LMFDB - Embedded newform 425.3.t.c.224.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(24,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 11])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.24"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.t (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,8,0,0,-8,-8,40,16,0,-8,-40,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			224.1
Root			$0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	425.224
Dual form			425.3.t.c.74.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.509666 + 1.23044i) q^{2} +(-0.523336 + 2.63099i) q^{3} +(1.57420 - 1.57420i) q^{4} +(-3.50400 + 0.696990i) q^{6} +(7.37170 + 4.92562i) q^{7} +(7.66104 + 3.17331i) q^{8} +(1.66671 + 0.690373i) q^{9} +(-1.61572 - 8.12279i) q^{11} +(3.31786 + 4.96553i) q^{12} +(16.1480 - 16.1480i) q^{13} +(-2.30358 + 11.5809i) q^{14} +2.13880i q^{16} +(-6.50562 - 15.7060i) q^{17} +2.40265i q^{18} +(1.20778 - 0.500280i) q^{19} +(-16.8171 + 16.8171i) q^{21} +(9.17115 - 6.12797i) q^{22} +(5.21946 + 26.2400i) q^{23} +(-12.3582 + 18.4954i) q^{24} +(28.0993 + 11.6391i) q^{26} +(-16.1016 + 24.0978i) q^{27} +(19.3584 - 3.85063i) q^{28} +(-13.7583 + 9.19303i) q^{29} +(2.68003 - 13.4734i) q^{31} +(28.0125 - 11.6032i) q^{32} +22.2165 q^{33} +(16.0096 - 16.0096i) q^{34} +(3.71051 - 1.53694i) q^{36} +(-3.77234 + 18.9648i) q^{37} +(1.23113 + 1.23113i) q^{38} +(34.0344 + 50.9361i) q^{39} +(-14.6853 + 21.9781i) q^{41} +(-29.2636 - 12.1214i) q^{42} +(-9.06895 + 21.8944i) q^{43} +(-15.3303 - 10.2434i) q^{44} +(-29.6266 + 19.7959i) q^{46} +(-26.8680 + 26.8680i) q^{47} +(-5.62714 - 1.11931i) q^{48} +(11.3288 + 27.3503i) q^{49} +(44.7268 - 8.89671i) q^{51} -50.8404i q^{52} +(-10.8340 - 26.1557i) q^{53} +(-37.8574 - 7.53030i) q^{54} +(40.8445 + 61.1281i) q^{56} +(0.684154 + 3.43947i) q^{57} +(-18.3236 - 12.2435i) q^{58} +(-9.12070 + 22.0193i) q^{59} +(-42.9373 - 28.6898i) q^{61} +(17.9442 - 3.56932i) q^{62} +(8.88596 + 13.2988i) q^{63} +(34.6035 + 34.6035i) q^{64} +(11.3230 + 27.3362i) q^{66} -70.4415 q^{67} +(-34.9654 - 14.4831i) q^{68} -71.7687 q^{69} +(-102.865 - 20.4612i) q^{71} +(10.5780 + 10.5780i) q^{72} +(29.5868 - 19.7693i) q^{73} +(-25.2578 + 5.02408i) q^{74} +(1.11375 - 2.68883i) q^{76} +(28.0991 - 67.8373i) q^{77} +(-45.3277 + 67.8377i) q^{78} +(1.41599 + 7.11865i) q^{79} +(-43.4936 - 43.4936i) q^{81} +(-34.5274 - 6.86792i) q^{82} +(124.385 - 51.5218i) q^{83} +52.9469i q^{84} -31.5619 q^{86} +(-16.9865 - 41.0090i) q^{87} +(13.3980 - 67.3563i) q^{88} +(-38.6522 + 38.6522i) q^{89} +(198.577 - 39.4995i) q^{91} +(49.5234 + 33.0905i) q^{92} +(34.0458 + 14.1023i) q^{93} +(-46.7533 - 19.3658i) q^{94} +(15.8678 + 79.7729i) q^{96} +(44.0470 + 65.9209i) 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} + 40 q^{8} + 16 q^{9} - 8 q^{11} - 40 q^{12} + 16 q^{13} - 8 q^{14} - 64 q^{21} - 56 q^{22} - 40 q^{23} + 80 q^{24} + 176 q^{26} - 16 q^{27} - 56 q^{28} - 48 q^{29}+ \cdots + 224 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^3 - 8 * q^6 - 8 * q^7 + 40 * q^8 + 16 * q^9 - 8 * q^11 - 40 * q^12 + 16 * q^13 - 8 * q^14 - 64 * q^21 - 56 * q^22 - 40 * q^23 + 80 * q^24 + 176 * q^26 - 16 * q^27 - 56 * q^28 - 48 * q^29 + 24 * q^31 + 88 * q^32 + 96 * q^33 + 136 * q^34 - 128 * q^36 + 128 * q^37 + 120 * q^38 - 48 * q^39 + 48 * q^41 + 128 * q^42 + 112 * q^43 - 120 * q^44 - 88 * q^46 - 192 * q^47 + 8 * q^48 - 16 * q^49 + 136 * q^51 - 128 * q^53 - 8 * q^54 - 120 * q^56 - 72 * q^57 - 32 * q^58 + 48 * q^59 - 160 * q^61 - 56 * q^62 - 168 * q^63 + 64 * q^64 - 8 * q^66 - 336 * q^67 - 272 * q^68 - 240 * q^69 + 40 * q^71 + 40 * q^72 - 48 * q^73 + 160 * q^74 + 80 * q^76 + 80 * q^77 + 304 * q^78 + 136 * q^79 - 424 * q^81 + 136 * q^82 + 336 * q^83 + 832 * q^86 + 80 * q^87 + 320 * q^88 - 160 * q^89 + 320 * q^91 + 184 * q^92 + 208 * q^93 - 32 * q^94 - 56 * q^96 + 104 * q^97 - 120 * q^98 + 224 * q^99

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 $

$2$	0.509666	+	1.23044i	0.254833	+	0.615221i	0.998582	−	0.0532379i	$-0.0169542\pi$
$2$	0.509666	+	1.23044i	0.254833	+	0.615221i	−0.743749	+	0.668459i	$0.766954\pi$
$3$	−0.523336	+	2.63099i	−0.174445	+	0.876995i	0.790080	+	0.613004i	$0.210039\pi$
$3$	−0.523336	+	2.63099i	−0.174445	+	0.876995i	−0.964525	+	0.263991i	$0.914961\pi$
$4$	1.57420	−	1.57420i	0.393549	−	0.393549i
$5$		0			0
$5$		0			0
$6$	−3.50400	+	0.696990i	−0.584001	+	0.116165i
$7$	7.37170	+	4.92562i	1.05310	+	0.703659i	0.956520	−	0.291666i	$-0.0942095\pi$
$7$	7.37170	+	4.92562i	1.05310	+	0.703659i	0.0965803	+	0.995325i	$0.469210\pi$
$8$	7.66104	+	3.17331i	0.957631	+	0.396664i
$9$	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	$-0.185356\pi$
$12$	3.31786	+	4.96553i	0.276488	+	0.413794i
$13$	16.1480	−	16.1480i	1.24216	−	1.24216i	0.283051	−	0.959105i	$-0.408654\pi$
$13$	16.1480	−	16.1480i	1.24216	−	1.24216i	0.959105	−	0.283051i	$-0.0913464\pi$
$14$	−2.30358	+	11.5809i	−0.164541	+	0.827205i
$15$		0			0
$16$			2.13880i			0.133675i
$17$	−6.50562	−	15.7060i	−0.382683	−	0.923880i
$17$	−6.50562	−	15.7060i	−0.382683	−	0.923880i
$18$			2.40265i			0.133480i
$19$	1.20778	−	0.500280i	0.0635675	−	0.0263305i	−0.350673	−	0.936498i	$-0.614047\pi$
$19$	1.20778	−	0.500280i	0.0635675	−	0.0263305i	0.414241	+	0.910167i	$0.364047\pi$
$20$		0			0
$21$	−16.8171	+	16.8171i	−0.800814	+	0.800814i
$22$	9.17115	−	6.12797i	0.416870	−	0.278544i
$23$	5.21946	+	26.2400i	0.226933	+	1.14087i	0.911303	+	0.411735i	$0.135077\pi$
$23$	5.21946	+	26.2400i	0.226933	+	1.14087i	−0.684370	+	0.729135i	$0.739923\pi$
$24$	−12.3582	+	18.4954i	−0.514926	+	0.770642i
$25$		0			0
$26$	28.0993	+	11.6391i	1.08074	+	0.447658i
$27$	−16.1016	+	24.0978i	−0.596356	+	0.892510i
$28$	19.3584	−	3.85063i	0.691372	−	0.137522i
$29$	−13.7583	+	9.19303i	−0.474425	+	0.317001i	−0.769694	−	0.638414i	$-0.779591\pi$
$29$	−13.7583	+	9.19303i	−0.474425	+	0.317001i	0.295268	+	0.955414i	$0.404591\pi$
$30$		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	$-0.00861839\pi$
$32$	28.0125	−	11.6032i	0.875391	−	0.362599i
$33$	22.2165			0.673228
$34$	16.0096	−	16.0096i	0.470870	−	0.470870i
$35$		0			0
$36$	3.71051	−	1.53694i	0.103070	−	0.0426929i
$37$	−3.77234	+	18.9648i	−0.101955	+	0.512563i	0.895732	+	0.444594i	$0.146652\pi$
$37$	−3.77234	+	18.9648i	−0.101955	+	0.512563i	−0.997687	+	0.0679693i	$0.978348\pi$
$38$	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	$0.291973\pi$
$42$	−29.2636	−	12.1214i	−0.696752	−	0.288604i
$43$	−9.06895	+	21.8944i	−0.210906	+	0.509172i	−0.993563	−	0.113281i	$-0.963864\pi$
$43$	−9.06895	+	21.8944i	−0.210906	+	0.509172i	0.782657	+	0.622453i	$0.213864\pi$
$44$	−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	$0.382459\pi$
$48$	−5.62714	−	1.11931i	−0.117232	−	0.0233189i
$49$	11.3288	+	27.3503i	0.231201	+	0.558169i
$50$		0			0
$51$	44.7268	−	8.89671i	0.876995	−	0.174445i
$52$		−	50.8404i		−	0.977699i
$53$	−10.8340	−	26.1557i	−0.204416	−	0.493503i	0.788111	−	0.615533i	$-0.211059\pi$
$53$	−10.8340	−	26.1557i	−0.204416	−	0.493503i	−0.992526	+	0.122031i	$0.961059\pi$
$54$	−37.8574	−	7.53030i	−0.701062	−	0.139450i
$55$		0			0
$56$	40.8445	+	61.1281i	0.729365	+	1.09157i
$57$	0.684154	+	3.43947i	0.0120027	+	0.0603416i
$58$	−18.3236	−	12.2435i	−0.315925	−	0.211094i
$59$	−9.12070	+	22.0193i	−0.154588	+	0.373209i	−0.982132	−	0.188192i	$-0.939737\pi$
