LMFDB - Embedded newform 225.4.h.a.91.7

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			91.7
Character	$\chi$	$=$	225.91
Dual form			225.4.h.a.136.7

$q$-expansion

$f(q)$	$=$	$q+(3.76530 + 2.73565i) q^{2} +(4.22155 + 12.9926i) q^{4} +(-5.34090 + 9.82216i) q^{5} -26.0445 q^{7} +(-8.14206 + 25.0587i) q^{8} +O(q^{10})$	\(q+(3.76530 + 2.73565i) q^{2} +(4.22155 + 12.9926i) q^{4} +(-5.34090 + 9.82216i) q^{5} -26.0445 q^{7} +(-8.14206 + 25.0587i) q^{8} +(-46.9800 + 22.3725i) q^{10} +(2.03543 + 1.47883i) q^{11} +(-32.0534 + 23.2881i) q^{13} +(-98.0653 - 71.2486i) q^{14} +(-10.7917 + 7.84062i) q^{16} +(26.2638 - 80.8316i) q^{17} +(-44.1360 + 135.837i) q^{19} +(-150.162 - 27.9275i) q^{20} +(3.61845 + 11.1365i) q^{22} +(127.177 + 92.3993i) q^{23} +(-67.9495 - 104.918i) q^{25} -184.399 q^{26} +(-109.948 - 338.386i) q^{28} +(30.9737 + 95.3273i) q^{29} +(-53.5715 + 164.876i) q^{31} +148.703 q^{32} +(320.018 - 232.506i) q^{34} +(139.101 - 255.813i) q^{35} +(48.0520 - 34.9118i) q^{37} +(-537.786 + 390.725i) q^{38} +(-202.644 - 213.809i) q^{40} +(-287.546 + 208.914i) q^{41} +109.742 q^{43} +(-10.6211 + 32.6885i) q^{44} +(226.086 + 695.821i) q^{46} +(17.9575 + 55.2674i) q^{47} +335.317 q^{49} +(31.1696 - 580.935i) q^{50} +(-437.888 - 318.144i) q^{52} +(120.787 + 371.745i) q^{53} +(-25.3963 + 12.0941i) q^{55} +(212.056 - 652.641i) q^{56} +(-144.157 + 443.669i) q^{58} +(333.759 - 242.490i) q^{59} +(-290.142 - 210.800i) q^{61} +(-652.756 + 474.255i) q^{62} +(646.244 + 469.524i) q^{64} +(-57.5458 - 439.213i) q^{65} +(108.468 - 333.831i) q^{67} +1161.09 q^{68} +(1223.57 - 582.681i) q^{70} +(-52.7887 - 162.467i) q^{71} +(754.724 + 548.339i) q^{73} +276.437 q^{74} -1951.19 q^{76} +(-53.0119 - 38.5154i) q^{77} +(-405.819 - 1248.98i) q^{79} +(-19.3744 - 147.874i) q^{80} -1654.21 q^{82} +(202.066 - 621.896i) q^{83} +(653.668 + 689.680i) q^{85} +(413.211 + 300.216i) q^{86} +(-53.6301 + 38.9646i) q^{88} +(857.273 + 622.845i) q^{89} +(834.814 - 606.528i) q^{91} +(-663.624 + 2042.42i) q^{92} +(-83.5770 + 257.224i) q^{94} +(-1098.48 - 1159.00i) q^{95} +(198.234 + 610.103i) q^{97} +(1262.57 + 917.308i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.76530	+	2.73565i	1.33123	+	0.967198i	0.999718	+	0.0237477i	$0.00755984\pi$
$2$	3.76530	+	2.73565i	1.33123	+	0.967198i	0.331515	+	0.943450i	$0.392440\pi$
$3$		0			0
$3$		0			0
$4$	4.22155	+	12.9926i	0.527694	+	1.62407i
$5$	−5.34090	+	9.82216i	−0.477705	+	0.878520i
$5$	−5.34090	+	9.82216i	−0.477705	+	0.878520i
$6$		0			0
$7$	−26.0445			−1.40627			−0.703136	−	0.711056i	$-0.748217\pi$
$7$	−26.0445			−1.40627			−0.703136	+	0.711056i	$0.748217\pi$
$8$	−8.14206	+	25.0587i	−0.359832	+	1.10745i
$9$		0			0
$10$	−46.9800	+	22.3725i	−1.48564	+	0.707481i
$11$	2.03543	+	1.47883i	0.0557915	+	0.0405349i	0.615331	−	0.788268i	$-0.289022\pi$
$11$	2.03543	+	1.47883i	0.0557915	+	0.0405349i	−0.559540	+	0.828803i	$0.689022\pi$
$12$		0			0
$13$	−32.0534	+	23.2881i	−0.683846	+	0.496843i	−0.874632	−	0.484788i	$-0.838897\pi$
$13$	−32.0534	+	23.2881i	−0.683846	+	0.496843i	0.190785	+	0.981632i	$0.438897\pi$
$14$	−98.0653	−	71.2486i	−1.87208	−	1.36014i
$15$		0			0
$16$	−10.7917	+	7.84062i	−0.168620	+	0.122510i
$17$	26.2638	−	80.8316i	0.374700	−	1.15321i	−0.568981	−	0.822351i	$-0.692662\pi$
$17$	26.2638	−	80.8316i	0.374700	−	1.15321i	0.943681	−	0.330857i	$-0.107338\pi$
$18$		0			0
$19$	−44.1360	+	135.837i	−0.532921	+	1.64016i	0.215179	+	0.976575i	$0.430967\pi$
$19$	−44.1360	+	135.837i	−0.532921	+	1.64016i	−0.748099	+	0.663587i	$0.769033\pi$
$20$	−150.162	−	27.9275i	−1.67886	−	0.312239i
$21$		0			0
$22$	3.61845	+	11.1365i	0.0350662	+	0.107923i
$23$	127.177	+	92.3993i	1.15296	+	0.837678i	0.988872	−	0.148768i	$-0.0475306\pi$
$23$	127.177	+	92.3993i	1.15296	+	0.837678i	0.164092	+	0.986445i	$0.447531\pi$
$24$		0			0
$25$	−67.9495	−	104.918i	−0.543596	−	0.839347i
$26$	−184.399			−1.39090
$27$		0			0
$28$	−109.948	−	338.386i	−0.742081	−	2.28389i
$29$	30.9737	+	95.3273i	0.198334	+	0.610408i	0.999921	+	0.0125312i	$0.00398890\pi$
$29$	30.9737	+	95.3273i	0.198334	+	0.610408i	−0.801588	+	0.597877i	$0.796011\pi$
$30$		0			0
$31$	−53.5715	+	164.876i	−0.310378	+	0.955246i	0.667237	+	0.744846i	$0.267477\pi$
$31$	−53.5715	+	164.876i	−0.310378	+	0.955246i	−0.977615	+	0.210401i	$0.932523\pi$
$32$	148.703			0.821476
$33$		0			0
$34$	320.018	−	232.506i	1.61419	−	1.17278i
$35$	139.101	−	255.813i	0.671783	−	1.23544i
$36$		0			0
$37$	48.0520	−	34.9118i	0.213506	−	0.155121i	−0.475893	−	0.879503i	$-0.657875\pi$
$37$	48.0520	−	34.9118i	0.213506	−	0.155121i	0.689398	+	0.724382i	$0.257875\pi$
$38$	−537.786	+	390.725i	−2.29580	+	1.66800i
$39$		0			0
$40$	−202.644	−	213.809i	−0.801022	−	0.845153i
$41$	−287.546	+	208.914i	−1.09530	+	0.795779i	−0.980286	−	0.197585i	$-0.936690\pi$
$41$	−287.546	+	208.914i	−1.09530	+	0.795779i	−0.115011	+	0.993364i	$0.536690\pi$
$42$		0			0
$43$	109.742			0.389198			0.194599	−	0.980883i	$-0.437659\pi$
$43$	109.742			0.389198			0.194599	+	0.980883i	$0.437659\pi$
$44$	−10.6211	+	32.6885i	−0.0363908	+	0.112000i
$45$		0			0
$46$	226.086	+	695.821i	0.724665	+	2.23029i
$47$	17.9575	+	55.2674i	0.0557312	+	0.171523i	0.975047	−	0.221997i	$-0.0712574\pi$
$47$	17.9575	+	55.2674i	0.0557312	+	0.171523i	−0.919316	+	0.393520i	$0.871257\pi$
$48$		0			0
$49$	335.317			0.977600
$50$	31.1696	−	580.935i	0.0881610	−	1.64313i
$51$		0			0
$52$	−437.888	−	318.144i	−1.16777	−	0.848436i
$53$	120.787	+	371.745i	0.313045	+	0.963455i	0.976552	+	0.215284i	$0.0690676\pi$
$53$	120.787	+	371.745i	0.313045	+	0.963455i	−0.663506	+	0.748171i	$0.730932\pi$
$54$		0			0
$55$	−25.3963	+	12.0941i	−0.0622626	+	0.0296502i
$56$	212.056	−	652.641i	0.506021	−	1.55737i
$57$		0			0
$58$	−144.157	+	443.669i	−0.326357	+	1.00442i
$59$	333.759	−	242.490i	0.736470	−	0.535077i	−0.155134	−	0.987893i	$-0.549581\pi$
