LMFDB - Embedded newform 1110.2.ba.a.529.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(529,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1110.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.ba (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.10
Character	$\chi$	$=$	1110.529
Dual form			1110.2.ba.a.619.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.05954 + 1.96911i) q^{5} -1.00000i q^{6} +(-3.29356 - 1.90154i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.05954 + 1.96911i) q^{5} -1.00000i q^{6} +(-3.29356 - 1.90154i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(1.17553 - 1.90214i) q^{10} -3.84960 q^{11} +(-0.866025 + 0.500000i) q^{12} +(1.22502 - 2.12180i) q^{13} +3.80308i q^{14} +(-0.0669680 + 2.23506i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.42715 - 5.93600i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.996184 - 0.575147i) q^{19} +(-2.23506 - 0.0669680i) q^{20} +(-1.90154 - 3.29356i) q^{21} +(1.92480 + 3.33385i) q^{22} +0.0656760 q^{23} +(0.866025 + 0.500000i) q^{24} +(-2.75477 + 4.17268i) q^{25} -2.45005 q^{26} +1.00000i q^{27} +(3.29356 - 1.90154i) q^{28} +2.70511i q^{29} +(1.96911 - 1.05954i) q^{30} -8.12994i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.33385 - 1.92480i) q^{33} +(-3.42715 + 5.93600i) q^{34} +(0.254685 - 8.50013i) q^{35} -1.00000 q^{36} +(4.13579 - 4.46040i) q^{37} +1.15029i q^{38} +(2.12180 - 1.22502i) q^{39} +(1.05954 + 1.96911i) q^{40} +(0.239768 - 0.415291i) q^{41} +(-1.90154 + 3.29356i) q^{42} -10.0403 q^{43} +(1.92480 - 3.33385i) q^{44} +(-1.17553 + 1.90214i) q^{45} +(-0.0328380 - 0.0568771i) q^{46} -1.94212i q^{47} -1.00000i q^{48} +(3.73171 + 6.46351i) q^{49} +(4.99103 + 0.299356i) q^{50} -6.85430i q^{51} +(1.22502 + 2.12180i) q^{52} +(4.83010 - 2.78866i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-4.07879 - 7.58027i) q^{55} +(-3.29356 - 1.90154i) q^{56} +(-0.575147 - 0.996184i) q^{57} +(2.34269 - 1.35255i) q^{58} +(1.87894 - 1.08481i) q^{59} +(-1.90214 - 1.17553i) q^{60} +(-4.07230 - 2.35114i) q^{61} +(-7.04073 + 4.06497i) q^{62} -3.80308i q^{63} +1.00000 q^{64} +(5.47601 + 0.164075i) q^{65} +3.84960i q^{66} +(-6.70598 - 3.87170i) q^{67} +6.85430 q^{68} +(0.0568771 + 0.0328380i) q^{69} +(-7.48867 + 4.02950i) q^{70} +(-3.72085 + 6.44470i) q^{71} +(0.500000 + 0.866025i) q^{72} -6.82160i q^{73} +(-5.93072 - 1.35150i) q^{74} +(-4.47204 + 2.23627i) q^{75} +(0.996184 - 0.575147i) q^{76} +(12.6789 + 7.32017i) q^{77} +(-2.12180 - 1.22502i) q^{78} +(2.57370 + 1.48593i) q^{79} +(1.17553 - 1.90214i) q^{80} +(-0.500000 + 0.866025i) q^{81} -0.479537 q^{82} +(4.83322 - 2.79046i) q^{83} +3.80308 q^{84} +(8.05742 - 13.0378i) q^{85} +(5.02016 + 8.69516i) q^{86} +(-1.35255 + 2.34269i) q^{87} -3.84960 q^{88} +(6.89417 - 3.98035i) q^{89} +(2.23506 + 0.0669680i) q^{90} +(-8.06938 + 4.65886i) q^{91} +(-0.0328380 + 0.0568771i) q^{92} +(4.06497 - 7.04073i) q^{93} +(-1.68192 + 0.971059i) q^{94} +(0.0770330 - 2.57098i) q^{95} +(-0.866025 + 0.500000i) q^{96} -2.90742 q^{97} +(3.73171 - 6.46351i) q^{98} +(-1.92480 - 3.33385i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	$ 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 - 14 * q^13 - 2 * q^15 - 18 * q^16 + 18 * q^18 + 6 * q^19 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * q^70 - 24 * q^71 + 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 - 24 * q^77 - 6 * q^78 + 2 * q^80 - 18 * q^81 - 20 * q^82 + 36 * q^83 + 26 * q^85 - 10 * q^87 + 4 * q^88 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.05954	+	1.96911i	0.473839	+	0.880611i
$5$	1.05954	+	1.96911i	0.473839	+	0.880611i
$6$		−	1.00000i		−	0.408248i
$7$	−3.29356	−	1.90154i	−1.24485	−	0.718715i	−0.274773	−	0.961509i	$-0.588603\pi$
$7$	−3.29356	−	1.90154i	−1.24485	−	0.718715i	−0.970078	+	0.242795i	$0.921936\pi$
$8$	1.00000			0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.17553	−	1.90214i	0.371735	−	0.601509i
$11$	−3.84960			−1.16070			−0.580349	−	0.814368i	$-0.697084\pi$
$11$	−3.84960			−1.16070			−0.580349	+	0.814368i	$0.697084\pi$
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$	1.22502	−	2.12180i	0.339760	−	0.588482i	−0.644627	−	0.764497i	$-0.722987\pi$
$13$	1.22502	−	2.12180i	0.339760	−	0.588482i	0.984387	+	0.176015i	$0.0563208\pi$
$14$			3.80308i			1.01642i
$15$	−0.0669680	+	2.23506i	−0.0172911	+	0.577091i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.42715	−	5.93600i	−0.831206	−	1.43969i	−0.897082	−	0.441863i	$-0.854318\pi$
$17$	−3.42715	−	5.93600i	−0.831206	−	1.43969i	0.0658765	−	0.997828i	$-0.479016\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−0.996184	−	0.575147i	−0.228540	−	0.131948i	0.381358	−	0.924427i	$-0.375456\pi$
$19$	−0.996184	−	0.575147i	−0.228540	−	0.131948i	−0.609899	+	0.792480i	$0.708790\pi$
$20$	−2.23506	−	0.0669680i	−0.499776	−	0.0149745i
$21$	−1.90154	−	3.29356i	−0.414950	−	0.718715i
$22$	1.92480	+	3.33385i	0.410369	+	0.710779i
$23$	0.0656760			0.0136944			0.00684720	−	0.999977i	$-0.497820\pi$
$23$	0.0656760			0.0136944			0.00684720	+	0.999977i	$0.497820\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−2.75477	+	4.17268i	−0.550953	+	0.834536i
$26$	−2.45005			−0.480493
$27$			1.00000i			0.192450i
$28$	3.29356	−	1.90154i	0.622425	−	0.359357i
$29$			2.70511i			0.502326i	0.967945	+	0.251163i	$0.0808131\pi$
$29$			2.70511i			0.502326i	−0.967945	+	0.251163i	$0.919187\pi$
$30$	1.96911	−	1.05954i	0.359508	−	0.193444i
$31$		−	8.12994i		−	1.46018i	−0.683351	−	0.730090i	$-0.739478\pi$
$31$		−	8.12994i		−	1.46018i	0.683351	−	0.730090i	$-0.260522\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−3.33385	−	1.92480i	−0.580349	−	0.335065i
$34$	−3.42715	+	5.93600i	−0.587751	+	1.01802i
$35$	0.254685	−	8.50013i	0.0430496	−	1.43678i
$36$	−1.00000			−0.166667
$37$	4.13579	−	4.46040i	0.679920	−	0.733286i
$37$	4.13579	−	4.46040i	0.679920	−	0.733286i
$38$			1.15029i			0.186602i
$39$	2.12180	−	1.22502i	0.339760	−	0.196161i
$40$	1.05954	+	1.96911i	0.167527	+	0.311343i
$41$	0.239768	−	0.415291i	0.0374455	−	0.0648575i	−0.846695	−	0.532078i	$-0.821411\pi$
$41$	0.239768	−	0.415291i	0.0374455	−	0.0648575i	0.884141	+	0.467221i	$0.154745\pi$
$42$	−1.90154	+	3.29356i	−0.293414	+	0.508208i
$43$	−10.0403			−1.53113			−0.765567	−	0.643357i	$-0.777541\pi$
$43$	−10.0403			−1.53113			−0.765567	+	0.643357i	$0.777541\pi$
$44$	1.92480	−	3.33385i	0.290174	−	0.502597i
$45$	−1.17553	+	1.90214i	−0.175237	+	0.283554i
$46$	−0.0328380	−	0.0568771i	−0.00484170	−	0.00838607i
$47$		−	1.94212i		−	0.283287i	−0.989918	−	0.141643i	$-0.954761\pi$
$47$		−	1.94212i		−	0.283287i	0.989918	−	0.141643i	$-0.0452386\pi$
$48$		−	1.00000i		−	0.144338i
$49$	3.73171	+	6.46351i	0.533101	+	0.923359i
$50$	4.99103	+	0.299356i	0.705838	+	0.0423353i
$51$		−	6.85430i		−	0.959794i
$52$	1.22502	+	2.12180i	0.169880	+	0.294241i
$53$	4.83010	−	2.78866i	0.663465	−	0.383052i	−0.130131	−	0.991497i	$-0.541540\pi$
$53$	4.83010	−	2.78866i	0.663465	−	0.383052i	0.793596	+	0.608445i	$0.208206\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−4.07879	−	7.58027i	−0.549984	−	1.02212i
$56$	−3.29356	−	1.90154i	−0.440121	−	0.254104i
$57$	−0.575147	−	0.996184i	−0.0761801	−	0.131948i
$58$	2.34269	−	1.35255i	0.307611	−	0.177599i
$59$	1.87894	−	1.08481i	0.244617	−	0.141230i	−0.372680	−	0.927960i	$-0.621561\pi$
$59$	1.87894	−	1.08481i	0.244617	−	0.141230i	0.617297	+	0.786730i	$0.288228\pi$
$60$	−1.90214	−	1.17553i	−0.245565	−	0.151760i
$61$	−4.07230	−	2.35114i	−0.521405	−	0.301033i	0.216105	−	0.976370i	$-0.430665\pi$
$61$	−4.07230	−	2.35114i	−0.521405	−	0.301033i	−0.737509	+	0.675337i	$0.763998\pi$
$62$	−7.04073	+	4.06497i	−0.894174	+	0.516252i
$63$		−	3.80308i		−	0.479143i
$64$	1.00000			0.125000
$65$	5.47601	+	0.164075i	0.679215	+	0.0203510i
$66$			3.84960i			0.473853i
$67$	−6.70598	−	3.87170i	−0.819266	−	0.473003i	0.0308975	−	0.999523i	$-0.490163\pi$
$67$	−6.70598	−	3.87170i	−0.819266	−	0.473003i	−0.850163	+	0.526519i	$0.823497\pi$
$68$	6.85430			0.831206
$69$	0.0568771	+	0.0328380i	0.00684720	+	0.00395323i
$70$	−7.48867	+	4.02950i	−0.895068	+	0.481618i
$71$	−3.72085	+	6.44470i	−0.441583	+	0.764845i	−0.997807	−	0.0661878i	$-0.978916\pi$
$71$	−3.72085	+	6.44470i	−0.441583	+	0.764845i	0.556224	+	0.831032i	$0.312250\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$		−	6.82160i		−	0.798408i	−0.916862	−	0.399204i	$-0.869287\pi$
$73$		−	6.82160i		−	0.798408i	0.916862	−	0.399204i	$-0.130713\pi$
$74$	−5.93072	−	1.35150i	−0.689432	−	0.157109i
$75$	−4.47204	+	2.23627i	−0.516386	+	0.258222i
$76$	0.996184	−	0.575147i	0.114270	−	0.0659739i
$77$	12.6789	+	7.32017i	1.44489	+	0.834210i
