LMFDB - Embedded newform 225.4.h.d.46.6

Newspace parameters

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			46.6
Character	$\chi$	$=$	225.46
Dual form			225.4.h.d.181.6

$q$-expansion

$f(q)$	$=$	$q+(-0.626289 + 1.92752i) q^{2} +(3.14904 + 2.28791i) q^{4} +(-3.12321 + 10.7352i) q^{5} -16.4425 q^{7} +(-19.4994 + 14.1671i) q^{8} +O(q^{10})$	\(q+(-0.626289 + 1.92752i) q^{2} +(3.14904 + 2.28791i) q^{4} +(-3.12321 + 10.7352i) q^{5} -16.4425 q^{7} +(-19.4994 + 14.1671i) q^{8} +(-18.7364 - 12.7434i) q^{10} +(-1.41112 + 4.34299i) q^{11} +(-17.0513 - 52.4784i) q^{13} +(10.2977 - 31.6932i) q^{14} +(-5.47256 - 16.8428i) q^{16} +(-1.72699 + 1.25473i) q^{17} +(22.2151 - 16.1402i) q^{19} +(-34.3964 + 26.6601i) q^{20} +(-7.48743 - 5.43993i) q^{22} +(-30.4050 + 93.5770i) q^{23} +(-105.491 - 67.0569i) q^{25} +111.832 q^{26} +(-51.7780 - 37.6189i) q^{28} +(2.70250 + 1.96348i) q^{29} +(54.6052 - 39.6730i) q^{31} -156.928 q^{32} +(-1.33692 - 4.11462i) q^{34} +(51.3533 - 176.514i) q^{35} +(-56.4702 - 173.797i) q^{37} +(17.1975 + 52.9285i) q^{38} +(-91.1869 - 253.578i) q^{40} +(11.7884 + 36.2811i) q^{41} -252.976 q^{43} +(-14.3801 + 10.4477i) q^{44} +(-161.329 - 117.213i) q^{46} +(-35.6846 - 25.9263i) q^{47} -72.6451 q^{49} +(195.321 - 161.339i) q^{50} +(66.3708 - 204.268i) q^{52} +(-163.853 - 119.046i) q^{53} +(-42.2158 - 28.7128i) q^{55} +(320.618 - 232.943i) q^{56} +(-5.47720 + 3.97942i) q^{58} +(36.4118 + 112.064i) q^{59} +(-248.210 + 763.911i) q^{61} +(42.2718 + 130.099i) q^{62} +(142.063 - 437.225i) q^{64} +(616.623 - 19.1484i) q^{65} +(523.504 - 380.348i) q^{67} -8.30906 q^{68} +(308.072 + 209.533i) q^{70} +(-798.476 - 580.127i) q^{71} +(-256.874 + 790.578i) q^{73} +370.365 q^{74} +106.884 q^{76} +(23.2023 - 71.4095i) q^{77} +(822.092 + 597.285i) q^{79} +(197.904 - 6.14563i) q^{80} -77.3154 q^{82} +(-926.758 + 673.329i) q^{83} +(-8.07608 - 22.4584i) q^{85} +(158.436 - 487.616i) q^{86} +(-34.0117 - 104.677i) q^{88} +(-349.060 + 1074.29i) q^{89} +(280.365 + 862.874i) q^{91} +(-309.843 + 225.114i) q^{92} +(72.3224 - 52.5453i) q^{94} +(103.887 + 288.894i) q^{95} +(457.822 + 332.627i) q^{97} +(45.4968 - 140.025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 72 q^{4} + 20 q^{7} + O(q^{10}) $	$ 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.626289	+	1.92752i	−0.221427	+	0.681481i	0.777208	+	0.629244i	$0.216635\pi$
$2$	−0.626289	+	1.92752i	−0.221427	+	0.681481i	−0.998635	+	0.0522374i	$0.983365\pi$
$3$		0			0
$3$		0			0
$4$	3.14904	+	2.28791i	0.393630	+	0.285989i
$5$	−3.12321	+	10.7352i	−0.279349	+	0.960190i
$5$	−3.12321	+	10.7352i	−0.279349	+	0.960190i
$6$		0			0
$7$	−16.4425			−0.887810			−0.443905	−	0.896074i	$-0.646407\pi$
$7$	−16.4425			−0.887810			−0.443905	+	0.896074i	$0.646407\pi$
$8$	−19.4994	+	14.1671i	−0.861759	+	0.626104i
$9$		0			0
$10$	−18.7364	−	12.7434i	−0.592496	−	0.402982i
$11$	−1.41112	+	4.34299i	−0.0386790	+	0.119042i	−0.968532	−	0.248890i	$-0.919934\pi$
$11$	−1.41112	+	4.34299i	−0.0386790	+	0.119042i	0.929853	+	0.367932i	$0.119934\pi$
$12$		0			0
$13$	−17.0513	−	52.4784i	−0.363782	−	1.11961i	−0.950740	−	0.309989i	$-0.899675\pi$
$13$	−17.0513	−	52.4784i	−0.363782	−	1.11961i	0.586958	−	0.809617i	$-0.300325\pi$
$14$	10.2977	−	31.6932i	0.196585	−	0.605026i
$15$		0			0
$16$	−5.47256	−	16.8428i	−0.0855087	−	0.263169i
$17$	−1.72699	+	1.25473i	−0.0246386	+	0.0179010i	−0.600036	−	0.799973i	$-0.704847\pi$
$17$	−1.72699	+	1.25473i	−0.0246386	+	0.0179010i	0.575398	+	0.817874i	$0.304847\pi$
$18$		0			0
$19$	22.2151	−	16.1402i	0.268237	−	0.194885i	−0.445534	−	0.895265i	$-0.646986\pi$
$19$	22.2151	−	16.1402i	0.268237	−	0.194885i	0.713770	+	0.700380i	$0.246986\pi$
$20$	−34.3964	+	26.6601i	−0.384564	+	0.298069i
$21$		0			0
$22$	−7.48743	−	5.43993i	−0.0725602	−	0.0527181i
$23$	−30.4050	+	93.5770i	−0.275647	+	0.848354i	0.713400	+	0.700757i	$0.247154\pi$
$23$	−30.4050	+	93.5770i	−0.275647	+	0.848354i	−0.989047	+	0.147598i	$0.952846\pi$
$24$		0			0
$25$	−105.491	−	67.0569i	−0.843929	−	0.536455i
$26$	111.832			0.843542
$27$		0			0
$28$	−51.7780	−	37.6189i	−0.349469	−	0.253904i
$29$	2.70250	+	1.96348i	0.0173049	+	0.0125728i	0.596404	−	0.802684i	$-0.296596\pi$
$29$	2.70250	+	1.96348i	0.0173049	+	0.0125728i	−0.579099	+	0.815257i	$0.696596\pi$
$30$		0			0
$31$	54.6052	−	39.6730i	0.316367	−	0.229854i	−0.418257	−	0.908329i	$-0.637359\pi$
$31$	54.6052	−	39.6730i	0.316367	−	0.229854i	0.734624	+	0.678475i	$0.237359\pi$
$32$	−156.928			−0.866914
$33$		0			0
$34$	−1.33692	−	4.11462i	−0.00674353	−	0.0207545i
$35$	51.3533	−	176.514i	0.248008	−	0.852466i
$36$		0			0
$37$	−56.4702	−	173.797i	−0.250909	−	0.772219i	−0.994608	−	0.103704i	$-0.966930\pi$
$37$	−56.4702	−	173.797i	−0.250909	−	0.772219i	0.743699	−	0.668515i	$-0.233070\pi$
$38$	17.1975	+	52.9285i	0.0734159	+	0.225951i
$39$		0			0
$40$	−91.1869	−	253.578i	−0.360448	−	1.00235i
$41$	11.7884	+	36.2811i	0.0449035	+	0.138199i	0.970995	−	0.239101i	$-0.0768527\pi$
$41$	11.7884	+	36.2811i	0.0449035	+	0.138199i	−0.926091	+	0.377300i	$0.876853\pi$
$42$		0			0
$43$	−252.976			−0.897173			−0.448586	−	0.893739i	$-0.648072\pi$
$43$	−252.976			−0.897173			−0.448586	+	0.893739i	$0.648072\pi$
$44$	−14.3801	+	10.4477i	−0.0492699	+	0.0357967i
$45$		0			0
$46$	−161.329	−	117.213i	−0.517102	−	0.375697i
$47$	−35.6846	−	25.9263i	−0.110747	−	0.0804627i	0.531033	−	0.847351i	$-0.321804\pi$
$47$	−35.6846	−	25.9263i	−0.110747	−	0.0804627i	−0.641780	+	0.766888i	$0.721804\pi$
$48$		0			0
$49$	−72.6451			−0.211793
$50$	195.321	−	161.339i	0.552452	−	0.456336i
$51$		0			0
$52$	66.3708	−	204.268i	0.177000	−	0.544749i
$53$	−163.853	−	119.046i	−0.424659	−	0.308533i	0.354851	−	0.934923i	$-0.384532\pi$
$53$	−163.853	−	119.046i	−0.424659	−	0.308533i	−0.779510	+	0.626390i	$0.784532\pi$
$54$		0			0
$55$	−42.2158	−	28.7128i	−0.103498	−	0.0703934i
$56$	320.618	−	232.943i	0.765078	−	0.555862i
$57$		0			0
$58$	−5.47720	+	3.97942i	−0.0123999	+	0.00900903i
