LMFDB - Embedded newform 546.2.bv.a.515.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(317,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			515.22
Character	$\chi$	$=$	546.515
Dual form			546.2.bv.a.317.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-1.45090 - 0.945993i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.31362 - 0.619932i) q^{5} +(-1.15662 - 1.28928i) q^{6} +(-1.72913 + 2.00252i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.21019 + 2.74507i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-1.45090 - 0.945993i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.31362 - 0.619932i) q^{5} +(-1.15662 - 1.28928i) q^{6} +(-1.72913 + 2.00252i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.21019 + 2.74507i) q^{9} +(-2.07433 - 1.19762i) q^{10} +(4.27634 - 1.14584i) q^{11} +(-0.783515 - 1.54470i) q^{12} +(2.93829 + 2.08961i) q^{13} +(-2.18851 + 1.48675i) q^{14} +(2.77036 + 3.08812i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.783047 + 1.35628i) q^{17} +(0.458480 + 2.96476i) q^{18} +(-1.62713 + 6.07252i) q^{19} +(-1.69368 - 1.69368i) q^{20} +(4.40317 - 1.26970i) q^{21} +4.42719 q^{22} +(1.38798 + 2.40405i) q^{23} +(-0.357020 - 1.69486i) q^{24} +(0.638379 + 0.368568i) q^{25} +(2.29734 + 2.77889i) q^{26} +(0.840957 - 5.12765i) q^{27} +(-2.49874 + 0.869667i) q^{28} +10.1305i q^{29} +(1.87670 + 3.69992i) q^{30} +(3.55563 - 0.952728i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-7.28848 - 2.38289i) q^{33} +(-1.10740 + 1.10740i) q^{34} +(5.24198 - 3.56112i) q^{35} +(-0.324478 + 2.98240i) q^{36} +(3.11607 + 0.834949i) q^{37} +(-3.14337 + 5.44447i) q^{38} +(-2.28639 - 5.81140i) q^{39} +(-1.19762 - 2.07433i) q^{40} +(-3.20200 + 3.20200i) q^{41} +(4.58175 - 0.0868122i) q^{42} -4.41157i q^{43} +(4.27634 + 1.14584i) q^{44} +(-1.09817 - 7.10129i) q^{45} +(0.718471 + 2.68137i) q^{46} +(2.70018 - 10.0772i) q^{47} +(0.0938065 - 1.72951i) q^{48} +(-1.02019 - 6.92526i) q^{49} +(0.521234 + 0.521234i) q^{50} +(2.41915 - 1.22706i) q^{51} +(1.49983 + 3.27880i) q^{52} +(-1.99674 - 1.15282i) q^{53} +(2.13944 - 4.73527i) q^{54} -10.6041 q^{55} +(-2.63868 + 0.193314i) q^{56} +(8.10536 - 7.27134i) q^{57} +(-2.62195 + 9.78527i) q^{58} +(-13.4331 + 3.59938i) q^{59} +(0.855145 + 4.05957i) q^{60} +(6.28923 + 10.8933i) q^{61} +3.68106 q^{62} +(-7.58966 - 2.32316i) q^{63} +1.00000i q^{64} +(-5.50266 - 6.65609i) q^{65} +(-6.42339 - 4.18809i) q^{66} +(1.94157 - 0.520241i) q^{67} +(-1.35628 + 0.783047i) q^{68} +(0.260403 - 4.80104i) q^{69} +(5.98505 - 2.08305i) q^{70} +(-2.32126 + 2.32126i) q^{71} +(-1.08532 + 2.79680i) q^{72} +(-0.292666 - 1.09224i) q^{73} +(2.79379 + 1.61300i) q^{74} +(-0.577558 - 1.13866i) q^{75} +(-4.44540 + 4.44540i) q^{76} +(-5.09979 + 10.5448i) q^{77} +(-0.704385 - 6.20515i) q^{78} +(-1.69077 - 2.92850i) q^{79} +(-0.619932 - 2.31362i) q^{80} +(-6.07086 + 6.64414i) q^{81} +(-3.92163 + 2.26416i) q^{82} +(-3.01433 + 3.01433i) q^{83} +(4.44810 + 1.10199i) q^{84} +(2.65247 - 2.65247i) q^{85} +(1.14180 - 4.26125i) q^{86} +(9.58334 - 14.6982i) q^{87} +(3.83406 + 2.21360i) q^{88} +(-1.07667 + 4.01819i) q^{89} +(0.777201 - 7.14354i) q^{90} +(-9.26518 + 2.27077i) q^{91} +2.77596i q^{92} +(-6.06012 - 1.98129i) q^{93} +(5.21635 - 9.03498i) q^{94} +(7.52910 - 13.0408i) q^{95} +(0.538240 - 1.64630i) q^{96} +(1.97173 + 1.97173i) q^{97} +(0.806966 - 6.95333i) q^{98} +(8.32062 + 10.3522i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−1.45090	−	0.945993i	−0.837675	−	0.546169i
$3$	−1.45090	−	0.945993i	−0.837675	−	0.546169i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−2.31362	−	0.619932i	−1.03468	−	0.277242i	−0.298773	−	0.954324i	$-0.596577\pi$
$5$	−2.31362	−	0.619932i	−1.03468	−	0.277242i	−0.735907	+	0.677082i	$0.763244\pi$
$6$	−1.15662	−	1.28928i	−0.472187	−	0.526346i
$7$	−1.72913	+	2.00252i	−0.653552	+	0.756882i
$7$	−1.72913	+	2.00252i	−0.653552	+	0.756882i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.21019	+	2.74507i	0.403398	+	0.915025i
$10$	−2.07433	−	1.19762i	−0.655961	−	0.378719i
$11$	4.27634	−	1.14584i	1.28936	−	0.345484i	0.451945	−	0.892046i	$-0.350730\pi$
$11$	4.27634	−	1.14584i	1.28936	−	0.345484i	0.837419	+	0.546562i	$0.184064\pi$
$12$	−0.783515	−	1.54470i	−0.226181	−	0.445917i
$13$	2.93829	+	2.08961i	0.814935	+	0.579553i
$13$	2.93829	+	2.08961i	0.814935	+	0.579553i
$14$	−2.18851	+	1.48675i	−0.584903	+	0.397352i
$15$	2.77036	+	3.08812i	0.715305	+	0.797349i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.783047	+	1.35628i	−0.189917	+	0.328946i	−0.945222	−	0.326427i	$-0.894155\pi$
$17$	−0.783047	+	1.35628i	−0.189917	+	0.328946i	0.755305	+	0.655373i	$0.227489\pi$
$18$	0.458480	+	2.96476i	0.108065	+	0.698800i
$19$	−1.62713	+	6.07252i	−0.373289	+	1.39313i	0.482541	+	0.875874i	$0.339714\pi$
$19$	−1.62713	+	6.07252i	−0.373289	+	1.39313i	−0.855829	+	0.517259i	$0.826953\pi$
$20$	−1.69368	−	1.69368i	−0.378719	−	0.378719i
$21$	4.40317	−	1.26970i	0.960849	−	0.277071i
$22$	4.42719			0.943880
$23$	1.38798	+	2.40405i	0.289414	+	0.501279i	0.973670	−	0.227962i	$-0.0732063\pi$
$23$	1.38798	+	2.40405i	0.289414	+	0.501279i	−0.684256	+	0.729242i	$0.739873\pi$
$24$	−0.357020	−	1.69486i	−0.0728763	−	0.345961i
$25$	0.638379	+	0.368568i	0.127676	+	0.0737136i
$26$	2.29734	+	2.77889i	0.450545	+	0.544985i
$27$	0.840957	−	5.12765i	0.161842	−	0.986817i
$28$	−2.49874	+	0.869667i	−0.472217	+	0.164352i
$29$			10.1305i			1.88118i	0.339547	+	0.940589i	$0.389726\pi$
$29$			10.1305i			1.88118i	−0.339547	+	0.940589i	$0.610274\pi$
$30$	1.87670	+	3.69992i	0.342637	+	0.675510i
$31$	3.55563	−	0.952728i	0.638610	−	0.171115i	0.0750363	−	0.997181i	$-0.476093\pi$
$31$	3.55563	−	0.952728i	0.638610	−	0.171115i	0.563574	+	0.826066i	$0.309426\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−7.28848	−	2.38289i	−1.26876	−	0.414808i
$34$	−1.10740	+	1.10740i	−0.189917	+	0.189917i
$35$	5.24198	−	3.56112i	0.886057	−	0.601939i
$36$	−0.324478	+	2.98240i	−0.0540797	+	0.497067i
$37$	3.11607	+	0.834949i	0.512279	+	0.137265i	0.505693	−	0.862714i	$-0.331237\pi$
$37$	3.11607	+	0.834949i	0.512279	+	0.137265i	0.00658613	+	0.999978i	$0.497904\pi$
$38$	−3.14337	+	5.44447i	−0.509922	+	0.883210i
$39$	−2.28639	−	5.81140i	−0.366116	−	0.930569i
$40$	−1.19762	−	2.07433i	−0.189360	−	0.327981i
$41$	−3.20200	+	3.20200i	−0.500068	+	0.500068i	−0.911459	−	0.411391i	$-0.865043\pi$
$41$	−3.20200	+	3.20200i	−0.500068	+	0.500068i	0.411391	+	0.911459i	$0.365043\pi$
$42$	4.58175	−	0.0868122i	0.706980	−	0.0133954i
$43$		−	4.41157i		−	0.672758i	−0.941727	−	0.336379i	$-0.890798\pi$
$43$		−	4.41157i		−	0.672758i	0.941727	−	0.336379i	$-0.109202\pi$
$44$	4.27634	+	1.14584i	0.644682	+	0.172742i
$45$	−1.09817	−	7.10129i	−0.163705	−	1.05860i
$46$	0.718471	+	2.68137i	0.105933	+	0.395346i
$47$	2.70018	−	10.0772i	0.393862	−	1.46991i	−0.429848	−	0.902901i	$-0.641433\pi$
$47$	2.70018	−	10.0772i	0.393862	−	1.46991i	0.823710	−	0.567011i	$-0.191900\pi$
$48$	0.0938065	−	1.72951i	0.0135398	−	0.249633i
$49$	−1.02019	−	6.92526i	−0.145741	−	0.989323i
$50$	0.521234	+	0.521234i	0.0737136	+	0.0737136i
$51$	2.41915	−	1.22706i	0.338749	−	0.171823i
$52$	1.49983	+	3.27880i	0.207989	+	0.454687i
$53$	−1.99674	−	1.15282i	−0.274273	−	0.158352i	0.356555	−	0.934274i	$-0.383951\pi$
$53$	−1.99674	−	1.15282i	−0.274273	−	0.158352i	−0.630828	+	0.775923i	$0.717285\pi$
$54$	2.13944	−	4.73527i	0.291140	−	0.644389i
$55$	−10.6041			−1.42986
$56$	−2.63868	+	0.193314i	−0.352608	+	0.0258326i
$57$	8.10536	−	7.27134i	1.07358	−	0.963113i
$58$	−2.62195	+	9.78527i	−0.344279	+	1.28487i
$59$	−13.4331	+	3.59938i	−1.74884	+	0.468600i	−0.984378	−	0.176070i	$-0.943661\pi$
$59$	−13.4331	+	3.59938i	−1.74884	+	0.468600i	−0.764461	+	0.644670i	$0.776995\pi$
$60$	0.855145	+	4.05957i	0.110399	+	0.524089i
$61$	6.28923	+	10.8933i	0.805254	+	1.39474i	0.916120	+	0.400905i	$0.131304\pi$
$61$	6.28923	+	10.8933i	0.805254	+	1.39474i	−0.110866	+	0.993835i	$0.535362\pi$
$62$	3.68106			0.467495
$63$	−7.58966	−	2.32316i	−0.956207	−	0.292691i
$64$			1.00000i			0.125000i
$65$	−5.50266	−	6.65609i	−0.682521	−	0.825586i
$66$	−6.42339	−	4.18809i	−0.790665	−	0.515518i
$67$	1.94157	−	0.520241i	0.237200	−	0.0635576i	−0.138261	−	0.990396i	$-0.544151\pi$
$67$	1.94157	−	0.520241i	0.237200	−	0.0635576i	0.375461	+	0.926838i	$0.377484\pi$
$68$	−1.35628	+	0.783047i	−0.164473	+	0.0949584i
$69$	0.260403	−	4.80104i	0.0313488	−	0.577978i
$70$	5.98505	−	2.08305i	0.715350	−	0.248973i
$71$	−2.32126	+	2.32126i	−0.275483	+	0.275483i	−0.831303	−	0.555820i	$-0.812404\pi$
$71$	−2.32126	+	2.32126i	−0.275483	+	0.275483i	0.555820	+	0.831303i	$0.312404\pi$
$72$	−1.08532	+	2.79680i	−0.127907	+	0.329606i
$73$	−0.292666	−	1.09224i	−0.0342539	−	0.127837i	0.946682	−	0.322170i	$-0.104412\pi$
$73$	−0.292666	−	1.09224i	−0.0342539	−	0.127837i	−0.980936	+	0.194333i	$0.937746\pi$
$74$	2.79379	+	1.61300i	0.324772	+	0.187507i
$75$	−0.577558	−	1.13866i	−0.0666906	−	0.131481i
$76$	−4.44540	+	4.44540i	−0.509922	+	0.509922i
$77$	−5.09979	+	10.5448i	−0.581175	+	1.20169i
$78$	−0.704385	−	6.20515i	−0.0797559	−	0.702594i
$79$	−1.69077	−	2.92850i	−0.190227	−	0.329482i	0.755099	−	0.655611i	$-0.227589\pi$
