LMFDB - Embedded newform 425.3.u.b.326.1

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			326.1
Root			$0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	425.326
Dual form			425.3.u.b.176.1

$q$-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 $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

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

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	−0.668459	−	0.743749i	$-0.733046\pi$
$2$	−1.23044	+	0.509666i	−0.615221	+	0.254833i	0.0532379	+	0.998582i	$0.483046\pi$
$3$	2.63099	+	0.523336i	0.876995	+	0.174445i	0.613004	−	0.790080i	$-0.289961\pi$
$3$	2.63099	+	0.523336i	0.876995	+	0.174445i	0.263991	+	0.964525i	$0.414961\pi$
$4$	−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	0.291666	+	0.956520i	$0.405790\pi$
$7$	−4.92562	+	7.37170i	−0.703659	+	1.05310i	−0.995325	+	0.0965803i	$0.969210\pi$
$8$	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	−0.982077	−	0.188479i	$-0.939644\pi$
$11$	−1.61572	−	8.12279i	−0.146884	−	0.738436i	0.835193	−	0.549957i	$-0.185356\pi$
$12$	−4.96553	+	3.31786i	−0.413794	+	0.276488i
$13$	−16.1480	−	16.1480i	−1.24216	−	1.24216i	−0.959105	−	0.283051i	$-0.908654\pi$
$13$	−16.1480	−	16.1480i	−1.24216	−	1.24216i	−0.283051	−	0.959105i	$-0.591346\pi$
$14$	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	−0.414241	−	0.910167i	$-0.635953\pi$
$19$	−1.20778	+	0.500280i	−0.0635675	+	0.0263305i	0.350673	+	0.936498i	$0.385953\pi$
$20$		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	0.411735	−	0.911303i	$-0.364923\pi$
$23$	26.2400	−	5.21946i	1.14087	−	0.226933i	0.729135	+	0.684370i	$0.239923\pi$
$24$	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	−0.295268	−	0.955414i	$-0.595409\pi$
$29$	13.7583	−	9.19303i	0.474425	−	0.317001i	0.769694	+	0.638414i	$0.220409\pi$
$30$		0			0
$31$	2.68003	−	13.4734i	0.0864526	−	0.434627i	−0.913181	−	0.407555i	$-0.866382\pi$
$31$	2.68003	−	13.4734i	0.0864526	−	0.434627i	0.999633	−	0.0270721i	$-0.00861839\pi$
$32$	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	−0.0679693	−	0.997687i	$-0.521652\pi$
$37$	−18.9648	−	3.77234i	−0.512563	−	0.101955i	−0.444594	+	0.895732i	$0.646652\pi$
$38$	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	−0.966175	−	0.257888i	$-0.916973\pi$
$41$	−14.6853	+	21.9781i	−0.358178	+	0.536051i	0.607997	+	0.793939i	$0.291973\pi$
$42$	12.1214	−	29.2636i	0.288604	−	0.696752i
$43$	21.8944	+	9.06895i	0.509172	+	0.210906i	0.622453	−	0.782657i	$-0.286136\pi$
$43$	21.8944	+	9.06895i	0.509172	+	0.210906i	−0.113281	+	0.993563i	$0.536136\pi$
$44$	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	0.360932	−	0.932592i	$-0.382459\pi$
$47$	−26.8680	−	26.8680i	−0.571660	−	0.571660i	−0.932592	+	0.360932i	$0.882459\pi$
$48$	−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	−0.615533	−	0.788111i	$-0.711059\pi$
$53$	−26.1557	+	10.8340i	−0.493503	+	0.204416i	0.122031	+	0.992526i	$0.461059\pi$
$54$	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	−0.827544	−	0.561401i	$-0.810263\pi$
$59$	9.12070	−	22.0193i	0.154588	−	0.373209i	0.982132	+	0.188192i	$0.0602627\pi$
$60$		0			0
$61$	−42.9373	−	28.6898i	−0.703890	−	0.470324i	0.151401	−	0.988472i	$-0.451622\pi$
$61$	−42.9373	−	28.6898i	−0.703890	−	0.470324i	−0.855291	+	0.518148i	$0.826622\pi$
$62$	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	$-0.823810\pi$
$67$		−	70.4415i		−	1.05137i	0.850681	−	0.525683i	$-0.176190\pi$
$68$	−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	−0.592883	−	0.805289i	$-0.702010\pi$
$71$	−102.865	−	20.4612i	−1.44881	−	0.288185i	−0.855923	+	0.517104i	$0.827010\pi$
$72$	−10.5780	+	10.5780i	−0.146916	+	0.146916i
$73$	−19.7693	−	29.5868i	−0.270812	−	0.405299i	0.670990	−	0.741466i	$-0.265869\pi$
$73$	−19.7693	−	29.5868i	−0.270812	−	0.405299i	−0.941802	+	0.336167i	$0.890869\pi$
