LMFDB - Embedded newform 405.3.g.f.82.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(82,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.82"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 256x^{12} + 15630x^{8} + 235936x^{4} + 28561 $ x^16 + 256x^12 + 15630x^8 + 235936*x^4 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			82.5
Root			$-0.417936 + 0.417936i$ of defining polynomial
Character	$\chi$	$=$	405.82
Dual form			405.3.g.f.163.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.417936 + 0.417936i) q^{2} -3.65066i q^{4} +(-0.0756586 - 4.99943i) q^{5} +(7.04922 + 7.04922i) q^{7} +(3.19748 - 3.19748i) q^{8} +(2.05782 - 2.12106i) q^{10} +15.2860 q^{11} +(-9.18886 + 9.18886i) q^{13} +5.89224i q^{14} -11.9300 q^{16} +(5.30588 + 5.30588i) q^{17} -32.8227i q^{19} +(-18.2512 + 0.276204i) q^{20} +(6.38857 + 6.38857i) q^{22} +(24.9765 - 24.9765i) q^{23} +(-24.9886 + 0.756499i) q^{25} -7.68071 q^{26} +(25.7343 - 25.7343i) q^{28} -36.3319i q^{29} -1.39975 q^{31} +(-17.7759 - 17.7759i) q^{32} +4.43503i q^{34} +(34.7087 - 35.7754i) q^{35} +(15.9479 + 15.9479i) q^{37} +(13.7178 - 13.7178i) q^{38} +(-16.2275 - 15.7437i) q^{40} +10.2902 q^{41} +(-36.7295 + 36.7295i) q^{43} -55.8040i q^{44} +20.8771 q^{46} +(-8.44960 - 8.44960i) q^{47} +50.3829i q^{49} +(-10.7598 - 10.1274i) q^{50} +(33.5454 + 33.5454i) q^{52} +(-42.9031 + 42.9031i) q^{53} +(-1.15652 - 76.4213i) q^{55} +45.0795 q^{56} +(15.1844 - 15.1844i) q^{58} +0.115635i q^{59} +4.25557 q^{61} +(-0.585006 - 0.585006i) q^{62} +32.8615i q^{64} +(46.6343 + 45.2438i) q^{65} +(42.8151 + 42.8151i) q^{67} +(19.3700 - 19.3700i) q^{68} +(29.4578 - 0.445798i) q^{70} +64.5971 q^{71} +(12.7587 - 12.7587i) q^{73} +13.3304i q^{74} -119.825 q^{76} +(107.754 + 107.754i) q^{77} +13.6288i q^{79} +(0.902603 + 59.6429i) q^{80} +(4.30062 + 4.30062i) q^{82} +(-22.4863 + 22.4863i) q^{83} +(26.1249 - 26.9278i) q^{85} -30.7011 q^{86} +(48.8768 - 48.8768i) q^{88} -68.7586i q^{89} -129.549 q^{91} +(-91.1806 - 91.1806i) q^{92} -7.06278i q^{94} +(-164.095 + 2.48332i) q^{95} +(-10.6904 - 10.6904i) q^{97} +(-21.0568 + 21.0568i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 40 q^{7} - 56 q^{10} - 44 q^{13} - 32 q^{16} + 32 q^{22} - 92 q^{25} + 176 q^{28} + 320 q^{31} + 4 q^{37} - 528 q^{40} + 256 q^{43} - 16 q^{46} - 308 q^{52} - 364 q^{55} + 492 q^{58} + 8 q^{61} + 88 q^{67}+ \cdots + 304 q^{97}+O(q^{100}) $ 16 * q + 40 * q^7 - 56 * q^10 - 44 * q^13 - 32 * q^16 + 32 * q^22 - 92 * q^25 + 176 * q^28 + 320 * q^31 + 4 * q^37 - 528 * q^40 + 256 * q^43 - 16 * q^46 - 308 * q^52 - 364 * q^55 + 492 * q^58 + 8 * q^61 + 88 * q^67 - 36 * q^70 + 364 * q^73 - 912 * q^76 + 32 * q^82 + 64 * q^85 + 840 * q^88 + 224 * q^91 + 304 * q^97

Character values

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

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	0.417936	+	0.417936i	0.208968	+	0.208968i	0.803829	−	0.594861i	$-0.202793\pi$
$2$	0.417936	+	0.417936i	0.208968	+	0.208968i	−0.594861	+	0.803829i	$0.702793\pi$
$3$		0			0
$3$		0			0
$4$		−	3.65066i		−	0.912665i
$5$	−0.0756586	−	4.99943i	−0.0151317	−	0.999886i
$5$	−0.0756586	−	4.99943i	−0.0151317	−	0.999886i
$6$		0			0
$7$	7.04922	+	7.04922i	1.00703	+	1.00703i	0.999975	+	0.00705568i	$0.00224591\pi$
$7$	7.04922	+	7.04922i	1.00703	+	1.00703i	0.00705568	+	0.999975i	$0.497754\pi$
$8$	3.19748	−	3.19748i	0.399685	−	0.399685i
$9$		0			0
$10$	2.05782	−	2.12106i	0.205782	−	0.212106i
$11$	15.2860			1.38964			0.694819	−	0.719185i	$-0.255485\pi$
$11$	15.2860			1.38964			0.694819	+	0.719185i	$0.255485\pi$
$12$		0			0
$13$	−9.18886	+	9.18886i	−0.706836	+	0.706836i	−0.965869	−	0.259033i	$-0.916596\pi$
$13$	−9.18886	+	9.18886i	−0.706836	+	0.706836i	0.259033	+	0.965869i	$0.416596\pi$
$14$			5.89224i			0.420874i
$15$		0			0
$16$	−11.9300			−0.745622
$17$	5.30588	+	5.30588i	0.312111	+	0.312111i	0.845727	−	0.533616i	$-0.179167\pi$
$17$	5.30588	+	5.30588i	0.312111	+	0.312111i	−0.533616	+	0.845727i	$0.679167\pi$
$18$		0			0
$19$		−	32.8227i		−	1.72751i	−0.503910	−	0.863756i	$-0.668106\pi$
$19$		−	32.8227i		−	1.72751i	0.503910	−	0.863756i	$-0.331894\pi$
$20$	−18.2512	+	0.276204i	−0.912560	+	0.0138102i
$21$		0			0
$22$	6.38857	+	6.38857i	0.290390	+	0.290390i
$23$	24.9765	−	24.9765i	1.08593	−	1.08593i	0.0899910	−	0.995943i	$-0.471316\pi$
$23$	24.9765	−	24.9765i	1.08593	−	1.08593i	0.995943	−	0.0899910i	$-0.0286838\pi$
$24$		0			0
$25$	−24.9886	+	0.756499i	−0.999542	+	0.0302600i
$26$	−7.68071			−0.295412
$27$		0			0
$28$	25.7343	−	25.7343i	0.919082	−	0.919082i
$29$		−	36.3319i		−	1.25283i	−0.779492	−	0.626413i	$-0.784523\pi$
$29$		−	36.3319i		−	1.25283i	0.779492	−	0.626413i	$-0.215477\pi$
$30$		0			0
$31$	−1.39975			−0.0451532			−0.0225766	−	0.999745i	$-0.507187\pi$
$31$	−1.39975			−0.0451532			−0.0225766	+	0.999745i	$0.507187\pi$
$32$	−17.7759	−	17.7759i	−0.555496	−	0.555496i
$33$		0			0
$34$			4.43503i			0.130442i
$35$	34.7087	−	35.7754i	0.991677	−	1.02215i
$36$		0			0
$37$	15.9479	+	15.9479i	0.431025	+	0.431025i	0.888977	−	0.457952i	$-0.151417\pi$
$37$	15.9479	+	15.9479i	0.431025	+	0.431025i	−0.457952	+	0.888977i	$0.651417\pi$
$38$	13.7178	−	13.7178i	0.360994	−	0.360994i
$39$		0			0
$40$	−16.2275	−	15.7437i	−0.405688	−	0.393592i
$41$	10.2902			0.250979			0.125490	−	0.992095i	$-0.459950\pi$
$41$	10.2902			0.250979			0.125490	+	0.992095i	$0.459950\pi$
$42$		0			0
$43$	−36.7295	+	36.7295i	−0.854173	+	0.854173i	−0.990644	−	0.136471i	$-0.956424\pi$
$43$	−36.7295	+	36.7295i	−0.854173	+	0.854173i	0.136471	+	0.990644i	$0.456424\pi$
$44$		−	55.8040i		−	1.26827i
$45$		0			0
$46$	20.8771			0.453850
$47$	−8.44960	−	8.44960i	−0.179779	−	0.179779i	0.611481	−	0.791259i	$-0.290574\pi$
$47$	−8.44960	−	8.44960i	−0.179779	−	0.179779i	−0.791259	+	0.611481i	$0.790574\pi$
$48$		0			0
$49$			50.3829i			1.02822i
$50$	−10.7598	−	10.1274i	−0.215195	−	0.202549i
$51$		0			0
$52$	33.5454	+	33.5454i	0.645104	+	0.645104i
$53$	−42.9031	+	42.9031i	−0.809493	+	0.809493i	−0.984557	−	0.175064i	$-0.943987\pi$
$53$	−42.9031	+	42.9031i	−0.809493	+	0.809493i	0.175064	+	0.984557i	$0.443987\pi$
$54$		0			0
$55$	−1.15652	−	76.4213i	−0.0210276	−	1.38948i
$56$	45.0795			0.804991
$57$		0			0
$58$	15.1844	−	15.1844i	0.261800	−	0.261800i
$59$			0.115635i			0.00195991i	1.00000		0.000979955i	$0.000311929\pi$
$59$			0.115635i			0.00195991i	−1.00000		0.000979955i	$0.999688\pi$
$60$		0			0
$61$	4.25557			0.0697634			0.0348817	−	0.999391i	$-0.488895\pi$
$61$	4.25557			0.0697634			0.0348817	+	0.999391i	$0.488895\pi$
$62$	−0.585006	−	0.585006i	−0.00943557	−	0.00943557i
$63$		0			0
$64$			32.8615i			0.513460i
$65$	46.6343	+	45.2438i	0.717450	+	0.696059i
$66$		0			0
$67$	42.8151	+	42.8151i	0.639032	+	0.639032i	0.950317	−	0.311285i	$-0.100759\pi$
$67$	42.8151	+	42.8151i	0.639032	+	0.639032i	−0.311285	+	0.950317i	$0.600759\pi$
$68$	19.3700	−	19.3700i	0.284852	−	0.284852i
$69$		0			0
$70$	29.4578	−	0.445798i	0.420826	−	0.00636855i
$71$	64.5971			0.909819			0.454910	−	0.890538i	$-0.349672\pi$
