LMFDB - Embedded newform 144.4.k.b.109.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [144,4,Mod(37,144)] 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("144.37"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(144, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	144.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$8.49627504083$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.8
Character	$\chi$	$=$	144.109
Dual form			144.4.k.b.37.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.987020 - 2.65062i) q^{2} +(-6.05158 - 5.23243i) q^{4} +(11.8955 - 11.8955i) q^{5} +0.485059i q^{7} +(-19.8422 + 10.8759i) q^{8} +(-19.7893 - 43.2714i) q^{10} +(30.9469 - 30.9469i) q^{11} +(-18.4511 - 18.4511i) q^{13} +(1.28571 + 0.478764i) q^{14} +(9.24327 + 63.3290i) q^{16} -135.964 q^{17} +(65.8832 + 65.8832i) q^{19} +(-134.229 + 9.74414i) q^{20} +(-51.4834 - 112.574i) q^{22} -128.108i q^{23} -158.004i q^{25} +(-67.1184 + 30.6952i) q^{26} +(2.53804 - 2.93538i) q^{28} +(-6.64817 - 6.64817i) q^{29} -15.1323 q^{31} +(176.984 + 38.0066i) q^{32} +(-134.199 + 360.389i) q^{34} +(5.77001 + 5.77001i) q^{35} +(51.4363 - 51.4363i) q^{37} +(239.660 - 109.603i) q^{38} +(-106.658 + 365.407i) q^{40} +410.253i q^{41} +(69.9911 - 69.9911i) q^{43} +(-349.206 + 25.3501i) q^{44} +(-339.567 - 126.446i) q^{46} +487.269 q^{47} +342.765 q^{49} +(-418.809 - 155.953i) q^{50} +(15.1142 + 208.202i) q^{52} +(217.138 - 217.138i) q^{53} -736.257i q^{55} +(-5.27547 - 9.62466i) q^{56} +(-24.1837 + 11.0599i) q^{58} +(293.944 - 293.944i) q^{59} +(207.076 + 207.076i) q^{61} +(-14.9359 + 40.1099i) q^{62} +(275.428 - 431.605i) q^{64} -438.968 q^{65} +(284.693 + 284.693i) q^{67} +(822.798 + 711.423i) q^{68} +(20.9892 - 9.59899i) q^{70} +614.701i q^{71} -486.171i q^{73} +(-85.5694 - 187.107i) q^{74} +(-53.9681 - 743.427i) q^{76} +(15.0111 + 15.0111i) q^{77} +960.347 q^{79} +(863.281 + 643.375i) q^{80} +(1087.42 + 404.928i) q^{82} +(-463.472 - 463.472i) q^{83} +(-1617.36 + 1617.36i) q^{85} +(-116.437 - 254.603i) q^{86} +(-277.480 + 950.633i) q^{88} -1278.38i q^{89} +(8.94987 - 8.94987i) q^{91} +(-670.318 + 775.258i) q^{92} +(480.945 - 1291.57i) q^{94} +1567.42 q^{95} -994.918 q^{97} +(338.316 - 908.539i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{4} - 84 q^{8} + 72 q^{10} + 40 q^{11} + 348 q^{14} - 192 q^{16} + 24 q^{19} - 80 q^{20} + 704 q^{22} + 20 q^{26} - 344 q^{28} - 400 q^{29} - 744 q^{31} + 960 q^{32} - 704 q^{34} + 456 q^{35}+ \cdots - 6760 q^{98}+O(q^{100}) $ 24 * q - 20 * q^4 - 84 * q^8 + 72 * q^10 + 40 * q^11 + 348 * q^14 - 192 * q^16 + 24 * q^19 - 80 * q^20 + 704 * q^22 + 20 * q^26 - 344 * q^28 - 400 * q^29 - 744 * q^31 + 960 * q^32 - 704 * q^34 + 456 * q^35 + 16 * q^37 - 1256 * q^38 + 1744 * q^40 + 1240 * q^43 + 200 * q^44 - 1432 * q^46 - 1176 * q^49 - 708 * q^50 + 1008 * q^52 - 752 * q^53 - 1344 * q^56 + 1936 * q^58 + 1376 * q^59 - 912 * q^61 + 996 * q^62 - 56 * q^64 - 976 * q^65 - 2256 * q^67 + 1568 * q^68 - 1760 * q^70 + 2740 * q^74 - 1880 * q^76 - 1904 * q^77 + 5992 * q^79 - 712 * q^80 - 40 * q^82 - 2680 * q^83 - 240 * q^85 + 1712 * q^86 - 3936 * q^88 - 3496 * q^91 - 5296 * q^92 + 5272 * q^94 + 7728 * q^95 - 6760 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	0.987020	−	2.65062i	0.348964	−	0.937136i
$2$	0.987020	−	2.65062i	0.348964	−	0.937136i
$3$		0			0
$3$		0			0
$4$	−6.05158	−	5.23243i	−0.756448	−	0.654054i
$5$	11.8955	−	11.8955i	1.06396	−	1.06396i	0.0661534	−	0.997809i	$-0.478927\pi$
$5$	11.8955	−	11.8955i	1.06396	−	1.06396i	0.997809	−	0.0661534i	$-0.0210727\pi$
$6$		0			0
$7$			0.485059i			0.0261907i	0.999914	+	0.0130954i	$0.00416851\pi$
$7$			0.485059i			0.0261907i	−0.999914	+	0.0130954i	$0.995831\pi$
$8$	−19.8422	+	10.8759i	−0.876911	+	0.480653i
$9$		0			0
$10$	−19.7893	−	43.2714i	−0.625793	−	1.36836i
$11$	30.9469	−	30.9469i	0.848260	−	0.848260i	−0.141656	−	0.989916i	$-0.545243\pi$
$11$	30.9469	−	30.9469i	0.848260	−	0.848260i	0.989916	+	0.141656i	$0.0452428\pi$
$12$		0			0
$13$	−18.4511	−	18.4511i	−0.393647	−	0.393647i	0.482338	−	0.875985i	$-0.339788\pi$
$13$	−18.4511	−	18.4511i	−0.393647	−	0.393647i	−0.875985	+	0.482338i	$0.839788\pi$
$14$	1.28571	+	0.478764i	0.0245443	+	0.00913964i
$15$		0			0
$16$	9.24327	+	63.3290i	0.144426	+	0.989516i
$17$	−135.964			−1.93977			−0.969886	−	0.243558i	$-0.921685\pi$
$17$	−135.964			−1.93977			−0.969886	+	0.243558i	$0.921685\pi$
$18$		0			0
$19$	65.8832	+	65.8832i	0.795508	+	0.795508i	0.982384	−	0.186876i	$-0.0598362\pi$
$19$	65.8832	+	65.8832i	0.795508	+	0.795508i	−0.186876	+	0.982384i	$0.559836\pi$
$20$	−134.229	+	9.74414i	−1.50072	+	0.108943i
$21$		0			0
$22$	−51.4834	−	112.574i	−0.498922	−	1.09095i
$23$		−	128.108i		−	1.16141i	−0.814114	−	0.580705i	$-0.802777\pi$
$23$		−	128.108i		−	1.16141i	0.814114	−	0.580705i	$-0.197223\pi$
$24$		0			0
$25$		−	158.004i		−	1.26403i
$26$	−67.1184	+	30.6952i	−0.506269	+	0.231532i
$27$		0			0
$28$	2.53804	−	2.93538i	0.0171302	−	0.0198119i
$29$	−6.64817	−	6.64817i	−0.0425702	−	0.0425702i	0.685501	−	0.728071i	$-0.259583\pi$
$29$	−6.64817	−	6.64817i	−0.0425702	−	0.0425702i	−0.728071	+	0.685501i	$0.759583\pi$
$30$		0			0
$31$	−15.1323			−0.0876722			−0.0438361	−	0.999039i	$-0.513958\pi$
$31$	−15.1323			−0.0876722			−0.0438361	+	0.999039i	$0.513958\pi$
$32$	176.984	+	38.0066i	0.977710	+	0.209959i
$33$		0			0
$34$	−134.199	+	360.389i	−0.676912	+	1.81783i
$35$	5.77001	+	5.77001i	0.0278660	+	0.0278660i
$36$		0			0
$37$	51.4363	−	51.4363i	0.228542	−	0.228542i	−0.583541	−	0.812084i	$-0.698333\pi$
$37$	51.4363	−	51.4363i	0.228542	−	0.228542i	0.812084	+	0.583541i	$0.198333\pi$
$38$	239.660	−	109.603i	1.02310	−	0.467895i
$39$		0			0
$40$	−106.658	+	365.407i	−0.421604	+	1.44440i
$41$			410.253i			1.56270i	0.624092	+	0.781350i	$0.285469\pi$
$41$			410.253i			1.56270i	−0.624092	+	0.781350i	$0.714531\pi$
$42$		0			0
$43$	69.9911	−	69.9911i	0.248222	−	0.248222i	−0.572019	−	0.820241i	$-0.693839\pi$
$43$	69.9911	−	69.9911i	0.248222	−	0.248222i	0.820241	+	0.572019i	$0.193839\pi$
$44$	−349.206	+	25.3501i	−1.19647	+	0.0868562i
$45$		0			0
$46$	−339.567	−	126.446i	−1.08840	−	0.405291i
$47$	487.269			1.51225			0.756123	−	0.654430i	$-0.227091\pi$
$47$	487.269			1.51225			0.756123	+	0.654430i	$0.227091\pi$
$48$		0			0
$49$	342.765			0.999314
$50$	−418.809	−	155.953i	−1.18457	−	0.441103i
$51$		0			0
$52$	15.1142	+	208.202i	0.0403068	+	0.555239i
$53$	217.138	−	217.138i	0.562757	−	0.562757i	−0.367333	−	0.930090i	$-0.619729\pi$
$53$	217.138	−	217.138i	0.562757	−	0.562757i	0.930090	+	0.367333i	$0.119729\pi$
$54$		0			0
$55$		−	736.257i		−	1.80503i
$56$	−5.27547	−	9.62466i	−0.0125887	−	0.0229670i
$57$		0			0
$58$	−24.1837	+	11.0599i	−0.0547495	+	0.0250386i
$59$	293.944	−	293.944i	0.648613	−	0.648613i	−0.304044	−	0.952658i	$-0.598337\pi$
$59$	293.944	−	293.944i	0.648613	−	0.648613i	0.952658	+	0.304044i	$0.0983371\pi$
$60$		0			0
$61$	207.076	+	207.076i	0.434646	+	0.434646i	0.890205	−	0.455559i	$-0.150561\pi$
$61$	207.076	+	207.076i	0.434646	+	0.434646i	−0.455559	+	0.890205i	$0.650561\pi$
$62$	−14.9359	+	40.1099i	−0.0305945	+	0.0821608i
$63$		0			0
$64$	275.428	−	431.605i	0.537946	−	0.842979i
$65$	−438.968			−0.837651
$66$		0			0
$67$	284.693	+	284.693i	0.519115	+	0.519115i	0.917304	−	0.398188i	$-0.130361\pi$