$59$	333.759	−	242.490i	0.736470	−	0.535077i	0.891604	+	0.452817i	$0.149581\pi$
$60$		0			0
$61$	−290.142	−	210.800i	−0.608998	−	0.442463i	0.240064	−	0.970757i	$-0.422832\pi$
$61$	−290.142	−	210.800i	−0.608998	−	0.442463i	−0.849061	+	0.528294i	$0.822832\pi$
$62$	−652.756	+	474.255i	−1.33710	+	0.971459i
$63$		0			0
$64$	646.244	+	469.524i	1.26220	+	0.917039i
$65$	−57.5458	−	439.213i	−0.109810	−	0.838118i
$66$		0			0
$67$	108.468	−	333.831i	0.197783	−	0.608715i	−0.802149	−	0.597123i	$-0.796310\pi$
$67$	108.468	−	333.831i	0.197783	−	0.608715i	0.999933	−	0.0115915i	$-0.00368977\pi$
$68$	1161.09			2.07062
$69$		0			0
$70$	1223.57	−	582.681i	2.08921	−	0.994910i
$71$	−52.7887	−	162.467i	−0.0882376	−	0.271567i	0.897195	−	0.441635i	$-0.145601\pi$
$71$	−52.7887	−	162.467i	−0.0882376	−	0.271567i	−0.985432	+	0.170068i	$0.945601\pi$
$72$		0			0
$73$	754.724	+	548.339i	1.21005	+	0.879154i	0.995236	−	0.0975001i	$-0.0310846\pi$
$73$	754.724	+	548.339i	1.21005	+	0.879154i	0.214817	+	0.976654i	$0.431085\pi$
$74$	276.437			0.434258
$75$		0			0
$76$	−1951.19			−2.94496
$77$	−53.0119	−	38.5154i	−0.0784580	−	0.0570030i
$78$		0			0
$79$	−405.819	−	1248.98i	−0.577952	−	1.77875i	−0.625898	−	0.779905i	$-0.715267\pi$
$79$	−405.819	−	1248.98i	−0.577952	−	1.77875i	0.0479457	−	0.998850i	$-0.484733\pi$
$80$	−19.3744	−	147.874i	−0.0270766	−	0.206660i
$81$		0			0
$82$	−1654.21			−2.22777
$83$	202.066	−	621.896i	0.267225	−	0.822433i	−0.723948	−	0.689855i	$-0.757674\pi$
$83$	202.066	−	621.896i	0.267225	−	0.822433i	0.991173	−	0.132578i	$-0.0423255\pi$
$84$		0			0
$85$	653.668	+	689.680i	0.834121	+	0.880075i
$86$	413.211	+	300.216i	0.518113	+	0.376431i
$87$		0			0
$88$	−53.6301	+	38.9646i	−0.0649658	+	0.0472004i
$89$	857.273	+	622.845i	1.02102	+	0.741814i	0.966492	−	0.256698i	$-0.0826346\pi$
$89$	857.273	+	622.845i	1.02102	+	0.741814i	0.0545280	+	0.998512i	$0.482635\pi$
$90$		0			0
$91$	834.814	−	606.528i	0.961674	−	0.698697i
$92$	−663.624	+	2042.42i	−0.752039	+	2.31454i
$93$		0			0
$94$	−83.5770	+	257.224i	−0.0917054	+	0.282240i
$95$	−1098.48	−	1159.00i	−1.18634	−	1.25169i
$96$		0			0
$97$	198.234	+	610.103i	0.207502	+	0.638624i	0.999601	+	0.0282327i	$0.00898793\pi$
$97$	198.234	+	610.103i	0.207502	+	0.638624i	−0.792100	+	0.610392i	$0.791012\pi$
$98$	1262.57	+	917.308i	1.30141	+	0.945532i
$99$		0			0
$100$	1076.31	−	1325.76i	1.07631	−	1.32576i
$101$	−864.030			−0.851229			−0.425615	−	0.904904i	$-0.639942\pi$
$101$	−864.030			−0.851229			−0.425615	+	0.904904i	$0.639942\pi$
$102$		0			0
$103$	566.152	+	1742.44i	0.541598	+	1.66687i	0.728944	+	0.684574i	$0.240012\pi$
$103$	566.152	+	1742.44i	0.541598	+	1.66687i	−0.187345	+	0.982294i	$0.559988\pi$
$104$	−322.589	−	992.828i	−0.304159	−	0.936104i
$105$		0			0
$106$	−562.163	+	1730.16i	−0.515115	+	1.58536i
$107$	1037.99			0.937816			0.468908	−	0.883247i	$-0.344648\pi$
$107$	1037.99			0.937816			0.468908	+	0.883247i	$0.344648\pi$
$108$		0			0
$109$	−1259.67	+	915.201i	−1.10692	+	0.804224i	−0.982176	−	0.187966i	$-0.939811\pi$
$109$	−1259.67	+	915.201i	−1.10692	+	0.804224i	−0.124743	+	0.992189i	$0.539811\pi$
$110$	−128.710	−	23.9377i	−0.111564	−	0.0207488i
$111$		0			0
$112$	281.064	−	204.205i	0.237126	−	0.172282i
$113$	−788.953	+	573.208i	−0.656800	+	0.477193i	−0.865581	−	0.500769i	$-0.833051\pi$
$113$	−788.953	+	573.208i	−0.656800	+	0.477193i	0.208781	+	0.977963i	$0.433051\pi$
$114$		0			0
$115$	−1586.80	+	755.654i	−1.28669	+	0.612740i
$116$	−1107.79	+	804.858i	−0.886689	+	0.644217i
$117$		0			0
$118$	1920.07			1.49794
$119$	−684.027	+	2105.22i	−0.526930	+	1.62172i
$120$		0			0
$121$	−409.346	−	1259.84i	−0.307547	−	0.946534i
$122$	−515.794	−	1587.45i	−0.382769	−	1.17804i
$123$		0			0
$124$	−2368.33			−1.71518
$125$	1393.44	−	107.052i	0.997062	−	0.0766002i
$126$		0			0
$127$	832.392	+	604.768i	0.581597	+	0.422555i	0.839300	−	0.543669i	$-0.182965\pi$
$127$	832.392	+	604.768i	0.581597	+	0.422555i	−0.257702	+	0.966224i	$0.582965\pi$
$128$	781.235	+	2404.39i	0.539469	+	1.66032i
$129$		0			0
$130$	984.855	−	1811.19i	0.664442	−	1.22194i
$131$	825.045	−	2539.23i	0.550264	−	1.69354i	−0.157870	−	0.987460i	$-0.550463\pi$
$131$	825.045	−	2539.23i	0.550264	−	1.69354i	0.708134	−	0.706078i	$-0.249537\pi$
$132$		0			0
$133$	1149.50	−	3537.80i	0.749431	−	2.30651i
$134$	1321.66	−	960.241i	0.852044	−	0.619046i
$135$		0			0
$136$	1811.69	+	1316.27i	1.14229	+	0.829921i
$137$	−986.533	+	716.758i	−0.615221	+	0.446984i	−0.851249	−	0.524762i	$-0.824154\pi$
$137$	−986.533	+	716.758i	−0.615221	+	0.446984i	0.236028	+	0.971746i	$0.424154\pi$
$138$		0			0
$139$	−708.126	−	514.484i	−0.432104	−	0.313942i	0.350386	−	0.936606i	$-0.386051\pi$
$139$	−708.126	−	514.484i	−0.432104	−	0.313942i	−0.782490	+	0.622664i	$0.786051\pi$
$140$	3910.90	+	727.357i	2.36094	+	0.439092i
$141$		0			0
$142$	245.687	−	756.148i	0.145194	−	0.446863i
$143$	−99.6816			−0.0582923
$144$		0			0
$145$	−1101.75	−	204.905i	−0.631001	−	0.117355i
$146$	1341.70	+	4129.32i	0.760546	+	2.34072i
$147$		0			0
$148$	656.449	+	476.938i	0.364593	+	0.264893i
$149$	819.633			0.450650			0.225325	−	0.974284i	$-0.427656\pi$
$149$	819.633			0.450650			0.225325	+	0.974284i	$0.427656\pi$
$150$		0			0
$151$	567.457			0.305821			0.152911	−	0.988240i	$-0.451135\pi$
$151$	567.457			0.305821			0.152911	+	0.988240i	$0.451135\pi$
$152$	−3044.53	−	2211.98i	−1.62463	−	1.18036i
$153$		0			0
$154$	−94.2409	−	290.044i	−0.0493126	−	0.151769i
$155$	−1333.32	−	1406.78i	−0.690934	−	0.729000i
$156$		0			0
$157$	−1643.63			−0.835516			−0.417758	−	0.908558i	$-0.637184\pi$
$157$	−1643.63			−0.835516			−0.417758	+	0.908558i	$0.637184\pi$
$158$	1888.75	−	5812.97i	0.951018	−	2.92693i
$159$		0			0
$160$	−794.208	+	1460.58i	−0.392423	+	0.721683i
$161$	−3312.26	−	2406.49i	−1.62138	−	1.17800i
$162$		0			0
