−30.6460	−	21.1534i	−1.31636	−	0.908616i
$543$	0.315134	−	20.8634i	0.0135237	−	0.895333i
$544$	−18.7544	+	23.9382i	−0.804087	+	1.02634i
$545$	0.307997	+	0.446211i	0.0131931	+	0.0191136i
$546$	31.8733	−	13.7324i	1.36405	−	0.587691i
$547$	−8.19641	+	11.8746i	−0.350453	+	0.507719i	−0.958079	−	0.286504i	$-0.907507\pi$
$547$	−8.19641	+	11.8746i	−0.350453	+	0.507719i	0.607626	+	0.794224i	$0.292122\pi$
$548$	−11.1514	−	35.7861i	−0.476364	−	1.52871i
$549$	0.445624	−	2.92795i	0.0190188	−	0.124962i
$550$	36.3998	+	4.41974i	1.55209	+	0.188458i
$551$	−4.85445	+	26.4899i	−0.206807	+	1.12851i
$552$	−0.760508	+	0.224440i	−0.0323694	+	0.00955282i
$553$	7.47232	−	40.7751i	0.317755	−	1.73393i
$554$	20.0455	+	9.02175i	0.851652	+	0.383297i
$555$	12.7392	−	1.35192i	0.540749	−	0.0573857i
$556$	0.253789	+	0.483554i	0.0107630	+	0.0205073i
$557$	0.318328	−	1.02155i	0.0134880	−	0.0432844i	−0.947732	−	0.319069i	$-0.896630\pi$
$557$	0.318328	−	1.02155i	0.0134880	−	0.0432844i	0.961220	+	0.275784i	$0.0889376\pi$
$558$	−35.6601	−	33.5682i	−1.50961	−	1.42106i
$559$	21.3224	−	3.88556i	0.901840	−	0.164342i
$560$	2.75032	+	11.1585i	0.116222	+	0.471532i
$561$	9.92473	−	30.2341i	0.419022	−	1.27649i
$562$	−1.61087	−	13.2667i	−0.0679502	−	0.559621i
$563$	18.8897	−	9.91407i	0.796105	−	0.417828i	−0.0170650	−	0.999854i	$-0.505432\pi$
$563$	18.8897	−	9.91407i	0.796105	−	0.417828i	0.813170	+	0.582026i	$0.197740\pi$
$564$	0.748951	+	16.5176i	0.0315365	+	0.695515i
$565$	2.18264	+	4.84964i	0.0918246	+	0.204026i
$566$	−0.0528521	+	0.873750i	−0.00222154	+	0.0367264i
$567$	22.9348	+	8.69798i	0.963169	+	0.365281i
$568$	−3.99001	−	0.983450i	−0.167417	−	0.0412646i
$569$	−31.7563	+	28.1337i	−1.33129	+	1.17942i	−0.362379	+	0.932031i	$0.618036\pi$
$569$	−31.7563	+	28.1337i	−1.33129	+	1.17942i	−0.968915	+	0.247393i	$0.920426\pi$
$570$	2.76662	−	13.9088i	0.115881	−	0.582575i
$571$	−5.49537	−	10.4706i	−0.229974	−	0.438179i	0.742936	−	0.669362i	$-0.233433\pi$
$571$	−5.49537	−	10.4706i	−0.229974	−	0.438179i	−0.972910	+	0.231183i	$0.925740\pi$
$572$	−4.55483	−	37.8266i	−0.190447	−	1.58161i
$573$	2.07455	−	2.27162i	0.0866657	−	0.0948983i
$574$	42.1551	+	18.9725i	1.75952	+	0.791896i
$575$	5.18391	+	0.629441i	0.216184	+	0.0262495i
$576$	−23.2008	+	15.0005i	−0.966700	+	0.625019i
$577$	−23.4223	+	23.4223i	−0.975085	+	0.975085i	−0.999697	−	0.0246121i	$-0.992165\pi$
$577$	−23.4223	+	23.4223i	−0.975085	+	0.975085i	0.0246121	+	0.999697i	$0.492165\pi$
$578$	−1.77401	−	5.69299i	−0.0737890	−	0.236797i
$579$	3.85838	−	19.3974i	0.160349	−	0.806128i
$580$	−18.9037	+	3.46423i	−0.784934	+	0.143844i