$59$	36.4118	+	112.064i	0.0803460	+	0.247280i	0.983159	−	0.182755i	$-0.0585014\pi$
$59$	36.4118	+	112.064i	0.0803460	+	0.247280i	−0.902813	+	0.430034i	$0.858501\pi$
$60$		0			0
$61$	−248.210	+	763.911i	−0.520984	+	1.60342i	0.251139	+	0.967951i	$0.419195\pi$
$61$	−248.210	+	763.911i	−0.520984	+	1.60342i	−0.772123	+	0.635473i	$0.780805\pi$
$62$	42.2718	+	130.099i	0.0865892	+	0.266494i
$63$		0			0
$64$	142.063	−	437.225i	0.277467	−	0.853954i
$65$	616.623	−	19.1484i	1.17666	−	0.0365395i
$66$		0			0
$67$	523.504	−	380.348i	0.954571	−	0.693536i	0.00268734	−	0.999996i	$-0.499145\pi$
$67$	523.504	−	380.348i	0.954571	−	0.693536i	0.951884	+	0.306460i	$0.0991446\pi$
$68$	−8.30906			−0.0148180
$69$		0			0
$70$	308.072	+	209.533i	0.526024	+	0.357772i
$71$	−798.476	−	580.127i	−1.33467	−	0.969696i	−0.999622	−	0.0274953i	$-0.991247\pi$
$71$	−798.476	−	580.127i	−1.33467	−	0.969696i	−0.335050	−	0.942200i	$-0.608753\pi$
$72$		0			0
$73$	−256.874	+	790.578i	−0.411847	+	1.26754i	0.503193	+	0.864174i	$0.332158\pi$
$73$	−256.874	+	790.578i	−0.411847	+	1.26754i	−0.915040	+	0.403362i	$0.867842\pi$
$74$	370.365			0.581811
$75$		0			0
$76$	106.884			0.161321
$77$	23.2023	−	71.4095i	0.0343396	−	0.105687i
$78$		0			0
$79$	822.092	+	597.285i	1.17079	+	0.850630i	0.991104	−	0.133093i	$-0.0424909\pi$
$79$	822.092	+	597.285i	1.17079	+	0.850630i	0.179689	+	0.983724i	$0.442491\pi$
$80$	197.904	−	6.14563i	0.276579	−	0.00858878i
$81$		0			0
$82$	−77.3154			−0.104123
$83$	−926.758	+	673.329i	−1.22560	+	0.890452i	−0.996553	−	0.0829629i	$-0.973562\pi$
$83$	−926.758	+	673.329i	−1.22560	+	0.890452i	−0.229049	+	0.973415i	$0.573562\pi$
$84$		0			0
$85$	−8.07608	−	22.4584i	−0.0103056	−	0.0286583i
$86$	158.436	−	487.616i	0.198658	−	0.611406i
$87$		0			0
$88$	−34.0117	−	104.677i	−0.0412006	−	0.126802i
$89$	−349.060	+	1074.29i	−0.415733	+	1.27949i	0.495861	+	0.868402i	$0.334853\pi$
$89$	−349.060	+	1074.29i	−0.415733	+	1.27949i	−0.911594	+	0.411093i	$0.865147\pi$
$90$		0			0
$91$	280.365	+	862.874i	0.322969	+	0.993998i
$92$	−309.843	+	225.114i	−0.351123	+	0.255106i
$93$		0			0
$94$	72.3224	−	52.5453i	0.0793562	−	0.0576557i
$95$	103.887	+	288.894i	0.112195	+	0.311999i
$96$		0			0
$97$	457.822	+	332.627i	0.479224	+	0.348177i	0.801025	−	0.598630i	$-0.204288\pi$
$97$	457.822	+	332.627i	0.479224	+	0.348177i	−0.321801	+	0.946807i	$0.604288\pi$
$98$	45.4968	−	140.025i	0.0468967	−	0.144333i
$99$		0			0
$100$	−178.776	−	452.519i	−0.178776	−	0.452519i
$101$	−732.732			−0.721877			−0.360938	−	0.932590i	$-0.617544\pi$
$101$	−732.732			−0.721877			−0.360938	+	0.932590i	$0.617544\pi$
$102$		0			0
$103$	148.901	+	108.183i	0.142443	+	0.103491i	0.656725	−	0.754130i	$-0.271941\pi$
$103$	148.901	+	108.183i	0.142443	+	0.103491i	−0.514282	+	0.857621i	$0.671941\pi$
$104$	1075.96	+	781.728i	1.01448	+	0.737065i
$105$		0			0
$106$	332.083	−	241.272i	0.304290	−	0.221080i
$107$	−1461.97			−1.32088			−0.660440	−	0.750879i	$-0.729630\pi$
$107$	−1461.97			−1.32088			−0.660440	+	0.750879i	$0.729630\pi$
$108$		0			0
$109$	551.250	+	1696.57i	0.484405	+	1.49085i	0.832840	+	0.553514i	$0.186713\pi$
$109$	551.250	+	1696.57i	0.484405	+	1.49085i	−0.348435	+	0.937333i	$0.613287\pi$
$110$	81.7838	−	63.3893i	0.0708889	−	0.0549448i
$111$		0			0
$112$	89.9823	+	276.937i	0.0759155	+	0.233644i
$113$	602.823	+	1855.30i	0.501848	+	1.54453i	0.806006	+	0.591907i	$0.201625\pi$
$113$	602.823	+	1855.30i	0.501848	+	1.54453i	−0.304158	+	0.952622i	$0.598375\pi$
$114$		0			0
$115$	−909.611	−	618.666i	−0.737580	−	0.501660i
$116$	4.01802	+	12.3662i	0.00321606	+	0.00989803i
$117$		0			0
$118$	−238.810			−0.186307
$119$	28.3959	−	20.6308i	0.0218744	−	0.0158926i
$120$		0			0
$121$	1059.93	+	770.085i	0.796342	+	0.578576i
$122$	−1317.00	−	956.859i	−0.977343	−	0.710081i
$123$		0			0
$124$	262.722			0.190267
$125$	1049.34	−	923.040i	0.750849	−	0.660474i
$126$		0			0
$127$	−286.464	+	881.645i	−0.200154	+	0.616011i	0.799724	+	0.600368i	$0.204979\pi$
$127$	−286.464	+	881.645i	−0.200154	+	0.616011i	−0.999878	+	0.0156424i	$0.995021\pi$
$128$	−261.874	−	190.263i	−0.180833	−	0.131383i
$129$		0			0
$130$	−349.275	+	1200.55i	−0.235642	+	0.809960i
$131$	2108.91	−	1532.21i	1.40654	−	1.02191i	0.412720	−	0.910858i	$-0.364579\pi$
$131$	2108.91	−	1532.21i	1.40654	−	1.02191i	0.993815	−	0.111050i	$-0.0354213\pi$
$132$		0			0
$133$	−365.271	+	265.385i	−0.238143	+	0.173021i
$134$	405.264	+	1247.27i	0.261265	+	0.804090i
$135$		0			0
$136$	15.8992	−	48.9328i	0.0100246	−	0.0308526i
$137$	−902.756	−	2778.40i	−0.562976	−	1.73266i	−0.673890	−	0.738831i	$-0.735378\pi$
$137$	−902.756	−	2778.40i	−0.562976	−	1.73266i	0.110915	−	0.993830i	$-0.464622\pi$
$138$		0			0
$139$	308.366	−	949.054i	0.188167	−	0.579120i	−0.811821	−	0.583906i	$-0.801524\pi$
$139$	308.366	−	949.054i	0.188167	−	0.579120i	0.999989	+	0.00478634i	$0.00152355\pi$
$140$	565.562	−	438.358i	0.341420	−	0.264629i
$141$		0			0
$142$	1618.28	−	1175.75i	0.956361	−	0.694837i
$143$	251.974			0.147351
$144$		0			0
$145$	−29.5190	+	22.8797i	−0.0169063	+	0.0131038i
$146$	−1362.98	−	990.261i	−0.772608	−	0.561333i
$147$		0			0
$148$	219.806	−	676.494i	0.122081	−	0.375726i
$149$	2608.22			1.43405			0.717026	−	0.697046i	$-0.245503\pi$
$149$	2608.22			1.43405			0.717026	+	0.697046i	$0.245503\pi$
$150$		0			0
$151$	−434.771			−0.234312			−0.117156	−	0.993114i	$-0.537378\pi$
$151$	−434.771			−0.234312			−0.117156	+	0.993114i	$0.537378\pi$
$152$	−204.520	+	629.448i	−0.109137	+	0.335888i
$153$		0			0
$154$	123.112	+	89.4459i	0.0644197	+	0.0468036i
$155$	255.356	+	710.107i	0.132327	+	0.367982i
$156$		0			0
$157$	−2183.01			−1.10970			−0.554851	−	0.831949i	$-0.687225\pi$
$157$	−2183.01			−1.10970			−0.554851	+	0.831949i	$0.687225\pi$
$158$	−1666.15	+	1210.53i	−0.838933	+	0.609521i
$159$		0			0
$160$	490.120	−	1684.66i	0.242171	−	0.832402i
$161$	499.933	−	1538.64i	0.244722	−	0.753178i
$162$		0			0
