LMFDB - Embedded newform 405.3.h.c.269.1

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			269.1
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	405.269
Dual form			405.3.h.c.134.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{4} +(-4.55842 + 2.05446i) q^{5} +(8.61684 + 4.97494i) q^{7} -7.00000 q^{8} +(0.500000 - 4.97494i) q^{10} +(-8.61684 - 4.97494i) q^{11} +(-17.2337 + 9.94987i) q^{13} +(-8.61684 + 4.97494i) q^{14} +(-2.50000 + 4.33013i) q^{16} +22.0000 q^{17} -4.00000 q^{19} +(-12.1753 - 8.76144i) q^{20} +(8.61684 - 4.97494i) q^{22} +(10.0000 + 17.3205i) q^{23} +(16.5584 - 18.7302i) q^{25} -19.8997i q^{26} +29.8496i q^{28} +(-34.4674 - 19.8997i) q^{29} +(-14.5000 - 25.1147i) q^{31} +(-16.5000 - 28.5788i) q^{32} +(-11.0000 + 19.0526i) q^{34} +(-49.5000 - 4.97494i) q^{35} +(2.00000 - 3.46410i) q^{38} +(31.9090 - 14.3812i) q^{40} +(-34.4674 + 19.8997i) q^{41} +(-17.2337 - 9.94987i) q^{43} -29.8496i q^{44} -20.0000 q^{46} +(-29.0000 + 50.2295i) q^{47} +(25.0000 + 43.3013i) q^{49} +(7.94158 + 23.7051i) q^{50} +(-51.7011 - 29.8496i) q^{52} +31.0000 q^{53} +(49.5000 + 4.97494i) q^{55} +(-60.3179 - 34.8246i) q^{56} +(34.4674 - 19.8997i) q^{58} +(-34.4674 + 19.8997i) q^{59} +(-22.0000 + 38.1051i) q^{61} +29.0000 q^{62} +13.0000 q^{64} +(58.1168 - 80.7616i) q^{65} +(-17.2337 + 9.94987i) q^{67} +(33.0000 + 57.1577i) q^{68} +(29.0584 - 40.3808i) q^{70} +59.6992i q^{71} -89.5489i q^{73} +(-6.00000 - 10.3923i) q^{76} +(-49.5000 - 85.7365i) q^{77} +(5.00000 - 8.66025i) q^{79} +(2.50000 - 24.8747i) q^{80} -39.7995i q^{82} +(-9.50000 + 16.4545i) q^{83} +(-100.285 + 45.1980i) q^{85} +(17.2337 - 9.94987i) q^{86} +(60.3179 + 34.8246i) q^{88} +59.6992i q^{89} -198.000 q^{91} +(-30.0000 + 51.9615i) q^{92} +(-29.0000 - 50.2295i) q^{94} +(18.2337 - 8.21782i) q^{95} +(112.019 + 64.6742i) q^{97} -50.0000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

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

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	−0.963525	−	0.267617i	$-0.913764\pi$
$2$	−0.500000	+	0.866025i	−0.250000	+	0.433013i	0.713525	+	0.700629i	$0.247097\pi$
$3$		0			0
$3$		0			0
$4$	1.50000	+	2.59808i	0.375000	+	0.649519i
$5$	−4.55842	+	2.05446i	−0.911684	+	0.410891i
$5$	−4.55842	+	2.05446i	−0.911684	+	0.410891i
$6$		0			0
$7$	8.61684	+	4.97494i	1.23098	+	0.710705i	0.967234	−	0.253887i	$-0.0817093\pi$
$7$	8.61684	+	4.97494i	1.23098	+	0.710705i	0.263744	+	0.964593i	$0.415043\pi$
$8$	−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	$-0.482718\pi$
$11$	−8.61684	−	4.97494i	−0.783349	−	0.452267i	−0.837616	+	0.546259i	$0.816051\pi$
$12$		0			0
$13$	−17.2337	+	9.94987i	−1.32567	+	0.765375i	−0.984626	−	0.174673i	$-0.944113\pi$
$13$	−17.2337	+	9.94987i	−1.32567	+	0.765375i	−0.341042	+	0.940048i	$0.610780\pi$
$14$	−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	$0.533568\pi$
$20$	−12.1753	−	8.76144i	−0.608763	−	0.438072i
$21$		0			0
$22$	8.61684	−	4.97494i	0.391675	−	0.226134i
$23$	10.0000	+	17.3205i	0.434783	+	0.753066i	0.997278	−	0.0737349i	$-0.0234919\pi$
$23$	10.0000	+	17.3205i	0.434783	+	0.753066i	−0.562495	+	0.826801i	$0.690159\pi$
$24$		0			0
$25$	16.5584	−	18.7302i	0.662337	−	0.749206i
$26$		−	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	$-0.574055\pi$
$29$	−34.4674	−	19.8997i	−1.18853	−	0.686198i	−0.957972	+	0.286860i	$0.907388\pi$
$30$		0			0
$31$	−14.5000	−	25.1147i	−0.467742	−	0.810153i	0.531579	−	0.847009i	$-0.321599\pi$
$31$	−14.5000	−	25.1147i	−0.467742	−	0.810153i	−0.999321	+	0.0368561i	$0.988266\pi$
$32$	−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
$40$	31.9090	−	14.3812i	0.797724	−	0.359530i
$41$	−34.4674	+	19.8997i	−0.840668	+	0.485360i	−0.857491	−	0.514499i	$-0.827978\pi$
$41$	−34.4674	+	19.8997i	−0.840668	+	0.485360i	0.0168234	+	0.999858i	$0.494645\pi$
$42$		0			0
$43$	−17.2337	−	9.94987i	−0.400783	−	0.231392i	0.286039	−	0.958218i	$-0.407661\pi$
$43$	−17.2337	−	9.94987i	−0.400783	−	0.231392i	−0.686822	+	0.726826i	$0.740995\pi$
$44$		−	29.8496i		−	0.678401i
$45$		0			0
$46$	−20.0000			−0.434783
$47$	−29.0000	+	50.2295i	−0.617021	+	1.06871i	0.373005	+	0.927829i	$0.378327\pi$
$47$	−29.0000	+	50.2295i	−0.617021	+	1.06871i	−0.990026	+	0.140883i	$0.955006\pi$
$48$		0			0
$49$	25.0000	+	43.3013i	0.510204	+	0.883699i