$581$	−31.1364	−	35.1457i	−1.29175	−	1.45809i
$582$	26.9615	−	23.1685i	1.11759	−	0.960365i
$583$	33.6994	−	15.1669i	1.39569	−	0.628148i
$584$	1.12748	−	2.97292i	0.0466555	−	0.123020i
$585$	4.05422	+	11.7867i	0.167621	+	0.487318i
$586$	23.5101	+	61.9910i	0.971193	+	2.56083i
$587$	19.5787	+	19.5787i	0.808098	+	0.808098i	0.984346	−	0.176247i	$-0.0563959\pi$
$587$	19.5787	+	19.5787i	0.808098	+	0.808098i	−0.176247	+	0.984346i	$0.556396\pi$
$588$	0.928225	−	1.30225i	0.0382794	−	0.0537038i
$589$	−27.6931	+	3.36255i	−1.14107	+	0.138551i
$590$	10.3364	+	3.22095i	0.425543	+	0.132604i
$591$	5.82654	+	0.440851i	0.239672	+	0.0181342i
$592$	−23.1026	+	4.23371i	−0.949512	+	0.174005i
$593$	−4.53243	+	14.5451i	−0.186125	+	0.597295i	0.813746	+	0.581220i	$0.197425\pi$
$593$	−4.53243	+	14.5451i	−0.186125	+	0.597295i	−0.999871	+	0.0160743i	$0.994883\pi$
$594$	31.3779	−	41.3217i	1.28745	−	1.69545i
$595$	11.0170	+	4.17821i	0.451655	+	0.171290i
$596$	10.9973	−	10.9973i	0.450468	−	0.450468i
$597$	15.1635	−	1.60919i	0.620601	−	0.0658599i
$598$	−1.24990	−	10.3801i	−0.0511122	−	0.424473i
$599$	18.5094	+	7.01970i	0.756274	+	0.286817i	0.702450	−	0.711733i	$-0.252090\pi$
$599$	18.5094	+	7.01970i	0.756274	+	0.286817i	0.0538247	+	0.998550i	$0.482859\pi$
$600$	−2.01936	+	0.338622i	−0.0824401	+	0.0138242i
$601$	2.57769	−	3.73442i	0.105146	−	0.152330i	−0.766879	−	0.641792i	$-0.778191\pi$
$601$	2.57769	−	3.73442i	0.105146	−	0.152330i	0.872025	+	0.489462i	$0.162807\pi$
$602$	25.0048	−	22.1523i	1.01912	−	0.902862i
$603$	−13.3240	+	38.6116i	−0.542596	+	1.57239i
$604$	43.5048	−	2.63156i	1.77019	−	0.107077i
$605$	−14.2801	+	4.44985i	−0.580567	+	0.180912i
$606$	11.4791	+	19.6532i	0.466306	+	0.798355i
$607$	−7.84010	−	4.11480i	−0.318220	−	0.167015i	0.298049	−	0.954551i	$-0.403664\pi$
$607$	−7.84010	−	4.11480i	−0.318220	−	0.167015i	−0.616269	+	0.787536i	$0.711356\pi$
$608$	−3.40439	+	28.0377i	−0.138066	+	1.13708i
$609$	−28.3768	−	22.9318i	−1.14988	−	0.929242i
$610$	1.07801	−	2.05398i	0.0436475	−	0.0831634i
$611$	−15.8323	−	1.93837i	−0.640508	−	0.0784180i
$612$	−0.733542	+	24.2764i	−0.0296517	+	0.981316i
$613$	−29.3970	+	1.77819i	−1.18733	+	0.0718204i	−0.642205	−	0.766533i	$-0.721980\pi$
$613$	−29.3970	+	1.77819i	−1.18733	+	0.0718204i	−0.545127	+	0.838353i	$0.683519\pi$
$614$	13.4453	+	15.1766i	0.542609	+	0.612479i
$615$	−7.93674	+	14.5826i	−0.320040	+	0.588028i
$616$	−2.64973	−	3.38213i	−0.106761	−	0.136270i
$617$	−0.0788011	−	0.00476659i	−0.00317241	−	0.000191896i	0.0587922	−	0.998270i	$-0.481275\pi$
$617$	−0.0788011	−	0.00476659i	−0.00317241	−	0.000191896i	−0.0619646	+	0.998078i	$0.519737\pi$
