LMFDB - Embedded newform 731.2.m.c.87.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.11
Character	$\chi$	$=$	731.87
Dual form			731.2.m.c.689.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.624813 - 0.624813i) q^{2} +(2.88236 - 1.19391i) q^{3} -1.21922i q^{4} +(-1.21824 - 2.94109i) q^{5} +(-2.54691 - 1.05496i) q^{6} +(0.920964 - 2.22340i) q^{7} +(-2.01141 + 2.01141i) q^{8} +(4.76125 - 4.76125i) q^{9} +O(q^{10})$	\(q+(-0.624813 - 0.624813i) q^{2} +(2.88236 - 1.19391i) q^{3} -1.21922i q^{4} +(-1.21824 - 2.94109i) q^{5} +(-2.54691 - 1.05496i) q^{6} +(0.920964 - 2.22340i) q^{7} +(-2.01141 + 2.01141i) q^{8} +(4.76125 - 4.76125i) q^{9} +(-1.07646 + 2.59880i) q^{10} +(0.310479 + 0.128605i) q^{11} +(-1.45564 - 3.51423i) q^{12} +5.45402i q^{13} +(-1.96464 + 0.813780i) q^{14} +(-7.02282 - 7.02282i) q^{15} +0.0750704 q^{16} +(3.54745 - 2.10134i) q^{17} -5.94978 q^{18} +(2.89789 + 2.89789i) q^{19} +(-3.58584 + 1.48530i) q^{20} -7.50820i q^{21} +(-0.113638 - 0.274345i) q^{22} +(6.21903 + 2.57601i) q^{23} +(-3.39616 + 8.19905i) q^{24} +(-3.63039 + 3.63039i) q^{25} +(3.40774 - 3.40774i) q^{26} +(4.45738 - 10.7611i) q^{27} +(-2.71081 - 1.12286i) q^{28} +(1.31012 + 3.16292i) q^{29} +8.77589i q^{30} +(-8.18548 + 3.39054i) q^{31} +(3.97591 + 3.97591i) q^{32} +1.04846 q^{33} +(-3.52943 - 0.903547i) q^{34} -7.66119 q^{35} +(-5.80500 - 5.80500i) q^{36} +(-8.11528 + 3.36146i) q^{37} -3.62128i q^{38} +(6.51162 + 15.7204i) q^{39} +(8.36612 + 3.46536i) q^{40} +(3.16704 - 7.64591i) q^{41} +(-4.69122 + 4.69122i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(0.156797 - 0.378542i) q^{44} +(-19.8036 - 8.20293i) q^{45} +(-2.27621 - 5.49525i) q^{46} -4.38757i q^{47} +(0.216380 - 0.0896274i) q^{48} +(0.854402 + 0.854402i) q^{49} +4.53662 q^{50} +(7.71620 - 10.2922i) q^{51} +6.64964 q^{52} +(6.74607 + 6.74607i) q^{53} +(-9.50868 + 3.93862i) q^{54} -1.06982i q^{55} +(2.61974 + 6.32460i) q^{56} +(11.8126 + 4.89293i) q^{57} +(1.15765 - 2.79481i) q^{58} +(-5.55757 + 5.55757i) q^{59} +(-8.56235 + 8.56235i) q^{60} +(-3.77139 + 9.10493i) q^{61} +(7.23284 + 2.99594i) q^{62} +(-6.20124 - 14.9711i) q^{63} -5.11854i q^{64} +(16.0408 - 6.64431i) q^{65} +(-0.655089 - 0.655089i) q^{66} -1.86246 q^{67} +(-2.56199 - 4.32511i) q^{68} +21.0010 q^{69} +(4.78681 + 4.78681i) q^{70} +(7.01102 - 2.90406i) q^{71} +19.1536i q^{72} +(-3.81569 - 9.21189i) q^{73} +(7.17081 + 2.97025i) q^{74} +(-6.12972 + 14.7984i) q^{75} +(3.53316 - 3.53316i) q^{76} +(0.571880 - 0.571880i) q^{77} +(5.75379 - 13.8909i) q^{78} +(-0.280713 - 0.116275i) q^{79} +(-0.0914538 - 0.220789i) q^{80} -16.1387i q^{81} +(-6.75606 + 2.79845i) q^{82} +(-7.70045 - 7.70045i) q^{83} -9.15413 q^{84} +(-10.5019 - 7.87344i) q^{85} +0.883619 q^{86} +(7.55249 + 7.55249i) q^{87} +(-0.883178 + 0.365824i) q^{88} +1.50936i q^{89} +(7.24826 + 17.4988i) q^{90} +(12.1265 + 5.02295i) q^{91} +(3.14072 - 7.58236i) q^{92} +(-19.5455 + 19.5455i) q^{93} +(-2.74141 + 2.74141i) q^{94} +(4.99264 - 12.0533i) q^{95} +(16.2069 + 6.71312i) q^{96} +(-3.59196 - 8.67175i) q^{97} -1.06768i q^{98} +(2.09059 - 0.865950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.624813	−	0.624813i	−0.441809	−	0.441809i	0.450810	−	0.892620i	$-0.351135\pi$
$2$	−0.624813	−	0.624813i	−0.441809	−	0.441809i	−0.892620	+	0.450810i	$0.851135\pi$
$3$	2.88236	−	1.19391i	1.66413	−	0.689306i	0.665749	−	0.746175i	$-0.268112\pi$
$3$	2.88236	−	1.19391i	1.66413	−	0.689306i	0.998382	+	0.0568699i	$0.0181120\pi$
$4$		−	1.21922i		−	0.609609i
$5$	−1.21824	−	2.94109i	−0.544814	−	1.31530i	−0.921292	−	0.388872i	$-0.872865\pi$
$5$	−1.21824	−	2.94109i	−0.544814	−	1.31530i	0.376478	−	0.926426i	$-0.377135\pi$
$6$	−2.54691	−	1.05496i	−1.03977	−	0.430687i
$7$	0.920964	−	2.22340i	0.348092	−	0.840367i	−0.648754	−	0.760998i	$-0.724710\pi$
$7$	0.920964	−	2.22340i	0.348092	−	0.840367i	0.996845	−	0.0793689i	$-0.0252905\pi$
$8$	−2.01141	+	2.01141i	−0.711140	+	0.711140i
$9$	4.76125	−	4.76125i	1.58708	−	1.58708i
$10$	−1.07646	+	2.59880i	−0.340407	+	0.821814i
$11$	0.310479	+	0.128605i	0.0936131	+	0.0387758i	0.428999	−	0.903305i	$-0.358867\pi$
$11$	0.310479	+	0.128605i	0.0936131	+	0.0387758i	−0.335385	+	0.942081i	$0.608867\pi$
$12$	−1.45564	−	3.51423i	−0.420207	−	1.01447i
$13$			5.45402i			1.51267i	0.654183	+	0.756336i	$0.273013\pi$
$13$			5.45402i			1.51267i	−0.654183	+	0.756336i	$0.726987\pi$
$14$	−1.96464	+	0.813780i	−0.525072	+	0.217492i
$15$	−7.02282	−	7.02282i	−1.81328	−	1.81328i
$16$	0.0750704			0.0187676
$17$	3.54745	−	2.10134i	0.860382	−	0.509649i
$17$	3.54745	−	2.10134i	0.860382	−	0.509649i
$18$	−5.94978			−1.40238
$19$	2.89789	+	2.89789i	0.664822	+	0.664822i	0.956513	−	0.291691i	$-0.0942179\pi$
$19$	2.89789	+	2.89789i	0.664822	+	0.664822i	−0.291691	+	0.956513i	$0.594218\pi$
$20$	−3.58584	+	1.48530i	−0.801817	+	0.332124i
$21$		−	7.50820i		−	1.63842i
$22$	−0.113638	−	0.274345i	−0.0242276	−	0.0584906i
$23$	6.21903	+	2.57601i	1.29676	+	0.537135i	0.920993	−	0.389580i	$-0.127380\pi$
$23$	6.21903	+	2.57601i	1.29676	+	0.537135i	0.375765	+	0.926715i	$0.377380\pi$
$24$	−3.39616	+	8.19905i	−0.693238	+	1.67362i
$25$	−3.63039	+	3.63039i	−0.726077	+	0.726077i
$26$	3.40774	−	3.40774i	0.668313	−	0.668313i
$27$	4.45738	−	10.7611i	0.857823	−	2.07097i
$28$	−2.71081	−	1.12286i	−0.512296	−	0.212200i
$29$	1.31012	+	3.16292i	0.243284	+	0.587339i	0.997605	−	0.0691665i	$-0.0220340\pi$
$29$	1.31012	+	3.16292i	0.243284	+	0.587339i	−0.754321	+	0.656505i	$0.772034\pi$
$30$			8.77589i			1.60225i
$31$	−8.18548	+	3.39054i	−1.47016	+	0.608958i	−0.966895	−	0.255176i	$-0.917867\pi$
$31$	−8.18548	+	3.39054i	−1.47016	+	0.608958i	−0.503261	+	0.864134i	$0.667867\pi$
$32$	3.97591	+	3.97591i	0.702849	+	0.702849i
$33$	1.04846			0.182513
$34$	−3.52943	−	0.903547i	−0.605293	−	0.154957i
$35$	−7.66119			−1.29498
$36$	−5.80500	−	5.80500i	−0.967500	−	0.967500i
$37$	−8.11528	+	3.36146i	−1.33414	+	0.552620i	−0.931834	−	0.362884i	$-0.881792\pi$
$37$	−8.11528	+	3.36146i	−1.33414	+	0.552620i	−0.402309	+	0.915504i	$0.631792\pi$
$38$		−	3.62128i		−	0.587449i
$39$	6.51162	+	15.7204i	1.04269	+	2.51728i
$40$	8.36612	+	3.46536i	1.32280	+	0.547922i
$41$	3.16704	−	7.64591i	0.494608	−	1.19409i	−0.457742	−	0.889085i	$-0.651342\pi$
$41$	3.16704	−	7.64591i	0.494608	−	1.19409i	0.952351	−	0.305005i	$-0.0986582\pi$
$42$	−4.69122	+	4.69122i	−0.723870	+	0.723870i
$43$	−0.707107	+	0.707107i	−0.107833	+	0.107833i
$43$	−0.707107	+	0.707107i	−0.107833	+	0.107833i
$44$	0.156797	−	0.378542i	0.0236381	−	0.0570674i
$45$	−19.8036	−	8.20293i	−2.95215	−	1.22282i
$46$	−2.27621	−	5.49525i	−0.335609	−	0.810231i
$47$		−	4.38757i		−	0.639993i	−0.947419	−	0.319997i	$-0.896318\pi$
$47$		−	4.38757i		−	0.639993i	0.947419	−	0.319997i	$-0.103682\pi$
$48$	0.216380	−	0.0896274i	0.0312317	−	0.0129366i
$49$	0.854402	+	0.854402i	0.122057	+	0.122057i
$50$	4.53662			0.641575
$51$	7.71620	−	10.2922i	1.08048	−	1.44119i
$52$	6.64964			0.922139
$53$	6.74607	+	6.74607i	0.926644	+	0.926644i	0.997487	−	0.0708435i	$-0.0225691\pi$
$53$	6.74607	+	6.74607i	0.926644	+	0.926644i	−0.0708435	+	0.997487i	$0.522569\pi$
$54$	−9.50868	+	3.93862i	−1.29397	+	0.535979i
$55$		−	1.06982i		−	0.144255i
$56$	2.61974	+	6.32460i	0.350077	+	0.845161i
$57$	11.8126	+	4.89293i	1.56462	+	0.648085i
$58$	1.15765	−	2.79481i	0.152007	−	0.366977i
$59$	−5.55757	+	5.55757i	−0.723534	+	0.723534i	−0.969323	−	0.245789i	$-0.920953\pi$
$59$	−5.55757	+	5.55757i	−0.723534	+	0.723534i	0.245789	+	0.969323i	$0.420953\pi$
$60$	−8.56235	+	8.56235i	−1.10539	+	1.10539i
$61$	−3.77139	+	9.10493i	−0.482876	+	1.16577i	0.475360	+	0.879791i	$0.342318\pi$
$61$	−3.77139	+	9.10493i	−0.482876	+	1.16577i	−0.958237	+	0.285976i	$0.907682\pi$
$62$	7.23284	+	2.99594i	0.918572	+	0.380485i
$63$	−6.20124	−	14.9711i	−0.781282	−	1.88618i
$64$		−	5.11854i		−	0.639818i
$65$	16.0408	−	6.64431i	1.98961	−	0.824125i
$66$	−0.655089	−	0.655089i	−0.0806358	−	0.0806358i
$67$	−1.86246			−0.227536			−0.113768	−	0.993507i	$-0.536292\pi$
$67$	−1.86246			−0.227536			−0.113768	+	0.993507i	$0.536292\pi$
$68$	−2.56199	−	4.32511i	−0.310687	−	0.524497i
$69$	21.0010			2.52822
$70$	4.78681	+	4.78681i	0.572133	+	0.572133i
$71$	7.01102	−	2.90406i	0.832055	−	0.344648i	0.0743389	−	0.997233i	$-0.476315\pi$
$71$	7.01102	−	2.90406i	0.832055	−	0.344648i	0.757716	+	0.652585i	$0.226315\pi$
$72$			19.1536i			2.25728i
$73$	−3.81569	−	9.21189i	−0.446593	−	1.07817i	−0.973590	−	0.228303i	$-0.926682\pi$
$73$	−3.81569	−	9.21189i	−0.446593	−	1.07817i	0.526997	−	0.849867i	$-0.323318\pi$
$74$	7.17081	+	2.97025i	0.833590	+	0.345284i
$75$	−6.12972	+	14.7984i	−0.707799	+	1.70878i
$76$	3.53316	−	3.53316i	0.405281	−	0.405281i
