LMFDB - Embedded newform 133.2.g.a.102.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [133,2,Mod(30,133)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(133, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("133.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 133 = 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	133.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			102.6
Character	$\chi$	$=$	133.102
Dual form			133.2.g.a.30.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0371811 + 0.0643995i) q^{2} +1.39660 q^{3} +(0.997235 + 1.72726i) q^{4} +(1.23136 - 2.13278i) q^{5} +(-0.0519269 + 0.0899401i) q^{6} +(-2.54166 + 0.734810i) q^{7} -0.297037 q^{8} -1.04952 q^{9} +O(q^{10})$	\(q+(-0.0371811 + 0.0643995i) q^{2} +1.39660 q^{3} +(0.997235 + 1.72726i) q^{4} +(1.23136 - 2.13278i) q^{5} +(-0.0519269 + 0.0899401i) q^{6} +(-2.54166 + 0.734810i) q^{7} -0.297037 q^{8} -1.04952 q^{9} +(0.0915665 + 0.158598i) q^{10} +(0.231887 - 0.401640i) q^{11} +(1.39273 + 2.41229i) q^{12} +(0.0203793 - 0.0352981i) q^{13} +(0.0471804 - 0.191003i) q^{14} +(1.71971 - 2.97863i) q^{15} +(-1.98343 + 3.43539i) q^{16} +3.00534 q^{17} +(0.0390222 - 0.0675885i) q^{18} +(-0.864338 - 4.27234i) q^{19} +4.91182 q^{20} +(-3.54968 + 1.02623i) q^{21} +(0.0172436 + 0.0298668i) q^{22} -4.22537 q^{23} -0.414841 q^{24} +(-0.532495 - 0.922308i) q^{25} +(0.00151545 + 0.00262484i) q^{26} -5.65554 q^{27} +(-3.80385 - 3.65734i) q^{28} +(1.44097 - 2.49583i) q^{29} +(0.127881 + 0.221497i) q^{30} +(-2.97334 + 5.14997i) q^{31} +(-0.444529 - 0.769947i) q^{32} +(0.323853 - 0.560929i) q^{33} +(-0.111742 + 0.193542i) q^{34} +(-1.56252 + 6.32562i) q^{35} +(-1.04662 - 1.81279i) q^{36} +(-0.655675 - 1.13566i) q^{37} +(0.307274 + 0.103187i) q^{38} +(0.0284617 - 0.0492971i) q^{39} +(-0.365760 + 0.633515i) q^{40} +(3.80562 + 6.59153i) q^{41} +(0.0658919 - 0.266754i) q^{42} +(-5.56677 - 9.64193i) q^{43} +0.924984 q^{44} +(-1.29234 + 2.23839i) q^{45} +(0.157104 - 0.272112i) q^{46} +2.93898 q^{47} +(-2.77005 + 4.79786i) q^{48} +(5.92011 - 3.73528i) q^{49} +0.0791948 q^{50} +4.19724 q^{51} +0.0812920 q^{52} +(-2.65488 - 4.59839i) q^{53} +(0.210279 - 0.364214i) q^{54} +(-0.571073 - 0.989128i) q^{55} +(0.754969 - 0.218266i) q^{56} +(-1.20713 - 5.96674i) q^{57} +(0.107154 + 0.185595i) q^{58} +12.3229 q^{59} +6.85983 q^{60} -1.86263 q^{61} +(-0.221104 - 0.382963i) q^{62} +(2.66752 - 0.771197i) q^{63} -7.86759 q^{64} +(-0.0501886 - 0.0869292i) q^{65} +(0.0240824 + 0.0417119i) q^{66} +(5.86906 + 10.1655i) q^{67} +(2.99703 + 5.19100i) q^{68} -5.90114 q^{69} +(-0.349271 - 0.335819i) q^{70} +(7.89435 + 13.6734i) q^{71} +0.311746 q^{72} +8.91233 q^{73} +0.0975147 q^{74} +(-0.743680 - 1.28809i) q^{75} +(6.51751 - 5.75347i) q^{76} +(-0.294250 + 1.19123i) q^{77} +(0.00211647 + 0.00366584i) q^{78} +(-2.15812 + 3.73798i) q^{79} +(4.88462 + 8.46041i) q^{80} -4.74995 q^{81} -0.565989 q^{82} -5.39339 q^{83} +(-5.31244 - 5.10783i) q^{84} +(3.70065 - 6.40972i) q^{85} +0.827914 q^{86} +(2.01245 - 3.48567i) q^{87} +(-0.0688791 + 0.119302i) q^{88} +7.22996 q^{89} +(-0.0961008 - 0.166452i) q^{90} +(-0.0258601 + 0.104691i) q^{91} +(-4.21369 - 7.29832i) q^{92} +(-4.15255 + 7.19243i) q^{93} +(-0.109274 + 0.189268i) q^{94} +(-10.1763 - 3.41735i) q^{95} +(-0.620828 - 1.07530i) q^{96} +(0.356016 + 0.616637i) q^{97} +(0.0204341 + 0.520134i) q^{98} +(-0.243370 + 0.421529i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9}+O(q^{10}) $ 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9} + 16 q^{10} - q^{11} - 2 q^{12} + 6 q^{13} - q^{14} - 9 q^{15} - 9 q^{16} - 16 q^{17} + 5 q^{18} - 4 q^{19} - 21 q^{21} - 2 q^{22} + 18 q^{23} + 16 q^{24} - 14 q^{25} + q^{26} - 18 q^{27} - 14 q^{28} - 2 q^{29} - 9 q^{30} + 11 q^{31} + 24 q^{32} + 3 q^{33} + 6 q^{34} + 38 q^{35} - 7 q^{36} - 14 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 20 q^{41} - 36 q^{42} + 2 q^{43} - 4 q^{44} - 12 q^{45} - 6 q^{46} + 39 q^{48} + 18 q^{49} + 22 q^{50} - 42 q^{51} - 22 q^{52} + 7 q^{53} - 43 q^{54} + 9 q^{55} - 21 q^{56} + 21 q^{57} + 35 q^{58} - 84 q^{59} + 12 q^{60} - 12 q^{61} - 19 q^{62} + 9 q^{63} - 2 q^{64} - 27 q^{65} + 3 q^{66} - 14 q^{67} + 51 q^{68} - 34 q^{69} + 33 q^{70} + q^{71} - 36 q^{72} + 42 q^{73} + 50 q^{74} + 31 q^{75} - 70 q^{76} - 20 q^{77} + 57 q^{78} - 5 q^{79} + 13 q^{80} - 56 q^{81} + 24 q^{82} + 10 q^{83} + 129 q^{84} - 27 q^{85} - 36 q^{86} + 53 q^{87} - 36 q^{88} + 2 q^{89} + 27 q^{90} - 9 q^{91} - 72 q^{92} + 34 q^{93} + 12 q^{94} - 11 q^{95} - 94 q^{96} + 31 q^{97} - 26 q^{98} + 43 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9 + 16 * q^10 - q^11 - 2 * q^12 + 6 * q^13 - q^14 - 9 * q^15 - 9 * q^16 - 16 * q^17 + 5 * q^18 - 4 * q^19 - 21 * q^21 - 2 * q^22 + 18 * q^23 + 16 * q^24 - 14 * q^25 + q^26 - 18 * q^27 - 14 * q^28 - 2 * q^29 - 9 * q^30 + 11 * q^31 + 24 * q^32 + 3 * q^33 + 6 * q^34 + 38 * q^35 - 7 * q^36 - 14 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 20 * q^41 - 36 * q^42 + 2 * q^43 - 4 * q^44 - 12 * q^45 - 6 * q^46 + 39 * q^48 + 18 * q^49 + 22 * q^50 - 42 * q^51 - 22 * q^52 + 7 * q^53 - 43 * q^54 + 9 * q^55 - 21 * q^56 + 21 * q^57 + 35 * q^58 - 84 * q^59 + 12 * q^60 - 12 * q^61 - 19 * q^62 + 9 * q^63 - 2 * q^64 - 27 * q^65 + 3 * q^66 - 14 * q^67 + 51 * q^68 - 34 * q^69 + 33 * q^70 + q^71 - 36 * q^72 + 42 * q^73 + 50 * q^74 + 31 * q^75 - 70 * q^76 - 20 * q^77 + 57 * q^78 - 5 * q^79 + 13 * q^80 - 56 * q^81 + 24 * q^82 + 10 * q^83 + 129 * q^84 - 27 * q^85 - 36 * q^86 + 53 * q^87 - 36 * q^88 + 2 * q^89 + 27 * q^90 - 9 * q^91 - 72 * q^92 + 34 * q^93 + 12 * q^94 - 11 * q^95 - 94 * q^96 + 31 * q^97 - 26 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$.

$n$	$78$	$115$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.0371811	+	0.0643995i	−0.0262910	+	0.0455373i	−0.878872	−	0.477059i	$-0.841703\pi$
$2$	−0.0371811	+	0.0643995i	−0.0262910	+	0.0455373i	0.852581	+	0.522596i	$0.175036\pi$
$3$	1.39660			0.806325			0.403163	−	0.915128i	$-0.367911\pi$
$3$	1.39660			0.806325			0.403163	+	0.915128i	$0.367911\pi$
$4$	0.997235	+	1.72726i	0.498618	+	0.863631i
$5$	1.23136	−	2.13278i	0.550681	−	0.953807i	−0.447545	−	0.894262i	$-0.647701\pi$
$5$	1.23136	−	2.13278i	0.550681	−	0.953807i	0.998226	−	0.0595457i	$-0.0189652\pi$
$6$	−0.0519269	+	0.0899401i	−0.0211991	+	0.0367179i
$7$	−2.54166	+	0.734810i	−0.960659	+	0.277732i
$7$	−2.54166	+	0.734810i	−0.960659	+	0.277732i
$8$	−0.297037			−0.105019
$9$	−1.04952			−0.349840
$10$	0.0915665	+	0.158598i	0.0289559	+	0.0501531i
$11$	0.231887	−	0.401640i	0.0699166	−	0.121099i	−0.828948	−	0.559326i	$-0.811060\pi$
$11$	0.231887	−	0.401640i	0.0699166	−	0.121099i	0.898864	+	0.438227i	$0.144393\pi$
$12$	1.39273	+	2.41229i	0.402048	+	0.696367i
$13$	0.0203793	−	0.0352981i	0.00565221	−	0.00978992i	−0.863185	−	0.504887i	$-0.831534\pi$
$13$	0.0203793	−	0.0352981i	0.00565221	−	0.00978992i	0.868838	+	0.495097i	$0.164868\pi$
$14$	0.0471804	−	0.191003i	0.0126095	−	0.0510477i
$15$	1.71971	−	2.97863i	0.444028	−	0.769079i
$16$	−1.98343	+	3.43539i	−0.495857	+	0.858849i
$17$	3.00534			0.728901			0.364451	−	0.931223i	$-0.381257\pi$
$17$	3.00534			0.728901			0.364451	+	0.931223i	$0.381257\pi$
$18$	0.0390222	−	0.0675885i	0.00919763	−	0.0159308i
$19$	−0.864338	−	4.27234i	−0.198293	−	0.980143i
$19$	−0.864338	−	4.27234i	−0.198293	−	0.980143i
$20$	4.91182			1.09832
$21$	−3.54968	+	1.02623i	−0.774603	+	0.223942i
$22$	0.0172436	+	0.0298668i	0.00367635	+	0.00636763i
$23$	−4.22537			−0.881051			−0.440525	−	0.897740i	$-0.645208\pi$
$23$	−4.22537			−0.881051			−0.440525	+	0.897740i	$0.645208\pi$
$24$	−0.414841			−0.0846791
$25$	−0.532495	−	0.922308i	−0.106499	−	0.184462i
$26$	0.00151545	+	0.00262484i	0.000297204	+	0.000514773i
$27$	−5.65554			−1.08841
$28$	−3.80385	−	3.65734i	−0.718859	−	0.691172i
$29$	1.44097	−	2.49583i	0.267581	−	0.463464i	−0.700655	−	0.713500i	$-0.747109\pi$
$29$	1.44097	−	2.49583i	0.267581	−	0.463464i	0.968237	+	0.250035i	$0.0804423\pi$
$30$	0.127881	+	0.221497i	0.0233479	+	0.0404397i
$31$	−2.97334	+	5.14997i	−0.534027	+	0.924962i	0.465182	+	0.885215i	$0.345989\pi$
$31$	−2.97334	+	5.14997i	−0.534027	+	0.924962i	−0.999210	+	0.0397476i	$0.987345\pi$
$32$	−0.444529	−	0.769947i	−0.0785824	−	0.136109i
$33$	0.323853	−	0.560929i	0.0563755	−	0.0976453i
$34$	−0.111742	+	0.193542i	−0.0191635	+	0.0331922i
$35$	−1.56252	+	6.32562i	−0.264113	+	1.06922i
$36$	−1.04662	−	1.81279i	−0.174436	−	0.302132i
$37$	−0.655675	−	1.13566i	−0.107792	−	0.186702i	0.807083	−	0.590438i	$-0.201045\pi$
$37$	−0.655675	−	1.13566i	−0.107792	−	0.186702i	−0.914876	+	0.403736i	$0.867711\pi$
$38$	0.307274	+	0.103187i	0.0498464	+	0.0167392i
$39$	0.0284617	−	0.0492971i	0.00455752	−	0.00789386i
$40$	−0.365760	+	0.633515i	−0.0578317	+	0.100167i
$41$	3.80562	+	6.59153i	0.594339	+	1.02942i	0.993640	+	0.112605i	$0.0359194\pi$
$41$	3.80562	+	6.59153i	0.594339	+	1.02942i	−0.399301	+	0.916820i	$0.630747\pi$
$42$	0.0658919	−	0.266754i	0.0101673	−	0.0411610i
$43$	−5.56677	−	9.64193i	−0.848924	−	1.47038i	−0.882169	−	0.470933i	$-0.843917\pi$
$43$	−5.56677	−	9.64193i	−0.848924	−	1.47038i	0.0332448	−	0.999447i	$-0.489416\pi$
$44$	0.924984			0.139447
$45$	−1.29234	+	2.23839i	−0.192650	+	0.333680i
$46$	0.157104	−	0.272112i	0.0231637	−	0.0401207i
$47$	2.93898			0.428694			0.214347	−	0.976758i	$-0.431238\pi$
