LMFDB - Embedded newform 1110.2.ba.b.619.9

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			619.9
Character	$\chi$	$=$	1110.619
Dual form			1110.2.ba.b.529.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.23506 + 0.0669680i) q^{5} +1.00000i q^{6} +(3.29356 - 1.90154i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.23506 + 0.0669680i) 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} +(-1.96911 + 1.05954i) 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} +(-1.05954 - 1.96911i) q^{20} +(-1.90154 + 3.29356i) q^{21} +(-1.92480 + 3.33385i) q^{22} -0.0656760 q^{23} +(0.866025 - 0.500000i) q^{24} +(4.99103 + 0.299356i) q^{25} -2.45005 q^{26} +1.00000i q^{27} +(-3.29356 - 1.90154i) q^{28} -2.70511i q^{29} +(-0.0669680 + 2.23506i) q^{30} +8.12994i q^{31} +(0.500000 + 0.866025i) q^{32} +(3.33385 - 1.92480i) q^{33} +(-3.42715 - 5.93600i) q^{34} +(7.48867 - 4.02950i) q^{35} -1.00000 q^{36} +(-4.13579 - 4.46040i) q^{37} +1.15029i q^{38} +(2.12180 + 1.22502i) q^{39} +(-2.23506 - 0.0669680i) 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} +(2.75477 - 4.17268i) q^{50} +6.85430i q^{51} +(-1.22502 + 2.12180i) q^{52} +(-4.83010 - 2.78866i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-8.60410 - 0.257800i) 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} +(-2.59591 - 4.82440i) q^{65} -3.84960i q^{66} +(6.70598 - 3.87170i) q^{67} -6.85430 q^{68} +(0.0568771 - 0.0328380i) q^{69} +(0.254685 - 8.50013i) 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} +(-1.05954 - 1.96911i) 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} +(-2.26505 + 1.21878i) 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} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9	$ 36 q + 18 q^{2} - 18 q^{4} + 4 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} - 2 q^{20} + 2 q^{22} + 20 q^{23} - 2 q^{25} + 28 q^{26} - 2 q^{30} + 18 q^{32} + 6 q^{33} - 20 q^{35} - 36 q^{36} - 20 q^{37} + 6 q^{39} - 4 q^{40} + 10 q^{41} - 2 q^{44} + 2 q^{45} + 10 q^{46} + 10 q^{49} - 4 q^{50} + 14 q^{52} + 12 q^{53} + 40 q^{55} - 8 q^{57} - 30 q^{58} + 18 q^{59} - 4 q^{60} - 6 q^{61} + 12 q^{62} + 36 q^{64} - 32 q^{65} - 36 q^{67} + 12 q^{69} - 40 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} - 2 q^{90} - 36 q^{91} - 10 q^{92} - 12 q^{93} + 12 q^{94} + 18 q^{95} - 52 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 + 4 * 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 - 2 * q^20 + 2 * q^22 + 20 * q^23 - 2 * q^25 + 28 * q^26 - 2 * q^30 + 18 * q^32 + 6 * q^33 - 20 * q^35 - 36 * q^36 - 20 * q^37 + 6 * q^39 - 4 * q^40 + 10 * q^41 - 2 * q^44 + 2 * q^45 + 10 * q^46 + 10 * q^49 - 4 * q^50 + 14 * q^52 + 12 * q^53 + 40 * q^55 - 8 * q^57 - 30 * q^58 + 18 * q^59 - 4 * q^60 - 6 * q^61 + 12 * q^62 + 36 * q^64 - 32 * q^65 - 36 * q^67 + 12 * q^69 - 40 * 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 - 2 * q^90 - 36 * q^91 - 10 * q^92 - 12 * q^93 + 12 * q^94 + 18 * 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

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
$5$	2.23506	+	0.0669680i	0.999551	+	0.0299490i
$5$	2.23506	+	0.0669680i	0.999551	+	0.0299490i
$6$			1.00000i			0.408248i
$7$	3.29356	−	1.90154i	1.24485	−	0.718715i	0.274773	−	0.961509i	$-0.411397\pi$
$7$	3.29356	−	1.90154i	1.24485	−	0.718715i	0.970078	+	0.242795i	$0.0780641\pi$
$8$	−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	$-0.277013\pi$
$13$	−1.22502	−	2.12180i	−0.339760	−	0.588482i	−0.984387	+	0.176015i	$0.943679\pi$
$14$		−	3.80308i		−	1.01642i
$15$	−1.96911	+	1.05954i	−0.508421	+	0.273571i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.42715	−	5.93600i	0.831206	−	1.43969i	−0.0658765	−	0.997828i	$-0.520984\pi$
$17$	3.42715	−	5.93600i	0.831206	−	1.43969i	0.897082	−	0.441863i	$-0.145682\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−0.996184	+	0.575147i	−0.228540	+	0.131948i	−0.609899	−	0.792480i	$-0.708790\pi$
$19$	−0.996184	+	0.575147i	−0.228540	+	0.131948i	0.381358	+	0.924427i	$0.375456\pi$
$20$	−1.05954	−	1.96911i	−0.236920	−	0.440306i
$21$	−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	$-0.502180\pi$
$23$	−0.0656760			−0.0136944			−0.00684720	+	0.999977i	$0.502180\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	4.99103	+	0.299356i	0.998206	+	0.0598712i
$26$	−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	$-0.919187\pi$
$29$		−	2.70511i		−	0.502326i	0.967945	−	0.251163i	$-0.0808131\pi$
$30$	−0.0669680	+	2.23506i	−0.0122266	+	0.408065i
$31$			8.12994i			1.46018i	0.683351	+	0.730090i	$0.260522\pi$
$31$			8.12994i			1.46018i	−0.683351	+	0.730090i	$0.739478\pi$
$32$	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
$35$	7.48867	−	4.02950i	1.26582	−	0.681110i
$36$	−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
$40$	−2.23506	−	0.0669680i	−0.353395	−	0.0105886i
$41$	0.239768	+	0.415291i	0.0374455	+	0.0648575i	0.884141	−	0.467221i	$-0.154745\pi$
$41$	0.239768	+	0.415291i	0.0374455	+	0.0648575i	−0.846695	+	0.532078i	$0.821411\pi$
$42$	1.90154	+	3.29356i	0.293414	+	0.508208i
$43$	10.0403			1.53113			0.765567	−	0.643357i	$-0.222459\pi$
$43$	10.0403			1.53113			0.765567	+	0.643357i	$0.222459\pi$
$44$	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
$50$	2.75477	−	4.17268i	0.389583	−	0.590106i
$51$			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	$-0.458460\pi$
$53$	−4.83010	−	2.78866i	−0.663465	−	0.383052i	−0.793596	+	0.608445i	$0.791794\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−8.60410	−	0.257800i	−1.16018	−	0.0347618i
$56$	−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	0.617297	−	0.786730i	$-0.288228\pi$
$59$	1.87894	+	1.08481i	0.244617	+	0.141230i	−0.372680	+	0.927960i	$0.621561\pi$
$60$	1.90214	+	1.17553i	0.245565	+	0.151760i
$61$	−4.07230	+	2.35114i	−0.521405	+	0.301033i	−0.737509	−	0.675337i	$-0.763998\pi$
