LMFDB - Embedded newform 170.3.j.c.123.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,3,Mod(47,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("170.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	170.j (of order $4$, 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:	$4.63216449413$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 112 x^{16} + 5012 x^{14} + 115076 x^{12} + 1458640 x^{10} + 10354784 x^{8} + 40404568 x^{6} + \cdots + 160000 $ x^18 + 112x^16 + 5012x^14 + 115076x^12 + 1458640x^10 + 10354784x^8 + 40404568x^6 + 80183744x^4 + 62990500x^2 + 160000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			123.3
Root			$2.16902i$ of defining polynomial
Character	$\chi$	$=$	170.123
Dual form			170.3.j.c.47.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} -2.16902 q^{3} +2.00000i q^{4} +(-4.97231 + 0.525481i) q^{5} +(-2.16902 - 2.16902i) q^{6} +3.57697 q^{7} +(-2.00000 + 2.00000i) q^{8} -4.29533 q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} -2.16902 q^{3} +2.00000i q^{4} +(-4.97231 + 0.525481i) q^{5} +(-2.16902 - 2.16902i) q^{6} +3.57697 q^{7} +(-2.00000 + 2.00000i) q^{8} -4.29533 q^{9} +(-5.49779 - 4.44683i) q^{10} +(-5.42716 - 5.42716i) q^{11} -4.33805i q^{12} +(-14.1969 - 14.1969i) q^{13} +(3.57697 + 3.57697i) q^{14} +(10.7851 - 1.13978i) q^{15} -4.00000 q^{16} +(-7.66690 + 15.1730i) q^{17} +(-4.29533 - 4.29533i) q^{18} -19.5300 q^{19} +(-1.05096 - 9.94462i) q^{20} -7.75853 q^{21} -10.8543i q^{22} -0.490779i q^{23} +(4.33805 - 4.33805i) q^{24} +(24.4477 - 5.22571i) q^{25} -28.3939i q^{26} +28.8379 q^{27} +7.15393i q^{28} +(35.8284 + 35.8284i) q^{29} +(11.9248 + 9.64528i) q^{30} +(-33.8951 + 33.8951i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(11.7716 + 11.7716i) q^{33} +(-22.8399 + 7.50606i) q^{34} +(-17.7858 + 1.87963i) q^{35} -8.59067i q^{36} -58.6179i q^{37} +(-19.5300 - 19.5300i) q^{38} +(30.7935 + 30.7935i) q^{39} +(8.89366 - 10.9956i) q^{40} +(36.7037 + 36.7037i) q^{41} +(-7.75853 - 7.75853i) q^{42} +(-36.2161 + 36.2161i) q^{43} +(10.8543 - 10.8543i) q^{44} +(21.3577 - 2.25712i) q^{45} +(0.490779 - 0.490779i) q^{46} +(12.3196 - 12.3196i) q^{47} +8.67610 q^{48} -36.2053 q^{49} +(29.6734 + 19.2220i) q^{50} +(16.6297 - 32.9105i) q^{51} +(28.3939 - 28.3939i) q^{52} +(15.9881 - 15.9881i) q^{53} +(28.8379 + 28.8379i) q^{54} +(29.8374 + 24.1336i) q^{55} +(-7.15393 + 7.15393i) q^{56} +42.3611 q^{57} +71.6568i q^{58} -91.3768 q^{59} +(2.27956 + 21.5701i) q^{60} +(-5.96556 - 5.96556i) q^{61} -67.7902 q^{62} -15.3643 q^{63} -8.00000i q^{64} +(78.0517 + 63.1313i) q^{65} +23.5433i q^{66} +(64.0344 - 64.0344i) q^{67} +(-30.3459 - 15.3338i) q^{68} +1.06451i q^{69} +(-19.6654 - 15.9062i) q^{70} +(-76.1597 + 76.1597i) q^{71} +(8.59067 - 8.59067i) q^{72} +31.8471 q^{73} +(58.6179 - 58.6179i) q^{74} +(-53.0277 + 11.3347i) q^{75} -39.0601i q^{76} +(-19.4128 - 19.4128i) q^{77} +61.5870i q^{78} +(-12.8725 + 12.8725i) q^{79} +(19.8892 - 2.10192i) q^{80} -23.8921 q^{81} +73.4075i q^{82} +(-30.3700 + 30.3700i) q^{83} -15.5171i q^{84} +(30.1491 - 79.4735i) q^{85} -72.4323 q^{86} +(-77.7127 - 77.7127i) q^{87} +21.7086 q^{88} -18.4285i q^{89} +(23.6148 + 19.1006i) q^{90} +(-50.7819 - 50.7819i) q^{91} +0.981558 q^{92} +(73.5193 - 73.5193i) q^{93} +24.6392 q^{94} +(97.1094 - 10.2627i) q^{95} +(8.67610 + 8.67610i) q^{96} +42.5377i q^{97} +(-36.2053 - 36.2053i) q^{98} +(23.3114 + 23.3114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 18 q^{2} - 8 q^{3} + 18 q^{5} - 8 q^{6} - 28 q^{7} - 36 q^{8} + 62 q^{9}+O(q^{10}) $ 18 * q + 18 * q^2 - 8 * q^3 + 18 * q^5 - 8 * q^6 - 28 * q^7 - 36 * q^8 + 62 * q^9	$ 18 q + 18 q^{2} - 8 q^{3} + 18 q^{5} - 8 q^{6} - 28 q^{7} - 36 q^{8} + 62 q^{9} + 26 q^{10} - 8 q^{11} - 22 q^{13} - 28 q^{14} + 28 q^{15} - 72 q^{16} - 58 q^{17} + 62 q^{18} + 48 q^{19} + 16 q^{20} - 64 q^{21} + 16 q^{24} - 62 q^{25} + 28 q^{27} + 74 q^{29} + 28 q^{30} - 16 q^{31} - 72 q^{32} + 84 q^{33} - 70 q^{34} - 28 q^{35} + 48 q^{38} - 60 q^{39} - 20 q^{40} + 18 q^{41} - 64 q^{42} - 48 q^{43} + 16 q^{44} + 270 q^{45} - 40 q^{46} - 44 q^{47} + 32 q^{48} + 214 q^{49} - 46 q^{50} + 52 q^{51} + 44 q^{52} + 58 q^{53} + 28 q^{54} + 52 q^{55} + 56 q^{56} - 136 q^{57} - 80 q^{59} - 254 q^{61} - 32 q^{62} - 312 q^{63} + 194 q^{65} + 336 q^{67} - 24 q^{68} - 12 q^{70} - 8 q^{71} - 124 q^{72} - 772 q^{73} + 144 q^{74} - 268 q^{75} - 76 q^{77} - 444 q^{79} - 72 q^{80} + 450 q^{81} + 244 q^{83} + 126 q^{85} - 96 q^{86} + 92 q^{87} + 32 q^{88} + 446 q^{90} + 288 q^{91} - 80 q^{92} - 88 q^{94} + 92 q^{95} + 32 q^{96} + 214 q^{98} + 128 q^{99}+O(q^{100}) $ 18 * q + 18 * q^2 - 8 * q^3 + 18 * q^5 - 8 * q^6 - 28 * q^7 - 36 * q^8 + 62 * q^9 + 26 * q^10 - 8 * q^11 - 22 * q^13 - 28 * q^14 + 28 * q^15 - 72 * q^16 - 58 * q^17 + 62 * q^18 + 48 * q^19 + 16 * q^20 - 64 * q^21 + 16 * q^24 - 62 * q^25 + 28 * q^27 + 74 * q^29 + 28 * q^30 - 16 * q^31 - 72 * q^32 + 84 * q^33 - 70 * q^34 - 28 * q^35 + 48 * q^38 - 60 * q^39 - 20 * q^40 + 18 * q^41 - 64 * q^42 - 48 * q^43 + 16 * q^44 + 270 * q^45 - 40 * q^46 - 44 * q^47 + 32 * q^48 + 214 * q^49 - 46 * q^50 + 52 * q^51 + 44 * q^52 + 58 * q^53 + 28 * q^54 + 52 * q^55 + 56 * q^56 - 136 * q^57 - 80 * q^59 - 254 * q^61 - 32 * q^62 - 312 * q^63 + 194 * q^65 + 336 * q^67 - 24 * q^68 - 12 * q^70 - 8 * q^71 - 124 * q^72 - 772 * q^73 + 144 * q^74 - 268 * q^75 - 76 * q^77 - 444 * q^79 - 72 * q^80 + 450 * q^81 + 244 * q^83 + 126 * q^85 - 96 * q^86 + 92 * q^87 + 32 * q^88 + 446 * q^90 + 288 * q^91 - 80 * q^92 - 88 * q^94 + 92 * q^95 + 32 * q^96 + 214 * q^98 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	−2.16902			−0.723008			−0.361504	−	0.932371i	$-0.617737\pi$
$3$	−2.16902			−0.723008			−0.361504	+	0.932371i	$0.617737\pi$
$4$			2.00000i			0.500000i
$5$	−4.97231	+	0.525481i	−0.994462	+	0.105096i
$5$	−4.97231	+	0.525481i	−0.994462	+	0.105096i
$6$	−2.16902	−	2.16902i	−0.361504	−	0.361504i
$7$	3.57697			0.510995			0.255498	−	0.966810i	$-0.417761\pi$
$7$	3.57697			0.510995			0.255498	+	0.966810i	$0.417761\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	−4.29533			−0.477259
$10$	−5.49779	−	4.44683i	−0.549779	−	0.444683i
$11$	−5.42716	−	5.42716i	−0.493378	−	0.493378i	0.415991	−	0.909369i	$-0.363435\pi$
$11$	−5.42716	−	5.42716i	−0.493378	−	0.493378i	−0.909369	+	0.415991i	$0.863435\pi$
$12$		−	4.33805i		−	0.361504i
$13$	−14.1969	−	14.1969i	−1.09207	−	1.09207i	−0.995307	−	0.0967638i	$-0.969151\pi$
$13$	−14.1969	−	14.1969i	−1.09207	−	1.09207i	−0.0967638	−	0.995307i	$-0.530849\pi$
$14$	3.57697	+	3.57697i	0.255498	+	0.255498i
$15$	10.7851	−	1.13978i	0.719004	−	0.0759854i
$16$	−4.00000			−0.250000
$17$	−7.66690	+	15.1730i	−0.450994	+	0.892527i
$17$	−7.66690	+	15.1730i	−0.450994	+	0.892527i
$18$	−4.29533	−	4.29533i	−0.238630	−	0.238630i
$19$	−19.5300			−1.02790			−0.513948	−	0.857821i	$-0.671818\pi$
$19$	−19.5300			−1.02790			−0.513948	+	0.857821i	$0.671818\pi$
$20$	−1.05096	−	9.94462i	−0.0525481	−	0.497231i
$21$	−7.75853			−0.369454
$22$		−	10.8543i		−	0.493378i
$23$		−	0.490779i		−	0.0213382i	−0.999943	−	0.0106691i	$-0.996604\pi$
$23$		−	0.490779i		−	0.0213382i	0.999943	−	0.0106691i	$-0.00339615\pi$
$24$	4.33805	−	4.33805i	0.180752	−	0.180752i
$25$	24.4477	−	5.22571i	0.977910	−	0.209028i
$26$		−	28.3939i		−	1.09207i
$27$	28.8379			1.06807
$28$			7.15393i			0.255498i
$29$	35.8284	+	35.8284i	1.23546	+	1.23546i	0.961836	+	0.273626i	$0.0882231\pi$
$29$	35.8284	+	35.8284i	1.23546	+	1.23546i	0.273626	+	0.961836i	$0.411777\pi$
$30$	11.9248	+	9.64528i	0.397495	+	0.321509i
$31$	−33.8951	+	33.8951i	−1.09339	+	1.09339i	−0.0982269	+	0.995164i	$0.531317\pi$
$31$	−33.8951	+	33.8951i	−1.09339	+	1.09339i	−0.995164	+	0.0982269i	$0.968683\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	11.7716	+	11.7716i	0.356716	+	0.356716i
$34$	−22.8399	+	7.50606i	−0.671761	+	0.220766i
$35$	−17.7858	+	1.87963i	−0.508165	+	0.0537036i
$36$		−	8.59067i		−	0.238630i
$37$		−	58.6179i		−	1.58427i	−0.610347	−	0.792134i	$-0.708970\pi$
$37$		−	58.6179i		−	1.58427i	0.610347	−	0.792134i	$-0.291030\pi$
$38$	−19.5300	−	19.5300i	−0.513948	−	0.513948i
$39$	30.7935	+	30.7935i	0.789576	+	0.789576i
$40$	8.89366	−	10.9956i	0.222341	−	0.274890i
$41$	36.7037	+	36.7037i	0.895213	+	0.895213i	0.995008	−	0.0997952i	$-0.0318188\pi$
$41$	36.7037	+	36.7037i	0.895213	+	0.895213i	−0.0997952	+	0.995008i	$0.531819\pi$
$42$	−7.75853	−	7.75853i	−0.184727	−	0.184727i
$43$	−36.2161	+	36.2161i	−0.842236	+	0.842236i	−0.989149	−	0.146914i	$-0.953066\pi$
$43$	−36.2161	+	36.2161i	−0.842236	+	0.842236i	0.146914	+	0.989149i	$0.453066\pi$
$44$	10.8543	−	10.8543i	0.246689	−	0.246689i
$45$	21.3577	−	2.25712i	0.474616	−	0.0501581i
$46$	0.490779	−	0.490779i	0.0106691	−	0.0106691i
