LMFDB - Embedded newform 360.4.q.e.241.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [360,4,Mod(121,360)] 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("360.121"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(360, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	360.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$21.2406876021$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
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} - 6 x^{19} + 9 x^{18} + 228 x^{17} - 1491 x^{16} + 5274 x^{15} + 540 x^{14} + \cdots + 205891132094649 $ x^20 - 6x^19 + 9x^18 + 228x^17 - 1491x^16 + 5274x^15 + 540x^14 + 88290x^13 + 125226x^12 - 4588326x^11 + 44794134x^10 - 123884802x^9 + 91289754x^8 + 1737812070x^7 + 286978140x^6 + 75676135518x^5 - 577643949099x^4 + 2384960530284x^3 + 2541865828329x^2 - 45753584909922*x + 205891132094649
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{15} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			241.1
Root			$-2.09215 + 4.75635i$ of defining polynomial
Character	$\chi$	$=$	360.241
Dual form			360.4.q.e.121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.16520 + 0.566318i) q^{3} +(2.50000 + 4.33013i) q^{5} +(1.57018 - 2.71963i) q^{7} +(26.3586 - 5.85030i) q^{9} +(-7.30996 + 12.6612i) q^{11} +(-27.3440 - 47.3612i) q^{13} +(-15.3652 - 20.9502i) q^{15} +45.7952 q^{17} -50.3457 q^{19} +(-6.57012 + 14.9367i) q^{21} +(9.94951 + 17.2331i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(-132.834 + 45.1453i) q^{27} +(82.1830 - 142.345i) q^{29} +(123.317 + 213.592i) q^{31} +(30.5871 - 69.5375i) q^{33} +15.7018 q^{35} +268.484 q^{37} +(168.059 + 229.144i) q^{39} +(166.114 + 287.718i) q^{41} +(55.4147 - 95.9811i) q^{43} +(91.2289 + 99.5102i) q^{45} +(-17.8310 + 30.8843i) q^{47} +(166.569 + 288.506i) q^{49} +(-236.541 + 25.9347i) q^{51} +482.657 q^{53} -73.0996 q^{55} +(260.046 - 28.5117i) q^{57} +(164.766 + 285.383i) q^{59} +(-80.0901 + 138.720i) q^{61} +(25.4771 - 80.8717i) q^{63} +(136.720 - 236.806i) q^{65} +(145.738 + 252.425i) q^{67} +(-61.1506 - 83.3776i) q^{69} +191.669 q^{71} +866.440 q^{73} +(52.3038 - 118.909i) q^{75} +(22.9559 + 39.7608i) q^{77} +(-369.794 + 640.503i) q^{79} +(660.548 - 308.411i) q^{81} +(244.041 - 422.691i) q^{83} +(114.488 + 198.299i) q^{85} +(-343.879 + 781.783i) q^{87} +173.938 q^{89} -171.740 q^{91} +(-757.920 - 1033.41i) q^{93} +(-125.864 - 218.003i) q^{95} +(-744.116 + 1288.85i) q^{97} +(-118.608 + 376.497i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{3} + 50 q^{5} + 22 q^{7} - 6 q^{9} + 50 q^{11} - 16 q^{13} - 68 q^{17} + 212 q^{19} - 60 q^{21} + 50 q^{23} - 250 q^{25} + 630 q^{27} - 64 q^{29} - 22 q^{31} - 330 q^{33} + 220 q^{35} + 600 q^{37}+ \cdots + 5562 q^{99}+O(q^{100}) $ 20 * q + 6 * q^3 + 50 * q^5 + 22 * q^7 - 6 * q^9 + 50 * q^11 - 16 * q^13 - 68 * q^17 + 212 * q^19 - 60 * q^21 + 50 * q^23 - 250 * q^25 + 630 * q^27 - 64 * q^29 - 22 * q^31 - 330 * q^33 + 220 * q^35 + 600 * q^37 + 306 * q^39 - 198 * q^41 - 382 * q^43 - 90 * q^45 + 128 * q^47 - 1230 * q^49 - 1506 * q^51 - 1128 * q^53 + 500 * q^55 + 294 * q^57 - 200 * q^59 - 232 * q^61 + 1908 * q^63 + 80 * q^65 - 1316 * q^67 - 1344 * q^69 - 228 * q^71 + 828 * q^73 - 150 * q^75 + 616 * q^77 - 300 * q^79 + 2814 * q^81 - 1082 * q^83 - 170 * q^85 - 4794 * q^87 - 768 * q^89 + 1972 * q^91 + 348 * q^93 + 530 * q^95 - 1354 * q^97 + 5562 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−5.16520	+	0.566318i	−0.994043	+	0.108988i
$3$	−5.16520	+	0.566318i	−0.994043	+	0.108988i
$4$		0			0
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$		0			0
$7$	1.57018	−	2.71963i	0.0847818	−	0.146846i	−0.820516	−	0.571623i	$-0.806314\pi$
$7$	1.57018	−	2.71963i	0.0847818	−	0.146846i	0.905298	+	0.424777i	$0.139647\pi$
$8$		0			0
$9$	26.3586	−	5.85030i	0.976243	−	0.216678i
$10$		0			0
$11$	−7.30996	+	12.6612i	−0.200367	+	0.347046i	−0.948647	−	0.316338i	$-0.897547\pi$
$11$	−7.30996	+	12.6612i	−0.200367	+	0.347046i	0.748280	+	0.663383i	$0.230880\pi$
$12$		0			0
$13$	−27.3440	−	47.3612i	−0.583374	−	1.01043i	−0.995076	−	0.0991143i	$-0.968399\pi$
$13$	−27.3440	−	47.3612i	−0.583374	−	1.01043i	0.411703	−	0.911318i	$-0.364934\pi$
$14$		0			0
$15$	−15.3652	−	20.9502i	−0.264486	−	0.360621i
$16$		0			0
$17$	45.7952			0.653351			0.326676	−	0.945137i	$-0.394072\pi$
$17$	45.7952			0.653351			0.326676	+	0.945137i	$0.394072\pi$
$18$		0			0
$19$	−50.3457			−0.607900			−0.303950	−	0.952688i	$-0.598306\pi$
$19$	−50.3457			−0.607900			−0.303950	+	0.952688i	$0.598306\pi$
$20$		0			0
$21$	−6.57012	+	14.9367i	−0.0682723	+	0.155212i
$22$		0			0
$23$	9.94951	+	17.2331i	0.0902007	+	0.156232i	0.907595	−	0.419846i	$-0.137916\pi$
$23$	9.94951	+	17.2331i	0.0902007	+	0.156232i	−0.817395	+	0.576078i	$0.804582\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$		0			0
$27$	−132.834	+	45.1453i	−0.946813	+	0.321786i
$28$		0			0
$29$	82.1830	−	142.345i	0.526242	−	0.911477i	−0.473291	−	0.880906i	$-0.656934\pi$
$29$	82.1830	−	142.345i	0.526242	−	0.911477i	0.999533	−	0.0305711i	$-0.00973259\pi$
$30$		0			0
$31$	123.317	+	213.592i	0.714466	+	1.23749i	0.963165	+	0.268911i	$0.0866636\pi$
$31$	123.317	+	213.592i	0.714466	+	1.23749i	−0.248699	+	0.968581i	$0.580003\pi$
$32$		0			0
$33$	30.5871	−	69.5375i	0.161349	−	0.366816i
$34$		0			0
$35$	15.7018			0.0758312
$36$		0			0
$37$	268.484			1.19293			0.596467	−	0.802637i	$-0.296571\pi$
$37$	268.484			1.19293			0.596467	+	0.802637i	$0.296571\pi$
$38$		0			0
$39$	168.059	+	229.144i	0.690023	+	0.940833i
$40$		0			0
$41$	166.114	+	287.718i	0.632747	+	1.09595i	0.986988	+	0.160795i	$0.0514059\pi$
$41$	166.114	+	287.718i	0.632747	+	1.09595i	−0.354241	+	0.935154i	$0.615261\pi$
$42$		0			0
$43$	55.4147	−	95.9811i	0.196527	−	0.340395i	−0.750873	−	0.660447i	$-0.770367\pi$
$43$	55.4147	−	95.9811i	0.196527	−	0.340395i	0.947400	+	0.320052i	$0.103700\pi$
$44$		0			0
$45$	91.2289	+	99.5102i	0.302213	+	0.329647i
$46$		0			0
$47$	−17.8310	+	30.8843i	−0.0553388	+	0.0958496i	−0.892368	−	0.451309i	$-0.850957\pi$
$47$	−17.8310	+	30.8843i	−0.0553388	+	0.0958496i	0.837029	+	0.547159i	$0.184291\pi$
$48$		0			0
$49$	166.569	+	288.506i	0.485624	+	0.841126i
$50$		0			0
$51$	−236.541	+	25.9347i	−0.649459	+	0.0712075i
$52$		0			0
$53$	482.657			1.25091			0.625453	−	0.780262i	$-0.284914\pi$
$53$	482.657			1.25091			0.625453	+	0.780262i	$0.284914\pi$
$54$		0			0
$55$	−73.0996			−0.179214
$56$		0			0
$57$	260.046	−	28.5117i	0.604279	−	0.0662538i
$58$		0			0
$59$	164.766	+	285.383i	0.363572	+	0.629724i	0.988546	−	0.150921i	$-0.0482239\pi$
$59$	164.766	+	285.383i	0.363572	+	0.629724i	−0.624974	+	0.780645i	$0.714891\pi$
