LMFDB - Embedded newform 189.4.o.a.62.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(62,189)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("189.62");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			62.11
Character	$\chi$	$=$	189.62
Dual form			189.4.o.a.125.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0847887 + 0.0489528i) q^{2} +(-3.99521 - 6.91990i) q^{4} +(-9.06347 - 15.6984i) q^{5} +(12.7516 + 13.4312i) q^{7} -1.56555i q^{8} +O(q^{10})$	\(q+(0.0847887 + 0.0489528i) q^{2} +(-3.99521 - 6.91990i) q^{4} +(-9.06347 - 15.6984i) q^{5} +(12.7516 + 13.4312i) q^{7} -1.56555i q^{8} -1.77473i q^{10} +(-32.0537 - 18.5062i) q^{11} +(-16.3673 + 9.44964i) q^{13} +(0.423698 + 1.76304i) q^{14} +(-31.8850 + 55.2265i) q^{16} +62.5187 q^{17} +70.2680i q^{19} +(-72.4209 + 125.437i) q^{20} +(-1.81186 - 3.13823i) q^{22} +(-140.692 + 81.2288i) q^{23} +(-101.793 + 176.311i) q^{25} -1.85034 q^{26} +(41.9972 - 141.900i) q^{28} +(-82.5015 - 47.6323i) q^{29} +(110.611 - 63.8612i) q^{31} +(-16.2534 + 9.38392i) q^{32} +(5.30088 + 3.06046i) q^{34} +(95.2742 - 321.913i) q^{35} -378.832 q^{37} +(-3.43981 + 5.95793i) q^{38} +(-24.5766 + 14.1893i) q^{40} +(-99.1937 - 171.809i) q^{41} +(160.692 - 278.327i) q^{43} +295.744i q^{44} -15.9055 q^{46} +(-79.3885 + 137.505i) q^{47} +(-17.7932 + 342.538i) q^{49} +(-17.2618 + 9.96610i) q^{50} +(130.781 + 75.5066i) q^{52} -191.780i q^{53} +670.922i q^{55} +(21.0272 - 19.9633i) q^{56} +(-4.66346 - 8.07736i) q^{58} +(106.918 + 185.187i) q^{59} +(-190.929 - 110.233i) q^{61} +12.5047 q^{62} +508.323 q^{64} +(296.688 + 171.293i) q^{65} +(68.2947 + 118.290i) q^{67} +(-249.775 - 432.623i) q^{68} +(23.8367 - 22.6306i) q^{70} +458.924i q^{71} -967.869i q^{73} +(-32.1207 - 18.5449i) q^{74} +(486.248 - 280.735i) q^{76} +(-160.176 - 666.503i) q^{77} +(298.318 - 516.702i) q^{79} +1155.96 q^{80} -19.4232i q^{82} +(-180.715 + 313.007i) q^{83} +(-566.636 - 981.443i) q^{85} +(27.2498 - 15.7327i) q^{86} +(-28.9724 + 50.1817i) q^{88} -35.4987 q^{89} +(-335.629 - 99.3336i) q^{91} +(1124.19 + 649.052i) q^{92} +(-13.4625 + 7.77258i) q^{94} +(1103.09 - 636.872i) q^{95} +(-1151.63 - 664.894i) q^{97} +(-18.2769 + 28.1723i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) $ 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7	$ 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7} + 18 q^{11} - 204 q^{14} - 242 q^{16} - 34 q^{22} + 102 q^{23} - 352 q^{25} + 300 q^{28} - 246 q^{29} - 1068 q^{32} + 328 q^{37} - 170 q^{43} + 968 q^{46} - 79 q^{49} - 288 q^{50} - 1212 q^{56} - 538 q^{58} - 808 q^{64} - 4350 q^{65} - 590 q^{67} + 384 q^{70} + 5304 q^{74} + 2787 q^{77} - 302 q^{79} - 612 q^{85} + 13692 q^{86} + 1294 q^{88} + 210 q^{91} + 10194 q^{92} - 6336 q^{95}+O(q^{100}) $ 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7 + 18 * q^11 - 204 * q^14 - 242 * q^16 - 34 * q^22 + 102 * q^23 - 352 * q^25 + 300 * q^28 - 246 * q^29 - 1068 * q^32 + 328 * q^37 - 170 * q^43 + 968 * q^46 - 79 * q^49 - 288 * q^50 - 1212 * q^56 - 538 * q^58 - 808 * q^64 - 4350 * q^65 - 590 * q^67 + 384 * q^70 + 5304 * q^74 + 2787 * q^77 - 302 * q^79 - 612 * q^85 + 13692 * q^86 + 1294 * q^88 + 210 * q^91 + 10194 * q^92 - 6336 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.0847887	+	0.0489528i	0.0299773	+	0.0173074i	0.514914	−	0.857242i	$-0.327824\pi$
$2$	0.0847887	+	0.0489528i	0.0299773	+	0.0173074i	−0.484936	+	0.874549i	$0.661157\pi$
$3$		0			0
$3$		0			0
$4$	−3.99521	−	6.91990i	−0.499401	−	0.864988i
$5$	−9.06347	−	15.6984i	−0.810661	−	1.40411i	−0.912402	−	0.409296i	$-0.865774\pi$
$5$	−9.06347	−	15.6984i	−0.810661	−	1.40411i	0.101740	−	0.994811i	$-0.467559\pi$
$6$		0			0
$7$	12.7516	+	13.4312i	0.688522	+	0.725216i
$7$	12.7516	+	13.4312i	0.688522	+	0.725216i
$8$		−	1.56555i		−	0.0691882i
$9$		0			0
$10$		−	1.77473i		−	0.0561218i
$11$	−32.0537	−	18.5062i	−0.878595	−	0.507257i	−0.00840042	−	0.999965i	$-0.502674\pi$
$11$	−32.0537	−	18.5062i	−0.878595	−	0.507257i	−0.870195	+	0.492707i	$0.836007\pi$
$12$		0			0
$13$	−16.3673	+	9.44964i	−0.349189	+	0.201605i	−0.664328	−	0.747441i	$-0.731282\pi$
$13$	−16.3673	+	9.44964i	−0.349189	+	0.201605i	0.315139	+	0.949046i	$0.397949\pi$
$14$	0.423698	+	1.76304i	0.00808843	+	0.0336566i
$15$		0			0
$16$	−31.8850	+	55.2265i	−0.498203	+	0.862914i
$17$	62.5187			0.891941			0.445971	−	0.895048i	$-0.352859\pi$
$17$	62.5187			0.891941			0.445971	+	0.895048i	$0.352859\pi$
$18$		0			0
$19$			70.2680i			0.848452i	0.905556	+	0.424226i	$0.139454\pi$
$19$			70.2680i			0.848452i	−0.905556	+	0.424226i	$0.860546\pi$
$20$	−72.4209	+	125.437i	−0.809690	+	1.40242i
$21$		0			0
$22$	−1.81186	−	3.13823i	−0.0175586	−	0.0304124i
$23$	−140.692	+	81.2288i	−1.27550	+	0.736408i	−0.976017	−	0.217695i	$-0.930146\pi$
$23$	−140.692	+	81.2288i	−1.27550	+	0.736408i	−0.299479	+	0.954103i	$0.596813\pi$
$24$		0			0
$25$	−101.793	+	176.311i	−0.814344	+	1.41048i
$26$	−1.85034			−0.0139570
$27$		0			0
$28$	41.9972	−	141.900i	0.283454	−	0.957736i
$29$	−82.5015	−	47.6323i	−0.528281	−	0.305003i	0.212035	−	0.977262i	$-0.431991\pi$
$29$	−82.5015	−	47.6323i	−0.528281	−	0.305003i	−0.740316	+	0.672259i	$0.765324\pi$
$30$		0			0
$31$	110.611	−	63.8612i	0.640848	−	0.369994i	−0.144093	−	0.989564i	$-0.546027\pi$
$31$	110.611	−	63.8612i	0.640848	−	0.369994i	0.784941	+	0.619570i	$0.212693\pi$
$32$	−16.2534	+	9.38392i	−0.0897883	+	0.0518393i
$33$		0			0
$34$	5.30088	+	3.06046i	0.0267380	+	0.0154372i
$35$	95.2742	−	321.913i	0.460122	−	1.55466i
$36$		0			0
$37$	−378.832			−1.68323			−0.841617	−	0.540075i	$-0.818396\pi$
$37$	−378.832			−1.68323			−0.841617	+	0.540075i	$0.818396\pi$
$38$	−3.43981	+	5.95793i	−0.0146845	+	0.0254343i
$39$		0			0
$40$	−24.5766	+	14.1893i	−0.0971476	+	0.0560882i
$41$	−99.1937	−	171.809i	−0.377840	−	0.654439i	0.612907	−	0.790155i	$-0.290000\pi$
$41$	−99.1937	−	171.809i	−0.377840	−	0.654439i	−0.990748	+	0.135716i	$0.956667\pi$
$42$		0			0
$43$	160.692	−	278.327i	0.569892	−	0.987081i	−0.426685	−	0.904401i	$-0.640319\pi$
$43$	160.692	−	278.327i	0.569892	−	0.987081i	0.996576	−	0.0826806i	$-0.0263481\pi$
$44$			295.744i			1.01330i
$45$		0			0
$46$	−15.9055			−0.0509813
$47$	−79.3885	+	137.505i	−0.246383	+	0.426748i	−0.962520	−	0.271212i	$-0.912575\pi$
$47$	−79.3885	+	137.505i	−0.246383	+	0.426748i	0.716136	+	0.697960i	$0.245909\pi$
$48$		0			0
$49$	−17.7932	+	342.538i	−0.0518754	+	0.998654i
$50$	−17.2618	+	9.96610i	−0.0488237	+	0.0281884i
$51$		0			0
$52$	130.781	+	75.5066i	0.348771	+	0.201363i
$53$		−	191.780i		−	0.497039i	−0.968627	−	0.248519i	$-0.920056\pi$
$53$		−	191.780i		−	0.497039i	0.968627	−	0.248519i	$-0.0799440\pi$
$54$		0			0
$55$			670.922i			1.64486i
$56$	21.0272	−	19.9633i	0.0501764	−	0.0476376i
$57$		0			0
$58$	−4.66346	−	8.07736i	−0.0105576	−	0.0182864i
$59$	106.918	+	185.187i	0.235924	+	0.408632i	0.959541	−	0.281570i	$-0.0908551\pi$
$59$	106.918	+	185.187i	0.235924	+	0.408632i	−0.723617	+	0.690202i	$0.757522\pi$
$60$		0			0
$61$	−190.929	−	110.233i	−0.400754	−	0.231375i	0.286055	−	0.958213i	$-0.407656\pi$
$61$	−190.929	−	110.233i	−0.400754	−	0.231375i	−0.686809	+	0.726838i	$0.740989\pi$
$62$	12.5047			0.0256145
$63$		0			0
$64$	508.323			0.992818
$65$	296.688	+	171.293i	0.566149	+	0.326866i
$66$		0			0
$67$	68.2947	+	118.290i	0.124530	+	0.215693i	0.921549	−	0.388262i	$-0.126924\pi$