$78$	−2.12180	−	1.22502i	−0.240247	−	0.138706i
$79$	2.57370	+	1.48593i	0.289564	+	0.167180i	0.637745	−	0.770247i	$-0.279867\pi$
$79$	2.57370	+	1.48593i	0.289564	+	0.167180i	−0.348181	+	0.937427i	$0.613201\pi$
$80$	1.17553	−	1.90214i	0.131428	−	0.212666i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.479537			−0.0529560
$83$	4.83322	−	2.79046i	0.530515	−	0.306293i	−0.210711	−	0.977548i	$-0.567578\pi$
$83$	4.83322	−	2.79046i	0.530515	−	0.306293i	0.741226	+	0.671255i	$0.234245\pi$
$84$	3.80308			0.414950
$85$	8.05742	−	13.0378i	0.873950	−	1.41415i
$86$	5.02016	+	8.69516i	0.541337	+	0.937624i
$87$	−1.35255	+	2.34269i	−0.145009	+	0.251163i
$88$	−3.84960			−0.410369
$89$	6.89417	−	3.98035i	0.730781	−	0.421916i	−0.0879270	−	0.996127i	$-0.528024\pi$
$89$	6.89417	−	3.98035i	0.730781	−	0.421916i	0.818708	+	0.574211i	$0.194691\pi$
$90$	2.23506	+	0.0669680i	0.235597	+	0.00705905i
$91$	−8.06938	+	4.65886i	−0.845901	+	0.488381i
$92$	−0.0328380	+	0.0568771i	−0.00342360	+	0.00592985i
$93$	4.06497	−	7.04073i	0.421518	−	0.730090i
$94$	−1.68192	+	0.971059i	−0.173477	+	0.100157i
$95$	0.0770330	−	2.57098i	0.00790342	−	0.263777i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−2.90742			−0.295204			−0.147602	−	0.989047i	$-0.547155\pi$
$97$	−2.90742			−0.295204			−0.147602	+	0.989047i	$0.547155\pi$
$98$	3.73171	−	6.46351i	0.376960	−	0.652913i
$99$	−1.92480	−	3.33385i	−0.193450	−	0.335065i
$100$	−2.23627	−	4.47204i	−0.223627	−	0.447204i
$101$	2.83091			0.281686			0.140843	−	0.990032i	$-0.455019\pi$
$101$	2.83091			0.281686			0.140843	+	0.990032i	$0.455019\pi$
$102$	−5.93600	+	3.42715i	−0.587751	+	0.339338i
$103$	−16.9217			−1.66734			−0.833672	−	0.552260i	$-0.813765\pi$
$103$	−16.9217			−1.66734			−0.833672	+	0.552260i	$0.813765\pi$
$104$	1.22502	−	2.12180i	0.120123	−	0.208060i
$105$	4.47063	−	7.23399i	0.436289	−	0.705965i
$106$	−4.83010	−	2.78866i	−0.469141	−	0.270858i
$107$	7.61741	+	4.39791i	0.736403	+	0.425162i	0.820760	−	0.571273i	$-0.193550\pi$
$107$	7.61741	+	4.39791i	0.736403	+	0.425162i	−0.0843572	+	0.996436i	$0.526884\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	−9.23933	+	5.33433i	−0.884968	+	0.510936i	−0.872293	−	0.488983i	$-0.837368\pi$
$109$	−9.23933	+	5.33433i	−0.884968	+	0.510936i	−0.0126746	+	0.999920i	$0.504035\pi$
$110$	−4.52531	+	7.32247i	−0.431472	+	0.698170i
$111$	5.81190	−	1.79493i	0.551642	−	0.170367i
$112$			3.80308i			0.359357i
$113$	2.96968	+	5.14363i	0.279364	+	0.483872i	0.971227	−	0.238157i	$-0.0765432\pi$
$113$	2.96968	+	5.14363i	0.279364	+	0.483872i	−0.691863	+	0.722029i	$0.743210\pi$
$114$	−0.575147	+	0.996184i	−0.0538675	+	0.0933012i
$115$	0.0695862	+	0.129323i	0.00648894	+	0.0120594i
$116$	−2.34269	−	1.35255i	−0.217514	−	0.125582i
$117$	2.45005			0.226507
$118$	−1.87894	−	1.08481i	−0.172970	−	0.0998646i
$119$			26.0675i			2.38960i
$120$	−0.0669680	+	2.23506i	−0.00611332	+	0.204033i
$121$	3.81941			0.347219
$122$			4.70229i			0.425725i
$123$	0.415291	−	0.239768i	0.0374455	−	0.0216192i
$124$	7.04073	+	4.06497i	0.632276	+	0.365045i
$125$	−11.1352	−	1.00332i	−0.995965	−	0.0897396i
$126$	−3.29356	+	1.90154i	−0.293414	+	0.169403i
$127$	−15.2426	+	8.80034i	−1.35257	+	0.780904i	−0.988608	−	0.150512i	$-0.951908\pi$
$127$	−15.2426	+	8.80034i	−1.35257	+	0.780904i	−0.363957	+	0.931416i	$0.618574\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−8.69516	−	5.02016i	−0.765567	−	0.442000i
$130$	−2.59591	−	4.82440i	−0.227677	−	0.423128i
$131$	−13.6533	+	7.88276i	−1.19290	+	0.688720i	−0.958963	−	0.283532i	$-0.908494\pi$
$131$	−13.6533	+	7.88276i	−1.19290	+	0.688720i	−0.233935	+	0.972252i	$0.575160\pi$
$132$	3.33385	−	1.92480i	0.290174	−	0.167532i
$133$	2.18733	+	3.78857i	0.189666	+	0.328511i
$134$			7.74340i			0.668928i
$135$	−1.96911	+	1.05954i	−0.169474	+	0.0911904i
$136$	−3.42715	−	5.93600i	−0.293876	−	0.509008i
$137$			17.0977i			1.46075i	0.683044	+	0.730377i	$0.260656\pi$
$137$			17.0977i			1.46075i	−0.683044	+	0.730377i	$0.739344\pi$
$138$		−	0.0656760i		−	0.00559072i
$139$	−8.88756	−	15.3937i	−0.753833	−	1.30568i	−0.945952	−	0.324306i	$-0.894869\pi$
$139$	−8.88756	−	15.3937i	−0.753833	−	1.30568i	0.192119	−	0.981372i	$-0.438464\pi$
$140$	7.23399	+	4.47063i	0.611384	+	0.377837i
$141$	0.971059	−	1.68192i	0.0817779	−	0.141643i
$142$	7.44169			0.624493
$143$	−4.71585	+	8.16808i	−0.394359	+	0.683050i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−5.32665	+	2.86616i	−0.442354	+	0.238022i
$146$	−5.90768	+	3.41080i	−0.488923	+	0.282280i
$147$			7.46342i			0.615572i
$148$	1.79493	+	5.81190i	0.147542	+	0.477736i
$149$	1.67946			0.137587			0.0687934	−	0.997631i	$-0.478085\pi$
$149$	1.67946			0.137587			0.0687934	+	0.997631i	$0.478085\pi$
$150$	4.17268	+	2.75477i	0.340698	+	0.224926i
$151$	7.33222	−	12.6998i	0.596687	−	1.03349i	−0.396619	−	0.917983i	$-0.629817\pi$
$151$	7.33222	−	12.6998i	0.596687	−	1.03349i	0.993306	−	0.115510i	$-0.0368501\pi$
$152$	−0.996184	−	0.575147i	−0.0808012	−	0.0466506i
$153$	3.42715	−	5.93600i	0.277069	−	0.479897i
$154$		−	14.6403i		−	1.17975i
$155$	16.0087	−	8.61397i	1.28585	−	0.691890i
$156$			2.45005i			0.196161i
$157$	−14.2552	+	8.23027i	−1.13769	+	0.656847i	−0.945858	−	0.324581i	$-0.894777\pi$
$157$	−14.2552	+	8.23027i	−1.13769	+	0.656847i	−0.191834	+	0.981427i	$0.561443\pi$
$158$		−	2.97186i		−	0.236428i
$159$	5.57732			0.442310
$160$	−2.23506	−	0.0669680i	−0.176697	−	0.00529429i
$161$	−0.216308	−	0.124886i	−0.0170475	−	0.00984237i
$162$	1.00000			0.0785674
$163$	9.83152	+	17.0287i	0.770064	+	1.33379i	0.937527	+	0.347911i	$0.113109\pi$
$163$	9.83152	+	17.0287i	0.770064	+	1.33379i	−0.167464	+	0.985878i	$0.553558\pi$
$164$	0.239768	+	0.415291i	0.0187228	+	0.0324288i
$165$	0.257800	−	8.60410i	0.0200697	−	0.669829i
$166$	−4.83322	−	2.79046i	−0.375131	−	0.216582i
$167$	−5.34341	+	9.25505i	−0.413485	+	0.716177i	−0.995268	−	0.0971667i	$-0.969022\pi$
$167$	−5.34341	+	9.25505i	−0.413485	+	0.716177i	0.581783	+	0.813344i	$0.302355\pi$
$168$	−1.90154	−	3.29356i	−0.146707	−	0.254104i
$169$	3.49864	+	6.05982i	0.269126	+	0.466140i
$170$	−15.3198	−	0.459019i	−1.17498	−	0.0352051i
$171$		−	1.15029i		−	0.0879652i
$172$	5.02016	−	8.69516i	0.382783	−	0.663000i
$173$	−9.41553	+	5.43606i	−0.715849	+	0.413296i	−0.813223	−	0.581952i	$-0.802289\pi$
$173$	−9.41553	+	5.43606i	−0.715849	+	0.413296i	0.0973739	+	0.995248i	$0.468956\pi$
$174$	2.70511			0.205074
$175$	17.0075	−	8.50470i	1.28565	−	0.642895i
$176$	1.92480	+	3.33385i	0.145087	+	0.251298i
$177$	2.16961			0.163078
$178$	−6.89417	−	3.98035i	−0.516740	−	0.298340i
$179$		−	8.35895i		−	0.624777i	−0.949954	−	0.312388i	$-0.898871\pi$
$179$		−	8.35895i		−	0.624777i	0.949954	−	0.312388i	$-0.101129\pi$
$180$	−1.05954	−	1.96911i	−0.0789732	−	0.146769i
$181$	9.39587	−	16.2741i	0.698389	−	1.20965i	−0.270635	−	0.962682i	$-0.587234\pi$
$181$	9.39587	−	16.2741i	0.698389	−	1.20965i	0.969025	−	0.246964i	$-0.0794329\pi$
$182$	8.06938	+	4.65886i	0.598142	+	0.345338i
$183$	−2.35114	−	4.07230i	−0.173802	−	0.301033i
$184$	0.0656760			0.00484170
$185$	13.1650	+	3.41786i	0.967913	+	0.251286i
$186$	−8.12994			−0.596116
$187$	13.1932	+	22.8512i	0.964779	+	1.67105i
$188$	1.68192	+	0.971059i	0.122667	+	0.0708217i
$189$	1.90154	−	3.29356i	0.138317	−	0.239572i
$190$	−2.26505	+	1.21878i	−0.164324	+	0.0884195i
$191$			13.1251i			0.949699i	0.880067	+	0.474850i	$0.157498\pi$
$191$			13.1251i			0.949699i	−0.880067	+	0.474850i	$0.842502\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−1.77545			−0.127800			−0.0639000	−	0.997956i	$-0.520354\pi$
$193$	−1.77545			−0.127800			−0.0639000	+	0.997956i	$0.520354\pi$
$194$	1.45371	+	2.51790i	0.104370	+	0.180775i
$195$	4.66033	+	2.88010i	0.333733	+	0.206248i
$196$	−7.46342			−0.533101
$197$	17.9982	−	10.3913i	1.28232	−	0.740347i	0.305047	−	0.952337i	$-0.401328\pi$
$197$	17.9982	−	10.3913i	1.28232	−	0.740347i	0.977272	+	0.211990i	$0.0679944\pi$
$198$	−1.92480	+	3.33385i	−0.136790	+	0.236926i
$199$		−	22.9945i		−	1.63003i	−0.579437	−	0.815017i	$-0.696727\pi$
$199$		−	22.9945i		−	1.63003i	0.579437	−	0.815017i	$-0.303273\pi$
$200$	−2.75477	+	4.17268i	−0.194791	+	0.295053i
$201$	−3.87170	−	6.70598i	−0.273089	−	0.473003i
$202$	−1.41545	−	2.45164i	−0.0995909	−	0.172496i
$203$	5.14388	−	8.90945i	0.361029	−	0.625321i
$204$	5.93600	+	3.42715i	0.415603	+	0.239948i
$205$	1.07180	+	0.0321136i	0.0748574	+	0.00224291i
$206$	8.46084	+	14.6546i	0.589495	+	1.02104i
$207$	0.0328380	+	0.0568771i	0.00228240	+	0.00395323i
$208$	−2.45005			−0.169880
$209$	3.83491	+	2.21409i	0.265266	+	0.153152i
$210$	−8.50013	−	0.254685i	−0.586565	−	0.0175749i
$211$	19.2357			1.32424			0.662120	−	0.749398i	$-0.269657\pi$
