LMFDB - Embedded newform 225.4.h.a.91.6

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:	$28$
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			91.6
Character	$\chi$	$=$	225.91
Dual form			225.4.h.a.136.6

$q$-expansion

$f(q)$	$=$	$q+(3.16070 + 2.29638i) q^{2} +(2.24451 + 6.90789i) q^{4} +(11.0852 + 1.45535i) q^{5} +22.0918 q^{7} +(0.889297 - 2.73697i) q^{8} +O(q^{10})$	\(q+(3.16070 + 2.29638i) q^{2} +(2.24451 + 6.90789i) q^{4} +(11.0852 + 1.45535i) q^{5} +22.0918 q^{7} +(0.889297 - 2.73697i) q^{8} +(31.6950 + 30.0558i) q^{10} +(-31.5999 - 22.9587i) q^{11} +(55.3321 - 40.2012i) q^{13} +(69.8255 + 50.7312i) q^{14} +(56.1056 - 40.7631i) q^{16} +(-31.1744 + 95.9450i) q^{17} +(-29.0621 + 89.4438i) q^{19} +(14.8275 + 79.8420i) q^{20} +(-47.1559 - 145.131i) q^{22} +(-130.565 - 94.8612i) q^{23} +(120.764 + 32.2658i) q^{25} +267.205 q^{26} +(49.5852 + 152.608i) q^{28} +(15.8462 + 48.7695i) q^{29} +(-80.4233 + 247.517i) q^{31} +247.918 q^{32} +(-318.859 + 231.665i) q^{34} +(244.892 + 32.1513i) q^{35} +(70.1129 - 50.9400i) q^{37} +(-297.254 + 215.967i) q^{38} +(13.8413 - 29.0457i) q^{40} +(-42.4765 + 30.8610i) q^{41} -53.3748 q^{43} +(87.6698 - 269.820i) q^{44} +(-194.840 - 599.656i) q^{46} +(-74.7809 - 230.152i) q^{47} +145.047 q^{49} +(307.604 + 379.302i) q^{50} +(401.899 + 291.997i) q^{52} +(-18.2798 - 56.2594i) q^{53} +(-316.879 - 300.491i) q^{55} +(19.6461 - 60.4646i) q^{56} +(-61.9084 + 190.534i) q^{58} +(-524.396 + 380.996i) q^{59} +(-530.204 - 385.216i) q^{61} +(-822.588 + 597.645i) q^{62} +(334.749 + 243.209i) q^{64} +(671.875 - 365.111i) q^{65} +(240.635 - 740.598i) q^{67} -732.749 q^{68} +(700.198 + 663.986i) q^{70} +(-69.2398 - 213.098i) q^{71} +(-281.749 - 204.703i) q^{73} +338.583 q^{74} -683.098 q^{76} +(-698.099 - 507.198i) q^{77} +(49.9257 + 153.655i) q^{79} +(681.267 - 370.214i) q^{80} -205.124 q^{82} +(12.3245 - 37.9308i) q^{83} +(-485.209 + 1018.20i) q^{85} +(-168.702 - 122.569i) q^{86} +(-90.9391 + 66.0711i) q^{88} +(-375.213 - 272.608i) q^{89} +(1222.39 - 888.115i) q^{91} +(362.236 - 1114.85i) q^{92} +(292.157 - 899.167i) q^{94} +(-452.331 + 949.208i) q^{95} +(177.512 + 546.326i) q^{97} +(458.449 + 333.082i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

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 $

$2$	3.16070	+	2.29638i	1.11748	+	0.811894i	0.983825	−	0.179135i	$-0.0573298\pi$
$2$	3.16070	+	2.29638i	1.11748	+	0.811894i	0.133651	+	0.991028i	$0.457330\pi$
$3$		0			0
$3$		0			0
$4$	2.24451	+	6.90789i	0.280564	+	0.863487i
$5$	11.0852	+	1.45535i	0.991492	+	0.130171i
$5$	11.0852	+	1.45535i	0.991492	+	0.130171i
$6$		0			0
$7$	22.0918			1.19284			0.596422	−	0.802671i	$-0.296589\pi$
$7$	22.0918			1.19284			0.596422	+	0.802671i	$0.296589\pi$
$8$	0.889297	−	2.73697i	0.0393017	−	0.120958i
$9$		0			0
$10$	31.6950	+	30.0558i	1.00228	+	0.950448i
$11$	−31.5999	−	22.9587i	−0.866158	−	0.629301i	0.0633953	−	0.997988i	$-0.479807\pi$
$11$	−31.5999	−	22.9587i	−0.866158	−	0.629301i	−0.929553	+	0.368688i	$0.879807\pi$
$12$		0			0
$13$	55.3321	−	40.2012i	1.18049	−	0.857676i	0.188264	−	0.982119i	$-0.439714\pi$
$13$	55.3321	−	40.2012i	1.18049	−	0.857676i	0.992227	+	0.124442i	$0.0397141\pi$
$14$	69.8255	+	50.7312i	1.33297	+	0.968462i
$15$		0			0
$16$	56.1056	−	40.7631i	0.876650	−	0.636923i
$17$	−31.1744	+	95.9450i	−0.444759	+	1.36883i	0.437988	+	0.898981i	$0.355691\pi$
$17$	−31.1744	+	95.9450i	−0.444759	+	1.36883i	−0.882747	+	0.469848i	$0.844309\pi$
$18$		0			0
$19$	−29.0621	+	89.4438i	−0.350910	+	1.07999i	0.607433	+	0.794371i	$0.292199\pi$
$19$	−29.0621	+	89.4438i	−0.350910	+	1.07999i	−0.958343	+	0.285619i	$0.907801\pi$
$20$	14.8275	+	79.8420i	0.165776	+	0.892661i
$21$		0			0
$22$	−47.1559	−	145.131i	−0.456985	−	1.40646i
$23$	−130.565	−	94.8612i	−1.18368	−	0.859997i	−0.191102	−	0.981570i	$-0.561206\pi$
$23$	−130.565	−	94.8612i	−1.18368	−	0.859997i	−0.992582	+	0.121573i	$0.961206\pi$
$24$		0			0
$25$	120.764	+	32.2658i	0.966111	+	0.258126i
$26$	267.205			2.01551
$27$		0			0
$28$	49.5852	+	152.608i	0.334669	+	1.03000i
$29$	15.8462	+	48.7695i	0.101468	+	0.312285i	0.988885	−	0.148681i	$-0.0475029\pi$
$29$	15.8462	+	48.7695i	0.101468	+	0.312285i	−0.887418	+	0.460966i	$0.847503\pi$
$30$		0			0
$31$	−80.4233	+	247.517i	−0.465950	+	1.43405i	0.391834	+	0.920036i	$0.371841\pi$
$31$	−80.4233	+	247.517i	−0.465950	+	1.43405i	−0.857784	+	0.514011i	$0.828159\pi$
$32$	247.918			1.36957
$33$		0			0
$34$	−318.859	+	231.665i	−1.60835	+	1.16854i
$35$	244.892	+	32.1513i	1.18269	+	0.155273i
$36$		0			0
$37$	70.1129	−	50.9400i	0.311527	−	0.226337i	−0.421025	−	0.907049i	$-0.638329\pi$
$37$	70.1129	−	50.9400i	0.311527	−	0.226337i	0.732551	+	0.680712i	$0.238329\pi$
$38$	−297.254	+	215.967i	−1.26897	+	0.921961i
$39$		0			0
$40$	13.8413	−	29.0457i	0.0547126	−	0.114813i
$41$	−42.4765	+	30.8610i	−0.161798	+	0.117553i	−0.665738	−	0.746185i	$-0.731883\pi$
$41$	−42.4765	+	30.8610i	−0.161798	+	0.117553i	0.503940	+	0.863739i	$0.331883\pi$
$42$		0			0
$43$	−53.3748			−0.189293			−0.0946463	−	0.995511i	$-0.530172\pi$
$43$	−53.3748			−0.189293			−0.0946463	+	0.995511i	$0.530172\pi$
$44$	87.6698	−	269.820i	0.300380	−	0.924475i
$45$		0			0
$46$	−194.840	−	599.656i	−0.624512	−	1.92205i
$47$	−74.7809	−	230.152i	−0.232083	−	0.714279i	−0.997495	−	0.0707380i	$-0.977465\pi$
$47$	−74.7809	−	230.152i	−0.232083	−	0.714279i	0.765412	−	0.643541i	$-0.222535\pi$
$48$		0			0
$49$	145.047			0.422876
$50$	307.604	+	379.302i	0.870035	+	1.07283i
$51$		0			0
$52$	401.899	+	291.997i	1.07179	+	0.778705i
$53$	−18.2798	−	56.2594i	−0.0473759	−	0.145808i	0.924570	−	0.381012i	$-0.124424\pi$
$53$	−18.2798	−	56.2594i	−0.0473759	−	0.145808i	−0.971946	+	0.235204i	$0.924424\pi$
$54$		0			0
$55$	−316.879	−	300.491i	−0.776872	−	0.736695i
$56$	19.6461	−	60.4646i	0.0468808	−	0.144284i
$57$		0			0
