LMFDB - Embedded newform 279.2.bb.a.103.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [279,2,Mod(7,279)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(279, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 28]))

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

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

chi := DirichletCharacter("279.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 279 = 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	279.bb (of order $15$, degree $8$, 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:	$2.22782621639$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			103.22
Character	$\chi$	$=$	279.103
Dual form			279.2.bb.a.214.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.161525 - 1.53681i) q^{2} +(0.550909 + 1.64210i) q^{3} +(-0.379403 - 0.0806445i) q^{4} -1.41277 q^{5} +(2.61259 - 0.581402i) q^{6} +(1.37134 + 4.22056i) q^{7} +(0.769815 - 2.36925i) q^{8} +(-2.39300 + 1.80930i) q^{9} +(-0.228198 + 2.17116i) q^{10} +(4.07876 + 0.866967i) q^{11} +(-0.0765897 - 0.667445i) q^{12} +(-1.26368 + 0.918119i) q^{13} +(6.70772 - 1.42577i) q^{14} +(-0.778307 - 2.31991i) q^{15} +(-4.22543 - 1.88128i) q^{16} +(-1.19367 - 1.32570i) q^{17} +(2.39402 + 3.96983i) q^{18} +(5.06637 - 2.25569i) q^{19} +(0.536008 + 0.113932i) q^{20} +(-6.17511 + 4.57703i) q^{21} +(1.99119 - 6.12824i) q^{22} +(1.76280 + 1.95778i) q^{23} +(4.31464 - 0.0411243i) q^{24} -3.00408 q^{25} +(1.20686 + 2.09034i) q^{26} +(-4.28938 - 2.93279i) q^{27} +(-0.179926 - 1.71188i) q^{28} +(0.456042 - 4.33895i) q^{29} +(-3.69098 + 0.821386i) q^{30} +(3.52023 + 4.31369i) q^{31} +(-1.08252 + 1.87497i) q^{32} +(0.823376 + 7.17536i) q^{33} +(-2.23016 + 1.62031i) q^{34} +(-1.93739 - 5.96268i) q^{35} +(1.05382 - 0.493470i) q^{36} +(4.15722 - 7.20052i) q^{37} +(-2.64823 - 8.15040i) q^{38} +(-2.20382 - 1.56930i) q^{39} +(-1.08757 + 3.34720i) q^{40} +(-6.39798 - 4.64840i) q^{41} +(6.03660 + 10.2293i) q^{42} +(-9.48607 - 6.89203i) q^{43} +(-1.47757 - 0.657859i) q^{44} +(3.38075 - 2.55612i) q^{45} +(3.29348 - 2.39285i) q^{46} +(-3.40870 - 1.51765i) q^{47} +(0.761431 - 7.97500i) q^{48} +(-10.2695 + 7.46120i) q^{49} +(-0.485236 + 4.61671i) q^{50} +(1.51934 - 2.69047i) q^{51} +(0.553486 - 0.246428i) q^{52} +(-2.83644 + 0.602903i) q^{53} +(-5.19999 + 6.11824i) q^{54} +(-5.76234 - 1.22482i) q^{55} +11.0552 q^{56} +(6.49519 + 7.07681i) q^{57} +(-6.59449 - 1.40170i) q^{58} +(3.78905 + 1.68699i) q^{59} +(0.108204 + 0.942946i) q^{60} +(5.16862 + 8.95232i) q^{61} +(7.19794 - 4.71316i) q^{62} +(-10.9179 - 7.61864i) q^{63} +(-4.77728 - 3.47090i) q^{64} +(1.78529 - 1.29709i) q^{65} +(11.1602 - 0.106371i) q^{66} +6.35170 q^{67} +(0.345970 + 0.599238i) q^{68} +(-2.24374 + 3.97325i) q^{69} +(-9.47645 + 2.01428i) q^{70} +(8.09339 - 1.72030i) q^{71} +(2.44450 + 7.06243i) q^{72} +(-2.56962 + 2.85385i) q^{73} +(-10.3943 - 7.55194i) q^{74} +(-1.65498 - 4.93301i) q^{75} +(-2.10410 + 0.447241i) q^{76} +(1.93429 + 18.4036i) q^{77} +(-2.76768 + 3.13337i) q^{78} +(-0.459260 + 1.41346i) q^{79} +(5.96955 + 2.65782i) q^{80} +(2.45289 - 8.65929i) q^{81} +(-8.17716 + 9.08165i) q^{82} +(-13.9084 + 6.19244i) q^{83} +(2.71197 - 1.23855i) q^{84} +(1.68638 + 1.87291i) q^{85} +(-12.1240 + 13.4651i) q^{86} +(7.37624 - 1.64150i) q^{87} +(5.19395 - 8.99618i) q^{88} +(-2.59365 - 7.98244i) q^{89} +(-3.38219 - 5.60846i) q^{90} +(-5.60793 - 4.07440i) q^{91} +(-0.510925 - 0.884948i) q^{92} +(-5.14420 + 8.15703i) q^{93} +(-2.88293 + 4.99338i) q^{94} +(-7.15761 + 3.18677i) q^{95} +(-3.67526 - 0.744663i) q^{96} +(7.24842 - 8.05019i) q^{97} +(9.80768 + 16.9874i) q^{98} +(-11.3291 + 5.30503i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 3 q^{2} - 11 q^{3} + 25 q^{4} - 6 q^{5} - 8 q^{6} - 5 q^{7} - 29 q^{8} - 11 q^{9} - 30 q^{10} - 14 q^{11} - 8 q^{12} + q^{13} - 2 q^{14} - 26 q^{15} + 25 q^{16} - 26 q^{17} - 3 q^{18} - 20 q^{19}+ \cdots - 74 q^{99}+O(q^{100}) $ 240 * q - 3 * q^2 - 11 * q^3 + 25 * q^4 - 6 * q^5 - 8 * q^6 - 5 * q^7 - 29 * q^8 - 11 * q^9 - 30 * q^10 - 14 * q^11 - 8 * q^12 + q^13 - 2 * q^14 - 26 * q^15 + 25 * q^16 - 26 * q^17 - 3 * q^18 - 20 * q^19 - 84 * q^20 + q^21 - 11 * q^22 - 6 * q^23 + 14 * q^24 + 174 * q^25 + 22 * q^26 + 70 * q^27 - 60 * q^28 - 15 * q^29 - 6 * q^30 - 20 * q^31 - 24 * q^32 - 40 * q^33 + 25 * q^34 - 15 * q^35 - 8 * q^36 + 2 * q^37 + 37 * q^38 - q^39 + 6 * q^40 - 23 * q^41 - 134 * q^42 + 9 * q^43 - 77 * q^44 - 127 * q^45 - 2 * q^46 - 32 * q^47 + 26 * q^48 - 41 * q^49 - 37 * q^50 + 13 * q^51 + 3 * q^52 - 56 * q^53 - 29 * q^54 - 30 * q^55 - 62 * q^56 - 40 * q^57 + 76 * q^58 - 3 * q^59 + 41 * q^60 - q^61 - 51 * q^62 + 77 * q^63 - 51 * q^64 + 25 * q^65 - 130 * q^66 - 16 * q^67 + 87 * q^68 + 32 * q^69 - 90 * q^70 - 7 * q^71 + 112 * q^72 - 11 * q^73 - 9 * q^74 - 157 * q^75 + 12 * q^76 + 10 * q^77 + 50 * q^78 + 24 * q^79 + 142 * q^80 + 61 * q^81 - 2 * q^82 + 60 * q^83 + 132 * q^84 - 33 * q^85 - 152 * q^86 - 88 * q^87 + 2 * q^88 + 58 * q^89 + 96 * q^90 + 72 * q^92 + 31 * q^93 + 2 * q^94 - 63 * q^95 + 137 * q^96 - 30 * q^97 + 33 * q^98 - 74 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/279\mathbb{Z}\right)^\times$.

$n$	$127$	$218$
$\chi(n)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.161525	−	1.53681i	0.114216	−	1.08669i	−0.775869	−	0.630894i	$-0.782688\pi$
$2$	0.161525	−	1.53681i	0.114216	−	1.08669i	0.890085	−	0.455795i	$-0.150645\pi$
$3$	0.550909	+	1.64210i	0.318067	+	0.948068i
$3$	0.550909	+	1.64210i	0.318067	+	0.948068i
$4$	−0.379403	−	0.0806445i	−0.189701	−	0.0403222i
$5$	−1.41277			−0.631809			−0.315905	−	0.948791i	$-0.602308\pi$
$5$	−1.41277			−0.631809			−0.315905	+	0.948791i	$0.602308\pi$
$6$	2.61259	−	0.581402i	1.06658	−	0.237356i
$7$	1.37134	+	4.22056i	0.518320	+	1.59522i	0.777160	+	0.629303i	$0.216660\pi$
$7$	1.37134	+	4.22056i	0.518320	+	1.59522i	−0.258840	+	0.965920i	$0.583340\pi$
$8$	0.769815	−	2.36925i	0.272171	−	0.837655i
$9$	−2.39300	+	1.80930i	−0.797666	+	0.603099i
$10$	−0.228198	+	2.17116i	−0.0721625	+	0.686581i
$11$	4.07876	+	0.866967i	1.22979	+	0.261400i	0.776589	−	0.630007i	$-0.216948\pi$
$11$	4.07876	+	0.866967i	1.22979	+	0.261400i	0.453203	+	0.891408i	$0.350281\pi$
$12$	−0.0765897	−	0.667445i	−0.0221095	−	0.192675i
$13$	−1.26368	+	0.918119i	−0.350483	+	0.254640i	−0.749071	−	0.662489i	$-0.769500\pi$
$13$	−1.26368	+	0.918119i	−0.350483	+	0.254640i	0.398589	+	0.917130i	$0.369500\pi$
$14$	6.70772	−	1.42577i	1.79271	−	0.381053i
$15$	−0.778307	−	2.31991i	−0.200958	−	0.598998i
$16$	−4.22543	−	1.88128i	−1.05636	−	0.470320i
$17$	−1.19367	−	1.32570i	−0.289507	−	0.321530i	0.580794	−	0.814051i	$-0.302742\pi$
$17$	−1.19367	−	1.32570i	−0.289507	−	0.321530i	−0.870301	+	0.492521i	$0.836076\pi$
$18$	2.39402	+	3.96983i	0.564275	+	0.935699i
$19$	5.06637	−	2.25569i	1.16230	−	0.517491i	0.267329	−	0.963605i	$-0.413859\pi$
$19$	5.06637	−	2.25569i	1.16230	−	0.517491i	0.894976	+	0.446114i	$0.147192\pi$
$20$	0.536008	+	0.113932i	0.119855	+	0.0254760i
$21$	−6.17511	+	4.57703i	−1.34752	+	0.998791i
$22$	1.99119	−	6.12824i	0.424522	−	1.30655i
$23$	1.76280	+	1.95778i	0.367568	+	0.408226i	0.898348	−	0.439283i	$-0.144768\pi$
$23$	1.76280	+	1.95778i	0.367568	+	0.408226i	−0.530780	+	0.847510i	$0.678101\pi$
$24$	4.31464	−	0.0411243i	0.880723	−	0.00839446i
$25$	−3.00408			−0.600817
$26$	1.20686	+	2.09034i	0.236685	+	0.409950i
$27$	−4.28938	−	2.93279i	−0.825491	−	0.564416i
$28$	−0.179926	−	1.71188i	−0.0340029	−	0.323516i
$29$	0.456042	−	4.33895i	0.0846849	−	0.805723i	−0.866930	−	0.498430i	$-0.833910\pi$
$29$	0.456042	−	4.33895i	0.0846849	−	0.805723i	0.951615	−	0.307293i	$-0.0994232\pi$
$30$	−3.69098	+	0.821386i	−0.673878	+	0.149964i
$31$	3.52023	+	4.31369i	0.632253	+	0.774762i
$31$	3.52023	+	4.31369i	0.632253	+	0.774762i
$32$	−1.08252	+	1.87497i	−0.191364	+	0.331451i
$33$	0.823376	+	7.17536i	0.143331	+	1.24907i
$34$	−2.23016	+	1.62031i	−0.382470	+	0.277880i
$35$	−1.93739	−	5.96268i	−0.327479	−	1.00788i
$36$	1.05382	−	0.493470i	0.175637	−	0.0822450i
$37$	4.15722	−	7.20052i	0.683444	−	1.18376i	−0.290480	−	0.956881i	$-0.593815\pi$
$37$	4.15722	−	7.20052i	0.683444	−	1.18376i	0.973923	−	0.226878i	$-0.0728518\pi$
$38$	−2.64823	−	8.15040i	−0.429599	−	1.32217i
$39$	−2.20382	−	1.56930i	−0.352894	−	0.251289i
$40$	−1.08757	+	3.34720i	−0.171960	+	0.529238i
$41$	−6.39798	−	4.64840i	−0.999197	−	0.725959i	−0.0372808	−	0.999305i	$-0.511870\pi$
$41$	−6.39798	−	4.64840i	−0.999197	−	0.725959i	−0.961916	+	0.273346i	$0.911870\pi$
$42$	6.03660	+	10.2293i	0.931468	+	1.57841i
$43$	−9.48607	−	6.89203i	−1.44661	−	1.05102i	−0.986608	−	0.163108i	$-0.947848\pi$
$43$	−9.48607	−	6.89203i	−1.44661	−	1.05102i	−0.460003	−	0.887917i	$-0.652152\pi$
$44$	−1.47757	−	0.657859i	−0.222753	−	0.0991759i
$45$	3.38075	−	2.55612i	0.503973	−	0.381044i
$46$	3.29348	−	2.39285i	0.485597	−	0.352807i
$47$	−3.40870	−	1.51765i	−0.497209	−	0.221372i	0.142782	−	0.989754i	$-0.454395\pi$
$47$	−3.40870	−	1.51765i	−0.497209	−	0.221372i	−0.639991	+	0.768382i	$0.721062\pi$
$48$	0.761431	−	7.97500i	0.109903	−	1.15109i
$49$	−10.2695	+	7.46120i	−1.46707	+	1.06589i
$50$	−0.485236	+	4.61671i	−0.0686227	+	0.652901i
$51$	1.51934	−	2.69047i	0.212750	−	0.376741i
$52$	0.553486	−	0.246428i	0.0767547	−	0.0341734i
$53$	−2.83644	+	0.602903i	−0.389615	+	0.0828151i	−0.398554	−	0.917145i	$-0.630488\pi$
$53$	−2.83644	+	0.602903i	−0.389615	+	0.0828151i	0.00893930	+	0.999960i	$0.497154\pi$
$54$	−5.19999	+	6.11824i	−0.707629	+	0.832587i
$55$	−5.76234	−	1.22482i	−0.776994	−	0.165155i
$56$	11.0552			1.47732
$57$	6.49519	+	7.07681i	0.860308	+	0.937347i
$58$	−6.59449	−	1.40170i	−0.865899	−	0.184052i
