LMFDB - Embedded newform 140.2.o.a.131.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(31,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("140.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.o (of order $6$, degree $2$, 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:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.14
Character	$\chi$	$=$	140.131
Dual form			140.2.o.a.31.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17265 + 0.790498i) q^{2} +(0.331177 + 0.573616i) q^{3} +(0.750225 + 1.85396i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.0650866 + 0.934447i) q^{6} +(-1.68748 + 2.03775i) q^{7} +(-0.585797 + 2.76710i) q^{8} +(1.28064 - 2.21814i) q^{9} +O(q^{10})$	\(q+(1.17265 + 0.790498i) q^{2} +(0.331177 + 0.573616i) q^{3} +(0.750225 + 1.85396i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.0650866 + 0.934447i) q^{6} +(-1.68748 + 2.03775i) q^{7} +(-0.585797 + 2.76710i) q^{8} +(1.28064 - 2.21814i) q^{9} +(-0.620297 - 1.27092i) q^{10} +(3.12892 - 1.80648i) q^{11} +(-0.815002 + 1.04433i) q^{12} -5.83027i q^{13} +(-3.58966 + 1.05561i) q^{14} -0.662355i q^{15} +(-2.87432 + 2.78177i) q^{16} +(-1.18483 + 0.684063i) q^{17} +(3.25518 - 1.58876i) q^{18} +(-2.04788 + 3.54704i) q^{19} +(0.277265 - 1.98069i) q^{20} +(-1.72774 - 0.293111i) q^{21} +(5.09715 + 0.355029i) q^{22} +(-2.81042 - 1.62259i) q^{23} +(-1.78126 + 0.580378i) q^{24} +(0.500000 + 0.866025i) q^{25} +(4.60882 - 6.83688i) q^{26} +3.68354 q^{27} +(-5.04389 - 1.59975i) q^{28} +5.19327 q^{29} +(0.523590 - 0.776712i) q^{30} +(-4.43405 - 7.67999i) q^{31} +(-5.56957 + 0.989905i) q^{32} +(2.07245 + 1.19653i) q^{33} +(-1.93014 - 0.134439i) q^{34} +(2.48027 - 0.920998i) q^{35} +(5.07311 + 0.710155i) q^{36} +(-5.39789 + 9.34942i) q^{37} +(-5.20538 + 2.54059i) q^{38} +(3.34434 - 1.93085i) q^{39} +(1.89087 - 2.10348i) q^{40} +0.832730i q^{41} +(-1.79433 - 1.70949i) q^{42} -3.10642i q^{43} +(5.69653 + 4.44561i) q^{44} +(-2.21814 + 1.28064i) q^{45} +(-2.01298 - 4.12437i) q^{46} +(-3.44801 + 5.97212i) q^{47} +(-2.54758 - 0.727497i) q^{48} +(-1.30481 - 6.87732i) q^{49} +(-0.0982654 + 1.41080i) q^{50} +(-0.784778 - 0.453092i) q^{51} +(10.8091 - 4.37402i) q^{52} +(3.70876 + 6.42376i) q^{53} +(4.31952 + 2.91183i) q^{54} -3.61296 q^{55} +(-4.65012 - 5.86314i) q^{56} -2.71285 q^{57} +(6.08989 + 4.10527i) q^{58} +(3.73928 + 6.47663i) q^{59} +(1.22798 - 0.496915i) q^{60} +(1.28652 + 0.742772i) q^{61} +(0.871427 - 12.5111i) q^{62} +(2.35894 + 6.35269i) q^{63} +(-7.31368 - 3.24192i) q^{64} +(-2.91513 + 5.04916i) q^{65} +(1.48441 + 3.04138i) q^{66} +(2.19763 - 1.26880i) q^{67} +(-2.15711 - 1.68343i) q^{68} -2.14947i q^{69} +(3.63655 + 0.880642i) q^{70} +3.52502i q^{71} +(5.38762 + 4.84305i) q^{72} +(-4.47721 + 2.58492i) q^{73} +(-13.7206 + 6.69660i) q^{74} +(-0.331177 + 0.573616i) q^{75} +(-8.11244 - 1.13561i) q^{76} +(-1.59884 + 9.42434i) q^{77} +(5.44808 + 0.379472i) q^{78} +(-9.82082 - 5.67005i) q^{79} +(3.88012 - 0.971925i) q^{80} +(-2.62202 - 4.54148i) q^{81} +(-0.658272 + 0.976503i) q^{82} +6.49145 q^{83} +(-0.752777 - 3.42306i) q^{84} +1.36813 q^{85} +(2.45562 - 3.64275i) q^{86} +(1.71989 + 2.97894i) q^{87} +(3.16580 + 9.71626i) q^{88} +(8.13303 + 4.69560i) q^{89} +(-3.61345 - 0.251686i) q^{90} +(11.8806 + 9.83847i) q^{91} +(0.899777 - 6.42771i) q^{92} +(2.93691 - 5.08688i) q^{93} +(-8.76426 + 4.27758i) q^{94} +(3.54704 - 2.04788i) q^{95} +(-2.41234 - 2.86696i) q^{96} +0.343189i q^{97} +(3.90642 - 9.09615i) q^{98} -9.25383i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9	$ 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38} - 62 q^{42} - 18 q^{44} + 12 q^{45} + 2 q^{46} - 16 q^{49} + 4 q^{50} - 36 q^{52} - 8 q^{53} + 12 q^{54} - 4 q^{56} + 48 q^{57} + 2 q^{58} + 14 q^{60} + 24 q^{61} + 4 q^{64} + 4 q^{65} + 24 q^{66} + 60 q^{68} - 4 q^{70} + 4 q^{72} - 72 q^{73} + 38 q^{74} - 40 q^{77} + 120 q^{78} - 36 q^{81} + 42 q^{82} - 20 q^{84} + 28 q^{86} + 4 q^{88} - 60 q^{89} - 4 q^{92} - 8 q^{93} + 18 q^{94} - 60 q^{96} + 78 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 - 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 - 8 * q^22 + 36 * q^24 + 16 * q^25 + 30 * q^26 + 2 * q^28 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 - 60 * q^38 - 62 * q^42 - 18 * q^44 + 12 * q^45 + 2 * q^46 - 16 * q^49 + 4 * q^50 - 36 * q^52 - 8 * q^53 + 12 * q^54 - 4 * q^56 + 48 * q^57 + 2 * q^58 + 14 * q^60 + 24 * q^61 + 4 * q^64 + 4 * q^65 + 24 * q^66 + 60 * q^68 - 4 * q^70 + 4 * q^72 - 72 * q^73 + 38 * q^74 - 40 * q^77 + 120 * q^78 - 36 * q^81 + 42 * q^82 - 20 * q^84 + 28 * q^86 + 4 * q^88 - 60 * q^89 - 4 * q^92 - 8 * q^93 + 18 * q^94 - 60 * q^96 + 78 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.17265	+	0.790498i	0.829190	+	0.558967i
$2$	1.17265	+	0.790498i	0.829190	+	0.558967i
$3$	0.331177	+	0.573616i	0.191205	+	0.331177i	0.945650	−	0.325186i	$-0.105427\pi$
$3$	0.331177	+	0.573616i	0.191205	+	0.331177i	−0.754445	+	0.656364i	$0.772094\pi$
$4$	0.750225	+	1.85396i	0.375113	+	0.926979i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−0.0650866	+	0.934447i	−0.0265715	+	0.381486i
$7$	−1.68748	+	2.03775i	−0.637808	+	0.770195i
$7$	−1.68748	+	2.03775i	−0.637808	+	0.770195i
$8$	−0.585797	+	2.76710i	−0.207111	+	0.978318i
$9$	1.28064	−	2.21814i	0.426881	−	0.739380i
$10$	−0.620297	−	1.27092i	−0.196155	−	0.401899i
$11$	3.12892	−	1.80648i	0.943404	−	0.544674i	0.0523781	−	0.998627i	$-0.483320\pi$
$11$	3.12892	−	1.80648i	0.943404	−	0.544674i	0.891026	+	0.453953i	$0.149987\pi$
$12$	−0.815002	+	1.04433i	−0.235271	+	0.301472i
$13$		−	5.83027i		−	1.61703i	−0.588478	−	0.808513i	$-0.700273\pi$
$13$		−	5.83027i		−	1.61703i	0.588478	−	0.808513i	$-0.299727\pi$
$14$	−3.58966	+	1.05561i	−0.959378	+	0.282125i
$15$		−	0.662355i		−	0.171019i
$16$	−2.87432	+	2.78177i	−0.718581	+	0.695443i
$17$	−1.18483	+	0.684063i	−0.287364	+	0.165910i	−0.636752	−	0.771068i	$-0.719723\pi$
$17$	−1.18483	+	0.684063i	−0.287364	+	0.165910i	0.349389	+	0.936978i	$0.386389\pi$
$18$	3.25518	−	1.58876i	0.767254	−	0.374474i
$19$	−2.04788	+	3.54704i	−0.469817	+	0.813747i	−0.999404	−	0.0345086i	$-0.989013\pi$
$19$	−2.04788	+	3.54704i	−0.469817	+	0.813747i	0.529588	+	0.848255i	$0.322347\pi$
$20$	0.277265	−	1.98069i	0.0619983	−	0.442895i
$21$	−1.72774	−	0.293111i	−0.377024	−	0.0639622i
$22$	5.09715	+	0.355029i	1.08672	+	0.0756925i
$23$	−2.81042	−	1.62259i	−0.586012	−	0.338334i	0.177507	−	0.984120i	$-0.443197\pi$
$23$	−2.81042	−	1.62259i	−0.586012	−	0.338334i	−0.763519	+	0.645785i	$0.776530\pi$
$24$	−1.78126	+	0.580378i	−0.363597	+	0.118469i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	4.60882	−	6.83688i	0.903863	−	1.34082i
$27$	3.68354			0.708898
$28$	−5.04389	−	1.59975i	−0.953205	−	0.302325i
$29$	5.19327			0.964365			0.482183	−	0.876071i	$-0.339844\pi$
$29$	5.19327			0.964365			0.482183	+	0.876071i	$0.339844\pi$
$30$	0.523590	−	0.776712i	0.0955940	−	0.141807i
$31$	−4.43405	−	7.67999i	−0.796378	−	1.37937i	−0.921960	−	0.387284i	$-0.873413\pi$
$31$	−4.43405	−	7.67999i	−0.796378	−	1.37937i	0.125582	−	0.992083i	$-0.459920\pi$
$32$	−5.56957	+	0.989905i	−0.984570	+	0.174992i
$33$	2.07245	+	1.19653i	0.360768	+	0.208289i
$34$	−1.93014	−	0.134439i	−0.331017	−	0.0230562i
$35$	2.48027	−	0.920998i	0.419243	−	0.155677i
$36$	5.07311	+	0.710155i	0.845518	+	0.118359i
$37$	−5.39789	+	9.34942i	−0.887408	+	1.53704i	−0.0444796	+	0.999010i	$0.514163\pi$
$37$	−5.39789	+	9.34942i	−0.887408	+	1.53704i	−0.842928	+	0.538026i	$0.819170\pi$
$38$	−5.20538	+	2.54059i	−0.844425	+	0.412139i
$39$	3.34434	−	1.93085i	0.535522	−	0.309184i
$40$	1.89087	−	2.10348i	0.298972	−	0.332589i
$41$			0.832730i			0.130051i	0.997884	+	0.0650253i	$0.0207128\pi$
$41$			0.832730i			0.130051i	−0.997884	+	0.0650253i	$0.979287\pi$
$42$	−1.79433	−	1.70949i	−0.276871	−	0.263780i
$43$		−	3.10642i		−	0.473725i	−0.971543	−	0.236862i	$-0.923881\pi$
$43$		−	3.10642i		−	0.473725i	0.971543	−	0.236862i	$-0.0761190\pi$
$44$	5.69653	+	4.44561i	0.858785	+	0.670201i
$45$	−2.21814	+	1.28064i	−0.330661	+	0.190907i
$46$	−2.01298	−	4.12437i	−0.296798	−	0.608105i
$47$	−3.44801	+	5.97212i	−0.502943	+	0.871124i	0.497051	+	0.867721i	$0.334416\pi$
$47$	−3.44801	+	5.97212i	−0.502943	+	0.871124i	−0.999994	+	0.00340208i	$0.998917\pi$
$48$	−2.54758	−	0.727497i	−0.367712	−	0.105005i
$49$	−1.30481	−	6.87732i	−0.186402	−	0.982474i
$50$	−0.0982654	+	1.41080i	−0.0138968	+	0.199517i
$51$	−0.784778	−	0.453092i	−0.109891	−	0.0634456i
$52$	10.8091	−	4.37402i	1.49895	−	0.606567i
$53$	3.70876	+	6.42376i	0.509437	+	0.882371i	0.999940	+	0.0109318i	$0.00347978\pi$
$53$	3.70876	+	6.42376i	0.509437	+	0.882371i	−0.490503	+	0.871440i	$0.663187\pi$
$54$	4.31952	+	2.91183i	0.587812	+	0.396250i
$55$	−3.61296			−0.487172
$56$	−4.65012	−	5.86314i	−0.621399	−	0.783494i
$57$	−2.71285			−0.359326
$58$	6.08989	+	4.10527i	0.799642	+	0.539048i
$59$	3.73928	+	6.47663i	0.486813	+	0.843185i	0.999885	−	0.0151606i	$-0.00482595\pi$
$59$	3.73928	+	6.47663i	0.486813	+	0.843185i	−0.513072	+	0.858346i	$0.671493\pi$
$60$	1.22798	−	0.496915i	0.158531	−	0.0641515i
$61$	1.28652	+	0.742772i	0.164722	+	0.0951022i	0.580095	−	0.814549i	$-0.303016\pi$
$61$	1.28652	+	0.742772i	0.164722	+	0.0951022i	−0.415373	+	0.909651i	$0.636349\pi$
$62$	0.871427	−	12.5111i	0.110671	−	1.58891i
$63$	2.35894	+	6.35269i	0.297199	+	0.800364i
$64$	−7.31368	−	3.24192i	−0.914210	−	0.405240i
