LMFDB - Embedded newform 387.2.f.c.130.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(130,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, 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("387.130");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.f (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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			130.14
Character	$\chi$	$=$	387.130
Dual form			387.2.f.c.259.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.649321 + 1.12466i) q^{2} +(-1.24030 + 1.20899i) q^{3} +(0.156764 - 0.271524i) q^{4} +(1.38166 - 2.39311i) q^{5} +(-2.16505 - 0.609884i) q^{6} +(-0.516159 - 0.894013i) q^{7} +3.00445 q^{8} +(0.0766735 - 2.99902i) q^{9} +O(q^{10})$	\(q+(0.649321 + 1.12466i) q^{2} +(-1.24030 + 1.20899i) q^{3} +(0.156764 - 0.271524i) q^{4} +(1.38166 - 2.39311i) q^{5} +(-2.16505 - 0.609884i) q^{6} +(-0.516159 - 0.894013i) q^{7} +3.00445 q^{8} +(0.0766735 - 2.99902i) q^{9} +3.58856 q^{10} +(-1.47222 - 2.54996i) q^{11} +(0.133836 + 0.526297i) q^{12} +(1.68562 - 2.91958i) q^{13} +(0.670305 - 1.16100i) q^{14} +(1.17958 + 4.63858i) q^{15} +(1.63732 + 2.83592i) q^{16} +1.55106 q^{17} +(3.42265 - 1.86110i) q^{18} +0.820840 q^{19} +(-0.433190 - 0.750307i) q^{20} +(1.72105 + 0.484810i) q^{21} +(1.91188 - 3.31148i) q^{22} +(-4.29584 + 7.44062i) q^{23} +(-3.72641 + 3.63235i) q^{24} +(-1.31797 - 2.28279i) q^{25} +4.37804 q^{26} +(3.53070 + 3.81237i) q^{27} -0.323661 q^{28} +(0.623396 + 1.07975i) q^{29} +(-4.45089 + 4.33855i) q^{30} +(0.962734 - 1.66750i) q^{31} +(0.878152 - 1.52100i) q^{32} +(4.90886 + 1.38280i) q^{33} +(1.00714 + 1.74442i) q^{34} -2.85262 q^{35} +(-0.802286 - 0.490958i) q^{36} -4.44739 q^{37} +(0.532989 + 0.923164i) q^{38} +(1.43908 + 5.65905i) q^{39} +(4.15112 - 7.18996i) q^{40} +(-3.13620 + 5.43205i) q^{41} +(0.572266 + 2.25038i) q^{42} +(-0.500000 - 0.866025i) q^{43} -0.923165 q^{44} +(-7.07104 - 4.32711i) q^{45} -11.1575 q^{46} +(5.05055 + 8.74780i) q^{47} +(-5.45938 - 1.53788i) q^{48} +(2.96716 - 5.13927i) q^{49} +(1.71157 - 2.96453i) q^{50} +(-1.92378 + 1.87523i) q^{51} +(-0.528491 - 0.915373i) q^{52} +8.79973 q^{53} +(-1.99506 + 6.44628i) q^{54} -8.13642 q^{55} +(-1.55077 - 2.68601i) q^{56} +(-1.01809 + 0.992390i) q^{57} +(-0.809568 + 1.40221i) q^{58} +(-3.31596 + 5.74341i) q^{59} +(1.44440 + 0.406880i) q^{60} +(0.0348705 + 0.0603975i) q^{61} +2.50049 q^{62} +(-2.72074 + 1.47942i) q^{63} +8.83009 q^{64} +(-4.65791 - 8.06774i) q^{65} +(1.63225 + 6.41867i) q^{66} +(5.76481 - 9.98494i) q^{67} +(0.243152 - 0.421151i) q^{68} +(-3.66753 - 14.4222i) q^{69} +(-1.85227 - 3.20822i) q^{70} -5.88849 q^{71} +(0.230361 - 9.01039i) q^{72} +1.89767 q^{73} +(-2.88779 - 5.00179i) q^{74} +(4.39455 + 1.23792i) q^{75} +(0.128678 - 0.222878i) q^{76} +(-1.51980 + 2.63236i) q^{77} +(-5.43007 + 5.29302i) q^{78} +(-3.49563 - 6.05462i) q^{79} +9.04889 q^{80} +(-8.98824 - 0.459891i) q^{81} -8.14560 q^{82} +(-1.50913 - 2.61390i) q^{83} +(0.401436 - 0.391304i) q^{84} +(2.14304 - 3.71186i) q^{85} +(0.649321 - 1.12466i) q^{86} +(-2.07861 - 0.585534i) q^{87} +(-4.42320 - 7.66120i) q^{88} -15.2655 q^{89} +(0.275148 - 10.7622i) q^{90} -3.48019 q^{91} +(1.34687 + 2.33285i) q^{92} +(0.821924 + 3.23214i) q^{93} +(-6.55885 + 11.3603i) q^{94} +(1.13412 - 1.96436i) q^{95} +(0.749713 + 2.94817i) q^{96} +(1.93718 + 3.35530i) q^{97} +7.70656 q^{98} +(-7.76025 + 4.21970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 4 q^{2} - 7 q^{3} - 22 q^{4} - 9 q^{5} - 7 q^{7} + 24 q^{8} - 3 q^{9}+O(q^{10}) $ 38 * q - 4 * q^2 - 7 * q^3 - 22 * q^4 - 9 * q^5 - 7 * q^7 + 24 * q^8 - 3 * q^9	\( 38 q - 4 q^{2} - 7 q^{3} - 22 q^{4} - 9 q^{5} - 7 q^{7} + 24 q^{8} - 3 q^{9} - 14 q^{10} - 5 q^{11} + 11 q^{12} + 5 q^{13} - 17 q^{14} - 5 q^{15} - 24 q^{16} + 42 q^{17} - 23 q^{18} - 8 q^{19} - 21 q^{20} + 20 q^{22} - 22 q^{23} - 14 q^{24} - 10 q^{25} + 34 q^{26} - 4 q^{27} - 2 q^{28} - 30 q^{29} + 63 q^{30} + 5 q^{31} - 48 q^{32} - q^{33} + 6 q^{34} + 106 q^{35} - 20 q^{36} - 2 q^{37} - 21 q^{38} + 25 q^{39} - 16 q^{40} - 29 q^{41} - 47 q^{42} - 19 q^{43} + 58 q^{44} - 37 q^{45} - 32 q^{47} + 45 q^{48} + 10 q^{49} + 11 q^{50} - 53 q^{51} - q^{52} + 76 q^{53} - 41 q^{54} + 4 q^{55} - 46 q^{56} + 23 q^{57} - 30 q^{58} - 30 q^{59} - 87 q^{60} + 10 q^{61} + 50 q^{62} + 21 q^{63} + 28 q^{64} - 8 q^{65} + 91 q^{66} - 3 q^{67} - 47 q^{68} - 40 q^{69} - 56 q^{70} + 42 q^{71} + 3 q^{72} + 16 q^{73} - 28 q^{74} + 19 q^{75} + 36 q^{76} - 49 q^{77} - 105 q^{78} - 4 q^{79} + 140 q^{80} + 77 q^{81} - 8 q^{82} - 29 q^{83} + 145 q^{84} + 4 q^{85} - 4 q^{86} - 24 q^{87} + 47 q^{88} + 108 q^{89} - 8 q^{90} + 8 q^{91} - 12 q^{92} - 4 q^{93} + 23 q^{94} - 33 q^{95} - 147 q^{96} + 4 q^{97} + 98 q^{98} + 85 q^{99}+O(q^{100}) \) 38 * q - 4 * q^2 - 7 * q^3 - 22 * q^4 - 9 * q^5 - 7 * q^7 + 24 * q^8 - 3 * q^9 - 14 * q^10 - 5 * q^11 + 11 * q^12 + 5 * q^13 - 17 * q^14 - 5 * q^15 - 24 * q^16 + 42 * q^17 - 23 * q^18 - 8 * q^19 - 21 * q^20 + 20 * q^22 - 22 * q^23 - 14 * q^24 - 10 * q^25 + 34 * q^26 - 4 * q^27 - 2 * q^28 - 30 * q^29 + 63 * q^30 + 5 * q^31 - 48 * q^32 - q^33 + 6 * q^34 + 106 * q^35 - 20 * q^36 - 2 * q^37 - 21 * q^38 + 25 * q^39 - 16 * q^40 - 29 * q^41 - 47 * q^42 - 19 * q^43 + 58 * q^44 - 37 * q^45 - 32 * q^47 + 45 * q^48 + 10 * q^49 + 11 * q^50 - 53 * q^51 - q^52 + 76 * q^53 - 41 * q^54 + 4 * q^55 - 46 * q^56 + 23 * q^57 - 30 * q^58 - 30 * q^59 - 87 * q^60 + 10 * q^61 + 50 * q^62 + 21 * q^63 + 28 * q^64 - 8 * q^65 + 91 * q^66 - 3 * q^67 - 47 * q^68 - 40 * q^69 - 56 * q^70 + 42 * q^71 + 3 * q^72 + 16 * q^73 - 28 * q^74 + 19 * q^75 + 36 * q^76 - 49 * q^77 - 105 * q^78 - 4 * q^79 + 140 * q^80 + 77 * q^81 - 8 * q^82 - 29 * q^83 + 145 * q^84 + 4 * q^85 - 4 * q^86 - 24 * q^87 + 47 * q^88 + 108 * q^89 - 8 * q^90 + 8 * q^91 - 12 * q^92 - 4 * q^93 + 23 * q^94 - 33 * q^95 - 147 * q^96 + 4 * q^97 + 98 * q^98 + 85 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.649321	+	1.12466i	0.459139	+	0.795253i	0.998916	−	0.0465558i	$-0.0148245\pi$
$2$	0.649321	+	1.12466i	0.459139	+	0.795253i	−0.539776	+	0.841808i	$0.681491\pi$
$3$	−1.24030	+	1.20899i	−0.716086	+	0.698012i
$3$	−1.24030	+	1.20899i	−0.716086	+	0.698012i
$4$	0.156764	−	0.271524i	0.0783822	−	0.135762i
$5$	1.38166	−	2.39311i	0.617897	−	1.07023i	−0.371972	−	0.928244i	$-0.621318\pi$
$5$	1.38166	−	2.39311i	0.617897	−	1.07023i	0.989869	−	0.141985i	$-0.0453486\pi$
$6$	−2.16505	−	0.609884i	−0.883879	−	0.248984i
$7$	−0.516159	−	0.894013i	−0.195090	−	0.337905i	0.751840	−	0.659345i	$-0.229166\pi$
$7$	−0.516159	−	0.894013i	−0.195090	−	0.337905i	−0.946930	+	0.321440i	$0.895833\pi$
$8$	3.00445			1.06223
$9$	0.0766735	−	2.99902i	0.0255578	−	0.999673i
$10$	3.58856			1.13480
$11$	−1.47222	−	2.54996i	−0.443890	−	0.768841i	0.554084	−	0.832461i	$-0.313069\pi$
$11$	−1.47222	−	2.54996i	−0.443890	−	0.768841i	−0.997974	+	0.0636203i	$0.979735\pi$
$12$	0.133836	+	0.526297i	0.0386351	+	0.151929i
$13$	1.68562	−	2.91958i	0.467507	−	0.809747i	−0.531803	−	0.846868i	$-0.678485\pi$
$13$	1.68562	−	2.91958i	0.467507	−	0.809747i	0.999311	+	0.0371213i	$0.0118188\pi$
$14$	0.670305	−	1.16100i	0.179147	−	0.310291i
$15$	1.17958	+	4.63858i	0.304566	+	1.19768i
$16$	1.63732	+	2.83592i	0.409330	+	0.708981i
$17$	1.55106			0.376188			0.188094	−	0.982151i	$-0.439769\pi$
$17$	1.55106			0.376188			0.188094	+	0.982151i	$0.439769\pi$
$18$	3.42265	−	1.86110i	0.806727	−	0.438664i
$19$	0.820840			0.188314			0.0941568	−	0.995557i	$-0.469984\pi$
$19$	0.820840			0.188314			0.0941568	+	0.995557i	$0.469984\pi$
$20$	−0.433190	−	0.750307i	−0.0968643	−	0.167774i
$21$	1.72105	+	0.484810i	0.375563	+	0.105794i
$22$	1.91188	−	3.31148i	0.407615	−	0.706010i
$23$	−4.29584	+	7.44062i	−0.895745	+	1.55148i	−0.0628656	+	0.998022i	$0.520024\pi$
$23$	−4.29584	+	7.44062i	−0.895745	+	1.55148i	−0.832880	+	0.553454i	$0.813309\pi$
$24$	−3.72641	+	3.63235i	−0.760649	+	0.741451i
$25$	−1.31797	−	2.28279i	−0.263594	−	0.456558i
$26$	4.37804			0.858604
$27$	3.53070	+	3.81237i	0.679483	+	0.733692i
$28$	−0.323661			−0.0611662
$29$	0.623396	+	1.07975i	0.115762	+	0.200505i	0.918084	−	0.396386i	$-0.129736\pi$
$29$	0.623396	+	1.07975i	0.115762	+	0.200505i	−0.802322	+	0.596891i	$0.796402\pi$
$30$	−4.45089	+	4.33855i	−0.812617	+	0.792107i
$31$	0.962734	−	1.66750i	0.172912	−	0.299493i	−0.766525	−	0.642215i	$-0.778016\pi$
$31$	0.962734	−	1.66750i	0.172912	−	0.299493i	0.939437	+	0.342722i	$0.111349\pi$
$32$	0.878152	−	1.52100i	0.155237	−	0.268878i
$33$	4.90886	+	1.38280i	0.854524	+	0.240715i
$34$	1.00714	+	1.74442i	0.172723	+	0.299165i
$35$	−2.85262			−0.482181
$36$	−0.802286	−	0.490958i	−0.133714	−	0.0818264i
$37$	−4.44739			−0.731147			−0.365574	−	0.930782i	$-0.619127\pi$
$37$	−4.44739			−0.731147			−0.365574	+	0.930782i	$0.619127\pi$
$38$	0.532989	+	0.923164i	0.0864622	+	0.149757i
$39$	1.43908	+	5.65905i	0.230438	+	0.906174i
$40$	4.15112	−	7.18996i	0.656350	−	1.13683i
$41$	−3.13620	+	5.43205i	−0.489792	+	0.848344i	−0.999931	−	0.0117476i	$-0.996261\pi$
$41$	−3.13620	+	5.43205i	−0.489792	+	0.848344i	0.510139	+	0.860092i	$0.329594\pi$
$42$	0.572266	+	2.25038i	0.0883026	+	0.347242i
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i
$44$	−0.923165			−0.139172
$45$	−7.07104	−	4.32711i	−1.05409	−	0.645048i
$46$	−11.1575			−1.64509