$67$	284.693	+	284.693i	0.519115	+	0.519115i	−0.398188	+	0.917304i	$0.630361\pi$
$68$	822.798	+	711.423i	1.46734	+	1.26872i
$69$		0			0
$70$	20.9892	−	9.59899i	0.0358384	−	0.0163900i
$71$			614.701i			1.02749i	0.857944	+	0.513744i	$0.171742\pi$
$71$			614.701i			1.02749i	−0.857944	+	0.513744i	$0.828258\pi$
$72$		0			0
$73$		−	486.171i		−	0.779479i	−0.920925	−	0.389740i	$-0.872565\pi$
$73$		−	486.171i		−	0.779479i	0.920925	−	0.389740i	$-0.127435\pi$
$74$	−85.5694	−	187.107i	−0.134422	−	0.293928i
$75$		0			0
$76$	−53.9681	−	743.427i	−0.0814548	−	1.12207i
$77$	15.0111	+	15.0111i	0.0222166	+	0.0222166i
$78$		0			0
$79$	960.347			1.36769			0.683845	−	0.729628i	$-0.260307\pi$
$79$	960.347			1.36769			0.683845	+	0.729628i	$0.260307\pi$
$80$	863.281	+	643.375i	1.20647	+	0.899144i
$81$		0			0
$82$	1087.42	+	404.928i	1.46446	+	0.545327i
$83$	−463.472	−	463.472i	−0.612923	−	0.612923i	0.330784	−	0.943707i	$-0.392687\pi$
$83$	−463.472	−	463.472i	−0.612923	−	0.612923i	−0.943707	+	0.330784i	$0.892687\pi$
$84$		0			0
$85$	−1617.36	+	1617.36i	−2.06385	+	2.06385i
$86$	−116.437	−	254.603i	−0.145997	−	0.319238i
$87$		0			0
$88$	−277.480	+	950.633i	−0.336130	+	1.15157i
$89$		−	1278.38i		−	1.52257i	−0.648420	−	0.761283i	$-0.724570\pi$
$89$		−	1278.38i		−	1.52257i	0.648420	−	0.761283i	$-0.275430\pi$
$90$		0			0
$91$	8.94987	−	8.94987i	0.0103099	−	0.0103099i
$92$	−670.318	+	775.258i	−0.759625	+	0.878546i
$93$		0			0
$94$	480.945	−	1291.57i	0.527720	−	1.41718i
$95$	1567.42			1.69278
$96$		0			0
$97$	−994.918			−1.04143			−0.520714	−	0.853731i	$-0.674334\pi$
$97$	−994.918			−1.04143			−0.520714	+	0.853731i	$0.674334\pi$
$98$	338.316	−	908.539i	0.348725	−	0.936493i
$99$		0			0
$100$	−826.747	+	956.175i	−0.826747	+	0.956175i
$101$	−1317.80	+	1317.80i	−1.29828	+	1.29828i	−0.368750	+	0.929529i	$0.620214\pi$
$101$	−1317.80	+	1317.80i	−1.29828	+	1.29828i	−0.929529	+	0.368750i	$0.879786\pi$
$102$		0			0
$103$			1345.19i			1.28685i	0.765511	+	0.643423i	$0.222486\pi$
$103$			1345.19i			1.28685i	−0.765511	+	0.643423i	$0.777514\pi$
$104$	566.783	+	165.438i	0.534401	+	0.155986i
$105$		0			0
$106$	−361.230	−	789.868i	−0.330998	−	0.723762i
$107$	−437.734	+	437.734i	−0.395489	+	0.395489i	−0.876639	−	0.481149i	$-0.840219\pi$
$107$	−437.734	+	437.734i	−0.395489	+	0.395489i	0.481149	+	0.876639i	$0.340219\pi$
$108$		0			0
$109$	173.959	+	173.959i	0.152864	+	0.152864i	0.779396	−	0.626532i	$-0.215526\pi$
$109$	173.959	+	173.959i	0.152864	+	0.152864i	−0.626532	+	0.779396i	$0.715526\pi$
$110$	−1951.54	−	726.700i	−1.69156	−	0.629892i
$111$		0			0
$112$	−30.7183	+	4.48354i	−0.0259162	+	0.00378263i
$113$	−312.932			−0.260514			−0.130257	−	0.991480i	$-0.541580\pi$
$113$	−312.932			−0.260514			−0.130257	+	0.991480i	$0.541580\pi$
$114$		0			0
$115$	−1523.91	−	1523.91i	−1.23570	−	1.23570i
$116$	5.44583	+	75.0181i	0.00435891	+	0.0600453i
$117$		0			0
$118$	−489.005	−	1069.26i	−0.381496	−	0.834182i
$119$		−	65.9507i		−	0.0508041i
$120$		0			0
$121$		−	584.427i		−	0.439089i
$122$	753.269	−	344.492i	0.558998	−	0.255646i
$123$		0			0
$124$	91.5743	+	79.1787i	0.0663194	+	0.0573424i
$125$	−392.601	−	392.601i	−0.280922	−	0.280922i
$126$		0			0
$127$	1457.94			1.01867			0.509335	−	0.860569i	$-0.329892\pi$
$127$	1457.94			1.01867			0.509335	+	0.860569i	$0.329892\pi$
$128$	−872.169	−	1156.06i	−0.602262	−	0.798298i
$129$		0			0
$130$	−433.271	+	1163.54i	−0.292310	+	0.784993i
$131$	203.507	+	203.507i	0.135729	+	0.135729i	0.771707	−	0.635978i	$-0.219403\pi$
$131$	203.507	+	203.507i	0.135729	+	0.135729i	−0.635978	+	0.771707i	$0.719403\pi$
$132$		0			0
$133$	−31.9573	+	31.9573i	−0.0208349	+	0.0208349i
$134$	1035.61	−	473.615i	0.667634	−	0.305329i
$135$		0			0
$136$	2697.83	−	1478.74i	1.70101	−	0.932357i
$137$			432.979i			0.270014i	0.990845	+	0.135007i	$0.0431056\pi$
$137$			432.979i			0.270014i	−0.990845	+	0.135007i	$0.956894\pi$
$138$		0			0
$139$	−1058.62	+	1058.62i	−0.645975	+	0.645975i	−0.952018	−	0.306043i	$-0.900995\pi$
$139$	−1058.62	+	1058.62i	−0.645975	+	0.645975i	0.306043	+	0.952018i	$0.400995\pi$
$140$	−4.72649	−	65.1089i	−0.00285329	−	0.0393050i
$141$		0			0
$142$	1629.34	+	606.723i	0.962895	+	0.358557i
$143$	−1142.01			−0.667829
$144$		0			0
$145$	−158.166			−0.0905861
$146$	−1288.65	−	479.860i	−0.730478	−	0.272010i
$147$		0			0
$148$	−580.407	+	42.1339i	−0.322359	+	0.0234012i
$149$	−1703.13	+	1703.13i	−0.936414	+	0.936414i	−0.998096	−	0.0616815i	$-0.980354\pi$
$149$	−1703.13	+	1703.13i	−0.936414	+	0.936414i	0.0616815	+	0.998096i	$0.480354\pi$
$150$		0			0
$151$		−	541.560i		−	0.291864i	−0.989295	−	0.145932i	$-0.953382\pi$
$151$		−	541.560i		−	0.291864i	0.989295	−	0.145932i	$-0.0466182\pi$
$152$	−2023.81	−	590.729i	−1.07995	−	0.315227i
$153$		0			0
$154$	54.6050	−	24.9725i	0.0285727	−	0.0130671i
$155$	−180.006	+	180.006i	−0.0932800	+	0.0932800i
$156$		0			0
$157$	−8.94805	−	8.94805i	−0.00454861	−	0.00454861i	0.704829	−	0.709377i	$-0.251024\pi$
$157$	−8.94805	−	8.94805i	−0.00454861	−	0.00454861i	−0.709377	+	0.704829i	$0.751024\pi$
$158$	947.882	−	2545.52i	0.477275	−	1.28171i
$159$		0			0
$160$	2557.42	−	1653.21i	1.26364	−	0.816859i
$161$	62.1402			0.0304182
$162$		0			0
$163$	−1308.41	−	1308.41i	−0.628727	−	0.628727i	0.319021	−	0.947748i	$-0.396646\pi$
$163$	−1308.41	−	1308.41i	−0.628727	−	0.628727i	−0.947748	+	0.319021i	$0.896646\pi$
$164$	2146.62	−	2482.68i	1.02209	−	1.18210i
$165$		0			0
$166$	−1685.94	+	771.031i	−0.788281	+	0.360504i
$167$		−	2374.12i		−	1.10009i	−0.835135	−	0.550045i	$-0.814610\pi$
$167$		−	2374.12i		−	1.10009i	0.835135	−	0.550045i	$-0.185390\pi$
$168$		0			0
$169$		−	1516.12i		−	0.690084i
$170$	2690.63	+	5883.36i	1.21390	+	2.65431i
$171$		0			0
$172$	−789.781	+	57.3331i	−0.350118	+	0.0254163i
$173$	1310.49	+	1310.49i	0.575922	+	0.575922i	0.933777	−	0.357855i	$-0.116492\pi$
$173$	1310.49	+	1310.49i	0.575922	+	0.575922i	−0.357855	+	0.933777i	$0.616492\pi$
$174$		0			0
$175$	76.6414			0.0331060
$176$	2245.89	+	1673.79i	0.961877	+	0.716855i
$177$		0			0
$178$	−3388.51	−	1261.79i	−1.42685	−	0.531321i
$179$	−248.652	−	248.652i	−0.103828	−	0.103828i	0.653285	−	0.757112i	$-0.273390\pi$
$179$	−248.652	−	248.652i	−0.103828	−	0.103828i	−0.757112	+	0.653285i	$0.773390\pi$
$180$		0			0
$181$	1152.86	−	1152.86i	0.473434	−	0.473434i	−0.429590	−	0.903024i	$-0.641342\pi$
$181$	1152.86	−	1152.86i	0.473434	−	0.473434i	0.903024	+	0.429590i	$0.141342\pi$
$182$	−14.8890	−	32.5564i	−0.00606399	−	0.0132596i
$183$		0			0
$184$	1393.30	+	2541.96i	0.558235	+	1.01845i
$185$		−	1223.72i		−	0.486321i
$186$		0			0
$187$	−4207.67	+	4207.67i	−1.64543	+	1.64543i
$188$	−2948.75	−	2549.60i	−1.14393	−	0.989090i
$189$		0			0
$190$	1547.08	−	4154.65i	0.590721	−	1.58637i
$191$	457.697			0.173392			0.0866959	−	0.996235i	$-0.472369\pi$
$191$	457.697			0.173392			0.0866959	+	0.996235i	$0.472369\pi$
$192$		0			0
$193$	−61.7567			−0.0230329			−0.0115164	−	0.999934i	$-0.503666\pi$
$193$	−61.7567			−0.0230329			−0.0115164	+	0.999934i	$0.503666\pi$
$194$	−982.004	+	2637.15i	−0.363422	+	0.975960i
$195$		0			0
$196$	−2074.27	−	1793.49i	−0.755929	−	0.653606i
$197$	613.568	−	613.568i	0.221903	−	0.221903i	−0.587396	−	0.809299i	$-0.699847\pi$
$197$	613.568	−	613.568i	0.221903	−	0.221903i	0.809299	+	0.587396i	$0.199847\pi$
$198$		0			0
$199$			3343.30i			1.19095i	0.803372	+	0.595477i	$0.203037\pi$
