LMFDB - Embedded newform 425.3.u.b.176.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,3,Mod(126,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("425.126");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.u (of order $16$, degree $8$, 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:	$11.5804112353$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			176.1
Root			$0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	425.176
Dual form			425.3.u.b.326.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23044 - 0.509666i) q^{2} +(2.63099 - 0.523336i) q^{3} +(-1.57420 - 1.57420i) q^{4} +(-3.50400 - 0.696990i) q^{6} +(-4.92562 - 7.37170i) q^{7} +(3.17331 + 7.66104i) q^{8} +(-1.66671 + 0.690373i) q^{9} +O(q^{10})$	\(q+(-1.23044 - 0.509666i) q^{2} +(2.63099 - 0.523336i) q^{3} +(-1.57420 - 1.57420i) q^{4} +(-3.50400 - 0.696990i) q^{6} +(-4.92562 - 7.37170i) q^{7} +(3.17331 + 7.66104i) q^{8} +(-1.66671 + 0.690373i) q^{9} +(-1.61572 + 8.12279i) q^{11} +(-4.96553 - 3.31786i) q^{12} +(-16.1480 + 16.1480i) q^{13} +(2.30358 + 11.5809i) q^{14} -2.13880i q^{16} +(15.7060 + 6.50562i) q^{17} +2.40265 q^{18} +(-1.20778 - 0.500280i) q^{19} +(-16.8171 - 16.8171i) q^{21} +(6.12797 - 9.17115i) q^{22} +(26.2400 + 5.21946i) q^{23} +(12.3582 + 18.4954i) q^{24} +(28.0993 - 11.6391i) q^{26} +(-24.0978 + 16.1016i) q^{27} +(-3.85063 + 19.3584i) q^{28} +(13.7583 + 9.19303i) q^{29} +(2.68003 + 13.4734i) q^{31} +(11.6032 - 28.0125i) q^{32} +22.2165i q^{33} +(-16.0096 - 16.0096i) q^{34} +(3.71051 + 1.53694i) q^{36} +(-18.9648 + 3.77234i) q^{37} +(1.23113 + 1.23113i) q^{38} +(-34.0344 + 50.9361i) q^{39} +(-14.6853 - 21.9781i) q^{41} +(12.1214 + 29.2636i) q^{42} +(21.8944 - 9.06895i) q^{43} +(15.3303 - 10.2434i) q^{44} +(-29.6266 - 19.7959i) q^{46} +(-26.8680 + 26.8680i) q^{47} +(-1.11931 - 5.62714i) q^{48} +(-11.3288 + 27.3503i) q^{49} +(44.7268 + 8.89671i) q^{51} +50.8404 q^{52} +(-26.1557 - 10.8340i) q^{53} +(37.8574 - 7.53030i) q^{54} +(40.8445 - 61.1281i) q^{56} +(-3.43947 - 0.684154i) q^{57} +(-12.2435 - 18.3236i) q^{58} +(9.12070 + 22.0193i) q^{59} +(-42.9373 + 28.6898i) q^{61} +(3.56932 - 17.9442i) q^{62} +(13.2988 + 8.88596i) q^{63} +(-34.6035 + 34.6035i) q^{64} +(11.3230 - 27.3362i) q^{66} +70.4415i q^{67} +(-14.4831 - 34.9654i) q^{68} +71.7687 q^{69} +(-102.865 + 20.4612i) q^{71} +(-10.5780 - 10.5780i) q^{72} +(-19.7693 + 29.5868i) q^{73} +(25.2578 + 5.02408i) q^{74} +(1.11375 + 2.68883i) q^{76} +(67.8373 - 28.0991i) q^{77} +(67.8377 - 45.3277i) q^{78} +(-1.41599 + 7.11865i) q^{79} +(-43.4936 + 43.4936i) q^{81} +(6.86792 + 34.5274i) q^{82} +(-51.5218 + 124.385i) q^{83} +52.9469i q^{84} -31.5619 q^{86} +(41.0090 + 16.9865i) q^{87} +(-67.3563 + 13.3980i) q^{88} +(38.6522 + 38.6522i) q^{89} +(198.577 + 39.4995i) q^{91} +(-33.0905 - 49.5234i) q^{92} +(14.1023 + 34.0458i) q^{93} +(46.7533 - 19.3658i) q^{94} +(15.8678 - 79.7729i) q^{96} +(-65.9209 - 44.0470i) q^{97} +(27.8790 - 27.8790i) q^{98} +(-2.91482 - 14.6538i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} - 8 q^{6} - 8 q^{7} + 24 q^{8} - 16 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 - 8 * q^6 - 8 * q^7 + 24 * q^8 - 16 * q^9	$ 8 q + 8 q^{2} + 8 q^{3} - 8 q^{6} - 8 q^{7} + 24 q^{8} - 16 q^{9} - 8 q^{11} - 48 q^{12} - 16 q^{13} + 8 q^{14} - 56 q^{18} - 64 q^{21} + 104 q^{22} + 56 q^{23} - 80 q^{24} + 176 q^{26} - 40 q^{27} - 152 q^{28} + 48 q^{29} + 24 q^{31} - 88 q^{32} - 136 q^{34} - 128 q^{36} - 32 q^{37} + 120 q^{38} + 48 q^{39} + 48 q^{41} - 16 q^{42} + 232 q^{43} + 120 q^{44} - 88 q^{46} - 192 q^{47} - 136 q^{48} + 16 q^{49} + 136 q^{51} + 384 q^{52} + 32 q^{53} + 8 q^{54} - 120 q^{56} - 24 q^{57} - 240 q^{58} - 48 q^{59} - 160 q^{61} + 168 q^{62} - 56 q^{63} - 64 q^{64} - 8 q^{66} - 272 q^{68} + 240 q^{69} + 40 q^{71} - 40 q^{72} - 48 q^{73} - 160 q^{74} + 80 q^{76} + 48 q^{77} + 400 q^{78} - 136 q^{79} - 424 q^{81} + 64 q^{82} + 264 q^{83} + 832 q^{86} - 208 q^{87} - 264 q^{88} + 160 q^{89} + 320 q^{91} - 24 q^{92} + 64 q^{93} + 32 q^{94} - 56 q^{96} - 48 q^{97} + 120 q^{98} - 224 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^3 - 8 * q^6 - 8 * q^7 + 24 * q^8 - 16 * q^9 - 8 * q^11 - 48 * q^12 - 16 * q^13 + 8 * q^14 - 56 * q^18 - 64 * q^21 + 104 * q^22 + 56 * q^23 - 80 * q^24 + 176 * q^26 - 40 * q^27 - 152 * q^28 + 48 * q^29 + 24 * q^31 - 88 * q^32 - 136 * q^34 - 128 * q^36 - 32 * q^37 + 120 * q^38 + 48 * q^39 + 48 * q^41 - 16 * q^42 + 232 * q^43 + 120 * q^44 - 88 * q^46 - 192 * q^47 - 136 * q^48 + 16 * q^49 + 136 * q^51 + 384 * q^52 + 32 * q^53 + 8 * q^54 - 120 * q^56 - 24 * q^57 - 240 * q^58 - 48 * q^59 - 160 * q^61 + 168 * q^62 - 56 * q^63 - 64 * q^64 - 8 * q^66 - 272 * q^68 + 240 * q^69 + 40 * q^71 - 40 * q^72 - 48 * q^73 - 160 * q^74 + 80 * q^76 + 48 * q^77 + 400 * q^78 - 136 * q^79 - 424 * q^81 + 64 * q^82 + 264 * q^83 + 832 * q^86 - 208 * q^87 - 264 * q^88 + 160 * q^89 + 320 * q^91 - 24 * q^92 + 64 * q^93 + 32 * q^94 - 56 * q^96 - 48 * q^97 + 120 * q^98 - 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{15}{16}\right)$

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 $

$2$	−1.23044	−	0.509666i	−0.615221	−	0.254833i	0.0532379	−	0.998582i	$-0.483046\pi$
$2$	−1.23044	−	0.509666i	−0.615221	−	0.254833i	−0.668459	+	0.743749i	$0.733046\pi$
$3$	2.63099	−	0.523336i	0.876995	−	0.174445i	0.263991	−	0.964525i	$-0.414961\pi$
$3$	2.63099	−	0.523336i	0.876995	−	0.174445i	0.613004	+	0.790080i	$0.289961\pi$
$4$	−1.57420	−	1.57420i	−0.393549	−	0.393549i
$5$		0			0
$5$		0			0
$6$	−3.50400	−	0.696990i	−0.584001	−	0.116165i
$7$	−4.92562	−	7.37170i	−0.703659	−	1.05310i	−0.995325	−	0.0965803i	$-0.969210\pi$
$7$	−4.92562	−	7.37170i	−0.703659	−	1.05310i	0.291666	−	0.956520i	$-0.405790\pi$
$8$	3.17331	+	7.66104i	0.396664	+	0.957631i
$9$	−1.66671	+	0.690373i	−0.185190	+	0.0767081i
$10$		0			0
$11$	−1.61572	+	8.12279i	−0.146884	+	0.738436i	0.835193	+	0.549957i	$0.185356\pi$
$11$	−1.61572	+	8.12279i	−0.146884	+	0.738436i	−0.982077	+	0.188479i	$0.939644\pi$
$12$	−4.96553	−	3.31786i	−0.413794	−	0.276488i
$13$	−16.1480	+	16.1480i	−1.24216	+	1.24216i	−0.283051	+	0.959105i	$0.591346\pi$
$13$	−16.1480	+	16.1480i	−1.24216	+	1.24216i	−0.959105	+	0.283051i	$0.908654\pi$
$14$	2.30358	+	11.5809i	0.164541	+	0.827205i
$15$		0			0
$16$		−	2.13880i		−	0.133675i
$17$	15.7060	+	6.50562i	0.923880	+	0.382683i
$17$	15.7060	+	6.50562i	0.923880	+	0.382683i
$18$	2.40265			0.133480
$19$	−1.20778	−	0.500280i	−0.0635675	−	0.0263305i	0.350673	−	0.936498i	$-0.385953\pi$
$19$	−1.20778	−	0.500280i	−0.0635675	−	0.0263305i	−0.414241	+	0.910167i	$0.635953\pi$
$20$		0			0
$21$	−16.8171	−	16.8171i	−0.800814	−	0.800814i
$22$	6.12797	−	9.17115i	0.278544	−	0.416870i
$23$	26.2400	+	5.21946i	1.14087	+	0.226933i	0.729135	−	0.684370i	$-0.239923\pi$
$23$	26.2400	+	5.21946i	1.14087	+	0.226933i	0.411735	+	0.911303i	$0.364923\pi$
$24$	12.3582	+	18.4954i	0.514926	+	0.770642i
$25$		0			0
$26$	28.0993	−	11.6391i	1.08074	−	0.447658i
$27$	−24.0978	+	16.1016i	−0.892510	+	0.596356i
$28$	−3.85063	+	19.3584i	−0.137522	+	0.691372i
$29$	13.7583	+	9.19303i	0.474425	+	0.317001i	0.769694	−	0.638414i	$-0.220409\pi$
$29$	13.7583	+	9.19303i	0.474425	+	0.317001i	−0.295268	+	0.955414i	$0.595409\pi$
$30$		0			0
$31$	2.68003	+	13.4734i	0.0864526	+	0.434627i	0.999633	+	0.0270721i	$0.00861839\pi$
$31$	2.68003	+	13.4734i	0.0864526	+	0.434627i	−0.913181	+	0.407555i	$0.866382\pi$
$32$	11.6032	−	28.0125i	0.362599	−	0.875391i
$33$			22.2165i			0.673228i
$34$	−16.0096	−	16.0096i	−0.470870	−	0.470870i
$35$		0			0
$36$	3.71051	+	1.53694i	0.103070	+	0.0426929i
$37$	−18.9648	+	3.77234i	−0.512563	+	0.101955i	−0.444594	−	0.895732i	$-0.646652\pi$
$37$	−18.9648	+	3.77234i	−0.512563	+	0.101955i	−0.0679693	+	0.997687i	$0.521652\pi$
$38$	1.23113	+	1.23113i	0.0323982	+	0.0323982i
$39$	−34.0344	+	50.9361i	−0.872677	+	1.30605i
$40$		0			0
$41$	−14.6853	−	21.9781i	−0.358178	−	0.536051i	0.607997	−	0.793939i	$-0.291973\pi$
$41$	−14.6853	−	21.9781i	−0.358178	−	0.536051i	−0.966175	+	0.257888i	$0.916973\pi$
$42$	12.1214	+	29.2636i	0.288604	+	0.696752i
$43$	21.8944	−	9.06895i	0.509172	−	0.210906i	−0.113281	−	0.993563i	$-0.536136\pi$
$43$	21.8944	−	9.06895i	0.509172	−	0.210906i	0.622453	+	0.782657i	$0.286136\pi$
$44$	15.3303	−	10.2434i	0.348417	−	0.232805i
$45$		0			0
$46$	−29.6266	−	19.7959i	−0.644058	−	0.430345i
$47$	−26.8680	+	26.8680i	−0.571660	+	0.571660i	−0.932592	−	0.360932i	$-0.882459\pi$
$47$	−26.8680	+	26.8680i	−0.571660	+	0.571660i	0.360932	+	0.932592i	$0.382459\pi$
$48$	−1.11931	−	5.62714i	−0.0233189	−	0.117232i
$49$	−11.3288	+	27.3503i	−0.231201	+	0.558169i
$50$		0			0
$51$	44.7268	+	8.89671i	0.876995	+	0.174445i
$52$	50.8404			0.977699
$53$	−26.1557	−	10.8340i	−0.493503	−	0.204416i	0.122031	−	0.992526i	$-0.461059\pi$