$47$	5.05055	+	8.74780i	0.736698	+	1.27600i	0.953974	+	0.299888i	$0.0969494\pi$
$47$	5.05055	+	8.74780i	0.736698	+	1.27600i	−0.217276	+	0.976110i	$0.569717\pi$
$48$	−5.45938	−	1.53788i	−0.787993	−	0.221974i
$49$	2.96716	−	5.13927i	0.423880	−	0.734182i
$50$	1.71157	−	2.96453i	0.242053	−	0.419248i
$51$	−1.92378	+	1.87523i	−0.269383	+	0.262584i
$52$	−0.528491	−	0.915373i	−0.0732885	−	0.126939i
$53$	8.79973			1.20874			0.604368	−	0.796705i	$-0.293426\pi$
$53$	8.79973			1.20874			0.604368	+	0.796705i	$0.293426\pi$
$54$	−1.99506	+	6.44628i	−0.271493	+	0.877227i
$55$	−8.13642			−1.09711
$56$	−1.55077	−	2.68601i	−0.207230	−	0.358934i
$57$	−1.01809	+	0.992390i	−0.134849	+	0.131445i
$58$	−0.809568	+	1.40221i	−0.106301	+	0.184120i
$59$	−3.31596	+	5.74341i	−0.431701	+	0.747728i	−0.997020	−	0.0771446i	$-0.975420\pi$
$59$	−3.31596	+	5.74341i	−0.431701	+	0.747728i	0.565319	+	0.824872i	$0.308753\pi$
$60$	1.44440	+	0.406880i	0.186471	+	0.0525280i
$61$	0.0348705	+	0.0603975i	0.00446471	+	0.00773310i	0.868249	−	0.496128i	$-0.165246\pi$
$61$	0.0348705	+	0.0603975i	0.00446471	+	0.00773310i	−0.863784	+	0.503862i	$0.831912\pi$
$62$	2.50049			0.317563
$63$	−2.72074	+	1.47942i	−0.342781	+	0.186390i
$64$	8.83009			1.10376
$65$	−4.65791	−	8.06774i	−0.577743	−	1.00068i
$66$	1.63225	+	6.41867i	0.200916	+	0.790084i
$67$	5.76481	−	9.98494i	0.704283	−	1.21985i	−0.262667	−	0.964887i	$-0.584602\pi$
$67$	5.76481	−	9.98494i	0.704283	−	1.21985i	0.966950	−	0.254967i	$-0.0820647\pi$
$68$	0.243152	−	0.421151i	0.0294865	−	0.0510720i
$69$	−3.66753	−	14.4222i	−0.441519	−	1.73623i
$70$	−1.85227	−	3.20822i	−0.221388	−	0.383456i
$71$	−5.88849			−0.698835			−0.349418	−	0.936967i	$-0.613621\pi$
$71$	−5.88849			−0.698835			−0.349418	+	0.936967i	$0.613621\pi$
$72$	0.230361	−	9.01039i	0.0271483	−	1.06189i
$73$	1.89767			0.222105			0.111053	−	0.993815i	$-0.464578\pi$
$73$	1.89767			0.222105			0.111053	+	0.993815i	$0.464578\pi$
$74$	−2.88779	−	5.00179i	−0.335698	−	0.581447i
$75$	4.39455	+	1.23792i	0.507439	+	0.142943i
$76$	0.128678	−	0.222878i	0.0147604	−	0.0255658i
$77$	−1.51980	+	2.63236i	−0.173197	+	0.299986i
$78$	−5.43007	+	5.29302i	−0.614834	+	0.599316i
$79$	−3.49563	−	6.05462i	−0.393290	−	0.681198i	0.599592	−	0.800306i	$-0.295330\pi$
$79$	−3.49563	−	6.05462i	−0.393290	−	0.681198i	−0.992881	+	0.119109i	$0.961996\pi$
$80$	9.04889			1.01170
$81$	−8.98824	−	0.459891i	−0.998694	−	0.0510990i
$82$	−8.14560			−0.899531
$83$	−1.50913	−	2.61390i	−0.165649	−	0.286912i	0.771237	−	0.636549i	$-0.219639\pi$
$83$	−1.50913	−	2.61390i	−0.165649	−	0.286912i	−0.936886	+	0.349636i	$0.886305\pi$
$84$	0.401436	−	0.391304i	0.0438002	−	0.0426948i
$85$	2.14304	−	3.71186i	0.232446	−	0.402608i
$86$	0.649321	−	1.12466i	0.0700181	−	0.121275i
$87$	−2.07861	−	0.585534i	−0.222850	−	0.0627758i
$88$	−4.42320	−	7.66120i	−0.471514	−	0.816687i
$89$	−15.2655			−1.61814			−0.809071	−	0.587711i	$-0.800029\pi$
$89$	−15.2655			−1.61814			−0.809071	+	0.587711i	$0.800029\pi$
$90$	0.275148	−	10.7622i	0.0290031	−	1.13443i
$91$	−3.48019			−0.364823
$92$	1.34687	+	2.33285i	0.140421	+	0.243216i
$93$	0.821924	+	3.23214i	0.0852296	+	0.335157i
$94$	−6.55885	+	11.3603i	−0.676494	+	1.17172i
$95$	1.13412	−	1.96436i	0.116359	−	0.201539i
$96$	0.749713	+	2.94817i	0.0765172	+	0.300897i
$97$	1.93718	+	3.35530i	0.196691	+	0.340679i	0.947454	−	0.319893i	$-0.103647\pi$
$97$	1.93718	+	3.35530i	0.196691	+	0.340679i	−0.750763	+	0.660572i	$0.770314\pi$
$98$	7.70656			0.778480
$99$	−7.76025	+	4.21970i	−0.779934	+	0.424095i
$100$	−0.826443			−0.0826443
$101$	5.11490	+	8.85927i	0.508952	+	0.881530i	0.999946	+	0.0103677i	$0.00330019\pi$
$101$	5.11490	+	8.85927i	0.508952	+	0.881530i	−0.490994	+	0.871163i	$0.663366\pi$
$102$	−3.35814	−	0.945970i	−0.332505	−	0.0936650i
$103$	−6.33977	+	10.9808i	−0.624676	+	1.08197i	0.363927	+	0.931427i	$0.381436\pi$
$103$	−6.33977	+	10.9808i	−0.624676	+	1.08197i	−0.988603	+	0.150543i	$0.951898\pi$
$104$	5.06436	−	8.77173i	0.496601	−	0.860139i
$105$	3.53810	−	3.44880i	0.345283	−	0.336568i
$106$	5.71385	+	9.89668i	0.554978	+	0.961251i
$107$	10.2054			0.986597			0.493298	−	0.869860i	$-0.335791\pi$
$107$	10.2054			0.986597			0.493298	+	0.869860i	$0.335791\pi$
$108$	1.58864	−	0.361024i	0.152867	−	0.0347395i
$109$	−4.68029			−0.448290			−0.224145	−	0.974556i	$-0.571959\pi$
$109$	−4.68029			−0.448290			−0.224145	+	0.974556i	$0.571959\pi$
$110$	−5.28315	−	9.15068i	−0.503728	−	0.872483i
$111$	5.51609	−	5.37687i	0.523564	−	0.510350i
$112$	1.69023	−	2.92757i	0.159712	−	0.276630i
$113$	3.43891	−	5.95637i	0.323505	−	0.560328i	−0.657703	−	0.753277i	$-0.728472\pi$
$113$	3.43891	−	5.95637i	0.323505	−	0.560328i	0.981209	+	0.192949i	$0.0618053\pi$
$114$	−1.77716	−	0.500618i	−0.166447	−	0.0468871i
$115$	11.8708	+	20.5608i	1.10696	+	1.91731i
$116$	0.390905			0.0362946
$117$	−8.62664	−	5.27907i	−0.797534	−	0.488050i
$118$	−8.61248			−0.792843
$119$	−0.800595	−	1.38667i	−0.0733904	−	0.127116i
$120$	3.54398	+	13.9364i	0.323519	+	1.27221i
$121$	1.16515	−	2.01810i	0.105923	−	0.183464i
$122$	−0.0452843	+	0.0784347i	−0.00409985	+	0.00710114i
$123$	−2.67750	−	10.5290i	−0.241422	−	0.949368i
$124$	−0.301845	−	0.522811i	−0.0271065	−	0.0469498i
$125$	6.53266			0.584299
$126$	−3.43048	−	2.09928i	−0.305611	−	0.187018i
$127$	6.24851			0.554466			0.277233	−	0.960803i	$-0.410583\pi$
$127$	6.24851			0.554466			0.277233	+	0.960803i	$0.410583\pi$
$128$	3.97726	+	6.88882i	0.351544	+	0.608892i
$129$	1.66717	+	0.469632i	0.146786	+	0.0413488i
$130$	6.04896	−	10.4771i	0.530529	−	0.918903i
$131$	−5.77690	+	10.0059i	−0.504730	+	0.874219i	0.495255	+	0.868748i	$0.335075\pi$
$131$	−5.77690	+	10.0059i	−0.504730	+	0.874219i	−0.999985	+	0.00547079i	$0.998259\pi$
$132$	1.14500	−	1.11610i	0.0996593	−	0.0971440i
$133$	−0.423684	−	0.733842i	−0.0367380	−	0.0636322i
$134$	14.9728			1.29346
$135$	14.0016	−	3.18192i	1.20507	−	0.273856i
$136$	4.66009			0.399599
$137$	10.4557	+	18.1097i	0.893287	+	1.54722i	0.835911	+	0.548865i	$0.184940\pi$
$137$	10.4557	+	18.1097i	0.893287	+	1.54722i	0.0573759	+	0.998353i	$0.481727\pi$
$138$	13.8386	−	13.4894i	1.17802	−	1.14829i
$139$	−11.1311	+	19.2797i	−0.944131	+	1.63528i	−0.186648	+	0.982427i	$0.559762\pi$
$139$	−11.1311	+	19.2797i	−0.944131	+	1.63528i	−0.757482	+	0.652855i	$0.773571\pi$
$140$	−0.447190	+	0.774555i	−0.0377944	+	0.0654619i
$141$	−16.8402	−	4.74380i	−1.41820	−	0.399500i
$142$	−3.82352	−	6.62253i	−0.320863	−	0.555750i
$143$	−9.92641			−0.830088
$144$	8.63053	−	4.69292i	0.719211	−	0.391077i
$145$	3.44528			0.286115
$146$	1.23220	+	2.13423i	0.101977	+	0.176630i
$147$	2.53318	+	9.96150i	0.208933	+	0.821611i
$148$	−0.697193	+	1.20757i	−0.0573089	+	0.0992619i
$149$	−6.32942	+	10.9629i	−0.518526	+	0.898114i	0.481242	+	0.876588i	$0.340186\pi$
$149$	−6.32942	+	10.9629i	−0.518526	+	0.898114i	−0.999768	+	0.0215262i	$0.993147\pi$
$150$	1.46124	+	5.74617i	0.119309	+	0.469173i
$151$	1.88903	+	3.27189i	0.153727	+	0.266262i	0.932595	−	0.360925i	$-0.117539\pi$
$151$	1.88903	+	3.27189i	0.153727	+	0.266262i	−0.778868	+	0.627188i	$0.784206\pi$
$152$	2.46617			0.200033
$153$	0.118925	−	4.65167i	0.00961456	−	0.376065i
$154$	−3.94734			−0.318086
$155$	−2.66034	−	4.60785i	−0.213684	−	0.370111i
$156$	1.76216	+	0.496393i	0.141086	+	0.0397432i
$157$	−1.63812	+	2.83730i	−0.130736	+	0.226441i	−0.923960	−	0.382488i	$-0.875067\pi$
$157$	−1.63812	+	2.83730i	−0.130736	+	0.226441i	0.793225	+	0.608929i	$0.208401\pi$
$158$	4.53958	−	7.86278i	0.361149	−	0.625529i
$159$	−10.9143	+	10.6388i	−0.865559	+	0.843713i
$160$	−2.42661	−	4.20302i	−0.191841	−	0.332278i
$161$	8.86935			0.699002
$162$	−5.31904	−	10.4073i	−0.417903	−	0.817675i
$163$	−2.94951			−0.231023			−0.115512	−	0.993306i	$-0.536851\pi$
$163$	−2.94951			−0.231023			−0.115512	+	0.993306i	$0.536851\pi$
$164$	0.983288	+	1.70310i	0.0767819	+	0.132990i
$165$	10.0916	−	9.83687i	0.785628	−	0.765799i
$166$	1.95983	−	3.39452i	0.152112	−	0.263466i
$167$	−11.9581	+	20.7120i	−0.925342	+	1.60274i	−0.134331	+	0.990936i	$0.542889\pi$
$167$	−11.9581	+	20.7120i	−0.925342	+	1.60274i	−0.791011	+	0.611803i	$0.790445\pi$
$168$	5.17079	+	1.45658i	0.398935	+	0.112378i
$169$	0.817357	+	1.41570i	0.0628736	+	0.108900i
$170$	5.56609			0.426900
$171$	0.0629367	−	2.46172i	0.00481289	−	0.188252i
$172$	−0.313529			−0.0239063
$173$	−10.9038	−	18.8860i	−0.829004	−	1.43588i	−0.898821	−	0.438317i	$-0.855575\pi$
$173$	−10.9038	−	18.8860i	−0.829004	−	1.43588i	0.0698168	−	0.997560i	$-0.477759\pi$
$174$	−0.691160	−	2.71792i	−0.0523967	−	0.206045i
$175$	−1.36056	+	2.35656i	−0.102849	+	0.178139i
$176$	4.82099	−	8.35019i	0.363396	−	0.629419i
$177$	−2.83096	−	11.1325i	−0.212788	−	0.836770i
$178$	−9.91223	−	17.1685i	−0.742953	−	1.28683i
$179$	6.92878			0.517882			0.258941	−	0.965893i	$-0.416627\pi$
$179$	6.92878			0.517882			0.258941	+	0.965893i	$0.416627\pi$
$180$	−2.28340	+	1.24162i	−0.170195	+	0.0925447i
$181$	−11.0279			−0.819698			−0.409849	−	0.912153i	$-0.634419\pi$
$181$	−11.0279			−0.819698			−0.409849	+	0.912153i	$0.634419\pi$
$182$	−2.25976	−	3.91402i	−0.167505	−	0.290127i
$183$	−0.116270	−	0.0327526i	−0.00859492	−	0.00242114i
$184$	−12.9066	+	22.3549i	−0.951489	+	1.64803i
$185$	−6.14479	+	10.6431i	−0.451774	+	0.782495i
$186$	−3.10136	+	3.02308i	−0.227402	+	0.221663i
$187$	−2.28350	−	3.95514i	−0.166986	−	0.289229i