$47$	2.93898			0.428694			0.214347	+	0.976758i	$0.431238\pi$
$48$	−2.77005	+	4.79786i	−0.399822	+	0.692511i
$49$	5.92011	−	3.73528i	0.845730	−	0.533611i
$50$	0.0791948			0.0111998
$51$	4.19724			0.587731
$52$	0.0812920			0.0112732
$53$	−2.65488	−	4.59839i	−0.364676	−	0.631637i	0.624048	−	0.781386i	$-0.285487\pi$
$53$	−2.65488	−	4.59839i	−0.364676	−	0.631637i	−0.988724	+	0.149749i	$0.952154\pi$
$54$	0.210279	−	0.364214i	0.0286154	−	0.0495633i
$55$	−0.571073	−	0.989128i	−0.0770035	−	0.133374i
$56$	0.754969	−	0.218266i	0.100887	−	0.0291670i
$57$	−1.20713	−	5.96674i	−0.159888	−	0.790314i
$58$	0.107154	+	0.185595i	0.0140699	+	0.0243699i
$59$	12.3229			1.60431			0.802156	−	0.597115i	$-0.203686\pi$
$59$	12.3229			1.60431			0.802156	+	0.597115i	$0.203686\pi$
$60$	6.85983			0.885600
$61$	−1.86263			−0.238485			−0.119242	−	0.992865i	$-0.538047\pi$
$61$	−1.86263			−0.238485			−0.119242	+	0.992865i	$0.538047\pi$
$62$	−0.221104	−	0.382963i	−0.0280802	−	0.0486363i
$63$	2.66752	−	0.771197i	0.336077	−	0.0971617i
$64$	−7.86759			−0.983449
$65$	−0.0501886	−	0.0869292i	−0.00622513	−	0.0107822i
$66$	0.0240824	+	0.0417119i	0.00296434	+	0.00513438i
$67$	5.86906	+	10.1655i	0.717020	+	1.24191i	0.962175	+	0.272431i	$0.0878275\pi$
$67$	5.86906	+	10.1655i	0.717020	+	1.24191i	−0.245156	+	0.969484i	$0.578839\pi$
$68$	2.99703	+	5.19100i	0.363443	+	0.629502i
$69$	−5.90114			−0.710414
$70$	−0.349271	−	0.335819i	−0.0417458	−	0.0401380i
$71$	7.89435	+	13.6734i	0.936887	+	1.62274i	0.771233	+	0.636553i	$0.219640\pi$
$71$	7.89435	+	13.6734i	0.936887	+	1.62274i	0.165654	+	0.986184i	$0.447026\pi$
$72$	0.311746			0.0367397
$73$	8.91233			1.04311			0.521555	−	0.853218i	$-0.325352\pi$
$73$	8.91233			1.04311			0.521555	+	0.853218i	$0.325352\pi$
$74$	0.0975147			0.0113359
$75$	−0.743680	−	1.28809i	−0.0858727	−	0.148736i
$76$	6.51751	−	5.75347i	0.747610	−	0.659968i
$77$	−0.294250	+	1.19123i	−0.0335329	+	0.135753i
$78$	0.00211647	+	0.00366584i	0.000239643	+	0.000415075i
$79$	−2.15812	+	3.73798i	−0.242808	+	0.420555i	−0.961513	−	0.274760i	$-0.911402\pi$
$79$	−2.15812	+	3.73798i	−0.242808	+	0.420555i	0.718705	+	0.695315i	$0.244735\pi$
$80$	4.88462	+	8.46041i	0.546117	+	0.945903i
$81$	−4.74995			−0.527772
$82$	−0.565989			−0.0625030
$83$	−5.39339			−0.592001			−0.296001	−	0.955188i	$-0.595653\pi$
$83$	−5.39339			−0.592001			−0.296001	+	0.955188i	$0.595653\pi$
$84$	−5.31244	−	5.10783i	−0.579634	−	0.557310i
$85$	3.70065	−	6.40972i	0.401392	−	0.695231i
$86$	0.827914			0.0892762
$87$	2.01245	−	3.48567i	0.215758	−	0.373703i
$88$	−0.0688791	+	0.119302i	−0.00734254	+	0.0127177i
$89$	7.22996			0.766375			0.383187	−	0.923671i	$-0.374826\pi$
$89$	7.22996			0.766375			0.383187	+	0.923671i	$0.374826\pi$
$90$	−0.0961008	−	0.166452i	−0.0101299	−	0.0175455i
$91$	−0.0258601	+	0.104691i	−0.00271087	+	0.0109746i
$92$	−4.21369	−	7.29832i	−0.439307	−	0.760903i
$93$	−4.15255	+	7.19243i	−0.430600	+	0.745821i
$94$	−0.109274	+	0.189268i	−0.0112708	+	0.0195216i
$95$	−10.1763	−	3.41735i	−1.04406	−	0.350613i
$96$	−0.620828	−	1.07530i	−0.0633630	−	0.109748i
$97$	0.356016	+	0.616637i	0.0361479	+	0.0626100i	0.883533	−	0.468368i	$-0.155158\pi$
$97$	0.356016	+	0.616637i	0.0361479	+	0.0626100i	−0.847385	+	0.530978i	$0.821825\pi$
$98$	0.0204341	+	0.520134i	0.00206416	+	0.0525414i
$99$	−0.243370	+	0.421529i	−0.0244596	+	0.0423653i
$100$	1.06204	−	1.83952i	0.106204	−	0.183952i
$101$	−6.38072	−	11.0517i	−0.634905	−	1.09969i	−0.986535	−	0.163549i	$-0.947706\pi$
$101$	−6.38072	−	11.0517i	−0.634905	−	1.09969i	0.351630	−	0.936139i	$-0.385628\pi$
$102$	−0.156058	+	0.270300i	−0.0154520	+	0.0267637i
$103$	2.68797	+	4.65571i	0.264854	+	0.458741i	0.967525	−	0.252774i	$-0.0813429\pi$
$103$	2.68797	+	4.65571i	0.264854	+	0.458741i	−0.702671	+	0.711515i	$0.748010\pi$
$104$	−0.00605342	+	0.0104848i	−0.000593587	+	0.00102812i
$105$	−2.18220	+	8.83434i	−0.212961	+	0.862143i
$106$	0.394845			0.0383508
$107$	−8.90083	−	15.4167i	−0.860476	−	1.49039i	−0.871470	−	0.490449i	$-0.836833\pi$
$107$	−8.90083	−	15.4167i	−0.860476	−	1.49039i	0.0109941	−	0.999940i	$-0.496500\pi$
$108$	−5.63991	−	9.76860i	−0.542700	−	0.939984i
$109$	−4.17321			−0.399721			−0.199861	−	0.979824i	$-0.564049\pi$
$109$	−4.17321			−0.399721			−0.199861	+	0.979824i	$0.564049\pi$
$110$	0.0849324			0.00809799
$111$	−0.915713	−	1.58606i	−0.0869156	−	0.150542i
$112$	2.51684	−	10.1891i	0.237819	−	0.962776i
$113$	9.26868			0.871924			0.435962	−	0.899965i	$-0.356408\pi$
$113$	9.26868			0.871924			0.435962	+	0.899965i	$0.356408\pi$
$114$	0.429137	+	0.144111i	0.0401924	+	0.0134972i
$115$	−5.20295	+	9.01178i	−0.485178	+	0.840353i
$116$	5.74794			0.533683
$117$	−0.0213885	+	0.0370460i	−0.00197737	+	0.00342490i
$118$	−0.458180	+	0.793591i	−0.0421789	+	0.0730560i
$119$	−7.63856	+	2.20835i	−0.700225	+	0.202439i
$120$	−0.510819	+	0.884764i	−0.0466312	+	0.0807675i
$121$	5.39246	+	9.34001i	0.490223	+	0.849092i
$122$	0.0692544	−	0.119952i	0.00627000	−	0.0108600i
$123$	5.31492	+	9.20571i	0.479230	+	0.830051i
$124$	−11.8605			−1.06510
$125$	9.69083			0.866774
$126$	−0.0495167	+	0.200461i	−0.00441130	+	0.0178585i
$127$	−9.30152	+	16.1107i	−0.825377	+	1.42959i	0.0762545	+	0.997088i	$0.475704\pi$
$127$	−9.30152	+	16.1107i	−0.825377	+	1.42959i	−0.901631	+	0.432506i	$0.857629\pi$
$128$	1.18158	−	2.04656i	0.104438	−	0.180892i
$129$	−7.77453	−	13.4659i	−0.684509	−	1.18560i
$130$	0.00746426			0.000654659
$131$	−5.56836	+	9.64469i	−0.486510	+	0.842660i	−0.999880	−	0.0155073i	$-0.995064\pi$
$131$	−5.56836	+	9.64469i	−0.486510	+	0.842660i	0.513370	+	0.858168i	$0.328397\pi$
$132$	1.29183			0.112439
$133$	5.33622	+	10.2237i	0.462709	+	0.886510i
$134$	−0.872871			−0.0754046
$135$	−6.96401	+	12.0620i	−0.599366	+	1.03813i
$136$	−0.892697			−0.0765481
$137$	−5.45531	−	9.44887i	−0.466078	−	0.807271i	0.533171	−	0.846007i	$-0.321000\pi$
$137$	−5.45531	−	9.44887i	−0.466078	−	0.807271i	−0.999249	+	0.0387361i	$0.987667\pi$
$138$	0.219411	−	0.380030i	0.0186775	−	0.0323503i
$139$	7.25681	−	12.5692i	0.615515	−	1.06610i	−0.374779	−	0.927114i	$-0.622281\pi$
$139$	7.25681	−	12.5692i	0.615515	−	1.06610i	0.990294	−	0.138989i	$-0.0443853\pi$
$140$	−12.4842	+	3.60926i	−1.05511	+	0.305038i
$141$	4.10456			0.345666
$142$	−1.17408			−0.0985268
$143$	−0.00945141	−	0.0163703i	−0.000790367	−	0.00136896i
$144$	2.08164	−	3.60551i	0.173470	−	0.300459i
$145$	−3.54870	−	6.14654i	−0.294704	−	0.510442i
$146$	−0.331370	+	0.573950i	−0.0274244	+	0.0475004i
$147$	8.26800	−	5.21668i	0.681933	−	0.430264i
$148$	1.30772	−	2.26504i	0.107494	−	0.186185i
$149$	8.53019	−	14.7747i	0.698821	−	1.21039i	−0.270055	−	0.962845i	$-0.587042\pi$
$149$	8.53019	−	14.7747i	0.698821	−	1.21039i	0.968876	−	0.247548i	$-0.0796248\pi$
$150$	0.110603			0.00903072
$151$	−3.25140	+	5.63160i	−0.264595	+	0.458293i	−0.967458	−	0.253033i	$-0.918572\pi$
$151$	−3.25140	+	5.63160i	−0.264595	+	0.458293i	0.702862	+	0.711326i	$0.251905\pi$
$152$	0.256740	+	1.26905i	0.0208244	+	0.102933i
$153$	−3.15416			−0.254999
$154$	−0.0657739	−	0.0632406i	−0.00530021	−	0.00509608i
$155$	7.32250	+	12.6829i	0.588157	+	1.01872i
$156$	0.113532			0.00908984
$157$	−13.7859			−1.10023			−0.550116	−	0.835088i	$-0.685417\pi$
$157$	−13.7859			−1.10023			−0.550116	+	0.835088i	$0.685417\pi$
$158$	−0.160483	−	0.277964i	−0.0127673	−	0.0221136i
$159$	−3.70780	−	6.42209i	−0.294047	−	0.509305i
$160$	−2.18950			−0.173095
$161$	10.7395	−	3.10485i	0.846389	−	0.244696i
$162$	0.176608	−	0.305894i	0.0138757	−	0.0240333i
$163$	−5.74792	−	9.95569i	−0.450212	−	0.779790i	0.548187	−	0.836356i	$-0.315318\pi$
$163$	−5.74792	−	9.95569i	−0.450212	−	0.779790i	−0.998399	+	0.0565660i	$0.981985\pi$
$164$	−7.59020	+	13.1466i	−0.592695	+	1.02658i
$165$	−0.797558	−	1.38141i	−0.0620898	−	0.107543i
$166$	0.200532	−	0.347331i	0.0155643	−	0.0269581i
$167$	5.78896	−	10.0268i	0.447964	−	0.775896i	−0.550290	−	0.834974i	$-0.685483\pi$
$167$	5.78896	−	10.0268i	0.447964	−	0.775896i	0.998253	+	0.0590782i	$0.0188161\pi$
$168$	1.05439	−	0.304829i	0.0813477	−	0.0235181i
$169$	6.49917	+	11.2569i	0.499936	+	0.865915i
$170$	0.275188	+	0.476640i	0.0211060	+	0.0365566i
$171$	0.907139	+	4.48391i	0.0693706	+	0.342893i
$172$	11.1028	−	19.2305i	0.846577	−	1.46631i
$173$	12.6262	−	21.8693i	0.959955	−	1.66269i	0.237357	−	0.971423i	$-0.423719\pi$
$173$	12.6262	−	21.8693i	0.959955	−	1.66269i	0.722598	−	0.691268i	$-0.242948\pi$
$174$	0.149650	+	0.259202i	0.0113450	+	0.0196500i
$175$	2.03114	+	1.95291i	0.153540	+	0.147626i
$176$	0.919862	+	1.59325i	0.0693372	+	0.120096i
$177$	17.2102			1.29360
$178$	−0.268818	+	0.465606i	−0.0201487	+	0.0348986i
$179$	−10.2592	+	17.7695i	−0.766810	+	1.32815i	0.172474	+	0.985014i	$0.444824\pi$
$179$	−10.2592	+	17.7695i	−0.766810	+	1.32815i	−0.939284	+	0.343140i	$0.888509\pi$
$180$	−5.15505			−0.384235
$181$	−10.0368	+	17.3842i	−0.746029	+	1.29216i	0.203684	+	0.979037i	$0.434709\pi$
$181$	−10.0368	+	17.3842i	−0.746029	+	1.29216i	−0.949713	+	0.313123i	$0.898625\pi$
$182$	−0.00578052	−	0.00555789i	−0.000428481	−	0.000411978i
$183$	−2.60134			−0.192296
$184$	1.25509			0.0925267
$185$	−3.22949			−0.237437
$186$	−0.308793	−	0.534845i	−0.0226418	−	0.0392167i
$187$	0.696899	−	1.20706i	0.0509623	−	0.0882693i
$188$	2.93085	+	5.07638i	0.213754	+	0.370233i
$189$	14.3745	−	4.15575i	1.04559	−	0.302286i
$190$	0.598440	−	0.528286i	0.0434154	−	0.0383259i
