LMFDB - Embedded newform 429.2.i.e.133.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(100,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("429.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.i (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 10x^{8} - 6x^{7} + 46x^{6} - 31x^{5} + 111x^{4} - 36x^{3} + 145x^{2} - 72x + 81 $ x^10 - 2x^9 + 10x^8 - 6x^7 + 46x^6 - 31x^5 + 111x^4 - 36x^3 + 145x^2 - 72*x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.2
Root			$-0.665890 - 1.15336i$ of defining polynomial
Character	$\chi$	$=$	429.133
Dual form			429.2.i.e.100.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.665890 - 1.15336i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.113180 - 0.196033i) q^{4} -3.31232 q^{5} +(0.665890 - 1.15336i) q^{6} +(0.767139 - 1.32872i) q^{7} -2.96502 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.665890 - 1.15336i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.113180 - 0.196033i) q^{4} -3.31232 q^{5} +(0.665890 - 1.15336i) q^{6} +(0.767139 - 1.32872i) q^{7} -2.96502 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.20564 + 3.82029i) q^{10} +(0.500000 + 0.866025i) q^{11} +0.226360 q^{12} +(-1.88126 - 3.07585i) q^{13} -2.04332 q^{14} +(-1.65616 - 2.86856i) q^{15} +(1.74802 + 3.02766i) q^{16} +(-2.98471 + 5.16968i) q^{17} +1.33178 q^{18} +(-3.23053 + 5.59545i) q^{19} +(-0.374889 + 0.649326i) q^{20} +1.53428 q^{21} +(0.665890 - 1.15336i) q^{22} +(-2.66033 - 4.60783i) q^{23} +(-1.48251 - 2.56779i) q^{24} +5.97148 q^{25} +(-2.29483 + 4.21794i) q^{26} -1.00000 q^{27} +(-0.173649 - 0.300770i) q^{28} +(0.0956916 + 0.165743i) q^{29} +(-2.20564 + 3.82029i) q^{30} -9.38922 q^{31} +(-0.637043 + 1.10339i) q^{32} +(-0.500000 + 0.866025i) q^{33} +7.94997 q^{34} +(-2.54101 + 4.40116i) q^{35} +(0.113180 + 0.196033i) q^{36} +(-4.63312 - 8.02479i) q^{37} +8.60472 q^{38} +(1.72313 - 3.16715i) q^{39} +9.82111 q^{40} +(-0.125238 - 0.216919i) q^{41} +(-1.02166 - 1.76957i) q^{42} +(2.58307 - 4.47402i) q^{43} +0.226360 q^{44} +(1.65616 - 2.86856i) q^{45} +(-3.54298 + 6.13662i) q^{46} -4.36030 q^{47} +(-1.74802 + 3.02766i) q^{48} +(2.32300 + 4.02355i) q^{49} +(-3.97635 - 6.88724i) q^{50} -5.96943 q^{51} +(-0.815891 + 0.0206660i) q^{52} +7.13695 q^{53} +(0.665890 + 1.15336i) q^{54} +(-1.65616 - 2.86856i) q^{55} +(-2.27458 + 3.93970i) q^{56} -6.46106 q^{57} +(0.127440 - 0.220733i) q^{58} +(4.90095 - 8.48870i) q^{59} -0.749777 q^{60} +(-4.23019 + 7.32691i) q^{61} +(6.25219 + 10.8291i) q^{62} +(0.767139 + 1.32872i) q^{63} +8.68889 q^{64} +(6.23135 + 10.1882i) q^{65} +1.33178 q^{66} +(3.40525 + 5.89807i) q^{67} +(0.675620 + 1.17021i) q^{68} +(2.66033 - 4.60783i) q^{69} +6.76814 q^{70} +(3.70598 - 6.41895i) q^{71} +(1.48251 - 2.56779i) q^{72} +13.2687 q^{73} +(-6.17030 + 10.6873i) q^{74} +(2.98574 + 5.17145i) q^{75} +(0.731263 + 1.26658i) q^{76} +1.53428 q^{77} +(-4.80026 + 0.121588i) q^{78} -6.63833 q^{79} +(-5.79001 - 10.0286i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.166790 + 0.288888i) q^{82} -9.84383 q^{83} +(0.173649 - 0.300770i) q^{84} +(9.88633 - 17.1236i) q^{85} -6.88018 q^{86} +(-0.0956916 + 0.165743i) q^{87} +(-1.48251 - 2.56779i) q^{88} +(-2.68721 - 4.65439i) q^{89} -4.41129 q^{90} +(-5.53014 + 0.140075i) q^{91} -1.20439 q^{92} +(-4.69461 - 8.13131i) q^{93} +(2.90348 + 5.02898i) q^{94} +(10.7006 - 18.5339i) q^{95} -1.27409 q^{96} +(3.62188 - 6.27329i) q^{97} +(3.09372 - 5.35848i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} + 5 q^{11} - 12 q^{12} - 3 q^{13} - 6 q^{14} + 2 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 5 q^{19} - 28 q^{20} + 18 q^{21} - 2 q^{22} + 5 q^{23} - 9 q^{24} + 42 q^{25} + 20 q^{26} - 10 q^{27} + 11 q^{28} - 12 q^{29} - 5 q^{30} - 36 q^{31} + 35 q^{32} - 5 q^{33} - 6 q^{34} - 6 q^{36} + q^{37} + 74 q^{38} + 6 q^{39} - 62 q^{40} - 30 q^{41} - 3 q^{42} + 3 q^{43} - 12 q^{44} - 2 q^{45} - 24 q^{46} - 44 q^{47} + 4 q^{48} - 14 q^{49} - 18 q^{50} + 6 q^{51} + 35 q^{52} + 14 q^{53} - 2 q^{54} + 2 q^{55} - 27 q^{56} - 10 q^{57} + 3 q^{58} + 12 q^{59} - 56 q^{60} - 18 q^{61} + 28 q^{62} + 9 q^{63} + 110 q^{64} - 28 q^{65} - 4 q^{66} + 37 q^{67} + 8 q^{68} - 5 q^{69} - 32 q^{70} + 17 q^{71} + 9 q^{72} + 4 q^{73} + q^{74} + 21 q^{75} + 26 q^{76} + 18 q^{77} + 25 q^{78} - 12 q^{79} - 38 q^{80} - 5 q^{81} + 36 q^{82} + 8 q^{83} - 11 q^{84} + 41 q^{85} - 28 q^{86} + 12 q^{87} - 9 q^{88} - 14 q^{89} - 10 q^{90} + 35 q^{91} - 12 q^{92} - 18 q^{93} - 20 q^{94} + 7 q^{95} + 70 q^{96} + 15 q^{97} + 4 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 + 5 * q^11 - 12 * q^12 - 3 * q^13 - 6 * q^14 + 2 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 5 * q^19 - 28 * q^20 + 18 * q^21 - 2 * q^22 + 5 * q^23 - 9 * q^24 + 42 * q^25 + 20 * q^26 - 10 * q^27 + 11 * q^28 - 12 * q^29 - 5 * q^30 - 36 * q^31 + 35 * q^32 - 5 * q^33 - 6 * q^34 - 6 * q^36 + q^37 + 74 * q^38 + 6 * q^39 - 62 * q^40 - 30 * q^41 - 3 * q^42 + 3 * q^43 - 12 * q^44 - 2 * q^45 - 24 * q^46 - 44 * q^47 + 4 * q^48 - 14 * q^49 - 18 * q^50 + 6 * q^51 + 35 * q^52 + 14 * q^53 - 2 * q^54 + 2 * q^55 - 27 * q^56 - 10 * q^57 + 3 * q^58 + 12 * q^59 - 56 * q^60 - 18 * q^61 + 28 * q^62 + 9 * q^63 + 110 * q^64 - 28 * q^65 - 4 * q^66 + 37 * q^67 + 8 * q^68 - 5 * q^69 - 32 * q^70 + 17 * q^71 + 9 * q^72 + 4 * q^73 + q^74 + 21 * q^75 + 26 * q^76 + 18 * q^77 + 25 * q^78 - 12 * q^79 - 38 * q^80 - 5 * q^81 + 36 * q^82 + 8 * q^83 - 11 * q^84 + 41 * q^85 - 28 * q^86 + 12 * q^87 - 9 * q^88 - 14 * q^89 - 10 * q^90 + 35 * q^91 - 12 * q^92 - 18 * q^93 - 20 * q^94 + 7 * q^95 + 70 * q^96 + 15 * q^97 + 4 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.665890	−	1.15336i	−0.470856	−	0.815546i	0.528589	−	0.848878i	$-0.322721\pi$
$2$	−0.665890	−	1.15336i	−0.470856	−	0.815546i	−0.999444	+	0.0333322i	$0.989388\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.113180	−	0.196033i	0.0565900	−	0.0980167i
$5$	−3.31232			−1.48132			−0.740658	−	0.671882i	$-0.765486\pi$
$5$	−3.31232			−1.48132			−0.740658	+	0.671882i	$0.765486\pi$
$6$	0.665890	−	1.15336i	0.271849	−	0.470856i
$7$	0.767139	−	1.32872i	0.289951	−	0.502210i	−0.683847	−	0.729626i	$-0.739694\pi$
$7$	0.767139	−	1.32872i	0.289951	−	0.502210i	0.973798	+	0.227416i	$0.0730276\pi$
$8$	−2.96502			−1.04829
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.20564	+	3.82029i	0.697486	+	1.20808i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	0.226360			0.0653445
$13$	−1.88126	−	3.07585i	−0.521769	−	0.853087i
$13$	−1.88126	−	3.07585i	−0.521769	−	0.853087i
$14$	−2.04332			−0.546101
$15$	−1.65616	−	2.86856i	−0.427619	−	0.740658i
$16$	1.74802	+	3.02766i	0.437005	+	0.756915i
$17$	−2.98471	+	5.16968i	−0.723899	+	1.25383i	0.235526	+	0.971868i	$0.424319\pi$
$17$	−2.98471	+	5.16968i	−0.723899	+	1.25383i	−0.959425	+	0.281963i	$0.909015\pi$
$18$	1.33178			0.313904
$19$	−3.23053	+	5.59545i	−0.741135	+	1.28368i	0.210844	+	0.977520i	$0.432379\pi$
$19$	−3.23053	+	5.59545i	−0.741135	+	1.28368i	−0.951979	+	0.306164i	$0.900955\pi$
$20$	−0.374889	+	0.649326i	−0.0838276	+	0.145194i
$21$	1.53428			0.334807
$22$	0.665890	−	1.15336i	0.141968	−	0.245896i
$23$	−2.66033	−	4.60783i	−0.554718	−	0.960800i	−0.997925	−	0.0643806i	$-0.979493\pi$
$23$	−2.66033	−	4.60783i	−0.554718	−	0.960800i	0.443208	−	0.896419i	$-0.353840\pi$
$24$	−1.48251	−	2.56779i	−0.302616	−	0.524147i
$25$	5.97148			1.19430
$26$	−2.29483	+	4.21794i	−0.450054	+	0.827207i
$27$	−1.00000			−0.192450
$28$	−0.173649	−	0.300770i	−0.0328167	−	0.0568401i
$29$	0.0956916	+	0.165743i	0.0177695	+	0.0307777i	0.874773	−	0.484532i	$-0.161010\pi$
$29$	0.0956916	+	0.165743i	0.0177695	+	0.0307777i	−0.857004	+	0.515310i	$0.827677\pi$
$30$	−2.20564	+	3.82029i	−0.402694	+	0.697486i
$31$	−9.38922			−1.68635			−0.843177	−	0.537636i	$-0.819317\pi$
$31$	−9.38922			−1.68635			−0.843177	+	0.537636i	$0.819317\pi$
$32$	−0.637043	+	1.10339i	−0.112614	+	0.195054i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	7.94997			1.36341
$35$	−2.54101	+	4.40116i	−0.429509	+	0.743932i
$36$	0.113180	+	0.196033i	0.0188633	+	0.0326722i
$37$	−4.63312	−	8.02479i	−0.761680	−	1.31927i	−0.941984	−	0.335657i	$-0.891042\pi$
$37$	−4.63312	−	8.02479i	−0.761680	−	1.31927i	0.180305	−	0.983611i	$-0.442292\pi$
$38$	8.60472			1.39587
$39$	1.72313	−	3.16715i	0.275922	−	0.507149i
$40$	9.82111			1.55285
$41$	−0.125238	−	0.216919i	−0.0195589	−	0.0338770i	0.856080	−	0.516843i	$-0.172893\pi$
$41$	−0.125238	−	0.216919i	−0.0195589	−	0.0338770i	−0.875639	+	0.482966i	$0.839560\pi$
$42$	−1.02166	−	1.76957i	−0.157646	−	0.273050i
$43$	2.58307	−	4.47402i	0.393915	−	0.682281i	−0.599047	−	0.800714i	$-0.704454\pi$
$43$	2.58307	−	4.47402i	0.393915	−	0.682281i	0.992962	+	0.118433i	$0.0377870\pi$
$44$	0.226360			0.0341250
$45$	1.65616	−	2.86856i	0.246886	−	0.427619i
$46$	−3.54298	+	6.13662i	−0.522384	+	0.904796i
$47$	−4.36030			−0.636015			−0.318008	−	0.948088i	$-0.603014\pi$
$47$	−4.36030			−0.636015			−0.318008	+	0.948088i	$0.603014\pi$