$199$			3343.30i			1.19095i	−0.803372	+	0.595477i	$0.796963\pi$
$200$	1718.44	+	3135.16i	0.607561	+	1.10845i
$201$		0			0
$202$	2192.29	+	4793.69i	0.763610	+	1.66972i
$203$	3.22476	−	3.22476i	0.00111494	−	0.00111494i
$204$		0			0
$205$	4880.15	+	4880.15i	1.66266	+	1.66266i
$206$	3565.58	+	1327.73i	1.20595	+	0.449063i
$207$		0			0
$208$	997.940	−	1339.04i	0.332667	−	0.446372i
$209$	4077.77			1.34959
$210$		0			0
$211$	−445.986	−	445.986i	−0.145512	−	0.145512i	0.630598	−	0.776110i	$-0.282810\pi$
$211$	−445.986	−	445.986i	−0.145512	−	0.145512i	−0.776110	+	0.630598i	$0.782810\pi$
$212$	−2450.18	+	177.868i	−0.793770	+	0.0576226i
$213$		0			0
$214$	728.215	+	1592.32i	0.232616	+	0.508639i
$215$		−	1665.15i		−	0.528198i
$216$		0			0
$217$		−	7.34006i		−	0.00229620i
$218$	632.799	−	289.398i	0.196599	−	0.0899104i
$219$		0			0
$220$	−3852.41	+	4455.52i	−1.18059	+	1.36541i
$221$	2508.68	+	2508.68i	0.763585	+	0.763585i
$222$		0			0
$223$	6100.84			1.83203			0.916014	−	0.401146i	$-0.131388\pi$
$223$	6100.84			1.83203			0.916014	+	0.401146i	$0.131388\pi$
$224$	−18.4355	+	85.8480i	−0.00549898	+	0.0256070i
$225$		0			0
$226$	−308.870	+	829.463i	−0.0909103	+	0.244137i
$227$	3652.90	+	3652.90i	1.06807	+	1.06807i	0.997507	+	0.0705613i	$0.0224790\pi$
$227$	3652.90	+	3652.90i	1.06807	+	1.06807i	0.0705613	+	0.997507i	$0.477521\pi$
$228$		0			0
$229$	1707.86	−	1707.86i	0.492832	−	0.492832i	−0.416365	−	0.909197i	$-0.636696\pi$
$229$	1707.86	−	1707.86i	0.492832	−	0.492832i	0.909197	+	0.416365i	$0.136696\pi$
$230$	−5543.43	+	2535.17i	−1.58923	+	0.726802i
$231$		0			0
$232$	204.220	+	59.6095i	0.0577917	+	0.0168688i
$233$		−	3019.27i		−	0.848924i	−0.905446	−	0.424462i	$-0.860463\pi$
$233$		−	3019.27i		−	0.848924i	0.905446	−	0.424462i	$-0.139537\pi$
$234$		0			0
$235$	5796.29	−	5796.29i	1.60897	−	1.60897i
$236$	−3316.86	+	240.783i	−0.914870	+	0.0664138i
$237$		0			0
$238$	−174.810	−	65.0946i	−0.0476103	−	0.0177288i
$239$	−2964.22			−0.802256			−0.401128	−	0.916022i	$-0.631382\pi$
$239$	−2964.22			−0.802256			−0.401128	+	0.916022i	$0.631382\pi$
$240$		0			0
$241$	−2606.84			−0.696769			−0.348384	−	0.937352i	$-0.613270\pi$
$241$	−2606.84			−0.696769			−0.348384	+	0.937352i	$0.613270\pi$
$242$	−1549.09	−	576.841i	−0.411486	−	0.153226i
$243$		0			0
$244$	−169.626	−	2336.65i	−0.0445049	−	0.613069i
$245$	4077.35	−	4077.35i	1.06323	−	1.06323i
$246$		0			0
$247$		−	2431.23i		−	0.626298i
$248$	300.258	−	164.578i	0.0768807	−	0.0421399i
$249$		0			0
$250$	−1428.14	+	653.131i	−0.361294	+	0.165230i
$251$	−3018.73	+	3018.73i	−0.759126	+	0.759126i	−0.976163	−	0.217037i	$-0.930361\pi$
$251$	−3018.73	+	3018.73i	−0.759126	+	0.759126i	0.217037	+	0.976163i	$0.430361\pi$
$252$		0			0
$253$	−3964.56	−	3964.56i	−0.985177	−	0.985177i
$254$	1439.01	−	3864.44i	0.355479	−	0.954632i
$255$		0			0
$256$	−3925.12	+	1170.73i	−0.958282	+	0.285824i
$257$	−1988.50			−0.482644			−0.241322	−	0.970445i	$-0.577581\pi$
$257$	−1988.50			−0.482644			−0.241322	+	0.970445i	$0.577581\pi$
$258$		0			0
$259$	24.9496	+	24.9496i	0.00598570	+	0.00598570i
$260$	2656.45	+	2296.87i	0.633639	+	0.547869i
$261$		0			0
$262$	740.284	−	338.554i	0.174561	−	0.0798318i
$263$			6049.85i			1.41844i	0.704987	+	0.709220i	$0.250953\pi$
$263$			6049.85i			1.41844i	−0.704987	+	0.709220i	$0.749047\pi$
$264$		0			0
$265$		−	5165.90i		−	1.19751i
$266$	53.1641	+	116.249i	0.0122545	+	0.0267958i
$267$		0			0
$268$	−233.205	−	3212.47i	−0.0531540	−	0.732213i
$269$	−3883.56	−	3883.56i	−0.880242	−	0.880242i	0.113317	−	0.993559i	$-0.463852\pi$
$269$	−3883.56	−	3883.56i	−0.880242	−	0.880242i	−0.993559	+	0.113317i	$0.963852\pi$
$270$		0			0
$271$	−3321.60			−0.744549			−0.372275	−	0.928123i	$-0.621422\pi$
$271$	−3321.60			−0.744549			−0.372275	+	0.928123i	$0.621422\pi$
$272$	−1256.75	−	8610.47i	−0.280154	−	1.91944i
$273$		0			0
$274$	1147.66	+	427.359i	0.253039	+	0.0942251i
$275$	−4889.75	−	4889.75i	−1.07223	−	1.07223i
$276$		0			0
$277$	−3603.29	+	3603.29i	−0.781591	+	0.781591i	−0.980099	−	0.198508i	$-0.936390\pi$
$277$	−3603.29	+	3603.29i	−0.781591	+	0.781591i	0.198508	+	0.980099i	$0.436390\pi$
$278$	1761.11	+	3850.86i	0.379944	+	0.830789i
$279$		0			0
$280$	−177.244	−	51.7356i	−0.0378298	−	0.0110421i
$281$		−	823.661i		−	0.174859i	−0.996171	−	0.0874297i	$-0.972135\pi$
$281$		−	823.661i		−	0.174859i	0.996171	−	0.0874297i	$-0.0278653\pi$
$282$		0			0
$283$	−2003.74	+	2003.74i	−0.420883	+	0.420883i	−0.885508	−	0.464624i	$-0.846189\pi$
$283$	−2003.74	+	2003.74i	−0.420883	+	0.420883i	0.464624	+	0.885508i	$0.346189\pi$
$284$	3216.38	−	3719.91i	0.672032	−	0.777240i
$285$		0			0
$286$	−1127.19	+	3027.03i	−0.233049	+	0.625847i
$287$	−198.997			−0.0409283
$288$		0			0
$289$	13573.2			2.76272
$290$	−156.113	+	419.239i	−0.0316113	+	0.0848915i
$291$		0			0
$292$	−2543.86	+	2942.10i	−0.509822	+	0.589635i
$293$	1900.08	−	1900.08i	0.378852	−	0.378852i	−0.491836	−	0.870688i	$-0.663674\pi$
$293$	1900.08	−	1900.08i	0.378852	−	0.378852i	0.870688	+	0.491836i	$0.163674\pi$
$294$		0			0
$295$		−	6993.19i		−	1.38020i
$296$	−461.193	+	1580.03i	−0.0905618	+	0.310261i
$297$		0			0
$298$	2833.33	+	6195.37i	0.550772	+	1.20432i
$299$	−2363.74	+	2363.74i	−0.457185	+	0.457185i
$300$		0			0
$301$	33.9499	+	33.9499i	0.00650112	+	0.00650112i
$302$	−1435.47	−	534.531i	−0.273517	−	0.101850i
$303$		0			0
$304$	−3563.34	+	4781.30i	−0.672275	+	0.902060i
$305$	4926.54			0.924894
$306$		0			0
$307$	−3489.52	−	3489.52i	−0.648721	−	0.648721i	0.303963	−	0.952684i	$-0.401690\pi$
$307$	−3489.52	−	3489.52i	−0.648721	−	0.648721i	−0.952684	+	0.303963i	$0.901690\pi$
$308$	−12.2963	−	169.386i	−0.00227483	−	0.0313365i
$309$		0			0
$310$	299.457	+	654.796i	0.0548646	+	0.119967i
$311$			1471.68i			0.268332i	0.990959	+	0.134166i	$0.0428356\pi$
$311$			1471.68i			0.268332i	−0.990959	+	0.134166i	$0.957164\pi$
$312$		0			0
$313$		−	1258.85i		−	0.227331i	−0.993519	−	0.113665i	$-0.963741\pi$
$313$		−	1258.85i		−	0.227331i	0.993519	−	0.113665i	$-0.0362592\pi$
$314$	−32.5498	+	14.8860i	−0.00584997	+	0.00267537i
$315$		0			0
$316$	−5811.62	−	5024.95i	−1.03459	−	0.894543i
$317$	5902.41	+	5902.41i	1.04578	+	1.04578i	0.998901	+	0.0468795i	$0.0149277\pi$
$317$	5902.41	+	5902.41i	1.04578	+	1.04578i	0.0468795	+	0.998901i	$0.485072\pi$
$318$		0			0
$319$	−411.481			−0.0722211
$320$	−1857.80	−	8410.50i	−0.324544	−	1.46925i
$321$		0			0
$322$	61.3336	−	164.710i	0.0106149	−	0.0285060i
$323$	−8957.75	−	8957.75i	−1.54310	−	1.54310i
$324$		0			0
$325$	−2915.35	+	2915.35i	−0.497583	+	0.497583i
$326$	−4759.52	+	2176.67i	−0.808606	+	0.369799i
$327$		0			0
$328$	−4461.88	−	8140.33i	−0.751116	−	1.37035i
$329$			236.355i			0.0396068i
$330$		0			0
$331$	−3256.70	+	3256.70i	−0.540798	+	0.540798i	−0.923763	−	0.382965i	$-0.874903\pi$
$331$	−3256.70	+	3256.70i	−0.540798	+	0.540798i	0.382965	+	0.923763i	$0.374903\pi$
$332$	379.652	+	5229.82i	0.0627593	+	0.864529i
$333$		0			0
$334$	−6292.90	−	2343.31i	−1.03093	−	0.383893i
$335$	6773.10			1.10464
$336$		0			0
$337$	−4882.53			−0.789224			−0.394612	−	0.918848i	$-0.629121\pi$
$337$	−4882.53			−0.789224			−0.394612	+	0.918848i	$0.629121\pi$
$338$	−4018.65	−	1496.44i	−0.646703	−	0.240815i
$339$		0			0
$340$	18250.3	−	1324.85i	2.91106	−	0.211324i
$341$	−468.298	+	468.298i	−0.0743688	+	0.0743688i
$342$		0			0
$343$			332.637i			0.0523635i