$59$	−9.12070	+	22.0193i	−0.154588	+	0.373209i	0.827544	+	0.561401i	$0.189737\pi$
$60$		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	$0.826622\pi$
$62$	17.9442	−	3.56932i	0.289423	−	0.0575697i
$63$	8.88596	+	13.2988i	0.141047	+	0.211092i
$64$	34.6035	+	34.6035i	0.540679	+	0.540679i
$65$		0			0
$66$	11.3230	+	27.3362i	0.171561	+	0.414184i
$67$	−70.4415			−1.05137			−0.525683	−	0.850681i	$-0.676190\pi$
$67$	−70.4415			−1.05137			−0.525683	+	0.850681i	$0.676190\pi$
$68$	−34.9654	−	14.4831i	−0.514197	−	0.212987i
$69$	−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
$73$	29.5868	−	19.7693i	0.405299	−	0.270812i	−0.336167	−	0.941802i	$-0.609131\pi$
$73$	29.5868	−	19.7693i	0.405299	−	0.270812i	0.741466	+	0.670990i	$0.234131\pi$
$74$	−25.2578	+	5.02408i	−0.341321	+	0.0678930i
$75$		0			0
$76$	1.11375	−	2.68883i	0.0146546	−	0.0353793i
$77$	28.0991	−	67.8373i	0.364924	−	0.881003i
$78$	−45.3277	+	67.8377i	−0.581125	+	0.869715i
$79$	1.41599	+	7.11865i	0.0179239	+	0.0901095i	0.988712	−	0.149830i	$-0.0478725\pi$
$79$	1.41599	+	7.11865i	0.0179239	+	0.0901095i	−0.970788	+	0.239939i	$0.922873\pi$
$80$		0			0
$81$	−43.4936	−	43.4936i	−0.536958	−	0.536958i
$82$	−34.5274	−	6.86792i	−0.421066	−	0.0837551i
$83$	124.385	−	51.5218i	1.49861	−	0.620745i	0.525441	−	0.850830i	$-0.323901\pi$
$83$	124.385	−	51.5218i	1.49861	−	0.620745i	0.973170	+	0.230085i	$0.0739005\pi$
$84$			52.9469i			0.630320i
$85$		0			0
$86$	−31.5619			−0.366999
$87$	−16.9865	−	41.0090i	−0.195247	−	0.471368i
$88$	13.3980	−	67.3563i	0.152250	−	0.765412i
$89$	−38.6522	+	38.6522i	−0.434294	+	0.434294i	−0.890086	−	0.455792i	$-0.849356\pi$
$89$	−38.6522	+	38.6522i	−0.434294	+	0.434294i	0.455792	+	0.890086i	$0.349356\pi$
$90$		0			0
$91$	198.577	−	39.4995i	2.18217	−	0.434060i
$92$	49.5234	+	33.0905i	0.538298	+	0.359679i
$93$	34.0458	+	14.1023i	0.366084	+	0.151637i
$94$	−46.7533	−	19.3658i	−0.497375	−	0.206020i
$95$		0			0
$96$	15.8678	+	79.7729i	0.165290	+	0.830968i
$97$	44.0470	+	65.9209i	0.454092	+	0.679597i	0.985913	−	0.167260i	$-0.0534919\pi$
$97$	44.0470	+	65.9209i	0.454092	+	0.679597i	−0.531820	+	0.846857i	$0.678492\pi$
$98$	−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	$-0.245159\pi$
$102$	33.7426	+	50.4994i	0.330810	+	0.495092i
$103$			42.3283i			0.410954i	0.978662	+	0.205477i	$0.0658746\pi$
$103$			42.3283i			0.410954i	−0.978662	+	0.205477i	$0.934125\pi$
$104$	174.953	−	72.4681i	1.68224	−	0.696808i
$105$		0			0
$106$	26.6613	−	26.6613i	0.251522	−	0.251522i
$107$	−61.3221	+	40.9741i	−0.573104	+	0.382936i	−0.808086	−	0.589064i	$-0.799497\pi$
$107$	−61.3221	+	40.9741i	−0.573104	+	0.382936i	0.234983	+	0.972000i	$0.424497\pi$
$108$	12.5875	+	63.2818i	0.116551	+	0.585942i
$109$	116.798	−	174.800i	1.07154	−	1.60367i	0.315770	−	0.948836i	$-0.397737\pi$
$109$	116.798	−	174.800i	1.07154	−	1.60367i	0.755770	−	0.654837i	$-0.227263\pi$
$110$		0			0
$111$	−47.9220	−	19.8500i	−0.431730	−	0.178828i
$112$	−10.5349	+	15.7666i	−0.0940615	+	0.140773i
$113$	−140.877	+	28.0222i	−1.24670	+	0.247984i	−0.773969	−	0.633224i	$-0.781731\pi$
$113$	−140.877	+	28.0222i	−1.24670	+	0.247984i	−0.472729	+	0.881208i	$0.656731\pi$
$114$	−3.88338	+	2.59479i	−0.0340648	+	0.0227613i
$115$		0			0
$116$	−7.18670	+	36.1300i	−0.0619543	+	0.311465i
$117$	38.0622	−	15.7659i	0.325318	−	0.134751i
$118$	−31.7420			−0.269000
$119$	29.4040	−	147.824i	0.247092	−	1.24222i
$120$		0			0
$121$	48.4202	−	20.0563i	0.400167	−	0.165755i
$122$	13.4175	−	67.4541i	0.109979	−	0.552902i
$123$	−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
$127$	100.009	+	41.4251i	0.787472	+	0.326182i	0.739927	−	0.672687i	$-0.234860\pi$
$127$	100.009	+	41.4251i	0.787472	+	0.326182i	0.0475454	+	0.998869i	$0.484860\pi$
$128$	21.4713	−	51.8363i	0.167744	−	0.404971i
$129$	−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
$133$	11.3676	+	2.26116i	0.0854707	+	0.0170012i
$134$	−35.9016	−	86.6742i	−0.267923	−	0.646822i
$135$		0			0
$136$		−	140.968i		−	1.03653i
$137$			102.046i			0.744863i	0.928060	+	0.372431i	$0.121476\pi$
$137$			102.046i			0.744863i	−0.928060	+	0.372431i	$0.878524\pi$
$138$	−36.5780	−	88.3072i	−0.265058	−	0.639907i
$139$	−30.2420	−	6.01550i	−0.217568	−	0.0432770i	0.0851025	−	0.996372i	$-0.472878\pi$
$139$	−30.2420	−	6.01550i	−0.217568	−	0.0432770i	−0.302671	+	0.953095i	$0.597878\pi$
$140$		0			0
$141$	−56.6284	−	84.7504i	−0.401620	−	0.601067i
$142$	−27.2506	−	136.998i	−0.191906	−	0.964775i
$143$	−157.258	−	105.076i	−1.09970	−	0.734799i
$144$	−1.47657	+	3.56475i	−0.0102539	+	0.0247552i
$145$		0			0
$146$	39.4044	+	26.3292i	0.269893	+	0.180337i
$147$	−77.8870	+	15.4927i	−0.529843	+	0.105392i
$148$	23.9160	+	35.7928i	0.161595	+	0.241843i
$149$	−23.3099	−	23.3099i	−0.156443	−	0.156443i	0.624546	−	0.780988i	$-0.285284\pi$
$149$	−23.3099	−	23.3099i	−0.156443	−	0.156443i	−0.780988	+	0.624546i	$0.785284\pi$
$150$		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	$-0.279588\pi$
$152$	10.8404			0.0713185
$153$		−	30.6685i		−	0.200448i
$154$	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	$-0.364865\pi$
$157$	−78.3942	−	78.3942i	−0.499326	−	0.499326i	−0.911228	+	0.411902i	$0.864865\pi$
$158$	−8.03741	+	5.37042i	−0.0508697	+	0.0339900i
$159$	74.4850	−	14.8160i	0.468459	−	0.0931823i
$160$		0			0
$161$	−90.7719	+	219.143i	−0.563800	+	1.36113i
$162$	31.3491	−	75.6835i	0.193513	−	0.467182i
$163$	−90.7416	+	135.804i	−0.556697	+	0.833156i	−0.997935	−	0.0642345i	$-0.979539\pi$
$163$	−90.7416	+	135.804i	−0.556697	+	0.833156i	0.441238	+	0.897390i	$0.354539\pi$
$164$	11.4803	+	57.7154i	0.0700019	+	0.351923i
$165$		0			0
$166$	126.789	+	126.789i	0.763791	+	0.763791i
$167$	163.517	+	32.5256i	0.979145	+	0.194764i	0.658620	−	0.752476i	$-0.271141\pi$
$167$	163.517	+	32.5256i	0.979145	+	0.194764i	0.320525	+	0.947240i	$0.396141\pi$
$168$	−182.202	+	75.4707i	−1.08454	+	0.449230i
$169$		−	352.517i		−	2.08590i
$170$		0			0
$171$	2.35840			0.0137918
$172$	20.1898	+	48.7424i	0.117382	+	0.283386i
$173$	3.26113	−	16.3948i	0.0188504	−	0.0947676i	−0.970215	−	0.242246i	$-0.922116\pi$
$173$	3.26113	−	16.3948i	0.0188504	−	0.0947676i	0.989065	+	0.147479i	$0.0471158\pi$
$174$	41.8018	−	41.8018i	0.240240	−	0.240240i
$175$		0			0
$176$	17.3730	−	3.45570i	0.0987102	−	0.0196347i
$177$	−53.1594	−	35.5199i	−0.300335	−	0.200678i
$178$	−67.2590	−	27.8596i	−0.377859	−	0.156514i
$179$	35.7824	+	14.8215i	0.199901	+	0.0828019i	0.480388	−	0.877056i	$-0.340496\pi$
$179$	35.7824	+	14.8215i	0.199901	+	0.0828019i	−0.280487	+	0.959858i	$0.590496\pi$
$180$		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	$0.899428\pi$
$182$	149.810	+	224.207i	0.823132	+	1.23190i
$183$	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
$187$	−117.065	+	78.2203i	−0.626015	+	0.418290i
$188$			84.5912i			0.449953i
$189$	−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	$0.379898\pi$
$192$	−109.151	+	72.9320i	−0.568492	+	0.379854i
$193$	40.1233	+	201.713i	0.207893	+	1.04515i	0.933920	+	0.357482i	$0.116364\pi$
$193$	40.1233	+	201.713i	0.207893	+	1.04515i	−0.726028	+	0.687666i	$0.758636\pi$
$194$	−58.6627	+	87.7949i	−0.302385	+	0.452551i
$195$		0			0
$196$	60.8886	+	25.2209i	0.310656	+	0.128678i
$197$	−77.7868	+	116.416i	−0.394857	+	0.590945i	−0.974627	−	0.223835i	$-0.928142\pi$
$197$	−77.7868	+	116.416i	−0.394857	+	0.590945i	0.579770	+	0.814780i	$0.303142\pi$
