LMFDB - Embedded newform 405.3.n.a.179.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(44,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.44"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.n (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			179.34
Character	$\chi$	$=$	405.179
Dual form			405.3.n.a.224.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.60298 + 1.31138i) q^{2} +(8.19760 + 6.87860i) q^{4} +(-2.60972 - 4.26490i) q^{5} +(5.01113 + 5.97203i) q^{7} +(12.8469 + 22.2515i) q^{8} +(-3.80988 - 18.7887i) q^{10} +(9.63258 - 1.69848i) q^{11} +(-3.91628 - 10.7599i) q^{13} +(10.2234 + 28.0886i) q^{14} +(9.67410 + 54.8645i) q^{16} +(-4.13818 + 7.16754i) q^{17} +(6.12499 + 10.6088i) q^{19} +(7.94311 - 52.9131i) q^{20} +(36.9334 + 6.51235i) q^{22} +(-15.9927 - 13.4195i) q^{23} +(-11.3787 + 22.2604i) q^{25} -43.9034i q^{26} +83.4258i q^{28} +(-4.79335 + 13.1696i) q^{29} +(-32.9893 - 27.6813i) q^{31} +(-19.2458 + 109.148i) q^{32} +(-24.3092 + 20.3978i) q^{34} +(12.3925 - 36.9573i) q^{35} +(9.27687 + 5.35600i) q^{37} +(8.15609 + 46.2555i) q^{38} +(61.3736 - 112.861i) q^{40} +(-14.9116 - 40.9693i) q^{41} +(43.1958 - 7.61658i) q^{43} +(90.6472 + 52.3352i) q^{44} +(-40.0234 - 69.3225i) q^{46} +(57.2199 - 48.0132i) q^{47} +(-2.04496 + 11.5976i) q^{49} +(-70.1892 + 65.2820i) q^{50} +(41.9089 - 115.144i) q^{52} -2.58820 q^{53} +(-32.3822 - 36.6494i) q^{55} +(-68.5091 + 188.227i) q^{56} +(-34.5407 + 41.1640i) q^{58} +(-108.318 - 19.0993i) q^{59} +(12.2356 - 10.2669i) q^{61} +(-82.5593 - 142.997i) q^{62} +(-101.055 + 175.033i) q^{64} +(-35.6695 + 44.7829i) q^{65} +(-10.8906 - 29.9217i) q^{67} +(-83.2258 + 30.2917i) q^{68} +(93.1148 - 116.905i) q^{70} +(-65.2964 - 37.6989i) q^{71} +(6.13041 - 3.53939i) q^{73} +(26.4006 + 31.4631i) q^{74} +(-22.7635 + 129.098i) q^{76} +(58.4135 + 49.0147i) q^{77} +(-32.2143 - 11.7251i) q^{79} +(208.745 - 184.440i) q^{80} -167.166i q^{82} +(-24.1153 - 8.77724i) q^{83} +(41.3683 - 1.05634i) q^{85} +(165.622 + 29.2036i) q^{86} +(161.543 + 192.519i) q^{88} +(-66.9037 + 38.6269i) q^{89} +(44.6334 - 77.3073i) q^{91} +(-38.7945 - 220.015i) q^{92} +(269.126 - 97.9538i) q^{94} +(29.2609 - 53.8085i) q^{95} +(-88.6588 + 15.6329i) q^{97} +(-22.5768 + 39.1041i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 12 q^{4} - 3 q^{5} - 3 q^{10} - 6 q^{11} + 48 q^{14} + 12 q^{16} - 6 q^{19} - 63 q^{20} - 15 q^{25} - 96 q^{29} - 102 q^{31} + 12 q^{34} + 252 q^{35} + 117 q^{40} - 96 q^{41} + 666 q^{44} - 6 q^{46}+ \cdots + 543 q^{95}+O(q^{100}) $ 204 * q - 12 * q^4 - 3 * q^5 - 3 * q^10 - 6 * q^11 + 48 * q^14 + 12 * q^16 - 6 * q^19 - 63 * q^20 - 15 * q^25 - 96 * q^29 - 102 * q^31 + 12 * q^34 + 252 * q^35 + 117 * q^40 - 96 * q^41 + 666 * q^44 - 6 * q^46 + 60 * q^49 - 48 * q^50 - 12 * q^55 - 294 * q^56 - 510 * q^59 + 132 * q^61 - 486 * q^64 - 147 * q^65 - 141 * q^70 + 18 * q^71 + 954 * q^74 + 84 * q^76 - 48 * q^79 + 69 * q^85 + 1506 * q^86 - 792 * q^89 - 6 * q^91 + 492 * q^94 + 543 * q^95

Character values

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

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.60298	+	1.31138i	1.80149	+	0.655689i	0.998191	+	0.0601148i	$0.0191467\pi$
$2$	3.60298	+	1.31138i	1.80149	+	0.655689i	0.803300	+	0.595575i	$0.203076\pi$
$3$		0			0
$3$		0			0
$4$	8.19760	+	6.87860i	2.04940	+	1.71965i
$5$	−2.60972	−	4.26490i	−0.521944	−	0.852980i
$5$	−2.60972	−	4.26490i	−0.521944	−	0.852980i
$6$		0			0
$7$	5.01113	+	5.97203i	0.715875	+	0.853147i	0.994223	−	0.107334i	$-0.0342313\pi$
$7$	5.01113	+	5.97203i	0.715875	+	0.853147i	−0.278348	+	0.960480i	$0.589787\pi$
$8$	12.8469	+	22.2515i	1.60587	+	2.78144i
$9$		0			0
$10$	−3.80988	−	18.7887i	−0.380988	−	1.87887i
$11$	9.63258	−	1.69848i	0.875689	−	0.154408i	0.282303	−	0.959325i	$-0.408902\pi$
$11$	9.63258	−	1.69848i	0.875689	−	0.154408i	0.593387	+	0.804918i	$0.297791\pi$
$12$		0			0
$13$	−3.91628	−	10.7599i	−0.301252	−	0.827684i	−0.994283	−	0.106776i	$-0.965947\pi$
$13$	−3.91628	−	10.7599i	−0.301252	−	0.827684i	0.693031	−	0.720908i	$-0.256275\pi$
$14$	10.2234	+	28.0886i	0.730244	+	2.00633i
$15$		0			0
$16$	9.67410	+	54.8645i	0.604631	+	3.42903i
$17$	−4.13818	+	7.16754i	−0.243422	+	0.421620i	−0.961687	−	0.274150i	$-0.911603\pi$
$17$	−4.13818	+	7.16754i	−0.243422	+	0.421620i	0.718265	+	0.695770i	$0.244937\pi$
$18$		0			0
$19$	6.12499	+	10.6088i	0.322368	+	0.558358i	0.980976	−	0.194128i	$-0.0621878\pi$
$19$	6.12499	+	10.6088i	0.322368	+	0.558358i	−0.658608	+	0.752486i	$0.728854\pi$
$20$	7.94311	−	52.9131i	0.397155	−	2.64566i
$21$		0			0
$22$	36.9334	+	6.51235i	1.67879	+	0.296016i
$23$	−15.9927	−	13.4195i	−0.695334	−	0.583455i	0.225108	−	0.974334i	$-0.427727\pi$
$23$	−15.9927	−	13.4195i	−0.695334	−	0.583455i	−0.920442	+	0.390879i	$0.872171\pi$
$24$		0			0
$25$	−11.3787	+	22.2604i	−0.455149	+	0.890415i
$26$		−	43.9034i		−	1.68859i
$27$		0			0
$28$			83.4258i			2.97949i
$29$	−4.79335	+	13.1696i	−0.165288	+	0.454125i	−0.994491	−	0.104823i	$-0.966572\pi$
$29$	−4.79335	+	13.1696i	−0.165288	+	0.454125i	0.829203	+	0.558947i	$0.188795\pi$
$30$		0			0
$31$	−32.9893	−	27.6813i	−1.06417	−	0.892946i	−0.0696597	−	0.997571i	$-0.522191\pi$
$31$	−32.9893	−	27.6813i	−1.06417	−	0.892946i	−0.994512	+	0.104625i	$0.966636\pi$
$32$	−19.2458	+	109.148i	−0.601431	+	3.41089i
$33$		0			0
$34$	−24.3092	+	20.3978i	−0.714975	+	0.599935i
$35$	12.3925	−	36.9573i	0.354070	−	1.05592i
$36$		0			0
$37$	9.27687	+	5.35600i	0.250726	+	0.144757i	0.620097	−	0.784525i	$-0.287093\pi$
$37$	9.27687	+	5.35600i	0.250726	+	0.144757i	−0.369371	+	0.929282i	$0.620427\pi$
$38$	8.15609	+	46.2555i	0.214634	+	1.21725i
$39$		0			0
$40$	61.3736	−	112.861i	1.53434	−	2.82153i
$41$	−14.9116	−	40.9693i	−0.363698	−	0.999251i	−0.977711	−	0.209956i	$-0.932668\pi$
$41$	−14.9116	−	40.9693i	−0.363698	−	0.999251i	0.614013	−	0.789296i	$-0.289554\pi$
$42$		0			0
$43$	43.1958	−	7.61658i	1.00455	−	0.177130i	0.352911	−	0.935657i	$-0.385192\pi$
$43$	43.1958	−	7.61658i	1.00455	−	0.177130i	0.651641	+	0.758527i	$0.274081\pi$
$44$	90.6472	+	52.3352i	2.06016	+	1.18944i
$45$		0			0
$46$	−40.0234	−	69.3225i	−0.870074	−	1.50701i
$47$	57.2199	−	48.0132i	1.21745	−	1.02156i	0.218491	−	0.975839i	$-0.429887\pi$
$47$	57.2199	−	48.0132i	1.21745	−	1.02156i	0.998954	−	0.0457191i	$-0.0145579\pi$
$48$		0			0
$49$	−2.04496	+	11.5976i	−0.0417339	+	0.236685i
$50$	−70.1892	+	65.2820i	−1.40378	+	1.30564i
$51$		0			0
$52$	41.9089	−	115.144i	0.805941	−	2.21430i
$53$	−2.58820			−0.0488340			−0.0244170	−	0.999702i	$-0.507773\pi$
$53$	−2.58820			−0.0488340			−0.0244170	+	0.999702i	$0.507773\pi$
$54$		0			0
$55$	−32.3822	−	36.6494i	−0.588767	−	0.666353i
$56$	−68.5091	+	188.227i	−1.22338	+	3.36120i
$57$		0			0
$58$	−34.5407	+	41.1640i	−0.595529	+	0.709724i
$59$	−108.318	−	19.0993i	−1.83589	−	0.323717i	−0.855054	−	0.518539i	$-0.826476\pi$
$59$	−108.318	−	19.0993i	−1.83589	−	0.323717i	−0.980839	+	0.194821i	$0.937587\pi$
$60$		0			0
$61$	12.2356	−	10.2669i	0.200584	−	0.168310i	−0.536963	−	0.843606i	$-0.680428\pi$
$61$	12.2356	−	10.2669i	0.200584	−	0.168310i	0.737547	+	0.675296i	$0.235984\pi$
$62$	−82.5593	−	142.997i	−1.33160	−	2.30640i
$63$		0			0
$64$	−101.055	+	175.033i	−1.57899	+	2.73489i
$65$	−35.6695	+	44.7829i	−0.548761	+	0.688967i
$66$		0			0
$67$	−10.8906	−	29.9217i	−0.162546	−	0.446593i	0.831503	−	0.555520i	$-0.187481\pi$
$67$	−10.8906	−	29.9217i	−0.162546	−	0.446593i	−0.994050	+	0.108927i	$0.965259\pi$
$68$	−83.2258	+	30.2917i	−1.22391	+	0.445466i
$69$		0			0
$70$	93.1148	−	116.905i	1.33021	−	1.67007i
$71$	−65.2964	−	37.6989i	−0.919668	−	0.530970i	−0.0361385	−	0.999347i	$-0.511506\pi$
