LMFDB - Embedded newform 117.2.e.c.79.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(40,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("117.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.e (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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 3 x^{10} - x^{9} - 2 x^{8} + 9 x^{7} + 24 x^{6} + 27 x^{5} - 18 x^{4} - 27 x^{3} + \cdots + 729 $ x^12 - x^11 - 3x^10 - x^9 - 2x^8 + 9x^7 + 24x^6 + 27x^5 - 18x^4 - 27x^3 - 243x^2 - 243*x + 729
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.5
Root			$1.70358 - 0.312736i$ of defining polynomial
Character	$\chi$	$=$	117.79
Dual form			117.2.e.c.40.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10985 - 1.92231i) q^{2} +(-0.580954 - 1.63171i) q^{3} +(-1.46353 - 2.53491i) q^{4} +(1.13044 + 1.95798i) q^{5} +(-3.78144 - 0.694180i) q^{6} +(-0.183027 + 0.317013i) q^{7} -2.05779 q^{8} +(-2.32499 + 1.89590i) q^{9} +O(q^{10})$	\(q+(1.10985 - 1.92231i) q^{2} +(-0.580954 - 1.63171i) q^{3} +(-1.46353 - 2.53491i) q^{4} +(1.13044 + 1.95798i) q^{5} +(-3.78144 - 0.694180i) q^{6} +(-0.183027 + 0.317013i) q^{7} -2.05779 q^{8} +(-2.32499 + 1.89590i) q^{9} +5.01848 q^{10} +(-0.622629 + 1.07843i) q^{11} +(-3.28600 + 3.86073i) q^{12} +(0.500000 + 0.866025i) q^{13} +(0.406266 + 0.703673i) q^{14} +(2.53814 - 2.98206i) q^{15} +(0.643223 - 1.11409i) q^{16} -6.50614 q^{17} +(1.06414 + 6.57352i) q^{18} +7.78258 q^{19} +(3.30887 - 5.73113i) q^{20} +(0.623605 + 0.114479i) q^{21} +(1.38205 + 2.39378i) q^{22} +(-0.749331 - 1.29788i) q^{23} +(1.19548 + 3.35773i) q^{24} +(-0.0557990 + 0.0966466i) q^{25} +2.21970 q^{26} +(4.44428 + 2.69228i) q^{27} +1.07146 q^{28} +(-2.54916 + 4.41528i) q^{29} +(-2.91551 - 8.18873i) q^{30} +(-1.82625 - 3.16316i) q^{31} +(-3.48555 - 6.03715i) q^{32} +(2.12140 + 0.389438i) q^{33} +(-7.22084 + 12.5069i) q^{34} -0.827608 q^{35} +(8.20862 + 3.11891i) q^{36} -10.6628 q^{37} +(8.63749 - 14.9606i) q^{38} +(1.12263 - 1.31898i) q^{39} +(-2.32621 - 4.02912i) q^{40} +(3.98181 + 6.89670i) q^{41} +(0.912172 - 1.07171i) q^{42} +(-0.123894 + 0.214591i) q^{43} +3.64495 q^{44} +(-6.34041 - 2.40907i) q^{45} -3.32658 q^{46} +(-3.55746 + 6.16171i) q^{47} +(-2.19157 - 0.402318i) q^{48} +(3.43300 + 5.94613i) q^{49} +(0.123857 + 0.214526i) q^{50} +(3.77977 + 10.6162i) q^{51} +(1.46353 - 2.53491i) q^{52} -0.671391 q^{53} +(10.1079 - 5.55528i) q^{54} -2.81539 q^{55} +(0.376632 - 0.652346i) q^{56} +(-4.52132 - 12.6989i) q^{57} +(5.65837 + 9.80058i) q^{58} +(-3.71183 - 6.42908i) q^{59} +(-11.2739 - 2.06961i) q^{60} +(2.10558 - 3.64698i) q^{61} -8.10745 q^{62} +(-0.175489 - 1.08405i) q^{63} -12.9008 q^{64} +(-1.13044 + 1.95798i) q^{65} +(3.10306 - 3.64578i) q^{66} +(-2.60671 - 4.51496i) q^{67} +(9.52193 + 16.4925i) q^{68} +(-1.68244 + 1.97670i) q^{69} +(-0.918520 + 1.59092i) q^{70} -2.13514 q^{71} +(4.78433 - 3.90137i) q^{72} +2.73585 q^{73} +(-11.8341 + 20.4973i) q^{74} +(0.190116 + 0.0349007i) q^{75} +(-11.3900 - 19.7281i) q^{76} +(-0.227917 - 0.394763i) q^{77} +(-1.28954 - 3.62191i) q^{78} +(5.89866 - 10.2168i) q^{79} +2.90850 q^{80} +(1.81111 - 8.81589i) q^{81} +17.6768 q^{82} +(8.32209 - 14.4143i) q^{83} +(-0.622471 - 1.74832i) q^{84} +(-7.35482 - 12.7389i) q^{85} +(0.275008 + 0.476328i) q^{86} +(8.68542 + 1.59443i) q^{87} +(1.28124 - 2.21917i) q^{88} +3.06161 q^{89} +(-11.6679 + 9.51455i) q^{90} -0.366055 q^{91} +(-2.19334 + 3.79897i) q^{92} +(-4.10040 + 4.81757i) q^{93} +(7.89649 + 13.6771i) q^{94} +(8.79775 + 15.2382i) q^{95} +(-7.82596 + 9.19473i) q^{96} +(5.35408 - 9.27354i) q^{97} +15.2405 q^{98} +(-0.596985 - 3.68777i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 2 q^{3} - 6 q^{4} + 3 q^{5} - 7 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 - 2 * q^3 - 6 * q^4 + 3 * q^5 - 7 * q^6 - 12 * q^8 - 2 * q^9	\( 12 q + 2 q^{2} - 2 q^{3} - 6 q^{4} + 3 q^{5} - 7 q^{6} - 12 q^{8} - 2 q^{9} - 12 q^{10} + 7 q^{11} + 7 q^{12} + 6 q^{13} + 13 q^{14} - 12 q^{15} - 6 q^{16} - 28 q^{17} + 26 q^{18} - 6 q^{19} + 17 q^{20} - 18 q^{21} + 3 q^{22} + 17 q^{23} - 30 q^{24} - 3 q^{25} + 4 q^{26} + 13 q^{27} + 30 q^{28} + 14 q^{29} - 7 q^{30} - 6 q^{31} + 9 q^{32} + 19 q^{33} - 3 q^{34} - 26 q^{35} + 43 q^{36} - 18 q^{37} - 4 q^{38} - q^{39} + 6 q^{40} - 4 q^{41} - 17 q^{42} + 3 q^{43} - 26 q^{44} + 18 q^{45} + 9 q^{47} - 3 q^{48} - 21 q^{50} - 4 q^{51} + 6 q^{52} - 56 q^{53} + 35 q^{54} + 30 q^{55} + 16 q^{56} - 30 q^{57} - 18 q^{58} + 17 q^{59} - 31 q^{60} + 6 q^{61} + 8 q^{62} - 60 q^{64} - 3 q^{65} - 19 q^{66} + 12 q^{67} + 22 q^{68} - 13 q^{69} - 9 q^{70} + 2 q^{71} - 18 q^{73} - 27 q^{74} + 18 q^{75} + 3 q^{76} + 15 q^{77} - 2 q^{78} + 6 q^{79} + 48 q^{80} - 2 q^{81} + 54 q^{82} + 28 q^{83} + 31 q^{84} - 27 q^{85} - 6 q^{86} + 23 q^{87} + 9 q^{88} + 18 q^{89} + 26 q^{90} + 44 q^{92} + 2 q^{93} + 24 q^{94} + 32 q^{95} - 57 q^{96} - 34 q^{98} - 11 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 6 * q^4 + 3 * q^5 - 7 * q^6 - 12 * q^8 - 2 * q^9 - 12 * q^10 + 7 * q^11 + 7 * q^12 + 6 * q^13 + 13 * q^14 - 12 * q^15 - 6 * q^16 - 28 * q^17 + 26 * q^18 - 6 * q^19 + 17 * q^20 - 18 * q^21 + 3 * q^22 + 17 * q^23 - 30 * q^24 - 3 * q^25 + 4 * q^26 + 13 * q^27 + 30 * q^28 + 14 * q^29 - 7 * q^30 - 6 * q^31 + 9 * q^32 + 19 * q^33 - 3 * q^34 - 26 * q^35 + 43 * q^36 - 18 * q^37 - 4 * q^38 - q^39 + 6 * q^40 - 4 * q^41 - 17 * q^42 + 3 * q^43 - 26 * q^44 + 18 * q^45 + 9 * q^47 - 3 * q^48 - 21 * q^50 - 4 * q^51 + 6 * q^52 - 56 * q^53 + 35 * q^54 + 30 * q^55 + 16 * q^56 - 30 * q^57 - 18 * q^58 + 17 * q^59 - 31 * q^60 + 6 * q^61 + 8 * q^62 - 60 * q^64 - 3 * q^65 - 19 * q^66 + 12 * q^67 + 22 * q^68 - 13 * q^69 - 9 * q^70 + 2 * q^71 - 18 * q^73 - 27 * q^74 + 18 * q^75 + 3 * q^76 + 15 * q^77 - 2 * q^78 + 6 * q^79 + 48 * q^80 - 2 * q^81 + 54 * q^82 + 28 * q^83 + 31 * q^84 - 27 * q^85 - 6 * q^86 + 23 * q^87 + 9 * q^88 + 18 * q^89 + 26 * q^90 + 44 * q^92 + 2 * q^93 + 24 * q^94 + 32 * q^95 - 57 * q^96 - 34 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.10985	−	1.92231i	0.784782	−	1.35928i	−0.144348	−	0.989527i	$-0.546108\pi$
$2$	1.10985	−	1.92231i	0.784782	−	1.35928i	0.929129	−	0.369755i	$-0.120558\pi$
$3$	−0.580954	−	1.63171i	−0.335414	−	0.942071i
$3$	−0.580954	−	1.63171i	−0.335414	−	0.942071i
$4$	−1.46353	−	2.53491i	−0.731765	−	1.26745i
$5$	1.13044	+	1.95798i	0.505549	+	0.875637i	0.999979	+	0.00641945i	$0.00204339\pi$
$5$	1.13044	+	1.95798i	0.505549	+	0.875637i	−0.494430	+	0.869217i	$0.664623\pi$
$6$	−3.78144	−	0.694180i	−1.54377	−	0.283398i
$7$	−0.183027	+	0.317013i	−0.0691779	+	0.119820i	−0.898540	−	0.438892i	$-0.855371\pi$
$7$	−0.183027	+	0.317013i	−0.0691779	+	0.119820i	0.829362	+	0.558712i	$0.188704\pi$
$8$	−2.05779			−0.727539
$9$	−2.32499	+	1.89590i	−0.774995	+	0.631967i
$10$	5.01848			1.58698
$11$	−0.622629	+	1.07843i	−0.187730	+	0.325158i	−0.944493	−	0.328532i	$-0.893446\pi$
$11$	−0.622629	+	1.07843i	−0.187730	+	0.325158i	0.756763	+	0.653689i	$0.226780\pi$
$12$	−3.28600	+	3.86073i	−0.948587	+	1.11450i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	0.406266	+	0.703673i	0.108579	+	0.188064i
$15$	2.53814	−	2.98206i	0.655344	−	0.769964i
$16$	0.643223	−	1.11409i	0.160806	−	0.278524i
$17$	−6.50614			−1.57797			−0.788986	−	0.614412i	$-0.789393\pi$
$17$	−6.50614			−1.57797			−0.788986	+	0.614412i	$0.789393\pi$
$18$	1.06414	+	6.57352i	0.250820	+	1.54939i
$19$	7.78258			1.78545			0.892723	−	0.450606i	$-0.148792\pi$
$19$	7.78258			1.78545			0.892723	+	0.450606i	$0.148792\pi$
$20$	3.30887	−	5.73113i	0.739886	−	1.28152i
$21$	0.623605	+	0.114479i	0.136082	+	0.0249813i
$22$	1.38205	+	2.39378i	0.294654	+	0.510355i
$23$	−0.749331	−	1.29788i	−0.156246	−	0.270627i	0.777266	−	0.629172i	$-0.216606\pi$
$23$	−0.749331	−	1.29788i	−0.156246	−	0.270627i	−0.933512	+	0.358546i	$0.883273\pi$
$24$	1.19548	+	3.35773i	0.244027	+	0.685393i
$25$	−0.0557990	+	0.0966466i	−0.0111598	+	0.0193293i
$26$	2.21970			0.435319
$27$	4.44428	+	2.69228i	0.855302	+	0.518130i
$28$	1.07146			0.202488
$29$	−2.54916	+	4.41528i	−0.473367	+	0.819896i	−0.999535	−	0.0304843i	$-0.990295\pi$
$29$	−2.54916	+	4.41528i	−0.473367	+	0.819896i	0.526168	+	0.850381i	$0.323628\pi$
$30$	−2.91551	−	8.18873i	−0.532296	−	1.49505i
$31$	−1.82625	−	3.16316i	−0.328004	−	0.568120i	0.654112	−	0.756398i	$-0.273043\pi$
$31$	−1.82625	−	3.16316i	−0.328004	−	0.568120i	−0.982116	+	0.188278i	$0.939709\pi$
$32$	−3.48555	−	6.03715i	−0.616164	−	1.06723i
$33$	2.12140	+	0.389438i	0.369289	+	0.0677924i
$34$	−7.22084	+	12.5069i	−1.23836	+	2.14491i
$35$	−0.827608			−0.139891
$36$	8.20862	+	3.11891i	1.36810	+	0.519819i
$37$	−10.6628			−1.75296			−0.876480	−	0.481439i	$-0.840114\pi$
$37$	−10.6628			−1.75296			−0.876480	+	0.481439i	$0.840114\pi$
$38$	8.63749	−	14.9606i	1.40119	−	2.42692i
$39$	1.12263	−	1.31898i	0.179765	−	0.211206i
$40$	−2.32621	−	4.02912i	−0.367807	−	0.637060i
$41$	3.98181	+	6.89670i	0.621854	+	1.07708i	0.989140	+	0.146975i	$0.0469537\pi$
$41$	3.98181	+	6.89670i	0.621854	+	1.07708i	−0.367286	+	0.930108i	$0.619713\pi$
$42$	0.912172	−	1.07171i	0.140751	−	0.165369i
$43$	−0.123894	+	0.214591i	−0.0188937	+	0.0327249i	−0.875318	−	0.483548i	$-0.839348\pi$
$43$	−0.123894	+	0.214591i	−0.0188937	+	0.0327249i	0.856424	+	0.516273i	$0.172681\pi$
