LMFDB - Embedded newform 429.2.i.f.100.1

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} - x^{9} + 7x^{8} + 4x^{7} + 32x^{6} + 3x^{5} + 30x^{4} - 7x^{3} + 26x^{2} - 5x + 1 $ x^10 - x^9 + 7x^8 + 4x^7 + 32x^6 + 3x^5 + 30x^4 - 7x^3 + 26x^2 - 5x + 1
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			100.1
Root			$1.40131 - 2.42714i$ of defining polynomial
Character	$\chi$	$=$	429.100
Dual form			429.2.i.f.133.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.901309 + 1.56111i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.624717 - 1.08204i) q^{4} -2.90617 q^{5} +(-0.901309 - 1.56111i) q^{6} +(-0.704431 - 1.22011i) q^{7} -1.35298 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.901309 + 1.56111i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.624717 - 1.08204i) q^{4} -2.90617 q^{5} +(-0.901309 - 1.56111i) q^{6} +(-0.704431 - 1.22011i) q^{7} -1.35298 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.61936 - 4.53686i) q^{10} +(-0.500000 + 0.866025i) q^{11} +1.24943 q^{12} +(3.57513 + 0.467344i) q^{13} +2.53964 q^{14} +(1.45308 - 2.51681i) q^{15} +(2.46889 - 4.27624i) q^{16} +(-1.84007 - 3.18709i) q^{17} +1.80262 q^{18} +(1.19688 + 2.07305i) q^{19} +(1.81553 + 3.14460i) q^{20} +1.40886 q^{21} +(-0.901309 - 1.56111i) q^{22} +(2.79585 - 4.84255i) q^{23} +(0.676492 - 1.17172i) q^{24} +3.44581 q^{25} +(-3.95188 + 5.15997i) q^{26} +1.00000 q^{27} +(-0.880141 + 1.52445i) q^{28} +(0.960637 - 1.66387i) q^{29} +(2.61936 + 4.53686i) q^{30} -7.17211 q^{31} +(3.09749 + 5.36500i) q^{32} +(-0.500000 - 0.866025i) q^{33} +6.63389 q^{34} +(2.04720 + 3.54585i) q^{35} +(-0.624717 + 1.08204i) q^{36} +(-0.171130 + 0.296407i) q^{37} -4.31503 q^{38} +(-2.19230 + 2.86249i) q^{39} +3.93200 q^{40} +(0.0680848 - 0.117926i) q^{41} +(-1.26982 + 2.19939i) q^{42} +(-5.63932 - 9.76759i) q^{43} +1.24943 q^{44} +(1.45308 + 2.51681i) q^{45} +(5.03985 + 8.72927i) q^{46} +2.74417 q^{47} +(2.46889 + 4.27624i) q^{48} +(2.50755 - 4.34321i) q^{49} +(-3.10574 + 5.37930i) q^{50} +3.68014 q^{51} +(-1.72776 - 4.16040i) q^{52} -6.17071 q^{53} +(-0.901309 + 1.56111i) q^{54} +(1.45308 - 2.51681i) q^{55} +(0.953084 + 1.65079i) q^{56} -2.39376 q^{57} +(1.73166 + 2.99933i) q^{58} +(1.71613 + 2.97243i) q^{59} -3.63107 q^{60} +(0.380923 + 0.659778i) q^{61} +(6.46429 - 11.1965i) q^{62} +(-0.704431 + 1.22011i) q^{63} -1.29161 q^{64} +(-10.3899 - 1.35818i) q^{65} +1.80262 q^{66} +(4.67939 - 8.10495i) q^{67} +(-2.29905 + 3.98206i) q^{68} +(2.79585 + 4.84255i) q^{69} -7.38063 q^{70} +(1.52645 + 2.64389i) q^{71} +(0.676492 + 1.17172i) q^{72} -2.98113 q^{73} +(-0.308483 - 0.534308i) q^{74} +(-1.72290 + 2.98416i) q^{75} +(1.49542 - 2.59015i) q^{76} +1.40886 q^{77} +(-2.49273 - 6.00241i) q^{78} -10.6762 q^{79} +(-7.17501 + 12.4275i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.122731 + 0.212576i) q^{82} -16.9231 q^{83} +(-0.880141 - 1.52445i) q^{84} +(5.34755 + 9.26223i) q^{85} +20.3311 q^{86} +(0.960637 + 1.66387i) q^{87} +(0.676492 - 1.17172i) q^{88} +(7.51460 - 13.0157i) q^{89} -5.23871 q^{90} +(-1.94823 - 4.69127i) q^{91} -6.98646 q^{92} +(3.58606 - 6.21123i) q^{93} +(-2.47335 + 4.28396i) q^{94} +(-3.47833 - 6.02464i) q^{95} -6.19497 q^{96} +(-7.85009 - 13.5968i) q^{97} +(4.52016 + 7.82915i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - 5 q^{3} - 6 q^{4} - 8 q^{5} + 4 q^{6} + 3 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 - 5 * q^3 - 6 * q^4 - 8 * q^5 + 4 * q^6 + 3 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 4 q^{2} - 5 q^{3} - 6 q^{4} - 8 q^{5} + 4 q^{6} + 3 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} - 5 q^{11} + 12 q^{12} + 5 q^{13} + 14 q^{14} + 4 q^{15} - 12 q^{16} - 9 q^{17} - 8 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} + 4 q^{22} + 9 q^{23} + 9 q^{24} + 2 q^{25} - 12 q^{26} + 10 q^{27} - q^{28} - 8 q^{29} + 5 q^{30} - 12 q^{31} + 27 q^{32} - 5 q^{33} - 14 q^{34} + 2 q^{35} - 6 q^{36} + 17 q^{37} - 2 q^{38} + 2 q^{39} + 46 q^{40} + 6 q^{41} - 7 q^{42} - 13 q^{43} + 12 q^{44} + 4 q^{45} - 6 q^{46} - 32 q^{47} - 12 q^{48} + 18 q^{49} - 8 q^{50} + 18 q^{51} + 7 q^{52} - 26 q^{53} + 4 q^{54} + 4 q^{55} - q^{56} - 18 q^{57} + 11 q^{58} + 8 q^{59} - 12 q^{60} - 4 q^{61} + 22 q^{62} + 3 q^{63} + 22 q^{64} + 26 q^{65} - 8 q^{66} + 5 q^{67} - 34 q^{68} + 9 q^{69} + 8 q^{70} + 19 q^{71} + 9 q^{72} - 4 q^{73} - 27 q^{74} - q^{75} - 6 q^{76} - 6 q^{77} - 3 q^{78} - 16 q^{79} + 32 q^{80} - 5 q^{81} - 16 q^{82} - 20 q^{83} - q^{84} + 21 q^{85} + 8 q^{86} - 8 q^{87} + 9 q^{88} + 32 q^{89} - 10 q^{90} - 17 q^{91} - 84 q^{92} + 6 q^{93} - 66 q^{94} - 11 q^{95} - 54 q^{96} - 5 q^{97} - 18 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - 5 * q^3 - 6 * q^4 - 8 * q^5 + 4 * q^6 + 3 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 - 5 * q^11 + 12 * q^12 + 5 * q^13 + 14 * q^14 + 4 * q^15 - 12 * q^16 - 9 * q^17 - 8 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 + 4 * q^22 + 9 * q^23 + 9 * q^24 + 2 * q^25 - 12 * q^26 + 10 * q^27 - q^28 - 8 * q^29 + 5 * q^30 - 12 * q^31 + 27 * q^32 - 5 * q^33 - 14 * q^34 + 2 * q^35 - 6 * q^36 + 17 * q^37 - 2 * q^38 + 2 * q^39 + 46 * q^40 + 6 * q^41 - 7 * q^42 - 13 * q^43 + 12 * q^44 + 4 * q^45 - 6 * q^46 - 32 * q^47 - 12 * q^48 + 18 * q^49 - 8 * q^50 + 18 * q^51 + 7 * q^52 - 26 * q^53 + 4 * q^54 + 4 * q^55 - q^56 - 18 * q^57 + 11 * q^58 + 8 * q^59 - 12 * q^60 - 4 * q^61 + 22 * q^62 + 3 * q^63 + 22 * q^64 + 26 * q^65 - 8 * q^66 + 5 * q^67 - 34 * q^68 + 9 * q^69 + 8 * q^70 + 19 * q^71 + 9 * q^72 - 4 * q^73 - 27 * q^74 - q^75 - 6 * q^76 - 6 * q^77 - 3 * q^78 - 16 * q^79 + 32 * q^80 - 5 * q^81 - 16 * q^82 - 20 * q^83 - q^84 + 21 * q^85 + 8 * q^86 - 8 * q^87 + 9 * q^88 + 32 * q^89 - 10 * q^90 - 17 * q^91 - 84 * q^92 + 6 * q^93 - 66 * q^94 - 11 * q^95 - 54 * q^96 - 5 * q^97 - 18 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	−0.901309	+	1.56111i	−0.637322	+	1.10387i	0.348696	+	0.937236i	$0.386625\pi$
$2$	−0.901309	+	1.56111i	−0.637322	+	1.10387i	−0.986018	+	0.166638i	$0.946709\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.624717	−	1.08204i	−0.312359	−	0.541021i
$5$	−2.90617			−1.29968			−0.649839	−	0.760072i	$-0.725164\pi$
$5$	−2.90617			−1.29968			−0.649839	+	0.760072i	$0.725164\pi$
$6$	−0.901309	−	1.56111i	−0.367958	−	0.637322i
$7$	−0.704431	−	1.22011i	−0.266250	−	0.461159i	0.701640	−	0.712531i	$-0.252451\pi$
$7$	−0.704431	−	1.22011i	−0.266250	−	0.461159i	−0.967890	+	0.251373i	$0.919118\pi$
$8$	−1.35298			−0.478352
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	2.61936	−	4.53686i	0.828313	−	1.43468i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	1.24943			0.360681
$13$	3.57513	+	0.467344i	0.991564	+	0.129618i
$13$	3.57513	+	0.467344i	0.991564	+	0.129618i
$14$	2.53964			0.678748
$15$	1.45308	−	2.51681i	0.375185	−	0.649839i
$16$	2.46889	−	4.27624i	0.617223	−	1.06906i
$17$	−1.84007	−	3.18709i	−0.446282	−	0.772984i	0.551858	−	0.833938i	$-0.313919\pi$
$17$	−1.84007	−	3.18709i	−0.446282	−	0.772984i	−0.998141	+	0.0609543i	$0.980586\pi$
$18$	1.80262			0.424881
$19$	1.19688	+	2.07305i	0.274583	+	0.475591i	0.970030	−	0.242986i	$-0.0781270\pi$
$19$	1.19688	+	2.07305i	0.274583	+	0.475591i	−0.695447	+	0.718577i	$0.744794\pi$
$20$	1.81553	+	3.14460i	0.405966	+	0.703153i
$21$	1.40886			0.307439
$22$	−0.901309	−	1.56111i	−0.192160	−	0.332831i
$23$	2.79585	−	4.84255i	0.582975	−	1.00974i	−0.412150	−	0.911116i	$-0.635222\pi$
$23$	2.79585	−	4.84255i	0.582975	−	1.00974i	0.995125	−	0.0986256i	$-0.0314446\pi$
$24$	0.676492	−	1.17172i	0.138088	−	0.239176i
$25$	3.44581			0.689162
$26$	−3.95188	+	5.15997i	−0.775027	+	1.01195i
$27$	1.00000			0.192450
$28$	−0.880141	+	1.52445i	−0.166331	+	0.288094i
$29$	0.960637	−	1.66387i	0.178386	−	0.308973i	−0.762942	−	0.646467i	$-0.776246\pi$
$29$	0.960637	−	1.66387i	0.178386	−	0.308973i	0.941328	+	0.337494i	$0.109579\pi$
$30$	2.61936	+	4.53686i	0.478227	+	0.828313i
$31$	−7.17211			−1.28815			−0.644075	−	0.764963i	$-0.722757\pi$
$31$	−7.17211			−1.28815			−0.644075	+	0.764963i	$0.722757\pi$
$32$	3.09749	+	5.36500i	0.547563	+	0.948408i
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$	6.63389			1.13770
$35$	2.04720	+	3.54585i	0.346039	+	0.599357i
$36$	−0.624717	+	1.08204i	−0.104120	+	0.180340i
$37$	−0.171130	+	0.296407i	−0.0281337	+	0.0487290i	−0.879749	−	0.475438i	$-0.842290\pi$
$37$	−0.171130	+	0.296407i	−0.0281337	+	0.0487290i	0.851616	+	0.524167i	$0.175623\pi$
$38$	−4.31503			−0.699990
$39$	−2.19230	+	2.86249i	−0.351049	+	0.458365i
$40$	3.93200			0.621703
$41$	0.0680848	−	0.117926i	0.0106331	−	0.0184170i	−0.860660	−	0.509180i	$-0.829949\pi$
$41$	0.0680848	−	0.117926i	0.0106331	−	0.0184170i	0.871293	+	0.490763i	$0.163282\pi$
$42$	−1.26982	+	2.19939i	−0.195938	+	0.339374i
$43$	−5.63932	−	9.76759i	−0.859988	−	1.48954i	−0.871939	−	0.489615i	$-0.837137\pi$
$43$	−5.63932	−	9.76759i	−0.859988	−	1.48954i	0.0119505	−	0.999929i	$-0.496196\pi$
$44$	1.24943			0.188359
$45$	1.45308	+	2.51681i	0.216613	+	0.375185i