$59$	3.78905	+	1.68699i	0.493293	+	0.219628i	0.638278	−	0.769806i	$-0.279647\pi$
$59$	3.78905	+	1.68699i	0.493293	+	0.219628i	−0.144986	+	0.989434i	$0.546314\pi$
$60$	0.108204	+	0.942946i	0.0139690	+	0.121734i
$61$	5.16862	+	8.95232i	0.661775	+	1.14623i	0.980149	+	0.198262i	$0.0635298\pi$
$61$	5.16862	+	8.95232i	0.661775	+	1.14623i	−0.318374	+	0.947965i	$0.603137\pi$
$62$	7.19794	−	4.71316i	0.914139	−	0.598572i
$63$	−10.9179	−	7.61864i	−1.37552	−	0.959858i
$64$	−4.77728	−	3.47090i	−0.597160	−	0.433862i
$65$	1.78529	−	1.29709i	0.221438	−	0.160884i
$66$	11.1602	−	0.106371i	1.37372	−	0.0130934i
$67$	6.35170			0.775983			0.387992	−	0.921663i	$-0.373169\pi$
$67$	6.35170			0.775983			0.387992	+	0.921663i	$0.373169\pi$
$68$	0.345970	+	0.599238i	0.0419550	+	0.0726682i
$69$	−2.24374	+	3.97325i	−0.270115	+	0.478323i
$70$	−9.47645	+	2.01428i	−1.13265	+	0.240753i
$71$	8.09339	−	1.72030i	0.960509	−	0.204162i	0.299128	−	0.954213i	$-0.403304\pi$
$71$	8.09339	−	1.72030i	0.960509	−	0.204162i	0.661381	+	0.750050i	$0.269971\pi$
$72$	2.44450	+	7.06243i	0.288088	+	0.832315i
$73$	−2.56962	+	2.85385i	−0.300751	+	0.334018i	−0.874511	−	0.485005i	$-0.838818\pi$
$73$	−2.56962	+	2.85385i	−0.300751	+	0.334018i	0.573760	+	0.819024i	$0.305484\pi$
$74$	−10.3943	−	7.55194i	−1.20832	−	0.877895i
$75$	−1.65498	−	4.93301i	−0.191100	−	0.569615i
$76$	−2.10410	+	0.447241i	−0.241357	+	0.0513020i
$77$	1.93429	+	18.4036i	0.220433	+	2.09728i
$78$	−2.76768	+	3.13337i	−0.313379	+	0.354785i
$79$	−0.459260	+	1.41346i	−0.0516708	+	0.159026i	−0.973562	−	0.228422i	$-0.926643\pi$
$79$	−0.459260	+	1.41346i	−0.0516708	+	0.159026i	0.921891	+	0.387448i	$0.126643\pi$
$80$	5.96955	+	2.65782i	0.667416	+	0.297153i
$81$	2.45289	−	8.65929i	0.272543	−	0.962144i
$82$	−8.17716	+	9.08165i	−0.903016	+	1.00290i
$83$	−13.9084	+	6.19244i	−1.52665	+	0.679709i	−0.986784	−	0.162042i	$-0.948192\pi$
$83$	−13.9084	+	6.19244i	−1.52665	+	0.679709i	−0.539867	+	0.841751i	$0.681525\pi$
$84$	2.71197	−	1.23855i	0.295900	−	0.135137i
$85$	1.68638	+	1.87291i	0.182913	+	0.203146i
$86$	−12.1240	+	13.4651i	−1.30736	+	1.45197i
$87$	7.37624	−	1.64150i	0.790816	−	0.175987i
$88$	5.19395	−	8.99618i	0.553676	−	0.958996i
$89$	−2.59365	−	7.98244i	−0.274926	−	0.846136i	−0.989239	−	0.146310i	$-0.953260\pi$
$89$	−2.59365	−	7.98244i	−0.274926	−	0.846136i	0.714312	−	0.699827i	$-0.246740\pi$
$90$	−3.38219	−	5.60846i	−0.356515	−	0.591183i
$91$	−5.60793	−	4.07440i	−0.587870	−	0.427113i
$92$	−0.510925	−	0.884948i	−0.0532676	−	0.0922622i
$93$	−5.14420	+	8.15703i	−0.533429	+	0.845845i
$94$	−2.88293	+	4.99338i	−0.297352	+	0.515028i
$95$	−7.15761	+	3.18677i	−0.734355	+	0.326956i
$96$	−3.67526	−	0.744663i	−0.375105	−	0.0760018i
$97$	7.24842	−	8.05019i	0.735966	−	0.817373i	−0.252694	−	0.967546i	$-0.581317\pi$
$97$	7.24842	−	8.05019i	0.735966	−	0.817373i	0.988660	+	0.150173i	$0.0479832\pi$
$98$	9.80768	+	16.9874i	0.990725	+	1.71599i
$99$	−11.3291	+	5.30503i	−1.13861	+	0.533176i
$100$	1.13976	+	0.242263i	0.113976	+	0.0242263i
$101$	−4.57955	+	0.973413i	−0.455682	+	0.0968582i	−0.430034	−	0.902813i	$-0.641498\pi$
$101$	−4.57955	+	0.973413i	−0.455682	+	0.0968582i	−0.0256482	+	0.999671i	$0.508165\pi$
$102$	−3.88933	−	2.76951i	−0.385101	−	0.274223i
$103$	−0.866488	−	0.629540i	−0.0853776	−	0.0620304i	0.544278	−	0.838905i	$-0.316804\pi$
$103$	−0.866488	−	0.629540i	−0.0853776	−	0.0620304i	−0.629655	+	0.776875i	$0.716804\pi$
$104$	1.20245	+	3.70076i	0.117910	+	0.362889i
$105$	8.72400	−	6.46629i	0.851376	−	0.631045i
$106$	0.468392	+	4.45645i	0.0454943	+	0.432849i
$107$	6.29051	+	6.98632i	0.608126	+	0.675393i	0.966049	−	0.258358i	$-0.0831815\pi$
$107$	6.29051	+	6.98632i	0.608126	+	0.675393i	−0.357923	+	0.933751i	$0.616515\pi$
$108$	1.39089	+	1.45862i	0.133838	+	0.140356i
$109$	7.23552	−	5.25691i	0.693037	−	0.503521i	−0.184620	−	0.982810i	$-0.559105\pi$
$109$	7.23552	−	5.25691i	0.693037	−	0.503521i	0.877657	+	0.479289i	$0.159105\pi$
$110$	−2.81309	+	8.65779i	−0.268217	+	0.825488i
$111$	14.1142	+	2.85975i	1.33967	+	0.271436i
$112$	2.14555	−	20.4136i	0.202736	−	1.92890i
$113$	−4.53690	−	13.9631i	−0.426796	−	1.31354i	−0.901264	−	0.433270i	$-0.857360\pi$
$113$	−4.53690	−	13.9631i	−0.426796	−	1.31354i	0.474468	−	0.880273i	$-0.342640\pi$
$114$	11.9249	−	8.83879i	1.11687	−	0.827828i
$115$	−2.49042	−	2.76590i	−0.232233	−	0.257921i
$116$	−0.522936	+	1.60943i	−0.0485534	+	0.149432i
$117$	1.36284	−	4.48344i	0.125995	−	0.414494i
$118$	3.20462	−	5.55056i	0.295009	−	0.510971i
$119$	3.95828	−	6.85595i	0.362855	−	0.628484i
$120$	−6.09559	+	0.0580991i	−0.556449	+	0.00530370i
$121$	5.83563	+	2.59819i	0.530512	+	0.236199i
$122$	14.5929	−	6.49717i	1.32118	−	0.588226i
$123$	4.10845	−	13.0670i	0.370447	−	1.17821i
$124$	−0.987710	−	1.92051i	−0.0886989	−	0.172467i
$125$	11.3079			1.01141
$126$	−13.4719	+	15.5481i	−1.20017	+	1.38514i
$127$	−1.06414	−	10.1246i	−0.0944272	−	0.898414i	−0.934505	−	0.355949i	$-0.884158\pi$
$127$	−1.06414	−	10.1246i	−0.0944272	−	0.898414i	0.840078	−	0.542465i	$-0.182509\pi$
$128$	−9.00314	+	9.99900i	−0.795773	+	0.883795i
$129$	6.09146	−	19.3740i	0.536323	−	1.70578i
$130$	−1.70501	−	2.95317i	−0.149540	−	0.259010i
$131$	6.48100	−	7.19788i	0.566248	−	0.628882i	−0.390219	−	0.920722i	$-0.627601\pi$
$131$	6.48100	−	7.19788i	0.566248	−	0.628882i	0.956467	+	0.291840i	$0.0942675\pi$
$132$	0.266262	−	2.78875i	0.0231751	−	0.242729i
$133$	16.4680	+	18.2896i	1.42796	+	1.58591i
$134$	1.02596	−	9.76136i	0.0886294	−	0.843253i
$135$	6.05989	+	4.14335i	0.521553	+	0.356603i
$136$	−4.05982	+	1.80755i	−0.348127	+	0.154996i
$137$	0.695005	+	6.61253i	0.0593783	+	0.564947i	0.983252	+	0.182250i	$0.0583380\pi$
$137$	0.695005	+	6.61253i	0.0593783	+	0.564947i	−0.923874	+	0.382697i	$0.874995\pi$
$138$	5.74372	+	4.08999i	0.488938	+	0.348163i
$139$	1.05105	+	10.0001i	0.0891492	+	0.848198i	0.944138	+	0.329551i	$0.106897\pi$
$139$	1.05105	+	10.0001i	0.0891492	+	0.848198i	−0.854989	+	0.518647i	$0.826436\pi$
$140$	0.254194	+	2.41850i	0.0214833	+	0.204400i
$141$	0.614254	−	6.43351i	0.0517295	−	0.541800i
$142$	−1.33649	−	12.7159i	−0.112156	−	1.06709i
$143$	−5.95024	+	2.64922i	−0.497584	+	0.221539i
$144$	13.5152	−	3.14315i	1.12627	−	0.261929i
$145$	−0.644282	+	6.12994i	−0.0535047	+	0.509063i
$146$	3.97077	+	4.40999i	0.328623	+	0.364973i
$147$	−17.9096	−	12.7531i	−1.47716	−	1.05185i
$148$	−2.15794	+	2.39664i	−0.177382	+	0.197003i
$149$	−6.83665	−	11.8414i	−0.560080	−	0.970087i	−0.997489	−	0.0708243i	$-0.977437\pi$
$149$	−6.83665	−	11.8414i	−0.560080	−	0.970087i	0.437409	−	0.899263i	$-0.355896\pi$
$150$	−7.84843	+	1.74658i	−0.640822	+	0.142608i
$151$	6.19756	−	6.88309i	0.504351	−	0.560138i	−0.436175	−	0.899862i	$-0.643667\pi$
$151$	6.19756	−	6.88309i	0.504351	−	0.560138i	0.940525	+	0.339724i	$0.110334\pi$
$152$	−1.44413	−	13.7399i	−0.117134	−	1.11446i
$153$	5.25504	+	1.01270i	0.424845	+	0.0818723i
$154$	28.5952			2.30427
$155$	−4.97327	−	6.09425i	−0.399463	−	0.489502i
$156$	0.709580	+	0.773121i	0.0568118	+	0.0618992i
$157$	19.1614	−	8.53122i	1.52925	−	0.680866i	0.542048	−	0.840347i	$-0.317649\pi$
$157$	19.1614	−	8.53122i	1.52925	−	0.680866i	0.987201	+	0.159482i	$0.0509823\pi$
$158$	2.09803	+	0.934104i	0.166911	+	0.0743134i
$159$	−2.55265	−	4.32557i	−0.202438	−	0.343040i
$160$	1.52934	−	2.64890i	0.120905	−	0.209414i
$161$	−5.84555	+	10.1248i	−0.460694	+	0.797945i
$162$	−12.9115	−	5.16832i	−1.01442	−	0.406061i
$163$	−5.99564	+	18.4527i	−0.469615	+	1.44533i	0.383470	+	0.923553i	$0.374729\pi$
$163$	−5.99564	+	18.4527i	−0.469615	+	1.44533i	−0.853085	+	0.521773i	$0.825271\pi$
$164$	2.05254	+	2.27958i	0.160277	+	0.178005i
$165$	−1.16324	−	10.1371i	−0.0905581	−	0.789174i
$166$	7.27004	+	22.3749i	0.564265	+	1.73663i
$167$	−1.74333	+	16.5867i	−0.134903	+	1.28352i	0.692298	+	0.721612i	$0.256598\pi$
$167$	−1.74333	+	16.5867i	−0.134903	+	1.28352i	−0.827201	+	0.561906i	$0.810068\pi$
$168$	6.09043	+	18.1538i	0.469887	+	1.40060i
$169$	−3.26327	+	10.0433i	−0.251021	+	0.772562i
$170$	3.15070	−	2.28912i	0.241648	−	0.175567i
$171$	−8.04260	+	14.5644i	−0.615033	+	1.11377i
$172$	3.04323	+	3.37985i	0.232044	+	0.257711i
$173$	−0.521335	−	4.96017i	−0.0396364	−	0.377115i	−0.996302	−	0.0859250i	$-0.972615\pi$
$173$	−0.521335	−	4.96017i	−0.0396364	−	0.377115i	0.956665	−	0.291190i	$-0.0940512\pi$
$174$	−1.33122	−	11.6010i	−0.100920	−	0.879472i
$175$	−4.11964	−	12.6789i	−0.311415	−	0.958437i
$176$	−15.6035	−	11.3366i	−1.17616	−	0.854528i
$177$	−0.682795	+	7.15139i	−0.0513220	+	0.537531i
$178$	−12.6864	+	2.69658i	−0.950888	+	0.202118i
$179$	−9.34078	−	1.98544i	−0.698162	−	0.148399i	−0.154860	−	0.987936i	$-0.549493\pi$
$179$	−9.34078	−	1.98544i	−0.698162	−	0.148399i	−0.543302	+	0.839537i	$0.682826\pi$
$180$	−1.48880	+	0.697159i	−0.110969	+	0.0519631i
$181$	2.98599	+	5.17189i	0.221947	+	0.384424i	0.955399	−	0.295317i	$-0.0954254\pi$
$181$	2.98599	+	5.17189i	0.221947	+	0.384424i	−0.733452	+	0.679741i	$0.762092\pi$
$182$	−7.16740	+	7.96021i	−0.531283	+	0.590050i
$183$	−11.8532	+	13.4193i	−0.876213	+	0.991985i
$184$	5.99550	−	2.66937i	0.441994	−	0.196788i
$185$	−5.87320	+	10.1727i	−0.431806	+	0.747910i
$186$	11.7049	+	9.22323i	0.858245	+	0.676280i
$187$	−3.71934	−	6.44209i	−0.271985	−	0.471092i
$188$	1.17088	+	0.850693i	0.0853950	+	0.0620431i
$189$	6.49582	−	22.1255i	0.472501	−	1.60939i
$190$	3.74133	+	11.5146i	0.271425	+	0.835359i
$191$	8.32024	−	14.4111i	0.602031	−	1.04275i	−0.390482	−	0.920611i	$-0.627692\pi$
$191$	8.32024	−	14.4111i	0.602031	−	1.04275i	0.992513	−	0.122138i	$-0.0389750\pi$
$192$	3.06772	−	9.75693i	0.221394	−	0.704146i
$193$	4.10886	−	4.56335i	0.295762	−	0.328477i	−0.576888	−	0.816824i	$-0.695733\pi$
$193$	4.10886	−	4.56335i	0.295762	−	0.328477i	0.872650	+	0.488346i	$0.162400\pi$