$163$	1.56141	+	4.80554i	0.000750303	+	0.00230920i	0.951431	−	0.307862i	$-0.0996136\pi$
$163$	1.56141	+	4.80554i	0.000750303	+	0.00230920i	−0.950681	+	0.310171i	$0.899614\pi$
$164$	−45.8856	+	141.221i	−0.0218480	+	0.0672411i
$165$		0			0
$166$	−717.437	−	2208.04i	−0.335445	−	1.03239i
$167$	−182.453	+	132.560i	−0.0845428	+	0.0614239i	−0.629254	−	0.777200i	$-0.716639\pi$
$167$	−182.453	+	132.560i	−0.0845428	+	0.0614239i	0.544711	+	0.838624i	$0.316639\pi$
$168$		0			0
$169$	−685.824	+	498.280i	−0.312164	+	0.226800i
$170$	48.3470	−	1.50135i	0.0218120	−	0.000677343i
$171$		0			0
$172$	−796.631	−	578.786i	−0.353154	−	0.256582i
$173$	−1021.65	+	3144.32i	−0.448986	+	1.38184i	0.429066	+	0.903273i	$0.358843\pi$
$173$	−1021.65	+	3144.32i	−0.448986	+	1.38184i	−0.878052	+	0.478565i	$0.841157\pi$
$174$		0			0
$175$	1734.53	+	1102.58i	0.749248	+	0.476270i
$176$	80.8705			0.0346355
$177$		0			0
$178$	−1852.11	−	1345.64i	−0.779897	−	0.566629i
$179$	1464.76	+	1064.21i	0.611627	+	0.444373i	0.849987	−	0.526804i	$-0.176610\pi$
$179$	1464.76	+	1064.21i	0.611627	+	0.444373i	−0.238360	+	0.971177i	$0.576610\pi$
$180$		0			0
$181$	−1447.42	+	1051.61i	−0.594395	+	0.431854i	−0.843885	−	0.536524i	$-0.819737\pi$
$181$	−1447.42	+	1051.61i	−0.594395	+	0.431854i	0.249490	+	0.968377i	$0.419737\pi$
$182$	−1838.80			−0.748905
$183$		0			0
$184$	−732.838	−	2255.44i	−0.293617	−	0.903661i
$185$	2042.13	−	63.4155i	0.811568	−	0.0252022i
$186$		0			0
$187$	−3.01228	−	9.27085i	−0.00117797	−	0.00362541i
$188$	−53.0549	−	163.286i	−0.0205821	−	0.0633451i
$189$		0			0
$190$	−621.912	+	19.3126i	−0.237464	+	0.00737414i
$191$	−1406.35	−	4328.29i	−0.532774	−	1.63971i	−0.748411	−	0.663235i	$-0.769183\pi$
$191$	−1406.35	−	4328.29i	−0.532774	−	1.63971i	0.215637	−	0.976474i	$-0.430817\pi$
$192$		0			0
$193$	3534.94			1.31840			0.659199	−	0.751969i	$-0.270895\pi$
$193$	3534.94			1.31840			0.659199	+	0.751969i	$0.270895\pi$
$194$	−927.874	+	674.140i	−0.343389	+	0.249487i
$195$		0			0
$196$	−228.762	−	166.206i	−0.0833682	−	0.0605706i
$197$	−135.139	−	98.1842i	−0.0488744	−	0.0355093i	0.563080	−	0.826402i	$-0.309616\pi$
$197$	−135.139	−	98.1842i	−0.0488744	−	0.0355093i	−0.611954	+	0.790893i	$0.709616\pi$
$198$		0			0
$199$	−3173.44			−1.13045			−0.565224	−	0.824937i	$-0.691210\pi$
$199$	−3173.44			−1.13045			−0.565224	+	0.824937i	$0.691210\pi$
$200$	3007.01	−	186.938i	1.06314	−	0.0660925i
$201$		0			0
$202$	458.902	−	1412.36i	0.159843	−	0.491946i
$203$	−44.4358	−	32.2845i	−0.0153635	−	0.0111622i
$204$		0			0
$205$	−426.304	+	13.2383i	−0.145241	+	0.00451026i
$206$	−301.779	+	219.256i	−0.102068	+	0.0741566i
$207$		0			0
$208$	−790.569	+	574.382i	−0.263539	+	0.191472i
$209$	38.7485	+	119.256i	0.0128244	+	0.0394693i
$210$		0			0
$211$	842.745	−	2593.70i	0.274962	−	0.846245i	−0.714268	−	0.699873i	$-0.753240\pi$
$211$	842.745	−	2593.70i	0.274962	−	0.846245i	0.989229	−	0.146373i	$-0.0467599\pi$
$212$	−243.612	−	749.762i	−0.0789215	−	0.242895i
$213$		0			0
$214$	915.617	−	2817.98i	0.292478	−	0.900154i
$215$	790.097	−	2715.76i	0.250624	−	0.861456i
$216$		0			0
$217$	−897.844	+	652.322i	−0.280874	+	0.204067i
$218$	−3615.42			−1.12324
$219$		0			0
$220$	−67.2469	−	187.004i	−0.0206081	−	0.0573082i
$221$	95.2934	+	69.2347i	0.0290051	+	0.0210734i
$222$		0			0
$223$	−11.6372	+	35.8157i	−0.00349456	+	0.0107551i	−0.952789	−	0.303634i	$-0.901800\pi$
$223$	−11.6372	+	35.8157i	−0.00349456	+	0.0107551i	0.949294	+	0.314390i	$0.101800\pi$
$224$	2580.29			0.769655
$225$		0			0
$226$	−3953.67			−1.16369
$227$	−1025.04	+	3154.75i	−0.299710	+	0.922413i	0.681888	+	0.731456i	$0.261159\pi$
$227$	−1025.04	+	3154.75i	−0.299710	+	0.922413i	−0.981598	+	0.190957i	$0.938841\pi$
$228$		0			0
$229$	−3988.04	−	2897.48i	−1.15082	−	0.836118i	−0.162228	−	0.986753i	$-0.551868\pi$
$229$	−3988.04	−	2897.48i	−1.15082	−	0.836118i	−0.988589	+	0.150635i	$0.951868\pi$
$230$	1762.17	−	1365.83i	0.505192	−	0.391566i
$231$		0			0
$232$	−80.5141			−0.0227845
$233$	−5.77631	+	4.19673i	−0.00162411	+	0.00117999i	−0.588597	−	0.808427i	$-0.700320\pi$
$233$	−5.77631	+	4.19673i	−0.00162411	+	0.00117999i	0.586973	+	0.809607i	$0.300320\pi$
$234$		0			0
$235$	389.776	−	302.109i	0.108197	−	0.0838614i
$236$	−141.730	+	436.201i	−0.0390926	+	0.120315i
$237$		0			0
$238$	21.9823	+	67.6545i	0.00598698	+	0.0184260i
$239$	−2227.98	+	6857.03i	−0.602997	+	1.85583i	−0.0929815	+	0.995668i	$0.529640\pi$
$239$	−2227.98	+	6857.03i	−0.602997	+	1.85583i	−0.510015	+	0.860165i	$0.670360\pi$
$240$		0			0
$241$	−1061.81	−	3267.92i	−0.283806	−	0.873465i	−0.986754	−	0.162224i	$-0.948133\pi$
$241$	−1061.81	−	3267.92i	−0.283806	−	0.873465i	0.702948	−	0.711241i	$-0.251867\pi$
$242$	−2148.18	+	1560.74i	−0.570620	+	0.414580i
$243$		0			0
$244$	−2529.39	+	1837.71i	−0.663637	+	0.482160i
$245$	226.886	−	779.863i	0.0591642	−	0.203362i
$246$		0			0
$247$	−1225.81	−	890.601i	−0.315774	−	0.229424i
$248$	−502.715	+	1547.20i	−0.128719	+	0.396158i
$249$		0			0
$250$	1121.99	+	2600.72i	0.283842	+	0.657936i
$251$	1687.00			0.424233			0.212117	−	0.977244i	$-0.431964\pi$
$251$	1687.00			0.424233			0.212117	+	0.977244i	$0.431964\pi$
$252$		0			0
$253$	−363.499	−	264.097i	−0.0903279	−	0.0656271i
$254$	−1519.98	−	1104.33i	−0.375480	−	0.272802i
$255$		0			0
$256$	3506.15	−	2547.37i	0.855993	−	0.621915i
$257$	−2098.27			−0.509286			−0.254643	−	0.967035i	$-0.581958\pi$
$257$	−2098.27			−0.509286			−0.254643	+	0.967035i	$0.581958\pi$
$258$		0			0
$259$	928.509	+	2857.66i	0.222760	+	0.685584i
$260$	1985.58	+	1350.48i	0.473617	+	0.322128i
$261$		0			0
$262$	1632.58	+	5024.57i	0.384966	+	1.18480i
$263$	43.9940	+	135.400i	0.0103148	+	0.0317456i	0.956081	−	0.293101i	$-0.0946873\pi$
$263$	43.9940	+	135.400i	0.0103148	+	0.0317456i	−0.945767	+	0.324847i	$0.894687\pi$
$264$		0			0
$265$	1789.74	−	1387.19i	0.414878	−	0.321565i
$266$	−282.770	−	870.275i	−0.0651794	−	0.200601i
$267$		0			0
$268$	2518.74			0.574092