$71$	−65.2964	−	37.6989i	−0.919668	−	0.530970i	−0.883529	+	0.468377i	$0.844839\pi$
$72$		0			0
$73$	6.13041	−	3.53939i	0.0839782	−	0.0484849i	−0.457423	−	0.889249i	$-0.651227\pi$
$73$	6.13041	−	3.53939i	0.0839782	−	0.0484849i	0.541401	+	0.840764i	$0.317894\pi$
$74$	26.4006	+	31.4631i	0.356765	+	0.425177i
$75$		0			0
$76$	−22.7635	+	129.098i	−0.299519	+	1.69866i
$77$	58.4135	+	49.0147i	0.758617	+	0.636555i
$78$		0			0
$79$	−32.2143	−	11.7251i	−0.407776	−	0.148418i	0.129984	−	0.991516i	$-0.458507\pi$
$79$	−32.2143	−	11.7251i	−0.407776	−	0.148418i	−0.537760	+	0.843098i	$0.680730\pi$
$80$	208.745	−	184.440i	2.60931	−	2.30550i
$81$		0			0
$82$		−	167.166i		−	2.03862i
$83$	−24.1153	−	8.77724i	−0.290545	−	0.105750i	0.192636	−	0.981270i	$-0.438296\pi$
$83$	−24.1153	−	8.77724i	−0.290545	−	0.105750i	−0.483181	+	0.875520i	$0.660519\pi$
$84$		0			0
$85$	41.3683	−	1.05634i	0.486686	−	0.0124276i
$86$	165.622	+	29.2036i	1.92583	+	0.339577i
$87$		0			0
$88$	161.543	+	192.519i	1.83571	+	2.18772i
$89$	−66.9037	+	38.6269i	−0.751727	+	0.434010i	−0.826317	−	0.563205i	$-0.809568\pi$
$89$	−66.9037	+	38.6269i	−0.751727	+	0.434010i	0.0745907	+	0.997214i	$0.476235\pi$
$90$		0			0
$91$	44.6334	−	77.3073i	0.490477	−	0.849531i
$92$	−38.7945	−	220.015i	−0.421679	−	2.39146i
$93$		0			0
$94$	269.126	−	97.9538i	2.86304	−	1.04206i
$95$	29.2609	−	53.8085i	0.308010	−	0.566405i
$96$		0			0
$97$	−88.6588	+	15.6329i	−0.914008	+	0.161164i	−0.610823	−	0.791767i	$-0.709161\pi$
$97$	−88.6588	+	15.6329i	−0.914008	+	0.161164i	−0.303185	+	0.952932i	$0.598050\pi$
$98$	−22.5768	+	39.1041i	−0.230375	+	0.399021i
$99$		0			0
$100$	−246.398	+	104.212i	−2.46398	+	1.04212i
$101$	45.2669	+	53.9469i	0.448187	+	0.534128i	0.942077	−	0.335396i	$-0.108870\pi$
$101$	45.2669	+	53.9469i	0.448187	+	0.534128i	−0.493891	+	0.869524i	$0.664426\pi$
$102$		0			0
$103$	179.880	+	31.7177i	1.74641	+	0.307939i	0.953497	−	0.301401i	$-0.0974543\pi$
$103$	179.880	+	31.7177i	1.74641	+	0.307939i	0.792909	+	0.609340i	$0.208565\pi$
$104$	189.112	−	225.375i	1.81838	−	2.16706i
$105$		0			0
$106$	−9.32526	−	3.39412i	−0.0879741	−	0.0320200i
$107$	−39.8116			−0.372071			−0.186035	−	0.982543i	$-0.559564\pi$
$107$	−39.8116			−0.372071			−0.186035	+	0.982543i	$0.559564\pi$
$108$		0			0
$109$	−24.9651			−0.229038			−0.114519	−	0.993421i	$-0.536533\pi$
$109$	−24.9651			−0.229038			−0.114519	+	0.993421i	$0.536533\pi$
$110$	−68.6113	−	174.513i	−0.623739	−	1.58648i
$111$		0			0
$112$	−279.174	+	332.707i	−2.49263	+	2.97060i
$113$	−24.1751	+	137.104i	−0.213939	+	1.21331i	0.668799	+	0.743444i	$0.266809\pi$
$113$	−24.1751	+	137.104i	−0.213939	+	1.21331i	−0.882738	+	0.469866i	$0.844302\pi$
$114$		0			0
$115$	−15.4962	+	103.228i	−0.134750	+	0.897637i
$116$	−129.882	+	74.9877i	−1.11968	+	0.646445i
$117$		0			0
$118$	−365.220	−	210.860i	−3.09509	−	1.78695i
$119$	−63.5417	+	11.2041i	−0.533964	+	0.0941522i
$120$		0			0
$121$	−23.8010	+	8.66285i	−0.196702	+	0.0715938i
$122$	57.5486	−	20.9460i	0.471710	−	0.171688i
$123$		0			0
$124$	−80.0243	−	453.841i	−0.645358	−	3.66000i
$125$	124.634	−	9.56422i	0.997069	−	0.0765138i
$126$		0			0
$127$	141.775	−	81.8538i	1.11634	−	0.644518i	0.175874	−	0.984413i	$-0.443725\pi$
$127$	141.775	−	81.8538i	1.11634	−	0.644518i	0.940464	+	0.339895i	$0.110391\pi$
$128$	−254.026	+	213.153i	−1.98458	+	1.66526i
$129$		0			0
$130$	−187.244	+	114.576i	−1.44034	+	0.881351i
$131$	−68.0937	+	81.1509i	−0.519799	+	0.619472i	−0.960533	−	0.278165i	$-0.910274\pi$
$131$	−68.0937	+	81.1509i	−0.519799	+	0.619472i	0.440734	+	0.897638i	$0.354718\pi$
$132$		0			0
$133$	−32.6629	+	89.7406i	−0.245586	+	0.674742i
$134$		−	122.089i		−	0.911113i
$135$		0			0
$136$	−212.651			−1.56361
$137$	153.987	+	56.0467i	1.12399	+	0.409100i	0.836108	−	0.548565i	$-0.184826\pi$
$137$	153.987	+	56.0467i	1.12399	+	0.409100i	0.287885	+	0.957665i	$0.407048\pi$
$138$		0			0
$139$	50.1389	+	42.0716i	0.360712	+	0.302673i	0.805074	−	0.593174i	$-0.202125\pi$
$139$	50.1389	+	42.0716i	0.360712	+	0.302673i	−0.444363	+	0.895847i	$0.646570\pi$
$140$	355.803	−	217.718i	2.54145	−	1.55513i
$141$		0			0
$142$	−185.824	−	221.457i	−1.30862	−	1.55955i
$143$	−55.9994	−	96.9938i	−0.391604	−	0.678279i
$144$		0			0
$145$	68.6764	−	13.9259i	0.473630	−	0.0960404i
$146$	26.7293	−	4.71309i	0.183077	−	0.0322814i
$147$		0			0
$148$	39.2062	+	107.718i	0.264907	+	0.727825i
$149$	−24.8288	−	68.2166i	−0.166636	−	0.457829i	0.828066	−	0.560631i	$-0.189441\pi$
$149$	−24.8288	−	68.2166i	−0.166636	−	0.457829i	−0.994702	+	0.102802i	$0.967219\pi$
$150$		0			0
$151$	8.47334	+	48.0547i	0.0561148	+	0.318243i	0.999925	−	0.0122450i	$-0.00389781\pi$
$151$	8.47334	+	48.0547i	0.0561148	+	0.318243i	−0.943810	+	0.330488i	$0.892787\pi$
$152$	−157.375	+	272.581i	−1.03536	+	1.79329i
$153$		0			0
$154$	146.186	+	253.201i	0.949259	+	1.64416i
$155$	−31.9652	+	212.937i	−0.206227	+	1.37378i
$156$		0			0
$157$	107.804	+	19.0087i	0.686648	+	0.121075i	0.506078	−	0.862488i	$-0.331095\pi$
$157$	107.804	+	19.0087i	0.686648	+	0.121075i	0.180570	+	0.983562i	$0.442206\pi$
$158$	−100.692	−	84.4903i	−0.637289	−	0.534749i
$159$		0			0
$160$	515.733	−	202.765i	3.22333	−	1.26728i
$161$		−	162.755i		−	1.01090i
$162$		0			0
$163$			275.362i			1.68934i	0.535291	+	0.844668i	$0.320202\pi$
$163$			275.362i			1.68934i	−0.535291	+	0.844668i	$0.679798\pi$
$164$	159.572	−	438.421i	0.973001	−	2.67330i
$165$		0			0
$166$	−75.3766	−	63.2485i	−0.454076	−	0.381015i
$167$	−39.6434	+	224.829i	−0.237385	+	1.34628i	0.600146	+	0.799891i	$0.295109\pi$
$167$	−39.6434	+	224.829i	−0.237385	+	1.34628i	−0.837531	+	0.546389i	$0.816002\pi$
$168$		0			0
$169$	29.0234	−	24.3536i	0.171736	−	0.144104i
$170$	150.435	+	50.4435i	0.884910	+	0.296727i
$171$		0			0
$172$	406.493	+	234.689i	2.36333	+	1.36447i
$173$	−27.2423	−	154.498i	−0.157470	−	0.893055i	−0.956493	−	0.291755i	$-0.905761\pi$
$173$	−27.2423	−	154.498i	−0.157470	−	0.893055i	0.799023	−	0.601300i	$-0.205350\pi$
$174$		0			0
$175$	−189.960	+	43.5955i	−1.08548	+	0.249117i
$176$	186.373	+	512.056i	1.05894	+	2.90941i
$177$		0			0
$178$	−291.707	+	51.4359i	−1.63880	+	0.288966i
$179$	−27.5045	−	15.8797i	−0.153656	−	0.0887136i	0.421200	−	0.906968i	$-0.361609\pi$
$179$	−27.5045	−	15.8797i	−0.153656	−	0.0887136i	−0.574857	+	0.818254i	$0.694942\pi$
$180$		0			0
$181$	103.811	+	179.806i	0.573542	+	0.993404i	0.996198	+	0.0871137i	$0.0277643\pi$
$181$	103.811	+	179.806i	0.573542	+	0.993404i	−0.422657	+	0.906290i	$0.638902\pi$
$182$	262.193	−	220.006i	1.44062	−	1.20882i
$183$		0			0
$184$	93.1465	−	528.260i	0.506231	−	2.87098i
$185$	−1.36721	−	53.5426i	−0.00739034	−	0.289419i
$186$		0			0
$187$	−27.6874	+	76.0705i	−0.148061	+	0.406794i
$188$	799.330			4.25175
$189$		0			0
$190$	175.990	−	155.499i	0.926263	−	0.818415i
$191$	−46.4729	+	127.683i	−0.243314	+	0.668498i	0.756580	+	0.653901i	$0.226869\pi$
$191$	−46.4729	+	127.683i	−0.243314	+	0.668498i	−0.999893	+	0.0145972i	$0.995353\pi$
$192$		0			0
$193$	70.1004	−	83.5424i	0.363215	−	0.432862i	−0.553227	−	0.833030i	$-0.686604\pi$
$193$	70.1004	−	83.5424i	0.363215	−	0.432862i	0.916442	+	0.400168i	$0.131048\pi$
$194$	−339.937	−	59.9400i	−1.75225	−	0.308969i
$195$		0			0
$196$	−96.5388	+	81.0057i	−0.492545	+	0.413294i
$197$	−15.7639	−	27.3039i	−0.0800199	−	0.138598i	0.823238	−	0.567696i	$-0.192165\pi$
$197$	−15.7639	−	27.3039i	−0.0800199	−	0.138598i	−0.903258	+	0.429097i	$0.858832\pi$
$198$		0			0
$199$	145.414	−	251.865i	0.730724	−	1.26565i	−0.225850	−	0.974162i	$-0.572516\pi$
$199$	145.414	−	251.865i	0.730724	−	1.26565i	0.956574	−	0.291489i	$-0.0941508\pi$
$200$	−641.509	+	32.7834i	−3.20754	+	0.163917i