$60$		0			0
$61$	−80.0901	+	138.720i	−0.168106	+	0.291169i	−0.937754	−	0.347300i	$-0.887099\pi$
$61$	−80.0901	+	138.720i	−0.168106	+	0.291169i	0.769648	+	0.638469i	$0.220432\pi$
$62$		0			0
$63$	25.4771	−	80.8717i	0.0509493	−	0.161728i
$64$		0			0
$65$	136.720	−	236.806i	0.260893	−	0.451879i
$66$		0			0
$67$	145.738	+	252.425i	0.265742	+	0.460278i	0.967758	−	0.251883i	$-0.0810498\pi$
$67$	145.738	+	252.425i	0.265742	+	0.460278i	−0.702016	+	0.712161i	$0.747716\pi$
$68$		0			0
$69$	−61.1506	−	83.3776i	−0.106691	−	0.145471i
$70$		0			0
$71$	191.669			0.320380			0.160190	−	0.987086i	$-0.448789\pi$
$71$	191.669			0.320380			0.160190	+	0.987086i	$0.448789\pi$
$72$		0			0
$73$	866.440			1.38917			0.694583	−	0.719412i	$-0.255589\pi$
$73$	866.440			1.38917			0.694583	+	0.719412i	$0.255589\pi$
$74$		0			0
$75$	52.3038	−	118.909i	0.0805270	−	0.183072i
$76$		0			0
$77$	22.9559	+	39.7608i	0.0339749	+	0.0588463i
$78$		0			0
$79$	−369.794	+	640.503i	−0.526647	+	0.912180i	0.472871	+	0.881132i	$0.343218\pi$
$79$	−369.794	+	640.503i	−0.526647	+	0.912180i	−0.999518	+	0.0310478i	$0.990116\pi$
$80$		0			0
$81$	660.548	−	308.411i	0.906102	−	0.423060i
$82$		0			0
$83$	244.041	−	422.691i	0.322734	−	0.558992i	−0.658317	−	0.752741i	$-0.728731\pi$
$83$	244.041	−	422.691i	0.322734	−	0.558992i	0.981051	+	0.193749i	$0.0620646\pi$
$84$		0			0
$85$	114.488	+	198.299i	0.146094	+	0.253042i
$86$		0			0
$87$	−343.879	+	781.783i	−0.423767	+	0.963402i
$88$		0			0
$89$	173.938			0.207161			0.103581	−	0.994621i	$-0.466970\pi$
$89$	173.938			0.207161			0.103581	+	0.994621i	$0.466970\pi$
$90$		0			0
$91$	−171.740			−0.197838
$92$		0			0
$93$	−757.920	−	1033.41i	−0.845082	−	1.15225i
$94$		0			0
$95$	−125.864	−	218.003i	−0.135931	−	0.235439i
$96$		0			0
$97$	−744.116	+	1288.85i	−0.778902	+	1.34910i	0.153673	+	0.988122i	$0.450890\pi$
$97$	−744.116	+	1288.85i	−0.778902	+	1.34910i	−0.932575	+	0.360976i	$0.882444\pi$
$98$		0			0
$99$	−118.608	+	376.497i	−0.120410	+	0.382216i
$100$		0			0
$101$	197.683	−	342.397i	0.194754	−	0.337324i	−0.752066	−	0.659088i	$-0.770942\pi$
$101$	197.683	−	342.397i	0.194754	−	0.337324i	0.946820	+	0.321764i	$0.104276\pi$
$102$		0			0
$103$	−428.044	−	741.394i	−0.409480	−	0.709240i	0.585352	−	0.810779i	$-0.300956\pi$
$103$	−428.044	−	741.394i	−0.409480	−	0.709240i	−0.994831	+	0.101540i	$0.967623\pi$
$104$		0			0
$105$	−81.1030	+	8.89223i	−0.0753794	+	0.00826469i
$106$		0			0
$107$	423.634			0.382750			0.191375	−	0.981517i	$-0.438705\pi$
$107$	423.634			0.382750			0.191375	+	0.981517i	$0.438705\pi$
$108$		0			0
$109$	−840.730			−0.738783			−0.369391	−	0.929274i	$-0.620434\pi$
$109$	−840.730			−0.738783			−0.369391	+	0.929274i	$0.620434\pi$
$110$		0			0
$111$	−1386.78	+	152.048i	−1.18583	+	0.130016i
$112$		0			0
$113$	−853.149	−	1477.70i	−0.710243	−	1.23018i	−0.964766	−	0.263111i	$-0.915252\pi$
$113$	−853.149	−	1477.70i	−0.710243	−	1.23018i	0.254522	−	0.967067i	$-0.418082\pi$
$114$		0			0
$115$	−49.7475	+	86.1653i	−0.0403390	+	0.0698692i
$116$		0			0
$117$	−997.825	−	1088.40i	−0.788453	−	0.860024i
$118$		0			0
$119$	71.9068	−	124.546i	0.0553923	−	0.0959423i
$120$		0			0
$121$	558.629	+	967.574i	0.419706	+	0.726953i
$122$		0			0
$123$	−1020.95	−	1392.05i	−0.748423	−	1.02046i
$124$		0			0
$125$	−125.000			−0.0894427
$126$		0			0
$127$	1075.14			0.751205			0.375602	−	0.926781i	$-0.377436\pi$
$127$	1075.14			0.751205			0.375602	+	0.926781i	$0.377436\pi$
$128$		0			0
$129$	−231.872	+	527.144i	−0.158257	+	0.359786i
$130$		0			0
$131$	−443.630	−	768.390i	−0.295879	−	0.512477i	0.679310	−	0.733851i	$-0.262279\pi$
$131$	−443.630	−	768.390i	−0.295879	−	0.512477i	−0.975189	+	0.221374i	$0.928946\pi$
$132$		0			0
$133$	−79.0519	+	136.922i	−0.0515389	+	0.0892679i
$134$		0			0
$135$	−527.570	−	462.325i	−0.336341	−	0.294745i
$136$		0			0
$137$	988.251	−	1711.70i	0.616292	−	1.06745i	−0.373865	−	0.927483i	$-0.621968\pi$
$137$	988.251	−	1711.70i	0.616292	−	1.06745i	0.990156	−	0.139965i	$-0.0446992\pi$
$138$		0			0
$139$	906.632	+	1570.33i	0.553234	+	0.958229i	0.998039	+	0.0626017i	$0.0199398\pi$
$139$	906.632	+	1570.33i	0.553234	+	0.958229i	−0.444805	+	0.895628i	$0.646727\pi$
$140$		0			0
$141$	74.6105	−	169.621i	0.0445627	−	0.101310i
$142$		0			0
$143$	799.534			0.467555
$144$		0			0
$145$	821.830			0.470685
$146$		0			0
$147$	−1023.75	−	1395.86i	−0.574404	−	0.783188i
$148$		0			0
$149$	505.197	+	875.027i	0.277767	+	0.481107i	0.970830	−	0.239771i	$-0.0770722\pi$
$149$	505.197	+	875.027i	0.277767	+	0.481107i	−0.693062	+	0.720878i	$0.743739\pi$
$150$		0			0
$151$	−577.277	+	999.874i	−0.311114	+	0.538865i	−0.978604	−	0.205754i	$-0.934035\pi$
$151$	−577.277	+	999.874i	−0.311114	+	0.538865i	0.667490	+	0.744619i	$0.267369\pi$
$152$		0			0
$153$	1207.10	−	267.916i	0.637830	−	0.141567i
$154$		0			0
$155$	−616.587	+	1067.96i	−0.319519	+	0.553423i
$156$		0			0
$157$	−569.678	−	986.711i	−0.289587	−	0.501580i	0.684124	−	0.729366i	$-0.260185\pi$
$157$	−569.678	−	986.711i	−0.289587	−	0.501580i	−0.973711	+	0.227786i	$0.926851\pi$
$158$		0			0
$159$	−2493.02	+	273.338i	−1.24345	+	0.136334i
$160$		0			0
$161$	62.4901			0.0305895
$162$		0			0
$163$	−3320.87			−1.59577			−0.797886	−	0.602809i	$-0.794048\pi$
$163$	−3320.87			−1.59577			−0.797886	+	0.602809i	$0.794048\pi$
$164$		0			0
$165$	377.574	−	41.3977i	0.178146	−	0.0195321i
$166$		0			0
$167$	1076.63	+	1864.78i	0.498876	+	0.864078i	0.999999	−	0.00129774i	$-0.000413084\pi$
$167$	1076.63	+	1864.78i	0.498876	+	0.864078i	−0.501123	+	0.865376i	$0.667080\pi$
$168$		0			0
$169$	−396.887	+	687.428i	−0.180649	+	0.312894i
$170$		0			0
$171$	−1327.04	+	294.537i	−0.593458	+	0.131718i
$172$		0			0
$173$	1898.21	−	3287.80i	0.834211	−	1.44490i	−0.0604599	−	0.998171i	$-0.519257\pi$
$173$	1898.21	−	3287.80i	0.834211	−	1.44490i	0.894671	−	0.446725i	$-0.147410\pi$
$174$		0			0
$175$	39.2545	+	67.9908i	0.0169564	+	0.0293693i
$176$		0			0
$177$	−1012.67	−	1380.75i	−0.430038	−	0.586348i
$178$		0			0
$179$	1763.35			0.736305			0.368153	−	0.929765i	$-0.379990\pi$
$179$	1763.35			0.736305			0.368153	+	0.929765i	$0.379990\pi$
$180$		0			0
$181$	194.975			0.0800683			0.0400342	−	0.999198i	$-0.487253\pi$
$181$	194.975			0.0800683			0.0400342	+	0.999198i	$0.487253\pi$
$182$		0			0
$183$	335.122	−	761.874i	0.135371	−	0.307756i
$184$		0			0
$185$	671.211	+	1162.57i	0.266748	+	0.462022i
$186$		0			0
$187$	−334.761	+	579.823i	−0.130910	+	0.226743i
$188$		0			0
$189$	−85.7950	+	432.146i	−0.0330194	+	0.166318i
$190$		0			0
$191$	1718.62	−	2976.74i	0.651074	−	1.12769i	−0.331789	−	0.943354i	$-0.607652\pi$
$191$	1718.62	−	2976.74i	0.651074	−	1.12769i	0.982863	−	0.184339i	$-0.0590145\pi$
