LMFDB - Embedded newform 403.2.h.a.118.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

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("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.4
Character	$\chi$	$=$	403.118
Dual form			403.2.h.a.222.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.54088 q^{2} +(-0.945700 - 1.63800i) q^{3} +0.374297 q^{4} +(0.246770 - 0.427419i) q^{5} +(1.45721 + 2.52395i) q^{6} +(-2.41271 - 4.17893i) q^{7} +2.50501 q^{8} +(-0.288697 + 0.500038i) q^{9} +O(q^{10})$	\(q-1.54088 q^{2} +(-0.945700 - 1.63800i) q^{3} +0.374297 q^{4} +(0.246770 - 0.427419i) q^{5} +(1.45721 + 2.52395i) q^{6} +(-2.41271 - 4.17893i) q^{7} +2.50501 q^{8} +(-0.288697 + 0.500038i) q^{9} +(-0.380242 + 0.658599i) q^{10} +(0.323849 - 0.560922i) q^{11} +(-0.353973 - 0.613099i) q^{12} +(0.500000 - 0.866025i) q^{13} +(3.71768 + 6.43922i) q^{14} -0.933482 q^{15} -4.60850 q^{16} +(-1.77718 - 3.07816i) q^{17} +(0.444846 - 0.770496i) q^{18} +(-0.462401 - 0.800901i) q^{19} +(0.0923654 - 0.159982i) q^{20} +(-4.56340 + 7.90404i) q^{21} +(-0.499010 + 0.864311i) q^{22} +7.83617 q^{23} +(-2.36898 - 4.10320i) q^{24} +(2.37821 + 4.11918i) q^{25} +(-0.770438 + 1.33444i) q^{26} -4.58212 q^{27} +(-0.903071 - 1.56416i) q^{28} -10.2450 q^{29} +1.43838 q^{30} +(-5.48182 + 0.974513i) q^{31} +2.09111 q^{32} -1.22505 q^{33} +(2.73841 + 4.74307i) q^{34} -2.38154 q^{35} +(-0.108059 + 0.187163i) q^{36} +(4.36745 + 7.56465i) q^{37} +(0.712502 + 1.23409i) q^{38} -1.89140 q^{39} +(0.618161 - 1.07069i) q^{40} +(0.938480 - 1.62549i) q^{41} +(7.03163 - 12.1791i) q^{42} +(1.59757 + 2.76708i) q^{43} +(0.121216 - 0.209952i) q^{44} +(0.142484 + 0.246789i) q^{45} -12.0746 q^{46} -3.82248 q^{47} +(4.35825 + 7.54872i) q^{48} +(-8.14233 + 14.1029i) q^{49} +(-3.66452 - 6.34714i) q^{50} +(-3.36136 + 5.82204i) q^{51} +(0.187149 - 0.324151i) q^{52} +(-0.535195 + 0.926985i) q^{53} +7.06047 q^{54} +(-0.159832 - 0.276838i) q^{55} +(-6.04385 - 10.4683i) q^{56} +(-0.874585 + 1.51483i) q^{57} +15.7863 q^{58} +(-1.62553 - 2.81550i) q^{59} -0.349400 q^{60} -6.17126 q^{61} +(8.44680 - 1.50160i) q^{62} +2.78617 q^{63} +5.99486 q^{64} +(-0.246770 - 0.427419i) q^{65} +1.88766 q^{66} +(6.54194 - 11.3310i) q^{67} +(-0.665193 - 1.15215i) q^{68} +(-7.41066 - 12.8356i) q^{69} +3.66965 q^{70} +(7.81025 - 13.5277i) q^{71} +(-0.723187 + 1.25260i) q^{72} +(-2.94080 + 5.09361i) q^{73} +(-6.72970 - 11.6562i) q^{74} +(4.49814 - 7.79101i) q^{75} +(-0.173075 - 0.299775i) q^{76} -3.12541 q^{77} +2.91441 q^{78} +(3.56887 + 6.18146i) q^{79} +(-1.13724 + 1.96976i) q^{80} +(5.19940 + 9.00562i) q^{81} +(-1.44608 + 2.50469i) q^{82} +(6.37864 - 11.0481i) q^{83} +(-1.70807 + 2.95846i) q^{84} -1.75422 q^{85} +(-2.46166 - 4.26373i) q^{86} +(9.68874 + 16.7814i) q^{87} +(0.811242 - 1.40511i) q^{88} +8.62310 q^{89} +(-0.219550 - 0.380271i) q^{90} -4.82542 q^{91} +2.93306 q^{92} +(6.78041 + 8.05762i) q^{93} +5.88996 q^{94} -0.456427 q^{95} +(-1.97756 - 3.42524i) q^{96} -7.58140 q^{97} +(12.5463 - 21.7309i) q^{98} +(0.186988 + 0.323873i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) $ 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 + 15 * q^13 + 3 * q^14 + 4 * q^15 + 22 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 10 * q^20 - 15 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 20 * q^25 - 3 * q^26 + 4 * q^27 + 13 * q^28 + 26 * q^29 + 28 * q^30 + 19 * q^31 - 74 * q^32 + 2 * q^33 - 21 * q^34 - 30 * q^35 + 37 * q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 - 17 * q^40 + 7 * q^41 + 44 * q^42 + 15 * q^43 - 70 * q^44 + 15 * q^45 - 58 * q^46 - 24 * q^47 + 31 * q^48 - 29 * q^49 + 2 * q^50 + 25 * q^51 + 11 * q^52 + 4 * q^53 + 34 * q^54 + 13 * q^55 - 41 * q^56 + 8 * q^57 - 46 * q^58 + 27 * q^59 + 78 * q^60 + 8 * q^61 + 20 * q^62 - 112 * q^63 + 60 * q^64 - 7 * q^65 + 60 * q^66 + 29 * q^67 + 41 * q^68 - 23 * q^69 - 112 * q^70 + 29 * q^71 + 14 * q^72 - 10 * q^73 + 25 * q^74 - 18 * q^75 + 24 * q^76 - 72 * q^77 + 9 * q^79 - 11 * q^81 - 38 * q^82 - 13 * q^83 - 62 * q^84 + 108 * q^85 - 38 * q^86 - 18 * q^87 + 32 * q^88 + 6 * q^89 + 7 * q^90 + 12 * q^91 + 2 * q^92 + 37 * q^93 - 154 * q^94 - 28 * q^95 - 105 * q^96 - 84 * q^97 + 50 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.54088			−1.08956			−0.544782	−	0.838578i	$-0.683388\pi$
$2$	−1.54088			−1.08956			−0.544782	+	0.838578i	$0.683388\pi$
$3$	−0.945700	−	1.63800i	−0.546000	−	0.945700i	−0.998543	−	0.0539575i	$-0.982816\pi$
$3$	−0.945700	−	1.63800i	−0.546000	−	0.945700i	0.452543	−	0.891743i	$-0.350517\pi$
$4$	0.374297			0.187149
$5$	0.246770	−	0.427419i	0.110359	−	0.191147i	−0.805556	−	0.592520i	$-0.798133\pi$
$5$	0.246770	−	0.427419i	0.110359	−	0.191147i	0.915915	+	0.401372i	$0.131467\pi$
$6$	1.45721	+	2.52395i	0.594902	+	1.03040i
$7$	−2.41271	−	4.17893i	−0.911918	−	1.57949i	−0.811352	−	0.584558i	$-0.801268\pi$
$7$	−2.41271	−	4.17893i	−0.911918	−	1.57949i	−0.100567	−	0.994930i	$-0.532066\pi$
$8$	2.50501			0.885653
$9$	−0.288697	+	0.500038i	−0.0962323	+	0.166679i
$10$	−0.380242	+	0.658599i	−0.120243	+	0.208267i
$11$	0.323849	−	0.560922i	0.0976440	−	0.169124i	−0.813065	−	0.582173i	$-0.802203\pi$
$11$	0.323849	−	0.560922i	0.0976440	−	0.169124i	0.910709	+	0.413048i	$0.135536\pi$
$12$	−0.353973	−	0.613099i	−0.102183	−	0.176986i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	3.71768	+	6.43922i	0.993593	+	1.72095i
$15$	−0.933482			−0.241024
$16$	−4.60850			−1.15212
$17$	−1.77718	−	3.07816i	−0.431029	−	0.746564i	0.565933	−	0.824451i	$-0.308516\pi$
$17$	−1.77718	−	3.07816i	−0.431029	−	0.746564i	−0.996962	+	0.0778868i	$0.975183\pi$
$18$	0.444846	−	0.770496i	0.104851	−	0.181608i
$19$	−0.462401	−	0.800901i	−0.106082	−	0.183739i	0.808098	−	0.589048i	$-0.200497\pi$
$19$	−0.462401	−	0.800901i	−0.106082	−	0.183739i	−0.914180	+	0.405309i	$0.867164\pi$
$20$	0.0923654	−	0.159982i	0.0206535	−	0.0357730i
$21$	−4.56340	+	7.90404i	−0.995815	+	1.72480i
$22$	−0.499010	+	0.864311i	−0.106389	+	0.184272i
$23$	7.83617			1.63395			0.816977	−	0.576670i	$-0.195648\pi$
$23$	7.83617			1.63395			0.816977	+	0.576670i	$0.195648\pi$
$24$	−2.36898	−	4.10320i	−0.483567	−	0.837562i
$25$	2.37821	+	4.11918i	0.475642	+	0.823836i
$26$	−0.770438	+	1.33444i	−0.151095	+	0.261705i
$27$	−4.58212			−0.881829
$28$	−0.903071	−	1.56416i	−0.170664	−	0.295599i
$29$	−10.2450			−1.90246			−0.951229	−	0.308486i	$-0.900178\pi$
$29$	−10.2450			−1.90246			−0.951229	+	0.308486i	$0.900178\pi$
$30$	1.43838			0.262611
$31$	−5.48182	+	0.974513i	−0.984564	+	0.175028i
$31$	−5.48182	+	0.974513i	−0.984564	+	0.175028i
$32$	2.09111			0.369659
$33$	−1.22505			−0.213255
$34$	2.73841	+	4.74307i	0.469634	+	0.813429i
$35$	−2.38154			−0.402554
$36$	−0.108059	+	0.187163i	−0.0180098	+	0.0311938i
$37$	4.36745	+	7.56465i	0.718005	+	1.24362i	0.961789	+	0.273791i	$0.0882776\pi$
$37$	4.36745	+	7.56465i	0.718005	+	1.24362i	−0.243785	+	0.969829i	$0.578389\pi$
$38$	0.712502	+	1.23409i	0.115583	+	0.200196i
$39$	−1.89140			−0.302866
$40$	0.618161	−	1.07069i	0.0977398	−	0.169290i
$41$	0.938480	−	1.62549i	0.146566	−	0.253860i	−0.783390	−	0.621530i	$-0.786511\pi$
$41$	0.938480	−	1.62549i	0.146566	−	0.253860i	0.929956	+	0.367671i	$0.119845\pi$
$42$	7.03163	−	12.1791i	1.08500	−	1.87928i
$43$	1.59757	+	2.76708i	0.243628	+	0.421976i	0.961745	−	0.273946i	$-0.0883291\pi$
$43$	1.59757	+	2.76708i	0.243628	+	0.421976i	−0.718117	+	0.695922i	$0.754996\pi$
$44$	0.121216	−	0.209952i	0.0182739	−	0.0316514i
$45$	0.142484	+	0.246789i	0.0212402	+	0.0367891i
$46$	−12.0746			−1.78030
$47$	−3.82248			−0.557566			−0.278783	−	0.960354i	$-0.589931\pi$
$47$	−3.82248			−0.557566			−0.278783	+	0.960354i	$0.589931\pi$
$48$	4.35825	+	7.54872i	0.629060	+	1.08956i
$49$	−8.14233	+	14.1029i	−1.16319	+	2.01470i
$50$	−3.66452	−	6.34714i	−0.518242	−	0.897621i
$51$	−3.36136	+	5.82204i	−0.470684	+	0.815249i
$52$	0.187149	−	0.324151i	0.0259529	−	0.0449517i
$53$	−0.535195	+	0.926985i	−0.0735147	+	0.127331i	−0.900439	−	0.434981i	$-0.856755\pi$
$53$	−0.535195	+	0.926985i	−0.0735147	+	0.127331i	0.826925	+	0.562313i	$0.190088\pi$
$54$	7.06047			0.960809
$55$	−0.159832	−	0.276838i	−0.0215518	−	0.0373288i
$56$	−6.04385	−	10.4683i	−0.807643	−	1.39888i
$57$	−0.874585	+	1.51483i	−0.115842	+	0.200643i
$58$	15.7863			2.07285
$59$	−1.62553	−	2.81550i	−0.211626	−	0.366547i	0.740598	−	0.671949i	$-0.234543\pi$
$59$	−1.62553	−	2.81550i	−0.211626	−	0.366547i	−0.952224	+	0.305402i	$0.901209\pi$
$60$	−0.349400			−0.0451073
$61$	−6.17126			−0.790150			−0.395075	−	0.918649i	$-0.629281\pi$
$61$	−6.17126			−0.790150			−0.395075	+	0.918649i	$0.629281\pi$