$201$		0			0
$202$	92.3509	+	253.732i	0.457182	+	1.25610i
$203$	−102.669	+	37.3686i	−0.505760	+	0.184082i
$204$		0			0
$205$	−135.815	+	170.515i	−0.662511	+	0.831780i
$206$	606.510	+	350.169i	2.94422	+	1.69985i
$207$		0			0
$208$	552.450	−	318.957i	2.65601	−	1.53345i
$209$	77.0184	+	91.7869i	0.368509	+	0.439172i
$210$		0			0
$211$	−33.6259	+	190.702i	−0.159365	+	0.903802i	0.795322	+	0.606188i	$0.207302\pi$
$211$	−33.6259	+	190.702i	−0.159365	+	0.903802i	−0.954686	+	0.297614i	$0.903809\pi$
$212$	−21.2171	−	17.8032i	−0.100080	−	0.0839775i
$213$		0			0
$214$	−143.440	−	52.2080i	−0.670282	−	0.243963i
$215$	−145.213	−	164.348i	−0.675408	−	0.764411i
$216$		0			0
$217$		−	335.728i		−	1.54713i
$218$	−89.9489	−	32.7387i	−0.412610	−	0.150178i
$219$		0			0
$220$	−13.3595	−	523.181i	−0.0607249	−	2.37810i
$221$	93.3282	+	16.4563i	0.422300	+	0.0744628i
$222$		0			0
$223$	−41.0916	−	48.9710i	−0.184267	−	0.219601i	0.666001	−	0.745951i	$-0.268005\pi$
$223$	−41.0916	−	48.9710i	−0.184267	−	0.219601i	−0.850268	+	0.526350i	$0.823560\pi$
$224$	−748.280	+	432.020i	−3.34054	+	1.92866i
$225$		0			0
$226$	−266.898	+	462.280i	−1.18096	+	2.04549i
$227$	0.416906	+	2.36439i	0.00183659	+	0.0104158i	0.985712	−	0.168438i	$-0.0538722\pi$
$227$	0.416906	+	2.36439i	0.00183659	+	0.0104158i	−0.983876	+	0.178854i	$0.942761\pi$
$228$		0			0
$229$	−269.280	+	98.0101i	−1.17590	+	0.427992i	−0.854751	−	0.519038i	$-0.826290\pi$
$229$	−269.280	+	98.0101i	−1.17590	+	0.427992i	−0.321146	+	0.947030i	$0.604068\pi$
$230$	−191.204	+	351.608i	−0.831321	+	1.52873i
$231$		0			0
$232$	−354.624	+	62.5297i	−1.52855	+	0.269525i
$233$	−162.379	+	281.248i	−0.696904	+	1.20707i	0.272630	+	0.962119i	$0.412106\pi$
$233$	−162.379	+	281.248i	−0.696904	+	1.20707i	−0.969535	+	0.244955i	$0.921227\pi$
$234$		0			0
$235$	−354.100	−	118.736i	−1.50681	−	0.505260i
$236$	−756.568	−	901.642i	−3.20580	−	3.82052i
$237$		0			0
$238$	−243.632	−	42.9590i	−1.02367	−	0.180500i
$239$	−131.433	+	156.636i	−0.549931	+	0.655382i	−0.967383	−	0.253317i	$-0.918478\pi$
$239$	−131.433	+	156.636i	−0.549931	+	0.655382i	0.417453	+	0.908699i	$0.362923\pi$
$240$		0			0
$241$	−343.921	−	125.177i	−1.42706	−	0.519406i	−0.490970	−	0.871176i	$-0.663358\pi$
$241$	−343.921	−	125.177i	−1.42706	−	0.519406i	−0.936086	+	0.351770i	$0.885580\pi$
$242$	−97.1149			−0.401301
$243$		0			0
$244$	170.925			0.700511
$245$	54.7992	−	21.5448i	0.223670	−	0.0879381i
$246$		0			0
$247$	90.1624	−	107.451i	0.365030	−	0.435026i
$248$	192.140	−	1089.68i	0.774760	−	4.39388i
$249$		0			0
$250$	461.595	+	128.982i	1.84638	+	0.515928i
$251$	111.953	−	64.6362i	0.446028	−	0.257515i	−0.260123	−	0.965575i	$-0.583763\pi$
$251$	111.953	−	64.6362i	0.446028	−	0.257515i	0.706151	+	0.708061i	$0.250430\pi$
$252$		0			0
$253$	−176.844	−	102.101i	−0.698987	−	0.403560i
$254$	618.154	−	108.997i	2.43368	−	0.429123i
$255$		0			0
$256$	−435.087	+	158.359i	−1.69956	+	0.618589i
$257$	319.339	−	116.230i	1.24256	−	0.452256i	0.364681	−	0.931133i	$-0.381178\pi$
$257$	319.339	−	116.230i	1.24256	−	0.452256i	0.877882	+	0.478877i	$0.158956\pi$
$258$		0			0
$259$	14.5014	+	82.2413i	0.0559898	+	0.317534i
$260$	−600.447	+	121.756i	−2.30941	+	0.468291i
$261$		0			0
$262$	−351.760	+	203.089i	−1.34259	+	0.775147i
$263$	−153.344	+	128.671i	−0.583056	+	0.489242i	−0.885949	−	0.463783i	$-0.846492\pi$
$263$	−153.344	+	128.671i	−0.583056	+	0.489242i	0.302893	+	0.953024i	$0.402047\pi$
$264$		0			0
$265$	6.75449	+	11.0384i	0.0254886	+	0.0416545i
$266$	−235.368	+	280.501i	−0.884842	+	1.05451i
$267$		0			0
$268$	116.543	−	320.198i	0.434861	−	1.19477i
$269$			124.840i			0.464089i	0.972705	+	0.232044i	$0.0745414\pi$
$269$			124.840i			0.464089i	−0.972705	+	0.232044i	$0.925459\pi$
$270$		0			0
$271$	275.919			1.01815			0.509075	−	0.860722i	$-0.329988\pi$
$271$	275.919			1.01815			0.509075	+	0.860722i	$0.329988\pi$
$272$	−433.277	−	157.700i	−1.59293	−	0.579779i
$273$		0			0
$274$	481.314	+	403.870i	1.75662	+	1.47398i
$275$	−71.7976	+	233.752i	−0.261082	+	0.850006i
$276$		0			0
$277$	88.2597	+	105.184i	0.318627	+	0.379725i	0.901457	−	0.432870i	$-0.142499\pi$
$277$	88.2597	+	105.184i	0.318627	+	0.379725i	−0.582830	+	0.812594i	$0.698055\pi$
$278$	125.478	+	217.334i	0.451360	+	0.781778i
$279$		0			0
$280$	981.560	−	199.036i	3.50557	−	0.710843i
$281$	387.161	−	68.2669i	1.37780	−	0.242943i	0.564808	−	0.825222i	$-0.308950\pi$
$281$	387.161	−	68.2669i	1.37780	−	0.242943i	0.812989	+	0.582280i	$0.197839\pi$
$282$		0			0
$283$	68.9761	+	189.510i	0.243732	+	0.669648i	0.999884	+	0.0152514i	$0.00485486\pi$
$283$	68.9761	+	189.510i	0.243732	+	0.669648i	−0.756152	+	0.654396i	$0.772923\pi$
$284$	−275.958	−	758.188i	−0.971683	−	2.66968i
$285$		0			0
$286$	−74.5693	−	422.904i	−0.260732	−	1.47868i
$287$	169.946	−	294.355i	0.592146	−	1.02563i
$288$		0			0
$289$	110.251	+	190.960i	0.381491	+	0.660762i
$290$	265.702	+	39.8861i	0.916213	+	0.137538i
$291$		0			0
$292$	74.6007	+	13.1541i	0.255482	+	0.0450483i
$293$	12.8492	+	10.7817i	0.0438538	+	0.0367977i	0.664451	−	0.747332i	$-0.268665\pi$
$293$	12.8492	+	10.7817i	0.0438538	+	0.0367977i	−0.620597	+	0.784129i	$0.713110\pi$
$294$		0			0
$295$	201.222	+	511.808i	0.682109	+	1.73494i
$296$			275.232i			0.929839i
$297$		0			0
$298$		−	278.343i		−	0.934037i
$299$	−81.7601	+	224.634i	−0.273445	+	0.751284i
$300$		0			0
$301$	261.946	+	219.799i	0.870252	+	0.730228i
$302$	−32.4886	+	184.252i	−0.107578	+	0.610106i
$303$		0			0
$304$	−522.793	+	438.675i	−1.71971	+	1.44301i
$305$	−75.7189	−	25.3900i	−0.248259	−	0.0832458i
$306$		0			0
$307$	−324.909	−	187.586i	−1.05834	−	0.611030i	−0.133364	−	0.991067i	$-0.542578\pi$
$307$	−324.909	−	187.586i	−1.05834	−	0.611030i	−0.924971	+	0.380037i	$0.875911\pi$
$308$	141.697	+	803.606i	0.460056	+	2.60911i
$309$		0			0
$310$	−394.411	+	725.288i	−1.27229	+	2.33964i
$311$	−49.1638	−	135.076i	−0.158083	−	0.434330i	0.835213	−	0.549926i	$-0.185344\pi$
$311$	−49.1638	−	135.076i	−0.158083	−	0.434330i	−0.993296	+	0.115597i	$0.963122\pi$
$312$		0			0
$313$	−2.11086	+	0.372201i	−0.00674396	+	0.00118914i	−0.177019	−	0.984207i	$-0.556645\pi$
$313$	−2.11086	+	0.372201i	−0.00674396	+	0.00118914i	0.170275	+	0.985397i	$0.445534\pi$
$314$	363.488	+	209.860i	1.15760	+	0.668343i
$315$		0			0
$316$	−183.428	−	317.707i	−0.580468	−	1.00540i
$317$	56.8404	−	47.6947i	0.179307	−	0.150457i	−0.548717	−	0.836008i	$-0.684883\pi$
$317$	56.8404	−	47.6947i	0.179307	−	0.150457i	0.728024	+	0.685552i	$0.240439\pi$
$318$		0			0
$319$	−23.8039	+	134.999i	−0.0746205	+	0.423194i
$320$	1010.22	−	25.7962i	3.15695	−	0.0806130i
$321$		0			0
$322$	213.434	−	586.405i	0.662838	−	1.82113i
$323$	−101.385			−0.313886
$324$		0			0
$325$	284.082	+	35.2560i	0.874097	+	0.108480i
$326$	−361.103	+	992.123i	−1.10768	+	3.04332i
$327$		0			0
$328$	720.061	−	858.135i	2.19531	−	2.61627i
$329$	573.473	+	101.119i	1.74308	+	0.307352i
$330$		0			0
$331$	−84.9014	+	71.2408i	−0.256500	+	0.215229i	−0.761965	−	0.647618i	$-0.775765\pi$
$331$	−84.9014	+	71.2408i	−0.256500	+	0.215229i	0.505465	+	0.862847i	$0.331321\pi$
$332$	−137.312	−	237.832i	−0.413591	−	0.716360i
$333$		0			0
$334$	−437.670	+	758.067i	−1.31039	+	2.26966i
$335$	−99.1917	+	124.535i	−0.296095	+	0.371745i
$336$		0			0
$337$	−139.991	−	384.623i	−0.415405	−	1.14132i	−0.954276	−	0.298927i	$-0.903371\pi$
$337$	−139.991	−	384.623i	−0.415405	−	1.14132i	0.538871	−	0.842388i	$-0.318851\pi$
$338$	136.508	−	49.6847i	0.403869	−	0.146996i
$339$		0			0
$340$	346.387	+	275.897i	1.01879	+	0.811461i
$341$	−364.789	−	210.611i	−1.06976	−	0.617627i
$342$		0			0
$343$	251.314	−	145.096i	0.732693	−	0.423020i
