LMFDB - Embedded newform 405.3.g.h.163.4

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 = [20,2] 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:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} + 8 x^{17} + 245 x^{16} - 440 x^{15} + 422 x^{14} + 1724 x^{13} + \cdots + 11449 $ x^20 - 2x^19 + 2x^18 + 8x^17 + 245x^16 - 440x^15 + 422x^14 + 1724x^13 + 15070x^12 - 18240x^11 + 13542x^10 + 50064x^9 + 293818x^8 - 191648x^7 + 30530x^6 - 134164x^5 + 859529x^4 - 948950x^3 + 540800x^2 - 111280*x + 11449
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.4
Root			$-1.18732 - 1.18732i$ of defining polynomial
Character	$\chi$	$=$	405.163
Dual form			405.3.g.h.82.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18732 + 1.18732i) q^{2} +1.18052i q^{4} +(-2.02288 - 4.57252i) q^{5} +(-1.94050 + 1.94050i) q^{7} +(-6.15096 - 6.15096i) q^{8} +(7.83089 + 3.02725i) q^{10} +14.5360 q^{11} +(-4.15569 - 4.15569i) q^{13} -4.60801i q^{14} +9.88429 q^{16} +(5.66128 - 5.66128i) q^{17} +30.5333i q^{19} +(5.39796 - 2.38806i) q^{20} +(-17.2589 + 17.2589i) q^{22} +(15.9961 + 15.9961i) q^{23} +(-16.8159 + 18.4994i) q^{25} +9.86831 q^{26} +(-2.29080 - 2.29080i) q^{28} -1.74629i q^{29} +51.0538 q^{31} +(12.8680 - 12.8680i) q^{32} +13.4436i q^{34} +(12.7984 + 4.94758i) q^{35} +(2.78899 - 2.78899i) q^{37} +(-36.2529 - 36.2529i) q^{38} +(-15.6827 + 40.5681i) q^{40} -33.1234 q^{41} +(28.0046 + 28.0046i) q^{43} +17.1600i q^{44} -37.9852 q^{46} +(-30.1248 + 30.1248i) q^{47} +41.4689i q^{49} +(-1.99882 - 41.9306i) q^{50} +(4.90588 - 4.90588i) q^{52} +(-4.77052 - 4.77052i) q^{53} +(-29.4046 - 66.4660i) q^{55} +23.8719 q^{56} +(2.07341 + 2.07341i) q^{58} +80.6672i q^{59} +15.2319 q^{61} +(-60.6174 + 60.6174i) q^{62} +70.0941i q^{64} +(-10.5955 + 27.4085i) q^{65} +(45.2721 - 45.2721i) q^{67} +(6.68326 + 6.68326i) q^{68} +(-21.0702 + 9.32147i) q^{70} +45.4076 q^{71} +(92.0685 + 92.0685i) q^{73} +6.62288i q^{74} -36.0452 q^{76} +(-28.2071 + 28.2071i) q^{77} +32.5525i q^{79} +(-19.9948 - 45.1961i) q^{80} +(39.3283 - 39.3283i) q^{82} +(-4.89551 - 4.89551i) q^{83} +(-37.3384 - 14.4342i) q^{85} -66.5010 q^{86} +(-89.4101 - 89.4101i) q^{88} -35.7887i q^{89} +16.1283 q^{91} +(-18.8837 + 18.8837i) q^{92} -71.5359i q^{94} +(139.614 - 61.7653i) q^{95} +(43.7021 - 43.7021i) q^{97} +(-49.2370 - 49.2370i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 2 q^{5} + 2 q^{7} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 2 q^{13} - 28 q^{16} + 14 q^{17} + 114 q^{20} - 14 q^{22} - 82 q^{23} + 8 q^{25} - 56 q^{26} - 44 q^{28} + 4 q^{31} + 14 q^{32} + 176 q^{35}+ \cdots - 938 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 + 2 * q^5 + 2 * q^7 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 2 * q^13 - 28 * q^16 + 14 * q^17 + 114 * q^20 - 14 * q^22 - 82 * q^23 + 8 * q^25 - 56 * q^26 - 44 * q^28 + 4 * q^31 + 14 * q^32 + 176 * q^35 - 46 * q^37 - 330 * q^38 - 30 * q^40 + 28 * q^41 + 2 * q^43 - 68 * q^46 - 64 * q^47 + 458 * q^50 + 74 * q^52 - 304 * q^53 + 112 * q^55 + 192 * q^56 - 30 * q^58 - 92 * q^61 - 50 * q^62 + 326 * q^65 + 80 * q^67 - 626 * q^68 + 102 * q^70 + 124 * q^71 - 4 * q^73 + 96 * q^76 - 338 * q^77 + 722 * q^80 + 52 * q^82 - 370 * q^83 + 98 * q^85 + 328 * q^86 + 210 * q^88 + 76 * q^91 - 388 * q^92 + 360 * q^95 - 292 * q^97 - 938 * q^98

Character values

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

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−1.18732	+	1.18732i	−0.593662	+	0.593662i	−0.938619	−	0.344956i	$-0.887894\pi$
$2$	−1.18732	+	1.18732i	−0.593662	+	0.593662i	0.344956	+	0.938619i	$0.387894\pi$
$3$		0			0
$3$		0			0
$4$			1.18052i			0.295130i
$5$	−2.02288	−	4.57252i	−0.404577	−	0.914504i
$5$	−2.02288	−	4.57252i	−0.404577	−	0.914504i
$6$		0			0
$7$	−1.94050	+	1.94050i	−0.277215	+	0.277215i	−0.831996	−	0.554782i	$-0.812802\pi$
$7$	−1.94050	+	1.94050i	−0.277215	+	0.277215i	0.554782	+	0.831996i	$0.312802\pi$
$8$	−6.15096	−	6.15096i	−0.768870	−	0.768870i
$9$		0			0
$10$	7.83089	+	3.02725i	0.783089	+	0.302725i
$11$	14.5360			1.32145			0.660726	−	0.750628i	$-0.270249\pi$
$11$	14.5360			1.32145			0.660726	+	0.750628i	$0.270249\pi$
$12$		0			0
$13$	−4.15569	−	4.15569i	−0.319668	−	0.319668i	0.528971	−	0.848640i	$-0.322578\pi$
$13$	−4.15569	−	4.15569i	−0.319668	−	0.319668i	−0.848640	+	0.528971i	$0.822578\pi$
$14$		−	4.60801i		−	0.329144i
$15$		0			0
$16$	9.88429			0.617768
$17$	5.66128	−	5.66128i	0.333017	−	0.333017i	−0.520714	−	0.853731i	$-0.674334\pi$
$17$	5.66128	−	5.66128i	0.333017	−	0.333017i	0.853731	+	0.520714i	$0.174334\pi$
$18$		0			0
$19$			30.5333i			1.60701i	0.595295	+	0.803507i	$0.297035\pi$
$19$			30.5333i			1.60701i	−0.595295	+	0.803507i	$0.702965\pi$
$20$	5.39796	−	2.38806i	0.269898	−	0.119403i
$21$		0			0
$22$	−17.2589	+	17.2589i	−0.784496	+	0.784496i
$23$	15.9961	+	15.9961i	0.695483	+	0.695483i	0.963433	−	0.267950i	$-0.0863461\pi$
$23$	15.9961	+	15.9961i	0.695483	+	0.695483i	−0.267950	+	0.963433i	$0.586346\pi$
$24$		0			0
$25$	−16.8159	+	18.4994i	−0.672635	+	0.739974i
$26$	9.86831			0.379550
$27$		0			0
$28$	−2.29080	−	2.29080i	−0.0818144	−	0.0818144i
$29$		−	1.74629i		−	0.0602168i	−0.999547	−	0.0301084i	$-0.990415\pi$
$29$		−	1.74629i		−	0.0602168i	0.999547	−	0.0301084i	$-0.00958524\pi$
$30$		0			0
$31$	51.0538			1.64690			0.823448	−	0.567391i	$-0.192047\pi$
$31$	51.0538			1.64690			0.823448	+	0.567391i	$0.192047\pi$
$32$	12.8680	−	12.8680i	0.402124	−	0.402124i
$33$		0			0
$34$			13.4436i			0.395399i
$35$	12.7984	+	4.94758i	0.365668	+	0.141359i
$36$		0			0
$37$	2.78899	−	2.78899i	0.0753782	−	0.0753782i	−0.668413	−	0.743791i	$-0.733026\pi$
$37$	2.78899	−	2.78899i	0.0753782	−	0.0753782i	0.743791	+	0.668413i	$0.233026\pi$
$38$	−36.2529	−	36.2529i	−0.954024	−	0.954024i
$39$		0			0
$40$	−15.6827	+	40.5681i	−0.392068	+	1.01420i
$41$	−33.1234			−0.807888			−0.403944	−	0.914784i	$-0.632361\pi$
$41$	−33.1234			−0.807888			−0.403944	+	0.914784i	$0.632361\pi$
$42$		0			0
$43$	28.0046	+	28.0046i	0.651269	+	0.651269i	0.953299	−	0.302029i	$-0.0976641\pi$
$43$	28.0046	+	28.0046i	0.651269	+	0.651269i	−0.302029	+	0.953299i	$0.597664\pi$
$44$			17.1600i			0.390000i
$45$		0			0
$46$	−37.9852			−0.825764
$47$	−30.1248	+	30.1248i	−0.640954	+	0.640954i	−0.950790	−	0.309836i	$-0.899726\pi$
$47$	−30.1248	+	30.1248i	−0.640954	+	0.640954i	0.309836	+	0.950790i	$0.399726\pi$
$48$		0			0
$49$			41.4689i			0.846304i
$50$	−1.99882	−	41.9306i	−0.0399765	−	0.838613i
$51$		0			0
$52$	4.90588	−	4.90588i	0.0943438	−	0.0943438i
$53$	−4.77052	−	4.77052i	−0.0900098	−	0.0900098i	0.660668	−	0.750678i	$-0.270273\pi$
$53$	−4.77052	−	4.77052i	−0.0900098	−	0.0900098i	−0.750678	+	0.660668i	$0.770273\pi$
$54$		0			0
$55$	−29.4046	−	66.4660i	−0.534628	−	1.20847i
$56$	23.8719			0.426284
$57$		0			0
$58$	2.07341	+	2.07341i	0.0357484	+	0.0357484i
$59$			80.6672i			1.36724i	0.729838	+	0.683620i	$0.239596\pi$
$59$			80.6672i			1.36724i	−0.729838	+	0.683620i	$0.760404\pi$
$60$		0			0
$61$	15.2319			0.249703			0.124851	−	0.992175i	$-0.460155\pi$
$61$	15.2319			0.249703			0.124851	+	0.992175i	$0.460155\pi$
$62$	−60.6174	+	60.6174i	−0.977700	+	0.977700i