$188$	3.16698			0.230976
$189$	1.58591	−	5.12428i	0.115358	−	0.372736i
$190$	2.94564			0.213699
$191$	−12.6528	−	21.9152i	−0.915522	−	1.58573i	−0.806136	−	0.591731i	$-0.798445\pi$
$191$	−12.6528	−	21.9152i	−0.915522	−	1.58573i	−0.109386	−	0.993999i	$-0.534888\pi$
$192$	−10.9519	+	10.6755i	−0.790388	+	0.770439i
$193$	10.8578	−	18.8063i	0.781563	−	1.35371i	−0.149468	−	0.988767i	$-0.547756\pi$
$193$	10.8578	−	18.8063i	0.781563	−	1.35371i	0.931031	−	0.364940i	$-0.118911\pi$
$194$	−2.51570	+	4.35733i	−0.180617	+	0.312838i
$195$	15.5310	+	4.37501i	1.11220	+	0.313301i
$196$	−0.930290	−	1.61131i	−0.0664493	−	0.115094i
$197$	6.79869			0.484386			0.242193	−	0.970228i	$-0.422133\pi$
$197$	6.79869			0.484386			0.242193	+	0.970228i	$0.422133\pi$
$198$	−9.78460	−	5.98768i	−0.695361	−	0.425526i
$199$	27.2806			1.93387			0.966935	−	0.255022i	$-0.0820827\pi$
$199$	27.2806			1.93387			0.966935	+	0.255022i	$0.0820827\pi$
$200$	−3.95977	−	6.85852i	−0.279998	−	0.484971i
$201$	4.92164	+	19.3539i	0.347146	+	1.36512i
$202$	−6.64243	+	11.5050i	−0.467360	+	0.809491i
$203$	0.643542	−	1.11465i	0.0451678	−	0.0782329i
$204$	0.207588	+	0.816321i	0.0145341	+	0.0571539i
$205$	8.66632	+	15.0105i	0.605282	+	1.04838i
$206$	−16.4662			−1.14725
$207$	21.9852	+	13.4538i	1.52808	+	0.935105i
$208$	11.0396			0.765460
$209$	−1.20846	−	2.09311i	−0.0835906	−	0.144783i
$210$	6.17608	+	1.73977i	0.426190	+	0.120056i
$211$	−7.88503	+	13.6573i	−0.542828	+	0.940206i	0.455912	+	0.890025i	$0.349313\pi$
$211$	−7.88503	+	13.6573i	−0.542828	+	0.940206i	−0.998740	+	0.0501808i	$0.984020\pi$
$212$	1.37948	−	2.38934i	0.0947434	−	0.164100i
$213$	7.30348	−	7.11914i	0.500426	−	0.487795i
$214$	6.62661	+	11.4776i	0.452985	+	0.784594i
$215$	−2.76332			−0.188457
$216$	10.6078	+	11.4541i	0.721768	+	0.779351i
$217$	−1.98769			−0.134933
$218$	−3.03901	−	5.26372i	−0.205828	−	0.356504i
$219$	−2.35367	+	2.29427i	−0.159046	+	0.155032i
$220$	−1.27550	+	2.20923i	−0.0859942	+	0.148946i
$221$	2.61451	−	4.52846i	0.175871	−	0.304617i
$222$	9.62885	+	2.71240i	0.646246	+	0.182044i
$223$	−10.5956	−	18.3520i	−0.709531	−	1.22894i	−0.965031	−	0.262135i	$-0.915574\pi$
$223$	−10.5956	−	18.3520i	−0.709531	−	1.22894i	0.255500	−	0.966809i	$-0.417760\pi$
$224$	−1.81306			−0.121140
$225$	−6.94719	+	3.77759i	−0.463146	+	0.251839i
$226$	8.93183			0.594136
$227$	−0.776999	−	1.34580i	−0.0515712	−	0.0893240i	0.839087	−	0.543997i	$-0.183090\pi$
$227$	−0.776999	−	1.34580i	−0.0515712	−	0.0893240i	−0.890659	+	0.454673i	$0.849756\pi$
$228$	0.109858	+	0.432006i	0.00727552	+	0.0286103i
$229$	−0.990433	+	1.71548i	−0.0654496	+	0.113362i	−0.896893	−	0.442247i	$-0.854181\pi$
$229$	−0.990433	+	1.71548i	−0.0654496	+	0.113362i	0.831444	+	0.555609i	$0.187515\pi$
$230$	−15.4159	+	26.7011i	−1.01649	+	1.76062i
$231$	−1.29751	−	5.10233i	−0.0853699	−	0.335709i
$232$	1.87296	+	3.24406i	0.122966	+	0.212983i
$233$	−25.5390			−1.67311			−0.836557	−	0.547880i	$-0.815435\pi$
$233$	−25.5390			−1.67311			−0.836557	+	0.547880i	$0.815435\pi$
$234$	0.335680	−	13.1298i	0.0219441	−	0.858324i
$235$	27.9126			1.82081
$236$	1.03965	+	1.80072i	0.0676753	+	0.117217i
$237$	11.6556	+	3.28333i	0.757113	+	0.213275i
$238$	1.03969	−	1.80079i	0.0673929	−	0.116728i
$239$	7.98820	−	13.8360i	0.516714	−	0.894975i	−0.483098	−	0.875566i	$-0.660488\pi$
$239$	7.98820	−	13.8360i	0.516714	−	0.894975i	0.999812	−	0.0194082i	$-0.00617822\pi$
$240$	−11.2233	+	10.9400i	−0.724461	+	0.706176i
$241$	4.85761	+	8.41363i	0.312906	+	0.541969i	0.978990	−	0.203907i	$-0.0653641\pi$
$241$	4.85761	+	8.41363i	0.312906	+	0.541969i	−0.666084	+	0.745877i	$0.732031\pi$
$242$	3.02623			0.194533
$243$	11.7041	−	10.2963i	0.750818	−	0.660509i
$244$	0.0218658			0.00139981
$245$	−8.19922	−	14.2015i	−0.523829	−	0.907298i
$246$	10.1030	−	9.84797i	0.644141	−	0.627883i
$247$	1.38363	−	2.39651i	0.0880380	−	0.152486i
$248$	2.89248	−	5.00993i	0.183673	−	0.318131i
$249$	5.03196	+	1.41748i	0.318887	+	0.0898289i
$250$	4.24179	+	7.34700i	0.268274	+	0.464665i
$251$	5.91101			0.373100			0.186550	−	0.982445i	$-0.440269\pi$
$251$	5.91101			0.373100			0.186550	+	0.982445i	$0.440269\pi$
$252$	−0.0248162	+	0.970666i	−0.00156328	+	0.0611462i
$253$	25.2977			1.59045
$254$	4.05729	+	7.02743i	0.254577	+	0.440940i
$255$	1.82960	+	7.19473i	0.114574	+	0.450552i
$256$	3.66505	−	6.34806i	0.229066	−	0.396754i
$257$	−14.1947	+	24.5859i	−0.885439	+	1.53363i	−0.0402290	+	0.999190i	$0.512809\pi$
$257$	−14.1947	+	24.5859i	−0.885439	+	1.53363i	−0.845210	+	0.534435i	$0.820525\pi$
$258$	0.554351	+	2.17993i	0.0345124	+	0.135717i
$259$	2.29556	+	3.97603i	0.142639	+	0.247058i
$260$	−2.92078			−0.181139
$261$	3.28600	−	1.78679i	0.203398	−	0.110599i
$262$	−15.0043			−0.926966
$263$	−13.1146	−	22.7152i	−0.808683	−	1.40068i	−0.913777	−	0.406217i	$-0.866848\pi$
$263$	−13.1146	−	22.7152i	−0.808683	−	1.40068i	0.105094	−	0.994462i	$-0.466486\pi$
$264$	14.7484	+	4.15455i	0.907702	+	0.255695i
$265$	12.1582	−	21.0587i	0.746875	−	1.29362i
$266$	0.550214	−	0.952998i	0.0337358	−	0.0584321i
$267$	18.9338	−	18.4559i	1.15873	−	1.12948i
$268$	−1.80743	−	3.13056i	−0.110406	−	0.191230i
$269$	16.9061			1.03078			0.515392	−	0.856954i	$-0.327646\pi$
$269$	16.9061			1.03078			0.515392	+	0.856954i	$0.327646\pi$
$270$	12.6701	+	13.6809i	0.771079	+	0.832596i
$271$	14.9590			0.908693			0.454347	−	0.890825i	$-0.349873\pi$
$271$	14.9590			0.908693			0.454347	+	0.890825i	$0.349873\pi$
$272$	2.53959	+	4.39870i	0.153985	+	0.266710i
$273$	4.31647	−	4.20753i	0.261245	−	0.254651i
$274$	−13.5782	+	23.5180i	−0.820286	+	1.42078i
$275$	−3.88068	+	6.72153i	−0.234014	+	0.405323i
$276$	−4.49091	−	1.26507i	−0.270321	−	0.0761481i
$277$	−0.464342	−	0.804265i	−0.0278996	−	0.0483236i	0.851738	−	0.523967i	$-0.175549\pi$
$277$	−0.464342	−	0.804265i	−0.0278996	−	0.0483236i	−0.879638	+	0.475644i	$0.842215\pi$
$278$	−28.9107			−1.73395
$279$	−4.92706	−	3.01511i	−0.294976	−	0.180510i
$280$	−8.57055			−0.512188
$281$	−8.89911	−	15.4137i	−0.530876	−	0.919505i	−0.999351	−	0.0360276i	$-0.988530\pi$
$281$	−8.89911	−	15.4137i	−0.530876	−	0.919505i	0.468475	−	0.883477i	$-0.344804\pi$
$282$	−5.59955	−	22.0197i	−0.333449	−	1.31125i
$283$	−0.877006	+	1.51902i	−0.0521326	+	0.0902963i	−0.890914	−	0.454172i	$-0.849935\pi$
$283$	−0.877006	+	1.51902i	−0.0521326	+	0.0902963i	0.838781	+	0.544468i	$0.183269\pi$
$284$	−0.923105	+	1.59886i	−0.0547762	+	0.0948752i
$285$	0.968245	+	3.80753i	0.0573539	+	0.225539i
$286$	−6.44543	−	11.1638i	−0.381126	−	0.660130i
$287$	6.47510			0.382213
$288$	−4.49419	−	2.75021i	−0.264823	−	0.162058i
$289$	−14.5942			−0.858482
$290$	2.23710	+	3.87476i	0.131367	+	0.227534i
$291$	−6.45921	−	1.81953i	−0.378645	−	0.106663i
$292$	0.297487	−	0.515262i	0.0174091	−	0.0301534i
$293$	3.75036	−	6.49581i	0.219098	−	0.379489i	−0.735434	−	0.677596i	$-0.763022\pi$
$293$	3.75036	−	6.49581i	0.219098	−	0.379489i	0.954533	+	0.298107i	$0.0963551\pi$
$294$	−9.55842	+	9.31717i	−0.557459	+	0.543389i
$295$	9.16305	+	15.8709i	0.533493	+	0.924038i
$296$	−13.3620			−0.776648
$297$	4.52343	−	14.6158i	0.262476	−	0.848092i
$298$	−16.4393			−0.952303
$299$	14.4823	+	25.0841i	0.837535	+	1.45065i
$300$	1.02503	−	0.999163i	0.0591804	−	0.0576867i
$301$	−0.516159	+	0.894013i	−0.0297509	+	0.0515301i
$302$	−2.45317	+	4.24901i	−0.141164	+	0.244503i
$303$	−17.0548	−	4.80425i	−0.979772	−	0.275997i
$304$	1.34398	+	2.32784i	0.0770825	+	0.133511i
$305$	0.192717			0.0110349
$306$	5.30876	−	2.88668i	0.303481	−	0.165020i
$307$	24.5577			1.40158			0.700792	−	0.713365i	$-0.252830\pi$
$307$	24.5577			1.40158			0.700792	+	0.713365i	$0.252830\pi$
$308$	0.476500	+	0.825321i	0.0271511	+	0.0470271i
$309$	−5.41251	−	21.2842i	−0.307907	−	1.21082i
$310$	3.45483	−	5.98395i	0.196221	−	0.339865i
$311$	9.36086	−	16.2135i	0.530806	−	0.919382i	−0.468548	−	0.883438i	$-0.655223\pi$
$311$	9.36086	−	16.2135i	0.530806	−	0.919382i	0.999354	−	0.0359442i	$-0.0114439\pi$
$312$	4.32364	+	17.0023i	0.244778	+	0.962567i
$313$	0.549273	+	0.951369i	0.0310468	+	0.0537746i	0.881131	−	0.472872i	$-0.156783\pi$
$313$	0.549273	+	0.951369i	0.0310468	+	0.0537746i	−0.850085	+	0.526646i	$0.823449\pi$
$314$	−4.25466			−0.240104
$315$	−0.218721	+	8.55507i	−0.0123235	+	0.482024i
$316$	−2.19196			−0.123308
$317$	−1.25859	−	2.17995i	−0.0706896	−	0.122438i	0.828514	−	0.559968i	$-0.189187\pi$
$317$	−1.25859	−	2.17995i	−0.0706896	−	0.122438i	−0.899204	+	0.437530i	$0.855853\pi$
$318$	−19.0519	−	5.36682i	−1.06838	−	0.300956i
$319$	1.83555	−	3.17926i	0.102771	−	0.178005i
$320$	12.2002	−	21.1313i	0.682011	−	1.18128i
$321$	−12.6578	+	12.3383i	−0.706488	+	0.688657i
$322$	5.75905	+	9.97497i	0.320939	+	0.555883i
$323$	1.27318			0.0708414
$324$	−1.53391	+	2.36843i	−0.0852171	+	0.131579i
$325$	−8.88639			−0.492928
$326$	−1.91518	−	3.31718i	−0.106072	−	0.183722i
$327$	5.80494	−	5.65843i	0.321014	−	0.312912i
$328$	−9.42253	+	16.3203i	−0.520272	+	0.901138i
$329$	5.21377	−	9.03051i	0.287444	−	0.497868i
$330$	17.6158	+	4.96227i	0.969717	+	0.273164i
$331$	6.76996	+	11.7259i	0.372111	+	0.644515i	0.989890	−	0.141837i	$-0.0453008\pi$
$331$	6.76996	+	11.7259i	0.372111	+	0.644515i	−0.617779	+	0.786352i	$0.711967\pi$
$332$	−0.946314			−0.0519357
$333$	−0.340997	+	13.3378i	−0.0186865	+	0.730908i
$334$	−31.0585			−1.69944
$335$	−15.9300	−	27.5916i	−0.870349	−	1.50749i
