LMFDB - Embedded newform 225.4.h.a.181.4

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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.4
Character	$\chi$	$=$	225.181
Dual form			225.4.h.a.46.4

$q$-expansion

$f(q)$	$=$	$q+(0.177563 + 0.546483i) q^{2} +(6.20502 - 4.50821i) q^{4} +(9.45304 + 5.96993i) q^{5} -2.67744 q^{7} +(7.28438 + 5.29241i) q^{8} +O(q^{10})$	\(q+(0.177563 + 0.546483i) q^{2} +(6.20502 - 4.50821i) q^{4} +(9.45304 + 5.96993i) q^{5} -2.67744 q^{7} +(7.28438 + 5.29241i) q^{8} +(-1.58395 + 6.22597i) q^{10} +(19.4804 + 59.9545i) q^{11} +(4.38017 - 13.4808i) q^{13} +(-0.475414 - 1.46317i) q^{14} +(17.3621 - 53.4350i) q^{16} +(24.5906 + 17.8661i) q^{17} +(-22.2647 - 16.1762i) q^{19} +(85.5700 - 5.57276i) q^{20} +(-29.3052 + 21.2914i) q^{22} +(-35.9246 - 110.565i) q^{23} +(53.7199 + 112.868i) q^{25} +8.14478 q^{26} +(-16.6135 + 12.0704i) q^{28} +(-32.5312 + 23.6353i) q^{29} +(180.304 + 130.998i) q^{31} +104.316 q^{32} +(-5.39715 + 16.6107i) q^{34} +(-25.3099 - 15.9841i) q^{35} +(25.6160 - 78.8378i) q^{37} +(4.88665 - 15.0396i) q^{38} +(37.2642 + 93.5166i) q^{40} +(-44.5269 + 137.040i) q^{41} +433.956 q^{43} +(391.164 + 284.197i) q^{44} +(54.0428 - 39.2644i) q^{46} +(371.550 - 269.947i) q^{47} -335.831 q^{49} +(-52.1418 + 49.3982i) q^{50} +(-33.5952 - 103.395i) q^{52} +(-200.214 + 145.464i) q^{53} +(-173.775 + 683.049i) q^{55} +(-19.5034 - 14.1701i) q^{56} +(-18.6927 - 13.5810i) q^{58} +(-95.9388 + 295.269i) q^{59} +(0.644333 + 1.98305i) q^{61} +(-39.5730 + 121.793i) q^{62} +(-120.374 - 370.473i) q^{64} +(121.885 - 101.285i) q^{65} +(-529.476 - 384.687i) q^{67} +233.129 q^{68} +(4.24094 - 16.6696i) q^{70} +(-734.591 + 533.711i) q^{71} +(-271.486 - 835.547i) q^{73} +47.6320 q^{74} -211.079 q^{76} +(-52.1575 - 160.524i) q^{77} +(921.477 - 669.493i) q^{79} +(483.127 - 401.473i) q^{80} -82.7962 q^{82} +(-798.210 - 579.934i) q^{83} +(125.796 + 315.693i) q^{85} +(77.0546 + 237.150i) q^{86} +(-175.401 + 539.830i) q^{88} +(-305.549 - 940.383i) q^{89} +(-11.7276 + 36.0939i) q^{91} +(-721.361 - 524.100i) q^{92} +(213.495 + 155.113i) q^{94} +(-113.898 - 285.833i) q^{95} +(-1244.20 + 903.964i) q^{97} +(-59.6313 - 183.526i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) $ 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8	$ 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) $ 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8 + 165 * q^10 - 19 * q^11 + 4 * q^13 + 24 * q^14 - 66 * q^16 - 208 * q^17 + 42 * q^19 - 295 * q^20 - 89 * q^22 - 32 * q^23 + 95 * q^25 - 206 * q^26 - 482 * q^28 + 716 * q^29 + 637 * q^31 + 844 * q^32 - 90 * q^34 - 430 * q^35 + 216 * q^37 - 2314 * q^38 - 500 * q^40 + 38 * q^41 - 1392 * q^43 - 603 * q^44 + 1622 * q^46 + 536 * q^47 + 162 * q^49 + 2265 * q^50 - 1922 * q^52 - 1672 * q^53 - 1000 * q^55 - 3000 * q^56 - 827 * q^58 - 973 * q^59 - 2712 * q^61 - 1057 * q^62 + 4439 * q^64 + 4360 * q^65 + 2768 * q^67 + 1370 * q^68 + 3230 * q^70 + 1074 * q^71 - 1018 * q^73 + 1414 * q^74 - 11408 * q^76 - 1607 * q^77 - 1820 * q^79 + 1290 * q^80 + 1772 * q^82 - 4045 * q^83 + 1850 * q^85 + 3986 * q^86 + 2407 * q^88 - 4542 * q^89 + 4412 * q^91 + 1089 * q^92 + 5137 * q^94 + 720 * q^95 - 5977 * q^97 + 10689 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.177563	+	0.546483i	0.0627781	+	0.193211i	0.977526	−	0.210813i	$-0.0676112\pi$
$2$	0.177563	+	0.546483i	0.0627781	+	0.193211i	−0.914748	+	0.404024i	$0.867611\pi$
$3$		0			0
$3$		0			0
$4$	6.20502	−	4.50821i	0.775628	−	0.563526i
$5$	9.45304	+	5.96993i	0.845506	+	0.533967i
$5$	9.45304	+	5.96993i	0.845506	+	0.533967i
$6$		0			0
$7$	−2.67744			−0.144568			−0.0722840	−	0.997384i	$-0.523029\pi$
$7$	−2.67744			−0.144568			−0.0722840	+	0.997384i	$0.523029\pi$
$8$	7.28438	+	5.29241i	0.321927	+	0.233894i
$9$		0			0
$10$	−1.58395	+	6.22597i	−0.0500891	+	0.196882i
$11$	19.4804	+	59.9545i	0.533960	+	1.64336i	0.745885	+	0.666075i	$0.232027\pi$
$11$	19.4804	+	59.9545i	0.533960	+	1.64336i	−0.211924	+	0.977286i	$0.567973\pi$
$12$		0			0
$13$	4.38017	−	13.4808i	0.0934493	−	0.287607i	−0.893397	−	0.449268i	$-0.851685\pi$
$13$	4.38017	−	13.4808i	0.0934493	−	0.287607i	0.986846	+	0.161660i	$0.0516849\pi$
$14$	−0.475414	−	1.46317i	−0.00907569	−	0.0279321i
$15$		0			0
$16$	17.3621	−	53.4350i	0.271282	−	0.834922i
$17$	24.5906	+	17.8661i	0.350829	+	0.254892i	0.749217	−	0.662325i	$-0.230430\pi$
$17$	24.5906	+	17.8661i	0.350829	+	0.254892i	−0.398388	+	0.917217i	$0.630430\pi$
$18$		0			0
$19$	−22.2647	−	16.1762i	−0.268835	−	0.195320i	0.445198	−	0.895432i	$-0.353133\pi$
$19$	−22.2647	−	16.1762i	−0.268835	−	0.195320i	−0.714033	+	0.700112i	$0.753133\pi$
$20$	85.5700	−	5.57276i	0.956702	−	0.0623054i
$21$		0			0
$22$	−29.3052	+	21.2914i	−0.283995	+	0.206334i
$23$	−35.9246	−	110.565i	−0.325687	−	1.00236i	−0.971130	−	0.238553i	$-0.923327\pi$
$23$	−35.9246	−	110.565i	−0.325687	−	1.00236i	0.645443	−	0.763809i	$-0.276673\pi$
$24$		0			0
$25$	53.7199	+	112.868i	0.429759	+	0.902944i
$26$	8.14478			0.0614355
$27$		0			0
$28$	−16.6135	+	12.0704i	−0.112131	+	0.0814678i
$29$	−32.5312	+	23.6353i	−0.208307	+	0.151344i	−0.687047	−	0.726613i	$-0.741093\pi$
$29$	−32.5312	+	23.6353i	−0.208307	+	0.151344i	0.478740	+	0.877956i	$0.341093\pi$
$30$		0			0
$31$	180.304	+	130.998i	1.04463	+	0.758967i	0.971184	−	0.238333i	$-0.0766008\pi$
$31$	180.304	+	130.998i	1.04463	+	0.758967i	0.0734444	+	0.997299i	$0.476601\pi$
$32$	104.316			0.576270
$33$		0			0
$34$	−5.39715	+	16.6107i	−0.0272236	+	0.0837857i
$35$	−25.3099	−	15.9841i	−0.122233	−	0.0771944i
$36$		0			0
$37$	25.6160	−	78.8378i	0.113817	−	0.350293i	−0.877881	−	0.478878i	$-0.841044\pi$
$37$	25.6160	−	78.8378i	0.113817	−	0.350293i	0.991698	+	0.128585i	$0.0410435\pi$
$38$	4.88665	−	15.0396i	0.0208610	−	0.0642037i
$39$		0			0
$40$	37.2642	+	93.5166i	0.147300	+	0.369657i
$41$	−44.5269	+	137.040i	−0.169608	+	0.522000i	−0.999346	−	0.0361527i	$-0.988490\pi$
$41$	−44.5269	+	137.040i	−0.169608	+	0.522000i	0.829738	+	0.558153i	$0.188490\pi$
$42$		0			0
$43$	433.956			1.53901			0.769507	−	0.638638i	$-0.220502\pi$
$43$	433.956			1.53901			0.769507	+	0.638638i	$0.220502\pi$