$50$	7.94158	+	23.7051i	0.158832	+	0.474102i
$51$		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	$-0.776175\pi$
$59$	−34.4674	+	19.8997i	−0.584193	+	0.337284i	0.178605	+	0.983921i	$0.442842\pi$
$60$		0			0
$61$	−22.0000	+	38.1051i	−0.360656	+	0.624674i	−0.988069	−	0.154012i	$-0.950780\pi$
$61$	−22.0000	+	38.1051i	−0.360656	+	0.624674i	0.627413	+	0.778687i	$0.284114\pi$
$62$	29.0000			0.467742
$63$		0			0
$64$	13.0000			0.203125
$65$	58.1168	−	80.7616i	0.894105	−	1.24249i
$66$		0			0
$67$	−17.2337	+	9.94987i	−0.257219	+	0.148506i	−0.623065	−	0.782170i	$-0.714113\pi$
$67$	−17.2337	+	9.94987i	−0.257219	+	0.148506i	0.365846	+	0.930675i	$0.380780\pi$
$68$	33.0000	+	57.1577i	0.485294	+	0.840554i
$69$		0			0
$70$	29.0584	−	40.3808i	0.415120	−	0.576868i
$71$			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	−0.832644	−	0.553809i	$-0.813174\pi$
$79$	5.00000	−	8.66025i	0.0632911	−	0.109623i	0.895935	+	0.444186i	$0.146507\pi$
$80$	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	−0.917563	−	0.397591i	$-0.869846\pi$
$83$	−9.50000	+	16.4545i	−0.114458	+	0.198247i	0.803105	+	0.595837i	$0.203180\pi$
$84$		0			0
$85$	−100.285	+	45.1980i	−1.17983	+	0.531742i
$86$	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
$95$	18.2337	−	8.21782i	0.191934	−	0.0865034i
$96$		0			0
$97$	112.019	+	64.6742i	1.15483	+	0.666744i	0.950061	−	0.312065i	$-0.101021\pi$
$97$	112.019	+	64.6742i	1.15483	+	0.666744i	0.204774	+	0.978809i	$0.434354\pi$
$98$	−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	$-0.0174279\pi$
$101$	146.486	+	84.5739i	1.45036	+	0.837366i	0.451858	+	0.892090i	$0.350761\pi$
$102$		0			0
$103$	34.4674	−	19.8997i	0.334635	−	0.193201i	−0.323262	−	0.946309i	$-0.604780\pi$
$103$	34.4674	−	19.8997i	0.334635	−	0.193201i	0.657897	+	0.753108i	$0.271446\pi$
$104$	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	$0.341701\pi$
$110$	−29.0584	+	40.3808i	−0.264167	+	0.367098i
$111$		0			0
$112$	−43.0842	+	24.8747i	−0.384681	+	0.222095i
$113$	40.0000	+	69.2820i	0.353982	+	0.613115i	0.986943	−	0.161068i	$-0.0514940\pi$
$113$	40.0000	+	69.2820i	0.353982	+	0.613115i	−0.632961	+	0.774184i	$0.718161\pi$
$114$		0			0
$115$	−81.1684	−	58.4096i	−0.705813	−	0.507910i
$116$		−	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
$130$	40.8832	+	90.7115i	0.314486	+	0.697780i
$131$	146.486	−	84.5739i	1.11822	−	0.645603i	0.177271	−	0.984162i	$-0.443273\pi$
$131$	146.486	−	84.5739i	1.11822	−	0.645603i	0.940945	+	0.338559i	$0.109940\pi$
$132$		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	−0.629906	−	0.776671i	$-0.716907\pi$
$137$	49.0000	−	84.8705i	0.357664	−	0.619493i	0.987570	+	0.157179i	$0.0502399\pi$
$138$		0			0
$139$	32.0000	+	55.4256i	0.230216	+	0.398746i	0.957872	−	0.287197i	$-0.0927235\pi$
$139$	32.0000	+	55.4256i	0.230216	+	0.398746i	−0.727656	+	0.685943i	$0.759390\pi$
$140$	−61.3247	−	136.067i	−0.438034	−	0.971908i
$141$		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	$-0.677297\pi$
$149$	−8.61684	+	4.97494i	−0.0578312	+	0.0333888i	0.470806	+	0.882237i	$0.343963\pi$
$150$		0			0
$151$	−128.500	+	222.569i	−0.850993	+	1.47396i	0.0293194	+	0.999570i	$0.490666\pi$
$151$	−128.500	+	222.569i	−0.850993	+	1.47396i	−0.880313	+	0.474394i	$0.842667\pi$
$152$	28.0000			0.184211
$153$		0			0
$154$	99.0000			0.642857
$155$	117.694	+	84.6940i	0.759318	+	0.546413i
$156$		0			0
$157$	137.870	−	79.5990i	0.878150	−	0.507000i	0.00810182	−	0.999967i	$-0.497421\pi$
$157$	137.870	−	79.5990i	0.878150	−	0.507000i	0.870048	+	0.492967i	$0.164088\pi$
$158$	5.00000	+	8.66025i	0.0316456	+	0.0548117i
$159$		0			0
$160$	133.928	+	96.3759i	0.837050	+	0.602349i
$161$			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	0.942604	+	0.333913i	$0.108369\pi$
$167$	127.000	+	219.970i	0.760479	+	1.31719i	−0.182125	+	0.983275i	$0.558298\pi$
$168$		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	0.296034	+	0.955177i	$0.404336\pi$
$173$	−117.500	+	203.516i	−0.679191	+	1.17639i	−0.975225	+	0.221216i	$0.928998\pi$
$174$		0			0
$175$	235.863	−	79.0177i	1.34779	−	0.451530i
$176$	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	$-0.417210\pi$
$191$	−86.1684	−	49.7494i	−0.451144	−	0.260468i	−0.708313	+	0.705898i	$0.750543\pi$
$192$		0			0
$193$	−146.486	+	84.5739i	−0.758997	+	0.438207i	−0.828935	−	0.559344i	$-0.811053\pi$
