LMFDB - Embedded newform 405.3.h.c.134.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(134,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.134"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2,0,6,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			134.2
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	405.134
Dual form			405.3.h.c.269.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{4} +(4.05842 + 2.92048i) q^{5} +(-8.61684 + 4.97494i) q^{7} -7.00000 q^{8} +(0.500000 - 4.97494i) q^{10} +(8.61684 - 4.97494i) q^{11} +(17.2337 + 9.94987i) q^{13} +(8.61684 + 4.97494i) q^{14} +(-2.50000 - 4.33013i) q^{16} +22.0000 q^{17} -4.00000 q^{19} +(13.6753 - 6.16337i) q^{20} +(-8.61684 - 4.97494i) q^{22} +(10.0000 - 17.3205i) q^{23} +(7.94158 + 23.7051i) q^{25} -19.8997i q^{26} +29.8496i q^{28} +(34.4674 - 19.8997i) q^{29} +(-14.5000 + 25.1147i) q^{31} +(-16.5000 + 28.5788i) q^{32} +(-11.0000 - 19.0526i) q^{34} +(-49.5000 - 4.97494i) q^{35} +(2.00000 + 3.46410i) q^{38} +(-28.4090 - 20.4434i) q^{40} +(34.4674 + 19.8997i) q^{41} +(17.2337 - 9.94987i) q^{43} -29.8496i q^{44} -20.0000 q^{46} +(-29.0000 - 50.2295i) q^{47} +(25.0000 - 43.3013i) q^{49} +(16.5584 - 18.7302i) q^{50} +(51.7011 - 29.8496i) q^{52} +31.0000 q^{53} +(49.5000 + 4.97494i) q^{55} +(60.3179 - 34.8246i) q^{56} +(-34.4674 - 19.8997i) q^{58} +(34.4674 + 19.8997i) q^{59} +(-22.0000 - 38.1051i) q^{61} +29.0000 q^{62} +13.0000 q^{64} +(40.8832 + 90.7115i) q^{65} +(17.2337 + 9.94987i) q^{67} +(33.0000 - 57.1577i) q^{68} +(20.4416 + 45.3557i) q^{70} +59.6992i q^{71} -89.5489i q^{73} +(-6.00000 + 10.3923i) q^{76} +(-49.5000 + 85.7365i) q^{77} +(5.00000 + 8.66025i) q^{79} +(2.50000 - 24.8747i) q^{80} -39.7995i q^{82} +(-9.50000 - 16.4545i) q^{83} +(89.2853 + 64.2506i) q^{85} +(-17.2337 - 9.94987i) q^{86} +(-60.3179 + 34.8246i) q^{88} +59.6992i q^{89} -198.000 q^{91} +(-30.0000 - 51.9615i) q^{92} +(-29.0000 + 50.2295i) q^{94} +(-16.2337 - 11.6819i) q^{95} +(-112.019 + 64.6742i) q^{97} -50.0000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{4} - q^{5} - 28 q^{8} + 2 q^{10} - 10 q^{16} + 88 q^{17} - 16 q^{19} + 3 q^{20} + 40 q^{23} + 49 q^{25} - 58 q^{31} - 66 q^{32} - 44 q^{34} - 198 q^{35} + 8 q^{38} + 7 q^{40} - 80 q^{46}+ \cdots - 200 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^4 - q^5 - 28 * q^8 + 2 * q^10 - 10 * q^16 + 88 * q^17 - 16 * q^19 + 3 * q^20 + 40 * q^23 + 49 * q^25 - 58 * q^31 - 66 * q^32 - 44 * q^34 - 198 * q^35 + 8 * q^38 + 7 * q^40 - 80 * q^46 - 116 * q^47 + 100 * q^49 + 49 * q^50 + 124 * q^53 + 198 * q^55 - 88 * q^61 + 116 * q^62 + 52 * q^64 + 198 * q^65 + 132 * q^68 + 99 * q^70 - 24 * q^76 - 198 * q^77 + 20 * q^79 + 10 * q^80 - 38 * q^83 - 22 * q^85 - 792 * q^91 - 120 * q^92 - 116 * q^94 + 4 * q^95 - 200 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.250000	−	0.433013i	0.713525	−	0.700629i	$-0.247097\pi$
$2$	−0.500000	−	0.866025i	−0.250000	−	0.433013i	−0.963525	+	0.267617i	$0.913764\pi$
$3$		0			0
$3$		0			0
$4$	1.50000	−	2.59808i	0.375000	−	0.649519i
$5$	4.05842	+	2.92048i	0.811684	+	0.584096i
$5$	4.05842	+	2.92048i	0.811684	+	0.584096i
$6$		0			0
$7$	−8.61684	+	4.97494i	−1.23098	+	0.710705i	−0.967234	−	0.253887i	$-0.918291\pi$
$7$	−8.61684	+	4.97494i	−1.23098	+	0.710705i	−0.263744	+	0.964593i	$0.584957\pi$
$8$	−7.00000			−0.875000
$9$		0			0
$10$	0.500000	−	4.97494i	0.0500000	−	0.497494i
$11$	8.61684	−	4.97494i	0.783349	−	0.452267i	−0.0542666	−	0.998526i	$-0.517282\pi$
$11$	8.61684	−	4.97494i	0.783349	−	0.452267i	0.837616	+	0.546259i	$0.183949\pi$
$12$		0			0
$13$	17.2337	+	9.94987i	1.32567	+	0.765375i	0.984626	−	0.174673i	$-0.0558869\pi$
$13$	17.2337	+	9.94987i	1.32567	+	0.765375i	0.341042	+	0.940048i	$0.389220\pi$
$14$	8.61684	+	4.97494i	0.615489	+	0.355353i
$15$		0			0
$16$	−2.50000	−	4.33013i	−0.156250	−	0.270633i
$17$	22.0000			1.29412			0.647059	−	0.762440i	$-0.275999\pi$
$17$	22.0000			1.29412			0.647059	+	0.762440i	$0.275999\pi$
$18$		0			0
$19$	−4.00000			−0.210526			−0.105263	−	0.994444i	$-0.533568\pi$
$19$	−4.00000			−0.210526			−0.105263	+	0.994444i	$0.533568\pi$
$20$	13.6753	−	6.16337i	0.683763	−	0.308168i
$21$		0			0
$22$	−8.61684	−	4.97494i	−0.391675	−	0.226134i
$23$	10.0000	−	17.3205i	0.434783	−	0.753066i	−0.562495	−	0.826801i	$-0.690159\pi$
$23$	10.0000	−	17.3205i	0.434783	−	0.753066i	0.997278	+	0.0737349i	$0.0234919\pi$
$24$		0			0
$25$	7.94158	+	23.7051i	0.317663	+	0.948204i
$26$		−	19.8997i		−	0.765375i
$27$		0			0
$28$			29.8496i			1.06606i
$29$	34.4674	−	19.8997i	1.18853	−	0.686198i	0.230558	−	0.973059i	$-0.425945\pi$
$29$	34.4674	−	19.8997i	1.18853	−	0.686198i	0.957972	+	0.286860i	$0.0926116\pi$
$30$		0			0
$31$	−14.5000	+	25.1147i	−0.467742	+	0.810153i	−0.999321	−	0.0368561i	$-0.988266\pi$
$31$	−14.5000	+	25.1147i	−0.467742	+	0.810153i	0.531579	+	0.847009i	$0.321599\pi$
$32$	−16.5000	+	28.5788i	−0.515625	+	0.893089i
$33$		0			0
$34$	−11.0000	−	19.0526i	−0.323529	−	0.560369i
$35$	−49.5000	−	4.97494i	−1.41429	−	0.142141i
$36$		0			0
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	2.00000	+	3.46410i	0.0526316	+	0.0911606i
$39$		0			0
$40$	−28.4090	−	20.4434i	−0.710224	−	0.511084i
$41$	34.4674	+	19.8997i	0.840668	+	0.485360i	0.857491	−	0.514499i	$-0.172022\pi$
$41$	34.4674	+	19.8997i	0.840668	+	0.485360i	−0.0168234	+	0.999858i	$0.505355\pi$
$42$		0			0
$43$	17.2337	−	9.94987i	0.400783	−	0.231392i	−0.286039	−	0.958218i	$-0.592339\pi$
$43$	17.2337	−	9.94987i	0.400783	−	0.231392i	0.686822	+	0.726826i	$0.259005\pi$
$44$		−	29.8496i		−	0.678401i
$45$		0			0
$46$	−20.0000			−0.434783
$47$	−29.0000	−	50.2295i	−0.617021	−	1.06871i	−0.990026	−	0.140883i	$-0.955006\pi$
$47$	−29.0000	−	50.2295i	−0.617021	−	1.06871i	0.373005	−	0.927829i	$-0.378327\pi$
$48$		0			0
$49$	25.0000	−	43.3013i	0.510204	−	0.883699i
$50$	16.5584	−	18.7302i	0.331168	−	0.374603i
$51$		0			0
$52$	51.7011	−	29.8496i	0.994251	−	0.574031i
$53$	31.0000			0.584906			0.292453	−	0.956280i	$-0.405529\pi$
$53$	31.0000			0.584906			0.292453	+	0.956280i	$0.405529\pi$
$54$		0			0
$55$	49.5000	+	4.97494i	0.900000	+	0.0904534i
$56$	60.3179	−	34.8246i	1.07711	−	0.621867i
$57$		0			0
$58$	−34.4674	−	19.8997i	−0.594265	−	0.343099i
$59$	34.4674	+	19.8997i	0.584193	+	0.337284i	0.762798	−	0.646637i	$-0.223825\pi$
$59$	34.4674	+	19.8997i	0.584193	+	0.337284i	−0.178605	+	0.983921i	$0.557158\pi$
$60$		0			0
$61$	−22.0000	−	38.1051i	−0.360656	−	0.624674i	0.627413	−	0.778687i	$-0.284114\pi$
$61$	−22.0000	−	38.1051i	−0.360656	−	0.624674i	−0.988069	+	0.154012i	$0.950780\pi$
$62$	29.0000			0.467742
$63$		0			0
$64$	13.0000			0.203125
$65$	40.8832	+	90.7115i	0.628972	+	1.39556i
$66$		0			0
$67$	17.2337	+	9.94987i	0.257219	+	0.148506i	0.623065	−	0.782170i	$-0.285887\pi$
$67$	17.2337	+	9.94987i	0.257219	+	0.148506i	−0.365846	+	0.930675i	$0.619220\pi$
$68$	33.0000	−	57.1577i	0.485294	−	0.840554i
$69$		0			0
$70$	20.4416	+	45.3557i	0.292023	+	0.647939i
$71$			59.6992i			0.840834i	0.907331	+	0.420417i	$0.138116\pi$
$71$			59.6992i			0.840834i	−0.907331	+	0.420417i	$0.861884\pi$
$72$		0			0
$73$		−	89.5489i		−	1.22670i	−0.789812	−	0.613348i	$-0.789822\pi$
$73$		−	89.5489i		−	1.22670i	0.789812	−	0.613348i	$-0.210178\pi$
$74$		0			0