$163$	1035.78	−	752.538i	0.497721	−	0.361615i	−0.310425	−	0.950598i	$-0.600471\pi$
$163$	1035.78	−	752.538i	0.497721	−	0.361615i	0.808146	+	0.588982i	$0.200471\pi$
$164$	−3928.23	−	2854.03i	−1.87039	−	1.35892i
$165$		0			0
$166$	2462.13	−	1788.84i	1.15119	−	0.836391i
$167$	487.198	−	1499.44i	0.225752	−	0.694792i	−0.772463	−	0.635060i	$-0.780975\pi$
$167$	487.198	−	1499.44i	0.225752	−	0.694792i	0.998214	−	0.0597320i	$-0.0190246\pi$
$168$		0			0
$169$	−193.829	+	596.545i	−0.0882246	+	0.271527i
$170$	574.531	+	4385.06i	0.259203	+	1.97834i
$171$		0			0
$172$	463.282	+	1425.83i	0.205377	+	0.632086i
$173$	1797.33	+	1305.83i	0.789874	+	0.573877i	0.907926	−	0.419131i	$-0.137665\pi$
$173$	1797.33	+	1305.83i	0.789874	+	0.573877i	−0.118052	+	0.993007i	$0.537665\pi$
$174$		0			0
$175$	1769.71	+	2732.55i	0.764444	+	1.18035i
$176$	−33.5607			−0.0143735
$177$		0			0
$178$	1524.00	+	4690.39i	0.641734	+	1.97506i
$179$	−931.708	−	2867.50i	−0.389045	−	1.19736i	−0.933503	−	0.358570i	$-0.883264\pi$
$179$	−931.708	−	2867.50i	−0.389045	−	1.19736i	0.544458	−	0.838788i	$-0.316736\pi$
$180$		0			0
$181$	764.093	−	2351.64i	0.313782	−	0.965722i	−0.662471	−	0.749088i	$-0.730492\pi$
$181$	764.093	−	2351.64i	0.313782	−	0.965722i	0.976253	−	0.216634i	$-0.0695079\pi$
$182$	4802.57			1.95599
$183$		0			0
$184$	−3350.88	+	2434.56i	−1.34256	+	0.975425i
$185$	86.2684	+	658.435i	0.0342842	+	0.261671i
$186$		0			0
$187$	172.994	−	125.688i	0.0676502	−	0.0491508i
$188$	−642.259	+	466.628i	−0.249157	+	0.181023i
$189$		0			0
$190$	−965.494	−	7369.04i	−0.368654	−	2.81372i
$191$	−518.536	+	376.738i	−0.196439	+	0.142722i	−0.681657	−	0.731672i	$-0.738740\pi$
$191$	−518.536	+	376.738i	−0.196439	+	0.142722i	0.485218	+	0.874393i	$0.338740\pi$
$192$		0			0
$193$	−658.953			−0.245764			−0.122882	−	0.992421i	$-0.539214\pi$
$193$	−658.953			−0.245764			−0.122882	+	0.992421i	$0.539214\pi$
$194$	−922.615	+	2839.52i	−0.341443	+	1.05085i
$195$		0			0
$196$	1415.56	+	4356.63i	0.515873	+	1.58769i
$197$	−865.948	−	2665.12i	−0.313179	−	0.963866i	−0.976498	−	0.215529i	$-0.930853\pi$
$197$	−865.948	−	2665.12i	−0.313179	−	0.963866i	0.663318	−	0.748337i	$-0.269147\pi$
$198$		0			0
$199$	−2715.89			−0.967459			−0.483729	−	0.875218i	$-0.660718\pi$
$199$	−2715.89			−0.967459			−0.483729	+	0.875218i	$0.660718\pi$
$200$	3182.36	−	848.474i	1.12514	−	0.299981i
$201$		0			0
$202$	−3253.33	−	2363.68i	−1.13318	−	0.823307i
$203$	−806.696	−	2482.75i	−0.278911	−	0.858400i
$204$		0			0
$205$	−516.235	−	3940.11i	−0.175880	−	1.34239i
$206$	−2634.96	+	8109.58i	−0.891197	+	2.74282i
$207$		0			0
$208$	163.317	−	502.637i	0.0544421	−	0.167556i
$209$	−290.715	+	211.217i	−0.0962162	+	0.0699051i
$210$		0			0
$211$	1402.23	+	1018.78i	0.457505	+	0.332397i	0.792552	−	0.609805i	$-0.208752\pi$
$211$	1402.23	+	1018.78i	0.457505	+	0.332397i	−0.335047	+	0.942201i	$0.608752\pi$
$212$	−4320.02	+	3138.68i	−1.39953	+	1.01682i
$213$		0			0
$214$	3908.34	+	2839.58i	1.24845	+	0.907053i
$215$	−586.122	+	1077.90i	−0.185922	+	0.341918i
$216$		0			0
$217$	1395.24	−	4294.12i	0.436476	−	1.34334i
$218$	−7246.68			−2.25141
$219$		0			0
$220$	−264.345	−	278.909i	−0.0810098	−	0.0854728i
$221$	1040.57	+	3202.56i	0.316727	+	0.974784i
$222$		0			0
$223$	−3541.18	−	2572.82i	−1.06338	−	0.772594i	−0.0886732	−	0.996061i	$-0.528263\pi$
$223$	−3541.18	−	2572.82i	−1.06338	−	0.772594i	−0.974712	+	0.223467i	$0.928263\pi$
$224$	−3872.90			−1.15522
$225$		0			0
$226$	−4538.74			−1.33589
$227$	−1819.26	−	1321.77i	−0.531931	−	0.386471i	0.289148	−	0.957284i	$-0.406628\pi$
$227$	−1819.26	−	1321.77i	−0.531931	−	0.386471i	−0.821080	+	0.570814i	$0.806628\pi$
$228$		0			0
$229$	693.843	+	2135.43i	0.200220	+	0.616215i	0.999876	+	0.0157557i	$0.00501539\pi$
$229$	693.843	+	2135.43i	0.200220	+	0.616215i	−0.799656	+	0.600459i	$0.794985\pi$
$230$	−8041.97	−	1495.66i	−2.30553	−	0.428787i
$231$		0			0
$232$	−2640.97			−0.747362
$233$	−218.901	+	673.707i	−0.0615479	+	0.189425i	−0.977103	−	0.212768i	$-0.931752\pi$
$233$	−218.901	+	673.707i	−0.0615479	+	0.189425i	0.915555	+	0.402193i	$0.131752\pi$
$234$		0			0
$235$	−638.754	−	118.797i	−0.177310	−	0.0329764i
$236$	4559.56	+	3312.71i	1.25763	+	0.913725i
$237$		0			0
$238$	−8334.70	+	6055.52i	−2.26999	+	1.64925i
$239$	4411.37	+	3205.04i	1.19392	+	0.867435i	0.993673	−	0.112309i	$-0.0358248\pi$
$239$	4411.37	+	3205.04i	1.19392	+	0.867435i	0.200249	+	0.979745i	$0.435825\pi$
$240$		0			0
$241$	−4628.17	+	3362.56i	−1.23704	+	0.898762i	−0.997397	−	0.0720995i	$-0.977030\pi$
$241$	−4628.17	+	3362.56i	−1.23704	+	0.898762i	−0.239642	+	0.970861i	$0.577030\pi$
$242$	1905.16	−	5863.48i	0.506068	−	1.55752i
$243$		0			0
$244$	1514.00	−	4659.60i	0.397228	−	1.22254i
$245$	−1790.89	+	3293.53i	−0.467004	+	0.858841i
$246$		0			0
$247$	−1748.67	−	5381.87i	−0.450468	−	1.38640i
$248$	−3695.40	−	2684.86i	−0.946202	−	0.687456i
$249$		0			0
$250$	5539.56	+	3408.87i	1.40141	+	0.862383i
$251$	−2045.23			−0.514319			−0.257159	−	0.966369i	$-0.582787\pi$
$251$	−2045.23			−0.514319			−0.257159	+	0.966369i	$0.582787\pi$
$252$		0			0
$253$	122.217	+	376.145i	0.0303704	+	0.0934705i
$254$	1479.77	+	4554.26i	0.365547	+	1.12504i
$255$		0			0
$256$	−1661.25	+	5112.79i	−0.405578	+	1.24824i
$257$	−407.547			−0.0989186			−0.0494593	−	0.998776i	$-0.515750\pi$
$257$	−407.547			−0.0989186			−0.0494593	+	0.998776i	$0.515750\pi$
$258$		0			0
$259$	−1251.49	+	909.262i	−0.300247	+	0.218142i
$260$	5463.58	−	2601.83i	1.30322	−	0.620610i
$261$		0			0
$262$	10053.0	−	7303.91i	2.37052	−	1.72228i
$263$	−717.991	+	521.651i	−0.168339	+	0.122306i	−0.668765	−	0.743474i	$-0.733177\pi$
$263$	−717.991	+	521.651i	−0.168339	+	0.122306i	0.500426	+	0.865779i	$0.333177\pi$
$264$		0			0
$265$	−4296.45	−	799.062i	−0.995958	−	0.185230i
$266$	14006.4	−	10176.2i	3.22852	−	2.34566i
$267$		0			0
$268$	4795.23			1.09297