$47$	12.3196	−	12.3196i	0.262119	−	0.262119i	−0.563795	−	0.825914i	$-0.690659\pi$
$47$	12.3196	−	12.3196i	0.262119	−	0.262119i	0.825914	+	0.563795i	$0.190659\pi$
$48$	8.67610			0.180752
$49$	−36.2053			−0.738884
$50$	29.6734	+	19.2220i	0.593469	+	0.384441i
$51$	16.6297	−	32.9105i	0.326072	−	0.645304i
$52$	28.3939	−	28.3939i	0.546036	−	0.546036i
$53$	15.9881	−	15.9881i	0.301662	−	0.301662i	−0.540002	−	0.841664i	$-0.681576\pi$
$53$	15.9881	−	15.9881i	0.301662	−	0.301662i	0.841664	+	0.540002i	$0.181576\pi$
$54$	28.8379	+	28.8379i	0.534035	+	0.534035i
$55$	29.8374	+	24.1336i	0.542498	+	0.438793i
$56$	−7.15393	+	7.15393i	−0.127749	+	0.127749i
$57$	42.3611			0.743177
$58$			71.6568i			1.23546i
$59$	−91.3768			−1.54876			−0.774379	−	0.632722i	$-0.781938\pi$
$59$	−91.3768			−1.54876			−0.774379	+	0.632722i	$0.781938\pi$
$60$	2.27956	+	21.5701i	0.0379927	+	0.359502i
$61$	−5.96556	−	5.96556i	−0.0977961	−	0.0977961i	0.656516	−	0.754312i	$-0.272029\pi$
$61$	−5.96556	−	5.96556i	−0.0977961	−	0.0977961i	−0.754312	+	0.656516i	$0.772029\pi$
$62$	−67.7902			−1.09339
$63$	−15.3643			−0.243877
$64$		−	8.00000i		−	0.125000i
$65$	78.0517	+	63.1313i	1.20080	+	0.971251i
$66$			23.5433i			0.356716i
$67$	64.0344	−	64.0344i	0.955737	−	0.955737i	−0.0433244	−	0.999061i	$-0.513795\pi$
$67$	64.0344	−	64.0344i	0.955737	−	0.955737i	0.999061	+	0.0433244i	$0.0137949\pi$
$68$	−30.3459	−	15.3338i	−0.446263	−	0.225497i
$69$			1.06451i			0.0154277i
$70$	−19.6654	−	15.9062i	−0.280934	−	0.227231i
$71$	−76.1597	+	76.1597i	−1.07267	+	1.07267i	−0.0755289	+	0.997144i	$0.524065\pi$
$71$	−76.1597	+	76.1597i	−1.07267	+	1.07267i	−0.997144	+	0.0755289i	$0.975935\pi$
$72$	8.59067	−	8.59067i	0.119315	−	0.119315i
$73$	31.8471			0.436261			0.218131	−	0.975920i	$-0.430004\pi$
$73$	31.8471			0.436261			0.218131	+	0.975920i	$0.430004\pi$
$74$	58.6179	−	58.6179i	0.792134	−	0.792134i
$75$	−53.0277	+	11.3347i	−0.707037	+	0.151129i
$76$		−	39.0601i		−	0.513948i
$77$	−19.4128	−	19.4128i	−0.252114	−	0.252114i
$78$			61.5870i			0.789576i
$79$	−12.8725	+	12.8725i	−0.162943	+	0.162943i	−0.783869	−	0.620926i	$-0.786757\pi$
$79$	−12.8725	+	12.8725i	−0.162943	+	0.162943i	0.620926	+	0.783869i	$0.286757\pi$
$80$	19.8892	−	2.10192i	0.248616	−	0.0262740i
$81$	−23.8921			−0.294964
$82$			73.4075i			0.895213i
$83$	−30.3700	+	30.3700i	−0.365903	+	0.365903i	−0.865981	−	0.500077i	$-0.833305\pi$
$83$	−30.3700	+	30.3700i	−0.365903	+	0.365903i	0.500077	+	0.865981i	$0.333305\pi$
$84$		−	15.5171i		−	0.184727i
$85$	30.1491	−	79.4735i	0.354695	−	0.934982i
$86$	−72.4323			−0.842236
$87$	−77.7127	−	77.7127i	−0.893249	−	0.893249i
$88$	21.7086			0.246689
$89$		−	18.4285i		−	0.207062i	−0.994626	−	0.103531i	$-0.966986\pi$
$89$		−	18.4285i		−	0.207062i	0.994626	−	0.103531i	$-0.0330140\pi$
$90$	23.6148	+	19.1006i	0.262387	+	0.212229i
$91$	−50.7819	−	50.7819i	−0.558043	−	0.558043i
$92$	0.981558			0.0106691
$93$	73.5193	−	73.5193i	0.790531	−	0.790531i
$94$	24.6392			0.262119
$95$	97.1094	−	10.2627i	1.02220	−	0.108028i
$96$	8.67610	+	8.67610i	0.0903760	+	0.0903760i
$97$			42.5377i			0.438533i	0.975665	+	0.219266i	$0.0703664\pi$
$97$			42.5377i			0.438533i	−0.975665	+	0.219266i	$0.929634\pi$
$98$	−36.2053	−	36.2053i	−0.369442	−	0.369442i
$99$	23.3114	+	23.3114i	0.235469	+	0.235469i
$100$	10.4514	+	48.8955i	0.104514	+	0.488955i
$101$	14.6236			0.144788			0.0723940	−	0.997376i	$-0.476936\pi$
$101$	14.6236			0.144788			0.0723940	+	0.997376i	$0.476936\pi$
$102$	49.5402	−	16.2808i	0.485688	−	0.159616i
$103$	−61.2635	−	61.2635i	−0.594791	−	0.594791i	0.344130	−	0.938922i	$-0.388174\pi$
$103$	−61.2635	−	61.2635i	−0.594791	−	0.594791i	−0.938922	+	0.344130i	$0.888174\pi$
$104$	56.7877			0.546036
$105$	38.5778	−	4.07696i	0.367408	−	0.0388282i
$106$	31.9762			0.301662
$107$		−	60.7636i		−	0.567884i	−0.958841	−	0.283942i	$-0.908358\pi$
$107$		−	60.7636i		−	0.567884i	0.958841	−	0.283942i	$-0.0916423\pi$
$108$			57.6758i			0.534035i
$109$	21.7899	−	21.7899i	0.199907	−	0.199907i	−0.600053	−	0.799960i	$-0.704854\pi$
$109$	21.7899	−	21.7899i	0.199907	−	0.199907i	0.799960	+	0.600053i	$0.204854\pi$
$110$	5.70373	+	53.9710i	0.0518521	+	0.490646i
$111$			127.144i			1.14544i
$112$	−14.3079			−0.127749
$113$		−	163.408i		−	1.44609i	−0.690800	−	0.723046i	$-0.742741\pi$
$113$		−	163.408i		−	1.44609i	0.690800	−	0.723046i	$-0.257259\pi$
$114$	42.3611	+	42.3611i	0.371589	+	0.371589i
$115$	0.257895	+	2.44031i	0.00224256	+	0.0212200i
$116$	−71.6568	+	71.6568i	−0.617731	+	0.617731i
$117$	60.9805	+	60.9805i	0.521201	+	0.521201i
$118$	−91.3768	−	91.3768i	−0.774379	−	0.774379i
$119$	−27.4242	+	54.2732i	−0.230456	+	0.456077i
$120$	−19.2906	+	23.8497i	−0.160755	+	0.198747i
$121$		−	62.0919i		−	0.513157i
$122$		−	11.9311i		−	0.0977961i
$123$	−79.6113	−	79.6113i	−0.647246	−	0.647246i
$124$	−67.7902	−	67.7902i	−0.546695	−	0.546695i
$125$	−118.816	+	38.8307i	−0.950526	+	0.310645i
$126$	−15.3643	−	15.3643i	−0.121939	−	0.121939i
$127$	−124.928	−	124.928i	−0.983684	−	0.983684i	0.0161854	−	0.999869i	$-0.494848\pi$
$127$	−124.928	−	124.928i	−0.983684	−	0.983684i	−0.999869	+	0.0161854i	$0.994848\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$	78.5537	−	78.5537i	0.608943	−	0.608943i
$130$	14.9204	+	141.183i	0.114773	+	1.08602i
$131$	55.2981	−	55.2981i	0.422123	−	0.422123i	−0.463811	−	0.885934i	$-0.653518\pi$
$131$	55.2981	−	55.2981i	0.422123	−	0.422123i	0.885934	+	0.463811i	$0.153518\pi$
$132$	−23.5433	+	23.5433i	−0.178358	+	0.178358i
$133$	−69.8583			−0.525250
$134$	128.069			0.955737
$135$	−143.391	+	15.1538i	−1.06216	+	0.112250i
$136$	−15.0121	−	45.6797i	−0.110383	−	0.335880i
$137$	−102.509	+	102.509i	−0.748237	+	0.748237i	−0.974148	−	0.225911i	$-0.927464\pi$
$137$	−102.509	+	102.509i	−0.748237	+	0.748237i	0.225911	+	0.974148i	$0.427464\pi$
$138$	−1.06451	+	1.06451i	−0.00771385	+	0.00771385i
$139$	−77.6822	−	77.6822i	−0.558865	−	0.558865i	0.370119	−	0.928984i	$-0.379317\pi$
$139$	−77.6822	−	77.6822i	−0.558865	−	0.558865i	−0.928984	+	0.370119i	$0.879317\pi$
$140$	−3.75925	−	35.5716i	−0.0268518	−	0.254083i
$141$	−26.7215	+	26.7215i	−0.189514	+	0.189514i
$142$	−152.319			−1.07267
$143$			154.098i			1.07761i
$144$	17.1813			0.119315
$145$	−196.977	−	159.323i	−1.35846	−	1.09878i
$146$	31.8471	+	31.8471i	0.218131	+	0.218131i
$147$	78.5302			0.534219
$148$	117.236			0.792134
$149$			70.3853i			0.472385i	0.971706	+	0.236192i	$0.0758996\pi$
$149$			70.3853i			0.472385i	−0.971706	+	0.236192i	$0.924100\pi$
$150$	−64.3624	−	41.6931i	−0.429083	−	0.277954i
$151$			96.5321i			0.639285i	0.947538	+	0.319643i	$0.103563\pi$
$151$			96.5321i			0.639285i	−0.947538	+	0.319643i	$0.896437\pi$
$152$	39.0601	−	39.0601i	0.256974	−	0.256974i
$153$	32.9319	−	65.1729i	0.215241	−	0.425967i
$154$		−	38.8255i		−	0.252114i
$155$	150.726	−	186.348i	0.972425	−	1.20225i
$156$	−61.5870	+	61.5870i	−0.394788	+	0.394788i
$157$	38.5048	−	38.5048i	0.245254	−	0.245254i	−0.573766	−	0.819019i	$-0.694518\pi$
$157$	38.5048	−	38.5048i	0.245254	−	0.245254i	0.819019	+	0.573766i	$0.194518\pi$
$158$	−25.7450			−0.162943
$159$	−34.6786	+	34.6786i	−0.218104	+	0.218104i
$160$	21.9912	+	17.7873i	0.137445	+	0.111171i
$161$		−	1.75550i		−	0.0109037i
$162$	−23.8921	−	23.8921i	−0.147482	−	0.147482i
$163$			116.234i			0.713094i	0.934277	+	0.356547i	$0.116046\pi$
$163$			116.234i			0.713094i	−0.934277	+	0.356547i	$0.883954\pi$
$164$	−73.4075	+	73.4075i	−0.447606	+	0.447606i
$165$	−64.7180	−	52.3464i	−0.392230	−	0.317251i
$166$	−60.7399			−0.365903
$167$			195.018i			1.16777i	0.811835	+	0.583886i	$0.198469\pi$
$167$			195.018i			1.16777i	−0.811835	+	0.583886i	$0.801531\pi$
$168$	15.5171	−	15.5171i	0.0923634	−	0.0923634i
$169$			234.105i			1.38524i
$170$	109.623	−	49.3244i	0.644839	−	0.290143i
$171$	83.8880			0.490573
$172$	−72.4323	−	72.4323i	−0.421118	−	0.421118i
$173$	−91.6758			−0.529918			−0.264959	−	0.964260i	$-0.585358\pi$
$173$	−91.6758			−0.529918			−0.264959	+	0.964260i	$0.585358\pi$
$174$		−	155.425i		−	0.893249i
$175$	87.4487	−	18.6922i	0.499707	−	0.106812i
$176$	21.7086	+	21.7086i	0.123344	+	0.123344i
$177$	198.198			1.11977
$178$	18.4285	−	18.4285i	0.103531	−	0.103531i
$179$	−14.6680			−0.0819439			−0.0409720	−	0.999160i	$-0.513045\pi$
$179$	−14.6680			−0.0819439			−0.0409720	+	0.999160i	$0.513045\pi$
$180$	4.51423	+	42.7155i	0.0250791	+	0.237308i
$181$	101.874	+	101.874i	0.562841	+	0.562841i	0.930114	−	0.367272i	$-0.119708\pi$
$181$	101.874	+	101.874i	0.562841	+	0.562841i	−0.367272	+	0.930114i	$0.619708\pi$
$182$		−	101.564i		−	0.558043i
$183$	12.9394	+	12.9394i	0.0707074	+	0.0707074i
$184$	0.981558	+	0.981558i	0.00533455	+	0.00533455i
$185$	30.8026	+	291.467i	0.166501	+	1.57549i
$186$	147.039			0.790531
$187$	123.955	−	40.7366i	0.662864	−	0.217843i