$77$	0.571880	−	0.571880i	0.0651718	−	0.0651718i
$78$	5.75379	−	13.8909i	0.651488	−	1.57283i
$79$	−0.280713	−	0.116275i	−0.0315827	−	0.0130820i	0.366836	−	0.930286i	$-0.380441\pi$
$79$	−0.280713	−	0.116275i	−0.0315827	−	0.0130820i	−0.398419	+	0.917204i	$0.630441\pi$
$80$	−0.0914538	−	0.220789i	−0.0102248	−	0.0246850i
$81$		−	16.1387i		−	1.79319i
$82$	−6.75606	+	2.79845i	−0.746083	+	0.309037i
$83$	−7.70045	−	7.70045i	−0.845235	−	0.845235i	0.144299	−	0.989534i	$-0.453907\pi$
$83$	−7.70045	−	7.70045i	−0.845235	−	0.845235i	−0.989534	+	0.144299i	$0.953907\pi$
$84$	−9.15413			−0.998797
$85$	−10.5019	−	7.87344i	−1.13909	−	0.853994i
$86$	0.883619			0.0952830
$87$	7.55249	+	7.55249i	0.809712	+	0.809712i
$88$	−0.883178	+	0.365824i	−0.0941470	+	0.0389970i
$89$			1.50936i			0.159992i	0.996795	+	0.0799962i	$0.0254908\pi$
$89$			1.50936i			0.159992i	−0.996795	+	0.0799962i	$0.974509\pi$
$90$	7.24826	+	17.4988i	0.764034	+	1.84454i
$91$	12.1265	+	5.02295i	1.27120	+	0.526548i
$92$	3.14072	−	7.58236i	0.327442	−	0.790515i
$93$	−19.5455	+	19.5455i	−2.02677	+	2.02677i
$94$	−2.74141	+	2.74141i	−0.282755	+	0.282755i
$95$	4.99264	−	12.0533i	0.512234	−	1.23664i
$96$	16.2069	+	6.71312i	1.65411	+	0.685155i
$97$	−3.59196	−	8.67175i	−0.364708	−	0.880483i	−0.994598	−	0.103799i	$-0.966900\pi$
$97$	−3.59196	−	8.67175i	−0.364708	−	0.880483i	0.629891	−	0.776684i	$-0.283100\pi$
$98$		−	1.06768i		−	0.107852i
$99$	2.09059	−	0.865950i	0.210112	−	0.0870313i
$100$	4.42623	+	4.42623i	0.442623	+	0.442623i
$101$	−8.42993			−0.838810			−0.419405	−	0.907799i	$-0.637761\pi$
$101$	−8.42993			−0.838810			−0.419405	+	0.907799i	$0.637761\pi$
$102$	−11.2518	+	1.60949i	−1.11410	+	0.159363i
$103$	−0.399566			−0.0393704			−0.0196852	−	0.999806i	$-0.506266\pi$
$103$	−0.399566			−0.0393704			−0.0196852	+	0.999806i	$0.506266\pi$
$104$	−10.9703	−	10.9703i	−1.07572	−	1.07572i
$105$	−22.0823	+	9.14679i	−2.15501	+	0.892635i
$106$		−	8.43006i		−	0.818800i
$107$	−3.19770	−	7.71993i	−0.309133	−	0.746314i	−0.999734	−	0.0230773i	$-0.992654\pi$
$107$	−3.19770	−	7.71993i	−0.309133	−	0.746314i	0.690600	−	0.723237i	$-0.257346\pi$
$108$	−13.1201	−	5.43452i	−1.26248	−	0.522937i
$109$	2.34114	−	5.65200i	0.224240	−	0.541364i	−0.771217	−	0.636572i	$-0.780352\pi$
$109$	2.34114	−	5.65200i	0.224240	−	0.541364i	0.995457	+	0.0952084i	$0.0303517\pi$
$110$	−0.668437	+	0.668437i	−0.0637330	+	0.0637330i
$111$	−19.3779	+	19.3779i	−1.83927	+	1.83927i
$112$	0.0691371	−	0.166912i	0.00653284	−	0.0157717i
$113$	2.51351	+	1.04113i	0.236451	+	0.0979411i	0.497763	−	0.867313i	$-0.334155\pi$
$113$	2.51351	+	1.04113i	0.236451	+	0.0979411i	−0.261312	+	0.965254i	$0.584155\pi$
$114$	−4.32349	−	10.4378i	−0.404932	−	0.977592i
$115$		−	21.4290i		−	1.99826i
$116$	3.85628	−	1.59733i	0.358047	−	0.148308i
$117$	25.9679	+	25.9679i	2.40074	+	2.40074i
$118$	6.94488			0.639328
$119$	−1.40505	−	9.82266i	−0.128801	−	0.900442i
$120$	28.2515			2.57900
$121$	−7.69832	−	7.69832i	−0.699847	−	0.699847i
$122$	8.04529	−	3.33247i	0.728386	−	0.301707i
$123$		−	25.8194i		−	2.32806i
$124$	4.13380	+	9.97989i	0.371227	+	0.896220i
$125$	0.394526	+	0.163418i	0.0352875	+	0.0146166i
$126$	−5.47953	+	13.2287i	−0.488155	+	1.17851i
$127$	−6.78286	+	6.78286i	−0.601881	+	0.601881i	−0.940811	−	0.338930i	$-0.889935\pi$
$127$	−6.78286	+	6.78286i	−0.601881	+	0.601881i	0.338930	+	0.940811i	$0.389935\pi$
$128$	4.75369	−	4.75369i	0.420171	−	0.420171i
$129$	−1.19391	+	2.88236i	−0.105118	+	0.253778i
$130$	−14.1739	−	5.87103i	−1.24314	−	0.514924i
$131$	4.06901	+	9.82347i	0.355511	+	0.858280i	0.995920	+	0.0902455i	$0.0287652\pi$
$131$	4.06901	+	9.82347i	0.355511	+	0.858280i	−0.640408	+	0.768035i	$0.721235\pi$
$132$		−	1.27830i		−	0.111261i
$133$	9.11203	−	3.77433i	0.790113	−	0.327276i
$134$	1.16369	+	1.16369i	0.100528	+	0.100528i
$135$	−37.0795			−3.19129
$136$	−2.90872	+	11.3620i	−0.249420	+	0.974285i
$137$	−19.4855			−1.66476			−0.832378	−	0.554209i	$-0.813021\pi$
$137$	−19.4855			−1.66476			−0.832378	+	0.554209i	$0.813021\pi$
$138$	−13.1217	−	13.1217i	−1.11699	−	1.11699i
$139$	11.6492	−	4.82527i	0.988074	−	0.409274i	0.170664	−	0.985329i	$-0.445409\pi$
$139$	11.6492	−	4.82527i	0.988074	−	0.409274i	0.817411	+	0.576056i	$0.195409\pi$
$140$			9.34066i			0.789430i
$141$	−5.23838	−	12.6466i	−0.441151	−	1.06503i
$142$	−6.19506	−	2.56608i	−0.519878	−	0.215341i
$143$	−0.701413	+	1.69336i	−0.0586551	+	0.141606i
$144$	0.357429	−	0.357429i	0.0297857	−	0.0297857i
$145$	7.70639	−	7.70639i	0.639981	−	0.639981i
$146$	−3.37161	+	8.13980i	−0.279037	+	0.673654i
$147$	3.48277	+	1.44261i	0.287254	+	0.118985i
$148$	4.09835	+	9.89429i	0.336882	+	0.813306i
$149$			6.73779i			0.551982i	0.961160	+	0.275991i	$0.0890059\pi$
$149$			6.73779i			0.551982i	−0.961160	+	0.275991i	$0.910994\pi$
$150$	13.0762	−	5.41633i	1.06767	−	0.442242i
$151$	14.6666	+	14.6666i	1.19355	+	1.19355i	0.976063	+	0.217488i	$0.0697864\pi$
$151$	14.6666	+	14.6666i	1.19355	+	1.19355i	0.217488	+	0.976063i	$0.430214\pi$
$152$	−11.6577			−0.945563
$153$	6.88528	−	26.8953i	0.556642	−	2.17435i
$154$	−0.714636			−0.0575870
$155$	19.9438	+	19.9438i	1.60192	+	1.60192i
$156$	19.1666	−	7.93909i	1.53456	−	0.635636i
$157$			1.30295i			0.103987i	0.998647	+	0.0519934i	$0.0165575\pi$
$157$			1.30295i			0.103987i	−0.998647	+	0.0519934i	$0.983443\pi$
$158$	0.102743	+	0.248044i	0.00817379	+	0.0197333i
$159$	27.4988	+	11.3904i	2.18080	+	0.903316i
$160$	6.84991	−	16.5371i	0.541533	−	1.30738i
$161$	11.4550	−	11.4550i	0.902781	−	0.902781i
$162$	−10.0837	+	10.0837i	−0.792248	+	0.792248i
$163$	−3.13736	+	7.57426i	−0.245737	+	0.593262i	−0.997833	−	0.0657915i	$-0.979043\pi$
$163$	−3.13736	+	7.57426i	−0.245737	+	0.593262i	0.752096	+	0.659053i	$0.229043\pi$
$164$	−9.32203	−	3.86131i	−0.727928	−	0.301518i
$165$	−1.27727	−	3.08361i	−0.0994355	−	0.240059i
$166$			9.62268i			0.746865i
$167$	14.0237	−	5.80881i	1.08519	−	0.449499i	0.232861	−	0.972510i	$-0.425191\pi$
$167$	14.0237	−	5.80881i	1.08519	−	0.449499i	0.852326	+	0.523011i	$0.175191\pi$
$168$	15.1020	+	15.1020i	1.16515	+	1.16515i
$169$	−16.7463			−1.28818
$170$	1.64228	+	11.4811i	0.125957	+	0.880562i
$171$	27.5951			2.11025
$172$	0.862117	+	0.862117i	0.0657358	+	0.0657358i
$173$	−0.478666	+	0.198270i	−0.0363923	+	0.0150742i	−0.400805	−	0.916163i	$-0.631270\pi$
$173$	−0.478666	+	0.198270i	−0.0363923	+	0.0150742i	0.364413	+	0.931237i	$0.381270\pi$
$174$		−	9.43778i		−	0.715476i
$175$	4.72836	+	11.4153i	0.357430	+	0.862913i
$176$	0.0233078	+	0.00965441i	0.00175689	+	0.000727728i
$177$	−9.38367	+	22.6542i	−0.705320	+	1.70279i
$178$	0.943070	−	0.943070i	0.0706861	−	0.0706861i
$179$	−7.81595	+	7.81595i	−0.584192	+	0.584192i	−0.936052	−	0.351861i	$-0.885549\pi$
$179$	−7.81595	+	7.81595i	−0.584192	+	0.584192i	0.351861	+	0.936052i	$0.385549\pi$
$180$	−10.0012	+	24.1449i	−0.745443	+	1.79966i
$181$	−13.7034	−	5.67614i	−1.01857	−	0.421904i	−0.189993	−	0.981785i	$-0.560847\pi$
$181$	−13.7034	−	5.67614i	−1.01857	−	0.421904i	−0.828573	+	0.559882i	$0.810847\pi$
$182$	−4.43837	−	10.7152i	−0.328994	−	0.794262i
$183$			30.7464i			2.27284i
$184$	−17.6904	+	7.32761i	−1.30415	+	0.540199i
$185$	19.7727	+	19.7727i	1.45372	+	1.45372i
$186$	24.4245			1.79089
$187$	1.37165	−	0.196204i	0.100305	−	0.0143478i
$188$	−5.34941			−0.390146
$189$	−19.8211	−	19.8211i	−1.44177	−	1.44177i
$190$	−10.6505	+	4.41159i	−0.772670	+	0.320050i
$191$		−	16.2004i		−	1.17222i	−0.810231	−	0.586111i	$-0.800658\pi$
$191$		−	16.2004i		−	1.17222i	0.810231	−	0.586111i	$-0.199342\pi$
$192$	−6.11109	−	14.7535i	−0.441030	−	1.06474i
$193$	14.5157	+	6.01261i	1.04486	+	0.432797i	0.838056	−	0.545585i	$-0.183692\pi$
$193$	14.5157	+	6.01261i	1.04486	+	0.432797i	0.206808	+	0.978381i	$0.433692\pi$
$194$	−3.17392	+	7.66252i	−0.227874	+	0.550137i
$195$	38.3026	−	38.3026i	2.74290	−	2.74290i
$196$	1.04170	−	1.04170i	0.0744073	−	0.0744073i
$197$	5.61106	−	13.5463i	0.399771	−	0.965134i	−0.587948	−	0.808898i	$-0.700064\pi$
$197$	5.61106	−	13.5463i	0.399771	−	0.965134i	0.987720	−	0.156235i	$-0.0499358\pi$
$198$	−1.84728	−	0.765170i	−0.131281	−	0.0543782i
$199$	2.53066	+	6.10955i	0.179394	+	0.433095i	0.987840	−	0.155476i	$-0.0496910\pi$
$199$	2.53066	+	6.10955i	0.179394	+	0.433095i	−0.808446	+	0.588570i	$0.799691\pi$
$200$		−	14.6044i		−	1.03269i
$201$	−5.36829	+	2.22362i	−0.378650	+	0.156842i
$202$	5.26713	+	5.26713i	0.370594	+	0.370594i
$203$	8.23901			0.578265
$204$	−12.5484	−	9.40774i	−0.878562	−	0.658673i
$205$	−26.3455			−1.84005
$206$	0.249654	+	0.249654i	0.0173942	+	0.0173942i
$207$	41.8754	−	17.3453i	2.91054	−	1.20558i
$208$			0.409435i			0.0283892i