$74$	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	0.970788	−	0.239939i	$-0.0771275\pi$
$79$	−1.41599	−	7.11865i	−0.0179239	−	0.0901095i	−0.988712	+	0.149830i	$0.952127\pi$
$80$		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	−0.850830	−	0.525441i	$-0.823901\pi$
$83$	−51.5218	−	124.385i	−0.620745	−	1.49861i	0.230085	−	0.973170i	$-0.426099\pi$
$84$		−	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	−0.455792	−	0.890086i	$-0.650644\pi$
$89$	38.6522	−	38.6522i	0.434294	−	0.434294i	0.890086	+	0.455792i	$0.150644\pi$
$90$		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	−0.846857	−	0.531820i	$-0.821508\pi$
$97$	−65.9209	+	44.0470i	−0.679597	+	0.454092i	0.167260	+	0.985913i	$0.446508\pi$
$98$	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	$-0.754841\pi$
$101$		−	140.647i		−	1.39254i	0.717779	−	0.696271i	$-0.245159\pi$
$102$	−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	0.589064	−	0.808086i	$-0.299497\pi$
$107$	−40.9741	−	61.3221i	−0.382936	−	0.573104i	−0.972000	+	0.234983i	$0.924497\pi$
$108$	63.2818	−	12.5875i	0.585942	−	0.116551i
$109$	−116.798	+	174.800i	−1.07154	+	1.60367i	−0.315770	+	0.948836i	$0.602263\pi$
$109$	−116.798	+	174.800i	−1.07154	+	1.60367i	−0.755770	+	0.654837i	$0.772737\pi$
$110$		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	0.881208	+	0.472729i	$0.156731\pi$
$113$	28.0222	+	140.877i	0.247984	+	1.24670i	−0.633224	+	0.773969i	$0.718269\pi$
$114$	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	0.672687	+	0.739927i	$0.265140\pi$
$127$	−41.4251	+	100.009i	−0.326182	+	0.787472i	−0.998869	+	0.0475454i	$0.984860\pi$
$128$	−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	−0.813788	−	0.581162i	$-0.802598\pi$
$131$	−77.0656	+	51.4936i	−0.588287	+	0.393081i	0.225501	+	0.974243i	$0.427598\pi$
$132$	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	0.302671	−	0.953095i	$-0.402122\pi$
$139$	30.2420	+	6.01550i	0.217568	+	0.0432770i	−0.0851025	+	0.996372i	$0.527122\pi$
$140$		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	0.780988	−	0.624546i	$-0.214716\pi$
$149$	23.3099	+	23.3099i	0.156443	+	0.156443i	−0.624546	+	0.780988i	$0.714716\pi$
$150$		0			0
$151$	−53.9466	−	130.239i	−0.357262	−	0.862507i	−0.995683	−	0.0928198i	$-0.970412\pi$
$151$	−53.9466	−	130.239i	−0.357262	−	0.862507i	0.638421	−	0.769688i	$-0.279588\pi$
$152$			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	−0.411902	−	0.911228i	$-0.635135\pi$
$157$	78.3942	−	78.3942i	0.499326	−	0.499326i	0.911228	+	0.411902i	$0.135135\pi$
$158$	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	0.897390	−	0.441238i	$-0.145461\pi$
$163$	135.804	+	90.7416i	0.833156	+	0.556697i	−0.0642345	+	0.997935i	$0.520461\pi$
$164$	−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	0.752476	+	0.658620i	$0.228859\pi$
$167$	−32.5256	+	163.517i	−0.194764	+	0.979145i	−0.947240	+	0.320525i	$0.896141\pi$
$168$	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	0.147479	−	0.989065i	$-0.452884\pi$
$173$	−16.3948	−	3.26113i	−0.0947676	−	0.0188504i	−0.242246	+	0.970215i	$0.577884\pi$
$174$	−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	0.280487	−	0.959858i	$-0.409504\pi$
$179$	−35.7824	−	14.8215i	−0.199901	−	0.0828019i	−0.480388	+	0.877056i	$0.659504\pi$
$180$		0			0
$181$	8.42674	+	42.3641i	0.0465566	+	0.234056i	0.997057	−	0.0766687i	$-0.0244284\pi$
$181$	8.42674	+	42.3641i	0.0465566	+	0.234056i	−0.950500	+	0.310724i	$0.899428\pi$
$182$	−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	−0.929658	−	0.368424i	$-0.879898\pi$
$191$	−107.196	+	107.196i	−0.561234	+	0.561234i	0.368424	+	0.929658i	$0.379898\pi$
$192$	−72.9320	−	109.151i	−0.379854	−	0.568492i
$193$	201.713	−	40.1233i	1.04515	−	0.207893i	0.357482	−	0.933920i	$-0.383636\pi$
$193$	201.713	−	40.1233i	1.04515	−	0.207893i	0.687666	+	0.726028i	$0.258636\pi$
$194$	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	0.223835	−	0.974627i	$-0.428142\pi$