$188$	24.6392	+	24.6392i	0.131059	+	0.131059i
$189$	103.152			0.545779
$190$	107.372	+	86.8467i	0.565116	+	0.457088i
$191$	355.776			1.86270			0.931352	−	0.364121i	$-0.118630\pi$
$191$	355.776			1.86270			0.931352	+	0.364121i	$0.118630\pi$
$192$			17.3522i			0.0903760i
$193$			10.2748i			0.0532372i	0.999646	+	0.0266186i	$0.00847396\pi$
$193$			10.2748i			0.0532372i	−0.999646	+	0.0266186i	$0.991526\pi$
$194$	−42.5377	+	42.5377i	−0.219266	+	0.219266i
$195$	−169.296	−	136.933i	−0.868185	−	0.702222i
$196$		−	72.4106i		−	0.369442i
$197$	274.977			1.39582			0.697911	−	0.716185i	$-0.254113\pi$
$197$	274.977			1.39582			0.697911	+	0.716185i	$0.254113\pi$
$198$			46.6229i			0.235469i
$199$	−103.237	−	103.237i	−0.518777	−	0.518777i	0.398424	−	0.917201i	$-0.369557\pi$
$199$	−103.237	−	103.237i	−0.518777	−	0.518777i	−0.917201	+	0.398424i	$0.869557\pi$
$200$	−38.4441	+	59.3469i	−0.192220	+	0.296734i
$201$	−138.892	+	138.892i	−0.691005	+	0.691005i
$202$	14.6236	+	14.6236i	0.0723940	+	0.0723940i
$203$	128.157	+	128.157i	0.631315	+	0.631315i
$204$	65.8210	+	33.2594i	0.322652	+	0.163036i
$205$	−201.789	−	163.215i	−0.984339	−	0.796172i
$206$		−	122.527i		−	0.594791i
$207$			2.10806i			0.0101839i
$208$	56.7877	+	56.7877i	0.273018	+	0.273018i
$209$	105.993	+	105.993i	0.507141	+	0.507141i
$210$	42.6548	+	34.5008i	0.203118	+	0.164290i
$211$	49.1131	+	49.1131i	0.232763	+	0.232763i	0.813845	−	0.581082i	$-0.197370\pi$
$211$	49.1131	+	49.1131i	0.232763	+	0.232763i	−0.581082	+	0.813845i	$0.697370\pi$
$212$	31.9762	+	31.9762i	0.150831	+	0.150831i
$213$	165.192	−	165.192i	0.775551	−	0.775551i
$214$	60.7636	−	60.7636i	0.283942	−	0.283942i
$215$	161.047	−	199.109i	0.749056	−	0.926087i
$216$	−57.6758	+	57.6758i	−0.267018	+	0.267018i
$217$	−121.242	+	121.242i	−0.558717	+	0.558717i
$218$	43.5798			0.199907
$219$	−69.0771			−0.315421
$220$	−48.2673	+	59.6747i	−0.219397	+	0.271249i
$221$	324.256	−	106.563i	1.46722	−	0.482185i
$222$	−127.144	+	127.144i	−0.572720	+	0.572720i
$223$	33.0217	−	33.0217i	0.148079	−	0.148079i	−0.629180	−	0.777259i	$-0.716609\pi$
$223$	33.0217	−	33.0217i	0.148079	−	0.148079i	0.777259	+	0.629180i	$0.216609\pi$
$224$	−14.3079	−	14.3079i	−0.0638744	−	0.0638744i
$225$	−105.011	+	22.4462i	−0.466716	+	0.0997607i
$226$	163.408	−	163.408i	0.723046	−	0.723046i
$227$	−312.127			−1.37501			−0.687504	−	0.726181i	$-0.741293\pi$
$227$	−312.127			−1.37501			−0.687504	+	0.726181i	$0.741293\pi$
$228$			84.7222i			0.371589i
$229$	−285.284			−1.24578			−0.622890	−	0.782309i	$-0.714042\pi$
$229$	−285.284			−1.24578			−0.622890	+	0.782309i	$0.714042\pi$
$230$	−2.18241	+	2.69820i	−0.00948874	+	0.0117313i
$231$	42.1067	+	42.1067i	0.182280	+	0.182280i
$232$	−143.314			−0.617731
$233$	206.626			0.886809			0.443404	−	0.896322i	$-0.353771\pi$
$233$	206.626			0.886809			0.443404	+	0.896322i	$0.353771\pi$
$234$			121.961i			0.521201i
$235$	−54.7831	+	67.7305i	−0.233120	+	0.288215i
$236$		−	182.754i		−	0.774379i
$237$	27.9208	−	27.9208i	0.117809	−	0.117809i
$238$	−81.6974	+	26.8489i	−0.343266	+	0.112811i
$239$			459.515i			1.92266i	0.275406	+	0.961328i	$0.411188\pi$
$239$			459.515i			1.92266i	−0.275406	+	0.961328i	$0.588812\pi$
$240$	−43.1402	+	4.55912i	−0.179751	+	0.0189963i
$241$	214.253	−	214.253i	0.889019	−	0.889019i	−0.105410	−	0.994429i	$-0.533616\pi$
$241$	214.253	−	214.253i	0.889019	−	0.889019i	0.994429	+	0.105410i	$0.0336156\pi$
$242$	62.0919	−	62.0919i	0.256578	−	0.256578i
$243$	−207.719			−0.854809
$244$	11.9311	−	11.9311i	0.0488980	−	0.0488980i
$245$	180.024	−	19.0252i	0.734792	−	0.0776539i
$246$		−	159.223i		−	0.647246i
$247$	277.266	+	277.266i	1.12254	+	1.12254i
$248$		−	135.580i		−	0.546695i
$249$	65.8732	−	65.8732i	0.264551	−	0.264551i
$250$	−157.646	−	79.9851i	−0.630586	−	0.319940i
$251$	−285.323			−1.13674			−0.568372	−	0.822772i	$-0.692426\pi$
$251$	−285.323			−1.13674			−0.568372	+	0.822772i	$0.692426\pi$
$252$		−	30.7285i		−	0.121939i
$253$	−2.66353	+	2.66353i	−0.0105278	+	0.0105278i
$254$		−	249.856i		−	0.983684i
$255$	−65.3941	+	172.380i	−0.256448	+	0.676000i
$256$	16.0000			0.0625000
$257$	58.0070	+	58.0070i	0.225708	+	0.225708i	0.810897	−	0.585189i	$-0.198980\pi$
$257$	58.0070	+	58.0070i	0.225708	+	0.225708i	−0.585189	+	0.810897i	$0.698980\pi$
$258$	157.107			0.608943
$259$		−	209.674i		−	0.809554i
$260$	−126.263	+	156.103i	−0.485625	+	0.600398i
$261$	−153.895	−	153.895i	−0.589636	−	0.589636i
$262$	110.596			0.422123
$263$	−4.36671	+	4.36671i	−0.0166035	+	0.0166035i	−0.715360	−	0.698756i	$-0.753737\pi$
$263$	−4.36671	+	4.36671i	−0.0166035	+	0.0166035i	0.698756	+	0.715360i	$0.253737\pi$
$264$	−47.0865			−0.178358
$265$	−71.0964	+	87.8993i	−0.268288	+	0.331695i
$266$	−69.8583	−	69.8583i	−0.262625	−	0.262625i
$267$			39.9718i			0.149707i
$268$	128.069	+	128.069i	0.477868	+	0.477868i
$269$	−278.274	−	278.274i	−1.03448	−	1.03448i	−0.999384	−	0.0350916i	$-0.988828\pi$
$269$	−278.274	−	278.274i	−1.03448	−	1.03448i	−0.0350916	−	0.999384i	$-0.511172\pi$
$270$	−158.545	−	128.237i	−0.587203	−	0.474953i
$271$	−500.004			−1.84503			−0.922517	−	0.385957i	$-0.873871\pi$
$271$	−500.004			−1.84503			−0.922517	+	0.385957i	$0.873871\pi$
$272$	30.6676	−	60.6918i	0.112749	−	0.223132i
$273$	110.147	+	110.147i	0.403470	+	0.403470i
$274$	−205.017			−0.748237
$275$	−161.042	−	104.321i	−0.585609	−	0.379349i
$276$	−2.12902			−0.00771385
$277$			473.661i			1.70997i	0.518654	+	0.854984i	$0.326433\pi$
$277$			473.661i			1.70997i	−0.518654	+	0.854984i	$0.673567\pi$
$278$		−	155.364i		−	0.558865i
$279$	145.591	−	145.591i	0.521831	−	0.521831i
$280$	31.8123	−	39.3308i	0.113615	−	0.140467i
$281$			64.5806i			0.229824i	0.993376	+	0.114912i	$0.0366587\pi$
$281$			64.5806i			0.229824i	−0.993376	+	0.114912i	$0.963341\pi$
$282$	−53.4430			−0.189514
$283$			210.367i			0.743346i	0.928364	+	0.371673i	$0.121216\pi$
$283$			210.367i			0.743346i	−0.928364	+	0.371673i	$0.878784\pi$
$284$	−152.319	−	152.319i	−0.536336	−	0.536336i
$285$	−210.633	+	22.2600i	−0.739062	+	0.0781051i
$286$	−154.098	+	154.098i	−0.538804	+	0.538804i
$287$	131.288	+	131.288i	0.457449	+	0.457449i
$288$	17.1813	+	17.1813i	0.0596574	+	0.0596574i
$289$	−171.437	−	232.659i	−0.593209	−	0.805049i
$290$	−37.6543	−	356.300i	−0.129842	−	1.22862i
$291$		−	92.2652i		−	0.317063i
$292$			63.6942i			0.218131i
$293$	155.212	+	155.212i	0.529734	+	0.529734i	0.920493	−	0.390759i	$-0.127787\pi$
$293$	155.212	+	155.212i	0.529734	+	0.529734i	−0.390759	+	0.920493i	$0.627787\pi$
$294$	78.5302	+	78.5302i	0.267110	+	0.267110i
$295$	454.354	−	48.0167i	1.54018	−	0.162769i
$296$	117.236	+	117.236i	0.396067	+	0.396067i
$297$	−156.508	−	156.508i	−0.526962	−	0.526962i
$298$	−70.3853	+	70.3853i	−0.236192	+	0.236192i
$299$	−6.96755	+	6.96755i	−0.0233028	+	0.0233028i
$300$	−22.6694	−	106.055i	−0.0755646	−	0.353518i
$301$	−129.544	+	129.544i	−0.430378	+	0.430378i
$302$	−96.5321	+	96.5321i	−0.319643	+	0.319643i
$303$	−31.7189			−0.104683
$304$	78.1201			0.256974
$305$	32.7974	+	26.5278i	0.107532	+	0.0869765i
$306$	98.1048	−	32.2410i	0.320604	−	0.105363i
$307$	−99.4690	+	99.4690i	−0.324003	+	0.324003i	−0.850301	−	0.526297i	$-0.823580\pi$
$307$	−99.4690	+	99.4690i	−0.324003	+	0.324003i	0.526297	+	0.850301i	$0.323580\pi$
$308$	38.8255	−	38.8255i	0.126057	−	0.126057i
$309$	132.882	+	132.882i	0.430039	+	0.430039i
$310$	337.074	−	35.6225i	1.08734	−	0.114911i
$311$	62.5167	−	62.5167i	0.201018	−	0.201018i	−0.599418	−	0.800436i	$-0.704601\pi$
$311$	62.5167	−	62.5167i	0.201018	−	0.201018i	0.800436	+	0.599418i	$0.204601\pi$
$312$	−123.174			−0.394788
$313$		−	278.407i		−	0.889479i	−0.895660	−	0.444739i	$-0.853296\pi$
$313$		−	278.407i		−	0.889479i	0.895660	−	0.444739i	$-0.146704\pi$
$314$	77.0096			0.245254
$315$	76.3959	−	8.07363i	0.242527	−	0.0256306i
$316$	−25.7450	−	25.7450i	−0.0814716	−	0.0814716i
$317$	−372.514			−1.17512			−0.587562	−	0.809179i	$-0.699912\pi$
$317$	−372.514			−1.17512			−0.587562	+	0.809179i	$0.699912\pi$
$318$	−69.3572			−0.218104
$319$		−	388.893i		−	1.21910i
$320$	4.20385	+	39.7785i	0.0131370	+	0.124308i
$321$			131.798i			0.410585i
$322$	1.75550	−	1.75550i	0.00545186	−	0.00545186i
$323$	149.735	−	296.328i	0.463575	−	0.917425i
$324$		−	47.7842i		−	0.147482i
$325$	−421.272	−	272.894i	−1.29622	−	0.839673i
$326$	−116.234	+	116.234i	−0.356547	+	0.356547i
$327$	−47.2629	+	47.2629i	−0.144535	+	0.144535i
$328$	−146.815			−0.447606
$329$	44.0668	−	44.0668i	0.133942	−	0.133942i
$330$	−12.3715	−	117.064i	−0.0374895	−	0.354741i
$331$		−	500.515i		−	1.51213i	−0.654496	−	0.756065i	$-0.727119\pi$
$331$		−	500.515i		−	1.51213i	0.654496	−	0.756065i	$-0.272881\pi$
$332$	−60.7399	−	60.7399i	−0.182952	−	0.182952i
$333$			251.784i			0.756107i
$334$	−195.018	+	195.018i	−0.583886	+	0.583886i