$63$		0			0
$64$			70.0941i			1.09522i
$65$	−10.5955	+	27.4085i	−0.163008	+	0.421669i
$66$		0			0
$67$	45.2721	−	45.2721i	0.675703	−	0.675703i	−0.283322	−	0.959025i	$-0.591437\pi$
$67$	45.2721	−	45.2721i	0.675703	−	0.675703i	0.959025	+	0.283322i	$0.0914365\pi$
$68$	6.68326	+	6.68326i	0.0982832	+	0.0982832i
$69$		0			0
$70$	−21.0702	+	9.32147i	−0.301003	+	0.133164i
$71$	45.4076			0.639543			0.319772	−	0.947495i	$-0.396394\pi$
$71$	45.4076			0.639543			0.319772	+	0.947495i	$0.396394\pi$
$72$		0			0
$73$	92.0685	+	92.0685i	1.26121	+	1.26121i	0.950506	+	0.310707i	$0.100566\pi$
$73$	92.0685	+	92.0685i	1.26121	+	1.26121i	0.310707	+	0.950506i	$0.399434\pi$
$74$			6.62288i			0.0894984i
$75$		0			0
$76$	−36.0452			−0.474279
$77$	−28.2071	+	28.2071i	−0.366326	+	0.366326i
$78$		0			0
$79$			32.5525i			0.412057i	0.978546	+	0.206028i	$0.0660539\pi$
$79$			32.5525i			0.412057i	−0.978546	+	0.206028i	$0.933946\pi$
$80$	−19.9948	−	45.1961i	−0.249935	−	0.564951i
$81$		0			0
$82$	39.3283	−	39.3283i	0.479613	−	0.479613i
$83$	−4.89551	−	4.89551i	−0.0589820	−	0.0589820i	0.677001	−	0.735983i	$-0.263279\pi$
$83$	−4.89551	−	4.89551i	−0.0589820	−	0.0589820i	−0.735983	+	0.677001i	$0.763279\pi$
$84$		0			0
$85$	−37.3384	−	14.4342i	−0.439276	−	0.169814i
$86$	−66.5010			−0.773268
$87$		0			0
$88$	−89.4101	−	89.4101i	−1.01602	−	1.01602i
$89$		−	35.7887i		−	0.402121i	−0.979579	−	0.201060i	$-0.935561\pi$
$89$		−	35.7887i		−	0.402121i	0.979579	−	0.201060i	$-0.0644387\pi$
$90$		0			0
$91$	16.1283			0.177234
$92$	−18.8837	+	18.8837i	−0.205258	+	0.205258i
$93$		0			0
$94$		−	71.5359i		−	0.761020i
$95$	139.614	−	61.7653i	1.46962	−	0.650161i
$96$		0			0
$97$	43.7021	−	43.7021i	0.450537	−	0.450537i	−0.444995	−	0.895533i	$-0.646795\pi$
$97$	43.7021	−	43.7021i	0.450537	−	0.450537i	0.895533	+	0.444995i	$0.146795\pi$
$98$	−49.2370	−	49.2370i	−0.502419	−	0.502419i
$99$		0			0
$100$	−21.8389	−	19.8515i	−0.218389	−	0.198515i
$101$	109.176			1.08095			0.540475	−	0.841360i	$-0.318245\pi$
$101$	109.176			1.08095			0.540475	+	0.841360i	$0.318245\pi$
$102$		0			0
$103$	−82.9269	−	82.9269i	−0.805116	−	0.805116i	0.178774	−	0.983890i	$-0.442787\pi$
$103$	−82.9269	−	82.9269i	−0.805116	−	0.805116i	−0.983890	+	0.178774i	$0.942787\pi$
$104$			51.1230i			0.491567i
$105$		0			0
$106$	11.3283			0.106871
$107$	−24.4404	+	24.4404i	−0.228415	+	0.228415i	−0.812030	−	0.583615i	$-0.801638\pi$
$107$	−24.4404	+	24.4404i	−0.228415	+	0.228415i	0.583615	+	0.812030i	$0.301638\pi$
$108$		0			0
$109$		−	38.5655i		−	0.353812i	−0.984228	−	0.176906i	$-0.943391\pi$
$109$		−	38.5655i		−	0.353812i	0.984228	−	0.176906i	$-0.0566088\pi$
$110$	113.829	+	44.0039i	1.03481	+	0.400036i
$111$		0			0
$112$	−19.1805	+	19.1805i	−0.171254	+	0.171254i
$113$	−128.243	−	128.243i	−1.13490	−	1.13490i	−0.989351	−	0.145547i	$-0.953506\pi$
$113$	−128.243	−	128.243i	−1.13490	−	1.13490i	−0.145547	−	0.989351i	$-0.546494\pi$
$114$		0			0
$115$	40.7843	−	105.501i	0.354646	−	0.917399i
$116$	2.06153			0.0177718
$117$		0			0
$118$	−95.7782	−	95.7782i	−0.811679	−	0.811679i
$119$			21.9715i			0.184634i
$120$		0			0
$121$	90.2942			0.746233
$122$	−18.0852	+	18.0852i	−0.148239	+	0.148239i
$123$		0			0
$124$			60.2701i			0.486049i
$125$	118.605	+	39.4689i	0.948842	+	0.315751i
$126$		0			0
$127$	71.5886	−	71.5886i	0.563690	−	0.563690i	−0.366664	−	0.930353i	$-0.619500\pi$
$127$	71.5886	−	71.5886i	0.563690	−	0.563690i	0.930353	+	0.366664i	$0.119500\pi$
$128$	−31.7525	−	31.7525i	−0.248067	−	0.248067i
$129$		0			0
$130$	−19.9624	−	45.1230i	−0.153557	−	0.347100i
$131$	187.376			1.43035			0.715176	−	0.698945i	$-0.246347\pi$
$131$	187.376			1.43035			0.715176	+	0.698945i	$0.246347\pi$
$132$		0			0
$133$	−59.2499	−	59.2499i	−0.445488	−	0.445488i
$134$			107.505i			0.802279i
$135$		0			0
$136$	−69.6446			−0.512093
$137$	27.0279	−	27.0279i	0.197284	−	0.197284i	−0.601551	−	0.798835i	$-0.705450\pi$
$137$	27.0279	−	27.0279i	0.197284	−	0.197284i	0.798835	+	0.601551i	$0.205450\pi$
$138$		0			0
$139$			100.919i			0.726037i	0.931782	+	0.363018i	$0.118254\pi$
$139$			100.919i			0.726037i	−0.931782	+	0.363018i	$0.881746\pi$
$140$	−5.84071	+	15.1088i	−0.0417194	+	0.107920i
$141$		0			0
$142$	−53.9135	+	53.9135i	−0.379673	+	0.379673i
$143$	−60.4070	−	60.4070i	−0.422426	−	0.422426i
$144$		0			0
$145$	−7.98493	+	3.53253i	−0.0550685	+	0.0243623i
$146$	−218.630			−1.49747
$147$		0			0
$148$	3.29246	+	3.29246i	0.0222464	+	0.0222464i
$149$		−	48.9865i		−	0.328768i	−0.986396	−	0.164384i	$-0.947436\pi$
$149$		−	48.9865i		−	0.328768i	0.986396	−	0.164384i	$-0.0525637\pi$
$150$		0			0
$151$	102.200			0.676819			0.338409	−	0.940999i	$-0.390111\pi$
$151$	102.200			0.676819			0.338409	+	0.940999i	$0.390111\pi$
$152$	187.809	−	187.809i	1.23559	−	1.23559i
$153$		0			0
$154$		−	66.9819i		−	0.434947i
$155$	−103.276	−	233.445i	−0.666296	−	1.50609i
$156$		0			0
$157$	96.5973	−	96.5973i	0.615269	−	0.615269i	−0.329045	−	0.944314i	$-0.606727\pi$
$157$	96.5973	−	96.5973i	0.615269	−	0.615269i	0.944314	+	0.329045i	$0.106727\pi$
$158$	−38.6504	−	38.6504i	−0.244623	−	0.244623i
$159$		0			0
$160$	−84.8695	−	32.8087i	−0.530435	−	0.205054i
$161$	−62.0810			−0.385596
$162$		0			0
$163$	−150.604	−	150.604i	−0.923951	−	0.923951i	0.0733548	−	0.997306i	$-0.476629\pi$
$163$	−150.604	−	150.604i	−0.923951	−	0.923951i	−0.997306	+	0.0733548i	$0.976629\pi$
$164$		−	39.1029i		−	0.238432i
$165$		0			0
$166$	11.6251			0.0700308
$167$	−94.1465	+	94.1465i	−0.563752	+	0.563752i	−0.930371	−	0.366619i	$-0.880515\pi$
$167$	−94.1465	+	94.1465i	−0.563752	+	0.563752i	0.366619	+	0.930371i	$0.380515\pi$
$168$		0			0
$169$		−	134.460i		−	0.795624i
$170$	61.4709	−	27.1948i	0.361594	−	0.159969i
$171$		0			0
$172$	−33.0600	+	33.0600i	−0.192209	+	0.192209i
$173$	−103.567	−	103.567i	−0.598653	−	0.598653i	0.341301	−	0.939954i	$-0.389132\pi$
$173$	−103.567	−	103.567i	−0.598653	−	0.598653i	−0.939954	+	0.341301i	$0.889132\pi$
$174$		0			0
$175$	−3.26678	−	68.5293i	−0.0186673	−	0.391596i
$176$	143.678			0.816350
$177$		0			0
$178$	42.4929	+	42.4929i	0.238724	+	0.238724i
$179$			141.161i			0.788611i	0.918979	+	0.394305i	$0.129015\pi$
$179$			141.161i			0.788611i	−0.918979	+	0.394305i	$0.870985\pi$
$180$		0			0
$181$	182.292			1.00714			0.503568	−	0.863956i	$-0.332020\pi$
$181$	182.292			1.00714			0.503568	+	0.863956i	$0.332020\pi$
$182$	−19.1495	+	19.1495i	−0.105217	+	0.105217i
$183$		0			0
$184$		−	196.783i		−	1.06947i
$185$	−18.3945	−	7.11092i	−0.0994299	−	0.0384374i
$186$		0			0
$187$	82.2922	−	82.2922i	0.440065	−	0.440065i
$188$	−35.5630	−	35.5630i	−0.189165	−	0.189165i
$189$		0			0
$190$	−92.4317	+	239.103i	−0.486483	+	1.25843i
$191$	218.167			1.14224			0.571118	−	0.820868i	$-0.306510\pi$
$191$	218.167			1.14224			0.571118	+	0.820868i	$0.306510\pi$
$192$		0			0
$193$	155.557	+	155.557i	0.805996	+	0.805996i	0.984025	−	0.178030i	$-0.0569723\pi$
$193$	155.557	+	155.557i	0.805996	+	0.805996i	−0.178030	+	0.984025i	$0.556972\pi$
$194$			103.777i			0.534934i
$195$		0			0
$196$	−48.9549			−0.249770
$197$	−241.895	+	241.895i	−1.22789	+	1.22789i	−0.263133	+	0.964759i	$0.584756\pi$