$62$	8.44680	−	1.50160i	1.07274	−	0.190704i
$63$	2.78617			0.351024
$64$	5.99486			0.749357
$65$	−0.246770	−	0.427419i	−0.0306081	−	0.0530147i
$66$	1.88766			0.232354
$67$	6.54194	−	11.3310i	0.799225	−	1.38430i	−0.120897	−	0.992665i	$-0.538577\pi$
$67$	6.54194	−	11.3310i	0.799225	−	1.38430i	0.920122	−	0.391633i	$-0.128090\pi$
$68$	−0.665193	−	1.15215i	−0.0806665	−	0.139719i
$69$	−7.41066	−	12.8356i	−0.892139	−	1.54523i
$70$	3.66965			0.438608
$71$	7.81025	−	13.5277i	0.926906	−	1.60545i	0.138440	−	0.990371i	$-0.455791\pi$
$71$	7.81025	−	13.5277i	0.926906	−	1.60545i	0.788467	−	0.615078i	$-0.210875\pi$
$72$	−0.723187	+	1.25260i	−0.0852285	+	0.147620i
$73$	−2.94080	+	5.09361i	−0.344195	+	0.596162i	−0.985207	−	0.171368i	$-0.945181\pi$
$73$	−2.94080	+	5.09361i	−0.344195	+	0.596162i	0.641013	+	0.767530i	$0.278515\pi$
$74$	−6.72970	−	11.6562i	−0.782312	−	1.35500i
$75$	4.49814	−	7.79101i	0.519401	−	0.899629i
$76$	−0.173075	−	0.299775i	−0.0198531	−	0.0343866i
$77$	−3.12541			−0.356173
$78$	2.91441			0.329992
$79$	3.56887	+	6.18146i	0.401529	+	0.695468i	0.993911	−	0.110189i	$-0.0351456\pi$
$79$	3.56887	+	6.18146i	0.401529	+	0.695468i	−0.592382	+	0.805657i	$0.701812\pi$
$80$	−1.13724	+	1.96976i	−0.127147	+	0.220225i
$81$	5.19940	+	9.00562i	0.577711	+	1.00062i
$82$	−1.44608	+	2.50469i	−0.159693	+	0.276596i
$83$	6.37864	−	11.0481i	0.700147	−	1.21269i	−0.268268	−	0.963344i	$-0.586451\pi$
$83$	6.37864	−	11.0481i	0.700147	−	1.21269i	0.968415	−	0.249345i	$-0.0802154\pi$
$84$	−1.70807	+	2.95846i	−0.186365	+	0.322794i
$85$	−1.75422			−0.190272
$86$	−2.46166	−	4.26373i	−0.265448	−	0.459770i
$87$	9.68874	+	16.7814i	1.03874	+	1.79915i
$88$	0.811242	−	1.40511i	0.0864787	−	0.149786i
$89$	8.62310			0.914046			0.457023	−	0.889455i	$-0.348916\pi$
$89$	8.62310			0.914046			0.457023	+	0.889455i	$0.348916\pi$
$90$	−0.219550	−	0.380271i	−0.0231426	−	0.0400841i
$91$	−4.82542			−0.505841
$92$	2.93306			0.305792
$93$	6.78041	+	8.05762i	0.703095	+	0.835537i
$94$	5.88996			0.607503
$95$	−0.456427			−0.0468284
$96$	−1.97756	−	3.42524i	−0.201834	−	0.349587i
$97$	−7.58140			−0.769775			−0.384887	−	0.922964i	$-0.625760\pi$
$97$	−7.58140			−0.769775			−0.384887	+	0.922964i	$0.625760\pi$
$98$	12.5463	−	21.7309i	1.26737	−	2.19515i
$99$	0.186988	+	0.323873i	0.0187930	+	0.0325505i
$100$	0.890157	+	1.54180i	0.0890157	+	0.154180i
$101$	−17.6420			−1.75545			−0.877723	−	0.479168i	$-0.840938\pi$
$101$	−17.6420			−1.75545			−0.877723	+	0.479168i	$0.840938\pi$
$102$	5.17943	−	8.97104i	0.512840	−	0.888265i
$103$	2.55007	−	4.41686i	0.251266	−	0.435206i	−0.712608	−	0.701562i	$-0.752486\pi$
$103$	2.55007	−	4.41686i	0.251266	−	0.435206i	0.963875	+	0.266356i	$0.0858197\pi$
$104$	1.25250	−	2.16940i	0.122818	−	0.212727i
$105$	2.25222	+	3.90096i	0.219794	+	0.380695i
$106$	0.824669	−	1.42837i	0.0800989	−	0.138735i
$107$	4.27561	+	7.40557i	0.413338	+	0.715923i	0.995252	−	0.0973272i	$-0.0310293\pi$
$107$	4.27561	+	7.40557i	0.413338	+	0.715923i	−0.581914	+	0.813250i	$0.697696\pi$
$108$	−1.71507			−0.165033
$109$	12.6445			1.21112			0.605560	−	0.795800i	$-0.292949\pi$
$109$	12.6445			1.21112			0.605560	+	0.795800i	$0.292949\pi$
$110$	0.246282	+	0.426573i	0.0234820	+	0.0406721i
$111$	8.26060	−	14.3078i	0.784061	−	1.35803i
$112$	11.1190	+	19.2586i	1.05064	+	1.81977i
$113$	0.399411	−	0.691801i	0.0375735	−	0.0650792i	−0.846627	−	0.532187i	$-0.821371\pi$
$113$	0.399411	−	0.691801i	0.0375735	−	0.0650792i	0.884201	+	0.467107i	$0.154704\pi$
$114$	1.34763	−	2.33416i	0.126217	−	0.218614i
$115$	1.93373	−	3.34932i	0.180322	−	0.312326i
$116$	−3.83469			−0.356042
$117$	0.288697	+	0.500038i	0.0266900	+	0.0462285i
$118$	2.50474	+	4.33833i	0.230580	+	0.399376i
$119$	−8.57563	+	14.8534i	−0.786127	+	1.36161i
$120$	−2.33838			−0.213464
$121$	5.29024	+	9.16297i	0.480931	+	0.832997i
$122$	9.50915			0.860918
$123$	−3.55008			−0.320100
$124$	−2.05183	+	0.364758i	−0.184260	+	0.0327562i
$125$	4.81519			0.430683
$126$	−4.29314			−0.382463
$127$	−8.35693	−	14.4746i	−0.741558	−	1.28442i	−0.951786	−	0.306764i	$-0.900754\pi$
$127$	−8.35693	−	14.4746i	−0.741558	−	1.28442i	0.210228	−	0.977652i	$-0.432579\pi$
$128$	−13.4195			−1.18613
$129$	3.02165	−	5.23366i	0.266042	−	0.460798i
$130$	0.380242	+	0.658599i	0.0333494	+	0.0577629i
$131$	2.85755	+	4.94941i	0.249665	+	0.432432i	0.963433	−	0.267950i	$-0.0863462\pi$
$131$	2.85755	+	4.94941i	0.249665	+	0.432432i	−0.713768	+	0.700382i	$0.753013\pi$
$132$	−0.458535			−0.0399103
$133$	−2.23128	+	3.86468i	−0.193476	+	0.335111i
$134$	−10.0803	+	17.4596i	−0.870806	+	1.50828i
$135$	−1.13073	+	1.95848i	−0.0973177	+	0.168559i
$136$	−4.45184	−	7.71082i	−0.381742	−	0.661197i
$137$	8.18344	−	14.1741i	0.699158	−	1.21098i	−0.269601	−	0.962972i	$-0.586892\pi$
$137$	8.18344	−	14.1741i	0.699158	−	1.21098i	0.968759	−	0.248005i	$-0.0797750\pi$
$138$	11.4189	+	19.7781i	0.972042	+	1.68363i
$139$	−9.55911			−0.810793			−0.405396	−	0.914141i	$-0.632866\pi$
$139$	−9.55911			−0.810793			−0.405396	+	0.914141i	$0.632866\pi$
$140$	−0.891404			−0.0753374
$141$	3.61492	+	6.26122i	0.304431	+	0.527290i
$142$	−12.0346	+	20.8446i	−1.00992	+	1.74924i
$143$	−0.323849	−	0.560922i	−0.0270816	−	0.0469067i
$144$	1.33046	−	2.30442i	0.110872	−	0.192035i
$145$	−2.52817	+	4.37892i	−0.209953	+	0.363650i
$146$	4.53141	−	7.84862i	0.375022	−	0.649557i
$147$	30.8008			2.54041
$148$	1.63473	+	2.83143i	0.134374	+	0.232742i
$149$	−1.69087	−	2.92868i	−0.138522	−	0.239927i	0.788415	−	0.615143i	$-0.210902\pi$
$149$	−1.69087	−	2.92868i	−0.138522	−	0.239927i	−0.926937	+	0.375216i	$0.877568\pi$
$150$	−6.93108	+	12.0050i	−0.565920	+	0.980203i
$151$	−13.2830			−1.08096			−0.540478	−	0.841358i	$-0.681757\pi$
$151$	−13.2830			−1.08096			−0.540478	+	0.841358i	$0.681757\pi$
$152$	−1.15832	−	2.00626i	−0.0939519	−	0.162729i
$153$	2.05226			0.165916
$154$	4.81587			0.388074
$155$	−0.936224	+	2.58351i	−0.0751994	+	0.207513i
$156$	−0.707946			−0.0566810
$157$	3.71450			0.296450			0.148225	−	0.988954i	$-0.452644\pi$
$157$	3.71450			0.296450			0.148225	+	0.988954i	$0.452644\pi$
$158$	−5.49918	−	9.52486i	−0.437491	−	0.757757i
$159$	2.02454			0.160556
$160$	0.516023	−	0.893778i	0.0407952	−	0.0706594i
$161$	−18.9064	−	32.7468i	−1.49003	−	2.58081i
$162$	−8.01163	−	13.8765i	−0.629453	−	1.09024i
$163$	−22.8134			−1.78688			−0.893441	−	0.449182i	$-0.851716\pi$
$163$	−22.8134			−1.78688			−0.893441	+	0.449182i	$0.851716\pi$
$164$	0.351271	−	0.608418i	0.0274296	−	0.0475095i
$165$	−0.302307	+	0.523611i	−0.0235346	+	0.0407631i
$166$	−9.82869	+	17.0238i	−0.762854	+	1.32130i
$167$	−5.96434	−	10.3305i	−0.461534	−	0.799401i	0.537503	−	0.843262i	$-0.319368\pi$
$167$	−5.96434	−	10.3305i	−0.461534	−	0.799401i	−0.999038	+	0.0438605i	$0.986034\pi$
$168$	−11.4313	+	19.7997i	−0.881947	+	1.52758i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	2.70303			0.207313
$171$	0.533975			0.0408341
$172$	0.597968	+	1.03571i	0.0455946	+	0.0789722i
$173$	−2.03865	+	3.53105i	−0.154996	+	0.268460i	−0.933057	−	0.359727i	$-0.882870\pi$
$173$	−2.03865	+	3.53105i	−0.154996	+	0.268460i	0.778062	+	0.628188i	$0.216203\pi$
$174$	−14.9291	−	25.8580i	−1.13178	−	1.96029i
$175$	11.4759	−	19.8768i	0.867493	−	1.50254i
$176$	−1.49245	+	2.58501i	−0.112498	+	0.194852i
$177$	−3.07453	+	5.32524i	−0.231096	+	0.400269i
$178$	−13.2871			−0.995912
$179$	−6.35341	−	11.0044i	−0.474876	−	0.822510i	0.524710	−	0.851281i	$-0.324174\pi$
$179$	−6.35341	−	11.0044i	−0.474876	−	0.822510i	−0.999586	+	0.0287715i	$0.990840\pi$
$180$	0.0533312	+	0.0923724i	0.00397508	+	0.00688503i
$181$	−1.36266	+	2.36020i	−0.101286	+	0.175432i	−0.912215	−	0.409713i	$-0.865629\pi$
$181$	−1.36266	+	2.36020i	−0.101286	+	0.175432i	0.810929	+	0.585145i	$0.198962\pi$
$182$	7.43537			0.551146
$183$	5.83617	+	10.1085i	0.431422	+	0.747244i
$184$	19.6296			1.44712
$185$	4.31103			0.316953
$186$	−10.4478	−	12.4158i	−0.766067	−	0.910370i
$187$	−2.30215			−0.168350
$188$	−1.43074			−0.104348
$189$	11.0553	+	19.1484i	0.804156	+	1.39284i
$190$	0.703297			0.0510225
$191$	−1.76763	+	3.06163i	−0.127901	+	0.221532i	−0.922863	−	0.385128i	$-0.874157\pi$
$191$	−1.76763	+	3.06163i	−0.127901	+	0.221532i	0.794962	+	0.606659i	$0.207491\pi$
$192$	−5.66933	−	9.81958i	−0.409149	−	0.708667i
$193$	−5.57031	−	9.64807i	−0.400960	−	0.694483i	0.592882	−	0.805289i	$-0.297990\pi$
$193$	−5.57031	−	9.64807i	−0.400960	−	0.694483i	−0.993842	+	0.110806i	$0.964657\pi$
$194$	11.6820			0.838719
$195$	−0.466741	+	0.808419i	−0.0334240	+	0.0578921i
$196$	−3.04765	+	5.27869i	−0.217689	+	0.377049i
$197$	3.33043	−	5.76847i	0.237283	−	0.410987i	−0.722651	−	0.691214i	$-0.757076\pi$