$48$	−1.74802	+	3.02766i	−0.252305	+	0.437005i
$49$	2.32300	+	4.02355i	0.331857	+	0.574792i
$50$	−3.97635	−	6.88724i	−0.562341	−	0.974003i
$51$	−5.96943			−0.835887
$52$	−0.815891	+	0.0206660i	−0.113144	+	0.00286586i
$53$	7.13695			0.980335			0.490168	−	0.871628i	$-0.336936\pi$
$53$	7.13695			0.980335			0.490168	+	0.871628i	$0.336936\pi$
$54$	0.665890	+	1.15336i	0.0906162	+	0.156952i
$55$	−1.65616	−	2.86856i	−0.223317	−	0.386796i
$56$	−2.27458	+	3.93970i	−0.303954	+	0.526464i
$57$	−6.46106			−0.855789
$58$	0.127440	−	0.220733i	0.0167337	−	0.0289837i
$59$	4.90095	−	8.48870i	0.638050	−	1.10513i	−0.347810	−	0.937565i	$-0.613075\pi$
$59$	4.90095	−	8.48870i	0.638050	−	1.10513i	0.985860	−	0.167570i	$-0.0535920\pi$
$60$	−0.749777			−0.0967958
$61$	−4.23019	+	7.32691i	−0.541621	+	0.938114i	0.457191	+	0.889369i	$0.348856\pi$
$61$	−4.23019	+	7.32691i	−0.541621	+	0.938114i	−0.998811	+	0.0487457i	$0.984478\pi$
$62$	6.25219	+	10.8291i	0.794029	+	1.37530i
$63$	0.767139	+	1.32872i	0.0966504	+	0.167403i
$64$	8.68889			1.08611
$65$	6.23135	+	10.1882i	0.772904	+	1.26369i
$66$	1.33178			0.163931
$67$	3.40525	+	5.89807i	0.416018	+	0.720564i	0.995535	−	0.0943962i	$-0.0300920\pi$
$67$	3.40525	+	5.89807i	0.416018	+	0.720564i	−0.579517	+	0.814960i	$0.696759\pi$
$68$	0.675620	+	1.17021i	0.0819309	+	0.141909i
$69$	2.66033	−	4.60783i	0.320267	−	0.554718i
$70$	6.76814			0.808947
$71$	3.70598	−	6.41895i	0.439819	−	0.761790i	−0.557856	−	0.829938i	$-0.688376\pi$
$71$	3.70598	−	6.41895i	0.439819	−	0.761790i	0.997675	+	0.0681484i	$0.0217091\pi$
$72$	1.48251	−	2.56779i	0.174716	−	0.302616i
$73$	13.2687			1.55299			0.776495	−	0.630124i	$-0.216996\pi$
$73$	13.2687			1.55299			0.776495	+	0.630124i	$0.216996\pi$
$74$	−6.17030	+	10.6873i	−0.717282	+	1.24237i
$75$	2.98574	+	5.17145i	0.344764	+	0.597148i
$76$	0.731263	+	1.26658i	0.0838816	+	0.145287i
$77$	1.53428			0.174847
$78$	−4.80026	+	0.121588i	−0.543523	+	0.0137671i
$79$	−6.63833			−0.746870			−0.373435	−	0.927656i	$-0.621820\pi$
$79$	−6.63833			−0.746870			−0.373435	+	0.927656i	$0.621820\pi$
$80$	−5.79001	−	10.0286i	−0.647343	−	1.12123i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.166790	+	0.288888i	−0.0184188	+	0.0319023i
$83$	−9.84383			−1.08050			−0.540250	−	0.841504i	$-0.681670\pi$
$83$	−9.84383			−1.08050			−0.540250	+	0.841504i	$0.681670\pi$
$84$	0.173649	−	0.300770i	0.0189467	−	0.0328167i
$85$	9.88633	−	17.1236i	1.07232	−	1.85732i
$86$	−6.88018			−0.741909
$87$	−0.0956916	+	0.165743i	−0.0102592	+	0.0177695i
$88$	−1.48251	−	2.56779i	−0.158036	−	0.273727i
$89$	−2.68721	−	4.65439i	−0.284844	−	0.493364i	0.687728	−	0.725969i	$-0.258608\pi$
$89$	−2.68721	−	4.65439i	−0.284844	−	0.493364i	−0.972571	+	0.232605i	$0.925275\pi$
$90$	−4.41129			−0.464991
$91$	−5.53014	+	0.140075i	−0.579717	+	0.0146839i
$92$	−1.20439			−0.125566
$93$	−4.69461	−	8.13131i	−0.486809	−	0.843177i
$94$	2.90348	+	5.02898i	0.299471	+	0.518700i
$95$	10.7006	−	18.5339i	1.09785	−	1.90154i
$96$	−1.27409			−0.130036
$97$	3.62188	−	6.27329i	0.367747	−	0.636956i	−0.621466	−	0.783441i	$-0.713463\pi$
$97$	3.62188	−	6.27329i	0.367747	−	0.636956i	0.989213	+	0.146485i	$0.0467961\pi$
$98$	3.09372	−	5.35848i	0.312513	−	0.541289i
$99$	−1.00000			−0.100504
$100$	0.675852	−	1.17061i	0.0675852	−	0.117061i
$101$	−6.95194	−	12.0411i	−0.691744	−	1.19814i	−0.971266	−	0.237996i	$-0.923509\pi$
$101$	−6.95194	−	12.0411i	−0.691744	−	1.19814i	0.279522	−	0.960139i	$-0.409824\pi$
$102$	3.97498	+	6.88488i	0.393582	+	0.681704i
$103$	7.38140			0.727311			0.363655	−	0.931534i	$-0.381529\pi$
$103$	7.38140			0.727311			0.363655	+	0.931534i	$0.381529\pi$
$104$	5.57799	+	9.11996i	0.546967	+	0.894286i
$105$	−5.08202			−0.495955
$106$	−4.75243	−	8.23144i	−0.461596	−	0.799508i
$107$	−4.56684	−	7.91001i	−0.441493	−	0.764689i	0.556307	−	0.830977i	$-0.312218\pi$
$107$	−4.56684	−	7.91001i	−0.441493	−	0.764689i	−0.997801	+	0.0662876i	$0.978885\pi$
$108$	−0.113180	+	0.196033i	−0.0108907	+	0.0188633i
$109$	−17.4363			−1.67009			−0.835046	−	0.550180i	$-0.814559\pi$
$109$	−17.4363			−1.67009			−0.835046	+	0.550180i	$0.814559\pi$
$110$	−2.20564	+	3.82029i	−0.210300	+	0.364250i
$111$	4.63312	−	8.02479i	0.439756	−	0.761680i
$112$	5.36390			0.506841
$113$	7.79112	−	13.4946i	0.732927	−	1.26947i	−0.222700	−	0.974887i	$-0.571487\pi$
$113$	7.79112	−	13.4946i	0.732927	−	1.26947i	0.955627	−	0.294580i	$-0.0951797\pi$
$114$	4.30236	+	7.45191i	0.402953	+	0.697935i
$115$	8.81188	+	15.2626i	0.821712	+	1.42325i
$116$	0.0433215			0.00402230
$117$	3.60440	−	0.0912972i	0.333226	−	0.00844042i
$118$	−13.0540			−1.20172
$119$	4.57938	+	7.93172i	0.419791	+	0.727099i
$120$	4.91056	+	8.50533i	0.448270	+	0.776427i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	11.2674			1.02010
$123$	0.125238	−	0.216919i	0.0112923	−	0.0195589i
$124$	−1.06267	+	1.84060i	−0.0954307	+	0.165291i
$125$	−3.21785			−0.287813
$126$	1.02166	−	1.76957i	0.0910168	−	0.157646i
$127$	4.89422	+	8.47704i	0.434292	+	0.752216i	0.997238	−	0.0742783i	$-0.0236653\pi$
$127$	4.89422	+	8.47704i	0.434292	+	0.752216i	−0.562946	+	0.826494i	$0.690332\pi$
$128$	−4.51176	−	7.81460i	−0.398787	−	0.690719i
$129$	5.16615			0.454854
$130$	7.60123	−	13.9712i	0.666672	−	1.22535i
$131$	−5.90938			−0.516305			−0.258152	−	0.966104i	$-0.583114\pi$
$131$	−5.90938			−0.516305			−0.258152	+	0.966104i	$0.583114\pi$
$132$	0.113180	+	0.196033i	0.00985105	+	0.0170625i
$133$	4.95653	+	8.58497i	0.429786	+	0.744411i
$134$	4.53505	−	7.85494i	0.391769	−	0.678563i
$135$	3.31232			0.285079
$136$	8.84975	−	15.3282i	0.758860	−	1.31438i
$137$	0.509389	−	0.882288i	0.0435200	−	0.0753789i	−0.843445	−	0.537216i	$-0.819476\pi$
$137$	0.509389	−	0.882288i	0.0435200	−	0.0753789i	0.886965	+	0.461837i	$0.152809\pi$
$138$	−7.08596			−0.603197
$139$	−2.56219	+	4.43785i	−0.217322	+	0.376414i	−0.953989	−	0.299843i	$-0.903066\pi$
$139$	−2.56219	+	4.43785i	−0.217322	+	0.376414i	0.736666	+	0.676257i	$0.236399\pi$
$140$	0.575183	+	0.996246i	0.0486118	+	0.0841982i
$141$	−2.18015	−	3.77613i	−0.183602	−	0.318008i
$142$	−9.87112			−0.828366
$143$	1.72313	−	3.16715i	0.144096	−	0.264850i
$144$	−3.49604			−0.291337
$145$	−0.316962	−	0.548994i	−0.0263222	−	0.0455914i
$146$	−8.83553	−	15.3036i	−0.731234	−	1.26653i
$147$	−2.32300	+	4.02355i	−0.191597	+	0.331857i
$148$	−2.09750			−0.172414
$149$	−6.22726	+	10.7859i	−0.510157	+	0.883618i	0.489774	+	0.871850i	$0.337079\pi$
$149$	−6.22726	+	10.7859i	−0.510157	+	0.883618i	−0.999931	+	0.0117682i	$0.996254\pi$
$150$	3.97635	−	6.88724i	0.324668	−	0.562341i
$151$	11.4057			0.928182			0.464091	−	0.885787i	$-0.346381\pi$
$151$	11.4057			0.928182			0.464091	+	0.885787i	$0.346381\pi$
$152$	9.57860	−	16.5906i	0.776927	−	1.34568i
$153$	−2.98471	−	5.16968i	−0.241300	−	0.417944i
$154$	−1.02166	−	1.76957i	−0.0823278	−	0.142596i
$155$	31.1001			2.49802
$156$	−0.425843	−	0.696249i	−0.0340947	−	0.0557445i
$157$	−24.0934			−1.92286			−0.961430	−	0.275049i	$-0.911306\pi$
$157$	−24.0934			−1.92286			−0.961430	+	0.275049i	$0.911306\pi$
$158$	4.42040	+	7.65636i	0.351668	+	0.609107i
$159$	3.56847	+	6.18078i	0.282998	+	0.490168i
$160$	2.11009	−	3.65479i	0.166817	−	0.288936i
$161$	−8.16338			−0.643365
$162$	−0.665890	+	1.15336i	−0.0523173	+	0.0906162i
$163$	−1.03556	+	1.79365i	−0.0811115	+	0.140489i	−0.903728	−	0.428108i	$-0.859180\pi$
$163$	−1.03556	+	1.79365i	−0.0811115	+	0.140489i	0.822616	+	0.568597i	$0.192514\pi$
$164$	−0.0566977			−0.00442735
$165$	1.65616	−	2.86856i	0.128932	−	0.223317i
$166$	6.55491	+	11.3534i	0.508760	+	0.881198i
$167$	−0.218960	−	0.379249i	−0.0169436	−	0.0293472i	0.857429	−	0.514602i	$-0.172060\pi$
$167$	−0.218960	−	0.379249i	−0.0169436	−	0.0293472i	−0.874373	+	0.485255i	$0.838727\pi$
$168$	−4.54917			−0.350976
$169$	−5.92170	+	11.5730i	−0.455515	+	0.890228i
$170$	−26.3329			−2.01964
$171$	−3.23053	−	5.59545i	−0.247045	−	0.427894i
$172$	−0.584705	−	1.01274i	−0.0445833	−	0.0772206i
$173$	−1.09695	+	1.89997i	−0.0833995	+	0.144452i	−0.904708	−	0.426032i	$-0.859911\pi$
$173$	−1.09695	+	1.89997i	−0.0833995	+	0.144452i	0.821309	+	0.570484i	$0.193244\pi$
$174$	0.254881			0.0193224
$175$	4.58095	−	7.93444i	0.346288	−	0.599788i
$176$	−1.74802	+	3.02766i	−0.131762	+	0.228219i
$177$	9.80191			0.736757
$178$	−3.57878	+	6.19862i	−0.268241	+	0.464606i
$179$	9.30732	+	16.1208i	0.695662	+	1.20492i	0.969957	+	0.243276i	$0.0782222\pi$
$179$	9.30732	+	16.1208i	0.695662	+	1.20492i	−0.274295	+	0.961646i	$0.588444\pi$
$180$	−0.374889	−	0.649326i	−0.0279425	−	0.0483979i
$181$	−13.4000			−0.996015			−0.498007	−	0.867173i	$-0.665935\pi$
$181$	−13.4000			−0.996015			−0.498007	+	0.867173i	$0.665935\pi$
$182$	3.84403	+	6.28495i	0.284938	+	0.465871i
$183$	−8.46038			−0.625410
$184$	7.88795	+	13.6623i	0.581507	+	1.00720i
$185$	15.3464	+	26.5807i	1.12829	+	1.95425i
$186$	−6.25219	+	10.8291i	−0.458433	+	0.794029i
$187$	−5.96943			−0.436528
$188$	−0.493499	+	0.854765i	−0.0359921	+	0.0623401i