$193$	−146.486	+	84.5739i	−0.758997	+	0.438207i	0.0699388	+	0.997551i	$0.477720\pi$
$194$	−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	$0.372666\pi$
$200$	−115.909	+	131.111i	−0.579545	+	0.655555i
$201$		0			0
$202$	−146.486	+	84.5739i	−0.725180	+	0.418683i
$203$	−198.000	−	342.946i	−0.975369	−	1.68939i
$204$		0			0
$205$	116.234	−	161.523i	0.566994	−	0.787918i
$206$			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	−0.956943	−	0.290276i	$-0.906253\pi$
$211$	−154.000	−	266.736i	−0.729858	−	1.26415i	0.227085	−	0.973875i	$-0.427080\pi$
$212$	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
$220$	61.3247	+	136.067i	0.278749	+	0.618487i
$221$	−379.141	+	218.897i	−1.71557	+	0.990485i
$222$		0			0
$223$	34.4674	+	19.8997i	0.154562	+	0.0892365i	0.575286	−	0.817952i	$-0.304891\pi$
$223$	34.4674	+	19.8997i	0.154562	+	0.0892365i	−0.420724	+	0.907189i	$0.638224\pi$
$224$		−	328.346i		−	1.46583i
$225$		0			0
$226$	−80.0000			−0.353982
$227$	121.000	−	209.578i	0.533040	−	0.923252i	−0.466216	−	0.884671i	$-0.654383\pi$
$227$	121.000	−	209.578i	0.533040	−	0.923252i	0.999255	−	0.0385807i	$-0.0122837\pi$
$228$		0			0
$229$	53.0000	+	91.7987i	0.231441	+	0.400868i	0.958232	−	0.285991i	$-0.0923226\pi$
$229$	53.0000	+	91.7987i	0.231441	+	0.400868i	−0.726791	+	0.686858i	$0.758989\pi$
$230$	91.1684	−	41.0891i	0.396385	−	0.178648i
$231$		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	$-0.529989\pi$
$239$	172.337	−	99.4987i	0.721075	−	0.416313i	0.815148	+	0.579253i	$0.196655\pi$
$240$		0			0
$241$	−85.0000	+	147.224i	−0.352697	+	0.610889i	−0.986721	−	0.162424i	$-0.948069\pi$
$241$	−85.0000	+	147.224i	−0.352697	+	0.610889i	0.634024	+	0.773313i	$0.281402\pi$
$242$	22.0000			0.0909091
$243$		0			0
$244$	−132.000			−0.540984
$245$	−202.921	−	146.024i	−0.828249	−	0.596017i
$246$		0			0
$247$	68.9348	−	39.7995i	0.279088	−	0.161132i
$248$	101.500	+	175.803i	0.409274	+	0.708884i
$249$		0			0
$250$	−84.9021	−	91.7422i	−0.339609	−	0.366969i
$251$		−	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	0.997123	+	0.0757953i	$0.0241495\pi$
$257$	145.000	+	251.147i	0.564202	+	0.977227i	−0.432921	+	0.901432i	$0.642517\pi$
$258$		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	−0.750070	−	0.661359i	$-0.769980\pi$
$263$	52.0000	−	90.0666i	0.197719	−	0.342459i	0.947788	+	0.318900i	$0.103313\pi$
$264$		0			0
$265$	−141.311	+	63.6881i	−0.533249	+	0.240333i
$266$	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
$275$	−235.863	+	79.0177i	−0.857682	+	0.287337i
$276$		0			0
$277$	137.870	+	79.5990i	0.497724	+	0.287361i	0.727773	−	0.685818i	$-0.240555\pi$
$277$	137.870	+	79.5990i	0.497724	+	0.287361i	−0.230049	+	0.973179i	$0.573889\pi$
$278$	−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	$-0.460684\pi$
$281$	−189.571	−	109.449i	−0.674628	−	0.389497i	−0.797828	+	0.602885i	$0.794018\pi$
$282$		0			0
$283$	241.272	−	139.298i	0.852550	−	0.492220i	−0.00896047	−	0.999960i	$-0.502852\pi$
$283$	241.272	−	139.298i	0.852550	−	0.492220i	0.861510	+	0.507740i	$0.169519\pi$
$284$	−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
$290$	−116.234	+	161.523i	−0.400806	+	0.556976i
$291$		0			0
$292$	232.655	−	134.323i	0.796763	−	0.460011i
$293$	−143.000	−	247.683i	−0.488055	−	0.845335i	0.511851	−	0.859074i	$-0.328960\pi$
$293$	−143.000	−	247.683i	−0.488055	−	0.845335i	−0.999906	+	0.0137389i	$0.995627\pi$
$294$		0			0
$295$	116.234	−	161.523i	0.394013	−	0.547536i
$296$		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
$310$	−132.194	+	59.5792i	−0.426433	+	0.192191i
$311$	172.337	−	99.4987i	0.554138	−	0.319932i	−0.196651	−	0.980473i	$-0.563007\pi$
$311$	172.337	−	99.4987i	0.554138	−	0.319932i	0.750789	+	0.660542i	$0.229673\pi$
$312$		0			0
$313$	60.3179	+	34.8246i	0.192709	+	0.111261i	0.593250	−	0.805018i	$-0.297845\pi$
$313$	60.3179	+	34.8246i	0.192709	+	0.111261i	−0.400541	+	0.916279i	$0.631178\pi$
$314$			159.198i			0.507000i
$315$		0			0
$316$	30.0000			0.0949367
$317$	−270.500	+	468.520i	−0.853312	+	1.47798i	0.0248896	+	0.999690i	$0.492077\pi$
$317$	−270.500	+	468.520i	−0.853312	+	1.47798i	−0.878202	+	0.478290i	$0.841257\pi$
$318$		0			0
$319$	198.000	+	342.946i	0.620690	+	1.07507i
$320$	−59.2595	+	26.7079i	−0.185186	+	0.0834623i
