LMFDB - Embedded newform 187.2.g.d.103.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(69,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("187.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			103.2
Root			$0.535233 + 1.64728i$ of defining polynomial
Character	$\chi$	$=$	187.103
Dual form			187.2.g.d.69.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.363271i) q^{2} +(0.726216 - 2.23506i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(1.90126 - 1.38135i) q^{5} +(-1.17504 + 0.853718i) q^{6} +(0.273784 + 0.842620i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-2.04107 - 1.48292i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.363271i) q^{2} +(0.726216 - 2.23506i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(1.90126 - 1.38135i) q^{5} +(-1.17504 + 0.853718i) q^{6} +(0.273784 + 0.842620i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-2.04107 - 1.48292i) q^{9} -1.45243 q^{10} +(-1.62747 + 2.88987i) q^{11} -3.80252 q^{12} +(1.80902 + 1.31433i) q^{13} +(0.169208 - 0.520768i) q^{14} +(-1.70667 - 5.25259i) q^{15} +(-1.50000 + 1.08981i) q^{16} +(0.809017 - 0.587785i) q^{17} +(0.481831 + 1.48292i) q^{18} +(0.570466 - 1.75571i) q^{19} +(-3.07630 - 2.23506i) q^{20} +2.08214 q^{21} +(1.86354 - 0.853718i) q^{22} +0.547568 q^{23} +(4.25134 + 3.08878i) q^{24} +(0.161585 - 0.497306i) q^{25} +(-0.427051 - 1.31433i) q^{26} +(0.907093 - 0.659042i) q^{27} +(1.15977 - 0.842620i) q^{28} +(0.283225 + 0.871676i) q^{29} +(-1.05478 + 3.24628i) q^{30} +(0.114017 + 0.0828381i) q^{31} +5.61803 q^{32} +(5.27714 + 5.73618i) q^{33} -0.618034 q^{34} +(1.68448 + 1.22385i) q^{35} +(-1.26145 + 3.88234i) q^{36} +(-3.19835 - 9.84352i) q^{37} +(-0.923034 + 0.670623i) q^{38} +(4.25134 - 3.08878i) q^{39} +(1.62387 + 4.99775i) q^{40} +(-2.21859 + 6.82813i) q^{41} +(-1.04107 - 0.756380i) q^{42} -5.74597 q^{43} +(5.26078 + 1.05949i) q^{44} -5.92903 q^{45} +(-0.273784 - 0.198916i) q^{46} +(-3.73359 + 11.4908i) q^{47} +(1.34648 + 4.14404i) q^{48} +(5.02807 - 3.65311i) q^{49} +(-0.261449 + 0.189954i) q^{50} +(-0.726216 - 2.23506i) q^{51} +(1.11803 - 3.44095i) q^{52} +(6.15260 + 4.47013i) q^{53} -0.692958 q^{54} +(0.897653 + 7.74249i) q^{55} -1.98112 q^{56} +(-3.50985 - 2.55006i) q^{57} +(0.175042 - 0.538725i) q^{58} +(-0.927051 - 2.85317i) q^{59} +(-7.22957 + 5.25259i) q^{60} +(9.26882 - 6.73419i) q^{61} +(-0.0269157 - 0.0828381i) q^{62} +(0.690729 - 2.12584i) q^{63} +(0.190983 + 0.138757i) q^{64} +5.25495 q^{65} +(-0.554780 - 4.78512i) q^{66} -0.0587969 q^{67} +(-1.30902 - 0.951057i) q^{68} +(0.397653 - 1.22385i) q^{69} +(-0.397653 - 1.22385i) q^{70} +(-2.82723 + 2.05411i) q^{71} +(4.56397 - 3.31592i) q^{72} +(1.41472 + 4.35405i) q^{73} +(-1.97669 + 6.08363i) q^{74} +(-0.994165 - 0.722303i) q^{75} -2.98700 q^{76} +(-2.88064 - 0.580144i) q^{77} -3.24774 q^{78} +(-10.1832 - 7.39849i) q^{79} +(-1.34648 + 4.14404i) q^{80} +(-3.15311 - 9.70427i) q^{81} +(3.58976 - 2.60811i) q^{82} +(-9.27064 + 6.73551i) q^{83} +(-1.04107 - 3.20408i) q^{84} +(0.726216 - 2.23506i) q^{85} +(2.87298 + 2.08734i) q^{86} +2.15393 q^{87} +(-5.02111 - 5.45788i) q^{88} +13.1463 q^{89} +(2.96451 + 2.15384i) q^{90} +(-0.612199 + 1.88416i) q^{91} +(-0.273784 - 0.842620i) q^{92} +(0.267949 - 0.194676i) q^{93} +(6.04107 - 4.38909i) q^{94} +(-1.34064 - 4.12608i) q^{95} +(4.07991 - 12.5567i) q^{96} +(2.05158 + 1.49056i) q^{97} -3.84110 q^{98} +(7.60723 - 3.48499i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 6 q^{3} - 4 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{7} - 10 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 6 * q^3 - 4 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7 - 10 * q^8 + 2 * q^9	\( 8 q - 4 q^{2} + 6 q^{3} - 4 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{7} - 10 q^{8} + 2 q^{9} - 12 q^{10} - 2 q^{11} - 8 q^{12} + 10 q^{13} + 4 q^{14} + 14 q^{15} - 12 q^{16} + 2 q^{17} + 14 q^{18} - 4 q^{19} - 2 q^{20} - 20 q^{21} - 14 q^{22} + 4 q^{23} - 4 q^{25} + 10 q^{26} - 18 q^{27} + 14 q^{28} - 32 q^{30} - 4 q^{31} + 36 q^{32} + 6 q^{33} + 4 q^{34} - 6 q^{36} + 10 q^{37} + 2 q^{38} - 10 q^{40} - 10 q^{41} + 10 q^{42} + 16 q^{43} + 6 q^{44} + 40 q^{45} - 2 q^{46} + 10 q^{47} - 24 q^{48} - 14 q^{49} + 2 q^{50} - 6 q^{51} + 4 q^{53} + 64 q^{54} - 16 q^{55} - 20 q^{56} - 10 q^{57} - 10 q^{58} + 6 q^{59} - 22 q^{60} + 30 q^{61} + 12 q^{62} - 38 q^{63} + 6 q^{64} + 20 q^{65} - 28 q^{66} - 20 q^{67} - 6 q^{68} - 20 q^{69} + 20 q^{70} + 18 q^{71} + 10 q^{72} - 6 q^{73} - 40 q^{74} - 22 q^{75} + 12 q^{76} + 32 q^{77} + 20 q^{78} - 4 q^{79} + 24 q^{80} - 76 q^{81} - 20 q^{83} + 10 q^{84} + 6 q^{85} - 8 q^{86} + 36 q^{87} - 10 q^{88} - 48 q^{89} - 20 q^{90} - 10 q^{91} - 2 q^{92} + 16 q^{93} + 30 q^{94} + 10 q^{95} + 22 q^{96} + 12 q^{97} + 32 q^{98} + 22 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 6 * q^3 - 4 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7 - 10 * q^8 + 2 * q^9 - 12 * q^10 - 2 * q^11 - 8 * q^12 + 10 * q^13 + 4 * q^14 + 14 * q^15 - 12 * q^16 + 2 * q^17 + 14 * q^18 - 4 * q^19 - 2 * q^20 - 20 * q^21 - 14 * q^22 + 4 * q^23 - 4 * q^25 + 10 * q^26 - 18 * q^27 + 14 * q^28 - 32 * q^30 - 4 * q^31 + 36 * q^32 + 6 * q^33 + 4 * q^34 - 6 * q^36 + 10 * q^37 + 2 * q^38 - 10 * q^40 - 10 * q^41 + 10 * q^42 + 16 * q^43 + 6 * q^44 + 40 * q^45 - 2 * q^46 + 10 * q^47 - 24 * q^48 - 14 * q^49 + 2 * q^50 - 6 * q^51 + 4 * q^53 + 64 * q^54 - 16 * q^55 - 20 * q^56 - 10 * q^57 - 10 * q^58 + 6 * q^59 - 22 * q^60 + 30 * q^61 + 12 * q^62 - 38 * q^63 + 6 * q^64 + 20 * q^65 - 28 * q^66 - 20 * q^67 - 6 * q^68 - 20 * q^69 + 20 * q^70 + 18 * q^71 + 10 * q^72 - 6 * q^73 - 40 * q^74 - 22 * q^75 + 12 * q^76 + 32 * q^77 + 20 * q^78 - 4 * q^79 + 24 * q^80 - 76 * q^81 - 20 * q^83 + 10 * q^84 + 6 * q^85 - 8 * q^86 + 36 * q^87 - 10 * q^88 - 48 * q^89 - 20 * q^90 - 10 * q^91 - 2 * q^92 + 16 * q^93 + 30 * q^94 + 10 * q^95 + 22 * q^96 + 12 * q^97 + 32 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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	−	0.363271i	−0.353553	−	0.256872i	0.396805	−	0.917903i	$-0.370119\pi$
$2$	−0.500000	−	0.363271i	−0.353553	−	0.256872i	−0.750358	+	0.661031i	$0.770119\pi$
$3$	0.726216	−	2.23506i	0.419281	−	1.29041i	−0.489084	−	0.872237i	$-0.662669\pi$
$3$	0.726216	−	2.23506i	0.419281	−	1.29041i	0.908365	−	0.418178i	$-0.137331\pi$
$4$	−0.500000	−	1.53884i	−0.250000	−	0.769421i
$5$	1.90126	−	1.38135i	0.850269	−	0.617756i	−0.0749514	−	0.997187i	$-0.523880\pi$
$5$	1.90126	−	1.38135i	0.850269	−	0.617756i	0.925220	+	0.379431i	$0.123880\pi$
$6$	−1.17504	+	0.853718i	−0.479709	+	0.348529i
$7$	0.273784	+	0.842620i	0.103481	+	0.318480i	0.989371	−	0.145414i	$-0.0464515\pi$
$7$	0.273784	+	0.842620i	0.103481	+	0.318480i	−0.885890	+	0.463895i	$0.846452\pi$
$8$	−0.690983	+	2.12663i	−0.244299	+	0.751876i
$9$	−2.04107	−	1.48292i	−0.680356	−	0.494308i
$10$	−1.45243			−0.459299
$11$	−1.62747	+	2.88987i	−0.490702	+	0.871327i
$11$	−1.62747	+	2.88987i	−0.490702	+	0.871327i
$12$	−3.80252			−1.09769
$13$	1.80902	+	1.31433i	0.501731	+	0.364529i	0.809678	−	0.586875i	$-0.199642\pi$
$13$	1.80902	+	1.31433i	0.501731	+	0.364529i	−0.307947	+	0.951404i	$0.599642\pi$
$14$	0.169208	−	0.520768i	0.0452227	−	0.139181i
$15$	−1.70667	−	5.25259i	−0.440660	−	1.35621i
$16$	−1.50000	+	1.08981i	−0.375000	+	0.272453i
$17$	0.809017	−	0.587785i	0.196215	−	0.142559i
$17$	0.809017	−	0.587785i	0.196215	−	0.142559i
$18$	0.481831	+	1.48292i	0.113569	+	0.349528i
$19$	0.570466	−	1.75571i	0.130874	−	0.402789i	−0.864052	−	0.503403i	$-0.832081\pi$
$19$	0.570466	−	1.75571i	0.130874	−	0.402789i	0.994925	+	0.100615i	$0.0320810\pi$
$20$	−3.07630	−	2.23506i	−0.687882	−	0.499775i
$21$	2.08214			0.454359
$22$	1.86354	−	0.853718i	0.397309	−	0.182013i
$23$	0.547568			0.114176			0.0570879	−	0.998369i	$-0.481818\pi$
$23$	0.547568			0.114176			0.0570879	+	0.998369i	$0.481818\pi$
$24$	4.25134	+	3.08878i	0.867802	+	0.630495i
$25$	0.161585	−	0.497306i	0.0323169	−	0.0994612i
$26$	−0.427051	−	1.31433i	−0.0837516	−	0.257761i
$27$	0.907093	−	0.659042i	0.174570	−	0.126833i
$28$	1.15977	−	0.842620i	0.219175	−	0.159240i
$29$	0.283225	+	0.871676i	0.0525935	+	0.161866i	0.973903	−	0.226963i	$-0.0728797\pi$
$29$	0.283225	+	0.871676i	0.0525935	+	0.161866i	−0.921310	+	0.388829i	$0.872880\pi$
$30$	−1.05478	+	3.24628i	−0.192576	+	0.592687i
$31$	0.114017	+	0.0828381i	0.0204780	+	0.0148782i	0.597977	−	0.801513i	$-0.295971\pi$
$31$	0.114017	+	0.0828381i	0.0204780	+	0.0148782i	−0.577499	+	0.816391i	$0.695971\pi$
$32$	5.61803			0.993137
$33$	5.27714	+	5.73618i	0.918631	+	0.998540i
$34$	−0.618034			−0.105992
$35$	1.68448	+	1.22385i	0.284730	+	0.206868i
$36$	−1.26145	+	3.88234i	−0.210242	+	0.647057i
$37$	−3.19835	−	9.84352i	−0.525806	−	1.61826i	−0.762717	−	0.646733i	$-0.776135\pi$
$37$	−3.19835	−	9.84352i	−0.525806	−	1.61826i	0.236911	−	0.971531i	$-0.423865\pi$
$38$	−0.923034	+	0.670623i	−0.149736	+	0.108789i
$39$	4.25134	−	3.08878i	0.680760	−	0.494601i
$40$	1.62387	+	4.99775i	0.256756	+	0.790214i
$41$	−2.21859	+	6.82813i	−0.346486	+	1.06637i	0.614297	+	0.789075i	$0.289440\pi$
$41$	−2.21859	+	6.82813i	−0.346486	+	1.06637i	−0.960783	+	0.277300i	$0.910560\pi$
$42$	−1.04107	−	0.756380i	−0.160640	−	0.116712i
$43$	−5.74597			−0.876252			−0.438126	−	0.898914i	$-0.644358\pi$
$43$	−5.74597			−0.876252			−0.438126	+	0.898914i	$0.644358\pi$
$44$	5.26078	+	1.05949i	0.793093	+	0.159725i
$45$	−5.92903			−0.883847
$46$	−0.273784	−	0.198916i	−0.0403672	−	0.0293285i