$209$	0.527053	+	1.27242i	0.0364570	+	0.0880150i
$210$	19.5123	+	8.08227i	1.34648	+	0.557730i
$211$	1.38190	−	3.33621i	0.0951341	−	0.229674i	−0.869148	−	0.494553i	$-0.835332\pi$
$211$	1.38190	−	3.33621i	0.0951341	−	0.229674i	0.964282	+	0.264879i	$0.0853319\pi$
$212$	8.22493	−	8.22493i	0.564891	−	0.564891i
$213$	16.7411	−	16.7411i	1.14708	−	1.14708i
$214$	−2.82555	+	6.82147i	−0.193150	+	0.466306i
$215$	2.94109	+	1.21824i	0.200581	+	0.0830833i
$216$	12.6793	+	30.6105i	0.862716	+	2.08278i
$217$			21.3222i			1.44744i
$218$	−4.99422	+	2.06867i	−0.338251	+	0.140108i
$219$	−21.9964	−	21.9964i	−1.48638	−	1.48638i
$220$	−1.30434			−0.0879389
$221$	11.4607	+	19.3478i	0.770932	+	1.30148i
$222$	24.2151			1.62521
$223$	20.2557	+	20.2557i	1.35642	+	1.35642i	0.878284	+	0.478139i	$0.158689\pi$
$223$	20.2557	+	20.2557i	1.35642	+	1.35642i	0.478139	+	0.878284i	$0.341311\pi$
$224$	12.5017	−	5.17838i	0.835306	−	0.345995i
$225$			34.5703i			2.30469i
$226$	−0.919960	−	2.22098i	−0.0611948	−	0.147737i
$227$	−5.88537	−	2.43780i	−0.390626	−	0.161803i	0.178721	−	0.983900i	$-0.442804\pi$
$227$	−5.88537	−	2.43780i	−0.390626	−	0.161803i	−0.569347	+	0.822097i	$0.692804\pi$
$228$	5.96555	−	14.4021i	0.395078	−	0.953804i
$229$	−7.65871	+	7.65871i	−0.506102	+	0.506102i	−0.913328	−	0.407226i	$-0.866496\pi$
$229$	−7.65871	+	7.65871i	−0.506102	+	0.506102i	0.407226	+	0.913328i	$0.366496\pi$
$230$	−13.3891	+	13.3891i	−0.882850	+	0.882850i
$231$	0.965590	−	2.33114i	0.0635311	−	0.153378i
$232$	−8.99711	−	3.72672i	−0.590689	−	0.244671i
$233$	−5.24792	−	12.6696i	−0.343803	−	0.830013i	−0.997324	−	0.0731051i	$-0.976709\pi$
$233$	−5.24792	−	12.6696i	−0.343803	−	0.830013i	0.653522	−	0.756908i	$-0.273291\pi$
$234$		−	32.4502i		−	2.12134i
$235$	−12.9043	+	5.34512i	−0.841781	+	0.348677i
$236$	6.77589	+	6.77589i	0.441073	+	0.441073i
$237$	−0.947939			−0.0615753
$238$	−5.25943	+	7.01522i	−0.340918	+	0.454729i
$239$	21.8480			1.41323			0.706615	−	0.707598i	$-0.250221\pi$
$239$	21.8480			1.41323			0.706615	+	0.707598i	$0.250221\pi$
$240$	−0.527205	−	0.527205i	−0.0340310	−	0.0340310i
$241$	21.9606	−	9.09638i	1.41461	−	0.585949i	0.461107	−	0.887344i	$-0.347452\pi$
$241$	21.9606	−	9.09638i	1.41461	−	0.585949i	0.953499	+	0.301395i	$0.0974524\pi$
$242$			9.62001i			0.618398i
$243$	−5.89606	−	14.2344i	−0.378233	−	0.913134i
$244$	11.1009	+	4.59814i	0.710662	+	0.294366i
$245$	1.47201	−	3.55374i	0.0940432	−	0.227040i
$246$	−16.1323	+	16.1323i	−1.02856	+	1.02856i
$247$	−15.8051	+	15.8051i	−1.00566	+	1.00566i
$248$	9.64459	−	23.2841i	0.612432	−	1.47854i
$249$	−31.3891	−	13.0018i	−1.98921	−	0.823956i
$250$	−0.144399	−	0.348611i	−0.00913262	−	0.0220481i
$251$		−	19.7362i		−	1.24574i	−0.782325	−	0.622870i	$-0.785967\pi$
$251$		−	19.7362i		−	1.24574i	0.782325	−	0.622870i	$-0.214033\pi$
$252$	−18.2530	+	7.56066i	−1.14983	+	0.476277i
$253$	1.59959	+	1.59959i	0.100566	+	0.100566i
$254$	8.47603			0.531833
$255$	−39.6704	−	10.1558i	−2.48426	−	0.635978i
$256$	−16.1774			−1.01109
$257$	12.8291	+	12.8291i	0.800258	+	0.800258i	0.983136	−	0.182878i	$-0.0585413\pi$
$257$	12.8291	+	12.8291i	0.800258	+	0.800258i	−0.182878	+	0.983136i	$0.558541\pi$
$258$	2.54691	−	1.05496i	0.158563	−	0.0656791i
$259$			21.1393i			1.31353i
$260$	−8.10086	−	19.5572i	−0.502394	−	1.21289i
$261$	21.2972	+	8.82161i	1.31827	+	0.546044i
$262$	3.59546	−	8.68020i	0.222128	−	0.536264i
$263$	−10.8680	+	10.8680i	−0.670151	+	0.670151i	−0.957751	−	0.287600i	$-0.907143\pi$
$263$	−10.8680	+	10.8680i	−0.670151	+	0.670151i	0.287600	+	0.957751i	$0.407143\pi$
$264$	−2.10887	+	2.10887i	−0.129792	+	0.129792i
$265$	11.6225	−	28.0592i	0.713964	−	1.72366i
$266$	−8.05156	−	3.33506i	−0.493673	−	0.204486i
$267$	1.80205	+	4.35053i	0.110284	+	0.266248i
$268$			2.27075i			0.138708i
$269$	−17.1735	+	7.11348i	−1.04708	+	0.433716i	−0.838850	−	0.544363i	$-0.816772\pi$
$269$	−17.1735	+	7.11348i	−1.04708	+	0.433716i	−0.208234	+	0.978079i	$0.566772\pi$
$270$	23.1677	+	23.1677i	1.40994	+	1.40994i
$271$	−8.60890			−0.522953			−0.261477	−	0.965210i	$-0.584209\pi$
$271$	−8.60890			−0.522953			−0.261477	+	0.965210i	$0.584209\pi$
$272$	0.266308	−	0.157748i	0.0161473	−	0.00956489i
$273$	40.9498			2.47840
$274$	12.1748	+	12.1748i	0.735505	+	0.735505i
$275$	−1.59405	+	0.660275i	−0.0961246	+	0.0398161i
$276$		−	25.6048i		−	1.54123i
$277$	2.52682	+	6.10029i	0.151822	+	0.366531i	0.981431	−	0.191813i	$-0.0614368\pi$
$277$	2.52682	+	6.10029i	0.151822	+	0.366531i	−0.829609	+	0.558344i	$0.811437\pi$
$278$	−10.2935	−	4.26369i	−0.617361	−	0.255719i
$279$	−22.8299	+	55.1163i	−1.36679	+	3.29973i
$280$	15.4098	−	15.4098i	0.920911	−	0.920911i
$281$	−10.2182	+	10.2182i	−0.609566	+	0.609566i	−0.942833	−	0.333266i	$-0.891849\pi$
$281$	−10.2182	+	10.2182i	−0.609566	+	0.609566i	0.333266	+	0.942833i	$0.391849\pi$
$282$	−4.62873	+	11.1747i	−0.275637	+	0.665446i
$283$	−7.41958	−	3.07329i	−0.441048	−	0.182688i	0.151098	−	0.988519i	$-0.451719\pi$
$283$	−7.41958	−	3.07329i	−0.441048	−	0.182688i	−0.592146	+	0.805831i	$0.701719\pi$
$284$	−3.54068	−	8.54796i	−0.210101	−	0.507228i
$285$		−	40.7027i		−	2.41102i
$286$	1.49628	−	0.619781i	0.0884772	−	0.0366484i
$287$	−14.0832	−	14.0832i	−0.831305	−	0.831305i
$288$	37.8606			2.23096
$289$	8.16876	−	14.9088i	0.480515	−	0.876986i
$290$	−9.63010			−0.565499
$291$	−20.7066	−	20.7066i	−1.21384	−	1.21384i
$292$	−11.2313	+	4.65216i	−0.657262	+	0.272247i
$293$			25.6835i			1.50045i	0.661184	+	0.750224i	$0.270054\pi$
$293$			25.6835i			1.50045i	−0.661184	+	0.750224i	$0.729946\pi$
$294$	−1.27472	−	3.07744i	−0.0743431	−	0.179480i
$295$	23.1158	+	9.57488i	1.34585	+	0.557471i
$296$	9.56187	−	23.0844i	0.555773	−	1.34175i
$297$	2.76785	−	2.76785i	0.160607	−	0.160607i
$298$	4.20986	−	4.20986i	0.243871	−	0.243871i
$299$	−14.0496	+	33.9187i	−0.812509	+	1.96157i
$300$	18.0425	+	7.47346i	1.04169	+	0.431481i
$301$	0.920964	+	2.22340i	0.0530835	+	0.128155i
$302$		−	18.3278i		−	1.05464i
$303$	−24.2981	+	10.0646i	−1.39589	+	0.578196i
$304$	0.217546	+	0.217546i	0.0124771	+	0.0124771i
$305$	31.3729			1.79641
$306$	−21.1065	+	12.5025i	−1.20658	+	0.714720i
$307$	−27.6891			−1.58030			−0.790149	−	0.612915i	$-0.789997\pi$
$307$	−27.6891			−1.58030			−0.790149	+	0.612915i	$0.789997\pi$
$308$	−0.697247	−	0.697247i	−0.0397293	−	0.0397293i
$309$	−1.15169	+	0.477047i	−0.0655176	+	0.0271383i
$310$		−	24.9222i		−	1.41549i
$311$	−0.566280	−	1.36712i	−0.0321108	−	0.0775224i	0.907011	−	0.421108i	$-0.138359\pi$
$311$	−0.566280	−	1.36712i	−0.0321108	−	0.0775224i	−0.939121	+	0.343585i	$0.888359\pi$
$312$	−44.7177	−	18.5227i	−2.53164	−	1.04864i
$313$	−9.27711	+	22.3969i	−0.524373	+	1.26595i	0.410789	+	0.911730i	$0.365253\pi$
$313$	−9.27711	+	22.3969i	−0.524373	+	1.26595i	−0.935163	+	0.354219i	$0.884747\pi$
$314$	0.814100	−	0.814100i	0.0459423	−	0.0459423i
$315$	−36.4768	+	36.4768i	−2.05524	+	2.05524i
$316$	−0.141765	+	0.342251i	−0.00797490	+	0.0192531i
$317$	9.54907	+	3.95536i	0.536329	+	0.222155i	0.634373	−	0.773027i	$-0.281258\pi$
$317$	9.54907	+	3.95536i	0.536329	+	0.222155i	−0.0980435	+	0.995182i	$0.531258\pi$
$318$	−10.0648	−	24.2985i	−0.564403	−	1.36259i
$319$			1.15051i			0.0644161i
$320$	−15.0541	+	6.23562i	−0.841550	+	0.348582i
$321$	−18.4338	−	18.4338i	−1.02888	−	1.02888i
$322$	−14.3145			−0.797714
$323$	16.3696	+	4.19066i	0.910827	+	0.233175i
$324$	−19.6766			−1.09314
$325$	−19.8002	−	19.8002i	−1.09832	−	1.09832i
$326$	6.69275	−	2.77223i	0.370677	−	0.153540i
$327$		−	19.0862i		−	1.05547i
$328$	9.00883	+	21.7492i	0.497430	+	1.20090i
$329$	−9.75534	−	4.04079i	−0.537829	−	0.222776i
$330$	−1.12862	+	2.72473i	−0.0621286	+	0.149992i
$331$	−13.7256	+	13.7256i	−0.754427	+	0.754427i	−0.975302	−	0.220875i	$-0.929109\pi$
$331$	−13.7256	+	13.7256i	−0.754427	+	0.754427i	0.220875	+	0.975302i	$0.429109\pi$
$332$	−9.38853	+	9.38853i	−0.515263	+	0.515263i
$333$	−22.6341	+	54.6436i	−1.24034	+	2.99445i
$334$	−12.3916	−	5.13277i	−0.678039	−	0.280853i
$335$	2.26893	+	5.47768i	0.123965	+	0.299278i
$336$		−	0.563643i		−	0.0307492i
$337$	−5.48082	+	2.27023i	−0.298559	+	0.123667i	−0.526935	−	0.849906i	$-0.676659\pi$
$337$	−5.48082	+	2.27023i	−0.298559	+	0.123667i	0.228375	+	0.973573i	$0.426659\pi$
$338$	10.4633	+	10.4633i	0.569129	+	0.569129i
$339$	8.48784			0.460996
$340$	−9.59944	+	12.8041i	−0.520603	+	0.694399i
$341$	−2.97746			−0.161239
$342$	−17.2418	−	17.2418i	−0.932330	−	0.932330i
$343$	18.2504	−	7.55955i	0.985427	−	0.408177i
$344$		−	2.84456i		−	0.153368i
$345$	−25.5843	−	61.7659i	−1.37741	−	3.32537i
$346$	0.422958	+	0.175195i	0.0227384	+	0.00941854i
$347$	−3.75883	+	9.07461i	−0.201784	+	0.487151i	−0.992085	−	0.125569i	$-0.959924\pi$