$198$	19.5162	−	3.88201i	0.0985667	−	0.0196061i
$199$	123.283	−	82.3749i	0.619511	−	0.413944i	−0.205823	−	0.978589i	$-0.565987\pi$
$199$	123.283	−	82.3749i	0.619511	−	0.413944i	0.825334	+	0.564645i	$0.190987\pi$
$200$		0			0
$201$	36.8645	−	185.331i	0.183406	−	0.922043i
$202$	173.058	−	71.6828i	0.856721	−	0.354865i
$203$	−146.704			−0.722678
$204$	56.4036	−	84.4140i	0.276488	−	0.413794i
$205$		0			0
$206$	−52.0825	+	21.5733i	−0.252828	+	0.104725i
$207$	−9.41607	+	47.3378i	−0.0454883	+	0.228685i
$208$	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	$0.0263123\pi$
$212$	−58.2291	−	24.1193i	−0.274665	−	0.113770i
$213$	107.666	−	259.929i	0.505474	−	1.22032i
$214$	−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
$218$	274.610	+	54.6233i	1.25968	+	0.250565i
$219$	36.5289	+	88.1885i	0.166799	+	0.402687i
$220$		0			0
$221$	−358.673	−	148.567i	−1.62295	−	0.672250i
$222$		−	69.0821i		−	0.311181i
$223$	44.4897	+	107.408i	0.199506	+	0.481649i	0.991693	−	0.128629i	$-0.0410577\pi$
$223$	44.4897	+	107.408i	0.199506	+	0.481649i	−0.792187	+	0.610278i	$0.791058\pi$
$224$	263.653	+	52.4438i	1.17702	+	0.234124i
$225$		0			0
$226$	−106.280	−	159.059i	−0.470265	−	0.703801i
$227$	−29.9302	−	150.469i	−0.131851	−	0.662859i	−0.989015	−	0.147816i	$-0.952776\pi$
$227$	−29.9302	−	150.469i	−0.131851	−	0.662859i	0.857164	−	0.515044i	$-0.172224\pi$
$228$	6.49140	+	4.33742i	0.0284711	+	0.0190238i
$229$	−3.69064	+	8.91000i	−0.0161164	+	0.0389083i	−0.931733	−	0.363144i	$-0.881703\pi$
$229$	−3.69064	+	8.91000i	−0.0161164	+	0.0389083i	0.915617	+	0.402053i	$0.131703\pi$
$230$		0			0
$231$	163.774	+	109.430i	0.708977	+	0.473723i
$232$	−134.576	+	26.7687i	−0.580067	+	0.115382i
$233$	−216.700	−	324.315i	−0.930044	−	1.39191i	−0.919982	−	0.391960i	$-0.871797\pi$
$233$	−216.700	−	324.315i	−0.930044	−	1.39191i	−0.0100614	−	0.999949i	$-0.503203\pi$
$234$	38.7980	+	38.7980i	0.165803	+	0.165803i
$235$		0			0
$236$	20.3050	+	49.0206i	0.0860381	+	0.207714i
$237$	−19.4701			−0.0821523
$238$	196.875	−	39.1609i	0.827205	−	0.164541i
$239$	−372.281			−1.55766			−0.778831	−	0.627233i	$-0.784187\pi$
$239$	−372.281			−1.55766			−0.778831	+	0.627233i	$0.784187\pi$
$240$		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
$243$	−79.6872	+	53.2453i	−0.327931	+	0.219116i
$244$	−112.755	+	22.4284i	−0.462111	+	0.0919197i
$245$		0			0
$246$	36.1388	−	87.2468i	0.146906	−	0.354662i
$247$	11.4248	−	27.5818i	0.0462541	−	0.111667i
$248$	63.2872	−	94.7160i	0.255190	−	0.381919i
$249$	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	$0.607106\pi$
$252$	34.9232	+	6.94665i	0.138584	+	0.0275661i
$253$	204.709	−	84.7932i	0.809126	−	0.335151i
$254$			144.168i			0.567591i
$255$		0			0
$256$	270.472			1.05653
$257$	−162.362	−	391.977i	−0.631760	−	1.52520i	−0.837408	−	0.546578i	$-0.815930\pi$
$257$	−162.362	−	391.977i	−0.631760	−	1.52520i	0.205648	−	0.978626i	$-0.434070\pi$
$258$	16.5175	−	83.0389i	0.0640212	−	0.321856i
$259$	−121.222	+	121.222i	−0.468039	+	0.468039i
$260$		0			0
$261$	−29.2777	+	5.82370i	−0.112175	+	0.0223130i
$262$	−102.638	−	68.5803i	−0.391747	−	0.261757i
$263$	132.058	+	54.7003i	0.502122	+	0.207986i	0.619344	−	0.785120i	$-0.287399\pi$
$263$	132.058	+	54.7003i	0.502122	+	0.207986i	−0.117221	+	0.993106i	$0.537399\pi$
$264$	170.202	+	70.4999i	0.644704	+	0.267045i
$265$		0			0
$266$	3.01146	+	15.1396i	0.0113213	+	0.0569158i
$267$	−81.4652	−	121.921i	−0.305113	−	0.456634i
$268$	−110.889	+	110.889i	−0.413764	+	0.413764i
$269$	−8.93614	+	44.9250i	−0.0332199	+	0.167008i	−0.993834	−	0.110878i	$-0.964634\pi$
$269$	−8.93614	+	44.9250i	−0.0332199	+	0.167008i	0.960614	+	0.277886i	$0.0896337\pi$
$270$		0			0
$271$		−	329.809i		−	1.21701i	−0.793550	−	0.608504i	$-0.791770\pi$
$271$		−	329.809i		−	1.21701i	0.793550	−	0.608504i	$-0.208230\pi$
$272$	33.5918	−	13.9142i	0.123499	−	0.0511551i
$273$			543.126i			1.98947i
$274$	−125.562	+	52.0095i	−0.458255	+	0.189816i
$275$		0			0
$276$	−112.978	+	112.978i	−0.409341	+	0.409341i
$277$	−234.642	+	156.783i	−0.847082	+	0.566002i	−0.901629	−	0.432509i	$-0.857628\pi$
$277$	−234.642	+	156.783i	−0.847082	+	0.566002i	0.0545479	+	0.998511i	$0.482628\pi$
$278$	−8.01157	−	40.2769i	−0.0288186	−	0.144881i
$279$	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	$0.537313\pi$
$282$	75.4189	−	112.872i	0.267443	−	0.400257i
$283$	311.786	−	62.0182i	1.10172	−	0.219145i	0.389447	−	0.921049i	$-0.372666\pi$
$283$	311.786	−	62.0182i	1.10172	−	0.219145i	0.712272	+	0.701904i	$0.247666\pi$
$284$	−194.140	+	129.720i	−0.683592	+	0.456761i
$285$		0			0
$286$	49.1414	−	247.050i	0.171823	−	0.863813i
$287$	−216.511	+	89.6819i	−0.754395	+	0.312480i
$288$	54.6992			0.189928
$289$	−204.354	+	204.354i	−0.707107	+	0.707107i
$290$		0			0
$291$	−196.488	+	81.3882i	−0.675218	+	0.279684i
$292$	15.4548	−	77.6963i	0.0529272	−	0.266083i
$293$	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
$297$	221.757	+	91.8547i	0.746656	+	0.309275i
$298$	16.8013	−	40.5618i	0.0563801	−	0.136114i
$299$	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
$303$	370.039	+	73.6054i	1.22125	+	0.242922i
$304$	1.07000	+	2.58320i	0.00351972	+	0.00849736i
$305$		0			0
$306$	37.7359	−	15.6307i	0.123320	−	0.0510807i
$307$		−	4.80965i		−	0.0156666i	−0.999969	−	0.00783330i	$-0.997507\pi$
$307$		−	4.80965i		−	0.0156666i	0.999969	−	0.00783330i	$-0.00249344\pi$
$308$	−62.5557	−	151.023i	−0.203103	−	0.490334i
$309$	−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	$0.531397\pi$
$312$	99.1031	+	498.225i	0.317638	+	1.59688i
$313$	73.7441	+	49.2742i	0.235604	+	0.157426i	0.667768	−	0.744369i	$-0.267250\pi$
$313$	73.7441	+	49.2742i	0.235604	+	0.157426i	−0.432164	+	0.901795i	$0.642250\pi$
$314$	56.5047	−	136.414i	0.179951	−	0.434441i
$315$		0			0
$316$	13.4352	+	8.97712i	0.0425165	+	0.0284086i
$317$	117.988	−	23.4692i	0.372201	−	0.0740353i	−0.00544574	−	0.999985i	$-0.501733\pi$
$317$	117.988	−	23.4692i	0.372201	−	0.0740353i	0.377647	+	0.925950i	$0.376733\pi$
$318$	56.1927	+	84.0983i	0.176707	+	0.264460i
$319$	96.9027	+	96.9027i	0.303770	+	0.303770i
$320$		0			0
$321$	−75.7103	−	182.781i	−0.235858	−	0.569411i
$322$	−315.906			−0.981074
$323$	−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
$328$	−182.248	+	121.774i	−0.555634	+	0.371263i
$329$	−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	$0.0759262\pi$
$332$	114.701	−	276.912i	0.345484	−	0.834071i
$333$	−19.3802	+	29.0045i	−0.0581988	+	0.0871006i
$334$	43.3183	+	217.776i	0.129695	+	0.652023i
$335$		0			0
$336$	−35.9683	−	35.9683i	−0.107049	−	0.107049i
$337$	−539.044	−	107.223i	−1.59954	−	0.318168i	−0.686842	−	0.726807i	$-0.741004\pi$
$337$	−539.044	−	107.223i	−1.59954	−	0.318168i	−0.912696	+	0.408639i	$0.866004\pi$
$338$	433.752	−	179.666i	1.28329	−	0.531556i
$339$		−	385.310i		−	1.13661i
$340$		0			0
$341$	−113.772			−0.333642
$342$	1.20200	+	2.90187i	0.00351461	+	0.00848501i
$343$	33.5487	−	168.661i	0.0978097	−	0.491722i
$344$	−138.955	+	138.955i	−0.403940	+	0.403940i
$345$		0			0
$346$	21.8349	−	4.34324i	0.0631067	−	0.0125527i
$347$	212.258	+	141.826i	0.611695	+	0.408722i	0.822466	−	0.568814i	$-0.192597\pi$
$347$	212.258	+	141.826i	0.611695	+	0.408722i	−0.210771	+	0.977535i	$0.567597\pi$
$348$	−91.2964	−	37.8162i	−0.262346	−	0.108667i
$349$	513.215	+	212.580i	1.47053	+	0.609113i	0.966980	−	0.254854i	$-0.0820273\pi$