$53$	−26.1557	−	10.8340i	−0.493503	−	0.204416i	−0.615533	+	0.788111i	$0.711059\pi$
$54$	37.8574	−	7.53030i	0.701062	−	0.139450i
$55$		0			0
$56$	40.8445	−	61.1281i	0.729365	−	1.09157i
$57$	−3.43947	−	0.684154i	−0.0603416	−	0.0120027i
$58$	−12.2435	−	18.3236i	−0.211094	−	0.315925i
$59$	9.12070	+	22.0193i	0.154588	+	0.373209i	0.982132	−	0.188192i	$-0.0602627\pi$
$59$	9.12070	+	22.0193i	0.154588	+	0.373209i	−0.827544	+	0.561401i	$0.810263\pi$
$60$		0			0
$61$	−42.9373	+	28.6898i	−0.703890	+	0.470324i	−0.855291	−	0.518148i	$-0.826622\pi$
$61$	−42.9373	+	28.6898i	−0.703890	+	0.470324i	0.151401	+	0.988472i	$0.451622\pi$
$62$	3.56932	−	17.9442i	0.0575697	−	0.289423i
$63$	13.2988	+	8.88596i	0.211092	+	0.141047i
$64$	−34.6035	+	34.6035i	−0.540679	+	0.540679i
$65$		0			0
$66$	11.3230	−	27.3362i	0.171561	−	0.414184i
$67$			70.4415i			1.05137i	0.850681	+	0.525683i	$0.176190\pi$
$67$			70.4415i			1.05137i	−0.850681	+	0.525683i	$0.823810\pi$
$68$	−14.4831	−	34.9654i	−0.212987	−	0.514197i
$69$	71.7687			1.04013
$70$		0			0
$71$	−102.865	+	20.4612i	−1.44881	+	0.288185i	−0.855923	−	0.517104i	$-0.827010\pi$
$71$	−102.865	+	20.4612i	−1.44881	+	0.288185i	−0.592883	+	0.805289i	$0.702010\pi$
$72$	−10.5780	−	10.5780i	−0.146916	−	0.146916i
$73$	−19.7693	+	29.5868i	−0.270812	+	0.405299i	−0.941802	−	0.336167i	$-0.890869\pi$
$73$	−19.7693	+	29.5868i	−0.270812	+	0.405299i	0.670990	+	0.741466i	$0.265869\pi$
$74$	25.2578	+	5.02408i	0.341321	+	0.0678930i
$75$		0			0
$76$	1.11375	+	2.68883i	0.0146546	+	0.0353793i
$77$	67.8373	−	28.0991i	0.881003	−	0.364924i
$78$	67.8377	−	45.3277i	0.869715	−	0.581125i
$79$	−1.41599	+	7.11865i	−0.0179239	+	0.0901095i	−0.988712	−	0.149830i	$-0.952127\pi$
$79$	−1.41599	+	7.11865i	−0.0179239	+	0.0901095i	0.970788	+	0.239939i	$0.0771275\pi$
$80$		0			0
$81$	−43.4936	+	43.4936i	−0.536958	+	0.536958i
$82$	6.86792	+	34.5274i	0.0837551	+	0.421066i
$83$	−51.5218	+	124.385i	−0.620745	+	1.49861i	0.230085	+	0.973170i	$0.426099\pi$
$83$	−51.5218	+	124.385i	−0.620745	+	1.49861i	−0.850830	+	0.525441i	$0.823901\pi$
$84$			52.9469i			0.630320i
$85$		0			0
$86$	−31.5619			−0.366999
$87$	41.0090	+	16.9865i	0.471368	+	0.195247i
$88$	−67.3563	+	13.3980i	−0.765412	+	0.152250i
$89$	38.6522	+	38.6522i	0.434294	+	0.434294i	0.890086	−	0.455792i	$-0.150644\pi$
$89$	38.6522	+	38.6522i	0.434294	+	0.434294i	−0.455792	+	0.890086i	$0.650644\pi$
$90$		0			0
$91$	198.577	+	39.4995i	2.18217	+	0.434060i
$92$	−33.0905	−	49.5234i	−0.359679	−	0.538298i
$93$	14.1023	+	34.0458i	0.151637	+	0.366084i
$94$	46.7533	−	19.3658i	0.497375	−	0.206020i
$95$		0			0
$96$	15.8678	−	79.7729i	0.165290	−	0.830968i
$97$	−65.9209	−	44.0470i	−0.679597	−	0.454092i	0.167260	−	0.985913i	$-0.446508\pi$
$97$	−65.9209	−	44.0470i	−0.679597	−	0.454092i	−0.846857	+	0.531820i	$0.821508\pi$
$98$	27.8790	−	27.8790i	0.284480	−	0.284480i
$99$	−2.91482	−	14.6538i	−0.0294426	−	0.148018i
$100$		0			0
$101$			140.647i			1.39254i	0.717779	+	0.696271i	$0.245159\pi$
$101$			140.647i			1.39254i	−0.717779	+	0.696271i	$0.754841\pi$
$102$	−50.4994	−	33.7426i	−0.495092	−	0.330810i
$103$	42.3283			0.410954			0.205477	−	0.978662i	$-0.434125\pi$
$103$	42.3283			0.410954			0.205477	+	0.978662i	$0.434125\pi$
$104$	−174.953	−	72.4681i	−1.68224	−	0.696808i
$105$		0			0
$106$	26.6613	+	26.6613i	0.251522	+	0.251522i
$107$	−40.9741	+	61.3221i	−0.382936	+	0.573104i	−0.972000	−	0.234983i	$-0.924497\pi$
$107$	−40.9741	+	61.3221i	−0.382936	+	0.573104i	0.589064	+	0.808086i	$0.299497\pi$
$108$	63.2818	+	12.5875i	0.585942	+	0.116551i
$109$	−116.798	−	174.800i	−1.07154	−	1.60367i	−0.755770	−	0.654837i	$-0.772737\pi$
$109$	−116.798	−	174.800i	−1.07154	−	1.60367i	−0.315770	−	0.948836i	$-0.602263\pi$
$110$		0			0
$111$	−47.9220	+	19.8500i	−0.431730	+	0.178828i
$112$	−15.7666	+	10.5349i	−0.140773	+	0.0940615i
$113$	28.0222	−	140.877i	0.247984	−	1.24670i	−0.633224	−	0.773969i	$-0.718269\pi$
$113$	28.0222	−	140.877i	0.247984	−	1.24670i	0.881208	−	0.472729i	$-0.156731\pi$
$114$	3.88338	+	2.59479i	0.0340648	+	0.0227613i
$115$		0			0
$116$	−7.18670	−	36.1300i	−0.0619543	−	0.311465i
$117$	15.7659	−	38.0622i	0.134751	−	0.325318i
$118$		−	31.7420i		−	0.269000i
$119$	−29.4040	−	147.824i	−0.247092	−	1.24222i
$120$		0			0
$121$	48.4202	+	20.0563i	0.400167	+	0.165755i
$122$	67.4541	−	13.4175i	0.552902	−	0.109979i
$123$	−50.1387	−	50.1387i	−0.407632	−	0.407632i
$124$	16.9909	−	25.4287i	0.137024	−	0.205070i
$125$		0			0
$126$	−11.8345	−	17.7116i	−0.0939247	−	0.140568i
$127$	−41.4251	−	100.009i	−0.326182	−	0.787472i	−0.998869	−	0.0475454i	$-0.984860\pi$
$127$	−41.4251	−	100.009i	−0.326182	−	0.787472i	0.672687	−	0.739927i	$-0.265140\pi$
$128$	−51.8363	+	21.4713i	−0.404971	+	0.167744i
$129$	52.8577	−	35.3184i	0.409750	−	0.273786i
$130$		0			0
$131$	−77.0656	−	51.4936i	−0.588287	−	0.393081i	0.225501	−	0.974243i	$-0.427598\pi$
$131$	−77.0656	−	51.4936i	−0.588287	−	0.393081i	−0.813788	+	0.581162i	$0.802598\pi$
$132$	34.9732	−	34.9732i	0.264948	−	0.264948i
$133$	2.26116	+	11.3676i	0.0170012	+	0.0854707i
$134$	35.9016	−	86.6742i	0.267923	−	0.646822i
$135$		0			0
$136$			140.968i			1.03653i
$137$	−102.046			−0.744863			−0.372431	−	0.928060i	$-0.621476\pi$
$137$	−102.046			−0.744863			−0.372431	+	0.928060i	$0.621476\pi$
$138$	−88.3072	−	36.5780i	−0.639907	−	0.265058i
$139$	30.2420	−	6.01550i	0.217568	−	0.0432770i	−0.0851025	−	0.996372i	$-0.527122\pi$
$139$	30.2420	−	6.01550i	0.217568	−	0.0432770i	0.302671	+	0.953095i	$0.402122\pi$
$140$		0			0
$141$	−56.6284	+	84.7504i	−0.401620	+	0.601067i
$142$	136.998	+	27.2506i	0.964775	+	0.191906i
$143$	−105.076	−	157.258i	−0.734799	−	1.09970i
$144$	1.47657	+	3.56475i	0.0102539	+	0.0247552i
$145$		0			0
$146$	39.4044	−	26.3292i	0.269893	−	0.180337i
$147$	−15.4927	+	77.8870i	−0.105392	+	0.529843i
$148$	35.7928	+	23.9160i	0.241843	+	0.161595i
$149$	23.3099	−	23.3099i	0.156443	−	0.156443i	−0.624546	−	0.780988i	$-0.714716\pi$
$149$	23.3099	−	23.3099i	0.156443	−	0.156443i	0.780988	+	0.624546i	$0.214716\pi$
$150$		0			0
$151$	−53.9466	+	130.239i	−0.357262	+	0.862507i	0.638421	+	0.769688i	$0.279588\pi$
$151$	−53.9466	+	130.239i	−0.357262	+	0.862507i	−0.995683	+	0.0928198i	$0.970412\pi$
$152$		−	10.8404i		−	0.0713185i
$153$	−30.6685			−0.200448
$154$	−97.7910			−0.635006
$155$		0			0
$156$	133.760	−	26.6066i	0.857438	−	0.170555i
$157$	78.3942	+	78.3942i	0.499326	+	0.499326i	0.911228	−	0.411902i	$-0.135135\pi$
$157$	78.3942	+	78.3942i	0.499326	+	0.499326i	−0.411902	+	0.911228i	$0.635135\pi$
$158$	5.37042	−	8.03741i	0.0339900	−	0.0508697i
$159$	−74.4850	−	14.8160i	−0.468459	−	0.0931823i
$160$		0			0
$161$	−90.7719	−	219.143i	−0.563800	−	1.36113i
$162$	75.6835	−	31.3491i	0.467182	−	0.193513i
$163$	135.804	−	90.7416i	0.833156	−	0.556697i	−0.0642345	−	0.997935i	$-0.520461\pi$
$163$	135.804	−	90.7416i	0.833156	−	0.556697i	0.897390	+	0.441238i	$0.145461\pi$
$164$	−11.4803	+	57.7154i	−0.0700019	+	0.351923i
$165$		0			0
$166$	126.789	−	126.789i	0.763791	−	0.763791i
$167$	−32.5256	−	163.517i	−0.194764	−	0.979145i	−0.947240	−	0.320525i	$-0.896141\pi$
$167$	−32.5256	−	163.517i	−0.194764	−	0.979145i	0.752476	−	0.658620i	$-0.228859\pi$
$168$	75.4707	−	182.202i	0.449230	−	1.08454i
$169$		−	352.517i		−	2.08590i
$170$		0			0
$171$	2.35840			0.0137918
$172$	−48.7424	−	20.1898i	−0.283386	−	0.117382i
$173$	−16.3948	+	3.26113i	−0.0947676	+	0.0188504i	−0.242246	−	0.970215i	$-0.577884\pi$
$173$	−16.3948	+	3.26113i	−0.0947676	+	0.0188504i	0.147479	+	0.989065i	$0.452884\pi$
$174$	−41.8018	−	41.8018i	−0.240240	−	0.240240i
$175$		0			0
$176$	17.3730	+	3.45570i	0.0987102	+	0.0196347i
$177$	35.5199	+	53.1594i	0.200678	+	0.300335i
$178$	−27.8596	−	67.2590i	−0.156514	−	0.377859i
$179$	−35.7824	+	14.8215i	−0.199901	+	0.0828019i	−0.480388	−	0.877056i	$-0.659504\pi$
$179$	−35.7824	+	14.8215i	−0.199901	+	0.0828019i	0.280487	+	0.959858i	$0.409504\pi$
$180$		0			0
$181$	8.42674	−	42.3641i	0.0465566	−	0.234056i	−0.950500	−	0.310724i	$-0.899428\pi$
$181$	8.42674	−	42.3641i	0.0465566	−	0.234056i	0.997057	+	0.0766687i	$0.0244284\pi$
$182$	−224.207	−	149.810i	−1.23190	−	0.823132i
$183$	−97.9531	+	97.9531i	−0.535263	+	0.535263i
$184$	43.2811	+	217.589i	0.235223	+	1.18255i
$185$		0			0
$186$		−	49.0789i		−	0.263865i
$187$	−78.2203	+	117.065i	−0.418290	+	0.626015i
$188$	84.5912			0.449953
$189$	237.393	+	98.3313i	1.25605	+	0.520271i
$190$		0			0
$191$	−107.196	−	107.196i	−0.561234	−	0.561234i	0.368424	−	0.929658i	$-0.379898\pi$
$191$	−107.196	−	107.196i	−0.561234	−	0.561234i	−0.929658	+	0.368424i	$0.879898\pi$
$192$	−72.9320	+	109.151i	−0.379854	+	0.568492i
$193$	201.713	+	40.1233i	1.04515	+	0.207893i	0.687666	−	0.726028i	$-0.258636\pi$
$193$	201.713	+	40.1233i	1.04515	+	0.207893i	0.357482	+	0.933920i	$0.383636\pi$