$344$	724.413	+	863.322i	2.10585	+	2.50966i
$345$		0			0
$346$	104.453	−	592.380i	0.301886	−	1.71208i
$347$	219.470	+	184.158i	0.632480	+	0.530713i	0.901698	−	0.432366i	$-0.142321\pi$
$347$	219.470	+	184.158i	0.632480	+	0.530713i	−0.269219	+	0.963079i	$0.586765\pi$
$348$		0			0
$349$	−130.481	−	47.4911i	−0.373870	−	0.136078i	0.148249	−	0.988950i	$-0.452636\pi$
$349$	−130.481	−	47.4911i	−0.373870	−	0.136078i	−0.522119	+	0.852872i	$0.674858\pi$
$350$	−741.592	−	92.0354i	−2.11883	−	0.262958i
$351$		0			0
$352$			1084.07i			3.07974i
$353$	280.331	+	102.032i	0.794137	+	0.289042i	0.707055	−	0.707159i	$-0.250023\pi$
$353$	280.331	+	102.032i	0.794137	+	0.289042i	0.0870826	+	0.996201i	$0.472246\pi$
$354$		0			0
$355$	9.62331	+	376.866i	0.0271079	+	1.06159i
$356$	−814.148	−	143.556i	−2.28693	−	0.403248i
$357$		0			0
$358$	−78.2739	−	93.2833i	−0.218642	−	0.260568i
$359$	4.31662	−	2.49220i	0.0120240	−	0.00694207i	−0.493976	−	0.869476i	$-0.664457\pi$
$359$	4.31662	−	2.49220i	0.0120240	−	0.00694207i	0.506000	+	0.862534i	$0.331124\pi$
$360$		0			0
$361$	105.469	−	182.678i	0.292158	−	0.506032i
$362$	138.236	+	783.974i	0.381867	+	2.16567i
$363$		0			0
$364$	897.653	−	326.719i	2.46608	−	0.897579i
$365$	−31.0938	−	16.9088i	−0.0851885	−	0.0463254i
$366$		0			0
$367$	255.507	−	45.0529i	0.696205	−	0.122760i	0.185664	−	0.982613i	$-0.440556\pi$
$367$	255.507	−	45.0529i	0.696205	−	0.122760i	0.510541	+	0.859853i	$0.329445\pi$
$368$	581.537	−	1007.25i	1.58026	−	2.73710i
$369$		0			0
$370$	65.2885	−	194.706i	0.176455	−	0.526232i
$371$	−12.9698	−	15.4568i	−0.0349591	−	0.0416626i
$372$		0			0
$373$	−478.468	−	84.3667i	−1.28275	−	0.226184i	−0.509605	−	0.860408i	$-0.670209\pi$
$373$	−478.468	−	84.3667i	−1.28275	−	0.226184i	−0.773149	+	0.634224i	$0.781320\pi$
$374$	−199.515	+	237.772i	−0.533461	+	0.635755i
$375$		0			0
$376$	1803.47	+	656.408i	4.79646	+	1.74577i
$377$	160.476			0.425665
$378$		0			0
$379$	−556.277			−1.46775			−0.733875	−	0.679284i	$-0.762290\pi$
$379$	−556.277			−1.46775			−0.733875	+	0.679284i	$0.762290\pi$
$380$	609.996	−	239.826i	1.60525	−	0.631120i
$381$		0			0
$382$	−334.882	+	399.097i	−0.876655	+	1.04476i
$383$	−92.0688	+	522.148i	−0.240389	+	1.36331i	0.590574	+	0.806983i	$0.298901\pi$
$383$	−92.0688	+	522.148i	−0.240389	+	1.36331i	−0.830963	+	0.556328i	$0.812210\pi$
$384$		0			0
$385$	56.6001	−	377.042i	0.147013	−	0.979331i
$386$	362.126	−	209.074i	0.938151	−	0.541642i
$387$		0			0
$388$	−834.321	−	481.696i	−2.15031	−	1.24148i
$389$	203.603	−	35.9007i	0.523400	−	0.0922896i	0.0942954	−	0.995544i	$-0.469940\pi$
$389$	203.603	−	35.9007i	0.523400	−	0.0922896i	0.429105	+	0.903255i	$0.358829\pi$
$390$		0			0
$391$	162.365	−	59.0961i	0.415256	−	0.151141i
$392$	−284.335	+	103.489i	−0.725344	+	0.264004i
$393$		0			0
$394$	−20.9914	−	119.048i	−0.0532776	−	0.302152i
$395$	34.0642	+	167.990i	0.0862384	+	0.425291i
$396$		0			0
$397$	72.2431	−	41.7096i	0.181973	−	0.105062i	−0.406247	−	0.913764i	$-0.633163\pi$
$397$	72.2431	−	41.7096i	0.181973	−	0.105062i	0.588219	+	0.808702i	$0.299829\pi$
$398$	854.214	−	716.771i	2.14627	−	1.80093i
$399$		0			0
$400$	−1331.38	−	408.939i	−3.32846	−	1.02235i
$401$	319.064	−	380.246i	0.795671	−	0.948244i	−0.203855	−	0.979001i	$-0.565347\pi$
$401$	319.064	−	380.246i	0.795671	−	0.948244i	0.999527	+	0.0307567i	$0.00979170\pi$
$402$		0			0
$403$	−168.653	+	463.369i	−0.418493	+	1.14980i
$404$			753.608i			1.86537i
$405$		0			0
$406$	−418.920			−1.03182
$407$	98.4573	+	35.8355i	0.241910	+	0.0880479i
$408$		0			0
$409$	−217.774	−	182.734i	−0.532455	−	0.446783i	0.336493	−	0.941686i	$-0.390759\pi$
$409$	−217.774	−	182.734i	−0.532455	−	0.446783i	−0.868948	+	0.494903i	$0.835204\pi$
$410$	−712.948	+	436.258i	−1.73890	+	1.06404i
$411$		0			0
$412$	1256.41	+	1497.33i	3.04954	+	3.63430i
$413$	−428.732	−	742.585i	−1.03809	−	1.79803i
$414$		0			0
$415$	25.5000	+	125.755i	0.0614459	+	0.303025i
$416$	1249.80	−	220.373i	3.00432	−	0.529743i
$417$		0			0
$418$	157.129	+	431.707i	0.375906	+	1.03279i
$419$	−243.883	−	670.063i	−0.582060	−	1.59920i	−0.784655	−	0.619933i	$-0.787160\pi$
$419$	−243.883	−	670.063i	−0.582060	−	1.59920i	0.202595	−	0.979263i	$-0.435063\pi$
$420$		0			0
$421$	−24.1546	−	136.988i	−0.0573744	−	0.325386i	0.942589	−	0.333955i	$-0.108383\pi$
$421$	−24.1546	−	136.988i	−0.0573744	−	0.325386i	−0.999963	+	0.00856911i	$0.997272\pi$
$422$	−371.237	+	643.001i	−0.879707	+	1.52370i
$423$		0			0
$424$	−33.2505	−	57.5915i	−0.0784209	−	0.135829i
$425$	−112.465	−	173.675i	−0.264623	−	0.408647i
$426$		0			0
$427$	122.629	+	21.6227i	0.287186	+	0.0506387i
$428$	−326.359	−	273.848i	−0.762521	−	0.639831i
$429$		0			0
$430$	−307.676	−	782.573i	−0.715526	−	1.81994i
$431$		−	357.284i		−	0.828966i	−0.910057	−	0.414483i	$-0.863963\pi$
$431$		−	357.284i		−	0.828966i	0.910057	−	0.414483i	$-0.136037\pi$
$432$		0			0
$433$		−	61.8658i		−	0.142877i	−0.997445	−	0.0714386i	$-0.977241\pi$
$433$		−	61.8658i		−	0.142877i	0.997445	−	0.0714386i	$-0.0227590\pi$
$434$	440.266	−	1209.62i	1.01444	−	2.78715i
$435$		0			0
$436$	−204.654	−	171.725i	−0.469390	−	0.393865i
$437$	44.4092	−	251.857i	0.101623	−	0.576332i
$438$		0			0
$439$	−389.862	+	327.133i	−0.888068	+	0.745177i	−0.967822	−	0.251637i	$-0.919031\pi$
$439$	−389.862	+	327.133i	−0.888068	+	0.745177i	0.0797540	+	0.996815i	$0.474587\pi$
$440$	399.494	−	1191.39i	0.907941	−	2.70769i
$441$		0			0
$442$	314.680	+	181.680i	0.711945	+	0.411042i
$443$	−85.0329	−	482.245i	−0.191948	−	1.08859i	−0.916699	−	0.399579i	$-0.869156\pi$
$443$	−85.0329	−	482.245i	−0.191948	−	1.08859i	0.724751	−	0.689011i	$-0.241955\pi$
$444$		0			0
$445$	339.340	+	184.532i	0.762561	+	0.414679i
$446$	−83.8327	−	230.328i	−0.187966	−	0.516431i
$447$		0			0
$448$	−1551.70	+	273.607i	−3.46362	+	0.610730i
$449$	6.62400	+	3.82437i	0.0147528	+	0.00851752i	0.507358	−	0.861735i	$-0.330622\pi$
$449$	6.62400	+	3.82437i	0.0147528	+	0.00851752i	−0.492605	+	0.870253i	$0.663955\pi$
$450$		0			0
$451$	−213.223	−	369.313i	−0.472778	−	0.818876i
$452$	−1141.26	+	957.632i	−2.52491	+	2.11865i
$453$		0			0
$454$	−1.59851	+	9.06559i	−0.00352094	+	0.0199683i
$455$	−446.189	+	11.3935i	−0.980634	+	0.0250406i
$456$		0			0
$457$	54.2230	−	148.976i	0.118650	−	0.325988i	−0.866124	−	0.499830i	$-0.833396\pi$
$457$	54.2230	−	148.976i	0.118650	−	0.325988i	0.984774	+	0.173842i	$0.0556182\pi$
$458$	−1098.74			−2.39900
$459$		0			0
$460$	−837.097	+	739.631i	−1.81978	+	1.60789i
$461$	−292.341	+	803.199i	−0.634145	+	1.74230i	0.0352369	+	0.999379i	$0.488781\pi$
$461$	−292.341	+	803.199i	−0.634145	+	1.74230i	−0.669381	+	0.742919i	$0.733441\pi$
$462$		0			0
$463$	93.5751	−	111.518i	0.202106	−	0.240861i	−0.655466	−	0.755225i	$-0.727528\pi$
$463$	93.5751	−	111.518i	0.202106	−	0.240861i	0.857572	+	0.514364i	$0.171972\pi$
$464$	−768.916	−	135.581i	−1.65715	−	0.292200i
$465$		0			0
$466$	−953.871	+	800.392i	−2.04693	+	1.71758i
$467$	293.155	+	507.759i	0.627740	+	1.08728i	0.988004	+	0.154428i	$0.0493534\pi$
$467$	293.155	+	507.759i	0.627740	+	1.08728i	−0.360264	+	0.932851i	$0.617313\pi$
$468$		0			0
$469$	124.119	−	214.981i	0.264646	−	0.458381i
$470$	−1120.11	−	892.163i	−2.38321	−	1.89822i
$471$		0			0
$472$	−966.559	−	2655.60i	−2.04780	−	5.62627i
$473$	403.150	−	146.735i	0.852326	−	0.310221i
$474$		0			0
$475$	−305.851	+	15.6300i	−0.643896	+	0.0329053i
$476$	−597.957	−	345.231i	−1.25621	−	0.725275i
$477$		0			0
$478$	−678.962	+	391.999i	−1.42042	+	0.820081i
$479$	206.264	+	245.816i	0.430614	+	0.513186i	0.937099	−	0.349063i	$-0.113500\pi$
$479$	206.264	+	245.816i	0.430614	+	0.513186i	−0.506485	+	0.862249i	$0.669056\pi$
$480$		0			0