$269$	−1864.45	+	5738.18i	−0.422592	+	1.30061i	0.482688	+	0.875792i	$0.339660\pi$
$269$	−1864.45	+	5738.18i	−0.422592	+	1.30061i	−0.905281	+	0.424814i	$0.860340\pi$
$270$		0			0
$271$	2019.40	+	6215.08i	0.452656	+	1.39313i	0.873865	+	0.486169i	$0.161606\pi$
$271$	2019.40	+	6215.08i	0.452656	+	1.39313i	−0.421209	+	0.906964i	$0.638394\pi$
$272$	350.339	+	1078.23i	0.0780972	+	0.240358i
$273$		0			0
$274$	−5675.39			−1.25132
$275$	16.8496	−	314.040i	0.00369480	−	0.0688630i
$276$		0			0
$277$	4454.88	+	3236.66i	0.966309	+	0.702064i	0.954607	−	0.297867i	$-0.0962753\pi$
$277$	4454.88	+	3236.66i	0.966309	+	0.702064i	0.0117014	+	0.999932i	$0.496275\pi$
$278$	−1258.86	−	3874.37i	−0.271587	−	0.835860i
$279$		0			0
$280$	5277.77	+	5568.54i	1.12645	+	1.18851i
$281$	2323.54	−	7151.11i	0.493276	−	1.51815i	−0.326350	−	0.945249i	$-0.605819\pi$
$281$	2323.54	−	7151.11i	0.493276	−	1.51815i	0.819626	−	0.572898i	$-0.194181\pi$
$282$		0			0
$283$	1384.45	−	4260.88i	0.290801	−	0.894994i	−0.693798	−	0.720169i	$-0.744064\pi$
$283$	1384.45	−	4260.88i	0.290801	−	0.894994i	0.984600	−	0.174825i	$-0.0559359\pi$
$284$	1888.02	−	1371.73i	0.394483	−	0.286609i
$285$		0			0
$286$	−375.331	−	272.694i	−0.0776006	−	0.0563802i
$287$	7489.00	−	5441.08i	1.54028	−	1.11908i
$288$		0			0
$289$	−1869.26	−	1358.09i	−0.380471	−	0.276429i
$290$	−3587.86	−	3785.52i	−0.726504	−	0.766529i
$291$		0			0
$292$	−3938.24	+	12120.7i	−0.789275	+	2.42914i
$293$	6672.17			1.33035			0.665174	−	0.746688i	$-0.268357\pi$
$293$	6672.17			1.33035			0.665174	+	0.746688i	$0.268357\pi$
$294$		0			0
$295$	599.201	+	4573.35i	0.118261	+	0.902612i
$296$	483.602	+	1488.37i	0.0949622	+	0.292264i
$297$		0			0
$298$	3086.16	+	2242.23i	0.599921	+	0.435868i
$299$	−6228.25			−1.20464
$300$		0			0
$301$	−2858.18			−0.547318
$302$	2136.65	+	1552.36i	0.407120	+	0.295790i
$303$		0			0
$304$	−588.742	−	1811.96i	−0.111075	−	0.341852i
$305$	3620.13	−	1723.95i	0.679634	−	0.323650i
$306$		0			0
$307$	5433.28			1.01008			0.505039	−	0.863097i	$-0.331478\pi$
$307$	5433.28			1.01008			0.505039	+	0.863097i	$0.331478\pi$
$308$	276.622	−	851.356i	0.0511754	−	0.157502i
$309$		0			0
$310$	−1171.90	−	8944.42i	−0.214708	−	1.63874i
$311$	415.035	+	301.541i	0.0756736	+	0.0549801i	0.624979	−	0.780642i	$-0.285108\pi$
$311$	415.035	+	301.541i	0.0756736	+	0.0549801i	−0.549305	+	0.835622i	$0.685108\pi$
$312$		0			0
$313$	806.159	−	585.709i	0.145581	−	0.105771i	−0.512611	−	0.858621i	$-0.671322\pi$
$313$	806.159	−	585.709i	0.145581	−	0.105771i	0.658192	+	0.752850i	$0.271322\pi$
$314$	−6188.75	−	4496.39i	−1.11227	−	0.808109i
$315$		0			0
$316$	14514.4	−	10545.3i	2.58385	−	1.87728i
$317$	−1322.77	+	4071.07i	−0.234366	+	0.721305i	0.762838	+	0.646589i	$0.223805\pi$
$317$	−1322.77	+	4071.07i	−0.234366	+	0.721305i	−0.997205	+	0.0747164i	$0.976195\pi$
$318$		0			0
$319$	−77.9278	+	239.837i	−0.0136775	+	0.0420950i
$320$	−8063.27	+	3839.83i	−1.40859	+	0.670791i
$321$		0			0
$322$	−5888.30	−	18122.3i	−1.01908	−	3.13639i
$323$	9820.71	+	7135.17i	1.69176	+	1.22914i
$324$		0			0
$325$	4621.36	+	1780.57i	0.788760	+	0.303902i
$326$	5958.70			1.01234
$327$		0			0
$328$	−2893.90	−	8906.52i	−0.487162	−	1.49933i
$329$	−467.694	−	1439.41i	−0.0783732	−	0.241208i
$330$		0			0
$331$	−918.630	+	2827.25i	−0.152545	+	0.469486i	−0.997904	−	0.0647132i	$-0.979387\pi$
$331$	−918.630	+	2827.25i	−0.152545	+	0.469486i	0.845359	+	0.534199i	$0.179387\pi$
$332$	8933.07			1.47670
$333$		0			0
$334$	5936.39	−	4313.04i	0.972529	−	0.706584i
$335$	2699.62	+	2848.35i	0.440286	+	0.464543i
$336$		0			0
$337$	−1248.14	+	906.825i	−0.201752	+	0.146581i	−0.684074	−	0.729413i	$-0.739794\pi$
$337$	−1248.14	+	906.825i	−0.201752	+	0.146581i	0.482322	+	0.875994i	$0.339794\pi$
$338$	−2361.76	+	1715.92i	−0.380068	+	0.276136i
$339$		0			0
$340$	−6201.25	+	11404.4i	−0.989146	+	1.81908i
$341$	−352.865	+	256.371i	−0.0560373	+	0.0407135i
$342$		0			0
$343$	200.108			0.0315009
$344$	−893.526	+	2749.99i	−0.140046	+	0.431016i
$345$		0			0
$346$	3195.16	+	9833.70i	0.496454	+	1.52793i
$347$	1738.01	+	5349.05i	0.268880	+	0.827527i	0.990774	+	0.135524i	$0.0432717\pi$
$347$	1738.01	+	5349.05i	0.268880	+	0.827527i	−0.721894	+	0.692003i	$0.756728\pi$
$348$		0			0
$349$	3546.44			0.543945			0.271972	−	0.962305i	$-0.412324\pi$
$349$	3546.44			0.543945			0.271972	+	0.962305i	$0.412324\pi$
$350$	−811.798	+	15130.2i	−0.123978	+	2.31069i
$351$		0			0
$352$	302.675	+	219.906i	0.0458313	+	0.0332984i
$353$	592.091	+	1822.27i	0.0892742	+	0.274758i	0.985719	−	0.168397i	$-0.0538591\pi$
$353$	592.091	+	1822.27i	0.0892742	+	0.274758i	−0.896445	+	0.443155i	$0.853859\pi$
$354$		0			0
$355$	1877.72	+	349.221i	0.280729	+	0.0522105i
$356$	−4473.36	+	13767.6i	−0.665976	+	2.04966i
$357$		0			0
$358$	4336.32	−	13345.8i	0.640172	−	1.97025i
$359$	2130.22	−	1547.69i	0.313171	−	0.227532i	−0.420085	−	0.907485i	$-0.638000\pi$
$359$	2130.22	−	1547.69i	0.313171	−	0.227532i	0.733256	+	0.679953i	$0.238000\pi$
$360$		0			0
$361$	−10954.6	−	7958.96i	−1.59711	−	1.16037i
$362$	9310.28	−	6764.32i	1.35176	−	0.982112i
$363$		0			0
$364$	11404.6	+	8285.92i	1.64221	+	1.19313i
$365$	−9416.78	+	4484.39i	−1.35040	+	0.643079i
$366$		0			0
$367$	−2102.12	+	6469.65i	−0.298991	+	0.920199i	0.682861	+	0.730548i	$0.260735\pi$
$367$	−2102.12	+	6469.65i	−0.298991	+	0.920199i	−0.981852	+	0.189650i	$0.939265\pi$
$368$	−2096.92			−0.297037
$369$		0			0
$370$	−1476.42	+	2715.20i	−0.207447	+	0.381505i
$371$	−3145.85	−	9681.92i	−0.440227	−	1.35488i
$372$		0			0
$373$	5424.55	+	3941.17i	0.753010	+	0.547094i	0.896758	−	0.442520i	$-0.145916\pi$
$373$	5424.55	+	3941.17i	0.753010	+	0.547094i	−0.143748	+	0.989614i	$0.545916\pi$
$374$	995.212			0.137597
$375$		0			0
$376$	−1531.14			−0.210007
$377$	−3212.81	−	2334.24i	−0.438907	−	0.318885i
$378$		0			0