$79$	−1.69077	−	2.92850i	−0.190227	−	0.329482i	−0.945325	+	0.326129i	$0.894256\pi$
$80$	−0.619932	−	2.31362i	−0.0693105	−	0.258670i
$81$	−6.07086	+	6.64414i	−0.674540	+	0.738238i
$82$	−3.92163	+	2.26416i	−0.433072	+	0.250034i
$83$	−3.01433	+	3.01433i	−0.330866	+	0.330866i	−0.852915	−	0.522049i	$-0.825168\pi$
$83$	−3.01433	+	3.01433i	−0.330866	+	0.330866i	0.522049	+	0.852915i	$0.325168\pi$
$84$	4.44810	+	1.10199i	0.485328	+	0.120237i
$85$	2.65247	−	2.65247i	0.287701	−	0.287701i
$86$	1.14180	−	4.26125i	0.123123	−	0.459502i
$87$	9.58334	−	14.6982i	1.02744	−	1.57582i
$88$	3.83406	+	2.21360i	0.408712	+	0.235970i
$89$	−1.07667	+	4.01819i	−0.114127	+	0.425927i	−0.999220	−	0.0394865i	$-0.987428\pi$
$89$	−1.07667	+	4.01819i	−0.114127	+	0.425927i	0.885093	+	0.465414i	$0.154094\pi$
$90$	0.777201	−	7.14354i	0.0819242	−	0.752995i
$91$	−9.26518	+	2.27077i	−0.971255	+	0.238042i
$92$			2.77596i			0.289414i
$93$	−6.06012	−	1.98129i	−0.628405	−	0.205451i
$94$	5.21635	−	9.03498i	0.538025	−	0.931887i
$95$	7.52910	−	13.0408i	0.772469	−	1.33796i
$96$	0.538240	−	1.64630i	0.0549339	−	0.168025i
$97$	1.97173	+	1.97173i	0.200199	+	0.200199i	0.800085	−	0.599887i	$-0.204788\pi$
$97$	1.97173	+	1.97173i	0.200199	+	0.200199i	−0.599887	+	0.800085i	$0.704788\pi$
$98$	0.806966	−	6.95333i	0.0815158	−	0.702392i
$99$	8.32062	+	10.3522i	0.836253	+	1.04043i
$100$	0.368568	+	0.638379i	0.0368568	+	0.0638379i
$101$	4.49445	−	7.78461i	0.447214	−	0.774598i	−0.550989	−	0.834512i	$-0.685749\pi$
$101$	4.49445	−	7.78461i	0.447214	−	0.774598i	0.998204	+	0.0599144i	$0.0190828\pi$
$102$	2.65430	−	0.559126i	0.262815	−	0.0553618i
$103$	16.1944	−	9.34982i	1.59568	−	0.921265i	0.603371	−	0.797460i	$-0.293824\pi$
$103$	16.1944	−	9.34982i	1.59568	−	0.921265i	0.992307	−	0.123805i	$-0.0395097\pi$
$104$	0.600108	+	3.55526i	0.0588454	+	0.348622i
$105$	−10.9744	+	0.207935i	−1.07099	+	0.0202924i
$106$	−1.63033	−	1.63033i	−0.158352	−	0.158352i
$107$	0.182799	−	0.105539i	0.0176718	−	0.0102028i	−0.491138	−	0.871082i	$-0.663419\pi$
$107$	0.182799	−	0.105539i	0.0176718	−	0.0102028i	0.508810	+	0.860879i	$0.330086\pi$
$108$	3.29211	−	4.02020i	0.316784	−	0.386844i
$109$	−13.6372	+	3.65408i	−1.30621	+	0.349997i	−0.843794	−	0.536667i	$-0.819683\pi$
$109$	−13.6372	+	3.65408i	−1.30621	+	0.349997i	−0.462414	+	0.886664i	$0.653016\pi$
$110$	−10.2428	−	2.74456i	−0.976615	−	0.261683i
$111$	−3.73124	−	4.15921i	−0.354153	−	0.394774i
$112$	−2.59880	−	0.496214i	−0.245564	−	0.0468878i
$113$			7.74117i			0.728228i	0.931354	+	0.364114i	$0.118628\pi$
$113$			7.74117i			0.728228i	−0.931354	+	0.364114i	$0.881372\pi$
$114$	9.71114	−	4.92576i	0.909531	−	0.461339i
$115$	−1.72090	−	6.42250i	−0.160475	−	0.598902i
$116$	−5.06523	+	8.77323i	−0.470294	+	0.814574i
$117$	−2.18023	+	10.5946i	−0.201562	+	0.979476i
$118$	−13.9070			−1.28024
$119$	−1.36198	−	3.91326i	−0.124853	−	0.358728i
$120$	−0.224688	+	4.14257i	−0.0205112	+	0.378164i
$121$	7.44783	−	4.30001i	0.677075	−	0.390910i
$122$	3.25555	+	12.1499i	0.294743	+	1.10000i
$123$	7.67483	−	1.61670i	0.692016	−	0.145773i
$124$	3.55563	+	0.952728i	0.319305	+	0.0855575i
$125$	7.21995	+	7.21995i	0.645772	+	0.645772i
$126$	−6.72977	−	4.20835i	−0.599535	−	0.374910i
$127$		−	14.6274i		−	1.29797i	−0.760801	−	0.648985i	$-0.775194\pi$
$127$		−	14.6274i		−	1.29797i	0.760801	−	0.648985i	$-0.224806\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−4.17332	+	6.40073i	−0.367440	+	0.563553i
$130$	−3.59244	−	7.85348i	−0.315078	−	0.688796i
$131$	13.2073	−	7.62522i	1.15392	−	0.666219i	0.204084	−	0.978953i	$-0.434578\pi$
$131$	13.2073	−	7.62522i	1.15392	−	0.666219i	0.949841	+	0.312734i	$0.101245\pi$
$132$	−5.12056	−	5.70788i	−0.445687	−	0.496807i
$133$	−9.34683	−	13.7586i	−0.810473	−	1.19302i
$134$	2.01006			0.173642
$135$	−5.12444	+	11.3421i	−0.441042	+	0.976171i
$136$	−1.51273	+	0.405335i	−0.129716	+	0.0347572i
$137$	−11.7590	+	3.15082i	−1.00464	+	0.269193i	−0.723389	−	0.690441i	$-0.757417\pi$
$137$	−11.7590	+	3.15082i	−1.00464	+	0.269193i	−0.281253	+	0.959634i	$0.590750\pi$
$138$	1.49413	−	4.57006i	0.127189	−	0.389029i
$139$	−5.78743			−0.490884			−0.245442	−	0.969411i	$-0.578933\pi$
$139$	−5.78743			−0.490884			−0.245442	+	0.969411i	$0.578933\pi$
$140$	6.32025	−	0.463031i	0.534159	−	0.0391333i
$141$	−13.4507	+	12.0666i	−1.13275	+	1.01619i
$142$	−2.84295	+	1.64138i	−0.238575	+	0.137742i
$143$	14.9595	+	5.56906i	1.25097	+	0.465708i
$144$	−1.77221	+	2.42060i	−0.147684	+	0.201716i
$145$	6.28019	−	23.4380i	0.521541	−	1.94642i
$146$		−	1.13077i		−	0.0935835i
$147$	−5.07107	+	11.0129i	−0.418254	+	0.908330i
$148$	2.28112	+	2.28112i	0.187507	+	0.187507i
$149$	12.4133	+	3.32612i	1.01693	+	0.272487i	0.728524	−	0.685020i	$-0.240207\pi$
$149$	12.4133	+	3.32612i	1.01693	+	0.272487i	0.288410	+	0.957507i	$0.406873\pi$
$150$	−0.263172	−	1.24934i	−0.0214879	−	0.102008i
$151$	−3.31813	−	12.3834i	−0.270026	−	1.00775i	−0.959102	−	0.283061i	$-0.908650\pi$
$151$	−3.31813	−	12.3834i	−0.270026	−	1.00775i	0.689076	−	0.724689i	$-0.258017\pi$
$152$	−5.44447	+	3.14337i	−0.441605	+	0.254961i
$153$	−4.67072	−	0.508164i	−0.377605	−	0.0410826i
$154$	−7.65521	+	8.86554i	−0.616874	+	0.714406i
$155$	−8.81699			−0.708198
$156$	0.925626	−	6.17602i	0.0741094	−	0.494477i
$157$	9.81438	−	16.9990i	0.783273	−	1.35667i	−0.146752	−	0.989173i	$-0.546882\pi$
$157$	9.81438	−	16.9990i	0.783273	−	1.35667i	0.930025	−	0.367495i	$-0.119785\pi$
$158$	−0.875208	−	3.26632i	−0.0696278	−	0.259855i
$159$	1.80650	+	3.56151i	0.143265	+	0.282447i
$160$		−	2.39523i		−	0.189360i
$161$	−7.21417	−	1.37747i	−0.568556	−	0.108560i
$162$	−7.58363	+	4.84649i	−0.595827	+	0.380777i
$163$	−3.36505	−	0.901661i	−0.263571	−	0.0706236i	0.124614	−	0.992205i	$-0.460231\pi$
$163$	−3.36505	−	0.901661i	−0.263571	−	0.0706236i	−0.388184	+	0.921582i	$0.626898\pi$
$164$	−4.37401	+	1.17201i	−0.341553	+	0.0915188i
$165$	15.3855	+	10.0315i	1.19776	+	0.780947i
$166$	−3.69179	+	2.13146i	−0.286538	+	0.165433i
$167$	8.50343	+	8.50343i	0.658015	+	0.658015i	0.954910	−	0.296895i	$-0.0959511\pi$
$167$	8.50343	+	8.50343i	0.658015	+	0.658015i	−0.296895	+	0.954910i	$0.595951\pi$
$168$	4.01132	+	2.21570i	0.309480	+	0.170945i
$169$	4.26708	+	12.2797i	0.328237	+	0.944595i
$170$	3.24860	−	1.87558i	0.249156	−	0.143850i
$171$	−18.6387	+	2.88234i	−1.42533	+	0.220418i
$172$	2.20579	−	3.82053i	0.168190	−	0.291313i
$173$	4.22698	+	7.32134i	0.321371	+	0.556631i	0.980771	−	0.195161i	$-0.0625229\pi$
$173$	4.22698	+	7.32134i	0.321371	+	0.556631i	−0.659400	+	0.751792i	$0.729190\pi$
$174$	13.0610	−	11.7170i	0.990150	−	0.888267i
$175$	−1.84191	+	0.641063i	−0.139235	+	0.0484598i
$176$	3.13050	+	3.13050i	0.235970	+	0.235970i
$177$	22.8950	+	7.48528i	1.72089	+	0.562628i
$178$	−2.07997	+	3.60261i	−0.155900	+	0.270027i
$179$	−4.53130	+	7.84844i	−0.338685	+	0.586620i	−0.984186	−	0.177140i	$-0.943315\pi$
$179$	−4.53130	+	7.84844i	−0.338685	+	0.586620i	0.645501	+	0.763760i	$0.276649\pi$
$180$	2.59960	−	6.69898i	0.193763	−	0.499312i
$181$			17.2409i			1.28150i	0.767749	+	0.640751i	$0.221377\pi$
$181$			17.2409i			1.28150i	−0.767749	+	0.640751i	$0.778623\pi$
$182$	−9.53720	−	0.204608i	−0.706944	−	0.0151665i
$183$	1.17994	−	21.7546i	0.0872238	−	1.60814i
$184$	−0.718471	+	2.68137i	−0.0529664	+	0.197673i
$185$	−6.69178	−	3.86350i	−0.491990	−	0.284050i
$186$	−5.34083	−	3.48226i	−0.391609	−	0.255331i
$187$	−1.79450	+	6.69715i	−0.131226	+	0.489744i
$188$	7.37703	−	7.37703i	0.538025	−	0.538025i
$189$	8.81410	+	10.5504i	0.641132	+	0.767431i
$190$	10.6478	−	10.6478i	0.772469	−	0.772469i
$191$	8.61894	−	4.97615i	0.623645	−	0.360062i	−0.154642	−	0.987971i	$-0.549422\pi$
$191$	8.61894	−	4.97615i	0.623645	−	0.360062i	0.778287	+	0.627909i	$0.216089\pi$
$192$	0.945993	−	1.45090i	0.0682712	−	0.104709i
$193$	−0.0446354	−	0.166582i	−0.00321293	−	0.0119908i	0.964301	−	0.264809i	$-0.0853091\pi$
$193$	−0.0446354	−	0.166582i	−0.00321293	−	0.0119908i	−0.967514	+	0.252819i	$0.918642\pi$
$194$	1.39422	+	2.41486i	0.100099	+	0.173377i
$195$	1.68717	+	14.8628i	0.120820	+	1.06434i
$196$	2.57912	−	6.50754i	0.184223	−	0.464825i
$197$	9.15712	−	9.15712i	0.652418	−	0.652418i	−0.301157	−	0.953575i	$-0.597373\pi$
$197$	9.15712	−	9.15712i	0.652418	−	0.652418i	0.953575	+	0.301157i	$0.0973727\pi$
$198$	5.35776	+	12.1530i	0.380759	+	0.863674i
$199$	21.3942	+	12.3520i	1.51660	+	0.875608i	0.999810	+	0.0194938i	$0.00620546\pi$
$199$	21.3942	+	12.3520i	1.51660	+	0.875608i	0.516787	+	0.856114i	$0.327128\pi$
$200$	0.190785	+	0.712019i	0.0134905	+	0.0503473i
$201$	−3.30915	−	1.08189i	−0.233410	−	0.0763109i
$202$	6.35611	−	6.35611i	0.447214	−	0.447214i
$203$	−20.2865	−	17.5169i	−1.42383	−	1.22945i
$204$	2.70857	+	0.146910i	0.189638	+	0.0102858i
$205$	9.39322	−	5.42318i	0.656051	−	0.378771i
$206$	18.0625	−	4.83982i	1.25847	−	0.337206i
$207$	−4.91957	+	6.71947i	−0.341934	+	0.467036i
$208$	−0.340509	+	3.58944i	−0.0236101	+	0.248883i
$209$			27.8326i			1.92522i
$210$	−10.6542	−	2.63952i	−0.735212	−	0.182144i
$211$	19.4856			1.34144			0.670721	−	0.741710i	$-0.265985\pi$
$211$	19.4856			1.34144			0.670721	+	0.741710i	$0.265985\pi$
$212$	−1.15282	−	1.99674i	−0.0791758	−	0.137136i