$67$	68.2947	+	118.290i	0.124530	+	0.215693i	−0.797019	+	0.603954i	$0.793591\pi$
$68$	−249.775	−	432.623i	−0.445436	−	0.771518i
$69$		0			0
$70$	23.8367	−	22.6306i	0.0407004	−	0.0386411i
$71$			458.924i			0.767102i	0.923520	+	0.383551i	$0.125299\pi$
$71$			458.924i			0.767102i	−0.923520	+	0.383551i	$0.874701\pi$
$72$		0			0
$73$		−	967.869i		−	1.55179i	−0.630863	−	0.775894i	$-0.717299\pi$
$73$		−	967.869i		−	1.55179i	0.630863	−	0.775894i	$-0.282701\pi$
$74$	−32.1207	−	18.5449i	−0.0504588	−	0.0291324i
$75$		0			0
$76$	486.248	−	280.735i	0.733900	−	0.423718i
$77$	−160.176	−	666.503i	−0.237061	−	0.986429i
$78$		0			0
$79$	298.318	−	516.702i	0.424853	−	0.735868i	−0.571553	−	0.820565i	$-0.693659\pi$
$79$	298.318	−	516.702i	0.424853	−	0.735868i	0.996407	+	0.0846971i	$0.0269923\pi$
$80$	1155.96			1.61550
$81$		0			0
$82$		−	19.4232i		−	0.0261578i
$83$	−180.715	+	313.007i	−0.238988	+	0.413940i	−0.960424	−	0.278541i	$-0.910149\pi$
$83$	−180.715	+	313.007i	−0.238988	+	0.413940i	0.721436	+	0.692481i	$0.243482\pi$
$84$		0			0
$85$	−566.636	−	981.443i	−0.723063	−	1.25238i
$86$	27.2498	−	15.7327i	0.0341676	−	0.0197267i
$87$		0			0
$88$	−28.9724	+	50.1817i	−0.0350962	+	0.0607884i
$89$	−35.4987			−0.0422792			−0.0211396	−	0.999777i	$-0.506729\pi$
$89$	−35.4987			−0.0422792			−0.0211396	+	0.999777i	$0.506729\pi$
$90$		0			0
$91$	−335.629	−	99.3336i	−0.386631	−	0.114428i
$92$	1124.19	+	649.052i	1.27397	+	0.735525i
$93$		0			0
$94$	−13.4625	+	7.77258i	−0.0147718	+	0.00852851i
$95$	1103.09	−	636.872i	1.19132	−	0.687807i
$96$		0			0
$97$	−1151.63	−	664.894i	−1.20547	−	0.695977i	−0.243701	−	0.969850i	$-0.578362\pi$
$97$	−1151.63	−	664.894i	−1.20547	−	0.695977i	−0.961766	+	0.273874i	$0.911695\pi$
$98$	−18.2769	+	28.1723i	−0.0188392	+	0.0290391i
$99$		0			0
$100$	1626.74			1.62674
$101$	−457.491	+	792.398i	−0.450714	+	0.780659i	−0.998430	−	0.0560049i	$-0.982164\pi$
$101$	−457.491	+	792.398i	−0.450714	+	0.780659i	0.547717	+	0.836664i	$0.315497\pi$
$102$		0			0
$103$	−721.873	+	416.774i	−0.690566	+	0.398698i	−0.803824	−	0.594867i	$-0.797205\pi$
$103$	−721.873	+	416.774i	−0.690566	+	0.398698i	0.113258	+	0.993566i	$0.463871\pi$
$104$	14.7939	+	25.6238i	0.0139487	+	0.0241598i
$105$		0			0
$106$	9.38818	−	16.2608i	0.00860246	−	0.0148999i
$107$		−	1686.33i		−	1.52358i	−0.647822	−	0.761792i	$-0.724320\pi$
$107$		−	1686.33i		−	1.52358i	0.647822	−	0.761792i	$-0.275680\pi$
$108$		0			0
$109$	641.258			0.563499			0.281750	−	0.959488i	$-0.409085\pi$
$109$	641.258			0.563499			0.281750	+	0.959488i	$0.409085\pi$
$110$	−32.8435	+	56.8866i	−0.0284682	+	0.0493084i
$111$		0			0
$112$	−1148.34	+	275.973i	−0.968822	+	0.232830i
$113$	−1245.30	+	718.974i	−1.03671	+	0.598543i	−0.918899	−	0.394493i	$-0.870920\pi$
$113$	−1245.30	+	718.974i	−1.03671	+	0.598543i	−0.117809	+	0.993036i	$0.537587\pi$
$114$		0			0
$115$	2550.32	+	1472.43i	2.06799	+	1.19395i
$116$			761.203i			0.609275i
$117$		0			0
$118$			20.9357i			0.0163329i
$119$	797.213	+	839.700i	0.614121	+	0.646850i
$120$		0			0
$121$	19.4592	+	33.7044i	0.0146200	+	0.0253226i
$122$	−10.7924	−	18.6930i	−0.00800902	−	0.0138720i
$123$		0			0
$124$	−883.826	−	510.277i	−0.640080	−	0.369550i
$125$	1424.52			1.01931
$126$		0			0
$127$	−1845.03			−1.28914			−0.644568	−	0.764547i	$-0.722963\pi$
$127$	−1845.03			−1.28914			−0.644568	+	0.764547i	$0.722963\pi$
$128$	173.127	+	99.9552i	0.119550	+	0.0690224i
$129$		0			0
$130$	16.7705	+	29.0474i	0.0113144	+	0.0195971i
$131$	−1099.22	−	1903.91i	−0.733125	−	1.26981i	−0.955541	−	0.294858i	$-0.904728\pi$
$131$	−1099.22	−	1903.91i	−0.733125	−	1.26981i	0.222416	−	0.974952i	$-0.428606\pi$
$132$		0			0
$133$	−943.782	+	896.030i	−0.615311	+	0.584178i
$134$			13.3729i			0.00862119i
$135$		0			0
$136$		−	97.8761i		−	0.0617118i
$137$	−1869.64	−	1079.44i	−1.16594	−	0.673156i	−0.213220	−	0.977004i	$-0.568395\pi$
$137$	−1869.64	−	1079.44i	−1.16594	−	0.673156i	−0.952720	+	0.303848i	$0.901728\pi$
$138$		0			0
$139$	2521.54	−	1455.81i	1.53866	−	0.888348i	0.539746	−	0.841828i	$-0.318520\pi$
$139$	2521.54	−	1455.81i	1.53866	−	0.888348i	0.998917	−	0.0465196i	$-0.0148130\pi$
$140$	−2608.24	+	626.820i	−1.57455	+	0.378400i
$141$		0			0
$142$	−22.4656	+	38.9115i	−0.0132766	+	0.0229957i
$143$	699.508			0.409062
$144$		0			0
$145$			1726.85i			0.989017i
$146$	47.3799	−	82.0644i	0.0268574	−	0.0465185i
$147$		0			0
$148$	1513.51	+	2621.48i	0.840608	+	1.45598i
$149$	230.641	−	133.161i	0.126811	−	0.0732144i	−0.435253	−	0.900308i	$-0.643341\pi$
$149$	230.641	−	133.161i	0.126811	−	0.0732144i	0.562064	+	0.827094i	$0.310008\pi$
$150$		0			0
$151$	467.757	−	810.180i	0.252090	−	0.436632i	−0.712011	−	0.702168i	$-0.752215\pi$
$151$	467.757	−	810.180i	0.252090	−	0.436632i	0.964101	+	0.265536i	$0.0855488\pi$
$152$	110.008			0.0587029
$153$		0			0
$154$	19.0461	−	64.3529i	0.00996607	−	0.0336734i
$155$	−2005.04	−	1157.61i	−1.03902	−	0.599879i
$156$		0			0
$157$	872.747	−	503.881i	0.443648	−	0.256141i	−0.261496	−	0.965205i	$-0.584216\pi$
$157$	872.747	−	503.881i	0.443648	−	0.256141i	0.705144	+	0.709064i	$0.250882\pi$
$158$	50.5880	−	29.2070i	0.0254719	−	0.0147062i
$159$		0			0
$160$	294.625	+	170.102i	0.145576	+	0.0840483i
$161$	−2885.05	−	853.868i	−1.41226	−	0.417976i
$162$		0			0
$163$	−1801.27			−0.865561			−0.432780	−	0.901499i	$-0.642467\pi$
$163$	−1801.27			−0.865561			−0.432780	+	0.901499i	$0.642467\pi$
$164$	−792.599	+	1372.82i	−0.377388	+	0.653655i
$165$		0			0
$166$	−30.6451	+	17.6930i	−0.0143285	+	0.00827254i
$167$	817.899	+	1416.64i	0.378987	+	0.656425i	0.990915	−	0.134488i	$-0.0429390\pi$
$167$	817.899	+	1416.64i	0.378987	+	0.656425i	−0.611928	+	0.790914i	$0.709606\pi$
$168$		0			0
$169$	−919.908	+	1593.33i	−0.418711	+	0.725229i
$170$		−	110.954i		−	0.0500574i
$171$		0			0
$172$	−2568.00			−1.13842
$173$	399.759	−	692.402i	0.175683	−	0.304291i	−0.764715	−	0.644369i	$-0.777120\pi$
$173$	399.759	−	692.402i	0.175683	−	0.304291i	0.940397	+	0.340078i	$0.110453\pi$
$174$		0			0
$175$	−3666.08	+	881.043i	−1.58360	+	0.380575i
$176$	2044.06	−	1180.14i	0.875439	−	0.505435i
$177$		0			0
$178$	−3.00989	−	1.73776i	−0.00126742	−	0.000731745i
$179$			2940.19i			1.22771i	0.789418	+	0.613856i	$0.210382\pi$
$179$			2940.19i			1.22771i	−0.789418	+	0.613856i	$0.789618\pi$
$180$		0			0
$181$		−	376.924i		−	0.154788i	−0.997001	−	0.0773938i	$-0.975340\pi$
$181$		−	376.924i		−	0.154788i	0.997001	−	0.0773938i	$-0.0246599\pi$
$182$	−23.5949	−	24.8523i	−0.00960971	−	0.0101218i
$183$		0			0
$184$	127.168	+	220.261i	0.0509507	+	0.0882492i
$185$	3433.53	+	5947.06i	1.36453	+	2.36344i
$186$		0			0
$187$	−2003.95	−	1156.98i	−0.783656	−	0.452444i
$188$	1268.69			0.492176
$189$		0			0
$190$	124.707			0.0476167
$191$	−1586.09	−	915.732i	−0.600868	−	0.346911i	0.168515	−	0.985699i	$-0.446103\pi$
$191$	−1586.09	−	915.732i	−0.600868	−	0.346911i	−0.769383	+	0.638788i	$0.779436\pi$
$192$		0			0
$193$	190.008	+	329.104i	0.0708657	+	0.122743i	0.899281	−	0.437371i	$-0.144090\pi$
$193$	190.008	+	329.104i	0.0708657	+	0.122743i	−0.828415	+	0.560114i	$0.810757\pi$
$194$	−65.0968	−	112.751i	−0.0240911	−	0.0417270i
$195$		0			0
$196$	2441.42	−	1245.38i	0.889730	−	0.453857i
$197$		−	3579.56i		−	1.29458i	−0.762243	−	0.647291i	$-0.775902\pi$
$197$		−	3579.56i		−	1.29458i	0.762243	−	0.647291i	$-0.224098\pi$
$198$		0			0
$199$		−	881.304i		−	0.313939i	−0.987603	−	0.156970i	$-0.949827\pi$