$58$	−61.9084	+	190.534i	−0.140155	+	0.431352i
$59$	−524.396	+	380.996i	−1.15713	+	0.840703i	−0.989412	−	0.145132i	$-0.953639\pi$
$59$	−524.396	+	380.996i	−1.15713	+	0.840703i	−0.167716	+	0.985835i	$0.553639\pi$
$60$		0			0
$61$	−530.204	−	385.216i	−1.11288	−	0.808555i	−0.129765	−	0.991545i	$-0.541422\pi$
$61$	−530.204	−	385.216i	−1.11288	−	0.808555i	−0.983115	+	0.182990i	$0.941422\pi$
$62$	−822.588	+	597.645i	−1.68498	+	1.22421i
$63$		0			0
$64$	334.749	+	243.209i	0.653807	+	0.475018i
$65$	671.875	−	365.111i	1.28209	−	0.696714i
$66$		0			0
$67$	240.635	−	740.598i	0.438779	−	1.35042i	−0.450384	−	0.892835i	$-0.648713\pi$
$67$	240.635	−	740.598i	0.438779	−	1.35042i	0.889164	−	0.457589i	$-0.151287\pi$
$68$	−732.749			−1.30675
$69$		0			0
$70$	700.198	+	663.986i	1.19557	+	1.13374i
$71$	−69.2398	−	213.098i	−0.115736	−	0.356199i	0.876364	−	0.481650i	$-0.159962\pi$
$71$	−69.2398	−	213.098i	−0.115736	−	0.356199i	−0.992100	+	0.125451i	$0.959962\pi$
$72$		0			0
$73$	−281.749	−	204.703i	−0.451729	−	0.328200i	0.338549	−	0.940949i	$-0.390064\pi$
$73$	−281.749	−	204.703i	−0.451729	−	0.328200i	−0.790278	+	0.612748i	$0.790064\pi$
$74$	338.583			0.531886
$75$		0			0
$76$	−683.098			−1.03101
$77$	−698.099	−	507.198i	−1.03319	−	0.750657i
$78$		0			0
$79$	49.9257	+	153.655i	0.0711022	+	0.218830i	0.980293	−	0.197550i	$-0.0632985\pi$
$79$	49.9257	+	153.655i	0.0711022	+	0.218830i	−0.909191	+	0.416380i	$0.863299\pi$
$80$	681.267	−	370.214i	0.952099	−	0.517390i
$81$		0			0
$82$	−205.124			−0.276246
$83$	12.3245	−	37.9308i	0.0162986	−	0.0501620i	−0.942576	−	0.333991i	$-0.891605\pi$
$83$	12.3245	−	37.9308i	0.0162986	−	0.0501620i	0.958875	+	0.283829i	$0.0916047\pi$
$84$		0			0
$85$	−485.209	+	1018.20i	−0.619156	+	1.29929i
$86$	−168.702	−	122.569i	−0.211530	−	0.153685i
$87$		0			0
$88$	−90.9391	+	66.0711i	−0.110161	+	0.0800364i
$89$	−375.213	−	272.608i	−0.446882	−	0.324679i	0.341481	−	0.939889i	$-0.389071\pi$
$89$	−375.213	−	272.608i	−0.446882	−	0.324679i	−0.788364	+	0.615210i	$0.789071\pi$
$90$		0			0
$91$	1222.39	−	888.115i	1.40814	−	1.02307i
$92$	362.236	−	1114.85i	0.410497	−	1.26338i
$93$		0			0
$94$	292.157	−	899.167i	0.320571	−	0.986617i
$95$	−452.331	+	949.208i	−0.488508	+	1.02512i
$96$		0			0
$97$	177.512	+	546.326i	0.185810	+	0.571866i	0.999961	−	0.00878766i	$-0.00279724\pi$
$97$	177.512	+	546.326i	0.185810	+	0.571866i	−0.814151	+	0.580653i	$0.802797\pi$
$98$	458.449	+	333.082i	0.472554	+	0.343331i
$99$		0			0
$100$	48.1674	+	906.645i	0.0481674	+	0.906645i
$101$	1074.69			1.05877			0.529383	−	0.848383i	$-0.322423\pi$
$101$	1074.69			1.05877			0.529383	+	0.848383i	$0.322423\pi$
$102$		0			0
$103$	288.232	+	887.086i	0.275731	+	0.848613i	0.989025	+	0.147748i	$0.0472025\pi$
$103$	288.232	+	887.086i	0.275731	+	0.848613i	−0.713294	+	0.700865i	$0.752797\pi$
$104$	−60.8228	−	187.193i	−0.0573478	−	0.176498i
$105$		0			0
$106$	71.4162	−	219.797i	0.0654392	−	0.201401i
$107$	1102.95			0.996511			0.498255	−	0.867030i	$-0.333974\pi$
$107$	1102.95			0.996511			0.498255	+	0.867030i	$0.333974\pi$
$108$		0			0
$109$	1186.41	−	861.976i	1.04254	−	0.757453i	0.0717636	−	0.997422i	$-0.477137\pi$
$109$	1186.41	−	861.976i	1.04254	−	0.757453i	0.970781	+	0.239969i	$0.0771373\pi$
$110$	−311.517	−	1677.44i	−0.270018	−	1.45398i
$111$		0			0
$112$	1239.47	−	900.529i	1.04571	−	0.759750i
$113$	−1253.89	+	911.005i	−1.04386	+	0.758408i	−0.971035	−	0.238936i	$-0.923201\pi$
$113$	−1253.89	+	911.005i	−1.04386	+	0.758408i	−0.0728243	+	0.997345i	$0.523201\pi$
$114$		0			0
$115$	−1309.29	−	1241.58i	−1.06167	−	1.00676i
$116$	−301.327	+	218.927i	−0.241186	+	0.175232i
$117$		0			0
$118$	−2532.37			−1.97563
$119$	−688.699	+	2119.60i	−0.530528	+	1.63280i
$120$		0			0
$121$	60.1524	+	185.130i	0.0451934	+	0.139091i
$122$	−791.213	−	2435.10i	−0.587156	−	1.80708i
$123$		0			0
$124$	−1890.33			−1.36901
$125$	1291.74	+	533.427i	0.924291	+	0.381689i
$126$		0			0
$127$	−786.360	−	571.324i	−0.549434	−	0.399187i	0.278143	−	0.960540i	$-0.410281\pi$
$127$	−786.360	−	571.324i	−0.549434	−	0.399187i	−0.827577	+	0.561352i	$0.810281\pi$
$128$	−113.347	−	348.848i	−0.0782703	−	0.240891i
$129$		0			0
$130$	2962.03	+	388.878i	1.99836	+	0.262360i
$131$	360.986	−	1111.00i	0.240760	−	0.740982i	−0.755545	−	0.655096i	$-0.772628\pi$
$131$	360.986	−	1111.00i	0.240760	−	0.740982i	0.996305	−	0.0858855i	$-0.0273719\pi$
$132$		0			0
$133$	−642.032	+	1975.97i	−0.418581	+	1.28826i
$134$	2461.27	−	1788.22i	1.58673	−	1.15282i
$135$		0			0
$136$	234.876	+	170.647i	0.148091	+	0.107595i
$137$	867.865	−	630.541i	0.541217	−	0.393217i	−0.283320	−	0.959025i	$-0.591436\pi$
$137$	867.865	−	630.541i	0.541217	−	0.393217i	0.824537	+	0.565808i	$0.191436\pi$
$138$		0			0
$139$	276.953	+	201.218i	0.168999	+	0.122785i	0.669070	−	0.743200i	$-0.266693\pi$
$139$	276.953	+	201.218i	0.168999	+	0.122785i	−0.500071	+	0.865984i	$0.666693\pi$
$140$	327.565	+	1763.85i	0.197745	+	1.06480i
$141$		0			0
$142$	270.509	−	832.540i	0.159863	−	0.492009i
$143$	−2671.46			−1.56223
$144$		0			0
$145$	104.681	+	563.682i	0.0599539	+	0.322836i
$146$	−420.448	−	1294.01i	−0.238333	−	0.733512i
$147$		0			0
$148$	509.257	+	369.997i	0.282842	+	0.205497i
$149$	−1268.97			−0.697704			−0.348852	−	0.937178i	$-0.613428\pi$
$149$	−1268.97			−0.697704			−0.348852	+	0.937178i	$0.613428\pi$
$150$		0			0
$151$	−1863.93			−1.00453			−0.502266	−	0.864713i	$-0.667500\pi$
$151$	−1863.93			−1.00453			−0.502266	+	0.864713i	$0.667500\pi$
$152$	218.961	+	159.084i	0.116842	+	0.0848910i
$153$		0			0
$154$	−1041.76	−	3206.20i	−0.545112	−	1.67768i
$155$	−1251.73	+	2626.74i	−0.648656	+	1.36119i
$156$		0			0
$157$	−1891.87			−0.961705			−0.480852	−	0.876802i	$-0.659673\pi$
$157$	−1891.87			−0.961705			−0.480852	+	0.876802i	$0.659673\pi$
$158$	−195.051	+	600.307i	−0.0982118	+	0.302265i
$159$		0			0
$160$	2748.22	+	360.808i	1.35791	+	0.178277i
