LMFDB - Embedded newform 108.4.i.a.25.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [108,4,Mod(13,108)] 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("108.13"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(108, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, degree $6$, 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:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.8
Character	$\chi$	$=$	108.25
Dual form			108.4.i.a.13.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.14478 - 0.728858i) q^{3} +(-5.18194 + 4.34817i) q^{5} +(16.8240 - 6.12342i) q^{7} +(25.9375 - 7.49962i) q^{9} +(45.5667 + 38.2350i) q^{11} +(-5.02544 - 28.5007i) q^{13} +(-23.4908 + 26.1473i) q^{15} +(-14.6698 - 25.4089i) q^{17} +(13.7884 - 23.8822i) q^{19} +(82.0925 - 43.7660i) q^{21} +(-0.946050 - 0.344334i) q^{23} +(-13.7600 + 78.0370i) q^{25} +(127.977 - 57.4887i) q^{27} +(-15.4827 + 87.8069i) q^{29} +(-11.6374 - 4.23566i) q^{31} +(262.299 + 163.499i) q^{33} +(-60.5552 + 104.885i) q^{35} +(-186.599 - 323.199i) q^{37} +(-46.6278 - 142.967i) q^{39} +(38.3921 + 217.733i) q^{41} +(-415.169 - 348.368i) q^{43} +(-101.797 + 151.643i) q^{45} +(-575.029 + 209.294i) q^{47} +(-17.2036 + 14.4355i) q^{49} +(-93.9924 - 120.031i) q^{51} -51.1253 q^{53} -402.376 q^{55} +(53.5316 - 132.919i) q^{57} +(-326.874 + 274.280i) q^{59} +(488.734 - 177.884i) q^{61} +(390.449 - 285.000i) q^{63} +(149.967 + 125.838i) q^{65} +(38.0132 + 215.584i) q^{67} +(-5.11819 - 1.08199i) q^{69} +(-99.9846 - 173.178i) q^{71} +(-398.711 + 690.588i) q^{73} +(-13.9145 + 411.513i) q^{75} +(1000.74 + 364.240i) q^{77} +(227.171 - 1288.35i) q^{79} +(616.511 - 389.044i) q^{81} +(-11.1689 + 63.3422i) q^{83} +(186.500 + 67.8805i) q^{85} +(-15.6565 + 463.032i) q^{87} +(466.341 - 807.726i) q^{89} +(-259.070 - 448.722i) q^{91} +(-62.9590 - 13.3096i) q^{93} +(32.3931 + 183.711i) q^{95} +(915.498 + 768.194i) q^{97} +(1468.64 + 649.989i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45}+ \cdots - 5076 q^{99}+O(q^{100}) $ 54 * q + 12 * q^5 - 48 * q^9 - 87 * q^11 + 234 * q^15 + 204 * q^17 - 12 * q^21 + 96 * q^23 - 216 * q^25 + 27 * q^27 + 318 * q^29 - 54 * q^31 + 63 * q^33 + 6 * q^35 + 66 * q^39 + 867 * q^41 - 513 * q^43 - 306 * q^45 - 1548 * q^47 + 594 * q^49 - 1368 * q^51 - 1068 * q^53 - 1269 * q^57 - 1218 * q^59 - 54 * q^61 + 30 * q^63 + 96 * q^65 - 2997 * q^67 + 1476 * q^69 - 120 * q^71 - 216 * q^73 + 732 * q^75 + 3480 * q^77 + 2808 * q^79 + 3348 * q^81 + 4464 * q^83 + 2160 * q^85 + 4824 * q^87 + 4029 * q^89 + 270 * q^91 + 1164 * q^93 - 1650 * q^95 - 3483 * q^97 - 5076 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	5.14478	−	0.728858i	0.990113	−	0.140269i
$3$	5.14478	−	0.728858i	0.990113	−	0.140269i
$4$		0			0
$5$	−5.18194	+	4.34817i	−0.463487	+	0.388912i	−0.844412	−	0.535694i	$-0.820050\pi$
$5$	−5.18194	+	4.34817i	−0.463487	+	0.388912i	0.380925	+	0.924606i	$0.375606\pi$
$6$		0			0
$7$	16.8240	−	6.12342i	0.908409	−	0.330634i	0.154792	−	0.987947i	$-0.450529\pi$
$7$	16.8240	−	6.12342i	0.908409	−	0.330634i	0.753617	+	0.657313i	$0.228307\pi$
$8$		0			0
$9$	25.9375	−	7.49962i	0.960649	−	0.277764i
$10$		0			0
$11$	45.5667	+	38.2350i	1.24899	+	1.04803i	0.996766	+	0.0803571i	$0.0256061\pi$
$11$	45.5667	+	38.2350i	1.24899	+	1.04803i	0.252223	+	0.967669i	$0.418838\pi$
$12$		0			0
$13$	−5.02544	−	28.5007i	−0.107216	−	0.608052i	−0.990312	−	0.138860i	$-0.955656\pi$
$13$	−5.02544	−	28.5007i	−0.107216	−	0.608052i	0.883096	−	0.469192i	$-0.155455\pi$
$14$		0			0
$15$	−23.4908	+	26.1473i	−0.404353	+	0.450080i
$16$		0			0
$17$	−14.6698	−	25.4089i	−0.209291	−	0.362503i	0.742200	−	0.670178i	$-0.233782\pi$
$17$	−14.6698	−	25.4089i	−0.209291	−	0.362503i	−0.951491	+	0.307675i	$0.900449\pi$
$18$		0			0
$19$	13.7884	−	23.8822i	0.166488	−	0.288366i	−0.770695	−	0.637205i	$-0.780091\pi$
$19$	13.7884	−	23.8822i	0.166488	−	0.288366i	0.937183	+	0.348839i	$0.113424\pi$
$20$		0			0
$21$	82.0925	−	43.7660i	0.853050	−	0.454786i
$22$		0			0
$23$	−0.946050	−	0.344334i	−0.00857674	−	0.00312168i	0.337728	−	0.941244i	$-0.390342\pi$
$23$	−0.946050	−	0.344334i	−0.00857674	−	0.00312168i	−0.346305	+	0.938122i	$0.612564\pi$
$24$		0			0
$25$	−13.7600	+	78.0370i	−0.110080	+	0.624296i
$26$		0			0
$27$	127.977	−	57.4887i	0.912190	−	0.409767i
$28$		0			0
$29$	−15.4827	+	87.8069i	−0.0991404	+	0.562253i	0.894259	+	0.447549i	$0.147703\pi$
$29$	−15.4827	+	87.8069i	−0.0991404	+	0.562253i	−0.993400	+	0.114704i	$0.963408\pi$
$30$		0			0
$31$	−11.6374	−	4.23566i	−0.0674238	−	0.0245402i	0.308088	−	0.951358i	$-0.400311\pi$
$31$	−11.6374	−	4.23566i	−0.0674238	−	0.0245402i	−0.375512	+	0.926818i	$0.622533\pi$
$32$		0			0
$33$	262.299	+	163.499i	1.38365	+	0.862471i
$34$		0			0
$35$	−60.5552	+	104.885i	−0.292448	+	0.506536i
$36$		0			0
$37$	−186.599	−	323.199i	−0.829100	−	1.43604i	−0.898745	−	0.438472i	$-0.855520\pi$
$37$	−186.599	−	323.199i	−0.829100	−	1.43604i	0.0696442	−	0.997572i	$-0.477814\pi$
$38$		0			0
$39$	−46.6278	−	142.967i	−0.191447	−	0.587001i
$40$		0			0
$41$	38.3921	+	217.733i	0.146240	+	0.829369i	0.966363	+	0.257182i	$0.0827939\pi$
$41$	38.3921	+	217.733i	0.146240	+	0.829369i	−0.820123	+	0.572187i	$0.806095\pi$
$42$		0			0
$43$	−415.169	−	348.368i	−1.47239	−	1.23548i	−0.913882	−	0.405979i	$-0.866931\pi$
$43$	−415.169	−	348.368i	−1.47239	−	1.23548i	−0.558505	−	0.829501i	$-0.688625\pi$
$44$		0			0
$45$	−101.797	+	151.643i	−0.337223	+	0.502348i
$46$		0			0
$47$	−575.029	+	209.294i	−1.78461	+	0.649545i	−0.785063	+	0.619416i	$0.787369\pi$
$47$	−575.029	+	209.294i	−1.78461	+	0.649545i	−0.999546	+	0.0301286i	$0.990408\pi$
$48$		0			0
$49$	−17.2036	+	14.4355i	−0.0501562	+	0.0420861i
$50$		0			0
$51$	−93.9924	−	120.031i	−0.258070	−	0.329562i
$52$		0			0
$53$	−51.1253			−0.132502			−0.0662509	−	0.997803i	$-0.521104\pi$
$53$	−51.1253			−0.132502			−0.0662509	+	0.997803i	$0.521104\pi$
$54$		0			0
$55$	−402.376			−0.986480
$56$		0			0
$57$	53.5316	−	132.919i	0.124394	−	0.308868i
$58$		0			0
$59$	−326.874	+	274.280i	−0.721278	+	0.605224i	−0.927739	−	0.373231i	$-0.878250\pi$
$59$	−326.874	+	274.280i	−0.721278	+	0.605224i	0.206460	+	0.978455i	$0.433806\pi$
$60$		0			0
$61$	488.734	−	177.884i	1.02583	−	0.373373i	0.226341	−	0.974048i	$-0.427324\pi$
$61$	488.734	−	177.884i	1.02583	−	0.373373i	0.799493	+	0.600675i	$0.205101\pi$
$62$		0			0
$63$	390.449	−	285.000i	0.780824	−	0.569946i
$64$		0			0
$65$	149.967	+	125.838i	0.286172	+	0.240127i
$66$		0			0
$67$	38.0132	+	215.584i	0.0693143	+	0.393101i	0.999652	+	0.0263958i	$0.00840303\pi$
$67$	38.0132	+	215.584i	0.0693143	+	0.393101i	−0.930337	+	0.366705i	$0.880486\pi$
$68$		0			0
$69$	−5.11819	−	1.08199i	−0.00892982	−	0.00188777i
$70$		0			0
$71$	−99.9846	−	173.178i	−0.167127	−	0.289472i	0.770282	−	0.637704i	$-0.220116\pi$
$71$	−99.9846	−	173.178i	−0.167127	−	0.289472i	−0.937408	+	0.348232i	$0.886782\pi$
