LMFDB - Embedded newform 418.2.j.a.23.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(23,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("418.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.j (of order $9$, degree $6$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			23.3
Character	$\chi$	$=$	418.23
Dual form			418.2.j.a.309.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(0.291741 + 1.65454i) q^{3} +(0.766044 + 0.642788i) q^{4} +(1.53274 - 1.28612i) q^{5} +(-0.291741 + 1.65454i) q^{6} +(1.45368 - 2.51785i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.166674 - 0.0606642i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(0.291741 + 1.65454i) q^{3} +(0.766044 + 0.642788i) q^{4} +(1.53274 - 1.28612i) q^{5} +(-0.291741 + 1.65454i) q^{6} +(1.45368 - 2.51785i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.166674 - 0.0606642i) q^{9} +(1.88018 - 0.684329i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.840034 + 1.45498i) q^{12} +(-0.464402 + 2.63375i) q^{13} +(2.22717 - 1.86882i) q^{14} +(2.57510 + 2.16077i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-5.01723 - 1.82612i) q^{17} +0.177370 q^{18} +(-0.382995 - 4.34204i) q^{19} +2.00084 q^{20} +(4.58999 + 1.67062i) q^{21} +(0.173648 + 0.984808i) q^{22} +(-1.94137 - 1.62900i) q^{23} +(-1.28701 + 1.07993i) q^{24} +(-0.173061 + 0.981480i) q^{25} +(-1.33719 + 2.31608i) q^{26} +(2.66910 + 4.62302i) q^{27} +(2.73203 - 0.994376i) q^{28} +(-4.10678 + 1.49474i) q^{29} +(1.68078 + 2.91119i) q^{30} +(-4.86335 + 8.42357i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-1.28701 + 1.07993i) q^{33} +(-4.09009 - 3.43199i) q^{34} +(-1.01014 - 5.72880i) q^{35} +(0.166674 + 0.0606642i) q^{36} -7.63430 q^{37} +(1.12517 - 4.21118i) q^{38} -4.49315 q^{39} +(1.88018 + 0.684329i) q^{40} +(1.09725 + 6.22280i) q^{41} +(3.74179 + 3.13974i) q^{42} +(5.28878 - 4.43782i) q^{43} +(-0.173648 + 0.984808i) q^{44} +(0.177445 - 0.307344i) q^{45} +(-1.26714 - 2.19475i) q^{46} +(10.3041 - 3.75039i) q^{47} +(-1.57875 + 0.574617i) q^{48} +(-0.726375 - 1.25812i) q^{49} +(-0.498310 + 0.863099i) q^{50} +(1.55767 - 8.83399i) q^{51} +(-2.04870 + 1.71906i) q^{52} +(-6.56725 - 5.51057i) q^{53} +(0.926969 + 5.25710i) q^{54} +(1.88018 + 0.684329i) q^{55} +2.90736 q^{56} +(7.07236 - 1.90043i) q^{57} -4.37034 q^{58} +(-8.72132 - 3.17430i) q^{59} +(0.583728 + 3.31049i) q^{60} +(-6.59794 - 5.53633i) q^{61} +(-7.45108 + 6.25220i) q^{62} +(0.0895468 - 0.507845i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.67551 + 4.63412i) q^{65} +(-1.57875 + 0.574617i) q^{66} +(12.5072 - 4.55224i) q^{67} +(-2.66961 - 4.62391i) q^{68} +(2.12888 - 3.68732i) q^{69} +(1.01014 - 5.72880i) q^{70} +(3.47001 - 2.91168i) q^{71} +(0.135874 + 0.114011i) q^{72} +(0.426832 + 2.42069i) q^{73} +(-7.17389 - 2.61108i) q^{74} -1.67439 q^{75} +(2.49762 - 3.57238i) q^{76} +2.90736 q^{77} +(-4.22218 - 1.53675i) q^{78} +(-1.80744 - 10.2505i) q^{79} +(1.53274 + 1.28612i) q^{80} +(-6.46268 + 5.42283i) q^{81} +(-1.09725 + 6.22280i) q^{82} +(3.34076 - 5.78636i) q^{83} +(2.44228 + 4.23016i) q^{84} +(-10.0387 + 3.65379i) q^{85} +(6.48765 - 2.36131i) q^{86} +(-3.67124 - 6.35877i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(0.0912390 - 0.517442i) q^{89} +(0.271862 - 0.228119i) q^{90} +(5.95630 + 4.99793i) q^{91} +(-0.440072 - 2.49577i) q^{92} +(-15.3560 - 5.58913i) q^{93} +10.9654 q^{94} +(-6.17141 - 6.16262i) q^{95} -1.68007 q^{96} +(7.14717 + 2.60136i) q^{97} +(-0.252267 - 1.43068i) q^{98} +(0.135874 + 0.114011i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{8}+O(q^{10}) $ 24 * q + 12 * q^8	$ 24 q + 12 q^{8} + 12 q^{11} - 3 q^{12} - 3 q^{13} + 3 q^{14} + 27 q^{15} - 6 q^{18} - 21 q^{19} - 18 q^{20} + 15 q^{21} + 9 q^{23} + 36 q^{25} - 21 q^{27} - 3 q^{28} - 9 q^{30} - 27 q^{31} - 9 q^{34} - 45 q^{35} + 18 q^{37} + 9 q^{38} + 36 q^{39} - 18 q^{41} + 39 q^{42} - 48 q^{43} + 36 q^{45} - 18 q^{46} - 9 q^{47} + 6 q^{49} + 3 q^{50} - 18 q^{51} - 3 q^{52} - 36 q^{53} - 45 q^{54} + 18 q^{58} + 9 q^{59} - 9 q^{60} + 15 q^{61} - 33 q^{62} + 87 q^{63} - 12 q^{64} - 36 q^{65} + 33 q^{67} + 9 q^{68} - 18 q^{69} + 45 q^{70} - 9 q^{71} - 3 q^{73} + 3 q^{74} + 42 q^{75} + 9 q^{76} + 12 q^{78} + 15 q^{79} - 108 q^{81} + 18 q^{82} + 36 q^{83} - 9 q^{84} - 99 q^{85} - 33 q^{86} + 63 q^{87} - 12 q^{88} - 27 q^{89} - 36 q^{90} - 21 q^{91} - 9 q^{92} - 21 q^{93} + 54 q^{94} + 18 q^{95} - 6 q^{96} + 45 q^{97} + 39 q^{98}+O(q^{100}) $ 24 * q + 12 * q^8 + 12 * q^11 - 3 * q^12 - 3 * q^13 + 3 * q^14 + 27 * q^15 - 6 * q^18 - 21 * q^19 - 18 * q^20 + 15 * q^21 + 9 * q^23 + 36 * q^25 - 21 * q^27 - 3 * q^28 - 9 * q^30 - 27 * q^31 - 9 * q^34 - 45 * q^35 + 18 * q^37 + 9 * q^38 + 36 * q^39 - 18 * q^41 + 39 * q^42 - 48 * q^43 + 36 * q^45 - 18 * q^46 - 9 * q^47 + 6 * q^49 + 3 * q^50 - 18 * q^51 - 3 * q^52 - 36 * q^53 - 45 * q^54 + 18 * q^58 + 9 * q^59 - 9 * q^60 + 15 * q^61 - 33 * q^62 + 87 * q^63 - 12 * q^64 - 36 * q^65 + 33 * q^67 + 9 * q^68 - 18 * q^69 + 45 * q^70 - 9 * q^71 - 3 * q^73 + 3 * q^74 + 42 * q^75 + 9 * q^76 + 12 * q^78 + 15 * q^79 - 108 * q^81 + 18 * q^82 + 36 * q^83 - 9 * q^84 - 99 * q^85 - 33 * q^86 + 63 * q^87 - 12 * q^88 - 27 * q^89 - 36 * q^90 - 21 * q^91 - 9 * q^92 - 21 * q^93 + 54 * q^94 + 18 * q^95 - 6 * q^96 + 45 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	0.291741	+	1.65454i	0.168437	+	0.955252i	0.945450	+	0.325767i	$0.105623\pi$
$3$	0.291741	+	1.65454i	0.168437	+	0.955252i	−0.777013	+	0.629484i	$0.783266\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	1.53274	−	1.28612i	0.685460	−	0.575169i	−0.232136	−	0.972683i	$-0.574571\pi$
$5$	1.53274	−	1.28612i	0.685460	−	0.575169i	0.917596	+	0.397514i	$0.130127\pi$
$6$	−0.291741	+	1.65454i	−0.119103	+	0.675465i
$7$	1.45368	−	2.51785i	0.549440	−	0.951657i	−0.448873	−	0.893595i	$-0.648175\pi$
$7$	1.45368	−	2.51785i	0.549440	−	0.951657i	0.998313	−	0.0580620i	$-0.0184921\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.166674	−	0.0606642i	0.0555579	−	0.0202214i
$10$	1.88018	−	0.684329i	0.594565	−	0.216404i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−0.840034	+	1.45498i	−0.242497	+	0.420017i
$13$	−0.464402	+	2.63375i	−0.128802	+	0.730472i	0.850175	+	0.526500i	$0.176496\pi$
$13$	−0.464402	+	2.63375i	−0.128802	+	0.730472i	−0.978977	+	0.203971i	$0.934615\pi$
$14$	2.22717	−	1.86882i	0.595236	−	0.499462i
$15$	2.57510	+	2.16077i	0.664888	+	0.557907i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−5.01723	−	1.82612i	−1.21686	−	0.442900i	−0.347780	−	0.937576i	$-0.613065\pi$
$17$	−5.01723	−	1.82612i	−1.21686	−	0.442900i	−0.869078	+	0.494676i	$0.835287\pi$
$18$	0.177370			0.0418066
$19$	−0.382995	−	4.34204i	−0.0878652	−	0.996132i
$19$	−0.382995	−	4.34204i	−0.0878652	−	0.996132i
$20$	2.00084			0.447402
$21$	4.58999	+	1.67062i	1.00162	+	0.364559i
$22$	0.173648	+	0.984808i	0.0370219	+	0.209962i
$23$	−1.94137	−	1.62900i	−0.404803	−	0.339670i	0.417544	−	0.908657i	$-0.362891\pi$
$23$	−1.94137	−	1.62900i	−0.404803	−	0.339670i	−0.822347	+	0.568987i	$0.807336\pi$
$24$	−1.28701	+	1.07993i	−0.262709	+	0.220439i
$25$	−0.173061	+	0.981480i	−0.0346123	+	0.196296i
$26$	−1.33719	+	2.31608i	−0.262245	+	0.454221i
$27$	2.66910	+	4.62302i	0.513668	+	0.889700i
$28$	2.73203	−	0.994376i	0.516304	−	0.187919i
$29$	−4.10678	+	1.49474i	−0.762609	+	0.277567i	−0.693902	−	0.720070i	$-0.744110\pi$
$29$	−4.10678	+	1.49474i	−0.762609	+	0.277567i	−0.0687076	+	0.997637i	$0.521888\pi$
$30$	1.68078	+	2.91119i	0.306867	+	0.531509i
$31$	−4.86335	+	8.42357i	−0.873483	+	1.51292i	−0.0151140	+	0.999886i	$0.504811\pi$
$31$	−4.86335	+	8.42357i	−0.873483	+	1.51292i	−0.858369	+	0.513032i	$0.828522\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−1.28701	+	1.07993i	−0.224039	+	0.187991i
$34$	−4.09009	−	3.43199i	−0.701444	−	0.588581i
$35$	−1.01014	−	5.72880i	−0.170745	−	0.968344i
$36$	0.166674	+	0.0606642i	0.0277789	+	0.0101107i
$37$	−7.63430			−1.25507			−0.627536	−	0.778588i	$-0.715936\pi$
$37$	−7.63430			−1.25507			−0.627536	+	0.778588i	$0.715936\pi$
$38$	1.12517	−	4.21118i	0.182526	−	0.683143i
$39$	−4.49315			−0.719479
$40$	1.88018	+	0.684329i	0.297282	+	0.108202i
$41$	1.09725	+	6.22280i	0.171361	+	0.971839i	0.942260	+	0.334881i	$0.108696\pi$
$41$	1.09725	+	6.22280i	0.171361	+	0.971839i	−0.770899	+	0.636957i	$0.780193\pi$
$42$	3.74179	+	3.13974i	0.577371	+	0.484472i
$43$	5.28878	−	4.43782i	0.806532	−	0.676761i	−0.143245	−	0.989687i	$-0.545754\pi$
$43$	5.28878	−	4.43782i	0.806532	−	0.676761i	0.949777	+	0.312927i	$0.101309\pi$
$44$	−0.173648	+	0.984808i	−0.0261784	+	0.148465i
$45$	0.177445	−	0.307344i	0.0264520	−	0.0458162i
$46$	−1.26714	−	2.19475i	−0.186829	−	0.323598i
$47$	10.3041	−	3.75039i	1.50301	−	0.547050i	0.546171	−	0.837674i	$-0.316085\pi$
$47$	10.3041	−	3.75039i	1.50301	−	0.547050i	0.956838	+	0.290623i	$0.0938626\pi$
$48$	−1.57875	+	0.574617i	−0.227873	+	0.0829389i
$49$	−0.726375	−	1.25812i	−0.103768	−	0.179731i
$50$	−0.498310	+	0.863099i	−0.0704717	+	0.122061i
$51$	1.55767	−	8.83399i	0.218118	−	1.23701i
$52$	−2.04870	+	1.71906i	−0.284103	+	0.238391i
$53$	−6.56725	−	5.51057i	−0.902081	−	0.756936i	0.0685152	−	0.997650i	$-0.478174\pi$
$53$	−6.56725	−	5.51057i	−0.902081	−	0.756936i	−0.970596	+	0.240714i	$0.922618\pi$
$54$	0.926969	+	5.25710i	0.126144	+	0.715401i
$55$	1.88018	+	0.684329i	0.253523	+	0.0922749i
$56$	2.90736			0.388512
$57$	7.07236	−	1.90043i	0.936757	−	0.251719i
$58$	−4.37034			−0.573854
$59$	−8.72132	−	3.17430i	−1.13542	−	0.413259i	−0.295163	−	0.955447i	$-0.595374\pi$
