LMFDB - Embedded newform 87.2.g.b.82.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(7,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("87.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.g (of order $7$, 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:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} + 15 x^{16} - 32 x^{15} + 66 x^{14} - 115 x^{13} + 272 x^{12} - 387 x^{11} + 762 x^{10} + \cdots + 49 $ x^18 - 5x^17 + 15x^16 - 32x^15 + 66x^14 - 115x^13 + 272x^12 - 387x^11 + 762x^10 - 822x^9 + 2349x^8 - 3280x^7 + 7428x^6 - 15449x^5 + 23373x^4 - 19712x^3 + 7938x^2 - 392*x + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			82.3
Root			$-0.408260 + 1.78870i$ of defining polynomial
Character	$\chi$	$=$	87.82
Dual form			87.2.g.b.52.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.14392 + 1.43443i) q^{2} +(0.222521 + 0.974928i) q^{3} +(-0.303995 + 1.33189i) q^{4} +(-1.40816 - 1.76577i) q^{5} +(-1.14392 + 1.43443i) q^{6} +(0.165617 + 0.725615i) q^{7} +(1.04778 - 0.504584i) q^{8} +(-0.900969 + 0.433884i) q^{9} +(0.922058 - 4.03980i) q^{10} +(-5.68404 - 2.73729i) q^{11} -1.36614 q^{12} +(1.48289 + 0.714123i) q^{13} +(-0.851391 + 1.06761i) q^{14} +(1.40816 - 1.76577i) q^{15} +(4.38406 + 2.11125i) q^{16} +4.16595 q^{17} +(-1.65301 - 0.796048i) q^{18} +(-0.231613 + 1.01476i) q^{19} +(2.77988 - 1.33872i) q^{20} +(-0.670569 + 0.322929i) q^{21} +(-2.57563 - 11.2846i) q^{22} +(-2.85155 + 3.57573i) q^{23} +(0.725086 + 0.909229i) q^{24} +(-0.0224408 + 0.0983195i) q^{25} +(0.671949 + 2.94400i) q^{26} +(-0.623490 - 0.781831i) q^{27} -1.01678 q^{28} +(-4.68636 + 2.65293i) q^{29} +4.14369 q^{30} +(-2.20186 - 2.76105i) q^{31} +(1.46901 + 6.43615i) q^{32} +(1.40384 - 6.15063i) q^{33} +(4.76551 + 5.97577i) q^{34} +(1.04806 - 1.31422i) q^{35} +(-0.303995 - 1.33189i) q^{36} +(0.969034 - 0.466662i) q^{37} +(-1.72055 + 0.828574i) q^{38} +(-0.366244 + 1.60462i) q^{39} +(-2.36642 - 1.13961i) q^{40} -1.20065 q^{41} +(-1.23030 - 0.592479i) q^{42} +(-7.99734 + 10.0283i) q^{43} +(5.37367 - 6.73837i) q^{44} +(2.03484 + 0.979929i) q^{45} -8.39108 q^{46} +(7.10498 + 3.42158i) q^{47} +(-1.08277 + 4.74394i) q^{48} +(5.80769 - 2.79684i) q^{49} +(-0.166703 + 0.0802799i) q^{50} +(0.927012 + 4.06150i) q^{51} +(-1.40192 + 1.75795i) q^{52} +(-8.22494 - 10.3138i) q^{53} +(0.408260 - 1.78870i) q^{54} +(3.17058 + 13.8912i) q^{55} +(0.539663 + 0.676716i) q^{56} -1.04086 q^{57} +(-9.16625 - 3.68752i) q^{58} +11.0585 q^{59} +(1.92374 + 2.41229i) q^{60} +(1.43496 + 6.28696i) q^{61} +(1.44178 - 6.31683i) q^{62} +(-0.464048 - 0.581898i) q^{63} +(-1.48405 + 1.86094i) q^{64} +(-0.827164 - 3.62404i) q^{65} +(10.4285 - 5.02211i) q^{66} +(6.19652 - 2.98409i) q^{67} +(-1.26643 + 5.54858i) q^{68} +(-4.12061 - 1.98438i) q^{69} +3.08405 q^{70} +(2.95303 + 1.42211i) q^{71} +(-0.725086 + 0.909229i) q^{72} +(4.42081 - 5.54352i) q^{73} +(1.77789 + 0.856187i) q^{74} -0.100848 q^{75} +(-1.28114 - 0.616965i) q^{76} +(1.04484 - 4.57776i) q^{77} +(-2.72067 + 1.31020i) q^{78} +(-5.75663 + 2.77225i) q^{79} +(-2.44545 - 10.7142i) q^{80} +(0.623490 - 0.781831i) q^{81} +(-1.37344 - 1.72224i) q^{82} +(1.14686 - 5.02472i) q^{83} +(-0.226256 - 0.991291i) q^{84} +(-5.86631 - 7.35612i) q^{85} -23.5333 q^{86} +(-3.62923 - 3.97853i) q^{87} -7.33681 q^{88} +(5.80998 + 7.28549i) q^{89} +(0.922058 + 4.03980i) q^{90} +(-0.272586 + 1.19428i) q^{91} +(-3.89562 - 4.88495i) q^{92} +(2.20186 - 2.76105i) q^{93} +(3.21951 + 14.1056i) q^{94} +(2.11798 - 1.01997i) q^{95} +(-5.94790 + 2.86436i) q^{96} +(3.37522 - 14.7878i) q^{97} +(10.6554 + 5.13137i) q^{98} +6.30880 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{2}{7}\right)$	$1$

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 $

$2$	1.14392	+	1.43443i	0.808873	+	1.01429i	0.999468	+	0.0326259i	$0.0103870\pi$
$2$	1.14392	+	1.43443i	0.808873	+	1.01429i	−0.190595	+	0.981669i	$0.561042\pi$
$3$	0.222521	+	0.974928i	0.128473	+	0.562875i
$3$	0.222521	+	0.974928i	0.128473	+	0.562875i
$4$	−0.303995	+	1.33189i	−0.151997	+	0.665944i
$5$	−1.40816	−	1.76577i	−0.629746	−	0.789677i	0.359933	−	0.932978i	$-0.382800\pi$
$5$	−1.40816	−	1.76577i	−0.629746	−	0.789677i	−0.989679	+	0.143301i	$0.954228\pi$
$6$	−1.14392	+	1.43443i	−0.467003	+	0.585603i
$7$	0.165617	+	0.725615i	0.0625973	+	0.274257i	0.996534	−	0.0831805i	$-0.0265078\pi$
$7$	0.165617	+	0.725615i	0.0625973	+	0.274257i	−0.933937	+	0.357437i	$0.883651\pi$
$8$	1.04778	−	0.504584i	0.370446	−	0.178397i
$9$	−0.900969	+	0.433884i	−0.300323	+	0.144628i
$10$	0.922058	−	4.03980i	0.291580	−	1.27750i
$11$	−5.68404	−	2.73729i	−1.71380	−	0.825323i	−0.990936	−	0.134334i	$-0.957111\pi$
$11$	−5.68404	−	2.73729i	−1.71380	−	0.825323i	−0.722865	−	0.690989i	$-0.757175\pi$
$12$	−1.36614			−0.394370
$13$	1.48289	+	0.714123i	0.411280	+	0.198062i	0.628071	−	0.778156i	$-0.283845\pi$
$13$	1.48289	+	0.714123i	0.411280	+	0.198062i	−0.216791	+	0.976218i	$0.569559\pi$
$14$	−0.851391	+	1.06761i	−0.227544	+	0.285331i
$15$	1.40816	−	1.76577i	0.363584	−	0.455920i
$16$	4.38406	+	2.11125i	1.09602	+	0.527813i
$17$	4.16595			1.01039			0.505196	−	0.863005i	$-0.331420\pi$
$17$	4.16595			1.01039			0.505196	+	0.863005i	$0.331420\pi$
$18$	−1.65301	−	0.796048i	−0.389618	−	0.187630i
$19$	−0.231613	+	1.01476i	−0.0531356	+	0.232802i	−0.994522	−	0.104528i	$-0.966667\pi$
$19$	−0.231613	+	1.01476i	−0.0531356	+	0.232802i	0.941386	+	0.337330i	$0.109524\pi$
$20$	2.77988	−	1.33872i	0.621600	−	0.299347i
$21$	−0.670569	+	0.322929i	−0.146330	+	0.0704689i
$22$	−2.57563	−	11.2846i	−0.549127	−	2.40588i
$23$	−2.85155	+	3.57573i	−0.594590	+	0.745592i	−0.984524	−	0.175251i	$-0.943926\pi$
$23$	−2.85155	+	3.57573i	−0.594590	+	0.745592i	0.389934	+	0.920843i	$0.372498\pi$
$24$	0.725086	+	0.909229i	0.148008	+	0.185596i
$25$	−0.0224408	+	0.0983195i	−0.00448816	+	0.0196639i
$26$	0.671949	+	2.94400i	0.131780	+	0.577366i
$27$	−0.623490	−	0.781831i	−0.119991	−	0.150464i
$28$	−1.01678			−0.192154
$29$	−4.68636	+	2.65293i	−0.870235	+	0.492636i
$29$	−4.68636	+	2.65293i	−0.870235	+	0.492636i
$30$	4.14369			0.756531
$31$	−2.20186	−	2.76105i	−0.395466	−	0.495899i	0.543740	−	0.839254i	$-0.317008\pi$
$31$	−2.20186	−	2.76105i	−0.395466	−	0.495899i	−0.939206	+	0.343355i	$0.888437\pi$
$32$	1.46901	+	6.43615i	0.259687	+	1.13776i
$33$	1.40384	−	6.15063i	0.244377	−	1.07069i
$34$	4.76551	+	5.97577i	0.817279	+	1.02484i
$35$	1.04806	−	1.31422i	0.177154	−	0.222144i
$36$	−0.303995	−	1.33189i	−0.0506658	−	0.221981i
$37$	0.969034	−	0.466662i	0.159308	−	0.0767188i	−0.352531	−	0.935800i	$-0.614679\pi$
$37$	0.969034	−	0.466662i	0.159308	−	0.0767188i	0.511839	+	0.859081i	$0.328964\pi$
$38$	−1.72055	+	0.828574i	−0.279110	+	0.134412i
$39$	−0.366244	+	1.60462i	−0.0586460	+	0.256945i
$40$	−2.36642	−	1.13961i	−0.374163	−	0.180187i
$41$	−1.20065			−0.187510			−0.0937548	−	0.995595i	$-0.529887\pi$
$41$	−1.20065			−0.187510			−0.0937548	+	0.995595i	$0.529887\pi$
$42$	−1.23030	−	0.592479i	−0.189839	−	0.0914215i
$43$	−7.99734	+	10.0283i	−1.21958	+	1.52931i	−0.446804	+	0.894632i	$0.647438\pi$
$43$	−7.99734	+	10.0283i	−1.21958	+	1.52931i	−0.772778	+	0.634676i	$0.781133\pi$
$44$	5.37367	−	6.73837i	0.810112	−	1.01585i
$45$	2.03484	+	0.979929i	0.303337	+	0.146079i
$46$	−8.39108			−1.23720
$47$	7.10498	+	3.42158i	1.03637	+	0.499088i	0.873124	−	0.487497i	$-0.162090\pi$
$47$	7.10498	+	3.42158i	1.03637	+	0.499088i	0.163243	+	0.986586i	$0.447804\pi$
$48$	−1.08277	+	4.74394i	−0.156285	+	0.684729i
$49$	5.80769	−	2.79684i	0.829671	−	0.399548i
$50$	−0.166703	+	0.0802799i	−0.0235753	+	0.0113533i
$51$	0.927012	+	4.06150i	0.129808	+	0.568724i
$52$	−1.40192	+	1.75795i	−0.194412	+	0.243784i
$53$	−8.22494	−	10.3138i	−1.12978	−	1.41670i	−0.895797	−	0.444463i	$-0.853395\pi$
$53$	−8.22494	−	10.3138i	−1.12978	−	1.41670i	−0.233986	−	0.972240i	$-0.575177\pi$
$54$	0.408260	−	1.78870i	0.0555572	−	0.243412i
$55$	3.17058	+	13.8912i	0.427521	+	1.87309i
$56$	0.539663	+	0.676716i	0.0721155	+	0.0904300i
$57$	−1.04086			−0.137865
$58$	−9.16625	−	3.68752i	−1.20359	−	0.484195i
$59$	11.0585			1.43970			0.719849	−	0.694131i	$-0.244211\pi$
$59$	11.0585			1.43970			0.719849	+	0.694131i	$0.244211\pi$
$60$	1.92374	+	2.41229i	0.248353	+	0.311425i
$61$	1.43496	+	6.28696i	0.183728	+	0.804963i	0.979835	+	0.199808i	$0.0640318\pi$
$61$	1.43496	+	6.28696i	0.183728	+	0.804963i	−0.796108	+	0.605155i	$0.793111\pi$
$62$	1.44178	−	6.31683i	0.183106	−	0.802238i
$63$	−0.464048	−	0.581898i	−0.0584646	−	0.0733122i
$64$	−1.48405	+	1.86094i	−0.185506	+	0.232617i
$65$	−0.827164	−	3.62404i	−0.102597	−	0.449507i
$66$	10.4285	−	5.02211i	1.28366	−	0.618179i
$67$	6.19652	−	2.98409i	0.757026	−	0.364564i	−0.0152236	−	0.999884i	$-0.504846\pi$
$67$	6.19652	−	2.98409i	0.757026	−	0.364564i	0.772249	+	0.635320i	$0.219132\pi$
$68$	−1.26643	+	5.54858i	−0.153577	+	0.672864i
$69$	−4.12061	−	1.98438i	−0.496063	−	0.238892i
$70$	3.08405			0.368614
$71$	2.95303	+	1.42211i	0.350461	+	0.168773i	0.600829	−	0.799378i	$-0.294837\pi$
$71$	2.95303	+	1.42211i	0.350461	+	0.168773i	−0.250368	+	0.968151i	$0.580552\pi$