$211$	19.2357			1.32424			0.662120	+	0.749398i	$0.269657\pi$
$212$			5.57732i			0.383052i
$213$	−6.44470	+	3.72085i	−0.441583	+	0.254948i
$214$		−	8.79583i		−	0.601270i
$215$	−10.6381	−	19.7704i	−0.725511	−	1.34833i
$216$			1.00000i			0.0680414i
$217$	−15.4594	+	26.7765i	−1.04945	+	1.81771i
$218$	9.23933	+	5.33433i	0.625767	+	0.361287i
$219$	3.41080	−	5.90768i	0.230480	−	0.399204i
$220$	8.60410	+	0.257800i	0.580089	+	0.0173809i
$221$	−16.7933			−1.12964
$222$	−4.46040	−	4.13579i	−0.299363	−	0.277576i
$223$			21.9748i			1.47154i	0.677230	+	0.735771i	$0.263180\pi$
$223$			21.9748i			1.47154i	−0.677230	+	0.735771i	$0.736820\pi$
$224$	3.29356	−	1.90154i	0.220061	−	0.127052i
$225$	−4.99103	−	0.299356i	−0.332735	−	0.0199571i
$226$	2.96968	−	5.14363i	0.197540	−	0.342149i
$227$	5.60894	−	9.71497i	0.372278	−	0.644805i	−0.617637	−	0.786463i	$-0.711910\pi$
$227$	5.60894	−	9.71497i	0.372278	−	0.644805i	0.989916	+	0.141658i	$0.0452434\pi$
$228$	1.15029			0.0761801
$229$	−8.04647	+	13.9369i	−0.531726	+	0.920976i	0.467588	+	0.883946i	$0.345123\pi$
$229$	−8.04647	+	13.9369i	−0.531726	+	0.920976i	−0.999314	+	0.0370298i	$0.988210\pi$
$230$	0.0772040	−	0.124925i	0.00509068	−	0.00823731i
$231$	7.32017	+	12.6789i	0.481632	+	0.834210i
$232$			2.70511i			0.177599i
$233$		−	23.3335i		−	1.52863i	−0.644843	−	0.764315i	$-0.723077\pi$
$233$		−	23.3335i		−	1.52863i	0.644843	−	0.764315i	$-0.276923\pi$
$234$	−1.22502	−	2.12180i	−0.0800822	−	0.138706i
$235$	3.82424	−	2.05774i	0.249466	−	0.134232i
$236$			2.16961i			0.141230i
$237$	1.48593	+	2.57370i	0.0965214	+	0.167180i
$238$	22.5751	−	13.0337i	1.46332	−	0.844851i
$239$	−0.514328	+	0.296947i	−0.0332691	+	0.0192079i	−0.516542	−	0.856262i	$-0.672781\pi$
$239$	−0.514328	+	0.296947i	−0.0332691	+	0.0192079i	0.483273	+	0.875470i	$0.339448\pi$
$240$	1.96911	−	1.05954i	0.127105	−	0.0683928i
$241$	9.13422	+	5.27364i	0.588387	+	0.339705i	0.764459	−	0.644672i	$-0.223006\pi$
$241$	9.13422	+	5.27364i	0.588387	+	0.339705i	−0.176073	+	0.984377i	$0.556339\pi$
$242$	−1.90971	−	3.30771i	−0.122761	−	0.212627i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	4.07230	−	2.35114i	0.260702	−	0.150517i
$245$	−8.77346	+	14.1965i	−0.560516	+	0.906979i
$246$	−0.415291	−	0.239768i	−0.0264780	−	0.0152871i
$247$	−2.44070	+	1.40914i	−0.155298	+	0.0896612i
$248$		−	8.12994i		−	0.516252i
$249$	5.58092			0.353677
$250$	4.69872	+	10.1451i	0.297173	+	0.641629i
$251$		−	28.9037i		−	1.82439i	−0.409761	−	0.912193i	$-0.634388\pi$
$251$		−	28.9037i		−	1.82439i	0.409761	−	0.912193i	$-0.365612\pi$
$252$	3.29356	+	1.90154i	0.207475	+	0.119786i
$253$	−0.252826			−0.0158951
$254$	15.2426	+	8.80034i	0.956408	+	0.552182i
$255$	13.4969	−	7.26238i	0.845206	−	0.454788i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.71460	+	8.16592i	0.294089	+	0.509376i	0.974772	−	0.223201i	$-0.0716506\pi$
$257$	4.71460	+	8.16592i	0.294089	+	0.509376i	−0.680684	+	0.732577i	$0.738317\pi$
$258$			10.0403i			0.625082i
$259$	−22.1031	+	6.82625i	−1.37342	+	0.424163i
$260$	−2.88010	+	4.66033i	−0.178616	+	0.289021i
$261$	−2.34269	+	1.35255i	−0.145009	+	0.0837211i
$262$	13.6533	+	7.88276i	0.843506	+	0.486998i
$263$	27.0317	+	15.6068i	1.66685	+	0.962355i	0.969321	+	0.245796i	$0.0790495\pi$
$263$	27.0317	+	15.6068i	1.66685	+	0.962355i	0.697527	+	0.716559i	$0.254284\pi$
$264$	−3.33385	−	1.92480i	−0.205184	−	0.118463i
$265$	10.6088	+	6.55629i	0.651695	+	0.402750i
$266$	2.18733	−	3.78857i	0.134114	−	0.232292i
$267$	7.96070			0.487187
$268$	6.70598	−	3.87170i	0.409633	−	0.236502i
$269$	−2.05025			−0.125006			−0.0625031	−	0.998045i	$-0.519908\pi$
$269$	−2.05025			−0.125006			−0.0625031	+	0.998045i	$0.519908\pi$
$270$	1.90214	+	1.17553i	0.115760	+	0.0715404i
$271$	−3.28422	−	5.68843i	−0.199502	−	0.345547i	0.748865	−	0.662722i	$-0.230599\pi$
$271$	−3.28422	−	5.68843i	−0.199502	−	0.345547i	−0.948367	+	0.317175i	$0.897266\pi$
$272$	−3.42715	+	5.93600i	−0.207801	+	0.359923i
$273$	−9.31772			−0.563934
$274$	14.8070	−	8.54885i	0.894526	−	0.516455i
$275$	10.6047	−	16.0631i	0.639490	−	0.968644i
$276$	−0.0568771	+	0.0328380i	−0.00342360	+	0.00197662i
$277$	6.72455	−	11.6473i	0.404039	−	0.699816i	−0.590170	−	0.807279i	$-0.700939\pi$
$277$	6.72455	−	11.6473i	0.404039	−	0.699816i	0.994209	+	0.107463i	$0.0342726\pi$
$278$	−8.88756	+	15.3937i	−0.533041	+	0.923254i
$279$	7.04073	−	4.06497i	0.421518	−	0.243363i
$280$	0.254685	−	8.50013i	0.0152203	−	0.507980i
$281$	22.2706	−	12.8579i	1.32855	−	0.767040i	0.343477	−	0.939161i	$-0.388395\pi$
$281$	22.2706	−	12.8579i	1.32855	−	0.767040i	0.985076	+	0.172121i	$0.0550621\pi$
$282$	−1.94212			−0.115651
$283$	9.20159	−	15.9376i	0.546978	−	0.947394i	−0.451502	−	0.892270i	$-0.649111\pi$
$283$	9.20159	−	15.9376i	0.546978	−	0.947394i	0.998480	−	0.0551234i	$-0.0175552\pi$
$284$	−3.72085	−	6.44470i	−0.220792	−	0.382422i
$285$	1.35220	−	2.18802i	0.0800977	−	0.129607i
$286$	9.43169			0.557708
$287$	−1.57938	+	0.911858i	−0.0932281	+	0.0538253i
$288$	−1.00000			−0.0589256
$289$	−14.9907	+	25.9647i	−0.881807	+	1.52733i
$290$	5.14550	+	3.17993i	0.302154	+	0.186732i
$291$	−2.51790	−	1.45371i	−0.147602	−	0.0852180i
$292$	5.90768	+	3.41080i	0.345721	+	0.199602i
$293$	−13.9533	−	8.05596i	−0.815162	−	0.470634i	0.0335831	−	0.999436i	$-0.489308\pi$
$293$	−13.9533	−	8.05596i	−0.815162	−	0.470634i	−0.848745	+	0.528802i	$0.822641\pi$
$294$	6.46351	−	3.73171i	0.376960	−	0.217638i
$295$	4.12691	+	2.55044i	0.240278	+	0.148493i
$296$	4.13579	−	4.46040i	0.240388	−	0.259256i
$297$		−	3.84960i		−	0.223376i
$298$	−0.839730	−	1.45446i	−0.0486443	−	0.0842543i
$299$	0.0804546	−	0.139351i	0.00465281	−	0.00805891i
$300$	0.299356	−	4.99103i	0.0172833	−	0.288157i
$301$	33.0684	+	19.0921i	1.90603	+	1.10045i
$302$	−14.6644			−0.843843
$303$	2.45164	+	1.41545i	0.140843	+	0.0813156i
$304$			1.15029i			0.0659739i
$305$	0.314903	−	10.5099i	0.0180313	−	0.601796i
$306$	−6.85430			−0.391834
$307$		−	25.0434i		−	1.42930i	−0.699482	−	0.714650i	$-0.746586\pi$
$307$		−	25.0434i		−	1.42930i	0.699482	−	0.714650i	$-0.253414\pi$
$308$	−12.6789	+	7.32017i	−0.722447	+	0.417105i
$309$	−14.6546	−	8.46084i	−0.833672	−	0.481321i
$310$	−15.4643	−	9.55697i	−0.878312	−	0.542800i
$311$	−15.5003	+	8.94910i	−0.878941	+	0.507457i	−0.870309	−	0.492506i	$-0.836081\pi$
$311$	−15.5003	+	8.94910i	−0.878941	+	0.507457i	−0.00863174	+	0.999963i	$0.502748\pi$
$312$	2.12180	−	1.22502i	0.120123	−	0.0693532i
$313$	5.62602	+	9.74455i	0.318001	+	0.550795i	0.980071	−	0.198648i	$-0.0636550\pi$
$313$	5.62602	+	9.74455i	0.318001	+	0.550795i	−0.662070	+	0.749442i	$0.730322\pi$
$314$	14.2552	+	8.23027i	0.804470	+	0.464461i
$315$	7.48867	−	4.02950i	0.421939	−	0.227037i
$316$	−2.57370	+	1.48593i	−0.144782	+	0.0835900i
$317$	−2.29777	+	1.32662i	−0.129055	+	0.0745102i	−0.563138	−	0.826363i	$-0.690406\pi$
$317$	−2.29777	+	1.32662i	−0.129055	+	0.0745102i	0.434082	+	0.900873i	$0.357073\pi$
$318$	−2.78866	−	4.83010i	−0.156380	−	0.270858i
$319$		−	10.4136i		−	0.583049i
$320$	1.05954	+	1.96911i	0.0592299	+	0.110076i
$321$	4.39791	+	7.61741i	0.245468	+	0.425162i
$322$			0.249771i			0.0139192i
$323$			7.88447i			0.438703i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	5.47895	+	10.9567i	0.303918	+	0.607768i
$326$	9.83152	−	17.0287i	0.544517	−	0.943132i
$327$	−10.6687			−0.589979
$328$	0.239768	−	0.415291i	0.0132390	−	0.0229306i
$329$	−3.69301	+	6.39649i	−0.203602	+	0.352650i
$330$	−7.58027	+	4.07879i	−0.417280	+	0.224530i
$331$	15.6212	−	9.01889i	0.858618	−	0.495723i	−0.00493151	−	0.999988i	$-0.501570\pi$
$331$	15.6212	−	9.01889i	0.858618	−	0.495723i	0.863549	+	0.504265i	$0.168236\pi$
$332$			5.58092i			0.306293i
$333$	5.93072	+	1.35150i	0.325001	+	0.0740618i
$334$	10.6868			0.584756
$335$	0.518560	−	17.3070i	0.0283320	−	0.945582i
$336$	−1.90154	+	3.29356i	−0.103738	+	0.179679i
$337$	17.1397	+	9.89562i	0.933660	+	0.539049i	0.887967	−	0.459907i	$-0.152117\pi$
$337$	17.1397	+	9.89562i	0.933660	+	0.539049i	0.0456926	+	0.998956i	$0.485451\pi$
$338$	3.49864	−	6.05982i	0.190301	−	0.329611i
$339$			5.93935i			0.322581i
$340$	7.26238	+	13.4969i	0.393858	+	0.731969i
$341$			31.2970i			1.69483i
$342$	−0.996184	+	0.575147i	−0.0538675	+	0.0311004i
$343$		−	1.76242i		−	0.0951618i
$344$	−10.0403			−0.541337
$345$	−0.00439819	+	0.146790i	−0.000236791	+	0.00790292i
$346$	9.41553	+	5.43606i	0.506182	+	0.292244i
$347$	5.12556			0.275155			0.137577	−	0.990491i	$-0.456068\pi$
$347$	5.12556			0.275155			0.137577	+	0.990491i	$0.456068\pi$
$348$	−1.35255	−	2.34269i	−0.0725046	−	0.125582i
$349$	12.9643	+	22.4549i	0.693964	+	1.20198i	0.970529	+	0.240985i	$0.0774706\pi$
$349$	12.9643	+	22.4549i	0.693964	+	1.20198i	−0.276565	+	0.960995i	$0.589196\pi$