$72$		0			0
$73$	−398.711	+	690.588i	−0.639255	+	1.10722i	0.346342	+	0.938108i	$0.387424\pi$
$73$	−398.711	+	690.588i	−0.639255	+	1.10722i	−0.985597	+	0.169113i	$0.945910\pi$
$74$		0			0
$75$	−13.9145	+	411.513i	−0.0214227	+	0.633565i
$76$		0			0
$77$	1000.74	+	364.240i	1.48111	+	0.539078i
$78$		0			0
$79$	227.171	−	1288.35i	0.323529	−	1.83482i	−0.196290	−	0.980546i	$-0.562889\pi$
$79$	227.171	−	1288.35i	0.323529	−	1.83482i	0.519819	−	0.854277i	$-0.326000\pi$
$80$		0			0
$81$	616.511	−	389.044i	0.845694	−	0.533667i
$82$		0			0
$83$	−11.1689	+	63.3422i	−0.0147705	+	0.0837675i	−0.991302	−	0.131607i	$-0.957986\pi$
$83$	−11.1689	+	63.3422i	−0.0147705	+	0.0837675i	0.976531	+	0.215375i	$0.0690973\pi$
$84$		0			0
$85$	186.500	+	67.8805i	0.237986	+	0.0866197i
$86$		0			0
$87$	−15.6565	+	463.032i	−0.0192937	+	0.570601i
$88$		0			0
$89$	466.341	−	807.726i	0.555416	−	0.962009i	−0.442455	−	0.896791i	$-0.645892\pi$
$89$	466.341	−	807.726i	0.555416	−	0.962009i	0.997871	−	0.0652184i	$-0.0207744\pi$
$90$		0			0
$91$	−259.070	−	448.722i	−0.298439	−	0.516911i
$92$		0			0
$93$	−62.9590	−	13.3096i	−0.0701994	−	0.0148402i
$94$		0			0
$95$	32.3931	+	183.711i	0.0349839	+	0.198403i
$96$		0			0
$97$	915.498	+	768.194i	0.958296	+	0.804106i	0.980675	−	0.195644i	$-0.0626797\pi$
$97$	915.498	+	768.194i	0.958296	+	0.804106i	−0.0223792	+	0.999750i	$0.507124\pi$
$98$		0			0
$99$	1468.64	+	649.989i	1.49094	+	0.659862i
$100$		0			0
$101$	−934.108	+	339.987i	−0.920269	+	0.334951i	−0.758346	−	0.651853i	$-0.773992\pi$
$101$	−934.108	+	339.987i	−0.920269	+	0.334951i	−0.161924	+	0.986803i	$0.551770\pi$
$102$		0			0
$103$	−252.152	+	211.581i	−0.241216	+	0.202405i	−0.755379	−	0.655288i	$-0.772547\pi$
$103$	−252.152	+	211.581i	−0.241216	+	0.202405i	0.514163	+	0.857693i	$0.328103\pi$
$104$		0			0
$105$	−235.097	+	583.745i	−0.218506	+	0.542549i
$106$		0			0
$107$	−321.330			−0.290319			−0.145159	−	0.989408i	$-0.546369\pi$
$107$	−321.330			−0.290319			−0.145159	+	0.989408i	$0.546369\pi$
$108$		0			0
$109$	379.701			0.333658			0.166829	−	0.985986i	$-0.446647\pi$
$109$	379.701			0.333658			0.166829	+	0.985986i	$0.446647\pi$
$110$		0			0
$111$	−1195.58	−	1526.79i	−1.02234	−	1.30555i
$112$		0			0
$113$	1463.88	−	1228.34i	1.21867	−	1.02259i	0.219780	−	0.975549i	$-0.429466\pi$
$113$	1463.88	−	1228.34i	1.21867	−	1.02259i	0.998893	−	0.0470391i	$-0.0149785\pi$
$114$		0			0
$115$	6.39960	−	2.32926i	0.00518927	−	0.00188874i
$116$		0			0
$117$	−344.092	−	701.549i	−0.271892	−	0.554344i
$118$		0			0
$119$	−402.394	−	337.648i	−0.309978	−	0.260102i
$120$		0			0
$121$	383.283	+	2173.71i	0.287966	+	1.63314i
$122$		0			0
$123$	356.215	+	1092.20i	0.261129	+	0.800657i
$124$		0			0
$125$	−690.799	−	1196.50i	−0.494295	−	0.856145i
$126$		0			0
$127$	−84.0772	+	145.626i	−0.0587453	+	0.101750i	−0.893902	−	0.448262i	$-0.852043\pi$
$127$	−84.0772	+	145.626i	−0.0587453	+	0.101750i	0.835157	+	0.550011i	$0.185377\pi$
$128$		0			0
$129$	−2389.86	−	1489.68i	−1.63113	−	1.01674i
$130$		0			0
$131$	1884.63	+	685.949i	1.25695	+	0.457493i	0.882745	−	0.469852i	$-0.155693\pi$
$131$	1884.63	+	685.949i	1.25695	+	0.457493i	0.374207	+	0.927345i	$0.377915\pi$
$132$		0			0
$133$	85.7348	−	486.226i	0.0558958	−	0.317001i
$134$		0			0
$135$	−413.198	+	854.368i	−0.263425	+	0.544683i
$136$		0			0
$137$	−160.622	+	910.931i	−0.100167	+	0.568073i	0.892874	+	0.450306i	$0.148685\pi$
$137$	−160.622	+	910.931i	−0.100167	+	0.568073i	−0.993041	+	0.117768i	$0.962426\pi$
$138$		0			0
$139$	2389.86	+	869.838i	1.45831	+	0.530782i	0.944900	−	0.327360i	$-0.106159\pi$
$139$	2389.86	+	869.838i	1.45831	+	0.530782i	0.513412	+	0.858142i	$0.328381\pi$
$140$		0			0
$141$	−2805.85	+	1495.88i	−1.67585	+	0.893448i
$142$		0			0
$143$	860.732	−	1490.83i	0.503343	−	0.871815i
$144$		0			0
$145$	−301.569	−	522.332i	−0.172717	−	0.299154i
$146$		0			0
$147$	−77.9873	+	86.8066i	−0.0437570	+	0.0487054i
$148$		0			0
$149$	−353.990	−	2007.58i	−0.194631	−	1.10381i	−0.912943	−	0.408086i	$-0.866196\pi$
$149$	−353.990	−	2007.58i	−0.194631	−	1.10381i	0.718313	−	0.695720i	$-0.244915\pi$
$150$		0			0
$151$	631.192	+	529.633i	0.340170	+	0.285437i	0.796829	−	0.604205i	$-0.206509\pi$
$151$	631.192	+	529.633i	0.340170	+	0.285437i	−0.456658	+	0.889642i	$0.650954\pi$
$152$		0			0
$153$	−571.056	−	549.025i	−0.301746	−	0.290105i
$154$		0			0
$155$	78.7217	−	28.6523i	0.0407940	−	0.0148478i
$156$		0			0
$157$	−721.515	+	605.423i	−0.366772	+	0.307758i	−0.807483	−	0.589891i	$-0.799171\pi$
$157$	−721.515	+	605.423i	−0.366772	+	0.307758i	0.440711	+	0.897649i	$0.354726\pi$
$158$		0			0
$159$	−263.028	+	37.2631i	−0.131192	+	0.0185859i
$160$		0			0
$161$	−18.0248			−0.00882332
$162$		0			0
$163$	−3395.63			−1.63169			−0.815847	−	0.578267i	$-0.803729\pi$
$163$	−3395.63			−1.63169			−0.815847	+	0.578267i	$0.803729\pi$
$164$		0			0
$165$	−2070.14	+	293.275i	−0.976728	+	0.138372i
$166$		0			0
$167$	−2218.43	+	1861.48i	−1.02795	+	0.862550i	−0.990605	−	0.136752i	$-0.956334\pi$
$167$	−2218.43	+	1861.48i	−1.02795	+	0.862550i	−0.0373420	+	0.999303i	$0.511889\pi$
$168$		0			0
$169$	1277.47	−	464.961i	0.581461	−	0.211634i
$170$		0			0
$171$	178.530	−	722.854i	0.0798392	−	0.323263i
$172$		0			0
$173$	−1595.10	−	1338.45i	−0.701002	−	0.588211i	0.221056	−	0.975261i	$-0.429050\pi$
$173$	−1595.10	−	1338.45i	−0.701002	−	0.588211i	−0.922059	+	0.387050i	$0.873494\pi$
$174$		0			0
$175$	246.355	+	1397.15i	0.106416	+	0.603513i
$176$		0			0
$177$	−1481.79	+	1649.36i	−0.629253	+	0.700414i
$178$		0			0
$179$	−2179.06	−	3774.24i	−0.909890	−	1.57598i	−0.814215	−	0.580563i	$-0.802832\pi$
$179$	−2179.06	−	3774.24i	−0.909890	−	1.57598i	−0.0956752	−	0.995413i	$-0.530501\pi$
$180$		0			0
$181$	−1347.22	+	2333.45i	−0.553248	+	0.958254i	0.444789	+	0.895635i	$0.353279\pi$
$181$	−1347.22	+	2333.45i	−0.553248	+	0.958254i	−0.998038	+	0.0626187i	$0.980055\pi$
$182$		0			0
$183$	2384.77	−	1271.39i	0.963320	−	0.513574i
$184$		0			0
$185$	2372.27	+	863.436i	0.942772	+	0.343141i
$186$		0			0
$187$	303.053	−	1718.70i	0.118510	−	0.672105i
$188$		0			0
$189$	1801.05	−	1750.84i	0.693159	−	0.673837i
$190$		0			0
$191$	−523.862	+	2970.97i	−0.198457	+	1.12551i	0.708951	+	0.705258i	$0.249169\pi$
$191$	−523.862	+	2970.97i	−0.198457	+	1.12551i	−0.907408	+	0.420250i	$0.861942\pi$
$192$		0			0
$193$	1388.37	+	505.325i	0.517808	+	0.188467i	0.587686	−	0.809089i	$-0.300039\pi$
$193$	1388.37	+	505.325i	0.517808	+	0.188467i	−0.0698784	+	0.997556i	$0.522261\pi$
$194$		0			0
$195$	863.267	+	538.102i	0.317025	+	0.197612i
$196$		0			0
$197$	1889.39	−	3272.53i	0.683318	−	1.18354i	−0.290644	−	0.956831i	$-0.593869\pi$
$197$	1889.39	−	3272.53i	0.683318	−	1.18354i	0.973962	−	0.226711i	$-0.0727973\pi$
$198$		0			0
$199$	160.647	+	278.248i	0.0572258	+	0.0991180i	0.893219	−	0.449622i	$-0.148441\pi$