$75$		0			0
$76$	−6.00000	+	10.3923i	−0.0789474	+	0.136741i
$77$	−49.5000	+	85.7365i	−0.642857	+	1.11346i
$78$		0			0
$79$	5.00000	+	8.66025i	0.0632911	+	0.109623i	0.895935	−	0.444186i	$-0.146507\pi$
$79$	5.00000	+	8.66025i	0.0632911	+	0.109623i	−0.832644	+	0.553809i	$0.813174\pi$
$80$	2.50000	−	24.8747i	0.0312500	−	0.310934i
$81$		0			0
$82$		−	39.7995i		−	0.485360i
$83$	−9.50000	−	16.4545i	−0.114458	−	0.198247i	0.803105	−	0.595837i	$-0.203180\pi$
$83$	−9.50000	−	16.4545i	−0.114458	−	0.198247i	−0.917563	+	0.397591i	$0.869846\pi$
$84$		0			0
$85$	89.2853	+	64.2506i	1.05042	+	0.755889i
$86$	−17.2337	−	9.94987i	−0.200392	−	0.115696i
$87$		0			0
$88$	−60.3179	+	34.8246i	−0.685431	+	0.395734i
$89$			59.6992i			0.670778i	0.942080	+	0.335389i	$0.108868\pi$
$89$			59.6992i			0.670778i	−0.942080	+	0.335389i	$0.891132\pi$
$90$		0			0
$91$	−198.000			−2.17582
$92$	−30.0000	−	51.9615i	−0.326087	−	0.564799i
$93$		0			0
$94$	−29.0000	+	50.2295i	−0.308511	+	0.534356i
$95$	−16.2337	−	11.6819i	−0.170881	−	0.122968i
$96$		0			0
$97$	−112.019	+	64.6742i	−1.15483	+	0.666744i	−0.950061	−	0.312065i	$-0.898979\pi$
$97$	−112.019	+	64.6742i	−1.15483	+	0.666744i	−0.204774	+	0.978809i	$0.565646\pi$
$98$	−50.0000			−0.510204
$99$		0			0
$100$	73.5000	+	14.9248i	0.735000	+	0.149248i
$101$	−146.486	+	84.5739i	−1.45036	+	0.837366i	−0.998502	−	0.0547240i	$-0.982572\pi$
$101$	−146.486	+	84.5739i	−1.45036	+	0.837366i	−0.451858	+	0.892090i	$0.649239\pi$
$102$		0			0
$103$	−34.4674	−	19.8997i	−0.334635	−	0.193201i	0.323262	−	0.946309i	$-0.395220\pi$
$103$	−34.4674	−	19.8997i	−0.334635	−	0.193201i	−0.657897	+	0.753108i	$0.728554\pi$
$104$	−120.636	−	69.6491i	−1.15996	−	0.669703i
$105$		0			0
$106$	−15.5000	−	26.8468i	−0.146226	−	0.253272i
$107$	−29.0000			−0.271028			−0.135514	−	0.990775i	$-0.543269\pi$
$107$	−29.0000			−0.271028			−0.135514	+	0.990775i	$0.543269\pi$
$108$		0			0
$109$	104.000			0.954128			0.477064	−	0.878868i	$-0.341701\pi$
$109$	104.000			0.954128			0.477064	+	0.878868i	$0.341701\pi$
$110$	−20.4416	−	45.3557i	−0.185833	−	0.412325i
$111$		0			0
$112$	43.0842	+	24.8747i	0.384681	+	0.222095i
$113$	40.0000	−	69.2820i	0.353982	−	0.613115i	−0.632961	−	0.774184i	$-0.718161\pi$
$113$	40.0000	−	69.2820i	0.353982	−	0.613115i	0.986943	+	0.161068i	$0.0514940\pi$
$114$		0			0
$115$	91.1684	−	41.0891i	0.792769	−	0.357297i
$116$		−	119.398i		−	1.02930i
$117$		0			0
$118$		−	39.7995i		−	0.337284i
$119$	−189.571	+	109.449i	−1.59303	+	0.919736i
$120$		0			0
$121$	−11.0000	+	19.0526i	−0.0909091	+	0.157459i
$122$	−22.0000	+	38.1051i	−0.180328	+	0.312337i
$123$		0			0
$124$	43.5000	+	75.3442i	0.350806	+	0.607615i
$125$	−37.0000	+	119.398i	−0.296000	+	0.955188i
$126$		0			0
$127$			149.248i			1.17518i	0.809158	+	0.587591i	$0.199924\pi$
$127$			149.248i			1.17518i	−0.809158	+	0.587591i	$0.800076\pi$
$128$	59.5000	+	103.057i	0.464844	+	0.805133i
$129$		0			0
$130$	58.1168	−	80.7616i	0.447053	−	0.621243i
$131$	−146.486	−	84.5739i	−1.11822	−	0.645603i	−0.177271	−	0.984162i	$-0.556727\pi$
$131$	−146.486	−	84.5739i	−1.11822	−	0.645603i	−0.940945	+	0.338559i	$0.890060\pi$
$132$		0			0
$133$	34.4674	−	19.8997i	0.259153	−	0.149622i
$134$		−	19.8997i		−	0.148506i
$135$		0			0
$136$	−154.000			−1.13235
$137$	49.0000	+	84.8705i	0.357664	+	0.619493i	0.987570	−	0.157179i	$-0.0502399\pi$
$137$	49.0000	+	84.8705i	0.357664	+	0.619493i	−0.629906	+	0.776671i	$0.716907\pi$
$138$		0			0
$139$	32.0000	−	55.4256i	0.230216	−	0.398746i	−0.727656	−	0.685943i	$-0.759390\pi$
$139$	32.0000	−	55.4256i	0.230216	−	0.398746i	0.957872	+	0.287197i	$0.0927235\pi$
$140$	−87.1753	+	121.142i	−0.622680	+	0.865303i
$141$		0			0
$142$	51.7011	−	29.8496i	0.364092	−	0.210209i
$143$	198.000			1.38462
$144$		0			0
$145$	198.000	+	19.8997i	1.36552	+	0.137240i
$146$	−77.5516	+	44.7744i	−0.531175	+	0.306674i
$147$		0			0
$148$		0			0
$149$	8.61684	+	4.97494i	0.0578312	+	0.0333888i	0.528637	−	0.848848i	$-0.322703\pi$
$149$	8.61684	+	4.97494i	0.0578312	+	0.0333888i	−0.470806	+	0.882237i	$0.656037\pi$
$150$		0			0
$151$	−128.500	−	222.569i	−0.850993	−	1.47396i	−0.880313	−	0.474394i	$-0.842667\pi$
$151$	−128.500	−	222.569i	−0.850993	−	1.47396i	0.0293194	−	0.999570i	$-0.490666\pi$
$152$	28.0000			0.184211
$153$		0			0
$154$	99.0000			0.642857
$155$	−132.194	+	59.5792i	−0.852866	+	0.384382i
$156$		0			0
$157$	−137.870	−	79.5990i	−0.878150	−	0.507000i	−0.00810182	−	0.999967i	$-0.502579\pi$
$157$	−137.870	−	79.5990i	−0.878150	−	0.507000i	−0.870048	+	0.492967i	$0.835912\pi$
$158$	5.00000	−	8.66025i	0.0316456	−	0.0548117i
$159$		0			0
$160$	−150.428	+	67.7970i	−0.940175	+	0.423732i
$161$			198.997i			1.23601i
$162$		0			0
$163$			298.496i			1.83127i	0.402016	+	0.915633i	$0.368310\pi$
$163$			298.496i			1.83127i	−0.402016	+	0.915633i	$0.631690\pi$
$164$	103.402	−	59.6992i	0.630501	−	0.364020i
$165$		0			0
$166$	−9.50000	+	16.4545i	−0.0572289	+	0.0991234i
$167$	127.000	−	219.970i	0.760479	−	1.31719i	−0.182125	−	0.983275i	$-0.558298\pi$
$167$	127.000	−	219.970i	0.760479	−	1.31719i	0.942604	−	0.333913i	$-0.108369\pi$
$168$		0			0
$169$	113.500	+	196.588i	0.671598	+	1.16324i
$170$	11.0000	−	109.449i	0.0647059	−	0.643815i
$171$		0			0
$172$		−	59.6992i		−	0.347089i
$173$	−117.500	−	203.516i	−0.679191	−	1.17639i	−0.975225	−	0.221216i	$-0.928998\pi$
$173$	−117.500	−	203.516i	−0.679191	−	1.17639i	0.296034	−	0.955177i	$-0.404336\pi$
$174$		0			0
$175$	−186.363	−	164.754i	−1.06493	−	0.941453i
$176$	−43.0842	−	24.8747i	−0.244797	−	0.141333i
$177$		0			0
$178$	51.7011	−	29.8496i	0.290455	−	0.167695i
$179$			149.248i			0.833788i	0.908955	+	0.416894i	$0.136881\pi$
$179$			149.248i			0.833788i	−0.908955	+	0.416894i	$0.863119\pi$
$180$		0			0
$181$	−292.000			−1.61326			−0.806630	−	0.591057i	$-0.798711\pi$
$181$	−292.000			−1.61326			−0.806630	+	0.591057i	$0.798711\pi$
$182$	99.0000	+	171.473i	0.543956	+	0.942160i
$183$		0			0
$184$	−70.0000	+	121.244i	−0.380435	+	0.658932i
$185$		0			0
$186$		0			0
$187$	189.571	−	109.449i	1.01375	−	0.585287i
$188$	−174.000			−0.925532
$189$		0			0
$190$	−2.00000	+	19.8997i	−0.0105263	+	0.104736i
$191$	86.1684	−	49.7494i	0.451144	−	0.260468i	−0.257169	−	0.966366i	$-0.582790\pi$
$191$	86.1684	−	49.7494i	0.451144	−	0.260468i	0.708313	+	0.705898i	$0.249457\pi$
$192$		0			0
$193$	146.486	+	84.5739i	0.758997	+	0.438207i	0.828935	−	0.559344i	$-0.188947\pi$
$193$	146.486	+	84.5739i	0.758997	+	0.438207i	−0.0699388	+	0.997551i	$0.522280\pi$
$194$	112.019	+	64.6742i	0.577417	+	0.333372i
$195$		0			0
$196$	−75.0000	−	129.904i	−0.382653	−	0.662775i
$197$	−203.000			−1.03046			−0.515228	−	0.857053i	$-0.672293\pi$
$197$	−203.000			−1.03046			−0.515228	+	0.857053i	$0.672293\pi$
$198$		0			0
$199$	155.000			0.778894			0.389447	−	0.921049i	$-0.372666\pi$
$199$	155.000			0.778894			0.389447	+	0.921049i	$0.372666\pi$
$200$	−55.5910	−	165.936i	−0.277955	−	0.829678i
$201$		0			0
$202$	146.486	+	84.5739i	0.725180	+	0.418683i
$203$	−198.000	+	342.946i	−0.975369	+	1.68939i
$204$		0			0
$205$	81.7663	+	181.423i	0.398860	+	0.884990i
$206$			39.7995i			0.193201i
$207$		0			0
$208$		−	99.4987i		−	0.478359i
$209$	−34.4674	+	19.8997i	−0.164916	+	0.0952141i
$210$		0			0
