LMFDB - Embedded newform 585.2.i.e.391.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + \cdots + 268 $ x^16 - 5x^15 + 20x^14 - 44x^13 + 96x^12 - 107x^11 + 178x^10 - 19x^9 + 231x^8 + 326x^7 + 551x^6 + 859x^5 + 1118x^4 + 1215x^3 + 1103x^2 + 770*x + 268
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.6
Root			$0.466399 - 1.64781i$ of defining polynomial
Character	$\chi$	$=$	585.391
Dual form			585.2.i.e.196.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0336011 - 0.0581988i) q^{2} +(-0.332146 + 1.69991i) q^{3} +(0.997742 - 1.72814i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.110093 - 0.0377882i) q^{6} +(-1.23179 - 2.13352i) q^{7} -0.268505 q^{8} +(-2.77936 - 1.12923i) q^{9} +O(q^{10})$	\(q+(-0.0336011 - 0.0581988i) q^{2} +(-0.332146 + 1.69991i) q^{3} +(0.997742 - 1.72814i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.110093 - 0.0377882i) q^{6} +(-1.23179 - 2.13352i) q^{7} -0.268505 q^{8} +(-2.77936 - 1.12923i) q^{9} -0.0672022 q^{10} +(-1.60607 - 2.78180i) q^{11} +(2.60628 + 2.27006i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-0.0827788 + 0.143377i) q^{14} +(1.30609 + 1.13760i) q^{15} +(-1.98646 - 3.44065i) q^{16} -4.77678 q^{17} +(0.0276694 + 0.199699i) q^{18} -3.94903 q^{19} +(-0.997742 - 1.72814i) q^{20} +(4.03591 - 1.38528i) q^{21} +(-0.107932 + 0.186943i) q^{22} +(-2.13489 + 3.69773i) q^{23} +(0.0891830 - 0.456434i) q^{24} +(-0.500000 - 0.866025i) q^{25} -0.0672022 q^{26} +(2.84275 - 4.34957i) q^{27} -4.91602 q^{28} +(1.15314 + 1.99730i) q^{29} +(0.0223210 - 0.114237i) q^{30} +(3.81652 - 6.61041i) q^{31} +(-0.402000 + 0.696284i) q^{32} +(5.26224 - 1.80621i) q^{33} +(0.160505 + 0.278003i) q^{34} -2.46357 q^{35} +(-4.72456 + 3.67643i) q^{36} +4.87293 q^{37} +(0.132692 + 0.229829i) q^{38} +(1.30609 + 1.13760i) q^{39} +(-0.134253 + 0.232532i) q^{40} +(1.26518 - 2.19136i) q^{41} +(-0.216233 - 0.188338i) q^{42} +(2.28304 + 3.95433i) q^{43} -6.40978 q^{44} +(-2.36762 + 1.84238i) q^{45} +0.286938 q^{46} +(3.13284 + 5.42623i) q^{47} +(6.50858 - 2.23400i) q^{48} +(0.465404 - 0.806103i) q^{49} +(-0.0336011 + 0.0581988i) q^{50} +(1.58659 - 8.12007i) q^{51} +(-0.997742 - 1.72814i) q^{52} +12.4968 q^{53} +(-0.348659 - 0.0192939i) q^{54} -3.21214 q^{55} +(0.330741 + 0.572861i) q^{56} +(1.31166 - 6.71298i) q^{57} +(0.0774937 - 0.134223i) q^{58} +(-1.42509 + 2.46833i) q^{59} +(3.26907 - 1.12207i) q^{60} +(-6.35000 - 10.9985i) q^{61} -0.512957 q^{62} +(1.01433 + 7.32078i) q^{63} -7.89182 q^{64} +(-0.500000 - 0.866025i) q^{65} +(-0.281936 - 0.245566i) q^{66} +(6.75359 - 11.6976i) q^{67} +(-4.76599 + 8.25494i) q^{68} +(-5.57670 - 4.85729i) q^{69} +(0.0827788 + 0.143377i) q^{70} +7.79224 q^{71} +(0.746272 + 0.303205i) q^{72} +2.26796 q^{73} +(-0.163736 - 0.283599i) q^{74} +(1.63823 - 0.562306i) q^{75} +(-3.94012 + 6.82448i) q^{76} +(-3.95668 + 6.85316i) q^{77} +(0.0223210 - 0.114237i) q^{78} +(-4.56668 - 7.90972i) q^{79} -3.97292 q^{80} +(6.44966 + 6.27709i) q^{81} -0.170046 q^{82} +(-5.25595 - 9.10356i) q^{83} +(1.63284 - 8.35677i) q^{84} +(-2.38839 + 4.13681i) q^{85} +(0.153425 - 0.265740i) q^{86} +(-3.77824 + 1.29684i) q^{87} +(0.431239 + 0.746927i) q^{88} +0.966612 q^{89} +(0.186779 + 0.0758870i) q^{90} -2.46357 q^{91} +(4.26013 + 7.37876i) q^{92} +(9.96943 + 8.68335i) q^{93} +(0.210533 - 0.364655i) q^{94} +(-1.97452 + 3.41996i) q^{95} +(-1.05009 - 0.914630i) q^{96} +(9.39020 + 16.2643i) q^{97} -0.0625523 q^{98} +(1.32255 + 9.54524i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9} - 6 q^{10} - 6 q^{11} + 2 q^{12} + 8 q^{13} - 10 q^{14} + 5 q^{15} - 11 q^{16} - 4 q^{17} + 5 q^{18} - 20 q^{19} + 9 q^{20} + 11 q^{21} - 3 q^{22} - 6 q^{23} - 57 q^{24} - 8 q^{25} - 6 q^{26} - 14 q^{27} - 68 q^{28} - 14 q^{29} + 7 q^{30} + 31 q^{31} - q^{32} - 31 q^{33} + 7 q^{34} + 22 q^{35} + 2 q^{36} + 2 q^{37} - 9 q^{38} + 5 q^{39} - 6 q^{40} + 12 q^{41} - 26 q^{42} - 15 q^{43} + 32 q^{44} - 16 q^{45} - 64 q^{46} + 18 q^{47} - 4 q^{48} - 17 q^{49} - 3 q^{50} + 32 q^{51} + 9 q^{52} + 4 q^{53} + 2 q^{54} - 12 q^{55} - 16 q^{56} + 45 q^{57} + 42 q^{58} - 24 q^{59} - 8 q^{60} + 9 q^{61} - 40 q^{62} + 47 q^{63} - 60 q^{64} - 8 q^{65} + 55 q^{66} + 18 q^{67} + 14 q^{68} - 12 q^{69} + 10 q^{70} + 20 q^{71} - 9 q^{72} + 12 q^{73} + 37 q^{74} + 4 q^{75} + 53 q^{76} + 34 q^{77} + 7 q^{78} + 3 q^{79} - 22 q^{80} + 13 q^{81} - 68 q^{82} + 10 q^{83} + 22 q^{84} - 2 q^{85} - 60 q^{86} + 11 q^{87} + 14 q^{88} - 26 q^{89} + 19 q^{90} + 22 q^{91} - 5 q^{92} + 74 q^{93} - 17 q^{94} - 10 q^{95} + 13 q^{96} + 34 q^{97} - 60 q^{98} - 43 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9 - 6 * q^10 - 6 * q^11 + 2 * q^12 + 8 * q^13 - 10 * q^14 + 5 * q^15 - 11 * q^16 - 4 * q^17 + 5 * q^18 - 20 * q^19 + 9 * q^20 + 11 * q^21 - 3 * q^22 - 6 * q^23 - 57 * q^24 - 8 * q^25 - 6 * q^26 - 14 * q^27 - 68 * q^28 - 14 * q^29 + 7 * q^30 + 31 * q^31 - q^32 - 31 * q^33 + 7 * q^34 + 22 * q^35 + 2 * q^36 + 2 * q^37 - 9 * q^38 + 5 * q^39 - 6 * q^40 + 12 * q^41 - 26 * q^42 - 15 * q^43 + 32 * q^44 - 16 * q^45 - 64 * q^46 + 18 * q^47 - 4 * q^48 - 17 * q^49 - 3 * q^50 + 32 * q^51 + 9 * q^52 + 4 * q^53 + 2 * q^54 - 12 * q^55 - 16 * q^56 + 45 * q^57 + 42 * q^58 - 24 * q^59 - 8 * q^60 + 9 * q^61 - 40 * q^62 + 47 * q^63 - 60 * q^64 - 8 * q^65 + 55 * q^66 + 18 * q^67 + 14 * q^68 - 12 * q^69 + 10 * q^70 + 20 * q^71 - 9 * q^72 + 12 * q^73 + 37 * q^74 + 4 * q^75 + 53 * q^76 + 34 * q^77 + 7 * q^78 + 3 * q^79 - 22 * q^80 + 13 * q^81 - 68 * q^82 + 10 * q^83 + 22 * q^84 - 2 * q^85 - 60 * q^86 + 11 * q^87 + 14 * q^88 - 26 * q^89 + 19 * q^90 + 22 * q^91 - 5 * q^92 + 74 * q^93 - 17 * q^94 - 10 * q^95 + 13 * q^96 + 34 * q^97 - 60 * q^98 - 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	−0.0336011	−	0.0581988i	−0.0237596	−	0.0411528i	0.853901	−	0.520435i	$-0.174230\pi$
$2$	−0.0336011	−	0.0581988i	−0.0237596	−	0.0411528i	−0.877661	+	0.479282i	$0.840897\pi$
$3$	−0.332146	+	1.69991i	−0.191765	+	0.981441i
$3$	−0.332146	+	1.69991i	−0.191765	+	0.981441i
$4$	0.997742	−	1.72814i	0.498871	−	0.864070i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.110093	−	0.0377882i	0.0449453	−	0.0154270i
$7$	−1.23179	−	2.13352i	−0.465572	−	0.806394i	0.533656	−	0.845702i	$-0.320818\pi$
$7$	−1.23179	−	2.13352i	−0.465572	−	0.806394i	−0.999227	+	0.0393083i	$0.987485\pi$
$8$	−0.268505			−0.0949309
$9$	−2.77936	−	1.12923i	−0.926453	−	0.376412i
$10$	−0.0672022			−0.0212512
$11$	−1.60607	−	2.78180i	−0.484249	−	0.838744i	0.515587	−	0.856837i	$-0.327574\pi$
$11$	−1.60607	−	2.78180i	−0.484249	−	0.838744i	−0.999836	+	0.0180933i	$0.994240\pi$
$12$	2.60628	+	2.27006i	0.752368	+	0.655311i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	−0.0827788	+	0.143377i	−0.0221236	+	0.0383191i
$15$	1.30609	+	1.13760i	0.337231	+	0.293727i
$16$	−1.98646	−	3.44065i	−0.496615	−	0.860163i
$17$	−4.77678			−1.15854			−0.579269	−	0.815136i	$-0.696662\pi$
$17$	−4.77678			−1.15854			−0.579269	+	0.815136i	$0.696662\pi$
$18$	0.0276694	+	0.199699i	0.00652173	+	0.0470695i
$19$	−3.94903			−0.905970			−0.452985	−	0.891518i	$-0.649641\pi$
$19$	−3.94903			−0.905970			−0.452985	+	0.891518i	$0.649641\pi$
$20$	−0.997742	−	1.72814i	−0.223102	−	0.386424i
$21$	4.03591	−	1.38528i	0.880708	−	0.302293i
$22$	−0.107932	+	0.186943i	−0.0230111	+	0.0398564i
$23$	−2.13489	+	3.69773i	−0.445154	+	0.771030i	−0.998063	−	0.0622118i	$-0.980185\pi$
$23$	−2.13489	+	3.69773i	−0.445154	+	0.771030i	0.552908	+	0.833242i	$0.313518\pi$
$24$	0.0891830	−	0.456434i	0.0182044	−	0.0931691i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.0672022			−0.0131794
$27$	2.84275	−	4.34957i	0.547087	−	0.837076i
$28$	−4.91602			−0.929040
$29$	1.15314	+	1.99730i	0.214133	+	0.370890i	0.953004	−	0.302957i	$-0.0979740\pi$
$29$	1.15314	+	1.99730i	0.214133	+	0.370890i	−0.738871	+	0.673847i	$0.764641\pi$
$30$	0.0223210	−	0.114237i	0.00407523	−	0.0208568i
$31$	3.81652	−	6.61041i	0.685468	−	1.18726i	−0.287822	−	0.957684i	$-0.592931\pi$
$31$	3.81652	−	6.61041i	0.685468	−	1.18726i	0.973290	−	0.229581i	$-0.0737356\pi$
$32$	−0.402000	+	0.696284i	−0.0710642	+	0.123087i
$33$	5.26224	−	1.80621i	0.916039	−	0.314420i
$34$	0.160505	+	0.278003i	0.0275264	+	0.0476771i
$35$	−2.46357			−0.416420
$36$	−4.72456	+	3.67643i	−0.787426	+	0.612739i
$37$	4.87293			0.801105			0.400553	−	0.916274i	$-0.368818\pi$
$37$	4.87293			0.801105			0.400553	+	0.916274i	$0.368818\pi$
$38$	0.132692	+	0.229829i	0.0215255	+	0.0372832i
$39$	1.30609	+	1.13760i	0.209142	+	0.182162i
$40$	−0.134253	+	0.232532i	−0.0212272	+	0.0367666i
$41$	1.26518	−	2.19136i	0.197588	−	0.342233i	−0.750158	−	0.661259i	$-0.770022\pi$
$41$	1.26518	−	2.19136i	0.197588	−	0.342233i	0.947746	+	0.319026i	$0.103356\pi$
$42$	−0.216233	−	0.188338i	−0.0333654	−	0.0290612i
$43$	2.28304	+	3.95433i	0.348160	+	0.603030i	0.985923	−	0.167202i	$-0.0534734\pi$
$43$	2.28304	+	3.95433i	0.348160	+	0.603030i	−0.637763	+	0.770233i	$0.720140\pi$
$44$	−6.40978			−0.966311
$45$	−2.36762	+	1.84238i	−0.352945	+	0.274645i
$46$	0.286938			0.0423067
$47$	3.13284	+	5.42623i	0.456971	+	0.791497i	0.998799	−	0.0489922i	$-0.0156009\pi$
$47$	3.13284	+	5.42623i	0.456971	+	0.791497i	−0.541828	+	0.840489i	$0.682268\pi$
$48$	6.50858	−	2.23400i	0.939433	−	0.322450i
$49$	0.465404	−	0.806103i	0.0664863	−	0.115158i
$50$	−0.0336011	+	0.0581988i	−0.00475191	+	0.00823055i
