LMFDB - Embedded newform 63.4.o.a.20.13

Newspace parameters

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.o (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			20.13
Character	$\chi$	$=$	63.20
Dual form			63.4.o.a.41.13

$q$-expansion

$f(q)$	$=$	$q+(0.628557 + 0.362898i) q^{2} +(-2.99138 + 4.24872i) q^{3} +(-3.73661 - 6.47200i) q^{4} +(-5.53318 - 9.58374i) q^{5} +(-3.42210 + 1.58500i) q^{6} +(13.3114 - 12.8765i) q^{7} -11.2304i q^{8} +(-9.10332 - 25.4191i) q^{9} +O(q^{10})$	\(q+(0.628557 + 0.362898i) q^{2} +(-2.99138 + 4.24872i) q^{3} +(-3.73661 - 6.47200i) q^{4} +(-5.53318 - 9.58374i) q^{5} +(-3.42210 + 1.58500i) q^{6} +(13.3114 - 12.8765i) q^{7} -11.2304i q^{8} +(-9.10332 - 25.4191i) q^{9} -8.03191i q^{10} +(0.219645 + 0.126812i) q^{11} +(38.6754 + 3.48437i) q^{12} +(-12.3956 + 7.15663i) q^{13} +(13.0399 - 3.26296i) q^{14} +(57.2705 + 5.15965i) q^{15} +(-25.8174 + 44.7170i) q^{16} -92.5854 q^{17} +(3.50257 - 19.2809i) q^{18} -130.104i q^{19} +(-41.3506 + 71.6214i) q^{20} +(14.8894 + 95.0753i) q^{21} +(0.0920395 + 0.159417i) q^{22} +(-102.797 + 59.3500i) q^{23} +(47.7148 + 33.5944i) q^{24} +(1.26793 - 2.19612i) q^{25} -10.3885 q^{26} +(135.230 + 37.3606i) q^{27} +(-133.077 - 38.0370i) q^{28} +(248.320 + 143.368i) q^{29} +(34.1254 + 24.0265i) q^{30} +(214.225 - 123.683i) q^{31} +(-110.262 + 63.6597i) q^{32} +(-1.19583 + 0.553867i) q^{33} +(-58.1952 - 33.5990i) q^{34} +(-197.060 - 56.3252i) q^{35} +(-130.497 + 153.898i) q^{36} +188.615 q^{37} +(47.2144 - 81.7777i) q^{38} +(6.67351 - 74.0738i) q^{39} +(-107.629 + 62.1397i) q^{40} +(53.2437 + 92.2207i) q^{41} +(-25.1438 + 65.1636i) q^{42} +(-21.5586 + 37.3406i) q^{43} -1.89539i q^{44} +(-193.240 + 227.892i) q^{45} -86.1520 q^{46} +(-68.8818 + 119.307i) q^{47} +(-112.761 - 243.457i) q^{48} +(11.3890 - 342.811i) q^{49} +(1.59393 - 0.920258i) q^{50} +(276.958 - 393.370i) q^{51} +(92.6354 + 53.4830i) q^{52} -419.280i q^{53} +(71.4418 + 72.5580i) q^{54} -2.80669i q^{55} +(-144.609 - 149.493i) q^{56} +(552.775 + 389.190i) q^{57} +(104.056 + 180.230i) q^{58} +(-217.560 - 376.825i) q^{59} +(-180.604 - 389.934i) q^{60} +(-163.504 - 94.3989i) q^{61} +179.537 q^{62} +(-448.488 - 221.145i) q^{63} +320.670 q^{64} +(137.175 + 79.1977i) q^{65} +(-0.952645 - 0.0858263i) q^{66} +(-185.350 - 321.035i) q^{67} +(345.956 + 599.213i) q^{68} +(55.3435 - 614.296i) q^{69} +(-103.423 - 106.916i) q^{70} -26.1630i q^{71} +(-285.466 + 102.234i) q^{72} +728.545i