$197$	−241.895	+	241.895i	−1.22789	+	1.22789i	−0.964759	+	0.263133i	$0.915244\pi$
$198$		0			0
$199$		−	126.744i		−	0.636904i	−0.947939	−	0.318452i	$-0.896837\pi$
$199$		−	126.744i		−	0.636904i	0.947939	−	0.318452i	$-0.103163\pi$
$200$	217.223	−	10.3550i	1.08611	−	0.0517748i
$201$		0			0
$202$	−129.627	+	129.627i	−0.641719	+	0.641719i
$203$	3.38867	+	3.38867i	0.0166930	+	0.0166930i
$204$		0			0
$205$	67.0048	+	151.458i	0.326853	+	0.738817i
$206$	196.922			0.955934
$207$		0			0
$208$	−41.0760	−	41.0760i	−0.197481	−	0.197481i
$209$			443.831i			2.12359i
$210$		0			0
$211$	−209.613			−0.993429			−0.496714	−	0.867914i	$-0.665460\pi$
$211$	−209.613			−0.993429			−0.496714	+	0.867914i	$0.665460\pi$
$212$	5.63170	−	5.63170i	0.0265646	−	0.0265646i
$213$		0			0
$214$		−	58.0374i		−	0.271203i
$215$	71.4015	−	184.701i	0.332100	−	0.859077i
$216$		0			0
$217$	−99.0700	+	99.0700i	−0.456544	+	0.456544i
$218$	45.7897	+	45.7897i	0.210045	+	0.210045i
$219$		0			0
$220$	78.4645	−	34.7127i	0.356657	−	0.157785i
$221$	−47.0531			−0.212910
$222$		0			0
$223$	202.625	+	202.625i	0.908630	+	0.908630i	0.996162	−	0.0875316i	$-0.0278979\pi$
$223$	202.625	+	202.625i	0.908630	+	0.908630i	−0.0875316	+	0.996162i	$0.527898\pi$
$224$			49.9407i			0.222949i
$225$		0			0
$226$	304.533			1.34749
$227$	−135.036	+	135.036i	−0.594871	+	0.594871i	−0.938943	−	0.344072i	$-0.888193\pi$
$227$	−135.036	+	135.036i	−0.594871	+	0.594871i	0.344072	+	0.938943i	$0.388193\pi$
$228$		0			0
$229$			299.260i			1.30681i	0.757008	+	0.653406i	$0.226661\pi$
$229$			299.260i			1.30681i	−0.757008	+	0.653406i	$0.773339\pi$
$230$	76.8396	+	173.688i	0.334085	+	0.755165i
$231$		0			0
$232$	−10.7413	+	10.7413i	−0.0462989	+	0.0462989i
$233$	−54.0196	−	54.0196i	−0.231844	−	0.231844i	0.581618	−	0.813462i	$-0.302420\pi$
$233$	−54.0196	−	54.0196i	−0.231844	−	0.231844i	−0.813462	+	0.581618i	$0.802420\pi$
$234$		0			0
$235$	198.685	+	76.8073i	0.845469	+	0.326840i
$236$	−95.2293			−0.403514
$237$		0			0
$238$	−26.0872	−	26.0872i	−0.109610	−	0.109610i
$239$		−	147.060i		−	0.615314i	−0.951497	−	0.307657i	$-0.900455\pi$
$239$		−	147.060i		−	0.615314i	0.951497	−	0.307657i	$-0.0995450\pi$
$240$		0			0
$241$	−389.900			−1.61784			−0.808921	−	0.587918i	$-0.799948\pi$
$241$	−389.900			−1.61784			−0.808921	+	0.587918i	$0.799948\pi$
$242$	−107.209	+	107.209i	−0.443010	+	0.443010i
$243$		0			0
$244$			17.9815i			0.0736948i
$245$	189.617	−	83.8868i	0.773949	−	0.342395i
$246$		0			0
$247$	126.887	−	126.887i	0.513712	−	0.513712i
$248$	−314.030	−	314.030i	−1.26625	−	1.26625i
$249$		0			0
$250$	−187.685	+	93.9605i	−0.750741	+	0.375842i
$251$	−239.421			−0.953870			−0.476935	−	0.878938i	$-0.658252\pi$
$251$	−239.421			−0.953870			−0.476935	+	0.878938i	$0.658252\pi$
$252$		0			0
$253$	232.519	+	232.519i	0.919047	+	0.919047i
$254$			169.998i			0.669282i
$255$		0			0
$256$	−204.975			−0.800685
$257$	−17.1180	+	17.1180i	−0.0666071	+	0.0666071i	−0.739626	−	0.673019i	$-0.764997\pi$
$257$	−17.1180	+	17.1180i	−0.0666071	+	0.0666071i	0.673019	+	0.739626i	$0.264997\pi$
$258$		0			0
$259$			10.8241i			0.0417919i
$260$	−32.3563	−	12.5082i	−0.124447	−	0.0481085i
$261$		0			0
$262$	−222.476	+	222.476i	−0.849146	+	0.849146i
$263$	−74.9185	−	74.9185i	−0.284861	−	0.284861i	0.550183	−	0.835044i	$-0.314558\pi$
$263$	−74.9185	−	74.9185i	−0.284861	−	0.284861i	−0.835044	+	0.550183i	$0.814558\pi$
$264$		0			0
$265$	−12.1631	+	31.4635i	−0.0458985	+	0.118730i
$266$	140.698			0.528939
$267$		0			0
$268$	53.4446	+	53.4446i	0.199420	+	0.199420i
$269$		−	33.3603i		−	0.124016i	−0.998076	−	0.0620079i	$-0.980250\pi$
$269$		−	33.3603i		−	0.124016i	0.998076	−	0.0620079i	$-0.0197504\pi$
$270$		0			0
$271$	−89.2173			−0.329215			−0.164608	−	0.986359i	$-0.552636\pi$
$271$	−89.2173			−0.329215			−0.164608	+	0.986359i	$0.552636\pi$
$272$	55.9577	−	55.9577i	0.205727	−	0.205727i
$273$		0			0
$274$			64.1817i			0.234240i
$275$	−244.435	+	268.906i	−0.888855	+	0.977840i
$276$		0			0
$277$	−67.3186	+	67.3186i	−0.243027	+	0.243027i	−0.818101	−	0.575074i	$-0.804973\pi$
$277$	−67.3186	+	67.3186i	−0.243027	+	0.243027i	0.575074	+	0.818101i	$0.304973\pi$
$278$	−119.824	−	119.824i	−0.431021	−	0.431021i
$279$		0			0
$280$	−48.2901	−	109.155i	−0.172465	−	0.389838i
$281$	−299.660			−1.06640			−0.533202	−	0.845988i	$-0.679012\pi$
$281$	−299.660			−1.06640			−0.533202	+	0.845988i	$0.679012\pi$
$282$		0			0
$283$	2.98477	+	2.98477i	0.0105469	+	0.0105469i	0.712361	−	0.701814i	$-0.247626\pi$
$283$	2.98477	+	2.98477i	0.0105469	+	0.0105469i	−0.701814	+	0.712361i	$0.747626\pi$
$284$			53.6046i			0.188749i
$285$		0			0
$286$	143.445			0.501557
$287$	64.2761	−	64.2761i	0.223958	−	0.223958i
$288$		0			0
$289$			224.900i			0.778200i
$290$	5.28644	−	13.6750i	0.0182291	−	0.0471551i
$291$		0			0
$292$	−108.689	+	108.689i	−0.372222	+	0.372222i
$293$	81.1381	+	81.1381i	0.276922	+	0.276922i	0.831879	−	0.554957i	$-0.187265\pi$
$293$	81.1381	+	81.1381i	0.276922	+	0.276922i	−0.554957	+	0.831879i	$0.687265\pi$
$294$		0			0
$295$	368.852	−	163.180i	1.25035	−	0.553154i
$296$	−34.3100			−0.115912
$297$		0			0
$298$	58.1629	+	58.1629i	0.195177	+	0.195177i
$299$		−	132.950i		−	0.444648i
$300$		0			0
$301$	−108.686			−0.361083
$302$	−121.344	+	121.344i	−0.401802	+	0.401802i
$303$		0			0
$304$			301.800i			0.992762i
$305$	−30.8123	−	69.6480i	−0.101024	−	0.228354i
$306$		0			0
$307$	−148.857	+	148.857i	−0.484876	+	0.484876i	−0.906685	−	0.421809i	$-0.861395\pi$
$307$	−148.857	+	148.857i	−0.484876	+	0.484876i	0.421809	+	0.906685i	$0.361395\pi$
$308$	−33.2990	−	33.2990i	−0.108114	−	0.108114i
$309$		0			0
$310$	399.796	+	154.552i	1.28967	+	0.498556i
$311$	34.8637			0.112102			0.0560510	−	0.998428i	$-0.482149\pi$
$311$	34.8637			0.112102			0.0560510	+	0.998428i	$0.482149\pi$
$312$		0			0
$313$	119.051	+	119.051i	0.380354	+	0.380354i	0.871230	−	0.490876i	$-0.163323\pi$
$313$	119.051	+	119.051i	0.380354	+	0.380354i	−0.490876	+	0.871230i	$0.663323\pi$
$314$			229.385i			0.730524i
$315$		0			0
$316$	−38.4289			−0.121610
$317$	109.319	−	109.319i	0.344853	−	0.344853i	−0.513335	−	0.858188i	$-0.671590\pi$
$317$	109.319	−	109.319i	0.344853	−	0.344853i	0.858188	+	0.513335i	$0.171590\pi$
$318$		0			0
$319$		−	25.3839i		−	0.0795735i
$320$	320.507	−	141.792i	1.00158	−	0.443101i
$321$		0			0
$322$	73.7103	−	73.7103i	0.228914	−	0.228914i
$323$	172.857	+	172.857i	0.535162	+	0.535162i
$324$		0			0
$325$	146.759	−	6.99598i	0.451567	−	0.0215261i
$326$	357.632			1.09703
$327$		0			0
$328$	203.741	+	203.741i	0.621161	+	0.621161i
$329$		−	116.915i		−	0.355363i
$330$		0			0
$331$	−149.254			−0.450920			−0.225460	−	0.974252i	$-0.572388\pi$
$331$	−149.254			−0.450920			−0.225460	+	0.974252i	$0.572388\pi$
$332$	5.77925	−	5.77925i	0.0174074	−	0.0174074i
$333$		0			0
$334$		−	223.565i		−	0.669356i
$335$	−298.588	−	115.427i	−0.891307	−	0.344559i
$336$		0			0
$337$	−48.5749	+	48.5749i	−0.144139	+	0.144139i	−0.775494	−	0.631355i	$-0.782499\pi$
$337$	−48.5749	+	48.5749i	−0.144139	+	0.144139i	0.631355	+	0.775494i	$0.282499\pi$
$338$	159.648	+	159.648i	0.472332	+	0.472332i
$339$		0			0