$481$	21.2992	−	120.794i	0.0442811	−	0.251130i
$482$	−1074.99	−	902.020i	−2.23026	−	1.87141i
$483$		0			0
$484$	−254.699	−	92.7029i	−0.526238	−	0.191535i
$485$	298.047	+	337.323i	0.614531	+	0.695511i
$486$		0			0
$487$			392.682i			0.806328i	0.915128	+	0.403164i	$0.132090\pi$
$487$			392.682i			0.806328i	−0.915128	+	0.403164i	$0.867910\pi$
$488$	385.645	+	140.363i	0.790255	+	0.287629i
$489$		0			0
$490$	225.694	−	5.76312i	0.460600	−	0.0117615i
$491$	781.670	+	137.830i	1.59200	+	0.280712i	0.898242	−	0.439500i	$-0.144845\pi$
$491$	781.670	+	137.830i	1.59200	+	0.280712i	0.693754	+	0.720212i	$0.255956\pi$
$492$		0			0
$493$	−74.5580	−	88.8547i	−0.151233	−	0.180233i
$494$	465.763	−	268.908i	0.942840	−	0.544349i
$495$		0			0
$496$	1199.58	−	2077.73i	2.41851	−	4.18898i
$497$	−102.070	−	578.866i	−0.205371	−	1.16472i
$498$		0			0
$499$	−206.900	+	75.3054i	−0.414629	+	0.150913i	−0.540907	−	0.841082i	$-0.681919\pi$
$499$	−206.900	+	75.3054i	−0.414629	+	0.150913i	0.126278	+	0.991995i	$0.459697\pi$
$500$	1087.48	+	778.901i	2.17497	+	1.55780i
$501$		0			0
$502$	488.128	−	86.0701i	0.972366	−	0.171454i
$503$	274.373	−	475.228i	0.545473	−	0.944787i	−0.453104	−	0.891458i	$-0.649683\pi$
$503$	274.373	−	475.228i	0.545473	−	0.944787i	0.998577	−	0.0533293i	$-0.0169833\pi$
$504$		0			0
$505$	111.944	−	333.845i	0.221672	−	0.661079i
$506$	−503.272	−	599.776i	−0.994609	−	1.18533i
$507$		0			0
$508$	1725.25	+	304.209i	3.39617	+	0.598836i
$509$	−589.405	+	702.425i	−1.15797	+	1.38001i	−0.246241	+	0.969209i	$0.579196\pi$
$509$	−589.405	+	702.425i	−1.15797	+	1.38001i	−0.911725	+	0.410802i	$0.865249\pi$
$510$		0			0
$511$	51.8576	+	18.8746i	0.101483	+	0.0369366i
$512$	−448.851			−0.876663
$513$		0			0
$514$	1302.99			2.53501
$515$	−334.163	−	849.944i	−0.648861	−	1.65038i
$516$		0			0
$517$	469.626	−	559.679i	0.908368	−	1.08255i
$518$	−55.6013	+	315.331i	−0.107338	+	0.608746i
$519$		0			0
$520$	−1454.73	−	218.378i	−2.79756	−	0.419958i
$521$	−505.296	+	291.733i	−0.969858	+	0.559948i	−0.899193	−	0.437552i	$-0.855845\pi$
$521$	−505.296	+	291.733i	−0.969858	+	0.559948i	−0.0706651	+	0.997500i	$0.522512\pi$
$522$		0			0
$523$	787.733	+	454.798i	1.50618	+	0.869595i	0.999974	+	0.00718333i	$0.00228654\pi$
$523$	787.733	+	454.798i	1.50618	+	0.869595i	0.506208	+	0.862411i	$0.331047\pi$
$524$	−1116.41	+	196.853i	−2.13055	+	0.375674i
$525$		0			0
$526$	−721.230	+	262.506i	−1.37116	+	0.499062i
$527$	334.923	−	121.902i	0.635527	−	0.231313i
$528$		0			0
$529$	−16.1757	−	91.7369i	−0.0305779	−	0.173416i
$530$	9.86074	+	48.6290i	0.0186052	+	0.0917528i
$531$		0			0
$532$	−885.047	+	510.982i	−1.66362	+	0.960493i
$533$	−382.427	+	320.895i	−0.717500	+	0.602054i
$534$		0			0
$535$	103.897	+	169.792i	0.194200	+	0.317369i
$536$	525.893	−	626.735i	0.981143	−	1.16928i
$537$		0			0
$538$	−163.712	+	449.796i	−0.304298	+	0.836052i
$539$			115.188i			0.213707i
$540$		0			0
$541$	854.408			1.57931			0.789656	−	0.613550i	$-0.210259\pi$
$541$	854.408			1.57931			0.789656	+	0.613550i	$0.210259\pi$
$542$	994.130	+	361.834i	1.83419	+	0.667590i
$543$		0			0
$544$	−702.683	−	589.621i	−1.29170	−	1.08386i
$545$	65.1520	+	106.474i	0.119545	+	0.195365i
$546$		0			0
$547$	−342.347	−	407.993i	−0.625863	−	0.745874i	0.356204	−	0.934408i	$-0.384071\pi$
$547$	−342.347	−	407.993i	−0.625863	−	0.745874i	−0.982067	+	0.188534i	$0.939626\pi$
$548$	876.800	+	1518.66i	1.60000	+	2.77128i
$549$		0			0
$550$	−565.222	+	748.049i	−1.02768	+	1.36009i
$551$	−169.073	+	29.8121i	−0.306848	+	0.0541055i
$552$		0			0
$553$	−91.4077	−	251.140i	−0.165294	−	0.454142i
$554$	180.062	+	494.717i	0.325022	+	0.892991i
$555$		0			0
$556$	121.625	+	689.771i	0.218750	+	1.24060i
$557$	408.575	−	707.673i	0.733528	−	1.27051i	−0.221837	−	0.975084i	$-0.571205\pi$
$557$	408.575	−	707.673i	0.733528	−	1.27051i	0.955366	−	0.295425i	$-0.0954612\pi$
$558$		0			0
$559$	−251.120	−	434.953i	−0.449231	−	0.778091i
$560$	2147.53	+	322.378i	3.83487	+	0.575676i
$561$		0			0
$562$	1484.46	+	261.750i	2.64138	+	0.465747i
$563$	−217.558	−	182.553i	−0.386426	−	0.324250i	0.428793	−	0.903403i	$-0.358939\pi$
$563$	−217.558	−	182.553i	−0.386426	−	0.324250i	−0.815219	+	0.579153i	$0.803383\pi$
$564$		0			0
$565$	647.825	−	254.698i	1.14659	−	0.450794i
$566$			773.256i			1.36618i
$567$		0			0
$568$		−	1937.26i		−	3.41067i
$569$	146.231	−	401.765i	0.256996	−	0.706090i	−0.742353	−	0.670009i	$-0.766290\pi$
$569$	146.231	−	401.765i	0.256996	−	0.706090i	0.999349	−	0.0360812i	$-0.0114875\pi$
$570$		0			0
$571$	−795.674	−	667.649i	−1.39347	−	1.16926i	−0.963910	−	0.266227i	$-0.914223\pi$
$571$	−795.674	−	667.649i	−1.39347	−	1.16926i	−0.429564	−	0.903037i	$-0.641333\pi$
$572$	208.121	−	1180.31i	0.363848	−	2.06349i
$573$		0			0
$574$	998.323	−	837.692i	1.73924	−	1.45939i
$575$	480.699	−	203.307i	0.835998	−	0.353577i
$576$		0			0
$577$	13.7068	+	7.91361i	0.0237552	+	0.0137151i	0.511831	−	0.859086i	$-0.328968\pi$
$577$	13.7068	+	7.91361i	0.0237552	+	0.0137151i	−0.488075	+	0.872801i	$0.662301\pi$
$578$	146.811	+	832.607i	0.253998	+	1.44050i
$579$		0			0
$580$	658.772	+	358.239i	1.13581	+	0.617653i
$581$	−68.4267	−	188.001i	−0.117774	−	0.323582i
$582$		0			0
$583$	−24.9311	+	4.39602i	−0.0427635	+	0.00754035i
$584$	157.514	+	90.9406i	0.269715	+	0.155720i
$585$		0			0
$586$	32.1564	+	55.6965i	0.0548744	+	0.0950452i
$587$	88.9241	−	74.6162i	0.151489	−	0.127114i	−0.563893	−	0.825848i	$-0.690697\pi$
$587$	88.9241	−	74.6162i	0.151489	−	0.127114i	0.715382	+	0.698733i	$0.246253\pi$
$588$		0			0
$589$	91.6063	−	519.525i	0.155528	−	0.882046i
$590$	53.8258	+	2107.91i	0.0912301	+	3.57273i
$591$		0			0
$592$	−204.109	+	560.785i	−0.344779	+	0.947272i
$593$	70.0516			0.118131			0.0590654	−	0.998254i	$-0.481188\pi$
$593$	70.0516			0.118131			0.0590654	+	0.998254i	$0.481188\pi$
$594$		0			0
$595$	213.610	+	241.759i	0.359009	+	0.406318i
$596$	265.698	−	729.999i	0.445802	−	1.22483i
$597$		0			0
$598$	−589.160	+	702.134i	−0.985218	+	1.17414i
$599$	−102.432	−	18.0615i	−0.171005	−	0.0301528i	0.0874899	−	0.996165i	$-0.472115\pi$
$599$	−102.432	−	18.0615i	−0.171005	−	0.0301528i	−0.258495	+	0.966013i	$0.583227\pi$
$600$		0			0
$601$	405.512	−	340.265i	0.674729	−	0.566165i	−0.239732	−	0.970839i	$-0.577059\pi$
$601$	405.512	−	340.265i	0.674729	−	0.566165i	0.914461	+	0.404674i	$0.132615\pi$
$602$	655.547	+	1135.44i	1.08895	+	1.88611i
$603$		0			0
$604$	−261.088	+	452.218i	−0.432265	+	0.748705i
$605$	99.0601	+	78.9012i	0.163736	+	0.130415i
$606$		0			0
$607$	−355.728	−	977.354i	−0.586043	−	1.61014i	−0.777671	−	0.628671i	$-0.783599\pi$
$607$	−355.728	−	977.354i	−0.586043	−	1.61014i	0.191628	−	0.981468i	$-0.438623\pi$
$608$	−1275.81	+	464.358i	−2.09838	+	0.763747i
$609$		0			0
$610$	−239.518	−	190.776i	−0.392653	−	0.312747i
$611$	−740.707	−	427.647i	−1.21229	−	0.699914i
$612$		0			0
$613$	14.5370	−	8.39292i	0.0237145	−	0.0136916i	−0.488096	−	0.872790i	$-0.662308\pi$
$613$	14.5370	−	8.39292i	0.0237145	−	0.0136916i	0.511810	+	0.859098i	$0.328975\pi$
$614$	−924.645	−	1101.95i	−1.50594	−	1.79470i
$615$		0			0
$616$	−340.219	+	1929.48i	−0.552303	+	3.13227i
$617$	−536.704	−	450.348i	−0.869860	−	0.729899i	0.0942085	−	0.995552i	$-0.469968\pi$
$617$	−536.704	−	450.348i	−0.869860	−	0.729899i	−0.964069	+	0.265653i	$0.914412\pi$
$618$		0			0
$619$	235.061	+	85.5552i	0.379743	+	0.138215i	0.524837	−	0.851203i	$-0.324126\pi$
$619$	235.061	+	85.5552i	0.379743	+	0.138215i	−0.145094	+	0.989418i	$0.546348\pi$
$620$	−1726.74	+	1525.69i	−2.78507	+	2.46079i
$621$		0			0
$622$		−	551.151i		−	0.886094i
$623$	−565.943	−	205.987i	−0.908416	−	0.330636i
$624$		0			0
$625$	−366.049	−	506.590i	−0.585679	−	0.810543i