$61$	−4.07230	+	2.35114i	−0.521405	+	0.301033i	0.216105	+	0.976370i	$0.430665\pi$
$62$	7.04073	+	4.06497i	0.894174	+	0.516252i
$63$		−	3.80308i		−	0.479143i
$64$	1.00000			0.125000
$65$	−2.59591	−	4.82440i	−0.321983	−	0.598393i
$66$		−	3.84960i		−	0.473853i
$67$	6.70598	−	3.87170i	0.819266	−	0.473003i	−0.0308975	−	0.999523i	$-0.509837\pi$
$67$	6.70598	−	3.87170i	0.819266	−	0.473003i	0.850163	+	0.526519i	$0.176503\pi$
$68$	−6.85430			−0.831206
$69$	0.0568771	−	0.0328380i	0.00684720	−	0.00395323i
$70$	0.254685	−	8.50013i	0.0304407	−	1.01596i
$71$	−3.72085	−	6.44470i	−0.441583	−	0.764845i	0.556224	−	0.831032i	$-0.312250\pi$
$71$	−3.72085	−	6.44470i	−0.441583	−	0.764845i	−0.997807	+	0.0661878i	$0.978916\pi$
$72$	−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	−0.348181	−	0.937427i	$-0.613201\pi$
$79$	2.57370	−	1.48593i	0.289564	−	0.167180i	0.637745	+	0.770247i	$0.279867\pi$
$80$	−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	$-0.432422\pi$
$83$	−4.83322	−	2.79046i	−0.530515	−	0.306293i	−0.741226	+	0.671255i	$0.765755\pi$
$84$	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	0.818708	−	0.574211i	$-0.194691\pi$
$89$	6.89417	+	3.98035i	0.730781	+	0.421916i	−0.0879270	+	0.996127i	$0.528024\pi$
$90$	−1.05954	−	1.96911i	−0.111685	−	0.207562i
$91$	−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
$95$	−2.26505	+	1.21878i	−0.232390	+	0.125044i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	2.90742			0.295204			0.147602	−	0.989047i	$-0.452845\pi$
$97$	2.90742			0.295204			0.147602	+	0.989047i	$0.452845\pi$
$98$	−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	$-0.186235\pi$
$103$	16.9217			1.66734			0.833672	+	0.552260i	$0.186235\pi$
$104$	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	$-0.806450\pi$
$107$	−7.61741	+	4.39791i	−0.736403	+	0.425162i	0.0843572	+	0.996436i	$0.473116\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−9.23933	−	5.33433i	−0.884968	−	0.510936i	−0.0126746	−	0.999920i	$-0.504035\pi$
$109$	−9.23933	−	5.33433i	−0.884968	−	0.510936i	−0.872293	+	0.488983i	$0.837368\pi$
$110$	−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	$-0.923457\pi$
$113$	−2.96968	+	5.14363i	−0.279364	+	0.483872i	0.691863	+	0.722029i	$0.256790\pi$
$114$	−0.575147	−	0.996184i	−0.0538675	−	0.0933012i
$115$	−0.146790	−	0.00439819i	−0.0136883	−	0.000410134i
$116$	−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
$120$	1.96911	−	1.05954i	0.179754	−	0.0967220i
$121$	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	$-0.0480922\pi$
$127$	15.2426	+	8.80034i	1.35257	+	0.780904i	0.363957	+	0.931416i	$0.381426\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−8.69516	+	5.02016i	−0.765567	+	0.442000i
$130$	−5.47601	−	0.164075i	−0.480278	−	0.0143903i
$131$	−13.6533	−	7.88276i	−1.19290	−	0.688720i	−0.233935	−	0.972252i	$-0.575160\pi$
$131$	−13.6533	−	7.88276i	−1.19290	−	0.688720i	−0.958963	+	0.283532i	$0.908494\pi$
$132$	−3.33385	−	1.92480i	−0.290174	−	0.167532i
$133$	−2.18733	+	3.78857i	−0.189666	+	0.328511i
$134$		−	7.74340i		−	0.668928i
$135$	−0.0669680	+	2.23506i	−0.00576369	+	0.192364i
$136$	−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	0.192119	+	0.981372i	$0.438464\pi$
$139$	−8.88756	+	15.3937i	−0.753833	+	1.30568i	−0.945952	+	0.324306i	$0.894869\pi$
$140$	−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
$145$	0.181156	−	6.04610i	0.0150442	−	0.502101i
$146$	−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	$0.478085\pi$
$150$	−0.299356	+	4.99103i	−0.0244423	+	0.407516i
$151$	7.33222	+	12.6998i	0.596687	+	1.03349i	0.993306	+	0.115510i	$0.0368501\pi$
$151$	7.33222	+	12.6998i	0.596687	+	1.03349i	−0.396619	+	0.917983i	$0.629817\pi$
$152$	0.996184	−	0.575147i	0.0808012	−	0.0466506i
$153$	−3.42715	−	5.93600i	−0.277069	−	0.479897i
$154$			14.6403i			1.17975i
$155$	−0.544446	+	18.1709i	−0.0437309	+	1.45952i
$156$		−	2.45005i		−	0.196161i
$157$	14.2552	+	8.23027i	1.13769	+	0.656847i	0.945858	−	0.324581i	$-0.105223\pi$
$157$	14.2552	+	8.23027i	1.13769	+	0.656847i	0.191834	+	0.981427i	$0.438557\pi$
$158$		−	2.97186i		−	0.236428i
$159$	5.57732			0.442310
$160$	1.05954	+	1.96911i	0.0837637	+	0.155672i
$161$	−0.216308	+	0.124886i	−0.0170475	+	0.00984237i
$162$	−1.00000			−0.0785674
$163$	−9.83152	+	17.0287i	−0.770064	+	1.33379i	0.167464	+	0.985878i	$0.446442\pi$
$163$	−9.83152	+	17.0287i	−0.770064	+	1.33379i	−0.937527	+	0.347911i	$0.886891\pi$
$164$	0.239768	−	0.415291i	0.0187228	−	0.0324288i
$165$	7.58027	−	4.07879i	0.590123	−	0.317533i
$166$	−4.83322	+	2.79046i	−0.375131	+	0.216582i
$167$	5.34341	+	9.25505i	0.413485	+	0.716177i	0.995268	−	0.0971667i	$-0.0309780\pi$
$167$	5.34341	+	9.25505i	0.413485	+	0.716177i	−0.581783	+	0.813344i	$0.697645\pi$
$168$	1.90154	−	3.29356i	0.146707	−	0.254104i
$169$	3.49864	−	6.05982i	0.269126	−	0.466140i
$170$	−7.26238	−	13.4969i	−0.556999	−	1.03516i
$171$			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	$-0.197711\pi$
$173$	9.41553	+	5.43606i	0.715849	+	0.413296i	−0.0973739	+	0.995248i	$0.531044\pi$
$174$	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	$0.101129\pi$
$179$			8.35895i			0.624777i	−0.949954	+	0.312388i	$0.898871\pi$
$180$	−2.23506	−	0.0669680i	−0.166592	−	0.00499150i
$181$	9.39587	+	16.2741i	0.698389	+	1.20965i	0.969025	+	0.246964i	$0.0794329\pi$
$181$	9.39587	+	16.2741i	0.698389	+	1.20965i	−0.270635	+	0.962682i	$0.587234\pi$
$182$	−8.06938	+	4.65886i	−0.598142	+	0.345338i
$183$	2.35114	−	4.07230i	0.173802	−	0.301033i
$184$	0.0656760			0.00484170
$185$	−8.94506	−	10.2463i	−0.657654	−	0.753320i
$186$	−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
$190$	−0.0770330	+	2.57098i	−0.00558856	+	0.186519i
$191$		−	13.1251i		−	0.949699i	−0.880067	−	0.474850i	$-0.842502\pi$