$44$	3.64495			0.549496
$45$	−6.34041	−	2.40907i	−0.945172	−	0.359124i
$46$	−3.32658			−0.490477
$47$	−3.55746	+	6.16171i	−0.518909	+	0.898777i	0.480849	+	0.876803i	$0.340328\pi$
$47$	−3.55746	+	6.16171i	−0.518909	+	0.898777i	−0.999759	+	0.0219741i	$0.993005\pi$
$48$	−2.19157	−	0.402318i	−0.316325	−	0.0580696i
$49$	3.43300	+	5.94613i	0.490429	+	0.849448i
$50$	0.123857	+	0.214526i	0.0175160	+	0.0303386i
$51$	3.77977	+	10.6162i	0.529274	+	1.48656i
$52$	1.46353	−	2.53491i	0.202955	−	0.351528i
$53$	−0.671391			−0.0922226			−0.0461113	−	0.998936i	$-0.514683\pi$
$53$	−0.671391			−0.0922226			−0.0461113	+	0.998936i	$0.514683\pi$
$54$	10.1079	−	5.55528i	1.37551	−	0.755978i
$55$	−2.81539			−0.379627
$56$	0.376632	−	0.652346i	0.0503296	−	0.0871734i
$57$	−4.52132	−	12.6989i	−0.598863	−	1.68202i
$58$	5.65837	+	9.80058i	0.742980	+	1.28688i
$59$	−3.71183	−	6.42908i	−0.483239	−	0.836995i	0.516575	−	0.856242i	$-0.327207\pi$
$59$	−3.71183	−	6.42908i	−0.483239	−	0.836995i	−0.999815	+	0.0192464i	$0.993873\pi$
$60$	−11.2739	−	2.06961i	−1.45545	−	0.267185i
$61$	2.10558	−	3.64698i	0.269592	−	0.466947i	−0.699164	−	0.714961i	$-0.746444\pi$
$61$	2.10558	−	3.64698i	0.269592	−	0.466947i	0.968757	+	0.248014i	$0.0797778\pi$
$62$	−8.10745			−1.02965
$63$	−0.175489	−	1.08405i	−0.0221096	−	0.136578i
$64$	−12.9008			−1.61261
$65$	−1.13044	+	1.95798i	−0.140214	+	0.242858i
$66$	3.10306	−	3.64578i	0.381960	−	0.448765i
$67$	−2.60671	−	4.51496i	−0.318461	−	0.551590i	0.661706	−	0.749763i	$-0.269833\pi$
$67$	−2.60671	−	4.51496i	−0.318461	−	0.551590i	−0.980167	+	0.198173i	$0.936499\pi$
$68$	9.52193	+	16.4925i	1.15470	+	2.00001i
$69$	−1.68244	+	1.97670i	−0.202542	+	0.237967i
$70$	−0.918520	+	1.59092i	−0.109784	+	0.190152i
$71$	−2.13514			−0.253394			−0.126697	−	0.991941i	$-0.540438\pi$
$71$	−2.13514			−0.253394			−0.126697	+	0.991941i	$0.540438\pi$
$72$	4.78433	−	3.90137i	0.563839	−	0.459781i
$73$	2.73585			0.320207			0.160104	−	0.987100i	$-0.448817\pi$
$73$	2.73585			0.320207			0.160104	+	0.987100i	$0.448817\pi$
$74$	−11.8341	+	20.4973i	−1.37569	+	2.38277i
$75$	0.190116	+	0.0349007i	0.0219527	+	0.00402999i
$76$	−11.3900	−	19.7281i	−1.30653	−	2.26297i
$77$	−0.227917	−	0.394763i	−0.0259735	−	0.0449874i
$78$	−1.28954	−	3.62191i	−0.146012	−	0.410101i
$79$	5.89866	−	10.2168i	0.663651	−	1.14948i	−0.315998	−	0.948760i	$-0.602339\pi$
$79$	5.89866	−	10.2168i	0.663651	−	1.14948i	0.979649	−	0.200717i	$-0.0643273\pi$
$80$	2.90850			0.325181
$81$	1.81111	−	8.81589i	0.201235	−	0.979543i
$82$	17.6768			1.95208
$83$	8.32209	−	14.4143i	0.913468	−	1.58217i	0.104339	−	0.994542i	$-0.466727\pi$
$83$	8.32209	−	14.4143i	0.913468	−	1.58217i	0.809129	−	0.587631i	$-0.199939\pi$
$84$	−0.622471	−	1.74832i	−0.0679172	−	0.190758i
$85$	−7.35482	−	12.7389i	−0.797742	−	1.38173i
$86$	0.275008	+	0.476328i	0.0296549	+	0.0513637i
$87$	8.68542	+	1.59443i	0.931175	+	0.170941i
$88$	1.28124	−	2.21917i	0.136581	−	0.236565i
$89$	3.06161			0.324530			0.162265	−	0.986747i	$-0.448120\pi$
$89$	3.06161			0.324530			0.162265	+	0.986747i	$0.448120\pi$
$90$	−11.6679	+	9.51455i	−1.22990	+	1.00292i
$91$	−0.366055			−0.0383730
$92$	−2.19334	+	3.79897i	−0.228671	+	0.396070i
$93$	−4.10040	+	4.81757i	−0.425192	+	0.499559i
$94$	7.89649	+	13.6771i	0.814461	+	1.41069i
$95$	8.79775	+	15.2382i	0.902631	+	1.56340i
$96$	−7.82596	+	9.19473i	−0.798734	+	0.938433i
$97$	5.35408	−	9.27354i	0.543624	−	0.941585i	−0.455068	−	0.890457i	$-0.650385\pi$
$97$	5.35408	−	9.27354i	0.543624	−	0.941585i	0.998692	−	0.0511283i	$-0.0162817\pi$
$98$	15.2405			1.53952
$99$	−0.596985	−	3.68777i	−0.0599993	−	0.370635i
$100$	0.326654			0.0326654
$101$	1.31411	−	2.27611i	0.130759	−	0.226481i	−0.793210	−	0.608948i	$-0.791592\pi$
$101$	1.31411	−	2.27611i	0.130759	−	0.226481i	0.923969	+	0.382466i	$0.124925\pi$
$102$	24.6026	+	4.51644i	2.43602	+	0.447194i
$103$	6.57687	+	11.3915i	0.648039	+	1.12244i	0.983591	+	0.180414i	$0.0577438\pi$
$103$	6.57687	+	11.3915i	0.648039	+	1.12244i	−0.335552	+	0.942022i	$0.608923\pi$
$104$	−1.02890	−	1.78210i	−0.100891	−	0.174749i
$105$	0.480802	+	1.35042i	0.0469215	+	0.131787i
$106$	−0.745142	+	1.29062i	−0.0723746	+	0.125356i
$107$	−18.1083			−1.75059			−0.875296	−	0.483588i	$-0.839333\pi$
$107$	−18.1083			−1.75059			−0.875296	+	0.483588i	$0.839333\pi$
$108$	0.320346	−	15.2061i	0.0308253	−	1.46320i
$109$	−14.9274			−1.42979			−0.714893	−	0.699234i	$-0.753524\pi$
$109$	−14.9274			−1.42979			−0.714893	+	0.699234i	$0.753524\pi$
$110$	−3.12465	+	5.41206i	−0.297924	+	0.516019i
$111$	6.19462	+	17.3987i	0.587967	+	1.65141i
$112$	0.235455	+	0.407820i	0.0222484	+	0.0385353i
$113$	1.17883	+	2.04180i	0.110895	+	0.192076i	0.916132	−	0.400878i	$-0.131295\pi$
$113$	1.17883	+	2.04180i	0.110895	+	0.192076i	−0.805236	+	0.592954i	$0.797961\pi$
$114$	−29.4294	−	5.40251i	−2.75631	−	0.505992i
$115$	1.69415	−	2.93436i	0.157980	−	0.273630i
$116$	14.9231			1.38557
$117$	−2.80439	−	1.06555i	−0.259266	−	0.0985097i
$118$	−16.4783			−1.51695
$119$	1.19080	−	2.06253i	0.109161	−	0.189072i
$120$	−5.22295	+	6.13645i	−0.476788	+	0.560178i
$121$	4.72467	+	8.18336i	0.429515	+	0.743942i
$122$	−4.67376	−	8.09518i	−0.423142	−	0.732904i
$123$	8.94019	−	10.5038i	0.806110	−	0.947099i
$124$	−5.34554	+	9.25875i	−0.480044	+	0.831460i
$125$	11.0521			0.988531
$126$	−2.27866	−	0.865789i	−0.202999	−	0.0771306i
$127$	1.03484			0.0918273			0.0459136	−	0.998945i	$-0.485380\pi$
$127$	1.03484			0.0918273			0.0459136	+	0.998945i	$0.485380\pi$
$128$	−7.34689	+	12.7252i	−0.649379	+	1.12476i
$129$	0.422128	+	0.0774925i	0.0371663	+	0.00682284i
$130$	2.50924	+	4.34613i	0.220075	+	0.381181i
$131$	6.57671	+	11.3912i	0.574610	+	0.995254i	0.996084	+	0.0884133i	$0.0281796\pi$
$131$	6.57671	+	11.3912i	0.574610	+	0.995254i	−0.421474	+	0.906841i	$0.638487\pi$
$132$	−2.11755	−	5.94751i	−0.184309	−	0.517664i
$133$	−1.42443	+	2.46718i	−0.123513	+	0.213931i
$134$	−11.5722			−0.999689
$135$	−0.247438	+	11.7453i	−0.0212961	+	1.01087i
$136$	13.3883			1.14804
$137$	5.97201	−	10.3438i	0.510223	−	0.883732i	−0.489707	−	0.871887i	$-0.662896\pi$
$137$	5.97201	−	10.3438i	0.510223	−	0.883732i	0.999930	−	0.0118449i	$-0.00377043\pi$
$138$	1.93259	+	5.42803i	0.164513	+	0.462064i
$139$	−3.05767	−	5.29604i	−0.259348	−	0.449204i	0.706719	−	0.707494i	$-0.250174\pi$
$139$	−3.05767	−	5.29604i	−0.259348	−	0.449204i	−0.966067	+	0.258290i	$0.916841\pi$
$140$	1.21123	+	2.09791i	0.102367	+	0.177306i
$141$	12.1209	+	2.22510i	1.02076	+	0.187387i
$142$	−2.36968	+	4.10441i	−0.198859	+	0.344434i
$143$	−1.24526			−0.104134
$144$	0.616731	+	3.80974i	0.0513942	+	0.317478i
$145$	−11.5267			−0.957242
$146$	3.03638	−	5.25917i	0.251293	−	0.435252i
$147$	7.70798	−	9.05611i	0.635743	−	0.746935i
$148$	15.6054	+	27.0293i	1.28275	+	2.22179i
$149$	−0.338498	−	0.586296i	−0.0277308	−	0.0480312i	0.851827	−	0.523823i	$-0.175495\pi$
$149$	−0.338498	−	0.586296i	−0.0277308	−	0.0480312i	−0.879558	+	0.475792i	$0.842161\pi$
$150$	0.278091	−	0.326729i	0.0227060	−	0.0266773i
$151$	−3.05723	+	5.29527i	−0.248793	+	0.430923i	−0.963191	−	0.268817i	$-0.913367\pi$
$151$	−3.05723	+	5.29527i	−0.248793	+	0.430923i	0.714398	+	0.699740i	$0.246701\pi$
$152$	−16.0149			−1.29898
$153$	15.1267	−	12.3350i	1.22292	−	0.997226i
$154$	−1.01181			−0.0815341
$155$	4.12894	−	7.15153i	0.331644	−	0.574425i
$156$	−4.98649	−	0.915398i	−0.399239	−	0.0732905i
$157$	6.86743	+	11.8947i	0.548081	+	0.949303i	0.998406	+	0.0564389i	$0.0179746\pi$
$157$	6.86743	+	11.8947i	0.548081	+	0.949303i	−0.450325	+	0.892864i	$0.648692\pi$
$158$	−13.0932	−	22.6782i	−1.04164	−	1.80418i
$159$	0.390047	+	1.09552i	0.0309327	+	0.0868802i
$160$	7.88042	−	13.6493i	0.623002	−	1.07907i
$161$	0.548593			0.0432352
$162$	−14.9369	−	13.2658i	−1.17355	−	1.04226i
$163$	5.73203			0.448968			0.224484	−	0.974478i	$-0.427930\pi$
$163$	5.73203			0.448968			0.224484	+	0.974478i	$0.427930\pi$
$164$	11.6550	−	20.1870i	0.910102	−	1.57634i
$165$	1.63561	+	4.59391i	0.127332	+	0.357635i
$166$	−18.4725	−	31.9953i	−1.43375	−	2.48332i
$167$	−10.0638	−	17.4310i	−0.778759	−	1.34885i	−0.932658	−	0.360763i	$-0.882516\pi$
$167$	−10.0638	−	17.4310i	−0.778759	−	1.34885i	0.153899	−	0.988087i	$-0.450817\pi$
$168$	−1.28325	−	0.235573i	−0.0990048	−	0.0181749i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−32.6509			−2.50421
$171$	−18.0944	+	14.7550i	−1.38371	+	1.12834i
$172$	0.725292			0.0553030
$173$	5.97476	−	10.3486i	0.454253	−	0.786789i	−0.544392	−	0.838831i	$-0.683240\pi$
$173$	5.97476	−	10.3486i	0.454253	−	0.786789i	0.998645	+	0.0520421i	$0.0165730\pi$
$174$	12.7045	−	14.9265i	0.963126	−	1.13158i
$175$	−0.0204255	−	0.0353780i	−0.00154402	−	0.00267432i
$176$	0.800978	+	1.38734i	0.0603760	+	0.104574i
$177$	−8.33403	+	9.79165i	−0.626424	+	0.735986i
$178$	3.39792	−	5.88537i	0.254685	−	0.441127i
$179$	1.00164			0.0748663			0.0374332	−	0.999299i	$-0.488082\pi$
$179$	1.00164			0.0748663			0.0374332	+	0.999299i	$0.488082\pi$
$180$	3.17259	+	19.5981i	0.236471	+	1.46076i
$181$	−18.0190			−1.33934			−0.669670	−	0.742659i	$-0.733564\pi$
$181$	−18.0190			−1.33934			−0.669670	+	0.742659i	$0.733564\pi$
$182$	−0.406266	+	0.703673i	−0.0301144	+	0.0521597i
$183$	−7.17407	−	1.31698i	−0.530323	−	0.0973543i
$184$	1.54197	+	2.67076i	0.113675	+	0.196891i
$185$	−12.0537	−	20.8777i	−0.886207	−	1.53496i