$321$		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	−0.581415	−	0.813607i	$-0.697501\pi$
$331$	137.000	−	237.291i	0.413897	−	0.716891i	0.995312	+	0.0967162i	$0.0308339\pi$
$332$	−57.0000			−0.171687
$333$		0			0
$334$	−254.000			−0.760479
$335$	58.1168	−	80.7616i	0.173483	−	0.241079i
$336$		0			0
$337$	−379.141	+	218.897i	−1.12505	+	0.649547i	−0.942685	−	0.333685i	$-0.891708\pi$
$337$	−379.141	+	218.897i	−1.12505	+	0.649547i	−0.182363	+	0.983231i	$0.558375\pi$
$338$	113.500	+	196.588i	0.335799	+	0.581621i
$339$		0			0
$340$	−267.856	−	192.752i	−0.787811	−	0.566917i
$341$			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	0.965686	−	0.259713i	$-0.0836279\pi$
$347$	89.5000	+	155.019i	0.257925	+	0.446739i	−0.707761	+	0.706452i	$0.750295\pi$
$348$		0			0
$349$	−310.000	+	536.936i	−0.888252	+	1.53850i	−0.0463119	+	0.998927i	$0.514747\pi$
$349$	−310.000	+	536.936i	−0.888252	+	1.53850i	−0.841940	+	0.539571i	$0.818587\pi$
$350$	−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	−0.842472	−	0.538739i	$-0.818901\pi$
$353$	16.0000	−	27.7128i	0.0453258	−	0.0785066i	0.887798	+	0.460233i	$0.152234\pi$
$354$		0			0
$355$	−122.649	−	272.134i	−0.345491	−	0.766576i
$356$	−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
$365$	183.974	+	408.202i	0.504039	+	1.11836i
$366$		0			0
$367$	−301.590	−	174.123i	−0.821770	−	0.474449i	0.0292566	−	0.999572i	$-0.490686\pi$
$367$	−301.590	−	174.123i	−0.821770	−	0.474449i	−0.851026	+	0.525123i	$0.824019\pi$
$368$	−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	$-0.516849\pi$
$373$	292.973	−	169.148i	0.785450	−	0.453480i	0.838358	+	0.545120i	$0.183516\pi$
$374$	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	$0.393903\pi$
$380$	48.7011	+	35.0458i	0.128161	+	0.0922257i
$381$		0			0
$382$	86.1684	−	49.7494i	0.225572	−	0.130234i
$383$	−197.000	−	341.214i	−0.514360	−	0.890898i	−0.999861	−	0.0166620i	$-0.994696\pi$
$383$	−197.000	−	341.214i	−0.514360	−	0.890898i	0.485501	−	0.874236i	$-0.338637\pi$
$384$		0			0
$385$	401.784	+	289.128i	1.04359	+	0.750981i
$386$		−	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	$-0.337404\pi$
$389$	−8.61684	−	4.97494i	−0.0221513	−	0.0127890i	−0.511035	+	0.859560i	$0.670738\pi$
$390$		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
$400$	39.7079	+	118.525i	0.0992697	+	0.296314i
$401$	172.337	−	99.4987i	0.429768	−	0.248127i	−0.269480	−	0.963006i	$-0.586852\pi$
$401$	172.337	−	99.4987i	0.429768	−	0.248127i	0.699248	+	0.714879i	$0.253518\pi$
$402$		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	0.994280	−	0.106804i	$-0.0340616\pi$
$409$	165.500	+	286.654i	0.404645	+	0.700867i	−0.589635	+	0.807670i	$0.700728\pi$
$410$	81.7663	+	181.423i	0.199430	+	0.442495i
$411$		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	$-0.367547\pi$
$419$	585.945	−	338.296i	1.39844	−	0.807388i	0.994229	+	0.107278i	$0.0342136\pi$
$420$		0			0
$421$	−4.00000	+	6.92820i	−0.00950119	+	0.0164565i	−0.870737	−	0.491749i	$-0.836358\pi$
$421$	−4.00000	+	6.92820i	−0.00950119	+	0.0164565i	0.861236	+	0.508206i	$0.169691\pi$
$422$	308.000			0.729858
$423$		0			0
$424$	−217.000			−0.511792
$425$	364.285	−	412.063i	0.857142	−	0.969561i
$426$		0			0
$427$	−379.141	+	218.897i	−0.887918	+	0.512640i
$428$	−43.5000	−	75.3442i	−0.101636	−	0.176038i
$429$		0			0
$430$	−58.1168	+	80.7616i	−0.135155	+	0.187818i
$431$		−	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	−0.962096	−	0.272710i	$-0.912080\pi$
$439$	−107.500	+	186.195i	−0.244875	+	0.424135i	0.717222	+	0.696845i	$0.245413\pi$
$440$	−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	−0.953101	−	0.302651i	$-0.902128\pi$
$443$	−95.0000	+	164.545i	−0.214447	+	0.371433i	0.738654	+	0.674084i	$0.235462\pi$
$444$		0			0
$445$	−122.649	−	272.134i	−0.275617	−	0.611538i
$446$	−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
$455$	902.568	−	406.782i	1.98366	−	0.894027i
$456$		0			0
$457$	112.019	+	64.6742i	0.245118	+	0.141519i	0.617527	−	0.786550i	$-0.288135\pi$
$457$	112.019	+	64.6742i	0.245118	+	0.141519i	−0.372409	+	0.928069i	$0.621468\pi$
$458$	−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	$-0.399066\pi$
$461$	−163.720	−	94.5238i	−0.355141	−	0.205041i	−0.666947	+	0.745105i	$0.732399\pi$
$462$		0			0
$463$	−715.198	+	412.920i	−1.54470	+	0.891835i	−0.546172	+	0.837673i	$0.683916\pi$