q^{73} +(118.555 + 68.4480i) q^{74} +(5.53785 + 11.9565i) q^{75} +(-842.032 + 486.147i) q^{76} +(4.55669 - 1.14022i) q^{77} +(31.0759 - 44.1378i) q^{78} +(-48.6779 + 84.3125i) q^{79} +571.409 q^{80} +(-563.259 + 462.796i) q^{81} +77.2880i q^{82} +(401.359 - 695.174i) q^{83} +(559.691 - 451.623i) q^{84} +(512.291 + 887.315i) q^{85} +(-27.1017 + 15.6471i) q^{86} +(-1351.95 + 626.177i) q^{87} +(1.42415 - 2.46670i) q^{88} +236.618 q^{89} +(-204.164 + 73.1170i) q^{90} +(-72.8512 + 254.878i) q^{91} +(768.227 + 443.536i) q^{92} +(-115.333 + 1280.16i) q^{93} +(-86.5924 + 49.9941i) q^{94} +(-1246.88 + 719.887i) q^{95} +(59.3623 - 658.903i) q^{96} +(1268.09 + 732.133i) q^{97} +(131.564 - 211.343i) q^{98} +(1.22395 - 6.73758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44q - 6q^{2} + 78q^{4} + 5q^{7} + O(q^{10}) $	$ 44q - 6q^{2} + 78q^{4} + 5q^{7} - 18q^{11} + 204q^{14} + 66q^{15} - 242q^{16} - 210q^{18} - 57q^{21} - 34q^{22} - 102q^{23} - 352q^{25} + 300q^{28} + 246q^{29} - 144q^{30} + 1068q^{32} - 1818q^{36} + 328q^{37} - 798q^{39} - 1158q^{42} - 170q^{43} + 968q^{46} - 79q^{49} + 288q^{50} - 204q^{51} + 1212q^{56} + 324q^{57} - 538q^{58} + 5316q^{60} + 783q^{63} - 808q^{64} + 4350q^{65} - 590q^{67} + 384q^{70} + 4284q^{72} - 5304q^{74} - 2787q^{77} + 612q^{78} - 302q^{79} - 3720q^{81} + 7050q^{84} - 612q^{85} - 13692q^{86} + 1294q^{88} + 210q^{91} - 10194q^{92} - 4266q^{93} + 6336q^{95} + 1014q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.628557	+	0.362898i	0.222229	+	0.128304i	0.606982	−	0.794716i	$-0.292380\pi$
$2$	0.628557	+	0.362898i	0.222229	+	0.128304i	−0.384753	+	0.923019i	$0.625713\pi$
$3$	−2.99138	+	4.24872i	−0.575691	+	0.817667i
$3$	−2.99138	+	4.24872i	−0.575691	+	0.817667i
$4$	−3.73661	−	6.47200i	−0.467076	−	0.809000i
$5$	−5.53318	−	9.58374i	−0.494902	−	0.857196i	0.505080	−	0.863072i	$-0.331463\pi$
$5$	−5.53318	−	9.58374i	−0.494902	−	0.857196i	−0.999983	+	0.00587635i	$0.998129\pi$
$6$	−3.42210	+	1.58500i	−0.232845	+	0.107846i
$7$	13.3114	−	12.8765i	0.718750	−	0.695268i
$7$	13.3114	−	12.8765i	0.718750	−	0.695268i
$8$		−	11.2304i		−	0.496318i
$9$	−9.10332	−	25.4191i	−0.337160	−	0.941447i
$10$		−	8.03191i		−	0.253991i
$11$	0.219645	+	0.126812i	0.00602049	+	0.00347593i	0.503007	−	0.864282i	$-0.332227\pi$
$11$	0.219645	+	0.126812i	0.00602049	+	0.00347593i	−0.496987	+	0.867758i	$0.665560\pi$
$12$	38.6754	+	3.48437i	0.930384	+	0.0838208i
$13$	−12.3956	+	7.15663i	−0.264456	+	0.152684i	−0.626366	−	0.779529i	$-0.715458\pi$