$192$		0			0
$193$	1272.75	+	2204.47i	0.474686	+	0.822181i	0.999580	−	0.0289870i	$-0.00922813\pi$
$193$	1272.75	+	2204.47i	0.474686	+	0.822181i	−0.524893	+	0.851168i	$0.675895\pi$
$194$		0			0
$195$	−572.078	+	1300.58i	−0.210089	+	0.477622i
$196$		0			0
$197$	−3772.65			−1.36442			−0.682209	−	0.731158i	$-0.738980\pi$
$197$	−3772.65			−1.36442			−0.682209	+	0.731158i	$0.738980\pi$
$198$		0			0
$199$	−1011.51			−0.360321			−0.180160	−	0.983637i	$-0.557662\pi$
$199$	−1011.51			−0.360321			−0.180160	+	0.983637i	$0.557662\pi$
$200$		0			0
$201$	−895.718	−	1221.29i	−0.314324	−	0.428574i
$202$		0			0
$203$	−258.085	−	447.016i	−0.0892314	−	0.154553i
$204$		0			0
$205$	−830.569	+	1438.59i	−0.282973	+	0.490124i
$206$		0			0
$207$	363.073	+	396.031i	0.121910	+	0.132976i
$208$		0			0
$209$	368.025	−	637.438i	0.121803	−	0.210969i
$210$		0			0
$211$	−2104.05	−	3644.33i	−0.686488	−	1.18903i	−0.972967	−	0.230946i	$-0.925818\pi$
$211$	−2104.05	−	3644.33i	−0.686488	−	1.18903i	0.286478	−	0.958087i	$-0.407515\pi$
$212$		0			0
$213$	−990.010	+	108.546i	−0.318471	+	0.0349176i
$214$		0			0
$215$	554.147			0.175779
$216$		0			0
$217$	774.522			0.242295
$218$		0			0
$219$	−4475.34	+	490.681i	−1.38089	+	0.151403i
$220$		0			0
$221$	−1252.22	−	2168.91i	−0.381148	−	0.660167i
$222$		0			0
$223$	1576.10	−	2729.89i	0.473290	−	0.819762i	−0.526243	−	0.850335i	$-0.676400\pi$
$223$	1576.10	−	2729.89i	0.473290	−	0.819762i	0.999533	+	0.0305721i	$0.00973293\pi$
$224$		0			0
$225$	−202.819	+	643.808i	−0.0600947	+	0.190758i
$226$		0			0
$227$	1027.79	−	1780.18i	0.300515	−	0.520507i	−0.675738	−	0.737142i	$-0.736175\pi$
$227$	1027.79	−	1780.18i	0.300515	−	0.520507i	0.976253	+	0.216635i	$0.0695082\pi$
$228$		0			0
$229$	2339.71	+	4052.50i	0.675164	+	1.16942i	0.976421	+	0.215875i	$0.0692604\pi$
$229$	2339.71	+	4052.50i	0.675164	+	1.16942i	−0.301257	+	0.953543i	$0.597406\pi$
$230$		0			0
$231$	−141.089	−	192.372i	−0.0401861	−	0.0547929i
$232$		0			0
$233$	−707.658			−0.198971			−0.0994854	−	0.995039i	$-0.531720\pi$
$233$	−707.658			−0.198971			−0.0994854	+	0.995039i	$0.531720\pi$
$234$		0			0
$235$	−178.310			−0.0494965
$236$		0			0
$237$	1547.33	−	3517.75i	0.424093	−	0.964144i
$238$		0			0
$239$	3046.20	+	5276.18i	0.824446	+	1.42798i	0.902342	+	0.431021i	$0.141846\pi$
$239$	3046.20	+	5276.18i	0.824446	+	1.42798i	−0.0778960	+	0.996961i	$0.524820\pi$
$240$		0			0
$241$	−826.336	+	1431.26i	−0.220867	+	0.382553i	−0.955072	−	0.296375i	$-0.904222\pi$
$241$	−826.336	+	1431.26i	−0.220867	+	0.382553i	0.734204	+	0.678929i	$0.237555\pi$
$242$		0			0
$243$	−3237.20	+	1967.08i	−0.854596	+	0.519294i
$244$		0			0
$245$	−832.845	+	1442.53i	−0.217178	+	0.376163i
$246$		0			0
$247$	1376.65	+	2384.43i	0.354633	+	0.614242i
$248$		0			0
$249$	−1021.14	+	2321.49i	−0.259888	+	0.590836i
$250$		0			0
$251$	1497.98			0.376700			0.188350	−	0.982102i	$-0.439686\pi$
$251$	1497.98			0.376700			0.188350	+	0.982102i	$0.439686\pi$
$252$		0			0
$253$	−290.922			−0.0722929
$254$		0			0
$255$	−703.654	−	959.418i	−0.172802	−	0.235612i
$256$		0			0
$257$	−826.195	−	1431.01i	−0.200532	−	0.347331i	0.748168	−	0.663509i	$-0.230934\pi$
$257$	−826.195	−	1431.01i	−0.200532	−	0.347331i	−0.948700	+	0.316178i	$0.897600\pi$
$258$		0			0
$259$	421.569	−	730.179i	0.101139	−	0.175178i
$260$		0			0
$261$	1333.47	−	4232.81i	0.316243	−	1.00385i
$262$		0			0
$263$	2877.51	−	4983.99i	0.674657	−	1.16854i	−0.301912	−	0.953336i	$-0.597625\pi$
$263$	2877.51	−	4983.99i	0.674657	−	1.16854i	0.976569	−	0.215205i	$-0.0690419\pi$
$264$		0			0
$265$	1206.64	+	2089.97i	0.279711	+	0.484474i
$266$		0			0
$267$	−898.422	+	98.5041i	−0.205927	+	0.0225781i
$268$		0			0
$269$	−4242.00			−0.961484			−0.480742	−	0.876862i	$-0.659633\pi$
$269$	−4242.00			−0.961484			−0.480742	+	0.876862i	$0.659633\pi$
$270$		0			0
$271$	4037.67			0.905059			0.452529	−	0.891750i	$-0.350522\pi$
$271$	4037.67			0.905059			0.452529	+	0.891750i	$0.350522\pi$
$272$		0			0
$273$	887.071	−	97.2596i	0.196659	−	0.0215620i
$274$		0			0
$275$	−182.749	−	316.531i	−0.0400734	−	0.0694091i
$276$		0			0
$277$	−425.127	+	736.341i	−0.0922144	+	0.159720i	−0.908443	−	0.418010i	$-0.862728\pi$
$277$	−425.127	+	736.341i	−0.0922144	+	0.159720i	0.816228	+	0.577730i	$0.196061\pi$
$278$		0			0
$279$	4500.04	+	4908.53i	0.965629	+	1.05328i
$280$		0			0
$281$	2110.97	−	3656.30i	0.448149	−	0.776216i	−0.550117	−	0.835088i	$-0.685417\pi$
$281$	2110.97	−	3656.30i	0.448149	−	0.776216i	0.998266	+	0.0588713i	$0.0187502\pi$
$282$		0			0
$283$	−1225.85	−	2123.23i	−0.257488	−	0.445982i	0.708081	−	0.706132i	$-0.249561\pi$
$283$	−1225.85	−	2123.23i	−0.257488	−	0.445982i	−0.965568	+	0.260150i	$0.916228\pi$
$284$		0			0
$285$	773.574	+	1054.75i	0.160781	+	0.219221i
$286$		0			0
$287$	1043.32			0.214582
$288$		0			0
$289$	−2815.80			−0.573132
$290$		0			0
$291$	3113.61	−	7078.55i	0.627227	−	1.42595i
$292$		0			0
$293$	1912.62	+	3312.75i	0.381353	+	0.660523i	0.991256	−	0.131953i	$-0.0421249\pi$
$293$	1912.62	+	3312.75i	0.381353	+	0.660523i	−0.609903	+	0.792476i	$0.708792\pi$
$294$		0			0
$295$	−823.831	+	1426.92i	−0.162594	+	0.281621i
$296$		0			0
$297$	399.418	−	2011.85i	0.0780355	−	0.393062i
$298$		0			0
$299$	544.118	−	942.441i	0.105241	−	0.182283i
$300$		0			0
$301$	−174.022	−	301.416i	−0.0333239	−	0.0577186i
$302$		0			0
$303$	−827.166	+	1880.50i	−0.156830	+	0.356541i
$304$		0			0
$305$	−800.901			−0.150359
$306$		0			0
$307$	2771.63			0.515262			0.257631	−	0.966243i	$-0.417058\pi$
$307$	2771.63			0.515262			0.257631	+	0.966243i	$0.417058\pi$
$308$		0			0
$309$	2630.80	+	3587.04i	0.484339	+	0.660386i
$310$		0			0
$311$	4336.74	+	7511.46i	0.790721	+	1.36957i	0.925521	+	0.378696i	$0.123627\pi$
$311$	4336.74	+	7511.46i	0.790721	+	1.36957i	−0.134801	+	0.990873i	$0.543039\pi$
$312$		0			0
$313$	−1772.78	+	3070.55i	−0.320139	+	0.554497i	−0.980516	−	0.196437i	$-0.937063\pi$
$313$	−1772.78	+	3070.55i	−0.320139	+	0.554497i	0.660378	+	0.750934i	$0.270396\pi$
$314$		0			0
$315$	413.877	−	91.8602i	0.0740297	−	0.0164309i
$316$		0			0
$317$	−3081.76	+	5337.77i	−0.546022	+	0.945738i	0.452520	+	0.891754i	$0.350525\pi$
$317$	−3081.76	+	5337.77i	−0.546022	+	0.945738i	−0.998542	+	0.0539836i	$0.982808\pi$
$318$		0			0
$319$	1201.51	+	2081.08i	0.210883	+	0.365260i
$320$		0			0
$321$	−2188.16	+	239.912i	−0.380470	+	0.0417152i
$322$		0			0
$323$	−2305.59			−0.397172
$324$		0			0
$325$	1367.20			0.233349
$326$		0			0
$327$	4342.54	−	476.121i	0.734382	−	0.0805185i
$328$		0			0
$329$	55.9959	+	96.9878i	0.00938345	+	0.0162526i
$330$		0			0
$331$	4358.97	−	7549.96i	0.723839	−	1.25373i	−0.235611	−	0.971847i	$-0.575709\pi$