$463$	−715.198	+	412.920i	−1.54470	+	0.891835i	−0.998532	+	0.0541624i	$0.982751\pi$
$464$	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
$470$	235.388	+	169.388i	0.500827	+	0.360400i
$471$		0			0
$472$	241.272	−	139.298i	0.511169	−	0.295123i
$473$	99.0000	+	171.473i	0.209302	+	0.362522i
$474$		0			0
$475$	−66.2337	+	74.9206i	−0.139439	+	0.157728i
$476$			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	$-0.0543016\pi$
$479$	637.646	+	368.145i	1.33120	+	0.768571i	0.345719	+	0.938338i	$0.387635\pi$
$480$		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
$490$	227.921	−	102.723i	0.465145	−	0.209638i
$491$	249.888	−	144.273i	0.508938	−	0.293835i	−0.223459	−	0.974713i	$-0.571735\pi$
$491$	249.888	−	144.273i	0.508938	−	0.293835i	0.732397	+	0.680878i	$0.238402\pi$
$492$		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	0.683366	−	0.730076i	$-0.260515\pi$
$499$	−145.000	−	251.147i	−0.290581	−	0.503301i	−0.973947	+	0.226775i	$0.927182\pi$
$500$	−365.706	+	82.9689i	−0.731413	+	0.165938i
$501$		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	$-0.669778\pi$
$509$	−8.61684	+	4.97494i	−0.0169290	+	0.00977394i	0.491512	+	0.870871i	$0.336445\pi$
$510$		0			0
$511$	445.500	−	771.629i	0.871820	−	1.51004i
$512$	305.000			0.595703
$513$		0			0
$514$	−290.000			−0.564202
$515$	−116.234	+	161.523i	−0.225696	+	0.313637i
$516$		0			0
$517$	499.777	−	288.546i	0.966687	−	0.558117i
$518$		0			0
$519$		0			0
$520$	−406.818	+	565.331i	−0.782342	+	1.08718i
$521$			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
$535$	132.194	−	59.5792i	0.247092	−	0.111363i
$536$	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
$545$	−474.076	+	213.663i	−0.869864	+	0.392043i
$546$		0			0
$547$	86.1684	+	49.7494i	0.157529	+	0.0909495i	0.576692	−	0.816961i	$-0.304343\pi$
$547$	86.1684	+	49.7494i	0.157529	+	0.0909495i	−0.419163	+	0.907911i	$0.637676\pi$
$548$	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
$560$	145.292	−	201.904i	0.259450	−	0.360543i
$561$		0			0
$562$	189.571	−	109.449i	0.337314	−	0.194748i
$563$	467.500	+	809.734i	0.830373	+	1.43825i	0.897743	+	0.440520i	$0.145206\pi$
$563$	467.500	+	809.734i	0.830373	+	1.43825i	−0.0673697	+	0.997728i	$0.521461\pi$
$564$		0			0
$565$	−324.674	−	233.639i	−0.574644	−	0.413519i
$566$			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	$-0.564685\pi$
$569$	−654.880	−	378.095i	−1.15093	−	0.664491i	−0.949114	+	0.314932i	$0.898018\pi$
$570$		0			0
$571$	−253.000	−	438.209i	−0.443082	−	0.767441i	0.554834	−	0.831961i	$-0.312782\pi$
$571$	−253.000	−	438.209i	−0.443082	−	0.767441i	−0.997916	+	0.0645199i	$0.979448\pi$
$572$	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
$580$	245.299	+	544.269i	0.422929	+	0.938394i
$581$	−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	−0.807866	−	0.589367i	$-0.799377\pi$
$587$	62.5000	−	108.253i	0.106474	−	0.184418i	0.914339	+	0.404949i	$0.132711\pi$
$588$		0			0
$589$	58.0000	+	100.459i	0.0984720	+	0.170558i
$590$	81.7663	+	181.423i	0.138587	+	0.307496i
$591$		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	$-0.629571\pi$
$599$	120.636	−	69.6491i	0.201395	−	0.116276i	0.597306	+	0.802013i	$0.296238\pi$
$600$		0			0
$601$	−26.5000	+	45.8993i	−0.0440932	+	0.0763716i	−0.887230	−	0.461328i	$-0.847373\pi$
$601$	−26.5000	+	45.8993i	−0.0440932	+	0.0763716i	0.843137	+	0.537700i	$0.180707\pi$
$602$	198.000			0.328904
$603$		0			0
$604$	−771.000			−1.27649
$605$	89.2853	+	64.2506i	0.147579	+	0.106199i
$606$		0			0
$607$	344.674	−	198.997i	0.567832	−	0.327838i	−0.188451	−	0.982083i	$-0.560347\pi$
$607$	344.674	−	198.997i	0.567832	−	0.327838i	0.756283	+	0.654245i	$0.227013\pi$
$608$	66.0000	+	114.315i	0.108553	+	0.188019i
$609$		0			0
$610$	178.571	+	128.501i	0.292739	+	0.210658i
$611$		−	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	−0.803436	−	0.595391i	$-0.796997\pi$
$617$	−566.000	−	980.341i	−0.917342	−	1.58888i	−0.113906	−	0.993492i	$-0.536336\pi$
$618$		0			0
$619$	−151.000	+	261.540i	−0.243942	+	0.422520i	−0.961834	−	0.273635i	$-0.911774\pi$
$619$	−151.000	+	261.540i	−0.243942	+	0.422520i	0.717892	+	0.696155i	$0.245107\pi$
$620$	−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
$625$	−76.6373	−	620.284i	−0.122620	−	0.992454i
$626$	−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