$335$	−284.750	+	352.048i	−0.850000	+	1.05089i
$336$	31.0341			0.0923634
$337$			363.529i			1.07872i	0.842075	+	0.539360i	$0.181334\pi$
$337$			363.529i			1.07872i	−0.842075	+	0.539360i	$0.818666\pi$
$338$	−234.105	+	234.105i	−0.692620	+	0.692620i
$339$			354.437i			1.04554i
$340$	158.947	+	60.2982i	0.467491	+	0.177348i
$341$	367.908			1.07891
$342$	83.8880	+	83.8880i	0.245287	+	0.245287i
$343$	−304.777			−0.888561
$344$		−	144.865i		−	0.421118i
$345$	−0.559380	−	5.29308i	−0.00162139	−	0.0153423i
$346$	−91.6758	−	91.6758i	−0.264959	−	0.264959i
$347$	−110.158			−0.317458			−0.158729	−	0.987322i	$-0.550740\pi$
$347$	−110.158			−0.317458			−0.158729	+	0.987322i	$0.550740\pi$
$348$	155.425	−	155.425i	0.446625	−	0.446625i
$349$	378.019			1.08315			0.541574	−	0.840653i	$-0.317829\pi$
$349$	378.019			1.08315			0.541574	+	0.840653i	$0.317829\pi$
$350$	106.141	+	68.7566i	0.303260	+	0.196447i
$351$	−409.410	−	409.410i	−1.16641	−	1.16641i
$352$			43.4173i			0.123344i
$353$	−127.672	−	127.672i	−0.361678	−	0.361678i	0.502752	−	0.864431i	$-0.332321\pi$
$353$	−127.672	−	127.672i	−0.361678	−	0.361678i	−0.864431	+	0.502752i	$0.832321\pi$
$354$	198.198	+	198.198i	0.559883	+	0.559883i
$355$	338.669	−	418.710i	0.953998	−	1.17947i
$356$	36.8570			0.103531
$357$	59.4838	−	117.720i	0.166621	−	0.329747i
$358$	−14.6680	−	14.6680i	−0.0409720	−	0.0409720i
$359$	−314.191			−0.875183			−0.437592	−	0.899174i	$-0.644168\pi$
$359$	−314.191			−0.875183			−0.437592	+	0.899174i	$0.644168\pi$
$360$	−38.2012	+	47.2297i	−0.106115	+	0.131194i
$361$	20.4222			0.0565711
$362$			203.749i			0.562841i
$363$			134.679i			0.371016i
$364$	101.564	−	101.564i	0.279022	−	0.279022i
$365$	−158.354	+	16.7350i	−0.433845	+	0.0458494i
$366$			25.8789i			0.0707074i
$367$	371.103			1.01118			0.505590	−	0.862774i	$-0.331275\pi$
$367$	371.103			1.01118			0.505590	+	0.862774i	$0.331275\pi$
$368$			1.96312i			0.00533455i
$369$	−157.655	−	157.655i	−0.427249	−	0.427249i
$370$	−260.664	+	322.269i	−0.704497	+	0.870998i
$371$	57.1889	−	57.1889i	0.154148	−	0.154148i
$372$	147.039	+	147.039i	0.395265	+	0.395265i
$373$	179.918	+	179.918i	0.482354	+	0.482354i	0.905883	−	0.423529i	$-0.139209\pi$
$373$	179.918	+	179.918i	0.482354	+	0.482354i	−0.423529	+	0.905883i	$0.639209\pi$
$374$	164.692	+	83.2189i	0.440353	+	0.222510i
$375$	257.714	−	84.2247i	0.687238	−	0.224599i
$376$			49.2784i			0.131059i
$377$		−	1017.31i		−	2.69843i
$378$	103.152	+	103.152i	0.272889	+	0.272889i
$379$	6.73800	+	6.73800i	0.0177784	+	0.0177784i	0.715940	−	0.698162i	$-0.245998\pi$
$379$	6.73800	+	6.73800i	0.0177784	+	0.0177784i	−0.698162	+	0.715940i	$0.745998\pi$
$380$	20.5253	+	194.219i	0.0540140	+	0.511102i
$381$	270.971	+	270.971i	0.711211	+	0.711211i
$382$	355.776	+	355.776i	0.931352	+	0.931352i
$383$	25.8005	−	25.8005i	0.0673643	−	0.0673643i	−0.672622	−	0.739986i	$-0.734832\pi$
$383$	25.8005	−	25.8005i	0.0673643	−	0.0673643i	0.739986	+	0.672622i	$0.234832\pi$
$384$	−17.3522	+	17.3522i	−0.0451880	+	0.0451880i
$385$	106.727	+	86.3252i	0.277214	+	0.224221i
$386$	−10.2748	+	10.2748i	−0.0266186	+	0.0266186i
$387$	155.560	−	155.560i	0.401965	−	0.401965i
$388$	−85.0753			−0.219266
$389$	−21.6188			−0.0555752			−0.0277876	−	0.999614i	$-0.508846\pi$
$389$	−21.6188			−0.0555752			−0.0277876	+	0.999614i	$0.508846\pi$
$390$	−32.3628	−	306.229i	−0.0829815	−	0.785204i
$391$	7.44657	+	3.76275i	0.0190449	+	0.00962341i
$392$	72.4106	−	72.4106i	0.184721	−	0.184721i
$393$	−119.943	+	119.943i	−0.305198	+	0.305198i
$394$	274.977	+	274.977i	0.697911	+	0.697911i
$395$	57.2419	−	70.7704i	0.144916	−	0.179166i
$396$	−46.6229	+	46.6229i	−0.117735	+	0.117735i
$397$	−671.428			−1.69125			−0.845627	−	0.533775i	$-0.820773\pi$
$397$	−671.428			−1.69125			−0.845627	+	0.533775i	$0.820773\pi$
$398$		−	206.473i		−	0.518777i
$399$	151.524			0.379760
$400$	−97.7910	+	20.9028i	−0.244477	+	0.0522571i
$401$	−63.7363	−	63.7363i	−0.158943	−	0.158943i	0.623155	−	0.782098i	$-0.285851\pi$
$401$	−63.7363	−	63.7363i	−0.158943	−	0.158943i	−0.782098	+	0.623155i	$0.785851\pi$
$402$	−277.784			−0.691005
$403$	962.413			2.38812
$404$			29.2472i			0.0723940i
$405$	118.799	−	12.5548i	0.293331	−	0.0309996i
$406$			256.314i			0.631315i
$407$	−318.129	+	318.129i	−0.781643	+	0.781643i
$408$	32.5616	+	99.0804i	0.0798080	+	0.242844i
$409$		−	166.890i		−	0.408043i	−0.978966	−	0.204022i	$-0.934599\pi$
$409$		−	166.890i		−	0.408043i	0.978966	−	0.204022i	$-0.0654013\pi$
$410$	−38.5742	−	365.005i	−0.0940835	−	0.890255i
$411$	222.343	−	222.343i	0.540982	−	0.540982i
$412$	122.527	−	122.527i	0.297396	−	0.297396i
$413$	−326.852			−0.791408
$414$	−2.10806	+	2.10806i	−0.00509193	+	0.00509193i
$415$	135.050	−	166.968i	0.325422	−	0.402332i
$416$			113.575i			0.273018i
$417$	168.495	+	168.495i	0.404064	+	0.404064i
$418$			211.985i			0.507141i
$419$	−263.255	+	263.255i	−0.628293	+	0.628293i	−0.947638	−	0.319345i	$-0.896537\pi$
$419$	−263.255	+	263.255i	−0.628293	+	0.628293i	0.319345	+	0.947638i	$0.396537\pi$
$420$	8.15392	+	77.1556i	0.0194141	+	0.183704i
$421$	337.778			0.802324			0.401162	−	0.916007i	$-0.368606\pi$
$421$	337.778			0.802324			0.401162	+	0.916007i	$0.368606\pi$
$422$			98.2262i			0.232763i
$423$	−52.9168	+	52.9168i	−0.125099	+	0.125099i
$424$			63.9524i			0.150831i
$425$	−108.149	+	411.010i	−0.254468	+	0.967081i
$426$	330.385			0.775551
$427$	−21.3386	−	21.3386i	−0.0499733	−	0.0499733i
$428$	121.527			0.283942
$429$		−	334.242i		−	0.779119i
$430$	360.156	−	38.0618i	0.837571	−	0.0885157i
$431$	204.584	+	204.584i	0.474674	+	0.474674i	0.903423	−	0.428750i	$-0.141046\pi$
$431$	204.584	+	204.584i	0.474674	+	0.474674i	−0.428750	+	0.903423i	$0.641046\pi$
$432$	−115.352			−0.267018
$433$	147.904	−	147.904i	0.341580	−	0.341580i	−0.515381	−	0.856961i	$-0.672350\pi$
$433$	147.904	−	147.904i	0.341580	−	0.341580i	0.856961	+	0.515381i	$0.172350\pi$
$434$	−242.483			−0.558717
$435$	427.248	+	345.575i	0.982180	+	0.794425i
$436$	43.5798	+	43.5798i	0.0999537	+	0.0999537i
$437$			9.58493i			0.0219335i
$438$	−69.0771	−	69.0771i	−0.157710	−	0.157710i
$439$	84.4181	+	84.4181i	0.192296	+	0.192296i	0.796688	−	0.604391i	$-0.206584\pi$
$439$	84.4181	+	84.4181i	0.192296	+	0.192296i	−0.604391	+	0.796688i	$0.706584\pi$
$440$	−107.942	+	11.4075i	−0.245323	+	0.0259261i
$441$	155.514			0.352639
$442$	430.819	+	217.693i	0.974703	+	0.492518i
$443$	−536.961	−	536.961i	−1.21210	−	1.21210i	−0.970334	−	0.241769i	$-0.922273\pi$
$443$	−536.961	−	536.961i	−1.21210	−	1.21210i	−0.241769	−	0.970334i	$-0.577727\pi$
$444$	−254.287			−0.572720
$445$	9.68382	+	91.6322i	0.0217614	+	0.205915i
$446$	66.0434			0.148079
$447$		−	152.667i		−	0.341538i
$448$		−	28.6157i		−	0.0638744i
$449$	−74.4123	+	74.4123i	−0.165729	+	0.165729i	−0.785099	−	0.619370i	$-0.787388\pi$
$449$	−74.4123	+	74.4123i	−0.165729	+	0.165729i	0.619370	+	0.785099i	$0.287388\pi$
$450$	−127.457	−	82.5650i	−0.283239	−	0.183478i
$451$		−	398.394i		−	0.883356i
$452$	326.817			0.723046
$453$		−	209.380i		−	0.462208i
$454$	−312.127	−	312.127i	−0.687504	−	0.687504i
$455$	279.188	+	225.819i	0.613601	+	0.496304i
$456$	−84.7222	+	84.7222i	−0.185794	+	0.185794i
$457$	−415.477	−	415.477i	−0.909141	−	0.909141i	0.0870621	−	0.996203i	$-0.472252\pi$
$457$	−415.477	−	415.477i	−0.909141	−	0.909141i	−0.996203	+	0.0870621i	$0.972252\pi$
$458$	−285.284	−	285.284i	−0.622890	−	0.622890i
$459$	−221.097	+	437.556i	−0.481693	+	0.953282i
$460$	−4.88061	+	0.515790i	−0.0106100	+	0.00112128i
$461$			357.617i			0.775742i	0.921714	+	0.387871i	$0.126789\pi$
$461$			357.617i			0.775742i	−0.921714	+	0.387871i	$0.873211\pi$
$462$			84.2135i			0.182280i
$463$	627.616	+	627.616i	1.35554	+	1.35554i	0.879332	+	0.476209i	$0.157990\pi$
$463$	627.616	+	627.616i	1.35554	+	1.35554i	0.476209	+	0.879332i	$0.342010\pi$
$464$	−143.314	−	143.314i	−0.308866	−	0.308866i
$465$	−326.928	+	404.194i	−0.703071	+	0.869234i
$466$	206.626	+	206.626i	0.443404	+	0.443404i
$467$	−130.507	−	130.507i	−0.279458	−	0.279458i	0.553435	−	0.832893i	$-0.313317\pi$
$467$	−130.507	−	130.507i	−0.279458	−	0.279458i	−0.832893	+	0.553435i	$0.813317\pi$
$468$	−121.961	+	121.961i	−0.260601	+	0.260601i
$469$	229.049	−	229.049i	0.488377	−	0.488377i
$470$	−122.514	+	12.9474i	−0.260667	+	0.0275477i
$471$	−83.5178	+	83.5178i	−0.177320	+	0.177320i
$472$	182.754	−	182.754i	0.387190	−	0.387190i
$473$	393.101			0.831081
$474$	55.8416			0.117809
$475$	−477.465	+	102.058i	−1.00519	+	0.214859i
$476$	−108.546	−	54.8485i	−0.228038	−	0.115228i
$477$	−68.6742	+	68.6742i	−0.143971	+	0.143971i
$478$	−459.515	+	459.515i	−0.961328	+	0.961328i
$479$	309.664	+	309.664i	0.646480	+	0.646480i	0.952141	−	0.305661i	$-0.0988773\pi$
$479$	309.664	+	309.664i	0.646480	+	0.646480i	−0.305661	+	0.952141i	$0.598877\pi$