$191$	−1.42720	−	2.47198i	−0.103268	−	0.178866i	0.809761	−	0.586760i	$-0.199597\pi$
$191$	−1.42720	−	2.47198i	−0.103268	−	0.178866i	−0.913029	+	0.407894i	$0.866263\pi$
$192$	−10.9878			−0.792980
$193$	9.24515			0.665481			0.332740	−	0.943018i	$-0.392027\pi$
$193$	9.24515			0.665481			0.332740	+	0.943018i	$0.392027\pi$
$194$	−0.0529482			−0.00380146
$195$	−0.0700932	−	0.121405i	−0.00501948	−	0.00869399i
$196$	12.3555	+	6.50063i	0.882539	+	0.464330i
$197$	−19.9898			−1.42421			−0.712106	−	0.702072i	$-0.752259\pi$
$197$	−19.9898			−1.42421			−0.712106	+	0.702072i	$0.752259\pi$
$198$	−0.0180975	−	0.0313458i	−0.00128613	−	0.00222765i
$199$	−4.98872	−	8.64072i	−0.353641	−	0.612524i	0.633243	−	0.773953i	$-0.281723\pi$
$199$	−4.98872	−	8.64072i	−0.353641	−	0.612524i	−0.986884	+	0.161429i	$0.948390\pi$
$200$	0.158171	+	0.273960i	0.0111844	+	0.0193719i
$201$	8.19670	+	14.1971i	0.578151	+	1.00139i
$202$	0.948967			0.0667691
$203$	−1.82850	+	7.40240i	−0.128335	+	0.519547i
$204$	4.18564	+	7.24974i	0.293053	+	0.507583i
$205$	18.7444			1.30916
$206$	−0.399767			−0.0278531
$207$	4.43461			0.308227
$208$	0.0808418	+	0.140022i	0.00560537	+	0.00970879i
$209$	−1.91637	−	0.643549i	−0.132558	−	0.0445152i
$210$	−0.487790	−	0.469003i	−0.0336607	−	0.0323643i
$211$	10.5175	+	18.2169i	0.724058	+	1.25410i	0.959361	+	0.282183i	$0.0910584\pi$
$211$	10.5175	+	18.2169i	0.724058	+	1.25410i	−0.235303	+	0.971922i	$0.575608\pi$
$212$	5.29508	−	9.17135i	0.363668	−	0.629891i
$213$	11.0252	+	19.0962i	0.755436	+	1.30845i
$214$	1.32377			0.0904910
$215$	−27.4188			−1.86995
$216$	1.67991			0.114303
$217$	3.77297	−	15.2743i	0.256126	−	1.03689i
$218$	0.155165	−	0.268753i	0.0105091	−	0.0182022i
$219$	12.4469			0.841085
$220$	1.13899	−	1.97279i	0.0767906	−	0.133005i
$221$	0.0612468	−	0.106083i	0.00411990	−	0.00713588i
$222$	0.136189			0.00914039
$223$	−6.07733	−	10.5263i	−0.406968	−	0.704890i	0.587580	−	0.809166i	$-0.300081\pi$
$223$	−6.07733	−	10.5263i	−0.406968	−	0.704890i	−0.994548	+	0.104276i	$0.966747\pi$
$224$	1.69561	+	1.63030i	0.113293	+	0.108929i
$225$	0.558863	+	0.967979i	0.0372575	+	0.0645320i
$226$	−0.344619	+	0.596898i	−0.0229237	+	0.0397051i
$227$	4.75704	−	8.23944i	0.315736	−	0.546871i	−0.663858	−	0.747859i	$-0.731082\pi$
$227$	4.75704	−	8.23944i	0.315736	−	0.546871i	0.979594	+	0.200988i	$0.0644152\pi$
$228$	9.10233	−	8.03527i	0.602816	−	0.532149i
$229$	−3.27838	−	5.67833i	−0.216642	−	0.375235i	0.737137	−	0.675743i	$-0.236177\pi$
$229$	−3.27838	−	5.67833i	−0.216642	−	0.375235i	−0.953779	+	0.300508i	$0.902844\pi$
$230$	−0.386903	−	0.670135i	−0.0255116	−	0.0441874i
$231$	−0.410948	+	1.66366i	−0.0270384	+	0.109461i
$232$	−0.428022	+	0.741355i	−0.0281010	+	0.0486724i
$233$	2.95191	−	5.11286i	0.193386	−	0.334955i	−0.752984	−	0.658039i	$-0.771386\pi$
$233$	2.95191	−	5.11286i	0.193386	−	0.334955i	0.946370	+	0.323084i	$0.104720\pi$
$234$	−0.00159049	−	0.00275482i	−0.000103974	−	0.000180088i
$235$	3.61894	−	6.26818i	0.236073	−	0.408891i
$236$	12.2889	+	21.2850i	0.799938	+	1.38553i
$237$	−3.01403	+	5.22045i	−0.195782	+	0.339104i
$238$	0.141793	−	0.574028i	0.00919107	−	0.0372087i
$239$	−16.4354			−1.06312			−0.531560	−	0.847021i	$-0.678394\pi$
$239$	−16.4354			−1.06312			−0.531560	+	0.847021i	$0.678394\pi$
$240$	6.82185	+	11.8158i	0.440348	+	0.762706i
$241$	−6.77645	−	11.7372i	−0.436510	−	0.756057i	0.560908	−	0.827878i	$-0.310452\pi$
$241$	−6.77645	−	11.7372i	−0.436510	−	0.756057i	−0.997418	+	0.0718212i	$0.977119\pi$
$242$	−0.801989			−0.0515538
$243$	10.3329			0.662854
$244$	−1.85748	−	3.21724i	−0.118913	−	0.205963i
$245$	−0.676737	−	17.2258i	−0.0432351	−	1.10051i
$246$	−0.790457			−0.0503977
$247$	−0.168420	−	0.0565581i	−0.0107163	−	0.00359871i
$248$	0.883192	−	1.52973i	0.0560828	−	0.0971382i
$249$	−7.53239			−0.477346
$250$	−0.360315	+	0.624084i	−0.0227883	+	0.0394706i
$251$	6.67717	−	11.5652i	0.421459	−	0.729989i	−0.574623	−	0.818418i	$-0.694851\pi$
$251$	6.67717	−	11.5652i	0.421459	−	0.729989i	0.996082	+	0.0884294i	$0.0281848\pi$
$252$	3.99221	+	3.83845i	0.251486	+	0.241800i
$253$	−0.979809	+	1.69708i	−0.0616001	+	0.106694i
$254$	−0.691681	−	1.19803i	−0.0433999	−	0.0751709i
$255$	5.16832	−	8.95178i	0.323652	−	0.560582i
$256$	−7.77973	−	13.4749i	−0.486233	−	0.842180i
$257$	−17.5252			−1.09319			−0.546595	−	0.837397i	$-0.684076\pi$
$257$	−17.5252			−1.09319			−0.546595	+	0.837397i	$0.684076\pi$
$258$	1.15626			0.0719857
$259$	2.50100	+	2.40467i	0.155405	+	0.149419i
$260$	0.100100	−	0.173378i	0.00620792	−	0.0107524i
$261$	−1.51232	+	2.61942i	−0.0936106	+	0.162138i
$262$	−0.414075	−	0.717200i	−0.0255817	−	0.0443087i
$263$	−27.0354			−1.66708			−0.833538	−	0.552462i	$-0.813688\pi$
$263$	−27.0354			−1.66708			−0.833538	+	0.552462i	$0.813688\pi$
$264$	−0.0961963	+	0.166617i	−0.00592047	+	0.0102546i
$265$	−13.0765			−0.803280
$266$	−0.856810	−	0.0364798i	−0.0525344	−	0.00223672i
$267$	10.0973			0.617947
$268$	−11.7057	+	20.2748i	−0.715037	+	1.23848i
$269$	−8.02619			−0.489366			−0.244683	−	0.969603i	$-0.578684\pi$
$269$	−8.02619			−0.489366			−0.244683	+	0.969603i	$0.578684\pi$
$270$	−0.517858	−	0.896957i	−0.0315159	−	0.0545871i
$271$	−0.0747893	+	0.129539i	−0.00454313	+	0.00786893i	−0.868288	−	0.496060i	$-0.834779\pi$
$271$	−0.0747893	+	0.129539i	−0.00454313	+	0.00786893i	0.863745	+	0.503929i	$0.168113\pi$
$272$	−5.96086	+	10.3245i	−0.361430	+	0.626016i
$273$	−0.0361161	+	0.146211i	−0.00218584	+	0.00884907i
$274$	0.811336			0.0490146
$275$	−0.493915			−0.0297842
$276$	−5.88482	−	10.1928i	−0.354225	−	0.613535i
$277$	−0.395919	+	0.685751i	−0.0237884	+	0.0412028i	−0.877675	−	0.479257i	$-0.840906\pi$
$277$	−0.395919	+	0.685751i	−0.0237884	+	0.0412028i	0.853886	+	0.520460i	$0.174239\pi$
$278$	0.539632	+	0.934670i	0.0323650	+	0.0560578i
$279$	3.12058	−	5.40500i	0.186824	−	0.323589i
$280$	0.464126	−	1.87894i	0.0277368	−	0.112288i
$281$	−9.15738	+	15.8611i	−0.546284	+	0.946191i	0.452241	+	0.891896i	$0.350625\pi$
$281$	−9.15738	+	15.8611i	−0.546284	+	0.946191i	−0.998525	+	0.0542954i	$0.982709\pi$
$282$	−0.152612	+	0.264332i	−0.00908791	+	0.0157407i
$283$	1.63162			0.0969897			0.0484948	−	0.998823i	$-0.484558\pi$
$283$	1.63162			0.0969897			0.0484948	+	0.998823i	$0.484558\pi$
$284$	−15.7451	+	27.2712i	−0.934297	+	1.61825i
$285$	−14.2121	−	4.77266i	−0.841855	−	0.282708i
$286$	0.00140565			8.31181e−5
$287$	−14.5161	−	13.9571i	−0.856861	−	0.823859i
$288$	0.466542	+	0.808074i	0.0274912	+	0.0476162i
$289$	−7.96795			−0.468703
$290$	0.527778			0.0309922
$291$	0.497210	+	0.861193i	0.0291470	+	0.0504841i
$292$	8.88769	+	15.3939i	0.520113	+	0.900862i
$293$	−9.45139			−0.552156			−0.276078	−	0.961135i	$-0.589035\pi$
$293$	−9.45139			−0.552156			−0.276078	+	0.961135i	$0.589035\pi$
$294$	0.0285383	+	0.726417i	0.00166438	+	0.0423655i
$295$	15.1740	−	26.2821i	0.883463	−	1.53020i
$296$	0.194760	+	0.337334i	0.0113202	+	0.0196071i
$297$	−1.31145	+	2.27149i	−0.0760979	+	0.131805i
$298$	0.634323	+	1.09868i	0.0367454	+	0.0636448i
$299$	−0.0861103	+	0.149147i	−0.00497989	+	0.00862542i
$300$	1.48325	−	2.56906i	0.0856353	−	0.148325i
$301$	21.2338	+	20.4160i	1.22390	+	1.17676i
$302$	−0.241781	−	0.418777i	−0.0139129	−	0.0240979i
$303$	−8.91129	−	15.4348i	−0.511940	−	0.886706i
$304$	16.3915	+	5.50454i	0.940119	+	0.315707i
$305$	−2.29356	+	3.97257i	−0.131329	+	0.227469i
$306$	0.117275	−	0.203126i	0.00670416	−	0.0116120i
$307$	0.0850710	+	0.147347i	0.00485526	+	0.00840956i	0.868443	−	0.495789i	$-0.165121\pi$
$307$	0.0850710	+	0.147347i	0.00485526	+	0.00840956i	−0.863588	+	0.504199i	$0.831788\pi$
$308$	−2.35100	+	0.679687i	−0.133961	+	0.0387288i
$309$	3.75401	+	6.50214i	0.213558	+	0.369894i
$310$	−1.08903			−0.0618529
$311$	6.21567	−	10.7659i	0.352458	−	0.610476i	−0.634221	−	0.773152i	$-0.718679\pi$
$311$	6.21567	−	10.7659i	0.352458	−	0.610476i	0.986680	+	0.162676i	$0.0520125\pi$
$312$	−0.00845419	+	0.0146431i	−0.000478624	+	0.000829001i
$313$	−0.124369			−0.00702978			−0.00351489	−	0.999994i	$-0.501119\pi$
$313$	−0.124369			−0.00702978			−0.00351489	+	0.999994i	$0.501119\pi$
$314$	0.512573	−	0.887803i	0.0289262	−	0.0501016i
$315$	1.63989	−	6.63886i	0.0923974	−	0.374057i
$316$	−8.60862			−0.484273
$317$	−5.40619			−0.303642			−0.151821	−	0.988408i	$-0.548514\pi$
$317$	−5.40619			−0.303642			−0.151821	+	0.988408i	$0.548514\pi$
$318$	0.551439			0.0309232
$319$	−0.668284	−	1.15750i	−0.0374167	−	0.0648077i
$320$	−9.68784	+	16.7798i	−0.541567	+	0.938021i
$321$	−12.4309	−	21.5309i	−0.693823	−	1.20174i
$322$	−0.199355	+	0.807058i	−0.0111096	+	0.0449756i
$323$	−2.59763	−	12.8398i	−0.144536	−	0.714427i
$324$	−4.73682	−	8.20441i	−0.263157	−	0.455801i
$325$	−0.0434075			−0.00240782
$326$	0.854855			0.0473460
$327$	−5.82829			−0.322305
$328$	−1.13041	−	1.95793i	−0.0624166	−	0.108109i
$329$	−7.46989	+	2.15959i	−0.411828	+	0.119062i
$330$	0.118616			0.00652961
$331$	−4.14178	−	7.17377i	−0.227653	−	0.394306i	0.729459	−	0.684024i	$-0.239772\pi$
$331$	−4.14178	−	7.17377i	−0.227653	−	0.394306i	−0.957112	+	0.289718i	$0.906438\pi$
$332$	−5.37848	−	9.31579i	−0.295182	−	0.511271i
$333$	0.688143	+	1.19190i	0.0377100	+	0.0653157i
$334$	0.430480	+	0.745613i	0.0235548	+	0.0407981i
$335$	28.9077			1.57940
$336$	3.51501	−	14.2300i	0.191759	−	0.776310i
$337$	−2.04835	−	3.54784i	−0.111580	−	0.193263i	0.804827	−	0.593509i	$-0.202258\pi$