$349$	513.215	+	212.580i	1.47053	+	0.609113i	0.503549	+	0.863967i	$0.332027\pi$
$350$		0			0
$351$	129.122	+	649.141i	0.367869	+	1.84940i
$352$	−139.511	−	208.792i	−0.396337	−	0.593160i
$353$	−408.644	+	408.644i	−1.15763	+	1.15763i	−0.172648	+	0.984984i	$0.555232\pi$
$353$	−408.644	+	408.644i	−1.15763	+	1.15763i	−0.984984	+	0.172648i	$0.944768\pi$
$354$	16.6117	−	83.5128i	0.0469258	−	0.235912i
$355$		0			0
$356$			121.692i			0.341832i
$357$	373.534	+	154.723i	1.04631	+	0.433398i
$358$			51.5822i			0.144084i
$359$	159.526	−	66.0778i	0.444362	−	0.184061i	−0.149272	−	0.988796i	$-0.547693\pi$
$359$	159.526	−	66.0778i	0.444362	−	0.184061i	0.593634	+	0.804735i	$0.297693\pi$
$360$		0			0
$361$	−254.057	+	254.057i	−0.703759	+	0.703759i
$362$	−47.8317	+	31.9602i	−0.132132	+	0.0882877i
$363$	27.4279	+	137.889i	0.0755588	+	0.379860i
$364$	250.420	−	374.780i	0.687967	−	1.02962i
$365$		0			0
$366$	170.449	+	70.6023i	0.465708	+	0.192902i
$367$	11.3429	−	16.9759i	0.0309071	−	0.0462558i	−0.815694	−	0.578483i	$-0.803645\pi$
$367$	11.3429	−	16.9759i	0.0309071	−	0.0462558i	0.846601	+	0.532227i	$0.178645\pi$
$368$	−56.1220	+	11.1634i	−0.152505	+	0.0303352i
$369$	−39.6492	+	26.4927i	−0.107450	+	0.0717960i
$370$		0			0
$371$	48.9675	−	246.176i	0.131988	−	0.663547i
$372$	75.7946	−	31.3952i	0.203749	−	0.0843956i
$373$	−690.960			−1.85244			−0.926220	−	0.376983i	$-0.876961\pi$
$373$	−690.960			−1.85244			−0.926220	+	0.376983i	$0.876961\pi$
$374$	−155.910	−	104.175i	−0.416870	−	0.278544i
$375$		0			0
$376$	−291.098	+	120.577i	−0.774196	+	0.320682i
$377$	−73.7207	+	370.619i	−0.195546	+	0.983075i
$378$	−241.982	−	241.982i	−0.640164	−	0.640164i
$379$	97.1405	+	145.381i	0.256308	+	0.383591i	0.937200	−	0.348792i	$-0.113408\pi$
$379$	97.1405	+	145.381i	0.256308	+	0.383591i	−0.680893	+	0.732383i	$0.738408\pi$
$380$		0			0
$381$	−161.327	+	241.443i	−0.423431	+	0.633709i
$382$	−186.532	−	77.2642i	−0.488304	−	0.202262i
$383$	182.466	−	440.512i	0.476412	−	1.15016i	−0.484868	−	0.874588i	$-0.661132\pi$
$383$	182.466	−	440.512i	0.476412	−	1.15016i	0.961280	−	0.275574i	$-0.0888678\pi$
$384$	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
$388$	173.111	+	34.4340i	0.446163	+	0.0887473i
$389$	−84.5808	−	204.196i	−0.217431	−	0.524926i	0.777098	−	0.629379i	$-0.216691\pi$
$389$	−84.5808	−	204.196i	−0.217431	−	0.524926i	−0.994530	+	0.104453i	$0.966691\pi$
$390$		0			0
$391$	378.169	−	252.684i	0.967183	−	0.646251i
$392$			245.482i			0.626228i
$393$	−95.1478	−	229.707i	−0.242106	−	0.584496i
$394$	−182.889	−	36.3788i	−0.464184	−	0.0923320i
$395$		0			0
$396$	−18.4794	−	27.6564i	−0.0466652	−	0.0698395i
$397$	−23.6042	−	118.666i	−0.0594565	−	0.298908i	0.939603	−	0.342266i	$-0.111194\pi$
$397$	−23.6042	−	118.666i	−0.0594565	−	0.298908i	−0.999060	+	0.0433581i	$0.986194\pi$
$398$	164.191	+	109.709i	0.412539	+	0.275650i
$399$	−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	$0.461828\pi$
$402$	246.827	−	49.0970i	0.613998	−	0.122132i
$403$	−174.292	−	260.846i	−0.432486	−	0.647262i
$404$	−221.406	−	221.406i	−0.548034	−	0.548034i
$405$		0			0
$406$	−74.7699	−	180.510i	−0.184162	−	0.444607i
$407$	160.142			0.393471
$408$	370.886	+	73.7738i	0.909034	+	0.180818i
$409$	−136.013			−0.332550			−0.166275	−	0.986079i	$-0.553174\pi$
$409$	−136.013			−0.332550			−0.166275	+	0.986079i	$0.553174\pi$
$410$		0			0
$411$	−268.482	−	53.4044i	−0.653241	−	0.129938i
$412$	66.6331	+	66.6331i	0.161731	+	0.161731i
$413$	−175.694	+	117.395i	−0.425409	+	0.284249i
$414$	−63.0455	+	12.5405i	−0.152284	+	0.0302911i
$415$		0			0
$416$	264.979	−	639.715i	0.636968	−	1.53778i
$417$	31.6534	−	76.4181i	0.0759074	−	0.183257i
$418$	8.01105	−	11.9894i	0.0191652	−	0.0286827i
$419$	−73.0669	−	367.332i	−0.174384	−	0.876687i	−0.964571	−	0.263822i	$-0.915017\pi$
$419$	−73.0669	−	367.332i	−0.174384	−	0.876687i	0.790187	−	0.612865i	$-0.209983\pi$
$420$		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	$0.902223\pi$
$422$	267.357	+	53.1807i	0.633548	+	0.126021i
$423$	−63.3301	+	26.2322i	−0.149716	+	0.0620146i
$424$		−	234.759i		−	0.553678i
$425$		0			0
$426$	374.701			0.879580
$427$	−175.206	−	422.985i	−0.410319	−	0.990598i
$428$	−32.0318	+	161.034i	−0.0748405	+	0.376249i
$429$	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	$0.412056\pi$
$432$	−51.5402	−	34.4381i	−0.119306	−	0.0797177i
$433$	251.710	+	104.262i	0.581317	+	0.240790i	0.653910	−	0.756572i	$-0.273127\pi$
$433$	251.710	+	104.262i	0.581317	+	0.240790i	−0.0725929	+	0.997362i	$0.523127\pi$
$434$	149.860	+	62.0742i	0.345301	+	0.143028i
$435$		0			0
$436$	−91.3074	−	459.033i	−0.209421	−	1.05283i
$437$	19.4313	+	29.0810i	0.0444653	+	0.0665470i
$438$	−89.8934	+	89.8934i	−0.205236	+	0.205236i
$439$	28.7213	−	144.392i	0.0654244	−	0.328910i	−0.934187	−	0.356783i	$-0.883873\pi$
$439$	28.7213	−	144.392i	0.0654244	−	0.328910i	0.999611	+	0.0278730i	$0.00887340\pi$
$440$		0			0
$441$			53.4060i			0.121102i
$442$		−	517.046i		−	1.16979i
$443$			619.331i			1.39804i	0.715103	+	0.699019i	$0.246380\pi$
$443$			619.331i			1.39804i	−0.715103	+	0.699019i	$0.753620\pi$
$444$	−106.687	+	44.1910i	−0.240285	+	0.0995293i
$445$		0			0
$446$	−109.484	+	109.484i	−0.245480	+	0.245480i
$447$	73.5271	−	49.1292i	0.164490	−	0.109909i
$448$	84.6432	+	425.530i	0.188936	+	0.949844i
$449$	−348.576	+	521.681i	−0.776339	+	1.16187i	0.206687	+	0.978407i	$0.433732\pi$
$449$	−348.576	+	521.681i	−0.776339	+	1.16187i	−0.983026	+	0.183466i	$0.941268\pi$
$450$		0			0
$451$	202.251	+	83.7750i	0.448450	+	0.185754i
$452$	−177.656	+	265.880i	−0.393043	+	0.588231i
$453$	370.888	−	73.7743i	0.818738	−	0.162857i
$454$	169.889	−	113.516i	0.374205	−	0.250036i
$455$		0			0
$456$	−5.67318	+	28.5210i	−0.0124412	+	0.0625460i
$457$	127.865	−	52.9634i	0.279792	−	0.115894i	−0.238375	−	0.971173i	$-0.576615\pi$
$457$	127.865	−	52.9634i	0.279792	−	0.115894i	0.518167	+	0.855280i	$0.326615\pi$
$458$	−12.8442			−0.0280442
$459$	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	$0.425891\pi$
$462$	−51.1775	+	257.287i	−0.110774	+	0.556898i
$463$	−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
$467$	−7.06740	−	2.92741i	−0.0151336	−	0.00626855i	0.375104	−	0.926983i	$-0.377607\pi$
$467$	−7.06740	−	2.92741i	−0.0151336	−	0.00626855i	−0.390237	+	0.920714i	$0.627607\pi$
$468$	35.0988	−	84.7360i	0.0749974	−	0.181060i
$469$	−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
$473$	192.496	+	38.2899i	0.406969	+	0.0809512i
$474$	−9.92325	−	23.9568i	−0.0209351	−	0.0505419i
$475$		0			0
$476$	−186.416	−	278.992i	−0.391631	−	0.586117i
$477$		−	51.0733i		−	0.107072i
$478$	−189.739	−	458.071i	−0.396944	−	0.958307i
$479$	742.358	+	147.664i	1.54981	+	0.308276i	0.894493	−	0.447081i	$-0.147536\pi$
$479$	742.358	+	147.664i	1.54981	+	0.308276i	0.655314	+	0.755357i	$0.272536\pi$
$480$		0			0
$481$	245.329	+	367.160i	0.510039	+	0.763327i
$482$	36.1119	+	181.547i	0.0749209	+	0.376653i
$483$	−529.057	−	353.505i	−1.09536	−	0.731894i
$484$	44.6504	−	107.796i	0.0922529	−	0.222718i
$485$		0			0
$486$	−106.129	−	70.9132i	−0.218373	−	0.145912i
$487$	−8.66318	+	1.72321i	−0.0177889	+	0.00353843i	−0.203977	−	0.978976i	$-0.565387\pi$
$487$	−8.66318	+	1.72321i	−0.0177889	+	0.00353843i	0.186188	+	0.982514i	$0.440387\pi$
$488$	−237.903	−	356.047i	−0.487506	−	0.729605i
$489$	−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	$-0.328914\pi$