$71$	64.5971			0.909819			0.454910	+	0.890538i	$0.349672\pi$
$72$		0			0
$73$	12.7587	−	12.7587i	0.174776	−	0.174776i	−0.614298	−	0.789074i	$-0.710561\pi$
$73$	12.7587	−	12.7587i	0.174776	−	0.174776i	0.789074	+	0.614298i	$0.210561\pi$
$74$			13.3304i			0.180141i
$75$		0			0
$76$	−119.825			−1.57664
$77$	107.754	+	107.754i	1.39941	+	1.39941i
$78$		0			0
$79$			13.6288i			0.172516i	0.996273	+	0.0862582i	$0.0274910\pi$
$79$			13.6288i			0.172516i	−0.996273	+	0.0862582i	$0.972509\pi$
$80$	0.902603	+	59.6429i	0.0112825	+	0.745537i
$81$		0			0
$82$	4.30062	+	4.30062i	0.0524466	+	0.0524466i
$83$	−22.4863	+	22.4863i	−0.270920	+	0.270920i	−0.829470	−	0.558551i	$-0.811358\pi$
$83$	−22.4863	+	22.4863i	−0.270920	+	0.270920i	0.558551	+	0.829470i	$0.311358\pi$
$84$		0			0
$85$	26.1249	−	26.9278i	0.307352	−	0.316798i
$86$	−30.7011			−0.356989
$87$		0			0
$88$	48.8768	−	48.8768i	0.555418	−	0.555418i
$89$		−	68.7586i		−	0.772569i	−0.922380	−	0.386284i	$-0.873758\pi$
$89$		−	68.7586i		−	0.772569i	0.922380	−	0.386284i	$-0.126242\pi$
$90$		0			0
$91$	−129.549			−1.42361
$92$	−91.1806	−	91.1806i	−0.991093	−	0.991093i
$93$		0			0
$94$		−	7.06278i		−	0.0751360i
$95$	−164.095	+	2.48332i	−1.72731	+	0.0261402i
$96$		0			0
$97$	−10.6904	−	10.6904i	−0.110210	−	0.110210i	0.649851	−	0.760061i	$-0.274831\pi$
$97$	−10.6904	−	10.6904i	−0.110210	−	0.110210i	−0.760061	+	0.649851i	$0.774831\pi$
$98$	−21.0568	+	21.0568i	−0.214865	+	0.214865i
$99$		0			0
$100$	2.76172	+	91.2247i	0.0276172	+	0.912247i
$101$	−103.322			−1.02299			−0.511497	−	0.859285i	$-0.670909\pi$
$101$	−103.322			−1.02299			−0.511497	+	0.859285i	$0.670909\pi$
$102$		0			0
$103$	98.8239	−	98.8239i	0.959456	−	0.959456i	−0.0397539	−	0.999210i	$-0.512657\pi$
$103$	98.8239	−	98.8239i	0.959456	−	0.959456i	0.999210	+	0.0397539i	$0.0126574\pi$
$104$			58.7625i			0.565024i
$105$		0			0
$106$	−35.8615			−0.338316
$107$	3.49410	+	3.49410i	0.0326551	+	0.0326551i	0.723246	−	0.690591i	$-0.242649\pi$
$107$	3.49410	+	3.49410i	0.0326551	+	0.0326551i	−0.690591	+	0.723246i	$0.742649\pi$
$108$		0			0
$109$			196.002i			1.79818i	0.437760	+	0.899092i	$0.355772\pi$
$109$			196.002i			1.79818i	−0.437760	+	0.899092i	$0.644228\pi$
$110$	31.4558	−	32.4225i	0.285962	−	0.294750i
$111$		0			0
$112$	−84.0968	−	84.0968i	−0.750864	−	0.750864i
$113$	85.6607	−	85.6607i	0.758059	−	0.758059i	−0.217910	−	0.975969i	$-0.569924\pi$
$113$	85.6607	−	85.6607i	0.758059	−	0.758059i	0.975969	+	0.217910i	$0.0699238\pi$
$114$		0			0
$115$	−126.758	−	122.978i	−1.10224	−	1.06938i
$116$	−132.636			−1.14341
$117$		0			0
$118$	−0.0483278	+	0.0483278i	−0.000409558	+	0.000409558i
$119$			74.8046i			0.628610i
$120$		0			0
$121$	112.662			0.931093
$122$	1.77855	+	1.77855i	0.0145783	+	0.0145783i
$123$		0			0
$124$			5.11001i			0.0412098i
$125$	5.67266	+	124.871i	0.0453813	+	0.998970i
$126$		0			0
$127$	−24.3656	−	24.3656i	−0.191855	−	0.191855i	0.604642	−	0.796497i	$-0.293316\pi$
$127$	−24.3656	−	24.3656i	−0.191855	−	0.191855i	−0.796497	+	0.604642i	$0.793316\pi$
$128$	−84.8375	+	84.8375i	−0.662793	+	0.662793i
$129$		0			0
$130$	0.581111	+	38.3991i	0.00447009	+	0.295378i
$131$	−85.5580			−0.653115			−0.326557	−	0.945177i	$-0.605889\pi$
$131$	−85.5580			−0.653115			−0.326557	+	0.945177i	$0.605889\pi$
$132$		0			0
$133$	231.375	−	231.375i	1.73966	−	1.73966i
$134$			35.7880i			0.267074i
$135$		0			0
$136$	33.9309			0.249492
$137$	174.192	+	174.192i	1.27147	+	1.27147i	0.945315	+	0.326159i	$0.105755\pi$
$137$	174.192	+	174.192i	1.27147	+	1.27147i	0.326159	+	0.945315i	$0.394245\pi$
$138$		0			0
$139$			149.643i			1.07657i	0.842764	+	0.538283i	$0.180927\pi$
$139$			149.643i			1.07657i	−0.842764	+	0.538283i	$0.819073\pi$
$140$	−130.604	−	126.710i	−0.932884	−	0.905069i
$141$		0			0
$142$	26.9974	+	26.9974i	0.190123	+	0.190123i
$143$	−140.461	+	140.461i	−0.982246	+	0.982246i
$144$		0			0
$145$	−181.639	+	2.74882i	−1.25268	+	0.0189574i
$146$	10.6646			0.0730452
$147$		0			0
$148$	58.2205	−	58.2205i	0.393382	−	0.393382i
$149$			241.428i			1.62032i	0.586208	+	0.810160i	$0.300620\pi$
$149$			241.428i			1.62032i	−0.586208	+	0.810160i	$0.699380\pi$
$150$		0			0
$151$	43.2507			0.286429			0.143214	−	0.989692i	$-0.454256\pi$
$151$	43.2507			0.286429			0.143214	+	0.989692i	$0.454256\pi$
$152$	−104.950	−	104.950i	−0.690461	−	0.690461i
$153$		0			0
$154$			90.0688i			0.584862i
$155$	0.105903	+	6.99795i	0.000683246	+	0.0451481i
$156$		0			0
$157$	70.8404	+	70.8404i	0.451213	+	0.451213i	0.895757	−	0.444544i	$-0.146634\pi$
$157$	70.8404	+	70.8404i	0.451213	+	0.451213i	−0.444544	+	0.895757i	$0.646634\pi$
$158$	−5.69596	+	5.69596i	−0.0360504	+	0.0360504i
$159$		0			0
$160$	−87.5244	+	90.2141i	−0.547027	+	0.563838i
$161$	352.129			2.18714
$162$		0			0
$163$	−22.8092	+	22.8092i	−0.139934	+	0.139934i	−0.773603	−	0.633670i	$-0.781548\pi$
$163$	−22.8092	+	22.8092i	−0.139934	+	0.139934i	0.633670	+	0.773603i	$0.281548\pi$
$164$		−	37.5658i		−	0.229060i
$165$		0			0
$166$	−18.7957			−0.113227
$167$	115.961	+	115.961i	0.694374	+	0.694374i	0.963191	−	0.268817i	$-0.0866326\pi$
$167$	115.961	+	115.961i	0.694374	+	0.694374i	−0.268817	+	0.963191i	$0.586633\pi$
$168$		0			0
$169$			0.129597i			0.000766844i
$170$	22.1726	−	0.335548i	0.130427	−	0.00197381i
$171$		0			0
$172$	134.087	+	134.087i	0.779574	+	0.779574i
$173$	−110.903	+	110.903i	−0.641056	+	0.641056i	−0.950815	−	0.309759i	$-0.899752\pi$
$173$	−110.903	+	110.903i	−0.641056	+	0.641056i	0.309759	+	0.950815i	$0.399752\pi$
$174$		0			0
$175$	−181.482	−	170.817i	−1.03704	−	0.976097i
$176$	−182.361			−1.03614
$177$		0			0
$178$	28.7367	−	28.7367i	0.161442	−	0.161442i
$179$			141.760i			0.791958i	0.918260	+	0.395979i	$0.129595\pi$
$179$			141.760i			0.791958i	−0.918260	+	0.395979i	$0.870405\pi$
$180$		0			0
$181$	−125.175			−0.691573			−0.345786	−	0.938313i	$-0.612388\pi$
$181$	−125.175			−0.691573			−0.345786	+	0.938313i	$0.612388\pi$
$182$	−54.1430	−	54.1430i	−0.297489	−	0.297489i
$183$		0			0
$184$		−	159.724i		−	0.868064i
$185$	78.5240	−	80.9372i	0.424454	−	0.437498i
$186$		0			0
$187$	81.1058	+	81.1058i	0.433721	+	0.433721i
$188$	−30.8466	+	30.8466i	−0.164078	+	0.164078i
$189$		0			0
$190$	−69.6190	−	67.5432i	−0.366416	−	0.355491i
$191$	135.259			0.708160			0.354080	−	0.935215i	$-0.384794\pi$
$191$	135.259			0.708160			0.354080	+	0.935215i	$0.384794\pi$
$192$		0			0
$193$	50.2370	−	50.2370i	0.260296	−	0.260296i	−0.564879	−	0.825174i	$-0.691077\pi$
$193$	50.2370	−	50.2370i	0.260296	−	0.260296i	0.825174	+	0.564879i	$0.191077\pi$
$194$		−	8.93579i		−	0.0460608i
$195$		0			0
$196$	183.931			0.938422
$197$	−244.942	−	244.942i	−1.24336	−	1.24336i	−0.958599	−	0.284761i	$-0.908086\pi$
$197$	−244.942	−	244.942i	−1.24336	−	1.24336i	−0.284761	−	0.958599i	$-0.591914\pi$
$198$		0			0
$199$		−	87.9006i		−	0.441711i	−0.975306	−	0.220856i	$-0.929115\pi$
$199$		−	87.9006i		−	0.441711i	0.975306	−	0.220856i	$-0.0708850\pi$
$200$	−77.4816	+	82.3194i	−0.387408	+	0.411597i
$201$		0			0