$197$	3.33043	−	5.76847i	0.237283	−	0.410987i	0.959934	+	0.280227i	$0.0904097\pi$
$198$	−0.288126	−	0.499048i	−0.0204762	−	0.0354658i
$199$	−10.5114	+	18.2063i	−0.745136	+	1.29061i	0.204995	+	0.978763i	$0.434282\pi$
$199$	−10.5114	+	18.2063i	−0.745136	+	1.29061i	−0.950131	+	0.311850i	$0.899051\pi$
$200$	5.95743	+	10.3186i	0.421254	+	0.729633i
$201$	−24.7468			−1.74551
$202$	27.1842			1.91267
$203$	24.7183	+	42.8134i	1.73489	+	3.00491i
$204$	−1.25815	+	2.17917i	−0.0880879	+	0.152573i
$205$	−0.463178	−	0.802247i	−0.0323497	−	0.0560314i
$206$	−3.92935	+	6.80583i	−0.273771	+	0.474184i
$207$	−2.26228	+	3.91838i	−0.157239	+	0.272346i
$208$	−2.30425	+	3.99107i	−0.159771	+	0.276731i
$209$	−0.598991			−0.0414331
$210$	−3.47039	−	6.01090i	−0.239480	−	0.414791i
$211$	−8.22445	−	14.2452i	−0.566194	−	0.980677i	−0.996937	−	0.0782029i	$-0.975082\pi$
$211$	−8.22445	−	14.2452i	−0.566194	−	0.980677i	0.430743	−	0.902475i	$-0.358252\pi$
$212$	−0.200322	+	0.346968i	−0.0137582	+	0.0238299i
$213$	−29.5446			−2.02436
$214$	−6.58818	−	11.4111i	−0.450358	−	0.780044i
$215$	1.57694			0.107546
$216$	−11.4782			−0.780994
$217$	17.2985	+	20.5569i	1.17430	+	1.39550i
$218$	−19.4835			−1.31959
$219$	11.1245			0.751721
$220$	−0.0598248	−	0.103620i	−0.00403339	−	0.00698604i
$221$	−3.55436			−0.239092
$222$	−12.7286	+	22.0465i	−0.854284	+	1.47966i
$223$	8.81146	+	15.2619i	0.590059	+	1.02201i	0.994224	+	0.107326i	$0.0342290\pi$
$223$	8.81146	+	15.2619i	0.590059	+	1.02201i	−0.404165	+	0.914686i	$0.632438\pi$
$224$	−5.04524	−	8.73860i	−0.337099	−	0.583873i
$225$	−2.74633			−0.183088
$226$	−0.615443	+	1.06598i	−0.0409387	+	0.0709079i
$227$	−2.07315	+	3.59081i	−0.137600	+	0.238330i	−0.926588	−	0.376079i	$-0.877272\pi$
$227$	−2.07315	+	3.59081i	−0.137600	+	0.238330i	0.788988	+	0.614409i	$0.210606\pi$
$228$	−0.327355	+	0.566995i	−0.0216796	+	0.0375502i
$229$	5.70997	+	9.88996i	0.377326	+	0.653547i	0.990672	−	0.136267i	$-0.0435104\pi$
$229$	5.70997	+	9.88996i	0.377326	+	0.653547i	−0.613347	+	0.789814i	$0.710177\pi$
$230$	−2.97964	+	5.16089i	−0.196472	+	0.340299i
$231$	2.95570	+	5.11942i	0.194471	+	0.336833i
$232$	−25.6639			−1.68492
$233$	−14.4837			−0.948856			−0.474428	−	0.880294i	$-0.657345\pi$
$233$	−14.4837			−0.948856			−0.474428	+	0.880294i	$0.657345\pi$
$234$	−0.444846	−	0.770496i	−0.0290805	−	0.0503689i
$235$	−0.943274	+	1.63380i	−0.0615324	+	0.106577i
$236$	−0.608431	−	1.05383i	−0.0396055	−	0.0685988i
$237$	6.75016	−	11.6916i	0.438470	−	0.759452i
$238$	13.2140	−	22.8873i	0.856535	−	1.48356i
$239$	5.19645	−	9.00051i	0.336130	−	0.582194i	−0.647571	−	0.762005i	$-0.724215\pi$
$239$	5.19645	−	9.00051i	0.336130	−	0.582194i	0.983701	+	0.179811i	$0.0575485\pi$
$240$	4.30195			0.277690
$241$	−7.50537	−	12.9997i	−0.483463	−	0.837383i	0.516356	−	0.856374i	$-0.327288\pi$
$241$	−7.50537	−	12.9997i	−0.483463	−	0.837383i	−0.999820	+	0.0189909i	$0.993955\pi$
$242$	−8.15161	−	14.1190i	−0.524005	−	0.907604i
$243$	2.96097	−	5.12855i	0.189946	−	0.328996i
$244$	−2.30989			−0.147875
$245$	4.01857	+	6.96036i	0.256737	+	0.444681i
$246$	5.47023			0.348769
$247$	−0.924801			−0.0588437
$248$	−13.7320	+	2.44116i	−0.871982	+	0.155014i
$249$	−24.1291			−1.52912
$250$	−7.41960			−0.469257
$251$	3.78287	+	6.55213i	0.238773	+	0.413567i	0.960362	−	0.278754i	$-0.0899215\pi$
$251$	3.78287	+	6.55213i	0.238773	+	0.413567i	−0.721590	+	0.692321i	$0.756588\pi$
$252$	1.04285			0.0656937
$253$	2.53773	−	4.39548i	0.159546	−	0.276342i
$254$	12.8770	+	22.3036i	0.807975	+	1.39945i
$255$	1.65897	+	2.87341i	0.103888	+	0.179940i
$256$	8.68813			0.543008
$257$	8.29418	−	14.3659i	0.517377	−	0.896123i	−0.482419	−	0.875940i	$-0.660242\pi$
$257$	8.29418	−	14.3659i	0.517377	−	0.896123i	0.999796	−	0.0201828i	$-0.00642481\pi$
$258$	−4.65599	+	8.06441i	−0.289869	+	0.502068i
$259$	21.0748	−	36.5026i	1.30952	−	2.26816i
$260$	−0.0923654	−	0.159982i	−0.00572826	−	0.00992164i
$261$	2.95771	−	5.12291i	0.183078	−	0.317100i
$262$	−4.40312	−	7.62643i	−0.272026	−	0.471163i
$263$	13.4864			0.831609			0.415804	−	0.909454i	$-0.363500\pi$
$263$	13.4864			0.831609			0.415804	+	0.909454i	$0.363500\pi$
$264$	−3.06877			−0.188870
$265$	0.264140	+	0.457505i	0.0162260	+	0.0281043i
$266$	3.43812	−	5.95500i	0.210805	−	0.365124i
$267$	−8.15486	−	14.1246i	−0.499069	−	0.864414i
$268$	2.44863	−	4.24115i	0.149574	−	0.259070i
$269$	−0.191482	+	0.331656i	−0.0116748	+	0.0202214i	−0.871804	−	0.489855i	$-0.837050\pi$
$269$	−0.191482	+	0.331656i	−0.0116748	+	0.0202214i	0.860129	+	0.510077i	$0.170383\pi$
$270$	1.74231	−	3.01778i	0.106034	−	0.183656i
$271$	−1.55465			−0.0944385			−0.0472193	−	0.998885i	$-0.515036\pi$
$271$	−1.55465			−0.0944385			−0.0472193	+	0.998885i	$0.515036\pi$
$272$	8.19012	+	14.1857i	0.496599	+	0.860135i
$273$	4.56340	+	7.90404i	0.276189	+	0.478374i
$274$	−12.6097	+	21.8406i	−0.761777	+	1.31944i
$275$	3.08072			0.185774
$276$	−2.77379	−	4.80435i	−0.166963	−	0.289188i
$277$	6.56119			0.394224			0.197112	−	0.980381i	$-0.436844\pi$
$277$	6.56119			0.394224			0.197112	+	0.980381i	$0.436844\pi$
$278$	14.7294			0.883410
$279$	1.09529	−	3.02246i	0.0655734	−	0.180950i
$280$	−5.96577			−0.356523
$281$	12.8743			0.768017			0.384009	−	0.923329i	$-0.374543\pi$
$281$	12.8743			0.768017			0.384009	+	0.923329i	$0.374543\pi$
$282$	−5.57014	−	9.64776i	−0.331697	−	0.574516i
$283$	31.4749			1.87099			0.935496	−	0.353338i	$-0.114954\pi$
$283$	31.4749			1.87099			0.935496	+	0.353338i	$0.114954\pi$
$284$	2.92336	−	5.06340i	0.173469	−	0.300458i
$285$	0.431643	+	0.747627i	0.0255683	+	0.0442856i
$286$	0.499010	+	0.864311i	0.0295071	+	0.0511078i
$287$	−9.05712			−0.534625
$288$	−0.603697	+	1.04563i	−0.0355732	+	0.0616145i
$289$	2.18327	−	3.78154i	0.128428	−	0.222443i
$290$	3.89560	−	6.74738i	0.228757	−	0.396220i
$291$	7.16973	+	12.4183i	0.420297	+	0.727976i
$292$	−1.10073	+	1.90653i	−0.0644155	+	0.111571i
$293$	3.34130	+	5.78730i	0.195201	+	0.338098i	0.946966	−	0.321333i	$-0.104131\pi$
$293$	3.34130	+	5.78730i	0.195201	+	0.338098i	−0.751765	+	0.659431i	$0.770797\pi$
$294$	−47.4602			−2.76794
$295$	−1.60453			−0.0934193
$296$	10.9405	+	18.9495i	0.635903	+	1.10142i
$297$	−1.48391	+	2.57021i	−0.0861053	+	0.149139i
$298$	2.60543	+	4.51273i	0.150928	+	0.261415i
$299$	3.91808	−	6.78632i	0.226589	−	0.392463i
$300$	1.68364	−	2.91616i	0.0972052	−	0.168364i
$301$	7.70897	−	13.3523i	0.444337	−	0.769615i
$302$	20.4675			1.17777
$303$	16.6841	+	28.8976i	0.958474	+	1.66013i
$304$	2.13097	+	3.69095i	0.122220	+	0.211691i
$305$	−1.52288	+	2.63771i	−0.0872001	+	0.151035i
$306$	−3.16228			−0.180776
$307$	−9.28573	−	16.0833i	−0.529964	−	0.917925i	−0.999389	−	0.0349527i	$-0.988872\pi$
$307$	−9.28573	−	16.0833i	−0.529964	−	0.917925i	0.469425	−	0.882973i	$-0.344461\pi$
$308$	−1.16983			−0.0666574
$309$	−9.64642			−0.548766
$310$	1.44261	−	3.98087i	0.0819345	−	0.226098i
$311$	−3.95840			−0.224460			−0.112230	−	0.993682i	$-0.535799\pi$
$311$	−3.95840			−0.224460			−0.112230	+	0.993682i	$0.535799\pi$
$312$	−4.73797			−0.268235
$313$	−12.2628	−	21.2398i	−0.693134	−	1.20054i	−0.970806	−	0.239867i	$-0.922896\pi$
$313$	−12.2628	−	21.2398i	−0.693134	−	1.20054i	0.277672	−	0.960676i	$-0.410437\pi$
$314$	−5.72359			−0.323001
$315$	0.687543	−	1.19086i	0.0387387	−	0.0670973i
$316$	1.33582	+	2.31370i	0.0751456	+	0.130156i
$317$	−4.88535	−	8.46167i	−0.274389	−	0.475255i	0.695592	−	0.718437i	$-0.255142\pi$
$317$	−4.88535	−	8.46167i	−0.274389	−	0.475255i	−0.969981	+	0.243182i	$0.921809\pi$
$318$	−3.11956			−0.174936
$319$	−3.31784	+	5.74667i	−0.185764	+	0.321752i
$320$	1.47935	−	2.56231i	0.0826983	−	0.143238i
$321$	8.08688	−	14.0069i	0.451366	−	0.781788i
$322$	29.1324	+	50.4588i	1.62349	+	2.81196i
$323$	−1.64354	+	2.84669i	−0.0914489	+	0.158394i
$324$	1.94612	+	3.37078i	0.108118	+	0.187266i
$325$	4.75642			0.263839
$326$	35.1526			1.94692
$327$	−11.9579	−	20.7116i	−0.661272	−	1.14536i
$328$	2.35090	−	4.07187i	0.129807	−	0.224832i
$329$	9.22252	+	15.9739i	0.508454	+	0.880669i
$330$	0.465817	−	0.806819i	0.0256424	−	0.0444139i
$331$	−3.63431	+	6.29481i	−0.199760	+	0.345994i	−0.948450	−	0.316925i	$-0.897350\pi$
$331$	−3.63431	+	6.29481i	−0.199760	+	0.345994i	0.748691	+	0.662920i	$0.230683\pi$
$332$	2.38751	−	4.13529i	0.131032	−	0.226953i
$333$	−5.04348			−0.276381
$334$	9.19031	+	15.9181i	0.502871	+	0.870998i
$335$	−3.22871	−	5.59229i	−0.176403	−	0.305539i
$336$	21.0304	−	36.4257i	1.14730	−	1.98719i
$337$	1.88608			0.102741			0.0513706	−	0.998680i	$-0.483641\pi$
$337$	1.88608			0.102741			0.0513706	+	0.998680i	$0.483641\pi$