$379$	1202.29	+	3700.27i	0.162948	+	0.501504i	0.998879	−	0.0473310i	$-0.0150716\pi$
$379$	1202.29	+	3700.27i	0.162948	+	0.501504i	−0.835931	+	0.548835i	$0.815072\pi$
$380$	10421.1	−	19164.9i	1.40682	−	2.58721i
$381$		0			0
$382$	−2983.06			−0.399547
$383$	1743.53	−	5366.04i	0.232612	−	0.715906i	−0.764817	−	0.644247i	$-0.777171\pi$
$383$	1743.53	−	5366.04i	0.232612	−	0.715906i	0.997429	−	0.0716588i	$-0.0228293\pi$
$384$		0			0
$385$	661.435	−	314.984i	0.0875581	−	0.0416963i
$386$	−2481.15	−	1802.66i	−0.327169	−	0.237702i
$387$		0			0
$388$	−7089.96	+	5151.16i	−0.927676	+	0.673996i
$389$	−3785.35	−	2750.22i	−0.493380	−	0.358462i	0.313102	−	0.949719i	$-0.398632\pi$
$389$	−3785.35	−	2750.22i	−0.493380	−	0.358462i	−0.806483	+	0.591257i	$0.798632\pi$
$390$		0			0
$391$	10808.9	−	7853.14i	1.39803	−	1.01573i
$392$	−2730.17	+	8402.59i	−0.351771	+	1.08264i
$393$		0			0
$394$	4030.26	−	12403.9i	0.515334	−	1.58604i
$395$	14435.2	+	2684.68i	1.83876	+	0.341977i
$396$		0			0
$397$	2589.33	+	7969.14i	0.327342	+	1.00746i	0.970372	+	0.241614i	$0.0776769\pi$
$397$	2589.33	+	7969.14i	0.327342	+	1.00746i	−0.643030	+	0.765841i	$0.722323\pi$
$398$	−10226.1	−	7429.72i	−1.28791	−	0.935724i
$399$		0			0
$400$	1555.92	+	599.480i	0.194489	+	0.0749350i
$401$	−6042.30			−0.752464			−0.376232	−	0.926525i	$-0.622780\pi$
$401$	−6042.30			−0.752464			−0.376232	+	0.926525i	$0.622780\pi$
$402$		0			0
$403$	−2122.51	−	6532.42i	−0.262357	−	0.807451i
$404$	−3647.55	−	11226.0i	−0.449189	−	1.38246i
$405$		0			0
$406$	3754.49	−	11555.1i	0.458947	−	1.41249i
$407$	149.435			0.0181996
$408$		0			0
$409$	−5290.72	+	3843.93i	−0.639631	+	0.464719i	−0.859723	−	0.510760i	$-0.829364\pi$
$409$	−5290.72	+	3843.93i	−0.639631	+	0.464719i	0.220092	+	0.975479i	$0.429364\pi$
$410$	8834.99	−	16247.9i	1.06422	−	1.95714i
$411$		0			0
$412$	−20248.7	+	14711.6i	−2.42132	+	1.75919i
$413$	−8692.59	+	6315.54i	−1.03568	+	0.752463i
$414$		0			0
$415$	5029.14	+	5306.21i	0.594869	+	0.627642i
$416$	−4766.43	+	3463.01i	−0.561763	+	0.408145i
$417$		0			0
$418$	−1672.44			−0.195698
$419$	−4050.94	+	12467.5i	−0.472319	+	1.45365i	0.377221	+	0.926123i	$0.376880\pi$
$419$	−4050.94	+	12467.5i	−0.472319	+	1.45365i	−0.849540	+	0.527525i	$0.823120\pi$
$420$		0			0
$421$	1054.72	+	3246.11i	0.122100	+	0.375785i	0.993362	−	0.115034i	$-0.0366977\pi$
$421$	1054.72	+	3246.11i	0.122100	+	0.375785i	−0.871262	+	0.490819i	$0.836698\pi$
$422$	2492.79	+	7672.01i	0.287552	+	0.884995i
$423$		0			0
$424$	−10298.9			−1.17962
$425$	−10265.3	+	2736.91i	−1.17163	+	0.312376i
$426$		0			0
$427$	7556.60	+	5490.19i	0.856416	+	0.622223i
$428$	4381.93	+	13486.2i	0.494880	+	1.52308i
$429$		0			0
$430$	−5155.69	+	2455.20i	−0.578208	+	0.275350i
$431$	467.178	−	1437.83i	0.0522116	−	0.160691i	−0.921551	−	0.388258i	$-0.873077\pi$
$431$	467.178	−	1437.83i	0.0522116	−	0.160691i	0.973762	+	0.227567i	$0.0730771\pi$
$432$		0			0
$433$	−2665.17	+	8202.55i	−0.295797	+	0.910368i	0.687156	+	0.726510i	$0.258859\pi$
$433$	−2665.17	+	8202.55i	−0.295797	+	0.910368i	−0.982953	+	0.183858i	$0.941141\pi$
$434$	17000.7	−	12351.7i	1.88032	−	1.36613i
$435$		0			0
$436$	−17208.6	−	12502.8i	−1.89023	−	1.37333i
$437$	−18164.3	+	13197.1i	−1.98836	+	1.44463i
$438$		0			0
$439$	2854.86	+	2074.17i	0.310375	+	0.225501i	0.732058	−	0.681243i	$-0.238560\pi$
$439$	2854.86	+	2074.17i	0.310375	+	0.225501i	−0.421682	+	0.906744i	$0.638560\pi$
$440$	−96.2828	−	734.869i	−0.0104320	−	0.0796216i
$441$		0			0
$442$	−4843.00	+	14905.2i	−0.521172	+	1.60400i
$443$	9589.40			1.02846			0.514228	−	0.857653i	$-0.328078\pi$
$443$	9589.40			1.02846			0.514228	+	0.857653i	$0.328078\pi$
$444$		0			0
$445$	−10696.3	+	5093.71i	−1.13944	+	0.542618i
$446$	−6295.26	−	19374.8i	−0.668362	−	2.05701i
$447$		0			0
$448$	−16831.1	−	12228.5i	−1.77499	−	1.28961i
$449$	9820.81			1.03223			0.516117	−	0.856518i	$-0.327377\pi$
$449$	9820.81			1.03223			0.516117	+	0.856518i	$0.327377\pi$
$450$		0			0
$451$	−894.230			−0.0933650
$452$	−10778.1	−	7830.72i	−1.12159	−	0.814881i
$453$		0			0
$454$	−3234.15	−	9953.70i	−0.334331	−	1.02897i
$455$	1498.75	+	11439.1i	0.154423	+	1.17862i
$456$		0			0
$457$	1597.23			0.163491			0.0817455	−	0.996653i	$-0.473951\pi$
$457$	1597.23			0.163491			0.0817455	+	0.996653i	$0.473951\pi$
$458$	−3229.26	+	9938.63i	−0.329461	+	1.01398i
$459$		0			0
$460$	−16516.7	−	17426.6i	−1.67412	−	1.76635i
$461$	−3157.65	−	2294.17i	−0.319016	−	0.231779i	0.416740	−	0.909026i	$-0.363173\pi$
$461$	−3157.65	−	2294.17i	−0.319016	−	0.231779i	−0.735755	+	0.677247i	$0.763173\pi$
$462$		0			0
$463$	12670.8	−	9205.86i	1.27184	−	0.924044i	0.272563	−	0.962138i	$-0.412129\pi$
$463$	12670.8	−	9205.86i	1.27184	−	0.924044i	0.999274	+	0.0380937i	$0.0121285\pi$
$464$	−1081.68	−	785.890i	−0.108224	−	0.0786293i
$465$		0			0
$466$	−2667.25	+	1937.87i	−0.265146	+	0.192640i
$467$	1976.88	−	6084.21i	0.195887	−	0.602878i	−0.804078	−	0.594523i	$-0.797341\pi$
$467$	1976.88	−	6084.21i	0.195887	−	0.602878i	0.999965	−	0.00835414i	$-0.00265924\pi$
$468$		0			0
$469$	−2825.00	+	8694.46i	−0.278137	+	0.856019i
$470$	−2080.11	−	2194.71i	−0.204146	−	0.215393i
$471$		0			0
$472$	3359.00	+	10337.9i	0.327564	+	1.00814i
$473$	223.373	+	162.290i	0.0217139	+	0.0157761i
$474$		0			0
$475$	17250.8	−	4599.36i	1.66636	−	0.444280i
$476$	−30239.9			−2.91186
$477$		0			0
$478$	7842.22	+	24135.9i	0.750408	+	2.30952i
$479$	3178.50	+	9782.42i	0.303193	+	0.933132i	0.980345	+	0.197289i	$0.0632137\pi$
$479$	3178.50	+	9782.42i	0.303193	+	0.933132i	−0.677153	+	0.735843i	$0.736786\pi$
$480$		0			0
$481$	−727.197	+	2238.08i	−0.0689342	+	0.212158i
$482$	−26625.2			−2.51607
$483$		0			0
$484$	14640.5	−	10636.9i	1.37495	−	0.998960i
$485$	−7051.28	−	1311.41i	−0.660169	−	0.122780i
$486$		0			0
$487$	−1685.55	+	1224.62i	−0.156837	+	0.113949i	−0.663436	−	0.748233i	$-0.730902\pi$