$194$	−11.2008	−	12.4398i	−0.804172	−	0.893123i
$195$	3.11349	+	2.21705i	0.222961	+	0.158766i
$196$	4.49796	−	2.00262i	0.321283	−	0.143044i
$197$	−7.51763	+	8.34917i	−0.535609	+	0.594854i	−0.948834	−	0.315775i	$-0.897735\pi$
$197$	−7.51763	+	8.34917i	−0.535609	+	0.594854i	0.413225	+	0.910629i	$0.364402\pi$
$198$	6.32291	+	18.2675i	0.449349	+	1.29822i
$199$	1.71333	+	0.762823i	0.121455	+	0.0540751i	0.466564	−	0.884487i	$-0.345492\pi$
$199$	1.71333	+	0.762823i	0.121455	+	0.0540751i	−0.345110	+	0.938562i	$0.612158\pi$
$200$	−2.31259	+	7.11742i	−0.163525	+	0.503277i
$201$	3.49921	+	10.4301i	0.246815	+	0.735685i
$202$	0.756238	+	7.19513i	0.0532087	+	0.506247i
$203$	18.9382	−	4.02544i	1.32920	−	0.282531i
$204$	−0.793412	+	0.898243i	−0.0555499	+	0.0628896i
$205$	9.03887	+	6.56712i	0.631302	+	0.458668i
$206$	−1.10744	+	1.22994i	−0.0771593	+	0.0856941i
$207$	−7.76058	−	1.49555i	−0.539398	−	0.103948i
$208$	7.06684	−	1.50210i	0.489997	−	0.104152i
$209$	22.6201	−	4.80805i	1.56467	−	0.332580i
$210$	−8.52832	−	14.4516i	−0.588510	−	0.997256i
$211$	−2.71690	−	4.70581i	−0.187039	−	0.323961i	0.757223	−	0.653157i	$-0.226556\pi$
$211$	−2.71690	−	4.70581i	−0.187039	−	0.323961i	−0.944262	+	0.329196i	$0.893222\pi$
$212$	1.12477			0.0772497
$213$	7.28363	+	12.3424i	0.499066	+	0.845690i
$214$	11.7527	−	8.53886i	0.803400	−	0.583704i
$215$	13.4016	+	9.73685i	0.913983	+	0.664047i
$216$	−10.2505	+	7.90488i	−0.697460	+	0.537859i
$217$	−13.3788	+	20.7729i	−0.908210	+	1.41016i
$218$	−6.91016	−	11.9688i	−0.468015	−	0.810626i
$219$	−6.10194	−	2.64737i	−0.412331	−	0.178892i
$220$	2.08747	+	0.929402i	0.140737	+	0.0626603i
$221$	2.72557	+	0.579338i	0.183342	+	0.0389705i
$222$	6.67471	−	21.2290i	0.447977	−	1.42480i
$223$	−1.22705			−0.0821694			−0.0410847	−	0.999156i	$-0.513081\pi$
$223$	−1.22705			−0.0821694			−0.0410847	+	0.999156i	$0.513081\pi$
$224$	−9.39794	−	1.99759i	−0.627927	−	0.133470i
$225$	7.18877	−	5.43528i	0.479251	−	0.362352i
$226$	−22.1915	+	4.71696i	−1.47616	+	0.313767i
$227$	−20.5874	+	9.16609i	−1.36643	+	0.608375i	−0.953225	−	0.302263i	$-0.902258\pi$
$227$	−20.5874	+	9.16609i	−1.36643	+	0.608375i	−0.413207	+	0.910637i	$0.635591\pi$
$228$	−1.89358	−	3.20876i	−0.125406	−	0.212505i
$229$	−0.793202	+	7.54681i	−0.0524163	+	0.498707i	0.936547	+	0.350543i	$0.114003\pi$
$229$	−0.793202	+	7.54681i	−0.0524163	+	0.498707i	−0.988963	+	0.148164i	$0.952664\pi$
$230$	−4.65293	+	3.38055i	−0.306805	+	0.222907i
$231$	−29.1549	+	13.3150i	−1.91825	+	0.876062i
$232$	−9.92898	−	4.42067i	−0.651869	−	0.290231i
$233$	−8.41899	+	6.11675i	−0.551546	+	0.400722i	−0.828355	−	0.560203i	$-0.810723\pi$
$233$	−8.41899	+	6.11675i	−0.551546	+	0.400722i	0.276809	+	0.960925i	$0.410723\pi$
$234$	−6.67006	−	2.81862i	−0.436036	−	0.184259i
$235$	4.81570	+	2.14409i	0.314142	+	0.139865i
$236$	−1.30153	−	0.945616i	−0.0847223	−	0.0615544i
$237$	−2.57405	+	0.0245341i	−0.167202	+	0.00159366i
$238$	−9.89693	−	7.19054i	−0.641523	−	0.466094i
$239$	−5.55167	+	17.0863i	−0.359108	+	1.10522i	0.594481	+	0.804110i	$0.297358\pi$
$239$	−5.55167	+	17.0863i	−0.359108	+	1.10522i	−0.953589	+	0.301111i	$0.902642\pi$
$240$	−1.07573	+	11.2668i	−0.0694378	+	0.727271i
$241$	5.27286	+	16.2282i	0.339655	+	1.04535i	0.964383	+	0.264508i	$0.0852096\pi$
$241$	5.27286	+	16.2282i	0.339655	+	1.04535i	−0.624729	+	0.780842i	$0.714790\pi$
$242$	4.93553	−	8.54859i	0.317268	−	0.549524i
$243$	15.5708	−	0.742590i	0.998865	−	0.0476372i
$244$	−1.23903	−	3.81335i	−0.0793210	−	0.244125i
$245$	14.5084	−	10.5409i	0.926906	−	0.673436i
$246$	−19.4179	−	8.42456i	−1.23804	−	0.537130i
$247$	−4.33129	+	7.50201i	−0.275593	+	0.477342i
$248$	12.9301	−	5.01955i	0.821064	−	0.318742i
$249$	−17.8309	−	19.4276i	−1.12999	−	1.23118i
$250$	1.82652	−	17.3781i	0.115519	−	1.09909i
$251$	2.51881	+	23.9648i	0.158986	+	1.51265i	0.725286	+	0.688448i	$0.241708\pi$
$251$	2.51881	+	23.9648i	0.158986	+	1.51265i	−0.566300	+	0.824199i	$0.691626\pi$
$252$	3.52787	+	3.77100i	0.222235	+	0.237550i
$253$	5.49269	+	9.51361i	0.345322	+	0.598116i
$254$	−15.7315			−0.987083
$255$	−2.14647	+	3.80101i	−0.134417	+	0.238028i
$256$	6.00985	+	6.67462i	0.375616	+	0.417164i
$257$	−9.38733	+	28.8912i	−0.585565	+	1.80219i	0.0114223	+	0.999935i	$0.496364\pi$
$257$	−9.38733	+	28.8912i	−0.585565	+	1.80219i	−0.596988	+	0.802250i	$0.703636\pi$
$258$	−28.7902	−	12.4908i	−1.79240	−	0.777644i
$259$	36.0913	+	7.67144i	2.24260	+	0.476680i
$260$	−0.781947	+	0.348145i	−0.0484943	+	0.0215911i
$261$	6.75915	+	11.2082i	0.418381	+	0.693772i
$262$	−10.0149	−	11.1227i	−0.618725	−	0.687164i
$263$	−19.0018	−	8.46013i	−1.17170	−	0.521674i	−0.273761	−	0.961798i	$-0.588268\pi$
$263$	−19.0018	−	8.46013i	−1.17170	−	0.521674i	−0.897937	+	0.440124i	$0.854935\pi$
$264$	17.6340	+	3.57292i	1.08530	+	0.219898i
$265$	4.00723	−	0.851763i	0.246162	−	0.0523234i
$266$	30.7677	−	22.3540i	1.88649	−	1.37061i
$267$	11.6791	−	8.65663i	0.714750	−	0.529777i
$268$	−2.40985	−	0.512229i	−0.147205	−	0.0312894i
$269$	−2.53132	+	24.0839i	−0.154337	+	1.46842i	0.593659	+	0.804717i	$0.297683\pi$
$269$	−2.53132	+	24.0839i	−0.154337	+	1.46842i	−0.747996	+	0.663703i	$0.768984\pi$
$270$	7.34638	−	8.64366i	0.447086	−	0.526036i
$271$	5.60516	−	17.2509i	0.340489	−	1.04792i	−0.623465	−	0.781851i	$-0.714276\pi$
$271$	5.60516	−	17.2509i	0.340489	−	1.04792i	0.963955	−	0.266067i	$-0.0857243\pi$
$272$	2.54974	+	7.84729i	0.154601	+	0.475812i
$273$	3.60112	−	11.4534i	0.217950	−	0.693192i
$274$	10.2745			0.620704
$275$	−12.2529	−	2.60444i	−0.738880	−	0.157054i
$276$	1.17170	−	1.32652i	0.0705282	−	0.0798469i
$277$	1.73186	−	16.4776i	0.104057	−	0.990040i	−0.810542	−	0.585680i	$-0.800828\pi$
$277$	1.73186	−	16.4776i	0.104057	−	0.990040i	0.914600	−	0.404360i	$-0.132506\pi$
$278$	15.5380			0.931910
$279$	−16.2287	−	3.95352i	−0.971585	−	0.236691i
$280$	−15.6185			−0.933383
$281$	1.96241	−	18.6710i	0.117067	−	1.11382i	−0.765435	−	0.643513i	$-0.777476\pi$
$281$	1.96241	−	18.6710i	0.117067	−	1.11382i	0.882502	−	0.470308i	$-0.155857\pi$
$282$	−9.78788	−	1.98317i	−0.582860	−	0.118096i
$283$	−6.76446	−	1.43783i	−0.402105	−	0.0854701i	0.00241970	−	0.999997i	$-0.499230\pi$
$283$	−6.76446	−	1.43783i	−0.402105	−	0.0854701i	−0.404525	+	0.914527i	$0.632563\pi$
$284$	−3.20939			−0.190442
$285$	−9.17620	−	9.99790i	−0.543551	−	0.592225i
$286$	3.11023	+	9.57230i	0.183912	+	0.566022i
$287$	10.8451	−	33.3777i	0.640163	−	1.97022i
$288$	−0.801923	−	6.44540i	−0.0472538	−	0.379799i
$289$	1.44434	−	13.7420i	0.0849612	−	0.808351i
$290$	9.31649	+	1.98028i	0.547083	+	0.116286i
$291$	17.2125	+	7.46773i	1.00901	+	0.437766i
$292$	1.20507	−	0.875533i	0.0705212	−	0.0512367i
$293$	−15.7294	+	3.34338i	−0.918920	+	0.195322i	−0.643007	−	0.765860i	$-0.722313\pi$
$293$	−15.7294	+	3.34338i	−0.918920	+	0.195322i	−0.275913	+	0.961183i	$0.588980\pi$
$294$	−22.4919	+	25.4637i	−1.31175	+	1.48507i
$295$	−5.35305	−	2.38333i	−0.311667	−	0.138763i
$296$	−13.8595	−	15.3926i	−0.805568	−	0.894674i
$297$	−14.9527	−	15.6809i	−0.867643	−	0.909897i
$298$	−19.3023	+	8.59395i	−1.11815	+	0.497834i
$299$	−4.02509	−	0.855560i	−0.232777	−	0.0494783i
$300$	0.230082	+	2.00506i	0.0132838	+	0.115762i
$301$	16.0796	−	49.4879i	0.926813	−	2.85244i
$302$	−9.57695	−	10.6363i	−0.551091	−	0.612049i
$303$	−4.12136	−	6.98382i	−0.236766	−	0.401210i
$304$	−25.6512			−1.47120
$305$	−7.30207	−	12.6476i	−0.418115	−	0.724197i
$306$	2.40516	−	7.91242i	0.137494	−	0.452323i
$307$	0.828269	+	7.88046i	0.0472718	+	0.449761i	0.992399	+	0.123060i	$0.0392706\pi$
$307$	0.828269	+	7.88046i	0.0472718	+	0.449761i	−0.945127	+	0.326702i	$0.894063\pi$
$308$	0.750271	−	7.13835i	0.0427507	−	0.406745i
$309$	0.556414	−	1.76968i	0.0316533	−	0.100674i
$310$	−10.1690	+	6.65861i	−0.577562	+	0.378184i
$311$	3.37889	−	5.85241i	0.191599	−	0.331860i	−0.754181	−	0.656666i	$-0.771966\pi$
$311$	3.37889	−	5.85241i	0.191599	−	0.331860i	0.945780	+	0.324807i	$0.105299\pi$
$312$	−5.41458	+	4.01332i	−0.306540	+	0.227210i
$313$	−16.1233	+	11.7143i	−0.911343	+	0.662129i	−0.941354	−	0.337420i	$-0.890446\pi$
$313$	−16.1233	+	11.7143i	−0.911343	+	0.662129i	0.0300111	+	0.999550i	$0.490446\pi$
$314$	−10.0158	−	30.8255i	−0.565225	−	1.73958i
$315$	15.4244	+	10.7634i	0.869069	+	0.606447i
$316$	0.288232	−	0.499232i	0.0162143	−	0.0280840i
$317$	7.24296	+	22.2915i	0.406805	+	1.25202i	0.919379	+	0.393374i	$0.128692\pi$
$317$	7.24296	+	22.2915i	0.406805	+	1.25202i	−0.512574	+	0.858643i	$0.671308\pi$
$318$	−7.05991	+	3.22425i	−0.395900	+	0.180807i
$319$	5.62181	−	17.3022i	0.314761	−	0.968735i
$320$	6.74919	+	4.90357i	0.377291	+	0.274118i
$321$	−8.00675	+	14.1785i	−0.446893	+	0.791366i
$322$	14.6157	+	10.6189i	0.814500	+	0.591769i
$323$	−9.03794	−	4.02395i	−0.502885	−	0.223899i
$324$	−1.62896	+	3.08755i	−0.0904975	+	0.171530i
$325$	3.79621	−	2.75811i	0.210576	−	0.152992i
$326$	27.3898	+	12.1947i	1.51698	+	0.675404i
$327$	12.6185	+	8.98539i	0.697805	+	0.496893i
$328$	−15.9385	+	11.5800i	−0.880055	+	0.639397i
$329$	1.73084	−	16.4678i	0.0954243	−	0.907902i
$330$	−15.7667	+	0.150278i	−0.867930	+	0.00827253i
$331$	−8.00991	+	3.56624i	−0.440265	+	0.196018i	−0.614884	−	0.788618i	$-0.710797\pi$
$331$	−8.00991	+	3.56624i	−0.440265	+	0.196018i	0.174619	+	0.984636i	$0.444131\pi$
$332$	5.77629	−	1.22779i	0.317015	−	0.0673836i
$333$	3.07966	+	24.7525i	0.168764	+	1.35643i
$334$	25.2090	+	5.35835i	1.37938	+	0.293196i
$335$	−8.97348			−0.490273
$336$	34.7032	−	7.72280i	1.89321	−	0.421313i
$337$	6.90804	+	1.46835i	0.376305	+	0.0799860i	0.392181	−	0.919888i	$-0.371721\pi$
$337$	6.90804	+	1.46835i	0.376305	+	0.0799860i	−0.0158766	+	0.999874i	$0.505054\pi$
$338$	14.9076	+	6.63728i	0.810865	+	0.361020i