$213$	5.56381	−	1.17201i	0.381226	−	0.0803048i
$214$	0.203885	−	0.0546309i	0.0139373	−	0.00373449i
$215$	−2.73487	+	10.2067i	−0.186517	+	0.696090i
$216$	4.22044	−	3.03115i	0.287165	−	0.206244i
$217$	−4.24031	+	8.76762i	−0.287851	+	0.595185i
$218$	−14.1183			−0.956210
$219$	−0.608627	+	1.86159i	−0.0411272	+	0.125795i
$220$	−9.18346	−	5.30207i	−0.619149	−	0.357466i
$221$	−5.13491	+	2.34887i	−0.345411	+	0.158002i
$222$	−2.52762	−	4.98320i	−0.169643	−	0.334450i
$223$	−19.4025	−	19.4025i	−1.29929	−	1.29929i	−0.928860	−	0.370431i	$-0.879210\pi$
$223$	−19.4025	−	19.4025i	−1.29929	−	1.29929i	−0.370431	−	0.928860i	$-0.620790\pi$
$224$	−2.38182	−	1.15193i	−0.159142	−	0.0769662i
$225$	−0.239185	+	2.19844i	−0.0159457	+	0.146562i
$226$	−2.00356	+	7.47740i	−0.133275	+	0.497389i
$227$	1.12921	+	4.21428i	0.0749485	+	0.279712i	0.993222	−	0.116236i	$-0.0370829\pi$
$227$	1.12921	+	4.21428i	0.0749485	+	0.279712i	−0.918273	+	0.395948i	$0.870416\pi$
$228$	10.6551	−	2.24449i	0.705652	−	0.148645i
$229$	−4.77855	−	1.28041i	−0.315775	−	0.0846117i	0.0974504	−	0.995240i	$-0.468931\pi$
$229$	−4.77855	−	1.28041i	−0.315775	−	0.0846117i	−0.413226	+	0.910629i	$0.635598\pi$
$230$		−	6.64906i		−	0.438426i
$231$	17.3745	−	10.4750i	1.14316	−	0.689204i
$232$	−7.16331	+	7.16331i	−0.470294	+	0.470294i
$233$	−2.07390	−	3.59209i	−0.135865	−	0.235326i	0.790062	−	0.613027i	$-0.210048\pi$
$233$	−2.07390	−	3.59209i	−0.135865	−	0.235326i	−0.925928	+	0.377701i	$0.876715\pi$
$234$	−4.84804	+	9.66936i	−0.316926	+	0.632106i
$235$	−12.4944	+	21.6409i	−0.815042	+	1.41169i
$236$	−13.4331	−	3.59938i	−0.874419	−	0.234300i
$237$	−0.317211	+	5.84841i	−0.0206051	+	0.379895i
$238$	−0.302747	−	4.13242i	−0.0196242	−	0.267865i
$239$	17.2034	−	17.2034i	1.11279	−	1.11279i	0.120023	−	0.992771i	$-0.461703\pi$
$239$	17.2034	−	17.2034i	1.11279	−	1.11279i	0.992771	−	0.120023i	$-0.0382967\pi$
$240$	−1.28921	+	3.94327i	−0.0832181	+	0.254537i
$241$	−4.07282	−	15.2000i	−0.262353	−	0.979115i	−0.963851	−	0.266443i	$-0.914151\pi$
$241$	−4.07282	−	15.2000i	−0.262353	−	0.979115i	0.701497	−	0.712672i	$-0.252515\pi$
$242$	8.30697	−	2.22585i	0.533993	−	0.143083i
$243$	15.0935	−	3.89696i	0.968248	−	0.249990i
$244$			12.5785i			0.805254i
$245$	−1.93287	+	16.6548i	−0.123487	+	1.06404i
$246$	7.83175	+	0.424785i	0.499334	+	0.0270833i
$247$	−17.4702	+	14.4428i	−1.11160	+	0.918971i
$248$	3.18789	+	1.84053i	0.202431	+	0.116874i
$249$	7.22502	−	1.52194i	0.457867	−	0.0964492i
$250$	5.10527	+	8.84259i	0.322886	+	0.559255i
$251$	−11.0233			−0.695786			−0.347893	−	0.937534i	$-0.613103\pi$
$251$	−11.0233			−0.695786			−0.347893	+	0.937534i	$0.613103\pi$
$252$	−5.41125	−	5.80675i	−0.340877	−	0.365791i
$253$	8.69013	+	8.69013i	0.546344	+	0.546344i
$254$	3.78584	−	14.1290i	0.237545	−	0.886530i
$255$	−6.35768	+	1.33924i	−0.398133	+	0.0838663i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.19360	+	12.4597i	0.448725	+	0.777214i	0.998303	−	0.0582280i	$-0.0185450\pi$
$257$	7.19360	+	12.4597i	0.448725	+	0.777214i	−0.549579	+	0.835442i	$0.685212\pi$
$258$	−5.68774	+	5.10249i	−0.354103	+	0.317667i
$259$	−7.06011	+	4.79626i	−0.438694	+	0.298025i
$260$	−1.43740	−	8.51567i	−0.0891436	−	0.528120i
$261$	−27.8088	+	12.2598i	−1.72132	+	0.758863i
$262$	14.7308	−	3.94711i	0.910072	−	0.243853i
$263$	−17.6280	−	10.1775i	−1.08699	−	0.627574i	−0.154216	−	0.988037i	$-0.549285\pi$
$263$	−17.6280	−	10.1775i	−1.08699	−	0.627574i	−0.932773	+	0.360464i	$0.882619\pi$
$264$	−3.46877	−	6.83869i	−0.213488	−	0.420892i
$265$	3.90502	+	3.90502i	0.239883	+	0.239883i
$266$	−5.46737	−	15.7089i	−0.335226	−	0.963174i
$267$	5.36332	−	4.81145i	0.328230	−	0.294456i
$268$	1.94157	+	0.520241i	0.118600	+	0.0317788i
$269$	−1.64185	−	0.947920i	−0.100105	−	0.0577957i	0.449112	−	0.893476i	$-0.351741\pi$
$269$	−1.64185	−	0.947920i	−0.100105	−	0.0577957i	−0.549217	+	0.835680i	$0.685074\pi$
$270$	−7.88538	+	9.62930i	−0.479889	+	0.586021i
$271$	−8.87788	−	2.37882i	−0.539293	−	0.144503i	−0.0211167	−	0.999777i	$-0.506722\pi$
$271$	−8.87788	−	2.37882i	−0.539293	−	0.144503i	−0.518176	+	0.855274i	$0.673389\pi$
$272$	−1.56609			−0.0949584
$273$	15.5909	+	5.47015i	0.943607	+	0.331068i
$274$	−12.1738			−0.735449
$275$	3.15224	+	0.844641i	0.190087	+	0.0509338i
$276$	2.62604	−	4.02762i	0.158069	−	0.242435i
$277$	−7.03014	−	4.05885i	−0.422400	−	0.243873i	0.273704	−	0.961814i	$-0.411751\pi$
$277$	−7.03014	−	4.05885i	−0.422400	−	0.243873i	−0.696104	+	0.717941i	$0.745085\pi$
$278$	−5.59023	−	1.49790i	−0.335280	−	0.0898380i
$279$	6.91831	+	8.60748i	0.414188	+	0.515316i
$280$	6.22473	+	1.18855i	0.371999	+	0.0710293i
$281$	−6.69009	−	6.69009i	−0.399098	−	0.399098i	0.478817	−	0.877915i	$-0.341066\pi$
$281$	−6.69009	−	6.69009i	−0.399098	−	0.399098i	−0.877915	+	0.478817i	$0.841066\pi$
$282$	−16.1154	+	8.17418i	−0.959658	+	0.486765i
$283$	−5.14240	−	2.96897i	−0.305684	−	0.176487i	0.339309	−	0.940675i	$-0.389807\pi$
$283$	−5.14240	−	2.96897i	−0.305684	−	0.176487i	−0.644994	+	0.764188i	$0.723140\pi$
$284$	−3.17090	+	0.849641i	−0.188159	+	0.0504169i
$285$	−23.2604	+	11.7983i	−1.37783	+	0.698873i
$286$	13.0084	+	9.25109i	0.769201	+	0.547029i
$287$	−0.875384	−	11.9488i	−0.0516723	−	0.705313i
$288$	−2.33832	+	1.87943i	−0.137787	+	0.110747i
$289$	7.27367	+	12.5984i	0.427863	+	0.741081i
$290$	12.1324	−	21.0139i	0.712439	−	1.23398i
$291$	−0.995529	−	4.72601i	−0.0583590	−	0.277044i
$292$	0.292666	−	1.09224i	0.0171270	−	0.0639187i
$293$	−9.37657	−	9.37657i	−0.547785	−	0.547785i	0.378015	−	0.925800i	$-0.376607\pi$
$293$	−9.37657	−	9.37657i	−0.547785	−	0.547785i	−0.925800	+	0.378015i	$0.876607\pi$
$294$	−7.74863	+	9.32517i	−0.451909	+	0.543855i
$295$	33.3104			1.93941
$296$	1.61300	+	2.79379i	0.0937536	+	0.162386i
$297$	−2.27926	−	22.8912i	−0.132256	−	1.32828i
$298$	11.1294	+	6.42558i	0.644711	+	0.372224i
$299$	−0.945240	+	9.96413i	−0.0546646	+	0.576240i
$300$	0.0691482	−	1.27488i	0.00399227	−	0.0736054i
$301$	8.83427	+	7.62820i	0.509199	+	0.439682i
$302$		−	12.8203i		−	0.737724i
$303$	−13.8852	+	7.04294i	−0.797682	+	0.404606i
$304$	−6.07252	+	1.62713i	−0.348283	+	0.0933222i
$305$	−7.79779	−	29.1017i	−0.446500	−	1.66636i
$306$	−4.38005	−	1.69972i	−0.250391	−	0.0971665i
$307$	5.32762	−	5.32762i	0.304064	−	0.304064i	−0.538538	−	0.842601i	$-0.681023\pi$
$307$	5.32762	−	5.32762i	0.304064	−	0.304064i	0.842601	+	0.538538i	$0.181023\pi$
$308$	−9.68894	+	6.58214i	−0.552078	+	0.375052i
$309$	−32.3412	−	1.75415i	−1.83983	−	0.0997900i
$310$	−8.51656	−	2.28201i	−0.483708	−	0.129609i
$311$	17.2052	−	29.8002i	0.975616	−	1.68982i	0.297730	−	0.954650i	$-0.403770\pi$
$311$	17.2052	−	29.8002i	0.975616	−	1.68982i	0.677886	−	0.735167i	$-0.262896\pi$
$312$	2.49256	−	5.72601i	0.141113	−	0.324171i
$313$	−0.915865	−	1.58632i	−0.0517677	−	0.0896644i	0.838980	−	0.544162i	$-0.183152\pi$
$313$	−0.915865	−	1.58632i	−0.0517677	−	0.0896644i	−0.890748	+	0.454497i	$0.849819\pi$
$314$	13.8796	−	13.8796i	0.783273	−	0.783273i
$315$	16.1194	+	10.0800i	0.908223	+	0.567942i
$316$		−	3.38154i		−	0.190227i
$317$	−6.01057	−	1.61053i	−0.337587	−	0.0904562i	0.0860431	−	0.996291i	$-0.472578\pi$
$317$	−6.01057	−	1.61053i	−0.337587	−	0.0904562i	−0.423630	+	0.905835i	$0.639244\pi$
$318$	0.823156	+	3.90772i	0.0461603	+	0.219134i
$319$	11.6079	+	43.3212i	0.649917	+	2.42552i
$320$	0.619932	−	2.31362i	0.0346552	−	0.129335i
$321$	−0.365060	−	0.0198005i	−0.0203757	−	0.00110515i
$322$	−6.61183	−	3.19770i	−0.368463	−	0.178201i
$323$	−6.96191	−	6.96191i	−0.387371	−	0.387371i
$324$	−8.57959	+	2.71857i	−0.476644	+	0.151031i
$325$	1.10558	+	2.41692i	0.0613264	+	0.134067i
$326$	−3.01702	−	1.74188i	−0.167097	−	0.0964736i
$327$	23.2429	+	7.59902i	1.28533	+	0.420227i
$328$	−4.52831			−0.250034
$329$	15.5109	+	22.8320i	0.855141	+	1.25877i
$330$	12.2649	+	13.6717i	0.675162	+	0.752602i
$331$	−2.91891	+	10.8935i	−0.160438	+	0.598762i	0.838140	+	0.545455i	$0.183643\pi$
$331$	−2.91891	+	10.8935i	−0.160438	+	0.598762i	−0.998578	+	0.0533075i	$0.983024\pi$
$332$	−4.11766	+	1.10332i	−0.225986	+	0.0605527i
$333$	1.47905	+	9.56430i	0.0810517	+	0.524120i
$334$	6.01283	+	10.4145i	0.329008	+	0.569858i
$335$	−4.81455			−0.263047
$336$	3.30117	+	3.17840i	0.180094	+	0.173396i
$337$		−	32.9198i		−	1.79325i	−0.442786	−	0.896627i	$-0.646010\pi$
$337$		−	32.9198i		−	1.79325i	0.442786	−	0.896627i	$-0.353990\pi$
$338$	0.943450	+	12.9657i	0.0513169	+	0.705242i
$339$	7.32310	−	11.2316i	0.397736	−	0.610019i
$340$	3.62334	−	0.970871i	0.196503	−	0.0526529i
$341$	14.1134	−	8.14837i	0.764283	−	0.441259i
$342$	−18.7496	−	2.03991i	−1.01386	−	0.110306i
$343$	15.6320	+	9.93176i	0.844050	+	0.536265i
$344$	3.11945	−	3.11945i	0.168190	−	0.168190i
$345$	−3.57879	+	10.9463i	−0.192676	+	0.589331i
$346$	2.18805	+	8.16590i	0.117630	+	0.439001i
$347$	8.98451	+	5.18721i	0.482314	+	0.278464i	0.721380	−	0.692539i	$-0.243508\pi$
$347$	8.98451	+	5.18721i	0.482314	+	0.278464i	−0.239066	+	0.971003i	$0.576841\pi$
$348$	15.6485	−	7.93737i	0.838849	−	0.425488i
$349$	−18.4597	+	18.4597i	−0.988127	+	0.988127i	−0.999930	−	0.0118036i	$-0.996243\pi$
$349$	−18.4597	+	18.4597i	−0.988127	+	0.988127i	0.0118036	+	0.999930i	$0.496243\pi$