$618$	7.82365	+	46.6560i	0.314714	+	1.87678i
$619$	−12.2124	−	39.1909i	−0.490857	−	1.57522i	−0.785026	−	0.619463i	$-0.787350\pi$
$619$	−12.2124	−	39.1909i	−0.490857	−	1.57522i	0.294168	−	0.955754i	$-0.404957\pi$
$620$	−9.25147	−	17.6272i	−0.371548	−	0.707926i
$621$	4.46872	−	5.88487i	0.179324	−	0.236152i
$622$	−3.14817	−	0.190429i	−0.126230	−	0.00763551i
$623$	11.5245	−	2.84053i	0.461718	−	0.113803i
$624$	−9.04227	−	20.9874i	−0.361980	−	0.840169i
$625$	6.64616	+	1.63813i	0.265847	+	0.0655253i
$626$	6.21025	+	1.93519i	0.248212	+	0.0773459i
$627$	−6.63867	−	28.7993i	−0.265123	−	1.15013i
$628$	−11.4574	+	4.34521i	−0.457199	+	0.173393i
$629$	−9.88301	+	21.9591i	−0.394061	+	0.875568i
$630$	14.7585	+	12.2997i	0.587992	+	0.490030i
$631$	13.2667	+	21.9459i	0.528141	+	0.873652i	0.999968	−	0.00803962i	$-0.00255912\pi$
$631$	13.2667	+	21.9459i	0.528141	+	0.873652i	−0.471827	+	0.881691i	$0.656405\pi$
$632$	4.81638	+	0.882635i	0.191585	+	0.0351093i
$633$	10.9095	−	27.5056i	0.433613	−	1.09325i
$634$	49.3811	−	18.7278i	1.96118	−	0.743776i
$635$	−1.90245	+	0.592827i	−0.0754964	+	0.0235256i
$636$	−21.3924	+	18.3829i	−0.848265	+	0.728930i
$637$	1.08978	+	1.09195i	0.0431788	+	0.0432648i
$638$	−63.5134	+	43.8401i	−2.51452	+	1.73565i
$639$	35.3801	−	14.6550i	1.39962	−	0.579741i
$640$	−2.87254	+	0.708017i	−0.113547	+	0.0279868i
$641$	−0.819131	+	1.18672i	−0.0323537	+	0.0468724i	−0.838827	−	0.544398i	$-0.816758\pi$
$641$	−0.819131	+	1.18672i	−0.0323537	+	0.0468724i	0.806473	+	0.591271i	$0.201373\pi$
$642$	22.1440	+	4.40472i	0.873956	+	0.173840i
$643$	−5.20108	+	16.6909i	−0.205111	+	0.658224i	0.793646	+	0.608379i	$0.208180\pi$
$643$	−5.20108	+	16.6909i	−0.205111	+	0.658224i	−0.998757	+	0.0498440i	$0.984128\pi$
$644$	−5.15781	−	6.58346i	−0.203246	−	0.259425i
$645$	7.25572	+	9.55505i	0.285694	+	0.376230i
$646$	19.9530	+	17.6768i	0.785039	+	0.695484i
$647$	0.190874	+	0.276529i	0.00750404	+	0.0108715i	0.826718	−	0.562617i	$-0.190205\pi$
$647$	0.190874	+	0.276529i	0.00750404	+	0.0108715i	−0.819214	+	0.573488i	$0.805590\pi$
$648$	−1.02741	+	2.70907i	−0.0403605	+	0.106422i
$649$	22.3987	−	2.71970i	0.879228	−	0.106758i
$650$	0.0268391	−	26.9975i	0.00105272	−	1.05893i
$651$	13.9335	−	35.1300i	0.546096	−	1.37685i
$652$	19.2388	−	11.6303i	0.753451	−	0.455477i
$653$			31.5339i			1.23402i	0.786957	+	0.617008i	$0.211655\pi$
$653$			31.5339i			1.23402i	−0.786957	+	0.617008i	$0.788345\pi$
$654$	−1.60727	−	0.422006i	−0.0628493	−	0.0165017i
$655$	−6.40894	+	3.87434i	−0.250418	+	0.151383i
$656$	12.4927	−	27.7576i	0.487758	−	1.08375i
$657$	7.95654	+	28.5415i	0.310414	+	1.11351i