$13$	−12.3956	+	7.15663i	−0.264456	+	0.152684i	0.361909	+	0.932213i	$0.382125\pi$
$14$	13.0399	−	3.26296i	0.248932	−	0.0622901i
$15$	57.2705	+	5.15965i	0.985812	+	0.0888145i
$16$	−25.8174	+	44.7170i	−0.403397	+	0.698704i
$17$	−92.5854			−1.32090			−0.660449	−	0.750871i	$-0.729634\pi$
$17$	−92.5854			−1.32090			−0.660449	+	0.750871i	$0.729634\pi$
$18$	3.50257	−	19.2809i	0.0458646	−	0.252475i
$19$		−	130.104i		−	1.57094i	−0.618899	−	0.785470i	$-0.712421\pi$
$19$		−	130.104i		−	1.57094i	0.618899	−	0.785470i	$-0.287579\pi$
$20$	−41.3506	+	71.6214i	−0.462314	+	0.800752i
$21$	14.8894	+	95.0753i	0.154720	+	0.987958i
$22$	0.0920395	+	0.159417i	0.000891950	+	0.00154490i
$23$	−102.797	+	59.3500i	−0.931944	+	0.538058i	−0.887426	−	0.460951i	$-0.847509\pi$
$23$	−102.797	+	59.3500i	−0.931944	+	0.538058i	−0.0445181	+	0.999009i	$0.514175\pi$
$24$	47.7148	+	33.5944i	0.405823	+	0.285726i
$25$	1.26793	−	2.19612i	0.0101434	−	0.0175689i
$26$	−10.3885			−0.0783597
$27$	135.230	+	37.3606i	0.963891	+	0.266298i
$28$	−133.077	−	38.0370i	−0.898183	−	0.256726i
$29$	248.320	+	143.368i	1.59007	+	0.918025i	0.993294	+	0.115615i	$0.0368837\pi$
$29$	248.320	+	143.368i	1.59007	+	0.918025i	0.596772	+	0.802411i	$0.296450\pi$
$30$	34.1254	+	24.0265i	0.207680	+	0.146220i
$31$	214.225	−	123.683i	1.24116	−	0.716582i	0.271827	−	0.962346i	$-0.412372\pi$
$31$	214.225	−	123.683i	1.24116	−	0.716582i	0.969330	+	0.245764i	$0.0790388\pi$
$32$	−110.262	+	63.6597i	−0.609117	+	0.351674i
$33$	−1.19583	+	0.553867i	−0.00630810	+	0.00292170i
$34$	−58.1952	−	33.5990i	−0.293541	−	0.169476i
$35$	−197.060	−	56.3252i	−0.951692	−	0.272020i
$36$	−130.497	+	153.898i	−0.604151	+	0.712490i
$37$	188.615			0.838058			0.419029	−	0.907973i	$-0.362371\pi$
$37$	188.615			0.838058			0.419029	+	0.907973i	$0.362371\pi$
$38$	47.2144	−	81.7777i	0.201558	−	0.349108i
$39$	6.67351	−	74.0738i	0.0274004	−	0.304136i
$40$	−107.629	+	62.1397i	−0.425442	+	0.245629i
$41$	53.2437	+	92.2207i	0.202811	+	0.351279i	0.949433	−	0.313969i	$-0.101659\pi$
$41$	53.2437	+	92.2207i	0.202811	+	0.351279i	−0.746622	+	0.665249i	$0.768326\pi$
$42$	−25.1438	+	65.1636i	−0.0923755	+	0.239404i
$43$	−21.5586	+	37.3406i	−0.0764572	+	0.132428i	−0.901719	−	0.432323i	$-0.857694\pi$
$43$	−21.5586	+	37.3406i	−0.0764572	+	0.132428i	0.825262	+	0.564750i	$0.191028\pi$
$44$		−	1.89539i		−	0.00649410i
$45$	−193.240	+	227.892i	−0.640144	+	0.754937i
$46$	−86.1520			−0.276139