$197$	−116.416	−	77.7868i	−0.590945	−	0.394857i	−0.814780	+	0.579770i	$0.803142\pi$
$198$	−3.88201	−	19.5162i	−0.0196061	−	0.0985667i
$199$	−123.283	+	82.3749i	−0.619511	+	0.413944i	−0.825334	−	0.564645i	$-0.809013\pi$
$199$	−123.283	+	82.3749i	−0.619511	+	0.413944i	0.205823	+	0.978589i	$0.434013\pi$
$200$		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	−0.457660	−	0.889127i	$-0.651312\pi$
$211$	113.713	−	170.184i	0.538925	−	0.806559i	0.996585	+	0.0825683i	$0.0263123\pi$
$212$	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	−0.128629	−	0.991693i	$-0.541058\pi$
$223$	107.408	−	44.4897i	0.481649	−	0.199506i	0.610278	+	0.792187i	$0.291058\pi$
$224$	−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	0.147816	−	0.989015i	$-0.452776\pi$
$227$	150.469	−	29.9302i	0.662859	−	0.131851i	0.515044	+	0.857164i	$0.327776\pi$
$228$	4.33742	−	6.49140i	0.0190238	−	0.0284711i
$229$	3.69064	−	8.91000i	0.0161164	−	0.0389083i	−0.915617	−	0.402053i	$-0.868297\pi$
$229$	3.69064	−	8.91000i	0.0161164	−	0.0389083i	0.931733	+	0.363144i	$0.118297\pi$
$230$		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	−0.391960	+	0.919982i	$0.628203\pi$
$233$	−324.315	+	216.700i	−1.39191	+	0.930044i	−0.999949	+	0.0100614i	$0.996797\pi$
$234$	−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	0.469614	−	0.882872i	$-0.344393\pi$
$241$	136.315	+	27.1147i	0.565621	+	0.112509i	0.0960065	+	0.995381i	$0.469393\pi$
$242$	−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	0.943922	−	0.330168i	$-0.107106\pi$
$251$	154.052	+	154.052i	0.613754	+	0.613754i	−0.330168	+	0.943922i	$0.607106\pi$
$252$	−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	0.546578	−	0.837408i	$-0.315930\pi$
$257$	391.977	−	162.362i	1.52520	−	0.631760i	0.978626	+	0.205648i	$0.0659301\pi$
$258$	−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	−0.785120	−	0.619344i	$-0.787399\pi$
$263$	54.7003	−	132.058i	0.207986	−	0.502122i	0.993106	+	0.117221i	$0.0373987\pi$
$264$	−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	−0.960614	−	0.277886i	$-0.910366\pi$
$269$	8.93614	−	44.9250i	0.0332199	−	0.167008i	0.993834	+	0.110878i	$0.0353663\pi$
$270$		0			0
$271$		−	329.809i		−	1.21701i	−0.793550	−	0.608504i	$-0.791770\pi$
$271$		−	329.809i		−	1.21701i	0.793550	−	0.608504i	$-0.208230\pi$
$272$	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	0.432509	−	0.901629i	$-0.357628\pi$
$277$	−156.783	−	234.642i	−0.566002	−	0.847082i	−0.998511	+	0.0545479i	$0.982628\pi$
$278$	−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	0.619556	−	0.784953i	$-0.287313\pi$
$281$	141.231	+	58.4999i	0.502603	+	0.208185i	−0.116953	+	0.993137i	$0.537313\pi$
$282$	112.872	+	75.4189i	0.400257	+	0.267443i
$283$	−62.0182	−	311.786i	−0.219145	−	1.10172i	−0.921049	−	0.389447i	$-0.872666\pi$
$283$	−62.0182	−	311.786i	−0.219145	−	1.10172i	0.701904	−	0.712272i	$-0.252334\pi$
$284$	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	−0.659050	−	0.752099i	$-0.729042\pi$
$293$	27.2633	−	27.2633i	0.0930488	−	0.0930488i	0.752099	+	0.659050i	$0.229042\pi$
$294$	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	0.957074	+	0.289843i	$0.0936031\pi$
$311$	267.024	+	399.630i	0.858598	+	1.28498i	−0.0984763	+	0.995139i	$0.531397\pi$
$312$	−498.225	+	99.1031i	−1.59688	+	0.317638i
$313$	49.2742	−	73.7441i	0.157426	−	0.235604i	−0.744369	−	0.667768i	$-0.767250\pi$
$313$	49.2742	−	73.7441i	0.157426	−	0.235604i	0.901795	+	0.432164i	$0.142250\pi$
$314$	−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	0.999985	−	0.00544574i	$-0.00173344\pi$
$317$	23.4692	+	117.988i	0.0740353	+	0.372201i	−0.925950	+	0.377647i	$0.876733\pi$
$318$	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	−0.854157	−	0.520015i	$-0.825926\pi$
$331$	38.9023	−	93.9184i	0.117530	−	0.283741i	0.971687	+	0.236274i	$0.0759262\pi$