$480$	−47.6994	−	38.5811i	−0.0993737	−	0.0803773i
$481$	−832.194	+	832.194i	−1.73013	+	1.73013i
$482$	428.507			0.889019
$483$			3.80772i			0.00788348i
$484$	124.184			0.256578
$485$	−22.3527	−	211.510i	−0.0460881	−	0.436104i
$486$	−207.719	−	207.719i	−0.427404	−	0.427404i
$487$	873.511			1.79366			0.896828	−	0.442379i	$-0.145865\pi$
$487$	873.511			1.79366			0.896828	+	0.442379i	$0.145865\pi$
$488$	23.8622			0.0488980
$489$		−	252.115i		−	0.515572i
$490$	199.049	+	160.999i	0.406223	+	0.328569i
$491$			128.168i			0.261035i	0.991446	+	0.130517i	$0.0416639\pi$
$491$			128.168i			0.261035i	−0.991446	+	0.130517i	$0.958336\pi$
$492$	159.223	−	159.223i	0.323623	−	0.323623i
$493$	−818.316	+	268.930i	−1.65987	+	0.545497i
$494$			554.533i			1.12254i
$495$	−128.161	−	103.662i	−0.258912	−	0.209418i
$496$	135.580	−	135.580i	0.273348	−	0.273348i
$497$	−272.421	+	272.421i	−0.548130	+	0.548130i
$498$	131.746			0.264551
$499$	391.000	−	391.000i	0.783567	−	0.783567i	−0.196864	−	0.980431i	$-0.563076\pi$
$499$	391.000	−	391.000i	0.783567	−	0.783567i	0.980431	+	0.196864i	$0.0630757\pi$
$500$	−77.6613	−	237.631i	−0.155323	−	0.475263i
$501$		−	422.999i		−	0.844309i
$502$	−285.323	−	285.323i	−0.568372	−	0.568372i
$503$			121.284i			0.241121i	0.992706	+	0.120560i	$0.0384691\pi$
$503$			121.284i			0.241121i	−0.992706	+	0.120560i	$0.961531\pi$
$504$	30.7285	−	30.7285i	0.0609693	−	0.0609693i
$505$	−72.7130	+	7.68441i	−0.143986	+	0.0152167i
$506$	−5.32707			−0.0105278
$507$		−	507.780i		−	1.00154i
$508$	249.856	−	249.856i	0.491842	−	0.491842i
$509$			334.326i			0.656829i	0.944534	+	0.328414i	$0.106514\pi$
$509$			334.326i			0.656829i	−0.944534	+	0.328414i	$0.893486\pi$
$510$	−237.774	+	106.986i	−0.466224	+	0.209776i
$511$	113.916			0.222927
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−563.205			−1.09787
$514$			116.014i			0.225708i
$515$	336.814	+	272.428i	0.654008	+	0.528987i
$516$	157.107	+	157.107i	0.304472	+	0.304472i
$517$	−133.721			−0.258647
$518$	209.674	−	209.674i	0.404777	−	0.404777i
$519$	198.847			0.383135
$520$	−282.366	+	29.8409i	−0.543012	+	0.0573863i
$521$	487.684	+	487.684i	0.936053	+	0.936053i	0.998075	−	0.0620217i	$-0.0197548\pi$
$521$	487.684	+	487.684i	0.936053	+	0.936053i	−0.0620217	+	0.998075i	$0.519755\pi$
$522$		−	307.790i		−	0.589636i
$523$	282.623	+	282.623i	0.540389	+	0.540389i	0.923643	−	0.383254i	$-0.125197\pi$
$523$	282.623	+	282.623i	0.540389	+	0.540389i	−0.383254	+	0.923643i	$0.625197\pi$
$524$	110.596	+	110.596i	0.211061	+	0.211061i
$525$	−189.678	+	40.5438i	−0.361292	+	0.0772263i
$526$	−8.73343			−0.0166035
$527$	−254.419	−	774.160i	−0.482768	−	1.46899i
$528$	−47.0865	−	47.0865i	−0.0891790	−	0.0891790i
$529$	528.759			0.999545
$530$	−158.996	+	16.8029i	−0.299992	+	0.0317036i
$531$	392.494			0.739159
$532$		−	139.717i		−	0.262625i
$533$		−	1042.16i		−	1.95527i
$534$	−39.9718	+	39.9718i	−0.0748536	+	0.0748536i
$535$	31.9301	+	302.135i	0.0596824	+	0.564739i
$536$			256.137i			0.477868i
$537$	31.8152			0.0592461
$538$		−	556.548i		−	1.03448i
$539$	196.492	+	196.492i	0.364549	+	0.364549i
$540$	−30.3075	−	286.782i	−0.0561251	−	0.531078i
$541$	−532.489	+	532.489i	−0.984268	+	0.984268i	−0.999878	−	0.0156097i	$-0.995031\pi$
$541$	−532.489	+	532.489i	−0.984268	+	0.984268i	0.0156097	+	0.999878i	$0.495031\pi$
$542$	−500.004	−	500.004i	−0.922517	−	0.922517i
$543$	−220.968	−	220.968i	−0.406939	−	0.406939i
$544$	91.3594	−	30.0242i	0.167940	−	0.0551916i
$545$	−96.8960	+	119.796i	−0.177791	+	0.219810i
$546$			220.294i			0.403470i
$547$		−	116.556i		−	0.213082i	−0.994308	−	0.106541i	$-0.966022\pi$
$547$		−	116.556i		−	0.213082i	0.994308	−	0.106541i	$-0.0339775\pi$
$548$	−205.017	−	205.017i	−0.374119	−	0.374119i
$549$	25.6241	+	25.6241i	0.0466741	+	0.0466741i
$550$	−56.7215	−	265.363i	−0.103130	−	0.482479i
$551$	−699.730	−	699.730i	−1.26993	−	1.26993i
$552$	−2.12902	−	2.12902i	−0.00385693	−	0.00385693i
$553$	−46.0446	+	46.0446i	−0.0832632	+	0.0832632i
$554$	−473.661	+	473.661i	−0.854984	+	0.854984i
$555$	−66.8116	−	632.198i	−0.120381	−	1.13910i
$556$	155.364	−	155.364i	0.279432	−	0.279432i
$557$	−233.644	+	233.644i	−0.419468	+	0.419468i	−0.885020	−	0.465552i	$-0.845856\pi$
$557$	−233.644	+	233.644i	−0.419468	+	0.419468i	0.465552	+	0.885020i	$0.345856\pi$
$558$	291.182			0.521831
$559$	1028.32			1.83956
$560$	71.1431	−	7.51851i	0.127041	−	0.0134259i
$561$	−268.862	+	88.3586i	−0.479256	+	0.157502i
$562$	−64.5806	+	64.5806i	−0.114912	+	0.114912i
$563$	272.810	−	272.810i	0.484565	−	0.484565i	−0.422021	−	0.906586i	$-0.638679\pi$
$563$	272.810	−	272.810i	0.484565	−	0.484565i	0.906586	+	0.422021i	$0.138679\pi$
$564$	−53.4430	−	53.4430i	−0.0947571	−	0.0947571i
$565$	85.8680	+	812.517i	0.151979	+	1.43808i
$566$	−210.367	+	210.367i	−0.371673	+	0.371673i
$567$	−85.4613			−0.150725
$568$		−	304.639i		−	0.536336i
$569$	−1043.99			−1.83478			−0.917388	−	0.397993i	$-0.869707\pi$
$569$	−1043.99			−1.83478			−0.917388	+	0.397993i	$0.869707\pi$
$570$	−232.893	−	188.373i	−0.408583	−	0.330478i
$571$	−518.151	−	518.151i	−0.907444	−	0.907444i	0.0886213	−	0.996065i	$-0.471754\pi$
$571$	−518.151	−	518.151i	−0.907444	−	0.907444i	−0.996065	+	0.0886213i	$0.971754\pi$
$572$	−308.196			−0.538804
$573$	−771.688			−1.34675
$574$			262.576i			0.457449i
$575$	−2.56467	−	11.9984i	−0.00446029	−	0.0208668i
$576$			34.3627i			0.0596574i
$577$	746.286	−	746.286i	1.29339	−	1.29339i	0.360713	−	0.932677i	$-0.382533\pi$
$577$	746.286	−	746.286i	1.29339	−	1.29339i	0.932677	−	0.360713i	$-0.117467\pi$
$578$	61.2218	−	404.096i	0.105920	−	0.699129i
$579$		−	22.2862i		−	0.0384909i
$580$	318.646	−	393.954i	0.549389	−	0.679231i
$581$	−108.632	+	108.632i	−0.186975	+	0.186975i
$582$	92.2652	−	92.2652i	0.158531	−	0.158531i
$583$	−173.540			−0.297667
$584$	−63.6942	+	63.6942i	−0.109065	+	0.109065i
$585$	−335.258	−	271.170i	−0.573091	−	0.463538i
$586$			310.424i			0.529734i
$587$	162.845	+	162.845i	0.277419	+	0.277419i	0.832078	−	0.554659i	$-0.187151\pi$
$587$	162.845	+	162.845i	0.277419	+	0.277419i	−0.554659	+	0.832078i	$0.687151\pi$
$588$			157.060i			0.267110i
$589$	661.973	−	661.973i	1.12389	−	1.12389i
$590$	502.370	+	406.337i	0.851475	+	0.688707i
$591$	−596.432			−1.00919
$592$			234.472i			0.396067i
$593$	21.2579	−	21.2579i	0.0358481	−	0.0358481i	−0.688956	−	0.724804i	$-0.741930\pi$
$593$	21.2579	−	21.2579i	0.0358481	−	0.0358481i	0.724804	+	0.688956i	$0.241930\pi$
$594$		−	313.016i		−	0.526962i
$595$	107.842	−	284.274i	0.181248	−	0.477771i
$596$	−140.771			−0.236192
$597$	223.923	+	223.923i	0.375080	+	0.375080i
$598$	−13.9351			−0.0233028
$599$		−	315.250i		−	0.526293i	−0.964756	−	0.263147i	$-0.915240\pi$
$599$		−	315.250i		−	0.526293i	0.964756	−	0.263147i	$-0.0847603\pi$
$600$	83.3861	−	128.725i	0.138977	−	0.214541i
$601$	−60.9324	−	60.9324i	−0.101385	−	0.101385i	0.654595	−	0.755980i	$-0.272839\pi$
$601$	−60.9324	−	60.9324i	−0.101385	−	0.101385i	−0.755980	+	0.654595i	$0.772839\pi$
$602$	−259.088			−0.430378
$603$	−275.049	+	275.049i	−0.456134	+	0.456134i
$604$	−193.064			−0.319643
$605$	32.6281	+	308.740i	0.0539308	+	0.510315i
$606$	−31.7189	−	31.7189i	−0.0523414	−	0.0523414i
$607$			465.858i			0.767476i	0.923442	+	0.383738i	$0.125363\pi$
$607$			465.858i			0.767476i	−0.923442	+	0.383738i	$0.874637\pi$
$608$	78.1201	+	78.1201i	0.128487	+	0.128487i
$609$	−277.976	−	277.976i	−0.456446	−	0.456446i
$610$	6.26958	+	59.3252i	0.0102780	+	0.0972545i
$611$	−349.801			−0.572505
$612$	130.346	+	65.8638i	0.212983	+	0.107621i
$613$	31.6569	+	31.6569i	0.0516425	+	0.0516425i	0.732456	−	0.680814i	$-0.238374\pi$
$613$	31.6569	+	31.6569i	0.0516425	+	0.0516425i	−0.680814	+	0.732456i	$0.738374\pi$
$614$	−198.938			−0.324003
$615$	437.686	+	354.018i	0.711685	+	0.575639i
$616$	77.6510			0.126057
$617$		−	459.409i		−	0.744585i	−0.928116	−	0.372292i	$-0.878572\pi$
$617$		−	459.409i		−	0.744585i	0.928116	−	0.372292i	$-0.121428\pi$
$618$			265.764i			0.430039i
$619$	−592.708	+	592.708i	−0.957524	+	0.957524i	−0.999134	−	0.0416095i	$-0.986751\pi$
$619$	−592.708	+	592.708i	−0.957524	+	0.957524i	0.0416095	+	0.999134i	$0.486751\pi$
$620$	372.697	+	301.452i	0.601124	+	0.486212i
$621$		−	14.1530i		−	0.0227907i
$622$	125.033			0.201018
$623$		−	65.9181i		−	0.105808i
$624$	−123.174	−	123.174i	−0.197394	−	0.197394i
$625$	570.384	−	255.514i	0.912614	−	0.408822i
$626$	278.407	−	278.407i	0.444739	−	0.444739i
$627$	−229.900	−	229.900i	−0.366667	−	0.366667i
$628$	77.0096	+	77.0096i	0.122627	+	0.122627i
$629$	889.407	+	449.418i	1.41400	+	0.714496i
$630$	84.4695	+	68.3223i	0.134079	+	0.108448i
$631$			1120.27i			1.77539i	0.460432	+	0.887695i	$0.347695\pi$
$631$			1120.27i			1.77539i	−0.460432	+	0.887695i	$0.652305\pi$
$632$		−	51.4901i		−	0.0814716i