$161$	−2884.42	−	2095.65i	−1.41195	−	1.02584i
$162$		0			0
$163$	−2559.85	+	1859.84i	−1.23008	+	0.893705i	−0.996896	−	0.0787280i	$-0.974914\pi$
$163$	−2559.85	+	1859.84i	−1.23008	+	0.893705i	−0.233183	+	0.972433i	$0.574914\pi$
$164$	−308.524	−	224.155i	−0.146900	−	0.106729i
$165$		0			0
$166$	126.057	−	91.5861i	0.0589395	−	0.0428220i
$167$	−1089.41	+	3352.87i	−0.504798	+	1.55361i	0.296312	+	0.955091i	$0.404243\pi$
$167$	−1089.41	+	3352.87i	−0.504798	+	1.55361i	−0.801110	+	0.598517i	$0.795757\pi$
$168$		0			0
$169$	766.603	−	2359.36i	0.348932	−	1.07390i
$170$	−3871.78	+	2104.00i	−1.74678	+	0.949233i
$171$		0			0
$172$	−119.800	−	368.707i	−0.0531086	−	0.163452i
$173$	3140.81	+	2281.93i	1.38030	+	1.00285i	0.996852	+	0.0792825i	$0.0252629\pi$
$173$	3140.81	+	2281.93i	1.38030	+	1.00285i	0.383446	+	0.923563i	$0.374737\pi$
$174$		0			0
$175$	2667.89	+	712.808i	1.15242	+	0.307904i
$176$	−2708.80			−1.16013
$177$		0			0
$178$	−559.923	−	1723.27i	−0.235775	−	0.725641i
$179$	−154.209	−	474.606i	−0.0643917	−	0.198177i	0.913685	−	0.406424i	$-0.133224\pi$
$179$	−154.209	−	474.606i	−0.0643917	−	0.198177i	−0.978076	+	0.208247i	$0.933224\pi$
$180$		0			0
$181$	−1375.55	+	4233.49i	−0.564881	+	1.73853i	0.103422	+	0.994638i	$0.467021\pi$
$181$	−1375.55	+	4233.49i	−0.564881	+	1.73853i	−0.668304	+	0.743888i	$0.732979\pi$
$182$	5903.04			2.40419
$183$		0			0
$184$	−375.744	+	272.994i	−0.150545	+	0.109377i
$185$	851.352	−	462.642i	0.338339	−	0.183860i
$186$		0			0
$187$	3187.88	−	2316.13i	1.24664	−	0.905734i
$188$	1422.02	−	1033.16i	0.551656	−	0.400802i
$189$		0			0
$190$	−3609.43	+	1961.44i	−1.37819	+	0.748934i
$191$	3212.06	−	2333.70i	1.21684	−	0.884088i	0.221008	−	0.975272i	$-0.429065\pi$
$191$	3212.06	−	2333.70i	1.21684	−	0.884088i	0.995834	+	0.0911844i	$0.0290653\pi$
$192$		0			0
$193$	3115.35			1.16190			0.580952	−	0.813938i	$-0.302680\pi$
$193$	3115.35			1.16190			0.580952	+	0.813938i	$0.302680\pi$
$194$	−693.510	+	2134.41i	−0.256655	+	0.789904i
$195$		0			0
$196$	325.559	+	1001.97i	0.118644	+	0.365148i
$197$	445.849	+	1372.18i	0.161246	+	0.496263i	0.998740	−	0.0501827i	$-0.0159804\pi$
$197$	445.849	+	1372.18i	0.161246	+	0.496263i	−0.837494	+	0.546446i	$0.815980\pi$
$198$		0			0
$199$	−2015.36			−0.717916			−0.358958	−	0.933354i	$-0.616868\pi$
$199$	−2015.36			−0.717916			−0.358958	+	0.933354i	$0.616868\pi$
$200$	195.706	−	301.834i	0.0691924	−	0.106714i
$201$		0			0
$202$	3396.76	+	2467.89i	1.18315	+	0.859606i
$203$	350.070	+	1077.40i	0.121035	+	0.372507i
$204$		0			0
$205$	−515.775	+	280.283i	−0.175723	+	0.0954916i
$206$	−1126.07	+	3465.70i	−0.380861	+	1.17217i
$207$		0			0
$208$	1465.72	−	4511.02i	0.488602	−	1.50376i
$209$	2971.87	−	2159.19i	0.983582	−	0.714614i
$210$		0			0
$211$	192.025	+	139.514i	0.0626517	+	0.0455192i	0.618670	−	0.785651i	$-0.287672\pi$
$211$	192.025	+	139.514i	0.0626517	+	0.0455192i	−0.556019	+	0.831170i	$0.687672\pi$
$212$	347.605	−	252.550i	0.112611	−	0.0818169i
$213$		0			0
$214$	3486.11	+	2532.80i	1.11358	+	0.809061i
$215$	−591.671	−	77.6791i	−0.187682	−	0.0246403i
$216$		0			0
$217$	−1776.69	+	5468.10i	−0.555806	+	1.71059i
$218$	5729.31			1.77999
$219$		0			0
$220$	1364.52	−	2863.42i	0.418164	−	0.877508i
$221$	2132.15	+	6562.09i	0.648978	+	1.99735i
$222$		0			0
$223$	236.890	+	172.111i	0.0711361	+	0.0516834i	0.622785	−	0.782393i	$-0.286001\pi$
$223$	236.890	+	172.111i	0.0711361	+	0.0516834i	−0.551649	+	0.834076i	$0.686001\pi$
$224$	5476.95			1.63368
$225$		0			0
$226$	−6055.19			−1.78223
$227$	172.374	+	125.237i	0.0504003	+	0.0366180i	0.612700	−	0.790315i	$-0.290083\pi$
$227$	172.374	+	125.237i	0.0504003	+	0.0366180i	−0.562300	+	0.826933i	$0.690083\pi$
$228$		0			0
$229$	−1001.94	−	3083.67i	−0.289128	−	0.889845i	−0.985131	−	0.171806i	$-0.945040\pi$
$229$	−1001.94	−	3083.67i	−0.289128	−	0.889845i	0.696003	−	0.718039i	$-0.254960\pi$
$230$	−1287.13	−	6930.87i	−0.369004	−	1.98699i
$231$		0			0
$232$	147.573			0.0417613
$233$	1229.34	−	3783.53i	0.345652	−	1.06381i	−0.615582	−	0.788073i	$-0.711079\pi$
$233$	1229.34	−	3783.53i	0.345652	−	1.06381i	0.961234	−	0.275735i	$-0.0889211\pi$
$234$		0			0
$235$	−494.010	−	2660.12i	−0.137131	−	0.738412i
$236$	−3808.89	−	2767.32i	−1.05058	−	0.763294i
$237$		0			0
$238$	−7044.17	+	5117.89i	−1.91851	+	1.39388i
$239$	−3905.56	−	2837.55i	−1.05703	−	0.767975i	−0.0834914	−	0.996508i	$-0.526607\pi$
$239$	−3905.56	−	2837.55i	−1.05703	−	0.767975i	−0.973536	+	0.228533i	$0.926607\pi$
$240$		0			0
$241$	1630.46	−	1184.60i	0.435798	−	0.316625i	−0.348165	−	0.937433i	$-0.613195\pi$
$241$	1630.46	−	1184.60i	0.435798	−	0.316625i	0.783963	+	0.620808i	$0.213195\pi$
$242$	−235.006	+	723.273i	−0.0624245	+	0.192123i
$243$		0			0
$244$	1470.98	−	4527.21i	0.385942	−	1.18781i
$245$	1607.87	+	211.094i	0.419278	+	0.0550461i
$246$		0			0
$247$	1987.68	+	6117.45i	0.512036	+	1.57589i
$248$	605.929	+	440.233i	0.155147	+	0.112721i
$249$		0			0
$250$	2857.84	+	4652.32i	0.722981	+	1.17695i
$251$	278.293			0.0699830			0.0349915	−	0.999388i	$-0.488860\pi$
$251$	278.293			0.0699830			0.0349915	+	0.999388i	$0.488860\pi$
$252$		0			0
$253$	1947.96	+	5995.22i	0.484061	+	1.48979i
$254$	−1173.47	−	3611.57i	−0.289882	−	0.892165i
$255$		0			0
$256$	1465.73	−	4511.06i	0.357845	−	1.10133i
$257$	2149.20			0.521647			0.260823	−	0.965387i	$-0.416006\pi$
$257$	2149.20			0.521647			0.260823	+	0.965387i	$0.416006\pi$
$258$		0			0
$259$	1548.92	−	1125.36i	0.371603	−	0.269985i
$260$	4030.18	+	3821.75i	0.961311	+	0.911595i
$261$		0			0
$262$	3692.25	−	2682.58i	0.870641	−	0.632558i
$263$	−5778.91	+	4198.62i	−1.35492	+	0.984404i	−0.356165	+	0.934423i	$0.615916\pi$
$263$	−5778.91	+	4198.62i	−1.35492	+	0.984404i	−0.998750	+	0.0499805i	$0.984084\pi$
$264$		0			0
$265$	−120.758	−	650.251i	−0.0279929	−	0.150734i
$266$	−6566.86	+	4771.10i	−1.51368	+	1.09976i