$338$	0.770438	+	1.33444i	0.0419063	+	0.0725838i
$339$	−1.51089			−0.0820605
$340$	−0.656600			−0.0356091
$341$	−1.22865	+	3.39047i	−0.0665353	+	0.183604i
$342$	−0.822789			−0.0444913
$343$	44.8024			2.41910
$344$	4.00193	+	6.93155i	0.215770	+	0.373724i
$345$	−7.31492			−0.393822
$346$	3.14131	−	5.44090i	0.168878	−	0.292505i
$347$	6.40756	+	11.0982i	0.343976	+	0.595784i	0.985167	−	0.171597i	$-0.0548928\pi$
$347$	6.40756	+	11.0982i	0.343976	+	0.595784i	−0.641191	+	0.767381i	$0.721559\pi$
$348$	3.62647	+	6.28123i	0.194399	+	0.336709i
$349$	−23.7959			−1.27377			−0.636884	−	0.770960i	$-0.719777\pi$
$349$	−23.7959			−1.27377			−0.636884	+	0.770960i	$0.719777\pi$
$350$	−17.6829	+	30.6276i	−0.945189	+	1.63711i
$351$	−2.29106	+	3.96823i	−0.122288	+	0.211808i
$352$	0.677202	−	1.17295i	0.0360950	−	0.0625184i
$353$	−2.13763	−	3.70248i	−0.113775	−	0.197063i	0.803515	−	0.595285i	$-0.202961\pi$
$353$	−2.13763	−	3.70248i	−0.113775	−	0.197063i	−0.917289	+	0.398222i	$0.869627\pi$
$354$	4.73746	−	8.20553i	0.251793	−	0.436119i
$355$	−3.85467	−	6.67649i	−0.204585	−	0.354351i
$356$	3.22760			0.171063
$357$	32.4399			1.71690
$358$	9.78981	+	16.9565i	0.517408	+	0.896176i
$359$	6.04619	−	10.4723i	0.319106	−	0.552707i	−0.661196	−	0.750213i	$-0.729951\pi$
$359$	6.04619	−	10.4723i	0.319106	−	0.552707i	0.980302	+	0.197506i	$0.0632842\pi$
$360$	0.356922	+	0.618207i	0.0188115	+	0.0325824i
$361$	9.07237	−	15.7138i	0.477493	−	0.827043i
$362$	2.09969	−	3.63678i	0.110357	−	0.191145i
$363$	10.0060	−	17.3308i	0.525177	−	0.909633i
$364$	−1.80614			−0.0946675
$365$	1.45140	+	2.51390i	0.0759699	+	0.131584i
$366$	−8.99280	−	15.5760i	−0.470061	−	0.814170i
$367$	−6.44339	+	11.1603i	−0.336342	+	0.582561i	−0.983742	−	0.179589i	$-0.942523\pi$
$367$	−6.44339	+	11.1603i	−0.336342	+	0.582561i	0.647400	+	0.762151i	$0.275856\pi$
$368$	−36.1130			−1.88252
$369$	0.541873	+	0.938551i	0.0282088	+	0.0488590i
$370$	−6.64276			−0.345340
$371$	5.16508			0.268158
$372$	2.53789	+	3.01595i	0.131583	+	0.156370i
$373$	−0.823874			−0.0426586			−0.0213293	−	0.999773i	$-0.506790\pi$
$373$	−0.823874			−0.0426586			−0.0213293	+	0.999773i	$0.506790\pi$
$374$	3.54732			0.183428
$375$	−4.55372	−	7.88728i	−0.235153	−	0.407297i
$376$	−9.57533			−0.493810
$377$	−5.12252	+	8.87247i	−0.263823	+	0.456956i
$378$	−17.0349	−	29.5052i	−0.876179	−	1.51759i
$379$	−7.11663	−	12.3264i	−0.365557	−	0.633163i	0.623309	−	0.781976i	$-0.285788\pi$
$379$	−7.11663	−	12.3264i	−0.365557	−	0.633163i	−0.988865	+	0.148813i	$0.952455\pi$
$380$	−0.170839			−0.00876387
$381$	−15.8063	+	27.3773i	−0.809782	+	1.40258i
$382$	2.72370	−	4.71759i	0.139357	−	0.241373i
$383$	15.6548	−	27.1149i	0.799922	−	1.38551i	−0.119744	−	0.992805i	$-0.538207\pi$
$383$	15.6548	−	27.1149i	0.799922	−	1.38551i	0.919666	−	0.392702i	$-0.128459\pi$
$384$	12.6909	+	21.9812i	0.647628	+	1.12172i
$385$	−0.771258	+	1.33586i	−0.0393069	+	0.0680816i
$386$	8.58316	+	14.8665i	0.436871	+	0.756683i
$387$	−1.84486			−0.0937795
$388$	−2.83770			−0.144062
$389$	−9.58339	−	16.5989i	−0.485897	−	0.841598i	0.513972	−	0.857807i	$-0.328174\pi$
$389$	−9.58339	−	16.5989i	−0.485897	−	0.841598i	−0.999869	+	0.0162089i	$0.994840\pi$
$390$	0.719190	−	1.24567i	0.0364176	−	0.0630771i
$391$	−13.9263	−	24.1210i	−0.704282	−	1.21985i
$392$	−20.3966	+	35.3279i	−1.03018	+	1.78433i
$393$	5.40476	−	9.36132i	0.272634	−	0.472216i
$394$	−5.13178	+	8.88850i	−0.258535	+	0.447796i
$395$	3.52276			0.177249
$396$	0.0699892	+	0.121225i	0.00351709	+	0.00609178i
$397$	−7.13953	−	12.3660i	−0.358323	−	0.620634i	0.629358	−	0.777116i	$-0.283318\pi$
$397$	−7.13953	−	12.3660i	−0.358323	−	0.620634i	−0.987681	+	0.156482i	$0.949985\pi$
$398$	16.1968	−	28.0537i	0.811873	−	1.40621i
$399$	8.44047			0.422552
$400$	−10.9600	−	18.9832i	−0.547998	−	0.949161i
$401$	23.7398			1.18551			0.592754	−	0.805383i	$-0.298041\pi$
$401$	23.7398			1.18551			0.592754	+	0.805383i	$0.298041\pi$
$402$	38.1318			1.90184
$403$	−1.89696	+	5.23465i	−0.0944941	+	0.260756i
$404$	−6.60336			−0.328529
$405$	5.13223			0.255022
$406$	−38.0879	−	65.9701i	−1.89027	−	3.27404i
$407$	5.65757			0.280435
$408$	−8.42022	+	14.5842i	−0.416863	+	0.722027i
$409$	7.74135	+	13.4084i	0.382785	+	0.663003i	0.991459	−	0.130417i	$-0.0416316\pi$
$409$	7.74135	+	13.4084i	0.382785	+	0.663003i	−0.608674	+	0.793420i	$0.708298\pi$
$410$	0.713699	+	1.23616i	0.0352471	+	0.0610498i
$411$	−30.9563			−1.52696
$412$	0.954486	−	1.65322i	0.0470241	−	0.0814482i
$413$	−7.84386	+	13.5860i	−0.385971	+	0.668521i
$414$	3.48589	−	6.03774i	0.171322	−	0.296739i
$415$	−3.14812	−	5.45270i	−0.154535	−	0.267662i
$416$	1.04555	−	1.81095i	0.0512625	−	0.0887893i
$417$	9.04005	+	15.6578i	0.442693	+	0.766767i
$418$	0.922971			0.0451440
$419$	−20.5216			−1.00254			−0.501272	−	0.865290i	$-0.667134\pi$
$419$	−20.5216			−1.00254			−0.501272	+	0.865290i	$0.667134\pi$
$420$	0.843000	+	1.46012i	0.0411342	+	0.0712465i
$421$	4.04928	−	7.01357i	0.197350	−	0.341820i	−0.750318	−	0.661077i	$-0.770100\pi$
$421$	4.04928	−	7.01357i	0.197350	−	0.341820i	0.947668	+	0.319256i	$0.103433\pi$
$422$	12.6729	+	21.9500i	0.616905	+	1.06851i
$423$	1.10354	−	1.91138i	0.0536558	−	0.0929346i
$424$	−1.34067	+	2.32210i	−0.0651085	+	0.112771i
$425$	8.45301	−	14.6410i	0.410031	−	0.710194i
$426$	45.5246			2.20567
$427$	14.8895	+	25.7893i	0.720552	+	1.24803i
$428$	1.60035	+	2.77188i	0.0773557	+	0.133984i
$429$	−0.612527	+	1.06093i	−0.0295731	+	0.0512221i
$430$	−2.42986			−0.117178
$431$	−14.9335	−	25.8656i	−0.719323	−	1.24590i	−0.961268	−	0.275614i	$-0.911119\pi$
$431$	−14.9335	−	25.8656i	−0.719323	−	1.24590i	0.241945	−	0.970290i	$-0.422214\pi$
$432$	21.1167			1.01598
$433$	5.98188			0.287471			0.143735	−	0.989616i	$-0.454089\pi$
$433$	5.98188			0.287471			0.143735	+	0.989616i	$0.454089\pi$
$434$	−26.6548	−	31.6757i	−1.27947	−	1.52048i
$435$	9.56357			0.458538
$436$	4.73279			0.226659
$437$	−3.62345	−	6.27600i	−0.173333	−	0.300222i
$438$	−17.1414			−0.819048
$439$	5.03852	−	8.72697i	0.240475	−	0.416516i	−0.720374	−	0.693585i	$-0.756030\pi$
$439$	5.03852	−	8.72697i	0.240475	−	0.416516i	0.960850	+	0.277070i	$0.0893633\pi$
$440$	−0.400381	−	0.693480i	−0.0190874	−	0.0330604i
$441$	−4.70133	−	8.14294i	−0.223873	−	0.387759i
$442$	5.47682			0.260506
$443$	−1.53676	+	2.66175i	−0.0730138	+	0.126464i	−0.900221	−	0.435434i	$-0.856595\pi$
$443$	−1.53676	+	2.66175i	−0.0730138	+	0.126464i	0.827207	+	0.561897i	$0.189928\pi$
$444$	3.09192	−	5.35536i	0.146736	−	0.254154i
$445$	2.12792	−	3.68567i	0.100873	−	0.174718i
$446$	−13.5774	−	23.5167i	−0.642907	−	1.11355i
$447$	−3.19812	+	5.53930i	−0.151266	+	0.262000i
$448$	−14.4638	−	25.0521i	−0.683352	−	1.18360i
$449$	20.7999			0.981609			0.490804	−	0.871270i	$-0.336703\pi$
$449$	20.7999			0.981609			0.490804	+	0.871270i	$0.336703\pi$
$450$	4.23175			0.199487
$451$	−0.607851	−	1.05283i	−0.0286226	−	0.0495758i
$452$	0.149499	−	0.258939i	0.00703182	−	0.0121795i
$453$	12.5617	+	21.7576i	0.590202	+	1.02226i
$454$	3.19447	−	5.53299i	0.149924	−	0.259676i
$455$	−1.19077	+	2.06247i	−0.0558241	+	0.0966902i
$456$	−2.19084	+	3.79465i	−0.102595	+	0.177701i
$457$	19.5878			0.916278			0.458139	−	0.888881i	$-0.348516\pi$
$457$	19.5878			0.916278			0.458139	+	0.888881i	$0.348516\pi$
$458$	−8.79836	−	15.2392i	−0.411120	−	0.712081i
$459$	8.14324	+	14.1045i	0.380094	+	0.658342i
$460$	0.723791	−	1.25364i	0.0337469	−	0.0584514i
$461$	−11.4436			−0.532983			−0.266492	−	0.963837i	$-0.585864\pi$
$461$	−11.4436			−0.532983			−0.266492	+	0.963837i	$0.585864\pi$
$462$	−4.55437	−	7.88839i	−0.211888	−	0.367001i
$463$	−5.37108			−0.249615			−0.124808	−	0.992181i	$-0.539831\pi$
$463$	−5.37108			−0.249615			−0.124808	+	0.992181i	$0.539831\pi$
$464$	47.2143			2.19187
$465$	5.11718	−	0.909690i	0.237304	−	0.0421859i
$466$	22.3175			1.03384
$467$	−23.4431			−1.08482			−0.542409	−	0.840115i	$-0.682488\pi$
$467$	−23.4431			−1.08482			−0.542409	+	0.840115i	$0.682488\pi$
$468$	0.108059	+	0.187163i	0.00499501	+	0.00865160i
$469$	−63.1352			−2.91531
$470$	1.45347	−	2.51748i	0.0670434	−	0.116123i
$471$	−3.51281	−	6.08436i	−0.161862	−	0.280352i
$472$	−4.07196	−	7.05284i	−0.187427	−	0.324633i
$473$	2.06949			0.0951552
$474$	−10.4011	+	18.0153i	−0.477741	+	0.827471i
$475$	2.19937	−	3.80942i	0.100914	−	0.174788i
$476$	−3.20984	+	5.55960i	−0.147123	+	0.254824i
$477$	−0.309018	−	0.535235i	−0.0141490	−	0.0245067i
$478$	−8.00708	+	13.8687i	−0.366235	+	0.634338i
$479$	−11.4835	−	19.8900i	−0.524694	−	0.908797i	−0.999587	−	0.0287534i	$-0.990846\pi$
$479$	−11.4835	−	19.8900i	−0.524694	−	0.908797i	0.474892	−	0.880044i	$-0.342487\pi$
$480$	−1.95201			−0.0890968