$633$	−106.527	−	106.527i	−0.168290	−	0.168290i
$634$	−372.514	−	372.514i	−0.587562	−	0.587562i
$635$	686.827	+	555.533i	1.08162	+	0.874855i
$636$	−69.3572	−	69.3572i	−0.109052	−	0.109052i
$637$	514.004	+	514.004i	0.806914	+	0.806914i
$638$	388.893	−	388.893i	0.609550	−	0.609550i
$639$	327.132	−	327.132i	0.511943	−	0.511943i
$640$	−35.5746	+	43.9823i	−0.0555854	+	0.0687224i
$641$	−183.361	+	183.361i	−0.286054	+	0.286054i	−0.835518	−	0.549463i	$-0.814832\pi$
$641$	−183.361	+	183.361i	−0.286054	+	0.286054i	0.549463	+	0.835518i	$0.314832\pi$
$642$	−131.798	+	131.798i	−0.205292	+	0.205292i
$643$	−10.4617			−0.0162702			−0.00813510	−	0.999967i	$-0.502590\pi$
$643$	−10.4617			−0.0162702			−0.00813510	+	0.999967i	$0.502590\pi$
$644$	3.51100			0.00545186
$645$	−349.315	+	431.872i	−0.541573	+	0.669568i
$646$	446.063	−	146.594i	0.690500	−	0.226925i
$647$	−618.906	+	618.906i	−0.956578	+	0.956578i	−0.999096	−	0.0425181i	$-0.986462\pi$
$647$	−618.906	+	618.906i	−0.956578	+	0.956578i	0.0425181	+	0.999096i	$0.486462\pi$
$648$	47.7842	−	47.7842i	0.0737411	−	0.0737411i
$649$	495.916	+	495.916i	0.764123	+	0.764123i
$650$	−148.378	−	694.165i	−0.228274	−	1.06795i
$651$	262.976	−	262.976i	0.403957	−	0.403957i
$652$	−232.469			−0.356547
$653$			1013.59i			1.55220i	0.630610	+	0.776100i	$0.282805\pi$
$653$			1013.59i			1.55220i	−0.630610	+	0.776100i	$0.717195\pi$
$654$	−94.5257			−0.144535
$655$	−245.901	+	304.017i	−0.375422	+	0.464149i
$656$	−146.815	−	146.815i	−0.223803	−	0.223803i
$657$	−136.794			−0.208210
$658$	88.1335			0.133942
$659$		−	747.288i		−	1.13397i	−0.823727	−	0.566987i	$-0.808109\pi$
$659$		−	747.288i		−	1.13397i	0.823727	−	0.566987i	$-0.191891\pi$
$660$	104.693	−	129.436i	0.158626	−	0.196115i
$661$		−	145.785i		−	0.220552i	−0.993901	−	0.110276i	$-0.964827\pi$
$661$		−	145.785i		−	0.220552i	0.993901	−	0.110276i	$-0.0351735\pi$
$662$	500.515	−	500.515i	0.756065	−	0.756065i
$663$	−703.319	+	231.138i	−1.06081	+	0.348624i
$664$		−	121.480i		−	0.182952i
$665$	347.357	−	36.7092i	0.522341	−	0.0552018i
$666$	−251.784	+	251.784i	−0.378053	+	0.378053i
$667$	17.5838	−	17.5838i	0.0263626	−	0.0263626i
$668$	−390.036			−0.583886
$669$	−71.6248	+	71.6248i	−0.107063	+	0.107063i
$670$	−636.797	+	67.2977i	−0.950444	+	0.100444i
$671$			64.7521i			0.0965008i
$672$	31.0341	+	31.0341i	0.0461817	+	0.0461817i
$673$		−	749.755i		−	1.11405i	−0.830496	−	0.557025i	$-0.811943\pi$
$673$		−	749.755i		−	1.11405i	0.830496	−	0.557025i	$-0.188057\pi$
$674$	−363.529	+	363.529i	−0.539360	+	0.539360i
$675$	705.022	−	150.698i	1.04448	−	0.223257i
$676$	−468.211			−0.692620
$677$		−	1033.74i		−	1.52694i	−0.645843	−	0.763470i	$-0.723494\pi$
$677$		−	1033.74i		−	1.52694i	0.645843	−	0.763470i	$-0.276506\pi$
$678$	−354.437	+	354.437i	−0.522768	+	0.522768i
$679$			152.156i			0.224088i
$680$	98.6487	+	219.245i	0.145072	+	0.322419i
$681$	677.010			0.994141
$682$	367.908	+	367.908i	0.539455	+	0.539455i
$683$	−754.995			−1.10541			−0.552705	−	0.833377i	$-0.686404\pi$
$683$	−754.995			−1.10541			−0.552705	+	0.833377i	$0.686404\pi$
$684$			167.776i			0.245287i
$685$	455.838	−	563.570i	0.665457	−	0.822730i
$686$	−304.777	−	304.777i	−0.444281	−	0.444281i
$687$	618.787			0.900709
$688$	144.865	−	144.865i	0.210559	−	0.210559i
$689$	−453.964			−0.658874
$690$	4.73370	−	5.85246i	0.00686044	−	0.00848183i
$691$	107.980	+	107.980i	0.156266	+	0.156266i	0.780910	−	0.624644i	$-0.214756\pi$
$691$	107.980	+	107.980i	0.156266	+	0.156266i	−0.624644	+	0.780910i	$0.714756\pi$
$692$		−	183.352i		−	0.264959i
$693$	83.3843	+	83.3843i	0.120324	+	0.120324i
$694$	−110.158	−	110.158i	−0.158729	−	0.158729i
$695$	427.081	+	345.440i	0.614504	+	0.497035i
$696$	310.851			0.446625
$697$	−838.308	+	275.500i	−1.20274	+	0.395266i
$698$	378.019	+	378.019i	0.541574	+	0.541574i
$699$	−448.178			−0.641170
$700$	37.3844	+	174.897i	0.0534062	+	0.249854i
$701$	−331.643			−0.473100			−0.236550	−	0.971619i	$-0.576017\pi$
$701$	−331.643			−0.473100			−0.236550	+	0.971619i	$0.576017\pi$
$702$		−	818.819i		−	1.16641i
$703$			1144.81i			1.62846i
$704$	−43.4173	+	43.4173i	−0.0616722	+	0.0616722i
$705$	118.826	−	146.909i	0.168547	−	0.208382i
$706$		−	255.345i		−	0.361678i
$707$	52.3081			0.0739859
$708$			396.397i			0.559883i
$709$	542.637	+	542.637i	0.765356	+	0.765356i	0.977285	−	0.211929i	$-0.0679747\pi$
$709$	542.637	+	542.637i	0.765356	+	0.765356i	−0.211929	+	0.977285i	$0.567975\pi$
$710$	757.380	−	80.0410i	1.06673	−	0.112734i
$711$	55.2918	−	55.2918i	0.0777662	−	0.0777662i
$712$	36.8570	+	36.8570i	0.0517654	+	0.0517654i
$713$	16.6350	+	16.6350i	0.0233310	+	0.0233310i
$714$	177.204	−	58.2359i	0.248184	−	0.0815630i
$715$	−80.9755	−	766.222i	−0.113252	−	1.07164i
$716$		−	29.3359i		−	0.0409720i
$717$		−	996.699i		−	1.39010i
$718$	−314.191	−	314.191i	−0.437592	−	0.437592i
$719$	106.291	+	106.291i	0.147832	+	0.147832i	0.777149	−	0.629317i	$-0.216665\pi$
$719$	106.291	+	106.291i	0.147832	+	0.147832i	−0.629317	+	0.777149i	$0.716665\pi$
$720$	−85.4309	+	9.02846i	−0.118654	+	0.0125395i
$721$	−219.138	−	219.138i	−0.303936	−	0.303936i
$722$	20.4222	+	20.4222i	0.0282855	+	0.0282855i
$723$	−464.721	+	464.721i	−0.642768	+	0.642768i
$724$	−203.749	+	203.749i	−0.281421	+	0.281421i
$725$	1063.15	+	688.695i	1.46642	+	0.949924i
$726$	−134.679	+	134.679i	−0.185508	+	0.185508i
$727$	−372.647	+	372.647i	−0.512581	+	0.512581i	−0.915317	−	0.402735i	$-0.868060\pi$
$727$	−372.647	+	372.647i	−0.512581	+	0.512581i	0.402735	+	0.915317i	$0.368060\pi$
$728$	203.128			0.279022
$729$	665.576			0.912998
$730$	−175.089	−	141.619i	−0.239847	−	0.193998i
$731$	−271.840	−	827.171i	−0.371875	−	1.13156i
$732$	−25.8789	+	25.8789i	−0.0353537	+	0.0353537i
$733$	−164.197	+	164.197i	−0.224006	+	0.224006i	−0.810183	−	0.586177i	$-0.800632\pi$
$733$	−164.197	+	164.197i	−0.224006	+	0.224006i	0.586177	+	0.810183i	$0.300632\pi$
$734$	371.103	+	371.103i	0.505590	+	0.505590i
$735$	−390.477	+	41.2661i	−0.531261	+	0.0561444i
$736$	−1.96312	+	1.96312i	−0.00266728	+	0.00266728i
$737$	−695.049			−0.943079
$738$		−	315.309i		−	0.427249i
$739$	−1249.71			−1.69108			−0.845539	−	0.533914i	$-0.820721\pi$
$739$	−1249.71			−1.69108			−0.845539	+	0.533914i	$0.820721\pi$
$740$	−582.933	+	61.6052i	−0.787747	+	0.0832503i
$741$	−601.398	−	601.398i	−0.811603	−	0.811603i
$742$	114.378			0.154148
$743$	−179.193			−0.241175			−0.120588	−	0.992703i	$-0.538478\pi$
$743$	−179.193			−0.241175			−0.120588	+	0.992703i	$0.538478\pi$
$744$			294.077i			0.395265i
$745$	−36.9861	−	349.978i	−0.0496458	−	0.469769i
$746$			359.836i			0.482354i
$747$	130.449	−	130.449i	0.174631	−	0.174631i
$748$	81.4731	+	247.911i	0.108921	+	0.331432i
$749$		−	217.349i		−	0.290186i
$750$	341.939	+	173.490i	0.455919	+	0.231319i
$751$	258.792	−	258.792i	0.344597	−	0.344597i	−0.513495	−	0.858092i	$-0.671650\pi$
$751$	258.792	−	258.792i	0.344597	−	0.344597i	0.858092	+	0.513495i	$0.171650\pi$
$752$	−49.2784	+	49.2784i	−0.0655297	+	0.0655297i
$753$	618.872			0.821875
$754$	1017.31	−	1017.31i	1.34921	−	1.34921i
$755$	−50.7258	−	479.987i	−0.0671864	−	0.635745i
$756$			206.304i			0.272889i
$757$	−99.9123	−	99.9123i	−0.131985	−	0.131985i	0.638028	−	0.770013i	$-0.279750\pi$
$757$	−99.9123	−	99.9123i	−0.131985	−	0.131985i	−0.770013	+	0.638028i	$0.779750\pi$
$758$			13.4760i			0.0177784i
$759$	5.77727	−	5.77727i	0.00761169	−	0.00761169i
$760$	−173.693	+	214.744i	−0.228544	+	0.282558i
$761$	1054.31			1.38543			0.692716	−	0.721210i	$-0.256414\pi$
$761$	1054.31			1.38543			0.692716	+	0.721210i	$0.256414\pi$
$762$			541.943i			0.711211i
$763$	77.9418	−	77.9418i	0.102152	−	0.102152i
$764$			711.553i			0.931352i
$765$	−129.500	+	341.365i	−0.169282	+	0.446229i
$766$	51.6010			0.0673643
$767$	1297.27	+	1297.27i	1.69135	+	1.69135i
$768$	−34.7044			−0.0451880
$769$			1073.28i			1.39568i	0.716254	+	0.697839i	$0.245855\pi$
$769$			1073.28i			1.39568i	−0.716254	+	0.697839i	$0.754145\pi$
$770$	20.4021	+	193.052i	0.0264962	+	0.250717i
$771$	−125.819	−	125.819i	−0.163189	−	0.163189i
$772$	−20.5496			−0.0266186
$773$	680.194	−	680.194i	0.879940	−	0.879940i	−0.113588	−	0.993528i	$-0.536234\pi$
$773$	680.194	−	680.194i	0.879940	−	0.879940i	0.993528	+	0.113588i	$0.0362343\pi$
$774$	311.121			0.401965
$775$	−651.533	+	1005.79i	−0.840688	+	1.29779i
$776$	−85.0753	−	85.0753i	−0.109633	−	0.109633i
$777$			454.789i			0.585314i
$778$	−21.6188	−	21.6188i	−0.0277876	−	0.0277876i
$779$	−716.825	−	716.825i	−0.920186	−	0.920186i
$780$	273.867	−	338.592i	0.351111	−	0.434093i
$781$	826.662			1.05847
$782$	3.68382	+	11.2093i	0.00471076	+	0.0143342i
$783$	1033.22	+	1033.22i	1.31956	+	1.31956i
$784$	144.821			0.184721
$785$	−171.224	+	211.691i	−0.218120	+	0.269671i
$786$	−239.886			−0.305198
$787$		−	998.379i		−	1.26859i	−0.773092	−	0.634294i	$-0.781291\pi$