$186$	4.71005	+	13.2290i	0.345358	+	0.970000i
$187$	4.05092	−	7.01639i	0.296232	−	0.513089i
$188$	20.8258			1.51888
$189$	−1.66691	+	0.916133i	−0.121250	+	0.0666389i
$190$	39.0567			2.83347
$191$	−3.17383	+	5.49724i	−0.229651	+	0.397766i	−0.957705	−	0.287753i	$-0.907092\pi$
$191$	−3.17383	+	5.49724i	−0.229651	+	0.397766i	0.728054	+	0.685520i	$0.240425\pi$
$192$	7.49480	+	21.0505i	0.540890	+	1.51919i
$193$	1.41065	+	2.44333i	0.101541	+	0.175874i	0.912320	−	0.409478i	$-0.134289\pi$
$193$	1.41065	+	2.44333i	0.101541	+	0.175874i	−0.810779	+	0.585353i	$0.800956\pi$
$194$	−11.8844	−	20.5845i	−0.853253	−	1.47788i
$195$	3.85160	+	0.707061i	0.275819	+	0.0506337i
$196$	10.0486	−	17.4047i	0.717757	−	1.24319i
$197$	−3.40569			−0.242645			−0.121323	−	0.992613i	$-0.538714\pi$
$197$	−3.40569			−0.242645			−0.121323	+	0.992613i	$0.538714\pi$
$198$	−7.75161	−	2.94527i	−0.550883	−	0.209311i
$199$	6.75433			0.478802			0.239401	−	0.970921i	$-0.423049\pi$
$199$	6.75433			0.478802			0.239401	+	0.970921i	$0.423049\pi$
$200$	0.114823	−	0.198879i	0.00811918	−	0.0140628i
$201$	−5.85275	+	6.87640i	−0.412821	+	0.485024i
$202$	−2.91693	−	5.05228i	−0.205235	−	0.355477i
$203$	−0.933133	−	1.61623i	−0.0654931	−	0.113437i
$204$	21.3792	−	25.1184i	1.49684	−	1.75864i
$205$	−9.00241	+	15.5926i	−0.628756	+	1.08904i
$206$	29.1973			2.03428
$207$	4.20284	+	1.59689i	0.292117	+	0.110992i
$208$	1.28645			0.0891989
$209$	−4.84566	+	8.39293i	−0.335181	+	0.580551i
$210$	3.12955	+	0.574509i	0.215959	+	0.0396449i
$211$	−2.39771	−	4.15296i	−0.165065	−	0.285902i	0.771613	−	0.636092i	$-0.219450\pi$
$211$	−2.39771	−	4.15296i	−0.165065	−	0.285902i	−0.936679	+	0.350190i	$0.886117\pi$
$212$	0.982600	+	1.70191i	0.0674852	+	0.116888i
$213$	1.24042	+	3.48394i	0.0849920	+	0.238715i
$214$	−20.0974	+	34.8098i	−1.37383	+	2.37955i
$215$	−0.560221			−0.0382068
$216$	−9.14540	−	5.54015i	−0.622265	−	0.376959i
$217$	1.33702			0.0907625
$218$	−16.5672	+	28.6952i	−1.12207	+	1.94348i
$219$	−1.58940	−	4.46413i	−0.107402	−	0.301658i
$220$	4.12040	+	7.13674i	0.277797	+	0.481159i
$221$	−3.25307	−	5.63449i	−0.218825	−	0.379016i
$222$	40.3209	+	7.40193i	2.70616	+	0.496785i
$223$	4.86191	−	8.42108i	0.325578	−	0.563917i	−0.656052	−	0.754716i	$-0.727775\pi$
$223$	4.86191	−	8.42108i	0.325578	−	0.563917i	0.981629	+	0.190799i	$0.0611079\pi$
$224$	2.55181			0.170500
$225$	−0.0535008	−	0.330491i	−0.00356672	−	0.0220328i
$226$	5.23331			0.348115
$227$	−3.63401	+	6.29430i	−0.241198	+	0.417767i	−0.961056	−	0.276354i	$-0.910874\pi$
$227$	−3.63401	+	6.29430i	−0.241198	+	0.417767i	0.719858	+	0.694122i	$0.244207\pi$
$228$	−25.5736	+	30.0464i	−1.69365	+	1.98987i
$229$	0.388488	+	0.672880i	0.0256720	+	0.0444652i	0.878576	−	0.477603i	$-0.158494\pi$
$229$	0.388488	+	0.672880i	0.0256720	+	0.0444652i	−0.852904	+	0.522068i	$0.825161\pi$
$230$	−3.76050	−	6.51339i	−0.247960	−	0.429480i
$231$	−0.511732	+	0.601234i	−0.0336695	+	0.0395583i
$232$	5.24564	−	9.08571i	0.344393	−	0.596506i
$233$	11.4284			0.748701			0.374350	−	0.927287i	$-0.377866\pi$
$233$	11.4284			0.748701			0.374350	+	0.927287i	$0.377866\pi$
$234$	−5.16076	+	4.20833i	−0.337370	+	0.275107i
$235$	−16.0860			−1.04934
$236$	−10.8648	+	18.8183i	−0.707235	+	1.22497i
$237$	−20.0977	−	3.68945i	−1.30549	−	0.239656i
$238$	−2.64322	−	4.57820i	−0.171335	−	0.296760i
$239$	6.88693	+	11.9285i	0.445479	+	0.771592i	0.998085	−	0.0618504i	$-0.0197002\pi$
$239$	6.88693	+	11.9285i	0.445479	+	0.771592i	−0.552607	+	0.833442i	$0.686367\pi$
$240$	−1.68971	−	4.74585i	−0.109070	−	0.306343i
$241$	−8.18579	+	14.1782i	−0.527293	+	0.913299i	0.472201	+	0.881491i	$0.343460\pi$
$241$	−8.18579	+	14.1782i	−0.527293	+	0.913299i	−0.999494	+	0.0318076i	$0.989874\pi$
$242$	20.9747			1.34830
$243$	−15.4372	+	2.16641i	−0.990296	+	0.138975i
$244$	−12.3263			−0.789112
$245$	−7.76162	+	13.4435i	−0.495872	+	0.858875i
$246$	−10.2694	−	28.8435i	−0.654755	−	1.83900i
$247$	3.89129	+	6.73991i	0.247597	+	0.428850i
$248$	3.75804	+	6.50911i	0.238636	+	0.413329i
$249$	−28.3547	−	5.20524i	−1.79691	−	0.329869i
$250$	12.2662	−	21.2456i	0.775781	−	1.34369i
$251$	−3.64736			−0.230219			−0.115110	−	0.993353i	$-0.536722\pi$
$251$	−3.64736			−0.230219			−0.115110	+	0.993353i	$0.536722\pi$
$252$	−2.49114	+	2.03139i	−0.156927	+	0.127966i
$253$	1.86622			0.117328
$254$	1.14852	−	1.98929i	0.0720644	−	0.124819i
$255$	−16.5135	+	19.4017i	−1.03411	+	1.21498i
$256$	3.40703	+	5.90115i	0.212939	+	0.368822i
$257$	9.18143	+	15.9027i	0.572722	+	0.991983i	0.996285	+	0.0861168i	$0.0274458\pi$
$257$	9.18143	+	15.9027i	0.572722	+	0.991983i	−0.423563	+	0.905867i	$0.639221\pi$
$258$	0.617464	−	0.725459i	0.0384416	−	0.0451651i
$259$	1.95159	−	3.38026i	0.121266	−	0.210039i
$260$	6.61774			0.410415
$261$	−2.44417	−	15.0984i	−0.151290	−	0.934568i
$262$	29.1966			1.80377
$263$	1.96402	−	3.40179i	0.121107	−	0.209763i	−0.799098	−	0.601201i	$-0.794689\pi$
$263$	1.96402	−	3.40179i	0.121107	−	0.209763i	0.920204	+	0.391438i	$0.128022\pi$
$264$	−4.36540	−	0.801381i	−0.268672	−	0.0493216i
$265$	−0.758968	−	1.31457i	−0.0466230	−	0.0807535i
$266$	3.16179	+	5.47639i	0.193862	+	0.335779i
$267$	−1.77865	−	4.99567i	−0.108852	−	0.305730i
$268$	−7.63001	+	13.2156i	−0.466077	+	0.807269i
$269$	28.1752			1.71787			0.858937	−	0.512081i	$-0.171125\pi$
$269$	28.1752			1.71787			0.858937	+	0.512081i	$0.171125\pi$
$270$	22.3035	+	13.5112i	1.35735	+	0.822263i
$271$	24.6066			1.49474			0.747372	−	0.664406i	$-0.231315\pi$
$271$	24.6066			1.49474			0.747372	+	0.664406i	$0.231315\pi$
$272$	−4.18490	+	7.24846i	−0.253747	+	0.439502i
$273$	0.212661	+	0.597297i	0.0128708	+	0.0361501i
$274$	−13.2560	−	22.9601i	−0.800827	−	1.38707i
$275$	−0.0694841	−	0.120350i	−0.00419005	−	0.00725738i
$276$	7.47306	+	1.37187i	0.449826	+	0.0825770i
$277$	−11.6113	+	20.1114i	−0.697658	+	1.20838i	0.271618	+	0.962405i	$0.412441\pi$
$277$	−11.6113	+	20.1114i	−0.697658	+	1.20838i	−0.969276	+	0.245975i	$0.920892\pi$
$278$	−13.5742			−0.814127
$279$	10.2430	+	3.89190i	0.613235	+	0.233002i
$280$	1.70304			0.101776
$281$	6.66747	−	11.5484i	0.397748	−	0.688920i	−0.595700	−	0.803207i	$-0.703125\pi$
$281$	6.66747	−	11.5484i	0.397748	−	0.688920i	0.993448	+	0.114287i	$0.0364584\pi$
$282$	17.7297	−	20.8306i	1.05579	−	1.24044i
$283$	−7.55375	−	13.0835i	−0.449024	−	0.777733i	0.549299	−	0.835626i	$-0.314895\pi$
$283$	−7.55375	−	13.0835i	−0.449024	−	0.777733i	−0.998323	+	0.0578936i	$0.981562\pi$
$284$	3.12484	+	5.41238i	0.185425	+	0.321165i
$285$	19.7532	−	23.2081i	1.17008	−	1.37473i
$286$	−1.38205	+	2.39378i	−0.0817223	+	0.141547i
$287$	−2.91512			−0.172074
$288$	19.5497	+	7.42802i	1.15198	+	0.437700i
$289$	25.3299			1.48999
$290$	−12.7929	+	22.1580i	−0.751226	+	1.30116i
$291$	−18.2422	−	3.34883i	−1.06938	−	0.196312i
$292$	−4.00400	−	6.93513i	−0.234316	−	0.405848i
$293$	8.34607	+	14.4558i	0.487583	+	0.844518i	0.999898	−	0.0142793i	$-0.00454539\pi$
$293$	8.34607	+	14.4558i	0.487583	+	0.844518i	−0.512315	+	0.858797i	$0.671212\pi$
$294$	−8.85400	−	24.8681i	−0.516376	−	1.45034i
$295$	8.39202	−	14.5354i	0.488603	−	0.846284i
$296$	21.9419			1.27535
$297$	−5.67056	+	3.11653i	−0.329039	+	0.180840i
$298$	−1.50273			−0.0870506
$299$	0.749331	−	1.29788i	0.0433350	−	0.0750583i
$300$	−0.189771	−	0.533006i	−0.0109564	−	0.0307731i
$301$	−0.0453521	−	0.0785522i	−0.00261405	−	0.00452767i
$302$	6.78612	+	11.7539i	0.390497	+	0.676361i
$303$	−4.47740	−	0.821942i	−0.257220	−	0.0472193i
$304$	5.00593	−	8.67052i	0.287110	−	0.497289i
$305$	9.52096			0.545168
$306$	−6.92344	−	42.7682i	−0.395786	−	2.44490i
$307$	0.681417			0.0388905			0.0194453	−	0.999811i	$-0.493810\pi$
$307$	0.681417			0.0388905			0.0194453	+	0.999811i	$0.493810\pi$
$308$	−0.667125	+	1.15549i	−0.0380130	+	0.0658404i
$309$	14.7668	−	17.3495i	0.840053	−	0.986979i
$310$	−9.16500	−	15.8742i	−0.520537	−	0.901597i
$311$	2.98782	+	5.17506i	0.169424	+	0.293451i	0.938217	−	0.346046i	$-0.112476\pi$
$311$	2.98782	+	5.17506i	0.169424	+	0.293451i	−0.768794	+	0.639497i	$0.779143\pi$
$312$	−2.31014	+	2.71418i	−0.130786	+	0.153660i
$313$	−3.15592	+	5.46621i	−0.178383	+	0.308969i	−0.941327	−	0.337496i	$-0.890420\pi$
$313$	−3.15592	+	5.46621i	−0.178383	+	0.308969i	0.762944	+	0.646465i	$0.223753\pi$
$314$	30.4872			1.72049
$315$	1.92418	−	1.56906i	0.108415	−	0.0884067i
$316$	−34.5314			−1.94255
$317$	0.856360	−	1.48326i	0.0480980	−	0.0833081i	−0.840974	−	0.541075i	$-0.818017\pi$
$317$	0.856360	−	1.48326i	0.0480980	−	0.0833081i	0.889072	+	0.457767i	$0.151351\pi$
$318$	2.53882	+	0.466066i	0.142370	+	0.0261357i
$319$	−3.17437	−	5.49816i	−0.177730	−	0.307838i
$320$	−14.5837	−	25.2596i	−0.815251	−	1.41206i
$321$	10.5201	+	29.5475i	0.587173	+	1.64918i
$322$	0.608855	−	1.05457i	0.0339302	−	0.0587688i
$323$	−50.6346			−2.81738
$324$	−24.9981	+	8.31131i	−1.38878	+	0.461740i
$325$	−0.111598			−0.00619034
$326$	6.36169	−	11.0188i	0.352342	−	0.610274i
$327$	8.67213	+	24.3572i	0.479570	+	1.34696i
$328$	−8.19373	−	14.1920i	−0.452423	−	0.783620i
$329$	−1.30223	−	2.25552i	−0.0717941	−	0.124351i
$330$	10.6462	+	1.95439i	0.586055	+	0.107585i
$331$	4.23989	−	7.34370i	0.233045	−	0.403646i	−0.725658	−	0.688056i	$-0.758464\pi$
$331$	4.23989	−	7.34370i	0.233045	−	0.403646i	0.958703	+	0.284410i	$0.0917976\pi$