$336$	1.44302	+	5.67454i	0.0787232	+	0.309572i
$337$	1.22079	−	2.11448i	0.0665009	−	0.115183i	−0.830858	−	0.556485i	$-0.812150\pi$
$337$	1.22079	−	2.11448i	0.0665009	−	0.115183i	0.897359	+	0.441302i	$0.145483\pi$
$338$	−1.06145	+	1.83849i	−0.0577355	+	0.100001i
$339$	2.93593	+	11.5453i	0.159458	+	0.627054i
$340$	−0.671906	−	1.16377i	−0.0364392	−	0.0631145i
$341$	−5.66942			−0.307016
$342$	2.80945	−	1.52766i	0.151918	−	0.0826065i
$343$	−13.3523			−0.720958
$344$	−1.50222	−	2.60193i	−0.0809944	−	0.140286i
$345$	−39.5812	−	11.1498i	−2.13098	−	0.600286i
$346$	14.1602	−	24.5262i	0.761256	−	1.31853i
$347$	−0.939688	+	1.62759i	−0.0504451	+	0.0873735i	−0.890145	−	0.455677i	$-0.849397\pi$
$347$	−0.939688	+	1.62759i	−0.0504451	+	0.0873735i	0.839700	+	0.543050i	$0.182731\pi$
$348$	−0.484838	+	0.472601i	−0.0259901	+	0.0253341i
$349$	−12.0684	−	20.9031i	−0.646006	−	1.11892i	−0.984068	−	0.177792i	$-0.943105\pi$
$349$	−12.0684	−	20.9031i	−0.646006	−	1.11892i	0.338062	−	0.941124i	$-0.390229\pi$
$350$	−3.53377			−0.188888
$351$	17.0820	−	3.88194i	0.911767	−	0.207202i
$352$	−5.17132			−0.275632
$353$	6.77717	+	11.7384i	0.360712	+	0.624772i	0.988078	−	0.153953i	$-0.0492003\pi$
$353$	6.77717	+	11.7384i	0.360712	+	0.624772i	−0.627366	+	0.778724i	$0.715867\pi$
$354$	10.6820	−	10.4124i	0.567744	−	0.553414i
$355$	−8.13589	+	14.0918i	−0.431808	+	0.747914i
$356$	−2.39309	+	4.14495i	−0.126834	+	0.219682i
$357$	2.66945	+	0.751971i	0.141282	+	0.0397985i
$358$	4.49900	+	7.79250i	0.237780	+	0.411847i
$359$	−3.49289			−0.184348			−0.0921739	−	0.995743i	$-0.529382\pi$
$359$	−3.49289			−0.184348			−0.0921739	+	0.995743i	$0.529382\pi$
$360$	−21.2445	−	13.0006i	−1.11969	−	0.685191i
$361$	−18.3262			−0.964538
$362$	−7.16065	−	12.4026i	−0.376355	−	0.651867i
$363$	0.994735	+	3.91170i	0.0522101	+	0.205311i
$364$	−0.545570	+	0.944955i	−0.0285957	+	0.0495291i
$365$	2.62193	−	4.54132i	0.137238	−	0.237704i
$366$	−0.0386610	−	0.152031i	−0.00202084	−	0.00794677i
$367$	−14.5976	−	25.2838i	−0.761989	−	1.31980i	−0.941824	−	0.336107i	$-0.890890\pi$
$367$	−14.5976	−	25.2838i	−0.761989	−	1.31980i	0.179834	−	0.983697i	$-0.442444\pi$
$368$	−28.1347			−1.46662
$369$	16.0504	+	9.82201i	0.835549	+	0.511314i
$370$	−15.9598			−0.829708
$371$	−4.54206	−	7.86707i	−0.235812	−	0.408438i
$372$	1.00645	+	0.283512i	0.0521821	+	0.0146994i
$373$	2.95796	−	5.12334i	0.153157	−	0.265276i	−0.779229	−	0.626739i	$-0.784389\pi$
$373$	2.95796	−	5.12334i	0.153157	−	0.265276i	0.932387	+	0.361463i	$0.117723\pi$
$374$	2.96545	−	5.13632i	0.153340	−	0.265593i
$375$	−8.10243	+	7.89793i	−0.418408	+	0.407848i
$376$	15.1741	+	26.2823i	0.782544	+	1.35541i
$377$	4.20324			0.216478
$378$	6.79282	−	1.54369i	0.349385	−	0.0793990i
$379$	8.06235			0.414135			0.207067	−	0.978327i	$-0.433608\pi$
$379$	8.06235			0.414135			0.207067	+	0.978327i	$0.433608\pi$
$380$	−0.355580	−	0.615882i	−0.0182409	−	0.0315941i
$381$	−7.75001	+	7.55441i	−0.397045	+	0.387024i
$382$	16.4314	−	28.4600i	0.840704	−	1.45614i
$383$	−2.31912	+	4.01683i	−0.118501	+	0.205250i	−0.919174	−	0.393852i	$-0.871142\pi$
$383$	−2.31912	+	4.01683i	−0.118501	+	0.205250i	0.800673	+	0.599102i	$0.204476\pi$
$384$	−13.2615	−	3.73570i	−0.676749	−	0.190637i
$385$	4.19968	+	7.27406i	0.214036	+	0.370721i
$386$	28.2008			1.43539
$387$	−2.63556	+	1.43311i	−0.133973	+	0.0728490i
$388$	1.21472			0.0616683
$389$	9.06993	+	15.7096i	0.459864	+	0.796507i	0.998953	−	0.0457413i	$-0.0145650\pi$
$389$	9.06993	+	15.7096i	0.459864	+	0.796507i	−0.539090	+	0.842248i	$0.681232\pi$
$390$	5.16424	+	20.3079i	0.261501	+	1.02833i
$391$	−6.66313	+	11.5409i	−0.336969	+	0.583647i
$392$	8.91467	−	15.4407i	0.450259	−	0.779871i
$393$	−4.93197	−	19.3945i	−0.248785	−	0.978324i
$394$	4.41453	+	7.64619i	0.222401	+	0.385210i
$395$	−19.3191			−0.972050
$396$	−0.0707823	+	2.76859i	−0.00355694	+	0.139127i
$397$	32.4912			1.63069			0.815343	−	0.578979i	$-0.196549\pi$
$397$	32.4912			1.63069			0.815343	+	0.578979i	$0.196549\pi$
$398$	17.7139	+	30.6813i	0.887916	+	1.53792i
$399$	1.41270	+	0.397951i	0.0707236	+	0.0199225i
$400$	4.31588	−	7.47532i	0.215794	−	0.373766i
$401$	−2.47708	+	4.29042i	−0.123699	+	0.214254i	−0.921224	−	0.389033i	$-0.872809\pi$
$401$	−2.47708	+	4.29042i	−0.123699	+	0.214254i	0.797524	+	0.603287i	$0.206143\pi$
$402$	−18.5708	+	18.1021i	−0.926226	+	0.902848i
$403$	−3.24561	−	5.62156i	−0.161675	−	0.280030i
$404$	3.20734			0.159571
$405$	−13.5193	+	20.8744i	−0.671778	+	1.03726i
$406$	1.67146			0.0829533
$407$	6.54753	+	11.3407i	0.324549	+	0.562136i
$408$	−5.77989	+	5.63401i	−0.286147	+	0.278925i
$409$	−13.5836	+	23.5274i	−0.671664	+	1.16336i	0.305768	+	0.952106i	$0.401087\pi$
$409$	−13.5836	+	23.5274i	−0.671664	+	1.16336i	−0.977432	+	0.211250i	$0.932247\pi$
$410$	−11.2544	+	19.4933i	−0.555817	+	0.962704i
$411$	−34.8626	−	9.82063i	−1.71965	−	0.484416i
$412$	1.98770	+	3.44280i	0.0979269	+	0.169614i
$413$	6.84624			0.336881
$414$	−0.855486	+	33.4616i	−0.0420449	+	1.64455i
$415$	−8.34044			−0.409416
$416$	−2.96046	−	5.12767i	−0.145149	−	0.251405i
$417$	−9.50309	−	37.3700i	−0.465368	−	1.83002i
$418$	1.56935	−	2.71820i	0.0767595	−	0.132951i
$419$	−0.591184	+	1.02396i	−0.0288812	+	0.0500238i	−0.880105	−	0.474780i	$-0.842528\pi$
$419$	−0.591184	+	1.02396i	−0.0288812	+	0.0500238i	0.851224	+	0.524803i	$0.175861\pi$
$420$	−0.381784	−	1.50133i	−0.0186291	−	0.0732573i
$421$	−12.8870	−	22.3209i	−0.628072	−	1.08785i	−0.987938	−	0.154848i	$-0.950511\pi$
$421$	−12.8870	−	22.3209i	−0.628072	−	1.08785i	0.359867	−	0.933004i	$-0.382822\pi$
$422$	−20.4797			−0.996935
$423$	26.6221	−	14.4760i	1.29441	−	0.703846i
$424$	26.4383			1.28396
$425$	−2.04426	−	3.54075i	−0.0991610	−	0.171752i
$426$	12.7489	+	3.59130i	0.617686	+	0.173999i
$427$	0.0359974	−	0.0623493i	0.00174204	−	0.00301730i
$428$	1.59985	−	2.77102i	0.0773316	−	0.133942i
$429$	12.3117	−	12.0010i	0.594414	−	0.579412i
$430$	−1.79428	−	3.10779i	−0.0865280	−	0.149871i
$431$	−9.39722			−0.452648			−0.226324	−	0.974052i	$-0.572671\pi$
$431$	−9.39722			−0.452648			−0.226324	+	0.974052i	$0.572671\pi$
$432$	−5.03072	+	16.2549i	−0.242040	+	0.782062i
$433$	−21.5740			−1.03678			−0.518391	−	0.855144i	$-0.673469\pi$
$433$	−21.5740			−1.03678			−0.518391	+	0.855144i	$0.673469\pi$
$434$	−1.29065	−	2.23547i	−0.0619533	−	0.107306i
$435$	−4.27318	+	4.16532i	−0.204883	+	0.199712i
$436$	−0.733702	+	1.27081i	−0.0351380	+	0.0608607i
$437$	−3.52620	+	6.10756i	−0.168681	+	0.292164i
$438$	−4.10855	−	1.15736i	−0.196314	−	0.0553007i
$439$	−1.04927	−	1.81739i	−0.0500790	−	0.0867395i	0.839899	−	0.542742i	$-0.182614\pi$
$439$	−1.04927	−	1.81739i	−0.0500790	−	0.0867395i	−0.889978	+	0.456003i	$0.849281\pi$
$440$	−24.4454			−1.16539
$441$	−15.1853	−	9.29262i	−0.723109	−	0.442506i
$442$	6.79062			0.322997
$443$	−18.2063	−	31.5342i	−0.865007	−	1.49824i	−0.867040	−	0.498238i	$-0.833980\pi$
$443$	−18.2063	−	31.5342i	−0.865007	−	1.49824i	0.00203309	−	0.999998i	$-0.499353\pi$
$444$	−0.595221	−	2.34065i	−0.0282480	−	0.111082i
$445$	−21.0918	+	36.5320i	−0.999846	+	1.73178i
$446$	13.7598	−	23.8327i	0.651547	−	1.12851i
$447$	−5.40368	−	21.2494i	−0.255585	−	1.00506i
$448$	−4.55773	−	7.89422i	−0.215332	−	0.372967i
$449$	7.78784			0.367531			0.183765	−	0.982970i	$-0.441171\pi$
$449$	7.78784			0.367531			0.183765	+	0.982970i	$0.441171\pi$
$450$	−8.75945	−	5.36034i	−0.412924	−	0.252689i
$451$	18.4687			0.869655
$452$	−1.07820	−	1.86749i	−0.0507141	−	0.0878394i
$453$	−6.29864	−	1.77430i	−0.295936	−	0.0833637i
$454$	1.00904	−	1.74771i	0.0473567	−	0.0820243i
$455$	−4.80844	+	8.32847i	−0.225423	+	0.390445i
$456$	−3.05878	+	2.98158i	−0.143241	+	0.139625i
$457$	11.8008	+	20.4395i	0.552016	+	0.956120i	0.998129	+	0.0611431i	$0.0194746\pi$
$457$	11.8008	+	20.4395i	0.552016	+	0.956120i	−0.446113	+	0.894977i	$0.647192\pi$
$458$	−2.57243			−0.120202
$459$	5.47633	+	5.91324i	0.255613	+	0.276006i
$460$	7.44367			0.347063
$461$	−0.177184	−	0.306891i	−0.00825227	−	0.0142933i	0.861870	−	0.507130i	$-0.169293\pi$
$461$	−0.177184	−	0.306891i	−0.00825227	−	0.0142933i	−0.870122	+	0.492836i	$0.835960\pi$
$462$	4.89588	−	4.77231i	0.227777	−	0.222028i
$463$	5.49903	−	9.52459i	0.255561	−	0.442645i	−0.709486	−	0.704719i	$-0.751073\pi$
$463$	5.49903	−	9.52459i	0.255561	−	0.442645i	0.965048	+	0.262074i	$0.0844064\pi$
$464$	−2.04140	+	3.53581i	−0.0947695	+	0.164146i
$465$	8.87047	+	2.49877i	0.411358	+	0.115878i
$466$	−16.5830	−	28.7226i	−0.768192	−	1.33055i
$467$	0.429641			0.0198814			0.00994072	−	0.999951i	$-0.496836\pi$
$467$	0.429641			0.0198814			0.00994072	+	0.999951i	$0.496836\pi$
$468$	−2.78574	+	1.51477i	−0.128771	+	0.0700203i
$469$	−11.9022			−0.549593
$470$	18.1242	+	31.3921i	0.836008	+	1.44801i
$471$	−1.39853	−	5.49957i	−0.0644407	−	0.253407i
$472$	−9.96261	+	17.2557i	−0.458566	+	0.794260i
$473$	−1.47222	+	2.54996i	−0.0676926	+	0.117247i
$474$	3.87562	+	15.2405i	0.178013	+	0.700019i
$475$	−1.08184	−	1.87381i	−0.0496383	−	0.0859761i
$476$	−0.502019			−0.0230100
$477$	0.674706	−	26.3906i	0.0308927	−	1.20834i
$478$	20.7476			0.948975
$479$	0.666231	+	1.15395i	0.0304409	+	0.0527252i	0.880845	−	0.473406i	$-0.156976\pi$
$479$	0.666231	+	1.15395i	0.0304409	+	0.0527252i	−0.850404	+	0.526131i	$0.823642\pi$
$480$	8.09114	+	2.27923i	0.369308	+	0.104032i
$481$	−7.49663	+	12.9845i	−0.341817	+	0.592044i