$194$	58.6627	+	87.7949i	0.302385	+	0.452551i
$195$		0			0
$196$	60.8886	−	25.2209i	0.310656	−	0.128678i
$197$	−116.416	+	77.7868i	−0.590945	+	0.394857i	−0.814780	−	0.579770i	$-0.803142\pi$
$197$	−116.416	+	77.7868i	−0.590945	+	0.394857i	0.223835	+	0.974627i	$0.428142\pi$
$198$	−3.88201	+	19.5162i	−0.0196061	+	0.0985667i
$199$	−123.283	−	82.3749i	−0.619511	−	0.413944i	0.205823	−	0.978589i	$-0.434013\pi$
$199$	−123.283	−	82.3749i	−0.619511	−	0.413944i	−0.825334	+	0.564645i	$0.809013\pi$
$200$		0			0
$201$	36.8645	+	185.331i	0.183406	+	0.922043i
$202$	71.6828	−	173.058i	0.354865	−	0.856721i
$203$		−	146.704i		−	0.722678i
$204$	−56.4036	−	84.4140i	−0.276488	−	0.413794i
$205$		0			0
$206$	−52.0825	−	21.5733i	−0.252828	−	0.104725i
$207$	−47.3378	+	9.41607i	−0.228685	+	0.0454883i
$208$	34.5373	+	34.5373i	0.166045	+	0.166045i
$209$	6.01511	−	9.00225i	0.0287804	−	0.0430730i
$210$		0			0
$211$	113.713	+	170.184i	0.538925	+	0.806559i	0.996585	−	0.0825683i	$-0.0263123\pi$
$211$	113.713	+	170.184i	0.538925	+	0.806559i	−0.457660	+	0.889127i	$0.651312\pi$
$212$	24.1193	+	58.2291i	0.113770	+	0.274665i
$213$	−259.929	+	107.666i	−1.22032	+	0.505474i
$214$	81.6701	−	54.5702i	0.381636	−	0.255001i
$215$		0			0
$216$	−199.825	−	133.519i	−0.925115	−	0.618142i
$217$	86.1213	−	86.1213i	0.396872	−	0.396872i
$218$	54.6233	+	274.610i	0.250565	+	1.25968i
$219$	−36.5289	+	88.1885i	−0.166799	+	0.402687i
$220$		0			0
$221$	−358.673	+	148.567i	−1.62295	+	0.672250i
$222$	69.0821			0.311181
$223$	107.408	+	44.4897i	0.481649	+	0.199506i	0.610278	−	0.792187i	$-0.291058\pi$
$223$	107.408	+	44.4897i	0.481649	+	0.199506i	−0.128629	+	0.991693i	$0.541058\pi$
$224$	−263.653	+	52.4438i	−1.17702	+	0.234124i
$225$		0			0
$226$	−106.280	+	159.059i	−0.470265	+	0.703801i
$227$	150.469	+	29.9302i	0.662859	+	0.131851i	0.515044	−	0.857164i	$-0.327776\pi$
$227$	150.469	+	29.9302i	0.662859	+	0.131851i	0.147816	+	0.989015i	$0.452776\pi$
$228$	4.33742	+	6.49140i	0.0190238	+	0.0284711i
$229$	3.69064	+	8.91000i	0.0161164	+	0.0389083i	0.931733	−	0.363144i	$-0.118297\pi$
$229$	3.69064	+	8.91000i	0.0161164	+	0.0389083i	−0.915617	+	0.402053i	$0.868297\pi$
$230$		0			0
$231$	163.774	−	109.430i	0.708977	−	0.473723i
$232$	−26.7687	+	134.576i	−0.115382	+	0.580067i
$233$	−324.315	−	216.700i	−1.39191	−	0.930044i	−0.999949	−	0.0100614i	$-0.996797\pi$
$233$	−324.315	−	216.700i	−1.39191	−	0.930044i	−0.391960	−	0.919982i	$-0.628203\pi$
$234$	−38.7980	+	38.7980i	−0.165803	+	0.165803i
$235$		0			0
$236$	20.3050	−	49.0206i	0.0860381	−	0.207714i
$237$			19.4701i			0.0821523i
$238$	−39.1609	+	196.875i	−0.164541	+	0.827205i
$239$	372.281			1.55766			0.778831	−	0.627233i	$-0.215813\pi$
$239$	372.281			1.55766			0.778831	+	0.627233i	$0.215813\pi$
$240$		0			0
$241$	136.315	−	27.1147i	0.565621	−	0.112509i	0.0960065	−	0.995381i	$-0.469393\pi$
$241$	136.315	−	27.1147i	0.565621	−	0.112509i	0.469614	+	0.882872i	$0.344393\pi$
$242$	−49.3563	−	49.3563i	−0.203952	−	0.203952i
$243$	53.2453	−	79.6872i	0.219116	−	0.327931i
$244$	112.755	+	22.4284i	0.462111	+	0.0919197i
$245$		0			0
$246$	36.1388	+	87.2468i	0.146906	+	0.354662i
$247$	27.5818	−	11.4248i	0.111667	−	0.0462541i
$248$	−94.7160	+	63.2872i	−0.381919	+	0.255190i
$249$	−70.4583	+	354.218i	−0.282965	+	1.42256i
$250$		0			0
$251$	154.052	−	154.052i	0.613754	−	0.613754i	−0.330168	−	0.943922i	$-0.607106\pi$
$251$	154.052	−	154.052i	0.613754	−	0.613754i	0.943922	+	0.330168i	$0.107106\pi$
$252$	−6.94665	−	34.9232i	−0.0275661	−	0.138584i
$253$	−84.7932	+	204.709i	−0.335151	+	0.809126i
$254$			144.168i			0.567591i
$255$		0			0
$256$	270.472			1.05653
$257$	391.977	+	162.362i	1.52520	+	0.631760i	0.978626	−	0.205648i	$-0.0659301\pi$
$257$	391.977	+	162.362i	1.52520	+	0.631760i	0.546578	+	0.837408i	$0.315930\pi$
$258$	−83.0389	+	16.5175i	−0.321856	+	0.0640212i
$259$	121.222	+	121.222i	0.468039	+	0.468039i
$260$		0			0
$261$	−29.2777	−	5.82370i	−0.112175	−	0.0223130i
$262$	68.5803	+	102.638i	0.261757	+	0.391747i
$263$	54.7003	+	132.058i	0.207986	+	0.502122i	0.993106	−	0.117221i	$-0.0373987\pi$
$263$	54.7003	+	132.058i	0.207986	+	0.502122i	−0.785120	+	0.619344i	$0.787399\pi$
$264$	−170.202	+	70.4999i	−0.644704	+	0.267045i
$265$		0			0
$266$	3.01146	−	15.1396i	0.0113213	−	0.0569158i
$267$	121.921	+	81.4652i	0.456634	+	0.305113i
$268$	110.889	−	110.889i	0.413764	−	0.413764i
$269$	8.93614	+	44.9250i	0.0332199	+	0.167008i	0.993834	−	0.110878i	$-0.0353663\pi$
$269$	8.93614	+	44.9250i	0.0332199	+	0.167008i	−0.960614	+	0.277886i	$0.910366\pi$
$270$		0			0
$271$			329.809i			1.21701i	0.793550	+	0.608504i	$0.208230\pi$
$271$			329.809i			1.21701i	−0.793550	+	0.608504i	$0.791770\pi$
$272$	13.9142	−	33.5918i	0.0511551	−	0.123499i
$273$	543.126			1.98947
$274$	125.562	+	52.0095i	0.458255	+	0.189816i
$275$		0			0
$276$	−112.978	−	112.978i	−0.409341	−	0.409341i
$277$	−156.783	+	234.642i	−0.566002	+	0.847082i	−0.998511	−	0.0545479i	$-0.982628\pi$
$277$	−156.783	+	234.642i	−0.566002	+	0.847082i	0.432509	+	0.901629i	$0.357628\pi$
$278$	−40.2769	−	8.01157i	−0.144881	−	0.0288186i
$279$	−13.7685	−	20.6060i	−0.0493495	−	0.0738568i
$280$		0			0
$281$	141.231	−	58.4999i	0.502603	−	0.208185i	−0.116953	−	0.993137i	$-0.537313\pi$
$281$	141.231	−	58.4999i	0.502603	−	0.208185i	0.619556	+	0.784953i	$0.287313\pi$
$282$	112.872	−	75.4189i	0.400257	−	0.267443i
$283$	−62.0182	+	311.786i	−0.219145	+	1.10172i	0.701904	+	0.712272i	$0.252334\pi$
$283$	−62.0182	+	311.786i	−0.219145	+	1.10172i	−0.921049	+	0.389447i	$0.872666\pi$
$284$	194.140	+	129.720i	0.683592	+	0.456761i
$285$		0			0
$286$	49.1414	+	247.050i	0.171823	+	0.863813i
$287$	−89.6819	+	216.511i	−0.312480	+	0.754395i
$288$			54.6992i			0.189928i
$289$	204.354	+	204.354i	0.707107	+	0.707107i
$290$		0			0
$291$	−196.488	−	81.3882i	−0.675218	−	0.279684i
$292$	77.6963	−	15.4548i	0.266083	−	0.0529272i
$293$	27.2633	+	27.2633i	0.0930488	+	0.0930488i	0.752099	−	0.659050i	$-0.229042\pi$
$293$	27.2633	+	27.2633i	0.0930488	+	0.0930488i	−0.659050	+	0.752099i	$0.729042\pi$
$294$	58.7592	−	87.9393i	0.199861	−	0.299113i
$295$		0			0
$296$	−89.0814	−	133.320i	−0.300951	−	0.450404i
$297$	−91.8547	−	221.757i	−0.309275	−	0.746656i
$298$	−40.5618	+	16.8013i	−0.136114	+	0.0563801i
$299$	−508.008	+	339.440i	−1.69902	+	1.13525i
$300$		0			0
$301$	−174.697	−	116.729i	−0.580388	−	0.387803i
$302$	132.756	−	132.756i	0.439591	−	0.439591i
$303$	73.6054	+	370.039i	0.242922	+	1.22125i
$304$	−1.07000	+	2.58320i	−0.00351972	+	0.00849736i
$305$		0			0
$306$	37.7359	+	15.6307i	0.123320	+	0.0510807i
$307$	4.80965			0.0156666			0.00783330	−	0.999969i	$-0.497507\pi$
$307$	4.80965			0.0156666			0.00783330	+	0.999969i	$0.497507\pi$
$308$	−151.023	−	62.5557i	−0.490334	−	0.203103i
$309$	111.365	−	22.1519i	0.360405	−	0.0716890i
$310$		0			0
$311$	267.024	−	399.630i	0.858598	−	1.28498i	−0.0984763	−	0.995139i	$-0.531397\pi$
$311$	267.024	−	399.630i	0.858598	−	1.28498i	0.957074	−	0.289843i	$-0.0936031\pi$
$312$	−498.225	−	99.1031i	−1.59688	−	0.317638i
$313$	49.2742	+	73.7441i	0.157426	+	0.235604i	0.901795	−	0.432164i	$-0.142250\pi$
$313$	49.2742	+	73.7441i	0.157426	+	0.235604i	−0.744369	+	0.667768i	$0.767250\pi$
$314$	−56.5047	−	136.414i	−0.179951	−	0.434441i
$315$		0			0
$316$	13.4352	−	8.97712i	0.0425165	−	0.0284086i
$317$	23.4692	−	117.988i	0.0740353	−	0.372201i	−0.925950	−	0.377647i	$-0.876733\pi$
$317$	23.4692	−	117.988i	0.0740353	−	0.372201i	0.999985	+	0.00544574i	$0.00173344\pi$
$318$	84.0983	+	56.1927i	0.264460	+	0.176707i
$319$	−96.9027	+	96.9027i	−0.303770	+	0.303770i
$320$		0			0
$321$	−75.7103	+	182.781i	−0.235858	+	0.569411i
$322$			315.906i			0.981074i
$323$	−15.7147	−	15.7147i	−0.0486524	−	0.0486524i
$324$	136.935			0.422639
$325$		0			0
$326$	−213.347	+	42.4374i	−0.654440	+	0.130176i
$327$	−398.773	−	398.773i	−1.21949	−	1.21949i
$328$	121.774	−	182.248i	0.371263	−	0.555634i
$329$	330.405	+	65.7216i	1.00427	+	0.199762i
$330$		0			0
$331$	38.9023	+	93.9184i	0.117530	+	0.283741i	0.971687	−	0.236274i	$-0.0759262\pi$
$331$	38.9023	+	93.9184i	0.117530	+	0.283741i	−0.854157	+	0.520015i	$0.825926\pi$
$332$	276.912	−	114.701i	0.834071	−	0.345484i
$333$	29.0045	−	19.3802i	0.0871006	−	0.0581988i
$334$	−43.3183	+	217.776i	−0.129695	+	0.652023i
$335$		0			0
$336$	−35.9683	+	35.9683i	−0.107049	+	0.107049i
$337$	107.223	+	539.044i	0.318168	+	1.59954i	0.726807	+	0.686842i	$0.241004\pi$
$337$	107.223	+	539.044i	0.318168	+	1.59954i	−0.408639	+	0.912696i	$0.633996\pi$
$338$	−179.666	+	433.752i	−0.531556	+	1.28329i
$339$		−	385.310i		−	1.13661i
$340$		0			0
$341$	−113.772			−0.333642
$342$	−2.90187	−	1.20200i	−0.00848501	−	0.00351461i
$343$	−168.661	+	33.5487i	−0.491722	+	0.0978097i
$344$	138.955	+	138.955i	0.403940	+	0.403940i
$345$		0			0
$346$	21.8349	+	4.34324i	0.0631067	+	0.0125527i