$65$	−2.91513	+	5.04916i	−0.361578	+	0.626271i
$66$	1.48441	+	3.04138i	0.182718	+	0.374368i
$67$	2.19763	−	1.26880i	0.268484	−	0.155009i	−0.359715	−	0.933062i	$-0.617126\pi$
$67$	2.19763	−	1.26880i	0.268484	−	0.155009i	0.628198	+	0.778053i	$0.283793\pi$
$68$	−2.15711	−	1.68343i	−0.261589	−	0.204145i
$69$		−	2.14947i		−	0.258765i
$70$	3.63655	+	0.880642i	0.434650	+	0.105257i
$71$			3.52502i			0.418342i	0.977879	+	0.209171i	$0.0670766\pi$
$71$			3.52502i			0.418342i	−0.977879	+	0.209171i	$0.932923\pi$
$72$	5.38762	+	4.84305i	0.634937	+	0.570759i
$73$	−4.47721	+	2.58492i	−0.524018	+	0.302542i	−0.738577	−	0.674169i	$-0.764502\pi$
$73$	−4.47721	+	2.58492i	−0.524018	+	0.302542i	0.214559	+	0.976711i	$0.431169\pi$
$74$	−13.7206	+	6.69660i	−1.59498	+	0.778464i
$75$	−0.331177	+	0.573616i	−0.0382411	+	0.0662355i
$76$	−8.11244	−	1.13561i	−0.930561	−	0.130264i
$77$	−1.59884	+	9.42434i	−0.182205	+	1.07400i
$78$	5.44808	+	0.379472i	0.616873	+	0.0429668i
$79$	−9.82082	−	5.67005i	−1.10493	−	0.637931i	−0.167417	−	0.985886i	$-0.553543\pi$
$79$	−9.82082	−	5.67005i	−1.10493	−	0.637931i	−0.937511	+	0.347955i	$0.886876\pi$
$80$	3.88012	−	0.971925i	0.433811	−	0.108665i
$81$	−2.62202	−	4.54148i	−0.291336	−	0.504609i
$82$	−0.658272	+	0.976503i	−0.0726939	+	0.107837i
$83$	6.49145			0.712529			0.356264	−	0.934385i	$-0.384050\pi$
$83$	6.49145			0.712529			0.356264	+	0.934385i	$0.384050\pi$
$84$	−0.752777	−	3.42306i	−0.0821347	−	0.373486i
$85$	1.36813			0.148394
$86$	2.45562	−	3.64275i	0.264796	−	0.392808i
$87$	1.71989	+	2.97894i	0.184392	+	0.319376i
$88$	3.16580	+	9.71626i	0.337476	+	1.03576i
$89$	8.13303	+	4.69560i	0.862099	+	0.497733i	0.864715	−	0.502264i	$-0.167499\pi$
$89$	8.13303	+	4.69560i	0.862099	+	0.497733i	−0.00261566	+	0.999997i	$0.500833\pi$
$90$	−3.61345	−	0.251686i	−0.380891	−	0.0265300i
$91$	11.8806	+	9.83847i	1.24543	+	1.03135i
$92$	0.899777	−	6.42771i	0.0938083	−	0.670135i
$93$	2.93691	−	5.08688i	0.304544	−	0.527485i
$94$	−8.76426	+	4.27758i	−0.903965	+	0.441199i
$95$	3.54704	−	2.04788i	0.363919	−	0.210108i
$96$	−2.41234	−	2.86696i	−0.246208	−	0.292608i
$97$			0.343189i			0.0348455i	0.999848	+	0.0174228i	$0.00554612\pi$
$97$			0.343189i			0.0348455i	−0.999848	+	0.0174228i	$0.994454\pi$
$98$	3.90642	−	9.09615i	0.394608	−	0.918850i
$99$		−	9.25383i		−	0.930045i
$100$	−1.23046	+	1.57669i	−0.123046	+	0.157669i
$101$	3.92859	−	2.26817i	0.390910	−	0.225692i	−0.291645	−	0.956527i	$-0.594202\pi$
$101$	3.92859	−	2.26817i	0.390910	−	0.225692i	0.682554	+	0.730835i	$0.260869\pi$
$102$	−0.562104	−	1.15169i	−0.0556566	−	0.114034i
$103$	−3.06906	+	5.31577i	−0.302404	+	0.523778i	−0.976680	−	0.214701i	$-0.931122\pi$
$103$	−3.06906	+	5.31577i	−0.302404	+	0.523778i	0.674276	+	0.738479i	$0.264456\pi$
$104$	16.1329	+	3.41536i	1.58196	+	0.334903i
$105$	1.34971	+	1.11771i	0.131718	+	0.109077i
$106$	−0.728886	+	10.4646i	−0.0707957	+	1.01641i
$107$	−6.64066	−	3.83398i	−0.641976	−	0.370645i	0.143399	−	0.989665i	$-0.454197\pi$
$107$	−6.64066	−	3.83398i	−0.641976	−	0.370645i	−0.785375	+	0.619020i	$0.787530\pi$
$108$	2.76349	+	6.82914i	0.265917	+	0.657134i
$109$	−0.647616	−	1.12170i	−0.0620304	−	0.107440i	0.833342	−	0.552757i	$-0.186424\pi$
$109$	−0.647616	−	1.12170i	−0.0620304	−	0.107440i	−0.895373	+	0.445317i	$0.853091\pi$
$110$	−4.23675	−	2.85604i	−0.403958	−	0.272313i
$111$	−7.15064			−0.678709
$112$	−0.818178	−	10.5513i	−0.0773105	−	0.997007i
$113$	7.10591			0.668468			0.334234	−	0.942490i	$-0.391522\pi$
$113$	7.10591			0.668468			0.334234	+	0.942490i	$0.391522\pi$
$114$	−3.18123	−	2.14450i	−0.297950	−	0.200851i
$115$	1.62259	+	2.81042i	0.151308	+	0.262073i
$116$	3.89612	+	9.62810i	0.361746	+	0.893946i
$117$	−12.9323	−	7.46649i	−1.19560	−	0.690278i
$118$	−0.734884	+	10.5507i	−0.0676516	+	0.971273i
$119$	0.605436	−	3.56873i	0.0555002	−	0.327145i
$120$	1.83280	+	0.388005i	0.167311	+	0.0354199i
$121$	1.02675	−	1.77837i	0.0933405	−	0.161670i
$122$	0.921479	+	1.88800i	0.0834268	+	0.170932i
$123$	−0.477667	+	0.275781i	−0.0430698	+	0.0248664i
$124$	10.9119	−	13.9823i	0.979914	−	1.25564i
$125$		−	1.00000i		−	0.0894427i
$126$	−2.25558	+	9.31424i	−0.200943	+	0.829778i
$127$		−	17.0178i		−	1.51008i	−0.655677	−	0.755041i	$-0.727617\pi$
$127$		−	17.0178i		−	1.51008i	0.655677	−	0.755041i	$-0.272383\pi$
$128$	−6.01367	−	9.58310i	−0.531539	−	0.847034i
$129$	1.78189	−	1.02878i	0.156887	−	0.0905787i
$130$	−7.40979	+	3.61650i	−0.649882	+	0.317188i
$131$	−0.603066	+	1.04454i	−0.0526901	+	0.0912619i	−0.891167	−	0.453674i	$-0.850113\pi$
$131$	−0.603066	+	1.04454i	−0.0526901	+	0.0912619i	0.838477	+	0.544936i	$0.183446\pi$
$132$	−0.663512	+	4.73991i	−0.0577513	+	0.412556i
$133$	−3.77220	−	10.1586i	−0.327091	−	0.880865i
$134$	3.58005	+	0.249359i	0.309269	+	0.0215414i
$135$	−3.19004	−	1.84177i	−0.274555	−	0.158514i
$136$	−1.19880	−	3.67927i	−0.102796	−	0.315495i
$137$	−1.07245	−	1.85754i	−0.0916258	−	0.158701i	0.816570	−	0.577247i	$-0.195873\pi$
$137$	−1.07245	−	1.85754i	−0.0916258	−	0.158701i	−0.908195	+	0.418547i	$0.862540\pi$
$138$	1.69915	−	2.52058i	0.144641	−	0.214566i
$139$	−3.39555			−0.288007			−0.144004	−	0.989577i	$-0.545998\pi$
$139$	−3.39555			−0.288007			−0.144004	+	0.989577i	$0.545998\pi$
$140$	3.56826	+	3.90737i	0.301573	+	0.330233i
$141$	−4.56761			−0.384662
$142$	−2.78652	+	4.13362i	−0.233839	+	0.346885i
$143$	−10.5323	−	18.2424i	−0.880753	−	1.52551i
$144$	2.48938	+	9.93811i	0.207448	+	0.828176i
$145$	−4.49750	−	2.59663i	−0.373497	−	0.215639i
$146$	−7.29359	−	0.508017i	−0.603622	−	0.0420438i
$147$	3.51281	−	3.02607i	0.289732	−	0.249586i
$148$	−21.3831	−	2.99329i	−1.75768	−	0.246047i
$149$	9.54319	−	16.5293i	0.781808	−	1.35413i	−0.149079	−	0.988825i	$-0.547631\pi$
$149$	9.54319	−	16.5293i	0.781808	−	1.35413i	0.930887	−	0.365307i	$-0.119036\pi$
$150$	−0.841798	+	0.410857i	−0.0687325	+	0.0335463i
$151$	−8.31900	+	4.80298i	−0.676990	+	0.390861i	−0.798720	−	0.601703i	$-0.794489\pi$
$151$	−8.31900	+	4.80298i	−0.676990	+	0.390861i	0.121730	+	0.992563i	$0.461156\pi$
$152$	−8.61537	−	7.74455i	−0.698799	−	0.628166i
$153$			3.50416i			0.283295i
$154$	−9.32481	+	9.78759i	−0.751414	+	0.788706i
$155$			8.86809i			0.712302i
$156$	6.08873	+	4.75168i	0.487488	+	0.380439i
$157$	14.2568	−	8.23118i	1.13782	−	0.656919i	0.191928	−	0.981409i	$-0.438526\pi$
$157$	14.2568	−	8.23118i	1.13782	−	0.656919i	0.945889	+	0.324490i	$0.105193\pi$
$158$	−7.03424	−	14.4123i	−0.559614	−	1.14658i
$159$	−2.45651	+	4.25481i	−0.194814	+	0.337428i
$160$	5.31834	+	1.92750i	0.420452	+	0.152382i
$161$	8.04896	−	2.98881i	0.634347	−	0.235552i
$162$	0.515309	−	7.39828i	0.0404865	−	0.581264i
$163$	6.19738	+	3.57806i	0.485416	+	0.280255i	0.722671	−	0.691192i	$-0.242914\pi$
$163$	6.19738	+	3.57806i	0.485416	+	0.280255i	−0.237255	+	0.971447i	$0.576248\pi$
$164$	−1.54385	+	0.624735i	−0.120554	+	0.0487836i
$165$	−1.19653	−	2.07245i	−0.0931498	−	0.161340i
$166$	7.61221	+	5.13148i	0.590822	+	0.398280i
$167$	13.7127			1.06112			0.530562	−	0.847646i	$-0.321981\pi$
$167$	13.7127			1.06112			0.530562	+	0.847646i	$0.321981\pi$
$168$	1.82317	−	4.60912i	0.140661	−	0.355601i
$169$	−20.9920			−1.61477
$170$	1.60433	+	1.08150i	0.123047	+	0.0829473i
$171$	5.24522	+	9.08498i	0.401112	+	0.694746i
$172$	5.75917	−	2.33052i	0.439133	−	0.177700i
$173$	3.39862	+	1.96219i	0.258392	+	0.149183i	0.623601	−	0.781743i	$-0.285669\pi$
$173$	3.39862	+	1.96219i	0.258392	+	0.149183i	−0.365209	+	0.930926i	$0.619002\pi$
$174$	−0.338012	+	4.85283i	−0.0256246	+	0.367892i
$175$	−2.60848	−	0.442529i	−0.197183	−	0.0334521i
$176$	−3.96830	+	13.8963i	−0.299122	+	1.04748i
$177$	−2.47673	+	4.28982i	−0.186162	+	0.322443i
$178$	5.82534	+	11.9355i	0.436628	+	0.894600i
$179$	17.8002	−	10.2769i	1.33045	−	0.768134i	0.345079	−	0.938574i	$-0.387852\pi$
$179$	17.8002	−	10.2769i	1.33045	−	0.768134i	0.985368	+	0.170440i	$0.0545188\pi$
$180$	−4.03836	−	3.15157i	−0.301002	−	0.234904i
$181$			13.0603i			0.970762i	0.874303	+	0.485381i	$0.161319\pi$
$181$			13.0603i			0.970762i	−0.874303	+	0.485381i	$0.838681\pi$
$182$	6.15452	+	20.9287i	0.456203	+	1.55134i
$183$			0.983957i			0.0727362i
$184$	6.13622	−	6.82619i	0.452368	−	0.503234i
$185$	9.34942	−	5.39789i	0.687383	−	0.396861i
$186$	7.46514	−	3.64352i	0.547371	−	0.267156i
$187$	−2.47149	+	4.28075i	−0.180733	+	0.313039i
$188$	−13.6588	−	1.91202i	−0.996174	−	0.139449i
$189$	−6.21591	+	7.50612i	−0.452141	+	0.545990i
$190$	5.77829	+	0.402472i	0.419201	+	0.0291984i
$191$	−10.8038	−	6.23755i	−0.781733	−	0.451334i	0.0553113	−	0.998469i	$-0.482385\pi$
$191$	−10.8038	−	6.23755i	−0.781733	−	0.451334i	−0.837044	+	0.547136i	$0.815718\pi$
$192$	−0.562510	−	5.26890i	−0.0405956	−	0.380250i
$193$	−9.53225	−	16.5103i	−0.686147	−	1.18844i	−0.973075	−	0.230489i	$-0.925967\pi$
$193$	−9.53225	−	16.5103i	−0.686147	−	1.18844i	0.286928	−	0.957952i	$-0.407366\pi$
$194$	−0.271290	+	0.402441i	−0.0194775	+	0.0288936i
$195$	−3.86171			−0.276543
$196$	11.7714	−	7.57860i	0.840811	−	0.541329i
$197$	1.93188			0.137641			0.0688203	−	0.997629i	$-0.478076\pi$
$197$	1.93188			0.137641			0.0688203	+	0.997629i	$0.478076\pi$
$198$	7.31513	−	10.8515i	0.519864	−	0.771184i
$199$	10.2823	+	17.8094i	0.728892	+	1.26248i	0.957352	+	0.288924i	$0.0932976\pi$
$199$	10.2823	+	17.8094i	0.728892	+	1.26248i	−0.228460	+	0.973553i	$0.573369\pi$
$200$	−2.68928	+	0.876235i	−0.190161	+	0.0619591i
$201$	1.45561	+	0.840398i	0.102671	+	0.0592771i