$51$	1.58659	−	8.12007i	0.222167	−	1.13704i
$52$	−0.997742	−	1.72814i	−0.138362	−	0.239650i
$53$	12.4968			1.71657			0.858286	−	0.513172i	$-0.171530\pi$
$53$	12.4968			1.71657			0.858286	+	0.513172i	$0.171530\pi$
$54$	−0.348659	−	0.0192939i	−0.0474465	−	0.00262557i
$55$	−3.21214			−0.433125
$56$	0.330741	+	0.572861i	0.0441971	+	0.0765517i
$57$	1.31166	−	6.71298i	0.173733	−	0.889156i
$58$	0.0774937	−	0.134223i	0.0101754	−	0.0176244i
$59$	−1.42509	+	2.46833i	−0.185531	+	0.321350i	−0.943755	−	0.330644i	$-0.892734\pi$
$59$	−1.42509	+	2.46833i	−0.185531	+	0.321350i	0.758224	+	0.651994i	$0.226067\pi$
$60$	3.26907	−	1.12207i	0.422035	−	0.144859i
$61$	−6.35000	−	10.9985i	−0.813034	−	1.40822i	−0.910731	−	0.413000i	$-0.864481\pi$
$61$	−6.35000	−	10.9985i	−0.813034	−	1.40822i	0.0976967	−	0.995216i	$-0.468852\pi$
$62$	−0.512957			−0.0651457
$63$	1.01433	+	7.32078i	0.127794	+	0.922332i
$64$	−7.89182			−0.986477
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$	−0.281936	−	0.245566i	−0.0347040	−	0.0302271i
$67$	6.75359	−	11.6976i	0.825082	−	1.42908i	−0.0767741	−	0.997049i	$-0.524462\pi$
$67$	6.75359	−	11.6976i	0.825082	−	1.42908i	0.901856	−	0.432036i	$-0.142205\pi$
$68$	−4.76599	+	8.25494i	−0.577961	+	1.00106i
$69$	−5.57670	−	4.85729i	−0.671356	−	0.584749i
$70$	0.0827788	+	0.143377i	0.00989395	+	0.0171368i
$71$	7.79224			0.924769			0.462384	−	0.886680i	$-0.346994\pi$
$71$	7.79224			0.924769			0.462384	+	0.886680i	$0.346994\pi$
$72$	0.746272	+	0.303205i	0.0879490	+	0.0357331i
$73$	2.26796			0.265444			0.132722	−	0.991153i	$-0.457628\pi$
$73$	2.26796			0.265444			0.132722	+	0.991153i	$0.457628\pi$
$74$	−0.163736	−	0.283599i	−0.0190339	−	0.0329677i
$75$	1.63823	−	0.562306i	0.189167	−	0.0649295i
$76$	−3.94012	+	6.82448i	−0.451962	+	0.782822i
$77$	−3.95668	+	6.85316i	−0.450905	+	0.780990i
$78$	0.0223210	−	0.114237i	0.00252735	−	0.0129348i
$79$	−4.56668	−	7.90972i	−0.513791	−	0.889913i	−0.999872	−	0.0159988i	$-0.994907\pi$
$79$	−4.56668	−	7.90972i	−0.513791	−	0.889913i	0.486081	−	0.873914i	$-0.338426\pi$
$80$	−3.97292			−0.444186
$81$	6.44966	+	6.27709i	0.716629	+	0.697455i
$82$	−0.170046			−0.0187784
$83$	−5.25595	−	9.10356i	−0.576915	−	0.999246i	−0.995831	−	0.0912209i	$-0.970923\pi$
$83$	−5.25595	−	9.10356i	−0.576915	−	0.999246i	0.418916	−	0.908025i	$-0.362410\pi$
$84$	1.63284	−	8.35677i	0.178157	−	0.911798i
$85$	−2.38839	+	4.13681i	−0.259057	+	0.448700i
$86$	0.153425	−	0.265740i	0.0165442	−	0.0286555i
$87$	−3.77824	+	1.29684i	−0.405070	+	0.139036i
$88$	0.431239	+	0.746927i	0.0459702	+	0.0796227i
$89$	0.966612			0.102461			0.0512303	−	0.998687i	$-0.483686\pi$
$89$	0.966612			0.102461			0.0512303	+	0.998687i	$0.483686\pi$
$90$	0.186779	+	0.0758870i	0.0196882	+	0.00799920i
$91$	−2.46357			−0.258253
$92$	4.26013	+	7.37876i	0.444149	+	0.769289i
$93$	9.96943	+	8.68335i	1.03378	+	0.900422i
$94$	0.210533	−	0.364655i	0.0217149	−	0.0376113i
$95$	−1.97452	+	3.41996i	−0.202581	+	0.350881i
$96$	−1.05009	−	0.914630i	−0.107175	−	0.0933490i
$97$	9.39020	+	16.2643i	0.953431	+	1.65139i	0.737919	+	0.674889i	$0.235809\pi$
$97$	9.39020	+	16.2643i	0.953431	+	1.65139i	0.215511	+	0.976501i	$0.430858\pi$
$98$	−0.0625523			−0.00631874
$99$	1.32255	+	9.54524i	0.132921	+	0.959333i
$100$	−1.99548			−0.199548
$101$	9.27873	+	16.0712i	0.923268	+	1.59915i	0.794324	+	0.607495i	$0.207825\pi$
$101$	9.27873	+	16.0712i	0.923268	+	1.59915i	0.128944	+	0.991652i	$0.458841\pi$
$102$	−0.525890	+	0.180506i	−0.0520708	+	0.0178727i
$103$	−5.12815	+	8.88222i	−0.505292	+	0.875191i	0.494690	+	0.869070i	$0.335282\pi$
$103$	−5.12815	+	8.88222i	−0.505292	+	0.875191i	−0.999981	+	0.00612110i	$0.998052\pi$
$104$	−0.134253	+	0.232532i	−0.0131646	+	0.0228017i
$105$	0.818267	−	4.18784i	0.0798546	−	0.408691i
$106$	−0.419907	−	0.727300i	−0.0407850	−	0.0706417i
$107$	−13.3729			−1.29281			−0.646403	−	0.762996i	$-0.723727\pi$
$107$	−13.3729			−1.29281			−0.646403	+	0.762996i	$0.723727\pi$
$108$	−4.68035	−	9.25241i	−0.450367	−	0.890314i
$109$	−1.35788			−0.130061			−0.0650306	−	0.997883i	$-0.520715\pi$
$109$	−1.35788			−0.130061			−0.0650306	+	0.997883i	$0.520715\pi$
$110$	0.107932	+	0.186943i	0.0102909	+	0.0178243i
$111$	−1.61853	+	8.28353i	−0.153624	+	0.786238i
$112$	−4.89379	+	8.47630i	−0.462420	+	0.800935i
$113$	3.67848	−	6.37132i	0.346042	−	0.599363i	−0.639500	−	0.768791i	$-0.720859\pi$
$113$	3.67848	−	6.37132i	0.346042	−	0.599363i	0.985543	+	0.169428i	$0.0541920\pi$
$114$	−0.434761	+	0.149227i	−0.0407191	+	0.0139764i
$115$	2.13489	+	3.69773i	0.199079	+	0.344815i
$116$	4.60216			0.427300
$117$	−2.36762	+	1.84238i	−0.218887	+	0.170328i
$118$	0.191539			0.0176326
$119$	5.88397	+	10.1913i	0.539383	+	0.934238i
$120$	−0.350692	−	0.305452i	−0.0320136	−	0.0278838i
$121$	0.341067	−	0.590745i	0.0310061	−	0.0537041i
$122$	−0.426734	+	0.739125i	−0.0386347	+	0.0669172i
$123$	3.30488	+	2.87854i	0.297991	+	0.259549i
$124$	−7.61581	−	13.1910i	−0.683920	−	1.18458i
$125$	−1.00000			−0.0894427
$126$	0.391978	−	0.305019i	0.0349202	−	0.0271733i
$127$	−5.97693			−0.530367			−0.265183	−	0.964198i	$-0.585433\pi$
$127$	−5.97693			−0.530367			−0.265183	+	0.964198i	$0.585433\pi$
$128$	1.06917	+	1.85186i	0.0945025	+	0.163683i
$129$	−7.48030	+	2.56753i	−0.658603	+	0.226058i
$130$	−0.0336011	+	0.0581988i	−0.00294701	+	0.00510437i
$131$	−8.93670	+	15.4788i	−0.780803	+	1.35239i	0.150672	+	0.988584i	$0.451856\pi$
$131$	−8.93670	+	15.4788i	−0.780803	+	1.35239i	−0.931475	+	0.363806i	$0.881477\pi$
$132$	2.12898	−	10.8960i	0.185304	−	0.948377i
$133$	4.86436	+	8.42533i	0.421794	+	0.730568i
$134$	−0.907712			−0.0784144
$135$	−2.34547	−	4.63668i	−0.201866	−	0.399062i
$136$	1.28259			0.109981
$137$	−5.24653	−	9.08726i	−0.448241	−	0.776377i	0.550030	−	0.835145i	$-0.314616\pi$
$137$	−5.24653	−	9.08726i	−0.448241	−	0.776377i	−0.998272	+	0.0587679i	$0.981283\pi$
$138$	−0.0953054	+	0.487768i	−0.00811293	+	0.0415215i
$139$	5.35343	−	9.27241i	0.454072	−	0.786475i	−0.544563	−	0.838720i	$-0.683304\pi$
$139$	5.35343	−	9.27241i	0.454072	−	0.786475i	0.998634	+	0.0522449i	$0.0166376\pi$
$140$	−2.45801	+	4.25740i	−0.207740	+	0.359816i
$141$	−10.2646	+	3.52322i	−0.864439	+	0.296709i
$142$	−0.261828	−	0.453499i	−0.0219721	−	0.0380568i
$143$	−3.21214			−0.268613
$144$	1.63578	+	11.8060i	0.136315	+	0.983832i
$145$	2.30629			0.191527
$146$	−0.0762058	−	0.131992i	−0.00630684	−	0.0109238i
$147$	1.21572	+	1.05889i	0.100271	+	0.0873355i
$148$	4.86193	−	8.42111i	0.399648	−	0.692211i
$149$	10.1595	−	17.5968i	0.832300	−	1.44159i	−0.0639091	−	0.997956i	$-0.520357\pi$
$149$	10.1595	−	17.5968i	0.832300	−	1.44159i	0.896210	−	0.443631i	$-0.146310\pi$
$150$	−0.0877720	−	0.0764492i	−0.00716655	−	0.00624205i
$151$	8.51099	+	14.7415i	0.692615	+	1.19964i	0.970978	+	0.239168i	$0.0768747\pi$
$151$	8.51099	+	14.7415i	0.692615	+	1.19964i	−0.278363	+	0.960476i	$0.589792\pi$
$152$	1.06034			0.0860046
$153$	13.2764	+	5.39410i	1.07333	+	0.436087i
$154$	0.531794			0.0428532
$155$	−3.81652	−	6.61041i	−0.306550	−	0.530961i
$156$	3.26907	−	1.12207i	0.261735	−	0.0898376i
$157$	0.653935	−	1.13265i	0.0521897	−	0.0903952i	−0.838750	−	0.544516i	$-0.816713\pi$
$157$	0.653935	−	1.13265i	0.0521897	−	0.0903952i	0.890940	+	0.454121i	$0.150047\pi$
$158$	−0.306891	+	0.531550i	−0.0244149	+	0.0422879i
$159$	−4.15078	+	21.2434i	−0.329178	+	1.68471i
$160$	0.402000	+	0.696284i	0.0317809	+	0.0550461i
$161$	10.5189			0.829005
$162$	0.148604	−	0.586280i	0.0116754	−	0.0460625i
$163$	−9.81120			−0.768473			−0.384236	−	0.923235i	$-0.625535\pi$
$163$	−9.81120			−0.768473			−0.384236	+	0.923235i	$0.625535\pi$
$164$	−2.52465	−	4.37282i	−0.197142	−	0.341460i
$165$	1.06690	−	5.46034i	0.0830582	−	0.425087i
$166$	−0.353211	+	0.611779i	−0.0274145	+	0.0474833i
$167$	−4.08745	+	7.07968i	−0.316297	+	0.547842i	−0.979712	−	0.200409i	$-0.935773\pi$
$167$	−4.08745	+	7.07968i	−0.316297	+	0.547842i	0.663416	+	0.748251i	$0.269106\pi$
$168$	−1.08366	+	0.371955i	−0.0836064	+	0.0286970i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	0.321010			0.0246203
$171$	10.9758	+	4.45938i	0.839338	+	0.341018i
$172$	9.11152			0.694747
$173$	3.19885	+	5.54058i	0.243204	+	0.421242i	0.961625	−	0.274366i	$-0.0884681\pi$
$173$	3.19885	+	5.54058i	0.243204	+	0.421242i	−0.718421	+	0.695609i	$0.755135\pi$
$174$	0.202427	+	0.176314i	0.0153460	+	0.0133663i
$175$	−1.23179	+	2.13352i	−0.0931143	+	0.161279i
$176$	−6.38080	+	11.0519i	−0.480971	+	0.833066i
$177$	−3.72260	−	3.24237i	−0.279807	−	0.243712i
$178$	−0.0324792	−	0.0562557i	−0.00243442	−	0.00421654i
$179$	−15.6316			−1.16836			−0.584180	−	0.811624i	$-0.698584\pi$
$179$	−15.6316			−1.16836			−0.584180	+	0.811624i	$0.698584\pi$
$180$	0.821607	+	5.92980i	0.0612389	+	0.441981i
$181$	11.1033			0.825299			0.412650	−	0.910890i	$-0.364603\pi$
$181$	11.1033			0.825299			0.412650	+	0.910890i	$0.364603\pi$
$182$	0.0827788	+	0.143377i	0.00613597	+	0.0106278i
$183$	20.8056	−	7.14128i	1.53799	−	0.527899i
$184$	0.573228	−	0.992860i	0.0422589	−	0.0731946i
$185$	2.43647	−	4.22008i	0.179133	−	0.310267i
$186$	0.170377	−	0.871979i	0.0124926	−	0.0639366i
$187$	7.67185	+	13.2880i	0.561021	+	0.971717i
$188$	12.5030			0.911878
$189$	−12.7815	−	0.707298i	−0.929721	−	0.0514484i
$190$	0.265384			0.0192530
$191$	−7.79123	−	13.4948i	−0.563753	−	0.976450i	−0.997164	−	0.0752533i	$-0.976023\pi$