$347$	−141.826	−	212.258i	−0.408722	−	0.611695i	0.568814	−	0.822466i	$-0.307403\pi$
$347$	−141.826	−	212.258i	−0.408722	−	0.611695i	−0.977535	+	0.210771i	$0.932403\pi$
$348$	−37.8162	−	91.2964i	−0.108667	−	0.262346i
$349$	−513.215	+	212.580i	−1.47053	+	0.609113i	−0.966980	−	0.254854i	$-0.917973\pi$
$349$	−513.215	+	212.580i	−1.47053	+	0.609113i	−0.503549	+	0.863967i	$0.667973\pi$
$350$		0			0
$351$	129.122	−	649.141i	0.367869	−	1.84940i
$352$	208.792	+	139.511i	0.593160	+	0.396337i
$353$	408.644	−	408.644i	1.15763	−	1.15763i	0.172648	−	0.984984i	$-0.444768\pi$
$353$	408.644	−	408.644i	1.15763	−	1.15763i	0.984984	−	0.172648i	$-0.0552323\pi$
$354$	−16.6117	−	83.5128i	−0.0469258	−	0.235912i
$355$		0			0
$356$		−	121.692i		−	0.341832i
$357$	−154.723	−	373.534i	−0.433398	−	1.04631i
$358$	51.5822			0.144084
$359$	−159.526	−	66.0778i	−0.444362	−	0.184061i	0.149272	−	0.988796i	$-0.452307\pi$
$359$	−159.526	−	66.0778i	−0.444362	−	0.184061i	−0.593634	+	0.804735i	$0.702307\pi$
$360$		0			0
$361$	−254.057	−	254.057i	−0.703759	−	0.703759i
$362$	−31.9602	+	47.8317i	−0.0882877	+	0.132132i
$363$	137.889	+	27.4279i	0.379860	+	0.0755588i
$364$	−250.420	−	374.780i	−0.687967	−	1.02962i
$365$		0			0
$366$	170.449	−	70.6023i	0.465708	−	0.192902i
$367$	16.9759	−	11.3429i	0.0462558	−	0.0309071i	−0.532227	−	0.846601i	$-0.678645\pi$
$367$	16.9759	−	11.3429i	0.0462558	−	0.0309071i	0.578483	+	0.815694i	$0.303645\pi$
$368$	11.1634	−	56.1220i	0.0303352	−	0.152505i
$369$	39.6492	+	26.4927i	0.107450	+	0.0717960i
$370$		0			0
$371$	48.9675	+	246.176i	0.131988	+	0.663547i
$372$	31.3952	−	75.7946i	0.0843956	−	0.203749i
$373$		−	690.960i		−	1.85244i	−0.376983	−	0.926220i	$-0.623039\pi$
$373$		−	690.960i		−	1.85244i	0.376983	−	0.926220i	$-0.376961\pi$
$374$	155.910	−	104.175i	0.416870	−	0.278544i
$375$		0			0
$376$	−291.098	−	120.577i	−0.774196	−	0.320682i
$377$	−370.619	+	73.7207i	−0.983075	+	0.195546i
$378$	−241.982	−	241.982i	−0.640164	−	0.640164i
$379$	−97.1405	+	145.381i	−0.256308	+	0.383591i	−0.937200	−	0.348792i	$-0.886592\pi$
$379$	−97.1405	+	145.381i	−0.256308	+	0.383591i	0.680893	+	0.732383i	$0.261592\pi$
$380$		0			0
$381$	−161.327	−	241.443i	−0.423431	−	0.633709i
$382$	77.2642	+	186.532i	0.202262	+	0.488304i
$383$	−440.512	+	182.466i	−1.15016	+	0.476412i	−0.874588	−	0.484868i	$-0.838868\pi$
$383$	−440.512	+	182.466i	−1.15016	+	0.476412i	−0.275574	+	0.961280i	$0.588868\pi$
$384$	−125.144	+	83.6184i	−0.325895	+	0.217756i
$385$		0			0
$386$	−227.747	−	152.176i	−0.590019	−	0.394238i
$387$	−30.2306	+	30.2306i	−0.0781151	+	0.0781151i
$388$	34.4340	+	173.111i	0.0887473	+	0.446163i
$389$	84.5808	−	204.196i	0.217431	−	0.524926i	−0.777098	−	0.629379i	$-0.783309\pi$
$389$	84.5808	−	204.196i	0.217431	−	0.524926i	0.994530	+	0.104453i	$0.0333092\pi$
$390$		0			0
$391$	378.169	+	252.684i	0.967183	+	0.646251i
$392$	−245.482			−0.626228
$393$	−229.707	−	95.1478i	−0.584496	−	0.242106i
$394$	182.889	−	36.3788i	0.464184	−	0.0923320i
$395$		0			0
$396$	−18.4794	+	27.6564i	−0.0466652	+	0.0698395i
$397$	118.666	+	23.6042i	0.298908	+	0.0594565i	0.342266	−	0.939603i	$-0.388806\pi$
$397$	118.666	+	23.6042i	0.298908	+	0.0594565i	−0.0433581	+	0.999060i	$0.513806\pi$
$398$	109.709	+	164.191i	0.275650	+	0.412539i
$399$	11.8981	+	28.7246i	0.0298199	+	0.0719916i
$400$		0			0
$401$	434.146	−	290.087i	1.08266	−	0.723409i	0.119633	−	0.992818i	$-0.461828\pi$
$401$	434.146	−	290.087i	1.08266	−	0.723409i	0.963026	+	0.269409i	$0.0868282\pi$
$402$	49.0970	−	246.827i	0.122132	−	0.613998i
$403$	−260.846	−	174.292i	−0.647262	−	0.432486i
$404$	221.406	−	221.406i	0.548034	−	0.548034i
$405$		0			0
$406$	−74.7699	+	180.510i	−0.184162	+	0.444607i
$407$		−	160.142i		−	0.393471i
$408$	73.7738	+	370.886i	0.180818	+	0.909034i
$409$	136.013			0.332550			0.166275	−	0.986079i	$-0.446826\pi$
$409$	136.013			0.332550			0.166275	+	0.986079i	$0.446826\pi$
$410$		0			0
$411$	−268.482	+	53.4044i	−0.653241	+	0.129938i
$412$	−66.6331	−	66.6331i	−0.161731	−	0.161731i
$413$	117.395	−	175.694i	0.284249	−	0.425409i
$414$	63.0455	+	12.5405i	0.152284	+	0.0302911i
$415$		0			0
$416$	264.979	+	639.715i	0.636968	+	1.53778i
$417$	76.4181	−	31.6534i	0.183257	−	0.0759074i
$418$	−11.9894	+	8.01105i	−0.0286827	+	0.0191652i
$419$	73.0669	−	367.332i	0.174384	−	0.876687i	−0.790187	−	0.612865i	$-0.790017\pi$
$419$	73.0669	−	367.332i	0.174384	−	0.876687i	0.964571	−	0.263822i	$-0.0849832\pi$
$420$		0			0
$421$	−273.997	+	273.997i	−0.650824	+	0.650824i	−0.953192	−	0.302367i	$-0.902223\pi$
$421$	−273.997	+	273.997i	−0.650824	+	0.650824i	0.302367	+	0.953192i	$0.402223\pi$
$422$	−53.1807	−	267.357i	−0.126021	−	0.633548i
$423$	26.2322	−	63.3301i	0.0620146	−	0.149716i
$424$		−	234.759i		−	0.553678i
$425$		0			0
$426$	374.701			0.879580
$427$	422.985	+	175.206i	0.990598	+	0.410319i
$428$	161.034	−	32.0318i	0.376249	−	0.0748405i
$429$	−358.753	−	358.753i	−0.836254	−	0.836254i
$430$		0			0
$431$	67.5084	+	13.4283i	0.156632	+	0.0311561i	0.272783	−	0.962075i	$-0.412056\pi$
$431$	67.5084	+	13.4283i	0.156632	+	0.0311561i	−0.116151	+	0.993232i	$0.537056\pi$
$432$	34.4381	+	51.5402i	0.0797177	+	0.119306i
$433$	104.262	+	251.710i	0.240790	+	0.581317i	0.997362	−	0.0725929i	$-0.0231274\pi$
$433$	104.262	+	251.710i	0.240790	+	0.581317i	−0.756572	+	0.653910i	$0.773127\pi$
$434$	−149.860	+	62.0742i	−0.345301	+	0.143028i
$435$		0			0
$436$	−91.3074	+	459.033i	−0.209421	+	1.05283i
$437$	−29.0810	−	19.4313i	−0.0665470	−	0.0444653i
$438$	89.8934	−	89.8934i	0.205236	−	0.205236i
$439$	−28.7213	−	144.392i	−0.0654244	−	0.328910i	0.934187	−	0.356783i	$-0.116127\pi$
$439$	−28.7213	−	144.392i	−0.0654244	−	0.328910i	−0.999611	+	0.0278730i	$0.991127\pi$
$440$		0			0
$441$		−	53.4060i		−	0.121102i
$442$	517.046			1.16979
$443$	619.331			1.39804			0.699019	−	0.715103i	$-0.253620\pi$
$443$	619.331			1.39804			0.699019	+	0.715103i	$0.253620\pi$
$444$	106.687	+	44.1910i	0.240285	+	0.0995293i
$445$		0			0
$446$	−109.484	−	109.484i	−0.245480	−	0.245480i
$447$	49.1292	−	73.5271i	0.109909	−	0.164490i
$448$	425.530	+	84.6432i	0.949844	+	0.188936i
$449$	348.576	+	521.681i	0.776339	+	1.16187i	0.983026	+	0.183466i	$0.0587318\pi$
$449$	348.576	+	521.681i	0.776339	+	1.16187i	−0.206687	+	0.978407i	$0.566268\pi$
$450$		0			0
$451$	202.251	−	83.7750i	0.448450	−	0.185754i
$452$	−265.880	+	177.656i	−0.588231	+	0.393043i
$453$	−73.7743	+	370.888i	−0.162857	+	0.818738i
$454$	−169.889	−	113.516i	−0.374205	−	0.250036i
$455$		0			0
$456$	−5.67318	−	28.5210i	−0.0124412	−	0.0625460i
$457$	52.9634	−	127.865i	0.115894	−	0.279792i	−0.855280	−	0.518167i	$-0.826615\pi$
$457$	52.9634	−	127.865i	0.115894	−	0.279792i	0.971173	+	0.238375i	$0.0766147\pi$
$458$		−	12.8442i		−	0.0280442i
$459$	−483.229	+	96.1203i	−1.05279	+	0.209412i
$460$		0			0
$461$	−135.609	−	56.1709i	−0.294162	−	0.121846i	0.230722	−	0.973020i	$-0.425891\pi$
$461$	−135.609	−	56.1709i	−0.294162	−	0.121846i	−0.524884	+	0.851174i	$0.675891\pi$
$462$	−257.287	+	51.1775i	−0.556898	+	0.110774i
$463$	−522.332	−	522.332i	−1.12815	−	1.12815i	−0.990478	−	0.137669i	$-0.956039\pi$
$463$	−522.332	−	522.332i	−1.12815	−	1.12815i	−0.137669	−	0.990478i	$-0.543961\pi$
$464$	19.6620	−	29.4263i	0.0423750	−	0.0634187i
$465$		0			0
$466$	288.606	+	431.929i	0.619326	+	0.926887i
$467$	2.92741	+	7.06740i	0.00626855	+	0.0151336i	0.926983	−	0.375104i	$-0.122393\pi$
$467$	2.92741	+	7.06740i	0.00626855	+	0.0151336i	−0.920714	+	0.390237i	$0.872393\pi$
$468$	−84.7360	+	35.0988i	−0.181060	+	0.0749974i
$469$	519.274	−	346.968i	1.10719	−	0.739803i
$470$		0			0
$471$	247.281	+	165.228i	0.525012	+	0.350802i
$472$	−139.748	+	139.748i	−0.296077	+	0.296077i
$473$	38.2899	+	192.496i	0.0809512	+	0.406969i
$474$	9.92325	−	23.9568i	0.0209351	−	0.0505419i
$475$		0			0
$476$	−186.416	+	278.992i	−0.391631	+	0.586117i
$477$	51.0733			0.107072
$478$	−458.071	−	189.739i	−0.958307	−	0.396944i
$479$	−742.358	+	147.664i	−1.54981	+	0.308276i	−0.894493	−	0.447081i	$-0.852464\pi$
$479$	−742.358	+	147.664i	−1.54981	+	0.308276i	−0.655314	+	0.755357i	$0.727464\pi$
$480$		0			0
$481$	245.329	−	367.160i	0.510039	−	0.763327i
$482$	−181.547	−	36.1119i	−0.376653	−	0.0749209i
$483$	−353.505	−	529.057i	−0.731894	−	1.09536i
$484$	−44.6504	−	107.796i	−0.0922529	−	0.222718i
$485$		0			0
$486$	−106.129	+	70.9132i	−0.218373	+	0.145912i
$487$	−1.72321	+	8.66318i	−0.00353843	+	0.0177889i	−0.982514	−	0.186188i	$-0.940387\pi$
$487$	−1.72321	+	8.66318i	−0.00353843	+	0.0177889i	0.978976	+	0.203977i	$0.0653867\pi$
$488$	−356.047	−	237.903i	−0.729605	−	0.487506i
$489$	309.811	−	309.811i	0.633561	−	0.633561i
$490$		0			0
$491$	−224.608	+	542.252i	−0.457450	+	1.10438i	0.511976	+	0.859000i	$0.328914\pi$
$491$	−224.608	+	542.252i	−0.457450	+	1.10438i	−0.969426	+	0.245383i	$0.921086\pi$