$332$	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	−0.408639	−	0.912696i	$-0.633996\pi$
$337$	107.223	−	539.044i	0.318168	−	1.59954i	0.726807	−	0.686842i	$-0.241004\pi$
$338$	−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	−0.977535	−	0.210771i	$-0.932403\pi$
$347$	−141.826	+	212.258i	−0.408722	+	0.611695i	0.568814	+	0.822466i	$0.307403\pi$
$348$	−37.8162	+	91.2964i	−0.108667	+	0.262346i
$349$	−513.215	−	212.580i	−1.47053	−	0.609113i	−0.503549	−	0.863967i	$-0.667973\pi$
$349$	−513.215	−	212.580i	−1.47053	−	0.609113i	−0.966980	+	0.254854i	$0.917973\pi$
$350$		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	0.984984	+	0.172648i	$0.0552323\pi$
$353$	408.644	+	408.644i	1.15763	+	1.15763i	0.172648	+	0.984984i	$0.444768\pi$
$354$	−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	−0.593634	−	0.804735i	$-0.702307\pi$
$359$	−159.526	+	66.0778i	−0.444362	+	0.184061i	0.149272	+	0.988796i	$0.452307\pi$
$360$		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	0.578483	−	0.815694i	$-0.303645\pi$
$367$	16.9759	+	11.3429i	0.0462558	+	0.0309071i	−0.532227	+	0.846601i	$0.678645\pi$
$368$	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	$0.376961\pi$
$373$			690.960i			1.85244i	−0.376983	+	0.926220i	$0.623039\pi$
$374$	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	0.680893	−	0.732383i	$-0.261592\pi$
$379$	−97.1405	−	145.381i	−0.256308	−	0.383591i	−0.937200	+	0.348792i	$0.886592\pi$
$380$		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	−0.275574	−	0.961280i	$-0.588868\pi$
$383$	−440.512	−	182.466i	−1.15016	−	0.476412i	−0.874588	+	0.484868i	$0.838868\pi$
$384$	−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	0.994530	−	0.104453i	$-0.0333092\pi$
$389$	84.5808	+	204.196i	0.217431	+	0.524926i	−0.777098	+	0.629379i	$0.783309\pi$
$390$		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	−0.0433581	−	0.999060i	$-0.513806\pi$
$397$	118.666	−	23.6042i	0.298908	−	0.0594565i	0.342266	+	0.939603i	$0.388806\pi$
$398$	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	0.963026	−	0.269409i	$-0.0868282\pi$
$401$	434.146	+	290.087i	1.08266	+	0.723409i	0.119633	+	0.992818i	$0.461828\pi$
$402$	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	0.964571	+	0.263822i	$0.0849832\pi$
$419$	73.0669	+	367.332i	0.174384	+	0.876687i	−0.790187	+	0.612865i	$0.790017\pi$
$420$		0			0
$421$	−273.997	−	273.997i	−0.650824	−	0.650824i	0.302367	−	0.953192i	$-0.402223\pi$
$421$	−273.997	−	273.997i	−0.650824	−	0.650824i	−0.953192	+	0.302367i	$0.902223\pi$
$422$	−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	−0.116151	−	0.993232i	$-0.537056\pi$
$431$	67.5084	−	13.4283i	0.156632	−	0.0311561i	0.272783	+	0.962075i	$0.412056\pi$
$432$	34.4381	−	51.5402i	0.0797177	−	0.119306i
$433$	104.262	−	251.710i	0.240790	−	0.581317i	−0.756572	−	0.653910i	$-0.773127\pi$
$433$	104.262	−	251.710i	0.240790	−	0.581317i	0.997362	+	0.0725929i	$0.0231274\pi$
$434$	−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	−0.999611	−	0.0278730i	$-0.991127\pi$
$439$	−28.7213	+	144.392i	−0.0654244	+	0.328910i	0.934187	+	0.356783i	$0.116127\pi$
$440$		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	−0.206687	−	0.978407i	$-0.566268\pi$
$449$	348.576	−	521.681i	0.776339	−	1.16187i	0.983026	−	0.183466i	$-0.0587318\pi$
$450$		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	0.971173	−	0.238375i	$-0.0766147\pi$
$457$	52.9634	+	127.865i	0.115894	+	0.279792i	−0.855280	+	0.518167i	$0.826615\pi$
$458$			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	−0.524884	−	0.851174i	$-0.675891\pi$
$461$	−135.609	+	56.1709i	−0.294162	+	0.121846i	0.230722	+	0.973020i	$0.425891\pi$
$462$	−257.287	−	51.1775i	−0.556898	−	0.110774i
$463$	−522.332	+	522.332i	−1.12815	+	1.12815i	−0.137669	+	0.990478i	$0.543961\pi$
$463$	−522.332	+	522.332i	−1.12815	+	1.12815i	−0.990478	+	0.137669i	$0.956039\pi$