$191$	−7.79123	−	13.4948i	−0.563753	−	0.976450i	0.433411	−	0.901196i	$-0.357310\pi$
$192$	2.62124	−	13.4153i	0.189172	−	0.968169i
$193$	9.34800	−	16.1912i	0.672884	−	1.16547i	−0.304199	−	0.952609i	$-0.598389\pi$
$193$	9.34800	−	16.1912i	0.672884	−	1.16547i	0.977083	−	0.212860i	$-0.0682780\pi$
$194$	0.631042	−	1.09300i	0.0453062	−	0.0784726i
$195$	1.63823	−	0.562306i	0.117316	−	0.0402675i
$196$	−0.928706	−	1.60857i	−0.0663362	−	0.114898i
$197$	−10.2024			−0.726893			−0.363447	−	0.931615i	$-0.618400\pi$
$197$	−10.2024			−0.726893			−0.363447	+	0.931615i	$0.618400\pi$
$198$	0.511083	−	0.397701i	0.0363211	−	0.0282634i
$199$	−16.4798			−1.16822			−0.584112	−	0.811673i	$-0.698557\pi$
$199$	−16.4798			−1.16822			−0.584112	+	0.811673i	$0.698557\pi$
$200$	0.134253	+	0.232532i	0.00949309	+	0.0164425i
$201$	17.6416	+	15.3658i	1.24434	+	1.08382i
$202$	0.623551	−	1.08002i	0.0438729	−	0.0759900i
$203$	2.84085	−	4.92050i	0.199389	−	0.345351i
$204$	−12.4496	−	10.8436i	−0.871647	−	0.759203i
$205$	−1.26518	−	2.19136i	−0.0883641	−	0.153051i
$206$	0.689246			0.0480220
$207$	10.1092	−	7.86653i	0.702639	−	0.546762i
$208$	−3.97292			−0.275473
$209$	6.34243	+	10.9854i	0.438715	+	0.759877i
$210$	−0.271222	+	0.0930939i	−0.0187161	+	0.00642409i
$211$	12.5991	−	21.8223i	0.867359	−	1.50231i	0.00267240	−	0.999996i	$-0.499149\pi$
$211$	12.5991	−	21.8223i	0.867359	−	1.50231i	0.864686	−	0.502313i	$-0.167517\pi$
$212$	12.4686	−	21.5963i	0.856348	−	1.48324i
$213$	−2.58816	+	13.2461i	−0.177338	+	0.907606i
$214$	0.449344	+	0.778286i	0.0307165	+	0.0532025i
$215$	4.56607			0.311403
$216$	−0.763292	+	1.16788i	−0.0519355	+	0.0794644i
$217$	−18.8046			−1.27654
$218$	0.0456262	+	0.0790270i	0.00309020	+	0.00535238i
$219$	−0.753293	+	3.85531i	−0.0509029	+	0.260518i
$220$	−3.20489	+	5.55103i	−0.216074	+	0.374251i
$221$	−2.38839	+	4.13681i	−0.160660	+	0.278272i
$222$	0.536476	−	0.184139i	0.0360059	−	0.0123586i
$223$	−3.79219	−	6.56827i	−0.253944	−	0.439844i	0.710664	−	0.703531i	$-0.248395\pi$
$223$	−3.79219	−	6.56827i	−0.253944	−	0.439844i	−0.964608	+	0.263688i	$0.915061\pi$
$224$	1.98071			0.132342
$225$	0.411733	+	2.97161i	0.0274489	+	0.198107i
$226$	−0.494404			−0.0328873
$227$	−0.150519	−	0.260706i	−0.00999028	−	0.0173037i	0.860987	−	0.508627i	$-0.169847\pi$
$227$	−0.150519	−	0.260706i	−0.00999028	−	0.0173037i	−0.870977	+	0.491323i	$0.836513\pi$
$228$	−10.2923	−	8.96455i	−0.681623	−	0.593692i
$229$	2.31658	−	4.01244i	0.153084	−	0.265149i	−0.779276	−	0.626681i	$-0.784413\pi$
$229$	2.31658	−	4.01244i	0.153084	−	0.265149i	0.932360	+	0.361532i	$0.117746\pi$
$230$	0.143469	−	0.248496i	0.00946007	−	0.0163853i
$231$	−10.3355	−	9.00223i	−0.680028	−	0.592303i
$232$	−0.309625	−	0.536286i	−0.0203279	−	0.0352089i
$233$	5.62440			0.368466			0.184233	−	0.982883i	$-0.441020\pi$
$233$	5.62440			0.368466			0.184233	+	0.982883i	$0.441020\pi$
$234$	0.186779	+	0.0758870i	0.0122101	+	0.00496089i
$235$	6.26567			0.408727
$236$	2.84375	+	4.92552i	0.185112	+	0.320624i
$237$	14.9626	−	5.13574i	0.971924	−	0.333602i
$238$	0.395416	−	0.684880i	0.0256310	−	0.0443942i
$239$	−1.28093	+	2.21863i	−0.0828562	+	0.143511i	−0.904476	−	0.426525i	$-0.859738\pi$
$239$	−1.28093	+	2.21863i	−0.0828562	+	0.143511i	0.821619	+	0.570036i	$0.193071\pi$
$240$	1.31959	−	6.75359i	0.0851793	−	0.435943i
$241$	7.49149	+	12.9756i	0.482569	+	0.835835i	0.999800	−	0.0200114i	$-0.00637025\pi$
$241$	7.49149	+	12.9756i	0.482569	+	0.835835i	−0.517230	+	0.855846i	$0.673037\pi$
$242$	−0.0458409			−0.00294676
$243$	−12.8127	+	8.87890i	−0.821935	+	0.569582i
$244$	−25.3426			−1.62240
$245$	−0.465404	−	0.806103i	−0.0297336	−	0.0515001i
$246$	0.0564801	−	0.289062i	0.00360104	−	0.0184299i
$247$	−1.97452	+	3.41996i	−0.125635	+	0.217607i
$248$	−1.02476	+	1.77493i	−0.0650721	+	0.112708i
$249$	17.2209	−	5.91090i	1.09133	−	0.374588i
$250$	0.0336011	+	0.0581988i	0.00212512	+	0.00368082i
$251$	−7.27387			−0.459123			−0.229561	−	0.973294i	$-0.573729\pi$
$251$	−7.27387			−0.459123			−0.229561	+	0.973294i	$0.573729\pi$
$252$	13.6634	+	5.55134i	0.860712	+	0.349702i
$253$	13.7151			0.862262
$254$	0.200831	+	0.347850i	0.0126013	+	0.0218261i
$255$	−6.23889	−	5.43406i	−0.390695	−	0.340294i
$256$	−7.81997	+	13.5446i	−0.488748	+	0.846536i
$257$	4.53307	−	7.85150i	0.282765	−	0.489763i	−0.689300	−	0.724476i	$-0.742082\pi$
$257$	4.53307	−	7.85150i	0.282765	−	0.489763i	0.972065	+	0.234713i	$0.0754150\pi$
$258$	0.400773	+	0.349073i	0.0249510	+	0.0217323i
$259$	−6.00241	−	10.3965i	−0.372972	−	0.646006i
$260$	−1.99548			−0.123755
$261$	−0.949574	−	6.85339i	−0.0587772	−	0.424214i
$262$	1.20113			0.0742061
$263$	−13.7692	−	23.8490i	−0.849045	−	1.47059i	−0.882061	−	0.471135i	$-0.843844\pi$
$263$	−13.7692	−	23.8490i	−0.849045	−	1.47059i	0.0330158	−	0.999455i	$-0.489489\pi$
$264$	−1.41294	+	0.484976i	−0.0869605	+	0.0298482i
$265$	6.24841	−	10.8226i	0.383837	−	0.664825i
$266$	0.326896	−	0.566200i	0.0200433	−	0.0347160i
$267$	−0.321057	+	1.64315i	−0.0196483	+	0.100559i
$268$	−13.4767	−	23.3423i	−0.823219	−	1.42586i
$269$	−6.82403			−0.416069			−0.208034	−	0.978122i	$-0.566707\pi$
$269$	−6.82403			−0.416069			−0.208034	+	0.978122i	$0.566707\pi$
$270$	−0.191039	+	0.292301i	−0.0116262	+	0.0177889i
$271$	1.91734			0.116470			0.0582352	−	0.998303i	$-0.481453\pi$
$271$	1.91734			0.116470			0.0582352	+	0.998303i	$0.481453\pi$
$272$	9.48889	+	16.4352i	0.575348	+	0.996532i
$273$	0.818267	−	4.18784i	0.0495237	−	0.253460i
$274$	−0.352578	+	0.610684i	−0.0213000	+	0.0368927i
$275$	−1.60607	+	2.78180i	−0.0968498	+	0.167749i
$276$	−13.9582	+	4.79099i	−0.840184	+	0.288384i
$277$	13.6495	+	23.6416i	0.820119	+	1.42049i	0.905593	+	0.424148i	$0.139426\pi$
$277$	13.6495	+	23.6416i	0.820119	+	1.42049i	−0.0854740	+	0.996340i	$0.527240\pi$
$278$	−0.719524			−0.0431542
$279$	−18.0722	+	14.0629i	−1.08195	+	0.841927i
$280$	0.661482			0.0395311
$281$	0.328412	+	0.568826i	0.0195914	+	0.0339333i	0.875655	−	0.482937i	$-0.160430\pi$
$281$	0.328412	+	0.568826i	0.0195914	+	0.0339333i	−0.856063	+	0.516871i	$0.827097\pi$
$282$	0.549950	+	0.479006i	0.0327491	+	0.0285244i
$283$	2.50989	−	4.34726i	0.149198	−	0.258418i	−0.781734	−	0.623613i	$-0.785664\pi$
$283$	2.50989	−	4.34726i	0.149198	−	0.258418i	0.930931	+	0.365195i	$0.118998\pi$
$284$	7.77464	−	13.4661i	0.461340	−	0.799065i
$285$	−5.15778	−	4.49242i	−0.305521	−	0.266108i
$286$	0.107932	+	0.186943i	0.00638213	+	0.0110542i
$287$	−6.23373			−0.367966
$288$	1.90357	−	1.48127i	0.112169	−	0.0872847i
$289$	5.81760			0.342212
$290$	−0.0774937	−	0.134223i	−0.00455059	−	0.00788185i
$291$	−30.7667	+	10.5603i	−1.80358	+	0.619057i
$292$	2.26284	−	3.91935i	0.132422	−	0.229362i
$293$	6.11183	−	10.5860i	0.357057	−	0.618441i	−0.630411	−	0.776262i	$-0.717113\pi$
$293$	6.11183	−	10.5860i	0.357057	−	0.618441i	0.987468	+	0.157821i	$0.0504468\pi$
$294$	0.0207765	−	0.106333i	0.00121171	−	0.00620147i
$295$	1.42509	+	2.46833i	0.0829722	+	0.143712i
$296$	−1.30841			−0.0760497
$297$	−16.6653	−	0.922214i	−0.967018	−	0.0535123i
$298$	−1.36548			−0.0791004
$299$	2.13489	+	3.69773i	0.123464	+	0.213845i
$300$	0.662793	−	3.39213i	0.0382663	−	0.195845i
$301$	5.62443	−	9.74179i	0.324186	−	0.561507i
$302$	0.571957	−	0.990659i	0.0329124	−	0.0570060i
$303$	−30.4015	+	10.4350i	−1.74652	+	0.599473i
$304$	7.84460	+	13.5872i	0.449919	+	0.779282i
$305$	−12.7000			−0.727200
$306$	−0.132170	−	0.953917i	−0.00755568	−	0.0545318i
$307$	−1.01733			−0.0580619			−0.0290309	−	0.999579i	$-0.509242\pi$
$307$	−1.01733			−0.0580619			−0.0290309	+	0.999579i	$0.509242\pi$
$308$	7.89548	+	13.6754i	0.449887	+	0.779227i
$309$	−13.3956	−	11.6676i	−0.762051	−	0.663745i
$310$	−0.256479	+	0.444234i	−0.0145670	+	0.0252308i
$311$	11.1446	−	19.3030i	0.631952	−	1.09457i	−0.355200	−	0.934790i	$-0.615587\pi$
$311$	11.1446	−	19.3030i	0.631952	−	1.09457i	0.987152	−	0.159783i	$-0.0510793\pi$
$312$	−0.350692	−	0.305452i	−0.0198540	−	0.0172928i
$313$	11.8874	+	20.5896i	0.671915	+	1.16379i	0.977360	+	0.211581i	$0.0678613\pi$
$313$	11.8874	+	20.5896i	0.671915	+	1.16379i	−0.305445	+	0.952210i	$0.598805\pi$
$314$	−0.0878917			−0.00496001
$315$	6.84715	+	2.78195i	0.385793	+	0.156745i
$316$	−18.2255			−1.02526
$317$	−14.0187	−	24.2810i	−0.787366	−	1.36376i	−0.927575	−	0.373637i	$-0.878111\pi$
$317$	−14.0187	−	24.2810i	−0.787366	−	1.36376i	0.140209	−	0.990122i	$-0.455223\pi$
$318$	1.37581	−	0.472232i	0.0771517	−	0.0264815i
$319$	3.70406	−	6.41562i	0.207388	−	0.359206i
$320$	−3.94591	+	6.83451i	−0.220583	+	0.382061i
$321$	4.44175	−	22.7326i	0.247915	−	1.26881i
$322$	−0.353446	−	0.612187i	−0.0196968	−	0.0341159i
$323$	18.8636			1.04960
$324$	17.2828	−	4.88299i	0.960155	−	0.271277i
$325$	−1.00000			−0.0554700
$326$	0.329667	+	0.571000i	0.0182586	+	0.0316248i
$327$	0.451015	−	2.30827i	0.0249412	−	0.127647i
$328$	−0.339708	+	0.588391i	−0.0187572	+	0.0324885i
$329$	7.71797	−	13.3679i	0.425505	−	0.736997i
$330$	−0.353634	+	0.121381i	−0.0194669	+	0.00668181i
$331$	8.93018	+	15.4675i	0.490847	+	0.850172i	0.999944	−	0.0105370i	$-0.00335410\pi$
$331$	8.93018	+	15.4675i	0.490847	+	0.850172i	−0.509098	+	0.860709i	$0.670021\pi$
$332$	−20.9763			−1.15122
$333$	−13.5436	−	5.50269i	−0.742186	−	0.301545i
$334$	0.549372			0.0300603
$335$	−6.75359	−	11.6976i	−0.368988	−	0.639106i
$336$	−12.7835	−	11.1344i	−0.697395	−	0.607429i
$337$	−4.88581	+	8.46246i	−0.266147	+	0.460980i	−0.967863	−	0.251476i	$-0.919084\pi$