$487$	−1685.55	+	1224.62i	−0.156837	+	0.113949i	0.506599	+	0.862182i	$0.330902\pi$
$488$	7644.73	−	5554.22i	0.709141	−	0.515221i
$489$		0			0
$490$	−15753.2	+	7501.87i	−1.45236	+	0.691633i
$491$	14323.2	−	10406.4i	1.31649	−	0.956487i	0.316522	−	0.948585i	$-0.397485\pi$
$491$	14323.2	−	10406.4i	1.31649	−	0.956487i	0.999969	−	0.00790172i	$-0.00251522\pi$
$492$		0			0
$493$	8518.94			0.778243
$494$	8138.61	−	25048.1i	0.741242	−	2.28131i
$495$		0			0
$496$	−714.605	−	2199.33i	−0.0646909	−	0.199098i
$497$	1374.86	+	4231.37i	0.124086	+	0.381897i
$498$		0			0
$499$	5018.92			0.450256			0.225128	−	0.974329i	$-0.427720\pi$
$499$	5018.92			0.450256			0.225128	+	0.974329i	$0.427720\pi$
$500$	7273.35	+	17652.4i	0.650548	+	1.57888i
$501$		0			0
$502$	−7700.91	−	5595.04i	−0.684678	−	0.497448i
$503$	3109.30	+	9569.44i	0.275620	+	0.848270i	0.989055	+	0.147549i	$0.0471384\pi$
$503$	3109.30	+	9569.44i	0.275620	+	0.848270i	−0.713435	+	0.700721i	$0.752862\pi$
$504$		0			0
$505$	4614.70	−	8486.64i	0.406636	−	0.747822i
$506$	−568.818	+	1750.64i	−0.0499744	+	0.153805i
$507$		0			0
$508$	−4343.53	+	13368.0i	−0.379356	+	1.16754i
$509$	−4301.55	+	3125.26i	−0.374584	+	0.272151i	−0.759109	−	0.650963i	$-0.774365\pi$
$509$	−4301.55	+	3125.26i	−0.374584	+	0.272151i	0.384525	+	0.923114i	$0.374365\pi$
$510$		0			0
$511$	−19656.4	−	14281.2i	−1.70166	−	1.23633i
$512$	−3879.49	+	2818.62i	−0.334865	+	0.243294i
$513$		0			0
$514$	−1534.53	−	1114.90i	−0.131684	−	0.0956738i
$515$	−20138.3	−	3745.35i	−1.72310	−	0.320466i
$516$		0			0
$517$	−45.1798	+	139.049i	−0.00384334	+	0.0118286i
$518$	−7199.66			−0.610685
$519$		0			0
$520$	11474.6	+	2134.08i	0.967685	+	0.179972i
$521$	1938.78	+	5966.95i	0.163032	+	0.501760i	0.998886	−	0.0471916i	$-0.0150271\pi$
$521$	1938.78	+	5966.95i	0.163032	+	0.501760i	−0.835854	+	0.548952i	$0.815027\pi$
$522$		0			0
$523$	−11374.4	−	8264.02i	−0.950994	−	0.690937i	4.79448e−5	−	1.00000i	$-0.499985\pi$
$523$	−11374.4	−	8264.02i	−0.950994	−	0.690937i	−0.951042	+	0.309063i	$0.899985\pi$
$524$	36474.1			3.04080
$525$		0			0
$526$	−4130.50			−0.342392
$527$	11920.2	+	8660.54i	0.985299	+	0.715862i
$528$		0			0
$529$	3876.48	+	11930.6i	0.318606	+	0.980568i
$530$	−13991.5	−	14762.3i	−1.14670	−	1.20987i
$531$		0			0
$532$	50817.9			4.14142
$533$	4351.59	−	13392.8i	0.353637	−	1.08838i
$534$		0			0
$535$	−5543.80	+	10195.3i	−0.447999	+	0.823890i
$536$	7482.20	+	5436.14i	0.602951	+	0.438070i
$537$		0			0
$538$	−22717.8	+	16505.5i	−1.82051	+	1.32268i
$539$	682.515	+	495.876i	0.0545417	+	0.0396269i
$540$		0			0
$541$	16286.0	−	11832.5i	1.29425	−	0.940328i	0.294369	−	0.955692i	$-0.404890\pi$
$541$	16286.0	−	11832.5i	1.29425	−	0.940328i	0.999882	+	0.0153633i	$0.00489048\pi$
$542$	−9398.62	+	28926.0i	−0.744844	+	2.29239i
$543$		0			0
$544$	3905.50	−	12019.9i	0.307807	−	0.947332i
$545$	−2261.49	−	17260.6i	−0.177746	−	1.35663i
$546$		0			0
$547$	−4085.46	−	12573.8i	−0.319345	−	0.982843i	−0.973929	−	0.226854i	$-0.927156\pi$
$547$	−4085.46	−	12573.8i	−0.319345	−	0.982843i	0.654584	−	0.755989i	$-0.272844\pi$
$548$	−13477.3	−	9791.80i	−1.05058	−	0.763293i
$549$		0			0
$550$	922.547	−	1136.36i	0.0715228	−	0.0880991i
$551$	−14316.0			−1.10686
$552$		0			0
$553$	10569.4	+	32529.2i	0.812758	+	2.50141i
$554$	7919.57	+	24373.9i	0.607347	+	1.86922i
$555$		0			0
$556$	3695.09	−	11372.3i	0.281846	−	0.867434i
$557$	14165.4			1.07757			0.538786	−	0.842442i	$-0.318883\pi$
$557$	14165.4			1.07757			0.538786	+	0.842442i	$0.318883\pi$
$558$		0			0
$559$	−3517.60	+	2555.69i	−0.266152	+	0.193370i
$560$	504.598	+	3851.30i	0.0380771	+	0.290620i
$561$		0			0
$562$	28311.7	−	20569.7i	2.12501	−	1.54391i
$563$	9115.09	−	6622.50i	0.682336	−	0.495746i	−0.191796	−	0.981435i	$-0.561431\pi$
$563$	9115.09	−	6622.50i	0.682336	−	0.495746i	0.874132	+	0.485689i	$0.161431\pi$
$564$		0			0
$565$	−1416.42	−	10810.7i	−0.105467	−	0.804970i
$566$	16869.1	−	12256.1i	1.25276	−	0.910183i
$567$		0			0
$568$	4501.02			0.332497
$569$	2287.20	−	7039.27i	0.168514	−	0.518632i	−0.830764	−	0.556624i	$-0.812096\pi$
$569$	2287.20	−	7039.27i	0.168514	−	0.518632i	0.999278	+	0.0379926i	$0.0120963\pi$
$570$		0			0
$571$	−4038.92	−	12430.5i	−0.296013	−	0.911035i	−0.982879	−	0.184251i	$-0.941014\pi$
$571$	−4038.92	−	12430.5i	−0.296013	−	0.911035i	0.686866	−	0.726784i	$-0.258986\pi$
$572$	−420.811	−	1295.12i	−0.0307605	−	0.0946710i
$573$		0			0
$574$	43083.2			3.13285
$575$	1052.79	−	19621.7i	0.0763552	−	1.42310i
$576$		0			0
$577$	−6647.54	−	4829.72i	−0.479620	−	0.348464i	0.321559	−	0.946890i	$-0.395793\pi$
$577$	−6647.54	−	4829.72i	−0.479620	−	0.348464i	−0.801179	+	0.598425i	$0.795793\pi$
$578$	−3323.04	−	10227.3i	−0.239135	−	0.735982i
$579$		0			0
$580$	−1988.83	−	15179.6i	−0.142382	−	1.08672i
$581$	−5262.71	+	16197.0i	−0.375790	+	1.15656i
$582$		0			0
$583$	−303.893	+	935.286i	−0.0215883	+	0.0664418i
$584$	−19885.7	+	14447.8i	−1.40903	+	1.02372i
$585$		0			0
$586$	25122.7	+	18252.7i	1.77100	+	1.28671i
$587$	16152.0	−	11735.1i	1.13572	−	0.825145i	0.149199	−	0.988807i	$-0.452331\pi$
$587$	16152.0	−	11735.1i	1.13572	−	0.825145i	0.986517	+	0.163662i	$0.0523306\pi$
$588$		0			0
$589$	−20031.8	−	14554.0i	−1.40135	−	1.01814i
$590$	−10254.9	+	18859.2i	−0.715572	+	1.31597i
$591$		0			0
$592$	−244.832	+	753.515i	−0.0169975	+	0.0523130i
$593$	14429.9			0.999267			0.499634	−	0.866237i	$-0.333468\pi$
$593$	14429.9			0.999267			0.499634	+	0.866237i	$0.333468\pi$
$594$		0			0
$595$	−17024.5	−	17962.4i	−1.17300	−	1.23762i
$596$	3460.12	+	10649.2i	0.237805	+	0.731890i
$597$		0			0
$598$	−23451.2	−	17038.3i	−1.60366	−	1.16513i
$599$	7838.61			0.534686			0.267343	−	0.963601i	$-0.413854\pi$
$599$	7838.61			0.534686			0.267343	+	0.963601i	$0.413854\pi$
$600$		0			0
$601$	−25163.3			−1.70787			−0.853937	−	0.520376i	$-0.825792\pi$