$332$	−48.7185			−2.67377
$333$	24.7909	−	20.2157i	1.35853	−	1.10781i
$334$	−44.6771			−2.44462
$335$	5.89348	−	10.2078i	0.321995	−	0.557712i
$336$	0.528657	−	0.621119i	0.0288406	−	0.0338848i
$337$	13.8562	+	23.9997i	0.754796	+	1.30735i	0.945475	+	0.325693i	$0.105598\pi$
$337$	13.8562	+	23.9997i	0.754796	+	1.30735i	−0.190679	+	0.981652i	$0.561069\pi$
$338$	1.10985	+	1.92231i	0.0603678	+	0.104560i
$339$	2.64679	−	3.10971i	0.143754	−	0.168896i
$340$	−21.5280	+	37.2876i	−1.16752	+	2.02220i
$341$	4.54831			0.246305
$342$	8.28174	+	51.1589i	0.447825	+	2.76636i
$343$	−5.07572			−0.274063
$344$	0.254948	−	0.441584i	0.0137459	−	0.0238086i
$345$	−5.77226	−	1.05965i	−0.310768	−	0.0570494i
$346$	−13.2622	−	22.9707i	−0.712978	−	1.23491i
$347$	−4.71680	−	8.16974i	−0.253211	−	0.438575i	0.711197	−	0.702993i	$-0.248153\pi$
$347$	−4.71680	−	8.16974i	−0.253211	−	0.438575i	−0.964408	+	0.264418i	$0.914820\pi$
$348$	−8.66963	−	24.3502i	−0.464741	−	1.30531i
$349$	−4.24885	+	7.35922i	−0.227435	+	0.393930i	−0.957047	−	0.289932i	$-0.906367\pi$
$349$	−4.24885	+	7.35922i	−0.227435	+	0.393930i	0.729612	+	0.683861i	$0.239701\pi$
$350$	−0.0906768			−0.00484688
$351$	−0.109443	+	5.19500i	−0.00584164	+	0.277289i
$352$	8.68082			0.462689
$353$	2.21221	−	3.83166i	0.117744	−	0.203938i	−0.801129	−	0.598491i	$-0.795767\pi$
$353$	2.21221	−	3.83166i	0.117744	−	0.203938i	0.918873	+	0.394553i	$0.129100\pi$
$354$	9.57313	+	26.8879i	0.508806	+	1.42907i
$355$	−2.41365	−	4.18056i	−0.128103	−	0.221881i
$356$	−4.48075	−	7.76089i	−0.237479	−	0.411326i
$357$	−4.05726	−	0.744815i	−0.214733	−	0.0394198i
$358$	1.11167	−	1.92547i	0.0587537	−	0.101764i
$359$	−17.7104			−0.934721			−0.467360	−	0.884067i	$-0.654795\pi$
$359$	−17.7104			−0.934721			−0.467360	+	0.884067i	$0.654795\pi$
$360$	13.0472	+	4.95737i	0.687649	+	0.261276i
$361$	41.5685			2.18782
$362$	−19.9983	+	34.6381i	−1.05109	+	1.82054i
$363$	10.6081	−	12.4635i	0.556781	−	0.654162i
$364$	0.535732	+	0.927915i	0.0280800	+	0.0486360i
$365$	3.09272	+	5.35675i	0.161880	+	0.280385i
$366$	−10.4938	+	12.3292i	−0.548519	+	0.644456i
$367$	−16.8979	+	29.2680i	−0.882064	+	1.52778i	−0.0330208	+	0.999455i	$0.510513\pi$
$367$	−16.8979	+	29.2680i	−0.882064	+	1.52778i	−0.849043	+	0.528324i	$0.822821\pi$
$368$	−1.92795			−0.100501
$369$	−22.3331	−	8.48560i	−1.16262	−	0.441742i
$370$	−53.5112			−2.78192
$371$	0.122883	−	0.212839i	0.00637976	−	0.0110501i
$372$	18.2131	+	3.34349i	0.944308	+	0.173352i
$373$	−8.29259	−	14.3632i	−0.429374	−	0.743698i	0.567443	−	0.823412i	$-0.307933\pi$
$373$	−8.29259	−	14.3632i	−0.429374	−	0.743698i	−0.996818	+	0.0797143i	$0.974599\pi$
$374$	−8.99181	−	15.5743i	−0.464955	−	0.805326i
$375$	−6.42077	−	18.0339i	−0.331567	−	0.931266i
$376$	7.32051	−	12.6795i	0.377527	−	0.653895i
$377$	−5.09832			−0.262577
$378$	−0.0889259	+	4.22110i	−0.00457386	+	0.217110i
$379$	2.69355			0.138358			0.0691792	−	0.997604i	$-0.477962\pi$
$379$	2.69355			0.138358			0.0691792	+	0.997604i	$0.477962\pi$
$380$	25.7515	−	44.6030i	1.32103	−	2.28808i
$381$	−0.601195	−	1.68856i	−0.0308001	−	0.0865078i
$382$	7.04495	+	12.2022i	0.360451	+	0.624320i
$383$	1.96047	+	3.39564i	0.100175	+	0.173509i	0.911757	−	0.410730i	$-0.134726\pi$
$383$	1.96047	+	3.39564i	0.100175	+	0.173509i	−0.811581	+	0.584239i	$0.801393\pi$
$384$	25.0321	+	4.59528i	1.27741	+	0.234502i
$385$	0.515293	−	0.892514i	0.0262618	−	0.0454867i
$386$	6.26245			0.318751
$387$	−0.118792	−	0.733813i	−0.00603851	−	0.0373018i
$388$	−31.3434			−1.59122
$389$	−5.48433	+	9.49914i	−0.278066	+	0.481625i	−0.970904	−	0.239468i	$-0.923027\pi$
$389$	−5.48433	+	9.49914i	−0.278066	+	0.481625i	0.692838	+	0.721094i	$0.256360\pi$
$390$	5.63389	−	6.61927i	0.285283	−	0.335180i
$391$	4.87526	+	8.44419i	0.246552	+	0.427041i
$392$	−7.06440	−	12.2359i	−0.356806	−	0.618006i
$393$	14.7664	−	17.3491i	0.744867	−	0.875145i
$394$	−3.77980	+	6.54681i	−0.190424	+	0.329823i
$395$	26.6724			1.34203
$396$	−8.47444	+	6.91046i	−0.425857	+	0.347264i
$397$	20.2614			1.01689			0.508445	−	0.861095i	$-0.330221\pi$
$397$	20.2614			1.01689			0.508445	+	0.861095i	$0.330221\pi$
$398$	7.49629	−	12.9839i	0.375755	−	0.650827i
$399$	4.85326	+	0.890940i	0.242967	+	0.0446028i
$400$	0.0717823	+	0.124331i	0.00358912	+	0.00621653i
$401$	0.184306	+	0.319227i	0.00920380	+	0.0159415i	0.870591	−	0.492008i	$-0.163737\pi$
$401$	0.184306	+	0.319227i	0.00920380	+	0.0159415i	−0.861387	+	0.507950i	$0.830404\pi$
$402$	6.72294	+	18.8826i	0.335310	+	0.941778i
$403$	1.82625	−	3.16316i	0.0909720	−	0.157568i
$404$	−7.69297			−0.382740
$405$	19.3087	−	6.41973i	0.959458	−	0.318999i
$406$	−4.14255			−0.205591
$407$	6.63899	−	11.4991i	0.329083	−	0.569988i
$408$	−7.77797	−	21.8458i	−0.385067	−	1.08153i
$409$	−0.943623	−	1.63440i	−0.0466592	−	0.0808160i	0.841753	−	0.539863i	$-0.181524\pi$
$409$	−0.943623	−	1.63440i	−0.0466592	−	0.0808160i	−0.888412	+	0.459047i	$0.848191\pi$
$410$	19.9826	+	34.6109i	0.986872	+	1.70931i
$411$	−20.3476	−	3.73533i	−1.00367	−	0.184250i
$412$	19.2509	−	33.3435i	0.948424	−	1.64272i
$413$	2.71747			0.133718
$414$	7.73425	−	6.30687i	0.380117	−	0.309966i
$415$	37.6306			1.84721
$416$	3.48555	−	6.03715i	0.170893	−	0.295996i
$417$	−6.86526	+	8.06600i	−0.336193	+	0.394994i
$418$	10.7559	+	18.6298i	0.526088	+	0.911212i
$419$	3.76757	+	6.52563i	0.184058	+	0.318798i	0.943259	−	0.332059i	$-0.107743\pi$
$419$	3.76757	+	6.52563i	0.184058	+	0.318798i	−0.759201	+	0.650857i	$0.774410\pi$
$420$	2.71952	−	3.19517i	0.132699	−	0.155908i
$421$	−7.83212	+	13.5656i	−0.381714	+	0.661148i	−0.991307	−	0.131566i	$-0.957999\pi$
$421$	−7.83212	+	13.5656i	−0.381714	+	0.661148i	0.609593	+	0.792714i	$0.291333\pi$
$422$	−10.6444			−0.518161
$423$	−3.41094	−	21.0705i	−0.165846	−	1.02448i
$424$	1.38158			0.0670955
$425$	0.363036	−	0.628797i	0.0176098	−	0.0305011i
$426$	8.07390	+	1.48217i	0.391182	+	0.0718114i
$427$	0.770759	+	1.33499i	0.0372996	+	0.0646049i
$428$	26.5020	+	45.9028i	1.28102	+	2.21879i
$429$	0.723438	+	2.03191i	0.0349279	+	0.0981014i
$430$	−0.621761	+	1.07692i	−0.0299840	+	0.0519338i
$431$	8.24909			0.397345			0.198672	−	0.980066i	$-0.436337\pi$
$431$	8.24909			0.397345			0.198672	+	0.980066i	$0.436337\pi$
$432$	5.85812	−	3.21961i	0.281849	−	0.154904i
$433$	−35.8304			−1.72190			−0.860949	−	0.508692i	$-0.830129\pi$
$433$	−35.8304			−1.72190			−0.860949	+	0.508692i	$0.830129\pi$
$434$	1.48389	−	2.57016i	0.0712288	−	0.123372i
$435$	6.69649	+	18.8083i	0.321072	+	0.901790i
$436$	21.8467	+	37.8396i	1.04627	+	1.81219i
$437$	−5.83173	−	10.1009i	−0.278970	−	0.483189i
$438$	−10.3455	−	1.89917i	−0.494325	−	0.0907460i
$439$	−14.8270	+	25.6811i	−0.707653	+	1.22569i	0.258072	+	0.966126i	$0.416913\pi$
$439$	−14.8270	+	25.6811i	−0.707653	+	1.22569i	−0.965725	+	0.259566i	$0.916421\pi$
$440$	5.79347			0.276193
$441$	−19.2550	−	7.31604i	−0.916903	−	0.348383i
$442$	−14.4417			−0.686920
$443$	10.0467	−	17.4014i	0.477334	−	0.826767i	−0.522328	−	0.852745i	$-0.674936\pi$
$443$	10.0467	−	17.4014i	0.477334	−	0.826767i	0.999663	+	0.0259772i	$0.00826973\pi$
$444$	35.0381	−	41.1663i	1.66283	−	1.95367i
$445$	3.46097	+	5.99457i	0.164066	+	0.284170i
$446$	−10.7920	−	18.6922i	−0.511015	−	0.885103i
$447$	−0.760016	+	0.892943i	−0.0359475	+	0.0422347i
$448$	2.36121	−	4.08973i	0.111557	−	0.193222i
$449$	−23.9831			−1.13183			−0.565916	−	0.824463i	$-0.691477\pi$
$449$	−23.9831			−1.13183			−0.565916	+	0.824463i	$0.691477\pi$
$450$	−0.694686	−	0.263950i	−0.0327478	−	0.0124427i
$451$	−9.91677			−0.466962
$452$	3.45052	−	5.97647i	0.162299	−	0.281110i
$453$	10.4165	+	1.91221i	0.489409	+	0.0898435i
$454$	8.06641	+	13.9714i	0.378576	+	0.655712i
$455$	−0.413804	−	0.716729i	−0.0193994	−	0.0336008i
$456$	9.30393	+	26.1318i	0.435696	+	1.22373i
$457$	16.1383	−	27.9523i	0.754917	−	1.30755i	−0.190498	−	0.981688i	$-0.561010\pi$
$457$	16.1383	−	27.9523i	0.754917	−	1.30755i	0.945416	−	0.325867i	$-0.105656\pi$
$458$	1.72465			0.0805876
$459$	−28.9151	−	17.5164i	−1.34964	−	0.817594i
$460$	−9.91776			−0.462418
$461$	10.2015	−	17.6696i	0.475133	−	0.822954i	−0.524462	−	0.851434i	$-0.675733\pi$
$461$	10.2015	−	17.6696i	0.475133	−	0.822954i	0.999594	+	0.0284799i	$0.00906667\pi$
$462$	0.587816	+	1.65099i	0.0273477	+	0.0768109i
$463$	3.04455	+	5.27332i	0.141492	+	0.245072i	0.928059	−	0.372434i	$-0.121477\pi$
$463$	3.04455	+	5.27332i	0.141492	+	0.245072i	−0.786566	+	0.617506i	$0.788143\pi$
$464$	3.27936	+	5.68001i	0.152240	+	0.263688i
$465$	−14.0680	−	2.58254i	−0.652387	−	0.119762i
$466$	12.6838	−	21.9690i	0.587567	−	1.01770i
$467$	−34.1628			−1.58087			−0.790434	−	0.612548i	$-0.790145\pi$
$467$	−34.1628			−1.58087			−0.790434	+	0.612548i	$0.790145\pi$
$468$	1.40325	+	8.66833i	0.0648653	+	0.400694i
$469$	1.90840			0.0881218
$470$	−17.8531	+	30.9224i	−0.823500	+	1.42634i
$471$	15.4192	−	18.1160i	0.710477	−	0.834740i
$472$	7.63817	+	13.2297i	0.351575	+	0.608946i
$473$	−0.154280	−	0.267222i	−0.00709382	−	0.0122869i
$474$	−29.3977	+	34.5394i	−1.35028	+	1.58645i
$475$	−0.434260	+	0.752160i	−0.0199252	+	0.0345115i
$476$	−6.97110			−0.319520
$477$	1.56097	−	1.27289i	0.0714720	−	0.0582817i
$478$	30.5738			1.39841
$479$	−2.75116	+	4.76514i	−0.125704	+	0.217725i	−0.922008	−	0.387171i	$-0.873452\pi$
$479$	−2.75116	+	4.76514i	−0.125704	+	0.217725i	0.796304	+	0.604896i	$0.206785\pi$