$331$	4358.97	−	7549.96i	0.723839	−	1.25373i	0.959450	−	0.281878i	$-0.0909574\pi$
$332$		0			0
$333$	7076.87	−	1570.71i	1.16459	−	0.258482i
$334$		0			0
$335$	−728.689	+	1262.13i	−0.118843	+	0.205843i
$336$		0			0
$337$	3254.65	+	5637.22i	0.526090	+	0.911214i	0.999538	+	0.0303925i	$0.00967573\pi$
$337$	3254.65	+	5637.22i	0.526090	+	0.911214i	−0.473448	+	0.880822i	$0.656991\pi$
$338$		0			0
$339$	5243.53	+	7149.45i	0.840087	+	1.14544i
$340$		0			0
$341$	−3605.78			−0.572621
$342$		0			0
$343$	2123.32			0.334252
$344$		0			0
$345$	208.159	−	473.234i	0.0324838	−	0.0738494i
$346$		0			0
$347$	1852.56	+	3208.72i	0.286601	+	0.496407i	0.972996	−	0.230822i	$-0.0741414\pi$
$347$	1852.56	+	3208.72i	0.286601	+	0.496407i	−0.686395	+	0.727228i	$0.740808\pi$
$348$		0			0
$349$	−5113.11	+	8856.17i	−0.784237	+	1.35834i	0.145217	+	0.989400i	$0.453612\pi$
$349$	−5113.11	+	8856.17i	−0.784237	+	1.35834i	−0.929454	+	0.368938i	$0.879721\pi$
$350$		0			0
$351$	5770.35	+	5056.73i	0.877488	+	0.768969i
$352$		0			0
$353$	−1156.50	+	2003.11i	−0.174374	+	0.302025i	−0.939944	−	0.341327i	$-0.889124\pi$
$353$	−1156.50	+	2003.11i	−0.174374	+	0.302025i	0.765570	+	0.643352i	$0.222457\pi$
$354$		0			0
$355$	479.173	+	829.953i	0.0716391	+	0.124083i
$356$		0			0
$357$	−300.880	+	684.028i	−0.0446058	+	0.101408i
$358$		0			0
$359$	11018.9			1.61993			0.809967	−	0.586475i	$-0.199485\pi$
$359$	11018.9			1.61993			0.809967	+	0.586475i	$0.199485\pi$
$360$		0			0
$361$	−4324.31			−0.630458
$362$		0			0
$363$	−3433.38	−	4681.35i	−0.496435	−	0.676879i
$364$		0			0
$365$	2166.10	+	3751.80i	0.310627	+	0.538022i
$366$		0			0
$367$	6462.97	−	11194.2i	0.919248	−	1.59218i	0.118689	−	0.992932i	$-0.462131\pi$
$367$	6462.97	−	11194.2i	0.919248	−	1.59218i	0.800560	−	0.599253i	$-0.204536\pi$
$368$		0			0
$369$	6061.75	+	6612.01i	0.855182	+	0.932811i
$370$		0			0
$371$	757.859	−	1312.65i	0.106054	−	0.183691i
$372$		0			0
$373$	−1003.06	−	1737.36i	−0.139240	−	0.241171i	0.787969	−	0.615715i	$-0.211133\pi$
$373$	−1003.06	−	1737.36i	−0.139240	−	0.241171i	−0.927209	+	0.374544i	$0.877799\pi$
$374$		0			0
$375$	645.650	−	70.7898i	0.0889099	−	0.00974819i
$376$		0			0
$377$	−8988.85			−1.22798
$378$		0			0
$379$	−6167.89			−0.835945			−0.417972	−	0.908460i	$-0.637259\pi$
$379$	−6167.89			−0.835945			−0.417972	+	0.908460i	$0.637259\pi$
$380$		0			0
$381$	−5553.30	+	608.870i	−0.746730	+	0.0818724i
$382$		0			0
$383$	1344.31	+	2328.41i	0.179350	+	0.310643i	0.941658	−	0.336571i	$-0.109267\pi$
$383$	1344.31	+	2328.41i	0.179350	+	0.310643i	−0.762308	+	0.647214i	$0.775934\pi$
$384$		0			0
$385$	−114.780	+	198.804i	−0.0151941	+	0.0263169i
$386$		0			0
$387$	899.135	−	2854.12i	0.118102	−	0.374891i
$388$		0			0
$389$	857.500	−	1485.23i	0.111766	−	0.193584i	−0.804716	−	0.593660i	$-0.797683\pi$
$389$	857.500	−	1485.23i	0.111766	−	0.193584i	0.916482	+	0.400075i	$0.131016\pi$
$390$		0			0
$391$	455.640	+	789.191i	0.0589327	+	0.102074i
$392$		0			0
$393$	2726.59	+	3717.65i	0.349970	+	0.477177i
$394$		0			0
$395$	−3697.94			−0.471048
$396$		0			0
$397$	8048.37			1.01747			0.508735	−	0.860923i	$-0.330113\pi$
$397$	8048.37			1.01747			0.508735	+	0.860923i	$0.330113\pi$
$398$		0			0
$399$	330.777	−	751.998i	0.0415027	−	0.0943533i
$400$		0			0
$401$	−4821.71	−	8351.45i	−0.600461	−	1.04003i	−0.992751	−	0.120188i	$-0.961650\pi$
$401$	−4821.71	−	8351.45i	−0.600461	−	1.04003i	0.392290	−	0.919842i	$-0.371683\pi$
$402$		0			0
$403$	6743.97	−	11680.9i	0.833601	−	1.44384i
$404$		0			0
$405$	2986.83	+	2089.23i	0.366461	+	0.256333i
$406$		0			0
$407$	−1962.61	+	3399.34i	−0.239025	+	0.414003i
$408$		0			0
$409$	−7105.36	−	12306.8i	−0.859016	−	1.48786i	−0.872869	−	0.487955i	$-0.837743\pi$
$409$	−7105.36	−	12306.8i	−0.859016	−	1.48786i	0.0138525	−	0.999904i	$-0.495590\pi$
$410$		0			0
$411$	−4135.15	+	9400.94i	−0.496281	+	1.12826i
$412$		0			0
$413$	1034.85			0.123297
$414$		0			0
$415$	2440.41			0.288662
$416$		0			0
$417$	−5572.24	−	7597.64i	−0.654374	−	0.892225i
$418$		0			0
$419$	−1114.29	−	1930.01i	−0.129921	−	0.225029i	0.793725	−	0.608277i	$-0.208139\pi$
$419$	−1114.29	−	1930.01i	−0.129921	−	0.225029i	−0.923646	+	0.383248i	$0.874806\pi$
$420$		0			0
$421$	776.902	−	1345.63i	0.0899380	−	0.155777i	−0.817547	−	0.575862i	$-0.804666\pi$
$421$	776.902	−	1345.63i	0.0899380	−	0.155777i	0.907485	+	0.420085i	$0.138000\pi$
$422$		0			0
$423$	−289.319	+	918.382i	−0.0332557	+	0.105563i
$424$		0			0
$425$	−572.440	+	991.495i	−0.0653351	+	0.113164i
$426$		0			0
$427$	251.512	+	435.632i	0.0285047	+	0.0493716i
$428$		0			0
$429$	−4129.75	+	452.791i	−0.464770	+	0.0509579i
$430$		0			0
$431$	462.976			0.0517419			0.0258710	−	0.999665i	$-0.491764\pi$
$431$	462.976			0.0517419			0.0258710	+	0.999665i	$0.491764\pi$
$432$		0			0
$433$	−580.010			−0.0643729			−0.0321865	−	0.999482i	$-0.510247\pi$
$433$	−580.010			−0.0643729			−0.0321865	+	0.999482i	$0.510247\pi$
$434$		0			0
$435$	−4244.92	+	465.418i	−0.467881	+	0.0512990i
$436$		0			0
$437$	−500.915	−	867.610i	−0.0548330	−	0.0949735i
$438$		0			0
$439$	−1096.63	+	1899.41i	−0.119223	+	0.206501i	−0.919460	−	0.393183i	$-0.871374\pi$
$439$	−1096.63	+	1899.41i	−0.119223	+	0.206501i	0.800237	+	0.599684i	$0.204707\pi$
$440$		0			0
$441$	6078.37	+	6630.13i	0.656340	+	0.715919i
$442$		0			0
$443$	1710.70	−	2963.02i	0.183471	−	0.317781i	−0.759589	−	0.650403i	$-0.774600\pi$
$443$	1710.70	−	2963.02i	0.183471	−	0.317781i	0.943060	+	0.332622i	$0.107933\pi$
$444$		0			0
$445$	434.844	+	753.172i	0.0463227	+	0.0802332i
$446$		0			0
$447$	−3104.99	−	4233.58i	−0.328548	−	0.447968i
$448$		0			0
$449$	−13914.9			−1.46255			−0.731273	−	0.682085i	$-0.761074\pi$
$449$	−13914.9			−1.46255			−0.731273	+	0.682085i	$0.761074\pi$
$450$		0			0
$451$	−4857.14			−0.507126
$452$		0			0
$453$	2415.51	−	5491.47i	0.250531	−	0.569562i
$454$		0			0
$455$	−429.350	−	743.656i	−0.0442379	−	0.0766223i
$456$		0			0
$457$	−3864.00	+	6692.65i	−0.395515	+	0.685052i	−0.993167	−	0.116703i	$-0.962767\pi$
$457$	−3864.00	+	6692.65i	−0.395515	+	0.685052i	0.597652	+	0.801756i	$0.296101\pi$
$458$		0			0
$459$	−6083.17	+	2067.44i	−0.618601	+	0.210239i
$460$		0			0
$461$	−3464.26	+	6000.28i	−0.349993	+	0.606206i	−0.986248	−	0.165273i	$-0.947149\pi$
$461$	−3464.26	+	6000.28i	−0.349993	+	0.606206i	0.636255	+	0.771479i	$0.280483\pi$
$462$		0			0
$463$	−9738.83	−	16868.1i	−0.977541	−	1.69315i	−0.671280	−	0.741204i	$-0.734255\pi$
$463$	−9738.83	−	16868.1i	−0.977541	−	1.69315i	−0.306261	−	0.951948i	$-0.599078\pi$
$464$		0			0
$465$	2579.99	−	5865.41i	0.257299	−	0.584950i
$466$		0			0
$467$	−18244.0			−1.80777			−0.903887	−	0.427772i	$-0.859299\pi$