$199$		−	881.304i		−	0.313939i	0.987603	−	0.156970i	$-0.0501725\pi$
$200$	276.023	+	159.362i	0.0975889	+	0.0563430i
$201$		0			0
$202$	−77.5802	+	44.7909i	−0.0270224	+	0.0156014i
$203$	−412.269	−	1715.48i	−0.142540	−	0.593119i
$204$		0			0
$205$	−1798.08	+	3114.36i	−0.612601	+	1.06106i
$206$	−81.6089			−0.0276018
$207$		0			0
$208$		−	1205.21i		−	0.401760i
$209$	1300.39	−	2252.35i	0.430383	−	0.745446i
$210$		0			0
$211$	−418.581	−	725.004i	−0.136570	−	0.236547i	0.789626	−	0.613588i	$-0.210275\pi$
$211$	−418.581	−	725.004i	−0.136570	−	0.236547i	−0.926196	+	0.377042i	$0.876941\pi$
$212$	−1327.10	+	766.202i	−0.429932	+	0.248222i
$213$		0			0
$214$	82.5504	−	142.981i	0.0263693	−	0.0456730i
$215$	−5825.72			−1.84796
$216$		0			0
$217$	2268.20	+	671.301i	0.709563	+	0.210004i
$218$	54.3715	+	31.3914i	0.0168922	+	0.00975272i
$219$		0			0
$220$	4642.71	−	2680.47i	1.42278	−	0.821442i
$221$	−1023.26	+	590.779i	−0.311456	+	0.179819i
$222$		0			0
$223$	981.825	+	566.857i	0.294834	+	0.170222i	0.640120	−	0.768275i	$-0.278885\pi$
$223$	981.825	+	566.857i	0.294834	+	0.170222i	−0.345286	+	0.938497i	$0.612218\pi$
$224$	−333.294	−	98.6427i	−0.0994159	−	0.0294234i
$225$		0			0
$226$	−140.783			−0.0414370
$227$	1752.96	−	3036.21i	0.512545	−	0.887754i	−0.487349	−	0.873207i	$-0.662036\pi$
$227$	1752.96	−	3036.21i	0.512545	−	0.887754i	0.999894	−	0.0145471i	$-0.00463065\pi$
$228$		0			0
$229$	−2721.44	+	1571.23i	−0.785319	+	0.453404i	−0.838312	−	0.545191i	$-0.816457\pi$
$229$	−2721.44	+	1571.23i	−0.785319	+	0.453404i	0.0529930	+	0.998595i	$0.483124\pi$
$230$	144.159	+	249.691i	0.0413285	+	0.0715831i
$231$		0			0
$232$	−74.5707	+	129.160i	−0.0211026	+	0.0365508i
$233$			6882.00i			1.93500i	0.252872	+	0.967500i	$0.418625\pi$
$233$			6882.00i			1.93500i	−0.252872	+	0.967500i	$0.581375\pi$
$234$		0			0
$235$	2878.14			0.798933
$236$	854.317	−	1479.72i	0.235641	−	0.408142i
$237$		0			0
$238$	26.4890	+	110.223i	0.00721441	+	0.0300197i
$239$	1036.14	−	598.217i	0.280429	−	0.161906i	−0.353189	−	0.935552i	$-0.614903\pi$
$239$	1036.14	−	598.217i	0.280429	−	0.161906i	0.633617	+	0.773646i	$0.281569\pi$
$240$		0			0
$241$	3790.59	+	2188.50i	1.01317	+	0.584953i	0.912118	−	0.409928i	$-0.134446\pi$
$241$	3790.59	+	2188.50i	1.01317	+	0.584953i	0.101051	+	0.994881i	$0.467780\pi$
$242$			3.81033i			0.00101214i
$243$		0			0
$244$			1761.62i			0.462196i
$245$	5538.57	−	2825.26i	1.44427	−	0.736731i
$246$		0			0
$247$	−664.008	−	1150.09i	−0.171052	−	0.296270i
$248$	−99.9779	−	173.167i	−0.0255992	−	0.0443391i
$249$		0			0
$250$	120.783	+	69.7344i	0.0305561	+	0.0176416i
$251$	−5787.19			−1.45532			−0.727658	−	0.685940i	$-0.759391\pi$
$251$	−5787.19			−1.45532			−0.727658	+	0.685940i	$0.759391\pi$
$252$		0			0
$253$	6012.95			1.49419
$254$	−156.438	−	90.3195i	−0.0386448	−	0.0223116i
$255$		0			0
$256$	−2023.51	−	3504.81i	−0.494020	−	0.855667i
$257$	1074.45	+	1861.00i	0.260786	+	0.451695i	0.966451	−	0.256851i	$-0.0826848\pi$
$257$	1074.45	+	1861.00i	0.260786	+	0.451695i	−0.705665	+	0.708546i	$0.749351\pi$
$258$		0			0
$259$	−4830.72	−	5088.16i	−1.15894	−	1.22071i
$260$		−	2737.41i		−	0.652949i
$261$		0			0
$262$		−	215.240i		−	0.0507540i
$263$	1057.21	+	610.380i	0.247872	+	0.143109i	0.618789	−	0.785557i	$-0.287623\pi$
$263$	1057.21	+	610.380i	0.247872	+	0.143109i	−0.370917	+	0.928666i	$0.620957\pi$
$264$		0			0
$265$	−3010.64	+	1738.20i	−0.697895	+	0.402930i
$266$	−123.885	+	29.7724i	−0.0285560	+	0.00686265i
$267$		0			0
$268$	545.703	−	945.185i	0.124381	−	0.215434i
$269$	4430.56			1.00422			0.502112	−	0.864803i	$-0.332556\pi$
$269$	4430.56			1.00422			0.502112	+	0.864803i	$0.332556\pi$
$270$		0			0
$271$			111.259i			0.0249391i	0.999922	+	0.0124695i	$0.00396928\pi$
$271$			111.259i			0.0249391i	−0.999922	+	0.0124695i	$0.996031\pi$
$272$	−1993.41	+	3452.69i	−0.444368	+	0.769668i
$273$		0			0
$274$	−105.683	−	183.048i	−0.0233012	−	0.0403588i
$275$	6525.68	−	3767.60i	1.43096	−	0.826164i
$276$		0			0
$277$	1529.33	−	2648.87i	0.331727	−	0.574567i	−0.651124	−	0.758971i	$-0.725702\pi$
$277$	1529.33	−	2648.87i	0.331727	−	0.574567i	0.982850	+	0.184404i	$0.0590356\pi$
$278$	285.064			0.0615000
$279$		0			0
$280$	−503.971	−	149.156i	−0.107564	−	0.0318350i
$281$	4124.03	+	2381.01i	0.875513	+	0.505478i	0.869176	−	0.494502i	$-0.164650\pi$
$281$	4124.03	+	2381.01i	0.875513	+	0.505478i	0.00633670	+	0.999980i	$0.497983\pi$
$282$		0			0
$283$	3567.54	−	2059.72i	0.749358	−	0.432642i	−0.0761041	−	0.997100i	$-0.524248\pi$
$283$	3567.54	−	2059.72i	0.749358	−	0.432642i	0.825462	+	0.564458i	$0.190915\pi$
$284$	3175.71	−	1833.50i	0.663534	−	0.383091i
$285$		0			0
$286$	59.3104	+	34.2429i	0.0122626	+	0.00707980i
$287$	1042.71	−	3523.12i	0.214458	−	0.724611i
$288$		0			0
$289$	−1004.42			−0.204440
$290$	−84.5343	+	146.418i	−0.0171173	+	0.0296481i
$291$		0			0
$292$	−6697.56	+	3866.84i	−1.34228	+	0.774964i
$293$	1401.70	+	2427.81i	0.279482	+	0.484076i	0.971256	−	0.238037i	$-0.0765041\pi$
$293$	1401.70	+	2427.81i	0.279482	+	0.484076i	−0.691774	+	0.722114i	$0.743171\pi$
$294$		0			0
$295$	1938.09	−	3356.87i	0.382509	−	0.662524i
$296$			593.081i			0.116460i
$297$		0			0
$298$	26.0743			0.00506861
$299$	1535.17	−	2658.99i	0.296926	−	0.514291i
$300$		0			0
$301$	5787.35	−	1390.83i	1.10823	−	0.266333i
$302$	79.3211	−	45.7960i	0.0151140	−	0.00872605i
$303$		0			0
$304$	−3880.65	−	2240.50i	−0.732141	−	0.422702i
$305$			3996.38i			0.750268i
$306$		0			0
$307$		−	3959.31i		−	0.736058i	−0.929814	−	0.368029i	$-0.880033\pi$
$307$		−	3959.31i		−	0.736058i	0.929814	−	0.368029i	$-0.119967\pi$
$308$	−3972.20	+	3771.22i	−0.734860	+	0.697679i
$309$		0			0
$310$	−113.336	−	196.304i	−0.0207647	−	0.0359656i
$311$	2492.25	+	4316.71i	0.454413	+	0.787067i	0.998654	−	0.0518618i	$-0.0165155\pi$
$311$	2492.25	+	4316.71i	0.454413	+	0.787067i	−0.544241	+	0.838929i	$0.683182\pi$
$312$		0			0
$313$	699.706	+	403.976i	0.126357	+	0.0729522i	0.561846	−	0.827242i	$-0.310091\pi$
$313$	699.706	+	403.976i	0.126357	+	0.0729522i	−0.435489	+	0.900194i	$0.643425\pi$
$314$	98.6654			0.0177325
$315$		0			0
$316$	−4767.37			−0.848689
$317$	−2061.65	−	1190.29i	−0.365280	−	0.210894i	0.306115	−	0.951995i	$-0.400971\pi$
$317$	−2061.65	−	1190.29i	−0.365280	−	0.210894i	−0.671394	+	0.741100i	$0.734304\pi$
$318$		0			0
$319$	1762.99	+	3053.58i	0.309430	+	0.535949i
$320$	−4607.17	−	7979.85i	−0.804839	−	1.39402i
$321$		0			0
$322$	−202.821	−	213.630i	−0.0351017	−	0.0369724i
$323$			4393.06i			0.756769i
$324$		0			0
$325$		−	3847.63i		−	0.656702i
$326$	−152.727	−	88.1772i	−0.0259472	−	0.0149806i
$327$		0			0
$328$	−268.975	+	155.293i	−0.0452794	+	0.0261421i
$329$	−2859.19	+	687.127i	−0.479125	+	0.115145i
$330$		0			0
$331$	3727.74	−	6456.64i	0.619019	−	1.07217i	−0.370646	−	0.928774i	$-0.620864\pi$
$331$	3727.74	−	6456.64i	0.619019	−	1.07217i	0.989665	−	0.143398i	$-0.0458029\pi$
$332$	2887.97			0.477404
$333$		0			0
$334$			160.154i			0.0262372i
$335$	1237.97	−	2144.23i	0.201904	−	0.349707i
$336$		0			0
$337$	978.259	+	1694.39i	0.158128	+	0.273886i	0.934194	−	0.356766i	$-0.116121\pi$
$337$	978.259	+	1694.39i	0.158128	+	0.273886i	−0.776066	+	0.630652i	$0.782787\pi$
$338$	−155.996	+	90.0641i	−0.0251037	+	0.0144936i
$339$		0			0
$340$	−4527.66	+	7842.13i	−0.722196	+	1.25088i
$341$	−4727.31			−0.750728
$342$		0			0
$343$	−4827.58	+	4128.93i	−0.759956	+	0.649974i
$344$	−435.735	−	251.572i	−0.0682944	−	0.0394298i