$480$	−26.8499	−	4.92899i	−1.22553	−	0.224977i
$481$	−5.33142	−	9.23429i	−0.243092	−	0.421047i
$482$	18.1700	+	31.4713i	0.827620	+	1.43348i
$483$	−0.318707	−	0.895147i	−0.0145017	−	0.0407306i
$484$	13.8294	−	23.9532i	0.628608	−	1.08878i
$485$	24.2099			1.09932
$486$	−12.9684	+	32.0795i	−0.588260	+	1.45516i
$487$	9.28234			0.420623			0.210311	−	0.977634i	$-0.432552\pi$
$487$	9.28234			0.420623			0.210311	+	0.977634i	$0.432552\pi$
$488$	−4.33285	+	7.50471i	−0.196139	+	0.339722i
$489$	−3.33005	−	9.35305i	−0.150590	−	0.422959i
$490$	17.2285	+	29.8406i	0.778302	+	1.34806i
$491$	−15.8720	−	27.4912i	−0.716295	−	1.24066i	−0.962458	−	0.271431i	$-0.912503\pi$
$491$	−15.8720	−	27.4912i	−0.716295	−	1.24066i	0.246163	−	0.969228i	$-0.420830\pi$
$492$	−39.7105	−	7.28988i	−1.79029	−	0.328653i
$493$	16.5852	−	28.7264i	0.746960	−	1.29377i
$494$	17.2750			0.777238
$495$	6.54573	−	5.33770i	0.294209	−	0.239912i
$496$	−4.69874			−0.210980
$497$	0.390789	−	0.676866i	0.0175293	−	0.0303616i
$498$	−41.4756	+	48.7297i	−1.85857	+	2.18363i
$499$	8.78006	+	15.2075i	0.393050	+	0.680782i	0.992850	−	0.119368i	$-0.0380867\pi$
$499$	8.78006	+	15.2075i	0.393050	+	0.680782i	−0.599800	+	0.800150i	$0.704753\pi$
$500$	−16.1751	−	28.0161i	−0.723372	−	1.25292i
$501$	−22.5958	+	26.5478i	−1.00951	+	1.18607i
$502$	−4.04802	+	7.01137i	−0.180672	+	0.312933i
$503$	−9.35855			−0.417277			−0.208639	−	0.977993i	$-0.566903\pi$
$503$	−9.35855			−0.417277			−0.208639	+	0.977993i	$0.566903\pi$
$504$	0.361120	+	2.23075i	0.0160856	+	0.0993656i
$505$	5.94211			0.264421
$506$	2.07123	−	3.58747i	0.0920772	−	0.159482i
$507$	1.70358	+	0.312736i	0.0756588	+	0.0138891i
$508$	−1.51452	−	2.62322i	−0.0671959	−	0.116387i
$509$	9.93570	+	17.2091i	0.440392	+	0.762781i	0.997718	−	0.0675120i	$-0.0215061\pi$
$509$	9.93570	+	17.2091i	0.440392	+	0.762781i	−0.557326	+	0.830294i	$0.688173\pi$
$510$	18.9687	+	53.2770i	0.839948	+	2.35915i
$511$	−0.500736	+	0.867300i	−0.0221512	+	0.0383671i
$512$	−14.2624			−0.630315
$513$	34.5880	+	20.9529i	1.52710	+	0.925092i
$514$	40.7600			1.79785
$515$	−14.8696	+	25.7548i	−0.655231	+	1.13489i
$516$	−0.421361	−	1.18347i	−0.0185494	−	0.0520993i
$517$	−4.42996	−	7.67292i	−0.194830	−	0.337455i
$518$	−4.33194	−	7.50315i	−0.190335	−	0.329669i
$519$	−20.3570	−	3.73705i	−0.893573	−	0.164038i
$520$	2.32621	−	4.02912i	0.102011	−	0.176689i
$521$	25.6348			1.12308			0.561541	−	0.827449i	$-0.310209\pi$
$521$	25.6348			1.12308			0.561541	+	0.827449i	$0.310209\pi$
$522$	−31.7366	−	12.0585i	−1.38907	−	0.527786i
$523$	−37.5901			−1.64370			−0.821849	−	0.569705i	$-0.807057\pi$
$523$	−37.5901			−1.64370			−0.821849	+	0.569705i	$0.807057\pi$
$524$	19.2504	−	33.3427i	0.840959	−	1.45658i
$525$	−0.0458605	+	0.0538815i	−0.00200152	+	0.00235158i
$526$	−4.35954	−	7.55095i	−0.190085	−	0.329237i
$527$	11.8818	+	20.5800i	0.517581	+	0.896477i
$528$	1.79840	−	2.11295i	0.0782655	−	0.0919542i
$529$	10.3770	−	17.9735i	0.451174	−	0.781456i
$530$	−3.36936			−0.146356
$531$	20.8189	+	7.91025i	0.903462	+	0.343276i
$532$	8.33875			0.361531
$533$	−3.98181	+	6.89670i	−0.172471	+	0.298729i
$534$	−11.5773	−	2.12531i	−0.500998	−	0.0919710i
$535$	−20.4703	−	35.4557i	−0.885010	−	1.53288i
$536$	5.36407	+	9.29084i	0.231693	+	0.401303i
$537$	−0.581909	−	1.63440i	−0.0251112	−	0.0705294i
$538$	31.2702	−	54.1617i	1.34816	−	2.33507i
$539$	−8.54995			−0.368272
$540$	30.1354	−	16.5623i	1.29682	−	0.712730i
$541$	−17.6842			−0.760304			−0.380152	−	0.924924i	$-0.624128\pi$
$541$	−17.6842			−0.760304			−0.380152	+	0.924924i	$0.624128\pi$
$542$	27.3096	−	47.3016i	1.17305	−	2.03178i
$543$	10.4682	+	29.4018i	0.449233	+	1.26175i
$544$	22.6775	+	39.2786i	0.972289	+	1.68405i
$545$	−16.8746	−	29.2276i	−0.722827	−	1.25197i
$546$	1.38421	+	0.254108i	0.0592389	+	0.0108748i
$547$	11.8723	−	20.5635i	0.507623	−	0.879230i	−0.492338	−	0.870404i	$-0.663857\pi$
$547$	11.8723	−	20.5635i	0.507623	−	0.879230i	0.999961	−	0.00882531i	$-0.00280922\pi$
$548$	−34.9608			−1.49345
$549$	2.01886	+	12.4711i	0.0861629	+	0.532255i
$550$	−0.308468			−0.0131531
$551$	−19.8390	+	34.3622i	−0.845172	+	1.46388i
$552$	3.46211	−	4.06764i	0.147357	−	0.173130i
$553$	2.15923	+	3.73990i	0.0918199	+	0.159037i
$554$	25.7737	+	44.6413i	1.09502	+	1.89663i
$555$	−27.0637	+	31.7972i	−1.14879	+	1.34972i
$556$	−8.94998	+	15.5018i	−0.379564	+	0.657423i
$557$	2.59164			0.109811			0.0549056	−	0.998492i	$-0.482514\pi$
$557$	2.59164			0.109811			0.0549056	+	0.998492i	$0.482514\pi$
$558$	18.8497	−	15.3709i	0.797971	−	0.650703i
$559$	−0.247789			−0.0104803
$560$	−0.532336	+	0.922033i	−0.0224953	+	0.0389630i
$561$	−13.8021	−	2.53374i	−0.582727	−	0.106974i
$562$	−14.7998	−	25.6340i	−0.624291	−	1.08130i
$563$	2.73931	+	4.74462i	0.115448	+	0.199962i	0.917959	−	0.396676i	$-0.129836\pi$
$563$	2.73931	+	4.74462i	0.115448	+	0.199962i	−0.802511	+	0.596638i	$0.796503\pi$
$564$	−12.0988	−	33.9818i	−0.509453	−	1.43089i
$565$	−2.66521	+	4.61628i	−0.112126	+	0.194208i
$566$	−33.5341			−1.40954
$567$	2.46327	+	2.18770i	0.103447	+	0.0918746i
$568$	4.39367			0.184354
$569$	−12.7695	+	22.1174i	−0.535324	+	0.927208i	0.463824	+	0.885928i	$0.346477\pi$
$569$	−12.7695	+	22.1174i	−0.535324	+	0.927208i	−0.999148	+	0.0412807i	$0.986856\pi$
$570$	−22.6902	−	63.7294i	−0.950386	−	2.66933i
$571$	−3.14697	−	5.45071i	−0.131696	−	0.228105i	0.792634	−	0.609698i	$-0.208709\pi$
$571$	−3.14697	−	5.45071i	−0.131696	−	0.228105i	−0.924331	+	0.381593i	$0.875376\pi$
$572$	1.82247	+	3.15662i	0.0762014	+	0.131985i
$573$	10.8138	+	1.98515i	0.451752	+	0.0829307i
$574$	−3.23535	+	5.60378i	−0.135041	+	0.233897i
$575$	0.167248			0.00697471
$576$	29.9943	−	24.4587i	1.24976	−	1.01911i
$577$	2.79543			0.116375			0.0581877	−	0.998306i	$-0.481468\pi$
$577$	2.79543			0.116375			0.0581877	+	0.998306i	$0.481468\pi$
$578$	28.1124	−	48.6920i	1.16932	−	2.02532i
$579$	3.16728	−	3.72125i	0.131628	−	0.154650i
$580$	16.8697	+	29.2192i	0.700476	+	1.21326i
$581$	3.04634	+	5.27642i	0.126384	+	0.218903i
$582$	−26.6836	+	31.3506i	−1.10607	+	1.29953i
$583$	0.418027	−	0.724045i	0.0173129	−	0.0299869i
$584$	−5.62981			−0.232963
$585$	−1.08388	−	6.69549i	−0.0448131	−	0.276824i
$586$	37.0515			1.53058
$587$	12.2216	−	21.1684i	0.504438	−	0.873712i	−0.495549	−	0.868580i	$-0.665033\pi$
$587$	12.2216	−	21.1684i	0.504438	−	0.873712i	0.999987	−	0.00513194i	$-0.00163355\pi$
$588$	−34.2372	−	6.28513i	−1.41192	−	0.259194i
$589$	−14.2129	−	24.6175i	−0.585634	−	1.01435i
$590$	−18.6278	−	32.2642i	−0.766893	−	1.32830i
$591$	1.97855	+	5.55711i	0.0813866	+	0.228589i
$592$	−6.85858	+	11.8794i	−0.281886	+	0.488240i
$593$	9.19811			0.377721			0.188861	−	0.982004i	$-0.439521\pi$
$593$	9.19811			0.377721			0.188861	+	0.982004i	$0.439521\pi$
$594$	−0.302511	+	14.3595i	−0.0124122	+	0.589177i
$595$	5.38454			0.220744
$596$	−0.990803	+	1.71612i	−0.0405849	+	0.0702951i
$597$	−3.92396	−	11.0211i	−0.160597	−	0.451065i
$598$	−1.66329	−	2.88090i	−0.0680170	−	0.117809i
$599$	−15.8080	−	27.3802i	−0.645897	−	1.11873i	−0.984094	−	0.177651i	$-0.943150\pi$
$599$	−15.8080	−	27.3802i	−0.645897	−	1.11873i	0.338197	−	0.941075i	$-0.390183\pi$
$600$	−0.391220	−	0.0718184i	−0.0159715	−	0.00293197i
$601$	−18.1503	+	31.4372i	−0.740366	+	1.28235i	0.211963	+	0.977278i	$0.432014\pi$
$601$	−18.1503	+	31.4372i	−0.740366	+	1.28235i	−0.952329	+	0.305073i	$0.901319\pi$
$602$	−0.201336			−0.00820584
$603$	14.6205	+	5.55514i	0.595393	+	0.226223i
$604$	17.8974			0.728233
$605$	−10.6819	+	18.5016i	−0.434282	+	0.752198i
$606$	−6.54927	+	7.69474i	−0.266046	+	0.312578i
$607$	−23.7415	−	41.1215i	−0.963638	−	1.66907i	−0.713231	−	0.700929i	$-0.752769\pi$
$607$	−23.7415	−	41.1215i	−0.963638	−	1.66907i	−0.250407	−	0.968141i	$-0.580564\pi$
$608$	−27.1266	−	46.9846i	−1.10013	−	1.90548i
$609$	−2.09513	+	2.46156i	−0.0848988	+	0.0997476i
$610$	10.5668	−	18.3023i	0.427838	−	0.741037i
$611$	−7.11493			−0.287839
$612$	−53.4065	−	20.2921i	−2.15883	−	0.820259i
$613$	−20.0621			−0.810302			−0.405151	−	0.914250i	$-0.632781\pi$
$613$	−20.0621			−0.810302			−0.405151	+	0.914250i	$0.632781\pi$
$614$	0.756270	−	1.30990i	0.0305206	−	0.0528632i
$615$	30.6727	+	5.63076i	1.23684	+	0.227054i
$616$	0.469004	+	0.812339i	0.0188967	+	0.0327301i
$617$	−13.3414	−	23.1080i	−0.537106	−	0.930295i	−0.999058	−	0.0433901i	$-0.986184\pi$
$617$	−13.3414	−	23.1080i	−0.537106	−	0.930295i	0.461952	−	0.886905i	$-0.347149\pi$
$618$	−16.9623	−	47.6417i	−0.682324	−	1.91643i
$619$	7.64737	−	13.2456i	0.307374	−	0.532387i	−0.670413	−	0.741988i	$-0.733883\pi$
$619$	7.64737	−	13.2456i	0.307374	−	0.532387i	0.977787	+	0.209601i	$0.0672165\pi$
$620$	−24.1713			−0.970743
$621$	0.164018	−	7.78555i	0.00658183	−	0.312423i
$622$	13.2641			0.531843
$623$	−0.560358	+	0.970568i	−0.0224503	+	0.0388850i
$624$	−0.747365	−	2.09911i	−0.0299186	−	0.0840317i
$625$	12.7728	+	22.1231i	0.510911	+	0.884923i
$626$	7.00519	+	12.1333i	0.279984	+	0.484946i
$627$	16.5100	+	3.03083i	0.659345	+	0.121040i
$628$	20.1014	−	34.8166i	0.802132	−	1.38933i
$629$	69.3739			2.76612
$630$	−0.880689	−	5.44030i	−0.0350875	−	0.216747i
$631$	6.08024			0.242051			0.121025	−	0.992649i	$-0.461382\pi$
$631$	6.08024			0.242051			0.121025	+	0.992649i	$0.461382\pi$
$632$	−12.1382	+	21.0240i	−0.482832	+	0.836289i