$47$	−3.73359	+	11.4908i	−0.544599	+	1.67610i	0.177341	+	0.984149i	$0.443250\pi$
$47$	−3.73359	+	11.4908i	−0.544599	+	1.67610i	−0.721941	+	0.691955i	$0.756750\pi$
$48$	1.34648	+	4.14404i	0.194347	+	0.598140i
$49$	5.02807	−	3.65311i	0.718295	−	0.521872i
$50$	−0.261449	+	0.189954i	−0.0369745	+	0.0268636i
$51$	−0.726216	−	2.23506i	−0.101691	−	0.312971i
$52$	1.11803	−	3.44095i	0.155043	−	0.477175i
$53$	6.15260	+	4.47013i	0.845125	+	0.614019i	0.923798	−	0.382881i	$-0.125068\pi$
$53$	6.15260	+	4.47013i	0.845125	+	0.614019i	−0.0786727	+	0.996901i	$0.525068\pi$
$54$	−0.692958			−0.0942996
$55$	0.897653	+	7.74249i	0.121039	+	1.04400i
$56$	−1.98112			−0.264738
$57$	−3.50985	−	2.55006i	−0.464891	−	0.337763i
$58$	0.175042	−	0.538725i	0.0229842	−	0.0707381i
$59$	−0.927051	−	2.85317i	−0.120692	−	0.371451i	0.872400	−	0.488793i	$-0.162563\pi$
$59$	−0.927051	−	2.85317i	−0.120692	−	0.371451i	−0.993092	+	0.117342i	$0.962563\pi$
$60$	−7.22957	+	5.25259i	−0.933333	+	0.678106i
$61$	9.26882	−	6.73419i	1.18675	−	0.862225i	0.193834	−	0.981034i	$-0.437908\pi$
$61$	9.26882	−	6.73419i	1.18675	−	0.862225i	0.992917	+	0.118810i	$0.0379078\pi$
$62$	−0.0269157	−	0.0828381i	−0.00341830	−	0.0105204i
$63$	0.690729	−	2.12584i	0.0870237	−	0.267831i
$64$	0.190983	+	0.138757i	0.0238729	+	0.0173447i
$65$	5.25495			0.651796
$66$	−0.554780	−	4.78512i	−0.0682887	−	0.589008i
$67$	−0.0587969			−0.00718319			−0.00359159	−	0.999994i	$-0.501143\pi$
$67$	−0.0587969			−0.00718319			−0.00359159	+	0.999994i	$0.501143\pi$
$68$	−1.30902	−	0.951057i	−0.158742	−	0.115333i
$69$	0.397653	−	1.22385i	0.0478717	−	0.147334i
$70$	−0.397653	−	1.22385i	−0.0475286	−	0.146278i
$71$	−2.82723	+	2.05411i	−0.335531	+	0.243777i	−0.742774	−	0.669542i	$-0.766490\pi$
$71$	−2.82723	+	2.05411i	−0.335531	+	0.243777i	0.407243	+	0.913320i	$0.366490\pi$
$72$	4.56397	−	3.31592i	0.537869	−	0.390784i
$73$	1.41472	+	4.35405i	0.165580	+	0.509603i	0.999079	−	0.0429187i	$-0.0136657\pi$
$73$	1.41472	+	4.35405i	0.165580	+	0.509603i	−0.833499	+	0.552522i	$0.813666\pi$
$74$	−1.97669	+	6.08363i	−0.229786	+	0.707207i
$75$	−0.994165	−	0.722303i	−0.114796	−	0.0834044i
$76$	−2.98700			−0.342632
$77$	−2.88064	−	0.580144i	−0.328279	−	0.0661136i
$78$	−3.24774			−0.367734
$79$	−10.1832	−	7.39849i	−1.14569	−	0.832396i	−0.157792	−	0.987472i	$-0.550437\pi$
$79$	−10.1832	−	7.39849i	−1.14569	−	0.832396i	−0.987902	+	0.155077i	$0.950437\pi$
$80$	−1.34648	+	4.14404i	−0.150541	+	0.463317i
$81$	−3.15311	−	9.70427i	−0.350346	−	1.07825i
$82$	3.58976	−	2.60811i	0.396423	−	0.288018i
$83$	−9.27064	+	6.73551i	−1.01758	+	0.739318i	−0.965786	−	0.259339i	$-0.916495\pi$
$83$	−9.27064	+	6.73551i	−1.01758	+	0.739318i	−0.0517982	+	0.998658i	$0.516495\pi$
$84$	−1.04107	−	3.20408i	−0.113590	−	0.349593i
$85$	0.726216	−	2.23506i	0.0787692	−	0.242427i
$86$	2.87298	+	2.08734i	0.309802	+	0.225084i
$87$	2.15393			0.230926
$88$	−5.02111	−	5.45788i	−0.535252	−	0.581812i
$89$	13.1463			1.39351			0.696753	−	0.717311i	$-0.254627\pi$
$89$	13.1463			1.39351			0.696753	+	0.717311i	$0.254627\pi$
$90$	2.96451	+	2.15384i	0.312487	+	0.227035i
$91$	−0.612199	+	1.88416i	−0.0641759	+	0.197513i
$92$	−0.273784	−	0.842620i	−0.0285439	−	0.0878492i
$93$	0.267949	−	0.194676i	0.0277850	−	0.0201870i
$94$	6.04107	−	4.38909i	0.623089	−	0.452700i
$95$	−1.34064	−	4.12608i	−0.137547	−	0.423327i
$96$	4.07991	−	12.5567i	0.416404	−	1.28156i
$97$	2.05158	+	1.49056i	0.208307	+	0.151344i	0.687047	−	0.726613i	$-0.258906\pi$
$97$	2.05158	+	1.49056i	0.208307	+	0.151344i	−0.478740	+	0.877956i	$0.658906\pi$
$98$	−3.84110			−0.388010
$99$	7.60723	−	3.48499i	0.764556	−	0.350255i
$100$	−0.846068			−0.0846068
$101$	−12.8346	−	9.32488i	−1.27709	−	0.927861i	−0.277630	−	0.960688i	$-0.589549\pi$
$101$	−12.8346	−	9.32488i	−1.27709	−	0.927861i	−0.999461	+	0.0328275i	$0.989549\pi$
$102$	−0.448826	+	1.38135i	−0.0444404	+	0.136774i
$103$	−3.20667	−	9.86911i	−0.315963	−	0.972433i	−0.975356	−	0.220635i	$-0.929187\pi$
$103$	−3.20667	−	9.86911i	−0.315963	−	0.972433i	0.659394	−	0.751798i	$-0.270813\pi$
$104$	−4.04508	+	2.93893i	−0.396653	+	0.288185i
$105$	3.95868	−	2.87615i	0.386327	−	0.280683i
$106$	−1.45243	−	4.47013i	−0.141073	−	0.434177i
$107$	−0.735657	+	2.26412i	−0.0711186	+	0.218881i	−0.980298	−	0.197524i	$-0.936710\pi$
$107$	−0.735657	+	2.26412i	−0.0711186	+	0.218881i	0.909179	+	0.416405i	$0.136710\pi$
$108$	−1.46771	−	1.06635i	−0.141230	−	0.102610i
$109$	9.54848			0.914579			0.457289	−	0.889318i	$-0.348820\pi$
$109$	9.54848			0.914579			0.457289	+	0.889318i	$0.348820\pi$
$110$	2.36380	−	4.19733i	0.225379	−	0.400200i
$111$	−24.3236			−2.30869
$112$	−1.32897	−	0.965557i	−0.125576	−	0.0912365i
$113$	−3.13372	+	9.64460i	−0.294796	+	0.907288i	0.688494	+	0.725242i	$0.258272\pi$
$113$	−3.13372	+	9.64460i	−0.294796	+	0.907288i	−0.983290	+	0.182046i	$0.941728\pi$
$114$	0.828564	+	2.55006i	0.0776021	+	0.238835i
$115$	1.04107	−	0.756380i	0.0970801	−	0.0705328i
$116$	1.19976	−	0.871676i	0.111395	−	0.0809330i
$117$	−1.74328	−	5.36526i	−0.161166	−	0.496019i
$118$	−0.572949	+	1.76336i	−0.0527442	+	0.162330i
$119$	0.716775	+	0.520768i	0.0657067	+	0.0477387i
$120$	12.3496			1.12736
$121$	−5.70265	−	9.40637i	−0.518423	−	0.855124i
$122$	−7.08075			−0.641061
$123$	13.6501	+	9.91739i	1.23079	+	0.894221i
$124$	0.0704663	−	0.216873i	0.00632806	−	0.0194758i
$125$	3.25134	+	10.0066i	0.290809	+	0.895018i
$126$	−1.11762	+	0.812001i	−0.0995658	+	0.0723388i
$127$	−17.3692	+	12.6194i	−1.54126	+	1.11979i	−0.591728	+	0.806138i	$0.701554\pi$
$127$	−17.3692	+	12.6194i	−1.54126	+	1.11979i	−0.949536	+	0.313657i	$0.898446\pi$
$128$	−3.51722	−	10.8249i	−0.310881	−	0.956794i
$129$	−4.17281	+	12.8426i	−0.367396	+	1.13073i
$130$	−2.62747	−	1.90897i	−0.230445	−	0.167428i
$131$	16.2935			1.42357			0.711786	−	0.702396i	$-0.247886\pi$
$131$	16.2935			1.42357			0.711786	+	0.702396i	$0.247886\pi$
$132$	6.18850	−	10.9888i	0.538640	−	0.956449i
$133$	1.63558			0.141823
$134$	0.0293985	+	0.0213592i	0.00253964	+	0.00184516i
$135$	0.814254	−	2.50602i	0.0700799	−	0.215684i
$136$	0.690983	+	2.12663i	0.0592513	+	0.182357i
$137$	−10.2107	+	7.41850i	−0.872358	+	0.633805i	−0.931219	−	0.364461i	$-0.881253\pi$
$137$	−10.2107	+	7.41850i	−0.872358	+	0.633805i	0.0588608	+	0.998266i	$0.481253\pi$
$138$	−0.643415	+	0.467469i	−0.0547711	+	0.0397936i
$139$	2.58305	+	7.94983i	0.219092	+	0.674295i	0.998838	+	0.0481993i	$0.0153483\pi$
$139$	2.58305	+	7.94983i	0.219092	+	0.674295i	−0.779746	+	0.626096i	$0.784652\pi$
$140$	1.04107	−	3.20408i	0.0879863	−	0.270794i
$141$	22.9713	+	16.6896i	1.93453	+	1.40552i
$142$	2.15981			0.181248
$143$	−6.74236	+	3.08878i	−0.563825	+	0.258297i
$144$	4.67771			0.389809
$145$	1.74257	+	1.26605i	0.144712	+	0.105140i
$146$	0.874343	−	2.69095i	0.0723611	−	0.222705i
$147$	−4.51346	−	13.8910i	−0.372264	−	1.14571i
$148$	−13.5484	+	9.84352i	−1.11367	+	0.809132i
$149$	1.06645	−	0.774821i	0.0873669	−	0.0634758i	−0.543244	−	0.839575i	$-0.682804\pi$
$149$	1.06645	−	0.774821i	0.0873669	−	0.0634758i	0.630611	+	0.776099i	$0.282804\pi$
$150$	0.234691	+	0.722303i	0.0191624	+	0.0589758i
$151$	−4.75648	+	14.6390i	−0.387077	+	1.19130i	0.547885	+	0.836554i	$0.315433\pi$
$151$	−4.75648	+	14.6390i	−0.387077	+	1.19130i	−0.934962	+	0.354747i	$0.884567\pi$
$152$	3.33957	+	2.42634i	0.270875	+	0.196802i
$153$	−2.52290			−0.203964
$154$	1.22957	+	1.33652i	0.0990814	+	0.107700i
$155$	0.331203			0.0266029
$156$	−6.87882	−	4.99775i	−0.550746	−	0.400141i
$157$	−5.77064	+	17.7602i	−0.460547	+	1.41742i	0.403951	+	0.914781i	$0.367637\pi$
$157$	−5.77064	+	17.7602i	−0.460547	+	1.41742i	−0.864498	+	0.502637i	$0.832363\pi$
$158$	2.40392	+	7.39849i	0.191245	+	0.588593i
$159$	14.4591	−	10.5052i	1.14668	−	0.833115i
$160$	10.6813	−	7.76044i	0.844434	−	0.613517i
$161$	0.149915	+	0.461392i	0.0118150	+	0.0363627i
$162$	−1.94873	+	5.99757i	−0.153107	+	0.471214i
$163$	2.30653	+	1.67580i	0.180662	+	0.131258i	0.674441	−	0.738329i	$-0.264385\pi$
$163$	2.30653	+	1.67580i	0.180662	+	0.131258i	−0.493779	+	0.869587i	$0.664385\pi$
$164$	11.6167			0.907112
$165$	17.9568	+	3.61641i	1.39794	+	0.281537i
$166$	7.08214			0.549680
$167$	2.69794	+	1.96017i	0.208773	+	0.151682i	0.687258	−	0.726413i	$-0.258814\pi$
$167$	2.69794	+	1.96017i	0.208773	+	0.151682i	−0.478485	+	0.878096i	$0.658814\pi$
$168$	−1.43872	+	4.42793i	−0.111000	+	0.341622i
$169$	−2.47214	−	7.60845i	−0.190164	−	0.585266i
$170$	−1.17504	+	0.853718i	−0.0901216	+	0.0654772i
$171$	−3.76795	+	2.73758i	−0.288142	+	0.209348i
$172$	2.87298	+	8.84213i	0.219063	+	0.674206i
$173$	−6.36536	+	19.5906i	−0.483949	+	1.48944i	0.349547	+	0.936919i	$0.386335\pi$
$173$	−6.36536	+	19.5906i	−0.483949	+	1.48944i	−0.833497	+	0.552524i	$0.813665\pi$
$174$	−1.07697	−	0.782462i	−0.0816446	−	0.0593183i
$175$	0.463279			0.0350206
$176$	−0.708204	−	6.10844i	−0.0533829	−	0.460441i
$177$	−7.05025			−0.529930
$178$	−6.57315	−	4.77568i	−0.492679	−	0.357952i
$179$	7.79129	−	23.9791i	0.582348	−	1.79228i	−0.0273200	−	0.999627i	$-0.508697\pi$
$179$	7.79129	−	23.9791i	0.582348	−	1.79228i	0.609668	−	0.792657i	$-0.291303\pi$
$180$	2.96451	+	9.12383i	0.220962	+	0.680050i
$181$	−12.8492	+	9.33550i	−0.955074	+	0.693902i	−0.952002	−	0.306093i	$-0.900978\pi$
$181$	−12.8492	+	9.33550i	−0.955074	+	0.693902i	−0.00307284	+	0.999995i	$0.500978\pi$
$182$	0.990559	−	0.719683i	0.0734251	−	0.0533465i
$183$	−8.32018	−	25.6069i	−0.615045	−	1.89291i
$184$	−0.378360	+	1.16447i	−0.0278931	+	0.0858460i
$185$	−19.6782	−	14.2970i	−1.44677	−	1.05114i
$186$	−0.204695			−0.0150090