$269$	−2534.35	+	1841.31i	−0.574432	+	0.417349i	−0.836712	−	0.547643i	$-0.815525\pi$
$269$	−2534.35	+	1841.31i	−0.574432	+	0.417349i	0.262281	+	0.964992i	$0.415525\pi$
$270$		0			0
$271$	2812.49	+	2043.40i	0.630431	+	0.458035i	0.856550	−	0.516065i	$-0.172604\pi$
$271$	2812.49	+	2043.40i	0.630431	+	0.458035i	−0.226118	+	0.974100i	$0.572604\pi$
$272$	30.5841	+	22.2207i	0.00681778	+	0.00495341i
$273$		0			0
$274$	5920.80			1.30543
$275$	440.088	−	363.521i	0.0965030	−	0.0797133i
$276$		0			0
$277$	−1027.03	+	3160.87i	−0.222774	+	0.685626i	0.775736	+	0.631057i	$0.217379\pi$
$277$	−1027.03	+	3160.87i	−0.222774	+	0.685626i	−0.998510	+	0.0545694i	$0.982621\pi$
$278$	1636.19	+	1188.76i	0.352994	+	0.256465i
$279$		0			0
$280$	1499.34	+	4169.44i	0.320009	+	0.889899i
$281$	−2319.48	+	1685.20i	−0.492415	+	0.357760i	−0.806112	−	0.591763i	$-0.798432\pi$
$281$	−2319.48	+	1685.20i	−0.492415	+	0.357760i	0.313698	+	0.949523i	$0.398432\pi$
$282$		0			0
$283$	6659.26	−	4838.24i	1.39877	−	1.01627i	0.403933	−	0.914789i	$-0.367643\pi$
$283$	6659.26	−	4838.24i	1.39877	−	1.01627i	0.994838	−	0.101478i	$-0.0323571\pi$
$284$	−1187.15	−	3653.69i	−0.248045	−	0.763403i
$285$		0			0
$286$	−157.809	+	485.686i	−0.0326274	+	0.100417i
$287$	−193.831	−	596.550i	−0.0398658	−	0.122694i
$288$		0			0
$289$	−1516.79	+	4668.21i	−0.308730	+	0.950174i
$290$	−25.6136	−	71.2277i	−0.00518649	−	0.0144229i
$291$		0			0
$292$	−2617.68	+	1901.86i	−0.524617	+	0.381157i
$293$	−2288.26			−0.456251			−0.228125	−	0.973632i	$-0.573260\pi$
$293$	−2288.26			−0.456251			−0.228125	+	0.973632i	$0.573260\pi$
$294$		0			0
$295$	−1316.76	+	40.8901i	−0.259880	+	0.00807022i
$296$	3563.34	+	2588.92i	0.699713	+	0.508371i
$297$		0			0
$298$	−1633.50	+	5027.40i	−0.317538	+	0.977280i
$299$	5429.21			1.05010
$300$		0			0
$301$	4159.55			0.796519
$302$	272.292	−	838.029i	0.0518830	−	0.159679i
$303$		0			0
$304$	−393.420	−	285.836i	−0.0742242	−	0.0539271i
$305$	−7425.57	−	5050.45i	−1.39405	−	0.948157i
$306$		0			0
$307$	−2783.54			−0.517475			−0.258737	−	0.965948i	$-0.583306\pi$
$307$	−2783.54			−0.517475			−0.258737	+	0.965948i	$0.583306\pi$
$308$	236.444	−	171.786i	0.0437423	−	0.0317806i
$309$		0			0
$310$	−1528.67	+	47.4709i	−0.280073	+	0.00869731i
$311$	2462.79	−	7579.70i	0.449043	−	1.38201i	−0.428946	−	0.903330i	$-0.641115\pi$
$311$	2462.79	−	7579.70i	0.449043	−	1.38201i	0.877989	−	0.478681i	$-0.158885\pi$
$312$		0			0
$313$	−1489.79	−	4585.11i	−0.269035	−	0.828005i	−0.990736	−	0.135800i	$-0.956640\pi$
$313$	−1489.79	−	4585.11i	−0.269035	−	0.828005i	0.721701	−	0.692205i	$-0.243360\pi$
$314$	1367.20	−	4207.80i	0.245718	−	0.756242i
$315$		0			0
$316$	1222.27	+	3761.75i	0.217588	+	0.669668i
$317$	6986.98	−	5076.34i	1.23794	−	0.899418i	0.240484	−	0.970653i	$-0.422694\pi$
$317$	6986.98	−	5076.34i	1.23794	−	0.899418i	0.997460	+	0.0712347i	$0.0226939\pi$
$318$		0			0
$319$	−12.3409	+	8.96622i	−0.00216602	+	0.00157371i
$320$	4250.02	+	2890.63i	0.742448	+	0.504971i
$321$		0			0
$322$	2652.65	+	1927.26i	0.459088	+	0.333547i
$323$	−18.1136	+	55.7478i	−0.00312033	+	0.00960338i
$324$		0			0
$325$	−1720.28	+	6679.41i	−0.293612	+	1.14002i
$326$	−10.2407			−0.00173981
$327$		0			0
$328$	−743.866	−	540.450i	−0.125223	−	0.0909797i
$329$	586.742	+	426.293i	0.0983226	+	0.0714356i
$330$		0			0
$331$	1556.01	−	1130.51i	0.258388	−	0.187730i	−0.451048	−	0.892500i	$-0.648950\pi$
$331$	1556.01	−	1130.51i	0.258388	−	0.187730i	0.709436	+	0.704770i	$0.248950\pi$
$332$	−4458.92			−0.737093
$333$		0			0
$334$	−141.244	−	434.703i	−0.0231392	−	0.0712152i
$335$	2448.12	+	6807.86i	0.399269	+	1.11031i
$336$		0			0
$337$	721.800	+	2221.47i	0.116673	+	0.359084i	0.992292	−	0.123919i	$-0.0395462\pi$
$337$	721.800	+	2221.47i	0.116673	+	0.359084i	−0.875619	+	0.483003i	$0.839546\pi$
$338$	−530.921	−	1634.01i	−0.0854388	−	0.262953i
$339$		0			0
$340$	25.9509	−	89.1998i	0.00413937	−	0.0142280i
$341$	95.2447	+	293.133i	0.0151255	+	0.0465515i
$342$		0			0
$343$	6834.23			1.07584
$344$	4932.87	−	3583.94i	0.773147	−	0.561724i
$345$		0			0
$346$	−5420.88	−	3938.50i	−0.842279	−	0.611952i
$347$	5254.02	+	3817.27i	0.812826	+	0.590553i	0.914649	−	0.404250i	$-0.132467\pi$
$347$	5254.02	+	3817.27i	0.812826	+	0.590553i	−0.101822	+	0.994803i	$0.532467\pi$
$348$		0			0
$349$	4713.73			0.722980			0.361490	−	0.932376i	$-0.382268\pi$
$349$	4713.73			0.722980			0.361490	+	0.932376i	$0.382268\pi$
$350$	−3211.57	+	2652.81i	−0.490473	+	0.405140i
$351$		0			0
$352$	221.445	−	681.537i	0.0335314	−	0.103199i
$353$	3185.69	+	2314.54i	0.480331	+	0.348981i	0.801454	−	0.598056i	$-0.204060\pi$
$353$	3185.69	+	2314.54i	0.480331	+	0.348981i	−0.321123	+	0.947038i	$0.604060\pi$
$354$		0			0
$355$	8721.62	−	6759.98i	1.30393	−	1.01066i
$356$	−3557.10	+	2584.38i	−0.529567	+	0.384753i
$357$		0			0
$358$	−2968.65	+	2156.85i	−0.438262	+	0.318416i
$359$	−2913.64	−	8967.26i	−0.428345	−	1.31831i	−0.899754	−	0.436397i	$-0.856254\pi$
$359$	−2913.64	−	8967.26i	−0.428345	−	1.31831i	0.471409	−	0.881915i	$-0.343746\pi$
$360$		0			0
$361$	−1886.54	+	5806.18i	−0.275046	+	0.846506i
$362$	−1120.50	−	3448.53i	−0.162685	−	0.500693i
$363$		0			0
$364$	−1091.30	+	3358.68i	−0.157142	+	0.483633i
$365$	−7684.78	−	5226.75i	−1.10203	−	0.749536i
$366$		0			0
$367$	2067.94	−	1502.45i	0.294130	−	0.213698i	−0.430927	−	0.902387i	$-0.641813\pi$
$367$	2067.94	−	1502.45i	0.294130	−	0.213698i	0.725057	+	0.688689i	$0.241813\pi$
$368$	1742.49			0.246831
$369$		0			0
$370$	−1156.73	+	3975.96i	−0.162528	+	0.558649i
$371$	2694.14	+	1957.41i	0.377016	+	0.273918i
$372$		0			0
$373$	−3360.65	+	10343.0i	−0.466509	+	1.43577i	0.390565	+	0.920575i	$0.372280\pi$
$373$	−3360.65	+	10343.0i	−0.466509	+	1.43577i	−0.857074	+	0.515193i	$0.827720\pi$
$374$	19.7563			0.00273148
$375$		0			0
$376$	1063.13			0.145816
$377$	56.9593	−	175.303i	0.00778131	−	0.0239484i
$378$		0			0
$379$	−5989.27	−	4351.46i	−0.811737	−	0.589761i	0.102597	−	0.994723i	$-0.467285\pi$