$633$	−5.38349	+	6.32507i	−0.213974	+	0.251399i
$634$	−1.90086	−	3.29239i	−0.0754928	−	0.130757i
$635$	1.16983	+	2.02620i	0.0464232	+	0.0804073i
$636$	2.20619	−	2.59206i	0.0874811	−	0.102782i
$637$	−3.43300	+	5.94613i	−0.136020	+	0.235594i
$638$	−14.0923			−0.557918
$639$	4.96416	−	4.04801i	0.196379	−	0.160137i
$640$	−33.2209			−1.31317
$641$	6.61858	−	11.4637i	0.261418	−	0.452789i	−0.705201	−	0.709008i	$-0.749143\pi$
$641$	6.61858	−	11.4637i	0.261418	−	0.452789i	0.966619	+	0.256218i	$0.0824765\pi$
$642$	68.4753	+	12.5704i	2.70250	+	0.496114i
$643$	21.9855	+	38.0801i	0.867025	+	1.50173i	0.865022	+	0.501734i	$0.167304\pi$
$643$	21.9855	+	38.0801i	0.867025	+	1.50173i	0.00200304	+	0.999998i	$0.499362\pi$
$644$	−0.802882	−	1.39063i	−0.0316380	−	0.0547986i
$645$	0.325463	+	0.914121i	0.0128151	+	0.0359935i
$646$	−56.1967	+	97.3356i	−2.21103	+	3.82962i
$647$	17.6899			0.695460			0.347730	−	0.937595i	$-0.386953\pi$
$647$	17.6899			0.695460			0.347730	+	0.937595i	$0.386953\pi$
$648$	−3.72689	+	18.1412i	−0.146406	+	0.712655i
$649$	9.24438			0.362874
$650$	−0.123857	+	0.214526i	−0.00485807	+	0.00841442i
$651$	−0.776744	−	2.18163i	−0.0304430	−	0.0855047i
$652$	−8.38900	−	14.5302i	−0.328539	−	0.569046i
$653$	21.1552	+	36.6418i	0.827866	+	1.43391i	0.899709	+	0.436490i	$0.143779\pi$
$653$	21.1552	+	36.6418i	0.827866	+	1.43391i	−0.0718428	+	0.997416i	$0.522888\pi$
$654$	56.4471	+	10.3623i	2.20725	+	0.405198i
$655$	−14.8692	+	25.7542i	−0.580987	+	1.00630i
$656$	10.2448			0.399991
$657$	−6.36081	+	5.18691i	−0.248159	+	0.202360i
$658$	−5.78110			−0.225371
$659$	21.7571	−	37.6844i	0.847536	−	1.46798i	−0.0358650	−	0.999357i	$-0.511419\pi$
$659$	21.7571	−	37.6844i	0.847536	−	1.46798i	0.883401	−	0.468618i	$-0.155248\pi$
$660$	9.25136	−	10.8694i	0.360109	−	0.423092i
$661$	10.1142	+	17.5183i	0.393397	+	0.681384i	0.992895	−	0.118992i	$-0.0379663\pi$
$661$	10.1142	+	17.5183i	0.393397	+	0.681384i	−0.599498	+	0.800376i	$0.704633\pi$
$662$	−9.41127	−	16.3008i	−0.365779	−	0.633548i
$663$	−7.30399	+	8.58146i	−0.283663	+	0.333276i
$664$	−17.1251	+	29.6616i	−0.664583	+	1.15109i
$665$	−6.44092			−0.249768
$666$	−11.3467	−	70.0923i	−0.439677	−	2.71602i
$667$	7.64067			0.295848
$668$	−29.4573	+	51.0215i	−1.13974	+	1.97408i
$669$	−16.5653	−	3.04099i	−0.640453	−	0.117572i
$670$	−13.0817	−	22.6582i	−0.505392	−	0.875364i
$671$	2.62199	+	4.54143i	0.101221	+	0.175320i
$672$	−1.48248	−	4.16382i	−0.0571880	−	0.160623i
$673$	−8.22550	+	14.2470i	−0.317070	+	0.549181i	−0.979875	−	0.199611i	$-0.936032\pi$
$673$	−8.22550	+	14.2470i	−0.317070	+	0.549181i	0.662806	+	0.748791i	$0.269366\pi$
$674$	61.5132			2.36940
$675$	−0.508186	+	0.279298i	−0.0195601	+	0.0107502i
$676$	2.92706			0.112579
$677$	−8.55184	+	14.8122i	−0.328674	+	0.569280i	−0.982249	−	0.187582i	$-0.939935\pi$
$677$	−8.55184	+	14.8122i	−0.328674	+	0.569280i	0.653575	+	0.756862i	$0.273268\pi$
$678$	−3.04031	−	8.53927i	−0.116763	−	0.327949i
$679$	1.95989	+	3.39462i	0.0752136	+	0.130274i
$680$	15.1347	+	26.2140i	0.580388	+	1.00526i
$681$	12.3817	+	2.27298i	0.474467	+	0.0871007i
$682$	5.04793	−	8.74328i	0.193295	−	0.334797i
$683$	20.4528			0.782605			0.391302	−	0.920262i	$-0.372025\pi$
$683$	20.4528			0.782605			0.391302	+	0.920262i	$0.372025\pi$
$684$	63.8842	+	24.2732i	2.44267	+	0.928108i
$685$	27.0040			1.03177
$686$	−5.63328	+	9.75713i	−0.215080	+	0.372529i
$687$	0.872255	−	1.02481i	0.0332786	−	0.0390991i
$688$	0.159383	+	0.276060i	0.00607643	+	0.0105247i
$689$	−0.335695	−	0.581441i	−0.0127890	−	0.0221511i
$690$	−8.44331	+	9.92005i	−0.321431	+	0.377650i
$691$	−13.4542	+	23.3034i	−0.511823	+	0.886504i	0.488083	+	0.872797i	$0.337696\pi$
$691$	−13.4542	+	23.3034i	−0.511823	+	0.886504i	−0.999906	+	0.0137063i	$0.995637\pi$
$692$	−34.9769			−1.32962
$693$	1.27833	+	0.485711i	0.0485599	+	0.0184506i
$694$	−20.9398			−0.794862
$695$	6.91304	−	11.9737i	0.262226	−	0.454190i
$696$	−17.8728	−	3.28101i	−0.677465	−	0.124366i
$697$	−25.9062	−	44.8709i	−0.981268	−	1.69961i
$698$	9.43115	+	16.3352i	0.356974	+	0.618298i
$699$	−6.63939	−	18.6479i	−0.251125	−	0.705329i
$700$	−0.0597866	+	0.103553i	−0.00225972	+	0.00391395i
$701$	−41.0736			−1.55133			−0.775664	−	0.631146i	$-0.782585\pi$
$701$	−41.0736			−1.55133			−0.775664	+	0.631146i	$0.782585\pi$
$702$	9.86496	+	5.97605i	0.372329	+	0.225551i
$703$	−82.9843			−3.12981
$704$	8.03244	−	13.9126i	0.302734	−	0.524351i
$705$	9.34524	+	26.2478i	0.351962	+	0.988549i
$706$	−4.91043	−	8.50512i	−0.184807	−	0.320094i
$707$	0.481037	+	0.833181i	0.0180913	+	0.0313350i
$708$	37.0180	+	6.79561i	1.39122	+	0.255395i
$709$	15.9952	−	27.7046i	0.600714	−	1.04047i	−0.392000	−	0.919965i	$-0.628217\pi$
$709$	15.9952	−	27.7046i	0.600714	−	1.04047i	0.992713	−	0.120501i	$-0.0384501\pi$
$710$	−10.7151			−0.402132
$711$	5.65571	+	34.9371i	0.212106	+	1.31024i
$712$	−6.30014			−0.236108
$713$	−2.73693	+	4.74051i	−0.102499	+	0.177533i
$714$	−5.93472	+	6.97271i	−0.222101	+	0.260947i
$715$	−1.40769	−	2.43820i	−0.0526447	−	0.0911833i
$716$	−1.46593	−	2.53907i	−0.0547845	−	0.0948896i
$717$	15.4629	−	18.1674i	0.577474	−	0.678475i
$718$	−19.6559	+	34.0450i	−0.733552	+	1.27055i
$719$	−2.09070			−0.0779698			−0.0389849	−	0.999240i	$-0.512412\pi$
$719$	−2.09070			−0.0779698			−0.0389849	+	0.999240i	$0.512412\pi$
$720$	−6.76223	+	5.51424i	−0.252013	+	0.205504i
$721$	−4.81499			−0.179320
$722$	46.1348	−	79.9078i	1.71696	−	2.97386i
$723$	27.8904	+	5.11999i	1.03725	+	0.190414i
$724$	26.3713	+	45.6764i	0.980081	+	1.69755i
$725$	−0.284481	−	0.492736i	−0.0105654	−	0.0182997i
$726$	−12.1853	−	34.2247i	−0.452239	−	1.27020i
$727$	−20.7917	+	36.0123i	−0.771122	+	1.33562i	0.165827	+	0.986155i	$0.446971\pi$
$727$	−20.7917	+	36.0123i	−0.771122	+	1.33562i	−0.936949	+	0.349467i	$0.886363\pi$
$728$	0.753264			0.0279178
$729$	12.5033	+	23.9305i	0.463083	+	0.886315i
$730$	13.7298			0.508163
$731$	0.806074	−	1.39616i	0.0298137	−	0.0516389i
$732$	7.16103	+	20.1130i	0.264679	+	0.743400i
$733$	−20.8400	−	36.0959i	−0.769742	−	1.33323i	−0.937703	−	0.347438i	$-0.887052\pi$
$733$	−20.8400	−	36.0959i	−0.769742	−	1.33323i	0.167961	−	0.985794i	$-0.446282\pi$
$734$	37.5082	+	64.9662i	1.38445	+	2.39795i
$735$	26.4451	+	4.85468i	0.975443	+	0.179068i
$736$	−5.22366	+	9.04765i	−0.192547	+	0.333501i
$737$	6.49207			0.239138
$738$	−41.0984	+	33.5135i	−1.51285	+	1.23365i
$739$	0.873438			0.0321299			0.0160650	−	0.999871i	$-0.494886\pi$
$739$	0.873438			0.0321299			0.0160650	+	0.999871i	$0.494886\pi$
$740$	−35.2819	+	61.1101i	−1.29699	+	2.24645i
$741$	8.73695	−	10.2651i	0.320960	−	0.377096i
$742$	−0.272763	−	0.472439i	−0.0100134	−	0.0173438i
$743$	−2.68307	−	4.64721i	−0.0984323	−	0.170490i	0.812604	−	0.582817i	$-0.198049\pi$
$743$	−2.68307	−	4.64721i	−0.0984323	−	0.170490i	−0.911036	+	0.412327i	$0.864716\pi$
$744$	8.43777	−	9.91354i	0.309344	−	0.363448i
$745$	0.765305	−	1.32555i	0.0280386	−	0.0485643i
$746$	−36.8141			−1.34786
$747$	7.97933	+	49.2908i	0.291948	+	1.80346i
$748$	−23.7145			−0.867089
$749$	3.31431	−	5.74055i	0.121102	−	0.209755i
$750$	−41.7929	−	7.67216i	−1.52606	−	0.280148i
$751$	10.8555	+	18.8023i	0.396124	+	0.686107i	0.993244	−	0.116045i	$-0.0370216\pi$
$751$	10.8555	+	18.8023i	0.396124	+	0.686107i	−0.597120	+	0.802152i	$0.703688\pi$
$752$	4.57648	+	7.92670i	0.166887	+	0.289057i
$753$	2.11895	+	5.95145i	0.0772187	+	0.216883i
$754$	−5.65837	+	9.80058i	−0.206066	+	0.356916i
$755$	−13.8241			−0.503109
$756$	4.76189	+	2.88468i	0.173188	+	0.104915i
$757$	28.4465			1.03390			0.516952	−	0.856014i	$-0.327067\pi$
$757$	28.4465			1.03390			0.516952	+	0.856014i	$0.327067\pi$
$758$	2.98943	−	5.17785i	0.108581	−	0.188068i
$759$	−1.08419	−	3.04514i	−0.0393536	−	0.110532i
$760$	−18.1039	−	31.3569i	−0.656699	−	1.13744i
$761$	−25.2071	−	43.6599i	−0.913756	−	1.58267i	−0.808712	−	0.588204i	$-0.799835\pi$
$761$	−25.2071	−	43.6599i	−0.913756	−	1.58267i	−0.105044	−	0.994468i	$-0.533498\pi$
$762$	−3.91319	−	0.718366i	−0.141760	−	0.0260237i
$763$	2.73212	−	4.73218i	0.0989095	−	0.171316i
$764$	18.5800			0.672201
$765$	41.2516	+	15.6738i	1.49145	+	0.566687i
$766$	8.70331			0.314463
$767$	3.71183	−	6.42908i	0.134027	−	0.232141i
$768$	7.64966	−	8.98759i	0.276033	−	0.324312i
$769$	5.98351	+	10.3637i	0.215771	+	0.373726i	0.953511	−	0.301359i	$-0.0974402\pi$
$769$	5.98351	+	10.3637i	0.215771	+	0.373726i	−0.737740	+	0.675085i	$0.764107\pi$
$770$	−1.14379	−	1.98111i	−0.0412195	−	0.0713943i
$771$	20.6147	−	24.2202i	0.742420	−	0.872270i
$772$	4.12907	−	7.15176i	0.148608	−	0.257397i
$773$	−43.8095			−1.57572			−0.787859	−	0.615856i	$-0.788810\pi$
$773$	−43.8095			−1.57572			−0.787859	+	0.615856i	$0.788810\pi$
$774$	−1.54246	−	0.586067i	−0.0554426	−	0.0210657i
$775$	0.407611			0.0146418
$776$	−11.0176	+	19.0830i	−0.395508	+	0.685040i
$777$	−6.64940	−	1.22067i	−0.238546	−	0.0437912i
$778$	12.1736	+	21.0852i	0.436443	+	0.755941i
$779$	30.9887	+	53.6741i	1.11029	+	1.92307i
$780$	−3.84460	−	10.7983i	−0.137659	−	0.386640i
$781$	1.32940	−	2.30259i	0.0475697	−	0.0823931i
$782$	21.6432			0.773959
$783$	−23.2164	+	12.7597i	−0.829685	+	0.455993i
$784$	8.83274			0.315455
$785$	−15.5265	+	26.8926i	−0.554163	+	0.959839i
$786$	−16.9619	−	47.6406i	−0.605011	−	1.69928i
$787$	−24.8024	−	42.9589i	−0.884109	−	1.53132i	−0.846732	−	0.532020i	$-0.821433\pi$