$337$	−4.88581	+	8.46246i	−0.266147	+	0.460980i	0.701717	+	0.712456i	$0.252417\pi$
$338$	−0.0336011	+	0.0581988i	−0.00182766	+	0.00316560i
$339$	9.60884	+	8.36928i	0.521881	+	0.454557i
$340$	4.76599	+	8.25494i	0.258472	+	0.447687i
$341$	−24.5184			−1.32775
$342$	−0.109267	−	0.788617i	−0.00590849	−	0.0426435i
$343$	−19.5381			−1.05496
$344$	−0.613007	−	1.06176i	−0.0330511	−	0.0572462i
$345$	−6.99489	+	2.40092i	−0.376592	+	0.129261i
$346$	0.214970	−	0.372339i	0.0115569	−	0.0200171i
$347$	−10.5073	+	18.1991i	−0.564059	+	0.976978i	0.433078	+	0.901357i	$0.357428\pi$
$347$	−10.5073	+	18.1991i	−0.564059	+	0.976978i	−0.997137	+	0.0756219i	$0.975906\pi$
$348$	−1.52859	+	7.82323i	−0.0819410	+	0.419369i
$349$	4.61976	+	8.00166i	0.247290	+	0.428319i	0.962773	−	0.270311i	$-0.0871266\pi$
$349$	4.61976	+	8.00166i	0.247290	+	0.428319i	−0.715483	+	0.698630i	$0.753793\pi$
$350$	0.165558			0.00884942
$351$	−2.34547	−	4.63668i	−0.125192	−	0.247488i
$352$	2.58256			0.137651
$353$	−2.25362	−	3.90339i	−0.119948	−	0.207756i	0.799799	−	0.600268i	$-0.204940\pi$
$353$	−2.25362	−	3.90339i	−0.119948	−	0.207756i	−0.919747	+	0.392512i	$0.871606\pi$
$354$	−0.0636189	+	0.325598i	−0.00338131	+	0.0173053i
$355$	3.89612	−	6.74828i	0.206785	−	0.358161i
$356$	0.964429	−	1.67044i	0.0511146	−	0.0885332i
$357$	−19.2786	+	6.61718i	−1.02033	+	0.350218i
$358$	0.525239	+	0.909741i	0.0277597	+	0.0480813i
$359$	25.2752			1.33397			0.666986	−	0.745070i	$-0.267584\pi$
$359$	25.2752			1.33397			0.666986	+	0.745070i	$0.267584\pi$
$360$	0.635720	−	0.494688i	0.0335054	−	0.0260723i
$361$	−3.40514			−0.179218
$362$	−0.373082	−	0.646197i	−0.0196087	−	0.0339633i
$363$	0.890927	+	0.775995i	0.0467615	+	0.0407292i
$364$	−2.45801	+	4.25740i	−0.128835	+	0.223148i
$365$	1.13398	−	1.96411i	0.0593551	−	0.102806i
$366$	−1.11470	−	0.970905i	−0.0582665	−	0.0507500i
$367$	5.55336	+	9.61871i	0.289883	+	0.502092i	0.973782	−	0.227485i	$-0.0730502\pi$
$367$	5.55336	+	9.61871i	0.289883	+	0.502092i	−0.683898	+	0.729577i	$0.739717\pi$
$368$	16.9635			0.884282
$369$	−5.99095	+	4.66188i	−0.311876	+	0.242688i
$370$	−0.327472			−0.0170244
$371$	−15.3934	−	26.6622i	−0.799187	−	1.38423i
$372$	24.9530	−	8.56483i	1.29375	−	0.444066i
$373$	3.86823	−	6.69997i	0.200289	−	0.346911i	−0.748332	−	0.663324i	$-0.769145\pi$
$373$	3.86823	−	6.69997i	0.200289	−	0.346911i	0.948622	+	0.316413i	$0.102478\pi$
$374$	0.515565	−	0.892985i	0.0266592	−	0.0461751i
$375$	0.332146	−	1.69991i	0.0171520	−	0.0877827i
$376$	−0.841183	−	1.45697i	−0.0433807	−	0.0751376i
$377$	2.30629			0.118780
$378$	0.388310	+	0.767637i	0.0199725	+	0.0394830i
$379$	26.0870			1.34000			0.669999	−	0.742362i	$-0.266295\pi$
$379$	26.0870			1.34000			0.669999	+	0.742362i	$0.266295\pi$
$380$	3.94012	+	6.82448i	0.202124	+	0.350088i
$381$	1.98522	−	10.1602i	0.101706	−	0.520524i
$382$	−0.523588	+	0.906880i	−0.0267891	+	0.0464000i
$383$	0.421284	−	0.729686i	0.0215266	−	0.0372852i	−0.855061	−	0.518527i	$-0.826481\pi$
$383$	0.421284	−	0.729686i	0.0215266	−	0.0372852i	0.876588	+	0.481242i	$0.159814\pi$
$384$	−3.50311	+	1.20240i	−0.178768	+	0.0613599i
$385$	3.95668	+	6.85316i	0.201651	+	0.349269i
$386$	−1.25641			−0.0639497
$387$	−1.88000	−	13.5686i	−0.0955659	−	0.689730i
$388$	37.4760			1.90256
$389$	4.37726	+	7.58163i	0.221936	+	0.384404i	0.955396	−	0.295329i	$-0.0954291\pi$
$389$	4.37726	+	7.58163i	0.221936	+	0.384404i	−0.733460	+	0.679733i	$0.762096\pi$
$390$	−0.0877720	−	0.0764492i	−0.00444451	−	0.00387116i
$391$	10.1979	−	17.6632i	0.515729	−	0.893268i
$392$	−0.124963	+	0.216443i	−0.00631161	+	0.0109320i
$393$	−23.3442	−	20.3328i	−1.17756	−	1.02565i
$394$	0.342813	+	0.593769i	0.0172707	+	0.0299137i
$395$	−9.13335			−0.459549
$396$	17.8151	+	7.23815i	0.895241	+	0.363731i
$397$	−6.72904			−0.337721			−0.168860	−	0.985640i	$-0.554009\pi$
$397$	−6.72904			−0.337721			−0.168860	+	0.985640i	$0.554009\pi$
$398$	0.553740	+	0.959106i	0.0277565	+	0.0480757i
$399$	−15.9379	+	5.47052i	−0.797895	+	0.273869i
$400$	−1.98646	+	3.44065i	−0.0993231	+	0.172033i
$401$	14.4471	−	25.0231i	0.721453	−	1.24959i	−0.238964	−	0.971028i	$-0.576808\pi$
$401$	14.4471	−	25.0231i	0.721453	−	1.24959i	0.960417	−	0.278565i	$-0.0898589\pi$
$402$	0.301493	−	1.54302i	0.0150371	−	0.0769591i
$403$	−3.81652	−	6.61041i	−0.190115	−	0.329288i
$404$	37.0311			1.84237
$405$	8.66095	−	2.44702i	0.430366	−	0.121593i
$406$	−0.381823			−0.0189496
$407$	−7.82628	−	13.5555i	−0.387934	−	0.671922i
$408$	−0.426007	+	2.18028i	−0.0210905	+	0.107940i
$409$	9.19426	−	15.9249i	0.454627	−	0.787437i	−0.544040	−	0.839059i	$-0.683106\pi$
$409$	9.19426	−	15.9249i	0.454627	−	0.787437i	0.998667	+	0.0516225i	$0.0164392\pi$
$410$	−0.0850230	+	0.147264i	−0.00419898	+	0.00727285i
$411$	17.1901	−	5.90031i	0.847925	−	0.291041i
$412$	10.2331	+	17.7243i	0.504151	+	0.873215i
$413$	7.02164			0.345513
$414$	−0.797503	−	0.324020i	−0.0391952	−	0.0159247i
$415$	−10.5119			−0.516008
$416$	0.402000	+	0.696284i	0.0197097	+	0.0341381i
$417$	13.9841	+	12.1801i	0.684804	+	0.596463i
$418$	0.426225	−	0.738244i	0.0208474	−	0.0361087i
$419$	12.6003	−	21.8244i	0.615567	−	1.06619i	−0.374718	−	0.927139i	$-0.622261\pi$
$419$	12.6003	−	21.8244i	0.615567	−	1.06619i	0.990285	−	0.139054i	$-0.0444061\pi$
$420$	−6.42076	−	5.59246i	−0.313301	−	0.272884i
$421$	8.93227	+	15.4711i	0.435332	+	0.754017i	0.997323	−	0.0731263i	$-0.0232976\pi$
$421$	8.93227	+	15.4711i	0.435332	+	0.754017i	−0.561991	+	0.827144i	$0.689964\pi$
$422$	−1.69338			−0.0824322
$423$	−2.57978	−	18.6191i	−0.125433	−	0.905294i
$424$	−3.35546			−0.162956
$425$	2.38839	+	4.13681i	0.115854	+	0.200665i
$426$	0.857870	−	0.294454i	0.0415640	−	0.0142664i
$427$	−15.6437	+	27.0957i	−0.757051	+	1.31125i
$428$	−13.3427	+	23.1102i	−0.644943	+	1.11707i
$429$	1.06690	−	5.46034i	0.0515105	−	0.263628i
$430$	−0.153425	−	0.265740i	−0.00739881	−	0.0128151i
$431$	28.4290			1.36937			0.684687	−	0.728837i	$-0.259939\pi$
$431$	28.4290			1.36937			0.684687	+	0.728837i	$0.259939\pi$
$432$	−20.6124	−	1.14064i	−0.991714	−	0.0548789i
$433$	−20.4163			−0.981146			−0.490573	−	0.871400i	$-0.663212\pi$
$433$	−20.4163			−0.981146			−0.490573	+	0.871400i	$0.663212\pi$
$434$	0.631854	+	1.09440i	0.0303300	+	0.0525330i
$435$	−0.766024	+	3.92047i	−0.0367281	+	0.187972i
$436$	−1.35481	+	2.34661i	−0.0648838	+	0.112382i
$437$	8.43073	−	14.6025i	0.403297	−	0.698530i
$438$	0.249686	−	0.0857019i	0.0119305	−	0.00409500i
$439$	−4.91252	−	8.50874i	−0.234462	−	0.406100i	0.724654	−	0.689113i	$-0.241999\pi$
$439$	−4.91252	−	8.50874i	−0.234462	−	0.406100i	−0.959116	+	0.283013i	$0.908666\pi$
$440$	0.862477			0.0411170
$441$	−2.20380	+	1.71490i	−0.104943	+	0.0816619i
$442$	0.321010			0.0152689
$443$	9.82384	+	17.0154i	0.466745	+	0.808425i	0.999278	−	0.0379835i	$-0.0120934\pi$
$443$	9.82384	+	17.0154i	0.466745	+	0.808425i	−0.532534	+	0.846409i	$0.678760\pi$
$444$	12.7002	+	11.0619i	0.602726	+	0.524973i
$445$	0.483306	−	0.837110i	0.0229109	−	0.0396828i
$446$	−0.254844	+	0.441402i	−0.0120672	+	0.0209010i
$447$	26.5385	+	23.1149i	1.25523	+	1.09330i
$448$	9.72103	+	16.8373i	0.459276	+	0.795489i
$449$	27.3713			1.29173			0.645866	−	0.763451i	$-0.276496\pi$
$449$	27.3713			1.29173			0.645866	+	0.763451i	$0.276496\pi$
$450$	0.159110	−	0.123812i	0.00750050	−	0.00583654i
$451$	−8.12789			−0.382727
$452$	−7.34035	−	12.7139i	−0.345261	−	0.598010i
$453$	−27.8860	+	9.57156i	−1.31020	+	0.449711i
$454$	−0.0101152	+	0.0175200i	−0.000474729	+	0.000822255i
$455$	−1.23179	+	2.13352i	−0.0577470	+	0.100021i
$456$	−0.352187	+	1.80247i	−0.0164927	+	0.0844084i
$457$	12.2292	+	21.1815i	0.572056	+	0.990830i	0.996355	+	0.0853077i	$0.0271873\pi$
$457$	12.2292	+	21.1815i	0.572056	+	0.990830i	−0.424299	+	0.905522i	$0.639479\pi$
$458$	−0.311359			−0.0145488
$459$	−13.5792	+	20.7770i	−0.633821	+	0.969785i
$460$	8.52026			0.397259
$461$	−4.38036	−	7.58701i	−0.204014	−	0.353362i	0.745804	−	0.666165i	$-0.232065\pi$
$461$	−4.38036	−	7.58701i	−0.204014	−	0.353362i	−0.949818	+	0.312803i	$0.898732\pi$
$462$	−0.176634	+	0.904000i	−0.00821774	+	0.0420579i
$463$	−7.55160	+	13.0797i	−0.350952	+	0.607867i	−0.986417	−	0.164263i	$-0.947475\pi$
$463$	−7.55160	+	13.0797i	−0.350952	+	0.607867i	0.635464	+	0.772130i	$0.280809\pi$
$464$	4.58135	−	7.93513i	0.212684	−	0.368379i
$465$	12.5047	−	4.29210i	0.579892	−	0.199042i
$466$	−0.188986	−	0.327333i	−0.00875460	−	0.0151634i
$467$	−19.5484			−0.904591			−0.452296	−	0.891868i	$-0.649395\pi$
$467$	−19.5484			−0.904591			−0.452296	+	0.891868i	$0.649395\pi$
$468$	0.821607	+	5.92980i	0.0379788	+	0.274105i
$469$	−33.2759			−1.53654
$470$	−0.210533	−	0.364655i	−0.00971118	−	0.0168203i
$471$	1.70819	+	1.48783i	0.0787094	+	0.0685557i
$472$	0.382645	−	0.662761i	0.0176127	−	0.0305060i
$473$	7.33344	−	12.7019i	0.337192	−	0.584033i
$474$	−0.801653	−	0.698238i	−0.0368211	−	0.0320711i
$475$	1.97452	+	3.41996i	0.0905970	+	0.156919i
$476$	23.4827			1.07633
$477$	−34.7332	−	14.1119i	−1.59032	−	0.646137i
$478$	0.172162			0.00787451
$479$	−0.653565	−	1.13201i	−0.0298621	−	0.0517227i	0.850708	−	0.525638i	$-0.176173\pi$
$479$	−0.653565	−	1.13201i	−0.0298621	−	0.0517227i	−0.880570	+	0.473916i	$0.842840\pi$
$480$	−1.31714	+	0.452094i	−0.0601189	+	0.0206352i
$481$	2.43647	−	4.22008i	0.111093	−	0.192419i
$482$	0.503445	−	0.871992i	0.0229313	−	0.0397181i