$481$	8.73490			0.398277
$482$	11.5648	+	20.0309i	0.526764	+	0.912382i
$483$	−35.7596	+	61.9374i	−1.62712	+	2.81825i
$484$	1.98012	+	3.42968i	0.0900057	+	0.155894i
$485$	−1.87086	+	3.24043i	−0.0849516	+	0.147140i
$486$	−4.56248	+	7.90245i	−0.206958	+	0.358462i
$487$	−14.9009	+	25.8091i	−0.675223	+	1.16952i	0.301180	+	0.953567i	$0.402619\pi$
$487$	−14.9009	+	25.8091i	−0.675223	+	1.16952i	−0.976404	+	0.215954i	$0.930714\pi$
$488$	−15.4591			−0.699798
$489$	21.5746	+	37.3683i	0.975637	+	1.68985i
$490$	−6.19211	−	10.7251i	−0.279731	−	0.484509i
$491$	−13.3152	+	23.0625i	−0.600905	+	1.04080i	0.391779	+	0.920059i	$0.371860\pi$
$491$	−13.3152	+	23.0625i	−0.600905	+	1.04080i	−0.992684	+	0.120739i	$0.961474\pi$
$492$	−1.32879			−0.0599063
$493$	18.2073	+	31.5359i	0.820015	+	1.42031i
$494$	1.42500			0.0641140
$495$	0.184572			0.00829592
$496$	25.2629	−	4.49104i	1.13434	−	0.201654i
$497$	−75.3754			−3.38105
$498$	37.1800			1.66607
$499$	13.3118	+	23.0568i	0.595920	+	1.03216i	0.993416	+	0.114560i	$0.0365459\pi$
$499$	13.3118	+	23.0568i	0.595920	+	1.03216i	−0.397496	+	0.917604i	$0.630121\pi$
$500$	1.80231			0.0806018
$501$	−11.2810	+	19.5392i	−0.503996	+	0.872946i
$502$	−5.82894	−	10.0960i	−0.260158	−	0.450607i
$503$	−20.5685	−	35.6257i	−0.917105	−	1.58847i	−0.803790	−	0.594913i	$-0.797187\pi$
$503$	−20.5685	−	35.6257i	−0.917105	−	1.58847i	−0.113314	−	0.993559i	$-0.536147\pi$
$504$	6.97936			0.310886
$505$	−4.35352	+	7.54052i	−0.193729	+	0.335549i
$506$	−3.91033	+	6.77289i	−0.173835	+	0.301092i
$507$	−0.945700	+	1.63800i	−0.0420000	+	0.0727462i
$508$	−3.12798	−	5.41782i	−0.138782	−	0.240377i
$509$	−13.7969	+	23.8970i	−0.611539	+	1.05922i	0.379443	+	0.925215i	$0.376116\pi$
$509$	−13.7969	+	23.8970i	−0.611539	+	1.05922i	−0.990981	+	0.134001i	$0.957218\pi$
$510$	−2.55626	−	4.42757i	−0.113193	−	0.196056i
$511$	28.3812			1.25551
$512$	13.4518			0.594489
$513$	2.11877	+	3.66982i	0.0935462	+	0.162027i
$514$	−12.7803	+	22.1361i	−0.563715	+	0.976383i
$515$	−1.25856	−	2.17990i	−0.0554590	−	0.0960578i
$516$	1.13100	−	1.95894i	0.0497894	−	0.0862377i
$517$	−1.23790	+	2.14411i	−0.0544429	+	0.0942980i
$518$	−32.4736	+	56.2459i	−1.42681	+	2.47130i
$519$	7.71181			0.338511
$520$	−0.618161	−	1.07069i	−0.0271081	−	0.0469527i
$521$	9.50269	+	16.4591i	0.416320	+	0.721088i	0.995566	−	0.0940648i	$-0.0299861\pi$
$521$	9.50269	+	16.4591i	0.416320	+	0.721088i	−0.579246	+	0.815153i	$0.696653\pi$
$522$	−4.55747	+	7.89377i	−0.199475	+	0.345501i
$523$	33.2384			1.45341			0.726706	−	0.686949i	$-0.241050\pi$
$523$	33.2384			1.45341			0.726706	+	0.686949i	$0.241050\pi$
$524$	1.06957	+	1.85255i	0.0467245	+	0.0809291i
$525$	−43.4109			−1.89460
$526$	−20.7809			−0.906091
$527$	12.7419	+	15.1421i	0.555045	+	0.659598i
$528$	5.64566			0.245696
$529$	38.4055			1.66981
$530$	−0.407007	−	0.704958i	−0.0176793	−	0.0306214i
$531$	1.87714			0.0814610
$532$	−0.835161	+	1.44654i	−0.0362088	+	0.0627155i
$533$	−0.938480	−	1.62549i	−0.0406501	−	0.0704080i
$534$	12.5656	+	21.7643i	0.543768	+	0.941834i
$535$	4.22037			0.182462
$536$	16.3876	−	28.3841i	0.707836	−	1.22601i
$537$	−12.0168	+	20.8138i	−0.518565	+	0.898181i
$538$	0.295050	−	0.511041i	0.0127205	−	0.0220325i
$539$	5.27376	+	9.13443i	0.227157	+	0.393448i
$540$	−0.423229	+	0.733055i	−0.0182129	+	0.0315456i
$541$	−3.41298	−	5.91145i	−0.146735	−	0.254153i	0.783284	−	0.621664i	$-0.213543\pi$
$541$	−3.41298	−	5.91145i	−0.146735	−	0.254153i	−0.930019	+	0.367511i	$0.880210\pi$
$542$	2.39553			0.102897
$543$	5.15468			0.221208
$544$	−3.71627	−	6.43677i	−0.159334	−	0.275974i
$545$	3.12028	−	5.40448i	0.133658	−	0.231502i
$546$	−7.03163	−	12.1791i	−0.300926	−	0.521219i
$547$	−10.8451	+	18.7843i	−0.463703	+	0.803158i	−0.999142	−	0.0414164i	$-0.986813\pi$
$547$	−10.8451	+	18.7843i	−0.463703	+	0.803158i	0.535439	+	0.844574i	$0.320146\pi$
$548$	3.06304	−	5.30534i	0.130846	−	0.226633i
$549$	1.78163	−	3.08587i	0.0760379	−	0.131702i
$550$	−4.74700			−0.202413
$551$	4.73732	+	8.20527i	0.201816	+	0.349556i
$552$	−18.5638	−	32.1534i	−0.790126	−	1.36854i
$553$	17.2213	−	29.8281i	0.732323	−	1.26842i
$554$	−10.1100			−0.429532
$555$	−4.07694	−	7.06146i	−0.173056	−	0.299742i
$556$	−3.57795			−0.151739
$557$	−20.1678			−0.854536			−0.427268	−	0.904125i	$-0.640524\pi$
$557$	−20.1678			−0.854536			−0.427268	+	0.904125i	$0.640524\pi$
$558$	−1.68771	+	4.65723i	−0.0714463	+	0.197156i
$559$	3.19515			0.135140
$560$	10.9753			0.463792
$561$	2.17714	+	3.77092i	0.0919190	+	0.159208i
$562$	−19.8377			−0.836804
$563$	10.2444	−	17.7439i	0.431751	−	0.747814i	−0.565273	−	0.824904i	$-0.691229\pi$
$563$	10.2444	−	17.7439i	0.431751	−	0.747814i	0.997024	+	0.0770892i	$0.0245626\pi$
$564$	1.35305	+	2.34356i	0.0569738	+	0.0986816i
$565$	−0.197126	−	0.341432i	−0.00829314	−	0.0143641i
$566$	−48.4990			−2.03856
$567$	25.0893	−	43.4559i	1.05365	−	1.82498i
$568$	19.5647	−	33.8871i	0.820917	−	1.42187i
$569$	10.9262	−	18.9246i	0.458048	−	0.793363i	−0.540810	−	0.841145i	$-0.681882\pi$
$569$	10.9262	−	18.9246i	0.458048	−	0.793363i	0.998858	+	0.0477825i	$0.0152154\pi$
$570$	−0.665108	−	1.15200i	−0.0278583	−	0.0482520i
$571$	−3.42128	+	5.92583i	−0.143176	+	0.247988i	−0.928691	−	0.370855i	$-0.879065\pi$
$571$	−3.42128	+	5.92583i	−0.143176	+	0.247988i	0.785515	+	0.618843i	$0.212398\pi$
$572$	−0.121216	−	0.209952i	−0.00506828	−	0.00877852i
$573$	6.68660			0.279337
$574$	13.9559			0.582507
$575$	18.6360	+	32.2786i	0.777177	+	1.34611i
$576$	−1.73070	+	2.99765i	−0.0721124	+	0.124902i
$577$	−20.8845	−	36.1730i	−0.869434	−	1.50590i	−0.862576	−	0.505927i	$-0.831151\pi$
$577$	−20.8845	−	36.1730i	−0.869434	−	1.50590i	−0.00685740	−	0.999976i	$-0.502183\pi$
$578$	−3.36415	+	5.82688i	−0.139930	+	0.242366i
$579$	−10.5357	+	18.2484i	−0.437848	+	0.758376i
$580$	−0.946288	+	1.63902i	−0.0392925	+	0.0680566i
$581$	−61.5592			−2.55391
$582$	−11.0477	−	19.1351i	−0.457940	−	0.793176i
$583$	0.346644	+	0.600406i	0.0143565	+	0.0248663i
$584$	−7.36672	+	12.7595i	−0.304837	+	0.527993i
$585$	0.284967			0.0117819
$586$	−5.14853	−	8.91751i	−0.212684	−	0.368379i
$587$	38.8091			1.60182			0.800912	−	0.598782i	$-0.204349\pi$
$587$	38.8091			1.60182			0.800912	+	0.598782i	$0.204349\pi$
$588$	11.5287			0.475434
$589$	3.31528	+	3.93978i	0.136604	+	0.162336i
$590$	2.47238			0.101786
$591$	−12.5983			−0.518227
$592$	−20.1274	−	34.8616i	−0.827230	−	1.43280i
$593$	11.3344			0.465446			0.232723	−	0.972543i	$-0.425236\pi$
$593$	11.3344			0.465446			0.232723	+	0.972543i	$0.425236\pi$
$594$	2.28652	−	3.96038i	0.0938172	−	0.162496i
$595$	4.23242	+	7.33077i	0.173512	+	0.300532i
$596$	−0.632890	−	1.09620i	−0.0259242	−	0.0449020i
$597$	39.7627			1.62738
$598$	−6.03728	+	10.4569i	−0.246883	+	0.427613i
$599$	20.0942	−	34.8042i	0.821027	−	1.42206i	−0.0838915	−	0.996475i	$-0.526735\pi$
$599$	20.0942	−	34.8042i	0.821027	−	1.42206i	0.904918	−	0.425585i	$-0.139932\pi$
$600$	11.2679	−	19.5165i	0.460009	−	0.796759i
$601$	−2.87169	−	4.97391i	−0.117139	−	0.202890i	0.801494	−	0.598003i	$-0.204039\pi$
$601$	−2.87169	−	4.97391i	−0.117139	−	0.202890i	−0.918633	+	0.395113i	$0.870705\pi$
$602$	−11.8786	+	20.5743i	−0.484134	+	0.838544i
$603$	3.77727	+	6.54243i	0.153823	+	0.266428i
$604$	−4.97180			−0.202299
$605$	5.22190			0.212300
$606$	−25.7081	−	44.5277i	−1.04432	−	1.80881i
$607$	−1.21943	+	2.11211i	−0.0494950	+	0.0857279i	−0.889712	−	0.456523i	$-0.849095\pi$
$607$	−1.21943	+	2.11211i	−0.0494950	+	0.0857279i	0.840216	+	0.542251i	$0.182428\pi$
$608$	−0.966930	−	1.67477i	−0.0392142	−	0.0679210i
$609$	46.7522	−	80.9772i	1.89450	−	3.28136i
$610$	2.34658	−	4.06439i	0.0950101	−	0.164562i
$611$	−1.91124	+	3.31036i	−0.0773204	+	0.133923i
$612$	0.768157			0.0310509
$613$	3.19817	+	5.53939i	0.129173	+	0.223734i	0.923356	−	0.383944i	$-0.125434\pi$
$613$	3.19817	+	5.53939i	0.129173	+	0.223734i	−0.794184	+	0.607678i	$0.792101\pi$
$614$	14.3081	+	24.7824i	0.577430	+	1.00014i
$615$	−0.876054	+	1.51737i	−0.0353259	+	0.0611863i
$616$	−7.82917			−0.315446
$617$	11.7983	+	20.4352i	0.474981	+	0.822691i	0.999589	−	0.0286522i	$-0.00912154\pi$
$617$	11.7983	+	20.4352i	0.474981	+	0.822691i	−0.524608	+	0.851344i	$0.675788\pi$
$618$	14.8639			0.597915
$619$	30.3959			1.22172			0.610858	−	0.791740i	$-0.290825\pi$
$619$	30.3959			1.22172			0.610858	+	0.791740i	$0.290825\pi$
$620$	−0.350426	+	0.967001i	−0.0140735	+	0.0388357i
$621$	−35.9062			−1.44087
$622$	6.09940			0.244564
$623$	−20.8050	−	36.0354i	−0.833536	−	1.44373i
$624$	8.71651			0.348940
$625$	−10.7028	+	18.5378i	−0.428112	+	0.741512i
$626$	18.8954	+	32.7279i	0.755213	+	1.30807i