$344$	−627.562	+	2150.00i	−0.0983601	+	0.336977i
$345$		0			0
$346$	4767.09	−	2180.13i	0.740694	−	0.338741i
$347$	−1744.70	+	1744.70i	−0.269914	+	0.269914i	−0.829066	−	0.559151i	$-0.811127\pi$
$347$	−1744.70	+	1744.70i	−0.269914	+	0.269914i	0.559151	+	0.829066i	$0.311127\pi$
$348$		0			0
$349$	6212.48	+	6212.48i	0.952855	+	0.952855i	0.998938	−	0.0460825i	$-0.0146737\pi$
$349$	6212.48	+	6212.48i	0.952855	+	0.952855i	−0.0460825	+	0.998938i	$0.514674\pi$
$350$	75.6467	−	203.147i	0.0115528	−	0.0310248i
$351$		0			0
$352$	6653.32	−	4300.94i	1.00745	−	0.651253i
$353$	−683.045			−0.102988			−0.0514941	−	0.998673i	$-0.516398\pi$
$353$	−683.045			−0.102988			−0.0514941	+	0.998673i	$0.516398\pi$
$354$		0			0
$355$	7312.16	+	7312.16i	1.09321	+	1.09321i
$356$	−6689.06	+	7736.24i	−0.995841	+	1.15174i
$357$		0			0
$358$	−904.508	+	413.658i	−0.133533	+	0.0610684i
$359$			4019.67i			0.590947i	0.955351	+	0.295473i	$0.0954773\pi$
$359$			4019.67i			0.590947i	−0.955351	+	0.295473i	$0.904523\pi$
$360$		0			0
$361$			1822.20i			0.265665i
$362$	−1917.90	−	4193.70i	−0.278460	−	0.608884i
$363$		0			0
$364$	−100.990	+	7.33126i	−0.0145421	+	0.00105567i
$365$	−5783.23	−	5783.23i	−0.829337	−	0.829337i
$366$		0			0
$367$	−8041.99			−1.14384			−0.571919	−	0.820310i	$-0.693801\pi$
$367$	−8041.99			−1.14384			−0.571919	+	0.820310i	$0.693801\pi$
$368$	8112.97	−	1184.14i	1.14923	−	0.167738i
$369$		0			0
$370$	−3243.61	−	1207.83i	−0.455749	−	0.169709i
$371$	105.325	+	105.325i	0.0147390	+	0.0147390i
$372$		0			0
$373$	805.266	−	805.266i	0.111783	−	0.111783i	−0.649003	−	0.760786i	$-0.724814\pi$
$373$	805.266	−	805.266i	0.111783	−	0.111783i	0.760786	+	0.649003i	$0.224814\pi$
$374$	6999.89	+	15306.0i	0.967795	+	2.11619i
$375$		0			0
$376$	−9668.51	+	5299.51i	−1.32610	+	0.726865i
$377$			245.332i			0.0335152i
$378$		0			0
$379$	519.461	−	519.461i	0.0704034	−	0.0704034i	−0.671028	−	0.741432i	$-0.734147\pi$
$379$	519.461	−	519.461i	0.0704034	−	0.0704034i	0.741432	+	0.671028i	$0.234147\pi$
$380$	−9485.39	−	8201.44i	−1.28050	−	1.10717i
$381$		0			0
$382$	451.757	−	1213.18i	0.0605075	−	0.162492i
$383$	−2907.38			−0.387886			−0.193943	−	0.981013i	$-0.562128\pi$
$383$	−2907.38			−0.387886			−0.193943	+	0.981013i	$0.562128\pi$
$384$		0			0
$385$	357.128			0.0472752
$386$	−60.9552	+	163.694i	−0.00803766	+	0.0215849i
$387$		0			0
$388$	6020.83	+	5205.84i	0.787786	+	0.681151i
$389$	−6046.78	+	6046.78i	−0.788133	+	0.788133i	−0.981188	−	0.193055i	$-0.938160\pi$
$389$	−6046.78	+	6046.78i	−0.788133	+	0.788133i	0.193055	+	0.981188i	$0.438160\pi$
$390$		0			0
$391$			17418.1i			2.25287i
$392$	−6801.22	+	3727.88i	−0.876310	+	0.480323i
$393$		0			0
$394$	−1020.73	−	2231.94i	−0.130517	−	0.285390i
$395$	11423.8	−	11423.8i	1.45517	−	1.45517i
$396$		0			0
$397$	−4121.17	−	4121.17i	−0.520996	−	0.520996i	0.396876	−	0.917872i	$-0.370094\pi$
$397$	−4121.17	−	4121.17i	−0.520996	−	0.520996i	−0.917872	+	0.396876i	$0.870094\pi$
$398$	8861.81	+	3299.90i	1.11609	+	0.415601i
$399$		0			0
$400$	10006.2	−	1460.48i	1.25078	−	0.182560i
$401$	−3991.60			−0.497084			−0.248542	−	0.968621i	$-0.579951\pi$
$401$	−3991.60			−0.497084			−0.248542	+	0.968621i	$0.579951\pi$
$402$		0			0
$403$	279.207	+	279.207i	0.0345119	+	0.0345119i
$404$	14870.1	−	1079.47i	1.83122	−	0.132935i
$405$		0			0
$406$	−5.36471	−	11.7305i	−0.000655779	−	0.00143393i
$407$		−	3183.59i		−	0.387727i
$408$		0			0
$409$			7470.32i			0.903138i	0.892236	+	0.451569i	$0.149136\pi$
$409$			7470.32i			0.903138i	−0.892236	+	0.451569i	$0.850864\pi$
$410$	17752.2	−	8118.62i	2.13834	−	0.977927i
$411$		0			0
$412$	7038.59	−	8140.50i	0.841667	−	0.973431i
$413$	142.580	+	142.580i	0.0169877	+	0.0169877i
$414$		0			0
$415$	−11026.4			−1.30425
$416$	−2564.29	−	3966.82i	−0.302223	−	0.467522i
$417$		0			0
$418$	4024.84	−	10808.6i	0.470960	−	1.26475i
$419$	11052.5	+	11052.5i	1.28866	+	1.28866i	0.935601	+	0.353059i	$0.114858\pi$
$419$	11052.5	+	11052.5i	1.28866	+	1.28866i	0.353059	+	0.935601i	$0.385142\pi$
$420$		0			0
$421$	2747.59	−	2747.59i	0.318075	−	0.318075i	−0.529952	−	0.848027i	$-0.677790\pi$
$421$	2747.59	−	2747.59i	0.318075	−	0.318075i	0.848027	+	0.529952i	$0.177790\pi$
$422$	−1622.34	+	741.943i	−0.187143	+	0.0855858i
$423$		0			0
$424$	−1946.92	+	6670.06i	−0.222997	+	0.763979i
$425$			21482.9i			2.45194i
$426$		0			0
$427$	−100.444	+	100.444i	−0.0113837	+	0.0113837i
$428$	4939.40	−	358.569i	0.557838	−	0.0404955i
$429$		0			0
$430$	−4413.69	−	1643.54i	−0.494993	−	0.184322i
$431$	−11.7027			−0.00130789			−0.000653945	−	1.00000i	$-0.500208\pi$
$431$	−11.7027			−0.00130789			−0.000653945		1.00000i	$0.500208\pi$
$432$		0			0
$433$	−8291.16			−0.920202			−0.460101	−	0.887866i	$-0.652187\pi$
$433$	−8291.16			−0.920202			−0.460101	+	0.887866i	$0.652187\pi$
$434$	−19.4557	−	7.24479i	−0.00215185	−	0.000801292i
$435$		0			0
$436$	−142.498	−	1962.95i	−0.0156523	−	0.215615i
$437$	8440.19	−	8440.19i	0.923911	−	0.923911i
$438$		0			0
$439$		−	14287.6i		−	1.55332i	−0.629918	−	0.776661i	$-0.716912\pi$
$439$		−	14287.6i		−	1.55332i	0.629918	−	0.776661i	$-0.283088\pi$
$440$	8007.48	+	14609.0i	0.867594	+	1.58285i
$441$		0			0
$442$	9125.69	−	4173.45i	0.982047	−	0.449119i
$443$	5070.34	−	5070.34i	0.543790	−	0.543790i	−0.380847	−	0.924638i	$-0.624368\pi$
$443$	5070.34	−	5070.34i	0.543790	−	0.543790i	0.924638	+	0.380847i	$0.124368\pi$
$444$		0			0
$445$	−15207.0	−	15207.0i	−1.61995	−	1.61995i
$446$	6021.65	−	16171.0i	0.639313	−	1.71686i
$447$		0			0
$448$	209.354	+	133.599i	0.0220783	+	0.0140892i
$449$	−16521.3			−1.73650			−0.868249	−	0.496128i	$-0.834755\pi$
$449$	−16521.3			−1.73650			−0.868249	+	0.496128i	$0.834755\pi$
$450$		0			0
$451$	12696.1	+	12696.1i	1.32558	+	1.32558i
$452$	1893.73	+	1637.39i	0.197066	+	0.170391i
$453$		0			0
$454$	13287.9	−	6076.97i	1.37364	−	0.628208i
$455$		−	212.926i		−	0.0219387i
$456$		0			0
$457$		−	3323.22i		−	0.340161i	−0.985430	−	0.170080i	$-0.945597\pi$
$457$		−	3323.22i		−	0.340161i	0.985430	−	0.170080i	$-0.0544028\pi$
$458$	−2841.20	−	6212.58i	−0.289870	−	0.633832i
$459$		0			0
$460$	1248.31	+	17195.8i	0.126527	+	1.74295i
$461$	1193.80	+	1193.80i	0.120609	+	0.120609i	0.764835	−	0.644226i	$-0.222820\pi$
$461$	1193.80	+	1193.80i	0.120609	+	0.120609i	−0.644226	+	0.764835i	$0.722820\pi$
$462$		0			0
$463$	6199.48			0.622277			0.311139	−	0.950365i	$-0.399290\pi$
$463$	6199.48			0.622277			0.311139	+	0.950365i	$0.399290\pi$
$464$	359.571	−	482.473i	0.0359756	−	0.0482721i
$465$		0			0
$466$	−8002.95	−	2980.09i	−0.795557	−	0.296244i
$467$	2566.04	+	2566.04i	0.254265	+	0.254265i	0.822717	−	0.568451i	$-0.192457\pi$
$467$	2566.04	+	2566.04i	0.254265	+	0.254265i	−0.568451	+	0.822717i	$0.692457\pi$
$468$		0			0
$469$	−138.093	+	138.093i	−0.0135960	+	0.0135960i
$470$	−9642.72	−	21084.8i	−0.946352	−	2.06930i
$471$		0			0
$472$	−2635.59	+	9029.40i	−0.257018	+	0.880534i
$473$		−	4332.02i		−	0.421113i
$474$		0			0
$475$	10409.8	−	10409.8i	1.00555	−	1.00555i
$476$	−345.082	+	399.106i	−0.0332286	+	0.0384306i
$477$		0			0
$478$	−2925.74	+	7857.02i	−0.279959	+	0.751823i
$479$	−4563.85			−0.435339			−0.217670	−	0.976023i	$-0.569846\pi$
$479$	−4563.85			−0.435339			−0.217670	+	0.976023i	$0.569846\pi$
$480$		0			0
$481$	−1898.11			−0.179930
$482$	−2573.00	+	6909.74i	−0.243147	+	0.652967i
$483$		0			0
$484$	−3057.98	+	3536.71i	−0.287188	+	0.332148i