$211$	−154.000	+	266.736i	−0.729858	+	1.26415i	0.227085	+	0.973875i	$0.427080\pi$
$211$	−154.000	+	266.736i	−0.729858	+	1.26415i	−0.956943	+	0.290276i	$0.906253\pi$
$212$	46.5000	−	80.5404i	0.219340	−	0.379907i
$213$		0			0
$214$	14.5000	+	25.1147i	0.0677570	+	0.117359i
$215$	99.0000	+	9.94987i	0.460465	+	0.0462785i
$216$		0			0
$217$		−	288.546i		−	1.32971i
$218$	−52.0000	−	90.0666i	−0.238532	−	0.413150i
$219$		0			0
$220$	87.1753	−	121.142i	0.396251	−	0.550647i
$221$	379.141	+	218.897i	1.71557	+	0.990485i
$222$		0			0
$223$	−34.4674	+	19.8997i	−0.154562	+	0.0892365i	−0.575286	−	0.817952i	$-0.695109\pi$
$223$	−34.4674	+	19.8997i	−0.154562	+	0.0892365i	0.420724	+	0.907189i	$0.361776\pi$
$224$		−	328.346i		−	1.46583i
$225$		0			0
$226$	−80.0000			−0.353982
$227$	121.000	+	209.578i	0.533040	+	0.923252i	0.999255	+	0.0385807i	$0.0122837\pi$
$227$	121.000	+	209.578i	0.533040	+	0.923252i	−0.466216	+	0.884671i	$0.654383\pi$
$228$		0			0
$229$	53.0000	−	91.7987i	0.231441	−	0.400868i	−0.726791	−	0.686858i	$-0.758989\pi$
$229$	53.0000	−	91.7987i	0.231441	−	0.400868i	0.958232	+	0.285991i	$0.0923226\pi$
$230$	−81.1684	−	58.4096i	−0.352906	−	0.253955i
$231$		0			0
$232$	−241.272	+	139.298i	−1.03996	+	0.600423i
$233$	142.000			0.609442			0.304721	−	0.952442i	$-0.401437\pi$
$233$	142.000			0.609442			0.304721	+	0.952442i	$0.401437\pi$
$234$		0			0
$235$	29.0000	−	288.546i	0.123404	−	1.22786i
$236$	103.402	−	59.6992i	0.438145	−	0.252963i
$237$		0			0
$238$	189.571	+	109.449i	0.796515	+	0.459868i
$239$	−172.337	−	99.4987i	−0.721075	−	0.416313i	0.0940733	−	0.995565i	$-0.470011\pi$
$239$	−172.337	−	99.4987i	−0.721075	−	0.416313i	−0.815148	+	0.579253i	$0.803345\pi$
$240$		0			0
$241$	−85.0000	−	147.224i	−0.352697	−	0.610889i	0.634024	−	0.773313i	$-0.281402\pi$
$241$	−85.0000	−	147.224i	−0.352697	−	0.610889i	−0.986721	+	0.162424i	$0.948069\pi$
$242$	22.0000			0.0909091
$243$		0			0
$244$	−132.000			−0.540984
$245$	227.921	−	102.723i	0.930290	−	0.419277i
$246$		0			0
$247$	−68.9348	−	39.7995i	−0.279088	−	0.161132i
$248$	101.500	−	175.803i	0.409274	−	0.708884i
$249$		0			0
$250$	121.902	−	27.6563i	0.487609	−	0.110625i
$251$		−	358.195i		−	1.42707i	−0.700618	−	0.713537i	$-0.747092\pi$
$251$		−	358.195i		−	1.42707i	0.700618	−	0.713537i	$-0.252908\pi$
$252$		0			0
$253$		−	198.997i		−	0.786551i
$254$	129.253	−	74.6241i	0.508869	−	0.293796i
$255$		0			0
$256$	85.5000	−	148.090i	0.333984	−	0.578478i
$257$	145.000	−	251.147i	0.564202	−	0.977227i	−0.432921	−	0.901432i	$-0.642517\pi$
$257$	145.000	−	251.147i	0.564202	−	0.977227i	0.997123	−	0.0757953i	$-0.0241495\pi$
$258$		0			0
$259$		0			0
$260$	297.000	+	29.8496i	1.14231	+	0.114806i
$261$		0			0
$262$			169.148i			0.645603i
$263$	52.0000	+	90.0666i	0.197719	+	0.342459i	0.947788	−	0.318900i	$-0.103313\pi$
$263$	52.0000	+	90.0666i	0.197719	+	0.342459i	−0.750070	+	0.661359i	$0.769980\pi$
$264$		0			0
$265$	125.811	+	90.5349i	0.474759	+	0.341641i
$266$	−34.4674	−	19.8997i	−0.129577	−	0.0748111i
$267$		0			0
$268$	51.7011	−	29.8496i	0.192914	−	0.111379i
$269$			119.398i			0.443861i	0.975063	+	0.221930i	$0.0712357\pi$
$269$			119.398i			0.443861i	−0.975063	+	0.221930i	$0.928764\pi$
$270$		0			0
$271$	−121.000			−0.446494			−0.223247	−	0.974762i	$-0.571666\pi$
$271$	−121.000			−0.446494			−0.223247	+	0.974762i	$0.571666\pi$
$272$	−55.0000	−	95.2628i	−0.202206	−	0.350231i
$273$		0			0
$274$	49.0000	−	84.8705i	0.178832	−	0.309746i
$275$	186.363	+	164.754i	0.677682	+	0.599106i
$276$		0			0
$277$	−137.870	+	79.5990i	−0.497724	+	0.287361i	−0.727773	−	0.685818i	$-0.759445\pi$
$277$	−137.870	+	79.5990i	−0.497724	+	0.287361i	0.230049	+	0.973179i	$0.426111\pi$
$278$	−64.0000			−0.230216
$279$		0			0
$280$	346.500	+	34.8246i	1.23750	+	0.124373i
$281$	189.571	−	109.449i	0.674628	−	0.389497i	−0.123200	−	0.992382i	$-0.539316\pi$
$281$	189.571	−	109.449i	0.674628	−	0.389497i	0.797828	+	0.602885i	$0.205982\pi$
$282$		0			0
$283$	−241.272	−	139.298i	−0.852550	−	0.492220i	0.00896047	−	0.999960i	$-0.497148\pi$
$283$	−241.272	−	139.298i	−0.852550	−	0.492220i	−0.861510	+	0.507740i	$0.830481\pi$
$284$	155.103	+	89.5489i	0.546138	+	0.315313i
$285$		0			0
$286$	−99.0000	−	171.473i	−0.346154	−	0.599556i
$287$	−396.000			−1.37979
$288$		0			0
$289$	195.000			0.674740
$290$	−81.7663	−	181.423i	−0.281953	−	0.625596i
$291$		0			0
$292$	−232.655	−	134.323i	−0.796763	−	0.460011i
$293$	−143.000	+	247.683i	−0.488055	+	0.845335i	−0.999906	−	0.0137389i	$-0.995627\pi$
$293$	−143.000	+	247.683i	−0.488055	+	0.845335i	0.511851	+	0.859074i	$0.328960\pi$
$294$		0			0
$295$	81.7663	+	181.423i	0.277174	+	0.614993i
$296$		0			0
$297$		0			0
$298$		−	9.94987i		−	0.0333888i
$299$	344.674	−	198.997i	1.15276	−	0.665543i
$300$		0			0
$301$	−99.0000	+	171.473i	−0.328904	+	0.569678i
$302$	−128.500	+	222.569i	−0.425497	+	0.736982i
$303$		0			0
$304$	10.0000	+	17.3205i	0.0328947	+	0.0569754i
$305$	22.0000	−	218.897i	0.0721311	−	0.717696i
$306$		0			0
$307$			59.6992i			0.194460i	0.995262	+	0.0972300i	$0.0309983\pi$
$307$			59.6992i			0.194460i	−0.995262	+	0.0972300i	$0.969002\pi$
$308$	148.500	+	257.210i	0.482143	+	0.835096i
$309$		0			0
$310$	117.694	+	84.6940i	0.379659	+	0.273206i
$311$	−172.337	−	99.4987i	−0.554138	−	0.319932i	0.196651	−	0.980473i	$-0.436993\pi$
$311$	−172.337	−	99.4987i	−0.554138	−	0.319932i	−0.750789	+	0.660542i	$0.770327\pi$
$312$		0			0
$313$	−60.3179	+	34.8246i	−0.192709	+	0.111261i	−0.593250	−	0.805018i	$-0.702155\pi$
$313$	−60.3179	+	34.8246i	−0.192709	+	0.111261i	0.400541	+	0.916279i	$0.368822\pi$
$314$			159.198i			0.507000i
$315$		0			0
$316$	30.0000			0.0949367
$317$	−270.500	−	468.520i	−0.853312	−	1.47798i	−0.878202	−	0.478290i	$-0.841257\pi$
$317$	−270.500	−	468.520i	−0.853312	−	1.47798i	0.0248896	−	0.999690i	$-0.492077\pi$
$318$		0			0
$319$	198.000	−	342.946i	0.620690	−	1.07507i
$320$	52.7595	+	37.9663i	0.164873	+	0.118645i
$321$		0			0
$322$	172.337	−	99.4987i	0.535208	−	0.309002i
$323$	−88.0000			−0.272446
$324$		0			0
$325$	−99.0000	+	487.544i	−0.304615	+	1.50013i
$326$	258.505	−	149.248i	0.792961	−	0.457816i
$327$		0			0
$328$	−241.272	−	139.298i	−0.735584	−	0.424690i
$329$	499.777	+	288.546i	1.51908	+	0.877041i
$330$		0			0
$331$	137.000	+	237.291i	0.413897	+	0.716891i	0.995312	−	0.0967162i	$-0.0308339\pi$
$331$	137.000	+	237.291i	0.413897	+	0.716891i	−0.581415	+	0.813607i	$0.697501\pi$
$332$	−57.0000			−0.171687
$333$		0			0
$334$	−254.000			−0.760479
$335$	40.8832	+	90.7115i	0.122039	+	0.270780i
$336$		0			0
$337$	379.141	+	218.897i	1.12505	+	0.649547i	0.942685	−	0.333685i	$-0.108292\pi$
$337$	379.141	+	218.897i	1.12505	+	0.649547i	0.182363	+	0.983231i	$0.441625\pi$
$338$	113.500	−	196.588i	0.335799	−	0.581621i
$339$		0			0
$340$	300.856	−	135.594i	0.884870	−	0.398806i
$341$			288.546i			0.846177i
$342$		0			0
$343$			9.94987i			0.0290084i
$344$	−120.636	+	69.6491i	−0.350686	+	0.202468i
$345$		0			0
$346$	−117.500	+	203.516i	−0.339595	+	0.588196i
$347$	89.5000	−	155.019i	0.257925	−	0.446739i	−0.707761	−	0.706452i	$-0.750295\pi$
$347$	89.5000	−	155.019i	0.257925	−	0.446739i	0.965686	+	0.259713i	$0.0836279\pi$
$348$		0			0
$349$	−310.000	−	536.936i	−0.888252	−	1.53850i	−0.841940	−	0.539571i	$-0.818587\pi$