$199$	160.647	+	278.248i	0.0572258	+	0.0991180i	−0.835993	+	0.548740i	$0.815108\pi$
$200$		0			0
$201$	352.700	+	1081.43i	0.123769	+	0.379492i
$202$		0			0
$203$	277.198	+	1572.07i	0.0958399	+	0.543535i
$204$		0			0
$205$	−1145.68	−	961.343i	−0.390332	−	0.327527i
$206$		0			0
$207$	−27.1206	−	1.83616i	−0.00910633	−	0.000616530i
$208$		0			0
$209$	1541.43	−	561.034i	0.510157	−	0.185682i
$210$		0			0
$211$	973.780	−	817.098i	0.317714	−	0.266594i	−0.469957	−	0.882689i	$-0.655731\pi$
$211$	973.780	−	817.098i	0.317714	−	0.266594i	0.787672	+	0.616095i	$0.211286\pi$
$212$		0			0
$213$	−640.621	−	818.090i	−0.206078	−	0.263167i
$214$		0			0
$215$	3666.15			1.16293
$216$		0			0
$217$	−221.724			−0.0693622
$218$		0			0
$219$	−1547.94	+	3843.53i	−0.477626	+	1.18594i
$220$		0			0
$221$	−650.448	+	545.791i	−0.197981	+	0.166126i
$222$		0			0
$223$	4698.03	−	1709.94i	1.41078	−	0.513481i	0.479420	−	0.877585i	$-0.340847\pi$
$223$	4698.03	−	1709.94i	1.41078	−	0.513481i	0.931358	+	0.364104i	$0.118625\pi$
$224$		0			0
$225$	228.347	+	2127.28i	0.0676584	+	0.630306i
$226$		0			0
$227$	−907.775	−	761.713i	−0.265423	−	0.222717i	0.500356	−	0.865820i	$-0.333202\pi$
$227$	−907.775	−	761.713i	−0.265423	−	0.222717i	−0.765780	+	0.643103i	$0.777647\pi$
$228$		0			0
$229$	321.039	+	1820.70i	0.0926412	+	0.525394i	0.995445	+	0.0953410i	$0.0303941\pi$
$229$	321.039	+	1820.70i	0.0926412	+	0.525394i	−0.902803	+	0.430053i	$0.858495\pi$
$230$		0			0
$231$	5414.08	+	1144.54i	1.54208	+	0.325996i
$232$		0			0
$233$	1585.36	+	2745.93i	0.445754	+	0.772068i	0.998104	−	0.0615437i	$-0.0196024\pi$
$233$	1585.36	+	2745.93i	0.445754	+	0.772068i	−0.552351	+	0.833612i	$0.686269\pi$
$234$		0			0
$235$	2069.73	−	3584.87i	0.574528	−	0.995111i
$236$		0			0
$237$	229.721	−	6793.87i	0.0629620	−	1.86206i
$238$		0			0
$239$	5573.01	+	2028.41i	1.50832	+	0.548983i	0.958199	−	0.286104i	$-0.0923602\pi$
$239$	5573.01	+	2028.41i	1.50832	+	0.548983i	0.550119	+	0.835086i	$0.314582\pi$
$240$		0			0
$241$	−517.453	+	2934.62i	−0.138307	+	0.784380i	0.834192	+	0.551474i	$0.185935\pi$
$241$	−517.453	+	2934.62i	−0.138307	+	0.784380i	−0.972499	+	0.232906i	$0.925177\pi$
$242$		0			0
$243$	2888.26	−	2450.89i	0.762477	−	0.647016i
$244$		0			0
$245$	26.3800	−	149.608i	0.00687900	−	0.0390127i
$246$		0			0
$247$	−749.953	−	272.961i	−0.193192	−	0.0703161i
$248$		0			0
$249$	−11.2943	+	334.022i	−0.00287448	+	0.0850112i
$250$		0			0
$251$	−3456.30	+	5986.49i	−0.869162	+	1.50543i	−0.00630772	+	0.999980i	$0.502008\pi$
$251$	−3456.30	+	5986.49i	−0.869162	+	1.50543i	−0.862854	+	0.505453i	$0.831326\pi$
$252$		0			0
$253$	−29.9428	−	51.8624i	−0.00744066	−	0.0128876i
$254$		0			0
$255$	1008.98	+	213.298i	0.247783	+	0.0523814i
$256$		0			0
$257$	−882.257	−	5003.53i	−0.214139	−	1.21444i	−0.882395	−	0.470510i	$-0.844070\pi$
$257$	−882.257	−	5003.53i	−0.214139	−	1.21444i	0.668256	−	0.743931i	$-0.267041\pi$
$258$		0			0
$259$	−5118.43	−	4294.87i	−1.22797	−	1.03039i
$260$		0			0
$261$	256.935	+	2393.61i	0.0609344	+	0.567666i
$262$		0			0
$263$	−7196.97	+	2619.48i	−1.68739	+	0.614160i	−0.994293	−	0.106682i	$-0.965977\pi$
$263$	−7196.97	+	2619.48i	−1.68739	+	0.614160i	−0.693099	+	0.720843i	$0.743755\pi$
$264$		0			0
$265$	264.928	−	222.301i	0.0614129	−	0.0515316i
$266$		0			0
$267$	1810.50	−	4495.47i	0.414985	−	1.03041i
$268$		0			0
$269$	−6884.46			−1.56042			−0.780210	−	0.625518i	$-0.784888\pi$
$269$	−6884.46			−1.56042			−0.780210	+	0.625518i	$0.784888\pi$
$270$		0			0
$271$	−3232.55			−0.724588			−0.362294	−	0.932064i	$-0.618006\pi$
$271$	−3232.55			−0.724588			−0.362294	+	0.932064i	$0.618006\pi$
$272$		0			0
$273$	−1659.91	−	2119.75i	−0.367994	−	0.469939i
$274$		0			0
$275$	−3610.75	+	3029.78i	−0.791768	+	0.664372i
$276$		0			0
$277$	−2971.80	+	1081.65i	−0.644615	+	0.234621i	−0.643580	−	0.765379i	$-0.722552\pi$
$277$	−2971.80	+	1081.65i	−0.644615	+	0.234621i	−0.00103476	+	0.999999i	$0.500329\pi$
$278$		0			0
$279$	−333.611	−	22.5866i	−0.0715870	−	0.00484668i
$280$		0			0
$281$	3251.44	+	2728.28i	0.690266	+	0.579202i	0.918986	−	0.394290i	$-0.129009\pi$
$281$	3251.44	+	2728.28i	0.690266	+	0.579202i	−0.228720	+	0.973492i	$0.573454\pi$
$282$		0			0
$283$	−927.955	−	5262.69i	−0.194916	−	1.10542i	−0.912538	−	0.408991i	$-0.865881\pi$
$283$	−927.955	−	5262.69i	−0.194916	−	1.10542i	0.717623	−	0.696432i	$-0.245230\pi$
$284$		0			0
$285$	300.555	+	921.541i	0.0624678	+	0.191535i
$286$		0			0
$287$	1979.18	+	3428.04i	0.407063	+	0.705054i
$288$		0			0
$289$	2026.09	−	3509.30i	0.412394	−	0.714288i
$290$		0			0
$291$	5269.94	+	3284.92i	1.06161	+	0.661737i
$292$		0			0
$293$	2133.39	+	776.490i	0.425372	+	0.154823i	0.545830	−	0.837896i	$-0.316214\pi$
$293$	2133.39	+	776.490i	0.425372	+	0.154823i	−0.120459	+	0.992718i	$0.538437\pi$
$294$		0			0
$295$	501.229	−	2842.61i	0.0989243	−	0.561028i
$296$		0			0
$297$	8029.56	+	2273.62i	1.56876	+	0.444205i
$298$		0			0
$299$	−5.05944	+	28.6935i	−0.000978579	+	0.00554980i
$300$		0			0
$301$	−9118.00	−	3318.68i	−1.74602	−	0.635500i
$302$		0			0
$303$	−4557.98	+	2429.99i	−0.864188	+	0.460724i
$304$		0			0
$305$	−1759.12	+	3046.88i	−0.330252	+	0.572013i
$306$		0			0
$307$	−324.386	−	561.853i	−0.0603052	−	0.104452i	0.834297	−	0.551316i	$-0.185874\pi$
$307$	−324.386	−	561.853i	−0.0603052	−	0.104452i	−0.894602	+	0.446864i	$0.852541\pi$
$308$		0			0
$309$	−1143.05	+	1272.32i	−0.210440	+	0.234239i
$310$		0			0
$311$	−990.109	−	5615.19i	−0.180527	−	1.02382i	−0.931569	−	0.363565i	$-0.881559\pi$
$311$	−990.109	−	5615.19i	−0.180527	−	1.02382i	0.751042	−	0.660255i	$-0.229552\pi$
$312$		0			0
$313$	3737.23	+	3135.91i	0.674890	+	0.566300i	0.914508	−	0.404567i	$-0.132578\pi$
$313$	3737.23	+	3135.91i	0.674890	+	0.566300i	−0.239618	+	0.970867i	$0.577022\pi$
$314$		0			0
$315$	−784.057	+	3174.59i	−0.140243	+	0.567835i
$316$		0			0
$317$	6695.08	−	2436.81i	1.18623	−	0.431751i	0.327829	−	0.944737i	$-0.393683\pi$
$317$	6695.08	−	2436.81i	1.18623	−	0.431751i	0.858397	+	0.512987i	$0.171461\pi$
$318$		0			0
$319$	−4062.80	+	3409.09i	−0.713081	+	0.598346i
$320$		0			0
$321$	−1653.17	+	234.203i	−0.287448	+	0.0407226i
$322$		0			0
$323$	−809.093			−0.139378
$324$		0			0
$325$	2293.26			0.391407
$326$		0			0
$327$	1953.48	−	276.748i	0.330359	−	0.0468018i
$328$		0			0
$329$	−8392.68	+	7042.30i	−1.40639	+	1.18010i
$330$		0			0
$331$	−4873.32	+	1773.74i	−0.809250	+	0.294543i	−0.713314	−	0.700844i	$-0.752807\pi$
$331$	−4873.32	+	1773.74i	−0.809250	+	0.294543i	−0.0959363	+	0.995387i	$0.530584\pi$
$332$		0			0
$333$	−7263.80	−	6983.57i	−1.19536	−	1.14924i
$334$		0			0
$335$	−1134.38	−	951.855i	−0.185008	−	0.155240i
$336$		0			0
$337$	−1266.75	−	7184.10i	−0.204760	−	1.16125i	−0.897816	−	0.440370i	$-0.854847\pi$
$337$	−1266.75	−	7184.10i	−0.204760	−	1.16125i	0.693056	−	0.720884i	$-0.256264\pi$
$338$		0			0