$347$	−3.75883	+	9.07461i	−0.201784	+	0.487151i	0.790300	+	0.612719i	$0.209924\pi$
$348$	9.20813	−	9.20813i	0.493608	−	0.493608i
$349$	14.8671	−	14.8671i	0.795817	−	0.795817i	−0.186616	−	0.982433i	$-0.559752\pi$
$349$	14.8671	−	14.8671i	0.795817	−	0.795817i	0.982433	+	0.186616i	$0.0597520\pi$
$350$	4.17807	−	10.0867i	0.223327	−	0.539159i
$351$	58.6910	+	24.3106i	3.13270	+	1.29761i
$352$	0.723117	+	1.74576i	0.0385423	+	0.0930493i
$353$			11.3683i			0.605072i	0.953138	+	0.302536i	$0.0978332\pi$
$353$			11.3683i			0.605072i	−0.953138	+	0.302536i	$0.902167\pi$
$354$	20.0176	−	8.29158i	1.06393	−	0.440693i
$355$	−17.0822	−	17.0822i	−0.906630	−	0.906630i
$356$	1.84025			0.0975328
$357$	−15.7773	−	26.6349i	−0.835021	−	1.40967i
$358$	9.76701			0.516203
$359$	−19.3741	−	19.3741i	−1.02253	−	1.02253i	−0.999740	−	0.0227868i	$-0.992746\pi$
$359$	−19.3741	−	19.3741i	−1.02253	−	1.02253i	−0.0227868	−	0.999740i	$-0.507254\pi$
$360$	56.3326	−	23.3337i	2.96899	−	1.22980i
$361$		−	2.20447i		−	0.116025i
$362$	5.01554	+	12.1086i	0.263611	+	0.636413i
$363$	−31.3804	−	12.9982i	−1.64705	−	0.682229i
$364$	6.12407	−	14.7848i	0.320989	−	0.774935i
$365$	−22.4446	+	22.4446i	−1.17480	+	1.17480i
$366$	19.2107	−	19.2107i	1.00416	−	1.00416i
$367$	1.00100	−	2.41662i	0.0522517	−	0.126147i	−0.895598	−	0.444864i	$-0.853252\pi$
$367$	1.00100	−	2.41662i	0.0522517	−	0.126147i	0.947850	+	0.318717i	$0.103252\pi$
$368$	0.466865	+	0.193382i	0.0243370	+	0.0100807i
$369$	−21.3250	−	51.4831i	−1.11014	−	2.68010i
$370$		−	24.7085i		−	1.28453i
$371$	21.2121	−	8.78635i	1.10128	−	0.456164i
$372$	23.8302	+	23.8302i	1.23554	+	1.23554i
$373$	22.7759			1.17929			0.589645	−	0.807662i	$-0.299268\pi$
$373$	22.7759			1.17929			0.589645	+	0.807662i	$0.299268\pi$
$374$	−0.979616	−	0.734435i	−0.0506547	−	0.0379767i
$375$	1.33227			0.0687983
$376$	8.82520	+	8.82520i	0.455125	+	0.455125i
$377$	−17.2506	+	7.14543i	−0.888451	+	0.368008i
$378$			24.7689i			1.27398i
$379$	−5.57565	−	13.4608i	−0.286402	−	0.691436i	0.713556	−	0.700598i	$-0.247083\pi$
$379$	−5.57565	−	13.4608i	−0.286402	−	0.691436i	−0.999958	+	0.00916236i	$0.997083\pi$
$380$	−14.6956	−	6.08712i	−0.753868	−	0.312262i
$381$	−11.4525	+	27.6488i	−0.586729	+	1.41649i
$382$	−10.1222	+	10.1222i	−0.517899	+	0.517899i
$383$	8.45057	−	8.45057i	0.431804	−	0.431804i	−0.457438	−	0.889242i	$-0.651233\pi$
$383$	8.45057	−	8.45057i	0.431804	−	0.431804i	0.889242	+	0.457438i	$0.151233\pi$
$384$	8.02636	−	19.3773i	0.409594	−	0.988846i
$385$	−2.37864	−	0.985266i	−0.121227	−	0.0502138i
$386$	−5.31285	−	12.8264i	−0.270417	−	0.652844i
$387$			6.73342i			0.342279i
$388$	−10.5728	+	4.37938i	−0.536750	+	0.222329i
$389$	−7.11038	−	7.11038i	−0.360511	−	0.360511i	0.503490	−	0.864001i	$-0.332049\pi$
$389$	−7.11038	−	7.11038i	−0.360511	−	0.360511i	−0.864001	+	0.503490i	$0.832049\pi$
$390$	−47.8639			−2.42368
$391$	27.4747	−	3.93004i	1.38946	−	0.198751i
$392$	−3.43710			−0.173600
$393$	23.4567	+	23.4567i	1.18323	+	1.18323i
$394$	−11.9698	+	4.95804i	−0.603028	+	0.249782i
$395$			0.967256i			0.0486679i
$396$	−1.05578	−	2.54888i	−0.0530551	−	0.128086i
$397$	−23.8273	−	9.86958i	−1.19586	−	0.495340i	−0.306199	−	0.951968i	$-0.599057\pi$
$397$	−23.8273	−	9.86958i	−1.19586	−	0.495340i	−0.889658	+	0.456628i	$0.849057\pi$
$398$	2.23614	−	5.39851i	0.112087	−	0.270603i
$399$	21.7579	−	21.7579i	1.08926	−	1.08926i
$400$	−0.272535	+	0.272535i	−0.0136267	+	0.0136267i
$401$	5.36440	−	12.9508i	0.267886	−	0.646733i	−0.731498	−	0.681844i	$-0.761178\pi$
$401$	5.36440	−	12.9508i	0.267886	−	0.646733i	0.999383	+	0.0351108i	$0.0111784\pi$
$402$	4.74352	+	1.96483i	0.236585	+	0.0979969i
$403$	−18.4920	−	44.6438i	−0.921155	−	2.22386i
$404$			10.2779i			0.511346i
$405$	−47.4654	+	19.6608i	−2.35858	+	0.976954i
$406$	−5.14784	−	5.14784i	−0.255483	−	0.255483i
$407$	−2.95193			−0.146322
$408$	5.18128	+	36.2222i	0.256512	+	1.79326i
$409$	−12.4896			−0.617570			−0.308785	−	0.951132i	$-0.599922\pi$
$409$	−12.4896			−0.617570			−0.308785	+	0.951132i	$0.599922\pi$
$410$	16.4610	+	16.4610i	0.812952	+	0.812952i
$411$	−56.1641	+	23.2639i	−2.77037	+	1.14753i
$412$			0.487159i			0.0240006i
$413$	7.23840	+	17.4750i	0.356178	+	0.859891i
$414$	−37.0018	−	15.3267i	−1.81854	−	0.753265i
$415$	−13.2667	+	32.0288i	−0.651239	+	1.57223i
$416$	−21.6847	+	21.6847i	−1.06318	+	1.06318i
$417$	27.8163	−	27.8163i	1.36217	−	1.36217i
$418$	0.465714	−	1.12433i	0.0227788	−	0.0549929i
$419$	4.10240	+	1.69927i	0.200415	+	0.0830147i	0.480633	−	0.876922i	$-0.340407\pi$
$419$	4.10240	+	1.69927i	0.200415	+	0.0830147i	−0.280218	+	0.959936i	$0.590407\pi$
$420$	11.1519	+	26.9231i	0.544159	+	1.31372i
$421$			7.17673i			0.349773i	0.984589	+	0.174886i	$0.0559558\pi$
$421$			7.17673i			0.349773i	−0.984589	+	0.174886i	$0.944044\pi$
$422$	−2.94793	+	1.22107i	−0.143503	+	0.0594410i
$423$	−20.8903	−	20.8903i	−1.01572	−	1.01572i
$424$	−27.1382			−1.31795
$425$	−5.24993	+	20.5073i	−0.254659	+	0.994749i
$426$	−20.9201			−1.01358
$427$	16.7706	+	16.7706i	0.811587	+	0.811587i
$428$	−9.41228	+	3.89869i	−0.454960	+	0.188450i
$429$			5.71830i			0.276082i
$430$	−1.07646	−	2.59880i	−0.0519115	−	0.125326i
$431$	−11.6378	−	4.82053i	−0.560573	−	0.232197i	0.0843612	−	0.996435i	$-0.473115\pi$
$431$	−11.6378	−	4.82053i	−0.560573	−	0.232197i	−0.644934	+	0.764238i	$0.723115\pi$
$432$	0.334617	−	0.807837i	0.0160993	−	0.0388671i
$433$	15.8069	−	15.8069i	0.759632	−	0.759632i	−0.216623	−	0.976255i	$-0.569504\pi$
$433$	15.8069	−	15.8069i	0.759632	−	0.759632i	0.976255	+	0.216623i	$0.0695042\pi$
$434$	13.3224	−	13.3224i	0.639494	−	0.639494i
$435$	13.0118	−	31.4133i	0.623869	−	1.50615i
$436$	−6.89103	−	2.85436i	−0.330020	−	0.136699i
$437$	10.5571	+	25.4871i	0.505014	+	1.21921i
$438$			27.4872i			1.31339i
$439$	−27.9846	+	11.5916i	−1.33563	+	0.553237i	−0.932257	−	0.361797i	$-0.882163\pi$
$439$	−27.9846	+	11.5916i	−1.33563	+	0.553237i	−0.403376	+	0.915034i	$0.632163\pi$
$440$	2.15185	+	2.15185i	0.102585	+	0.102585i
$441$	8.13604			0.387430
$442$	4.92796	−	19.2496i	0.234399	−	0.915610i
$443$	25.3507			1.20445			0.602224	−	0.798327i	$-0.294281\pi$
$443$	25.3507			1.20445			0.602224	+	0.798327i	$0.294281\pi$
$444$	23.6258	+	23.6258i	1.12123	+	1.12123i
$445$	4.43918	−	1.83877i	0.210437	−	0.0871661i
$446$		−	25.3121i		−	1.19856i
$447$	8.04433	+	19.4207i	0.380484	+	0.918570i
$448$	−11.3806	−	4.71399i	−0.537682	−	0.222715i
$449$	1.80510	−	4.35791i	0.0851881	−	0.205662i	−0.875545	−	0.483137i	$-0.839497\pi$
$449$	1.80510	−	4.35791i	0.0851881	−	0.205662i	0.960733	+	0.277474i	$0.0894974\pi$
$450$	21.6000	−	21.6000i	1.01823	−	1.01823i
$451$	1.96660	−	1.96660i	0.0926036	−	0.0926036i
$452$	1.26936	−	3.06451i	0.0597058	−	0.144143i
$453$	59.7851	+	24.7638i	2.80895	+	1.16350i
$454$	2.15409	+	5.20042i	0.101096	+	0.244068i
$455$		−	41.7843i		−	1.95888i
$456$	−33.6016	+	13.9182i	−1.57354	+	0.651782i
$457$	17.9567	+	17.9567i	0.839980	+	0.839980i	0.988856	−	0.148875i	$-0.0475654\pi$
$457$	17.9567	+	17.9567i	0.839980	+	0.839980i	−0.148875	+	0.988856i	$0.547565\pi$
$458$	9.57052			0.447201
$459$	−6.80032	−	47.5408i	−0.317412	−	2.21901i
$460$	−26.1266			−1.21816
$461$	−25.1464	−	25.1464i	−1.17118	−	1.17118i	−0.981928	−	0.189256i	$-0.939392\pi$
$461$	−25.1464	−	25.1464i	−1.17118	−	1.17118i	−0.189256	−	0.981928i	$-0.560608\pi$
$462$	−2.05984	+	0.853213i	−0.0958324	+	0.0396951i
$463$			19.7152i			0.916244i	0.888889	+	0.458122i	$0.151478\pi$
$463$			19.7152i			0.916244i	−0.888889	+	0.458122i	$0.848522\pi$
$464$	0.0983514	+	0.237441i	0.00456585	+	0.0110229i
$465$	81.2962	+	33.6740i	3.77002	+	1.56159i
$466$	−4.63716	+	11.1951i	−0.214812	+	0.518603i
$467$	6.07948	−	6.07948i	0.281325	−	0.281325i	−0.552312	−	0.833637i	$-0.686254\pi$
$467$	6.07948	−	6.07948i	0.281325	−	0.281325i	0.833637	+	0.552312i	$0.186254\pi$
$468$	31.6606	−	31.6606i	1.46351	−	1.46351i
$469$	−1.71526	+	4.14101i	−0.0792034	+	0.191214i
$470$	11.4024	+	4.72305i	0.525956	+	0.217858i
$471$	1.55561	+	3.75557i	0.0716786	+	0.173048i
$472$		−	22.3571i		−	1.02907i
$473$	−0.310479	+	0.128605i	−0.0142759	+	0.00591325i
$474$	0.592284	+	0.592284i	0.0272045	+	0.0272045i
$475$	−21.0409			−0.965424
$476$	−11.9760	+	1.71306i	−0.548917	+	0.0785182i
$477$	64.2394			2.94132
$478$	−13.6509	−	13.6509i	−0.624378	−	0.624378i
$479$	−2.12619	+	0.880695i	−0.0971479	+	0.0402400i	−0.430728	−	0.902482i	$-0.641743\pi$
$479$	−2.12619	+	0.880695i	−0.0971479	+	0.0402400i	0.333580	+	0.942722i	$0.391743\pi$
$480$		−	55.8442i		−	2.54893i
$481$	−18.3335	−	44.2609i	−0.835933	−	2.01812i
$482$	−19.4048	−	8.03773i	−0.883864	−	0.366108i
$483$	19.3412	−	46.6937i	0.880054	−	2.12464i