$658$	−22.4192	+	10.0900i	−0.873990	+	0.393351i
$659$	−8.67878	−	35.2112i	−0.338077	−	1.37163i	−0.856340	−	0.516412i	$-0.827267\pi$
$659$	−8.67878	−	35.2112i	−0.338077	−	1.37163i	0.518263	−	0.855221i	$-0.326579\pi$
$660$	17.5363	−	11.7174i	0.682599	−	0.456099i
$661$	−10.3362	−	6.24844i	−0.402031	−	0.243036i	0.301848	−	0.953356i	$-0.402396\pi$
$661$	−10.3362	−	6.24844i	−0.402031	−	0.243036i	−0.703879	+	0.710320i	$0.748550\pi$
$662$	39.8031	+	35.2625i	1.54699	+	1.37051i
$663$	−22.9749	−	4.59374i	−0.892273	−	0.178406i
$664$	4.15143	−	3.67785i	0.161107	−	0.142728i
$665$	10.7641	−	1.97260i	0.417414	−	0.0764940i
$666$	−26.9124	+	28.5895i	−1.04283	+	1.10782i
$667$	−9.04532	+	6.24353i	−0.350236	+	0.241750i
$668$	−3.12173	−	1.88715i	−0.120783	−	0.0730162i
$669$	−17.3864	+	16.8689i	−0.672195	+	0.652191i
$670$	−19.7301	+	25.1836i	−0.762241	+	0.972928i
$671$	0.291892	−	4.82554i	0.0112684	−	0.186288i
$672$	−31.1576	−	22.2087i	−1.20193	−	0.856720i
$673$	20.2414	−	38.5667i	0.780248	−	1.48664i	−0.0910298	−	0.995848i	$-0.529016\pi$
$673$	20.2414	−	38.5667i	0.780248	−	1.48664i	0.871278	−	0.490790i	$-0.163292\pi$
$674$	19.1908	+	3.51684i	0.739200	+	0.135464i
$675$	13.2869	−	13.6945i	0.511413	−	0.527101i
$676$	−27.2506	+	6.65921i	−1.04810	+	0.256124i
$677$			2.71819i			0.104469i	0.998635	+	0.0522343i	$0.0166343\pi$
$677$			2.71819i			0.104469i	−0.998635	+	0.0522343i	$0.983366\pi$
$678$	−14.7610	−	6.91332i	−0.566891	−	0.265505i
$679$	24.2898	+	12.7483i	0.932159	+	0.489235i
$680$	−0.493533	+	1.30134i	−0.0189261	+	0.0499041i
$681$	16.0842	+	5.27985i	0.616349	+	0.202324i
$682$	−62.9284	−	49.3013i	−2.40965	−	1.88784i
$683$	18.2125	−	30.1272i	0.696883	−	1.15279i	−0.284119	−	0.958789i	$-0.591701\pi$
$683$	18.2125	−	30.1272i	0.696883	−	1.15279i	0.981002	−	0.193997i	$-0.0621451\pi$
$684$	11.0814	+	19.6478i	0.423708	+	0.751251i
$685$	11.3707	+	16.4733i	0.434453	+	0.629414i
$686$	−35.4623	−	8.74068i	−1.35396	−	0.333721i
$687$	−23.9063	−	1.80881i	−0.912082	−	0.0690106i
$688$	−14.5865	−	16.4648i	−0.556106	−	0.627714i
$689$	−14.0534	−	23.2995i	−0.535393	−	0.887639i
$690$	4.81217	−	3.21539i	0.183196	−	0.122408i
$691$	−6.93473	+	11.4714i	−0.263809	+	0.436394i	−0.959402	−	0.282042i	$-0.908988\pi$
$691$	−6.93473	+	11.4714i	−0.263809	+	0.436394i	0.695592	+	0.718437i	$0.255142\pi$
$692$	−11.4073	+	12.8762i	−0.433641	+	0.489480i
$693$	38.5679	+	10.7516i	1.46508	+	0.408419i
$694$	0.351380	+	0.780734i	0.0133382	+	0.0296363i
$695$	−0.206213	−	0.206213i	−0.00782210	−	0.00782210i
$696$	2.70871	−	3.35188i	0.102674	−	0.127053i
$697$	−16.1452	−	26.7074i	−0.611543	−	1.01162i