$349$	−310.000	−	536.936i	−0.888252	−	1.53850i	−0.0463119	−	0.998927i	$-0.514747\pi$
$350$	−49.5000	+	243.772i	−0.141429	+	0.696491i
$351$		0			0
$352$			328.346i			0.932801i
$353$	16.0000	+	27.7128i	0.0453258	+	0.0785066i	0.887798	−	0.460233i	$-0.152234\pi$
$353$	16.0000	+	27.7128i	0.0453258	+	0.0785066i	−0.842472	+	0.538739i	$0.818901\pi$
$354$		0			0
$355$	−174.351	+	242.285i	−0.491128	+	0.682492i
$356$	155.103	+	89.5489i	0.435683	+	0.251542i
$357$		0			0
$358$	129.253	−	74.6241i	0.361041	−	0.208447i
$359$		−	537.293i		−	1.49664i	−0.663339	−	0.748319i	$-0.730861\pi$
$359$		−	537.293i		−	1.49664i	0.663339	−	0.748319i	$-0.269139\pi$
$360$		0			0
$361$	−345.000			−0.955679
$362$	146.000	+	252.879i	0.403315	+	0.698562i
$363$		0			0
$364$	−297.000	+	514.419i	−0.815934	+	1.41324i
$365$	261.526	−	363.427i	0.716509	−	0.995691i
$366$		0			0
$367$	301.590	−	174.123i	0.821770	−	0.474449i	−0.0292566	−	0.999572i	$-0.509314\pi$
$367$	301.590	−	174.123i	0.821770	−	0.474449i	0.851026	+	0.525123i	$0.175981\pi$
$368$	−100.000			−0.271739
$369$		0			0
$370$		0			0
$371$	−267.122	+	154.223i	−0.720006	+	0.415696i
$372$		0			0
$373$	−292.973	−	169.148i	−0.785450	−	0.453480i	0.0529086	−	0.998599i	$-0.483151\pi$
$373$	−292.973	−	169.148i	−0.785450	−	0.453480i	−0.838358	+	0.545120i	$0.816484\pi$
$374$	−189.571	−	109.449i	−0.506873	−	0.292643i
$375$		0			0
$376$	203.000	+	351.606i	0.539894	+	0.935123i
$377$	792.000			2.10080
$378$		0			0
$379$	248.000			0.654354			0.327177	−	0.944963i	$-0.393903\pi$
$379$	248.000			0.654354			0.327177	+	0.944963i	$0.393903\pi$
$380$	−54.7011	+	24.6535i	−0.143950	+	0.0648776i
$381$		0			0
$382$	−86.1684	−	49.7494i	−0.225572	−	0.130234i
$383$	−197.000	+	341.214i	−0.514360	+	0.890898i	0.485501	+	0.874236i	$0.338637\pi$
$383$	−197.000	+	341.214i	−0.514360	+	0.890898i	−0.999861	+	0.0166620i	$0.994696\pi$
$384$		0			0
$385$	−451.284	+	203.391i	−1.17217	+	0.528289i
$386$		−	169.148i		−	0.438207i
$387$		0			0
$388$			388.045i			1.00012i
$389$	8.61684	−	4.97494i	0.0221513	−	0.0127890i	−0.488883	−	0.872349i	$-0.662596\pi$
$389$	8.61684	−	4.97494i	0.0221513	−	0.0127890i	0.511035	+	0.859560i	$0.329262\pi$
$390$		0			0
$391$	220.000	−	381.051i	0.562660	−	0.974555i
$392$	−175.000	+	303.109i	−0.446429	+	0.773237i
$393$		0			0
$394$	101.500	+	175.803i	0.257614	+	0.446201i
$395$	−5.00000	+	49.7494i	−0.0126582	+	0.125948i
$396$		0			0
$397$			59.6992i			0.150376i	0.997169	+	0.0751880i	$0.0239557\pi$
$397$			59.6992i			0.150376i	−0.997169	+	0.0751880i	$0.976044\pi$
$398$	−77.5000	−	134.234i	−0.194724	−	0.337271i
$399$		0			0
$400$	82.7921	−	93.6508i	0.206980	−	0.234127i
$401$	−172.337	−	99.4987i	−0.429768	−	0.248127i	0.269480	−	0.963006i	$-0.413148\pi$
$401$	−172.337	−	99.4987i	−0.429768	−	0.248127i	−0.699248	+	0.714879i	$0.746482\pi$
$402$		0			0
$403$	−499.777	+	288.546i	−1.24014	+	0.715996i
$404$			507.444i			1.25605i
$405$		0			0
$406$	396.000			0.975369
$407$		0			0
$408$		0			0
$409$	165.500	−	286.654i	0.404645	−	0.700867i	−0.589635	−	0.807670i	$-0.700728\pi$
$409$	165.500	−	286.654i	0.404645	−	0.700867i	0.994280	+	0.106804i	$0.0340616\pi$
$410$	116.234	−	161.523i	0.283497	−	0.393959i
$411$		0			0
$412$	−103.402	+	59.6992i	−0.250976	+	0.144901i
$413$	−396.000			−0.958838
$414$		0			0
$415$	9.50000	−	94.5238i	0.0228916	−	0.227768i
$416$	−568.712	+	328.346i	−1.36710	+	0.789293i
$417$		0			0
$418$	34.4674	+	19.8997i	0.0824578	+	0.0476071i
$419$	−585.945	−	338.296i	−1.39844	−	0.807388i	−0.404209	−	0.914667i	$-0.632453\pi$
$419$	−585.945	−	338.296i	−1.39844	−	0.807388i	−0.994229	+	0.107278i	$0.965786\pi$
$420$		0			0
$421$	−4.00000	−	6.92820i	−0.00950119	−	0.0164565i	0.861236	−	0.508206i	$-0.169691\pi$
$421$	−4.00000	−	6.92820i	−0.00950119	−	0.0164565i	−0.870737	+	0.491749i	$0.836358\pi$
$422$	308.000			0.729858
$423$		0			0
$424$	−217.000			−0.511792
$425$	174.715	+	521.512i	0.411093	+	1.22709i
$426$		0			0
$427$	379.141	+	218.897i	0.887918	+	0.512640i
$428$	−43.5000	+	75.3442i	−0.101636	+	0.176038i
$429$		0			0
$430$	−40.8832	−	90.7115i	−0.0950771	−	0.210957i
$431$		−	298.496i		−	0.692567i	−0.938130	−	0.346283i	$-0.887444\pi$
$431$		−	298.496i		−	0.692567i	0.938130	−	0.346283i	$-0.112556\pi$
$432$		0			0
$433$		−	686.541i		−	1.58555i	−0.609517	−	0.792773i	$-0.708637\pi$
$433$		−	686.541i		−	1.58555i	0.609517	−	0.792773i	$-0.291363\pi$
$434$	−249.888	+	144.273i	−0.575780	+	0.332427i
$435$		0			0
$436$	156.000	−	270.200i	0.357798	−	0.619725i
$437$	−40.0000	+	69.2820i	−0.0915332	+	0.158540i
$438$		0			0
$439$	−107.500	−	186.195i	−0.244875	−	0.424135i	0.717222	−	0.696845i	$-0.245413\pi$
$439$	−107.500	−	186.195i	−0.244875	−	0.424135i	−0.962096	+	0.272710i	$0.912080\pi$
$440$	−346.500	−	34.8246i	−0.787500	−	0.0791467i
$441$		0			0
$442$		−	437.794i		−	0.990485i
$443$	−95.0000	−	164.545i	−0.214447	−	0.371433i	0.738654	−	0.674084i	$-0.235462\pi$
$443$	−95.0000	−	164.545i	−0.214447	−	0.371433i	−0.953101	+	0.302651i	$0.902128\pi$
$444$		0			0
$445$	−174.351	+	242.285i	−0.391799	+	0.544460i
$446$	34.4674	+	19.8997i	0.0772811	+	0.0446183i
$447$		0			0
$448$	−112.019	+	64.6742i	−0.250042	+	0.144362i
$449$			119.398i			0.265921i	0.991121	+	0.132960i	$0.0424483\pi$
$449$			119.398i			0.265921i	−0.991121	+	0.132960i	$0.957552\pi$
$450$		0			0
$451$	396.000			0.878049
$452$	−120.000	−	207.846i	−0.265487	−	0.459836i
$453$		0			0
$454$	121.000	−	209.578i	0.266520	−	0.461626i
$455$	−803.568	−	578.255i	−1.76608	−	1.27089i
$456$		0			0
$457$	−112.019	+	64.6742i	−0.245118	+	0.141519i	−0.617527	−	0.786550i	$-0.711865\pi$
$457$	−112.019	+	64.6742i	−0.245118	+	0.141519i	0.372409	+	0.928069i	$0.378532\pi$
$458$	−106.000			−0.231441
$459$		0			0
$460$	30.0000	−	298.496i	0.0652174	−	0.648905i
$461$	163.720	−	94.5238i	0.355141	−	0.205041i	−0.311806	−	0.950146i	$-0.600934\pi$
$461$	163.720	−	94.5238i	0.355141	−	0.205041i	0.666947	+	0.745105i	$0.267601\pi$
$462$		0			0
$463$	715.198	+	412.920i	1.54470	+	0.891835i	0.998532	+	0.0541624i	$0.0172489\pi$
$463$	715.198	+	412.920i	1.54470	+	0.891835i	0.546172	+	0.837673i	$0.316084\pi$
$464$	−172.337	−	99.4987i	−0.371416	−	0.214437i
$465$		0			0
$466$	−71.0000	−	122.976i	−0.152361	−	0.263896i
$467$	193.000			0.413276			0.206638	−	0.978417i	$-0.433748\pi$
$467$	193.000			0.413276			0.206638	+	0.978417i	$0.433748\pi$
$468$		0			0
$469$	−198.000			−0.422175
$470$	−264.388	+	119.158i	−0.562529	+	0.253529i
$471$		0			0
$472$	−241.272	−	139.298i	−0.511169	−	0.295123i
$473$	99.0000	−	171.473i	0.209302	−	0.362522i
$474$		0			0
$475$	−31.7663	−	94.8204i	−0.0668764	−	0.199622i
$476$			656.692i			1.37960i
$477$		0			0
$478$			198.997i			0.416313i
$479$	−637.646	+	368.145i	−1.33120	+	0.768571i	−0.985484	−	0.169767i	$-0.945698\pi$
$479$	−637.646	+	368.145i	−1.33120	+	0.768571i	−0.345719	+	0.938338i	$0.612365\pi$
$480$		0			0
$481$		0			0
$482$	−85.0000	+	147.224i	−0.176349	+	0.305445i
$483$		0			0
$484$	33.0000	+	57.1577i	0.0681818	+	0.118094i
$485$	−643.500	−	64.6742i	−1.32680	−	0.133349i
$486$		0			0
$487$		−	477.594i		−	0.980686i	−0.871530	−	0.490343i	$-0.836872\pi$
$487$		−	477.594i		−	0.980686i	0.871530	−	0.490343i	$-0.163128\pi$
$488$	154.000	+	266.736i	0.315574	+	0.546590i
$489$		0			0