$350$	−15.8690	−	10.4766i	−0.848236	−	0.559997i
$351$	2.12180	+	1.22502i	0.113253	+	0.0653869i
$352$	1.92480	−	3.33385i	0.102592	−	0.177695i
$353$	2.11906	+	3.67032i	0.112786	+	0.195352i	0.916893	−	0.399134i	$-0.130689\pi$
$353$	2.11906	+	3.67032i	0.112786	+	0.195352i	−0.804106	+	0.594485i	$0.797356\pi$
$354$	−1.08481	−	1.87894i	−0.0576568	−	0.0998646i
$355$	−16.6327	−	0.498356i	−0.882770	−	0.0264500i
$356$			7.96070i			0.421916i
$357$	−13.0337	+	22.5751i	−0.689818	+	1.19480i
$358$	−7.23906	+	4.17947i	−0.382596	+	0.220892i
$359$	−11.0273			−0.582000			−0.291000	−	0.956723i	$-0.593988\pi$
$359$	−11.0273			−0.582000			−0.291000	+	0.956723i	$0.593988\pi$
$360$	−1.17553	+	1.90214i	−0.0619558	+	0.100252i
$361$	−8.83841	−	15.3086i	−0.465180	−	0.805715i
$362$	−18.7917			−0.987672
$363$	3.30771	+	1.90971i	0.173610	+	0.100234i
$364$		−	9.31772i		−	0.488381i
$365$	13.4325	−	7.22773i	0.703087	−	0.378317i
$366$	−2.35114	+	4.07230i	−0.122896	+	0.212863i
$367$	−0.710723	−	0.410336i	−0.0370994	−	0.0214194i	0.481336	−	0.876536i	$-0.340152\pi$
$367$	−0.710723	−	0.410336i	−0.0370994	−	0.0214194i	−0.518435	+	0.855117i	$0.673485\pi$
$368$	−0.0328380	−	0.0568771i	−0.00171180	−	0.00296492i
$369$	0.479537			0.0249637
$370$	−3.62257	−	13.1102i	−0.188328	−	0.681566i
$371$	−21.2110			−1.10122
$372$	4.06497	+	7.04073i	0.210759	+	0.365045i
$373$	−24.6060	−	14.2063i	−1.27405	−	0.735572i	−0.298301	−	0.954472i	$-0.596420\pi$
$373$	−24.6060	−	14.2063i	−1.27405	−	0.735572i	−0.975747	+	0.218899i	$0.929753\pi$
$374$	13.1932	−	22.8512i	0.682202	−	1.18161i
$375$	−9.14173	−	6.43651i	−0.472077	−	0.332380i
$376$		−	1.94212i		−	0.100157i
$377$	5.73971	+	3.31382i	0.295610	+	0.170670i
$378$	−3.80308			−0.195609
$379$	2.60445	+	4.51103i	0.133781	+	0.231716i	0.925131	−	0.379647i	$-0.123955\pi$
$379$	2.60445	+	4.51103i	0.133781	+	0.231716i	−0.791350	+	0.611364i	$0.790621\pi$
$380$	2.18802	+	1.35220i	0.112243	+	0.0693666i
$381$	−17.6007			−0.901710
$382$	11.3667	−	6.56255i	0.581570	−	0.335769i
$383$	−3.04474	+	5.27364i	−0.155579	+	0.269470i	−0.933270	−	0.359177i	$-0.883058\pi$
$383$	−3.04474	+	5.27364i	−0.155579	+	0.269470i	0.777691	+	0.628647i	$0.216391\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−0.980434	+	32.7221i	−0.0499676	+	1.66767i
$386$	0.887727	+	1.53759i	0.0451841	+	0.0782612i
$387$	−5.02016	−	8.69516i	−0.255189	−	0.442000i
$388$	1.45371	−	2.51790i	0.0738009	−	0.127827i
$389$	−24.6454	−	14.2290i	−1.24957	−	0.721441i	−0.278549	−	0.960422i	$-0.589853\pi$
$389$	−24.6454	−	14.2290i	−1.24957	−	0.721441i	−0.971024	+	0.238981i	$0.923187\pi$
$390$	0.164075	−	5.47601i	0.00830825	−	0.277289i
$391$	−0.225082	−	0.389853i	−0.0113829	−	0.0197157i
$392$	3.73171	+	6.46351i	0.188480	+	0.326457i
$393$	−15.7655			−0.795265
$394$	−17.9982	−	10.3913i	−0.906737	−	0.523505i
$395$	−0.199019	+	6.64229i	−0.0100137	+	0.334210i
$396$	3.84960			0.193450
$397$			34.7007i			1.74158i	0.491656	+	0.870790i	$0.336392\pi$
$397$			34.7007i			1.74158i	−0.491656	+	0.870790i	$0.663608\pi$
$398$	−19.9138	+	11.4972i	−0.998188	+	0.576304i
$399$			4.37466i			0.219007i
$400$	4.99103	+	0.299356i	0.249552	+	0.0149678i
$401$			1.30549i			0.0651933i	0.999469	+	0.0325967i	$0.0103777\pi$
$401$			1.30549i			0.0651933i	−0.999469	+	0.0325967i	$0.989622\pi$
$402$	−3.87170	+	6.70598i	−0.193103	+	0.334464i
$403$	−17.2501	−	9.95936i	−0.859289	−	0.496111i
$404$	−1.41545	+	2.45164i	−0.0704214	+	0.121973i
$405$	−2.23506	−	0.0669680i	−0.111061	−	0.00332767i
$406$	−10.2878			−0.510572
$407$	−15.9211	+	17.1708i	−0.789182	+	0.851123i
$408$		−	6.85430i		−	0.339338i
$409$	15.6275	−	9.02256i	0.772731	−	0.446137i	−0.0611167	−	0.998131i	$-0.519466\pi$
$409$	15.6275	−	9.02256i	0.772731	−	0.446137i	0.833848	+	0.551994i	$0.186133\pi$
$410$	−0.508087	−	0.944259i	−0.0250926	−	0.0466336i
$411$	−8.54885	+	14.8070i	−0.421684	+	0.730377i
$412$	8.46084	−	14.6546i	0.416836	−	0.721981i
$413$	−8.25121			−0.406016
$414$	0.0328380	−	0.0568771i	0.00161390	−	0.00279536i
$415$	10.6157	+	6.56053i	0.521104	+	0.322044i
$416$	1.22502	+	2.12180i	0.0600617	+	0.104030i
$417$		−	17.7751i		−	0.870452i
$418$		−	4.42817i		−	0.216589i
$419$	−2.21154	−	3.83049i	−0.108041	−	0.187132i	0.806936	−	0.590639i	$-0.201124\pi$
$419$	−2.21154	−	3.83049i	−0.108041	−	0.187132i	−0.914976	+	0.403507i	$0.867791\pi$
$420$	4.02950	+	7.48867i	0.196620	+	0.365410i
$421$		−	36.6940i		−	1.78835i	−0.447713	−	0.894177i	$-0.647761\pi$
$421$		−	36.6940i		−	1.78835i	0.447713	−	0.894177i	$-0.352239\pi$
$422$	−9.61784	−	16.6586i	−0.468189	−	0.810927i
$423$	1.68192	−	0.971059i	0.0817779	−	0.0472145i
$424$	4.83010	−	2.78866i	0.234570	−	0.135429i
$425$	34.2100	+	2.05187i	1.65943	+	0.0995305i
$426$	6.44470	+	3.72085i	0.312247	+	0.180276i
$427$	8.94159	+	15.4873i	0.432714	+	0.749482i
$428$	−7.61741	+	4.39791i	−0.368201	+	0.212581i
$429$	−8.16808	+	4.71585i	−0.394359	+	0.227683i
$430$	−11.8027	+	19.0981i	−0.569175	+	0.920991i
$431$	7.11522	+	4.10797i	0.342728	+	0.197874i	0.661478	−	0.749965i	$-0.269930\pi$
$431$	7.11522	+	4.10797i	0.342728	+	0.197874i	−0.318750	+	0.947839i	$0.603263\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$		−	35.2652i		−	1.69474i	−0.531005	−	0.847368i	$-0.678186\pi$
$433$		−	35.2652i		−	1.69474i	0.531005	−	0.847368i	$-0.321814\pi$
$434$	30.9188			1.48415
$435$	−6.04610	−	0.181156i	−0.289888	−	0.00868576i
$436$		−	10.6687i		−	0.510936i
$437$	−0.0654254	−	0.0377734i	−0.00312972	−	0.00180695i
$438$	−6.82160			−0.325949
$439$	−0.786419	−	0.454039i	−0.0375337	−	0.0216701i	0.481116	−	0.876657i	$-0.340232\pi$
$439$	−0.786419	−	0.454039i	−0.0375337	−	0.0216701i	−0.518649	+	0.854987i	$0.673565\pi$
$440$	−4.07879	−	7.58027i	−0.194449	−	0.361375i
$441$	−3.73171	+	6.46351i	−0.177700	+	0.307786i
$442$	8.39667	+	14.5435i	0.399389	+	0.691762i
$443$			35.0014i			1.66297i	0.555548	+	0.831484i	$0.312508\pi$
$443$			35.0014i			1.66297i	−0.555548	+	0.831484i	$0.687492\pi$
$444$	−1.35150	+	5.93072i	−0.0641394	+	0.281460i
$445$	15.1424	+	9.35803i	0.717817	+	0.443613i
$446$	19.0307	−	10.9874i	0.901132	−	0.520269i
$447$	1.45446	+	0.839730i	0.0687934	+	0.0397179i
$448$	−3.29356	−	1.90154i	−0.155606	−	0.0898393i
$449$	17.3266	+	10.0035i	0.817692	+	0.472095i	0.849620	−	0.527395i	$-0.176831\pi$
$449$	17.3266	+	10.0035i	0.817692	+	0.472095i	−0.0319278	+	0.999490i	$0.510165\pi$
$450$	2.23627	+	4.47204i	0.105419	+	0.210814i
$451$	−0.923012	+	1.59870i	−0.0434629	+	0.0752800i
$452$	−5.93935			−0.279364
$453$	12.6998	−	7.33222i	0.596687	−	0.344498i
$454$	−11.2179			−0.526481
$455$	−17.7236	−	10.9532i	−0.830895	−	0.513496i
$456$	−0.575147	−	0.996184i	−0.0269337	−	0.0466506i
$457$	−6.37769	+	11.0465i	−0.298336	+	0.516733i	−0.975755	−	0.218864i	$-0.929765\pi$
$457$	−6.37769	+	11.0465i	−0.298336	+	0.516733i	0.677420	+	0.735597i	$0.263098\pi$
$458$	16.0929			0.751974
$459$	5.93600	−	3.42715i	0.277069	−	0.159966i
$460$	−0.146790	−	0.00439819i	−0.00684413	−	0.000205067i
$461$	19.2166	−	11.0947i	0.895005	−	0.516731i	0.0194288	−	0.999811i	$-0.493815\pi$
$461$	19.2166	−	11.0947i	0.895005	−	0.516731i	0.875576	+	0.483080i	$0.160482\pi$
$462$	7.32017	−	12.6789i	0.340565	−	0.589876i
$463$	6.56761	−	11.3754i	0.305223	−	0.528661i	−0.672088	−	0.740471i	$-0.734602\pi$
$463$	6.56761	−	11.3754i	0.305223	−	0.528661i	0.977311	+	0.211810i	$0.0679358\pi$
$464$	2.34269	−	1.35255i	0.108757	−	0.0627908i
$465$	18.1709	+	0.544446i	0.842657	+	0.0252481i
$466$	−20.2074	+	11.6668i	−0.936091	+	0.540453i
$467$	2.63986			0.122158			0.0610790	−	0.998133i	$-0.480546\pi$
$467$	2.63986			0.122158			0.0610790	+	0.998133i	$0.480546\pi$
$468$	−1.22502	+	2.12180i	−0.0566267	+	0.0980803i
$469$	14.7244	+	25.5034i	0.679909	+	1.17764i
$470$	−3.69418	−	2.28301i	−0.170400	−	0.105308i
$471$	−16.4605			−0.758461
$472$	1.87894	−	1.08481i	0.0864852	−	0.0499323i
$473$	38.6512			1.77718
$474$	1.48593	−	2.57370i	0.0682509	−	0.118214i
$475$	5.14416	−	2.57236i	0.236030	−	0.118028i
$476$	−22.5751	−	13.0337i	−1.03473	−	0.597400i
$477$	4.83010	+	2.78866i	0.221155	+	0.127684i
$478$	0.514328	+	0.296947i	0.0235248	+	0.0135821i
$479$	−9.66298	+	5.57892i	−0.441513	+	0.254907i	−0.704239	−	0.709963i	$-0.748712\pi$
$479$	−9.66298	+	5.57892i	−0.441513	+	0.254907i	0.262726	+	0.964870i	$0.415378\pi$
$480$	−1.90214	−	1.17553i	−0.0868204	−	0.0536553i
$481$	−4.39765	−	14.2394i	−0.200516	−	0.649262i
$482$		−	10.5473i		−	0.480416i
$483$	−0.124886	−	0.216308i	−0.00568249	−	0.00984237i
$484$	−1.90971	+	3.30771i	−0.0868048	+	0.150350i
$485$	−3.08052	−	5.72502i	−0.139879	−	0.259960i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−25.4527			−1.15337			−0.576686	−	0.816966i	$-0.695654\pi$