$492$	−157.857			−0.320847
$493$	233.892	+	156.281i	0.474425	+	0.317001i
$494$	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
$498$	−399.934	+	267.228i	−0.803081	+	0.536602i
$499$	109.936	−	21.8676i	0.220312	−	0.0438229i	−0.0836997	−	0.996491i	$-0.526674\pi$
$499$	109.936	−	21.8676i	0.220312	−	0.0438229i	0.304012	+	0.952668i	$0.401674\pi$
$500$		0			0
$501$	−171.149	+	413.190i	−0.341614	+	0.824730i
$502$	−111.037	+	268.067i	−0.221190	+	0.533999i
$503$	−265.535	+	397.401i	−0.527902	+	0.790061i	−0.995588	−	0.0938335i	$-0.970088\pi$
$503$	−265.535	+	397.401i	−0.527902	+	0.790061i	0.467686	+	0.883895i	$0.345088\pi$
$504$	25.8746	+	130.080i	0.0513385	+	0.258096i
$505$		0			0
$506$	208.666	+	208.666i	0.412384	+	0.412384i
$507$	927.468	+	184.485i	1.82933	+	0.363875i
$508$	222.645	−	92.2226i	0.438278	−	0.181541i
$509$		−	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
$512$	51.9650	+	125.455i	0.101494	+	0.245029i
$513$	−7.39162	+	37.1602i	−0.0144086	+	0.0724370i
$514$	399.555	−	399.555i	0.777345	−	0.777345i
$515$		0			0
$516$	−138.807	+	27.6104i	−0.269005	+	0.0535084i
$517$	261.655	+	174.832i	0.506102	+	0.338166i
$518$	−210.940	−	87.3740i	−0.407219	−	0.168676i
$519$	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	$-0.259662\pi$
$522$	−22.0876	−	33.0564i	−0.0423134	−	0.0633265i
$523$	721.650	−	721.650i	1.37983	−	1.37983i	0.534934	−	0.844894i	$-0.320336\pi$
$523$	721.650	−	721.650i	1.37983	−	1.37983i	0.844894	−	0.534934i	$-0.179664\pi$
$524$	−40.2554	+	202.378i	−0.0768233	+	0.386217i
$525$		0			0
$526$			190.369i			0.361918i
$527$	−229.048	+	45.5605i	−0.434627	+	0.0864526i
$528$			47.5166i			0.0899935i
$529$	−172.563	+	71.4781i	−0.326207	+	0.135119i
$530$		0			0
$531$	−30.4031	+	30.4031i	−0.0572563	+	0.0572563i
$532$	21.4544	−	14.3353i	0.0403277	−	0.0269461i
$533$	117.764	+	592.041i	0.220946	+	1.11077i
$534$	108.497	−	162.377i	0.203178	−	0.304078i
$535$		0			0
$536$	−539.655	−	223.533i	−1.00682	−	0.417038i
$537$	−57.7215	+	86.3863i	−0.107489	+	0.160868i
$538$	−59.8321	+	11.9013i	−0.111212	+	0.0221215i
$539$	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	$-0.113580\pi$
$542$	405.812	−	168.093i	0.748730	−	0.310134i
$543$	−115.869			−0.213387
$544$	−364.477	−	364.477i	−0.669995	−	0.669995i
$545$		0			0
$546$	−668.285	+	276.813i	−1.22397	+	0.506983i
$547$	71.5805	−	359.860i	0.130860	−	0.657879i	−0.858550	−	0.512730i	$-0.828634\pi$
$547$	71.5805	−	359.860i	0.130860	−	0.657879i	0.989410	−	0.145148i	$-0.0463659\pi$
$548$	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
$552$	−549.823	−	227.744i	−0.996056	−	0.412580i
$553$	−24.6255	+	59.4512i	−0.0445307	+	0.107507i
$554$	−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	$0.190449\pi$
$558$	32.3719	+	6.43917i	0.0580141	+	0.0115397i
$559$	207.105	+	499.996i	0.370493	+	0.894448i
$560$		0			0
$561$	−144.532	−	348.932i	−0.257633	−	0.621981i
$562$			203.593i			0.362264i
$563$	−328.584	−	793.273i	−0.583631	−	1.40901i	−0.889499	−	0.456936i	$-0.848947\pi$
$563$	−328.584	−	793.273i	−0.583631	−	1.40901i	0.305868	−	0.952074i	$-0.401053\pi$
$564$	−222.558	−	44.2696i	−0.394607	−	0.0784922i
$565$		0			0
$566$	235.217	+	352.027i	0.415577	+	0.621955i
$567$	−106.389	−	534.854i	−0.187635	−	0.943306i
$568$	−723.125	−	483.177i	−1.27311	−	0.850663i
$569$	−120.952	+	292.003i	−0.212569	+	0.513187i	−0.993817	−	0.111034i	$-0.964584\pi$
$569$	−120.952	+	292.003i	−0.212569	+	0.513187i	0.781248	+	0.624221i	$0.214584\pi$
$570$		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	$0.611415\pi$
$572$	−412.966	+	82.1440i	−0.721968	+	0.143608i
$573$	−225.931	−	338.130i	−0.394295	−	0.590105i
$574$	−220.697	−	220.697i	−0.384489	−	0.384489i
$575$		0			0
$576$	33.7846	+	81.5632i	0.0586538	+	0.141603i
$577$	63.2031			0.109537			0.0547687	−	0.998499i	$-0.482558\pi$
$577$	63.2031			0.109537			0.0547687	+	0.998499i	$0.482558\pi$
$578$	−355.598	−	147.293i	−0.615221	−	0.254833i
$579$	−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
$583$	−194.952	+	130.263i	−0.334395	+	0.223435i
$584$	289.400	−	57.5653i	0.495548	−	0.0985706i
$585$		0			0
$586$	−19.6507	+	47.4411i	−0.0335337	+	0.0809575i
$587$	−283.753	+	685.040i	−0.483395	+	1.16702i	0.474592	+	0.880206i	$0.342596\pi$
$587$	−283.753	+	685.040i	−0.483395	+	1.16702i	−0.957987	+	0.286812i	$0.907404\pi$
$588$	−98.2209	+	146.998i	−0.167042	+	0.249997i
$589$	−3.50359	−	17.6137i	−0.00594837	−	0.0299045i
$590$		0			0
$591$	−265.581	−	265.581i	−0.449375	−	0.449375i
$592$	−40.5619	−	8.06826i	−0.0685167	−	0.0136288i
$593$	−185.647	+	76.8977i	−0.313065	+	0.129676i	−0.533683	−	0.845685i	$-0.679192\pi$
$593$	−185.647	+	76.8977i	−0.313065	+	0.129676i	0.220618	+	0.975360i	$0.429192\pi$
$594$			319.674i			0.538172i
$595$		0			0
$596$	−73.3889			−0.123136
$597$	152.209	+	367.465i	0.254956	+	0.615519i
$598$	−158.747	+	798.076i	−0.265464	+	1.33458i
$599$	−457.825	+	457.825i	−0.764316	+	0.764316i	−0.977099	−	0.212784i	$-0.931747\pi$
$599$	−457.825	+	457.825i	−0.764316	+	0.764316i	0.212784	+	0.977099i	$0.431747\pi$
$600$		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	$0.234003\pi$
$602$	−232.665	−	155.462i	−0.386487	−	0.258242i
$603$	−117.405	−	48.6309i	−0.194702	−	0.0806482i
$604$	−289.944	−	120.099i	−0.480040	−	0.198839i
$605$		0			0
$606$	98.0293	+	492.826i	0.161764	+	0.813245i
$607$	−577.021	−	863.573i	−0.950612	−	1.42269i	−0.905805	−	0.423695i	$-0.860733\pi$
$607$	−577.021	−	863.573i	−0.950612	−	1.42269i	−0.0448067	−	0.998996i	$-0.514267\pi$
$608$	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
$613$			626.391i			1.02185i	0.859627	+	0.510923i	$0.170696\pi$
$613$			626.391i			1.02185i	−0.859627	+	0.510923i	$0.829304\pi$
$614$	5.91799	−	2.45131i	0.00963842	−	0.00399237i
$615$		0			0
$616$	430.537	−	430.537i	0.698924	−	0.698924i
$617$	557.109	−	372.249i	0.902933	−	0.603320i	−0.0150736	−	0.999886i	$-0.504798\pi$
$617$	557.109	−	372.249i	0.902933	−	0.603320i	0.918006	+	0.396566i	$0.129798\pi$
$618$	−29.5024	−	148.319i	−0.0477385	−	0.239998i
$619$	437.249	−	654.389i	0.706379	−	1.05717i	−0.288635	−	0.957439i	$-0.593201\pi$
$619$	437.249	−	654.389i	0.706379	−	1.05717i	0.995014	−	0.0997323i	$-0.0317987\pi$
$620$		0			0
$621$	−716.368	−	296.729i	−1.15357	−	0.477825i
$622$	−355.628	+	532.235i	−0.571749	+	0.855684i
$623$	−475.318	+	94.5466i	−0.762950	+	0.151760i
$624$	−108.942	+	72.7926i	−0.174586	+	0.116655i
$625$		0			0
$626$	−23.0442	+	115.851i	−0.0368119	+	0.185066i
$627$	26.8327	−	11.1145i	0.0427954	−	0.0177264i
$628$	−246.816			−0.393019
$629$	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	$0.603698\pi$
$632$	−11.7417	+	59.0297i	−0.0185787	+	0.0934013i
$633$	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
$637$	624.591	+	258.714i	0.980520	+	0.406145i
$638$	−69.8452	+	168.621i	−0.109475	+	0.264297i
$639$	−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
$643$	724.957	+	144.203i	1.12746	+	0.224266i	0.723375	−	0.690456i	$-0.242590\pi$
$643$	724.957	+	144.203i	1.12746	+	0.224266i	0.404085	+	0.914721i	$0.367590\pi$
$644$	202.081	+	487.867i	0.313790	+	0.757557i
$645$		0			0
$646$	11.3268	−	27.3453i	0.0175338	−	0.0423303i
$647$			874.070i			1.35096i	0.737379	+	0.675479i	$0.236063\pi$
$647$			874.070i			1.35096i	−0.737379	+	0.675479i	$0.763937\pi$
$648$	−195.188	−	471.225i	−0.301216	−	0.727199i
$649$	193.595	+	38.5084i	0.298297	+	0.0593350i