$47$	−68.8818	+	119.307i	−0.213776	+	0.370270i	−0.952893	−	0.303306i	$-0.901909\pi$
$47$	−68.8818	+	119.307i	−0.213776	+	0.370270i	0.739118	+	0.673576i	$0.235243\pi$
$48$	−112.761	−	243.457i	−0.339075	−	0.732082i
$49$	11.3890	−	342.811i	0.0332041	−	0.999449i
$50$	1.59393	−	0.920258i	0.00450832	−	0.00260288i
$51$	276.958	−	393.370i	0.760429	−	1.08006i
$52$	92.6354	+	53.4830i	0.247043	+	0.142630i
$53$		−	419.280i		−	1.08665i	−0.839522	−	0.543325i	$-0.817165\pi$
$53$		−	419.280i		−	1.08665i	0.839522	−	0.543325i	$-0.182835\pi$
$54$	71.4418	+	72.5580i	0.180037	+	0.182850i
$55$		−	2.80669i		−	0.00688098i
$56$	−144.609	−	149.493i	−0.345074	−	0.356729i
$57$	552.775	+	389.190i	1.28451	+	0.904376i
$58$	104.056	+	180.230i	0.235572	+	0.408023i
$59$	−217.560	−	376.825i	−0.480066	−	0.831498i	0.519673	−	0.854365i	$-0.326054\pi$
$59$	−217.560	−	376.825i	−0.480066	−	0.831498i	−0.999739	+	0.0228670i	$0.992721\pi$
$60$	−180.604	−	389.934i	−0.388599	−	0.839005i
$61$	−163.504	−	94.3989i	−0.343189	−	0.198140i	0.318493	−	0.947925i	$-0.396823\pi$
$61$	−163.504	−	94.3989i	−0.343189	−	0.198140i	−0.661681	+	0.749785i	$0.730157\pi$
$62$	179.537			0.367761
$63$	−448.488	−	221.145i	−0.896892	−	0.442249i
$64$	320.670			0.626310
$65$	137.175	+	79.1977i	0.261760	+	0.151127i
$66$	−0.952645	−	0.0858263i	−0.00177670	−	0.000160068i
$67$	−185.350	−	321.035i	−0.337971	−	0.585383i	0.646080	−	0.763270i	$-0.276407\pi$
$67$	−185.350	−	321.035i	−0.337971	−	0.585383i	−0.984051	+	0.177887i	$0.943074\pi$
$68$	345.956	+	599.213i	0.616960	+	1.06861i
$69$	55.3435	−	614.296i	0.0965591	−	1.07178i
$70$	−103.423	−	106.916i	−0.176592	−	0.182556i
$71$		−	26.1630i		−	0.0437321i	−0.999761	−	0.0218661i	$-0.993039\pi$
$71$		−	26.1630i		−	0.0437321i	0.999761	−	0.0218661i	$-0.00696074\pi$
$72$	−285.466	+	102.234i	−0.467257	+	0.167339i
$73$			728.545i			1.16808i	0.811725	+	0.584039i	$0.198529\pi$
$73$			728.545i			1.16808i	−0.811725	+	0.584039i	$0.801471\pi$
$74$	118.555	+	68.4480i	0.186240	+	0.107526i
$75$	5.53785	+	11.9565i	0.00852607	+	0.0184082i
$76$	−842.032	+	486.147i	−1.27089	+	0.733749i
$77$	4.55669	−	1.14022i	0.00674393	−	0.00168753i
$78$	31.0759	−	44.1378i	0.0451109	−	0.0640721i
$79$	−48.6779	+	84.3125i	−0.0693251	+	0.120075i	−0.898604	−	0.438760i	$-0.855418\pi$
$79$	−48.6779	+	84.3125i	−0.0693251	+	0.120075i	0.829279	+	0.558834i	$0.188751\pi$
$80$	571.409			0.798568
$81$	−563.259	+	462.796i	−0.772646	+	0.634837i
$82$			77.2880i			0.104086i