$59$	−8.72132	−	3.17430i	−1.13542	−	0.413259i	−0.840257	+	0.542188i	$0.817596\pi$
$60$	0.583728	+	3.31049i	0.0753590	+	0.427382i
$61$	−6.59794	−	5.53633i	−0.844780	−	0.708855i	0.113853	−	0.993498i	$-0.463681\pi$
$61$	−6.59794	−	5.53633i	−0.844780	−	0.708855i	−0.958634	+	0.284643i	$0.908125\pi$
$62$	−7.45108	+	6.25220i	−0.946289	+	0.794031i
$63$	0.0895468	−	0.507845i	0.0112818	−	0.0639825i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.67551	+	4.63412i	0.331857	+	0.574792i
$66$	−1.57875	+	0.574617i	−0.194330	+	0.0707305i
$67$	12.5072	−	4.55224i	1.52800	−	0.556145i	0.564866	−	0.825183i	$-0.308928\pi$
$67$	12.5072	−	4.55224i	1.52800	−	0.556145i	0.963130	+	0.269038i	$0.0867057\pi$
$68$	−2.66961	−	4.62391i	−0.323738	−	0.560731i
$69$	2.12888	−	3.68732i	0.256287	−	0.443902i
$70$	1.01014	−	5.72880i	0.120735	−	0.684723i
$71$	3.47001	−	2.91168i	0.411814	−	0.345553i	−0.413225	−	0.910629i	$-0.635598\pi$
$71$	3.47001	−	2.91168i	0.411814	−	0.345553i	0.825039	+	0.565076i	$0.191153\pi$
$72$	0.135874	+	0.114011i	0.0160129	+	0.0134364i
$73$	0.426832	+	2.42069i	0.0499569	+	0.283320i	0.999544	−	0.0301824i	$-0.00960881\pi$
$73$	0.426832	+	2.42069i	0.0499569	+	0.283320i	−0.949587	+	0.313502i	$0.898498\pi$
$74$	−7.17389	−	2.61108i	−0.833948	−	0.303532i
$75$	−1.67439			−0.193342
$76$	2.49762	−	3.57238i	0.286496	−	0.409780i
$77$	2.90736			0.331325
$78$	−4.22218	−	1.53675i	−0.478067	−	0.174002i
$79$	−1.80744	−	10.2505i	−0.203353	−	1.15327i	−0.900010	−	0.435869i	$-0.856441\pi$
$79$	−1.80744	−	10.2505i	−0.203353	−	1.15327i	0.696657	−	0.717404i	$-0.254670\pi$
$80$	1.53274	+	1.28612i	0.171365	+	0.143792i
$81$	−6.46268	+	5.42283i	−0.718075	+	0.602537i
$82$	−1.09725	+	6.22280i	−0.121171	+	0.687194i
$83$	3.34076	−	5.78636i	0.366696	−	0.635136i	−0.622351	−	0.782738i	$-0.713822\pi$
$83$	3.34076	−	5.78636i	0.366696	−	0.635136i	0.989047	+	0.147602i	$0.0471556\pi$
$84$	2.44228	+	4.23016i	0.266475	+	0.461548i
$85$	−10.0387	+	3.65379i	−1.08885	+	0.396309i
$86$	6.48765	−	2.36131i	0.699582	−	0.254627i
$87$	−3.67124	−	6.35877i	−0.393598	−	0.681731i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	0.0912390	−	0.517442i	0.00967131	−	0.0548487i	−0.979590	−	0.201005i	$-0.935579\pi$
$89$	0.0912390	−	0.517442i	0.00967131	−	0.0548487i	0.989261	+	0.146156i	$0.0466903\pi$
$90$	0.271862	−	0.228119i	0.0286568	−	0.0240459i
$91$	5.95630	+	4.99793i	0.624390	+	0.523925i
$92$	−0.440072	−	2.49577i	−0.0458807	−	0.260202i
$93$	−15.3560	−	5.58913i	−1.59234	−	0.579566i
$94$	10.9654			1.13100
$95$	−6.17141	−	6.16262i	−0.633173	−	0.632272i
$96$	−1.68007			−0.171471
$97$	7.14717	+	2.60136i	0.725685	+	0.264128i	0.678337	−	0.734751i	$-0.262701\pi$
$97$	7.14717	+	2.60136i	0.725685	+	0.264128i	0.0473481	+	0.998878i	$0.484923\pi$
$98$	−0.252267	−	1.43068i	−0.0254828	−	0.144520i
$99$	0.135874	+	0.114011i	0.0136558	+	0.0114586i
$100$	−0.763456	+	0.640616i	−0.0763456	+	0.0640616i
$101$	0.496991	−	2.81858i	0.0494525	−	0.280459i	−0.950047	−	0.312108i	$-0.898965\pi$
$101$	0.496991	−	2.81858i	0.0494525	−	0.280459i	0.999499	+	0.0316492i	$0.0100759\pi$
$102$	4.48513	−	7.76848i	0.444095	−	0.769194i
$103$	7.52023	+	13.0254i	0.740990	+	1.28343i	0.952045	+	0.305958i	$0.0989768\pi$
$103$	7.52023	+	13.0254i	0.740990	+	1.28343i	−0.211055	+	0.977474i	$0.567690\pi$
$104$	−2.51310	+	0.914693i	−0.246430	+	0.0896930i
$105$	9.18386	−	3.34265i	0.896253	−	0.326209i
$106$	−4.28647	−	7.42438i	−0.416338	−	0.721119i
$107$	−8.70913	+	15.0847i	−0.841944	+	1.45829i	0.0463053	+	0.998927i	$0.485255\pi$
$107$	−8.70913	+	15.0847i	−0.841944	+	1.45829i	−0.888249	+	0.459362i	$0.848078\pi$
$108$	−0.926969	+	5.25710i	−0.0891976	+	0.505865i
$109$	3.59566	−	3.01712i	0.344402	−	0.288988i	−0.454135	−	0.890933i	$-0.650052\pi$
$109$	3.59566	−	3.01712i	0.344402	−	0.288988i	0.798538	+	0.601945i	$0.205607\pi$
$110$	1.53274	+	1.28612i	0.146141	+	0.122627i
$111$	−2.22724	−	12.6313i	−0.211400	−	1.19891i
$112$	2.73203	+	0.994376i	0.258152	+	0.0939597i
$113$	−6.85152			−0.644536			−0.322268	−	0.946648i	$-0.604445\pi$
$113$	−6.85152			−0.644536			−0.322268	+	0.946648i	$0.604445\pi$
$114$	7.29583	+	0.633068i	0.683317	+	0.0592922i
$115$	−5.07069			−0.472844
$116$	−4.10678	−	1.49474i	−0.381305	−	0.138784i
$117$	0.0823711	+	0.467150i	0.00761521	+	0.0431880i
$118$	−7.10969	−	5.96574i	−0.654500	−	0.549191i
$119$	−11.8914	+	9.97804i	−1.09008	+	0.914685i
$120$	−0.583728	+	3.31049i	−0.0532868	+	0.302205i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−4.30650	−	7.45908i	−0.389892	−	0.675313i
$123$	−9.97579	+	3.63089i	−0.899487	+	0.327386i
$124$	−9.14011	+	3.32673i	−0.820806	+	0.298749i
$125$	5.99915	+	10.3908i	0.536581	+	0.929385i
$126$	0.257840	−	0.446592i	0.0229702	−	0.0397855i
$127$	1.90206	−	10.7871i	0.168781	−	0.957204i	−0.776299	−	0.630365i	$-0.782905\pi$
$127$	1.90206	−	10.7871i	0.168781	−	0.957204i	0.945080	−	0.326839i	$-0.105984\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	8.88552	+	7.45583i	0.782326	+	0.656450i
$130$	0.929196	+	5.26973i	0.0814959	+	0.462186i
$131$	−1.57047	−	0.571605i	−0.137213	−	0.0499414i	0.272501	−	0.962156i	$-0.412149\pi$
$131$	−1.57047	−	0.571605i	−0.137213	−	0.0499414i	−0.409714	+	0.912214i	$0.634371\pi$
$132$	−1.68007			−0.146231
$133$	−11.4894	−	5.34762i	−0.996253	−	0.463697i
$134$	13.3099			1.14980
$135$	10.0368	+	3.65309i	0.863828	+	0.314408i
$136$	−0.927147	−	5.25811i	−0.0795022	−	0.450880i
$137$	8.19296	+	6.87471i	0.699972	+	0.587346i	0.921766	−	0.387747i	$-0.126747\pi$
$137$	8.19296	+	6.87471i	0.699972	+	0.587346i	−0.221794	+	0.975094i	$0.571191\pi$
$138$	3.26163	−	2.73683i	0.277648	−	0.232975i
$139$	−0.533586	+	3.02612i	−0.0452582	+	0.256672i	−0.999039	−	0.0438315i	$-0.986044\pi$
$139$	−0.533586	+	3.02612i	−0.0452582	+	0.256672i	0.953781	+	0.300503i	$0.0971546\pi$
$140$	2.90859	−	5.03782i	0.245821	−	0.425774i
$141$	9.21131	+	15.9545i	0.775733	+	1.34361i
$142$	4.25659	−	1.54927i	0.357205	−	0.130012i
$143$	−2.51310	+	0.914693i	−0.210156	+	0.0764905i
$144$	0.0886852	+	0.153607i	0.00739043	+	0.0128006i
$145$	−4.37219	+	7.57285i	−0.363090	+	0.628891i
$146$	−0.426832	+	2.42069i	−0.0353249	+	0.200337i
$147$	1.86970	−	1.56886i	0.154210	−	0.129398i
$148$	−5.84821	−	4.90723i	−0.480720	−	0.403372i
$149$	−2.42688	−	13.7635i	−0.198818	−	1.12755i	−0.906876	−	0.421398i	$-0.861539\pi$
$149$	−2.42688	−	13.7635i	−0.198818	−	1.12755i	0.708058	−	0.706155i	$-0.249572\pi$
$150$	−1.57341	−	0.572676i	−0.128469	−	0.0467588i
$151$	10.9675			0.892519			0.446260	−	0.894904i	$-0.352756\pi$
$151$	10.9675			0.892519			0.446260	+	0.894904i	$0.352756\pi$
$152$	3.56882	−	2.50270i	0.289469	−	0.202996i
$153$	−0.947021			−0.0765621
$154$	2.73203	+	0.994376i	0.220153	+	0.0801291i
$155$	3.37947	+	19.1660i	0.271446	+	1.53945i
$156$	−3.44195	−	2.88814i	−0.275577	−	0.231236i
$157$	−17.1567	+	14.3962i	−1.36926	+	1.14894i	−0.396257	+	0.918139i	$0.629691\pi$
$157$	−17.1567	+	14.3962i	−1.36926	+	1.14894i	−0.973000	+	0.230804i	$0.925864\pi$
$158$	1.80744	−	10.2505i	0.143792	−	0.815487i
$159$	7.20156	−	12.4735i	0.571121	−	0.989210i
$160$	1.00042	+	1.73278i	0.0790903	+	0.136988i
$161$	−6.92370	+	2.52002i	−0.545664	+	0.198606i
$162$	−7.92765	+	2.88543i	−0.622855	+	0.226701i
$163$	12.0294	+	20.8355i	0.942213	+	1.63196i	0.761237	+	0.648473i	$0.224592\pi$
$163$	12.0294	+	20.8355i	0.942213	+	1.63196i	0.180976	+	0.983488i	$0.442074\pi$
$164$	−3.15940	+	5.47224i	−0.246708	+	0.427310i
$165$	−0.583728	+	3.31049i	−0.0454432	+	0.257721i
$166$	5.11834	−	4.29480i	0.397260	−	0.333341i
$167$	−8.90964	−	7.47608i	−0.689449	−	0.578516i	0.229302	−	0.973355i	$-0.426356\pi$
$167$	−8.90964	−	7.47608i	−0.689449	−	0.578516i	−0.918750	+	0.394839i	$0.870800\pi$
$168$	0.848196	+	4.81036i	0.0654397	+	0.371127i
$169$	5.49502	+	2.00002i	0.422694	+	0.153848i
$170$	−10.6830			−0.819346
$171$	−0.327242	−	0.700469i	−0.0250248	−	0.0535662i
$172$	6.90402			0.526426
$173$	−0.401513	−	0.146139i	−0.0305265	−	0.0111107i	0.326712	−	0.945124i	$-0.394059\pi$
$173$	−0.401513	−	0.146139i	−0.0305265	−	0.0111107i	−0.357238	+	0.934013i	$0.616282\pi$
$174$	−1.27501	−	7.23092i	−0.0966580	−	0.548175i
$175$	2.21964	+	1.86250i	0.167789	+	0.140792i
$176$	−0.766044	+	0.642788i	−0.0577428	+	0.0484519i
$177$	2.70766	−	15.3559i	0.203520	−	1.15422i
$178$	0.262712	−	0.455031i	0.0196911	−	0.0341060i
$179$	−12.9182	−	22.3750i	−0.965551	−	1.67238i	−0.708127	−	0.706086i	$-0.750459\pi$
$179$	−12.9182	−	22.3750i	−0.965551	−	1.67238i	−0.257425	−	0.966298i	$-0.582874\pi$
$180$	0.333488	−	0.121380i	0.0248567	−	0.00904711i
$181$	2.79843	−	1.01854i	0.208005	−	0.0757077i	−0.235916	−	0.971773i	$-0.575809\pi$
$181$	2.79843	−	1.01854i	0.208005	−	0.0757077i	0.443922	+	0.896066i	$0.353587\pi$
$182$	3.88770	+	6.73369i	0.288175	+	0.499135i
$183$	7.23522	−	12.5318i	0.534843	−	0.926375i
$184$	0.440072	−	2.49577i	0.0324426	−	0.183991i
$185$	−11.7014	+	9.81861i	−0.860301	+	0.721879i
$186$	−12.5183	−	10.5041i	−0.917889	−	0.770200i
$187$	−0.927147	−	5.25811i	−0.0677997	−	0.384511i
$188$	10.3041	+	3.75039i	0.751504	+	0.273525i
$189$	15.5201			1.12892
$190$	−3.69148	−	7.90172i	−0.267808	−	0.573251i
$191$	−6.30344			−0.456101			−0.228050	−	0.973649i	$-0.573235\pi$
$191$	−6.30344			−0.456101			−0.228050	+	0.973649i	$0.573235\pi$
$192$	−1.57875	−	0.574617i	−0.113936	−	0.0414694i
$193$	0.707818	+	4.01424i	0.0509499	+	0.288951i	0.999627	−	0.0272939i	$-0.00868898\pi$
$193$	0.707818	+	4.01424i	0.0509499	+	0.288951i	−0.948678	+	0.316245i	$0.897578\pi$
$194$	5.82643	+	4.88895i	0.418313	+	0.351006i
$195$	−6.88681	+	5.77872i	−0.493175	+	0.413823i