$189$	−0.767139	+	1.32872i	−0.0558011	+	0.0966504i
$190$	−28.5016			−2.06772
$191$	−3.06177	+	5.30315i	−0.221542	+	0.383722i	−0.955276	−	0.295714i	$-0.904442\pi$
$191$	−3.06177	+	5.30315i	−0.221542	+	0.383722i	0.733734	+	0.679436i	$0.237776\pi$
$192$	4.34444	+	7.52480i	0.313533	+	0.543055i
$193$	−9.26563	−	16.0485i	−0.666954	−	1.15520i	−0.978751	−	0.205050i	$-0.934264\pi$
$193$	−9.26563	−	16.0485i	−0.666954	−	1.15520i	0.311797	−	0.950149i	$-0.399069\pi$
$194$	−9.64711			−0.692622
$195$	−5.70757	+	10.4906i	−0.408727	+	0.751248i
$196$	1.05167			0.0751190
$197$	9.35203	+	16.1982i	0.666305	+	1.15407i	0.978930	+	0.204197i	$0.0654583\pi$
$197$	9.35203	+	16.1982i	0.666305	+	1.15407i	−0.312625	+	0.949877i	$0.601208\pi$
$198$	0.665890	+	1.15336i	0.0473228	+	0.0819654i
$199$	6.67688	−	11.5647i	0.473311	−	0.819799i	−0.526222	−	0.850347i	$-0.676392\pi$
$199$	6.67688	−	11.5647i	0.473311	−	0.819799i	0.999533	+	0.0305480i	$0.00972525\pi$
$200$	−17.7056			−1.25197
$201$	−3.40525	+	5.89807i	−0.240188	+	0.416018i
$202$	−9.25846	+	16.0361i	−0.651423	+	1.12830i
$203$	0.293635			0.0206091
$204$	−0.675620	+	1.17021i	−0.0473028	+	0.0819309i
$205$	0.414829	+	0.718504i	0.0289729	+	0.0501825i
$206$	−4.91520	−	8.51338i	−0.342458	−	0.593155i
$207$	5.32067			0.369812
$208$	6.02414	−	11.0725i	0.417699	−	0.767738i
$209$	−6.46106			−0.446921
$210$	3.38407	+	5.86138i	0.233523	+	0.404474i
$211$	0.798547	+	1.38312i	0.0549743	+	0.0952182i	0.892203	−	0.451635i	$-0.149159\pi$
$211$	0.798547	+	1.38312i	0.0549743	+	0.0952182i	−0.837229	+	0.546853i	$0.815826\pi$
$212$	0.807760	−	1.39908i	0.0554772	−	0.0960892i
$213$	7.41197			0.507860
$214$	−6.08204	+	10.5344i	−0.415759	+	0.720116i
$215$	−8.55598	+	14.8194i	−0.583513	+	1.01067i
$216$	2.96502			0.201744
$217$	−7.20284	+	12.4757i	−0.488960	+	0.846904i
$218$	11.6106	+	20.1102i	0.786372	+	1.36204i
$219$	6.63437	+	11.4911i	0.448309	+	0.776495i
$220$	−0.749777			−0.0505500
$221$	21.5162	−	0.544992i	1.44733	−	0.0366601i
$222$	−12.3406			−0.828246
$223$	3.95402	+	6.84857i	0.264781	+	0.458614i	0.967506	−	0.252847i	$-0.0813670\pi$
$223$	3.95402	+	6.84857i	0.264781	+	0.458614i	−0.702725	+	0.711461i	$0.748034\pi$
$224$	0.977401	+	1.69291i	0.0653053	+	0.113112i
$225$	−2.98574	+	5.17145i	−0.199049	+	0.344764i
$226$	−20.7521			−1.38041
$227$	−7.44129	+	12.8887i	−0.493896	+	0.855453i	−0.999975	−	0.00703406i	$-0.997761\pi$
$227$	−7.44129	+	12.8887i	−0.493896	+	0.855453i	0.506079	+	0.862487i	$0.331094\pi$
$228$	−0.731263	+	1.26658i	−0.0484291	+	0.0838816i
$229$	−10.5735			−0.698716			−0.349358	−	0.936989i	$-0.613600\pi$
$229$	−10.5735			−0.698716			−0.349358	+	0.936989i	$0.613600\pi$
$230$	11.7355	−	20.3265i	0.773816	−	1.34029i
$231$	0.767139	+	1.32872i	0.0504740	+	0.0874236i
$232$	−0.283728	−	0.491431i	−0.0186277	−	0.0322640i
$233$	−2.70114			−0.176958			−0.0884789	−	0.996078i	$-0.528201\pi$
$233$	−2.70114			−0.176958			−0.0884789	+	0.996078i	$0.528201\pi$
$234$	−2.50543	−	4.09636i	−0.163785	−	0.267787i
$235$	14.4427			0.942139
$236$	−1.10938	−	1.92150i	−0.0722145	−	0.125079i
$237$	−3.31916	−	5.74896i	−0.215603	−	0.373435i
$238$	6.09873	−	10.5633i	0.395322	−	0.684718i
$239$	−1.21613			−0.0786647			−0.0393323	−	0.999226i	$-0.512523\pi$
$239$	−1.21613			−0.0786647			−0.0393323	+	0.999226i	$0.512523\pi$
$240$	5.79001	−	10.0286i	0.373743	−	0.647343i
$241$	1.73319	−	3.00197i	0.111644	−	0.193374i	−0.804789	−	0.593561i	$-0.797722\pi$
$241$	1.73319	−	3.00197i	0.111644	−	0.193374i	0.916433	+	0.400187i	$0.131055\pi$
$242$	1.33178			0.0856101
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	0.957546	+	1.65852i	0.0613006	+	0.106176i
$245$	−7.69451	−	13.3273i	−0.491584	−	0.851449i
$246$	−0.333579			−0.0212682
$247$	23.2882	−	0.589877i	1.48179	−	0.0375330i
$248$	27.8393			1.76780
$249$	−4.92192	−	8.52501i	−0.311914	−	0.540250i
$250$	2.14274	+	3.71133i	0.135519	+	0.234725i
$251$	−11.7325	+	20.3213i	−0.740551	+	1.28267i	0.211694	+	0.977336i	$0.432102\pi$
$251$	−11.7325	+	20.3213i	−0.740551	+	1.28267i	−0.952245	+	0.305335i	$0.901231\pi$
$252$	0.347299			0.0218778
$253$	2.66033	−	4.60783i	0.167254	−	0.289692i
$254$	6.51803	−	11.2896i	0.408978	−	0.708370i
$255$	19.7727			1.23821
$256$	2.68021	−	4.64226i	0.167513	−	0.290141i
$257$	−5.79581	−	10.0386i	−0.361533	−	0.626193i	0.626680	−	0.779276i	$-0.284413\pi$
$257$	−5.79581	−	10.0386i	−0.361533	−	0.626193i	−0.988213	+	0.153083i	$0.951080\pi$
$258$	−3.44009	−	5.95841i	−0.214171	−	0.370954i
$259$	−14.2170			−0.883400
$260$	2.70249	−	0.0684525i	0.167601	−	0.00424524i
$261$	−0.191383			−0.0118463
$262$	3.93500	+	6.81562i	0.243105	+	0.421070i
$263$	−4.24351	−	7.34997i	−0.261666	−	0.453219i	0.705019	−	0.709189i	$-0.250939\pi$
$263$	−4.24351	−	7.34997i	−0.261666	−	0.453219i	−0.966685	+	0.255970i	$0.917605\pi$
$264$	1.48251	−	2.56779i	0.0912423	−	0.158036i
$265$	−23.6399			−1.45219
$266$	6.60102	−	11.4333i	0.404734	−	0.701020i
$267$	2.68721	−	4.65439i	0.164455	−	0.284844i
$268$	1.54163			0.0941698
$269$	4.66801	−	8.08523i	0.284614	−	0.492965i	−0.687902	−	0.725804i	$-0.741468\pi$
$269$	4.66801	−	8.08523i	0.284614	−	0.492965i	0.972515	+	0.232838i	$0.0748013\pi$
$270$	−2.20564	−	3.82029i	−0.134231	−	0.232495i
$271$	9.70866	+	16.8159i	0.589759	+	1.02149i	0.994264	+	0.106957i	$0.0341107\pi$
$271$	9.70866	+	16.8159i	0.589759	+	1.02149i	−0.404504	+	0.914536i	$0.632556\pi$
$272$	−20.8694			−1.26539
$273$	−2.88638	−	4.71921i	−0.174692	−	0.285619i
$274$	−1.35679			−0.0819666
$275$	2.98574	+	5.17145i	0.180047	+	0.311850i
$276$	−0.602193	−	1.04303i	−0.0362478	−	0.0627830i
$277$	−6.68353	+	11.5762i	−0.401574	+	0.695547i	−0.993916	−	0.110140i	$-0.964870\pi$
$277$	−6.68353	+	11.5762i	−0.401574	+	0.695547i	0.592342	+	0.805687i	$0.298204\pi$
$278$	6.82456			0.409310
$279$	4.69461	−	8.13131i	0.281059	−	0.486809i
$280$	7.53416	−	13.0495i	0.450252	−	0.779859i
$281$	−5.90481			−0.352252			−0.176126	−	0.984368i	$-0.556357\pi$
$281$	−5.90481			−0.352252			−0.176126	+	0.984368i	$0.556357\pi$
$282$	−2.90348	+	5.02898i	−0.172900	+	0.299471i
$283$	−11.7998	−	20.4378i	−0.701425	−	1.21490i	−0.967966	−	0.251080i	$-0.919214\pi$
$283$	−11.7998	−	20.4378i	−0.701425	−	1.21490i	0.266541	−	0.963824i	$-0.414119\pi$
$284$	−0.838886	−	1.45299i	−0.0497787	−	0.0862193i
$285$	21.4011			1.26769
$286$	−4.80026	+	0.121588i	−0.283846	+	0.00718964i
$287$	−0.384300			−0.0226845
$288$	−0.637043	−	1.10339i	−0.0375381	−	0.0650179i
$289$	−9.31704	−	16.1376i	−0.548061	−	0.949269i
$290$	−0.422123	+	0.731139i	−0.0247879	+	0.0429340i
$291$	7.24377			0.424637
$292$	1.50176	−	2.60112i	0.0878836	−	0.152219i
$293$	−15.3754	+	26.6310i	−0.898243	+	1.55580i	−0.0685036	+	0.997651i	$0.521822\pi$
$293$	−15.3754	+	26.6310i	−0.898243	+	1.55580i	−0.829739	+	0.558151i	$0.811511\pi$
$294$	6.18744			0.360859
$295$	−16.2335	+	28.1173i	−0.945153	+	1.63705i
$296$	13.7373	+	23.7937i	0.798464	+	1.38298i
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$	16.5867			0.960841
$299$	−9.16821	+	16.8513i	−0.530211	+	0.974538i
$300$	1.35170			0.0780406
$301$	−3.96315	−	6.86438i	−0.228432	−	0.395657i
$302$	−7.59494	−	13.1548i	−0.437040	−	0.756975i
$303$	6.95194	−	12.0411i	0.399378	−	0.691744i
$304$	−22.5881			−1.29552
$305$	14.0118	−	24.2691i	0.802311	−	1.38964i
$306$	−3.97498	+	6.88488i	−0.227235	+	0.393582i
$307$	−16.4893			−0.941094			−0.470547	−	0.882375i	$-0.655943\pi$
$307$	−16.4893			−0.941094			−0.470547	+	0.882375i	$0.655943\pi$
$308$	0.173649	−	0.300770i	0.00989460	−	0.0171379i
$309$	3.69070	+	6.39248i	0.209956	+	0.363655i
$310$	−20.7093	−	35.8695i	−1.17621	−	2.03725i
$311$	18.2912			1.03720			0.518600	−	0.855017i	$-0.326453\pi$
$311$	18.2912			1.03720			0.518600	+	0.855017i	$0.326453\pi$
$312$	−5.10913	+	9.39066i	−0.289247	+	0.531642i
$313$	1.48698			0.0840490			0.0420245	−	0.999117i	$-0.486619\pi$
$313$	1.48698			0.0840490			0.0420245	+	0.999117i	$0.486619\pi$
$314$	16.0435	+	27.7882i	0.905390	+	1.56818i
$315$	−2.54101	−	4.40116i	−0.143170	−	0.247977i
$316$	−0.751326	+	1.30133i	−0.0422654	+	0.0732058i
$317$	18.9331			1.06339			0.531695	−	0.846936i	$-0.321555\pi$
$317$	18.9331			1.06339			0.531695	+	0.846936i	$0.321555\pi$
$318$	4.75243	−	8.23144i	0.266503	−	0.461596i
$319$	−0.0956916	+	0.165743i	−0.00535770	+	0.00927982i
$320$	−28.7804			−1.60887
$321$	4.56684	−	7.91001i	0.254896	−	0.441493i
$322$	5.43592	+	9.41528i	0.302932	+	0.524693i
$323$	−19.2844	−	33.4016i	−1.07301	−	1.85852i
$324$	−0.226360			−0.0125756
$325$	−11.2339	−	18.3674i	−0.623146	−	1.01884i
$326$	2.75828			0.152767
$327$	−8.71813	−	15.1003i	−0.482114	−	0.835046i
$328$	0.371334	+	0.643169i	0.0205035	+	0.0355130i
$329$	−3.34496	+	5.79363i	−0.184413	+	0.319413i
$330$	−4.41129			−0.242833
$331$	3.78998	−	6.56443i	0.208316	−	0.360814i	−0.742868	−	0.669438i	$-0.766535\pi$
$331$	3.78998	−	6.56443i	0.208316	−	0.360814i	0.951184	+	0.308624i	$0.0998684\pi$
$332$	−1.11412	+	1.92972i	−0.0611455	+	0.105907i
$333$	9.26623			0.507786
$334$	−0.291606	+	0.505077i	−0.0159560	+	0.0276366i