$191$		−	13.1251i		−	0.949699i	0.880067	−	0.474850i	$-0.157498\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	1.77545			0.127800			0.0639000	−	0.997956i	$-0.479646\pi$
$193$	1.77545			0.127800			0.0639000	+	0.997956i	$0.479646\pi$
$194$	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	$-0.598672\pi$
$197$	−17.9982	−	10.3913i	−1.28232	−	0.740347i	−0.977272	+	0.211990i	$0.932006\pi$
$198$	1.92480	+	3.33385i	0.136790	+	0.236926i
$199$			22.9945i			1.63003i	0.579437	+	0.815017i	$0.303273\pi$
$199$			22.9945i			1.63003i	−0.579437	+	0.815017i	$0.696727\pi$
$200$	−4.99103	−	0.299356i	−0.352919	−	0.0211677i
$201$	−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
$205$	0.508087	+	0.944259i	0.0354863	+	0.0659499i
$206$	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
$210$	4.02950	+	7.48867i	0.278062	+	0.516767i
$211$	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
$215$	22.4407	+	0.672380i	1.53045	+	0.0458559i
$216$		−	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
$220$	4.07879	+	7.58027i	0.274992	+	0.511062i
$221$	−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
$225$	2.75477	−	4.17268i	0.183651	−	0.278179i
$226$	2.96968	+	5.14363i	0.197540	+	0.342149i
$227$	−5.60894	−	9.71497i	−0.372278	−	0.644805i	0.617637	−	0.786463i	$-0.288090\pi$
$227$	−5.60894	−	9.71497i	−0.372278	−	0.644805i	−0.989916	+	0.141658i	$0.954757\pi$
$228$	−1.15029			−0.0761801
$229$	−8.04647	−	13.9369i	−0.531726	−	0.920976i	−0.999314	−	0.0370298i	$-0.988210\pi$
$229$	−8.04647	−	13.9369i	−0.531726	−	0.920976i	0.467588	−	0.883946i	$-0.345123\pi$
$230$	−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
$235$	0.130060	−	4.34076i	0.00848416	−	0.283160i
$236$		−	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	0.483273	−	0.875470i	$-0.339448\pi$
$239$	−0.514328	−	0.296947i	−0.0332691	−	0.0192079i	−0.516542	+	0.856262i	$0.672781\pi$
$240$	0.0669680	−	2.23506i	0.00432277	−	0.144273i
$241$	9.13422	−	5.27364i	0.588387	−	0.339705i	−0.176073	−	0.984377i	$-0.556339\pi$
$241$	9.13422	−	5.27364i	0.588387	−	0.339705i	0.764459	+	0.644672i	$0.223006\pi$
$242$	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
$250$	6.43651	−	9.14173i	0.407081	−	0.578174i
$251$			28.9037i			1.82439i	0.409761	+	0.912193i	$0.365612\pi$
$251$			28.9037i			1.82439i	−0.409761	+	0.912193i	$0.634388\pi$
$252$	−3.29356	+	1.90154i	−0.207475	+	0.119786i
$253$	0.252826			0.0158951
$254$	15.2426	−	8.80034i	0.956408	−	0.552182i
$255$	−0.459019	+	15.3198i	−0.0287449	+	0.959363i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.71460	+	8.16592i	−0.294089	+	0.509376i	−0.974772	−	0.223201i	$-0.928349\pi$
$257$	−4.71460	+	8.16592i	−0.294089	+	0.509376i	0.680684	+	0.732577i	$0.261683\pi$
$258$			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	−0.697527	+	0.716559i	$0.745716\pi$
$263$	−27.0317	+	15.6068i	−1.66685	+	0.962355i	−0.969321	+	0.245796i	$0.920951\pi$
$264$	−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	−0.948367	−	0.317175i	$-0.897266\pi$
$271$	−3.28422	+	5.68843i	−0.199502	+	0.345547i	0.748865	+	0.662722i	$0.230599\pi$
$272$	3.42715	+	5.93600i	0.207801	+	0.359923i
$273$	9.31772			0.563934
$274$	14.8070	+	8.54885i	0.894526	+	0.516455i
$275$	−19.2135	−	1.15240i	−1.15862	−	0.0694923i
$276$	−0.0568771	−	0.0328380i	−0.00342360	−	0.00197662i
$277$	−6.72455	−	11.6473i	−0.404039	−	0.699816i	0.590170	−	0.807279i	$-0.299061\pi$
$277$	−6.72455	−	11.6473i	−0.404039	−	0.699816i	−0.994209	+	0.107463i	$0.965727\pi$
$278$	8.88756	+	15.3937i	0.533041	+	0.923254i
$279$	7.04073	+	4.06497i	0.421518	+	0.243363i
$280$	−7.48867	+	4.02950i	−0.447534	+	0.240809i
$281$	22.2706	+	12.8579i	1.32855	+	0.767040i	0.985076	−	0.172121i	$-0.0550621\pi$
$281$	22.2706	+	12.8579i	1.32855	+	0.767040i	0.343477	+	0.939161i	$0.388395\pi$
$282$	1.94212			0.115651
$283$	−9.20159	−	15.9376i	−0.546978	−	0.947394i	−0.998480	−	0.0551234i	$-0.982445\pi$
$283$	−9.20159	−	15.9376i	−0.546978	−	0.947394i	0.451502	−	0.892270i	$-0.350889\pi$
$284$	−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	$-0.510692\pi$
$293$	13.9533	−	8.05596i	0.815162	−	0.470634i	0.848745	+	0.528802i	$0.177359\pi$
$294$	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
$300$	4.17268	+	2.75477i	0.240910	+	0.159046i
$301$	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
$305$	−9.25931	+	4.98224i	−0.530186	+	0.285283i
$306$	−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	−0.00863174	−	0.999963i	$-0.502748\pi$
$311$	−15.5003	−	8.94910i	−0.878941	−	0.507457i	−0.870309	+	0.492506i	$0.836081\pi$
$312$	−2.12180	−	1.22502i	−0.120123	−	0.0693532i
$313$	−5.62602	+	9.74455i	−0.318001	+	0.550795i	−0.980071	−	0.198648i	$-0.936345\pi$
$313$	−5.62602	+	9.74455i	−0.318001	+	0.550795i	0.662070	+	0.749442i	$0.269678\pi$
$314$	14.2552	−	8.23027i	0.804470	−	0.464461i
$315$	0.254685	−	8.50013i	0.0143499	−	0.478928i
$316$	−2.57370	−	1.48593i	−0.144782	−	0.0835900i
$317$	2.29777	+	1.32662i	0.129055	+	0.0745102i	0.563138	−	0.826363i	$-0.309594\pi$
$317$	2.29777	+	1.32662i	0.129055	+	0.0745102i	−0.434082	+	0.900873i	$0.642927\pi$
$318$	2.78866	−	4.83010i	0.156380	−	0.270858i
$319$			10.4136i			0.583049i
$320$	2.23506	+	0.0669680i	0.124944	+	0.00374363i
$321$	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
$330$	0.257800	−	8.60410i	0.0141914	−	0.473640i
$331$	15.6212	+	9.01889i	0.858618	+	0.495723i	0.863549	−	0.504265i	$-0.168236\pi$
$331$	15.6212	+	9.01889i	0.858618	+	0.495723i	−0.00493151	+	0.999988i	$0.501570\pi$
$332$			5.58092i			0.306293i
$333$	−5.93072	+	1.35150i	−0.325001	+	0.0740618i
$334$	10.6868			0.584756
$335$	15.2476	−	8.20441i	0.833064	−	0.448255i
$336$	−1.90154	−	3.29356i	−0.103738	−	0.179679i
$337$	−17.1397	+	9.89562i	−0.933660	+	0.539049i	−0.887967	−	0.459907i	$-0.847883\pi$
$337$	−17.1397	+	9.89562i	−0.933660	+	0.539049i	−0.0456926	+	0.998956i	$0.514549\pi$