$337$	−2.04835	−	3.54784i	−0.111580	−	0.193263i	−0.916408	+	0.400246i	$0.868925\pi$
$338$	−0.966584			−0.0525752
$339$	12.9446			0.703055
$340$	14.7617			0.800564
$341$	1.37896	+	2.38843i	0.0746748	+	0.129340i
$342$	−0.322490	−	0.108297i	−0.0174382	−	0.00585604i
$343$	−12.3022	+	13.8440i	−0.664257	+	0.747505i
$344$	1.65354	+	2.86401i	0.0891528	+	0.154417i
$345$	−7.26643	+	12.5858i	−0.391211	+	0.677598i
$346$	0.938914	+	1.62625i	0.0504763	+	0.0874275i
$347$	14.1795			0.761197			0.380598	−	0.924740i	$-0.375718\pi$
$347$	14.1795			0.761197			0.380598	+	0.924740i	$0.375718\pi$
$348$	8.02755			0.430322
$349$	15.1782			0.812469			0.406235	−	0.913769i	$-0.366842\pi$
$349$	15.1782			0.812469			0.406235	+	0.913769i	$0.366842\pi$
$350$	−0.201287	+	0.0581932i	−0.0107592	+	0.00311056i
$351$	−0.115256	+	0.199630i	−0.00615192	+	0.0106554i
$352$	−0.412322			−0.0219769
$353$	0.980901	−	1.69897i	0.0522081	−	0.0904271i	−0.838740	−	0.544532i	$-0.816707\pi$
$353$	0.980901	−	1.69897i	0.0522081	−	0.0904271i	0.890948	+	0.454105i	$0.150041\pi$
$354$	−0.639893	+	1.10833i	−0.0340099	+	0.0589069i
$355$	38.8832			2.06370
$356$	7.20997	+	12.4880i	0.382128	+	0.661865i
$357$	−10.6680	+	3.08417i	−0.564609	+	0.163232i
$358$	−0.762898	−	1.32138i	−0.0403204	−	0.0698370i
$359$	−0.139324	+	0.241316i	−0.00735324	+	0.0127362i	−0.869679	−	0.493618i	$-0.835674\pi$
$359$	−0.139324	+	0.241316i	−0.00735324	+	0.0127362i	0.862325	+	0.506355i	$0.169007\pi$
$360$	0.383872	−	0.664886i	0.0202318	−	0.0350426i
$361$	−17.5058	+	7.38549i	−0.921360	+	0.388710i
$362$	−0.746357	−	1.29273i	−0.0392277	−	0.0679443i
$363$	7.53108	+	13.0442i	0.395279	+	0.684644i
$364$	−0.206617	+	0.0597342i	−0.0108297	+	0.00313092i
$365$	10.9743	−	19.0080i	0.574420	−	0.994925i
$366$	0.0967205	−	0.167525i	0.00505566	−	0.00875666i
$367$	1.57769	+	2.73264i	0.0823547	+	0.142643i	0.904261	−	0.426980i	$-0.140423\pi$
$367$	1.57769	+	2.73264i	0.0823547	+	0.142643i	−0.821906	+	0.569623i	$0.807089\pi$
$368$	8.38071	−	14.5158i	0.436875	−	0.756689i
$369$	−3.99408	−	6.91794i	−0.207923	−	0.360134i
$370$	0.120076	−	0.207977i	0.00624244	−	0.0108122i
$371$	10.1268	+	9.73672i	0.525755	+	0.505506i
$372$	−16.5643			−0.858818
$373$	3.33873	+	5.78285i	0.172873	+	0.299424i	0.939423	−	0.342760i	$-0.111362\pi$
$373$	3.33873	+	5.78285i	0.172873	+	0.299424i	−0.766550	+	0.642184i	$0.778028\pi$
$374$	0.0518229	+	0.0897599i	0.00267970	+	0.00464137i
$375$	13.5342			0.698902
$376$	−0.872985			−0.0450208
$377$	−0.0587320	−	0.101727i	−0.00302485	−	0.00523920i
$378$	−0.266831	+	1.08022i	−0.0137243	+	0.0555608i
$379$	−7.77946			−0.399604			−0.199802	−	0.979836i	$-0.564030\pi$
$379$	−7.77946			−0.399604			−0.199802	+	0.979836i	$0.564030\pi$
$380$	−4.24547	−	20.9850i	−0.217788	−	1.07651i
$381$	−12.9905	+	22.5002i	−0.665522	+	1.15272i
$382$	0.212259			0.0108601
$383$	3.00862	−	5.21108i	0.153733	−	0.266274i	−0.778864	−	0.627193i	$-0.784204\pi$
$383$	3.00862	−	5.21108i	0.153733	−	0.266274i	0.932597	+	0.360919i	$0.117537\pi$
$384$	1.65020	−	2.85822i	0.0842112	−	0.145858i
$385$	2.17830	+	2.09440i	0.111016	+	0.106740i
$386$	−0.343745	+	0.595383i	−0.0174961	+	0.0303042i
$387$	5.84243	+	10.1194i	0.296987	+	0.514397i
$388$	−0.710063	+	1.22987i	−0.0360480	+	0.0624369i
$389$	15.9479	+	27.6226i	0.808593	+	1.40052i	0.913839	+	0.406078i	$0.133104\pi$
$389$	15.9479	+	27.6226i	0.808593	+	1.40052i	−0.105246	+	0.994446i	$0.533563\pi$
$390$	0.0104246			0.000527868
$391$	−12.6987			−0.642199
$392$	−1.75849	+	1.10952i	−0.0888173	+	0.0560391i
$393$	−7.77676	+	13.4697i	−0.392285	+	0.679458i
$394$	0.743241	−	1.28733i	0.0374439	−	0.0648548i
$395$	5.31485	+	9.20559i	0.267419	+	0.463184i
$396$	−0.970788			−0.0487840
$397$	−1.48740	+	2.57626i	−0.0746506	+	0.129299i	−0.900934	−	0.433956i	$-0.857117\pi$
$397$	−1.48740	+	2.57626i	−0.0746506	+	0.129299i	0.826284	+	0.563254i	$0.190451\pi$
$398$	0.741944			0.0371903
$399$	7.45254	+	14.2784i	0.373094	+	0.714816i
$400$	4.22465			0.211233
$401$	15.0020	−	25.9843i	0.749166	−	1.29759i	−0.199056	−	0.979988i	$-0.563788\pi$
$401$	15.0020	−	25.9843i	0.749166	−	1.29759i	0.948223	−	0.317606i	$-0.102879\pi$
$402$	−1.21905			−0.0608006
$403$	0.121189	+	0.209906i	0.00603687	+	0.0104562i
$404$	12.7262	−	22.0423i	0.633150	−	1.09665i
$405$	−5.84890	+	10.1306i	−0.290634	+	0.503393i
$406$	−0.408726	−	0.392984i	−0.0202847	−	0.0195034i
$407$	−0.608170			−0.0301459
$408$	−1.24674			−0.0617227
$409$	7.94029	+	13.7530i	0.392622	+	0.680042i	0.992795	−	0.119829i	$-0.0382347\pi$
$409$	7.94029	+	13.7530i	0.392622	+	0.680042i	−0.600172	+	0.799871i	$0.704901\pi$
$410$	−0.696936	+	1.20713i	−0.0344192	+	0.0596158i
$411$	−7.61886	−	13.1963i	−0.375811	−	0.650923i
$412$	−5.36108	+	9.28567i	−0.264122	+	0.457472i
$413$	−31.3208	+	9.05502i	−1.54120	+	0.445569i
$414$	−0.164883	+	0.285587i	−0.00810358	+	0.0140358i
$415$	−6.64120	+	11.5029i	−0.326004	+	0.564655i
$416$	−0.0362368			−0.00177666
$417$	10.1348	−	17.5541i	0.496305	−	0.859626i
$418$	0.112697	−	0.0994857i	0.00551219	−	0.00486600i
$419$	21.2562			1.03844			0.519218	−	0.854642i	$-0.326223\pi$
$419$	21.2562			1.03844			0.519218	+	0.854642i	$0.326223\pi$
$420$	−17.4354	+	5.04067i	−0.850760	+	0.245960i
$421$	−12.1277	−	21.0058i	−0.591067	−	1.02376i	−0.994089	−	0.108568i	$-0.965374\pi$
$421$	−12.1277	−	21.0058i	−0.591067	−	1.02376i	0.403022	−	0.915190i	$-0.367960\pi$
$422$	−1.56421			−0.0761448
$423$	−3.08451			−0.149974
$424$	0.788599	+	1.36589i	0.0382977	+	0.0663336i
$425$	−1.60033	−	2.77184i	−0.0776272	−	0.134454i
$426$	−1.63972			−0.0794446
$427$	4.73417	−	1.36868i	0.229103	−	0.0662349i
$428$	17.7524	−	30.7481i	0.858097	−	1.48627i
$429$	−0.0131998	−	0.0228627i	−0.000637293	−	0.00110382i
$430$	1.01946	−	1.76576i	0.0491627	−	0.0851523i
$431$	−0.127784	−	0.221329i	−0.00615516	−	0.0106610i	0.862931	−	0.505321i	$-0.168626\pi$
$431$	−0.127784	−	0.221329i	−0.00615516	−	0.0106610i	−0.869087	+	0.494660i	$0.835293\pi$
$432$	11.2174	−	19.4290i	0.539695	−	0.934779i
$433$	−16.0050	+	27.7215i	−0.769152	+	1.33221i	0.168871	+	0.985638i	$0.445988\pi$
$433$	−16.0050	+	27.7215i	−0.769152	+	1.33221i	−0.938023	+	0.346572i	$0.887346\pi$
$434$	0.843376	+	0.810894i	0.0404834	+	0.0389241i
$435$	−4.95611	−	8.58423i	−0.237627	−	0.411582i
$436$	−4.16168	−	7.20823i	−0.199308	−	0.345212i
$437$	3.65215	+	18.0522i	0.174706	+	0.863556i
$438$	−0.462790	+	0.801576i	−0.0221130	+	0.0383008i
$439$	14.7153	−	25.4876i	0.702323	−	1.21646i	−0.265326	−	0.964159i	$-0.585480\pi$
$439$	14.7153	−	25.4876i	0.702323	−	1.21646i	0.967649	−	0.252300i	$-0.0811870\pi$
$440$	0.169630	+	0.293808i	0.00808679	+	0.0140067i
$441$	−6.21327	+	3.92025i	−0.295870	+	0.186678i
$442$	0.00455444	+	0.00788852i	0.000216633	+	0.000375219i
$443$	−23.4103			−1.11226			−0.556128	−	0.831096i	$-0.687714\pi$
$443$	−23.4103			−1.11226			−0.556128	+	0.831096i	$0.687714\pi$
$444$	1.82636	−	3.16335i	0.0866753	−	0.150126i
$445$	8.90269	−	15.4199i	0.422028	−	0.730974i
$446$	0.903847			0.0427984
$447$	11.9132	−	20.6343i	0.563477	−	0.975970i
$448$	19.9968	−	5.78118i	0.944759	−	0.273135i
$449$	26.1946			1.23620			0.618099	−	0.786100i	$-0.287903\pi$
$449$	26.1946			1.23620			0.618099	+	0.786100i	$0.287903\pi$
$450$	−0.0831165			−0.00391815
$451$	3.52990			0.166217
$452$	9.24306	+	16.0094i	0.434757	+	0.753021i
$453$	−4.54090	+	7.86506i	−0.213350	+	0.369533i
$454$	0.353744	+	0.612702i	0.0166020	+	0.0287556i
$455$	0.191439	+	0.184066i	0.00897480	+	0.00862914i
$456$	0.358563	+	1.77234i	0.0167912	+	0.0829976i
$457$	16.1389	+	27.9534i	0.754946	+	1.30761i	0.945401	+	0.325910i	$0.105671\pi$
$457$	16.1389	+	27.9534i	0.754946	+	1.30761i	−0.190455	+	0.981696i	$0.560996\pi$
$458$	0.487575			0.0227829
$459$	−16.9968			−0.793343
$460$	−20.7543			−0.967673
$461$	13.5109	+	23.4015i	0.629264	+	1.08992i	0.987700	+	0.156363i	$0.0499769\pi$
$461$	13.5109	+	23.4015i	0.629264	+	1.08992i	−0.358436	+	0.933554i	$0.616690\pi$
$462$	−0.0918596	−	0.0883216i	−0.00427370	−	0.00410909i
$463$	32.1787			1.49547			0.747734	−	0.663998i	$-0.231142\pi$
$463$	32.1787			1.49547			0.747734	+	0.663998i	$0.231142\pi$
$464$	5.71611	+	9.90060i	0.265364	+	0.459624i
$465$	10.2266	+	17.7129i	0.474246	+	0.821418i
$466$	0.219510	+	0.380203i	0.0101686	+	0.0176126i
$467$	16.7939	+	29.0879i	0.777130	+	1.34603i	0.933589	+	0.358345i	$0.116659\pi$
$467$	16.7939	+	29.0879i	0.777130	+	1.34603i	−0.156459	+	0.987684i	$0.550008\pi$
$468$	−0.0853175			−0.00394380
$469$	−22.3869	−	21.5247i	−1.03373	−	0.993916i
$470$	0.269112	+	0.466115i	0.0124132	+	0.0215003i
$471$	−19.2533			−0.887145
$472$	−3.66037			−0.168482
$473$	−5.16345			−0.237416
$474$	−0.224129	−	0.388203i	−0.0102946	−	0.0178308i
$475$	−3.48016	+	3.07218i	−0.159681	+	0.140962i
$476$	−11.4318	−	10.9915i	−0.523977	−	0.503796i
$477$	2.78635	+	4.82610i	0.127578	+	0.220972i
$478$	0.611087	−	1.05843i	0.0279505	−	0.0484116i
$479$	−1.25610	−	2.17562i	−0.0573925	−	0.0994067i	0.835902	−	0.548879i	$-0.184945\pi$
$479$	−1.25610	−	2.17562i	−0.0573925	−	0.0994067i	−0.893294	+	0.449472i	$0.851612\pi$
$480$	−3.05785			−0.139571
$481$	−0.0534489			−0.00243706
$482$	1.00782			0.0459051
$483$	14.9987	−	4.33622i	0.682465	−	0.197305i
$484$	−10.7551	+	18.6284i	−0.488868	+	0.846744i
$485$	1.75353			0.0796239
$486$	−0.384187	+	0.665431i	−0.0174271	+	0.0301846i
$487$	18.3435	−	31.7718i	0.831222	−	1.43972i	−0.0658472	−	0.997830i	$-0.520975\pi$