$350$	−1.94507	+	0.142498i	−0.103968	+	0.00761686i
$351$	13.1858	−	13.3092i	0.703803	−	0.710395i
$352$	2.21360	+	3.83406i	0.117985	+	0.204356i
$353$	5.31054	+	19.8192i	0.282651	+	1.05487i	0.950539	+	0.310607i	$0.100532\pi$
$353$	5.31054	+	19.8192i	0.282651	+	1.05487i	−0.667887	+	0.744263i	$0.732801\pi$
$354$	20.1775	+	13.1559i	1.07242	+	0.699227i
$355$	6.80954	−	3.93149i	0.361413	−	0.208662i
$356$	−2.94152	+	2.94152i	−0.155900	+	0.155900i
$357$	−1.72582	+	6.96615i	−0.0913402	+	0.368688i
$358$	−6.40822	+	6.40822i	−0.338685	+	0.338685i
$359$	−3.61348	+	13.4857i	−0.190712	+	0.711748i	0.802623	+	0.596487i	$0.203437\pi$
$359$	−3.61348	+	13.4857i	−0.190712	+	0.711748i	−0.993335	+	0.115261i	$0.963230\pi$
$360$	4.24485	−	5.79789i	0.223723	−	0.305576i
$361$	−17.7735	−	10.2615i	−0.935448	−	0.540081i
$362$	−4.46226	+	16.6534i	−0.234531	+	0.875282i
$363$	−14.8738	−	0.806737i	−0.780672	−	0.0423427i
$364$	−9.15927	−	2.66604i	−0.480076	−	0.139739i
$365$			2.70846i			0.141767i
$366$	6.77023	−	20.7079i	0.353886	−	1.08242i
$367$	−6.69566	+	11.5972i	−0.349511	+	0.605370i	−0.986163	−	0.165781i	$-0.946985\pi$
$367$	−6.69566	+	11.5972i	−0.349511	+	0.605370i	0.636652	+	0.771151i	$0.280319\pi$
$368$	−1.38798	+	2.40405i	−0.0723534	+	0.125320i
$369$	−12.6648	−	4.91468i	−0.659301	−	0.255848i
$370$	−5.46382	−	5.46382i	−0.284050	−	0.284050i
$371$	5.76117	−	2.00513i	0.299105	−	0.104101i
$372$	−4.25757	−	4.74591i	−0.220745	−	0.246064i
$373$	12.2520	+	21.2210i	0.634383	+	1.09878i	0.986646	+	0.162882i	$0.0520791\pi$
$373$	12.2520	+	21.2210i	0.634383	+	1.09878i	−0.352263	+	0.935901i	$0.614588\pi$
$374$	−3.46670	+	6.00450i	−0.179259	+	0.310485i
$375$	−3.64537	−	17.3054i	−0.188246	−	0.893647i
$376$	9.03498	−	5.21635i	0.465943	−	0.269013i
$377$	−21.1687	+	29.7662i	−1.09024	+	1.53304i
$378$	5.78312	+	12.4722i	0.297451	+	0.641500i
$379$	−24.3733	−	24.3733i	−1.25197	−	1.25197i	−0.954834	−	0.297140i	$-0.903967\pi$
$379$	−24.3733	−	24.3733i	−1.25197	−	1.25197i	−0.297140	−	0.954834i	$-0.596033\pi$
$380$	13.0408	−	7.52910i	0.668978	−	0.386235i
$381$	−13.8374	+	21.2228i	−0.708911	+	1.08728i
$382$	9.61318	−	2.57584i	0.491853	−	0.131792i
$383$	12.3940	+	3.32095i	0.633302	+	0.169693i	0.561168	−	0.827702i	$-0.310352\pi$
$383$	12.3940	+	3.32095i	0.633302	+	0.169693i	0.0721342	+	0.997395i	$0.477019\pi$
$384$	1.28928	−	1.15662i	0.0657932	−	0.0590233i
$385$	18.3360	−	21.2350i	0.934489	−	1.08224i
$386$		−	0.172458i		−	0.00877789i
$387$	12.1101	−	5.33885i	0.615590	−	0.271389i
$388$	0.721702	+	2.69343i	0.0366389	+	0.136738i
$389$	11.6305	−	20.1446i	0.589690	−	1.02137i	−0.404583	−	0.914501i	$-0.632583\pi$
$389$	11.6305	−	20.1446i	0.589690	−	1.02137i	0.994273	−	0.106872i	$-0.0340835\pi$
$390$	−2.21709	+	14.7930i	−0.112267	+	0.749073i
$391$	−4.34741			−0.219858
$392$	4.17552	−	5.61828i	0.210896	−	0.283766i
$393$	−26.3758	−	1.43059i	−1.33048	−	0.0721638i
$394$	11.2151	−	6.47506i	0.565010	−	0.326209i
$395$	2.09633	+	7.82360i	0.105478	+	0.393648i
$396$	2.02978	+	13.1256i	0.102000	+	0.659584i
$397$	−11.9336	−	3.19761i	−0.598932	−	0.160483i	−0.0533998	−	0.998573i	$-0.517006\pi$
$397$	−11.9336	−	3.19761i	−0.598932	−	0.160483i	−0.545532	+	0.838090i	$0.683672\pi$
$398$	17.4683	+	17.4683i	0.875608	+	0.875608i
$399$	0.545766	+	28.8043i	0.0273225	+	1.44202i
$400$			0.737136i			0.0368568i
$401$	8.62573	−	32.1917i	0.430749	−	1.60758i	−0.320292	−	0.947319i	$-0.603781\pi$
$401$	8.62573	−	32.1917i	0.430749	−	1.60758i	0.751040	−	0.660256i	$-0.229552\pi$
$402$	−2.91638	−	1.90150i	−0.145456	−	0.0948382i
$403$	12.4383	+	4.63048i	0.619596	+	0.230661i
$404$	7.78461	−	4.49445i	0.387299	−	0.223607i
$405$	18.1646	−	11.6085i	0.902604	−	0.576830i
$406$	−15.0615	−	22.1706i	−0.747489	−	1.10031i
$407$	14.2821			0.707937
$408$	2.57826	+	0.842935i	0.127643	+	0.0417315i
$409$	27.7673	−	7.44021i	1.37300	−	0.367895i	0.504428	−	0.863454i	$-0.331703\pi$
$409$	27.7673	−	7.44021i	1.37300	−	0.367895i	0.868574	+	0.495559i	$0.165037\pi$
$410$	10.4768	−	2.80724i	0.517411	−	0.138640i
$411$	20.0418	+	6.55245i	0.988588	+	0.323209i
$412$	18.6996			0.921265
$413$	16.0198	−	33.1239i	0.788281	−	1.62992i
$414$	−6.49107	+	5.21723i	−0.319019	+	0.256413i
$415$	8.84269	−	5.10533i	0.434071	−	0.250611i
$416$	−1.25792	+	3.37900i	−0.0616747	+	0.165669i
$417$	8.39696	+	5.47487i	0.411201	+	0.268106i
$418$	−7.20360	+	26.8842i	−0.352340	+	1.31495i
$419$			4.41529i			0.215701i	0.994167	+	0.107850i	$0.0343968\pi$
$419$			4.41529i			0.215701i	−0.994167	+	0.107850i	$0.965603\pi$
$420$	−9.60804	−	5.30710i	−0.468825	−	0.258960i
$421$	9.77773	+	9.77773i	0.476537	+	0.476537i	0.904022	−	0.427485i	$-0.140600\pi$
$421$	9.77773	+	9.77773i	0.476537	+	0.476537i	−0.427485	+	0.904022i	$0.640600\pi$
$422$	18.8216	+	5.04324i	0.916222	+	0.245501i
$423$	30.9304	−	4.78318i	1.50389	−	0.232566i
$424$	−0.596742	−	2.22707i	−0.0289803	−	0.108156i
$425$	−0.999761	+	0.577212i	−0.0484955	+	0.0279989i
$426$	5.67756	+	0.307944i	0.275079	+	0.0149200i
$427$	−32.6889	−	6.24161i	−1.58193	−	0.302053i
$428$	0.211078			0.0102028
$429$	−16.4363	−	22.2317i	−0.793554	−	1.07336i
$430$	−5.28337	+	9.15106i	−0.254787	+	0.441303i
$431$	4.37529	+	16.3288i	0.210750	+	0.786531i	0.987619	+	0.156869i	$0.0501399\pi$
$431$	4.37529	+	16.3288i	0.210750	+	0.786531i	−0.776869	+	0.629662i	$0.783193\pi$
$432$	4.86115	−	1.83553i	0.233882	−	0.0883122i
$433$		−	20.3606i		−	0.978466i	−0.872153	−	0.489233i	$-0.837277\pi$
$433$		−	20.3606i		−	0.978466i	0.872153	−	0.489233i	$-0.162723\pi$
$434$	−6.36505	+	7.37140i	−0.305532	+	0.353839i
$435$	−31.2841	+	28.0650i	−1.49996	+	1.34562i
$436$	−13.6372	−	3.65408i	−0.653104	−	0.174999i
$437$	−16.8571	+	4.51684i	−0.806383	+	0.216070i
$438$	−1.06970	+	1.64063i	−0.0511124	+	0.0783925i
$439$	0.198379	−	0.114534i	0.00946813	−	0.00546643i	−0.495258	−	0.868746i	$-0.664927\pi$
$439$	0.198379	−	0.114534i	0.00946813	−	0.00546643i	0.504727	+	0.863279i	$0.331593\pi$
$440$	−7.49826	−	7.49826i	−0.357466	−	0.357466i
$441$	17.7757	−	11.1814i	0.846463	−	0.532447i
$442$	−5.56787	+	0.939825i	−0.264837	+	0.0447029i
$443$	−12.9015	+	7.44866i	−0.612967	+	0.353897i	−0.774126	−	0.633032i	$-0.781810\pi$
$443$	−12.9015	+	7.44866i	−0.612967	+	0.353897i	0.161159	+	0.986928i	$0.448477\pi$
$444$	−1.15174	−	5.46760i	−0.0546593	−	0.259481i
$445$	4.98201	−	8.62909i	0.236170	−	0.409058i
$446$	−13.7197	−	23.7632i	−0.649645	−	1.12522i
$447$	−14.8639	−	16.5687i	−0.703036	−	0.783674i
$448$	−2.00252	−	1.72913i	−0.0946103	−	0.0816939i
$449$	−0.539231	−	0.539231i	−0.0254479	−	0.0254479i	0.694268	−	0.719716i	$-0.255728\pi$
$449$	−0.539231	−	0.539231i	−0.0254479	−	0.0254479i	−0.719716	+	0.694268i	$0.755728\pi$
$450$	−0.800032	+	2.06162i	−0.0377139	+	0.0971857i
$451$	−10.0238	+	17.3618i	−0.472004	+	0.817536i
$452$	−3.87059	+	6.70405i	−0.182057	+	0.315332i
$453$	−6.90039	+	21.1060i	−0.324208	+	0.991647i
$454$			4.36294i			0.204763i
$455$	22.8438	+	0.490083i	1.07093	+	0.0229754i
$456$	10.8730	+	0.589737i	0.509173	+	0.0276170i
$457$	4.58034	−	17.0941i	0.214259	−	0.799627i	−0.772166	−	0.635420i	$-0.780827\pi$
$457$	4.58034	−	17.0941i	0.214259	−	0.799627i	0.986426	−	0.164207i	$-0.0525065\pi$
$458$	−4.28433	−	2.47356i	−0.200193	−	0.115582i
$459$	6.29601	+	5.15576i	0.293872	+	0.240650i
$460$	1.72090	−	6.42250i	0.0802376	−	0.299451i
$461$	−0.0481167	+	0.0481167i	−0.00224102	+	0.00224102i	−0.708226	−	0.705985i	$-0.750504\pi$
$461$	−0.0481167	+	0.0481167i	−0.00224102	+	0.00224102i	0.705985	+	0.708226i	$0.250504\pi$
$462$	19.4936	−	5.62120i	0.906927	−	0.261522i
$463$	−26.7322	+	26.7322i	−1.24235	+	1.24235i	−0.283324	+	0.959024i	$0.591437\pi$
$463$	−26.7322	+	26.7322i	−1.24235	+	1.24235i	−0.959024	+	0.283324i	$0.908563\pi$
$464$	−8.77323	+	5.06523i	−0.407287	+	0.235147i
$465$	12.7925	+	8.34081i	0.593239	+	0.386796i
$466$	−1.07353	−	4.00646i	−0.0497302	−	0.185596i
$467$	−5.35002	−	9.26651i	−0.247570	−	0.428803i	0.715281	−	0.698837i	$-0.246299\pi$
$467$	−5.35002	−	9.26651i	−0.247570	−	0.428803i	−0.962851	+	0.270033i	$0.912965\pi$
$468$	−7.18546	+	8.08512i	−0.332148	+	0.373735i
$469$	−2.31544	+	4.78760i	−0.106917	+	0.221071i
$470$	−17.6697	+	17.6697i	−0.815042	+	0.815042i
$471$	−30.3206	+	15.3794i	−1.39710	+	0.708647i
$472$	−12.0438	−	6.95348i	−0.554360	−	0.320060i
$473$	−5.05496	−	18.8654i	−0.232427	−	0.867430i
$474$	−1.82008	+	5.56703i	−0.0835991	+	0.255702i
$475$	−3.27686	+	3.27686i	−0.150353	+	0.150353i
$476$	0.777118	−	4.06997i	0.0356191	−	0.186547i
$477$	0.748128	−	6.87632i	0.0342544	−	0.314845i
$478$	21.0697	−	12.1646i	0.963708	−	0.556397i
$479$	13.0420	−	3.49459i	0.595904	−	0.159672i	0.0517541	−	0.998660i	$-0.483519\pi$
$479$	13.0420	−	3.49459i	0.595904	−	0.159672i	0.544150	+	0.838988i	$0.316852\pi$
$480$	−2.26587	+	3.47523i	−0.103422	+	0.158622i
$481$	7.41120	+	8.96469i	0.337922	+	0.408755i
$482$		−	15.7362i		−	0.716762i
$483$	9.16392	+	8.82312i	0.416973	+	0.401466i
$484$	8.60001			0.390910
$485$	−3.33949	−	5.78416i	−0.151638	−	0.262645i
$486$	15.5878	+	0.142310i	0.707077	+	0.00645533i
$487$	−10.7180	+	2.87187i	−0.485677	+	0.130137i	−0.493345	−	0.869834i	$-0.664226\pi$
$487$	−10.7180	+	2.87187i	−0.485677	+	0.130137i	0.00766762	+	0.999971i	$0.497559\pi$