$72$	−0.725086	+	0.909229i	−0.0854522	+	0.107154i
$73$	4.42081	−	5.54352i	0.517417	−	0.648820i	−0.452641	−	0.891693i	$-0.649518\pi$
$73$	4.42081	−	5.54352i	0.517417	−	0.648820i	0.970058	+	0.242872i	$0.0780896\pi$
$74$	1.77789	+	0.856187i	0.206676	+	0.0995298i
$75$	−0.100848			−0.0116449
$76$	−1.28114	−	0.616965i	−0.146957	−	0.0707707i
$77$	1.04484	−	4.57776i	0.119071	−	0.521684i
$78$	−2.72067	+	1.31020i	−0.308055	+	0.148351i
$79$	−5.75663	+	2.77225i	−0.647672	+	0.311902i	−0.728724	−	0.684808i	$-0.759886\pi$
$79$	−5.75663	+	2.77225i	−0.647672	+	0.311902i	0.0810523	+	0.996710i	$0.474172\pi$
$80$	−2.44545	−	10.7142i	−0.273410	−	1.19789i
$81$	0.623490	−	0.781831i	0.0692766	−	0.0868702i
$82$	−1.37344	−	1.72224i	−0.151672	−	0.190190i
$83$	1.14686	−	5.02472i	0.125884	−	0.551535i	−0.872171	−	0.489201i	$-0.837288\pi$
$83$	1.14686	−	5.02472i	0.125884	−	0.551535i	0.998055	−	0.0623339i	$-0.0198544\pi$
$84$	−0.226256	−	0.991291i	−0.0246865	−	0.108159i
$85$	−5.86631	−	7.35612i	−0.636290	−	0.797883i
$86$	−23.5333			−2.53766
$87$	−3.62923	−	3.97853i	−0.389094	−	0.426543i
$88$	−7.33681			−0.782106
$89$	5.80998	+	7.28549i	0.615857	+	0.772260i	0.987755	−	0.156013i	$-0.0498643\pi$
$89$	5.80998	+	7.28549i	0.615857	+	0.772260i	−0.371898	+	0.928274i	$0.621293\pi$
$90$	0.922058	+	4.03980i	0.0971934	+	0.425832i
$91$	−0.272586	+	1.19428i	−0.0285748	+	0.125194i
$92$	−3.89562	−	4.88495i	−0.406146	−	0.509291i
$93$	2.20186	−	2.76105i	0.228322	−	0.286307i
$94$	3.21951	+	14.1056i	0.332067	+	1.45488i
$95$	2.11798	−	1.01997i	0.217301	−	0.104646i
$96$	−5.94790	+	2.86436i	−0.607055	+	0.292342i
$97$	3.37522	−	14.7878i	0.342701	−	1.50147i	−0.450646	−	0.892703i	$-0.648806\pi$
$97$	3.37522	−	14.7878i	0.342701	−	1.50147i	0.793347	−	0.608769i	$-0.208337\pi$
$98$	10.6554	+	5.13137i	1.07636	+	0.518347i
$99$	6.30880			0.634059
$100$	−0.124129	−	0.0597772i	−0.0124129	−	0.00597772i
$101$	2.76928	−	3.47257i	0.275554	−	0.345534i	−0.624727	−	0.780843i	$-0.714790\pi$
$101$	2.76928	−	3.47257i	0.275554	−	0.345534i	0.900281	+	0.435310i	$0.143361\pi$
$102$	−4.76551	+	5.97577i	−0.471856	+	0.591689i
$103$	−13.8692	−	6.67906i	−1.36657	−	0.658108i	−0.400482	−	0.916305i	$-0.631157\pi$
$103$	−13.8692	−	6.67906i	−1.36657	−	0.658108i	−0.966092	+	0.258197i	$0.916872\pi$
$104$	1.91408			0.187691
$105$	1.51448	+	0.729337i	0.147798	+	0.0711760i
$106$	5.38568	−	23.5962i	0.523103	−	2.29187i
$107$	7.13273	−	3.43494i	0.689547	−	0.332068i	−0.0560855	−	0.998426i	$-0.517862\pi$
$107$	7.13273	−	3.43494i	0.689547	−	0.332068i	0.745632	+	0.666358i	$0.232148\pi$
$108$	1.23085	−	0.592746i	0.118438	−	0.0570370i
$109$	−0.932147	−	4.08400i	−0.0892835	−	0.391177i	0.910465	−	0.413585i	$-0.135724\pi$
$109$	−0.932147	−	4.08400i	−0.0892835	−	0.391177i	−0.999749	+	0.0224086i	$0.992867\pi$
$110$	−16.2991	+	20.4384i	−1.55406	+	1.94873i
$111$	0.670593	+	0.840897i	0.0636498	+	0.0798144i
$112$	−0.805882	+	3.53080i	−0.0761487	+	0.333629i
$113$	2.40874	+	10.5534i	0.226595	+	0.992779i	0.952394	+	0.304871i	$0.0986134\pi$
$113$	2.40874	+	10.5534i	0.226595	+	0.992779i	−0.725798	+	0.687907i	$0.758529\pi$
$114$	−1.19066	−	1.49304i	−0.111515	−	0.139836i
$115$	10.3294			0.963217
$116$	−2.10877	−	7.04818i	−0.195794	−	0.654407i
$117$	−1.64589			−0.152162
$118$	12.6501	+	15.8627i	1.16453	+	1.46028i
$119$	0.689952	+	3.02288i	0.0632478	+	0.277107i
$120$	0.584456	−	2.56067i	0.0533533	−	0.233756i
$121$	17.9571	+	22.5175i	1.63247	+	2.04705i
$122$	−7.37673	+	9.25012i	−0.667858	+	0.837467i
$123$	−0.267169	−	1.17054i	−0.0240898	−	0.105544i
$124$	4.34676	−	2.09329i	0.390350	−	0.187983i
$125$	−9.96901	+	4.80082i	−0.891655	+	0.429398i
$126$	0.303858	−	1.33129i	0.0270698	−	0.118601i
$127$	−7.27053	−	3.50130i	−0.645155	−	0.310690i	0.0825435	−	0.996587i	$-0.473696\pi$
$127$	−7.27053	−	3.50130i	−0.645155	−	0.310690i	−0.727698	+	0.685897i	$0.759410\pi$
$128$	8.83633			0.781029
$129$	−11.5565	−	5.56531i	−1.01749	−	0.489998i
$130$	4.25222	−	5.33212i	0.372945	−	0.467658i
$131$	−11.6622	+	14.6240i	−1.01893	+	1.27770i	−0.0587686	+	0.998272i	$0.518717\pi$
$131$	−11.6622	+	14.6240i	−1.01893	+	1.27770i	−0.960166	+	0.279432i	$0.909854\pi$
$132$	7.76518	+	3.73952i	0.675872	+	0.325483i
$133$	−0.774686			−0.0671738
$134$	11.3688	+	5.47492i	0.982113	+	0.472961i
$135$	−0.502565	+	2.20188i	−0.0432539	+	0.189508i
$136$	4.36500	−	2.10207i	0.374296	−	0.180251i
$137$	3.36252	−	1.61931i	0.287280	−	0.138347i	−0.284694	−	0.958618i	$-0.591892\pi$
$137$	3.36252	−	1.61931i	0.287280	−	0.138347i	0.571974	+	0.820272i	$0.306178\pi$
$138$	−1.86719	−	8.18070i	−0.158946	−	0.696388i
$139$	8.44508	−	10.5898i	0.716302	−	0.898214i	−0.281820	−	0.959467i	$-0.590938\pi$
$139$	8.44508	−	10.5898i	0.716302	−	0.898214i	0.998122	+	0.0612530i	$0.0195096\pi$
$140$	1.43179	+	1.79541i	0.121008	+	0.151740i
$141$	−1.75478	+	7.68822i	−0.147780	+	0.647465i
$142$	1.33812	+	5.86270i	0.112293	+	0.491986i
$143$	−6.47405	−	8.11820i	−0.541387	−	0.678878i
$144$	−4.86594			−0.405495
$145$	11.2836	+	4.53931i	0.937051	+	0.376969i
$146$	13.0088			1.07662
$147$	4.01905	+	5.03973i	0.331486	+	0.415670i
$148$	0.326960	+	1.43251i	0.0268760	+	0.117751i
$149$	0.458291	−	2.00790i	0.0375447	−	0.164494i	−0.952680	−	0.303975i	$-0.901686\pi$
$149$	0.458291	−	2.00790i	0.0375447	−	0.164494i	0.990225	+	0.139481i	$0.0445433\pi$
$150$	−0.115362	−	0.144659i	−0.00941927	−	0.0118114i
$151$	−7.77480	+	9.74929i	−0.632704	+	0.793386i	−0.990070	−	0.140578i	$-0.955104\pi$
$151$	−7.77480	+	9.74929i	−0.632704	+	0.793386i	0.357365	+	0.933965i	$0.383675\pi$
$152$	0.269354	+	1.18012i	0.0218475	+	0.0957200i
$153$	−3.75339	+	1.80754i	−0.303444	+	0.146131i
$154$	7.76169	−	3.73783i	0.625455	−	0.301203i
$155$	−1.77481	+	7.77597i	−0.142556	+	0.624581i
$156$	−2.02584	−	0.975591i	−0.162197	−	0.0781098i
$157$	−13.1146			−1.04666			−0.523329	−	0.852131i	$-0.675310\pi$
$157$	−13.1146			−1.04666			−0.523329	+	0.852131i	$0.675310\pi$
$158$	−10.5617	−	5.08625i	−0.840245	−	0.404641i
$159$	8.22494	−	10.3138i	0.652281	−	0.817934i
$160$	9.29618	−	11.6570i	0.734927	−	0.921570i
$161$	−3.06687	−	1.47693i	−0.241703	−	0.116398i
$162$	1.83470			0.144148
$163$	−9.80204	−	4.72041i	−0.767755	−	0.369731i	0.00865246	−	0.999963i	$-0.497246\pi$
$163$	−9.80204	−	4.72041i	−0.767755	−	0.369731i	−0.776407	+	0.630231i	$0.782960\pi$
$164$	0.364990	−	1.59913i	0.0285010	−	0.124871i
$165$	−12.8374	+	6.18218i	−0.999392	+	0.481282i
$166$	8.51952	−	4.10279i	0.661243	−	0.318438i
$167$	4.51248	+	19.7705i	0.349186	+	1.52988i	0.779033	+	0.626983i	$0.215710\pi$
$167$	4.51248	+	19.7705i	0.349186	+	1.52988i	−0.429847	+	0.902902i	$0.641432\pi$
$168$	−0.539663	+	0.676716i	−0.0416359	+	0.0522098i
$169$	−6.41637	−	8.04588i	−0.493567	−	0.618914i
$170$	3.84125	−	16.8296i	0.294610	−	1.29077i
$171$	−0.231613	−	1.01476i	−0.0177119	−	0.0776008i
$172$	−10.9255	−	13.7001i	−0.833060	−	1.04462i
$173$	−0.158953			−0.0120850			−0.00604249	−	0.999982i	$-0.501923\pi$
$173$	−0.158953			−0.0120850			−0.00604249	+	0.999982i	$0.501923\pi$
$174$	1.55538	−	9.75699i	0.117913	−	0.739675i
$175$	−0.0750587			−0.00567390
$176$	−19.1401	−	24.0009i	−1.44274	−	1.80913i
$177$	2.46075	+	10.7813i	0.184962	+	0.810369i
$178$	−3.80437	+	16.6680i	−0.285149	+	1.24932i
$179$	−8.97720	−	11.2571i	−0.670988	−	0.841392i	0.323502	−	0.946228i	$-0.395140\pi$
$179$	−8.97720	−	11.2571i	−0.670988	−	0.841392i	−0.994490	+	0.104836i	$0.966568\pi$
$180$	−1.92374	+	2.41229i	−0.143387	+	0.179801i
$181$	−2.87864	−	12.6121i	−0.213968	−	0.937453i	−0.961840	−	0.273611i	$-0.911782\pi$
$181$	−2.87864	−	12.6121i	−0.213968	−	0.937453i	0.747873	−	0.663842i	$-0.231075\pi$
$182$	−2.02492	+	0.975152i	−0.150097	+	0.0722831i
$183$	−5.81003	+	2.79796i	−0.429490	+	0.206831i
$184$	−1.18354	+	5.18543i	−0.0872517	+	0.382275i
$185$	−2.18857	−	1.05396i	−0.160907	−	0.0774887i
$186$	6.47928			0.475084
$187$	−23.6794	−	11.4034i	−1.73161	−	0.833900i
$188$	−6.71703	+	8.42289i	−0.489890	+	0.614302i
$189$	0.464048	−	0.581898i	0.0337545	−	0.0423268i
$190$	3.88588	+	1.87134i	0.281911	+	0.135761i
$191$	−5.61297			−0.406140			−0.203070	−	0.979164i	$-0.565092\pi$
$191$	−5.61297			−0.406140			−0.203070	+	0.979164i	$0.565092\pi$
$192$	−2.14451	−	1.03274i	−0.154767	−	0.0745317i
$193$	−2.01768	+	8.84002i	−0.145236	+	0.636319i	0.848935	+	0.528498i	$0.177245\pi$
$193$	−2.01768	+	8.84002i	−0.145236	+	0.636319i	−0.994170	+	0.107821i	$0.965613\pi$
$194$	25.0730	−	12.0745i	1.80014	−	0.866900i
$195$	3.34912	−	1.61285i	0.239835	−	0.115499i
$196$	1.95957	+	8.58542i	0.139969	+	0.613244i
$197$	6.01235	−	7.53925i	0.428362	−	0.537149i	−0.520072	−	0.854122i	$-0.674095\pi$
$197$	6.01235	−	7.53925i	0.428362	−	0.537149i	0.948435	+	0.316973i	$0.102667\pi$
$198$	7.21676	+	9.04953i	0.512873	+	0.643122i
$199$	−2.64957	+	11.6085i	−0.187823	+	0.822905i	0.789939	+	0.613186i	$0.210112\pi$
$199$	−2.64957	+	11.6085i	−0.187823	+	0.822905i	−0.977762	+	0.209720i	$0.932745\pi$
$200$	0.0260975	+	0.114340i	0.00184537	+	0.00808509i
$201$	4.28813	+	5.37714i	0.302461	+	0.379274i