$650$		0			0
$651$	181.514	+	271.654i	0.278823	+	0.417288i
$652$	70.9377	+	356.628i	0.108800	+	0.546976i
$653$	960.997	+	642.117i	1.47166	+	0.983335i	0.994524	+	0.104507i	$0.0333266\pi$
$653$	960.997	+	642.117i	1.47166	+	0.983335i	0.477140	+	0.878827i	$0.341673\pi$
$654$	−287.426	+	693.908i	−0.439489	+	1.06102i
$655$		0			0
$656$	−47.0066	−	31.4088i	−0.0716565	−	0.0478793i
$657$	62.9607	−	12.5237i	0.0958307	−	0.0190619i
$658$	−249.263	−	373.048i	−0.378819	−	0.566942i
$659$	318.726	+	318.726i	0.483651	+	0.483651i	0.906295	−	0.422645i	$-0.138898\pi$
$659$	318.726	+	318.726i	0.483651	+	0.483651i	−0.422645	+	0.906295i	$0.638898\pi$
$660$		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	$0.751688\pi$
$662$	135.388			0.204514
$663$	578.585	−	865.913i	0.872677	−	1.30605i
$664$	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
$668$	308.610	−	206.207i	0.461991	−	0.308693i
$669$	−305.871	+	60.8416i	−0.457207	+	0.0909441i
$670$		0			0
$671$	−163.666	+	395.126i	−0.243914	+	0.588861i
$672$	−275.958	+	666.221i	−0.410651	+	0.991400i
$673$	−522.061	+	781.320i	−0.775722	+	1.16095i	0.207446	+	0.978247i	$0.433485\pi$
$673$	−522.061	+	781.320i	−0.775722	+	1.16095i	−0.983168	+	0.182704i	$0.941515\pi$
$674$	−142.801	−	717.911i	−0.211871	−	1.06515i
$675$		0			0
$676$	−554.932	−	554.932i	−0.820905	−	0.820905i
$677$	1091.43	+	217.100i	1.61216	+	0.320679i	0.917218	−	0.398386i	$-0.130430\pi$
$677$	1091.43	+	217.100i	1.61216	+	0.320679i	0.694943	+	0.719065i	$0.255430\pi$
$678$	474.102	−	196.379i	0.699265	−	0.289645i
$679$			702.908i			1.03521i
$680$		0			0
$681$	411.546			0.604325
$682$	−57.9857	−	139.990i	−0.0850231	−	0.205264i
$683$	256.456	−	1289.29i	0.375484	−	1.88769i	−0.0789027	−	0.996882i	$-0.525142\pi$
$683$	256.456	−	1289.29i	0.375484	−	1.88769i	0.454387	−	0.890804i	$-0.349858\pi$
$684$	3.71259	−	3.71259i	0.00542776	−	0.00542776i
$685$		0			0
$686$	224.626	−	44.6809i	0.327443	−	0.0651325i
$687$	−21.5107	−	14.3730i	−0.0313110	−	0.0209213i
$688$	−46.8276	−	19.3966i	−0.0680634	−	0.0281928i
$689$	−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	$0.824785\pi$
$692$	−20.6750	−	30.9423i	−0.0298771	−	0.0447143i
$693$	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
$697$	440.724	+	87.6654i	0.632315	+	0.125775i
$698$			739.826i			1.05992i
$699$	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	$-0.0369420\pi$
$702$	−732.921	+	489.722i	−1.04405	+	0.697610i
$703$	4.93156	+	24.7926i	0.00701502	+	0.0352669i
$704$	225.167	−	336.987i	0.319840	−	0.478674i
$705$		0			0
$706$	−711.085	−	294.541i	−1.00720	−	0.417197i
$707$	692.771	−	1036.81i	0.979875	−	1.46649i
$708$	−139.599	+	27.7679i	−0.197173	+	0.0392202i
$709$	−433.937	+	289.947i	−0.612041	+	0.408953i	−0.822593	−	0.568630i	$-0.807474\pi$
$709$	−433.937	+	289.947i	−0.612041	+	0.408953i	0.210553	+	0.977583i	$0.432474\pi$
$710$		0			0
$711$	−2.55448	+	12.8423i	−0.00359281	+	0.0180623i
$712$	−418.771	+	173.461i	−0.588162	+	0.243625i
$713$	367.531			0.515472
$714$			538.469i			0.754159i
$715$		0			0
$716$	79.6605	−	32.9965i	0.111258	−	0.0460845i
$717$	194.828	−	979.467i	0.271727	−	1.36606i
$718$	162.610	+	162.610i	0.226476	+	0.226476i
$719$	345.349	+	516.851i	0.480318	+	0.718847i	0.989930	−	0.141557i	$-0.0452110\pi$
$719$	345.349	+	516.851i	0.480318	+	0.718847i	−0.509612	+	0.860404i	$0.670211\pi$
$720$		0			0
$721$	−208.493	+	312.032i	−0.289172	+	0.432776i
$722$	−442.087	−	183.118i	−0.612309	−	0.253627i
$723$	−142.677	+	344.452i	−0.197340	+	0.476420i
$724$	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	$0.306459\pi$
$728$	1646.65	+	327.540i	2.26189	+	0.449917i
$729$	−310.231	−	748.965i	−0.425557	−	1.02739i
$730$		0			0
$731$	402.871			0.551123
$732$		−	308.395i		−	0.421305i
$733$	−84.8211	−	204.776i	−0.115718	−	0.279367i	0.855400	−	0.517968i	$-0.173311\pi$
$733$	−84.8211	−	204.776i	−0.115718	−	0.279367i	−0.971118	+	0.238600i	$0.923311\pi$
$734$	26.6690	+	5.30478i	0.0363337	+	0.00722723i
$735$		0			0
$736$	450.677	+	674.487i	0.612334	+	0.916422i
$737$	113.814	+	572.182i	0.154429	+	0.776366i
$738$	−52.8056	−	35.2836i	−0.0715523	−	0.0478097i
$739$	−113.071	+	272.978i	−0.153006	+	0.369388i	−0.981733	−	0.190265i	$-0.939065\pi$
$739$	−113.071	+	272.978i	−0.153006	+	0.369388i	0.828727	+	0.559653i	$0.189065\pi$
$740$		0			0
$741$	66.5884	+	44.4929i	0.0898629	+	0.0600445i
$742$	327.862	−	65.2159i	0.441863	−	0.0878920i
$743$	415.988	+	622.570i	0.559876	+	0.837914i	0.998142	−	0.0609312i	$-0.0194070\pi$
$743$	415.988	+	622.570i	0.559876	+	0.837914i	−0.438265	+	0.898846i	$0.644407\pi$
$744$	216.076	+	216.076i	0.290425	+	0.290425i
$745$		0			0
$746$	−352.159	−	850.187i	−0.472063	−	1.13966i
$747$	242.882			0.325143
$748$	−61.1491	+	307.417i	−0.0817502	+	0.410986i
$749$	−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
$753$	−485.930	+	324.688i	−0.645326	+	0.431193i
$754$	−493.598	+	98.1828i	−0.654640	+	0.130216i
$755$		0			0
$756$	−218.910	+	528.496i	−0.289564	+	0.699069i
$757$	262.415	−	633.525i	0.346651	−	0.836889i	−0.650360	−	0.759626i	$-0.725382\pi$
$757$	262.415	−	633.525i	0.346651	−	0.836889i	0.997011	−	0.0772631i	$-0.0246182\pi$
$758$	−129.374	+	193.622i	−0.170678	+	0.255438i
$759$	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	$0.841464\pi$
$762$	−379.305	−	75.4484i	−0.497775	−	0.0990136i
$763$	1722.00	−	713.275i	2.25688	−	0.934830i
$764$			337.495i			0.441747i
$765$		0			0
$766$	635.021			0.829009
$767$	208.287	+	502.850i	0.271561	+	0.655606i
$768$	−141.547	+	711.607i	−0.184307	+	0.926572i
$769$	−303.275	+	303.275i	−0.394376	+	0.394376i	−0.876244	−	0.481868i	$-0.839959\pi$
$769$	−303.275	+	303.275i	−0.394376	+	0.394376i	0.481868	+	0.876244i	$0.339959\pi$
$770$		0			0
$771$	1116.26	−	222.037i	1.44780	−	0.287986i
$772$	380.699	+	254.375i	0.493133	+	0.329501i
$773$	192.675	+	79.8088i	0.249257	+	0.103246i	0.503814	−	0.863812i	$-0.331930\pi$
$773$	192.675	+	79.8088i	0.249257	+	0.103246i	−0.254557	+	0.967058i	$0.581930\pi$
$774$	−52.6045	−	21.7895i	−0.0679644	−	0.0281518i
$775$		0			0
$776$	128.258	+	644.798i	0.165281	+	0.830925i
$777$	−255.494	−	382.373i	−0.328821	−	0.492115i
$778$	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
$782$	503.653	+	336.530i	0.644058	+	0.430345i
$783$		−	479.568i		−	0.612475i
$784$	−58.4966	+	24.2301i	−0.0746130	+	0.0309057i
$785$		0			0
$786$	234.148	−	234.148i	0.297898	−	0.297898i
$787$	−919.662	+	614.498i	−1.16857	+	0.780811i	−0.979558	−	0.201164i	$-0.935527\pi$
$787$	−919.662	+	614.498i	−1.16857	+	0.780811i	−0.189009	+	0.981975i	$0.560527\pi$
$788$	60.8102	+	305.714i	0.0771703	+	0.387962i
$789$	−213.027	+	318.817i	−0.269996	+	0.404077i
$790$		0			0
$791$	−1176.53	−	487.334i	−1.48739	−	0.616099i
$792$	68.8315	−	103.014i	0.0869084	−	0.130068i
$793$	−1156.64	+	230.069i	−1.45856	+	0.290125i
$794$	133.982	−	89.5239i	0.168743	−	0.112750i
$795$		0			0
$796$	64.3970	−	323.746i	0.0809008	−	0.406716i
$797$	56.6619	−	23.4701i	0.0710940	−	0.0294481i	−0.346853	−	0.937919i	$-0.612750\pi$
$797$	56.6619	−	23.4701i	0.0710940	−	0.0294481i	0.417947	+	0.908471i	$0.362750\pi$
$798$	−41.4081			−0.0518899
$799$	596.781	+	247.195i	0.746910	+	0.309380i
$800$		0			0
$801$	−91.1062	+	37.7374i	−0.113741	+	0.0471129i
$802$	−135.666	+	682.039i	−0.169160	+	0.850423i
$803$	−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
$807$	−113.521	−	47.0217i	−0.140670	−	0.0582673i