$490$	−202.921	−	146.024i	−0.414125	−	0.298008i
$491$	−249.888	−	144.273i	−0.508938	−	0.293835i	0.223459	−	0.974713i	$-0.428265\pi$
$491$	−249.888	−	144.273i	−0.508938	−	0.293835i	−0.732397	+	0.680878i	$0.761598\pi$
$492$		0			0
$493$	758.282	−	437.794i	1.53810	−	0.888021i
$494$			79.5990i			0.161132i
$495$		0			0
$496$	145.000			0.292339
$497$	−297.000	−	514.419i	−0.597586	−	1.03505i
$498$		0			0
$499$	−145.000	+	251.147i	−0.290581	+	0.503301i	−0.973947	−	0.226775i	$-0.927182\pi$
$499$	−145.000	+	251.147i	−0.290581	+	0.503301i	0.683366	+	0.730076i	$0.260515\pi$
$500$	254.706	+	275.227i	0.509413	+	0.550453i
$501$		0			0
$502$	−310.206	+	179.098i	−0.617941	+	0.356768i
$503$	220.000			0.437376			0.218688	−	0.975795i	$-0.429822\pi$
$503$	220.000			0.437376			0.218688	+	0.975795i	$0.429822\pi$
$504$		0			0
$505$	−841.500	−	84.5739i	−1.66634	−	0.167473i
$506$	−172.337	+	99.4987i	−0.340587	+	0.196638i
$507$		0			0
$508$	387.758	+	223.872i	0.763303	+	0.440693i
$509$	8.61684	+	4.97494i	0.0169290	+	0.00977394i	0.508441	−	0.861097i	$-0.330222\pi$
$509$	8.61684	+	4.97494i	0.0169290	+	0.00977394i	−0.491512	+	0.870871i	$0.663555\pi$
$510$		0			0
$511$	445.500	+	771.629i	0.871820	+	1.51004i
$512$	305.000			0.595703
$513$		0			0
$514$	−290.000			−0.564202
$515$	−81.7663	−	181.423i	−0.158770	−	0.352277i
$516$		0			0
$517$	−499.777	−	288.546i	−0.966687	−	0.558117i
$518$		0			0
$519$		0			0
$520$	−286.182	−	634.980i	−0.550350	−	1.22112i
$521$			298.496i			0.572929i	0.958091	+	0.286465i	$0.0924801\pi$
$521$			298.496i			0.572929i	−0.958091	+	0.286465i	$0.907520\pi$
$522$		0			0
$523$			537.293i			1.02733i	0.857991	+	0.513665i	$0.171712\pi$
$523$			537.293i			1.02733i	−0.857991	+	0.513665i	$0.828288\pi$
$524$	−439.459	+	253.722i	−0.838662	+	0.484202i
$525$		0			0
$526$	52.0000	−	90.0666i	0.0988593	−	0.171229i
$527$	−319.000	+	552.524i	−0.605313	+	1.04843i
$528$		0			0
$529$	64.5000	+	111.717i	0.121928	+	0.211186i
$530$	15.5000	−	154.223i	0.0292453	−	0.290987i
$531$		0			0
$532$		−	119.398i		−	0.224433i
$533$	396.000	+	685.892i	0.742964	+	1.28685i
$534$		0			0
$535$	−117.694	−	84.6940i	−0.219989	−	0.158306i
$536$	−120.636	−	69.6491i	−0.225067	−	0.129942i
$537$		0			0
$538$	103.402	−	59.6992i	0.192197	−	0.110965i
$539$		−	497.494i		−	0.922994i
$540$		0			0
$541$	704.000			1.30129			0.650647	−	0.759380i	$-0.274498\pi$
$541$	704.000			1.30129			0.650647	+	0.759380i	$0.274498\pi$
$542$	60.5000	+	104.789i	0.111624	+	0.193338i
$543$		0			0
$544$	−363.000	+	628.734i	−0.667279	+	1.15576i
$545$	422.076	+	303.730i	0.774451	+	0.557303i
$546$		0			0
$547$	−86.1684	+	49.7494i	−0.157529	+	0.0909495i	−0.576692	−	0.816961i	$-0.695657\pi$
$547$	−86.1684	+	49.7494i	−0.157529	+	0.0909495i	0.419163	+	0.907911i	$0.362324\pi$
$548$	294.000			0.536496
$549$		0			0
$550$	49.5000	−	243.772i	0.0900000	−	0.443222i
$551$	−137.870	+	79.5990i	−0.250217	+	0.144463i
$552$		0			0
$553$	−86.1684	−	49.7494i	−0.155820	−	0.0899627i
$554$	137.870	+	79.5990i	0.248862	+	0.143680i
$555$		0			0
$556$	−96.0000	−	166.277i	−0.172662	−	0.299059i
$557$	−101.000			−0.181329			−0.0906643	−	0.995882i	$-0.528899\pi$
$557$	−101.000			−0.181329			−0.0906643	+	0.995882i	$0.528899\pi$
$558$		0			0
$559$	396.000			0.708408
$560$	102.208	+	226.779i	0.182514	+	0.404962i
$561$		0			0
$562$	−189.571	−	109.449i	−0.337314	−	0.194748i
$563$	467.500	−	809.734i	0.830373	−	1.43825i	−0.0673697	−	0.997728i	$-0.521461\pi$
$563$	467.500	−	809.734i	0.830373	−	1.43825i	0.897743	−	0.440520i	$-0.145206\pi$
$564$		0			0
$565$	364.674	−	164.356i	0.645440	−	0.290896i
$566$			278.596i			0.492220i
$567$		0			0
$568$		−	417.895i		−	0.735730i
$569$	654.880	−	378.095i	1.15093	−	0.664491i	0.201818	−	0.979423i	$-0.435315\pi$
$569$	654.880	−	378.095i	1.15093	−	0.664491i	0.949114	+	0.314932i	$0.101982\pi$
$570$		0			0
$571$	−253.000	+	438.209i	−0.443082	+	0.767441i	−0.997916	−	0.0645199i	$-0.979448\pi$
$571$	−253.000	+	438.209i	−0.443082	+	0.767441i	0.554834	+	0.831961i	$0.312782\pi$
$572$	297.000	−	514.419i	0.519231	−	0.899334i
$573$		0			0
$574$	198.000	+	342.946i	0.344948	+	0.597467i
$575$	490.000	+	99.4987i	0.852174	+	0.173041i
$576$		0			0
$577$			1074.59i			1.86237i	0.364549	+	0.931184i	$0.381223\pi$
$577$			1074.59i			1.86237i	−0.364549	+	0.931184i	$0.618777\pi$
$578$	−97.5000	−	168.875i	−0.168685	−	0.292171i
$579$		0			0
$580$	348.701	−	484.569i	0.601209	−	0.835465i
$581$	163.720	+	94.5238i	0.281790	+	0.162692i
$582$		0			0
$583$	267.122	−	154.223i	0.458186	−	0.264534i
$584$			626.842i			1.07336i
$585$		0			0
$586$	286.000			0.488055
$587$	62.5000	+	108.253i	0.106474	+	0.184418i	0.914339	−	0.404949i	$-0.132711\pi$
$587$	62.5000	+	108.253i	0.106474	+	0.184418i	−0.807866	+	0.589367i	$0.799377\pi$
$588$		0			0
$589$	58.0000	−	100.459i	0.0984720	−	0.170558i
$590$	116.234	−	161.523i	0.197006	−	0.273768i
$591$		0			0
$592$		0			0
$593$	−50.0000			−0.0843170			−0.0421585	−	0.999111i	$-0.513423\pi$
$593$	−50.0000			−0.0843170			−0.0421585	+	0.999111i	$0.513423\pi$
$594$		0			0
$595$	−1089.00	−	109.449i	−1.83025	−	0.183947i
$596$	25.8505	−	14.9248i	0.0433734	−	0.0250416i
$597$		0			0
$598$	−344.674	−	198.997i	−0.576378	−	0.332772i
$599$	−120.636	−	69.6491i	−0.201395	−	0.116276i	0.395911	−	0.918289i	$-0.370429\pi$
$599$	−120.636	−	69.6491i	−0.201395	−	0.116276i	−0.597306	+	0.802013i	$0.703762\pi$
$600$		0			0
$601$	−26.5000	−	45.8993i	−0.0440932	−	0.0763716i	0.843137	−	0.537700i	$-0.180707\pi$
$601$	−26.5000	−	45.8993i	−0.0440932	−	0.0763716i	−0.887230	+	0.461328i	$0.847373\pi$
$602$	198.000			0.328904
$603$		0			0
$604$	−771.000			−1.27649
$605$	−100.285	+	45.1980i	−0.165761	+	0.0747075i
$606$		0			0
$607$	−344.674	−	198.997i	−0.567832	−	0.327838i	0.188451	−	0.982083i	$-0.439653\pi$
$607$	−344.674	−	198.997i	−0.567832	−	0.327838i	−0.756283	+	0.654245i	$0.772987\pi$
$608$	66.0000	−	114.315i	0.108553	−	0.188019i
$609$		0			0
$610$	−200.571	+	90.3961i	−0.328804	+	0.148190i
$611$		−	1154.19i		−	1.88901i
$612$		0			0
$613$			895.489i			1.46083i	0.683004	+	0.730415i	$0.260673\pi$
$613$			895.489i			1.46083i	−0.683004	+	0.730415i	$0.739327\pi$
$614$	51.7011	−	29.8496i	0.0842037	−	0.0486150i
$615$		0			0
$616$	346.500	−	600.156i	0.562500	−	0.974279i
$617$	−566.000	+	980.341i	−0.917342	+	1.58888i	−0.113906	+	0.993492i	$0.536336\pi$
$617$	−566.000	+	980.341i	−0.917342	+	1.58888i	−0.803436	+	0.595391i	$0.796997\pi$
$618$		0			0
$619$	−151.000	−	261.540i	−0.243942	−	0.422520i	0.717892	−	0.696155i	$-0.245107\pi$
$619$	−151.000	−	261.540i	−0.243942	−	0.422520i	−0.961834	+	0.273635i	$0.911774\pi$
$620$	−43.5000	+	432.820i	−0.0701613	+	0.698096i
$621$		0			0
$622$			198.997i			0.319932i
$623$	−297.000	−	514.419i	−0.476726	−	0.825713i
$624$		0			0
$625$	−498.863	+	376.512i	−0.798180	+	0.602419i
$626$	60.3179	+	34.8246i	0.0963545	+	0.0556303i
$627$		0			0
$628$	−413.609	+	238.797i	−0.658612	+	0.380250i
$629$		0			0
$630$		0			0
$631$	1103.00			1.74802			0.874010	−	0.485909i	$-0.161511\pi$
$631$	1103.00			1.74802			0.874010	+	0.485909i	$0.161511\pi$
$632$	−35.0000	−	60.6218i	−0.0553797	−	0.0959205i
$633$		0			0
$634$	−270.500	+	468.520i	−0.426656	+	0.738990i
$635$	−435.876	+	605.712i	−0.686419	+	0.953877i
$636$		0			0