$335$	−11.2793	−	19.5363i	−0.616254	−	1.06738i
$336$	2.68195	+	4.64527i	0.146312	+	0.253420i
$337$	−21.4213			−1.16689			−0.583446	−	0.812152i	$-0.698296\pi$
$337$	−21.4213			−1.16689			−0.583446	+	0.812152i	$0.698296\pi$
$338$	17.2909	−	0.876501i	0.940504	−	0.0476754i
$339$	15.5822			0.846311
$340$	−2.23787	−	3.87610i	−0.121366	−	0.210211i
$341$	−4.69461	−	8.13131i	−0.254227	−	0.440335i
$342$	−4.30236	+	7.45191i	−0.232645	+	0.402953i
$343$	17.8682			0.964791
$344$	−7.65888	+	13.2656i	−0.412939	+	0.715231i
$345$	−8.81188	+	15.2626i	−0.474416	+	0.821712i
$346$	2.92179			0.157077
$347$	1.66215	−	2.87893i	0.0892289	−	0.154549i	−0.817957	−	0.575280i	$-0.804893\pi$
$347$	1.66215	−	2.87893i	0.0892289	−	0.154549i	0.907185	+	0.420731i	$0.138226\pi$
$348$	0.0216608	+	0.0375175i	0.00116114	+	0.00201115i
$349$	7.86429	+	13.6213i	0.420966	+	0.729134i	0.996034	−	0.0889713i	$-0.0283579\pi$
$349$	7.86429	+	13.6213i	0.420966	+	0.729134i	−0.575068	+	0.818105i	$0.695025\pi$
$350$	−12.2017			−0.652206
$351$	1.88126	+	3.07585i	0.100414	+	0.164177i
$352$	−1.27409			−0.0679090
$353$	10.8523	+	18.7967i	0.577610	+	1.00045i	0.995753	+	0.0920682i	$0.0293478\pi$
$353$	10.8523	+	18.7967i	0.577610	+	1.00045i	−0.418143	+	0.908381i	$0.637319\pi$
$354$	−6.52700	−	11.3051i	−0.346906	−	0.600859i
$355$	−12.2754	+	21.2616i	−0.651511	+	1.12845i
$356$	−1.21655			−0.0644772
$357$	−4.57938	+	7.93172i	−0.242366	+	0.419791i
$358$	12.3953	−	21.4693i	0.655113	−	1.13469i
$359$	22.8129			1.20402			0.602008	−	0.798490i	$-0.294367\pi$
$359$	22.8129			1.20402			0.602008	+	0.798490i	$0.294367\pi$
$360$	−4.91056	+	8.50533i	−0.258809	+	0.448270i
$361$	−11.3727	−	19.6981i	−0.598562	−	1.03674i
$362$	8.92294	+	15.4550i	0.468979	+	0.812296i
$363$	−1.00000			−0.0524864
$364$	−0.598442	+	1.09995i	−0.0313669	+	0.0576529i
$365$	−43.9504			−2.30047
$366$	5.63369	+	9.75783i	0.294478	+	0.510050i
$367$	1.42601	+	2.46993i	0.0744373	+	0.128929i	0.900841	−	0.434148i	$-0.142951\pi$
$367$	1.42601	+	2.46993i	0.0744373	+	0.128929i	−0.826404	+	0.563077i	$0.809617\pi$
$368$	9.30064	−	16.1092i	0.484829	−	0.839749i
$369$	0.250476			0.0130393
$370$	20.4380	−	35.3997i	1.06252	−	1.84034i
$371$	5.47503	−	9.48303i	0.284249	−	0.492334i
$372$	−2.12534			−0.110194
$373$	15.7325	−	27.2495i	0.814597	−	1.41092i	−0.0950195	−	0.995475i	$-0.530291\pi$
$373$	15.7325	−	27.2495i	0.814597	−	1.41092i	0.909617	−	0.415448i	$-0.136375\pi$
$374$	3.97498	+	6.88488i	0.205542	+	0.356008i
$375$	−1.60893	−	2.78674i	−0.0830846	−	0.143907i
$376$	12.9284			0.666731
$377$	0.329779	−	0.606139i	0.0169845	−	0.0312177i
$378$	2.04332			0.105097
$379$	7.04360	+	12.1999i	0.361805	+	0.626665i	0.988258	−	0.152794i	$-0.0488272\pi$
$379$	7.04360	+	12.1999i	0.361805	+	0.626665i	−0.626453	+	0.779459i	$0.715494\pi$
$380$	−2.42218	−	4.19534i	−0.124255	−	0.215216i
$381$	−4.89422	+	8.47704i	−0.250739	+	0.434292i
$382$	8.15522			0.417257
$383$	19.0267	−	32.9551i	0.972216	−	1.68393i	0.283386	−	0.959006i	$-0.408542\pi$
$383$	19.0267	−	32.9551i	0.972216	−	1.68393i	0.688831	−	0.724922i	$-0.258124\pi$
$384$	4.51176	−	7.81460i	0.230240	−	0.398787i
$385$	−5.08202			−0.259004
$386$	−12.3398	+	21.3731i	−0.628079	+	1.08786i
$387$	2.58307	+	4.47402i	0.131305	+	0.227427i
$388$	−0.819849	−	1.42002i	−0.0416215	−	0.0720906i
$389$	−30.5899			−1.55097			−0.775485	−	0.631366i	$-0.782495\pi$
$389$	−30.5899			−1.55097			−0.775485	+	0.631366i	$0.782495\pi$
$390$	15.9000	−	0.402738i	0.805129	−	0.0203934i
$391$	31.7613			1.60624
$392$	−6.88774	−	11.9299i	−0.347883	−	0.602552i
$393$	−2.95469	−	5.11767i	−0.149044	−	0.258152i
$394$	12.4549	−	21.5724i	0.627466	−	1.08680i
$395$	21.9883			1.10635
$396$	−0.113180	+	0.196033i	−0.00568751	+	0.00985105i
$397$	4.13070	−	7.15457i	0.207314	−	0.359078i	−0.743554	−	0.668676i	$-0.766861\pi$
$397$	4.13070	−	7.15457i	0.207314	−	0.359078i	0.950867	+	0.309598i	$0.100195\pi$
$398$	−17.7843			−0.891445
$399$	−4.95653	+	8.58497i	−0.248137	+	0.429786i
$400$	10.4383	+	18.0796i	0.521913	+	0.903981i
$401$	0.373736	+	0.647330i	0.0186635	+	0.0323261i	0.875206	−	0.483750i	$-0.160726\pi$
$401$	0.373736	+	0.647330i	0.0186635	+	0.0323261i	−0.856543	+	0.516076i	$0.827392\pi$
$402$	9.07010			0.452376
$403$	17.6636	+	28.8798i	0.879887	+	1.43861i
$404$	−3.14728			−0.156583
$405$	1.65616	+	2.86856i	0.0822953	+	0.142540i
$406$	−0.195529	−	0.338666i	−0.00970393	−	0.0168077i
$407$	4.63312	−	8.02479i	0.229655	−	0.397774i
$408$	17.6995			0.876256
$409$	15.9566	−	27.6376i	0.789003	−	1.36659i	−0.137575	−	0.990491i	$-0.543931\pi$
$409$	15.9566	−	27.6376i	0.789003	−	1.36659i	0.926578	−	0.376102i	$-0.122736\pi$
$410$	0.552461	−	0.956890i	0.0272841	−	0.0472574i
$411$	1.01878			0.0502526
$412$	0.835426	−	1.44700i	0.0411585	−	0.0712886i
$413$	−7.51942	−	13.0240i	−0.370007	−	0.640870i
$414$	−3.54298	−	6.13662i	−0.174128	−	0.301599i
$415$	32.6059			1.60056
$416$	4.59231	−	0.116320i	0.225157	−	0.00570308i
$417$	−5.12439			−0.250942
$418$	4.30236	+	7.45191i	0.210435	+	0.364485i
$419$	−2.69739	−	4.67202i	−0.131776	−	0.228243i	0.792585	−	0.609761i	$-0.208735\pi$
$419$	−2.69739	−	4.67202i	−0.131776	−	0.228243i	−0.924361	+	0.381518i	$0.875401\pi$
$420$	−0.575183	+	0.996246i	−0.0280661	+	0.0486118i
$421$	−34.9075			−1.70129			−0.850644	−	0.525742i	$-0.823788\pi$
$421$	−34.9075			−1.70129			−0.850644	+	0.525742i	$0.823788\pi$
$422$	1.06349	−	1.84202i	0.0517699	−	0.0896681i
$423$	2.18015	−	3.77613i	0.106003	−	0.183602i
$424$	−21.1612			−1.02768
$425$	−17.8232	+	30.8706i	−0.864550	+	1.49744i
$426$	−4.93556	−	8.54864i	−0.239129	−	0.414183i
$427$	6.49029	+	11.2415i	0.314087	+	0.544015i
$428$	−2.06750			−0.0999364
$429$	3.60440	−	0.0912972i	0.174022	−	0.00440787i
$430$	22.7894			1.09900
$431$	10.7617	+	18.6397i	0.518371	+	0.897844i	0.999772	+	0.0213442i	$0.00679459\pi$
$431$	10.7617	+	18.6397i	0.518371	+	0.897844i	−0.481401	+	0.876500i	$0.659872\pi$
$432$	−1.74802	−	3.02766i	−0.0841017	−	0.145668i
$433$	0.0945017	−	0.163682i	0.00454146	−	0.00786604i	−0.863746	−	0.503928i	$-0.831888\pi$
$433$	0.0945017	−	0.163682i	0.00454146	−	0.00786604i	0.868287	+	0.496062i	$0.165221\pi$
$434$	19.1852			0.920919
$435$	0.316962	−	0.548994i	0.0151971	−	0.0263222i
$436$	−1.97344	+	3.41809i	−0.0945104	+	0.163697i
$437$	34.3772			1.64448
$438$	8.83553	−	15.3036i	0.422178	−	0.731234i
$439$	4.95202	+	8.57715i	0.236347	+	0.409365i	0.959663	−	0.281152i	$-0.0907164\pi$
$439$	4.95202	+	8.57715i	0.236347	+	0.409365i	−0.723316	+	0.690517i	$0.757383\pi$
$440$	4.91056	+	8.50533i	0.234102	+	0.405476i
$441$	−4.64599			−0.221238
$442$	−14.9560	−	24.4529i	−0.711384	−	1.16311i
$443$	−29.5128			−1.40220			−0.701099	−	0.713064i	$-0.747307\pi$
$443$	−29.5128			−1.40220			−0.701099	+	0.713064i	$0.747307\pi$
$444$	−1.04875	−	1.81649i	−0.0497716	−	0.0862069i
$445$	8.90091	+	15.4168i	0.421944	+	0.730828i
$446$	5.26589	−	9.12079i	0.249347	−	0.431882i
$447$	−12.4545			−0.589078
$448$	6.66558	−	11.5451i	0.314919	−	0.545456i
$449$	−6.87594	+	11.9095i	−0.324496	+	0.562043i	−0.981410	−	0.191922i	$-0.938528\pi$
$449$	−6.87594	+	11.9095i	−0.324496	+	0.562043i	0.656915	+	0.753965i	$0.271861\pi$
$450$	7.95270			0.374894
$451$	0.125238	−	0.216919i	0.00589723	−	0.0102143i
$452$	−1.76360	−	3.05464i	−0.0829526	−	0.143678i
$453$	5.70285	+	9.87762i	0.267943	+	0.464091i
$454$	19.8203			0.930215
$455$	18.3176	−	0.463974i	0.858743	−	0.0217514i
$456$	19.1572			0.897118
$457$	−5.47947	−	9.49072i	−0.256319	−	0.443957i	0.708934	−	0.705275i	$-0.249176\pi$
$457$	−5.47947	−	9.49072i	−0.256319	−	0.443957i	−0.965253	+	0.261318i	$0.915843\pi$
$458$	7.04079	+	12.1950i	0.328995	+	0.569835i
$459$	2.98471	−	5.16968i	0.139315	−	0.241300i
$460$	3.98931			0.186003
$461$	−5.54454	+	9.60343i	−0.258235	+	0.447276i	−0.965769	−	0.259403i	$-0.916474\pi$
$461$	−5.54454	+	9.60343i	−0.258235	+	0.447276i	0.707534	+	0.706679i	$0.249808\pi$
$462$	1.02166	−	1.76957i	0.0475320	−	0.0823278i
$463$	−34.5360			−1.60502			−0.802512	−	0.596636i	$-0.796504\pi$
$463$	−34.5360			−1.60502			−0.802512	+	0.596636i	$0.796504\pi$
$464$	−0.334542	+	0.579444i	−0.0155307	+	0.0269000i
$465$	15.5501	+	26.9335i	0.721117	+	1.24901i
$466$	1.79867	+	3.11538i	0.0833216	+	0.144317i
$467$	16.9674			0.785157			0.392578	−	0.919719i	$-0.371583\pi$
$467$	16.9674			0.785157			0.392578	+	0.919719i	$0.371583\pi$
$468$	0.390048	−	0.716915i	0.0180300	−	0.0331394i
$469$	10.4492			0.482500
$470$	−9.61727	−	16.6576i	−0.443612	−	0.768358i
$471$	−12.0467	−	20.8655i	−0.555082	−	0.961430i
$472$	−14.5314	+	25.1692i	−0.668864	+	1.15851i
$473$	5.16615			0.237540
$474$	−4.42040	+	7.65636i	−0.203036	+	0.351668i
$475$	−19.2911	+	33.4131i	−0.885134	+	1.53310i
$476$	2.07318			0.0950239
$477$	−3.56847	+	6.18078i	−0.163389	+	0.282998i
$478$	0.809807	+	1.40263i	0.0370397	+	0.0641546i
$479$	19.6435	+	34.0235i	0.897534	+	1.55458i	0.830636	+	0.556815i	$0.187977\pi$
$479$	19.6435	+	34.0235i	0.897534	+	1.55458i	0.0668983	+	0.997760i	$0.478690\pi$
$480$	4.22018			0.192624