$488$	−3.25555	+	12.1499i	−0.147372	+	0.549998i
$489$	4.02936	+	4.49153i	0.182214	+	0.203114i
$490$	−6.17760	+	15.5871i	−0.279075	+	0.704152i
$491$	11.1964			0.505288			0.252644	−	0.967559i	$-0.418700\pi$
$491$	11.1964			0.505288			0.252644	+	0.967559i	$0.418700\pi$
$492$	7.45495	+	2.43732i	0.336095	+	0.109883i
$493$	−13.7397	−	7.93262i	−0.618805	−	0.357267i
$494$	−20.6129	+	9.42903i	−0.927420	+	0.424232i
$495$	−12.8331	−	29.1092i	−0.576804	−	1.30836i
$496$	2.60290	+	2.60290i	0.116874	+	0.116874i
$497$	−0.634602	−	8.66215i	−0.0284658	−	0.388551i
$498$	7.37274	+	0.399889i	0.330380	+	0.0179195i
$499$	3.09629	−	11.5555i	0.138609	−	0.517296i	−0.861348	−	0.508015i	$-0.830379\pi$
$499$	3.09629	−	11.5555i	0.138609	−	0.517296i	0.999957	−	0.00928036i	$-0.00295407\pi$
$500$	2.64268	+	9.86263i	0.118184	+	0.441070i
$501$	−4.29340	−	20.3818i	−0.191815	−	0.910590i
$502$	−10.6477	−	2.85305i	−0.475231	−	0.127338i
$503$		−	35.7511i		−	1.59406i	−0.603938	−	0.797031i	$-0.706403\pi$
$503$		−	35.7511i		−	1.59406i	0.603938	−	0.797031i	$-0.293597\pi$
$504$	−3.72397	−	7.00942i	−0.165879	−	0.312225i
$505$	−15.2244	+	15.2244i	−0.677475	+	0.677475i
$506$	6.14485	+	10.6432i	0.273172	+	0.473147i
$507$	5.42547	−	21.8532i	0.240954	−	0.970537i
$508$	7.31369	−	12.6677i	0.324492	−	0.562037i
$509$	−6.70678	−	1.79708i	−0.297273	−	0.0796540i	0.107100	−	0.994248i	$-0.465844\pi$
$509$	−6.70678	−	1.79708i	−0.297273	−	0.0796540i	−0.404373	+	0.914594i	$0.632510\pi$
$510$	−6.48766	−	0.351883i	−0.287279	−	0.0155817i
$511$	2.69330	+	1.30257i	0.119145	+	0.0576221i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	29.7694	+	13.4501i	1.31435	+	0.593835i
$514$	3.72368	+	13.8970i	0.164245	+	0.612969i
$515$	−43.2638	+	11.5925i	−1.90643	+	0.510827i
$516$	−6.81456	+	3.45653i	−0.299994	+	0.152165i
$517$		−	46.1875i		−	2.03133i
$518$	−8.06091	+	2.80554i	−0.354176	+	0.123268i
$519$	0.793037	−	14.6212i	0.0348104	−	0.641799i
$520$	0.815599	−	8.59753i	0.0357664	−	0.377027i
$521$	2.47233	+	1.42740i	0.108315	+	0.0625355i	0.553179	−	0.833063i	$-0.313415\pi$
$521$	2.47233	+	1.42740i	0.108315	+	0.0625355i	−0.444864	+	0.895598i	$0.646748\pi$
$522$	−30.0344	+	4.64461i	−1.31457	+	0.203289i
$523$	−7.41356	−	12.8407i	−0.324172	−	0.561483i	0.657172	−	0.753741i	$-0.271752\pi$
$523$	−7.41356	−	12.8407i	−0.324172	−	0.561483i	−0.981345	+	0.192258i	$0.938419\pi$
$524$	15.2504			0.666219
$525$	3.27886	+	0.812317i	0.143101	+	0.0354524i
$526$	−14.3932	−	14.3932i	−0.627574	−	0.627574i
$527$	−1.49206	+	5.56845i	−0.0649953	+	0.242566i
$528$	−1.58059	−	7.50345i	−0.0687865	−	0.326546i
$529$	7.64703	−	13.2450i	0.332479	−	0.575871i
$530$	2.76126	+	4.78265i	0.119942	+	0.207745i
$531$	−26.1372	−	32.5189i	−1.13426	−	1.41120i
$532$	−1.21531	−	16.5887i	−0.0526905	−	0.719211i
$533$	−16.0993	+	2.71747i	−0.697339	+	0.117707i
$534$	6.42586	−	3.25937i	0.278074	−	0.141047i
$535$	−0.488353	+	0.130854i	−0.0211133	+	0.00565730i
$536$	1.74076	+	1.00503i	0.0751894	+	0.0434106i
$537$	13.9990	−	7.10068i	0.604102	−	0.306417i
$538$	−1.34056	−	1.34056i	−0.0577957	−	0.0577957i
$539$	−12.2979	−	28.4458i	−0.529708	−	1.22525i
$540$	−10.1089	+	7.26031i	−0.435019	+	0.312434i
$541$	−27.8277	−	7.45641i	−1.19641	−	0.320576i	−0.394991	−	0.918685i	$-0.629252\pi$
$541$	−27.8277	−	7.45641i	−1.19641	−	0.320576i	−0.801415	+	0.598109i	$0.795919\pi$
$542$	−7.95969	−	4.59553i	−0.341898	−	0.197395i
$543$	16.3097	−	25.0147i	0.699917	−	1.07348i
$544$	−1.51273	−	0.405335i	−0.0648578	−	0.0173786i
$545$	33.8165			1.44854
$546$	13.6439	+	9.31899i	0.583906	+	0.398816i
$547$	8.76219			0.374644			0.187322	−	0.982299i	$-0.440019\pi$
$547$	8.76219			0.374644			0.187322	+	0.982299i	$0.440019\pi$
$548$	−11.7590	−	3.15082i	−0.502321	−	0.134597i
$549$	−22.2916	+	30.4474i	−0.951384	+	1.29946i
$550$	2.82622	+	1.63172i	0.120511	+	0.0695768i
$551$	−61.5174	−	16.4835i	−2.62073	−	0.702222i
$552$	3.57898	−	3.21072i	0.152332	−	0.136657i
$553$	8.78796	+	1.67797i	0.373702	+	0.0713545i
$554$	−5.74009	−	5.74009i	−0.243873	−	0.243873i
$555$	6.05423	+	11.9359i	0.256988	+	0.506652i
$556$	−5.01206	−	2.89372i	−0.212559	−	0.122721i
$557$	−10.2967	+	2.75899i	−0.436284	+	0.116902i	−0.470275	−	0.882520i	$-0.655845\pi$
$557$	−10.2967	+	2.75899i	−0.436284	+	0.116902i	0.0339903	+	0.999422i	$0.489178\pi$
$558$	4.45479	+	10.1048i	0.188587	+	0.427769i
$559$	9.21845	−	12.9625i	0.389899	−	0.548254i
$560$	5.70501	+	2.75913i	0.241081	+	0.116594i
$561$	8.93908	−	8.01928i	0.377408	−	0.338574i
$562$	−4.73061	−	8.19366i	−0.199549	−	0.345629i
$563$	5.59106	−	9.68401i	0.235635	−	0.408132i	−0.723822	−	0.689987i	$-0.757616\pi$
$563$	5.59106	−	9.68401i	0.235635	−	0.408132i	0.959457	+	0.281855i	$0.0909496\pi$
$564$	−17.6819	+	3.72468i	−0.744543	+	0.156837i
$565$	4.79900	−	17.9101i	0.201895	−	0.753484i
$566$	−4.19875	−	4.19875i	−0.176487	−	0.176487i
$567$	−2.80770	−	23.6457i	−0.117912	−	0.993024i
$568$	−3.28276			−0.137742
$569$	−15.1821	−	26.2962i	−0.636467	−	1.10239i	−0.986202	−	0.165544i	$-0.947062\pi$
$569$	−15.1821	−	26.2962i	−0.636467	−	1.10239i	0.349736	−	0.936848i	$-0.386271\pi$
$570$	−25.5215	+	5.37607i	−1.06898	+	0.225179i
$571$	33.2794	+	19.2139i	1.39270	+	0.804076i	0.993613	−	0.112838i	$-0.0359940\pi$
$571$	33.2794	+	19.2139i	1.39270	+	0.804076i	0.399086	+	0.916913i	$0.369327\pi$
$572$	10.1708	+	12.3027i	0.425261	+	0.514401i
$573$	−17.2126	−	0.933591i	−0.719066	−	0.0390013i
$574$	2.24701	−	11.7682i	0.0937884	−	0.491194i
$575$			2.04626i			0.0853349i
$576$	−2.74507	+	1.21019i	−0.114378	+	0.0504247i
$577$	−15.5293	+	4.16107i	−0.646495	+	0.173228i	−0.567144	−	0.823619i	$-0.691952\pi$
$577$	−15.5293	+	4.16107i	−0.646495	+	0.173228i	−0.0793513	+	0.996847i	$0.525285\pi$
$578$	3.76513	+	14.0517i	0.156609	+	0.584472i
$579$	−0.0928238	+	0.283917i	−0.00385763	+	0.0117992i
$580$	17.1578	−	17.1578i	0.712439	−	0.712439i
$581$	−0.824079	−	11.2485i	−0.0341886	−	0.466665i
$582$	0.261574	−	4.82264i	0.0108426	−	0.199905i
$583$	−9.85966	−	2.64189i	−0.408346	−	0.109416i
$584$	0.565387	−	0.979278i	0.0233959	−	0.0405228i
$585$	11.6122	−	23.1604i	0.480104	−	0.957563i
$586$	−6.63024	−	11.4839i	−0.273893	−	0.474396i
$587$	−25.3372	+	25.3372i	−1.04578	+	1.04578i	−0.0468791	+	0.998901i	$0.514928\pi$
$587$	−25.3372	+	25.3372i	−1.04578	+	1.04578i	−0.998901	+	0.0468791i	$0.985072\pi$
$588$	−9.89813	+	7.00193i	−0.408192	+	0.288755i
$589$			23.1419i			0.953544i
$590$	32.1754	+	8.62136i	1.32464	+	0.354936i
$591$	−21.9486	+	4.62345i	−0.902845	+	0.190183i
$592$	0.834949	+	3.11607i	0.0343162	+	0.128070i
$593$	−2.46209	+	9.18866i	−0.101106	+	0.377333i	−0.997874	−	0.0651675i	$-0.979242\pi$
$593$	−2.46209	+	9.18866i	−0.101106	+	0.377333i	0.896768	+	0.442500i	$0.145908\pi$
$594$	3.72308	−	22.7011i	0.152760	−	0.931437i
$595$	0.725150	+	9.89811i	0.0297283	+	0.405783i
$596$	9.08714	+	9.08714i	0.372224	+	0.372224i
$597$	−19.3559	−	38.1602i	−0.792185	−	1.56179i
$598$	−3.49194	+	9.37996i	−0.142796	+	0.383575i
$599$	9.76036	+	5.63515i	0.398798	+	0.230246i	0.685965	−	0.727634i	$-0.259380\pi$
$599$	9.76036	+	5.63515i	0.398798	+	0.230246i	−0.287167	+	0.957880i	$0.592714\pi$
$600$	0.396756	−	1.21355i	0.0161975	−	0.0495428i
$601$	4.45981			0.181919			0.0909596	−	0.995855i	$-0.471007\pi$
$601$	4.45981			0.181919			0.0909596	+	0.995855i	$0.471007\pi$
$602$	6.55892	+	9.65475i	0.267322	+	0.393498i
$603$	3.77777	+	4.70015i	0.153843	+	0.191405i
$604$	3.31813	−	12.3834i	0.135013	−	0.503875i
$605$	−19.8971	+	5.33142i	−0.808933	+	0.216753i
$606$	−15.2349	+	3.20921i	−0.618875	+	0.130365i
$607$	11.5858	+	20.0672i	0.470253	+	0.814502i	0.999421	−	0.0340152i	$-0.0108295\pi$
$607$	11.5858	+	20.0672i	0.470253	+	0.814502i	−0.529169	+	0.848517i	$0.677496\pi$
$608$	−6.28674			−0.254961
$609$	12.8626	+	44.6061i	0.521220	+	1.80753i
$610$		−	30.1283i		−	1.21986i
$611$	28.9913	−	23.9674i	1.17286	−	0.969618i
$612$	−3.79088	−	2.77544i	−0.153237	−	0.112191i
$613$	30.5664	−	8.19024i	1.23457	−	0.330801i	0.418210	−	0.908350i	$-0.362658\pi$
$613$	30.5664	−	8.19024i	1.23457	−	0.330801i	0.816356	+	0.577550i	$0.195991\pi$
$614$	6.52498	−	3.76720i	0.263327	−	0.152032i
$615$	−18.7589	−	1.01746i	−0.756430	−	0.0410279i
$616$	−11.0624	+	3.85018i	−0.445716	+	0.155128i
$617$	10.1965	−	10.1965i	0.410496	−	0.410496i	−0.471415	−	0.881911i	$-0.656257\pi$
$617$	10.1965	−	10.1965i	0.410496	−	0.410496i	0.881911	+	0.471415i	$0.156257\pi$
$618$	−30.7852	−	10.0649i	−1.23836	−	0.404869i
$619$	5.74324	+	21.4340i	0.230840	+	0.861507i	0.979980	+	0.199095i	$0.0638004\pi$
$619$	5.74324	+	21.4340i	0.230840	+	0.861507i	−0.749140	+	0.662412i	$0.769533\pi$
$620$	−7.63574	−	4.40850i	−0.306659	−	0.177049i
$621$	13.4944	−	5.09537i	0.541510	−	0.204470i
$622$	24.3318	−	24.3318i	0.975616	−	0.975616i
$623$	−6.18480	−	9.10405i	−0.247789	−	0.364746i
$624$	3.88963	−	4.88578i	0.155710	−	0.195588i
$625$	−14.0712	−	24.3720i	−0.562846	−	0.974878i
$626$	−0.474087	−	1.76932i	−0.0189483	−	0.0707161i
$627$	26.3294	−	40.3822i	1.05150	−	1.61271i
$628$	16.9990	−	9.81438i	0.678334	−	0.391636i
$629$	−3.57245	+	3.57245i	−0.142443	+	0.142443i
$630$	12.9612	+	13.9085i	0.516387	+	0.554128i