$487$	18.3435	−	31.7718i	0.831222	−	1.43972i	0.897069	−	0.441890i	$-0.145692\pi$
$488$	0.553270			0.0250453
$489$	−8.02752	−	13.9041i	−0.363017	−	0.628764i
$490$	1.13449	+	0.596890i	0.0512511	+	0.0269648i
$491$	−11.6559	−	20.1886i	−0.526023	−	0.911098i	−0.999540	−	0.0303138i	$-0.990349\pi$
$491$	−11.6559	−	20.1886i	−0.526023	−	0.911098i	0.473518	−	0.880784i	$-0.342984\pi$
$492$	−10.6005	+	18.3605i	−0.477905	+	0.827756i
$493$	4.33060	−	7.50082i	0.195040	−	0.337820i
$494$	0.00990435	−	0.00874327i	0.000445618	−	0.000393378i
$495$	0.599352	+	1.03811i	0.0269389	+	0.0466595i
$496$	−11.7948	−	20.4292i	−0.529602	−	0.917297i
$497$	−30.1122	−	28.9524i	−1.35071	−	1.29869i
$498$	0.280062	−	0.485082i	0.0125499	−	0.0217370i
$499$	−6.63132	+	11.4858i	−0.296858	+	0.514174i	−0.975416	−	0.220374i	$-0.929272\pi$
$499$	−6.63132	+	11.4858i	−0.296858	+	0.514174i	0.678557	+	0.734548i	$0.262606\pi$
$500$	9.66404	+	16.7386i	0.432189	+	0.748573i
$501$	8.08485	−	14.0034i	0.361204	−	0.625624i
$502$	0.496528	+	0.860012i	0.0221611	+	0.0383842i
$503$	−9.14566	+	15.8407i	−0.407785	+	0.706304i	−0.994641	−	0.103387i	$-0.967032\pi$
$503$	−9.14566	+	15.8407i	−0.407785	+	0.706304i	0.586856	+	0.809691i	$0.300365\pi$
$504$	−0.792354	+	0.229074i	−0.0352943	+	0.0102038i
$505$	−31.4278			−1.39852
$506$	−0.0728607	−	0.126198i	−0.00323905	−	0.00561021i
$507$	9.07672	+	15.7213i	0.403111	+	0.698209i
$508$	−37.1032			−1.64619
$509$	−27.6864			−1.22718			−0.613589	−	0.789626i	$-0.710275\pi$
$509$	−27.6864			−1.22718			−0.613589	+	0.789626i	$0.710275\pi$
$510$	0.384327	+	0.665674i	0.0170183	+	0.0294765i
$511$	−22.6521	+	6.54887i	−1.00207	+	0.289705i
$512$	5.88337			0.260011
$513$	4.88830	+	24.1624i	0.215824	+	1.06680i
$514$	0.651604	−	1.12861i	0.0287410	−	0.0497809i
$515$	13.2395			0.583400
$516$	15.5061	−	26.8573i	0.682616	−	1.18233i
$517$	0.681511	−	1.18041i	0.0299728	−	0.0519144i
$518$	−0.247850	+	0.0716548i	−0.0108899	+	0.00314833i
$519$	17.6338	−	30.5426i	0.774036	−	1.34067i
$520$	0.0149079	+	0.0258212i	0.000653754	+	0.00113234i
$521$	16.2321	−	28.1149i	0.711143	−	1.23174i	−0.253286	−	0.967391i	$-0.581511\pi$
$521$	16.2321	−	28.1149i	0.711143	−	1.23174i	0.964429	−	0.264344i	$-0.0851553\pi$
$522$	−0.112460	−	0.194786i	−0.00492223	−	0.00852555i
$523$	−9.19820			−0.402209			−0.201105	−	0.979570i	$-0.564453\pi$
$523$	−9.19820			−0.402209			−0.201105	+	0.979570i	$0.564453\pi$
$524$	−22.2119			−0.970330
$525$	2.83669	+	2.72743i	0.123803	+	0.119035i
$526$	1.00521	−	1.74107i	0.0438291	−	0.0759142i
$527$	−8.93588	+	15.4774i	−0.389253	+	0.674206i
$528$	1.28468	+	2.22512i	0.0559083	+	0.0968361i
$529$	−5.14623			−0.223749
$530$	0.486197	−	0.842117i	0.0211190	−	0.0365792i
$531$	−12.9332			−0.561252
$532$	−12.3376	+	19.4125i	−0.534903	+	0.841639i
$533$	0.310224			0.0134373
$534$	−0.375430	+	0.650263i	−0.0162464	+	0.0281397i
$535$	−43.8405			−1.89539
$536$	−1.74333	−	3.01953i	−0.0753003	−	0.130424i
$537$	−14.3280	+	24.8168i	−0.618299	+	1.07092i
$538$	0.298422	−	0.516883i	0.0128659	−	0.0222844i
$539$	−0.127442	−	3.24392i	−0.00548930	−	0.139725i
$540$	−27.7790			−1.19542
$541$	−6.86895			−0.295319			−0.147660	−	0.989038i	$-0.547174\pi$
$541$	−6.86895			−0.295319			−0.147660	+	0.989038i	$0.547174\pi$
$542$	−0.00556149	−	0.00963278i	−0.000238886	−	0.000413764i
$543$	−14.0173	+	24.2788i	−0.601542	+	1.04190i
$544$	−1.33596	−	2.31395i	−0.0572788	−	0.0992098i
$545$	−5.13873	+	8.90054i	−0.220119	+	0.381257i
$546$	−0.00807306	−	0.00776212i	−0.000345495	−	0.000332188i
$547$	4.90193	−	8.49039i	0.209591	−	0.363023i	−0.741995	−	0.670406i	$-0.766120\pi$
$547$	4.90193	−	8.49039i	0.209591	−	0.363023i	0.951586	+	0.307383i	$0.0994533\pi$
$548$	10.8804	−	18.8455i	0.464790	−	0.805039i
$549$	1.95486			0.0834315
$550$	0.0183643	−	0.0318078i	0.000783055	−	0.00135629i
$551$	−11.9085	−	3.99907i	−0.507321	−	0.170366i
$552$	1.75286			0.0746066
$553$	2.73852	−	11.0865i	0.116454	−	0.471446i
$554$	−0.0294413	−	0.0509939i	−0.00125084	−	0.00216652i
$555$	−4.51029			−0.191451
$556$	28.9470			1.22763
$557$	−0.183580	−	0.317970i	−0.00777854	−	0.0134728i	0.862110	−	0.506721i	$-0.169143\pi$
$557$	−0.183580	−	0.317970i	−0.00777854	−	0.0134728i	−0.869888	+	0.493248i	$0.835809\pi$
$558$	0.232053	+	0.401927i	0.00982357	+	0.0170149i
$559$	−0.453788			−0.0191932
$560$	−18.6319	−	17.9143i	−0.787340	−	0.757016i
$561$	0.973286	−	1.68578i	0.0410922	−	0.0711737i
$562$	−0.680962	−	1.17946i	−0.0287247	−	0.0497526i
$563$	17.3353	−	30.0256i	0.730594	−	1.26543i	−0.226035	−	0.974119i	$-0.572576\pi$
$563$	17.3353	−	30.0256i	0.730594	−	1.26543i	0.956630	−	0.291307i	$-0.0940902\pi$
$564$	4.09321	+	7.08965i	0.172355	+	0.298528i
$565$	11.4131	−	19.7680i	0.480152	−	0.831648i
$566$	−0.0606653	+	0.105075i	−0.00254995	+	0.00441665i
$567$	12.0728	−	3.49031i	0.507009	−	0.146579i
$568$	−2.34492	−	4.06152i	−0.0983905	−	0.170417i
$569$	17.5230	+	30.3507i	0.734602	+	1.27237i	0.954898	+	0.296935i	$0.0959646\pi$
$569$	17.5230	+	30.3507i	0.734602	+	1.27237i	−0.220295	+	0.975433i	$0.570702\pi$
$570$	0.835779	−	0.737802i	0.0350069	−	0.0309031i
$571$	−0.134809	+	0.233496i	−0.00564158	+	0.00977150i	−0.868832	−	0.495106i	$-0.835129\pi$
$571$	−0.134809	+	0.233496i	−0.00564158	+	0.00977150i	0.863191	+	0.504878i	$0.168462\pi$
$572$	0.0188506	−	0.0326501i	0.000788182	−	0.00136517i
$573$	−1.99322	−	3.45235i	−0.0832678	−	0.144224i
$574$	1.43855	−	0.415894i	0.0600440	−	0.0173591i
$575$	2.24999	+	3.89709i	0.0938310	+	0.162520i
$576$	8.25719			0.344050
$577$	−12.2188	+	21.1636i	−0.508676	+	0.881052i	0.491274	+	0.871005i	$0.336531\pi$
$577$	−12.2188	+	21.1636i	−0.508676	+	0.881052i	−0.999950	+	0.0100469i	$0.996802\pi$
$578$	0.296257	−	0.513132i	0.0123227	−	0.0213435i
$579$	12.9117			0.536594
$580$	7.07778	−	12.2591i	0.293889	−	0.509031i
$581$	13.7082	−	3.96312i	0.568711	−	0.164418i
$582$	−0.0739472			−0.00306521
$583$	−2.46253			−0.101988
$584$	−2.64729			−0.109546
$585$	0.0526739	+	0.0912339i	0.00217780	+	0.00377206i
$586$	0.351413	−	0.608665i	0.0145167	−	0.0251437i
$587$	22.5998	+	39.1441i	0.932795	+	1.61565i	0.778519	+	0.627621i	$0.215971\pi$
$587$	22.5998	+	39.1441i	0.932795	+	1.61565i	0.154277	+	0.988028i	$0.450695\pi$
$588$	17.2557	+	9.07875i	0.711613	+	0.374401i
$589$	24.5724	+	8.25181i	1.01249	+	0.340010i
$590$	1.12837	+	1.95439i	0.0464542	+	0.0804611i
$591$	−27.9176			−1.14838
$592$	5.20193			0.213798
$593$	7.64979			0.314139			0.157070	−	0.987588i	$-0.449795\pi$
$593$	7.64979			0.314139			0.157070	+	0.987588i	$0.449795\pi$
$594$	−0.0975220	−	0.168913i	−0.00400138	−	0.00693059i
$595$	−4.69589	+	19.0106i	−0.192513	+	0.779359i
$596$	34.0264			1.39378
$597$	−6.96723	−	12.0676i	−0.285150	−	0.493894i
$598$	−0.00640334	−	0.0110909i	−0.000261852	−	0.000453541i
$599$	−10.5226	−	18.2258i	−0.429944	−	0.744684i	0.566924	−	0.823770i	$-0.308133\pi$
$599$	−10.5226	−	18.2258i	−0.429944	−	0.744684i	−0.996868	+	0.0790858i	$0.974800\pi$
$600$	0.220901	+	0.382611i	0.00901823	+	0.0156200i
$601$	−12.7043			−0.518220			−0.259110	−	0.965848i	$-0.583429\pi$
$601$	−12.7043			−0.518220			−0.259110	+	0.965848i	$0.583429\pi$
$602$	−2.10428	+	0.608359i	−0.0857640	+	0.0247949i
$603$	−6.15969	−	10.6689i	−0.250842	−	0.434471i
$604$	−12.9697			−0.527728
$605$	26.5602			1.07983
$606$	1.32532			0.0538376
$607$	13.9021	+	24.0791i	0.564267	+	0.977339i	0.997117	+	0.0758732i	$0.0241744\pi$
$607$	13.9021	+	24.0791i	0.564267	+	0.977339i	−0.432851	+	0.901466i	$0.642492\pi$
$608$	−2.90525	+	2.56468i	−0.117824	+	0.104011i
$609$	−2.55367	+	10.3382i	−0.103480	+	0.418924i
$610$	−0.170554	−	0.295409i	−0.00690554	−	0.0119607i
$611$	0.0598944	−	0.103740i	0.00242307	−	0.00419688i
$612$	−3.14544	−	5.44806i	−0.127147	−	0.220225i
$613$	12.3266			0.497865			0.248932	−	0.968521i	$-0.419920\pi$
$613$	12.3266			0.497865			0.248932	+	0.968521i	$0.419920\pi$
$614$	−0.0126521			−0.000510598
$615$	26.1783			1.05561
$616$	0.0874032	−	0.353839i	0.00352157	−	0.0142566i
$617$	−6.25570	+	10.8352i	−0.251845	+	0.436209i	−0.964034	−	0.265779i	$-0.914371\pi$
$617$	−6.25570	+	10.8352i	−0.251845	+	0.436209i	0.712189	+	0.701988i	$0.247704\pi$
$618$	−0.558313			−0.0224586
$619$	20.1664	−	34.9293i	0.810557	−	1.40393i	−0.101918	−	0.994793i	$-0.532498\pi$
$619$	20.1664	−	34.9293i	0.810557	−	1.40393i	0.912475	−	0.409133i	$-0.134169\pi$
$620$	−14.6045	+	25.2957i	−0.586531	+	1.01590i
$621$	23.8968			0.958944
$622$	0.462210	+	0.800572i	0.0185329	+	0.0321000i
$623$	−18.3761	+	5.31265i	−0.736224	+	0.212847i
$624$	0.112903	+	0.195554i	0.00451975	+	0.00782844i
$625$	14.5954	−	25.2799i	0.583815	−	1.01120i
$626$	0.00462419	−	0.00800933i	0.000184820	−	0.000320117i
$627$	−2.67640	−	0.898778i	−0.106885	−	0.0358937i
$628$	−13.7478	−	23.8118i	−0.548595	−	0.950195i
$629$	−1.97052	−	3.41305i	−0.0785699	−	0.136087i
$630$	0.366566	+	0.352448i	0.0146043	+	0.0140419i
$631$	−1.05264	+	1.82323i	−0.0419049	+	0.0725815i	−0.886217	−	0.463270i	$-0.846676\pi$
$631$	−1.05264	+	1.82323i	−0.0419049	+	0.0725815i	0.844312	+	0.535852i	$0.180009\pi$
$632$	0.641043	−	1.11032i	0.0254993	−	0.0441661i
$633$	14.6888	+	25.4417i	0.583826	+	1.01122i
$634$	0.201008	−	0.348156i	0.00798304	−	0.0138270i
$635$	22.9070	+	39.6762i	0.909038	+	1.57450i
$636$	7.39509	−	12.8087i	0.293234	−	0.507897i
$637$	−0.0112002	−	0.285091i	−0.000443767	−	0.0112957i
$638$	0.0993901			0.00393489