$483$	−3.49381	+	17.8811i	−0.158974	+	0.813619i
$484$	−0.680593	−	1.17882i	−0.0309361	−	0.0535828i
$485$	18.7804			0.852774
$486$	0.947262	+	0.447343i	0.0429687	+	0.0202919i
$487$	30.3533			1.37544			0.687719	−	0.725977i	$-0.258612\pi$
$487$	30.3533			1.37544			0.687719	+	0.725977i	$0.258612\pi$
$488$	1.70501	+	2.95316i	0.0771821	+	0.133683i
$489$	3.25875	−	16.6781i	0.147366	−	0.754211i
$490$	−0.0312762	+	0.0541719i	−0.00141291	+	0.00244724i
$491$	−4.18858	+	7.25484i	−0.189028	+	0.327406i	−0.944926	−	0.327283i	$-0.893867\pi$
$491$	−4.18858	+	7.25484i	−0.189028	+	0.327406i	0.755898	+	0.654689i	$0.227200\pi$
$492$	8.27193	−	2.83925i	0.372928	−	0.128003i
$493$	−5.50831	−	9.54067i	−0.248082	−	0.429690i
$494$	0.265384			0.0119402
$495$	8.92770	+	3.62726i	0.401270	+	0.163033i
$496$	−30.3255			−1.36166
$497$	−9.59837	−	16.6249i	−0.430546	−	0.745727i
$498$	−0.922650	−	0.803626i	−0.0413449	−	0.0360113i
$499$	−6.43013	+	11.1373i	−0.287852	+	0.498574i	−0.973297	−	0.229550i	$-0.926274\pi$
$499$	−6.43013	+	11.1373i	−0.287852	+	0.498574i	0.685445	+	0.728125i	$0.259608\pi$
$500$	−0.997742	+	1.72814i	−0.0446204	+	0.0772848i
$501$	−10.6772	−	9.29977i	−0.477020	−	0.415483i
$502$	0.244410	+	0.423331i	0.0109086	+	0.0188942i
$503$	5.22447			0.232947			0.116474	−	0.993194i	$-0.462841\pi$
$503$	5.22447			0.232947			0.116474	+	0.993194i	$0.462841\pi$
$504$	−0.272354	−	1.96567i	−0.0121316	−	0.0875578i
$505$	18.5575			0.825796
$506$	−0.460843	−	0.798204i	−0.0204870	−	0.0354845i
$507$	1.63823	−	0.562306i	0.0727565	−	0.0249729i
$508$	−5.96344	+	10.3290i	−0.264585	+	0.458274i
$509$	−5.01119	+	8.67964i	−0.222117	+	0.384718i	−0.955451	−	0.295151i	$-0.904630\pi$
$509$	−5.01119	+	8.67964i	−0.222117	+	0.384718i	0.733334	+	0.679869i	$0.237963\pi$
$510$	−0.106622	+	0.545687i	−0.00472131	+	0.0241634i
$511$	−2.79364	−	4.83872i	−0.123583	−	0.214053i
$512$	5.32773			0.235455
$513$	−11.2261	+	17.1766i	−0.495644	+	0.758366i
$514$	−0.609264			−0.0268735
$515$	5.12815	+	8.88222i	0.225973	+	0.391397i
$516$	−3.02636	+	15.4887i	−0.133228	+	0.681853i
$517$	10.0631	−	17.4298i	0.442575	−	0.766563i
$518$	−0.403375	+	0.698667i	−0.0177233	+	0.0306976i
$519$	−10.4809	+	3.59747i	−0.460062	+	0.157911i
$520$	0.134253	+	0.232532i	0.00588737	+	0.0101972i
$521$	20.3192			0.890202			0.445101	−	0.895480i	$-0.353168\pi$
$521$	20.3192			0.890202			0.445101	+	0.895480i	$0.353168\pi$
$522$	−0.366952	+	0.285545i	−0.0160611	+	0.0124980i
$523$	−0.572523			−0.0250347			−0.0125173	−	0.999922i	$-0.503984\pi$
$523$	−0.572523			−0.0250347			−0.0125173	+	0.999922i	$0.503984\pi$
$524$	17.8330	+	30.8877i	0.779040	+	1.34934i
$525$	−3.21764	−	2.80256i	−0.140429	−	0.122314i
$526$	−0.925321	+	1.60270i	−0.0403459	+	0.0698811i
$527$	−18.2307	+	31.5765i	−0.794141	+	1.37549i
$528$	−16.6678	−	14.5176i	−0.725372	−	0.631797i
$529$	2.38452	+	4.13012i	0.103675	+	0.179570i
$530$	−0.839814			−0.0364792
$531$	6.74817	−	5.25112i	0.292846	−	0.227879i
$532$	19.4135			0.841683
$533$	−1.26518	−	2.19136i	−0.0548011	−	0.0949183i
$534$	0.106417	−	0.0365265i	0.00460512	−	0.00158066i
$535$	−6.68644	+	11.5813i	−0.289080	+	0.500702i
$536$	−1.81337	+	3.14086i	−0.0783258	+	0.135664i
$537$	5.19198	−	26.5723i	0.224050	−	1.14668i
$538$	0.229295	+	0.397151i	0.00988561	+	0.0171224i
$539$	−2.98989			−0.128784
$540$	−10.3530	−	0.572908i	−0.445522	−	0.0246541i
$541$	−23.5766			−1.01364			−0.506819	−	0.862052i	$-0.669179\pi$
$541$	−23.5766			−1.01364			−0.506819	+	0.862052i	$0.669179\pi$
$542$	−0.0644248	−	0.111587i	−0.00276728	−	0.00479308i
$543$	−3.68791	+	18.8745i	−0.158263	+	0.809982i
$544$	1.92026	−	3.32599i	0.0823306	−	0.142601i
$545$	−0.678940	+	1.17596i	−0.0290826	+	0.0503725i
$546$	−0.271222	+	0.0930939i	−0.0116072	+	0.00398405i
$547$	1.87854	+	3.25373i	0.0803205	+	0.139119i	0.903388	−	0.428825i	$-0.141072\pi$
$547$	1.87854	+	3.25373i	0.0803205	+	0.139119i	−0.823067	+	0.567944i	$0.807739\pi$
$548$	−20.9387			−0.894458
$549$	5.22901	+	37.7395i	0.223169	+	1.61068i
$550$	0.215863			0.00920443
$551$	−4.55380	−	7.88741i	−0.193998	−	0.336015i
$552$	1.49737	+	1.30421i	0.0637324	+	0.0555108i
$553$	−11.2503	+	19.4862i	−0.478413	+	0.828636i
$554$	0.917276	−	1.58877i	0.0389713	−	0.0675003i
$555$	6.36448	+	5.54345i	0.270157	+	0.235306i
$556$	−10.6827	−	18.5029i	−0.453046	−	0.784699i
$557$	−39.9225			−1.69157			−0.845785	−	0.533523i	$-0.820868\pi$
$557$	−39.9225			−1.69157			−0.845785	+	0.533523i	$0.820868\pi$
$558$	1.42569	+	0.579249i	0.0603544	+	0.0245216i
$559$	4.56607			0.193124
$560$	4.89379	+	8.47630i	0.206801	+	0.358189i
$561$	−25.1366	+	8.62785i	−1.06127	+	0.364268i
$562$	0.0220700	−	0.0382264i	0.000930967	−	0.00161248i
$563$	−16.7785	+	29.0612i	−0.707130	+	1.22478i	0.258788	+	0.965934i	$0.416677\pi$
$563$	−16.7785	+	29.0612i	−0.707130	+	1.22478i	−0.965917	+	0.258850i	$0.916656\pi$
$564$	−4.15284	+	21.2540i	−0.174866	+	0.894955i
$565$	−3.67848	−	6.37132i	−0.154755	−	0.268043i
$566$	−0.337340			−0.0141795
$567$	5.44768	−	21.4925i	0.228781	−	0.902600i
$568$	−2.09226			−0.0877892
$569$	−7.71687	−	13.3660i	−0.323508	−	0.560332i	0.657701	−	0.753279i	$-0.271529\pi$
$569$	−7.71687	−	13.3660i	−0.323508	−	0.560332i	−0.981209	+	0.192946i	$0.938196\pi$
$570$	−0.0881462	+	0.451127i	−0.00369204	+	0.0188956i
$571$	−19.9691	+	34.5875i	−0.835681	+	1.44744i	0.0577933	+	0.998329i	$0.481594\pi$
$571$	−19.9691	+	34.5875i	−0.835681	+	1.44744i	−0.893475	+	0.449114i	$0.851740\pi$
$572$	−3.20489	+	5.55103i	−0.134003	+	0.232100i
$573$	25.5277	−	8.76210i	1.06644	−	0.366042i
$574$	0.209460	+	0.362796i	0.00874270	+	0.0151428i
$575$	4.26977			0.178062
$576$	21.9342	+	8.91171i	0.913924	+	0.371321i
$577$	25.4359			1.05891			0.529455	−	0.848338i	$-0.322396\pi$
$577$	25.4359			1.05891			0.529455	+	0.848338i	$0.322396\pi$
$578$	−0.195478	−	0.338578i	−0.00813081	−	0.0140830i
$579$	24.4186	+	21.2686i	1.01480	+	0.883892i
$580$	2.30108	−	3.98558i	0.0955471	−	0.165492i
$581$	−12.9484	+	22.4273i	−0.537190	+	0.930441i
$582$	1.64839	+	1.43575i	0.0683281	+	0.0595136i
$583$	−20.0708	−	34.7637i	−0.831248	−	1.43976i
$584$	−0.608958			−0.0251989
$585$	0.411733	+	2.97161i	0.0170231	+	0.122861i
$586$	−0.821457			−0.0339341
$587$	20.4639	+	35.4446i	0.844637	+	1.46295i	0.885936	+	0.463807i	$0.153517\pi$
$587$	20.4639	+	35.4446i	0.844637	+	1.46295i	−0.0412991	+	0.999147i	$0.513150\pi$
$588$	3.04288	−	1.04443i	0.125486	−	0.0430717i
$589$	−15.0716	+	26.1047i	−0.621013	+	1.07563i
$590$	0.0957694	−	0.165877i	0.00394276	−	0.00682907i
$591$	3.38870	−	17.3432i	0.139393	−	0.713403i
$592$	−9.67990	−	16.7661i	−0.397841	−	0.689081i
$593$	−1.00808			−0.0413971			−0.0206985	−	0.999786i	$-0.506589\pi$
$593$	−1.00808			−0.0413971			−0.0206985	+	0.999786i	$0.506589\pi$
$594$	0.506300	+	1.00089i	0.0207738	+	0.0410669i
$595$	11.7679			0.482439
$596$	−20.2732	−	35.1141i	−0.830421	−	1.43833i
$597$	5.47371	−	28.0141i	0.224024	−	1.14654i
$598$	0.143469	−	0.248496i	0.00586688	−	0.0101617i
$599$	−0.939758	+	1.62771i	−0.0383975	+	0.0665064i	−0.884585	−	0.466378i	$-0.845559\pi$
$599$	−0.939758	+	1.62771i	−0.0383975	+	0.0665064i	0.846188	+	0.532884i	$0.178892\pi$
$600$	−0.439875	+	0.150982i	−0.0179578	+	0.00616382i
$601$	1.47264	+	2.55068i	0.0600702	+	0.104045i	0.894497	−	0.447075i	$-0.147534\pi$
$601$	1.47264	+	2.55068i	0.0600702	+	0.104045i	−0.834426	+	0.551119i	$0.814201\pi$
$602$	−0.755947			−0.0308101
$603$	−31.9799	+	24.8853i	−1.30232	+	1.01341i
$604$	33.9671			1.38210
$605$	−0.341067	−	0.590745i	−0.0138663	−	0.0240172i
$606$	1.62882	+	1.41870i	0.0661665	+	0.0576308i
$607$	−0.670347	+	1.16108i	−0.0272085	+	0.0471266i	−0.879309	−	0.476252i	$-0.841995\pi$
$607$	−0.670347	+	1.16108i	−0.0272085	+	0.0471266i	0.852101	+	0.523378i	$0.175328\pi$
$608$	1.58751	−	2.74965i	0.0643820	−	0.111513i
$609$	7.42081	+	6.46351i	0.300706	+	0.261914i
$610$	0.426734	+	0.739125i	0.0172780	+	0.0299263i
$611$	6.26567			0.253482
$612$	22.5682	−	17.5615i	0.912264	−	0.709882i
$613$	−20.1796			−0.815046			−0.407523	−	0.913195i	$-0.633607\pi$
$613$	−20.1796			−0.815046			−0.407523	+	0.913195i	$0.633607\pi$
$614$	0.0341833	+	0.0592072i	0.00137952	+	0.00238941i
$615$	4.14533	−	1.42284i	0.167156	−	0.0573743i
$616$	1.06239	−	1.84011i	0.0428048	−	0.0741402i
$617$	3.56739	−	6.17890i	0.143618	−	0.248753i	−0.785239	−	0.619193i	$-0.787460\pi$
$617$	3.56739	−	6.17890i	0.143618	−	0.248753i	0.928856	+	0.370440i	$0.120793\pi$
$618$	−0.228930	+	1.17165i	−0.00920893	+	0.0471308i
$619$	15.4477	+	26.7562i	0.620895	+	1.07542i	0.989319	+	0.145764i	$0.0465640\pi$
$619$	15.4477	+	26.7562i	0.620895	+	1.07542i	−0.368424	+	0.929658i	$0.620103\pi$
$620$	−15.2316			−0.611717
$621$	10.0146	+	19.7976i	0.401873	+	0.794448i
$622$	−1.49788			−0.0600596
$623$	−1.19066	−	2.06228i	−0.0477028	−	0.0826236i
$624$	1.31959	−	6.75359i	0.0528259	−	0.270360i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	0.798859	−	1.38366i	0.0319288	−	0.0553023i
$627$	−20.7808	+	7.13277i	−0.829904	+	0.284855i
$628$	−1.30492	−	2.26018i	−0.0520718	−	0.0901910i
$629$	−23.2769			−0.928112
$630$	−0.0681655	−	0.491973i	−0.00271578	−	0.0196007i
$631$	11.8799			0.472932			0.236466	−	0.971640i	$-0.424011\pi$
$631$	11.8799			0.472932			0.236466	+	0.971640i	$0.424011\pi$
$632$	1.22618	+	2.12380i	0.0487747	+	0.0844803i
$633$	32.9111	+	28.6655i	1.30810	+	1.13935i
$634$	−0.942085	+	1.63174i	−0.0374150	+	0.0648046i