$46$	5.03985	+	8.72927i	0.743085	+	1.28706i
$47$	2.74417			0.400278			0.200139	−	0.979767i	$-0.435861\pi$
$47$	2.74417			0.400278			0.200139	+	0.979767i	$0.435861\pi$
$48$	2.46889	+	4.27624i	0.356354	+	0.617223i
$49$	2.50755	−	4.34321i	0.358222	−	0.620458i
$50$	−3.10574	+	5.37930i	−0.439218	+	0.760748i
$51$	3.68014			0.515322
$52$	−1.72776	−	4.16040i	−0.239598	−	0.576944i
$53$	−6.17071			−0.847612			−0.423806	−	0.905753i	$-0.639306\pi$
$53$	−6.17071			−0.847612			−0.423806	+	0.905753i	$0.639306\pi$
$54$	−0.901309	+	1.56111i	−0.122653	+	0.212441i
$55$	1.45308	−	2.51681i	0.195934	−	0.339367i
$56$	0.953084	+	1.65079i	0.127361	+	0.220596i
$57$	−2.39376			−0.317061
$58$	1.73166	+	2.99933i	0.227378	+	0.393831i
$59$	1.71613	+	2.97243i	0.223422	+	0.386978i	0.955845	−	0.293872i	$-0.0949440\pi$
$59$	1.71613	+	2.97243i	0.223422	+	0.386978i	−0.732423	+	0.680850i	$0.761611\pi$
$60$	−3.63107			−0.468769
$61$	0.380923	+	0.659778i	0.0487722	+	0.0844759i	0.889381	−	0.457167i	$-0.151136\pi$
$61$	0.380923	+	0.659778i	0.0487722	+	0.0844759i	−0.840609	+	0.541643i	$0.817803\pi$
$62$	6.46429	−	11.1965i	0.820966	−	1.42195i
$63$	−0.704431	+	1.22011i	−0.0887500	+	0.153720i
$64$	−1.29161			−0.161451
$65$	−10.3899	−	1.35818i	−1.28871	−	0.168461i
$66$	1.80262			0.221887
$67$	4.67939	−	8.10495i	0.571679	−	0.990177i	−0.424715	−	0.905327i	$-0.639626\pi$
$67$	4.67939	−	8.10495i	0.571679	−	0.990177i	0.996394	−	0.0848496i	$-0.0270410\pi$
$68$	−2.29905	+	3.98206i	−0.278800	+	0.482896i
$69$	2.79585	+	4.84255i	0.336581	+	0.582975i
$70$	−7.38063			−0.882153
$71$	1.52645	+	2.64389i	0.181156	+	0.313772i	0.942275	−	0.334841i	$-0.108683\pi$
$71$	1.52645	+	2.64389i	0.181156	+	0.313772i	−0.761118	+	0.648613i	$0.775349\pi$
$72$	0.676492	+	1.17172i	0.0797253	+	0.138088i
$73$	−2.98113			−0.348914			−0.174457	−	0.984665i	$-0.555817\pi$
$73$	−2.98113			−0.348914			−0.174457	+	0.984665i	$0.555817\pi$
$74$	−0.308483	−	0.534308i	−0.0358604	−	0.0621121i
$75$	−1.72290	+	2.98416i	−0.198944	+	0.344581i
$76$	1.49542	−	2.59015i	0.171537	−	0.297110i
$77$	1.40886			0.160555
$78$	−2.49273	−	6.00241i	−0.282246	−	0.679639i
$79$	−10.6762			−1.20117			−0.600584	−	0.799561i	$-0.705065\pi$
$79$	−10.6762			−1.20117			−0.600584	+	0.799561i	$0.705065\pi$
$80$	−7.17501	+	12.4275i	−0.802191	+	1.38943i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.122731	+	0.212576i	0.0135534	+	0.0234751i
$83$	−16.9231			−1.85755			−0.928775	−	0.370644i	$-0.879137\pi$
$83$	−16.9231			−1.85755			−0.928775	+	0.370644i	$0.879137\pi$
$84$	−0.880141	−	1.52445i	−0.0960312	−	0.166331i
$85$	5.34755	+	9.26223i	0.580023	+	1.00463i
$86$	20.3311			2.19236
$87$	0.960637	+	1.66387i	0.102991	+	0.178386i
$88$	0.676492	−	1.17172i	0.0721143	−	0.124906i
$89$	7.51460	−	13.0157i	0.796546	−	1.37966i	−0.125306	−	0.992118i	$-0.539991\pi$
$89$	7.51460	−	13.0157i	0.796546	−	1.37966i	0.921853	−	0.387541i	$-0.126675\pi$
$90$	−5.23871			−0.552209
$91$	−1.94823	−	4.69127i	−0.204230	−	0.491779i
$92$	−6.98646			−0.728389
$93$	3.58606	−	6.21123i	0.371857	−	0.644075i
$94$	−2.47335	+	4.28396i	−0.255106	+	0.441857i
$95$	−3.47833	−	6.02464i	−0.356869	−	0.618115i
$96$	−6.19497			−0.632272
$97$	−7.85009	−	13.5968i	−0.797056	−	1.38054i	−0.921525	−	0.388318i	$-0.873056\pi$
$97$	−7.85009	−	13.5968i	−0.797056	−	1.38054i	0.124469	−	0.992223i	$-0.460277\pi$
$98$	4.52016	+	7.82915i	0.456605	+	0.790864i
$99$	1.00000			0.100504
$100$	−2.15266	−	3.72851i	−0.215266	−	0.372851i
$101$	−0.548407	+	0.949869i	−0.0545685	+	0.0945155i	−0.892019	−	0.451997i	$-0.850712\pi$
$101$	−0.548407	+	0.949869i	−0.0545685	+	0.0945155i	0.837451	+	0.546513i	$0.184045\pi$
$102$	−3.31694	+	5.74511i	−0.328426	+	0.568851i
$103$	−2.19361			−0.216143			−0.108072	−	0.994143i	$-0.534468\pi$
$103$	−2.19361			−0.216143			−0.108072	+	0.994143i	$0.534468\pi$
$104$	−4.83710	−	0.632308i	−0.474316	−	0.0620029i
$105$	−4.09439			−0.399572
$106$	5.56172	−	9.63318i	0.540202	−	0.935657i
$107$	3.17063	−	5.49169i	0.306516	−	0.530901i	−0.671082	−	0.741383i	$-0.734170\pi$
$107$	3.17063	−	5.49169i	0.306516	−	0.530901i	0.977598	+	0.210482i	$0.0675033\pi$
$108$	−0.624717	−	1.08204i	−0.0601135	−	0.104120i
$109$	−16.6691			−1.59661			−0.798307	−	0.602251i	$-0.794271\pi$
$109$	−16.6691			−1.59661			−0.798307	+	0.602251i	$0.794271\pi$
$110$	2.61936	+	4.53686i	0.249746	+	0.432572i
$111$	−0.171130	−	0.296407i	−0.0162430	−	0.0281337i
$112$	−6.95666			−0.657342
$113$	−5.57921	−	9.66348i	−0.524848	−	0.909063i	−0.999581	−	0.0289337i	$-0.990789\pi$
$113$	−5.57921	−	9.66348i	−0.524848	−	0.909063i	0.474733	−	0.880130i	$-0.342545\pi$
$114$	2.15752	−	3.73693i	0.202070	−	0.349995i
$115$	−8.12520	+	14.0733i	−0.757679	+	1.31234i
$116$	−2.40051			−0.222881
$117$	−1.38284	−	3.32983i	−0.127843	−	0.307843i
$118$	−6.18707			−0.569566
$119$	−2.59240	+	4.49018i	−0.237645	+	0.411614i
$120$	−1.96600	+	3.40521i	−0.179470	+	0.310852i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−1.37332			−0.124334
$123$	0.0680848	+	0.117926i	0.00613900	+	0.0106331i
$124$	4.48054	+	7.76053i	0.402365	+	0.696916i
$125$	4.51674			0.403989
$126$	−1.26982	−	2.19939i	−0.113125	−	0.195938i
$127$	−6.23779	+	10.8042i	−0.553514	+	0.958715i	0.444503	+	0.895777i	$0.353380\pi$
$127$	−6.23779	+	10.8042i	−0.553514	+	0.958715i	−0.998017	+	0.0629374i	$0.979953\pi$
$128$	−5.03083	+	8.71366i	−0.444667	+	0.770186i
$129$	11.2786			0.993029
$130$	11.4848	−	14.9957i	1.00729	−	1.31521i
$131$	4.07537			0.356067			0.178033	−	0.984024i	$-0.443027\pi$
$131$	4.07537			0.356067			0.178033	+	0.984024i	$0.443027\pi$
$132$	−0.624717	+	1.08204i	−0.0543747	+	0.0941797i
$133$	1.68624	−	2.92065i	0.146215	−	0.253252i
$134$	8.43516	+	14.6101i	0.728687	+	1.26212i
$135$	−2.90617			−0.250123
$136$	2.48958	+	4.31208i	0.213480	+	0.369758i
$137$	−2.72779	−	4.72467i	−0.233051	−	0.403656i	0.725653	−	0.688060i	$-0.241538\pi$
$137$	−2.72779	−	4.72467i	−0.233051	−	0.403656i	−0.958704	+	0.284404i	$0.908204\pi$
$138$	−10.0797			−0.858041
$139$	8.68818	+	15.0484i	0.736921	+	1.27639i	0.953875	+	0.300204i	$0.0970546\pi$
$139$	8.68818	+	15.0484i	0.736921	+	1.27639i	−0.216954	+	0.976182i	$0.569612\pi$
$140$	2.55784	−	4.43030i	0.216177	−	0.374429i
$141$	−1.37208	+	2.37652i	−0.115550	+	0.200139i
$142$	−5.50321			−0.461819
$143$	−2.19230	+	2.86249i	−0.183329	+	0.239373i
$144$	−4.93778			−0.411482
$145$	−2.79177	+	4.83549i	−0.231844	+	0.401566i
$146$	2.68692	−	4.65388i	0.222371	−	0.385158i
$147$	2.50755	+	4.34321i	0.206819	+	0.358222i
$148$	0.427633			0.0351512
$149$	6.93673	+	12.0148i	0.568279	+	0.984288i	0.996736	+	0.0807260i	$0.0257239\pi$
$149$	6.93673	+	12.0148i	0.568279	+	0.984288i	−0.428457	+	0.903562i	$0.640943\pi$
$150$	−3.10574	−	5.37930i	−0.253583	−	0.439218i
$151$	−18.6348			−1.51648			−0.758239	−	0.651977i	$-0.773940\pi$
$151$	−18.6348			−1.51648			−0.758239	+	0.651977i	$0.773940\pi$
$152$	−1.61936	−	2.80481i	−0.131347	−	0.227500i
$153$	−1.84007	+	3.18709i	−0.148761	+	0.257661i
$154$	−1.26982	+	2.19939i	−0.102325	+	0.177232i
$155$	20.8434			1.67418
$156$	4.46690	+	0.583916i	0.357638	+	0.0467507i
$157$	9.23600			0.737113			0.368557	−	0.929605i	$-0.379852\pi$
$157$	9.23600			0.737113			0.368557	+	0.929605i	$0.379852\pi$
$158$	9.62258	−	16.6668i	0.765531	−	1.32594i
$159$	3.08535	−	5.34399i	0.244685	−	0.423806i
$160$	−9.00181	−	15.5916i	−0.711656	−	1.23262i
$161$	−7.87793			−0.620868
$162$	−0.901309	−	1.56111i	−0.0708136	−	0.122653i
$163$	−3.95485	−	6.85001i	−0.309768	−	0.536534i	0.668543	−	0.743673i	$-0.266918\pi$
$163$	−3.95485	−	6.85001i	−0.309768	−	0.536534i	−0.978312	+	0.207139i	$0.933585\pi$
$164$	−0.170135			−0.0132853
$165$	1.45308	+	2.51681i	0.113122	+	0.195934i
$166$	15.2529	−	26.4189i	1.18386	−	2.05050i
$167$	10.3312	−	17.8941i	0.799449	−	1.38469i	−0.120526	−	0.992710i	$-0.538458\pi$
$167$	10.3312	−	17.8941i	0.799449	−	1.38469i	0.919975	−	0.391977i	$-0.128209\pi$
$168$	−1.90617			−0.147064
$169$	12.5632	+	3.34163i	0.966398	+	0.257049i
$170$	−19.2792			−1.47865
$171$	1.19688	−	2.07305i	0.0915276	−	0.158530i
$172$	−7.04596	+	12.2040i	−0.537250	+	0.930544i
$173$	−1.68737	−	2.92261i	−0.128288	−	0.222202i	0.794725	−	0.606969i	$-0.207615\pi$
$173$	−1.68737	−	2.92261i	−0.128288	−	0.222202i	−0.923013	+	0.384768i	$0.874282\pi$
$174$	−3.46332			−0.262554
$175$	−2.42734	−	4.20427i	−0.183489	−	0.317813i
$176$	2.46889	+	4.27624i	0.186100	+	0.322334i
$177$	−3.43227			−0.257985
$178$	13.5460	+	23.4623i	1.01531	+	1.75857i
$179$	−6.41737	+	11.1152i	−0.479657	+	0.830789i	−0.999728	−	0.0233334i	$-0.992572\pi$
$179$	−6.41737	+	11.1152i	−0.479657	+	0.830789i	0.520071	+	0.854123i	$0.325905\pi$
$180$	1.81553	−	3.14460i	0.135322	−	0.234384i
$181$	22.3924			1.66441			0.832206	−	0.554466i	$-0.187078\pi$
$181$	22.3924			1.66441			0.832206	+	0.554466i	$0.187078\pi$
$182$	9.07956	+	1.18689i	0.673022	+	0.0879778i
$183$	−0.761846			−0.0563173
$184$	−3.78274	+	6.55189i	−0.278867	+	0.483012i
$185$	0.497334	−	0.861408i	0.0365647	−	0.0633319i
$186$	6.46429	+	11.1965i	0.473985	+	0.820966i
$187$	3.68014			0.269118