$626$	−8.09349	−	1.42710i	−0.0129289	−	0.00227971i
$627$		0			0
$628$	752.979	+	897.365i	1.19901	+	1.42892i
$629$	−76.7787	+	44.3282i	−0.122065	+	0.0704741i
$630$		0			0
$631$	−567.250	+	982.505i	−0.898969	+	1.55706i	−0.0701553	+	0.997536i	$0.522349\pi$
$631$	−567.250	+	982.505i	−0.898969	+	1.55706i	−0.828814	+	0.559524i	$0.810984\pi$
$632$	−152.955	−	867.448i	−0.242017	−	1.37254i
$633$		0			0
$634$	267.341	−	97.3041i	0.421673	−	0.153476i
$635$	−719.091	−	391.040i	−1.13243	−	0.615811i
$636$		0			0
$637$	132.797	−	23.4157i	0.208473	−	0.0367594i
$638$	−262.800	+	455.183i	−0.411912	+	0.713452i
$639$		0			0
$640$	1572.01	+	527.125i	2.45627	+	0.823633i
$641$	540.058	+	643.616i	0.842524	+	1.00408i	0.999863	+	0.0165365i	$0.00526398\pi$
$641$	540.058	+	643.616i	0.842524	+	1.00408i	−0.157339	+	0.987545i	$0.550292\pi$
$642$		0			0
$643$	−704.771	−	124.270i	−1.09607	−	0.193266i	−0.403757	−	0.914866i	$-0.632296\pi$
$643$	−704.771	−	124.270i	−1.09607	−	0.193266i	−0.692310	+	0.721600i	$0.743407\pi$
$644$	1119.53	−	1334.20i	1.73840	−	2.07174i
$645$		0			0
$646$	−365.290	−	132.955i	−0.565464	−	0.205812i
$647$	54.6299			0.0844358			0.0422179	−	0.999108i	$-0.486558\pi$
$647$	54.6299			0.0844358			0.0422179	+	0.999108i	$0.486558\pi$
$648$		0			0
$649$	−1075.82			−1.65766
$650$	977.307	+	499.565i	1.50355	+	0.768562i
$651$		0			0
$652$	−1894.10	+	2257.30i	−2.90506	+	3.46212i
$653$	76.2276	−	432.308i	0.116734	−	0.662034i	−0.869142	−	0.494562i	$-0.835329\pi$
$653$	76.2276	−	432.308i	0.116734	−	0.662034i	0.985877	−	0.167472i	$-0.0535604\pi$
$654$		0			0
$655$	523.806	+	78.6316i	0.799703	+	0.120048i
$656$	2103.51	−	1214.46i	3.20656	−	1.85131i
$657$		0			0
$658$	1933.61	+	1116.37i	2.93861	+	1.69661i
$659$	−1007.40	+	177.632i	−1.52868	+	0.269548i	−0.873838	−	0.486217i	$-0.838377\pi$
$659$	−1007.40	+	177.632i	−1.52868	+	0.269548i	−0.654843	+	0.755765i	$0.727265\pi$
$660$		0			0
$661$	653.995	−	238.035i	0.989403	−	0.360113i	0.203914	−	0.978989i	$-0.434634\pi$
$661$	653.995	−	238.035i	0.989403	−	0.360113i	0.785489	+	0.618876i	$0.212412\pi$
$662$	−399.322	+	145.341i	−0.603205	+	0.219549i
$663$		0			0
$664$	−114.500	−	649.362i	−0.172440	−	0.977955i
$665$	467.976	−	94.8938i	0.703723	−	0.142698i
$666$		0			0
$667$	253.388	−	146.293i	0.379891	−	0.219330i
$668$	−1871.49	+	1570.36i	−2.80163	+	2.35084i
$669$		0			0
$670$	−520.698	+	318.618i	−0.777161	+	0.475550i
$671$	100.423	−	119.679i	0.149661	−	0.178359i
$672$		0			0
$673$	254.284	−	698.639i	0.377836	−	1.03810i	−0.594415	−	0.804159i	$-0.702616\pi$
$673$	254.284	−	698.639i	0.377836	−	1.03810i	0.972251	−	0.233939i	$-0.0751615\pi$
$674$		−	1569.37i		−	2.32845i
$675$		0			0
$676$	405.441			0.599765
$677$	−732.006	−	266.428i	−1.08125	−	0.393542i	−0.260877	−	0.965372i	$-0.584012\pi$
$677$	−732.006	−	266.428i	−1.08125	−	0.393542i	−0.820372	+	0.571830i	$0.806234\pi$
$678$		0			0
$679$	−537.640	−	451.134i	−0.791812	−	0.664409i
$680$	554.961	+	906.937i	0.816119	+	1.33373i
$681$		0			0
$682$	−1038.14	−	1237.20i	−1.52219	−	1.81408i
$683$	396.792	+	687.263i	0.580954	+	1.00624i	0.995367	+	0.0961530i	$0.0306538\pi$
$683$	396.792	+	687.263i	0.580954	+	1.00624i	−0.414412	+	0.910089i	$0.636013\pi$
$684$		0			0
$685$	−162.829	−	803.005i	−0.237707	−	1.17227i
$686$	1095.75	−	193.211i	1.59731	−	0.281649i
$687$		0			0
$688$	835.760	+	2296.23i	1.21477	+	3.33755i
$689$	10.1361	+	27.8488i	0.0147114	+	0.0404192i
$690$		0			0
$691$	70.9748	+	402.518i	0.102713	+	0.582516i	0.992109	+	0.125378i	$0.0400143\pi$
$691$	70.9748	+	402.518i	0.102713	+	0.582516i	−0.889396	+	0.457138i	$0.848875\pi$
$692$	839.412	−	1453.90i	1.21302	−	2.10102i
$693$		0			0
$694$	549.248	+	951.325i	0.791424	+	1.37079i
$695$	48.5824	−	323.632i	0.0699027	−	0.465658i
$696$		0			0
$697$	355.356	+	62.6589i	0.509836	+	0.0898979i
$698$	−407.841	−	342.219i	−0.584299	−	0.490285i
$699$		0			0
$700$	−1857.09	−	949.279i	−2.65299	−	1.35611i
$701$			101.996i			0.145500i	0.997350	+	0.0727502i	$0.0231776\pi$
$701$			101.996i			0.145500i	−0.997350	+	0.0727502i	$0.976822\pi$
$702$		0			0
$703$			131.222i			0.186660i
$704$	−676.133	+	1857.66i	−0.960417	+	2.63872i
$705$		0			0
$706$	876.224	+	735.239i	1.24111	+	1.04141i
$707$	−95.3347	+	540.670i	−0.134844	+	0.764738i
$708$		0			0
$709$	736.947	−	618.372i	1.03942	−	0.872175i	0.0474760	−	0.998872i	$-0.484882\pi$
$709$	736.947	−	618.372i	1.03942	−	0.872175i	0.991941	+	0.126698i	$0.0404378\pi$
$710$	−459.541	+	1370.46i	−0.647241	+	1.93023i
$711$		0			0
$712$	−1719.01	−	992.472i	−2.41434	−	1.39392i
$713$	156.119	+	885.397i	0.218961	+	1.24179i
$714$		0			0
$715$	−267.526	+	491.959i	−0.374162	+	0.688054i
$716$	−116.241	−	319.368i	−0.162347	−	0.446045i
$717$		0			0
$718$	18.8209	−	3.31864i	0.0262130	−	0.00462206i
$719$	13.4440	+	7.76189i	0.0186982	+	0.0107954i	0.509320	−	0.860577i	$-0.329897\pi$
$719$	13.4440	+	7.76189i	0.0186982	+	0.0107954i	−0.490622	+	0.871373i	$0.663230\pi$
$720$		0			0
$721$	711.982	+	1233.19i	0.987492	+	1.71039i
$722$	619.562	−	519.874i	0.858119	−	0.720048i
$723$		0			0
$724$	−385.813	+	2188.05i	−0.532890	+	3.02217i
$725$	−238.618	−	256.555i	−0.329129	−	0.353869i
$726$		0			0
$727$	−81.8003	+	224.744i	−0.112518	+	0.309139i	−0.983152	−	0.182792i	$-0.941487\pi$
$727$	−81.8003	+	224.744i	−0.112518	+	0.309139i	0.870634	+	0.491931i	$0.163709\pi$
$728$	2293.61			3.15056
$729$		0			0
$730$	−89.8567	−	101.698i	−0.123091	−	0.139312i
$731$	−124.160	+	341.126i	−0.169849	+	0.466657i
$732$		0			0
$733$	−817.513	+	974.274i	−1.11530	+	1.32916i	−0.176653	+	0.984273i	$0.556527\pi$
$733$	−817.513	+	974.274i	−1.11530	+	1.32916i	−0.938645	+	0.344886i	$0.887918\pi$
$734$	979.670	+	172.742i	1.33470	+	0.235344i
$735$		0			0
$736$	1772.50	−	1487.31i	2.40829	−	2.02080i
$737$	−155.726	−	269.726i	−0.211298	−	0.365978i
$738$		0			0
$739$	542.460	−	939.569i	0.734046	−	1.27141i	−0.221094	−	0.975252i	$-0.570963\pi$
$739$	542.460	−	939.569i	0.734046	−	1.27141i	0.955140	−	0.296153i	$-0.0957039\pi$
$740$	357.090	−	448.325i	0.482554	−	0.605844i
$741$		0			0
$742$	−26.4603	−	72.6990i	−0.0356608	−	0.0979771i
$743$	980.589	−	356.905i	1.31977	−	0.480357i	0.416385	−	0.909188i	$-0.363297\pi$
$743$	980.589	−	356.905i	1.31977	−	0.480357i	0.903384	+	0.428832i	$0.141075\pi$
$744$		0			0
$745$	−226.141	+	283.918i	−0.303544	+	0.381099i
$746$	−1613.27	−	931.424i	−2.16257	−	1.24856i
$747$		0			0
$748$	−750.229	+	433.145i	−1.00298	+	0.579071i
$749$	−199.501	−	237.756i	−0.266356	−	0.317431i
$750$		0			0
$751$	223.514	−	1267.61i	0.297622	−	1.68790i	−0.358727	−	0.933443i	$-0.616789\pi$
$751$	223.514	−	1267.61i	0.297622	−	1.68790i	0.656349	−	0.754457i	$-0.272100\pi$
$752$	3187.77	+	2674.86i	4.23906	+	3.55699i
$753$		0			0
$754$	578.191	+	210.444i	0.766832	+	0.279104i
$755$	182.835	−	161.547i	0.242166	−	0.213970i
$756$		0			0
$757$			906.234i			1.19714i	0.801071	+	0.598569i	$0.204264\pi$
$757$			906.234i			1.19714i	−0.801071	+	0.598569i	$0.795736\pi$
$758$	−2004.26	−	729.490i	−2.64414	−	0.962388i
$759$		0			0
$760$	1573.23	−	40.1727i	2.07004	−	0.0528588i
$761$	1063.75	+	187.569i	1.39784	+	0.246476i	0.821254	−	0.570562i	$-0.193275\pi$
$761$	1063.75	+	187.569i	1.39784	+	0.246476i	0.576583	+	0.817039i	$0.304386\pi$
$762$		0			0
$763$	−125.103	−	149.092i	−0.163962	−	0.195403i
$764$	−1259.25	+	727.027i	−1.64823	+	0.951606i
$765$		0			0
$766$	−1016.46	+	1760.55i	−1.32697	+	2.29837i
$767$	218.696	+	1240.29i	0.285131	+	1.61706i
$768$		0			0
$769$	−28.4739	+	10.3637i	−0.0370272	+	0.0134768i	−0.360467	−	0.932772i	$-0.617383\pi$
$769$	−28.4739	+	10.3637i	−0.0370272	+	0.0134768i	0.323440	+	0.946249i	$0.395161\pi$