$635$	−2.98847	+	5.17618i	−0.118594	+	0.205410i
$636$	32.5702	+	28.3686i	1.29149	+	1.12489i
$637$	−0.465404	−	0.806103i	−0.0184400	−	0.0319390i
$638$	−0.497842			−0.0197098
$639$	−21.6574	−	8.79926i	−0.856754	−	0.348094i
$640$	2.13835			0.0845256
$641$	−12.5654	−	21.7639i	−0.496302	−	0.859621i	0.503689	−	0.863885i	$-0.331976\pi$
$641$	−12.5654	−	21.7639i	−0.496302	−	0.859621i	−0.999991	+	0.00426452i	$0.998643\pi$
$642$	−1.47226	+	0.505337i	−0.0581055	+	0.0199441i
$643$	18.9486	−	32.8199i	0.747258	−	1.29429i	−0.201874	−	0.979411i	$-0.564703\pi$
$643$	18.9486	−	32.8199i	0.747258	−	1.29429i	0.949132	−	0.314877i	$-0.101963\pi$
$644$	10.4951	−	18.1781i	0.413567	−	0.716318i
$645$	−1.51660	+	7.76189i	−0.0597162	+	0.305624i
$646$	−0.633839	−	1.09784i	−0.0249381	−	0.0431940i
$647$	−5.59065			−0.219791			−0.109896	−	0.993943i	$-0.535052\pi$
$647$	−5.59065			−0.219791			−0.109896	+	0.993943i	$0.535052\pi$
$648$	−1.73177	−	1.68543i	−0.0680302	−	0.0662100i
$649$	9.15521			0.359373
$650$	0.0336011	+	0.0581988i	0.00131794	+	0.00228274i
$651$	6.24587	−	31.9660i	0.244795	−	1.25285i
$652$	−9.78905	+	16.9551i	−0.383369	+	0.664014i
$653$	4.29248	−	7.43479i	0.167978	−	0.290946i	−0.769731	−	0.638368i	$-0.779610\pi$
$653$	4.29248	−	7.43479i	0.167978	−	0.290946i	0.937709	+	0.347422i	$0.112943\pi$
$654$	−0.149493	+	0.0513118i	−0.00584564	+	0.00200645i
$655$	8.93670	+	15.4788i	0.349186	+	0.604807i
$656$	−10.0529			−0.392501
$657$	−6.30346	−	2.56106i	−0.245922	−	0.0999163i
$658$	−1.03733			−0.0404393
$659$	9.85987	+	17.0778i	0.384086	+	0.665257i	0.991642	−	0.129020i	$-0.0411832\pi$
$659$	9.85987	+	17.0778i	0.384086	+	0.665257i	−0.607556	+	0.794277i	$0.707850\pi$
$660$	−8.37174	−	7.29177i	−0.325870	−	0.283832i
$661$	−17.6742	+	30.6127i	−0.687448	+	1.19069i	0.285213	+	0.958464i	$0.407936\pi$
$661$	−17.6742	+	30.6127i	−0.687448	+	1.19069i	−0.972661	+	0.232230i	$0.925398\pi$
$662$	0.600127	−	1.03945i	0.0233246	−	0.0403994i
$663$	−6.23889	−	5.43406i	−0.242299	−	0.211041i
$664$	1.41125	+	2.44436i	0.0547671	+	0.0948594i
$665$	9.72873			0.377264
$666$	0.134831	+	0.973119i	0.00522459	+	0.0377076i
$667$	−9.84732			−0.381290
$668$	8.15645	+	14.1274i	0.315582	+	0.546605i
$669$	12.4250	−	4.26474i	0.480378	−	0.164884i
$670$	−0.453856	+	0.786102i	−0.0175340	+	0.0303698i
$671$	−20.3971	+	35.3288i	−0.787422	+	1.36385i
$672$	−0.657886	+	3.36702i	−0.0253785	+	0.129886i
$673$	−8.53274	−	14.7791i	−0.328913	−	0.569694i	0.653383	−	0.757027i	$-0.273349\pi$
$673$	−8.53274	−	14.7791i	−0.328913	−	0.569694i	−0.982296	+	0.187333i	$0.940016\pi$
$674$	0.656674			0.0252941
$675$	−5.18821	−	0.287102i	−0.199694	−	0.0110506i
$676$	−1.99548			−0.0767494
$677$	5.54423	+	9.60290i	0.213082	+	0.369069i	0.952678	−	0.303982i	$-0.0983164\pi$
$677$	5.54423	+	9.60290i	0.213082	+	0.369069i	−0.739595	+	0.673052i	$0.764983\pi$
$678$	0.164214	−	0.840440i	0.00630662	−	0.0322769i
$679$	23.1335	−	40.0683i	0.887780	−	1.53768i
$680$	0.641295	−	1.11076i	0.0245925	−	0.0425955i
$681$	0.493170	−	0.169275i	0.0188983	−	0.00648663i
$682$	0.823846	+	1.42694i	0.0315467	+	0.0546405i
$683$	−42.5037			−1.62636			−0.813179	−	0.582014i	$-0.802265\pi$
$683$	−42.5037			−1.62636			−0.813179	+	0.582014i	$0.802265\pi$
$684$	18.6574	−	14.5184i	0.713385	−	0.555123i
$685$	−10.4931			−0.400919
$686$	0.656502	+	1.13710i	0.0250654	+	0.0434145i
$687$	6.05132	+	5.27069i	0.230872	+	0.201089i
$688$	9.07033	−	15.7103i	0.345803	−	0.598948i
$689$	6.24841	−	10.8226i	0.238046	−	0.412307i
$690$	0.374766	+	0.326421i	0.0142671	+	0.0124266i
$691$	−0.656332	−	1.13680i	−0.0249681	−	0.0432460i	0.853271	−	0.521467i	$-0.174615\pi$
$691$	−0.656332	−	1.13680i	−0.0249681	−	0.0432460i	−0.878239	+	0.478221i	$0.841282\pi$
$692$	12.7665			0.485310
$693$	18.7358	−	14.5794i	0.711716	−	0.553825i
$694$	1.41222			0.0536072
$695$	−5.35343	−	9.27241i	−0.203067	−	0.351722i
$696$	1.01448	−	0.348208i	0.0384536	−	0.0131988i
$697$	−6.04349	+	10.4676i	−0.228914	+	0.396490i
$698$	0.310458	−	0.537729i	0.0117510	−	0.0203534i
$699$	−1.86812	+	9.56094i	−0.0706589	+	0.361628i
$700$	2.45801	+	4.25740i	0.0929040	+	0.160915i
$701$	21.2054			0.800916			0.400458	−	0.916315i	$-0.368851\pi$
$701$	21.2054			0.800916			0.400458	+	0.916315i	$0.368851\pi$
$702$	−0.191039	+	0.292301i	−0.00721029	+	0.0110322i
$703$	−19.2434			−0.725778
$704$	12.6748	+	21.9534i	0.477700	+	0.827401i
$705$	−2.08112	+	10.6511i	−0.0783795	+	0.401142i
$706$	−0.151448	+	0.262316i	−0.00569983	+	0.00987240i
$707$	22.8588	−	39.5926i	0.859694	−	1.48903i
$708$	−9.31746	+	3.19812i	−0.350172	+	0.120193i
$709$	−24.6030	−	42.6136i	−0.923985	−	1.60039i	−0.793186	−	0.608980i	$-0.791579\pi$
$709$	−24.6030	−	42.6136i	−0.923985	−	1.60039i	−0.130799	−	0.991409i	$-0.541754\pi$
$710$	−0.523655			−0.0196524
$711$	3.76050	+	27.1408i	0.141030	+	1.01786i
$712$	−0.259540			−0.00972669
$713$	16.2957	+	28.2249i	0.610278	+	1.05703i
$714$	1.03290	+	0.899650i	0.0386551	+	0.0336685i
$715$	−1.60607	+	2.78180i	−0.0600637	+	0.104033i
$716$	−15.5963	+	27.0136i	−0.582861	+	1.00955i
$717$	−3.34601	−	2.91436i	−0.124959	−	0.108839i
$718$	−0.849273	−	1.47098i	−0.0316946	−	0.0548966i
$719$	−31.1080			−1.16013			−0.580067	−	0.814569i	$-0.696974\pi$
$719$	−31.1080			−1.16013			−0.580067	+	0.814569i	$0.696974\pi$
$720$	11.0422	+	4.48636i	0.411518	+	0.167197i
$721$	25.2671			0.940998
$722$	0.114417	+	0.198175i	0.00425814	+	0.00737532i
$723$	−24.5456	+	8.42502i	−0.912862	+	0.313330i
$724$	11.0782	−	19.1880i	0.411718	−	0.713116i
$725$	1.15314	−	1.99730i	0.0428267	−	0.0741780i
$726$	0.0152259	−	0.0779251i	0.000565085	−	0.00289207i
$727$	−15.0470	−	26.0622i	−0.558062	−	0.966592i	−0.997658	−	0.0683968i	$-0.978212\pi$
$727$	−15.0470	−	26.0622i	−0.558062	−	0.966592i	0.439596	−	0.898196i	$-0.355122\pi$
$728$	0.661482			0.0245162
$729$	−10.8376	−	24.7295i	−0.401392	−	0.915906i
$730$	−0.152412			−0.00564101
$731$	−10.9056	−	18.8890i	−0.403356	−	0.698634i
$732$	8.41747	−	43.0801i	0.311118	−	1.59229i
$733$	6.49987	−	11.2581i	0.240078	−	0.415827i	−0.720658	−	0.693290i	$-0.756160\pi$
$733$	6.49987	−	11.2581i	0.240078	−	0.415827i	0.960736	+	0.277463i	$0.0894936\pi$
$734$	0.373198	−	0.646398i	0.0137750	−	0.0238590i
$735$	1.52488	−	0.523399i	0.0562461	−	0.0193059i
$736$	−1.71645	−	2.97297i	−0.0632691	−	0.109585i
$737$	−43.3870			−1.59818
$738$	0.472618	+	0.192022i	0.0173973	+	0.00706842i
$739$	43.9402			1.61637			0.808183	−	0.588932i	$-0.200451\pi$
$739$	43.9402			1.61637			0.808183	+	0.588932i	$0.200451\pi$
$740$	−4.86193	−	8.42111i	−0.178728	−	0.309566i
$741$	−5.15778	−	4.49242i	−0.189476	−	0.165033i
$742$	−1.03447	+	1.79176i	−0.0379767	+	0.0657775i
$743$	24.4254	−	42.3061i	0.896081	−	1.55206i	0.0636208	−	0.997974i	$-0.479735\pi$
$743$	24.4254	−	42.3061i	0.896081	−	1.55206i	0.832461	−	0.554084i	$-0.186931\pi$
$744$	−2.67684	−	2.33153i	−0.0981379	−	0.0854779i
$745$	−10.1595	−	17.5968i	−0.372216	−	0.644697i
$746$	−0.519907			−0.0190351
$747$	4.32809	+	31.2373i	0.158357	+	1.14291i
$748$	30.6181			1.11951
$749$	16.4725	+	28.5313i	0.601894	+	1.04251i
$750$	−0.110093	+	0.0377882i	−0.00402003	+	0.00137983i
$751$	16.7071	−	28.9376i	0.609651	−	1.05595i	−0.381647	−	0.924308i	$-0.624643\pi$
$751$	16.7071	−	28.9376i	0.609651	−	1.05595i	0.991298	−	0.131638i	$-0.0420238\pi$
$752$	12.4465	−	21.5580i	0.453878	−	0.786139i
$753$	2.41599	−	12.3649i	0.0880435	−	0.450602i
$754$	−0.0774937	−	0.134223i	−0.00282216	−	0.00488812i
$755$	17.0220			0.619493
$756$	−13.9750	+	21.3826i	−0.508266	+	0.777678i
$757$	45.6922			1.66071			0.830356	−	0.557233i	$-0.188137\pi$
$757$	45.6922			1.66071			0.830356	+	0.557233i	$0.188137\pi$
$758$	−0.876551	−	1.51823i	−0.0318378	−	0.0551446i
$759$	−4.55543	+	23.3144i	−0.165351	+	0.846259i
$760$	0.530168	−	0.918278i	0.0192312	−	0.0333094i
$761$	2.43929	−	4.22497i	0.0884242	−	0.153155i	−0.818421	−	0.574619i	$-0.805150\pi$
$761$	2.43929	−	4.22497i	0.0884242	−	0.153155i	0.906845	+	0.421464i	$0.138484\pi$
$762$	−0.658018	+	0.225857i	−0.0238375	+	0.00818195i
$763$	1.67262	+	2.89706i	0.0605528	+	0.104881i
$764$	−31.0945			−1.12496
$765$	11.3096	−	8.80063i	0.408900	−	0.318187i
$766$	−0.0566225			−0.00204585
$767$	1.42509	+	2.46833i	0.0514572	+	0.0891264i
$768$	−20.4271	−	17.7920i	−0.737101	−	0.642013i
$769$	−5.62978	+	9.75106i	−0.203015	+	0.351632i	−0.949498	−	0.313772i	$-0.898407\pi$
$769$	−5.62978	+	9.75106i	−0.203015	+	0.351632i	0.746483	+	0.665404i	$0.231741\pi$
$770$	0.265897	−	0.460548i	0.00958227	−	0.0165970i
$771$	11.8412	+	10.3136i	0.426449	+	0.371436i
$772$	−18.6538	−	32.3093i	−0.671364	−	1.16284i
$773$	17.8461			0.641880			0.320940	−	0.947100i	$-0.396001\pi$
$773$	17.8461			0.641880			0.320940	+	0.947100i	$0.396001\pi$
$774$	−0.726506	+	0.565333i	−0.0261137	+	0.0203205i
$775$	−7.63305			−0.274187
$776$	−2.52132	−	4.36705i	−0.0905101	−	0.156768i
$777$	19.6667	−	6.75038i	0.705540	−	0.242169i
$778$	0.294161	−	0.509502i	0.0105462	−	0.0182665i
$779$	−4.99624	+	8.65375i	−0.179009	+	0.310053i
$780$	0.662793	−	3.39213i	0.0237318	−	0.121458i
$781$	−12.5149	−	21.6764i	−0.447818	−	0.775644i
$782$	−1.37064			−0.0490140
$783$	11.9655	+	0.662140i	0.427612	+	0.0236630i
$784$	−3.69803			−0.132072
$785$	−0.653935	−	1.13265i	−0.0233399	−	0.0404259i
$786$	−0.398951	+	2.04181i	−0.0142301	+	0.0728289i
$787$	−12.3557	+	21.4006i	−0.440432	+	0.762850i	−0.997721	−	0.0674682i	$-0.978508\pi$