$464$	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	−0.920714	−	0.390237i	$-0.872393\pi$
$467$	2.92741	−	7.06740i	0.00626855	−	0.0151336i	0.926983	+	0.375104i	$0.122393\pi$
$468$	−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	−0.655314	−	0.755357i	$-0.727464\pi$
$479$	−742.358	−	147.664i	−1.54981	−	0.308276i	−0.894493	+	0.447081i	$0.852464\pi$
$480$		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	0.978976	−	0.203977i	$-0.0653867\pi$
$487$	−1.72321	−	8.66318i	−0.00353843	−	0.0177889i	−0.982514	+	0.186188i	$0.940387\pi$
$488$	−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	−0.969426	−	0.245383i	$-0.921086\pi$
$491$	−224.608	−	542.252i	−0.457450	−	1.10438i	0.511976	−	0.859000i	$-0.328914\pi$
$492$		−	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	−0.304012	−	0.952668i	$-0.598326\pi$
$499$	−109.936	+	21.8676i	−0.220312	+	0.0438229i	0.0836997	+	0.996491i	$0.473326\pi$
$500$		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	0.883895	−	0.467686i	$-0.154912\pi$
$503$	397.401	+	265.535i	0.790061	+	0.527902i	−0.0938335	+	0.995588i	$0.529912\pi$
$504$	−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	$0.0741820\pi$
$509$			235.103i			0.461891i	−0.972967	+	0.230946i	$0.925818\pi$
$510$		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	−0.911840	−	0.410546i	$-0.865338\pi$
$521$	−118.016	−	593.308i	−0.226519	−	1.13879i	0.685321	−	0.728241i	$-0.259662\pi$
$522$	33.0564	−	22.0876i	0.0633265	−	0.0423134i
$523$	−721.650	−	721.650i	−1.37983	−	1.37983i	−0.844894	−	0.534934i	$-0.820336\pi$
$523$	−721.650	−	721.650i	−1.37983	−	1.37983i	−0.534934	−	0.844894i	$-0.679664\pi$
$524$	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	−0.732016	−	0.681288i	$-0.761420\pi$
$541$	110.903	−	557.546i	0.204996	−	1.03058i	0.937012	−	0.349297i	$-0.113580\pi$
$542$	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	0.512730	−	0.858550i	$-0.328634\pi$
$547$	359.860	+	71.5805i	0.657879	+	0.130860i	0.145148	+	0.989410i	$0.453634\pi$
$548$	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	0.826287	−	0.563249i	$-0.190449\pi$
$557$	146.512	+	146.512i	0.263038	+	0.263038i	−0.563249	+	0.826287i	$0.690449\pi$
$558$	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	−0.952074	−	0.305868i	$-0.901053\pi$
$563$	−793.273	+	328.584i	−1.40901	+	0.583631i	−0.456936	+	0.889499i	$0.651053\pi$
$564$	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	−0.781248	−	0.624221i	$-0.785416\pi$
$569$	120.952	−	292.003i	0.212569	−	0.513187i	0.993817	+	0.111034i	$0.0354164\pi$
$570$		0			0
$571$	224.810	+	150.213i	0.393713	+	0.263071i	0.736631	−	0.676294i	$-0.236415\pi$
$571$	224.810	+	150.213i	0.393713	+	0.263071i	−0.342918	+	0.939365i	$0.611415\pi$
$572$	−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	$0.0174421\pi$
$577$			63.2031i			0.109537i	−0.998499	+	0.0547687i	$0.982558\pi$
$578$	−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	−0.286812	−	0.957987i	$-0.592596\pi$
$587$	−685.040	−	283.753i	−1.16702	−	0.483395i	−0.880206	+	0.474592i	$0.842596\pi$
$588$	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	0.975360	−	0.220618i	$-0.0708075\pi$
$593$	76.8977	+	185.647i	0.129676	+	0.313065i	−0.845685	+	0.533683i	$0.820808\pi$
$594$		−	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	−0.212784	−	0.977099i	$-0.568253\pi$
$599$	457.825	−	457.825i	0.764316	−	0.764316i	0.977099	+	0.212784i	$0.0682529\pi$
$600$		0			0
$601$	703.378	−	139.911i	1.17035	−	0.232796i	0.428611	−	0.903489i	$-0.359003\pi$
$601$	703.378	−	139.911i	1.17035	−	0.232796i	0.741735	+	0.670693i	$0.234003\pi$
$602$	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	0.423695	−	0.905805i	$-0.360733\pi$
$607$	863.573	−	577.021i	1.42269	−	0.950612i	0.998996	−	0.0448067i	$-0.0142672\pi$
$608$	−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	0.999886	−	0.0150736i	$-0.00479825\pi$
$617$	372.249	+	557.109i	0.603320	+	0.902933i	−0.396566	+	0.918006i	$0.629798\pi$