$787$	−24.8024	−	42.9589i	−0.884109	−	1.53132i	−0.0373767	−	0.999301i	$-0.511900\pi$
$788$	4.98433	+	8.63311i	0.177559	+	0.307542i
$789$	−6.69176	−	1.22844i	−0.238233	−	0.0437338i
$790$	29.6023	−	51.2727i	1.05320	−	1.82420i
$791$	−0.863036			−0.0306860
$792$	1.22847	+	7.58865i	0.0436518	+	0.269651i
$793$	4.21117			0.149543
$794$	22.4871	−	38.9488i	0.798037	−	1.38224i
$795$	−1.70408	+	2.00212i	−0.0604375	+	0.0710081i
$796$	−9.88516	−	17.1216i	−0.350370	−	0.606859i
$797$	2.28023	+	3.94947i	0.0807698	+	0.139897i	0.903581	−	0.428418i	$-0.140929\pi$
$797$	2.28023	+	3.94947i	0.0807698	+	0.139897i	−0.822811	+	0.568315i	$0.807595\pi$
$798$	7.09905	−	8.34068i	0.251304	−	0.295257i
$799$	23.1454	−	40.0889i	0.818824	−	1.41825i
$800$	0.777960			0.0275051
$801$	−7.11819	+	5.80450i	−0.251509	+	0.205092i
$802$	0.818207			0.0288919
$803$	−1.70342	+	2.95041i	−0.0601124	+	0.104118i
$804$	25.9967	+	4.77236i	0.916833	+	0.168308i
$805$	0.620153	+	1.07414i	0.0218575	+	0.0378583i
$806$	−4.05372	−	7.02125i	−0.142786	−	0.247313i
$807$	−16.3685	−	45.9739i	−0.576199	−	1.61836i
$808$	−2.70417	+	4.68376i	−0.0951323	+	0.164774i
$809$	−47.1352			−1.65718			−0.828592	−	0.559852i	$-0.810858\pi$
$809$	−47.1352			−1.65718			−0.828592	+	0.559852i	$0.810858\pi$
$810$	9.08903	−	44.2424i	0.319356	−	1.55452i
$811$	16.8933			0.593203			0.296601	−	0.955001i	$-0.404147\pi$
$811$	16.8933			0.593203			0.296601	+	0.955001i	$0.404147\pi$
$812$	−2.73134	+	4.73081i	−0.0958511	+	0.166019i
$813$	−14.2953	−	40.1509i	−0.501358	−	1.40816i
$814$	−14.7366	−	25.5245i	−0.516516	−	0.894632i
$815$	6.47973	+	11.2232i	0.226975	+	0.393133i
$816$	14.2586	+	2.61754i	0.499152	+	0.0916322i
$817$	−0.964217	+	1.67007i	−0.0337337	+	0.0584285i
$818$	−4.18912			−0.146469
$819$	0.851072	−	0.694004i	0.0297389	−	0.0242505i
$820$	52.7012			1.84040
$821$	−12.1876	+	21.1095i	−0.425349	+	0.736727i	−0.996453	−	0.0841514i	$-0.973182\pi$
$821$	−12.1876	+	21.1095i	−0.425349	+	0.736727i	0.571104	+	0.820878i	$0.306515\pi$
$822$	−29.7633	+	34.9689i	−1.03811	+	1.21968i
$823$	17.8670	+	30.9465i	0.622803	+	1.07873i	0.988961	+	0.148174i	$0.0473395\pi$
$823$	17.8670	+	30.9465i	0.622803	+	1.07873i	−0.366158	+	0.930553i	$0.619327\pi$
$824$	−13.5338	−	23.4413i	−0.471473	−	0.816616i
$825$	−0.156010	+	0.183296i	−0.00543157	+	0.00638155i
$826$	3.01598	−	5.22383i	0.104939	−	0.181760i
$827$	25.4444			0.884790			0.442395	−	0.896820i	$-0.354129\pi$
$827$	25.4444			0.884790			0.442395	+	0.896820i	$0.354129\pi$
$828$	−2.10300	−	12.9909i	−0.0730843	−	0.451465i
$829$	−54.8739			−1.90585			−0.952924	−	0.303208i	$-0.901942\pi$
$829$	−54.8739			−1.90585			−0.952924	+	0.303208i	$0.901942\pi$
$830$	41.7642	−	72.3378i	1.44966	−	2.51088i
$831$	39.5618	+	7.26258i	1.37238	+	0.251936i
$832$	−6.45042	−	11.1725i	−0.223628	−	0.387335i
$833$	−22.3356	−	38.6864i	−0.773883	−	1.34040i
$834$	7.88599	+	22.1492i	0.273069	+	0.766965i
$835$	22.7530	−	39.4094i	0.787402	−	1.36382i
$836$	28.3671			0.981096
$837$	0.399741	−	18.9747i	0.0138171	−	0.655863i
$838$	16.7258			0.577781
$839$	−20.0429	+	34.7153i	−0.691956	+	1.19850i	0.279240	+	0.960221i	$0.409918\pi$
$839$	−20.0429	+	34.7153i	−0.691956	+	1.19850i	−0.971196	+	0.238282i	$0.923416\pi$
$840$	−0.989390	−	2.77888i	−0.0341372	−	0.0958805i
$841$	1.50355	+	2.60423i	0.0518466	+	0.0898009i
$842$	17.3849	+	30.1116i	0.599124	+	1.03771i
$843$	−22.7172	−	4.17032i	−0.782422	−	0.143634i
$844$	−7.01825	+	12.1560i	−0.241578	+	0.418426i
$845$	−2.26088			−0.0777768
$846$	−44.2897	−	16.8281i	−1.52271	−	0.578563i
$847$	−3.45897			−0.118852
$848$	−0.431854	+	0.747992i	−0.0148299	+	0.0256862i
$849$	−16.9601	+	19.9265i	−0.582070	+	0.683875i
$850$	−0.805830	−	1.39574i	−0.0276398	−	0.0478735i
$851$	7.99000	+	13.8391i	0.273894	+	0.474398i
$852$	7.01607	−	8.24318i	0.240366	−	0.282407i
$853$	−4.43754	+	7.68604i	−0.151938	+	0.263165i	−0.931940	−	0.362612i	$-0.881885\pi$
$853$	−4.43754	+	7.68604i	−0.151938	+	0.263165i	0.780002	+	0.625778i	$0.215218\pi$
$854$	3.42170			0.117088
$855$	−49.3447	−	18.7488i	−1.68755	−	0.641196i
$856$	37.2630			1.27362
$857$	11.8214	−	20.4753i	0.403812	−	0.699423i	−0.590370	−	0.807132i	$-0.701018\pi$
$857$	11.8214	−	20.4753i	0.403812	−	0.699423i	0.994182	+	0.107710i	$0.0343516\pi$
$858$	4.70887	+	0.864434i	0.160758	+	0.0295113i
$859$	2.22752	+	3.85817i	0.0760019	+	0.131639i	0.901522	−	0.432734i	$-0.142451\pi$
$859$	2.22752	+	3.85817i	0.0760019	+	0.131639i	−0.825520	+	0.564373i	$0.809118\pi$
$860$	0.819900	+	1.42011i	0.0279584	+	0.0484253i
$861$	1.69355	+	4.75665i	0.0577161	+	0.162106i
$862$	9.15524	−	15.8573i	0.311829	−	0.540103i
$863$	12.3681			0.421015			0.210508	−	0.977592i	$-0.432488\pi$
$863$	12.3681			0.421015			0.210508	+	0.977592i	$0.432488\pi$
$864$	0.762939	−	36.2149i	0.0259557	−	1.23205i
$865$	27.0165			0.918588
$866$	−39.7663	+	68.8772i	−1.35131	+	2.34054i
$867$	−14.7155	−	41.3312i	−0.499765	−	1.40368i
$868$	−1.95676	−	3.38921i	−0.0664168	−	0.115037i
$869$	7.34536	+	12.7225i	0.249174	+	0.431582i
$870$	43.5876	+	8.00162i	1.47776	+	0.271280i
$871$	2.60671	−	4.51496i	0.0883251	−	0.152984i
$872$	30.7174			1.04022
$873$	5.13356	+	31.7116i	0.173745	+	1.07328i
$874$	−25.8894			−0.875721
$875$	−2.02284	+	3.50366i	−0.0683845	+	0.118445i
$876$	−8.99001	+	10.5624i	−0.303744	+	0.356869i
$877$	−25.2064	−	43.6588i	−0.851161	−	1.47425i	−0.880162	−	0.474674i	$-0.842566\pi$
$877$	−25.2064	−	43.6588i	−0.851161	−	1.47425i	0.0290011	−	0.999579i	$-0.490767\pi$
$878$	32.9114	+	57.0043i	1.11071	+	1.92380i
$879$	18.7391	−	22.0166i	0.632054	−	0.742601i
$880$	−1.81092	+	3.13660i	−0.0610461	+	0.105735i
$881$	27.4128			0.923560			0.461780	−	0.886994i	$-0.347211\pi$
$881$	27.4128			0.923560			0.461780	+	0.886994i	$0.347211\pi$
$882$	−35.4338	+	28.8944i	−1.19312	+	0.972925i
$883$	−48.6454			−1.63705			−0.818524	−	0.574473i	$-0.805207\pi$
$883$	−48.6454			−1.63705			−0.818524	+	0.574473i	$0.805207\pi$
$884$	−9.52193	+	16.4925i	−0.320257	+	0.554702i
$885$	−28.5930	−	5.24898i	−0.961144	−	0.176443i
$886$	−22.3007	−	38.6259i	−0.749207	−	1.29766i
$887$	6.12948	+	10.6166i	0.205808	+	0.356470i	0.950390	−	0.311061i	$-0.100684\pi$
$887$	6.12948	+	10.6166i	0.205808	+	0.356470i	−0.744582	+	0.667531i	$0.767351\pi$
$888$	−12.7472	−	35.8029i	−0.427769	−	1.20147i
$889$	−0.189404	+	0.328058i	−0.00635242	+	0.0110027i
$890$	15.3646			0.515023
$891$	8.37963	+	7.44218i	0.280728	+	0.249322i
$892$	−28.4622			−0.952985
$893$	−27.6862	+	47.9540i	−0.926485	+	1.60472i
$894$	0.873015	+	2.45202i	0.0291980	+	0.0820078i
$895$	1.13230	+	1.96120i	0.0378486	+	0.0655557i
$896$	−2.68936	−	4.65812i	−0.0898454	−	0.155617i
$897$	−2.55310	−	0.468686i	−0.0852454	−	0.0156490i
$898$	−26.6176	+	46.1031i	−0.888242	+	1.53848i
$899$	18.6216			0.621066
$900$	−0.759465	+	0.619303i	−0.0253155	+	0.0206434i
$901$	4.36816			0.145525
$902$	−11.0061	+	19.0631i	−0.366463	+	0.634733i
$903$	−0.101827	+	0.119637i	−0.00338860	+	0.00398127i
$904$	−2.42579	−	4.20160i	−0.0806807	−	0.139743i
$905$	−20.3694	−	35.2808i	−0.677102	−	1.17277i
$906$	15.2366	−	17.9015i	0.506202	−	0.594737i
$907$	3.24782	−	5.62539i	0.107842	−	0.186788i	−0.807054	−	0.590478i	$-0.798939\pi$
$907$	3.24782	−	5.62539i	0.107842	−	0.186788i	0.914896	+	0.403690i	$0.132273\pi$
$908$	21.2739			0.706001
$909$	1.25999	+	7.78335i	0.0417912	+	0.258157i
$910$	−1.83704			−0.0608973
$911$	0.0807935	−	0.139938i	0.00267681	−	0.00463636i	−0.864684	−	0.502316i	$-0.832481\pi$
$911$	0.0807935	−	0.139938i	0.00267681	−	0.00463636i	0.867361	+	0.497680i	$0.165815\pi$
$912$	−17.0560	−	3.13107i	−0.564782	−	0.103680i
$913$	10.3632	+	17.9495i	0.342970	+	0.594042i
$914$	−35.8221	−	62.0457i	−1.18489	−	2.05229i
$915$	−5.53124	−	15.5355i	−0.182857	−	0.513587i
$916$	1.13713	−	1.96956i	0.0375717	−	0.0650761i
$917$	−4.81488			−0.159001
$918$	−65.7634	+	36.1435i	−2.17051	+	1.19291i
$919$	27.8344			0.918173			0.459087	−	0.888392i	$-0.348177\pi$
$919$	27.8344			0.918173			0.459087	+	0.888392i	$0.348177\pi$
$920$	−3.48621	+	6.03829i	−0.114937	+	0.199077i
$921$	−0.395872	−	1.11188i	−0.0130444	−	0.0366376i
$922$	−22.6443	−	39.2211i	−0.745751	−	1.29168i
$923$	−1.06757	−	1.84908i	−0.0351395	−	0.0608633i
$924$	2.27301	+	0.417269i	0.0747764	+	0.0137271i
$925$	0.594975	−	1.03053i	0.0195627	−	0.0338835i
$926$	13.5160			0.444162
$927$	−36.8883	−	14.0159i	−1.21157	−	0.460343i
$928$	35.5409			1.16669
$929$	−22.0041	+	38.1122i	−0.721931	+	1.25042i	0.238294	+	0.971193i	$0.423412\pi$
$929$	−22.0041	+	38.1122i	−0.721931	+	1.25042i	−0.960225	+	0.279228i	$0.909921\pi$
$930$	−20.5778	+	24.1769i	−0.674772	+	0.792791i
$931$	26.7176	+	46.2762i	0.875634	+	1.51664i
$932$	−16.7258	−	28.9700i	−0.547873	−	0.948944i
$933$	6.70844	−	7.88175i	0.219624	−	0.258037i
$934$	−37.9156	+	65.6717i	−1.24064	+	2.14884i
$935$	18.3173			0.599040
$936$	5.77085	+	2.19267i	0.188626	+	0.0716696i
$937$	14.8899			0.486433			0.243217	−	0.969972i	$-0.421797\pi$
$937$	14.8899			0.486433			0.243217	+	0.969972i	$0.421797\pi$
$938$	2.11804	−	3.66855i	0.0691564	−	0.119782i
$939$	10.7527	+	1.97394i	0.350903	+	0.0644172i
$940$	23.5424	+	40.7766i	0.767867	+	1.32999i
$941$	−7.23889	−	12.5381i	−0.235981	−	0.408731i	0.723576	−	0.690244i	$-0.242497\pi$
$941$	−7.23889	−	12.5381i	−0.235981	−	0.408731i	−0.959557	+	0.281513i	$0.909164\pi$