$339$	20.4295	−	15.1425i	1.10958	−	0.822427i
$340$	−0.488776	−	0.846584i	−0.0265076	−	0.0459125i
$341$	10.6183	+	20.6464i	0.575016	+	1.11807i
$342$	21.0837	+	14.7125i	1.14008	+	0.795560i
$343$	−20.4419	−	14.8519i	−1.10376	−	0.801926i
$344$	−23.6314	+	17.1692i	−1.27412	+	0.925703i
$345$	3.16989	−	5.61329i	0.170661	−	0.302209i
$346$	−7.70706			−0.414334
$347$	5.68131	+	9.84031i	0.304988	+	0.528255i	0.977259	−	0.212050i	$-0.0680141\pi$
$347$	5.68131	+	9.84031i	0.304988	+	0.528255i	−0.672270	+	0.740306i	$0.734681\pi$
$348$	−2.93094	+	0.0279358i	−0.157115	+	0.00149751i
$349$	18.8477	−	4.00621i	1.00890	−	0.214448i	0.326318	−	0.945260i	$-0.394192\pi$
$349$	18.8477	−	4.00621i	1.00890	−	0.214448i	0.682579	+	0.730812i	$0.260859\pi$
$350$	−20.1506	+	4.28313i	−1.07709	+	0.228943i
$351$	8.11306	−	0.232041i	0.433043	−	0.0123854i
$352$	−6.04086	+	6.70905i	−0.321979	+	0.357594i
$353$	3.35208	+	2.43543i	0.178413	+	0.129625i	0.673408	−	0.739271i	$-0.264830\pi$
$353$	3.35208	+	2.43543i	0.178413	+	0.129625i	−0.494995	+	0.868896i	$0.664830\pi$
$354$	10.8800	+	2.20446i	0.578268	+	0.117166i
$355$	−11.4341	+	2.43039i	−0.606858	+	0.128992i
$356$	0.340298	+	3.23772i	0.0180358	+	0.171599i
$357$	13.4388	+	2.72290i	0.711258	+	0.144111i
$358$	−4.56002	+	14.0343i	−0.241005	+	0.741736i
$359$	24.8411	+	11.0600i	1.31106	+	0.583722i	0.938818	−	0.344413i	$-0.111922\pi$
$359$	24.8411	+	11.0600i	1.31106	+	0.583722i	0.372243	+	0.928135i	$0.378589\pi$
$360$	−3.45352	−	9.97758i	−0.182016	−	0.525864i
$361$	7.86647	−	8.73660i	0.414025	−	0.459821i
$362$	8.43054	−	3.75352i	0.443099	−	0.197280i
$363$	−1.05159	+	11.0141i	−0.0551943	+	0.578089i
$364$	1.79908	+	1.99808i	0.0942976	+	0.104728i
$365$	3.63028	−	4.03183i	0.190017	−	0.211036i
$366$	18.7084	+	20.3837i	0.977902	+	1.06547i
$367$	−13.9043	+	24.0829i	−0.725797	+	1.25712i	0.232848	+	0.972513i	$0.425195\pi$
$367$	−13.9043	+	24.0829i	−0.725797	+	1.25712i	−0.958645	+	0.284604i	$0.908138\pi$
$368$	−3.76543	−	11.5888i	−0.196286	−	0.604108i
$369$	23.7207	−	0.452221i	1.23485	−	0.0235417i
$370$	14.6848	+	10.6691i	0.763427	+	0.554662i
$371$	−6.43433	−	11.1446i	−0.334054	−	0.578598i
$372$	2.60954	−	2.67995i	0.135298	−	0.138949i
$373$	−12.3231	+	21.3443i	−0.638068	+	1.10517i	0.347789	+	0.937573i	$0.386933\pi$
$373$	−12.3231	+	21.3443i	−0.638068	+	1.10517i	−0.985856	+	0.167593i	$0.946401\pi$
$374$	−10.5010	+	4.67537i	−0.542996	+	0.241757i
$375$	6.22963	+	18.5688i	0.321697	+	0.958887i
$376$	−6.21975	+	6.90773i	−0.320759	+	0.356239i
$377$	3.40738	+	5.90176i	0.175489	+	0.303956i
$378$	−32.9534	−	13.5567i	−1.69494	−	0.697280i
$379$	−24.5949	−	5.22781i	−1.26336	−	0.268535i	−0.472935	−	0.881098i	$-0.656805\pi$
$379$	−24.5949	−	5.22781i	−1.26336	−	0.268535i	−0.790422	+	0.612563i	$0.790139\pi$
$380$	2.97261	−	0.631848i	0.152492	−	0.0324131i
$381$	16.0394	−	7.32517i	0.821724	−	0.375280i
$382$	−20.8032	−	15.1144i	−1.06438	−	0.773319i
$383$	−3.21460	−	9.89353i	−0.164259	−	0.505536i	0.834722	−	0.550671i	$-0.185628\pi$
$383$	−3.21460	−	9.89353i	−0.164259	−	0.505536i	−0.998981	+	0.0451352i	$0.985628\pi$
$384$	−21.3793	−	9.27554i	−1.09101	−	0.473340i
$385$	−2.73271	−	26.0000i	−0.139272	−	1.32508i
$386$	−6.34933	−	7.05164i	−0.323172	−	0.358919i
$387$	35.1699	−	0.670492i	1.78779	−	0.0340830i
$388$	−3.39927	+	2.46972i	−0.172572	+	0.125381i
$389$	−9.28281	+	28.5696i	−0.470657	+	1.44853i	0.381069	+	0.924547i	$0.375556\pi$
$389$	−9.28281	+	28.5696i	−0.470657	+	1.44853i	−0.851726	+	0.523987i	$0.824444\pi$
$390$	3.91010	−	4.42673i	0.197996	−	0.224156i
$391$	0.491245	−	4.67389i	0.0248433	−	0.236369i
$392$	9.77184	+	30.0746i	0.493552	+	1.51900i
$393$	15.3901	+	6.67709i	0.776328	+	0.336815i
$394$	11.6168	+	12.9018i	0.585246	+	0.649982i
$395$	0.648828	−	1.99689i	0.0326461	−	0.100474i
$396$	4.72610	−	1.09912i	0.237495	−	0.0552327i
$397$	0.863906	−	1.49633i	0.0433582	−	0.0750986i	−0.843532	−	0.537079i	$-0.819528\pi$
$397$	0.863906	−	1.49633i	0.0433582	−	0.0750986i	0.886890	+	0.461981i	$0.152861\pi$
$398$	1.44906	−	2.50985i	0.0726348	−	0.125807i
$399$	−20.9610	+	37.1181i	−1.04936	+	1.85823i
$400$	12.6935	+	5.65153i	0.634677	+	0.282577i
$401$	−12.1259	+	5.39881i	−0.605540	+	0.269604i	−0.686519	−	0.727112i	$-0.740862\pi$
$401$	−12.1259	+	5.39881i	−0.605540	+	0.269604i	0.0809787	+	0.996716i	$0.474195\pi$
$402$	16.5944	−	3.69289i	0.827651	−	0.184184i
$403$	−8.40894	−	2.21915i	−0.418879	−	0.110544i
$404$	1.81599			0.0903490
$405$	−3.46536	+	12.2336i	−0.172195	+	0.607891i
$406$	−3.12734	−	29.7547i	−0.155207	−	1.47670i
$407$	23.1989	−	25.7650i	1.14993	−	1.27712i
$408$	−5.20477	−	5.67084i	−0.257674	−	0.280749i
$409$	−11.9365	−	20.6747i	−0.590223	−	1.02230i	−0.994202	−	0.107528i	$-0.965707\pi$
$409$	−11.9365	−	20.6747i	−0.590223	−	1.02230i	0.403979	−	0.914768i	$-0.367627\pi$
$410$	11.5524	−	12.8303i	0.570534	−	0.633642i
$411$	−10.4756	+	4.78417i	−0.516722	+	0.235986i
$412$	0.277979	+	0.308727i	0.0136950	+	0.0152099i
$413$	−1.92397	+	18.3054i	−0.0946726	+	0.900749i
$414$	−3.55191	+	11.6850i	−0.174567	+	0.574285i
$415$	19.6494	−	8.74849i	0.964552	−	0.429446i
$416$	−0.353492	−	3.36325i	−0.0173314	−	0.164897i
$417$	−15.8422	+	7.23508i	−0.775794	+	0.354304i
$418$	−3.73535	−	35.5394i	−0.182702	−	1.73829i
$419$	−1.50811	−	14.3488i	−0.0736762	−	0.700982i	−0.967553	−	0.252669i	$-0.918692\pi$
$419$	−1.50811	−	14.3488i	−0.0736762	−	0.700982i	0.893877	−	0.448313i	$-0.147975\pi$
$420$	−3.83138	+	1.74978i	−0.186952	+	0.0853807i
$421$	−0.812774	−	7.73303i	−0.0396122	−	0.376885i	−0.996312	−	0.0858075i	$-0.972653\pi$
$421$	−0.812774	−	7.73303i	−0.0396122	−	0.376885i	0.956700	−	0.291077i	$-0.0940137\pi$
$422$	−7.67079	+	3.41525i	−0.373408	+	0.166252i
$423$	10.9029	−	2.53561i	0.530116	−	0.123286i
$424$	−0.755105	+	7.18434i	−0.0366711	+	0.348903i
$425$	3.58588	+	3.98252i	0.173941	+	0.193181i
$426$	20.1445	−	9.19995i	0.976004	−	0.445739i
$427$	−30.6959	+	34.0912i	−1.48548	+	1.64979i
$428$	−1.82323	−	3.15792i	−0.0881290	−	0.152644i
$429$	−7.62832	−	8.31142i	−0.368299	−	0.401279i
$430$	17.1284	−	19.0230i	0.826004	−	0.917371i
$431$	−2.32585	−	22.1290i	−0.112032	−	1.06592i	−0.895676	−	0.444706i	$-0.853308\pi$
$431$	−2.32585	−	22.1290i	−0.112032	−	1.06592i	0.783644	−	0.621210i	$-0.213359\pi$
$432$	12.6070	+	20.4618i	0.606557	+	0.984470i
$433$	−5.47868			−0.263288			−0.131644	−	0.991297i	$-0.542026\pi$
$433$	−5.47868			−0.263288			−0.131644	+	0.991297i	$0.542026\pi$
$434$	29.7631	+	23.9160i	1.42867	+	1.14800i
$435$	−10.4209	+	2.31906i	−0.499645	+	0.111190i
$436$	−3.16912	+	1.41098i	−0.151773	+	0.0675738i
$437$	13.3471	+	5.94253i	0.638480	+	0.284270i
$438$	−5.05412	+	8.94992i	−0.241495	+	0.427643i
$439$	0.699441	−	1.21147i	0.0333825	−	0.0578202i	−0.848851	−	0.528631i	$-0.822705\pi$
$439$	0.699441	−	1.21147i	0.0333825	−	0.0578202i	0.882234	+	0.470811i	$0.156039\pi$
$440$	−7.33784	+	12.7095i	−0.349818	+	0.605902i
$441$	11.0753	−	36.4351i	0.527394	−	1.73501i
$442$	1.33058	−	4.09511i	0.0632893	−	0.194785i
$443$	1.25216	+	1.39067i	0.0594921	+	0.0660726i	0.772156	−	0.635433i	$-0.219178\pi$
$443$	1.25216	+	1.39067i	0.0594921	+	0.0660726i	−0.712664	+	0.701505i	$0.752512\pi$
$444$	−5.12436	−	2.22323i	−0.243191	−	0.105510i
$445$	3.66423	+	11.2773i	0.173701	+	0.534597i
$446$	−0.198200	+	1.88575i	−0.00938504	+	0.0892927i
$447$	15.6785	−	17.7500i	0.741565	−	0.839547i
$448$	8.09785	−	24.9226i	0.382587	−	1.17748i
$449$	23.2851	−	16.9176i	1.09889	−	0.798392i	0.118014	−	0.993012i	$-0.462347\pi$
$449$	23.2851	−	16.9176i	1.09889	−	0.798392i	0.980879	+	0.194620i	$0.0623473\pi$
$450$	−7.19183	−	11.9257i	−0.339026	−	0.562184i
$451$	−22.0658	−	24.5066i	−1.03904	−	1.15397i
$452$	0.595261	+	5.66353i	0.0279987	+	0.266390i
$453$	14.7170	+	6.38508i	0.691467	+	0.299997i
$454$	10.7612	+	33.1194i	0.505046	+	1.55437i
$455$	7.92270	+	5.75618i	0.371422	+	0.269854i
$456$	21.7668	−	9.94086i	1.01932	−	0.465523i
$457$	−20.2831	+	4.31131i	−0.948805	+	0.201675i	−0.656224	−	0.754566i	$-0.727847\pi$
$457$	−20.2831	+	4.31131i	−0.948805	+	0.201675i	−0.292581	+	0.956241i	$0.594514\pi$
$458$	11.4699	+	2.43800i	0.535953	+	0.113920i
$459$	1.23208	+	9.18721i	0.0575086	+	0.428822i
$460$	0.721819	+	1.25023i	0.0336550	+	0.0582921i
$461$	8.58479	−	9.53438i	0.399834	−	0.444060i	−0.509285	−	0.860598i	$-0.670090\pi$
$461$	8.58479	−	9.53438i	0.399834	−	0.444060i	0.909118	+	0.416538i	$0.136757\pi$
$462$	15.7534	+	46.9563i	0.732913	+	2.18461i
$463$	13.6127	−	6.06076i	0.632635	−	0.281667i	−0.0652588	−	0.997868i	$-0.520787\pi$
$463$	13.6127	−	6.06076i	0.632635	−	0.281667i	0.697894	+	0.716201i	$0.254121\pi$
$464$	−10.0898	+	17.4760i	−0.468406	+	0.811302i
$465$	7.26756	−	11.5240i	0.337025	−	0.534413i
$466$	8.04041	+	13.9264i	0.372465	+	0.645128i
$467$	−6.02533	−	4.37766i	−0.278819	−	0.202574i	0.439583	−	0.898202i	$-0.355126\pi$
$467$	−6.02533	−	4.37766i	−0.278819	−	0.202574i	−0.718402	+	0.695628i	$0.755126\pi$
$468$	−0.878630	+	1.59112i	−0.0406147	+	0.0735496i
$469$	8.71036	+	26.8077i	0.402207	+	1.23787i
$470$	4.07291	−	7.05449i	0.187870	−	0.325400i
$471$	24.5653	+	26.7651i	1.13191	+	1.23327i
$472$	6.91377	−	7.67852i	0.318232	−	0.353433i
$473$	−32.7162	−	36.3350i	−1.50429	−	1.67069i
$474$	−0.378070	+	3.95979i	−0.0173653	+	0.181879i
$475$	−15.2198	+	6.77629i	−0.698332	+	0.310918i
$476$	−2.05468	+	2.28195i	−0.0941760	+	0.104593i
$477$	5.69676	−	6.57471i	0.260837	−	0.301035i
$478$	25.3617	+	11.2917i	1.16002	+	0.516472i
$479$	−0.344165	+	1.05923i	−0.0157253	+	0.0483975i	−0.958611	−	0.284718i	$-0.908100\pi$
$479$	−0.344165	+	1.05923i	−0.0157253	+	0.0483975i	0.942886	+	0.333116i	$0.108100\pi$
$480$	5.19230	+	1.05204i	0.236995	+	0.0480187i
$481$	1.35753	+	12.9160i	0.0618979	+	0.588919i
$482$	25.7914	−	5.48212i	1.17476	−	0.249704i