$770$	698.374	−	1284.25i	0.906980	−	1.66786i
$771$		0			0
$772$	1149.31	−	202.654i	1.48874	−	0.262506i
$773$	−188.396	+	326.311i	−0.243720	+	0.422136i	−0.961771	−	0.273855i	$-0.911701\pi$
$773$	−188.396	+	326.311i	−0.243720	+	0.422136i	0.718051	+	0.695991i	$0.245035\pi$
$774$		0			0
$775$	991.573	−	419.376i	1.27945	−	0.541131i
$776$	−1486.85	−	1771.96i	−1.91604	−	2.28345i
$777$		0			0
$778$	780.656	+	137.651i	1.00341	+	0.176929i
$779$	343.302	−	409.131i	0.440695	−	0.525200i
$780$		0			0
$781$	−693.004	−	252.233i	−0.887329	−	0.322961i
$782$	662.496			0.847182
$783$		0			0
$784$	−656.078			−0.836834
$785$	−200.267	−	509.380i	−0.255118	−	0.648891i
$786$		0			0
$787$	−287.757	+	342.936i	−0.365638	+	0.435751i	−0.917227	−	0.398366i	$-0.869578\pi$
$787$	−287.757	+	342.936i	−0.365638	+	0.435751i	0.551588	+	0.834116i	$0.314022\pi$
$788$	58.5864	−	332.260i	0.0743482	−	0.421650i
$789$		0			0
$790$	−97.5658	+	649.936i	−0.123501	+	0.822704i
$791$	−939.933	+	542.671i	−1.18828	+	0.686056i
$792$		0			0
$793$	−158.389	−	91.4460i	−0.199734	−	0.115316i
$794$	314.988	−	55.5409i	0.396710	−	0.0699507i
$795$		0			0
$796$	2924.52	−	1064.44i	3.67402	−	1.33723i
$797$	1344.71	−	489.434i	1.68721	−	0.614095i	0.692943	−	0.720993i	$-0.256314\pi$
$797$	1344.71	−	489.434i	1.68721	−	0.614095i	0.994270	+	0.106898i	$0.0340917\pi$
$798$		0			0
$799$	107.350	+	608.813i	0.134356	+	0.761969i
$800$	−2210.69	−	1670.39i	−2.76336	−	2.08799i
$801$		0			0
$802$	1648.23	−	951.606i	2.05515	−	1.18654i
$803$	53.0401	−	44.5059i	0.0660524	−	0.0554246i
$804$		0			0
$805$	−694.135	+	424.746i	−0.862280	+	0.527634i
$806$	−1215.31	+	1448.34i	−1.50782	+	1.79695i
$807$		0			0
$808$	−618.862	+	1700.31i	−0.765918	+	2.10434i
$809$			1430.32i			1.76801i	0.467474	+	0.884007i	$0.345164\pi$
$809$			1430.32i			1.76801i	−0.467474	+	0.884007i	$0.654836\pi$
$810$		0			0
$811$	−1216.28			−1.49973			−0.749866	−	0.661589i	$-0.769882\pi$
$811$	−1216.28			−1.49973			−0.749866	+	0.661589i	$0.769882\pi$
$812$	−1098.69	−	399.889i	−1.35306	−	0.492474i
$813$		0			0
$814$	307.746	+	258.229i	0.378066	+	0.317235i
$815$	1174.39	−	718.617i	1.44097	−	0.881738i
$816$		0			0
$817$	345.376	+	411.604i	0.422737	+	0.503799i
$818$	−545.003	−	943.973i	−0.666263	−	1.15400i
$819$		0			0
$820$	−2286.26	+	463.596i	−2.78812	+	0.565361i
$821$	290.704	−	51.2590i	0.354086	−	0.0624349i	0.00622377	−	0.999981i	$-0.498019\pi$
$821$	290.704	−	51.2590i	0.354086	−	0.0624349i	0.347862	+	0.937546i	$0.386908\pi$
$822$		0			0
$823$	−119.432	−	328.138i	−0.145118	−	0.398710i	0.845744	−	0.533590i	$-0.179157\pi$
$823$	−119.432	−	328.138i	−0.145118	−	0.398710i	−0.990862	+	0.134880i	$0.956935\pi$
$824$	1605.14	+	4410.08i	1.94798	+	5.35203i
$825$		0			0
$826$	−570.903	−	3237.75i	−0.691166	−	3.91980i
$827$	−740.937	+	1283.34i	−0.895933	+	1.55180i	−0.0632873	+	0.997995i	$0.520158\pi$
$827$	−740.937	+	1283.34i	−0.895933	+	1.55180i	−0.832646	+	0.553806i	$0.813175\pi$
$828$		0			0
$829$	39.5851	+	68.5634i	0.0477504	+	0.0827062i	0.888913	−	0.458077i	$-0.151461\pi$
$829$	39.5851	+	68.5634i	0.0477504	+	0.0827062i	−0.841162	+	0.540783i	$0.818128\pi$
$830$	−73.0366	+	486.535i	−0.0879959	+	0.586186i
$831$		0			0
$832$	2279.10	+	401.866i	2.73930	+	0.483013i
$833$	−74.6636	−	62.6502i	−0.0896321	−	0.0752103i
$834$		0			0
$835$	1062.33	−	417.665i	1.27225	−	0.500198i
$836$			1282.21i			1.53375i
$837$		0			0
$838$		−	2734.05i		−	3.26259i
$839$	−44.6871	+	122.777i	−0.0532624	+	0.146337i	−0.963471	−	0.267813i	$-0.913699\pi$
$839$	−44.6871	+	122.777i	−0.0532624	+	0.146337i	0.910208	+	0.414150i	$0.135921\pi$
$840$		0			0
$841$	493.781	+	414.331i	0.587135	+	0.492665i
$842$	92.6139	−	525.240i	0.109993	−	0.623800i
$843$		0			0
$844$	−1587.42	+	1332.00i	−1.88082	+	1.57820i
$845$	−179.609	−	60.2261i	−0.212554	−	0.0712735i
$846$		0			0
$847$	−171.005	−	98.7295i	−0.201894	−	0.116564i
$848$	−25.0385	−	142.001i	−0.0295266	−	0.167454i
$849$		0			0
$850$	−177.456	−	773.232i	−0.208771	−	0.909685i
$851$	−76.4874	−	210.147i	−0.0898794	−	0.246942i
$852$		0			0
$853$	590.303	−	104.086i	0.692032	−	0.122024i	0.183439	−	0.983031i	$-0.441277\pi$
$853$	590.303	−	104.086i	0.692032	−	0.122024i	0.508593	+	0.861007i	$0.330166\pi$
$854$	413.473	+	238.719i	0.484160	+	0.279530i
$855$		0			0
$856$	−511.456	−	885.868i	−0.597495	−	1.03489i
$857$	−214.669	+	180.129i	−0.250489	+	0.210186i	−0.759383	−	0.650644i	$-0.774499\pi$
$857$	−214.669	+	180.129i	−0.250489	+	0.210186i	0.508894	+	0.860829i	$0.330055\pi$
$858$		0			0
$859$	−272.385	+	1544.77i	−0.317095	+	1.79834i	0.243126	+	0.969995i	$0.421827\pi$
$859$	−272.385	+	1544.77i	−0.317095	+	1.79834i	−0.560222	+	0.828343i	$0.689284\pi$
$860$	−59.9084	−	2346.12i	−0.0696610	−	2.72805i
$861$		0			0
$862$	468.535	−	1287.29i	0.543544	−	1.49337i
$863$	−282.809			−0.327704			−0.163852	−	0.986485i	$-0.552392\pi$
$863$	−282.809			−0.327704			−0.163852	+	0.986485i	$0.552392\pi$
$864$		0			0
$865$	−587.826	+	519.383i	−0.679567	+	0.600443i
$866$	81.1295	−	222.902i	0.0936831	−	0.257392i
$867$		0			0
$868$	2309.34	−	2752.16i	2.66053	−	3.17069i
$869$	−330.222	−	58.2270i	−0.380002	−	0.0670046i
$870$		0			0
$871$	−279.304	+	234.364i	−0.320670	+	0.269074i
$872$	−320.725	−	555.512i	−0.367804	−	0.637055i
$873$		0			0
$874$	490.286	−	849.200i	0.560968	−	0.971625i
$875$	681.672	+	696.387i	0.779054	+	0.795871i
$876$		0			0
$877$	488.442	+	1341.98i	0.556946	+	1.53020i	0.824043	+	0.566527i	$0.191713\pi$
$877$	488.442	+	1341.98i	0.556946	+	1.53020i	−0.267097	+	0.963670i	$0.586065\pi$
$878$	−1833.66	+	667.398i	−2.08845	+	0.760134i
$879$		0			0
$880$	1697.48	−	2131.18i	1.92896	−	2.42180i
$881$	998.678	+	576.587i	1.13357	+	0.654469i	0.944831	−	0.327558i	$-0.106226\pi$
$881$	998.678	+	576.587i	1.13357	+	0.654469i	0.188742	+	0.982027i	$0.439559\pi$
$882$		0			0
$883$	−23.9284	+	13.8151i	−0.0270990	+	0.0156456i	−0.513488	−	0.858097i	$-0.671647\pi$
$883$	−23.9284	+	13.8151i	−0.0270990	+	0.0156456i	0.486389	+	0.873742i	$0.338314\pi$
$884$	651.871	+	776.870i	0.737411	+	0.878812i
$885$		0			0
$886$	326.034	−	1849.03i	0.367984	−	2.08694i
$887$	−168.475	−	141.368i	−0.189938	−	0.159377i	0.542860	−	0.839823i	$-0.317342\pi$
$887$	−168.475	−	141.368i	−0.189938	−	0.159377i	−0.732798	+	0.680446i	$0.761786\pi$
$888$		0			0
$889$	1199.28	+	436.504i	1.34903	+	0.491006i
$890$	980.643	+	1109.87i	1.10185	+	1.24704i
$891$		0			0
$892$		−	684.097i		−	0.766925i
$893$	859.834	+	312.954i	0.962861	+	0.350453i
$894$		0			0
$895$	4.05358	+	158.746i	0.00452914	+	0.177369i
$896$	−2545.91	−	448.913i	−2.84142	−	0.501019i
$897$		0			0
$898$	18.8510	+	22.4657i	0.0209922	+	0.0250175i
$899$	522.682	−	301.770i	0.581403	−	0.335673i
$900$		0			0
$901$	10.7105	−	18.5511i	0.0118873	−	0.0205894i
$902$	−283.930	−	1610.25i	−0.314778	−	1.78519i
$903$		0			0
$904$	−3361.35	+	1223.43i	−3.71830	+	1.35335i
$905$	495.937	−	911.987i	0.547997	−	1.00772i
$906$		0			0
$907$	−871.694	+	153.703i	−0.961073	+	0.169463i	−0.632109	−	0.774879i	$-0.717811\pi$
$907$	−871.694	+	153.703i	−0.961073	+	0.169463i	−0.328964	+	0.944342i	$0.606700\pi$
$908$	−12.8461	+	22.2501i	−0.0141477	+	0.0245045i
$909$		0			0
$910$	−1622.55	−	544.072i	−1.78302	−	0.597881i
$911$	−695.382	−	828.724i	−0.763317	−	0.909686i	0.234736	−	0.972059i	$-0.424577\pi$
$911$	−695.382	−	828.724i	−0.763317	−	0.909686i	−0.998053	+	0.0623734i	$0.980133\pi$
$912$		0			0
$913$	−247.200	−	43.5881i	−0.270756	−	0.0477416i
$914$	390.729	−	465.653i	0.427493	−	0.509467i
$915$		0			0
$916$	−2881.62	−	1048.83i	−3.14588	−	1.14501i
$917$	−825.861			−0.900612
$918$		0			0
$919$	−227.334			−0.247371			−0.123686	−	0.992321i	$-0.539471\pi$