$482$	−6.30830	+	10.9263i	−0.287335	+	0.497679i
$483$	−11.0006	+	10.7230i	−0.500546	+	0.487912i
$484$	−0.365308	−	0.632732i	−0.0166049	−	0.0287606i
$485$	10.7061			0.486139
$486$	19.1795	+	6.47748i	0.870002	+	0.293824i
$487$	−17.8776			−0.810113			−0.405057	−	0.914292i	$-0.632748\pi$
$487$	−17.8776			−0.810113			−0.405057	+	0.914292i	$0.632748\pi$
$488$	0.104767	+	0.181461i	0.00474256	+	0.00821435i
$489$	3.65826	−	3.56593i	0.165432	−	0.161257i
$490$	10.6478	−	18.4426i	0.481021	−	0.833152i
$491$	11.4781	−	19.8806i	0.517998	−	0.897199i	−0.481783	−	0.876290i	$-0.660011\pi$
$491$	11.4781	−	19.8806i	0.517998	−	0.897199i	0.999781	−	0.0209087i	$-0.00665593\pi$
$492$	−3.27861	−	0.923568i	−0.147811	−	0.0416376i
$493$	0.966927	+	1.67477i	0.0435482	+	0.0754277i
$494$	3.59367			0.161687
$495$	−0.623848	+	24.4013i	−0.0280399	+	1.09676i
$496$	6.30522			0.283113
$497$	3.03939	+	5.26439i	0.136335	+	0.236140i
$498$	1.67318	+	6.57962i	0.0749770	+	0.294840i
$499$	−4.72216	+	8.17902i	−0.211393	+	0.366143i	−0.952151	−	0.305629i	$-0.901133\pi$
$499$	−4.72216	+	8.17902i	−0.211393	+	0.366143i	0.740758	+	0.671772i	$0.234467\pi$
$500$	1.02409	−	1.77377i	0.0457986	−	0.0793255i
$501$	−10.2091	−	40.1462i	−0.456107	−	1.79360i
$502$	3.83815	+	6.64786i	0.171305	+	0.296709i
$503$	44.4176			1.98048			0.990241	−	0.139366i	$-0.0445066\pi$
$503$	44.4176			1.98048			0.990241	+	0.139366i	$0.0445066\pi$
$504$	−8.17431	+	4.44485i	−0.364113	+	0.197989i
$505$	28.2682			1.25792
$506$	16.4263	+	28.4512i	0.730238	+	1.26481i
$507$	−2.72534	−	0.767715i	−0.121037	−	0.0340954i
$508$	0.979544	−	1.69662i	0.0434602	−	0.0752753i
$509$	−21.3394	+	36.9609i	−0.945852	+	1.63826i	−0.191815	+	0.981431i	$0.561437\pi$
$509$	−21.3394	+	36.9609i	−0.945852	+	1.63826i	−0.754037	+	0.656832i	$0.771896\pi$
$510$	−6.90361	+	6.72937i	−0.305697	+	0.297981i
$511$	−0.979498	−	1.69654i	−0.0433304	−	0.0750505i
$512$	25.4282			1.12378
$513$	2.89814	+	3.12935i	0.127956	+	0.138164i
$514$	−36.8676			−1.62616
$515$	17.5188	+	30.3435i	0.771971	+	1.33709i
$516$	0.388869	−	0.379054i	0.0171190	−	0.0166869i
$517$	14.8710	−	25.7573i	0.654026	−	1.13281i
$518$	−2.98111	+	5.16344i	−0.130983	+	0.226868i
$519$	36.3570	+	10.2416i	1.59590	+	0.449556i
$520$	−13.9944	−	24.2391i	−0.613697	−	1.06295i
$521$	−30.0291			−1.31560			−0.657799	−	0.753194i	$-0.728512\pi$
$521$	−30.0291			−1.31560			−0.657799	+	0.753194i	$0.728512\pi$
$522$	4.14319	+	2.53542i	0.181343	+	0.110972i
$523$	−20.0700			−0.877599			−0.438799	−	0.898585i	$-0.644596\pi$
$523$	−20.0700			−0.877599			−0.438799	+	0.898585i	$0.644596\pi$
$524$	1.81122	+	3.13713i	0.0791237	+	0.137046i
$525$	−1.16157	−	4.56775i	−0.0506949	−	0.199353i
$526$	17.0312	−	29.4989i	0.742596	−	1.28621i
$527$	1.49326	−	2.58641i	0.0650475	−	0.112666i
$528$	4.11587	+	16.1853i	0.179120	+	0.704373i
$529$	−25.4085	−	44.0089i	−1.10472	−	1.91343i
$530$	31.5784			1.37168
$531$	16.9703	+	10.3850i	0.736450	+	0.450670i
$532$	−0.265674			−0.0115184
$533$	10.5729	+	18.3128i	0.457963	+	0.793214i
$534$	33.0507	+	9.31021i	1.43024	+	0.402892i
$535$	14.1004	−	24.4227i	0.609615	−	1.05588i
$536$	17.3200	−	29.9992i	0.748112	−	1.29577i
$537$	−8.59375	+	8.37685i	−0.370848	+	0.361488i
$538$	10.9775	+	19.0136i	0.473274	+	0.819734i
$539$	−17.4732			−0.752625
$540$	1.33099	−	4.30059i	0.0572767	−	0.185068i
$541$	25.4769			1.09534			0.547669	−	0.836695i	$-0.315515\pi$
$541$	25.4769			1.09534			0.547669	+	0.836695i	$0.315515\pi$
$542$	9.71318	+	16.8237i	0.417217	+	0.722641i
$543$	13.6779	−	13.3327i	0.586974	−	0.572159i
$544$	1.36207	−	2.35917i	0.0583982	−	0.101149i
$545$	−6.46656	+	11.2004i	−0.276997	+	0.479773i
$546$	7.53480	+	2.12252i	0.322460	+	0.0908353i
$547$	12.7230	+	22.0368i	0.543994	+	0.942226i	0.998669	+	0.0515683i	$0.0164220\pi$
$547$	12.7230	+	22.0368i	0.543994	+	0.942226i	−0.454675	+	0.890657i	$0.650245\pi$
$548$	6.55629			0.280071
$549$	0.183807	−	0.0999464i	0.00784469	−	0.00426561i
$550$	−10.0792			−0.429779
$551$	0.511708	+	0.886305i	0.0217995	+	0.0377579i
$552$	−11.0189	−	43.3308i	−0.468996	−	1.84428i
$553$	−3.60860	+	6.25028i	−0.153453	+	0.265789i
$554$	0.603015	−	1.04445i	0.0256196	−	0.0443745i
$555$	−5.24605	−	20.6296i	−0.222682	−	0.875677i
$556$	3.48993	+	6.04474i	0.148006	+	0.256354i
$557$	43.3451			1.83659			0.918295	−	0.395898i	$-0.129567\pi$
$557$	43.3451			1.83659			0.918295	+	0.395898i	$0.129567\pi$
$558$	0.191722	−	7.49903i	0.00811622	−	0.317459i
$559$	−3.37124			−0.142588
$560$	−4.67066	−	8.08982i	−0.197371	−	0.341857i
$561$	7.61396	+	2.14481i	0.321462	+	0.0905542i
$562$	11.5568	−	20.0169i	0.487492	−	0.844361i
$563$	19.1697	−	33.2028i	0.807905	−	1.39933i	−0.106407	−	0.994323i	$-0.533935\pi$
$563$	19.1697	−	33.2028i	0.807905	−	1.39933i	0.914312	−	0.405010i	$-0.132732\pi$
$564$	−3.92800	+	3.82886i	−0.165399	+	0.161224i
$565$	−9.50281	−	16.4593i	−0.399786	−	0.692450i
$566$	−2.27783			−0.0957445
$567$	4.22821	+	8.27298i	0.177568	+	0.347433i
$568$	−17.6916			−0.742325
$569$	2.85151	+	4.93897i	0.119542	+	0.207052i	0.919586	−	0.392888i	$-0.128524\pi$
$569$	2.85151	+	4.93897i	0.119542	+	0.207052i	−0.800044	+	0.599941i	$0.795191\pi$
$570$	−3.65347	+	3.56125i	−0.153027	+	0.149165i
$571$	−21.5962	+	37.4056i	−0.903771	+	1.56538i	−0.0812121	+	0.996697i	$0.525879\pi$
$571$	−21.5962	+	37.4056i	−0.903771	+	1.56538i	−0.822559	+	0.568680i	$0.807454\pi$
$572$	−1.55611	+	2.69526i	−0.0650641	+	0.112694i
$573$	42.1885	+	11.8843i	1.76245	+	0.496473i
$574$	4.20442	+	7.28227i	0.175489	+	0.303956i
$575$	22.6472			0.944452
$576$	0.677034	−	26.4816i	0.0282098	−	1.10340i
$577$	1.62734			0.0677469			0.0338735	−	0.999426i	$-0.489216\pi$
$577$	1.62734			0.0677469			0.0338735	+	0.999426i	$0.489216\pi$
$578$	−9.47632	−	16.4135i	−0.394163	−	0.682710i
$579$	9.26975	+	36.4524i	0.385238	+	1.51491i
$580$	0.540098	−	0.935477i	0.0224263	−	0.0388436i
$581$	−1.55791	+	2.69837i	−0.0646328	+	0.111947i
$582$	−2.14776	−	8.44585i	−0.0890274	−	0.350092i
$583$	−12.9551	−	22.4389i	−0.536546	−	0.929325i
$584$	5.70144			0.235927
$585$	−24.5525	+	13.3506i	−1.01512	+	0.551979i
$586$	9.74075			0.402387
$587$	22.8904	+	39.6473i	0.944786	+	1.63642i	0.756179	+	0.654365i	$0.227064\pi$
$587$	22.8904	+	39.6473i	0.944786	+	1.63642i	0.188607	+	0.982053i	$0.439603\pi$
$588$	3.10190	+	0.873789i	0.127920	+	0.0360344i
$589$	0.790251	−	1.36876i	0.0325617	−	0.0563986i
$590$	−11.8995	+	20.6106i	−0.489896	+	0.848524i
$591$	−8.43239	+	8.21956i	−0.346862	+	0.338108i
$592$	−7.28181	−	12.6125i	−0.299281	−	0.518369i
$593$	22.1612			0.910051			0.455026	−	0.890478i	$-0.349630\pi$
$593$	22.1612			0.910051			0.455026	+	0.890478i	$0.349630\pi$
$594$	19.3749	−	4.40301i	0.794961	−	0.180658i
$595$	−4.42460			−0.181391
$596$	1.98446	+	3.43718i	0.0812865	+	0.140792i
$597$	−33.8360	+	32.9820i	−1.38482	+	1.34987i
$598$	−18.8074	+	32.5753i	−0.769091	+	1.33210i
$599$	16.3016	−	28.2351i	0.666063	−	1.15366i	−0.312932	−	0.949775i	$-0.601311\pi$
$599$	16.3016	−	28.2351i	0.666063	−	1.15366i	0.978996	−	0.203880i	$-0.0653554\pi$
$600$	13.2032	+	3.71927i	0.539018	+	0.151839i
$601$	−0.818207	−	1.41718i	−0.0333753	−	0.0578078i	0.848855	−	0.528625i	$-0.177292\pi$
$601$	−0.818207	−	1.41718i	−0.0333753	−	0.0578078i	−0.882231	+	0.470818i	$0.843959\pi$
$602$	−1.34061			−0.0546392
$603$	−29.5030	−	18.0543i	−1.20146	−	0.735230i
$604$	1.18453			0.0481977
$605$	−3.21968	−	5.57666i	−0.130899	−	0.226723i
$606$	−5.67090	−	22.3003i	−0.230365	−	0.905887i
$607$	−4.95802	+	8.58754i	−0.201240	+	0.348557i	−0.948928	−	0.315492i	$-0.897830\pi$
$607$	−4.95802	+	8.58754i	−0.201240	+	0.348557i	0.747688	+	0.664050i	$0.231164\pi$
$608$	0.720822	−	1.24850i	0.0292332	−	0.0506334i
$609$	0.549418	+	2.16053i	0.0222635	+	0.0875492i
$610$	0.125135	+	0.216740i	0.00506657	+	0.00877555i
$611$	34.0533			1.37765
$612$	−1.24440	−	0.761507i	−0.0503017	−	0.0307821i
$613$	26.3963			1.06614			0.533068	−	0.846072i	$-0.321039\pi$
$613$	26.3963			1.06614			0.533068	+	0.846072i	$0.321039\pi$
$614$	15.9459	+	27.6190i	0.643523	+	1.11461i
$615$	−28.8964	−	8.13997i	−1.16522	−	0.328235i
$616$	−4.56614	+	7.90879i	−0.183975	+	0.318654i
$617$	9.98736	−	17.2986i	0.402076	−	0.696416i	−0.591900	−	0.806011i	$-0.701622\pi$
$617$	9.98736	−	17.2986i	0.402076	−	0.696416i	0.993976	+	0.109595i	$0.0349555\pi$
$618$	20.4230	−	19.9075i	0.821532	−	0.800797i
$619$	−18.0421	−	31.2499i	−0.725174	−	1.25604i	−0.958902	−	0.283737i	$-0.908426\pi$
$619$	−18.0421	−	31.2499i	−0.725174	−	1.25604i	0.233728	−	0.972302i	$-0.424907\pi$
$620$	−1.66819			−0.0669960
$621$	−43.5337	+	9.89320i	−1.74695	+	0.397000i
$622$	24.3128			0.974855
$623$	7.87943	+	13.6476i	0.315683	+	0.546779i
$624$	−13.6924	+	13.3468i	−0.548135	+	0.534300i
$625$	15.6158	−	27.0473i	0.624630	−	1.08189i
$626$	−0.713309	+	1.23549i	−0.0285096	+	0.0493800i
$627$	4.02939	+	1.13506i	0.160919	+	0.0453299i
$628$	0.513597	+	0.889576i	0.0204947	+	0.0354979i
$629$	−6.89819			−0.275049
$630$	−9.76354	+	5.30900i	−0.388989	+	0.211516i
$631$	−46.6716			−1.85797			−0.928984	−	0.370120i	$-0.879317\pi$
$631$	−46.6716			−1.85797			−0.928984	+	0.370120i	$0.879317\pi$
$632$	−10.5024	−	18.1908i	−0.417765	−	0.723590i
$633$	−6.73176	−	26.4720i	−0.267564	−	1.05217i
$634$	1.63446	−	2.83097i	0.0649128	−	0.112432i
$635$	8.63332	−	14.9534i	0.342603	−	0.593406i
$636$	1.17772	+	4.63127i	0.0466997	+	0.183642i