$487$	−25.4527			−1.15337			−0.576686	+	0.816966i	$0.695654\pi$
$488$	−4.07230	−	2.35114i	−0.184344	−	0.106431i
$489$			19.6630i			0.889193i
$490$	16.6812	+	0.499811i	0.753581	+	0.0225791i
$491$	16.1537			0.729007			0.364503	−	0.931202i	$-0.381239\pi$
$491$	16.1537			0.729007			0.364503	+	0.931202i	$0.381239\pi$
$492$			0.479537i			0.0216192i
$493$	16.0575	−	9.27082i	0.723195	−	0.417537i
$494$	2.44070	+	1.40914i	0.109812	+	0.0634001i
$495$	4.52531	−	7.32247i	0.203398	−	0.329121i
$496$	−7.04073	+	4.06497i	−0.316138	+	0.182522i
$497$	24.5097	−	14.1507i	1.09941	−	0.634745i
$498$	−2.79046	−	4.83322i	−0.125044	−	0.216582i
$499$	−26.9210	−	15.5428i	−1.20515	−	0.695793i	−0.243453	−	0.969913i	$-0.578280\pi$
$499$	−26.9210	−	15.5428i	−1.20515	−	0.695793i	−0.961696	+	0.274119i	$0.911614\pi$
$500$	6.43651	−	9.14173i	0.287850	−	0.408831i
$501$	−9.25505	+	5.34341i	−0.413485	+	0.238726i
$502$	−25.0313	+	14.4519i	−1.11720	+	0.645018i
$503$	5.22198	+	9.04473i	0.232836	+	0.403284i	0.958642	−	0.284616i	$-0.0918660\pi$
$503$	5.22198	+	9.04473i	0.232836	+	0.403284i	−0.725805	+	0.687900i	$0.758533\pi$
$504$		−	3.80308i		−	0.169403i
$505$	2.99945	+	5.57435i	0.133474	+	0.248056i
$506$	0.126413	+	0.218954i	0.00561975	+	0.00973370i
$507$			6.99728i			0.310760i
$508$		−	17.6007i		−	0.780904i
$509$	−7.95848	−	13.7845i	−0.352753	−	0.610987i	0.633977	−	0.773352i	$-0.281421\pi$
$509$	−7.95848	−	13.7845i	−0.352753	−	0.610987i	−0.986731	+	0.162365i	$0.948088\pi$
$510$	−13.0378	−	8.05742i	−0.577325	−	0.356789i
$511$	−12.9715	+	22.4674i	−0.573827	+	0.993898i
$512$	1.00000			0.0441942
$513$	0.575147	−	0.996184i	0.0253934	−	0.0439826i
$514$	4.71460	−	8.16592i	0.207952	−	0.360183i
$515$	−17.9291	−	33.3206i	−0.790053	−	1.46828i
$516$	8.69516	−	5.02016i	0.382783	−	0.221000i
$517$			7.47637i			0.328810i
$518$	16.9633	+	15.7288i	0.745324	+	0.691082i
$519$	−10.8721			−0.477233
$520$	5.47601	+	0.164075i	0.240139	+	0.00719515i
$521$	−14.8542	+	25.7282i	−0.650774	+	1.12717i	0.332161	+	0.943223i	$0.392222\pi$
$521$	−14.8542	+	25.7282i	−0.650774	+	1.12717i	−0.982935	+	0.183951i	$0.941111\pi$
$522$	2.34269	+	1.35255i	0.102537	+	0.0591997i
$523$	18.5161	−	32.0708i	0.809651	−	1.40236i	−0.103455	−	0.994634i	$-0.532990\pi$
$523$	18.5161	−	32.0708i	0.809651	−	1.40236i	0.913106	−	0.407723i	$-0.133677\pi$
$524$		−	15.7655i		−	0.688720i
$525$	18.9813	+	1.13847i	0.828411	+	0.0496871i
$526$		−	31.2136i		−	1.36098i
$527$	−48.2593	+	27.8625i	−2.10221	+	1.21371i
$528$			3.84960i			0.167532i
$529$	−22.9957			−0.999812
$530$	0.373502	−	12.4657i	0.0162239	−	0.541474i
$531$	1.87894	+	1.08481i	0.0815391	+	0.0470766i
$532$	−4.37466			−0.189666
$533$	−0.587443	−	1.01748i	−0.0254450	−	0.0440720i
$534$	−3.98035	−	6.89417i	−0.172247	−	0.298340i
$535$	−0.589039	+	19.6592i	−0.0254664	+	0.849943i
$536$	−6.70598	−	3.87170i	−0.289654	−	0.167232i
$537$	4.17947	−	7.23906i	0.180358	−	0.312388i
$538$	1.02513	+	1.77557i	0.0441963	+	0.0765503i
$539$	−14.3656	−	24.8819i	−0.618770	−	1.07174i
$540$	0.0669680	−	2.23506i	0.00288185	−	0.0961819i
$541$		−	5.98204i		−	0.257188i	−0.991697	−	0.128594i	$-0.958954\pi$
$541$		−	5.98204i		−	0.257188i	0.991697	−	0.128594i	$-0.0410464\pi$
$542$	−3.28422	+	5.68843i	−0.141069	+	0.244339i
$543$	16.2741	−	9.39587i	0.698389	−	0.403215i
$544$	6.85430			0.293876
$545$	−20.2933	−	12.5413i	−0.869269	−	0.537211i
$546$	4.65886	+	8.06938i	0.199381	+	0.345338i
$547$	−7.81210			−0.334021			−0.167011	−	0.985955i	$-0.553411\pi$
$547$	−7.81210			−0.334021			−0.167011	+	0.985955i	$0.553411\pi$
$548$	−14.8070	−	8.54885i	−0.632525	−	0.365189i
$549$		−	4.70229i		−	0.200689i
$550$	−19.2135	−	1.15240i	−0.819265	−	0.0491385i
$551$	1.55584	−	2.69479i	0.0662809	−	0.114802i
$552$	0.0568771	+	0.0328380i	0.00242085	+	0.00139768i
$553$	−5.65110	−	9.78800i	−0.240309	−	0.416228i
$554$	−13.4491			−0.571398
$555$	9.69233	+	9.54247i	0.411416	+	0.405055i
$556$	17.7751			0.753833
$557$	1.26410	+	2.18949i	0.0535618	+	0.0927717i	0.891563	−	0.452896i	$-0.149609\pi$
$557$	1.26410	+	2.18949i	0.0535618	+	0.0927717i	−0.838001	+	0.545668i	$0.816276\pi$
$558$	−7.04073	−	4.06497i	−0.298058	−	0.172084i
$559$	−12.2996	+	21.3035i	−0.520218	+	0.901044i
$560$	−7.48867	+	4.02950i	−0.316454	+	0.170278i
$561$			26.3863i			1.11403i
$562$	−22.2706	−	12.8579i	−0.939428	−	0.542379i
$563$	−6.95366			−0.293062			−0.146531	−	0.989206i	$-0.546811\pi$
$563$	−6.95366			−0.293062			−0.146531	+	0.989206i	$0.546811\pi$
$564$	0.971059	+	1.68192i	0.0408889	+	0.0708217i
$565$	−6.98188	+	11.2975i	−0.293730	+	0.475288i
$566$	−18.4032			−0.773544
$567$	3.29356	−	1.90154i	0.138317	−	0.0798572i
$568$	−3.72085	+	6.44470i	−0.156123	+	0.270413i
$569$		−	18.5866i		−	0.779192i	−0.920986	−	0.389596i	$-0.872615\pi$
$569$		−	18.5866i		−	0.779192i	0.920986	−	0.389596i	$-0.127385\pi$
$570$	−2.57098	−	0.0770330i	−0.107687	−	0.00322656i
$571$	0.540231	+	0.935708i	0.0226080	+	0.0391582i	0.877108	−	0.480293i	$-0.159470\pi$
$571$	0.540231	+	0.935708i	0.0226080	+	0.0391582i	−0.854500	+	0.519451i	$0.826136\pi$
$572$	−4.71585	−	8.16808i	−0.197179	−	0.341525i
$573$	−6.56255	+	11.3667i	−0.274155	+	0.474850i
$574$	1.57938	+	0.911858i	0.0659222	+	0.0380602i
$575$	−0.180922	+	0.274045i	−0.00754497	+	0.0114285i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	13.4705	+	23.3317i	0.560786	+	0.971310i	0.997428	+	0.0716745i	$0.0228343\pi$
$577$	13.4705	+	23.3317i	0.560786	+	0.971310i	−0.436642	+	0.899635i	$0.643832\pi$
$578$	29.9814			1.24706
$579$	−1.53759	−	0.887727i	−0.0639000	−	0.0368927i
$580$	0.181156	−	6.04610i	0.00752209	−	0.251050i
$581$	−21.2247			−0.880549
$582$			2.90742i			0.120516i
$583$	−18.5939	+	10.7352i	−0.770082	+	0.444607i
$584$		−	6.82160i		−	0.282280i
$585$	2.59591	+	4.82440i	0.107328	+	0.199464i
$586$			16.1119i			0.665577i
$587$	7.31683	−	12.6731i	0.301998	−	0.523076i	−0.674590	−	0.738192i	$-0.735680\pi$
$587$	7.31683	−	12.6731i	0.301998	−	0.523076i	0.976588	+	0.215116i	$0.0690130\pi$
$588$	−6.46351	−	3.73171i	−0.266551	−	0.153893i
$589$	−4.67591	+	8.09892i	−0.192668	+	0.333710i
$590$	0.145295	−	4.84923i	0.00598169	−	0.199640i
$591$	20.7825			0.854880
$592$	−5.93072	−	1.35150i	−0.243751	−	0.0555463i
$593$		−	8.93492i		−	0.366913i	−0.983028	−	0.183457i	$-0.941271\pi$
$593$		−	8.93492i		−	0.366913i	0.983028	−	0.183457i	$-0.0587287\pi$
$594$	−3.33385	+	1.92480i	−0.136790	+	0.0789755i
$595$	−51.3296	+	27.6194i	−2.10431	+	1.13229i
$596$	−0.839730	+	1.45446i	−0.0343967	+	0.0595768i
$597$	11.4972	−	19.9138i	0.470550	−	0.815017i
$598$	−0.160909			−0.00658007
$599$	−20.5035	+	35.5132i	−0.837752	+	1.45103i	0.0540178	+	0.998540i	$0.482797\pi$
$599$	−20.5035	+	35.5132i	−0.837752	+	1.45103i	−0.891770	+	0.452489i	$0.850536\pi$
$600$	−4.47204	+	2.23627i	−0.182570	+	0.0912952i
$601$	−20.0982	−	34.8112i	−0.819824	−	1.41998i	−0.905812	−	0.423680i	$-0.860738\pi$
$601$	−20.0982	−	34.8112i	−0.819824	−	1.41998i	0.0859879	−	0.996296i	$-0.472595\pi$
$602$		−	38.1841i		−	1.55627i
$603$		−	7.74340i		−	0.315335i
$604$	7.33222	+	12.6998i	0.298344	+	0.516746i
$605$	4.04681	+	7.52083i	0.164526	+	0.305765i
$606$		−	2.83091i		−	0.114998i
$607$	−11.0397	−	19.1214i	−0.448089	−	0.776114i	0.550172	−	0.835051i	$-0.314562\pi$
$607$	−11.0397	−	19.1214i	−0.448089	−	0.776114i	−0.998262	+	0.0589376i	$0.981229\pi$
$608$	0.996184	−	0.575147i	0.0404006	−	0.0233253i
$609$	8.90945	−	5.14388i	0.361029	−	0.208440i
$610$	−9.25931	+	4.98224i	−0.374898	+	0.201725i
$611$	−4.12079	−	2.37914i	−0.166709	−	0.0962496i
$612$	3.42715	+	5.93600i	0.138534	+	0.239948i
$613$	0.146782	−	0.0847445i	0.00592846	−	0.00342280i	−0.497033	−	0.867732i	$-0.665577\pi$
$613$	0.146782	−	0.0847445i	0.00592846	−	0.00342280i	0.502961	+	0.864309i	$0.332244\pi$
$614$	−21.6882	+	12.5217i	−0.875264	+	0.505334i
$615$	0.912145	+	0.563709i	0.0367812	+	0.0227309i
$616$	12.6789	+	7.32017i	0.510847	+	0.294938i
$617$	−36.7353	+	21.2091i	−1.47891	+	0.853848i	−0.999715	−	0.0238625i	$-0.992404\pi$
$617$	−36.7353	+	21.2091i	−1.47891	+	0.853848i	−0.479192	+	0.877710i	$0.659070\pi$
$618$			16.9217i			0.680690i
$619$	−36.2920			−1.45870			−0.729349	−	0.684142i	$-0.760177\pi$
$619$	−36.2920			−1.45870			−0.729349	+	0.684142i	$0.760177\pi$
$620$	−0.544446	+	18.1709i	−0.0218655	+	0.729762i
$621$			0.0656760i			0.00263549i
$622$	15.5003	+	8.94910i	0.621505	+	0.358826i
$623$	−30.2752			−1.21295
$624$	−2.12180	−	1.22502i	−0.0849400	−	0.0490402i
$625$	−9.82254	−	22.9895i	−0.392902	−	0.919581i
$626$	5.62602	−	9.74455i	0.224861	−	0.389471i
$627$	2.21409	+	3.83491i	0.0884221	+	0.153152i
$628$		−	16.4605i		−	0.656847i
$629$	−40.6509	−	9.26359i	−1.62086	−	0.369363i