$345$		0			0
$346$	67.7900	−	39.1386i	0.0105330	−	0.00608122i
$347$	1191.69	−	688.024i	0.184361	−	0.106441i	−0.404979	−	0.914326i	$-0.632721\pi$
$347$	1191.69	−	688.024i	0.184361	−	0.106441i	0.589340	+	0.807885i	$0.299388\pi$
$348$		0			0
$349$	8098.04	+	4675.41i	1.24206	+	0.717103i	0.969513	−	0.245040i	$-0.0788011\pi$
$349$	8098.04	+	4675.41i	1.24206	+	0.717103i	0.272546	+	0.962143i	$0.412134\pi$
$350$	−353.972	−	104.762i	−0.0540588	−	0.0159994i
$351$		0			0
$352$	694.643			0.105184
$353$	−338.836	+	586.881i	−0.0510890	+	0.0884887i	−0.890439	−	0.455103i	$-0.849603\pi$
$353$	−338.836	+	586.881i	−0.0510890	+	0.0884887i	0.839350	+	0.543591i	$0.182936\pi$
$354$		0			0
$355$	7204.37	−	4159.44i	1.07709	−	0.621860i
$356$	141.825	+	245.647i	0.0211143	+	0.0365710i
$357$		0			0
$358$	−143.931	+	249.295i	−0.0212485	+	0.0368035i
$359$			1662.36i			0.244390i	0.992506	+	0.122195i	$0.0389933\pi$
$359$			1662.36i			0.244390i	−0.992506	+	0.122195i	$0.961007\pi$
$360$		0			0
$361$	1921.41			0.280129
$362$	18.4515	−	31.9589i	0.00267897	−	0.00464012i
$363$		0			0
$364$	653.528	+	2719.38i	0.0941048	+	0.391577i
$365$	−15194.0	+	8772.25i	−2.17888	+	1.25797i
$366$		0			0
$367$	−2653.41	−	1531.94i	−0.377402	−	0.217893i	0.299285	−	0.954164i	$-0.403252\pi$
$367$	−2653.41	−	1531.94i	−0.377402	−	0.217893i	−0.676687	+	0.736270i	$0.736585\pi$
$368$		−	10359.9i		−	1.46752i
$369$		0			0
$370$			672.324i			0.0944661i
$371$	2575.84	−	2445.51i	0.360460	−	0.342222i
$372$		0			0
$373$	3900.06	+	6755.10i	0.541387	+	0.937711i	0.998825	+	0.0484687i	$0.0154341\pi$
$373$	3900.06	+	6755.10i	0.541387	+	0.937711i	−0.457437	+	0.889242i	$0.651233\pi$
$374$	−113.275	−	196.198i	−0.0156613	−	0.0271261i
$375$		0			0
$376$	215.271	+	124.287i	0.0295259	+	0.0170468i
$377$	1800.43			0.245960
$378$		0			0
$379$	−6855.89			−0.929191			−0.464595	−	0.885523i	$-0.653800\pi$
$379$	−6855.89			−0.929191			−0.464595	+	0.885523i	$0.653800\pi$
$380$	−8814.18	−	5088.87i	−1.18989	−	0.686983i
$381$		0			0
$382$	−89.6552	−	155.287i	−0.0120083	−	0.0207989i
$383$	5511.46	+	9546.14i	0.735307	+	1.27359i	0.954588	+	0.297928i	$0.0962955\pi$
$383$	5511.46	+	9546.14i	0.735307	+	1.27359i	−0.219281	+	0.975662i	$0.570371\pi$
$384$		0			0
$385$	−9011.27	+	8555.33i	−1.19288	+	1.13252i
$386$			37.2057i			0.00490601i
$387$		0			0
$388$			10625.6i			1.39029i
$389$	−9460.70	−	5462.14i	−1.23310	−	0.711931i	−0.265426	−	0.964131i	$-0.585513\pi$
$389$	−9460.70	−	5462.14i	−1.23310	−	0.711931i	−0.967675	+	0.252200i	$0.918846\pi$
$390$		0			0
$391$	−8795.90	+	5078.32i	−1.13767	+	0.656833i
$392$	536.261	+	27.8562i	0.0690950	+	0.00358916i
$393$		0			0
$394$	175.229	−	303.506i	0.0224059	−	0.0388081i
$395$	−10815.2			−1.37765
$396$		0			0
$397$			7203.22i			0.910627i	0.890331	+	0.455314i	$0.150473\pi$
$397$			7203.22i			0.910627i	−0.890331	+	0.455314i	$0.849527\pi$
$398$	43.1423	−	74.7246i	0.00543348	−	0.00941107i
$399$		0			0
$400$	−6491.34	−	11243.3i	−0.811418	−	1.40542i
$401$	10633.1	−	6139.03i	1.32417	−	0.764510i	0.339778	−	0.940506i	$-0.389648\pi$
$401$	10633.1	−	6139.03i	1.32417	−	0.764510i	0.984391	+	0.175996i	$0.0563146\pi$
$402$		0			0
$403$	−1206.93	+	2090.46i	−0.149185	+	0.258396i
$404$	7311.09			0.900347
$405$		0			0
$406$	49.0218	−	165.635i	0.00599239	−	0.0202471i
$407$	12143.0	+	7010.75i	1.47888	+	0.853832i
$408$		0			0
$409$	−735.497	+	424.639i	−0.0889193	+	0.0513376i	−0.543800	−	0.839215i	$-0.683015\pi$
$409$	−735.497	+	424.639i	−0.0889193	+	0.0513376i	0.454881	+	0.890552i	$0.349682\pi$
$410$	−304.913	+	176.042i	−0.0367283	+	0.0212051i
$411$		0			0
$412$	5768.07	+	3330.19i	0.689738	+	0.398221i
$413$	−1123.91	+	3797.46i	−0.133908	+	0.452448i
$414$		0			0
$415$	6551.61			0.774954
$416$	177.349	−	307.178i	0.0209021	−	0.0362035i
$417$		0			0
$418$	220.517	−	127.316i	0.0258035	−	0.0148977i
$419$	−3109.74	−	5386.23i	−0.362579	−	0.628006i	0.625805	−	0.779979i	$-0.284771\pi$
$419$	−3109.74	−	5386.23i	−0.362579	−	0.628006i	−0.988385	+	0.151973i	$0.951437\pi$
$420$		0			0
$421$	−1012.07	+	1752.95i	−0.117162	+	0.202930i	−0.918642	−	0.395091i	$-0.870713\pi$
$421$	−1012.07	+	1752.95i	−0.117162	+	0.202930i	0.801480	+	0.598021i	$0.204046\pi$
$422$		−	81.9628i		−	0.00945471i
$423$		0			0
$424$	−300.242			−0.0343892
$425$	−6363.96	+	11022.7i	−0.726347	+	1.25807i
$426$		0			0
$427$	−954.094	−	3970.05i	−0.108131	−	0.449940i
$428$	−11669.2	+	6737.23i	−1.31788	+	0.760879i
$429$		0			0
$430$	−493.955	−	285.185i	−0.0553968	−	0.0319834i
$431$		−	6519.65i		−	0.728633i	−0.931275	−	0.364316i	$-0.881303\pi$
$431$		−	6519.65i		−	0.728633i	0.931275	−	0.364316i	$-0.118697\pi$
$432$		0			0
$433$		−	17767.9i		−	1.97199i	−0.166772	−	0.985996i	$-0.553334\pi$
$433$		−	17767.9i		−	1.97199i	0.166772	−	0.985996i	$-0.446666\pi$
$434$	159.455	+	167.953i	0.0176362	+	0.0185761i
$435$		0			0
$436$	−2561.96	−	4437.45i	−0.281412	−	0.487420i
$437$	−5707.79	−	9886.17i	−0.624806	−	1.08220i
$438$		0			0
$439$	1280.80	+	739.472i	0.139247	+	0.0803942i	0.568005	−	0.823025i	$-0.307715\pi$
$439$	1280.80	+	739.472i	0.139247	+	0.0803942i	−0.428758	+	0.903419i	$0.641049\pi$
$440$	1050.36			0.113805
$441$		0			0
$442$	−115.681			−0.0124488
$443$	−13484.2	−	7785.09i	−1.44617	−	0.834945i	−0.447918	−	0.894075i	$-0.647834\pi$
$443$	−13484.2	−	7785.09i	−1.44617	−	0.834945i	−0.998250	+	0.0591295i	$0.981168\pi$
$444$		0			0
$445$	321.741	+	557.272i	0.0342742	+	0.0593646i
$446$	55.4985	+	96.1262i	0.00589222	+	0.0102056i
$447$		0			0
$448$	6481.93	+	6827.38i	0.683577	+	0.720007i
$449$		−	6120.30i		−	0.643284i	−0.946861	−	0.321642i	$-0.895765\pi$
$449$		−	6120.30i		−	0.643284i	0.946861	−	0.321642i	$-0.104235\pi$
$450$		0			0
$451$			7342.80i			0.766649i
$452$	9950.46	+	5744.90i	1.03547	+	0.597826i
$453$		0			0
$454$	297.262	−	171.624i	0.0307295	−	0.0177417i
$455$	1482.58	+	6169.14i	0.152757	+	0.635634i
$456$		0			0
$457$	−3498.22	+	6059.10i	−0.358074	+	0.620203i	−0.987639	−	0.156745i	$-0.949900\pi$
$457$	−3498.22	+	6059.10i	−0.358074	+	0.620203i	0.629565	+	0.776948i	$0.283233\pi$
$458$	−307.663			−0.0313890
$459$		0			0
$460$		−	23530.6i		−	2.38505i
$461$	1833.17	−	3175.15i	0.185205	−	0.320784i	−0.758441	−	0.651742i	$-0.774038\pi$
$461$	1833.17	−	3175.15i	0.185205	−	0.320784i	0.943646	+	0.330958i	$0.107372\pi$
$462$		0			0
$463$	3513.71	+	6085.92i	0.352691	+	0.610878i	0.986720	−	0.162431i	$-0.0519335\pi$
$463$	3513.71	+	6085.92i	0.352691	+	0.610878i	−0.634029	+	0.773309i	$0.718600\pi$
$464$	5261.13	−	3037.51i	0.526383	−	0.303907i
$465$		0			0
$466$	−336.893	+	583.516i	−0.0334898	+	0.0580061i
$467$	13367.8			1.32460			0.662301	−	0.749238i	$-0.269580\pi$
$467$	13367.8			1.32460			0.662301	+	0.749238i	$0.269580\pi$
$468$		0			0
$469$	−717.906	+	2425.66i	−0.0706819	+	0.238820i
$470$	244.034	+	140.893i	0.0239499	+	0.0138275i
$471$		0			0
$472$	289.919	−	167.385i	0.0282725	−	0.0163231i
$473$	−10301.6	+	5947.61i	−1.00141	+	0.578163i
$474$		0			0
$475$	−12389.0	−	7152.79i	−1.19673	−	0.690932i
$476$	2625.61	−	8871.41i	0.252825	−	0.854245i
$477$		0			0
$478$	117.138			0.0112087
$479$	−3497.20	+	6057.33i	−0.333593	+	0.577800i	−0.983214	−	0.182458i	$-0.941594\pi$
$479$	−3497.20	+	6057.33i	−0.333593	+	0.577800i	0.649620	+	0.760259i	$0.274928\pi$
$480$		0			0
$481$	6200.45	−	3579.83i	0.587767	−	0.339348i
$482$	214.266	+	371.120i	0.0202481	+	0.0350707i
$483$		0			0