$467$	−18244.0			−1.80777			−0.903887	+	0.427772i	$0.859299\pi$
$468$		0			0
$469$	915.339			0.0901203
$470$		0			0
$471$	3501.29	+	4773.94i	0.342529	+	0.467031i
$472$		0			0
$473$	810.159	+	1403.24i	0.0787551	+	0.136408i
$474$		0			0
$475$	629.321	−	1090.02i	0.0607900	−	0.105291i
$476$		0			0
$477$	12722.1	−	2823.69i	1.22119	−	0.271043i
$478$		0			0
$479$	2243.72	−	3886.24i	0.214025	−	0.370703i	−0.738945	−	0.673765i	$-0.764676\pi$
$479$	2243.72	−	3886.24i	0.214025	−	0.370703i	0.952971	+	0.303063i	$0.0980091\pi$
$480$		0			0
$481$	−7341.43	−	12715.7i	−0.695926	−	1.20538i
$482$		0			0
$483$	−322.774	+	35.3893i	−0.0304073	+	0.00333389i
$484$		0			0
$485$	−7441.16			−0.696671
$486$		0			0
$487$	−2136.17			−0.198766			−0.0993832	−	0.995049i	$-0.531687\pi$
$487$	−2136.17			−0.198766			−0.0993832	+	0.995049i	$0.531687\pi$
$488$		0			0
$489$	17153.0	−	1880.67i	1.58627	−	0.173920i
$490$		0			0
$491$	7048.39	+	12208.2i	0.647840	+	1.12209i	0.983638	+	0.180158i	$0.0576609\pi$
$491$	7048.39	+	12208.2i	0.647840	+	1.12209i	−0.335797	+	0.941934i	$0.609006\pi$
$492$		0			0
$493$	3763.59	−	6518.73i	0.343821	−	0.595515i
$494$		0			0
$495$	−1926.80	+	427.654i	−0.174956	+	0.0388316i
$496$		0			0
$497$	300.956	−	521.270i	0.0271624	−	0.0470466i
$498$		0			0
$499$	−10083.5	−	17465.2i	−0.904612	−	1.56683i	−0.821437	−	0.570299i	$-0.806827\pi$
$499$	−10083.5	−	17465.2i	−0.904612	−	1.56683i	−0.0831753	−	0.996535i	$-0.526506\pi$
$500$		0			0
$501$	−6617.08	−	9022.25i	−0.590078	−	0.804559i
$502$		0			0
$503$	−19912.3			−1.76510			−0.882551	−	0.470217i	$-0.844175\pi$
$503$	−19912.3			−1.76510			−0.882551	+	0.470217i	$0.844175\pi$
$504$		0			0
$505$	1976.83			0.174193
$506$		0			0
$507$	1660.70	−	3775.47i	0.145472	−	0.330719i
$508$		0			0
$509$	9789.42	+	16955.8i	0.852472	+	1.47652i	0.878971	+	0.476876i	$0.158231\pi$
$509$	9789.42	+	16955.8i	0.852472	+	1.47652i	−0.0264988	+	0.999649i	$0.508436\pi$
$510$		0			0
$511$	1360.47	−	2356.40i	0.117776	−	0.203994i
$512$		0			0
$513$	6687.63	−	2272.87i	0.575567	−	0.195614i
$514$		0			0
$515$	2140.22	−	3706.97i	0.183125	−	0.317182i
$516$		0			0
$517$	−260.688	−	451.526i	−0.0221761	−	0.0384102i
$518$		0			0
$519$	−7942.71	+	18057.2i	−0.671765	+	1.52721i
$520$		0			0
$521$	−18389.9			−1.54640			−0.773200	−	0.634163i	$-0.781345\pi$
$521$	−18389.9			−1.54640			−0.773200	+	0.634163i	$0.781345\pi$
$522$		0			0
$523$	−20546.3			−1.71783			−0.858916	−	0.512116i	$-0.828862\pi$
$523$	−20546.3			−1.71783			−0.858916	+	0.512116i	$0.828862\pi$
$524$		0			0
$525$	−241.262	−	328.956i	−0.0200563	−	0.0273463i
$526$		0			0
$527$	5647.34	+	9781.49i	0.466797	+	0.808517i
$528$		0			0
$529$	5885.51	−	10194.0i	0.483728	−	0.837841i
$530$		0			0
$531$	6012.57	+	6558.36i	0.491381	+	0.535986i
$532$		0			0
$533$	9084.42	−	15734.7i	0.738255	−	1.27870i
$534$		0			0
$535$	1059.09	+	1834.39i	0.0855856	+	0.148239i
$536$		0			0
$537$	−9108.03	+	998.615i	−0.731919	+	0.0802485i
$538$		0			0
$539$	−4870.45			−0.389212
$540$		0			0
$541$	4660.74			0.370390			0.185195	−	0.982702i	$-0.440708\pi$
$541$	4660.74			0.370390			0.185195	+	0.982702i	$0.440708\pi$
$542$		0			0
$543$	−1007.08	+	110.418i	−0.0795914	+	0.00872649i
$544$		0			0
$545$	−2101.83	−	3640.47i	−0.165197	−	0.286129i
$546$		0			0
$547$	1458.99	−	2527.04i	0.114044	−	0.197529i	−0.803353	−	0.595503i	$-0.796953\pi$
$547$	1458.99	−	2527.04i	0.114044	−	0.197529i	0.917397	+	0.397973i	$0.130286\pi$
$548$		0			0
$549$	−1299.51	+	4125.02i	−0.101023	+	0.320676i
$550$		0			0
$551$	−4137.56	+	7166.47i	−0.319902	+	0.554087i
$552$		0			0
$553$	1161.29	+	2011.41i	0.0893002	+	0.154672i
$554$		0			0
$555$	−4125.33	−	5624.80i	−0.315514	−	0.430197i
$556$		0			0
$557$	−14120.6			−1.07417			−0.537084	−	0.843529i	$-0.680474\pi$
$557$	−14120.6			−1.07417			−0.537084	+	0.843529i	$0.680474\pi$
$558$		0			0
$559$	−6061.04			−0.458595
$560$		0			0
$561$	1400.74	−	3184.48i	0.105418	−	0.239660i
$562$		0			0
$563$	−6642.62	−	11505.4i	−0.497252	−	0.861266i	0.502743	−	0.864436i	$-0.332324\pi$
$563$	−6642.62	−	11505.4i	−0.497252	−	0.861266i	−0.999995	+	0.00316990i	$0.998991\pi$
$564$		0			0
$565$	4265.74	−	7388.49i	0.317630	−	0.550152i
$566$		0			0
$567$	198.416	−	2280.71i	0.0146961	−	0.168926i
$568$		0			0
$569$	6058.65	−	10493.9i	0.446383	−	0.773158i	−0.551765	−	0.834000i	$-0.686045\pi$
$569$	6058.65	−	10493.9i	0.446383	−	0.773158i	0.998147	+	0.0608422i	$0.0193787\pi$
$570$		0			0
$571$	3443.57	+	5964.44i	0.252380	+	0.437135i	0.964181	−	0.265247i	$-0.0854534\pi$
$571$	3443.57	+	5964.44i	0.252380	+	0.437135i	−0.711801	+	0.702381i	$0.752120\pi$
$572$		0			0
$573$	−7191.24	+	16348.7i	−0.524290	+	1.19193i
$574$		0			0
$575$	−497.475			−0.0360803
$576$		0			0
$577$	6389.22			0.460982			0.230491	−	0.973074i	$-0.425967\pi$
$577$	6389.22			0.460982			0.230491	+	0.973074i	$0.425967\pi$
$578$		0			0
$579$	−7822.43	−	10665.7i	−0.561467	−	0.765548i
$580$		0			0
$581$	−766.376	−	1327.40i	−0.0547240	−	0.0947848i
$582$		0			0
$583$	−3528.20	+	6111.03i	−0.250640	+	0.434121i
$584$		0			0
$585$	2218.36	−	7041.71i	0.156782	−	0.497674i
$586$		0			0
$587$	−12313.1	+	21327.0i	−0.865787	+	1.49959i	0.000476796		1.00000i	$0.499848\pi$
$587$	−12313.1	+	21327.0i	−0.865787	+	1.49959i	−0.866264	+	0.499587i	$0.833485\pi$
$588$		0			0
$589$	−6208.50	−	10753.4i	−0.434324	−	0.752271i
$590$		0			0
$591$	19486.5	−	2136.52i	1.35629	−	0.148705i
$592$		0			0
$593$	18703.3			1.29520			0.647598	−	0.761982i	$-0.275774\pi$
$593$	18703.3			1.29520			0.647598	+	0.761982i	$0.275774\pi$
$594$		0			0
$595$	719.068			0.0495444
$596$		0			0
$597$	5224.64	−	572.835i	0.358174	−	0.0392707i
$598$		0			0
$599$	1258.93	+	2180.54i	0.0858741	+	0.148738i	0.905763	−	0.423784i	$-0.139298\pi$
$599$	1258.93	+	2180.54i	0.0858741	+	0.148738i	−0.819889	+	0.572522i	$0.805965\pi$
$600$		0			0
$601$	−10579.5	+	18324.2i	−0.718048	+	1.24369i	0.243725	+	0.969844i	$0.421631\pi$
$601$	−10579.5	+	18324.2i	−0.718048	+	1.24369i	−0.961772	+	0.273851i	$0.911703\pi$
$602$		0			0
$603$	5318.20	+	5800.96i	0.359161	+	0.391763i
$604$		0			0
$605$	−2793.14	+	4837.87i	−0.187698	+	0.325103i
$606$		0			0
$607$	14378.7	+	24904.7i	0.961474	+	1.66532i	0.718804	+	0.695213i	$0.244690\pi$
$607$	14378.7	+	24904.7i	0.961474	+	1.66532i	0.242670	+	0.970109i	$0.421977\pi$
$608$		0			0
$609$	1586.21	+	2162.77i	0.105544	+	0.143908i
$610$		0			0
$611$	1950.29			0.129133
$612$		0			0
$613$	12342.1			0.813205			0.406602	−	0.913605i	$-0.366713\pi$
$613$	12342.1			0.813205			0.406602	+	0.913605i	$0.366713\pi$
$614$		0			0
$615$	3475.36	−	7900.96i	0.227870	−	0.518045i
$616$		0			0
$617$	666.521	+	1154.45i	0.0434897	+	0.0753263i	0.886951	−	0.461864i	$-0.152819\pi$