$630$	−7.23399	−	4.47063i	−0.288209	−	0.178114i
$631$	1.44160	−	0.832307i	0.0573891	−	0.0331336i	−0.471031	−	0.882117i	$-0.656118\pi$
$631$	1.44160	−	0.832307i	0.0573891	−	0.0331336i	0.528420	+	0.848983i	$0.322785\pi$
$632$	2.57370	+	1.48593i	0.102376	+	0.0591070i
$633$	16.6586	+	9.61784i	0.662120	+	0.382275i
$634$	2.29777	+	1.32662i	0.0912560	+	0.0526867i
$635$	−33.4789	−	20.6901i	−1.32857	−	0.821061i
$636$	−2.78866	+	4.83010i	−0.110577	+	0.191526i
$637$	18.2857			0.724506
$638$	−9.01843	+	5.20679i	−0.357043	+	0.206139i
$639$	−7.44169			−0.294389
$640$	1.17553	−	1.90214i	0.0464668	−	0.0751886i
$641$	6.48865	+	11.2387i	0.256286	+	0.443901i	0.965244	−	0.261350i	$-0.0841677\pi$
$641$	6.48865	+	11.2387i	0.256286	+	0.443901i	−0.708958	+	0.705251i	$0.750834\pi$
$642$	4.39791	−	7.61741i	0.173572	−	0.300635i
$643$	−20.0143			−0.789285			−0.394643	−	0.918835i	$-0.629132\pi$
$643$	−20.0143			−0.789285			−0.394643	+	0.918835i	$0.629132\pi$
$644$	0.216308	−	0.124886i	0.00852374	−	0.00492118i
$645$	0.672380	−	22.4407i	0.0264749	−	0.883604i
$646$	6.82815	−	3.94223i	0.268650	−	0.155105i
$647$	25.0163	−	43.3294i	0.983491	−	1.70346i	0.335030	−	0.942207i	$-0.391253\pi$
$647$	25.0163	−	43.3294i	0.983491	−	1.70346i	0.648460	−	0.761248i	$-0.275413\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−7.23317	+	4.17607i	−0.283927	+	0.163925i
$650$	6.74930	−	10.2233i	0.264729	−	0.400989i
$651$	−26.7765	+	15.4594i	−1.04945	+	0.605902i
$652$	−19.6630			−0.770064
$653$	−3.28047	+	5.68194i	−0.128375	+	0.222351i	−0.923047	−	0.384687i	$-0.874309\pi$
$653$	−3.28047	+	5.68194i	−0.128375	+	0.222351i	0.794672	+	0.607039i	$0.207643\pi$
$654$	5.33433	+	9.23933i	0.208589	+	0.361287i
$655$	−29.9882	−	18.5328i	−1.17174	−	0.724137i
$656$	−0.479537			−0.0187228
$657$	5.90768	−	3.41080i	0.230480	−	0.133068i
$658$	7.38603			0.287937
$659$	23.8790	−	41.3596i	0.930193	−	1.61114i	0.147203	−	0.989106i	$-0.452973\pi$
$659$	23.8790	−	41.3596i	0.930193	−	1.61114i	0.782989	−	0.622035i	$-0.213694\pi$
$660$	7.32247	+	4.52531i	0.285027	+	0.176148i
$661$	31.6257	+	18.2591i	1.23010	+	0.710197i	0.967050	−	0.254586i	$-0.0819391\pi$
$661$	31.6257	+	18.2591i	1.23010	+	0.710197i	0.263047	+	0.964783i	$0.415272\pi$
$662$	−15.6212	−	9.01889i	−0.607134	−	0.350529i
$663$	−14.5435	−	8.39667i	−0.564821	−	0.326100i
$664$	4.83322	−	2.79046i	0.187565	−	0.108291i
$665$	−5.14254	+	8.32122i	−0.199419	+	0.322683i
$666$	−1.79493	−	5.81190i	−0.0695520	−	0.225207i
$667$			0.177661i			0.00687906i
$668$	−5.34341	−	9.25505i	−0.206743	−	0.358089i
$669$	−10.9874	+	19.0307i	−0.424798	+	0.735771i
$670$	−15.2476	+	8.20441i	−0.589065	+	0.316964i
$671$	15.6767	+	9.05096i	0.605193	+	0.349408i
$672$	3.80308			0.146707
$673$	3.39834	+	1.96203i	0.130996	+	0.0756307i	0.564066	−	0.825730i	$-0.309236\pi$
$673$	3.39834	+	1.96203i	0.130996	+	0.0756307i	−0.433070	+	0.901360i	$0.642570\pi$
$674$		−	19.7912i		−	0.762330i
$675$	−4.17268	−	2.75477i	−0.160607	−	0.106031i
$676$	−6.99728			−0.269126
$677$		−	26.4675i		−	1.01723i	−0.860994	−	0.508615i	$-0.830158\pi$
$677$		−	26.4675i		−	1.01723i	0.860994	−	0.508615i	$-0.169842\pi$
$678$	5.14363	−	2.96968i	0.197540	−	0.114050i
$679$	9.57577	+	5.52857i	0.367484	+	0.212167i
$680$	8.05742	−	13.0378i	0.308988	−	0.499978i
$681$	9.71497	−	5.60894i	0.372278	−	0.214935i
$682$	27.1040	−	15.6485i	1.03787	−	0.599212i
$683$	−6.60542	−	11.4409i	−0.252749	−	0.437774i	0.711533	−	0.702653i	$-0.248001\pi$
$683$	−6.60542	−	11.4409i	−0.252749	−	0.437774i	−0.964282	+	0.264879i	$0.914668\pi$
$684$	0.996184	+	0.575147i	0.0380901	+	0.0219913i
$685$	−33.6672	+	18.1156i	−1.28636	+	0.692163i
$686$	−1.52630	+	0.881211i	−0.0582745	+	0.0336448i
$687$	−13.9369	+	8.04647i	−0.531726	+	0.306992i
$688$	5.02016	+	8.69516i	0.191392	+	0.331500i
$689$		−	13.6647i		−	0.520583i
$690$	0.129323	−	0.0695862i	0.00492325	−	0.00264910i
$691$	23.9934	+	41.5579i	0.912753	+	1.58094i	0.810158	+	0.586212i	$0.199381\pi$
$691$	23.9934	+	41.5579i	0.912753	+	1.58094i	0.102596	+	0.994723i	$0.467285\pi$
$692$		−	10.8721i		−	0.413296i
$693$			14.6403i			0.556140i
$694$	−2.56278	−	4.43887i	−0.0972818	−	0.168497i
$695$	20.8952	−	33.8108i	0.792599	−	1.28252i
$696$	−1.35255	+	2.34269i	−0.0512685	+	0.0887996i
$697$	−3.28689			−0.124500
$698$	12.9643	−	22.4549i	0.490707	−	0.849929i
$699$	11.6668	−	20.2074i	0.441278	−	0.764315i
$700$	−1.13847	+	18.9813i	−0.0430303	+	0.717425i
$701$	−13.4755	+	7.78011i	−0.508964	+	0.293851i	−0.732408	−	0.680866i	$-0.761603\pi$
$701$	−13.4755	+	7.78011i	−0.508964	+	0.293851i	0.223444	+	0.974717i	$0.428270\pi$
$702$		−	2.45005i		−	0.0924710i
$703$	−6.68540	+	2.06469i	−0.252145	+	0.0778714i
$704$	−3.84960			−0.145087
$705$	4.34076	+	0.130060i	0.163482	+	0.00489833i
$706$	2.11906	−	3.67032i	0.0797520	−	0.138134i
$707$	−9.32377	−	5.38308i	−0.350656	−	0.202452i
$708$	−1.08481	+	1.87894i	−0.0407695	+	0.0706149i
$709$		−	0.120714i		−	0.00453352i	−0.999997	−	0.00226676i	$-0.999278\pi$
$709$		−	0.120714i		−	0.00453352i	0.999997	−	0.00226676i	$-0.000721533\pi$
$710$	7.88475	+	14.6535i	0.295909	+	0.549936i
$711$			2.97186i			0.111453i
$712$	6.89417	−	3.98035i	0.258370	−	0.149170i
$713$		−	0.533942i		−	0.0199963i
$714$	26.0675			0.975550
$715$	−21.0804	−	0.631622i	−0.788364	−	0.0236213i
$716$	7.23906	+	4.17947i	0.270536	+	0.156194i
$717$	−0.593895			−0.0221794
$718$	5.51366	+	9.54994i	0.205768	+	0.356401i
$719$	10.4447	+	18.0907i	0.389521	+	0.674671i	0.992385	−	0.123173i	$-0.0393072\pi$
$719$	10.4447	+	18.0907i	0.389521	+	0.674671i	−0.602864	+	0.797844i	$0.705974\pi$
$720$	2.23506	+	0.0669680i	0.0832960	+	0.00249575i
$721$	55.7327	+	32.1773i	2.07559	+	1.19834i
$722$	−8.83841	+	15.3086i	−0.328932	+	0.569726i
$723$	5.27364	+	9.13422i	0.196129	+	0.339705i
$724$	9.39587	+	16.2741i	0.349195	+	0.604823i
$725$	−11.2876	−	7.45194i	−0.419210	−	0.276758i
$726$		−	3.81941i		−	0.141752i
$727$	14.7316	−	25.5159i	0.546364	−	0.946331i	−0.452155	−	0.891939i	$-0.649345\pi$
$727$	14.7316	−	25.5159i	0.546364	−	0.946331i	0.998520	−	0.0543916i	$-0.0173219\pi$
$728$	−8.06938	+	4.65886i	−0.299071	+	0.172669i
$729$	−1.00000			−0.0370370
$730$	−12.9756	−	8.01898i	−0.480250	−	0.296796i
$731$	34.4097	+	59.5993i	1.27269	+	2.20436i
$732$	4.70229			0.173802
$733$	17.4475	+	10.0733i	0.644438	+	0.372067i	0.786322	−	0.617817i	$-0.211983\pi$
$733$	17.4475	+	10.0733i	0.644438	+	0.372067i	−0.141884	+	0.989883i	$0.545316\pi$
$734$			0.820672i			0.0302915i
$735$	−14.6963	+	7.90776i	−0.542080	+	0.291682i
$736$	−0.0328380	+	0.0568771i	−0.00121043	+	0.00209652i
$737$	25.8153	+	14.9045i	0.950920	+	0.549014i
$738$	−0.239768	−	0.415291i	−0.00882599	−	0.0152871i
$739$	−5.60635			−0.206233			−0.103116	−	0.994669i	$-0.532881\pi$
$739$	−5.60635			−0.206233			−0.103116	+	0.994669i	$0.532881\pi$
$740$	−9.54247	+	9.69233i	−0.350788	+	0.356297i
$741$	−2.81827			−0.103532
$742$	10.6055	+	18.3692i	0.389340	+	0.674356i
$743$	−9.93130	−	5.73384i	−0.364344	−	0.210354i	0.306641	−	0.951825i	$-0.400795\pi$
$743$	−9.93130	−	5.73384i	−0.364344	−	0.210354i	−0.670985	+	0.741471i	$0.734128\pi$
$744$	4.06497	−	7.04073i	0.149029	−	0.258126i
$745$	1.77945	+	3.30704i	0.0651940	+	0.121160i
$746$			28.4125i			1.04026i
$747$	4.83322	+	2.79046i	0.176838	+	0.102098i
$748$	−26.3863			−0.964779
$749$	−16.7256	−	28.9696i	−0.611141	−	1.05853i
$750$	−1.00332	+	11.1352i	−0.0366360	+	0.406601i
$751$	4.70945			0.171850			0.0859252	−	0.996302i	$-0.472615\pi$
$751$	4.70945			0.171850			0.0859252	+	0.996302i	$0.472615\pi$
$752$	−1.68192	+	0.971059i	−0.0613334	+	0.0354109i
$753$	14.4519	−	25.0313i	0.526655	−	0.912193i
$754$		−	6.62764i		−	0.241364i
$755$	32.7760	+	0.982048i	1.19284	+	0.0357404i
$756$	1.90154	+	3.29356i	0.0691583	+	0.119786i
$757$	−15.3612	−	26.6063i	−0.558311	−	0.967022i	−0.997638	−	0.0686950i	$-0.978116\pi$
$757$	−15.3612	−	26.6063i	−0.558311	−	0.967022i	0.439327	−	0.898327i	$-0.355217\pi$
$758$	2.60445	−	4.51103i	0.0945978	−	0.163848i
$759$	−0.218954	−	0.126413i	−0.00794753	−	0.00458851i
$760$	0.0770330	−	2.57098i	0.00279428	−	0.0932594i
$761$	−1.51563	−	2.62515i	−0.0549415	−	0.0951615i	0.837247	−	0.546826i	$-0.184164\pi$
$761$	−1.51563	−	2.62515i	−0.0549415	−	0.0951615i	−0.892188	+	0.451664i	$0.850831\pi$
$762$	8.80034	+	15.2426i	0.318803	+	0.552182i
$763$	40.5738			1.46887
$764$	−11.3667	−	6.56255i	−0.411232	−	0.237425i
$765$	15.3198	+	0.459019i	0.553889	+	0.0165959i
$766$	6.08947			0.220022
$767$		−	5.31565i		−	0.191937i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$			32.6155i			1.17615i	0.808808	+	0.588073i	$0.200113\pi$
$769$			32.6155i			1.17615i	−0.808808	+	0.588073i	$0.799887\pi$
$770$	28.8284	−	15.5120i	1.03890	−	0.559012i