$484$	155.487	−	269.312i	0.0146025	−	0.0252923i
$485$			24105.0i			2.25681i
$486$		0			0
$487$	−8233.24			−0.766086			−0.383043	−	0.923731i	$-0.625124\pi$
$487$	−8233.24			−0.766086			−0.383043	+	0.923731i	$0.625124\pi$
$488$	−172.575	+	298.909i	−0.0160084	+	0.0277274i
$489$		0			0
$490$	607.912	+	31.5782i	0.0560463	+	0.00291134i
$491$	12925.9	−	7462.77i	1.18806	−	0.685927i	0.230195	−	0.973145i	$-0.426064\pi$
$491$	12925.9	−	7462.77i	1.18806	−	0.685927i	0.957865	+	0.287218i	$0.0927303\pi$
$492$		0			0
$493$	−5157.89	−	2977.91i	−0.471196	−	0.272045i
$494$		−	130.020i		−	0.0118419i
$495$		0			0
$496$			8144.86i			0.737329i
$497$	−6163.89	+	5852.01i	−0.556314	+	0.528166i
$498$		0			0
$499$	−4165.46	−	7214.80i	−0.373691	−	0.647252i	0.616439	−	0.787402i	$-0.288575\pi$
$499$	−4165.46	−	7214.80i	−0.373691	−	0.647252i	−0.990130	+	0.140151i	$0.955241\pi$
$500$	−5691.27	−	9857.56i	−0.509042	−	0.881687i
$501$		0			0
$502$	−490.688	−	283.299i	−0.0436265	−	0.0251878i
$503$	15511.0			1.37495			0.687475	−	0.726208i	$-0.258719\pi$
$503$	15511.0			1.37495			0.687475	+	0.726208i	$0.258719\pi$
$504$		0			0
$505$	16585.8			1.46150
$506$	509.830	+	294.350i	0.0447919	+	0.0258606i
$507$		0			0
$508$	7371.29	+	12767.4i	0.643795	+	1.11509i
$509$	−1816.15	−	3145.66i	−0.158152	−	0.273927i	0.776050	−	0.630671i	$-0.217220\pi$
$509$	−1816.15	−	3145.66i	−0.158152	−	0.273927i	−0.934202	+	0.356744i	$0.883887\pi$
$510$		0			0
$511$	12999.6	−	12341.9i	1.12538	−	1.06844i
$512$		−	1995.51i		−	0.172246i
$513$		0			0
$514$			210.388i			0.0180542i
$515$	13085.4	+	7554.83i	1.11963	+	0.646419i
$516$		0			0
$517$	5089.39	−	2938.36i	0.432942	−	0.249959i
$518$	−160.510	−	667.896i	−0.0136147	−	0.0566518i
$519$		0			0
$520$	268.168	−	464.481i	0.0226153	−	0.0391708i
$521$	−531.760			−0.0447156			−0.0223578	−	0.999750i	$-0.507117\pi$
$521$	−531.760			−0.0447156			−0.0223578	+	0.999750i	$0.507117\pi$
$522$		0			0
$523$			14041.2i			1.17395i	0.809604	+	0.586977i	$0.199682\pi$
$523$			14041.2i			1.17395i	−0.809604	+	0.586977i	$0.800318\pi$
$524$	−8783.23	+	15213.0i	−0.732247	+	1.26829i
$525$		0			0
$526$	59.7596	+	103.507i	0.00495369	+	0.00858005i
$527$	6915.24	−	3992.52i	0.571599	−	0.330013i
$528$		0			0
$529$	7112.74	−	12319.6i	0.584592	−	1.01254i
$530$	−340.358			−0.0278947
$531$		0			0
$532$	9971.04	+	2951.06i	0.812593	+	0.240497i
$533$	3247.06	+	1874.69i	0.263876	+	0.152349i
$534$		0			0
$535$	−26472.6	+	15284.0i	−2.13927	+	1.23511i
$536$	185.189	−	106.919i	0.0149234	−	0.00861602i
$537$		0			0
$538$	375.662	+	216.888i	0.0301040	+	0.0173805i
$539$	6909.42	−	10650.3i	0.552152	−	0.851098i
$540$		0			0
$541$	−11065.4			−0.879372			−0.439686	−	0.898151i	$-0.644910\pi$
$541$	−11065.4			−0.879372			−0.439686	+	0.898151i	$0.644910\pi$
$542$	−5.44642	+	9.43348i	−0.000431631	+	0.000747606i
$543$		0			0
$544$	−1016.14	+	586.670i	−0.0800860	+	0.0462376i
$545$	−5812.03	−	10066.7i	−0.456807	−	0.791213i
$546$		0			0
$547$	6024.28	−	10434.4i	0.470895	−	0.815614i	−0.528551	−	0.848902i	$-0.677264\pi$
$547$	6024.28	−	10434.4i	0.470895	−	0.815614i	0.999446	+	0.0332874i	$0.0105977\pi$
$548$			17250.3i			1.34470i
$549$		0			0
$550$	737.739			0.0571950
$551$	3347.02	−	5797.22i	0.258780	−	0.448221i
$552$		0			0
$553$	10744.0	−	2582.02i	0.826184	−	0.198551i
$554$	259.339	−	149.729i	0.0198885	−	0.0114827i
$555$		0			0
$556$	−20148.1	−	11632.5i	−1.53682	−	0.887283i
$557$			2546.80i			0.193737i	0.995297	+	0.0968684i	$0.0308826\pi$
$557$			2546.80i			0.193737i	−0.995297	+	0.0968684i	$0.969117\pi$
$558$		0			0
$559$			6073.94i			0.459571i
$560$	14740.3	+	15525.9i	1.11231	+	1.17158i
$561$		0			0
$562$	233.114	+	403.766i	0.0174970	+	0.0303057i
$563$	−11536.2	−	19981.3i	−0.863578	−	1.49576i	−0.868452	−	0.495772i	$-0.834885\pi$
$563$	−11536.2	−	19981.3i	−0.863578	−	1.49576i	0.00487467	−	0.999988i	$-0.498448\pi$
$564$		0			0
$565$	22573.5	+	13032.8i	1.68084	+	0.970432i
$566$	403.316			0.0299517
$567$		0			0
$568$	718.468			0.0530744
$569$	5471.39	+	3158.91i	0.403115	+	0.232739i	0.687827	−	0.725874i	$-0.258565\pi$
$569$	5471.39	+	3158.91i	0.403115	+	0.232739i	−0.284712	+	0.958613i	$0.591898\pi$
$570$		0			0
$571$	−9276.07	−	16066.6i	−0.679845	−	1.17753i	−0.975027	−	0.222085i	$-0.928714\pi$
$571$	−9276.07	−	16066.6i	−0.679845	−	1.17753i	0.295182	−	0.955441i	$-0.404620\pi$
$572$	−2794.68	−	4840.53i	−0.204286	−	0.353833i
$573$		0			0
$574$	260.877	−	247.677i	0.0189700	−	0.0180102i
$575$		−	33074.1i		−	2.39876i
$576$		0			0
$577$		−	2684.61i		−	0.193695i	−0.995299	−	0.0968473i	$-0.969124\pi$
$577$		−	2684.61i		−	0.193695i	0.995299	−	0.0968473i	$-0.0308758\pi$
$578$	−85.1631	−	49.1689i	−0.00612858	−	0.00353834i
$579$		0			0
$580$	11949.7	−	6899.14i	0.855488	−	0.493916i
$581$	−6508.46	+	1564.13i	−0.464744	+	0.111689i
$582$		0			0
$583$	−3549.13	+	6147.27i	−0.252127	+	0.436696i
$584$	−1515.25			−0.107365
$585$		0			0
$586$			274.468i			0.0193484i
$587$	9124.16	−	15803.5i	0.641558	−	1.11121i	−0.343527	−	0.939143i	$-0.611622\pi$
$587$	9124.16	−	15803.5i	0.641558	−	1.11121i	0.985085	−	0.172068i	$-0.0550448\pi$
$588$		0			0
$589$	4487.40	+	7772.40i	0.313922	+	0.543729i
$590$	328.656	−	189.750i	0.0229332	−	0.0132405i
$591$		0			0
$592$	12079.1	−	20921.6i	0.838593	−	1.45249i
$593$	10331.8			0.715473			0.357736	−	0.933823i	$-0.383549\pi$
$593$	10331.8			0.715473			0.357736	+	0.933823i	$0.383549\pi$
$594$		0			0
$595$	5956.41	−	20125.6i	0.410402	−	1.38667i
$596$	−1842.92	−	1064.01i	−0.126659	−	0.0731266i
$597$		0			0
$598$	260.329	−	150.301i	0.0178021	−	0.0102781i
$599$	3453.17	−	1993.69i	0.235547	−	0.135993i	−0.377581	−	0.925976i	$-0.623244\pi$
$599$	3453.17	−	1993.69i	0.235547	−	0.135993i	0.613129	+	0.789983i	$0.289911\pi$
$600$		0			0
$601$	−15935.6	−	9200.43i	−1.08158	−	0.624448i	−0.150255	−	0.988647i	$-0.548010\pi$
$601$	−15935.6	−	9200.43i	−1.08158	−	0.624448i	−0.931321	+	0.364199i	$0.881343\pi$
$602$	558.786	+	165.380i	0.0378313	+	0.0111966i
$603$		0			0
$604$	−7475.15			−0.503576
$605$	352.736	−	610.957i	0.0237038	−	0.0410561i
$606$		0			0
$607$	12276.2	−	7087.68i	0.820883	−	0.473937i	−0.0298377	−	0.999555i	$-0.509499\pi$
$607$	12276.2	−	7087.68i	0.820883	−	0.473937i	0.850721	+	0.525618i	$0.176166\pi$
$608$	−659.389	−	1142.10i	−0.0439832	−	0.0761811i
$609$		0			0
$610$	−195.634	+	338.848i	−0.0129852	+	0.0224910i
$611$		−	3000.77i		−	0.198688i
$612$		0			0
$613$	−2164.43			−0.142611			−0.0713054	−	0.997455i	$-0.522716\pi$
$613$	−2164.43			−0.142611			−0.0713054	+	0.997455i	$0.522716\pi$
$614$	193.819	−	335.705i	0.0127393	−	0.0220650i
$615$		0			0
$616$	−1043.44	+	250.763i	−0.0682492	+	0.0164018i
$617$	−2799.72	+	1616.42i	−0.182678	+	0.105469i	−0.588550	−	0.808460i	$-0.700301\pi$
$617$	−2799.72	+	1616.42i	−0.182678	+	0.105469i	0.405872	+	0.913930i	$0.366968\pi$
$618$		0			0
$619$	18943.3	+	10936.9i	1.23004	+	0.710166i	0.967039	−	0.254629i	$-0.0819532\pi$
$619$	18943.3	+	10936.9i	1.23004	+	0.710166i	0.263005	+	0.964795i	$0.415287\pi$
$620$			18499.5i			1.19832i
$621$		0			0
$622$			488.010i			0.0314589i
$623$	−452.665	−	476.789i	−0.0291102	−	0.0306616i
$624$		0			0
$625$	−187.001	−	323.895i	−0.0119680	−	0.0207292i
$626$	39.5514	+	68.5051i	0.00252523	+	0.00437383i
$627$		0			0
$628$	−6973.61	−	4026.22i	−0.443117	−	0.255834i
$629$	−23684.1			−1.50135
$630$		0			0
$631$	−9979.57			−0.629604			−0.314802	−	0.949157i	$-0.601938\pi$