$637$	−10.0030	−	17.3257i	−0.396334	−	0.686471i
$638$	4.76744			0.188745
$639$	−0.451491	+	17.6597i	−0.0178607	+	0.698607i
$640$	21.9809			0.868871
$641$	0.383789	+	0.664742i	0.0151588	+	0.0262557i	0.873505	−	0.486815i	$-0.161841\pi$
$641$	0.383789	+	0.664742i	0.0151588	+	0.0262557i	−0.858347	+	0.513070i	$0.828508\pi$
$642$	−22.0953	−	6.22414i	−0.872033	−	0.245647i
$643$	−14.4053	+	24.9507i	−0.568090	+	0.983960i	0.428665	+	0.903463i	$0.358984\pi$
$643$	−14.4053	+	24.9507i	−0.568090	+	0.983960i	−0.996755	+	0.0804966i	$0.974349\pi$
$644$	1.39040	−	2.40824i	0.0547893	−	0.0948979i
$645$	3.42734	−	3.34083i	0.134951	−	0.131545i
$646$	0.826700	+	1.43189i	0.0325261	+	0.0563368i
$647$	−5.46805			−0.214971			−0.107486	−	0.994207i	$-0.534280\pi$
$647$	−5.46805			−0.214971			−0.107486	+	0.994207i	$0.534280\pi$
$648$	−27.0047	−	1.38172i	−1.06084	−	0.0542789i
$649$	19.5272			0.766511
$650$	−5.77012	−	9.99415i	−0.226323	−	0.392003i
$651$	2.46533	−	2.40311i	0.0966240	−	0.0941852i
$652$	−0.462378	+	0.800861i	−0.0181081	+	0.0313642i
$653$	−2.85758	+	4.94948i	−0.111826	+	0.193688i	−0.916506	−	0.400020i	$-0.869003\pi$
$653$	−2.85758	+	4.94948i	−0.111826	+	0.193688i	0.804681	+	0.593708i	$0.202337\pi$
$654$	10.1331	+	2.85443i	0.396234	+	0.111617i
$655$	15.9634	+	27.6495i	0.623743	+	1.08035i
$656$	−20.5398			−0.801946
$657$	0.145501	−	5.69115i	0.00567653	−	0.222033i
$658$	13.5416			0.527908
$659$	−18.2149	−	31.5491i	−0.709552	−	1.22898i	−0.965023	−	0.262163i	$-0.915564\pi$
$659$	−18.2149	−	31.5491i	−0.709552	−	1.22898i	0.255471	−	0.966817i	$-0.417769\pi$
$660$	−1.08895	−	4.28217i	−0.0423871	−	0.166683i
$661$	9.85404	−	17.0677i	0.383278	−	0.663856i	−0.608251	−	0.793745i	$-0.708129\pi$
$661$	9.85404	−	17.0677i	0.383278	−	0.663856i	0.991529	+	0.129888i	$0.0414619\pi$
$662$	−8.79176	+	15.2278i	−0.341701	+	0.591844i
$663$	2.23211	+	8.77756i	0.0866879	+	0.340892i
$664$	−4.53411	−	7.85331i	−0.175958	−	0.304768i
$665$	−2.34155			−0.0908013
$666$	−15.2219	+	8.27703i	−0.589836	+	0.320728i
$667$	−10.7120			−0.414772
$668$	3.74919	+	6.49379i	0.145061	+	0.251252i
$669$	35.3291	+	9.95203i	1.36590	+	0.384768i
$670$	20.6874	−	35.8316i	0.799223	−	1.38429i
$671$	0.102674	−	0.177836i	0.00396368	−	0.00686530i
$672$	2.24874	−	2.19198i	0.0867469	−	0.0845574i
$673$	1.68997	+	2.92712i	0.0651437	+	0.112832i	0.896758	−	0.442522i	$-0.145916\pi$
$673$	1.68997	+	2.92712i	0.0651437	+	0.112832i	−0.831614	+	0.555354i	$0.812583\pi$
$674$	3.17075			0.122133
$675$	4.04950	−	13.0844i	0.155865	−	0.503620i
$676$	0.512530			0.0197127
$677$	8.48897	+	14.7033i	0.326258	+	0.565095i	0.981766	−	0.190093i	$-0.0608790\pi$
$677$	8.48897	+	14.7033i	0.326258	+	0.565095i	−0.655508	+	0.755188i	$0.727546\pi$
$678$	−11.0781	+	10.7985i	−0.425453	+	0.414714i
$679$	1.99979	−	3.46373i	0.0767447	−	0.132926i
$680$	6.43866	−	11.1521i	0.246911	−	0.427663i
$681$	2.59077	+	0.729808i	0.0992786	+	0.0279663i
$682$	−3.68127	−	6.37615i	−0.140963	−	0.244155i
$683$	−10.3202			−0.394890			−0.197445	−	0.980314i	$-0.563264\pi$
$683$	−10.3202			−0.394890			−0.197445	+	0.980314i	$0.563264\pi$
$684$	−0.658548	−	0.402998i	−0.0251802	−	0.0154090i
$685$	57.7846			2.20784
$686$	−8.66994	−	15.0168i	−0.331020	−	0.573343i
$687$	−0.845572	−	3.32513i	−0.0322606	−	0.126862i
$688$	1.63732	−	2.83592i	0.0624223	−	0.108119i
$689$	14.8330	−	25.6915i	0.565093	−	0.978770i
$690$	−13.1612	−	51.7551i	−0.501037	−	1.97028i
$691$	−2.11921	−	3.67057i	−0.0806184	−	0.139635i	0.822897	−	0.568190i	$-0.192356\pi$
$691$	−2.11921	−	3.67057i	−0.0806184	−	0.139635i	−0.903516	+	0.428555i	$0.859023\pi$
$692$	−6.83733			−0.259916
$693$	7.77798	+	4.75973i	0.295461	+	0.180807i
$694$	−2.44064			−0.0926453
$695$	30.7589	+	53.2760i	1.16675	+	2.02087i
$696$	−6.24507	−	1.75920i	−0.236719	−	0.0666825i
$697$	−4.86444	+	8.42546i	−0.184254	+	0.319137i
$698$	15.6725	−	27.1456i	0.593214	−	1.02748i
$699$	31.6759	−	30.8764i	1.19809	−	1.16785i
$700$	0.426576	+	0.738850i	0.0161230	+	0.0279259i
$701$	−4.89904			−0.185034			−0.0925171	−	0.995711i	$-0.529491\pi$
$701$	−4.89904			−0.185034			−0.0925171	+	0.995711i	$0.529491\pi$
$702$	15.4575	+	16.6907i	0.583407	+	0.629951i
$703$	−3.65060			−0.137685
$704$	−12.9998	−	22.5163i	−0.489949	−	0.848617i
$705$	−34.6199	+	33.7461i	−1.30386	+	1.27095i
$706$	−8.80111	+	15.2440i	−0.331234	+	0.573715i
$707$	5.28020	−	9.14558i	0.198582	−	0.343955i
$708$	−3.46653	−	0.976504i	−0.130280	−	0.0366993i
$709$	17.1625	+	29.7264i	0.644552	+	1.11640i	0.984405	+	0.175918i	$0.0562894\pi$
$709$	17.1625	+	29.7264i	0.644552	+	1.11640i	−0.339853	+	0.940479i	$0.610377\pi$
$710$	−21.1312			−0.793041
$711$	−18.4259	+	10.0192i	−0.691027	+	0.375751i
$712$	−45.8644			−1.71884
$713$	8.27151	+	14.3267i	0.309770	+	0.536538i
$714$	0.887622	+	3.49049i	0.0332184	+	0.130628i
$715$	−13.7149	+	23.7549i	−0.512909	+	0.888385i
$716$	1.08619	−	1.88133i	0.0405927	−	0.0703086i
$717$	6.81985	+	26.8184i	0.254692	+	1.00155i
$718$	−2.26801	−	3.92831i	−0.0846413	−	0.146603i
$719$	−13.6554			−0.509260			−0.254630	−	0.967039i	$-0.581954\pi$
$719$	−13.6554			−0.509260			−0.254630	+	0.967039i	$0.581954\pi$
$720$	0.693810	−	27.1378i	0.0258568	−	1.01137i
$721$	13.0893			0.487471
$722$	−11.8996	−	20.6107i	−0.442857	−	0.767051i
$723$	−16.1969	−	4.56258i	−0.602369	−	0.169684i
$724$	−1.72878	+	2.99434i	−0.0642497	+	0.111284i
$725$	1.64323	−	2.84616i	0.0610282	−	0.105704i
$726$	−3.75342	+	3.65869i	−0.139303	+	0.135787i
$727$	−19.1619	−	33.1895i	−0.710677	−	1.23093i	−0.964603	−	0.263705i	$-0.915055\pi$
$727$	−19.1619	−	33.1895i	−0.710677	−	1.23093i	0.253926	−	0.967224i	$-0.418278\pi$
$728$	−10.4561			−0.387527
$729$	−2.06838	+	26.9207i	−0.0766067	+	0.997061i
$730$	6.80990			0.252046
$731$	−0.775532	−	1.34326i	−0.0286841	−	0.0496823i
$732$	−0.0271201	+	0.0264356i	−0.00100239	+	0.000977088i
$733$	−2.13197	+	3.69269i	−0.0787463	+	0.136393i	−0.902709	−	0.430251i	$-0.858425\pi$
$733$	−2.13197	+	3.69269i	−0.0787463	+	0.136393i	0.823963	+	0.566644i	$0.191758\pi$
$734$	18.9571	−	32.8346i	0.699718	−	1.21195i
$735$	27.3389	+	7.70123i	1.00841	+	0.284064i
$736$	7.54480	+	13.0680i	0.278105	+	0.481692i
$737$	−33.9482			−1.25050
$738$	−0.624551	+	24.4288i	−0.0229900	+	0.899237i
$739$	−33.6314			−1.23715			−0.618576	−	0.785725i	$-0.712290\pi$
$739$	−33.6314			−1.23715			−0.618576	+	0.785725i	$0.712290\pi$
$740$	1.92657	+	3.33691i	0.0708220	+	0.122667i
$741$	1.18126	+	4.64518i	0.0433946	+	0.170645i
$742$	5.89851	−	10.2165i	0.216541	−	0.375060i
$743$	−8.45867	+	14.6508i	−0.310318	+	0.537487i	−0.978431	−	0.206573i	$-0.933769\pi$
$743$	−8.45867	+	14.6508i	−0.310318	+	0.537487i	0.668113	+	0.744060i	$0.267102\pi$
$744$	2.46943	+	9.71079i	0.0905336	+	0.356015i
$745$	17.4902	+	30.2939i	0.640792	+	1.10988i
$746$	7.68266			0.281282
$747$	−7.95484	+	4.32551i	−0.291052	+	0.158262i
$748$	−1.43189			−0.0523550
$749$	−5.26762	−	9.12379i	−0.192475	−	0.333376i
$750$	−14.1435	−	3.98417i	−0.516449	−	0.145481i
$751$	4.64235	−	8.04079i	0.169402	−	0.293412i	−0.768808	−	0.639480i	$-0.779150\pi$
$751$	4.64235	−	8.04079i	0.169402	−	0.293412i	0.938210	+	0.346067i	$0.112483\pi$
$752$	−16.5387	+	28.6459i	−0.603106	+	1.04461i
$753$	−7.33141	+	7.14637i	−0.267172	+	0.260428i
$754$	2.72925	+	4.72720i	0.0993935	+	0.172155i
$755$	10.4400			0.379949
$756$	−1.14275	−	1.23392i	−0.0415614	−	0.0448771i
$757$	−34.5024			−1.25401			−0.627005	−	0.779015i	$-0.715719\pi$
$757$	−34.5024			−1.25401			−0.627005	+	0.779015i	$0.715719\pi$
$758$	5.23505	+	9.06737i	0.190146	+	0.329342i
$759$	−31.3766	+	30.5847i	−1.13890	+	1.11015i
$760$	3.40741	−	5.90181i	0.123600	−	0.214081i
$761$	7.97924	−	13.8204i	0.289247	−	0.500991i	−0.684383	−	0.729123i	$-0.739928\pi$
$761$	7.97924	−	13.8204i	0.289247	−	0.500991i	0.973630	+	0.228132i	$0.0732617\pi$
$762$	−13.5284	−	3.81087i	−0.490081	−	0.138053i
$763$	2.41577	+	4.18424i	0.0874567	+	0.151480i
$764$	−7.93401			−0.287042
$765$	−10.9676	−	6.71163i	−0.396535	−	0.242660i
$766$	−6.02341			−0.217635
$767$	11.1789	+	19.3624i	0.403647	+	0.699136i
$768$	3.12900	+	12.3045i	0.112908	+	0.444000i
$769$	7.85906	−	13.6123i	0.283405	−	0.490872i	−0.688816	−	0.724936i	$-0.741869\pi$
$769$	7.85906	−	13.6123i	0.283405	−	0.490872i	0.972221	+	0.234064i	$0.0752026\pi$
$770$	−5.45388	+	9.44640i	−0.196544	+	0.340425i
$771$	−12.1185	−	47.6550i	−0.436439	−	1.71625i
$772$	−3.40424	−	5.89631i	−0.122521	−	0.212213i
$773$	0.818514			0.0294399			0.0147200	−	0.999892i	$-0.495314\pi$
$773$	0.818514			0.0294399			0.0147200	+	0.999892i	$0.495314\pi$
$774$	−3.32308	−	2.03356i	−0.119446	−	0.0730947i
$775$	−5.07542			−0.182314
$776$	5.82016	+	10.0808i	0.208931	+	0.361880i
$777$	−7.65417	−	2.15614i	−0.274592	−	0.0773511i
$778$	−11.7786	+	20.4011i	−0.422283	+	0.731415i
$779$	−2.57432	+	4.45885i	−0.0922345	+	0.159755i
$780$	3.62263	−	3.53120i	0.129711	−	0.126437i
$781$	8.66914	+	15.0154i	0.310206	+	0.537293i
$782$	−17.3060			−0.618863
$783$	−1.91540	+	6.18890i	−0.0684509	+	0.221173i
$784$	19.4328			0.694028
$785$	4.52664	+	7.84037i	0.161563	+	0.279835i
$786$	18.6097	−	18.1400i	0.663787	−	0.647034i
$787$	−18.3210	+	31.7329i	−0.653074	+	1.13116i	0.329299	+	0.944226i	$0.393188\pi$
$787$	−18.3210	+	31.7329i	−0.653074	+	1.13116i	−0.982373	+	0.186932i	$0.940146\pi$
$788$	1.06579	−	1.84601i	0.0379673	−	0.0657612i