$202$	−43.1821	−	43.1821i	−0.213773	−	0.213773i
$203$	256.112	−	256.112i	1.26163	−	1.26163i
$204$		0			0
$205$	−0.778538	−	51.4449i	−0.00379775	−	0.250951i
$206$	82.6041			0.400991
$207$		0			0
$208$	109.623	−	109.623i	0.527032	−	0.527032i
$209$		−	501.729i		−	2.40062i
$210$		0			0
$211$	19.1156			0.0905950			0.0452975	−	0.998974i	$-0.485576\pi$
$211$	19.1156			0.0905950			0.0452975	+	0.998974i	$0.485576\pi$
$212$	156.625	+	156.625i	0.738796	+	0.738796i
$213$		0			0
$214$			2.92061i			0.0136477i
$215$	186.405	+	180.847i	0.867001	+	0.841150i
$216$		0			0
$217$	−9.86714	−	9.86714i	−0.0454707	−	0.0454707i
$218$	−81.9162	+	81.9162i	−0.375762	+	0.375762i
$219$		0			0
$220$	−278.988	+	4.22205i	−1.26813	+	0.0191912i
$221$	−97.5100			−0.441222
$222$		0			0
$223$	−275.150	+	275.150i	−1.23386	+	1.23386i	−0.271388	+	0.962470i	$0.587483\pi$
$223$	−275.150	+	275.150i	−1.23386	+	1.23386i	−0.962470	+	0.271388i	$0.912517\pi$
$224$		−	250.612i		−	1.11880i
$225$		0			0
$226$	71.6013			0.316820
$227$	−3.37865	−	3.37865i	−0.0148839	−	0.0148839i	0.699626	−	0.714510i	$-0.253350\pi$
$227$	−3.37865	−	3.37865i	−0.0148839	−	0.0148839i	−0.714510	+	0.699626i	$0.753350\pi$
$228$		0			0
$229$			290.400i			1.26812i	0.773283	+	0.634061i	$0.218613\pi$
$229$			290.400i			1.26812i	−0.773283	+	0.634061i	$0.781387\pi$
$230$	−1.57953	−	104.374i	−0.00686753	−	0.453798i
$231$		0			0
$232$	−116.171	−	116.171i	−0.500736	−	0.500736i
$233$	41.5335	−	41.5335i	0.178255	−	0.178255i	−0.612340	−	0.790595i	$-0.709771\pi$
$233$	41.5335	−	41.5335i	0.178255	−	0.178255i	0.790595	+	0.612340i	$0.209771\pi$
$234$		0			0
$235$	−41.6039	+	42.8825i	−0.177038	+	0.182479i
$236$	0.422143			0.00178874
$237$		0			0
$238$	−31.2635	+	31.2635i	−0.131359	+	0.131359i
$239$			353.502i			1.47909i	0.673108	+	0.739544i	$0.264959\pi$
$239$			353.502i			1.47909i	−0.673108	+	0.739544i	$0.735041\pi$
$240$		0			0
$241$	−336.159			−1.39485			−0.697425	−	0.716658i	$-0.745671\pi$
$241$	−336.159			−1.39485			−0.697425	+	0.716658i	$0.745671\pi$
$242$	47.0856	+	47.0856i	0.194569	+	0.194569i
$243$		0			0
$244$		−	15.5356i		−	0.0636706i
$245$	251.886	−	3.81190i	1.02810	−	0.0155588i
$246$		0			0
$247$	301.604	+	301.604i	1.22107	+	1.22107i
$248$	−4.47568	+	4.47568i	−0.0180471	+	0.0180471i
$249$		0			0
$250$	−49.8173	+	54.5589i	−0.199269	+	0.218236i
$251$	−284.670			−1.13414			−0.567071	−	0.823669i	$-0.691923\pi$
$251$	−284.670			−1.13414			−0.567071	+	0.823669i	$0.691923\pi$
$252$		0			0
$253$	381.791	−	381.791i	1.50905	−	1.50905i
$254$		−	20.3665i		−	0.0801832i
$255$		0			0
$256$	60.5326			0.236456
$257$	−233.124	−	233.124i	−0.907098	−	0.907098i	0.0889390	−	0.996037i	$-0.471652\pi$
$257$	−233.124	−	233.124i	−0.907098	−	0.907098i	−0.996037	+	0.0889390i	$0.971652\pi$
$258$		0			0
$259$			224.841i			0.868112i
$260$	165.170	−	170.246i	0.635269	−	0.654792i
$261$		0			0
$262$	−35.7577	−	35.7577i	−0.136480	−	0.136480i
$263$	27.0122	−	27.0122i	0.102708	−	0.102708i	−0.653885	−	0.756594i	$-0.726862\pi$
$263$	27.0122	−	27.0122i	0.102708	−	0.102708i	0.756594	+	0.653885i	$0.226862\pi$
$264$		0			0
$265$	217.737	+	211.245i	0.821650	+	0.797152i
$266$	193.399			0.727065
$267$		0			0
$268$	156.304	−	156.304i	0.583222	−	0.583222i
$269$		−	371.565i		−	1.38128i	−0.723198	−	0.690641i	$-0.757329\pi$
$269$		−	371.565i		−	1.38128i	0.723198	−	0.690641i	$-0.242671\pi$
$270$		0			0
$271$	301.604			1.11293			0.556464	−	0.830872i	$-0.312158\pi$
$271$	301.604			1.11293			0.556464	+	0.830872i	$0.312158\pi$
$272$	−63.2989	−	63.2989i	−0.232717	−	0.232717i
$273$		0			0
$274$			145.602i			0.531394i
$275$	−381.975	+	11.5639i	−1.38900	+	0.0420504i
$276$		0			0
$277$	115.928	+	115.928i	0.418513	+	0.418513i	0.884691	−	0.466178i	$-0.154369\pi$
$277$	115.928	+	115.928i	0.418513	+	0.418513i	−0.466178	+	0.884691i	$0.654369\pi$
$278$	−62.5410	+	62.5410i	−0.224968	+	0.224968i
$279$		0			0
$280$	−3.41065	−	225.372i	−0.0121809	−	0.804899i
$281$	175.645			0.625070			0.312535	−	0.949906i	$-0.398822\pi$
$281$	175.645			0.625070			0.312535	+	0.949906i	$0.398822\pi$
$282$		0			0
$283$	73.2061	−	73.2061i	0.258679	−	0.258679i	−0.565838	−	0.824517i	$-0.691447\pi$
$283$	73.2061	−	73.2061i	0.258679	−	0.258679i	0.824517	+	0.565838i	$0.191447\pi$
$284$		−	235.822i		−	0.830360i
$285$		0			0
$286$	−117.407			−0.410515
$287$	72.5375	+	72.5375i	0.252744	+	0.252744i
$288$		0			0
$289$		−	232.695i		−	0.805174i
$290$	−77.0622	−	74.7645i	−0.265732	−	0.257809i
$291$		0			0
$292$	−46.5775	−	46.5775i	−0.159512	−	0.159512i
$293$	391.391	−	391.391i	1.33580	−	1.33580i	0.435724	−	0.900080i	$-0.356492\pi$
$293$	391.391	−	391.391i	1.33580	−	1.33580i	0.900080	−	0.435724i	$-0.143508\pi$
$294$		0			0
$295$	0.578107	−	0.00874875i	0.00195968	−	2.96568e-5i
$296$	101.987			0.344549
$297$		0			0
$298$	−100.901	+	100.901i	−0.338595	+	0.338595i
$299$			459.011i			1.53515i
$300$		0			0
$301$	−517.828			−1.72036
$302$	18.0760	+	18.0760i	0.0598544	+	0.0598544i
$303$		0			0
$304$			391.574i			1.28807i
$305$	−0.321970	−	21.2754i	−0.00105564	−	0.0697554i
$306$		0			0
$307$	156.225	+	156.225i	0.508875	+	0.508875i	0.914181	−	0.405306i	$-0.132835\pi$
$307$	156.225	+	156.225i	0.508875	+	0.508875i	−0.405306	+	0.914181i	$0.632835\pi$
$308$	393.375	−	393.375i	1.27719	−	1.27719i
$309$		0			0
$310$	−2.88043	+	2.96895i	−0.00929172	+	0.00957727i
$311$	67.9519			0.218495			0.109247	−	0.994015i	$-0.465156\pi$
$311$	67.9519			0.218495			0.109247	+	0.994015i	$0.465156\pi$
$312$		0			0
$313$	132.201	−	132.201i	0.422368	−	0.422368i	−0.463650	−	0.886018i	$-0.653461\pi$
$313$	132.201	−	132.201i	0.422368	−	0.422368i	0.886018	+	0.463650i	$0.153461\pi$
$314$			59.2134i			0.188578i
$315$		0			0
$316$	49.7541			0.157450
$317$	−304.297	−	304.297i	−0.959927	−	0.959927i	0.0393008	−	0.999227i	$-0.487487\pi$
$317$	−304.297	−	304.297i	−0.959927	−	0.959927i	−0.999227	+	0.0393008i	$0.987487\pi$
$318$		0			0
$319$		−	555.370i		−	1.74097i
$320$	164.289	−	2.48625i	0.513402	−	0.00776954i
$321$		0			0
$322$	147.167	+	147.167i	0.457041	+	0.457041i
$323$	174.154	−	174.154i	0.539175	−	0.539175i
$324$		0			0
$325$	222.665	−	236.568i	0.685123	−	0.727901i
$326$	−19.0655			−0.0584832
$327$		0			0
$328$	32.9026	−	32.9026i	0.100313	−	0.100313i
$329$		−	119.126i		−	0.362086i
$330$		0			0
$331$	−324.790			−0.981240			−0.490620	−	0.871374i	$-0.663230\pi$
$331$	−324.790			−0.981240			−0.490620	+	0.871374i	$0.663230\pi$
$332$	82.0900	+	82.0900i	0.247259	+	0.247259i
$333$		0			0
$334$			96.9281i			0.290204i
$335$	210.812	−	217.291i	0.629289	−	0.648629i
$336$		0			0
$337$	−110.297	−	110.297i	−0.327291	−	0.327291i	0.524265	−	0.851555i	$-0.324340\pi$
$337$	−110.297	−	110.297i	−0.327291	−	0.327291i	−0.851555	+	0.524265i	$0.824340\pi$
$338$	−0.0541631	+	0.0541631i	−0.000160246	+	0.000160246i
$339$		0			0
$340$	−98.3043	−	95.3733i	−0.289130	−	0.280510i
$341$	−21.3966			−0.0627466
$342$		0			0
$343$	−9.74822	+	9.74822i	−0.0284205	+	0.0284205i
$344$			234.884i			0.682801i
$345$		0			0
$346$	−92.7004			−0.267920