$339$	6636.05	−	7386.50i	1.06319	−	1.18342i
$340$		0			0
$341$	−368.327	−	637.961i	−0.0584927	−	0.101312i
$342$		0			0
$343$	−3271.52	+	5666.44i	−0.515002	+	0.892009i
$344$		0			0
$345$	31.2268	−	16.6480i	0.00487303	−	0.00259796i
$346$		0			0
$347$	−3010.74	−	1095.82i	−0.465777	−	0.169529i	0.0984612	−	0.995141i	$-0.468608\pi$
$347$	−3010.74	−	1095.82i	−0.465777	−	0.169529i	−0.564239	+	0.825612i	$0.690830\pi$
$348$		0			0
$349$	−322.003	+	1826.17i	−0.0493881	+	0.280094i	−0.999493	−	0.0318364i	$-0.989864\pi$
$349$	−322.003	+	1826.17i	−0.0493881	+	0.280094i	0.950105	+	0.311930i	$0.100976\pi$
$350$		0			0
$351$	−2281.61	−	3358.52i	−0.346961	−	0.510726i
$352$		0			0
$353$	57.4469	−	325.798i	0.00866173	−	0.0491231i	−0.980171	−	0.198156i	$-0.936505\pi$
$353$	57.4469	−	325.798i	0.00866173	−	0.0491231i	0.988832	+	0.149033i	$0.0476159\pi$
$354$		0			0
$355$	1271.12	+	462.651i	0.190040	+	0.0691689i
$356$		0			0
$357$	−2316.32	−	1443.84i	−0.343397	−	0.214051i
$358$		0			0
$359$	2668.13	−	4621.33i	0.392251	−	0.679399i	−0.600495	−	0.799629i	$-0.705030\pi$
$359$	2668.13	−	4621.33i	0.392251	−	0.679399i	0.992746	+	0.120229i	$0.0383630\pi$
$360$		0			0
$361$	3049.26	+	5281.47i	0.444563	+	0.770006i
$362$		0			0
$363$	3556.23	+	10903.9i	0.514198	+	1.57660i
$364$		0			0
$365$	−936.693	−	5312.25i	−0.134325	−	0.761797i
$366$		0			0
$367$	1992.63	+	1672.02i	0.283418	+	0.237816i	0.773403	−	0.633915i	$-0.218553\pi$
$367$	1992.63	+	1672.02i	0.283418	+	0.237816i	−0.489984	+	0.871731i	$0.662998\pi$
$368$		0			0
$369$	2628.71	+	5359.52i	0.370854	+	0.756113i
$370$		0			0
$371$	−860.130	+	313.062i	−0.120366	+	0.0438096i
$372$		0			0
$373$	4976.72	−	4175.97i	0.690844	−	0.579687i	−0.228308	−	0.973589i	$-0.573319\pi$
$373$	4976.72	−	4175.97i	0.690844	−	0.579687i	0.919153	+	0.393902i	$0.128875\pi$
$374$		0			0
$375$	−4426.08	−	5652.23i	−0.609499	−	0.778346i
$376$		0			0
$377$	2580.37			0.352508
$378$		0			0
$379$	5410.32			0.733271			0.366635	−	0.930365i	$-0.380510\pi$
$379$	5410.32			0.733271			0.366635	+	0.930365i	$0.380510\pi$
$380$		0			0
$381$	−326.418	+	810.494i	−0.0438922	+	0.108984i
$382$		0			0
$383$	−6463.74	+	5423.72i	−0.862354	+	0.723601i	−0.962474	−	0.271374i	$-0.912522\pi$
$383$	−6463.74	+	5423.72i	−0.862354	+	0.723601i	0.100120	+	0.994975i	$0.468077\pi$
$384$		0			0
$385$	−6769.57	+	2463.92i	−0.896128	+	0.326164i
$386$		0			0
$387$	−13381.1	−	5922.20i	−1.75762	−	0.777887i
$388$		0			0
$389$	8970.57	+	7527.21i	1.16922	+	0.981091i	0.999990	−	0.00448556i	$-0.00142780\pi$
$389$	8970.57	+	7527.21i	1.16922	+	0.981091i	0.169229	+	0.985577i	$0.445872\pi$
$390$		0			0
$391$	5.12924	+	29.0894i	0.000663419	+	0.00376244i
$392$		0			0
$393$	10196.0	+	2155.43i	1.30870	+	0.276659i
$394$		0			0
$395$	4424.78	+	7663.95i	0.563633	+	0.976241i
$396$		0			0
$397$	6759.21	−	11707.3i	0.854496	−	1.48003i	−0.0226159	−	0.999744i	$-0.507199\pi$
$397$	6759.21	−	11707.3i	0.854496	−	1.48003i	0.877112	−	0.480286i	$-0.159467\pi$
$398$		0			0
$399$	86.6970	−	2564.01i	0.0108779	−	0.321707i
$400$		0			0
$401$	6064.01	+	2207.12i	0.755168	+	0.274859i	0.690779	−	0.723066i	$-0.257268\pi$
$401$	6064.01	+	2207.12i	0.755168	+	0.274859i	0.0643893	+	0.997925i	$0.479490\pi$
$402$		0			0
$403$	−62.2364	+	352.960i	−0.00769284	+	0.0436283i
$404$		0			0
$405$	−1503.10	+	4696.70i	−0.184419	+	0.576249i
$406$		0			0
$407$	3854.82	−	21861.7i	0.469475	−	2.66252i
$408$		0			0
$409$	5073.67	+	1846.66i	0.613390	+	0.223256i	0.629986	−	0.776606i	$-0.283061\pi$
$409$	5073.67	+	1846.66i	0.613390	+	0.223256i	−0.0165958	+	0.999862i	$0.505283\pi$
$410$		0			0
$411$	−162.424	+	4803.61i	−0.0194934	+	0.576507i
$412$		0			0
$413$	−3819.79	+	6616.07i	−0.455108	+	0.788270i
$414$		0			0
$415$	−217.546	−	376.800i	−0.0257323	−	0.0445696i
$416$		0			0
$417$	12929.3	+	2733.26i	1.51835	+	0.320979i
$418$		0			0
$419$	−1598.37	−	9064.78i	−0.186361	−	1.05691i	−0.924194	−	0.381923i	$-0.875262\pi$
$419$	−1598.37	−	9064.78i	−0.186361	−	1.05691i	0.737833	−	0.674983i	$-0.235849\pi$
$420$		0			0
$421$	6648.55	+	5578.80i	0.769669	+	0.645829i	0.940624	−	0.339450i	$-0.110241\pi$
$421$	6648.55	+	5578.80i	0.769669	+	0.645829i	−0.170955	+	0.985279i	$0.554685\pi$
$422$		0			0
$423$	−13345.2	+	9741.06i	−1.53396	+	1.11968i
$424$		0			0
$425$	2184.69	−	795.162i	0.249348	−	0.0907553i
$426$		0			0
$427$	7133.18	−	5985.45i	0.808428	−	0.678351i
$428$		0			0
$429$	3341.67	−	8297.35i	0.376078	−	0.933799i
$430$		0			0
$431$	13477.8			1.50628			0.753138	−	0.657862i	$-0.228539\pi$
$431$	13477.8			1.50628			0.753138	+	0.657862i	$0.228539\pi$
$432$		0			0
$433$	12659.9			1.40507			0.702533	−	0.711651i	$-0.252052\pi$
$433$	12659.9			1.40507			0.702533	+	0.711651i	$0.252052\pi$
$434$		0			0
$435$	−1932.21	−	2467.48i	−0.212971	−	0.271970i
$436$		0			0
$437$	−21.2680	+	17.8460i	−0.00232811	+	0.00195352i
$438$		0			0
$439$	−8751.79	+	3185.39i	−0.951480	+	0.346311i	−0.770689	−	0.637211i	$-0.780088\pi$
$439$	−8751.79	+	3185.39i	−0.951480	+	0.346311i	−0.180791	+	0.983522i	$0.557866\pi$
$440$		0			0
$441$	−337.958	+	503.442i	−0.0364926	+	0.0543616i
$442$		0			0
$443$	−3512.25	−	2947.12i	−0.376686	−	0.316077i	0.434714	−	0.900569i	$-0.356850\pi$
$443$	−3512.25	−	2947.12i	−0.376686	−	0.316077i	−0.811400	+	0.584492i	$0.801294\pi$
$444$		0			0
$445$	1095.58	+	6213.32i	0.116709	+	0.661887i
$446$		0			0
$447$	−3284.44	−	10070.5i	−0.347536	−	1.06559i
$448$		0			0
$449$	530.524	+	918.895i	0.0557616	+	0.0965820i	0.892559	−	0.450931i	$-0.148908\pi$
$449$	530.524	+	918.895i	0.0557616	+	0.0965820i	−0.836797	+	0.547513i	$0.815575\pi$
$450$		0			0
$451$	−6575.61	+	11389.3i	−0.686548	+	1.18914i
$452$		0			0
$453$	3633.37	+	2264.80i	0.376845	+	0.234899i
$454$		0			0
$455$	3293.61	+	1198.77i	0.339355	+	0.123515i
$456$		0			0
$457$	−2136.23	+	12115.2i	−0.218662	+	1.24009i	0.655775	+	0.754956i	$0.272342\pi$
$457$	−2136.23	+	12115.2i	−0.218662	+	1.24009i	−0.874437	+	0.485139i	$0.838769\pi$
$458$		0			0
$459$	−3338.12	−	2408.39i	−0.339455	−	0.244911i
$460$		0			0
$461$	−30.2863	+	171.762i	−0.00305981	+	0.0173531i	−0.986299	−	0.164965i	$-0.947249\pi$
$461$	−30.2863	+	171.762i	−0.00305981	+	0.0173531i	0.983240	+	0.182318i	$0.0583600\pi$
$462$		0			0
$463$	8366.64	+	3045.21i	0.839808	+	0.305665i	0.725878	−	0.687824i	$-0.241434\pi$
$463$	8366.64	+	3045.21i	0.839808	+	0.305665i	0.113930	+	0.993489i	$0.463656\pi$
$464$		0			0
$465$	384.122	−	204.787i	0.0383080	−	0.0204232i
$466$		0			0
$467$	1326.26	−	2297.15i	0.131418	−	0.227622i	−0.792806	−	0.609475i	$-0.791380\pi$
$467$	1326.26	−	2297.15i	0.131418	−	0.227622i	0.924223	+	0.381853i	$0.124714\pi$
$468$		0			0
$469$	1959.64	+	3394.20i	0.192938	+	0.334179i
$470$		0			0
$471$	−3270.77	+	3640.65i	−0.319977	+	0.356162i
$472$		0			0
$473$	−5598.02	−	31748.0i	−0.544181	−	3.08620i
$474$		0			0
$475$	1673.97	+	1404.63i	0.161699	+	0.135681i