$789$	43.7285	+	12.3181i	1.55678	+	0.438536i
$790$	−12.5443	−	21.7274i	−0.446306	−	0.773025i
$791$	−7.10009			−0.252450
$792$	−23.3152	+	12.6778i	−0.828471	+	0.450488i
$793$	0.235114			0.00834914
$794$	21.0972	+	36.5414i	0.748712	+	1.29681i
$795$	10.3800	+	40.8183i	0.368140	+	1.44767i
$796$	4.27663	−	7.40733i	0.151581	−	0.262546i
$797$	−6.01770	+	10.4230i	−0.213158	+	0.369200i	−0.952701	−	0.303909i	$-0.901708\pi$
$797$	−6.01770	+	10.4230i	−0.213158	+	0.369200i	0.739543	+	0.673109i	$0.235042\pi$
$798$	0.469739	+	1.84720i	0.0166286	+	0.0653903i
$799$	7.83372	+	13.5684i	0.277137	+	0.480016i
$800$	−4.62951			−0.163678
$801$	−1.17046	+	45.7816i	−0.0413562	+	1.61761i
$802$	−6.43367			−0.227181
$803$	−2.79378	−	4.83897i	−0.0985904	−	0.170764i
$804$	6.02658	+	1.69766i	0.212541	+	0.0598718i
$805$	12.2544	−	21.2253i	0.431912	−	0.748093i
$806$	4.21489	−	7.30040i	0.148463	−	0.257146i
$807$	−20.9686	+	20.4394i	−0.738130	+	0.719500i
$808$	15.3674	+	26.6172i	0.540625	+	0.936390i
$809$	−8.87248			−0.311940			−0.155970	−	0.987762i	$-0.549850\pi$
$809$	−8.87248			−0.311940			−0.155970	+	0.987762i	$0.549850\pi$
$810$	−32.2549	−	1.65035i	−1.13332	−	0.0579873i
$811$	9.69230			0.340343			0.170171	−	0.985414i	$-0.445568\pi$
$811$	9.69230			0.340343			0.170171	+	0.985414i	$0.445568\pi$
$812$	−0.201769	−	0.349474i	−0.00708070	−	0.0122641i
$813$	−18.5536	+	18.0853i	−0.650702	+	0.634279i
$814$	−8.50290	+	14.7275i	−0.298027	+	0.516197i
$815$	−4.07522	+	7.05848i	−0.142749	+	0.247248i
$816$	−8.46784	−	2.38535i	−0.296434	−	0.0835039i
$817$	−0.410420	−	0.710869i	−0.0143588	−	0.0248701i
$818$	−35.2804			−1.23355
$819$	−0.266839	+	10.4372i	−0.00932409	+	0.364704i
$820$	5.43428			0.189773
$821$	−5.13985	−	8.90248i	−0.179382	−	0.310699i	0.762287	−	0.647239i	$-0.224076\pi$
$821$	−5.13985	−	8.90248i	−0.179382	−	0.310699i	−0.941669	+	0.336540i	$0.890743\pi$
$822$	−11.5922	−	45.5852i	−0.404325	−	1.58997i
$823$	−20.9587	+	36.3015i	−0.730573	+	1.26539i	0.226066	+	0.974112i	$0.427413\pi$
$823$	−20.9587	+	36.3015i	−0.730573	+	1.26539i	−0.956639	+	0.291277i	$0.905920\pi$
$824$	−19.0475	+	32.9912i	−0.663551	+	1.14930i
$825$	−3.31309	−	13.0284i	−0.115347	−	0.453591i
$826$	4.44541	+	7.69967i	0.154675	+	0.267906i
$827$	27.5477			0.957927			0.478963	−	0.877835i	$-0.341013\pi$
$827$	27.5477			0.957927			0.478963	+	0.877835i	$0.341013\pi$
$828$	7.09953	−	3.86042i	0.246726	−	0.134159i
$829$	−23.3262			−0.810154			−0.405077	−	0.914283i	$-0.632755\pi$
$829$	−23.3262			−0.810154			−0.405077	+	0.914283i	$0.632755\pi$
$830$	−5.41562	−	9.38014i	−0.187979	−	0.325589i
$831$	1.54827	+	0.436140i	0.0537090	+	0.0151295i
$832$	14.8842	−	25.7802i	0.516017	−	0.893767i
$833$	4.60226	−	7.97134i	0.159459	−	0.276191i
$834$	35.8579	−	34.9529i	1.24166	−	1.21032i
$835$	33.0439	+	57.2338i	1.14353	+	1.98066i
$836$	−0.757771			−0.0262081
$837$	9.75627	−	2.21715i	0.337226	−	0.0766359i
$838$	−1.53547			−0.0530421
$839$	−4.31079	−	7.46651i	−0.148825	−	0.257773i	0.781968	−	0.623318i	$-0.214216\pi$
$839$	−4.31079	−	7.46651i	−0.148825	−	0.257773i	−0.930793	+	0.365545i	$0.880882\pi$
$840$	10.6300	−	10.3617i	0.366771	−	0.357514i
$841$	13.7228	−	23.7685i	0.473198	−	0.819604i
$842$	16.7355	−	28.9868i	0.576745	−	0.998951i
$843$	29.6726	+	8.35862i	1.02198	+	0.287886i
$844$	2.47218	+	4.28195i	0.0850961	+	0.147391i
$845$	4.51724			0.155398
$846$	33.5668	+	20.5412i	1.15405	+	0.706220i
$847$	−2.40561			−0.0826577
$848$	14.4080	+	24.9554i	0.494772	+	0.856971i
$849$	−0.748735	−	2.94433i	−0.0256965	−	0.101049i
$850$	2.65476	−	4.59817i	0.0910574	−	0.157716i
$851$	19.1053	−	33.0914i	0.654922	−	1.13436i
$852$	−0.788091	−	3.09909i	−0.0269996	−	0.106173i
$853$	−21.3858	−	37.0412i	−0.732235	−	1.26827i	−0.955926	−	0.293608i	$-0.905144\pi$
$853$	−21.3858	−	37.0412i	−0.732235	−	1.26827i	0.223691	−	0.974660i	$-0.428189\pi$
$854$	0.0934955			0.00319935
$855$	−5.80419	−	3.55187i	−0.198499	−	0.121471i
$856$	30.6617			1.04799
$857$	−22.2710	−	38.5744i	−0.760762	−	1.31768i	−0.942458	−	0.334323i	$-0.891492\pi$
$857$	−22.2710	−	38.5744i	−0.760762	−	1.31768i	0.181697	−	0.983355i	$-0.441841\pi$
$858$	21.4912	+	6.05396i	0.733698	+	0.206679i
$859$	15.9851	−	27.6871i	0.545406	−	0.944671i	−0.453175	−	0.891422i	$-0.649709\pi$
$859$	15.9851	−	27.6871i	0.545406	−	0.944671i	0.998581	−	0.0532497i	$-0.0169579\pi$
$860$	−0.433190	+	0.750307i	−0.0147717	+	0.0255853i
$861$	−8.03105	+	7.82835i	−0.273697	+	0.266789i
$862$	−6.10181	−	10.5687i	−0.207829	−	0.359970i
$863$	−39.0037			−1.32770			−0.663851	−	0.747865i	$-0.731079\pi$
$863$	−39.0037			−1.32770			−0.663851	+	0.747865i	$0.731079\pi$
$864$	8.89912	−	2.02236i	0.302754	−	0.0688020i
$865$	−60.2616			−2.04896
$866$	−14.0085	−	24.2634i	−0.476028	−	0.824504i
$867$	18.1011	−	17.6443i	0.614747	−	0.599231i
$868$	−0.311600	+	0.539706i	−0.0105764	+	0.0183188i
$869$	−10.2927	+	17.8274i	−0.349155	+	0.604754i
$870$	−7.45922	−	2.10123i	−0.252891	−	0.0712382i
$871$	−19.4346	−	33.6617i	−0.658515	−	1.14058i
$872$	−14.0617			−0.476188
$873$	10.2111	−	5.55238i	0.345594	−	0.187920i
$874$	−9.15855			−0.309792
$875$	−3.37189	−	5.84028i	−0.113991	−	0.197437i
$876$	0.253976	+	0.998737i	0.00858106	+	0.0337442i
$877$	25.0560	−	43.3983i	0.846082	−	1.46546i	−0.0385964	−	0.999255i	$-0.512289\pi$
$877$	25.0560	−	43.3983i	0.846082	−	1.46546i	0.884678	−	0.466202i	$-0.154378\pi$
$878$	1.36263	−	2.36014i	0.0459865	−	0.0796510i
$879$	3.20183	+	12.5909i	0.107995	+	0.424680i
$880$	−13.3219	−	23.0743i	−0.449082	−	0.777833i
$881$	−30.9354			−1.04224			−0.521120	−	0.853483i	$-0.674486\pi$
$881$	−30.9354			−1.04224			−0.521120	+	0.853483i	$0.674486\pi$
$882$	0.590889	−	23.1121i	0.0198963	−	0.778226i
$883$	35.3840			1.19077			0.595383	−	0.803442i	$-0.297000\pi$
$883$	35.3840			1.19077			0.595383	+	0.803442i	$0.297000\pi$
$884$	−0.819723	−	1.41980i	−0.0275703	−	0.0477531i
$885$	−30.5527	−	8.60653i	−1.02702	−	0.289305i
$886$	23.6435	−	40.9517i	0.794318	−	1.37580i
$887$	−24.4733	+	42.3890i	−0.821733	+	1.42328i	0.0826579	+	0.996578i	$0.473659\pi$
$887$	−24.4733	+	42.3890i	−0.821733	+	1.42328i	−0.904391	+	0.426705i	$0.859674\pi$
$888$	16.5728	−	16.1545i	0.556147	−	0.542110i
$889$	−3.22522	−	5.58625i	−0.108171	−	0.187357i
$890$	−54.7813			−1.83627
$891$	12.0599	+	23.5967i	0.404023	+	0.790518i
$892$	−6.64402			−0.222458
$893$	4.14569	+	7.18055i	0.138730	+	0.240288i
$894$	20.3896	−	19.8750i	0.681931	−	0.664719i
$895$	9.57322	−	16.5813i	0.319998	−	0.554252i
$896$	4.10580	−	7.11145i	0.137165	−	0.237577i
$897$	−48.2889	−	13.6027i	−1.61232	−	0.454183i
$898$	5.05681	+	8.75865i	0.168748	+	0.292280i
$899$	2.40066			0.0800664
$900$	−0.0633662	+	2.47852i	−0.00211221	+	0.0826173i
$901$	13.6489			0.454712
$902$	11.9921	+	20.7709i	0.399293	+	0.691596i
$903$	−0.440665	−	1.73287i	−0.0146644	−	0.0576664i
$904$	10.3320	−	17.8956i	0.343638	−	0.595198i
$905$	−15.2368	+	26.3909i	−0.506489	+	0.877265i
$906$	−2.09437	−	8.23590i	−0.0695807	−	0.273619i
$907$	−14.1919	−	24.5811i	−0.471234	−	0.816202i	0.528224	−	0.849105i	$-0.322858\pi$
$907$	−14.1919	−	24.5811i	−0.471234	−	0.816202i	−0.999459	+	0.0329029i	$0.989525\pi$
$908$	−0.487223			−0.0161691
$909$	26.9613	−	14.6604i	0.894250	−	0.486256i
$910$	−12.4889			−0.414003
$911$	−2.89932	−	5.02177i	−0.0960588	−	0.166379i	0.813991	−	0.580877i	$-0.197290\pi$
$911$	−2.89932	−	5.02177i	−0.0960588	−	0.166379i	−0.910050	+	0.414499i	$0.863957\pi$
$912$	−4.48128	−	1.26235i	−0.148390	−	0.0418007i
$913$	−4.44355	+	7.69645i	−0.147060	+	0.254715i
$914$	−15.3250	+	26.5436i	−0.506905	+	0.877984i
$915$	−0.239026	+	0.232993i	−0.00790195	+	0.00770251i
$916$	0.310529	+	0.537852i	0.0102602	+	0.0177711i
$917$	11.9272			0.393871
$918$	−3.09446	+	9.99859i	−0.102132	+	0.330003i
$919$	−46.2912			−1.52701			−0.763503	−	0.645804i	$-0.776522\pi$
$919$	−46.2912			−1.52701			−0.763503	+	0.645804i	$0.776522\pi$
$920$	35.6651	+	61.7738i	1.17585	+	2.03662i
$921$	−30.4589	+	29.6901i	−1.00365	+	0.978323i
$922$	0.230098	−	0.398542i	0.00757788	−	0.0131253i
$923$	−9.92577	+	17.1919i	−0.326711	+	0.565879i
$924$	−1.58881	−	0.447559i	−0.0522680	−	0.0147236i
$925$	5.86153	+	10.1525i	0.192726	+	0.333811i
$926$	14.2825			0.469353
$927$	32.4456	+	19.8550i	1.06565	+	0.652125i
$928$	2.18974			0.0718819
$929$	−21.1201	−	36.5811i	−0.692928	−	1.20019i	−0.970874	−	0.239589i	$-0.922987\pi$
$929$	−21.1201	−	36.5811i	−0.692928	−	1.20019i	0.277947	−	0.960596i	$-0.410346\pi$
$930$	2.94953	+	11.5987i	0.0967188	+	0.380338i
$931$	2.43557	−	4.21852i	0.0798224	−	0.138256i
$932$	−4.00360	+	6.93444i	−0.131142	+	0.227145i
$933$	7.99174	+	31.4267i	0.261638	+	1.02887i
$934$	0.278975	+	0.483199i	0.00912835	+	0.0158108i
$935$	−12.6201			−0.412722
$936$	−25.9183	−	15.8607i	−0.847166	−	0.518422i
$937$	34.2767			1.11977			0.559886	−	0.828570i	$-0.310845\pi$
$937$	34.2767			1.11977			0.559886	+	0.828570i	$0.310845\pi$
$938$	−7.72836	−	13.3859i	−0.252340	−	0.437066i
$939$	−1.83146	−	0.515913i	−0.0597674	−	0.0168362i
$940$	4.37569	−	7.57892i	0.142719	−	0.247197i
$941$	15.2021	−	26.3309i	0.495576	−	0.858362i	−0.504411	−	0.863463i	$-0.668291\pi$
$941$	15.2021	−	26.3309i	0.495576	−	0.858362i	0.999987	+	0.00510142i	$0.00162384\pi$
$942$	5.27704	−	5.14385i	0.171935	−	0.167596i
$943$	−26.9452	−	46.6705i	−0.877457	−	1.51980i
$944$	−21.7171			−0.706833