$187$	0.381966	+	3.29456i	0.0279321	+	0.240922i
$188$	19.5493			1.42578
$189$	0.803669	+	0.583900i	0.0584583	+	0.0424725i
$190$	−0.828564	+	2.55006i	−0.0601103	+	0.185001i
$191$	−0.432016	−	1.32961i	−0.0312596	−	0.0962072i	0.934209	−	0.356725i	$-0.116107\pi$
$191$	−0.432016	−	1.32961i	−0.0312596	−	0.0962072i	−0.965469	+	0.260518i	$0.916107\pi$
$192$	0.448826	−	0.326091i	0.0323912	−	0.0235336i
$193$	18.4788	−	13.4257i	1.33014	−	0.966400i	0.330390	−	0.943844i	$-0.392820\pi$
$193$	18.4788	−	13.4257i	1.33014	−	0.966400i	0.999746	−	0.0225560i	$-0.00718041\pi$
$194$	−0.484313	−	1.49056i	−0.0347717	−	0.107016i
$195$	3.81623	−	11.7451i	0.273286	−	0.841087i
$196$	−8.13558	−	5.91085i	−0.581113	−	0.422203i
$197$	−0.858245			−0.0611474			−0.0305737	−	0.999533i	$-0.509733\pi$
$197$	−0.858245			−0.0611474			−0.0305737	+	0.999533i	$0.509733\pi$
$198$	−5.06962	−	1.02099i	−0.360282	−	0.0725588i
$199$	−0.143651			−0.0101832			−0.00509159	−	0.999987i	$-0.501621\pi$
$199$	−0.143651			−0.0101832			−0.00509159	+	0.999987i	$0.501621\pi$
$200$	0.945932	+	0.687260i	0.0668875	+	0.0485966i
$201$	−0.0426993	+	0.131415i	−0.00301178	+	0.00926929i
$202$	3.02984	+	9.32488i	0.213179	+	0.656097i
$203$	−0.656949	+	0.477301i	−0.0461088	+	0.0335000i
$204$	−3.07630	+	2.23506i	−0.215384	+	0.156486i
$205$	5.21388	+	16.0467i	0.364153	+	1.12075i
$206$	−1.98183	+	6.09945i	−0.138081	+	0.424969i
$207$	−1.11762	−	0.812001i	−0.0776802	−	0.0564379i
$208$	−4.14590			−0.287466
$209$	4.14536	+	4.50595i	0.286741	+	0.311683i
$210$	−3.02416			−0.208687
$211$	3.38424	+	2.45880i	0.232981	+	0.169270i	0.698150	−	0.715951i	$-0.254007\pi$
$211$	3.38424	+	2.45880i	0.232981	+	0.169270i	−0.465170	+	0.885222i	$0.654007\pi$
$212$	3.80252	−	11.7029i	0.261158	−	0.803762i
$213$	2.53787	+	7.81077i	0.173892	+	0.535185i
$214$	1.19032	−	0.864816i	0.0813684	−	0.0591176i
$215$	−10.9246	+	7.93716i	−0.745049	+	0.541310i
$216$	0.774750	+	2.38444i	0.0527151	+	0.162240i
$217$	−0.0385851	+	0.118753i	−0.00261932	+	0.00806145i
$218$	−4.77424	−	3.46869i	−0.323352	−	0.234929i
$219$	10.7590			0.727024
$220$	11.4656	−	5.25259i	0.773013	−	0.354129i
$221$	2.23607			0.150414
$222$	12.1618	+	8.83606i	0.816246	+	0.593037i
$223$	2.96008	−	9.11020i	0.198222	−	0.610064i	−0.801702	−	0.597724i	$-0.796072\pi$
$223$	2.96008	−	9.11020i	0.198222	−	0.610064i	0.999924	−	0.0123403i	$-0.00392814\pi$
$224$	1.53813	+	4.73387i	0.102770	+	0.316295i
$225$	−1.06727	+	0.775418i	−0.0711514	+	0.0516945i
$226$	5.07047	−	3.68391i	0.337282	−	0.245050i
$227$	0.992788	+	3.05549i	0.0658937	+	0.202800i	0.978582	−	0.205856i	$-0.0659978\pi$
$227$	0.992788	+	3.05549i	0.0658937	+	0.202800i	−0.912689	+	0.408656i	$0.865998\pi$
$228$	−2.16921	+	6.67613i	−0.143659	+	0.442138i
$229$	−0.541686	−	0.393558i	−0.0357956	−	0.0260070i	0.569744	−	0.821823i	$-0.307043\pi$
$229$	−0.541686	−	0.393558i	−0.0357956	−	0.0260070i	−0.605539	+	0.795815i	$0.707043\pi$
$230$	−0.795305			−0.0524409
$231$	−3.38862	+	6.01709i	−0.222955	+	0.395896i
$232$	−2.04943			−0.134552
$233$	−17.1063	−	12.4285i	−1.12067	−	0.814216i	−0.136361	−	0.990659i	$-0.543541\pi$
$233$	−17.1063	−	12.4285i	−1.12067	−	0.814216i	−0.984311	+	0.176443i	$0.943541\pi$
$234$	−1.07741	+	3.31592i	−0.0704323	+	0.216768i
$235$	8.77424	+	27.0043i	0.572368	+	1.76157i
$236$	−3.92705	+	2.85317i	−0.255629	+	0.185726i
$237$	−23.9313	+	17.3871i	−1.55450	+	1.12941i
$238$	−0.169208	−	0.520768i	−0.0109681	−	0.0337564i
$239$	2.53303	−	7.79588i	0.163848	−	0.504273i	−0.835101	−	0.550096i	$-0.814591\pi$
$239$	2.53303	−	7.79588i	0.163848	−	0.504273i	0.998950	+	0.0458230i	$0.0145910\pi$
$240$	8.28435	+	6.01893i	0.534752	+	0.388520i
$241$	−12.8106			−0.825200			−0.412600	−	0.910912i	$-0.635379\pi$
$241$	−12.8106			−0.825200			−0.412600	+	0.910912i	$0.635379\pi$
$242$	−0.565737	+	6.77479i	−0.0363669	+	0.435500i
$243$	−20.6158			−1.32251
$244$	−14.9973	−	10.8961i	−0.960101	−	0.697554i
$245$	4.51346	−	13.8910i	0.288354	−	0.887463i
$246$	−3.22236	−	9.91739i	−0.205450	−	0.632310i
$247$	3.33957	−	2.42634i	0.212492	−	0.154384i
$248$	−0.254949	+	0.185232i	−0.0161893	+	0.0117622i
$249$	8.32181	+	25.6119i	0.527373	+	1.62309i
$250$	2.00944	−	6.18442i	0.127088	−	0.391137i
$251$	−18.9473	−	13.7660i	−1.19594	−	0.868903i	−0.202063	−	0.979373i	$-0.564764\pi$
$251$	−18.9473	−	13.7660i	−1.19594	−	0.868903i	−0.993879	+	0.110470i	$0.964764\pi$
$252$	−3.61670			−0.227831
$253$	−0.891153	+	1.58240i	−0.0560263	+	0.0994845i
$254$	13.2689			0.832563
$255$	−4.46812	−	3.24628i	−0.279804	−	0.203290i
$256$	−2.02786	+	6.24112i	−0.126742	+	0.390070i
$257$	−1.82483	−	5.61625i	−0.113830	−	0.350332i	0.877871	−	0.478896i	$-0.158963\pi$
$257$	−1.82483	−	5.61625i	−0.113830	−	0.350332i	−0.991701	+	0.128565i	$0.958963\pi$
$258$	6.75175	−	4.90544i	0.420346	−	0.305399i
$259$	7.41869	−	5.38999i	0.460975	−	0.334918i
$260$	−2.62747	−	8.08654i	−0.162949	−	0.501506i
$261$	0.714547	−	2.19915i	0.0442293	−	0.136124i
$262$	−8.14677	−	5.91897i	−0.503309	−	0.365675i
$263$	−27.4381			−1.69191			−0.845953	−	0.533258i	$-0.820968\pi$
$263$	−27.4381			−1.69191			−0.845953	+	0.533258i	$0.820968\pi$
$264$	−15.8451	+	7.25890i	−0.975200	+	0.446754i
$265$	17.8725			1.09790
$266$	−0.817792	−	0.594161i	−0.0501421	−	0.0364303i
$267$	9.54706	−	29.3828i	0.584271	−	1.79820i
$268$	0.0293985	+	0.0904792i	0.00179580	+	0.00552690i
$269$	16.8375	−	12.2332i	1.02660	−	0.745869i	0.0589749	−	0.998259i	$-0.481217\pi$
$269$	16.8375	−	12.2332i	1.02660	−	0.745869i	0.967625	+	0.252391i	$0.0812168\pi$
$270$	−1.31749	+	0.957214i	−0.0801800	+	0.0582542i
$271$	3.24576	+	9.98943i	0.197166	+	0.606815i	0.999944	+	0.0105373i	$0.00335418\pi$
$271$	3.24576	+	9.98943i	0.197166	+	0.606815i	−0.802778	+	0.596277i	$0.796646\pi$
$272$	−0.572949	+	1.76336i	−0.0347401	+	0.106919i
$273$	3.76662	+	2.73661i	0.227966	+	0.165627i
$274$	7.80027			0.471232
$275$	1.17417	+	1.27631i	0.0708053	+	0.0769644i
$276$	−2.08214			−0.125330
$277$	14.3698	+	10.4403i	0.863400	+	0.627297i	0.928808	−	0.370562i	$-0.120835\pi$
$277$	14.3698	+	10.4403i	0.863400	+	0.627297i	−0.0654080	+	0.997859i	$0.520835\pi$
$278$	1.59642	−	4.91326i	0.0957467	−	0.294678i
$279$	−0.109874	−	0.338156i	−0.00657796	−	0.0202449i
$280$	−3.76662	+	2.73661i	−0.225099	+	0.163544i
$281$	7.65662	−	5.56286i	0.456756	−	0.331852i	−0.335502	−	0.942040i	$-0.608906\pi$
$281$	7.65662	−	5.56286i	0.456756	−	0.331852i	0.792257	+	0.610187i	$0.208906\pi$
$282$	−5.42278	−	16.6896i	−0.322922	−	0.993851i
$283$	9.50903	−	29.2658i	0.565253	−	1.73967i	−0.101945	−	0.994790i	$-0.532507\pi$
$283$	9.50903	−	29.2658i	0.565253	−	1.73967i	0.667198	−	0.744880i	$-0.267493\pi$
$284$	4.57456	+	3.32361i	0.271450	+	0.197220i
$285$	−10.1956			−0.603938
$286$	4.49325	+	0.904915i	0.265691	+	0.0535087i
$287$	−6.36093			−0.375474
$288$	−11.4668	−	8.33111i	−0.675687	−	0.490915i
$289$	0.309017	−	0.951057i	0.0181775	−	0.0559445i
$290$	−0.411364	−	1.26605i	−0.0241562	−	0.0743450i
$291$	4.82140	−	3.50295i	0.282635	−	0.205347i
$292$	5.99283	−	4.35405i	0.350704	−	0.254801i
$293$	−6.13998	−	18.8969i	−0.358702	−	1.10397i	−0.953832	−	0.300341i	$-0.902900\pi$
$293$	−6.13998	−	18.8969i	−0.358702	−	1.10397i	0.595130	−	0.803629i	$-0.297100\pi$
$294$	−2.78947	+	8.58511i	−0.162685	+	0.500694i
$295$	−5.70378	−	4.14404i	−0.332087	−	0.241275i
$296$	23.1435			1.34519
$297$	0.428271	+	3.69395i	0.0248508	+	0.214345i
$298$	−0.814695			−0.0471940
$299$	0.990559	+	0.719683i	0.0572855	+	0.0416204i
$300$	−0.614428	+	1.89101i	−0.0354740	+	0.109178i
$301$	−1.57315	−	4.84167i	−0.0906750	−	0.279069i
$302$	7.69615	−	5.59158i	0.442864	−	0.321759i
$303$	−30.1624	+	21.9143i	−1.73278	+	1.25894i
$304$	1.05770	+	3.25527i	0.0606634	+	0.186703i
$305$	8.32018	−	25.6069i	0.476412	−	1.46625i
$306$	1.26145	+	0.916497i	0.0721123	+	0.0523926i
$307$	−17.7219			−1.01144			−0.505720	−	0.862698i	$-0.668773\pi$
$307$	−17.7219			−1.01144			−0.505720	+	0.862698i	$0.668773\pi$
$308$	0.547568	+	4.72291i	0.0312006	+	0.269113i
$309$	−24.3868			−1.38732
$310$	−0.165602	−	0.120317i	−0.00940554	−	0.00683353i
$311$	−0.848267	+	2.61070i	−0.0481008	+	0.148039i	−0.972222	−	0.234060i	$-0.924799\pi$
$311$	−0.848267	+	2.61070i	−0.0481008	+	0.148039i	0.924121	+	0.382099i	$0.124799\pi$
$312$	3.63108	+	11.1753i	0.205569	+	0.632678i
$313$	24.6184	−	17.8863i	1.39152	−	1.01100i	0.395820	−	0.918328i	$-0.370461\pi$
$313$	24.6184	−	17.8863i	1.39152	−	1.01100i	0.995697	−	0.0926677i	$-0.0295394\pi$
$314$	9.33708	−	6.78379i	0.526922	−	0.382831i
$315$	−1.62327	−	4.99592i	−0.0914610	−	0.281488i
$316$	−6.29353	+	19.3695i	−0.354039	+	1.08962i
$317$	18.8362	+	13.6853i	1.05794	+	0.768642i	0.973707	−	0.227804i	$-0.0731546\pi$
$317$	18.8362	+	13.6853i	1.05794	+	0.768642i	0.0842375	+	0.996446i	$0.473155\pi$
$318$	−11.0458			−0.619418
$319$	−2.97997	−	0.600149i	−0.166846	−	0.0336019i
$320$	0.554780			0.0310131
$321$	4.52620	+	3.28848i	0.252628	+	0.183545i
$322$	0.0926527	−	0.285156i	0.00516333	−	0.0158911i
$323$	−0.570466	−	1.75571i	−0.0317416	−	0.0976906i
$324$	−13.3568	+	9.70427i	−0.742044	+	0.539126i
$325$	0.945932	−	0.687260i	0.0524709	−	0.0381223i
$326$	−0.544499	−	1.67580i	−0.0301570	−	0.0928137i
$327$	6.93426	−	21.3415i	0.383466	−	1.18019i
$328$	−12.9879	−	9.43624i	−0.717135	−	0.521029i
$329$	−10.7046			−0.590162
$330$	−7.66468	−	8.33141i	−0.421927	−	0.458629i
$331$	24.9901			1.37358			0.686789	−	0.726857i	$-0.259020\pi$
$331$	24.9901			1.37358			0.686789	+	0.726857i	$0.259020\pi$
$332$	15.0002	+	10.8983i	0.823243	+	0.598121i
$333$	−8.06912	+	24.8342i	−0.442185	+	1.36091i