$485$	−11835.0	+	11835.0i	−1.10804	+	1.10804i
$486$		0			0
$487$		−	1099.80i		−	0.102334i	−0.998690	−	0.0511672i	$-0.983706\pi$
$487$		−	1099.80i		−	0.102334i	0.998690	−	0.0511672i	$-0.0162941\pi$
$488$	−6361.00	−	1856.71i	−0.590060	−	0.172232i
$489$		0			0
$490$	−6783.07	−	14831.9i	−0.625363	−	1.36742i
$491$	−11017.7	+	11017.7i	−1.01267	+	1.01267i	−0.0127523	+	0.999919i	$0.504059\pi$
$491$	−11017.7	+	11017.7i	−1.01267	+	1.01267i	−0.999919	+	0.0127523i	$0.995941\pi$
$492$		0			0
$493$	903.913	+	903.913i	0.0825764	+	0.0825764i
$494$	−6444.28	−	2399.68i	−0.586927	−	0.218556i
$495$		0			0
$496$	−139.872	−	958.312i	−0.0126622	−	0.0867530i
$497$	−298.167			−0.0269107
$498$		0			0
$499$	−3603.08	−	3603.08i	−0.323238	−	0.323238i	0.526770	−	0.850008i	$-0.323403\pi$
$499$	−3603.08	−	3603.08i	−0.323238	−	0.323238i	−0.850008	+	0.526770i	$0.823403\pi$
$500$	321.598	+	4430.11i	0.0287646	+	0.396241i
$501$		0			0
$502$	5021.96	+	10981.1i	0.446496	+	0.976312i
$503$		−	17947.0i		−	1.59089i	−0.606028	−	0.795443i	$-0.707238\pi$
$503$		−	17947.0i		−	1.59089i	0.606028	−	0.795443i	$-0.292762\pi$
$504$		0			0
$505$			31351.7i			2.76264i
$506$	−14421.7	+	6595.45i	−1.26704	+	0.579453i
$507$		0			0
$508$	−8822.82	−	7628.56i	−0.770570	−	0.666265i
$509$	−1844.54	−	1844.54i	−0.160625	−	0.160625i	0.622219	−	0.782843i	$-0.286231\pi$
$509$	−1844.54	−	1844.54i	−0.160625	−	0.160625i	−0.782843	+	0.622219i	$0.786231\pi$
$510$		0			0
$511$	235.822			0.0204151
$512$	−771.004	+	11559.6i	−0.0665506	+	0.997783i
$513$		0			0
$514$	−1962.69	+	5270.77i	−0.168426	+	0.452303i
$515$	16001.6	+	16001.6i	1.36916	+	1.36916i
$516$		0			0
$517$	15079.5	−	15079.5i	1.28278	−	1.28278i
$518$	90.7578	−	41.5062i	0.00769821	−	0.00352062i
$519$		0			0
$520$	8710.11	−	4774.19i	0.734545	−	0.402619i
$521$			5221.57i			0.439081i	0.975603	+	0.219541i	$0.0704558\pi$
$521$			5221.57i			0.439081i	−0.975603	+	0.219541i	$0.929544\pi$
$522$		0			0
$523$	−581.412	+	581.412i	−0.0486106	+	0.0486106i	−0.730994	−	0.682384i	$-0.760943\pi$
$523$	−581.412	+	581.412i	−0.0486106	+	0.0486106i	0.682384	+	0.730994i	$0.260943\pi$
$524$	−166.702	−	2296.37i	−0.0138977	−	0.191446i
$525$		0			0
$526$	16035.9	+	5971.33i	1.32927	+	0.494985i
$527$	2057.45			0.170064
$528$		0			0
$529$	−4244.75			−0.348874
$530$	−13692.9	−	5098.85i	−1.12223	−	0.417887i
$531$		0			0
$532$	360.606	−	26.1777i	0.0293877	−	0.00213336i
$533$	7569.61	−	7569.61i	0.615152	−	0.615152i
$534$		0			0
$535$			10414.1i			0.841572i
$536$	−8745.23	−	2552.64i	−0.704732	−	0.205704i
$537$		0			0
$538$	−14127.0	+	6460.70i	−1.13208	+	0.517733i
$539$	10607.5	−	10607.5i	0.847678	−	0.847678i
$540$		0			0
$541$	4813.94	+	4813.94i	0.382564	+	0.382564i	0.872025	−	0.489461i	$-0.162806\pi$
$541$	4813.94	+	4813.94i	0.382564	+	0.382564i	−0.489461	+	0.872025i	$0.662806\pi$
$542$	−3278.49	+	8804.30i	−0.259821	+	0.697744i
$543$		0			0
$544$	−24063.5	−	5167.53i	−1.89654	−	0.407272i
$545$	4138.64			0.325284
$546$		0			0
$547$	−10287.7	−	10287.7i	−0.804154	−	0.804154i	0.179588	−	0.983742i	$-0.442524\pi$
$547$	−10287.7	−	10287.7i	−0.804154	−	0.804154i	−0.983742	+	0.179588i	$0.942524\pi$
$548$	2265.53	−	2620.21i	0.176604	−	0.204251i
$549$		0			0
$550$	−17787.1	+	8134.59i	−1.37899	+	0.630654i
$551$		−	876.006i		−	0.0677298i
$552$		0			0
$553$			465.825i			0.0358208i
$554$	5994.44	+	13107.5i	0.459710	+	1.00520i
$555$		0			0
$556$	11945.4	−	867.162i	0.911149	−	0.0661436i
$557$	−16473.4	−	16473.4i	−1.25315	−	1.25315i	−0.954302	−	0.298843i	$-0.903399\pi$
$557$	−16473.4	−	16473.4i	−1.25315	−	1.25315i	−0.298843	−	0.954302i	$-0.596601\pi$
$558$		0			0
$559$	−2582.82			−0.195424
$560$	−312.075	+	418.743i	−0.0235492	+	0.0315984i
$561$		0			0
$562$	−2183.21	−	812.970i	−0.163867	−	0.0610197i
$563$	3846.62	+	3846.62i	0.287950	+	0.287950i	0.836269	−	0.548319i	$-0.184732\pi$
$563$	3846.62	+	3846.62i	0.287950	+	0.287950i	−0.548319	+	0.836269i	$0.684732\pi$
$564$		0			0
$565$	−3722.47	+	3722.47i	−0.277178	+	0.277178i
$566$	3333.42	+	7288.89i	0.247552	+	0.541298i
$567$		0			0
$568$	−6685.45	−	12197.0i	−0.493865	−	0.901015i
$569$		−	16206.0i		−	1.19401i	−0.802239	−	0.597003i	$-0.796358\pi$
$569$		−	16206.0i		−	1.19401i	0.802239	−	0.597003i	$-0.203642\pi$
$570$		0			0
$571$	15842.4	−	15842.4i	1.16109	−	1.16109i	0.176858	−	0.984236i	$-0.443407\pi$
$571$	15842.4	−	15842.4i	1.16109	−	1.16109i	0.984236	−	0.176858i	$-0.0565933\pi$
$572$	6910.96	+	5975.49i	0.505178	+	0.436797i
$573$		0			0
$574$	−196.414	+	527.466i	−0.0142825	+	0.0383554i
$575$	−20241.7			−1.46806
$576$		0			0
$577$	−18218.5			−1.31446			−0.657231	−	0.753689i	$-0.728272\pi$
$577$	−18218.5			−1.31446			−0.657231	+	0.753689i	$0.728272\pi$
$578$	13397.1	−	35977.5i	0.964090	−	2.58904i
$579$		0			0
$580$	957.156	+	827.594i	0.0685237	+	0.0592482i
$581$	224.811	−	224.811i	0.0160529	−	0.0160529i
$582$		0			0
$583$		−	13439.5i		−	0.954728i
$584$	5287.56	+	9646.71i	0.374659	+	0.683534i
$585$		0			0
$586$	−3160.97	−	6911.79i	−0.222830	−	0.487241i
$587$	−3225.64	+	3225.64i	−0.226808	+	0.226808i	−0.811358	−	0.584550i	$-0.801271\pi$
$587$	−3225.64	+	3225.64i	−0.226808	+	0.226808i	0.584550	+	0.811358i	$0.301271\pi$
$588$		0			0
$589$	−996.964	−	996.964i	−0.0697439	−	0.0697439i
$590$	−18536.3	−	6902.42i	−1.29344	−	0.481641i
$591$		0			0
$592$	3732.85	+	2781.97i	0.259154	+	0.193139i
$593$	15436.7			1.06898			0.534492	−	0.845174i	$-0.320503\pi$
$593$	15436.7			1.06898			0.534492	+	0.845174i	$0.320503\pi$
$594$		0			0
$595$	−784.514	−	784.514i	−0.0540537	−	0.0540537i
$596$	19218.1	−	1395.11i	1.32081	−	0.0958827i
$597$		0			0
$598$	3932.31	+	8598.43i	0.268903	+	0.587986i
$599$		−	13650.7i		−	0.931142i	−0.885010	−	0.465571i	$-0.845849\pi$
$599$		−	13650.7i		−	0.931142i	0.885010	−	0.465571i	$-0.154151\pi$
$600$		0			0
$601$			27042.7i			1.83543i	0.397236	+	0.917716i	$0.369969\pi$
$601$			27042.7i			1.83543i	−0.397236	+	0.917716i	$0.630031\pi$
$602$	123.497	−	56.4790i	0.00836109	−	0.00382377i
$603$		0			0
$604$	−2833.68	+	3277.30i	−0.190895	+	0.220780i
$605$	−6952.03	−	6952.03i	−0.467174	−	0.467174i
$606$		0			0
$607$	−3562.32			−0.238205			−0.119102	−	0.992882i	$-0.538002\pi$
$607$	−3562.32			−0.238205			−0.119102	+	0.992882i	$0.538002\pi$
$608$	9156.31	+	14164.3i	0.610752	+	0.944800i
$609$		0			0
$610$	4862.59	−	13058.4i	0.322755	−	0.866752i
$611$	−8990.64	−	8990.64i	−0.595290	−	0.595290i
$612$		0			0
$613$	11418.0	−	11418.0i	0.752315	−	0.752315i	−0.222595	−	0.974911i	$-0.571453\pi$
$613$	11418.0	−	11418.0i	0.752315	−	0.752315i	0.974911	+	0.222595i	$0.0714529\pi$
$614$	−12693.6	+	5805.17i	−0.834321	+	0.381559i
$615$		0			0
$616$	−461.114	−	134.594i	−0.0301604	−	0.00880350i
$617$		−	3981.62i		−	0.259796i	−0.991527	−	0.129898i	$-0.958535\pi$
$617$		−	3981.62i		−	0.259796i	0.991527	−	0.129898i	$-0.0414649\pi$
$618$		0			0
$619$	6160.23	−	6160.23i	0.400001	−	0.400001i	−0.478232	−	0.878233i	$-0.658722\pi$
$619$	6160.23	−	6160.23i	0.400001	−	0.400001i	0.878233	+	0.478232i	$0.158722\pi$
$620$	2031.19	−	147.451i	0.131572	−	0.00955126i
$621$		0			0
$622$	3900.87	+	1452.58i	0.251464	+	0.0936384i
$623$	620.092			0.0398771
$624$		0			0
$625$	10410.2			0.666252
$626$	−3336.74	−	1242.51i	−0.213040	−	0.0793304i
$627$		0			0
$628$	7.32978	+	100.970i	0.000465748	+	0.00641583i
$629$	−6993.48	+	6993.48i	−0.443320	+	0.443320i