$627$	0.566466	+	0.981148i	0.0226225	+	0.0391833i
$628$	1.39033			0.0554802
$629$	15.5235	−	26.8875i	0.618962	−	1.07207i
$630$	−1.05942	+	1.83497i	−0.0422082	+	0.0731068i
$631$	−6.53709	+	11.3226i	−0.260237	+	0.450745i	−0.966305	−	0.257400i	$-0.917134\pi$
$631$	−6.53709	+	11.3226i	−0.260237	+	0.450745i	0.706067	+	0.708145i	$0.250468\pi$
$632$	8.94003	+	15.4846i	0.355615	+	0.615944i
$633$	−15.5557	+	26.9433i	−0.618284	+	1.07090i
$634$	7.52772	+	13.0384i	0.298964	+	0.517820i
$635$	−8.24897			−0.327350
$636$	0.757778			0.0300479
$637$	8.14233	+	14.1029i	0.322611	+	0.558778i
$638$	5.11239	−	8.85491i	0.202401	−	0.350569i
$639$	4.50959	+	7.81084i	0.178397	+	0.308992i
$640$	−3.31154	+	5.73576i	−0.130900	+	0.226726i
$641$	3.25627	−	5.64003i	0.128615	−	0.222768i	−0.794525	−	0.607231i	$-0.792280\pi$
$641$	3.25627	−	5.64003i	0.128615	−	0.222768i	0.923140	+	0.384463i	$0.125614\pi$
$642$	−12.4609	+	21.5829i	−0.491792	+	0.851808i
$643$	−36.5200			−1.44021			−0.720104	−	0.693866i	$-0.755906\pi$
$643$	−36.5200			−1.44021			−0.720104	+	0.693866i	$0.755906\pi$
$644$	−7.07661	−	12.2571i	−0.278858	−	0.482996i
$645$	−1.49131	−	2.58302i	−0.0587202	−	0.101706i
$646$	2.53249	−	4.38640i	0.0996394	−	0.172580i
$647$	−2.08056			−0.0817954			−0.0408977	−	0.999163i	$-0.513022\pi$
$647$	−2.08056			−0.0817954			−0.0408977	+	0.999163i	$0.513022\pi$
$648$	13.0245	+	22.5591i	0.511652	+	0.886207i
$649$	−2.10570			−0.0826560
$650$	−7.32905			−0.287469
$651$	17.3131	−	47.7756i	0.678555	−	1.87247i
$652$	−8.53898			−0.334412
$653$	−26.1173			−1.02205			−0.511025	−	0.859566i	$-0.670734\pi$
$653$	−26.1173			−1.02205			−0.511025	+	0.859566i	$0.670734\pi$
$654$	18.4256	+	31.9141i	0.720497	+	1.24794i
$655$	2.82063			0.110211
$656$	−4.32498	+	7.49109i	−0.168862	+	0.292478i
$657$	−1.69800	−	2.94102i	−0.0662453	−	0.114740i
$658$	−14.2108	−	24.6138i	−0.553993	−	0.959544i
$659$	−14.5636			−0.567318			−0.283659	−	0.958925i	$-0.591548\pi$
$659$	−14.5636			−0.567318			−0.283659	+	0.958925i	$0.591548\pi$
$660$	−0.113153	+	0.195986i	−0.00440446	+	0.00762875i
$661$	−14.9561	+	25.9047i	−0.581723	+	1.00757i	0.413552	+	0.910481i	$0.364288\pi$
$661$	−14.9561	+	25.9047i	−0.581723	+	1.00757i	−0.995275	+	0.0970938i	$0.969045\pi$
$662$	5.60002	−	9.69952i	0.217651	−	0.376983i
$663$	3.36136	+	5.82204i	0.130544	+	0.226109i
$664$	15.9785	−	27.6756i	0.620087	−	1.07402i
$665$	1.10123	+	1.90738i	0.0427037	+	0.0739649i
$666$	7.77137			0.301135
$667$	−80.2819			−3.10853
$668$	−2.23244	−	3.86669i	−0.0863756	−	0.149607i
$669$	16.6660	−	28.8664i	0.644345	−	1.11604i
$670$	4.97504	+	8.61702i	0.192203	+	0.332905i
$671$	−1.99856	+	3.46160i	−0.0771534	+	0.133634i
$672$	−9.54256	+	16.5282i	−0.368112	+	0.637589i
$673$	18.7818	−	32.5310i	0.723983	−	1.25398i	−0.235408	−	0.971897i	$-0.575642\pi$
$673$	18.7818	−	32.5310i	0.723983	−	1.25398i	0.959391	−	0.282079i	$-0.0910242\pi$
$674$	−2.90621			−0.111943
$675$	−10.8972	−	18.8746i	−0.419435	−	0.726482i
$676$	−0.187149	−	0.324151i	−0.00719803	−	0.0124673i
$677$	−7.13690	+	12.3615i	−0.274293	+	0.475090i	−0.969957	−	0.243278i	$-0.921777\pi$
$677$	−7.13690	+	12.3615i	−0.274293	+	0.475090i	0.695663	+	0.718368i	$0.255111\pi$
$678$	2.32810			0.0894101
$679$	18.2917	+	31.6822i	0.701972	+	1.21585i
$680$	−4.39433			−0.168515
$681$	7.84233			0.300519
$682$	1.89320	−	5.22429i	0.0724944	−	0.200048i
$683$	22.0127			0.842293			0.421146	−	0.906993i	$-0.361628\pi$
$683$	22.0127			0.842293			0.421146	+	0.906993i	$0.361628\pi$
$684$	0.199865			0.00764204
$685$	−4.03886	−	6.99550i	−0.154317	−	0.267284i
$686$	−69.0348			−2.63576
$687$	10.7998	−	18.7059i	0.412040	−	0.713674i
$688$	−7.36242	−	12.7521i	−0.280690	−	0.486169i
$689$	0.535195	+	0.926985i	0.0203893	+	0.0353153i
$690$	11.2714			0.429094
$691$	−22.6405	+	39.2146i	−0.861287	+	1.49179i	0.00940023	+	0.999956i	$0.497008\pi$
$691$	−22.6405	+	39.2146i	−0.861287	+	1.49179i	−0.870687	+	0.491837i	$0.836326\pi$
$692$	−0.763061	+	1.32166i	−0.0290072	+	0.0502420i
$693$	0.902296	−	1.56282i	0.0342754	−	0.0593667i
$694$	−9.87326	−	17.1010i	−0.374784	−	0.649144i
$695$	−2.35890	+	4.08574i	−0.0894783	+	0.154981i
$696$	24.2704	+	42.0375i	0.919965	+	1.59343i
$697$	−6.67139			−0.252697
$698$	36.6666			1.38785
$699$	13.6972	+	23.7242i	0.518075	+	0.897333i
$700$	4.29538	−	7.43982i	0.162350	−	0.281199i
$701$	4.70328	+	8.14633i	0.177641	+	0.307683i	0.941072	−	0.338206i	$-0.109820\pi$
$701$	4.70328	+	8.14633i	0.177641	+	0.307683i	−0.763431	+	0.645889i	$0.776487\pi$
$702$	3.53024	−	6.11455i	0.133240	−	0.230779i
$703$	4.03902	−	6.99580i	0.152335	−	0.263851i
$704$	1.94143	−	3.36265i	0.0731702	−	0.126735i
$705$	3.56822			0.134387
$706$	3.29382	+	5.70507i	0.123965	+	0.214713i
$707$	42.5651	+	73.7248i	1.60082	+	2.77271i
$708$	−1.15079	+	1.99322i	−0.0432492	+	0.0749099i
$709$	6.15573			0.231183			0.115592	−	0.993297i	$-0.463124\pi$
$709$	6.15573			0.231183			0.115592	+	0.993297i	$0.463124\pi$
$710$	5.93957	+	10.2876i	0.222908	+	0.386088i
$711$	−4.12128			−0.154560
$712$	21.6009			0.809528
$713$	−42.9564	+	7.63645i	−1.60873	+	0.285987i
$714$	−49.9858			−1.87067
$715$	−0.319665			−0.0119548
$716$	−2.37806	−	4.11893i	−0.0888724	−	0.153932i
$717$	−19.6571			−0.734108
$718$	−9.31642	+	16.1365i	−0.347686	+	0.602210i
$719$	18.3589	+	31.7986i	0.684673	+	1.18589i	0.973540	+	0.228518i	$0.0733881\pi$
$719$	18.3589	+	31.7986i	0.684673	+	1.18589i	−0.288867	+	0.957369i	$0.593279\pi$
$720$	−0.656635	−	1.13733i	−0.0244714	−	0.0423856i
$721$	−24.6103			−0.916537
$722$	−13.9794	+	24.2130i	−0.520259	+	0.901115i
$723$	−14.1957	+	24.5876i	−0.527942	+	0.914422i
$724$	−0.510041	+	0.883417i	−0.0189555	+	0.0328319i
$725$	−24.3649	−	42.2012i	−0.904888	−	1.56731i
$726$	−15.4180	+	26.7047i	−0.572214	+	0.991103i
$727$	−18.1515	−	31.4393i	−0.673201	−	1.16602i	−0.976991	−	0.213280i	$-0.931585\pi$
$727$	−18.1515	−	31.4393i	−0.673201	−	1.16602i	0.303790	−	0.952739i	$-0.401748\pi$
$728$	−12.0877			−0.448000
$729$	19.9956			0.740579
$730$	−2.23643	−	3.87361i	−0.0827741	−	0.143369i
$731$	5.67835	−	9.83520i	0.210021	−	0.363768i
$732$	2.18446	+	3.78360i	0.0807400	+	0.139846i
$733$	7.49662	−	12.9845i	0.276894	−	0.479594i	−0.693717	−	0.720247i	$-0.744028\pi$
$733$	7.49662	−	12.9845i	0.276894	−	0.479594i	0.970611	+	0.240653i	$0.0773616\pi$
$734$	9.92845	−	17.1966i	0.366466	−	0.634738i
$735$	7.60072	−	13.1648i	0.280357	−	0.485592i
$736$	16.3863			0.604006
$737$	−4.23719	−	7.33904i	−0.156079	−	0.270337i
$738$	−0.834958	−	1.44619i	−0.0307352	−	0.0532350i
$739$	7.39624	−	12.8107i	0.272075	−	0.471248i	−0.697318	−	0.716762i	$-0.745623\pi$
$739$	7.39624	−	12.8107i	0.272075	−	0.471248i	0.969393	+	0.245514i	$0.0789567\pi$
$740$	1.61361			0.0593173
$741$	0.874585	+	1.51483i	0.0321287	+	0.0556485i
$742$	−7.95874			−0.292175
$743$	8.77518			0.321930			0.160965	−	0.986960i	$-0.448539\pi$
$743$	8.77518			0.321930			0.160965	+	0.986960i	$0.448539\pi$
$744$	16.9850	+	20.1844i	0.622699	+	0.739996i
$745$	−1.66903			−0.0611485
$746$	1.26949			0.0464792
$747$	3.68299	+	6.37912i	0.134753	+	0.233400i
$748$	−0.861688			−0.0315064
$749$	20.6316	−	35.7350i	0.753862	−	1.30573i
$750$	7.01672	+	12.1533i	0.256214	+	0.443776i
$751$	6.29866	+	10.9096i	0.229841	+	0.398097i	0.957761	−	0.287566i	$-0.0928460\pi$
$751$	6.29866	+	10.9096i	0.229841	+	0.398097i	−0.727920	+	0.685662i	$0.759513\pi$
$752$	17.6159			0.642385
$753$	7.15493	−	12.3927i	0.260740	−	0.451615i
$754$	7.89317	−	13.6714i	0.287452	−	0.497882i
$755$	−3.27785	+	5.67740i	−0.119293	+	0.206622i
$756$	4.13797	+	7.16718i	0.150497	+	0.260668i
$757$	−0.343813	+	0.595501i	−0.0124961	+	0.0216438i	−0.872206	−	0.489139i	$-0.837311\pi$
$757$	−0.343813	+	0.595501i	−0.0124961	+	0.0216438i	0.859710	+	0.510783i	$0.170644\pi$
$758$	10.9658	+	18.9934i	0.398297	+	0.689871i
$759$	−9.59973			−0.348448
$760$	−1.14335			−0.0414737
$761$	22.4999	+	38.9709i	0.815620	+	1.41269i	0.908882	+	0.417053i	$0.136937\pi$
$761$	22.4999	+	38.9709i	0.815620	+	1.41269i	−0.0932623	+	0.995642i	$0.529730\pi$
$762$	24.3556	−	42.1851i	0.882308	−	1.52820i
$763$	−30.5074	−	52.8404i	−1.10444	−	1.91295i
$764$	−0.661620	+	1.14596i	−0.0239366	+	0.0414594i
$765$	0.506438	−	0.877176i	0.0183103	−	0.0317144i
$766$	−24.1221	+	41.7807i	−0.871566	+	1.50960i
$767$	−3.25106			−0.117389
$768$	−8.21637	−	14.2312i	−0.296483	−	0.513523i
$769$	2.97666	+	5.15572i	0.107341	+	0.185920i	0.914692	−	0.404151i	$-0.132433\pi$
$769$	2.97666	+	5.15572i	0.107341	+	0.185920i	−0.807351	+	0.590071i	$0.799100\pi$
$770$	1.18841	−	2.05839i	0.0428274	−	0.0741793i
$771$	−31.3752			−1.12995
$772$	−2.08495	−	3.61125i	−0.0750391	−	0.129972i