$618$	−148.319	+	29.5024i	−0.239998	+	0.0477385i
$619$	−437.249	+	654.389i	−0.706379	+	1.05717i	0.288635	+	0.957439i	$0.406799\pi$
$619$	−437.249	+	654.389i	−0.706379	+	1.05717i	−0.995014	+	0.0997323i	$0.968201\pi$
$620$		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	−0.896221	−	0.443608i	$-0.853698\pi$
$631$	−767.465	+	317.894i	−1.21627	+	0.503794i	−0.320046	+	0.947402i	$0.603698\pi$
$632$	−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	−0.966050	−	0.258357i	$-0.916819\pi$
$641$	−703.209	+	469.870i	−1.09705	+	0.733026i	−0.131001	+	0.991382i	$0.541819\pi$
$642$	186.314	+	186.314i	0.290209	+	0.290209i
$643$	144.203	−	724.957i	0.224266	−	1.12746i	−0.690456	−	0.723375i	$-0.742590\pi$
$643$	144.203	−	724.957i	0.224266	−	1.12746i	0.914721	−	0.404085i	$-0.132410\pi$
$644$	−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	0.104507	−	0.994524i	$-0.466673\pi$
$653$	642.117	−	960.997i	0.983335	−	1.47166i	0.878827	−	0.477140i	$-0.158327\pi$
$654$	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	0.422645	−	0.906295i	$-0.361102\pi$
$659$	−318.726	−	318.726i	−0.483651	−	0.483651i	−0.906295	+	0.422645i	$0.861102\pi$
$660$		0			0
$661$	191.121	+	461.408i	0.289140	+	0.698045i	0.999986	−	0.00530241i	$-0.00168782\pi$
$661$	191.121	+	461.408i	0.289140	+	0.698045i	−0.710846	+	0.703347i	$0.751688\pi$
$662$			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	0.978247	−	0.207446i	$-0.0665151\pi$
$673$	781.320	+	522.061i	1.16095	+	0.775722i	0.182704	+	0.983168i	$0.441515\pi$
$674$	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	0.398386	+	0.917218i	$0.369570\pi$
$677$	−217.100	+	1091.43i	−0.320679	+	1.61216i	−0.719065	+	0.694943i	$0.755430\pi$
$678$	−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	−0.890804	−	0.454387i	$-0.849858\pi$
$683$	−1289.29	−	256.456i	−1.88769	−	0.375484i	−0.996882	+	0.0789027i	$0.974858\pi$
$684$	−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	0.987582	+	0.157103i	$0.0502154\pi$
$691$	93.4894	+	470.003i	0.135296	+	0.680178i	−0.852286	+	0.523075i	$0.824785\pi$
$692$	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	0.115796	−	0.993273i	$-0.463058\pi$
$701$	777.458	−	777.458i	1.10907	−	1.10907i	0.993273	−	0.115796i	$-0.0369420\pi$
$702$	−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	−0.210553	−	0.977583i	$-0.567526\pi$
$709$	433.937	−	289.947i	0.612041	−	0.408953i	0.822593	+	0.568630i	$0.192526\pi$
$710$		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	0.509612	−	0.860404i	$-0.329789\pi$
$719$	−345.349	−	516.851i	−0.480318	−	0.718847i	−0.989930	+	0.141557i	$0.954789\pi$
$720$		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	0.571250	−	0.820776i	$-0.306459\pi$
$727$	−181.405	−	181.405i	−0.249526	−	0.249526i	−0.820776	+	0.571250i	$0.806459\pi$
$728$	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	−0.517968	−	0.855400i	$-0.673311\pi$
$733$	−204.776	+	84.8211i	−0.279367	+	0.115718i	0.238600	+	0.971118i	$0.423311\pi$
$734$	−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	−0.828727	−	0.559653i	$-0.810935\pi$
$739$	113.071	−	272.978i	0.153006	−	0.369388i	0.981733	+	0.190265i	$0.0609346\pi$
$740$		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	−0.0609312	−	0.998142i	$-0.519407\pi$
$743$	622.570	−	415.988i	0.837914	−	0.559876i	0.898846	+	0.438265i	$0.144407\pi$
$744$	−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	−0.282003	−	0.959414i	$-0.590999\pi$
$751$	−683.178	−	135.892i	−0.909691	−	0.180949i	−0.627688	+	0.778465i	$0.715999\pi$
$752$	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	0.759626	−	0.650360i	$-0.225382\pi$
$757$	633.525	+	262.415i	0.836889	+	0.346651i	0.0772631	+	0.997011i	$0.475382\pi$
$758$	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	0.477718	−	0.878513i	$-0.341464\pi$
$761$	−305.005	−	305.005i	−0.400795	−	0.400795i	−0.878513	+	0.477718i	$0.841464\pi$