$267$		0			0
$268$	5656.08			1.28918
$269$	−273.812	+	842.706i	−0.0620617	+	0.191006i	−0.977280	−	0.211952i	$-0.932018\pi$
$269$	−273.812	+	842.706i	−0.0620617	+	0.191006i	0.915218	+	0.402958i	$0.132018\pi$
$270$		0			0
$271$	−238.067	−	732.696i	−0.0533637	−	0.164237i	0.920823	−	0.389981i	$-0.127519\pi$
$271$	−238.067	−	732.696i	−0.0533637	−	0.164237i	−0.974187	+	0.225745i	$0.927519\pi$
$272$	2161.96	+	6653.82i	0.481941	+	1.48326i
$273$		0			0
$274$	4191.02			0.924047
$275$	−3075.35	−	3792.18i	−0.674366	−	0.831552i
$276$		0			0
$277$	6061.62	+	4404.02i	1.31483	+	0.955278i	0.999981	+	0.00613595i	$0.00195315\pi$
$277$	6061.62	+	4404.02i	1.31483	+	0.955278i	0.314847	+	0.949142i	$0.398047\pi$
$278$	413.291	+	1271.98i	0.0891639	+	0.274418i
$279$		0			0
$280$	305.779	−	641.671i	0.0652635	−	0.136954i
$281$	−678.424	+	2087.98i	−0.144026	+	0.443267i	−0.996884	−	0.0788752i	$-0.974867\pi$
$281$	−678.424	+	2087.98i	−0.144026	+	0.443267i	0.852858	+	0.522143i	$0.174867\pi$
$282$		0			0
$283$	1728.33	−	5319.25i	0.363033	−	1.11730i	−0.588170	−	0.808737i	$-0.700151\pi$
$283$	1728.33	−	5319.25i	0.363033	−	1.11730i	0.951203	−	0.308564i	$-0.0998485\pi$
$284$	1316.65	−	956.602i	0.275101	−	0.199873i
$285$		0			0
$286$	−8443.67	−	6134.69i	−1.74575	−	1.26836i
$287$	−938.382	+	681.775i	−0.193000	+	0.140223i
$288$		0			0
$289$	−4258.90	−	3094.27i	−0.866864	−	0.629814i
$290$	−963.562	+	2022.02i	−0.195111	+	0.409437i
$291$		0			0
$292$	781.675	−	2405.75i	0.156658	−	0.482143i
$293$	2905.73			0.579367			0.289684	−	0.957122i	$-0.406450\pi$
$293$	2905.73			0.579367			0.289684	+	0.957122i	$0.406450\pi$
$294$		0			0
$295$	−6367.53	+	3460.24i	−1.25672	+	0.682926i
$296$	−77.0703	−	237.198i	−0.0151339	−	0.0465772i
$297$		0			0
$298$	−4010.83	−	2914.04i	−0.779667	−	0.566461i
$299$	−11038.0			−2.13493
$300$		0			0
$301$	−1179.14			−0.225796
$302$	−5891.32	−	4280.29i	−1.12254	−	0.815573i
$303$		0			0
$304$	2015.46	+	6202.96i	0.380246	+	1.17028i
$305$	−5316.80	−	5041.83i	−0.998161	−	0.946540i
$306$		0			0
$307$	−1896.85			−0.352635			−0.176317	−	0.984333i	$-0.556419\pi$
$307$	−1896.85			−0.352635			−0.176317	+	0.984333i	$0.556419\pi$
$308$	1936.78	−	5960.80i	0.358306	−	1.10275i
$309$		0			0
$310$	−9988.35	+	5427.87i	−1.83000	+	0.994459i
$311$	7137.00	+	5185.33i	1.30129	+	0.945444i	0.999967	−	0.00807744i	$-0.00257116\pi$
$311$	7137.00	+	5185.33i	1.30129	+	0.945444i	0.301325	+	0.953522i	$0.402571\pi$
$312$		0			0
$313$	6034.71	−	4384.47i	1.08978	−	0.791774i	0.110420	−	0.993885i	$-0.464780\pi$
$313$	6034.71	−	4384.47i	1.08978	−	0.791774i	0.979363	+	0.202111i	$0.0647803\pi$
$314$	−5979.63	−	4344.46i	−1.07468	−	0.780802i
$315$		0			0
$316$	−949.376	+	689.762i	−0.169008	+	0.122792i
$317$	1742.87	−	5364.01i	0.308799	−	0.950387i	−0.669433	−	0.742873i	$-0.733463\pi$
$317$	1742.87	−	5364.01i	0.308799	−	0.950387i	0.978232	−	0.207514i	$-0.0665372\pi$
$318$		0			0
$319$	618.946	−	1904.92i	0.108634	−	0.334342i
$320$	3356.81	+	3183.21i	0.586410	+	0.556083i
$321$		0			0
$322$	−4304.36	−	13247.5i	−0.744946	−	2.29271i
$323$	−7675.70	−	5576.72i	−1.32225	−	0.960672i
$324$		0			0
$325$	7979.25	−	3069.51i	1.36187	−	0.523895i
$326$	−12361.8			−2.10018
$327$		0			0
$328$	46.6915	+	143.702i	0.00786009	+	0.0241909i
$329$	−1652.04	−	5084.47i	−0.276839	−	0.852023i
$330$		0			0
$331$	1361.95	−	4191.66i	0.226162	−	0.696055i	−0.772010	−	0.635611i	$-0.780748\pi$
$331$	1361.95	−	4191.66i	0.226162	−	0.696055i	0.998172	−	0.0604442i	$-0.0192517\pi$
$332$	289.684			0.0478870
$333$		0			0
$334$	−11142.8	+	8095.69i	−1.82546	+	1.32628i
$335$	3745.32	−	7859.48i	0.610832	−	1.28182i
$336$		0			0
$337$	−3620.77	+	2630.64i	−0.585269	+	0.425223i	−0.840620	−	0.541626i	$-0.817809\pi$
$337$	−3620.77	+	2630.64i	−0.585269	+	0.425223i	0.255351	+	0.966848i	$0.417809\pi$
$338$	7841.00	−	5696.82i	1.26182	−	0.916763i
$339$		0			0
$340$	−8122.68	−	1066.41i	−1.29563	−	0.170100i
$341$	8224.05	−	5975.12i	1.30603	−	0.948888i
$342$		0			0
$343$	−4373.14			−0.688418
$344$	−47.4660	+	146.085i	−0.00743952	+	0.0228965i
$345$		0			0
$346$	4686.97	+	14425.0i	0.728246	+	2.24131i
$347$	216.151	+	665.244i	0.0334397	+	0.102917i	0.966383	−	0.257106i	$-0.0827689\pi$
$347$	216.151	+	665.244i	0.0334397	+	0.102917i	−0.932944	+	0.360023i	$0.882769\pi$
$348$		0			0
$349$	−7119.97			−1.09204			−0.546022	−	0.837771i	$-0.683858\pi$
$349$	−7119.97			−1.09204			−0.546022	+	0.837771i	$0.683858\pi$
$350$	6795.51	+	8379.46i	1.03782	+	1.27972i
$351$		0			0
$352$	−7834.19	−	5691.87i	−1.18626	−	0.861868i
$353$	1094.30	+	3367.90i	0.164996	+	0.507806i	0.999036	−	0.0438984i	$-0.0139778\pi$
$353$	1094.30	+	3367.90i	0.164996	+	0.507806i	−0.834040	+	0.551704i	$0.813978\pi$
$354$		0			0
$355$	−457.405	−	2463.01i	−0.0683846	−	0.368233i
$356$	1040.98	−	3203.80i	0.154977	−	0.476970i
$357$		0			0
$358$	602.470	−	1854.21i	0.0889428	−	0.273738i
$359$	9430.47	−	6851.64i	1.38641	−	1.00729i	0.390161	−	0.920747i	$-0.372419\pi$
$359$	9430.47	−	6851.64i	1.38641	−	1.00729i	0.996248	−	0.0865388i	$-0.0275807\pi$
$360$		0			0
$361$	−1606.55	−	1167.22i	−0.234224	−	0.170174i
$362$	−14069.4	+	10222.0i	−2.04274	+	1.48414i
$363$		0			0
$364$	8878.66	+	6450.72i	1.27848	+	0.928873i
$365$	−2825.33	−	2679.22i	−0.405164	−	0.384210i
$366$		0			0
$367$	22.7126	−	69.9022i	0.00323048	−	0.00994241i	−0.949428	−	0.313984i	$-0.898336\pi$
$367$	22.7126	−	69.9022i	0.00323048	−	0.00994241i	0.952659	+	0.304042i	$0.0983362\pi$
$368$	−11192.3			−1.58543
$369$		0			0
$370$	3753.27	+	492.758i	0.527360	+	0.0692359i
$371$	−403.833	−	1242.87i	−0.0565121	−	0.173926i
$372$		0			0
$373$	−2082.90	−	1513.32i	−0.289139	−	0.210071i	0.433755	−	0.901031i	$-0.357188\pi$
$373$	−2082.90	−	1513.32i	−0.289139	−	0.210071i	−0.722894	+	0.690959i	$0.757188\pi$
$374$	15394.7			2.12845
$375$		0			0
$376$	−696.422			−0.0955193