$188$	−1.71433	−	2.96931i	−0.125030	−	0.216559i
$189$	−0.704431	−	1.22011i	−0.0512398	−	0.0887500i
$190$	12.5402			0.909762
$191$	1.68276	+	2.91463i	0.121760	+	0.210895i	0.920462	−	0.390832i	$-0.127813\pi$
$191$	1.68276	+	2.91463i	0.121760	+	0.210895i	−0.798702	+	0.601727i	$0.794479\pi$
$192$	0.645805	−	1.11857i	0.0466070	−	0.0807256i
$193$	−9.42520	+	16.3249i	−0.678441	+	1.17509i	0.297010	+	0.954874i	$0.404011\pi$
$193$	−9.42520	+	16.3249i	−0.678441	+	1.17509i	−0.975450	+	0.220219i	$0.929323\pi$
$194$	28.3015			2.03193
$195$	6.37119	−	8.31886i	0.456250	−	0.595726i
$196$	−6.26605			−0.447575
$197$	7.15007	−	12.3843i	0.509422	−	0.882344i	−0.490519	−	0.871431i	$-0.663193\pi$
$197$	7.15007	−	12.3843i	0.509422	−	0.882344i	0.999940	−	0.0109134i	$-0.00347392\pi$
$198$	−0.901309	+	1.56111i	−0.0640533	+	0.110944i
$199$	11.7108	+	20.2837i	0.830157	+	1.43787i	0.897914	+	0.440171i	$0.145082\pi$
$199$	11.7108	+	20.2837i	0.830157	+	1.43787i	−0.0677572	+	0.997702i	$0.521584\pi$
$200$	−4.66212			−0.329662
$201$	4.67939	+	8.10495i	0.330059	+	0.571679i
$202$	−0.988569	−	1.71225i	−0.0695555	−	0.120474i
$203$	−2.70681			−0.189981
$204$	−2.29905	−	3.98206i	−0.160965	−	0.278800i
$205$	−0.197866	+	0.342714i	−0.0138196	+	0.0239362i
$206$	1.97712	−	3.42448i	0.137753	−	0.238595i
$207$	−5.59170			−0.388650
$208$	10.8251	−	14.1343i	0.750585	−	0.980040i
$209$	−2.39376			−0.165580
$210$	3.69031	−	6.39181i	0.254656	−	0.441077i
$211$	−3.30355	+	5.72192i	−0.227426	+	0.393913i	−0.957044	−	0.289941i	$-0.906364\pi$
$211$	−3.30355	+	5.72192i	−0.227426	+	0.393913i	0.729619	+	0.683854i	$0.239698\pi$
$212$	3.85495	+	6.67697i	0.264759	+	0.458576i
$213$	−3.05290			−0.209181
$214$	5.71543	+	9.89942i	0.390699	+	0.676710i
$215$	16.3888	+	28.3863i	1.11771	+	1.93593i
$216$	−1.35298			−0.0920589
$217$	5.05226	+	8.75077i	0.342970	+	0.594041i
$218$	15.0240	−	26.0224i	1.01756	−	1.76246i
$219$	1.49056	−	2.58173i	0.100723	−	0.174457i
$220$	−3.63107			−0.244806
$221$	−5.08903	−	12.2542i	−0.342325	−	0.824309i
$222$	0.616966			0.0414081
$223$	−0.176270	+	0.305309i	−0.0118039	+	0.0204450i	−0.871867	−	0.489743i	$-0.837091\pi$
$223$	−0.176270	+	0.305309i	−0.0118039	+	0.0204450i	0.860063	+	0.510188i	$0.170424\pi$
$224$	4.36393	−	7.55855i	0.291578	−	0.505027i
$225$	−1.72290	−	2.98416i	−0.114860	−	0.198944i
$226$	20.1144			1.33799
$227$	4.10506	+	7.11017i	0.272462	+	0.471919i	0.969492	−	0.245124i	$-0.0788286\pi$
$227$	4.10506	+	7.11017i	0.272462	+	0.471919i	−0.697029	+	0.717043i	$0.745495\pi$
$228$	1.49542	+	2.59015i	0.0990367	+	0.171537i
$229$	7.80991			0.516093			0.258047	−	0.966132i	$-0.416921\pi$
$229$	7.80991			0.516093			0.258047	+	0.966132i	$0.416921\pi$
$230$	−14.6466	−	25.3687i	−0.965771	−	1.67276i
$231$	−0.704431	+	1.22011i	−0.0463482	+	0.0802774i
$232$	−1.29973	+	2.25119i	−0.0853312	+	0.147798i
$233$	−7.15319			−0.468621			−0.234311	−	0.972162i	$-0.575283\pi$
$233$	−7.15319			−0.468621			−0.234311	+	0.972162i	$0.575283\pi$
$234$	6.44461	+	0.842443i	0.421297	+	0.0550722i
$235$	−7.97502			−0.520233
$236$	2.14420	−	3.71386i	0.139575	−	0.241752i
$237$	5.33811	−	9.24588i	0.346748	−	0.600584i
$238$	−4.67312	−	8.09408i	−0.302913	−	0.524661i
$239$	−12.8357			−0.830275			−0.415138	−	0.909759i	$-0.636267\pi$
$239$	−12.8357			−0.830275			−0.415138	+	0.909759i	$0.636267\pi$
$240$	−7.17501	−	12.4275i	−0.463145	−	0.802191i
$241$	−8.70249	−	15.0732i	−0.560577	−	0.970948i	−0.997446	−	0.0714226i	$-0.977246\pi$
$241$	−8.70249	−	15.0732i	−0.560577	−	0.970948i	0.436869	−	0.899525i	$-0.356087\pi$
$242$	1.80262			0.115877
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	0.475938	−	0.824349i	0.0304688	−	0.0527736i
$245$	−7.28737	+	12.6221i	−0.465573	+	0.806396i
$246$	−0.245462			−0.0156501
$247$	3.31017	+	7.97080i	0.210621	+	0.507170i
$248$	9.70375			0.616188
$249$	8.46154	−	14.6558i	0.536229	−	0.928775i
$250$	−4.07098	+	7.05114i	−0.257471	+	0.445953i
$251$	6.83438	+	11.8375i	0.431383	+	0.747176i	0.996993	−	0.0774964i	$-0.0246926\pi$
$251$	6.83438	+	11.8375i	0.431383	+	0.747176i	−0.565610	+	0.824673i	$0.691359\pi$
$252$	1.76028			0.110887
$253$	2.79585	+	4.84255i	0.175773	+	0.304449i
$254$	−11.2444	−	19.4758i	−0.705533	−	1.22202i
$255$	−10.6951			−0.669753
$256$	−10.3603	−	17.9445i	−0.647518	−	1.12153i
$257$	10.6347	−	18.4198i	0.663372	−	1.14899i	−0.316351	−	0.948642i	$-0.602458\pi$
$257$	10.6347	−	18.4198i	0.663372	−	1.14899i	0.979724	−	0.200353i	$-0.0642088\pi$
$258$	−10.1655	+	17.6072i	−0.632879	+	1.09618i
$259$	0.482199			0.0299624
$260$	5.02117	+	12.0908i	0.311400	+	0.749842i
$261$	−1.92127			−0.118924
$262$	−3.67317	+	6.36212i	−0.226929	+	0.393053i
$263$	−7.32697	+	12.6907i	−0.451800	+	0.782541i	−0.998498	−	0.0547892i	$-0.982551\pi$
$263$	−7.32697	+	12.6907i	−0.451800	+	0.782541i	0.546698	+	0.837330i	$0.315885\pi$
$264$	0.676492	+	1.17172i	0.0416352	+	0.0721143i
$265$	17.9331			1.10162
$266$	3.03964	+	5.26481i	0.186372	+	0.322806i
$267$	7.51460	+	13.0157i	0.459886	+	0.796546i
$268$	−11.6932			−0.714275
$269$	−8.39052	−	14.5328i	−0.511579	−	0.886081i	−0.999910	−	0.0134221i	$-0.995727\pi$
$269$	−8.39052	−	14.5328i	−0.511579	−	0.886081i	0.488331	−	0.872658i	$-0.337606\pi$
$270$	2.61936	−	4.53686i	0.159409	−	0.276104i
$271$	−14.2006	+	24.5962i	−0.862626	+	1.49411i	0.00676017	+	0.999977i	$0.497848\pi$
$271$	−14.2006	+	24.5962i	−0.862626	+	1.49411i	−0.869386	+	0.494134i	$0.835485\pi$
$272$	−18.1717			−1.10182
$273$	5.03687	+	0.658423i	0.304845	+	0.0398496i
$274$	9.83434			0.594114
$275$	−1.72290	+	2.98416i	−0.103895	+	0.179952i
$276$	3.49323	−	6.05045i	0.210268	−	0.364194i
$277$	−4.74570	−	8.21980i	−0.285142	−	0.493880i	0.687502	−	0.726183i	$-0.258707\pi$
$277$	−4.74570	−	8.21980i	−0.285142	−	0.493880i	−0.972644	+	0.232303i	$0.925374\pi$
$278$	−31.3229			−1.87863
$279$	3.58606	+	6.21123i	0.214692	+	0.371857i
$280$	−2.76982	−	4.79747i	−0.165528	−	0.286704i
$281$	21.7208			1.29575			0.647876	−	0.761746i	$-0.275657\pi$
$281$	21.7208			1.29575			0.647876	+	0.761746i	$0.275657\pi$
$282$	−2.47335	−	4.28396i	−0.147286	−	0.255106i
$283$	−7.76918	+	13.4566i	−0.461830	+	0.799912i	−0.999052	−	0.0435283i	$-0.986140\pi$
$283$	−7.76918	+	13.4566i	−0.461830	+	0.799912i	0.537223	+	0.843440i	$0.319473\pi$
$284$	1.90720	−	3.30336i	0.113171	−	0.196019i
$285$	6.95666			0.412077
$286$	−2.49273	−	6.00241i	−0.147398	−	0.354930i
$287$	−0.191844			−0.0113242
$288$	3.09749	−	5.36500i	0.182521	−	0.316136i
$289$	1.72829	−	2.99349i	0.101664	−	0.176088i
$290$	−5.03250	−	8.71655i	−0.295519	−	0.511853i
$291$	15.7002			0.920361
$292$	1.86236	+	3.22570i	0.108986	+	0.188770i
$293$	−2.07081	−	3.58674i	−0.120978	−	0.209540i	0.799176	−	0.601097i	$-0.205270\pi$
$293$	−2.07081	−	3.58674i	−0.120978	−	0.209540i	−0.920154	+	0.391558i	$0.871936\pi$
$294$	−9.04032			−0.527242
$295$	−4.98737	−	8.63838i	−0.290376	−	0.502946i
$296$	0.231537	−	0.401033i	0.0134578	−	0.0233096i
$297$	−0.500000	+	0.866025i	−0.0290129	+	0.0502519i
$298$	−25.0086			−1.44871
$299$	12.2587	−	16.0061i	0.708937	−	0.925659i
$300$	4.30531			0.248567
$301$	−7.94503	+	13.7612i	−0.457944	+	0.793182i
$302$	16.7957	−	29.0910i	0.966484	−	1.67400i
$303$	−0.548407	−	0.949869i	−0.0315052	−	0.0545685i
$304$	11.8198			0.677915
$305$	−1.10703	−	1.91743i	−0.0633881	−	0.109791i
$306$	−3.31694	−	5.74511i	−0.189617	−	0.328426i
$307$	28.0449			1.60061			0.800304	−	0.599595i	$-0.204672\pi$
$307$	28.0449			1.60061			0.800304	+	0.599595i	$0.204672\pi$
$308$	−0.880141	−	1.52445i	−0.0501507	−	0.0868635i
$309$	1.09681	−	1.89972i	0.0623951	−	0.108072i
$310$	−18.7863	+	32.5388i	−1.06699	+	1.84808i
$311$	−21.4758			−1.21778			−0.608889	−	0.793255i	$-0.708385\pi$
$311$	−21.4758			−1.21778			−0.608889	+	0.793255i	$0.708385\pi$
$312$	2.96614	−	3.87290i	0.167925	−	0.219260i
$313$	−23.8001			−1.34526			−0.672630	−	0.739979i	$-0.734835\pi$
$313$	−23.8001			−1.34526			−0.672630	+	0.739979i	$0.734835\pi$
$314$	−8.32450	+	14.4185i	−0.469778	+	0.813680i
$315$	2.04720	−	3.54585i	0.115346	−	0.199786i
$316$	6.66962	+	11.5521i	0.375196	+	0.649858i
$317$	−16.3873			−0.920401			−0.460200	−	0.887815i	$-0.652222\pi$
$317$	−16.3873			−0.920401			−0.460200	+	0.887815i	$0.652222\pi$
$318$	5.56172	+	9.63318i	0.311886	+	0.540202i
$319$	0.960637	+	1.66387i	0.0537853	+	0.0931589i
$320$	3.75363			0.209835
$321$	3.17063	+	5.49169i	0.176967	+	0.306516i
$322$	7.10045	−	12.2983i	0.395693	−	0.685360i
$323$	4.40468	−	7.62912i	0.245083	−	0.424496i
$324$	1.24943			0.0694130
$325$	12.3192	+	1.61038i	0.683348	+	0.0893277i
$326$	14.2582			0.789688
$327$	8.33456	−	14.4359i	0.460902	−	0.798307i
$328$	−0.0921176	+	0.159552i	−0.00508635	+	0.00880981i
$329$	−1.93308	−	3.34819i	−0.106574	−	0.184592i
$330$	−5.23871			−0.288382
$331$	−8.10697	−	14.0417i	−0.445599	−	0.771801i	0.552494	−	0.833517i	$-0.313676\pi$
$331$	−8.10697	−	14.0417i	−0.445599	−	0.771801i	−0.998094	+	0.0617158i	$0.980343\pi$
$332$	10.5721	+	18.3115i	0.580222	+	1.00497i
$333$	0.342261			0.0187558
$334$	18.6231	+	32.2562i	1.01901	+	1.76498i