$476$		0			0
$477$	−1326.06	+	383.420i	−0.127288	+	0.0368042i
$478$		0			0
$479$	18164.9	−	6611.48i	1.73272	−	0.630660i	0.733905	−	0.679252i	$-0.237696\pi$
$479$	18164.9	−	6611.48i	1.73272	−	0.630660i	0.998819	+	0.0485928i	$0.0154736\pi$
$480$		0			0
$481$	−8273.67	+	6942.43i	−0.784297	+	0.658103i
$482$		0			0
$483$	−92.7337	+	13.1375i	−0.00873609	+	0.00123764i
$484$		0			0
$485$	−8084.29			−0.756884
$486$		0			0
$487$	6386.49			0.594249			0.297125	−	0.954839i	$-0.403972\pi$
$487$	6386.49			0.594249			0.297125	+	0.954839i	$0.403972\pi$
$488$		0			0
$489$	−17469.8	+	2474.93i	−1.61556	+	0.228876i
$490$		0			0
$491$	−13082.9	+	10977.9i	−1.20249	+	1.00901i	−0.202936	+	0.979192i	$0.565048\pi$
$491$	−13082.9	+	10977.9i	−1.20249	+	1.00901i	−0.999555	+	0.0298176i	$0.990507\pi$
$492$		0			0
$493$	2458.20	−	894.712i	0.224568	−	0.0817359i
$494$		0			0
$495$	−10436.7	+	3017.67i	−0.947662	+	0.274009i
$496$		0			0
$497$	−2742.58	−	2301.30i	−0.247528	−	0.207701i
$498$		0			0
$499$	−1145.21	−	6494.83i	−0.102739	−	0.582662i	−0.992099	−	0.125455i	$-0.959961\pi$
$499$	−1145.21	−	6494.83i	−0.102739	−	0.582662i	0.889360	−	0.457207i	$-0.151150\pi$
$500$		0			0
$501$	−10056.6	+	11193.8i	−0.896796	+	0.998211i
$502$		0			0
$503$	−3417.70	−	5919.63i	−0.302958	−	0.524738i	0.673847	−	0.738871i	$-0.264641\pi$
$503$	−3417.70	−	5919.63i	−0.302958	−	0.524738i	−0.976805	+	0.214133i	$0.931307\pi$
$504$		0			0
$505$	3362.17	−	5823.45i	0.296267	−	0.513149i
$506$		0			0
$507$	6233.41	−	3323.21i	0.546026	−	0.291103i
$508$		0			0
$509$	−435.292	−	158.433i	−0.0379056	−	0.0137965i	0.322998	−	0.946400i	$-0.395309\pi$
$509$	−435.292	−	158.433i	−0.0379056	−	0.0137965i	−0.360903	+	0.932603i	$0.617532\pi$
$510$		0			0
$511$	−2479.14	+	14059.9i	−0.214620	+	1.21717i
$512$		0			0
$513$	391.638	−	3849.05i	0.0337061	−	0.331266i
$514$		0			0
$515$	386.650	−	2192.80i	0.0330831	−	0.187624i
$516$		0			0
$517$	−34204.5	−	12449.4i	−2.90970	−	1.05904i
$518$		0			0
$519$	−9181.99	−	5723.43i	−0.776579	−	0.484067i
$520$		0			0
$521$	−5085.58	+	8808.49i	−0.427646	+	0.740704i	−0.996663	−	0.0816212i	$-0.973990\pi$
$521$	−5085.58	+	8808.49i	−0.427646	+	0.740704i	0.569018	+	0.822325i	$0.307324\pi$
$522$		0			0
$523$	4957.61	+	8586.84i	0.414496	+	0.717928i	0.995375	−	0.0960616i	$-0.0306246\pi$
$523$	4957.61	+	8586.84i	0.414496	+	0.717928i	−0.580879	+	0.813990i	$0.697291\pi$
$524$		0			0
$525$	2285.77	+	7008.48i	0.190017	+	0.582619i
$526$		0			0
$527$	63.0949	+	357.829i	0.00521529	+	0.0295774i
$528$		0			0
$529$	−9319.69	−	7820.15i	−0.765981	−	0.642734i
$530$		0			0
$531$	−6421.32	+	9565.59i	−0.524786	+	0.781754i
$532$		0			0
$533$	6012.60	−	2188.41i	0.488620	−	0.177843i
$534$		0			0
$535$	1665.11	−	1397.19i	0.134559	−	0.112908i
$536$		0			0
$537$	−13961.6	−	17829.4i	−1.12195	−	1.43277i
$538$		0			0
$539$	−1335.85			−0.106752
$540$		0			0
$541$	12272.1			0.975264			0.487632	−	0.873049i	$-0.337861\pi$
$541$	12272.1			0.975264			0.487632	+	0.873049i	$0.337861\pi$
$542$		0			0
$543$	−5230.39	+	12987.0i	−0.413365	+	1.02638i
$544$		0			0
$545$	−1967.59	+	1651.00i	−0.154646	+	0.129764i
$546$		0			0
$547$	17044.4	−	6203.64i	1.33229	−	0.484915i	0.424915	−	0.905233i	$-0.360304\pi$
$547$	17044.4	−	6203.64i	1.33229	−	0.484915i	0.907377	+	0.420318i	$0.138082\pi$
$548$		0			0
$549$	11342.5	−	8279.20i	0.881758	−	0.643621i
$550$		0			0
$551$	1883.54	+	1580.48i	0.145629	+	0.122197i
$552$		0			0
$553$	−4067.21	−	23066.3i	−0.312758	−	1.77374i
$554$		0			0
$555$	12834.1	+	2713.14i	0.981583	+	0.207507i
$556$		0			0
$557$	1502.66	+	2602.69i	0.114309	+	0.197988i	0.917503	−	0.397729i	$-0.130201\pi$
$557$	1502.66	+	2602.69i	0.114309	+	0.197988i	−0.803195	+	0.595717i	$0.796868\pi$
$558$		0			0
$559$	−7842.33	+	13583.3i	−0.593373	+	1.02775i
$560$		0			0
$561$	306.454	−	9063.21i	0.0230633	−	0.682084i
$562$		0			0
$563$	2205.13	+	802.602i	0.165071	+	0.0600811i	0.423234	−	0.906020i	$-0.360895\pi$
$563$	2205.13	+	802.602i	0.165071	+	0.0600811i	−0.258163	+	0.966101i	$0.583117\pi$
$564$		0			0
$565$	−2244.71	+	12730.4i	−0.167143	+	0.947913i
$566$		0			0
$567$	7989.89	−	10320.4i	0.591788	−	0.764403i
$568$		0			0
$569$	−3585.08	+	20332.0i	−0.264138	+	1.49800i	0.507341	+	0.861745i	$0.330628\pi$
$569$	−3585.08	+	20332.0i	−0.264138	+	1.49800i	−0.771479	+	0.636255i	$0.780483\pi$
$570$		0			0
$571$	10022.8	+	3648.01i	0.734575	+	0.267363i	0.682100	−	0.731259i	$-0.261067\pi$
$571$	10022.8	+	3648.01i	0.734575	+	0.267363i	0.0524748	+	0.998622i	$0.483289\pi$
$572$		0			0
$573$	−529.742	+	15666.8i	−0.0386218	+	1.14222i
$574$		0			0
$575$	39.8885	−	69.0889i	0.00289298	−	0.00501079i
$576$		0			0
$577$	−5276.40	−	9138.99i	−0.380692	−	0.659378i	0.610469	−	0.792040i	$-0.290981\pi$
$577$	−5276.40	−	9138.99i	−0.380692	−	0.659378i	−0.991161	+	0.132662i	$0.957648\pi$
$578$		0			0
$579$	7511.16	+	1587.86i	0.539125	+	0.113971i
$580$		0			0
$581$	199.965	+	1134.06i	0.0142787	+	0.0809788i
$582$		0			0
$583$	−2329.61	−	1954.78i	−0.165493	−	0.138865i
$584$		0			0
$585$	4833.52	+	2139.22i	0.341609	+	0.151189i
$586$		0			0
$587$	−5519.40	+	2008.90i	−0.388092	+	0.141254i	−0.528695	−	0.848812i	$-0.677318\pi$
$587$	−5519.40	+	2008.90i	−0.388092	+	0.141254i	0.140602	+	0.990066i	$0.455096\pi$
$588$		0			0
$589$	−261.618	+	219.524i	−0.0183018	+	0.0153571i
$590$		0			0
$591$	7335.31	−	18213.5i	0.510549	−	1.26769i
$592$		0			0
$593$	−10619.0			−0.735360			−0.367680	−	0.929952i	$-0.619848\pi$
$593$	−10619.0			−0.735360			−0.367680	+	0.929952i	$0.619848\pi$
$594$		0			0
$595$	3553.33			0.244828
$596$		0			0
$597$	1029.29	+	1314.44i	0.0705632	+	0.0901111i
$598$		0			0
$599$	−291.282	+	244.414i	−0.0198689	+	0.0166719i	−0.652668	−	0.757644i	$-0.726350\pi$
$599$	−291.282	+	244.414i	−0.0198689	+	0.0166719i	0.632799	+	0.774316i	$0.281906\pi$
$600$		0			0
$601$	−2760.03	+	1004.57i	−0.187327	+	0.0681816i	−0.433981	−	0.900922i	$-0.642891\pi$
$601$	−2760.03	+	1004.57i	−0.187327	+	0.0681816i	0.246653	+	0.969104i	$0.420669\pi$
$602$		0			0
$603$	2602.77	+	5306.63i	0.175776	+	0.358379i
$604$		0			0
$605$	−11437.8	−	9597.45i	−0.768616	−	0.644945i
$606$		0			0
$607$	4004.42	+	22710.2i	0.267766	+	1.51858i	0.761040	+	0.648705i	$0.224689\pi$
$607$	4004.42	+	22710.2i	0.267766	+	1.51858i	−0.493274	+	0.869874i	$0.664200\pi$
$608$		0			0
$609$	2571.94	+	7885.91i	0.171133	+	0.524718i
$610$		0			0
$611$	8854.79	+	15336.9i	0.586295	+	1.01549i
$612$		0			0
$613$	7919.71	−	13717.3i	0.521818	−	0.903814i	−0.477860	−	0.878436i	$-0.658588\pi$
$613$	7919.71	−	13717.3i	0.521818	−	0.903814i	0.999678	−	0.0253787i	$-0.00807915\pi$
$614$		0			0
$615$	−6594.98	−	4110.86i	−0.432415	−	0.269538i
$616$		0			0
$617$	7369.88	+	2682.42i	0.480875	+	0.175024i	0.571072	−	0.820900i	$-0.306528\pi$
$617$	7369.88	+	2682.42i	0.480875	+	0.175024i	−0.0901973	+	0.995924i	$0.528750\pi$
$618$		0			0