$202$	6.39986	+	0.445766i	0.450293	+	0.0313640i
$203$	−8.76354	+	10.5826i	−0.615080	+	0.742750i
$204$	0.251253	−	1.79487i	0.0175912	−	0.125666i
$205$	0.416365	−	0.721165i	0.0290802	−	0.0503684i
$206$	−7.80105	+	3.80746i	−0.543525	+	0.265278i
$207$	−7.19828	+	4.15593i	−0.500315	+	0.288857i
$208$	16.2185	+	16.7581i	1.12455	+	1.16196i
$209$			14.7979i			1.02359i
$210$	0.699191	+	2.37763i	0.0482488	+	0.164072i
$211$			9.98398i			0.687326i	0.939093	+	0.343663i	$0.111668\pi$
$211$			9.98398i			0.687326i	−0.939093	+	0.343663i	$0.888332\pi$
$212$	−9.12698	+	11.6952i	−0.626843	+	0.803227i
$213$	−2.02200	+	1.16741i	−0.138545	+	0.0799893i
$214$	−4.75642	−	9.74536i	−0.325142	−	0.666179i
$215$	−1.55321	+	2.69024i	−0.105928	+	0.183473i
$216$	−2.15781	+	10.1927i	−0.146820	+	0.693528i
$217$	23.1322	+	3.92439i	1.57032	+	0.266405i
$218$	0.127277	−	1.82731i	0.00862026	−	0.123761i
$219$	−2.96550	−	1.71213i	−0.200390	−	0.115695i
$220$	−2.71054	−	6.69828i	−0.182744	−	0.451598i
$221$	3.98827	+	6.90789i	0.268280	+	0.464675i
$222$	−8.38521	−	5.65257i	−0.562778	−	0.379375i
$223$	16.8179			1.12621			0.563106	−	0.826384i	$-0.309606\pi$
$223$	16.8179			1.12621			0.563106	+	0.826384i	$0.309606\pi$
$224$	7.38137	−	13.0198i	0.493188	−	0.869922i
$225$	2.56129			0.170752
$226$	8.33276	+	5.61721i	0.554287	+	0.373651i
$227$	−9.91692	−	17.1766i	−0.658209	−	1.14005i	−0.981079	−	0.193608i	$-0.937981\pi$
$227$	−9.91692	−	17.1766i	−0.658209	−	1.14005i	0.322870	−	0.946443i	$-0.395352\pi$
$228$	−2.03525	−	5.02951i	−0.134788	−	0.333088i
$229$	12.0664	+	6.96655i	0.797371	+	0.460363i	0.842551	−	0.538616i	$-0.181053\pi$
$229$	12.0664	+	6.96655i	0.797371	+	0.460363i	−0.0451798	+	0.998979i	$0.514386\pi$
$230$	−0.318890	+	4.57830i	−0.0210270	+	0.301884i
$231$	−5.93545	+	2.20401i	−0.390524	+	0.145013i
$232$	−3.04220	+	14.3703i	−0.199730	+	0.943455i
$233$	−5.11283	+	8.85568i	−0.334953	+	0.580155i	−0.983476	−	0.181040i	$-0.942054\pi$
$233$	−5.11283	+	8.85568i	−0.334953	+	0.580155i	0.648523	+	0.761195i	$0.275387\pi$
$234$	−9.26289	−	18.9786i	−0.605534	−	1.24067i
$235$	5.97212	−	3.44801i	0.389578	−	0.224923i
$236$	−9.20209	+	11.7914i	−0.599005	+	0.767555i
$237$		−	7.51117i		−	0.487903i
$238$	3.53104	−	3.70628i	0.228883	−	0.240242i
$239$			17.0835i			1.10504i	0.833501	+	0.552518i	$0.186333\pi$
$239$			17.0835i			1.10504i	−0.833501	+	0.552518i	$0.813667\pi$
$240$	1.84252	+	1.90382i	0.118934	+	0.122891i
$241$	−16.0074	+	9.24185i	−1.03112	+	0.595320i	−0.917307	−	0.398182i	$-0.869641\pi$
$241$	−16.0074	+	9.24185i	−1.03112	+	0.595320i	−0.113818	+	0.993502i	$0.536308\pi$
$242$	2.60982	−	1.27377i	0.167765	−	0.0818813i
$243$	7.26203	−	12.5782i	0.465859	−	0.806892i
$244$	−0.411889	+	2.94240i	−0.0263685	+	0.188368i
$245$	−2.30866	+	6.60834i	−0.147495	+	0.422191i
$246$	−0.778142	−	0.0541995i	−0.0496125	−	0.00345564i
$247$	20.6802	+	11.9397i	1.31585	+	0.759706i
$248$	23.8488	−	7.77053i	1.51440	−	0.493429i
$249$	2.14982	+	3.72360i	0.136239	+	0.235973i
$250$	0.790498	−	1.17265i	0.0499955	−	0.0741650i
$251$	16.5313			1.04344			0.521722	−	0.853116i	$-0.325290\pi$
$251$	16.5313			1.04344			0.521722	+	0.853116i	$0.325290\pi$
$252$	−10.0079	+	9.13933i	−0.630438	+	0.575724i
$253$	−11.7247			−0.737128
$254$	13.4525	−	19.9559i	0.844086	−	1.25215i
$255$	0.453092	+	0.784778i	0.0283737	+	0.0491447i
$256$	0.523471	−	15.9914i	0.0327169	−	0.999465i
$257$	−5.36502	−	3.09749i	−0.334660	−	0.193216i	0.323248	−	0.946314i	$-0.395225\pi$
$257$	−5.36502	−	3.09749i	−0.334660	−	0.193216i	−0.657908	+	0.753098i	$0.728559\pi$
$258$	2.90279	+	0.202186i	0.180720	+	0.0125876i
$259$	−9.94290	−	26.7765i	−0.617822	−	1.66381i
$260$	−11.5479	−	1.61653i	−0.716173	−	0.100253i
$261$	6.65072	−	11.5194i	0.411669	−	0.713032i
$262$	−1.53289	+	0.748160i	−0.0947025	+	0.0462215i
$263$	−18.3196	+	10.5768i	−1.12963	+	0.652194i	−0.943842	−	0.330396i	$-0.892818\pi$
$263$	−18.3196	+	10.5768i	−1.12963	+	0.652194i	−0.185790	+	0.982589i	$0.559484\pi$
$264$	−4.52496	+	5.03376i	−0.278492	+	0.309806i
$265$		−	7.41752i		−	0.455655i
$266$	3.60691	−	14.8945i	0.221154	−	0.913237i
$267$			6.22031i			0.380677i
$268$	4.00103	+	3.12243i	0.244402	+	0.190733i
$269$	−26.8352	+	15.4933i	−1.63617	+	0.944642i	−0.654033	+	0.756466i	$0.726924\pi$
$269$	−26.8352	+	15.4933i	−1.63617	+	0.944642i	−0.982135	+	0.188177i	$0.939742\pi$
$270$	−2.28489	−	4.68148i	−0.139054	−	0.284906i
$271$	11.5190	−	19.9516i	0.699732	−	1.21197i	−0.268827	−	0.963188i	$-0.586636\pi$
$271$	11.5190	−	19.9516i	0.699732	−	1.21197i	0.968559	−	0.248783i	$-0.0800306\pi$
$272$	1.50268	−	5.26215i	0.0911134	−	0.319065i
$273$	−1.70892	+	10.0732i	−0.103428	+	0.609657i
$274$	0.210770	−	3.02602i	0.0127331	−	0.182809i
$275$	3.12892	+	1.80648i	0.188681	+	0.108935i
$276$	3.98502	−	1.61258i	0.239870	−	0.0970662i
$277$	−3.47281	−	6.01508i	−0.208661	−	0.361411i	0.742632	−	0.669700i	$-0.233577\pi$
$277$	−3.47281	−	6.01508i	−0.208661	−	0.361411i	−0.951293	+	0.308288i	$0.900244\pi$
$278$	−3.98180	−	2.68418i	−0.238813	−	0.160986i
$279$	−22.7137			−1.35984
$280$	1.09556	+	7.40269i	0.0654720	+	0.442395i
$281$	−4.24391			−0.253170			−0.126585	−	0.991956i	$-0.540402\pi$
$281$	−4.24391			−0.253170			−0.126585	+	0.991956i	$0.540402\pi$
$282$	−5.35621	−	3.61068i	−0.318958	−	0.215013i
$283$	−4.26599	−	7.38891i	−0.253587	−	0.439225i	0.710924	−	0.703269i	$-0.248277\pi$
$283$	−4.26599	−	7.38891i	−0.253587	−	0.439225i	−0.964511	+	0.264044i	$0.914944\pi$
$284$	−6.53523	+	2.64456i	−0.387795	+	0.156926i
$285$	2.34940	+	1.35643i	0.139166	+	0.0803477i
$286$	2.06992	−	29.7178i	0.122397	−	1.75725i
$287$	−1.69689	−	1.40522i	−0.100164	−	0.0829473i
$288$	−4.93688	+	13.6218i	−0.290909	+	0.802672i
$289$	−7.56412	+	13.1014i	−0.444948	+	0.770673i
$290$	−3.22137	−	6.60021i	−0.189165	−	0.387578i
$291$	−0.196859	+	0.113656i	−0.0115401	+	0.00666265i
$292$	−8.15125	−	6.36129i	−0.477016	−	0.372267i
$293$			25.2319i			1.47406i	0.675857	+	0.737032i	$0.263773\pi$
$293$			25.2319i			1.47406i	−0.675857	+	0.737032i	$0.736227\pi$
$294$	6.51141	−	0.771656i	0.379753	−	0.0450039i
$295$		−	7.47856i		−	0.435419i
$296$	−22.7087	−	20.4134i	−1.31992	−	1.18650i
$297$	11.5255	−	6.65425i	0.668777	−	0.386119i
$298$	24.2572	−	11.8392i	1.40518	−	0.685828i
$299$	−9.46017	+	16.3855i	−0.547096	+	0.947597i
$300$	−1.31192	−	0.183648i	−0.0757436	−	0.0106029i
$301$	6.33009	+	5.24203i	0.364861	+	0.302145i
$302$	−13.5520	−	0.943933i	−0.779832	−	0.0543172i
$303$	2.60212	+	1.50234i	0.149488	+	0.0863070i
$304$	−3.98078	−	15.8921i	−0.228313	−	0.911474i
$305$	−0.742772	−	1.28652i	−0.0425310	−	0.0736658i
$306$	−2.77003	+	4.10916i	−0.158352	+	0.234905i
$307$	−29.2635			−1.67016			−0.835078	−	0.550132i	$-0.814577\pi$
$307$	−29.2635			−1.67016			−0.835078	+	0.550132i	$0.814577\pi$
$308$	−18.6718	+	4.10619i	−1.06393	+	0.233972i
$309$	−4.06561			−0.231285
$310$	−7.01021	+	10.3992i	−0.398153	+	0.590634i
$311$	−11.3730	−	19.6987i	−0.644906	−	1.11701i	−0.984323	−	0.176374i	$-0.943563\pi$
$311$	−11.3730	−	19.6987i	−0.644906	−	1.11701i	0.339417	−	0.940636i	$-0.389770\pi$
$312$	3.38376	+	10.3852i	0.191568	+	0.587946i
$313$	5.70261	+	3.29240i	0.322331	+	0.186098i	0.652431	−	0.757848i	$-0.273749\pi$
$313$	5.70261	+	3.29240i	0.322331	+	0.186098i	−0.330100	+	0.943946i	$0.607083\pi$
$314$	23.2250	+	1.61768i	1.31066	+	0.0912910i
$315$	1.13344	−	6.68106i	0.0638624	−	0.376435i
$316$	3.14421	−	22.4612i	0.176876	−	1.26354i
$317$	7.06086	−	12.2298i	0.396577	−	0.686892i	−0.596724	−	0.802447i	$-0.703531\pi$
$317$	7.06086	−	12.2298i	0.396577	−	0.686892i	0.993301	+	0.115555i	$0.0368646\pi$
$318$	−6.24405	+	3.04754i	−0.350149	+	0.170897i
$319$	16.2493	−	9.38153i	0.909786	−	0.525265i
$320$	4.71288	+	6.46443i	0.263458	+	0.361372i
$321$		−	5.07891i		−	0.283477i
$322$	11.8013	+	2.85785i	0.657660	+	0.159262i
$323$		−	5.60352i		−	0.311788i
$324$	6.45260	−	8.26825i	0.358478	−	0.459347i
$325$	5.04916	−	2.91513i	0.280077	−	0.161703i
$326$	4.43892	+	9.09483i	0.245849	+	0.503716i
$327$	0.428952	−	0.742966i	0.0237211	−	0.0410861i
$328$	−2.30425	−	0.487811i	−0.127231	−	0.0269349i
$329$	−6.35122	−	17.1040i	−0.350154	−	0.942974i
$330$	0.235155	−	3.37612i	0.0129449	−	0.185849i
$331$	17.5997	+	10.1612i	0.967368	+	0.558510i	0.898433	−	0.439111i	$-0.144707\pi$
$331$	17.5997	+	10.1612i	0.967368	+	0.558510i	0.0689349	+	0.997621i	$0.478040\pi$
$332$	4.87005	+	12.0349i	0.267279	+	0.660499i
$333$	13.8255	+	23.9466i	0.757635	+	1.31226i
$334$	16.0803	+	10.8399i	0.879873	+	0.593133i
$335$	−2.53761			−0.138644
$336$	5.78145	−	3.96368i	0.315404	−	0.216237i
$337$	15.7704			0.859067			0.429533	−	0.903051i	$-0.358678\pi$
$337$	15.7704			0.859067			0.429533	+	0.903051i	$0.358678\pi$
$338$	−24.6164	−	16.5942i	−1.33895	−	0.902604i
$339$	2.35332	+	4.07607i	0.127815	+	0.221381i
$340$	1.02640	+	2.53645i	0.0556645	+	0.137558i
$341$	−27.7475	−	16.0200i	−1.50261	−	0.867534i
$342$	−1.03085	+	14.7999i	−0.0557418	+	0.800285i
$343$	16.2161	+	8.94647i	0.875585	+	0.483064i
$344$	8.59578	+	1.81973i	0.463453	+	0.0981134i
$345$	−1.07473	+	1.86149i	−0.0578617	+	0.100219i
$346$	2.43429	+	4.98757i	0.130868	+	0.268133i
$347$	−2.63950	+	1.52392i	−0.141696	+	0.0818082i	−0.569172	−	0.822218i	$-0.692736\pi$
$347$	−2.63950	+	1.52392i	−0.141696	+	0.0818082i	0.427476	+	0.904027i	$0.359403\pi$
$348$	−4.23252	+	5.42348i	−0.226887	+	0.290729i
$349$			8.40462i			0.449889i	0.974372	+	0.224944i	$0.0722201\pi$