$340$	17.0399	−	44.0788i	0.0501173	−	0.129644i
$341$	742.116			2.17629
$342$		0			0
$343$	−175.555	−	175.555i	−0.511822	−	0.511822i
$344$		−	344.510i		−	1.00148i
$345$		0			0
$346$	245.935			0.710795
$347$	14.4128	−	14.4128i	0.0415356	−	0.0415356i	−0.686034	−	0.727570i	$-0.740650\pi$
$347$	14.4128	−	14.4128i	0.0415356	−	0.0415356i	0.727570	+	0.686034i	$0.240650\pi$
$348$		0			0
$349$			138.391i			0.396537i	0.980148	+	0.198268i	$0.0635318\pi$
$349$			138.391i			0.396537i	−0.980148	+	0.198268i	$0.936468\pi$
$350$	85.2452	+	77.4878i	0.243558	+	0.221394i
$351$		0			0
$352$	187.048	−	187.048i	0.531388	−	0.531388i
$353$	−16.5350	−	16.5350i	−0.0468412	−	0.0468412i	0.683298	−	0.730139i	$-0.260545\pi$
$353$	−16.5350	−	16.5350i	−0.0468412	−	0.0468412i	−0.730139	+	0.683298i	$0.760545\pi$
$354$		0			0
$355$	−91.8543	−	207.627i	−0.258744	−	0.584865i
$356$	42.2494			0.118678
$357$		0			0
$358$	−167.604	−	167.604i	−0.468168	−	0.468168i
$359$		−	401.663i		−	1.11884i	−0.828885	−	0.559419i	$-0.811024\pi$
$359$		−	401.663i		−	1.11884i	0.828885	−	0.559419i	$-0.188976\pi$
$360$		0			0
$361$	−571.281			−1.58250
$362$	−216.439	+	216.439i	−0.597899	+	0.597899i
$363$		0			0
$364$			19.0397i			0.0523070i
$365$	234.741	−	607.229i	0.643127	−	1.66364i
$366$		0			0
$367$	−444.467	+	444.467i	−1.21108	+	1.21108i	−0.240410	+	0.970672i	$0.577282\pi$
$367$	−444.467	+	444.467i	−1.21108	+	1.21108i	−0.970672	+	0.240410i	$0.922718\pi$
$368$	158.110	+	158.110i	0.429647	+	0.429647i
$369$		0			0
$370$	30.2832	−	13.3973i	0.0818466	−	0.0362090i
$371$	18.5144			0.0499041
$372$		0			0
$373$	264.172	+	264.172i	0.708235	+	0.708235i	0.966164	−	0.257929i	$-0.0830401\pi$
$373$	264.172	+	264.172i	0.708235	+	0.708235i	−0.257929	+	0.966164i	$0.583040\pi$
$374$			195.415i			0.522500i
$375$		0			0
$376$	370.593			0.985620
$377$	−7.25702	+	7.25702i	−0.0192494	+	0.0192494i
$378$		0			0
$379$		−	223.796i		−	0.590491i	−0.955421	−	0.295246i	$-0.904599\pi$
$379$		−	223.796i		−	0.590491i	0.955421	−	0.295246i	$-0.0954015\pi$
$380$	72.9152	+	164.817i	0.191882	+	0.433730i
$381$		0			0
$382$	−259.035	+	259.035i	−0.678103	+	0.678103i
$383$	−25.1535	−	25.1535i	−0.0656750	−	0.0656750i	0.673506	−	0.739181i	$-0.264787\pi$
$383$	−25.1535	−	25.1535i	−0.0656750	−	0.0656750i	−0.739181	+	0.673506i	$0.764787\pi$
$384$		0			0
$385$	186.037	+	71.9178i	0.483213	+	0.186799i
$386$	−369.394			−0.956978
$387$		0			0
$388$	51.5913	+	51.5913i	0.132967	+	0.132967i
$389$		−	208.194i		−	0.535204i	−0.963530	−	0.267602i	$-0.913769\pi$
$389$		−	208.194i		−	0.535204i	0.963530	−	0.267602i	$-0.0862312\pi$
$390$		0			0
$391$	181.117			0.463215
$392$	255.074	−	255.074i	0.650698	−	0.650698i
$393$		0			0
$394$		−	574.416i		−	1.45791i
$395$	148.847	−	65.8499i	0.376828	−	0.166709i
$396$		0			0
$397$	231.955	−	231.955i	0.584269	−	0.584269i	−0.351805	−	0.936073i	$-0.614432\pi$
$397$	231.955	−	231.955i	0.584269	−	0.584269i	0.936073	+	0.351805i	$0.114432\pi$
$398$	150.486	+	150.486i	0.378106	+	0.378106i
$399$		0			0
$400$	−166.213	+	182.853i	−0.415533	+	0.457132i
$401$	−94.0606			−0.234565			−0.117283	−	0.993099i	$-0.537418\pi$
$401$	−94.0606			−0.234565			−0.117283	+	0.993099i	$0.537418\pi$
$402$		0			0
$403$	−212.164	−	212.164i	−0.526461	−	0.526461i
$404$			128.884i			0.319021i
$405$		0			0
$406$	−8.04691			−0.0198200
$407$	40.5407	−	40.5407i	0.0996086	−	0.0996086i
$408$		0			0
$409$		−	682.148i		−	1.66784i	−0.551883	−	0.833922i	$-0.686090\pi$
$409$		−	682.148i		−	1.66784i	0.551883	−	0.833922i	$-0.313910\pi$
$410$	−259.386	−	100.273i	−0.632648	−	0.244568i
$411$		0			0
$412$	97.8970	−	97.8970i	0.237614	−	0.237614i
$413$	−156.535	−	156.535i	−0.379019	−	0.379019i
$414$		0			0
$415$	−12.4818	+	32.2878i	−0.0300765	+	0.0778020i
$416$	−106.951			−0.257093
$417$		0			0
$418$	−526.971	−	526.971i	−1.26070	−	1.26070i
$419$			209.749i			0.500595i	0.968169	+	0.250298i	$0.0805285\pi$
$419$			209.749i			0.500595i	−0.968169	+	0.250298i	$0.919472\pi$
$420$		0			0
$421$	−5.89649			−0.0140059			−0.00700296	−	0.999975i	$-0.502229\pi$
$421$	−5.89649			−0.0140059			−0.00700296	+	0.999975i	$0.502229\pi$
$422$	248.879	−	248.879i	0.589761	−	0.589761i
$423$		0			0
$424$			58.6866i			0.138412i
$425$	9.53059	+	199.929i	0.0224249	+	0.470422i
$426$		0			0
$427$	−29.5575	+	29.5575i	−0.0692212	+	0.0692212i
$428$	−28.8524	−	28.8524i	−0.0674122	−	0.0674122i
$429$		0			0
$430$	134.524	+	304.077i	0.312846	+	0.707157i
$431$	−623.625			−1.44693			−0.723463	−	0.690364i	$-0.757451\pi$
$431$	−623.625			−1.44693			−0.723463	+	0.690364i	$0.757451\pi$
$432$		0			0
$433$	342.585	+	342.585i	0.791190	+	0.791190i	0.981688	−	0.190497i	$-0.0610100\pi$
$433$	342.585	+	342.585i	0.791190	+	0.791190i	−0.190497	+	0.981688i	$0.561010\pi$
$434$		−	235.256i		−	0.542066i
$435$		0			0
$436$	45.5274			0.104421
$437$	−488.414	+	488.414i	−1.11765	+	1.11765i
$438$		0			0
$439$		−	470.070i		−	1.07077i	−0.844607	−	0.535387i	$-0.820166\pi$
$439$		−	470.070i		−	1.07077i	0.844607	−	0.535387i	$-0.179834\pi$
$440$	−227.963	+	589.696i	−0.518098	+	1.34022i
$441$		0			0
$442$	55.8673	−	55.8673i	0.126397	−	0.126397i
$443$	113.854	+	113.854i	0.257007	+	0.257007i	0.823836	−	0.566829i	$-0.191830\pi$
$443$	113.854	+	113.854i	0.257007	+	0.257007i	−0.566829	+	0.823836i	$0.691830\pi$
$444$		0			0
$445$	−163.645	+	72.3965i	−0.367741	+	0.162689i
$446$	−481.162			−1.07884
$447$		0			0
$448$	−136.018	−	136.018i	−0.303611	−	0.303611i
$449$		−	540.377i		−	1.20351i	−0.798680	−	0.601756i	$-0.794468\pi$
$449$		−	540.377i		−	1.20351i	0.798680	−	0.601756i	$-0.205532\pi$
$450$		0			0
$451$	−481.481			−1.06759
$452$	151.394	−	151.394i	0.334943	−	0.334943i
$453$		0			0
$454$		−	320.662i		−	0.706305i
$455$	−32.6256	−	73.7468i	−0.0717046	−	0.162081i
$456$		0			0
$457$	−91.8236	+	91.8236i	−0.200927	+	0.200927i	−0.800397	−	0.599470i	$-0.795378\pi$
$457$	−91.8236	+	91.8236i	−0.200927	+	0.200927i	0.599470	+	0.800397i	$0.295378\pi$
$458$	−355.319	−	355.319i	−0.775805	−	0.775805i
$459$		0			0
$460$	124.546	+	48.1467i	0.270752	+	0.104667i
$461$	767.971			1.66588			0.832941	−	0.553362i	$-0.186656\pi$
$461$	767.971			1.66588			0.832941	+	0.553362i	$0.186656\pi$
$462$		0			0
$463$	−390.218	−	390.218i	−0.842803	−	0.842803i	0.146420	−	0.989223i	$-0.453225\pi$
$463$	−390.218	−	390.218i	−0.842803	−	0.842803i	−0.989223	+	0.146420i	$0.953225\pi$
$464$		−	17.2608i		−	0.0372000i
$465$		0			0
$466$	128.278			0.275274
$467$	−118.969	+	118.969i	−0.254752	+	0.254752i	−0.822916	−	0.568163i	$-0.807654\pi$
$467$	−118.969	+	118.969i	−0.254752	+	0.254752i	0.568163	+	0.822916i	$0.307654\pi$
$468$		0			0
$469$			175.701i			0.374629i
$470$	−327.099	+	144.709i	−0.695956	+	0.307891i
$471$		0			0
$472$	496.181	−	496.181i	1.05123	−	1.05123i
$473$	407.073	+	407.073i	0.860620	+	0.860620i
$474$		0			0
$475$	−564.846	−	513.444i	−1.18915	−	1.08093i
$476$	−25.9378			−0.0544911
$477$		0			0
$478$	174.608	+	174.608i	0.365289	+	0.365289i
$479$			308.304i			0.643641i	0.946801	+	0.321820i	$0.104295\pi$
$479$			308.304i			0.643641i	−0.946801	+	0.321820i	$0.895705\pi$
$480$		0			0
$481$	−23.1804			−0.0481921
$482$	462.938	−	462.938i	0.960451	−	0.960451i