$631$	−9979.57			−0.629604			−0.314802	+	0.949157i	$0.601938\pi$
$632$	−808.923	−	467.032i	−0.0509134	−	0.0293948i
$633$		0			0
$634$	−116.536	−	201.847i	−0.00730007	−	0.0126441i
$635$	16722.4	+	28964.0i	1.04505	+	1.81008i
$636$		0			0
$637$	−2945.64	−	5774.55i	−0.183219	−	0.359178i
$638$			345.212i			0.0214217i
$639$		0			0
$640$		−	3623.76i		−	0.223815i
$641$	−13685.3	−	7901.22i	−0.843272	−	0.486864i	0.0151029	−	0.999886i	$-0.495192\pi$
$641$	−13685.3	−	7901.22i	−0.843272	−	0.486864i	−0.858375	+	0.513022i	$0.828526\pi$
$642$		0			0
$643$	−10980.9	+	6339.83i	−0.673476	+	0.388831i	−0.797392	−	0.603461i	$-0.793788\pi$
$643$	−10980.9	+	6339.83i	−0.673476	+	0.388831i	0.123917	+	0.992293i	$0.460454\pi$
$644$	5617.70	+	23375.7i	0.343740	+	1.43033i
$645$		0			0
$646$	−215.053	+	372.482i	−0.0130977	+	0.0226859i
$647$	−20710.7			−1.25846			−0.629230	−	0.777219i	$-0.716630\pi$
$647$	−20710.7			−1.25846			−0.629230	+	0.777219i	$0.716630\pi$
$648$		0			0
$649$		−	7914.57i		−	0.478696i
$650$	188.352	−	326.235i	0.0113658	−	0.0196862i
$651$		0			0
$652$	7196.45	+	12464.6i	0.432262	+	0.748699i
$653$	1355.80	−	782.771i	0.0812505	−	0.0469100i	−0.458824	−	0.888527i	$-0.651729\pi$
$653$	1355.80	−	782.771i	0.0812505	−	0.0469100i	0.540075	+	0.841617i	$0.318396\pi$
$654$		0			0
$655$	−19925.5	+	34512.0i	−1.18863	+	2.05877i
$656$	12651.2			0.752966
$657$		0			0
$658$	−276.063	−	81.7044i	−0.0163557	−	0.00484069i
$659$	15480.8	+	8937.83i	0.915091	+	0.528328i	0.882066	−	0.471126i	$-0.156152\pi$
$659$	15480.8	+	8937.83i	0.915091	+	0.528328i	0.0330256	+	0.999455i	$0.489486\pi$
$660$		0			0
$661$	−21911.3	+	12650.5i	−1.28934	+	0.744399i	−0.978536	−	0.206076i	$-0.933930\pi$
$661$	−21911.3	+	12650.5i	−1.28934	+	0.744399i	−0.310801	+	0.950475i	$0.600597\pi$
$662$	632.141	−	364.967i	0.0371131	−	0.0214272i
$663$		0			0
$664$	490.028	+	282.918i	0.0286397	+	0.0165352i
$665$	22620.2	+	6694.72i	1.31906	+	0.390391i
$666$		0			0
$667$	15476.4			0.898427
$668$	6535.35	−	11319.6i	0.378533	−	0.655639i
$669$		0			0
$670$	209.932	−	121.204i	0.0121051	−	0.00698886i
$671$	4079.99	+	7066.75i	0.234734	+	0.406571i
$672$		0			0
$673$	−16774.4	+	29054.1i	−0.960781	+	1.66412i	−0.240233	+	0.970715i	$0.577224\pi$
$673$	−16774.4	+	29054.1i	−0.960781	+	1.66412i	−0.720548	+	0.693405i	$0.756110\pi$
$674$			191.554i			0.0109472i
$675$		0			0
$676$	14700.9			0.836419
$677$	−16134.2	+	27945.3i	−0.915935	+	1.58645i	−0.110408	+	0.993886i	$0.535216\pi$
$677$	−16134.2	+	27945.3i	−0.915935	+	1.58645i	−0.805527	+	0.592559i	$0.798118\pi$
$678$		0			0
$679$	−5754.82	−	23946.2i	−0.325257	−	1.35342i
$680$	−1536.50	+	887.097i	−0.0866500	+	0.0500274i
$681$		0			0
$682$	−400.823	−	231.415i	−0.0225048	−	0.0129932i
$683$			14942.5i			0.837126i	0.908188	+	0.418563i	$0.137466\pi$
$683$			14942.5i			0.837126i	−0.908188	+	0.418563i	$0.862534\pi$
$684$		0			0
$685$			39133.7i			2.18281i
$686$	−611.447	+	113.763i	−0.0340308	+	0.00633160i
$687$		0			0
$688$	10247.4	+	17748.9i	0.567844	+	0.983534i
$689$	1812.26	+	3138.92i	0.100205	+	0.173561i
$690$		0			0
$691$	−9734.42	−	5620.17i	−0.535912	−	0.309409i	0.207509	−	0.978233i	$-0.433464\pi$
$691$	−9734.42	−	5620.17i	−0.535912	−	0.309409i	−0.743420	+	0.668824i	$0.766798\pi$
$692$	−6388.47			−0.350944
$693$		0			0
$694$	134.723			0.00736889
$695$	−45707.8	−	26389.4i	−2.49467	−	1.44030i
$696$		0			0
$697$	−6201.46	−	10741.2i	−0.337012	−	0.583721i
$698$	457.748	+	792.843i	0.0248224	+	0.0429936i
$699$		0			0
$700$	20743.5	+	21849.0i	1.12004	+	1.17973i
$701$		−	19409.2i		−	1.04576i	−0.852407	−	0.522879i	$-0.824858\pi$
$701$		−	19409.2i		−	1.04576i	0.852407	−	0.522879i	$-0.175142\pi$
$702$		0			0
$703$		−	26619.8i		−	1.42814i
$704$	−16293.6	−	9407.13i	−0.872285	−	0.503614i
$705$		0			0
$706$	−57.4589	+	33.1739i	−0.00306302	+	0.00176844i
$707$	−16476.6	+	3959.70i	−0.876472	+	0.210636i
$708$		0			0
$709$	866.108	−	1500.14i	0.0458778	−	0.0794627i	−0.842175	−	0.539205i	$-0.818725\pi$
$709$	866.108	−	1500.14i	0.0458778	−	0.0794627i	0.888052	+	0.459742i	$0.152058\pi$
$710$	814.465			0.0430512
$711$		0			0
$712$			55.5750i			0.00292522i
$713$	−10374.7	+	17969.6i	−0.544932	+	0.943851i
$714$		0			0
$715$	−6339.97	−	10981.2i	−0.331610	−	0.574366i
$716$	20345.8	−	11746.7i	1.06196	−	0.613120i
$717$		0			0
$718$	−81.3772	+	140.949i	−0.00422976	+	0.00732616i
$719$	−36946.9			−1.91639			−0.958197	−	0.286109i	$-0.907638\pi$
$719$	−36946.9			−1.91639			−0.958197	+	0.286109i	$0.907638\pi$
$720$		0			0
$721$	−14802.8	−	4381.08i	−0.764612	−	0.226297i
$722$	162.914	+	94.0582i	0.00839753	+	0.00484832i
$723$		0			0
$724$	−2608.28	+	1505.89i	−0.133889	+	0.0773011i
$725$	16796.2	−	9697.26i	0.860405	−	0.496755i
$726$		0			0
$727$	−1776.00	−	1025.38i	−0.0906029	−	0.0523096i	0.454014	−	0.890995i	$-0.349992\pi$
$727$	−1776.00	−	1025.38i	−0.0906029	−	0.0523096i	−0.544617	+	0.838685i	$0.683325\pi$
$728$	−155.512	+	525.444i	−0.00791710	+	0.0267503i
$729$		0			0
$730$	−1717.70			−0.0870892
$731$	10046.3	−	17400.6i	0.508310	−	0.880419i
$732$		0			0
$733$	27156.6	−	15678.9i	1.36842	−	0.790058i	0.377694	−	0.925931i	$-0.376717\pi$
$733$	27156.6	−	15678.9i	1.36842	−	0.790058i	0.990726	+	0.135873i	$0.0433839\pi$
$734$	−149.986	−	259.783i	−0.00754234	−	0.0130637i
$735$		0			0
$736$	1524.49	−	2640.49i	0.0763498	−	0.132242i
$737$		−	5055.50i		−	0.252675i
$738$		0			0
$739$	1233.93			0.0614219			0.0307109	−	0.999528i	$-0.490223\pi$
$739$	1233.93			0.0614219			0.0307109	+	0.999528i	$0.490223\pi$
$740$	27435.4	−	47519.4i	1.36290	−	2.36061i
$741$		0			0
$742$	338.116	−	81.2570i	0.0167286	−	0.00402027i
$743$	−26190.4	+	15121.0i	−1.29318	+	0.746618i	−0.979217	−	0.202818i	$-0.934990\pi$
$743$	−26190.4	+	15121.0i	−1.29318	+	0.746618i	−0.313963	+	0.949435i	$0.601657\pi$
$744$		0			0
$745$	−4180.81	−	2413.79i	−0.205602	−	0.118704i
$746$			763.675i			0.0374801i
$747$		0			0
$748$			18489.6i			0.903803i
$749$	22649.4	−	21503.4i	1.10493	−	1.04902i
$750$		0			0
$751$	−2746.70	−	4757.42i	−0.133460	−	0.231159i	0.791548	−	0.611107i	$-0.209275\pi$
$751$	−2746.70	−	4757.42i	−0.133460	−	0.231159i	−0.925008	+	0.379947i	$0.875942\pi$
$752$	−5062.61	−	8768.70i	−0.245498	−	0.425215i
$753$		0			0
$754$	152.656	+	88.1361i	0.00737323	+	0.00425693i
$755$	−16958.0			−0.817438
$756$		0			0
$757$	−31971.7			−1.53505			−0.767523	−	0.641021i	$-0.778511\pi$
$757$	−31971.7			−1.53505			−0.767523	+	0.641021i	$0.778511\pi$
$758$	−581.302	−	335.615i	−0.0278547	−	0.0160819i
$759$		0			0
$760$	−997.055	−	1726.95i	−0.0475881	−	0.0824251i
$761$	8220.51	+	14238.3i	0.391581	+	0.678238i	0.992658	−	0.120953i	$-0.0385949\pi$
$761$	8220.51	+	14238.3i	0.391581	+	0.678238i	−0.601077	+	0.799191i	$0.705262\pi$
$762$		0			0
$763$	8177.07	+	8612.86i	0.387982	+	0.408658i
$764$			14634.2i			0.692991i
$765$		0			0
$766$			1079.21i			0.0509051i
$767$	−3499.90	−	2020.67i	−0.164764	−	0.0951266i
$768$		0			0
$769$	1220.92	−	704.900i	0.0572531	−	0.0330551i	−0.471100	−	0.882080i	$-0.656143\pi$
$769$	1220.92	−	704.900i	0.0572531	−	0.0330551i	0.528353	+	0.849025i	$0.322810\pi$
$770$	−1182.86	+	284.268i	−0.0553602	+	0.0133043i
$771$		0			0
$772$	1518.24	−	2629.67i	0.0707808	−	0.122596i
$773$	9575.08			0.445526			0.222763	−	0.974873i	$-0.428492\pi$
$773$	9575.08			0.445526			0.222763	+	0.974873i	$0.428492\pi$
$774$		0			0
$775$			26002.5i			1.20521i
$776$	−1040.92	+	1802.93i	−0.0481534	+	0.0834041i