$630$		0			0
$631$		−	670.100i		−	0.0422761i	−0.999777	−	0.0211381i	$-0.993271\pi$
$631$		−	670.100i		−	0.0422761i	0.999777	−	0.0211381i	$-0.00672896\pi$
$632$	−19055.4	+	10444.7i	−1.19934	+	0.657384i
$633$		0			0
$634$	21470.8	−	9819.25i	1.34498	−	0.615098i
$635$	17342.8	−	17342.8i	1.08383	−	1.08383i
$636$		0			0
$637$	−6324.38	−	6324.38i	−0.393377	−	0.393377i
$638$	−406.140	+	1090.68i	−0.0252026	+	0.0676810i
$639$		0			0
$640$	−24126.7	−	3377.01i	−1.49014	−	0.208575i
$641$	3038.11			0.187204			0.0936022	−	0.995610i	$-0.470162\pi$
$641$	3038.11			0.187204			0.0936022	+	0.995610i	$0.470162\pi$
$642$		0			0
$643$	11363.4	+	11363.4i	0.696934	+	0.696934i	0.963748	−	0.266814i	$-0.0859710\pi$
$643$	11363.4	+	11363.4i	0.696934	+	0.696934i	−0.266814	+	0.963748i	$0.585971\pi$
$644$	−376.046	−	325.144i	−0.0230098	−	0.0198952i
$645$		0			0
$646$	−32585.1	+	14902.1i	−1.98459	+	0.907610i
$647$			25695.9i			1.56137i	0.624923	+	0.780687i	$0.285131\pi$
$647$			25695.9i			1.56137i	−0.624923	+	0.780687i	$0.714869\pi$
$648$		0			0
$649$		−	18193.3i		−	1.10039i
$650$	4849.97	+	10605.0i	0.292664	+	0.639941i
$651$		0			0
$652$	1071.78	+	14764.1i	0.0643775	+	0.886821i
$653$	20933.8	+	20933.8i	1.25452	+	1.25452i	0.953673	+	0.300847i	$0.0972692\pi$
$653$	20933.8	+	20933.8i	1.25452	+	1.25452i	0.300847	+	0.953673i	$0.402731\pi$
$654$		0			0
$655$	4841.61			0.288821
$656$	−25980.9	+	3792.08i	−1.54632	+	0.225695i
$657$		0			0
$658$	626.486	+	233.287i	0.0371170	+	0.0138214i
$659$	−5253.27	−	5253.27i	−0.310529	−	0.310529i	0.534586	−	0.845114i	$-0.320468\pi$
$659$	−5253.27	−	5253.27i	−0.310529	−	0.310529i	−0.845114	+	0.534586i	$0.820468\pi$
$660$		0			0
$661$	3182.14	−	3182.14i	0.187248	−	0.187248i	−0.607257	−	0.794505i	$-0.707730\pi$
$661$	3182.14	−	3182.14i	0.187248	−	0.187248i	0.794505	+	0.607257i	$0.207730\pi$
$662$	5417.84	+	11846.7i	0.318082	+	0.695521i
$663$		0			0
$664$	14237.0	+	4155.63i	0.832082	+	0.242876i
$665$			760.293i			0.0443352i
$666$		0			0
$667$	−851.686	+	851.686i	−0.0494414	+	0.0494414i
$668$	−12422.4	+	14367.2i	−0.719519	+	0.832161i
$669$		0			0
$670$	6685.19	−	17952.9i	0.385480	−	1.03520i
$671$	12816.8			0.737385
$672$		0			0
$673$	27736.4			1.58865			0.794325	−	0.607493i	$-0.207825\pi$
$673$	27736.4			1.58865			0.794325	+	0.607493i	$0.207825\pi$
$674$	−4819.16	+	12941.7i	−0.275411	+	0.739610i
$675$		0			0
$676$	−7932.97	+	9174.90i	−0.451353	+	0.522013i
$677$	−6076.45	+	6076.45i	−0.344959	+	0.344959i	−0.858228	−	0.513269i	$-0.828434\pi$
$677$	−6076.45	+	6076.45i	−0.344959	+	0.344959i	0.513269	+	0.858228i	$0.328434\pi$
$678$		0			0
$679$		−	482.594i		−	0.0272758i
$680$	14501.7	−	49682.2i	0.817816	−	2.80180i
$681$		0			0
$682$	779.061	+	1703.50i	0.0437416	+	0.0956457i
$683$	2360.09	−	2360.09i	0.132220	−	0.132220i	−0.637900	−	0.770120i	$-0.720197\pi$
$683$	2360.09	−	2360.09i	0.132220	−	0.132220i	0.770120	+	0.637900i	$0.220197\pi$
$684$		0			0
$685$	5150.48	+	5150.48i	0.287284	+	0.287284i
$686$	881.694	+	328.319i	0.0490717	+	0.0182730i
$687$		0			0
$688$	5079.42	+	3785.52i	0.281469	+	0.209770i
$689$	−8012.84			−0.443055
$690$		0			0
$691$	10248.5	+	10248.5i	0.564211	+	0.564211i	0.930501	−	0.366290i	$-0.119372\pi$
$691$	10248.5	+	10248.5i	0.564211	+	0.564211i	−0.366290	+	0.930501i	$0.619372\pi$
$692$	−1073.48	−	14787.6i	−0.0589707	−	0.812340i
$693$		0			0
$694$	2902.48	+	6346.58i	0.158756	+	0.347137i
$695$			25185.4i			1.37459i
$696$		0			0
$697$		−	55779.7i		−	3.03128i
$698$	22598.8	−	10335.1i	1.22547	−	0.560442i
$699$		0			0
$700$	−463.802	−	401.021i	−0.0250429	−	0.0216531i
$701$	5637.61	+	5637.61i	0.303751	+	0.303751i	0.842480	−	0.538728i	$-0.181095\pi$
$701$	5637.61	+	5637.61i	0.303751	+	0.303751i	−0.538728	+	0.842480i	$0.681095\pi$
$702$		0			0
$703$	6777.57			0.363614
$704$	−4833.20	−	21880.5i	−0.258747	−	1.17138i
$705$		0			0
$706$	−674.179	+	1810.49i	−0.0359392	+	0.0965139i
$707$	−639.212	−	639.212i	−0.0340029	−	0.0340029i
$708$		0			0
$709$	−1798.00	+	1798.00i	−0.0952402	+	0.0952402i	−0.753122	−	0.657881i	$-0.771453\pi$
$709$	−1798.00	+	1798.00i	−0.0952402	+	0.0952402i	0.657881	+	0.753122i	$0.271453\pi$
$710$	26599.0	−	12164.5i	1.40598	−	0.642994i
$711$		0			0
$712$	13903.6	+	25366.0i	0.731826	+	1.33516i
$713$			1938.57i			0.101823i
$714$		0			0
$715$	−13584.7	+	13584.7i	−0.710545	+	0.710545i
$716$	203.683	+	2805.80i	0.0106313	+	0.146449i
$717$		0			0
$718$	10654.6	+	3967.49i	0.553797	+	0.206219i
$719$	35035.3			1.81724			0.908622	−	0.417620i	$-0.137136\pi$
$719$	35035.3			1.81724			0.908622	+	0.417620i	$0.137136\pi$
$720$		0			0
$721$	−652.495			−0.0337034
$722$	4829.96	+	1798.55i	0.248965	+	0.0927078i
$723$		0			0
$724$	−13008.9	+	944.364i	−0.667780	+	0.0484765i
$725$	−1050.44	+	1050.44i	−0.0538101	+	0.0538101i
$726$		0			0
$727$			24515.4i			1.25066i	0.780362	+	0.625328i	$0.215035\pi$
$727$			24515.4i			1.25066i	−0.780362	+	0.625328i	$0.784965\pi$
$728$	−80.2472	+	274.923i	−0.00408539	+	0.0139963i
$729$		0			0
$730$	−21037.3	+	9620.98i	−1.06661	+	0.487792i
$731$	−9516.28	+	9516.28i	−0.481494	+	0.481494i
$732$		0			0
$733$	−23583.9	−	23583.9i	−1.18839	−	1.18839i	−0.977512	−	0.210878i	$-0.932368\pi$
$733$	−23583.9	−	23583.9i	−1.18839	−	1.18839i	−0.210878	−	0.977512i	$-0.567632\pi$
$734$	−7937.60	+	21316.3i	−0.399159	+	1.07193i
$735$		0			0
$736$	4868.96	−	22673.2i	0.243848	−	1.13552i
$737$	17620.7			0.880689
$738$		0			0
$739$	−17246.2	−	17246.2i	−0.858472	−	0.858472i	0.132686	−	0.991158i	$-0.457640\pi$
$739$	−17246.2	−	17246.2i	−0.858472	−	0.858472i	−0.991158	+	0.132686i	$0.957640\pi$
$740$	−6403.01	+	7405.42i	−0.318080	+	0.367877i
$741$		0			0
$742$	383.133	−	175.218i	0.0189559	−	0.00866908i
$743$		−	14249.5i		−	0.703587i	−0.936078	−	0.351793i	$-0.885572\pi$
$743$		−	14249.5i		−	0.703587i	0.936078	−	0.351793i	$-0.114428\pi$
$744$		0			0
$745$			40519.0i			1.99262i
$746$	−1339.64	−	2929.27i	−0.0657477	−	0.143764i
$747$		0			0
$748$	47479.4	−	3446.71i	2.32088	−	0.168481i
$749$	−212.327	−	212.327i	−0.0103582	−	0.0103582i
$750$		0			0
$751$	10260.0			0.498524			0.249262	−	0.968436i	$-0.419812\pi$
$751$	10260.0			0.498524			0.249262	+	0.968436i	$0.419812\pi$
$752$	4503.96	+	30858.3i	0.218408	+	1.49639i
$753$		0			0
$754$	650.282	+	242.148i	0.0314083	+	0.0116956i
$755$	−6442.11	−	6442.11i	−0.310533	−	0.310533i
$756$		0			0
$757$	−18953.4	+	18953.4i	−0.910005	+	0.910005i	−0.996272	−	0.0862671i	$-0.972506\pi$
$757$	−18953.4	+	18953.4i	−0.910005	+	0.910005i	0.0862671	+	0.996272i	$0.472506\pi$
$758$	−864.175	−	1889.61i	−0.0414093	−	0.0905459i
$759$		0			0
$760$	−31101.2	+	17047.2i	−1.48442	+	0.813640i
$761$			24434.3i			1.16392i	0.813218	+	0.581960i	$0.197714\pi$
$761$			24434.3i			1.16392i	−0.813218	+	0.581960i	$0.802286\pi$
$762$		0			0
$763$	−84.3802	+	84.3802i	−0.00400363	+	0.00400363i
$764$	−2769.79	−	2394.87i	−0.131162	−	0.113408i
$765$		0			0
$766$	−2869.65	+	7706.37i	−0.135358	+	0.363502i
$767$	−10847.1			−0.510649
$768$		0			0
$769$	−6752.03			−0.316625			−0.158312	−	0.987389i	$-0.550605\pi$
$769$	−6752.03			−0.316625			−0.158312	+	0.987389i	$0.550605\pi$
$770$	352.493	−	946.612i	0.0164974	−	0.0443033i
$771$		0			0
$772$	373.726	+	323.138i	0.0174232	+	0.0150648i
$773$	18608.6	−	18608.6i	0.865854	−	0.865854i	−0.126157	−	0.992010i	$-0.540264\pi$
$773$	18608.6	−	18608.6i	0.865854	−	0.865854i	0.992010	+	0.126157i	$0.0402642\pi$