$619$	3859.29	−	21887.1i	0.250594	−	1.42119i	−0.556539	−	0.830821i	$-0.687871\pi$
$619$	3859.29	−	21887.1i	0.250594	−	1.42119i	0.807133	−	0.590369i	$-0.201018\pi$
$620$		0			0
$621$	−140.868	+	10.3204i	−0.00910278	+	0.000666899i
$622$		0			0
$623$	2899.66	−	16444.8i	0.186472	−	1.05754i
$624$		0			0
$625$	−525.504	−	191.268i	−0.0336323	−	0.0122411i
$626$		0			0
$627$	7521.40	−	4009.88i	0.479068	−	0.255405i
$628$		0			0
$629$	−5474.75	+	9482.54i	−0.347047	+	0.601103i
$630$		0			0
$631$	−2964.46	−	5134.59i	−0.187026	−	0.323938i	0.757232	−	0.653146i	$-0.226551\pi$
$631$	−2964.46	−	5134.59i	−0.187026	−	0.323938i	−0.944257	+	0.329209i	$0.893218\pi$
$632$		0			0
$633$	4414.33	−	4913.54i	0.277179	−	0.308524i
$634$		0			0
$635$	−197.523	−	1120.21i	−0.0123440	−	0.0700065i
$636$		0			0
$637$	497.879	+	417.770i	0.0309681	+	0.0259853i
$638$		0			0
$639$	−3892.13	−	3741.97i	−0.240955	−	0.231659i
$640$		0			0
$641$	3853.21	−	1402.45i	0.237430	−	0.0864175i	−0.220565	−	0.975372i	$-0.570790\pi$
$641$	3853.21	−	1402.45i	0.237430	−	0.0864175i	0.457995	+	0.888955i	$0.348568\pi$
$642$		0			0
$643$	237.689	−	199.444i	0.0145778	−	0.0122322i	−0.635470	−	0.772126i	$-0.719193\pi$
$643$	237.689	−	199.444i	0.0145778	−	0.0122322i	0.650047	+	0.759894i	$0.274749\pi$
$644$		0			0
$645$	18861.5	−	2672.10i	1.15143	−	0.163122i
$646$		0			0
$647$	17190.2			1.04454			0.522268	−	0.852781i	$-0.325086\pi$
$647$	17190.2			1.04454			0.522268	+	0.852781i	$0.325086\pi$
$648$		0			0
$649$	−25381.7			−1.53516
$650$		0			0
$651$	−1140.72	+	161.605i	−0.0686764	+	0.00972934i
$652$		0			0
$653$	−5085.19	+	4266.98i	−0.304746	+	0.255712i	−0.782316	−	0.622881i	$-0.785962\pi$
$653$	−5085.19	+	4266.98i	−0.304746	+	0.255712i	0.477571	+	0.878593i	$0.341518\pi$
$654$		0			0
$655$	−12748.7	+	4640.13i	−0.760506	+	0.276802i
$656$		0			0
$657$	−5162.43	+	20902.3i	−0.306554	+	1.24121i
$658$		0			0
$659$	−1245.58	−	1045.16i	−0.0736279	−	0.0617812i	0.605231	−	0.796050i	$-0.293081\pi$
$659$	−1245.58	−	1045.16i	−0.0736279	−	0.0617812i	−0.678859	+	0.734269i	$0.737525\pi$
$660$		0			0
$661$	−1371.31	−	7777.07i	−0.0806924	−	0.457629i	−0.998203	−	0.0599185i	$-0.980916\pi$
$661$	−1371.31	−	7777.07i	−0.0806924	−	0.457629i	0.917511	−	0.397711i	$-0.130195\pi$
$662$		0			0
$663$	−2948.61	+	3282.06i	−0.172722	+	0.192254i
$664$		0			0
$665$	1669.92	+	2892.39i	0.0973785	+	0.168665i
$666$		0			0
$667$	44.8823	−	77.7385i	0.00260547	−	0.00451281i
$668$		0			0
$669$	22924.0	−	12221.5i	1.32481	−	0.706293i
$670$		0			0
$671$	29071.4	+	10581.1i	1.67256	+	0.608763i
$672$		0			0
$673$	2739.40	−	15535.9i	0.156904	−	0.889846i	−0.800121	−	0.599839i	$-0.795231\pi$
$673$	2739.40	−	15535.9i	0.156904	−	0.889846i	0.957025	−	0.290007i	$-0.0936576\pi$
$674$		0			0
$675$	2725.28	+	10778.0i	0.155402	+	0.614584i
$676$		0			0
$677$	−5133.84	+	29115.5i	−0.291447	+	1.65288i	0.389856	+	0.920876i	$0.372525\pi$
$677$	−5133.84	+	29115.5i	−0.291447	+	1.65288i	−0.681303	+	0.732002i	$0.738586\pi$
$678$		0			0
$679$	20106.3	+	7318.09i	1.13639	+	0.413612i
$680$		0			0
$681$	−5225.48	−	3257.21i	−0.294039	−	0.183284i
$682$		0			0
$683$	12777.3	−	22131.0i	0.715829	−	1.23985i	−0.246810	−	0.969064i	$-0.579382\pi$
$683$	12777.3	−	22131.0i	0.715829	−	1.23985i	0.962639	−	0.270788i	$-0.0872843\pi$
$684$		0			0
$685$	−3128.55	−	5418.80i	−0.174505	−	0.302251i
$686$		0			0
$687$	2978.71	+	9133.12i	0.165422	+	0.507205i
$688$		0			0
$689$	256.927	+	1457.11i	0.0142063	+	0.0805680i
$690$		0			0
$691$	−16424.3	−	13781.6i	−0.904212	−	0.758724i	0.0667969	−	0.997767i	$-0.478722\pi$
$691$	−16424.3	−	13781.6i	−0.904212	−	0.758724i	−0.971009	+	0.239042i	$0.923166\pi$
$692$		0			0
$693$	28688.4	+	1942.31i	1.57256	+	0.106468i
$694$		0			0
$695$	−16166.3	+	5884.06i	−0.882336	+	0.321144i
$696$		0			0
$697$	4969.13	−	4169.60i	0.270042	−	0.226592i
$698$		0			0
$699$	10157.7	+	12971.7i	0.549644	+	0.701910i
$700$		0			0
$701$	−11587.1			−0.624308			−0.312154	−	0.950031i	$-0.601051\pi$
$701$	−11587.1			−0.624308			−0.312154	+	0.950031i	$0.601051\pi$
$702$		0			0
$703$	−10291.6			−0.552142
$704$		0			0
$705$	8035.43	−	19951.9i	0.429265	−	1.06586i
$706$		0			0
$707$	−13633.5	+	11439.9i	−0.725235	+	0.608544i
$708$		0			0
$709$	8347.62	−	3038.29i	0.442174	−	0.160938i	−0.111332	−	0.993783i	$-0.535512\pi$
$709$	8347.62	−	3038.29i	0.442174	−	0.160938i	0.553506	+	0.832845i	$0.313289\pi$
$710$		0			0
$711$	−3769.90	−	35120.4i	−0.198850	−	1.85249i
$712$		0			0
$713$	9.55107	+	8.01430i	0.000501669	+	0.000420951i
$714$		0			0
$715$	2022.12	+	11468.0i	0.105766	+	0.599831i
$716$		0			0
$717$	30150.3	+	6373.79i	1.57041	+	0.331985i
$718$		0			0
$719$	−4391.89	−	7606.97i	−0.227802	−	0.394565i	0.729354	−	0.684136i	$-0.239821\pi$
$719$	−4391.89	−	7606.97i	−0.227802	−	0.394565i	−0.957156	+	0.289571i	$0.906487\pi$
$720$		0			0
$721$	−2946.60	+	5103.66i	−0.152201	+	0.263620i
$722$		0			0
$723$	−523.261	+	15475.1i	−0.0269160	+	0.796026i
$724$		0			0
$725$	−6639.15	−	2416.45i	−0.340099	−	0.123786i
$726$		0			0
$727$	2189.91	−	12419.6i	0.111718	−	0.633587i	−0.876604	−	0.481212i	$-0.840197\pi$
$727$	2189.91	−	12419.6i	0.111718	−	0.633587i	0.988323	−	0.152375i	$-0.0486921\pi$
$728$		0			0
$729$	13073.1	−	14714.4i	0.664182	−	0.747571i
$730$		0			0
$731$	−2761.19	+	15659.5i	−0.139707	+	0.792320i
$732$		0			0
$733$	5389.52	+	1961.62i	0.271578	+	0.0988462i	0.474219	−	0.880407i	$-0.342730\pi$
$733$	5389.52	+	1961.62i	0.271578	+	0.0988462i	−0.202642	+	0.979253i	$0.564953\pi$
$734$		0			0
$735$	26.6760	−	788.929i	0.00133872	−	0.0395919i
$736$		0			0
$737$	−6510.71	+	11276.9i	−0.325407	+	0.563622i
$738$		0			0
$739$	−6949.01	−	12036.0i	−0.345904	−	0.599124i	0.639613	−	0.768697i	$-0.279095\pi$
$739$	−6949.01	−	12036.0i	−0.345904	−	0.599124i	−0.985518	+	0.169573i	$0.945761\pi$
$740$		0			0
$741$	−4057.29	−	857.713i	−0.201145	−	0.0425221i
$742$		0			0
$743$	2458.80	+	13944.6i	0.121406	+	0.688528i	0.983378	+	0.181572i	$0.0581184\pi$
$743$	2458.80	+	13944.6i	0.121406	+	0.688528i	−0.861972	+	0.506956i	$0.830770\pi$
$744$		0			0
$745$	10563.6	+	8863.95i	0.519492	+	0.435906i
$746$		0			0
$747$	185.348	+	1726.70i	0.00907835	+	0.0845739i
$748$		0			0
$749$	−5406.04	+	1967.64i	−0.263728	+	0.0959892i
$750$		0			0
$751$	−8216.97	+	6894.86i	−0.399256	+	0.335016i	−0.820206	−	0.572068i	$-0.806141\pi$
$751$	−8216.97	+	6894.86i	−0.399256	+	0.335016i	0.420950	+	0.907084i	$0.361697\pi$
$752$		0			0
$753$	−13418.6	+	33318.3i	−0.649404	+	1.61247i
$754$		0			0
$755$	−5573.74			−0.268674
$756$		0			0
$757$	−12941.7			−0.621366			−0.310683	−	0.950514i	$-0.600558\pi$
$757$	−12941.7			−0.621366			−0.310683	+	0.950514i	$0.600558\pi$
$758$		0			0
$759$	−191.849	−	244.997i	−0.00917482	−	0.0117165i
$760$		0			0
$761$	−16885.2	+	14168.4i	−0.804323	+	0.674907i	−0.949245	−	0.314536i	$-0.898151\pi$