$635$	−306.624	−	680.336i	−0.482872	−	1.07140i
$636$		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	$-0.433813\pi$
$641$	−344.674	−	198.997i	−0.537713	−	0.310448i	−0.744151	+	0.668011i	$0.767146\pi$
$642$		0			0
$643$	241.272	−	139.298i	0.375228	−	0.216638i	−0.300512	−	0.953778i	$-0.597158\pi$
$643$	241.272	−	139.298i	0.375228	−	0.216638i	0.675740	+	0.737140i	$0.263824\pi$
$644$	−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
$650$	−372.725	−	329.508i	−0.573424	−	0.506936i
$651$		0			0
$652$	−775.516	+	447.744i	−1.18944	+	0.686724i
$653$	−3.50000	−	6.06218i	−0.00535988	−	0.00928358i	0.863333	−	0.504635i	$-0.168373\pi$
$653$	−3.50000	−	6.06218i	−0.00535988	−	0.00928358i	−0.868693	+	0.495351i	$0.835039\pi$
$654$		0			0
$655$	−493.993	+	686.473i	−0.754188	+	1.04805i
$656$		−	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	$-0.594875\pi$
$659$	−835.834	−	482.569i	−1.26834	−	0.732275i	−0.974673	+	0.223634i	$0.928208\pi$
$660$		0			0
$661$	320.000	+	554.256i	0.484115	+	0.838512i	0.999834	−	0.0182463i	$-0.00580831\pi$
$661$	320.000	+	554.256i	0.484115	+	0.838512i	−0.515719	+	0.856758i	$0.672475\pi$
$662$	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
$670$	40.8832	+	90.7115i	0.0610196	+	0.135390i
$671$	379.141	−	218.897i	0.565039	−	0.326225i
$672$		0			0
$673$	267.122	+	154.223i	0.396913	+	0.229158i	0.685151	−	0.728401i	$-0.259736\pi$
$673$	267.122	+	154.223i	0.396913	+	0.229158i	−0.288238	+	0.957559i	$0.593070\pi$
$674$		−	437.794i		−	0.649547i
$675$		0			0
$676$	681.000			1.00740
$677$	−11.0000	+	19.0526i	−0.0162482	+	0.0281426i	−0.874035	−	0.485863i	$-0.838506\pi$
$677$	−11.0000	+	19.0526i	−0.0162482	+	0.0281426i	0.857787	+	0.514005i	$0.171839\pi$
$678$		0			0
$679$	643.500	+	1114.57i	0.947717	+	1.64149i
$680$	701.997	−	316.386i	1.03235	−	0.465274i
$681$		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	−0.650219	−	0.759747i	$-0.725323\pi$
$691$	230.000	−	398.372i	0.332851	−	0.576515i	0.983070	+	0.183232i	$0.0586561\pi$
$692$	−705.000			−1.01879
$693$		0			0
$694$	−179.000			−0.257925
$695$	−259.739	−	186.911i	−0.373725	−	0.268936i
$696$		0			0
$697$	−758.282	+	437.794i	−1.08792	+	0.628113i
$698$	−310.000	−	536.936i	−0.444126	−	0.769249i
$699$		0			0
$700$	559.088	+	494.263i	0.798697	+	0.706090i
$701$		−	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	−0.607940	−	0.793983i	$-0.708004\pi$
$709$	272.000	−	471.118i	0.383639	−	0.664482i	0.991579	+	0.129501i	$0.0413374\pi$
$710$	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
$715$	−902.568	+	406.782i	−1.26233	+	0.568926i
$716$	−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
$725$	−943.451	+	316.071i	−1.30131	+	0.435960i
$726$		0			0
$727$	1197.74	+	691.516i	1.64751	+	0.951192i	0.978057	+	0.208339i	$0.0668059\pi$
$727$	1197.74	+	691.516i	1.64751	+	0.951192i	0.669456	+	0.742852i	$0.266527\pi$
$728$	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	$-0.523636\pi$
$733$	551.478	−	318.396i	0.752357	−	0.434374i	0.826545	+	0.562871i	$0.190303\pi$
$734$	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	0.994335	−	0.106294i	$-0.0338984\pi$
$743$	301.000	+	521.347i	0.405114	+	0.701679i	−0.589220	+	0.807972i	$0.700565\pi$
$744$		0			0
$745$	29.0584	−	40.3808i	0.0390046	−	0.0542024i
$746$			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	0.632234	−	0.774778i	$-0.282138\pi$
$751$	−266.500	−	461.592i	−0.354860	−	0.614636i	−0.987094	+	0.160142i	$0.948805\pi$
$752$	−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
$760$	−127.636	+	57.5248i	−0.167942	+	0.0756905i
$761$	−861.684	+	497.494i	−1.13231	+	0.653737i	−0.944514	−	0.328472i	$-0.893466\pi$
$761$	−861.684	+	497.494i	−1.13231	+	0.653737i	−0.187792	+	0.982209i	$0.560133\pi$
$762$		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	0.599523	−	0.800357i	$-0.295357\pi$
$769$	−302.500	−	523.945i	−0.393368	−	0.681333i	−0.992891	+	0.119024i	$0.962023\pi$
$770$	−451.284	+	203.391i	−0.586083	+	0.264144i
$771$		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
$785$	−464.935	+	646.093i	−0.592274	+	0.823048i
$786$		0			0
$787$	448.076	−	258.697i	0.569347	−	0.328712i	−0.187542	−	0.982257i	$-0.560052\pi$
$787$	448.076	−	258.697i	0.569347	−	0.328712i	0.756888	+	0.653544i	$0.226719\pi$
$788$	−304.500	−	527.409i	−0.386421	−	0.669301i