$774$		0			0
$775$			2390.96i			0.110821i
$776$	19741.4	−	10820.7i	0.913240	−	0.500566i
$777$		0			0
$778$	10059.4	+	21996.0i	0.463557	+	1.01362i
$779$	−27028.8	+	27028.8i	−1.24314	+	1.24314i
$780$		0			0
$781$	19023.1	+	19023.1i	0.871576	+	0.871576i
$782$	46168.9	+	17192.1i	2.11125	+	0.786172i
$783$		0			0
$784$	3168.27	+	21706.9i	0.144327	+	0.988837i
$785$	−212.883			−0.00967911
$786$		0			0
$787$	23406.2	+	23406.2i	1.06016	+	1.06016i	0.998071	+	0.0620850i	$0.0197750\pi$
$787$	23406.2	+	23406.2i	1.06016	+	1.06016i	0.0620850	+	0.998071i	$0.480225\pi$
$788$	−6923.51	+	502.603i	−0.312995	+	0.0227214i
$789$		0			0
$790$	−19004.6	−	41555.6i	−0.855890	−	1.87150i
$791$		−	151.790i		−	0.00682307i
$792$		0			0
$793$		−	7641.56i		−	0.342194i
$794$	−14991.3	+	6855.98i	−0.670054	+	0.306435i
$795$		0			0
$796$	17493.6	−	20232.2i	0.778949	−	0.900895i
$797$	−1487.10	−	1487.10i	−0.0660925	−	0.0660925i	0.673288	−	0.739380i	$-0.264881\pi$
$797$	−1487.10	−	1487.10i	−0.0660925	−	0.0660925i	−0.739380	+	0.673288i	$0.764881\pi$
$798$		0			0
$799$	−66251.1			−2.93341
$800$	6005.20	−	27964.3i	0.265395	−	1.23586i
$801$		0			0
$802$	−3939.79	+	10580.2i	−0.173465	+	0.465835i
$803$	−15045.5	−	15045.5i	−0.661201	−	0.661201i
$804$		0			0
$805$	739.186	−	739.186i	0.0323638	−	0.0323638i
$806$	1015.65	−	464.489i	0.0443857	−	0.0202989i
$807$		0			0
$808$	11815.8	−	40480.4i	0.514454	−	1.76250i
$809$			10505.2i			0.456542i	0.973598	+	0.228271i	$0.0733072\pi$
$809$			10505.2i			0.456542i	−0.973598	+	0.228271i	$0.926693\pi$
$810$		0			0
$811$	−27073.1	+	27073.1i	−1.17221	+	1.17221i	−0.190531	+	0.981681i	$0.561021\pi$
$811$	−27073.1	+	27073.1i	−1.17221	+	1.17221i	−0.981681	+	0.190531i	$0.938979\pi$
$812$	−36.3882	+	2.64155i	−0.00157263	+	0.000114163i
$813$		0			0
$814$	−8438.49	−	3142.27i	−0.363352	−	0.135303i
$815$	−31128.3			−1.33788
$816$		0			0
$817$	9222.48			0.394925
$818$	19801.0	+	7373.36i	0.846363	+	0.315163i
$819$		0			0
$820$	−3997.56	−	55067.7i	−0.170245	−	2.34518i
$821$	9907.96	−	9907.96i	0.421182	−	0.421182i	−0.464429	−	0.885610i	$-0.653740\pi$
$821$	9907.96	−	9907.96i	0.421182	−	0.421182i	0.885610	+	0.464429i	$0.153740\pi$
$822$		0			0
$823$		−	17501.8i		−	0.741281i	−0.928776	−	0.370640i	$-0.879138\pi$
$823$		−	17501.8i		−	0.741281i	0.928776	−	0.370640i	$-0.120862\pi$
$824$	−14630.1	−	26691.5i	−0.618526	−	1.12845i
$825$		0			0
$826$	518.655	−	237.196i	0.0218478	−	0.00999166i
$827$	−7074.02	+	7074.02i	−0.297446	+	0.297446i	−0.840013	−	0.542567i	$-0.817453\pi$
$827$	−7074.02	+	7074.02i	−0.297446	+	0.297446i	0.542567	+	0.840013i	$0.317453\pi$
$828$		0			0
$829$	21066.1	+	21066.1i	0.882576	+	0.882576i	0.993796	−	0.111220i	$-0.0354758\pi$
$829$	21066.1	+	21066.1i	0.882576	+	0.882576i	−0.111220	+	0.993796i	$0.535476\pi$
$830$	−10883.3	+	29226.9i	−0.455138	+	1.22226i
$831$		0			0
$832$	−13045.5	+	2881.63i	−0.543597	+	0.120075i
$833$	−46603.7			−1.93844
$834$		0			0
$835$	−28241.3	−	28241.3i	−1.17046	−	1.17046i
$836$	−24677.0	−	21336.7i	−1.02090	−	0.882708i
$837$		0			0
$838$	40204.9	−	18386.9i	1.65735	−	0.757953i
$839$		−	30444.6i		−	1.25276i	−0.779519	−	0.626379i	$-0.784536\pi$
$839$		−	30444.6i		−	1.25276i	0.779519	−	0.626379i	$-0.215464\pi$
$840$		0			0
$841$		−	24300.6i		−	0.996376i
$842$	−4570.90	−	9994.76i	−0.187083	−	0.409076i
$843$		0			0
$844$	365.329	+	5032.52i	0.0148994	+	0.205244i
$845$	−18034.9	−	18034.9i	−0.734224	−	0.734224i
$846$		0			0
$847$	283.482			0.0115001
$848$	15758.2	+	11744.0i	0.638134	+	0.475580i
$849$		0			0
$850$	56943.0	+	21204.1i	2.29780	+	0.855639i
$851$	−6589.41	−	6589.41i	−0.265431	−	0.265431i
$852$		0			0
$853$	−882.218	+	882.218i	−0.0354122	+	0.0354122i	−0.724591	−	0.689179i	$-0.757971\pi$
$853$	−882.218	+	882.218i	−0.0354122	+	0.0354122i	0.689179	+	0.724591i	$0.257971\pi$
$854$	167.099	+	365.380i	0.00669557	+	0.0146406i
$855$		0			0
$856$	3924.86	−	13446.4i	0.156716	−	0.536902i
$857$		−	8006.81i		−	0.319145i	−0.987186	−	0.159572i	$-0.948988\pi$
$857$		−	8006.81i		−	0.319145i	0.987186	−	0.159572i	$-0.0510116\pi$
$858$		0			0
$859$	−20266.0	+	20266.0i	−0.804967	+	0.804967i	−0.983867	−	0.178900i	$-0.942746\pi$
$859$	−20266.0	+	20266.0i	−0.804967	+	0.804967i	0.178900	+	0.983867i	$0.442746\pi$
$860$	−8712.81	+	10076.8i	−0.345470	+	0.399554i
$861$		0			0
$862$	−11.5508	+	31.0195i	−0.000456407	+	0.00122567i
$863$	−41478.0			−1.63607			−0.818034	−	0.575169i	$-0.804936\pi$
$863$	−41478.0			−1.63607			−0.818034	+	0.575169i	$0.804936\pi$
$864$		0			0
$865$	31177.7			1.22552
$866$	−8183.54	+	21976.7i	−0.321118	+	0.862355i
$867$		0			0
$868$	−38.4064	+	44.4190i	−0.00150184	+	0.00173696i
$869$	29719.8	−	29719.8i	1.16016	−	1.16016i
$870$		0			0
$871$		−	10505.8i		−	0.408696i
$872$	−5343.69	−	1559.77i	−0.207523	−	0.0605738i
$873$		0			0
$874$	−14041.1	−	30702.4i	−0.543418	−	1.18824i
$875$	190.435	−	190.435i	0.00735756	−	0.00735756i
$876$		0			0
$877$	6027.15	+	6027.15i	0.232067	+	0.232067i	0.813555	−	0.581488i	$-0.197529\pi$
$877$	6027.15	+	6027.15i	0.232067	+	0.232067i	−0.581488	+	0.813555i	$0.697529\pi$
$878$	−37870.9	−	14102.1i	−1.45567	−	0.542054i
$879$		0			0
$880$	46626.4	−	6805.42i	1.78611	−	0.260694i
$881$	40154.3			1.53556			0.767782	−	0.640712i	$-0.221361\pi$
$881$	40154.3			1.53556			0.767782	+	0.640712i	$0.221361\pi$
$882$		0			0
$883$	4435.93	+	4435.93i	0.169061	+	0.169061i	0.786567	−	0.617505i	$-0.211857\pi$
$883$	4435.93	+	4435.93i	0.169061	+	0.169061i	−0.617505	+	0.786567i	$0.711857\pi$
$884$	−2054.98	−	28308.0i	−0.0781861	−	1.07704i
$885$		0			0
$886$	−8435.02	−	18444.1i	−0.319842	−	0.699369i
$887$			3275.31i			0.123984i	0.998077	+	0.0619921i	$0.0197454\pi$
$887$			3275.31i			0.123984i	−0.998077	+	0.0619921i	$0.980255\pi$
$888$		0			0
$889$			707.186i			0.0266797i
$890$	−55317.5	+	25298.3i	−2.08342	+	0.952811i
$891$		0			0
$892$	−36919.7	−	31922.2i	−1.38583	−	1.19825i
$893$	32102.9	+	32102.9i	1.20300	+	1.20300i
$894$		0			0
$895$	−5915.67			−0.220937
$896$	560.758	−	423.054i	0.0209080	−	0.0157737i
$897$		0			0
$898$	−16306.8	+	43791.7i	−0.605976	+	1.62734i
$899$	100.602	+	100.602i	0.00373222	+	0.00373222i
$900$		0			0
$901$	−29522.9	+	29522.9i	−1.09162	+	1.09162i
$902$	46183.8	−	21121.2i	1.70482	−	0.779666i
$903$		0			0
$904$	6209.26	−	3403.42i	0.228448	−	0.125217i
$905$		−	27427.7i		−	1.00743i
$906$		0			0
$907$	18595.8	−	18595.8i	0.680775	−	0.680775i	−0.279400	−	0.960175i	$-0.590135\pi$
$907$	18595.8	−	18595.8i	0.680775	−	0.680775i	0.960175	+	0.279400i	$0.0901354\pi$
$908$	−2992.27	−	41219.4i	−0.109363	−	1.50651i
$909$		0			0
$910$	−564.385	−	210.162i	−0.0205596	−	0.00765583i
$911$	25144.8			0.914472			0.457236	−	0.889345i	$-0.348839\pi$
$911$	25144.8			0.914472			0.457236	+	0.889345i	$0.348839\pi$
$912$		0			0
$913$	−28686.1			−1.03984
$914$	−8808.59	−	3280.08i	−0.318777	−	0.118704i
$915$		0			0
$916$	−19271.5	+	1398.99i	−0.695141	+	0.0504628i
$917$	−98.7128	+	98.7128i	−0.00355484	+	0.00355484i
$918$		0			0
$919$		−	18292.8i		−	0.656608i	−0.944572	−	0.328304i	$-0.893523\pi$
$919$		−	18292.8i		−	0.656608i	0.944572	−	0.328304i	$-0.106477\pi$
$920$	46811.7	+	13663.8i	1.67754	+	0.489655i
$921$		0			0
$922$	4342.61	−	1986.00i	0.155115	−	0.0709387i
$923$	11341.9	−	11341.9i	0.404467	−	0.404467i
$924$		0			0
$925$	−8127.14	−	8127.14i	−0.288885	−	0.288885i