$617$	666.521	+	1154.45i	0.0434897	+	0.0753263i	−0.843461	+	0.537190i	$0.819486\pi$
$618$		0			0
$619$	1037.12	−	1796.34i	0.0673429	−	0.116641i	−0.830388	−	0.557186i	$-0.811881\pi$
$619$	1037.12	−	1796.34i	0.0673429	−	0.116641i	0.897731	+	0.440544i	$0.145215\pi$
$620$		0			0
$621$	−2099.63	−	1839.96i	−0.135676	−	0.118897i
$622$		0			0
$623$	273.114	−	473.047i	0.0175635	−	0.0304209i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−1539.93	+	3500.92i	−0.0980844	+	0.222987i
$628$		0			0
$629$	12295.3			0.779405
$630$		0			0
$631$	9839.77			0.620785			0.310392	−	0.950609i	$-0.399540\pi$
$631$	9839.77			0.620785			0.310392	+	0.950609i	$0.399540\pi$
$632$		0			0
$633$	12931.7	+	17632.1i	0.811989	+	1.10713i
$634$		0			0
$635$	2687.84	+	4655.48i	0.167975	+	0.290940i
$636$		0			0
$637$	9109.32	−	15777.8i	0.566600	−	0.981381i
$638$		0			0
$639$	5052.13	−	1121.32i	0.312769	−	0.0694191i
$640$		0			0
$641$	7909.90	−	13700.3i	0.487398	−	0.844198i	−0.512497	−	0.858689i	$-0.671279\pi$
$641$	7909.90	−	13700.3i	0.487398	−	0.844198i	0.999895	+	0.0144910i	$0.00461279\pi$
$642$		0			0
$643$	−7355.81	−	12740.6i	−0.451143	−	0.781402i	0.547315	−	0.836927i	$-0.315650\pi$
$643$	−7355.81	−	12740.6i	−0.451143	−	0.781402i	−0.998457	+	0.0555249i	$0.982317\pi$
$644$		0			0
$645$	−2862.28	+	313.824i	−0.174732	+	0.0191578i
$646$		0			0
$647$	−16466.5			−1.00056			−0.500281	−	0.865863i	$-0.666770\pi$
$647$	−16466.5			−1.00056			−0.500281	+	0.865863i	$0.666770\pi$
$648$		0			0
$649$	−4817.73			−0.291391
$650$		0			0
$651$	−4000.56	+	438.626i	−0.240852	+	0.0264072i
$652$		0			0
$653$	4076.89	+	7061.38i	0.244320	+	0.423175i	0.961940	−	0.273260i	$-0.0881019\pi$
$653$	4076.89	+	7061.38i	0.244320	+	0.423175i	−0.717620	+	0.696435i	$0.754769\pi$
$654$		0			0
$655$	2218.15	−	3841.95i	0.132321	−	0.229187i
$656$		0			0
$657$	22838.1	−	5068.93i	1.35616	−	0.301001i
$658$		0			0
$659$	15003.6	−	25987.0i	0.886886	−	1.53613i	0.0433494	−	0.999060i	$-0.486197\pi$
$659$	15003.6	−	25987.0i	0.886886	−	1.53613i	0.843537	−	0.537072i	$-0.180470\pi$
$660$		0			0
$661$	−10689.5	−	18514.8i	−0.629008	−	1.08947i	−0.987751	−	0.156037i	$-0.950128\pi$
$661$	−10689.5	−	18514.8i	−0.629008	−	1.08947i	0.358744	−	0.933436i	$-0.383205\pi$
$662$		0			0
$663$	7696.28	+	10493.7i	0.450828	+	0.614694i
$664$		0			0
$665$	−790.519			−0.0460978
$666$		0			0
$667$	3270.72			0.189869
$668$		0			0
$669$	−6594.90	+	14993.0i	−0.381126	+	0.866462i
$670$		0			0
$671$	−1170.91	−	2028.08i	−0.0673659	−	0.116681i
$672$		0			0
$673$	−12310.3	+	21322.0i	−0.705091	+	1.22125i	0.261568	+	0.965185i	$0.415760\pi$
$673$	−12310.3	+	21322.0i	−0.705091	+	1.22125i	−0.966659	+	0.256068i	$0.917573\pi$
$674$		0			0
$675$	683.002	−	3440.26i	0.0389463	−	0.196171i
$676$		0			0
$677$	−13782.0	+	23871.1i	−0.782399	+	1.35515i	0.148142	+	0.988966i	$0.452671\pi$
$677$	−13782.0	+	23871.1i	−0.782399	+	1.35515i	−0.930541	+	0.366188i	$0.880663\pi$
$678$		0			0
$679$	2336.79	+	4047.44i	0.132073	+	0.228758i
$680$		0			0
$681$	−4300.59	+	9777.07i	−0.241996	+	0.550159i
$682$		0			0
$683$	−9068.36			−0.508040			−0.254020	−	0.967199i	$-0.581753\pi$
$683$	−9068.36			−0.508040			−0.254020	+	0.967199i	$0.581753\pi$
$684$		0			0
$685$	9882.51			0.551228
$686$		0			0
$687$	−14380.1	−	19606.9i	−0.798594	−	1.08887i
$688$		0			0
$689$	−13197.8	−	22859.2i	−0.729746	−	1.26396i
$690$		0			0
$691$	−11432.8	+	19802.2i	−0.629413	+	1.09018i	0.358256	+	0.933623i	$0.383371\pi$
$691$	−11432.8	+	19802.2i	−0.629413	+	1.09018i	−0.987670	+	0.156553i	$0.949962\pi$
$692$		0			0
$693$	837.698	+	913.739i	0.0459185	+	0.0500867i
$694$		0			0
$695$	−4533.16	+	7851.66i	−0.247414	+	0.428533i
$696$		0			0
$697$	7607.22	+	13176.1i	0.413406	+	0.716040i
$698$		0			0
$699$	3655.19	−	400.760i	0.197786	−	0.0216854i
$700$		0			0
$701$	2080.10			0.112075			0.0560373	−	0.998429i	$-0.482153\pi$
$701$	2080.10			0.112075			0.0560373	+	0.998429i	$0.482153\pi$
$702$		0			0
$703$	−13517.0			−0.725185
$704$		0			0
$705$	921.009	−	100.980i	0.0492017	−	0.00539453i
$706$		0			0
$707$	−620.796	−	1075.25i	−0.0330232	−	0.0571979i
$708$		0			0
$709$	11853.8	−	20531.4i	0.627898	−	1.08755i	−0.360074	−	0.932924i	$-0.617249\pi$
$709$	11853.8	−	20531.4i	0.627898	−	1.08755i	0.987973	−	0.154628i	$-0.0494180\pi$
$710$		0			0
$711$	−6000.12	+	19046.1i	−0.316487	+	1.00462i
$712$		0			0
$713$	−2453.89	+	4250.27i	−0.128891	+	0.223245i
$714$		0			0
$715$	1998.83	+	3462.08i	0.104548	+	0.181083i
$716$		0			0
$717$	−18722.3	−	25527.4i	−0.975168	−	1.32962i
$718$		0			0
$719$	12675.0			0.657438			0.328719	−	0.944428i	$-0.393383\pi$
$719$	12675.0			0.657438			0.328719	+	0.944428i	$0.393383\pi$
$720$		0			0
$721$	−2688.43			−0.138866
$722$		0			0
$723$	3457.64	−	7860.69i	0.177858	−	0.404346i
$724$		0			0
$725$	2054.58	+	3558.63i	0.105248	+	0.182295i
$726$		0			0
$727$	9534.79	−	16514.7i	0.486418	−	0.842500i	−0.513460	−	0.858113i	$-0.671637\pi$
$727$	9534.79	−	16514.7i	0.486418	−	0.842500i	0.999878	+	0.0156129i	$0.00496995\pi$
$728$		0			0
$729$	15606.8	−	11993.7i	0.792908	−	0.609342i
$730$		0			0
$731$	2537.73	−	4395.48i	0.128401	−	0.222397i
$732$		0			0
$733$	11079.3	+	19189.9i	0.558285	+	0.966978i	0.997640	+	0.0686641i	$0.0218737\pi$
$733$	11079.3	+	19189.9i	0.558285	+	0.966978i	−0.439355	+	0.898313i	$0.644793\pi$
$734$		0			0
$735$	3484.88	−	7922.61i	0.174887	−	0.397592i
$736$		0			0
$737$	−4261.35			−0.212983
$738$		0			0
$739$	−15425.3			−0.767834			−0.383917	−	0.923368i	$-0.625425\pi$
$739$	−15425.3			−0.767834			−0.383917	+	0.923368i	$0.625425\pi$
$740$		0			0
$741$	−8461.03	−	11536.4i	−0.419465	−	0.571932i
$742$		0			0
$743$	17721.2	+	30694.0i	0.875004	+	1.51555i	0.856759	+	0.515717i	$0.172475\pi$
$743$	17721.2	+	30694.0i	0.875004	+	1.51555i	0.0182450	+	0.999834i	$0.494192\pi$
$744$		0			0
$745$	−2525.98	+	4375.13i	−0.124221	+	0.215158i
$746$		0			0
$747$	3959.70	−	12569.2i	0.193946	−	0.615642i
$748$		0			0
$749$	665.183	−	1152.13i	0.0324503	−	0.0562055i
$750$		0			0
$751$	8106.23	+	14040.4i	0.393875	+	0.682212i	0.992957	−	0.118476i	$-0.0378008\pi$
$751$	8106.23	+	14040.4i	0.393875	+	0.682212i	−0.599082	+	0.800688i	$0.704468\pi$
$752$		0			0
$753$	−7737.37	+	848.334i	−0.374456	+	0.0410558i
$754$		0			0
$755$	−5772.77			−0.278269
$756$		0			0
$757$	20286.0			0.973984			0.486992	−	0.873407i	$-0.338094\pi$
$757$	20286.0			0.973984			0.486992	+	0.873407i	$0.338094\pi$
$758$		0			0
$759$	1502.67	−	164.755i	0.0718623	−	0.00787906i
$760$		0			0
$761$	17748.5	+	30741.2i	0.845442	+	1.46435i	0.885237	+	0.465140i	$0.153996\pi$
$761$	17748.5	+	30741.2i	0.845442	+	1.46435i	−0.0397950	+	0.999208i	$0.512670\pi$