$773$	34.6083			1.24477			0.622387	−	0.782709i	$-0.286163\pi$
$773$	34.6083			1.24477			0.622387	+	0.782709i	$0.286163\pi$
$774$	2.84270			0.102179
$775$	−17.0511	−	20.2630i	−0.612494	−	0.727868i
$776$	−18.9915			−0.681754
$777$	−79.7217			−2.86000
$778$	14.7668	+	25.5769i	0.529416	+	0.916975i
$779$	−1.73582			−0.0621920
$780$	−0.174700	+	0.302589i	−0.00625526	+	0.0108344i
$781$	−5.05868	−	8.76189i	−0.181014	−	0.313525i
$782$	21.4587	+	37.1675i	0.767360	+	1.32911i
$783$	46.9440			1.67764
$784$	37.5239	−	64.9933i	1.34014	−	2.32119i
$785$	0.916629	−	1.58765i	0.0327159	−	0.0566656i
$786$	−8.32807	+	14.4246i	−0.297052	+	0.514510i
$787$	−3.87100	−	6.70476i	−0.137986	−	0.238999i	0.788748	−	0.614717i	$-0.210730\pi$
$787$	−3.87100	−	6.70476i	−0.137986	−	0.238999i	−0.926734	+	0.375718i	$0.877396\pi$
$788$	1.24657	−	2.15912i	0.0444072	−	0.0769156i
$789$	−12.7541	−	22.0908i	−0.454058	−	0.786452i
$790$	−5.42813			−0.193124
$791$	−3.85465			−0.137056
$792$	0.468406	+	0.811304i	0.0166441	+	0.0288284i
$793$	−3.08563	+	5.34447i	−0.109574	+	0.189788i
$794$	11.0011	+	19.0545i	0.390416	+	0.676220i
$795$	0.499595	−	0.865324i	0.0177188	−	0.0306899i
$796$	−3.93440	+	6.81458i	−0.139451	+	0.241537i
$797$	4.19934	−	7.27348i	0.148748	−	0.257640i	−0.782017	−	0.623257i	$-0.785809\pi$
$797$	4.19934	−	7.27348i	0.148748	−	0.257640i	0.930765	+	0.365618i	$0.119142\pi$
$798$	−13.0057			−0.460397
$799$	6.79323	+	11.7662i	0.240327	+	0.416259i
$800$	4.97309	+	8.61365i	0.175825	+	0.304538i
$801$	−2.48946	+	4.31187i	−0.0879608	+	0.152353i
$802$	−36.5801			−1.29169
$803$	1.90475	+	3.29912i	0.0672171	+	0.116423i
$804$	−9.26268			−0.326669
$805$	−18.6621			−0.657754
$806$	2.92297	−	8.06594i	0.102957	−	0.284111i
$807$	0.724337			0.0254979
$808$	−44.1933			−1.55472
$809$	26.4168	+	45.7553i	0.928766	+	1.60867i	0.785389	+	0.619002i	$0.212463\pi$
$809$	26.4168	+	45.7553i	0.928766	+	1.60867i	0.143377	+	0.989668i	$0.454204\pi$
$810$	−7.90812			−0.277863
$811$	10.6115	−	18.3796i	0.372619	−	0.645396i	−0.617348	−	0.786690i	$-0.711793\pi$
$811$	10.6115	−	18.3796i	0.372619	−	0.645396i	0.989968	+	0.141294i	$0.0451264\pi$
$812$	9.25200	+	16.0249i	0.324682	+	0.562365i
$813$	1.47024	+	2.54653i	0.0515635	+	0.0893105i
$814$	−8.71761			−0.305552
$815$	−5.62966	+	9.75086i	−0.197198	+	0.341558i
$816$	15.4908	−	26.8308i	0.542286	−	0.939267i
$817$	1.47744	−	2.55900i	0.0516891	−	0.0895281i
$818$	−11.9285	−	20.6607i	−0.417069	−	0.722384i
$819$	1.39308	−	2.41289i	0.0486783	−	0.0843133i
$820$	−0.173366	−	0.300279i	−0.00605421	−	0.0104862i
$821$	−28.3378			−0.988996			−0.494498	−	0.869179i	$-0.664648\pi$
$821$	−28.3378			−0.988996			−0.494498	+	0.869179i	$0.664648\pi$
$822$	47.6998			1.66372
$823$	−12.7907	−	22.1542i	−0.445856	−	0.772246i	0.552255	−	0.833675i	$-0.313767\pi$
$823$	−12.7907	−	22.1542i	−0.445856	−	0.772246i	−0.998111	+	0.0614294i	$0.980434\pi$
$824$	6.38795	−	11.0643i	0.222535	−	0.385441i
$825$	−2.91344	−	5.04622i	−0.101433	−	0.175687i
$826$	12.0864	−	20.9343i	0.420540	−	0.728397i
$827$	0.866810	−	1.50136i	0.0301419	−	0.0522074i	−0.850561	−	0.525877i	$-0.823737\pi$
$827$	0.866810	−	1.50136i	0.0301419	−	0.0522074i	0.880703	+	0.473669i	$0.157071\pi$
$828$	−0.846765	+	1.46664i	−0.0294271	+	0.0509692i
$829$	20.6237			0.716291			0.358145	−	0.933666i	$-0.383409\pi$
$829$	20.6237			0.716291			0.358145	+	0.933666i	$0.383409\pi$
$830$	4.85086	+	8.40193i	0.168376	+	0.291635i
$831$	−6.20492	−	10.7472i	−0.215246	−	0.372817i
$832$	2.99743	−	5.19170i	0.103917	−	0.179990i
$833$	57.8815			2.00547
$834$	−13.9296	−	24.1268i	−0.482342	−	0.835441i
$835$	−5.88729			−0.203738
$836$	−0.224201			−0.00775415
$837$	25.1183	−	4.46533i	0.868217	−	0.154344i
$838$	31.6212			1.09234
$839$	−44.7880			−1.54625			−0.773127	−	0.634251i	$-0.781309\pi$
$839$	−44.7880			−1.54625			−0.773127	+	0.634251i	$0.781309\pi$
$840$	5.64183	+	9.77193i	0.194662	+	0.337164i
$841$	75.9610			2.61935
$842$	−6.23944	+	10.8070i	−0.215025	+	0.372435i
$843$	−12.1752	−	21.0881i	−0.419338	−	0.726314i
$844$	−3.07839	−	5.33193i	−0.105963	−	0.183532i
$845$	−0.493540			−0.0169783
$846$	−1.70041	+	2.94520i	−0.0584614	+	0.101258i
$847$	25.5276	−	44.2152i	0.877140	−	1.51925i
$848$	2.46644	−	4.27201i	0.0846980	−	0.146701i
$849$	−29.7659	−	51.5560i	−1.02156	−	1.76940i
$850$	−13.0250	+	22.5600i	−0.446755	+	0.773802i
$851$	34.2241	+	59.2778i	1.17319	+	2.03202i
$852$	−11.0585			−0.378857
$853$	5.66653			0.194018			0.0970092	−	0.995283i	$-0.469072\pi$
$853$	5.66653			0.194018			0.0970092	+	0.995283i	$0.469072\pi$
$854$	−22.9428	−	39.7381i	−0.785087	−	1.35981i
$855$	0.131769	−	0.228231i	0.00450641	−	0.00780533i
$856$	10.7104	+	18.5510i	0.366074	+	0.634060i
$857$	12.7708	−	22.1196i	0.436241	−	0.755591i	−0.561155	−	0.827711i	$-0.689643\pi$
$857$	12.7708	−	22.1196i	0.436241	−	0.755591i	0.997396	+	0.0721195i	$0.0229763\pi$
$858$	0.943828	−	1.63476i	0.0322218	−	0.0558097i
$859$	−27.7391	+	48.0456i	−0.946447	+	1.63929i	−0.193618	+	0.981077i	$0.562022\pi$
$859$	−27.7391	+	48.0456i	−0.946447	+	1.63929i	−0.752828	+	0.658217i	$0.771311\pi$
$860$	0.590243			0.0201271
$861$	8.56531	+	14.8356i	0.291905	+	0.505595i
$862$	23.0107	+	39.8557i	0.783748	+	1.35749i
$863$	−14.5103	+	25.1326i	−0.493938	+	0.855525i	−0.999976	−	0.00698609i	$-0.997776\pi$
$863$	−14.5103	+	25.1326i	−0.493938	+	0.855525i	0.506038	+	0.862511i	$0.331110\pi$
$864$	−9.58170			−0.325976
$865$	1.00616	+	1.74271i	0.0342103	+	0.0592541i
$866$	−9.21733			−0.313218
$867$	−8.25888			−0.280486
$868$	6.47477	+	7.69441i	0.219768	+	0.261165i
$869$	4.62309			0.156828
$870$	−14.7363			−0.499606
$871$	−6.54194	−	11.3310i	−0.221665	−	0.383935i
$872$	31.6744			1.07263
$873$	2.18873	−	3.79099i	0.0740772	−	0.128306i
$874$	5.58328	+	9.67053i	0.188857	+	0.327111i
$875$	−11.6176	−	20.1223i	−0.392748	−	0.680260i
$876$	4.16385			0.140684
$877$	−5.68033	+	9.83861i	−0.191811	+	0.332226i	−0.945850	−	0.324603i	$-0.894769\pi$
$877$	−5.68033	+	9.83861i	−0.191811	+	0.332226i	0.754039	+	0.656829i	$0.228103\pi$
$878$	−7.76373	+	13.4472i	−0.262013	+	0.453820i
$879$	6.31974	−	10.9461i	0.213159	−	0.369203i
$880$	0.736587	+	1.27581i	0.0248303	+	0.0430074i
$881$	16.3416	−	28.3046i	0.550564	−	0.953605i	−0.447670	−	0.894199i	$-0.647746\pi$
$881$	16.3416	−	28.3046i	0.550564	−	0.953605i	0.998234	−	0.0594059i	$-0.0189206\pi$
$882$	7.24417	+	12.5473i	0.243924	+	0.422488i
$883$	27.4760			0.924641			0.462320	−	0.886713i	$-0.347017\pi$
$883$	27.4760			0.924641			0.462320	+	0.886713i	$0.347017\pi$
$884$	−1.33039			−0.0447457
$885$	1.51740	+	2.62822i	0.0510069	+	0.0883466i
$886$	2.36796	−	4.10143i	0.0795532	−	0.137790i
$887$	−7.28011	−	12.6095i	−0.244442	−	0.423386i	0.717532	−	0.696525i	$-0.245272\pi$
$887$	−7.28011	−	12.6095i	−0.244442	−	0.423386i	−0.961975	+	0.273139i	$0.911938\pi$
$888$	20.6928	−	35.8411i	0.694406	−	1.20275i
$889$	−40.3257	+	69.8462i	−1.35248	+	2.34257i
$890$	−3.27887	+	5.67916i	−0.109908	+	0.190366i
$891$	6.73527			0.225640
$892$	3.29811	+	5.71249i	0.110429	+	0.191268i
$893$	1.76752	+	3.06143i	0.0591477	+	0.102447i
$894$	4.92790	−	8.53538i	0.164814	−	0.285466i
$895$	−6.27133			−0.209627
$896$	32.3774	+	56.0794i	1.08165	+	1.87348i
$897$	−14.8213			−0.494870
$898$	−32.0501			−1.06952
$899$	56.1615	−	9.98393i	1.87309	−	0.332983i
$900$	−1.02794			−0.0342648
$901$	3.80455			0.126748
$902$	0.936622	+	1.62228i	0.0311861	+	0.0540159i
$903$	−29.1615			−0.970433
$904$	1.00053	−	1.73296i	0.0332771	−	0.0576376i
$905$	0.672529	+	1.16485i	0.0223556	+	0.0387211i
$906$	−19.3561	−	33.5257i	−0.643063	−	1.11382i
$907$	8.11182			0.269348			0.134674	−	0.990890i	$-0.457001\pi$
$907$	8.11182			0.269348			0.134674	+	0.990890i	$0.457001\pi$
$908$	−0.775976	+	1.34403i	−0.0257517	+	0.0446032i
$909$	5.09320	−	8.82168i	0.168931	−	0.292597i
$910$	1.83483	−	3.17801i	0.0608239	−	0.105350i
$911$	−8.76672	−	15.1844i	−0.290454	−	0.503082i	0.683463	−	0.729985i	$-0.260473\pi$
$911$	−8.76672	−	15.1844i	−0.290454	−	0.503082i	−0.973917	+	0.226903i	$0.927140\pi$
$912$	4.03052	−	6.98107i	0.133464	−	0.231166i
$913$	−4.13143	−	7.15584i	−0.136730	−	0.236824i
$914$	−30.1823			−0.998343
$915$	5.76077			0.190445
$916$	2.13723	+	3.70179i	0.0706160	+	0.122310i
$917$	13.7889	−	23.8830i	0.455348	−	0.788686i
$918$	−12.5477	−	21.7333i	−0.414137	−	0.717305i
$919$	−26.3198	+	45.5872i	−0.868210	+	1.50378i	−0.00438489	+	0.999990i	$0.501396\pi$
$919$	−26.3198	+	45.5872i	−0.868210	+	1.50378i	−0.863825	+	0.503793i	$0.831938\pi$
$920$	4.84401	−	8.39007i	0.159702	−	0.276613i
$921$	−17.5630	+	30.4200i	−0.578721	+	1.00237i
$922$	17.6332			0.580719
$923$	−7.81025	−	13.5277i	−0.257078	−	0.445271i