$338$	−3.49864	−	6.05982i	−0.190301	−	0.329611i
$339$		−	5.93935i		−	0.322581i
$340$	−15.3198	−	0.459019i	−0.830833	−	0.0248938i
$341$		−	31.2970i		−	1.69483i
$342$	0.996184	+	0.575147i	0.0538675	+	0.0311004i
$343$		−	1.76242i		−	0.0951618i
$344$	−10.0403			−0.541337
$345$	0.129323	−	0.0695862i	0.00696252	−	0.00374639i
$346$	9.41553	−	5.43606i	0.506182	−	0.292244i
$347$	−5.12556			−0.275155			−0.137577	−	0.990491i	$-0.543932\pi$
$347$	−5.12556			−0.275155			−0.137577	+	0.990491i	$0.543932\pi$
$348$	1.35255	−	2.34269i	0.0725046	−	0.125582i
$349$	12.9643	−	22.4549i	0.693964	−	1.20198i	−0.276565	−	0.960995i	$-0.589196\pi$
$349$	12.9643	−	22.4549i	0.693964	−	1.20198i	0.970529	−	0.240985i	$-0.0774706\pi$
$350$	1.13847	−	18.9813i	0.0608540	−	1.01459i
$351$	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	$-0.869311\pi$
$353$	−2.11906	+	3.67032i	−0.112786	+	0.195352i	0.804106	+	0.594485i	$0.202644\pi$
$354$	−1.08481	+	1.87894i	−0.0576568	+	0.0998646i
$355$	−7.88475	−	14.6535i	−0.418479	−	0.777727i
$356$		−	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
$365$	0.456829	−	15.2467i	0.0239115	−	0.798050i
$366$	−2.35114	−	4.07230i	−0.122896	−	0.212863i
$367$	0.710723	−	0.410336i	0.0370994	−	0.0214194i	−0.481336	−	0.876536i	$-0.659848\pi$
$367$	0.710723	−	0.410336i	0.0370994	−	0.0214194i	0.518435	+	0.855117i	$0.326515\pi$
$368$	0.0328380	−	0.0568771i	0.00171180	−	0.00296492i
$369$	0.479537			0.0249637
$370$	−13.3461	+	2.62352i	−0.693828	+	0.136390i
$371$	−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	$-0.403580\pi$
$373$	24.6060	−	14.2063i	1.27405	−	0.735572i	0.975747	+	0.218899i	$0.0702466\pi$
$374$	13.1932	+	22.8512i	0.682202	+	1.18161i
$375$	−10.1451	+	4.69872i	−0.523888	+	0.242641i
$376$			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	−0.791350	−	0.611364i	$-0.790621\pi$
$379$	2.60445	−	4.51103i	0.133781	−	0.231716i	0.925131	+	0.379647i	$0.123955\pi$
$380$	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	$-0.116942\pi$
$383$	3.04474	+	5.27364i	0.155579	+	0.269470i	−0.777691	+	0.628647i	$0.783609\pi$
$384$			1.00000i			0.0510310i
$385$	−28.8284	+	15.5120i	−1.46923	+	0.790563i
$386$	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	−0.971024	−	0.238981i	$-0.923187\pi$
$389$	−24.6454	+	14.2290i	−1.24957	+	0.721441i	−0.278549	+	0.960422i	$0.589853\pi$
$390$	4.82440	−	2.59591i	0.244293	−	0.131449i
$391$	−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
$395$	5.85190	−	3.14879i	0.294441	−	0.158433i
$396$	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
$400$	−2.75477	+	4.17268i	−0.137738	+	0.208634i
$401$		−	1.30549i		−	0.0651933i	−0.999469	−	0.0325967i	$-0.989622\pi$
$401$		−	1.30549i		−	0.0651933i	0.999469	−	0.0325967i	$-0.0103777\pi$
$402$	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
$405$	−1.05954	−	1.96911i	−0.0526488	−	0.0978457i
$406$	−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	0.833848	−	0.551994i	$-0.186133\pi$
$409$	15.6275	+	9.02256i	0.772731	+	0.446137i	−0.0611167	+	0.998131i	$0.519466\pi$
$410$	1.07180	+	0.0321136i	0.0529322	+	0.00158598i
$411$	−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	−0.914976	−	0.403507i	$-0.867791\pi$
$419$	−2.21154	+	3.83049i	−0.108041	+	0.187132i	0.806936	+	0.590639i	$0.201124\pi$
$420$	8.50013	+	0.254685i	0.414764	+	0.0124273i
$421$			36.6940i			1.78835i	0.447713	+	0.894177i	$0.352239\pi$
$421$			36.6940i			1.78835i	−0.447713	+	0.894177i	$0.647761\pi$
$422$	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
$425$	18.8820	−	28.6008i	0.915911	−	1.38734i
$426$	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	−0.318750	−	0.947839i	$-0.603263\pi$
$431$	7.11522	−	4.10797i	0.342728	−	0.197874i	0.661478	+	0.749965i	$0.269930\pi$
$432$	−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
$435$	2.86616	+	5.32665i	0.137422	+	0.255393i
$436$			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	−0.518649	−	0.854987i	$-0.673565\pi$
$439$	−0.786419	+	0.454039i	−0.0375337	+	0.0216701i	0.481116	+	0.876657i	$0.340232\pi$
$440$	8.60410	+	0.257800i	0.410185	+	0.0122901i
$441$	−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	−0.0319278	−	0.999490i	$-0.510165\pi$
$449$	17.3266	−	10.0035i	0.817692	−	0.472095i	0.849620	+	0.527395i	$0.176831\pi$
$450$	−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	$-0.0702352\pi$
$457$	6.37769	+	11.0465i	0.298336	+	0.516733i	−0.677420	+	0.735597i	$0.736902\pi$
$458$	−16.0929			−0.751974
$459$	5.93600	+	3.42715i	0.277069	+	0.159966i
$460$	0.0695862	+	0.129323i	0.00324447	+	0.00602972i
$461$	19.2166	+	11.0947i	0.895005	+	0.516731i	0.875576	−	0.483080i	$-0.160482\pi$
$461$	19.2166	+	11.0947i	0.895005	+	0.516731i	0.0194288	+	0.999811i	$0.493815\pi$
$462$	−7.32017	−	12.6789i	−0.340565	−	0.589876i
$463$	−6.56761	−	11.3754i	−0.305223	−	0.528661i	0.672088	−	0.740471i	$-0.265398\pi$
$463$	−6.56761	−	11.3754i	−0.305223	−	0.528661i	−0.977311	+	0.211810i	$0.932064\pi$
$464$	2.34269	+	1.35255i	0.108757	+	0.0627908i
$465$	−8.61397	−	16.0087i	−0.399463	−	0.742386i
$466$	−20.2074	−	11.6668i	−0.936091	−	0.540453i
$467$	−2.63986			−0.122158			−0.0610790	−	0.998133i	$-0.519454\pi$
$467$	−2.63986			−0.122158			−0.0610790	+	0.998133i	$0.519454\pi$
$468$	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	0.262726	−	0.964870i	$-0.415378\pi$
$479$	−9.66298	−	5.57892i	−0.441513	−	0.254907i	−0.704239	+	0.709963i	$0.748712\pi$
$480$	−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
$485$	6.49827	+	0.194704i	0.295071	+	0.00884106i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	25.4527			1.15337			0.576686	−	0.816966i	$-0.304346\pi$
$487$	25.4527			1.15337			0.576686	+	0.816966i	$0.304346\pi$
$488$	4.07230	−	2.35114i	0.184344	−	0.106431i
$489$		−	19.6630i		−	0.889193i