$698$			40.4989i			1.53291i
$699$	34.9523	+	9.17707i	1.32202	+	0.347109i
$700$	−11.1725	−	18.4816i	−0.422281	−	0.698538i
$701$	0.580150	−	4.77797i	0.0219120	−	0.180461i	−0.977644	−	0.210268i	$-0.932566\pi$
$701$	0.580150	−	4.77797i	0.0219120	−	0.180461i	0.999556	+	0.0298071i	$0.00948929\pi$
$702$	−32.9684	−	19.3002i	−1.24431	−	0.728440i
$703$	2.69583	+	22.2021i	0.101675	+	0.837370i
$704$	−35.4997	+	27.8122i	−1.33794	+	1.04821i
$705$	−3.00600	−	8.30223i	−0.113212	−	0.312680i
$706$	35.7808	−	40.3881i	1.34663	−	1.52003i
$707$	−10.8317	+	13.8256i	−0.407366	+	0.519964i
$708$	−15.8090	+	6.82984i	−0.594139	+	0.256681i
$709$	0.949439	+	0.295857i	0.0356569	+	0.0111111i	0.315280	−	0.948999i	$-0.397902\pi$
$709$	0.949439	+	0.295857i	0.0356569	+	0.0111111i	−0.279623	+	0.960110i	$0.590209\pi$
$710$	29.9395	−	1.81101i	1.12361	−	0.0679659i
$711$	−41.0260	+	19.9757i	−1.53859	+	0.749146i
$712$	0.335525	+	1.36128i	0.0125743	+	0.0510161i
$713$	−8.96201	−	7.02128i	−0.335630	−	0.262949i
$714$	−33.9558	+	12.2944i	−1.27076	+	0.460106i
$715$	8.33174	+	18.5617i	0.311590	+	0.694167i
$716$	16.8199	+	11.6099i	0.628587	+	0.433883i
$717$	2.11554	+	46.6565i	0.0790061	+	1.74242i
$718$	−10.6426	−	28.0621i	−0.397176	−	1.04727i
$719$	6.04736	−	49.8045i	0.225529	−	1.85739i	−0.237938	−	0.971280i	$-0.576472\pi$
$719$	6.04736	−	49.8045i	0.225529	−	1.85739i	0.463467	−	0.886114i	$-0.346605\pi$
$720$	8.09888	−	9.71793i	0.301827	−	0.362166i
$721$	−31.2412	+	18.8860i	−1.16348	+	0.703351i
$722$	−13.7557	−	2.52082i	−0.511933	−	0.0938152i
$723$	26.7803	−	33.1392i	0.995972	−	1.23246i
$724$	9.21817	+	24.3063i	0.342591	+	0.903337i
$725$	−25.1303	+	13.1894i	−0.933315	+	0.489842i
$726$	24.3060	−	38.8687i	0.902081	−	1.44255i
$727$	−0.428980	+	1.74044i	−0.0159100	+	0.0645494i	−0.978360	−	0.206909i	$-0.933660\pi$
$727$	−0.428980	+	1.74044i	−0.0159100	+	0.0645494i	0.962450	+	0.271458i	$0.0875058\pi$
$728$	−2.23913	+	2.23468i	−0.0829875	+	0.0828227i
$729$	−7.25040	−	26.0083i	−0.268533	−	0.963270i
$730$	−1.40121	+	23.1648i	−0.0518612	+	0.857368i
$731$	−22.3879	+	2.71839i	−0.828047	+	0.100543i
$732$	0.828818	+	3.59551i	0.0306340	+	0.132894i
$733$	24.6085	−	7.66830i	0.908934	−	0.283235i	0.192833	−	0.981232i	$-0.438233\pi$
$733$	24.6085	−	7.66830i	0.908934	−	0.283235i	0.716101	+	0.697996i	$0.245925\pi$
$734$	24.2894	−	10.9318i	0.896538	−	0.403499i
$735$	−0.266352	+	0.811398i	−0.00982452	+	0.0299289i
$736$	−9.07353	+	7.10865i	−0.334455	+	0.262028i
$737$	−15.9559	+	64.7358i	−0.587745	+	2.38457i
$738$	−10.6799	−	49.7519i	−0.393132	−	1.83139i
$739$	0.991703	+	16.3948i	0.0364804	+	0.603093i	0.969778	+	0.243989i	$0.0784561\pi$