$484$	−9.38593	+	9.38593i	−0.426633	+	0.426633i
$485$	−21.1286	+	21.1286i	−0.959398	+	0.959398i
$486$	−5.20987	+	12.5777i	−0.236325	+	0.570538i
$487$	−38.3269	−	15.8755i	−1.73676	−	0.719389i	−0.999018	−	0.0443052i	$-0.985893\pi$
$487$	−38.3269	−	15.8755i	−1.73676	−	0.719389i	−0.737741	−	0.675084i	$-0.764107\pi$
$488$	−10.7279	−	25.8995i	−0.485631	−	1.17242i
$489$			25.5775i			1.15665i
$490$	−3.14015	+	1.30069i	−0.141858	+	0.0587594i
$491$	7.60261	+	7.60261i	0.343101	+	0.343101i	0.857532	−	0.514431i	$-0.171997\pi$
$491$	7.60261	+	7.60261i	0.343101	+	0.343101i	−0.514431	+	0.857532i	$0.671997\pi$
$492$	−31.4795			−1.41921
$493$	11.2939	+	8.46726i	0.508654	+	0.381346i
$494$	19.7505			0.888617
$495$	−5.09368	−	5.09368i	−0.228944	−	0.228944i
$496$	−0.614487	+	0.254529i	−0.0275913	+	0.0114287i
$497$		−	18.2628i		−	0.819201i
$498$	11.4886	+	27.7360i	0.514818	+	1.24288i
$499$	20.3602	+	8.43346i	0.911447	+	0.377534i	0.788610	−	0.614893i	$-0.210801\pi$
$499$	20.3602	+	8.43346i	0.911447	+	0.377534i	0.122837	+	0.992427i	$0.460801\pi$
$500$	0.199242	−	0.481014i	0.00891039	−	0.0215116i
$501$	33.4861	−	33.4861i	1.49605	−	1.49605i
$502$	−12.3314	+	12.3314i	−0.550379	+	0.550379i
$503$	0.550878	−	1.32994i	0.0245624	−	0.0592989i	−0.911122	−	0.412136i	$-0.864783\pi$
$503$	0.550878	−	1.32994i	0.0245624	−	0.0592989i	0.935685	+	0.352837i	$0.114783\pi$
$504$	42.5862	+	17.6398i	1.89694	+	0.785739i
$505$	10.2697	+	24.7932i	0.456995	+	1.10328i
$506$		−	1.99889i		−	0.0888617i
$507$	−48.2689	+	19.9936i	−2.14370	+	0.887948i
$508$	8.26978	+	8.26978i	0.366912	+	0.366912i
$509$	16.3855			0.726274			0.363137	−	0.931736i	$-0.381706\pi$
$509$	16.3855			0.726274			0.363137	+	0.931736i	$0.381706\pi$
$510$	18.4411	+	31.1320i	0.816586	+	1.37855i
$511$	−23.9959			−1.06151
$512$	0.600467	+	0.600467i	0.0265372	+	0.0265372i
$513$	44.1014	−	18.2674i	1.94712	−	0.806525i
$514$		−	16.0316i		−	0.707123i
$515$	0.486768	+	1.17516i	0.0214496	+	0.0517838i
$516$	3.51423	+	1.45564i	0.154705	+	0.0640810i
$517$	0.564263	−	1.36225i	0.0248162	−	0.0599117i
$518$	13.2081	−	13.2081i	0.580331	−	0.580331i
$519$	−1.14297	+	1.14297i	−0.0501708	+	0.0501708i
$520$	−18.9001	+	45.6290i	−0.828826	+	2.00096i
$521$	38.4312	+	15.9187i	1.68370	+	0.697412i	0.999492	−	0.0318725i	$-0.0101471\pi$
$521$	38.4312	+	15.9187i	1.68370	+	0.697412i	0.684210	+	0.729285i	$0.260147\pi$
$522$	−7.79494	−	18.8186i	−0.341175	−	0.823670i
$523$		−	24.2374i		−	1.05983i	−0.848051	−	0.529915i	$-0.822224\pi$
$523$		−	24.2374i		−	1.05983i	0.848051	−	0.529915i	$-0.177776\pi$
$524$	11.9769	−	4.96101i	0.523215	−	0.216723i
$525$	27.2577	+	27.2577i	1.18962	+	1.18962i
$526$	13.5810			0.592158
$527$	−21.9129	+	29.2282i	−0.954541	+	1.27320i
$528$	0.0787080			0.00342533
$529$	15.7771	+	15.7771i	0.685960	+	0.685960i
$530$	−24.7936	+	10.2698i	−1.07696	+	0.446094i
$531$			52.9220i			2.29662i
$532$	−4.60173	−	11.1096i	−0.199510	−	0.481660i
$533$	41.7009	+	17.2731i	1.80627	+	0.748180i
$534$	1.59232	−	3.84421i	0.0689066	−	0.166355i
$535$	−18.8095	+	18.8095i	−0.813204	+	0.813204i
$536$	3.74618	−	3.74618i	0.161810	−	0.161810i
$537$	−13.1968	+	31.8599i	−0.569485	+	1.37486i
$538$	15.1748	+	6.28560i	0.654231	+	0.270991i
$539$	0.155394	+	0.375154i	0.00669329	+	0.0161590i
$540$			45.2079i			1.94544i
$541$	20.5470	−	8.51085i	0.883385	−	0.365910i	0.105576	−	0.994411i	$-0.466331\pi$
$541$	20.5470	−	8.51085i	0.883385	−	0.365910i	0.777809	+	0.628501i	$0.216331\pi$
$542$	5.37895	+	5.37895i	0.231046	+	0.231046i
$543$	−46.2749			−1.98585
$544$	22.4591	+	5.74960i	0.962925	+	0.246512i
$545$	−19.4751			−0.834223
$546$	−25.5860	−	25.5860i	−1.09498	−	1.09498i
$547$	11.6509	−	4.82595i	0.498156	−	0.206343i	−0.119436	−	0.992842i	$-0.538109\pi$
$547$	11.6509	−	4.82595i	0.498156	−	0.206343i	0.617591	+	0.786499i	$0.288109\pi$
$548$			23.7570i			1.01485i
$549$	25.3943	+	61.3073i	1.08380	+	2.61653i
$550$	1.40853	+	0.583432i	0.0600598	+	0.0248776i
$551$	−5.36919	+	12.9624i	−0.228735	+	0.552216i
$552$	−42.2416	+	42.2416i	−1.79792	+	1.79792i
$553$	−0.517054	+	0.517054i	−0.0219874	+	0.0219874i
$554$	2.23275	−	5.39033i	0.0948604	−	0.229013i
$555$	80.5990	+	33.3852i	3.42124	+	1.41712i
$556$	−5.88305	−	14.2029i	−0.249497	−	0.602339i
$557$		−	21.8585i		−	0.926173i	−0.886313	−	0.463086i	$-0.846742\pi$
$557$		−	21.8585i		−	0.926173i	0.886313	−	0.463086i	$-0.153258\pi$
$558$	48.7018	−	20.1729i	2.06171	−	0.853988i
$559$	−3.85657	−	3.85657i	−0.163116	−	0.163116i
$560$	−0.575128			−0.0243036
$561$	3.71934	−	2.20316i	0.157031	−	0.0930175i
$562$	12.7689			0.538624
$563$	−30.4159	−	30.4159i	−1.28188	−	1.28188i	−0.939597	−	0.342281i	$-0.888800\pi$
$563$	−30.4159	−	30.4159i	−1.28188	−	1.28188i	−0.342281	−	0.939597i	$-0.611200\pi$
$564$	−15.4189	+	6.38672i	−0.649253	+	0.268930i
$565$		−	8.66080i		−	0.364363i
$566$	2.71562	+	6.55608i	0.114146	+	0.275573i
$567$	−35.8828	−	14.8632i	−1.50694	−	0.624194i
$568$	−8.26077	+	19.9433i	−0.346614	+	0.836801i
$569$	14.5172	−	14.5172i	0.608594	−	0.608594i	−0.333985	−	0.942578i	$-0.608393\pi$
$569$	14.5172	−	14.5172i	0.608594	−	0.608594i	0.942578	+	0.333985i	$0.108393\pi$
$570$	−25.4316	+	25.4316i	−1.06521	+	1.06521i
$571$	0.0919704	−	0.222036i	0.00384884	−	0.00929193i	−0.921943	−	0.387325i	$-0.873399\pi$
$571$	0.0919704	−	0.222036i	0.00384884	−	0.00929193i	0.925792	+	0.378033i	$0.123399\pi$
$572$	2.06458	+	0.855175i	0.0863242	+	0.0357567i
$573$	−19.3419	−	46.6955i	−0.808019	−	1.95073i
$574$			17.5987i			0.734557i
$575$	−31.9294	+	13.2256i	−1.33155	+	0.551545i
$576$	−24.3706	−	24.3706i	−1.01544	−	1.01544i
$577$	−27.7861			−1.15675			−0.578376	−	0.815770i	$-0.696313\pi$
$577$	−27.7861			−1.15675			−0.578376	+	0.815770i	$0.696313\pi$
$578$	−14.4191	+	4.21125i	−0.599757	+	0.175165i
$579$	49.0180			2.03712
$580$	−9.39577	−	9.39577i	−0.390138	−	0.390138i
$581$	−24.2130	+	10.0294i	−1.00453	+	0.416088i
$582$			25.8755i			1.07257i
$583$	1.22694	+	2.96209i	0.0508146	+	0.122677i
$584$	26.2038	+	10.8540i	1.08432	+	0.449140i
$585$	44.7389	−	108.009i	1.84973	−	4.46564i
$586$	16.0474	−	16.0474i	0.662912	−	0.662912i
$587$	1.91046	−	1.91046i	0.0788530	−	0.0788530i	−0.666580	−	0.745433i	$-0.732243\pi$
$587$	1.91046	−	1.91046i	0.0788530	−	0.0788530i	0.745433	+	0.666580i	$0.232243\pi$
$588$	1.75886	−	4.24626i	0.0725341	−	0.175113i
$589$	−33.5460	−	13.8952i	−1.38224	−	0.572542i
$590$	−8.46054	−	20.4256i	−0.348315	−	0.840907i
$591$		−	45.7444i		−	1.88167i
$592$	−0.609217	+	0.252346i	−0.0250387	+	0.0103714i
$593$	18.4755	+	18.4755i	0.758700	+	0.758700i	0.976086	−	0.217386i	$-0.0697531\pi$
$593$	18.4755	+	18.4755i	0.758700	+	0.758700i	−0.217386	+	0.976086i	$0.569753\pi$
$594$	−3.45877			−0.141915
$595$	−27.1777	+	16.0988i	−1.11418	+	0.659984i
$596$	8.21484			0.336493
$597$	14.5885	+	14.5885i	0.597069	+	0.597069i
$598$	29.9712	−	12.4145i	1.22561	−	0.507666i
$599$		−	2.48091i		−	0.101367i	−0.998715	−	0.0506837i	$-0.983860\pi$
$599$		−	2.48091i		−	0.101367i	0.998715	−	0.0506837i	$-0.0161400\pi$
$600$	−17.4364	−	42.0951i	−0.711836	−	1.71852i
$601$	18.8319	+	7.80044i	0.768170	+	0.318187i	0.732131	−	0.681164i	$-0.238526\pi$
$601$	18.8319	+	7.80044i	0.768170	+	0.318187i	0.0360393	+	0.999350i	$0.488526\pi$
$602$	0.813780	−	1.96464i	0.0331672	−	0.0800727i
$603$	−8.86766	+	8.86766i	−0.361119	+	0.361119i
$604$	17.8818	−	17.8818i	0.727600	−	0.727600i
$605$	−13.2631	+	32.0199i	−0.539220	+	1.30179i
$606$	21.4703	+	8.89327i	0.872169	+	0.361264i
$607$	−4.09532	−	9.88698i	−0.166224	−	0.401300i	0.818716	−	0.574199i	$-0.194687\pi$
$607$	−4.09532	−	9.88698i	−0.166224	−	0.401300i	−0.984940	+	0.172899i	$0.944687\pi$
$608$			23.0435i			0.934538i
$609$	23.7478	−	9.83666i	0.962309	−	0.398601i
$610$	−19.6022	−	19.6022i	−0.793670	−	0.793670i
$611$	23.9299			0.968100
$612$	−32.7912	−	8.39466i	−1.32551	−	0.339334i
$613$	−21.8975			−0.884431			−0.442216	−	0.896909i	$-0.645807\pi$
$613$	−21.8975			−0.884431			−0.442216	+	0.896909i	$0.645807\pi$
$614$	17.3005	+	17.3005i	0.698190	+	0.698190i
$615$	−75.9373	+	31.4543i	−3.06209	+	1.26836i
$616$			2.30057i			0.0926926i
$617$	−5.24036	−	12.6514i	−0.210969	−	0.509324i	0.782604	−	0.622520i	$-0.213891\pi$
$617$	−5.24036	−	12.6514i	−0.210969	−	0.509324i	−0.993573	+	0.113196i	$0.963891\pi$
$618$	1.01766	+	0.421528i	0.0409362	+	0.0169563i
$619$	4.12163	−	9.95049i	0.165662	−	0.399944i	−0.819147	−	0.573584i	$-0.805553\pi$
$619$	4.12163	−	9.95049i	0.165662	−	0.399944i	0.984809	+	0.173640i	$0.0555528\pi$
$620$	24.3158	−	24.3158i	0.976546	−	0.976546i
$621$	55.4412	−	55.4412i	2.22478	−	2.22478i
$622$	−0.500376	+	1.20801i	−0.0200632	+	0.0484370i
$623$	3.35593	+	1.39007i	0.134452	+	0.0556920i