$44$	391.164	+	284.197i	1.34023	+	0.973736i
$45$		0			0
$46$	54.0428	−	39.2644i	0.173221	−	0.125853i
$47$	371.550	−	269.947i	1.15311	−	0.837783i	0.164218	−	0.986424i	$-0.447490\pi$
$47$	371.550	−	269.947i	1.15311	−	0.837783i	0.988891	+	0.148641i	$0.0474898\pi$
$48$		0			0
$49$	−335.831			−0.979100
$50$	−52.1418	+	49.3982i	−0.147479	+	0.139719i
$51$		0			0
$52$	−33.5952	−	103.395i	−0.0895925	−	0.275737i
$53$	−200.214	+	145.464i	−0.518897	+	0.377001i	−0.816188	−	0.577786i	$-0.803917\pi$
$53$	−200.214	+	145.464i	−0.518897	+	0.377001i	0.297291	+	0.954787i	$0.403917\pi$
$54$		0			0
$55$	−173.775	+	683.049i	−0.426034	+	1.67459i
$56$	−19.5034	−	14.1701i	−0.0465403	−	0.0338135i
$57$		0			0
$58$	−18.6927	−	13.5810i	−0.0423184	−	0.0307461i
$59$	−95.9388	+	295.269i	−0.211698	+	0.651539i	0.787674	+	0.616092i	$0.211285\pi$
$59$	−95.9388	+	295.269i	−0.211698	+	0.651539i	−0.999372	+	0.0354462i	$0.988715\pi$
$60$		0			0
$61$	0.644333	+	1.98305i	0.00135243	+	0.00416236i	0.951730	−	0.306935i	$-0.0993034\pi$
$61$	0.644333	+	1.98305i	0.00135243	+	0.00416236i	−0.950378	+	0.311097i	$0.899303\pi$
$62$	−39.5730	+	121.793i	−0.0810610	+	0.249480i
$63$		0			0
$64$	−120.374	−	370.473i	−0.235105	−	0.723580i
$65$	121.885	−	101.285i	0.232585	−	0.193275i
$66$		0			0
$67$	−529.476	−	384.687i	−0.965460	−	0.701448i	−0.0110477	−	0.999939i	$-0.503517\pi$
$67$	−529.476	−	384.687i	−0.965460	−	0.701448i	−0.954412	+	0.298491i	$0.903517\pi$
$68$	233.129			0.415751
$69$		0			0
$70$	4.24094	−	16.6696i	0.00724127	−	0.0284629i
$71$	−734.591	+	533.711i	−1.22789	+	0.892111i	−0.996730	−	0.0808056i	$-0.974251\pi$
$71$	−734.591	+	533.711i	−1.22789	+	0.892111i	−0.231156	+	0.972917i	$0.574251\pi$
$72$		0			0
$73$	−271.486	−	835.547i	−0.435274	−	1.33964i	−0.892805	−	0.450443i	$-0.851266\pi$
$73$	−271.486	−	835.547i	−0.435274	−	1.33964i	0.457531	−	0.889194i	$-0.348734\pi$
$74$	47.6320			0.0748258
$75$		0			0
$76$	−211.079			−0.318584
$77$	−52.1575	−	160.524i	−0.0771935	−	0.237577i
$78$		0			0
$79$	921.477	−	669.493i	1.31233	−	0.953466i	0.312339	−	0.949971i	$-0.398887\pi$
$79$	921.477	−	669.493i	1.31233	−	0.953466i	0.999994	−	0.00349520i	$-0.00111256\pi$
$80$	483.127	−	401.473i	0.675191	−	0.561075i
$81$		0			0
$82$	−82.7962			−0.111504
$83$	−798.210	−	579.934i	−1.05560	−	0.766940i	−0.0823324	−	0.996605i	$-0.526237\pi$
$83$	−798.210	−	579.934i	−1.05560	−	0.766940i	−0.973270	+	0.229665i	$0.926237\pi$
$84$		0			0
$85$	125.796	+	315.693i	0.160524	+	0.402844i
$86$	77.0546	+	237.150i	0.0966164	+	0.297355i
$87$		0			0
$88$	−175.401	+	539.830i	−0.212476	+	0.653932i
$89$	−305.549	−	940.383i	−0.363911	−	1.12000i	−0.950660	−	0.310235i	$-0.899592\pi$
$89$	−305.549	−	940.383i	−0.363911	−	1.12000i	0.586748	−	0.809769i	$-0.300408\pi$
$90$		0			0
$91$	−11.7276	+	36.0939i	−0.0135098	+	0.0415788i
$92$	−721.361	−	524.100i	−0.817469	−	0.593926i
$93$		0			0
$94$	213.495	+	155.113i	0.234259	+	0.170199i
$95$	−113.898	−	285.833i	−0.123007	−	0.308693i
$96$		0			0
$97$	−1244.20	+	903.964i	−1.30236	+	0.946223i	−0.999976	−	0.00696215i	$-0.997784\pi$
$97$	−1244.20	+	903.964i	−1.30236	+	0.946223i	−0.302388	+	0.953185i	$0.597784\pi$
$98$	−59.6313	−	183.526i	−0.0614660	−	0.189173i
$99$		0			0
$100$	842.166	+	458.167i	0.842166	+	0.458167i
$101$	266.284			0.262339			0.131170	−	0.991360i	$-0.458127\pi$
$101$	266.284			0.262339			0.131170	+	0.991360i	$0.458127\pi$
$102$		0			0
$103$	630.873	−	458.356i	0.603512	−	0.438477i	−0.243612	−	0.969873i	$-0.578332\pi$
$103$	630.873	−	458.356i	0.603512	−	0.438477i	0.847124	+	0.531396i	$0.178332\pi$
$104$	103.253	−	75.0174i	0.0973534	−	0.0707314i
$105$		0			0
$106$	−115.044	−	83.5847i	−0.105416	−	0.0765893i
$107$	−526.990			−0.476132			−0.238066	−	0.971249i	$-0.576513\pi$
$107$	−526.990			−0.476132			−0.238066	+	0.971249i	$0.576513\pi$
$108$		0			0
$109$	−18.0367	+	55.5114i	−0.0158496	+	0.0487800i	−0.958669	−	0.284525i	$-0.908164\pi$
$109$	−18.0367	+	55.5114i	−0.0158496	+	0.0487800i	0.942819	+	0.333305i	$0.108164\pi$
$110$	−404.131	+	26.3191i	−0.350294	+	0.0228130i
$111$		0			0
$112$	−46.4858	+	143.069i	−0.0392187	+	0.120703i
$113$	14.5997	−	44.9333i	0.0121542	−	0.0374068i	−0.944795	−	0.327661i	$-0.893740\pi$
$113$	14.5997	−	44.9333i	0.0121542	−	0.0374068i	0.956950	+	0.290254i	$0.0937397\pi$
$114$		0			0
$115$	320.466	−	1259.64i	0.259857	−	1.02141i
$116$	−95.3039	+	293.315i	−0.0762823	+	0.234773i
$117$		0			0
$118$	−178.395			−0.139174
$119$	−65.8397	−	47.8354i	−0.0507186	−	0.0368493i
$120$		0			0
$121$	−2138.26	+	1553.54i	−1.60651	+	1.16719i
$122$	−0.969296	+	0.704235i	−0.000719311	+	0.000522610i
$123$		0			0
$124$	1709.35			1.23794
$125$	−165.997	+	1387.65i	−0.118778	+	0.992921i
$126$		0			0
$127$	−485.405	−	1493.92i	−0.339155	−	1.04381i	−0.964639	−	0.263575i	$-0.915098\pi$
$127$	−485.405	−	1493.92i	−0.339155	−	1.04381i	0.625484	−	0.780237i	$-0.284902\pi$
$128$	856.231	−	622.088i	0.591257	−	0.429573i
$129$		0			0
$130$	76.9929	+	48.6238i	0.0519440	+	0.0328045i
$131$	−2344.50	−	1703.38i	−1.56366	−	1.13607i	−0.932923	−	0.360076i	$-0.882751\pi$
$131$	−2344.50	−	1703.38i	−1.56366	−	1.13607i	−0.630741	−	0.775993i	$-0.717249\pi$
$132$		0			0
$133$	59.6122	+	43.3108i	0.0388649	+	0.0282370i
$134$	116.210	−	357.656i	0.0749177	−	0.230573i
$135$		0			0
$136$	84.5724	+	260.287i	0.0533237	+	0.164113i
$137$	−402.958	+	1240.18i	−0.251292	+	0.773398i	0.743245	+	0.669019i	$0.233286\pi$
$137$	−402.958	+	1240.18i	−0.251292	+	0.773398i	−0.994538	+	0.104379i	$0.966714\pi$
$138$		0			0
$139$	381.913	+	1175.41i	0.233047	+	0.717243i	0.997375	+	0.0724158i	$0.0230709\pi$
$139$	381.913	+	1175.41i	0.233047	+	0.717243i	−0.764328	+	0.644828i	$0.776929\pi$
$140$	−229.108	+	14.9207i	−0.138308	+	0.00900736i
$141$		0			0
$142$	−422.101	−	306.674i	−0.249450	−	0.181236i
$143$	893.562			0.522541
$144$		0			0
$145$	−448.620	+	29.2165i	−0.256937	+	0.0167331i
$146$	408.407	−	296.725i	0.231507	−	0.168200i
$147$		0			0
$148$	−196.470	−	604.672i	−0.109120	−	0.335836i
$149$	810.211			0.445470			0.222735	−	0.974879i	$-0.428501\pi$
$149$	810.211			0.445470			0.222735	+	0.974879i	$0.428501\pi$