$349$			8.40462i			0.449889i	−0.974372	+	0.224944i	$0.927780\pi$
$350$	−2.70902	−	2.58093i	−0.144803	−	0.137957i
$351$		−	21.4761i		−	1.14631i
$352$	−15.6385	+	13.1586i	−0.833533	+	0.701358i
$353$	0.374834	−	0.216411i	0.0199504	−	0.0115184i	−0.489992	−	0.871727i	$-0.663000\pi$
$353$	0.374834	−	0.216411i	0.0199504	−	0.0115184i	0.509942	+	0.860209i	$0.329667\pi$
$354$	−6.29544	+	3.07262i	−0.334599	+	0.163308i
$355$	1.76251	−	3.05275i	0.0935442	−	0.162023i
$356$	−2.60385	+	18.6011i	−0.138004	+	0.985854i
$357$	2.24759	−	0.834594i	0.118955	−	0.0441714i
$358$	28.9973	+	2.01973i	1.53255	+	0.106746i
$359$	23.3662	+	13.4905i	1.23322	+	0.712002i	0.967700	−	0.252103i	$-0.0811222\pi$
$359$	23.3662	+	13.4905i	1.23322	+	0.712002i	0.265522	+	0.964105i	$0.414456\pi$
$360$	−2.24429	−	6.88801i	−0.118284	−	0.363030i
$361$	1.11234	+	1.92663i	0.0585442	+	0.101402i
$362$	−10.3241	+	15.3151i	−0.542623	+	0.804946i
$363$	1.36014			0.0713888
$364$	−9.32699	+	29.4072i	−0.488867	+	1.54136i
$365$	5.16984			0.270602
$366$	−0.777816	+	1.15384i	−0.0406571	+	0.0603121i
$367$	10.4106	+	18.0317i	0.543430	+	0.941248i	0.998704	+	0.0508965i	$0.0162079\pi$
$367$	10.4106	+	18.0317i	0.543430	+	0.941248i	−0.455274	+	0.890351i	$0.650459\pi$
$368$	12.5917	−	3.15408i	0.656390	−	0.164418i
$369$	1.84711	+	1.06643i	0.0961568	+	0.0555161i
$370$	15.2306	+	1.06085i	0.791804	+	0.0551511i
$371$	−19.3485	−	3.28247i	−1.00452	−	0.170417i
$372$	11.6342	+	1.62860i	0.603206	+	0.0844392i
$373$	8.83072	−	15.2953i	0.457237	−	0.791958i	−0.541576	−	0.840652i	$-0.682172\pi$
$373$	8.83072	−	15.2953i	0.457237	−	0.791958i	0.998814	+	0.0486931i	$0.0155056\pi$
$374$	−6.28212	+	3.06612i	−0.324841	+	0.158545i
$375$	0.573616	−	0.331177i	0.0296214	−	0.0171019i
$376$	−14.5056	−	13.0394i	−0.748071	−	0.672457i
$377$		−	30.2781i		−	1.55940i
$378$	−13.2227	+	3.88840i	−0.680101	+	0.199998i
$379$			15.0551i			0.773331i	0.922220	+	0.386665i	$0.126373\pi$
$379$			15.0551i			0.773331i	−0.922220	+	0.386665i	$0.873627\pi$
$380$	6.45777	+	5.03969i	0.331277	+	0.258531i
$381$	9.76166	−	5.63590i	0.500105	−	0.288736i
$382$	−7.73828	−	15.8548i	−0.395925	−	0.811204i
$383$	15.1753	−	26.2843i	0.775420	−	1.34307i	−0.159138	−	0.987256i	$-0.550871\pi$
$383$	15.1753	−	26.2843i	0.775420	−	1.34307i	0.934558	−	0.355811i	$-0.115795\pi$
$384$	3.50542	−	6.62324i	0.178885	−	0.337991i
$385$	6.09681	−	7.36229i	0.310722	−	0.375217i
$386$	1.87338	−	26.8961i	0.0953527	−	1.36898i
$387$	−6.89047	−	3.97822i	−0.350262	−	0.202224i
$388$	−0.636258	+	0.257469i	−0.0323011	+	0.0130710i
$389$	3.13909	+	5.43706i	0.159158	+	0.275670i	0.934565	−	0.355792i	$-0.115789\pi$
$389$	3.13909	+	5.43706i	0.159158	+	0.275670i	−0.775407	+	0.631462i	$0.782455\pi$
$390$	−4.52844	−	3.05267i	−0.229306	−	0.154578i
$391$	4.43983			0.224532
$392$	19.7946	+	0.418170i	0.999777	+	0.0211208i
$393$	−0.798887			−0.0402985
$394$	2.26542	+	1.52715i	0.114130	+	0.0769365i
$395$	5.67005	+	9.82082i	0.285291	+	0.494139i
$396$	17.1562	−	6.94246i	0.862132	−	0.348872i
$397$	−8.41956	−	4.86104i	−0.422566	−	0.243968i	0.273609	−	0.961841i	$-0.411783\pi$
$397$	−8.41956	−	4.86104i	−0.422566	−	0.243968i	−0.696174	+	0.717873i	$0.745116\pi$
$398$	−2.02079	+	29.0124i	−0.101293	+	1.45426i
$399$	4.57789	−	5.52810i	0.229181	−	0.276751i
$400$	−3.84625	−	1.09835i	−0.192312	−	0.0549175i
$401$	−3.49372	+	6.05130i	−0.174468	+	0.302188i	−0.939977	−	0.341238i	$-0.889154\pi$
$401$	−3.49372	+	6.05130i	−0.174468	+	0.302188i	0.765509	+	0.643425i	$0.222487\pi$
$402$	1.04259	+	2.13615i	0.0519999	+	0.106542i
$403$	−44.7764	+	25.8517i	−2.23047	+	1.28776i
$404$	7.15243	+	5.58181i	0.355847	+	0.277705i
$405$			5.24405i			0.260579i
$406$	−18.6421	+	5.48209i	−0.925190	+	0.272071i
$407$			39.0048i			1.93339i
$408$	1.71347	−	1.90614i	0.0848295	−	0.0943680i
$409$	1.94474	−	1.12280i	0.0961611	−	0.0555186i	−0.451148	−	0.892449i	$-0.648985\pi$
$409$	1.94474	−	1.12280i	0.0961611	−	0.0555186i	0.547309	+	0.836930i	$0.315652\pi$
$410$	1.05833	−	0.516540i	0.0522673	−	0.0255101i
$411$	0.710344	−	1.23035i	0.0350387	−	0.0606888i
$412$	−12.1577	−	1.70189i	−0.598967	−	0.0838459i
$413$	−19.5077	−	3.30948i	−0.959910	−	0.162849i
$414$	−11.7263	−	0.816769i	−0.576318	−	0.0401420i
$415$	−5.62176	−	3.24572i	−0.275961	−	0.159326i
$416$	5.77141	+	32.4721i	0.282967	+	1.59207i
$417$	−1.12453	−	1.94774i	−0.0550685	−	0.0953814i
$418$	−11.6977	+	17.3527i	−0.572152	+	0.848750i
$419$	−18.3565			−0.896775			−0.448388	−	0.893839i	$-0.648002\pi$
$419$	−18.3565			−0.896775			−0.448388	+	0.893839i	$0.648002\pi$
$420$	−1.05960	+	3.34084i	−0.0517034	+	0.163016i
$421$	2.27310			0.110784			0.0553921	−	0.998465i	$-0.482359\pi$
$421$	2.27310			0.110784			0.0553921	+	0.998465i	$0.482359\pi$
$422$	−7.89232	+	11.7077i	−0.384192	+	0.569924i
$423$	8.83133	+	15.2963i	0.429394	+	0.743732i
$424$	−19.9478	+	6.49949i	−0.968749	+	0.315643i
$425$	−1.18483	−	0.684063i	−0.0574728	−	0.0331819i
$426$	−3.29394	−	0.229431i	−0.159592	−	0.0111160i
$427$	−3.68456	+	1.36818i	−0.178308	+	0.0662110i
$428$	2.12606	−	15.1879i	0.102767	−	0.734133i
$429$	6.97610	−	12.0830i	0.336809	−	0.583371i
$430$	−3.94800	+	1.92690i	−0.190390	+	0.0929236i
$431$	−11.1379	+	6.43048i	−0.536494	+	0.309745i	−0.743657	−	0.668561i	$-0.766910\pi$
$431$	−11.1379	+	6.43048i	−0.536494	+	0.309745i	0.207163	+	0.978307i	$0.433577\pi$
$432$	−10.5877	+	10.2468i	−0.509401	+	0.492999i
$433$		−	33.6307i		−	1.61619i	−0.589054	−	0.808094i	$-0.700499\pi$
$433$		−	33.6307i		−	1.61619i	0.589054	−	0.808094i	$-0.299501\pi$
$434$	24.0238	+	22.8879i	1.15318	+	1.09866i
$435$		−	3.43978i		−	0.164925i
$436$	1.59373	−	2.04218i	0.0763260	−	0.0978029i
$437$	11.5108	−	6.64577i	0.550637	−	0.317910i
$438$	−2.12406	−	4.35196i	−0.101492	−	0.207945i
$439$	12.4435	−	21.5528i	0.593896	−	1.02866i	−0.399806	−	0.916600i	$-0.630922\pi$
$439$	12.4435	−	21.5528i	0.593896	−	1.02866i	0.993702	−	0.112058i	$-0.0357442\pi$
$440$	2.11646	−	9.99743i	0.100898	−	0.476609i
$441$	−16.9258	−	5.91313i	−0.805992	−	0.281578i
$442$	−0.783818	+	11.2533i	−0.0372824	+	0.535263i
$443$	6.88293	+	3.97386i	0.327018	+	0.188804i	0.654516	−	0.756048i	$-0.272872\pi$
$443$	6.88293	+	3.97386i	0.327018	+	0.188804i	−0.327498	+	0.944852i	$0.606206\pi$
$444$	−5.36459	−	13.2570i	−0.254592	−	0.629149i
$445$	−4.69560	−	8.13303i	−0.222593	−	0.385542i
$446$	19.7216	+	13.2946i	0.933845	+	0.629515i
$447$	12.6420			0.597944
$448$	18.9479	−	9.43274i	0.895205	−	0.445655i
$449$	14.3027			0.674988			0.337494	−	0.941328i	$-0.390421\pi$
$449$	14.3027			0.674988			0.337494	+	0.941328i	$0.390421\pi$
$450$	3.00350	+	2.02469i	0.141586	+	0.0954449i
$451$	1.50431	+	2.60554i	0.0708352	+	0.122690i
$452$	5.33104	+	13.1741i	0.250751	+	0.619656i
$453$	−5.51013	−	3.18127i	−0.258888	−	0.149469i
$454$	1.94898	−	27.9815i	0.0914702	−	1.31324i
$455$	−5.36967	−	14.4607i	−0.251734	−	0.677927i
$456$	1.58918	−	7.50673i	0.0744202	−	0.351535i
$457$	−11.0893	+	19.2073i	−0.518737	+	0.898478i	0.481026	+	0.876706i	$0.340264\pi$
$457$	−11.0893	+	19.2073i	−0.518737	+	0.898478i	−0.999763	+	0.0217719i	$0.993069\pi$
$458$	8.64267	+	17.7078i	0.403845	+	0.827432i
$459$	−4.36438	+	2.51977i	−0.203712	+	0.117613i
$460$	−3.99308	+	5.11667i	−0.186178	+	0.238566i
$461$		−	32.8587i		−	1.53038i	−0.643803	−	0.765192i	$-0.722644\pi$
$461$		−	32.8587i		−	1.53038i	0.643803	−	0.765192i	$-0.277356\pi$
$462$	−8.70248	−	2.10743i	−0.404876	−	0.0980465i
$463$		−	3.31392i		−	0.154011i	−0.997031	−	0.0770055i	$-0.975464\pi$
$463$		−	3.31392i		−	0.154011i	0.997031	−	0.0770055i	$-0.0245359\pi$
$464$	−14.9271	+	14.4465i	−0.692974	+	0.670661i
$465$	−5.08688	+	2.93691i	−0.235898	+	0.136196i
$466$	−12.9960	+	6.34295i	−0.602027	+	0.293832i
$467$	17.5667	−	30.4264i	0.812890	−	1.40797i	−0.0979429	−	0.995192i	$-0.531226\pi$
$467$	17.5667	−	30.4264i	0.812890	−	1.40797i	0.910833	−	0.412775i	$-0.135440\pi$
$468$	4.14039	−	29.5776i	0.191390	−	1.36722i
$469$	−1.12297	+	6.61930i	−0.0518538	+	0.305651i
$470$	9.72886	+	0.677640i	0.448759	+	0.0312572i
$471$	9.44307	+	5.45196i	0.435114	+	0.251213i
$472$	−20.1119	+	6.55298i	−0.925727	+	0.301625i
$473$	−5.61169	−	9.71973i	−0.258026	−	0.446914i
$474$	5.93757	−	8.80799i	0.272721	−	0.404564i
$475$	−4.09577			−0.187927
$476$	7.07049	−	1.55490i	0.324075	−	0.0712686i
$477$	18.9984			0.869877
$478$	−13.5044	+	20.0329i	−0.617679	+	0.916285i
$479$	11.1633	+	19.3354i	0.510065	+	0.883459i	0.999932	+	0.0116615i	$0.00371206\pi$
$479$	11.1633	+	19.3354i	0.510065	+	0.883459i	−0.489867	+	0.871797i	$0.662955\pi$
$480$	0.655668	+	3.68903i	0.0299270	+	0.168380i
$481$	54.5097	+	31.4712i	2.48543	+	1.43496i
$482$	−26.0767	−	1.81631i	−1.18776	−	0.0827306i
$483$	4.38007	+	3.62719i	0.199300	+	0.165043i
$484$	4.06732	+	0.569361i	0.184878	+	0.0258800i
$485$	0.171594	−	0.297210i	0.00779170	−	0.0134956i
$486$	18.4589	−	9.00923i	0.837311	−	0.408667i
$487$	−6.22255	+	3.59259i	−0.281971	+	0.162796i	−0.634315	−	0.773074i	$-0.718718\pi$
$487$	−6.22255	+	3.59259i	−0.281971	+	0.162796i	0.352344	+	0.935870i	$0.385385\pi$
$488$	−2.80896	+	3.12481i	−0.127156	+	0.141454i
$489$			4.73989i			0.214345i
$490$	−7.93113	+	5.92429i	−0.358292	+	0.267632i
$491$		−	5.80059i		−	0.261777i	−0.991397	−	0.130889i	$-0.958217\pi$
$491$		−	5.80059i		−	0.261777i	0.991397	−	0.130889i	$-0.0417830\pi$
$492$	−0.869645	−	0.678677i	−0.0392066	−	0.0305971i
$493$	−6.15314	+	3.55252i	−0.277124	+	0.159997i
$494$	14.8124	+	30.3488i	0.666439	+	1.36546i