$347$	294.595	+	294.595i	0.848977	+	0.848977i	0.990006	−	0.141028i	$-0.0450408\pi$
$347$	294.595	+	294.595i	0.848977	+	0.848977i	−0.141028	+	0.990006i	$0.545041\pi$
$348$		0			0
$349$			226.876i			0.650075i	0.945701	+	0.325038i	$0.105377\pi$
$349$			226.876i			0.650075i	−0.945701	+	0.325038i	$0.894623\pi$
$350$	−4.45747	−	147.238i	−0.0127356	−	0.420681i
$351$		0			0
$352$	−271.722	−	271.722i	−0.771939	−	0.771939i
$353$	106.849	−	106.849i	0.302688	−	0.302688i	−0.539377	−	0.842065i	$-0.681340\pi$
$353$	106.849	−	106.849i	0.302688	−	0.302688i	0.842065	+	0.539377i	$0.181340\pi$
$354$		0			0
$355$	−4.88733	−	322.949i	−0.0137671	−	0.909715i
$356$	−251.014			−0.705096
$357$		0			0
$358$	−59.2467	+	59.2467i	−0.165494	+	0.165494i
$359$		−	24.9262i		−	0.0694324i	−0.999397	−	0.0347162i	$-0.988947\pi$
$359$		−	24.9262i		−	0.0694324i	0.999397	−	0.0347162i	$-0.0110527\pi$
$360$		0			0
$361$	−716.332			−1.98430
$362$	−52.3150	−	52.3150i	−0.144516	−	0.144516i
$363$		0			0
$364$			472.938i			1.29928i
$365$	−64.7513	−	62.8207i	−0.177401	−	0.172111i
$366$		0			0
$367$	24.9623	+	24.9623i	0.0680172	+	0.0680172i	0.740297	−	0.672280i	$-0.234685\pi$
$367$	24.9623	+	24.9623i	0.0680172	+	0.0680172i	−0.672280	+	0.740297i	$0.734685\pi$
$368$	−297.968	+	297.968i	−0.809696	+	0.809696i
$369$		0			0
$370$	66.6445	−	1.00856i	0.180120	−	0.00272584i
$371$	−604.867			−1.63037
$372$		0			0
$373$	−431.058	+	431.058i	−1.15565	+	1.15565i	−0.170251	+	0.985401i	$0.554458\pi$
$373$	−431.058	+	431.058i	−1.15565	+	1.15565i	−0.985401	+	0.170251i	$0.945542\pi$
$374$			67.7940i			0.181267i
$375$		0			0
$376$	−54.0349			−0.143710
$377$	333.849	+	333.849i	0.885541	+	0.885541i
$378$		0			0
$379$		−	227.751i		−	0.600925i	−0.953794	−	0.300463i	$-0.902859\pi$
$379$		−	227.751i		−	0.600925i	0.953794	−	0.300463i	$-0.0971411\pi$
$380$	9.06576	+	599.055i	0.0238573	+	1.57646i
$381$		0			0
$382$	56.5294	+	56.5294i	0.147983	+	0.147983i
$383$	−315.603	+	315.603i	−0.824029	+	0.824029i	−0.986683	−	0.162654i	$-0.947995\pi$
$383$	−315.603	+	315.603i	−0.824029	+	0.824029i	0.162654	+	0.986683i	$0.447995\pi$
$384$		0			0
$385$	530.558	−	546.863i	1.37807	−	1.42042i
$386$	41.9917			0.108787
$387$		0			0
$388$	−39.0270	+	39.0270i	−0.100585	+	0.100585i
$389$			7.14102i			0.0183574i	0.999958	+	0.00917868i	$0.00292171\pi$
$389$			7.14102i			0.0183574i	−0.999958	+	0.00917868i	$0.997078\pi$
$390$		0			0
$391$	265.044			0.677863
$392$	161.098	+	161.098i	0.410965	+	0.410965i
$393$		0			0
$394$		−	204.740i		−	0.519644i
$395$	68.1362	−	1.03114i	0.172497	−	0.00261047i
$396$		0			0
$397$	266.344	+	266.344i	0.670891	+	0.670891i	0.957921	−	0.287031i	$-0.0926682\pi$
$397$	266.344	+	266.344i	0.670891	+	0.670891i	−0.287031	+	0.957921i	$0.592668\pi$
$398$	36.7368	−	36.7368i	0.0923035	−	0.0923035i
$399$		0			0
$400$	298.112	−	9.02500i	0.745281	−	0.0225625i
$401$	314.543			0.784398			0.392199	−	0.919880i	$-0.371715\pi$
$401$	314.543			0.784398			0.392199	+	0.919880i	$0.371715\pi$
$402$		0			0
$403$	12.8621	−	12.8621i	0.0319159	−	0.0319159i
$404$			377.195i			0.933650i
$405$		0			0
$406$	214.076			0.527282
$407$	243.780	+	243.780i	0.598969	+	0.598969i
$408$		0			0
$409$		−	307.573i		−	0.752011i	−0.926617	−	0.376006i	$-0.877297\pi$
$409$		−	307.573i		−	0.752011i	0.926617	−	0.376006i	$-0.122703\pi$
$410$	21.1753	−	21.8260i	0.0516470	−	0.0532342i
$411$		0			0
$412$	−360.773	−	360.773i	−0.875661	−	0.875661i
$413$	−0.815133	+	0.815133i	−0.00197369	+	0.00197369i
$414$		0			0
$415$	114.120	+	110.718i	0.274988	+	0.266789i
$416$	326.680			0.785289
$417$		0			0
$418$	209.690	−	209.690i	0.501652	−	0.501652i
$419$		−	302.942i		−	0.723012i	−0.932370	−	0.361506i	$-0.882263\pi$
$419$		−	302.942i		−	0.723012i	0.932370	−	0.361506i	$-0.117737\pi$
$420$		0			0
$421$	510.098			1.21163			0.605817	−	0.795604i	$-0.292846\pi$
$421$	510.098			1.21163			0.605817	+	0.795604i	$0.292846\pi$
$422$	7.98907	+	7.98907i	0.0189314	+	0.0189314i
$423$		0			0
$424$			274.364i			0.647085i
$425$	−136.600	−	128.572i	−0.321412	−	0.302523i
$426$		0			0
$427$	29.9984	+	29.9984i	0.0702539	+	0.0702539i
$428$	12.7558	−	12.7558i	0.0298032	−	0.0298032i
$429$		0			0
$430$	2.32280	+	153.488i	0.00540186	+	0.356949i
$431$	−499.696			−1.15939			−0.579693	−	0.814835i	$-0.696828\pi$
$431$	−499.696			−1.15939			−0.579693	+	0.814835i	$0.696828\pi$
$432$		0			0
$433$	−449.536	+	449.536i	−1.03819	+	1.03819i	−0.0389487	+	0.999241i	$0.512401\pi$
$433$	−449.536	+	449.536i	−1.03819	+	1.03819i	−0.999241	+	0.0389487i	$0.987599\pi$
$434$		−	8.24766i		−	0.0190038i
$435$		0			0
$436$	715.537			1.64114
$437$	−819.796	−	819.796i	−1.87596	−	1.87596i
$438$		0			0
$439$		−	570.377i		−	1.29926i	−0.760249	−	0.649632i	$-0.774923\pi$
$439$		−	570.377i		−	1.29926i	0.760249	−	0.649632i	$-0.225077\pi$
$440$	−248.054	−	240.658i	−0.563759	−	0.546950i
$441$		0			0
$442$	−40.7529	−	40.7529i	−0.0922012	−	0.0922012i
$443$	−610.181	+	610.181i	−1.37738	+	1.37738i	−0.528371	+	0.849014i	$0.677197\pi$
$443$	−610.181	+	610.181i	−1.37738	+	1.37738i	−0.849014	+	0.528371i	$0.822803\pi$
$444$		0			0
$445$	−343.754	+	5.20218i	−0.772480	+	0.0116903i
$446$	−229.990			−0.515673
$447$		0			0
$448$	−231.648	+	231.648i	−0.517070	+	0.517070i
$449$		−	36.3143i		−	0.0808781i	−0.999182	−	0.0404390i	$-0.987124\pi$
$449$		−	36.3143i		−	0.0808781i	0.999182	−	0.0404390i	$-0.0128757\pi$
$450$		0			0
$451$	157.295			0.348770
$452$	−312.718	−	312.718i	−0.691854	−	0.691854i
$453$		0			0
$454$		−	2.82412i		−	0.00622053i
$455$	9.80146	+	647.669i	0.0215417	+	1.42345i
$456$		0			0
$457$	−143.824	−	143.824i	−0.314714	−	0.314714i	0.532019	−	0.846733i	$-0.321434\pi$
$457$	−143.824	−	143.824i	−0.314714	−	0.314714i	−0.846733	+	0.532019i	$0.821434\pi$
$458$	−121.368	+	121.368i	−0.264997	+	0.264997i
$459$		0			0
$460$	−448.952	+	462.749i	−0.975983	+	1.00598i
$461$	245.025			0.531508			0.265754	−	0.964041i	$-0.414379\pi$
$461$	245.025			0.531508			0.265754	+	0.964041i	$0.414379\pi$
$462$		0			0
$463$	147.086	−	147.086i	0.317680	−	0.317680i	−0.530195	−	0.847876i	$-0.677881\pi$
$463$	147.086	−	147.086i	0.317680	−	0.317680i	0.847876	+	0.530195i	$0.177881\pi$
$464$			433.438i			0.934134i
$465$		0			0
$466$	34.7166			0.0744992
$467$	−563.699	−	563.699i	−1.20706	−	1.20706i	−0.971974	−	0.235090i	$-0.924461\pi$
$467$	−563.699	−	563.699i	−1.20706	−	1.20706i	−0.235090	−	0.971974i	$-0.575539\pi$
$468$		0			0
$469$			603.626i			1.28705i
$470$	−35.3099	+	0.534360i	−0.0751274	+	0.00113694i
$471$		0			0
$472$	0.369740	+	0.369740i	0.000783347	+	0.000783347i
$473$	−561.447	+	561.447i	−1.18699	+	1.18699i
$474$		0			0
$475$	24.8304	+	820.193i	0.0522745	+	1.72672i
$476$	273.086			0.573710
$477$		0			0
$478$	−147.741	+	147.741i	−0.309082	+	0.309082i
$479$		−	196.141i		−	0.409480i	−0.978816	−	0.204740i	$-0.934365\pi$
$479$		−	196.141i		−	0.409480i	0.978816	−	0.204740i	$-0.0656348\pi$
$480$		0			0
$481$	−293.087			−0.609328
$482$	−140.493	−	140.493i	−0.291479	−	0.291479i
$483$		0			0
$484$		−	411.292i		−	0.849776i