$335$	−13.5991	+	23.5543i	−0.742998	+	1.28691i
$336$	3.47833	−	6.02464i	0.189758	−	0.328671i
$337$	13.9667			0.760816			0.380408	−	0.924819i	$-0.375784\pi$
$337$	13.9667			0.760816			0.380408	+	0.924819i	$0.375784\pi$
$338$	−16.5400	+	16.6007i	−0.899656	+	0.902959i
$339$	11.1584			0.606042
$340$	6.68141	−	11.5725i	0.362350	−	0.627609i
$341$	3.58606	−	6.21123i	0.194196	−	0.336357i
$342$	2.15752	+	3.73693i	0.116665	+	0.202070i
$343$	−16.9276			−0.914006
$344$	7.62991	+	13.2154i	0.411377	+	0.712526i
$345$	−8.12520	−	14.0733i	−0.437446	−	0.757679i
$346$	6.08336			0.327044
$347$	2.18258	+	3.78034i	0.117167	+	0.202940i	0.918644	−	0.395086i	$-0.129285\pi$
$347$	2.18258	+	3.78034i	0.117167	+	0.202940i	−0.801477	+	0.598026i	$0.795952\pi$
$348$	1.20025	−	2.07890i	0.0643403	−	0.111441i
$349$	13.0950	−	22.6812i	0.700958	−	1.21409i	−0.267173	−	0.963649i	$-0.586089\pi$
$349$	13.0950	−	22.6812i	0.700958	−	1.21409i	0.968131	−	0.250446i	$-0.0805772\pi$
$350$	8.75112			0.467767
$351$	3.57513	+	0.467344i	0.190827	+	0.0249450i
$352$	−6.19497			−0.330193
$353$	−14.3710	+	24.8914i	−0.764894	+	1.32483i	0.175409	+	0.984496i	$0.443875\pi$
$353$	−14.3710	+	24.8914i	−0.764894	+	1.32483i	−0.940303	+	0.340339i	$0.889458\pi$
$354$	3.09354	−	5.35816i	0.164420	−	0.284783i
$355$	−4.43612	−	7.68358i	−0.235445	−	0.407802i
$356$	−18.7780			−0.995233
$357$	−2.59240	−	4.49018i	−0.137205	−	0.237645i
$358$	−11.5681	−	20.0365i	−0.611391	−	1.05896i
$359$	−32.8065			−1.73146			−0.865730	−	0.500511i	$-0.833146\pi$
$359$	−32.8065			−1.73146			−0.865730	+	0.500511i	$0.833146\pi$
$360$	−1.96600	−	3.40521i	−0.103617	−	0.179470i
$361$	6.63497	−	11.4921i	0.349209	−	0.604847i
$362$	−20.1825	+	34.9570i	−1.06077	+	1.83730i
$363$	1.00000			0.0524864
$364$	−3.85906	+	5.03878i	−0.202270	+	0.264104i
$365$	8.66365			0.453476
$366$	0.686659	−	1.18933i	0.0358922	−	0.0621672i
$367$	−11.9410	+	20.6824i	−0.623313	+	1.07961i	0.365551	+	0.930791i	$0.380880\pi$
$367$	−11.9410	+	20.6824i	−0.623313	+	1.07961i	−0.988864	+	0.148819i	$0.952453\pi$
$368$	−13.8053	−	23.9115i	−0.719650	−	1.24647i
$369$	−0.136170			−0.00708871
$370$	0.896503	+	1.55279i	0.0466070	+	0.0807257i
$371$	4.34684	+	7.52895i	0.225677	+	0.390883i
$372$	−8.96108			−0.464611
$373$	−10.4506	−	18.1010i	−0.541111	−	0.937232i	−0.998841	−	0.0481406i	$-0.984670\pi$
$373$	−10.4506	−	18.1010i	−0.541111	−	0.937232i	0.457729	−	0.889092i	$-0.348663\pi$
$374$	−3.31694	+	5.74511i	−0.171515	+	0.297073i
$375$	−2.25837	+	3.91161i	−0.116622	+	0.201995i
$376$	−3.71282			−0.191474
$377$	4.21201	−	5.49962i	0.216929	−	0.283245i
$378$	2.53964			0.130625
$379$	15.8980	−	27.5362i	0.816628	−	1.41444i	−0.0915258	−	0.995803i	$-0.529174\pi$
$379$	15.8980	−	27.5362i	0.816628	−	1.41444i	0.908153	−	0.418638i	$-0.137492\pi$
$380$	−4.34594	+	7.52740i	−0.222942	+	0.386147i
$381$	−6.23779	−	10.8042i	−0.319572	−	0.553514i
$382$	−6.06675			−0.310402
$383$	11.5713	+	20.0421i	0.591267	+	1.02410i	0.994062	+	0.108814i	$0.0347053\pi$
$383$	11.5713	+	20.0421i	0.591267	+	1.02410i	−0.402795	+	0.915290i	$0.631961\pi$
$384$	−5.03083	−	8.71366i	−0.256729	−	0.444667i
$385$	−4.09439			−0.208669
$386$	−16.9900	−	29.4276i	−0.864770	−	1.49783i
$387$	−5.63932	+	9.76759i	−0.286663	+	0.496514i
$388$	−9.80818	+	16.9883i	−0.497935	+	0.862448i
$389$	−22.3577			−1.13358			−0.566790	−	0.823862i	$-0.691815\pi$
$389$	−22.3577			−1.13358			−0.566790	+	0.823862i	$0.691815\pi$
$390$	7.24428	+	17.4440i	0.366828	+	0.883312i
$391$	−20.5782			−1.04068
$392$	−3.39268	+	5.87629i	−0.171356	+	0.296797i
$393$	−2.03768	+	3.52937i	−0.102788	+	0.178033i
$394$	12.8889	+	22.3241i	0.649331	+	1.12467i
$395$	31.0269			1.56113
$396$	−0.624717	−	1.08204i	−0.0313932	−	0.0543747i
$397$	−11.3445	−	19.6492i	−0.569363	−	0.986166i	−0.996629	−	0.0820403i	$-0.973856\pi$
$397$	−11.3445	−	19.6492i	−0.569363	−	0.986166i	0.427266	−	0.904126i	$-0.359477\pi$
$398$	−42.2202			−2.11631
$399$	1.68624	+	2.92065i	0.0844174	+	0.146215i
$400$	8.50733	−	14.7351i	0.425366	−	0.736756i
$401$	16.1986	−	28.0568i	0.808921	−	1.40109i	−0.104691	−	0.994505i	$-0.533385\pi$
$401$	16.1986	−	28.0568i	0.808921	−	1.40109i	0.913612	−	0.406587i	$-0.133281\pi$
$402$	−16.8703			−0.841415
$403$	−25.6413	−	3.35184i	−1.27728	−	0.166967i
$404$	1.37040			0.0681798
$405$	1.45308	−	2.51681i	0.0722043	−	0.125062i
$406$	2.43967	−	4.22564i	0.121079	−	0.209715i
$407$	−0.171130	−	0.296407i	−0.00848262	−	0.0146923i
$408$	−4.97917			−0.246505
$409$	13.4471	+	23.2911i	0.664918	+	1.15167i	0.979308	+	0.202378i	$0.0648668\pi$
$409$	13.4471	+	23.2911i	0.664918	+	1.15167i	−0.314390	+	0.949294i	$0.601800\pi$
$410$	−0.356677	−	0.617782i	−0.0176150	−	0.0305101i
$411$	5.45558			0.269104
$412$	1.37039	+	2.37358i	0.0675142	+	0.116938i
$413$	2.41780	−	4.18775i	0.118972	−	0.206066i
$414$	5.03985	−	8.72927i	0.247695	−	0.429020i
$415$	49.1813			2.41422
$416$	8.56663	+	20.6282i	0.420014	+	1.01138i
$417$	−17.3764			−0.850924
$418$	2.15752	−	3.73693i	0.105528	−	0.182779i
$419$	−11.8033	+	20.4439i	−0.576628	+	0.998748i	0.419235	+	0.907878i	$0.362298\pi$
$419$	−11.8033	+	20.4439i	−0.576628	+	0.998748i	−0.995863	+	0.0908706i	$0.971035\pi$
$420$	2.55784	+	4.43030i	0.124810	+	0.216177i
$421$	25.3078			1.23343			0.616714	−	0.787187i	$-0.288463\pi$
$421$	25.3078			1.23343			0.616714	+	0.787187i	$0.288463\pi$
$422$	−5.95504	−	10.3144i	−0.289887	−	0.502099i
$423$	−1.37208	−	2.37652i	−0.0667130	−	0.115550i
$424$	8.34887			0.405457
$425$	−6.34053	−	10.9821i	−0.307561	−	0.532711i
$426$	2.75161	−	4.76592i	0.133316	−	0.230910i
$427$	0.536668	−	0.929536i	0.0259712	−	0.0449834i
$428$	−7.92298			−0.382972
$429$	−1.38284	−	3.32983i	−0.0667639	−	0.160766i
$430$	−59.0856			−2.84936
$431$	−6.79470	+	11.7688i	−0.327289	+	0.566881i	−0.981973	−	0.189021i	$-0.939468\pi$
$431$	−6.79470	+	11.7688i	−0.327289	+	0.566881i	0.654684	+	0.755903i	$0.272802\pi$
$432$	2.46889	−	4.27624i	0.118785	−	0.205741i
$433$	−5.76282	−	9.98150i	−0.276944	−	0.479680i	0.693680	−	0.720283i	$-0.255988\pi$
$433$	−5.76282	−	9.98150i	−0.276944	−	0.479680i	−0.970624	+	0.240603i	$0.922655\pi$
$434$	−18.2146			−0.874329
$435$	−2.79177	−	4.83549i	−0.133855	−	0.231844i
$436$	10.4135	+	18.0367i	0.498716	+	0.863801i
$437$	13.3852			0.640299
$438$	2.68692	+	4.65388i	0.128386	+	0.222371i
$439$	−7.63403	+	13.2225i	−0.364353	+	0.631077i	−0.988672	−	0.150092i	$-0.952043\pi$
$439$	−7.63403	+	13.2225i	−0.364353	+	0.631077i	0.624320	+	0.781169i	$0.285376\pi$
$440$	−1.96600	+	3.40521i	−0.0937253	+	0.162337i
$441$	−5.01511			−0.238815
$442$	23.7170	+	3.10031i	1.12810	+	0.147466i
$443$	18.5447			0.881086			0.440543	−	0.897731i	$-0.354786\pi$
$443$	18.5447			0.881086			0.440543	+	0.897731i	$0.354786\pi$
$444$	−0.213816	+	0.370341i	−0.0101473	+	0.0175756i
$445$	−21.8387	+	37.8257i	−1.03525	+	1.79311i
$446$	−0.317748	−	0.550356i	−0.0150458	−	0.0260601i
$447$	−13.8735			−0.656192
$448$	0.909850	+	1.57591i	0.0429864	+	0.0744546i
$449$	−6.02668	−	10.4385i	−0.284417	−	0.492624i	0.688051	−	0.725662i	$-0.258467\pi$
$449$	−6.02668	−	10.4385i	−0.284417	−	0.492624i	−0.972468	+	0.233038i	$0.925133\pi$
$450$	6.21148			0.292812
$451$	0.0680848	+	0.117926i	0.00320599	+	0.00555294i
$452$	−6.97086	+	12.0739i	−0.327882	+	0.567908i
$453$	9.31739	−	16.1382i	0.437769	−	0.758239i
$454$	−14.7997			−0.694585
$455$	5.66187	+	13.6336i	0.265433	+	0.639154i
$456$	3.23871			0.151667
$457$	−9.44307	+	16.3559i	−0.441728	+	0.765096i	−0.997818	−	0.0660266i	$-0.978968\pi$
$457$	−9.44307	+	16.3559i	−0.441728	+	0.765096i	0.556090	+	0.831122i	$0.312301\pi$
$458$	−7.03915	+	12.1922i	−0.328918	+	0.569702i
$459$	−1.84007	−	3.18709i	−0.0858871	−	0.148761i
$460$	20.3038			0.946670
$461$	−4.94289	−	8.56134i	−0.230213	−	0.398741i	0.727657	−	0.685941i	$-0.240609\pi$
$461$	−4.94289	−	8.56134i	−0.230213	−	0.398741i	−0.957871	+	0.287199i	$0.907276\pi$
$462$	−1.26982	−	2.19939i	−0.0590774	−	0.102325i
$463$	12.2452			0.569081			0.284540	−	0.958664i	$-0.408159\pi$
$463$	12.2452			0.569081			0.284540	+	0.958664i	$0.408159\pi$
$464$	−4.74342	−	8.21584i	−0.220208	−	0.381411i
$465$	−10.4217	+	18.0509i	−0.483294	+	0.837089i
$466$	6.44724	−	11.1669i	0.298663	−	0.517299i
$467$	42.4158			1.96277			0.981385	−	0.192051i	$-0.0615139\pi$
$467$	42.4158			1.96277			0.981385	+	0.192051i	$0.0615139\pi$
$468$	−2.73913	+	3.57649i	−0.126617	+	0.165323i
$469$	−13.1852			−0.608838
$470$	7.18796	−	12.4499i	0.331556	−	0.574271i
$471$	−4.61800	+	7.99861i	−0.212786	+	0.368557i
$472$	−2.32190	−	4.02165i	−0.106874	−	0.185111i
$473$	11.2786			0.518592
$474$	9.62258	+	16.6668i	0.441980	+	0.765531i
$475$	4.12421	+	7.14335i	0.189232	+	0.327759i
$476$	6.47808			0.296922
$477$	3.08535	+	5.34399i	0.141269	+	0.244685i
$478$	11.5690	−	20.0380i	0.529153	−	0.916519i
$479$	14.1978	−	24.5913i	0.648715	−	1.12361i	−0.334715	−	0.942319i	$-0.608640\pi$
$479$	14.1978	−	24.5913i	0.648715	−	1.12361i	0.983430	−	0.181288i	$-0.0580266\pi$
$480$	18.0036			0.821749
$481$	−0.750338	+	0.979717i	−0.0342125	+	0.0446713i
$482$	31.3746			1.42907