$771$			9.42920i			0.339584i
$772$	0.887727	−	1.53759i	0.0319500	−	0.0553390i
$773$	−0.947360	−	0.546959i	−0.0340742	−	0.0196727i	0.482866	−	0.875694i	$-0.339596\pi$
$773$	−0.947360	−	0.546959i	−0.0340742	−	0.0196727i	−0.516940	+	0.856021i	$0.672929\pi$
$774$	−5.02016	+	8.69516i	−0.180446	+	0.312541i
$775$	33.9236	+	22.3961i	1.21857	+	0.804490i
$776$	−2.90742			−0.104370
$777$	−22.5550	−	5.13986i	−0.809156	−	0.184392i
$778$			28.4581i			1.02027i
$779$	−0.477707	+	0.275804i	−0.0171156	+	0.00988171i
$780$	−4.82440	+	2.59591i	−0.172741	+	0.0929486i
$781$	14.3238	−	24.8095i	0.512545	−	0.887753i
$782$	−0.225082	+	0.389853i	−0.00804890	+	0.0139411i
$783$	−2.70511			−0.0966727
$784$	3.73171	−	6.46351i	0.133275	−	0.230840i
$785$	−31.3102	−	19.3498i	−1.11751	−	0.690625i
$786$	7.88276	+	13.6533i	0.281169	+	0.486998i
$787$		−	51.7135i		−	1.84339i	−0.387920	−	0.921693i	$-0.626806\pi$
$787$		−	51.7135i		−	1.84339i	0.387920	−	0.921693i	$-0.373194\pi$
$788$			20.7825i			0.740347i
$789$	15.6068	+	27.0317i	0.555616	+	0.962355i
$790$	5.85190	−	3.14879i	0.208201	−	0.112029i
$791$		−	22.5878i		−	0.803131i
$792$	−1.92480	−	3.33385i	−0.0683948	−	0.118463i
$793$	−9.97732	+	5.76041i	−0.354305	+	0.204558i
$794$	30.0517	−	17.3504i	1.06650	−	0.615741i
$795$	5.90937	+	10.9823i	0.209584	+	0.389503i
$796$	19.9138	+	11.4972i	0.705826	+	0.407509i
$797$	−0.709094	−	1.22819i	−0.0251174	−	0.0435046i	0.853193	−	0.521595i	$-0.174663\pi$
$797$	−0.709094	−	1.22819i	−0.0251174	−	0.0435046i	−0.878311	+	0.478090i	$0.841329\pi$
$798$	3.78857	−	2.18733i	0.134114	−	0.0774307i
$799$	−11.5284	+	6.65593i	−0.407846	+	0.235470i
$800$	−2.23627	−	4.47204i	−0.0790639	−	0.158110i
$801$	6.89417	+	3.98035i	0.243594	+	0.140639i
$802$	1.13059	−	0.652747i	0.0399226	−	0.0230493i
$803$			26.2604i			0.926710i
$804$	7.74340			0.273089
$805$	0.0167267	−	0.558255i	0.000589538	−	0.0196759i
$806$			19.9187i			0.701607i
$807$	−1.77557	−	1.02513i	−0.0625031	−	0.0360862i
$808$	2.83091			0.0995909
$809$	27.6721	+	15.9765i	0.972899	+	0.561704i	0.900119	−	0.435645i	$-0.143480\pi$
$809$	27.6721	+	15.9765i	0.972899	+	0.561704i	0.0727802	+	0.997348i	$0.476813\pi$
$810$	1.05954	+	1.96911i	0.0372283	+	0.0691874i
$811$	13.5475	−	23.4650i	0.475718	−	0.823967i	−0.523896	−	0.851783i	$-0.675522\pi$
$811$	13.5475	−	23.4650i	0.475718	−	0.823967i	0.999613	+	0.0278156i	$0.00885512\pi$
$812$	5.14388	+	8.90945i	0.180515	+	0.312661i
$813$		−	6.56843i		−	0.230365i
$814$	22.8309	+	5.20273i	0.800222	+	0.182356i
$815$	−23.1145	+	37.4018i	−0.809664	+	1.31013i
$816$	−5.93600	+	3.42715i	−0.207801	+	0.119974i
$817$	10.0020	+	5.77466i	0.349926	+	0.202030i
$818$	−15.6275	−	9.02256i	−0.546404	−	0.315466i
$819$	−8.06938	−	4.65886i	−0.281967	−	0.162794i
$820$	−0.563709	+	0.912145i	−0.0196856	+	0.0318535i
$821$	3.08741	−	5.34755i	0.107751	−	0.186631i	−0.807108	−	0.590404i	$-0.798968\pi$
$821$	3.08741	−	5.34755i	0.107751	−	0.186631i	0.914859	+	0.403774i	$0.132302\pi$
$822$	17.0977			0.596351
$823$	41.9378	−	24.2128i	1.46186	−	0.844005i	0.462763	−	0.886482i	$-0.346858\pi$
$823$	41.9378	−	24.2128i	1.46186	−	0.844005i	0.999097	+	0.0424769i	$0.0135249\pi$
$824$	−16.9217			−0.589495
$825$	17.2155	−	8.60873i	0.599368	−	0.299717i
$826$	4.12561	+	7.14576i	0.143548	+	0.248633i
$827$	25.4747	−	44.1235i	0.885842	−	1.53432i	0.0410959	−	0.999155i	$-0.486915\pi$
$827$	25.4747	−	44.1235i	0.885842	−	1.53432i	0.844746	−	0.535168i	$-0.179752\pi$
$828$	−0.0656760			−0.00228240
$829$	28.4803	−	16.4431i	0.989162	−	0.571093i	0.0841386	−	0.996454i	$-0.473186\pi$
$829$	28.4803	−	16.4431i	0.989162	−	0.571093i	0.905024	+	0.425361i	$0.139853\pi$
$830$	0.373743	−	12.4737i	0.0129728	−	0.432969i
$831$	11.6473	−	6.72455i	0.404039	−	0.233272i
$832$	1.22502	−	2.12180i	0.0424700	−	0.0735602i
$833$	25.5783	−	44.3028i	0.886234	−	1.53500i
$834$	−15.3937	+	8.88756i	−0.533041	+	0.307751i
$835$	−23.8857	−	0.715675i	−0.826600	−	0.0247670i
$836$	−3.83491	+	2.21409i	−0.132633	+	0.0765758i
$837$	8.12994			0.281012
$838$	−2.21154	+	3.83049i	−0.0763962	+	0.132322i
$839$	13.7575	+	23.8286i	0.474960	+	0.822656i	0.999589	−	0.0286758i	$-0.00912903\pi$
$839$	13.7575	+	23.8286i	0.474960	+	0.822656i	−0.524628	+	0.851331i	$0.675796\pi$
$840$	4.47063	−	7.23399i	0.154251	−	0.249596i
$841$	21.6824			0.747668
$842$	−31.7779	+	18.3470i	−1.09514	+	0.632279i
$843$	25.7159			0.885702
$844$	−9.61784	+	16.6586i	−0.331060	+	0.573412i
$845$	−8.22550	+	13.3098i	−0.282966	+	0.457871i
$846$	−1.68192	−	0.971059i	−0.0578257	−	0.0333857i
$847$	−12.5795	−	7.26276i	−0.432236	−	0.249552i
$848$	−4.83010	−	2.78866i	−0.165866	−	0.0957629i
$849$	15.9376	−	9.20159i	0.546978	−	0.315798i
$850$	−15.3280	−	30.6527i	−0.525747	−	1.05138i
$851$	0.271623	−	0.292942i	0.00931110	−	0.0100419i
$852$		−	7.44169i		−	0.254948i
$853$	−2.55653	−	4.42804i	−0.0875340	−	0.151613i	0.818934	−	0.573887i	$-0.194565\pi$
$853$	−2.55653	−	4.42804i	−0.0875340	−	0.151613i	−0.906468	+	0.422274i	$0.861232\pi$
$854$	8.94159	−	15.4873i	0.305975	−	0.529964i
$855$	2.26505	−	1.21878i	0.0774632	−	0.0416814i
$856$	7.61741	+	4.39791i	0.260358	+	0.150318i
$857$	−37.2126			−1.27116			−0.635580	−	0.772035i	$-0.719239\pi$
$857$	−37.2126			−1.27116			−0.635580	+	0.772035i	$0.719239\pi$
$858$	8.16808	+	4.71585i	0.278854	+	0.160996i
$859$			5.99631i			0.204591i	0.994754	+	0.102296i	$0.0326188\pi$
$859$			5.99631i			0.204591i	−0.994754	+	0.102296i	$0.967381\pi$
$860$	22.4407	+	0.672380i	0.765223	+	0.0229280i
$861$	−1.82372			−0.0621521
$862$		−	8.21595i		−	0.279836i
$863$	−42.5951	+	24.5923i	−1.44995	+	0.837130i	−0.998478	−	0.0551536i	$-0.982435\pi$
$863$	−42.5951	+	24.5923i	−1.44995	+	0.837130i	−0.451475	+	0.892284i	$0.649102\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	−20.6803	−	12.7805i	−0.703150	−	0.434549i
$866$	−30.5405	+	17.6326i	−1.03781	+	0.599180i
$867$	−25.9647	+	14.9907i	−0.881807	+	0.509111i
$868$	−15.4594	−	26.7765i	−0.524726	−	0.908853i
$869$	−9.90772	−	5.72023i	−0.336096	−	0.194045i
$870$	2.86616	+	5.32665i	0.0971720	+	0.180590i
$871$	−16.4299	+	9.48584i	−0.556708	+	0.321415i
$872$	−9.23933	+	5.33433i	−0.312883	+	0.180643i
$873$	−1.45371	−	2.51790i	−0.0492006	−	0.0852180i
$874$			0.0755468i			0.00255541i
$875$	34.7667	+	24.4786i	1.17533	+	0.827527i
$876$	3.41080	+	5.90768i	0.115240	+	0.199602i
$877$			13.5009i			0.455892i	0.973674	+	0.227946i	$0.0732010\pi$
$877$			13.5009i			0.455892i	−0.973674	+	0.227946i	$0.926799\pi$
$878$			0.908079i			0.0306462i
$879$	−8.05596	−	13.9533i	−0.271721	−	0.470634i
$880$	−4.52531	+	7.32247i	−0.152548	+	0.246840i
$881$	20.6610	−	35.7860i	0.696088	−	1.20566i	−0.273725	−	0.961808i	$-0.588256\pi$
$881$	20.6610	−	35.7860i	0.696088	−	1.20566i	0.969813	−	0.243851i	$-0.0784109\pi$
$882$	7.46342			0.251306
$883$	−17.4829	+	30.2812i	−0.588345	+	1.01904i	0.406105	+	0.913827i	$0.366887\pi$
$883$	−17.4829	+	30.2812i	−0.588345	+	1.01904i	−0.994449	+	0.105217i	$0.966446\pi$
$884$	8.39667	−	14.5435i	0.282411	−	0.489150i
$885$	2.29878	+	4.27220i	0.0772728	+	0.143608i
$886$	30.3121	−	17.5007i	1.01836	−	0.587948i
$887$		−	10.8976i		−	0.365907i	−0.983122	−	0.182953i	$-0.941434\pi$
$887$		−	10.8976i		−	0.365907i	0.983122	−	0.182953i	$-0.0585657\pi$
$888$	5.81190	−	1.79493i	0.195035	−	0.0602338i
$889$	66.9368			2.24499
$890$	0.533113	−	17.7927i	0.0178700	−	0.596412i
$891$	1.92480	−	3.33385i	0.0644832	−	0.111688i
$892$	−19.0307	−	10.9874i	−0.637196	−	0.367886i
$893$	−1.11700	+	1.93471i	−0.0373791	+	0.0647425i
$894$		−	1.67946i		−	0.0561695i
$895$	16.4597	−	8.85661i	0.550186	−	0.296044i
$896$			3.80308i			0.127052i
$897$	0.139351	−	0.0804546i	0.00465281	−	0.00268630i
$898$		−	20.0070i		−	0.667643i
$899$	21.9924			0.733487
$900$	2.75477	−	4.17268i	0.0918255	−	0.139089i
$901$	−33.1069	−	19.1143i	−1.10295	−	0.636790i
$902$	1.84602			0.0614659
$903$	19.0921	+	33.0684i	0.635344	+	1.10045i
$904$	2.96968	+	5.14363i	0.0987699	+	0.171075i
$905$	42.0007	+	1.25845i	1.39615	+	0.0418321i
$906$	−12.6998	−	7.33222i	−0.421922	−	0.243597i
$907$	18.2511	−	31.6119i	0.606018	−	1.04965i	−0.385871	−	0.922553i	$-0.626099\pi$
$907$	18.2511	−	31.6119i	0.606018	−	1.04965i	0.991890	−	0.127102i	$-0.0405676\pi$
$908$	5.60894	+	9.71497i	0.186139	+	0.322402i
$909$	1.41545	+	2.45164i	0.0469476	+	0.0813156i
$910$	−0.623989	+	20.8257i	−0.0206850	+	0.690365i
$911$		−	33.5547i		−	1.11172i	−0.831277	−	0.555858i	$-0.812390\pi$
$911$		−	33.5547i		−	1.11172i	0.831277	−	0.555858i	$-0.187610\pi$
$912$	−0.575147	+	0.996184i	−0.0190450	+	0.0329870i
$913$	−18.6060	+	10.7422i	−0.615768	+	0.355514i
$914$	12.7554			0.421910
$915$	5.52767	−	8.94440i	0.182739	−	0.295693i