$787$	−12.3557	+	21.4006i	−0.440432	+	0.762850i	0.557290	+	0.830318i	$0.311841\pi$
$788$	−10.1794	+	17.6312i	−0.362626	+	0.628087i
$789$	45.1144	−	15.4850i	1.60611	−	0.551281i
$790$	0.306891	+	0.531550i	0.0109187	+	0.0189117i
$791$	−18.1244			−0.644430
$792$	−0.355110	−	2.56295i	−0.0126183	−	0.0910704i
$793$	−12.7000			−0.450990
$794$	0.226103	+	0.391622i	0.00802410	+	0.0138981i
$795$	16.3220	+	14.2164i	0.578880	+	0.504203i
$796$	−16.4426	+	28.4794i	−0.582793	+	1.00943i
$797$	−19.8688	+	34.4139i	−0.703791	+	1.21900i	0.263336	+	0.964704i	$0.415177\pi$
$797$	−19.8688	+	34.4139i	−0.703791	+	1.21900i	−0.967126	+	0.254297i	$0.918156\pi$
$798$	0.853910	+	0.743754i	0.0302281	+	0.0263286i
$799$	−14.9649	−	25.9199i	−0.529419	−	0.916980i
$800$	0.804000			0.0284257
$801$	−2.68656	−	1.09153i	−0.0949249	−	0.0385674i
$802$	−1.94175			−0.0685657
$803$	−3.64250	−	6.30900i	−0.128541	−	0.222640i
$804$	44.1559	−	15.1560i	1.55726	−	0.534512i
$805$	5.25945	−	9.10963i	0.185371	−	0.321072i
$806$	−0.256479	+	0.444234i	−0.00903408	+	0.0156475i
$807$	2.26658	−	11.6002i	0.0797873	−	0.408347i
$808$	−2.49139	−	4.31521i	−0.0876467	−	0.151808i
$809$	40.0717			1.40885			0.704423	−	0.709780i	$-0.251206\pi$
$809$	40.0717			1.40885			0.704423	+	0.709780i	$0.251206\pi$
$810$	−0.433431	−	0.421834i	−0.0152292	−	0.0148218i
$811$	49.6910			1.74489			0.872444	−	0.488714i	$-0.162534\pi$
$811$	49.6910			1.74489			0.872444	+	0.488714i	$0.162534\pi$
$812$	−5.66887	−	9.81878i	−0.198939	−	0.344572i
$813$	−0.636838	+	3.25930i	−0.0223349	+	0.114309i
$814$	−0.525943	+	0.910960i	−0.0184343	+	0.0319291i
$815$	−4.90560	+	8.49675i	−0.171836	+	0.297628i
$816$	−31.0900	+	10.6713i	−1.08837	+	0.373571i
$817$	−9.01578	−	15.6158i	−0.315422	−	0.546327i
$818$	−1.23575			−0.0432070
$819$	6.84715	+	2.78195i	0.239259	+	0.0972093i
$820$	−5.04930			−0.176329
$821$	−9.44011	−	16.3507i	−0.329462	−	0.570645i	0.652943	−	0.757407i	$-0.273534\pi$
$821$	−9.44011	−	16.3507i	−0.329462	−	0.570645i	−0.982405	+	0.186762i	$0.940201\pi$
$822$	−0.920997	−	0.802186i	−0.0321235	−	0.0279795i
$823$	14.2363	−	24.6580i	0.496247	−	0.859525i	−0.503744	−	0.863853i	$-0.668044\pi$
$823$	14.2363	−	24.6580i	0.496247	−	0.859525i	0.999991	+	0.00432845i	$0.00137779\pi$
$824$	1.37694	−	2.38492i	0.0479678	−	0.0830827i
$825$	−4.19534	−	3.65413i	−0.146063	−	0.127221i
$826$	−0.235935	−	0.408651i	−0.00820923	−	0.0142188i
$827$	−15.9961			−0.556239			−0.278120	−	0.960546i	$-0.589711\pi$
$827$	−15.9961			−0.556239			−0.278120	+	0.960546i	$0.589711\pi$
$828$	−3.50807	−	25.3189i	−0.121914	−	0.879893i
$829$	20.7729			0.721474			0.360737	−	0.932668i	$-0.382525\pi$
$829$	20.7729			0.721474			0.360737	+	0.932668i	$0.382525\pi$
$830$	0.353211	+	0.611779i	0.0122601	+	0.0212352i
$831$	−44.7222	+	15.3504i	−1.55139	+	0.532499i
$832$	−3.94591	+	6.83451i	−0.136800	+	0.236944i
$833$	−2.22313	+	3.85058i	−0.0770269	+	0.133415i
$834$	0.238987	−	1.22312i	0.00827545	−	0.0423533i
$835$	4.08745	+	7.07968i	0.141452	+	0.245002i
$836$	25.3124			0.875449
$837$	−17.9031	−	35.3920i	−0.618821	−	1.22333i
$838$	−1.69354			−0.0585024
$839$	8.59202	+	14.8818i	0.296630	+	0.513777i	0.975363	−	0.220608i	$-0.0708040\pi$
$839$	8.59202	+	14.8818i	0.296630	+	0.513777i	−0.678733	+	0.734385i	$0.737471\pi$
$840$	−0.219709	+	1.12446i	−0.00758068	+	0.0387975i
$841$	11.8405	−	20.5084i	0.408294	−	0.707186i
$842$	0.600268	−	1.03969i	0.0206866	−	0.0358302i
$843$	−1.07603	+	0.369336i	−0.0370605	+	0.0127206i
$844$	−25.1413	−	43.5460i	−0.865400	−	1.49892i
$845$	−1.00000			−0.0344010
$846$	−0.996928	+	0.775764i	−0.0342751	+	0.0266713i
$847$	−1.68049			−0.0577422
$848$	−24.8245	−	42.9972i	−0.852476	−	1.47653i
$849$	6.55628	+	5.71051i	0.225011	+	0.195984i
$850$	0.160505	−	0.278003i	0.00550527	−	0.00953542i
$851$	−10.4032	+	18.0188i	−0.356616	+	0.617676i
$852$	20.3087	+	17.6889i	0.695766	+	0.606011i
$853$	−16.5366	−	28.6423i	−0.566203	−	0.980693i	−0.996937	−	0.0782138i	$-0.975078\pi$
$853$	−16.5366	−	28.6423i	−0.566203	−	0.980693i	0.430733	−	0.902479i	$-0.358255\pi$
$854$	2.10258			0.0719488
$855$	9.34983	−	7.27561i	0.319757	−	0.248821i
$856$	3.59069			0.122727
$857$	19.8148	+	34.3202i	0.676859	+	1.17235i	0.975922	+	0.218121i	$0.0699927\pi$
$857$	19.8148	+	34.3202i	0.676859	+	1.17235i	−0.299063	+	0.954233i	$0.596674\pi$
$858$	−0.353634	+	0.121381i	−0.0120729	+	0.00414388i
$859$	0.586442	−	1.01575i	0.0200091	−	0.0346569i	−0.855847	−	0.517228i	$-0.826964\pi$
$859$	0.586442	−	1.01575i	0.0200091	−	0.0346569i	0.875857	+	0.482571i	$0.160297\pi$
$860$	4.55576	−	7.89081i	0.155350	−	0.269074i
$861$	2.07051	−	10.5968i	0.0705628	−	0.361137i
$862$	−0.955244	−	1.65453i	−0.0325357	−	0.0563536i
$863$	−54.3303			−1.84943			−0.924713	−	0.380665i	$-0.875695\pi$
$863$	−54.3303			−1.84943			−0.924713	+	0.380665i	$0.875695\pi$
$864$	1.88576	+	3.72789i	0.0641547	+	0.126825i
$865$	6.39771			0.217529
$866$	0.686011	+	1.18821i	0.0233116	+	0.0403769i
$867$	−1.93230	+	9.88938i	−0.0656242	+	0.335861i
$868$	−18.7621	+	32.4969i	−0.636827	+	1.10302i
$869$	−14.6688	+	25.4071i	−0.497606	+	0.861878i
$870$	0.253906	−	0.0871503i	0.00860821	−	0.00295467i
$871$	−6.75359	−	11.6976i	−0.228837	−	0.396357i
$872$	0.364598			0.0123468
$873$	−7.73251	−	55.8081i	−0.261706	−	1.88882i
$874$	−1.13313			−0.0383286
$875$	1.23179	+	2.13352i	0.0416420	+	0.0721260i
$876$	5.91093	+	5.14840i	0.199712	+	0.173948i
$877$	−23.8867	+	41.3730i	−0.806597	+	1.39707i	0.108610	+	0.994084i	$0.465360\pi$
$877$	−23.8867	+	41.3730i	−0.806597	+	1.39707i	−0.915207	+	0.402983i	$0.867973\pi$
$878$	−0.330132	+	0.571806i	−0.0111414	+	0.0192975i
$879$	15.9652	+	13.9056i	0.538492	+	0.469026i
$880$	6.38080	+	11.0519i	0.215097	+	0.372558i
$881$	28.0225			0.944101			0.472050	−	0.881572i	$-0.343514\pi$
$881$	28.0225			0.944101			0.472050	+	0.881572i	$0.343514\pi$
$882$	0.173855	+	0.0706363i	0.00585401	+	0.00237845i
$883$	−2.71952			−0.0915191			−0.0457595	−	0.998952i	$-0.514571\pi$
$883$	−2.71952			−0.0915191			−0.0457595	+	0.998952i	$0.514571\pi$
$884$	4.76599	+	8.25494i	0.160298	+	0.277644i
$885$	−4.66928	+	1.60268i	−0.156956	+	0.0538734i
$886$	0.660183	−	1.14347i	0.0221793	−	0.0384157i
$887$	2.38124	−	4.12442i	0.0799541	−	0.138485i	−0.823276	−	0.567642i	$-0.807856\pi$
$887$	2.38124	−	4.12442i	0.0799541	−	0.138485i	0.903230	+	0.429157i	$0.141189\pi$
$888$	0.434583	−	2.22417i	0.0145836	−	0.0746383i
$889$	7.36230	+	12.7519i	0.246924	+	0.427685i
$890$	−0.0649584			−0.00217741
$891$	7.10299	−	28.0231i	0.237959	−	0.938810i
$892$	−15.1345			−0.506741
$893$	−12.3717	−	21.4284i	−0.414002	−	0.717073i
$894$	0.453541	−	2.32119i	0.0151687	−	0.0776323i
$895$	−7.81580	+	13.5374i	−0.261253	+	0.452504i
$896$	2.63399	−	4.56220i	0.0879953	−	0.152412i
$897$	−6.99489	+	2.40092i	−0.233552	+	0.0801643i
$898$	−0.919706	−	1.59298i	−0.0306910	−	0.0531584i
$899$	17.6040			0.587126
$900$	5.54616	+	2.25337i	0.184872	+	0.0751123i
$901$	−59.6946			−1.98871
$902$	0.273106	+	0.473033i	0.00909343	+	0.0157503i
$903$	14.6920	+	12.7967i	0.488919	+	0.425847i
$904$	−0.987692	+	1.71073i	−0.0328501	+	0.0568981i
$905$	5.55163	−	9.61571i	0.184543	−	0.319637i
$906$	1.49405	+	1.30132i	0.0496366	+	0.0432334i
$907$	11.5731	+	20.0452i	0.384278	+	0.665589i	0.991669	−	0.128814i	$-0.0411171\pi$
$907$	11.5731	+	20.0452i	0.384278	+	0.665589i	−0.607391	+	0.794403i	$0.707784\pi$
$908$	−0.600715			−0.0199354
$909$	−7.64072	−	55.1455i	−0.253427	−	1.82906i
$910$	0.165558			0.00548818
$911$	5.77944	+	10.0103i	0.191481	+	0.331655i	0.945741	−	0.324920i	$-0.105338\pi$
$911$	5.77944	+	10.0103i	0.191481	+	0.331655i	−0.754260	+	0.656576i	$0.772004\pi$
$912$	−25.7026	+	8.82213i	−0.851098	+	0.292130i
$913$	−16.8829	+	29.2420i	−0.558741	+	0.967768i
$914$	0.821826	−	1.42344i	0.0271836	−	0.0470834i
$915$	4.21826	−	21.5888i	0.139451	−	0.713704i
$916$	−4.62270	−	8.00676i	−0.152738	−	0.264551i
$917$	44.0324			1.45408
$918$	1.66547	+	0.0921627i	0.0549686	+	0.00304182i
$919$	−45.9902			−1.51708			−0.758538	−	0.651629i	$-0.774086\pi$
$919$	−45.9902			−1.51708			−0.758538	+	0.651629i	$0.774086\pi$
$920$	−0.573228	−	0.992860i	−0.0188988	−	0.0327336i
$921$	0.337901	−	1.72936i	0.0111342	−	0.0569843i
$922$	−0.294370	+	0.509864i	−0.00969456	+	0.0167915i
$923$	3.89612	−	6.74828i	0.128242	−	0.222122i
$924$	−25.8693	+	8.87935i	−0.851037	+	0.292109i
$925$	−2.43647	−	4.22008i	−0.0801105	−	0.138756i
$926$	1.01497			0.0333539
$927$	24.2831	−	18.8960i	0.797561	−	0.620625i
$928$	−1.85425			−0.0608689
$929$	−21.3396	−	36.9613i	−0.700130	−	1.21266i	−0.968421	−	0.249322i	$-0.919792\pi$
$929$	−21.3396	−	36.9613i	−0.700130	−	1.21266i	0.268291	−	0.963338i	$-0.413541\pi$
$930$	−0.669968	−	0.583540i	−0.0219691	−	0.0191350i
$931$	−1.83790	+	3.18333i	−0.0602346	+	0.104329i
$932$	5.61169	−	9.71974i	0.183817	−	0.318381i
$933$	29.1116	+	25.3562i	0.953073	+	0.830124i
$934$	0.656847	+	1.13769i	0.0214927	+	0.0372264i
$935$	15.3437			0.501792
$936$	0.635720	−	0.494688i	0.0207791	−	0.0161694i
$937$	−47.1687			−1.54093			−0.770467	−	0.637480i	$-0.779977\pi$
$937$	−47.1687			−1.54093			−0.770467	+	0.637480i	$0.779977\pi$
$938$	1.11811	+	1.93662i	0.0365075	+	0.0632328i
$939$	−38.9487	+	13.3687i	−1.27104	+	0.436271i
$940$	6.25152	−	10.8280i	0.203902	−	0.353169i
$941$	−20.0891	+	34.7954i	−0.654887	+	1.13430i	0.327035	+	0.945012i	$0.393950\pi$