$196$	0.252267	−	1.43068i	0.0180191	−	0.102191i
$197$	8.05786	−	13.9566i	0.574099	−	0.994369i	−0.422040	−	0.906577i	$-0.638686\pi$
$197$	8.05786	−	13.9566i	0.574099	−	0.994369i	0.996139	−	0.0877914i	$-0.0279809\pi$
$198$	0.0886852	+	0.153607i	0.00630258	+	0.0109164i
$199$	3.24707	−	1.18184i	0.230179	−	0.0837782i	−0.224356	−	0.974507i	$-0.572028\pi$
$199$	3.24707	−	1.18184i	0.230179	−	0.0837782i	0.454535	+	0.890729i	$0.349806\pi$
$200$	−0.936517	+	0.340864i	−0.0662218	+	0.0241028i
$201$	11.1807	+	19.3656i	0.788629	+	1.36595i
$202$	1.43103	−	2.47862i	0.100687	−	0.174395i
$203$	−2.20640	+	12.5131i	−0.154859	+	0.878249i
$204$	6.87163	−	5.76598i	0.481110	−	0.403699i
$205$	9.68505	+	8.12672i	0.676433	+	0.567595i
$206$	2.61175	+	14.8120i	0.181969	+	1.03200i
$207$	−0.422397	−	0.153740i	−0.0293586	−	0.0106857i
$208$	−2.67438			−0.185435
$209$	3.56882	−	2.50270i	0.246860	−	0.173116i
$210$	9.77326			0.674419
$211$	6.35130	+	2.31168i	0.437241	+	0.159143i	0.551256	−	0.834336i	$-0.314149\pi$
$211$	6.35130	+	2.31168i	0.437241	+	0.159143i	−0.114014	+	0.993479i	$0.536371\pi$
$212$	−1.48867	−	8.44269i	−0.102243	−	0.579846i
$213$	5.82985	+	4.89182i	0.399455	+	0.335182i
$214$	−13.3432	+	11.1962i	−0.912120	+	0.765360i
$215$	2.39875	−	13.6040i	0.163594	−	0.927785i
$216$	−2.66910	+	4.62302i	−0.181609	+	0.314556i
$217$	14.1395	+	24.4904i	0.959853	+	1.66251i
$218$	4.41073	−	1.60538i	0.298733	−	0.108730i
$219$	−3.88061	+	1.41243i	−0.262227	+	0.0954429i
$220$	1.00042	+	1.73278i	0.0674485	+	0.116824i
$221$	7.13957	−	12.3661i	0.480260	−	0.831834i
$222$	2.22724	−	12.6313i	0.149482	−	0.847756i
$223$	−2.87904	+	2.41580i	−0.192795	+	0.161774i	−0.734075	−	0.679068i	$-0.762384\pi$
$223$	−2.87904	+	2.41580i	−0.192795	+	0.161774i	0.541281	+	0.840842i	$0.317940\pi$
$224$	2.22717	+	1.86882i	0.148809	+	0.124866i
$225$	0.0306960	+	0.174085i	0.00204640	+	0.0116057i
$226$	−6.43832	−	2.34336i	−0.428271	−	0.155878i
$227$	−6.21529			−0.412523			−0.206262	−	0.978497i	$-0.566130\pi$
$227$	−6.21529			−0.412523			−0.206262	+	0.978497i	$0.566130\pi$
$228$	6.63932	+	3.09021i	0.439700	+	0.204654i
$229$	1.95132			0.128947			0.0644733	−	0.997919i	$-0.479463\pi$
$229$	1.95132			0.128947			0.0644733	+	0.997919i	$0.479463\pi$
$230$	−4.76489	−	1.73428i	−0.314188	−	0.114355i
$231$	0.848196	+	4.81036i	0.0558072	+	0.316498i
$232$	−3.34787	−	2.80920i	−0.219799	−	0.184433i
$233$	−6.45616	+	5.41736i	−0.422957	+	0.354903i	−0.829287	−	0.558823i	$-0.811253\pi$
$233$	−6.45616	+	5.41736i	−0.422957	+	0.354903i	0.406330	+	0.913727i	$0.366809\pi$
$234$	−0.0823711	+	0.467150i	−0.00538477	+	0.0305385i
$235$	10.9700	−	19.0007i	0.715606	−	1.23947i
$236$	−4.64052	−	8.03762i	−0.302072	−	0.523204i
$237$	16.4326	−	5.98099i	1.06741	−	0.388507i
$238$	−14.5869	+	5.30920i	−0.945529	+	0.344144i
$239$	1.61190	+	2.79190i	0.104265	+	0.180593i	0.913438	−	0.406978i	$-0.133418\pi$
$239$	1.61190	+	2.79190i	0.104265	+	0.180593i	−0.809172	+	0.587571i	$0.800084\pi$
$240$	−1.68078	+	2.91119i	−0.108494	+	0.187917i
$241$	−2.87259	+	16.2913i	−0.185040	+	1.04941i	0.740864	+	0.671655i	$0.234416\pi$
$241$	−2.87259	+	16.2913i	−0.185040	+	1.04941i	−0.925904	+	0.377759i	$0.876695\pi$
$242$	−0.766044	+	0.642788i	−0.0492432	+	0.0413200i
$243$	1.41015	+	1.18326i	0.0904612	+	0.0759060i
$244$	−1.49563	−	8.48215i	−0.0957481	−	0.543014i
$245$	−2.73143	−	0.994159i	−0.174505	−	0.0635145i
$246$	−10.6160			−0.676852
$247$	11.6137	+	1.00774i	0.738964	+	0.0641207i
$248$	−9.72670			−0.617646
$249$	10.5484	+	3.83932i	0.668480	+	0.243307i
$250$	2.08348	+	11.8160i	0.131771	+	0.747311i
$251$	−17.6375	−	14.7996i	−1.11327	−	0.934143i	−0.115023	−	0.993363i	$-0.536694\pi$
$251$	−17.6375	−	14.7996i	−1.11327	−	0.934143i	−0.998245	+	0.0592201i	$0.981139\pi$
$252$	0.395034	−	0.331472i	0.0248848	−	0.0208808i
$253$	0.440072	−	2.49577i	0.0276671	−	0.156908i
$254$	5.47678	−	9.48606i	0.343644	−	0.595208i
$255$	−8.97406	−	15.5435i	−0.561977	−	0.973373i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	15.3858	−	5.59997i	0.959740	−	0.349317i	0.185808	−	0.982586i	$-0.440510\pi$
$257$	15.3858	−	5.59997i	0.959740	−	0.349317i	0.773932	+	0.633269i	$0.218287\pi$
$258$	5.79961	+	10.0452i	0.361068	+	0.625388i
$259$	−11.0978	+	19.2220i	−0.689586	+	1.19440i
$260$	−0.929196	+	5.26973i	−0.0576263	+	0.326815i
$261$	−0.593814	+	0.498269i	−0.0367561	+	0.0308421i
$262$	−1.28026	−	1.07427i	−0.0790948	−	0.0663684i
$263$	−1.64339	−	9.32012i	−0.101336	−	0.574703i	−0.992621	−	0.121260i	$-0.961307\pi$
$263$	−1.64339	−	9.32012i	−0.101336	−	0.574703i	0.891285	−	0.453443i	$-0.149805\pi$
$264$	−1.57875	−	0.574617i	−0.0971652	−	0.0353652i
$265$	−17.1531			−1.05371
$266$	−8.96747	−	8.95471i	−0.549831	−	0.549048i
$267$	0.882749			0.0540233
$268$	12.5072	+	4.55224i	0.763998	+	0.278072i
$269$	0.626952	+	3.55562i	0.0382259	+	0.216790i	0.997937	−	0.0641982i	$-0.0204490\pi$
$269$	0.626952	+	3.55562i	0.0382259	+	0.216790i	−0.959711	+	0.280988i	$0.909338\pi$
$270$	8.18205	+	6.86555i	0.497944	+	0.417824i
$271$	−5.86552	+	4.92176i	−0.356305	+	0.298976i	−0.803316	−	0.595553i	$-0.796933\pi$
$271$	−5.86552	+	4.92176i	−0.356305	+	0.298976i	0.447011	+	0.894529i	$0.352489\pi$
$272$	0.927147	−	5.25811i	0.0562166	−	0.318820i
$273$	−6.53160	+	11.3131i	−0.395310	+	0.684698i
$274$	5.34758	+	9.26227i	0.323059	+	0.559554i
$275$	−0.936517	+	0.340864i	−0.0564741	+	0.0205549i
$276$	4.00098	−	1.45624i	0.240831	−	0.0876552i
$277$	15.4999	+	26.8465i	0.931296	+	1.61305i	0.781109	+	0.624394i	$0.214654\pi$
$277$	15.4999	+	26.8465i	0.931296	+	1.61305i	0.150187	+	0.988658i	$0.452013\pi$
$278$	−1.53640	+	2.66112i	−0.0921471	+	0.159604i
$279$	−0.299583	+	1.69902i	−0.0179355	+	0.101718i
$280$	4.45622	−	3.73921i	0.266310	−	0.223461i
$281$	3.72840	+	3.12850i	0.222418	+	0.186631i	0.747187	−	0.664614i	$-0.231404\pi$
$281$	3.72840	+	3.12850i	0.222418	+	0.186631i	−0.524769	+	0.851245i	$0.675848\pi$
$282$	3.19906	+	18.1427i	0.190501	+	1.08038i
$283$	20.1958	+	7.35068i	1.20052	+	0.436952i	0.863405	−	0.504512i	$-0.168328\pi$
$283$	20.1958	+	7.35068i	1.20052	+	0.436952i	0.337112	+	0.941464i	$0.390550\pi$
$284$	4.52977			0.268793
$285$	8.39588	−	12.0088i	0.497329	−	0.711337i
$286$	−2.67438			−0.158140
$287$	17.2631	+	6.28326i	1.01901	+	0.370889i
$288$	0.0308000	+	0.174676i	0.00181491	+	0.0102929i
$289$	8.81515	+	7.39679i	0.518538	+	0.435105i
$290$	−6.69858	+	5.62077i	−0.393354	+	0.330063i
$291$	−2.21894	+	12.5842i	−0.130077	+	0.737701i
$292$	−1.22901	+	2.12871i	−0.0719226	+	0.124574i
$293$	−2.03912	−	3.53186i	−0.119127	−	0.206333i	0.800295	−	0.599606i	$-0.204676\pi$
$293$	−2.03912	−	3.53186i	−0.119127	−	0.206333i	−0.919422	+	0.393273i	$0.871343\pi$
$294$	2.29352	−	0.834775i	0.133761	−	0.0486851i
$295$	−17.4500	+	6.35129i	−1.01598	+	0.369786i
$296$	−3.81715	−	6.61150i	−0.221867	−	0.384285i
$297$	−2.66910	+	4.62302i	−0.154877	+	0.268255i
$298$	2.42688	−	13.7635i	0.140586	−	0.797301i
$299$	5.19196	−	4.35657i	0.300259	−	0.251947i
$300$	−1.28266	−	1.07628i	−0.0740543	−	0.0621389i
$301$	−3.48555	−	19.7675i	−0.200904	−	1.13938i
$302$	10.3060	+	3.75109i	0.593046	+	0.215851i
$303$	4.80846			0.276239
$304$	4.20957	−	1.13116i	0.241435	−	0.0648767i
$305$	−17.2333			−0.986775
$306$	−0.889908	−	0.323900i	−0.0508727	−	0.0185161i
$307$	−2.85761	−	16.2063i	−0.163092	−	0.924943i	−0.951010	−	0.309162i	$-0.899952\pi$
$307$	−2.85761	−	16.2063i	−0.163092	−	0.924943i	0.787917	−	0.615781i	$-0.211160\pi$
$308$	2.22717	+	1.86882i	0.126905	+	0.106486i
$309$	−19.3572	+	16.2426i	−1.10119	+	0.924009i
$310$	−3.37947	+	19.1660i	−0.191941	+	1.08855i
$311$	−6.94856	+	12.0353i	−0.394017	+	0.682457i	−0.992975	−	0.118323i	$-0.962248\pi$
$311$	−6.94856	+	12.0353i	−0.394017	+	0.682457i	0.598958	+	0.800780i	$0.295582\pi$
$312$	−2.24657	−	3.89118i	−0.127187	−	0.220295i
$313$	11.9536	−	4.35075i	0.675657	−	0.245919i	0.0186751	−	0.999826i	$-0.494055\pi$
$313$	11.9536	−	4.35075i	0.675657	−	0.245919i	0.656981	+	0.753907i	$0.271833\pi$
$314$	−21.0459	+	7.66007i	−1.18769	+	0.432283i
$315$	−0.515897	−	0.893561i	−0.0290675	−	0.0503464i
$316$	5.20432	−	9.01415i	0.292766	−	0.507086i
$317$	−2.08601	+	11.8304i	−0.117162	+	0.664460i	0.868495	+	0.495698i	$0.165088\pi$
$317$	−2.08601	+	11.8304i	−0.117162	+	0.664460i	−0.985657	+	0.168761i	$0.946023\pi$
$318$	11.0334	−	9.25814i	0.618724	−	0.519171i
$319$	−3.34787	−	2.80920i	−0.187445	−	0.157285i
$320$	0.347443	+	1.97045i	0.0194227	+	0.110151i
$321$	−27.4991	−	10.0088i	−1.53485	−	0.558639i
$322$	−7.36805			−0.410606
$323$	−6.00753	+	22.4844i	−0.334268	+	1.25107i
$324$	−8.43643			−0.468690
$325$	−2.50461	−	0.911602i	−0.138931	−	0.0505666i
$326$	4.17776	+	23.6932i	0.231385	+	1.31225i
$327$	6.04096	+	5.06897i	0.334066	+	0.280315i
$328$	−4.84048	+	4.06165i	−0.267271	+	0.224267i
$329$	5.53597	−	31.3961i	0.305208	−	1.73092i
$330$	−1.68078	+	2.91119i	−0.0925238	+	0.160256i
$331$	−2.43472	−	4.21706i	−0.133824	−	0.231790i	0.791323	−	0.611398i	$-0.209392\pi$
$331$	−2.43472	−	4.21706i	−0.133824	−	0.231790i	−0.925148	+	0.379607i	$0.876059\pi$
$332$	6.27857	−	2.28521i	0.344581	−	0.125417i
$333$	−1.27244	+	0.463129i	−0.0697291	+	0.0253793i
$334$	−5.81535	−	10.0725i	−0.318202	−	0.551142i
$335$	13.3155	−	23.0631i	0.727503	−	1.26007i
$336$	−0.848196	+	4.81036i	−0.0462729	+	0.262427i
$337$	25.9012	−	21.7337i	1.41093	−	1.18391i	0.454934	−	0.890525i	$-0.349663\pi$
$337$	25.9012	−	21.7337i	1.41093	−	1.18391i	0.955995	−	0.293384i	$-0.0947814\pi$
$338$	4.47958	+	3.75881i	0.243657	+	0.204452i
$339$	−1.99887	−	11.3361i	−0.108564	−	0.615694i
$340$	−10.0387	−	3.65379i	−0.544425	−	0.198155i