$739$	0.991703	+	16.3948i	0.0364804	+	0.603093i	−0.933298	+	0.359104i	$0.883082\pi$
$740$	−14.1321	+	7.41710i	−0.519507	+	0.272658i
$741$	−20.4681	+	7.38791i	−0.751915	+	0.271402i
$742$	−37.1352	−	19.4901i	−1.36328	−	0.715503i
$743$	−13.5880	+	30.1913i	−0.498495	+	1.10761i	0.475225	+	0.879864i	$0.342367\pi$
$743$	−13.5880	+	30.1913i	−0.498495	+	1.10761i	−0.973720	+	0.227747i	$0.926864\pi$
$744$	4.14958	+	1.64583i	0.152131	+	0.0603392i
$745$	−3.85966	+	7.35397i	−0.141407	+	0.269429i
$746$	−18.0419	−	18.0419i	−0.660560	−	0.660560i
$747$	−10.8476	+	50.5336i	−0.396894	+	1.84893i
$748$	2.39369	+	39.5724i	0.0875220	+	1.44691i
$749$	3.14055	+	17.1374i	0.114753	+	0.626189i
$750$	31.4955	−	15.9281i	1.15005	−	0.581612i
$751$	7.49929	+	5.17639i	0.273653	+	0.188889i	0.696985	−	0.717085i	$-0.254524\pi$
$751$	7.49929	+	5.17639i	0.273653	+	0.188889i	−0.423332	+	0.905975i	$0.639140\pi$
$752$	6.64393	+	14.7622i	0.242279	+	0.538323i
$753$	12.4930	−	17.5270i	0.455270	−	0.638718i
$754$	37.6380	+	42.5697i	1.37070	+	1.55030i
$755$	−21.7622	+	8.25330i	−0.792006	+	0.300368i
$756$	−30.5557	+	0.461567i	−1.11130	+	0.0167870i
$757$	8.27843	−	21.8284i	0.300885	−	0.793367i	−0.696256	−	0.717794i	$-0.745152\pi$
$757$	8.27843	−	21.8284i	0.300885	−	0.793367i	0.997140	−	0.0755735i	$-0.0240788\pi$
$758$	4.07482	+	33.5592i	0.148004	+	1.21892i
$759$	6.39509	−	10.2267i	0.232127	−	0.371204i
$760$	0.233004	+	1.27146i	0.00845196	+	0.0461208i
$761$	4.24296	+	23.1531i	0.153807	+	0.839299i	0.966512	+	0.256623i	$0.0826099\pi$
$761$	4.24296	+	23.1531i	0.153807	+	0.839299i	−0.812704	+	0.582676i	$0.802006\pi$
$762$	3.23815	−	5.17825i	0.117306	−	0.187588i
$763$	−0.154568	−	1.27299i	−0.00559575	−	0.0460852i
$764$	−1.35909	+	3.58363i	−0.0491703	+	0.129651i
$765$	−3.48283	−	12.4935i	−0.125922	−	0.451703i
$766$	70.8021	−	26.8517i	2.55818	−	0.970191i
$767$	−3.95972	−	16.1342i	−0.142977	−	0.582573i
$768$	−13.2536	+	18.5941i	−0.478250	+	0.670958i
$769$	−9.20315	−	20.4486i	−0.331874	−	0.737394i	0.668104	−	0.744068i	$-0.267106\pi$
$769$	−9.20315	−	20.4486i	−0.331874	−	0.737394i	−0.999978

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+(-0.367556 + 2.00569i) q^{2} +(1.27896 + 1.16801i) q^{3} +(-2.01765 - 0.765194i) q^{4} +(1.15023 + 0.0695764i) q^{5} +(-2.81276 + 2.13589i) q^{6} +(-2.33236 - 1.40996i) q^{7} +(0.166545 - 0.275500i) q^{8} +(0.271498 + 2.98769i) q^{9} +(-0.562324 + 2.28144i) q^{10} +(0.882698 + 4.81672i) q^{11} +(-1.68675 - 3.33530i) q^{12} +(3.44336 - 1.06924i) q^{13} +(3.68521 - 4.15974i) q^{14} +(1.38984 + 1.43247i) q^{15} +(-2.73904 - 2.42658i) q^{16} +(-3.64273 + 0.897854i) q^{17} +(-6.09216 - 0.553602i) q^{18} +(-2.46391 + 2.46391i) q^{19} +(-2.26753 - 1.02053i) q^{20} +(-1.33615 - 4.52751i) q^{21} -9.98528 q^{22} -1.42206 q^{23} +(0.534792 - 0.157827i) q^{24} +(-3.64535 - 0.442625i) q^{25} +(0.878934 + 7.29931i) q^{26} +(-3.14242 + 4.13826i) q^{27} +(3.62699 + 4.62951i) q^{28} +(6.36070 - 4.39047i) q^{29} +(-3.38394 + 2.26108i) q^{30} +(6.30211 + 4.93739i) q^{31} +(6.38054 - 4.99883i) q^{32} +(-4.49705 + 7.19142i) q^{33} +(-0.461905 - 7.63620i) q^{34} +(-2.58466 - 1.78406i) q^{35} +(1.73837 - 6.23586i) q^{36} +(3.95841 - 5.05254i) q^{37} +(-4.03620 - 5.84745i) q^{38} +(5.65282 + 2.65436i) q^{39} +(0.210734 - 0.305301i) q^{40} +(2.47472 + 7.94166i) q^{41} +(9.57187 - 1.01579i) q^{42} +(5.96732 + 0.724564i) q^{43} +(1.90475 - 10.3939i) q^{44} +(0.104414 + 3.45543i) q^{45} +(0.522688 - 2.85221i) q^{46} +(-4.03414 - 1.81562i) q^{47} +(-0.668863 - 6.30273i) q^{48} +(0.198843 + 0.378864i) q^{49} +(2.22764 - 7.14873i) q^{50} +(-5.70763 - 3.10643i) q^{51} +(-7.76567 - 0.477486i) q^{52} +(-1.80602 - 7.32731i) q^{53} +(-7.14504 - 7.82375i) q^{54} +(0.680179 + 5.60178i) q^{55} +(-0.776886 + 0.407741i) q^{56} +(-6.02912 + 0.273377i) q^{57} +(6.46800 + 14.3713i) q^{58} +(0.278202 - 4.59922i) q^{59} +(-1.70810 - 3.95373i) q^{60} +(-0.958535 - 0.236258i) q^{61} +(-12.2192 + 10.8253i) q^{62} +(3.57929 - 7.35116i) q^{63} +(4.27975 + 8.15438i) q^{64} +(4.03506 - 0.990300i) q^{65} +(-12.7708 - 11.6629i) q^{66} +(12.4158 + 5.58789i) q^{67} +(8.03680 + 0.975844i) q^{68} +(-1.81877 - 1.66099i) q^{69} +(4.52827 - 4.52827i) q^{70} +(-3.79765 - 12.1871i) q^{71} +(0.868324 + 0.422788i) q^{72} +(9.71480 - 1.78030i) q^{73} +(8.67888 + 9.79643i) q^{74} +(-4.14528 - 4.82391i) q^{75} +(6.85667 - 3.08594i) q^{76} +(4.73262 - 12.4789i) q^{77} +(-7.40155 + 10.3622i) q^{78} +(5.39362 + 14.2218i) q^{79} +(-2.98170 - 2.98170i) q^{80} +(-8.85258 + 1.62231i) q^{81} +(-16.8381 + 2.04451i) q^{82} +(16.4482 + 5.12546i) q^{83} +(-0.768532 + 10.1573i) q^{84} +(-4.25247 + 0.779294i) q^{85} +(-3.64657 + 11.7023i) q^{86} +(13.2632 + 1.81411i) q^{87} +(1.47401 + 0.559020i) q^{88} +(-3.07950 + 3.07950i) q^{89} +(-6.96889 - 1.06064i) q^{90} +(-9.53873 - 2.36115i) q^{91} +(2.86923 + 1.08815i) q^{92} +(2.29325 + 13.6757i) q^{93} +(5.12434 - 7.42389i) q^{94} +(-3.00550 + 2.66264i) q^{95} +(13.9992 + 1.05921i) q^{96} +(-10.0469 + 0.607726i) q^{97} +(-0.832968 + 0.259563i) q^{98} +(-14.1512 + 3.94496i) 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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