$789$		0			0
$790$	−40.5842	−	29.2048i	−0.0513724	−	0.0369681i
$791$			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	0.951765	−	0.306827i	$-0.0992672\pi$
$797$	167.500	+	290.119i	0.210163	+	0.364013i	−0.741602	+	0.670840i	$0.765934\pi$
$798$		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
$805$	−408.832	−	907.115i	−0.507865	−	1.12685i
$806$	−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
$815$	−613.247	−	1360.67i	−0.752451	−	1.66954i
$816$		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	$-0.570779\pi$
$821$	−965.087	−	557.193i	−1.17550	−	0.678676i	−0.954970	+	0.296704i	$0.904113\pi$
$822$		0			0
$823$	−818.600	+	472.619i	−0.994654	+	0.574264i	−0.906662	−	0.421857i	$-0.861378\pi$
$823$	−818.600	+	472.619i	−0.994654	+	0.574264i	−0.0879918	+	0.996121i	$0.528045\pi$
$824$	−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	$0.364218\pi$
$830$	77.1100	+	55.4891i	0.0929036	+	0.0668544i
$831$		0			0
$832$	−224.038	+	129.348i	−0.269276	+	0.155467i
$833$	550.000	+	952.628i	0.660264	+	1.14361i
$834$		0			0
$835$	−1030.84	−	741.802i	−1.23454	−	0.888386i
$836$			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	$-0.0759063\pi$
$839$	1051.25	+	606.942i	1.25299	+	0.723412i	0.281284	+	0.959624i	$0.409240\pi$
$840$		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
$850$	174.715	+	521.512i	0.205547	+	0.613544i
$851$		0			0
$852$		0			0
$853$	−637.646	−	368.145i	−0.747534	−	0.431589i	0.0772682	−	0.997010i	$-0.475380\pi$
$853$	−637.646	−	368.145i	−0.747534	−	0.431589i	−0.824802	+	0.565421i	$0.808714\pi$
$854$		−	437.794i		−	0.512640i
$855$		0			0
$856$	203.000			0.237150
$857$	−77.0000	+	133.368i	−0.0898483	+	0.155622i	−0.907447	−	0.420167i	$-0.861972\pi$
$857$	−77.0000	+	133.368i	−0.0898483	+	0.155622i	0.817599	+	0.575789i	$0.195305\pi$
$858$		0			0
$859$	566.000	+	980.341i	0.658906	+	1.14126i	0.980899	+	0.194516i	$0.0623137\pi$
$859$	566.000	+	980.341i	0.658906	+	1.14126i	−0.321994	+	0.946742i	$0.604353\pi$
$860$	122.649	+	272.134i	0.142616	+	0.316435i
$861$		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
$875$	−912.823	+	844.766i	−1.04323	+	0.965446i
$876$		0			0
$877$	1430.40	−	825.840i	1.63101	−	0.941664i	0.647228	−	0.762296i	$-0.275928\pi$
$877$	1430.40	−	825.840i	1.63101	−	0.941664i	0.983782	−	0.179368i	$-0.0574053\pi$
$878$	−107.500	−	186.195i	−0.122437	−	0.212068i
$879$		0			0
$880$	−145.292	+	201.904i	−0.165105	+	0.229436i
$881$		−	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	0.985555	−	0.169356i	$-0.0541689\pi$
$887$	307.000	+	531.740i	0.346110	+	0.599481i	−0.639444	+	0.768837i	$0.720836\pi$
$888$		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
$895$	−306.624	−	680.336i	−0.342596	−	0.760152i
$896$	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
$905$	1331.06	−	599.901i	1.47078	−	0.662874i
$906$		0			0
$907$	344.674	+	198.997i	0.380015	+	0.219402i	0.677825	−	0.735223i	$-0.262923\pi$
$907$	344.674	+	198.997i	0.380015	+	0.219402i	−0.297810	+	0.954625i	$0.596256\pi$
$908$	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	$-0.0395939\pi$
$911$	1258.06	+	726.341i	1.38097	+	0.797301i	0.388691	+	0.921368i	$0.372927\pi$
$912$		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	$0.532441\pi$
$920$	568.179	+	408.867i	0.617586	+	0.444421i
$921$		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	$-0.214693\pi$
$929$	585.945	+	338.296i	0.630727	+	0.364150i	−0.150307	+	0.988639i	$0.548026\pi$
$930$		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
$940$	793.165	−	357.475i	0.843793	−	0.380293i
$941$	−267.122	+	154.223i	−0.283871	+	0.163893i	−0.635174	−	0.772369i	$-0.719072\pi$
$941$	−267.122	+	154.223i	−0.283871	+	0.163893i	0.351304	+	0.936262i	$0.385738\pi$
$942$		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	−0.225090	−	0.974338i	$-0.572268\pi$
$947$	692.500	−	1199.45i	0.731257	−	1.26657i	0.956346	−	0.292236i	$-0.0943991\pi$
$948$		0			0
$949$	891.000	+	1543.26i	0.938883	+	1.62619i
$950$	−31.7663	−	94.8204i	−0.0334382	−	0.0998109i
$951$		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
$965$	493.993	−	686.473i	0.511910	−	0.711371i
$966$		0			0
$967$	60.3179	−	34.8246i	0.0623763	−	0.0360130i	−0.468487	−	0.883470i	$-0.655201\pi$
$967$	60.3179	−	34.8246i	0.0623763	−	0.0360130i	0.530864	+	0.847457i	$0.321868\pi$