$377$	2837.39	+	2061.48i	0.387621	+	0.281623i
$378$		0			0
$379$	18.7531	+	57.7162i	0.00254164	+	0.00782238i	0.952319	−	0.305103i	$-0.0986910\pi$
$379$	18.7531	+	57.7162i	0.00254164	+	0.00782238i	−0.949778	+	0.312926i	$0.898691\pi$
$380$	−7572.29	−	994.148i	−1.02224	−	0.134207i
$381$		0			0
$382$	15511.4			2.07758
$383$	−1174.60	+	3615.05i	−0.156708	+	0.482299i	−0.998330	−	0.0577690i	$-0.981601\pi$
$383$	−1174.60	+	3615.05i	−0.156708	+	0.482299i	0.841622	+	0.540068i	$0.181601\pi$
$384$		0			0
$385$	−7000.42	−	6638.38i	−0.926687	−	0.878762i
$386$	9846.67	+	7154.02i	1.29840	+	0.943343i
$387$		0			0
$388$	−3375.53	+	2452.47i	−0.441667	+	0.320890i
$389$	7911.32	+	5747.91i	1.03116	+	0.749179i	0.968540	−	0.248858i	$-0.0800554\pi$
$389$	7911.32	+	5747.91i	1.03116	+	0.749179i	0.0626169	+	0.998038i	$0.480055\pi$
$390$		0			0
$391$	13171.8	−	9569.84i	1.70364	−	1.23777i
$392$	128.989	−	396.989i	0.0166198	−	0.0511504i
$393$		0			0
$394$	−1741.86	+	5360.89i	−0.222725	+	0.685477i
$395$	329.814	+	1775.96i	0.0420120	+	0.226224i
$396$		0			0
$397$	−4430.53	−	13635.8i	−0.560106	−	1.72383i	−0.682063	−	0.731294i	$-0.738917\pi$
$397$	−4430.53	−	13635.8i	−0.560106	−	1.72383i	0.121957	−	0.992535i	$-0.461083\pi$
$398$	−6369.95	−	4628.04i	−0.802253	−	0.582871i
$399$		0			0
$400$	8090.78	−	3112.42i	1.01135	−	0.389052i
$401$	−2086.59			−0.259849			−0.129924	−	0.991524i	$-0.541473\pi$
$401$	−2086.59			−0.259849			−0.129924	+	0.991524i	$0.541473\pi$
$402$		0			0
$403$	5500.49	+	16928.8i	0.679899	+	2.09251i
$404$	2412.15	+	7423.83i	0.297052	+	0.914231i
$405$		0			0
$406$	−1367.67	+	4209.24i	−0.167183	+	0.514535i
$407$	−3385.08			−0.412266
$408$		0			0
$409$	338.014	−	245.582i	0.0408649	−	0.0296901i	−0.567165	−	0.823604i	$-0.691960\pi$
$409$	338.014	−	245.582i	0.0408649	−	0.0296901i	0.608030	+	0.793914i	$0.291960\pi$
$410$	−2273.85	−	298.528i	−0.273896	−	0.0359591i
$411$		0			0
$412$	−5480.95	+	3982.15i	−0.655406	+	0.476180i
$413$	−11584.8	+	8416.88i	−1.38027	+	1.00283i
$414$		0			0
$415$	191.822	−	402.534i	0.0226896	−	0.0476136i
$416$	13717.8	−	9966.58i	1.61676	−	1.17464i
$417$		0			0
$418$	14351.5			1.67932
$419$	385.525	−	1186.52i	0.0449502	−	0.138342i	−0.926063	−	0.377370i	$-0.876829\pi$
$419$	385.525	−	1186.52i	0.0449502	−	0.138342i	0.971013	+	0.239027i	$0.0768286\pi$
$420$		0			0
$421$	3257.63	+	10026.0i	0.377119	+	1.16065i	0.942038	+	0.335507i	$0.108908\pi$
$421$	3257.63	+	10026.0i	0.377119	+	1.16065i	−0.564919	+	0.825147i	$0.691092\pi$
$422$	286.554	+	881.924i	0.0330551	+	0.101733i
$423$		0			0
$424$	−170.237			−0.0194987
$425$	−6860.49	+	10580.8i	−0.783018	+	1.20764i
$426$		0			0
$427$	−11713.2	−	8510.10i	−1.32749	−	0.964480i
$428$	2475.59	+	7619.09i	0.279585	+	0.860473i
$429$		0			0
$430$	−1691.71	−	1604.22i	−0.189725	−	0.179913i
$431$	2759.44	−	8492.68i	0.308393	−	0.949137i	−0.669996	−	0.742365i	$-0.733704\pi$
$431$	2759.44	−	8492.68i	0.308393	−	0.949137i	0.978389	−	0.206772i	$-0.0662958\pi$
$432$		0			0
$433$	750.382	−	2309.44i	0.0832819	−	0.256315i	−0.900741	−	0.434356i	$-0.856976\pi$
$433$	750.382	−	2309.44i	0.0832819	−	0.256315i	0.984023	+	0.178041i	$0.0569759\pi$
$434$	−18172.4	+	13203.1i	−2.00992	+	1.46029i
$435$		0			0
$436$	8617.34	+	6260.87i	0.946550	+	0.687709i
$437$	12279.2	−	8921.39i	1.34416	−	0.976586i
$438$		0			0
$439$	7139.64	+	5187.25i	0.776211	+	0.563950i	0.903839	−	0.427872i	$-0.140737\pi$
$439$	7139.64	+	5187.25i	0.776211	+	0.563950i	−0.127629	+	0.991822i	$0.540737\pi$
$440$	−1104.24	+	600.064i	−0.119642	+	0.0650157i
$441$		0			0
$442$	−8329.98	+	25637.0i	−0.896418	+	2.75889i
$443$	11494.3			1.23275			0.616377	−	0.787451i	$-0.288600\pi$
$443$	11494.3			1.23275			0.616377	+	0.787451i	$0.288600\pi$
$444$		0			0
$445$	−3762.58	−	3567.99i	−0.400816	−	0.380087i
$446$	353.506	+	1087.98i	0.0375314	+	0.115510i
$447$		0			0
$448$	7395.20	+	5372.93i	0.779889	+	0.566623i
$449$	−1582.63			−0.166345			−0.0831727	−	0.996535i	$-0.526505\pi$
$449$	−1582.63			−0.166345			−0.0831727	+	0.996535i	$0.526505\pi$
$450$		0			0
$451$	2050.78			0.214119
$452$	−9107.50	−	6616.98i	−0.947745	−	0.688577i
$453$		0			0
$454$	257.230	+	791.673i	0.0265912	+	0.0818394i
$455$	14842.9	−	8065.94i	1.52933	−	0.831071i
$456$		0			0
$457$	6765.77			0.692537			0.346269	−	0.938135i	$-0.387449\pi$
$457$	6765.77			0.692537			0.346269	+	0.938135i	$0.387449\pi$
$458$	3914.43	−	12047.4i	0.399366	−	1.22912i
$459$		0			0
$460$	5637.96	−	11831.1i	0.571459	−	1.19920i
$461$	9394.53	+	6825.53i	0.949126	+	0.689580i	0.950600	−	0.310419i	$-0.100469\pi$
$461$	9394.53	+	6825.53i	0.949126	+	0.689580i	−0.00147406	+	0.999999i	$0.500469\pi$
$462$		0			0
$463$	3221.48	−	2340.54i	0.323358	−	0.234934i	−0.414249	−	0.910164i	$-0.635956\pi$
$463$	3221.48	−	2340.54i	0.323358	−	0.234934i	0.737607	+	0.675230i	$0.235956\pi$
$464$	2877.05	+	2090.30i	0.287853	+	0.209137i
$465$		0			0
$466$	12574.0	−	9135.55i	1.24996	−	0.908147i
$467$	−3420.76	+	10528.0i	−0.338959	+	1.04321i	0.625780	+	0.779999i	$0.284781\pi$
$467$	−3420.76	+	10528.0i	−0.338959	+	1.04321i	−0.964739	+	0.263208i	$0.915219\pi$
$468$		0			0
$469$	5316.05	−	16361.1i	0.523395	−	1.61085i
$470$	4547.23	−	9542.26i	0.446272	−	0.936493i
$471$		0			0
$472$	576.433	+	1774.08i	0.0562129	+	0.173005i
$473$	1686.64	+	1225.42i	0.163957	+	0.119122i
$474$		0			0
$475$	−6395.62	+	9863.87i	−0.617792	+	0.952812i
$476$	−16187.7			−1.55875
$477$		0			0
$478$	−5828.19	−	17937.3i	−0.557688	−	1.71639i
$479$	305.633	+	940.643i	0.0291540	+	0.0897267i	0.964575	−	0.263810i	$-0.0849791\pi$
$479$	305.633	+	940.643i	0.0291540	+	0.0897267i	−0.935421	+	0.353536i	$0.884979\pi$
$480$		0			0
$481$	1831.65	−	5637.24i	0.173630	−	0.534378i
$482$	7873.69			0.744059
$483$		0			0
$484$	−1143.85	+	831.052i	−0.107424	+	0.0780477i
$485$	1172.66	+	6314.48i	0.109789	+	0.591187i
$486$		0			0