$762$	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	−0.481868	−	0.876244i	$-0.660041\pi$
$769$	303.275	−	303.275i	0.394376	−	0.394376i	0.876244	+	0.481868i	$0.160041\pi$
$770$		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	−0.863812	−	0.503814i	$-0.831930\pi$
$773$	79.8088	−	192.675i	0.103246	−	0.249257i	0.967058	+	0.254557i	$0.0819297\pi$
$774$	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	−0.981975	−	0.189009i	$-0.939473\pi$
$787$	−614.498	−	919.662i	−0.780811	−	1.16857i	0.201164	−	0.979558i	$-0.435527\pi$
$788$	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	0.937919	−	0.346853i	$-0.112750\pi$
$797$	23.4701	+	56.6619i	0.0294481	+	0.0710940i	−0.908471	+	0.417947i	$0.862750\pi$
$798$			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	0.898218	−	0.439551i	$-0.144862\pi$
$809$	676.209	+	451.829i	0.835858	+	0.558503i	−0.0623592	+	0.998054i	$0.519862\pi$
$810$		0			0
$811$	961.868	−	642.700i	1.18603	−	0.792478i	0.203587	−	0.979057i	$-0.434740\pi$
$811$	961.868	−	642.700i	1.18603	−	0.792478i	0.982440	+	0.186579i	$0.0597399\pi$
$812$	−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	0.997803	+	0.0662547i	$0.0211050\pi$
$821$	555.958	+	832.050i	0.677172	+	1.01346i	−0.320631	+	0.947204i	$0.603895\pi$
$822$	357.570	−	71.1252i	0.435000	−	0.0865270i
$823$	−30.1009	+	45.0492i	−0.0365746	+	0.0547378i	−0.849306	−	0.527900i	$-0.822979\pi$
$823$	−30.1009	+	45.0492i	−0.0365746	+	0.0547378i	0.812732	+	0.582638i	$0.197979\pi$
$824$	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	−0.998528	−	0.0542461i	$-0.982724\pi$
$827$	−80.0267	−	402.321i	−0.0967675	−	0.486483i	0.901760	−	0.432237i	$-0.142276\pi$
$828$	89.3418	−	59.6963i	0.107901	−	0.0720970i
$829$	−153.097	−	153.097i	−0.184677	−	0.184677i	0.608713	−	0.793390i	$-0.291686\pi$
$829$	−153.097	−	153.097i	−0.184677	−	0.184677i	−0.793390	+	0.608713i	$0.791686\pi$
$830$		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	−0.358106	−	0.933681i	$-0.616577\pi$
$839$	−278.253	+	55.3480i	−0.331648	+	0.0659690i	0.0264576	+	0.999650i	$0.491577\pi$
$840$		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	0.511615	−	0.859215i	$-0.329047\pi$
$853$	559.124	+	111.217i	0.655479	+	0.130383i	0.143864	+	0.989598i	$0.454047\pi$
$854$	−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	−0.0945445	−	0.995521i	$-0.530139\pi$
$857$	738.200	−	1104.79i	0.861377	−	1.28914i	0.955922	−	0.293622i	$-0.0948605\pi$
$858$	258.581	−	624.269i	0.301376	−	0.727586i
$859$	260.316	+	107.826i	0.303046	+	0.125526i	0.529024	−	0.848607i	$-0.322558\pi$
$859$	260.316	+	107.826i	0.303046	+	0.125526i	−0.225979	+	0.974132i	$0.572558\pi$
$860$		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	0.680887	−	0.732388i	$-0.261594\pi$
$863$	−44.4457	−	44.4457i	−0.0515014	−	0.0515014i	−0.732388	+	0.680887i	$0.761594\pi$
$864$	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	0.323139	−	0.946351i	$-0.395262\pi$
$877$	−374.931	−	250.521i	−0.427515	−	0.285657i	−0.750655	+	0.660695i	$0.770262\pi$
$878$	−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	−0.704452	−	0.709752i	$-0.748807\pi$
$881$	192.046	−	965.483i	0.217987	−	1.09589i	0.922439	−	0.386143i	$-0.126193\pi$
$882$	−27.2192	−	65.7130i	−0.0308608	−	0.0745046i
$883$		−	908.452i		−	1.02882i	−0.857543	−	0.514412i	$-0.828010\pi$
$883$		−	908.452i		−	1.02882i	0.857543	−	0.514412i	$-0.171990\pi$
$884$	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	0.0546769	−	0.998504i	$-0.482587\pi$
$887$	−245.627	−	48.8583i	−0.276919	−	0.0550827i	−0.331596	+	0.943421i	$0.607587\pi$
$888$	−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	−0.995281	−	0.0970321i	$-0.969065\pi$
$907$	−1703.05	+	338.757i	−1.87767	+	0.373492i	−0.882387	+	0.470524i	$0.844065\pi$
$908$	−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	0.914401	+	0.404811i	$0.132663\pi$