$481$	−15.9669	+	29.3475i	−0.728030	+	1.33813i
$482$	−4.61645			−0.210274
$483$	−4.08169	−	7.06970i	−0.185723	−	0.321682i
$484$	0.113180	+	0.196033i	0.00514454	+	0.00891061i
$485$	−11.9968	+	20.7791i	−0.544749	+	0.943532i
$486$	−1.33178			−0.0604108
$487$	−4.31211	+	7.46880i	−0.195401	+	0.338444i	−0.947032	−	0.321140i	$-0.895934\pi$
$487$	−4.31211	+	7.46880i	−0.195401	+	0.338444i	0.751631	+	0.659584i	$0.229267\pi$
$488$	12.5426	−	21.7245i	0.567778	−	0.983420i
$489$	−2.07112			−0.0936595
$490$	−10.2474	+	17.7490i	−0.462930	+	0.801819i
$491$	2.25630	+	3.90803i	0.101826	+	0.176367i	0.912437	−	0.409218i	$-0.134198\pi$
$491$	2.25630	+	3.90803i	0.101826	+	0.176367i	−0.810611	+	0.585585i	$0.800865\pi$
$492$	−0.0283489	−	0.0491017i	−0.00127807	−	0.00221367i
$493$	−1.14245			−0.0514533
$494$	−16.1877	−	26.4668i	−0.728321	−	1.19080i
$495$	3.31232			0.148878
$496$	−16.4126	−	28.4274i	−0.736945	−	1.27643i
$497$	−5.68601	−	9.84846i	−0.255052	−	0.441764i
$498$	−6.55491	+	11.3534i	−0.293733	+	0.508760i
$499$	−27.9477			−1.25111			−0.625556	−	0.780179i	$-0.715128\pi$
$499$	−27.9477			−1.25111			−0.625556	+	0.780179i	$0.715128\pi$
$500$	−0.364196	+	0.630807i	−0.0162874	+	0.0282105i
$501$	0.218960	−	0.379249i	0.00978239	−	0.0169436i
$502$	31.2503			1.39477
$503$	7.21658	−	12.4995i	0.321771	−	0.557324i	−0.659082	−	0.752071i	$-0.729055\pi$
$503$	7.21658	−	12.4995i	0.321771	−	0.557324i	0.980854	+	0.194747i	$0.0623885\pi$
$504$	−2.27458	−	3.93970i	−0.101318	−	0.175488i
$505$	23.0271	+	39.8840i	1.02469	+	1.77482i
$506$	−7.08596			−0.315009
$507$	−12.9833	+	0.658142i	−0.576610	+	0.0292291i
$508$	2.21571			0.0983063
$509$	−15.6725	−	27.1456i	−0.694671	−	1.20321i	−0.970291	−	0.241939i	$-0.922217\pi$
$509$	−15.6725	−	27.1456i	−0.694671	−	1.20321i	0.275620	−	0.961267i	$-0.411117\pi$
$510$	−13.1664	−	22.8049i	−0.583019	−	1.00982i
$511$	10.1790	−	17.6305i	0.450291	−	0.779927i
$512$	−25.1859			−1.11307
$513$	3.23053	−	5.59545i	0.142631	−	0.247045i
$514$	−7.71875	+	13.3693i	−0.340460	+	0.589693i
$515$	−24.4496			−1.07738
$516$	0.584705	−	1.01274i	0.0257402	−	0.0445833i
$517$	−2.18015	−	3.77613i	−0.0958829	−	0.166074i
$518$	9.46695	+	16.3972i	0.415954	+	0.720453i
$519$	−2.19390			−0.0963015
$520$	−18.4761	−	30.2083i	−0.810231	−	1.32472i
$521$	−6.91319			−0.302873			−0.151436	−	0.988467i	$-0.548390\pi$
$521$	−6.91319			−0.302873			−0.151436	+	0.988467i	$0.548390\pi$
$522$	0.127440	+	0.220733i	0.00557791	+	0.00966122i
$523$	−5.34776	−	9.26260i	−0.233841	−	0.405025i	0.725094	−	0.688650i	$-0.241796\pi$
$523$	−5.34776	−	9.26260i	−0.233841	−	0.405025i	−0.958935	+	0.283625i	$0.908463\pi$
$524$	−0.668823	+	1.15844i	−0.0292177	+	0.0506065i
$525$	9.16191			0.399858
$526$	−5.65142	+	9.78855i	−0.246414	+	0.426801i
$527$	28.0241	−	48.5392i	1.22075	−	2.11440i
$528$	−3.49604			−0.152146
$529$	−2.65475	+	4.59816i	−0.115424	+	0.199920i
$530$	15.7416	+	27.2652i	0.683770	+	1.18432i
$531$	4.90095	+	8.48870i	0.212683	+	0.368378i
$532$	2.24392			0.0972863
$533$	−0.431603	+	0.793294i	−0.0186948	+	0.0343614i
$534$	−7.15755			−0.309738
$535$	15.1269	+	26.2005i	0.653991	+	1.13275i
$536$	−10.0967	−	17.4879i	−0.436109	−	0.755363i
$537$	−9.30732	+	16.1208i	−0.401641	+	0.695662i
$538$	−12.4335			−0.536048
$539$	−2.32300	+	4.02355i	−0.100059	+	0.173306i
$540$	0.374889	−	0.649326i	0.0161326	−	0.0279425i
$541$	20.7302			0.891263			0.445632	−	0.895216i	$-0.352979\pi$
$541$	20.7302			0.891263			0.445632	+	0.895216i	$0.352979\pi$
$542$	12.9298	−	22.3951i	0.555383	−	0.961952i
$543$	−6.70001	−	11.6048i	−0.287525	−	0.498007i
$544$	−3.80278	−	6.58661i	−0.163043	−	0.282399i
$545$	57.7545			2.47393
$546$	−3.52091	+	6.47150i	−0.150681	+	0.276955i
$547$	27.3491			1.16936			0.584681	−	0.811263i	$-0.301219\pi$
$547$	27.3491			1.16936			0.584681	+	0.811263i	$0.301219\pi$
$548$	−0.115305	−	0.199715i	−0.00492560	−	0.00853138i
$549$	−4.23019	−	7.32691i	−0.180540	−	0.312705i
$550$	3.97635	−	6.88724i	0.169552	−	0.293673i
$551$	−1.23654			−0.0526784
$552$	−7.88795	+	13.6623i	−0.335734	+	0.581507i
$553$	−5.09252	+	8.82050i	−0.216556	+	0.375086i
$554$	17.8020			0.756334
$555$	−15.3464	+	26.5807i	−0.651417	+	1.12829i
$556$	0.579978	+	1.00455i	0.0245965	+	0.0426025i
$557$	−0.527569	−	0.913776i	−0.0223538	−	0.0387179i	0.854632	−	0.519234i	$-0.173783\pi$
$557$	−0.527569	−	0.913776i	−0.0223538	−	0.0387179i	−0.876986	+	0.480516i	$0.840449\pi$
$558$	−12.5044			−0.529353
$559$	−18.6208	+	0.471655i	−0.787578	+	0.0199489i
$560$	−17.7670			−0.750791
$561$	−2.98471	−	5.16968i	−0.126015	−	0.218264i
$562$	3.93196	+	6.81035i	0.165860	+	0.287277i
$563$	8.96049	−	15.5200i	0.377640	−	0.654091i	−0.613079	−	0.790022i	$-0.710069\pi$
$563$	8.96049	−	15.5200i	0.377640	−	0.654091i	0.990718	+	0.135931i	$0.0434025\pi$
$564$	−0.986997			−0.0415601
$565$	−25.8067	+	44.6985i	−1.08570	+	1.88048i
$566$	−15.7147	+	27.2187i	−0.660540	+	1.14409i
$567$	−1.53428			−0.0644336
$568$	−10.9883	+	19.0323i	−0.461060	+	0.798579i
$569$	0.472909	+	0.819102i	0.0198254	+	0.0343386i	0.875768	−	0.482732i	$-0.160356\pi$
$569$	0.472909	+	0.819102i	0.0198254	+	0.0343386i	−0.855943	+	0.517071i	$0.827022\pi$
$570$	−14.2508	−	24.6831i	−0.596901	−	1.03386i
$571$	−23.7421			−0.993576			−0.496788	−	0.867872i	$-0.665487\pi$
$571$	−23.7421			−0.993576			−0.496788	+	0.867872i	$0.665487\pi$
$572$	−0.425843	−	0.696249i	−0.0178054	−	0.0291116i
$573$	−6.12355			−0.255815
$574$	0.255901	+	0.443234i	0.0106811	+	0.0185002i
$575$	−15.8861	−	27.5156i	−0.662497	−	1.14748i
$576$	−4.34444	+	7.52480i	−0.181018	+	0.313533i
$577$	15.5611			0.647819			0.323910	−	0.946088i	$-0.395003\pi$
$577$	15.5611			0.647819			0.323910	+	0.946088i	$0.395003\pi$
$578$	−12.4082	+	21.4917i	−0.516115	+	0.893938i
$579$	9.26563	−	16.0485i	0.385066	−	0.666954i
$580$	−0.143495			−0.00595830
$581$	−7.55159	+	13.0797i	−0.313293	+	0.542639i
$582$	−4.82355	−	8.35464i	−0.199943	−	0.346311i
$583$	3.56847	+	6.18078i	0.147791	+	0.255982i
$584$	−39.3421			−1.62799
$585$	−11.9389	+	0.302406i	−0.493614	+	0.0125029i
$586$	40.9534			1.69177
$587$	9.53036	+	16.5071i	0.393360	+	0.681320i	0.992890	−	0.119032i	$-0.0379792\pi$
$587$	9.53036	+	16.5071i	0.393360	+	0.681320i	−0.599530	+	0.800352i	$0.704646\pi$
$588$	0.525833	+	0.910770i	0.0216850	+	0.0375595i
$589$	30.3322	−	52.5369i	1.24982	−	2.16474i
$590$	43.2390			1.78012
$591$	−9.35203	+	16.1982i	−0.384691	+	0.666305i
$592$	16.1976	−	28.0550i	0.665716	−	1.15305i
$593$	−27.7776			−1.14069			−0.570344	−	0.821406i	$-0.693190\pi$
$593$	−27.7776			−1.14069			−0.570344	+	0.821406i	$0.693190\pi$
$594$	−0.665890	+	1.15336i	−0.0273218	+	0.0473228i
$595$	−15.1684	−	26.2724i	−0.621843	−	1.07706i
$596$	1.40960	+	2.44150i	0.0577395	+	0.100008i
$597$	13.3538			0.546533
$598$	25.5406	−	0.646928i	1.04443	−	0.0264549i
$599$	13.5670			0.554332			0.277166	−	0.960822i	$-0.410605\pi$
$599$	13.5670			0.554332			0.277166	+	0.960822i	$0.410605\pi$
$600$	−8.85279	−	15.3335i	−0.361414	−	0.625987i
$601$	4.11014	+	7.11897i	0.167656	+	0.290389i	0.937595	−	0.347728i	$-0.113047\pi$
$601$	4.11014	+	7.11897i	0.167656	+	0.290389i	−0.769939	+	0.638117i	$0.779714\pi$
$602$	−5.27805	+	9.14185i	−0.215117	+	0.372594i
$603$	−6.81051			−0.277345
$604$	1.29090	−	2.23590i	0.0525258	−	0.0909774i
$605$	1.65616	−	2.86856i	0.0673325	−	0.116623i
$606$	−18.5169			−0.752198
$607$	−12.5123	+	21.6719i	−0.507858	+	0.879637i	0.492100	+	0.870539i	$0.336229\pi$
$607$	−12.5123	+	21.6719i	−0.507858	+	0.879637i	−0.999959	+	0.00909803i	$0.997104\pi$
$608$	−4.11598	−	7.12908i	−0.166925	−	0.289122i
$609$	0.146818	+	0.254295i	0.00594935	+	0.0103046i
$610$	−37.3212			−1.51109
$611$	8.20287	+	13.4116i	0.331853	+	0.542576i
$612$	−1.35124			−0.0546206
$613$	−7.17192	−	12.4221i	−0.289671	−	0.501725i	0.684060	−	0.729426i	$-0.260213\pi$
$613$	−7.17192	−	12.4221i	−0.289671	−	0.501725i	−0.973731	+	0.227700i	$0.926879\pi$
$614$	10.9801	+	19.0180i	0.443120	+	0.767506i
$615$	−0.414829	+	0.718504i	−0.0167275	+	0.0289729i
$616$	−4.54917			−0.183291
$617$	18.0651	−	31.2896i	0.727273	−	1.25967i	−0.230759	−	0.973011i	$-0.574121\pi$
$617$	18.0651	−	31.2896i	0.727273	−	1.25967i	0.958032	−	0.286663i	$-0.0925459\pi$
$618$	4.91520	−	8.51338i	0.197718	−	0.342458i
$619$	1.55323			0.0624295			0.0312147	−	0.999513i	$-0.490062\pi$
$619$	1.55323			0.0624295			0.0312147	+	0.999513i	$0.490062\pi$
$620$	3.51991	−	6.09667i	0.141363	−	0.244848i
$621$	2.66033	+	4.60783i	0.106756	+	0.184906i
$622$	−12.1799	−	21.0963i	−0.488371	−	0.845884i
$623$	−8.24586			−0.330363
$624$	12.6011	−	0.319179i	0.504448	−	0.0127774i
$625$	−19.1988			−0.767953
$626$	−0.990165	−	1.71502i	−0.0395750	−	0.0685458i
$627$	−3.23053	−	5.59545i	−0.129015	−	0.223461i
$628$	−2.72689	+	4.72311i	−0.108815	+	0.188472i
$629$	55.3141			2.20552
$630$	−3.38407	+	5.86138i	−0.134825	+	0.233523i
$631$	4.38718	−	7.59882i	0.174651	−	0.302504i	−0.765390	−	0.643567i	$-0.777454\pi$
$631$	4.38718	−	7.59882i	0.174651	−	0.302504i	0.940040	+	0.341063i	$0.110787\pi$