$341$	−9.72670			−0.526730
$342$	−0.0679320	−	0.770149i	−0.00367334	−	0.0416449i
$343$	16.1279			0.870823
$344$	6.48765	+	2.36131i	0.349791	+	0.127313i
$345$	−1.47933	−	8.38968i	−0.0796443	−	0.451685i
$346$	−0.327317	−	0.274651i	−0.0175966	−	0.0147653i
$347$	13.3037	−	11.1631i	0.714181	−	0.599269i	−0.211588	−	0.977359i	$-0.567863\pi$
$347$	13.3037	−	11.1631i	0.714181	−	0.599269i	0.925769	+	0.378090i	$0.123419\pi$
$348$	1.27501	−	7.23092i	0.0683475	−	0.387618i
$349$	−0.316102	+	0.547504i	−0.0169205	+	0.0293072i	−0.874362	−	0.485275i	$-0.838720\pi$
$349$	−0.316102	+	0.547504i	−0.0169205	+	0.0293072i	0.857441	+	0.514582i	$0.172053\pi$
$350$	1.44877	+	2.50934i	0.0774399	+	0.134130i
$351$	−13.4154	+	4.88281i	−0.716062	+	0.260625i
$352$	−0.939693	+	0.342020i	−0.0500858	+	0.0182297i
$353$	−3.78480	−	6.55547i	−0.201445	−	0.348912i	0.747549	−	0.664206i	$-0.231230\pi$
$353$	−3.78480	−	6.55547i	−0.201445	−	0.348912i	−0.948994	+	0.315294i	$0.897897\pi$
$354$	7.79639	−	13.5037i	0.414373	−	0.717716i
$355$	1.57384	−	8.92568i	0.0835306	−	0.473726i
$356$	0.402498	−	0.337736i	0.0213324	−	0.0179000i
$357$	−19.9783	−	16.7638i	−1.05736	−	0.887233i
$358$	−4.48644	−	25.4439i	−0.237116	−	1.34475i
$359$	5.91736	+	2.15374i	0.312306	+	0.113670i	0.493418	−	0.869792i	$-0.335747\pi$
$359$	5.91736	+	2.15374i	0.312306	+	0.113670i	−0.181112	+	0.983463i	$0.557970\pi$
$360$	0.354890			0.0187044
$361$	−18.7066	+	3.32596i	−0.984559	+	0.175051i
$362$	2.97802			0.156521
$363$	−1.57875	−	0.574617i	−0.0828628	−	0.0301596i
$364$	1.35018	+	7.65727i	0.0707689	+	0.401350i
$365$	3.76751	+	3.16131i	0.197200	+	0.165471i
$366$	11.0850	−	9.30142i	0.579422	−	0.486193i
$367$	3.89650	−	22.0982i	0.203396	−	1.15351i	−0.696549	−	0.717509i	$-0.745282\pi$
$367$	3.89650	−	22.0982i	0.203396	−	1.15351i	0.899944	−	0.436005i	$-0.143607\pi$
$368$	1.26714	−	2.19475i	0.0660541	−	0.114409i
$369$	0.560384	+	0.970613i	0.0291724	+	0.0505281i
$370$	−14.3538	+	5.22437i	−0.746221	+	0.271602i
$371$	−23.4215	+	8.52472i	−1.21598	+	0.442581i
$372$	−8.17076	−	14.1522i	−0.423634	−	0.733756i
$373$	16.8652	−	29.2114i	0.873248	−	1.51251i	0.0146309	−	0.999893i	$-0.495343\pi$
$373$	16.8652	−	29.2114i	0.873248	−	1.51251i	0.858617	−	0.512617i	$-0.171324\pi$
$374$	0.927147	−	5.25811i	0.0479417	−	0.271891i
$375$	−15.4419	+	12.9573i	−0.797417	+	0.669112i
$376$	8.39999	+	7.04843i	0.433196	+	0.363495i
$377$	−2.02959	−	11.5104i	−0.104529	−	0.592816i
$378$	14.5841	+	5.30818i	0.750125	+	0.273023i
$379$	26.4601			1.35916			0.679582	−	0.733599i	$-0.262161\pi$
$379$	26.4601			1.35916			0.679582	+	0.733599i	$0.262161\pi$
$380$	−0.766314	−	8.68775i	−0.0393111	−	0.445672i
$381$	18.4027			0.942800
$382$	−5.92329	−	2.15590i	−0.303062	−	0.110306i
$383$	5.06339	+	28.7159i	0.258727	+	1.46732i	0.786321	+	0.617819i	$0.211983\pi$
$383$	5.06339	+	28.7159i	0.258727	+	1.46732i	−0.527593	+	0.849497i	$0.676905\pi$
$384$	−1.28701	−	1.07993i	−0.0656773	−	0.0551098i
$385$	4.45622	−	3.73921i	0.227110	−	0.190568i
$386$	−0.707818	+	4.01424i	−0.0360270	+	0.204319i
$387$	0.612284	−	1.06051i	0.0311241	−	0.0539086i
$388$	3.80293	+	6.58687i	0.193065	+	0.334398i
$389$	−35.1656	+	12.7992i	−1.78296	+	0.648946i	−0.783339	+	0.621595i	$0.786485\pi$
$389$	−35.1656	+	12.7992i	−1.78296	+	0.648946i	−0.999626	+	0.0273507i	$0.991293\pi$
$390$	−8.44792	+	3.07479i	−0.427777	+	0.155698i
$391$	6.76554	+	11.7183i	0.342148	+	0.592618i
$392$	0.726375	−	1.25812i	0.0366875	−	0.0635445i
$393$	0.487575	−	2.76518i	0.0245949	−	0.139485i
$394$	12.3454	−	10.3590i	0.621950	−	0.521878i
$395$	−15.9537	−	13.3867i	−0.802718	−	0.673560i
$396$	0.0308000	+	0.174676i	0.00154776	+	0.00877778i
$397$	0.367658	+	0.133817i	0.0184523	+	0.00671607i	0.351230	−	0.936289i	$-0.385764\pi$
$397$	0.367658	+	0.133817i	0.0184523	+	0.00671607i	−0.332778	+	0.943005i	$0.607986\pi$
$398$	3.45546			0.173207
$399$	5.49595	−	20.5698i	0.275142	−	1.02978i
$400$	−0.996621			−0.0498310
$401$	−5.77834	−	2.10314i	−0.288557	−	0.105026i	0.193686	−	0.981063i	$-0.437956\pi$
$401$	−5.77834	−	2.10314i	−0.288557	−	0.105026i	−0.482243	+	0.876037i	$0.660178\pi$
$402$	3.88303	+	22.0218i	0.193668	+	1.09835i
$403$	−19.9271	−	16.7208i	−0.992637	−	0.832922i
$404$	2.19246	−	1.83970i	0.109079	−	0.0915283i
$405$	−2.93118	+	16.6235i	−0.145651	+	0.826030i
$406$	−6.35308	+	11.0039i	−0.315298	+	0.546112i
$407$	−3.81715	−	6.61150i	−0.189209	−	0.327720i
$408$	8.42930	−	3.06801i	0.417312	−	0.151889i
$409$	−22.5280	+	8.19952i	−1.11394	+	0.405440i	−0.832436	−	0.554121i	$-0.813055\pi$
$409$	−22.5280	+	8.19952i	−1.11394	+	0.405440i	−0.281501	+	0.959561i	$0.590832\pi$
$410$	6.32147	+	10.9491i	0.312195	+	0.540738i
$411$	−8.98429	+	15.5613i	−0.443162	+	0.767580i
$412$	−2.61175	+	14.8120i	−0.128672	+	0.729733i
$413$	−20.6704	+	17.3446i	−1.01713	+	0.853470i
$414$	−0.344341	−	0.288936i	−0.0169234	−	0.0142004i
$415$	−2.32145	−	13.1656i	−0.113955	−	0.646273i
$416$	−2.51310	−	0.914693i	−0.123215	−	0.0448465i
$417$	−5.16251			−0.252809
$418$	4.20957	−	1.13116i	0.205897	−	0.0553271i
$419$	−19.6640			−0.960648			−0.480324	−	0.877091i	$-0.659481\pi$
$419$	−19.6640			−0.960648			−0.480324	+	0.877091i	$0.659481\pi$
$420$	9.18386	+	3.34265i	0.448126	+	0.163105i
$421$	−1.46781	−	8.32438i	−0.0715368	−	0.405705i	−0.999458	−	0.0329283i	$-0.989517\pi$
$421$	−1.46781	−	8.32438i	−0.0715368	−	0.405705i	0.927921	−	0.372777i	$-0.121594\pi$
$422$	5.17763	+	4.34454i	0.252043	+	0.211489i
$423$	1.48991	−	1.25018i	0.0724418	−	0.0607859i
$424$	1.48867	−	8.44269i	0.0722964	−	0.410013i
$425$	2.66059	−	4.60828i	0.129058	−	0.223535i
$426$	3.80516	+	6.59074i	0.184361	+	0.319322i
$427$	−23.5310	+	8.56457i	−1.13874	+	0.414468i
$428$	−16.3678	+	5.95740i	−0.791168	+	0.287962i
$429$	−2.24657	−	3.89118i	−0.108466	−	0.187868i
$430$	6.90693	−	11.9632i	0.333082	−	0.576915i
$431$	6.66403	−	37.7936i	0.320995	−	1.82045i	−0.215445	−	0.976516i	$-0.569120\pi$
$431$	6.66403	−	37.7936i	0.320995	−	1.82045i	0.536440	−	0.843938i	$-0.319769\pi$
$432$	−4.08930	+	3.43133i	−0.196746	+	0.165090i
$433$	7.29311	+	6.11965i	0.350484	+	0.294091i	0.800985	−	0.598685i	$-0.204310\pi$
$433$	7.29311	+	6.11965i	0.350484	+	0.294091i	−0.450500	+	0.892776i	$0.648754\pi$
$434$	4.91060	+	27.8494i	0.235716	+	1.33681i
$435$	−13.8052	−	5.02467i	−0.661907	−	0.240914i
$436$	4.69381			0.224792
$437$	−6.32965	+	9.05339i	−0.302788	+	0.433083i
$438$	−4.12966			−0.197323
$439$	12.1363	+	4.41726i	0.579235	+	0.210824i	0.614988	−	0.788536i	$-0.289161\pi$
$439$	12.1363	+	4.41726i	0.579235	+	0.210824i	−0.0357534	+	0.999361i	$0.511383\pi$
$440$	0.347443	+	1.97045i	0.0165637	+	0.0939374i
$441$	−0.197390	−	0.165630i	−0.00939953	−	0.00788715i
$442$	10.9385	−	9.17846i	0.520289	−	0.436575i
$443$	4.05580	−	23.0016i	0.192697	−	1.09284i	−0.722963	−	0.690886i	$-0.757221\pi$
$443$	4.05580	−	23.0016i	0.192697	−	1.09284i	0.915660	−	0.401953i	$-0.131668\pi$
$444$	6.41307	−	11.1078i	0.304351	−	0.527151i
$445$	−0.525646	−	0.910446i	−0.0249180	−	0.0431593i
$446$	−3.53167	+	1.28542i	−0.167229	+	0.0608665i
$447$	22.0644	−	8.03077i	1.04361	−	0.379843i
$448$	1.45368	+	2.51785i	0.0686800	+	0.118957i
$449$	7.88451	−	13.6564i	0.372093	−	0.644484i	−0.617794	−	0.786340i	$-0.711974\pi$
$449$	7.88451	−	13.6564i	0.372093	−	0.644484i	0.989887	+	0.141856i	$0.0453068\pi$
$450$	−0.0306960	+	0.174085i	−0.00144702	+	0.00820647i
$451$	−4.84048	+	4.06165i	−0.227929	+	0.191255i
$452$	−5.24857	−	4.40407i	−0.246872	−	0.207150i
$453$	3.19966	+	18.1461i	0.150333	+	0.852580i
$454$	−5.84046	−	2.12575i	−0.274106	−	0.0997666i
$455$	15.5574			0.729340
$456$	5.18200	+	5.17463i	0.242670	+	0.242324i
$457$	−18.8267			−0.880677			−0.440338	−	0.897832i	$-0.645142\pi$
$457$	−18.8267			−0.880677			−0.440338	+	0.897832i	$0.645142\pi$
$458$	1.83364	+	0.667389i	0.0856802	+	0.0311851i
$459$	−4.94930	−	28.0689i	−0.231013	−	1.31014i
$460$	−3.88437	−	3.25938i	−0.181110	−	0.151969i
$461$	−21.9841	+	18.4469i	−1.02390	+	0.859157i	−0.990113	−	0.140272i	$-0.955202\pi$
$461$	−21.9841	+	18.4469i	−1.02390	+	0.859157i	−0.0337903	+	0.999429i	$0.510758\pi$
$462$	−0.848196	+	4.81036i	−0.0394616	+	0.223798i
$463$	−15.2904	+	26.4838i	−0.710605	+	1.23080i	0.254025	+	0.967198i	$0.418245\pi$
$463$	−15.2904	+	26.4838i	−0.710605	+	1.23080i	−0.964630	+	0.263607i	$0.915088\pi$
$464$	−2.18517	−	3.78483i	−0.101444	−	0.175706i
$465$	−30.7250	+	11.1830i	−1.42484	+	0.518598i
$466$	−7.91965	+	2.88252i	−0.366871	+	0.133530i
$467$	17.7529	+	30.7489i	0.821505	+	1.42289i	0.904562	+	0.426343i	$0.140198\pi$
$467$	17.7529	+	30.7489i	0.821505	+	1.42289i	−0.0830570	+	0.996545i	$0.526468\pi$
$468$	−0.237178	+	0.410805i	−0.0109636	+	0.0189894i
$469$	6.71959	−	38.1087i	0.310282	−	1.75970i
$470$	16.8071	−	14.1028i	0.775252	−	0.650514i
$471$	−28.8245	−	24.1866i	−1.32816	−	1.11446i
$472$	−1.61164	−	9.14004i	−0.0741815	−	0.420704i
$473$	6.48765	+	2.36131i	0.298303	+	0.108573i
$474$	17.4872			0.803215
$475$	4.32791	+	0.375537i	0.198578	+	0.0172308i
$476$	−15.5231			−0.711499
$477$	−1.42888	−	0.520070i	−0.0654240	−	0.0238124i
$478$	0.559809	+	3.17483i	0.0256051	+	0.145213i
$479$	0.119976	+	0.100672i	0.00548183	+	0.00459981i	0.645524	−	0.763740i	$-0.276639\pi$
$479$	0.119976	+	0.100672i	0.00548183	+	0.00459981i	−0.640043	+	0.768339i	$0.721083\pi$
$480$	−2.57510	+	2.16077i	−0.117537	+	0.0986250i
$481$	3.54538	−	20.1069i	0.161656	−	0.916794i
$482$	−8.27130	+	14.3263i	−0.376748	+	0.652546i
$483$	−6.18942	−	10.7204i	−0.281628	−	0.487794i
$484$	−0.939693	+	0.342020i	−0.0427133	+	0.0155464i
$485$	14.3004	−	5.20491i	0.649347	−	0.236343i