$150$		0			0
$151$	−3447.19			−1.85781			−0.928903	−	0.370324i	$-0.879247\pi$
$151$	−3447.19			−1.85781			−0.928903	+	0.370324i	$0.879247\pi$
$152$	−76.5730	−	235.667i	−0.0408611	−	0.125758i
$153$		0			0
$154$	78.4626	−	57.0064i	0.0410565	−	0.0298293i
$155$	922.366	+	2314.73i	0.477976	+	1.19951i
$156$		0			0
$157$	−804.338			−0.408873			−0.204437	−	0.978880i	$-0.565536\pi$
$157$	−804.338			−0.408873			−0.204437	+	0.978880i	$0.565536\pi$
$158$	529.487	+	384.695i	0.266606	+	0.193700i
$159$		0			0
$160$	986.104	+	622.760i	0.487240	+	0.307709i
$161$	96.1858	+	296.029i	0.0470839	+	0.144909i
$162$		0			0
$163$	976.108	−	3004.15i	0.469047	−	1.44358i	−0.384774	−	0.923011i	$-0.625720\pi$
$163$	976.108	−	3004.15i	0.469047	−	1.44358i	0.853821	−	0.520567i	$-0.174280\pi$
$164$	341.514	+	1051.07i	0.162608	+	0.500456i
$165$		0			0
$166$	175.191	−	539.184i	0.0819126	−	0.252101i
$167$	−2278.34	−	1655.31i	−1.05571	−	0.767018i	−0.0824199	−	0.996598i	$-0.526265\pi$
$167$	−2278.34	−	1655.31i	−1.05571	−	0.767018i	−0.973290	+	0.229580i	$0.926265\pi$
$168$		0			0
$169$	1614.86	+	1173.27i	0.735032	+	0.534032i
$170$	−150.184	+	124.801i	−0.0677565	+	0.0563048i
$171$		0			0
$172$	2692.70	−	1956.36i	1.19370	−	0.867276i
$173$	1133.19	+	3487.61i	0.498006	+	1.53270i	0.812219	+	0.583352i	$0.198259\pi$
$173$	1133.19	+	3487.61i	0.498006	+	1.53270i	−0.314213	+	0.949352i	$0.601741\pi$
$174$		0			0
$175$	−143.832	−	302.197i	−0.0621294	−	0.130537i
$176$	3541.89			1.51693
$177$		0			0
$178$	459.649	−	333.955i	0.193552	−	0.140623i
$179$	1965.97	−	1428.36i	0.820912	−	0.596427i	−0.0960617	−	0.995375i	$-0.530625\pi$
$179$	1965.97	−	1428.36i	0.820912	−	0.596427i	0.916974	+	0.398948i	$0.130625\pi$
$180$		0			0
$181$	2655.62	+	1929.42i	1.09056	+	0.792336i	0.979493	−	0.201477i	$-0.0645743\pi$
$181$	2655.62	+	1929.42i	1.09056	+	0.792336i	0.111064	+	0.993813i	$0.464574\pi$
$182$	−21.8071			−0.00888160
$183$		0			0
$184$	323.465	−	995.522i	0.129599	−	0.398863i
$185$	712.805	−	592.331i	0.283278	−	0.235400i
$186$		0			0
$187$	−592.120	+	1822.36i	−0.231551	+	0.712642i
$188$	1088.50	−	3350.05i	0.422271	−	1.29962i
$189$		0			0
$190$	135.979	−	112.997i	0.0519208	−	0.0431455i
$191$	−659.004	+	2028.21i	−0.249654	+	0.768355i	0.745183	+	0.666861i	$0.232362\pi$
$191$	−659.004	+	2028.21i	−0.249654	+	0.768355i	−0.994836	+	0.101494i	$0.967638\pi$
$192$		0			0
$193$	−3868.32			−1.44274			−0.721368	−	0.692552i	$-0.756486\pi$
$193$	−3868.32			−1.44274			−0.721368	+	0.692552i	$0.756486\pi$
$194$	−714.925	−	519.423i	−0.264581	−	0.192229i
$195$		0			0
$196$	−2083.84	+	1514.00i	−0.759417	+	0.551749i
$197$	−1428.32	+	1037.74i	−0.516568	+	0.375308i	−0.815309	−	0.579026i	$-0.803433\pi$
$197$	−1428.32	+	1037.74i	−0.516568	+	0.375308i	0.298742	+	0.954334i	$0.403433\pi$
$198$		0			0
$199$	3952.78			1.40807			0.704033	−	0.710167i	$-0.251381\pi$
$199$	3952.78			1.40807			0.704033	+	0.710167i	$0.251381\pi$
$200$	−206.027	+	1106.48i	−0.0728417	+	0.391200i
$201$		0			0
$202$	47.2823	+	145.520i	0.0164692	+	0.0506869i
$203$	87.1002	−	63.2820i	0.0301145	−	0.0218794i
$204$		0			0
$205$	−1239.03	+	1029.62i	−0.422135	+	0.350789i
$206$	362.504	+	263.374i	0.122606	+	0.0890784i
$207$		0			0
$208$	−644.296	−	468.109i	−0.214778	−	0.156046i
$209$	536.113	−	1649.99i	0.177434	−	0.546086i
$210$		0			0
$211$	1472.71	+	4532.54i	0.480501	+	1.47883i	0.838392	+	0.545067i	$0.183496\pi$
$211$	1472.71	+	4532.54i	0.480501	+	1.47883i	−0.357891	+	0.933763i	$0.616504\pi$
$212$	−586.551	+	1805.22i	−0.190021	+	0.584825i
$213$		0			0
$214$	−93.5741	−	287.991i	−0.0298906	−	0.0919939i
$215$	4102.20	+	2590.69i	1.30125	+	0.821783i
$216$		0			0
$217$	−482.751	−	350.739i	−0.151020	−	0.109722i
$218$	−33.5387			−0.0104199
$219$		0			0
$220$	2001.05	+	5021.75i	0.613231	+	1.53894i
$221$	348.560	−	253.244i	0.106094	−	0.0770816i
$222$		0			0
$223$	−679.879	−	2092.45i	−0.204162	−	0.628345i	−0.999747	−	0.0225031i	$-0.992836\pi$
$223$	−679.879	−	2092.45i	−0.204162	−	0.628345i	0.795585	−	0.605842i	$-0.207164\pi$
$224$	−279.300			−0.0833102
$225$		0			0
$226$	27.1477			0.00799042
$227$	−301.326	−	927.386i	−0.0881045	−	0.271158i	0.897291	−	0.441440i	$-0.145532\pi$
$227$	−301.326	−	927.386i	−0.0881045	−	0.271158i	−0.985395	+	0.170282i	$0.945532\pi$
$228$		0			0
$229$	−1289.94	+	937.197i	−0.372235	+	0.270444i	−0.758137	−	0.652095i	$-0.773890\pi$
$229$	−1289.94	+	937.197i	−0.372235	+	0.270444i	0.385902	+	0.922540i	$0.373890\pi$
$230$	745.274	−	48.5362i	0.213661	−	0.0139147i
$231$		0			0
$232$	−362.057			−0.102458
$233$	−3787.94	−	2752.10i	−1.06505	−	0.773802i	−0.0900318	−	0.995939i	$-0.528697\pi$
$233$	−3787.94	−	2752.10i	−1.06505	−	0.773802i	−0.975016	+	0.222137i	$0.928697\pi$
$234$		0			0
$235$	5123.84	−	333.691i	1.42231	−	0.0926282i
$236$	735.834	+	2264.66i	0.202961	+	0.624649i
$237$		0			0
$238$	14.4505	−	44.4741i	0.00393566	−	0.0121127i
$239$	−22.3460	−	68.7738i	−0.00604787	−	0.0186134i	0.947987	−	0.318309i	$-0.103115\pi$
$239$	−22.3460	−	68.7738i	−0.00604787	−	0.0186134i	−0.954035	+	0.299695i	$0.903115\pi$
$240$		0			0
$241$	566.484	−	1743.46i	0.151413	−	0.466000i	−0.846367	−	0.532600i	$-0.821215\pi$
$241$	566.484	−	1743.46i	0.151413	−	0.466000i	0.997780	+	0.0665998i	$0.0212151\pi$
$242$	−1228.66	−	892.672i	−0.326368	−	0.237120i
$243$		0			0
$244$	12.9381	+	9.40010i	0.00339459	+	0.00246631i
$245$	−3174.63	−	2004.89i	−0.827835	−	0.522807i
$246$		0			0
$247$	−315.591	+	229.290i	−0.0812979	+	0.0590664i
$248$	620.103	+	1908.48i	0.158776	+	0.488664i
$249$		0			0
$250$	−787.802	+	155.681i	−0.199300	+	0.0393844i
$251$	211.935			0.0532956			0.0266478	−	0.999645i	$-0.491517\pi$
$251$	211.935			0.0532956			0.0266478	+	0.999645i	$0.491517\pi$
$252$		0			0
$253$	5929.02	−	4307.69i	1.47334	−	1.07044i
$254$	730.214	−	530.531i	0.180385	−	0.131057i
$255$		0			0
$256$	−2029.15	−	1474.26i	−0.495398	−	0.359927i
$257$	7074.89			1.71720			0.858599	−	0.512648i	$-0.171335\pi$
$257$	7074.89			1.71720			0.858599	+	0.512648i	$0.171335\pi$
$258$		0			0
$259$	−68.5851	+	211.083i	−0.0164543	+	0.0506412i
$260$	299.686	−	1177.96i	0.0714836	−	0.280977i
$261$		0			0