$202$	8.14899			0.573361
$203$	−2.70114	−	2.96112i	−0.189583	−	0.207830i
$204$	−5.69127			−0.398469
$205$	1.69070	+	2.12007i	0.118083	+	0.148072i
$206$	−6.28462	−	27.5347i	−0.437870	−	1.91843i
$207$	1.01771	−	4.45887i	0.0707355	−	0.309913i
$208$	4.99339	+	6.26152i	0.346230	+	0.434158i
$209$	4.09419	−	5.13395i	0.283201	−	0.355123i
$210$	0.686265	+	3.00672i	0.0473568	+	0.207484i
$211$	5.22041	−	2.51402i	0.359388	−	0.173072i	−0.245473	−	0.969404i	$-0.578943\pi$
$211$	5.22041	−	2.51402i	0.359388	−	0.173072i	0.604861	+	0.796331i	$0.293229\pi$
$212$	16.2371	−	7.81937i	1.11517	−	0.537037i
$213$	−0.729339	+	3.19544i	−0.0499735	+	0.218948i
$214$	13.0864	+	6.30210i	0.894571	+	0.430803i
$215$	28.9692			1.97569
$216$	−1.04778	−	0.504584i	−0.0712923	−	0.0343326i
$217$	1.63879	−	2.05498i	0.111248	−	0.139501i
$218$	4.79191	−	6.00887i	0.324549	−	0.406972i
$219$	6.38826	+	3.07642i	0.431678	+	0.207885i
$220$	−19.4654			−1.31236
$221$	6.17765	+	2.97500i	0.415554	+	0.200120i
$222$	−0.439103	+	1.92384i	−0.0294707	+	0.129119i
$223$	9.35393	−	4.50461i	0.626385	−	0.301651i	−0.0936325	−	0.995607i	$-0.529848\pi$
$223$	9.35393	−	4.50461i	0.626385	−	0.301651i	0.720018	+	0.693956i	$0.244134\pi$
$224$	−4.42687	+	2.13187i	−0.295783	+	0.142442i
$225$	−0.0224408	−	0.0983195i	−0.00149605	−	0.00655464i
$226$	−12.3827	+	15.5274i	−0.823683	+	1.03287i
$227$	0.871753	+	1.09314i	0.0578603	+	0.0725545i	0.809920	−	0.586541i	$-0.199511\pi$
$227$	0.871753	+	1.09314i	0.0578603	+	0.0725545i	−0.752059	+	0.659095i	$0.770939\pi$
$228$	0.316415	−	1.38631i	0.0209551	−	0.0918104i
$229$	1.53344	+	6.71844i	0.101333	+	0.443967i	0.999986	+	0.00530751i	$0.00168944\pi$
$229$	1.53344	+	6.71844i	0.101333	+	0.443967i	−0.898653	+	0.438660i	$0.855453\pi$
$230$	11.8159	+	14.8167i	0.779121	+	0.976986i
$231$	4.69549			0.308940
$232$	−3.57165	+	5.14434i	−0.234490	+	0.337743i
$233$	−0.133957			−0.00877579			−0.00438789	−	0.999990i	$-0.501397\pi$
$233$	−0.133957			−0.00877579			−0.00438789	+	0.999990i	$0.501397\pi$
$234$	−1.88276	−	2.36091i	−0.123080	−	0.154337i
$235$	−3.96319	−	17.3639i	−0.258530	−	1.13269i
$236$	−3.36173	+	14.7287i	−0.218830	+	0.958757i
$237$	−3.98371	−	4.99542i	−0.258770	−	0.324487i
$238$	−3.54685	+	4.44761i	−0.229908	+	0.288296i
$239$	−2.30911	−	10.1169i	−0.149364	−	0.654405i	−0.993062	−	0.117588i	$-0.962484\pi$
$239$	−2.30911	−	10.1169i	−0.149364	−	0.654405i	0.843699	−	0.536817i	$-0.180373\pi$
$240$	9.90143	−	4.76828i	0.639135	−	0.307791i
$241$	−7.62763	+	3.67328i	−0.491339	+	0.236616i	−0.663112	−	0.748520i	$-0.730765\pi$
$241$	−7.62763	+	3.67328i	−0.491339	+	0.236616i	0.171773	+	0.985137i	$0.445050\pi$
$242$	−11.7583	+	51.5165i	−0.755852	+	3.31160i
$243$	0.900969	+	0.433884i	0.0577972	+	0.0278337i
$244$	−8.80974			−0.563986
$245$	−13.1167	−	6.31668i	−0.837996	−	0.403558i
$246$	1.37344	−	1.72224i	0.0875676	−	0.109806i
$247$	−1.06812	+	1.33938i	−0.0679630	+	0.0852229i
$248$	−3.70024	−	1.78194i	−0.234966	−	0.113154i
$249$	5.15394			0.326618
$250$	−18.2902	−	8.80809i	−1.15677	−	0.557072i
$251$	−1.68037	+	7.36218i	−0.106064	+	0.464697i	0.893804	+	0.448458i	$0.148026\pi$
$251$	−1.68037	+	7.36218i	−0.106064	+	0.464697i	−0.999868	+	0.0162393i	$0.994831\pi$
$252$	0.916090	−	0.441166i	0.0577083	−	0.0277908i
$253$	25.9961	−	12.5191i	1.63436	−	0.787068i
$254$	−3.29453	−	14.4343i	−0.206717	−	0.905686i
$255$	5.86631	−	7.35612i	0.367362	−	0.460658i
$256$	13.0761	+	16.3970i	0.817259	+	1.02481i
$257$	−4.74187	+	20.7755i	−0.295789	+	1.29594i	0.580542	+	0.814230i	$0.302841\pi$
$257$	−4.74187	+	20.7755i	−0.295789	+	1.29594i	−0.876332	+	0.481708i	$0.840017\pi$
$258$	−5.23664	−	22.9432i	−0.326019	−	1.42838i
$259$	0.499105	+	0.625858i	0.0310129	+	0.0388890i
$260$	5.07827			0.314941
$261$	3.07120	−	4.42354i	0.190103	−	0.273810i
$262$	−34.3177			−2.12016
$263$	−16.0972	−	20.1853i	−0.992597	−	1.24468i	−0.969537	−	0.244943i	$-0.921231\pi$
$263$	−16.0972	−	20.1853i	−0.992597	−	1.24468i	−0.0230593	−	0.999734i	$-0.507341\pi$
$264$	−1.63259	−	7.15286i	−0.100479	−	0.440228i
$265$	−6.62973	+	29.0467i	−0.407261	+	1.78433i
$266$	−0.886178	−	1.11123i	−0.0543350	−	0.0681340i
$267$	−5.80998	+	7.28549i	−0.355565	+	0.445865i
$268$	2.09076	+	9.16021i	0.127713	+	0.559549i
$269$	−17.2204	+	8.29293i	−1.04995	+	0.505629i	−0.877593	−	0.479406i	$-0.840852\pi$
$269$	−17.2204	+	8.29293i	−1.04995	+	0.505629i	−0.172356	+	0.985035i	$0.555138\pi$
$270$	−3.73334	+	1.79788i	−0.227204	+	0.109415i
$271$	0.775056	−	3.39574i	0.0470813	−	0.206277i	−0.945916	−	0.324411i	$-0.894834\pi$
$271$	0.775056	−	3.39574i	0.0470813	−	0.206277i	0.992998	+	0.118134i	$0.0376912\pi$
$272$	18.2638	+	8.79538i	1.10741	+	0.533298i
$273$	−1.22499			−0.0741399
$274$	6.16924	+	2.97095i	0.372697	+	0.179481i
$275$	0.396683	−	0.497425i	0.0239209	−	0.0299958i
$276$	3.89562	−	4.88495i	0.234489	−	0.294039i
$277$	9.16006	+	4.41125i	0.550375	+	0.265047i	0.688337	−	0.725391i	$-0.258341\pi$
$277$	9.16006	+	4.41125i	0.550375	+	0.265047i	−0.137962	+	0.990437i	$0.544055\pi$
$278$	24.8508			1.49045
$279$	3.18178	+	1.53227i	0.190488	+	0.0917343i
$280$	0.434996	−	1.90584i	0.0259960	−	0.113896i
$281$	0.969638	−	0.466953i	0.0578437	−	0.0278561i	−0.404738	−	0.914433i	$-0.632637\pi$
$281$	0.969638	−	0.466953i	0.0578437	−	0.0278561i	0.462582	+	0.886576i	$0.346923\pi$
$282$	−13.0355	+	6.27758i	−0.776255	+	0.373825i
$283$	−2.03116	−	8.89909i	−0.120740	−	0.528996i	−0.998733	−	0.0503227i	$-0.983975\pi$
$283$	−2.03116	−	8.89909i	−0.120740	−	0.528996i	0.877993	−	0.478673i	$-0.158882\pi$
$284$	−2.79179	+	3.50080i	−0.165662	+	0.207734i
$285$	1.46569	+	1.83792i	0.0868200	+	0.108869i
$286$	4.23919	−	18.5731i	0.250669	−	1.09825i
$287$	−0.198847	−	0.871208i	−0.0117376	−	0.0514258i
$288$	−4.11607	−	5.16139i	−0.242542	−	0.304138i
$289$	0.355162			0.0208919
$290$	6.39619	+	21.3781i	0.375597	+	1.25537i
$291$	15.1681			0.889169
$292$	6.03944	+	7.57322i	0.353432	+	0.443189i
$293$	3.06458	+	13.4268i	0.179035	+	0.784402i	0.982077	+	0.188480i	$0.0603562\pi$
$293$	3.06458	+	13.4268i	0.179035	+	0.784402i	−0.803042	+	0.595922i	$0.796787\pi$
$294$	−2.63167	+	11.5301i	−0.153482	+	0.672448i
$295$	−15.5721	−	19.5268i	−0.906644	−	1.13690i
$296$	0.779864	−	0.977918i	0.0453287	−	0.0568403i
$297$	1.40384	+	6.15063i	0.0814591	+	0.356896i
$298$	3.40445	−	1.63949i	0.197214	−	0.0949734i
$299$	−6.78205	+	3.26607i	−0.392216	+	0.188881i
$300$	0.0306572	−	0.134318i	0.00177000	−	0.00775486i
$301$	−8.60121	−	4.14212i	−0.495765	−	0.238748i
$302$	−22.8784			−1.31651
$303$	4.00173	+	1.92713i	0.229893	+	0.110711i
$304$	−3.15783	+	3.95979i	−0.181114	+	0.227109i
$305$	9.08069	−	11.3868i	0.519959	−	0.652008i
$306$	−6.88637	−	3.31630i	−0.393667	−	0.189580i
$307$	3.43747			0.196187			0.0980934	−	0.995177i	$-0.468726\pi$
$307$	3.43747			0.196187			0.0980934	+	0.995177i	$0.468726\pi$
$308$	5.77943	+	2.78323i	0.329314	+	0.158589i
$309$	3.42541	−	15.0077i	0.194865	−	0.853759i
$310$	−13.1843	+	6.34923i	−0.748819	+	0.360612i
$311$	26.9582	−	12.9824i	1.52866	−	0.736163i	0.534609	−	0.845100i	$-0.320459\pi$
$311$	26.9582	−	12.9824i	1.52866	−	0.736163i	0.994049	+	0.108937i	$0.0347446\pi$
$312$	0.425922	+	1.86609i	0.0241131	+	0.105646i
$313$	19.0975	−	23.9476i	1.07946	−	1.35360i	0.148315	−	0.988940i	$-0.452615\pi$
$313$	19.0975	−	23.9476i	1.07946	−	1.35360i	0.931142	−	0.364657i	$-0.118814\pi$
$314$	−15.0020	−	18.8119i	−0.846613	−	1.06162i
$315$	−0.374047	+	1.63880i	−0.0210751	+	0.0923362i
$316$	−1.94234	−	8.50993i	−0.109265	−	0.478721i
$317$	2.76481	+	3.46696i	0.155287	+	0.194724i	0.853389	−	0.521274i	$-0.174543\pi$
$317$	2.76481	+	3.46696i	0.155287	+	0.194724i	−0.698102	+	0.715998i	$0.745972\pi$
$318$	24.2030			1.35724
$319$	33.8993	−	2.25141i	1.89799	−	0.126055i
$320$	5.37575			0.300514
$321$	4.93600	+	6.18955i	0.275501	+	0.345467i
$322$	−1.38970	−	6.08869i	−0.0774452	−	0.339310i
$323$	−0.964888	+	4.22745i	−0.0536878	+	0.235222i
$324$	0.851774	+	1.06809i	0.0473208	+	0.0593384i
$325$	−0.103489	+	0.129772i	−0.00574056	+	0.00719844i
$326$	−4.44164	−	19.4601i	−0.246000	−	1.07780i
$327$	3.77419	−	1.81755i	0.208713	−	0.100511i
$328$	−1.25801	+	0.605827i	−0.0694622	+	0.0334512i
$329$	−1.30604	+	5.72215i	−0.0720045	+	0.315472i
$330$	−23.5529	−	11.3425i	−1.29654	−	0.624382i
$331$	−12.6242			−0.693891			−0.346946	−	0.937885i	$-0.612781\pi$
$331$	−12.6242			−0.693891			−0.346946	+	0.937885i	$0.612781\pi$
$332$	6.34372	+	3.05498i	0.348157	+	0.167664i
$333$	−0.670593	+	0.840897i	−0.0367482	+	0.0460808i
$334$	−23.1974	+	29.0887i	−1.26931	+	1.59166i
$335$	−13.9949	−	6.73958i	−0.764622	−	0.368223i
$336$	−3.62160			−0.197574
$337$	15.3978	+	7.41521i	0.838774	+	0.403932i	0.803398	−	0.595442i	$-0.203023\pi$
$337$	15.3978	+	7.41521i	0.838774	+	0.403932i	0.0353753	+	0.999374i	$0.488737\pi$
$338$	4.20143	−	18.4077i	0.228528	−	1.00125i
$339$	−9.75279	+	4.69670i	−0.529699	+	0.255090i
$340$	11.5808	−	5.57704i	0.628059	−	0.302458i
$341$	4.95768	+	21.7210i	0.268473	+	1.17626i
$342$	1.19066	−	1.49304i	0.0643834	−	0.0807343i
$343$	6.23961	+	7.82423i	0.336908	+	0.422469i