$483$		0			0
$484$			106.594i			0.220236i
$485$	−288.233	−	111.425i	−0.594295	−	0.229741i
$486$		0			0
$487$	337.366	−	337.366i	0.692744	−	0.692744i	−0.270091	−	0.962835i	$-0.587054\pi$
$487$	337.366	−	337.366i	0.692744	−	0.692744i	0.962835	+	0.270091i	$0.0870538\pi$
$488$	−93.6905	−	93.6905i	−0.191989	−	0.191989i
$489$		0			0
$490$	−125.537	+	324.738i	−0.256197	+	0.662731i
$491$	−114.904			−0.234021			−0.117011	−	0.993131i	$-0.537331\pi$
$491$	−114.904			−0.234021			−0.117011	+	0.993131i	$0.537331\pi$
$492$		0			0
$493$	−9.88622	−	9.88622i	−0.0200532	−	0.0200532i
$494$			301.312i			0.609943i
$495$		0			0
$496$	504.630			1.01740
$497$	−88.1135	+	88.1135i	−0.177291	+	0.177291i
$498$		0			0
$499$		−	423.796i		−	0.849290i	−0.905360	−	0.424645i	$-0.860399\pi$
$499$		−	423.796i		−	0.849290i	0.905360	−	0.424645i	$-0.139601\pi$
$500$	−46.5939	+	140.016i	−0.0931878	+	0.280032i
$501$		0			0
$502$	284.271	−	284.271i	0.566277	−	0.566277i
$503$	429.215	+	429.215i	0.853309	+	0.853309i	0.990539	−	0.137230i	$-0.0438199\pi$
$503$	429.215	+	429.215i	0.853309	+	0.853309i	−0.137230	+	0.990539i	$0.543820\pi$
$504$		0			0
$505$	−220.850	−	499.209i	−0.437327	−	0.988533i
$506$	−552.151			−1.09121
$507$		0			0
$508$	84.5118	+	84.5118i	0.166362	+	0.166362i
$509$			294.127i			0.577853i	0.957351	+	0.288926i	$0.0932983\pi$
$509$			294.127i			0.577853i	−0.957351	+	0.288926i	$0.906702\pi$
$510$		0			0
$511$	−357.318			−0.699253
$512$	370.382	−	370.382i	0.723403	−	0.723403i
$513$		0			0
$514$		−	40.6493i		−	0.0790843i
$515$	−211.434	+	546.937i	−0.410551	+	1.06201i
$516$		0			0
$517$	−437.893	+	437.893i	−0.846989	+	0.846989i
$518$	−12.8517	−	12.8517i	−0.0248103	−	0.0248103i
$519$		0			0
$520$	233.761	−	103.416i	0.449540	−	0.198877i
$521$	659.361			1.26557			0.632784	−	0.774328i	$-0.281912\pi$
$521$	659.361			1.26557			0.632784	+	0.774328i	$0.281912\pi$
$522$		0			0
$523$	−179.405	−	179.405i	−0.343031	−	0.343031i	0.514475	−	0.857506i	$-0.327987\pi$
$523$	−179.405	−	179.405i	−0.343031	−	0.343031i	−0.857506	+	0.514475i	$0.827987\pi$
$524$			221.201i			0.422140i
$525$		0			0
$526$	177.905			0.338223
$527$	289.030	−	289.030i	0.548444	−	0.548444i
$528$		0			0
$529$		−	17.2485i		−	0.0326059i
$530$	−22.9159	−	51.7990i	−0.0432375	−	0.0977339i
$531$		0			0
$532$	69.9457	−	69.9457i	0.131477	−	0.131477i
$533$	137.651	+	137.651i	0.258256	+	0.258256i
$534$		0			0
$535$	161.194	+	62.3142i	0.301298	+	0.116475i
$536$	−556.934			−1.03906
$537$		0			0
$538$	39.6095	+	39.6095i	0.0736235	+	0.0736235i
$539$			602.790i			1.11835i
$540$		0			0
$541$	−423.058			−0.781992			−0.390996	−	0.920392i	$-0.627869\pi$
$541$	−423.058			−0.781992			−0.390996	+	0.920392i	$0.627869\pi$
$542$	105.930	−	105.930i	0.195443	−	0.195443i
$543$		0			0
$544$		−	145.699i		−	0.267828i
$545$	−176.341	+	78.0135i	−0.323562	+	0.143144i
$546$		0			0
$547$	343.688	−	343.688i	0.628315	−	0.628315i	−0.319329	−	0.947644i	$-0.603457\pi$
$547$	343.688	−	343.688i	0.628315	−	0.628315i	0.947644	+	0.319329i	$0.103457\pi$
$548$	31.9070	+	31.9070i	0.0582244	+	0.0582244i
$549$		0			0
$550$	−29.0548	−	609.502i	−0.0528270	−	1.10819i
$551$	53.3198			0.0967692
$552$		0			0
$553$	−63.1682	−	63.1682i	−0.114228	−	0.114228i
$554$		−	159.858i		−	0.288552i
$555$		0			0
$556$	−119.137			−0.214275
$557$	−771.430	+	771.430i	−1.38497	+	1.38497i	−0.549440	+	0.835533i	$0.685159\pi$
$557$	−771.430	+	771.430i	−1.38497	+	1.38497i	−0.835533	+	0.549440i	$0.814841\pi$
$558$		0			0
$559$		−	232.757i		−	0.416380i
$560$	126.503	+	48.9033i	0.225898	+	0.0873272i
$561$		0			0
$562$	355.793	−	355.793i	0.633084	−	0.633084i
$563$	269.750	+	269.750i	0.479130	+	0.479130i	0.904853	−	0.425723i	$-0.139980\pi$
$563$	269.750	+	269.750i	0.479130	+	0.479130i	−0.425723	+	0.904853i	$0.639980\pi$
$564$		0			0
$565$	−326.974	+	845.818i	−0.578716	+	1.49702i
$566$	−7.08778			−0.0125226
$567$		0			0
$568$	−279.300	−	279.300i	−0.491726	−	0.491726i
$569$		−	538.867i		−	0.947042i	−0.880783	−	0.473521i	$-0.842983\pi$
$569$		−	538.867i		−	0.947042i	0.880783	−	0.473521i	$-0.157017\pi$
$570$		0			0
$571$	298.401			0.522593			0.261296	−	0.965259i	$-0.415850\pi$
$571$	298.401			0.522593			0.261296	+	0.965259i	$0.415850\pi$
$572$	71.3117	−	71.3117i	0.124671	−	0.124671i
$573$		0			0
$574$			152.633i			0.265911i
$575$	−564.907	+	26.9290i	−0.982446	+	0.0468330i
$576$		0			0
$577$	−616.326	+	616.326i	−1.06816	+	1.06816i	−0.0706547	+	0.997501i	$0.522509\pi$
$577$	−616.326	+	616.326i	−1.06816	+	1.06816i	−0.997501	+	0.0706547i	$0.977491\pi$
$578$	−267.029	−	267.029i	−0.461988	−	0.461988i
$579$		0			0
$580$	−4.17023	−	9.42637i	−0.00719005	−	0.0162524i
$581$	18.9995			0.0327013
$582$		0			0
$583$	−69.3441	−	69.3441i	−0.118944	−	0.118944i
$584$		−	1132.62i		−	1.93942i
$585$		0			0
$586$	−192.675			−0.328796
$587$	−47.0108	+	47.0108i	−0.0800866	+	0.0800866i	−0.746015	−	0.665929i	$-0.768035\pi$
$587$	−47.0108	+	47.0108i	−0.0800866	+	0.0800866i	0.665929	+	0.746015i	$0.268035\pi$
$588$		0			0
$589$			1558.84i			2.64659i
$590$	−244.200	+	631.696i	−0.413897	+	1.07067i
$591$		0			0
$592$	27.5672	−	27.5672i	0.0465662	−	0.0465662i
$593$	687.903	+	687.903i	1.16004	+	1.16004i	0.984467	+	0.175572i	$0.0561776\pi$
$593$	687.903	+	687.903i	1.16004	+	1.16004i	0.175572	+	0.984467i	$0.443822\pi$
$594$		0			0
$595$	100.465	−	44.4457i	0.168849	−	0.0746987i
$596$	57.8296			0.0970295
$597$		0			0
$598$	157.855	+	157.855i	0.263971	+	0.263971i
$599$		−	758.685i		−	1.26659i	−0.773912	−	0.633293i	$-0.781703\pi$
$599$		−	758.685i		−	1.26659i	0.773912	−	0.633293i	$-0.218297\pi$
$600$		0			0
$601$	1013.35			1.68611			0.843057	−	0.537825i	$-0.180754\pi$
$601$	1013.35			1.68611			0.843057	+	0.537825i	$0.180754\pi$
$602$	129.045	−	129.045i	0.214361	−	0.214361i
$603$		0			0
$604$			120.649i			0.199750i
$605$	−182.655	−	412.872i	−0.301909	−	0.682433i
$606$		0			0
$607$	−21.3419	+	21.3419i	−0.0351597	+	0.0351597i	−0.724468	−	0.689308i	$-0.757915\pi$
$607$	−21.3419	+	21.3419i	−0.0351597	+	0.0351597i	0.689308	+	0.724468i	$0.257915\pi$
$608$	392.902	+	392.902i	0.646220	+	0.646220i
$609$		0			0
$610$	119.279	+	46.1106i	0.195539	+	0.0755911i
$611$	250.379			0.409785
$612$		0			0
$613$	−280.031	−	280.031i	−0.456820	−	0.456820i	0.440790	−	0.897610i	$-0.354698\pi$
$613$	−280.031	−	280.031i	−0.456820	−	0.456820i	−0.897610	+	0.440790i	$0.854698\pi$
$614$		−	353.483i		−	0.575705i
$615$		0			0
$616$	347.001			0.563313
$617$	376.272	−	376.272i	0.609841	−	0.609841i	−0.333064	−	0.942904i	$-0.608082\pi$
$617$	376.272	−	376.272i	0.609841	−	0.609841i	0.942904	+	0.333064i	$0.108082\pi$
$618$		0			0
$619$			291.842i			0.471473i	0.971817	+	0.235736i	$0.0757502\pi$
$619$			291.842i			0.471473i	−0.971817	+	0.235736i	$0.924250\pi$
$620$	275.586	−	121.919i	0.444494	−	0.196644i
$621$		0			0
$622$	−41.3945	+	41.3945i	−0.0665507	+	0.0665507i
$623$	69.4481	+	69.4481i	0.111474	+	0.111474i
$624$		0			0
$625$	−59.4521	−	622.166i	−0.0951234	−	0.995465i
$626$	−282.704			−0.451603
$627$		0			0
$628$	114.035	+	114.035i	0.181585	+	0.181585i
$629$		−	31.5785i		−	0.0502044i
$630$		0			0
$631$	872.307			1.38242			0.691210	−	0.722654i	$-0.257078\pi$