$808$	446.315	−	1077.50i	0.552370	−	1.33354i
$809$	−676.209	−	451.829i	−0.835858	−	0.558503i	0.0623592	−	0.998054i	$-0.480138\pi$
$809$	−676.209	−	451.829i	−0.835858	−	0.558503i	−0.898218	+	0.439551i	$0.855138\pi$
$810$		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
$813$	867.724	+	172.601i	1.06731	+	0.212301i
$814$	81.6192	+	197.046i	0.100269	+	0.242071i
$815$		0			0
$816$	19.0282	+	95.6614i	0.0233189	+	0.117232i
$817$			30.9806i			0.0379200i
$818$	−69.3211	−	167.356i	−0.0847446	−	0.204592i
$819$	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	$0.603895\pi$
$822$	−71.1252	−	357.570i	−0.0865270	−	0.435000i
$823$	−45.0492	−	30.1009i	−0.0547378	−	0.0365746i	0.527900	−	0.849306i	$-0.322979\pi$
$823$	−45.0492	−	30.1009i	−0.0547378	−	0.0365746i	−0.582638	+	0.812732i	$0.697979\pi$
$824$	−134.321	+	324.279i	−0.163011	+	0.393542i
$825$		0			0
$826$	−233.993	−	156.349i	−0.283284	−	0.189285i
$827$	−402.321	+	80.0267i	−0.486483	+	0.0967675i	−0.432237	−	0.901760i	$-0.642276\pi$
$827$	−402.321	+	80.0267i	−0.486483	+	0.0967675i	−0.0542461	+	0.998528i	$0.517276\pi$
$828$	59.6963	+	89.3418i	0.0720970	+	0.107901i
$829$	153.097	+	153.097i	0.184677	+	0.184677i	0.793390	−	0.608713i	$-0.208314\pi$
$829$	153.097	+	153.097i	0.184677	+	0.184677i	−0.608713	+	0.793390i	$0.708314\pi$
$830$		0			0
$831$	−289.696	−	699.389i	−0.348612	−	0.841623i
$832$	1117.56			1.34322
$833$	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
$838$	414.741	−	277.121i	0.494918	−	0.330694i
$839$	278.253	−	55.3480i	0.331648	−	0.0659690i	−0.0264576	−	0.999650i	$-0.508423\pi$
$839$	278.253	−	55.3480i	0.331648	−	0.0659690i	0.358106	+	0.933681i	$0.383423\pi$
$840$		0			0
$841$	−217.057	+	524.021i	−0.258094	+	0.623093i
$842$	197.491	−	476.785i	0.234549	−	0.566252i
$843$	−227.824	+	340.963i	−0.270254	+	0.404463i
$844$	−88.8960	−	446.910i	−0.105327	−	0.529515i
$845$		0			0
$846$	−64.5544	−	64.5544i	−0.0763054	−	0.0763054i
$847$	455.729	+	90.6502i	0.538051	+	0.107025i
$848$	55.9416	−	23.1718i	0.0659689	−	0.0273252i
$849$			852.762i			1.00443i
$850$		0			0
$851$	−517.327			−0.607905
$852$	−239.692	−	578.667i	−0.281328	−	0.679187i
$853$	−111.217	+	559.124i	−0.130383	+	0.655479i	0.859215	+	0.511615i	$0.170953\pi$
$853$	−111.217	+	559.124i	−0.130383	+	0.655479i	−0.989598	+	0.143864i	$0.954047\pi$
$854$	431.162	−	431.162i	0.504874	−	0.504874i
$855$		0			0
$856$	−599.815	+	119.311i	−0.700718	+	0.139382i
$857$	−1104.79	−	738.200i	−1.28914	−	0.861377i	−0.293622	−	0.955922i	$-0.594861\pi$
$857$	−1104.79	−	738.200i	−1.28914	−	0.861377i	−0.995521	+	0.0945445i	$0.969861\pi$
$858$	624.269	+	258.581i	0.727586	+	0.301376i
$859$	−260.316	−	107.826i	−0.303046	−	0.125526i	0.225979	−	0.974132i	$-0.427442\pi$
$859$	−260.316	−	107.826i	−0.303046	−	0.125526i	−0.529024	+	0.848607i	$0.677442\pi$
$860$		0			0
$861$	−122.644	−	616.572i	−0.142443	−	0.716111i
$862$	50.9295	+	76.2213i	0.0590829	+	0.0884238i
$863$	44.4457	−	44.4457i	0.0515014	−	0.0515014i	−0.680887	−	0.732388i	$-0.738406\pi$
$863$	44.4457	−	44.4457i	0.0515014	−	0.0515014i	0.732388	+	0.680887i	$0.238406\pi$
$864$	−171.436	+	861.869i	−0.198422	+	0.997533i
$865$		0			0
$866$			362.854i			0.419000i
$867$	−430.707	−	644.598i	−0.496778	−	0.743481i
$868$		−	271.144i		−	0.312378i
$869$	55.5355	−	23.0035i	0.0639073	−	0.0264713i
$870$		0			0
$871$	−1137.49	+	1137.49i	−1.30596	+	1.30596i
$872$	1449.49	−	968.518i	1.66226	−	1.11069i
$873$	27.9034	+	140.280i	0.0319626	+	0.160687i
$874$	−25.8790	+	38.7307i	−0.0296099	+	0.0443143i
$875$		0			0
$876$	196.330	+	81.3225i	0.224121	+	0.0928339i
$877$	−250.521	+	374.931i	−0.285657	+	0.427515i	−0.946351	−	0.323139i	$-0.895262\pi$
$877$	−250.521	+	374.931i	−0.285657	+	0.427515i	0.660695	+	0.750655i	$0.270262\pi$
$878$	192.304	−	38.2516i	0.219025	−	0.0435668i
$879$	−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	$-0.126193\pi$
$882$	−65.7130	+	27.2192i	−0.0745046	+	0.0308608i
$883$	908.452			1.02882			0.514412	−	0.857543i	$-0.328010\pi$
$883$	908.452			1.02882			0.514412	+	0.857543i	$0.328010\pi$
$884$	−798.496	+	330.748i	−0.903276	+	0.374149i
$885$		0			0
$886$	−762.051	+	315.652i	−0.860103	+	0.356266i
$887$	−48.8583	+	245.627i	−0.0550827	+	0.276919i	−0.998504	−	0.0546769i	$-0.982587\pi$
$887$	−48.8583	+	245.627i	−0.0550827	+	0.276919i	0.943421	+	0.331596i	$0.107587\pi$
$888$	−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
$892$	239.117	+	99.0454i	0.268068	+	0.111037i
$893$	−19.0092	+	45.8922i	−0.0212869	+	0.0513911i
$894$	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
$898$	−819.556	−	163.020i	−0.912646	−	0.181537i
$899$	86.9888	+	210.010i	0.0967617	+	0.233604i
$900$		0			0
$901$	−340.317	+	340.317i	−0.377711	+	0.377711i
$902$			291.555i			0.323232i
$903$	−215.687	−	520.713i	−0.238856	−	0.576648i
$904$	−1168.19	−	232.367i	−1.29224	−	0.257043i
$905$		0			0
$906$	279.804	+	418.756i	0.308835	+	0.462204i
$907$	338.757	+	1703.05i	0.373492	+	1.87767i	0.470524	+	0.882387i	$0.344065\pi$
$907$	338.757	+	1703.05i	0.373492	+	1.87767i	−0.0970321	+	0.995281i	$0.530935\pi$
$908$	−283.984	−	189.752i	−0.312758	−	0.208978i
$909$	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	$0.242337\pi$
$912$	−7.35633	+	1.46326i	−0.00806615	+	0.00160446i
$913$	−619.472	−	927.106i	−0.678502	−	1.01545i
$914$	130.337	+	130.337i	0.142600	+	0.142600i
$915$		0			0
$916$	8.21630	+	19.8359i	0.00896976	+	0.0216549i
$917$	−821.743			−0.896121
$918$	128.015	+	643.575i	0.139450	+	0.701062i
$919$	506.869			0.551544			0.275772	−	0.961223i	$-0.411067\pi$
$919$	506.869			0.551544			0.275772	+	0.961223i	$0.411067\pi$
$920$		0			0
$921$	12.6541	+	2.51706i	0.0137395	+	0.00273296i
$922$	−138.230	−	138.230i	−0.149924	−	0.149924i
$923$	−1991.48	+	1330.66i	−2.15761	+	1.44167i
$924$	430.077	−	85.5476i	0.465451	−	0.0925839i
$925$		0			0
$926$	376.485	−	908.914i	0.406571	−	0.981549i
$927$	−29.2223	+	70.5489i	−0.0315235	+	0.0761045i
$928$	−278.737	+	417.160i	−0.300364	+	0.449526i
$929$	−272.070	−	1367.79i	−0.292863	−	1.47232i	−0.794510	−	0.607251i	$-0.792272\pi$
$929$	−272.070	−	1367.79i	−0.292863	−	1.47232i	0.501646	−	0.865073i	$-0.332728\pi$
$930$		0			0
$931$	27.3656	+	27.3656i	0.0293937	+	0.0293937i
$932$	−851.665	−	169.407i	−0.913803	−	0.181767i
$933$	−1191.16	+	493.396i	−1.27670	+	0.528827i
$934$		−	10.1880i		−	0.0109080i
$935$		0			0
$936$	341.626			0.364985
$937$	−76.7261	−	185.233i	−0.0818848	−	0.197687i	0.877634	−	0.479331i	$-0.159121\pi$
$937$	−76.7261	−	185.233i	−0.0818848	−	0.197687i	−0.959519	+	0.281643i	$0.909121\pi$
$938$	162.268	−	815.774i	0.172993	−	0.869695i
$939$	−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	$0.738841\pi$
$942$	329.334	+	220.054i	0.349611	+	0.233603i
$943$	−653.355	−	270.628i	−0.692847	−	0.286987i
$944$	−47.0948	−	19.5073i	−0.0498886	−	0.0206645i
$945$		0			0
$946$	50.9953	+	256.371i	0.0539063	+	0.271005i
$947$	−565.096	−	845.726i	−0.596723	−	0.893058i	0.403033	−	0.915186i	$-0.367956\pi$
$947$	−565.096	−	845.726i	−0.596723	−	0.893058i	−0.999755	+	0.0221273i	$0.992956\pi$
$948$	−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
$952$	694.356	−	1039.18i	0.729365	−	1.09157i
$953$		−	297.230i		−	0.311889i	−0.987766	−	0.155945i	$-0.950158\pi$
$953$		−	297.230i		−	0.311889i	0.987766	−	0.155945i	$-0.0498421\pi$
$954$	62.8428	−	26.0303i	0.0658730	−	0.0272855i