$486$	0.920411	+	1.59420i	0.0417507	+	0.0723143i
$487$	−3.78737	+	6.55993i	−0.171622	+	0.297259i	−0.938987	−	0.343952i	$-0.888234\pi$
$487$	−3.78737	+	6.55993i	−0.171622	+	0.297259i	0.767365	+	0.641211i	$0.221568\pi$
$488$	1.49563	−	8.48215i	0.0677041	−	0.383969i
$489$	−30.9638	+	25.9817i	−1.40023	+	1.17493i
$490$	−2.22668	−	1.86841i	−0.100591	−	0.0844060i
$491$	2.26562	+	12.8490i	0.102246	+	0.579866i	0.992285	+	0.123981i	$0.0395662\pi$
$491$	2.26562	+	12.8490i	0.102246	+	0.579866i	−0.890039	+	0.455885i	$0.849323\pi$
$492$	−9.97579	−	3.63089i	−0.449743	−	0.163693i
$493$	23.3342			1.05092
$494$	10.5687	+	4.91909i	0.475507	+	0.221320i
$495$	0.354890			0.0159511
$496$	−9.14011	−	3.32673i	−0.410403	−	0.149374i
$497$	−2.28689	−	12.9696i	−0.102581	−	0.581766i
$498$	8.59916	+	7.21555i	0.385338	+	0.323337i
$499$	−2.68247	+	2.25086i	−0.120084	+	0.100762i	−0.700852	−	0.713307i	$-0.747197\pi$
$499$	−2.68247	+	2.25086i	−0.120084	+	0.100762i	0.580768	+	0.814069i	$0.302752\pi$
$500$	−2.08348	+	11.8160i	−0.0931762	+	0.528429i
$501$	9.77019	−	16.9225i	0.436500	−	0.756040i
$502$	−11.5120	−	19.9395i	−0.513808	−	0.889941i
$503$	−2.43970	+	0.887979i	−0.108781	+	0.0395930i	−0.395837	−	0.918321i	$-0.629546\pi$
$503$	−2.43970	+	0.887979i	−0.108781	+	0.0395930i	0.287056	+	0.957914i	$0.407323\pi$
$504$	0.484580	−	0.176373i	0.0215849	−	0.00785627i
$505$	−2.86327	−	4.95933i	−0.127414	−	0.220687i
$506$	1.26714	−	2.19475i	0.0563311	−	0.0975684i
$507$	−1.70601	+	9.67524i	−0.0757663	+	0.429692i
$508$	8.39091	−	7.04081i	0.372286	−	0.312385i
$509$	3.09688	+	2.59859i	0.137267	+	0.115181i	0.708836	−	0.705373i	$-0.249221\pi$
$509$	3.09688	+	2.59859i	0.137267	+	0.115181i	−0.571569	+	0.820554i	$0.693665\pi$
$510$	−3.11666	−	17.6754i	−0.138008	−	0.782682i
$511$	6.71540	+	2.44420i	0.297072	+	0.108125i
$512$	−1.00000			−0.0441942
$513$	19.0511	−	13.3599i	0.841125	−	0.589855i
$514$	16.3732			0.722192
$515$	28.2787	+	10.2926i	1.24611	+	0.453547i
$516$	2.01418	+	11.4230i	0.0886695	+	0.502870i
$517$	8.39999	+	7.04843i	0.369431	+	0.309989i
$518$	−17.0029	+	14.2671i	−0.747063	+	0.626860i
$519$	0.124655	−	0.706956i	0.00547177	−	0.0310319i
$520$	−2.67551	+	4.63412i	−0.117329	+	0.203220i
$521$	−3.45612	−	5.98618i	−0.151416	−	0.262259i	0.780333	−	0.625365i	$-0.215050\pi$
$521$	−3.45612	−	5.98618i	−0.151416	−	0.262259i	−0.931748	+	0.363105i	$0.881716\pi$
$522$	−0.728420	+	0.265123i	−0.0318821	+	0.0116041i
$523$	−2.32630	+	0.846706i	−0.101722	+	0.0370239i	−0.392380	−	0.919803i	$-0.628348\pi$
$523$	−2.32630	+	0.846706i	−0.101722	+	0.0370239i	0.290658	+	0.956827i	$0.406126\pi$
$524$	−0.835631	−	1.44736i	−0.0365047	−	0.0632280i
$525$	−2.43403	+	4.21586i	−0.106230	+	0.183995i
$526$	1.64339	−	9.32012i	0.0716551	−	0.406376i
$527$	39.7830	−	33.3819i	1.73298	−	1.45414i
$528$	−1.28701	−	1.07993i	−0.0560098	−	0.0469978i
$529$	−2.87864	−	16.3256i	−0.125158	−	0.709809i
$530$	−16.1186	−	5.86671i	−0.700149	−	0.254834i
$531$	−1.64618			−0.0714382
$532$	−5.36397	−	11.4817i	−0.232558	−	0.497796i
$533$	−16.8989			−0.731972
$534$	0.829512	+	0.301918i	0.0358965	+	0.0130653i
$535$	6.05186	+	34.3218i	0.261645	+	1.48386i
$536$	10.1959	+	8.55542i	0.440398	+	0.369538i
$537$	33.2516	−	27.9014i	1.43491	−	1.20404i
$538$	−0.626952	+	3.55562i	−0.0270298	+	0.153294i
$539$	0.726375	−	1.25812i	0.0312872	−	0.0541910i
$540$	5.34045	+	9.24994i	0.229817	+	0.398054i
$541$	11.6605	−	4.24406i	0.501322	−	0.182466i	−0.0789664	−	0.996877i	$-0.525162\pi$
$541$	11.6605	−	4.24406i	0.501322	−	0.182466i	0.580289	+	0.814411i	$0.302940\pi$
$542$	−7.19513	+	2.61881i	−0.309057	+	0.112488i
$543$	2.50164	+	4.33297i	0.107356	+	0.185945i
$544$	2.66961	−	4.62391i	0.114459	−	0.198248i
$545$	1.63083	−	9.24890i	0.0698571	−	0.396179i
$546$	−10.0070	+	8.39686i	−0.428260	+	0.359353i
$547$	−11.6595	−	9.78351i	−0.498525	−	0.418313i	0.358544	−	0.933513i	$-0.383273\pi$
$547$	−11.6595	−	9.78351i	−0.498525	−	0.418313i	−0.857070	+	0.515200i	$0.827718\pi$
$548$	1.85719	+	10.5327i	0.0793354	+	0.449933i
$549$	−1.43556	−	0.522501i	−0.0612682	−	0.0222998i
$550$	−0.996621			−0.0424961
$551$	8.06312	+	17.2593i	0.343500	+	0.735271i
$552$	4.25775			0.181222
$553$	−28.4367	−	10.3501i	−1.20925	−	0.440131i
$554$	5.38304	+	30.5288i	0.228704	+	1.29704i
$555$	−19.6591	−	16.4959i	−0.834482	−	0.700214i
$556$	−2.35390	+	1.97516i	−0.0998276	+	0.0837653i
$557$	1.77831	−	10.0853i	0.0753494	−	0.427327i	−0.923675	−	0.383176i	$-0.874830\pi$
$557$	1.77831	−	10.0853i	0.0753494	−	0.427327i	0.999025	−	0.0441518i	$-0.0140585\pi$
$558$	−0.862614	+	1.49409i	−0.0365174	+	0.0632499i
$559$	9.23199	+	15.9903i	0.390472	+	0.676317i
$560$	5.46636	−	1.98959i	0.230996	−	0.0840756i
$561$	8.42930	−	3.06801i	0.355885	−	0.129532i
$562$	2.43354	+	4.21502i	0.102653	+	0.177800i
$563$	−22.8848	+	39.6376i	−0.964478	+	1.67052i	−0.253466	+	0.967344i	$0.581571\pi$
$563$	−22.8848	+	39.6376i	−0.964478	+	1.67052i	−0.711011	+	0.703180i	$0.751763\pi$
$564$	−3.19906	+	18.1427i	−0.134705	+	0.763947i
$565$	−10.5016	+	8.81186i	−0.441804	+	0.370718i
$566$	16.4638	+	13.8148i	0.692025	+	0.580678i
$567$	4.25920	+	24.1551i	0.178870	+	1.01442i
$568$	4.25659	+	1.54927i	0.178603	+	0.0650061i
$569$	−15.8811			−0.665771			−0.332886	−	0.942967i	$-0.608022\pi$
$569$	−15.8811			−0.665771			−0.332886	+	0.942967i	$0.608022\pi$
$570$	11.9968	−	8.41298i	0.502490	−	0.352381i
$571$	3.10895			0.130106			0.0650528	−	0.997882i	$-0.479278\pi$
$571$	3.10895			0.130106			0.0650528	+	0.997882i	$0.479278\pi$
$572$	−2.51310	−	0.914693i	−0.105078	−	0.0382452i
$573$	−1.83897	−	10.4293i	−0.0768241	−	0.435691i
$574$	14.0730	+	11.8087i	0.587397	+	0.492884i
$575$	1.93481	−	1.62350i	0.0806870	−	0.0677045i
$576$	−0.0308000	+	0.174676i	−0.00128333	+	0.00727815i
$577$	5.48624	−	9.50245i	0.228395	−	0.395592i	−0.728938	−	0.684580i	$-0.759986\pi$
$577$	5.48624	−	9.50245i	0.228395	−	0.395592i	0.957333	+	0.288988i	$0.0933189\pi$
$578$	5.75368	+	9.96567i	0.239322	+	0.414517i
$579$	−6.43523	+	2.34223i	−0.267439	+	0.0973399i
$580$	−8.21702	+	2.99075i	−0.341193	+	0.124184i
$581$	−9.71279	−	16.8231i	−0.402955	−	0.697938i
$582$	−6.38918	+	11.0664i	−0.264840	+	0.458717i
$583$	1.48867	−	8.44269i	0.0616546	−	0.349661i
$584$	−1.88296	+	1.57999i	−0.0779174	+	0.0653805i
$585$	0.727063	+	0.610078i	0.0300603	+	0.0252236i
$586$	−0.708179	−	4.01628i	−0.0292546	−	0.165911i
$587$	7.45802	+	2.71450i	0.307825	+	0.112039i	0.491314	−	0.870983i	$-0.336517\pi$
$587$	7.45802	+	2.71450i	0.307825	+	0.112039i	−0.183489	+	0.983022i	$0.558739\pi$
$588$	2.44072			0.100654
$589$	38.4381	+	17.8907i	1.58382	+	0.737172i
$590$	−18.5699			−0.764511
$591$	25.4427	+	9.26037i	1.04657	+	0.380921i
$592$	−1.32568	−	7.51832i	−0.0544852	−	0.309001i
$593$	9.11342	+	7.64706i	0.374243	+	0.314027i	0.810437	−	0.585825i	$-0.199230\pi$
$593$	9.11342	+	7.64706i	0.374243	+	0.314027i	−0.436194	+	0.899853i	$0.643674\pi$
$594$	−4.08930	+	3.43133i	−0.167786	+	0.140789i
$595$	−5.39338	+	30.5874i	−0.221107	+	1.25396i
$596$	6.98793	−	12.1035i	0.286237	−	0.495777i
$597$	2.90271	+	5.02763i	0.118800	+	0.205767i
$598$	6.36888	−	2.31808i	0.260443	−	0.0947935i
$599$	31.0716	−	11.3091i	1.26955	−	0.462079i	0.382587	−	0.923919i	$-0.375033\pi$
$599$	31.0716	−	11.3091i	1.26955	−	0.462079i	0.886963	+	0.461841i	$0.152811\pi$
$600$	−0.837196	−	1.45007i	−0.0341784	−	0.0591987i
$601$	−20.5545	+	35.6014i	−0.838434	+	1.45221i	0.0527704	+	0.998607i	$0.483195\pi$
$601$	−20.5545	+	35.6014i	−0.838434	+	1.45221i	−0.891204	+	0.453603i	$0.850138\pi$
$602$	3.48555	−	19.7675i	0.142060	−	0.805664i
$603$	1.80846	−	1.51748i	0.0736461	−	0.0617964i
$604$	8.40156	+	7.04975i	0.341855	+	0.286850i
$605$	0.347443	+	1.97045i	0.0141256	+	0.0801101i
$606$	4.51847	+	1.64459i	0.183550	+	0.0668068i
$607$	16.8657			0.684558			0.342279	−	0.939598i	$-0.388801\pi$
$607$	16.8657			0.684558			0.342279	+	0.939598i	$0.388801\pi$
$608$	4.34258	+	0.376811i	0.176115	+	0.0152817i
$609$	−21.3472			−0.865033
$610$	−16.1940	−	5.89413i	−0.655675	−	0.238646i
$611$	5.09235	+	28.8802i	0.206015	+	1.16837i
$612$	−0.725460	−	0.608733i	−0.0293250	−	0.0246066i
$613$	−4.23633	+	3.55470i	−0.171104	+	0.143573i	−0.724318	−	0.689466i	$-0.757845\pi$
$613$	−4.23633	+	3.55470i	−0.171104	+	0.143573i	0.553215	+	0.833039i	$0.313401\pi$
$614$	2.85761	−	16.2063i	0.115324	−	0.654033i
$615$	−10.6205	+	18.3952i	−0.428260	+	0.741768i
$616$	1.45368	+	2.51785i	0.0585705	+	0.101447i
$617$	22.4555	−	8.17313i	0.904024	−	0.329038i	0.152160	−	0.988356i	$-0.451377\pi$
$617$	22.4555	−	8.17313i	0.904024	−	0.329038i	0.751864	+	0.659318i	$0.229155\pi$
$618$	−23.7451	+	8.64251i	−0.955168	+	0.347653i
$619$	24.2140	+	41.9399i	0.973244	+	1.68571i	0.685613	+	0.727966i	$0.259534\pi$
$619$	24.2140	+	41.9399i	0.973244	+	1.68571i	0.287630	+	0.957742i	$0.407133\pi$
$620$	−9.73081	+	16.8543i	−0.390799	+	0.676883i
$621$	2.34919	−	13.3229i	0.0942699	−	0.534631i
$622$	−10.6458	+	8.93290i	−0.426858	+	0.358177i
$623$	−1.17021	−	0.981921i	−0.0468834	−	0.0393398i
$624$	−0.780227	−	4.42489i	−0.0312341	−	0.177137i
$625$	17.8764	+	6.50647i	0.715055	+	0.260259i
$626$	12.7207			0.508423
$627$	5.18200	+	5.17463i	0.206949	+	0.206655i
$628$	−22.3965			−0.893719
$629$	38.3031	+	13.9412i	1.52724	+	0.555871i
$630$	−0.179169	−	1.01612i	−0.00713828	−	0.0404832i
$631$	−0.446914	−	0.375005i	−0.0177914	−	0.0149287i	0.633849	−	0.773457i	$-0.281474\pi$
$631$	−0.446914	−	0.375005i	−0.0177914	−	0.0149287i	−0.651640	+	0.758528i	$0.725919\pi$
$632$	7.97348	−	6.69055i	0.317168	−	0.266136i
$633$	−1.97185	+	11.1829i	−0.0783740	+	0.444481i