$485$	−52.6370	+	54.2546i	−0.108530	+	0.111865i
$486$		0			0
$487$	381.697	+	381.697i	0.783771	+	0.783771i	0.980465	−	0.196694i	$-0.0630205\pi$
$487$	381.697	+	381.697i	0.783771	+	0.783771i	−0.196694	+	0.980465i	$0.563021\pi$
$488$	13.6071	−	13.6071i	0.0278834	−	0.0278834i
$489$		0			0
$490$	106.865	+	103.679i	0.218092	+	0.211589i
$491$	200.579			0.408512			0.204256	−	0.978917i	$-0.434522\pi$
$491$	200.579			0.408512			0.204256	+	0.978917i	$0.434522\pi$
$492$		0			0
$493$	192.773	−	192.773i	0.391020	−	0.391020i
$494$			252.102i			0.510327i
$495$		0			0
$496$	16.6990			0.0336673
$497$	455.359	+	455.359i	0.916216	+	0.916216i
$498$		0			0
$499$		−	365.151i		−	0.731766i	−0.930661	−	0.365883i	$-0.880767\pi$
$499$		−	365.151i		−	0.731766i	0.930661	−	0.365883i	$-0.119233\pi$
$500$	455.862	−	20.7090i	0.911725	−	0.0414179i
$501$		0			0
$502$	−118.974	−	118.974i	−0.236999	−	0.236999i
$503$	−14.5648	+	14.5648i	−0.0289558	+	0.0289558i	−0.721436	−	0.692481i	$-0.756518\pi$
$503$	−14.5648	+	14.5648i	−0.0289558	+	0.0289558i	0.692481	+	0.721436i	$0.256518\pi$
$504$		0			0
$505$	7.81722	+	516.552i	0.0154796	+	1.02288i
$506$	319.128			0.630688
$507$		0			0
$508$	−88.9507	+	88.9507i	−0.175100	+	0.175100i
$509$			194.591i			0.382301i	0.981561	+	0.191150i	$0.0612218\pi$
$509$			194.591i			0.382301i	−0.981561	+	0.191150i	$0.938778\pi$
$510$		0			0
$511$	179.877			0.352010
$512$	364.649	+	364.649i	0.712205	+	0.712205i
$513$		0			0
$514$		−	194.862i		−	0.379109i
$515$	−501.540	−	486.586i	−0.973864	−	0.944828i
$516$		0			0
$517$	−129.161	−	129.161i	−0.249827	−	0.249827i
$518$	−93.9690	+	93.9690i	−0.181407	+	0.181407i
$519$		0			0
$520$	293.779	−	4.44588i	0.564959	−	0.00854978i
$521$	−381.214			−0.731697			−0.365848	−	0.930674i	$-0.619221\pi$
$521$	−381.214			−0.731697			−0.365848	+	0.930674i	$0.619221\pi$
$522$		0			0
$523$	−367.754	+	367.754i	−0.703162	+	0.703162i	−0.965088	−	0.261926i	$-0.915642\pi$
$523$	−367.754	+	367.754i	−0.703162	+	0.703162i	0.261926	+	0.965088i	$0.415642\pi$
$524$			312.343i			0.596075i
$525$		0			0
$526$	22.5787			0.0429254
$527$	−7.42691	−	7.42691i	−0.0140928	−	0.0140928i
$528$		0			0
$529$		−	718.648i		−	1.35850i
$530$	2.71323	+	179.287i	0.00511930	+	0.338277i
$531$		0			0
$532$	−844.670	−	844.670i	−1.58772	−	1.58772i
$533$	−94.5548	+	94.5548i	−0.177401	+	0.177401i
$534$		0			0
$535$	17.2041	−	17.7328i	0.0321572	−	0.0331455i
$536$	273.801			0.510824
$537$		0			0
$538$	155.290	−	155.290i	0.288643	−	0.288643i
$539$			770.154i			1.42886i
$540$		0			0
$541$	−378.213			−0.699100			−0.349550	−	0.936918i	$-0.613665\pi$
$541$	−378.213			−0.699100			−0.349550	+	0.936918i	$0.613665\pi$
$542$	126.051	+	126.051i	0.232566	+	0.232566i
$543$		0			0
$544$		−	188.634i		−	0.346753i
$545$	979.898	−	14.8292i	1.79798	−	0.0272096i
$546$		0			0
$547$	574.894	+	574.894i	1.05099	+	1.05099i	0.998628	+	0.0523664i	$0.0166764\pi$
$547$	574.894	+	574.894i	1.05099	+	1.05099i	0.0523664	+	0.998628i	$0.483324\pi$
$548$	635.915	−	635.915i	1.16043	−	1.16043i
$549$		0			0
$550$	−164.474	−	154.808i	−0.299044	−	0.281469i
$551$	−1192.51			−2.16427
$552$		0			0
$553$	−96.0723	+	96.0723i	−0.173729	+	0.173729i
$554$			96.9010i			0.174912i
$555$		0			0
$556$	546.295			0.982544
$557$	201.989	+	201.989i	0.362637	+	0.362637i	0.864783	−	0.502146i	$-0.167456\pi$
$557$	201.989	+	201.989i	0.362637	+	0.362637i	−0.502146	+	0.864783i	$0.667456\pi$
$558$		0			0
$559$		−	675.004i		−	1.20752i
$560$	−414.073	+	426.799i	−0.739417	+	0.762140i
$561$		0			0
$562$	73.4081	+	73.4081i	0.130619	+	0.130619i
$563$	−527.292	+	527.292i	−0.936576	+	0.936576i	−0.998105	−	0.0615292i	$-0.980402\pi$
$563$	−527.292	+	527.292i	−0.936576	+	0.936576i	0.0615292	+	0.998105i	$0.480402\pi$
$564$		0			0
$565$	−434.735	−	421.773i	−0.769443	−	0.746502i
$566$	61.1909			0.108111
$567$		0			0
$568$	206.548	−	206.548i	0.363641	−	0.363641i
$569$		−	394.275i		−	0.692927i	−0.938063	−	0.346463i	$-0.887382\pi$
$569$		−	394.275i		−	0.692927i	0.938063	−	0.346463i	$-0.112618\pi$
$570$		0			0
$571$	13.1614			0.0230498			0.0115249	−	0.999934i	$-0.496331\pi$
$571$	13.1614			0.0230498			0.0115249	+	0.999934i	$0.496331\pi$
$572$	512.776	+	512.776i	0.896461	+	0.896461i
$573$		0			0
$574$			60.6320i			0.105631i
$575$	−605.231	+	643.021i	−1.05258	+	1.11830i
$576$		0			0
$577$	375.907	+	375.907i	0.651485	+	0.651485i	0.953350	−	0.301866i	$-0.0976094\pi$
$577$	375.907	+	375.907i	0.651485	+	0.651485i	−0.301866	+	0.953350i	$0.597609\pi$
$578$	97.2516	−	97.2516i	0.168255	−	0.168255i
$579$		0			0
$580$	10.0350	+	663.102i	0.0173017	+	1.14328i
$581$	−317.022			−0.545649
$582$		0			0
$583$	−655.818	+	655.818i	−1.12490	+	1.12490i
$584$		−	81.5912i		−	0.139711i
$585$		0			0
$586$	327.152			0.558280
$587$	636.233	+	636.233i	1.08387	+	1.08387i	0.996144	+	0.0877277i	$0.0279605\pi$
$587$	636.233	+	636.233i	1.08387	+	1.08387i	0.0877277	+	0.996144i	$0.472039\pi$
$588$		0			0
$589$			45.9436i			0.0780028i
$590$	0.245268	+	0.237955i	0.000415708	+	0.000403314i
$591$		0			0
$592$	−190.258	−	190.258i	−0.321382	−	0.321382i
$593$	695.567	−	695.567i	1.17296	−	1.17296i	0.191463	−	0.981500i	$-0.438677\pi$
$593$	695.567	−	695.567i	1.17296	−	1.17296i	0.981500	−	0.191463i	$-0.0613233\pi$
$594$		0			0
$595$	373.980	−	5.65961i	0.628538	−	0.00951195i
$596$	881.371			1.47881
$597$		0			0
$598$	−191.837	+	191.837i	−0.320798	+	0.320798i
$599$		−	869.925i		−	1.45230i	−0.687538	−	0.726148i	$-0.741309\pi$
$599$		−	869.925i		−	1.45230i	0.687538	−	0.726148i	$-0.258691\pi$
$600$		0			0
$601$	−17.3041			−0.0287921			−0.0143961	−	0.999896i	$-0.504583\pi$
$601$	−17.3041			−0.0287921			−0.0143961	+	0.999896i	$0.504583\pi$
$602$	−216.419	−	216.419i	−0.359499	−	0.359499i
$603$		0			0
$604$		−	157.894i		−	0.261413i
$605$	−8.52387	−	563.247i	−0.0140890	−	0.930987i
$606$		0			0
$607$	−816.896	−	816.896i	−1.34579	−	1.34579i	−0.890176	−	0.455616i	$-0.849419\pi$
$607$	−816.896	−	816.896i	−1.34579	−	1.34579i	−0.455616	−	0.890176i	$-0.650581\pi$
$608$	−583.453	+	583.453i	−0.959627	+	0.959627i
$609$		0			0
$610$	8.75718	−	9.02631i	0.0143560	−	0.0147972i
$611$	155.285			0.254148
$612$		0			0
$613$	−345.194	+	345.194i	−0.563122	+	0.563122i	−0.930193	−	0.367071i	$-0.880361\pi$
$613$	−345.194	+	345.194i	−0.563122	+	0.563122i	0.367071	+	0.930193i	$0.380361\pi$
$614$			130.584i			0.212677i
$615$		0			0
$616$	689.086			1.11865
$617$	−290.255	−	290.255i	−0.470429	−	0.470429i	0.431624	−	0.902053i	$-0.357941\pi$
$617$	−290.255	−	290.255i	−0.470429	−	0.470429i	−0.902053	+	0.431624i	$0.857941\pi$
$618$		0			0
$619$			1069.79i			1.72825i	0.503277	+	0.864125i	$0.332127\pi$
$619$			1069.79i			1.72825i	−0.503277	+	0.864125i	$0.667873\pi$
$620$	25.5471	−	0.386616i	0.0412051	−	0.000623575i
$621$		0			0
$622$	28.3995	+	28.3995i	0.0456584	+	0.0456584i
$623$	484.694	−	484.694i	0.778001	−	0.778001i
$624$		0			0
$625$	623.855	−	37.8076i	0.998169	−	0.0604922i
$626$	110.503			0.176523
$627$		0			0
$628$	258.614	−	258.614i	0.411806	−	0.411806i
$629$			169.236i			0.269055i