$344$	−3.31930	+	14.5428i	−0.178965	+	0.784096i
$345$	2.29850	+	10.0704i	0.123747	+	0.542171i
$346$	−0.181830	−	0.228007i	−0.00977522	−	0.0122577i
$347$	5.48266			0.294325			0.147162	−	0.989112i	$-0.452986\pi$
$347$	5.48266			0.294325			0.147162	+	0.989112i	$0.452986\pi$
$348$	6.40222	−	3.62427i	0.343195	−	0.194281i
$349$	−20.4824			−1.09640			−0.548198	−	0.836349i	$-0.684686\pi$
$349$	−20.4824			−1.09640			−0.548198	+	0.836349i	$0.684686\pi$
$350$	−0.0858611	−	0.107666i	−0.00458947	−	0.00575501i
$351$	−0.366244	−	1.60462i	−0.0195487	−	0.0856482i
$352$	9.26769	−	40.6044i	0.493970	−	2.16422i
$353$	−11.7746	−	14.7649i	−0.626699	−	0.785856i	0.362571	−	0.931956i	$-0.381899\pi$
$353$	−11.7746	−	14.7649i	−0.626699	−	0.785856i	−0.989270	+	0.146100i	$0.953328\pi$
$354$	−12.6501	+	15.8627i	−0.672343	+	0.843092i
$355$	−1.64722	−	7.21693i	−0.0874252	−	0.383035i
$356$	−11.4697	+	5.52349i	−0.607890	+	0.292745i
$357$	−2.79356	+	1.34531i	−0.147851	+	0.0712012i
$358$	5.87826	−	25.7543i	0.310676	−	1.36116i
$359$	3.87037	+	1.86387i	0.204270	+	0.0983714i	0.533222	−	0.845975i	$-0.320981\pi$
$359$	3.87037	+	1.86387i	0.204270	+	0.0983714i	−0.328952	+	0.944347i	$0.606695\pi$
$360$	2.62652			0.138430
$361$	16.1423	+	7.77373i	0.849595	+	0.409144i
$362$	14.7983	−	18.5565i	0.777781	−	0.975307i
$363$	−17.9571	+	22.5175i	−0.942505	+	1.18186i
$364$	−1.50778	−	0.726108i	−0.0790291	−	0.0380584i
$365$	−16.0138			−0.838199
$366$	−10.6597	−	5.13343i	−0.557190	−	0.268329i
$367$	−3.04134	+	13.3250i	−0.158757	+	0.695558i	0.831409	+	0.555660i	$0.187534\pi$
$367$	−3.04134	+	13.3250i	−0.158757	+	0.695558i	−0.990166	+	0.139898i	$0.955323\pi$
$368$	−20.0507	+	9.65589i	−1.04521	+	0.503348i
$369$	1.08175	−	0.520941i	0.0563135	−	0.0271191i
$370$	−0.991716	−	4.34499i	−0.0515569	−	0.225885i
$371$	6.12162	−	7.67627i	0.317819	−	0.398532i
$372$	3.00805	+	3.77197i	0.155960	+	0.195568i
$373$	−2.78499	+	12.2018i	−0.144201	+	0.631787i	0.850231	+	0.526409i	$0.176462\pi$
$373$	−2.78499	+	12.2018i	−0.144201	+	0.631787i	−0.994432	+	0.105377i	$0.966395\pi$
$374$	−10.7300	−	47.0110i	−0.554833	−	2.43088i
$375$	−6.89877	−	8.65078i	−0.356251	−	0.446724i
$376$	9.17092			0.472954
$377$	−8.84388	+	0.587364i	−0.455483	+	0.0302508i
$378$	1.36552			0.0702350
$379$	6.92755	+	8.68688i	0.355845	+	0.446215i	0.927244	−	0.374457i	$-0.122171\pi$
$379$	6.92755	+	8.68688i	0.355845	+	0.446215i	−0.571400	+	0.820672i	$0.693599\pi$
$380$	0.714626	+	3.13098i	0.0366595	+	0.160616i
$381$	1.79567	−	7.86735i	0.0919951	−	0.403057i
$382$	−6.42079	−	8.05141i	−0.328516	−	0.411946i
$383$	9.69544	−	12.1577i	0.495414	−	0.621229i	−0.469774	−	0.882787i	$-0.655665\pi$
$383$	9.69544	−	12.1577i	0.495414	−	0.621229i	0.965188	+	0.261557i	$0.0842360\pi$
$384$	1.96627	+	8.61478i	0.100341	+	0.439621i
$385$	−9.55458	+	4.60124i	−0.486946	+	0.234501i
$386$	−14.9885	+	7.21806i	−0.762892	+	0.367389i
$387$	2.85422	−	12.5051i	0.145088	−	0.635672i
$388$	18.6696	+	8.99081i	0.947806	+	0.456439i
$389$	−0.482991			−0.0244886			−0.0122443	−	0.999925i	$-0.503898\pi$
$389$	−0.482991			−0.0244886			−0.0122443	+	0.999925i	$0.503898\pi$
$390$	6.14464	+	2.95910i	0.311146	+	0.149840i
$391$	−11.8794	+	14.8963i	−0.600769	+	0.753340i
$392$	4.67394	−	5.86094i	0.236070	−	0.296022i
$393$	−16.8524	−	8.11570i	−0.850092	−	0.409383i
$394$	17.6922			0.891318
$395$	13.0014	+	6.26114i	0.654171	+	0.315032i
$396$	−1.91784	+	8.40261i	−0.0963752	+	0.422247i
$397$	7.00415	−	3.37302i	0.351528	−	0.169287i	−0.249783	−	0.968302i	$-0.580359\pi$
$397$	7.00415	−	3.37302i	0.351528	−	0.169287i	0.601311	+	0.799015i	$0.294645\pi$
$398$	−19.6825	+	9.47858i	−0.986593	+	0.475118i
$399$	−0.172384	−	0.755263i	−0.00862998	−	0.0378104i
$400$	−0.305959	+	0.383661i	−0.0152980	+	0.0191830i
$401$	−0.967205	−	1.21284i	−0.0482999	−	0.0605662i	0.757095	−	0.653305i	$-0.226618\pi$
$401$	−0.967205	−	1.21284i	−0.0482999	−	0.0605662i	−0.805395	+	0.592739i	$0.798047\pi$
$402$	−2.80786	+	12.3020i	−0.140043	+	0.613569i
$403$	−1.29339	−	5.66673i	−0.0644286	−	0.282280i
$404$	3.78323	+	4.74401i	0.188222	+	0.236024i
$405$	−2.25851			−0.112226
$406$	1.15763	−	7.26188i	0.0574524	−	0.360401i
$407$	−6.78542			−0.336341
$408$	3.02067	+	3.78780i	0.149546	+	0.187524i
$409$	−2.26265	−	9.91331i	−0.111881	−	0.490182i	−0.999558	−	0.0297161i	$-0.990540\pi$
$409$	−2.26265	−	9.91331i	−0.111881	−	0.490182i	0.887678	−	0.460465i	$-0.152317\pi$
$410$	−1.10707	+	4.85037i	−0.0546741	+	0.239543i
$411$	2.32694	+	2.91789i	0.114779	+	0.143929i
$412$	13.1119	−	16.4418i	0.645978	−	0.810031i
$413$	1.83148	+	8.02423i	0.0901211	+	0.394846i
$414$	7.56010	−	3.64075i	0.371559	−	0.178933i
$415$	−10.4875	+	5.05050i	−0.514809	+	0.247919i
$416$	−2.41782	+	10.5932i	−0.118543	+	0.519373i
$417$	12.2035	+	5.87689i	0.597607	+	0.287793i
$418$	12.0477			0.589273
$419$	13.5322	+	6.51676i	0.661091	+	0.318364i	0.734174	−	0.678961i	$-0.237570\pi$
$419$	13.5322	+	6.51676i	0.661091	+	0.318364i	−0.0730834	+	0.997326i	$0.523284\pi$
$420$	−1.43179	+	1.79541i	−0.0698641	+	0.0876069i
$421$	−5.34856	+	6.70689i	−0.260673	+	0.326874i	−0.894894	−	0.446278i	$-0.852749\pi$
$421$	−5.34856	+	6.70689i	−0.260673	+	0.326874i	0.634221	+	0.773151i	$0.281321\pi$
$422$	9.57791	+	4.61248i	0.466246	+	0.224532i
$423$	−7.88593			−0.383427
$424$	−13.8221	−	6.65636i	−0.671260	−	0.323262i
$425$	−0.0934873	+	0.409595i	−0.00453480	+	0.0198683i
$426$	−5.41794	+	2.60914i	−0.262500	+	0.126413i
$427$	−4.32426	+	2.08245i	−0.209266	+	0.100777i
$428$	2.40664	+	10.5442i	0.116329	+	0.509673i
$429$	6.47405	−	8.11820i	0.312570	−	0.391950i
$430$	33.1385	+	41.5543i	1.59808	+	2.00393i
$431$	2.09048	−	9.15897i	0.100695	−	0.441172i	−0.899298	−	0.437336i	$-0.855922\pi$
$431$	2.09048	−	9.15897i	0.100695	−	0.441172i	0.999993	−	0.00383572i	$-0.00122095\pi$
$432$	−1.08277	−	4.74394i	−0.0520950	−	0.228243i
$433$	13.8607	+	17.3808i	0.666102	+	0.835266i	0.993992	−	0.109450i	$-0.0349090\pi$
$433$	13.8607	+	17.3808i	0.666102	+	0.835266i	−0.327890	+	0.944716i	$0.606338\pi$
$434$	4.82237			0.231481
$435$	−1.91466	+	12.0108i	−0.0918011	+	0.575872i
$436$	5.72280			0.274072
$437$	−2.96806	−	3.72183i	−0.141982	−	0.178039i
$438$	2.89474	+	12.6827i	0.138316	+	0.606002i
$439$	0.625294	−	2.73959i	0.0298437	−	0.130754i	−0.957812	−	0.287397i	$-0.907210\pi$
$439$	0.625294	−	2.73959i	0.0298437	−	0.130754i	0.987655	+	0.156643i	$0.0500673\pi$
$440$	10.3314	+	12.9551i	0.492528	+	0.617611i
$441$	−4.01905	+	5.03973i	−0.191383	+	0.239987i
$442$	2.79931	+	12.2646i	0.133150	+	0.583366i
$443$	4.43329	−	2.13496i	0.210632	−	0.101435i	−0.325593	−	0.945510i	$-0.605564\pi$
$443$	4.43329	−	2.13496i	0.210632	−	0.101435i	0.536225	+	0.844075i	$0.319850\pi$
$444$	−1.32384	+	0.637526i	−0.0628265	+	0.0302556i
$445$	4.68314	−	20.5182i	0.222002	−	0.972656i
$446$	17.1617	+	8.26464i	0.812630	+	0.391342i
$447$	2.05954			0.0974130
$448$	−1.59611	−	0.768644i	−0.0754089	−	0.0363150i
$449$	−23.6873	+	29.7029i	−1.11787	+	1.40177i	−0.212494	+	0.977162i	$0.568159\pi$
$449$	−23.6873	+	29.7029i	−1.11787	+	1.40177i	−0.905378	+	0.424606i	$0.860413\pi$
$450$	0.115362	−	0.144659i	0.00543822	−	0.00681931i
$451$	6.82452	+	3.28652i	0.321354	+	0.154756i
$452$	−14.7882			−0.695576
$453$	−11.2349	−	5.41045i	−0.527862	−	0.254205i
$454$	−0.570822	+	2.50094i	−0.0267900	+	0.117375i
$455$	2.49267	−	1.20040i	0.116858	−	0.0562758i
$456$	−1.09059	+	0.525201i	−0.0510716	+	0.0245948i
$457$	1.03622	+	4.53998i	0.0484723	+	0.212371i	0.993364	−	0.115012i	$-0.0366905\pi$
$457$	1.03622	+	4.53998i	0.0484723	+	0.212371i	−0.944892	+	0.327383i	$0.893833\pi$
$458$	−7.88300	+	9.88497i	−0.368348	+	0.461894i
$459$	−2.59743	−	3.25707i	−0.121238	−	0.152027i
$460$	−3.14007	+	13.7575i	−0.146406	+	0.641448i
$461$	4.44300	+	19.4661i	0.206931	+	0.906625i	0.966595	+	0.256309i	$0.0825064\pi$
$461$	4.44300	+	19.4661i	0.206931	+	0.906625i	−0.759664	+	0.650316i	$0.774636\pi$
$462$	5.37126	+	6.73534i	0.249893	+	0.313357i
$463$	−19.4998			−0.906230			−0.453115	−	0.891452i	$-0.649687\pi$
$463$	−19.4998			−0.906230			−0.453115	+	0.891452i	$0.649687\pi$
$464$	−26.1463	+	1.73650i	−1.21381	+	0.0806150i
$465$	−7.97594			−0.369875
$466$	−0.153236	−	0.192151i	−0.00709850	−	0.00890123i
$467$	−7.69529	−	33.7153i	−0.356095	−	1.56016i	−0.762824	−	0.646607i	$-0.776188\pi$
$467$	−7.69529	−	33.7153i	−0.356095	−	1.56016i	0.406728	−	0.913549i	$-0.366670\pi$
$468$	0.500340	−	2.19213i	0.0231282	−	0.101331i
$469$	3.19155	+	4.00207i	0.147372	+	0.184799i
$470$	20.3737	−	25.5478i	0.939768	−	1.17843i
$471$	−2.91827	−	12.7858i	−0.134467	−	0.589137i
$472$	11.5869	−	5.57995i	0.533330	−	0.256838i
$473$	72.9076	−	35.1104i	3.35230	−	1.61438i
$474$	2.60853	−	11.4287i	0.119814	−	0.524938i
$475$	−0.0945734	−	0.0455441i	−0.00433932	−	0.00208971i
$476$	−4.23587			−0.194151
$477$	11.8854	+	5.72370i	0.544195	+	0.262070i
$478$	11.8705	−	14.8851i	0.542943	−	0.680829i
$479$	3.84596	−	4.82268i	0.175726	−	0.220354i	−0.686166	−	0.727445i	$-0.740708\pi$
$479$	3.84596	−	4.82268i	0.175726	−	0.220354i	0.861893	+	0.507091i	$0.169279\pi$