$483$	−19.8463	−	4.02115i	−0.903038	−	0.182969i
$484$	−2.00452	−	1.45637i	−0.0911147	−	0.0661987i
$485$	−10.2403	+	11.3731i	−0.464990	+	0.516424i
$486$	1.37385	−	24.0493i	0.0623192	−	1.09090i
$487$	−28.6358	+	6.08672i	−1.29761	+	0.275816i	−0.804397	−	0.594092i	$-0.797511\pi$
$487$	−28.6358	+	6.08672i	−1.29761	+	0.275816i	−0.493214	+	0.869908i	$0.664178\pi$
$488$	25.1891	−	5.35412i	1.14026	−	0.242369i
$489$	−33.6042	+	0.320293i	−1.51964	+	0.0144842i
$490$	−13.8560	−	23.9993i	−0.625949	−	1.08418i
$491$	18.7565			0.846470			0.423235	−	0.906020i	$-0.360894\pi$
$491$	18.7565			0.846470			0.423235	+	0.906020i	$0.360894\pi$
$492$	−2.61254	+	4.62632i	−0.117782	+	0.208571i
$493$	−6.29652	+	4.57469i	−0.283581	+	0.206034i
$494$	10.8296	+	7.86814i	0.487245	+	0.354004i
$495$	16.0053	−	7.49479i	0.719387	−	0.336866i
$496$	−6.75922	−	24.8498i	−0.303498	−	1.11579i
$497$	18.3595	+	31.7995i	0.823535	+	1.42640i
$498$	−32.7367	+	24.2647i	−1.46697	+	1.08733i
$499$	−39.9349	−	17.7802i	−1.78773	−	0.795950i	−0.977835	−	0.209379i	$-0.932856\pi$
$499$	−39.9349	−	17.7802i	−1.78773	−	0.795950i	−0.809898	−	0.586571i	$-0.800478\pi$
$500$	−4.29025	−	0.911921i	−0.191866	−	0.0407824i
$501$	−28.1975	+	6.27503i	−1.25977	+	0.280348i
$502$	37.2363			1.66194
$503$	10.4450	+	2.22015i	0.465719	+	0.0989916i	0.434794	−	0.900530i	$-0.356821\pi$
$503$	10.4450	+	2.22015i	0.465719	+	0.0989916i	0.0309252	+	0.999522i	$0.490155\pi$
$504$	−26.4552	+	20.0022i	−1.17841	+	0.890969i
$505$	6.46984	−	1.37521i	0.287904	−	0.0611959i
$506$	15.5078	−	6.90453i	0.689407	−	0.306944i
$507$	−18.2899	+	0.174327i	−0.812283	+	0.00774214i
$508$	−0.412757	+	3.92712i	−0.0183131	+	0.174238i
$509$	10.2968	−	7.48104i	0.456396	−	0.331591i	−0.335720	−	0.941962i	$-0.608979\pi$
$509$	10.2968	−	7.48104i	0.456396	−	0.331591i	0.792116	+	0.610371i	$0.208979\pi$
$510$	5.49472	+	3.91268i	0.243310	+	0.173256i
$511$	−15.5687	−	6.93163i	−0.688719	−	0.306637i
$512$	−10.5423	+	7.65940i	−0.465906	+	0.338501i
$513$	−28.3470	−	5.18309i	−1.25155	−	0.228839i
$514$	42.8841	+	19.0932i	1.89153	+	0.842166i
$515$	1.22415	+	0.889395i	0.0539424	+	0.0391914i
$516$	−3.87352	+	6.85929i	−0.170522	+	0.301963i
$517$	−12.5875	−	9.14535i	−0.553597	−	0.402212i
$518$	17.6192	−	54.2263i	0.774143	−	2.38257i
$519$	7.85790	−	3.58869i	0.344924	−	0.157526i
$520$	−1.69878	−	5.22831i	−0.0744965	−	0.229277i
$521$	−1.83649	+	3.18090i	−0.0804582	+	0.139358i	−0.903447	−	0.428700i	$-0.858972\pi$
$521$	−1.83649	+	3.18090i	−0.0804582	+	0.139358i	0.822989	+	0.568058i	$0.192305\pi$
$522$	18.3167	−	8.57712i	0.801700	−	0.375410i
$523$	−1.55322	−	4.78032i	−0.0679175	−	0.209029i	0.911338	−	0.411660i	$-0.135051\pi$
$523$	−1.55322	−	4.78032i	−0.0679175	−	0.209029i	−0.979255	+	0.202631i	$0.935051\pi$
$524$	−3.03938	+	2.20824i	−0.132776	+	0.0964673i
$525$	18.5506	−	13.7498i	0.809613	−	0.600090i
$526$	−16.0709	+	27.8356i	−0.700724	+	1.21369i
$527$	1.51669	−	9.81590i	0.0660679	−	0.427587i
$528$	10.0198	−	31.8680i	0.436054	−	1.38687i
$529$	1.67869	−	15.9717i	0.0729865	−	0.694420i
$530$	−0.661730	−	6.29594i	−0.0287437	−	0.273478i
$531$	−12.1195	+	2.81854i	−0.525940	+	0.122314i
$532$	−4.77306	−	8.26718i	−0.206938	−	0.358428i
$533$	12.3528			0.535060
$534$	−11.4171	−	19.3468i	−0.494068	−	0.837220i
$535$	−8.88703	−	9.87005i	−0.384220	−	0.426719i
$536$	4.88963	−	15.0487i	0.211200	−	0.650006i
$537$	−1.88562	−	16.4323i	−0.0813703	−	0.709106i
$538$	36.6035	+	7.78031i	1.57809	+	0.335433i
$539$	−48.3553	+	21.5291i	−2.08281	+	0.927326i
$540$	−1.96500	−	2.06070i	−0.0845602	−	0.0886782i
$541$	12.5267	+	13.9124i	0.538567	+	0.598139i	0.949593	−	0.313484i	$-0.101496\pi$
$541$	12.5267	+	13.9124i	0.538567	+	0.598139i	−0.411027	+	0.911623i	$0.634830\pi$
$542$	−25.6060	−	11.4005i	−1.09987	−	0.489695i
$543$	−6.84777	+	7.75255i	−0.293866	+	0.332694i
$544$	3.77782	−	0.803001i	0.161973	−	0.0344284i
$545$	−10.2221	+	7.42680i	−0.437867	+	0.318129i
$546$	−17.0201	−	7.38426i	−0.728391	−	0.316017i
$547$	2.53650	+	0.539151i	0.108453	+	0.0230524i	0.261819	−	0.965117i	$-0.415678\pi$
$547$	2.53650	+	0.539151i	0.108453	+	0.0230524i	−0.153365	+	0.988170i	$0.549011\pi$
$548$	0.269578	−	2.56486i	0.0115158	−	0.109565i
$549$	−28.5659	−	12.0713i	−1.21916	−	0.515191i
$550$	−5.98169	+	18.4098i	−0.255060	+	0.784995i
$551$	−7.47687	−	23.0114i	−0.318525	−	0.980320i
$552$	7.68635	+	8.37464i	0.327153	+	0.356448i
$553$	−6.59539			−0.280464
$554$	−25.0431	−	5.32308i	−1.06398	−	0.226156i
$555$	−19.9402	−	4.04017i	−0.846413	−	0.171496i
$556$	0.407681	−	3.87883i	0.0172895	−	0.164499i
$557$	−25.0535			−1.06155			−0.530776	−	0.847512i	$-0.678100\pi$
$557$	−25.0535			−1.06155			−0.530776	+	0.847512i	$0.678100\pi$
$558$	−8.69715	+	24.3018i	−0.368180	+	1.02878i
$559$	18.3151			0.774646
$560$	−3.03117	+	28.8397i	−0.128090	+	1.21870i
$561$	8.52955	−	9.65655i	0.360118	−	0.407700i
$562$	−28.3769	−	6.03169i	−1.19701	−	0.254432i
$563$	44.1267			1.85972			0.929859	−	0.367917i	$-0.119929\pi$
$563$	44.1267			1.85972			0.929859	+	0.367917i	$0.119929\pi$
$564$	−0.751877	+	2.39135i	−0.0316597	+	0.100694i
$565$	6.40959	+	19.7267i	0.269654	+	0.829908i
$566$	−3.30230	+	10.1634i	−0.138806	+	0.427202i
$567$	39.9109	−	1.52231i	1.67610	−	0.0639308i
$568$	2.15459	−	20.4995i	0.0904046	−	0.860142i
$569$	17.2381	+	3.66406i	0.722657	+	0.153606i	0.554535	−	0.832161i	$-0.312896\pi$
$569$	17.2381	+	3.66406i	0.722657	+	0.153606i	0.168123	+	0.985766i	$0.446230\pi$
$570$	−16.8471	+	12.4872i	−0.705646	+	0.523030i
$571$	23.6110	−	17.1544i	0.988089	−	0.717889i	0.0285874	−	0.999591i	$-0.490899\pi$
$571$	23.6110	−	17.1544i	0.988089	−	0.717889i	0.959502	+	0.281702i	$0.0908991\pi$
$572$	2.47118	−	0.525265i	0.103325	−	0.0219624i
$573$	28.2481	+	5.72349i	1.18008	+	0.239102i
$574$	−49.5434	−	22.0581i	−2.06790	−	0.920689i
$575$	−5.29559	−	5.88135i	−0.220841	−	0.245269i
$576$	17.7119	−	0.337667i	0.737996	−	0.0140694i
$577$	−7.01105	+	3.12152i	−0.291874	+	0.129951i	−0.547450	−	0.836838i	$-0.684401\pi$
$577$	−7.01105	+	3.12152i	−0.291874	+	0.129951i	0.255576	+	0.966789i	$0.417735\pi$
$578$	−20.8855	−	4.43935i	−0.868723	−	0.184653i
$579$	9.75710	+	4.23318i	0.405491	+	0.175925i
$580$	0.738788	−	2.27376i	0.0306765	−	0.0944125i
$581$	−45.2089	−	50.2095i	−1.87558	−	2.08304i
$582$	14.2567	−	25.2461i	0.590961	−	1.04648i
$583$	−12.0918			−0.500793
$584$	4.78335	+	8.28500i	0.197936	+	0.342836i
$585$	−1.92538	+	6.33406i	−0.0796046	+	0.261881i
$586$	2.59745	+	24.7131i	0.107300	+	1.02089i
$587$	1.13721	−	10.8198i	0.0469378	−	0.446583i	−0.945662	−	0.325151i	$-0.894585\pi$
$587$	1.13721	−	10.8198i	0.0469378	−	0.446583i	0.992600	−	0.121432i	$-0.0387485\pi$
$588$	5.76648	+	6.28285i	0.237806	+	0.259100i
$589$	27.5652	+	13.9142i	1.13580	+	0.573325i
$590$	−4.52739	+	7.84166i	−0.186390	+	0.322836i
$591$	−17.8517	−	7.74508i	−0.734321	−	0.318590i
$592$	−31.1123	+	22.6044i	−1.27871	+	0.929035i
$593$	−12.0627	−	37.1251i	−0.495354	−	1.52454i	−0.816404	−	0.577482i	$-0.804035\pi$
$593$	−12.0627	−	37.1251i	−0.495354	−	1.52454i	0.321049	−	0.947063i	$-0.395965\pi$
$594$	−26.5138	+	20.4466i	−1.08787	+	0.838934i
$595$	−5.59214	+	9.68587i	−0.229255	+	0.397082i
$596$	1.63890	+	5.04400i	0.0671318	+	0.206610i
$597$	−0.308745	+	3.23370i	−0.0126361	+	0.132347i
$598$	−1.96499	+	6.04762i	−0.0803544	+	0.247305i
$599$	2.73738	+	1.98882i	0.111846	+	0.0812610i	0.642302	−	0.766451i	$-0.277979\pi$
$599$	2.73738	+	1.98882i	0.111846	+	0.0812610i	−0.530456	+	0.847712i	$0.677979\pi$
$600$	−12.9616	+	0.123541i	−0.529153	+	0.00504353i
$601$	−16.5520	−	12.0257i	−0.675171	−	0.490541i	0.196581	−	0.980488i	$-0.437016\pi$
$601$	−16.5520	−	12.0257i	−0.675171	−	0.490541i	−0.871752	+	0.489947i	$0.837016\pi$
$602$	−73.4563	−	32.7049i	−2.99386	−	1.33295i
$603$	−15.1996	+	11.4921i	−0.618976	+	0.467995i
$604$	−2.90645	+	2.11166i	−0.118262	+	0.0859223i
$605$	−8.24440	−	3.67064i	−0.335183	−	0.149233i
$606$	−11.3985	+	5.20568i	−0.463033	+	0.211466i
$607$	4.15738	−	3.02051i	0.168743	−	0.122599i	−0.500209	−	0.865905i	$-0.666743\pi$
$607$	4.15738	−	3.02051i	0.168743	−	0.122599i	0.668951	+	0.743306i	$0.266743\pi$
$608$	−1.25506	+	11.9411i	−0.0508995	+	0.484277i
$609$	17.0434	+	28.8808i	0.690634	+	1.17031i
$610$	−20.6164	+	9.17900i	−0.834733	+	0.371647i
$611$	5.70089	−	1.21176i	0.230633	−	0.0490227i
$612$	−1.91211	−	0.808012i	−0.0772923	−	0.0326620i
$613$	−9.74374	−	2.07110i	−0.393546	−	0.0836508i	0.00688819	−	0.999976i	$-0.497807\pi$
$613$	−9.74374	−	2.07110i	−0.393546	−	0.0836508i	−0.400434	+	0.916325i	$0.631141\pi$
$614$	12.2446			0.494150
$615$	−5.80429	+	18.4606i	−0.234052	+	0.744404i
$616$	45.0916	+	9.58452i	1.81679	+	0.386171i
$617$	−15.4677	−	6.88666i	−0.622706	−	0.277247i	0.0710320	−	0.997474i	$-0.477371\pi$
$617$	−15.4677	−	6.88666i	−0.622706	−	0.277247i	−0.693738	+	0.720228i	$0.744037\pi$
$618$	−2.62979	−	1.14095i	−0.105786	−	0.0458958i
$619$	15.2545	+	26.4215i	0.613129	+	1.06197i	0.990710	+	0.135994i	$0.0434229\pi$
$619$	15.2545	+	26.4215i	0.613129	+	1.06197i	−0.377580	+	0.925977i	$0.623244\pi$
$620$	1.39541	+	2.71324i	0.0560408	+	0.108966i
$621$	−1.81953	−	13.5676i	−0.0730150	−	0.544448i
$622$	−8.44827	−	6.13803i	−0.338745	−	0.246113i
$623$	30.1336	−	21.8933i	1.20728	−	0.877138i
$624$	6.35979	+	10.7770i	0.254596	+	0.431424i
$625$	−0.955051			−0.0382020
$626$	15.3983	+	26.6706i	0.615439	+	1.06597i
$627$	20.3569	+	34.4957i	0.812977	+	1.37763i
$628$	−7.95789	+	1.69150i	−0.317555	+	0.0674983i
$629$	−14.5081	+	3.08379i	−0.578476	+	0.122959i
$630$	19.0327	−	21.9659i	0.758281	−	0.875142i
$631$	1.44515	−	1.60500i	0.0575304	−	0.0638940i	−0.713693	−	0.700459i	$-0.752979\pi$
$631$	1.44515	−	1.60500i	0.0575304	−	0.0638940i	0.771223	+	0.636565i	$0.219645\pi$