$631$	872.307			1.38242			0.691210	+	0.722654i	$0.257078\pi$
$632$	200.229	−	200.229i	0.316818	−	0.316818i
$633$		0			0
$634$			259.593i			0.409453i
$635$	−472.156	−	182.525i	−0.743552	−	0.287441i
$636$		0			0
$637$	172.332	−	172.332i	0.270537	−	0.270537i
$638$	30.1390	+	30.1390i	0.0472398	+	0.0472398i
$639$		0			0
$640$	−80.9574	+	209.421i	−0.126496	+	0.327220i
$641$	−1017.59			−1.58751			−0.793754	−	0.608239i	$-0.791876\pi$
$641$	−1017.59			−1.58751			−0.793754	+	0.608239i	$0.791876\pi$
$642$		0			0
$643$	−224.082	−	224.082i	−0.348494	−	0.348494i	0.511055	−	0.859548i	$-0.329255\pi$
$643$	−224.082	−	224.082i	−0.348494	−	0.348494i	−0.859548	+	0.511055i	$0.829255\pi$
$644$		−	73.2879i		−	0.113801i
$645$		0			0
$646$	−410.476			−0.635412
$647$	638.406	−	638.406i	0.986717	−	0.986717i	−0.0131963	−	0.999913i	$-0.504201\pi$
$647$	638.406	−	638.406i	0.986717	−	0.986717i	0.999913	+	0.0131963i	$0.00420064\pi$
$648$		0			0
$649$			1172.58i			1.80674i
$650$	−165.944	+	182.557i	−0.255299	+	0.280857i
$651$		0			0
$652$	177.791	−	177.791i	0.272686	−	0.272686i
$653$	460.726	+	460.726i	0.705552	+	0.705552i	0.965597	−	0.260044i	$-0.0837371\pi$
$653$	460.726	+	460.726i	0.705552	+	0.705552i	−0.260044	+	0.965597i	$0.583737\pi$
$654$		0			0
$655$	−379.040	−	856.781i	−0.578687	−	1.30806i
$656$	−327.401			−0.499088
$657$		0			0
$658$	138.815	+	138.815i	0.210966	+	0.210966i
$659$		−	501.894i		−	0.761600i	−0.924658	−	0.380800i	$-0.875649\pi$
$659$		−	501.894i		−	0.761600i	0.924658	−	0.380800i	$-0.124351\pi$
$660$		0			0
$661$	−968.928			−1.46585			−0.732926	−	0.680308i	$-0.761846\pi$
$661$	−968.928			−1.46585			−0.732926	+	0.680308i	$0.761846\pi$
$662$	177.213	−	177.213i	0.267694	−	0.267694i
$663$		0			0
$664$			60.2241i			0.0906990i
$665$	−151.066	+	390.777i	−0.227166	+	0.587634i
$666$		0			0
$667$	27.9338	−	27.9338i	0.0418798	−	0.0418798i
$668$	−111.142	−	111.142i	−0.166380	−	0.166380i
$669$		0			0
$670$	491.570	−	217.471i	0.733687	−	0.324583i
$671$	221.410			0.329970
$672$		0			0
$673$	285.971	+	285.971i	0.424919	+	0.424919i	0.886893	−	0.461974i	$-0.152859\pi$
$673$	285.971	+	285.971i	0.424919	+	0.424919i	−0.461974	+	0.886893i	$0.652859\pi$
$674$		−	115.348i		−	0.171140i
$675$		0			0
$676$	158.733			0.234813
$677$	−89.6227	+	89.6227i	−0.132382	+	0.132382i	−0.770193	−	0.637811i	$-0.779840\pi$
$677$	−89.6227	+	89.6227i	−0.132382	+	0.132382i	0.637811	+	0.770193i	$0.279840\pi$
$678$		0			0
$679$			169.608i			0.249791i
$680$	140.883	+	318.451i	0.207181	+	0.468311i
$681$		0			0
$682$	−881.133	+	881.133i	−1.29198	+	1.29198i
$683$	−227.456	−	227.456i	−0.333025	−	0.333025i	0.520709	−	0.853734i	$-0.325668\pi$
$683$	−227.456	−	227.456i	−0.333025	−	0.333025i	−0.853734	+	0.520709i	$0.825668\pi$
$684$		0			0
$685$	−178.260	−	68.9112i	−0.260233	−	0.100600i
$686$	416.882			0.607699
$687$		0			0
$688$	276.805	+	276.805i	0.402333	+	0.402333i
$689$			39.6496i			0.0575466i
$690$		0			0
$691$	−1029.07			−1.48925			−0.744626	−	0.667482i	$-0.767372\pi$
$691$	−1029.07			−1.48925			−0.744626	+	0.667482i	$0.767372\pi$
$692$	122.263	−	122.263i	0.176681	−	0.176681i
$693$		0			0
$694$			34.2254i			0.0493162i
$695$	461.455	−	204.148i	0.663964	−	0.293738i
$696$		0			0
$697$	−187.521	+	187.521i	−0.269040	+	0.269040i
$698$	−164.316	−	164.316i	−0.235409	−	0.235409i
$699$		0			0
$700$	80.9002	−	3.85650i	0.115572	−	0.00550928i
$701$	−921.196			−1.31412			−0.657058	−	0.753840i	$-0.728200\pi$
$701$	−921.196			−1.31412			−0.657058	+	0.753840i	$0.728200\pi$
$702$		0			0
$703$	85.1571	+	85.1571i	0.121134	+	0.121134i
$704$			1018.89i			1.44728i
$705$		0			0
$706$	39.2647			0.0556158
$707$	−211.856	+	211.856i	−0.299655	+	0.299655i
$708$		0			0
$709$			1034.64i			1.45929i	0.683827	+	0.729645i	$0.260314\pi$
$709$			1034.64i			1.45929i	−0.683827	+	0.729645i	$0.739686\pi$
$710$	355.582	+	137.460i	0.500819	+	0.193606i
$711$		0			0
$712$	−220.135	+	220.135i	−0.309179	+	0.309179i
$713$	816.663	+	816.663i	1.14539	+	1.14539i
$714$		0			0
$715$	−154.016	+	398.408i	−0.215407	+	0.557214i
$716$	−166.644			−0.232743
$717$		0			0
$718$	476.904	+	476.904i	0.664211	+	0.664211i
$719$			111.687i			0.155336i	0.996979	+	0.0776681i	$0.0247475\pi$
$719$			111.687i			0.155336i	−0.996979	+	0.0776681i	$0.975253\pi$
$720$		0			0
$721$	321.840			0.446380
$722$	678.296	−	678.296i	0.939468	−	0.939468i
$723$		0			0
$724$			215.199i			0.297236i
$725$	32.3052	+	29.3653i	0.0445588	+	0.0405039i
$726$		0			0
$727$	970.969	−	970.969i	1.33558	−	1.33558i	0.435295	−	0.900288i	$-0.356644\pi$
$727$	970.969	−	970.969i	1.33558	−	1.33558i	0.900288	−	0.435295i	$-0.143356\pi$
$728$	−99.2042	−	99.2042i	−0.136270	−	0.136270i
$729$		0			0
$730$	442.264	+	999.692i	0.605841	+	1.36944i
$731$	317.084			0.433767
$732$		0			0
$733$	271.116	+	271.116i	0.369872	+	0.369872i	0.867431	−	0.497558i	$-0.165770\pi$
$733$	271.116	+	271.116i	0.369872	+	0.369872i	−0.497558	+	0.867431i	$0.665770\pi$
$734$		−	1055.45i		−	1.43795i
$735$		0			0
$736$	411.675			0.559342
$737$	658.073	−	658.073i	0.892908	−	0.892908i
$738$		0			0
$739$			108.074i			0.146243i	0.997323	+	0.0731215i	$0.0232961\pi$
$739$			108.074i			0.146243i	−0.997323	+	0.0731215i	$0.976704\pi$
$740$	8.39459	−	21.7151i	0.0113440	−	0.0293448i
$741$		0			0
$742$	−21.9826	+	21.9826i	−0.0296262	+	0.0296262i
$743$	−801.778	−	801.778i	−1.07911	−	1.07911i	−0.996589	−	0.0825189i	$-0.973704\pi$
$743$	−801.778	−	801.778i	−1.07911	−	1.07911i	−0.0825189	−	0.996589i	$-0.526296\pi$
$744$		0			0
$745$	−223.992	+	99.0940i	−0.300660	+	0.133012i
$746$	−627.315			−0.840905
$747$		0			0
$748$	97.1476	+	97.1476i	0.129876	+	0.129876i
$749$		−	94.8534i		−	0.126640i
$750$		0			0
$751$	−247.816			−0.329982			−0.164991	−	0.986295i	$-0.552759\pi$
$751$	−247.816			−0.329982			−0.164991	+	0.986295i	$0.552759\pi$
$752$	−297.762	+	297.762i	−0.395961	+	0.395961i
$753$		0			0
$754$		−	17.2329i		−	0.0228553i
$755$	−206.738	−	467.310i	−0.273825	−	0.618954i
$756$		0			0
$757$	794.781	−	794.781i	1.04991	−	1.04991i	0.0512222	−	0.998687i	$-0.483688\pi$
$757$	794.781	−	794.781i	1.04991	−	1.04991i	0.998687	−	0.0512222i	$-0.0163117\pi$
$758$	265.719	+	265.719i	0.350552	+	0.350552i
$759$		0			0
$760$	−1238.68	−	478.845i	−1.62984	−	0.630059i
$761$	1470.22			1.93196			0.965980	−	0.258617i	$-0.0832666\pi$
$761$	1470.22			1.93196			0.965980	+	0.258617i	$0.0832666\pi$
$762$		0			0
$763$	74.8364	+	74.8364i	0.0980818	+	0.0980818i
$764$			257.551i			0.337109i
$765$		0			0
$766$	59.7308			0.0779776
$767$	335.228	−	335.228i	0.437064	−	0.437064i
$768$		0			0
$769$			381.177i			0.495679i	0.968801	+	0.247840i	$0.0797206\pi$
$769$			381.177i			0.495679i	−0.968801	+	0.247840i	$0.920279\pi$
$770$	−306.276	+	135.497i	−0.397761	+	0.175970i
$771$		0			0
$772$	−183.638	+	183.638i	−0.237874	+	0.237874i
$773$	−325.772	−	325.772i	−0.421438	−	0.421438i	0.464260	−	0.885699i	$-0.346320\pi$
$773$	−325.772	−	325.772i	−0.421438	−	0.421438i	−0.885699	+	0.464260i	$0.846320\pi$
$774$		0			0
$775$	−858.515	+	944.462i	−1.10776	+	1.21866i
$776$	−537.620			−0.692809
$777$		0			0
$778$	247.194	+	247.194i	0.317730	+	0.317730i