$483$	3.93897	−	6.82249i	0.179229	−	0.310434i
$484$	−0.624717	+	1.08204i	−0.0283962	+	0.0491837i
$485$	22.8137	+	39.5145i	1.03592	+	1.79426i
$486$	1.80262			0.0817685
$487$	−7.85330	−	13.6023i	−0.355867	−	0.616380i	0.631399	−	0.775458i	$-0.282481\pi$
$487$	−7.85330	−	13.6023i	−0.355867	−	0.616380i	−0.987266	+	0.159079i	$0.949148\pi$
$488$	−0.515382	−	0.892668i	−0.0233303	−	0.0404092i
$489$	7.90971			0.357689
$490$	−13.1363	−	22.7528i	−0.593440	−	1.02787i
$491$	7.64508	−	13.2417i	0.345018	−	0.597588i	−0.640339	−	0.768092i	$-0.721206\pi$
$491$	7.64508	−	13.2417i	0.345018	−	0.597588i	0.985357	+	0.170504i	$0.0545396\pi$
$492$	0.0850675	−	0.147341i	0.00383514	−	0.00664266i
$493$	−7.07055			−0.318442
$494$	−15.4268	−	2.01660i	−0.694085	−	0.0907312i
$495$	−2.90617			−0.130623
$496$	−17.7072	+	30.6697i	−0.795075	+	1.37711i
$497$	2.15056	−	3.72487i	0.0964656	−	0.167083i
$498$	15.2529	+	26.4189i	0.683500	+	1.18386i
$499$	16.8318			0.753496			0.376748	−	0.926316i	$-0.377042\pi$
$499$	16.8318			0.753496			0.376748	+	0.926316i	$0.377042\pi$
$500$	−2.82168	−	4.88730i	−0.126190	−	0.218567i
$501$	10.3312	+	17.8941i	0.461562	+	0.799449i
$502$	−24.6396			−1.09972
$503$	−9.98757	−	17.2990i	−0.445324	−	0.771323i	0.552751	−	0.833346i	$-0.313578\pi$
$503$	−9.98757	−	17.2990i	−0.445324	−	0.771323i	−0.998075	+	0.0620231i	$0.980245\pi$
$504$	0.953084	−	1.65079i	0.0424537	−	0.0735320i
$505$	1.59376	−	2.76048i	0.0709215	−	0.122840i
$506$	−10.0797			−0.448097
$507$	−9.17553	+	9.20922i	−0.407500	+	0.408996i
$508$	15.5874			0.691580
$509$	−15.9912	+	27.6975i	−0.708796	+	1.22767i	0.256508	+	0.966542i	$0.417428\pi$
$509$	−15.9912	+	27.6975i	−0.708796	+	1.22767i	−0.965304	+	0.261129i	$0.915905\pi$
$510$	9.63959	−	16.6963i	0.426848	−	0.739323i
$511$	2.10000	+	3.63730i	0.0928984	+	0.160905i
$512$	17.2280			0.761375
$513$	1.19688	+	2.07305i	0.0528435	+	0.0915276i
$514$	19.1703	+	33.2039i	0.845564	+	1.46456i
$515$	6.37501			0.280916
$516$	−7.04596	−	12.2040i	−0.310181	−	0.537250i
$517$	−1.37208	+	2.37652i	−0.0603442	+	0.104519i
$518$	−0.434610	+	0.752767i	−0.0190957	+	0.0330747i
$519$	3.37474			0.148134
$520$	14.0574	+	1.83759i	0.616459	+	0.0805838i
$521$	−18.5052			−0.810726			−0.405363	−	0.914156i	$-0.632855\pi$
$521$	−18.5052			−0.810726			−0.405363	+	0.914156i	$0.632855\pi$
$522$	1.73166	−	2.99933i	0.0757928	−	0.131277i
$523$	13.2516	−	22.9524i	0.579450	−	1.00364i	−0.416092	−	0.909323i	$-0.636601\pi$
$523$	13.2516	−	22.9524i	0.579450	−	1.00364i	0.995542	−	0.0943150i	$-0.0300661\pi$
$524$	−2.54595	−	4.40972i	−0.111221	−	0.192640i
$525$	4.85467			0.211875
$526$	−13.2077	−	22.8765i	−0.575884	−	0.997461i
$527$	13.1972	+	22.8582i	0.574878	+	0.995718i
$528$	−4.93778			−0.214889
$529$	−4.13353	−	7.15948i	−0.179719	−	0.311282i
$530$	−16.1633	+	27.9956i	−0.702088	+	1.21605i
$531$	1.71613	−	2.97243i	0.0744739	−	0.128993i
$532$	−4.21369			−0.182686
$533$	0.298525	−	0.389784i	0.0129305	−	0.0168834i
$534$	−27.0919			−1.17238
$535$	−9.21437	+	15.9598i	−0.398372	+	0.690001i
$536$	−6.33114	+	10.9659i	−0.273464	+	0.473653i
$537$	−6.41737	−	11.1152i	−0.276930	−	0.479657i
$538$	30.2498			1.30416
$539$	2.50755	+	4.34321i	0.108008	+	0.187075i
$540$	1.81553	+	3.14460i	0.0781281	+	0.135322i
$541$	−19.6689			−0.845633			−0.422817	−	0.906215i	$-0.638959\pi$
$541$	−19.6689			−0.845633			−0.422817	+	0.906215i	$0.638959\pi$
$542$	−25.5983	−	44.3375i	−1.09954	−	1.90446i
$543$	−11.1962	+	19.3924i	−0.480474	+	0.832206i
$544$	11.3992	−	19.7440i	0.488736	−	0.846515i
$545$	48.4433			2.07508
$546$	−5.56766	+	7.26969i	−0.238274	+	0.311114i
$547$	−7.89573			−0.337597			−0.168798	−	0.985651i	$-0.553989\pi$
$547$	−7.89573			−0.337597			−0.168798	+	0.985651i	$0.553989\pi$
$548$	−3.40820	+	5.90317i	−0.145591	+	0.252171i
$549$	0.380923	−	0.659778i	0.0162574	−	0.0281586i
$550$	−3.10574	−	5.37930i	−0.132429	−	0.229374i
$551$	4.59906			0.195927
$552$	−3.78274	−	6.55189i	−0.161004	−	0.278867i
$553$	7.52067	+	13.0262i	0.319811	+	0.553929i
$554$	17.1094			0.726908
$555$	0.497334	+	0.861408i	0.0211106	+	0.0365647i
$556$	10.8553	−	18.8019i	0.460368	−	0.797380i
$557$	20.9427	−	36.2738i	0.887369	−	1.53697i	0.0443955	−	0.999014i	$-0.485864\pi$
$557$	20.9427	−	36.2738i	0.887369	−	1.53697i	0.842974	−	0.537955i	$-0.180803\pi$
$558$	−12.9286			−0.547311
$559$	−15.5965	−	37.5560i	−0.659662	−	1.58845i
$560$	20.2172			0.854333
$561$	−1.84007	+	3.18709i	−0.0776878	+	0.134559i
$562$	−19.5771	+	33.9086i	−0.825812	+	1.43035i
$563$	2.23717	+	3.87490i	0.0942856	+	0.163308i	0.909310	−	0.416119i	$-0.136610\pi$
$563$	2.23717	+	3.87490i	0.0942856	+	0.163308i	−0.815025	+	0.579426i	$0.803277\pi$
$564$	3.42866			0.144373
$565$	16.2141	+	28.0837i	0.682133	+	1.18149i
$566$	−14.0049	−	24.2571i	−0.588668	−	1.01960i
$567$	1.40886			0.0591667
$568$	−2.06526	−	3.57713i	−0.0866564	−	0.150093i
$569$	15.7687	−	27.3123i	0.661060	−	1.14499i	−0.319277	−	0.947661i	$-0.603440\pi$
$569$	15.7687	−	27.3123i	0.661060	−	1.14499i	0.980337	−	0.197328i	$-0.0632265\pi$
$570$	−6.27010	+	10.8601i	−0.262626	+	0.454881i
$571$	15.7405			0.658718			0.329359	−	0.944205i	$-0.393167\pi$
$571$	15.7405			0.658718			0.329359	+	0.944205i	$0.393167\pi$
$572$	4.46690	+	0.583916i	0.186770	+	0.0244147i
$573$	−3.36552			−0.140597
$574$	0.172911	−	0.299491i	0.00721717	−	0.0125005i
$575$	9.63396	−	16.6865i	0.401764	−	0.695875i
$576$	0.645805	+	1.11857i	0.0269085	+	0.0466070i
$577$	15.8739			0.660841			0.330421	−	0.943834i	$-0.392809\pi$
$577$	15.8739			0.660841			0.330421	+	0.943834i	$0.392809\pi$
$578$	3.11545	+	5.39612i	0.129586	+	0.224449i
$579$	−9.42520	−	16.3249i	−0.391698	−	0.678441i
$580$	6.97627			0.289674
$581$	11.9212	+	20.6480i	0.494573	+	0.856625i
$582$	−14.1507	+	24.5098i	−0.586566	+	1.01596i
$583$	3.08535	−	5.34399i	0.127782	−	0.221325i
$584$	4.03341			0.166904
$585$	4.01875	+	9.67704i	0.166155	+	0.400096i
$586$	7.46575			0.308407
$587$	−7.52675	+	13.0367i	−0.310662	+	0.538083i	−0.978506	−	0.206219i	$-0.933884\pi$
$587$	−7.52675	+	13.0367i	−0.310662	+	0.538083i	0.667844	+	0.744302i	$0.267218\pi$
$588$	3.13302	−	5.42656i	0.129204	−	0.223787i
$589$	−8.58414	−	14.8682i	−0.353703	−	0.612632i
$590$	17.9807			0.740252
$591$	7.15007	+	12.3843i	0.294115	+	0.509422i
$592$	0.845005	+	1.46359i	0.0347295	+	0.0601533i
$593$	6.09765			0.250401			0.125200	−	0.992131i	$-0.460043\pi$
$593$	6.09765			0.250401			0.125200	+	0.992131i	$0.460043\pi$
$594$	−0.901309	−	1.56111i	−0.0369812	−	0.0640533i
$595$	7.53396	−	13.0492i	0.308862	−	0.534965i
$596$	8.66699	−	15.0117i	0.355014	−	0.614902i
$597$	−23.4216			−0.958582
$598$	13.9386	+	33.5637i	0.569990	+	1.37252i
$599$	28.9368			1.18232			0.591162	−	0.806553i	$-0.298669\pi$
$599$	28.9368			1.18232			0.591162	+	0.806553i	$0.298669\pi$
$600$	2.33106	−	4.03752i	0.0951652	−	0.164831i
$601$	−3.68684	+	6.38579i	−0.150389	+	0.260482i	−0.931371	−	0.364073i	$-0.881386\pi$
$601$	−3.68684	+	6.38579i	−0.150389	+	0.260482i	0.780981	+	0.624554i	$0.214719\pi$
$602$	−14.3219	−	24.8062i	−0.583715	−	1.01102i
$603$	−9.35878			−0.381119
$604$	11.6415	+	20.1636i	0.473685	+	0.820446i
$605$	1.45308	+	2.51681i	0.0590763	+	0.102323i
$606$	1.97714			0.0803157
$607$	−11.9548	−	20.7062i	−0.485229	−	0.840441i	0.514627	−	0.857414i	$-0.327930\pi$
$607$	−11.9548	−	20.7062i	−0.485229	−	0.840441i	−0.999856	+	0.0169733i	$0.994597\pi$
$608$	−7.41463	+	12.8425i	−0.300703	+	0.520833i
$609$	1.35341	−	2.34417i	0.0548428	−	0.0949904i
$610$	3.99109			0.161595
$611$	9.81078	+	1.28247i	0.396901	+	0.0518832i
$612$	4.59809			0.185867
$613$	−0.922977	+	1.59864i	−0.0372787	+	0.0645686i	−0.884063	−	0.467368i	$-0.845202\pi$
$613$	−0.922977	+	1.59864i	−0.0372787	+	0.0645686i	0.846784	+	0.531937i	$0.178536\pi$
$614$	−25.2771	+	43.7813i	−1.02010	+	1.76687i
$615$	−0.197866	−	0.342714i	−0.00797872	−	0.0138196i
$616$	−1.90617			−0.0768017
$617$	0.374827	+	0.649219i	0.0150900	+	0.0261366i	0.873472	−	0.486875i	$-0.161863\pi$
$617$	0.374827	+	0.649219i	0.0150900	+	0.0261366i	−0.858382	+	0.513011i	$0.828530\pi$
$618$	1.97712	+	3.42448i	0.0795316	+	0.137753i
$619$	−40.6177			−1.63256			−0.816282	−	0.577654i	$-0.803968\pi$
$619$	−40.6177			−1.63256			−0.816282	+	0.577654i	$0.803968\pi$
$620$	−13.0212	−	22.5534i	−0.522944	−	0.905766i
$621$	2.79585	−	4.84255i	0.112194	−	0.194325i
$622$	19.3563	−	33.5261i	0.776117	−	1.34427i
$623$	−21.1741			−0.848322
$624$	6.82814	+	16.4420i	0.273344	+	0.658206i
$625$	−30.3554			−1.21422
$626$	21.4512	−	37.1546i	0.857363	−	1.48500i
$627$	1.19688	−	2.07305i	0.0477987	−	0.0827898i
$628$	−5.76989	−	9.99374i	−0.230244	−	0.398794i
$629$	1.25957			0.0502222
$630$	3.69031	+	6.39181i	0.147026	+	0.254656i
$631$	−6.96959	−	12.0717i	−0.277455	−	0.480566i	0.693296	−	0.720652i	$-0.256158\pi$
$631$	−6.96959	−	12.0717i	−0.277455	−	0.480566i	−0.970752	+	0.240086i	$0.922824\pi$
$632$	14.4448			0.574581
$633$	−3.30355	−	5.72192i	−0.131304	−	0.227426i
$634$	14.7700	−	25.5824i	0.586592	−	1.01601i
$635$	18.1281	−	31.3987i	0.719390	−	1.24602i
$636$	−7.70990			−0.305717