$624$	0.488830	+	1.18014i	0.0195688	+	0.0472434i
$625$			24.3113i			0.972452i
$626$	19.7903	−	8.19743i	0.790981	−	0.327635i
$627$	3.03831	+	3.03831i	0.121338	+	0.121338i
$628$	1.58858			0.0633912
$629$	−21.7250	+	28.9775i	−0.866231	+	1.15541i
$630$	45.5824			1.81605
$631$	−21.5640	−	21.5640i	−0.858447	−	0.858447i	0.132708	−	0.991155i	$-0.457633\pi$
$631$	−21.5640	−	21.5640i	−0.858447	−	0.858447i	−0.991155	+	0.132708i	$0.957633\pi$
$632$	0.798506	−	0.330752i	0.0317629	−	0.0131566i
$633$		−	11.2660i		−	0.447784i
$634$	−3.49503	−	8.43774i	−0.138805	−	0.335105i
$635$	28.2122	+	11.6859i	1.11957	+	0.463739i
$636$	13.8874	−	33.5271i	0.550670	−	1.32943i
$637$	−4.65992	+	4.65992i	−0.184633	+	0.184633i
$638$	0.718852	−	0.718852i	0.0284596	−	0.0284596i
$639$	19.5542	−	47.2081i	0.773554	−	1.86752i
$640$	−19.7722	−	8.18992i	−0.781565	−	0.323735i
$641$	9.65860	+	23.3179i	0.381492	+	0.921003i	0.991678	+	0.128744i	$0.0410947\pi$
$641$	9.65860	+	23.3179i	0.381492	+	0.921003i	−0.610186	+	0.792258i	$0.708905\pi$
$642$			23.0354i			0.909134i
$643$	−18.5426	+	7.68059i	−0.731248	+	0.302893i	−0.717065	−	0.697007i	$-0.754515\pi$
$643$	−18.5426	+	7.68059i	−0.731248	+	0.302893i	−0.0141833	+	0.999899i	$0.504515\pi$
$644$	−13.9661	−	13.9661i	−0.550343	−	0.550343i
$645$	9.93176			0.391063
$646$	−7.60953	−	12.8463i	−0.299393	−	0.505430i
$647$	−41.8015			−1.64339			−0.821693	−	0.569930i	$-0.806970\pi$
$647$	−41.8015			−1.64339			−0.821693	+	0.569930i	$0.806970\pi$
$648$	32.4615	+	32.4615i	1.27521	+	1.27521i
$649$	−2.44024	+	1.01078i	−0.0957879	+	0.0396766i
$650$			24.7428i			0.970494i
$651$	25.4568	+	61.4582i	0.997731	+	2.40874i
$652$	9.23467	+	3.82513i	0.361658	+	0.149804i
$653$	7.08207	−	17.0976i	0.277143	−	0.669082i	−0.722611	−	0.691254i	$-0.757058\pi$
$653$	7.08207	−	17.0976i	0.277143	−	0.669082i	0.999754	+	0.0221728i	$0.00705839\pi$
$654$	−11.9253	+	11.9253i	−0.466317	+	0.466317i
$655$	23.9347	−	23.9347i	0.935206	−	0.935206i
$656$	0.237751	−	0.573981i	0.00928261	−	0.0224102i
$657$	−62.0275	−	25.6927i	−2.41993	−	1.00237i
$658$	3.57052	+	8.62000i	0.139193	+	0.336043i
$659$			10.7730i			0.419658i	0.977738	+	0.209829i	$0.0672908\pi$
$659$			10.7730i			0.419658i	−0.977738	+	0.209829i	$0.932709\pi$
$660$	−3.75959	+	1.55727i	−0.146342	+	0.0606168i
$661$	4.11861	+	4.11861i	0.160195	+	0.160195i	0.782653	−	0.622458i	$-0.213866\pi$
$661$	4.11861	+	4.11861i	0.160195	+	0.160195i	−0.622458	+	0.782653i	$0.713866\pi$
$662$	17.1518			0.666625
$663$	56.1336	+	42.0843i	2.18005	+	1.63442i
$664$	30.9775			1.20216
$665$	−22.2013	−	22.2013i	−0.860929	−	0.860929i
$666$	48.2841	−	19.9999i	1.87097	−	0.774981i
$667$			23.0452i			0.892312i
$668$	−7.08221	−	17.0980i	−0.274019	−	0.661540i
$669$	82.5678	+	34.2007i	3.19226	+	1.32228i
$670$	2.00487	−	4.84018i	0.0774549	−	0.186993i
$671$	−2.34188	+	2.34188i	−0.0904071	+	0.0904071i
$672$	29.8519	−	29.8519i	1.15156	−	1.15156i
$673$	−8.19181	+	19.7768i	−0.315771	+	0.762339i	0.683698	+	0.729765i	$0.260370\pi$
$673$	−8.19181	+	19.7768i	−0.315771	+	0.762339i	−0.999469	+	0.0325740i	$0.989630\pi$
$674$	4.84295	+	2.00602i	0.186544	+	0.0772689i
$675$	22.8848	+	55.2488i	0.880837	+	2.12653i
$676$			20.4174i			0.785285i
$677$	7.07753	−	2.93161i	0.272012	−	0.112671i	−0.242508	−	0.970149i	$-0.577970\pi$
$677$	7.07753	−	2.93161i	0.272012	−	0.112671i	0.514520	+	0.857478i	$0.327970\pi$
$678$	−5.30331	−	5.30331i	−0.203672	−	0.203672i
$679$	−22.5888			−0.866880
$680$	36.9603	−	5.28686i	1.41736	−	0.202742i
$681$	−19.8743			−0.761584
$682$	1.86036	+	1.86036i	0.0712367	+	0.0712367i
$683$	−17.9875	+	7.45067i	−0.688273	+	0.285092i	−0.699281	−	0.714847i	$-0.746496\pi$
$683$	−17.9875	+	7.45067i	−0.688273	+	0.285092i	0.0110074	+	0.999939i	$0.496496\pi$
$684$		−	33.6445i		−	1.28643i
$685$	23.7380	+	57.3086i	0.906982	+	2.18965i
$686$	−16.1264	−	6.67976i	−0.615708	−	0.255034i
$687$	−12.9313	+	31.2190i	−0.493361	+	1.19108i
$688$	−0.0530828	+	0.0530828i	−0.00202376	+	0.00202376i
$689$	−36.7932	+	36.7932i	−1.40171	+	1.40171i
$690$	−22.6068	+	54.5775i	−0.860624	+	2.07773i
$691$	21.2962	+	8.82117i	0.810145	+	0.335573i	0.749012	−	0.662557i	$-0.230529\pi$
$691$	21.2962	+	8.82117i	0.810145	+	0.335573i	0.0611332	+	0.998130i	$0.480529\pi$
$692$	0.241734	+	0.583598i	0.00918936	+	0.0221851i
$693$		−	5.44573i		−	0.206866i
$694$	8.01850	−	3.32137i	0.304378	−	0.126077i
$695$	−28.3831	−	28.3831i	−1.07663	−	1.07663i
$696$	−30.3823			−1.15164
$697$	−4.83173	−	33.7785i	−0.183015	−	1.27945i
$698$	−18.5783			−0.703199
$699$	−30.2528	−	30.2528i	−1.14427	−	1.14427i
$700$	13.9177	−	5.76490i	0.526040	−	0.217893i
$701$		−	34.0976i		−	1.28785i	−0.765089	−	0.643924i	$-0.777305\pi$
$701$		−	34.0976i		−	1.28785i	0.765089	−	0.643924i	$-0.222695\pi$
$702$	−21.4813	−	51.8605i	−0.810760	−	1.95735i
$703$	−33.2583	−	13.7760i	−1.25436	−	0.519573i
$704$	0.658269	−	1.58920i	0.0248094	−	0.0598953i
$705$	−30.8131	+	30.8131i	−1.16049	+	1.16049i
$706$	7.10303	−	7.10303i	0.267326	−	0.267326i
$707$	−7.76366	+	18.7431i	−0.291983	+	0.704908i
$708$	27.6204	+	11.4407i	1.03804	+	0.429969i
$709$	−7.25734	−	17.5208i	−0.272555	−	0.658006i	0.727036	−	0.686599i	$-0.240897\pi$
$709$	−7.25734	−	17.5208i	−0.272555	−	0.658006i	−0.999591	+	0.0285932i	$0.990897\pi$
$710$			21.3464i			0.801115i
$711$	−1.89016	+	0.782931i	−0.0708866	+	0.0293622i
$712$	−3.03595	−	3.03595i	−0.113777	−	0.113777i
$713$	−59.6398			−2.23353
$714$	−6.78401	+	26.4997i	−0.253885	+	0.991725i
$715$	5.83482			0.218210
$716$	9.52935	+	9.52935i	0.356129	+	0.356129i
$717$	62.9738	−	26.0846i	2.35180	−	0.974147i
$718$			24.2104i			0.903524i
$719$	−15.3426	−	37.0403i	−0.572183	−	1.38137i	−0.899693	−	0.436523i	$-0.856210\pi$
$719$	−15.3426	−	37.0403i	−0.572183	−	1.38137i	0.327510	−	0.944848i	$-0.393790\pi$
$720$	−1.48667	−	0.615797i	−0.0554047	−	0.0229494i
$721$	−0.367986	+	0.888397i	−0.0137045	+	0.0330856i
$722$	−1.37738	+	1.37738i	−0.0512607	+	0.0512607i
$723$	52.4381	−	52.4381i	1.95019	−	1.95019i
$724$	−6.92045	+	16.7074i	−0.257196	+	0.620927i
$725$	−16.2389	−	6.72636i	−0.603096	−	0.249811i
$726$	11.4854	+	27.7283i	0.426265	+	1.02909i
$727$		−	13.1530i		−	0.487819i	−0.969798	−	0.243910i	$-0.921570\pi$
$727$		−	13.1530i		−	0.487819i	0.969798	−	0.243910i	$-0.0784300\pi$
$728$	−34.4945	+	14.2881i	−1.27845	+	0.529552i
$729$	0.246218	+	0.246218i	0.00911918	+	0.00911918i
$730$	28.0473			1.03808
$731$	−1.02255	+	3.99429i	−0.0378205	+	0.147734i
$732$	37.4866			1.38554
$733$	27.2575	+	27.2575i	1.00678	+	1.00678i	0.999977	+	0.00680041i	$0.00216465\pi$
$733$	27.2575	+	27.2575i	1.00678	+	1.00678i	0.00680041	+	0.999977i	$0.497835\pi$
$734$	−2.13537	+	0.884500i	−0.0788180	+	0.0326475i
$735$		−	12.0006i		−	0.442649i
$736$	14.4843	+	34.9683i	0.533900	+	1.28895i
$737$	−0.578257	−	0.239522i	−0.0213004	−	0.00882290i
$738$	−18.8432	+	45.4914i	−0.693627	+	1.67456i
$739$	−7.83798	+	7.83798i	−0.288325	+	0.288325i	−0.836418	−	0.548093i	$-0.815354\pi$
$739$	−7.83798	+	7.83798i	−0.288325	+	0.288325i	0.548093	+	0.836418i	$0.315354\pi$
$740$	24.1073	−	24.1073i	0.886201	−	0.886201i
$741$	−26.6861	+	64.4261i	−0.980340	+	2.36675i
$742$	−18.7434	−	7.76378i	−0.688093	−	0.285017i
$743$	−5.25184	−	12.6791i	−0.192671	−	0.465150i	0.797791	−	0.602934i	$-0.206002\pi$
$743$	−5.25184	−	12.6791i	−0.192671	−	0.465150i	−0.990462	+	0.137784i	$0.956002\pi$
$744$		−	78.6279i		−	2.88264i
$745$	19.8165	−	8.20826i	0.726020	−	0.300727i
$746$	−14.2307	−	14.2307i	−0.521021	−	0.521021i
$747$	−73.3275			−2.68291
$748$	−0.239215	−	1.67234i	−0.00874657	−	0.0611469i
$749$	−20.1095			−0.734784
$750$	−0.832422	−	0.832422i	−0.0303957	−	0.0303957i
$751$	50.1528	−	20.7740i	1.83010	−	0.758053i	0.862274	−	0.506441i	$-0.169039\pi$
$751$	50.1528	−	20.7740i	1.83010	−	0.758053i	0.967828	−	0.251612i	$-0.0809607\pi$
$752$		−	0.329377i		−	0.0120111i
$753$	−23.5633	−	56.8869i	−0.858695	−	2.07307i
$754$	15.2429	+	6.31384i	0.555115	+	0.229936i
$755$	25.2684	−	61.0033i	0.919611	−	2.22014i
$756$	−24.1662	+	24.1662i	−0.878918	+	0.878918i
$757$	−21.8212	+	21.8212i	−0.793104	+	0.793104i	−0.981998	−	0.188894i	$-0.939510\pi$
$757$	−21.8212	+	21.8212i	−0.793104	+	0.793104i	0.188894	+	0.981998i	$0.439510\pi$
$758$	−4.92675	+	11.8942i	−0.178948	+	0.432018i
$759$	6.52038	+	2.70083i	0.236675	+	0.0980339i
$760$	14.2019	+	34.2863i	0.515156	+	1.24370i
$761$		−	21.0626i		−	0.763517i	−0.924262	−	0.381759i	$-0.875319\pi$
$761$		−	21.0626i		−	0.763517i	0.924262	−	0.381759i	$-0.124681\pi$
$762$	24.4310	−	10.1196i	0.885040	−	0.366596i
$763$	−10.4106	−	10.4106i	−0.376888	−	0.376888i
$764$	−19.7519			−0.714597
$765$	−87.4894	+	12.5147i	−3.16319	+	0.452468i
$766$	−10.5600			−0.381550