$634$	−6.00643	+	10.4035i	−0.238546	+	0.413174i
$635$	−10.9582	−	18.9801i	−0.434862	−	0.753203i
$636$	13.5345	−	4.92615i	0.536678	−	0.195335i
$637$	3.65090	−	1.32882i	0.144654	−	0.0526498i
$638$	−2.18517	−	3.78483i	−0.0865117	−	0.149843i
$639$	0.401724	−	0.695806i	0.0158919	−	0.0275257i
$640$	−0.347443	+	1.97045i	−0.0137339	+	0.0778888i
$641$	20.7878	−	17.4430i	0.821069	−	0.688958i	−0.132153	−	0.991229i	$-0.542189\pi$
$641$	20.7878	−	17.4430i	0.821069	−	0.688958i	0.953222	+	0.302271i	$0.0977447\pi$
$642$	−22.4174	−	18.8105i	−0.884746	−	0.742390i
$643$	5.59812	+	31.7485i	0.220768	+	1.25204i	0.870612	+	0.491971i	$0.163723\pi$
$643$	5.59812	+	31.7485i	0.220768	+	1.25204i	−0.649844	+	0.760068i	$0.725166\pi$
$644$	−6.92370	−	2.52002i	−0.272832	−	0.0993028i
$645$	23.2082			0.913823
$646$	−13.3354	+	19.0738i	−0.524673	+	0.750447i
$647$	33.2829			1.30848			0.654242	−	0.756285i	$-0.272988\pi$
$647$	33.2829			1.30848			0.654242	+	0.756285i	$0.272988\pi$
$648$	−7.92765	−	2.88543i	−0.311427	−	0.113350i
$649$	−1.61164	−	9.14004i	−0.0632622	−	0.358778i
$650$	−2.04177	−	1.71325i	−0.0800850	−	0.0671993i
$651$	−36.3953	+	30.5393i	−1.42644	+	1.19693i
$652$	−4.17776	+	23.6932i	−0.163614	+	0.927899i
$653$	1.62201	−	2.80940i	0.0634741	−	0.109940i	−0.832542	−	0.553962i	$-0.813115\pi$
$653$	1.62201	−	2.80940i	0.0634741	−	0.109940i	0.896016	+	0.444022i	$0.146449\pi$
$654$	3.94296	+	6.82940i	0.154182	+	0.267051i
$655$	−3.14227	+	1.14369i	−0.122779	+	0.0446878i
$656$	−5.93773	+	2.16116i	−0.231829	+	0.0843790i
$657$	0.217991	+	0.377571i	0.00850463	+	0.0147304i
$658$	15.9402	−	27.6092i	0.621414	−	1.07632i
$659$	−6.32658	+	35.8798i	−0.246449	+	1.39768i	0.570655	+	0.821190i	$0.306689\pi$
$659$	−6.32658	+	35.8798i	−0.246449	+	1.39768i	−0.817104	+	0.576490i	$0.804422\pi$
$660$	−2.57510	+	2.16077i	−0.100236	+	0.0841077i
$661$	−18.6006	−	15.6078i	−0.723481	−	0.607073i	0.204865	−	0.978790i	$-0.434325\pi$
$661$	−18.6006	−	15.6078i	−0.723481	−	0.607073i	−0.928346	+	0.371718i	$0.878769\pi$
$662$	−0.845569	−	4.79546i	−0.0328640	−	0.186381i
$663$	22.5432	+	8.20504i	0.875504	+	0.318657i
$664$	6.68152			0.259293
$665$	−24.4878	+	6.58018i	−0.949597	+	0.255169i
$666$	−1.35410			−0.0524702
$667$	10.4077	+	3.78809i	0.402988	+	0.146676i
$668$	−2.01965	−	11.4540i	−0.0781427	−	0.443169i
$669$	−4.83698	−	4.05871i	−0.187009	−	0.156919i
$670$	20.4005	−	17.1181i	0.788140	−	0.661328i
$671$	1.49563	−	8.48215i	0.0577383	−	0.327450i
$672$	−2.44228	+	4.23016i	−0.0942131	+	0.163182i
$673$	9.19132	+	15.9198i	0.354299	+	0.613664i	0.986998	−	0.160734i	$-0.0513861\pi$
$673$	9.19132	+	15.9198i	0.354299	+	0.613664i	−0.632699	+	0.774398i	$0.718053\pi$
$674$	31.7725	−	11.5643i	1.22383	−	0.445438i
$675$	−4.99932	+	1.81960i	−0.192424	+	0.0700365i
$676$	2.92384	+	5.06423i	0.112455	+	0.194778i
$677$	4.56600	−	7.90855i	0.175486	−	0.303950i	−0.764844	−	0.644216i	$-0.777184\pi$
$677$	4.56600	−	7.90855i	0.175486	−	0.303950i	0.940329	+	0.340266i	$0.110517\pi$
$678$	1.99887	−	11.3361i	0.0767660	−	0.435362i
$679$	16.9395	−	14.2140i	0.650080	−	0.545482i
$680$	−8.18363	−	6.86688i	−0.313828	−	0.263333i
$681$	−1.81325	−	10.2835i	−0.0694840	−	0.394063i
$682$	−9.14011	−	3.32673i	−0.349993	−	0.127387i
$683$	−28.0940			−1.07499			−0.537494	−	0.843267i	$-0.680629\pi$
$683$	−28.0940			−1.07499			−0.537494	+	0.843267i	$0.680629\pi$
$684$	0.199571	−	0.746938i	0.00763080	−	0.0285599i
$685$	21.3993			0.817627
$686$	15.1552	+	5.51605i	0.578629	+	0.210604i
$687$	0.569278	+	3.22854i	0.0217193	+	0.123176i
$688$	5.28878	+	4.43782i	0.201633	+	0.169190i
$689$	17.5633	−	14.7374i	0.669110	−	0.561450i
$690$	1.47933	−	8.38968i	0.0563170	−	0.319390i
$691$	−18.5435	+	32.1183i	−0.705428	+	1.22184i	0.261109	+	0.965309i	$0.415912\pi$
$691$	−18.5435	+	32.1183i	−0.705428	+	1.22184i	−0.966537	+	0.256528i	$0.917421\pi$
$692$	−0.213641	−	0.370037i	−0.00812140	−	0.0140667i
$693$	0.484580	−	0.176373i	0.0184077	−	0.00669985i
$694$	16.3194	−	5.93978i	0.619477	−	0.225471i
$695$	3.07410	+	5.32449i	0.116607	+	0.201969i
$696$	3.67124	−	6.35877i	0.139158	−	0.241028i
$697$	5.85846	−	33.2250i	0.221905	−	1.25849i
$698$	−0.484296	+	0.406372i	−0.0183309	+	0.0153814i
$699$	−10.8468	−	9.10154i	−0.410263	−	0.344252i
$700$	0.503152	+	2.85352i	0.0190174	+	0.107853i
$701$	−14.0835	−	5.12596i	−0.531925	−	0.193605i	0.0620725	−	0.998072i	$-0.480229\pi$
$701$	−14.0835	−	5.12596i	−0.531925	−	0.193605i	−0.593998	+	0.804467i	$0.702451\pi$
$702$	−14.2764			−0.538828
$703$	2.92390	+	33.1484i	0.110277	+	1.25022i
$704$	−1.00000			−0.0376889
$705$	34.6378	+	12.6071i	1.30454	+	0.474812i
$706$	−1.31445	−	7.45461i	−0.0494699	−	0.280558i
$707$	−6.37429	−	5.34866i	−0.239730	−	0.201157i
$708$	11.9448	−	10.0228i	0.448912	−	0.376682i
$709$	6.30388	−	35.7511i	0.236747	−	1.34266i	−0.602156	−	0.798379i	$-0.705691\pi$
$709$	6.30388	−	35.7511i	0.236747	−	1.34266i	0.838903	−	0.544281i	$-0.183198\pi$
$710$	4.53169	−	7.84911i	0.170071	−	0.294572i
$711$	−0.923092	−	1.59884i	−0.0346187	−	0.0599613i
$712$	0.493737	−	0.179706i	0.0185036	−	0.00673476i
$713$	23.1635	−	8.43084i	0.867482	−	0.315738i
$714$	−13.0399	−	22.5858i	−0.488006	−	0.845252i
$715$	−2.67551	+	4.63412i	−0.100059	+	0.173306i
$716$	4.48644	−	25.4439i	0.167666	−	0.950882i
$717$	−4.14907	+	3.48148i	−0.154950	+	0.130018i
$718$	4.82387	+	4.04771i	0.180025	+	0.151059i
$719$	−4.73183	−	26.8356i	−0.176468	−	1.00080i	−0.936436	−	0.350838i	$-0.885897\pi$
$719$	−4.73183	−	26.8356i	−0.176468	−	1.00080i	0.759969	−	0.649960i	$-0.225214\pi$
$720$	0.333488	+	0.121380i	0.0124284	+	0.00452355i
$721$	43.7280			1.62852
$722$	−18.7160	−	3.27266i	−0.696538	−	0.121796i
$723$	−27.7927			−1.03362
$724$	2.79843	+	1.01854i	0.104003	+	0.0378539i
$725$	−0.756337	−	4.28940i	−0.0280897	−	0.159304i
$726$	−1.28701	−	1.07993i	−0.0477653	−	0.0400799i
$727$	29.3619	−	24.6376i	1.08897	−	0.913757i	0.0923388	−	0.995728i	$-0.470566\pi$
$727$	29.3619	−	24.6376i	1.08897	−	0.913757i	0.996635	+	0.0819704i	$0.0261213\pi$
$728$	−1.35018	+	7.65727i	−0.0500411	+	0.283797i
$729$	−14.2010	+	24.5968i	−0.525963	+	0.910994i
$730$	2.45907	+	4.25923i	0.0910141	+	0.157641i
$731$	−34.6391	+	12.6076i	−1.28117	+	0.466308i
$732$	13.5978	−	4.94918i	0.502588	−	0.182927i
$733$	−13.8268	−	23.9487i	−0.510704	−	0.884566i	−0.999923	−	0.0124046i	$-0.996051\pi$
$733$	−13.8268	−	23.9487i	−0.510704	−	0.884566i	0.489219	−	0.872161i	$-0.337282\pi$
$734$	11.2195	−	19.4328i	0.414120	−	0.717277i
$735$	0.848010	−	4.80931i	0.0312793	−	0.177394i
$736$	1.94137	−	1.62900i	0.0715597	−	0.0600458i
$737$	10.1959	+	8.55542i	0.375573	+	0.315143i
$738$	0.194619	+	1.10374i	0.00716403	+	0.0406293i
$739$	−3.80072	−	1.38335i	−0.139812	−	0.0508873i	0.271167	−	0.962532i	$-0.412591\pi$
$739$	−3.80072	−	1.38335i	−0.139812	−	0.0508873i	−0.410978	+	0.911645i	$0.634813\pi$
$740$	−15.2750			−0.561522
$741$	1.72085	+	19.5094i	0.0632172	+	0.716697i
$742$	−24.9246			−0.915011
$743$	−8.30443	−	3.02256i	−0.304660	−	0.110887i	0.185166	−	0.982707i	$-0.440718\pi$
$743$	−8.30443	−	3.02256i	−0.304660	−	0.110887i	−0.489826	+	0.871820i	$0.662940\pi$
$744$	−2.83768	−	16.0933i	−0.104034	−	0.590007i
$745$	−21.4213	−	17.9746i	−0.784816	−	0.658539i
$746$	25.8390	−	21.6815i	0.946034	−	0.793817i
$747$	0.205791	−	1.16710i	0.00752950	−	0.0427019i
$748$	2.66961	−	4.62391i	0.0976108	−	0.169067i
$749$	25.3206	+	43.8566i	0.925195	+	1.60248i
$750$	−18.9423	+	6.89443i	−0.691675	+	0.251749i
$751$	8.14780	−	2.96556i	0.297317	−	0.108215i	−0.189054	−	0.981967i	$-0.560542\pi$
$751$	8.14780	−	2.96556i	0.297317	−	0.108215i	0.486372	+	0.873752i	$0.338320\pi$
$752$	5.48270	+	9.49632i	0.199934	+	0.346295i
$753$	19.3410	−	33.4996i	0.704826	−	1.22079i
$754$	2.02959	−	11.5104i	0.0739134	−	0.419184i
$755$	16.8102	−	14.1054i	0.611787	−	0.513350i
$756$	11.8891	+	9.97611i	0.432401	+	0.362828i
$757$	−0.0233162	−	0.132233i	−0.000847441	−	0.00480607i	0.984381	−	0.176051i	$-0.0563323\pi$
$757$	−0.0233162	−	0.132233i	−0.000847441	−	0.00480607i	−0.985229	+	0.171245i	$0.945221\pi$
$758$	24.8644	+	9.04989i	0.903114	+	0.328707i
$759$	4.25775			0.154547
$760$	2.25128	−	8.42591i	0.0816627	−	0.305640i
$761$	−3.19351			−0.115765			−0.0578823	−	0.998323i	$-0.518435\pi$
$761$	−3.19351			−0.115765			−0.0578823	+	0.998323i	$0.518435\pi$
$762$	17.2929	+	6.29410i	0.626456	+	0.228011i
$763$	−2.36970	−	13.4393i	−0.0857891	−	0.486534i
$764$	−4.82871	−	4.05177i	−0.174697	−	0.146588i
$765$	−1.45153	+	1.21798i	−0.0524803	+	0.0440362i
$766$	−5.06339	+	28.7159i	−0.182948	+	1.03755i
$767$	12.4105	−	21.4957i	0.448118	−	0.776164i
$768$	−0.840034	−	1.45498i	−0.0303121	−	0.0525021i
$769$	−40.4710	+	14.7302i	−1.45942	+	0.531186i	−0.945206	−	0.326475i	$-0.894139\pi$
$769$	−40.4710	+	14.7302i	−1.45942	+	0.531186i	−0.514215	+	0.857661i	$0.671917\pi$
$770$	5.46636	−	1.98959i	0.196994	−	0.0716999i
$771$	13.7541	+	23.8227i	0.495341	+	0.857955i
$772$	−2.03808	+	3.53006i	−0.0733521	+	0.127050i
$773$	−5.13275	+	29.1093i	−0.184612	+	1.04699i	0.741841	+	0.670576i	$0.233953\pi$
$773$	−5.13275	+	29.1093i	−0.184612	+	1.04699i	−0.926453	+	0.376411i	$0.877158\pi$
$774$	0.938073	−	0.787137i	0.0337183	−	0.0282931i
$775$	−7.42591	−	6.23108i	−0.266746	−	0.223827i
$776$	1.32074	+	7.49031i	0.0474120	+	0.268887i
$777$	−35.0414	−	12.7540i	−1.25710	−	0.457548i
$778$	−37.4224			−1.34166
$779$	26.5994	−	7.14760i	0.953023	−	0.256089i
$780$	−8.99009			−0.321897
$781$	4.25659	+	1.54927i	0.152313	+	0.0554374i
$782$	2.34965	+	13.3255i	0.0840232	+	0.476519i
$783$	−17.8716	−	14.9961i	−0.638680	−	0.535916i
$784$	1.11287	−	0.933809i	0.0397454	−	0.0333503i