$779$		−	1011.37i		−	1.29829i
$780$		0			0
$781$	660.043			0.845125
$782$	−215.045	+	215.045i	−0.274993	+	0.274993i
$783$		0			0
$784$			409.891i			0.522820i
$785$	−637.098	−	246.288i	−0.811590	−	0.313743i
$786$		0			0
$787$	−247.695	+	247.695i	−0.314733	+	0.314733i	−0.846740	−	0.532007i	$-0.821438\pi$
$787$	−247.695	+	247.695i	−0.314733	+	0.314733i	0.532007	+	0.846740i	$0.321438\pi$
$788$	−285.562	−	285.562i	−0.362388	−	0.362388i
$789$		0			0
$790$	−98.5444	+	254.915i	−0.124740	+	0.322677i
$791$	497.714			0.629221
$792$		0			0
$793$	−63.2989	−	63.2989i	−0.0798220	−	0.0798220i
$794$			550.811i			0.693717i
$795$		0			0
$796$	149.624			0.187970
$797$	−88.6624	+	88.6624i	−0.111245	+	0.111245i	−0.760538	−	0.649293i	$-0.775065\pi$
$797$	−88.6624	+	88.6624i	−0.111245	+	0.111245i	0.649293	+	0.760538i	$0.275065\pi$
$798$		0			0
$799$			341.090i			0.426896i
$800$	21.6629	+	454.436i	0.0270786	+	0.568045i
$801$		0			0
$802$	111.680	−	111.680i	0.139252	−	0.139252i
$803$	1338.30	+	1338.30i	1.66663	+	1.66663i
$804$		0			0
$805$	125.583	+	283.867i	0.156003	+	0.352629i
$806$	503.815			0.625080
$807$		0			0
$808$	−671.537	−	671.537i	−0.831110	−	0.831110i
$809$		−	717.779i		−	0.887242i	−0.896214	−	0.443621i	$-0.853694\pi$
$809$		−	717.779i		−	0.887242i	0.896214	−	0.443621i	$-0.146306\pi$
$810$		0			0
$811$	771.312			0.951063			0.475532	−	0.879699i	$-0.342256\pi$
$811$	771.312			0.951063			0.475532	+	0.879699i	$0.342256\pi$
$812$	−4.00040	+	4.00040i	−0.00492660	+	0.00492660i
$813$		0			0
$814$			96.2699i			0.118268i
$815$	−383.986	+	993.294i	−0.471148	+	1.21877i
$816$		0			0
$817$	−855.071	+	855.071i	−1.04660	+	1.04660i
$818$	809.931	+	809.931i	0.990136	+	0.990136i
$819$		0			0
$820$	−178.799	+	79.1006i	−0.218047	+	0.0964641i
$821$	−607.334			−0.739749			−0.369874	−	0.929082i	$-0.620599\pi$
$821$	−607.334			−0.739749			−0.369874	+	0.929082i	$0.620599\pi$
$822$		0			0
$823$	386.961	+	386.961i	0.470184	+	0.470184i	0.901974	−	0.431790i	$-0.142118\pi$
$823$	386.961	+	386.961i	0.470184	+	0.470184i	−0.431790	+	0.901974i	$0.642118\pi$
$824$			1020.16i			1.23806i
$825$		0			0
$826$	371.715			0.450019
$827$	−54.4673	+	54.4673i	−0.0658613	+	0.0658613i	−0.739270	−	0.673409i	$-0.764829\pi$
$827$	−54.4673	+	54.4673i	−0.0658613	+	0.0658613i	0.673409	+	0.739270i	$0.264829\pi$
$828$		0			0
$829$		−	533.549i		−	0.643605i	−0.946807	−	0.321803i	$-0.895711\pi$
$829$		−	533.549i		−	0.643605i	0.946807	−	0.321803i	$-0.104289\pi$
$830$	−23.5162	−	53.1560i	−0.0283328	−	0.0640434i
$831$		0			0
$832$	291.289	−	291.289i	0.350107	−	0.350107i
$833$	234.767	+	234.767i	0.281833	+	0.281833i
$834$		0			0
$835$	620.934	+	240.039i	0.743634	+	0.287472i
$836$	−523.951			−0.626736
$837$		0			0
$838$	−249.041	−	249.041i	−0.297185	−	0.297185i
$839$		−	1523.91i		−	1.81635i	−0.418594	−	0.908173i	$-0.637477\pi$
$839$		−	1523.91i		−	1.81635i	0.418594	−	0.908173i	$-0.362523\pi$
$840$		0			0
$841$	837.950			0.996374
$842$	7.00105	−	7.00105i	0.00831478	−	0.00831478i
$843$		0			0
$844$		−	247.453i		−	0.293191i
$845$	−614.823	+	271.998i	−0.727601	+	0.321891i
$846$		0			0
$847$	−175.216	+	175.216i	−0.206867	+	0.206867i
$848$	−47.1532	−	47.1532i	−0.0556052	−	0.0556052i
$849$		0			0
$850$	−248.697	−	226.065i	−0.292585	−	0.265959i
$851$	89.2261			0.104849
$852$		0			0
$853$	−516.097	−	516.097i	−0.605037	−	0.605037i	0.336608	−	0.941645i	$-0.390720\pi$
$853$	−516.097	−	516.097i	−0.605037	−	0.605037i	−0.941645	+	0.336608i	$0.890720\pi$
$854$		−	70.1886i		−	0.0821880i
$855$		0			0
$856$	300.664			0.351243
$857$	−849.288	+	849.288i	−0.991001	+	0.991001i	−0.999960	−	0.00895907i	$-0.997148\pi$
$857$	−849.288	+	849.288i	−0.991001	+	0.991001i	0.00895907	+	0.999960i	$0.497148\pi$
$858$		0			0
$859$		−	1140.75i		−	1.32799i	−0.747736	−	0.663996i	$-0.768859\pi$
$859$		−	1140.75i		−	1.32799i	0.747736	−	0.663996i	$-0.231141\pi$
$860$	218.044	+	84.2909i	0.253539	+	0.0980127i
$861$		0			0
$862$	740.445	−	740.445i	0.858985	−	0.858985i
$863$	1189.86	+	1189.86i	1.37874	+	1.37874i	0.846744	+	0.532000i	$0.178559\pi$
$863$	1189.86	+	1189.86i	1.37874	+	1.37874i	0.532000	+	0.846744i	$0.321441\pi$
$864$		0			0
$865$	−264.058	+	683.066i	−0.305269	+	0.789671i
$866$	−813.520			−0.939400
$867$		0			0
$868$	−116.954	−	116.954i	−0.134740	−	0.134740i
$869$			473.182i			0.544513i
$870$		0			0
$871$	−376.274			−0.432002
$872$	−237.215	+	237.215i	−0.272035	+	0.272035i
$873$		0			0
$874$		−	1159.81i		−	1.32702i
$875$	−306.743	+	153.564i	−0.350564	+	0.175502i
$876$		0			0
$877$	1024.94	−	1024.94i	1.16869	−	1.16869i	0.186170	−	0.982518i	$-0.440393\pi$
$877$	1024.94	−	1024.94i	1.16869	−	1.16869i	0.982518	−	0.186170i	$-0.0596075\pi$
$878$	558.125	+	558.125i	0.635678	+	0.635678i
$879$		0			0
$880$	−290.643	−	656.969i	−0.330276	−	0.746556i
$881$	127.177			0.144355			0.0721777	−	0.997392i	$-0.477005\pi$
$881$	127.177			0.144355			0.0721777	+	0.997392i	$0.477005\pi$
$882$		0			0
$883$	−363.077	−	363.077i	−0.411186	−	0.411186i	0.470966	−	0.882151i	$-0.343905\pi$
$883$	−363.077	−	363.077i	−0.411186	−	0.411186i	−0.882151	+	0.470966i	$0.843905\pi$
$884$		−	55.5471i		−	0.0628361i
$885$		0			0
$886$	−270.364			−0.305151
$887$	−1092.05	+	1092.05i	−1.23118	+	1.23118i	−0.267664	+	0.963512i	$0.586252\pi$
$887$	−1092.05	+	1092.05i	−1.23118	+	1.23118i	−0.963512	+	0.267664i	$0.913748\pi$
$888$		0			0
$889$			277.836i			0.312526i
$890$	108.341	−	280.258i	0.121732	−	0.314896i
$891$		0			0
$892$	−239.202	+	239.202i	−0.268164	+	0.268164i
$893$	−919.809	−	919.809i	−1.03002	−	1.03002i
$894$		0			0
$895$	645.463	−	285.553i	0.721188	−	0.319054i
$896$	123.232			0.137535
$897$		0			0
$898$	641.603	+	641.603i	0.714480	+	0.714480i
$899$		−	89.1545i		−	0.0991708i
$900$		0			0
$901$	−54.0145			−0.0599495
$902$	571.674	−	571.674i	0.633785	−	0.633785i
$903$		0			0
$904$			1577.64i			1.74518i
$905$	−368.755	−	833.532i	−0.407464	−	0.921030i
$906$		0			0
$907$	−243.135	+	243.135i	−0.268065	+	0.268065i	−0.828320	−	0.560255i	$-0.810703\pi$
$907$	−243.135	+	243.135i	−0.268065	+	0.268065i	0.560255	+	0.828320i	$0.310703\pi$
$908$	−159.412	−	159.412i	−0.175564	−	0.175564i
$909$		0			0
$910$	126.298	+	48.8242i	0.138790	+	0.0536530i
$911$	19.2816			0.0211653			0.0105826	−	0.999944i	$-0.496631\pi$
$911$	19.2816			0.0211653			0.0105826	+	0.999944i	$0.496631\pi$
$912$		0			0
$913$	−71.1609	−	71.1609i	−0.0779418	−	0.0779418i
$914$		−	218.049i		−	0.238566i
$915$		0			0
$916$	−353.283			−0.385680
$917$	−363.604	+	363.604i	−0.396514	+	0.396514i
$918$		0			0
$919$		−	947.679i		−	1.03121i	−0.856827	−	0.515603i	$-0.827568\pi$
$919$		−	947.679i		−	1.03121i	0.856827	−	0.515603i	$-0.172432\pi$
$920$	−899.794	+	398.069i	−0.978037	+	0.432684i
$921$		0			0
$922$	−911.831	+	911.831i	−0.988971	+	0.988971i
$923$	−188.700	−	188.700i	−0.204442	−	0.204442i
$924$		0			0
$925$	4.69518	+	98.4939i	0.00507587	+	0.106480i
$926$	926.630			1.00068
$927$		0			0
$928$	−22.4712	−	22.4712i	−0.0242146	−	0.0242146i
$929$		−	250.477i		−	0.269620i	−0.990871	−	0.134810i	$-0.956958\pi$
$929$		−	250.477i		−	0.269620i	0.990871	−	0.134810i	$-0.0430424\pi$
$930$		0			0
$931$	−1266.18			−1.36002