$379$	−5989.27	−	4351.46i	−0.811737	−	0.589761i	−0.914334	+	0.404962i	$0.867285\pi$
$380$	−333.820	+	1147.42i	−0.0450648	+	0.154899i
$381$		0			0
$382$	9223.65			1.23540
$383$	5046.70	−	3666.64i	0.673301	−	0.489182i	−0.197828	−	0.980237i	$-0.563389\pi$
$383$	5046.70	−	3666.64i	0.673301	−	0.489182i	0.871128	+	0.491055i	$0.163389\pi$
$384$		0			0
$385$	694.132	+	472.110i	0.0918864	+	0.0624959i
$386$	−2213.90	+	6813.67i	−0.291928	+	0.898463i
$387$		0			0
$388$	680.678	+	2094.91i	0.0890624	+	0.274106i
$389$	−2416.91	+	7438.49i	−0.315019	+	0.969528i	0.660728	+	0.750625i	$0.270248\pi$
$389$	−2416.91	+	7438.49i	−0.315019	+	0.969528i	−0.975747	+	0.218903i	$0.929752\pi$
$390$		0			0
$391$	−64.9047	−	199.756i	−0.00839481	−	0.0258366i
$392$	1416.53	−	1029.17i	0.182515	−	0.132605i
$393$		0			0
$394$	273.888	−	198.991i	0.0350210	−	0.0254443i
$395$	−8979.57	+	6959.92i	−1.14383	+	0.886560i
$396$		0			0
$397$	−6541.82	−	4752.91i	−0.827013	−	0.600860i	0.0916994	−	0.995787i	$-0.470770\pi$
$397$	−6541.82	−	4752.91i	−0.827013	−	0.600860i	−0.918713	+	0.394926i	$0.870770\pi$
$398$	1987.49	−	6116.87i	0.250311	−	0.770379i
$399$		0			0
$400$	−552.120	+	2143.74i	−0.0690150	+	0.267967i
$401$	−1345.64			−0.167576			−0.0837882	−	0.996484i	$-0.526702\pi$
$401$	−1345.64			−0.167576			−0.0837882	+	0.996484i	$0.526702\pi$
$402$		0			0
$403$	−3013.06	−	2189.12i	−0.372435	−	0.270590i
$404$	−2307.40	−	1676.43i	−0.284153	−	0.206449i
$405$		0			0
$406$	90.0587	−	65.4315i	0.0110087	−	0.00799830i
$407$	834.486			0.101631
$408$		0			0
$409$	917.900	+	2825.00i	0.110971	+	0.341534i	0.991085	−	0.133228i	$-0.0425342\pi$
$409$	917.900	+	2825.00i	0.110971	+	0.341534i	−0.880114	+	0.474762i	$0.842534\pi$
$410$	241.472	−	830.000i	0.0290865	−	0.0999776i
$411$		0			0
$412$	221.382	+	681.344i	0.0264726	+	0.0814743i
$413$	−598.700	−	1842.61i	−0.0713320	−	0.219537i
$414$		0			0
$415$	−4333.90	−	12051.9i	−0.512633	−	1.42556i
$416$	2675.82	+	8235.34i	0.315368	+	0.970603i
$417$		0			0
$418$	−254.136			−0.0297373
$419$	−12542.9	+	9112.94i	−1.46243	+	1.06252i	−0.479713	+	0.877425i	$0.659259\pi$
$419$	−12542.9	+	9112.94i	−1.46243	+	1.06252i	−0.982721	+	0.185095i	$0.940741\pi$
$420$		0			0
$421$	−1956.11	−	1421.19i	−0.226448	−	0.164524i	0.468776	−	0.883317i	$-0.344695\pi$
$421$	−1956.11	−	1421.19i	−0.226448	−	0.164524i	−0.695225	+	0.718793i	$0.744695\pi$
$422$	4471.61	+	3248.81i	0.515816	+	0.374763i
$423$		0			0
$424$	4881.57			0.559127
$425$	266.320	−	16.5564i	0.0303962	−	0.00188965i
$426$		0			0
$427$	4081.18	−	12560.6i	0.462535	−	1.42354i
$428$	−4603.81	−	3344.86i	−0.519938	−	0.377757i
$429$		0			0
$430$	4739.85	+	3223.78i	0.531571	+	0.361545i
$431$	−6422.91	+	4666.52i	−0.717821	+	0.521527i	−0.885687	−	0.464282i	$-0.846312\pi$
$431$	−6422.91	+	4666.52i	−0.717821	+	0.521527i	0.167866	+	0.985810i	$0.446312\pi$
$432$		0			0
$433$	1146.40	−	832.906i	0.127234	−	0.0924409i	−0.522348	−	0.852732i	$-0.674944\pi$
$433$	1146.40	−	832.906i	0.127234	−	0.0924409i	0.649582	+	0.760291i	$0.274944\pi$
$434$	−695.054	−	2139.15i	−0.0768747	−	0.236596i
$435$		0			0
$436$	−2145.70	+	6603.79i	−0.235689	+	0.725377i
$437$	834.902	+	2569.57i	0.0913931	+	0.281279i
$438$		0			0
$439$	4154.10	−	12785.0i	0.451628	−	1.38997i	−0.423422	−	0.905933i	$-0.639171\pi$
$439$	4154.10	−	12785.0i	0.451628	−	1.38997i	0.875049	−	0.484034i	$-0.160829\pi$
$440$	1229.96	−	38.1948i	0.133264	−	0.00413833i
$441$		0			0
$442$	−193.132	+	140.319i	−0.0207836	+	0.0151002i
$443$	13347.6			1.43152			0.715759	−	0.698347i	$-0.246081\pi$
$443$	13347.6			1.43152			0.715759	+	0.698347i	$0.246081\pi$
$444$		0			0
$445$	−10442.6	−	7102.49i	−1.11242	−	0.756608i
$446$	−61.7472	−	44.8619i	−0.00655564	−	0.00476295i
$447$		0			0
$448$	−2335.87	+	7189.05i	−0.246338	+	0.758149i
$449$	3063.89			0.322035			0.161017	−	0.986952i	$-0.448522\pi$
$449$	3063.89			0.322035			0.161017	+	0.986952i	$0.448522\pi$
$450$		0			0
$451$	−174.203			−0.0181883
$452$	−2346.45	+	7221.62i	−0.244176	+	0.751496i
$453$		0			0
$454$	−5438.86	−	3951.57i	−0.562243	−	0.408494i
$455$	−10138.8	+	314.847i	−1.04465	+	0.0324401i
$456$		0			0
$457$	−185.070			−0.0189435			−0.00947177	−	0.999955i	$-0.503015\pi$
$457$	−185.070			−0.0189435			−0.00947177	+	0.999955i	$0.503015\pi$
$458$	8082.62	−	5872.37i	0.824620	−	0.599122i
$459$		0			0
$460$	−1448.95	−	4029.31i	−0.146864	−	0.408408i
$461$	−2389.28	+	7353.45i	−0.241388	+	0.742916i	0.754822	+	0.655930i	$0.227723\pi$
$461$	−2389.28	+	7353.45i	−0.241388	+	0.742916i	−0.996210	+	0.0869857i	$0.972277\pi$
$462$		0			0
$463$	−4560.19	−	14034.8i	−0.457732	−	1.40875i	−0.867897	−	0.496744i	$-0.834529\pi$
$463$	−4560.19	−	14034.8i	−0.457732	−	1.40875i	0.410165	−	0.912011i	$-0.365471\pi$
$464$	18.2810	−	56.2630i	0.00182903	−	0.00562919i
$465$		0			0
$466$	−4.47165	−	13.7623i	−0.000444517	−	0.00136808i
$467$	11511.6	−	8363.69i	1.14067	−	0.828748i	0.153460	−	0.988155i	$-0.450958\pi$
$467$	11511.6	−	8363.69i	1.14067	−	0.828748i	0.987213	+	0.159407i	$0.0509582\pi$
$468$		0			0
$469$	−8607.71	+	6253.87i	−0.847478	+	0.615729i
$470$	338.209	+	940.509i	0.0331923	+	0.0923031i
$471$		0			0
$472$	−2297.63	−	1669.33i	−0.224062	−	0.162790i
$473$	356.980	−	1098.67i	0.0347018	−	0.106801i
$474$		0			0
$475$	−3425.81	+	212.973i	−0.330920	+	0.0205724i
$476$	136.621			0.0131555
$477$		0			0
$478$	−11821.7	−	8588.96i	−1.13120	−	0.821862i
$479$	−13254.4	−	9629.85i	−1.26431	−	0.918578i	−0.265354	−	0.964151i	$-0.585489\pi$
$479$	−13254.4	−	9629.85i	−1.26431	−	0.918578i	−0.998961	+	0.0455728i	$0.985489\pi$
$480$		0			0
$481$	−8157.72	+	5926.93i	−0.773305	+	0.561839i
$482$	6963.98			0.658092
$483$		0			0
$484$	1575.88	+	4850.06i	0.147998	+	0.455490i
$485$	−5000.71	+	3875.97i	−0.468186	+	0.362884i
$486$		0			0
$487$	−4049.02	−	12461.6i	−0.376752	−	1.15952i	−0.942289	−	0.334801i	$-0.891331\pi$
$487$	−4049.02	−	12461.6i	−0.376752	−	1.15952i	0.565536	−	0.824723i	$-0.308669\pi$