$924$	1.10631	+	1.91619i	0.0363949	+	0.0630379i
$925$	−20.7734	+	35.9806i	−0.683026	+	1.18304i
$926$	8.27616			0.271972
$927$	1.47240	+	2.55027i	0.0483599	+	0.0837617i
$928$	−21.4235			−0.703261
$929$	23.3226			0.765190			0.382595	−	0.923916i	$-0.375030\pi$
$929$	23.3226			0.765190			0.382595	+	0.923916i	$0.375030\pi$
$930$	−7.88494	+	1.40172i	−0.258557	+	0.0459642i
$931$	15.0601			0.493574
$932$	−5.42119			−0.177577
$933$	3.74346	+	6.48386i	0.122555	+	0.212272i
$934$	36.1229			1.18198
$935$	−0.568101	+	0.983980i	−0.0185789	+	0.0321796i
$936$	0.723187	+	1.25260i	0.0236381	+	0.0409424i
$937$	3.80078	+	6.58315i	0.124166	+	0.215062i	0.921407	−	0.388600i	$-0.127041\pi$
$937$	3.80078	+	6.58315i	0.124166	+	0.215062i	−0.797241	+	0.603662i	$0.793708\pi$
$938$	97.2834			3.17642
$939$	−23.1938	+	40.1729i	−0.756902	+	1.31099i
$940$	−0.353065	+	0.611526i	−0.0115157	+	0.0199458i
$941$	1.54905	−	2.68304i	0.0504977	−	0.0874647i	−0.839672	−	0.543094i	$-0.817253\pi$
$941$	1.54905	−	2.68304i	0.0504977	−	0.0874647i	0.890169	+	0.455630i	$0.150586\pi$
$942$	5.41280	+	9.37524i	0.176358	+	0.305462i
$943$	7.35409	−	12.7377i	0.239482	−	0.414795i
$944$	7.49125	+	12.9752i	0.243819	+	0.422307i
$945$	10.9125			0.354983
$946$	−3.18883			−0.103678
$947$	−2.61092	−	4.52225i	−0.0848436	−	0.146953i	0.820481	−	0.571674i	$-0.193706\pi$
$947$	−2.61092	−	4.52225i	−0.0848436	−	0.146953i	−0.905325	+	0.424720i	$0.860372\pi$
$948$	2.52657	−	4.37614i	0.0820590	−	0.142130i
$949$	2.94080	+	5.09361i	0.0954624	+	0.165346i
$950$	−3.38896	+	5.86985i	−0.109952	+	0.190443i
$951$	−9.24015	+	16.0044i	−0.299632	+	0.518979i
$952$	−21.4820	+	37.2079i	−0.696236	+	1.20592i
$953$	0.398142			0.0128971			0.00644855	−	0.999979i	$-0.497947\pi$
$953$	0.398142			0.0128971			0.00644855	+	0.999979i	$0.497947\pi$
$954$	0.476159	+	0.824731i	0.0154162	+	0.0267017i
$955$	0.872398	+	1.51104i	0.0282301	+	0.0488960i
$956$	1.94502	−	3.36887i	0.0629063	−	0.108957i
$957$	12.5507			0.405708
$958$	17.6946	+	30.6480i	0.571688	+	0.990193i
$959$	−78.9770			−2.55030
$960$	−5.59609			−0.180613
$961$	29.1006	−	10.6842i	0.938731	−	0.344652i
$962$	−13.4594			−0.433948
$963$	−4.93742			−0.159106
$964$	−2.80924	−	4.86574i	−0.0904795	−	0.156715i
$965$	−5.49835			−0.176998
$966$	55.1010	−	95.4378i	1.77285	−	3.07066i
$967$	5.15568	+	8.92989i	0.165795	+	0.287166i	0.936937	−	0.349497i	$-0.113648\pi$
$967$	5.15568	+	8.92989i	0.165795	+	0.287166i	−0.771142	+	0.636663i	$0.780314\pi$
$968$	13.2521	+	22.9533i	0.425938	+	0.737747i
$969$	6.21717			0.199724
$970$	2.88277	−	4.99310i	0.0925601	−	0.160319i
$971$	18.7291	−	32.4398i	0.601046	−	1.04104i	−0.391617	−	0.920128i	$-0.628084\pi$
$971$	18.7291	−	32.4398i	0.601046	−	1.04104i	0.992663	−	0.120914i	$-0.0385824\pi$
$972$	1.10828	−	1.91960i	0.0355482	−	0.0615712i
$973$	23.0633	+	39.9469i	0.739377	+	1.28064i
$974$	22.9604	−	39.7686i	0.735699	−	1.27427i
$975$	−4.49814	−	7.79101i	−0.144056	−	0.249512i
$976$	28.4403			0.910350
$977$	21.5365			0.689014			0.344507	−	0.938784i	$-0.388046\pi$
$977$	21.5365			0.689014			0.344507	+	0.938784i	$0.388046\pi$
$978$	−33.2438	−	57.5799i	−1.06302	−	1.84120i
$979$	2.79258	−	4.83689i	0.0892512	−	0.154588i
$980$	1.50414	+	2.60525i	0.0480480	+	0.0832215i
$981$	−3.65042	+	6.32271i	−0.116549	+	0.201869i
$982$	20.5170	−	35.5365i	0.654724	−	1.13402i
$983$	−12.2892	+	21.2855i	−0.391963	+	0.678901i	−0.992708	−	0.120540i	$-0.961537\pi$
$983$	−12.2892	+	21.2855i	−0.391963	+	0.678901i	0.600745	+	0.799441i	$0.294871\pi$
$984$	−8.89297			−0.283498
$985$	−1.64370	−	2.84697i	−0.0523727	−	0.0907121i
$986$	−28.0552	−	48.5930i	−0.893458	−	1.54751i
$987$	17.4435	−	30.2130i	0.555232	−	0.961690i
$988$	−0.346151			−0.0110125
$989$	12.5189	+	21.6833i	0.398077	+	0.689489i
$990$	−0.284403			−0.00903893
$991$	−11.8543			−0.376563			−0.188282	−	0.982115i	$-0.560292\pi$
$991$	−11.8543			−0.376563			−0.188282	+	0.982115i	$0.560292\pi$
$992$	−11.4631	+	2.03781i	−0.363953	+	0.0647006i
$993$	13.7479			0.436276
$994$	116.144			3.68387
$995$	5.18782	+	8.98556i	0.164465	+	0.284862i
$996$	−9.03147			−0.286173
$997$	12.9276	−	22.3913i	0.409423	−	0.709141i	−0.585403	−	0.810743i	$-0.699064\pi$
$997$	12.9276	−	22.3913i	0.409423	−	0.709141i	0.994825	+	0.101602i	$0.0323968\pi$
$998$	−20.5119	−	35.5277i	−0.649293	−	1.12461i
$999$	−20.0122	−	34.6621i	−0.633157	−	1.09666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.a.118.4	✓	30
31.5	even	3	inner	403.2.h.a.222.4	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.a.118.4	✓	30	1.1	even	1	trivial
403.2.h.a.222.4	yes	30	31.5	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.54088 q^{2} +(-0.945700 - 1.63800i) q^{3} +0.374297 q^{4} +(0.246770 - 0.427419i) q^{5} +(1.45721 + 2.52395i) q^{6} +(-2.41271 - 4.17893i) q^{7} +2.50501 q^{8} +(-0.288697 + 0.500038i) q^{9} +O(q^{10})\)	\(q-1.54088 q^{2} +(-0.945700 - 1.63800i) q^{3} +0.374297 q^{4} +(0.246770 - 0.427419i) q^{5} +(1.45721 + 2.52395i) q^{6} +(-2.41271 - 4.17893i) q^{7} +2.50501 q^{8} +(-0.288697 + 0.500038i) q^{9} +(-0.380242 + 0.658599i) q^{10} +(0.323849 - 0.560922i) q^{11} +(-0.353973 - 0.613099i) q^{12} +(0.500000 - 0.866025i) q^{13} +(3.71768 + 6.43922i) q^{14} -0.933482 q^{15} -4.60850 q^{16} +(-1.77718 - 3.07816i) q^{17} +(0.444846 - 0.770496i) q^{18} +(-0.462401 - 0.800901i) q^{19} +(0.0923654 - 0.159982i) q^{20} +(-4.56340 + 7.90404i) q^{21} +(-0.499010 + 0.864311i) q^{22} +7.83617 q^{23} +(-2.36898 - 4.10320i) q^{24} +(2.37821 + 4.11918i) q^{25} +(-0.770438 + 1.33444i) q^{26} -4.58212 q^{27} +(-0.903071 - 1.56416i) q^{28} -10.2450 q^{29} +1.43838 q^{30} +(-5.48182 + 0.974513i) q^{31} +2.09111 q^{32} -1.22505 q^{33} +(2.73841 + 4.74307i) q^{34} -2.38154 q^{35} +(-0.108059 + 0.187163i) q^{36} +(4.36745 + 7.56465i) q^{37} +(0.712502 + 1.23409i) q^{38} -1.89140 q^{39} +(0.618161 - 1.07069i) q^{40} +(0.938480 - 1.62549i) q^{41} +(7.03163 - 12.1791i) q^{42} +(1.59757 + 2.76708i) q^{43} +(0.121216 - 0.209952i) q^{44} +(0.142484 + 0.246789i) q^{45} -12.0746 q^{46} -3.82248 q^{47} +(4.35825 + 7.54872i) q^{48} +(-8.14233 + 14.1029i) q^{49} +(-3.66452 - 6.34714i) q^{50} +(-3.36136 + 5.82204i) q^{51} +(0.187149 - 0.324151i) q^{52} +(-0.535195 + 0.926985i) q^{53} +7.06047 q^{54} +(-0.159832 - 0.276838i) q^{55} +(-6.04385 - 10.4683i) q^{56} +(-0.874585 + 1.51483i) q^{57} +15.7863 q^{58} +(-1.62553 - 2.81550i) q^{59} -0.349400 q^{60} -6.17126 q^{61} +(8.44680 - 1.50160i) q^{62} +2.78617 q^{63} +5.99486 q^{64} +(-0.246770 - 0.427419i) q^{65} +1.88766 q^{66} +(6.54194 - 11.3310i) q^{67} +(-0.665193 - 1.15215i) q^{68} +(-7.41066 - 12.8356i) q^{69} +3.66965 q^{70} +(7.81025 - 13.5277i) q^{71} +(-0.723187 + 1.25260i) q^{72} +(-2.94080 + 5.09361i) q^{73} +(-6.72970 - 11.6562i) q^{74} +(4.49814 - 7.79101i) q^{75} +(-0.173075 - 0.299775i) q^{76} -3.12541 q^{77} +2.91441 q^{78} +(3.56887 + 6.18146i) q^{79} +(-1.13724 + 1.96976i) q^{80} +(5.19940 + 9.00562i) q^{81} +(-1.44608 + 2.50469i) q^{82} +(6.37864 - 11.0481i) q^{83} +(-1.70807 + 2.95846i) q^{84} -1.75422 q^{85} +(-2.46166 - 4.26373i) q^{86} +(9.68874 + 16.7814i) q^{87} +(0.811242 - 1.40511i) q^{88} +8.62310 q^{89} +(-0.219550 - 0.380271i) q^{90} -4.82542 q^{91} +2.93306 q^{92} +(6.78041 + 8.05762i) q^{93} +5.88996 q^{94} -0.456427 q^{95} +(-1.97756 - 3.42524i) q^{96} -7.58140 q^{97} +(12.5463 - 21.7309i) q^{98} +(0.186988 + 0.323873i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 + 15 * q^13 + 3 * q^14 + 4 * q^15 + 22 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 10 * q^20 - 15 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 20 * q^25 - 3 * q^26 + 4 * q^27 + 13 * q^28 + 26 * q^29 + 28 * q^30 + 19 * q^31 - 74 * q^32 + 2 * q^33 - 21 * q^34 - 30 * q^35 + 37 * q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 - 17 * q^40 + 7 * q^41 + 44 * q^42 + 15 * q^43 - 70 * q^44 + 15 * q^45 - 58 * q^46 - 24 * q^47 + 31 * q^48 - 29 * q^49 + 2 * q^50 + 25 * q^51 + 11 * q^52 + 4 * q^53 + 34 * q^54 + 13 * q^55 - 41 * q^56 + 8 * q^57 - 46 * q^58 + 27 * q^59 + 78 * q^60 + 8 * q^61 + 20 * q^62 - 112 * q^63 + 60 * q^64 - 7 * q^65 + 60 * q^66 + 29 * q^67 + 41 * q^68 - 23 * q^69 - 112 * q^70 + 29 * q^71 + 14 * q^72 - 10 * q^73 + 25 * q^74 - 18 * q^75 + 24 * q^76 - 72 * q^77 + 9 * q^79 - 11 * q^81 - 38 * q^82 - 13 * q^83 - 62 * q^84 + 108 * q^85 - 38 * q^86 - 18 * q^87 + 32 * q^88 + 6 * q^89 + 7 * q^90 + 12 * q^91 + 2 * q^92 + 37 * q^93 - 154 * q^94 - 28 * q^95 - 105 * q^96 - 84 * q^97 + 50 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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