$492$			157.857i			0.320847i
$493$	156.281	+	233.892i	0.317001	+	0.474425i
$494$	−39.7607			−0.0804871
$495$		0			0
$496$	28.8169	−	5.73204i	0.0580986	−	0.0115565i
$497$	657.508	+	657.508i	1.32295	+	1.32295i
$498$	267.228	−	399.934i	0.536602	−	0.803081i
$499$	−109.936	−	21.8676i	−0.220312	−	0.0438229i	0.0836997	−	0.996491i	$-0.473326\pi$
$499$	−109.936	−	21.8676i	−0.220312	−	0.0438229i	−0.304012	+	0.952668i	$0.598326\pi$
$500$		0			0
$501$	−171.149	−	413.190i	−0.341614	−	0.824730i
$502$	−268.067	+	111.037i	−0.533999	+	0.221190i
$503$	397.401	−	265.535i	0.790061	−	0.527902i	−0.0938335	−	0.995588i	$-0.529912\pi$
$503$	397.401	−	265.535i	0.790061	−	0.527902i	0.883895	+	0.467686i	$0.154912\pi$
$504$	−25.8746	+	130.080i	−0.0513385	+	0.258096i
$505$		0			0
$506$	208.666	−	208.666i	0.412384	−	0.412384i
$507$	−184.485	−	927.468i	−0.363875	−	1.82933i
$508$	−92.2226	+	222.645i	−0.181541	+	0.438278i
$509$		−	235.103i		−	0.461891i	−0.972967	−	0.230946i	$-0.925818\pi$
$509$		−	235.103i		−	0.461891i	0.972967	−	0.230946i	$-0.0741820\pi$
$510$		0			0
$511$	315.481			0.617380
$512$	−125.455	−	51.9650i	−0.245029	−	0.101494i
$513$	37.1602	−	7.39162i	0.0724370	−	0.0144086i
$514$	−399.555	−	399.555i	−0.777345	−	0.777345i
$515$		0			0
$516$	−138.807	−	27.6104i	−0.269005	−	0.0535084i
$517$	−174.832	−	261.655i	−0.338166	−	0.506102i
$518$	−87.3740	−	210.940i	−0.168676	−	0.407219i
$519$	−41.4278	+	17.1600i	−0.0798223	+	0.0330635i
$520$		0			0
$521$	−118.016	+	593.308i	−0.226519	+	1.13879i	0.685321	+	0.728241i	$0.259662\pi$
$521$	−118.016	+	593.308i	−0.226519	+	1.13879i	−0.911840	+	0.410546i	$0.865338\pi$
$522$	33.0564	+	22.0876i	0.0633265	+	0.0423134i
$523$	−721.650	+	721.650i	−1.37983	+	1.37983i	−0.534934	+	0.844894i	$0.679664\pi$
$523$	−721.650	+	721.650i	−1.37983	+	1.37983i	−0.844894	+	0.534934i	$0.820336\pi$
$524$	40.2554	+	202.378i	0.0768233	+	0.386217i
$525$		0			0
$526$		−	190.369i		−	0.361918i
$527$	−45.5605	+	229.048i	−0.0864526	+	0.434627i
$528$	47.5166			0.0899935
$529$	172.563	+	71.4781i	0.326207	+	0.135119i
$530$		0			0
$531$	−30.4031	−	30.4031i	−0.0572563	−	0.0572563i
$532$	14.3353	−	21.4544i	0.0269461	−	0.0403277i
$533$	592.041	+	117.764i	1.11077	+	0.220946i
$534$	−108.497	−	162.377i	−0.203178	−	0.304078i
$535$		0			0
$536$	−539.655	+	223.533i	−1.00682	+	0.417038i
$537$	−86.3863	+	57.7215i	−0.160868	+	0.107489i
$538$	11.9013	−	59.8321i	0.0221215	−	0.111212i
$539$	−203.856	−	136.212i	−0.378212	−	0.252713i
$540$		0			0
$541$	110.903	+	557.546i	0.204996	+	1.03058i	0.937012	+	0.349297i	$0.113580\pi$
$541$	110.903	+	557.546i	0.204996	+	1.03058i	−0.732016	+	0.681288i	$0.761420\pi$
$542$	168.093	−	405.812i	0.310134	−	0.748730i
$543$		−	115.869i		−	0.213387i
$544$	364.477	−	364.477i	0.669995	−	0.669995i
$545$		0			0
$546$	−668.285	−	276.813i	−1.22397	−	0.506983i
$547$	359.860	−	71.5805i	0.657879	−	0.130860i	0.145148	−	0.989410i	$-0.453634\pi$
$547$	359.860	−	71.5805i	0.657879	−	0.130860i	0.512730	+	0.858550i	$0.328634\pi$
$548$	160.641	+	160.641i	0.293140	+	0.293140i
$549$	51.7573	−	77.4602i	0.0942755	−	0.141093i
$550$		0			0
$551$	−12.0180	−	17.9862i	−0.0218112	−	0.0326428i
$552$	227.744	+	549.823i	0.412580	+	0.996056i
$553$	59.4512	−	24.6255i	0.107507	−	0.0445307i
$554$	312.501	−	208.806i	0.564081	−	0.376907i
$555$		0			0
$556$	−57.0764	−	38.1372i	−0.102655	−	0.0685922i
$557$	146.512	−	146.512i	0.263038	−	0.263038i	−0.563249	−	0.826287i	$-0.690449\pi$
$557$	146.512	−	146.512i	0.263038	−	0.263038i	0.826287	+	0.563249i	$0.190449\pi$
$558$	6.43917	+	32.3719i	0.0115397	+	0.0580141i
$559$	−207.105	+	499.996i	−0.370493	+	0.894448i
$560$		0			0
$561$	−144.532	+	348.932i	−0.257633	+	0.621981i
$562$	−203.593			−0.362264
$563$	−793.273	−	328.584i	−1.40901	−	0.583631i	−0.456936	−	0.889499i	$-0.651053\pi$
$563$	−793.273	−	328.584i	−1.40901	−	0.583631i	−0.952074	+	0.305868i	$0.901053\pi$
$564$	222.558	−	44.2696i	0.394607	−	0.0784922i
$565$		0			0
$566$	235.217	−	352.027i	0.415577	−	0.621955i
$567$	534.854	+	106.389i	0.943306	+	0.187635i
$568$	−483.177	−	723.125i	−0.850663	−	1.27311i
$569$	120.952	+	292.003i	0.212569	+	0.513187i	0.993817	−	0.111034i	$-0.0354164\pi$
$569$	120.952	+	292.003i	0.212569	+	0.513187i	−0.781248	+	0.624221i	$0.785416\pi$
$570$		0			0
$571$	224.810	−	150.213i	0.393713	−	0.263071i	−0.342918	−	0.939365i	$-0.611415\pi$
$571$	224.810	−	150.213i	0.393713	−	0.263071i	0.736631	+	0.676294i	$0.236415\pi$
$572$	−82.1440	+	412.966i	−0.143608	+	0.721968i
$573$	−338.130	−	225.931i	−0.590105	−	0.394295i
$574$	220.697	−	220.697i	0.384489	−	0.384489i
$575$		0			0
$576$	33.7846	−	81.5632i	0.0586538	−	0.141603i
$577$		−	63.2031i		−	0.109537i	−0.998499	−	0.0547687i	$-0.982558\pi$
$577$		−	63.2031i		−	0.109537i	0.998499	−	0.0547687i	$-0.0174421\pi$
$578$	−147.293	−	355.598i	−0.254833	−	0.615221i
$579$	551.703			0.952855
$580$		0			0
$581$	1170.70	−	232.868i	2.01498	−	0.400805i
$582$	200.287	+	200.287i	0.344136	+	0.344136i
$583$	130.263	−	194.952i	0.223435	−	0.334395i
$584$	−289.400	−	57.5653i	−0.495548	−	0.0985706i
$585$		0			0
$586$	−19.6507	−	47.4411i	−0.0335337	−	0.0809575i
$587$	−685.040	+	283.753i	−1.16702	+	0.483395i	−0.880206	−	0.474592i	$-0.842596\pi$
$587$	−685.040	+	283.753i	−1.16702	+	0.483395i	−0.286812	+	0.957987i	$0.592596\pi$
$588$	146.998	−	98.2209i	0.249997	−	0.167042i
$589$	3.50359	−	17.6137i	0.00594837	−	0.0299045i
$590$		0			0
$591$	−265.581	+	265.581i	−0.449375	+	0.449375i
$592$	8.06826	+	40.5619i	0.0136288	+	0.0685167i
$593$	76.8977	−	185.647i	0.129676	−	0.313065i	−0.845685	−	0.533683i	$-0.820808\pi$
$593$	76.8977	−	185.647i	0.129676	−	0.313065i	0.975360	+	0.220618i	$0.0708075\pi$
$594$			319.674i			0.538172i
$595$		0			0
$596$	−73.3889			−0.123136
$597$	−367.465	−	152.209i	−0.615519	−	0.254956i
$598$	798.076	−	158.747i	1.33458	−	0.265464i
$599$	457.825	+	457.825i	0.764316	+	0.764316i	0.977099	−	0.212784i	$-0.0682529\pi$
$599$	457.825	+	457.825i	0.764316	+	0.764316i	−0.212784	+	0.977099i	$0.568253\pi$
$600$		0			0
$601$	703.378	+	139.911i	1.17035	+	0.232796i	0.741735	−	0.670693i	$-0.234003\pi$
$601$	703.378	+	139.911i	1.17035	+	0.232796i	0.428611	+	0.903489i	$0.359003\pi$
$602$	155.462	+	232.665i	0.258242	+	0.386487i
$603$	−48.6309	−	117.405i	−0.0806482	−	0.194702i
$604$	289.944	−	120.099i	0.480040	−	0.198839i
$605$		0			0
$606$	98.0293	−	492.826i	0.161764	−	0.813245i
$607$	863.573	+	577.021i	1.42269	+	0.950612i	0.998996	+	0.0448067i	$0.0142672\pi$
$607$	863.573	+	577.021i	1.42269	+	0.950612i	0.423695	+	0.905805i	$0.360733\pi$
$608$	−28.0282	+	28.0282i	−0.0460990	+	0.0460990i
$609$	−76.7753	−	385.975i	−0.126068	−	0.633786i
$610$		0			0
$611$		−	867.731i		−	1.42018i
$612$	48.2783	+	48.2783i	0.0788861	+	0.0788861i
$613$	626.391			1.02185			0.510923	−	0.859627i	$-0.329304\pi$
$613$	626.391			1.02185			0.510923	+	0.859627i	$0.329304\pi$
$614$	−5.91799	−	2.45131i	−0.00963842	−	0.00399237i
$615$		0			0
$616$	430.537	+	430.537i	0.698924	+	0.698924i
$617$	372.249	−	557.109i	0.603320	−	0.902933i	−0.396566	−	0.918006i	$-0.629798\pi$
$617$	372.249	−	557.109i	0.603320	−	0.902933i	0.999886	+	0.0150736i	$0.00479825\pi$
$618$	−148.319	−	29.5024i	−0.239998	−	0.0477385i
$619$	−437.249	−	654.389i	−0.706379	−	1.05717i	−0.995014	−	0.0997323i	$-0.968201\pi$
$619$	−437.249	−	654.389i	−0.706379	−	1.05717i	0.288635	−	0.957439i	$-0.406799\pi$
$620$		0			0
$621$	−716.368	+	296.729i	−1.15357	+	0.477825i
$622$	−532.235	+	355.628i	−0.855684	+	0.571749i
$623$	94.5466	−	475.318i	0.151760	−	0.762950i
$624$	108.942	+	72.7926i	0.174586	+	0.116655i
$625$		0			0
$626$	−23.0442	−	115.851i	−0.0368119	−	0.185066i
$627$	11.1145	−	26.8327i	0.0177264	−	0.0427954i
$628$		−	246.816i		−	0.393019i
$629$	−322.402	−	64.1298i	−0.512563	−	0.101955i
$630$		0			0
$631$	−767.465	−	317.894i	−1.21627	−	0.503794i	−0.320046	−	0.947402i	$-0.603698\pi$
$631$	−767.465	−	317.894i	−1.21627	−	0.503794i	−0.896221	+	0.443608i	$0.853698\pi$
$632$	−59.0297	+	11.7417i	−0.0934013	+	0.0185787i
$633$	388.241	+	388.241i	0.613336	+	0.613336i
$634$	−89.0118	+	133.216i	−0.140397	+	0.210119i
$635$		0			0
$636$	93.9308	+	140.577i	0.147690	+	0.221034i
$637$	−258.714	−	624.591i	−0.406145	−	0.980520i
$638$	168.621	−	69.8452i	0.264297	−	0.109475i
$639$	157.320	−	105.118i	0.246198	−	0.164504i
$640$		0			0
$641$	−703.209	−	469.870i	−1.09705	−	0.733026i	−0.131001	−	0.991382i	$-0.541819\pi$
$641$	−703.209	−	469.870i	−1.09705	−	0.733026i	−0.966050	+	0.258357i	$0.916819\pi$
$642$	186.314	−	186.314i	0.290209	−	0.290209i
$643$	144.203	+	724.957i	0.224266	+	1.12746i	0.914721	+	0.404085i	$0.132410\pi$
$643$	144.203	+	724.957i	0.224266	+	1.12746i	−0.690456	+	0.723375i	$0.742590\pi$
$644$	−202.081	+	487.867i	−0.313790	+	0.757557i
$645$		0			0
$646$	11.3268	+	27.3453i	0.0175338	+	0.0423303i