$968$	77.0000	+	133.368i	0.0795455	+	0.137777i
$969$		0			0
$970$	377.759	−	524.950i	0.389443	−	0.541186i
$971$			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	−0.998936	−	0.0461168i	$-0.985315\pi$
$977$	−527.000	−	912.791i	−0.539406	−	0.934279i	0.459530	−	0.888162i	$-0.348018\pi$
$978$		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	−0.256155	−	0.966636i	$-0.582456\pi$
$983$	697.000	−	1207.24i	0.709054	−	1.22812i	0.965208	−	0.261482i	$-0.0842111\pi$
$984$		0			0
$985$	925.360	−	417.055i	0.939451	−	0.423406i
$986$	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
$995$	−706.555	+	318.441i	−0.710106	+	0.320041i
$996$		0			0
$997$	396.375	+	228.847i	0.397568	+	0.229536i	0.685434	−	0.728135i	$-0.259613\pi$
$997$	396.375	+	228.847i	0.397568	+	0.229536i	−0.287866	+	0.957671i	$0.592946\pi$
$998$	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.269.1		4
3.2	odd	2		405.3.h.h.269.2		4
5.4	even	2		405.3.h.h.269.1		4
9.2	odd	6		135.3.d.a.134.2	yes	2
9.4	even	3	inner	405.3.h.c.134.2		4
9.5	odd	6		405.3.h.h.134.1		4
9.7	even	3		135.3.d.f.134.1	yes	2
15.14	odd	2	inner	405.3.h.c.269.2		4
36.7	odd	6		2160.3.c.d.1889.1		2
36.11	even	6		2160.3.c.c.1889.2		2
45.2	even	12		675.3.c.q.26.2		4
45.4	even	6		405.3.h.h.134.2		4
45.7	odd	12		675.3.c.q.26.4		4
45.14	odd	6	inner	405.3.h.c.134.1		4
45.29	odd	6		135.3.d.f.134.2	yes	2
45.34	even	6		135.3.d.a.134.1	✓	2
45.38	even	12		675.3.c.q.26.3		4
45.43	odd	12		675.3.c.q.26.1		4
180.79	odd	6		2160.3.c.c.1889.1		2
180.119	even	6		2160.3.c.d.1889.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.d.a.134.1	✓	2	45.34	even	6
135.3.d.a.134.2	yes	2	9.2	odd	6
135.3.d.f.134.1	yes	2	9.7	even	3
135.3.d.f.134.2	yes	2	45.29	odd	6
405.3.h.c.134.1		4	45.14	odd	6	inner
405.3.h.c.134.2		4	9.4	even	3	inner
405.3.h.c.269.1		4	1.1	even	1	trivial
405.3.h.c.269.2		4	15.14	odd	2	inner
405.3.h.h.134.1		4	9.5	odd	6
405.3.h.h.134.2		4	45.4	even	6
405.3.h.h.269.1		4	5.4	even	2
405.3.h.h.269.2		4	3.2	odd	2
675.3.c.q.26.1		4	45.43	odd	12
675.3.c.q.26.2		4	45.2	even	12
675.3.c.q.26.3		4	45.38	even	12
675.3.c.q.26.4		4	45.7	odd	12
2160.3.c.c.1889.1		2	180.79	odd	6
2160.3.c.c.1889.2		2	36.11	even	6
2160.3.c.d.1889.1		2	36.7	odd	6
2160.3.c.d.1889.2		2	180.119	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{4} +(-4.55842 + 2.05446i) q^{5} +(8.61684 + 4.97494i) q^{7} -7.00000 q^{8} +(0.500000 - 4.97494i) q^{10} +(-8.61684 - 4.97494i) q^{11} +(-17.2337 + 9.94987i) q^{13} +(-8.61684 + 4.97494i) q^{14} +(-2.50000 + 4.33013i) q^{16} +22.0000 q^{17} -4.00000 q^{19} +(-12.1753 - 8.76144i) q^{20} +(8.61684 - 4.97494i) q^{22} +(10.0000 + 17.3205i) q^{23} +(16.5584 - 18.7302i) q^{25} -19.8997i q^{26} +29.8496i q^{28} +(-34.4674 - 19.8997i) q^{29} +(-14.5000 - 25.1147i) q^{31} +(-16.5000 - 28.5788i) q^{32} +(-11.0000 + 19.0526i) q^{34} +(-49.5000 - 4.97494i) q^{35} +(2.00000 - 3.46410i) q^{38} +(31.9090 - 14.3812i) q^{40} +(-34.4674 + 19.8997i) q^{41} +(-17.2337 - 9.94987i) q^{43} -29.8496i q^{44} -20.0000 q^{46} +(-29.0000 + 50.2295i) q^{47} +(25.0000 + 43.3013i) q^{49} +(7.94158 + 23.7051i) q^{50} +(-51.7011 - 29.8496i) q^{52} +31.0000 q^{53} +(49.5000 + 4.97494i) q^{55} +(-60.3179 - 34.8246i) q^{56} +(34.4674 - 19.8997i) q^{58} +(-34.4674 + 19.8997i) q^{59} +(-22.0000 + 38.1051i) q^{61} +29.0000 q^{62} +13.0000 q^{64} +(58.1168 - 80.7616i) q^{65} +(-17.2337 + 9.94987i) q^{67} +(33.0000 + 57.1577i) q^{68} +(29.0584 - 40.3808i) q^{70} +59.6992i q^{71} -89.5489i q^{73} +(-6.00000 - 10.3923i) q^{76} +(-49.5000 - 85.7365i) q^{77} +(5.00000 - 8.66025i) q^{79} +(2.50000 - 24.8747i) q^{80} -39.7995i q^{82} +(-9.50000 + 16.4545i) q^{83} +(-100.285 + 45.1980i) q^{85} +(17.2337 - 9.94987i) q^{86} +(60.3179 + 34.8246i) q^{88} +59.6992i q^{89} -198.000 q^{91} +(-30.0000 + 51.9615i) q^{92} +(-29.0000 - 50.2295i) q^{94} +(18.2337 - 8.21782i) q^{95} +(112.019 + 64.6742i) q^{97} -50.0000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{4} - q^{5} - 28 q^{8} + 2 q^{10} - 10 q^{16} + 88 q^{17} - 16 q^{19} + 3 q^{20} + 40 q^{23} + 49 q^{25} - 58 q^{31} - 66 q^{32} - 44 q^{34} - 198 q^{35} + 8 q^{38} + 7 q^{40} - 80 q^{46}+ \cdots - 200 q^{98}+O(q^{100}) \) 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

L-functions

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