$631$	1.47612	−	1.47612i	0.0587634	−	0.0587634i	−0.677114	−	0.735878i	$-0.736770\pi$
$631$	1.47612	−	1.47612i	0.0587634	−	0.0587634i	0.735878	+	0.677114i	$0.236770\pi$
$632$	0.875208	−	3.26632i	0.0348139	−	0.129927i
$633$	−28.2715	−	18.4332i	−1.12369	−	0.732655i
$634$	−5.38893	−	3.11130i	−0.214022	−	0.123565i
$635$	−9.06797	+	33.8421i	−0.359851	+	1.34298i
$636$	−0.216283	+	3.98761i	−0.00857620	+	0.158119i
$637$	11.4735	−	22.4802i	0.454596	−	0.890698i
$638$			44.8494i			1.77561i
$639$	−9.18121	−	3.56286i	−0.363203	−	0.140945i
$640$	1.19762	−	2.07433i	0.0473399	−	0.0819952i
$641$	16.3674	−	28.3492i	0.646473	−	1.11972i	−0.337486	−	0.941331i	$-0.609576\pi$
$641$	16.3674	−	28.3492i	0.646473	−	1.11972i	0.983959	−	0.178394i	$-0.0570902\pi$
$642$	−0.347497	−	0.113610i	−0.0137146	−	0.00448384i
$643$	16.7721	+	16.7721i	0.661425	+	0.661425i	0.955716	−	0.294291i	$-0.0950833\pi$
$643$	16.7721	+	16.7721i	0.661425	+	0.661425i	−0.294291	+	0.955716i	$0.595083\pi$
$644$	−5.55892	−	4.80001i	−0.219052	−	0.189147i
$645$	13.6235	−	12.2217i	0.536423	−	0.481227i
$646$	−4.92281	−	8.52656i	−0.193685	−	0.335473i
$647$	9.50981	−	16.4715i	0.373869	−	0.647561i	−0.616288	−	0.787521i	$-0.711364\pi$
$647$	9.50981	−	16.4715i	0.373869	−	0.647561i	0.990157	+	0.139960i	$0.0446975\pi$
$648$	−8.99087	+	0.405370i	−0.353195	+	0.0159245i
$649$	−53.3201	+	30.7844i	−2.09300	+	1.20839i
$650$	0.442361	+	2.62071i	0.0173508	+	0.102793i
$651$	14.4463	−	8.70960i	0.566197	−	0.341356i
$652$	−2.46338	−	2.46338i	−0.0964736	−	0.0964736i
$653$	24.8991	−	14.3755i	0.974376	−	0.562556i	0.0738086	−	0.997272i	$-0.476485\pi$
$653$	24.8991	−	14.3755i	0.974376	−	0.562556i	0.900568	+	0.434716i	$0.143151\pi$
$654$	20.4841	+	13.3558i	0.800993	+	0.522253i
$655$	−35.2837	+	9.45424i	−1.37865	+	0.369408i
$656$	−4.37401	−	1.17201i	−0.170776	−	0.0457594i
$657$	2.64411	−	2.12521i	0.103156	−	0.0829125i
$658$	9.07297	+	26.0685i	0.353701	+	1.01626i
$659$			17.8592i			0.695697i	0.937551	+	0.347849i	$0.113088\pi$
$659$			17.8592i			0.695697i	−0.937551	+	0.347849i	$0.886912\pi$
$660$	8.30851	+	16.3802i	0.323408	+	0.637600i
$661$	10.3914	+	38.7812i	0.404178	+	1.50841i	0.805567	+	0.592505i	$0.201861\pi$
$661$	10.3914	+	38.7812i	0.404178	+	1.50841i	−0.401389	+	0.915908i	$0.631472\pi$
$662$	−5.63890	+	9.76687i	−0.219162	+	0.379600i
$663$	9.67223	+	1.44962i	0.375638	+	0.0562985i
$664$	−4.26291			−0.165433
$665$	13.0956	+	37.6264i	0.507826	+	1.45909i
$666$	−1.04677	+	9.62121i	−0.0405614	+	0.372814i
$667$	−24.3541	+	14.0609i	−0.942995	+	0.544439i
$668$	3.11247	+	11.6159i	0.120425	+	0.449433i
$669$	9.79639	+	46.5057i	0.378750	+	1.79802i
$670$	−4.65050	−	1.24610i	−0.179665	−	0.0481410i
$671$	39.3768	+	39.3768i	1.52013	+	1.52013i
$672$	2.36606	+	3.92451i	0.0912727	+	0.151391i
$673$			40.4652i			1.55982i	0.625891	+	0.779910i	$0.284735\pi$
$673$			40.4652i			1.55982i	−0.625891	+	0.779910i	$0.715265\pi$
$674$	8.52027	−	31.7981i	0.328188	−	1.22482i
$675$	2.42674	−	2.96343i	0.0934052	−	0.114063i
$676$	−2.44447	+	12.7681i	−0.0940182	+	0.491081i
$677$	27.5012	−	15.8778i	1.05696	−	0.610234i	0.132368	−	0.991201i	$-0.457742\pi$
$677$	27.5012	−	15.8778i	1.05696	−	0.610234i	0.924589	+	0.380966i	$0.124409\pi$
$678$	9.98053	−	8.95357i	0.383300	−	0.343860i
$679$	−7.35781	+	0.539044i	−0.282367	+	0.0206866i
$680$	3.75116			0.143850
$681$	2.34831	−	7.18271i	0.0899874	−	0.275242i
$682$	15.7415	−	4.21791i	0.602771	−	0.161512i
$683$	−25.8136	+	6.91674i	−0.987730	+	0.264662i	−0.716297	−	0.697796i	$-0.754164\pi$
$683$	−25.8136	+	6.91674i	−0.987730	+	0.264662i	−0.271433	+	0.962457i	$0.587498\pi$
$684$	−17.5827	−	6.82315i	−0.672292	−	0.260890i
$685$	29.1592			1.11412
$686$	12.5288	+	13.6392i	0.478353	+	0.520748i
$687$	5.72191	+	6.37821i	0.218305	+	0.243344i
$688$	3.82053	−	2.20579i	0.145656	−	0.0840948i
$689$	−3.45805	−	7.55970i	−0.131741	−	0.288002i
$690$	−6.28997	+	9.64710i	−0.239455	+	0.367259i
$691$	5.75591	−	21.4813i	0.218965	−	0.817189i	−0.765768	−	0.643117i	$-0.777641\pi$
$691$	5.75591	−	21.4813i	0.218965	−	0.817189i	0.984733	−	0.174072i	$-0.0556925\pi$
$692$			8.45396i			0.321371i
$693$	−35.1179	−	1.23809i	−1.33402	−	0.0470312i
$694$	7.33582	+	7.33582i	0.278464	+	0.278464i
$695$	13.3899	+	3.58781i	0.507908	+	0.136094i
$696$	17.1697	−	3.61677i	0.650814	−	0.137093i
$697$	−1.83548	−	6.85012i	−0.0695239	−	0.259467i
$698$	−22.6085	+	13.0530i	−0.855743	+	0.494063i
$699$	−0.389090	+	7.17364i	−0.0147167	+	0.271332i
$700$	−1.91567	−	0.365777i	−0.0724056	−	0.0138251i
$701$	27.4373			1.03629			0.518145	−	0.855293i	$-0.326623\pi$
$701$	27.4373			1.03629			0.518145	+	0.855293i	$0.326623\pi$
$702$	16.1811	−	9.44302i	0.610718	−	0.356404i
$703$	−10.1405	+	17.5638i	−0.382456	+	0.662433i
$704$	1.14584	+	4.27634i	0.0431855	+	0.161171i
$705$	38.6001	−	19.5791i	1.45376	−	0.737390i
$706$			20.5183i			0.772218i
$707$	7.81735	+	22.4609i	0.294002	+	0.844728i
$708$	16.0850	+	17.9299i	0.604511	+	0.673848i
$709$	30.0036	+	8.03944i	1.12681	+	0.301927i	0.773636	−	0.633631i	$-0.218436\pi$
$709$	30.0036	+	8.03944i	1.12681	+	0.301927i	0.353173	+	0.935558i	$0.385103\pi$
$710$	7.59505	−	2.03509i	0.285037	−	0.0763755i
$711$	5.99280	−	8.18535i	0.224747	−	0.306975i
$712$	−3.60261	+	2.07997i	−0.135014	+	0.0779501i
$713$	7.22555	+	7.22555i	0.270599	+	0.270599i
$714$	−3.46999	+	6.28211i	−0.129861	+	0.235102i
$715$	−31.1580	−	22.1585i	−1.16524	−	0.828681i
$716$	−7.84844	+	4.53130i	−0.293310	+	0.169343i
$717$	−41.2346	+	8.68602i	−1.53993	+	0.324385i
$718$	−6.98071	+	12.0909i	−0.260518	+	0.451230i
$719$	23.0599	+	39.9409i	0.859990	+	1.48955i	0.871938	+	0.489617i	$0.162863\pi$
$719$	23.0599	+	39.9409i	0.859990	+	1.48955i	−0.0119481	+	0.999929i	$0.503803\pi$
$720$	5.60081	−	4.50168i	0.208730	−	0.167768i
$721$	−9.27902	+	48.5967i	−0.345569	+	1.80983i
$722$	−14.5120	−	14.5120i	−0.540081	−	0.540081i
$723$	−8.46983	+	25.9064i	−0.314996	+	0.963469i
$724$	−8.62043	+	14.9310i	−0.320376	+	0.554907i
$725$	−3.73376	+	6.46707i	−0.138668	+	0.240181i
$726$	−14.1582	−	4.62887i	−0.525460	−	0.171793i
$727$			15.1685i			0.562568i	0.959625	+	0.281284i	$0.0907603\pi$
$727$			15.1685i			0.562568i	−0.959625	+	0.281284i	$0.909240\pi$
$728$	−8.15715	−	4.94579i	−0.302324	−	0.183303i
$729$	−25.5856	−	8.62427i	−0.947614	−	0.319417i
$730$	−0.701002	+	2.61618i	−0.0259453	+	0.0968290i
$731$	5.98331	+	3.45447i	0.221301	+	0.127768i
$732$	11.8991	−	18.2500i	0.439805	−	0.674541i
$733$	9.88490	−	36.8909i	0.365107	−	1.36260i	−0.502169	−	0.864770i	$-0.667464\pi$
$733$	9.88490	−	36.8909i	0.365107	−	1.36260i	0.867276	−	0.497828i	$-0.165869\pi$
$734$	−9.46909	+	9.46909i	−0.349511	+	0.349511i
$735$	18.5598	−	22.3359i	0.684587	−	0.823874i
$736$	−1.96290	+	1.96290i	−0.0723534	+	0.0723534i
$737$	7.70668	−	4.44945i	0.283879	−	0.163898i
$738$	−10.9612	−	8.02510i	−0.403488	−	0.295408i
$739$	−10.3712	−	38.7059i	−0.381511	−	1.42382i	−0.843594	−	0.536982i	$-0.819564\pi$
$739$	−10.3712	−	38.7059i	−0.381511	−	1.42382i	0.462083	−	0.886837i	$-0.347102\pi$
$740$	−3.86350	−	6.69178i	−0.142025	−	0.245995i
$741$	39.0101	−	4.42828i	1.43307	−	0.162677i
$742$	6.08383	−	0.445710i	0.223344	−	0.0163625i
$743$	−9.57433	+	9.57433i	−0.351248	+	0.351248i	−0.860574	−	0.509326i	$-0.829895\pi$
$743$	−9.57433	+	9.57433i	−0.351248	+	0.351248i	0.509326	+	0.860574i	$0.329895\pi$
$744$	−2.88417	−	5.68614i	−0.105739	−	0.208464i
$745$	−26.6576	−	15.3908i	−0.976658	−	0.563874i
$746$	6.34209	+	23.6690i	0.232200	+	0.866583i
$747$	−11.9225	−	4.62664i	−0.436221	−	0.169280i
$748$	−4.90265	+	4.90265i	−0.179259	+	0.179259i
$749$	−0.104740	+	0.548549i	−0.00382710	+	0.0200435i
$750$	0.957816	−	17.6592i	0.0349745	−	0.644824i
$751$	−10.3768	+	5.99105i	−0.378655	+	0.218616i	−0.677233	−	0.735769i	$-0.736821\pi$
$751$	−10.3768	+	5.99105i	−0.378655	+	0.218616i	0.298578	+	0.954385i	$0.403488\pi$
$752$	10.0772	−	2.70018i	0.367478	−	0.0984654i
$753$	15.9937	+	10.4280i	0.582843	+	0.380017i
$754$	−28.1514	+	23.2731i	−1.02521	+	0.847556i
$755$			30.7075i			1.11756i
$756$	2.35802	+	13.5440i	0.0857603	+	0.492590i
$757$	33.6799			1.22412			0.612059	−	0.790812i	$-0.290342\pi$
$757$	33.6799			1.22412			0.612059	+	0.790812i	$0.290342\pi$
$758$	−17.2345	−	29.8511i	−0.625987	−	1.08424i
$759$	−4.38766	−	20.8293i	−0.159262	−	0.756054i
$760$	14.5451	−	3.89735i	0.527606	−	0.141372i
$761$	5.12621	−	19.1313i	0.185825	−	0.693509i	−0.808627	−	0.588321i	$-0.799789\pi$
$761$	5.12621	−	19.1313i	0.185825	−	0.693509i	0.994452	−	0.105187i	$-0.0335442\pi$
$762$	−18.8588	+	16.9183i	−0.683181	+	0.612884i
$763$	16.2632	−	33.6272i	0.588767	−	1.21739i
$764$	9.95230			0.360062
$765$	10.4912	+	4.07122i	0.379311	+	0.147195i
$766$	11.1121	+	6.41559i	0.401497	+	0.231805i
$767$	−46.9916	−	17.4938i	−1.69677	−	0.631666i
$768$	1.54470	−	0.783515i	0.0557396	−	0.0282727i
$769$	18.5957	+	18.5957i	0.670578	+	0.670578i	0.957849	−	0.287272i	$-0.0927482\pi$
$769$	18.5957	+	18.5957i	0.670578	+	0.670578i	−0.287272	+	0.957849i	$0.592748\pi$
$770$	23.2072	−	15.7658i	0.836331	−	0.568159i
$771$	1.34961	−	24.8828i	0.0486052	−	0.896132i
$772$	0.0446354	−	0.166582i	0.00160646	−	0.00599541i
$773$	4.59473	+	17.1478i	0.165261	+	0.616762i	0.998007	+	0.0631066i	$0.0201008\pi$