$942$	−17.7117	−	49.7465i	−0.577078	−	1.62083i
$943$	5.96739	−	10.3358i	0.194325	−	0.336581i
$944$	−9.55014			−0.310831
$945$	−3.67812	−	2.22815i	−0.119649	−	0.0724818i
$946$	−0.684912			−0.0222684
$947$	7.02194	−	12.1623i	0.228182	−	0.395223i	−0.729087	−	0.684421i	$-0.760055\pi$
$947$	7.02194	−	12.1623i	0.228182	−	0.395223i	0.957269	+	0.289198i	$0.0933885\pi$
$948$	20.0612	+	56.3455i	0.651557	+	1.83002i
$949$	1.36793	+	2.36932i	0.0444047	+	0.0769113i
$950$	0.963926	+	1.66957i	0.0312739	+	0.0541679i
$951$	−2.91776	−	0.535630i	−0.0946149	−	0.0173690i
$952$	−2.45042	+	4.24426i	−0.0794186	+	0.137557i
$953$	33.5892			1.08806			0.544030	−	0.839066i	$-0.316898\pi$
$953$	33.5892			1.08806			0.544030	+	0.839066i	$0.316898\pi$
$954$	−0.714452	−	4.41340i	−0.0231312	−	0.142889i
$955$	−14.3513			−0.464399
$956$	20.1585	−	34.9155i	0.651971	−	1.12925i
$957$	−7.12727	+	8.37384i	−0.230392	+	0.270688i
$958$	6.10674	+	10.5772i	0.197300	+	0.341733i
$959$	2.18608	+	3.78641i	0.0705923	+	0.122269i
$960$	−32.7441	+	38.4711i	−1.05681	+	1.24165i
$961$	8.82962	−	15.2934i	0.284827	−	0.493334i
$962$	−23.6683			−0.763096
$963$	42.1014	−	34.3315i	1.35670	−	1.10632i
$964$	47.9206			1.54342
$965$	−3.18933	+	5.52408i	−0.102668	+	0.177826i
$966$	−2.07447	−	0.380822i	−0.0667450	−	0.0122528i
$967$	11.4261	+	19.7906i	0.367439	+	0.636422i	0.989164	−	0.146813i	$-0.0469015\pi$
$967$	11.4261	+	19.7906i	0.367439	+	0.636422i	−0.621726	+	0.783235i	$0.713568\pi$
$968$	−9.72237	−	16.8396i	−0.312489	−	0.541246i
$969$	29.4163	+	82.6212i	0.944989	+	2.65417i
$970$	26.8693	−	46.5391i	0.862723	−	1.49428i
$971$	−47.2156			−1.51522			−0.757610	−	0.652708i	$-0.773633\pi$
$971$	−47.2156			−1.51522			−0.757610	+	0.652708i	$0.773633\pi$
$972$	28.0844	+	35.9612i	0.900808	+	1.15346i
$973$	2.23855			0.0717646
$974$	10.3020	−	17.8436i	0.330097	−	0.571745i
$975$	0.0648333	+	0.182096i	0.00207633	+	0.00583174i
$976$	−2.70872	−	4.69163i	−0.0867039	−	0.150176i
$977$	−10.8029	−	18.7112i	−0.345616	−	0.598624i	0.639850	−	0.768500i	$-0.278997\pi$
$977$	−10.8029	−	18.7112i	−0.345616	−	0.598624i	−0.985465	+	0.169876i	$0.945663\pi$
$978$	−21.6753	−	3.97907i	−0.693101	−	0.127237i
$979$	−1.90625	+	3.30171i	−0.0609239	+	0.105523i
$980$	45.4374			1.45145
$981$	34.7060	−	28.3009i	1.10808	−	0.903578i
$982$	−70.4622			−2.24854
$983$	6.22344	−	10.7793i	0.198497	−	0.343806i	−0.749544	−	0.661954i	$-0.769727\pi$
$983$	6.22344	−	10.7793i	0.198497	−	0.343806i	0.948041	+	0.318148i	$0.103061\pi$
$984$	−18.3970	+	21.6147i	−0.586476	+	0.689051i
$985$	−3.84993	−	6.66828i	−0.122669	−	0.212469i
$986$	−36.8142	−	63.7640i	−1.17240	−	2.03066i
$987$	−2.92384	+	3.43522i	−0.0930667	+	0.109344i
$988$	11.3900	−	19.7281i	0.362365	−	0.627635i
$989$	0.371352			0.0118083
$990$	−2.99596	−	18.5070i	−0.0952178	−	0.588191i
$991$	40.1832			1.27646			0.638231	−	0.769845i	$-0.279666\pi$
$991$	40.1832			1.27646			0.638231	+	0.769845i	$0.279666\pi$
$992$	−12.7310	+	22.0507i	−0.404209	+	0.700110i
$993$	−14.4460	−	2.65193i	−0.458430	−	0.0841566i
$994$	−0.867433	−	1.50244i	−0.0275133	−	0.0476545i
$995$	7.63538	+	13.2249i	0.242058	+	0.419256i
$996$	28.3032	+	79.4947i	0.896821	+	2.51888i
$997$	−13.8166	+	23.9311i	−0.437577	+	0.757906i	−0.997502	−	0.0706374i	$-0.977497\pi$
$997$	−13.8166	+	23.9311i	−0.437577	+	0.757906i	0.559925	+	0.828543i	$0.310830\pi$
$998$	38.9782			1.23383
$999$	−47.3886	−	28.7073i	−1.49931	−	0.908260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.e.c.79.5	yes	12
3.2	odd	2		351.2.e.c.235.2		12
9.2	odd	6		1053.2.a.m.1.5		6
9.4	even	3	inner	117.2.e.c.40.5	✓	12
9.5	odd	6		351.2.e.c.118.2		12
9.7	even	3		1053.2.a.l.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.e.c.40.5	✓	12	9.4	even	3	inner
117.2.e.c.79.5	yes	12	1.1	even	1	trivial
351.2.e.c.118.2		12	9.5	odd	6
351.2.e.c.235.2		12	3.2	odd	2
1053.2.a.l.1.2		6	9.7	even	3
1053.2.a.m.1.5		6	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10985 - 1.92231i) q^{2} +(-0.580954 - 1.63171i) q^{3} +(-1.46353 - 2.53491i) q^{4} +(1.13044 + 1.95798i) q^{5} +(-3.78144 - 0.694180i) q^{6} +(-0.183027 + 0.317013i) q^{7} -2.05779 q^{8} +(-2.32499 + 1.89590i) q^{9} +O(q^{10})\)	\(q+(1.10985 - 1.92231i) q^{2} +(-0.580954 - 1.63171i) q^{3} +(-1.46353 - 2.53491i) q^{4} +(1.13044 + 1.95798i) q^{5} +(-3.78144 - 0.694180i) q^{6} +(-0.183027 + 0.317013i) q^{7} -2.05779 q^{8} +(-2.32499 + 1.89590i) q^{9} +5.01848 q^{10} +(-0.622629 + 1.07843i) q^{11} +(-3.28600 + 3.86073i) q^{12} +(0.500000 + 0.866025i) q^{13} +(0.406266 + 0.703673i) q^{14} +(2.53814 - 2.98206i) q^{15} +(0.643223 - 1.11409i) q^{16} -6.50614 q^{17} +(1.06414 + 6.57352i) q^{18} +7.78258 q^{19} +(3.30887 - 5.73113i) q^{20} +(0.623605 + 0.114479i) q^{21} +(1.38205 + 2.39378i) q^{22} +(-0.749331 - 1.29788i) q^{23} +(1.19548 + 3.35773i) q^{24} +(-0.0557990 + 0.0966466i) q^{25} +2.21970 q^{26} +(4.44428 + 2.69228i) q^{27} +1.07146 q^{28} +(-2.54916 + 4.41528i) q^{29} +(-2.91551 - 8.18873i) q^{30} +(-1.82625 - 3.16316i) q^{31} +(-3.48555 - 6.03715i) q^{32} +(2.12140 + 0.389438i) q^{33} +(-7.22084 + 12.5069i) q^{34} -0.827608 q^{35} +(8.20862 + 3.11891i) q^{36} -10.6628 q^{37} +(8.63749 - 14.9606i) q^{38} +(1.12263 - 1.31898i) q^{39} +(-2.32621 - 4.02912i) q^{40} +(3.98181 + 6.89670i) q^{41} +(0.912172 - 1.07171i) q^{42} +(-0.123894 + 0.214591i) q^{43} +3.64495 q^{44} +(-6.34041 - 2.40907i) q^{45} -3.32658 q^{46} +(-3.55746 + 6.16171i) q^{47} +(-2.19157 - 0.402318i) q^{48} +(3.43300 + 5.94613i) q^{49} +(0.123857 + 0.214526i) q^{50} +(3.77977 + 10.6162i) q^{51} +(1.46353 - 2.53491i) q^{52} -0.671391 q^{53} +(10.1079 - 5.55528i) q^{54} -2.81539 q^{55} +(0.376632 - 0.652346i) q^{56} +(-4.52132 - 12.6989i) q^{57} +(5.65837 + 9.80058i) q^{58} +(-3.71183 - 6.42908i) q^{59} +(-11.2739 - 2.06961i) q^{60} +(2.10558 - 3.64698i) q^{61} -8.10745 q^{62} +(-0.175489 - 1.08405i) q^{63} -12.9008 q^{64} +(-1.13044 + 1.95798i) q^{65} +(3.10306 - 3.64578i) q^{66} +(-2.60671 - 4.51496i) q^{67} +(9.52193 + 16.4925i) q^{68} +(-1.68244 + 1.97670i) q^{69} +(-0.918520 + 1.59092i) q^{70} -2.13514 q^{71} +(4.78433 - 3.90137i) q^{72} +2.73585 q^{73} +(-11.8341 + 20.4973i) q^{74} +(0.190116 + 0.0349007i) q^{75} +(-11.3900 - 19.7281i) q^{76} +(-0.227917 - 0.394763i) q^{77} +(-1.28954 - 3.62191i) q^{78} +(5.89866 - 10.2168i) q^{79} +2.90850 q^{80} +(1.81111 - 8.81589i) q^{81} +17.6768 q^{82} +(8.32209 - 14.4143i) q^{83} +(-0.622471 - 1.74832i) q^{84} +(-7.35482 - 12.7389i) q^{85} +(0.275008 + 0.476328i) q^{86} +(8.68542 + 1.59443i) q^{87} +(1.28124 - 2.21917i) q^{88} +3.06161 q^{89} +(-11.6679 + 9.51455i) q^{90} -0.366055 q^{91} +(-2.19334 + 3.79897i) q^{92} +(-4.10040 + 4.81757i) q^{93} +(7.89649 + 13.6771i) q^{94} +(8.79775 + 15.2382i) q^{95} +(-7.82596 + 9.19473i) q^{96} +(5.35408 - 9.27354i) q^{97} +15.2405 q^{98} +(-0.596985 - 3.68777i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 2 q^{3} - 6 q^{4} + 3 q^{5} - 7 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 - 2 * q^3 - 6 * q^4 + 3 * q^5 - 7 * q^6 - 12 * q^8 - 2 * q^9	\( 12 q + 2 q^{2} - 2 q^{3} - 6 q^{4} + 3 q^{5} - 7 q^{6} - 12 q^{8} - 2 q^{9} - 12 q^{10} + 7 q^{11} + 7 q^{12} + 6 q^{13} + 13 q^{14} - 12 q^{15} - 6 q^{16} - 28 q^{17} + 26 q^{18} - 6 q^{19} + 17 q^{20} - 18 q^{21} + 3 q^{22} + 17 q^{23} - 30 q^{24} - 3 q^{25} + 4 q^{26} + 13 q^{27} + 30 q^{28} + 14 q^{29} - 7 q^{30} - 6 q^{31} + 9 q^{32} + 19 q^{33} - 3 q^{34} - 26 q^{35} + 43 q^{36} - 18 q^{37} - 4 q^{38} - q^{39} + 6 q^{40} - 4 q^{41} - 17 q^{42} + 3 q^{43} - 26 q^{44} + 18 q^{45} + 9 q^{47} - 3 q^{48} - 21 q^{50} - 4 q^{51} + 6 q^{52} - 56 q^{53} + 35 q^{54} + 30 q^{55} + 16 q^{56} - 30 q^{57} - 18 q^{58} + 17 q^{59} - 31 q^{60} + 6 q^{61} + 8 q^{62} - 60 q^{64} - 3 q^{65} - 19 q^{66} + 12 q^{67} + 22 q^{68} - 13 q^{69} - 9 q^{70} + 2 q^{71} - 18 q^{73} - 27 q^{74} + 18 q^{75} + 3 q^{76} + 15 q^{77} - 2 q^{78} + 6 q^{79} + 48 q^{80} - 2 q^{81} + 54 q^{82} + 28 q^{83} + 31 q^{84} - 27 q^{85} - 6 q^{86} + 23 q^{87} + 9 q^{88} + 18 q^{89} + 26 q^{90} + 44 q^{92} + 2 q^{93} + 24 q^{94} + 32 q^{95} - 57 q^{96} - 34 q^{98} - 11 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 6 * q^4 + 3 * q^5 - 7 * q^6 - 12 * q^8 - 2 * q^9 - 12 * q^10 + 7 * q^11 + 7 * q^12 + 6 * q^13 + 13 * q^14 - 12 * q^15 - 6 * q^16 - 28 * q^17 + 26 * q^18 - 6 * q^19 + 17 * q^20 - 18 * q^21 + 3 * q^22 + 17 * q^23 - 30 * q^24 - 3 * q^25 + 4 * q^26 + 13 * q^27 + 30 * q^28 + 14 * q^29 - 7 * q^30 - 6 * q^31 + 9 * q^32 + 19 * q^33 - 3 * q^34 - 26 * q^35 + 43 * q^36 - 18 * q^37 - 4 * q^38 - q^39 + 6 * q^40 - 4 * q^41 - 17 * q^42 + 3 * q^43 - 26 * q^44 + 18 * q^45 + 9 * q^47 - 3 * q^48 - 21 * q^50 - 4 * q^51 + 6 * q^52 - 56 * q^53 + 35 * q^54 + 30 * q^55 + 16 * q^56 - 30 * q^57 - 18 * q^58 + 17 * q^59 - 31 * q^60 + 6 * q^61 + 8 * q^62 - 60 * q^64 - 3 * q^65 - 19 * q^66 + 12 * q^67 + 22 * q^68 - 13 * q^69 - 9 * q^70 + 2 * q^71 - 18 * q^73 - 27 * q^74 + 18 * q^75 + 3 * q^76 + 15 * q^77 - 2 * q^78 + 6 * q^79 + 48 * q^80 - 2 * q^81 + 54 * q^82 + 28 * q^83 + 31 * q^84 - 27 * q^85 - 6 * q^86 + 23 * q^87 + 9 * q^88 + 18 * q^89 + 26 * q^90 + 44 * q^92 + 2 * q^93 + 24 * q^94 + 32 * q^95 - 57 * q^96 - 34 * q^98 - 11 * q^99

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