$647$	−874.070			−1.35096			−0.675479	−	0.737379i	$-0.736063\pi$
$647$	−874.070			−1.35096			−0.675479	+	0.737379i	$0.736063\pi$
$648$	−471.225	−	195.188i	−0.727199	−	0.301216i
$649$	−193.595	+	38.5084i	−0.298297	+	0.0593350i
$650$		0			0
$651$	181.514	−	271.654i	0.278823	−	0.417288i
$652$	−356.628	−	70.9377i	−0.546976	−	0.108800i
$653$	642.117	+	960.997i	0.983335	+	1.47166i	0.878827	+	0.477140i	$0.158327\pi$
$653$	642.117	+	960.997i	0.983335	+	1.47166i	0.104507	+	0.994524i	$0.466673\pi$
$654$	287.426	+	693.908i	0.439489	+	1.06102i
$655$		0			0
$656$	−47.0066	+	31.4088i	−0.0716565	+	0.0478793i
$657$	12.5237	−	62.9607i	0.0190619	−	0.0958307i
$658$	−373.048	−	249.263i	−0.566942	−	0.378819i
$659$	−318.726	+	318.726i	−0.483651	+	0.483651i	−0.906295	−	0.422645i	$-0.861102\pi$
$659$	−318.726	+	318.726i	−0.483651	+	0.483651i	0.422645	+	0.906295i	$0.361102\pi$
$660$		0			0
$661$	191.121	−	461.408i	0.289140	−	0.698045i	−0.710846	−	0.703347i	$-0.751688\pi$
$661$	191.121	−	461.408i	0.289140	−	0.698045i	0.999986	+	0.00530241i	$0.00168782\pi$
$662$		−	135.388i		−	0.204514i
$663$	−865.913	+	578.585i	−1.30605	+	0.872677i
$664$	−1116.41			−1.68134
$665$		0			0
$666$	−45.5658	+	9.06360i	−0.0684171	+	0.0136090i
$667$	313.036	+	313.036i	0.469320	+	0.469320i
$668$	−206.207	+	308.610i	−0.308693	+	0.461991i
$669$	305.871	+	60.8416i	0.457207	+	0.0909441i
$670$		0			0
$671$	−163.666	−	395.126i	−0.243914	−	0.588861i
$672$	−666.221	+	275.958i	−0.991400	+	0.410651i
$673$	781.320	−	522.061i	1.16095	−	0.775722i	0.182704	−	0.983168i	$-0.441515\pi$
$673$	781.320	−	522.061i	1.16095	−	0.775722i	0.978247	+	0.207446i	$0.0665151\pi$
$674$	142.801	−	717.911i	0.211871	−	1.06515i
$675$		0			0
$676$	−554.932	+	554.932i	−0.820905	+	0.820905i
$677$	−217.100	−	1091.43i	−0.320679	−	1.61216i	−0.719065	−	0.694943i	$-0.755430\pi$
$677$	−217.100	−	1091.43i	−0.320679	−	1.61216i	0.398386	−	0.917218i	$-0.369570\pi$
$678$	−196.379	+	474.102i	−0.289645	+	0.699265i
$679$			702.908i			1.03521i
$680$		0			0
$681$	411.546			0.604325
$682$	139.990	+	57.9857i	0.205264	+	0.0850231i
$683$	−1289.29	+	256.456i	−1.88769	+	0.375484i	−0.996882	−	0.0789027i	$-0.974858\pi$
$683$	−1289.29	+	256.456i	−1.88769	+	0.375484i	−0.890804	+	0.454387i	$0.849858\pi$
$684$	−3.71259	−	3.71259i	−0.00542776	−	0.00542776i
$685$		0			0
$686$	224.626	+	44.6809i	0.327443	+	0.0651325i
$687$	14.3730	+	21.5107i	0.0209213	+	0.0313110i
$688$	−19.3966	−	46.8276i	−0.0281928	−	0.0680634i
$689$	597.310	−	247.414i	0.866923	−	0.359091i
$690$		0			0
$691$	93.4894	−	470.003i	0.135296	−	0.680178i	−0.852286	−	0.523075i	$-0.824785\pi$
$691$	93.4894	−	470.003i	0.135296	−	0.680178i	0.987582	−	0.157103i	$-0.0502154\pi$
$692$	30.9423	+	20.6750i	0.0447143	+	0.0298771i
$693$	−93.6660	+	93.6660i	−0.135160	+	0.135160i
$694$	66.3285	+	333.456i	0.0955742	+	0.480484i
$695$		0			0
$696$			368.075i			0.528844i
$697$	−87.6654	−	440.724i	−0.125775	−	0.632315i
$698$	739.826			1.05992
$699$	−966.675	−	400.410i	−1.38294	−	0.572832i
$700$		0			0
$701$	777.458	+	777.458i	1.10907	+	1.10907i	0.993273	+	0.115796i	$0.0369420\pi$
$701$	777.458	+	777.458i	1.10907	+	1.10907i	0.115796	+	0.993273i	$0.463058\pi$
$702$	−489.722	+	732.921i	−0.697610	+	1.04405i
$703$	24.7926	+	4.93156i	0.0352669	+	0.00701502i
$704$	−225.167	−	336.987i	−0.319840	−	0.478674i
$705$		0			0
$706$	−711.085	+	294.541i	−1.00720	+	0.417197i
$707$	1036.81	−	692.771i	1.46649	−	0.979875i
$708$	27.7679	−	139.599i	0.0392202	−	0.197173i
$709$	433.937	+	289.947i	0.612041	+	0.408953i	0.822593	−	0.568630i	$-0.192526\pi$
$709$	433.937	+	289.947i	0.612041	+	0.408953i	−0.210553	+	0.977583i	$0.567526\pi$
$710$		0			0
$711$	−2.55448	−	12.8423i	−0.00359281	−	0.0180623i
$712$	−173.461	+	418.771i	−0.243625	+	0.588162i
$713$			367.531i			0.515472i
$714$			538.469i			0.754159i
$715$		0			0
$716$	79.6605	+	32.9965i	0.111258	+	0.0460845i
$717$	979.467	−	194.828i	1.36606	−	0.271727i
$718$	162.610	+	162.610i	0.226476	+	0.226476i
$719$	−345.349	+	516.851i	−0.480318	+	0.718847i	−0.989930	−	0.141557i	$-0.954789\pi$
$719$	−345.349	+	516.851i	−0.480318	+	0.718847i	0.509612	+	0.860404i	$0.329789\pi$
$720$		0			0
$721$	−208.493	−	312.032i	−0.289172	−	0.432776i
$722$	183.118	+	442.087i	0.253627	+	0.612309i
$723$	344.452	−	142.677i	0.476420	−	0.197340i
$724$	−79.9548	+	53.4241i	−0.110435	+	0.0737902i
$725$		0			0
$726$	−155.686	−	104.026i	−0.214443	−	0.143286i
$727$	−181.405	+	181.405i	−0.249526	+	0.249526i	−0.820776	−	0.571250i	$-0.806459\pi$
$727$	−181.405	+	181.405i	−0.249526	+	0.249526i	0.571250	+	0.820776i	$0.306459\pi$
$728$	327.540	+	1646.65i	0.449917	+	2.26189i
$729$	310.231	−	748.965i	0.425557	−	1.02739i
$730$		0			0
$731$	402.871			0.551123
$732$	308.395			0.421305
$733$	−204.776	−	84.8211i	−0.279367	−	0.115718i	0.238600	−	0.971118i	$-0.423311\pi$
$733$	−204.776	−	84.8211i	−0.279367	−	0.115718i	−0.517968	+	0.855400i	$0.673311\pi$
$734$	−26.6690	+	5.30478i	−0.0363337	+	0.00722723i
$735$		0			0
$736$	450.677	−	674.487i	0.612334	−	0.916422i
$737$	−572.182	−	113.814i	−0.776366	−	0.154429i
$738$	−35.2836	−	52.8056i	−0.0478097	−	0.0715523i
$739$	113.071	+	272.978i	0.153006	+	0.369388i	0.981733	−	0.190265i	$-0.0609346\pi$
$739$	113.071	+	272.978i	0.153006	+	0.369388i	−0.828727	+	0.559653i	$0.810935\pi$
$740$		0			0
$741$	66.5884	−	44.4929i	0.0898629	−	0.0600445i
$742$	65.2159	−	327.862i	0.0878920	−	0.441863i
$743$	622.570	+	415.988i	0.837914	+	0.559876i	0.898846	−	0.438265i	$-0.144407\pi$
$743$	622.570	+	415.988i	0.837914	+	0.559876i	−0.0609312	+	0.998142i	$0.519407\pi$
$744$	−216.076	+	216.076i	−0.290425	+	0.290425i
$745$		0			0
$746$	−352.159	+	850.187i	−0.472063	+	1.13966i
$747$		−	242.882i		−	0.325143i
$748$	307.417	−	61.1491i	0.410986	−	0.0817502i
$749$	653.871			0.872992
$750$		0			0
$751$	−683.178	+	135.892i	−0.909691	+	0.180949i	−0.627688	−	0.778465i	$-0.715999\pi$
$751$	−683.178	+	135.892i	−0.909691	+	0.180949i	−0.282003	+	0.959414i	$0.590999\pi$
$752$	57.4652	+	57.4652i	0.0764165	+	0.0764165i
$753$	324.688	−	485.930i	0.431193	−	0.645326i
$754$	493.598	+	98.1828i	0.654640	+	0.130216i
$755$		0			0
$756$	−218.910	−	528.496i	−0.289564	−	0.699069i
$757$	633.525	−	262.415i	0.836889	−	0.346651i	0.0772631	−	0.997011i	$-0.475382\pi$
$757$	633.525	−	262.415i	0.836889	−	0.346651i	0.759626	+	0.650360i	$0.225382\pi$
$758$	193.622	−	129.374i	0.255438	−	0.170678i
$759$	−115.958	+	582.962i	−0.152778	+	0.768066i
$760$		0			0
$761$	−305.005	+	305.005i	−0.400795	+	0.400795i	−0.878513	−	0.477718i	$-0.841464\pi$
$761$	−305.005	+	305.005i	−0.400795	+	0.400795i	0.477718	+	0.878513i	$0.341464\pi$
$762$	75.4484	+	379.305i	0.0990136	+	0.497775i
$763$	−713.275	+	1722.00i	−0.934830	+	2.25688i
$764$			337.495i			0.441747i
$765$		0			0
$766$	635.021			0.829009
$767$	−502.850	−	208.287i	−0.655606	−	0.271561i
$768$	711.607	−	141.547i	0.926572	−	0.184307i
$769$	303.275	+	303.275i	0.394376	+	0.394376i	0.876244	−	0.481868i	$-0.160041\pi$
$769$	303.275	+	303.275i	0.394376	+	0.394376i	−0.481868	+	0.876244i	$0.660041\pi$
$770$		0			0
$771$	1116.26	+	222.037i	1.44780	+	0.287986i
$772$	−254.375	−	380.699i	−0.329501	−	0.493133i
$773$	79.8088	+	192.675i	0.103246	+	0.249257i	0.967058	−	0.254557i	$-0.0819297\pi$
$773$	79.8088	+	192.675i	0.103246	+	0.249257i	−0.863812	+	0.503814i	$0.831930\pi$
$774$	52.6045	−	21.7895i	0.0679644	−	0.0281518i
$775$		0			0
$776$	128.258	−	644.798i	0.165281	−	0.830925i
$777$	382.373	+	255.494i	0.492115	+	0.328821i
$778$	−208.144	+	208.144i	−0.267537	+	0.267537i
$779$	6.74144	+	33.8915i	0.00865396	+	0.0435064i
$780$		0			0
$781$		−	868.612i		−	1.11218i
$782$	−336.530	−	503.653i	−0.430345	−	0.644058i
$783$	−479.568			−0.612475
$784$	58.4966	+	24.2301i	0.0746130	+	0.0309057i
$785$		0			0
$786$	234.148	+	234.148i	0.297898	+	0.297898i
$787$	−614.498	+	919.662i	−0.780811	+	1.16857i	0.201164	+	0.979558i	$0.435527\pi$
$787$	−614.498	+	919.662i	−0.780811	+	1.16857i	−0.981975	+	0.189009i	$0.939473\pi$
$788$	305.714	+	60.8102i	0.387962	+	0.0771703i
$789$	213.027	+	318.817i	0.269996	+	0.404077i
$790$		0			0
$791$	−1176.53	+	487.334i	−1.48739	+	0.616099i
$792$	103.014	−	68.8315i	0.130068	−	0.0869084i
$793$	230.069	−	1156.64i	0.290125	−	1.45856i
$794$	−133.982	−	89.5239i	−0.168743	−	0.112750i
$795$		0			0
$796$	64.3970	+	323.746i	0.0809008	+	0.406716i
$797$	23.4701	−	56.6619i	0.0294481	−	0.0710940i	−0.908471	−	0.417947i	$-0.862750\pi$
$797$	23.4701	−	56.6619i	0.0294481	−	0.0710940i	0.937919	+	0.346853i	$0.112750\pi$
$798$		−	41.4081i		−	0.0518899i
$799$	−596.781	+	247.195i	−0.746910	+	0.309380i
$800$		0			0
$801$	−91.1062	−	37.7374i	−0.113741	−	0.0471129i
$802$	−682.039	+	135.666i	−0.850423	+	0.169160i
$803$	−208.386	−	208.386i	−0.259509	−	0.259509i
$804$	233.715	−	349.779i	0.290690	−	0.435049i