$490$	−7.90776	−	14.6963i	−0.357236	−	0.663910i
$491$	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	−0.961696	−	0.274119i	$-0.911614\pi$
$499$	−26.9210	+	15.5428i	−1.20515	+	0.695793i	−0.243453	+	0.969913i	$0.578280\pi$
$500$	−4.69872	−	10.1451i	−0.210133	−	0.453701i
$501$	−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	$-0.908134\pi$
$503$	−5.22198	+	9.04473i	−0.232836	+	0.403284i	0.725805	+	0.687900i	$0.241467\pi$
$504$			3.80308i			0.169403i
$505$	6.32726	+	0.189580i	0.281559	+	0.00843621i
$506$	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	−0.986731	−	0.162365i	$-0.948088\pi$
$509$	−7.95848	+	13.7845i	−0.352753	+	0.610987i	0.633977	+	0.773352i	$0.281421\pi$
$510$	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
$515$	37.8211	+	1.13321i	1.66660	+	0.0499353i
$516$	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
$520$	2.59591	+	4.82440i	0.113838	+	0.211564i
$521$	−14.8542	−	25.7282i	−0.650774	−	1.12717i	−0.982935	−	0.183951i	$-0.941111\pi$
$521$	−14.8542	−	25.7282i	−0.650774	−	1.12717i	0.332161	−	0.943223i	$-0.392222\pi$
$522$	−2.34269	+	1.35255i	−0.102537	+	0.0591997i
$523$	−18.5161	−	32.0708i	−0.809651	−	1.40236i	−0.913106	−	0.407723i	$-0.866323\pi$
$523$	−18.5161	−	32.0708i	−0.809651	−	1.40236i	0.103455	−	0.994634i	$-0.467010\pi$
$524$			15.7655i			0.688720i
$525$	−10.4766	+	15.8690i	−0.457236	+	0.692582i
$526$			31.2136i			1.36098i
$527$	48.2593	+	27.8625i	2.10221	+	1.21371i
$528$			3.84960i			0.167532i
$529$	−22.9957			−0.999812
$530$	−10.9823	+	5.90937i	−0.477042	+	0.256687i
$531$	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
$535$	−17.3199	+	9.31950i	−0.748806	+	0.402917i
$536$	−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
$540$	1.96911	−	1.05954i	0.0847369	−	0.0455952i
$541$			5.98204i			0.257188i	0.991697	+	0.128594i	$0.0410464\pi$
$541$			5.98204i			0.257188i	−0.991697	+	0.128594i	$0.958954\pi$
$542$	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	$-0.446589\pi$
$547$	7.81210			0.334021			0.167011	+	0.985955i	$0.446589\pi$
$548$	14.8070	−	8.54885i	0.632525	−	0.365189i
$549$			4.70229i			0.200689i
$550$	−10.6047	+	16.0631i	−0.452188	+	0.684935i
$551$	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
$555$	12.8698	+	4.40099i	0.546292	+	0.186812i
$556$	17.7751			0.753833
$557$	−1.26410	+	2.18949i	−0.0535618	+	0.0927717i	−0.891563	−	0.452896i	$-0.850391\pi$
$557$	−1.26410	+	2.18949i	−0.0535618	+	0.0927717i	0.838001	+	0.545668i	$0.183724\pi$
$558$	7.04073	−	4.06497i	0.298058	−	0.172084i
$559$	−12.2996	−	21.3035i	−0.520218	−	0.901044i
$560$	−0.254685	+	8.50013i	−0.0107624	+	0.359196i
$561$		−	26.3863i		−	1.11403i
$562$	22.2706	−	12.8579i	0.939428	−	0.542379i
$563$	6.95366			0.293062			0.146531	−	0.989206i	$-0.453189\pi$
$563$	6.95366			0.293062			0.146531	+	0.989206i	$0.453189\pi$
$564$	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	$0.127385\pi$
$569$			18.5866i			0.779192i	−0.920986	+	0.389596i	$0.872615\pi$
$570$	−1.21878	−	2.26505i	−0.0510490	−	0.0948727i
$571$	0.540231	−	0.935708i	0.0226080	−	0.0391582i	−0.854500	−	0.519451i	$-0.826136\pi$
$571$	0.540231	−	0.935708i	0.0226080	−	0.0391582i	0.877108	+	0.480293i	$0.159470\pi$
$572$	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
$575$	−0.327791	−	0.0196605i	−0.0136698	−	0.000819900i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−13.4705	+	23.3317i	−0.560786	+	0.971310i	0.436642	+	0.899635i	$0.356168\pi$
$577$	−13.4705	+	23.3317i	−0.560786	+	0.971310i	−0.997428	+	0.0716745i	$0.977166\pi$
$578$	−29.9814			−1.24706
$579$	−1.53759	+	0.887727i	−0.0639000	+	0.0368927i
$580$	−5.32665	+	2.86616i	−0.221177	+	0.119011i
$581$	−21.2247			−0.880549
$582$			2.90742i			0.120516i
$583$	18.5939	+	10.7352i	0.770082	+	0.444607i
$584$			6.82160i			0.282280i
$585$	−5.47601	−	0.164075i	−0.226405	−	0.00678365i
$586$		−	16.1119i		−	0.665577i
$587$	−7.31683	−	12.6731i	−0.301998	−	0.523076i	0.674590	−	0.738192i	$-0.264320\pi$
$587$	−7.31683	−	12.6731i	−0.301998	−	0.523076i	−0.976588	+	0.215116i	$0.930987\pi$
$588$	6.46351	−	3.73171i	0.266551	−	0.153893i
$589$	−4.67591	−	8.09892i	−0.192668	−	0.333710i
$590$	4.27220	−	2.29878i	0.175884	−	0.0946395i
$591$	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
$595$	1.74569	−	58.2625i	0.0715661	−	2.38853i
$596$	−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	−0.891770	−	0.452489i	$-0.850536\pi$
$599$	−20.5035	−	35.5132i	−0.837752	−	1.45103i	0.0540178	−	0.998540i	$-0.482797\pi$
$600$	4.47204	−	2.23627i	0.182570	−	0.0912952i
$601$	−20.0982	+	34.8112i	−0.819824	+	1.41998i	0.0859879	+	0.996296i	$0.472595\pi$
$601$	−20.0982	+	34.8112i	−0.819824	+	1.41998i	−0.905812	+	0.423680i	$0.860738\pi$
$602$		−	38.1841i		−	1.55627i
$603$		−	7.74340i		−	0.315335i
$604$	7.33222	−	12.6998i	0.298344	−	0.516746i
$605$	8.53663	+	0.255778i	0.347064	+	0.0103989i
$606$			2.83091i			0.114998i
$607$	11.0397	−	19.1214i	0.448089	−	0.776114i	−0.550172	−	0.835051i	$-0.685438\pi$
$607$	11.0397	−	19.1214i	0.448089	−	0.776114i	0.998262	+	0.0589376i	$0.0187713\pi$
$608$	−0.996184	−	0.575147i	−0.0404006	−	0.0233253i
$609$	8.90945	+	5.14388i	0.361029	+	0.208440i
$610$	−0.314903	+	10.5099i	−0.0127500	+	0.425534i
$611$	−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	$-0.334423\pi$
$613$	−0.146782	−	0.0847445i	−0.00592846	−	0.00342280i	−0.502961	+	0.864309i	$0.667756\pi$
$614$	−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	$-0.00759641\pi$
$617$	36.7353	+	21.2091i	1.47891	+	0.853848i	0.479192	+	0.877710i	$0.340930\pi$
$618$			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	$0.760177\pi$
$620$	16.0087	−	8.61397i	0.642926	−	0.345945i
$621$		−	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
$625$	24.8208	+	2.98819i	0.992831	+	0.119528i
$626$	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	0.528420	−	0.848983i	$-0.322785\pi$