$639$	−8.28527	−	14.3505i	−0.327760	−	0.567698i
$640$	−2.90991	−	5.04011i	−0.115024	−	0.199228i
$641$	26.6714			1.05346			0.526728	−	0.850034i	$-0.323419\pi$
$641$	26.6714			1.05346			0.526728	+	0.850034i	$0.323419\pi$
$642$	1.84877			0.0729652
$643$	−14.8014	−	25.6368i	−0.583711	−	1.01102i	−0.995035	−	0.0995273i	$-0.968267\pi$
$643$	−14.8014	−	25.6368i	−0.583711	−	1.01102i	0.411324	−	0.911489i	$-0.365066\pi$
$644$	16.0727	+	15.4536i	0.633352	+	0.608958i
$645$	−38.2930			−1.50778
$646$	0.923461	+	0.310113i	0.0363331	+	0.0122012i
$647$	2.03357	−	3.52225i	0.0799479	−	0.138474i	−0.823279	−	0.567636i	$-0.807858\pi$
$647$	2.03357	−	3.52225i	0.0799479	−	0.138474i	0.903227	+	0.429163i	$0.141191\pi$
$648$	1.41091			0.0554259
$649$	2.85753	−	4.94939i	0.112168	−	0.194281i
$650$	0.00161394	−	0.00279542i	6.33039e−5	−	0.000109646i
$651$	5.26932	−	21.3321i	0.206521	−	0.836070i
$652$	11.4641	−	19.8563i	0.448967	−	0.777634i
$653$	−10.7657	−	18.6468i	−0.421296	−	0.729705i	0.574771	−	0.818314i	$-0.305091\pi$
$653$	−10.7657	−	18.6468i	−0.421296	−	0.729705i	−0.996066	+	0.0886091i	$0.971758\pi$
$654$	0.216702	−	0.375339i	0.00847373	−	0.0146769i
$655$	13.7133	+	23.7522i	0.535824	+	0.928074i
$656$	−30.1927			−1.17883
$657$	−9.35366			−0.364921
$658$	0.138662	−	0.561353i	0.00540561	−	0.0218838i
$659$	−12.0860	+	20.9335i	−0.470802	+	0.815453i	−0.999442	−	0.0333929i	$-0.989369\pi$
$659$	−12.0860	+	20.9335i	−0.470802	+	0.815453i	0.528640	+	0.848846i	$0.322702\pi$
$660$	1.59071	−	2.75518i	0.0619182	−	0.107245i
$661$	21.7151	+	37.6117i	0.844620	+	1.46292i	0.885951	+	0.463779i	$0.153507\pi$
$661$	21.7151	+	37.6117i	0.844620	+	1.46292i	−0.0413308	+	0.999146i	$0.513160\pi$
$662$	0.615983			0.0239409
$663$	0.0855370	−	0.148154i	0.00332198	−	0.00575384i
$664$	1.60204			0.0621711
$665$	28.3758	+	1.20814i	1.10036	+	0.0468495i
$666$	−0.102344			−0.00396573
$667$	−6.08863	+	10.5458i	−0.235753	+	0.408336i
$668$	23.0918			0.893450
$669$	−8.48758	−	14.7009i	−0.328149	−	0.568370i
$670$	−1.07482	+	1.86164i	−0.0415239	+	0.0719214i
$671$	−0.431919	+	0.748106i	−0.0166741	+	0.0288803i
$672$	2.36808	+	2.27687i	0.0913507	+	0.0878323i
$673$	−37.2020			−1.43403			−0.717015	−	0.697057i	$-0.754492\pi$
$673$	−37.2020			−1.43403			−0.717015	+	0.697057i	$0.754492\pi$
$674$	0.304639			0.0117342
$675$	3.01155	+	5.21615i	0.115914	+	0.200770i
$676$	−12.9624	+	22.4515i	−0.498554	+	0.863521i
$677$	13.7084	+	23.7436i	0.526856	+	0.912541i	0.999510	+	0.0312931i	$0.00996254\pi$
$677$	13.7084	+	23.7436i	0.526856	+	0.912541i	−0.472654	+	0.881248i	$0.656704\pi$
$678$	−0.481294	+	0.833626i	−0.0184840	+	0.0320152i
$679$	−1.35798	−	1.30568i	−0.0521146	−	0.0501074i
$680$	−1.09923	+	1.90392i	−0.0421536	+	0.0730122i
$681$	6.64367	−	11.5072i	0.254586	−	0.440956i
$682$	−0.205084			−0.00785309
$683$	2.21838	−	3.84234i	0.0848838	−	0.147023i	−0.820458	−	0.571707i	$-0.806281\pi$
$683$	2.21838	−	3.84234i	0.0848838	−	0.147023i	0.905342	+	0.424684i	$0.139615\pi$
$684$	−6.84025	+	6.03838i	−0.261544	+	0.230883i
$685$	−26.8698			−1.02664
$686$	−0.434136	−	1.30699i	−0.0165754	−	0.0499011i
$687$	−4.57858	−	7.93033i	−0.174684	−	0.302561i
$688$	44.1651			1.68378
$689$	−0.216419			−0.00824490
$690$	−0.540347	−	0.935908i	−0.0205707	−	0.0356294i
$691$	−6.30259	−	10.9164i	−0.239762	−	0.415280i	0.720884	−	0.693056i	$-0.243736\pi$
$691$	−6.30259	−	10.9164i	−0.239762	−	0.415280i	−0.960646	+	0.277776i	$0.910403\pi$
$692$	50.3653			1.91460
$693$	0.308821	−	1.25022i	0.0117311	−	0.0474918i
$694$	−0.527210	+	0.913154i	−0.0200126	+	0.0346629i
$695$	−17.8715	−	30.9543i	−0.677905	−	1.17417i
$696$	−0.597773	+	1.03537i	−0.0226585	+	0.0392457i
$697$	11.4372	+	19.8098i	0.433214	+	0.750349i
$698$	−0.564341	+	0.977467i	−0.0213606	+	0.0369977i
$699$	4.12263	−	7.14060i	0.155932	−	0.270082i
$700$	−1.34767	+	5.45583i	−0.0509370	+	0.206211i
$701$	−10.9505	−	18.9668i	−0.413594	−	0.716365i	0.581686	−	0.813413i	$-0.302393\pi$
$701$	−10.9505	−	18.9668i	−0.413594	−	0.716365i	−0.995280	+	0.0970481i	$0.969060\pi$
$702$	−0.00857070	−	0.0148449i	−0.000323480	−	0.000560284i
$703$	−4.28521	+	3.78286i	−0.161620	+	0.142673i
$704$	−1.82439	+	3.15994i	−0.0687594	+	0.119095i
$705$	5.05419	−	8.75412i	0.190352	−	0.329699i
$706$	0.0729419	+	0.126339i	0.00274520	+	0.00475483i
$707$	24.3386	+	23.4012i	0.915346	+	0.880091i
$708$	17.1626	+	29.7265i	0.645010	+	1.11719i
$709$	−10.8098			−0.405972			−0.202986	−	0.979182i	$-0.565065\pi$
$709$	−10.8098			−0.405972			−0.202986	+	0.979182i	$0.565065\pi$
$710$	−1.44572	+	2.50406i	−0.0542568	+	0.0939755i
$711$	2.26499	−	3.92308i	0.0849438	−	0.147127i
$712$	−2.14757			−0.0804835
$713$	12.5635	−	21.7606i	0.470505	−	0.814939i
$714$	0.198027	−	0.801685i	0.00741099	−	0.0300023i
$715$	−0.0465524			−0.00174096
$716$	−40.9234			−1.52938
$717$	−22.9537			−0.857221
$718$	−0.0103604	−	0.0179448i	−0.000386648	−	0.000669694i
$719$	−7.67831	+	13.2992i	−0.286353	+	0.495977i	−0.972936	−	0.231074i	$-0.925776\pi$
$719$	−7.67831	+	13.2992i	−0.286353	+	0.495977i	0.686584	+	0.727051i	$0.259110\pi$
$720$	−5.12651	−	8.87937i	−0.191054	−	0.330914i
$721$	−10.2530	−	9.85809i	−0.381841	−	0.367135i
$722$	0.175264	−	1.40197i	0.00652264	−	0.0521758i
$723$	−9.46397	−	16.3921i	−0.351969	−	0.609628i
$724$	−40.0362			−1.48793
$725$	−3.06923			−0.113988
$726$	−1.12005			−0.0415691
$727$	11.4128	+	19.7676i	0.423279	+	0.733141i	0.996258	−	0.0864293i	$-0.0275457\pi$
$727$	11.4128	+	19.7676i	0.423279	+	0.733141i	−0.572979	+	0.819570i	$0.694212\pi$
$728$	0.00768141	−	0.0310970i	0.000284692	−	0.00115253i
$729$	28.6807			1.06225
$730$	0.816071	+	1.41348i	0.0302042	+	0.0523151i
$731$	−16.7300	−	28.9772i	−0.618782	−	1.07176i
$732$	−2.59414	−	4.49319i	−0.0958824	−	0.166073i
$733$	23.3863	+	40.5062i	0.863792	+	1.49613i	0.868242	+	0.496141i	$0.165250\pi$
$733$	23.3863	+	40.5062i	0.863792	+	1.49613i	−0.00444994	+	0.999990i	$0.501416\pi$
$734$	−0.234641			−0.00866074
$735$	−0.945128	−	24.0574i	−0.0348616	−	0.887371i
$736$	1.87830	+	3.25331i	0.0692351	+	0.119919i
$737$	5.44384			0.200526
$738$	0.594016			0.0218660
$739$	−19.5509			−0.719193			−0.359596	−	0.933108i	$-0.617086\pi$
$739$	−19.5509			−0.719193			−0.359596	+	0.933108i	$0.617086\pi$
$740$	−3.22056	−	5.57817i	−0.118390	−	0.205058i
$741$	−0.235215	−	0.0789888i	−0.00864083	−	0.00290173i
$742$	−1.00356	+	0.290136i	−0.0368420	+	0.0106512i
$743$	15.5475	+	26.9290i	0.570381	+	0.987929i	0.996527	+	0.0832748i	$0.0265379\pi$
$743$	15.5475	+	26.9290i	0.570381	+	0.987929i	−0.426145	+	0.904655i	$0.640129\pi$
$744$	1.23346	−	2.13642i	0.0452210	−	0.0783250i
$745$	−21.0075	−	36.3860i	−0.769654	−	1.33308i
$746$	−0.496550			−0.0181800
$747$	5.66046			0.207106
$748$	2.77989			0.101643
$749$	33.9513	+	32.6436i	1.24055	+	1.19277i
$750$	−0.503215	+	0.871594i	−0.0183748	+	0.0318261i
$751$	16.5517			0.603980			0.301990	−	0.953311i	$-0.402349\pi$
$751$	16.5517			0.603980			0.301990	+	0.953311i	$0.402349\pi$
$752$	−5.82924	+	10.0965i	−0.212571	+	0.368183i
$753$	9.32531	−	16.1519i	0.339833	−	0.588608i
$754$	0.00873487			0.000318105
$755$	8.00729	+	13.8690i	0.291415	+	0.504746i
$756$	21.5128	+	20.6842i	0.782413	+	0.752279i
$757$	−12.0807	−	20.9244i	−0.439081	−	0.760510i	0.558538	−	0.829479i	$-0.311362\pi$
$757$	−12.0807	−	20.9244i	−0.439081	−	0.760510i	−0.997619	+	0.0689689i	$0.978029\pi$
$758$	0.289248	−	0.500993i	0.0105060	−	0.0181969i
$759$	−1.36840	+	2.37014i	−0.0496697	+	0.0860305i
$760$	3.02273	+	1.01508i	0.109646	+	0.0368209i
$761$	−18.3935	−	31.8584i	−0.666763	−	1.15487i	−0.978804	−	0.204799i	$-0.934346\pi$
$761$	−18.3935	−	31.8584i	−0.666763	−	1.15487i	0.312041	−	0.950069i	$-0.398987\pi$
$762$	−0.965999	−	1.67316i	−0.0349945	−	0.0606122i
$763$	10.6069	−	3.06652i	0.383996	−	0.111015i
$764$	2.84650	−	4.93028i	0.102983	−	0.178371i
$765$	−3.88390	+	6.72712i	−0.140423	+	0.243220i
$766$	0.223727	+	0.387507i	0.00808360	+	0.0140012i
$767$	0.251134	−	0.434976i	0.00906791	−	0.0157061i
$768$	−10.8651	−	18.8190i	−0.392062	−	0.679071i
$769$	3.36008	−	5.81983i	0.121168	−	0.209868i	−0.799061	−	0.601250i	$-0.794669\pi$
$769$	3.36008	−	5.81983i	0.121168	−	0.209868i	0.920228	+	0.391382i	$0.128003\pi$
$770$	−0.215870	+	0.0624092i	−0.00777940	+	0.00224907i
$771$	−24.4756			−0.881466
$772$	9.21959	+	15.9688i	0.331820	+	0.574730i
$773$	−20.7019	−	35.8567i	−0.744594	−	1.28967i	−0.950384	−	0.311078i	$-0.899310\pi$
$773$	−20.7019	−	35.8567i	−0.744594	−	1.28967i	0.205790	−	0.978596i	$-0.434024\pi$
$774$	−0.868911			−0.0312324
$775$	6.33315			0.227493
$776$	−0.105750	−	0.183164i	−0.00379620	−	0.00657522i
$777$	3.49289	+	3.35836i	0.125307	+	0.120480i
$778$	−2.37185			−0.0850348
$779$	24.8720	−	21.9562i	0.891130	−	0.786664i
$780$	0.139799	−	0.242139i	0.00500560	−	0.00866996i
$781$	7.32240			0.262016
$782$	0.472150	−	0.817788i	0.0168840	−	0.0292440i
$783$	−8.14946	+	14.1153i	−0.291238	+	0.504439i
$784$	1.09006	+	27.7466i	0.0389308	+	0.990949i
$785$	−16.9754	+	29.4022i	−0.605877	+	1.04941i
$786$	−0.578296	−	1.00164i	−0.0206271	−	0.0357272i
$787$	4.64956	−	8.05328i	0.165739	−	0.287068i	−0.771178	−	0.636619i	$-0.780332\pi$
$787$	4.64956	−	8.05328i	0.165739	−	0.287068i	0.936917	+	0.349551i	$0.113666\pi$
$788$	−19.9345	−	34.5276i	−0.710137	−	1.22999i
$789$	−37.7576			−1.34421
$790$	−0.790447			−0.0281228
$791$	−23.5579	+	6.81072i	−0.837622	+	0.242161i
$792$	0.0722900	−	0.125210i	0.00256871	−	0.00444914i