$488$	−5982.49	−	18412.2i	−0.554948	−	1.70795i
$489$		0			0
$490$	1361.11	+	925.747i	0.125487	+	0.0853490i
$491$	−570.719	−	1756.49i	−0.0524566	−	0.161445i	0.921396	−	0.388624i	$-0.127050\pi$
$491$	−570.719	−	1756.49i	−0.0524566	−	0.161445i	−0.973853	+	0.227180i	$0.927050\pi$
$492$		0			0
$493$	−7.13082			−0.000651432
$494$	2484.36	−	1804.99i	0.226269	−	0.164394i
$495$		0			0
$496$	−967.034	−	702.591i	−0.0875426	−	0.0636034i
$497$	13128.9	+	9538.72i	1.18493	+	0.860906i
$498$		0			0
$499$	17773.8			1.59451			0.797257	−	0.603640i	$-0.206284\pi$
$499$	17773.8			1.59451			0.797257	+	0.603640i	$0.206284\pi$
$500$	5416.26	−	505.886i	0.484445	−	0.0452478i
$501$		0			0
$502$	−1056.55	+	3251.73i	−0.0939366	+	0.289107i
$503$	1358.97	+	987.353i	0.120465	+	0.0875227i	0.646386	−	0.763010i	$-0.276279\pi$
$503$	1358.97	+	987.353i	0.120465	+	0.0875227i	−0.525922	+	0.850533i	$0.676279\pi$
$504$		0			0
$505$	2288.48	−	7866.06i	0.201655	−	0.693139i
$506$	736.708	−	535.249i	0.0647246	−	0.0470252i
$507$		0			0
$508$	−2919.21	+	2120.93i	−0.254959	+	0.185239i
$509$	−5876.65	−	18086.5i	−0.511744	−	1.57499i	−0.789129	−	0.614228i	$-0.789468\pi$
$509$	−5876.65	−	18086.5i	−0.511744	−	1.57499i	0.277385	−	0.960759i	$-0.410532\pi$
$510$		0			0
$511$	4223.65	−	12999.1i	0.365642	−	1.12533i
$512$	1914.02	+	5890.75i	0.165212	+	0.508470i
$513$		0			0
$514$	1314.12	−	4044.46i	0.112769	−	0.347069i
$515$	−1626.42	+	1260.61i	−0.139162	+	0.107862i
$516$		0			0
$517$	162.953	−	118.392i	0.0138620	−	0.0100714i
$518$	−6089.71			−0.516538
$519$		0			0
$520$	−11752.5	+	9109.16i	−0.991117	+	0.768198i
$521$	−1611.58	−	1170.88i	−0.135517	−	0.0984592i	0.517961	−	0.855404i	$-0.326691\pi$
$521$	−1611.58	−	1170.88i	−0.135517	−	0.0984592i	−0.653479	+	0.756945i	$0.726691\pi$
$522$		0			0
$523$	−3681.59	+	11330.8i	−0.307810	+	0.947342i	0.670803	+	0.741635i	$0.265949\pi$
$523$	−3681.59	+	11330.8i	−0.307810	+	0.947342i	−0.978614	+	0.205707i	$0.934051\pi$
$524$	10146.6			0.845909
$525$		0			0
$526$	−288.538			−0.0239180
$527$	−44.5235	+	137.029i	−0.00368022	+	0.0113265i
$528$		0			0
$529$	2011.12	+	1461.17i	0.165293	+	0.120093i
$530$	1552.95	+	4318.54i	0.127275	+	0.353934i
$531$		0			0
$532$	−1757.43			−0.143222
$533$	1702.96	−	1237.28i	0.138393	−	0.100549i
$534$		0			0
$535$	4566.05	−	15694.6i	0.368986	−	1.26829i
$536$	−4819.57	+	14833.1i	−0.388384	+	1.19532i
$537$		0			0
$538$	−1961.93	−	6038.21i	−0.157221	−	0.483876i
$539$	102.511	−	315.497i	0.00819196	−	0.0252123i
$540$		0			0
$541$	3650.27	+	11234.4i	0.290088	+	0.892798i	0.984827	+	0.173537i	$0.0555196\pi$
$541$	3650.27	+	11234.4i	0.290088	+	0.892798i	−0.694740	+	0.719261i	$0.744480\pi$
$542$	−5700.12	+	4141.38i	−0.451736	+	0.328206i
$543$		0			0
$544$	271.013	−	196.902i	0.0213595	−	0.0155186i
$545$	−19934.8	+	619.049i	−1.56681	+	0.0486553i
$546$		0			0
$547$	6225.01	+	4522.74i	0.486586	+	0.353525i	0.803870	−	0.594805i	$-0.202771\pi$
$547$	6225.01	+	4522.74i	0.486586	+	0.353525i	−0.317284	+	0.948331i	$0.602771\pi$
$548$	3513.92	−	10814.7i	0.273918	−	0.843033i
$549$		0			0
$550$	425.072	+	1075.95i	0.0329548	+	0.0834156i
$551$	91.7274			0.00709205
$552$		0			0
$553$	−13517.2	−	9820.84i	−1.03944	−	0.755198i
$554$	−5449.43	−	3959.24i	−0.417914	−	0.303632i
$555$		0			0
$556$	3142.41	−	2283.09i	0.239690	−	0.174145i
$557$	20699.8			1.57465			0.787324	−	0.616540i	$-0.211466\pi$
$557$	20699.8			1.57465			0.787324	+	0.616540i	$0.211466\pi$
$558$		0			0
$559$	4313.55	+	13275.8i	0.326375	+	1.00448i
$560$	−3254.02	+	101.049i	−0.245549	+	0.00762521i
$561$		0			0
$562$	−1795.59	−	5526.26i	−0.134773	−	0.414789i
$563$	5732.09	+	17641.6i	0.429092	+	1.32061i	0.899021	+	0.437905i	$0.144279\pi$
$563$	5732.09	+	17641.6i	0.429092	+	1.32061i	−0.469929	+	0.882704i	$0.655721\pi$
$564$		0			0
$565$	−21799.8	+	676.965i	−1.62323	+	0.0504073i
$566$	5155.18	+	15866.0i	0.382841	+	1.17826i
$567$		0			0
$568$	23788.5			1.75730
$569$	131.419	−	95.4817i	0.00968257	−	0.00703480i	−0.582933	−	0.812520i	$-0.698095\pi$
$569$	131.419	−	95.4817i	0.00968257	−	0.00703480i	0.592616	+	0.805485i	$0.298095\pi$
$570$		0			0
$571$	13305.3	+	9666.86i	0.975147	+	0.708486i	0.956619	−	0.291343i	$-0.0941020\pi$
$571$	13305.3	+	9666.86i	0.975147	+	0.708486i	0.0185281	+	0.999828i	$0.494102\pi$
$572$	793.478	+	576.495i	0.0580017	+	0.0421407i
$573$		0			0
$574$	1271.26			0.0924412
$575$	9482.44	−	7832.67i	0.687731	−	0.568078i
$576$		0			0
$577$	−1917.80	+	5902.39i	−0.138369	+	0.425857i	−0.996099	−	0.0882441i	$-0.971874\pi$
$577$	−1917.80	+	5902.39i	−0.138369	+	0.425857i	0.857729	+	0.514101i	$0.171874\pi$
$578$	−8048.11	−	5847.29i	−0.579165	−	0.420788i
$579$		0			0
$580$	−145.303	+	4.51220i	−0.0104024	+	0.000323032i
$581$	15238.2	−	11071.2i	1.08810	−	0.790552i
$582$		0			0
$583$	748.232	−	543.622i	0.0531537	−	0.0386184i
$584$	−6191.33	−	19054.9i	−0.438697	−	1.35017i
$585$		0			0
$586$	1433.11	−	4410.66i	0.101026	−	0.310926i
$587$	−4296.85	−	13224.4i	−0.302130	−	0.929860i	−0.980733	−	0.195354i	$-0.937414\pi$
$587$	−4296.85	−	13224.4i	−0.302130	−	0.929860i	0.678603	−	0.734505i	$-0.262586\pi$
$588$		0			0
$589$	572.729	−	1762.68i	0.0400660	−	0.123311i
$590$	745.854	−	2563.68i	0.0520446	−	0.178890i
$591$		0			0
$592$	−2618.20	+	1902.23i	−0.181769	+	0.132063i
$593$	11389.2			0.788698			0.394349	−	0.918961i	$-0.370970\pi$
$593$	11389.2			0.788698			0.394349	+	0.918961i	$0.370970\pi$
$594$		0			0
$595$	132.791	+	369.272i	0.00914939	+	0.0254431i
$596$	8213.40	+	5967.38i	0.564486	+	0.410123i
$597$		0			0
$598$	−3400.26	+	10464.9i	−0.232520	+	0.715622i
$599$	−12576.2			−0.857844			−0.428922	−	0.903342i	$-0.641106\pi$
$599$	−12576.2			−0.857844			−0.428922	+	0.903342i	$0.641106\pi$
$600$		0			0
$601$	2154.43			0.146225			0.0731124	−	0.997324i	$-0.476707\pi$
$601$	2154.43			0.146225			0.0731124	+	0.997324i	$0.476707\pi$
$602$	−2605.08	+	8017.61i	−0.176371	+	0.542813i
$603$		0			0