$334$	−0.636897	−	1.96017i	−0.0348495	−	0.107256i
$335$	−0.111788	+	0.0812189i	−0.00610764	+	0.00443746i
$336$	−3.12320	+	2.26914i	−0.170385	+	0.123792i
$337$	2.31457	+	7.12351i	0.126083	+	0.388042i	0.994097	−	0.108497i	$-0.0346038\pi$
$337$	2.31457	+	7.12351i	0.126083	+	0.388042i	−0.868014	+	0.496539i	$0.834604\pi$
$338$	−1.52786	+	4.70228i	−0.0831048	+	0.255770i
$339$	19.2805	+	14.0081i	1.04717	+	0.760817i
$340$	−3.80252			−0.206220
$341$	−0.424950	+	0.194676i	−0.0230124	+	0.0105423i
$342$	2.87846			0.155649
$343$	9.47221	+	6.88196i	0.511451	+	0.371591i
$344$	3.97037	−	12.2195i	0.214068	−	0.658833i
$345$	−0.934517	−	2.87615i	−0.0503127	−	0.154847i
$346$	10.2994	−	7.48293i	0.553698	−	0.402285i
$347$	−5.83878	+	4.24212i	−0.313442	+	0.227729i	−0.733372	−	0.679827i	$-0.762055\pi$
$347$	−5.83878	+	4.24212i	−0.313442	+	0.227729i	0.419930	+	0.907557i	$0.362055\pi$
$348$	−1.07697	−	3.31456i	−0.0577314	−	0.177679i
$349$	2.60929	−	8.03056i	0.139672	−	0.429866i	−0.856615	−	0.515955i	$-0.827437\pi$
$349$	2.60929	−	8.03056i	0.139672	−	0.429866i	0.996287	+	0.0860893i	$0.0274370\pi$
$350$	−0.231640	−	0.168296i	−0.0123817	−	0.00899580i
$351$	2.50714			0.133821
$352$	−9.14321	+	16.2354i	−0.487335	+	0.865348i
$353$	2.83573			0.150931			0.0754653	−	0.997148i	$-0.475956\pi$
$353$	2.83573			0.150931			0.0754653	+	0.997148i	$0.475956\pi$
$354$	3.52513	+	2.56115i	0.187358	+	0.136124i
$355$	−2.53787	+	7.81077i	−0.134696	+	0.414553i
$356$	−6.57315	−	20.2301i	−0.348376	−	1.07219i
$357$	1.68448	−	1.22385i	0.0891523	−	0.0647729i
$358$	−12.6066	+	9.15921i	−0.666278	+	0.484079i
$359$	4.72614	+	14.5456i	0.249436	+	0.767685i	0.994875	+	0.101111i	$0.0322398\pi$
$359$	4.72614	+	14.5456i	0.249436	+	0.767685i	−0.745439	+	0.666574i	$0.767760\pi$
$360$	4.09686	−	12.6088i	0.215923	−	0.664543i
$361$	12.6142	+	9.16477i	0.663906	+	0.482356i
$362$	9.81592			0.515914
$363$	−25.1652	+	5.91473i	−1.32083	+	0.310443i
$364$	3.20552			0.168015
$365$	8.70419	+	6.32396i	0.455598	+	0.331011i
$366$	−5.14215	+	15.8259i	−0.268785	+	0.827234i
$367$	−7.61667	−	23.4417i	−0.397587	−	1.22365i	−0.926928	−	0.375238i	$-0.877561\pi$
$367$	−7.61667	−	23.4417i	−0.397587	−	1.22365i	0.529341	−	0.848409i	$-0.322439\pi$
$368$	−0.821352	+	0.596747i	−0.0428159	+	0.0311076i
$369$	14.6539	−	10.6467i	0.762851	−	0.554243i
$370$	4.64539	+	14.2970i	0.241502	+	0.743268i
$371$	−2.08214	+	6.40815i	−0.108099	+	0.332695i
$372$	−0.433551	−	0.314993i	−0.0224786	−	0.0163316i
$373$	−20.2953			−1.05085			−0.525425	−	0.850840i	$-0.676094\pi$
$373$	−20.2953			−1.05085			−0.525425	+	0.850840i	$0.676094\pi$
$374$	1.00583	−	1.78604i	0.0520105	−	0.0923537i
$375$	24.7266			1.27687
$376$	−21.8568	−	15.8799i	−1.12718	−	0.818943i
$377$	−0.633309	+	1.94913i	−0.0326171	+	0.100385i
$378$	−0.189721	−	0.583900i	−0.00975817	−	0.0300326i
$379$	10.2266	−	7.43008i	0.525307	−	0.381658i	−0.293293	−	0.956023i	$-0.594751\pi$
$379$	10.2266	−	7.43008i	0.525307	−	0.381658i	0.818599	+	0.574365i	$0.194751\pi$
$380$	−5.67906	+	4.12608i	−0.291330	+	0.211663i
$381$	15.5915	+	47.9856i	0.798776	+	2.45838i
$382$	−0.267001	+	0.821744i	−0.0136610	+	0.0420441i
$383$	−3.79167	−	2.75481i	−0.193745	−	0.140764i	0.486684	−	0.873578i	$-0.338206\pi$
$383$	−3.79167	−	2.75481i	−0.193745	−	0.140764i	−0.680429	+	0.732814i	$0.738206\pi$
$384$	−26.7486			−1.36501
$385$	−6.27821	+	2.87615i	−0.319967	+	0.146582i
$386$	−14.1166			−0.718515
$387$	11.7279	+	8.52082i	0.596163	+	0.433138i
$388$	1.26795	−	3.90235i	0.0643704	−	0.198112i
$389$	−0.451846	−	1.39064i	−0.0229095	−	0.0705082i	0.938948	−	0.344059i	$-0.111802\pi$
$389$	−0.451846	−	1.39064i	−0.0229095	−	0.0705082i	−0.961858	+	0.273551i	$0.911802\pi$
$390$	−6.17479	+	4.48625i	−0.312673	+	0.227170i
$391$	0.442992	−	0.321852i	0.0224030	−	0.0162768i
$392$	4.29448	+	13.2171i	0.216904	+	0.667562i
$393$	11.8326	−	36.4171i	0.596877	−	1.83700i
$394$	0.429123	+	0.311776i	0.0216189	+	0.0157070i
$395$	−29.5807			−1.48837
$396$	−9.16647	−	9.96383i	−0.460632	−	0.500701i
$397$	−11.6050			−0.582440			−0.291220	−	0.956656i	$-0.594061\pi$
$397$	−11.6050			−0.582440			−0.291220	+	0.956656i	$0.594061\pi$
$398$	0.0718257	+	0.0521845i	0.00360030	+	0.00261577i
$399$	1.18779	−	3.65564i	0.0594638	−	0.183011i
$400$	0.299594	+	0.922056i	0.0149797	+	0.0461028i
$401$	2.14234	−	1.55650i	0.106983	−	0.0777279i	−0.533007	−	0.846111i	$-0.678938\pi$
$401$	2.14234	−	1.55650i	0.106983	−	0.0777279i	0.639991	+	0.768383i	$0.278938\pi$
$402$	0.0690889	−	0.0501960i	0.00344584	−	0.00250355i
$403$	0.0973820	+	0.299711i	0.00485094	+	0.0149297i
$404$	−7.93222	+	24.4129i	−0.394643	+	1.21459i
$405$	−19.3998	−	14.0948i	−0.963985	−	0.700376i
$406$	0.501864			0.0249071
$407$	33.6517	+	6.77726i	1.66805	+	0.335936i
$408$	5.25495			0.260159
$409$	−15.9343	−	11.5769i	−0.787900	−	0.572443i	0.119440	−	0.992841i	$-0.461890\pi$
$409$	−15.9343	−	11.5769i	−0.787900	−	0.572443i	−0.907339	+	0.420399i	$0.861890\pi$
$410$	3.22236	−	9.91739i	0.159141	−	0.489785i
$411$	9.16565	+	28.2090i	0.452108	+	1.39145i
$412$	−13.5837	+	9.86911i	−0.669219	+	0.486216i
$413$	2.15033	−	1.56230i	0.105811	−	0.0768759i
$414$	0.263835	+	0.812001i	0.0129668	+	0.0399076i
$415$	−8.32181	+	25.6119i	−0.408502	+	1.25724i
$416$	10.1631	+	7.38394i	0.498288	+	0.362027i
$417$	19.6442			0.961982
$418$	−0.435797	−	3.75887i	−0.0213156	−	0.183852i
$419$	25.0359			1.22308			0.611542	−	0.791212i	$-0.290549\pi$
$419$	25.0359			1.22308			0.611542	+	0.791212i	$0.290549\pi$
$420$	−6.40528	−	4.65371i	−0.312545	−	0.227078i
$421$	−10.2641	+	31.5898i	−0.500243	+	1.53959i	0.308379	+	0.951263i	$0.400213\pi$
$421$	−10.2641	+	31.5898i	−0.500243	+	1.53959i	−0.808623	+	0.588327i	$0.799787\pi$
$422$	−0.798911	−	2.45880i	−0.0388904	−	0.119692i
$423$	24.6605	−	17.9169i	1.19903	−	0.871148i
$424$	−13.7576	+	9.99551i	−0.668130	+	0.485425i
$425$	−0.161585	−	0.497306i	−0.00783800	−	0.0241229i
$426$	1.56849	−	4.82732i	0.0759937	−	0.233884i
$427$	8.21202	+	5.96638i	0.397407	+	0.288733i
$428$	3.85195			0.186191
$429$	2.00721	+	17.3127i	0.0969091	+	0.835866i
$430$	8.34563			0.402462
$431$	24.9995	+	18.1632i	1.20419	+	0.874892i	0.994690	−	0.102918i	$-0.0328178\pi$
$431$	24.9995	+	18.1632i	1.20419	+	0.874892i	0.209496	+	0.977810i	$0.432818\pi$
$432$	−0.642407	+	1.97713i	−0.0309078	+	0.0951245i
$433$	7.07907	+	21.7871i	0.340198	+	1.04702i	0.964104	+	0.265523i	$0.0855447\pi$
$433$	7.07907	+	21.7871i	0.340198	+	1.04702i	−0.623906	+	0.781499i	$0.714455\pi$
$434$	0.0624319	−	0.0453595i	0.00299683	−	0.00217732i
$435$	4.09518	−	2.97532i	0.196349	−	0.142656i
$436$	−4.77424	−	14.6936i	−0.228645	−	0.703696i
$437$	0.312369	−	0.961373i	0.0149426	−	0.0459887i
$438$	−5.37948	−	3.90842i	−0.257042	−	0.186752i
$439$	−4.65523			−0.222182			−0.111091	−	0.993810i	$-0.535435\pi$
$439$	−4.65523			−0.222182			−0.111091	+	0.993810i	$0.535435\pi$
$440$	−17.0856	−	3.44095i	−0.814526	−	0.164041i
$441$	−15.6799			−0.746662
$442$	−1.11803	−	0.812299i	−0.0531795	−	0.0386371i
$443$	2.52881	−	7.78288i	0.120148	−	0.369776i	−0.872838	−	0.488009i	$-0.837723\pi$
$443$	2.52881	−	7.78288i	0.120148	−	0.369776i	0.992986	+	0.118234i	$0.0377231\pi$
$444$	12.1618	+	37.4301i	0.577173	+	1.77636i
$445$	24.9945	−	18.1596i	1.18485	−	0.860847i
$446$	−4.78952	+	3.47979i	−0.226790	+	0.164773i
$447$	−0.957301	−	2.94627i	−0.0452788	−	0.139354i
$448$	−0.0646316	+	0.198916i	−0.00305356	+	0.00939788i
$449$	−31.9394	−	23.2053i	−1.50731	−	1.09513i	−0.967352	−	0.253436i	$-0.918439\pi$
$449$	−31.9394	−	23.2053i	−1.50731	−	1.09513i	−0.539961	−	0.841690i	$-0.681561\pi$
$450$	0.815323			0.0384347
$451$	−16.1217	−	17.5240i	−0.759140	−	0.825175i
$452$	16.4084			0.771785
$453$	29.2648	+	21.2621i	1.37498	+	0.998980i
$454$	0.613577	−	1.88839i	0.0287966	−	0.0886268i
$455$	1.43872	+	4.42793i	0.0674482	+	0.207584i
$456$	7.84827	−	5.70210i	0.367529	−	0.267025i
$457$	21.9525	−	15.9494i	1.02689	−	0.746081i	0.0592083	−	0.998246i	$-0.481142\pi$
$457$	21.9525	−	15.9494i	1.02689	−	0.746081i	0.967684	+	0.252164i	$0.0811424\pi$
$458$	0.127875	+	0.393558i	0.00597520	+	0.0183898i
$459$	0.346479	−	1.06635i	0.0161722	−	0.0497730i
$460$	−1.68448	−	1.22385i	−0.0785394	−	0.0570622i
$461$	−20.4847			−0.954066			−0.477033	−	0.878885i	$-0.658288\pi$
$461$	−20.4847			−0.954066			−0.477033	+	0.878885i	$0.658288\pi$
$462$	3.88015	−	1.77756i	0.180521	−	0.0826994i
$463$	−7.88153			−0.366286			−0.183143	−	0.983086i	$-0.558627\pi$
$463$	−7.88153			−0.366286			−0.183143	+	0.983086i	$0.558627\pi$
$464$	−1.37480	−	0.998851i	−0.0638235	−	0.0463705i
$465$	0.240525	−	0.740261i	0.0111541	−	0.0343288i
$466$	4.03825	+	12.4285i	0.187068	+	0.575738i
$467$	−14.6337	+	10.6320i	−0.677168	+	0.491991i	−0.872417	−	0.488762i	$-0.837448\pi$
$467$	−14.6337	+	10.6320i	−0.677168	+	0.491991i	0.195249	+	0.980754i	$0.437448\pi$
$468$	−7.38465	+	5.36526i	−0.341356	+	0.248009i
$469$	−0.0160977	−	0.0495435i	−0.000743320	−	0.00228771i
$470$	5.42278	−	16.6896i	0.250134	−	0.769834i
$471$	35.5044	+	25.7955i	1.63596	+	1.18859i
$472$	6.70820			0.308770
$473$	9.35142	−	16.6051i	0.429979	−	0.763502i
$474$	18.2819			0.839714
$475$	−0.780949	−	0.567393i	−0.0358324	−	0.0260338i
$476$	0.442992	−	1.36339i	0.0203045	−	0.0624908i
$477$	−5.92903	−	18.2477i	−0.271471	−	0.835503i
$478$	−4.09853	+	2.97776i	−0.187463	+	0.136200i
$479$	0.339822	−	0.246895i	0.0155269	−	0.0112809i	−0.579995	−	0.814620i	$-0.696945\pi$
$479$	0.339822	−	0.246895i	0.0155269	−	0.0112809i	0.595522	+	0.803339i	$0.296945\pi$
$480$	−9.58813	−	29.5092i	−0.437636	−	1.34691i
$481$	7.15173	−	22.0108i	0.326091	−	1.00360i