$785$	−7.78152	+	44.1312i	−0.277734	+	1.57511i
$786$	1.40392	−	2.43166i	0.0500761	−	0.0867343i
$787$	−26.0251	−	45.0768i	−0.927695	−	1.60681i	−0.787169	−	0.616737i	$-0.788454\pi$
$787$	−26.0251	−	45.0768i	−0.927695	−	1.60681i	−0.140525	−	0.990077i	$-0.544879\pi$
$788$	15.1438	−	5.51190i	0.539477	−	0.196353i
$789$	14.9411	−	5.43812i	0.531917	−	0.193602i
$790$	−10.4130	−	18.0359i	−0.370479	−	0.641689i
$791$	−9.95992	+	17.2511i	−0.354134	+	0.613378i
$792$	−0.0308000	+	0.174676i	−0.00109443	+	0.00620683i
$793$	17.6454	−	14.8063i	0.626608	−	0.525786i
$794$	0.299718	+	0.251493i	0.0106366	+	0.00892516i
$795$	−5.00426	−	28.3806i	−0.177483	−	1.00656i
$796$	3.24707	+	1.18184i	0.115089	+	0.0418891i
$797$	26.1475			0.926191			0.463096	−	0.886308i	$-0.346739\pi$
$797$	26.1475			0.926191			0.463096	+	0.886308i	$0.346739\pi$
$798$	12.1998	−	17.4495i	0.431868	−	0.617707i
$799$	−58.5468			−2.07124
$800$	−0.936517	−	0.340864i	−0.0331109	−	0.0120514i
$801$	−0.0161831	−	0.0917788i	−0.000571801	−	0.00324285i
$802$	−4.71055	−	3.95262i	−0.166335	−	0.139572i
$803$	−1.88296	+	1.57999i	−0.0664482	+	0.0557566i
$804$	−3.88303	+	22.0218i	−0.136944	+	0.776648i
$805$	−7.37116	+	12.7672i	−0.259799	+	0.449986i
$806$	−13.0065	−	22.5279i	−0.458133	−	0.793510i
$807$	−5.70002	+	2.07464i	−0.200650	+	0.0730307i
$808$	2.68946	−	0.978882i	0.0946147	−	0.0344369i
$809$	18.6761	+	32.3479i	0.656617	+	1.13729i	0.981486	+	0.191534i	$0.0613463\pi$
$809$	18.6761	+	32.3479i	0.656617	+	1.13729i	−0.324869	+	0.945759i	$0.605320\pi$
$810$	−8.43999	+	14.6185i	−0.296551	+	0.513642i
$811$	−7.22227	+	40.9595i	−0.253608	+	1.43828i	0.546012	+	0.837778i	$0.316145\pi$
$811$	−7.22227	+	40.9595i	−0.253608	+	1.43828i	−0.799620	+	0.600506i	$0.794966\pi$
$812$	−9.73348	+	8.16736i	−0.341578	+	0.286618i
$813$	−9.85448	−	8.26889i	−0.345612	−	0.290003i
$814$	−1.32568	−	7.51832i	−0.0464651	−	0.263517i
$815$	45.2347	+	16.4641i	1.58450	+	0.576712i
$816$	8.97027			0.314022
$817$	−21.2948	−	21.2644i	−0.745009	−	0.743949i
$818$	−23.9738			−0.838224
$819$	1.29595	+	0.471689i	0.0452843	+	0.0164821i
$820$	2.19542	+	12.4509i	0.0766675	+	0.434803i
$821$	−34.1340	−	28.6418i	−1.19128	−	0.999606i	−0.999836	−	0.0181032i	$-0.994237\pi$
$821$	−34.1340	−	28.6418i	−1.19128	−	0.999606i	−0.191448	−	0.981503i	$-0.561318\pi$
$822$	−13.7647	+	11.5500i	−0.480100	+	0.402852i
$823$	−1.80740	+	10.2503i	−0.0630020	+	0.357302i	0.936967	+	0.349418i	$0.113621\pi$
$823$	−1.80740	+	10.2503i	−0.0630020	+	0.357302i	−0.999969	+	0.00788392i	$0.997490\pi$
$824$	−7.52023	+	13.0254i	−0.261980	+	0.453762i
$825$	−0.837196	−	1.45007i	−0.0291474	−	0.0504848i
$826$	−25.3560	+	9.22884i	−0.882250	+	0.321113i
$827$	−31.1094	+	11.3229i	−1.08178	+	0.393736i	−0.820570	−	0.571546i	$-0.806344\pi$
$827$	−31.1094	+	11.3229i	−1.08178	+	0.393736i	−0.261211	+	0.965282i	$0.584122\pi$
$828$	−0.224753	−	0.389283i	−0.00781069	−	0.0135285i
$829$	0.711322	−	1.23205i	0.0247052	−	0.0427907i	−0.853408	−	0.521243i	$-0.825469\pi$
$829$	0.711322	−	1.23205i	0.0247052	−	0.0427907i	0.878114	+	0.478452i	$0.158802\pi$
$830$	2.32145	−	13.1656i	0.0805786	−	0.456984i
$831$	−39.8968	+	33.4774i	−1.38401	+	1.16132i
$832$	−2.04870	−	1.71906i	−0.0710258	−	0.0595977i
$833$	1.34691	+	7.63872i	0.0466678	+	0.264666i
$834$	−4.85118	−	1.76568i	−0.167982	−	0.0611406i
$835$	−23.2712			−0.805334
$836$	4.34258	+	0.376811i	0.150191	+	0.0130323i
$837$	−51.9231			−1.79472
$838$	−18.4781	−	6.72548i	−0.638315	−	0.232328i
$839$	−5.35719	−	30.3822i	−0.184951	−	1.04891i	−0.926019	−	0.377478i	$-0.876791\pi$
$839$	−5.35719	−	30.3822i	−0.184951	−	1.04891i	0.741068	−	0.671430i	$-0.234320\pi$
$840$	7.48675	+	6.28213i	0.258317	+	0.216754i
$841$	−7.58394	+	6.36368i	−0.261515	+	0.219437i
$842$	1.46781	−	8.32438i	0.0505842	−	0.286877i
$843$	−4.08851	+	7.08152i	−0.140816	+	0.243900i
$844$	3.37946	+	5.85339i	0.116326	+	0.201482i
$845$	10.9947	−	4.00173i	0.378228	−	0.137664i
$846$	1.82764	−	0.665208i	0.0628357	−	0.0228703i
$847$	1.45368	+	2.51785i	0.0499491	+	0.0865143i
$848$	4.28647	−	7.42438i	0.147198	−	0.254954i
$849$	−6.27008	+	35.5594i	−0.215189	+	1.22039i
$850$	4.07627	−	3.42039i	0.139815	−	0.117319i
$851$	14.8210	+	12.4363i	0.508057	+	0.426310i
$852$	1.32152	+	7.49471i	0.0452745	+	0.256765i
$853$	−38.8932	−	14.1560i	−1.33168	−	0.484691i	−0.424496	−	0.905430i	$-0.639549\pi$
$853$	−38.8932	−	14.1560i	−1.33168	−	0.484691i	−0.907182	+	0.420738i	$0.861771\pi$
$854$	−25.0411			−0.856889
$855$	−1.40246	−	0.652763i	−0.0479632	−	0.0223240i
$856$	−17.4183			−0.595344
$857$	42.3813	+	15.4255i	1.44772	+	0.526927i	0.941953	−	0.335744i	$-0.108988\pi$
$857$	42.3813	+	15.4255i	1.44772	+	0.526927i	0.505766	+	0.862671i	$0.331210\pi$
$858$	−0.780227	−	4.42489i	−0.0266365	−	0.151063i
$859$	−15.6869	−	13.1629i	−0.535232	−	0.449113i	0.334672	−	0.942335i	$-0.391375\pi$
$859$	−15.6869	−	13.1629i	−0.535232	−	0.449113i	−0.869903	+	0.493222i	$0.835819\pi$
$860$	10.5820	−	8.87938i	0.360844	−	0.302784i
$861$	−5.35958	+	30.3957i	−0.182654	+	1.03588i
$862$	19.1883	−	33.2351i	0.653557	−	1.13199i
$863$	−8.89518	−	15.4069i	−0.302796	−	0.524457i	0.673972	−	0.738756i	$-0.264587\pi$
$863$	−8.89518	−	15.4069i	−0.302796	−	0.524457i	−0.976768	+	0.214299i	$0.931253\pi$
$864$	−5.01627	+	1.82577i	−0.170657	+	0.0621140i
$865$	−0.803365	+	0.292401i	−0.0273152	+	0.00994194i
$866$	4.76024	+	8.24498i	0.161760	+	0.280176i
$867$	−9.66658	+	16.7430i	−0.328294	+	0.568622i
$868$	−4.91060	+	27.8494i	−0.166677	+	0.945271i
$869$	7.97348	−	6.69055i	0.270482	−	0.226961i
$870$	−11.2541	−	9.44328i	−0.381549	−	0.320157i
$871$	6.18113	+	35.0549i	0.209439	+	1.18779i
$872$	4.41073	+	1.60538i	0.149366	+	0.0543649i
$873$	1.34905			0.0456586
$874$	−9.04437	+	6.34254i	−0.305930	+	0.214540i
$875$	34.8834			1.17927
$876$	−3.88061	−	1.41243i	−0.131114	−	0.0477214i
$877$	−7.44215	−	42.2066i	−0.251304	−	1.42521i	−0.805385	−	0.592752i	$-0.798042\pi$
$877$	−7.44215	−	42.2066i	−0.251304	−	1.42521i	0.554082	−	0.832462i	$-0.313070\pi$
$878$	9.89361	+	8.30173i	0.333893	+	0.280170i
$879$	5.24872	−	4.40420i	0.177035	−	0.148550i
$880$	−0.347443	+	1.97045i	−0.0117123	+	0.0664238i
$881$	−18.0254	+	31.2209i	−0.607292	+	1.05186i	0.384393	+	0.923170i	$0.374411\pi$
$881$	−18.0254	+	31.2209i	−0.607292	+	1.05186i	−0.991685	+	0.128691i	$0.958923\pi$
$882$	−0.128837	−	0.223153i	−0.00433818	−	0.00751395i
$883$	31.0365	−	11.2964i	1.04446	−	0.380152i	0.237891	−	0.971292i	$-0.423544\pi$
$883$	31.0365	−	11.2964i	1.04446	−	0.380152i	0.806569	+	0.591139i	$0.201322\pi$
$884$	13.4180	−	4.88376i	0.451296	−	0.164258i
$885$	−15.5994	−	27.0189i	−0.524367	−	0.908230i
$886$	11.6782	−	20.2273i	0.392337	−	0.679548i
$887$	−5.69522	+	32.2992i	−0.191227	+	1.08450i	0.726463	+	0.687205i	$0.241163\pi$
$887$	−5.69522	+	32.2992i	−0.191227	+	1.08450i	−0.917690	+	0.397297i	$0.869948\pi$
$888$	9.82540	−	8.24449i	0.329719	−	0.276667i
$889$	−24.3954	−	20.4702i	−0.818196	−	0.686548i
$890$	−0.182555	−	1.03532i	−0.00611926	−	0.0347040i
$891$	−7.92765	−	2.88543i	−0.265586	−	0.0966655i
$892$	−3.75832			−0.125838
$893$	−20.2308	−	43.3045i	−0.676997	−	1.44913i
$894$	23.4804			0.785302
$895$	−48.5770	−	17.6806i	−1.62375	−	0.590997i
$896$	0.504858	+	2.86319i	0.0168661	+	0.0956525i
$897$	8.72285	+	7.31934i	0.291247	+	0.244386i
$898$	12.0798	−	10.1361i	0.403107	−	0.338247i
$899$	7.38161	−	41.8632i	0.246190	−	1.39622i
$900$	−0.0883855	+	0.153088i	−0.00294618	+	0.00510294i
$901$	22.8864	+	39.6405i	0.762457	+	1.32061i
$902$	−5.93773	+	2.16116i	−0.197705	+	0.0719587i
$903$	31.6894	−	11.5340i	1.05456	−	0.383827i
$904$	−3.42576	−	5.93359i	−0.113939	−	0.197348i
$905$	2.97928	−	5.16026i	0.0990346	−	0.171533i
$906$	−3.19966	+	18.1461i	−0.106301	+	0.602865i
$907$	5.13126	−	4.30564i	0.170381	−	0.142966i	−0.553610	−	0.832776i	$-0.686750\pi$
$907$	5.13126	−	4.30564i	0.170381	−	0.142966i	0.723991	+	0.689810i	$0.242306\pi$
$908$	−4.76119	−	3.99511i	−0.158006	−	0.132582i
$909$	−0.0881515	−	0.499932i	−0.00292380	−	0.0165817i
$910$	14.6191	+	5.32093i	0.484620	+	0.176387i
$911$	−22.1684			−0.734473			−0.367236	−	0.930128i	$-0.619696\pi$
$911$	−22.1684			−0.734473			−0.367236	+	0.930128i	$0.619696\pi$
$912$	3.09966	+	6.63491i	0.102640	+	0.219704i
$913$	6.68152			0.221126
$914$	−17.6913	−	6.43912i	−0.585177	−	0.212987i
$915$	−5.02765	−	28.5132i	−0.166209	−	0.942618i
$916$	1.49479	+	1.25428i	0.0493894	+	0.0414426i
$917$	−3.72218	+	3.12328i	−0.122917	+	0.103140i
$918$	4.94930	−	28.0689i	0.163351	−	0.926410i
$919$	−26.2213	+	45.4166i	−0.864961	+	1.49816i	0.00212474	+	0.999998i	$0.499324\pi$
$919$	−26.2213	+	45.4166i	−0.864961	+	1.49816i	−0.867086	+	0.498159i	$0.834010\pi$
$920$	−2.53535	−	4.39135i	−0.0835879	−	0.144778i
$921$	25.9804	−	9.45608i	0.856083	−	0.311589i
$922$	−26.9675	+	9.81538i	−0.888128	+	0.323252i
$923$	6.05717	+	10.4913i	0.199374	+	0.345326i
$924$	−2.44228	+	4.23016i	−0.0803452	+	0.139162i
$925$	1.32120	−	7.49291i	0.0434409	−	0.246365i
$926$	−23.4263	+	19.6570i	−0.769835	+	0.645968i
$927$	2.04360	+	1.71478i	0.0671206	+	0.0563209i
$928$	−0.758902	−	4.30394i	−0.0249122	−	0.141284i
$929$	44.2704	+	16.1131i	1.45246	+	0.528654i	0.943279	−	0.332002i	$-0.107724\pi$
$929$	44.2704	+	16.1131i	1.45246	+	0.528654i	0.509186	+	0.860656i	$0.329946\pi$
$930$	−32.6968			−1.07217
$931$	−5.18460	+	3.63580i	−0.169918	+	0.119159i
$932$	−8.42792			−0.276066
$933$	−21.9401	−	7.98553i	−0.718285	−	0.261434i
$934$	6.16551	+	34.9663i	0.201741	+	1.14413i
$935$	−8.18363	−	6.86688i	−0.267633	−	0.224571i
$936$	−0.363378	+	0.304910i	−0.0118774	+	0.00996631i