$955$		0			0
$956$	−586.045	+	586.045i	−0.613017	+	0.613017i
$957$	−305.662	+	204.237i	−0.319396	+	0.213414i
$958$	196.662	+	988.688i	0.205284	+	1.03203i
$959$	−502.640	+	752.255i	−0.524130	+	0.784416i
$960$		0			0
$961$	713.498	+	295.540i	0.742453	+	0.307534i
$962$	−326.734	+	488.992i	−0.339640	+	0.508308i
$963$	−130.493	+	25.9567i	−0.135507	+	0.0269540i
$964$	257.270	−	171.902i	0.266878	−	0.178322i
$965$		0			0
$966$	165.325	−	831.144i	0.171144	−	0.860397i
$967$	1093.12	−	452.787i	1.13043	−	0.468239i	0.262502	−	0.964931i	$-0.415452\pi$
$967$	1093.12	−	452.787i	1.13043	−	0.468239i	0.867927	+	0.496692i	$0.165452\pi$
$968$	434.595			0.448961
$969$	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	$0.283215\pi$
$972$	−41.6248	+	209.262i	−0.0428239	+	0.215290i
$973$	−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
$977$	−302.204	−	125.177i	−0.309318	−	0.128124i	0.222624	−	0.974904i	$-0.428538\pi$
$977$	−302.204	−	125.177i	−0.309318	−	0.128124i	−0.531942	+	0.846781i	$0.678538\pi$
$978$	223.305	−	539.105i	0.228328	−	0.551232i
$979$	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
$983$	−1004.98	−	199.903i	−1.02236	−	0.203360i	−0.344683	−	0.938719i	$-0.612014\pi$
$983$	−1004.98	−	199.903i	−1.02236	−	0.203360i	−0.677678	+	0.735359i	$0.737014\pi$
$984$	−225.009	−	543.221i	−0.228668	−	0.552053i
$985$		0			0
$986$	−73.0887	+	367.442i	−0.0741265	+	0.372659i
$987$		−	903.685i		−	0.915587i
$988$	−25.4344	−	61.4041i	−0.0257433	−	0.0621499i
$989$	−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	$0.879262\pi$
$992$	−81.2600	−	408.521i	−0.0819153	−	0.411816i
$993$	226.739	+	151.502i	0.228338	+	0.152570i
$994$	473.916	−	1144.14i	0.476777	−	1.15104i
$995$		0			0
$996$	668.524	+	446.693i	0.671209	+	0.448487i
$997$	−1233.85	+	245.429i	−1.23757	+	0.246167i	−0.770146	−	0.637867i	$-0.779817\pi$
$997$	−1233.85	+	245.429i	−1.23757	+	0.246167i	−0.467421	+	0.884035i	$0.654817\pi$
$998$	82.9374	+	124.125i	0.0831037	+	0.124373i
$999$	−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.t.c.224.1		8
5.2	odd	4		425.3.u.b.326.1		8
5.3	odd	4		17.3.e.a.3.1	✓	8
5.4	even	2		425.3.t.a.224.1		8
15.8	even	4		153.3.p.b.37.1		8
17.6	odd	16		425.3.t.a.74.1		8
20.3	even	4		272.3.bh.c.241.1		8
85.3	even	16		289.3.e.l.214.1		8
85.8	odd	8		289.3.e.d.158.1		8
85.13	odd	4		289.3.e.i.65.1		8
85.23	even	16		17.3.e.a.6.1	yes	8
85.28	even	16		289.3.e.c.40.1		8
85.33	odd	4		289.3.e.c.224.1		8
85.38	odd	4		289.3.e.m.65.1		8
85.43	odd	8		289.3.e.b.158.1		8
85.48	even	16		289.3.e.k.214.1		8
85.53	odd	8		289.3.e.l.131.1		8
85.57	even	16		425.3.u.b.176.1		8
85.58	even	16		289.3.e.i.249.1		8
85.63	even	16		289.3.e.b.75.1		8
85.73	even	16		289.3.e.d.75.1		8
85.74	odd	16	inner	425.3.t.c.74.1		8
85.78	even	16		289.3.e.m.249.1		8
85.83	odd	8		289.3.e.k.131.1		8
255.23	odd	16		153.3.p.b.91.1		8
340.23	odd	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	5.3	odd	4
17.3.e.a.6.1	yes	8	85.23	even	16
153.3.p.b.37.1		8	15.8	even	4
153.3.p.b.91.1		8	255.23	odd	16
272.3.bh.c.193.1		8	340.23	odd	16
272.3.bh.c.241.1		8	20.3	even	4
289.3.e.b.75.1		8	85.63	even	16
289.3.e.b.158.1		8	85.43	odd	8
289.3.e.c.40.1		8	85.28	even	16
289.3.e.c.224.1		8	85.33	odd	4
289.3.e.d.75.1		8	85.73	even	16
289.3.e.d.158.1		8	85.8	odd	8
289.3.e.i.65.1		8	85.13	odd	4
289.3.e.i.249.1		8	85.58	even	16
289.3.e.k.131.1		8	85.83	odd	8
289.3.e.k.214.1		8	85.48	even	16
289.3.e.l.131.1		8	85.53	odd	8
289.3.e.l.214.1		8	85.3	even	16
289.3.e.m.65.1		8	85.38	odd	4
289.3.e.m.249.1		8	85.78	even	16
425.3.t.a.74.1		8	17.6	odd	16
425.3.t.a.224.1		8	5.4	even	2
425.3.t.c.74.1		8	85.74	odd	16	inner
425.3.t.c.224.1		8	1.1	even	1	trivial
425.3.u.b.176.1		8	85.57	even	16
425.3.u.b.326.1		8	5.2	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.t (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.509666 + 1.23044i) q^{2} +(-0.523336 + 2.63099i) q^{3} +(1.57420 - 1.57420i) q^{4} +(-3.50400 + 0.696990i) q^{6} +(7.37170 + 4.92562i) q^{7} +(7.66104 + 3.17331i) q^{8} +(1.66671 + 0.690373i) q^{9} +(-1.61572 - 8.12279i) q^{11} +(3.31786 + 4.96553i) q^{12} +(16.1480 - 16.1480i) q^{13} +(-2.30358 + 11.5809i) q^{14} +2.13880i q^{16} +(-6.50562 - 15.7060i) q^{17} +2.40265i q^{18} +(1.20778 - 0.500280i) q^{19} +(-16.8171 + 16.8171i) q^{21} +(9.17115 - 6.12797i) q^{22} +(5.21946 + 26.2400i) q^{23} +(-12.3582 + 18.4954i) q^{24} +(28.0993 + 11.6391i) q^{26} +(-16.1016 + 24.0978i) q^{27} +(19.3584 - 3.85063i) q^{28} +(-13.7583 + 9.19303i) q^{29} +(2.68003 - 13.4734i) q^{31} +(28.0125 - 11.6032i) q^{32} +22.2165 q^{33} +(16.0096 - 16.0096i) q^{34} +(3.71051 - 1.53694i) q^{36} +(-3.77234 + 18.9648i) q^{37} +(1.23113 + 1.23113i) q^{38} +(34.0344 + 50.9361i) q^{39} +(-14.6853 + 21.9781i) q^{41} +(-29.2636 - 12.1214i) q^{42} +(-9.06895 + 21.8944i) q^{43} +(-15.3303 - 10.2434i) q^{44} +(-29.6266 + 19.7959i) q^{46} +(-26.8680 + 26.8680i) q^{47} +(-5.62714 - 1.11931i) q^{48} +(11.3288 + 27.3503i) q^{49} +(44.7268 - 8.89671i) q^{51} -50.8404i q^{52} +(-10.8340 - 26.1557i) q^{53} +(-37.8574 - 7.53030i) q^{54} +(40.8445 + 61.1281i) q^{56} +(0.684154 + 3.43947i) q^{57} +(-18.3236 - 12.2435i) q^{58} +(-9.12070 + 22.0193i) q^{59} +(-42.9373 - 28.6898i) q^{61} +(17.9442 - 3.56932i) q^{62} +(8.88596 + 13.2988i) q^{63} +(34.6035 + 34.6035i) q^{64} +(11.3230 + 27.3362i) q^{66} -70.4415 q^{67} +(-34.9654 - 14.4831i) q^{68} -71.7687 q^{69} +(-102.865 - 20.4612i) q^{71} +(10.5780 + 10.5780i) q^{72} +(29.5868 - 19.7693i) q^{73} +(-25.2578 + 5.02408i) q^{74} +(1.11375 - 2.68883i) q^{76} +(28.0991 - 67.8373i) q^{77} +(-45.3277 + 67.8377i) q^{78} +(1.41599 + 7.11865i) q^{79} +(-43.4936 - 43.4936i) q^{81} +(-34.5274 - 6.86792i) q^{82} +(124.385 - 51.5218i) q^{83} +52.9469i q^{84} -31.5619 q^{86} +(-16.9865 - 41.0090i) q^{87} +(13.3980 - 67.3563i) q^{88} +(-38.6522 + 38.6522i) q^{89} +(198.577 - 39.4995i) q^{91} +(49.5234 + 33.0905i) q^{92} +(34.0458 + 14.1023i) q^{93} +(-46.7533 - 19.3658i) q^{94} +(15.8678 + 79.7729i) q^{96} +(44.0470 + 65.9209i) q^{97} +(-27.8790 + 27.8790i) q^{98} +(2.91482 - 14.6538i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} - 8 q^{6} - 8 q^{7} + 40 q^{8} + 16 q^{9} - 8 q^{11} - 40 q^{12} + 16 q^{13} - 8 q^{14} - 64 q^{21} - 56 q^{22} - 40 q^{23} + 80 q^{24} + 176 q^{26} - 16 q^{27} - 56 q^{28} - 48 q^{29}+ \cdots + 224 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 - 8 * q^6 - 8 * q^7 + 40 * q^8 + 16 * q^9 - 8 * q^11 - 40 * q^12 + 16 * q^13 - 8 * q^14 - 64 * q^21 - 56 * q^22 - 40 * q^23 + 80 * q^24 + 176 * q^26 - 16 * q^27 - 56 * q^28 - 48 * q^29 + 24 * q^31 + 88 * q^32 + 96 * q^33 + 136 * q^34 - 128 * q^36 + 128 * q^37 + 120 * q^38 - 48 * q^39 + 48 * q^41 + 128 * q^42 + 112 * q^43 - 120 * q^44 - 88 * q^46 - 192 * q^47 + 8 * q^48 - 16 * q^49 + 136 * q^51 - 128 * q^53 - 8 * q^54 - 120 * q^56 - 72 * q^57 - 32 * q^58 + 48 * q^59 - 160 * q^61 - 56 * q^62 - 168 * q^63 + 64 * q^64 - 8 * q^66 - 336 * q^67 - 272 * q^68 - 240 * q^69 + 40 * q^71 + 40 * q^72 - 48 * q^73 + 160 * q^74 + 80 * q^76 + 80 * q^77 + 304 * q^78 + 136 * q^79 - 424 * q^81 + 136 * q^82 + 336 * q^83 + 832 * q^86 + 80 * q^87 + 320 * q^88 - 160 * q^89 + 320 * q^91 + 184 * q^92 + 208 * q^93 - 32 * q^94 - 56 * q^96 + 104 * q^97 - 120 * q^98 + 224 * q^99

Introduction

L-functions

Modular forms

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