$262$	514.572	−	1583.69i	0.121337	−	0.373437i
$263$	1562.26	−	4808.14i	0.366286	−	1.12731i	−0.582886	−	0.812554i	$-0.698077\pi$
$263$	1562.26	−	4808.14i	0.366286	−	1.12731i	0.949172	−	0.314758i	$-0.101923\pi$
$264$		0			0
$265$	−2761.04	+	179.814i	−0.640036	+	0.0416825i
$266$	−13.0837	+	40.2675i	−0.00301584	+	0.00928179i
$267$		0			0
$268$	−5019.66			−1.14412
$269$	1867.63	+	1356.91i	0.423314	+	0.307556i	0.778970	−	0.627061i	$-0.215742\pi$
$269$	1867.63	+	1356.91i	0.423314	+	0.307556i	−0.355656	+	0.934617i	$0.615742\pi$
$270$		0			0
$271$	475.680	−	345.602i	0.106625	−	0.0774679i	−0.533195	−	0.845992i	$-0.679009\pi$
$271$	475.680	−	345.602i	0.106625	−	0.0774679i	0.639820	+	0.768525i	$0.279009\pi$
$272$	1381.62	−	1003.81i	0.307989	−	0.223767i
$273$		0			0
$274$	−749.287			−0.165205
$275$	−5720.46	+	5419.47i	−1.25439	+	1.18839i
$276$		0			0
$277$	−936.066	−	2880.92i	−0.203042	−	0.624900i	−0.999788	−	0.0205857i	$-0.993447\pi$
$277$	−936.066	−	2880.92i	−0.203042	−	0.624900i	0.796746	−	0.604315i	$-0.206553\pi$
$278$	−574.527	+	417.419i	−0.123949	+	0.0900543i
$279$		0			0
$280$	−99.7724	−	250.385i	−0.0212948	−	0.0534405i
$281$	−4977.64	−	3616.47i	−1.05673	−	0.767759i	−0.0832489	−	0.996529i	$-0.526530\pi$
$281$	−4977.64	−	3616.47i	−1.05673	−	0.767759i	−0.973481	+	0.228770i	$0.926530\pi$
$282$		0			0
$283$	4502.63	+	3271.35i	0.945773	+	0.687144i	0.949803	−	0.312848i	$-0.101283\pi$
$283$	4502.63	+	3271.35i	0.945773	+	0.687144i	−0.00403070	+	0.999992i	$0.501283\pi$
$284$	−2152.07	+	6623.38i	−0.449654	+	1.38389i
$285$		0			0
$286$	158.664	+	488.316i	0.0328041	+	0.100961i
$287$	119.218	−	366.915i	0.0245199	−	0.0754645i
$288$		0			0
$289$	−1232.70	−	3793.86i	−0.250906	−	0.772209i
$290$	−95.6247	−	239.976i	−0.0193630	−	0.0485926i
$291$		0			0
$292$	−5451.40	−	3960.67i	−1.09253	−	0.793770i
$293$	−2865.97			−0.571440			−0.285720	−	0.958313i	$-0.592233\pi$
$293$	−2865.97			−0.571440			−0.285720	+	0.958313i	$0.592233\pi$
$294$		0			0
$295$	−2669.65	+	2218.44i	−0.526892	+	0.437840i
$296$	603.838	−	438.714i	0.118572	−	0.0861478i
$297$		0			0
$298$	143.864	+	442.767i	0.0279658	+	0.0860698i
$299$	−1647.85			−0.318722
$300$		0			0
$301$	−1161.89			−0.222492
$302$	−612.095	−	1883.83i	−0.116629	−	0.358948i
$303$		0			0
$304$	−1250.94	+	908.859i	−0.236007	+	0.171469i
$305$	−5.74779	+	22.5925i	−0.00107907	+	0.00424145i
$306$		0			0
$307$	−1957.38			−0.363888			−0.181944	−	0.983309i	$-0.558239\pi$
$307$	−1957.38			−0.363888			−0.181944	+	0.983309i	$0.558239\pi$
$308$	−1047.32	−	760.920i	−0.193755	−	0.140771i
$309$		0			0
$310$	−1101.18	+	915.069i	−0.201752	+	0.167653i
$311$	−1081.33	−	3327.99i	−0.197159	−	0.606794i	−0.999945	−	0.0105260i	$-0.996649\pi$
$311$	−1081.33	−	3327.99i	−0.197159	−	0.606794i	0.802785	−	0.596268i	$-0.203351\pi$
$312$		0			0
$313$	132.624	−	408.176i	0.0239501	−	0.0737107i	−0.938367	−	0.345640i	$-0.887662\pi$
$313$	132.624	−	408.176i	0.0239501	−	0.0737107i	0.962317	+	0.271930i	$0.0876618\pi$
$314$	−142.821	−	439.557i	−0.0256683	−	0.0789989i
$315$		0			0
$316$	2699.57	−	8308.43i	0.480579	−	1.47907i
$317$	3210.73	+	2332.73i	0.568873	+	0.413310i	0.834696	−	0.550712i	$-0.185644\pi$
$317$	3210.73	+	2332.73i	0.568873	+	0.413310i	−0.265823	+	0.964022i	$0.585644\pi$
$318$		0			0
$319$	−2050.77	−	1489.97i	−0.359940	−	0.261512i
$320$	1073.80	−	4220.72i	0.187585	−	0.737329i
$321$		0			0
$322$	−144.696	+	105.128i	−0.0250422	+	0.0181942i
$323$	−258.495	−	795.566i	−0.0445296	−	0.137048i
$324$		0			0
$325$	1756.85	−	229.805i	0.299854	−	0.0392225i
$326$	1815.04			0.308361
$327$		0			0
$328$	−1049.62	+	762.594i	−0.176694	+	0.128376i
$329$	−994.801	+	722.765i	−0.166703	+	0.121117i
$330$		0			0
$331$	4997.11	+	3630.61i	0.829807	+	0.602890i	0.919505	−	0.393079i	$-0.128590\pi$
$331$	4997.11	+	3630.61i	0.829807	+	0.602890i	−0.0896980	+	0.995969i	$0.528590\pi$
$332$	−7567.38			−1.25094
$333$		0			0
$334$	500.051	−	1539.00i	0.0819209	−	0.252127i
$335$	−2708.61	−	6797.40i	−0.441752	−	1.10860i
$336$		0			0
$337$	−2557.17	+	7870.15i	−0.413346	+	1.27215i	0.500375	+	0.865809i	$0.333195\pi$
$337$	−2557.17	+	7870.15i	−0.413346	+	1.27215i	−0.913722	+	0.406341i	$0.866805\pi$
$338$	−354.431	+	1090.83i	−0.0570370	+	0.175542i
$339$		0			0
$340$	2203.78	+	1391.77i	0.351520	+	0.221997i
$341$	−4341.55	+	13361.9i	−0.689466	+	2.12196i
$342$		0			0
$343$	1817.53			0.286114
$344$	3161.10	+	2296.67i	0.495450	+	0.359966i
$345$		0			0
$346$	−1704.71	+	1238.54i	−0.264872	+	0.192440i
$347$	3062.22	−	2224.83i	0.473743	−	0.344194i	−0.325156	−	0.945661i	$-0.605417\pi$
$347$	3062.22	−	2224.83i	0.473743	−	0.344194i	0.798898	+	0.601466i	$0.205417\pi$
$348$		0			0
$349$	−7094.08			−1.08807			−0.544037	−	0.839061i	$-0.683105\pi$
$349$	−7094.08			−1.08807			−0.544037	+	0.839061i	$0.683105\pi$
$350$	139.606	−	132.261i	0.0213208	−	0.0201989i
$351$		0			0
$352$	2032.12	+	6254.22i	0.307706	+	0.947020i
$353$	−1416.95	+	1029.47i	−0.213644	+	0.155222i	−0.689461	−	0.724323i	$-0.742153\pi$
$353$	−1416.95	+	1029.47i	−0.213644	+	0.155222i	0.475817	+	0.879544i	$0.342153\pi$
$354$		0			0
$355$	−10130.3	+	659.740i	−1.51454	+	0.0986348i
$356$	−6135.38	−	4457.62i	−0.913412	−	0.663633i
$357$		0			0
$358$	1129.66	+	820.744i	0.166772	+	0.121167i
$359$	101.297	−	311.759i	0.0148920	−	0.0458329i	−0.943334	−	0.331844i	$-0.892329\pi$
$359$	101.297	−	311.759i	0.0148920	−	0.0458329i	0.958226	+	0.286011i	$0.0923293\pi$
$360$		0			0
$361$	−1885.50	−	5802.98i	−0.274895	−	0.846039i
$362$	−582.856	+	1793.85i	−0.0846250	+	0.260449i
$363$		0			0
$364$	89.9489	+	276.834i	0.0129522	+	0.0398628i
$365$	2421.79	−	9519.21i	0.347294	−	1.36509i
$366$		0			0
$367$	4716.67	+	3426.86i	0.670867	+	0.487413i	0.870315	−	0.492495i	$-0.163915\pi$
$367$	4716.67	+	3426.86i	0.670867	+	0.487413i	−0.199448	+	0.979908i	$0.563915\pi$
$368$	−6531.74			−0.925246
$369$		0			0
$370$	450.267	+	284.360i	0.0632656	+	0.0399545i
$371$	536.061	−	389.471i	0.0750159	−	0.0545022i
$372$		0			0
$373$	887.259	+	2730.70i	0.123165	+	0.379063i	0.993562	−	0.113287i	$-0.0361380\pi$
$373$	887.259	+	2730.70i	0.123165	+	0.379063i	−0.870397	+	0.492350i	$0.836138\pi$