$793$	−0.0379591	+	0.0657471i	−0.00134797	+	0.00233475i
$794$	−0.110606	−	0.191576i	−0.00392527	−	0.00679877i
$795$	−18.2625			−0.647705
$796$	9.94985	−	17.2336i	0.352663	−	0.610831i
$797$	7.07919			0.250758			0.125379	−	0.992109i	$-0.459985\pi$
$797$	7.07919			0.250758			0.125379	+	0.992109i	$0.459985\pi$
$798$	−1.19662	−	0.0509476i	−0.0423598	−	0.00180353i
$799$	8.83261			0.312475
$800$	−0.473419	+	0.819985i	−0.0167379	+	0.0289908i
$801$	−7.58798			−0.268108
$802$	1.11558	+	1.93225i	0.0393926	+	0.0682301i
$803$	2.06666	−	3.57955i	0.0729307	−	0.126320i
$804$	−16.3481	+	28.3157i	−0.576552	+	0.998618i
$805$	6.60221	−	26.7281i	0.232697	−	0.942042i
$806$	−0.0180238			−0.000634861
$807$	−11.2094			−0.394588
$808$	1.89531	+	3.28278i	0.0666768	+	0.115488i
$809$	0.998642	−	1.72970i	0.0351104	−	0.0608129i	−0.847936	−	0.530098i	$-0.822155\pi$
$809$	0.998642	−	1.72970i	0.0351104	−	0.0608129i	0.883047	+	0.469285i	$0.155488\pi$
$810$	−0.434937	−	0.753332i	−0.0152821	−	0.0264694i
$811$	18.0891	−	31.3312i	0.635193	−	1.10019i	−0.351282	−	0.936270i	$-0.614254\pi$
$811$	18.0891	−	31.3312i	0.635193	−	1.10019i	0.986474	−	0.163916i	$-0.0524126\pi$
$812$	−14.6093	+	4.22364i	−0.512687	+	0.148221i
$813$	−0.104450	+	0.180913i	−0.00366324	+	0.00634491i
$814$	0.0226124	−	0.0391658i	0.000792565	−	0.00137276i
$815$	−28.3110			−0.991692
$816$	−8.32492	+	14.4192i	−0.291430	+	0.504772i
$817$	−36.3821	+	32.1170i	−1.27285	+	1.12363i
$818$	−1.18091			−0.0412897
$819$	0.0271406	−	0.109875i	0.000948371	−	0.00383934i
$820$	18.6925	+	32.3764i	0.652772	+	1.13063i
$821$	46.1400			1.61030			0.805148	−	0.593073i	$-0.202086\pi$
$821$	46.1400			1.61030			0.805148	+	0.593073i	$0.202086\pi$
$822$	1.13311			0.0395217
$823$	8.28377	+	14.3479i	0.288754	+	0.500137i	0.973513	−	0.228633i	$-0.0734257\pi$
$823$	8.28377	+	14.3479i	0.288754	+	0.500137i	−0.684759	+	0.728770i	$0.740092\pi$
$824$	−0.798429	−	1.38292i	−0.0278146	−	0.0481763i
$825$	−0.689799			−0.0240157
$826$	0.581401	−	2.35372i	0.0202295	−	0.0818963i
$827$	−6.38108	+	11.0524i	−0.221892	+	0.384328i	−0.955382	−	0.295372i	$-0.904557\pi$
$827$	−6.38108	+	11.0524i	−0.221892	+	0.384328i	0.733491	+	0.679700i	$0.237890\pi$
$828$	4.42235	+	7.65973i	0.153687	+	0.266194i
$829$	−7.47588	+	12.9486i	−0.259648	+	0.449723i	−0.966148	−	0.257990i	$-0.916940\pi$
$829$	−7.47588	+	12.9486i	−0.259648	+	0.449723i	0.706500	+	0.707713i	$0.250273\pi$
$830$	−0.493854	−	0.855380i	−0.0171419	−	0.0296907i
$831$	−0.552938	+	0.957717i	−0.0191812	+	0.0332228i
$832$	−0.160336	+	0.277711i	−0.00555866	+	0.00962789i
$833$	17.7919	−	11.2258i	0.616453	−	0.388950i
$834$	0.753648	+	1.30536i	0.0260967	+	0.0452008i
$835$	−14.2566	−	24.6932i	−0.493370	−	0.854542i
$836$	−0.799498	−	3.95185i	−0.0276512	−	0.136678i
$837$	16.8158	−	29.1259i	0.581241	−	1.00674i
$838$	−0.790330	+	1.36889i	−0.0273015	+	0.0472876i
$839$	−17.4124	−	30.1592i	−0.601144	−	1.04121i	−0.992648	−	0.121035i	$-0.961379\pi$
$839$	−17.4124	−	30.1592i	−0.601144	−	1.04121i	0.391504	−	0.920176i	$-0.371955\pi$
$840$	0.648196	−	2.62413i	0.0223649	−	0.0905410i
$841$	10.3472	+	17.9219i	0.356801	+	0.617997i
$842$	1.80368			0.0621589
$843$	−12.7892	+	22.1515i	−0.440482	+	0.762938i
$844$	−20.9769	+	36.3331i	−0.722056	+	1.25064i
$845$	32.0113			1.10122
$846$	0.114685	−	0.198641i	0.00394296	−	0.00682941i
$847$	−20.5689	−	19.7767i	−0.706757	−	0.679537i
$848$	21.0630			0.723308
$849$	2.27871			0.0782052
$850$	0.238007			0.00816358
$851$	2.77047	+	4.79859i	0.0949705	+	0.164494i
$852$	−21.9895	+	38.0869i	−0.753347	+	1.30484i
$853$	−1.08613	−	1.88124i	−0.0371886	−	0.0644125i	0.846832	−	0.531860i	$-0.178507\pi$
$853$	−1.08613	−	1.88124i	−0.0371886	−	0.0644125i	−0.884021	+	0.467448i	$0.845174\pi$
$854$	−0.0878794	+	0.355767i	−0.00300717	+	0.0121741i
$855$	10.6802	+	3.58658i	0.365255	+	0.122658i
$856$	2.64388	+	4.57933i	0.0903659	+	0.156518i
$857$	−38.3712			−1.31074			−0.655368	−	0.755309i	$-0.727487\pi$
$857$	−38.3712			−1.31074			−0.655368	+	0.755309i	$0.727487\pi$
$858$	0.00196313			6.70202e−5
$859$	−40.6917			−1.38838			−0.694191	−	0.719791i	$-0.744238\pi$
$859$	−40.6917			−1.38838			−0.694191	+	0.719791i	$0.744238\pi$
$860$	−27.3430	−	47.3594i	−0.932388	−	1.61494i
$861$	−20.2732	−	19.4924i	−0.690908	−	0.664298i
$862$	0.0190046			0.000647300
$863$	8.39723	+	14.5444i	0.285845	+	0.495098i	0.972814	−	0.231589i	$-0.0743924\pi$
$863$	8.39723	+	14.5444i	0.285845	+	0.495098i	−0.686969	+	0.726687i	$0.741059\pi$
$864$	2.51405	+	4.35447i	0.0855298	+	0.148142i
$865$	−31.0949	−	53.8579i	−1.05726	−	1.83122i
$866$	−1.19017	−	2.06143i	−0.0404435	−	0.0700502i
$867$	−11.1280			−0.377927
$868$	30.1453	−	8.71519i	1.02320	−	0.295813i
$869$	1.00088	+	1.73358i	0.0339526	+	0.0588076i
$870$	0.737093			0.0249898
$871$	0.478430			0.0162110
$872$	1.23960			0.0419782
$873$	−0.373645	−	0.647173i	−0.0126460	−	0.0219035i
$874$	−1.29835	−	0.436005i	−0.0439172	−	0.0147481i
$875$	−24.6308	+	7.12092i	−0.832674	+	0.240731i
$876$	12.4125	+	21.4991i	0.419380	+	0.726387i
$877$	−14.2718	+	24.7194i	−0.481923	+	0.834715i	−0.999785	−	0.0207495i	$-0.993395\pi$
$877$	−14.2718	+	24.7194i	−0.481923	+	0.834715i	0.517862	+	0.855464i	$0.326728\pi$
$878$	1.09426	+	1.89532i	0.0369295	+	0.0639638i
$879$	−13.1998			−0.445217
$880$	4.53072			0.152731
$881$	−46.6625			−1.57210			−0.786050	−	0.618163i	$-0.787877\pi$
$881$	−46.6625			−1.57210			−0.786050	+	0.618163i	$0.787877\pi$
$882$	−0.0214460	−	0.545890i	−0.000722125	−	0.0183811i
$883$	−9.20274	+	15.9396i	−0.309697	+	0.536411i	−0.978296	−	0.207212i	$-0.933561\pi$
$883$	−9.20274	+	15.9396i	−0.309697	+	0.536411i	0.668599	+	0.743623i	$0.266894\pi$
$884$	0.244310			0.00821703
$885$	21.1919	−	36.7055i	0.712359	−	1.23384i
$886$	0.870420	−	1.50761i	0.0292423	−	0.0506492i
$887$	7.33258			0.246204			0.123102	−	0.992394i	$-0.460716\pi$
$887$	7.33258			0.246204			0.123102	+	0.992394i	$0.460716\pi$
$888$	0.272001	+	0.471119i	0.00912775	+	0.0158097i
$889$	11.8030	−	47.7829i	0.395861	−	1.60259i
$890$	0.662023	+	1.14666i	0.0221911	+	0.0384360i
$891$	−1.10145	+	1.90777i	−0.0369001	+	0.0639128i
$892$	12.1211	−	20.9943i	0.405843	−	0.702941i
$893$	−2.54027	−	12.5563i	−0.0850068	−	0.420181i
$894$	0.885894	+	1.53441i	0.0296287	+	0.0513184i
$895$	25.2656	+	43.7613i	0.844536	+	1.46278i
$896$	−1.49935	+	6.06991i	−0.0500899	+	0.202782i
$897$	−0.120261	+	0.208299i	−0.00401541	+	0.00695489i
$898$	−0.973942	+	1.68692i	−0.0325009	+	0.0562932i
$899$	8.56898	+	14.8419i	0.285791	+	0.495005i
$900$	−1.11464	+	1.93061i	−0.0371545	+	0.0643535i
$901$	−7.97881	−	13.8197i	−0.265813	−	0.460401i
$902$	−0.131245	+	0.227324i	−0.00437000	+	0.00756906i
$903$	29.6551	+	28.5129i	0.986860	+	0.948851i
$904$	−2.75314			−0.0915682
$905$	24.7178	+	42.8125i	0.821648	+	1.42314i
$906$	−0.337671	−	0.584863i	−0.0112184	−	0.0194308i
$907$	48.5716			1.61279			0.806396	−	0.591375i	$-0.201415\pi$
$907$	48.5716			1.61279			0.806396	+	0.591375i	$0.201415\pi$
$908$	18.9756			0.629726
$909$	6.69669	+	11.5990i	0.222115	+	0.384715i
$910$	−0.0189716	+	0.00548481i	−0.000628904	+	0.000181820i
$911$	−18.2738			−0.605437			−0.302718	−	0.953080i	$-0.597894\pi$
$911$	−18.2738			−0.605437			−0.302718	+	0.953080i	$0.597894\pi$
$912$	22.8924	+	7.68762i	0.758042	+	0.254562i
$913$	−1.25066	+	2.16620i	−0.0413907	+	0.0716908i
$914$	−2.40025			−0.0793931
$915$	−3.20318	+	5.54807i	−0.105894	+	0.183414i
$916$	6.53864	−	11.3253i	0.216043	−	0.374197i
$917$	7.06589	−	28.6052i	0.233336	−	0.944628i
$918$	0.631959	−	1.09459i	0.0208578	−	0.0361267i
$919$	3.17716	+	5.50300i	0.104805	+	0.181527i	0.913658	−	0.406483i	$-0.133245\pi$
$919$	3.17716	+	5.50300i	0.104805	+	0.181527i	−0.808854	+	0.588010i	$0.799912\pi$
$920$	1.54547	−	2.67683i	0.0509527	−	0.0882526i
$921$	0.118810	+	0.205785i	0.00391492	+	0.00678084i
$922$	−2.00939			−0.0661759
$923$	0.643527			0.0211819
$924$	−3.28340	+	0.949249i	−0.108016	+	0.0312280i
$925$	−0.698286	+	1.20947i	−0.0229595	+	0.0397670i
$926$	−1.19644	+	2.07229i	−0.0393173	+	0.0680996i
$927$	−2.82108	−	4.88625i	−0.0926564	−	0.160486i
$928$	−2.56221			−0.0841087
$929$	18.6602	−	32.3205i	0.612222	−	1.06040i	−0.378643	−	0.925543i	$-0.623609\pi$
$929$	18.6602	−	32.3205i	0.612222	−	1.06040i	0.990865	−	0.134857i	$-0.0430575\pi$
$930$	−1.52094			−0.0498736
$931$	−21.0754	−	22.0642i	−0.690717	−	0.723125i
$932$	11.7750			0.385703
$933$	8.68078	−	15.0356i	0.284196	−	0.492242i
$934$	−2.49766			−0.0817261
$935$	−1.71627	−	2.97266i	−0.0561279	−	0.0972164i
$936$	0.00635318	−	0.0110040i	0.000207660	−	0.000359678i
$937$	20.8321	−	36.0823i	0.680556	−	1.17876i	−0.294256	−	0.955727i	$-0.595072\pi$
$937$	20.8321	−	36.0823i	0.680556	−	1.17876i	0.974812	−	0.223030i	$-0.0715948\pi$
$938$	2.21854	−	0.641394i	0.0724381	−	0.0209423i
$939$	−0.173694			−0.00566829
$940$	14.4357			0.470841
$941$	28.2881	+	48.9965i	0.922167	+	1.59724i	0.796055	+	0.605224i	$0.206916\pi$
$941$	28.2881	+	48.9965i	0.922167	+	1.59724i	0.126112	+	0.992016i	$0.459750\pi$
$942$	0.715858	−	1.23990i	0.0233239	−	0.0403982i
$943$	−16.0802	−	27.8517i	−0.523643	−	0.906976i
$944$	−24.4417	+	42.3342i	−0.795508	+	1.37786i
$945$	8.83688	−	35.7748i	0.287464	−	1.16375i
$946$	0.191982	−	0.332523i	0.00624189	−	0.0108113i
$947$	10.4225	−	18.0524i	0.338687	−	0.586623i	−0.645499	−	0.763761i	$-0.723351\pi$