$604$	−1369.11	−	994.717i	−0.0922323	−	0.0670107i
$605$	−11577.4	+	8973.49i	−0.778000	+	0.603015i
$606$		0			0
$607$	9937.94			0.664528			0.332264	−	0.943186i	$-0.392187\pi$
$607$	9937.94			0.664528			0.332264	+	0.943186i	$0.392187\pi$
$608$	−3486.18	+	2532.86i	−0.232538	+	0.168949i
$609$		0			0
$610$	14385.4	−	11149.9i	0.954832	−	0.740075i
$611$	−752.106	+	2314.74i	−0.0497986	+	0.153264i
$612$		0			0
$613$	3184.38	+	9800.52i	0.209814	+	0.645741i	0.999481	+	0.0322059i	$0.0102532\pi$
$613$	3184.38	+	9800.52i	0.209814	+	0.645741i	−0.789667	+	0.613535i	$0.789747\pi$
$614$	1743.30	−	5365.32i	0.114583	−	0.352649i
$615$		0			0
$616$	559.236	+	1721.15i	0.0365783	+	0.112577i
$617$	13637.9	−	9908.50i	0.889854	−	0.646517i	−0.0459856	−	0.998942i	$-0.514643\pi$
$617$	13637.9	−	9908.50i	0.889854	−	0.646517i	0.935840	+	0.352425i	$0.114643\pi$
$618$		0			0
$619$	−6572.78	+	4775.40i	−0.426789	+	0.310080i	−0.780364	−	0.625326i	$-0.784966\pi$
$619$	−6572.78	+	4775.40i	−0.426789	+	0.310080i	0.353575	+	0.935406i	$0.384966\pi$
$620$	−820.537	+	2820.39i	−0.0531509	+	0.182693i
$621$		0			0
$622$	13067.6	+	9494.17i	0.842385	+	0.612028i
$623$	5739.40	−	17664.1i	0.369092	−	1.13595i
$624$		0			0
$625$	6631.74	+	14147.8i	0.424432	+	0.905460i
$626$	9770.92			0.623841
$627$		0			0
$628$	−6874.40	−	4994.54i	−0.436813	−	0.317363i
$629$	315.592	+	229.291i	0.0200055	+	0.0145348i
$630$		0			0
$631$	−9984.59	+	7254.23i	−0.629921	+	0.457665i	−0.856373	−	0.516358i	$-0.827287\pi$
$631$	−9984.59	+	7254.23i	−0.629921	+	0.457665i	0.226452	+	0.974022i	$0.427287\pi$
$632$	−24492.1			−1.54152
$633$		0			0
$634$	5408.87	+	16646.8i	0.338823	+	1.04279i
$635$	−8569.99	−	5828.83i	−0.535574	−	0.364268i
$636$		0			0
$637$	1238.69	+	3812.30i	0.0770466	+	0.237125i
$638$	−9.55357	−	29.4029i	−0.000592836	−	0.00182456i
$639$		0			0
$640$	2860.41	−	2217.05i	0.176668	−	0.136932i
$641$	4664.84	+	14356.9i	0.287442	+	0.884654i	0.985656	+	0.168766i	$0.0539781\pi$
$641$	4664.84	+	14356.9i	0.287442	+	0.884654i	−0.698215	+	0.715889i	$0.746022\pi$
$642$		0			0
$643$	21379.1			1.31121			0.655606	−	0.755103i	$-0.272413\pi$
$643$	21379.1			1.31121			0.655606	+	0.755103i	$0.272413\pi$
$644$	5094.58	−	3701.43i	0.311731	−	0.226486i
$645$		0			0
$646$	−96.1107	−	69.8285i	−0.00585360	−	0.00425289i
$647$	7903.05	+	5741.90i	0.480218	+	0.348899i	0.801410	−	0.598115i	$-0.204084\pi$
$647$	7903.05	+	5741.90i	0.480218	+	0.348899i	−0.321192	+	0.947014i	$0.604084\pi$
$648$		0			0
$649$	−538.074			−0.0325443
$650$	−11797.3	−	7499.12i	−0.711889	−	0.452522i
$651$		0			0
$652$	−6.07770	+	18.7052i	−0.000365063	+	0.00112355i
$653$	10418.9	+	7569.74i	0.624382	+	0.453640i	0.854449	−	0.519535i	$-0.173895\pi$
$653$	10418.9	+	7569.74i	0.624382	+	0.453640i	−0.230068	+	0.973175i	$0.573895\pi$
$654$		0			0
$655$	9862.10	+	27425.1i	0.588312	+	1.63601i
$656$	546.562	−	397.100i	0.0325300	−	0.0236344i
$657$		0			0
$658$	−1189.16	+	863.974i	−0.0704532	+	0.0511873i
$659$	1499.44	+	4614.81i	0.0886343	+	0.272788i	0.985542	−	0.169429i	$-0.0541922\pi$
$659$	1499.44	+	4614.81i	0.0886343	+	0.272788i	−0.896908	+	0.442217i	$0.854192\pi$
$660$		0			0
$661$	−2892.29	+	8901.56i	−0.170192	+	0.523798i	−0.999381	−	0.0351704i	$-0.988803\pi$
$661$	−2892.29	+	8901.56i	−0.170192	+	0.523798i	0.829189	+	0.558968i	$0.188803\pi$
$662$	1204.57	+	3707.27i	0.0707202	+	0.217655i
$663$		0			0
$664$	8532.07	−	26259.0i	0.498657	−	1.53471i
$665$	−1708.16	−	4750.13i	−0.0996081	−	0.276996i
$666$		0			0
$667$	−265.907	+	193.192i	−0.0154362	+	0.0112151i
$668$	−877.838			−0.0508452
$669$		0			0
$670$	−14655.5	+	455.107i	−0.845062	+	0.0262423i
$671$	−2967.40	−	2155.95i	−0.170723	−	0.124038i
$672$		0			0
$673$	−8985.41	+	27654.2i	−0.514654	+	1.58394i	0.269257	+	0.963068i	$0.413222\pi$
$673$	−8985.41	+	27654.2i	−0.514654	+	1.58394i	−0.783911	+	0.620873i	$0.786778\pi$
$674$	−4733.99			−0.270544
$675$		0			0
$676$	−3299.71			−0.187740
$677$	−1446.09	+	4450.60i	−0.0820940	+	0.252659i	−0.983676	−	0.179949i	$-0.942407\pi$
$677$	−1446.09	+	4450.60i	−0.0820940	+	0.252659i	0.901582	+	0.432608i	$0.142407\pi$
$678$		0			0
$679$	−7527.72	−	5469.21i	−0.425460	−	0.309115i
$680$	475.649	+	323.510i	0.0268240	+	0.0182442i
$681$		0			0
$682$	−624.671			−0.0350731
$683$	−13511.7	+	9816.80i	−0.756968	+	0.549970i	−0.897979	−	0.440038i	$-0.854965\pi$
$683$	−13511.7	+	9816.80i	−0.756968	+	0.549970i	0.141011	+	0.990008i	$0.454965\pi$
$684$		0			0
$685$	32646.3	−	1013.79i	1.82095	−	0.0565472i
$686$	−4280.21	+	13173.1i	−0.238220	+	0.733166i
$687$		0			0
$688$	1384.42	+	4260.82i	0.0767161	+	0.236108i
$689$	−3453.45	+	10628.6i	−0.190952	+	0.587689i
$690$		0			0
$691$	−3623.18	−	11151.0i	−0.199468	−	0.613899i	−0.999895	−	0.0144691i	$-0.995394\pi$
$691$	−3623.18	−	11151.0i	−0.199468	−	0.613899i	0.800428	−	0.599429i	$-0.204606\pi$
$692$	−10411.1	+	7564.14i	−0.571925	+	0.415528i
$693$		0			0
$694$	−10648.4	+	7736.52i	−0.582432	+	0.423162i
$695$	9225.23	+	6274.48i	0.503501	+	0.342453i
$696$		0			0
$697$	−65.8813	−	47.8656i	−0.00358025	−	0.00260120i
$698$	−2952.16	+	9085.80i	−0.160087	+	0.492697i
$699$		0			0
$700$	2939.51	+	7440.54i	0.158719	+	0.401751i
$701$	−19249.4			−1.03714			−0.518572	−	0.855034i	$-0.673536\pi$
$701$	−19249.4			−1.03714			−0.518572	+	0.855034i	$0.673536\pi$
$702$		0			0
$703$	−4059.62	−	2949.49i	−0.217797	−	0.158239i
$704$	1698.39	+	1233.95i	0.0909242	+	0.0660603i
$705$		0			0
$706$	−6456.48	+	4690.90i	−0.344182	+	0.250063i
$707$	12047.9			0.640890
$708$		0			0
$709$	1993.96	+	6136.79i	0.105620	+	0.325066i	0.989876	−	0.141938i	$-0.0453334\pi$
$709$	1993.96	+	6136.79i	0.105620	+	0.325066i	−0.884255	+	0.467004i	$0.845333\pi$
$710$	7567.74	+	21044.8i	0.400017	+	1.11239i
$711$		0			0
$712$	−8413.23	−	25893.3i	−0.442836	−	1.36291i
$713$	2052.21	+	6316.05i	0.107792	+	0.331750i
$714$		0			0
$715$	−786.969	+	2705.01i	−0.0411622	+	0.141485i
$716$	2177.77	+	6702.48i	0.113669	+	0.349837i
$717$		0			0