$487$	−9577.72	+	6958.62i	−0.891187	+	0.647485i	−0.936187	−	0.351502i	$-0.885671\pi$
$487$	−9577.72	+	6958.62i	−0.891187	+	0.647485i	0.0450004	+	0.998987i	$0.485671\pi$
$488$	−1525.83	+	1108.58i	−0.141540	+	0.102835i
$489$		0			0
$490$	4597.25	+	4359.49i	0.423842	+	0.401922i
$491$	10575.2	−	7683.33i	0.971999	−	0.706199i	0.0160929	−	0.999871i	$-0.494877\pi$
$491$	10575.2	−	7683.33i	0.971999	−	0.706199i	0.955906	+	0.293672i	$0.0948772\pi$
$492$		0			0
$493$	−5173.18			−0.472593
$494$	−7765.54	+	23899.9i	−0.707264	+	2.17673i
$495$		0			0
$496$	5577.38	+	17165.4i	0.504903	+	1.55393i
$497$	−1529.63	−	4707.72i	−0.138055	−	0.424889i
$498$		0			0
$499$	107.268			0.00962323			0.00481162	−	0.999988i	$-0.498468\pi$
$499$	107.268			0.00962323			0.00481162	+	0.999988i	$0.498468\pi$
$500$	−785.542	+	10120.5i	−0.0702610	+	0.905201i
$501$		0			0
$502$	879.602	+	639.068i	0.0782043	+	0.0568187i
$503$	1599.76	+	4923.56i	0.141809	+	0.436443i	0.996587	−	0.0825511i	$-0.0263068\pi$
$503$	1599.76	+	4923.56i	0.141809	+	0.436443i	−0.854778	+	0.518994i	$0.826307\pi$
$504$		0			0
$505$	11913.1	+	1564.05i	1.04976	+	0.137820i
$506$	−7610.38	+	23422.3i	−0.668622	+	2.05781i
$507$		0			0
$508$	2181.65	−	6714.43i	0.190542	−	0.586427i
$509$	−4039.84	+	2935.11i	−0.351793	+	0.255593i	−0.749621	−	0.661868i	$-0.769764\pi$
$509$	−4039.84	+	2935.11i	−0.351793	+	0.255593i	0.397828	+	0.917460i	$0.369764\pi$
$510$		0			0
$511$	−6224.34	−	4522.24i	−0.538842	−	0.391492i
$512$	12617.9	−	9167.42i	1.08913	−	0.791302i
$513$		0			0
$514$	6792.96	+	4935.38i	0.582928	+	0.423522i
$515$	1904.09	+	10253.0i	0.162921	+	0.877285i
$516$		0			0
$517$	−2920.92	+	8989.66i	−0.248475	+	0.764729i
$518$	7479.91			0.634456
$519$		0			0
$520$	−401.802	−	2163.60i	−0.0338849	−	0.182462i
$521$	−4258.29	−	13105.7i	−0.358079	−	1.10205i	−0.954203	−	0.299161i	$-0.903293\pi$
$521$	−4258.29	−	13105.7i	−0.358079	−	1.10205i	0.596124	−	0.802893i	$-0.296707\pi$
$522$		0			0
$523$	−17345.4	−	12602.2i	−1.45021	−	1.05364i	−0.985781	−	0.168034i	$-0.946258\pi$
$523$	−17345.4	−	12602.2i	−1.45021	−	1.05364i	−0.464433	−	0.885608i	$-0.653742\pi$
$524$	8484.91			0.707376
$525$		0			0
$526$	−27907.0			−2.31332
$527$	−21240.9	−	15432.4i	−1.75573	−	1.27561i
$528$		0			0
$529$	4288.83	+	13199.7i	0.352497	+	1.08487i
$530$	1111.55	−	2332.56i	0.0910990	−	0.191169i
$531$		0			0
$532$	−15090.9			−1.22983
$533$	−1109.67	+	3415.21i	−0.0901785	+	0.277541i
$534$		0			0
$535$	12226.5	+	1605.19i	0.988032	+	0.129716i
$536$	−1813.00	−	1317.22i	−0.146100	−	0.106148i
$537$		0			0
$538$	−2800.61	+	2034.76i	−0.224429	+	0.163057i
$539$	−4583.46	−	3330.08i	−0.366278	−	0.266116i
$540$		0			0
$541$	19412.5	−	14104.0i	1.54272	−	1.12085i	0.594113	−	0.804382i	$-0.297503\pi$
$541$	19412.5	−	14104.0i	1.54272	−	1.12085i	0.948603	−	0.316467i	$-0.102497\pi$
$542$	930.091	−	2862.53i	0.0737100	−	0.226856i
$543$		0			0
$544$	−7728.70	+	23786.5i	−0.609127	+	1.87470i
$545$	14406.1	−	7828.55i	1.13227	−	0.615299i
$546$		0			0
$547$	−6911.76	−	21272.2i	−0.540266	−	1.66277i	−0.731987	−	0.681319i	$-0.761407\pi$
$547$	−6911.76	−	21272.2i	−0.540266	−	1.66277i	0.191721	−	0.981450i	$-0.438593\pi$
$548$	6303.64	+	4579.86i	0.491383	+	0.357011i
$549$		0			0
$550$	−1011.97	−	19048.1i	−0.0784555	−	1.47675i
$551$	−4822.65			−0.372871
$552$		0			0
$553$	1102.95	+	3394.52i	0.0848138	+	0.261030i
$554$	9045.63	+	27839.6i	0.693704	+	2.13500i
$555$		0			0
$556$	−768.369	+	2364.80i	−0.0586081	+	0.180377i
$557$	−5920.24			−0.450357			−0.225178	−	0.974318i	$-0.572297\pi$
$557$	−5920.24			−0.450357			−0.225178	+	0.974318i	$0.572297\pi$
$558$		0			0
$559$	−2953.34	+	2145.73i	−0.223458	+	0.162352i
$560$	15050.4	−	8178.69i	1.13571	−	0.617165i
$561$		0			0
$562$	−6939.08	+	5041.54i	−0.520832	+	0.378407i
$563$	−2602.59	+	1890.89i	−0.194824	+	0.141548i	−0.680921	−	0.732357i	$-0.738420\pi$
$563$	−2602.59	+	1890.89i	−0.194824	+	0.141548i	0.486097	+	0.873905i	$0.338420\pi$
$564$		0			0
$565$	−15225.5	+	8273.83i	−1.13370	+	0.616076i
$566$	17677.7	−	12843.6i	1.31281	−	0.953813i
$567$		0			0
$568$	−644.819			−0.0476338
$569$	−1869.17	+	5752.70i	−0.137714	+	0.423841i	−0.996002	−	0.0893271i	$-0.971528\pi$
$569$	−1869.17	+	5752.70i	−0.137714	+	0.423841i	0.858288	+	0.513168i	$0.171528\pi$
$570$		0			0
$571$	1450.75	+	4464.95i	0.106326	+	0.327237i	0.990039	−	0.140791i	$-0.0449646\pi$
$571$	1450.75	+	4464.95i	0.106326	+	0.327237i	−0.883714	+	0.468028i	$0.844965\pi$
$572$	−5996.11	−	18454.1i	−0.438304	−	1.34896i
$573$		0			0
$574$	−4531.56			−0.329518
$575$	−12706.8	−	15668.6i	−0.921583	−	1.13639i
$576$		0			0
$577$	15913.7	+	11562.0i	1.14817	+	0.834197i	0.988237	−	0.152930i	$-0.0488709\pi$
$577$	15913.7	+	11562.0i	1.14817	+	0.834197i	0.159937	+	0.987127i	$0.448871\pi$
$578$	−6355.47	−	19560.1i	−0.457358	−	1.40760i
$579$		0			0
$580$	−3658.89	+	1988.32i	−0.261944	+	0.142345i
$581$	272.269	−	837.958i	0.0194417	−	0.0598354i
$582$		0			0
$583$	−714.003	+	2197.47i	−0.0507221	+	0.156107i
$584$	−810.824	+	589.098i	−0.0574523	+	0.0417415i
$585$		0			0
$586$	9184.14	+	6672.67i	0.647429	+	0.470384i
$587$	−8058.17	+	5854.60i	−0.566603	+	0.411661i	−0.833870	−	0.551961i	$-0.813880\pi$
$587$	−8058.17	+	5854.60i	−0.566603	+	0.411661i	0.267266	+	0.963623i	$0.413880\pi$
$588$		0			0
$589$	−19801.6	−	14386.7i	−1.38525	−	1.00644i
$590$	−28071.9	−	3685.49i	−1.95882	−	0.257168i
$591$		0			0
$592$	1857.25	−	5716.04i	0.128940	−	0.396837i
$593$	24115.5			1.66999			0.834995	−	0.550257i	$-0.185470\pi$
$593$	24115.5			1.66999			0.834995	+	0.550257i	$0.185470\pi$
$594$		0			0
$595$	−10719.1	+	22493.9i	−0.738557	+	1.54985i
$596$	−2848.21	−	8765.89i	−0.195750	−	0.602458i
$597$		0			0
$598$	−34887.8	−	25347.4i	−2.38573	−	1.73333i
$599$	−13381.7			−0.912790			−0.456395	−	0.889777i	$-0.650860\pi$
$599$	−13381.7			−0.912790			−0.456395	+	0.889777i	$0.650860\pi$
$600$		0			0