$480$	13.4334	+	6.46917i	0.613146	+	0.295276i
$481$	1.77023			0.0807154
$482$	−13.9945	−	6.73937i	−0.637430	−	0.306970i
$483$	0.757454	−	3.31862i	0.0344654	−	0.151003i
$484$	−35.4497	+	17.0717i	−1.61135	+	0.775985i
$485$	−30.8647	+	14.8636i	−1.40149	+	0.674923i
$486$	0.408260	+	1.78870i	0.0185191	+	0.0811373i
$487$	4.08151	−	5.11806i	0.184951	−	0.231921i	−0.680709	−	0.732554i	$-0.738328\pi$
$487$	4.08151	−	5.11806i	0.184951	−	0.231921i	0.865660	+	0.500633i	$0.166899\pi$
$488$	4.67582	+	5.86329i	0.211664	+	0.265419i
$489$	2.42090	−	10.6067i	0.109477	−	0.479650i
$490$	−5.94363	−	26.0408i	−0.268506	−	1.17640i
$491$	11.3529	+	14.2361i	0.512349	+	0.642465i	0.968965	−	0.247199i	$-0.0795100\pi$
$491$	11.3529	+	14.2361i	0.512349	+	0.642465i	−0.456616	+	0.889664i	$0.650939\pi$
$492$	1.64025			0.0739483
$493$	−19.5232	+	11.0520i	−0.879279	+	0.497756i
$494$	−3.14309			−0.141414
$495$	−8.88377	−	11.1399i	−0.399296	−	0.500701i
$496$	−3.82383	−	16.7533i	−0.171695	−	0.752245i
$497$	−0.542829	+	2.37829i	−0.0243492	+	0.106681i
$498$	5.89569	+	7.39296i	0.264192	+	0.331287i
$499$	10.4457	−	13.0985i	0.467614	−	0.586369i	−0.490971	−	0.871176i	$-0.663358\pi$
$499$	10.4457	−	13.0985i	0.467614	−	0.586369i	0.958585	+	0.284806i	$0.0919293\pi$
$500$	−3.36363	−	14.7370i	−0.150426	−	0.659059i
$501$	−18.2707	+	8.79869i	−0.816273	+	0.393096i
$502$	−12.4827	+	6.01137i	−0.557132	+	0.268301i
$503$	−0.739155	+	3.23845i	−0.0329573	+	0.144395i	−0.988730	−	0.149712i	$-0.952165\pi$
$503$	−0.739155	+	3.23845i	−0.0329573	+	0.144395i	0.955772	+	0.294108i	$0.0950224\pi$
$504$	−0.779836	−	0.375549i	−0.0347367	−	0.0167283i
$505$	−10.0313			−0.446389
$506$	47.6952	+	22.9688i	2.12031	+	1.02109i
$507$	6.41637	−	8.04588i	0.284961	−	0.357330i
$508$	6.87354	−	8.61914i	0.304964	−	0.382413i
$509$	−16.9609	−	8.16792i	−0.751777	−	0.362036i	0.0184308	−	0.999830i	$-0.494133\pi$
$509$	−16.9609	−	8.16792i	−0.751777	−	0.362036i	−0.770207	+	0.637794i	$0.779847\pi$
$510$	17.2624			0.764393
$511$	4.75462	+	2.28971i	0.210332	+	0.101291i
$512$	−4.62970	+	20.2840i	−0.204606	+	0.896436i
$513$	0.937782	−	0.451612i	0.0414041	−	0.0199391i
$514$	−35.2253	+	16.9636i	−1.55372	+	0.748232i
$515$	7.73632	+	33.8950i	0.340903	+	1.49359i
$516$	10.9255	−	13.7001i	0.480967	−	0.603114i
$517$	−31.0191	−	38.8967i	−1.36422	−	1.71068i
$518$	−0.326813	+	1.43186i	−0.0143594	+	0.0629125i
$519$	−0.0353704	−	0.154968i	−0.00155259	−	0.00680234i
$520$	−2.69532	−	3.37982i	−0.118198	−	0.148215i
$521$	−3.09335			−0.135522			−0.0677611	−	0.997702i	$-0.521586\pi$
$521$	−3.09335			−0.135522			−0.0677611	+	0.997702i	$0.521586\pi$
$522$	9.85847	−	0.654748i	0.431493	−	0.0286575i
$523$	34.6039			1.51312			0.756561	−	0.653924i	$-0.226878\pi$
$523$	34.6039			1.51312			0.756561	+	0.653924i	$0.226878\pi$
$524$	−15.9322	−	19.9784i	−0.696003	−	0.872760i
$525$	−0.0167021	−	0.0731768i	−0.000728940	−	0.00319370i
$526$	10.5404	−	46.1806i	0.459585	−	2.01357i
$527$	−9.17285	−	11.5024i	−0.399576	−	0.501052i
$528$	19.1401	−	24.0009i	0.832964	−	1.04450i
$529$	0.463462	+	2.03056i	0.0201505	+	0.0882852i
$530$	−49.2494	+	23.7172i	−2.13926	+	1.03021i
$531$	−9.96339	+	4.79811i	−0.432374	+	0.208220i
$532$	0.235500	−	1.03179i	0.0102102	−	0.0447339i
$533$	−1.78043	−	0.857410i	−0.0771190	−	0.0371385i
$534$	−17.0967			−0.739845
$535$	−16.1093	−	7.75783i	−0.696466	−	0.335400i
$536$	4.98686	−	6.25333i	0.215400	−	0.270103i
$537$	8.97720	−	11.2571i	0.387395	−	0.485778i
$538$	−31.5944	−	15.2151i	−1.36213	−	0.655968i
$539$	−40.6669			−1.75165
$540$	−2.77988	−	1.33872i	−0.119627	−	0.0576093i
$541$	−6.17721	+	27.0641i	−0.265579	+	1.16358i	0.649518	+	0.760346i	$0.274971\pi$
$541$	−6.17721	+	27.0641i	−0.265579	+	1.16358i	−0.915098	+	0.403232i	$0.867887\pi$
$542$	5.75755	−	2.77269i	0.247308	−	0.119097i
$543$	11.6554	−	5.61293i	0.500180	−	0.240874i
$544$	6.11982	+	26.8127i	0.262385	+	1.14959i
$545$	−5.89881	+	7.39687i	−0.252677	+	0.316847i
$546$	−1.40129	−	1.75716i	−0.0599697	−	0.0751997i
$547$	7.27014	−	31.8526i	0.310849	−	1.36192i	−0.542272	−	0.840203i	$-0.682436\pi$
$547$	7.27014	−	31.8526i	0.310849	−	1.36192i	0.853120	−	0.521714i	$-0.174707\pi$
$548$	1.13454	+	4.97076i	0.0484653	+	0.212340i
$549$	−4.02066	−	5.04175i	−0.171598	−	0.215177i
$550$	1.16729			0.0497736
$551$	−1.60667	−	5.37000i	−0.0684464	−	0.228769i
$552$	−5.31878			−0.226382
$553$	−2.96498	−	3.71796i	−0.126084	−	0.158104i
$554$	4.15074	+	18.1856i	0.176348	+	0.772631i
$555$	0.540532	−	2.36823i	0.0229443	−	0.100526i
$556$	11.5371	+	14.4671i	0.489284	+	0.613543i
$557$	27.0722	−	33.9474i	1.14708	−	1.43840i	0.266928	−	0.963717i	$-0.413991\pi$
$557$	27.0722	−	33.9474i	1.14708	−	1.43840i	0.880157	−	0.474683i	$-0.157437\pi$
$558$	1.44178	+	6.31683i	0.0610352	+	0.267413i
$559$	−19.0206	+	9.15986i	−0.804488	+	0.387421i
$560$	7.36939	−	3.54891i	0.311414	−	0.149969i
$561$	5.84833	−	25.6232i	0.246917	−	1.08181i
$562$	1.77900	+	0.856721i	0.0750425	+	0.0361386i
$563$	−0.551999			−0.0232640			−0.0116320	−	0.999932i	$-0.503703\pi$
$563$	−0.551999			−0.0232640			−0.0116320	+	0.999932i	$0.503703\pi$
$564$	−9.70639	−	4.67435i	−0.408713	−	0.196826i
$565$	15.2430	−	19.1141i	0.641277	−	0.804136i
$566$	10.4416	−	13.0934i	0.438895	−	0.550356i
$567$	0.670569	+	0.322929i	0.0281612	+	0.0135617i
$568$	3.81170			0.159935
$569$	25.1874	+	12.1296i	1.05591	+	0.508499i	0.879540	−	0.475825i	$-0.157850\pi$
$569$	25.1874	+	12.1296i	1.05591	+	0.508499i	0.176369	+	0.984324i	$0.443565\pi$
$570$	−0.959732	+	4.20486i	−0.0401988	+	0.176122i
$571$	−29.9930	+	14.4439i	−1.25517	+	0.604457i	−0.938893	−	0.344210i	$-0.888147\pi$
$571$	−29.9930	+	14.4439i	−1.25517	+	0.604457i	−0.316276	+	0.948667i	$0.602432\pi$
$572$	12.7806	−	6.15481i	0.534384	−	0.257346i
$573$	−1.24900	−	5.47224i	−0.0521779	−	0.228606i
$574$	1.02222	−	1.28182i	0.0426667	−	0.0535023i
$575$	−0.287573	−	0.360606i	−0.0119926	−	0.0150383i
$576$	0.529650	−	2.32055i	0.0220688	−	0.0966895i
$577$	−4.30983	−	18.8826i	−0.179421	−	0.786093i	−0.981898	−	0.189410i	$-0.939342\pi$
$577$	−4.30983	−	18.8826i	−0.179421	−	0.786093i	0.802477	−	0.596682i	$-0.203515\pi$
$578$	0.406277	+	0.509455i	0.0168989	+	0.0211905i
$579$	−9.06736			−0.376827
$580$	−9.47599	+	13.6485i	−0.393469	+	0.566725i
$581$	3.83595			0.159142
$582$	17.3511	+	21.7575i	0.719225	+	0.901879i
$583$	18.5192	+	81.1378i	0.766986	+	3.36038i
$584$	1.83486	−	8.03906i	0.0759271	−	0.332659i
$585$	2.31766	+	2.90626i	0.0958235	+	0.120159i
$586$	−15.7542	+	19.7551i	−0.650799	+	0.816076i
$587$	−1.29711	−	5.68302i	−0.0535376	−	0.234564i	0.941079	−	0.338187i	$-0.109814\pi$
$587$	−1.29711	−	5.68302i	−0.0535376	−	0.234564i	−0.994617	+	0.103623i	$0.966956\pi$
$588$	−7.93412	+	3.82087i	−0.327198	+	0.157570i
$589$	3.31179	−	1.59487i	0.136460	−	0.0657156i
$590$	10.1966	−	44.6742i	0.419787	−	1.83921i
$591$	8.68809	+	4.18397i	0.357380	+	0.172105i
$592$	5.23355			0.215098
$593$	2.04748	+	0.986017i	0.0840801	+	0.0404909i	0.475451	−	0.879742i	$-0.342285\pi$
$593$	2.04748	+	0.986017i	0.0840801	+	0.0404909i	−0.391371	+	0.920233i	$0.627999\pi$
$594$	−7.21676	+	9.04953i	−0.296107	+	0.371307i
$595$	4.36615	−	5.47498i	0.178995	−	0.224452i
$596$	2.53498	+	1.22078i	0.103837	+	0.0500053i
$597$	−11.9070			−0.487323
$598$	−12.4431	−	5.99226i	−0.508835	−	0.245042i
$599$	−6.75720	+	29.6052i	−0.276092	+	1.20964i	0.626597	+	0.779343i	$0.284447\pi$
$599$	−6.75720	+	29.6052i	−0.276092	+	1.20964i	−0.902689	+	0.430294i	$0.858410\pi$
$600$	−0.105666	+	0.0508863i	−0.00431381	+	0.00207742i
$601$	−17.9698	+	8.65379i	−0.733003	+	0.352996i	−0.762864	−	0.646559i	$-0.776208\pi$
$601$	−17.9698	+	8.65379i	−0.733003	+	0.352996i	0.0298616	+	0.999554i	$0.490493\pi$
$602$	−3.89750	−	17.0761i	−0.158850	−	0.695969i
$603$	−4.28813	+	5.37714i	−0.174626	+	0.218974i
$604$	−10.6215	−	13.3189i	−0.432181	−	0.541938i
$605$	14.4744	−	63.4164i	0.588467	−	2.57824i
$606$	1.81332	+	7.94468i	0.0736612	+	0.322731i
$607$	21.1629	+	26.5375i	0.858977	+	1.07712i	0.996244	+	0.0865894i	$0.0275968\pi$
$607$	21.1629	+	26.5375i	0.858977	+	1.07712i	−0.137267	+	0.990534i	$0.543832\pi$
$608$	−6.87141			−0.278672
$609$	2.28582	−	3.29233i	0.0926261	−	0.133412i
$610$	26.7212			1.08191
$611$	8.09248	+	10.1477i	0.327387	+	0.410530i
$612$	−1.26643	−	5.54858i	−0.0511923	−	0.224288i
$613$	−5.90946	+	25.8910i	−0.238681	+	1.04573i	0.703519	+	0.710677i	$0.251611\pi$
$613$	−5.90946	+	25.8910i	−0.238681	+	1.04573i	−0.942200	+	0.335052i	$0.891246\pi$
$614$	3.93219	+	4.93081i	0.158690	+	0.198991i
$615$	−1.69070	+	2.12007i	−0.0681755	+	0.0854894i
$616$	−1.21510	−	5.32369i	−0.0489577	−	0.214498i
$617$	0.763697	−	0.367777i	0.0307453	−	0.0148062i	−0.418448	−	0.908241i	$-0.637426\pi$
$617$	0.763697	−	0.367777i	0.0307453	−	0.0148062i	0.449193	+	0.893435i	$0.351711\pi$
$618$	25.4459	−	12.2541i	1.02358	−	0.492932i
$619$	−9.82554	+	43.0485i	−0.394922	+	1.73027i	0.252016	+	0.967723i	$0.418906\pi$
$619$	−9.82554	+	43.0485i	−0.394922	+	1.73027i	−0.646938	+	0.762543i	$0.723951\pi$
$620$	−9.81718	−	4.72770i	−0.394267	−	0.189869i
$621$	4.57353			0.183530