$374$	−1101.03			−0.152227
$375$		0			0
$376$	4135.18			0.567169
$377$	176.130	+	542.073i	0.0240615	+	0.0740535i
$378$		0			0
$379$	8973.27	−	6519.46i	1.21616	−	0.883594i	0.220387	−	0.975412i	$-0.429268\pi$
$379$	8973.27	−	6519.46i	1.21616	−	0.883594i	0.995776	+	0.0918182i	$0.0292678\pi$
$380$	−1995.33	−	1260.12i	−0.269364	−	0.170113i
$381$		0			0
$382$	−1225.39			−0.164127
$383$	579.752	+	421.215i	0.0773472	+	0.0561960i	0.625787	−	0.779994i	$-0.284778\pi$
$383$	579.752	+	421.215i	0.0773472	+	0.0561960i	−0.548440	+	0.836190i	$0.684778\pi$
$384$		0			0
$385$	465.272	−	1828.82i	0.0615908	−	0.242092i
$386$	−686.872	−	2113.97i	−0.0905722	−	0.278753i
$387$		0			0
$388$	−3645.02	+	11218.2i	−0.476928	+	1.46783i
$389$	−2338.83	−	7198.19i	−0.304842	−	0.938207i	−0.979736	−	0.200293i	$-0.935811\pi$
$389$	−2338.83	−	7198.19i	−0.304842	−	0.938207i	0.674894	−	0.737915i	$-0.264189\pi$
$390$		0			0
$391$	1091.95	−	3360.68i	0.141234	−	0.434673i
$392$	−2446.32	−	1777.36i	−0.315199	−	0.229005i
$393$		0			0
$394$	−820.724	−	596.291i	−0.104943	−	0.0762454i
$395$	12707.6	−	827.584i	1.61870	−	0.105418i
$396$		0			0
$397$	−576.649	+	418.960i	−0.0728997	+	0.0529648i	−0.623638	−	0.781713i	$-0.714346\pi$
$397$	−576.649	+	418.960i	−0.0728997	+	0.0529648i	0.550739	+	0.834678i	$0.314346\pi$
$398$	701.868	+	2160.13i	0.0883957	+	0.272054i
$399$		0			0
$400$	6963.79	−	910.899i	0.870473	−	0.113862i
$401$	5539.33			0.689828			0.344914	−	0.938634i	$-0.387908\pi$
$401$	5539.33			0.689828			0.344914	+	0.938634i	$0.387908\pi$
$402$		0			0
$403$	2555.72	−	1856.84i	0.315904	−	0.229518i
$404$	1652.30	−	1200.47i	0.203478	−	0.147835i
$405$		0			0
$406$	50.0484	+	36.3623i	0.00611788	+	0.00444490i
$407$	5225.69			0.636432
$408$		0			0
$409$	−2701.55	+	8314.52i	−0.326609	+	1.00520i	0.644100	+	0.764941i	$0.277232\pi$
$409$	−2701.55	+	8314.52i	−0.326609	+	1.00520i	−0.970709	+	0.240258i	$0.922768\pi$
$410$	−782.676	−	494.288i	−0.0942771	−	0.0595393i
$411$		0			0
$412$	1848.21	−	5688.21i	0.221007	−	0.680190i
$413$	256.870	−	790.564i	0.0306047	−	0.0941916i
$414$		0			0
$415$	−4083.35	−	10247.4i	−0.482997	−	1.21211i
$416$	456.922	−	1406.26i	0.0538521	−	0.165740i
$417$		0			0
$418$	996.884			0.116649
$419$	2623.21	+	1905.87i	0.305853	+	0.222215i	0.730115	−	0.683324i	$-0.239467\pi$
$419$	2623.21	+	1905.87i	0.305853	+	0.222215i	−0.424262	+	0.905539i	$0.639467\pi$
$420$		0			0
$421$	1410.17	−	1024.55i	0.163249	−	0.118607i	−0.503162	−	0.864192i	$-0.667830\pi$
$421$	1410.17	−	1024.55i	0.163249	−	0.118607i	0.666410	+	0.745585i	$0.267830\pi$
$422$	−2215.46	+	1609.63i	−0.255561	+	0.185676i
$423$		0			0
$424$	−2228.29			−0.255225
$425$	−695.508	+	3735.26i	−0.0793813	+	0.426321i
$426$		0			0
$427$	−1.72516	−	5.30950i	−0.000195518	−	0.000601744i
$428$	−3269.99	+	2375.78i	−0.369301	+	0.268313i
$429$		0			0
$430$	−687.366	+	2701.79i	−0.0770878	+	0.303005i
$431$	5437.70	+	3950.72i	0.607715	+	0.441531i	0.848609	−	0.529021i	$-0.177441\pi$
$431$	5437.70	+	3950.72i	0.607715	+	0.441531i	−0.240894	+	0.970551i	$0.577441\pi$
$432$		0			0
$433$	4669.15	+	3392.34i	0.518210	+	0.376502i	0.815929	−	0.578152i	$-0.196226\pi$
$433$	4669.15	+	3392.34i	0.518210	+	0.376502i	−0.297719	+	0.954654i	$0.596226\pi$
$434$	105.954	−	326.094i	0.0117188	−	0.0360668i
$435$		0			0
$436$	138.339	+	425.763i	0.0151955	+	0.0467668i
$437$	−988.668	+	3042.81i	−0.108225	+	0.333083i
$438$		0			0
$439$	−1919.93	−	5908.95i	−0.208732	−	0.642412i	−0.999539	−	0.0303466i	$-0.990339\pi$
$439$	−1919.93	−	5908.95i	−0.208732	−	0.642412i	0.790807	−	0.612065i	$-0.209661\pi$
$440$	−4880.82	+	4055.90i	−0.528827	+	0.439449i
$441$		0			0
$442$	200.285	+	145.516i	0.0215534	+	0.0156594i
$443$	6346.31			0.680638			0.340319	−	0.940310i	$-0.389465\pi$
$443$	6346.31			0.680638			0.340319	+	0.940310i	$0.389465\pi$
$444$		0			0
$445$	2725.65	−	10713.6i	0.290356	−	1.14129i
$446$	1022.77	−	743.085i	0.108586	−	0.0788926i
$447$		0			0
$448$	322.293	+	991.917i	0.0339887	+	0.104606i
$449$	2732.09			0.287161			0.143581	−	0.989639i	$-0.454138\pi$
$449$	2732.09			0.287161			0.143581	+	0.989639i	$0.454138\pi$
$450$		0			0
$451$	−9083.55			−0.948399
$452$	−111.977	−	344.631i	−0.0116526	−	0.0358630i
$453$		0			0
$454$	453.297	−	329.339i	0.0468596	−	0.0340455i
$455$	−326.340	+	271.184i	−0.0336243	+	0.0279413i
$456$		0			0
$457$	11572.5			1.18455			0.592276	−	0.805735i	$-0.298230\pi$
$457$	11572.5			1.18455			0.592276	+	0.805735i	$0.298230\pi$
$458$	−741.209	−	538.520i	−0.0756210	−	0.0549419i
$459$		0			0
$460$	−3690.22	−	9260.81i	−0.374038	−	0.938669i
$461$	1118.62	+	3442.75i	0.113013	+	0.347819i	0.991527	−	0.129897i	$-0.0414647\pi$
$461$	1118.62	+	3442.75i	0.113013	+	0.347819i	−0.878514	+	0.477716i	$0.841465\pi$
$462$		0			0
$463$	−3882.35	+	11948.7i	−0.389694	+	1.19935i	0.543324	+	0.839523i	$0.317166\pi$
$463$	−3882.35	+	11948.7i	−0.389694	+	1.19935i	−0.933018	+	0.359831i	$0.882834\pi$
$464$	698.143	+	2148.66i	0.0698502	+	0.214977i
$465$		0			0
$466$	831.377	−	2558.72i	0.0826455	−	0.254357i
$467$	14107.1	+	10249.4i	1.39786	+	1.01561i	0.994951	+	0.100366i	$0.0320012\pi$
$467$	14107.1	+	10249.4i	1.39786	+	1.01561i	0.402910	+	0.915240i	$0.367999\pi$
$468$		0			0
$469$	1417.64	+	1029.97i	0.139575	+	0.101407i
$470$	1092.16	+	2740.84i	0.107187	+	0.268991i
$471$		0			0
$472$	−2261.54	+	1643.11i	−0.220542	+	0.160233i
$473$	8453.64	+	26017.6i	0.821773	+	2.52916i
$474$		0			0
$475$	629.722	−	3381.95i	0.0608287	−	0.326683i
$476$	−624.189			−0.0601043
$477$		0			0
$478$	33.6159	−	24.4234i	0.00321665	−	0.00233703i
$479$	−555.095	+	403.300i	−0.0529497	+	0.0384702i	−0.613945	−	0.789349i	$-0.710418\pi$
$479$	−555.095	+	403.300i	−0.0529497	+	0.0384702i	0.560996	+	0.827819i	$0.310418\pi$
$480$		0			0
$481$	−950.593	−	690.646i	−0.0901108	−	0.0654693i
$482$	1053.36			0.0995417
$483$		0			0
$484$	−6264.27	+	19279.4i	−0.588305	+	1.81062i
$485$	−17158.1	+	1117.42i	−1.60641	+	0.104618i
$486$		0			0
$487$	1216.53	−	3744.08i	0.113195	−	0.348379i	−0.878371	−	0.477979i	$-0.841369\pi$
$487$	1216.53	−	3744.08i	0.113195	−	0.348379i	0.991566	+	0.129600i	$0.0413694\pi$