$601$	23840.2			1.61807			0.809037	−	0.587758i	$-0.199989\pi$
$601$	23840.2			1.61807			0.809037	+	0.587758i	$0.199989\pi$
$602$	−3726.92	−	2707.76i	−0.252322	−	0.183323i
$603$		0			0
$604$	−4183.61	−	12875.8i	−0.281835	−	0.867400i
$605$	397.373	+	2139.75i	0.0267033	+	0.143790i
$606$		0			0
$607$	−17213.0			−1.15100			−0.575499	−	0.817803i	$-0.695192\pi$
$607$	−17213.0			−1.15100			−0.575499	+	0.817803i	$0.695192\pi$
$608$	−7205.00	+	22174.7i	−0.480594	+	1.47912i
$609$		0			0
$610$	−5226.83	−	28145.1i	−0.346932	−	1.86814i
$611$	−13390.2	−	9728.52i	−0.886593	−	0.644147i
$612$		0			0
$613$	−6213.79	+	4514.58i	−0.409417	+	0.297459i	−0.773366	−	0.633960i	$-0.781428\pi$
$613$	−6213.79	+	4514.58i	−0.409417	+	0.297459i	0.363949	+	0.931419i	$0.381428\pi$
$614$	−5995.37	−	4355.89i	−0.394061	−	0.286302i
$615$		0			0
$616$	−2009.01	+	1459.63i	−0.131404	+	0.0954709i
$617$	−5822.57	+	17920.0i	−0.379915	+	1.16926i	0.560187	+	0.828366i	$0.310729\pi$
$617$	−5822.57	+	17920.0i	−0.379915	+	1.16926i	−0.940102	+	0.340893i	$0.889271\pi$
$618$		0			0
$619$	−8736.42	+	26887.9i	−0.567280	+	1.74591i	0.0937989	+	0.995591i	$0.470099\pi$
$619$	−8736.42	+	26887.9i	−0.567280	+	1.74591i	−0.661079	+	0.750317i	$0.729901\pi$
$620$	−20954.8	−	2751.10i	−1.35736	−	0.178205i
$621$		0			0
$622$	10650.4	+	32778.5i	0.686562	+	2.11302i
$623$	−8289.12	−	6022.40i	−0.533060	−	0.387291i
$624$		0			0
$625$	13542.8	+	7793.08i	0.866742	+	0.498757i
$626$	29142.3			1.86064
$627$		0			0
$628$	−4246.32	−	13068.8i	−0.269820	−	0.830419i
$629$	2701.71	+	8315.01i	0.171263	+	0.527092i
$630$		0			0
$631$	−2799.20	+	8615.05i	−0.176600	+	0.543518i	−0.999703	−	0.0243738i	$-0.992241\pi$
$631$	−2799.20	+	8615.05i	−0.176600	+	0.543518i	0.823103	+	0.567892i	$0.192241\pi$
$632$	464.950			0.0292638
$633$		0			0
$634$	17826.5	−	12951.7i	1.11669	−	0.811322i
$635$	−7885.49	−	7477.68i	−0.492797	−	0.467311i
$636$		0			0
$637$	8025.74	−	5831.04i	0.499201	−	0.362691i
$638$	6330.72	−	4599.54i	0.392846	−	0.285419i
$639$		0			0
$640$	−748.785	−	4032.01i	−0.0462474	−	0.249030i
$641$	−6259.41	+	4547.73i	−0.385697	+	0.280225i	−0.763690	−	0.645583i	$-0.776614\pi$
$641$	−6259.41	+	4547.73i	−0.385697	+	0.280225i	0.377993	+	0.925809i	$0.376614\pi$
$642$		0			0
$643$	20694.2			1.26921			0.634604	−	0.772837i	$-0.281163\pi$
$643$	20694.2			1.26921			0.634604	+	0.772837i	$0.281163\pi$
$644$	8002.44	−	24629.0i	0.489659	−	1.50701i
$645$		0			0
$646$	−11454.3	−	35252.7i	−0.697620	−	2.14705i
$647$	−2688.19	−	8273.39i	−0.163344	−	0.502721i	0.835566	−	0.549389i	$-0.185140\pi$
$647$	−2688.19	−	8273.39i	−0.163344	−	0.502721i	−0.998910	+	0.0466682i	$0.985140\pi$
$648$		0			0
$649$	25318.1			1.53131
$650$	32268.8	+	8621.59i	1.94721	+	0.520256i
$651$		0			0
$652$	−18593.2	−	13508.7i	−1.11682	−	0.811416i
$653$	−3741.70	−	11515.8i	−0.224233	−	0.690118i	−0.998369	−	0.0570980i	$-0.981815\pi$
$653$	−3741.70	−	11515.8i	−0.224233	−	0.690118i	0.774136	−	0.633020i	$-0.218185\pi$
$654$		0			0
$655$	5618.51	−	11790.3i	0.335165	−	0.703337i
$656$	−1125.18	+	3462.95i	−0.0669679	+	0.206106i
$657$		0			0
$658$	6454.27	−	19864.2i	0.382391	−	1.17688i
$659$	−1436.42	+	1043.62i	−0.0849091	+	0.0616901i	−0.629430	−	0.777057i	$-0.716712\pi$
$659$	−1436.42	+	1043.62i	−0.0849091	+	0.0616901i	0.544521	+	0.838747i	$0.316712\pi$
$660$		0			0
$661$	9947.42	+	7227.23i	0.585340	+	0.425275i	0.840645	−	0.541586i	$-0.182176\pi$
$661$	9947.42	+	7227.23i	0.585340	+	0.425275i	−0.255305	+	0.966861i	$0.582176\pi$
$662$	13930.4	−	10121.0i	0.817853	−	0.594205i
$663$		0			0
$664$	−92.8555	−	67.4634i	−0.00542694	−	0.00394291i
$665$	−9992.80	+	20969.7i	−0.582713	+	1.22281i
$666$		0			0
$667$	2557.37	−	7870.78i	0.148459	−	0.456908i
$668$	−25606.4			−1.48315
$669$		0			0
$670$	29886.2	−	16240.8i	1.72329	−	0.936470i
$671$	7910.36	+	24345.6i	0.455106	+	1.40067i
$672$		0			0
$673$	23862.6	+	17337.2i	1.36677	+	0.993016i	0.997982	+	0.0635025i	$0.0202271\pi$
$673$	23862.6	+	17337.2i	1.36677	+	0.993016i	0.368788	+	0.929514i	$0.379773\pi$
$674$	−17485.1			−0.999260
$675$		0			0
$676$	18018.9			1.02520
$677$	27342.4	+	19865.4i	1.55222	+	1.12776i	0.942043	+	0.335491i	$0.108902\pi$
$677$	27342.4	+	19865.4i	1.55222	+	1.12776i	0.610178	+	0.792264i	$0.291098\pi$
$678$		0			0
$679$	3921.55	+	12069.3i	0.221643	+	0.682146i
$680$	2355.30	+	2233.49i	0.132826	+	0.125956i
$681$		0			0
$682$	39714.9			2.22986
$683$	659.833	−	2030.76i	0.0369661	−	0.113770i	−0.930871	−	0.365349i	$-0.880950\pi$
$683$	659.833	−	2030.76i	0.0369661	−	0.113770i	0.967837	+	0.251579i	$0.0809498\pi$
$684$		0			0
$685$	10538.1	−	5726.63i	0.587797	−	0.319421i
$686$	−13822.2	−	10042.4i	−0.769291	−	0.558923i
$687$		0			0
$688$	−2994.62	+	2175.72i	−0.165943	+	0.120565i
$689$	−3273.16	−	2378.09i	−0.180983	−	0.131492i
$690$		0			0
$691$	−17933.3	+	13029.3i	−0.987285	+	0.717305i	−0.959325	−	0.282304i	$-0.908901\pi$
$691$	−17933.3	+	13029.3i	−0.987285	+	0.717305i	−0.0279602	+	0.999609i	$0.508901\pi$
$692$	−8713.77	+	26818.2i	−0.478682	+	1.47323i
$693$		0			0
$694$	−844.467	+	2599.00i	−0.0461895	+	0.142157i
$695$	2777.24	+	2633.61i	0.151578	+	0.143739i
$696$		0			0
$697$	−1636.78	−	5037.49i	−0.0889489	−	0.273757i
$698$	−22504.1	−	16350.2i	−1.22033	−	0.886623i
$699$		0			0
$700$	1064.10	+	20029.4i	0.0574561	+	1.08149i
$701$	−12304.2			−0.662941			−0.331471	−	0.943466i	$-0.607545\pi$
$701$	−12304.2			−0.662941			−0.331471	+	0.943466i	$0.607545\pi$
$702$		0			0
$703$	2518.64	+	7751.59i	0.135124	+	0.415870i
$704$	−4994.28	−	15370.8i	−0.267371	−	0.822882i
$705$		0			0
$706$	−4275.25	+	13157.9i	−0.227905	+	0.701420i
$707$	23741.8			1.26294
$708$		0			0
$709$	−9554.64	+	6941.85i	−0.506110	+	0.367711i	−0.811346	−	0.584566i	$-0.801265\pi$
$709$	−9554.64	+	6941.85i	−0.506110	+	0.367711i	0.305236	+	0.952277i	$0.401265\pi$
$710$	4210.28	−	8835.20i	0.222548	−	0.467013i
$711$		0			0