$637$	861.684	−	497.494i	1.35272	−	0.780995i
$638$	−396.000			−0.620690
$639$		0			0
$640$	−59.5000	+	592.018i	−0.0929688	+	0.925027i
$641$	344.674	−	198.997i	0.537713	−	0.310448i	−0.206439	−	0.978460i	$-0.566187\pi$
$641$	344.674	−	198.997i	0.537713	−	0.310448i	0.744151	+	0.668011i	$0.232854\pi$
$642$		0			0
$643$	−241.272	−	139.298i	−0.375228	−	0.216638i	0.300512	−	0.953778i	$-0.402842\pi$
$643$	−241.272	−	139.298i	−0.375228	−	0.216638i	−0.675740	+	0.737140i	$0.736176\pi$
$644$	517.011	+	298.496i	0.802812	+	0.463503i
$645$		0			0
$646$	44.0000	+	76.2102i	0.0681115	+	0.117973i
$647$	−1256.00			−1.94127			−0.970634	−	0.240562i	$-0.922668\pi$
$647$	−1256.00			−1.94127			−0.970634	+	0.240562i	$0.922668\pi$
$648$		0			0
$649$	396.000			0.610169
$650$	471.725	−	158.035i	0.725731	−	0.243131i
$651$		0			0
$652$	775.516	+	447.744i	1.18944	+	0.686724i
$653$	−3.50000	+	6.06218i	−0.00535988	+	0.00928358i	−0.868693	−	0.495351i	$-0.835039\pi$
$653$	−3.50000	+	6.06218i	−0.00535988	+	0.00928358i	0.863333	+	0.504635i	$0.168373\pi$
$654$		0			0
$655$	−347.507	−	771.047i	−0.530545	−	1.17717i
$656$		−	198.997i		−	0.303350i
$657$		0			0
$658$		−	577.093i		−	0.877041i
$659$	835.834	−	482.569i	1.26834	−	0.732275i	0.293664	−	0.955909i	$-0.405125\pi$
$659$	835.834	−	482.569i	1.26834	−	0.732275i	0.974673	+	0.223634i	$0.0717921\pi$
$660$		0			0
$661$	320.000	−	554.256i	0.484115	−	0.838512i	−0.515719	−	0.856758i	$-0.672475\pi$
$661$	320.000	−	554.256i	0.484115	−	0.838512i	0.999834	+	0.0182463i	$0.00580831\pi$
$662$	137.000	−	237.291i	0.206949	−	0.358446i
$663$		0			0
$664$	66.5000	+	115.181i	0.100151	+	0.173466i
$665$	198.000	+	19.8997i	0.297744	+	0.0299244i
$666$		0			0
$667$		−	795.990i		−	1.19339i
$668$	−381.000	−	659.911i	−0.570359	−	0.987891i
$669$		0			0
$670$	58.1168	−	80.7616i	0.0867416	−	0.120540i
$671$	−379.141	−	218.897i	−0.565039	−	0.326225i
$672$		0			0
$673$	−267.122	+	154.223i	−0.396913	+	0.229158i	−0.685151	−	0.728401i	$-0.740264\pi$
$673$	−267.122	+	154.223i	−0.396913	+	0.229158i	0.288238	+	0.957559i	$0.406930\pi$
$674$		−	437.794i		−	0.649547i
$675$		0			0
$676$	681.000			1.00740
$677$	−11.0000	−	19.0526i	−0.0162482	−	0.0281426i	0.857787	−	0.514005i	$-0.171839\pi$
$677$	−11.0000	−	19.0526i	−0.0162482	−	0.0281426i	−0.874035	+	0.485863i	$0.838506\pi$
$678$		0			0
$679$	643.500	−	1114.57i	0.947717	−	1.64149i
$680$	−624.997	−	449.754i	−0.919113	−	0.661403i
$681$		0			0
$682$	249.888	−	144.273i	0.366405	−	0.211544i
$683$	166.000			0.243045			0.121523	−	0.992589i	$-0.461222\pi$
$683$	166.000			0.243045			0.121523	+	0.992589i	$0.461222\pi$
$684$		0			0
$685$	−49.0000	+	487.544i	−0.0715328	+	0.711743i
$686$	8.61684	−	4.97494i	0.0125610	−	0.00725210i
$687$		0			0
$688$	−86.1684	−	49.7494i	−0.125245	−	0.0723101i
$689$	534.244	+	308.446i	0.775391	+	0.447672i
$690$		0			0
$691$	230.000	+	398.372i	0.332851	+	0.576515i	0.983070	−	0.183232i	$-0.0586561\pi$
$691$	230.000	+	398.372i	0.332851	+	0.576515i	−0.650219	+	0.759747i	$0.725323\pi$
$692$	−705.000			−1.01879
$693$		0			0
$694$	−179.000			−0.257925
$695$	291.739	−	131.485i	0.419768	−	0.189187i
$696$		0			0
$697$	758.282	+	437.794i	1.08792	+	0.628113i
$698$	−310.000	+	536.936i	−0.444126	+	0.769249i
$699$		0			0
$700$	−707.588	+	237.053i	−1.01084	+	0.338647i
$701$		−	268.647i		−	0.383233i	−0.981470	−	0.191617i	$-0.938627\pi$
$701$		−	268.647i		−	0.383233i	0.981470	−	0.191617i	$-0.0613730\pi$
$702$		0			0
$703$		0			0
$704$	112.019	−	64.6742i	0.159118	−	0.0918667i
$705$		0			0
$706$	16.0000	−	27.7128i	0.0226629	−	0.0392533i
$707$	841.500	−	1457.52i	1.19024	−	2.06156i
$708$		0			0
$709$	272.000	+	471.118i	0.383639	+	0.664482i	0.991579	−	0.129501i	$-0.0413374\pi$
$709$	272.000	+	471.118i	0.383639	+	0.664482i	−0.607940	+	0.793983i	$0.708004\pi$
$710$	297.000	+	29.8496i	0.418310	+	0.0420417i
$711$		0			0
$712$		−	417.895i		−	0.586931i
$713$	290.000	+	502.295i	0.406732	+	0.704481i
$714$		0			0
$715$	803.568	+	578.255i	1.12387	+	0.808749i
$716$	387.758	+	223.872i	0.541561	+	0.312671i
$717$		0			0
$718$	−465.310	+	268.647i	−0.648063	+	0.374160i
$719$		−	358.195i		−	0.498186i	−0.968480	−	0.249093i	$-0.919868\pi$
$719$		−	358.195i		−	0.498186i	0.968480	−	0.249093i	$-0.0801324\pi$
$720$		0			0
$721$	396.000			0.549237
$722$	172.500	+	298.779i	0.238920	+	0.413821i
$723$		0			0
$724$	−438.000	+	758.638i	−0.604972	+	1.04784i
$725$	745.451	+	659.017i	1.02821	+	0.908989i
$726$		0			0
$727$	−1197.74	+	691.516i	−1.64751	+	0.951192i	−0.669456	+	0.742852i	$0.733473\pi$
$727$	−1197.74	+	691.516i	−1.64751	+	0.951192i	−0.978057	+	0.208339i	$0.933194\pi$
$728$	1386.00			1.90385
$729$		0			0
$730$	−445.500	−	44.7744i	−0.610274	−	0.0613348i
$731$	379.141	−	218.897i	0.518661	−	0.299449i
$732$		0			0
$733$	−551.478	−	318.396i	−0.752357	−	0.434374i	0.0741876	−	0.997244i	$-0.476364\pi$
$733$	−551.478	−	318.396i	−0.752357	−	0.434374i	−0.826545	+	0.562871i	$0.809697\pi$
$734$	−301.590	−	174.123i	−0.410885	−	0.237225i
$735$		0			0
$736$	330.000	+	571.577i	0.448370	+	0.776599i
$737$	198.000			0.268657
$738$		0			0
$739$	−958.000			−1.29635			−0.648173	−	0.761493i	$-0.724467\pi$
$739$	−958.000			−1.29635			−0.648173	+	0.761493i	$0.724467\pi$
$740$		0			0
$741$		0			0
$742$	267.122	+	154.223i	0.360003	+	0.207848i
$743$	301.000	−	521.347i	0.405114	−	0.701679i	−0.589220	−	0.807972i	$-0.700565\pi$
$743$	301.000	−	521.347i	0.405114	−	0.701679i	0.994335	+	0.106294i	$0.0338984\pi$
$744$		0			0
$745$	20.4416	+	45.3557i	0.0274384	+	0.0608802i
$746$			338.296i			0.453480i
$747$		0			0
$748$		−	656.692i		−	0.877930i
$749$	249.888	−	144.273i	0.333629	−	0.192621i
$750$		0			0
$751$	−266.500	+	461.592i	−0.354860	+	0.614636i	−0.987094	−	0.160142i	$-0.948805\pi$
$751$	−266.500	+	461.592i	−0.354860	+	0.614636i	0.632234	+	0.774778i	$0.282138\pi$
$752$	−145.000	+	251.147i	−0.192819	+	0.333973i
$753$		0			0
$754$	−396.000	−	685.892i	−0.525199	−	0.909671i
$755$	128.500	−	1278.56i	0.170199	−	1.69346i
$756$		0			0
$757$			895.489i			1.18294i	0.806325	+	0.591472i	$0.201453\pi$
$757$			895.489i			1.18294i	−0.806325	+	0.591472i	$0.798547\pi$
$758$	−124.000	−	214.774i	−0.163588	−	0.283343i
$759$		0			0
$760$	113.636	+	81.7735i	0.149521	+	0.107597i
$761$	861.684	+	497.494i	1.13231	+	0.653737i	0.944514	−	0.328472i	$-0.106534\pi$
$761$	861.684	+	497.494i	1.13231	+	0.653737i	0.187792	+	0.982209i	$0.439867\pi$
$762$		0			0
$763$	−896.152	+	517.393i	−1.17451	+	0.678104i
$764$		−	298.496i		−	0.390702i
$765$		0			0
$766$	394.000			0.514360
$767$	396.000	+	685.892i	0.516297	+	0.894253i
$768$		0			0
$769$	−302.500	+	523.945i	−0.393368	+	0.681333i	−0.992891	−	0.119024i	$-0.962023\pi$
$769$	−302.500	+	523.945i	−0.393368	+	0.681333i	0.599523	+	0.800357i	$0.295357\pi$
$770$	401.784	+	289.128i	0.521797	+	0.375490i
$771$		0			0
$772$	439.459	−	253.722i	0.569247	−	0.328655i
$773$	886.000			1.14618			0.573092	−	0.819491i	$-0.305744\pi$
$773$	886.000			1.14618			0.573092	+	0.819491i	$0.305744\pi$
$774$		0			0
$775$	−710.500	−	144.273i	−0.916774	−	0.186159i
$776$	784.133	−	452.719i	1.01048	−	0.583401i
$777$		0			0
$778$	−8.61684	−	4.97494i	−0.0110756	−	0.00639452i
$779$	−137.870	−	79.5990i	−0.176983	−	0.102181i
$780$		0			0
$781$	297.000	+	514.419i	0.380282	+	0.658667i