$83$	401.359	−	695.174i	0.530781	−	0.919340i	−0.468573	−	0.883425i	$-0.655232\pi$
$83$	401.359	−	695.174i	0.530781	−	0.919340i	0.999355	−	0.0359157i	$-0.0114348\pi$
$84$	559.691	−	451.623i	0.726992	−	0.586620i
$85$	512.291	+	887.315i	0.653715	+	1.13227i
$86$	−27.1017	+	15.6471i	−0.0339819	+	0.0196195i
$87$	−1351.95	+	626.177i	−1.66603	+	0.771647i
$88$	1.42415	−	2.46670i	0.00172517	−	0.00298808i
$89$	236.618			0.281814			0.140907	−	0.990023i	$-0.454998\pi$
$89$	236.618			0.281814			0.140907	+	0.990023i	$0.454998\pi$
$90$	−204.164	+	73.1170i	−0.239119	+	0.0856357i
$91$	−72.8512	+	254.878i	−0.0839218	+	0.293610i
$92$	768.227	+	443.536i	0.870578	+	0.502628i
$93$	−115.333	+	1280.16i	−0.128597	+	1.42738i
$94$	−86.5924	+	49.9941i	−0.0950141	+	0.0548564i
$95$	−1246.88	+	719.887i	−1.34660	+	0.777462i
$96$	59.3623	−	658.903i	0.0631108	−	0.700510i
$97$	1268.09	+	732.133i	1.32737	+	0.766360i	0.984893	−	0.173165i	$-0.0553995\pi$
$97$	1268.09	+	732.133i	1.32737	+	0.766360i	0.342481	+	0.939525i	$0.388733\pi$
$98$	131.564	−	211.343i	0.135612	−	0.217846i
$99$	1.22395	−	6.73758i	0.00124254	−	0.00683992i
$100$	−18.9510			−0.0189510
$101$	783.722	−	1357.45i	0.772112	−	1.33734i	−0.164292	−	0.986412i	$-0.552534\pi$
$101$	783.722	−	1357.45i	0.772112	−	1.33734i	0.936404	−	0.350925i	$-0.114133\pi$
$102$	316.837	−	146.748i	0.307564	−	0.142453i
$103$	−86.8588	+	50.1479i	−0.0830918	+	0.0479730i	−0.540970	−	0.841042i	$-0.681943\pi$
$103$	−86.8588	+	50.1479i	−0.0830918	+	0.0479730i	0.457878	+	0.889015i	$0.348609\pi$
$104$	80.3717	+	139.208i	0.0757798	+	0.131254i
$105$	828.791	−	668.764i	0.770303	−	0.621568i
$106$	152.156	−	263.541i	0.139421	−	0.241485i
$107$		−	553.381i		−	0.499976i	−0.968249	−	0.249988i	$-0.919573\pi$
$107$		−	553.381i		−	0.499976i	0.968249	−	0.249988i	$-0.0804266\pi$
$108$	−263.505	−	1014.81i	−0.234775	−	0.904169i
$109$	−400.600			−0.352023			−0.176012	−	0.984388i	$-0.556320\pi$
$109$	−400.600			−0.352023			−0.176012	+	0.984388i	$0.556320\pi$
$110$	1.01854	−	1.76417i	0.000882856	−	0.00152915i
$111$	−564.219	+	801.374i	−0.482462	+	0.685253i
$112$	232.134	+	927.687i	0.195845	+	0.782663i
$113$	−617.417	+	356.466i	−0.513997	+	0.296756i	−0.734475	−	0.678635i	$-0.762572\pi$
$113$	−617.417	+	356.466i	−0.513997	+	0.296756i	0.220478	+	0.975392i	$0.429238\pi$
$114$	206.215	+	445.229i	0.169419	+	0.365785i
$115$	1137.59	+	656.788i	0.922442	+	0.532572i
$116$		−	2142.84i		−	1.71515i
$117$	294.756	+	249.937i	0.232908	+	0.197493i