$712$	−1079.80	+	784.519i	−0.0568358	+	0.0412937i
$713$	33980.3	−	24688.1i	1.78481	−	1.29674i
$714$		0			0
$715$	−29613.7	−	3887.91i	−1.54894	−	0.203356i
$716$	2932.41	−	2130.52i	0.153058	−	0.111203i
$717$		0			0
$718$	45540.8			2.36709
$719$	9386.90	−	28889.9i	0.486888	−	1.49849i	−0.342340	−	0.939576i	$-0.611219\pi$
$719$	9386.90	−	28889.9i	0.486888	−	1.49849i	0.829228	−	0.558911i	$-0.188781\pi$
$720$		0			0
$721$	6367.55	+	19597.3i	0.328904	+	1.01226i
$722$	−2397.42	−	7378.48i	−0.123577	−	0.380331i
$723$		0			0
$724$	−32332.0			−1.65968
$725$	340.060	+	6400.88i	0.0174200	+	0.327893i
$726$		0			0
$727$	−24645.5	−	17906.0i	−1.25729	−	0.913475i	−0.258668	−	0.965966i	$-0.583284\pi$
$727$	−24645.5	−	17906.0i	−1.25729	−	0.913475i	−0.998621	+	0.0524916i	$0.983284\pi$
$728$	−1343.68	−	4135.43i	−0.0684069	−	0.210535i
$729$		0			0
$730$	−2777.52	−	14956.2i	−0.140823	−	0.758295i
$731$	1663.93	−	5121.05i	0.0841896	−	0.259109i
$732$		0			0
$733$	−7869.55	+	24220.0i	−0.396546	+	1.22044i	0.531205	+	0.847244i	$0.321740\pi$
$733$	−7869.55	+	24220.0i	−0.396546	+	1.22044i	−0.927751	+	0.373200i	$0.878260\pi$
$734$	232.310	−	168.783i	0.0116822	−	0.00848759i
$735$		0			0
$736$	−32369.5	−	23517.8i	−1.62113	−	1.17782i
$737$	−24607.2	+	17878.2i	−1.22988	+	0.893557i
$738$		0			0
$739$	−19811.5	−	14393.9i	−0.986167	−	0.716492i	−0.0270884	−	0.999633i	$-0.508624\pi$
$739$	−19811.5	−	14393.9i	−0.986167	−	0.716492i	−0.959078	+	0.283141i	$0.908624\pi$
$740$	5106.75	+	4842.64i	0.253686	+	0.240566i
$741$		0			0
$742$	1577.71	−	4855.70i	0.0780588	−	0.240240i
$743$	−11738.9			−0.579622			−0.289811	−	0.957084i	$-0.593592\pi$
$743$	−11738.9			−0.579622			−0.289811	+	0.957084i	$0.593592\pi$
$744$		0			0
$745$	−14066.8	−	1846.79i	−0.691768	−	0.0908206i
$746$	−3108.27	−	9566.29i	−0.152550	−	0.469499i
$747$		0			0
$748$	23154.8	+	16823.0i	1.13185	+	0.822338i
$749$	24366.2			1.18868
$750$		0			0
$751$	−12224.7			−0.593989			−0.296995	−	0.954879i	$-0.595984\pi$
$751$	−12224.7			−0.593989			−0.296995	+	0.954879i	$0.595984\pi$
$752$	−13577.3	−	9864.51i	−0.658397	−	0.478353i
$753$		0			0
$754$	4234.18	+	13031.5i	0.204509	+	0.629414i
$755$	−20662.0	−	2712.67i	−0.995985	−	0.130761i
$756$		0			0
$757$	−22653.2			−1.08764			−0.543822	−	0.839201i	$-0.683023\pi$
$757$	−22653.2			−1.08764			−0.543822	+	0.839201i	$0.683023\pi$
$758$	−73.2654	+	225.488i	−0.00351071	+	0.0108049i
$759$		0			0
$760$	2195.70	+	2082.15i	0.104798	+	0.0993782i
$761$	6237.17	+	4531.57i	0.297106	+	0.215860i	0.726344	−	0.687331i	$-0.241218\pi$
$761$	6237.17	+	4531.57i	0.297106	+	0.215860i	−0.429238	+	0.903191i	$0.641218\pi$
$762$		0			0
$763$	26209.9	−	19042.6i	1.24359	−	0.903523i
$764$	23330.5	+	16950.6i	1.10480	+	0.802684i
$765$		0			0
$766$	−12014.1	+	8728.75i	−0.566693	+	0.411727i
$767$	−13699.5	+	42162.7i	−0.644928	+	1.98488i
$768$		0			0
$769$	8640.68	−	26593.3i	0.405190	−	1.24705i	−0.515547	−	0.856861i	$-0.672411\pi$
$769$	8640.68	−	26593.3i	0.405190	−	1.24705i	0.920737	−	0.390184i	$-0.127589\pi$
$770$	−6881.96	−	37057.6i	−0.322089	−	1.73437i
$771$		0			0
$772$	6992.42	+	21520.5i	0.325988	+	1.00329i
$773$	31856.0	+	23144.7i	1.48225	+	1.07692i	0.976823	+	0.214049i	$0.0686653\pi$
$773$	31856.0	+	23144.7i	1.48225	+	1.07692i	0.505428	+	0.862869i	$0.331335\pi$
$774$		0			0
$775$	−17698.6	+	27296.3i	−0.820324	+	1.26517i
$776$	1653.14			0.0764746
$777$		0			0
$778$	11805.9	+	36334.8i	0.544039	+	1.67438i
$779$	−1525.87	−	4696.15i	−0.0701797	−	0.215991i
$780$		0			0
$781$	−2704.48	+	8323.54i	−0.123910	+	0.381357i
$782$	63608.0			2.90872
$783$		0			0
$784$	8137.92	−	5912.55i	0.370714	−	0.269340i
$785$	−20971.8	−

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)

\(f(q)\)	\(=\)	\(q+(3.16070 + 2.29638i) q^{2} +(2.24451 + 6.90789i) q^{4} +(11.0852 + 1.45535i) q^{5} +22.0918 q^{7} +(0.889297 - 2.73697i) q^{8} +O(q^{10})\)	\(q+(3.16070 + 2.29638i) q^{2} +(2.24451 + 6.90789i) q^{4} +(11.0852 + 1.45535i) q^{5} +22.0918 q^{7} +(0.889297 - 2.73697i) q^{8} +(31.6950 + 30.0558i) q^{10} +(-31.5999 - 22.9587i) q^{11} +(55.3321 - 40.2012i) q^{13} +(69.8255 + 50.7312i) q^{14} +(56.1056 - 40.7631i) q^{16} +(-31.1744 + 95.9450i) q^{17} +(-29.0621 + 89.4438i) q^{19} +(14.8275 + 79.8420i) q^{20} +(-47.1559 - 145.131i) q^{22} +(-130.565 - 94.8612i) q^{23} +(120.764 + 32.2658i) q^{25} +267.205 q^{26} +(49.5852 + 152.608i) q^{28} +(15.8462 + 48.7695i) q^{29} +(-80.4233 + 247.517i) q^{31} +247.918 q^{32} +(-318.859 + 231.665i) q^{34} +(244.892 + 32.1513i) q^{35} +(70.1129 - 50.9400i) q^{37} +(-297.254 + 215.967i) q^{38} +(13.8413 - 29.0457i) q^{40} +(-42.4765 + 30.8610i) q^{41} -53.3748 q^{43} +(87.6698 - 269.820i) q^{44} +(-194.840 - 599.656i) q^{46} +(-74.7809 - 230.152i) q^{47} +145.047 q^{49} +(307.604 + 379.302i) q^{50} +(401.899 + 291.997i) q^{52} +(-18.2798 - 56.2594i) q^{53} +(-316.879 - 300.491i) q^{55} +(19.6461 - 60.4646i) q^{56} +(-61.9084 + 190.534i) q^{58} +(-524.396 + 380.996i) q^{59} +(-530.204 - 385.216i) q^{61} +(-822.588 + 597.645i) q^{62} +(334.749 + 243.209i) q^{64} +(671.875 - 365.111i) q^{65} +(240.635 - 740.598i) q^{67} -732.749 q^{68} +(700.198 + 663.986i) q^{70} +(-69.2398 - 213.098i) q^{71} +(-281.749 - 204.703i) q^{73} +338.583 q^{74} -683.098 q^{76} +(-698.099 - 507.198i) q^{77} +(49.9257 + 153.655i) q^{79} +(681.267 - 370.214i) q^{80} -205.124 q^{82} +(12.3245 - 37.9308i) q^{83} +(-485.209 + 1018.20i) q^{85} +(-168.702 - 122.569i) q^{86} +(-90.9391 + 66.0711i) q^{88} +(-375.213 - 272.608i) q^{89} +(1222.39 - 888.115i) q^{91} +(362.236 - 1114.85i) q^{92} +(292.157 - 899.167i) q^{94} +(-452.331 + 949.208i) q^{95} +(177.512 + 546.326i) q^{97} +(458.449 + 333.082i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) 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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