$632$	19.6828			0.782940
$633$	−0.798547	+	1.38312i	−0.0317394	+	0.0549743i
$634$	−12.6074	−	21.8366i	−0.500703	−	0.867243i
$635$	−16.2112	−	28.0787i	−0.643323	−	1.11427i
$636$	1.61552			0.0640595
$637$	8.00566	−	14.7145i	0.317196	−	0.583011i
$638$	0.254881			0.0100908
$639$	3.70598	+	6.41895i	0.146606	+	0.253930i
$640$	14.9444	+	25.8845i	0.590729	+	1.02317i
$641$	−10.4180	+	18.0444i	−0.411485	+	0.712713i	−0.995052	−	0.0993520i	$-0.968323\pi$
$641$	−10.4180	+	18.0444i	−0.411485	+	0.712713i	0.583567	+	0.812065i	$0.301656\pi$
$642$	−12.1641			−0.480078
$643$	7.20933	−	12.4869i	0.284308	−	0.492436i	−0.688133	−	0.725585i	$-0.741569\pi$
$643$	7.20933	−	12.4869i	0.284308	−	0.492436i	0.972441	+	0.233148i	$0.0749028\pi$
$644$	−0.923931	+	1.60030i	−0.0364080	+	0.0630605i
$645$	−17.1120			−0.673782
$646$	−25.6826	+	44.4836i	−1.01047	+	1.75018i
$647$	−3.62301	−	6.27524i	−0.142435	−	0.246705i	0.785978	−	0.618255i	$-0.212160\pi$
$647$	−3.62301	−	6.27524i	−0.142435	−	0.246705i	−0.928413	+	0.371550i	$0.878827\pi$
$648$	1.48251	+	2.56779i	0.0582386	+	0.100872i
$649$	9.80191			0.384759
$650$	−13.7036	+	25.1874i	−0.537498	+	0.987930i
$651$	−14.4057			−0.564603
$652$	0.234410	+	0.406010i	0.00918020	+	0.0159006i
$653$	−17.2639	−	29.9019i	−0.675589	−	1.17015i	−0.976296	−	0.216437i	$-0.930556\pi$
$653$	−17.2639	−	29.9019i	−0.675589	−	1.17015i	0.300708	−	0.953716i	$-0.402777\pi$
$654$	−11.6106	+	20.1102i	−0.454012	+	0.786372i
$655$	19.5738			0.764811
$656$	0.437837	−	0.758356i	0.0170947	−	0.0296088i
$657$	−6.63437	+	11.4911i	−0.258832	+	0.448309i
$658$	8.90950			0.347328
$659$	4.76906	−	8.26026i	0.185776	−	0.321774i	−0.758062	−	0.652183i	$-0.773853\pi$
$659$	4.76906	−	8.26026i	0.185776	−	0.321774i	0.943838	+	0.330409i	$0.107187\pi$
$660$	−0.374889	−	0.649326i	−0.0145925	−	0.0252750i
$661$	15.6376	+	27.0852i	0.608233	+	1.05349i	0.991532	+	0.129866i	$0.0414547\pi$
$661$	15.6376	+	27.0852i	0.608233	+	1.05349i	−0.383299	+	0.923624i	$0.625212\pi$
$662$	−10.0948			−0.392347
$663$	11.2301	+	18.3611i	0.436140	+	0.713085i
$664$	29.1872			1.13268
$665$	−16.4176	−	28.4362i	−0.636649	−	1.10271i
$666$	−6.17030	−	10.6873i	−0.239094	−	0.414123i
$667$	0.509143	−	0.881862i	0.0197141	−	0.0341458i
$668$	−0.0991273			−0.00383535
$669$	−3.95402	+	6.84857i	−0.152871	+	0.264781i
$670$	−15.0215	+	26.0181i	−0.580333	+	1.00517i
$671$	−8.46038			−0.326610
$672$	−0.977401	+	1.69291i	−0.0377041	+	0.0653053i
$673$	−2.78682	−	4.82691i	−0.107424	−	0.186064i	0.807302	−	0.590139i	$-0.200927\pi$
$673$	−2.78682	−	4.82691i	−0.107424	−	0.186064i	−0.914726	+	0.404075i	$0.867594\pi$
$674$	14.2642	+	24.7064i	0.549438	+	0.951655i
$675$	−5.97148			−0.229842
$676$	1.59847	+	2.47068i	0.0614796	+	0.0950261i
$677$	−39.2831			−1.50977			−0.754885	−	0.655857i	$-0.772308\pi$
$677$	−39.2831			−1.50977			−0.754885	+	0.655857i	$0.772308\pi$
$678$	−10.3761	−	17.9719i	−0.398490	−	0.690206i
$679$	−5.55697	−	9.62496i	−0.213257	−	0.369372i
$680$	−29.3132	+	50.7720i	−1.12411	+	1.94702i
$681$	−14.8826			−0.570302
$682$	−6.25219	+	10.8291i	−0.239409	+	0.414668i
$683$	8.17058	−	14.1519i	0.312638	−	0.541506i	−0.666294	−	0.745689i	$-0.732121\pi$
$683$	8.17058	−	14.1519i	0.312638	−	0.541506i	0.978933	+	0.204183i	$0.0654539\pi$
$684$	−1.46253			−0.0559211
$685$	−1.68726	+	2.92242i	−0.0644669	+	0.111660i
$686$	−11.8983	−	20.6084i	−0.454277	−	0.786832i
$687$	−5.28675	−	9.15692i	−0.201702	−	0.349358i
$688$	18.0611			0.688572
$689$	−13.4265	−	21.9522i	−0.511508	−	0.836311i
$690$	23.4710			0.893525
$691$	−10.9603	−	18.9837i	−0.416948	−	0.722175i	0.578683	−	0.815553i	$-0.303567\pi$
$691$	−10.9603	−	18.9837i	−0.416948	−	0.722175i	−0.995631	+	0.0933780i	$0.970233\pi$
$692$	0.248305	+	0.430078i	0.00943915	+	0.0163491i
$693$	−0.767139	+	1.32872i	−0.0291412	+	0.0504740i
$694$	−4.42724			−0.168056
$695$	8.48681	−	14.6996i	0.321923	−	0.557587i
$696$	0.283728	−	0.491431i	0.0107547	−	0.0186277i
$697$	1.49520			0.0566347
$698$	10.4735	−	18.1406i	0.396428	−	0.686634i
$699$	−1.35057	−	2.33926i	−0.0510833	−	0.0884789i
$700$	−1.03694	−	1.79604i	−0.0391928	−	0.0678839i
$701$	−35.1458			−1.32744			−0.663718	−	0.747982i	$-0.731023\pi$
$701$	−35.1458			−1.32744			−0.663718	+	0.747982i	$0.731023\pi$
$702$	2.29483	−	4.21794i	0.0866129	−	0.159196i
$703$	59.8697			2.25803
$704$	4.34444	+	7.52480i	0.163737	+	0.283601i
$705$	7.22136	+	12.5078i	0.271972	+	0.471070i
$706$	14.4529	−	25.0331i	0.543942	−	0.942135i
$707$	−21.3324			−0.802288
$708$	1.10938	−	1.92150i	0.0416930	−	0.0722145i
$709$	13.6455	−	23.6347i	0.512468	−	0.887621i	−0.487428	−	0.873163i	$-0.662065\pi$
$709$	13.6455	−	23.6347i	0.512468	−	0.887621i	0.999895	−	0.0144571i	$-0.00460199\pi$
$710$	32.6963			1.22707
$711$	3.31916	−	5.74896i	0.124478	−	0.215603i
$712$	7.96764	+	13.8004i	0.298600	+	0.517190i
$713$	24.9785	+	43.2640i	0.935451	+	1.62025i
$714$	12.1975			0.456478
$715$	−5.70757	+	10.4906i	−0.213451	+	0.392327i
$716$	4.21361			0.157470
$717$	−0.608063	−	1.05320i	−0.0227085	−	0.0393323i
$718$	−15.1909	−	26.3113i	−0.566918	−	0.981931i
$719$	−1.88633	+	3.26723i	−0.0703484	+	0.121847i	−0.899054	−	0.437838i	$-0.855744\pi$
$719$	−1.88633	+	3.26723i	−0.0703484	+	0.121847i	0.828706	+	0.559685i	$0.189078\pi$
$720$	11.5800			0.431562
$721$	5.66256	−	9.80783i	0.210885	−	0.365263i
$722$	−15.1459	+	26.2335i	−0.563673	+	0.976310i
$723$	3.46638			0.128916
$724$	−1.51661	+	2.62685i	−0.0563645	+	0.0976261i
$725$	0.571421	+	0.989730i	0.0212220	+	0.0367576i
$726$	0.665890	+	1.15336i	0.0247135	+	0.0428051i
$727$	−41.9955			−1.55753			−0.778764	−	0.627317i	$-0.784153\pi$
$727$	−41.9955			−1.55753			−0.778764	+	0.627317i	$0.784153\pi$
$728$	16.3970	−	0.415326i	0.607713	−	0.0153930i
$729$	1.00000			0.0370370
$730$	29.2661	+	50.6904i	1.08319	+	1.87614i
$731$	15.4195	+	26.7073i	0.570310	+	0.987806i
$732$	−0.957546	+	1.65852i	−0.0353919	+	0.0613006i
$733$	−10.8123			−0.399360			−0.199680	−	0.979861i	$-0.563990\pi$
$733$	−10.8123			−0.399360			−0.199680	+	0.979861i	$0.563990\pi$
$734$	1.89914	−	3.28940i	0.0700985	−	0.121414i
$735$	7.69451	−	13.3273i	0.283816	−	0.491584i
$736$	6.77899			0.249877
$737$	−3.40525	+	5.89807i	−0.125434	+	0.217258i
$738$	−0.166790	−	0.288888i	−0.00613961	−	0.0106341i
$739$	−4.27316	−	7.40133i	−0.157191	−	0.272262i	0.776664	−	0.629915i	$-0.216910\pi$
$739$	−4.27316	−	7.40133i	−0.157191	−	0.272262i	−0.933855	+	0.357653i	$0.883577\pi$
$740$	6.94761			0.255399
$741$	12.1550	+	19.8733i	0.446524	+	0.730062i
$742$	−14.5831			−0.535362
$743$	−7.51343	−	13.0137i	−0.275641	−	0.477425i	0.694655	−	0.719343i	$-0.255557\pi$
$743$	−7.51343	−	13.0137i	−0.275641	−	0.477425i	−0.970297	+	0.241918i	$0.922223\pi$
$744$	13.9196	+	24.1095i	0.510318	+	0.883898i
$745$	20.6267	−	35.7265i	0.755703	−	1.30892i
$746$	−41.9044			−1.53423
$747$	4.92192	−	8.52501i	0.180083	−	0.311914i
$748$	−0.675620	+	1.17021i	−0.0247031	+	0.0427870i
$749$	−14.0136			−0.512046
$750$	−2.14274	+	3.71133i	−0.0782417	+	0.135519i
$751$	23.2294	+	40.2345i	0.847652	+	1.46818i	0.883298	+	0.468812i	$0.155318\pi$
$751$	23.2294	+	40.2345i	0.847652	+	1.46818i	−0.0356454	+	0.999365i	$0.511349\pi$
$752$	−7.62190	−	13.2015i	−0.277942	−	0.481410i
$753$	−23.4651			−0.855114
$754$	−0.918690	+	0.0232699i	−0.0334567	+	0.000847439i
$755$	−37.7793			−1.37493
$756$	0.173649	+	0.300770i	0.00631557	+	0.0109389i
$757$	1.70395	+	2.95134i	0.0619313	+	0.107268i	0.895329	−	0.445406i	$-0.146941\pi$
$757$	1.70395	+	2.95134i	0.0619313	+	0.107268i	−0.833397	+	0.552674i	$0.813607\pi$
$758$	9.38053	−	16.2476i	0.340716	−	0.590138i
$759$	5.32067			0.193128
$760$	−31.7274	+	54.9535i	−1.15087	+	1.99337i
$761$	−16.1553	+	27.9818i	−0.585629	+	1.01434i	0.409167	+	0.912459i	$0.365819\pi$
$761$	−16.1553	+	27.9818i	−0.585629	+	1.01434i	−0.994797	+	0.101880i	$0.967514\pi$
$762$	13.0361			0.472247
$763$	−13.3760	+	23.1680i	−0.484245	+	0.838737i
$764$	0.693063	+	1.20042i	0.0250741	+	0.0434297i
$765$	9.88633	+	17.1236i	0.357441	+	0.619106i
$766$	−50.6787			−1.83109
$767$	−35.3299	+	0.894886i	−1.27569	+	0.0323125i
$768$	5.36042			0.193428
$769$	2.24803	+	3.89369i	0.0810659	+	0.140410i	0.903708	−	0.428149i	$-0.140834\pi$
$769$	2.24803	+	3.89369i	0.0810659	+	0.140410i	−0.822642	+	0.568559i	$0.807501\pi$
$770$	3.38407	+	5.86138i	0.121953	+	0.211229i
$771$	5.79581	−	10.0386i	0.208731	−	0.361533i
$772$	−4.19473			−0.150972
$773$	7.10256	−	12.3020i	0.255461	−	0.442472i	−0.709559	−	0.704646i	$-0.751106\pi$
$773$	7.10256	−	12.3020i	0.255461	−	0.442472i	0.965021	+	0.262174i	$0.0844393\pi$
$774$	3.44009	−	5.95841i	0.123651	−	0.214171i
$775$	−56.0675			−2.01401
$776$	−10.7390	+	18.6004i	−0.385507	+	0.667717i
$777$	−7.10849	−	12.3123i	−0.255016	−	0.441700i
$778$	20.3695	+	35.2811i	0.730283	+	1.26489i
$779$	1.61834			0.0579831
$780$	1.41053	+	2.30620i	0.0505050	+	0.0825752i
$781$	7.41197			0.265221
$782$	−21.1496	−	36.6321i	−0.756307	−	1.30996i
$783$	−0.0956916	−	0.165743i	−0.00341974	−	0.00592316i
$784$	−8.12129	+	14.0665i	−0.290046	+	0.502375i