$773$	4.59473	+	17.1478i	0.165261	+	0.616762i	−0.832746	+	0.553655i	$0.813233\pi$
$774$	13.0792	−	2.02262i	0.470124	−	0.0727015i
$775$	2.62098	+	0.702291i	0.0941485	+	0.0252270i
$776$			2.78844i			0.100099i
$777$	14.7807	−	0.280056i	0.530255	−	0.0100469i
$778$	16.4480	−	16.4480i	0.589690	−	0.589690i
$779$	−14.2341	−	24.6543i	−0.509991	−	0.883331i
$780$	−5.97025	+	13.7151i	−0.213769	+	0.491080i
$781$	−7.26670	+	12.5863i	−0.260023	+	0.450373i
$782$	−4.19928	−	1.12519i	−0.150166	−	0.0402368i
$783$	51.9454	+	8.51928i	1.85638	+	0.304454i
$784$	5.48736	−	4.34614i	0.195977	−	0.155219i
$785$	−33.2449	+	33.2449i	−1.18656	+	1.18656i
$786$	−25.1068	−	8.20840i	−0.895529	−	0.292784i
$787$	−3.60620	−	13.4585i	−0.128547	−	0.479745i	0.871394	−	0.490584i	$-0.163216\pi$
$787$	−3.60620	−	13.4585i	−0.128547	−	0.479745i	−0.999941	+	0.0108390i	$0.996550\pi$
$788$	12.5089	−	3.35174i	0.445610	−	0.119401i
$789$	15.9485	+	31.4425i	0.567782	+	1.11938i
$790$			8.09958i			0.288170i
$791$	−15.5019	−	13.3855i	−0.551183	−	0.475935i
$792$	−1.43653	+	13.2037i	−0.0510448	+	0.469171i
$793$	−4.28308	+	45.1496i	−0.152097	+	1.60331i
$794$	−10.6994	−	6.17730i	−0.379708	−	0.219224i
$795$	−1.97165	−	9.35989i	−0.0699272	−	0.331961i
$796$	12.3520	+	21.3942i	0.437804	+	0.758299i
$797$	−37.4575			−1.32681			−0.663406	−	0.748260i	$-0.730890\pi$
$797$	−37.4575			−1.32681			−0.663406	+	0.748260i	$0.730890\pi$
$798$	−6.92793	+	27.9641i	−0.245246	+	0.989917i
$799$	11.5531	+	11.5531i	0.408720	+	0.408720i
$800$	−0.190785	+	0.712019i	−0.00674526	+	0.0251737i
$801$	−12.3332	+	1.90725i	−0.435772	+	0.0673893i
$802$	16.6636	−	28.8623i	0.588413	−	1.01916i
$803$	−2.50307	−	4.33545i	−0.0883316	−	0.152995i
$804$	−2.32486	−	2.59152i	−0.0819916	−	0.0913960i
$805$	15.8369	+	7.65923i	0.558177	+	0.269952i
$806$	10.8160	+	7.69197i	0.380978	+	0.270938i
$807$	1.48542	+	2.92851i	0.0522893	+	0.103088i
$808$	8.68261	−	2.32650i	0.305453	−	0.0818459i
$809$	−25.4158	−	14.6738i	−0.893570	−	0.515903i	−0.0184616	−	0.999830i	$-0.505877\pi$
$809$	−25.4158	−	14.6738i	−0.893570	−	0.515903i	−0.875109	+	0.483927i	$0.839210\pi$
$810$	20.5501	−	6.51159i	0.722057	−	0.228794i
$811$	6.12152	+	6.12152i	0.214956	+	0.214956i	0.806369	−	0.591413i	$-0.201430\pi$
$811$	6.12152	+	6.12152i	0.214956	+	0.214956i	−0.591413	+	0.806369i	$0.701430\pi$
$812$	−8.81012	−	25.3133i	−0.309175	−	0.888323i
$813$	10.6305	+	11.8498i	0.372829	+	0.415592i
$814$	13.7954	+	3.69648i	0.483530	+	0.129561i
$815$	7.22646	+	4.17220i	0.253132	+	0.146146i
$816$	2.27224	+	1.48151i	0.0795443	+	0.0518634i
$817$	26.7894	+	7.17819i	0.937241	+	0.251133i
$818$	28.7468			1.00511
$819$	−17.4461	−	22.6855i	−0.609616	−	0.792697i
$820$	10.8464			0.378771
$821$	16.1287	+	4.32168i	0.562897	+	0.150828i	0.529037	−	0.848599i	$-0.322553\pi$
$821$	16.1287	+	4.32168i	0.562897	+	0.150828i	0.0338600	+	0.999427i	$0.489220\pi$
$822$	17.6630	+	11.5164i	0.616067	+	0.401680i
$823$	−38.0539	−	21.9705i	−1.32648	−	0.765842i	−0.341724	−	0.939800i	$-0.611011\pi$
$823$	−38.0539	−	21.9705i	−1.32648	−	0.765842i	−0.984753	+	0.173958i	$0.944344\pi$
$824$	18.0625	+	4.83982i	0.629236	+	0.168603i
$825$	−3.77455	−	4.20749i	−0.131413	−	0.146486i
$826$	24.0470	−	27.8490i	0.836702	−	0.968990i
$827$	14.3734	+	14.3734i	0.499812	+	0.499812i	0.911379	−	0.411567i	$-0.135018\pi$
$827$	14.3734	+	14.3734i	0.499812	+	0.499812i	−0.411567	+	0.911379i	$0.635018\pi$
$828$	−7.62021	+	3.35945i	−0.264821	+	0.116749i
$829$	11.7954	+	6.81010i	0.409672	+	0.236524i	0.690649	−	0.723190i	$-0.257325\pi$
$829$	11.7954	+	6.81010i	0.409672	+	0.236524i	−0.280977	+	0.959715i	$0.590658\pi$
$830$	9.86274	−	2.64271i	0.342341	−	0.0917299i
$831$	6.36035	+	12.5394i	0.220638	+	0.434988i
$832$	−2.08961	+	2.93829i	−0.0724441	+	0.101867i
$833$	10.1914	+	4.03915i	0.353112	+	0.139948i
$834$	6.69384	+	7.46161i	0.231789	+	0.258375i
$835$	−14.4021	−	24.9452i	−0.498406	−	0.863265i
$836$	−13.9163	+	24.1037i	−0.481305	+	0.833645i
$837$	−1.89512	−	19.0332i	−0.0655051	−	0.657885i
$838$	−1.14276	+	4.26484i	−0.0394760	+	0.147326i
$839$	−8.70868	−	8.70868i	−0.300657	−	0.300657i	0.540614	−	0.841271i	$-0.318192\pi$
$839$	−8.70868	−	8.70868i	−0.300657	−	0.300657i	−0.841271	+	0.540614i	$0.818192\pi$
$840$	−7.90708	−	7.61301i	−0.272820	−	0.262674i
$841$	−73.6261			−2.53883
$842$	6.91390	+	11.9752i	0.238269	+	0.412693i
$843$	3.37784	+	16.0354i	0.116339	+	0.552289i
$844$	16.8750	+	9.74279i	0.580862	+	0.335361i
$845$	−2.25978	−	31.0559i	−0.0777388	−	1.06836i
$846$	31.1145	+	3.38518i	1.06974	+	0.116385i
$847$	−4.26745	+	22.3497i	−0.146631	+	0.767946i
$848$		−	2.30563i		−	0.0791758i
$849$	4.65246	+	9.17234i	0.159672	+	0.314794i
$850$	−1.11509	+	0.298787i	−0.0382472	+	0.0102483i
$851$	2.31778	+	8.65009i	0.0794526	+	0.296521i
$852$	5.40440	+	1.76691i	0.185152	+	0.0605334i
$853$	−11.4339	+	11.4339i	−0.391491	+	0.391491i	−0.875219	−	0.483728i	$-0.839282\pi$
$853$	−11.4339	+	11.4339i	−0.391491	+	0.391491i	0.483728	+	0.875219i	$0.339282\pi$
$854$	−29.9596	−	14.4895i	−1.02520	−	0.495819i
$855$	44.9096	+	4.88606i	1.53587	+	0.167100i
$856$	0.203885	+	0.0546309i	0.00696866	+	0.00186725i
$857$	−0.490885	+	0.850238i	−0.0167683	+	0.0290436i	−0.874288	−	0.485408i	$-0.838671\pi$
$857$	−0.490885	+	0.850238i	−0.0167683	+	0.0290436i	0.857519	+	0.514451i	$0.172004\pi$
$858$	−10.1223	−	25.7282i	−0.345570	−	0.878346i
$859$	−3.31652	−	5.74438i	−0.113158	−	0.195996i	0.803884	−	0.594786i	$-0.202763\pi$
$859$	−3.31652	−	5.74438i	−0.113158	−	0.195996i	−0.917042	+	0.398791i	$0.869430\pi$
$860$	−7.47181	+	7.47181i	−0.254787	+	0.254787i
$861$	−10.0334	+	18.1645i	−0.341936	+	0.619045i
$862$			16.9048i			0.575780i
$863$	26.3591	+	7.06289i	0.897273	+	0.240424i	0.677845	−	0.735205i	$-0.262914\pi$
$863$	26.3591	+	7.06289i	0.897273	+	0.240424i	0.219428	+	0.975629i	$0.429581\pi$
$864$	5.17058	−	0.514831i	0.175907	−	0.0175149i
$865$	−5.24088	−	19.5592i	−0.178195	−	0.665033i
$866$	5.26970	−	19.6668i	0.179072	−	0.668305i
$867$	1.36464	−	25.1598i	0.0463455	−	0.854470i
$868$	−8.05602	+	5.47283i	−0.273439	+	0.185760i
$869$	−10.5859	−	10.5859i	−0.359102	−	0.359102i
$870$	−37.4819	+	19.0118i	−1.27075	+	0.644562i
$871$	6.79198	+	2.52849i	0.230138	+	0.0856747i
$872$	−12.2268	−	7.05914i	−0.414051	−	0.239053i
$873$	−3.02637	+	7.79871i	−0.102427	+	0.263946i
$874$	−17.4517			−0.590313
$875$	−26.9424	+	1.97384i	−0.910818	+	0.0667279i
$876$	−1.45788	+	1.30787i	−0.0492573	+	0.0441888i
$877$	3.87893	−	14.4763i	0.130982	−	0.488832i	−0.869000	−	0.494812i	$-0.835237\pi$
$877$	3.87893	−	14.4763i	0.130982	−	0.488832i	0.999982	+	0.00598037i	$0.00190362\pi$
$878$	0.221263	−	0.0592873i	0.00746728	−	0.00200085i
$879$	4.73425	+	22.4746i	0.159682	+	0.758049i
$880$	−5.30207	−	9.18346i	−0.178733	−	0.309574i
$881$	−18.1075			−0.610059			−0.305029	−	0.952343i	$-0.598666\pi$
$881$	−18.1075			−0.610059			−0.305029	+	0.952343i	$0.598666\pi$
$882$	20.0640	−	6.19970i	0.675590	−	0.208755i
$883$		−	24.2504i		−	0.816090i	−0.912962	−	0.408045i	$-0.866211\pi$
$883$		−	24.2504i		−	0.816090i	0.912962	−	0.408045i	$-0.133789\pi$
$884$	−5.62140	−	0.533270i	−0.189068	−	0.0179358i
$885$	−48.3299	−	31.5114i	−1.62459	−	1.05924i
$886$	−14.3897	+	3.85571i	−0.483432	+	0.129535i
$887$	−26.6769	+	15.4019i	−0.895723	+	0.517146i	−0.875810	−	0.482656i	$-0.839672\pi$
$887$	−26.6769	+	15.4019i	−0.895723	+	0.517146i	−0.0199127	+	0.999802i	$0.506339\pi$
$888$	0.302619	−	5.57939i	0.0101552	−	0.187232i
$889$	29.2916	+	25.2927i	0.982410	+	0.848290i
$890$	7.04562	−	7.04562i	0.236170	−	0.236170i
$891$	−18.3479	+	35.3688i	−0.614679	+	1.18490i
$892$	−7.10183	−	26.5044i	−0.237787	−	0.887432i
$893$	56.8005	+	32.7938i	1.90076	+	1.09740i
$894$	−10.0691	−	19.8512i	−0.336761	−	0.663924i
$895$	15.3492	−	15.3492i	0.513066	−	0.513066i
$896$	−1.48675	−	2.18851i	−0.0496690	−	0.0731129i
$897$	10.7974	−	13.5627i	0.360516	−	0.452846i
$898$	−0.381294	−	0.660421i	−0.0127240	−	0.0220385i
$899$	9.65157	+	36.0201i	0.321898	+	1.20134i
$900$	−1.30636	+	1.78431i	−0.0435453	+	0.0594770i
$901$	3.12708	−	1.80542i	0.104178	−	0.0601472i
$902$	−14.1759	+	14.1759i	−0.472004	+	0.472004i
$903$	−5.60137	−	19.4249i	−0.186402	−	0.646419i
$904$	−5.47384	+	5.47384i	−0.182057	+	0.182057i
$905$	10.6881	−	39.8887i	0.355286	−	1.32595i
$906$	−12.1279	+	18.6009i	−0.402922	+	0.617973i
$907$	14.1814	+	8.18765i	0.470886	+	0.271866i	0.716611	−	0.697473i	$-0.245692\pi$
$907$	14.1814	+	8.18765i	0.470886	+	0.271866i	−0.245724	+	0.969340i	$0.579026\pi$
$908$	−1.12921	+	4.21428i	−0.0374742	+	0.139856i
$909$	26.8085	+	2.91670i	0.889182	+	0.0967410i
$910$	21.9386	+	6.38579i	0.727257	+	0.211687i
$911$			50.4961i			1.67301i	0.547958	+	0.836506i	$0.315405\pi$
$911$			50.4961i			1.67301i	−0.547958	+	0.836506i	$0.684595\pi$
$912$	10.3498	+	3.38377i	0.342718	+	0.112048i
$913$	−9.43636	+	16.3443i	−0.312298	+	0.540916i
$914$	8.84855	−	15.3261i	0.292684	−	0.506943i
$915$	−16.2163	+	49.6002i	−0.536094	+	1.63973i
$916$	−3.49814	−	3.49814i	−0.115582	−	0.115582i
$917$	−7.56748	+	39.6329i	−0.249900	+	1.30879i
$918$	4.74707	+	6.60961i	0.156677	+	0.218150i
$919$	−27.5436	−	47.7070i	−0.908581	−	1.57371i	−0.816037	−	0.578000i	$-0.803833\pi$