$495$	−4.62691	+	8.01405i	−0.207964	+	0.360205i
$496$	34.1089	+	9.74027i	1.53153	+	0.437351i
$497$	−7.18308	−	5.94840i	−0.322205	−	0.266822i
$498$	−0.422506	+	6.06591i	−0.0189329	+	0.271820i
$499$	−34.3466	−	19.8300i	−1.53757	−	0.887715i	−0.998980	−	0.0451448i	$-0.985625\pi$
$499$	−34.3466	−	19.8300i	−1.53757	−	0.887715i	−0.538587	−	0.842570i	$-0.681042\pi$
$500$	1.85396	−	0.750225i	0.0829115	−	0.0335511i
$501$	4.54135	+	7.86585i	0.202892	+	0.351420i
$502$	19.3854	+	13.0679i	0.865213	+	0.583250i
$503$	8.22384			0.366683			0.183341	−	0.983049i	$-0.441309\pi$
$503$	8.22384			0.366683			0.183341	+	0.983049i	$0.441309\pi$
$504$	−18.9604	+	2.80603i	−0.844563	+	0.124991i
$505$	−4.53635			−0.201865
$506$	−13.7490	−	9.26839i	−0.611220	−	0.412030i
$507$	−6.95209	−	12.0414i	−0.308753	−	0.534776i
$508$	31.5502	−	12.7672i	1.39982	−	0.566451i
$509$	−28.2081	−	16.2860i	−1.25030	−	0.721863i	−0.279134	−	0.960252i	$-0.590047\pi$
$509$	−28.2081	−	16.2860i	−1.25030	−	0.721863i	−0.971170	+	0.238389i	$0.923381\pi$
$510$	−0.0890466	+	1.27844i	−0.00394305	+	0.0566103i
$511$	2.28781	−	13.4854i	0.101207	−	0.596560i
$512$	13.2550	−	18.3386i	0.585796	−	0.810459i
$513$	−7.54347	+	13.0657i	−0.333052	+	0.576864i
$514$	−3.84273	−	7.87332i	−0.169496	−	0.347277i
$515$	5.31577	−	3.06906i	0.234241	−	0.135239i
$516$	3.24413	+	2.53174i	0.142815	+	0.111454i
$517$			24.9150i			1.09576i
$518$	9.50722	−	39.2594i	0.417723	−	1.72496i
$519$			2.59934i			0.114098i
$520$	−12.2639	−	11.0243i	−0.537806	−	0.483446i
$521$	−4.88783	+	2.82199i	−0.214140	+	0.123634i	−0.603234	−	0.797564i	$-0.706121\pi$
$521$	−4.88783	+	2.82199i	−0.214140	+	0.123634i	0.389094	+	0.921198i	$0.372788\pi$
$522$	16.9050	−	8.25085i	0.739913	−	0.361130i
$523$	1.36705	−	2.36780i	0.0597770	−	0.103537i	−0.834588	−	0.550874i	$-0.814294\pi$
$523$	1.36705	−	2.36780i	0.0597770	−	0.103537i	0.894365	+	0.447338i	$0.147628\pi$
$524$	−2.38897	−	0.334418i	−0.104363	−	0.0146091i
$525$	−0.610027	−	1.64282i	−0.0266238	−	0.0716986i
$526$	−29.8434	−	2.07867i	−1.30123	−	0.0906342i
$527$	10.5072	+	6.06633i	0.457701	+	0.264254i
$528$	−9.28538	+	2.32588i	−0.404094	+	0.101221i
$529$	−6.23437	−	10.7982i	−0.271060	−	0.469489i
$530$	5.86354	−	8.69817i	0.254696	−	0.377824i
$531$	19.1547			0.831245
$532$	16.0037	−	14.6148i	0.693848	−	0.633630i
$533$	4.85504			0.210295
$534$	−4.91714	+	7.29426i	−0.212786	+	0.315653i
$535$	3.83398	+	6.64066i	0.165758	+	0.287101i
$536$	2.22354	+	6.82433i	0.0960423	+	0.294766i
$537$	11.7900	+	6.80697i	0.508777	+	0.293743i
$538$	−43.7157	−	3.04491i	−1.88472	−	0.131275i
$539$	−16.5064	−	19.1614i	−0.710980	−	0.825341i
$540$	1.02132	−	7.29595i	0.0439505	−	0.313968i
$541$	−14.1500	+	24.5085i	−0.608355	+	1.05370i	0.383157	+	0.923683i	$0.374837\pi$
$541$	−14.1500	+	24.5085i	−0.608355	+	1.05370i	−0.991512	+	0.130018i	$0.958497\pi$
$542$	29.2795	−	14.2905i	1.25766	−	0.613828i
$543$	−7.49157	+	4.32526i	−0.321494	+	0.185615i
$544$	5.92184	−	4.98280i	0.253897	−	0.213636i
$545$			1.29523i			0.0554817i
$546$	−9.96680	+	10.4614i	−0.426540	+	0.447708i
$547$		−	20.7596i		−	0.887616i	−0.896122	−	0.443808i	$-0.853627\pi$
$547$		−	20.7596i		−	0.887616i	0.896122	−	0.443808i	$-0.146373\pi$
$548$	2.63922	−	3.38186i	0.112742	−	0.144466i
$549$	3.29514	−	1.90245i	0.140633	−	0.0811946i
$550$	2.24111	+	4.59178i	0.0955613	+	0.195794i
$551$	−10.6352	+	18.4207i	−0.453075	+	0.784749i
$552$	5.94779	+	1.25915i	0.253155	+	0.0535930i
$553$	28.1266	−	10.4442i	1.19606	−	0.444133i
$554$	0.682514	−	9.79885i	0.0289973	−	0.416313i
$555$	6.19263	+	3.57532i	0.262863	+	0.151764i
$556$	−2.54743	−	6.29521i	−0.108035	−	0.266977i
$557$	9.37876	+	16.2445i	0.397391	+	0.688301i	0.993403	−	0.114674i	$-0.0365825\pi$
$557$	9.37876	+	16.2445i	0.397391	+	0.688301i	−0.596012	+	0.802975i	$0.703249\pi$
$558$	−26.6353	−	17.9552i	−1.12756	−	0.760102i
$559$	−18.1113			−0.766025
$560$	−4.56710	+	9.54681i	−0.192995	+	0.403426i
$561$	−3.27401			−0.138229
$562$	−4.97662	−	3.35480i	−0.209926	−	0.141514i
$563$	−16.6870	−	28.9028i	−0.703274	−	1.21811i	−0.967311	−	0.253594i	$-0.918387\pi$
$563$	−16.6870	−	28.9028i	−0.703274	−	1.21811i	0.264037	−	0.964513i	$-0.414946\pi$
$564$	−3.42673	−	8.46815i	−0.144292	−	0.356573i
$565$	−6.15390	−	3.55296i	−0.258897	−	0.149474i
$566$	0.838399	−	12.0369i	0.0352405	−	0.505948i
$567$	13.6790	+	2.32064i	0.574464	+	0.0974579i
$568$	−9.75407	−	2.06494i	−0.409272	−	0.0866431i
$569$	−6.51501	+	11.2843i	−0.273124	+	0.473064i	−0.969660	−	0.244457i	$-0.921390\pi$
$569$	−6.51501	+	11.2843i	−0.273124	+	0.473064i	0.696536	+	0.717521i	$0.254723\pi$
$570$	1.68277	+	3.44781i	0.0704837	+	0.144413i
$571$	−28.5406	+	16.4779i	−1.19439	+	0.689579i	−0.959298	−	0.282395i	$-0.908871\pi$
$571$	−28.5406	+	16.4779i	−1.19439	+	0.689579i	−0.235088	+	0.971974i	$0.575538\pi$
$572$	25.9191	−	33.2123i	1.08373	−	1.38868i
$573$		−	8.26295i		−	0.345190i
$574$	−0.879042	−	2.98922i	−0.0366905	−	0.124768i
$575$		−	3.24519i		−	0.135334i
$576$	−16.5572	+	12.0710i	−0.689885	+	0.502959i
$577$	−31.5124	+	18.1937i	−1.31188	+	0.757414i	−0.982407	−	0.186751i	$-0.940204\pi$
$577$	−31.5124	+	18.1937i	−1.31188	+	0.757414i	−0.329473	+	0.944165i	$0.606871\pi$
$578$	−19.2267	+	9.38400i	−0.799727	+	0.390323i
$579$	6.31373	−	10.9357i	0.262390	−	0.454472i
$580$	1.43991	−	10.2862i	0.0597890	−	0.427113i
$581$	−10.9542	+	13.2279i	−0.454457	+	0.548786i
$582$	−0.320692	−	0.0223370i	−0.0132931	−	0.000925898i
$583$	23.2088	+	13.3996i	0.961210	+	0.554955i
$584$	−4.52999	−	13.9031i	−0.187452	−	0.575316i
$585$	7.46649	+	12.9323i	0.308702	+	0.534687i
$586$	−19.9458	+	29.5883i	−0.823953	+	1.22228i
$587$	−28.4245			−1.17321			−0.586603	−	0.809875i	$-0.699535\pi$
$587$	−28.4245			−1.17321			−0.586603	+	0.809875i	$0.699535\pi$
$588$	8.24561	+	4.24238i	0.340043	+	0.174953i
$589$	36.3217			1.49661
$590$	5.91179	−	8.76975i	0.243385	−	0.361045i
$591$	0.639794	+	1.10816i	0.0263176	+	0.0455835i
$592$	−10.4927	−	41.8890i	−0.431247	−	1.72163i
$593$	6.55710	+	3.78574i	0.269268	+	0.155462i	0.628555	−	0.777765i	$-0.283647\pi$
$593$	6.55710	+	3.78574i	0.269268	+	0.155462i	−0.359287	+	0.933227i	$0.616980\pi$
$594$	18.7756	+	1.30777i	0.770371	+	0.0536583i
$595$	−2.30869	+	2.78789i	−0.0946469	+	0.114292i
$596$	37.8042	+	5.29198i	1.54852	+	0.216768i
$597$	−6.81052	+	11.7962i	−0.278736	+	0.482785i
$598$	−24.0462	+	11.7362i	−0.983321	+	0.479930i
$599$	41.0937	−	23.7255i	1.67904	−	0.969397i	0.716772	−	0.697307i	$-0.245619\pi$
$599$	41.0937	−	23.7255i	1.67904	−	0.969397i	0.962272	−	0.272090i	$-0.0877147\pi$
$600$	−1.39325	−	1.25242i	−0.0568792	−	0.0511300i
$601$			13.3242i			0.543506i	0.962367	+	0.271753i	$0.0876034\pi$
$601$			13.3242i			0.543506i	−0.962367	+	0.271753i	$0.912397\pi$
$602$	3.27918	+	11.1510i	0.133650	+	0.454481i
$603$		−	6.49954i		−	0.264682i
$604$	−15.1456	−	11.8198i	−0.616267	−	0.480939i
$605$	−1.77837	+	1.02675i	−0.0723012	+	0.0417431i
$606$	1.86379	+	3.81869i	0.0757113	+	0.155124i
$607$	7.54080	−	13.0610i	0.306072	−	0.530132i	−0.671428	−	0.741070i	$-0.734319\pi$
$607$	7.54080	−	13.0610i	0.306072	−	0.530132i	0.977499	+	0.210938i	$0.0676520\pi$
$608$	7.89460	−	21.7827i	0.320168	−	0.883405i
$609$	−8.97261	−	1.52221i	−0.363588	−	0.0616829i
$610$	0.145978	−	2.09580i	0.00591046	−	0.0848564i
$611$	34.8191	+	20.1028i	1.40863	+	0.813272i
$612$	−6.49657	+	2.62891i	−0.262608	+	0.106267i
$613$	2.60234	+	4.50739i	0.105108	+	0.182052i	0.913782	−	0.406205i	$-0.133148\pi$
$613$	2.60234	+	4.50739i	0.105108	+	0.182052i	−0.808675	+	0.588256i	$0.799815\pi$
$614$	−34.3159	−	23.1327i	−1.38488	−	0.933561i
$615$	0.551563			0.0222412
$616$	−25.1415	−	9.94491i	−1.01298	−	0.400692i
$617$	−35.7404			−1.43885			−0.719426	−	0.694569i	$-0.755595\pi$
$617$	−35.7404			−1.43885			−0.719426	+	0.694569i	$0.755595\pi$
$618$	−4.76755	−	3.21386i	−0.191779	−	0.129280i
$619$	19.1219	+	33.1200i	0.768573	+	1.33121i	0.938337	+	0.345722i	$0.112366\pi$
$619$	19.1219	+	33.1200i	0.768573	+	1.33121i	−0.169764	+	0.985485i	$0.554301\pi$
$620$	−16.4411	+	6.65307i	−0.660290	+	0.267194i
$621$	−10.3523	−	5.97690i	−0.415423	−	0.239845i
$622$	2.23515	−	32.0901i	0.0896215	−	1.28670i
$623$	−23.2928	+	8.64929i	−0.933205	+	0.346526i
$624$	−4.24151	+	14.8531i	−0.169796	+	0.594599i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	4.08454	+	8.36874i	0.163251	+	0.334482i
$627$	−8.48828	+	4.90071i	−0.338989	+	0.195716i
$628$	25.9561	+	20.2563i	1.03576	+	0.808315i
$629$		−	14.7700i		−	0.588918i
$630$	6.61050	−	6.93858i	0.263369	−	0.276440i
$631$		−	12.0334i		−	0.479042i	−0.970891	−	0.239521i	$-0.923010\pi$
$631$		−	12.0334i		−	0.479042i	0.970891	−	0.239521i	$-0.0769904\pi$
$632$	21.4426	−	23.8537i	0.852941	−	0.948849i
$633$	−5.72697	+	3.30647i	−0.227627	+	0.131420i
$634$	17.9475	−	8.75966i	0.712788	−	0.347891i
$635$	−8.50888	+	14.7378i	−0.337665	+	0.584852i
$636$	−9.73118	−	1.36221i	−0.385866	−	0.0540152i
$637$	−40.0966	+	7.60740i	−1.58869	+	0.301416i
$638$	26.4709	+	1.84376i	1.04799	+	0.0729952i
$639$	7.81897	+	4.51429i	0.309314	+	0.178582i
$640$	0.416448	+	11.3060i	0.0164615	+	0.446911i
$641$	−11.4676	−	19.8625i	−0.452944	−	0.784522i	0.545624	−	0.838030i	$-0.316293\pi$
$641$	−11.4676	−	19.8625i	−0.452944	−	0.784522i	−0.998567	+	0.0535086i	$0.982960\pi$
$642$	4.01487	−	5.95580i	0.158454	−	0.235057i
$643$	−1.23955			−0.0488833			−0.0244416	−	0.999701i	$-0.507781\pi$