$482$	6.40528	+	4.65371i	0.291752	+	0.211970i
$483$	1.14011			0.0518768
$484$	−11.6236	+	13.4787i	−0.528345	+	0.612667i
$485$	5.95958			0.270610
$486$	10.3079	+	7.48914i	0.467576	+	0.339714i
$487$	1.90351	−	5.85839i	0.0862560	−	0.265469i	−0.898620	−	0.438727i	$-0.855430\pi$
$487$	1.90351	−	5.85839i	0.0862560	−	0.265469i	0.984876	+	0.173258i	$0.0554295\pi$
$488$	7.91652	+	24.3645i	0.358364	+	1.10293i
$489$	5.42055	−	3.93826i	0.245126	−	0.178094i
$490$	−7.30293	+	5.30589i	−0.329913	+	0.239696i
$491$	−10.0791	−	31.0202i	−0.454862	−	1.39992i	−0.871297	−	0.490756i	$-0.836721\pi$
$491$	−10.0791	−	31.0202i	−0.454862	−	1.39992i	0.416435	−	0.909165i	$-0.363279\pi$
$492$	8.43624	−	25.9641i	0.380335	−	1.17055i
$493$	0.741491	+	0.538725i	0.0333951	+	0.0242630i
$494$	−2.55120			−0.114784
$495$	9.64934	−	17.1341i	0.433706	−	0.770120i
$496$	−0.261303			−0.0117329
$497$	−2.50488	−	1.81990i	−0.112359	−	0.0816338i
$498$	5.14316	−	15.8290i	0.230471	−	0.709315i
$499$	4.38333	+	13.4905i	0.196225	+	0.603917i	0.999960	+	0.00893049i	$0.00284270\pi$
$499$	4.38333	+	13.4905i	0.196225	+	0.603917i	−0.803736	+	0.594987i	$0.797157\pi$
$500$	13.7729	−	10.0066i	0.615943	−	0.447509i
$501$	6.34039	−	4.60656i	0.283268	−	0.205806i
$502$	4.47285	+	13.7660i	0.199633	+	0.614407i
$503$	7.71627	−	23.7482i	0.344051	−	1.05888i	−0.618038	−	0.786148i	$-0.712072\pi$
$503$	7.71627	−	23.7482i	0.344051	−	1.05888i	0.962090	−	0.272733i	$-0.0879276\pi$
$504$	4.04360	+	2.93785i	0.180116	+	0.130862i
$505$	−37.2828			−1.65906
$506$	1.02042	−	0.467469i	0.0453630	−	0.0207815i
$507$	−18.8007			−0.834967
$508$	28.1039	+	20.4187i	1.24691	+	0.905933i
$509$	−0.147873	+	0.455105i	−0.00655434	+	0.0201722i	−0.954280	−	0.298914i	$-0.903376\pi$
$509$	−0.147873	+	0.455105i	−0.00655434	+	0.0201722i	0.947726	+	0.319086i	$0.103376\pi$
$510$	1.05478	+	3.24628i	0.0467064	+	0.143748i
$511$	−3.28148	+	2.38414i	−0.145164	+	0.105468i
$512$	−15.1353	+	10.9964i	−0.668890	+	0.485977i
$513$	−0.639623	−	1.96856i	−0.0282401	−	0.0869140i
$514$	−1.12781	+	3.47103i	−0.0497454	+	0.153101i
$515$	−19.7294	−	14.3342i	−0.869380	−	0.631641i
$516$	21.8491			0.961855
$517$	−27.1305	−	29.4905i	−1.19320	−	1.29699i
$518$	−5.66737			−0.249010
$519$	39.1635	+	28.4540i	1.71909	+	1.24899i
$520$	−3.63108	+	11.1753i	−0.159233	+	0.490070i
$521$	−11.3703	−	34.9943i	−0.498143	−	1.53313i	−0.812001	−	0.583656i	$-0.801621\pi$
$521$	−11.3703	−	34.9943i	−0.498143	−	1.53313i	0.313858	−	0.949470i	$-0.398379\pi$
$522$	−1.15616	+	0.840000i	−0.0506038	+	0.0367658i
$523$	−10.2466	+	7.44458i	−0.448052	+	0.325529i	−0.788826	−	0.614616i	$-0.789311\pi$
$523$	−10.2466	+	7.44458i	−0.448052	+	0.325529i	0.340774	+	0.940145i	$0.389311\pi$
$524$	−8.14677	−	25.0732i	−0.355893	−	1.09533i
$525$	0.336441	−	1.03546i	0.0146835	−	0.0451911i
$526$	13.7191	+	9.96747i	0.598179	+	0.434603i
$527$	0.140933			0.00613912
$528$	−14.1671	−	2.85317i	−0.616542	−	0.124168i
$529$	−22.7002			−0.986964
$530$	−8.93624	−	6.49256i	−0.388165	−	0.282019i
$531$	−2.33886	+	7.19826i	−0.101498	+	0.312378i
$532$	−0.817792	−	2.51691i	−0.0354558	−	0.109122i
$533$	−12.9879	+	9.43624i	−0.562567	+	0.408729i
$534$	−15.4475	+	11.2232i	−0.668477	+	0.485677i
$535$	1.72886	+	5.32087i	0.0747450	+	0.230041i
$536$	0.0406277	−	0.125039i	0.00175485	−	0.00540087i
$537$	−47.9367	−	34.8280i	−2.06862	−	1.50294i
$538$	−12.8627			−0.554550
$539$	2.37393	+	20.4758i	0.102252	+	0.881954i
$540$	−4.26349			−0.183471
$541$	−31.6960	−	23.0285i	−1.36272	−	0.990073i	−0.998267	−	0.0588508i	$-0.981256\pi$
$541$	−31.6960	−	23.0285i	−1.36272	−	0.990073i	−0.364452	−	0.931222i	$-0.618744\pi$
$542$	2.00599	−	6.17381i	0.0861647	−	0.265188i
$543$	11.5341	+	35.4984i	0.494977	+	1.52338i
$544$	4.54508	−	3.30220i	0.194869	−	0.141581i
$545$	18.1541	−	13.1898i	0.777638	−	0.564987i
$546$	−0.889178	−	2.73661i	−0.0380533	−	0.117116i
$547$	−7.75314	+	23.8617i	−0.331500	+	1.02025i	0.636920	+	0.770930i	$0.280208\pi$
$547$	−7.75314	+	23.8617i	−0.331500	+	1.02025i	−0.968420	+	0.249323i	$0.919792\pi$
$548$	16.5212	+	12.0034i	0.705752	+	0.512759i
$549$	−28.9046			−1.23362
$550$	−0.123440	−	1.06470i	−0.00526348	−	0.0453989i
$551$	1.69198			0.0720809
$552$	2.32790	+	1.69132i	0.0990819	+	0.0719872i
$553$	3.44614	−	10.6061i	0.146545	−	0.451018i
$554$	−3.39226	−	10.4403i	−0.144123	−	0.443566i
$555$	−46.2454	+	33.5993i	−1.96301	+	1.42621i
$556$	10.9420	−	7.94983i	0.464044	−	0.337148i
$557$	−2.04675	−	6.29923i	−0.0867234	−	0.266907i	0.898285	−	0.439413i	$-0.144814\pi$
$557$	−2.04675	−	6.29923i	−0.0867234	−	0.266907i	−0.985008	+	0.172506i	$0.944814\pi$
$558$	−0.0679056	+	0.208992i	−0.00287467	+	0.00884734i
$559$	−10.3946	−	7.55208i	−0.439643	−	0.319419i
$560$	−3.86049			−0.163136
$561$	7.64093	+	1.53884i	0.322600	+	0.0649700i
$562$	−5.84914			−0.246731
$563$	12.9177	+	9.38529i	0.544418	+	0.395543i	0.825723	−	0.564076i	$-0.190767\pi$
$563$	12.9177	+	9.38529i	0.544418	+	0.395543i	−0.281305	+	0.959618i	$0.590767\pi$
$564$	14.1970	−	43.6939i	0.597802	−	1.83985i
$565$	7.36451	+	22.6656i	0.309827	+	0.953550i
$566$	−15.3859	+	11.1785i	−0.646719	+	0.469869i
$567$	7.31375	−	5.31375i	0.307148	−	0.223156i
$568$	−2.41475	−	7.43182i	−0.101320	−	0.311832i
$569$	4.24832	−	13.0750i	0.178099	−	0.548132i	−0.821662	−	0.569974i	$-0.806953\pi$
$569$	4.24832	−	13.0750i	0.178099	−	0.548132i	0.999761	+	0.0218421i	$0.00695311\pi$
$570$	5.09782	+	3.70378i	0.213524	+	0.155134i
$571$	36.7370			1.53740			0.768698	−	0.639612i	$-0.220905\pi$
$571$	36.7370			1.53740			0.768698	+	0.639612i	$0.220905\pi$
$572$	8.12433	+	8.83104i	0.339695	+	0.369244i
$573$	−3.28550			−0.137254
$574$	3.18047	+	2.31074i	0.132750	+	0.0964486i
$575$	0.0884785	−	0.272309i	0.00368981	−	0.0113561i
$576$	−0.184043	−	0.566426i	−0.00766846	−	0.0236011i
$577$	−9.54160	+	6.93238i	−0.397222	+	0.288599i	−0.768409	−	0.639960i	$-0.778951\pi$
$577$	−9.54160	+	6.93238i	−0.397222	+	0.288599i	0.371186	+	0.928558i	$0.378951\pi$
$578$	−0.500000	+	0.363271i	−0.0207973	+	0.0151101i
$579$	−16.5876	−	51.0513i	−0.689356	−	2.12162i
$580$	1.07697	−	3.31456i	0.0447186	−	0.137630i
$581$	−8.21363	−	5.96755i	−0.340759	−	0.247576i
$582$	−3.68322			−0.152674
$583$	−22.9313	+	10.5052i	−0.949716	+	0.435080i
$584$	−10.2370			−0.423609
$585$	−10.7257	−	7.79268i	−0.443453	−	0.322188i
$586$	−3.79472	+	11.6789i	−0.156758	+	0.482453i
$587$	8.82242	+	27.1526i	0.364140	+	1.12071i	0.950518	+	0.310671i	$0.100554\pi$
$587$	8.82242	+	27.1526i	0.364140	+	1.12071i	−0.586377	+	0.810038i	$0.699446\pi$
$588$	−19.1193	+	13.8910i	−0.788467	+	0.572855i
$589$	0.210483	−	0.152925i	0.00867279	−	0.00630115i
$590$	1.34648	+	4.14404i	0.0554337	+	0.170607i
$591$	−0.623271	+	1.91823i	−0.0256380	+	0.0789055i
$592$	15.5251	+	11.2797i	0.638079	+	0.463591i
$593$	−13.0714			−0.536780			−0.268390	−	0.963310i	$-0.586492\pi$
$593$	−13.0714			−0.536780			−0.268390	+	0.963310i	$0.586492\pi$
$594$	1.12777	−	2.00255i	0.0462730	−	0.0821658i
$595$	2.08214			0.0853592
$596$	−1.72555	−	1.25369i	−0.0706813	−	0.0513530i
$597$	−0.104322	+	0.321070i	−0.00426962	+	0.0131405i
$598$	−0.233839	−	0.719683i	−0.00956240	−	0.0294300i
$599$	−11.7435	+	8.53214i	−0.479826	+	0.348614i	−0.801258	−	0.598319i	$-0.795836\pi$
$599$	−11.7435	+	8.53214i	−0.479826	+	0.348614i	0.321432	+	0.946933i	$0.395836\pi$
$600$	2.22302	−	1.61512i	0.0907545	−	0.0659370i
$601$	−5.90572	−	18.1759i	−0.240899	−	0.741411i	−0.996284	−	0.0861299i	$-0.972550\pi$
$601$	−5.90572	−	18.1759i	−0.240899	−	0.741411i	0.755385	−	0.655282i	$-0.227450\pi$
$602$	−0.972262	+	2.99231i	−0.0396264	+	0.121958i
$603$	0.120009	+	0.0871913i	0.00488713	+	0.00355070i
$604$	24.9053			1.01338
$605$	−23.8357	−	10.0066i	−0.969057	−	0.406826i
$606$	23.0420			0.936018
$607$	−30.5363	−	22.1859i	−1.23943	−	0.900499i	−0.241870	−	0.970309i	$-0.577761\pi$
$607$	−30.5363	−	22.1859i	−1.23943	−	0.900499i	−0.997560	+	0.0698097i	$0.977761\pi$
$608$	3.20490	−	9.86366i	0.129976	−	0.400024i
$609$	0.589712	+	1.81495i	0.0238963	+	0.0735454i
$610$	−13.4623	+	9.78096i	−0.545074	+	0.396019i
$611$	−21.8568	+	15.8799i	−0.884231	+	0.642431i
$612$	1.26145	+	3.88234i	0.0509911	+	0.156934i
$613$	10.8411	−	33.3655i	0.437868	−	1.34762i	−0.452251	−	0.891891i	$-0.649379\pi$
$613$	10.8411	−	33.3655i	0.437868	−	1.34762i	0.890119	−	0.455728i	$-0.150621\pi$
$614$	8.86093	+	6.43784i	0.357598	+	0.259810i
$615$	39.6517			1.59891
$616$	3.22422	−	5.72517i	0.129908	−	0.230674i
$617$	0.667823			0.0268855			0.0134428	−	0.999910i	$-0.495721\pi$
$617$	0.667823			0.0268855			0.0134428	+	0.999910i	$0.495721\pi$
$618$	12.1934	+	8.85903i	0.490491	+	0.356363i
$619$	6.59728	−	20.3044i	0.265167	−	0.816101i	−0.726488	−	0.687180i	$-0.758849\pi$
$619$	6.59728	−	20.3044i	0.265167	−	0.816101i	0.991655	−	0.128921i	$-0.0411515\pi$
$620$	−0.165602	−	0.509670i	−0.00665072	−	0.0204688i
$621$	0.496695	−	0.360870i	0.0199317	−	0.0144812i
$622$	1.37253	−	0.997198i	0.0550333	−	0.0399840i
$623$	3.59925	+	11.0773i	0.144201	+	0.443804i
$624$	−3.01082	+	9.26635i	−0.120529	+	0.370951i
$625$	22.1194	+	16.0707i	0.884776	+	0.642827i
$626$	−18.8068			−0.751672
$627$	13.0815	−	5.99285i	0.522425	−	0.239331i
$628$	30.2154			1.20573
$629$	−8.37339	−	6.08363i	−0.333869	−	0.242570i
$630$	−1.00324	+	3.08765i	−0.0399699	+	0.123015i
$631$	−3.18492	−	9.80219i	−0.126790	−	0.390219i	0.867433	−	0.497554i	$-0.165768\pi$
$631$	−3.18492	−	9.80219i	−0.126790	−	0.390219i	−0.994223	+	0.107335i	$0.965768\pi$
$632$	22.7702	−	16.5435i	0.905751	−	0.658066i
$633$	7.95325	−	5.77838i	0.316113	−	0.229670i