$631$	1.44160	+	0.832307i	0.0573891	+	0.0331336i	−0.471031	+	0.882117i	$0.656118\pi$
$632$	−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	−0.708958	−	0.705251i	$-0.750834\pi$
$641$	6.48865	−	11.2387i	0.256286	−	0.443901i	0.965244	+	0.261350i	$0.0841677\pi$
$642$	−4.39791	−	7.61741i	−0.173572	−	0.300635i
$643$	20.0143			0.789285			0.394643	−	0.918835i	$-0.370868\pi$
$643$	20.0143			0.789285			0.394643	+	0.918835i	$0.370868\pi$
$644$	0.216308	+	0.124886i	0.00852374	+	0.00492118i
$645$	−19.7704	+	10.6381i	−0.778461	+	0.418874i
$646$	6.82815	+	3.94223i	0.268650	+	0.155105i
$647$	−25.0163	−	43.3294i	−0.983491	−	1.70346i	−0.648460	−	0.761248i	$-0.724587\pi$
$647$	−25.0163	−	43.3294i	−0.983491	−	1.70346i	−0.335030	−	0.942207i	$-0.608747\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−7.23317	−	4.17607i	−0.283927	−	0.163925i
$650$	−12.2283	−	0.733435i	−0.479631	−	0.0287677i
$651$	−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	$-0.125691\pi$
$653$	3.28047	+	5.68194i	0.128375	+	0.222351i	−0.794672	+	0.607039i	$0.792357\pi$
$654$	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	0.782989	+	0.622035i	$0.213694\pi$
$659$	23.8790	+	41.3596i	0.930193	+	1.61114i	0.147203	+	0.989106i	$0.452973\pi$
$660$	−7.32247	−	4.52531i	−0.285027	−	0.176148i
$661$	31.6257	−	18.2591i	1.23010	−	0.710197i	0.263047	−	0.964783i	$-0.415272\pi$
$661$	31.6257	−	18.2591i	1.23010	−	0.710197i	0.967050	+	0.254586i	$0.0819391\pi$
$662$	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
$670$	0.518560	−	17.3070i	0.0200337	−	0.668628i
$671$	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	$-0.690764\pi$
$673$	−3.39834	+	1.96203i	−0.130996	+	0.0756307i	0.433070	+	0.901360i	$0.357430\pi$
$674$			19.7912i			0.762330i
$675$	−0.299356	+	4.99103i	−0.0115222	+	0.192105i
$676$	−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	$-0.751999\pi$
$683$	6.60542	−	11.4409i	0.252749	−	0.437774i	0.964282	+	0.264879i	$0.0853319\pi$
$684$	0.996184	−	0.575147i	0.0380901	−	0.0219913i
$685$	−1.14500	+	38.2145i	−0.0437482	+	1.46010i
$686$	−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
$690$	0.00439819	−	0.146790i	0.000167436	−	0.00558821i
$691$	23.9934	−	41.5579i	0.912753	−	1.58094i	0.102596	−	0.994723i	$-0.467285\pi$
$691$	23.9934	−	41.5579i	0.912753	−	1.58094i	0.810158	−	0.586212i	$-0.199381\pi$
$692$		−	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
$700$	−15.8690	−	10.4766i	−0.599793	−	0.395978i
$701$	−13.4755	−	7.78011i	−0.508964	−	0.293851i	0.223444	−	0.974717i	$-0.428270\pi$
$701$	−13.4755	−	7.78011i	−0.508964	−	0.293851i	−0.732408	+	0.680866i	$0.761603\pi$
$702$		−	2.45005i		−	0.0924710i
$703$	6.68540	+	2.06469i	0.252145	+	0.0778714i
$704$	−3.84960			−0.145087
$705$	2.05774	+	3.82424i	0.0774991	+	0.144029i
$706$	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	$0.000721533\pi$
$709$			0.120714i			0.00453352i	−0.999997	+	0.00226676i	$0.999278\pi$
$710$	−16.6327	−	0.498356i	−0.624213	−	0.0187030i
$711$		−	2.97186i		−	0.111453i
$712$	−6.89417	−	3.98035i	−0.258370	−	0.149170i
$713$		−	0.533942i		−	0.0199963i
$714$	26.0675			0.975550
$715$	9.99322	+	18.5720i	0.373725	+	0.694554i
$716$	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	−0.602864	−	0.797844i	$-0.705974\pi$
$719$	10.4447	−	18.0907i	0.389521	−	0.674671i	0.992385	+	0.123173i	$0.0393072\pi$
$720$	1.05954	+	1.96911i	0.0394866	+	0.0733843i
$721$	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
$725$	0.809790	−	13.5013i	0.0300749	−	0.501425i
$726$			3.81941i			0.141752i
$727$	−14.7316	−	25.5159i	−0.546364	−	0.946331i	−0.998520	−	0.0543916i	$-0.982678\pi$
$727$	−14.7316	−	25.5159i	−0.546364	−	0.946331i	0.452155	−	0.891939i	$-0.350655\pi$
$728$	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	$-0.788017\pi$
$733$	−17.4475	+	10.0733i	−0.644438	+	0.372067i	0.141884	+	0.989883i	$0.454684\pi$
$734$		−	0.820672i		−	0.0302915i
$735$	−0.499811	+	16.6812i	−0.0184358	+	0.615296i
$736$	−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	$0.532881\pi$
$740$	−4.40099	+	12.8698i	−0.161784	+	0.473103i
$741$	−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	$-0.599205\pi$
$743$	9.93130	−	5.73384i	0.364344	−	0.210354i	0.670985	+	0.741471i	$0.265872\pi$
$744$	4.06497	+	7.04073i	0.149029	+	0.258126i
$745$	3.75370	+	0.112470i	0.137525	+	0.00412059i
$746$		−	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
$755$	15.5375	+	28.8758i	0.565468	+	1.05090i
$756$	1.90154	−	3.29356i	0.0691583	−	0.119786i
$757$	15.3612	−	26.6063i	0.558311	−	0.967022i	−0.439327	−	0.898327i	$-0.644783\pi$
$757$	15.3612	−	26.6063i	0.558311	−	0.967022i	0.997638	−	0.0686950i	$-0.0218835\pi$
$758$	−2.60445	−	4.51103i	−0.0945978	−	0.163848i
$759$	−0.218954	+	0.126413i	−0.00794753	+	0.00458851i
$760$	2.26505	−	1.21878i	0.0821621	−	0.0442098i
$761$	−1.51563	+	2.62515i	−0.0549415	+	0.0951615i	−0.892188	−	0.451664i	$-0.850831\pi$
$761$	−1.51563	+	2.62515i	−0.0549415	+	0.0951615i	0.837247	+	0.546826i	$0.184164\pi$
$762$	−8.80034	+	15.2426i	−0.318803	+	0.552182i
$763$	−40.5738			−1.46887
$764$	−11.3667	+	6.56255i	−0.411232	+	0.237425i
$765$	−7.26238	−	13.4969i	−0.262572	−	0.487980i
$766$	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	$-0.799887\pi$
$769$		−	32.6155i		−	1.17615i	0.808808	−	0.588073i	$-0.200113\pi$
$770$	−0.980434	+	32.7221i	−0.0353324	+	1.17922i
$771$		−	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	$-0.660404\pi$
$773$	0.947360	−	0.546959i	0.0340742	−	0.0196727i	0.516940	+	0.856021i	$0.327071\pi$
$774$	−5.02016	−	8.69516i	−0.180446	−	0.312541i
$775$	−2.43374	+	40.5768i	−0.0874227	+	1.45756i
$776$	−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
$780$	0.164075	−	5.47601i	0.00587482	−	0.196073i
$781$	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