$637$	10.9946	−	14.3557i	0.435622	−	0.568792i
$638$	−3.46332			−0.137114
$639$	1.52645	−	2.64389i	0.0603854	−	0.104591i
$640$	14.6204	−	25.3233i	0.577924	−	1.00099i
$641$	−19.9399	−	34.5370i	−0.787580	−	1.36413i	−0.927445	−	0.373959i	$-0.878000\pi$
$641$	−19.9399	−	34.5370i	−0.787580	−	1.36413i	0.139865	−	0.990171i	$-0.455333\pi$
$642$	−11.4309			−0.451140
$643$	−4.08268	−	7.07141i	−0.161005	−	0.278869i	0.774224	−	0.632911i	$-0.218140\pi$
$643$	−4.08268	−	7.07141i	−0.161005	−	0.278869i	−0.935229	+	0.354042i	$0.884807\pi$
$644$	4.92148	+	8.52425i	0.193933	+	0.335903i
$645$	−32.7776			−1.29062
$646$	7.93995	+	13.7524i	0.312393	+	0.541081i
$647$	−7.49759	+	12.9862i	−0.294761	+	0.510540i	−0.974929	−	0.222515i	$-0.928573\pi$
$647$	−7.49759	+	12.9862i	−0.294761	+	0.510540i	0.680169	+	0.733056i	$0.261907\pi$
$648$	0.676492	−	1.17172i	0.0265751	−	0.0460294i
$649$	−3.43227			−0.134728
$650$	−13.6174	+	17.7803i	−0.534119	+	0.697400i
$651$	−10.1045			−0.396027
$652$	−4.94133	+	8.55864i	−0.193517	+	0.335182i
$653$	−10.4219	+	18.0513i	−0.407841	+	0.706401i	−0.994648	−	0.103326i	$-0.967051\pi$
$653$	−10.4219	+	18.0513i	−0.407841	+	0.706401i	0.586807	+	0.809727i	$0.300385\pi$
$654$	15.0240	+	26.0224i	0.587487	+	1.01756i
$655$	−11.8437			−0.462772
$656$	−0.336188	−	0.582295i	−0.0131259	−	0.0227348i
$657$	1.49056	+	2.58173i	0.0581524	+	0.100723i
$658$	6.96921			0.271688
$659$	−14.7195	−	25.4948i	−0.573389	−	0.993138i	−0.996215	−	0.0869272i	$-0.972295\pi$
$659$	−14.7195	−	25.4948i	−0.573389	−	0.993138i	0.422826	−	0.906211i	$-0.361038\pi$
$660$	1.81553	−	3.14460i	0.0706695	−	0.122403i
$661$	15.5971	−	27.0150i	0.606657	−	1.05076i	−0.385130	−	0.922862i	$-0.625843\pi$
$661$	15.5971	−	27.0150i	0.606657	−	1.05076i	0.991787	−	0.127899i	$-0.0408232\pi$
$662$	29.2276			1.13596
$663$	13.1570	+	1.71989i	0.510975	+	0.0667950i
$664$	22.8967			0.888563
$665$	−4.90049	+	8.48789i	−0.190033	+	0.329146i
$666$	−0.308483	+	0.534308i	−0.0119535	+	0.0207040i
$667$	−5.37159	−	9.30387i	−0.207989	−	0.360247i
$668$	−25.8162			−0.998860
$669$	−0.176270	−	0.305309i	−0.00681501	−	0.0118039i
$670$	−24.5140	−	42.4595i	−0.947058	−	1.64035i
$671$	−0.761846			−0.0294107
$672$	4.36393	+	7.55855i	0.168342	+	0.291578i
$673$	0.693334	−	1.20089i	0.0267261	−	0.0462909i	−0.852353	−	0.522967i	$-0.824825\pi$
$673$	0.693334	−	1.20089i	0.0267261	−	0.0462909i	0.879079	+	0.476676i	$0.158158\pi$
$674$	−12.5883	+	21.8036i	−0.484884	+	0.839845i
$675$	3.44581			0.132629
$676$	−4.23265	−	15.6815i	−0.162794	−	0.603133i
$677$	23.5904			0.906654			0.453327	−	0.891344i	$-0.350237\pi$
$677$	23.5904			0.906654			0.453327	+	0.891344i	$0.350237\pi$
$678$	−10.0572	+	17.4196i	−0.386244	+	0.668994i
$679$	−11.0597	+	19.1560i	−0.424432	+	0.735139i
$680$	−7.23514	−	12.5316i	−0.277455	−	0.480566i
$681$	−8.21012			−0.314613
$682$	6.46429	+	11.1965i	0.247530	+	0.428735i
$683$	−9.73997	−	16.8701i	−0.372690	−	0.645517i	0.617289	−	0.786737i	$-0.288231\pi$
$683$	−9.73997	−	16.8701i	−0.372690	−	0.645517i	−0.989978	+	0.141219i	$0.954898\pi$
$684$	−2.99084			−0.114358
$685$	7.92742	+	13.7307i	0.302891	+	0.524623i
$686$	15.2570	−	26.4260i	0.582516	−	1.00895i
$687$	−3.90496	+	6.76358i	−0.148983	+	0.258047i
$688$	−55.6915			−2.12322
$689$	−22.0611	−	2.88384i	−0.840462	−	0.109866i
$690$	29.2933			1.11518
$691$	16.9880	−	29.4241i	0.646254	−	1.11935i	−0.337756	−	0.941234i	$-0.609668\pi$
$691$	16.9880	−	29.4241i	0.646254	−	1.11935i	0.984010	−	0.178112i	$-0.0569988\pi$
$692$	−2.10826	+	3.65161i	−0.0801438	+	0.138813i
$693$	−0.704431	−	1.22011i	−0.0267591	−	0.0463482i
$694$	−7.86873			−0.298693
$695$	−25.2493	−	43.7331i	−0.957760	−	1.65889i
$696$	−1.29973	−	2.25119i	−0.0492660	−	0.0853312i
$697$	−0.501123			−0.0189814
$698$	23.6052	+	40.8855i	0.893472	+	1.54754i
$699$	3.57660	−	6.19485i	0.135279	−	0.234311i
$700$	−3.03280	+	5.25296i	−0.114629	+	0.198543i
$701$	−4.91282			−0.185555			−0.0927773	−	0.995687i	$-0.529574\pi$
$701$	−4.91282			−0.185555			−0.0927773	+	0.995687i	$0.529574\pi$
$702$	−3.95188	+	5.15997i	−0.149154	+	0.194751i
$703$	−0.819289			−0.0309001
$704$	0.645805	−	1.11857i	0.0243397	−	0.0421576i
$705$	3.98751	−	6.90657i	0.150178	−	0.260116i
$706$	−25.9055	−	44.8697i	−0.974967	−	1.68869i
$707$	1.54526			0.0581155
$708$	2.14420	+	3.71386i	0.0805839	+	0.139575i
$709$	−4.41523	−	7.64740i	−0.165817	−	0.287204i	0.771128	−	0.636680i	$-0.219693\pi$
$709$	−4.41523	−	7.64740i	−0.165817	−	0.287204i	−0.936945	+	0.349476i	$0.886360\pi$
$710$	15.9933			0.600216
$711$	5.33811	+	9.24588i	0.200195	+	0.346748i
$712$	−10.1671	+	17.6100i	−0.381029	+	0.659962i
$713$	−20.0521	+	34.7313i	−0.750958	+	1.30070i
$714$	9.34623			0.349774
$715$	6.37119	−	8.31886i	0.238269	−	0.311108i
$716$	16.0362			0.599299
$717$	6.41787	−	11.1161i	0.239680	−	0.415138i
$718$	29.5688	−	51.2147i	1.10350	−	1.91131i
$719$	13.1970	+	22.8578i	0.492164	+	0.852453i	0.999959	−	0.00902447i	$-0.00287262\pi$
$719$	13.1970	+	22.8578i	0.492164	+	0.852453i	−0.507795	+	0.861478i	$0.669539\pi$
$720$	14.3500			0.534794
$721$	1.54525	+	2.67645i	0.0575481	+	0.0996762i
$722$	11.9603	+	20.7159i	0.445117	+	0.770965i
$723$	17.4050			0.647298
$724$	−13.9889	−	24.2295i	−0.519894	−	0.900482i
$725$	3.31017	−	5.73339i	0.122937	−	0.212933i
$726$	−0.901309	+	1.56111i	−0.0334507	+	0.0579384i
$727$	18.0047			0.667756			0.333878	−	0.942616i	$-0.391643\pi$
$727$	18.0047			0.667756			0.333878	+	0.942616i	$0.391643\pi$
$728$	2.63592	+	6.34721i	0.0976936	+	0.235243i
$729$	1.00000			0.0370370
$730$	−7.80863	+	13.5249i	−0.289010	+	0.500581i
$731$	−20.7535	+	35.9461i	−0.767595	+	1.32951i
$732$	0.475938	+	0.824349i	0.0175912	+	0.0304688i
$733$	7.43903			0.274767			0.137383	−	0.990518i	$-0.456131\pi$
$733$	7.43903			0.274767			0.137383	+	0.990518i	$0.456131\pi$
$734$	−21.5250	−	37.2824i	−0.794502	−	1.37612i
$735$	−7.28737	−	12.6221i	−0.268799	−	0.465573i
$736$	34.6404			1.27686
$737$	4.67939	+	8.10495i	0.172368	+	0.298549i
$738$	0.122731	−	0.212576i	0.00451779	−	0.00782504i
$739$	6.52566	−	11.3028i	0.240050	−	0.415779i	−0.720678	−	0.693270i	$-0.756169\pi$
$739$	6.52566	−	11.3028i	0.240050	−	0.415779i	0.960728	+	0.277490i	$0.0895027\pi$
$740$	−1.24277			−0.0456852
$741$	−8.55800	−	1.11871i	−0.314386	−	0.0410967i
$742$	−15.6714			−0.575315
$743$	1.89661	−	3.28502i	0.0695797	−	0.120516i	−0.829137	−	0.559046i	$-0.811168\pi$
$743$	1.89661	−	3.28502i	0.0695797	−	0.120516i	0.898716	+	0.438530i	$0.144501\pi$
$744$	−4.85187	+	8.40369i	−0.177878	+	0.308094i
$745$	−20.1593	−	34.9169i	−0.738579	−	1.27926i
$746$	37.6769			1.37945
$747$	8.46154	+	14.6558i	0.309592	+	0.536229i
$748$	−2.29905	−	3.98206i	−0.0840614	−	0.145599i
$749$	−8.93396			−0.326440
$750$	−4.07098	−	7.05114i	−0.148651	−	0.257471i
$751$	−7.10884	+	12.3129i	−0.259405	+	0.449303i	−0.966083	−	0.258233i	$-0.916860\pi$
$751$	−7.10884	+	12.3129i	−0.259405	+	0.449303i	0.706677	+	0.707536i	$0.250193\pi$
$752$	6.77506	−	11.7347i	0.247061	−	0.427922i
$753$	−13.6688			−0.498118
$754$	4.78921	+	11.5323i	0.174413	+	0.419981i
$755$	54.1558			1.97093
$756$	−0.880141	+	1.52445i	−0.0320104	+	0.0554437i
$757$	−11.5235	+	19.9593i	−0.418830	+	0.725434i	−0.995822	−	0.0913154i	$-0.970893\pi$
$757$	−11.5235	+	19.9593i	−0.418830	+	0.725434i	0.576992	+	0.816749i	$0.304226\pi$
$758$	28.6581	+	49.6373i	1.04091	+	1.80291i
$759$	−5.59170			−0.202966
$760$	4.70612	+	8.15124i	0.170709	+	0.295677i
$761$	16.8109	+	29.1173i	0.609394	+	1.05550i	0.991340	+	0.131317i	$0.0419205\pi$
$761$	16.8109	+	29.1173i	0.609394	+	1.05550i	−0.381947	+	0.924184i	$0.624746\pi$
$762$	22.4887			0.814680
$763$	11.7423	+	20.3382i	0.425098	+	0.736292i
$764$	2.10250	−	3.64163i	0.0760657	−	0.131750i
$765$	5.34755	−	9.26223i	0.193341	−	0.334876i
$766$	−41.7174			−1.50731
$767$	4.74626	+	11.4289i	0.171378	+	0.412672i
$768$	20.7206			0.747689
$769$	−12.4722	+	21.6025i	−0.449760	+	0.779007i	−0.998370	−	0.0570715i	$-0.981824\pi$
$769$	−12.4722	+	21.6025i	−0.449760	+	0.779007i	0.548610	+	0.836078i	$0.315157\pi$
$770$	3.69031	−	6.39181i	0.132990	−	0.230345i
$771$	10.6347	+	18.4198i	0.382998	+	0.663372i
$772$	23.5523			0.847667
$773$	23.7783	+	41.1853i	0.855247	+	1.48133i	0.876416	+	0.481555i	$0.159928\pi$
$773$	23.7783	+	41.1853i	0.855247	+	1.48133i	−0.0211691	+	0.999776i	$0.506739\pi$
$774$	−10.1655	−	17.6072i	−0.365393	−	0.632879i
$775$	−24.7137			−0.887743
$776$	10.6210	+	18.3962i	0.381273	+	0.660385i
$777$	−0.241099	+	0.417596i	−0.00864939	+	0.0149812i
$778$	20.1512	−	34.9029i	0.722455	−	1.25133i
$779$	0.325957			0.0116786
$780$	−12.9816	−	1.69696i	−0.464814	−	0.0607608i
$781$	−3.05290			−0.109241
$782$	18.5473	−	32.1249i	0.663251	−	1.14879i
$783$	0.960637	−	1.66387i	0.0343304	−	0.0594619i
$784$	−12.3818	−	21.4458i	−0.442205	−	0.765922i
$785$	−26.8414			−0.958010
$786$	−3.67317	−	6.36212i	−0.131018	−	0.226929i
$787$	−0.521877	−	0.903918i	−0.0186029	−	0.0322212i	0.856574	−	0.516024i	$-0.172589\pi$
$787$	−0.521877	−	0.903918i	−0.0186029	−	0.0322212i	−0.875177	+	0.483803i	$0.839255\pi$