$919$	−227.334			−0.247371			−0.123686	+	0.992321i	$0.539471\pi$
$920$	−2496.06	+	981.351i	−2.71311	+	1.06669i
$921$		0			0
$922$	−2106.60	+	2510.54i	−2.28481	+	2.72293i
$923$	−149.917	+	850.222i	−0.162424	+	0.921150i
$924$		0			0
$925$	−224.786	+	145.562i	−0.243011	+	0.157364i
$926$	483.392	−	279.087i	0.522022	−	0.301389i
$927$		0			0
$928$	−1345.19	−	776.646i	−1.44956	−	0.836903i
$929$	195.920	−	34.5460i	0.210894	−	0.0371862i	−0.0672031	−	0.997739i	$-0.521408\pi$
$929$	195.920	−	34.5460i	0.210894	−	0.0371862i	0.278097	+	0.960553i	$0.410296\pi$
$930$		0			0
$931$	−135.562	+	49.3404i	−0.145609	+	0.0529972i
$932$	−3265.71	+	1188.62i	−3.50398	+	1.27534i
$933$		0			0
$934$	390.367	+	2213.88i	0.417952	+	2.37033i
$935$	396.690	−	80.4388i	0.424267	−	0.0860308i
$936$		0			0
$937$	−634.949	+	366.588i	−0.677640	+	0.391236i	−0.798965	−	0.601377i	$-0.794619\pi$
$937$	−634.949	+	366.588i	−0.677640	+	0.391236i	0.121325	+	0.992613i	$0.461286\pi$
$938$	729.120	−	611.804i	0.777313	−	0.652243i
$939$		0			0
$940$	−2086.03	−	3409.06i	−2.21918	−	3.62666i
$941$	489.023	−	582.795i	0.519684	−	0.619336i	−0.440822	−	0.897595i	$-0.645313\pi$
$941$	489.023	−	582.795i	0.519684	−	0.619336i	0.960506	+	0.278259i	$0.0897574\pi$
$942$		0			0
$943$	−311.309	+	855.315i	−0.330126	+	0.907015i
$944$		−	6127.57i		−	6.49107i
$945$		0			0
$946$	1644.97			1.73887
$947$	−570.175	−	207.527i	−0.602085	−	0.219141i	0.0229512	−	0.999737i	$-0.492694\pi$
$947$	−570.175	−	207.527i	−0.602085	−	0.219141i	−0.625037	+	0.780595i	$0.714916\pi$
$948$		0			0
$949$	−62.0919	−	52.1013i	−0.0654288	−	0.0549013i
$950$	−1122.47	−	344.771i	−1.18155	−	0.362917i
$951$		0			0
$952$	−1065.62	−	1269.96i	−1.11935	−	1.33399i
$953$	283.652	+	491.299i	0.297641	+	0.515529i	0.975596	−	0.219574i	$-0.0704669\pi$
$953$	283.652	+	491.299i	0.297641	+	0.515529i	−0.677955	+	0.735104i	$0.737134\pi$
$954$		0			0
$955$	665.837	−	135.015i	0.697212	−	0.141377i
$956$	−2154.88	+	379.963i	−2.25405	+	0.397451i
$957$		0			0
$958$	420.808	+	1156.16i	0.439257	+	1.20685i
$959$	436.936	+	1200.47i	0.455616	+	1.25179i
$960$		0			0
$961$	155.163	+	879.975i	0.161460	+	0.915687i
$962$	235.147	−	407.286i	0.244435	−	0.423375i
$963$		0			0
$964$	−1958.28	−	3391.84i	−2.03141	−	3.51851i
$965$	−539.243	−	80.9489i	−0.558801	−	0.0838849i
$966$		0			0
$967$	−935.891	−	165.023i	−0.967830	−	0.170654i	−0.332677	−	0.943041i	$-0.607952\pi$
$967$	−935.891	−	165.023i	−0.967830	−	0.170654i	−0.635153	+	0.772386i	$0.719063\pi$
$968$	−498.531	−	418.317i	−0.515012	−	0.432146i
$969$		0			0
$970$	631.501	+	1606.22i	0.651032	+	1.65590i
$971$		−	935.107i		−	0.963035i	−0.876436	−	0.481518i	$-0.840086\pi$
$971$		−	935.107i		−	0.963035i	0.876436	−	0.481518i	$-0.159914\pi$
$972$		0			0
$973$			510.257i			0.524416i
$974$	−514.954	+	1414.83i	−0.528700	+	1.45259i
$975$		0			0
$976$	681.658	+	571.979i	0.698420	+	0.586044i
$977$	−146.223	+	829.272i	−0.149665	+	0.848795i	0.813837	+	0.581094i	$0.197375\pi$
$977$	−146.223	+	829.272i	−0.149665	+	0.848795i	−0.963502	+	0.267701i	$0.913736\pi$
$978$		0			0
$979$	−578.848	+	485.711i	−0.591265	+	0.496130i
$980$	597.420	+	200.326i	0.609612	+	0.204414i
$981$		0			0
$982$	2635.60	+	1521.66i	2.68391	+	1.54955i
$983$	−107.632	−	610.411i	−0.109493	−	0.620967i	−0.989330	−	0.145691i	$-0.953459\pi$
$983$	−107.632	−	610.411i	−0.109493	−	0.620967i	0.879837	−	0.475276i	$-0.157652\pi$
$984$		0			0
$985$	−75.3090	+	138.487i	−0.0764558	+	0.140596i
$986$	−152.109	−	417.916i	−0.154269	−	0.423850i
$987$		0			0
$988$	1478.23	−	260.652i	1.49618	−	0.263818i
$989$	−793.027	−	457.854i	−0.801847	−	0.462947i
$990$		0			0
$991$	971.444	+	1682.59i	0.980266	+	1.69787i	0.661330	+	0.750095i	$0.269992\pi$
$991$	971.444	+	1682.59i	0.980266	+	1.69787i	0.318936	+	0.947776i	$0.396674\pi$
$992$	3656.28	−	3067.98i	3.68576	−	3.09272i
$993$		0			0
$994$	391.357	−	2219.50i	0.393719	−	2.23289i
$995$	−1453.67	+	37.1195i	−1.46097	+	0.0373061i
$996$		0			0
$997$	328.542	−	902.662i	0.329531	−	0.905378i	−0.658700	−	0.752406i	$-0.728893\pi$
$997$	328.542	−	902.662i	0.329531	−	0.905378i	0.988231	−	0.152972i	$-0.0488844\pi$
$998$	−844.210			−0.845902
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.n.a.179.34		204
3.2	odd	2		135.3.n.a.104.1	yes	204
5.4	even	2	inner	405.3.n.a.179.1		204
15.14	odd	2		135.3.n.a.104.34	yes	204
27.7	even	9		135.3.n.a.74.34	yes	204
27.20	odd	18	inner	405.3.n.a.224.1		204
135.34	even	18		135.3.n.a.74.1	✓	204
135.74	odd	18	inner	405.3.n.a.224.34		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.n.a.74.1	✓	204	135.34	even	18
135.3.n.a.74.34	yes	204	27.7	even	9
135.3.n.a.104.1	yes	204	3.2	odd	2
135.3.n.a.104.34	yes	204	15.14	odd	2
405.3.n.a.179.1		204	5.4	even	2	inner
405.3.n.a.179.34		204	1.1	even	1	trivial
405.3.n.a.224.1		204	27.20	odd	18	inner
405.3.n.a.224.34		204	135.74	odd	18	inner

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.n (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.60298 + 1.31138i) q^{2} +(8.19760 + 6.87860i) q^{4} +(-2.60972 - 4.26490i) q^{5} +(5.01113 + 5.97203i) q^{7} +(12.8469 + 22.2515i) q^{8} +(-3.80988 - 18.7887i) q^{10} +(9.63258 - 1.69848i) q^{11} +(-3.91628 - 10.7599i) q^{13} +(10.2234 + 28.0886i) q^{14} +(9.67410 + 54.8645i) q^{16} +(-4.13818 + 7.16754i) q^{17} +(6.12499 + 10.6088i) q^{19} +(7.94311 - 52.9131i) q^{20} +(36.9334 + 6.51235i) q^{22} +(-15.9927 - 13.4195i) q^{23} +(-11.3787 + 22.2604i) q^{25} -43.9034i q^{26} +83.4258i q^{28} +(-4.79335 + 13.1696i) q^{29} +(-32.9893 - 27.6813i) q^{31} +(-19.2458 + 109.148i) q^{32} +(-24.3092 + 20.3978i) q^{34} +(12.3925 - 36.9573i) q^{35} +(9.27687 + 5.35600i) q^{37} +(8.15609 + 46.2555i) q^{38} +(61.3736 - 112.861i) q^{40} +(-14.9116 - 40.9693i) q^{41} +(43.1958 - 7.61658i) q^{43} +(90.6472 + 52.3352i) q^{44} +(-40.0234 - 69.3225i) q^{46} +(57.2199 - 48.0132i) q^{47} +(-2.04496 + 11.5976i) q^{49} +(-70.1892 + 65.2820i) q^{50} +(41.9089 - 115.144i) q^{52} -2.58820 q^{53} +(-32.3822 - 36.6494i) q^{55} +(-68.5091 + 188.227i) q^{56} +(-34.5407 + 41.1640i) q^{58} +(-108.318 - 19.0993i) q^{59} +(12.2356 - 10.2669i) q^{61} +(-82.5593 - 142.997i) q^{62} +(-101.055 + 175.033i) q^{64} +(-35.6695 + 44.7829i) q^{65} +(-10.8906 - 29.9217i) q^{67} +(-83.2258 + 30.2917i) q^{68} +(93.1148 - 116.905i) q^{70} +(-65.2964 - 37.6989i) q^{71} +(6.13041 - 3.53939i) q^{73} +(26.4006 + 31.4631i) q^{74} +(-22.7635 + 129.098i) q^{76} +(58.4135 + 49.0147i) q^{77} +(-32.2143 - 11.7251i) q^{79} +(208.745 - 184.440i) q^{80} -167.166i q^{82} +(-24.1153 - 8.77724i) q^{83} +(41.3683 - 1.05634i) q^{85} +(165.622 + 29.2036i) q^{86} +(161.543 + 192.519i) q^{88} +(-66.9037 + 38.6269i) q^{89} +(44.6334 - 77.3073i) q^{91} +(-38.7945 - 220.015i) q^{92} +(269.126 - 97.9538i) q^{94} +(29.2609 - 53.8085i) q^{95} +(-88.6588 + 15.6329i) q^{97} +(-22.5768 + 39.1041i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 12 q^{4} - 3 q^{5} - 3 q^{10} - 6 q^{11} + 48 q^{14} + 12 q^{16} - 6 q^{19} - 63 q^{20} - 15 q^{25} - 96 q^{29} - 102 q^{31} + 12 q^{34} + 252 q^{35} + 117 q^{40} - 96 q^{41} + 666 q^{44} - 6 q^{46}+ \cdots + 543 q^{95}+O(q^{100}) \) 204 * q - 12 * q^4 - 3 * q^5 - 3 * q^10 - 6 * q^11 + 48 * q^14 + 12 * q^16 - 6 * q^19 - 63 * q^20 - 15 * q^25 - 96 * q^29 - 102 * q^31 + 12 * q^34 + 252 * q^35 + 117 * q^40 - 96 * q^41 + 666 * q^44 - 6 * q^46 + 60 * q^49 - 48 * q^50 - 12 * q^55 - 294 * q^56 - 510 * q^59 + 132 * q^61 - 486 * q^64 - 147 * q^65 - 141 * q^70 + 18 * q^71 + 954 * q^74 + 84 * q^76 - 48 * q^79 + 69 * q^85 + 1506 * q^86 - 792 * q^89 - 6 * q^91 + 492 * q^94 + 543 * q^95

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