$945$	−10.0717	−	10.8753i	−0.327634	−	0.353772i
$946$	−3.82377			−0.124321
$947$	−18.1345	−	31.4099i	−0.589293	−	1.02068i	−0.994325	−	0.106383i	$-0.966073\pi$
$947$	−18.1345	−	31.4099i	−0.589293	−	1.02068i	0.405033	−	0.914302i	$-0.367260\pi$
$948$	2.71869	−	2.65007i	0.0882988	−	0.0860702i
$949$	3.19875	−	5.54040i	0.103836	−	0.179849i
$950$	1.40493	−	2.43340i	0.0455818	−	0.0789501i
$951$	4.19657	+	1.18215i	0.136083	+	0.0383339i
$952$	−2.40534	−	4.16618i	−0.0779577	−	0.135027i
$953$	−21.1687			−0.685722			−0.342861	−	0.939386i	$-0.611396\pi$
$953$	−21.1687			−0.685722			−0.342861	+	0.939386i	$0.611396\pi$
$954$	30.1184	−	16.3771i	0.975121	−	0.530230i
$955$	−69.9273			−2.26279
$956$	−2.50453	−	4.33797i	−0.0810023	−	0.140300i
$957$	1.56708	+	6.16240i	0.0506565	+	0.199202i
$958$	−0.865196	+	1.49856i	−0.0279532	+	0.0484164i
$959$	10.7936	−	18.6950i	0.348542	−	0.603692i
$960$	10.4158	+	40.9591i	0.336168	+	1.32195i
$961$	13.6463	+	23.6361i	0.440203	+	0.762454i
$962$	−19.4709			−0.627766
$963$	0.782486	−	30.6063i	0.0252153	−	0.986275i
$964$	3.04600			0.0981051
$965$	−30.0036	−	51.9678i	−0.965851	−	1.67290i
$966$	−19.2026	−	5.40928i	−0.617834	−	0.174041i
$967$	1.59049	−	2.75482i	0.0511468	−	0.0885889i	−0.839318	−	0.543640i	$-0.817046\pi$
$967$	1.59049	−	2.75482i	0.0511468	−	0.0885889i	0.890465	+	0.455051i	$0.150379\pi$
$968$	3.50063	−	6.06327i	0.112515	−	0.194881i
$969$	−1.57912	+	1.53926i	−0.0507285	+	0.0494482i
$970$	6.95170	+	12.0407i	0.223206	+	0.386603i
$971$	−23.4998			−0.754145			−0.377072	−	0.926184i	$-0.623069\pi$
$971$	−23.4998			−0.754145			−0.377072	+	0.926184i	$0.623069\pi$
$972$	−0.960911	−	4.79204i	−0.0308212	−	0.153705i
$973$	22.9817			0.736760
$974$	−11.6083	−	20.1062i	−0.371955	−	0.644245i
$975$	11.0218	−	10.7436i	0.352979	−	0.344070i
$976$	−0.114188	+	0.197780i	−0.00365508	+	0.00633079i
$977$	−20.2314	+	35.0418i	−0.647260	+	1.12109i	0.336515	+	0.941678i	$0.390752\pi$
$977$	−20.2314	+	35.0418i	−0.647260	+	1.12109i	−0.983775	+	0.179409i	$0.942582\pi$
$978$	6.38584	+	1.79886i	0.204197	+	0.0575211i
$979$	22.4742	+	38.9264i	0.718278	+	1.24409i
$980$	−5.14138			−0.164235
$981$	−0.358854	+	14.0363i	−0.0114573	+	0.448144i
$982$	29.8118			0.951333
$983$	−20.9320	−	36.2552i	−0.667626	−	1.15636i	−0.978566	−	0.205933i	$-0.933977\pi$
$983$	−20.9320	−	36.2552i	−0.667626	−	1.15636i	0.310940	−	0.950430i	$-0.399356\pi$
$984$	−8.04439	−	31.6338i	−0.256446	−	1.00845i
$985$	9.39348	−	16.2700i	0.299301	−	0.518405i
$986$	−1.25569	+	2.17492i	−0.0399894	+	0.0692636i
$987$	4.45120	+	17.5039i	0.141683	+	0.557156i
$988$	−0.433807	−	0.751375i	−0.0138012	−	0.0239044i
$989$	8.59169			0.273200
$990$	−27.8481	+	15.1427i	−0.885072	+	0.481265i
$991$	−18.0897			−0.574638			−0.287319	−	0.957835i	$-0.592764\pi$
$991$	−18.0897			−0.574638			−0.287319	+	0.957835i	$0.592764\pi$
$992$	−1.69085	−	2.92864i	−0.0536846	−	0.0929845i
$993$	−22.5733	−	6.35879i	−0.716343	−	0.201790i
$994$	−3.94709	+	6.83655i	−0.125194	+	0.216842i
$995$	37.6925	−	65.2854i	1.19493	−	2.06968i
$996$	1.17371	−	1.14409i	0.0371904	−	0.0362518i
$997$	18.6698	+	32.3370i	0.591278	+	1.02412i	0.994061	+	0.108828i	$0.0347096\pi$
$997$	18.6698	+	32.3370i	0.591278	+	1.02412i	−0.402783	+	0.915296i	$0.631957\pi$
$998$	−12.2648			−0.388235
$999$	−15.7024	−	16.9551i	−0.496802	−	0.536437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.f.c.130.14	✓	38
3.2	odd	2		1161.2.f.c.388.6		38
9.2	odd	6		1161.2.f.c.775.6		38
9.4	even	3		3483.2.a.s.1.6		19
9.5	odd	6		3483.2.a.r.1.14		19
9.7	even	3	inner	387.2.f.c.259.14	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.f.c.130.14	✓	38	1.1	even	1	trivial
387.2.f.c.259.14	yes	38	9.7	even	3	inner
1161.2.f.c.388.6		38	3.2	odd	2
1161.2.f.c.775.6		38	9.2	odd	6
3483.2.a.r.1.14		19	9.5	odd	6
3483.2.a.s.1.6		19	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.649321 + 1.12466i) q^{2} +(-1.24030 + 1.20899i) q^{3} +(0.156764 - 0.271524i) q^{4} +(1.38166 - 2.39311i) q^{5} +(-2.16505 - 0.609884i) q^{6} +(-0.516159 - 0.894013i) q^{7} +3.00445 q^{8} +(0.0766735 - 2.99902i) q^{9} +O(q^{10})\)	\(q+(0.649321 + 1.12466i) q^{2} +(-1.24030 + 1.20899i) q^{3} +(0.156764 - 0.271524i) q^{4} +(1.38166 - 2.39311i) q^{5} +(-2.16505 - 0.609884i) q^{6} +(-0.516159 - 0.894013i) q^{7} +3.00445 q^{8} +(0.0766735 - 2.99902i) q^{9} +3.58856 q^{10} +(-1.47222 - 2.54996i) q^{11} +(0.133836 + 0.526297i) q^{12} +(1.68562 - 2.91958i) q^{13} +(0.670305 - 1.16100i) q^{14} +(1.17958 + 4.63858i) q^{15} +(1.63732 + 2.83592i) q^{16} +1.55106 q^{17} +(3.42265 - 1.86110i) q^{18} +0.820840 q^{19} +(-0.433190 - 0.750307i) q^{20} +(1.72105 + 0.484810i) q^{21} +(1.91188 - 3.31148i) q^{22} +(-4.29584 + 7.44062i) q^{23} +(-3.72641 + 3.63235i) q^{24} +(-1.31797 - 2.28279i) q^{25} +4.37804 q^{26} +(3.53070 + 3.81237i) q^{27} -0.323661 q^{28} +(0.623396 + 1.07975i) q^{29} +(-4.45089 + 4.33855i) q^{30} +(0.962734 - 1.66750i) q^{31} +(0.878152 - 1.52100i) q^{32} +(4.90886 + 1.38280i) q^{33} +(1.00714 + 1.74442i) q^{34} -2.85262 q^{35} +(-0.802286 - 0.490958i) q^{36} -4.44739 q^{37} +(0.532989 + 0.923164i) q^{38} +(1.43908 + 5.65905i) q^{39} +(4.15112 - 7.18996i) q^{40} +(-3.13620 + 5.43205i) q^{41} +(0.572266 + 2.25038i) q^{42} +(-0.500000 - 0.866025i) q^{43} -0.923165 q^{44} +(-7.07104 - 4.32711i) q^{45} -11.1575 q^{46} +(5.05055 + 8.74780i) q^{47} +(-5.45938 - 1.53788i) q^{48} +(2.96716 - 5.13927i) q^{49} +(1.71157 - 2.96453i) q^{50} +(-1.92378 + 1.87523i) q^{51} +(-0.528491 - 0.915373i) q^{52} +8.79973 q^{53} +(-1.99506 + 6.44628i) q^{54} -8.13642 q^{55} +(-1.55077 - 2.68601i) q^{56} +(-1.01809 + 0.992390i) q^{57} +(-0.809568 + 1.40221i) q^{58} +(-3.31596 + 5.74341i) q^{59} +(1.44440 + 0.406880i) q^{60} +(0.0348705 + 0.0603975i) q^{61} +2.50049 q^{62} +(-2.72074 + 1.47942i) q^{63} +8.83009 q^{64} +(-4.65791 - 8.06774i) q^{65} +(1.63225 + 6.41867i) q^{66} +(5.76481 - 9.98494i) q^{67} +(0.243152 - 0.421151i) q^{68} +(-3.66753 - 14.4222i) q^{69} +(-1.85227 - 3.20822i) q^{70} -5.88849 q^{71} +(0.230361 - 9.01039i) q^{72} +1.89767 q^{73} +(-2.88779 - 5.00179i) q^{74} +(4.39455 + 1.23792i) q^{75} +(0.128678 - 0.222878i) q^{76} +(-1.51980 + 2.63236i) q^{77} +(-5.43007 + 5.29302i) q^{78} +(-3.49563 - 6.05462i) q^{79} +9.04889 q^{80} +(-8.98824 - 0.459891i) q^{81} -8.14560 q^{82} +(-1.50913 - 2.61390i) q^{83} +(0.401436 - 0.391304i) q^{84} +(2.14304 - 3.71186i) q^{85} +(0.649321 - 1.12466i) q^{86} +(-2.07861 - 0.585534i) q^{87} +(-4.42320 - 7.66120i) q^{88} -15.2655 q^{89} +(0.275148 - 10.7622i) q^{90} -3.48019 q^{91} +(1.34687 + 2.33285i) q^{92} +(0.821924 + 3.23214i) q^{93} +(-6.55885 + 11.3603i) q^{94} +(1.13412 - 1.96436i) q^{95} +(0.749713 + 2.94817i) q^{96} +(1.93718 + 3.35530i) q^{97} +7.70656 q^{98} +(-7.76025 + 4.21970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 4 q^{2} - 7 q^{3} - 22 q^{4} - 9 q^{5} - 7 q^{7} + 24 q^{8} - 3 q^{9}+O(q^{10}) \) 38 * q - 4 * q^2 - 7 * q^3 - 22 * q^4 - 9 * q^5 - 7 * q^7 + 24 * q^8 - 3 * q^9	\( 38 q - 4 q^{2} - 7 q^{3} - 22 q^{4} - 9 q^{5} - 7 q^{7} + 24 q^{8} - 3 q^{9} - 14 q^{10} - 5 q^{11} + 11 q^{12} + 5 q^{13} - 17 q^{14} - 5 q^{15} - 24 q^{16} + 42 q^{17} - 23 q^{18} - 8 q^{19} - 21 q^{20} + 20 q^{22} - 22 q^{23} - 14 q^{24} - 10 q^{25} + 34 q^{26} - 4 q^{27} - 2 q^{28} - 30 q^{29} + 63 q^{30} + 5 q^{31} - 48 q^{32} - q^{33} + 6 q^{34} + 106 q^{35} - 20 q^{36} - 2 q^{37} - 21 q^{38} + 25 q^{39} - 16 q^{40} - 29 q^{41} - 47 q^{42} - 19 q^{43} + 58 q^{44} - 37 q^{45} - 32 q^{47} + 45 q^{48} + 10 q^{49} + 11 q^{50} - 53 q^{51} - q^{52} + 76 q^{53} - 41 q^{54} + 4 q^{55} - 46 q^{56} + 23 q^{57} - 30 q^{58} - 30 q^{59} - 87 q^{60} + 10 q^{61} + 50 q^{62} + 21 q^{63} + 28 q^{64} - 8 q^{65} + 91 q^{66} - 3 q^{67} - 47 q^{68} - 40 q^{69} - 56 q^{70} + 42 q^{71} + 3 q^{72} + 16 q^{73} - 28 q^{74} + 19 q^{75} + 36 q^{76} - 49 q^{77} - 105 q^{78} - 4 q^{79} + 140 q^{80} + 77 q^{81} - 8 q^{82} - 29 q^{83} + 145 q^{84} + 4 q^{85} - 4 q^{86} - 24 q^{87} + 47 q^{88} + 108 q^{89} - 8 q^{90} + 8 q^{91} - 12 q^{92} - 4 q^{93} + 23 q^{94} - 33 q^{95} - 147 q^{96} + 4 q^{97} + 98 q^{98} + 85 q^{99}+O(q^{100}) \) 38 * q - 4 * q^2 - 7 * q^3 - 22 * q^4 - 9 * q^5 - 7 * q^7 + 24 * q^8 - 3 * q^9 - 14 * q^10 - 5 * q^11 + 11 * q^12 + 5 * q^13 - 17 * q^14 - 5 * q^15 - 24 * q^16 + 42 * q^17 - 23 * q^18 - 8 * q^19 - 21 * q^20 + 20 * q^22 - 22 * q^23 - 14 * q^24 - 10 * q^25 + 34 * q^26 - 4 * q^27 - 2 * q^28 - 30 * q^29 + 63 * q^30 + 5 * q^31 - 48 * q^32 - q^33 + 6 * q^34 + 106 * q^35 - 20 * q^36 - 2 * q^37 - 21 * q^38 + 25 * q^39 - 16 * q^40 - 29 * q^41 - 47 * q^42 - 19 * q^43 + 58 * q^44 - 37 * q^45 - 32 * q^47 + 45 * q^48 + 10 * q^49 + 11 * q^50 - 53 * q^51 - q^52 + 76 * q^53 - 41 * q^54 + 4 * q^55 - 46 * q^56 + 23 * q^57 - 30 * q^58 - 30 * q^59 - 87 * q^60 + 10 * q^61 + 50 * q^62 + 21 * q^63 + 28 * q^64 - 8 * q^65 + 91 * q^66 - 3 * q^67 - 47 * q^68 - 40 * q^69 - 56 * q^70 + 42 * q^71 + 3 * q^72 + 16 * q^73 - 28 * q^74 + 19 * q^75 + 36 * q^76 - 49 * q^77 - 105 * q^78 - 4 * q^79 + 140 * q^80 + 77 * q^81 - 8 * q^82 - 29 * q^83 + 145 * q^84 + 4 * q^85 - 4 * q^86 - 24 * q^87 + 47 * q^88 + 108 * q^89 - 8 * q^90 + 8 * q^91 - 12 * q^92 - 4 * q^93 + 23 * q^94 - 33 * q^95 - 147 * q^96 + 4 * q^97 + 98 * q^98 + 85 * q^99

Introduction

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