$805$		0			0
$806$	232.126	+	347.401i	0.287997	+	0.431018i
$807$	47.0217	+	113.521i	0.0582673	+	0.140670i
$808$	−1077.50	+	446.315i	−1.33354	+	0.552370i
$809$	676.209	−	451.829i	0.835858	−	0.558503i	−0.0623592	−	0.998054i	$-0.519862\pi$
$809$	676.209	−	451.829i	0.835858	−	0.558503i	0.898218	+	0.439551i	$0.144862\pi$
$810$		0			0
$811$	961.868	+	642.700i	1.18603	+	0.792478i	0.982440	−	0.186579i	$-0.0597399\pi$
$811$	961.868	+	642.700i	1.18603	+	0.792478i	0.203587	+	0.979057i	$0.434740\pi$
$812$	−230.941	+	230.941i	−0.284410	+	0.284410i
$813$	172.601	+	867.724i	0.212301	+	1.06731i
$814$	−81.6192	+	197.046i	−0.100269	+	0.242071i
$815$		0			0
$816$	19.0282	−	95.6614i	0.0233189	−	0.117232i
$817$	−30.9806			−0.0379200
$818$	−167.356	−	69.3211i	−0.204592	−	0.0847446i
$819$	−358.240	+	71.2583i	−0.437411	+	0.0870065i
$820$		0			0
$821$	555.958	−	832.050i	0.677172	−	1.01346i	−0.320631	−	0.947204i	$-0.603895\pi$
$821$	555.958	−	832.050i	0.677172	−	1.01346i	0.997803	−	0.0662547i	$-0.0211050\pi$
$822$	357.570	+	71.1252i	0.435000	+	0.0865270i
$823$	−30.1009	−	45.0492i	−0.0365746	−	0.0547378i	0.812732	−	0.582638i	$-0.197979\pi$
$823$	−30.1009	−	45.0492i	−0.0365746	−	0.0547378i	−0.849306	+	0.527900i	$0.822979\pi$
$824$	134.321	+	324.279i	0.163011	+	0.393542i
$825$		0			0
$826$	−233.993	+	156.349i	−0.283284	+	0.189285i
$827$	−80.0267	+	402.321i	−0.0967675	+	0.486483i	0.901760	+	0.432237i	$0.142276\pi$
$827$	−80.0267	+	402.321i	−0.0967675	+	0.486483i	−0.998528	+	0.0542461i	$0.982724\pi$
$828$	89.3418	+	59.6963i	0.107901	+	0.0720970i
$829$	−153.097	+	153.097i	−0.184677	+	0.184677i	−0.793390	−	0.608713i	$-0.791686\pi$
$829$	−153.097	+	153.097i	−0.184677	+	0.184677i	0.608713	+	0.793390i	$0.291686\pi$
$830$		0			0
$831$	−289.696	+	699.389i	−0.348612	+	0.841623i
$832$		−	1117.56i		−	1.34322i
$833$	−355.861	+	355.861i	−0.427204	+	0.427204i
$834$	−110.161			−0.132087
$835$		0			0
$836$	−23.6403	+	4.70235i	−0.0282779	+	0.00562482i
$837$	−281.527	−	281.527i	−0.336352	−	0.336352i
$838$	−277.121	+	414.741i	−0.330694	+	0.494918i
$839$	−278.253	−	55.3480i	−0.331648	−	0.0659690i	0.0264576	−	0.999650i	$-0.491577\pi$
$839$	−278.253	−	55.3480i	−0.331648	−	0.0659690i	−0.358106	+	0.933681i	$0.616577\pi$
$840$		0			0
$841$	−217.057	−	524.021i	−0.258094	−	0.623093i
$842$	476.785	−	197.491i	0.566252	−	0.234549i
$843$	340.963	−	227.824i	0.404463	−	0.270254i
$844$	88.8960	−	446.910i	0.105327	−	0.529515i
$845$		0			0
$846$	−64.5544	+	64.5544i	−0.0763054	+	0.0763054i
$847$	−90.6502	−	455.729i	−0.107025	−	0.538051i
$848$	−23.1718	+	55.9416i	−0.0273252	+	0.0659689i
$849$			852.762i			1.00443i
$850$		0			0
$851$	−517.327			−0.607905
$852$	578.667	+	239.692i	0.679187	+	0.281328i
$853$	559.124	−	111.217i	0.655479	−	0.130383i	0.143864	−	0.989598i	$-0.454047\pi$
$853$	559.124	−	111.217i	0.655479	−	0.130383i	0.511615	+	0.859215i	$0.329047\pi$
$854$	−431.162	−	431.162i	−0.504874	−	0.504874i
$855$		0			0
$856$	−599.815	−	119.311i	−0.700718	−	0.139382i
$857$	738.200	+	1104.79i	0.861377	+	1.28914i	0.955922	+	0.293622i	$0.0948605\pi$
$857$	738.200	+	1104.79i	0.861377	+	1.28914i	−0.0945445	+	0.995521i	$0.530139\pi$
$858$	258.581	+	624.269i	0.301376	+	0.727586i
$859$	260.316	−	107.826i	0.303046	−	0.125526i	−0.225979	−	0.974132i	$-0.572558\pi$
$859$	260.316	−	107.826i	0.303046	−	0.125526i	0.529024	+	0.848607i	$0.322558\pi$
$860$		0			0
$861$	−122.644	+	616.572i	−0.142443	+	0.716111i
$862$	−76.2213	−	50.9295i	−0.0884238	−	0.0590829i
$863$	−44.4457	+	44.4457i	−0.0515014	+	0.0515014i	−0.732388	−	0.680887i	$-0.761594\pi$
$863$	−44.4457	+	44.4457i	−0.0515014	+	0.0515014i	0.680887	+	0.732388i	$0.261594\pi$
$864$	171.436	+	861.869i	0.198422	+	0.997533i
$865$		0			0
$866$		−	362.854i		−	0.419000i
$867$	644.598	+	430.707i	0.743481	+	0.496778i
$868$	−271.144			−0.312378
$869$	−55.5355	−	23.0035i	−0.0639073	−	0.0264713i
$870$		0			0
$871$	−1137.49	−	1137.49i	−1.30596	−	1.30596i
$872$	968.518	−	1449.49i	1.11069	−	1.66226i
$873$	140.280	+	27.9034i	0.160687	+	0.0319626i
$874$	25.8790	+	38.7307i	0.0296099	+	0.0443143i
$875$		0			0
$876$	196.330	−	81.3225i	0.224121	−	0.0928339i
$877$	−374.931	+	250.521i	−0.427515	+	0.285657i	−0.750655	−	0.660695i	$-0.770262\pi$
$877$	−374.931	+	250.521i	−0.427515	+	0.285657i	0.323139	+	0.946351i	$0.395262\pi$
$878$	−38.2516	+	192.304i	−0.0435668	+	0.219025i
$879$	85.9972	+	57.4615i	0.0978353	+	0.0653714i
$880$		0			0
$881$	192.046	+	965.483i	0.217987	+	1.09589i	0.922439	+	0.386143i	$0.126193\pi$
$881$	192.046	+	965.483i	0.217987	+	1.09589i	−0.704452	+	0.709752i	$0.748807\pi$
$882$	−27.2192	+	65.7130i	−0.0308608	+	0.0745046i
$883$			908.452i			1.02882i	0.857543	+	0.514412i	$0.171990\pi$
$883$			908.452i			1.02882i	−0.857543	+	0.514412i	$0.828010\pi$
$884$	798.496	+	330.748i	0.903276	+	0.374149i
$885$		0			0
$886$	−762.051	−	315.652i	−0.860103	−	0.356266i
$887$	−245.627	+	48.8583i	−0.276919	+	0.0550827i	−0.331596	−	0.943421i	$-0.607587\pi$
$887$	−245.627	+	48.8583i	−0.276919	+	0.0550827i	0.0546769	+	0.998504i	$0.482587\pi$
$888$	−304.143	−	304.143i	−0.342503	−	0.342503i
$889$	−533.193	+	797.979i	−0.599767	+	0.897614i
$890$		0			0
$891$	−283.016	−	423.563i	−0.317638	−	0.475379i
$892$	−99.0454	−	239.117i	−0.111037	−	0.268068i
$893$	45.8922	−	19.0092i	0.0513911	−	0.0212869i
$894$	−97.9249	+	65.4313i	−0.109536	+	0.0731894i
$895$		0			0
$896$	413.605	+	276.362i	0.461613	+	0.308440i
$897$	−1158.92	+	1158.92i	−1.29200	+	1.29200i
$898$	−163.020	−	819.556i	−0.181537	−	0.912646i
$899$	−86.9888	+	210.010i	−0.0967617	+	0.233604i
$900$		0			0
$901$	−340.317	−	340.317i	−0.377711	−	0.377711i
$902$	−291.555			−0.323232
$903$	−520.713	−	215.687i	−0.576648	−	0.238856i
$904$	1168.19	−	232.367i	1.29224	−	0.257043i
$905$		0			0
$906$	279.804	−	418.756i	0.308835	−	0.462204i
$907$	−1703.05	−	338.757i	−1.87767	−	0.373492i	−0.882387	−	0.470524i	$-0.844065\pi$
$907$	−1703.05	−	338.757i	−1.87767	−	0.373492i	−0.995281	+	0.0970321i	$0.969065\pi$
$908$	−189.752	−	283.984i	−0.208978	−	0.312758i
$909$	−97.0986	−	234.417i	−0.106819	−	0.257884i
$910$		0			0
$911$	1492.51	−	997.265i	1.63832	−	1.09469i	0.723922	−	0.689882i	$-0.242337\pi$
$911$	1492.51	−	997.265i	1.63832	−	1.09469i	0.914401	−	0.404811i	$-0.132663\pi$
$912$	−1.46326	+	7.35633i	−0.00160446	+	0.00806615i
$913$	−927.106	−	619.472i	−1.01545	−	0.678502i
$914$	−130.337	+	130.337i	−0.142600	+	0.142600i
$915$		0			0
$916$	8.21630	−	19.8359i	0.00896976	−	0.0216549i
$917$			821.743i			0.896121i
$918$	643.575	+	128.015i	0.701062	+	0.139450i
$919$	−506.869			−0.551544			−0.275772	−	0.961223i	$-0.588933\pi$
$919$	−506.869			−0.551544			−0.275772	+	0.961223i	$0.588933\pi$
$920$		0			0
$921$	12.6541	−	2.51706i	0.0137395	−	0.00273296i
$922$	138.230	+	138.230i	0.149924	+	0.149924i
$923$	1330.66	−	1991.48i	1.44167	−	2.15761i
$924$	−430.077	−	85.5476i	−0.465451	−	0.0925839i
$925$		0			0
$926$	376.485	+	908.914i	0.406571	+	0.981549i
$927$	−70.5489	+	29.2223i	−0.0761045	+	0.0315235i
$928$	417.160	−	278.737i	0.449526	−	0.300364i
$929$	272.070	−	1367.79i	0.292863	−	1.47232i	−0.501646	−	0.865073i	$-0.667272\pi$
$929$	272.070	−	1367.79i	0.292863	−	1.47232i	0.794510	−	0.607251i	$-0.207728\pi$
$930$		0			0
$931$	27.3656	−	27.3656i	0.0293937	−	0.0293937i
$932$	169.407	+	851.665i	0.181767	+	0.913803i
$933$	493.396	−	1191.16i	0.528827	−	1.27670i
$934$		−	10.1880i		−	0.0109080i
$935$		0			0
$936$	341.626			0.364985
$937$	185.233	+	76.7261i	0.197687	+	0.0818848i	0.479331	−	0.877634i	$-0.340879\pi$
$937$	185.233	+	76.7261i	0.197687	+	0.0818848i	−0.281643	+	0.959519i	$0.590879\pi$
$938$	−815.774	+	162.268i	−0.869695	+	0.172993i
$939$	168.233	+	168.233i	0.179162	+	0.179162i
$940$		0			0
$941$	−1497.87	−	297.945i	−1.59179	−	0.316626i	−0.681889	−	0.731456i	$-0.738841\pi$
$941$	−1497.87	−	297.945i	−1.59179	−	0.316626i	−0.909899	+	0.414830i	$0.863841\pi$
$942$	−220.054	−	329.334i	−0.233603	−	0.349611i
$943$	−270.628	−	653.355i	−0.286987	−	0.692847i
$944$	47.0948	−	19.5073i	0.0498886	−	0.0206645i
$945$		0			0
$946$	50.9953	−	256.371i	0.0539063	−	0.271005i
$947$	845.726	+	565.096i	0.893058	+	0.596723i	0.915186	−	0.403033i	$-0.132044\pi$
$947$	845.726	+	565.096i	0.893058	+	0.596723i	−0.0221273	+	0.999755i	$0.507044\pi$
$948$	30.6498	−	30.6498i	0.0323310	−	0.0323310i
$949$	−158.534	−	797.004i	−0.167054	−	0.839835i
$950$		0			0
$951$		−	322.706i		−	0.339334i
$952$	1039.18	−	694.356i	1.09157	−	0.729365i
$953$	−297.230			−0.311889			−0.155945	−	0.987766i	$-0.549842\pi$
$953$	−297.230			−0.311889			−0.155945	+	0.987766i	$0.549842\pi$
$954$	−62.8428	−	26.0303i	−0.0658730	−	0.0272855i
$955$		0			0
$956$	−586.045	−	586.045i	−0.613017	−	0.613017i
$957$	−204.237	+	305.662i	−0.213414	+	0.319396i
$958$	988.688	+	196.662i	1.03203	+	0.205284i