$787$		−	998.379i		−	1.26859i	0.773092	−	0.634294i	$-0.218709\pi$
$788$			549.954i			0.697911i
$789$	9.47151	−	9.47151i	0.0120044	−	0.0120044i
$790$	128.012	−	13.5285i	0.162041	−	0.0171247i
$791$		−	584.506i		−	0.738946i
$792$	−93.2458			−0.117735
$793$			169.385i			0.213601i
$794$	−671.428	−	671.428i	−0.845627	−	0.845627i
$795$	154.210	−	190.656i	0.193975	−	0.239818i
$796$	206.473	−	206.473i	0.259389	−	0.259389i
$797$	421.516	+	421.516i	0.528878	+	0.528878i	0.920238	−	0.391360i	$-0.127995\pi$
$797$	421.516	+	421.516i	0.528878	+	0.528878i	−0.391360	+	0.920238i	$0.627995\pi$
$798$	151.524	+	151.524i	0.189880	+	0.189880i
$799$	92.4716	+	281.378i	0.115734	+	0.352162i
$800$	−118.694	−	76.8881i	−0.148367	−	0.0961102i
$801$			79.1565i			0.0988221i
$802$		−	127.473i		−	0.158943i
$803$	−172.839	−	172.839i	−0.215242	−	0.215242i
$804$	−277.784	−	277.784i	−0.345503	−	0.345503i
$805$	0.922482	+	8.72889i	0.00114594	+	0.0108433i
$806$	962.413	+	962.413i	1.19406	+	1.19406i
$807$	603.583	+	603.583i	0.747934	+	0.747934i
$808$	−29.2472	+	29.2472i	−0.0361970	+	0.0361970i
$809$	903.879	−	903.879i	1.11728	−	1.11728i	0.125140	−	0.992139i	$-0.460062\pi$
$809$	903.879	−	903.879i	1.11728	−	1.11728i	0.992139	−	0.125140i	$-0.0399380\pi$
$810$	131.354	+	106.244i	0.162165	+	0.131166i
$811$	1.47020	−	1.47020i	0.00181282	−	0.00181282i	−0.706200	−	0.708013i	$-0.749592\pi$
$811$	1.47020	−	1.47020i	0.00181282	−	0.00181282i	0.708013	+	0.706200i	$0.249592\pi$
$812$	−256.314	+	256.314i	−0.315658	+	0.315658i
$813$	1084.52			1.33397
$814$	−636.257			−0.781643
$815$	−61.0789	−	577.953i	−0.0749434	−	0.709144i
$816$	−66.5188	+	131.642i	−0.0815181	+	0.161326i
$817$	707.302	−	707.302i	0.865731	−	0.865731i
$818$	166.890	−	166.890i	0.204022	−	0.204022i
$819$	218.125	+	218.125i	0.266331	+	0.266331i
$820$	326.430	−	403.579i	0.398086	−	0.492169i
$821$	−61.4844	+	61.4844i	−0.0748897	+	0.0748897i	−0.743559	−	0.668670i	$-0.766864\pi$
$821$	−61.4844	+	61.4844i	−0.0748897	+	0.0748897i	0.668670	+	0.743559i	$0.266864\pi$
$822$	444.687			0.540982
$823$			567.160i			0.689137i	0.938761	+	0.344569i	$0.111975\pi$
$823$			567.160i			0.689137i	−0.938761	+	0.344569i	$0.888025\pi$
$824$	245.054			0.297396
$825$	349.305	+	226.275i	0.423400	+	0.274272i
$826$	−326.852	−	326.852i	−0.395704	−	0.395704i
$827$	−703.344			−0.850476			−0.425238	−	0.905081i	$-0.639810\pi$
$827$	−703.344			−0.850476			−0.425238	+	0.905081i	$0.639810\pi$
$828$	−4.21612			−0.00509193
$829$			258.643i			0.311994i	0.987758	+	0.155997i	$0.0498590\pi$
$829$			258.643i			0.311994i	−0.987758	+	0.155997i	$0.950141\pi$
$830$	302.018	−	31.9177i	0.363877	−	0.0384550i
$831$		−	1027.38i		−	1.23632i
$832$	−113.575	+	113.575i	−0.136509	+	0.136509i
$833$	277.583	−	549.342i	0.333232	−	0.659474i
$834$			336.989i			0.404064i
$835$	−102.478	−	969.690i	−0.122728	−	1.16131i
$836$	−211.985	+	211.985i	−0.253571	+	0.253571i
$837$	−977.464	+	977.464i	−1.16782	+	1.16782i
$838$	−526.510			−0.628293
$839$	60.3640	−	60.3640i	0.0719476	−	0.0719476i	−0.670217	−	0.742165i	$-0.733799\pi$
$839$	60.3640	−	60.3640i	0.0719476	−	0.0719476i	0.742165	+	0.670217i	$0.233799\pi$
$840$	−69.0017	+	85.3095i	−0.0821449	+	0.101559i
$841$			1726.35i			2.05273i
$842$	337.778	+	337.778i	0.401162	+	0.401162i
$843$		−	140.077i		−	0.166165i
$844$	−98.2262	+	98.2262i	−0.116382	+	0.116382i
$845$	−123.018	−	1164.04i	−0.145583	−	1.37757i
$846$	−105.834			−0.125099
$847$		−	222.101i		−	0.262221i
$848$	−63.9524	+	63.9524i	−0.0754156	+	0.0754156i
$849$		−	456.291i		−	0.537445i
$850$	−519.158	+	302.861i	−0.610775	+	0.356307i
$851$	−28.7684			−0.0338055
$852$	330.385	+	330.385i	0.387775	+	0.387775i
$853$	121.219			0.142109			0.0710545	−	0.997472i	$-0.477364\pi$
$853$	121.219			0.142109			0.0710545	+	0.997472i	$0.477364\pi$
$854$		−	42.6772i		−	0.0499733i
$855$	−417.117	+	44.0815i	−0.487856	+	0.0515574i
$856$	121.527	+	121.527i	0.141971	+	0.141971i
$857$	−570.157			−0.665294			−0.332647	−	0.943051i	$-0.607942\pi$
$857$	−570.157			−0.665294			−0.332647	+	0.943051i	$0.607942\pi$
$858$	334.242	−	334.242i	0.389559	−	0.389559i
$859$	228.094			0.265534			0.132767	−	0.991147i	$-0.457614\pi$
$859$	228.094			0.265534			0.132767	+	0.991147i	$0.457614\pi$
$860$	398.217	+	322.094i	0.463044	+	0.374528i
$861$	−284.767	−	284.767i	−0.330740	−	0.330740i
$862$			409.169i			0.474674i
$863$	−427.130	−	427.130i	−0.494937	−	0.494937i	0.414921	−	0.909857i	$-0.363809\pi$
$863$	−427.130	−	427.130i	−0.494937	−	0.494937i	−0.909857	+	0.414921i	$0.863809\pi$
$864$	−115.352	−	115.352i	−0.133509	−	0.133509i
$865$	455.840	−	48.1739i	0.526983	−	0.0556923i
$866$	295.809			0.341580
$867$	371.852	+	504.643i	0.428895	+	0.582057i
$868$	−242.483	−	242.483i	−0.279359	−	0.279359i
$869$	139.722			0.160785
$870$	81.6731	+	772.823i	0.0938771	+	0.888303i
$871$	−1818.18			−2.08746
$872$			87.1597i			0.0999537i
$873$		−	182.713i		−	0.209294i
$874$	−9.58493	+	9.58493i	−0.0109667	+	0.0109667i
$875$	−425.000	+	138.896i	−0.485714	+	0.158738i
$876$		−	138.154i		−	0.157710i
$877$	−689.902			−0.786661			−0.393331	−	0.919397i	$-0.628677\pi$
$877$	−689.902			−0.786661			−0.393331	+	0.919397i	$0.628677\pi$
$878$			168.836i			0.192296i
$879$	−336.659	−	336.659i	−0.383002	−	0.383002i
$880$	−119.349	−	96.5346i	−0.135624	−	0.109698i
$881$	707.552	−	707.552i	0.803124	−	0.803124i	−0.180459	−	0.983583i	$-0.557758\pi$
$881$	707.552	−	707.552i	0.803124	−	0.803124i	0.983583	+	0.180459i	$0.0577583\pi$
$882$	155.514	+	155.514i	0.176320	+	0.176320i
$883$	−465.384	−	465.384i	−0.527049	−	0.527049i	0.392642	−	0.919691i	$-0.371561\pi$
$883$	−465.384	−	465.384i	−0.527049	−	0.527049i	−0.919691	+	0.392642i	$0.871561\pi$
$884$	213.126	+	648.512i	0.241093	+	0.733610i
$885$	−985.504	+	104.149i	−1.11356	+	0.117683i
$886$		−	1073.92i		−	1.21210i
$887$		−	264.697i		−	0.298418i	−0.988806	−	0.149209i	$-0.952327\pi$
$887$		−	264.697i		−	0.298418i	0.988806	−	0.149209i	$-0.0476727\pi$
$888$	−254.287	−	254.287i	−0.286360	−	0.286360i
$889$	−446.863	−	446.863i	−0.502658	−	0.502658i
$890$	−81.9483	+	101.316i	−0.0920768	+	0.113838i
$891$	129.666	+	129.666i	0.145529	+	0.145529i
$892$	66.0434	+	66.0434i	0.0740396	+	0.0740396i
$893$	−240.602	+	240.602i	−0.269431	+	0.269431i
$894$	152.667	−	152.667i	0.170769	−	0.170769i
$895$	72.9337	−	7.70773i	0.0814901	−	0.00861199i
$896$	28.6157	−	28.6157i	0.0319372	−	0.0319372i
$897$	15.1128	−	15.1128i	0.0168481	−	0.0168481i
$898$	−148.825			−0.165729
$899$	−2428.82			−2.70169
$900$	−44.8923	−	210.022i	−0.0498804	−	0.233358i
$901$	120.008	+	365.166i	0.133194	+	0.405290i
$902$	398.394	−	398.394i	0.441678	−	0.441678i
$903$	280.984	−	280.984i	0.311167	−	0.311167i
$904$	326.817	+	326.817i	0.361523	+	0.361523i
$905$	−560.083	−	453.018i	−0.618877	−	0.500572i
$906$	209.380	−	209.380i	0.231104	−	0.231104i
$907$	562.701			0.620398			0.310199	−	0.950672i	$-0.399604\pi$
$907$	562.701			0.620398			0.310199	+	0.950672i	$0.399604\pi$
$908$		−	624.253i		−	0.687504i
$909$	−62.8132			−0.0691014
$910$	53.3699	+	505.007i	0.0586482	+	0.554953i
$911$	−464.900	−	464.900i	−0.510318	−	0.510318i	0.404306	−	0.914624i	$-0.367513\pi$
$911$	−464.900	−	464.900i	−0.510318	−	0.510318i	−0.914624	+	0.404306i	$0.867513\pi$
$912$	−169.444			−0.185794
$913$	329.645			0.361057
$914$		−	830.955i		−	0.909141i
$915$	−71.1384	−	57.5395i	−0.0777469	−	0.0628847i
$916$		−	570.567i		−	0.622890i
$917$	197.799	−	197.799i	0.215703	−	0.215703i
$918$	−658.654	+	216.459i	−0.717488	+	0.235794i
$919$			246.854i			0.268611i	0.990940	+	0.134306i	$0.0428804\pi$
$919$			246.854i			0.268611i	−0.990940	+	0.134306i	$0.957120\pi$
$920$	−5.39640	−	4.36482i	−0.00586565	−	0.00474437i
$921$	215.751	−	215.751i	0.234257	−	0.234257i
$922$	−357.617	+	357.617i	−0.387871	+	0.387871i
$923$	2162.47			2.34287
$924$	−84.2135	+	84.2135i	−0.0911401	+	0.0911401i
$925$	−306.320	−	1433.08i	−0.331157	−	1.54927i
$926$			1255.23i			1.35554i
$927$	263.147	+	263.147i	0.283870	+	0.283870i
$928$		−	286.627i		−	0.308866i
$929$	369.839	−	369.839i	0.398104	−	0.398104i	−0.479460	−	0.877564i	$-0.659167\pi$
$929$	369.839	−	369.839i	0.398104	−	0.398104i	0.877564	+	0.479460i	$0.159167\pi$
$930$	−731.122	+	77.2660i	−0.786153	+	0.0830817i
$931$	707.091			0.759496
$932$			413.253i			0.443404i
$933$	−135.600	+	135.600i	−0.145338	+	0.145338i
$934$		−	261.014i		−	0.279458i
$935$	−594.939	+	267.691i	−0.636298	+	0.286301i
$936$	−243.922			−0.260601
$937$	−976.945	−	976.945i	−1.04263	−	1.04263i	−0.999050	−	0.0435808i	$-0.986123\pi$
$937$	−976.945	−	976.945i	−1.04263	−	1.04263i	−0.0435808	−	0.999050i	$-0.513877\pi$
$938$	458.097			0.488377
$939$			603.871i			0.643100i
$940$	−135.461	−	109.566i	−0.144108	−	0.116560i