$488$	−5.80157	+	17.8554i	−0.000538165	+	0.00165630i
$489$		0			0
$490$	531.942	−	2090.88i	0.0490422	−	0.192768i
$491$	6027.95	−	18552.1i	0.554048	−	1.70518i	−0.144397	−	0.989520i	$-0.546124\pi$
$491$	6027.95	−	18552.1i	0.554048	−	1.70518i	0.698445	−	0.715664i	$-0.253876\pi$
$492$		0			0
$493$	−1222.23			−0.111656
$494$	−181.341	−	131.752i	−0.0165160	−	0.0119996i
$495$		0			0
$496$	10130.3	−	7360.12i	0.917067	−	0.666288i
$497$	1966.82	−	1428.98i	0.177513	−	0.128971i
$498$		0			0
$499$	−8132.04			−0.729539			−0.364770	−	0.931098i	$-0.618852\pi$
$499$	−8132.04			−0.729539			−0.364770	+	0.931098i	$0.618852\pi$
$500$	5225.80	+	9358.74i	0.467410	+	0.837071i
$501$		0			0
$502$	37.6318	+	115.819i	0.00334579	+	0.0102973i
$503$	17482.4	−	12701.7i	1.54971	−	1.12593i	0.605845	−	0.795582i	$-0.292835\pi$
$503$	17482.4	−	12701.7i	1.54971	−	1.12593i	0.943860	−	0.330345i	$-0.107165\pi$
$504$		0			0
$505$	2517.20	+	1589.70i	0.221809	+	0.140081i
$506$	3406.86	+	2475.23i	0.299315	+	0.217465i
$507$		0			0
$508$	−9746.86	−	7081.51i	−0.851274	−	0.618487i
$509$	−4650.20	+	14311.8i	−0.404944	+	1.24629i	0.515999	+	0.856589i	$0.327421\pi$
$509$	−4650.20	+	14311.8i	−0.404944	+	1.24629i	−0.920942	+	0.389699i	$0.872579\pi$
$510$		0			0
$511$	726.886	+	2237.12i	0.0629267	+	0.193668i
$512$	3061.77	−	9423.15i	0.264282	−	0.813376i
$513$		0			0
$514$	1256.24	+	3866.31i	0.107802	+	0.331782i
$515$	8700.01	−	566.590i	0.744405	−	0.0484795i
$516$		0			0
$517$	23422.5	+	17017.4i	1.99250	+	1.44763i
$518$	−127.532			−0.0108174
$519$		0			0
$520$	1423.90	−	92.7318i	0.120081	−	0.00782030i
$521$	6623.59	−	4812.32i	0.556977	−	0.404667i	−0.273375	−	0.961908i	$-0.588140\pi$
$521$	6623.59	−	4812.32i	0.556977	−	0.404667i	0.830351	+	0.557240i	$0.188140\pi$
$522$		0			0
$523$	4169.76	+	12833.2i	0.348625	+	1.07296i	0.959614	+	0.281319i	$0.0907720\pi$
$523$	4169.76	+	12833.2i	0.348625	+	1.07296i	−0.610989	+	0.791639i	$0.709228\pi$
$524$	−22226.9			−1.85303
$525$		0			0
$526$	2904.97			0.240804
$527$	2093.34	+	6442.65i	0.173031	+	0.532535i
$528$		0			0
$529$	−1090.64	+	792.396i	−0.0896392	+	0.0651267i
$530$	−588.525	−	1476.94i	−0.0482338	−	0.121045i
$531$		0			0
$532$	565.149			0.0460570
$533$	1652.37	+	1200.51i	0.134281	+	0.0975611i
$534$		0			0
$535$	−4981.66	−	3146.09i	−0.402572	−	0.254238i
$536$	−1820.98	−	5604.41i	−0.146743	−	0.451630i
$537$		0			0
$538$	−409.908	+	1261.57i	−0.0328483	+	0.101097i
$539$	−6542.13	−	20134.6i	−0.522801	−	1.60902i
$540$		0			0
$541$	−2450.73	+	7542.58i	−0.194760	+	0.599410i	0.805219	+	0.592977i	$0.202048\pi$
$541$	−2450.73	+	7542.58i	−0.194760	+	0.599410i	−0.999979	+	0.00643276i	$0.997952\pi$
$542$	273.329	+	198.585i	0.0216614	+	0.0157379i
$543$		0			0
$544$	2565.20	+	1863.72i	0.202172	+	0.146887i
$545$	−501.901	+	417.073i	−0.0394478	+	0.0327806i
$546$		0			0
$547$	11905.8	−	8650.05i	0.930629	−	0.676142i	−0.0155174	−	0.999880i	$-0.504940\pi$
$547$	11905.8	−	8650.05i	0.930629	−	0.676142i	0.946147	+	0.323738i	$0.104940\pi$
$548$	3090.62	+	9511.95i	0.240921	+	0.741479i
$549$		0			0
$550$	−3977.39	−	2163.84i	−0.308357	−	0.167757i
$551$	1106.63			0.0855606
$552$		0			0
$553$	−2467.20	+	1792.52i	−0.189721	+	0.137841i
$554$	1408.16	−	1023.09i	0.107991	−	0.0784601i
$555$		0			0
$556$	7668.77	+	5571.69i	0.584943	+	0.424986i
$557$	−22711.9			−1.72771			−0.863856	−	0.503739i	$-0.831957\pi$
$557$	−22711.9			−1.72771			−0.863856	+	0.503739i	$0.831957\pi$
$558$		0			0
$559$	1900.80	−	5850.06i	0.143820	−	0.442632i
$560$	−1293.54	+	1074.92i	−0.0976110	+	0.0811134i
$561$		0			0
$562$	1092.49	−	3362.35i	0.0820000	−	0.252370i
$563$	−715.529	+	2202.17i	−0.0535630	+	0.164850i	−0.974260	−	0.225429i	$-0.927622\pi$
$563$	−715.529	+	2202.17i	−0.0535630	+	0.164850i	0.920697	+	0.390279i	$0.127622\pi$
$564$		0			0
$565$	406.260	−	337.597i	0.0302504	−	0.0251377i
$566$	−988.238	+	3041.48i	−0.0733900	+	0.225871i
$567$		0			0
$568$	−8175.66			−0.603949
$569$	−5246.99	−	3812.16i	−0.386582	−	0.280868i	0.377472	−	0.926021i	$-0.376794\pi$
$569$	−5246.99	−	3812.16i	−0.386582	−	0.280868i	−0.764053	+	0.645153i	$0.776794\pi$
$570$		0			0
$571$	1237.96	−	899.434i	0.0907307	−	0.0659197i	−0.541495	−	0.840704i	$-0.682142\pi$
$571$	1237.96	−	899.434i	0.0907307	−	0.0659197i	0.632226	+	0.774784i	$0.282142\pi$
$572$	5544.57	−	4028.36i	0.405297	−	0.294466i
$573$		0			0
$574$	221.682			0.0161199
$575$	10549.3	−	9994.25i	0.765109	−	0.724851i
$576$		0			0
$577$	2455.32	+	7556.70i	0.177151	+	0.545216i	0.999725	−	0.0234424i	$-0.00746262\pi$
$577$	2455.32	+	7556.70i	0.177151	+	0.545216i	−0.822574	+	0.568658i	$0.807463\pi$
$578$	1854.40	−	1347.30i	0.133448	−	0.0969556i
$579$		0			0
$580$	−2651.98	+	2203.76i	−0.189858	+	0.157769i
$581$	2137.16	+	1552.74i	0.152606	+	0.110875i
$582$		0			0
$583$	−12621.5	−	9170.06i	−0.896619	−	0.651432i
$584$	2444.45	−	7523.26i	0.173206	−	0.533073i
$585$		0			0
$586$	−508.891	−	1566.21i	−0.0358739	−	0.110409i
$587$	863.957	−	2658.98i	0.0607484	−	0.186964i	−0.916077	−	0.401003i	$-0.868662\pi$
$587$	863.957	−	2658.98i	0.0607484	−	0.186964i	0.976825	+	0.214038i	$0.0686618\pi$
$588$		0			0
$589$	−1895.34	−	5833.26i	−0.132591	−	0.408074i
$590$	−1686.37	−	1065.01i	−0.117673	−	0.0743145i
$591$		0			0
$592$	−3767.95	−	2737.58i	−0.261591	−	0.190057i
$593$	−18900.9			−1.30889			−0.654443	−	0.756112i	$-0.727097\pi$
$593$	−18900.9			−1.30889			−0.654443	+	0.756112i	$0.727097\pi$
$594$		0			0
$595$	−336.812	−	845.248i	−0.0232066	−	0.0582383i
$596$	5027.38	−	3652.60i	0.345519	−	0.251034i
$597$		0			0
$598$	−292.598	−	900.524i	−0.0200087	−	0.0615806i
$599$	−5146.04			−0.351021			−0.175511	−	0.984478i	$-0.556158\pi$
$599$	−5146.04			−0.351021			−0.175511	+	0.984478i	$0.556158\pi$
$600$		0			0
$601$	−1011.92			−0.0686805			−0.0343403	−	0.999410i	$-0.510933\pi$
$601$	−1011.92			−0.0686805			−0.0343403	+	0.999410i	$0.510933\pi$
$602$	−206.309	−	634.953i	−0.0139676	−	0.0429879i
$603$		0			0
$604$	−21389.9	+	15540.7i	−1.44096	+	1.04692i
$605$	−29487.5	+	1920.38i	−1.98155	+	0.129049i
$606$		0			0
$607$	10173.3			0.680263			0.340131	−	0.940378i	$-0.389528\pi$
$607$	10173.3			0.680263			0.340131	+	0.940378i	$0.389528\pi$