$643$	−1.23955			−0.0488833			−0.0244416	+	0.999701i	$0.507781\pi$
$644$	11.5797	+	12.6802i	0.456303	+	0.499668i
$645$	−2.05755			−0.0810160
$646$	4.42958	−	6.57098i	0.174279	−	0.258532i
$647$	−7.07077	−	12.2469i	−0.277981	−	0.481477i	0.692902	−	0.721032i	$-0.256332\pi$
$647$	−7.07077	−	12.2469i	−0.277981	−	0.481477i	−0.970883	+	0.239555i	$0.922998\pi$
$648$	14.1027	−	4.59502i	0.554006	−	0.180509i
$649$	23.3998	+	13.5099i	0.918523	+	0.530309i
$650$	8.22532	+	0.572914i	0.322624	+	0.0224715i
$651$	5.40978	+	14.5687i	0.212026	+	0.570992i
$652$	−1.98414	+	14.1740i	−0.0777049	+	0.555098i
$653$	8.54579	−	14.8017i	0.334423	−	0.579237i	−0.648951	−	0.760830i	$-0.724792\pi$
$653$	8.54579	−	14.8017i	0.334423	−	0.579237i	0.983374	+	0.181593i	$0.0581254\pi$
$654$	1.09032	−	0.532155i	0.0426350	−	0.0208089i
$655$	1.04454	−	0.603066i	0.0408136	−	0.0235637i
$656$	−2.31647	−	2.39354i	−0.0904428	−	0.0934519i
$657$			13.2414i			0.516598i
$658$	6.07292	−	25.0777i	0.236747	−	0.977629i
$659$			3.45765i			0.134691i	0.997730	+	0.0673455i	$0.0214530\pi$
$659$			3.45765i			0.134691i	−0.997730	+	0.0673455i	$0.978547\pi$
$660$	2.94457	−	3.77312i	0.114617	−	0.146869i
$661$	13.1317	−	7.58160i	0.510765	−	0.294890i	−0.222383	−	0.974959i	$-0.571384\pi$
$661$	13.1317	−	7.58160i	0.510765	−	0.294890i	0.733148	+	0.680069i	$0.238050\pi$
$662$	12.6059	+	25.8281i	0.489943	+	1.00384i
$663$	−2.64165	+	4.57547i	−0.102593	+	0.177697i
$664$	−3.80267	+	17.9625i	−0.147572	+	0.697079i
$665$	−1.81250	+	10.6837i	−0.0702857	+	0.414297i
$666$	−2.71715	+	39.0100i	−0.105287	+	1.51161i
$667$	−14.5952	−	8.42657i	−0.565130	−	0.326278i
$668$	10.2876	+	25.4229i	0.398041	+	0.983640i
$669$	5.56972	+	9.64704i	0.215338	+	0.372976i
$670$	−2.97573	−	2.00597i	−0.114963	−	0.0774976i
$671$	5.36721			0.207199
$672$	9.91291	−	0.0777937i	0.382399	−	0.00300096i
$673$	−11.2116			−0.432175			−0.216087	−	0.976374i	$-0.569330\pi$
$673$	−11.2116			−0.432175			−0.216087	+	0.976374i	$0.569330\pi$
$674$	18.4932	+	12.4664i	0.712330	+	0.480190i
$675$	1.84177	+	3.19004i	0.0708898	+	0.122785i
$676$	−15.7488	−	38.9184i	−0.605722	−	1.49686i
$677$	3.18383	+	1.83818i	0.122364	+	0.0706471i	0.559933	−	0.828538i	$-0.310827\pi$
$677$	3.18383	+	1.83818i	0.122364	+	0.0706471i	−0.437568	+	0.899185i	$0.644160\pi$
$678$	−0.462500	+	6.64010i	−0.0177622	+	0.255011i
$679$	−0.699331	−	0.579125i	−0.0268379	−	0.0222248i
$680$	−0.801444	+	3.78574i	−0.0307340	+	0.145176i
$681$	6.56852	−	11.3770i	0.251706	−	0.435968i
$682$	−19.8744	−	40.7203i	−0.761029	−	1.55926i
$683$	36.5356	−	21.0938i	1.39800	−	0.807133i	0.403814	−	0.914841i	$-0.367684\pi$
$683$	36.5356	−	21.0938i	1.39800	−	0.807133i	0.994183	+	0.107708i	$0.0343511\pi$
$684$	−12.9081	+	16.5402i	−0.493553	+	0.632430i
$685$			2.14490i			0.0819526i
$686$	11.9436	+	23.3099i	0.456010	+	0.889975i
$687$			9.22865i			0.352095i
$688$	8.64136	+	8.92886i	0.329449	+	0.340410i
$689$	37.4523	−	21.6231i	1.42682	−	0.823773i
$690$	−2.73179	+	1.33331i	−0.103998	+	0.0507582i
$691$	−11.5615	+	20.0251i	−0.439820	+	0.761790i	−0.997675	−	0.0681478i	$-0.978291\pi$
$691$	−11.5615	+	20.0251i	−0.439820	+	0.761790i	0.557855	+	0.829938i	$0.311624\pi$
$692$	−1.08809	+	7.77298i	−0.0413631	+	0.295485i
$693$	18.8569	+	15.6157i	0.716316	+	0.593190i
$694$	−4.29987	−	0.299497i	−0.163221	−	0.0113688i
$695$	2.94063	+	1.69778i	0.111545	+	0.0644003i
$696$	−9.25053	+	3.01406i	−0.350640	+	0.114248i
$697$	−0.569640	−	0.986645i	−0.0215766	−	0.0373718i
$698$	−6.64384	+	9.85569i	−0.251473	+	0.373043i
$699$	−6.77301			−0.256179
$700$	−1.13652	−	5.16801i	−0.0429563	−	0.195332i
$701$	29.3192			1.10737			0.553686	−	0.832725i	$-0.313221\pi$
$701$	29.3192			1.10737			0.553686	+	0.832725i	$0.313221\pi$
$702$	16.9768	−	25.1839i	0.640747	−	0.950506i
$703$	−22.1085	−	38.2931i	−0.833839	−	1.44425i
$704$	−28.7404	+	3.06834i	−1.08319	+	0.115642i
$705$	3.95566	+	2.28380i	0.148979	+	0.0860130i
$706$	0.610622	+	0.0425314i	0.0229811	+	0.00160069i
$707$	−2.00747	+	11.8330i	−0.0754986	+	0.445025i
$708$	−9.81126	−	1.37342i	−0.368730	−	0.0516163i
$709$	−1.67720	+	2.90499i	−0.0629884	+	0.109099i	−0.895800	−	0.444458i	$-0.853396\pi$
$709$	−1.67720	+	2.90499i	−0.0629884	+	0.109099i	0.832811	+	0.553557i	$0.186730\pi$
$710$	4.48000	−	2.18656i	0.168132	−	0.0820600i
$711$	−25.1539	+	14.5226i	−0.943346	+	0.544641i
$712$	−17.7575	+	19.7542i	−0.665491	+	0.740321i
$713$			28.7786i			1.07777i
$714$	3.29538	+	0.798024i	0.123327	+	0.0298653i
$715$			21.0645i			0.787769i
$716$	32.4071	+	25.2908i	1.21111	+	0.945160i
$717$	−9.79934	+	5.65765i	−0.365963	+	0.211289i
$718$	16.7362	+	34.2906i	0.624591	+	1.27972i
$719$	−15.5142	+	26.8714i	−0.578583	+	1.00213i	0.417059	+	0.908879i	$0.363061\pi$
$719$	−15.5142	+	26.8714i	−0.578583	+	1.00213i	−0.995642	+	0.0932556i	$0.970273\pi$
$720$	2.81319	−	9.85134i	0.104841	−	0.367138i
$721$	−5.65320	−	15.2242i	−0.210536	−	0.566980i
$722$	−0.218609	+	3.13857i	−0.00813579	+	0.116805i
$723$	−10.6025	−	6.12138i	−0.394313	−	0.227657i
$724$	−24.2132	+	9.79814i	−0.899876	+	0.364145i
$725$	2.59663	+	4.49750i	0.0964365	+	0.167033i
$726$	1.59497	+	1.07519i	0.0591949	+	0.0399039i
$727$	37.9906			1.40899			0.704497	−	0.709707i	$-0.251173\pi$
$727$	37.9906			1.40899			0.704497	+	0.709707i	$0.251173\pi$
$728$	−34.1837	+	27.1115i	−1.26693	+	1.00482i
$729$	−6.11207			−0.226373
$730$	6.06242	+	4.08675i	0.224380	+	0.151257i
$731$	2.12499	+	3.68058i	0.0785955	+	0.136131i
$732$	−1.82421	+	0.738189i	−0.0674249	+	0.0272843i
$733$	−26.8252	−	15.4876i	−0.990813	−	0.572046i	−0.0852956	−	0.996356i	$-0.527183\pi$
$733$	−26.8252	−	15.4876i	−0.990813	−	0.572046i	−0.905517	+	0.424310i	$0.860517\pi$
$734$	−2.04601	+	29.3745i	−0.0755195	+	1.08423i
$735$	−4.55522	+	0.864248i	−0.168022	+	0.0318783i
$736$	17.2590	+	6.25511i	0.636176	+	0.230566i
$737$	4.58414	−	7.93996i	0.168859	−	0.292472i
$738$	1.32301	+	2.71069i	0.0487006	+	0.0997819i
$739$	2.53077	−	1.46114i	0.0930957	−	0.0537488i	−0.452729	−	0.891648i	$-0.649550\pi$
$739$	2.53077	−	1.46114i	0.0930957	−	0.0537488i	0.545825	+	0.837899i	$0.316216\pi$
$740$	17.0216	+	13.2838i	0.625728	+	0.488322i
$741$			15.8167i			0.581039i
$742$	−20.0942	−	19.1441i	−0.737682	−	0.702802i
$743$			36.6505i			1.34457i	0.740290	+	0.672287i	$0.234688\pi$
$743$			36.6505i			1.34457i	−0.740290	+	0.672287i	$0.765312\pi$
$744$	12.3555	+	11.1066i	0.452974	+	0.407188i
$745$	−16.5293	+	9.54319i	−0.605586	+	0.349635i
$746$	22.4462	−	10.9553i	0.821815	−	0.401104i
$747$	8.31323	−	14.3989i	0.304165	−	0.526829i
$748$	−9.79051	−	1.37052i	−0.357976	−	0.0501110i
$749$	19.0187	−	7.06219i	0.694927	−	0.258047i
$750$	0.934447	+	0.0650866i	0.0341212	+	0.00237663i
$751$	−31.3355	−	18.0915i	−1.14345	−	0.660170i	−0.196166	−	0.980571i	$-0.562849\pi$
$751$	−31.3355	−	18.0915i	−1.14345	−	0.660170i	−0.947282	+	0.320401i	$0.896182\pi$
$752$	−6.70241	−	26.7574i	−0.244412	−	0.975741i
$753$	5.47478	+	9.48259i	0.199512	+	0.345565i
$754$	23.9348	−	35.5057i	0.871654	−	1.29304i
$755$	9.60595			0.349596
$756$	−18.5794	−	5.89276i	−0.675725	−	0.214318i
$757$	−1.44394			−0.0524807			−0.0262404	−	0.999656i	$-0.508354\pi$
$757$	−1.44394			−0.0524807			−0.0262404	+	0.999656i	$0.508354\pi$
$758$	−11.9011	+	17.6544i	−0.432266	+	0.641238i
$759$	−3.88297	−	6.72550i	−0.140943	−	0.244120i
$760$	3.58885	+	11.0147i	0.130181	+	0.399544i
$761$	−24.4509	−	14.1167i	−0.886343	−	0.511730i	−0.0135983	−	0.999908i	$-0.504329\pi$
$761$	−24.4509	−	14.1167i	−0.886343	−	0.511730i	−0.872744	+	0.488177i	$0.837662\pi$
$762$	15.9022	+	1.10763i	0.576076	+	0.0401251i
$763$	3.37859	+	0.573178i	0.122313	+	0.0207505i
$764$	3.45891	−	24.7093i	0.125139	−	0.893951i
$765$	1.75208	−	3.03469i	0.0633466	−	0.109720i
$766$	38.5730	−	18.8264i	1.39370	−	0.680224i
$767$	37.7605	−	21.8010i	1.36345	−	0.787189i
$768$	9.34630	−	4.99573i	0.337256	−	0.180268i
$769$		−	38.3866i		−	1.38426i	−0.721774	−	0.692129i	$-0.756673\pi$
$769$		−	38.3866i		−	1.38426i	0.721774	−	0.692129i	$-0.243327\pi$
$770$	12.9693	−	3.81390i	0.467382	−	0.137443i
$771$		−	4.10328i		−	0.147776i
$772$	23.4582	−	30.0589i	0.844278	−	1.08184i
$773$	16.5252	−	9.54086i	0.594372	−	0.343161i	−0.172452	−	0.985018i	$-0.555169\pi$
$773$	16.5252	−	9.54086i	0.594372	−	0.343161i	0.766824	+	0.641857i	$0.221836\pi$
$774$	−4.93535	−	10.1120i	−0.177398	−	0.363467i
$775$	4.43405	−	7.67999i	0.159276	−	0.275874i
$776$	−0.949638	−	0.201039i	−0.0340900	−	0.00721688i
$777$	12.0666	−	14.5712i	0.432886	−	0.522738i
$778$	−0.616928	+	8.85722i	−0.0221179	+	0.317547i
$779$	−2.95373	−	1.70533i	−0.105828	−	0.0611000i
$780$	−2.89715	−	7.15944i	−0.103735	−	0.256349i
$781$	6.36787	+	11.0295i	0.227860	+	0.394666i
$782$	5.20637	+	3.50967i	0.186179	+	0.125506i
$783$	19.1296			0.683637
$784$	22.8816	+	16.1379i	0.817199	+	0.576355i
$785$	−16.4624			−0.587567
$786$	−0.936816	−	0.631519i	−0.0334151	−	0.0225255i
$787$	2.55107	+	4.41858i	0.0909358	+	0.157505i	0.907905	−	0.419176i	$-0.137681\pi$
$787$	2.55107	+	4.41858i	0.0909358	+	0.157505i	−0.816969	+	0.576681i	$0.804348\pi$
$788$	1.44934	+	3.58162i	0.0516308	+	0.127590i
$789$	−12.1340	−	7.00559i	−0.431983	−	0.249406i
$790$	−1.11434	+	15.9986i	−0.0396464	+	0.569203i
$791$	−11.9911	+	14.4800i	−0.426354	+	0.514851i
$792$	25.6063	+	5.42087i	0.909879	+	0.192622i
$793$	4.33056	−	7.50075i	0.153783	−	0.266359i
$794$	−6.03058	−	12.3560i	−0.214017	−	0.438496i
$795$	4.25481	−	2.45651i	0.150902	−	0.0871236i
$796$	−25.3039	+	32.4240i	−0.896874	+	1.14924i