$622$	49.4603	+	23.8188i	1.98318	+	0.955047i
$623$	−4.32423	+	5.42241i	−0.173246	+	0.217244i
$624$	−4.99339	+	6.26152i	−0.199896	+	0.250661i
$625$	22.9694	+	11.0615i	0.918775	+	0.442458i
$626$	56.1972			2.24609
$627$	5.91628	+	2.84913i	0.236273	+	0.113783i
$628$	3.98676	−	17.4671i	0.159089	−	0.697015i
$629$	4.03695	−	1.94409i	0.160964	−	0.0775161i
$630$	−2.77863	+	1.33812i	−0.110703	+	0.0533119i
$631$	1.04715	+	4.58785i	0.0416862	+	0.182639i	0.991485	−	0.130223i	$-0.0415693\pi$
$631$	1.04715	+	4.58785i	0.0416862	+	0.182639i	−0.949798	+	0.312862i	$0.898712\pi$
$632$	−4.63285	+	5.80941i	−0.184285	+	0.231086i
$633$	3.61264	+	4.53011i	0.143589	+	0.180056i
$634$	−1.81039	+	7.93185i	−0.0718999	+	0.315014i
$635$	4.05554	+	17.7685i	0.160939	+	0.705120i
$636$	11.2364	+	14.0900i	0.445553	+	0.558706i
$637$	10.6095			0.420362
$638$	42.0075	+	46.0507i	1.66309	+	1.82316i
$639$	−3.27762			−0.129661
$640$	−12.4429	−	15.6029i	−0.491850	−	0.616760i
$641$	−5.84782	−	25.6210i	−0.230975	−	1.01197i	−0.948833	−	0.315778i	$-0.897734\pi$
$641$	−5.84782	−	25.6210i	−0.230975	−	1.01197i	0.717858	−	0.696190i	$-0.245123\pi$
$642$	−3.23208	+	14.1607i	−0.127560	+	0.558878i
$643$	−13.3662	−	16.7607i	−0.527111	−	0.660976i	0.444991	−	0.895535i	$-0.353207\pi$
$643$	−13.3662	−	16.7607i	−0.527111	−	0.660976i	−0.972102	+	0.234559i	$0.924636\pi$
$644$	2.89941	−	3.63575i	0.114253	−	0.143268i
$645$	6.44626	+	28.2429i	0.253821	+	1.11206i
$646$	−7.16774	+	3.45180i	−0.282011	+	0.135809i
$647$	−28.2997	+	13.6284i	−1.11258	+	0.535788i	−0.897591	−	0.440829i	$-0.854685\pi$
$647$	−28.2997	+	13.6284i	−1.11258	+	0.535788i	−0.214985	+	0.976617i	$0.568970\pi$
$648$	0.258780	−	1.13379i	0.0101658	−	0.0445395i
$649$	−62.8570	−	30.2704i	−2.46735	−	1.18822i
$650$	−0.304532			−0.0119447
$651$	2.36812	+	1.14043i	0.0928140	+	0.0446969i
$652$	9.26682	−	11.6202i	0.362917	−	0.455083i
$653$	−21.5031	+	26.9641i	−0.841483	+	1.05519i	0.156239	+	0.987719i	$0.450063\pi$
$653$	−21.5031	+	26.9641i	−0.841483	+	1.05519i	−0.997722	+	0.0674669i	$0.978508\pi$
$654$	6.92452	+	3.33467i	0.270770	+	0.130396i
$655$	42.2448			1.65064
$656$	−5.26371	−	2.53487i	−0.205514	−	0.0989701i
$657$	−1.57777	+	6.91266i	−0.0615546	+	0.269689i
$658$	−9.70202	+	4.67225i	−0.378224	+	0.182143i
$659$	−21.3410	+	10.2773i	−0.831326	+	0.400346i	−0.800612	−	0.599183i	$-0.795492\pi$
$659$	−21.3410	+	10.2773i	−0.831326	+	0.400346i	−0.0307137	+	0.999528i	$0.509778\pi$
$660$	−4.33146	−	18.9774i	−0.168602	−	0.738692i
$661$	−19.9534	+	25.0208i	−0.776099	+	0.973197i	−0.999999	−	0.00141483i	$-0.999550\pi$
$661$	−19.9534	+	25.0208i	−0.776099	+	0.973197i	0.223900	+	0.974612i	$0.428121\pi$
$662$	−14.4411	−	18.1086i	−0.561270	−	0.703810i
$663$	−1.52575	+	6.68477i	−0.0592554	+	0.259615i
$664$	−1.33374	−	5.84348i	−0.0517590	−	0.226771i
$665$	1.09088	+	1.36792i	0.0423024	+	0.0530456i
$666$	−1.97331			−0.0764642
$667$	3.87725	−	24.3221i	0.150128	−	0.941757i
$668$	−27.7038			−1.07189
$669$	6.47312	+	8.11704i	0.250265	+	0.313823i
$670$	−6.34156	−	27.7842i	−0.244996	−	1.07340i
$671$	9.05287	−	39.6632i	0.349482	−	1.53118i
$672$	−3.06349	−	3.84150i	−0.118177	−	0.148189i
$673$	7.45946	−	9.35386i	0.287541	−	0.360565i	−0.616991	−	0.786970i	$-0.711649\pi$
$673$	7.45946	−	9.35386i	0.287541	−	0.360565i	0.904532	+	0.426405i	$0.140220\pi$
$674$	6.97729	+	30.5695i	0.268755	+	1.17749i
$675$	0.0908609	−	0.0437563i	0.00349724	−	0.00168418i
$676$	12.6667	−	6.09998i	0.487182	−	0.234615i
$677$	8.91349	−	39.0526i	0.342573	−	1.50091i	−0.451048	−	0.892500i	$-0.648950\pi$
$677$	8.91349	−	39.0526i	0.342573	−	1.50091i	0.793621	−	0.608412i	$-0.208193\pi$
$678$	−17.8935	−	8.61705i	−0.687195	−	0.330936i
$679$	11.2892			0.433241
$680$	−9.85837	−	4.74754i	−0.378051	−	0.182060i
$681$	−0.871753	+	1.09314i	−0.0334056	+	0.0418893i
$682$	−25.4861	+	31.9585i	−0.975912	+	1.22376i
$683$	18.7031	+	9.00695i	0.715655	+	0.344641i	0.756024	−	0.654543i	$-0.227139\pi$
$683$	18.7031	+	9.00695i	0.715655	+	0.344641i	−0.0403691	+	0.999185i	$0.512853\pi$
$684$	1.42196			0.0543699
$685$	−7.59428	−	3.65721i	−0.290162	−	0.139735i
$686$	−4.08569	+	17.9006i	−0.155992	+	0.683447i
$687$	−6.20877	+	2.98999i	−0.236879	+	0.114075i
$688$	−56.2332	+	27.0805i	−2.14387	+	1.03243i
$689$	−4.83141	−	21.1678i	−0.184062	−	0.806429i
$690$	−11.8159	+	14.8167i	−0.449825	+	0.564063i
$691$	2.08045	+	2.60881i	0.0791442	+	0.0992437i	0.819827	−	0.572611i	$-0.194069\pi$
$691$	2.08045	+	2.60881i	0.0791442	+	0.0992437i	−0.740683	+	0.671855i	$0.765498\pi$
$692$	0.0483209	−	0.211708i	0.00183688	−	0.00804792i
$693$	1.04484	+	4.57776i	0.0396903	+	0.173895i
$694$	6.27173	+	7.86449i	0.238071	+	0.298532i
$695$	−30.5911			−1.16039
$696$	−5.81013	−	2.33738i	−0.220232	−	0.0885980i
$697$	−5.00184			−0.189458
$698$	−23.4302	−	29.3805i	−0.886845	−	1.11207i
$699$	−0.0298081	−	0.130598i	−0.00112745	−	0.00493967i
$700$	0.0228174	−	0.0999697i	0.000862418	−	0.00377850i
$701$	14.9843	+	18.7898i	0.565951	+	0.709680i	0.979645	−	0.200736i	$-0.0643334\pi$
$701$	14.9843	+	18.7898i	0.565951	+	0.709680i	−0.413695	+	0.910416i	$0.635762\pi$
$702$	1.88276	−	2.36091i	0.0710602	−	0.0891067i
$703$	0.249111	+	1.09142i	0.00939538	+	0.0411639i
$704$	13.5293	−	6.51536i	0.509904	−	0.245557i
$705$	16.0466	−	7.72765i	0.604351	−	0.291040i
$706$	7.70999	−	33.7797i	0.290169	−	1.27132i
$707$	2.97839	+	1.43432i	0.112014	+	0.0539430i
$708$	−15.1075			−0.567774
$709$	42.6554	+	20.5417i	1.60196	+	0.771461i	0.999641	−	0.0267971i	$-0.00853079\pi$
$709$	42.6554	+	20.5417i	1.60196	+	0.771461i	0.602315	+	0.798258i	$0.294245\pi$
$710$	8.46789	−	10.6184i	0.317794	−	0.398502i
$711$	3.98371	−	4.99542i	0.149401	−	0.187343i
$712$	9.76372	+	4.70196i	0.365911	+	0.176213i
$713$	16.1515			0.604878
$714$	−5.12535	−	2.46824i	−0.191811	−	0.0923715i
$715$	−5.21841	+	22.8634i	−0.195158	+	0.855041i
$716$	17.7221	−	8.53454i	0.662308	−	0.318951i
$717$	9.34938	−	4.50242i	0.349159	−	0.168146i
$718$	1.75380	+	7.68389i	0.0654512	+	0.286760i
$719$	18.0229	−	22.6001i	0.672142	−	0.842840i	−0.322462	−	0.946582i	$-0.604510\pi$
$719$	18.0229	−	22.6001i	0.672142	−	0.842840i	0.994604	+	0.103743i	$0.0330819\pi$
$720$	6.85200	+	8.59214i	0.255359	+	0.320210i
$721$	2.54945	−	11.1699i	0.0949465	−	0.415988i
$722$	7.31464	+	32.0475i	0.272223	+	1.19269i
$723$	−5.27849	−	6.61901i	−0.196309	−	0.246164i
$724$	17.6730			0.656813
$725$	−0.155669	−	0.520295i	−0.00578140	−	0.0193233i
$726$	−52.8413			−1.96113
$727$	2.28644	+	2.86711i	0.0847994	+	0.106335i	0.822421	−	0.568879i	$-0.192623\pi$
$727$	2.28644	+	2.86711i	0.0847994	+	0.106335i	−0.737622	+	0.675214i	$0.764051\pi$
$728$	0.317003	+	1.38888i	0.0117489	+	0.0514754i
$729$	−0.222521	+	0.974928i	−0.00824152	+	0.0361084i
$730$	−18.3185	−	22.9706i	−0.677997	−	0.850181i
$731$	−33.3165	+	41.7776i	−1.23226	+	1.54520i
$732$	−1.96035	−	8.58887i	−0.0724567	−	0.317454i
$733$	37.0632	−	17.8487i	1.36896	−	0.659257i	0.402345	−	0.915488i	$-0.368195\pi$
$733$	37.0632	−	17.8487i	1.36896	−	0.659257i	0.966616	+	0.256231i	$0.0824808\pi$
$734$	−22.5928	+	10.8801i	−0.833915	+	0.401592i
$735$	3.23956	−	14.1934i	0.119493	−	0.523533i
$736$	−27.2029	−	13.1002i	−1.00271	−	0.482881i
$737$	−43.3896			−1.59827
$738$	1.98468	+	0.955773i	0.0730572	+	0.0351825i
$739$	26.7814	−	33.5828i	0.985168	−	1.23536i	0.0132816	−	0.999912i	$-0.495772\pi$
$739$	26.7814	−	33.5828i	0.985168	−	1.23536i	0.971886	−	0.235450i	$-0.0756563\pi$
$740$	2.06907	−	2.59453i	0.0760605	−	0.0953768i
$741$	−1.54348	−	0.743301i	−0.0567012	−	0.0273058i
$742$	18.0137			0.661304
$743$	−25.4955	−	12.2780i	−0.935340	−	0.450436i	−0.0968168	−	0.995302i	$-0.530866\pi$
$743$	−25.4955	−	12.2780i	−0.935340	−	0.450436i	−0.838523	+	0.544866i	$0.816580\pi$
$744$	0.913885	−	4.00399i	0.0335046	−	0.146793i
$745$	−4.19084	+	2.01820i	−0.153541	+	0.0739413i
$746$	−20.6885	+	9.96304i	−0.757458	+	0.364773i
$747$	1.14686	+	5.02472i	0.0419614	+	0.183845i
$748$	22.3865	−	28.0717i	0.818530	−	1.02640i
$749$	3.67374	+	4.60673i	0.134236	+	0.168326i
$750$	4.51730	−	19.7916i	0.164949	−	0.722687i
$751$	−11.6033	−	50.8373i	−0.423410	−	1.85508i	−0.511961	−	0.859009i	$-0.671081\pi$
$751$	−11.6033	−	50.8373i	−0.423410	−	1.85508i	0.0885513	−	0.996072i	$-0.471776\pi$
$752$	23.9249	+	30.0008i	0.872450	+	1.09402i
$753$	−7.55152			−0.275193
$754$	−10.9592	−	12.0140i	−0.399111	−	0.437525i
$755$	28.1631			1.02496
$756$	0.633954	+	0.794953i	0.0230567	+	0.0289122i
$757$	9.09782	+	39.8602i	0.330666	+	1.44874i	0.817844	+	0.575439i	$0.195169\pi$
$757$	9.09782	+	39.8602i	0.330666	+	1.44874i	−0.487179	+	0.873302i	$0.661974\pi$
$758$	−4.53615	+	19.8742i	−0.164760	+	0.721863i
$759$	17.9899	+	22.5586i	0.652991	+	0.818825i
$760$	1.70452	−	2.13740i	0.0618295	−	0.0775317i
$761$	2.91709	+	12.7806i	0.105744	+	0.463296i	0.999880	+	0.0154996i	$0.00493387\pi$
$761$	2.91709	+	12.7806i	0.105744	+	0.463296i	−0.894136	+	0.447796i	$0.852209\pi$
$762$	13.3393	−	6.42385i	0.483231	−	0.232712i
$763$	2.80903	−	1.35276i	0.101694	−	0.0489732i
$764$	1.70631	−	7.47584i	0.0617322	−	0.270467i
$765$	8.47706	+	4.08234i	0.306489	+	0.147597i