$632$	2.99528	+	2.17620i	0.119146	+	0.0865645i
$633$	6.23065	−	7.05390i	0.247646	−	0.280367i
$634$	35.4278	−	7.53041i	1.40702	−	0.299071i
$635$	1.50338	+	14.3037i	0.0596600	+	0.567627i
$636$	0.619647	+	1.84699i	0.0245706	+	0.0732380i
$637$	6.12707	−	18.8572i	0.242763	−	0.747149i
$638$	−25.6821	−	11.4344i	−1.01676	−	0.452692i
$639$	−16.2549	+	18.7600i	−0.643035	+	0.742135i
$640$	12.7194	−	14.1263i	0.502777	−	0.558390i
$641$	13.9168	−	6.19614i	0.549679	−	0.244733i	−0.113054	−	0.993589i	$-0.536063\pi$
$641$	13.9168	−	6.19614i	0.549679	−	0.244733i	0.662733	+	0.748856i	$0.269397\pi$
$642$	20.4964	+	14.5950i	0.808927	+	0.576021i
$643$	23.5132	+	26.1141i	0.927271	+	1.02984i	0.999473	+	0.0324487i	$0.0103306\pi$
$643$	23.5132	+	26.1141i	0.927271	+	1.02984i	−0.0722025	+	0.997390i	$0.523003\pi$
$644$	3.03433	−	3.36996i	0.119569	−	0.132795i
$645$	−8.60583	+	27.3709i	−0.338854	+	1.07773i
$646$	−7.64391	+	13.2396i	−0.300746	+	0.520907i
$647$	10.0915	+	31.0583i	0.396736	+	1.22103i	0.927601	+	0.373572i	$0.121867\pi$
$647$	10.0915	+	31.0583i	0.396736	+	1.22103i	−0.530865	+	0.847456i	$0.678133\pi$
$648$	−18.6277	−	12.4775i	−0.731766	−	0.490164i
$649$	13.9921	+	10.1658i	0.549236	+	0.399043i
$650$	−3.62551	−	6.27956i	−0.142204	−	0.246305i
$651$	−41.4818	−	10.5253i	−1.62580	−	0.412520i
$652$	3.76287	−	6.51748i	0.147365	−	0.255244i
$653$	−22.9643	+	10.2243i	−0.898661	+	0.400110i	−0.803467	−	0.595349i	$-0.797014\pi$
$653$	−22.9643	+	10.2243i	−0.898661	+	0.400110i	−0.0951937	+	0.995459i	$0.530347\pi$
$654$	15.8470	−	17.9409i	0.619669	−	0.701544i
$655$	−9.15616	+	10.1689i	−0.357761	+	0.397333i
$656$	18.2892	+	31.6779i	0.714075	+	1.23681i
$657$	0.985631	−	11.4785i	0.0384531	−	0.447818i
$658$	−25.0284	−	5.31995i	−0.975708	−	0.207393i
$659$	10.6851	−	2.27119i	0.416234	−	0.0884732i	0.00496559	−	0.999988i	$-0.498419\pi$
$659$	10.6851	−	2.27119i	0.416234	−	0.0884732i	0.411268	+	0.911515i	$0.365086\pi$
$660$	−0.376167	+	3.93986i	−0.0146423	+	0.153359i
$661$	15.4321	+	11.2121i	0.600239	+	0.436099i	0.845964	−	0.533241i	$-0.179026\pi$
$661$	15.4321	+	11.2121i	0.600239	+	0.436099i	−0.245725	+	0.969340i	$0.579026\pi$
$662$	4.18684	+	12.8858i	0.162726	+	0.500819i
$663$	0.550209	+	4.79483i	0.0213684	+	0.186216i
$664$	3.96449	+	37.7196i	0.153852	+	1.46380i
$665$	−23.2655	−	25.8390i	−0.902198	−	1.00199i
$666$	38.5374	−	0.734691i	1.49329	−	0.0284687i
$667$	9.29864	−	6.75586i	0.360045	−	0.261588i
$668$	1.99905	−	6.15245i	0.0773456	−	0.238045i
$669$	−0.675993	−	2.01494i	−0.0261354	−	0.0779022i
$670$	−1.44944	+	13.7905i	−0.0559969	+	0.532775i
$671$	13.3202	+	40.9954i	0.514221	+	1.58261i
$672$	−1.89716	−	16.5329i	−0.0731844	−	0.637770i
$673$	−27.5274	−	30.5722i	−1.06110	−	1.17847i	−0.983391	−	0.181497i	$-0.941906\pi$
$673$	−27.5274	−	30.5722i	−1.06110	−	1.17847i	−0.0777107	−	0.996976i	$-0.524761\pi$
$674$	3.37240	−	10.3792i	0.129900	−	0.399791i
$675$	12.8856	+	8.81035i	0.495969	+	0.339111i
$676$	2.04803	−	3.54729i	0.0787704	−	0.136434i
$677$	−3.87411	+	6.71015i	−0.148894	+	0.257892i	−0.930819	−	0.365481i	$-0.880905\pi$
$677$	−3.87411	+	6.71015i	−0.148894	+	0.257892i	0.781925	+	0.623373i	$0.214238\pi$
$678$	−19.9712	−	33.8422i	−0.766991	−	1.29970i
$679$	43.9164	+	19.5529i	1.68536	+	0.750370i
$680$	5.73559	−	2.55365i	0.219950	−	0.0979279i
$681$	−26.3934	−	28.7569i	−1.01140	−	1.10197i
$682$	33.4448	−	12.9835i	1.28067	−	0.497163i
$683$	37.7850			1.44580			0.722902	−	0.690951i	$-0.242808\pi$
$683$	37.7850			1.44580			0.722902	+	0.690951i	$0.242808\pi$
$684$	4.22592	−	4.87719i	0.161582	−	0.186484i
$685$	−0.981882	−	9.34198i	−0.0375158	−	0.356939i
$686$	−26.1264	+	29.0163i	−0.997511	+	1.10785i
$687$	−12.8296	+	2.85509i	−0.489480	+	0.108928i
$688$	27.1168	+	46.9678i	1.03382	+	1.79063i
$689$	3.03082	−	3.36607i	0.115465	−	0.128237i
$690$	−8.11454	−	5.77820i	−0.308915	−	0.219972i
$691$	−20.1242	−	22.3502i	−0.765561	−	0.850241i	0.226758	−	0.973951i	$-0.427187\pi$
$691$	−20.1242	−	22.3502i	−0.765561	−	0.850241i	−0.992318	+	0.123710i	$0.960521\pi$
$692$	−0.202215	+	1.92394i	−0.00768705	+	0.0731374i
$693$	−37.9263	−	40.5400i	−1.44070	−	1.53999i
$694$	16.0404	−	7.14163i	0.608884	−	0.271093i
$695$	−1.48490	−	14.1278i	−0.0563253	−	0.535899i
$696$	1.78922	−	18.7398i	0.0678203	−	0.710330i
$697$	1.47466	+	14.0305i	0.0558568	+	0.531442i
$698$	−3.11240	−	29.6125i	−0.117806	−	1.12085i
$699$	−14.6824	−	10.4551i	−0.555341	−	0.395447i
$700$	0.540514	+	5.14265i	0.0204295	+	0.194374i
$701$	12.8598	−	5.72554i	0.485707	−	0.216251i	−0.149248	−	0.988800i	$-0.547685\pi$
$701$	12.8598	−	5.72554i	0.485707	−	0.216251i	0.634955	+	0.772549i	$0.281019\pi$
$702$	0.953862	−	12.5057i	0.0360012	−	0.471998i
$703$	4.81986	−	45.8579i	0.181785	−	1.72957i
$704$	−16.4762	−	18.2987i	−0.620971	−	0.689658i
$705$	−0.867799	+	9.08907i	−0.0326832	+	0.342314i
$706$	4.28423	−	4.75812i	0.161239	−	0.179074i
$707$	−10.3885	−	17.9934i	−0.390699	−	0.676711i
$708$	0.835774	−	2.65819i	0.0314103	−	0.0999010i
$709$	−23.3840	+	25.9706i	−0.878204	+	0.975345i	−0.999852	−	0.0172287i	$-0.994516\pi$
$709$	−23.3840	+	25.9706i	−0.878204	+	0.975345i	0.121647	+	0.992573i	$0.461182\pi$
$710$	1.88816	+	17.9646i	0.0708612	+	0.674200i
$711$	−1.45835	−	4.21334i	−0.0546926	−	0.158012i
$712$	−20.9090			−0.783597
$713$	−2.23983	+	14.4960i	−0.0838822	+	0.542880i
$714$	6.35530	−	20.2131i	0.237841	−	0.756457i
$715$	8.40631	−	3.74273i	0.314378	−	0.139970i
$716$	3.38380	+	1.50656i	0.126459	+	0.0563030i
$717$	−31.1159	+	0.296576i	−1.16205	+	0.0110758i
$718$	21.0095	−	36.3896i	0.784069	−	1.35805i
$719$	−1.89135	+	3.27591i	−0.0705354	+	0.122171i	−0.899136	−	0.437669i	$-0.855804\pi$
$719$	−1.89135	+	3.27591i	−0.0705354	+	0.122171i	0.828601	+	0.559840i	$0.189137\pi$
$720$	−19.0939	+	4.44054i	−0.711588	+	0.165489i
$721$	1.46876	−	4.52038i	0.0546996	−	0.168348i
$722$	−12.1559	−	13.5005i	−0.452394	−	0.502435i
$723$	−23.7435	+	17.5988i	−0.883030	+	0.654508i
$724$	−0.715809	−	2.20303i	−0.0266028	−	0.0818751i
$725$	−1.36999	+	13.0346i	−0.0508801	+	0.484092i
$726$	16.7567	+	3.39515i	0.621899	+	0.126006i
$727$	11.5332	−	35.4956i	0.427744	−	1.31646i	−0.472598	−	0.881278i	$-0.656684\pi$
$727$	11.5332	−	35.4956i	0.427744	−	1.31646i	0.900342	−	0.435183i	$-0.143316\pi$
$728$	−13.9703	+	10.1500i	−0.517774	+	0.376185i
$729$	9.79748	+	25.1597i	0.362870	+	0.931840i
$730$	−5.60978	−	6.23029i	−0.207627	−	0.230594i
$731$	2.18643	+	20.8025i	0.0808681	+	0.769408i
$732$	5.57932	−	4.13543i	0.206218	−	0.152850i
$733$	−15.2381	−	46.8979i	−0.562831	−	1.73221i	−0.674310	−	0.738448i	$-0.735559\pi$
$733$	−15.2381	−	46.8979i	−0.562831	−	1.73221i	0.111479	−	0.993767i	$-0.464441\pi$
$734$	34.7650	+	25.2582i	1.28320	+	0.932298i
$735$	25.3021	+	18.0171i	0.933282	+	0.664572i
$736$	−5.57905	+	1.18586i	−0.205646	+	0.0437115i
$737$	25.9070	+	5.50671i	0.954298	+	0.202842i
$738$	3.13652	−	36.5273i	0.115457	−	1.34459i
$739$	5.03815	+	8.72634i	0.185331	+	0.321003i	0.943688	−	0.330836i	$-0.107331\pi$
$739$	5.03815	+	8.72634i	0.185331	+	0.321003i	−0.758357	+	0.651840i	$0.773997\pi$
$740$	3.04868	−	3.38590i	0.112072	−	0.124468i
$741$	−14.7052	−	2.97949i	−0.540210	−	0.109454i
$742$	−18.1664	+	8.08821i	−0.666910	+	0.296928i
$743$	9.85737	−	17.0735i	0.361632	−	0.626365i	−0.626598	−	0.779343i	$-0.715553\pi$
$743$	9.85737	−	17.0735i	0.361632	−	0.626365i	0.988230	+	0.152978i	$0.0488864\pi$
$744$	15.3659	+	18.4673i	0.563343	+	0.677043i
$745$	9.65860	+	16.7292i	0.353864	+	0.612910i
$746$	30.8117	+	22.3860i	1.12809	+	0.819609i
$747$	22.0789	−	39.9830i	0.807826	−	1.46290i
$748$	0.891609	+	2.74409i	0.0326004	+	0.100334i
$749$	−20.8597	+	36.1301i	−0.762199	+	1.32017i
$750$	29.5429	−	6.57444i	1.07875	−	0.240065i
$751$	−22.5422	+	25.0357i	−0.822577	+	0.913565i	−0.997475	−	0.0710220i	$-0.977374\pi$
$751$	−22.5422	+	25.0357i	−0.822577	+	0.913565i	0.174897	+	0.984587i	$0.444041\pi$
$752$	11.5481	+	12.8254i	0.421115	+	0.467696i
$753$	−37.9651	+	17.3386i	−1.38352	+	0.631853i
$754$	9.62027	−	4.28322i	0.350350	−	0.155986i
$755$	−8.75572	+	9.72422i	−0.318653	+	0.353900i
$756$	−4.24883	+	7.87060i	−0.154528	+	0.286251i
$757$	40.1749	+	17.8870i	1.46018	+	0.650114i	0.974574	−	0.224064i	$-0.0719325\pi$
$757$	40.1749	+	17.8870i	1.46018	+	0.650114i	0.485606	+	0.874178i	$0.338599\pi$
$758$	−12.0069	+	36.9533i	−0.436109	+	1.34221i
$759$	−12.5964	+	14.2607i	−0.457219	+	0.517630i
$760$	2.04022	+	19.4114i	0.0740064	+	0.704124i
$761$	6.11680	−	1.30017i	0.221734	−	0.0471310i	−0.0957049	−	0.995410i	$-0.530511\pi$
$761$	6.11680	−	1.30017i	0.221734	−	0.0471310i	0.317439	+	0.948279i	$0.397177\pi$
$762$	−8.66663	−	25.8327i	−0.313959	−	0.935822i
$763$	32.1095	+	23.3289i	1.16244	+	0.844565i
$764$	−4.31889	+	4.79661i	−0.156252	+	0.173535i
$765$	−7.42415	−	1.43072i	−0.268421	−	0.0517277i
$766$	−15.7237	+	3.34218i	−0.568121	+	0.120758i
$767$	−6.33702	+	1.34698i	−0.228817	+	0.0486365i
$768$	−7.64952	+	13.5459i	−0.276028	+	0.488795i
$769$	6.28300	+	10.8825i	0.226571	+	0.392432i	0.956790	−	0.290781i	$-0.0939152\pi$
$769$	6.28300	+	10.8825i	0.226571	+	0.392432i	−0.730219	+	0.683213i	$0.760582\pi$
$770$	−40.3985			−1.45586
$771$	−52.6139	+	0.501480i	−1.89484	+	0.0180604i
$772$	−1.92692	+	1.39999i	−0.0693515	+	0.0503868i
$773$	29.2580	+	21.2572i	1.05234	+	0.764568i	0.972656	−	0.232252i	$-0.0746094\pi$
$773$	29.2580	+	21.2572i	1.05234	+	0.764568i	0.0796822	+	0.996820i	$0.474609\pi$
$774$	4.65041	−	54.1578i	0.167155	−	1.94666i
$775$	−10.5751	−	12.9587i	−0.379868	−	0.465490i
$776$	−13.4929	−	23.3705i	−0.484368	−	0.838950i
$777$	7.28572	+	63.4918i	0.261374	+	2.27776i
$778$	42.4066	+	18.8806i	1.52035	+	0.676903i
$779$	−42.8999	−	9.11866i	−1.53705	−	0.326710i