$797$			25.6101i			0.907155i	0.891217	+	0.453578i	$0.149852\pi$
$797$			25.6101i			0.907155i	−0.891217	+	0.453578i	$0.850148\pi$
$798$	9.73822	−	2.86373i	0.344729	−	0.101375i
$799$		−	9.43461i		−	0.333772i
$800$	−3.64207	−	4.32843i	−0.128767	−	0.153033i
$801$	20.8310	−	12.0268i	0.736027	−	0.424946i
$802$	−8.88046	+	4.33429i	−0.313580	+	0.153049i
$803$	−9.33922	+	16.1760i	−0.329574	+	0.570839i
$804$	−0.466026	+	3.32913i	−0.0164355	+	0.117409i
$805$	−8.46501	−	1.43609i	−0.298352	−	0.0506156i
$806$	−72.9429	−	5.08065i	−2.56930	−	0.178958i
$807$	−17.7744	−	10.2621i	−0.625688	−	0.361241i
$808$	3.97491	+	12.1995i	0.139837	+	0.429177i
$809$	−25.2381	−	43.7136i	−0.887323	−	1.53689i	−0.843028	−	0.537870i	$-0.819229\pi$
$809$	−25.2381	−	43.7136i	−0.887323	−	1.53689i	−0.0442955	−	0.999018i	$-0.514104\pi$
$810$	−4.14541	+	6.14944i	−0.145655	+	0.216069i
$811$	−3.15050			−0.110629			−0.0553145	−	0.998469i	$-0.517616\pi$
$811$	−3.15050			−0.110629			−0.0553145	+	0.998469i	$0.517616\pi$
$812$	−26.1942	−	8.30794i	−0.919238	−	0.291552i
$813$	15.2594			0.535170
$814$	−30.8332	+	45.7390i	−1.08070	+	1.60315i
$815$	−3.57806	−	6.19738i	−0.125334	−	0.217085i
$816$	3.51611	−	0.880743i	0.123088	−	0.0308322i
$817$	11.0186	+	6.36159i	0.385492	+	0.222564i
$818$	3.16807	+	0.220664i	0.110769	+	0.00771533i
$819$	37.0379	−	13.7533i	1.29421	−	0.480578i
$820$	1.64938	+	0.230887i	0.0575988	+	0.00806292i
$821$	17.7416	−	30.7294i	0.619187	−	1.07246i	−0.370448	−	0.928853i	$-0.620796\pi$
$821$	17.7416	−	30.7294i	0.619187	−	1.07246i	0.989634	−	0.143609i	$-0.0458709\pi$
$822$	1.80558	−	0.881249i	0.0629767	−	0.0307371i
$823$	7.28440	−	4.20565i	0.253918	−	0.146600i	−0.367639	−	0.929969i	$-0.619834\pi$
$823$	7.28440	−	4.20565i	0.253918	−	0.146600i	0.621557	+	0.783369i	$0.286500\pi$
$824$	−12.9114	−	11.6064i	−0.449790	−	0.404327i
$825$			2.39306i			0.0833157i
$826$	−20.2596	−	19.3017i	−0.704921	−	0.671591i
$827$		−	4.33435i		−	0.150720i	−0.997156	−	0.0753601i	$-0.975989\pi$
$827$		−	4.33435i		−	0.150720i	0.997156	−	0.0753601i	$-0.0240106\pi$
$828$	−13.1053	−	10.2274i	−0.455439	−	0.355428i
$829$	20.9404	−	12.0899i	0.727289	−	0.419900i	−0.0901408	−	0.995929i	$-0.528732\pi$
$829$	20.9404	−	12.0899i	0.727289	−	0.419900i	0.817429	+	0.576029i	$0.195398\pi$
$830$	−4.02663	−	8.25009i	−0.139766	−	0.286365i
$831$	2.30023	−	3.98412i	0.0797942	−	0.138208i
$832$	−18.9013	+	42.6407i	−0.655283	+	1.47830i
$833$	6.25050	+	7.25589i	0.216567	+	0.251402i
$834$	0.221005	−	3.17296i	0.00765277	−	0.109871i
$835$	−11.8756	−	6.85637i	−0.410971	−	0.237274i
$836$	−27.4346	+	11.1017i	−0.948846	+	0.383961i
$837$	−16.3330	−	28.2896i	−0.564551	−	0.977831i
$838$	−21.5258	−	14.5108i	−0.743597	−	0.501267i
$839$	−18.3056			−0.631979			−0.315989	−	0.948763i	$-0.602336\pi$
$839$	−18.3056			−0.631979			−0.315989	+	0.948763i	$0.602336\pi$
$840$	−3.88348	+	3.08003i	−0.133993	+	0.106271i
$841$	−2.02999			−0.0699998
$842$	2.66556	+	1.79688i	0.0918611	+	0.0619246i
$843$	−1.40549	−	2.43437i	−0.0484075	−	0.0838442i
$844$	−18.5099	+	7.49024i	−0.637137	+	0.257825i
$845$	18.1796	+	10.4960i	0.625399	+	0.361074i
$846$	−1.73563	+	24.9184i	−0.0596722	+	0.856712i
$847$	1.89126	+	5.09322i	0.0649845	+	0.175005i
$848$	−28.5296	−	8.14704i	−0.979711	−	0.279770i
$849$	2.82560	−	4.89408i	0.0969743	−	0.167964i
$850$	−0.848645	−	1.73877i	−0.0291083	−	0.0596395i
$851$	30.3407	−	17.5172i	1.04006	−	0.600481i
$852$	−3.68128	−	2.87290i	−0.126119	−	0.0984238i
$853$		−	16.9533i		−	0.580469i	−0.956956	−	0.290234i	$-0.906267\pi$
$853$		−	16.9533i		−	0.580469i	0.956956	−	0.290234i	$-0.0937332\pi$
$854$	−5.40225	−	1.30823i	−0.184861	−	0.0447668i
$855$		−	10.4904i		−	0.358765i
$856$	14.4991	−	16.1294i	0.495569	−	0.551292i
$857$	−43.7988	+	25.2872i	−1.49614	+	0.863795i	−0.999990	−	0.00444284i	$-0.998586\pi$
$857$	−43.7988	+	25.2872i	−1.49614	+	0.863795i	−0.496147	+	0.868238i	$0.665252\pi$
$858$	17.7321	−	8.65451i	0.605364	−	0.295460i
$859$	−2.51925	+	4.36346i	−0.0859555	+	0.148879i	−0.905798	−	0.423710i	$-0.860728\pi$
$859$	−2.51925	+	4.36346i	−0.0859555	+	0.148879i	0.819842	+	0.572589i	$0.194061\pi$
$860$	−6.15285	−	0.861301i	−0.209810	−	0.0293701i
$861$	0.244083	−	1.43874i	0.00831832	−	0.0490321i
$862$	−18.1442	−	1.26379i	−0.617993	−	0.0430448i
$863$	−10.1686	−	5.87084i	−0.346143	−	0.199846i	0.316842	−	0.948478i	$-0.397377\pi$
$863$	−10.1686	−	5.87084i	−0.346143	−	0.199846i	−0.662985	+	0.748633i	$0.730711\pi$
$864$	−20.5157	+	3.64636i	−0.697960	+	0.124052i
$865$	−1.96219	−	3.39862i	−0.0667166	−	0.115556i
$866$	26.5850	−	39.4371i	0.903395	−	1.34013i
$867$	−10.0203			−0.340306
$868$	10.0787	+	45.8304i	0.342095	+	1.55559i
$869$	−40.9714			−1.38986
$870$	2.71914	−	4.03367i	0.0921876	−	0.136754i
$871$	−7.39747	−	12.8128i	−0.250654	−	0.434145i
$872$	3.48324	−	1.13493i	0.117957	−	0.0384335i
$873$	0.761240	+	0.439502i	0.0257641	+	0.0148749i
$874$	18.7517	+	1.30610i	0.634284	+	0.0441795i
$875$	2.03775	+	1.68748i	0.0688884	+	0.0570473i
$876$	0.949429	−	6.78241i	0.0320782	−	0.229156i
$877$	12.0912	−	20.9426i	0.408290	−	0.707180i	−0.586408	−	0.810016i	$-0.699458\pi$
$877$	12.0912	−	20.9426i	0.408290	−	0.707180i	0.994698	+	0.102836i	$0.0327917\pi$
$878$	31.6293	−	15.4373i	1.06744	−	0.520985i
$879$	−14.4734	+	8.35624i	−0.488177	+	0.281849i
$880$	10.3848	−	10.0504i	0.350072	−	0.338800i
$881$		−	19.6285i		−	0.661301i	−0.943753	−	0.330651i	$-0.892732\pi$
$881$		−	19.6285i		−	0.661301i	0.943753	−	0.330651i	$-0.107268\pi$
$882$	−15.1738	−	20.3139i	−0.510928	−	0.684004i
$883$		−	11.2418i		−	0.378315i	−0.981947	−	0.189158i	$-0.939424\pi$
$883$		−	11.2418i		−	0.378315i	0.981947	−	0.189158i	$-0.0605757\pi$
$884$	−9.81483	+	12.5766i	−0.330108	+	0.422995i
$885$	4.28982	−	2.47673i	0.144201	−	0.0832544i
$886$	4.92995	+	10.1009i	0.165625	+	0.339346i
$887$	−20.9050	+	36.2085i	−0.701920	+	1.21576i	0.265871	+	0.964009i	$0.414340\pi$
$887$	−20.9050	+	36.2085i	−0.701920	+	1.21576i	−0.967792	+	0.251753i	$0.918993\pi$
$888$	4.18882	−	19.7865i	0.140568	−	0.663993i
$889$	34.6779	+	28.7172i	1.16306	+	0.963143i
$890$	0.922831	−	13.2491i	0.0309334	−	0.444110i
$891$	−16.4082	−	9.47327i	−0.549695	−	0.317366i
$892$	12.6173	+	31.1798i	0.422457	+	1.04398i
$893$	−14.1222	−	24.4604i	−0.472583	−	0.818537i
$894$	14.8246	+	9.99344i	0.495809	+	0.334231i
$895$	−20.5539			−0.687040
$896$	29.6759	+	3.91696i	0.991401	+	0.130856i
$897$	−12.5320			−0.418430
$898$	16.7721	+	11.3063i	0.559693	+	0.377296i
$899$	−23.0272	−	39.8842i	−0.768000	−	1.33021i
$900$	1.92154	+	4.74852i	0.0640514	+	0.158284i
$901$	−8.78851	−	5.07405i	−0.292788	−	0.169041i
$902$	−0.295644	+	4.24455i	−0.00984385	+	0.141328i
$903$	−0.910527	+	5.36708i	−0.0303005	+	0.178605i
$904$	−4.16262	+	19.6628i	−0.138447	+	0.653974i
$905$	6.53013	−	11.3105i	0.217069	−	0.375974i
$906$	−3.94667	−	8.08627i	−0.131119	−	0.268648i
$907$	−18.8870	+	10.9044i	−0.627133	+	0.362076i	−0.779641	−	0.626227i	$-0.784598\pi$
$907$	−18.8870	+	10.9044i	−0.627133	+	0.362076i	0.152508	+	0.988302i	$0.451265\pi$
$908$	24.4048	−	31.2719i	0.809901	−	1.03779i
$909$		−	11.6189i		−	0.385374i
$910$	5.13438	−	21.2020i	0.170203	−	0.702841i
$911$			2.40991i			0.0798440i	0.999203	+	0.0399220i	$0.0127109\pi$
$911$			2.40991i			0.0798440i	−0.999203	+	0.0399220i	$0.987289\pi$
$912$	7.79761	−	7.54654i	0.258205	−	0.249891i
$913$	20.3112	−	11.7267i	0.672202	−	0.388096i
$914$	−28.1872	+	13.7574i	−0.932350	+	0.455053i
$915$	0.491978	−	0.852131i	0.0162643	−	0.0281706i
$916$	−3.86316	+	27.5971i	−0.127642	+	0.911835i
$917$	−1.11085	−	2.99154i	−0.0366833	−	0.0987893i
$918$	−7.10977	−	0.495214i	−0.234657	−	0.0163445i
$919$	−13.1661	−	7.60145i	−0.434310	−	0.250749i	0.266871	−	0.963732i	$-0.414010\pi$
$919$	−13.1661	−	7.60145i	−0.434310	−	0.250749i	−0.701181	+	0.712983i	$0.747343\pi$
$920$	−8.72722	+	2.84355i	−0.287728	+	0.0937490i
$921$	−9.69140	−	16.7860i	−0.319343	−	0.553118i
$922$	25.9748	−	38.5318i	0.855433	−	1.26898i
$923$	20.5518			0.676470
$924$	−8.53906	−	9.35058i	−0.280914	−	0.307611i
$925$	−10.7958			−0.354963
$926$	2.61965	−	3.88607i	0.0860870	−	0.127704i
$927$	7.86074	+	13.6152i	0.258181	+	0.447182i
$928$	−28.9242	+	5.14084i	−0.949485	+	0.168756i
$929$	18.0735	+	10.4347i	0.592971	+	0.342352i	0.766272	−	0.642517i	$-0.222110\pi$
$929$	18.0735	+	10.4347i	0.592971	+	0.342352i	−0.173300	+	0.984869i	$0.555443\pi$
$930$	−8.28676	−	0.577194i	−0.271734	−	0.0189269i
$931$	27.0662	+	9.45573i	0.887059	+	0.309899i
$932$	−20.2538	−	2.83522i	−0.663437	−	0.0928706i
$933$	7.53299	−	13.0475i	0.246619	−	0.427157i
$934$	44.6517	−	21.7932i	1.46105	−	0.713094i
$935$	4.28075	−	2.47149i	0.139995	−	0.0808264i
$936$	28.2363	−	31.4112i	0.922931	−	1.02671i
$937$			10.9083i			0.356358i	0.983998	+	0.178179i	$0.0570206\pi$
$937$			10.9083i			0.356358i	−0.983998	+	0.178179i	$0.942979\pi$
$938$	−6.54939	+	6.87443i	−0.213845	+	0.224458i
$939$			4.36148i			0.142331i
$940$	10.8729	+	8.48528i	0.354635	+	0.276759i
$941$	−42.7569	+	24.6857i	−1.39383	+	0.804730i	−0.993737	−	0.111743i	$-0.964357\pi$
$941$	−42.7569	+	24.6857i	−1.39383	+	0.804730i	−0.400097	+	0.916473i	$0.631023\pi$
$942$	6.76367	+	13.8580i	0.220372	+	0.451517i
$943$	1.35118	−	2.34032i	0.0440006	−	0.0762113i
$944$	−28.7644	−	8.21408i	−0.936202	−	0.267346i
$945$	9.13620	−	3.39254i	0.297201	−	0.110359i
$946$	1.10287	−	15.8339i	0.0358574	−	0.514804i