$916$	−8.04647	−	13.9369i	−0.265863	−	0.460488i
$917$	59.9575			1.97997
$918$	−5.93600	−	3.42715i	−0.195917	−	0.113113i
$919$			8.13814i			0.268452i	0.990951	+	0.134226i	$0.0428549\pi$
$919$			8.13814i			0.268452i	−0.990951	+	0.134226i	$0.957145\pi$
$920$	0.0695862	+	0.129323i	0.00229419	+	0.00426366i
$921$	12.5217	−	21.6882i	0.412603	−	0.714650i
$922$	−19.2166	−	11.0947i	−0.632864	−	0.365384i
$923$	9.11624	+	15.7898i	0.300065	+	0.519727i
$924$	−14.6403			−0.481632
$925$	7.21871	+	29.5447i	0.237350	+	0.971424i
$926$	−13.1352			−0.431650
$927$	−8.46084	−	14.6546i	−0.277891	−	0.481321i
$928$	−2.34269	−	1.35255i	−0.0769027	−	0.0443998i
$929$	−3.73445	+	6.46826i	−0.122523	+	0.212217i	−0.920762	−	0.390124i	$-0.872432\pi$
$929$	−3.73445	+	6.46826i	−0.122523	+	0.212217i	0.798239	+	0.602341i	$0.205765\pi$
$930$	−8.61397	−	16.0087i	−0.282463	−	0.524947i
$931$		−	8.58513i		−	0.281366i
$932$	20.2074	+	11.6668i	0.661917	+	0.382158i
$933$	−17.8982			−0.585961
$934$	−1.31993	−	2.28618i	−0.0431894	−	0.0748062i
$935$	−31.0179	+	50.1904i	−1.01439	+	1.64140i
$936$	2.45005			0.0800822
$937$	49.2427	−	28.4303i	1.60869	−	0.928777i	0.619024	−	0.785372i	$-0.287528\pi$
$937$	49.2427	−	28.4303i	1.60869	−	0.928777i	0.989664	−	0.143405i	$-0.0458052\pi$
$938$	14.7244	−	25.5034i	0.480768	−	0.832715i
$939$			11.2520i			0.367196i
$940$	−0.130060	+	4.34076i	−0.00424208	+	0.141580i
$941$	29.4403	+	50.9920i	0.959725	+	1.66229i	0.723165	+	0.690676i	$0.242687\pi$
$941$	29.4403	+	50.9920i	0.959725	+	1.66229i	0.236561	+	0.971617i	$0.423980\pi$
$942$	8.23027	+	14.2552i	0.268157	+	0.464461i
$943$	0.0157470	−	0.0272747i	0.000512794	−	0.000888185i
$944$	−1.87894	−	1.08481i	−0.0611543	−	0.0353075i
$945$	8.50013	+	0.254685i	0.276509	+	0.00828490i
$946$	−19.3256	−	33.4729i	−0.628329	−	1.08830i
$947$	28.7838	+	49.8551i	0.935349	+	1.62007i	0.774010	+	0.633174i	$0.218248\pi$
$947$	28.7838	+	49.8551i	0.935349	+	1.62007i	0.161339	+	0.986899i	$0.448419\pi$
$948$	−2.97186			−0.0965214
$949$	−14.4741	−	8.35661i	−0.469848	−	0.271267i
$950$	−4.79981	−	3.16879i	−0.155727	−	0.102809i
$951$	−2.65323			−0.0860370
$952$			26.0675i			0.844851i
$953$	−17.2207	+	9.94235i	−0.557832	+	0.322064i	−0.752275	−	0.658850i	$-0.771043\pi$
$953$	−17.2207	+	9.94235i	−0.557832	+	0.322064i	0.194443	+	0.980914i	$0.437710\pi$
$954$		−	5.57732i		−	0.180572i
$955$	−25.8447	+	13.9065i	−0.836316	+	0.450005i
$956$		−	0.593895i		−	0.0192079i
$957$	5.20679	−	9.01843i	0.168312	−	0.291525i
$958$	9.66298	+	5.57892i	0.312197	+	0.180247i
$959$	32.5120	−	56.3124i	1.04987	−	1.81842i
$960$	−0.0669680	+	2.23506i	−0.00216138	+	0.0721364i
$961$	−35.0959			−1.13213
$962$	−10.1329	+	10.9282i	−0.326697	+	0.352339i
$963$			8.79583i			0.283442i
$964$	−9.13422	+	5.27364i	−0.294193	+	0.169853i
$965$	−1.88116	−	3.49606i	−0.0605567	−	0.112542i
$966$	−0.124886	+	0.216308i	−0.00401813	+	0.00695960i
$967$	0.967950	−	1.67654i	0.0311272	−	0.0539139i	−0.850042	−	0.526715i	$-0.823424\pi$
$967$	0.967950	−	1.67654i	0.0311272	−	0.0539139i	0.881169	+	0.472801i	$0.156757\pi$
$968$	3.81941			0.122761
$969$	−3.94223	+	6.82815i	−0.126643	+	0.219352i
$970$	−3.41775	+	5.53032i	−0.109737	+	0.177568i
$971$	−24.1484	−	41.8262i	−0.774957	−	1.34227i	−0.934818	−	0.355126i	$-0.884438\pi$
$971$	−24.1484	−	41.8262i	−0.774957	−	1.34227i	0.159861	−	0.987140i	$-0.448895\pi$
$972$		−	1.00000i		−	0.0320750i
$973$			67.6002i			2.16716i
$974$	12.7264	+	22.0427i	0.407779	+	0.706294i
$975$	−0.733435	+	12.2283i	−0.0234887	+	0.391617i
$976$			4.70229i			0.150517i
$977$	−11.5097	−	19.9353i	−0.368226	−	0.637787i	0.621062	−	0.783761i	$-0.286702\pi$
$977$	−11.5097	−	19.9353i	−0.368226	−	0.637787i	−0.989288	+	0.145975i	$0.953368\pi$
$978$	17.0287	−	9.83152i	0.544517	−	0.314377i
$979$	−26.5398	+	15.3228i	−0.848215	+	0.489717i
$980$	−7.90776	−	14.6963i	−0.252604	−	0.469455i
$981$	−9.23933	−	5.33433i	−0.294989	−	0.170312i
$982$	−8.07686	−	13.9895i	−0.257743	−	0.446424i
$983$	39.1296	−	22.5915i	1.24804	−	0.720557i	0.277323	−	0.960777i	$-0.410553\pi$
$983$	39.1296	−	22.5915i	1.24804	−	0.720557i	0.970719	+	0.240219i	$0.0772194\pi$
$984$	0.415291	−	0.239768i	0.0132390	−	0.00764353i
$985$	39.5313	+	24.4305i	1.25957	+	0.778419i
$986$	−16.0575	−	9.27082i	−0.511376	−	0.295243i
$987$	−6.39649	+	3.69301i	−0.203602	+	0.117550i
$988$		−	2.81827i		−	0.0896612i
$989$	−0.659408			−0.0209679
$990$	−8.60410	−	0.257800i	−0.273456	−	0.00819342i
$991$		−	33.6103i		−	1.06767i	−0.845589	−	0.533834i	$-0.820751\pi$
$991$		−	33.6103i		−	1.06767i	0.845589	−	0.533834i	$-0.179249\pi$
$992$	7.04073	+	4.06497i	0.223543	+	0.129063i
$993$	18.0378			0.572412
$994$	−24.5097	−	14.1507i	−0.777400	−	0.448832i
$995$	45.2786	−	24.3635i	1.43543	−	0.772374i
$996$	−2.79046	+	4.83322i	−0.0884192	+	0.153146i
$997$	−0.517102	−	0.895647i	−0.0163768	−	0.0283654i	0.857721	−	0.514116i	$-0.171880\pi$
$997$	−0.517102	−	0.895647i	−0.0163768	−	0.0283654i	−0.874098	+	0.485750i	$0.838546\pi$
$998$			31.0857i			0.984000i
$999$	4.46040	+	4.13579i	0.141121	+	0.130851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.a.529.10	✓	36
5.4	even	2		1110.2.ba.b.529.9	yes	36
37.27	even	6		1110.2.ba.b.619.9	yes	36
185.64	even	6	inner	1110.2.ba.a.619.10	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.10	✓	36	1.1	even	1	trivial
1110.2.ba.a.619.10	yes	36	185.64	even	6	inner
1110.2.ba.b.529.9	yes	36	5.4	even	2
1110.2.ba.b.619.9	yes	36	37.27	even	6

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.05954 + 1.96911i) q^{5} -1.00000i q^{6} +(-3.29356 - 1.90154i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.05954 + 1.96911i) q^{5} -1.00000i q^{6} +(-3.29356 - 1.90154i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(1.17553 - 1.90214i) q^{10} -3.84960 q^{11} +(-0.866025 + 0.500000i) q^{12} +(1.22502 - 2.12180i) q^{13} +3.80308i q^{14} +(-0.0669680 + 2.23506i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.42715 - 5.93600i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.996184 - 0.575147i) q^{19} +(-2.23506 - 0.0669680i) q^{20} +(-1.90154 - 3.29356i) q^{21} +(1.92480 + 3.33385i) q^{22} +0.0656760 q^{23} +(0.866025 + 0.500000i) q^{24} +(-2.75477 + 4.17268i) q^{25} -2.45005 q^{26} +1.00000i q^{27} +(3.29356 - 1.90154i) q^{28} +2.70511i q^{29} +(1.96911 - 1.05954i) q^{30} -8.12994i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.33385 - 1.92480i) q^{33} +(-3.42715 + 5.93600i) q^{34} +(0.254685 - 8.50013i) q^{35} -1.00000 q^{36} +(4.13579 - 4.46040i) q^{37} +1.15029i q^{38} +(2.12180 - 1.22502i) q^{39} +(1.05954 + 1.96911i) q^{40} +(0.239768 - 0.415291i) q^{41} +(-1.90154 + 3.29356i) q^{42} -10.0403 q^{43} +(1.92480 - 3.33385i) q^{44} +(-1.17553 + 1.90214i) q^{45} +(-0.0328380 - 0.0568771i) q^{46} -1.94212i q^{47} -1.00000i q^{48} +(3.73171 + 6.46351i) q^{49} +(4.99103 + 0.299356i) q^{50} -6.85430i q^{51} +(1.22502 + 2.12180i) q^{52} +(4.83010 - 2.78866i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-4.07879 - 7.58027i) q^{55} +(-3.29356 - 1.90154i) q^{56} +(-0.575147 - 0.996184i) q^{57} +(2.34269 - 1.35255i) q^{58} +(1.87894 - 1.08481i) q^{59} +(-1.90214 - 1.17553i) q^{60} +(-4.07230 - 2.35114i) q^{61} +(-7.04073 + 4.06497i) q^{62} -3.80308i q^{63} +1.00000 q^{64} +(5.47601 + 0.164075i) q^{65} +3.84960i q^{66} +(-6.70598 - 3.87170i) q^{67} +6.85430 q^{68} +(0.0568771 + 0.0328380i) q^{69} +(-7.48867 + 4.02950i) q^{70} +(-3.72085 + 6.44470i) q^{71} +(0.500000 + 0.866025i) q^{72} -6.82160i q^{73} +(-5.93072 - 1.35150i) q^{74} +(-4.47204 + 2.23627i) q^{75} +(0.996184 - 0.575147i) q^{76} +(12.6789 + 7.32017i) q^{77} +(-2.12180 - 1.22502i) q^{78} +(2.57370 + 1.48593i) q^{79} +(1.17553 - 1.90214i) q^{80} +(-0.500000 + 0.866025i) q^{81} -0.479537 q^{82} +(4.83322 - 2.79046i) q^{83} +3.80308 q^{84} +(8.05742 - 13.0378i) q^{85} +(5.02016 + 8.69516i) q^{86} +(-1.35255 + 2.34269i) q^{87} -3.84960 q^{88} +(6.89417 - 3.98035i) q^{89} +(2.23506 + 0.0669680i) q^{90} +(-8.06938 + 4.65886i) q^{91} +(-0.0328380 + 0.0568771i) q^{92} +(4.06497 - 7.04073i) q^{93} +(-1.68192 + 0.971059i) q^{94} +(0.0770330 - 2.57098i) q^{95} +(-0.866025 + 0.500000i) q^{96} -2.90742 q^{97} +(3.73171 - 6.46351i) q^{98} +(-1.92480 - 3.33385i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 - 14 * q^13 - 2 * q^15 - 18 * q^16 + 18 * q^18 + 6 * q^19 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * q^70 - 24 * q^71 + 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 - 24 * q^77 - 6 * q^78 + 2 * q^80 - 18 * q^81 - 20 * q^82 + 36 * q^83 + 26 * q^85 - 10 * q^87 + 4 * q^88 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * q^98 + 2 * q^99

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