$630$		0			0
$631$	629.240			0.997211			0.498606	−	0.866829i	$-0.333846\pi$
$631$	629.240			0.997211			0.498606	+	0.866829i	$0.333846\pi$
$632$	43.5778	+	43.5778i	0.0689523	+	0.0689523i
$633$		0			0
$634$		−	254.353i		−	0.401188i
$635$	−119.971	+	123.658i	−0.188930	+	0.194737i
$636$		0			0
$637$	−462.961	−	462.961i	−0.726784	−	0.726784i
$638$	232.109	−	232.109i	0.363807	−	0.363807i
$639$		0			0
$640$	430.558	+	417.720i	0.672746	+	0.652688i
$641$	−767.625			−1.19754			−0.598771	−	0.800920i	$-0.704344\pi$
$641$	−767.625			−1.19754			−0.598771	+	0.800920i	$0.704344\pi$
$642$		0			0
$643$	−573.042	+	573.042i	−0.891200	+	0.891200i	−0.994636	−	0.103436i	$-0.967016\pi$
$643$	−573.042	+	573.042i	−0.891200	+	0.891200i	0.103436	+	0.994636i	$0.467016\pi$
$644$		−	1285.50i		−	1.99612i
$645$		0			0
$646$	145.570			0.225340
$647$	−294.799	−	294.799i	−0.455641	−	0.455641i	0.441581	−	0.897221i	$-0.354418\pi$
$647$	−294.799	−	294.799i	−0.455641	−	0.455641i	−0.897221	+	0.441581i	$0.854418\pi$
$648$		0			0
$649$			1.76759i			0.00272356i
$650$	191.930	−	5.81045i	0.295276	−	0.00893915i
$651$		0			0
$652$	83.2685	+	83.2685i	0.127712	+	0.127712i
$653$	631.887	−	631.887i	0.967667	−	0.967667i	−0.0318263	−	0.999493i	$-0.510132\pi$
$653$	631.887	−	631.887i	0.967667	−	0.967667i	0.999493	+	0.0318263i	$0.0101323\pi$
$654$		0			0
$655$	6.47320	+	427.741i	0.00988274	+	0.653040i
$656$	−122.761			−0.187136
$657$		0			0
$658$	49.7871	−	49.7871i	0.0756642	−	0.0756642i
$659$		−	302.347i		−	0.458796i	−0.973333	−	0.229398i	$-0.926324\pi$
$659$		−	302.347i		−	0.458796i	0.973333	−	0.229398i	$-0.0736758\pi$
$660$		0			0
$661$	−530.910			−0.803192			−0.401596	−	0.915817i	$-0.631544\pi$
$661$	−530.910			−0.803192			−0.401596	+	0.915817i	$0.631544\pi$
$662$	−135.741	−	135.741i	−0.205047	−	0.205047i
$663$		0			0
$664$			143.799i			0.216565i
$665$	−1174.25	−	1139.23i	−1.76578	−	1.71313i
$666$		0			0
$667$	−907.443	−	907.443i	−1.36048	−	1.36048i
$668$	423.332	−	423.332i	0.633731	−	0.633731i
$669$		0			0
$670$	178.919	−	2.70767i	0.267044	−	0.00404129i
$671$	65.0507			0.0969458
$672$		0			0
$673$	−251.666	+	251.666i	−0.373947	+	0.373947i	−0.868912	−	0.494966i	$-0.835181\pi$
$673$	−251.666	+	251.666i	−0.373947	+	0.373947i	0.494966	+	0.868912i	$0.335181\pi$
$674$		−	92.1941i		−	0.136787i
$675$		0			0
$676$	0.473113			0.000699872
$677$	−97.3766	−	97.3766i	−0.143835	−	0.143835i	0.631522	−	0.775358i	$-0.282430\pi$
$677$	−97.3766	−	97.3766i	−0.143835	−	0.143835i	−0.775358	+	0.631522i	$0.782430\pi$
$678$		0			0
$679$		−	150.718i		−	0.221970i
$680$	−2.56717	−	169.635i	−0.00377524	−	0.249464i
$681$		0			0
$682$	−8.94240	−	8.94240i	−0.0131120	−	0.0131120i
$683$	58.2071	−	58.2071i	0.0852226	−	0.0852226i	−0.663210	−	0.748433i	$-0.730807\pi$
$683$	58.2071	−	58.2071i	0.0852226	−	0.0852226i	0.748433	+	0.663210i	$0.230807\pi$
$684$		0			0
$685$	857.681	−	884.039i	1.25209	−	1.29057i
$686$	−8.14825			−0.0118779
$687$		0			0
$688$	438.181	−	438.181i	0.636891	−	0.636891i
$689$		−	788.462i		−	1.14436i
$690$		0			0
$691$	−122.157			−0.176783			−0.0883915	−	0.996086i	$-0.528173\pi$
$691$	−122.157			−0.176783			−0.0883915	+	0.996086i	$0.528173\pi$
$692$	404.868	+	404.868i	0.585070	+	0.585070i
$693$		0			0
$694$			246.244i			0.354818i
$695$	748.128	−	11.3218i	1.07644	−	0.0162903i
$696$		0			0
$697$	54.5983	+	54.5983i	0.0783333	+	0.0783333i
$698$	−94.8197	+	94.8197i	−0.135845	+	0.135845i
$699$		0			0
$700$	−623.595	+	662.531i	−0.890849	+	0.946472i
$701$	663.953			0.947151			0.473576	−	0.880753i	$-0.342963\pi$
$701$	663.953			0.947151			0.473576	+	0.880753i	$0.342963\pi$
$702$		0			0
$703$	523.455	−	523.455i	0.744602	−	0.744602i
$704$			502.321i			0.713524i
$705$		0			0
$706$	89.3119			0.126504
$707$	−728.341	−	728.341i	−1.03019	−	1.03019i
$708$		0			0
$709$		−	964.553i		−	1.36044i	−0.733007	−	0.680221i	$-0.761884\pi$
$709$		−	964.553i		−	1.36044i	0.733007	−	0.680221i	$-0.238116\pi$
$710$	132.929	−	137.014i	0.187224	−	0.192978i
$711$		0			0
$712$	−219.855	−	219.855i	−0.308784	−	0.308784i
$713$	−34.9608	+	34.9608i	−0.0490334	+	0.0490334i
$714$		0			0
$715$	712.852	+	691.598i	0.996996	+	0.967270i
$716$	517.519			0.722792
$717$		0			0
$718$	10.4176	−	10.4176i	0.0145091	−	0.0145091i
$719$			171.152i			0.238042i	0.992892	+	0.119021i	$0.0379756\pi$
$719$			171.152i			0.238042i	−0.992892	+	0.119021i	$0.962024\pi$
$720$		0			0
$721$	1393.26			1.93240
$722$	−299.381	−	299.381i	−0.414655	−	0.414655i
$723$		0			0
$724$			456.970i			0.631174i
$725$	27.4851	+	907.882i	0.0379104	+	1.25225i
$726$		0			0
$727$	−536.540	−	536.540i	−0.738019	−	0.738019i	0.234175	−	0.972194i	$-0.424761\pi$
$727$	−536.540	−	536.540i	−0.738019	−	0.738019i	−0.972194	+	0.234175i	$0.924761\pi$
$728$	−414.229	+	414.229i	−0.568996	+	0.568996i
$729$		0			0
$730$	−0.806868	−	53.3169i	−0.00110530	−	0.0730368i
$731$	−389.764			−0.533193
$732$		0			0
$733$	−384.894	+	384.894i	−0.525094	+	0.525094i	−0.919105	−	0.394012i	$-0.871087\pi$
$733$	−384.894	+	384.894i	−0.525094	+	0.525094i	0.394012	+	0.919105i	$0.371087\pi$
$734$			20.8653i			0.0284268i
$735$		0			0
$736$	−887.958			−1.20646
$737$	654.473	+	654.473i	0.888023	+	0.888023i
$738$		0			0
$739$		−	900.167i		−	1.21809i	−0.793136	−	0.609044i	$-0.791553\pi$
$739$		−	900.167i		−	1.21809i	0.793136	−	0.609044i	$-0.208447\pi$
$740$	−295.474	−	286.664i	−0.399289	−	0.387384i
$741$		0			0
$742$	−252.795	−	252.795i	−0.340695	−	0.340695i
$743$	−109.710	+	109.710i	−0.147658	+	0.147658i	−0.777071	−	0.629413i	$-0.783295\pi$
$743$	−109.710	+	109.710i	−0.147658	+	0.147658i	0.629413	+	0.777071i	$0.283295\pi$
$744$		0			0
$745$	1207.00	−	18.2661i	1.62014	−	0.0245182i
$746$	−360.309			−0.482988
$747$		0			0
$748$	296.090	−	296.090i	0.395842	−	0.395842i
$749$			49.2613i			0.0657694i
$750$		0			0
$751$	−73.6090			−0.0980147			−0.0490074	−	0.998798i	$-0.515606\pi$
$751$	−73.6090			−0.0980147			−0.0490074	+	0.998798i	$0.515606\pi$
$752$	100.803	+	100.803i	0.134047	+	0.134047i
$753$		0			0
$754$			279.055i			0.370099i
$755$	−3.27229	−	216.229i	−0.00433416	−	0.286396i
$756$		0			0
$757$	−562.868	−	562.868i	−0.743551	−	0.743551i	0.229708	−	0.973260i	$-0.426223\pi$
$757$	−562.868	−	562.868i	−0.743551	−	0.743551i	−0.973260	+	0.229708i	$0.926223\pi$
$758$	95.1852	−	95.1852i	0.125574	−	0.125574i
$759$		0			0
$760$	−516.750	+	532.631i	−0.679934	+	0.700830i
$761$	1444.65			1.89836			0.949182	−	0.314728i	$-0.101913\pi$
$761$	1444.65			1.89836			0.949182	+	0.314728i	$0.101913\pi$
$762$		0			0
$763$	−1381.66	+	1381.66i	−1.81083	+	1.81083i
$764$		−	493.783i		−	0.646313i
$765$		0			0
$766$	−263.804			−0.344391
$767$	−1.06255	−	1.06255i	−0.00138533	−	0.00138533i
$768$		0			0
$769$			1062.29i			1.38139i	0.723144	+	0.690697i	$0.242696\pi$
$769$			1062.29i			1.38139i	−0.723144	+	0.690697i	$0.757304\pi$
$770$	450.293	−	6.81448i	0.584796	−	0.00884997i
$771$		0			0
$772$	−183.398	−	183.398i	−0.237563	−	0.237563i
$773$	772.859	−	772.859i	0.999818	−	0.999818i	−0.000181879	−	1.00000i	$-0.500058\pi$