$941$	224.787	+	224.787i	0.238881	+	0.238881i	0.816387	−	0.577505i	$-0.195974\pi$
$941$	224.787	+	224.787i	0.238881	+	0.238881i	−0.577505	+	0.816387i	$0.695974\pi$
$942$	−167.036			−0.177320
$943$	18.0134	−	18.0134i	0.0191022	−	0.0191022i
$944$	365.507			0.387190
$945$	−512.905	+	54.2045i	−0.542756	+	0.0573593i
$946$	393.101	+	393.101i	0.415540	+	0.415540i
$947$		−	108.091i		−	0.114140i	−0.998370	−	0.0570701i	$-0.981824\pi$
$947$		−	108.091i		−	0.114140i	0.998370	−	0.0570701i	$-0.0181759\pi$
$948$	55.8416	+	55.8416i	0.0589047	+	0.0589047i
$949$	−452.131	−	452.131i	−0.476428	−	0.476428i
$950$	−579.523	−	375.407i	−0.610025	−	0.395165i
$951$	807.992			0.849624
$952$	−53.6978	−	163.395i	−0.0564053	−	0.171633i
$953$	−1171.23	−	1171.23i	−1.22900	−	1.22900i	−0.964344	−	0.264653i	$-0.914743\pi$
$953$	−1171.23	−	1171.23i	−1.22900	−	1.22900i	−0.264653	−	0.964344i	$-0.585257\pi$
$954$	−137.348			−0.143971
$955$	−1769.03	+	186.954i	−1.85239	+	0.195763i
$956$	−919.030			−0.961328
$957$			843.518i			0.881419i
$958$			619.328i			0.646480i
$959$	−366.669	+	366.669i	−0.382346	+	0.382346i
$960$	−9.11825	−	86.2805i	−0.00949817	−	0.0898755i
$961$		−	1336.76i		−	1.39101i
$962$	−1664.39			−1.73013
$963$			261.000i			0.271028i
$964$	428.507	+	428.507i	0.444509	+	0.444509i
$965$	−5.39920	−	51.0894i	−0.00559503	−	0.0529424i
$966$	−3.80772	+	3.80772i	−0.00394174	+	0.00394174i
$967$	−1246.64	−	1246.64i	−1.28918	−	1.28918i	−0.935286	−	0.353892i	$-0.884858\pi$
$967$	−1246.64	−	1246.64i	−1.28918	−	1.28918i	−0.353892	−	0.935286i	$-0.615142\pi$
$968$	124.184	+	124.184i	0.128289	+	0.128289i
$969$	−324.778	+	642.743i	−0.335169	+	0.663306i
$970$	189.158	−	233.863i	0.195008	−	0.241096i
$971$			1862.45i			1.91807i	0.283288	+	0.959035i	$0.408575\pi$
$971$			1862.45i			1.91807i	−0.283288	+	0.959035i	$0.591425\pi$
$972$		−	415.437i		−	0.427404i
$973$	−277.867	−	277.867i	−0.285577	−	0.285577i
$974$	873.511	+	873.511i	0.896828	+	0.896828i
$975$	913.749	+	591.913i	0.937178	+	0.607090i
$976$	23.8622	+	23.8622i	0.0244490	+	0.0244490i
$977$	783.919	+	783.919i	0.802373	+	0.802373i	0.983466	−	0.181093i	$-0.0579635\pi$
$977$	783.919	+	783.919i	0.802373	+	0.802373i	−0.181093	+	0.983466i	$0.557963\pi$
$978$	252.115	−	252.115i	0.257786	−	0.257786i
$979$	−100.014	+	100.014i	−0.102160	+	0.102160i
$980$	38.0504	+	360.048i	0.0388269	+	0.367396i
$981$	−93.5950	+	93.5950i	−0.0954077	+	0.0954077i
$982$	−128.168	+	128.168i	−0.130517	+	0.130517i
$983$	−1382.40			−1.40631			−0.703154	−	0.711037i	$-0.748226\pi$
$983$	−1382.40			−1.40631			−0.703154	+	0.711037i	$0.748226\pi$
$984$	318.445			0.323623
$985$	−1367.27	+	144.495i	−1.38809	+	0.146696i
$986$	−1087.25	−	549.386i	−1.10268	−	0.557186i
$987$	−95.5819	+	95.5819i	−0.0968408	+	0.0968408i
$988$	−554.533	+	554.533i	−0.561268	+	0.561268i
$989$	17.7741	+	17.7741i	0.0179718	+	0.0179718i
$990$	−24.4994	−	231.823i	−0.0247469	−	0.234165i
$991$	556.790	−	556.790i	0.561847	−	0.561847i	−0.367985	−	0.929832i	$-0.619952\pi$
$991$	556.790	−	556.790i	0.561847	−	0.561847i	0.929832	+	0.367985i	$0.119952\pi$
$992$	271.161			0.273348
$993$			1085.63i			1.09328i
$994$	−544.842			−0.548130
$995$	567.574	+	459.076i	0.570426	+	0.461383i
$996$	131.746	+	131.746i	0.132276	+	0.132276i
$997$	589.695			0.591470			0.295735	−	0.955270i	$-0.404435\pi$
$997$	589.695			0.591470			0.295735	+	0.955270i	$0.404435\pi$
$998$	782.000			0.783567
$999$		−	1690.42i		−	1.69211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.3.j.c.123.3	yes	18
5.2	odd	4		170.3.e.c.157.7	yes	18
17.13	even	4		170.3.e.c.13.3	✓	18
85.47	odd	4	inner	170.3.j.c.47.3	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.3.e.c.13.3	✓	18	17.13	even	4
170.3.e.c.157.7	yes	18	5.2	odd	4
170.3.j.c.47.3	yes	18	85.47	odd	4	inner
170.3.j.c.123.3	yes	18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	170.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} -2.16902 q^{3} +2.00000i q^{4} +(-4.97231 + 0.525481i) q^{5} +(-2.16902 - 2.16902i) q^{6} +3.57697 q^{7} +(-2.00000 + 2.00000i) q^{8} -4.29533 q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} -2.16902 q^{3} +2.00000i q^{4} +(-4.97231 + 0.525481i) q^{5} +(-2.16902 - 2.16902i) q^{6} +3.57697 q^{7} +(-2.00000 + 2.00000i) q^{8} -4.29533 q^{9} +(-5.49779 - 4.44683i) q^{10} +(-5.42716 - 5.42716i) q^{11} -4.33805i q^{12} +(-14.1969 - 14.1969i) q^{13} +(3.57697 + 3.57697i) q^{14} +(10.7851 - 1.13978i) q^{15} -4.00000 q^{16} +(-7.66690 + 15.1730i) q^{17} +(-4.29533 - 4.29533i) q^{18} -19.5300 q^{19} +(-1.05096 - 9.94462i) q^{20} -7.75853 q^{21} -10.8543i q^{22} -0.490779i q^{23} +(4.33805 - 4.33805i) q^{24} +(24.4477 - 5.22571i) q^{25} -28.3939i q^{26} +28.8379 q^{27} +7.15393i q^{28} +(35.8284 + 35.8284i) q^{29} +(11.9248 + 9.64528i) q^{30} +(-33.8951 + 33.8951i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(11.7716 + 11.7716i) q^{33} +(-22.8399 + 7.50606i) q^{34} +(-17.7858 + 1.87963i) q^{35} -8.59067i q^{36} -58.6179i q^{37} +(-19.5300 - 19.5300i) q^{38} +(30.7935 + 30.7935i) q^{39} +(8.89366 - 10.9956i) q^{40} +(36.7037 + 36.7037i) q^{41} +(-7.75853 - 7.75853i) q^{42} +(-36.2161 + 36.2161i) q^{43} +(10.8543 - 10.8543i) q^{44} +(21.3577 - 2.25712i) q^{45} +(0.490779 - 0.490779i) q^{46} +(12.3196 - 12.3196i) q^{47} +8.67610 q^{48} -36.2053 q^{49} +(29.6734 + 19.2220i) q^{50} +(16.6297 - 32.9105i) q^{51} +(28.3939 - 28.3939i) q^{52} +(15.9881 - 15.9881i) q^{53} +(28.8379 + 28.8379i) q^{54} +(29.8374 + 24.1336i) q^{55} +(-7.15393 + 7.15393i) q^{56} +42.3611 q^{57} +71.6568i q^{58} -91.3768 q^{59} +(2.27956 + 21.5701i) q^{60} +(-5.96556 - 5.96556i) q^{61} -67.7902 q^{62} -15.3643 q^{63} -8.00000i q^{64} +(78.0517 + 63.1313i) q^{65} +23.5433i q^{66} +(64.0344 - 64.0344i) q^{67} +(-30.3459 - 15.3338i) q^{68} +1.06451i q^{69} +(-19.6654 - 15.9062i) q^{70} +(-76.1597 + 76.1597i) q^{71} +(8.59067 - 8.59067i) q^{72} +31.8471 q^{73} +(58.6179 - 58.6179i) q^{74} +(-53.0277 + 11.3347i) q^{75} -39.0601i q^{76} +(-19.4128 - 19.4128i) q^{77} +61.5870i q^{78} +(-12.8725 + 12.8725i) q^{79} +(19.8892 - 2.10192i) q^{80} -23.8921 q^{81} +73.4075i q^{82} +(-30.3700 + 30.3700i) q^{83} -15.5171i q^{84} +(30.1491 - 79.4735i) q^{85} -72.4323 q^{86} +(-77.7127 - 77.7127i) q^{87} +21.7086 q^{88} -18.4285i q^{89} +(23.6148 + 19.1006i) q^{90} +(-50.7819 - 50.7819i) q^{91} +0.981558 q^{92} +(73.5193 - 73.5193i) q^{93} +24.6392 q^{94} +(97.1094 - 10.2627i) q^{95} +(8.67610 + 8.67610i) q^{96} +42.5377i q^{97} +(-36.2053 - 36.2053i) q^{98} +(23.3114 + 23.3114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 18 q^{2} - 8 q^{3} + 18 q^{5} - 8 q^{6} - 28 q^{7} - 36 q^{8} + 62 q^{9}+O(q^{10}) \) 18 * q + 18 * q^2 - 8 * q^3 + 18 * q^5 - 8 * q^6 - 28 * q^7 - 36 * q^8 + 62 * q^9	\( 18 q + 18 q^{2} - 8 q^{3} + 18 q^{5} - 8 q^{6} - 28 q^{7} - 36 q^{8} + 62 q^{9} + 26 q^{10} - 8 q^{11} - 22 q^{13} - 28 q^{14} + 28 q^{15} - 72 q^{16} - 58 q^{17} + 62 q^{18} + 48 q^{19} + 16 q^{20} - 64 q^{21} + 16 q^{24} - 62 q^{25} + 28 q^{27} + 74 q^{29} + 28 q^{30} - 16 q^{31} - 72 q^{32} + 84 q^{33} - 70 q^{34} - 28 q^{35} + 48 q^{38} - 60 q^{39} - 20 q^{40} + 18 q^{41} - 64 q^{42} - 48 q^{43} + 16 q^{44} + 270 q^{45} - 40 q^{46} - 44 q^{47} + 32 q^{48} + 214 q^{49} - 46 q^{50} + 52 q^{51} + 44 q^{52} + 58 q^{53} + 28 q^{54} + 52 q^{55} + 56 q^{56} - 136 q^{57} - 80 q^{59} - 254 q^{61} - 32 q^{62} - 312 q^{63} + 194 q^{65} + 336 q^{67} - 24 q^{68} - 12 q^{70} - 8 q^{71} - 124 q^{72} - 772 q^{73} + 144 q^{74} - 268 q^{75} - 76 q^{77} - 444 q^{79} - 72 q^{80} + 450 q^{81} + 244 q^{83} + 126 q^{85} - 96 q^{86} + 92 q^{87} + 32 q^{88} + 446 q^{90} + 288 q^{91} - 80 q^{92} - 88 q^{94} + 92 q^{95} + 32 q^{96} + 214 q^{98} + 128 q^{99}+O(q^{100}) \) 18 * q + 18 * q^2 - 8 * q^3 + 18 * q^5 - 8 * q^6 - 28 * q^7 - 36 * q^8 + 62 * q^9 + 26 * q^10 - 8 * q^11 - 22 * q^13 - 28 * q^14 + 28 * q^15 - 72 * q^16 - 58 * q^17 + 62 * q^18 + 48 * q^19 + 16 * q^20 - 64 * q^21 + 16 * q^24 - 62 * q^25 + 28 * q^27 + 74 * q^29 + 28 * q^30 - 16 * q^31 - 72 * q^32 + 84 * q^33 - 70 * q^34 - 28 * q^35 + 48 * q^38 - 60 * q^39 - 20 * q^40 + 18 * q^41 - 64 * q^42 - 48 * q^43 + 16 * q^44 + 270 * q^45 - 40 * q^46 - 44 * q^47 + 32 * q^48 + 214 * q^49 - 46 * q^50 + 52 * q^51 + 44 * q^52 + 58 * q^53 + 28 * q^54 + 52 * q^55 + 56 * q^56 - 136 * q^57 - 80 * q^59 - 254 * q^61 - 32 * q^62 - 312 * q^63 + 194 * q^65 + 336 * q^67 - 24 * q^68 - 12 * q^70 - 8 * q^71 - 124 * q^72 - 772 * q^73 + 144 * q^74 - 268 * q^75 - 76 * q^77 - 444 * q^79 - 72 * q^80 + 450 * q^81 + 244 * q^83 + 126 * q^85 - 96 * q^86 + 92 * q^87 + 32 * q^88 + 446 * q^90 + 288 * q^91 - 80 * q^92 - 88 * q^94 + 92 * q^95 + 32 * q^96 + 214 * q^98 + 128 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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