$785$	79.8050			2.84836
$786$	−3.93500	+	6.81562i	−0.140357	+	0.243105i
$787$	−10.2171	+	17.6965i	−0.364200	+	0.630813i	−0.988647	−	0.150254i	$-0.951991\pi$
$787$	−10.2171	+	17.6965i	−0.364200	+	0.630813i	0.624447	+	0.781067i	$0.285324\pi$
$788$	4.23385			0.150825
$789$	4.24351	−	7.34997i	0.151073	−	0.261666i
$790$	−14.6418	−	25.3603i	−0.520931	−	0.902280i
$791$	−11.9537	−	20.7045i	−0.425026	−	0.736167i
$792$	2.96502			0.105358
$793$	30.4946	−	0.772409i	1.08289	−	0.0274290i
$794$	−11.0024			−0.390459
$795$	−11.8199	−	20.4727i	−0.419210	−	0.726093i
$796$	−1.51138	−	2.61778i	−0.0535694	−	0.0927848i
$797$	−10.9921	+	19.0389i	−0.389360	+	0.674391i	−0.992364	−	0.123347i	$-0.960637\pi$
$797$	−10.9921	+	19.0389i	−0.389360	+	0.674391i	0.603003	+	0.797739i	$0.293970\pi$
$798$	13.2020			0.467347
$799$	13.0143	−	22.5413i	0.460411	−	0.797456i
$800$	−3.80409	+	6.58888i	−0.134495	+	0.232952i
$801$	5.37442			0.189896
$802$	0.497735	−	0.862102i	0.0175756	−	0.0304419i
$803$	6.63437	+	11.4911i	0.234122	+	0.405511i
$804$	0.770813	+	1.33509i	0.0271845	+	0.0470849i
$805$	27.0397			0.953026
$806$	21.5467	−	39.6032i	0.758950	−	1.39496i
$807$	9.33602			0.328644
$808$	20.6127	+	35.7022i	0.725151	+	1.25600i
$809$	−6.13174	−	10.6205i	−0.215580	−	0.373396i	0.737872	−	0.674941i	$-0.235831\pi$
$809$	−6.13174	−	10.6205i	−0.215580	−	0.373396i	−0.953452	+	0.301545i	$0.902498\pi$
$810$	2.20564	−	3.82029i	0.0774984	−	0.134231i
$811$	39.8424			1.39906			0.699528	−	0.714605i	$-0.253394\pi$
$811$	39.8424			1.39906			0.699528	+	0.714605i	$0.253394\pi$
$812$	0.0332336	−	0.0575623i	0.00116627	−	0.00202004i
$813$	−9.70866	+	16.8159i	−0.340498	+	0.589759i
$814$	−12.3406			−0.432537
$815$	3.43012	−	5.94114i	0.120152	−	0.208109i
$816$	−10.4347	−	18.0734i	−0.365287	−	0.632696i
$817$	16.6894	+	28.9069i	0.583889	+	1.01132i
$818$	−42.5014			−1.48603
$819$	2.64376	−	4.85928i	0.0923805	−	0.169797i
$820$	0.187801			0.00655830
$821$	−5.29007	−	9.16267i	−0.184625	−	0.319779i	0.758825	−	0.651294i	$-0.225774\pi$
$821$	−5.29007	−	9.16267i	−0.184625	−	0.319779i	−0.943450	+	0.331515i	$0.892440\pi$
$822$	−0.678394	−	1.17501i	−0.0236617	−	0.0409833i
$823$	20.3806	−	35.3002i	0.710422	−	1.23049i	−0.254277	−	0.967131i	$-0.581838\pi$
$823$	20.3806	−	35.3002i	0.710422	−	1.23049i	0.964699	−	0.263355i	$-0.0848291\pi$
$824$	−21.8860			−0.762435
$825$	−2.98574	+	5.17145i	−0.103950	+	0.180047i
$826$	−10.0142	+	17.3451i	−0.348439	+	0.603515i
$827$	46.8352			1.62862			0.814309	−	0.580432i	$-0.197116\pi$
$827$	46.8352			1.62862			0.814309	+	0.580432i	$0.197116\pi$
$828$	0.602193	−	1.04303i	0.0209277	−	0.0362478i
$829$	2.65127	+	4.59214i	0.0920825	+	0.159492i	0.908387	−	0.418130i	$-0.137314\pi$
$829$	2.65127	+	4.59214i	0.0920825	+	0.159492i	−0.816305	+	0.577621i	$0.803981\pi$
$830$	−21.7120	−	37.6063i	−0.753634	−	1.30533i
$831$	−13.3671			−0.463698
$832$	−16.3461	−	26.7257i	−0.566698	−	0.926547i
$833$	−27.7339			−0.960923
$834$	3.41228	+	5.91024i	0.118158	+	0.204655i
$835$	0.725264	+	1.25619i	0.0250988	+	0.0434724i
$836$	−0.731263	+	1.26658i	−0.0252913	+	0.0438057i
$837$	9.38922			0.324539
$838$	−3.59234	+	6.22211i	−0.124095	+	0.214939i
$839$	−27.2169	+	47.1411i	−0.939633	+	1.62749i	−0.173477	+	0.984838i	$0.555500\pi$
$839$	−27.2169	+	47.1411i	−0.939633	+	1.62749i	−0.766156	+	0.642655i	$0.777833\pi$
$840$	15.0683			0.519906
$841$	14.4817	−	25.0830i	0.499368	−	0.864932i
$842$	23.2446	+	40.2608i	0.801061	+	1.38748i
$843$	−2.95241	−	5.11372i	−0.101686	−	0.176126i
$844$	0.361518			0.0124440
$845$	19.6146	−	38.3334i	0.674762	−	1.31871i
$846$	−5.80697			−0.199648
$847$	0.767139	+	1.32872i	0.0263592	+	0.0456555i
$848$	12.4755	+	21.6083i	0.428412	+	0.742031i
$849$	11.7998	−	20.4378i	0.404968	−	0.701425i
$850$	47.4731			1.62831
$851$	−24.6513	+	42.6973i	−0.845035	+	1.46364i
$852$	0.838886	−	1.45299i	0.0287398	−	0.0497787i
$853$	54.3590			1.86122			0.930609	−	0.366014i	$-0.119278\pi$
$853$	54.3590			1.86122			0.930609	+	0.366014i	$0.119278\pi$
$854$	8.64364	−	14.9712i	0.295779	−	0.512305i
$855$	10.7006	+	18.5339i	0.365952	+	0.633847i
$856$	13.5408	+	23.4534i	0.462815	+	0.801619i
$857$	8.18928			0.279741			0.139870	−	0.990170i	$-0.455331\pi$
$857$	8.18928			0.279741			0.139870	+	0.990170i	$0.455331\pi$
$858$	−2.50543	−	4.09636i	−0.0855340	−	0.139847i
$859$	−1.40511			−0.0479418			−0.0239709	−	0.999713i	$-0.507631\pi$
$859$	−1.40511			−0.0479418			−0.0239709	+	0.999713i	$0.507631\pi$
$860$	1.93673	+	3.35451i	0.0660419	+	0.114388i
$861$	−0.192150	−	0.332813i	−0.00654845	−	0.0113422i
$862$	14.3322	−	24.8240i	0.488156	−	0.845510i
$863$	−42.9555			−1.46222			−0.731112	−	0.682258i	$-0.760998\pi$
$863$	−42.9555			−1.46222			−0.731112	+	0.682258i	$0.760998\pi$
$864$	0.637043	−	1.10339i	0.0216726	−	0.0375381i
$865$	3.63345	−	6.29332i	0.123541	−	0.213979i
$866$	−0.251711			−0.00855349
$867$	9.31704	−	16.1376i	0.316423	−	0.548061i
$868$	1.63043	+	2.82399i	0.0553405	+	0.0958526i
$869$	−3.31916	−	5.74896i	−0.112595	−	0.195020i
$870$	−0.844247			−0.0286226
$871$	11.7354	−	21.5699i	0.397639	−	0.730867i
$872$	51.6989			1.75075
$873$	3.62188	+	6.27329i	0.122582	+	0.212319i
$874$	−22.8914	−	39.6491i	−0.774314	−	1.34115i
$875$	−2.46854	+	4.27564i	−0.0834519	+	0.144543i
$876$	3.00351			0.101479
$877$	6.41374	−	11.1089i	0.216577	−	0.375122i	−0.737183	−	0.675694i	$-0.763844\pi$
$877$	6.41374	−	11.1089i	0.216577	−	0.375122i	0.953759	+	0.300572i	$0.0971776\pi$
$878$	6.59501	−	11.4229i	0.222571	−	0.385504i
$879$	−30.7509			−1.03720
$880$	5.79001	−	10.0286i	0.195181	−	0.338064i
$881$	−16.1964	−	28.0530i	−0.545671	−	0.945129i	−0.998564	−	0.0535647i	$-0.982942\pi$
$881$	−16.1964	−	28.0530i	−0.545671	−	0.945129i	0.452894	−	0.891564i	$-0.350392\pi$
$882$	3.09372	+	5.35848i	0.104171	+	0.180430i
$883$	51.2086			1.72331			0.861654	−	0.507497i	$-0.169429\pi$
$883$	51.2086			1.72331			0.861654	+	0.507497i	$0.169429\pi$
$884$	2.32836	−	4.27957i	0.0783113	−	0.143938i
$885$	−32.4671			−1.09137
$886$	19.6523	+	34.0388i	0.660233	+	1.14356i
$887$	6.83571	+	11.8398i	0.229521	+	0.397541i	0.957666	−	0.287881i	$-0.0929508\pi$
$887$	6.83571	+	11.8398i	0.229521	+	0.397541i	−0.728146	+	0.685423i	$0.759618\pi$
$888$	−13.7373	+	23.7937i	−0.460994	+	0.798464i
$889$	15.0182			0.503694
$890$	11.8541	−	20.5318i	0.397349	−	0.688229i
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	1.79006			0.0599358
$893$	14.0861	−	24.3978i	0.471373	−	0.816442i
$894$	8.29334	+	14.3645i	0.277371	+	0.480421i
$895$	−30.8289	−	53.3971i	−1.03050	−	1.78487i
$896$	−13.8446			−0.462515
$897$	−19.1778	+	0.485762i	−0.640328	+	0.0162191i
$898$	18.3145			0.611162
$899$	−0.898470	−	1.55620i	−0.0299657	−	0.0519020i
$900$	0.675852	+	1.17061i	0.0225284	+	0.0390203i
$901$	−21.3017	+	36.8957i	−0.709664	+	1.22917i
$902$	−0.333579			−0.0111070
$903$	3.96315	−	6.86438i	0.131886	−	0.228432i
$904$	−23.1009	+	40.0119i	−0.768323	+	1.33077i
$905$	44.3852			1.47541
$906$	7.59494	−	13.1548i	0.252325	−	0.437040i
$907$	−11.5671	−	20.0348i	−0.384080	−	0.665246i	0.607561	−	0.794273i	$-0.292148\pi$
$907$	−11.5671	−	20.0348i	−0.384080	−	0.665246i	−0.991641	+	0.129027i	$0.958815\pi$
$908$	1.68441	+	2.91748i	0.0558991	+	0.0968201i
$909$	13.9039			0.461163
$910$	−12.7327	−	20.8178i	−0.422083	−	0.690103i
$911$	14.6236			0.484503			0.242252	−	0.970213i	$-0.422114\pi$
$911$	14.6236			0.484503			0.242252	+	0.970213i	$0.422114\pi$
$912$	−11.2941	−	19.5619i	−0.373984	−	0.647760i
$913$	−4.92192	−	8.52501i	−0.162892	−	0.282137i
$914$	−7.29745	+	12.6396i	−0.241378	+	0.418080i
$915$	28.0235			0.926429
$916$	−1.19671	+	2.07276i	−0.0395403	+	0.0684859i
$917$	−4.53331	+	7.85193i	−0.149703	+	0.259294i
$918$	−7.94997			−0.262388
$919$	−8.65152	+	14.9849i	−0.285387	+	0.494305i	−0.972703	−	0.232054i	$-0.925456\pi$
$919$	−8.65152	+	14.9849i	−0.285387	+	0.494305i	0.687316	+	0.726359i	$0.258789\pi$
$920$	−26.1274	−	45.2540i	−0.861396	−	1.49198i
$921$	−8.24465	−	14.2802i	−0.271671	−	0.470547i
$922$	14.7682			0.486366
$923$	−26.7157	+	0.676692i	−0.879357	+	0.0222736i
$924$	0.347299			0.0114253
$925$	−27.6666	−	47.9199i	−0.909671	−	1.57560i
$926$	22.9972	+	39.8323i	0.755735	+	1.30897i
$927$	−3.69070	+	6.39248i	−0.121218	+	0.209956i
$928$	−0.243839			−0.00800440
$929$	4.73600	−	8.20299i	0.155383	−	0.269131i	−0.777815	−	0.628493i	$-0.783672\pi$
$929$	4.73600	−	8.20299i	0.155383	−	0.269131i	0.933198	+	0.359361i	$0.117005\pi$
$930$	20.7093	−	35.8695i	0.679084	−	1.17621i
$931$	−30.0181			−0.983802
$932$	−0.305715	+	0.529515i	−0.0100140	+	0.0173448i
$933$	9.14561	+	15.8407i	0.299414	+	0.518600i
$934$	−11.2984	−	19.5694i	−0.369695	−	0.640331i
$935$	19.7727			0.646635
$936$	−10.6871	+	0.270698i	−0.349319	+	0.00884805i
$937$	2.35834			0.0770436			0.0385218	−	0.999258i	$-0.487735\pi$
$937$	2.35834			0.0770436			0.0385218	+	0.999258i	$0.487735\pi$
$938$	−6.95803	−	12.0517i	−0.227188	−	0.393500i
$939$	0.743490	+	1.28776i	0.0242629	+	0.0420245i
$940$	1.63463	−	2.83126i	0.0533157	−	0.0923454i