$773$	772.859	−	772.859i	0.999818	−	0.999818i	1.00000		0.000181879i	$5.78938e-5\pi$
$774$		0			0
$775$	34.9777	−	1.05891i	0.0451326	−	0.00136634i
$776$	−68.3647			−0.0880988
$777$		0			0
$778$	−2.98448	+	2.98448i	−0.00383610	+	0.00383610i
$779$		−	337.751i		−	0.433570i
$780$		0			0
$781$	987.433			1.26432
$782$	110.772	+	110.772i	0.141652	+	0.141652i
$783$		0			0
$784$		−	601.065i		−	0.766665i
$785$	348.802	−	359.521i	0.444333	−	0.457989i
$786$		0			0
$787$	−311.022	−	311.022i	−0.395199	−	0.395199i	0.481337	−	0.876536i	$-0.340151\pi$
$787$	−311.022	−	311.022i	−0.395199	−	0.395199i	−0.876536	+	0.481337i	$0.840151\pi$
$788$	−894.199	+	894.199i	−1.13477	+	1.13477i
$789$		0			0
$790$	28.9075	+	28.0456i	0.0365918	+	0.0355007i
$791$	1207.68			1.52678
$792$		0			0
$793$	−39.1038	+	39.1038i	−0.0493112	+	0.0493112i
$794$			222.629i			0.280389i
$795$		0			0
$796$	−320.895			−0.403135
$797$	166.738	+	166.738i	0.209207	+	0.209207i	0.803931	−	0.594723i	$-0.202738\pi$
$797$	166.738	+	166.738i	0.209207	+	0.209207i	−0.594723	+	0.803931i	$0.702738\pi$
$798$		0			0
$799$		−	89.6652i		−	0.112222i
$800$	457.641	+	430.746i	0.572051	+	0.538433i
$801$		0			0
$802$	131.459	+	131.459i	0.163914	+	0.163914i
$803$	195.029	−	195.029i	0.242876	−	0.242876i
$804$		0			0
$805$	−26.6416	−	1760.44i	−0.0330951	−	2.18689i
$806$	10.7511			0.0133388
$807$		0			0
$808$	−330.371	+	330.371i	−0.408875	+	0.408875i
$809$		−	522.911i		−	0.646367i	−0.946336	−	0.323184i	$-0.895247\pi$
$809$		−	522.911i		−	0.646367i	0.946336	−	0.323184i	$-0.104753\pi$
$810$		0			0
$811$	−1339.90			−1.65215			−0.826076	−	0.563558i	$-0.809432\pi$
$811$	−1339.90			−1.65215			−0.826076	+	0.563558i	$0.809432\pi$
$812$	−934.976	−	934.976i	−1.15145	−	1.15145i
$813$		0			0
$814$			203.769i			0.250331i
$815$	115.758	+	112.307i	0.142035	+	0.137800i
$816$		0			0
$817$	1205.56	+	1205.56i	1.47559	+	1.47559i
$818$	128.546	−	128.546i	0.157146	−	0.157146i
$819$		0			0
$820$	−187.808	+	2.84218i	−0.229034	+	0.00346607i
$821$	1191.75			1.45158			0.725789	−	0.687917i	$-0.241475\pi$
$821$	1191.75			1.45158			0.725789	+	0.687917i	$0.241475\pi$
$822$		0			0
$823$	−146.323	+	146.323i	−0.177792	+	0.177792i	−0.790393	−	0.612600i	$-0.790124\pi$
$823$	−146.323	+	146.323i	−0.177792	+	0.177792i	0.612600	+	0.790393i	$0.290124\pi$
$824$		−	631.976i		−	0.766961i
$825$		0			0
$826$	−0.681347			−0.000824875
$827$	−245.326	−	245.326i	−0.296645	−	0.296645i	0.543053	−	0.839698i	$-0.317268\pi$
$827$	−245.326	−	245.326i	−0.296645	−	0.296645i	−0.839698	+	0.543053i	$0.817268\pi$
$828$		0			0
$829$			469.286i			0.566087i	0.959107	+	0.283044i	$0.0913441\pi$
$829$			469.286i			0.566087i	−0.959107	+	0.283044i	$0.908656\pi$
$830$	1.42206	+	93.9677i	0.00171332	+	0.113214i
$831$		0			0
$832$	−301.960	−	301.960i	−0.362932	−	0.362932i
$833$	−267.326	+	267.326i	−0.320919	+	0.320919i
$834$		0			0
$835$	570.963	−	588.510i	0.683788	−	0.704802i
$836$	−1831.64			−2.19096
$837$		0			0
$838$	126.610	−	126.610i	0.151086	−	0.151086i
$839$		−	0.354307i		−	0.000422297i	−1.00000		0.000211148i	$-0.999933\pi$
$839$		−	0.354307i		−	0.000422297i	1.00000		0.000211148i	$-6.72106e-5\pi$
$840$		0			0
$841$	−479.009			−0.569571
$842$	213.188	+	213.188i	0.253193	+	0.253193i
$843$		0			0
$844$		−	69.7844i		−	0.0826829i
$845$	0.647909	−	0.00980510i	0.000766756	−	1.16037e-5i
$846$		0			0
$847$	794.181	+	794.181i	0.937640	+	0.937640i
$848$	511.833	−	511.833i	0.603576	−	0.603576i
$849$		0			0
$850$	−3.35510	−	110.825i	−0.00394718	−	0.130382i
$851$	796.647			0.936130
$852$		0			0
$853$	340.358	−	340.358i	0.399012	−	0.399012i	−0.478872	−	0.877885i	$-0.658954\pi$
$853$	340.358	−	340.358i	0.399012	−	0.399012i	0.877885	+	0.478872i	$0.158954\pi$
$854$			25.0748i			0.0293616i
$855$		0			0
$856$	22.3446			0.0261035
$857$	540.094	+	540.094i	0.630215	+	0.630215i	0.948122	−	0.317907i	$-0.102980\pi$
$857$	540.094	+	540.094i	0.630215	+	0.630215i	−0.317907	+	0.948122i	$0.602980\pi$
$858$		0			0
$859$		−	1231.06i		−	1.43314i	−0.697517	−	0.716568i	$-0.745712\pi$
$859$		−	1231.06i		−	1.43314i	0.697517	−	0.716568i	$-0.254288\pi$
$860$	660.212	−	680.502i	0.767689	−	0.791281i
$861$		0			0
$862$	−208.841	−	208.841i	−0.242274	−	0.242274i
$863$	−448.174	+	448.174i	−0.519321	+	0.519321i	−0.917366	−	0.398045i	$-0.869689\pi$
$863$	−448.174	+	448.174i	−0.519321	+	0.519321i	0.398045	+	0.917366i	$0.369689\pi$
$864$		0			0
$865$	562.841	+	546.059i	0.650683	+	0.631283i
$866$	−375.754			−0.433897
$867$		0			0
$868$	−36.0216	+	36.0216i	−0.0414995	+	0.0414995i
$869$			208.330i			0.239735i
$870$		0			0
$871$	−786.845			−0.903381
$872$	626.713	+	626.713i	0.718708	+	0.718708i
$873$		0			0
$874$		−	685.244i		−	0.784032i
$875$	−840.256	+	920.232i	−0.960293	+	1.05169i
$876$		0			0
$877$	1161.34	+	1161.34i	1.32421	+	1.32421i	0.910329	+	0.413886i	$0.135829\pi$
$877$	1161.34	+	1161.34i	1.32421	+	1.32421i	0.413886	+	0.910329i	$0.364171\pi$
$878$	238.381	−	238.381i	0.271504	−	0.271504i
$879$		0			0
$880$	13.7972	+	911.703i	0.0156786	+	1.03603i
$881$	−503.847			−0.571904			−0.285952	−	0.958244i	$-0.592310\pi$
$881$	−503.847			−0.571904			−0.285952	+	0.958244i	$0.592310\pi$
$882$		0			0
$883$	−125.515	+	125.515i	−0.142147	+	0.142147i	−0.774599	−	0.632453i	$-0.782048\pi$
$883$	−125.515	+	125.515i	−0.142147	+	0.142147i	0.632453	+	0.774599i	$0.282048\pi$
$884$			355.976i			0.402688i
$885$		0			0
$886$	−510.033			−0.575658
$887$	−795.852	−	795.852i	−0.897240	−	0.897240i	0.0979510	−	0.995191i	$-0.468771\pi$
$887$	−795.852	−	795.852i	−0.897240	−	0.897240i	−0.995191	+	0.0979510i	$0.968771\pi$
$888$		0			0
$889$		−	343.517i		−	0.386409i
$890$	−145.841	−	141.493i	−0.163866	−	0.158981i
$891$		0			0
$892$	1004.48	+	1004.48i	1.12610	+	1.12610i
$893$	−277.339	+	277.339i	−0.310570	+	0.310570i
$894$		0			0
$895$	708.721	−	10.7254i	0.791867	−	0.0119837i
$896$	−1196.08			−1.33491
$897$		0			0
$898$	15.1770	−	15.1770i	0.0169009	−	0.0169009i
$899$			50.8556i			0.0565691i
$900$		0			0
$901$	−455.278			−0.505303
$902$	65.7394	+	65.7394i	0.0728818	+	0.0728818i
$903$		0			0
$904$		−	547.797i		−	0.605970i
$905$	9.47054	+	625.802i	0.0104647	+	0.691494i
$906$		0			0
$907$	160.363	+	160.363i	0.176806	+	0.176806i	0.789962	−	0.613156i	$-0.210100\pi$
$907$	160.363	+	160.363i	0.176806	+	0.176806i	−0.613156	+	0.789962i	$0.710100\pi$
$908$	−12.3343	+	12.3343i	−0.0135841	+	0.0135841i
$909$		0			0
$910$	−266.587	+	274.780i	−0.292953	+	0.301956i
$911$	845.063			0.927621			0.463810	−	0.885934i	$-0.346482\pi$
$911$	845.063			0.927621			0.463810	+	0.885934i	$0.346482\pi$
$912$		0			0
$913$	−343.727	+	343.727i	−0.376480	+	0.376480i
$914$		−	120.219i		−	0.131530i
$915$		0			0
$916$	1060.15			1.15737
$917$	−603.117	−	603.117i	−0.657706	−	0.657706i
$918$		0			0
$919$			316.538i			0.344438i	0.985059	+	0.172219i	$0.0550936\pi$
$919$			316.538i			0.344438i	−0.985059	+	0.172219i	$0.944906\pi$
$920$	−798.527	+	12.0845i	−0.867964	+	0.0131353i
$921$		0			0
$922$	102.405	+	102.405i	0.111068	+	0.111068i