$767$	−30.3111	−	30.3111i	−1.09447	−	1.09447i
$768$	−46.6291	+	19.3144i	−1.68258	+	0.696949i
$769$		−	14.1304i		−	0.509556i	−0.967000	−	0.254778i	$-0.917998\pi$
$769$		−	14.1304i		−	0.509556i	0.967000	−	0.254778i	$-0.0820023\pi$
$770$	0.870599	+	2.10181i	0.0313742	+	0.0757441i
$771$	52.2949	+	21.6613i	1.88336	+	0.780112i
$772$	7.33068	−	17.6978i	0.263837	−	0.636959i
$773$	4.80239	−	4.80239i	0.172730	−	0.172730i	−0.615448	−	0.788178i	$-0.711025\pi$
$773$	4.80239	−	4.80239i	0.172730	−	0.172730i	0.788178	+	0.615448i	$0.211025\pi$
$774$	4.20713	−	4.20713i	0.151222	−	0.151222i
$775$	17.4075	−	42.0254i	0.625296	−	1.50960i
$776$	24.6673	+	10.2175i	0.885505	+	0.366788i
$777$	25.2385	+	60.9311i	0.905426	+	2.18589i
$778$			8.88531i			0.318554i
$779$	31.3347	−	12.9793i	1.12268	−	0.465031i
$780$	−46.6992	−	46.6992i	−1.67210	−	1.67210i
$781$	2.55025			0.0912552
$782$	−19.6221	−	14.7110i	−0.701685	−	0.526065i
$783$	39.8760			1.42505
$784$	0.0641403	+	0.0641403i	0.00229072	+	0.00229072i
$785$	3.83210	−	1.58731i	0.136773	−	0.0566534i
$786$		−	29.3121i		−	1.04553i
$787$	17.2753	+	41.7063i	0.615798	+	1.48667i	0.856541	+	0.516079i	$0.172609\pi$
$787$	17.2753	+	41.7063i	0.615798	+	1.48667i	−0.240743	+	0.970589i	$0.577391\pi$
$788$	−16.5159	−	6.84111i	−0.588354	−	0.243704i
$789$	−18.3501	+	44.3010i	−0.653280	+	1.57716i
$790$	0.604354	−	0.604354i	0.0215019	−	0.0215019i
$791$	4.62969	−	4.62969i	0.164613	−	0.164613i
$792$	−2.46325	+	5.94681i	−0.0875277	+	0.211311i
$793$	−49.6585	−	20.5692i	−1.76342	−	0.730434i
$794$	8.72094	+	21.0542i	0.309495	+	0.747186i
$795$		−	94.7528i		−	3.36054i
$796$	7.44888	−	3.08543i	0.264018	−	0.109360i
$797$	16.3821	+	16.3821i	0.580283	+	0.580283i	0.934981	−	0.354698i	$-0.115416\pi$
$797$	16.3821	+	16.3821i	0.580283	+	0.580283i	−0.354698	+	0.934981i	$0.615416\pi$
$798$	−27.1893			−0.962489
$799$	−9.21977	−	15.5647i	−0.326172	−	0.550639i
$800$	−28.8682			−1.02064
$801$	7.18646	+	7.18646i	0.253921	+	0.253921i
$802$	−11.4436	+	4.74009i	−0.404087	+	0.167378i
$803$		−	3.35082i		−	0.118248i
$804$	2.71108	+	6.54512i	0.0956123	+	0.230829i
$805$	−47.6452	−	19.7353i	−1.67927	−	0.695577i
$806$	−16.3399	+	39.4481i	−0.575549	+	1.38950i
$807$	−41.0072	+	41.0072i	−1.44352	+	1.44352i
$808$	16.9560	−	16.9560i	0.596511	−	0.596511i
$809$	−6.97793	+	16.8462i	−0.245331	+	0.592281i	−0.997796	−	0.0663505i	$-0.978864\pi$
$809$	−6.97793	+	16.8462i	−0.245331	+	0.592281i	0.752465	+	0.658632i	$0.228864\pi$
$810$	41.9413	+	17.3727i	1.47367	+	0.610414i
$811$	13.9622	+	33.7077i	0.490278	+	1.18364i	0.954579	+	0.297959i	$0.0963059\pi$
$811$	13.9622	+	33.7077i	0.490278	+	1.18364i	−0.464300	+	0.885678i	$0.653694\pi$
$812$		−	10.0452i		−	0.352516i
$813$	−24.8139	+	10.2783i	−0.870263	+	0.360475i
$814$	1.84440	+	1.84440i	0.0646462	+	0.0646462i
$815$	26.0987			0.914196
$816$	0.579258	−	0.772636i	0.0202781	−	0.0270477i
$817$	−4.09824			−0.143379
$818$	7.80365	+	7.80365i	0.272848	+	0.272848i
$819$	81.6527	−	33.8217i	2.85318	−	1.18182i
$820$			32.1210i			1.12171i
$821$	4.01459	+	9.69209i	0.140110	+	0.338256i	0.978322	−	0.207088i	$-0.0663988\pi$
$821$	4.01459	+	9.69209i	0.140110	+	0.338256i	−0.838212	+	0.545345i	$0.816399\pi$
$822$	49.6277	+	20.5564i	1.73096	+	0.716988i
$823$	−9.03353	+	21.8089i	−0.314889	+	0.760210i	0.684621	+	0.728900i	$0.259968\pi$
$823$	−9.03353	+	21.8089i	−0.314889	+	0.760210i	−0.999510	+	0.0313101i	$0.990032\pi$
$824$	0.803691	−	0.803691i	0.0279979	−	0.0279979i
$825$	−3.80630	+	3.80630i	−0.132518	+	0.132518i
$826$	6.39598	−	15.4413i	0.222545	−	0.537271i
$827$	2.63746	+	1.09247i	0.0917136	+	0.0379890i	0.428069	−	0.903746i	$-0.359194\pi$
$827$	2.63746	+	1.09247i	0.0917136	+	0.0379890i	−0.336355	+	0.941735i	$0.609194\pi$
$828$	−21.1478	−	51.0552i	−0.734935	−	1.77429i
$829$		−	7.66903i		−	0.266356i	−0.991092	−	0.133178i	$-0.957482\pi$
$829$		−	7.66903i		−	0.266356i	0.991092	−	0.133178i	$-0.0425182\pi$
$830$	28.3012	−	11.7227i	0.982349	−	0.406902i
$831$	14.5664	+	14.5664i	0.505304	+	0.505304i
$832$	27.9166			0.967834
$833$	4.82633	+	1.23556i	0.167222	+	0.0428095i
$834$	−34.7600			−1.20364
$835$	−34.1685	−	34.1685i	−1.18245	−	1.18245i
$836$	1.55135	−	0.642592i	0.0536547	−	0.0222245i
$837$			103.197i			3.56702i
$838$	−1.50150	−	3.62495i	−0.0518686	−	0.125222i
$839$	−43.5084	−	18.0218i	−1.50208	−	0.622180i	−0.528172	−	0.849138i	$-0.677122\pi$
$839$	−43.5084	−	18.0218i	−1.50208	−	0.622180i	−0.973905	+	0.226957i	$0.927122\pi$
$840$	26.0186	−	62.8145i	0.897727	−	2.16730i
$841$	12.2185	−	12.2185i	0.421327	−	0.421327i
$842$	4.48411	−	4.48411i	0.154533	−	0.154533i
$843$	−17.2529	+	41.6521i	−0.594221	+	1.43458i
$844$	−4.06756	−	1.68484i	−0.140011	−	0.0579946i
$845$	20.4010	+	49.2525i	0.701817	+	1.69434i
$846$			26.1051i			0.897511i
$847$	−24.2063	+	10.0266i	−0.831739	+	0.344518i
$848$	0.506430	+	0.506430i	0.0173909	+	0.0173909i
$849$	−25.0551			−0.859890
$850$	16.0934	−	9.53298i	0.552000	−	0.326979i
$851$	−59.1283			−2.02689
$852$	−20.4110	−	20.4110i	−0.699270	−	0.699270i
$853$	−17.6180	+	7.29762i	−0.603229	+	0.249866i	−0.663330	−	0.748327i	$-0.730858\pi$
$853$	−17.6180	+	7.29762i	−0.603229	+	0.249866i	0.0601015	+	0.998192i	$0.480858\pi$
$854$		−	20.9570i		−	0.717133i
$855$	−33.6175	−	81.1599i	−1.14970	−	2.77561i
$856$	21.9598	+	9.09605i	0.750571	+	0.310897i
$857$	5.22687	−	12.6188i	0.178547	−	0.431049i	−0.809116	−	0.587650i	$-0.800053\pi$
$857$	5.22687	−	12.6188i	0.178547	−	0.431049i	0.987662	+	0.156600i	$0.0500534\pi$
$858$	3.57287	−	3.57287i	0.121976	−	0.121976i
$859$	11.3842	−	11.3842i	0.388424	−	0.388424i	−0.485701	−	0.874125i	$-0.661436\pi$
$859$	11.3842	−	11.3842i	0.388424	−	0.388424i	0.874125	+	0.485701i	$0.161436\pi$
$860$	1.48530	−	3.58584i	0.0506484	−	0.122276i
$861$	−57.4070	−	23.7787i	−1.95642	−	0.810377i
$862$	4.25951	+	10.2834i	0.145079	+	0.350253i
$863$		−	49.6163i		−	1.68896i	−0.535587	−	0.844480i	$-0.679910\pi$
$863$		−	49.6163i		−	1.68896i	0.535587	−	0.844480i	$-0.320090\pi$
$864$	60.5072	−	25.0629i	2.05850	−	0.852657i
$865$	1.16626	+	1.16626i	0.0396541	+	0.0396541i
$866$	−19.7527			−0.671225
$867$	5.74553	−	52.7252i	0.195128	−	1.79064i
$868$	25.9964			0.882375
$869$	−0.0722022	−	0.0722022i	−0.00244929	−	0.00244929i
$870$	−27.7574	+	11.4975i	−0.941064	+	0.389801i
$871$		−	10.1579i		−	0.344188i
$872$	6.65951	+	16.0775i	0.225519	+	0.544452i
$873$	−58.3905	−	24.1862i	−1.97622	−	0.818577i
$874$	9.32844	−	22.5208i	0.315539	−	0.761779i
$875$	0.726689	−	0.726689i	0.0245666	−	0.0245666i
$876$	−26.8184	+	26.8184i	−0.906109	+	0.906109i
$877$	−6.09712	+	14.7198i	−0.205885	+	0.497051i	−0.992768	−	0.120052i	$-0.961694\pi$
$877$	−6.09712	+	14.7198i	−0.205885	+	0.497051i	0.786882	+	0.617103i	$0.211694\pi$
$878$	24.7277	+	10.2426i	0.834520	+	0.345670i
$879$	30.6639	+	74.0291i	1.03427	+	2.49694i
$880$		−	0.0803118i		−	0.00270731i
$881$	48.7359	−	20.1871i	1.64195	−	0.680119i	0.645460	−	0.763794i	$-0.276666\pi$
$881$	48.7359	−	20.1871i	1.64195	−	0.680119i	0.996493	+	0.0836748i	$0.0266657\pi$
$882$	−5.08350	−	5.08350i	−0.171170	−	0.171170i
$883$	−0.453187			−0.0152510			−0.00762548	−	0.999971i	$-0.502427\pi$
$883$	−0.453187			−0.0152510			−0.00762548	+	0.999971i	$0.502427\pi$
$884$	23.5892	−	13.9731i	0.793392	−	0.469967i
$885$	78.0596			2.62395
$886$	−15.8394	−	15.8394i	−0.532137	−	0.532137i
$887$	−4.27590	+	1.77113i	−0.143571	+	0.0594689i	−0.453312	−	0.891352i	$-0.649758\pi$
$887$	−4.27590	+	1.77113i	−0.143571	+	0.0594689i	0.309741	+	0.950821i	$0.399758\pi$
$888$		−	77.9536i		−	2.61595i
$889$	8.83426	+	21.3278i	0.296292	+	0.715311i
$890$	−3.92255	−	1.62477i	−0.131484	−	0.0544625i
$891$	2.07551	−	5.01074i	0.0695324	−	0.167866i
$892$	24.6961	−	24.6961i	0.826888	−	0.826888i
$893$	12.7147	−	12.7147i	0.425481	−	0.425481i
$894$	7.10812	−	17.1605i	0.237731	−	0.573934i
$895$	32.5092	+	13.4657i	1.08666	+	0.450110i
$896$	−6.19140	−	14.9474i	−0.206840	−	0.499356i
$897$			114.540i			3.82438i
$898$	−3.85073	+	1.59502i	−0.128500	+	0.0532266i
$899$	−21.4480	−	21.4480i	−0.715330	−	0.715330i
$900$	42.1488			1.40496
$901$	38.1071	+	9.75555i	1.26953	+	0.325005i
$902$	−2.45751			−0.0818262
$903$	5.30910	+	5.30910i	0.176676	+	0.176676i
$904$	−7.14982	+	2.96155i	−0.237799	+	0.0984998i
$905$			47.2179i			1.56958i
$906$	−21.8817	−	52.8272i	−0.726972	−	1.75507i
$907$	7.46823	+	3.09344i	0.247978	+	0.102716i	0.503211	−	0.864164i	$-0.332152\pi$
$907$	7.46823	+	3.09344i	0.247978	+	0.102716i	−0.255232	+	0.966880i	$0.582152\pi$
$908$	−2.97221	+	7.17555i	−0.0986363	+	0.238129i
$909$	−40.1370	+	40.1370i	−1.33126	+	1.33126i
$910$	−26.1073	+	26.1073i	−0.865450	+	0.865450i