$941$	−20.0891	+	34.7954i	−0.654887	+	1.13430i	−0.981922	+	0.189285i	$0.939383\pi$
$942$	0.0291929	−	0.149408i	0.000951156	−	0.00486796i
$943$	5.40204	+	9.35660i	0.175914	+	0.304693i
$944$	11.3236			0.368551
$945$	−7.00331	+	10.7155i	−0.227818	+	0.348575i
$946$	−0.985646			−0.0320461
$947$	0.402966	+	0.697957i	0.0130946	+	0.0226806i	0.872498	−	0.488617i	$-0.162498\pi$
$947$	0.402966	+	0.697957i	0.0130946	+	0.0226806i	−0.859404	+	0.511297i	$0.829165\pi$
$948$	6.05352	−	30.9816i	0.196609	−	1.00623i
$949$	1.13398	−	1.96411i	0.0368105	−	0.0637577i
$950$	0.132692	−	0.229829i	0.00430509	−	0.00745664i
$951$	45.9317	−	15.7655i	1.48944	−	0.511233i
$952$	−1.57988	−	2.73643i	−0.0512041	−	0.0886881i
$953$	−8.33532			−0.270007			−0.135004	−	0.990845i	$-0.543105\pi$
$953$	−8.33532			−0.270007			−0.135004	+	0.990845i	$0.543105\pi$
$954$	0.345779	+	2.49560i	0.0111950	+	0.0807981i
$955$	−15.5825			−0.504236
$956$	2.55607	+	4.42724i	0.0826691	+	0.143187i
$957$	9.67566	+	8.42748i	0.312770	+	0.272422i
$958$	−0.0439210	+	0.0760733i	−0.00141902	+	0.00245782i
$959$	−12.9252	+	22.3871i	−0.417377	+	0.722918i
$960$	−10.3074	−	8.97773i	−0.332670	−	0.289755i
$961$	−13.6317	−	23.6108i	−0.439732	−	0.761638i
$962$	−0.327472			−0.0105581
$963$	37.1680	+	15.1011i	1.19772	+	0.486627i
$964$	29.8983			0.962960
$965$	−9.34800	−	16.1912i	−0.300923	−	0.521214i
$966$	1.15806	−	0.397490i	0.0372598	−	0.0127890i
$967$	21.0963	−	36.5398i	0.678410	−	1.17504i	−0.297049	−	0.954862i	$-0.596002\pi$
$967$	21.0963	−	36.5398i	0.678410	−	1.17504i	0.975459	−	0.220179i	$-0.0706642\pi$
$968$	−0.0915782	+	0.158618i	−0.00294344	+	0.00509818i
$969$	−6.26549	+	32.0664i	−0.201277	+	1.03012i
$970$	−0.631042	−	1.09300i	−0.0202615	−	0.0350940i
$971$	25.3293			0.812856			0.406428	−	0.913683i	$-0.366774\pi$
$971$	25.3293			0.812856			0.406428	+	0.913683i	$0.366774\pi$
$972$	2.56021	+	31.0010i	0.0821188	+	0.994357i
$973$	−26.3771			−0.845611
$974$	−1.01990	−	1.76652i	−0.0326798	−	0.0566031i
$975$	0.332146	−	1.69991i	0.0106372	−	0.0544405i
$976$	−25.2281	+	43.6963i	−0.807531	+	1.39868i
$977$	−18.0466	+	31.2575i	−0.577360	+	1.00002i	0.418420	+	0.908253i	$0.362584\pi$
$977$	−18.0466	+	31.2575i	−0.577360	+	1.00002i	−0.995781	+	0.0917641i	$0.970749\pi$
$978$	−1.08014	+	0.370747i	−0.0345392	+	0.0118552i
$979$	−1.55245	−	2.68892i	−0.0496165	−	0.0859382i
$980$	−1.85741			−0.0593329
$981$	3.77403	+	1.53336i	0.120496	+	0.0489566i
$982$	0.562964			0.0179649
$983$	30.4781	+	52.7897i	0.972102	+	1.68373i	0.689186	+	0.724584i	$0.257968\pi$
$983$	30.4781	+	52.7897i	0.972102	+	1.68373i	0.282916	+	0.959145i	$0.408698\pi$
$984$	−0.887377	−	0.772903i	−0.0282885	−	0.0246393i
$985$	−5.10122	+	8.83557i	−0.162538	+	0.281525i
$986$	−0.370170	+	0.641154i	−0.0117886	+	0.0204185i
$987$	20.1607	+	17.5599i	0.641722	+	0.558939i
$988$	3.94012	+	6.82448i	0.125352	+	0.217116i
$989$	−19.4961			−0.619939
$990$	−0.0888780	−	0.641461i	−0.00282473	−	0.0203870i
$991$	56.5677			1.79693			0.898466	−	0.439042i	$-0.144682\pi$
$991$	56.5677			1.79693			0.898466	+	0.439042i	$0.144682\pi$
$992$	3.06848	+	5.31477i	0.0974244	+	0.168744i
$993$	−29.2594	+	10.0430i	−0.928521	+	0.318704i
$994$	−0.645032	+	1.11723i	−0.0204592	+	0.0354363i
$995$	−8.23991	+	14.2719i	−0.261223	+	0.452451i
$996$	6.96720	−	35.6577i	0.220764	−	1.12986i
$997$	1.18890	+	2.05924i	0.0376530	+	0.0652169i	0.884238	−	0.467037i	$-0.154679\pi$
$997$	1.18890	+	2.05924i	0.0376530	+	0.0652169i	−0.846585	+	0.532254i	$0.821345\pi$
$998$	0.864237			0.0273569
$999$	13.8525	−	21.1952i	0.438274	−	0.670586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.e.391.6	yes	16
3.2	odd	2		1755.2.i.f.1171.3		16
9.2	odd	6		1755.2.i.f.586.3		16
9.4	even	3		5265.2.a.bf.1.3		8
9.5	odd	6		5265.2.a.ba.1.6		8
9.7	even	3	inner	585.2.i.e.196.6	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.e.196.6	✓	16	9.7	even	3	inner
585.2.i.e.391.6	yes	16	1.1	even	1	trivial
1755.2.i.f.586.3		16	9.2	odd	6
1755.2.i.f.1171.3		16	3.2	odd	2
5265.2.a.ba.1.6		8	9.5	odd	6
5265.2.a.bf.1.3		8	9.4	even	3

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0336011 - 0.0581988i) q^{2} +(-0.332146 + 1.69991i) q^{3} +(0.997742 - 1.72814i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.110093 - 0.0377882i) q^{6} +(-1.23179 - 2.13352i) q^{7} -0.268505 q^{8} +(-2.77936 - 1.12923i) q^{9} +O(q^{10})\)	\(q+(-0.0336011 - 0.0581988i) q^{2} +(-0.332146 + 1.69991i) q^{3} +(0.997742 - 1.72814i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.110093 - 0.0377882i) q^{6} +(-1.23179 - 2.13352i) q^{7} -0.268505 q^{8} +(-2.77936 - 1.12923i) q^{9} -0.0672022 q^{10} +(-1.60607 - 2.78180i) q^{11} +(2.60628 + 2.27006i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-0.0827788 + 0.143377i) q^{14} +(1.30609 + 1.13760i) q^{15} +(-1.98646 - 3.44065i) q^{16} -4.77678 q^{17} +(0.0276694 + 0.199699i) q^{18} -3.94903 q^{19} +(-0.997742 - 1.72814i) q^{20} +(4.03591 - 1.38528i) q^{21} +(-0.107932 + 0.186943i) q^{22} +(-2.13489 + 3.69773i) q^{23} +(0.0891830 - 0.456434i) q^{24} +(-0.500000 - 0.866025i) q^{25} -0.0672022 q^{26} +(2.84275 - 4.34957i) q^{27} -4.91602 q^{28} +(1.15314 + 1.99730i) q^{29} +(0.0223210 - 0.114237i) q^{30} +(3.81652 - 6.61041i) q^{31} +(-0.402000 + 0.696284i) q^{32} +(5.26224 - 1.80621i) q^{33} +(0.160505 + 0.278003i) q^{34} -2.46357 q^{35} +(-4.72456 + 3.67643i) q^{36} +4.87293 q^{37} +(0.132692 + 0.229829i) q^{38} +(1.30609 + 1.13760i) q^{39} +(-0.134253 + 0.232532i) q^{40} +(1.26518 - 2.19136i) q^{41} +(-0.216233 - 0.188338i) q^{42} +(2.28304 + 3.95433i) q^{43} -6.40978 q^{44} +(-2.36762 + 1.84238i) q^{45} +0.286938 q^{46} +(3.13284 + 5.42623i) q^{47} +(6.50858 - 2.23400i) q^{48} +(0.465404 - 0.806103i) q^{49} +(-0.0336011 + 0.0581988i) q^{50} +(1.58659 - 8.12007i) q^{51} +(-0.997742 - 1.72814i) q^{52} +12.4968 q^{53} +(-0.348659 - 0.0192939i) q^{54} -3.21214 q^{55} +(0.330741 + 0.572861i) q^{56} +(1.31166 - 6.71298i) q^{57} +(0.0774937 - 0.134223i) q^{58} +(-1.42509 + 2.46833i) q^{59} +(3.26907 - 1.12207i) q^{60} +(-6.35000 - 10.9985i) q^{61} -0.512957 q^{62} +(1.01433 + 7.32078i) q^{63} -7.89182 q^{64} +(-0.500000 - 0.866025i) q^{65} +(-0.281936 - 0.245566i) q^{66} +(6.75359 - 11.6976i) q^{67} +(-4.76599 + 8.25494i) q^{68} +(-5.57670 - 4.85729i) q^{69} +(0.0827788 + 0.143377i) q^{70} +7.79224 q^{71} +(0.746272 + 0.303205i) q^{72} +2.26796 q^{73} +(-0.163736 - 0.283599i) q^{74} +(1.63823 - 0.562306i) q^{75} +(-3.94012 + 6.82448i) q^{76} +(-3.95668 + 6.85316i) q^{77} +(0.0223210 - 0.114237i) q^{78} +(-4.56668 - 7.90972i) q^{79} -3.97292 q^{80} +(6.44966 + 6.27709i) q^{81} -0.170046 q^{82} +(-5.25595 - 9.10356i) q^{83} +(1.63284 - 8.35677i) q^{84} +(-2.38839 + 4.13681i) q^{85} +(0.153425 - 0.265740i) q^{86} +(-3.77824 + 1.29684i) q^{87} +(0.431239 + 0.746927i) q^{88} +0.966612 q^{89} +(0.186779 + 0.0758870i) q^{90} -2.46357 q^{91} +(4.26013 + 7.37876i) q^{92} +(9.96943 + 8.68335i) q^{93} +(0.210533 - 0.364655i) q^{94} +(-1.97452 + 3.41996i) q^{95} +(-1.05009 - 0.914630i) q^{96} +(9.39020 + 16.2643i) q^{97} -0.0625523 q^{98} +(1.32255 + 9.54524i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9} - 6 q^{10} - 6 q^{11} + 2 q^{12} + 8 q^{13} - 10 q^{14} + 5 q^{15} - 11 q^{16} - 4 q^{17} + 5 q^{18} - 20 q^{19} + 9 q^{20} + 11 q^{21} - 3 q^{22} - 6 q^{23} - 57 q^{24} - 8 q^{25} - 6 q^{26} - 14 q^{27} - 68 q^{28} - 14 q^{29} + 7 q^{30} + 31 q^{31} - q^{32} - 31 q^{33} + 7 q^{34} + 22 q^{35} + 2 q^{36} + 2 q^{37} - 9 q^{38} + 5 q^{39} - 6 q^{40} + 12 q^{41} - 26 q^{42} - 15 q^{43} + 32 q^{44} - 16 q^{45} - 64 q^{46} + 18 q^{47} - 4 q^{48} - 17 q^{49} - 3 q^{50} + 32 q^{51} + 9 q^{52} + 4 q^{53} + 2 q^{54} - 12 q^{55} - 16 q^{56} + 45 q^{57} + 42 q^{58} - 24 q^{59} - 8 q^{60} + 9 q^{61} - 40 q^{62} + 47 q^{63} - 60 q^{64} - 8 q^{65} + 55 q^{66} + 18 q^{67} + 14 q^{68} - 12 q^{69} + 10 q^{70} + 20 q^{71} - 9 q^{72} + 12 q^{73} + 37 q^{74} + 4 q^{75} + 53 q^{76} + 34 q^{77} + 7 q^{78} + 3 q^{79} - 22 q^{80} + 13 q^{81} - 68 q^{82} + 10 q^{83} + 22 q^{84} - 2 q^{85} - 60 q^{86} + 11 q^{87} + 14 q^{88} - 26 q^{89} + 19 q^{90} + 22 q^{91} - 5 q^{92} + 74 q^{93} - 17 q^{94} - 10 q^{95} + 13 q^{96} + 34 q^{97} - 60 q^{98} - 43 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9 - 6 * q^10 - 6 * q^11 + 2 * q^12 + 8 * q^13 - 10 * q^14 + 5 * q^15 - 11 * q^16 - 4 * q^17 + 5 * q^18 - 20 * q^19 + 9 * q^20 + 11 * q^21 - 3 * q^22 - 6 * q^23 - 57 * q^24 - 8 * q^25 - 6 * q^26 - 14 * q^27 - 68 * q^28 - 14 * q^29 + 7 * q^30 + 31 * q^31 - q^32 - 31 * q^33 + 7 * q^34 + 22 * q^35 + 2 * q^36 + 2 * q^37 - 9 * q^38 + 5 * q^39 - 6 * q^40 + 12 * q^41 - 26 * q^42 - 15 * q^43 + 32 * q^44 - 16 * q^45 - 64 * q^46 + 18 * q^47 - 4 * q^48 - 17 * q^49 - 3 * q^50 + 32 * q^51 + 9 * q^52 + 4 * q^53 + 2 * q^54 - 12 * q^55 - 16 * q^56 + 45 * q^57 + 42 * q^58 - 24 * q^59 - 8 * q^60 + 9 * q^61 - 40 * q^62 + 47 * q^63 - 60 * q^64 - 8 * q^65 + 55 * q^66 + 18 * q^67 + 14 * q^68 - 12 * q^69 + 10 * q^70 + 20 * q^71 - 9 * q^72 + 12 * q^73 + 37 * q^74 + 4 * q^75 + 53 * q^76 + 34 * q^77 + 7 * q^78 + 3 * q^79 - 22 * q^80 + 13 * q^81 - 68 * q^82 + 10 * q^83 + 22 * q^84 - 2 * q^85 - 60 * q^86 + 11 * q^87 + 14 * q^88 - 26 * q^89 + 19 * q^90 + 22 * q^91 - 5 * q^92 + 74 * q^93 - 17 * q^94 - 10 * q^95 + 13 * q^96 + 34 * q^97 - 60 * q^98 - 43 * q^99

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