$761$	−16885.2	+	14168.4i	−0.804323	+	0.674907i	0.144923	+	0.989443i	$0.453707\pi$
$762$		0			0
$763$	6388.07	−	2325.07i	0.303098	−	0.110319i
$764$		0			0
$765$	5346.43	+	361.972i	0.252681	+	0.0171073i
$766$		0			0
$767$	9459.87	+	7937.77i	0.445340	+	0.373685i
$768$		0			0
$769$	−2620.50	−	14861.6i	−0.122884	−	0.696908i	−0.982542	−	0.186039i	$-0.940435\pi$
$769$	−2620.50	−	14861.6i	−0.122884	−	0.696908i	0.859659	−	0.510869i	$-0.170676\pi$
$770$		0			0
$771$	−8185.88	−	25099.0i	−0.382370	−	1.17240i
$772$		0			0
$773$	−16889.2	−	29253.0i	−0.785852	−	1.36113i	−0.928489	−	0.371360i	$-0.878892\pi$
$773$	−16889.2	−	29253.0i	−0.785852	−	1.36113i	0.142637	−	0.989775i	$-0.454442\pi$
$774$		0			0
$775$	490.669	−	849.864i	0.0227424	−	0.0393910i
$776$		0			0
$777$	−29463.5	−	18365.6i	−1.36036	−	0.847954i
$778$		0			0
$779$	5729.31	+	2085.30i	0.263509	+	0.0959095i
$780$		0			0
$781$	2065.51	−	11714.1i	0.0946347	−	0.536700i
$782$		0			0
$783$	3066.48	+	12127.3i	0.139958	+	0.553506i
$784$		0			0
$785$	1106.37	−	6274.53i	0.0503032	−	0.285284i
$786$		0			0
$787$	−25567.2	−	9305.71i	−1.15803	−	0.421490i	−0.309640	−	0.950854i	$-0.600208\pi$
$787$	−25567.2	−	9305.71i	−1.15803	−	0.421490i	−0.848395	+	0.529364i	$0.822431\pi$
$788$		0			0
$789$	−35117.6	+	18722.2i	−1.58456	+	0.844777i
$790$		0			0
$791$	17106.6	−	29629.5i	0.768952	−	1.33186i
$792$		0			0
$793$	−7525.94	−	13035.3i	−0.337016	−	0.583729i
$794$		0			0
$795$	1200.97	−	1336.79i	0.0535775	−	0.0596364i
$796$		0			0
$797$	2911.06	+	16509.5i	0.129379	+	0.733746i	0.978610	+	0.205724i	$0.0659549\pi$
$797$	2911.06	+	16509.5i	0.129379	+	0.733746i	−0.849231	+	0.528022i	$0.822934\pi$
$798$		0			0
$799$	13753.5	+	11540.5i	0.608965	+	0.510982i
$800$		0			0
$801$	6038.09	−	24447.8i	0.266349	−	1.07843i
$802$		0			0
$803$	−44572.6	+	16223.1i	−1.95882	+	0.712952i
$804$		0			0
$805$	93.4036	−	78.3749i	0.00408950	−	0.00343150i
$806$		0			0
$807$	−35419.0	+	5017.79i	−1.54499	+	0.218878i
$808$		0			0
$809$	8398.15			0.364973			0.182487	−	0.983208i	$-0.441585\pi$
$809$	8398.15			0.364973			0.182487	+	0.983208i	$0.441585\pi$
$810$		0			0
$811$	−38336.5			−1.65990			−0.829949	−	0.557839i	$-0.811631\pi$
$811$	−38336.5			−1.65990			−0.829949	+	0.557839i	$0.811631\pi$
$812$		0			0
$813$	−16630.8	+	2356.07i	−0.717425	+	0.101637i
$814$		0			0
$815$	17596.0	−	14764.8i	0.756269	−	0.634585i
$816$		0			0
$817$	−14044.3	+	5111.72i	−0.601406	+	0.218894i
$818$		0			0
$819$	−10084.9	−	9695.82i	−0.430274	−	0.413674i
$820$		0			0
$821$	21752.9	+	18252.8i	0.924703	+	0.775918i	0.974859	−	0.222824i	$-0.0715274\pi$
$821$	21752.9	+	18252.8i	0.924703	+	0.775918i	−0.0501561	+	0.998741i	$0.515972\pi$
$822$		0			0
$823$	4570.67	+	25921.6i	0.193589	+	1.09790i	0.914414	+	0.404780i	$0.132652\pi$
$823$	4570.67	+	25921.6i	0.193589	+	1.09790i	−0.720825	+	0.693117i	$0.756237\pi$
$824$		0			0
$825$	−16368.2	+	18219.3i	−0.690750	+	0.768864i
$826$		0			0
$827$	−8653.68	−	14988.6i	−0.363867	−	0.630236i	0.624727	−	0.780843i	$-0.285210\pi$
$827$	−8653.68	−	14988.6i	−0.363867	−	0.630236i	−0.988594	+	0.150608i	$0.951877\pi$
$828$		0			0
$829$	−3848.42	+	6665.66i	−0.161232	+	0.279262i	−0.935311	−	0.353827i	$-0.884880\pi$
$829$	−3848.42	+	6665.66i	−0.161232	+	0.279262i	0.774079	+	0.633089i	$0.218213\pi$
$830$		0			0
$831$	−14500.9	+	7730.86i	−0.605332	+	0.322720i
$832$		0			0
$833$	619.164	+	225.357i	0.0257536	+	0.00937354i
$834$		0			0
$835$	3401.74	−	19292.2i	0.140984	−	0.799562i
$836$		0			0
$837$	−1732.82	+	126.952i	−0.0715591	+	0.00524265i
$838$		0			0
$839$	2024.34	−	11480.6i	0.0832992	−	0.472413i	−0.914411	−	0.404786i	$-0.867346\pi$
$839$	2024.34	−	11480.6i	0.0832992	−	0.472413i	0.997711	−	0.0676272i	$-0.0215429\pi$
$840$		0			0
$841$	15447.8	+	5622.55i	0.633393	+	0.230536i
$842$		0			0
$843$	18716.5	+	11666.6i	0.764686	+	0.476653i
$844$		0			0
$845$	−4598.05	+	7964.05i	−0.187192	+	0.324227i
$846$		0			0
$847$	19758.9	+	34223.4i	0.801562	+	1.38835i
$848$		0			0
$849$	−8609.88	−	26399.1i	−0.348045	−	1.06715i
$850$		0			0
$851$	65.2437	+	370.015i	0.00262811	+	0.0149048i
$852$		0			0
$853$	16135.3	+	13539.1i	0.647668	+	0.543458i	0.906362	−	0.422501i	$-0.138848\pi$
$853$	16135.3	+	13539.1i	0.647668	+	0.543458i	−0.258694	+	0.965959i	$0.583292\pi$
$854$		0			0
$855$	2217.96	+	4522.06i	0.0887165	+	0.180879i
$856$		0			0
$857$	10298.8	−	3748.45i	0.410501	−	0.149410i	−0.128511	−	0.991708i	$-0.541020\pi$
$857$	10298.8	−	3748.45i	0.410501	−	0.149410i	0.539012	+	0.842298i	$0.318798\pi$
$858$		0			0
$859$	−5778.78	+	4848.97i	−0.229534	+	0.192602i	−0.750300	−	0.661098i	$-0.770091\pi$
$859$	−5778.78	+	4848.97i	−0.229534	+	0.192602i	0.520766	+	0.853699i	$0.325646\pi$
$860$		0			0
$861$	12681.0	+	16194.0i	0.501936	+	0.640986i
$862$		0			0
$863$	−26268.2			−1.03613			−0.518065	−	0.855341i	$-0.673348\pi$
$863$	−26268.2			−1.03613			−0.518065	+	0.855341i	$0.673348\pi$
$864$		0			0
$865$	14085.5			0.553668
$866$		0			0
$867$	7866.03	−	19531.3i	0.308125	−	0.765072i
$868$		0			0
$869$	59611.6	−	50020.1i	2.32703	−	1.95261i
$870$		0			0
$871$	5953.26	−	2166.81i	0.231594	−	0.0842934i
$872$		0			0
$873$	29506.9	+	13059.2i	1.14394	+	0.506284i
$874$		0			0
$875$	−18948.6	−	15899.8i	−0.732093	−	0.614299i
$876$		0			0
$877$	8371.42	+	47476.7i	0.322329	+	1.82802i	0.527814	+	0.849360i	$0.323012\pi$
$877$	8371.42	+	47476.7i	0.322329	+	1.82802i	−0.205485	+	0.978660i	$0.565877\pi$
$878$		0			0
$879$	11541.8	+	2439.93i	0.442883	+	0.0936257i
$880$		0			0
$881$	−8868.20	−	15360.2i	−0.339134	−	0.587398i	0.645136	−	0.764068i	$-0.276801\pi$
$881$	−8868.20	−	15360.2i	−0.339134	−	0.587398i	−0.984270	+	0.176670i	$0.943467\pi$
$882$		0			0
$883$	17748.2	−	30740.7i	0.676413	−	1.17158i	−0.299640	−	0.954052i	$-0.596867\pi$
$883$	17748.2	−	30740.7i	0.676413	−	1.17158i	0.976054	−	0.217530i	$-0.0698000\pi$
$884$		0			0
$885$	506.854	−	14989.9i	0.0192517	−	0.569357i
$886$		0			0
$887$	−2797.75	−	1018.30i	−0.105907	−	0.0385469i	0.288523	−	0.957473i	$-0.406836\pi$
$887$	−2797.75	−	1018.30i	−0.105907	−	0.0385469i	−0.394430	+	0.918926i	$0.629058\pi$
$888$		0			0
$889$	−522.783	+	2964.85i	−0.0197228	+	0.111854i
$890$		0			0
$891$	42967.5	+	5844.88i	1.61556	+	0.219765i
$892$		0			0
$893$	−2930.34	+	16618.8i	−0.109810	+	0.622762i
$894$		0			0
$895$	27702.8	+	10083.0i	1.03464	+	0.376578i
$896$		0			0
$897$	−5.11623	+	151.310i	−0.000190441	+	0.00563219i
$898$		0			0
$899$	552.099	−	956.264i	0.0204822	−	0.0354763i
$900$		0			0
$901$	749.998	+	1299.03i	0.0277315	+	0.0480323i
$902$		0			0
$903$	−49328.9	−	10428.2i	−1.81790	−	0.384305i
$904$		0			0
$905$	−3165.02	−	17949.7i	−0.116253	−	0.659303i
$906$		0			0
$907$	−3444.78	−	2890.51i	−0.126110	−	0.105819i	0.577551	−	0.816354i	$-0.304008\pi$
$907$	−3444.78	−	2890.51i	−0.126110	−	0.105819i	−0.703661	+	0.710535i	$0.748453\pi$
$908$		0			0
$909$	−21678.7	+	15823.9i	−0.791019	+	0.577388i