$911$	−3.75144	+	9.05677i	−0.124291	+	0.300064i	−0.973761	−	0.227572i	$-0.926921\pi$
$911$	−3.75144	+	9.05677i	−0.124291	+	0.300064i	0.849471	+	0.527636i	$0.176921\pi$
$912$	0.886775	+	0.367314i	0.0293641	+	0.0121630i
$913$	−1.40052	−	3.38115i	−0.0463504	−	0.111900i
$914$		−	22.4392i		−	0.742222i
$915$	90.4280	−	37.4565i	2.98946	−	1.23827i
$916$	9.33764	+	9.33764i	0.308524	+	0.308524i
$917$	25.5889			0.845021
$918$	−25.4551	+	33.9530i	−0.840145	+	1.12062i
$919$	41.4778			1.36823			0.684114	−	0.729375i	$-0.260189\pi$
$919$	41.4778			1.36823			0.684114	+	0.729375i	$0.260189\pi$
$920$	43.1024	+	43.1024i	1.42104	+	1.42104i
$921$	−79.8098	+	33.0583i	−2.62982	+	1.08931i
$922$			31.4236i			1.03488i
$923$	15.8388	+	38.2382i	0.521340	+	1.25863i
$924$	−2.84217	−	1.17726i	−0.0935005	−	0.0387292i
$925$	17.2582	−	41.6650i	0.567446	−	1.36994i
$926$	12.3183	−	12.3183i	0.404805	−	0.404805i
$927$	−1.90243	+	1.90243i	−0.0624841	+	0.0624841i
$928$	−7.36654	+	17.7844i	−0.241819	+	0.583802i
$929$	54.4376	+	22.5488i	1.78604	+	0.739802i	0.991101	+	0.133115i	$0.0424980\pi$
$929$	54.4376	+	22.5488i	1.78604	+	0.739802i	0.794940	+	0.606687i	$0.207502\pi$
$930$	−29.7550	−	71.8349i	−0.975704	−	2.35556i
$931$			4.95193i			0.162293i
$932$	−15.4470	+	6.39836i	−0.505984	+	0.209585i
$933$	−3.26445	−	3.26445i	−0.106873	−	0.106873i
$934$	−7.59707			−0.248584
$935$	−2.24805	−	3.79513i	−0.0735193	−	0.124114i
$936$	−104.464			−3.41452
$937$	24.1077	+	24.1077i	0.787564	+	0.787564i	0.981094	−	0.193530i	$-0.0619938\pi$
$937$	24.1077	+	24.1077i	0.787564	+	0.787564i	−0.193530	+	0.981094i	$0.561994\pi$
$938$	3.65907	−	1.51564i	0.119473	−	0.0494873i
$939$			75.6320i			2.46816i
$940$	6.51687	+	15.7331i	0.212557	+	0.513157i
$941$	26.0015	+	10.7702i	0.847626	+	0.351098i	0.763856	−	0.645387i	$-0.223304\pi$
$941$	26.0015	+	10.7702i	0.847626	+	0.351098i	0.0837702	+	0.996485i	$0.473304\pi$
$942$	1.37456	−	3.31849i	0.0447857	−	0.108122i
$943$	39.3918	−	39.3918i	1.28277	−	1.28277i
$944$	−0.417209	+	0.417209i	−0.0135790	+	0.0135790i
$945$	−34.1488	+	82.4426i	−1.11086	+	2.68186i
$946$	0.274345	+	0.113638i	0.00891974	+	0.00369468i
$947$	18.9200	+	45.6768i	0.614816	+	1.48430i	0.857652	+	0.514230i	$0.171922\pi$
$947$	18.9200	+	45.6768i	0.614816	+	1.48430i	−0.242836	+	0.970067i	$0.578078\pi$
$948$			1.15574i			0.0375368i
$949$	50.2418	−	20.8108i	1.63092	−	0.675549i
$950$	13.1466	+	13.1466i	0.426533	+	0.426533i
$951$	32.2462			1.04565
$952$	22.5835	+	16.9312i	0.731936	+	0.548745i
$953$	40.8578			1.32351			0.661757	−	0.749718i	$-0.269811\pi$
$953$	40.8578			1.32351			0.661757	+	0.749718i	$0.269811\pi$
$954$	−40.1376	−	40.1376i	−1.29950	−	1.29950i
$955$	−47.6470	+	19.7360i	−1.54182	+	0.638643i
$956$		−	26.6375i		−	0.861518i
$957$	1.37361	+	3.31618i	0.0444024	+	0.107197i
$958$	1.87874	+	0.778199i	0.0606993	+	0.0251425i
$959$	−17.9454	+	43.3240i	−0.579487	+	1.39901i
$960$	−35.9466	+	35.9466i	−1.16017	+	1.16017i
$961$	33.5860	−	33.5860i	1.08342	−	1.08342i
$962$	−16.1998	+	39.1097i	−0.522302	+	1.26095i
$963$	−51.9815	−	21.5315i	−1.67508	−	0.693842i
$964$	−11.0905	−	26.7748i	−0.357200	−	0.862357i
$965$		−	50.0169i		−	1.61010i
$966$	−41.2594	+	17.0902i	−1.32750	+	0.549869i
$967$	26.1838	+	26.1838i	0.842013	+	0.842013i	0.989120	−	0.147108i	$-0.0469964\pi$
$967$	26.1838	+	26.1838i	0.842013	+	0.842013i	−0.147108	+	0.989120i	$0.546996\pi$
$968$	30.9689			0.995379
$969$	52.1862	−	7.46482i	1.67646	−	0.239804i
$970$	26.4028			0.847742
$971$	−19.1226	−	19.1226i	−0.613675	−	0.613675i	0.330227	−	0.943902i	$-0.392875\pi$
$971$	−19.1226	−	19.1226i	−0.613675	−	0.613675i	−0.943902	+	0.330227i	$0.892875\pi$
$972$	−17.3548	+	7.18859i	−0.556655	+	0.230574i
$973$		−	30.3448i		−	0.972810i
$974$	14.0279	+	33.8664i	0.449483	+	1.08515i
$975$	−80.7110	−	33.4316i	−2.58482	−	1.07067i
$976$	−0.283119	+	0.683510i	−0.00906243	+	0.0218786i
$977$	−43.4258	+	43.4258i	−1.38931	+	1.38931i	−0.562554	+	0.826761i	$0.690181\pi$
$977$	−43.4258	+	43.4258i	−1.38931	+	1.38931i	−0.826761	+	0.562554i	$0.809819\pi$
$978$	15.9811	−	15.9811i	0.511020	−	0.511020i
$979$	−0.194112	+	0.468627i	−0.00620383	+	0.0149774i
$980$	−4.33279	−	1.79470i	−0.138406	−	0.0573296i
$981$	−15.7639	−	38.0573i	−0.503301	−	1.21508i
$982$		−	9.50041i		−	0.303170i
$983$	−12.6539	+	5.24142i	−0.403597	+	0.167175i	−0.575241	−	0.817984i	$-0.695092\pi$
$983$	−12.6539	+	5.24142i	−0.403597	+	0.167175i	0.171645	+	0.985159i	$0.445092\pi$
$984$	51.9334	+	51.9334i	1.65558	+	1.65558i
$985$	−46.6765			−1.48724
$986$	−1.76615	−	12.3471i	−0.0562455	−	0.393210i
$987$	−32.9427			−1.04858
$988$	19.2699	+	19.2699i	0.613058	+	0.613058i
$989$	−6.21903	+	2.57601i	−0.197754	+	0.0819123i
$990$			6.36519i			0.202299i
$991$	2.59660	+	6.26874i	0.0824836	+	0.199133i	0.959741	−	0.280888i	$-0.0906290\pi$
$991$	2.59660	+	6.26874i	0.0824836	+	0.199133i	−0.877257	+	0.480021i	$0.840629\pi$
$992$	−46.0252	−	19.0643i	−1.46130	−	0.605291i
$993$	−23.1749	+	55.9492i	−0.735434	+	1.77550i
$994$	−11.4109	+	11.4109i	−0.361930	+	0.361930i
$995$	14.8858	−	14.8858i	0.471912	−	0.471912i
$996$	−15.8520	+	38.2702i	−0.502291	+	1.21264i
$997$	35.9963	+	14.9102i	1.14002	+	0.472210i	0.871174	−	0.490975i	$-0.163359\pi$
$997$	35.9963	+	14.9102i	1.14002	+	0.472210i	0.268841	+	0.963184i	$0.413359\pi$
$998$	−7.45197	−	17.9906i	−0.235888	−	0.569484i
$999$			102.312i			3.23702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.c.87.11	✓	128
17.9	even	8	inner	731.2.m.c.689.11	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.c.87.11	✓	128	1.1	even	1	trivial
731.2.m.c.689.11	yes	128	17.9	even	8	inner

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.624813 - 0.624813i) q^{2} +(2.88236 - 1.19391i) q^{3} -1.21922i q^{4} +(-1.21824 - 2.94109i) q^{5} +(-2.54691 - 1.05496i) q^{6} +(0.920964 - 2.22340i) q^{7} +(-2.01141 + 2.01141i) q^{8} +(4.76125 - 4.76125i) q^{9} +O(q^{10})\)	\(q+(-0.624813 - 0.624813i) q^{2} +(2.88236 - 1.19391i) q^{3} -1.21922i q^{4} +(-1.21824 - 2.94109i) q^{5} +(-2.54691 - 1.05496i) q^{6} +(0.920964 - 2.22340i) q^{7} +(-2.01141 + 2.01141i) q^{8} +(4.76125 - 4.76125i) q^{9} +(-1.07646 + 2.59880i) q^{10} +(0.310479 + 0.128605i) q^{11} +(-1.45564 - 3.51423i) q^{12} +5.45402i q^{13} +(-1.96464 + 0.813780i) q^{14} +(-7.02282 - 7.02282i) q^{15} +0.0750704 q^{16} +(3.54745 - 2.10134i) q^{17} -5.94978 q^{18} +(2.89789 + 2.89789i) q^{19} +(-3.58584 + 1.48530i) q^{20} -7.50820i q^{21} +(-0.113638 - 0.274345i) q^{22} +(6.21903 + 2.57601i) q^{23} +(-3.39616 + 8.19905i) q^{24} +(-3.63039 + 3.63039i) q^{25} +(3.40774 - 3.40774i) q^{26} +(4.45738 - 10.7611i) q^{27} +(-2.71081 - 1.12286i) q^{28} +(1.31012 + 3.16292i) q^{29} +8.77589i q^{30} +(-8.18548 + 3.39054i) q^{31} +(3.97591 + 3.97591i) q^{32} +1.04846 q^{33} +(-3.52943 - 0.903547i) q^{34} -7.66119 q^{35} +(-5.80500 - 5.80500i) q^{36} +(-8.11528 + 3.36146i) q^{37} -3.62128i q^{38} +(6.51162 + 15.7204i) q^{39} +(8.36612 + 3.46536i) q^{40} +(3.16704 - 7.64591i) q^{41} +(-4.69122 + 4.69122i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(0.156797 - 0.378542i) q^{44} +(-19.8036 - 8.20293i) q^{45} +(-2.27621 - 5.49525i) q^{46} -4.38757i q^{47} +(0.216380 - 0.0896274i) q^{48} +(0.854402 + 0.854402i) q^{49} +4.53662 q^{50} +(7.71620 - 10.2922i) q^{51} +6.64964 q^{52} +(6.74607 + 6.74607i) q^{53} +(-9.50868 + 3.93862i) q^{54} -1.06982i q^{55} +(2.61974 + 6.32460i) q^{56} +(11.8126 + 4.89293i) q^{57} +(1.15765 - 2.79481i) q^{58} +(-5.55757 + 5.55757i) q^{59} +(-8.56235 + 8.56235i) q^{60} +(-3.77139 + 9.10493i) q^{61} +(7.23284 + 2.99594i) q^{62} +(-6.20124 - 14.9711i) q^{63} -5.11854i q^{64} +(16.0408 - 6.64431i) q^{65} +(-0.655089 - 0.655089i) q^{66} -1.86246 q^{67} +(-2.56199 - 4.32511i) q^{68} +21.0010 q^{69} +(4.78681 + 4.78681i) q^{70} +(7.01102 - 2.90406i) q^{71} +19.1536i q^{72} +(-3.81569 - 9.21189i) q^{73} +(7.17081 + 2.97025i) q^{74} +(-6.12972 + 14.7984i) q^{75} +(3.53316 - 3.53316i) q^{76} +(0.571880 - 0.571880i) q^{77} +(5.75379 - 13.8909i) q^{78} +(-0.280713 - 0.116275i) q^{79} +(-0.0914538 - 0.220789i) q^{80} -16.1387i q^{81} +(-6.75606 + 2.79845i) q^{82} +(-7.70045 - 7.70045i) q^{83} -9.15413 q^{84} +(-10.5019 - 7.87344i) q^{85} +0.883619 q^{86} +(7.55249 + 7.55249i) q^{87} +(-0.883178 + 0.365824i) q^{88} +1.50936i q^{89} +(7.24826 + 17.4988i) q^{90} +(12.1265 + 5.02295i) q^{91} +(3.14072 - 7.58236i) q^{92} +(-19.5455 + 19.5455i) q^{93} +(-2.74141 + 2.74141i) q^{94} +(4.99264 - 12.0533i) q^{95} +(16.2069 + 6.71312i) q^{96} +(-3.59196 - 8.67175i) q^{97} -1.06768i q^{98} +(2.09059 - 0.865950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

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