$959$	502.640	+	752.255i	0.524130	+	0.784416i
$960$		0			0
$961$	713.498	−	295.540i	0.742453	−	0.307534i
$962$	−488.992	+	326.734i	−0.508308	+	0.339640i
$963$	25.9567	−	130.493i	0.0269540	−	0.135507i
$964$	−257.270	−	171.902i	−0.266878	−	0.178322i
$965$		0			0
$966$	165.325	+	831.144i	0.171144	+	0.860397i
$967$	452.787	−	1093.12i	0.468239	−	1.13043i	−0.496692	−	0.867927i	$-0.665452\pi$
$967$	452.787	−	1093.12i	0.468239	−	1.13043i	0.964931	−	0.262502i	$-0.0845477\pi$
$968$			434.595i			0.448961i
$969$	−49.5693	−	33.1212i	−0.0511551	−	0.0341808i
$970$		0			0
$971$	510.211	+	211.336i	0.525449	+	0.217648i	0.629608	−	0.776913i	$-0.283215\pi$
$971$	510.211	+	211.336i	0.525449	+	0.217648i	−0.104160	+	0.994561i	$0.533215\pi$
$972$	−209.262	+	41.6248i	−0.215290	+	0.0428239i
$973$	−193.305	−	193.305i	−0.198669	−	0.198669i
$974$	6.53565	−	9.78129i	0.00671011	−	0.0100424i
$975$		0			0
$976$	61.3616	+	91.8341i	0.0628705	+	0.0940923i
$977$	125.177	+	302.204i	0.128124	+	0.309318i	0.974904	−	0.222624i	$-0.0714623\pi$
$977$	125.177	+	302.204i	0.128124	+	0.309318i	−0.846781	+	0.531942i	$0.821462\pi$
$978$	−539.105	+	223.305i	−0.551232	+	0.228328i
$979$	−376.415	+	251.512i	−0.384489	+	0.256907i
$980$		0			0
$981$	315.345	+	210.707i	0.321453	+	0.214788i
$982$	552.735	−	552.735i	0.562866	−	0.562866i
$983$	−199.903	−	1004.98i	−0.203360	−	1.02236i	−0.938719	−	0.344683i	$-0.887986\pi$
$983$	−199.903	−	1004.98i	−0.203360	−	1.02236i	0.735359	−	0.677678i	$-0.237014\pi$
$984$	225.009	−	543.221i	0.228668	−	0.552053i
$985$		0			0
$986$	−73.0887	−	367.442i	−0.0741265	−	0.372659i
$987$	903.685			0.915587
$988$	−61.4041	−	25.4344i	−0.0621499	−	0.0257433i
$989$	621.844	−	123.692i	0.628760	−	0.125068i
$990$		0			0
$991$	−229.264	+	343.118i	−0.231346	+	0.346234i	−0.928921	−	0.370278i	$-0.879262\pi$
$991$	−229.264	+	343.118i	−0.231346	+	0.346234i	0.697575	+	0.716512i	$0.254262\pi$
$992$	408.521	+	81.2600i	0.411816	+	0.0819153i
$993$	151.502	+	226.739i	0.152570	+	0.228338i
$994$	−473.916	−	1144.14i	−0.476777	−	1.15104i
$995$		0			0
$996$	668.524	−	446.693i	0.671209	−	0.448487i
$997$	−245.429	+	1233.85i	−0.246167	+	1.23757i	0.637867	+	0.770146i	$0.279817\pi$
$997$	−245.429	+	1233.85i	−0.246167	+	1.23757i	−0.884035	+	0.467421i	$0.845183\pi$
$998$	124.125	+	82.9374i	0.124373	+	0.0831037i
$999$	396.270	−	396.270i	0.396666	−	0.396666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.u.b.176.1		8
5.2	odd	4		425.3.t.c.74.1		8
5.3	odd	4		425.3.t.a.74.1		8
5.4	even	2		17.3.e.a.6.1	yes	8
15.14	odd	2		153.3.p.b.91.1		8
17.3	odd	16	inner	425.3.u.b.326.1		8
20.19	odd	2		272.3.bh.c.193.1		8
85.3	even	16		425.3.t.c.224.1		8
85.4	even	4		289.3.e.i.249.1		8
85.9	even	8		289.3.e.l.214.1		8
85.14	odd	16		289.3.e.c.224.1		8
85.19	even	8		289.3.e.b.75.1		8
85.24	odd	16		289.3.e.d.158.1		8
85.29	odd	16		289.3.e.m.65.1		8
85.37	even	16		425.3.t.a.224.1		8
85.39	odd	16		289.3.e.i.65.1		8
85.44	odd	16		289.3.e.b.158.1		8
85.49	even	8		289.3.e.d.75.1		8
85.54	odd	16		17.3.e.a.3.1	✓	8
85.59	even	8		289.3.e.k.214.1		8
85.64	even	4		289.3.e.m.249.1		8
85.74	odd	16		289.3.e.l.131.1		8
85.79	odd	16		289.3.e.k.131.1		8
85.84	even	2		289.3.e.c.40.1		8
255.224	even	16		153.3.p.b.37.1		8
340.139	even	16		272.3.bh.c.241.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.3.1	✓	8	85.54	odd	16
17.3.e.a.6.1	yes	8	5.4	even	2
153.3.p.b.37.1		8	255.224	even	16
153.3.p.b.91.1		8	15.14	odd	2
272.3.bh.c.193.1		8	20.19	odd	2
272.3.bh.c.241.1		8	340.139	even	16
289.3.e.b.75.1		8	85.19	even	8
289.3.e.b.158.1		8	85.44	odd	16
289.3.e.c.40.1		8	85.84	even	2
289.3.e.c.224.1		8	85.14	odd	16
289.3.e.d.75.1		8	85.49	even	8
289.3.e.d.158.1		8	85.24	odd	16
289.3.e.i.65.1		8	85.39	odd	16
289.3.e.i.249.1		8	85.4	even	4
289.3.e.k.131.1		8	85.79	odd	16
289.3.e.k.214.1		8	85.59	even	8
289.3.e.l.131.1		8	85.74	odd	16
289.3.e.l.214.1		8	85.9	even	8
289.3.e.m.65.1		8	85.29	odd	16
289.3.e.m.249.1		8	85.64	even	4
425.3.t.a.74.1		8	5.3	odd	4
425.3.t.a.224.1		8	85.37	even	16
425.3.t.c.74.1		8	5.2	odd	4
425.3.t.c.224.1		8	85.3	even	16
425.3.u.b.176.1		8	1.1	even	1	trivial
425.3.u.b.326.1		8	17.3	odd	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.u (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23044 - 0.509666i) q^{2} +(2.63099 - 0.523336i) q^{3} +(-1.57420 - 1.57420i) q^{4} +(-3.50400 - 0.696990i) q^{6} +(-4.92562 - 7.37170i) q^{7} +(3.17331 + 7.66104i) q^{8} +(-1.66671 + 0.690373i) q^{9} +O(q^{10})\)	\(q+(-1.23044 - 0.509666i) q^{2} +(2.63099 - 0.523336i) q^{3} +(-1.57420 - 1.57420i) q^{4} +(-3.50400 - 0.696990i) q^{6} +(-4.92562 - 7.37170i) q^{7} +(3.17331 + 7.66104i) q^{8} +(-1.66671 + 0.690373i) q^{9} +(-1.61572 + 8.12279i) q^{11} +(-4.96553 - 3.31786i) q^{12} +(-16.1480 + 16.1480i) q^{13} +(2.30358 + 11.5809i) q^{14} -2.13880i q^{16} +(15.7060 + 6.50562i) q^{17} +2.40265 q^{18} +(-1.20778 - 0.500280i) q^{19} +(-16.8171 - 16.8171i) q^{21} +(6.12797 - 9.17115i) q^{22} +(26.2400 + 5.21946i) q^{23} +(12.3582 + 18.4954i) q^{24} +(28.0993 - 11.6391i) q^{26} +(-24.0978 + 16.1016i) q^{27} +(-3.85063 + 19.3584i) q^{28} +(13.7583 + 9.19303i) q^{29} +(2.68003 + 13.4734i) q^{31} +(11.6032 - 28.0125i) q^{32} +22.2165i q^{33} +(-16.0096 - 16.0096i) q^{34} +(3.71051 + 1.53694i) q^{36} +(-18.9648 + 3.77234i) q^{37} +(1.23113 + 1.23113i) q^{38} +(-34.0344 + 50.9361i) q^{39} +(-14.6853 - 21.9781i) q^{41} +(12.1214 + 29.2636i) q^{42} +(21.8944 - 9.06895i) q^{43} +(15.3303 - 10.2434i) q^{44} +(-29.6266 - 19.7959i) q^{46} +(-26.8680 + 26.8680i) q^{47} +(-1.11931 - 5.62714i) q^{48} +(-11.3288 + 27.3503i) q^{49} +(44.7268 + 8.89671i) q^{51} +50.8404 q^{52} +(-26.1557 - 10.8340i) q^{53} +(37.8574 - 7.53030i) q^{54} +(40.8445 - 61.1281i) q^{56} +(-3.43947 - 0.684154i) q^{57} +(-12.2435 - 18.3236i) q^{58} +(9.12070 + 22.0193i) q^{59} +(-42.9373 + 28.6898i) q^{61} +(3.56932 - 17.9442i) q^{62} +(13.2988 + 8.88596i) q^{63} +(-34.6035 + 34.6035i) q^{64} +(11.3230 - 27.3362i) q^{66} +70.4415i q^{67} +(-14.4831 - 34.9654i) q^{68} +71.7687 q^{69} +(-102.865 + 20.4612i) q^{71} +(-10.5780 - 10.5780i) q^{72} +(-19.7693 + 29.5868i) q^{73} +(25.2578 + 5.02408i) q^{74} +(1.11375 + 2.68883i) q^{76} +(67.8373 - 28.0991i) q^{77} +(67.8377 - 45.3277i) q^{78} +(-1.41599 + 7.11865i) q^{79} +(-43.4936 + 43.4936i) q^{81} +(6.86792 + 34.5274i) q^{82} +(-51.5218 + 124.385i) q^{83} +52.9469i q^{84} -31.5619 q^{86} +(41.0090 + 16.9865i) q^{87} +(-67.3563 + 13.3980i) q^{88} +(38.6522 + 38.6522i) q^{89} +(198.577 + 39.4995i) q^{91} +(-33.0905 - 49.5234i) q^{92} +(14.1023 + 34.0458i) q^{93} +(46.7533 - 19.3658i) q^{94} +(15.8678 - 79.7729i) q^{96} +(-65.9209 - 44.0470i) q^{97} +(27.8790 - 27.8790i) q^{98} +(-2.91482 - 14.6538i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} - 8 q^{6} - 8 q^{7} + 24 q^{8} - 16 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 - 8 * q^6 - 8 * q^7 + 24 * q^8 - 16 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} - 8 q^{6} - 8 q^{7} + 24 q^{8} - 16 q^{9} - 8 q^{11} - 48 q^{12} - 16 q^{13} + 8 q^{14} - 56 q^{18} - 64 q^{21} + 104 q^{22} + 56 q^{23} - 80 q^{24} + 176 q^{26} - 40 q^{27} - 152 q^{28} + 48 q^{29} + 24 q^{31} - 88 q^{32} - 136 q^{34} - 128 q^{36} - 32 q^{37} + 120 q^{38} + 48 q^{39} + 48 q^{41} - 16 q^{42} + 232 q^{43} + 120 q^{44} - 88 q^{46} - 192 q^{47} - 136 q^{48} + 16 q^{49} + 136 q^{51} + 384 q^{52} + 32 q^{53} + 8 q^{54} - 120 q^{56} - 24 q^{57} - 240 q^{58} - 48 q^{59} - 160 q^{61} + 168 q^{62} - 56 q^{63} - 64 q^{64} - 8 q^{66} - 272 q^{68} + 240 q^{69} + 40 q^{71} - 40 q^{72} - 48 q^{73} - 160 q^{74} + 80 q^{76} + 48 q^{77} + 400 q^{78} - 136 q^{79} - 424 q^{81} + 64 q^{82} + 264 q^{83} + 832 q^{86} - 208 q^{87} - 264 q^{88} + 160 q^{89} + 320 q^{91} - 24 q^{92} + 64 q^{93} + 32 q^{94} - 56 q^{96} - 48 q^{97} + 120 q^{98} - 224 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 - 8 * q^6 - 8 * q^7 + 24 * q^8 - 16 * q^9 - 8 * q^11 - 48 * q^12 - 16 * q^13 + 8 * q^14 - 56 * q^18 - 64 * q^21 + 104 * q^22 + 56 * q^23 - 80 * q^24 + 176 * q^26 - 40 * q^27 - 152 * q^28 + 48 * q^29 + 24 * q^31 - 88 * q^32 - 136 * q^34 - 128 * q^36 - 32 * q^37 + 120 * q^38 + 48 * q^39 + 48 * q^41 - 16 * q^42 + 232 * q^43 + 120 * q^44 - 88 * q^46 - 192 * q^47 - 136 * q^48 + 16 * q^49 + 136 * q^51 + 384 * q^52 + 32 * q^53 + 8 * q^54 - 120 * q^56 - 24 * q^57 - 240 * q^58 - 48 * q^59 - 160 * q^61 + 168 * q^62 - 56 * q^63 - 64 * q^64 - 8 * q^66 - 272 * q^68 + 240 * q^69 + 40 * q^71 - 40 * q^72 - 48 * q^73 - 160 * q^74 + 80 * q^76 + 48 * q^77 + 400 * q^78 - 136 * q^79 - 424 * q^81 + 64 * q^82 + 264 * q^83 + 832 * q^86 - 208 * q^87 - 264 * q^88 + 160 * q^89 + 320 * q^91 - 24 * q^92 + 64 * q^93 + 32 * q^94 - 56 * q^96 - 48 * q^97 + 120 * q^98 - 224 * q^99

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