$118$		−	315.808i		−	0.246377i
$119$	−1232.45	+	1192.18i	−0.949396	+	0.918378i
$120$	57.9449	−	643.170i	0.0440802	−	0.489276i
$121$	−665.468	−	1152.62i	−0.499976	−	0.865984i
$122$	−68.5143	−	118.670i	−0.0508442	−	0.0880648i
$123$	−551.092	−	49.6494i	−0.403986	−	0.0363962i
$124$	−1600.95	−	924.307i	−1.15943	−	0.669397i
$125$	−1411.36			−1.00988
$126$	−201.647	−	301.758i	−0.142573	−	0.213355i
$127$	102.170			0.0713865			0.0356932	−	0.999363i	$-0.488636\pi$
$127$	102.170			0.0713865			0.0356932	+	0.999363i	$0.488636\pi$
$128$	1083.65	+	625.648i	0.748300	+	0.432031i
$129$	−94.1600	−	203.297i	−0.0642661	−	0.138754i
$130$	57.4814	+	99.5606i	0.0387804	+	0.0671696i
$131$	236.423	+	409.496i	0.157682	+	0.273113i	0.934032	−	0.357188i	$-0.116265\pi$
$131$	236.423	+	409.496i	0.157682	+	0.273113i	−0.776350	+	0.630302i	$0.782931\pi$
$132$	8.05298	+	5.66982i	0.00531001	+	0.00373859i
$133$	−1675.29	−	1731.87i	−1.09222	−	1.12911i
$134$		−	269.052i		−	0.173452i
$135$	−390.198	−	1502.73i	−0.248762	−	0.958035i
$136$			1039.77i			0.655585i
$137$	2268.47	+	1309.70i	1.41466	+	0.816756i	0.995823	−	0.0913039i	$-0.0291035\pi$
$137$	2268.47	+	1309.70i	1.41466	+	0.816756i	0.418840	+	0.908060i	$0.362437\pi$
$138$	257.713	−	366.036i	0.158971	−	0.225790i
$139$	1075.92	−	621.185i	0.656537	−	0.379052i	−0.134419	−	0.990925i	$-0.542917\pi$
$139$	1075.92	−	621.185i	0.656537	−	0.379052i	0.790956	+	0.611873i	$0.209583\pi$
$140$	371.800	+	1485.84i	0.224449	+	0.896973i
$141$	−300.850	−	649.552i	−0.179689	−	0.387958i
$142$	9.49451	−	16.4450i	0.00561100	−	0.00971853i
$143$	−3.63018			−0.00212287
$144$	1371.69	+	249.181i	0.793802	+	0.144202i
$145$		−	3173.12i		−	1.81733i
$146$	−264.387	+	457.932i	−0.149869	+	0.259581i
$147$	1422.44	+	1073.87i	0.798101	+	0.602523i
$148$	−704.781	−	1220.72i	−0.391437	−	0.677989i
$149$	973.891	−	562.276i	0.535465	−	0.309151i	−0.207774	−	0.978177i	$-0.566622\pi$
$149$	973.891	−	562.276i	0.535465	−	0.309151i	0.743239	+	0.669026i	$0.233289\pi$
$150$	−0.858135	+	9.52502i	−0.000467109	+	0.00518476i
$151$	237.798	−	411.879i	0.128157	−	0.221975i	−0.794805	−	0.606864i	$-0.792427\pi$
$151$	237.798	−	411.879i	0.128157	−	0.221975i	0.922963	+	0.384889i	$0.125760\pi$
$152$	−1461.12			−0.779686
$153$	842.835	+	2353.44i	0.445354	+	1.24356i
$154$	3.27792	+	0.936921i	0.00171521	+	0.000490255i
$155$	−2370.68	−	1368.71i	−1.22850	−	0.709276i
$156$	−504.342	+	233.594i	−0.258844	+	0.119888i