$780$	−1.00247	−	1.09224i	−0.0358943	−	0.0391085i
$781$	34.5024			1.23459
$782$	−7.10353	−	1.50990i	−0.254022	−	0.0539940i
$783$	−14.6814	+	17.2739i	−0.524670	+	0.617319i
$784$	57.4295	−	12.2070i	2.05105	−	0.435965i
$785$	−27.0707	+	12.0526i	−0.966194	+	0.430177i
$786$	12.7473	−	22.5732i	0.454682	−	0.805158i
$787$	2.15416	−	20.4954i	0.0767874	−	0.730583i	−0.886612	−	0.462514i	$-0.846948\pi$
$787$	2.15416	−	20.4954i	0.0767874	−	0.730583i	0.963400	−	0.268070i	$-0.0863858\pi$
$788$	3.52552	−	2.56144i	0.125591	−	0.0912475i
$789$	3.42416	−	35.8636i	0.121903	−	1.27678i
$790$	−2.96404	−	1.31967i	−0.105456	−	0.0469519i
$791$	52.7107	−	38.2966i	1.87418	−	1.36167i
$792$	3.84765	+	30.9252i	0.136720	+	1.09888i
$793$	−14.7508	−	6.56748i	−0.523816	−	0.233218i
$794$	−2.16003	−	1.56935i	−0.0766566	−	0.0556943i
$795$	3.60630	+	6.11104i	0.127902	+	0.216736i
$796$	−0.588523	−	0.427587i	−0.0208597	−	0.0151554i
$797$	10.3682	−	31.9099i	0.367259	−	1.13031i	−0.581296	−	0.813693i	$-0.697454\pi$
$797$	10.3682	−	31.9099i	0.367259	−	1.13031i	0.948554	−	0.316614i	$-0.102546\pi$
$798$	53.6578	+	38.2086i	1.89946	+	1.35257i
$799$	2.05690	+	6.33049i	0.0727679	+	0.223957i
$800$	3.25197	−	5.63258i	0.114974	−	0.199142i
$801$	20.6492	+	14.4093i	0.729604	+	0.509127i
$802$	6.33831	+	19.5073i	0.223814	+	0.688827i
$803$	−12.9551	+	9.41239i	−0.457174	+	0.332156i
$804$	−0.486475	−	4.23941i	−0.0171566	−	0.149512i
$805$	8.25841	−	14.3040i	0.291071	−	0.504149i
$806$	−4.76867	+	12.5645i	−0.167969	+	0.442566i
$807$	−40.9427	+	9.11134i	−1.44125	+	0.320734i
$808$	−1.21915	+	11.5994i	−0.0428895	+	0.408066i
$809$	1.88641	+	17.9480i	0.0663226	+	0.631018i	0.976309	+	0.216380i	$0.0694250\pi$
$809$	1.88641	+	17.9480i	0.0663226	+	0.631018i	−0.909987	+	0.414638i	$0.863908\pi$
$810$	18.2410	+	7.30164i	0.640922	+	0.256553i
$811$	−9.24360	−	16.0104i	−0.324587	−	0.562201i	0.656842	−	0.754028i	$-0.271892\pi$
$811$	−9.24360	−	16.0104i	−0.324587	−	0.562201i	−0.981429	+	0.191828i	$0.938559\pi$
$812$	−7.50984			−0.263544
$813$	31.4157	−	0.299433i	1.10180	−	0.0105016i
$814$	−35.8488	−	39.8141i	−1.25650	−	1.39548i
$815$	8.47045	−	26.0694i	0.296707	−	0.913170i
$816$	−11.4814	+	8.51007i	−0.401929	+	0.297912i
$817$	−63.6062	−	13.5199i	−2.22530	−	0.473002i
$818$	−33.7011	+	15.0047i	−1.17833	+	0.524627i
$819$	20.7916	−	0.396378i	0.726516	−	0.0138506i
$820$	−2.89977	−	3.22052i	−0.101264	−	0.112465i
$821$	22.7162	+	10.1139i	0.792799	+	0.352977i	0.762851	−	0.646575i	$-0.223799\pi$
$821$	22.7162	+	10.1139i	0.792799	+	0.352977i	0.0299483	+	0.999551i	$0.490466\pi$
$822$	5.66030	+	16.8717i	0.197426	+	0.588469i
$823$	2.15909	−	0.458929i	0.0752612	−	0.0159973i	−0.170127	−	0.985422i	$-0.554418\pi$
$823$	2.15909	−	0.458929i	0.0752612	−	0.0159973i	0.245388	+	0.969425i	$0.421085\pi$
$824$	−2.15857	+	1.56829i	−0.0751974	+	0.0546341i
$825$	−2.47349	−	21.5554i	−0.0861159	−	0.750462i
$826$	27.8212	+	5.91357i	0.968022	+	0.205759i
$827$	0.727296	−	6.91976i	0.0252906	−	0.240624i	−0.974572	−	0.224073i	$-0.928065\pi$
$827$	0.727296	−	6.91976i	0.0252906	−	0.240624i	0.999863	−	0.0165511i	$-0.00526861\pi$
$828$	2.82378	+	1.19326i	0.0981330	+	0.0414688i
$829$	−10.9899	+	33.8236i	−0.381697	+	1.17474i	0.557152	+	0.830411i	$0.311894\pi$
$829$	−10.9899	+	33.8236i	−0.381697	+	1.17474i	−0.938848	+	0.344331i	$0.888106\pi$
$830$	−10.2709	−	31.6105i	−0.356508	−	1.09722i
$831$	28.0119	−	6.23374i	0.971723	−	0.216246i
$832$	9.22366			0.319773
$833$	22.1497	+	4.70806i	0.767440	+	0.163124i
$834$	8.56005	+	25.5151i	0.296410	+	0.883514i
$835$	2.46293	−	23.4332i	0.0852331	−	0.810939i
$836$	−8.96987			−0.310229
$837$	−2.44844	−	28.8272i	−0.0846304	−	0.996412i
$838$	−22.2949			−0.770165
$839$	−2.04805	+	19.4859i	−0.0707065	+	0.672727i	0.900560	+	0.434732i	$0.143157\pi$
$839$	−2.04805	+	19.4859i	−0.0707065	+	0.672727i	−0.971266	+	0.237995i	$0.923510\pi$
$840$	−8.60437	−	25.6472i	−0.296879	−	0.884911i
$841$	9.74775	+	2.07195i	0.336129	+	0.0714465i
$842$	−12.0155			−0.414081
$843$	31.7409	−	7.06357i	1.09321	−	0.243282i
$844$	0.651301	+	2.00450i	0.0224187	+	0.0689977i
$845$	4.61025	−	14.1889i	0.158597	−	0.488112i
$846$	−2.13566	−	17.1652i	−0.0734256	−	0.590153i
$847$	−2.96317	+	28.1927i	−0.101816	+	0.968712i
$848$	13.1194	+	2.78861i	0.450522	+	0.0957614i
$849$	−1.36554	−	11.9000i	−0.0468651	−	0.408408i
$850$	6.69960	−	4.86754i	0.229794	−	0.166955i
$851$	21.4254	−	4.55411i	0.734454	−	0.156113i
$852$	−1.76808	−	5.27014i	−0.0605734	−	0.180552i
$853$	−3.01226	−	1.34114i	−0.103138	−	0.0459199i	0.354519	−	0.935049i	$-0.384645\pi$
$853$	−3.01226	−	1.34114i	−0.103138	−	0.0459199i	−0.457657	+	0.889129i	$0.651311\pi$
$854$	47.4336	+	52.6804i	1.62314	+	1.80269i
$855$	11.3623	−	20.5762i	0.388583	−	0.703691i
$856$	21.3948	−	9.52559i	0.731260	−	0.325578i
$857$	−15.9658	−	3.39364i	−0.545382	−	0.115925i	−0.0730222	−	0.997330i	$-0.523264\pi$
$857$	−15.9658	−	3.39364i	−0.545382	−	0.115925i	−0.472360	+	0.881406i	$0.656598\pi$
$858$	−14.0052	+	10.3808i	−0.478131	+	0.354394i
$859$	4.43593	−	13.6524i	0.151352	−	0.465813i	−0.846421	−	0.532514i	$-0.821247\pi$
$859$	4.43593	−	13.6524i	0.151352	−	0.465813i	0.997773	+	0.0667010i	$0.0212473\pi$
$860$	−4.29938	−	4.77495i	−0.146608	−	0.162824i
$861$	60.7842	−	0.579354i	2.07152	−	0.0197443i
$862$	−34.3838			−1.17112
$863$	−9.24855	−	16.0190i	−0.314824	−	0.545292i	0.664576	−	0.747221i	$-0.268612\pi$
$863$	−9.24855	−	16.0190i	−0.314824	−	0.545292i	−0.979400	+	0.201929i	$0.935279\pi$
$864$	10.1422	−	4.86767i	0.345045	−	0.165601i
$865$	0.736526	+	7.00758i	0.0250426	+	0.238265i
$866$	−0.884945	+	8.41969i	−0.0300717	+	0.286113i
$867$	23.3614	−	5.19882i	0.793396	−	0.176561i
$868$	6.75116	−	6.80238i	0.229149	−	0.230888i
$869$	−3.09863	+	5.36698i	−0.105114	+	0.182062i
$870$	1.88071	+	16.3896i	0.0637621	+	0.555659i
$871$	−8.02653	+	5.83161i	−0.271969	+	0.197597i
$872$	−6.88491	−	21.1896i	−0.233153	−	0.717570i
$873$	−2.78028	+	32.3786i	−0.0940983	+	1.09585i
$874$	11.2884	−	19.5522i	0.381837	−	0.661362i
$875$	15.5071	+	47.7258i	0.524234	+	1.61343i
$876$	2.10160	+	1.49651i	0.0710064	+	0.0505622i
$877$	−14.6318	+	45.0321i	−0.494081	+	1.52063i	0.324302	+	0.945954i	$0.394871\pi$
$877$	−14.6318	+	45.0321i	−0.494081	+	1.52063i	−0.818383	+	0.574673i	$0.805129\pi$
$878$	−1.74882	−	1.27059i	−0.0590198	−	0.0428804i
$879$	−14.1556	−	23.9873i	−0.477457	−	0.809073i
$880$	22.0441	+	16.0160i	0.743107	+	0.539899i
$881$	−35.7745	−	15.9278i	−1.20527	−	0.536622i	−0.296951	−	0.954893i	$-0.595970\pi$
$881$	−35.7745	−	15.9278i	−1.20527	−	0.536622i	−0.908323	+	0.418270i	$0.862636\pi$
$882$	−54.2050	−	22.9058i	−1.82518	−	0.771279i
$883$	1.65322	−	1.20113i	0.0556352	−	0.0404213i	−0.559620	−	0.828749i	$-0.689053\pi$
$883$	1.65322	−	1.20113i	0.0556352	−	0.0404213i	0.615255	+	0.788328i	$0.289053\pi$
$884$	−0.987368	−	0.439605i	−0.0332088	−	0.0147855i
$885$	0.964632	−	10.1033i	0.0324257	−	0.339617i
$886$	2.33945	−	1.69971i	0.0785953	−	0.0571029i
$887$	1.42031	−	13.5133i	0.0476893	−	0.453733i	−0.944456	−	0.328639i	$-0.893410\pi$
$887$	1.42031	−	13.5133i	0.0476893	−	0.453733i	0.992145	−	0.125094i	$-0.0399233\pi$
$888$	17.6408	−	31.2386i	0.591987	−	1.04830i
$889$	41.2723	−	18.3756i	1.38423	−	0.616298i
$890$	17.9230	−	3.80965i	0.600780	−	0.127700i
$891$	17.5121	−	33.1926i	0.586676	−	1.11199i
$892$	0.465546	+	0.0989549i	0.0155876	+	0.00331326i
$893$	−20.6931			−0.692467
$894$	−24.7460	−	26.9619i	−0.827629	−	0.901741i
$895$	13.1964	+	2.80497i	0.441106	+	0.0937599i
$896$	−54.5478	−	24.2863i	−1.82232	−	0.811347i
$897$	−0.812543	−	7.08095i	−0.0271300	−	0.236426i
$898$	−22.2381	−	38.5174i	−0.742094	−	1.28534i
$899$	20.3223	−	13.3069i	0.677786	−	0.443810i
$900$	−3.16576	+	1.48242i	−0.105525	+	0.0494142i
$901$	4.18504	+	3.04061i	0.139424	+	0.101297i
$902$	−41.2261	+	29.9525i	−1.37268	+	0.997310i
$903$	90.1226	−	0.858988i	2.99909	−	0.0285853i
$904$	−36.5747			−1.21646
$905$	−4.21852	−	7.30669i	−0.140228	−	0.242883i
$906$	12.1898	−	21.5859i	0.404980	−	0.717145i
$907$	55.7203	−	11.8437i	1.85016	−	0.393264i	0.857529	−	0.514435i	$-0.171998\pi$
$907$	55.7203	−	11.8437i	1.85016	−	0.393264i	0.992632	+	0.121171i	$0.0386649\pi$
$908$	8.55009	−	1.81738i	0.283745	−	0.0603118i
$909$	9.19766	−	10.6151i	0.305067	−	0.352082i
$910$	10.1259	−	11.2459i	0.335670	−	0.372799i
$911$	30.7820	+	22.3644i	1.01985	+	0.740966i	0.966252	−	0.257597i	$-0.0829306\pi$
$911$	30.7820	+	22.3644i	1.01985	+	0.740966i	0.0535993	+	0.998563i	$0.482931\pi$
$912$	−14.1315	−	42.1219i	−0.467939	−	1.39479i
$913$	−62.0978	+	13.1993i	−2.05514	+	0.436833i
$914$	3.34943	+	31.8677i	0.110789	+	1.05409i
$915$	16.7458	−	18.9584i	0.553599	−	0.626745i
$916$	0.909552	−	2.79931i	0.0300524	−	0.0924919i
$917$	39.2668	+	17.4827i	1.29670	+	0.577330i
$918$	14.3180	−	0.409509i	0.472565	−	0.0135158i
$919$	−7.27187	+	8.07623i	−0.239877	+	0.266410i	−0.851048	−	0.525088i	$-0.824032\pi$
$919$	−7.27187	+	8.07623i	−0.239877	+	0.266410i	0.611171	+	0.791499i	$0.290699\pi$
$920$	−8.47025	+	3.77120i	−0.279256	+	0.124333i
$921$	−12.4842	+	5.70152i	−0.411369	+	0.187871i
$922$	−13.2659	−	14.7332i	−0.436888	−	0.485214i
$923$	−8.64804	+	9.60462i	−0.284654	+	0.316140i
$924$	12.1352	−	2.70056i	0.399220	−	0.0888419i
$925$	−12.4887	+	21.6310i	−0.410624	+	0.711222i
$926$	−7.11545	−	21.8991i	−0.233828	−	0.719649i
$927$	3.21253	−	0.0612449i	0.105513	−	0.00201155i
$928$	7.64174	+	5.55205i	0.250853	+	0.182255i
$929$	−21.7692	−	37.7054i	−0.714226	−	1.23708i	−0.963257	−	0.268580i	$-0.913446\pi$
$929$	−21.7692	−	37.7054i	−0.714226	−	1.23708i	0.249032	−	0.968495i	$-0.419888\pi$
$930$	−16.5363	−	13.0303i	−0.542247	−	0.427280i
$931$	−35.1987	+	60.9659i	−1.15359	+	1.99808i
$932$	3.68747	−	1.64177i	0.120787	−	0.0537779i