$601$	−25163.3			−1.70787			−0.853937	+	0.520376i	$0.825792\pi$
$602$	−10761.9	−	7818.97i	−0.728608	−	0.529365i
$603$		0			0
$604$	2395.55	+	7372.74i	0.161380	+	0.496677i
$605$	14560.6	+	2708.01i	0.978466	+	0.181977i
$606$		0			0
$607$	−563.698			−0.0376932			−0.0188466	−	0.999822i	$-0.505999\pi$
$607$	−563.698			−0.0376932			−0.0188466	+	0.999822i	$0.505999\pi$
$608$	−6563.16	+	20199.3i	−0.437781	+	1.34735i
$609$		0			0
$610$	18347.0	+	3412.21i	1.21778	+	0.226486i
$611$	−1862.67	−	1353.31i	−0.123332	−	0.0896057i
$612$		0			0
$613$	5449.70	−	3959.44i	0.359072	−	0.260881i	−0.393593	−	0.919285i	$-0.628768\pi$
$613$	5449.70	−	3959.44i	0.359072	−	0.260881i	0.752665	+	0.658404i	$0.228768\pi$
$614$	20457.9	+	14863.6i	1.34465	+	0.976945i
$615$		0			0
$616$	1396.77	−	1014.81i	0.0913595	−	0.0663766i
$617$	3151.55	−	9699.47i	0.205635	−	0.632878i	−0.794052	−	0.607850i	$-0.792032\pi$
$617$	3151.55	−	9699.47i	0.205635	−	0.632878i	0.999687	−	0.0250287i	$-0.00796772\pi$
$618$		0			0
$619$	2342.12	−	7208.30i	0.152080	−	0.468055i	−0.845773	−	0.533543i	$-0.820860\pi$
$619$	2342.12	−	7208.30i	0.152080	−	0.468055i	0.997853	+	0.0654878i	$0.0208604\pi$
$620$	12649.0	−	23262.1i	0.819348	−	1.50682i
$621$		0			0
$622$	737.821	+	2270.78i	0.0475626	+	0.146383i
$623$	−22327.3	−	16221.7i	−1.43583	−	1.04319i
$624$		0			0
$625$	−6390.73	+	14258.3i	−0.409006	+	0.912531i
$626$	4637.72			0.296103
$627$		0			0
$628$	−6938.67	−	21355.0i	−0.440896	−	1.35694i
$629$	−1559.95	−	4801.04i	−0.0988861	−	0.304340i
$630$		0			0
$631$	1413.93	−	4351.64i	0.0892042	−	0.274542i	−0.896496	−	0.443052i	$-0.853896\pi$
$631$	1413.93	−	4351.64i	0.0892042	−	0.274542i	0.985700	+	0.168510i	$0.0538956\pi$
$632$	34602.1			2.17784
$633$		0			0
$634$	−16117.6	+	11710.1i	−1.00964	+	0.733547i
$635$	−10385.9	+	4945.88i	−0.649055	+	0.309088i
$636$		0			0
$637$	−10748.0	+	7808.90i	−0.668528	+	0.485714i
$638$	−949.532	+	689.875i	−0.0589221	+	0.0428094i
$639$		0			0
$640$	−27788.8	−	5168.22i	−1.71633	−	0.319206i
$641$	−14330.6	+	10411.8i	−0.883034	+	0.641562i	−0.934052	−	0.357136i	$-0.883753\pi$
$641$	−14330.6	+	10411.8i	−0.883034	+	0.641562i	0.0510186	+	0.998698i	$0.483753\pi$
$642$		0			0
$643$	−13212.2			−0.810323			−0.405162	−	0.914245i	$-0.632785\pi$
$643$	−13212.2			−0.810323			−0.405162	+	0.914245i	$0.632785\pi$
$644$	17283.8	−	53193.9i	1.05757	−	3.25487i
$645$		0			0
$646$	17458.6	+	53732.0i	1.06331	+	3.27254i
$647$	−1302.73	−	4009.39i	−0.0791586	−	0.243625i	0.903644	−	0.428284i	$-0.140882\pi$
$647$	−1302.73	−	4009.39i	−0.0791586	−	0.243625i	−0.982803	+	0.184659i	$0.940882\pi$
$648$		0			0
$649$	1037.95			0.0627780
$650$	12529.8	+	19346.8i	0.756091	+	1.16745i
$651$		0			0
$652$	14150.0	+	10280.6i	0.849935	+	0.617514i
$653$	−8093.51	−	24909.3i	−0.485028	−	1.49276i	−0.831940	−	0.554866i	$-0.812770\pi$
$653$	−8093.51	−	24909.3i	−0.485028	−	1.49276i	0.346911	−	0.937898i	$-0.387230\pi$
$654$		0			0
$655$	20534.2	+	21665.5i	1.22494	+	1.29243i
$656$	1465.09	−	4509.08i	0.0871983	−	0.268369i
$657$		0			0
$658$	2176.72	−	6699.26i	0.128963	−	0.396906i
$659$	−10410.7	+	7563.80i	−0.615391	+	0.447107i	−0.851308	−	0.524666i	$-0.824190\pi$
$659$	−10410.7	+	7563.80i	−0.615391	+	0.447107i	0.235918	+	0.971773i	$0.424190\pi$
$660$		0			0
$661$	17474.6	+	12696.0i	1.02827	+	0.747078i	0.967961	−	0.251102i	$-0.0807929\pi$
$661$	17474.6	+	12696.0i	1.02827	+	0.747078i	0.0603043	+	0.998180i	$0.480793\pi$
$662$	−11193.3	+	8132.40i	−0.657159	+	0.477454i
$663$		0			0
$664$	13938.6	+	10127.0i	0.814645	+	0.591874i
$665$	28609.5	+	30185.6i	1.66831	+	1.76022i
$666$		0			0
$667$	−4869.04	+	14985.4i	−0.282654	+	0.869918i
$668$	21538.4			1.24752
$669$		0			0
$670$	2372.79	+	18110.1i	0.136819	+	1.04426i
$671$	−278.827	−	858.140i	−0.0160417	−	0.0493713i
$672$		0			0
$673$	−8553.18	−	6214.25i	−0.489897	−	0.355931i	0.315248	−	0.949009i	$-0.397912\pi$
$673$	−8553.18	−	6214.25i	−0.489897	−	0.355931i	−0.805145	+	0.593078i	$0.797912\pi$
$674$	−7180.37			−0.410352
$675$		0			0
$676$	−8568.93			−0.487536
$677$	−12670.0	−	9205.29i	−0.719272	−	0.522582i	0.166879	−	0.985977i	$-0.446631\pi$
$677$	−12670.0	−	9205.29i	−0.719272	−	0.522582i	−0.886152	+	0.463395i	$0.846631\pi$
$678$		0			0
$679$	−5162.92	−	15889.8i	−0.291804	−	0.898079i
$680$	−22604.7	+	10764.6i	−1.27478	+	0.607066i
$681$		0			0
$682$	−2029.98			−0.113977
$683$	−7323.05	+	22538.0i	−0.410261	+	1.26265i	0.506160	+	0.862440i	$0.331065\pi$
$683$	−7323.05	+	22538.0i	−0.410261	+	1.26265i	−0.916421	+	0.400215i	$0.868935\pi$
$684$		0			0
$685$	−1771.13	−	13518.0i	−0.0987906	−	0.754010i
$686$	753.466	+	547.425i	0.0419351	+	0.0304676i
$687$		0			0
$688$	−1184.30	+	860.446i	−0.0656266	+	0.0476805i
$689$	−12528.9	−	9102.77i	−0.692761	−	0.503320i
$690$		0			0
$691$	−3580.95	+	2601.71i	−0.197143	+	0.143233i	−0.681978	−	0.731373i	$-0.738880\pi$
$691$	−3580.95	+	2601.71i	−0.197143	+	0.143233i	0.484835	+	0.874606i	$0.338880\pi$
$692$	−9378.67	+	28864.6i	−0.515207	+	1.58564i
$693$		0			0
$694$	−8088.99	+	24895.3i	−0.442441	+	1.36169i
$695$	8835.37	−	4207.52i	0.482223	−	0.229641i
$696$		0			0
$697$	9334.84	+	28729.7i	0.507292	+	1.56128i
$698$	13353.4	+	9701.82i	0.724118	+	0.526102i
$699$		0			0
$700$	−28032.0	+	34528.7i	−1.51358	+	1.86438i
$701$	−5192.49			−0.279768			−0.139884	−	0.990168i	$-0.544673\pi$
$701$	−5192.49			−0.279768			−0.139884	+	0.990168i	$0.544673\pi$
$702$		0			0
$703$	2621.48	+	8068.10i	0.140642	+	0.432851i
$704$	621.041	+	1911.37i	0.0332477	+	0.102326i
$705$		0			0
$706$	−2755.69	+	8481.13i	−0.146900	+	0.452113i
$707$	22503.2			1.19706
$708$		0			0
$709$	906.237	−	658.420i	0.0480035	−	0.0348766i	−0.563525	−	0.826099i	$-0.690555\pi$
$709$	906.237	−	658.420i	0.0480035	−	0.0348766i	0.611528	+	0.791223i	$0.290555\pi$
$710$	6114.81	+	6451.69i	0.323218	+	0.341025i
$711$		0			0