$608$	−2322.56	−	1687.44i	−0.154922	−	0.112557i
$609$		0			0
$610$	−13.3670	+	0.870530i	−0.000887238	+	5.77815e-5i
$611$	−2011.64	−	6191.20i	−0.133195	−	0.409933i
$612$		0			0
$613$	6821.12	−	20993.3i	0.449433	−	1.38321i	−0.428115	−	0.903724i	$-0.640822\pi$
$613$	6821.12	−	20993.3i	0.449433	−	1.38321i	0.877548	−	0.479489i	$-0.159178\pi$
$614$	−347.559	−	1069.68i	−0.0228442	−	0.0703071i
$615$		0			0
$616$	469.626	−	1445.36i	0.0307171	−	0.0945376i
$617$	−18690.4	−	13579.4i	−1.21953	−	0.886039i	−0.223467	−	0.974712i	$-0.571737\pi$
$617$	−18690.4	−	13579.4i	−1.21953	−	0.886039i	−0.996061	+	0.0886729i	$0.971737\pi$
$618$		0			0
$619$	−1080.02	−	784.684i	−0.0701290	−	0.0509517i	0.552168	−	0.833733i	$-0.313801\pi$
$619$	−1080.02	−	784.684i	−0.0701290	−	0.0509517i	−0.622297	+	0.782781i	$0.713801\pi$
$620$	16158.6	+	10204.7i	1.04669	+	0.661019i
$621$		0			0
$622$	1626.69	−	1181.86i	0.104862	−	0.0761868i
$623$	818.087	+	2517.81i	0.0526099	+	0.161917i
$624$		0			0
$625$	−9853.35	+	12126.5i	−0.630614	+	0.776096i
$626$	246.610			0.0157453
$627$		0			0
$628$	−4990.93	+	3626.12i	−0.317133	+	0.230411i
$629$	2038.44	−	1481.01i	0.129218	−	0.0938820i
$630$		0			0
$631$	5073.00	+	3685.75i	0.320052	+	0.232531i	0.736198	−	0.676767i	$-0.236619\pi$
$631$	5073.00	+	3685.75i	0.320052	+	0.232531i	−0.416146	+	0.909298i	$0.636619\pi$
$632$	10255.6			0.645485
$633$		0			0
$634$	−704.692	+	2168.82i	−0.0441434	+	0.135859i
$635$	4330.06	−	17019.9i	0.270603	−	1.06365i
$636$		0			0
$637$	−1471.00	+	4527.27i	−0.0914962	+	0.281596i
$638$	450.102	−	1385.27i	0.0279306	−	0.0859616i
$639$		0			0
$640$	11807.8	−	768.986i	0.729288	−	0.0474951i
$641$	−2824.44	+	8692.72i	−0.174038	+	0.535635i	−0.999588	−	0.0286942i	$-0.990865\pi$
$641$	−2824.44	+	8692.72i	−0.174038	+	0.535635i	0.825550	+	0.564329i	$0.190865\pi$
$642$		0			0
$643$	−12262.8			−0.752095			−0.376047	−	0.926600i	$-0.622717\pi$
$643$	−12262.8			−0.752095			−0.376047	+	0.926600i	$0.622717\pi$
$644$	1931.40	+	1403.24i	0.118180	+	0.0858626i
$645$		0			0
$646$	388.864	−	282.527i	0.0236837	−	0.0172072i
$647$	−13172.3	+	9570.20i	−0.800394	+	0.581520i	−0.911030	−	0.412341i	$-0.864711\pi$
$647$	−13172.3	+	9570.20i	−0.800394	+	0.581520i	0.110636	+	0.993861i	$0.464711\pi$
$648$		0			0
$649$	−19571.7			−1.18375
$650$	437.537	+	919.284i	0.0264025	+	0.0554728i
$651$		0			0
$652$	−7486.58	−	23041.3i	−0.449689	−	1.38400i
$653$	3811.13	−	2768.95i	0.228393	−	0.165938i	−0.467703	−	0.883886i	$-0.654918\pi$
$653$	3811.13	−	2768.95i	0.228393	−	0.165938i	0.696097	+	0.717948i	$0.254918\pi$
$654$		0			0
$655$	−11993.6	−	30098.6i	−0.715464	−	1.79550i
$656$	6549.63	+	4758.59i	0.389817	+	0.283219i
$657$		0			0
$658$	−571.619	−	415.306i	−0.0338663	−	0.0246053i
$659$	−5153.02	+	15859.4i	−0.304603	+	0.937471i	0.675222	+	0.737614i	$0.264048\pi$
$659$	−5153.02	+	15859.4i	−0.304603	+	0.937471i	−0.979825	+	0.199857i	$0.935952\pi$
$660$		0			0
$661$	−5801.03	−	17853.7i	−0.341352	−	1.05057i	−0.963508	−	0.267680i	$-0.913743\pi$
$661$	−5801.03	−	17853.7i	−0.341352	−	1.05057i	0.622156	−	0.782894i	$-0.286257\pi$
$662$	−1096.77	+	3375.50i	−0.0643913	+	0.198176i
$663$		0			0
$664$	−2745.22	−	8448.91i	−0.160444	−	0.493797i
$665$	304.954	+	765.299i	0.0177829	+	0.0446271i
$666$		0			0
$667$	3781.90	+	2747.71i	0.219544	+	0.159508i
$668$	−21599.7			−1.25107
$669$		0			0
$670$	3233.72	−	2687.18i	0.186462	−	0.154947i
$671$	−106.341	+	77.2614i	−0.00611812	+	0.00444507i
$672$		0			0
$673$	9259.20	+	28496.9i	0.530336	+	1.63221i	0.753517	+	0.657429i	$0.228356\pi$
$673$	9259.20	+	28496.9i	0.530336	+	1.63221i	−0.223181	+	0.974777i	$0.571644\pi$
$674$	−4754.96			−0.271742
$675$		0			0
$676$	15309.6			0.871052
$677$	6669.63	+	20527.0i	0.378633	+	1.16531i	0.940995	+	0.338421i	$0.109893\pi$
$677$	6669.63	+	20527.0i	0.378633	+	1.16531i	−0.562362	+	0.826891i	$0.690107\pi$
$678$		0			0
$679$	3331.26	−	2420.30i	0.188280	−	0.136793i
$680$	−754.429	+	2965.40i	−0.0425456	+	0.167232i
$681$		0			0
$682$	−8072.96			−0.453269
$683$	4810.04	+	3494.70i	0.269474	+	0.195784i	0.714313	−	0.699826i	$-0.246739\pi$
$683$	4810.04	+	3494.70i	0.269474	+	0.195784i	−0.444839	+	0.895610i	$0.646739\pi$
$684$		0			0
$685$	−11213.0	+	9317.82i	−0.625438	+	0.519731i
$686$	322.726	+	993.248i	0.0179617	+	0.0552804i
$687$		0			0
$688$	7534.37	−	23188.4i	0.417508	−	1.28496i
$689$	1084.00	+	3336.20i	0.0599377	+	0.184469i
$690$		0			0
$691$	−4660.89	+	14344.7i	−0.256597	+	0.789725i	0.736914	+	0.675987i	$0.236282\pi$
$691$	−4660.89	+	14344.7i	−0.256597	+	0.789725i	−0.993511	+	0.113738i	$0.963718\pi$
$692$	22754.4	+	16532.0i	1.24999	+	0.908168i
$693$		0			0
$694$	1759.57	+	1278.40i	0.0962427	+	0.0699244i
$695$	−3406.86	+	13391.2i	−0.185942	+	0.730872i
$696$		0			0
$697$	−3543.31	+	2574.37i	−0.192557	+	0.139901i
$698$	−1259.65	−	3876.80i	−0.0683071	−	0.210228i
$699$		0			0
$700$	−2254.84	−	1226.71i	−0.121750	−	0.0662363i
$701$	−29869.3			−1.60934			−0.804671	−	0.593722i	$-0.797658\pi$
$701$	−29869.3			−1.60934			−0.804671	+	0.593722i	$0.797658\pi$
$702$		0			0
$703$	−1845.63	+	1340.93i	−0.0990174	+	0.0719403i
$704$	19866.6	−	14433.9i	1.06357	−	0.772726i
$705$		0			0
$706$	−814.186	−	591.541i	−0.0434027	−	0.0315339i
$707$	−712.959			−0.0379259
$708$		0			0
$709$	3546.30	−	10914.4i	0.187848	−	0.578136i	−0.812138	−	0.583465i	$-0.801696\pi$
$709$	3546.30	−	10914.4i	0.187848	−	0.578136i	0.999986	+	0.00532961i	$0.00169648\pi$
$710$	−2159.31	−	5418.91i	−0.114137	−	0.286434i
$711$		0			0
$712$	2751.16	−	8467.19i	0.144809	−	0.445676i
$713$	8006.43	−	24641.2i	0.420537	−	1.29428i
$714$		0			0
$715$	8446.87	+	5334.50i	0.441811	+	0.279020i
$716$	5759.52	−	17726.0i	0.300619	−	0.925211i
$717$		0			0
$718$	188.358			0.00979031
$719$	7033.06	+	5109.81i	0.364797	+	0.265040i	0.755050	−	0.655667i	$-0.227613\pi$
$719$	7033.06	+	5109.81i	0.364797	+	0.265040i	−0.390253	+	0.920707i	$0.627613\pi$
$720$		0			0
$721$	−1689.12	+	1227.22i	−0.0872484	+	0.0633897i
$722$	2836.44	−	2060.79i	0.146207	−	0.106225i
$723$		0			0
$724$	25176.4			1.29237
$725$	−4415.24	−	2402.05i	−0.226177	−	0.123048i
$726$		0			0