$926$	6119.02	−	16432.5i	0.217153	−	0.583158i
$927$		0			0
$928$	−923.949	−	1429.30i	−0.0326833	−	0.0505593i
$929$	−16680.0			−0.589078			−0.294539	−	0.955640i	$-0.595166\pi$
$929$	−16680.0			−0.589078			−0.294539	+	0.955640i	$0.595166\pi$
$930$		0			0
$931$	22582.4	+	22582.4i	0.794962	+	0.794962i
$932$	−15798.2	+	18271.4i	−0.555242	+	0.642167i
$933$		0			0
$934$	9334.32	−	4268.86i	0.327011	−	0.149552i
$935$			100104.i			3.50135i
$936$		0			0
$937$		−	2053.17i		−	0.0715839i	−0.999359	−	0.0357920i	$-0.988605\pi$
$937$		−	2053.17i		−	0.0715839i	0.999359	−	0.0357920i	$-0.0113954\pi$
$938$	229.731	+	502.332i	0.00799679	+	0.0174858i
$939$		0			0
$940$	−65405.5	+	4748.02i	−2.26946	+	0.164748i
$941$	17468.5	+	17468.5i	0.605160	+	0.605160i	0.941677	−	0.336517i	$-0.109249\pi$
$941$	17468.5	+	17468.5i	0.605160	+	0.605160i	−0.336517	+	0.941677i	$0.609249\pi$
$942$		0			0
$943$	52556.8			1.81494
$944$	21332.1	+	15898.1i	0.735490	+	0.548136i
$945$		0			0
$946$	−11482.6	−	4275.80i	−0.394641	−	0.146954i
$947$	−22999.8	−	22999.8i	−0.789223	−	0.789223i	0.192144	−	0.981367i	$-0.438456\pi$
$947$	−22999.8	−	22999.8i	−0.789223	−	0.789223i	−0.981367	+	0.192144i	$0.938456\pi$
$948$		0			0
$949$	−8970.37	+	8970.37i	−0.306839	+	0.306839i
$950$	−17317.8	−	37867.2i	−0.591435	−	1.29324i
$951$		0			0
$952$	717.275	+	1308.61i	0.0244191	+	0.0445507i
$953$		−	29341.4i		−	0.997336i	−0.866793	−	0.498668i	$-0.833823\pi$
$953$		−	29341.4i		−	0.997336i	0.866793	−	0.498668i	$-0.166177\pi$
$954$		0			0
$955$	5444.52	−	5444.52i	0.184482	−	0.184482i
$956$	17938.2	+	15510.1i	0.606865	+	0.524719i
$957$		0			0
$958$	−4504.61	+	12097.0i	−0.151918	+	0.407972i
$959$	−210.020			−0.00707186
$960$		0			0
$961$	−29562.0			−0.992314
$962$	−1873.47	+	5031.17i	−0.0627891	+	0.168619i
$963$		0			0
$964$	15775.5	+	13640.1i	0.527069	+	0.455724i
$965$	−734.625	+	734.625i	−0.0245061	+	0.0245061i
$966$		0			0
$967$			8861.99i			0.294708i	0.989084	+	0.147354i	$0.0470756\pi$
$967$			8861.99i			0.294708i	−0.989084	+	0.147354i	$0.952924\pi$
$968$	6356.19	+	11596.3i	0.211049	+	0.385042i
$969$		0			0
$970$	19688.7	+	43051.5i	0.651718	+	1.42505i
$971$	−38037.4	+	38037.4i	−1.25714	+	1.25714i	−0.304681	+	0.952454i	$0.598550\pi$
$971$	−38037.4	+	38037.4i	−1.25714	+	1.25714i	−0.952454	+	0.304681i	$0.901450\pi$
$972$		0			0
$973$	−513.491	−	513.491i	−0.0169186	−	0.0169186i
$974$	−2915.16	−	1085.53i	−0.0959013	−	0.0357111i
$975$		0			0
$976$	−11199.9	+	15028.0i	−0.367315	+	0.492863i
$977$	−26081.9			−0.854078			−0.427039	−	0.904233i	$-0.640443\pi$
$977$	−26081.9			−0.854078			−0.427039	+	0.904233i	$0.640443\pi$
$978$		0			0
$979$	−39562.1	−	39562.1i	−1.29153	−	1.29153i
$980$	−46008.8	+	3339.95i	−1.49969	+	0.108868i
$981$		0			0
$982$	18329.0	+	40078.4i	0.595624	+	1.30240i
$983$		−	28987.6i		−	0.940552i	−0.882520	−	0.470276i	$-0.844154\pi$
$983$		−	28987.6i		−	0.940552i	0.882520	−	0.470276i	$-0.155846\pi$
$984$		0			0
$985$		−	14597.3i		−	0.472193i
$986$	3288.11	−	1503.75i	0.106202	−	0.0485691i
$987$		0			0
$988$	−12721.3	+	14712.8i	−0.409633	+	0.473762i
$989$	−8966.45	−	8966.45i	−0.288288	−	0.288288i
$990$		0			0
$991$	33373.6			1.06977			0.534887	−	0.844923i	$-0.320354\pi$
$991$	33373.6			1.06977			0.534887	+	0.844923i	$0.320354\pi$
$992$	−2678.18	−	575.127i	−0.0857180	−	0.0184076i
$993$		0			0
$994$	−294.297	+	790.327i	−0.00939086	+	0.0252189i
$995$	39770.1	+	39770.1i	1.26713	+	1.26713i
$996$		0			0
$997$	−5283.79	+	5283.79i	−0.167843	+	0.167843i	−0.786031	−	0.618188i	$-0.787867\pi$
$997$	−5283.79	+	5283.79i	−0.167843	+	0.167843i	0.618188	+	0.786031i	$0.287867\pi$
$998$	−13106.7	+	5994.08i	−0.415717	+	0.190120i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.4.k.b.109.8		24
3.2	odd	2		48.4.j.a.13.5	✓	24
4.3	odd	2		576.4.k.b.145.12		24
12.11	even	2		192.4.j.a.145.1		24
16.5	even	4	inner	144.4.k.b.37.8		24
16.11	odd	4		576.4.k.b.433.12		24
24.5	odd	2		384.4.j.b.289.6		24
24.11	even	2		384.4.j.a.289.7		24
48.5	odd	4		48.4.j.a.37.5	yes	24
48.11	even	4		192.4.j.a.49.1		24
48.29	odd	4		384.4.j.b.97.6		24
48.35	even	4		384.4.j.a.97.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.5	✓	24	3.2	odd	2
48.4.j.a.37.5	yes	24	48.5	odd	4
144.4.k.b.37.8		24	16.5	even	4	inner
144.4.k.b.109.8		24	1.1	even	1	trivial
192.4.j.a.49.1		24	48.11	even	4
192.4.j.a.145.1		24	12.11	even	2
384.4.j.a.97.7		24	48.35	even	4
384.4.j.a.289.7		24	24.11	even	2
384.4.j.b.97.6		24	48.29	odd	4
384.4.j.b.289.6		24	24.5	odd	2
576.4.k.b.145.12		24	4.3	odd	2
576.4.k.b.433.12		24	16.11	odd	4

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.987020 - 2.65062i) q^{2} +(-6.05158 - 5.23243i) q^{4} +(11.8955 - 11.8955i) q^{5} +0.485059i q^{7} +(-19.8422 + 10.8759i) q^{8} +(-19.7893 - 43.2714i) q^{10} +(30.9469 - 30.9469i) q^{11} +(-18.4511 - 18.4511i) q^{13} +(1.28571 + 0.478764i) q^{14} +(9.24327 + 63.3290i) q^{16} -135.964 q^{17} +(65.8832 + 65.8832i) q^{19} +(-134.229 + 9.74414i) q^{20} +(-51.4834 - 112.574i) q^{22} -128.108i q^{23} -158.004i q^{25} +(-67.1184 + 30.6952i) q^{26} +(2.53804 - 2.93538i) q^{28} +(-6.64817 - 6.64817i) q^{29} -15.1323 q^{31} +(176.984 + 38.0066i) q^{32} +(-134.199 + 360.389i) q^{34} +(5.77001 + 5.77001i) q^{35} +(51.4363 - 51.4363i) q^{37} +(239.660 - 109.603i) q^{38} +(-106.658 + 365.407i) q^{40} +410.253i q^{41} +(69.9911 - 69.9911i) q^{43} +(-349.206 + 25.3501i) q^{44} +(-339.567 - 126.446i) q^{46} +487.269 q^{47} +342.765 q^{49} +(-418.809 - 155.953i) q^{50} +(15.1142 + 208.202i) q^{52} +(217.138 - 217.138i) q^{53} -736.257i q^{55} +(-5.27547 - 9.62466i) q^{56} +(-24.1837 + 11.0599i) q^{58} +(293.944 - 293.944i) q^{59} +(207.076 + 207.076i) q^{61} +(-14.9359 + 40.1099i) q^{62} +(275.428 - 431.605i) q^{64} -438.968 q^{65} +(284.693 + 284.693i) q^{67} +(822.798 + 711.423i) q^{68} +(20.9892 - 9.59899i) q^{70} +614.701i q^{71} -486.171i q^{73} +(-85.5694 - 187.107i) q^{74} +(-53.9681 - 743.427i) q^{76} +(15.0111 + 15.0111i) q^{77} +960.347 q^{79} +(863.281 + 643.375i) q^{80} +(1087.42 + 404.928i) q^{82} +(-463.472 - 463.472i) q^{83} +(-1617.36 + 1617.36i) q^{85} +(-116.437 - 254.603i) q^{86} +(-277.480 + 950.633i) q^{88} -1278.38i q^{89} +(8.94987 - 8.94987i) q^{91} +(-670.318 + 775.258i) q^{92} +(480.945 - 1291.57i) q^{94} +1567.42 q^{95} -994.918 q^{97} +(338.316 - 908.539i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} - 84 q^{8} + 72 q^{10} + 40 q^{11} + 348 q^{14} - 192 q^{16} + 24 q^{19} - 80 q^{20} + 704 q^{22} + 20 q^{26} - 344 q^{28} - 400 q^{29} - 744 q^{31} + 960 q^{32} - 704 q^{34} + 456 q^{35}+ \cdots - 6760 q^{98}+O(q^{100}) \) 24 * q - 20 * q^4 - 84 * q^8 + 72 * q^10 + 40 * q^11 + 348 * q^14 - 192 * q^16 + 24 * q^19 - 80 * q^20 + 704 * q^22 + 20 * q^26 - 344 * q^28 - 400 * q^29 - 744 * q^31 + 960 * q^32 - 704 * q^34 + 456 * q^35 + 16 * q^37 - 1256 * q^38 + 1744 * q^40 + 1240 * q^43 + 200 * q^44 - 1432 * q^46 - 1176 * q^49 - 708 * q^50 + 1008 * q^52 - 752 * q^53 - 1344 * q^56 + 1936 * q^58 + 1376 * q^59 - 912 * q^61 + 996 * q^62 - 56 * q^64 - 976 * q^65 - 2256 * q^67 + 1568 * q^68 - 1760 * q^70 + 2740 * q^74 - 1880 * q^76 - 1904 * q^77 + 5992 * q^79 - 712 * q^80 - 40 * q^82 - 2680 * q^83 - 240 * q^85 + 1712 * q^86 - 3936 * q^88 - 3496 * q^91 - 5296 * q^92 + 5272 * q^94 + 7728 * q^95 - 6760 * q^98

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