$718$	19109.3			0.993251
$719$	−17508.2	+	12720.5i	−0.908132	+	0.659797i	−0.940542	−	0.339678i	$-0.889682\pi$
$719$	−17508.2	+	12720.5i	−0.908132	+	0.659797i	0.0324096	+	0.999475i	$0.489682\pi$
$720$		0			0
$721$	−2448.30	−	1778.79i	−0.126462	−	0.0918803i
$722$	−10010.0	−	7272.70i	−0.515975	−	0.374878i
$723$		0			0
$724$	−6963.96			−0.357477
$725$	−153.425	−	388.352i	−0.00785939	−	0.0198938i
$726$		0			0
$727$	−6051.62	+	18625.0i	−0.308724	+	0.950155i	0.669537	+	0.742778i	$0.266492\pi$
$727$	−6051.62	+	18625.0i	−0.308724	+	0.950155i	−0.978261	+	0.207376i	$0.933508\pi$
$728$	−17691.4	−	12853.5i	−0.900668	−	0.654374i
$729$		0			0
$730$	14887.6	−	11539.1i	0.754813	−	0.585043i
$731$	436.885	−	317.416i	0.0221050	−	0.0160603i
$732$		0			0
$733$	8314.98	−	6041.19i	0.418992	−	0.304415i	−0.358240	−	0.933629i	$-0.616623\pi$
$733$	8314.98	−	6041.19i	0.418992	−	0.304415i	0.777232	+	0.629214i	$0.216623\pi$
$734$	1600.87	+	4926.97i	0.0805029	+	0.247762i
$735$		0			0
$736$	4771.40	−	14684.9i	0.238962	−	0.735450i
$737$	913.119	+	2810.29i	0.0456380	+	0.140459i
$738$		0			0
$739$	8283.58	−	25494.2i	0.412336	−	1.26904i	−0.502276	−	0.864707i	$-0.667504\pi$
$739$	8283.58	−	25494.2i	0.412336	−	1.26904i	0.914612	−	0.404333i	$-0.132496\pi$
$740$	6575.83	+	4472.51i	0.326665	+	0.222179i
$741$		0			0
$742$	−5460.26	+	3967.11i	−0.270152	+	0.196277i
$743$	3369.02			0.166349			0.0831746	−	0.996535i	$-0.473494\pi$
$743$	3369.02			0.166349			0.0831746	+	0.996535i	$0.473494\pi$
$744$		0			0
$745$	−8146.03	+	27999.9i	−0.400601	+	1.37696i
$746$	−17831.6	−	12955.5i	−0.875151	−	0.635835i
$747$		0			0
$748$	11.7251	−	36.0861i	0.000573144	−	0.00176396i
$749$	24038.4			1.17269
$750$		0			0
$751$	6458.58			0.313817			0.156909	−	0.987613i	$-0.449847\pi$
$751$	6458.58			0.313817			0.156909	+	0.987613i	$0.449847\pi$
$752$	−241.386	+	742.911i	−0.0117054	+	0.0360255i
$753$		0			0
$754$	302.227	+	219.581i	0.0145974	+	0.0106056i
$755$	1357.88	−	4667.37i	0.0654548	−	0.224984i
$756$		0			0
$757$	−5810.90			−0.278997			−0.139499	−	0.990222i	$-0.544549\pi$
$757$	−5810.90			−0.278997			−0.139499	+	0.990222i	$0.544549\pi$
$758$	12138.5	−	8819.17i	0.581651	−	0.422594i
$759$		0			0
$760$	−6118.52	−	4161.47i	−0.292029	−	0.198622i
$761$	10479.9	−	32253.9i	0.499208	−	1.53640i	−0.311087	−	0.950382i	$-0.600693\pi$
$761$	10479.9	−	32253.9i	0.499208	−	1.53640i	0.810295	−	0.586023i	$-0.199307\pi$
$762$		0			0
$763$	−9063.92	−	27895.9i	−0.430060	−	1.32359i
$764$	5474.11	−	16847.6i	0.259223	−	0.797806i
$765$		0			0
$766$	3906.83	+	12024.0i	0.184281	+	0.567160i
$767$	5260.07	−	3821.66i	0.247627	−	0.179912i
$768$		0			0
$769$	−29641.8	+	21536.0i	−1.39000	+	1.00990i	−0.394137	+	0.919052i	$0.628956\pi$
$769$	−29641.8	+	21536.0i	−1.39000	+	1.00990i	−0.995865	+	0.0908440i	$0.971044\pi$
$770$	−1344.73	+	1042.28i	−0.0629359	+	0.0487806i
$771$		0			0
$772$	11131.7	+	8087.64i	0.518961	+	0.377047i
$773$	136.048	−	418.714i	0.00633030	−	0.0194827i	−0.947841	−	0.318742i	$-0.896740\pi$
$773$	136.048	−	418.714i	0.00633030	−	0.0194827i	0.954172	+	0.299259i	$0.0967396\pi$
$774$		0			0
$775$	−8420.71	+	523.493i	−0.390298	+	0.0242638i
$776$	−13639.6			−0.630971
$777$		0			0
$778$	−12824.1	−	9317.29i	−0.590961	−	0.429359i
$779$	847.465	+	615.720i	0.0389777	+	0.0283189i
$780$		0			0
$781$	3646.23	−	2649.14i	0.167058	−	0.121375i
$782$	425.683			0.0194660
$783$		0			0
$784$	397.554	+	1223.55i	0.0181102	+	0.0557374i
$785$	6818.01	−	23435.2i	0.309994	−	1.06553i
$786$		0			0
$787$	7874.56	+	24235.4i	0.356668	+	1.09771i	0.955036	+	0.296490i	$0.0958163\pi$
$787$	7874.56	+	24235.4i	0.356668	+	1.09771i	−0.598368	+	0.801222i	$0.704184\pi$

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.626289 + 1.92752i) q^{2} +(3.14904 + 2.28791i) q^{4} +(-3.12321 + 10.7352i) q^{5} -16.4425 q^{7} +(-19.4994 + 14.1671i) q^{8} +O(q^{10})\)	\(q+(-0.626289 + 1.92752i) q^{2} +(3.14904 + 2.28791i) q^{4} +(-3.12321 + 10.7352i) q^{5} -16.4425 q^{7} +(-19.4994 + 14.1671i) q^{8} +(-18.7364 - 12.7434i) q^{10} +(-1.41112 + 4.34299i) q^{11} +(-17.0513 - 52.4784i) q^{13} +(10.2977 - 31.6932i) q^{14} +(-5.47256 - 16.8428i) q^{16} +(-1.72699 + 1.25473i) q^{17} +(22.2151 - 16.1402i) q^{19} +(-34.3964 + 26.6601i) q^{20} +(-7.48743 - 5.43993i) q^{22} +(-30.4050 + 93.5770i) q^{23} +(-105.491 - 67.0569i) q^{25} +111.832 q^{26} +(-51.7780 - 37.6189i) q^{28} +(2.70250 + 1.96348i) q^{29} +(54.6052 - 39.6730i) q^{31} -156.928 q^{32} +(-1.33692 - 4.11462i) q^{34} +(51.3533 - 176.514i) q^{35} +(-56.4702 - 173.797i) q^{37} +(17.1975 + 52.9285i) q^{38} +(-91.1869 - 253.578i) q^{40} +(11.7884 + 36.2811i) q^{41} -252.976 q^{43} +(-14.3801 + 10.4477i) q^{44} +(-161.329 - 117.213i) q^{46} +(-35.6846 - 25.9263i) q^{47} -72.6451 q^{49} +(195.321 - 161.339i) q^{50} +(66.3708 - 204.268i) q^{52} +(-163.853 - 119.046i) q^{53} +(-42.2158 - 28.7128i) q^{55} +(320.618 - 232.943i) q^{56} +(-5.47720 + 3.97942i) q^{58} +(36.4118 + 112.064i) q^{59} +(-248.210 + 763.911i) q^{61} +(42.2718 + 130.099i) q^{62} +(142.063 - 437.225i) q^{64} +(616.623 - 19.1484i) q^{65} +(523.504 - 380.348i) q^{67} -8.30906 q^{68} +(308.072 + 209.533i) q^{70} +(-798.476 - 580.127i) q^{71} +(-256.874 + 790.578i) q^{73} +370.365 q^{74} +106.884 q^{76} +(23.2023 - 71.4095i) q^{77} +(822.092 + 597.285i) q^{79} +(197.904 - 6.14563i) q^{80} -77.3154 q^{82} +(-926.758 + 673.329i) q^{83} +(-8.07608 - 22.4584i) q^{85} +(158.436 - 487.616i) q^{86} +(-34.0117 - 104.677i) q^{88} +(-349.060 + 1074.29i) q^{89} +(280.365 + 862.874i) q^{91} +(-309.843 + 225.114i) q^{92} +(72.3224 - 52.5453i) q^{94} +(103.887 + 288.894i) q^{95} +(457.822 + 332.627i) q^{97} +(45.4968 - 140.025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 72 q^{4} + 20 q^{7} + O(q^{10}) \)	\( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97} + O(q^{100}) \)

Introduction

L-functions

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