$634$	−4.44662	−	13.6853i	−0.176598	−	0.543512i
$635$	−15.5915	+	47.9856i	−0.618729	+	1.90425i
$636$	−23.3954	−	16.9977i	−0.927687	−	0.674004i
$637$	13.8972			0.550629
$638$	1.27197	+	1.38261i	0.0503576	+	0.0547381i
$639$	8.81665			0.348781
$640$	−21.6401	−	15.7224i	−0.855398	−	0.621483i
$641$	0.853251	−	2.62604i	0.0337014	−	0.103722i	−0.932791	−	0.360418i	$-0.882634\pi$
$641$	0.853251	−	2.62604i	0.0337014	−	0.103722i	0.966492	+	0.256696i	$0.0826340\pi$
$642$	−1.06849	−	3.28848i	−0.0421700	−	0.129786i
$643$	21.2261	−	15.4217i	0.837075	−	0.608171i	−0.0844768	−	0.996425i	$-0.526922\pi$
$643$	21.2261	−	15.4217i	0.837075	−	0.608171i	0.921552	+	0.388255i	$0.126922\pi$
$644$	0.635051	−	0.461392i	0.0250245	−	0.0181814i
$645$	9.80647	+	30.1812i	0.386129	+	1.18838i
$646$	−0.352568	+	1.08509i	−0.0138716	+	0.0426923i
$647$	−9.82934	−	7.14143i	−0.386431	−	0.280759i	0.377560	−	0.925985i	$-0.376763\pi$
$647$	−9.82934	−	7.14143i	−0.386431	−	0.280759i	−0.763992	+	0.645226i	$0.776763\pi$
$648$	22.8161			0.896302
$649$	9.75403	+	1.96441i	0.382879	+	0.0771098i
$650$	−0.722628			−0.0283438
$651$	0.237398	+	0.172480i	0.00930438	+	0.00676003i
$652$	1.42552	−	4.38729i	0.0558275	−	0.171819i
$653$	2.32371	+	7.15163i	0.0909337	+	0.279865i	0.986173	−	0.165721i	$-0.0529952\pi$
$653$	2.32371	+	7.15163i	0.0909337	+	0.279865i	−0.895239	+	0.445586i	$0.852995\pi$
$654$	−11.2199	+	8.15172i	−0.438732	+	0.318757i
$655$	30.9782	−	22.5070i	1.21042	−	0.879421i
$656$	−4.11350	−	12.6600i	−0.160605	−	0.494292i
$657$	3.56919	−	10.9848i	0.139247	−	0.428559i
$658$	5.35228	+	3.88866i	0.208654	+	0.151596i
$659$	25.6257			0.998236			0.499118	−	0.866534i	$-0.333657\pi$
$659$	25.6257			0.998236			0.499118	+	0.866534i	$0.333657\pi$
$660$	−3.41334	−	29.4409i	−0.132864	−	1.14599i
$661$	−13.8782			−0.539800			−0.269900	−	0.962888i	$-0.586991\pi$
$661$	−13.8782			−0.539800			−0.269900	+	0.962888i	$0.586991\pi$
$662$	−12.4950	−	9.07817i	−0.485633	−	0.352833i
$663$	1.62387	−	4.99775i	0.0630658	−	0.194097i
$664$	−7.91807	−	24.3693i	−0.307281	−	0.945713i
$665$	3.10967	−	2.25931i	0.120588	−	0.0876122i
$666$	13.0561	−	9.48582i	0.505914	−	0.367568i
$667$	0.155085	+	0.477301i	0.00600490	+	0.0184812i
$668$	1.66742	−	5.13179i	0.0645144	−	0.198555i
$669$	−18.2122	−	13.2320i	−0.704125	−	0.511577i
$670$	0.0853986			0.00329923
$671$	4.37614	+	37.7454i	0.168939	+	1.45714i
$672$	11.6975			0.451241
$673$	38.2037	+	27.7566i	1.47265	+	1.06994i	0.979836	+	0.199802i	$0.0640299\pi$
$673$	38.2037	+	27.7566i	1.47265	+	1.06994i	0.492809	+	0.870137i	$0.335970\pi$
$674$	1.43048	−	4.40257i	0.0551001	−	0.169581i
$675$	−0.181173	−	0.557594i	−0.00697336	−	0.0214618i
$676$	−10.4721	+	7.60845i	−0.402774	+	0.292633i
$677$	−11.3110	+	8.21790i	−0.434716	+	0.315839i	−0.783532	−	0.621352i	$-0.786584\pi$
$677$	−11.3110	+	8.21790i	−0.434716	+	0.315839i	0.348816	+	0.937191i	$0.386584\pi$
$678$	−4.55152	−	14.0081i	−0.174800	−	0.537979i
$679$	−0.694288	+	2.13680i	−0.0266443	+	0.0820028i
$680$	4.25134	+	3.08878i	0.163032	+	0.118449i
$681$	7.55019			0.289324
$682$	0.283196	+	0.0570340i	0.0108441	+	0.00218395i
$683$	16.5450			0.633077			0.316538	−	0.948580i	$-0.397479\pi$
$683$	16.5450			0.633077			0.316538	+	0.948580i	$0.397479\pi$
$684$	6.09667	+	4.42949i	0.233112	+	0.169366i
$685$	−9.16565	+	28.2090i	−0.350201	+	1.07781i
$686$	−2.23609	−	6.88196i	−0.0853742	−	0.262755i
$687$	−1.27301	+	0.924895i	−0.0485683	+	0.0352869i
$688$	8.61895	−	6.26203i	0.328594	−	0.238738i
$689$	5.25495	+	16.1731i	0.200198	+	0.616145i
$690$	−0.577563	+	1.77756i	−0.0219875	+	0.0676704i
$691$	18.5705	+	13.4922i	0.706454	+	0.513269i	0.882028	−	0.471198i	$-0.156178\pi$
$691$	18.5705	+	13.4922i	0.706454	+	0.513269i	−0.175574	+	0.984466i	$0.556178\pi$
$692$	33.3295			1.26700
$693$	5.01926	+	5.45587i	0.190666	+	0.207251i
$694$	4.46043			0.169316
$695$	15.8925	+	11.5466i	0.602837	+	0.437987i
$696$	−1.48833	+	4.58061i	−0.0564150	+	0.173628i
$697$	2.21859	+	6.82813i	0.0840352	+	0.258634i
$698$	−4.22192	+	3.06740i	−0.159802	+	0.116103i
$699$	−40.2013	+	29.2079i	−1.52055	+	1.10475i
$700$	−0.231640	−	0.712914i	−0.00875516	−	0.0269456i
$701$	−5.33141	+	16.4084i	−0.201364	+	0.619736i	0.798479	+	0.602023i	$0.205639\pi$
$701$	−5.33141	+	16.4084i	−0.201364	+	0.619736i	−0.999843	+	0.0177130i	$0.994361\pi$
$702$	−1.25357	−	0.910773i	−0.0473130	−	0.0343749i
$703$	−19.1070			−0.720633
$704$	−0.711810	+	0.326091i	−0.0268273	+	0.0122900i
$705$	66.7284			2.51314
$706$	−1.41786	−	1.03014i	−0.0533620	−	0.0387698i
$707$	4.34343	−	13.3677i	0.163351	−	0.502744i
$708$	3.52513	+	10.8492i	0.132482	+	0.407739i
$709$	−14.6554	+	10.6477i	−0.550394	+	0.399884i	−0.827931	−	0.560831i	$-0.810482\pi$
$709$	−14.6554	+	10.6477i	−0.550394	+	0.399884i	0.277537	+	0.960715i	$0.410482\pi$
$710$	4.10636	−	2.98345i	0.154109	−	0.111967i
$711$	9.81311	+	30.2017i	0.368020	+	1.13265i
$712$	−9.08387	+	27.9573i	−0.340433	+	1.04774i
$713$	0.0624319	+	0.0453595i	0.00233809	+	0.00169872i
$714$	−1.28683			−0.0481584
$715$	−8.55230	+	15.1861i	−0.319838	+	0.567928i
$716$	−40.7957			−1.52461
$717$	−15.5847	−	11.3230i	−0.582023	−	0.422864i
$718$	2.92091	−	8.98965i	0.109008	−	0.335491i
$719$	−3.38557	−	10.4197i	−0.126261	−	0.388590i	0.867868	−	0.496795i	$-0.165490\pi$
$719$	−3.38557	−	10.4197i	−0.126261	−	0.388590i	−0.994129	+	0.108205i	$0.965490\pi$
$720$	8.89354	−	6.46153i	0.331443	−	0.240807i
$721$	7.43798	−	5.40401i	0.277005	−	0.201256i
$722$	−2.97781	−	9.16477i	−0.110823	−	0.341077i
$723$	−9.30323	+	28.6324i	−0.345991	+	1.06485i
$724$	20.7905	+	15.1052i	0.772671	+	0.561379i
$725$	0.479254			0.0177991
$726$	14.7312	+	6.18442i	0.546728	+	0.229525i
$727$	33.2288			1.23239			0.616195	−	0.787594i	$-0.288673\pi$
$727$	33.2288			1.23239			0.616195	+	0.787594i	$0.288673\pi$
$728$	−3.58388	−	2.60384i	−0.132827	−	0.0965047i
$729$	−5.51221	+	16.9648i	−0.204156	+	0.628328i
$730$	−2.05478	−	6.32396i	−0.0760508	−	0.234060i
$731$	−4.64858	+	3.37739i	−0.171934	+	0.124917i
$732$	−35.2448	+	25.6069i	−1.30269	+	0.946457i
$733$	−3.88843	−	11.9674i	−0.143623	−	0.442025i	0.853209	−	0.521570i	$-0.174653\pi$
$733$	−3.88843	−	11.9674i	−0.143623	−	0.442025i	−0.996831	+	0.0795448i	$0.974653\pi$
$734$	−4.70736	+	14.4878i	−0.173752	+	0.534754i
$735$	−27.7695	−	20.1757i	−1.02429	−	0.744193i
$736$	3.07625			0.113392
$737$	0.0956905	−	0.169915i	0.00352481	−	0.00625891i
$738$	−11.1946			−0.412078
$739$	−25.9720	−	18.8698i	−0.955396	−	0.694136i	−0.00331894	−	0.999994i	$-0.501056\pi$
$739$	−25.9720	−	18.8698i	−0.955396	−	0.694136i	−0.952077	+	0.305859i	$0.901056\pi$
$740$	−12.1618	+	37.4301i	−0.447076	+	1.37596i
$741$	−2.99777	−	9.22619i	−0.110126	−	0.338933i
$742$	3.36897	−	2.44770i	0.123679	−	0.0898578i
$743$	−20.3729	+	14.8017i	−0.747408	+	0.543023i	−0.895022	−	0.446022i	$-0.852840\pi$
$743$	−20.3729	+	14.8017i	−0.747408	+	0.543023i	0.147615	+	0.989045i	$0.452840\pi$
$744$	0.228856	+	0.704346i	0.00839027	+	0.0258226i
$745$	0.957301	−	2.94627i	0.0350728	−	0.107943i
$746$	10.1476	+	7.37269i	0.371531	+	0.269933i
$747$	28.9102			1.05777
$748$	4.87882	−	2.23506i	0.178387	−	0.0817220i
$749$	−2.10920			−0.0770686
$750$	−12.3633	−	8.98245i	−0.451443	−	0.327993i
$751$	−4.51709	+	13.9022i	−0.164831	+	0.507298i	−0.999024	−	0.0441752i	$-0.985934\pi$
$751$	−4.51709	+	13.9022i	−0.164831	+	0.507298i	0.834193	+	0.551473i	$0.185934\pi$
$752$	−6.92245	−	21.3051i	−0.252436	−	0.776917i
$753$	−44.5277	+	32.3513i	−1.62268	+	1.17895i
$754$	1.02472	−	0.744500i	0.0373180	−	0.0271131i
$755$	11.1781	+	34.4028i	0.406814	+	1.25205i
$756$	0.496695	−	1.52867i	0.0180646	−	0.0555972i
$757$	15.7625	+	11.4521i	0.572897	+	0.416234i	0.836156	−	0.548491i	$-0.184798\pi$
$757$	15.7625	+	11.4521i	0.572897	+	0.416234i	−0.263259	+	0.964725i	$0.584798\pi$
$758$	−7.81245			−0.283761
$759$	2.88959	+	3.14095i	0.104885	+	0.114009i
$760$	9.70099			0.351892
$761$	0.414670	+	0.301275i	0.0150318	+	0.0109212i	0.595276	−	0.803521i	$-0.297043\pi$
$761$	0.414670	+	0.301275i	0.0150318	+	0.0109212i	−0.580244	+	0.814443i	$0.697043\pi$
$762$	9.63606	−	29.6568i	0.349078	−	1.07435i
$763$	2.61422	+	8.04574i	0.0946411	+	0.291275i
$764$	−1.83005	+	1.32961i	−0.0662089	+	0.0481036i
$765$	−4.79668	+	3.48499i	−0.173424	+	0.126000i
$766$	0.895092	+	2.75481i	0.0323410	+	0.0995353i
$767$	2.07295	−	6.37988i	0.0748499	−	0.230364i
$768$	12.4766	+	9.06481i	0.450212	+	0.327098i
$769$	−15.9496			−0.575159			−0.287579	−	0.957757i	$-0.592851\pi$
$769$	−15.9496			−0.575159			−0.287579	+	0.957757i	$0.592851\pi$
$770$	4.18393	+	0.842620i	0.150778	+	0.0303659i
$771$	−13.8779			−0.499800
$772$	−29.8994	−	21.7232i	−1.07610	−	0.781834i
$773$	−7.61351	+	23.4320i	−0.273839	+	0.842789i	0.715685	+	0.698423i	$0.246114\pi$
$773$	−7.61351	+	23.4320i	−0.273839	+	0.842789i	−0.989524	+	0.144367i	$0.953886\pi$
$774$	−2.76858	−	8.52082i	−0.0995147	−	0.306275i
$775$	0.0596192	−	0.0433159i	0.00214159	−	0.00155595i
$776$	−4.58748	+	3.33300i	−0.164681	+	0.119648i
$777$	−6.65940	−	20.4955i	−0.238905	−	0.735273i
$778$	−0.279256	+	0.859463i	−0.0100118	+	0.0308132i
$779$	10.7226	+	7.79043i	0.384177	+	0.279121i
$780$	−19.9820			−0.715472
$781$	−1.33484	−	11.5133i	−0.0477643	−	0.411979i
$782$	−0.338415			−0.0121017
$783$	0.831382	+	0.604034i	0.0297112	+	0.0215864i
$784$	−3.56090	+	10.9593i	−0.127175	+	0.391404i
$785$	13.5615	+	41.7380i	0.484030	+	1.48969i
$786$	−19.1456	+	13.9101i	−0.682901	+	0.496156i
$787$	15.3842	−	11.1773i	0.548389	−	0.398428i	−0.278802	−	0.960349i	$-0.589937\pi$
$787$	15.3842	−	11.1773i	0.548389	−	0.398428i	0.827191	+	0.561921i	$0.189937\pi$