$910$		0			0
$911$	−3923.42	+	1428.01i	−0.142688	+	0.0519342i	−0.412377	−	0.911013i	$-0.635301\pi$
$911$	−3923.42	+	1428.01i	−0.142688	+	0.0519342i	0.269689	+	0.962947i	$0.413079\pi$
$912$		0			0
$913$	−2930.82	+	2459.25i	−0.106239	+	0.0891449i
$914$		0			0
$915$	−6829.54	+	16957.7i	−0.246751	+	0.612682i
$916$		0			0
$917$	35907.3			1.29309
$918$		0			0
$919$	−25666.6			−0.921287			−0.460643	−	0.887585i	$-0.652381\pi$
$919$	−25666.6			−0.921287			−0.460643	+	0.887585i	$0.652381\pi$
$920$		0			0
$921$	−2078.41	−	2654.18i	−0.0743603	−	0.0949601i
$922$		0			0
$923$	−4433.24	+	3719.93i	−0.158095	+	0.132658i
$924$		0			0
$925$	27789.1	−	10114.4i	0.987785	−	0.359524i
$926$		0			0
$927$	−4953.43	+	7378.93i	−0.175504	+	0.261441i
$928$		0			0
$929$	−20279.1	−	17016.2i	−0.716185	−	0.600950i	0.210142	−	0.977671i	$-0.432607\pi$
$929$	−20279.1	−	17016.2i	−0.716185	−	0.600950i	−0.926327	+	0.376720i	$0.877052\pi$
$930$		0			0
$931$	107.542	+	609.903i	0.00378578	+	0.0214702i
$932$		0			0
$933$	−9186.56	−	28167.3i	−0.322352	−	0.988376i
$934$		0			0
$935$	5902.78	+	10223.9i	0.206462	+	0.357602i
$936$		0			0
$937$	−17460.8	+	30243.1i	−0.608774	+	1.05443i	0.382669	+	0.923885i	$0.375005\pi$
$937$	−17460.8	+	30243.1i	−0.608774	+	1.05443i	−0.991443	+	0.130542i	$0.958328\pi$
$938$		0			0
$939$	21512.9	+	13409.7i	0.747652	+	0.466036i
$940$		0			0
$941$	46488.1	+	16920.3i	1.61049	+	0.586169i	0.981536	−	0.191276i	$-0.0612627\pi$
$941$	46488.1	+	16920.3i	1.61049	+	0.586169i	0.628950	+	0.777446i	$0.283485\pi$
$942$		0			0
$943$	38.6519	−	219.206i	0.00133476	−	0.00756980i
$944$		0			0
$945$	−1719.98	+	16904.0i	−0.0592072	+	0.581893i
$946$		0			0
$947$	4727.28	−	26809.7i	0.162213	−	0.919956i	−0.789678	−	0.613521i	$-0.789753\pi$
$947$	4727.28	−	26809.7i	0.162213	−	0.919956i	0.951891	−	0.306435i	$-0.0991363\pi$
$948$		0			0
$949$	21685.9	+	7893.04i	0.741787	+	0.269988i
$950$		0			0
$951$	32668.6	−	17416.6i	1.11394	−	0.593872i
$952$		0			0
$953$	15252.7	−	26418.4i	0.518450	−	0.897982i	−0.481320	−	0.876545i	$-0.659842\pi$
$953$	15252.7	−	26418.4i	0.518450	−	0.897982i	0.999770	−	0.0214371i	$-0.00682417\pi$
$954$		0			0
$955$	−10203.7	−	17673.3i	−0.345741	−	0.598841i
$956$		0			0
$957$	−18417.4	+	20500.2i	−0.622102	+	0.692454i
$958$		0			0
$959$	2875.72	+	16309.0i	0.0968320	+	0.549161i
$960$		0			0
$961$	−22703.7	−	19050.7i	−0.762101	−	0.639478i
$962$		0			0
$963$	−8334.50	+	2409.85i	−0.278894	+	0.0806400i
$964$		0			0
$965$	−9391.68	+	3418.29i	−0.313294	+	0.114030i
$966$		0			0
$967$	11428.8	−	9589.87i	0.380066	−	0.318914i	−0.432662	−	0.901556i	$-0.642426\pi$
$967$	11428.8	−	9589.87i	0.380066	−	0.318914i	0.812728	+	0.582643i	$0.197981\pi$
$968$		0			0
$969$	−4162.61	+	589.714i	−0.138000	+	0.0195504i
$970$		0			0
$971$	16017.3			0.529373			0.264686	−	0.964335i	$-0.414732\pi$
$971$	16017.3			0.529373			0.264686	+	0.964335i	$0.414732\pi$
$972$		0			0
$973$	45533.3			1.50024
$974$		0			0
$975$	11798.3	−	1671.46i	0.387537	−	0.0549022i
$976$		0			0
$977$	21806.5	−	18297.8i	0.714075	−	0.599180i	−0.211664	−	0.977342i	$-0.567888\pi$
$977$	21806.5	−	18297.8i	0.714075	−	0.599180i	0.925739	+	0.378163i	$0.123444\pi$
$978$		0			0
$979$	52133.1	−	18974.9i	1.70192	−	0.619448i
$980$		0			0
$981$	9848.50	−	2847.61i	0.320528	−	0.0926782i
$982$		0			0
$983$	18350.6	+	15398.0i	0.595417	+	0.499614i	0.889969	−	0.456022i	$-0.150726\pi$
$983$	18350.6	+	15398.0i	0.595417	+	0.499614i	−0.294552	+	0.955635i	$0.595170\pi$
$984$		0			0
$985$	4438.76	+	25173.5i	0.143584	+	0.814307i
$986$		0			0
$987$	−38045.7	+	42348.1i	−1.22696	+	1.36571i
$988$		0			0
$989$	272.816	+	472.530i	0.00877152	+	0.0151927i
$990$		0			0
$991$	−8682.28	+	15038.1i	−0.278306	+	0.482041i	−0.970964	−	0.239226i	$-0.923106\pi$
$991$	−8682.28	+	15038.1i	−0.278306	+	0.482041i	0.692658	+	0.721267i	$0.256440\pi$
$992$		0			0
$993$	−23779.4	+	12677.5i	−0.759935	+	0.405144i
$994$		0			0
$995$	−2042.33	−	743.348i	−0.0650716	−	0.0236841i
$996$		0			0
$997$	−3733.89	+	21175.9i	−0.118609	+	0.672667i	0.866290	+	0.499541i	$0.166498\pi$
$997$	−3733.89	+	21175.9i	−0.118609	+	0.672667i	−0.984900	+	0.173126i	$0.944613\pi$
$998$		0			0
$999$	−42460.7	−	30634.7i	−1.34474	−	0.970208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.i.a.25.8	yes	54
3.2	odd	2		324.4.i.a.73.6		54
27.13	even	9	inner	108.4.i.a.13.8	✓	54
27.14	odd	18		324.4.i.a.253.6		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.i.a.13.8	✓	54	27.13	even	9	inner
108.4.i.a.25.8	yes	54	1.1	even	1	trivial
324.4.i.a.73.6		54	3.2	odd	2
324.4.i.a.253.6		54	27.14	odd	18

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(5.14478 - 0.728858i) q^{3} +(-5.18194 + 4.34817i) q^{5} +(16.8240 - 6.12342i) q^{7} +(25.9375 - 7.49962i) q^{9} +(45.5667 + 38.2350i) q^{11} +(-5.02544 - 28.5007i) q^{13} +(-23.4908 + 26.1473i) q^{15} +(-14.6698 - 25.4089i) q^{17} +(13.7884 - 23.8822i) q^{19} +(82.0925 - 43.7660i) q^{21} +(-0.946050 - 0.344334i) q^{23} +(-13.7600 + 78.0370i) q^{25} +(127.977 - 57.4887i) q^{27} +(-15.4827 + 87.8069i) q^{29} +(-11.6374 - 4.23566i) q^{31} +(262.299 + 163.499i) q^{33} +(-60.5552 + 104.885i) q^{35} +(-186.599 - 323.199i) q^{37} +(-46.6278 - 142.967i) q^{39} +(38.3921 + 217.733i) q^{41} +(-415.169 - 348.368i) q^{43} +(-101.797 + 151.643i) q^{45} +(-575.029 + 209.294i) q^{47} +(-17.2036 + 14.4355i) q^{49} +(-93.9924 - 120.031i) q^{51} -51.1253 q^{53} -402.376 q^{55} +(53.5316 - 132.919i) q^{57} +(-326.874 + 274.280i) q^{59} +(488.734 - 177.884i) q^{61} +(390.449 - 285.000i) q^{63} +(149.967 + 125.838i) q^{65} +(38.0132 + 215.584i) q^{67} +(-5.11819 - 1.08199i) q^{69} +(-99.9846 - 173.178i) q^{71} +(-398.711 + 690.588i) q^{73} +(-13.9145 + 411.513i) q^{75} +(1000.74 + 364.240i) q^{77} +(227.171 - 1288.35i) q^{79} +(616.511 - 389.044i) q^{81} +(-11.1689 + 63.3422i) q^{83} +(186.500 + 67.8805i) q^{85} +(-15.6565 + 463.032i) q^{87} +(466.341 - 807.726i) q^{89} +(-259.070 - 448.722i) q^{91} +(-62.9590 - 13.3096i) q^{93} +(32.3931 + 183.711i) q^{95} +(915.498 + 768.194i) q^{97} +(1468.64 + 649.989i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45}+ \cdots - 5076 q^{99}+O(q^{100}) \) 54 * q + 12 * q^5 - 48 * q^9 - 87 * q^11 + 234 * q^15 + 204 * q^17 - 12 * q^21 + 96 * q^23 - 216 * q^25 + 27 * q^27 + 318 * q^29 - 54 * q^31 + 63 * q^33 + 6 * q^35 + 66 * q^39 + 867 * q^41 - 513 * q^43 - 306 * q^45 - 1548 * q^47 + 594 * q^49 - 1368 * q^51 - 1068 * q^53 - 1269 * q^57 - 1218 * q^59 - 54 * q^61 + 30 * q^63 + 96 * q^65 - 2997 * q^67 + 1476 * q^69 - 120 * q^71 - 216 * q^73 + 732 * q^75 + 3480 * q^77 + 2808 * q^79 + 3348 * q^81 + 4464 * q^83 + 2160 * q^85 + 4824 * q^87 + 4029 * q^89 + 270 * q^91 + 1164 * q^93 - 1650 * q^95 - 3483 * q^97 - 5076 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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