$932$	63.7713	−	63.7713i	0.0684241	−	0.0684241i
$933$		0			0
$934$		−	282.510i		−	0.302474i
$935$	−542.750	−	209.815i	−0.580481	−	0.224401i
$936$		0			0
$937$	−773.708	+	773.708i	−0.825729	+	0.825729i	−0.986923	−	0.161194i	$-0.948466\pi$
$937$	−773.708	+	773.708i	−0.825729	+	0.825729i	0.161194	+	0.986923i	$0.448466\pi$
$938$	−208.614	−	208.614i	−0.222403	−	0.222403i
$939$		0			0
$940$	−90.6727	+	234.552i	−0.0964603	+	0.249524i
$941$	−1422.82			−1.51203			−0.756017	−	0.654552i	$-0.772857\pi$
$941$	−1422.82			−1.51203			−0.756017	+	0.654552i	$0.772857\pi$
$942$		0			0
$943$	−529.846	−	529.846i	−0.561873	−	0.561873i
$944$			797.338i			0.844638i
$945$		0			0
$946$	−966.657			−1.02184
$947$	−713.742	+	713.742i	−0.753688	+	0.753688i	−0.975165	−	0.221478i	$-0.928912\pi$
$947$	−713.742	+	713.742i	−0.753688	+	0.753688i	0.221478	+	0.975165i	$0.428912\pi$
$948$		0			0
$949$		−	765.216i		−	0.806340i
$950$	1280.28	−	61.0307i	1.34766	−	0.0642428i
$951$		0			0
$952$	135.146	−	135.146i	0.141960	−	0.141960i
$953$	−1340.68	−	1340.68i	−1.40680	−	1.40680i	−0.775700	−	0.631102i	$-0.782603\pi$
$953$	−1340.68	−	1340.68i	−1.40680	−	1.40680i	−0.631102	−	0.775700i	$-0.717397\pi$
$954$		0			0
$955$	−441.327	−	997.574i	−0.462122	−	1.04458i
$956$	173.608			0.181598
$957$		0			0
$958$	−366.057	−	366.057i	−0.382105	−	0.382105i
$959$			104.895i			0.109380i
$960$		0			0
$961$	1645.49			1.71227
$962$	27.5226	−	27.5226i	0.0286098	−	0.0286098i
$963$		0			0
$964$		−	460.285i		−	0.477474i
$965$	396.614	−	1025.96i	0.410999	−	1.06317i
$966$		0			0
$967$	614.274	−	614.274i	0.635237	−	0.635237i	−0.314140	−	0.949377i	$-0.601716\pi$
$967$	614.274	−	614.274i	0.635237	−	0.635237i	0.949377	+	0.314140i	$0.101716\pi$
$968$	−555.396	−	555.396i	−0.573756	−	0.573756i
$969$		0			0
$970$	474.523	−	209.929i	0.489199	−	0.216422i
$971$	−35.3368			−0.0363922			−0.0181961	−	0.999834i	$-0.505792\pi$
$971$	−35.3368			−0.0363922			−0.0181961	+	0.999834i	$0.505792\pi$
$972$		0			0
$973$	−195.834	−	195.834i	−0.201268	−	0.201268i
$974$			801.126i			0.822511i
$975$		0			0
$976$	150.556			0.154258
$977$	496.574	−	496.574i	0.508264	−	0.508264i	−0.405729	−	0.913993i	$-0.632982\pi$
$977$	496.574	−	496.574i	0.508264	−	0.508264i	0.913993	+	0.405729i	$0.132982\pi$
$978$		0			0
$979$		−	520.224i		−	0.531383i
$980$	99.0301	+	223.847i	0.101051	+	0.228416i
$981$		0			0
$982$	136.429	−	136.429i	0.138929	−	0.138929i
$983$	−29.5716	−	29.5716i	−0.0300830	−	0.0300830i	0.691905	−	0.721988i	$-0.256772\pi$
$983$	−29.5716	−	29.5716i	−0.0300830	−	0.0300830i	−0.721988	+	0.691905i	$0.756772\pi$
$984$		0			0
$985$	1595.39	+	616.744i	1.61969	+	0.626136i
$986$	23.4763			0.0238096
$987$		0			0
$988$	149.793	+	149.793i	0.151612	+	0.151612i
$989$			895.929i			0.905894i
$990$		0			0
$991$	805.965			0.813284			0.406642	−	0.913588i	$-0.366700\pi$
$991$	805.965			0.813284			0.406642	+	0.913588i	$0.366700\pi$
$992$	656.959	−	656.959i	0.662257	−	0.662257i
$993$		0			0
$994$		−	209.239i		−	0.210502i
$995$	−579.539	+	256.388i	−0.582452	+	0.257677i
$996$		0			0
$997$	149.614	−	149.614i	0.150064	−	0.150064i	−0.628083	−	0.778147i	$-0.716160\pi$
$997$	149.614	−	149.614i	0.150064	−	0.150064i	0.778147	+	0.628083i	$0.216160\pi$
$998$	503.183	+	503.183i	0.504192	+	0.504192i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.g.h.163.4		20
3.2	odd	2		405.3.g.g.163.7		20
5.2	odd	4	inner	405.3.g.h.82.4		20
9.2	odd	6		135.3.l.a.118.4		40
9.4	even	3		45.3.k.a.43.4	yes	40
9.5	odd	6		135.3.l.a.73.7		40
9.7	even	3		45.3.k.a.13.7	yes	40
15.2	even	4		405.3.g.g.82.7		20
45.2	even	12		135.3.l.a.37.7		40
45.4	even	6		225.3.o.b.43.7		40
45.7	odd	12		45.3.k.a.22.4	yes	40
45.13	odd	12		225.3.o.b.7.4		40
45.22	odd	12		45.3.k.a.7.7	✓	40
45.32	even	12		135.3.l.a.127.4		40
45.34	even	6		225.3.o.b.193.4		40
45.43	odd	12		225.3.o.b.157.7		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.7	✓	40	45.22	odd	12
45.3.k.a.13.7	yes	40	9.7	even	3
45.3.k.a.22.4	yes	40	45.7	odd	12
45.3.k.a.43.4	yes	40	9.4	even	3
135.3.l.a.37.7		40	45.2	even	12
135.3.l.a.73.7		40	9.5	odd	6
135.3.l.a.118.4		40	9.2	odd	6
135.3.l.a.127.4		40	45.32	even	12
225.3.o.b.7.4		40	45.13	odd	12
225.3.o.b.43.7		40	45.4	even	6
225.3.o.b.157.7		40	45.43	odd	12
225.3.o.b.193.4		40	45.34	even	6
405.3.g.g.82.7		20	15.2	even	4
405.3.g.g.163.7		20	3.2	odd	2
405.3.g.h.82.4		20	5.2	odd	4	inner
405.3.g.h.163.4		20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.18732 + 1.18732i) q^{2} +1.18052i q^{4} +(-2.02288 - 4.57252i) q^{5} +(-1.94050 + 1.94050i) q^{7} +(-6.15096 - 6.15096i) q^{8} +(7.83089 + 3.02725i) q^{10} +14.5360 q^{11} +(-4.15569 - 4.15569i) q^{13} -4.60801i q^{14} +9.88429 q^{16} +(5.66128 - 5.66128i) q^{17} +30.5333i q^{19} +(5.39796 - 2.38806i) q^{20} +(-17.2589 + 17.2589i) q^{22} +(15.9961 + 15.9961i) q^{23} +(-16.8159 + 18.4994i) q^{25} +9.86831 q^{26} +(-2.29080 - 2.29080i) q^{28} -1.74629i q^{29} +51.0538 q^{31} +(12.8680 - 12.8680i) q^{32} +13.4436i q^{34} +(12.7984 + 4.94758i) q^{35} +(2.78899 - 2.78899i) q^{37} +(-36.2529 - 36.2529i) q^{38} +(-15.6827 + 40.5681i) q^{40} -33.1234 q^{41} +(28.0046 + 28.0046i) q^{43} +17.1600i q^{44} -37.9852 q^{46} +(-30.1248 + 30.1248i) q^{47} +41.4689i q^{49} +(-1.99882 - 41.9306i) q^{50} +(4.90588 - 4.90588i) q^{52} +(-4.77052 - 4.77052i) q^{53} +(-29.4046 - 66.4660i) q^{55} +23.8719 q^{56} +(2.07341 + 2.07341i) q^{58} +80.6672i q^{59} +15.2319 q^{61} +(-60.6174 + 60.6174i) q^{62} +70.0941i q^{64} +(-10.5955 + 27.4085i) q^{65} +(45.2721 - 45.2721i) q^{67} +(6.68326 + 6.68326i) q^{68} +(-21.0702 + 9.32147i) q^{70} +45.4076 q^{71} +(92.0685 + 92.0685i) q^{73} +6.62288i q^{74} -36.0452 q^{76} +(-28.2071 + 28.2071i) q^{77} +32.5525i q^{79} +(-19.9948 - 45.1961i) q^{80} +(39.3283 - 39.3283i) q^{82} +(-4.89551 - 4.89551i) q^{83} +(-37.3384 - 14.4342i) q^{85} -66.5010 q^{86} +(-89.4101 - 89.4101i) q^{88} -35.7887i q^{89} +16.1283 q^{91} +(-18.8837 + 18.8837i) q^{92} -71.5359i q^{94} +(139.614 - 61.7653i) q^{95} +(43.7021 - 43.7021i) q^{97} +(-49.2370 - 49.2370i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 2 q^{5} + 2 q^{7} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 2 q^{13} - 28 q^{16} + 14 q^{17} + 114 q^{20} - 14 q^{22} - 82 q^{23} + 8 q^{25} - 56 q^{26} - 44 q^{28} + 4 q^{31} + 14 q^{32} + 176 q^{35}+ \cdots - 938 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^5 + 2 * q^7 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 2 * q^13 - 28 * q^16 + 14 * q^17 + 114 * q^20 - 14 * q^22 - 82 * q^23 + 8 * q^25 - 56 * q^26 - 44 * q^28 + 4 * q^31 + 14 * q^32 + 176 * q^35 - 46 * q^37 - 330 * q^38 - 30 * q^40 + 28 * q^41 + 2 * q^43 - 68 * q^46 - 64 * q^47 + 458 * q^50 + 74 * q^52 - 304 * q^53 + 112 * q^55 + 192 * q^56 - 30 * q^58 - 92 * q^61 - 50 * q^62 + 326 * q^65 + 80 * q^67 - 626 * q^68 + 102 * q^70 + 124 * q^71 - 4 * q^73 + 96 * q^76 - 338 * q^77 + 722 * q^80 + 52 * q^82 - 370 * q^83 + 98 * q^85 + 328 * q^86 + 210 * q^88 + 76 * q^91 - 388 * q^92 + 360 * q^95 - 292 * q^97 - 938 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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