$911$	1492.51	+	997.265i	1.63832	+	1.09469i	0.723922	+	0.689882i	$0.242337\pi$
$912$	−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	0.794510	+	0.607251i	$0.207728\pi$
$929$	272.070	+	1367.79i	0.292863	+	1.47232i	−0.501646	+	0.865073i	$0.667272\pi$
$930$		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	−0.281643	−	0.959519i	$-0.590879\pi$
$937$	185.233	−	76.7261i	0.197687	−	0.0818848i	0.479331	+	0.877634i	$0.340879\pi$
$938$	−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	−0.909899	−	0.414830i	$-0.863841\pi$
$941$	−1497.87	+	297.945i	−1.59179	+	0.316626i	−0.681889	+	0.731456i	$0.738841\pi$
$942$	−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	−0.0221273	−	0.999755i	$-0.507044\pi$
$947$	845.726	−	565.096i	0.893058	−	0.596723i	0.915186	+	0.403033i	$0.132044\pi$
$948$	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	0.964931	+	0.262502i	$0.0845477\pi$
$967$	452.787	+	1093.12i	0.468239	+	1.13043i	−0.496692	+	0.867927i	$0.665452\pi$
$968$		−	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	−0.104160	−	0.994561i	$-0.533215\pi$
$971$	510.211	−	211.336i	0.525449	−	0.217648i	0.629608	+	0.776913i	$0.283215\pi$
$972$	−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	−0.846781	−	0.531942i	$-0.821462\pi$
$977$	125.177	−	302.204i	0.128124	−	0.309318i	0.974904	+	0.222624i	$0.0714623\pi$
$978$	−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	0.735359	+	0.677678i	$0.237014\pi$
$983$	−199.903	+	1004.98i	−0.203360	+	1.02236i	−0.938719	+	0.344683i	$0.887986\pi$
$984$	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	0.697575	−	0.716512i	$-0.254262\pi$
$991$	−229.264	−	343.118i	−0.231346	−	0.346234i	−0.928921	+	0.370278i	$0.879262\pi$
$992$	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	−0.884035	−	0.467421i	$-0.845183\pi$
$997$	−245.429	−	1233.85i	−0.246167	−	1.23757i	0.637867	−	0.770146i	$-0.279817\pi$
$998$	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.326.1		8
5.2	odd	4		425.3.t.a.224.1		8
5.3	odd	4		425.3.t.c.224.1		8
5.4	even	2		17.3.e.a.3.1	✓	8
15.14	odd	2		153.3.p.b.37.1		8
17.6	odd	16	inner	425.3.u.b.176.1		8
20.19	odd	2		272.3.bh.c.241.1		8
85.4	even	4		289.3.e.m.65.1		8
85.9	even	8		289.3.e.b.158.1		8
85.14	odd	16		289.3.e.k.214.1		8
85.19	even	8		289.3.e.l.131.1		8
85.23	even	16		425.3.t.a.74.1		8
85.24	odd	16		289.3.e.i.249.1		8
85.29	odd	16		289.3.e.b.75.1		8
85.39	odd	16		289.3.e.d.75.1		8
85.44	odd	16		289.3.e.m.249.1		8
85.49	even	8		289.3.e.k.131.1		8
85.54	odd	16		289.3.e.l.214.1		8
85.57	even	16		425.3.t.c.74.1		8
85.59	even	8		289.3.e.d.158.1		8
85.64	even	4		289.3.e.i.65.1		8
85.74	odd	16		17.3.e.a.6.1	yes	8
85.79	odd	16		289.3.e.c.40.1		8
85.84	even	2		289.3.e.c.224.1		8
255.74	even	16		153.3.p.b.91.1		8
340.159	even	16		272.3.bh.c.193.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.3.1	✓	8	5.4	even	2
17.3.e.a.6.1	yes	8	85.74	odd	16
153.3.p.b.37.1		8	15.14	odd	2
153.3.p.b.91.1		8	255.74	even	16
272.3.bh.c.193.1		8	340.159	even	16
272.3.bh.c.241.1		8	20.19	odd	2
289.3.e.b.75.1		8	85.29	odd	16
289.3.e.b.158.1		8	85.9	even	8
289.3.e.c.40.1		8	85.79	odd	16
289.3.e.c.224.1		8	85.84	even	2
289.3.e.d.75.1		8	85.39	odd	16
289.3.e.d.158.1		8	85.59	even	8
289.3.e.i.65.1		8	85.64	even	4
289.3.e.i.249.1		8	85.24	odd	16
289.3.e.k.131.1		8	85.49	even	8
289.3.e.k.214.1		8	85.14	odd	16
289.3.e.l.131.1		8	85.19	even	8
289.3.e.l.214.1		8	85.54	odd	16
289.3.e.m.65.1		8	85.4	even	4
289.3.e.m.249.1		8	85.44	odd	16
425.3.t.a.74.1		8	85.23	even	16
425.3.t.a.224.1		8	5.2	odd	4
425.3.t.c.74.1		8	85.57	even	16
425.3.t.c.224.1		8	5.3	odd	4
425.3.u.b.176.1		8	17.6	odd	16	inner
425.3.u.b.326.1		8	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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
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

Introduction

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