$777$		0			0
$778$	−534.773	−	926.255i	−0.0246434	−	0.0426836i
$779$	12072.6	−	6970.15i	0.555260	−	0.320579i
$780$		0			0
$781$	8492.94	−	14710.2i	0.389118	−	0.673972i
$782$	−994.391			−0.0454723
$783$		0			0
$784$	−18349.8	−	11904.5i	−0.835907	−	0.542297i
$785$	−15820.2	−	9133.82i	−0.719297	−	0.415286i
$786$		0			0
$787$	985.646	−	569.063i	0.0446436	−	0.0257750i	−0.477512	−	0.878625i	$-0.658461\pi$
$787$	985.646	−	569.063i	0.0446436	−	0.0257750i	0.522156	+	0.852850i	$0.325128\pi$
$788$	−24770.2	+	14301.1i	−1.11980	+	0.646516i
$789$		0			0
$790$	−917.006	−	529.434i	−0.0412982	−	0.0238436i
$791$	−25536.2	−	7557.78i	−1.14787	−	0.339726i
$792$		0			0
$793$	4166.65			0.186585
$794$	−352.617	+	610.751i	−0.0157606	+	0.0272982i
$795$		0			0
$796$	−6098.53	+	3520.99i	−0.271554	+	0.156782i
$797$	−10685.7	−	18508.2i	−0.474914	−	0.822576i	0.524673	−	0.851304i	$-0.324188\pi$
$797$	−10685.7	−	18508.2i	−0.474914	−	0.822576i	−0.999587	+	0.0287282i	$0.990854\pi$
$798$		0			0
$799$	−4963.27	+	8596.63i	−0.219759	+	0.380634i
$800$		−	3820.87i		−	0.168860i
$801$		0			0
$802$	1202.09			0.0529267
$803$	−17911.6	+	31023.8i	−0.787156	+	1.36339i
$804$		0			0
$805$	12744.2	+	53029.7i	0.557982	+	2.32180i
$806$	−204.668	+	118.165i	−0.00894433	+	0.00516401i
$807$		0			0
$808$	1240.54	+	716.225i	0.0540124	+	0.0311841i
$809$		−	16824.0i		−	0.731150i	−0.930782	−	0.365575i	$-0.880872\pi$
$809$		−	16824.0i		−	0.731150i	0.930782	−	0.365575i	$-0.119128\pi$
$810$		0			0
$811$		−	32964.6i		−	1.42731i	−0.700500	−	0.713653i	$-0.747039\pi$
$811$		−	32964.6i		−	1.42731i	0.700500	−	0.713653i	$-0.252961\pi$
$812$	−10223.9	+	9706.56i	−0.441856	+	0.419499i
$813$		0			0
$814$	686.391	+	1188.86i	0.0295553	+	0.0511912i
$815$	16325.8	+	28277.0i	0.701677	+	1.21534i
$816$		0			0
$817$	19557.5	+	11291.5i	0.837491	+	0.483526i
$818$	−83.1491			−0.00355408
$819$		0			0
$820$	28734.8			1.22373
$821$	18735.6	+	10817.0i	0.796438	+	0.459824i	0.842224	−	0.539127i	$-0.181246\pi$
$821$	18735.6	+	10817.0i	0.796438	+	0.459824i	−0.0457860	+	0.998951i	$0.514579\pi$
$822$		0			0
$823$	12194.5	+	21121.4i	0.516492	+	0.894590i	0.999817	+	0.0191488i	$0.00609561\pi$
$823$	12194.5	+	21121.4i	0.516492	+	0.894590i	−0.483325	+	0.875441i	$0.660571\pi$
$824$	652.480	+	1130.13i	0.0275852	+	0.0477790i
$825$		0			0
$826$	−281.191	+	266.963i	−0.0118449	+	0.0112456i
$827$			29015.7i			1.22004i	0.792385	+	0.610022i	$0.208839\pi$
$827$			29015.7i			1.22004i	−0.792385	+	0.610022i	$0.791161\pi$
$828$		0			0
$829$			17685.2i			0.740931i	0.928846	+	0.370466i	$0.120802\pi$
$829$			17685.2i			0.740931i	−0.928846	+	0.370466i	$0.879198\pi$
$830$	555.502	+	320.720i	0.0232311	+	0.0134125i
$831$		0			0
$832$	−8319.85	+	4803.47i	−0.346682	+	0.200157i
$833$	−1112.41	+	21415.0i	−0.0462698	+	0.890741i
$834$		0			0
$835$	14826.0	−	25679.4i	0.614461	−	1.06428i
$836$	−20781.4			−0.859735
$837$		0			0
$838$		−	608.922i		−	0.0251013i
$839$	18875.6	−	32693.4i	0.776706	−	1.34529i	−0.157124	−	0.987579i	$-0.550222\pi$
$839$	18875.6	−	32693.4i	0.776706	−	1.34529i	0.933831	−	0.357716i	$-0.116444\pi$
$840$		0			0
$841$	−7656.83	−	13262.0i	−0.313946	−	0.543771i
$842$	−171.623	+	99.0869i	−0.00702439	+	0.00405553i
$843$		0			0
$844$	−3344.64	+	5793.08i	−0.136407	+	0.236263i
$845$	33350.3			1.35773
$846$		0			0
$847$	−204.553	+	691.145i	−0.00829815	+	0.0280378i
$848$	10591.4	+	6114.92i	0.428902	+	0.247626i
$849$		0			0
$850$	−1079.18	+	623.067i	−0.0435479	+	0.0251424i
$851$	53298.8	−	30772.1i	2.14696	−	1.23955i
$852$		0			0
$853$	−19616.3	−	11325.5i	−0.787398	−	0.454605i	0.0516476	−	0.998665i	$-0.483553\pi$
$853$	−19616.3	−	11325.5i	−0.787398	−	0.454605i	−0.839046	+	0.544061i	$0.816886\pi$
$854$	113.449	−	383.321i	0.00454583	−	0.0153595i
$855$		0			0
$856$	−2640.03			−0.105414
$857$	−6080.19	+	10531.2i	−0.242351	+	0.419765i	−0.961384	−	0.275212i	$-0.911252\pi$
$857$	−6080.19	+	10531.2i	−0.242351	+	0.419765i	0.719032	+	0.694977i	$0.244585\pi$
$858$		0			0
$859$	−12189.4	+	7037.53i	−0.484163	+	0.279531i	−0.722150	−	0.691737i	$-0.756846\pi$
$859$	−12189.4	+	7037.53i	−0.484163	+	0.279531i	0.237987	+	0.971268i	$0.423512\pi$
$860$	23274.9	+	40313.4i	0.922871	+	1.59846i
$861$		0			0
$862$	319.155	−	552.793i	0.0126107	−	0.0218425i
$863$			8687.35i			0.342666i	0.985213	+	0.171333i	$0.0548074\pi$
$863$			8687.35i			0.342666i	−0.985213	+	0.171333i	$0.945193\pi$
$864$		0			0
$865$	−14492.8			−0.569676
$866$	869.789	−	1506.52i	0.0341301	−	0.0591150i
$867$		0			0
$868$	−4416.57	−	18377.7i	−0.172705	−	0.718640i
$869$	−19124.4	+	11041.5i	−0.746549	+	0.431020i
$870$		0			0
$871$	−2235.59	−	1290.72i	−0.0869692	−	0.0502117i
$872$		−	1003.92i		−	0.0389875i
$873$		0			0
$874$		−	1117.65i		−	0.0432551i
$875$	18165.0	+	19133.0i	0.701814	+	0.739217i
$876$		0			0
$877$	−1604.18	−	2778.53i	−0.0617667	−	0.106983i	0.833488	−	0.552537i	$-0.186340\pi$
$877$	−1604.18	−	2778.53i	−0.0617667	−	0.106983i	−0.895255	+	0.445554i	$0.853007\pi$
$878$	72.3984	+	125.398i	0.00278283	+	0.00482001i
$879$		0			0
$880$	−37052.6	−	21392.4i	−1.41937	−	0.819473i
$881$	36469.9			1.39467			0.697334	−	0.716746i	$-0.254369\pi$
$881$	36469.9			1.39467			0.697334	+	0.716746i	$0.254369\pi$
$882$		0			0
$883$	4262.90			0.162467			0.0812333	−	0.996695i	$-0.474114\pi$
$883$	4262.90			0.162467			0.0812333	+	0.996695i	$0.474114\pi$
$884$	8176.27	+	4720.57i	0.311083	+	0.179604i
$885$		0			0
$886$	−762.203	−	1320.18i	−0.0289015	−	0.0500589i
$887$	−16289.3	−	28214.0i	−0.616620	−	1.06802i	−0.990098	−	0.140379i	$-0.955168\pi$
$887$	−16289.3	−	28214.0i	−0.616620	−	1.06802i	0.373478	−	0.927639i	$-0.378165\pi$
$888$		0			0
$889$	−23527.1	−	24781.0i	−0.887598	−	0.934901i
$890$			63.0005i			0.00237279i
$891$		0			0
$892$		−	9058.85i		−	0.340037i
$893$	−9662.20	−	5578.47i	−0.362075	−	0.209044i
$894$		0			0
$895$	46156.3	−	26648.4i	1.72384	−	0.995258i
$896$	865.136	+	3599.89i	0.0322569	+	0.134223i
$897$		0			0
$898$	299.605	−	518.932i	0.0111336	−	0.0192839i
$899$	−12167.4			−0.451397
$900$		0			0
$901$		−	11989.9i		−	0.443329i
$902$	−359.450	+	622.586i	−0.0132687	+	0.0229821i
$903$		0			0
$904$	1125.59	+	1949.58i	0.0414121	+	0.0717279i
$905$	−5917.10	+	3416.24i	−0.217338	+	0.125480i
$906$		0			0
$907$	−2421.00	+	4193.30i	−0.0886307	+	0.153513i	−0.906933	−	0.421276i	$-0.861582\pi$
$907$	−2421.00	+	4193.30i	−0.0886307	+	0.153513i	0.818302	+	0.574789i	$0.194916\pi$
$908$	−28013.7			−1.02386
$909$		0			0
$910$	−176.290	+	595.650i	−0.00642193	+	0.0216985i
$911$	30705.9	+	17728.1i	1.11672	+	0.644740i	0.940562	−	0.339622i	$-0.110299\pi$
$911$	30705.9	+	17728.1i	1.11672	+	0.644740i	0.176160	+	0.984362i	$0.443633\pi$
$912$		0			0
$913$	11585.1	−	6688.69i	0.419948	−	0.242457i
$914$	−593.219	+	342.495i	−0.0214682	+	0.0123947i
$915$		0			0
$916$	21745.5	+	12554.7i	0.784378	+	0.452861i
$917$	11554.9	−	39041.7i	0.416113	−	1.40597i
$918$		0			0
$919$	16541.1			0.593732			0.296866	−	0.954919i	$-0.404059\pi$
$919$	16541.1			0.593732			0.296866	+	0.954919i	$0.404059\pi$
$920$	2305.16	−	3992.66i	0.0826076	−	0.143080i
$921$		0			0
$922$	310.865	−	179.478i	0.0111039	−	0.00641084i
$923$	−4336.67	−	7511.33i	−0.154651	−	0.267864i
$924$		0			0
$925$	38562.5	−	66792.1i	1.37073	−	2.37418i
$926$			688.023i			0.0244167i
$927$		0			0
$928$	1787.91			0.0632446
$929$	20349.3	−	35246.0i	0.718664	−	1.24476i	−0.242866	−	0.970060i	$-0.578087\pi$