$712$	−22587.6	+	16410.9i	−1.18892	+	0.863798i
$713$	−22047.5	+	16018.4i	−1.15804	+	0.841368i
$714$		0			0
$715$	532.390	−	979.089i	0.0278465	−	0.0512110i
$716$	33323.0	−	24210.6i	1.73930	−	1.26368i
$717$		0			0
$718$	12254.8			0.636973
$719$	−7041.08	+	21670.2i	−0.365213	+	1.12401i	0.584635	+	0.811297i	$0.301238\pi$
$719$	−7041.08	+	21670.2i	−0.365213	+	1.12401i	−0.949848	+	0.312713i	$0.898762\pi$
$720$		0			0
$721$	−14745.2	−	45380.9i	−0.761634	−	2.34407i
$722$	−19474.3	−	59935.7i	−1.00382	−	3.08944i
$723$		0			0
$724$	33779.5			1.73399
$725$	7896.94	−	9727.16i	0.404531	−	0.498286i
$726$		0			0
$727$	−25911.7	−	18825.9i	−1.32188	−	0.960406i	−0.999907	−	0.0136585i	$-0.995652\pi$
$727$	−25911.7	−	18825.9i	−1.32188	−	0.960406i	−0.321978	−	0.946747i	$-0.604348\pi$
$728$	8401.69	+	25857.7i	0.427730	+	1.31642i
$729$		0			0
$730$	−47724.7	−	8875.93i	−2.41969	−	0.450018i
$731$	2882.24	−	8870.62i	0.145832	−	0.448826i
$732$		0			0
$733$	6712.80	−	20659.9i	0.338258	−	1.04105i	−0.626837	−	0.779151i	$-0.715651\pi$
$733$	6712.80	−	20659.9i	0.338258	−	1.04105i	0.965095	−	0.261901i	$-0.0843492\pi$
$734$	−25613.8	+	18609.5i	−1.28804	+	0.935816i
$735$		0			0
$736$	18911.6	+	13740.0i	0.947132	+	0.688132i
$737$	714.458	−	519.084i	0.0357088	−	0.0259440i
$738$		0			0
$739$	−24270.5	−	17633.5i	−1.20812	−	0.877754i	−0.213066	−	0.977038i	$-0.568345\pi$
$739$	−24270.5	−	17633.5i	−1.20812	−	0.877754i	−0.995059	+	0.0992837i	$0.968345\pi$
$740$	−8190.60	+	3900.47i	−0.406882	+	0.193762i
$741$		0			0
$742$	14641.3	−	45061.2i	0.724391	−	2.22945i
$743$	5551.03			0.274088			0.137044	−	0.990565i	$-0.456240\pi$
$743$	5551.03			0.274088			0.137044	+	0.990565i	$0.456240\pi$
$744$		0			0
$745$	−4377.58	+	8050.56i	−0.215278	+	0.395906i
$746$	9643.40	+	29679.3i	0.473284	+	1.45662i
$747$		0			0
$748$	2363.31	+	1717.05i	0.115523	+	0.0839324i
$749$	−27033.9			−1.31882
$750$		0			0
$751$	5337.87			0.259363			0.129682	−	0.991556i	$-0.458604\pi$
$751$	5337.87			0.259363			0.129682	+	0.991556i	$0.458604\pi$
$752$	−627.122	−	455.631i	−0.0304106	−	0.0220946i
$753$		0			0
$754$	−5711.51	−	17578.2i	−0.275863	−	0.849020i
$755$	−3030.73	+	5573.66i	−0.146092	+	0.268670i
$756$		0			0
$757$	−17462.2			−0.838409			−0.419205	−	0.907892i	$-0.637691\pi$
$757$	−17462.2			−0.838409			−0.419205	+	0.907892i	$0.637691\pi$
$758$	−5595.65	+	17221.6i	−0.268131	+	0.825222i
$759$		0			0
$760$	37987.0	−	18089.9i	1.81307	−	0.863406i
$761$	11011.7	+	8000.49i	0.524540	+	0.381100i	0.818311	−	0.574775i	$-0.194911\pi$
$761$	11011.7	+	8000.49i	0.524540	+	0.381100i	−0.293772	+	0.955876i	$0.594911\pi$
$762$		0			0
$763$	32807.4	−	23836.0i	1.55663	−	1.13096i
$764$	−7083.83	−	5146.71i	−0.335450	−	0.243719i
$765$		0			0
$766$	21244.5	−	15435.1i	1.00208	−	0.728056i
$767$	−5050.96	+	15545.2i	−0.237783	+	0.731820i
$768$		0			0
$769$	−7403.09	+	22784.4i	−0.347155	+	1.06843i	0.613265	+	0.789877i	$0.289856\pi$
$769$	−7403.09	+	22784.4i	−0.347155	+	1.06843i	−0.960420	+	0.278556i	$0.910144\pi$
$770$	3352.19	+	623.446i	0.156889	+	0.0291785i
$771$		0			0
$772$	−2781.80	−	8561.50i	−0.129688	−	0.399139i
$773$	−28541.9	−	20736.9i	−1.32805	−	0.964883i	−0.999794	−	0.0202938i	$-0.993540\pi$
$773$	−28541.9	−	20736.9i	−1.32805	−	0.964883i	−0.328254	−	0.944590i	$-0.606460\pi$
$774$		0			0
$775$	20938.7	−	5582.62i	0.970504	−	0.258753i
$776$	−16902.4			−0.781909
$777$		0			0
$778$	−6729.34	−	20710.8i	−0.310101	−	0.954393i
$779$	−15687.1	−	48280.0i	−0.721501	−	2.22055i
$780$		0			0
$781$	132.813	−	408.756i	0.00608505	−	0.0187278i
$782$	62182.2			2.84352
$783$		0			0
$784$	−3618.63	+	2629.09i	−0.164843	+	0.119765i
$785$	8778.47	−

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)

\(f(q)\)	\(=\)	\(q+(3.76530 + 2.73565i) q^{2} +(4.22155 + 12.9926i) q^{4} +(-5.34090 + 9.82216i) q^{5} -26.0445 q^{7} +(-8.14206 + 25.0587i) q^{8} +O(q^{10})\)	\(q+(3.76530 + 2.73565i) q^{2} +(4.22155 + 12.9926i) q^{4} +(-5.34090 + 9.82216i) q^{5} -26.0445 q^{7} +(-8.14206 + 25.0587i) q^{8} +(-46.9800 + 22.3725i) q^{10} +(2.03543 + 1.47883i) q^{11} +(-32.0534 + 23.2881i) q^{13} +(-98.0653 - 71.2486i) q^{14} +(-10.7917 + 7.84062i) q^{16} +(26.2638 - 80.8316i) q^{17} +(-44.1360 + 135.837i) q^{19} +(-150.162 - 27.9275i) q^{20} +(3.61845 + 11.1365i) q^{22} +(127.177 + 92.3993i) q^{23} +(-67.9495 - 104.918i) q^{25} -184.399 q^{26} +(-109.948 - 338.386i) q^{28} +(30.9737 + 95.3273i) q^{29} +(-53.5715 + 164.876i) q^{31} +148.703 q^{32} +(320.018 - 232.506i) q^{34} +(139.101 - 255.813i) q^{35} +(48.0520 - 34.9118i) q^{37} +(-537.786 + 390.725i) q^{38} +(-202.644 - 213.809i) q^{40} +(-287.546 + 208.914i) q^{41} +109.742 q^{43} +(-10.6211 + 32.6885i) q^{44} +(226.086 + 695.821i) q^{46} +(17.9575 + 55.2674i) q^{47} +335.317 q^{49} +(31.1696 - 580.935i) q^{50} +(-437.888 - 318.144i) q^{52} +(120.787 + 371.745i) q^{53} +(-25.3963 + 12.0941i) q^{55} +(212.056 - 652.641i) q^{56} +(-144.157 + 443.669i) q^{58} +(333.759 - 242.490i) q^{59} +(-290.142 - 210.800i) q^{61} +(-652.756 + 474.255i) q^{62} +(646.244 + 469.524i) q^{64} +(-57.5458 - 439.213i) q^{65} +(108.468 - 333.831i) q^{67} +1161.09 q^{68} +(1223.57 - 582.681i) q^{70} +(-52.7887 - 162.467i) q^{71} +(754.724 + 548.339i) q^{73} +276.437 q^{74} -1951.19 q^{76} +(-53.0119 - 38.5154i) q^{77} +(-405.819 - 1248.98i) q^{79} +(-19.3744 - 147.874i) q^{80} -1654.21 q^{82} +(202.066 - 621.896i) q^{83} +(653.668 + 689.680i) q^{85} +(413.211 + 300.216i) q^{86} +(-53.6301 + 38.9646i) q^{88} +(857.273 + 622.845i) q^{89} +(834.814 - 606.528i) q^{91} +(-663.624 + 2042.42i) q^{92} +(-83.5770 + 257.224i) q^{94} +(-1098.48 - 1159.00i) q^{95} +(198.234 + 610.103i) q^{97} +(1262.57 + 917.308i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) 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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