$788$	−17.8671			−0.636489
$789$	−7.32697	−	12.6907i	−0.260847	−	0.451800i
$790$	−27.9648	+	48.4365i	−0.994944	+	1.72329i
$791$	−7.86034	+	13.6145i	−0.279482	+	0.484076i
$792$	−1.35298			−0.0480762
$793$	1.05351	+	2.53682i	0.0374112	+	0.0900850i
$794$	40.8996			1.45147
$795$	−8.96656	+	15.5305i	−0.318011	+	0.550811i
$796$	14.6319	−	25.3432i	0.518613	−	0.898264i
$797$	17.0522	+	29.5353i	0.604020	+	1.04619i	0.992206	+	0.124612i	$0.0397687\pi$
$797$	17.0522	+	29.5353i	0.604020	+	1.04619i	−0.388185	+	0.921581i	$0.626898\pi$
$798$	−6.07928			−0.215204
$799$	−5.04946	−	8.74592i	−0.178637	−	0.309408i
$800$	10.6733	+	18.4868i	0.377360	+	0.653606i
$801$	−15.0292			−0.531031
$802$	29.2000	+	50.5758i	1.03109	+	1.78589i
$803$	1.49056	−	2.58173i	0.0526008	−	0.0911073i
$804$	5.84659	−	10.1266i	0.206193	−	0.357138i
$805$	22.8946			0.806928
$806$	28.3433	−	37.0079i	0.998351	−	1.30355i
$807$	16.7810			0.590720
$808$	0.741986	−	1.28516i	0.0261030	−	0.0452117i
$809$	13.7471	−	23.8107i	0.483322	−	0.837139i	−0.516494	−	0.856291i	$-0.672763\pi$
$809$	13.7471	−	23.8107i	0.483322	−	0.837139i	0.999817	+	0.0191519i	$0.00609661\pi$
$810$	2.61936	+	4.53686i	0.0920348	+	0.159409i
$811$	27.9591			0.981778			0.490889	−	0.871222i	$-0.336672\pi$
$811$	27.9591			0.981778			0.490889	+	0.871222i	$0.336672\pi$
$812$	1.69099	+	2.92888i	0.0593422	+	0.102784i
$813$	−14.2006	−	24.5962i	−0.498037	−	0.862626i
$814$	0.616966			0.0216246
$815$	11.4935	+	19.9073i	0.402599	+	0.697321i
$816$	9.08586	−	15.7372i	0.318069	−	0.550911i
$817$	13.4992	−	23.3812i	0.472276	−	0.818006i
$818$	−48.4801			−1.69507
$819$	−3.08865	+	4.03285i	−0.107926	+	0.140919i
$820$	0.494441			0.0172666
$821$	−20.9045	+	36.2077i	−0.729574	+	1.26366i	0.227490	+	0.973780i	$0.426948\pi$
$821$	−20.9045	+	36.2077i	−0.729574	+	1.26366i	−0.957064	+	0.289878i	$0.906385\pi$
$822$	−4.91717	+	8.51679i	−0.171506	+	0.297057i
$823$	8.70855	+	15.0836i	0.303561	+	0.525783i	0.976940	−	0.213515i	$-0.0684911\pi$
$823$	8.70855	+	15.0836i	0.303561	+	0.525783i	−0.673379	+	0.739297i	$0.735158\pi$
$824$	2.96792			0.103392
$825$	−1.72290	−	2.98416i	−0.0599838	−	0.103895i
$826$	4.35837	+	7.54891i	0.151647	+	0.262660i
$827$	−34.9915			−1.21677			−0.608387	−	0.793641i	$-0.708183\pi$
$827$	−34.9915			−1.21677			−0.608387	+	0.793641i	$0.708183\pi$
$828$	3.49323	+	6.05045i	0.121398	+	0.210268i
$829$	−1.73570	+	3.00632i	−0.0602834	+	0.104414i	−0.894592	−	0.446884i	$-0.852534\pi$
$829$	−1.73570	+	3.00632i	−0.0602834	+	0.104414i	0.834309	+	0.551298i	$0.185867\pi$
$830$	−44.3276	+	76.7776i	−1.53863	+	2.66499i
$831$	9.49141			0.329253
$832$	−4.61768	−	0.603626i	−0.160089	−	0.0209270i
$833$	−18.4563			−0.639472
$834$	15.6615	−	27.1265i	0.542312	−	0.939313i
$835$	−30.0241	+	52.0032i	−1.03903	+	1.79965i
$836$	1.49542	+	2.59015i	0.0517202	+	0.0895820i
$837$	−7.17211			−0.247904
$838$	−21.2768	−	36.8525i	−0.734995	−	1.27305i
$839$	−27.5672	−	47.7479i	−0.951727	−	1.64844i	−0.741686	−	0.670747i	$-0.765974\pi$
$839$	−27.5672	−	47.7479i	−0.951727	−	1.64844i	−0.210041	−	0.977693i	$-0.567360\pi$
$840$	5.53964			0.191136
$841$	12.6544	+	21.9180i	0.436357	+	0.755793i
$842$	−22.8102	+	39.5084i	−0.786091	+	1.36155i
$843$	−10.8604	+	18.8107i	−0.374052	+	0.647876i
$844$	8.25514			0.284154
$845$	−36.5107	−	9.71135i	−1.25601	−	0.334081i
$846$	4.94669			0.170071
$847$	−0.704431	+	1.22011i	−0.0242045	+	0.0419235i
$848$	−15.2348	+	26.3875i	−0.523165	+	0.906149i
$849$	−7.76918	−	13.4566i	−0.266637	−	0.461830i
$850$	22.8591			0.784061
$851$	0.956910	+	1.65742i	0.0328024	+	0.0568155i
$852$	1.90720	+	3.30336i	0.0653395	+	0.113171i
$853$	34.9221			1.19571			0.597855	−	0.801604i	$-0.296020\pi$
$853$	34.9221			1.19571			0.597855	+	0.801604i	$0.296020\pi$
$854$	0.967408	+	1.67560i	0.0331040	+	0.0573378i
$855$	−3.47833	+	6.02464i	−0.118956	+	0.206038i
$856$	−4.28981	+	7.43016i	−0.146623	+	0.253958i
$857$	−23.2086			−0.792790			−0.396395	−	0.918080i	$-0.629739\pi$
$857$	−23.2086			−0.792790			−0.396395	+	0.918080i	$0.629739\pi$
$858$	6.44461	+	0.842443i	0.220015	+	0.0287605i
$859$	26.8142			0.914889			0.457444	−	0.889238i	$-0.348765\pi$
$859$	26.8142			0.914889			0.457444	+	0.889238i	$0.348765\pi$
$860$	20.4767	−	35.4668i	0.698251	−	1.20941i
$861$	0.0959222	−	0.166142i	0.00326902	−	0.00566211i
$862$	−12.2483	−	21.2146i	−0.417177	−	0.722572i
$863$	−26.5007			−0.902096			−0.451048	−	0.892500i	$-0.648950\pi$
$863$	−26.5007			−0.902096			−0.451048	+	0.892500i	$0.648950\pi$
$864$	3.09749	+	5.36500i	0.105379	+	0.182521i
$865$	4.90377	+	8.49358i	0.166733	+	0.288791i
$866$	20.7763			0.706009
$867$	1.72829	+	2.99349i	0.0586959	+	0.101664i
$868$	6.31247	−	10.9335i	0.214259	−	0.371108i
$869$	5.33811	−	9.24588i	0.181083	−	0.313645i
$870$	10.0650			0.341235
$871$	20.5173	−	26.7894i	0.695201	−	0.907724i
$872$	22.5531			0.763743
$873$	−7.85009	+	13.5968i	−0.265685	+	0.460181i
$874$	−12.0642	+	20.8958i	−0.408077	+	0.706809i
$875$	−3.18173	−	5.51092i	−0.107562	−	0.186303i
$876$	−3.72472			−0.125847
$877$	10.2439	+	17.7429i	0.345911	+	0.599136i	0.985519	−	0.169566i	$-0.0542365\pi$
$877$	10.2439	+	17.7429i	0.345911	+	0.599136i	−0.639608	+	0.768701i	$0.720903\pi$
$878$	−13.7613	−	23.8352i	−0.464420	−	0.804399i
$879$	4.14161			0.139693
$880$	−7.17501	−	12.4275i	−0.241870	−	0.418930i
$881$	−22.6724	+	39.2697i	−0.763852	+	1.32303i	0.176999	+	0.984211i	$0.443361\pi$
$881$	−22.6724	+	39.2697i	−0.763852	+	1.32303i	−0.940851	+	0.338820i	$0.889972\pi$
$882$	4.52016	−	7.82915i	0.152202	−	0.263621i
$883$	−31.1709			−1.04898			−0.524491	−	0.851416i	$-0.675745\pi$
$883$	−31.1709			−1.04898			−0.524491	+	0.851416i	$0.675745\pi$
$884$	−10.0804	+	13.1620i	−0.339040	+	0.442685i
$885$	9.97474			0.335297
$886$	−16.7145	+	28.9504i	−0.561536	+	0.972608i
$887$	−19.5965	+	33.9422i	−0.657987	+	1.13967i	0.323149	+	0.946348i	$0.395258\pi$
$887$	−19.5965	+	33.9422i	−0.657987	+	1.13967i	−0.981136	+	0.193319i	$0.938075\pi$
$888$	0.231537	+	0.401033i	0.00776986	+	0.0134578i
$889$	17.5764			0.589493
$890$	−39.3668	−	68.1854i	−1.31958	−	2.28558i
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	0.440477			0.0147482
$893$	3.28444	+	5.68881i	0.109909	+	0.190369i
$894$	12.5043	−	21.6580i	0.418206	−	0.724353i
$895$	18.6499	−	32.3026i	0.623399	−	1.07976i
$896$	14.1755			0.473570
$897$	7.73240	+	18.6194i	0.258177	+	0.621683i
$898$	21.7276			0.725060
$899$	−6.88979	+	11.9335i	−0.229788	+	0.398004i
$900$	−2.15266	+	3.72851i	−0.0717552	+	0.124284i
$901$	11.3545	+	19.6666i	0.378274	+	0.655190i
$902$	−0.245462			−0.00817299
$903$	−7.94503	−	13.7612i	−0.264394	−	0.457944i
$904$	7.54858	+	13.0745i	0.251062	+	0.434852i
$905$	−65.0760			−2.16320
$906$	16.7957	+	29.0910i	0.558000	+	0.966484i
$907$	−13.6017	+	23.5589i	−0.451638	+	0.782259i	−0.998488	−	0.0549710i	$-0.982493\pi$
$907$	−13.6017	+	23.5589i	−0.451638	+	0.782259i	0.546850	+	0.837230i	$0.315827\pi$
$908$	5.12901	−	8.88370i	0.170212	−	0.294816i
$909$	1.09681			0.0363790
$910$	−26.3867	−	3.44929i	−0.874712	−	0.114343i
$911$	6.55704			0.217244			0.108622	−	0.994083i	$-0.465356\pi$
$911$	6.55704			0.217244			0.108622	+	0.994083i	$0.465356\pi$
$912$	−5.90992	+	10.2363i	−0.195697	+	0.338957i
$913$	8.46154	−	14.6558i	0.280036	−	0.485037i
$914$	−17.0223	−	29.4834i	−0.563046	−	0.975225i
$915$	2.21405			0.0731943
$916$	−4.87899	−	8.45065i	−0.161206	−	0.279217i
$917$	−2.87082	−	4.97240i	−0.0948028	−	0.164203i
$918$	6.63389			0.218951
$919$	−8.99063	−	15.5722i	−0.296573	−	0.513680i	0.678776	−	0.734345i	$-0.262511\pi$
$919$	−8.99063	−	15.5722i	−0.296573	−	0.513680i	−0.975350	+	0.220665i	$0.929177\pi$
$920$	10.9933	−	19.0409i	0.362437	−	0.627760i
$921$	−14.0225	+	24.2876i	−0.462056	+	0.800304i
$922$	17.8203			0.586880
$923$	4.22166	+	10.1656i	0.138958	+	0.334606i
$924$	1.76028			0.0579090
$925$	−0.589683	+	1.02136i	−0.0193887	+	0.0335821i
$926$	−11.0367	+	19.1161i	−0.362688	+	0.628193i
$927$	1.09681	+	1.89972i	0.0360239	+	0.0623951i
$928$	11.9022			0.390710
$929$	3.40346	+	5.89497i	0.111664	+	0.193408i	0.916441	−	0.400169i	$-0.131049\pi$
$929$	3.40346	+	5.89497i	0.111664	+	0.193408i	−0.804777	+	0.593577i	$0.797715\pi$
$930$	−18.7863	−	32.5388i	−0.616027	−	1.06699i
$931$	12.0049			0.393446
$932$	4.46872	+	7.74006i	0.146378	+	0.253534i
$933$	10.7379	−	18.5986i	0.351543	−	0.608889i
$934$	−38.2298	+	66.2159i	−1.25092	+	2.16665i
$935$	−10.6951			−0.349767
$936$	1.87095	+	4.50520i	0.0611540	+	0.147257i
$937$	16.8541			0.550600			0.275300	−	0.961358i	$-0.411223\pi$
$937$	16.8541			0.550600			0.275300	+	0.961358i	$0.411223\pi$
$938$	11.8840	−	20.5837i	0.388026	−	0.672080i
$939$	11.9000	−	20.6115i	0.388343	−	0.672630i
$940$	4.98213	+	8.62930i	0.162499	+	0.281457i
$941$	−41.9816			−1.36856			−0.684280	−	0.729219i	$-0.739883\pi$
$941$	−41.9816			−1.36856			−0.684280	+	0.729219i	$0.739883\pi$
$942$	−8.32450	−	14.4185i	−0.271227	−	0.469778i
$943$	−0.380710	−	0.659408i	−0.0123976	−	0.0214733i
$944$	16.9478			0.551604
$945$	2.04720	+	3.54585i	0.0665953	+	0.115346i
$946$	−10.1655	+	17.6072i	−0.330510	+	0.572461i