$788$	0.429123	+	1.32070i	0.0152869	+	0.0470481i
$789$	−19.9260	+	61.3259i	−0.709384	+	2.18326i
$790$	14.7903	+	10.7458i	0.526217	+	0.382319i
$791$	−8.98470			−0.319459
$792$	2.15481	+	18.5858i	0.0765679	+	0.660418i
$793$	25.6184			0.909735
$794$	5.80252	+	4.21578i	0.205924	+	0.149612i
$795$	12.9793	−	39.9461i	0.460328	−	1.41674i
$796$	0.0718257	+	0.221057i	0.00254580	+	0.00783515i
$797$	6.35883	−	4.61996i	0.225241	−	0.163647i	−0.469442	−	0.882964i	$-0.655545\pi$
$797$	6.35883	−	4.61996i	0.225241	−	0.163647i	0.694683	+	0.719316i	$0.255545\pi$
$798$	−1.92188	+	1.39633i	−0.0680339	+	0.0494295i
$799$	3.73359	+	11.4908i	0.132085	+	0.406515i
$800$	0.907787	−	2.79388i	0.0320951	−	0.0987787i
$801$	−26.8325	−	19.4950i	−0.948080	−	0.688820i
$802$	−1.63660			−0.0577904
$803$	−14.8850	−	2.99776i	−0.525281	−	0.105789i
$804$	0.223576			0.00788493
$805$	0.922369	+	0.670140i	0.0325092	+	0.0236193i
$806$	0.0601854	−	0.185232i	0.00211994	−	0.00652450i
$807$	−15.1142	−	46.5168i	−0.532046	−	1.63747i
$808$	28.6990	−	20.8511i	1.00963	−	0.733538i
$809$	2.32173	−	1.68684i	0.0816278	−	0.0593061i	−0.546223	−	0.837640i	$-0.683935\pi$
$809$	2.32173	−	1.68684i	0.0816278	−	0.0593061i	0.627851	+	0.778334i	$0.283935\pi$
$810$	4.57968	+	14.0948i	0.160914	+	0.495241i
$811$	13.4964	−	41.5375i	0.473921	−	1.45858i	−0.373486	−	0.927636i	$-0.621837\pi$
$811$	13.4964	−	41.5375i	0.473921	−	1.45858i	0.847407	−	0.530944i	$-0.178163\pi$
$812$	1.06297	+	0.772290i	0.0373028	+	0.0271021i
$813$	24.6841			0.865710
$814$	−14.3639	−	15.6133i	−0.503453	−	0.547247i
$815$	6.70017			0.234697
$816$	3.52513	+	2.56115i	0.123404	+	0.0896584i
$817$	−3.27788	+	10.0883i	−0.114679	+	0.352944i
$818$	3.76158	+	11.5769i	0.131520	+	0.404778i
$819$	4.04360	−	2.93785i	0.141295	−	0.102657i
$820$	22.0864	−	16.0467i	0.771289	−	0.560374i
$821$	−5.69072	−	17.5142i	−0.198607	−	0.611251i	−0.999916	−	0.0129989i	$-0.995862\pi$
$821$	−5.69072	−	17.5142i	−0.198607	−	0.611251i	0.801308	−	0.598252i	$-0.204138\pi$
$822$	5.66468	−	17.4341i	0.197578	−	0.608084i
$823$	5.84185	+	4.24435i	0.203634	+	0.147949i	0.684929	−	0.728610i	$-0.259833\pi$
$823$	5.84185	+	4.24435i	0.203634	+	0.147949i	−0.481295	+	0.876559i	$0.659833\pi$
$824$	23.2037			0.808338
$825$	3.70534	−	1.69747i	0.129003	−	0.0590985i
$826$	−1.64270			−0.0571570
$827$	36.6265	+	26.6107i	1.27363	+	0.925344i	0.999341	−	0.0363036i	$-0.0115583\pi$
$827$	36.6265	+	26.6107i	1.27363	+	0.925344i	0.274287	+	0.961648i	$0.411558\pi$
$828$	−0.690729	+	2.12584i	−0.0240045	+	0.0738782i
$829$	12.1098	+	37.2703i	0.420592	+	1.29445i	0.907152	+	0.420803i	$0.138251\pi$
$829$	12.1098	+	37.2703i	0.420592	+	1.29445i	−0.486560	+	0.873647i	$0.661749\pi$
$830$	13.4650	−	9.78287i	0.467376	−	0.339569i
$831$	33.7703	−	24.5356i	1.17148	−	0.851130i
$832$	0.163119	+	0.502029i	0.00565513	+	0.0174047i
$833$	1.92055	−	5.91085i	0.0665432	−	0.204799i
$834$	−9.82211	−	7.13618i	−0.340112	−	0.247106i
$835$	7.83715			0.271216
$836$	4.86127	−	8.63203i	0.168130	−	0.298545i
$837$	0.158018			0.00546189
$838$	−12.5180	−	9.09483i	−0.432426	−	0.314176i
$839$	16.3406	−	50.2913i	0.564142	−	1.73625i	−0.106346	−	0.994329i	$-0.533915\pi$
$839$	16.3406	−	50.2913i	0.564142	−	1.73625i	0.670488	−	0.741920i	$-0.266085\pi$
$840$	3.38111	+	10.4060i	0.116660	+	0.359041i
$841$	22.7819	−	16.5520i	0.785582	−	0.570759i
$842$	16.6077	−	12.0662i	0.572340	−	0.415829i
$843$	−6.87298	−	21.1529i	−0.236718	−	0.728543i
$844$	2.09158	−	6.43721i	0.0719950	−	0.221578i
$845$	−15.2101	−	11.0508i	−0.523242	−	0.380158i
$846$	−18.8389			−0.647695
$847$	6.36470	−	7.38048i	0.218694	−	0.253596i
$848$	−14.1005			−0.484213
$849$	−58.5053	−	42.5066i	−2.00790	−	1.45882i
$850$	−0.0998647	+	0.307352i	−0.00342533	+	0.0105421i
$851$	−1.75131	−	5.38999i	−0.0600343	−	0.184767i
$852$	10.7506	−	7.81077i	0.368310	−	0.267593i
$853$	−18.4614	+	13.4130i	−0.632105	+	0.459251i	−0.857129	−	0.515102i	$-0.827754\pi$
$853$	−18.4614	+	13.4130i	−0.632105	+	0.459251i	0.225024	+	0.974353i	$0.427754\pi$
$854$	−1.93859	−	5.96638i	−0.0663373	−	0.204165i
$855$	−3.38231	+	10.4097i	−0.115673	+	0.356003i
$856$	−4.30661	−	3.12894i	−0.147197	−	0.106945i
$857$	−31.4787			−1.07529			−0.537646	−	0.843171i	$-0.680686\pi$
$857$	−31.4787			−1.07529			−0.537646	+	0.843171i	$0.680686\pi$
$858$	5.28561	−	9.38553i	0.180448	−	0.320417i
$859$	−44.0216			−1.50200			−0.750998	−	0.660304i	$-0.770427\pi$
$859$	−44.0216			−1.50200			−0.750998	+	0.660304i	$0.770427\pi$
$860$	17.6763	+	12.8426i	0.602758	+	0.437929i
$861$	−4.61941	+	14.2171i	−0.157429	+	0.484517i
$862$	−5.90159	−	18.1632i	−0.201009	−	0.618642i
$863$	33.8974	−	24.6279i	1.15388	−	0.838345i	0.164890	−	0.986312i	$-0.447273\pi$
$863$	33.8974	−	24.6279i	1.15388	−	0.838345i	0.988992	+	0.147967i	$0.0472731\pi$
$864$	5.09608	−	3.70252i	0.173372	−	0.125962i
$865$	14.9591	+	46.0395i	0.508626	+	1.56539i
$866$	4.37510	−	13.4652i	0.148672	−	0.457566i
$867$	−1.90126	−	1.38135i	−0.0645701	−	0.0469129i
$868$	0.202034			0.00685748
$869$	37.9535	−	17.3871i	1.28748	−	0.589817i
$870$	−3.12844			−0.106064
$871$	−0.106365	−	0.0772784i	−0.00360403	−	0.00261848i
$872$	−6.59784	+	20.3061i	−0.223431	+	0.687650i
$873$	−1.97703	−	6.08468i	−0.0669124	−	0.205935i
$874$	−0.505424	+	0.367212i	−0.0170962	+	0.0124211i
$875$	−7.54160	+	5.47929i	−0.254953	+	0.185234i
$876$	−5.37948	−	16.5563i	−0.181756	−	0.559387i
$877$	0.142858	−	0.439672i	0.00482398	−	0.0148467i	−0.948616	−	0.316431i	$-0.897515\pi$
$877$	0.142858	−	0.439672i	0.00482398	−	0.0148467i	0.953440	+	0.301584i	$0.0975155\pi$
$878$	2.32762	+	1.69111i	0.0785532	+	0.0570722i
$879$	−46.6948			−1.57498
$880$	−9.78435	−	10.6355i	−0.329830	−	0.358521i
$881$	−20.7745			−0.699910			−0.349955	−	0.936767i	$-0.613803\pi$
$881$	−20.7745			−0.699910			−0.349955	+	0.936767i	$0.613803\pi$
$882$	7.83995	+	5.69606i	0.263985	+	0.191796i
$883$	−4.13443	+	12.7245i	−0.139135	+	0.428213i	−0.996210	−	0.0869782i	$-0.972279\pi$
$883$	−4.13443	+	12.7245i	−0.139135	+	0.428213i	0.857075	+	0.515191i	$0.172279\pi$
$884$	−1.11803	−	3.44095i	−0.0376036	−	0.115732i
$885$	−13.4044	+	9.73883i	−0.450583	+	0.327367i
$886$	−4.09170	+	2.97280i	−0.137463	+	0.0998731i
$887$	6.81368	+	20.9703i	0.228781	+	0.704115i	0.997886	+	0.0649926i	$0.0207024\pi$
$887$	6.81368	+	20.9703i	0.228781	+	0.704115i	−0.769105	+	0.639123i	$0.779298\pi$
$888$	16.8072	−	51.7272i	0.564012	−	1.73585i
$889$	−15.3888	−	11.1806i	−0.516124	−	0.374986i
$890$	−19.0941			−0.640036
$891$	33.1757	+	6.68140i	1.11143	+	0.223835i
$892$	−15.4992			−0.518952
$893$	18.0447	+	13.1102i	0.603842	+	0.438717i
$894$	−0.591644	+	1.82089i	−0.0197875	+	0.0608998i
$895$	−18.3102	−	56.3530i	−0.612042	−	1.88367i
$896$	8.15831	−	5.92736i	0.272550	−	0.198019i
$897$	2.32790	−	1.69132i	0.0777263	−	0.0564714i
$898$	7.53987	+	23.2053i	0.251609	+	0.774372i
$899$	−0.0399156	+	0.122847i	−0.00133126	+	0.00409719i
$900$	1.72688	+	1.25465i	0.0575627	+	0.0418218i
$901$	7.60503			0.253360
$902$	1.69485	+	14.6186i	0.0564325	+	0.486745i
$903$	−11.9639			−0.398133
$904$	−18.3451	−	13.3285i	−0.610150	−	0.443300i
$905$	−11.5341	+	35.4984i	−0.383407	+	1.18001i
$906$	−6.90847	−	21.2621i	−0.229519	−	0.706385i
$907$	−16.7599	+	12.1768i	−0.556502	+	0.404322i	−0.830177	−	0.557500i	$-0.811761\pi$
$907$	−16.7599	+	12.1768i	−0.556502	+	0.404322i	0.273675	+	0.961822i	$0.411761\pi$
$908$	4.20552	−	3.05549i	0.139565	−	0.101400i
$909$	12.3682	+	38.0654i	0.410228	+	1.26255i
$910$	0.889178	−	2.73661i	0.0294760	−	0.0907177i
$911$	5.92810	+	4.30702i	0.196407	+	0.142698i	0.681642	−	0.731686i	$-0.261266\pi$
$911$	5.92810	+	4.30702i	0.196407	+	0.142698i	−0.485235	+	0.874384i	$0.661266\pi$
$912$	8.04386			0.266359
$913$	−4.37700	−	37.7528i	−0.144858	−	1.24943i
$914$	−16.7702			−0.554708
$915$	−51.1907	−	37.1923i	−1.69231	−	1.22954i
$916$	−0.334780	+	1.03035i	−0.0110615	+	0.0340437i
$917$	4.46091	+	13.7293i	0.147312	+	0.453380i
$918$	−0.560614	+	0.407310i	−0.0185030	+	0.0134432i
$919$	9.04795	−	6.57372i	0.298464	−	0.216847i	−0.428467	−	0.903558i	$-0.640946\pi$
$919$	9.04795	−	6.57372i	0.298464	−	0.216847i	0.726931	+	0.686711i	$0.240946\pi$
$920$	0.889178	+	2.73661i	0.0293153	+	0.0902233i
$921$	−12.8699	+	39.6095i	−0.424078	+	1.30518i
$922$	10.2423	+	7.44149i	0.337313	+	0.245072i
$923$	−7.81428			−0.257210
$924$	10.9537	+	2.20601i	0.360349	+	0.0725723i
$925$	−5.41204			−0.177947
$926$	3.94076	+	2.86313i	0.129502	+	0.0940884i
$927$	−8.09010	+	24.8988i	−0.265714	+	0.817783i
$928$	1.59117	+	4.89710i	0.0522326	+	0.160755i
$929$	−21.2319	+	15.4259i	−0.696596	+	0.506107i	−0.878822	−	0.477150i	$-0.841670\pi$
$929$	−21.2319	+	15.4259i	−0.696596	+	0.506107i	0.182226	+	0.983257i	$0.441670\pi$
$930$	−0.389178	+	0.282754i	−0.0127617	+	0.00927188i
$931$	−3.54547	−	10.9118i	−0.116198	−	0.357621i
$932$	−10.5723	+	32.5381i	−0.346307	+	1.06582i
$933$	5.21905	+	3.79186i	0.170864	+	0.124140i
$934$	11.1792			0.365794
$935$	5.27714	+	5.73618i	0.172581	+	0.187593i
$936$	12.6145			0.412318
$937$	−15.0573	−	10.9398i	−0.491900	−	0.357386i	0.314014	−	0.949418i	$-0.398326\pi$
$937$	−15.0573	−	10.9398i	−0.491900	−	0.357386i	−0.805915	+	0.592032i	$0.798326\pi$
$938$	−0.00994890	+	0.0306196i	−0.000324843	+	0.000999764i
$939$	−22.0988	−	68.0131i	−0.721167	−	2.21952i
$940$	37.1683	−	27.0043i	1.21230	−	0.880784i
$941$	31.8654	−	23.1516i	1.03878	−	0.754719i	0.0687345	−	0.997635i	$-0.478104\pi$
$941$	31.8654	−	23.1516i	1.03878	−	0.754719i	0.970047	+	0.242916i	$0.0781039\pi$
$942$	−8.38146	−	25.7955i	−0.273083	−	0.840462i