$790$	0.199019	−	6.64229i	0.00708079	−	0.236322i
$791$			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
$795$	12.4657	+	0.373502i	0.442112	+	0.0132467i
$796$	19.9138	−	11.4972i	0.705826	−	0.407509i
$797$	0.709094	−	1.22819i	0.0251174	−	0.0435046i	−0.853193	−	0.521595i	$-0.825337\pi$
$797$	0.709094	−	1.22819i	0.0251174	−	0.0435046i	0.878311	+	0.478090i	$0.158671\pi$
$798$	−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
$805$	−0.491826	+	0.264642i	−0.0173346	+	0.00932740i
$806$		−	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	0.0727802	−	0.997348i	$-0.476813\pi$
$809$	27.6721	−	15.9765i	0.972899	−	0.561704i	0.900119	+	0.435645i	$0.143480\pi$
$810$	−2.23506	−	0.0669680i	−0.0785322	−	0.00235302i
$811$	13.5475	+	23.4650i	0.475718	+	0.823967i	0.999613	−	0.0278156i	$-0.00885512\pi$
$811$	13.5475	+	23.4650i	0.475718	+	0.823967i	−0.523896	+	0.851783i	$0.675522\pi$
$812$	−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	0.914859	−	0.403774i	$-0.132302\pi$
$821$	3.08741	+	5.34755i	0.107751	+	0.186631i	−0.807108	+	0.590404i	$0.798968\pi$
$822$	−17.0977			−0.596351
$823$	−41.9378	−	24.2128i	−1.46186	−	0.844005i	−0.462763	−	0.886482i	$-0.653142\pi$
$823$	−41.9378	−	24.2128i	−1.46186	−	0.844005i	−0.999097	+	0.0424769i	$0.986475\pi$
$824$	−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	−0.844746	−	0.535168i	$-0.820248\pi$
$827$	−25.4747	−	44.1235i	−0.885842	−	1.53432i	−0.0410959	−	0.999155i	$-0.513085\pi$
$828$	0.0656760			0.00228240
$829$	28.4803	+	16.4431i	0.989162	+	0.571093i	0.905024	−	0.425361i	$-0.139853\pi$
$829$	28.4803	+	16.4431i	0.989162	+	0.571093i	0.0841386	+	0.996454i	$0.473186\pi$
$830$	−10.9894	+	5.91319i	−0.381449	+	0.205250i
$831$	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
$835$	11.3231	+	21.0435i	0.391851	+	0.728240i
$836$	−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	−0.524628	−	0.851331i	$-0.675796\pi$
$839$	13.7575	−	23.8286i	0.474960	−	0.822656i	0.999589	+	0.0286758i	$0.00912903\pi$
$840$	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	$-0.805435\pi$
$853$	2.55653	−	4.42804i	0.0875340	−	0.151613i	0.906468	+	0.422274i	$0.138768\pi$
$854$	8.94159	+	15.4873i	0.305975	+	0.529964i
$855$	−0.0770330	+	2.57098i	−0.00263447	+	0.0879258i
$856$	7.61741	−	4.39791i	0.260358	−	0.150318i
$857$	37.2126			1.27116			0.635580	−	0.772035i	$-0.280761\pi$
$857$	37.2126			1.27116			0.635580	+	0.772035i	$0.280761\pi$
$858$	−8.16808	+	4.71585i	−0.278854	+	0.160996i
$859$		−	5.99631i		−	0.204591i	−0.994754	−	0.102296i	$-0.967381\pi$
$859$		−	5.99631i		−	0.204591i	0.994754	−	0.102296i	$-0.0326188\pi$
$860$	−10.6381	−	19.7704i	−0.362755	−	0.674167i
$861$	−1.82372			−0.0621521
$862$		−	8.21595i		−	0.279836i
$863$	42.5951	+	24.5923i	1.44995	+	0.837130i	0.998478	−	0.0551536i	$-0.0175648\pi$
$863$	42.5951	+	24.5923i	1.44995	+	0.837130i	0.451475	+	0.892284i	$0.350898\pi$
$864$	−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
$870$	6.04610	+	0.181156i	0.204982	+	0.00614176i
$871$	−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
$875$	38.5824	−	17.8696i	1.30432	−	0.604102i
$876$	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	0.969813	+	0.243851i	$0.0784109\pi$
$881$	20.6610	+	35.7860i	0.696088	+	1.20566i	−0.273725	+	0.961808i	$0.588256\pi$
$882$	−7.46342			−0.251306
$883$	17.4829	+	30.2812i	0.588345	+	1.01904i	0.994449	+	0.105217i	$0.0335536\pi$
$883$	17.4829	+	30.2812i	0.588345	+	1.01904i	−0.406105	+	0.913827i	$0.633113\pi$
$884$	8.39667	+	14.5435i	0.282411	+	0.489150i
$885$	−4.84923	−	0.145295i	−0.163005	−	0.00488403i
$886$	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
$890$	15.6755	−	8.43466i	0.525443	−	0.282730i
$891$	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
$895$	−0.559782	+	18.6828i	−0.0187115	+	0.624497i
$896$		−	3.80308i		−	0.127052i
$897$	−0.139351	−	0.0804546i	−0.00465281	−	0.00268630i
$898$		−	20.0070i		−	0.667643i
$899$	21.9924			0.733487
$900$	−4.99103	−	0.299356i	−0.166368	−	0.00997853i
$901$	−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
$905$	19.9105	+	37.0029i	0.661848	+	1.23002i
$906$	−12.6998	+	7.33222i	−0.421922	+	0.243597i
$907$	−18.2511	−	31.6119i	−0.606018	−	1.04965i	−0.991890	−	0.127102i	$-0.959432\pi$
$907$	−18.2511	−	31.6119i	−0.606018	−	1.04965i	0.385871	−	0.922553i	$-0.373901\pi$
$908$	−5.60894	+	9.71497i	−0.186139	+	0.322402i
$909$	1.41545	−	2.45164i	0.0469476	−	0.0813156i
$910$	−18.3476	+	9.87246i	−0.608217	+	0.327269i
$911$			33.5547i			1.11172i	0.831277	+	0.555858i	$0.187610\pi$
$911$			33.5547i			1.11172i	−0.831277	+	0.555858i	$0.812390\pi$
$912$	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	$-0.957145\pi$
$919$		−	8.13814i		−	0.268452i	0.990951	−	0.134226i	$-0.0428549\pi$
$920$	0.146790	+	0.00439819i	0.00483953	+	0.000145004i
$921$	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
$925$	−19.3066	−	23.5001i	−0.634798	−	0.772678i
$926$	−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	0.798239	−	0.602341i	$-0.205765\pi$
$929$	−3.73445	−	6.46826i	−0.122523	−	0.212217i	−0.920762	+	0.390124i	$0.872432\pi$
$930$	−18.1709	−	0.544446i	−0.595849	−	0.0178531i
$931$			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	−0.989664	−	0.143405i	$-0.954195\pi$
$937$	−49.2427	−	28.4303i	−1.60869	−	0.928777i	−0.619024	−	0.785372i	$-0.712472\pi$
$938$	−14.7244	−	25.5034i	−0.480768	−	0.832715i
$939$		−	11.2520i		−	0.367196i
$940$	−3.82424	+	2.05774i	−0.124733	+	0.0671162i
$941$	29.4403	−	50.9920i	0.959725	−	1.66229i	0.236561	−	0.971617i	$-0.423980\pi$
$941$	29.4403	−	50.9920i	0.959725	−	1.66229i	0.723165	−	0.690676i	$-0.242687\pi$
$942$	−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
$945$	4.02950	+	7.48867i	0.131080	+	0.243607i
$946$	−19.3256	+	33.4729i	−0.628329	+	1.08830i