$929$	20349.3	−	35246.0i	0.718664	−	1.24476i	0.961529	−	0.274702i	$-0.0885793\pi$
$930$		0			0
$931$	−24069.5	−	1250.30i	−0.847309	−	0.0440137i
$932$	47622.8	−	27495.0i	1.67375	−	0.966341i
$933$		0			0
$934$	1133.44	+	654.392i	0.0397080	+	0.0229254i
$935$			41945.1i			1.46712i
$936$		0			0
$937$		−	13937.5i		−	0.485933i	−0.970035	−	0.242967i	$-0.921879\pi$
$937$		−	13937.5i		−	0.485933i	0.970035	−	0.242967i	$-0.0781205\pi$
$938$	−179.613	+	170.525i	−0.00625222	+	0.00593587i
$939$		0			0
$940$	−11498.8	−	19916.5i	−0.398988	−	0.691068i
$941$	−16191.6	−	28044.6i	−0.560925	−	0.971550i	−0.997416	−	0.0718418i	$-0.977112\pi$
$941$	−16191.6	−	28044.6i	−0.560925	−	0.971550i	0.436491	−	0.899709i	$-0.356221\pi$
$942$		0			0
$943$	27911.6	+	16114.8i	0.963868	+	0.556489i
$944$	−13636.3			−0.470152
$945$		0			0
$946$	−1164.61			−0.0400261
$947$	−6500.78	−	3753.23i	−0.223070	−	0.128789i	0.384301	−	0.923208i	$-0.374442\pi$
$947$	−6500.78	−	3753.23i	−0.223070	−	0.128789i	−0.607371	+	0.794418i	$0.707776\pi$
$948$		0			0
$949$	9146.02	+	15841.4i	0.312848	+	0.541868i
$950$	−700.298	−	1212.95i	−0.0239165	−	0.0414246i
$951$		0			0
$952$	1314.59	−	1248.08i	0.0447544	−	0.0424899i
$953$			469.935i			0.0159735i	0.999968	+	0.00798673i	$0.00254228\pi$
$953$			469.935i			0.0159735i	−0.999968	+	0.00798673i	$0.997458\pi$
$954$		0			0
$955$			33198.8i			1.12491i
$956$	−8279.21	−	4780.00i	−0.280093	−	0.161712i
$957$		0			0
$958$	−593.046	+	342.395i	−0.0200005	+	0.0115473i
$959$	−9342.77	−	38876.0i	−0.314592	−	1.30904i
$960$		0			0
$961$	−6739.00	+	11672.3i	−0.226209	+	0.391806i
$962$	700.970			0.0234929
$963$		0			0
$964$		−	34974.1i		−	1.16850i
$965$	3444.27	−	5965.64i	0.114896	−	0.199006i
$966$		0			0
$967$	−16008.3	−	27727.1i	−0.532359	−	0.922073i	−0.999286	−	0.0377773i	$-0.987972\pi$
$967$	−16008.3	−	27727.1i	−0.532359	−	0.922073i	0.466927	−	0.884296i	$-0.345361\pi$
$968$	52.7659	−	30.4644i	0.00175203	−	0.00101153i
$969$		0			0
$970$	−1180.01	+	2043.83i	−0.0390595	+	0.0676530i
$971$	2588.27			0.0855424			0.0427712	−	0.999085i	$-0.486381\pi$
$971$	2588.27			0.0855424			0.0427712	+	0.999085i	$0.486381\pi$
$972$		0			0
$973$	51706.9	+	15303.3i	1.70365	+	0.504216i
$974$	−698.086	−	403.040i	−0.0229652	−	0.0132590i
$975$		0			0
$976$	12175.6	−	7029.57i	0.399314	−	0.230544i
$977$	31756.0	−	18334.4i	1.03988	−	0.600376i	0.120083	−	0.992764i	$-0.461684\pi$
$977$	31756.0	−	18334.4i	1.03988	−	0.600376i	0.919800	+	0.392387i	$0.128351\pi$
$978$		0			0
$979$	1137.86	+	656.946i	0.0371464	+	0.0214465i
$980$	−41678.2	−	27038.8i	−1.35853	−	0.881351i
$981$		0			0
$982$	1461.29			0.0474865
$983$	−4505.33	+	7803.46i	−0.146183	+	0.253196i	−0.929814	−	0.368031i	$-0.880032\pi$
$983$	−4505.33	+	7803.46i	−0.146183	+	0.253196i	0.783631	+	0.621227i	$0.213365\pi$
$984$		0			0
$985$	−56193.3	+	32443.2i	−1.81773	+	1.04947i
$986$	−291.554	−	504.986i	−0.00941679	−	0.0163104i
$987$		0			0
$988$	−5305.70	+	9189.73i	−0.170847	+	0.295915i
$989$			52211.4i			1.67869i
$990$		0			0
$991$	13431.5			0.430540			0.215270	−	0.976555i	$-0.430937\pi$
$991$	13431.5			0.430540			0.215270	+	0.976555i	$0.430937\pi$
$992$	−1198.54	+	2075.93i	−0.0383604	+	0.0664422i
$993$		0			0
$994$	−809.100	+	194.445i	−0.0258180	+	0.00620465i
$995$	−13835.0	+	7987.67i	−0.440805	+	0.254499i
$996$		0			0
$997$	13651.7	+	7881.82i	0.433655	+	0.250371i	0.700902	−	0.713257i	$-0.252781\pi$
$997$	13651.7	+	7881.82i	0.433655	+	0.250371i	−0.267248	+	0.963628i	$0.586114\pi$
$998$		−	815.644i		−	0.0258705i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.o.a.62.11		44
3.2	odd	2		63.4.o.a.20.11	✓	44
7.6	odd	2	inner	189.4.o.a.62.12		44
9.2	odd	6		567.4.c.c.566.4		44
9.4	even	3		63.4.o.a.41.12	yes	44
9.5	odd	6	inner	189.4.o.a.125.12		44
9.7	even	3		567.4.c.c.566.41		44
21.20	even	2		63.4.o.a.20.12	yes	44
63.13	odd	6		63.4.o.a.41.11	yes	44
63.20	even	6		567.4.c.c.566.42		44
63.34	odd	6		567.4.c.c.566.3		44
63.41	even	6	inner	189.4.o.a.125.11		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.11	✓	44	3.2	odd	2
63.4.o.a.20.12	yes	44	21.20	even	2
63.4.o.a.41.11	yes	44	63.13	odd	6
63.4.o.a.41.12	yes	44	9.4	even	3
189.4.o.a.62.11		44	1.1	even	1	trivial
189.4.o.a.62.12		44	7.6	odd	2	inner
189.4.o.a.125.11		44	63.41	even	6	inner
189.4.o.a.125.12		44	9.5	odd	6	inner
567.4.c.c.566.3		44	63.34	odd	6
567.4.c.c.566.4		44	9.2	odd	6
567.4.c.c.566.41		44	9.7	even	3
567.4.c.c.566.42		44	63.20	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0847887 + 0.0489528i) q^{2} +(-3.99521 - 6.91990i) q^{4} +(-9.06347 - 15.6984i) q^{5} +(12.7516 + 13.4312i) q^{7} -1.56555i q^{8} +O(q^{10})\)	\(q+(0.0847887 + 0.0489528i) q^{2} +(-3.99521 - 6.91990i) q^{4} +(-9.06347 - 15.6984i) q^{5} +(12.7516 + 13.4312i) q^{7} -1.56555i q^{8} -1.77473i q^{10} +(-32.0537 - 18.5062i) q^{11} +(-16.3673 + 9.44964i) q^{13} +(0.423698 + 1.76304i) q^{14} +(-31.8850 + 55.2265i) q^{16} +62.5187 q^{17} +70.2680i q^{19} +(-72.4209 + 125.437i) q^{20} +(-1.81186 - 3.13823i) q^{22} +(-140.692 + 81.2288i) q^{23} +(-101.793 + 176.311i) q^{25} -1.85034 q^{26} +(41.9972 - 141.900i) q^{28} +(-82.5015 - 47.6323i) q^{29} +(110.611 - 63.8612i) q^{31} +(-16.2534 + 9.38392i) q^{32} +(5.30088 + 3.06046i) q^{34} +(95.2742 - 321.913i) q^{35} -378.832 q^{37} +(-3.43981 + 5.95793i) q^{38} +(-24.5766 + 14.1893i) q^{40} +(-99.1937 - 171.809i) q^{41} +(160.692 - 278.327i) q^{43} +295.744i q^{44} -15.9055 q^{46} +(-79.3885 + 137.505i) q^{47} +(-17.7932 + 342.538i) q^{49} +(-17.2618 + 9.96610i) q^{50} +(130.781 + 75.5066i) q^{52} -191.780i q^{53} +670.922i q^{55} +(21.0272 - 19.9633i) q^{56} +(-4.66346 - 8.07736i) q^{58} +(106.918 + 185.187i) q^{59} +(-190.929 - 110.233i) q^{61} +12.5047 q^{62} +508.323 q^{64} +(296.688 + 171.293i) q^{65} +(68.2947 + 118.290i) q^{67} +(-249.775 - 432.623i) q^{68} +(23.8367 - 22.6306i) q^{70} +458.924i q^{71} -967.869i q^{73} +(-32.1207 - 18.5449i) q^{74} +(486.248 - 280.735i) q^{76} +(-160.176 - 666.503i) q^{77} +(298.318 - 516.702i) q^{79} +1155.96 q^{80} -19.4232i q^{82} +(-180.715 + 313.007i) q^{83} +(-566.636 - 981.443i) q^{85} +(27.2498 - 15.7327i) q^{86} +(-28.9724 + 50.1817i) q^{88} -35.4987 q^{89} +(-335.629 - 99.3336i) q^{91} +(1124.19 + 649.052i) q^{92} +(-13.4625 + 7.77258i) q^{94} +(1103.09 - 636.872i) q^{95} +(-1151.63 - 664.894i) q^{97} +(-18.2769 + 28.1723i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7	\( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7} + 18 q^{11} - 204 q^{14} - 242 q^{16} - 34 q^{22} + 102 q^{23} - 352 q^{25} + 300 q^{28} - 246 q^{29} - 1068 q^{32} + 328 q^{37} - 170 q^{43} + 968 q^{46} - 79 q^{49} - 288 q^{50} - 1212 q^{56} - 538 q^{58} - 808 q^{64} - 4350 q^{65} - 590 q^{67} + 384 q^{70} + 5304 q^{74} + 2787 q^{77} - 302 q^{79} - 612 q^{85} + 13692 q^{86} + 1294 q^{88} + 210 q^{91} + 10194 q^{92} - 6336 q^{95}+O(q^{100}) \) 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7 + 18 * q^11 - 204 * q^14 - 242 * q^16 - 34 * q^22 + 102 * q^23 - 352 * q^25 + 300 * q^28 - 246 * q^29 - 1068 * q^32 + 328 * q^37 - 170 * q^43 + 968 * q^46 - 79 * q^49 - 288 * q^50 - 1212 * q^56 - 538 * q^58 - 808 * q^64 - 4350 * q^65 - 590 * q^67 + 384 * q^70 + 5304 * q^74 + 2787 * q^77 - 302 * q^79 - 612 * q^85 + 13692 * q^86 + 1294 * q^88 + 210 * q^91 + 10194 * q^92 - 6336 * q^95

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