$727$	4671.47	+	14377.3i	0.238315	+	0.733459i	0.996664	+	0.0816103i	$0.0260063\pi$
$727$	4671.47	+	14377.3i	0.238315	+	0.733459i	−0.758349	+	0.651849i	$0.773994\pi$
$728$	−276.452	+	200.854i	−0.0140742	+	0.0102255i
$729$		0			0
$730$	5632.11	−	366.792i	0.285553	−	0.0185967i
$731$	10671.2	+	7753.11i	0.539931	+	0.392283i
$732$		0			0
$733$	27204.2	+	19765.0i	1.37082	+	0.995959i	0.997673	+	0.0681872i	$0.0217215\pi$
$733$	27204.2	+	19765.0i	1.37082	+	0.995959i	0.373148	+	0.927772i	$0.378278\pi$
$734$	−1035.22	+	3186.06i	−0.0520579	+	0.160218i
$735$		0			0
$736$	−3747.51	−	11533.7i	−0.187684	−	0.577631i
$737$	12749.3	−	39238.4i	0.637215	−	1.96115i
$738$		0			0
$739$	−2946.68	−	9068.95i	−0.146678	−	0.451430i	0.850545	−	0.525903i	$-0.176273\pi$
$739$	−2946.68	−	9068.95i	−0.146678	−	0.451430i	−0.997223	+	0.0744731i	$0.976273\pi$
$740$	1752.61	−	6888.90i	0.0870640	−	0.342218i
$741$		0			0
$742$	308.024	+	223.793i	0.0152398	+	0.0110724i
$743$	−39282.1			−1.93960			−0.969798	−	0.243909i	$-0.921570\pi$
$743$	−39282.1			−1.93960			−0.969798	+	0.243909i	$0.921570\pi$
$744$		0			0
$745$	7658.96	+	4836.90i	0.376648	+	0.237866i
$746$	−1334.74	+	969.744i	−0.0655070	+	0.0475936i
$747$		0			0
$748$	4541.46	+	13977.2i	0.221995	+	0.683230i
$749$	1410.98			0.0688333
$750$		0			0
$751$	15625.4			0.759226			0.379613	−	0.925145i	$-0.376057\pi$
$751$	15625.4			0.759226			0.379613	+	0.925145i	$0.376057\pi$
$752$	−7973.73	−	24540.6i	−0.386665	−	1.19003i
$753$		0			0
$754$	−264.960	+	192.504i	−0.0127974	+	0.00929788i
$755$	−32586.4	−	20579.5i	−1.57078	−	0.992006i
$756$		0			0
$757$	−28389.3			−1.36305			−0.681524	−	0.731796i	$-0.738682\pi$
$757$	−28389.3			−1.36305			−0.681524	+	0.731796i	$0.738682\pi$
$758$	5156.10	+	3746.13i	0.247069	+	0.179506i
$759$		0			0
$760$	683.070	−	2684.91i	0.0326021	−	0.128147i
$761$	2807.36	+	8640.18i	0.133728	+	0.411572i	0.995390	−	0.0959105i	$-0.0305763\pi$
$761$	2807.36	+	8640.18i	0.133728	+	0.411572i	−0.861662	+	0.507482i	$0.830576\pi$
$762$		0			0
$763$	48.2922	−	148.628i	0.00229134	−	0.00705203i
$764$	5054.45	+	15556.0i	0.239350	+	0.736644i
$765$		0			0
$766$	−127.244	+	391.617i	−0.00600198	+	0.0184722i
$767$	3560.23	+	2586.66i	0.167604	+	0.121772i
$768$		0			0
$769$	−10201.3	−	7411.64i	−0.478370	−	0.347556i	0.322324	−	0.946629i	$-0.395536\pi$
$769$	−10201.3	−	7411.64i	−0.478370	−	0.347556i	−0.800694	+	0.599073i	$0.795536\pi$
$770$	1082.03	−	70.4677i	0.0506413	−	0.00329803i
$771$		0			0
$772$	−24003.0	+	17439.2i	−1.11903	+	0.813020i
$773$	3920.38	+	12065.7i	0.182415	+	0.561414i	0.999894	−	0.0145432i	$-0.00462941\pi$
$773$	3920.38	+	12065.7i	0.182415	+	0.561414i	−0.817480	+	0.575957i	$0.804629\pi$
$774$		0			0
$775$	−5099.61	+	27387.7i	−0.236366	+	1.26941i
$776$	−13847.4			−0.640582
$777$		0			0
$778$	3518.40	−	2556.27i	0.162135	−	0.117798i
$779$	3208.16	−	2330.87i	0.147554	−	0.107204i
$780$		0			0
$781$	−46308.6	−	33645.1i	−2.12170	−	1.54151i
$782$	2030.45			0.0928499
$783$		0			0
$784$	−5830.73	+	17945.1i	−0.265613	+	0.817472i

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)

\(f(q)\)	\(=\)	\(q+(0.177563 + 0.546483i) q^{2} +(6.20502 - 4.50821i) q^{4} +(9.45304 + 5.96993i) q^{5} -2.67744 q^{7} +(7.28438 + 5.29241i) q^{8} +O(q^{10})\)	\(q+(0.177563 + 0.546483i) q^{2} +(6.20502 - 4.50821i) q^{4} +(9.45304 + 5.96993i) q^{5} -2.67744 q^{7} +(7.28438 + 5.29241i) q^{8} +(-1.58395 + 6.22597i) q^{10} +(19.4804 + 59.9545i) q^{11} +(4.38017 - 13.4808i) q^{13} +(-0.475414 - 1.46317i) q^{14} +(17.3621 - 53.4350i) q^{16} +(24.5906 + 17.8661i) q^{17} +(-22.2647 - 16.1762i) q^{19} +(85.5700 - 5.57276i) q^{20} +(-29.3052 + 21.2914i) q^{22} +(-35.9246 - 110.565i) q^{23} +(53.7199 + 112.868i) q^{25} +8.14478 q^{26} +(-16.6135 + 12.0704i) q^{28} +(-32.5312 + 23.6353i) q^{29} +(180.304 + 130.998i) q^{31} +104.316 q^{32} +(-5.39715 + 16.6107i) q^{34} +(-25.3099 - 15.9841i) q^{35} +(25.6160 - 78.8378i) q^{37} +(4.88665 - 15.0396i) q^{38} +(37.2642 + 93.5166i) q^{40} +(-44.5269 + 137.040i) q^{41} +433.956 q^{43} +(391.164 + 284.197i) q^{44} +(54.0428 - 39.2644i) q^{46} +(371.550 - 269.947i) q^{47} -335.831 q^{49} +(-52.1418 + 49.3982i) q^{50} +(-33.5952 - 103.395i) q^{52} +(-200.214 + 145.464i) q^{53} +(-173.775 + 683.049i) q^{55} +(-19.5034 - 14.1701i) q^{56} +(-18.6927 - 13.5810i) q^{58} +(-95.9388 + 295.269i) q^{59} +(0.644333 + 1.98305i) q^{61} +(-39.5730 + 121.793i) q^{62} +(-120.374 - 370.473i) q^{64} +(121.885 - 101.285i) q^{65} +(-529.476 - 384.687i) q^{67} +233.129 q^{68} +(4.24094 - 16.6696i) q^{70} +(-734.591 + 533.711i) q^{71} +(-271.486 - 835.547i) q^{73} +47.6320 q^{74} -211.079 q^{76} +(-52.1575 - 160.524i) q^{77} +(921.477 - 669.493i) q^{79} +(483.127 - 401.473i) q^{80} -82.7962 q^{82} +(-798.210 - 579.934i) q^{83} +(125.796 + 315.693i) q^{85} +(77.0546 + 237.150i) q^{86} +(-175.401 + 539.830i) q^{88} +(-305.549 - 940.383i) q^{89} +(-11.7276 + 36.0939i) q^{91} +(-721.361 - 524.100i) q^{92} +(213.495 + 155.113i) q^{94} +(-113.898 - 285.833i) q^{95} +(-1244.20 + 903.964i) q^{97} +(-59.6313 - 183.526i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8	\( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) \) 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8 + 165 * q^10 - 19 * q^11 + 4 * q^13 + 24 * q^14 - 66 * q^16 - 208 * q^17 + 42 * q^19 - 295 * q^20 - 89 * q^22 - 32 * q^23 + 95 * q^25 - 206 * q^26 - 482 * q^28 + 716 * q^29 + 637 * q^31 + 844 * q^32 - 90 * q^34 - 430 * q^35 + 216 * q^37 - 2314 * q^38 - 500 * q^40 + 38 * q^41 - 1392 * q^43 - 603 * q^44 + 1622 * q^46 + 536 * q^47 + 162 * q^49 + 2265 * q^50 - 1922 * q^52 - 1672 * q^53 - 1000 * q^55 - 3000 * q^56 - 827 * q^58 - 973 * q^59 - 2712 * q^61 - 1057 * q^62 + 4439 * q^64 + 4360 * q^65 + 2768 * q^67 + 1370 * q^68 + 3230 * q^70 + 1074 * q^71 - 1018 * q^73 + 1414 * q^74 - 11408 * q^76 - 1607 * q^77 - 1820 * q^79 + 1290 * q^80 + 1772 * q^82 - 4045 * q^83 + 1850 * q^85 + 3986 * q^86 + 2407 * q^88 - 4542 * q^89 + 4412 * q^91 + 1089 * q^92 + 5137 * q^94 + 720 * q^95 - 5977 * q^97 + 10689 * q^98

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