$941$	31.5104			1.02721			0.513605	−	0.858026i	$-0.328310\pi$
$941$	31.5104			1.02721			0.513605	+	0.858026i	$0.328310\pi$
$942$	−16.0435	+	27.7882i	−0.522727	+	0.905390i
$943$	−0.666350	+	1.15415i	−0.0216993	+	0.0375843i
$944$	34.2679			1.11532
$945$	2.54101	−	4.40116i	0.0826591	−	0.143170i
$946$	−3.44009	−	5.95841i	−0.111847	−	0.193725i
$947$	9.92068	+	17.1831i	0.322379	+	0.558377i	0.980978	−	0.194117i	$-0.0621841\pi$
$947$	9.92068	+	17.1831i	0.322379	+	0.558377i	−0.658599	+	0.752494i	$0.728851\pi$
$948$	−1.50265			−0.0488038
$949$	−24.9620	−	40.8127i	−0.810301	−	1.32484i
$950$	51.3829			1.66708
$951$	9.46656	+	16.3966i	0.306974	+	0.531695i
$952$	−13.5780	−	23.5177i	−0.440064	−	0.762214i
$953$	−23.7390	+	41.1172i	−0.768983	+	1.33192i	0.169132	+	0.985593i	$0.445904\pi$
$953$	−23.7390	+	41.1172i	−0.768983	+	1.33192i	−0.938115	+	0.346324i	$0.887430\pi$
$954$	9.50485			0.307731
$955$	10.1416	−	17.5657i	0.328174	−	0.568414i
$956$	−0.137641	+	0.238401i	−0.00445163	+	0.00771045i
$957$	−0.191383			−0.00618654
$958$	26.1608	−	45.3119i	0.845218	−	1.46396i
$959$	−0.781544	−	1.35367i	−0.0252374	−	0.0437124i
$960$	−14.3902	−	24.9245i	−0.464442	−	0.804436i
$961$	57.1575			1.84379
$962$	44.4804	−	1.12666i	1.43410	−	0.0363250i
$963$	9.13369			0.294329
$964$	−0.392324	−	0.679526i	−0.0126359	−	0.0218860i
$965$	30.6907	+	53.1579i	0.987970	+	1.71121i
$966$	−5.43592	+	9.41528i	−0.174898	+	0.302932i
$967$	−44.3349			−1.42572			−0.712858	−	0.701309i	$-0.752599\pi$
$967$	−44.3349			−1.42572			−0.712858	+	0.701309i	$0.752599\pi$
$968$	1.48251	−	2.56779i	0.0476497	−	0.0825318i
$969$	19.2844	−	33.4016i	0.619505	−	1.07301i
$970$	31.9543			1.02599
$971$	9.09560	−	15.7540i	0.291892	−	0.505571i	−0.682365	−	0.731011i	$-0.739049\pi$
$971$	9.09560	−	15.7540i	0.291892	−	0.505571i	0.974257	+	0.225440i	$0.0723820\pi$
$972$	−0.113180	−	0.196033i	−0.00363025	−	0.00628778i
$973$	3.93112	+	6.80889i	0.126026	+	0.218283i
$974$	11.4856			0.368022
$975$	10.2896	−	18.9125i	0.329532	−	0.605686i
$976$	−29.5779			−0.946764
$977$	7.28215	+	12.6131i	0.232977	+	0.403527i	0.958683	−	0.284478i	$-0.0918201\pi$
$977$	7.28215	+	12.6131i	0.232977	+	0.403527i	−0.725706	+	0.688005i	$0.758487\pi$
$978$	1.37914	+	2.38874i	0.0441001	+	0.0763836i
$979$	2.68721	−	4.65439i	0.0858836	−	0.148755i
$980$	−3.48346			−0.111275
$981$	8.71813	−	15.1003i	0.278349	−	0.482114i
$982$	3.00490	−	5.20464i	0.0958902	−	0.166087i
$983$	−49.1745			−1.56842			−0.784212	−	0.620493i	$-0.786933\pi$
$983$	−49.1745			−1.56842			−0.784212	+	0.620493i	$0.786933\pi$
$984$	−0.371334	+	0.643169i	−0.0118377	+	0.0205035i
$985$	−30.9769	−	53.6536i	−0.987007	−	1.70955i
$986$	0.760746	+	1.31765i	0.0242271	+	0.0419625i
$987$	−6.68991			−0.212942
$988$	2.52013	−	4.63203i	0.0801759	−	0.147365i
$989$	−27.4874			−0.874047
$990$	−2.20564	−	3.82029i	−0.0701000	−	0.121417i
$991$	21.8636	+	37.8688i	0.694520	+	1.20294i	0.970342	+	0.241735i	$0.0777165\pi$
$991$	21.8636	+	37.8688i	0.694520	+	1.20294i	−0.275822	+	0.961209i	$0.588950\pi$
$992$	5.98134	−	10.3600i	0.189908	−	0.328930i
$993$	7.57995			0.240543
$994$	−7.57252	+	13.1160i	−0.240186	+	0.416014i
$995$	−22.1160	+	38.3060i	−0.701123	+	1.21438i
$996$	−2.22825			−0.0706048
$997$	−2.02494	+	3.50731i	−0.0641306	+	0.111078i	−0.896308	−	0.443432i	$-0.853761\pi$
$997$	−2.02494	+	3.50731i	−0.0641306	+	0.111078i	0.832177	+	0.554510i	$0.187094\pi$
$998$	18.6101	+	32.2337i	0.589093	+	1.02034i
$999$	4.63312	+	8.02479i	0.146585	+	0.253893i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.e.133.2	yes	10
13.3	even	3		5577.2.a.o.1.4		5
13.9	even	3	inner	429.2.i.e.100.2	✓	10
13.10	even	6		5577.2.a.u.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.e.100.2	✓	10	13.9	even	3	inner
429.2.i.e.133.2	yes	10	1.1	even	1	trivial
5577.2.a.o.1.4		5	13.3	even	3
5577.2.a.u.1.2		5	13.10	even	6

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.665890 - 1.15336i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.113180 - 0.196033i) q^{4} -3.31232 q^{5} +(0.665890 - 1.15336i) q^{6} +(0.767139 - 1.32872i) q^{7} -2.96502 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.665890 - 1.15336i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.113180 - 0.196033i) q^{4} -3.31232 q^{5} +(0.665890 - 1.15336i) q^{6} +(0.767139 - 1.32872i) q^{7} -2.96502 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.20564 + 3.82029i) q^{10} +(0.500000 + 0.866025i) q^{11} +0.226360 q^{12} +(-1.88126 - 3.07585i) q^{13} -2.04332 q^{14} +(-1.65616 - 2.86856i) q^{15} +(1.74802 + 3.02766i) q^{16} +(-2.98471 + 5.16968i) q^{17} +1.33178 q^{18} +(-3.23053 + 5.59545i) q^{19} +(-0.374889 + 0.649326i) q^{20} +1.53428 q^{21} +(0.665890 - 1.15336i) q^{22} +(-2.66033 - 4.60783i) q^{23} +(-1.48251 - 2.56779i) q^{24} +5.97148 q^{25} +(-2.29483 + 4.21794i) q^{26} -1.00000 q^{27} +(-0.173649 - 0.300770i) q^{28} +(0.0956916 + 0.165743i) q^{29} +(-2.20564 + 3.82029i) q^{30} -9.38922 q^{31} +(-0.637043 + 1.10339i) q^{32} +(-0.500000 + 0.866025i) q^{33} +7.94997 q^{34} +(-2.54101 + 4.40116i) q^{35} +(0.113180 + 0.196033i) q^{36} +(-4.63312 - 8.02479i) q^{37} +8.60472 q^{38} +(1.72313 - 3.16715i) q^{39} +9.82111 q^{40} +(-0.125238 - 0.216919i) q^{41} +(-1.02166 - 1.76957i) q^{42} +(2.58307 - 4.47402i) q^{43} +0.226360 q^{44} +(1.65616 - 2.86856i) q^{45} +(-3.54298 + 6.13662i) q^{46} -4.36030 q^{47} +(-1.74802 + 3.02766i) q^{48} +(2.32300 + 4.02355i) q^{49} +(-3.97635 - 6.88724i) q^{50} -5.96943 q^{51} +(-0.815891 + 0.0206660i) q^{52} +7.13695 q^{53} +(0.665890 + 1.15336i) q^{54} +(-1.65616 - 2.86856i) q^{55} +(-2.27458 + 3.93970i) q^{56} -6.46106 q^{57} +(0.127440 - 0.220733i) q^{58} +(4.90095 - 8.48870i) q^{59} -0.749777 q^{60} +(-4.23019 + 7.32691i) q^{61} +(6.25219 + 10.8291i) q^{62} +(0.767139 + 1.32872i) q^{63} +8.68889 q^{64} +(6.23135 + 10.1882i) q^{65} +1.33178 q^{66} +(3.40525 + 5.89807i) q^{67} +(0.675620 + 1.17021i) q^{68} +(2.66033 - 4.60783i) q^{69} +6.76814 q^{70} +(3.70598 - 6.41895i) q^{71} +(1.48251 - 2.56779i) q^{72} +13.2687 q^{73} +(-6.17030 + 10.6873i) q^{74} +(2.98574 + 5.17145i) q^{75} +(0.731263 + 1.26658i) q^{76} +1.53428 q^{77} +(-4.80026 + 0.121588i) q^{78} -6.63833 q^{79} +(-5.79001 - 10.0286i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.166790 + 0.288888i) q^{82} -9.84383 q^{83} +(0.173649 - 0.300770i) q^{84} +(9.88633 - 17.1236i) q^{85} -6.88018 q^{86} +(-0.0956916 + 0.165743i) q^{87} +(-1.48251 - 2.56779i) q^{88} +(-2.68721 - 4.65439i) q^{89} -4.41129 q^{90} +(-5.53014 + 0.140075i) q^{91} -1.20439 q^{92} +(-4.69461 - 8.13131i) q^{93} +(2.90348 + 5.02898i) q^{94} +(10.7006 - 18.5339i) q^{95} -1.27409 q^{96} +(3.62188 - 6.27329i) q^{97} +(3.09372 - 5.35848i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} + 5 q^{11} - 12 q^{12} - 3 q^{13} - 6 q^{14} + 2 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 5 q^{19} - 28 q^{20} + 18 q^{21} - 2 q^{22} + 5 q^{23} - 9 q^{24} + 42 q^{25} + 20 q^{26} - 10 q^{27} + 11 q^{28} - 12 q^{29} - 5 q^{30} - 36 q^{31} + 35 q^{32} - 5 q^{33} - 6 q^{34} - 6 q^{36} + q^{37} + 74 q^{38} + 6 q^{39} - 62 q^{40} - 30 q^{41} - 3 q^{42} + 3 q^{43} - 12 q^{44} - 2 q^{45} - 24 q^{46} - 44 q^{47} + 4 q^{48} - 14 q^{49} - 18 q^{50} + 6 q^{51} + 35 q^{52} + 14 q^{53} - 2 q^{54} + 2 q^{55} - 27 q^{56} - 10 q^{57} + 3 q^{58} + 12 q^{59} - 56 q^{60} - 18 q^{61} + 28 q^{62} + 9 q^{63} + 110 q^{64} - 28 q^{65} - 4 q^{66} + 37 q^{67} + 8 q^{68} - 5 q^{69} - 32 q^{70} + 17 q^{71} + 9 q^{72} + 4 q^{73} + q^{74} + 21 q^{75} + 26 q^{76} + 18 q^{77} + 25 q^{78} - 12 q^{79} - 38 q^{80} - 5 q^{81} + 36 q^{82} + 8 q^{83} - 11 q^{84} + 41 q^{85} - 28 q^{86} + 12 q^{87} - 9 q^{88} - 14 q^{89} - 10 q^{90} + 35 q^{91} - 12 q^{92} - 18 q^{93} - 20 q^{94} + 7 q^{95} + 70 q^{96} + 15 q^{97} + 4 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 + 5 * q^11 - 12 * q^12 - 3 * q^13 - 6 * q^14 + 2 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 5 * q^19 - 28 * q^20 + 18 * q^21 - 2 * q^22 + 5 * q^23 - 9 * q^24 + 42 * q^25 + 20 * q^26 - 10 * q^27 + 11 * q^28 - 12 * q^29 - 5 * q^30 - 36 * q^31 + 35 * q^32 - 5 * q^33 - 6 * q^34 - 6 * q^36 + q^37 + 74 * q^38 + 6 * q^39 - 62 * q^40 - 30 * q^41 - 3 * q^42 + 3 * q^43 - 12 * q^44 - 2 * q^45 - 24 * q^46 - 44 * q^47 + 4 * q^48 - 14 * q^49 - 18 * q^50 + 6 * q^51 + 35 * q^52 + 14 * q^53 - 2 * q^54 + 2 * q^55 - 27 * q^56 - 10 * q^57 + 3 * q^58 + 12 * q^59 - 56 * q^60 - 18 * q^61 + 28 * q^62 + 9 * q^63 + 110 * q^64 - 28 * q^65 - 4 * q^66 + 37 * q^67 + 8 * q^68 - 5 * q^69 - 32 * q^70 + 17 * q^71 + 9 * q^72 + 4 * q^73 + q^74 + 21 * q^75 + 26 * q^76 + 18 * q^77 + 25 * q^78 - 12 * q^79 - 38 * q^80 - 5 * q^81 + 36 * q^82 + 8 * q^83 - 11 * q^84 + 41 * q^85 - 28 * q^86 + 12 * q^87 - 9 * q^88 - 14 * q^89 - 10 * q^90 + 35 * q^91 - 12 * q^92 - 18 * q^93 - 20 * q^94 + 7 * q^95 + 70 * q^96 + 15 * q^97 + 4 * q^98 - 10 * q^99

Introduction

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