$947$	−4.91811	+	8.51841i	−0.159817	+	0.276811i	−0.934803	−	0.355168i	$-0.884424\pi$
$947$	−4.91811	+	8.51841i	−0.159817	+	0.276811i	0.774986	+	0.631979i	$0.217757\pi$
$948$	−13.3392			−0.433238
$949$	−10.6579	−	1.39321i	−0.345971	−	0.0452255i
$950$	−14.8688			−0.482407
$951$	8.19364	−	14.1918i	0.265697	−	0.460200i
$952$	3.50748	−	6.07513i	0.113678	−	0.196896i
$953$	19.1147	+	33.1077i	0.619187	+	1.07246i	0.989634	+	0.143610i	$0.0458709\pi$
$953$	19.1147	+	33.1077i	0.619187	+	1.07246i	−0.370448	+	0.928853i	$0.620796\pi$
$954$	−11.1234			−0.360135
$955$	−4.89038	−	8.47039i	−0.158249	−	0.274095i
$956$	8.01871	+	13.8888i	0.259344	+	0.449196i
$957$	−1.92127			−0.0621060
$958$	25.5933	+	44.3288i	0.826881	+	1.43220i
$959$	−3.84308	+	6.65642i	−0.124100	+	0.214947i
$960$	−1.87682	+	3.25074i	−0.0605740	+	0.104917i
$961$	20.4392			0.659328
$962$	−0.853163	−	2.05439i	−0.0275071	−	0.0662363i
$963$	−6.34125			−0.204344
$964$	−10.8732	+	18.8329i	−0.350202	+	0.606568i
$965$	27.3912	−	47.4430i	0.881754	−	1.52724i
$966$	7.10045	+	12.2983i	0.228453	+	0.395693i
$967$	−21.0319			−0.676341			−0.338170	−	0.941085i	$-0.609808\pi$
$967$	−21.0319			−0.676341			−0.338170	+	0.941085i	$0.609808\pi$
$968$	0.676492	+	1.17172i	0.0217433	+	0.0376604i
$969$	4.40468	+	7.62912i	0.141499	+	0.245083i
$970$	−82.2488			−2.64085
$971$	−19.7620	−	34.2288i	−0.634194	−	1.09846i	−0.986685	−	0.162641i	$-0.947999\pi$
$971$	−19.7620	−	34.2288i	−0.634194	−	1.09846i	0.352492	−	0.935815i	$-0.385335\pi$
$972$	−0.624717	+	1.08204i	−0.0200378	+	0.0347065i
$973$	12.2404	−	21.2011i	0.392411	−	0.679675i
$974$	28.3130			0.907207
$975$	−7.55425	+	9.86358i	−0.241929	+	0.315887i
$976$	3.76183			0.120413
$977$	21.4732	−	37.1926i	0.686987	−	1.18990i	−0.285820	−	0.958283i	$-0.592266\pi$
$977$	21.4732	−	37.1926i	0.686987	−	1.18990i	0.972808	−	0.231614i	$-0.0744006\pi$
$978$	−7.12909	+	12.3480i	−0.227963	+	0.394844i
$979$	7.51460	+	13.0157i	0.240168	+	0.415983i
$980$	18.2102			0.581703
$981$	8.33456	+	14.4359i	0.266102	+	0.460902i
$982$	13.7812	+	23.8697i	0.439775	+	0.761712i
$983$	−38.9916			−1.24364			−0.621819	−	0.783161i	$-0.713606\pi$
$983$	−38.9916			−1.24364			−0.621819	+	0.783161i	$0.713606\pi$
$984$	−0.0921176	−	0.159552i	−0.00293660	−	0.00508635i
$985$	−20.7793	+	35.9908i	−0.662084	+	1.14676i
$986$	6.37276	−	11.0379i	0.202950	−	0.351520i
$987$	3.86616			0.123061
$988$	6.55682	−	8.56124i	0.208600	−	0.272369i
$989$	−63.0667			−2.00541
$990$	2.61936	−	4.53686i	0.0832486	−	0.144191i
$991$	25.3523	−	43.9115i	0.805344	−	1.39490i	−0.110715	−	0.993852i	$-0.535314\pi$
$991$	25.3523	−	43.9115i	0.805344	−	1.39490i	0.916059	−	0.401044i	$-0.131353\pi$
$992$	−22.2155	−	38.4784i	−0.705343	−	1.22169i
$993$	16.2139			0.514534
$994$	3.87663	+	6.71453i	0.122959	+	0.212972i
$995$	−34.0335	−	58.9478i	−1.07894	−	1.86877i
$996$	−21.1443			−0.669982
$997$	20.1395	+	34.8826i	0.637823	+	1.10474i	0.985909	+	0.167280i	$0.0534983\pi$
$997$	20.1395	+	34.8826i	0.637823	+	1.10474i	−0.348086	+	0.937463i	$0.613168\pi$
$998$	−15.1707	+	26.2764i	−0.480220	+	0.831765i
$999$	−0.171130	+	0.296407i	−0.00541433	+	0.00937789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.f.100.1	✓	10
13.3	even	3	inner	429.2.i.f.133.1	yes	10
13.4	even	6		5577.2.a.w.1.1		5
13.9	even	3		5577.2.a.n.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.f.100.1	✓	10	1.1	even	1	trivial
429.2.i.f.133.1	yes	10	13.3	even	3	inner
5577.2.a.n.1.5		5	13.9	even	3
5577.2.a.w.1.1		5	13.4	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)

\(f(q)\)	\(=\)	\(q+(-0.901309 + 1.56111i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.624717 - 1.08204i) q^{4} -2.90617 q^{5} +(-0.901309 - 1.56111i) q^{6} +(-0.704431 - 1.22011i) q^{7} -1.35298 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.901309 + 1.56111i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.624717 - 1.08204i) q^{4} -2.90617 q^{5} +(-0.901309 - 1.56111i) q^{6} +(-0.704431 - 1.22011i) q^{7} -1.35298 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.61936 - 4.53686i) q^{10} +(-0.500000 + 0.866025i) q^{11} +1.24943 q^{12} +(3.57513 + 0.467344i) q^{13} +2.53964 q^{14} +(1.45308 - 2.51681i) q^{15} +(2.46889 - 4.27624i) q^{16} +(-1.84007 - 3.18709i) q^{17} +1.80262 q^{18} +(1.19688 + 2.07305i) q^{19} +(1.81553 + 3.14460i) q^{20} +1.40886 q^{21} +(-0.901309 - 1.56111i) q^{22} +(2.79585 - 4.84255i) q^{23} +(0.676492 - 1.17172i) q^{24} +3.44581 q^{25} +(-3.95188 + 5.15997i) q^{26} +1.00000 q^{27} +(-0.880141 + 1.52445i) q^{28} +(0.960637 - 1.66387i) q^{29} +(2.61936 + 4.53686i) q^{30} -7.17211 q^{31} +(3.09749 + 5.36500i) q^{32} +(-0.500000 - 0.866025i) q^{33} +6.63389 q^{34} +(2.04720 + 3.54585i) q^{35} +(-0.624717 + 1.08204i) q^{36} +(-0.171130 + 0.296407i) q^{37} -4.31503 q^{38} +(-2.19230 + 2.86249i) q^{39} +3.93200 q^{40} +(0.0680848 - 0.117926i) q^{41} +(-1.26982 + 2.19939i) q^{42} +(-5.63932 - 9.76759i) q^{43} +1.24943 q^{44} +(1.45308 + 2.51681i) q^{45} +(5.03985 + 8.72927i) q^{46} +2.74417 q^{47} +(2.46889 + 4.27624i) q^{48} +(2.50755 - 4.34321i) q^{49} +(-3.10574 + 5.37930i) q^{50} +3.68014 q^{51} +(-1.72776 - 4.16040i) q^{52} -6.17071 q^{53} +(-0.901309 + 1.56111i) q^{54} +(1.45308 - 2.51681i) q^{55} +(0.953084 + 1.65079i) q^{56} -2.39376 q^{57} +(1.73166 + 2.99933i) q^{58} +(1.71613 + 2.97243i) q^{59} -3.63107 q^{60} +(0.380923 + 0.659778i) q^{61} +(6.46429 - 11.1965i) q^{62} +(-0.704431 + 1.22011i) q^{63} -1.29161 q^{64} +(-10.3899 - 1.35818i) q^{65} +1.80262 q^{66} +(4.67939 - 8.10495i) q^{67} +(-2.29905 + 3.98206i) q^{68} +(2.79585 + 4.84255i) q^{69} -7.38063 q^{70} +(1.52645 + 2.64389i) q^{71} +(0.676492 + 1.17172i) q^{72} -2.98113 q^{73} +(-0.308483 - 0.534308i) q^{74} +(-1.72290 + 2.98416i) q^{75} +(1.49542 - 2.59015i) q^{76} +1.40886 q^{77} +(-2.49273 - 6.00241i) q^{78} -10.6762 q^{79} +(-7.17501 + 12.4275i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.122731 + 0.212576i) q^{82} -16.9231 q^{83} +(-0.880141 - 1.52445i) q^{84} +(5.34755 + 9.26223i) q^{85} +20.3311 q^{86} +(0.960637 + 1.66387i) q^{87} +(0.676492 - 1.17172i) q^{88} +(7.51460 - 13.0157i) q^{89} -5.23871 q^{90} +(-1.94823 - 4.69127i) q^{91} -6.98646 q^{92} +(3.58606 - 6.21123i) q^{93} +(-2.47335 + 4.28396i) q^{94} +(-3.47833 - 6.02464i) q^{95} -6.19497 q^{96} +(-7.85009 - 13.5968i) q^{97} +(4.52016 + 7.82915i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - 5 q^{3} - 6 q^{4} - 8 q^{5} + 4 q^{6} + 3 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 - 5 * q^3 - 6 * q^4 - 8 * q^5 + 4 * q^6 + 3 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 4 q^{2} - 5 q^{3} - 6 q^{4} - 8 q^{5} + 4 q^{6} + 3 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} - 5 q^{11} + 12 q^{12} + 5 q^{13} + 14 q^{14} + 4 q^{15} - 12 q^{16} - 9 q^{17} - 8 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} + 4 q^{22} + 9 q^{23} + 9 q^{24} + 2 q^{25} - 12 q^{26} + 10 q^{27} - q^{28} - 8 q^{29} + 5 q^{30} - 12 q^{31} + 27 q^{32} - 5 q^{33} - 14 q^{34} + 2 q^{35} - 6 q^{36} + 17 q^{37} - 2 q^{38} + 2 q^{39} + 46 q^{40} + 6 q^{41} - 7 q^{42} - 13 q^{43} + 12 q^{44} + 4 q^{45} - 6 q^{46} - 32 q^{47} - 12 q^{48} + 18 q^{49} - 8 q^{50} + 18 q^{51} + 7 q^{52} - 26 q^{53} + 4 q^{54} + 4 q^{55} - q^{56} - 18 q^{57} + 11 q^{58} + 8 q^{59} - 12 q^{60} - 4 q^{61} + 22 q^{62} + 3 q^{63} + 22 q^{64} + 26 q^{65} - 8 q^{66} + 5 q^{67} - 34 q^{68} + 9 q^{69} + 8 q^{70} + 19 q^{71} + 9 q^{72} - 4 q^{73} - 27 q^{74} - q^{75} - 6 q^{76} - 6 q^{77} - 3 q^{78} - 16 q^{79} + 32 q^{80} - 5 q^{81} - 16 q^{82} - 20 q^{83} - q^{84} + 21 q^{85} + 8 q^{86} - 8 q^{87} + 9 q^{88} + 32 q^{89} - 10 q^{90} - 17 q^{91} - 84 q^{92} + 6 q^{93} - 66 q^{94} - 11 q^{95} - 54 q^{96} - 5 q^{97} - 18 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - 5 * q^3 - 6 * q^4 - 8 * q^5 + 4 * q^6 + 3 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 - 5 * q^11 + 12 * q^12 + 5 * q^13 + 14 * q^14 + 4 * q^15 - 12 * q^16 - 9 * q^17 - 8 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 + 4 * q^22 + 9 * q^23 + 9 * q^24 + 2 * q^25 - 12 * q^26 + 10 * q^27 - q^28 - 8 * q^29 + 5 * q^30 - 12 * q^31 + 27 * q^32 - 5 * q^33 - 14 * q^34 + 2 * q^35 - 6 * q^36 + 17 * q^37 - 2 * q^38 + 2 * q^39 + 46 * q^40 + 6 * q^41 - 7 * q^42 - 13 * q^43 + 12 * q^44 + 4 * q^45 - 6 * q^46 - 32 * q^47 - 12 * q^48 + 18 * q^49 - 8 * q^50 + 18 * q^51 + 7 * q^52 - 26 * q^53 + 4 * q^54 + 4 * q^55 - q^56 - 18 * q^57 + 11 * q^58 + 8 * q^59 - 12 * q^60 - 4 * q^61 + 22 * q^62 + 3 * q^63 + 22 * q^64 + 26 * q^65 - 8 * q^66 + 5 * q^67 - 34 * q^68 + 9 * q^69 + 8 * q^70 + 19 * q^71 + 9 * q^72 - 4 * q^73 - 27 * q^74 - q^75 - 6 * q^76 - 6 * q^77 - 3 * q^78 - 16 * q^79 + 32 * q^80 - 5 * q^81 - 16 * q^82 - 20 * q^83 - q^84 + 21 * q^85 + 8 * q^86 - 8 * q^87 + 9 * q^88 + 32 * q^89 - 10 * q^90 - 17 * q^91 - 84 * q^92 + 6 * q^93 - 66 * q^94 - 11 * q^95 - 54 * q^96 - 5 * q^97 - 18 * q^98 + 10 * q^99

Introduction

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