$923$	−593.574	+	593.574i	−0.643092	+	0.643092i
$924$		0			0
$925$	−410.580	−	386.451i	−0.443871	−	0.417785i
$926$	122.945			0.132770
$927$		0			0
$928$	−645.832	+	645.832i	−0.695940	+	0.695940i
$929$		−	548.992i		−	0.590949i	−0.955351	−	0.295475i	$-0.904522\pi$
$929$		−	548.992i		−	0.590949i	0.955351	−	0.295475i	$-0.0954777\pi$
$930$		0			0
$931$	1653.70			1.77627
$932$	−151.625	−	151.625i	−0.162687	−	0.162687i
$933$		0			0
$934$		−	471.180i		−	0.504475i
$935$	399.346	−	411.619i	0.427108	−	0.440234i
$936$		0			0
$937$	−331.821	−	331.821i	−0.354131	−	0.354131i	0.507513	−	0.861644i	$-0.330565\pi$
$937$	−331.821	−	331.821i	−0.354131	−	0.354131i	−0.861644	+	0.507513i	$0.830565\pi$
$938$	−252.277	+	252.277i	−0.268952	+	0.268952i
$939$		0			0
$940$	156.549	+	151.882i	0.166542	+	0.161576i
$941$	−1077.94			−1.14553			−0.572765	−	0.819720i	$-0.694129\pi$
$941$	−1077.94			−1.14553			−0.572765	+	0.819720i	$0.694129\pi$
$942$		0			0
$943$	257.012	−	257.012i	0.272547	−	0.272547i
$944$		−	1.37952i		−	0.00146135i
$945$		0			0
$946$	−469.297			−0.496086
$947$	287.398	+	287.398i	0.303483	+	0.303483i	0.842375	−	0.538892i	$-0.181157\pi$
$947$	287.398	+	287.398i	0.303483	+	0.303483i	−0.538892	+	0.842375i	$0.681157\pi$
$948$		0			0
$949$			234.475i			0.247076i
$950$	−332.410	+	353.165i	−0.349905	+	0.371753i
$951$		0			0
$952$	239.186	+	239.186i	0.251246	+	0.251246i
$953$	−318.146	+	318.146i	−0.333837	+	0.333837i	−0.854042	−	0.520205i	$-0.825856\pi$
$953$	−318.146	+	318.146i	−0.333837	+	0.333837i	0.520205	+	0.854042i	$0.325856\pi$
$954$		0			0
$955$	−10.2335	−	676.215i	−0.0107157	−	0.708079i
$956$	1290.52			1.34991
$957$		0			0
$958$	81.9742	−	81.9742i	0.0855681	−	0.0855681i
$959$			2455.83i			2.56083i
$960$		0			0
$961$	−959.041			−0.997961
$962$	−122.491	−	122.491i	−0.127330	−	0.127330i
$963$		0			0
$964$			1227.20i			1.27303i
$965$	−254.957	−	247.356i	−0.264204	−	0.256327i
$966$		0			0
$967$	971.848	+	971.848i	1.00501	+	1.00501i	0.999987	+	0.00502589i	$0.00159980\pi$
$967$	971.848	+	971.848i	1.00501	+	1.00501i	0.00502589	+	0.999987i	$0.498400\pi$
$968$	360.236	−	360.236i	0.372144	−	0.372144i
$969$		0			0
$970$	−44.6738	+	0.676069i	−0.0460555	+	0.000696978i
$971$	−137.755			−0.141869			−0.0709347	−	0.997481i	$-0.522598\pi$
$971$	−137.755			−0.141869			−0.0709347	+	0.997481i	$0.522598\pi$
$972$		0			0
$973$	−1054.86	+	1054.86i	−1.08414	+	1.08414i
$974$			319.049i			0.327566i
$975$		0			0
$976$	−50.7687			−0.0520171
$977$	237.000	+	237.000i	0.242579	+	0.242579i	0.817916	−	0.575337i	$-0.195129\pi$
$977$	237.000	+	237.000i	0.242579	+	0.242579i	−0.575337	+	0.817916i	$0.695129\pi$
$978$		0			0
$979$		−	1051.05i		−	1.07359i
$980$	−13.9159	−	919.548i	−0.0141999	−	0.938315i
$981$		0			0
$982$	83.8293	+	83.8293i	0.0853659	+	0.0853659i
$983$	−609.523	+	609.523i	−0.620064	+	0.620064i	−0.945548	−	0.325484i	$-0.894473\pi$
$983$	−609.523	+	609.523i	−0.620064	+	0.620064i	0.325484	+	0.945548i	$0.394473\pi$
$984$		0			0
$985$	−1206.04	+	1243.10i	−1.22440	+	1.26203i
$986$	161.133			0.163421
$987$		0			0
$988$	1101.05	−	1101.05i	1.11443	−	1.11443i
$989$			1834.74i			1.85515i
$990$		0			0
$991$	745.194			0.751962			0.375981	−	0.926627i	$-0.377306\pi$
$991$	745.194			0.751962			0.375981	+	0.926627i	$0.377306\pi$
$992$	24.8818	+	24.8818i	0.0250825	+	0.0250825i
$993$		0			0
$994$			380.622i			0.382919i
$995$	−439.453	+	6.65043i	−0.441661	+	0.00668385i
$996$		0			0
$997$	−439.058	−	439.058i	−0.440379	−	0.440379i	0.451761	−	0.892139i	$-0.350796\pi$
$997$	−439.058	−	439.058i	−0.440379	−	0.440379i	−0.892139	+	0.451761i	$0.850796\pi$
$998$	152.610	−	152.610i	0.152916	−	0.152916i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.g.f.82.5	yes	16
3.2	odd	2	inner	405.3.g.f.82.4	✓	16
5.3	odd	4	inner	405.3.g.f.163.5	yes	16
9.2	odd	6		405.3.l.m.352.2		16
9.4	even	3		405.3.l.m.217.2		16
9.5	odd	6		405.3.l.j.217.3		16
9.7	even	3		405.3.l.j.352.3		16
15.8	even	4	inner	405.3.g.f.163.4	yes	16
45.13	odd	12		405.3.l.j.298.3		16
45.23	even	12		405.3.l.m.298.2		16
45.38	even	12		405.3.l.j.28.3		16
45.43	odd	12		405.3.l.m.28.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.g.f.82.4	✓	16	3.2	odd	2	inner
405.3.g.f.82.5	yes	16	1.1	even	1	trivial
405.3.g.f.163.4	yes	16	15.8	even	4	inner
405.3.g.f.163.5	yes	16	5.3	odd	4	inner
405.3.l.j.28.3		16	45.38	even	12
405.3.l.j.217.3		16	9.5	odd	6
405.3.l.j.298.3		16	45.13	odd	12
405.3.l.j.352.3		16	9.7	even	3
405.3.l.m.28.2		16	45.43	odd	12
405.3.l.m.217.2		16	9.4	even	3
405.3.l.m.298.2		16	45.23	even	12
405.3.l.m.352.2		16	9.2	odd	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.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.417936 + 0.417936i) q^{2} -3.65066i q^{4} +(-0.0756586 - 4.99943i) q^{5} +(7.04922 + 7.04922i) q^{7} +(3.19748 - 3.19748i) q^{8} +(2.05782 - 2.12106i) q^{10} +15.2860 q^{11} +(-9.18886 + 9.18886i) q^{13} +5.89224i q^{14} -11.9300 q^{16} +(5.30588 + 5.30588i) q^{17} -32.8227i q^{19} +(-18.2512 + 0.276204i) q^{20} +(6.38857 + 6.38857i) q^{22} +(24.9765 - 24.9765i) q^{23} +(-24.9886 + 0.756499i) q^{25} -7.68071 q^{26} +(25.7343 - 25.7343i) q^{28} -36.3319i q^{29} -1.39975 q^{31} +(-17.7759 - 17.7759i) q^{32} +4.43503i q^{34} +(34.7087 - 35.7754i) q^{35} +(15.9479 + 15.9479i) q^{37} +(13.7178 - 13.7178i) q^{38} +(-16.2275 - 15.7437i) q^{40} +10.2902 q^{41} +(-36.7295 + 36.7295i) q^{43} -55.8040i q^{44} +20.8771 q^{46} +(-8.44960 - 8.44960i) q^{47} +50.3829i q^{49} +(-10.7598 - 10.1274i) q^{50} +(33.5454 + 33.5454i) q^{52} +(-42.9031 + 42.9031i) q^{53} +(-1.15652 - 76.4213i) q^{55} +45.0795 q^{56} +(15.1844 - 15.1844i) q^{58} +0.115635i q^{59} +4.25557 q^{61} +(-0.585006 - 0.585006i) q^{62} +32.8615i q^{64} +(46.6343 + 45.2438i) q^{65} +(42.8151 + 42.8151i) q^{67} +(19.3700 - 19.3700i) q^{68} +(29.4578 - 0.445798i) q^{70} +64.5971 q^{71} +(12.7587 - 12.7587i) q^{73} +13.3304i q^{74} -119.825 q^{76} +(107.754 + 107.754i) q^{77} +13.6288i q^{79} +(0.902603 + 59.6429i) q^{80} +(4.30062 + 4.30062i) q^{82} +(-22.4863 + 22.4863i) q^{83} +(26.1249 - 26.9278i) q^{85} -30.7011 q^{86} +(48.8768 - 48.8768i) q^{88} -68.7586i q^{89} -129.549 q^{91} +(-91.1806 - 91.1806i) q^{92} -7.06278i q^{94} +(-164.095 + 2.48332i) q^{95} +(-10.6904 - 10.6904i) q^{97} +(-21.0568 + 21.0568i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 40 q^{7} - 56 q^{10} - 44 q^{13} - 32 q^{16} + 32 q^{22} - 92 q^{25} + 176 q^{28} + 320 q^{31} + 4 q^{37} - 528 q^{40} + 256 q^{43} - 16 q^{46} - 308 q^{52} - 364 q^{55} + 492 q^{58} + 8 q^{61} + 88 q^{67}+ \cdots + 304 q^{97}+O(q^{100}) \) 16 * q + 40 * q^7 - 56 * q^10 - 44 * q^13 - 32 * q^16 + 32 * q^22 - 92 * q^25 + 176 * q^28 + 320 * q^31 + 4 * q^37 - 528 * q^40 + 256 * q^43 - 16 * q^46 - 308 * q^52 - 364 * q^55 + 492 * q^58 + 8 * q^61 + 88 * q^67 - 36 * q^70 + 364 * q^73 - 912 * q^76 + 32 * q^82 + 64 * q^85 + 840 * q^88 + 224 * q^91 + 304 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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