$766$	28.5302			1.03084
$767$	16.3986	+	7.89714i	0.592119	+	0.285149i
$768$	−13.0761	+	16.3970i	−0.471845	+	0.591674i
$769$	22.3639	−	28.0435i	0.806464	−	1.01127i	−0.193083	−	0.981182i	$-0.561849\pi$
$769$	22.3639	−	28.0435i	0.806464	−	1.01127i	0.999547	−	0.0300916i	$-0.00957990\pi$
$770$	−17.5298	−	8.44192i	−0.631731	−	0.304226i
$771$	−21.3098			−0.767452
$772$	−11.1606	−	5.37464i	−0.401677	−	0.193437i
$773$	8.47794	−	37.1443i	0.304930	−	1.33599i	−0.557654	−	0.830073i	$-0.688298\pi$
$773$	8.47794	−	37.1443i	0.304930	−	1.33599i	0.862584	−	0.505913i	$-0.168844\pi$
$774$	21.2027	−	10.2107i	0.762116	−	0.367016i
$775$	0.320876	−	0.154526i	0.0115262	−	0.00555073i
$776$	−3.92520	−	17.1974i	−0.140906	−	0.617351i
$777$	−0.499105	+	0.625858i	−0.0179053	+	0.0224525i
$778$	−0.552503	−	0.692817i	−0.0198082	−	0.0248387i
$779$	0.278085	−	1.21837i	0.00996345	−	0.0436527i
$780$	1.13002	+	4.95095i	0.0404612	+	0.177272i
$781$	−12.8924	−	16.1666i	−0.461328	−	0.578487i
$782$	−34.9569			−1.25005
$783$	4.99604	+	2.00987i	0.178544	+	0.0718270i
$784$	31.3661			1.12022
$785$	18.4674	+	23.1573i	0.659129	+	0.826521i
$786$	−7.63641	−	33.4573i	−0.272382	−	1.19338i
$787$	3.60754	−	15.8057i	0.128595	−	0.563411i	−0.869044	−	0.494735i	$-0.835265\pi$
$787$	3.60754	−	15.8057i	0.128595	−	0.563411i	0.997639	−	0.0686766i	$-0.0218777\pi$
$788$	8.21370	+	10.2997i	0.292601	+	0.366910i
$789$	16.0972	−	20.1853i	0.573076	−	0.718615i
$790$	5.89137	+	25.8118i	0.209606	+	0.918343i
$791$	−7.25876	+	3.49563i	−0.258092	+	0.124290i
$792$	6.61023	−	3.18332i	0.234884	−	0.113114i
$793$	−2.36178	+	10.3476i	−0.0838691	+	0.367455i
$794$	12.8505	+	6.18849i	0.456049	+	0.219621i
$795$	−29.7937			−1.05667
$796$	−14.6558	−	7.05785i	−0.519460	−	0.250159i
$797$	−17.9769	+	22.5423i	−0.636774	+	0.798490i	−0.990595	−	0.136824i	$-0.956311\pi$
$797$	−17.9769	+	22.5423i	−0.636774	+	0.798490i	0.353821	+	0.935313i	$0.384882\pi$
$798$	0.886178	−	1.11123i	0.0313704	−	0.0393372i
$799$	29.5990	+	14.2541i	1.04714	+	0.504275i
$800$	−0.665765			−0.0235384
$801$	−8.39567	−	4.04314i	−0.296646	−	0.142857i
$802$	0.633324	−	2.77478i	0.0223635	−	0.0979807i
$803$	−40.3023	+	19.4085i	−1.42224	+	0.684913i
$804$	−8.46531	+	4.07668i	−0.298548	+	0.143773i
$805$	1.71071	+	7.49513i	0.0602948	+	0.264169i
$806$	6.64899	−	8.33757i	0.234201	−	0.293678i
$807$	−11.9169	−	14.9433i	−0.419495	−	0.526031i
$808$	1.14939	−	5.03582i	0.0404355	−	0.177160i
$809$	2.83736	+	12.4313i	0.0997564	+	0.437062i	0.999999	+	0.00167197i	$0.000532206\pi$
$809$	2.83736	+	12.4313i	0.0997564	+	0.437062i	−0.900242	+	0.435390i	$0.856611\pi$
$810$	−2.58355	−	3.23967i	−0.0907766	−	0.113830i
$811$	11.6687			0.409742			0.204871	−	0.978789i	$-0.434323\pi$
$811$	11.6687			0.409742			0.204871	+	0.978789i	$0.434323\pi$
$812$	4.76501	−	2.69745i	0.167219	−	0.0946620i
$813$	3.48307			0.122157
$814$	−7.76197	−	9.73320i	−0.272057	−	0.341148i
$815$	5.46763	+	23.9552i	0.191523	+	0.839115i
$816$	−4.51079	+	19.7630i	−0.157909	+	0.691845i
$817$	−8.32410	−	10.4381i	−0.291223	−	0.365183i
$818$	11.6317	−	14.5856i	0.406691	−	0.509975i
$819$	−0.272586	−	1.19428i	−0.00952493	−	0.0417315i
$820$	−3.33766	+	1.60733i	−0.116556	+	0.0561304i
$821$	40.9280	−	19.7099i	1.42840	−	0.687880i	0.449698	−	0.893180i	$-0.351531\pi$
$821$	40.9280	−	19.7099i	1.42840	−	0.687880i	0.978699	+	0.205301i	$0.0658172\pi$
$822$	−1.52368	+	6.67566i	−0.0531443	+	0.232840i
$823$	10.0382	+	4.83414i	0.349909	+	0.168507i	0.600579	−	0.799565i	$-0.294937\pi$
$823$	10.0382	+	4.83414i	0.349909	+	0.168507i	−0.250670	+	0.968073i	$0.580651\pi$
$824$	−17.9020			−0.623646
$825$	0.573224	+	0.276050i	0.0199571	+	0.00961083i
$826$	−9.41513	+	11.8062i	−0.327594	+	0.410790i
$827$	5.49909	−	6.89564i	0.191222	−	0.239785i	−0.676973	−	0.736008i	$-0.736709\pi$
$827$	5.49909	−	6.89564i	0.191222	−	0.239785i	0.868195	+	0.496223i	$0.165280\pi$
$828$	5.62933	+	2.71094i	0.195633	+	0.0942118i
$829$	−40.1793			−1.39548			−0.697742	−	0.716349i	$-0.745812\pi$
$829$	−40.1793			−1.39548			−0.697742	+	0.716349i	$0.745812\pi$
$830$	−19.2414	−	9.26616i	−0.667878	−	0.321633i
$831$	−2.26235	+	9.91200i	−0.0784800	+	0.343843i
$832$	−3.52962	+	1.69977i	−0.122367	+	0.0589290i
$833$	24.1946	−	11.6515i	0.838293	−	0.403700i
$834$	5.52982	+	24.2277i	0.191482	+	0.838938i
$835$	28.5558	−	35.8079i	0.988216	−	1.23918i
$836$	5.59324	+	7.01370i	0.193446	+	0.242574i
$837$	−0.785835	+	3.44297i	−0.0271624	+	0.119006i
$838$	6.13190	+	26.8656i	0.211823	+	0.928057i
$839$	−19.8914	−	24.9430i	−0.686726	−	0.861128i	0.309228	−	0.950988i	$-0.399929\pi$
$839$	−19.8914	−	24.9430i	−0.686726	−	0.861128i	−0.995954	+	0.0898602i	$0.971358\pi$
$840$	1.95486			0.0674489
$841$	14.9240	−	24.8651i	0.514619	−	0.857419i
$842$	−15.7389			−0.542398
$843$	0.671010	+	0.841420i	0.0231108	+	0.0289801i
$844$	1.76141	+	7.71725i	0.0606303	+	0.265639i
$845$	−5.17193	+	22.6597i	−0.177920	+	0.779517i
$846$	−9.02087	−	11.3118i	−0.310144	−	0.388908i
$847$	−13.3650	+	16.7592i	−0.459228	+	0.575854i
$848$	−14.2837	−	62.5811i	−0.490505	−	2.14904i
$849$	8.22399	−	3.96047i	0.282247	−	0.135923i
$850$	−0.694476	+	0.334442i	−0.0238203	+	0.0114713i
$851$	−1.09459	+	4.79572i	−0.0375221	+	0.164395i
$852$	−4.03426	−	1.94280i	−0.138211	−	0.0665591i
$853$	7.50388			0.256928			0.128464	−	0.991714i	$-0.458995\pi$
$853$	7.50388			0.256928			0.128464	+	0.991714i	$0.458995\pi$
$854$	−7.93374	−	3.82069i	−0.271487	−	0.130741i
$855$	−1.46569	+	1.83792i	−0.0501256	+	0.0628555i
$856$	5.74031	−	7.19812i	0.196200	−	0.246027i
$857$	−9.86686	−	4.75163i	−0.337045	−	0.162313i	0.257703	−	0.966224i	$-0.417034\pi$
$857$	−9.86686	−	4.75163i	−0.337045	−	0.162313i	−0.594749	+	0.803912i	$0.702749\pi$
$858$	19.0508			0.650383
$859$	10.3409	+	4.97993i	0.352828	+	0.169913i	0.601899	−	0.798572i	$-0.294411\pi$
$859$	10.3409	+	4.97993i	0.352828	+	0.169913i	−0.249071	+	0.968485i	$0.580125\pi$
$860$	−8.80649	+	38.5838i	−0.300299	+	1.31570i
$861$	0.805117	−	0.387724i	0.0274383	−	0.0132136i
$862$	15.5292	−	7.47848i	0.528928	−	0.254718i
$863$	1.67556	+	7.34109i	0.0570366	+	0.249894i	0.995406	−	0.0957391i	$-0.0305215\pi$
$863$	1.67556	+	7.34109i	0.0570366	+	0.249894i	−0.938370	+	0.345633i	$0.887664\pi$
$864$	4.11607	−	5.16139i	0.140032	−	0.175594i
$865$	0.223831	+	0.280675i	0.00761047	+	0.00954323i
$866$	−9.07596	+	39.7644i	−0.308414	+	1.35125i
$867$	0.0790310	+	0.346258i	0.00268403	+	0.0117595i
$868$	2.23882	+	2.80739i	0.0759904	+	0.0952889i
$869$	40.3093			1.36740
$870$	−19.4188	+	10.9929i	−0.658360	+	0.372694i
$871$	11.3198			0.383556
$872$	−3.03741	−	3.80879i	−0.102860	−	0.128982i
$873$	3.37522	+	14.7878i	0.114234	+	0.500491i
$874$	1.94348	−	8.51496i	0.0657393	−	0.288023i
$875$	−5.13458	−	6.43856i	−0.173581	−	0.217663i
$876$	−6.03944	+	7.57322i	−0.204054	+	0.255875i
$877$	−6.09091	−	26.6860i	−0.205675	−	0.901123i	−0.967406	−	0.253229i	$-0.918507\pi$
$877$	−6.09091	−	26.6860i	−0.205675	−	0.901123i	0.761731	−	0.647894i	$-0.224350\pi$
$878$	4.64504	−	2.23693i	0.156762	−	0.0754928i
$879$	−12.4082	+	5.97549i	−0.418519	+	0.201548i
$880$	−15.4279	+	67.5939i	−0.520073	+	2.27859i
$881$	−23.6427	−	11.3857i	−0.796541	−	0.383594i	−0.00908042	−	0.999959i	$-0.502890\pi$
$881$	−23.6427	−	11.3857i	−0.796541	−	0.383594i	−0.787461	+	0.616365i	$0.788605\pi$
$882$	−11.8266			−0.398222
$883$	−27.3771	−	13.1841i	−0.921313	−	0.443681i	−0.0877734	−	0.996140i	$-0.527975\pi$
$883$	−27.3771	−	13.1841i	−0.921313	−	0.443681i	−0.833540	+	0.552459i	$0.813689\pi$
$884$	−5.84034	+	7.32355i	−0.196432	+	0.246318i
$885$	15.5721	−	19.5268i	0.523451	−	0.656387i
$886$	8.13378	+	3.91702i	0.273260	+	0.131595i
$887$	8.08209			0.271370			0.135685	−	0.990752i	$-0.456676\pi$
$887$	8.08209			0.271370			0.135685	+	0.990752i	$0.456676\pi$
$888$	1.12694	+	0.542704i	0.0378175	+	0.0182119i
$889$	1.33647	−	5.85548i	0.0448239	−	0.196386i
$890$	34.7890	−	16.7535i	1.16613	−	0.561579i
$891$	−5.68404	+	2.73729i	−0.190422	+	0.0917026i
$892$	3.15610	+	13.8278i	0.105674	+	0.462988i
$893$	−5.11769	+	6.41738i	−0.171257	+	0.214750i
$894$	2.35595	+	2.95427i	0.0787947	+	0.0988055i
$895$	−7.23609	+	31.7034i	−0.241876	+	1.05973i
$896$	1.46344	+	6.41177i	0.0488903	+	0.214202i
$897$	−4.69333	−	5.88525i	−0.156706	−	0.196503i
$898$	−69.7031			−2.32602
$899$	17.6436	+	7.09789i	0.588446	+	0.236728i
$900$	0.137772			0.00459241
$901$	−34.2647	−	42.9666i	−1.14152	−	1.43143i
$902$	3.09243	+	13.5488i	0.102967	+	0.451126i
$903$	2.12432	−	9.30726i	0.0706930	−	0.309726i
$904$	7.84889	+	9.84220i	0.261050	+	0.327347i
$905$	−18.2166	+	22.8429i	−0.605540	+	0.759323i
$906$	−5.09093	−	22.3048i	−0.169135	−	0.741028i
$907$	−7.16202	+	3.44905i	−0.237811	+	0.114524i	−0.548994	−	0.835826i	$-0.684989\pi$
$907$	−7.16202	+	3.44905i	−0.237811	+	0.114524i	0.311183	+	0.950350i	$0.399275\pi$
$908$	−1.72095	+	0.828767i	−0.0571118	+	0.0275036i
$909$	−0.988346	+	4.33022i	−0.0327814	+	0.143624i
$910$	4.57330	+	2.20239i	0.151604	+	0.0730084i
$911$	−5.66777			−0.187782			−0.0938908	−	0.995583i	$-0.529930\pi$
$911$	−5.66777			−0.187782			−0.0938908	+	0.995583i	$0.529930\pi$