$947$	12.6081	+	7.27929i	0.409708	+	0.236545i	0.690664	−	0.723175i	$-0.257318\pi$
$947$	12.6081	+	7.27929i	0.409708	+	0.236545i	−0.280956	+	0.959721i	$0.590651\pi$
$948$	13.9254	−	5.63507i	0.452276	−	0.183019i
$949$	15.0708	+	26.1034i	0.489218	+	0.847351i
$950$	−4.80291	−	3.23770i	−0.155827	−	0.105045i
$951$	9.35358			0.303311
$952$	9.52036	+	3.76585i	0.308557	+	0.122052i
$953$	−9.87954			−0.320030			−0.160015	−	0.987115i	$-0.551154\pi$
$953$	−9.87954			−0.320030			−0.160015	+	0.987115i	$0.551154\pi$
$954$	22.2785	+	15.0182i	0.721293	+	0.486232i
$955$	6.23755	+	10.8038i	0.201843	+	0.349602i
$956$	−31.6720	+	12.8164i	−1.02435	+	0.414513i
$957$	10.7628	+	6.21390i	0.347912	+	0.200867i
$958$	−2.19394	+	31.4983i	−0.0708829	+	1.01766i
$959$	5.59494	+	0.949183i	0.180670	+	0.0306507i
$960$	−2.14730	+	4.84425i	−0.0693038	+	0.156348i
$961$	−23.8215	+	41.2601i	−0.768437	+	1.33097i
$962$	39.0430	+	79.9945i	1.25880	+	2.57913i
$963$	−17.0086	+	9.81993i	−0.548095	+	0.316443i
$964$	−29.1431	−	22.7435i	−0.938637	−	0.732519i
$965$			19.0645i			0.613708i
$966$	2.26901	+	7.71586i	0.0730042	+	0.248254i
$967$		−	15.5047i		−	0.498597i	−0.968427	−	0.249298i	$-0.919800\pi$
$967$		−	15.5047i		−	0.498597i	0.968427	−	0.249298i	$-0.0802000\pi$
$968$	4.31948	+	3.88287i	0.138833	+	0.124800i
$969$	3.21427	−	1.85576i	0.103257	−	0.0596156i
$970$	0.436165	−	0.212879i	0.0140044	−	0.00683514i
$971$	16.5173	−	28.6089i	0.530067	−	0.918102i	−0.469318	−	0.883029i	$-0.655500\pi$
$971$	16.5173	−	28.6089i	0.530067	−	0.918102i	0.999385	−	0.0350732i	$-0.0111664\pi$
$972$	28.7676	+	4.02701i	0.922721	+	0.129166i
$973$	5.72993	−	6.91927i	0.183693	−	0.221822i
$974$	−10.1368	−	0.706056i	−0.324805	−	0.0226235i
$975$	3.34434	+	1.93085i	0.107104	+	0.0618368i
$976$	−5.76409	+	1.44384i	−0.184504	+	0.0462161i
$977$	25.4860	+	44.1430i	0.815369	+	1.41226i	0.909062	+	0.416660i	$0.136799\pi$
$977$	25.4860	+	44.1430i	0.815369	+	1.41226i	−0.0936930	+	0.995601i	$0.529867\pi$
$978$	−3.74687	+	5.55824i	−0.119812	+	0.177733i
$979$	33.9301			1.08441
$980$	−13.9836	+	0.677585i	−0.446689	+	0.0216447i
$981$	−3.31746			−0.105918
$982$	4.58536	−	6.80208i	0.146325	−	0.217063i
$983$	12.2642	+	21.2423i	0.391168	+	0.677523i	0.992604	−	0.121398i	$-0.0387378\pi$
$983$	12.2642	+	21.2423i	0.391168	+	0.677523i	−0.601436	+	0.798921i	$0.705404\pi$
$984$	−0.483298	−	1.48330i	−0.0154070	−	0.0472860i
$985$	−1.67306	−	0.965939i	−0.0533080	−	0.0307774i
$986$	−10.0238	−	0.698180i	−0.319221	−	0.0222346i
$987$	7.70775	−	9.30762i	0.245340	−	0.296265i
$988$	−6.62093	+	47.2977i	−0.210640	+	1.50474i
$989$	−5.04046	+	8.73034i	−0.160277	+	0.277609i
$990$	−11.7609	+	5.74013i	−0.373784	+	0.182433i
$991$	45.8274	−	26.4585i	1.45576	−	0.840481i	0.456957	−	0.889489i	$-0.348939\pi$
$991$	45.8274	−	26.4585i	1.45576	−	0.840481i	0.998798	+	0.0490078i	$0.0156059\pi$
$992$	32.2982	+	38.3850i	1.02547	+	1.21872i
$993$			13.4606i			0.427160i
$994$	−3.72106	−	12.6536i	−0.118025	−	0.401348i
$995$		−	20.5646i		−	0.651941i
$996$	−5.29054	+	6.77921i	−0.167637	+	0.214808i
$997$	14.7423	−	8.51148i	0.466894	−	0.269561i	−0.248045	−	0.968749i	$-0.579788\pi$
$997$	14.7423	−	8.51148i	0.466894	−	0.269561i	0.714939	+	0.699187i	$0.246455\pi$
$998$	−24.6011	−	50.4047i	−0.778733	−	1.59553i
$999$	−19.8834	+	34.4390i	−0.629082	+	1.08960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.o.a.131.14	yes	32
4.3	odd	2	inner	140.2.o.a.131.2	yes	32
5.2	odd	4		700.2.t.d.299.5		32
5.3	odd	4		700.2.t.c.299.12		32
5.4	even	2		700.2.p.c.551.3		32
7.2	even	3		980.2.g.a.391.17		32
7.3	odd	6	inner	140.2.o.a.31.2	✓	32
7.4	even	3		980.2.o.f.31.2		32
7.5	odd	6		980.2.g.a.391.18		32
7.6	odd	2		980.2.o.f.411.14		32
20.3	even	4		700.2.t.c.299.7		32
20.7	even	4		700.2.t.d.299.10		32
20.19	odd	2		700.2.p.c.551.15		32
28.3	even	6	inner	140.2.o.a.31.14	yes	32
28.11	odd	6		980.2.o.f.31.14		32
28.19	even	6		980.2.g.a.391.19		32
28.23	odd	6		980.2.g.a.391.20		32
28.27	even	2		980.2.o.f.411.2		32
35.3	even	12		700.2.t.d.199.10		32
35.17	even	12		700.2.t.c.199.7		32
35.24	odd	6		700.2.p.c.451.15		32
140.3	odd	12		700.2.t.d.199.5		32
140.59	even	6		700.2.p.c.451.3		32
140.87	odd	12		700.2.t.c.199.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.2	✓	32	7.3	odd	6	inner
140.2.o.a.31.14	yes	32	28.3	even	6	inner
140.2.o.a.131.2	yes	32	4.3	odd	2	inner
140.2.o.a.131.14	yes	32	1.1	even	1	trivial
700.2.p.c.451.3		32	140.59	even	6
700.2.p.c.451.15		32	35.24	odd	6
700.2.p.c.551.3		32	5.4	even	2
700.2.p.c.551.15		32	20.19	odd	2
700.2.t.c.199.7		32	35.17	even	12
700.2.t.c.199.12		32	140.87	odd	12
700.2.t.c.299.7		32	20.3	even	4
700.2.t.c.299.12		32	5.3	odd	4
700.2.t.d.199.5		32	140.3	odd	12
700.2.t.d.199.10		32	35.3	even	12
700.2.t.d.299.5		32	5.2	odd	4
700.2.t.d.299.10		32	20.7	even	4
980.2.g.a.391.17		32	7.2	even	3
980.2.g.a.391.18		32	7.5	odd	6
980.2.g.a.391.19		32	28.19	even	6
980.2.g.a.391.20		32	28.23	odd	6
980.2.o.f.31.2		32	7.4	even	3
980.2.o.f.31.14		32	28.11	odd	6
980.2.o.f.411.2		32	28.27	even	2
980.2.o.f.411.14		32	7.6	odd	2

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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17265 + 0.790498i) q^{2} +(0.331177 + 0.573616i) q^{3} +(0.750225 + 1.85396i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.0650866 + 0.934447i) q^{6} +(-1.68748 + 2.03775i) q^{7} +(-0.585797 + 2.76710i) q^{8} +(1.28064 - 2.21814i) q^{9} +O(q^{10})\)	\(q+(1.17265 + 0.790498i) q^{2} +(0.331177 + 0.573616i) q^{3} +(0.750225 + 1.85396i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.0650866 + 0.934447i) q^{6} +(-1.68748 + 2.03775i) q^{7} +(-0.585797 + 2.76710i) q^{8} +(1.28064 - 2.21814i) q^{9} +(-0.620297 - 1.27092i) q^{10} +(3.12892 - 1.80648i) q^{11} +(-0.815002 + 1.04433i) q^{12} -5.83027i q^{13} +(-3.58966 + 1.05561i) q^{14} -0.662355i q^{15} +(-2.87432 + 2.78177i) q^{16} +(-1.18483 + 0.684063i) q^{17} +(3.25518 - 1.58876i) q^{18} +(-2.04788 + 3.54704i) q^{19} +(0.277265 - 1.98069i) q^{20} +(-1.72774 - 0.293111i) q^{21} +(5.09715 + 0.355029i) q^{22} +(-2.81042 - 1.62259i) q^{23} +(-1.78126 + 0.580378i) q^{24} +(0.500000 + 0.866025i) q^{25} +(4.60882 - 6.83688i) q^{26} +3.68354 q^{27} +(-5.04389 - 1.59975i) q^{28} +5.19327 q^{29} +(0.523590 - 0.776712i) q^{30} +(-4.43405 - 7.67999i) q^{31} +(-5.56957 + 0.989905i) q^{32} +(2.07245 + 1.19653i) q^{33} +(-1.93014 - 0.134439i) q^{34} +(2.48027 - 0.920998i) q^{35} +(5.07311 + 0.710155i) q^{36} +(-5.39789 + 9.34942i) q^{37} +(-5.20538 + 2.54059i) q^{38} +(3.34434 - 1.93085i) q^{39} +(1.89087 - 2.10348i) q^{40} +0.832730i q^{41} +(-1.79433 - 1.70949i) q^{42} -3.10642i q^{43} +(5.69653 + 4.44561i) q^{44} +(-2.21814 + 1.28064i) q^{45} +(-2.01298 - 4.12437i) q^{46} +(-3.44801 + 5.97212i) q^{47} +(-2.54758 - 0.727497i) q^{48} +(-1.30481 - 6.87732i) q^{49} +(-0.0982654 + 1.41080i) q^{50} +(-0.784778 - 0.453092i) q^{51} +(10.8091 - 4.37402i) q^{52} +(3.70876 + 6.42376i) q^{53} +(4.31952 + 2.91183i) q^{54} -3.61296 q^{55} +(-4.65012 - 5.86314i) q^{56} -2.71285 q^{57} +(6.08989 + 4.10527i) q^{58} +(3.73928 + 6.47663i) q^{59} +(1.22798 - 0.496915i) q^{60} +(1.28652 + 0.742772i) q^{61} +(0.871427 - 12.5111i) q^{62} +(2.35894 + 6.35269i) q^{63} +(-7.31368 - 3.24192i) q^{64} +(-2.91513 + 5.04916i) q^{65} +(1.48441 + 3.04138i) q^{66} +(2.19763 - 1.26880i) q^{67} +(-2.15711 - 1.68343i) q^{68} -2.14947i q^{69} +(3.63655 + 0.880642i) q^{70} +3.52502i q^{71} +(5.38762 + 4.84305i) q^{72} +(-4.47721 + 2.58492i) q^{73} +(-13.7206 + 6.69660i) q^{74} +(-0.331177 + 0.573616i) q^{75} +(-8.11244 - 1.13561i) q^{76} +(-1.59884 + 9.42434i) q^{77} +(5.44808 + 0.379472i) q^{78} +(-9.82082 - 5.67005i) q^{79} +(3.88012 - 0.971925i) q^{80} +(-2.62202 - 4.54148i) q^{81} +(-0.658272 + 0.976503i) q^{82} +6.49145 q^{83} +(-0.752777 - 3.42306i) q^{84} +1.36813 q^{85} +(2.45562 - 3.64275i) q^{86} +(1.71989 + 2.97894i) q^{87} +(3.16580 + 9.71626i) q^{88} +(8.13303 + 4.69560i) q^{89} +(-3.61345 - 0.251686i) q^{90} +(11.8806 + 9.83847i) q^{91} +(0.899777 - 6.42771i) q^{92} +(2.93691 - 5.08688i) q^{93} +(-8.76426 + 4.27758i) q^{94} +(3.54704 - 2.04788i) q^{95} +(-2.41234 - 2.86696i) q^{96} +0.343189i q^{97} +(3.90642 - 9.09615i) q^{98} -9.25383i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9	\( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38} - 62 q^{42} - 18 q^{44} + 12 q^{45} + 2 q^{46} - 16 q^{49} + 4 q^{50} - 36 q^{52} - 8 q^{53} + 12 q^{54} - 4 q^{56} + 48 q^{57} + 2 q^{58} + 14 q^{60} + 24 q^{61} + 4 q^{64} + 4 q^{65} + 24 q^{66} + 60 q^{68} - 4 q^{70} + 4 q^{72} - 72 q^{73} + 38 q^{74} - 40 q^{77} + 120 q^{78} - 36 q^{81} + 42 q^{82} - 20 q^{84} + 28 q^{86} + 4 q^{88} - 60 q^{89} - 4 q^{92} - 8 q^{93} + 18 q^{94} - 60 q^{96} + 78 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 - 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 - 8 * q^22 + 36 * q^24 + 16 * q^25 + 30 * q^26 + 2 * q^28 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 - 60 * q^38 - 62 * q^42 - 18 * q^44 + 12 * q^45 + 2 * q^46 - 16 * q^49 + 4 * q^50 - 36 * q^52 - 8 * q^53 + 12 * q^54 - 4 * q^56 + 48 * q^57 + 2 * q^58 + 14 * q^60 + 24 * q^61 + 4 * q^64 + 4 * q^65 + 24 * q^66 + 60 * q^68 - 4 * q^70 + 4 * q^72 - 72 * q^73 + 38 * q^74 - 40 * q^77 + 120 * q^78 - 36 * q^81 + 42 * q^82 - 20 * q^84 + 28 * q^86 + 4 * q^88 - 60 * q^89 - 4 * q^92 - 8 * q^93 + 18 * q^94 - 60 * q^96 + 78 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more