$762$		0			0
$763$	−1320.10	+	2286.48i	−0.0626354	+	0.108488i
$764$		0			0
$765$	4177.85	+	4557.09i	0.197452	+	0.215375i
$766$		0			0
$767$	9010.72	−	15607.0i	0.424196	−	0.734729i
$768$		0			0
$769$	−17945.3	−	31082.3i	−0.841516	−	1.45755i	−0.888613	−	0.458658i	$-0.848330\pi$
$769$	−17945.3	−	31082.3i	−0.841516	−	1.45755i	0.0470967	−	0.998890i	$-0.485003\pi$
$770$		0			0
$771$	5077.87	+	6923.57i	0.237192	+	0.323407i
$772$		0			0
$773$	22725.0			1.05739			0.528694	−	0.848812i	$-0.322682\pi$
$773$	22725.0			1.05739			0.528694	+	0.848812i	$0.322682\pi$
$774$		0			0
$775$	−6165.87			−0.285786
$776$		0			0
$777$	−1763.98	+	4010.26i	−0.0814443	+	0.185158i
$778$		0			0
$779$	−8363.12	−	14485.3i	−0.384647	−	0.666228i
$780$		0			0
$781$	−1401.10	+	2426.77i	−0.0641935	+	0.111186i
$782$		0			0
$783$	−4490.50	+	22618.5i	−0.204952	+	1.03234i
$784$		0			0
$785$	2848.39	−	4933.55i	0.129507	−	0.224313i
$786$		0			0
$787$	16475.1	+	28535.6i	0.746217	+	1.29249i	0.949624	+	0.313391i	$0.101465\pi$
$787$	16475.1	+	28535.6i	0.746217	+	1.29249i	−0.203407	+	0.979094i	$0.565202\pi$
$788$		0			0
$789$	−12040.4	+	27372.9i	−0.543281	+	1.23511i
$790$		0			0
$791$	−5358.39			−0.240863
$792$		0			0
$793$	8759.93			0.392275
$794$		0			0
$795$	−7416.13	−	10111.7i	−0.330847	−	0.451103i
$796$		0			0
$797$	9869.56	+	17094.6i	0.438642	+	0.759751i	0.997585	−	0.0694555i	$-0.0221262\pi$
$797$	9869.56	+	17094.6i	0.438642	+	0.759751i	−0.558943	+	0.829206i	$0.688793\pi$
$798$		0			0
$799$	−816.576	+	1414.35i	−0.0361557	+	0.0626235i
$800$		0			0
$801$	4584.75	−	1017.59i	0.202240	−	0.0448872i
$802$		0			0
$803$	−6333.64	+	10970.2i	−0.278343	+	0.482104i
$804$		0			0
$805$	156.225	+	270.590i	0.00684002	+	0.0118473i
$806$		0			0
$807$	21910.8	−	2402.32i	0.955757	−	0.104790i
$808$		0			0
$809$	32852.8			1.42774			0.713870	−	0.700278i	$-0.246941\pi$
$809$	32852.8			1.42774			0.713870	+	0.700278i	$0.246941\pi$
$810$		0			0
$811$	20122.0			0.871245			0.435623	−	0.900129i	$-0.356528\pi$
$811$	20122.0			0.871245			0.435623	+	0.900129i	$0.356528\pi$
$812$		0			0
$813$	−20855.4	+	2286.61i	−0.899667	+	0.0986406i
$814$		0			0
$815$	−8302.18	−	14379.8i	−0.356825	−	0.618040i
$816$		0			0
$817$	−2789.89	+	4832.24i	−0.119469	+	0.206926i
$818$		0			0
$819$	−4526.82	+	1004.73i	−0.193138	+	0.0428670i
$820$		0			0
$821$	12567.8	−	21768.0i	0.534249	−	0.925347i	−0.464950	−	0.885337i	$-0.653928\pi$
$821$	12567.8	−	21768.0i	0.534249	−	0.925347i	0.999199	−	0.0400102i	$-0.0127390\pi$
$822$		0			0
$823$	11558.9	+	20020.6i	0.489572	+	0.847963i	0.999928	−	0.0119999i	$-0.00381978\pi$
$823$	11558.9	+	20020.6i	0.489572	+	0.847963i	−0.510356	+	0.859963i	$0.670486\pi$
$824$		0			0
$825$	1123.19	+	1531.45i	0.0473994	+	0.0646281i
$826$		0			0
$827$	6362.04			0.267509			0.133754	−	0.991015i	$-0.457297\pi$
$827$	6362.04			0.267509			0.133754	+	0.991015i	$0.457297\pi$
$828$		0			0
$829$	−21021.5			−0.880706			−0.440353	−	0.897825i	$-0.645147\pi$
$829$	−21021.5			−0.880706			−0.440353	+	0.897825i	$0.645147\pi$
$830$		0			0
$831$	1778.86	−	4044.10i	0.0742575	−	0.168819i
$832$		0			0
$833$	7628.07	+	13212.2i	0.317283	+	0.549550i
$834$		0			0
$835$	−5383.16	+	9323.90i	−0.223104	+	0.386427i
$836$		0			0
$837$	−26023.4	−	22805.1i	−1.07467	−	0.941767i
$838$		0			0
$839$	23031.0	−	39890.9i	0.947698	−	1.64146i	0.197441	−	0.980315i	$-0.436737\pi$
$839$	23031.0	−	39890.9i	0.947698	−	1.64146i	0.750257	−	0.661146i	$-0.229930\pi$
$840$		0			0
$841$	−1313.60	−	2275.23i	−0.0538605	−	0.0932891i
$842$		0			0
$843$	−8832.94	+	20081.0i	−0.360881	+	0.820435i
$844$		0			0
$845$	−3968.87			−0.161578
$846$		0			0
$847$	3508.60			0.142334
$848$		0			0
$849$	7534.17	+	10272.7i	0.304561	+	0.415262i
$850$		0			0
$851$	2671.29	+	4626.81i	0.107604	+	0.186375i
$852$		0			0
$853$	−8792.39	+	15228.9i	−0.352926	+	0.611285i	−0.986761	−	0.162183i	$-0.948147\pi$
$853$	−8792.39	+	15228.9i	−0.352926	+	0.611285i	0.633835	+	0.773468i	$0.281480\pi$
$854$		0			0
$855$	−4592.99	−	5009.91i	−0.183716	−	0.200392i
$856$		0			0
$857$	5156.94	−	8932.09i	0.205552	−	0.356026i	−0.744757	−	0.667336i	$-0.767434\pi$
$857$	5156.94	−	8932.09i	0.205552	−	0.356026i	0.950308	+	0.311310i	$0.100768\pi$
$858$		0			0
$859$	15293.9	+	26489.9i	0.607476	+	1.05218i	0.991655	+	0.128921i	$0.0411514\pi$
$859$	15293.9	+	26489.9i	0.607476	+	1.05218i	−0.384178	+	0.923259i	$0.625515\pi$
$860$		0			0
$861$	−5388.93	+	590.849i	−0.213303	+	0.0233868i
$862$		0			0
$863$	−3387.21			−0.133606			−0.0668029	−	0.997766i	$-0.521280\pi$
$863$	−3387.21			−0.133606			−0.0668029	+	0.997766i	$0.521280\pi$
$864$		0			0
$865$	18982.1			0.746141
$866$		0			0
$867$	14544.2	−	1594.64i	0.569718	−	0.0624646i
$868$		0			0
$869$	−5406.36	−	9364.10i	−0.211045	−	0.365541i
$870$		0			0
$871$	7970.10	−	13804.6i	0.310053	−	0.537028i
$872$		0			0
$873$	−12073.7	+	38325.4i	−0.468078	+	1.48582i
$874$		0			0
$875$	−196.273	+	339.954i	−0.00758312	+	0.0131343i
$876$		0			0
$877$	9232.83	+	15991.7i	0.355497	+	0.615738i	0.987203	−	0.159470i	$-0.0509784\pi$
$877$	9232.83	+	15991.7i	0.355497	+	0.615738i	−0.631706	+	0.775208i	$0.717645\pi$
$878$		0			0
$879$	−11755.1	−	16027.9i	−0.451070	−	0.615025i
$880$		0			0
$881$	20662.0			0.790148			0.395074	−	0.918649i	$-0.370719\pi$
$881$	20662.0			0.790148			0.395074	+	0.918649i	$0.370719\pi$
$882$		0			0
$883$	386.519			0.0147309			0.00736545	−	0.999973i	$-0.497655\pi$
$883$	386.519			0.0147309			0.00736545	+	0.999973i	$0.497655\pi$
$884$		0			0
$885$	3447.16	−	7836.86i	0.130932	−	0.297665i
$886$		0			0
$887$	−6678.06	−	11566.7i	−0.252793	−	0.437850i	0.711501	−	0.702685i	$-0.248016\pi$
$887$	−6678.06	−	11566.7i	−0.252793	−	0.437850i	−0.964294	+	0.264835i	$0.914682\pi$
$888$		0			0
$889$	1688.16	−	2923.98i	0.0636885	−	0.110312i
$890$		0			0
$891$	−923.722	+	10617.8i	−0.0347316	+	0.399226i
$892$		0			0
$893$	897.717	−	1554.89i	0.0336405	−	0.0582670i
$894$		0			0
$895$	4408.36	+	7635.51i	0.164643	+	0.285170i
$896$		0			0
$897$	−2276.76	+	5176.04i	−0.0847478	+	0.192668i
$898$		0			0
$899$	40538.4			1.50393
$900$		0			0
$901$	22103.4			0.817281
$902$		0			0
$903$	1069.56	+	1458.32i	0.0394160	+	0.0537429i
$904$		0			0
$905$	487.437	+	844.266i	0.0179038	+	0.0310103i
$906$		0			0
$907$	−14680.6	+	25427.6i	−0.537445	+	0.930882i	0.461596	+	0.887090i	$0.347277\pi$
$907$	−14680.6	+	25427.6i	−0.537445	+	0.930882i	−0.999041	+	0.0437913i	$0.986056\pi$
$908$		0			0
$909$	3207.51	−	10181.6i	0.117037	−	0.371509i
$910$		0			0
$911$	3836.01	−	6644.16i	0.139509	−	0.241636i	−0.787802	−	0.615929i	$-0.788781\pi$
$911$	3836.01	−	6644.16i	0.139509	−	0.241636i	0.927311	+	0.374292i	$0.122114\pi$
$912$		0			0