$937$	4.16611	−	23.6272i	0.136101	−	0.771866i	−0.837986	−	0.545692i	$-0.816267\pi$
$937$	4.16611	−	23.6272i	0.136101	−	0.771866i	0.974087	−	0.226174i	$-0.0726219\pi$
$938$	19.3483	−	33.5122i	0.631744	−	1.09421i
$939$	10.6859	+	18.5084i	0.348720	+	0.604000i
$940$	20.6169	−	7.50395i	0.672450	−	0.244752i
$941$	36.4695	−	13.2738i	1.18887	−	0.432714i	0.329544	−	0.944140i	$-0.393105\pi$
$941$	36.4695	−	13.2738i	1.18887	−	0.432714i	0.859327	+	0.511427i	$0.170883\pi$
$942$	−18.8139	−	32.5866i	−0.612989	−	1.06173i
$943$	8.00679	−	13.8682i	0.260737	−	0.451610i
$944$	1.61164	−	9.14004i	0.0524543	−	0.297483i
$945$	23.7882	−	19.9606i	0.773829	−	0.649320i
$946$	5.28878	+	4.43782i	0.171953	+	0.144286i
$947$	5.56770	+	31.5760i	0.180926	+	1.02608i	0.931079	+	0.364818i	$0.118869\pi$
$947$	5.56770	+	31.5760i	0.180926	+	1.02608i	−0.750153	+	0.661264i	$0.770020\pi$
$948$	16.4326	+	5.98099i	0.533707	+	0.194253i
$949$	−6.57371			−0.213392
$950$	3.93846	+	1.83312i	0.127781	+	0.0594743i
$951$	−20.1824			−0.654461
$952$	−14.5869	−	5.30920i	−0.472765	−	0.172072i
$953$	−2.06755	−	11.7257i	−0.0669745	−	0.379831i	−0.999809	−	0.0195270i	$-0.993784\pi$
$953$	−2.06755	−	11.7257i	−0.0669745	−	0.379831i	0.932835	−	0.360304i	$-0.117327\pi$
$954$	−1.16483	−	0.977413i	−0.0377129	−	0.0316449i
$955$	−9.66151	+	8.10697i	−0.312639	+	0.262335i
$956$	−0.559809	+	3.17483i	−0.0181055	+	0.102681i
$957$	3.67124	−	6.35877i	0.118674	−	0.205550i
$958$	0.0783086	+	0.135635i	0.00253004	+	0.00438215i
$959$	29.2194	−	10.6350i	0.943545	−	0.343422i
$960$	−3.15883	+	1.14972i	−0.101951	+	0.0371070i
$961$	−31.8044	−	55.0868i	−1.02595	−	1.77699i
$962$	10.2085	−	17.6817i	0.329136	−	0.570080i
$963$	−0.536483	+	3.04255i	−0.0172879	+	0.0980447i
$964$	−12.6724	+	10.6334i	−0.408150	+	0.342478i
$965$	6.24768	+	5.24243i	0.201120	+	0.168760i
$966$	−2.14956	−	12.1908i	−0.0691610	−	0.392232i
$967$	−15.7159	−	5.72011i	−0.505389	−	0.183946i	0.0767275	−	0.997052i	$-0.475553\pi$
$967$	−15.7159	−	5.72011i	−0.505389	−	0.183946i	−0.582116	+	0.813106i	$0.697775\pi$
$968$	−1.00000			−0.0321412
$969$	−38.9541	−	3.38009i	−1.25139	−	0.108584i
$970$	15.2181			0.488625
$971$	−46.4297	−	16.8990i	−1.49000	−	0.542315i	−0.536550	−	0.843869i	$-0.680273\pi$
$971$	−46.4297	−	16.8990i	−1.49000	−	0.542315i	−0.953449	+	0.301553i	$0.902495\pi$
$972$	0.319655	+	1.81285i	0.0102529	+	0.0581473i
$973$	6.84364	+	5.74250i	0.219397	+	0.184096i
$974$	−5.80259	+	4.86896i	−0.185927	+	0.156011i
$975$	0.777590	−	4.40993i	0.0249028	−	0.141231i
$976$	4.30650	−	7.45908i	0.137848	−	0.238759i
$977$	−9.97859	−	17.2834i	−0.319243	−	0.552946i	0.661087	−	0.750309i	$-0.270095\pi$
$977$	−9.97859	−	17.2834i	−0.319243	−	0.552946i	−0.980330	+	0.197364i	$0.936762\pi$
$978$	−37.9827	+	13.8246i	−1.21455	+	0.442061i
$979$	0.493737	−	0.179706i	0.0157799	−	0.00574342i
$980$	−1.45336	−	2.51730i	−0.0464260	−	0.0804121i
$981$	0.416271	−	0.721002i	0.0132905	−	0.0230198i
$982$	−2.26562	+	12.8490i	−0.0722989	+	0.410027i
$983$	26.1986	−	21.9832i	0.835606	−	0.701156i	−0.120965	−	0.992657i	$-0.538599\pi$
$983$	26.1986	−	21.9832i	0.835606	−	0.701156i	0.956571	+	0.291500i	$0.0941545\pi$
$984$	−8.13234	−	6.82384i	−0.259250	−	0.217536i
$985$	−5.59930	−	31.7552i	−0.178408	−	1.01180i
$986$	21.9270	+	7.98078i	0.698299	+	0.254160i
$987$	53.5612			1.70487
$988$	8.24887	+	8.23713i	0.262432	+	0.262058i
$989$	−17.4967			−0.556362
$990$	0.333488	+	0.121380i	0.0105989	+	0.00385770i
$991$	−4.04660	−	22.9494i	−0.128545	−	0.729013i	−0.979139	−	0.203191i	$-0.934869\pi$
$991$	−4.04660	−	22.9494i	−0.128545	−	0.729013i	0.850595	−	0.525822i	$-0.176242\pi$
$992$	−7.45108	−	6.25220i	−0.236572	−	0.198508i
$993$	6.26700	−	5.25864i	0.198877	−	0.166878i
$994$	2.28689	−	12.9696i	0.0725358	−	0.411371i
$995$	3.45692	−	5.98756i	0.109592	−	0.189818i
$996$	5.61270	+	9.72149i	0.177845	+	0.308037i
$997$	−34.0224	+	12.3831i	−1.07750	+	0.392178i	−0.818976	−	0.573828i	$-0.805458\pi$
$997$	−34.0224	+	12.3831i	−1.07750	+	0.392178i	−0.258523	+	0.966005i	$0.583236\pi$
$998$	−3.29054	+	1.19766i	−0.104160	+	0.0379112i
$999$	−20.3767	−	35.2935i	−0.644690	−	1.11664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.j.a.23.3	✓	24
19.5	even	9	inner	418.2.j.a.309.3	yes	24
19.9	even	9		7942.2.a.bt.1.9		12
19.10	odd	18		7942.2.a.bx.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.a.23.3	✓	24	1.1	even	1	trivial
418.2.j.a.309.3	yes	24	19.5	even	9	inner
7942.2.a.bt.1.9		12	19.9	even	9
7942.2.a.bx.1.4		12	19.10	odd	18

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.j (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.291741 + 1.65454i) q^{3} +(0.766044 + 0.642788i) q^{4} +(1.53274 - 1.28612i) q^{5} +(-0.291741 + 1.65454i) q^{6} +(1.45368 - 2.51785i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.166674 - 0.0606642i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.291741 + 1.65454i) q^{3} +(0.766044 + 0.642788i) q^{4} +(1.53274 - 1.28612i) q^{5} +(-0.291741 + 1.65454i) q^{6} +(1.45368 - 2.51785i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.166674 - 0.0606642i) q^{9} +(1.88018 - 0.684329i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.840034 + 1.45498i) q^{12} +(-0.464402 + 2.63375i) q^{13} +(2.22717 - 1.86882i) q^{14} +(2.57510 + 2.16077i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-5.01723 - 1.82612i) q^{17} +0.177370 q^{18} +(-0.382995 - 4.34204i) q^{19} +2.00084 q^{20} +(4.58999 + 1.67062i) q^{21} +(0.173648 + 0.984808i) q^{22} +(-1.94137 - 1.62900i) q^{23} +(-1.28701 + 1.07993i) q^{24} +(-0.173061 + 0.981480i) q^{25} +(-1.33719 + 2.31608i) q^{26} +(2.66910 + 4.62302i) q^{27} +(2.73203 - 0.994376i) q^{28} +(-4.10678 + 1.49474i) q^{29} +(1.68078 + 2.91119i) q^{30} +(-4.86335 + 8.42357i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-1.28701 + 1.07993i) q^{33} +(-4.09009 - 3.43199i) q^{34} +(-1.01014 - 5.72880i) q^{35} +(0.166674 + 0.0606642i) q^{36} -7.63430 q^{37} +(1.12517 - 4.21118i) q^{38} -4.49315 q^{39} +(1.88018 + 0.684329i) q^{40} +(1.09725 + 6.22280i) q^{41} +(3.74179 + 3.13974i) q^{42} +(5.28878 - 4.43782i) q^{43} +(-0.173648 + 0.984808i) q^{44} +(0.177445 - 0.307344i) q^{45} +(-1.26714 - 2.19475i) q^{46} +(10.3041 - 3.75039i) q^{47} +(-1.57875 + 0.574617i) q^{48} +(-0.726375 - 1.25812i) q^{49} +(-0.498310 + 0.863099i) q^{50} +(1.55767 - 8.83399i) q^{51} +(-2.04870 + 1.71906i) q^{52} +(-6.56725 - 5.51057i) q^{53} +(0.926969 + 5.25710i) q^{54} +(1.88018 + 0.684329i) q^{55} +2.90736 q^{56} +(7.07236 - 1.90043i) q^{57} -4.37034 q^{58} +(-8.72132 - 3.17430i) q^{59} +(0.583728 + 3.31049i) q^{60} +(-6.59794 - 5.53633i) q^{61} +(-7.45108 + 6.25220i) q^{62} +(0.0895468 - 0.507845i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.67551 + 4.63412i) q^{65} +(-1.57875 + 0.574617i) q^{66} +(12.5072 - 4.55224i) q^{67} +(-2.66961 - 4.62391i) q^{68} +(2.12888 - 3.68732i) q^{69} +(1.01014 - 5.72880i) q^{70} +(3.47001 - 2.91168i) q^{71} +(0.135874 + 0.114011i) q^{72} +(0.426832 + 2.42069i) q^{73} +(-7.17389 - 2.61108i) q^{74} -1.67439 q^{75} +(2.49762 - 3.57238i) q^{76} +2.90736 q^{77} +(-4.22218 - 1.53675i) q^{78} +(-1.80744 - 10.2505i) q^{79} +(1.53274 + 1.28612i) q^{80} +(-6.46268 + 5.42283i) q^{81} +(-1.09725 + 6.22280i) q^{82} +(3.34076 - 5.78636i) q^{83} +(2.44228 + 4.23016i) q^{84} +(-10.0387 + 3.65379i) q^{85} +(6.48765 - 2.36131i) q^{86} +(-3.67124 - 6.35877i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(0.0912390 - 0.517442i) q^{89} +(0.271862 - 0.228119i) q^{90} +(5.95630 + 4.99793i) q^{91} +(-0.440072 - 2.49577i) q^{92} +(-15.3560 - 5.58913i) q^{93} +10.9654 q^{94} +(-6.17141 - 6.16262i) q^{95} -1.68007 q^{96} +(7.14717 + 2.60136i) q^{97} +(-0.252267 - 1.43068i) q^{98} +(0.135874 + 0.114011i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{8}+O(q^{10}) \) 24 * q + 12 * q^8	\( 24 q + 12 q^{8} + 12 q^{11} - 3 q^{12} - 3 q^{13} + 3 q^{14} + 27 q^{15} - 6 q^{18} - 21 q^{19} - 18 q^{20} + 15 q^{21} + 9 q^{23} + 36 q^{25} - 21 q^{27} - 3 q^{28} - 9 q^{30} - 27 q^{31} - 9 q^{34} - 45 q^{35} + 18 q^{37} + 9 q^{38} + 36 q^{39} - 18 q^{41} + 39 q^{42} - 48 q^{43} + 36 q^{45} - 18 q^{46} - 9 q^{47} + 6 q^{49} + 3 q^{50} - 18 q^{51} - 3 q^{52} - 36 q^{53} - 45 q^{54} + 18 q^{58} + 9 q^{59} - 9 q^{60} + 15 q^{61} - 33 q^{62} + 87 q^{63} - 12 q^{64} - 36 q^{65} + 33 q^{67} + 9 q^{68} - 18 q^{69} + 45 q^{70} - 9 q^{71} - 3 q^{73} + 3 q^{74} + 42 q^{75} + 9 q^{76} + 12 q^{78} + 15 q^{79} - 108 q^{81} + 18 q^{82} + 36 q^{83} - 9 q^{84} - 99 q^{85} - 33 q^{86} + 63 q^{87} - 12 q^{88} - 27 q^{89} - 36 q^{90} - 21 q^{91} - 9 q^{92} - 21 q^{93} + 54 q^{94} + 18 q^{95} - 6 q^{96} + 45 q^{97} + 39 q^{98}+O(q^{100}) \) 24 * q + 12 * q^8 + 12 * q^11 - 3 * q^12 - 3 * q^13 + 3 * q^14 + 27 * q^15 - 6 * q^18 - 21 * q^19 - 18 * q^20 + 15 * q^21 + 9 * q^23 + 36 * q^25 - 21 * q^27 - 3 * q^28 - 9 * q^30 - 27 * q^31 - 9 * q^34 - 45 * q^35 + 18 * q^37 + 9 * q^38 + 36 * q^39 - 18 * q^41 + 39 * q^42 - 48 * q^43 + 36 * q^45 - 18 * q^46 - 9 * q^47 + 6 * q^49 + 3 * q^50 - 18 * q^51 - 3 * q^52 - 36 * q^53 - 45 * q^54 + 18 * q^58 + 9 * q^59 - 9 * q^60 + 15 * q^61 - 33 * q^62 + 87 * q^63 - 12 * q^64 - 36 * q^65 + 33 * q^67 + 9 * q^68 - 18 * q^69 + 45 * q^70 - 9 * q^71 - 3 * q^73 + 3 * q^74 + 42 * q^75 + 9 * q^76 + 12 * q^78 + 15 * q^79 - 108 * q^81 + 18 * q^82 + 36 * q^83 - 9 * q^84 - 99 * q^85 - 33 * q^86 + 63 * q^87 - 12 * q^88 - 27 * q^89 - 36 * q^90 - 21 * q^91 - 9 * q^92 - 21 * q^93 + 54 * q^94 + 18 * q^95 - 6 * q^96 + 45 * q^97 + 39 * q^98

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