$947$	10.4225	−	18.0524i	0.338687	−	0.586623i	0.984186	+	0.177138i	$0.0566839\pi$
$948$	−12.0228			−0.390481
$949$	0.181627	−	0.314588i	0.00589588	−	0.0102120i
$950$	−0.0684511	−	0.338348i	−0.00222085	−	0.0109774i
$951$	−7.55026			−0.244834
$952$	2.26894	−	0.655963i	0.0735366	−	0.0212599i
$953$	20.7241	+	35.8952i	0.671320	+	1.16276i	0.977530	+	0.210796i	$0.0676056\pi$
$953$	20.7241	+	35.8952i	0.671320	+	1.16276i	−0.306210	+	0.951964i	$0.599061\pi$
$954$	−0.414398			−0.0134166
$955$	−7.02957			−0.227472
$956$	−16.3900	−	28.3883i	−0.530090	−	0.918144i
$957$	−0.933324	−	1.61656i	−0.0301701	−	0.0522561i
$958$	0.186812			0.00603562
$959$	20.8087	+	20.0072i	0.671947	+	0.646067i
$960$	−13.5300	+	23.4346i	−0.436679	+	0.756350i
$961$	−2.18148	−	3.77844i	−0.0703704	−	0.121885i
$962$	0.00198729	−	0.00344208i	6.40727e−5	−	0.000110977i
$963$	9.34159	+	16.1801i	0.301029	+	0.521397i
$964$	13.5154	−	23.4094i	0.435303	−	0.753967i
$965$	11.3841	−	19.7179i	0.366467	−	0.634740i
$966$	−0.278418	+	1.12713i	−0.00895795	+	0.0362650i
$967$	8.31013	+	14.3936i	0.267236	+	0.462866i	0.968147	−	0.250383i	$-0.0805565\pi$
$967$	8.31013	+	14.3936i	0.267236	+	0.462866i	−0.700911	+	0.713248i	$0.747223\pi$
$968$	−1.60176	−	2.77433i	−0.0514825	−	0.0891704i
$969$	−3.62783	−	17.9321i	−0.116543	−	0.576061i
$970$	−0.0651983	+	0.112927i	−0.00209339	+	0.00362586i
$971$	10.9770	−	19.0127i	0.352268	−	0.610146i	−0.634379	−	0.773023i	$-0.718744\pi$
$971$	10.9770	−	19.0127i	0.352268	−	0.610146i	0.986646	+	0.162877i	$0.0520773\pi$
$972$	10.3043	+	17.8476i	0.330510	+	0.572461i
$973$	−9.20843	+	37.2790i	−0.295209	+	1.19511i
$974$	1.36406	+	2.36262i	0.0437073	+	0.0757033i
$975$	−0.0606228			−0.00194148
$976$	3.69438	−	6.39886i	0.118254	−	0.204822i
$977$	7.17224	−	12.4227i	0.229460	−	0.397437i	−0.728188	−	0.685377i	$-0.759637\pi$
$977$	7.17224	−	12.4227i	0.229460	−	0.397437i	0.957648	+	0.287941i	$0.0929706\pi$
$978$	1.19389			0.0381763
$979$	1.67654	−	2.90384i	0.0535823	−	0.0928073i
$980$	29.0785	−	18.3470i	0.928879	−	0.586074i
$981$	4.37987			0.139838
$982$	1.73351			0.0553186
$983$	−34.2861			−1.09356			−0.546778	−	0.837278i	$-0.684146\pi$
$983$	−34.2861			−1.09356			−0.546778	+	0.837278i	$0.684146\pi$
$984$	−1.57873	−	2.73444i	−0.0503281	−	0.0871708i
$985$	−24.6146	+	42.6338i	−0.784287	+	1.35842i
$986$	0.322032	+	0.557777i	0.0102556	+	0.0177632i
$987$	−10.4324	+	3.01607i	−0.332067	+	0.0960026i
$988$	−0.0702637	−	0.347307i	−0.00223539	−	0.0110493i
$989$	23.5217	+	40.7407i	0.747946	+	1.29548i
$990$	−0.0891382			−0.00283300
$991$	30.4969			0.968767			0.484384	−	0.874856i	$-0.339044\pi$
$991$	30.4969			0.968767			0.484384	+	0.874856i	$0.339044\pi$
$992$	5.28694			0.167861
$993$	−5.78440	−	10.0189i	−0.183562	−	0.317939i
$994$	2.98412	−	0.862727i	0.0946506	−	0.0273640i
$995$	−24.5716			−0.778973
$996$	−7.51156	−	13.0104i	−0.238013	−	0.412250i
$997$	6.38802	+	11.0644i	0.202311	+	0.350412i	0.949273	−	0.314454i	$-0.101822\pi$
$997$	6.38802	+	11.0644i	0.202311	+	0.350412i	−0.746962	+	0.664867i	$0.768488\pi$
$998$	−0.493119	−	0.854107i	−0.0156094	−	0.0270363i
$999$	3.70820	+	6.42279i	0.117322	+	0.203208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.g.a.102.6	yes	24
7.2	even	3		133.2.h.a.121.7	yes	24
7.3	odd	6		931.2.e.e.197.6		24
7.4	even	3		931.2.e.f.197.6		24
7.5	odd	6		931.2.h.h.520.7		24
7.6	odd	2		931.2.g.h.900.6		24
19.11	even	3		133.2.h.a.11.7	yes	24
133.11	even	3		931.2.e.f.638.6		24
133.30	even	3	inner	133.2.g.a.30.6	✓	24
133.68	odd	6		931.2.g.h.30.6		24
133.87	odd	6		931.2.e.e.638.6		24
133.125	odd	6		931.2.h.h.410.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.g.a.30.6	✓	24	133.30	even	3	inner
133.2.g.a.102.6	yes	24	1.1	even	1	trivial
133.2.h.a.11.7	yes	24	19.11	even	3
133.2.h.a.121.7	yes	24	7.2	even	3
931.2.e.e.197.6		24	7.3	odd	6
931.2.e.e.638.6		24	133.87	odd	6
931.2.e.f.197.6		24	7.4	even	3
931.2.e.f.638.6		24	133.11	even	3
931.2.g.h.30.6		24	133.68	odd	6
931.2.g.h.900.6		24	7.6	odd	2
931.2.h.h.410.7		24	133.125	odd	6
931.2.h.h.520.7		24	7.5	odd	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:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0371811 + 0.0643995i) q^{2} +1.39660 q^{3} +(0.997235 + 1.72726i) q^{4} +(1.23136 - 2.13278i) q^{5} +(-0.0519269 + 0.0899401i) q^{6} +(-2.54166 + 0.734810i) q^{7} -0.297037 q^{8} -1.04952 q^{9} +O(q^{10})\)	\(q+(-0.0371811 + 0.0643995i) q^{2} +1.39660 q^{3} +(0.997235 + 1.72726i) q^{4} +(1.23136 - 2.13278i) q^{5} +(-0.0519269 + 0.0899401i) q^{6} +(-2.54166 + 0.734810i) q^{7} -0.297037 q^{8} -1.04952 q^{9} +(0.0915665 + 0.158598i) q^{10} +(0.231887 - 0.401640i) q^{11} +(1.39273 + 2.41229i) q^{12} +(0.0203793 - 0.0352981i) q^{13} +(0.0471804 - 0.191003i) q^{14} +(1.71971 - 2.97863i) q^{15} +(-1.98343 + 3.43539i) q^{16} +3.00534 q^{17} +(0.0390222 - 0.0675885i) q^{18} +(-0.864338 - 4.27234i) q^{19} +4.91182 q^{20} +(-3.54968 + 1.02623i) q^{21} +(0.0172436 + 0.0298668i) q^{22} -4.22537 q^{23} -0.414841 q^{24} +(-0.532495 - 0.922308i) q^{25} +(0.00151545 + 0.00262484i) q^{26} -5.65554 q^{27} +(-3.80385 - 3.65734i) q^{28} +(1.44097 - 2.49583i) q^{29} +(0.127881 + 0.221497i) q^{30} +(-2.97334 + 5.14997i) q^{31} +(-0.444529 - 0.769947i) q^{32} +(0.323853 - 0.560929i) q^{33} +(-0.111742 + 0.193542i) q^{34} +(-1.56252 + 6.32562i) q^{35} +(-1.04662 - 1.81279i) q^{36} +(-0.655675 - 1.13566i) q^{37} +(0.307274 + 0.103187i) q^{38} +(0.0284617 - 0.0492971i) q^{39} +(-0.365760 + 0.633515i) q^{40} +(3.80562 + 6.59153i) q^{41} +(0.0658919 - 0.266754i) q^{42} +(-5.56677 - 9.64193i) q^{43} +0.924984 q^{44} +(-1.29234 + 2.23839i) q^{45} +(0.157104 - 0.272112i) q^{46} +2.93898 q^{47} +(-2.77005 + 4.79786i) q^{48} +(5.92011 - 3.73528i) q^{49} +0.0791948 q^{50} +4.19724 q^{51} +0.0812920 q^{52} +(-2.65488 - 4.59839i) q^{53} +(0.210279 - 0.364214i) q^{54} +(-0.571073 - 0.989128i) q^{55} +(0.754969 - 0.218266i) q^{56} +(-1.20713 - 5.96674i) q^{57} +(0.107154 + 0.185595i) q^{58} +12.3229 q^{59} +6.85983 q^{60} -1.86263 q^{61} +(-0.221104 - 0.382963i) q^{62} +(2.66752 - 0.771197i) q^{63} -7.86759 q^{64} +(-0.0501886 - 0.0869292i) q^{65} +(0.0240824 + 0.0417119i) q^{66} +(5.86906 + 10.1655i) q^{67} +(2.99703 + 5.19100i) q^{68} -5.90114 q^{69} +(-0.349271 - 0.335819i) q^{70} +(7.89435 + 13.6734i) q^{71} +0.311746 q^{72} +8.91233 q^{73} +0.0975147 q^{74} +(-0.743680 - 1.28809i) q^{75} +(6.51751 - 5.75347i) q^{76} +(-0.294250 + 1.19123i) q^{77} +(0.00211647 + 0.00366584i) q^{78} +(-2.15812 + 3.73798i) q^{79} +(4.88462 + 8.46041i) q^{80} -4.74995 q^{81} -0.565989 q^{82} -5.39339 q^{83} +(-5.31244 - 5.10783i) q^{84} +(3.70065 - 6.40972i) q^{85} +0.827914 q^{86} +(2.01245 - 3.48567i) q^{87} +(-0.0688791 + 0.119302i) q^{88} +7.22996 q^{89} +(-0.0961008 - 0.166452i) q^{90} +(-0.0258601 + 0.104691i) q^{91} +(-4.21369 - 7.29832i) q^{92} +(-4.15255 + 7.19243i) q^{93} +(-0.109274 + 0.189268i) q^{94} +(-10.1763 - 3.41735i) q^{95} +(-0.620828 - 1.07530i) q^{96} +(0.356016 + 0.616637i) q^{97} +(0.0204341 + 0.520134i) q^{98} +(-0.243370 + 0.421529i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9}+O(q^{10}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9} + 16 q^{10} - q^{11} - 2 q^{12} + 6 q^{13} - q^{14} - 9 q^{15} - 9 q^{16} - 16 q^{17} + 5 q^{18} - 4 q^{19} - 21 q^{21} - 2 q^{22} + 18 q^{23} + 16 q^{24} - 14 q^{25} + q^{26} - 18 q^{27} - 14 q^{28} - 2 q^{29} - 9 q^{30} + 11 q^{31} + 24 q^{32} + 3 q^{33} + 6 q^{34} + 38 q^{35} - 7 q^{36} - 14 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 20 q^{41} - 36 q^{42} + 2 q^{43} - 4 q^{44} - 12 q^{45} - 6 q^{46} + 39 q^{48} + 18 q^{49} + 22 q^{50} - 42 q^{51} - 22 q^{52} + 7 q^{53} - 43 q^{54} + 9 q^{55} - 21 q^{56} + 21 q^{57} + 35 q^{58} - 84 q^{59} + 12 q^{60} - 12 q^{61} - 19 q^{62} + 9 q^{63} - 2 q^{64} - 27 q^{65} + 3 q^{66} - 14 q^{67} + 51 q^{68} - 34 q^{69} + 33 q^{70} + q^{71} - 36 q^{72} + 42 q^{73} + 50 q^{74} + 31 q^{75} - 70 q^{76} - 20 q^{77} + 57 q^{78} - 5 q^{79} + 13 q^{80} - 56 q^{81} + 24 q^{82} + 10 q^{83} + 129 q^{84} - 27 q^{85} - 36 q^{86} + 53 q^{87} - 36 q^{88} + 2 q^{89} + 27 q^{90} - 9 q^{91} - 72 q^{92} + 34 q^{93} + 12 q^{94} - 11 q^{95} - 94 q^{96} + 31 q^{97} - 26 q^{98} + 43 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9 + 16 * q^10 - q^11 - 2 * q^12 + 6 * q^13 - q^14 - 9 * q^15 - 9 * q^16 - 16 * q^17 + 5 * q^18 - 4 * q^19 - 21 * q^21 - 2 * q^22 + 18 * q^23 + 16 * q^24 - 14 * q^25 + q^26 - 18 * q^27 - 14 * q^28 - 2 * q^29 - 9 * q^30 + 11 * q^31 + 24 * q^32 + 3 * q^33 + 6 * q^34 + 38 * q^35 - 7 * q^36 - 14 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 20 * q^41 - 36 * q^42 + 2 * q^43 - 4 * q^44 - 12 * q^45 - 6 * q^46 + 39 * q^48 + 18 * q^49 + 22 * q^50 - 42 * q^51 - 22 * q^52 + 7 * q^53 - 43 * q^54 + 9 * q^55 - 21 * q^56 + 21 * q^57 + 35 * q^58 - 84 * q^59 + 12 * q^60 - 12 * q^61 - 19 * q^62 + 9 * q^63 - 2 * q^64 - 27 * q^65 + 3 * q^66 - 14 * q^67 + 51 * q^68 - 34 * q^69 + 33 * q^70 + q^71 - 36 * q^72 + 42 * q^73 + 50 * q^74 + 31 * q^75 - 70 * q^76 - 20 * q^77 + 57 * q^78 - 5 * q^79 + 13 * q^80 - 56 * q^81 + 24 * q^82 + 10 * q^83 + 129 * q^84 - 27 * q^85 - 36 * q^86 + 53 * q^87 - 36 * q^88 + 2 * q^89 + 27 * q^90 - 9 * q^91 - 72 * q^92 + 34 * q^93 + 12 * q^94 - 11 * q^95 - 94 * q^96 + 31 * q^97 - 26 * q^98 + 43 * q^99

Introduction

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