$913$	3567.86	+	6179.71i	0.129331	+	0.224007i
$914$		0			0
$915$	4136.81	−	453.565i	0.149463	−	0.0163873i
$916$		0			0
$917$	−2786.32			−0.100341
$918$		0			0
$919$	−25818.6			−0.926742			−0.463371	−	0.886164i	$-0.653360\pi$
$919$	−25818.6			−0.926742			−0.463371	+	0.886164i	$0.653360\pi$
$920$		0			0
$921$	−14316.0	+	1569.63i	−0.512193	+	0.0561574i
$922$		0			0
$923$	−5241.00	−	9077.68i	−0.186901	−	0.323722i
$924$		0			0
$925$	−3356.06	+	5812.86i	−0.119293	+	0.206622i
$926$		0			0
$927$	−15620.0	−	17037.9i	−0.553428	−	0.603665i
$928$		0			0
$929$	13689.5	−	23710.9i	0.483463	−	0.837383i	−0.516356	−	0.856374i	$-0.672712\pi$
$929$	13689.5	−	23710.9i	0.483463	−	0.837383i	0.999820	+	0.0189908i	$0.00604531\pi$
$930$		0			0
$931$	−8386.04	−	14525.0i	−0.295211	−	0.511320i
$932$		0			0
$933$	−26654.0	−	36342.2i	−0.935277	−	1.27523i
$934$		0			0
$935$	−3347.61			−0.117089
$936$		0			0
$937$	−4696.47			−0.163743			−0.0818713	−	0.996643i	$-0.526090\pi$
$937$	−4696.47			−0.163743			−0.0818713	+	0.996643i	$0.526090\pi$
$938$		0			0
$939$	7417.86	−	16863.9i	0.257798	−	0.586085i
$940$		0			0
$941$	−1419.08	−	2457.92i	−0.0491612	−	0.0851497i	0.840398	−	0.541970i	$-0.182321\pi$
$941$	−1419.08	−	2457.92i	−0.0491612	−	0.0851497i	−0.889559	+	0.456821i	$0.848988\pi$
$942$		0			0
$943$	−3305.50	+	5725.30i	−0.114148	+	0.197711i
$944$		0			0
$945$	−2085.74	+	708.863i	−0.0717979	+	0.0244014i
$946$		0			0
$947$	−23449.9	+	40616.5i	−0.804668	+	1.39373i	0.111847	+	0.993725i	$0.464323\pi$
$947$	−23449.9	+	40616.5i	−0.804668	+	1.39373i	−0.916515	+	0.400000i	$0.869010\pi$
$948$		0			0
$949$	−23691.9	−	41035.6i	−0.810403	−	1.40366i
$950$		0			0
$951$	12895.0	−	29315.9i	0.439695	−	0.999614i
$952$		0			0
$953$	32713.6			1.11196			0.555980	−	0.831196i	$-0.312343\pi$
$953$	32713.6			1.11196			0.555980	+	0.831196i	$0.312343\pi$
$954$		0			0
$955$	17186.2			0.582338
$956$		0			0
$957$	−7384.59	−	10068.7i	−0.249436	−	0.340100i
$958$		0			0
$959$	−3103.47	−	5375.36i	−0.104501	−	0.181001i
$960$		0			0
$961$	−15518.8	+	26879.4i	−0.520923	+	0.902266i
$962$		0			0
$963$	11166.4	−	2478.39i	0.373657	−	0.0829334i
$964$		0			0
$965$	−6363.75	+	11022.3i	−0.212286	+	0.367691i
$966$		0			0
$967$	12065.4	+	20897.8i	0.401236	+	0.694962i	0.993875	−	0.110506i	$-0.0352473\pi$
$967$	12065.4	+	20897.8i	0.401236	+	0.694962i	−0.592639	+	0.805468i	$0.701914\pi$
$968$		0			0
$969$	11908.8	−	1305.70i	0.394806	−	0.0432870i
$970$		0			0
$971$	−21198.9			−0.700623			−0.350312	−	0.936633i	$-0.613924\pi$
$971$	−21198.9			−0.700623			−0.350312	+	0.936633i	$0.613924\pi$
$972$		0			0
$973$	5694.31			0.187617
$974$		0			0
$975$	−7061.86	+	774.270i	−0.231959	+	0.0254323i
$976$		0			0
$977$	2070.13	+	3585.57i	0.0677885	+	0.117413i	0.897928	−	0.440143i	$-0.145072\pi$
$977$	2070.13	+	3585.57i	0.0677885	+	0.117413i	−0.830139	+	0.557556i	$0.811739\pi$
$978$		0			0
$979$	−1271.48	+	2202.26i	−0.0415082	+	0.0718944i
$980$		0			0
$981$	−22160.4	+	4918.52i	−0.721232	+	0.160078i
$982$		0			0
$983$	−11969.4	+	20731.6i	−0.388367	+	0.672672i	−0.992230	−	0.124417i	$-0.960294\pi$
$983$	−11969.4	+	20731.6i	−0.388367	+	0.672672i	0.603863	+	0.797088i	$0.293627\pi$
$984$		0			0
$985$	−9431.62	−	16336.1i	−0.305093	−	0.528436i
$986$		0			0
$987$	−344.156	−	469.250i	−0.0110989	−	0.0151331i
$988$		0			0
$989$	2205.40			0.0709075
$990$		0			0
$991$	−40688.9			−1.30426			−0.652131	−	0.758106i	$-0.726125\pi$
$991$	−40688.9			−1.30426			−0.652131	+	0.758106i	$0.726125\pi$
$992$		0			0
$993$	−18239.3	+	41465.6i	−0.582886	+	1.32515i
$994$		0			0
$995$	−2528.77	−	4379.95i	−0.0805702	−	0.139552i
$996$		0			0
$997$	1689.21	−	2925.80i	0.0536589	−	0.0929400i	−0.837948	−	0.545750i	$-0.816245\pi$
$997$	1689.21	−	2925.80i	0.0536589	−	0.0929400i	0.891607	+	0.452810i	$0.149578\pi$
$998$		0			0
$999$	−35663.9	+	12120.8i	−1.12949	+	0.383869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.4.q.e.241.1	yes	20
3.2	odd	2		1080.4.q.e.721.6		20
9.4	even	3	inner	360.4.q.e.121.1	✓	20
9.5	odd	6		1080.4.q.e.361.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.4.q.e.121.1	✓	20	9.4	even	3	inner
360.4.q.e.241.1	yes	20	1.1	even	1	trivial
1080.4.q.e.361.6		20	9.5	odd	6
1080.4.q.e.721.6		20	3.2	odd	2

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	360.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.16520 + 0.566318i) q^{3} +(2.50000 + 4.33013i) q^{5} +(1.57018 - 2.71963i) q^{7} +(26.3586 - 5.85030i) q^{9} +(-7.30996 + 12.6612i) q^{11} +(-27.3440 - 47.3612i) q^{13} +(-15.3652 - 20.9502i) q^{15} +45.7952 q^{17} -50.3457 q^{19} +(-6.57012 + 14.9367i) q^{21} +(9.94951 + 17.2331i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(-132.834 + 45.1453i) q^{27} +(82.1830 - 142.345i) q^{29} +(123.317 + 213.592i) q^{31} +(30.5871 - 69.5375i) q^{33} +15.7018 q^{35} +268.484 q^{37} +(168.059 + 229.144i) q^{39} +(166.114 + 287.718i) q^{41} +(55.4147 - 95.9811i) q^{43} +(91.2289 + 99.5102i) q^{45} +(-17.8310 + 30.8843i) q^{47} +(166.569 + 288.506i) q^{49} +(-236.541 + 25.9347i) q^{51} +482.657 q^{53} -73.0996 q^{55} +(260.046 - 28.5117i) q^{57} +(164.766 + 285.383i) q^{59} +(-80.0901 + 138.720i) q^{61} +(25.4771 - 80.8717i) q^{63} +(136.720 - 236.806i) q^{65} +(145.738 + 252.425i) q^{67} +(-61.1506 - 83.3776i) q^{69} +191.669 q^{71} +866.440 q^{73} +(52.3038 - 118.909i) q^{75} +(22.9559 + 39.7608i) q^{77} +(-369.794 + 640.503i) q^{79} +(660.548 - 308.411i) q^{81} +(244.041 - 422.691i) q^{83} +(114.488 + 198.299i) q^{85} +(-343.879 + 781.783i) q^{87} +173.938 q^{89} -171.740 q^{91} +(-757.920 - 1033.41i) q^{93} +(-125.864 - 218.003i) q^{95} +(-744.116 + 1288.85i) q^{97} +(-118.608 + 376.497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{3} + 50 q^{5} + 22 q^{7} - 6 q^{9} + 50 q^{11} - 16 q^{13} - 68 q^{17} + 212 q^{19} - 60 q^{21} + 50 q^{23} - 250 q^{25} + 630 q^{27} - 64 q^{29} - 22 q^{31} - 330 q^{33} + 220 q^{35} + 600 q^{37}+ \cdots + 5562 q^{99}+O(q^{100}) \) 20 * q + 6 * q^3 + 50 * q^5 + 22 * q^7 - 6 * q^9 + 50 * q^11 - 16 * q^13 - 68 * q^17 + 212 * q^19 - 60 * q^21 + 50 * q^23 - 250 * q^25 + 630 * q^27 - 64 * q^29 - 22 * q^31 - 330 * q^33 + 220 * q^35 + 600 * q^37 + 306 * q^39 - 198 * q^41 - 382 * q^43 - 90 * q^45 + 128 * q^47 - 1230 * q^49 - 1506 * q^51 - 1128 * q^53 + 500 * q^55 + 294 * q^57 - 200 * q^59 - 232 * q^61 + 1908 * q^63 + 80 * q^65 - 1316 * q^67 - 1344 * q^69 - 228 * q^71 + 828 * q^73 - 150 * q^75 + 616 * q^77 - 300 * q^79 + 2814 * q^81 - 1082 * q^83 - 170 * q^85 - 4794 * q^87 - 768 * q^89 + 1972 * q^91 + 348 * q^93 + 530 * q^95 - 1354 * q^97 + 5562 * q^99

Introduction

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