$782$	−440.000			−0.562660
$783$		0			0
$784$	−250.000			−0.318878
$785$	−327.065	−	725.692i	−0.416644	−	0.924448i
$786$		0			0
$787$	−448.076	−	258.697i	−0.569347	−	0.328712i	0.187542	−	0.982257i	$-0.439948\pi$
$787$	−448.076	−	258.697i	−0.569347	−	0.328712i	−0.756888	+	0.653544i	$0.773281\pi$
$788$	−304.500	+	527.409i	−0.386421	+	0.669301i
$789$		0			0
$790$	45.5842	−	20.5446i	0.0577015	−	0.0260058i
$791$			795.990i			1.00631i
$792$		0			0
$793$		−	875.589i		−	1.10415i
$794$	51.7011	−	29.8496i	0.0651147	−	0.0375940i
$795$		0			0
$796$	232.500	−	402.702i	0.292085	−	0.505907i
$797$	167.500	−	290.119i	0.210163	−	0.364013i	−0.741602	−	0.670840i	$-0.765934\pi$
$797$	167.500	−	290.119i	0.210163	−	0.364013i	0.951765	+	0.306827i	$0.0992672\pi$
$798$		0			0
$799$	−638.000	−	1105.05i	−0.798498	−	1.38304i
$800$	−808.500	−	164.173i	−1.01063	−	0.205216i
$801$		0			0
$802$			198.997i			0.248127i
$803$	−445.500	−	771.629i	−0.554795	−	0.960932i
$804$		0			0
$805$	−581.168	+	807.616i	−0.721948	+	1.00325i
$806$	499.777	+	288.546i	0.620071	+	0.357998i
$807$		0			0
$808$	1025.40	−	592.018i	1.26906	−	0.732695i
$809$			417.895i			0.516557i	0.966070	+	0.258279i	$0.0831552\pi$
$809$			417.895i			0.516557i	−0.966070	+	0.258279i	$0.916845\pi$
$810$		0			0
$811$	−700.000			−0.863132			−0.431566	−	0.902081i	$-0.642039\pi$
$811$	−700.000			−0.863132			−0.431566	+	0.902081i	$0.642039\pi$
$812$	594.000	+	1028.84i	0.731527	+	1.26704i
$813$		0			0
$814$		0			0
$815$	−871.753	+	1211.42i	−1.06964	+	1.48641i
$816$		0			0
$817$	−68.9348	+	39.7995i	−0.0843755	+	0.0487142i
$818$	−331.000			−0.404645
$819$		0			0
$820$	594.000	+	59.6992i	0.724390	+	0.0728040i
$821$	965.087	−	557.193i	1.17550	−	0.678676i	0.220532	−	0.975380i	$-0.429221\pi$
$821$	965.087	−	557.193i	1.17550	−	0.678676i	0.954970	+	0.296704i	$0.0958874\pi$
$822$		0			0
$823$	818.600	+	472.619i	0.994654	+	0.574264i	0.906662	−	0.421857i	$-0.138622\pi$
$823$	818.600	+	472.619i	0.994654	+	0.574264i	0.0879918	+	0.996121i	$0.471955\pi$
$824$	241.272	+	139.298i	0.292805	+	0.169051i
$825$		0			0
$826$	198.000	+	342.946i	0.239709	+	0.415189i
$827$	−230.000			−0.278114			−0.139057	−	0.990284i	$-0.544407\pi$
$827$	−230.000			−0.278114			−0.139057	+	0.990284i	$0.544407\pi$
$828$		0			0
$829$	686.000			0.827503			0.413752	−	0.910390i	$-0.364218\pi$
$829$	686.000			0.827503			0.413752	+	0.910390i	$0.364218\pi$
$830$	−86.6100	+	39.0347i	−0.104349	+	0.0470297i
$831$		0			0
$832$	224.038	+	129.348i	0.269276	+	0.155467i
$833$	550.000	−	952.628i	0.660264	−	1.14361i
$834$		0			0
$835$	1157.84	−	521.832i	1.38663	−	0.624948i
$836$			119.398i			0.142821i
$837$		0			0
$838$			676.591i			0.807388i
$839$	−1051.25	+	606.942i	−1.25299	+	0.723412i	−0.971701	−	0.236213i	$-0.924094\pi$
$839$	−1051.25	+	606.942i	−1.25299	+	0.723412i	−0.281284	+	0.959624i	$0.590760\pi$
$840$		0			0
$841$	371.500	−	643.457i	0.441736	−	0.765109i
$842$	−4.00000	+	6.92820i	−0.00475059	+	0.00822827i
$843$		0			0
$844$	462.000	+	800.207i	0.547393	+	0.948113i
$845$	−113.500	+	1129.31i	−0.134320	+	1.33646i
$846$		0			0
$847$		−	218.897i		−	0.258438i
$848$	−77.5000	−	134.234i	−0.0913915	−	0.158295i
$849$		0			0
$850$	364.285	−	412.063i	0.428571	−	0.484780i
$851$		0			0
$852$		0			0
$853$	637.646	−	368.145i	0.747534	−	0.431589i	−0.0772682	−	0.997010i	$-0.524620\pi$
$853$	637.646	−	368.145i	0.747534	−	0.431589i	0.824802	+	0.565421i	$0.191286\pi$
$854$		−	437.794i		−	0.512640i
$855$		0			0
$856$	203.000			0.237150
$857$	−77.0000	−	133.368i	−0.0898483	−	0.155622i	0.817599	−	0.575789i	$-0.195305\pi$
$857$	−77.0000	−	133.368i	−0.0898483	−	0.155622i	−0.907447	+	0.420167i	$0.861972\pi$
$858$		0			0
$859$	566.000	−	980.341i	0.658906	−	1.14126i	−0.321994	−	0.946742i	$-0.604353\pi$
$859$	566.000	−	980.341i	0.658906	−	1.14126i	0.980899	−	0.194516i	$-0.0623137\pi$
$860$	174.351	−	242.285i	0.202733	−	0.281726i
$861$		0			0
$862$	−258.505	+	149.248i	−0.299890	+	0.173142i
$863$	−1040.00			−1.20510			−0.602549	−	0.798082i	$-0.705848\pi$
$863$	−1040.00			−1.20510			−0.602549	+	0.798082i	$0.705848\pi$
$864$		0			0
$865$	117.500	−	1169.11i	0.135838	−	1.35157i
$866$	−594.562	+	343.271i	−0.686561	+	0.396386i
$867$		0			0
$868$	−749.665	−	432.820i	−0.863670	−	0.498640i
$869$	86.1684	+	49.7494i	0.0991582	+	0.0572490i
$870$		0			0
$871$	198.000	+	342.946i	0.227325	+	0.393738i
$872$	−728.000			−0.834862
$873$		0			0
$874$	80.0000			0.0915332
$875$	−275.177	−	1212.91i	−0.314488	−	1.38618i
$876$		0			0
$877$	−1430.40	−	825.840i	−1.63101	−	0.941664i	−0.983782	−	0.179368i	$-0.942595\pi$
$877$	−1430.40	−	825.840i	−1.63101	−	0.941664i	−0.647228	−	0.762296i	$-0.724072\pi$
$878$	−107.500	+	186.195i	−0.122437	+	0.212068i
$879$		0			0
$880$	−102.208	−	226.779i	−0.116145	−	0.257703i
$881$		−	417.895i		−	0.474341i	−0.971468	−	0.237171i	$-0.923780\pi$
$881$		−	417.895i		−	0.474341i	0.971468	−	0.237171i	$-0.0762201\pi$
$882$		0			0
$883$		−	238.797i		−	0.270438i	−0.990816	−	0.135219i	$-0.956826\pi$
$883$		−	238.797i		−	0.270438i	0.990816	−	0.135219i	$-0.0431738\pi$
$884$	1137.42	−	656.692i	1.28668	−	0.742864i
$885$		0			0
$886$	−95.0000	+	164.545i	−0.107223	+	0.185717i
$887$	307.000	−	531.740i	0.346110	−	0.599481i	−0.639444	−	0.768837i	$-0.720836\pi$
$887$	307.000	−	531.740i	0.346110	−	0.599481i	0.985555	+	0.169356i	$0.0541689\pi$
$888$		0			0
$889$	−742.500	−	1286.05i	−0.835208	−	1.44662i
$890$	297.000	+	29.8496i	0.333708	+	0.0335389i
$891$		0			0
$892$			119.398i			0.133855i
$893$	116.000	+	200.918i	0.129899	+	0.224992i
$894$		0			0
$895$	−435.876	+	605.712i	−0.487013	+	0.676773i
$896$	−1025.40	−	592.018i	−1.14442	−	0.660734i
$897$		0			0
$898$	103.402	−	59.6992i	0.115147	−	0.0664802i
$899$			1154.19i			1.28385i
$900$		0			0
$901$	682.000			0.756937
$902$	−198.000	−	342.946i	−0.219512	−	0.380206i
$903$		0			0
$904$	−280.000	+	484.974i	−0.309735	+	0.536476i
$905$	−1185.06	−	852.781i	−1.30946	−	0.942299i
$906$		0			0
$907$	−344.674	+	198.997i	−0.380015	+	0.219402i	−0.677825	−	0.735223i	$-0.737077\pi$
$907$	−344.674	+	198.997i	−0.380015	+	0.219402i	0.297810	+	0.954625i	$0.403744\pi$
$908$	726.000			0.799559
$909$		0			0
$910$	−99.0000	+	985.038i	−0.108791	+	1.08246i
$911$	−1258.06	+	726.341i	−1.38097	+	0.797301i	−0.992274	−	0.124067i	$-0.960406\pi$
$911$	−1258.06	+	726.341i	−1.38097	+	0.797301i	−0.388691	+	0.921368i	$0.627073\pi$
$912$		0			0
$913$	−163.720	−	94.5238i	−0.179321	−	0.103531i
$914$	112.019	+	64.6742i	0.122559	+	0.0707595i
$915$		0			0
$916$	−159.000	−	275.396i	−0.173581	−	0.300651i
$917$	1683.00			1.83533
$918$		0			0
$919$	−187.000			−0.203482			−0.101741	−	0.994811i	$-0.532441\pi$
$919$	−187.000			−0.203482			−0.101741	+	0.994811i	$0.532441\pi$
$920$	−638.179	+	287.624i	−0.693673	+	0.312635i
$921$		0			0
$922$	−163.720	−	94.5238i	−0.177571	−	0.102520i
$923$	−594.000	+	1028.84i	−0.643554	+	1.11467i
$924$		0			0
$925$		0			0
$926$		−	825.840i		−	0.891835i
$927$		0			0
$928$			1313.38i			1.41528i
$929$	−585.945	+	338.296i	−0.630727	+	0.364150i	−0.781034	−	0.624489i	$-0.785307\pi$
$929$	−585.945	+	338.296i	−0.630727	+	0.364150i	0.150307	+	0.988639i	$0.451974\pi$
$930$		0			0
$931$	−100.000	+	173.205i	−0.107411	+	0.186042i
$932$	213.000	−	368.927i	0.228541	−	0.395844i