$919$	−27.5436	−	47.7070i	−0.908581	−	1.57371i	−0.0925444	−	0.995709i	$-0.529500\pi$
$920$	3.32453	−	5.75826i	0.109607	−	0.189844i
$921$	−12.7697	+	2.68993i	−0.420777	+	0.0886361i
$922$	−0.0589307	+	0.0340237i	−0.00194078	+	0.00112051i
$923$	−11.6711	+	1.97001i	−0.384158	+	0.0648437i
$924$	20.2843	−	0.384334i	0.667304	−	0.0126437i
$925$	1.68150	+	1.68150i	0.0552873	+	0.0552873i
$926$	−32.7401	+	18.9025i	−1.07591	+	0.621174i
$927$	45.2643	+	33.1396i	1.48667	+	1.08845i
$928$	−9.78527	+	2.62195i	−0.321217	+	0.0860699i
$929$	−40.1682	−	10.7630i	−1.31788	−	0.353124i	−0.469695	−	0.882829i	$-0.655636\pi$
$929$	−40.1682	−	10.7630i	−1.31788	−	0.353124i	−0.848182	+	0.529705i	$0.822303\pi$
$930$	10.1979	+	11.3676i	0.334401	+	0.372757i
$931$	43.7138	+	5.07318i	1.43266	+	0.166267i
$932$		−	4.14779i		−	0.135865i
$933$	−53.1537	+	26.9611i	−1.74018	+	0.882665i
$934$	−2.76938	−	10.3355i	−0.0906168	−	0.338186i
$935$	8.30355	−	14.3822i	0.271555	−	0.470347i
$936$	−9.03320	+	5.94989i	−0.295260	+	0.194478i
$937$	9.60676			0.313839			0.156920	−	0.987611i	$-0.449844\pi$
$937$	9.60676			0.313839			0.156920	+	0.987611i	$0.449844\pi$
$938$	−3.47566	+	4.02518i	−0.113484	+	0.131427i
$939$	−0.171828	+	3.16799i	−0.00560740	+	0.103384i
$940$	−21.6409	+	12.4944i	−0.705847	+	0.407521i
$941$	−0.535677	−	1.99918i	−0.0174626	−	0.0651713i	0.956645	−	0.291257i	$-0.0940736\pi$
$941$	−0.535677	−	1.99918i	−0.0174626	−	0.0651713i	−0.974107	+	0.226086i	$0.927407\pi$
$942$	−33.2679	+	7.00785i	−1.08393	+	0.228328i
$943$	−12.1421	−	3.25346i	−0.395400	−	0.105947i
$944$	−9.83370	−	9.83370i	−0.320060	−	0.320060i
$945$	−13.8519	−	29.8738i	−0.450602	−	0.971795i
$946$		−	19.5309i		−	0.635003i
$947$	−12.5387	+	46.7952i	−0.407454	+	1.52064i	0.392030	+	0.919952i	$0.371773\pi$
$947$	−12.5387	+	46.7952i	−0.407454	+	1.52064i	−0.799484	+	0.600687i	$0.794894\pi$
$948$	−3.19892	+	4.90627i	−0.103896	+	0.159348i
$949$	1.42242	−	3.82088i	0.0461738	−	0.124031i
$950$	−4.01332	+	2.31709i	−0.130209	+	0.0751764i
$951$	7.19716	+	8.02266i	0.233384	+	0.260153i
$952$	1.80402	−	3.73016i	0.0584687	−	0.120895i
$953$	47.8347			1.54952			0.774759	−	0.632257i	$-0.217871\pi$
$953$	47.8347			1.54952			0.774759	+	0.632257i	$0.217871\pi$
$954$	2.50236	−	6.44839i	0.0810169	−	0.208774i
$955$	−23.0258	+	6.16975i	−0.745097	+	0.199648i
$956$	23.5002	−	6.29687i	0.760052	−	0.203655i
$957$	24.1398	−	73.8356i	0.780328	−	2.38676i
$958$	13.5021			0.436232
$959$	14.0234	−	28.9959i	0.452838	−	0.936327i
$960$	−3.08812	+	2.77036i	−0.0996687	+	0.0894131i
$961$	−15.1120	+	8.72490i	−0.487483	+	0.281448i
$962$	4.83844	+	10.5774i	0.155998	+	0.341029i
$963$	0.510933	+	0.374073i	0.0164646	+	0.0120543i
$964$	4.07282	−	15.2000i	0.131177	−	0.489558i
$965$			0.413077i			0.0132974i
$966$	6.56808	+	10.8943i	0.211324	+	0.350517i
$967$	26.3458	+	26.3458i	0.847225	+	0.847225i	0.989786	−	0.142561i	$-0.0455336\pi$
$967$	26.3458	+	26.3458i	0.847225	+	0.847225i	−0.142561	+	0.989786i	$0.545534\pi$
$968$	8.30697	+	2.22585i	0.266996	+	0.0715414i
$969$	3.51508	+	16.6869i	0.112921	+	0.536061i
$970$	−1.72864	−	6.45139i	−0.0555034	−	0.207142i
$971$	16.3495	−	9.43942i	0.524682	−	0.302925i	−0.214166	−	0.976797i	$-0.568703\pi$
$971$	16.3495	−	9.43942i	0.524682	−	0.302925i	0.738848	+	0.673872i	$0.235370\pi$
$972$	15.0198	+	4.17188i	0.481761	+	0.133813i
$973$	10.0073	−	11.5895i	0.320818	−	0.371541i
$974$	−11.0961			−0.355540
$975$	0.682313	−	4.55257i	0.0218515	−	0.145799i
$976$	−6.28923	+	10.8933i	−0.201313	+	0.348685i
$977$	10.9632	+	40.9152i	0.350743	+	1.30899i	0.885757	+	0.464149i	$0.153640\pi$
$977$	10.9632	+	40.9152i	0.350743	+	1.30899i	−0.535014	+	0.844843i	$0.679694\pi$
$978$	2.72957	+	5.38136i	0.0872821	+	0.172077i
$979$			18.4168i			0.588604i
$980$	−10.0013	+	13.4571i	−0.319481	+	0.429871i
$981$	−26.5344	−	33.0130i	−0.847178	−	1.05402i
$982$	10.8149	+	2.89785i	0.345118	+	0.0924741i
$983$	29.9257	−	8.01856i	0.954481	−	0.255752i	0.252218	−	0.967670i	$-0.418840\pi$
$983$	29.9257	−	8.01856i	0.954481	−	0.255752i	0.702263	+	0.711918i	$0.252173\pi$
$984$	6.57010	+	4.28375i	0.209447	+	0.136561i
$985$	−26.8629	+	15.5093i	−0.855922	+	0.494167i
$986$	−11.2184	−	11.2184i	−0.357267	−	0.357267i
$987$	−0.905685	−	47.8000i	−0.0288283	−	1.52149i
$988$	−22.3510	+	3.77272i	−0.711080	+	0.120026i
$989$	10.6056	−	6.12317i	0.337240	−	0.194705i
$990$	−4.86179	−	31.4387i	−0.154518	−	0.999189i
$991$	9.20860	−	15.9498i	0.292521	−	0.506661i	−0.681884	−	0.731460i	$-0.738839\pi$
$991$	9.20860	−	15.9498i	0.292521	−	0.506661i	0.974405	+	0.224799i	$0.0721726\pi$
$992$	1.84053	+	3.18789i	0.0584369	+	0.101216i
$993$	14.5402	−	13.0441i	0.461420	−	0.413942i
$994$	1.62895	−	8.53125i	0.0516672	−	0.270595i
$995$	−41.8407	−	41.8407i	−1.32644	−	1.32644i
$996$	7.01802	+	2.29447i	0.222375	+	0.0727030i
$997$	0.141931	−	0.245832i	0.00449501	−	0.00778559i	−0.863769	−	0.503888i	$-0.831903\pi$
$997$	0.141931	−	0.245832i	0.00449501	−	0.00778559i	0.868264	+	0.496102i	$0.165236\pi$
$998$	5.98157	−	10.3604i	0.189343	−	0.327952i
$999$	6.90181	−	15.2760i	0.218364	−	0.483310i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.515.22	yes	144
3.2	odd	2	inner	546.2.bv.a.515.16	yes	144
7.2	even	3	inner	546.2.bv.a.359.16	yes	144
13.5	odd	4	inner	546.2.bv.a.473.22	yes	144
21.2	odd	6	inner	546.2.bv.a.359.22	yes	144
39.5	even	4	inner	546.2.bv.a.473.16	yes	144
91.44	odd	12	inner	546.2.bv.a.317.16	✓	144
273.44	even	12	inner	546.2.bv.a.317.22	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.16	✓	144	91.44	odd	12	inner
546.2.bv.a.317.22	yes	144	273.44	even	12	inner
546.2.bv.a.359.16	yes	144	7.2	even	3	inner
546.2.bv.a.359.22	yes	144	21.2	odd	6	inner
546.2.bv.a.473.16	yes	144	39.5	even	4	inner
546.2.bv.a.473.22	yes	144	13.5	odd	4	inner
546.2.bv.a.515.16	yes	144	3.2	odd	2	inner
546.2.bv.a.515.22	yes	144	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.45090 - 0.945993i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.31362 - 0.619932i) q^{5} +(-1.15662 - 1.28928i) q^{6} +(-1.72913 + 2.00252i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.21019 + 2.74507i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.45090 - 0.945993i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.31362 - 0.619932i) q^{5} +(-1.15662 - 1.28928i) q^{6} +(-1.72913 + 2.00252i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.21019 + 2.74507i) q^{9} +(-2.07433 - 1.19762i) q^{10} +(4.27634 - 1.14584i) q^{11} +(-0.783515 - 1.54470i) q^{12} +(2.93829 + 2.08961i) q^{13} +(-2.18851 + 1.48675i) q^{14} +(2.77036 + 3.08812i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.783047 + 1.35628i) q^{17} +(0.458480 + 2.96476i) q^{18} +(-1.62713 + 6.07252i) q^{19} +(-1.69368 - 1.69368i) q^{20} +(4.40317 - 1.26970i) q^{21} +4.42719 q^{22} +(1.38798 + 2.40405i) q^{23} +(-0.357020 - 1.69486i) q^{24} +(0.638379 + 0.368568i) q^{25} +(2.29734 + 2.77889i) q^{26} +(0.840957 - 5.12765i) q^{27} +(-2.49874 + 0.869667i) q^{28} +10.1305i q^{29} +(1.87670 + 3.69992i) q^{30} +(3.55563 - 0.952728i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-7.28848 - 2.38289i) q^{33} +(-1.10740 + 1.10740i) q^{34} +(5.24198 - 3.56112i) q^{35} +(-0.324478 + 2.98240i) q^{36} +(3.11607 + 0.834949i) q^{37} +(-3.14337 + 5.44447i) q^{38} +(-2.28639 - 5.81140i) q^{39} +(-1.19762 - 2.07433i) q^{40} +(-3.20200 + 3.20200i) q^{41} +(4.58175 - 0.0868122i) q^{42} -4.41157i q^{43} +(4.27634 + 1.14584i) q^{44} +(-1.09817 - 7.10129i) q^{45} +(0.718471 + 2.68137i) q^{46} +(2.70018 - 10.0772i) q^{47} +(0.0938065 - 1.72951i) q^{48} +(-1.02019 - 6.92526i) q^{49} +(0.521234 + 0.521234i) q^{50} +(2.41915 - 1.22706i) q^{51} +(1.49983 + 3.27880i) q^{52} +(-1.99674 - 1.15282i) q^{53} +(2.13944 - 4.73527i) q^{54} -10.6041 q^{55} +(-2.63868 + 0.193314i) q^{56} +(8.10536 - 7.27134i) q^{57} +(-2.62195 + 9.78527i) q^{58} +(-13.4331 + 3.59938i) q^{59} +(0.855145 + 4.05957i) q^{60} +(6.28923 + 10.8933i) q^{61} +3.68106 q^{62} +(-7.58966 - 2.32316i) q^{63} +1.00000i q^{64} +(-5.50266 - 6.65609i) q^{65} +(-6.42339 - 4.18809i) q^{66} +(1.94157 - 0.520241i) q^{67} +(-1.35628 + 0.783047i) q^{68} +(0.260403 - 4.80104i) q^{69} +(5.98505 - 2.08305i) q^{70} +(-2.32126 + 2.32126i) q^{71} +(-1.08532 + 2.79680i) q^{72} +(-0.292666 - 1.09224i) q^{73} +(2.79379 + 1.61300i) q^{74} +(-0.577558 - 1.13866i) q^{75} +(-4.44540 + 4.44540i) q^{76} +(-5.09979 + 10.5448i) q^{77} +(-0.704385 - 6.20515i) q^{78} +(-1.69077 - 2.92850i) q^{79} +(-0.619932 - 2.31362i) q^{80} +(-6.07086 + 6.64414i) q^{81} +(-3.92163 + 2.26416i) q^{82} +(-3.01433 + 3.01433i) q^{83} +(4.44810 + 1.10199i) q^{84} +(2.65247 - 2.65247i) q^{85} +(1.14180 - 4.26125i) q^{86} +(9.58334 - 14.6982i) q^{87} +(3.83406 + 2.21360i) q^{88} +(-1.07667 + 4.01819i) q^{89} +(0.777201 - 7.14354i) q^{90} +(-9.26518 + 2.27077i) q^{91} +2.77596i q^{92} +(-6.06012 - 1.98129i) q^{93} +(5.21635 - 9.03498i) q^{94} +(7.52910 - 13.0408i) q^{95} +(0.538240 - 1.64630i) q^{96} +(1.97173 + 1.97173i) q^{97} +(0.806966 - 6.95333i) q^{98} +(8.32062 + 10.3522i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

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