$933$	11.4717	+	2.32434i	0.375567	+	0.0760954i
$934$	−7.70088	+	8.55269i	−0.251980	+	0.279853i
$935$	5.25457	+	9.10118i	0.171843	+	0.297641i
$936$	−9.57323	−	6.68032i	−0.312911	−	0.218353i
$937$	46.7424	+	9.93541i	1.52701	+	0.324576i	0.893465	−	0.449132i	$-0.148267\pi$
$937$	46.7424	+	9.93541i	1.52701	+	0.324576i	0.633543	+	0.773708i	$0.281600\pi$
$938$	42.6054	−	9.05605i	1.39111	−	0.295691i
$939$	−28.1185	−	20.0226i	−0.917612	−	0.653413i
$940$	−1.65418	−	1.20183i	−0.0539534	−	0.0391994i
$941$	1.30474	+	4.01557i	0.0425332	+	0.130904i	0.970068	−	0.242832i	$-0.0780765\pi$
$941$	1.30474	+	4.01557i	0.0425332	+	0.130904i	−0.927535	+	0.373736i	$0.878077\pi$
$942$	45.1008	−	33.4290i	1.46946	−	1.08918i
$943$	−2.17777	−	20.7201i	−0.0709178	−	0.674738i
$944$	−12.8367	−	14.2565i	−0.417798	−	0.464011i
$945$	−9.17709	+	31.2581i	−0.298531	+	1.01683i
$946$	−61.1246	+	44.4096i	−1.98733	+	1.44388i
$947$	6.59396	−	20.2941i	0.214275	−	0.659471i	−0.784929	−	0.619585i	$-0.787301\pi$
$947$	6.59396	−	20.2941i	0.214275	−	0.659471i	0.999204	−	0.0398853i	$-0.0126993\pi$
$948$	0.978579	+	0.198275i	0.0317828	+	0.00643966i
$949$	0.627008	−	5.96558i	0.0203535	−	0.193651i
$950$	7.95550	+	24.4845i	0.258110	+	0.794382i
$951$	−32.6148	+	24.1743i	−1.05761	+	0.783904i
$952$	−13.1963	−	14.6560i	−0.427694	−	0.475002i
$953$	1.08300	−	3.33312i	0.0350817	−	0.107970i	−0.931982	−	0.362504i	$-0.881922\pi$
$953$	1.08300	−	3.33312i	0.0350817	−	0.107970i	0.967064	+	0.254534i	$0.0819219\pi$
$954$	−9.18391	−	9.81682i	−0.297340	−	0.317831i
$955$	−11.7546	+	20.3595i	−0.380369	+	0.658818i
$956$	3.48424	−	6.03487i	0.112688	−	0.195182i
$957$	31.5090	−	0.300323i	1.01854	−	0.00970806i
$958$	1.57225	+	0.700010i	0.0507970	+	0.0226163i
$959$	−26.9555	+	12.0014i	−0.870439	+	0.387545i
$960$	−4.33398	+	13.7843i	−0.139879	+	0.444886i
$961$	−6.21592	+	30.3704i	−0.200513	+	0.979691i
$962$	20.0687			0.647042
$963$	−27.6935	−	5.33685i	−0.892411	−	0.171978i
$964$	−0.691822	−	6.58225i	−0.0222821	−	0.212000i
$965$	−5.80487	+	6.44696i	−0.186865	+	0.207535i
$966$	−9.38544	+	29.8505i	−0.301971	+	0.960424i
$967$	−3.23638	−	5.60558i	−0.104075	−	0.180263i	0.809285	−	0.587416i	$-0.199855\pi$
$967$	−3.23638	−	5.60558i	−0.104075	−	0.180263i	−0.913360	+	0.407153i	$0.866522\pi$
$968$	10.6481	−	11.8259i	0.342243	−	0.380100i
$969$	1.62866	−	17.0581i	0.0523200	−	0.547984i
$970$	15.8242	+	17.5745i	0.508083	+	0.564284i
$971$	−3.60282	+	34.2785i	−0.115620	+	1.10005i	0.770771	+	0.637113i	$0.219871\pi$
$971$	−3.60282	+	34.2785i	−0.115620	+	1.10005i	−0.886391	+	0.462938i	$0.846795\pi$
$972$	−5.96747	−	0.973955i	−0.191407	−	0.0312396i
$973$	−40.7647	+	18.1496i	−1.30686	+	0.581850i
$974$	4.72874	+	44.9910i	0.151519	+	1.44160i
$975$	6.62046	+	4.71430i	0.212024	+	0.150978i
$976$	−4.99781	−	47.5510i	−0.159976	−	1.52207i
$977$	4.65965	+	44.3336i	0.149075	+	1.41836i	0.771775	+	0.635896i	$0.219369\pi$
$977$	4.65965	+	44.3336i	0.149075	+	1.41836i	−0.622700	+	0.782461i	$0.713964\pi$
$978$	−4.93571	+	51.6951i	−0.157827	+	1.65303i
$979$	−3.65837	−	34.8070i	−0.116922	−	1.11244i
$980$	−6.35458	+	2.82924i	−0.202990	+	0.0903768i
$981$	−7.80328	+	25.6710i	−0.249139	+	0.819612i
$982$	3.02965	−	28.8252i	0.0966801	−	0.919850i
$983$	13.0657	+	14.5109i	0.416732	+	0.462827i	0.914561	−	0.404448i	$-0.132536\pi$
$983$	13.0657	+	14.5109i	0.416732	+	0.462827i	−0.497830	+	0.867275i	$0.665870\pi$
$984$	−27.7962	−	19.7931i	−0.886109	−	0.630981i
$985$	10.6207	−	11.7954i	0.338403	−	0.375834i
$986$	6.01339	+	10.4155i	0.191505	+	0.331697i
$987$	27.9954	−	6.23006i	0.891104	−	0.198305i
$988$	2.24830	−	2.49699i	0.0715279	−	0.0794398i
$989$	−3.22890	−	30.7209i	−0.102673	−	0.976868i
$990$	−8.93280	−	25.8078i	−0.283903	−	0.820225i
$991$	−2.33718			−0.0742430			−0.0371215	−	0.999311i	$-0.511819\pi$
$991$	−2.33718			−0.0742430			−0.0371215	+	0.999311i	$0.511819\pi$
$992$	−11.8988	+	1.93070i	−0.377786	+	0.0612997i
$993$	−10.2689	−	11.1884i	−0.325873	−	0.355054i
$994$	51.8354	−	23.0786i	1.64412	−	0.732009i
$995$	−2.42054	−	1.07769i	−0.0767361	−	0.0341651i
$996$	5.19836	+	8.80885i	0.164716	+	0.279119i
$997$	15.5342	−	26.9060i	0.491973	−	0.852122i	−0.507984	−	0.861366i	$-0.669609\pi$
$997$	15.5342	−	26.9060i	0.491973	−	0.852122i	0.999957	+	0.00924414i	$0.00294254\pi$
$998$	−33.7753	+	58.5005i	−1.06914	+	1.85180i
$999$	−38.9495	+	18.6935i	−1.23231	+	0.591436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	279.2.bb.a.103.22	yes	240
3.2	odd	2		837.2.be.a.10.9		240
9.2	odd	6		837.2.bd.a.289.22		240
9.7	even	3		279.2.ba.a.196.9	yes	240
31.28	even	15		279.2.ba.a.121.9	✓	240
93.59	odd	30		837.2.bd.a.307.22		240
279.214	even	15	inner	279.2.bb.a.214.22	yes	240
279.245	odd	30		837.2.be.a.586.9		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
279.2.ba.a.121.9	✓	240	31.28	even	15
279.2.ba.a.196.9	yes	240	9.7	even	3
279.2.bb.a.103.22	yes	240	1.1	even	1	trivial
279.2.bb.a.214.22	yes	240	279.214	even	15	inner
837.2.bd.a.289.22		240	9.2	odd	6
837.2.bd.a.307.22		240	93.59	odd	30
837.2.be.a.10.9		240	3.2	odd	2
837.2.be.a.586.9		240	279.245	odd	30

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:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	279.bb (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.161525 - 1.53681i) q^{2} +(0.550909 + 1.64210i) q^{3} +(-0.379403 - 0.0806445i) q^{4} -1.41277 q^{5} +(2.61259 - 0.581402i) q^{6} +(1.37134 + 4.22056i) q^{7} +(0.769815 - 2.36925i) q^{8} +(-2.39300 + 1.80930i) q^{9} +(-0.228198 + 2.17116i) q^{10} +(4.07876 + 0.866967i) q^{11} +(-0.0765897 - 0.667445i) q^{12} +(-1.26368 + 0.918119i) q^{13} +(6.70772 - 1.42577i) q^{14} +(-0.778307 - 2.31991i) q^{15} +(-4.22543 - 1.88128i) q^{16} +(-1.19367 - 1.32570i) q^{17} +(2.39402 + 3.96983i) q^{18} +(5.06637 - 2.25569i) q^{19} +(0.536008 + 0.113932i) q^{20} +(-6.17511 + 4.57703i) q^{21} +(1.99119 - 6.12824i) q^{22} +(1.76280 + 1.95778i) q^{23} +(4.31464 - 0.0411243i) q^{24} -3.00408 q^{25} +(1.20686 + 2.09034i) q^{26} +(-4.28938 - 2.93279i) q^{27} +(-0.179926 - 1.71188i) q^{28} +(0.456042 - 4.33895i) q^{29} +(-3.69098 + 0.821386i) q^{30} +(3.52023 + 4.31369i) q^{31} +(-1.08252 + 1.87497i) q^{32} +(0.823376 + 7.17536i) q^{33} +(-2.23016 + 1.62031i) q^{34} +(-1.93739 - 5.96268i) q^{35} +(1.05382 - 0.493470i) q^{36} +(4.15722 - 7.20052i) q^{37} +(-2.64823 - 8.15040i) q^{38} +(-2.20382 - 1.56930i) q^{39} +(-1.08757 + 3.34720i) q^{40} +(-6.39798 - 4.64840i) q^{41} +(6.03660 + 10.2293i) q^{42} +(-9.48607 - 6.89203i) q^{43} +(-1.47757 - 0.657859i) q^{44} +(3.38075 - 2.55612i) q^{45} +(3.29348 - 2.39285i) q^{46} +(-3.40870 - 1.51765i) q^{47} +(0.761431 - 7.97500i) q^{48} +(-10.2695 + 7.46120i) q^{49} +(-0.485236 + 4.61671i) q^{50} +(1.51934 - 2.69047i) q^{51} +(0.553486 - 0.246428i) q^{52} +(-2.83644 + 0.602903i) q^{53} +(-5.19999 + 6.11824i) q^{54} +(-5.76234 - 1.22482i) q^{55} +11.0552 q^{56} +(6.49519 + 7.07681i) q^{57} +(-6.59449 - 1.40170i) q^{58} +(3.78905 + 1.68699i) q^{59} +(0.108204 + 0.942946i) q^{60} +(5.16862 + 8.95232i) q^{61} +(7.19794 - 4.71316i) q^{62} +(-10.9179 - 7.61864i) q^{63} +(-4.77728 - 3.47090i) q^{64} +(1.78529 - 1.29709i) q^{65} +(11.1602 - 0.106371i) q^{66} +6.35170 q^{67} +(0.345970 + 0.599238i) q^{68} +(-2.24374 + 3.97325i) q^{69} +(-9.47645 + 2.01428i) q^{70} +(8.09339 - 1.72030i) q^{71} +(2.44450 + 7.06243i) q^{72} +(-2.56962 + 2.85385i) q^{73} +(-10.3943 - 7.55194i) q^{74} +(-1.65498 - 4.93301i) q^{75} +(-2.10410 + 0.447241i) q^{76} +(1.93429 + 18.4036i) q^{77} +(-2.76768 + 3.13337i) q^{78} +(-0.459260 + 1.41346i) q^{79} +(5.96955 + 2.65782i) q^{80} +(2.45289 - 8.65929i) q^{81} +(-8.17716 + 9.08165i) q^{82} +(-13.9084 + 6.19244i) q^{83} +(2.71197 - 1.23855i) q^{84} +(1.68638 + 1.87291i) q^{85} +(-12.1240 + 13.4651i) q^{86} +(7.37624 - 1.64150i) q^{87} +(5.19395 - 8.99618i) q^{88} +(-2.59365 - 7.98244i) q^{89} +(-3.38219 - 5.60846i) q^{90} +(-5.60793 - 4.07440i) q^{91} +(-0.510925 - 0.884948i) q^{92} +(-5.14420 + 8.15703i) q^{93} +(-2.88293 + 4.99338i) q^{94} +(-7.15761 + 3.18677i) q^{95} +(-3.67526 - 0.744663i) q^{96} +(7.24842 - 8.05019i) q^{97} +(9.80768 + 16.9874i) q^{98} +(-11.3291 + 5.30503i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 3 q^{2} - 11 q^{3} + 25 q^{4} - 6 q^{5} - 8 q^{6} - 5 q^{7} - 29 q^{8} - 11 q^{9} - 30 q^{10} - 14 q^{11} - 8 q^{12} + q^{13} - 2 q^{14} - 26 q^{15} + 25 q^{16} - 26 q^{17} - 3 q^{18} - 20 q^{19}+ \cdots - 74 q^{99}+O(q^{100}) \) 240 * q - 3 * q^2 - 11 * q^3 + 25 * q^4 - 6 * q^5 - 8 * q^6 - 5 * q^7 - 29 * q^8 - 11 * q^9 - 30 * q^10 - 14 * q^11 - 8 * q^12 + q^13 - 2 * q^14 - 26 * q^15 + 25 * q^16 - 26 * q^17 - 3 * q^18 - 20 * q^19 - 84 * q^20 + q^21 - 11 * q^22 - 6 * q^23 + 14 * q^24 + 174 * q^25 + 22 * q^26 + 70 * q^27 - 60 * q^28 - 15 * q^29 - 6 * q^30 - 20 * q^31 - 24 * q^32 - 40 * q^33 + 25 * q^34 - 15 * q^35 - 8 * q^36 + 2 * q^37 + 37 * q^38 - q^39 + 6 * q^40 - 23 * q^41 - 134 * q^42 + 9 * q^43 - 77 * q^44 - 127 * q^45 - 2 * q^46 - 32 * q^47 + 26 * q^48 - 41 * q^49 - 37 * q^50 + 13 * q^51 + 3 * q^52 - 56 * q^53 - 29 * q^54 - 30 * q^55 - 62 * q^56 - 40 * q^57 + 76 * q^58 - 3 * q^59 + 41 * q^60 - q^61 - 51 * q^62 + 77 * q^63 - 51 * q^64 + 25 * q^65 - 130 * q^66 - 16 * q^67 + 87 * q^68 + 32 * q^69 - 90 * q^70 - 7 * q^71 + 112 * q^72 - 11 * q^73 - 9 * q^74 - 157 * q^75 + 12 * q^76 + 10 * q^77 + 50 * q^78 + 24 * q^79 + 142 * q^80 + 61 * q^81 - 2 * q^82 + 60 * q^83 + 132 * q^84 - 33 * q^85 - 152 * q^86 - 88 * q^87 + 2 * q^88 + 58 * q^89 + 96 * q^90 + 72 * q^92 + 31 * q^93 + 2 * q^94 - 63 * q^95 + 137 * q^96 - 30 * q^97 + 33 * q^98 - 74 * q^99

Introduction

L-functions

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