$933$		0			0
$934$	−96.5000	−	167.143i	−0.103319	−	0.178954i
$935$	1089.00	+	109.449i	1.16471	+	0.117057i
$936$		0			0
$937$		−	985.038i		−	1.05127i	−0.850711	−	0.525634i	$-0.823828\pi$
$937$		−	985.038i		−	1.05127i	0.850711	−	0.525634i	$-0.176172\pi$
$938$	99.0000	+	171.473i	0.105544	+	0.182807i
$939$		0			0
$940$	−706.165	−	508.164i	−0.751240	−	0.540600i
$941$	267.122	+	154.223i	0.283871	+	0.163893i	0.635174	−	0.772369i	$-0.280928\pi$
$941$	267.122	+	154.223i	0.283871	+	0.163893i	−0.351304	+	0.936262i	$0.614262\pi$
$942$		0			0
$943$	689.348	−	397.995i	0.731015	−	0.422052i
$944$		−	198.997i		−	0.210802i
$945$		0			0
$946$	−198.000			−0.209302
$947$	692.500	+	1199.45i	0.731257	+	1.26657i	0.956346	+	0.292236i	$0.0943991\pi$
$947$	692.500	+	1199.45i	0.731257	+	1.26657i	−0.225090	+	0.974338i	$0.572268\pi$
$948$		0			0
$949$	891.000	−	1543.26i	0.938883	−	1.62619i
$950$	−66.2337	+	74.9206i	−0.0697197	+	0.0788638i
$951$		0			0
$952$	1326.99	−	766.140i	1.39390	−	0.804769i
$953$	−1496.00			−1.56978			−0.784890	−	0.619635i	$-0.787280\pi$
$953$	−1496.00			−1.56978			−0.784890	+	0.619635i	$0.787280\pi$
$954$		0			0
$955$	495.000	+	49.7494i	0.518325	+	0.0520936i
$956$	−517.011	+	298.496i	−0.540806	+	0.312235i
$957$		0			0
$958$	637.646	+	368.145i	0.665602	+	0.384285i
$959$	−844.451	−	487.544i	−0.880553	−	0.508388i
$960$		0			0
$961$	60.0000	+	103.923i	0.0624350	+	0.108141i
$962$		0			0
$963$		0			0
$964$	−510.000			−0.529046
$965$	347.507	+	771.047i	0.360111	+	0.799013i
$966$		0			0
$967$	−60.3179	−	34.8246i	−0.0623763	−	0.0360130i	0.468487	−	0.883470i	$-0.344799\pi$
$967$	−60.3179	−	34.8246i	−0.0623763	−	0.0360130i	−0.530864	+	0.847457i	$0.678132\pi$
$968$	77.0000	−	133.368i	0.0795455	−	0.137777i
$969$		0			0
$970$	265.741	+	589.624i	0.273959	+	0.607860i
$971$			746.241i			0.768528i	0.923223	+	0.384264i	$0.125545\pi$
$971$			746.241i			0.768528i	−0.923223	+	0.384264i	$0.874455\pi$
$972$		0			0
$973$			636.792i			0.654462i
$974$	−413.609	+	238.797i	−0.424649	+	0.245171i
$975$		0			0
$976$	−110.000	+	190.526i	−0.112705	+	0.195211i
$977$	−527.000	+	912.791i	−0.539406	+	0.934279i	0.459530	+	0.888162i	$0.348018\pi$
$977$	−527.000	+	912.791i	−0.539406	+	0.934279i	−0.998936	+	0.0461168i	$0.985315\pi$
$978$		0			0
$979$	297.000	+	514.419i	0.303371	+	0.525454i
$980$	75.0000	−	746.241i	0.0765306	−	0.761470i
$981$		0			0
$982$			288.546i			0.293835i
$983$	697.000	+	1207.24i	0.709054	+	1.22812i	0.965208	+	0.261482i	$0.0842111\pi$
$983$	697.000	+	1207.24i	0.709054	+	1.22812i	−0.256155	+	0.966636i	$0.582456\pi$
$984$		0			0
$985$	−823.860	−	592.858i	−0.836406	−	0.601886i
$986$	−758.282	−	437.794i	−0.769049	−	0.444011i
$987$		0			0
$988$	−206.804	+	119.398i	−0.209316	+	0.120849i
$989$		−	397.995i		−	0.402422i
$990$		0			0
$991$	−265.000			−0.267407			−0.133703	−	0.991021i	$-0.542687\pi$
$991$	−265.000			−0.267407			−0.133703	+	0.991021i	$0.542687\pi$
$992$	−478.500	−	828.786i	−0.482359	−	0.835470i
$993$		0			0
$994$	−297.000	+	514.419i	−0.298793	+	0.517524i
$995$	629.055	+	452.675i	0.632216	+	0.454949i
$996$		0			0
$997$	−396.375	+	228.847i	−0.397568	+	0.229536i	−0.685434	−	0.728135i	$-0.740387\pi$
$997$	−396.375	+	228.847i	−0.397568	+	0.229536i	0.287866	+	0.957671i	$0.407054\pi$
$998$	290.000			0.290581
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.h.c.134.2		4
3.2	odd	2		405.3.h.h.134.1		4
5.4	even	2		405.3.h.h.134.2		4
9.2	odd	6		405.3.h.h.269.2		4
9.4	even	3		135.3.d.f.134.1	yes	2
9.5	odd	6		135.3.d.a.134.2	yes	2
9.7	even	3	inner	405.3.h.c.269.1		4
15.14	odd	2	inner	405.3.h.c.134.1		4
36.23	even	6		2160.3.c.c.1889.2		2
36.31	odd	6		2160.3.c.d.1889.1		2
45.4	even	6		135.3.d.a.134.1	✓	2
45.13	odd	12		675.3.c.q.26.1		4
45.14	odd	6		135.3.d.f.134.2	yes	2
45.22	odd	12		675.3.c.q.26.4		4
45.23	even	12		675.3.c.q.26.3		4
45.29	odd	6	inner	405.3.h.c.269.2		4
45.32	even	12		675.3.c.q.26.2		4
45.34	even	6		405.3.h.h.269.1		4
180.59	even	6		2160.3.c.d.1889.2		2
180.139	odd	6		2160.3.c.c.1889.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.d.a.134.1	✓	2	45.4	even	6
135.3.d.a.134.2	yes	2	9.5	odd	6
135.3.d.f.134.1	yes	2	9.4	even	3
135.3.d.f.134.2	yes	2	45.14	odd	6
405.3.h.c.134.1		4	15.14	odd	2	inner
405.3.h.c.134.2		4	1.1	even	1	trivial
405.3.h.c.269.1		4	9.7	even	3	inner
405.3.h.c.269.2		4	45.29	odd	6	inner
405.3.h.h.134.1		4	3.2	odd	2
405.3.h.h.134.2		4	5.4	even	2
405.3.h.h.269.1		4	45.34	even	6
405.3.h.h.269.2		4	9.2	odd	6
675.3.c.q.26.1		4	45.13	odd	12
675.3.c.q.26.2		4	45.32	even	12
675.3.c.q.26.3		4	45.23	even	12
675.3.c.q.26.4		4	45.22	odd	12
2160.3.c.c.1889.1		2	180.139	odd	6
2160.3.c.c.1889.2		2	36.23	even	6
2160.3.c.d.1889.1		2	36.31	odd	6
2160.3.c.d.1889.2		2	180.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{4} +(4.05842 + 2.92048i) q^{5} +(-8.61684 + 4.97494i) q^{7} -7.00000 q^{8} +(0.500000 - 4.97494i) q^{10} +(8.61684 - 4.97494i) q^{11} +(17.2337 + 9.94987i) q^{13} +(8.61684 + 4.97494i) q^{14} +(-2.50000 - 4.33013i) q^{16} +22.0000 q^{17} -4.00000 q^{19} +(13.6753 - 6.16337i) q^{20} +(-8.61684 - 4.97494i) q^{22} +(10.0000 - 17.3205i) q^{23} +(7.94158 + 23.7051i) q^{25} -19.8997i q^{26} +29.8496i q^{28} +(34.4674 - 19.8997i) q^{29} +(-14.5000 + 25.1147i) q^{31} +(-16.5000 + 28.5788i) q^{32} +(-11.0000 - 19.0526i) q^{34} +(-49.5000 - 4.97494i) q^{35} +(2.00000 + 3.46410i) q^{38} +(-28.4090 - 20.4434i) q^{40} +(34.4674 + 19.8997i) q^{41} +(17.2337 - 9.94987i) q^{43} -29.8496i q^{44} -20.0000 q^{46} +(-29.0000 - 50.2295i) q^{47} +(25.0000 - 43.3013i) q^{49} +(16.5584 - 18.7302i) q^{50} +(51.7011 - 29.8496i) q^{52} +31.0000 q^{53} +(49.5000 + 4.97494i) q^{55} +(60.3179 - 34.8246i) q^{56} +(-34.4674 - 19.8997i) q^{58} +(34.4674 + 19.8997i) q^{59} +(-22.0000 - 38.1051i) q^{61} +29.0000 q^{62} +13.0000 q^{64} +(40.8832 + 90.7115i) q^{65} +(17.2337 + 9.94987i) q^{67} +(33.0000 - 57.1577i) q^{68} +(20.4416 + 45.3557i) q^{70} +59.6992i q^{71} -89.5489i q^{73} +(-6.00000 + 10.3923i) q^{76} +(-49.5000 + 85.7365i) q^{77} +(5.00000 + 8.66025i) q^{79} +(2.50000 - 24.8747i) q^{80} -39.7995i q^{82} +(-9.50000 - 16.4545i) q^{83} +(89.2853 + 64.2506i) q^{85} +(-17.2337 - 9.94987i) q^{86} +(-60.3179 + 34.8246i) q^{88} +59.6992i q^{89} -198.000 q^{91} +(-30.0000 - 51.9615i) q^{92} +(-29.0000 + 50.2295i) q^{94} +(-16.2337 - 11.6819i) q^{95} +(-112.019 + 64.6742i) q^{97} -50.0000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{4} - q^{5} - 28 q^{8} + 2 q^{10} - 10 q^{16} + 88 q^{17} - 16 q^{19} + 3 q^{20} + 40 q^{23} + 49 q^{25} - 58 q^{31} - 66 q^{32} - 44 q^{34} - 198 q^{35} + 8 q^{38} + 7 q^{40} - 80 q^{46}+ \cdots - 200 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^4 - q^5 - 28 * q^8 + 2 * q^10 - 10 * q^16 + 88 * q^17 - 16 * q^19 + 3 * q^20 + 40 * q^23 + 49 * q^25 - 58 * q^31 - 66 * q^32 - 44 * q^34 - 198 * q^35 + 8 * q^38 + 7 * q^40 - 80 * q^46 - 116 * q^47 + 100 * q^49 + 49 * q^50 + 124 * q^53 + 198 * q^55 - 88 * q^61 + 116 * q^62 + 52 * q^64 + 198 * q^65 + 132 * q^68 + 99 * q^70 - 24 * q^76 - 198 * q^77 + 20 * q^79 + 10 * q^80 - 38 * q^83 - 22 * q^85 - 792 * q^91 - 120 * q^92 - 116 * q^94 + 4 * q^95 - 200 * q^98

Introduction

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