$947$	−28.7838	+	49.8551i	−0.935349	+	1.62007i	−0.161339	+	0.986899i	$0.551581\pi$
$947$	−28.7838	+	49.8551i	−0.935349	+	1.62007i	−0.774010	+	0.633174i	$0.781752\pi$
$948$	2.97186			0.0965214
$949$	−14.4741	+	8.35661i	−0.469848	+	0.271267i
$950$	−0.344347	+	5.74116i	−0.0111721	+	0.186268i
$951$	−2.65323			−0.0860370
$952$			26.0675i			0.844851i
$953$	17.2207	+	9.94235i	0.557832	+	0.322064i	0.752275	−	0.658850i	$-0.228957\pi$
$953$	17.2207	+	9.94235i	0.557832	+	0.322064i	−0.194443	+	0.980914i	$0.562290\pi$
$954$			5.57732i			0.180572i
$955$	0.878962	−	29.3355i	0.0284426	−	0.949273i
$956$			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
$960$	−1.96911	+	1.05954i	−0.0635527	+	0.0341964i
$961$	−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
$965$	3.96826	+	0.118899i	0.127743	+	0.00382749i
$966$	−0.124886	−	0.216308i	−0.00401813	−	0.00695960i
$967$	−0.967950	−	1.67654i	−0.0311272	−	0.0539139i	0.850042	−	0.526715i	$-0.176576\pi$
$967$	−0.967950	−	1.67654i	−0.0311272	−	0.0539139i	−0.881169	+	0.472801i	$0.843243\pi$
$968$	−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	0.159861	+	0.987140i	$0.448895\pi$
$971$	−24.1484	+	41.8262i	−0.774957	+	1.34227i	−0.934818	+	0.355126i	$0.884438\pi$
$972$		−	1.00000i		−	0.0320750i
$973$			67.6002i			2.16716i
$974$	12.7264	−	22.0427i	0.407779	−	0.706294i
$975$	10.2233	+	6.74930i	0.327406	+	0.216151i
$976$		−	4.70229i		−	0.150517i
$977$	11.5097	−	19.9353i	0.368226	−	0.637787i	−0.621062	−	0.783761i	$-0.713298\pi$
$977$	11.5097	−	19.9353i	0.368226	−	0.637787i	0.989288	+	0.145975i	$0.0466318\pi$
$978$	−17.0287	−	9.83152i	−0.544517	−	0.314377i
$979$	−26.5398	−	15.3228i	−0.848215	−	0.489717i
$980$	−16.6812	−	0.499811i	−0.532862	−	0.0159659i
$981$	−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	$-0.589447\pi$
$983$	−39.1296	−	22.5915i	−1.24804	−	0.720557i	−0.970719	+	0.240219i	$0.922781\pi$
$984$	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
$990$	4.07879	+	7.58027i	0.129632	+	0.240917i
$991$			33.6103i			1.06767i	0.845589	+	0.533834i	$0.179249\pi$
$991$			33.6103i			1.06767i	−0.845589	+	0.533834i	$0.820751\pi$
$992$	−7.04073	+	4.06497i	−0.223543	+	0.129063i
$993$	−18.0378			−0.572412
$994$	−24.5097	+	14.1507i	−0.777400	+	0.448832i
$995$	−1.53989	+	51.3941i	−0.0488179	+	1.62930i
$996$	−2.79046	−	4.83322i	−0.0884192	−	0.153146i
$997$	0.517102	−	0.895647i	0.0163768	−	0.0283654i	−0.857721	−	0.514116i	$-0.828120\pi$
$997$	0.517102	−	0.895647i	0.0163768	−	0.0283654i	0.874098	+	0.485750i	$0.161454\pi$
$998$			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.b.619.9	yes	36
5.4	even	2		1110.2.ba.a.619.10	yes	36
37.11	even	6		1110.2.ba.a.529.10	✓	36
185.159	even	6	inner	1110.2.ba.b.529.9	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.10	✓	36	37.11	even	6
1110.2.ba.a.619.10	yes	36	5.4	even	2
1110.2.ba.b.529.9	yes	36	185.159	even	6	inner
1110.2.ba.b.619.9	yes	36	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.23506 + 0.0669680i) q^{5} +1.00000i q^{6} +(3.29356 - 1.90154i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.23506 + 0.0669680i) 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} +(-1.96911 + 1.05954i) 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} +(-1.05954 - 1.96911i) q^{20} +(-1.90154 + 3.29356i) q^{21} +(-1.92480 + 3.33385i) q^{22} -0.0656760 q^{23} +(0.866025 - 0.500000i) q^{24} +(4.99103 + 0.299356i) q^{25} -2.45005 q^{26} +1.00000i q^{27} +(-3.29356 - 1.90154i) q^{28} -2.70511i q^{29} +(-0.0669680 + 2.23506i) q^{30} +8.12994i q^{31} +(0.500000 + 0.866025i) q^{32} +(3.33385 - 1.92480i) q^{33} +(-3.42715 - 5.93600i) q^{34} +(7.48867 - 4.02950i) q^{35} -1.00000 q^{36} +(-4.13579 - 4.46040i) q^{37} +1.15029i q^{38} +(2.12180 + 1.22502i) q^{39} +(-2.23506 - 0.0669680i) 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} +(2.75477 - 4.17268i) q^{50} +6.85430i q^{51} +(-1.22502 + 2.12180i) q^{52} +(-4.83010 - 2.78866i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-8.60410 - 0.257800i) 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} +(-2.59591 - 4.82440i) q^{65} -3.84960i q^{66} +(6.70598 - 3.87170i) q^{67} -6.85430 q^{68} +(0.0568771 - 0.0328380i) q^{69} +(0.254685 - 8.50013i) 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} +(-1.05954 - 1.96911i) 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} +(-2.26505 + 1.21878i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} + 14 q^{13} + 2 q^{15} - 18 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{20} + 2 q^{22} + 20 q^{23} - 2 q^{25} + 28 q^{26} - 2 q^{30} + 18 q^{32} + 6 q^{33} - 20 q^{35} - 36 q^{36} - 20 q^{37} + 6 q^{39} - 4 q^{40} + 10 q^{41} - 2 q^{44} + 2 q^{45} + 10 q^{46} + 10 q^{49} - 4 q^{50} + 14 q^{52} + 12 q^{53} + 40 q^{55} - 8 q^{57} - 30 q^{58} + 18 q^{59} - 4 q^{60} - 6 q^{61} + 12 q^{62} + 36 q^{64} - 32 q^{65} - 36 q^{67} + 12 q^{69} - 40 q^{70} - 24 q^{71} - 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} + 24 q^{77} + 6 q^{78} - 2 q^{80} - 18 q^{81} + 20 q^{82} - 36 q^{83} + 26 q^{85} + 10 q^{87} - 4 q^{88} - 2 q^{90} - 36 q^{91} - 10 q^{92} - 12 q^{93} + 12 q^{94} + 18 q^{95} - 52 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 + 4 * 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 - 2 * q^20 + 2 * q^22 + 20 * q^23 - 2 * q^25 + 28 * q^26 - 2 * q^30 + 18 * q^32 + 6 * q^33 - 20 * q^35 - 36 * q^36 - 20 * q^37 + 6 * q^39 - 4 * q^40 + 10 * q^41 - 2 * q^44 + 2 * q^45 + 10 * q^46 + 10 * q^49 - 4 * q^50 + 14 * q^52 + 12 * q^53 + 40 * q^55 - 8 * q^57 - 30 * q^58 + 18 * q^59 - 4 * q^60 - 6 * q^61 + 12 * q^62 + 36 * q^64 - 32 * q^65 - 36 * q^67 + 12 * q^69 - 40 * 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 - 2 * q^90 - 36 * q^91 - 10 * q^92 - 12 * q^93 + 12 * q^94 + 18 * q^95 - 52 * q^97 - 10 * q^98 + 2 * q^99

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