$912$	−4.56319	−	2.19752i	−0.151102	−	0.0727671i
$913$	−20.2729	+	25.4214i	−0.670935	+	0.841326i
$914$	−5.32692	+	6.67975i	−0.176199	+	0.220946i
$915$	13.1220	+	6.31921i	0.433799	+	0.208907i
$916$	−9.41436			−0.311059
$917$	−12.5428	−	6.04031i	−0.414201	−	0.199469i
$918$	1.70079	−	7.45166i	0.0561345	−	0.245941i
$919$	−24.1751	+	11.6421i	−0.797464	+	0.384038i	−0.787812	−	0.615915i	$-0.788786\pi$
$919$	−24.1751	+	11.6421i	−0.797464	+	0.384038i	−0.00965109	+	0.999953i	$0.503072\pi$
$920$	10.8229	−	5.21203i	0.356820	−	0.171835i
$921$	0.764909	+	3.35128i	0.0252046	+	0.110429i
$922$	−22.8403	+	28.6408i	−0.752204	+	0.943234i
$923$	3.36347	+	4.21766i	0.110710	+	0.138826i
$924$	−1.42740	+	6.25386i	−0.0469581	+	0.205737i
$925$	0.0241361	+	0.105747i	0.000793591	+	0.00347695i
$926$	−22.3061	−	27.9710i	−0.733025	−	0.919185i
$927$	15.3937			0.505594
$928$	−23.9589	−	26.2650i	−0.786491	−	0.862189i
$929$	−24.4580			−0.802441			−0.401220	−	0.915982i	$-0.631414\pi$
$929$	−24.4580			−0.802441			−0.401220	+	0.915982i	$0.631414\pi$
$930$	−9.12383	−	11.4409i	−0.299182	−	0.375163i
$931$	1.49299	+	6.54121i	0.0489308	+	0.214380i
$932$	0.0407221	−	0.178415i	0.00133390	−	0.00584418i
$933$	18.6556	+	23.3934i	0.610758	+	0.765866i
$934$	39.5594	−	49.6059i	1.29442	−	1.62315i
$935$	13.2085	+	57.8702i	0.431964	+	1.89256i
$936$	−1.72452	+	0.830487i	−0.0563678	+	0.0271453i
$937$	−30.8489	+	14.8560i	−1.00779	+	0.485325i	−0.863575	−	0.504221i	$-0.831780\pi$
$937$	−30.8489	+	14.8560i	−1.00779	+	0.485325i	−0.144214	+	0.989547i	$0.546065\pi$
$938$	−2.08982	+	9.15609i	−0.0682350	+	0.298957i
$939$	27.5968	+	13.2899i	0.900586	+	0.433699i
$940$	24.3315			0.793606
$941$	34.3095	+	16.5226i	1.11846	+	0.538621i	0.899416	−	0.437094i	$-0.143992\pi$
$941$	34.3095	+	16.5226i	1.11846	+	0.538621i	0.219042	+	0.975715i	$0.429707\pi$
$942$	15.0020	−	18.8119i	0.488792	−	0.612926i
$943$	3.42371	−	4.29320i	0.111491	−	0.139806i
$944$	48.4813	+	23.3473i	1.57793	+	0.759891i
$945$	−1.68095			−0.0546813
$946$	133.764	+	64.4173i	4.34904	+	2.09439i
$947$	11.0693	−	48.4979i	0.359705	−	1.57597i	−0.394223	−	0.919015i	$-0.628986\pi$
$947$	11.0693	−	48.4979i	0.359705	−	1.57597i	0.753929	−	0.656956i	$-0.228156\pi$
$948$	7.86436	−	3.78728i	0.255422	−	0.123005i
$949$	10.5143	−	5.06344i	0.341310	−	0.164366i
$950$	−0.0428545	−	0.187758i	−0.00139038	−	0.00609166i
$951$	−2.76481	+	3.46696i	−0.0896551	+	0.112424i
$952$	2.24821	+	2.81917i	0.0728650	+	0.0913698i
$953$	2.13183	−	9.34015i	0.0690567	−	0.302557i	−0.928591	−	0.371104i	$-0.878979\pi$
$953$	2.13183	−	9.34015i	0.0690567	−	0.302557i	0.997648	+	0.0685472i	$0.0218364\pi$
$954$	5.38568	+	23.5962i	0.174368	+	0.763955i
$955$	7.90393	+	9.91122i	0.255765	+	0.320720i
$956$	14.1765			0.458500
$957$	9.73826	+	32.5484i	0.314793	+	1.05214i
$958$	11.3173			0.365644
$959$	1.73188	+	2.17171i	0.0559254	+	0.0701282i
$960$	1.19622	+	5.24097i	0.0386078	+	0.169152i
$961$	4.12296	−	18.0639i	0.132999	−	0.582706i
$962$	2.02500	+	2.53927i	0.0652885	+	0.0818692i
$963$	−4.93600	+	6.18955i	−0.159060	+	0.199455i
$964$	−2.57363	−	11.2758i	−0.0828910	−	0.363169i
$965$	18.4507	−	8.88537i	0.593948	−	0.286030i
$966$	5.62680	−	2.70972i	0.181039	−	0.0871839i
$967$	−10.0491	+	44.0282i	−0.323159	+	1.41585i	0.508739	+	0.860921i	$0.330112\pi$
$967$	−10.0491	+	44.0282i	−0.323159	+	1.41585i	−0.831898	+	0.554929i	$0.812745\pi$
$968$	30.1771	+	14.5325i	0.969928	+	0.467093i
$969$	−4.33617			−0.139298
$970$	−56.6275	−	27.2704i	−1.81820	−	0.875599i
$971$	11.3267	−	14.2032i	0.363491	−	0.455803i	−0.566133	−	0.824314i	$-0.691561\pi$
$971$	11.3267	−	14.2032i	0.363491	−	0.455803i	0.929623	+	0.368511i	$0.120132\pi$
$972$	−0.851774	+	1.06809i	−0.0273207	+	0.0342590i
$973$	9.08275	+	4.37402i	0.291180	+	0.140225i
$974$	12.0104			0.384838
$975$	−0.149547	−	0.0720178i	−0.00478932	−	0.00230642i
$976$	−6.98242	+	30.5920i	−0.223502	+	0.979226i
$977$	−1.28858	+	0.620547i	−0.0412253	+	0.0198531i	−0.454383	−	0.890807i	$-0.650140\pi$
$977$	−1.28858	+	0.620547i	−0.0412253	+	0.0198531i	0.413158	+	0.910660i	$0.364426\pi$
$978$	17.9838	−	8.66056i	0.575060	−	0.276934i
$979$	−13.0817	−	57.3146i	−0.418092	−	1.83178i
$980$	12.4005	−	15.5497i	0.396120	−	0.496718i
$981$	2.61182	+	3.27512i	0.0833890	+	0.104566i
$982$	−7.43386	+	32.5698i	−0.237224	+	1.03935i
$983$	−9.15928	−	40.1294i	−0.292136	−	1.27993i	−0.881547	−	0.472097i	$-0.843497\pi$
$983$	−9.15928	−	40.1294i	−0.292136	−	1.27993i	0.589411	−	0.807833i	$-0.299360\pi$
$984$	−0.870572	−	1.09166i	−0.0277528	−	0.0348010i
$985$	−21.7789			−0.693933
$986$	−38.1862	−	15.3620i	−1.21610	−	0.489227i
$987$	−5.86930			−0.186822
$988$	−1.45920	−	1.82978i	−0.0464234	−	0.0582131i
$989$	−13.0539	−	57.1927i	−0.415089	−	1.81862i
$990$	5.81708	−	25.4863i	0.184879	−	0.810008i
$991$	−2.45327	−	3.07630i	−0.0779307	−	0.0977220i	0.741338	−	0.671132i	$-0.234192\pi$
$991$	−2.45327	−	3.07630i	−0.0779307	−	0.0977220i	−0.819269	+	0.573410i	$0.805620\pi$
$992$	14.5360	−	18.2275i	0.461517	−	0.578724i
$993$	−2.80916	−	12.3077i	−0.0891460	−	0.390574i
$994$	−4.03244	+	1.94192i	−0.127901	+	0.0615940i
$995$	24.2290	−	11.6681i	0.768110	−	0.369902i
$996$	−1.56677	+	6.86447i	−0.0496450	+	0.217509i
$997$	42.2291	+	20.3364i	1.33741	+	0.644062i	0.959481	−	0.281774i	$-0.0909227\pi$
$997$	42.2291	+	20.3364i	1.33741	+	0.644062i	0.377927	+	0.925835i	$0.376637\pi$
$998$	30.7379			0.972992
$999$	−0.969034	−	0.466662i	−0.0306589	−	0.0147645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.g.b.82.3	yes	18
3.2	odd	2		261.2.k.b.82.1		18
29.9	even	14		2523.2.a.q.1.2		9
29.20	even	7		2523.2.a.p.1.8		9
29.23	even	7	inner	87.2.g.b.52.3	✓	18
87.20	odd	14		7569.2.a.bl.1.2		9
87.23	odd	14		261.2.k.b.226.1		18
87.38	odd	14		7569.2.a.bk.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.b.52.3	✓	18	29.23	even	7	inner
87.2.g.b.82.3	yes	18	1.1	even	1	trivial
261.2.k.b.82.1		18	3.2	odd	2
261.2.k.b.226.1		18	87.23	odd	14
2523.2.a.p.1.8		9	29.20	even	7
2523.2.a.q.1.2		9	29.9	even	14
7569.2.a.bk.1.8		9	87.38	odd	14
7569.2.a.bl.1.2		9	87.20	odd	14

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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14392 + 1.43443i) q^{2} +(0.222521 + 0.974928i) q^{3} +(-0.303995 + 1.33189i) q^{4} +(-1.40816 - 1.76577i) q^{5} +(-1.14392 + 1.43443i) q^{6} +(0.165617 + 0.725615i) q^{7} +(1.04778 - 0.504584i) q^{8} +(-0.900969 + 0.433884i) q^{9} +(0.922058 - 4.03980i) q^{10} +(-5.68404 - 2.73729i) q^{11} -1.36614 q^{12} +(1.48289 + 0.714123i) q^{13} +(-0.851391 + 1.06761i) q^{14} +(1.40816 - 1.76577i) q^{15} +(4.38406 + 2.11125i) q^{16} +4.16595 q^{17} +(-1.65301 - 0.796048i) q^{18} +(-0.231613 + 1.01476i) q^{19} +(2.77988 - 1.33872i) q^{20} +(-0.670569 + 0.322929i) q^{21} +(-2.57563 - 11.2846i) q^{22} +(-2.85155 + 3.57573i) q^{23} +(0.725086 + 0.909229i) q^{24} +(-0.0224408 + 0.0983195i) q^{25} +(0.671949 + 2.94400i) q^{26} +(-0.623490 - 0.781831i) q^{27} -1.01678 q^{28} +(-4.68636 + 2.65293i) q^{29} +4.14369 q^{30} +(-2.20186 - 2.76105i) q^{31} +(1.46901 + 6.43615i) q^{32} +(1.40384 - 6.15063i) q^{33} +(4.76551 + 5.97577i) q^{34} +(1.04806 - 1.31422i) q^{35} +(-0.303995 - 1.33189i) q^{36} +(0.969034 - 0.466662i) q^{37} +(-1.72055 + 0.828574i) q^{38} +(-0.366244 + 1.60462i) q^{39} +(-2.36642 - 1.13961i) q^{40} -1.20065 q^{41} +(-1.23030 - 0.592479i) q^{42} +(-7.99734 + 10.0283i) q^{43} +(5.37367 - 6.73837i) q^{44} +(2.03484 + 0.979929i) q^{45} -8.39108 q^{46} +(7.10498 + 3.42158i) q^{47} +(-1.08277 + 4.74394i) q^{48} +(5.80769 - 2.79684i) q^{49} +(-0.166703 + 0.0802799i) q^{50} +(0.927012 + 4.06150i) q^{51} +(-1.40192 + 1.75795i) q^{52} +(-8.22494 - 10.3138i) q^{53} +(0.408260 - 1.78870i) q^{54} +(3.17058 + 13.8912i) q^{55} +(0.539663 + 0.676716i) q^{56} -1.04086 q^{57} +(-9.16625 - 3.68752i) q^{58} +11.0585 q^{59} +(1.92374 + 2.41229i) q^{60} +(1.43496 + 6.28696i) q^{61} +(1.44178 - 6.31683i) q^{62} +(-0.464048 - 0.581898i) q^{63} +(-1.48405 + 1.86094i) q^{64} +(-0.827164 - 3.62404i) q^{65} +(10.4285 - 5.02211i) q^{66} +(6.19652 - 2.98409i) q^{67} +(-1.26643 + 5.54858i) q^{68} +(-4.12061 - 1.98438i) q^{69} +3.08405 q^{70} +(2.95303 + 1.42211i) q^{71} +(-0.725086 + 0.909229i) q^{72} +(4.42081 - 5.54352i) q^{73} +(1.77789 + 0.856187i) q^{74} -0.100848 q^{75} +(-1.28114 - 0.616965i) q^{76} +(1.04484 - 4.57776i) q^{77} +(-2.72067 + 1.31020i) q^{78} +(-5.75663 + 2.77225i) q^{79} +(-2.44545 - 10.7142i) q^{80} +(0.623490 - 0.781831i) q^{81} +(-1.37344 - 1.72224i) q^{82} +(1.14686 - 5.02472i) q^{83} +(-0.226256 - 0.991291i) q^{84} +(-5.86631 - 7.35612i) q^{85} -23.5333 q^{86} +(-3.62923 - 3.97853i) q^{87} -7.33681 q^{88} +(5.80998 + 7.28549i) q^{89} +(0.922058 + 4.03980i) q^{90} +(-0.272586 + 1.19428i) q^{91} +(-3.89562 - 4.88495i) q^{92} +(2.20186 - 2.76105i) q^{93} +(3.21951 + 14.1056i) q^{94} +(2.11798 - 1.01997i) q^{95} +(-5.94790 + 2.86436i) q^{96} +(3.37522 - 14.7878i) q^{97} +(10.6554 + 5.13137i) q^{98} +6.30880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more