$943$	−1.21483	+	3.73886i	−0.0395603	+	0.121754i
$944$	4.50000	+	3.26944i	0.146463	+	0.106411i
$945$	2.33455			0.0759429
$946$	−10.7079	+	4.90544i	−0.348142	+	0.159490i
$947$	13.9913			0.454656			0.227328	−	0.973818i	$-0.427001\pi$
$947$	13.9913			0.454656			0.227328	+	0.973818i	$0.427001\pi$
$948$	38.7216	+	28.1329i	1.25762	+	0.913714i
$949$	−3.16340	+	9.73595i	−0.102688	+	0.316042i
$950$	0.184357	+	0.567393i	0.00598133	+	0.0184086i
$951$	44.2666	−	32.1616i	1.43544	−	1.04291i
$952$	−1.60276	+	1.16447i	−0.0519457	+	0.0377408i
$953$	9.45542	+	29.1008i	0.306291	+	0.942667i	0.979192	+	0.202935i	$0.0650480\pi$
$953$	9.45542	+	29.1008i	0.306291	+	0.942667i	−0.672901	+	0.739733i	$0.734952\pi$
$954$	−3.66434	+	11.2777i	−0.118637	+	0.365128i
$955$	−2.65803	−	1.93117i	−0.0860117	−	0.0624911i
$956$	−13.2631			−0.428960
$957$	−3.50547	+	6.22458i	−0.113316	+	0.201212i
$958$	−0.259601			−0.00838732
$959$	−9.04650	−	6.57266i	−0.292127	−	0.212242i
$960$	0.402890	−	1.23997i	0.0130032	−	0.0400198i
$961$	−9.57339	−	29.4639i	−0.308819	−	0.950447i
$962$	−11.5717	+	8.40737i	−0.373088	+	0.271064i
$963$	4.85904	−	3.53030i	0.156580	−	0.113762i
$964$	6.40528	+	19.7134i	0.206300	+	0.634926i
$965$	16.5876	−	51.0513i	0.533973	−	1.64340i
$966$	−0.570055	−	0.414169i	−0.0183412	−	0.0133257i
$967$	12.6806			0.407779			0.203890	−	0.978994i	$-0.434642\pi$
$967$	12.6806			0.407779			0.203890	+	0.978994i	$0.434642\pi$
$968$	23.9443	−	5.62777i	0.769598	−	0.180884i
$969$	−4.33842			−0.139370
$970$	−2.97979	−	2.16494i	−0.0956752	−	0.0695121i
$971$	0.484822	−	1.49213i	0.0155587	−	0.0478847i	−0.942976	−	0.332861i	$-0.891986\pi$
$971$	0.484822	−	1.49213i	0.0155587	−	0.0478847i	0.958534	+	0.284977i	$0.0919859\pi$
$972$	10.3079	+	31.7245i	0.330626	+	1.01756i
$973$	−5.99148	+	4.35307i	−0.192078	+	0.139553i
$974$	−3.07994	+	2.23770i	−0.0986875	+	0.0717007i
$975$	−0.849119	−	2.61332i	−0.0271936	−	0.0836932i
$976$	−6.56421	+	20.2026i	−0.210115	+	0.646669i
$977$	−40.5344	−	29.4500i	−1.29681	−	0.942189i	−0.296893	−	0.954911i	$-0.595950\pi$
$977$	−40.5344	−	29.4500i	−1.29681	−	0.942189i	−0.999919	+	0.0127220i	$0.995950\pi$
$978$	−4.14093			−0.132412
$979$	−21.3953	+	37.9911i	−0.683796	+	1.21420i
$980$	−23.6328			−0.754921
$981$	−19.4891	−	14.1597i	−0.622239	−	0.452083i
$982$	−6.22921	+	19.1715i	−0.198782	+	0.611788i
$983$	11.7567	+	36.1835i	0.374981	+	1.15407i	0.943491	+	0.331397i	$0.107520\pi$
$983$	11.7567	+	36.1835i	0.374981	+	1.15407i	−0.568510	+	0.822676i	$0.692480\pi$
$984$	−30.5226	+	22.1760i	−0.973025	+	0.706944i
$985$	−1.63175	+	1.18553i	−0.0519917	+	0.0377742i
$986$	−0.175042	−	0.538725i	−0.00557449	−	0.0171565i
$987$	−7.77383	+	23.9254i	−0.247444	+	0.761554i
$988$	−5.40353	−	3.92590i	−0.171909	−	0.124899i
$989$	−3.14631			−0.100047
$990$	−11.0490	+	5.06172i	−0.351160	+	0.160872i
$991$	−43.4586			−1.38051			−0.690254	−	0.723567i	$-0.742501\pi$
$991$	−43.4586			−1.38051			−0.690254	+	0.723567i	$0.742501\pi$
$992$	0.640550	+	0.465387i	0.0203375	+	0.0147761i
$993$	18.1482	−	55.8544i	0.575915	−	1.77249i
$994$	0.591322	+	1.81990i	0.0187556	+	0.0577238i
$995$	−0.273119	+	0.198432i	−0.00865844	+	0.00629073i
$996$	35.2518	−	25.6119i	1.11699	−	0.811544i
$997$	−10.5485	−	32.4649i	−0.334074	−	1.02817i	−0.967176	−	0.254106i	$-0.918219\pi$
$997$	−10.5485	−	32.4649i	−0.334074	−	1.02817i	0.633103	−	0.774068i	$-0.281781\pi$
$998$	2.70904	−	8.33758i	0.0857533	−	0.263922i
$999$	−9.38849	−	6.82114i	−0.297039	−	0.215811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.d.103.2	yes	8
11.3	even	5	inner	187.2.g.d.69.2	✓	8
11.5	even	5		2057.2.a.q.1.4		4
11.6	odd	10		2057.2.a.t.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.d.69.2	✓	8	11.3	even	5	inner
187.2.g.d.103.2	yes	8	1.1	even	1	trivial
2057.2.a.q.1.4		4	11.5	even	5
2057.2.a.t.1.2		4	11.6	odd	10

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.363271i) q^{2} +(0.726216 - 2.23506i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(1.90126 - 1.38135i) q^{5} +(-1.17504 + 0.853718i) q^{6} +(0.273784 + 0.842620i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-2.04107 - 1.48292i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.363271i) q^{2} +(0.726216 - 2.23506i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(1.90126 - 1.38135i) q^{5} +(-1.17504 + 0.853718i) q^{6} +(0.273784 + 0.842620i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-2.04107 - 1.48292i) q^{9} -1.45243 q^{10} +(-1.62747 + 2.88987i) q^{11} -3.80252 q^{12} +(1.80902 + 1.31433i) q^{13} +(0.169208 - 0.520768i) q^{14} +(-1.70667 - 5.25259i) q^{15} +(-1.50000 + 1.08981i) q^{16} +(0.809017 - 0.587785i) q^{17} +(0.481831 + 1.48292i) q^{18} +(0.570466 - 1.75571i) q^{19} +(-3.07630 - 2.23506i) q^{20} +2.08214 q^{21} +(1.86354 - 0.853718i) q^{22} +0.547568 q^{23} +(4.25134 + 3.08878i) q^{24} +(0.161585 - 0.497306i) q^{25} +(-0.427051 - 1.31433i) q^{26} +(0.907093 - 0.659042i) q^{27} +(1.15977 - 0.842620i) q^{28} +(0.283225 + 0.871676i) q^{29} +(-1.05478 + 3.24628i) q^{30} +(0.114017 + 0.0828381i) q^{31} +5.61803 q^{32} +(5.27714 + 5.73618i) q^{33} -0.618034 q^{34} +(1.68448 + 1.22385i) q^{35} +(-1.26145 + 3.88234i) q^{36} +(-3.19835 - 9.84352i) q^{37} +(-0.923034 + 0.670623i) q^{38} +(4.25134 - 3.08878i) q^{39} +(1.62387 + 4.99775i) q^{40} +(-2.21859 + 6.82813i) q^{41} +(-1.04107 - 0.756380i) q^{42} -5.74597 q^{43} +(5.26078 + 1.05949i) q^{44} -5.92903 q^{45} +(-0.273784 - 0.198916i) q^{46} +(-3.73359 + 11.4908i) q^{47} +(1.34648 + 4.14404i) q^{48} +(5.02807 - 3.65311i) q^{49} +(-0.261449 + 0.189954i) q^{50} +(-0.726216 - 2.23506i) q^{51} +(1.11803 - 3.44095i) q^{52} +(6.15260 + 4.47013i) q^{53} -0.692958 q^{54} +(0.897653 + 7.74249i) q^{55} -1.98112 q^{56} +(-3.50985 - 2.55006i) q^{57} +(0.175042 - 0.538725i) q^{58} +(-0.927051 - 2.85317i) q^{59} +(-7.22957 + 5.25259i) q^{60} +(9.26882 - 6.73419i) q^{61} +(-0.0269157 - 0.0828381i) q^{62} +(0.690729 - 2.12584i) q^{63} +(0.190983 + 0.138757i) q^{64} +5.25495 q^{65} +(-0.554780 - 4.78512i) q^{66} -0.0587969 q^{67} +(-1.30902 - 0.951057i) q^{68} +(0.397653 - 1.22385i) q^{69} +(-0.397653 - 1.22385i) q^{70} +(-2.82723 + 2.05411i) q^{71} +(4.56397 - 3.31592i) q^{72} +(1.41472 + 4.35405i) q^{73} +(-1.97669 + 6.08363i) q^{74} +(-0.994165 - 0.722303i) q^{75} -2.98700 q^{76} +(-2.88064 - 0.580144i) q^{77} -3.24774 q^{78} +(-10.1832 - 7.39849i) q^{79} +(-1.34648 + 4.14404i) q^{80} +(-3.15311 - 9.70427i) q^{81} +(3.58976 - 2.60811i) q^{82} +(-9.27064 + 6.73551i) q^{83} +(-1.04107 - 3.20408i) q^{84} +(0.726216 - 2.23506i) q^{85} +(2.87298 + 2.08734i) q^{86} +2.15393 q^{87} +(-5.02111 - 5.45788i) q^{88} +13.1463 q^{89} +(2.96451 + 2.15384i) q^{90} +(-0.612199 + 1.88416i) q^{91} +(-0.273784 - 0.842620i) q^{92} +(0.267949 - 0.194676i) q^{93} +(6.04107 - 4.38909i) q^{94} +(-1.34064 - 4.12608i) q^{95} +(4.07991 - 12.5567i) q^{96} +(2.05158 + 1.49056i) q^{97} -3.84110 q^{98} +(7.60723 - 3.48499i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 6 q^{3} - 4 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{7} - 10 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 6 * q^3 - 4 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7 - 10 * q^8 + 2 * q^9	\( 8 q - 4 q^{2} + 6 q^{3} - 4 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{7} - 10 q^{8} + 2 q^{9} - 12 q^{10} - 2 q^{11} - 8 q^{12} + 10 q^{13} + 4 q^{14} + 14 q^{15} - 12 q^{16} + 2 q^{17} + 14 q^{18} - 4 q^{19} - 2 q^{20} - 20 q^{21} - 14 q^{22} + 4 q^{23} - 4 q^{25} + 10 q^{26} - 18 q^{27} + 14 q^{28} - 32 q^{30} - 4 q^{31} + 36 q^{32} + 6 q^{33} + 4 q^{34} - 6 q^{36} + 10 q^{37} + 2 q^{38} - 10 q^{40} - 10 q^{41} + 10 q^{42} + 16 q^{43} + 6 q^{44} + 40 q^{45} - 2 q^{46} + 10 q^{47} - 24 q^{48} - 14 q^{49} + 2 q^{50} - 6 q^{51} + 4 q^{53} + 64 q^{54} - 16 q^{55} - 20 q^{56} - 10 q^{57} - 10 q^{58} + 6 q^{59} - 22 q^{60} + 30 q^{61} + 12 q^{62} - 38 q^{63} + 6 q^{64} + 20 q^{65} - 28 q^{66} - 20 q^{67} - 6 q^{68} - 20 q^{69} + 20 q^{70} + 18 q^{71} + 10 q^{72} - 6 q^{73} - 40 q^{74} - 22 q^{75} + 12 q^{76} + 32 q^{77} + 20 q^{78} - 4 q^{79} + 24 q^{80} - 76 q^{81} - 20 q^{83} + 10 q^{84} + 6 q^{85} - 8 q^{86} + 36 q^{87} - 10 q^{88} - 48 q^{89} - 20 q^{90} - 10 q^{91} - 2 q^{92} + 16 q^{93} + 30 q^{94} + 10 q^{95} + 22 q^{96} + 12 q^{97} + 32 q^{98} + 22 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 6 * q^3 - 4 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7 - 10 * q^8 + 2 * q^9 - 12 * q^10 - 2 * q^11 - 8 * q^12 + 10 * q^13 + 4 * q^14 + 14 * q^15 - 12 * q^16 + 2 * q^17 + 14 * q^18 - 4 * q^19 - 2 * q^20 - 20 * q^21 - 14 * q^22 + 4 * q^23 - 4 * q^25 + 10 * q^26 - 18 * q^27 + 14 * q^28 - 32 * q^30 - 4 * q^31 + 36 * q^32 + 6 * q^33 + 4 * q^34 - 6 * q^36 + 10 * q^37 + 2 * q^38 - 10 * q^40 - 10 * q^41 + 10 * q^42 + 16 * q^43 + 6 * q^44 + 40 * q^45 - 2 * q^46 + 10 * q^47 - 24 * q^48 - 14 * q^49 + 2 * q^50 - 6 * q^51 + 4 * q^53 + 64 * q^54 - 16 * q^55 - 20 * q^56 - 10 * q^57 - 10 * q^58 + 6 * q^59 - 22 * q^60 + 30 * q^61 + 12 * q^62 - 38 * q^63 + 6 * q^64 + 20 * q^65 - 28 * q^66 - 20 * q^67 - 6 * q^68 - 20 * q^69 + 20 * q^70 + 18 * q^71 + 10 * q^72 - 6 * q^73 - 40 * q^74 - 22 * q^75 + 12 * q^76 + 32 * q^77 + 20 * q^78 - 4 * q^79 + 24 * q^80 - 76 * q^81 - 20 * q^83 + 10 * q^84 + 6 * q^85 - 8 * q^86 + 36 * q^87 - 10 * q^88 - 48 * q^89 - 20 * q^90 - 10 * q^91 - 2 * q^92 + 16 * q^93 + 30 * q^94 + 10 * q^95 + 22 * q^96 + 12 * q^97 + 32 * q^98 + 22 * q^99

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