$157$	1674.30	−	966.660i	0.851108	−	0.491388i	−0.00991644	−	0.999951i	$-0.503157\pi$
$157$	1674.30	−	966.660i	0.851108	−	0.491388i	0.861025	+	0.508563i	$0.169823\pi$
$158$	−61.1936	+	35.3302i	−0.0308121	+	0.0177893i
$159$	1781.40	+	1254.22i	0.888519	+	0.625575i
$160$	1220.20	+	704.481i	0.602906	+	0.348088i
$161$	−604.156	+	2113.71i	−0.295740	+	1.03468i
$162$	−521.988	+	86.4882i	−0.253156	+	0.0419454i
$163$	−743.323			−0.357187			−0.178594	−	0.983923i	$-0.557155\pi$
$163$	−743.323			−0.357187			−0.178594	+	0.983923i	$0.557155\pi$
$164$	397.902	−	689.186i	0.189457	−	0.328149i
$165$	11.9249	+	8.39587i	0.00562636	+	0.00396132i
$166$	504.554	−	291.304i	0.235910	−	0.136202i
$167$	−1811.60	−	3137.78i	−0.839435	−	1.45394i	−0.890368	−	0.455242i	$-0.849553\pi$
$167$	−1811.60	−	3137.78i	−0.839435	−	1.45394i	0.0509327	−	0.998702i	$-0.483781\pi$
$168$	1067.73	−	167.213i	0.490341	−	0.0767904i
$169$	−996.065	+	1725.24i	−0.453375	+	0.785269i
$170$			743.638i			0.335496i
$171$	−3307.12	+	1184.38i	−1.47896	+	0.529658i
$172$	322.225			0.142845
$173$	−1648.50	+	2855.29i	−0.724470	+	1.25482i	0.234722	+	0.972063i	$0.424582\pi$
$173$	−1648.50	+	2855.29i	−0.724470	+	1.25482i	−0.959192	+	0.282756i	$0.908751\pi$
$174$	−1077.02	−	97.0313i	−0.469244	−	0.0422754i
$175$	−11.4005	−	45.5601i	−0.00492453	−	0.0196801i
$176$	−11.3413	+	6.54791i	−0.00485729	+	0.00280436i
$177$	2251.83	+	202.873i	0.956259	+	0.0861519i
$178$	148.728	+	85.8680i	0.0626270	+	0.0361577i
$179$			2746.77i			1.14695i	0.819225	+	0.573473i	$0.194404\pi$
$179$			2746.77i			1.14695i	−0.819225	+	0.573473i	$0.805596\pi$
$180$	2196.98	+	399.103i	0.909740	+	0.165263i
$181$		−	738.434i		−	0.303245i	−0.988438	−	0.151622i	$-0.951550\pi$
$181$		−	738.434i		−	0.303245i	0.988438	−	0.151622i	$-0.0484498\pi$
$182$	−138.286	+	133.768i	−0.0563210	+	0.0544810i
$183$	890.177	−	412.299i	0.359583	−	0.166547i
$184$	666.524	+	1154.45i	0.267048	+	0.462541i
$185$	−1043.64	−	1807.64i	−0.414757	−	0.718380i
$186$	−537.062	+	762.801i	−0.211716	+	0.300706i
$187$	−20.3359	−	11.7409i	−0.00795245	−	0.00459135i
$188$	1029.54			0.399398
$189$	2281.18	−	1243.97i	0.877945	−	0.478761i
$190$	−1044.98			−0.399005
$191$	−2879.69	−	1662.59i	−1.09093	−	0.629848i	−0.157105	−	0.987582i	$-0.550216\pi$
$191$	−2879.69	−	1662.59i	−1.09093	−	0.629848i	−0.933823	+	0.357734i	$0.883549\pi$
$192$	−959.247	+	1362.44i	−0.360561	+	0.512113i
$193$	1660.75	+	2876.50i	0.619394	+	1.07282i	0.989596	+	0.143871i	$0.0459550\pi$
$193$	1660.75	+	2876.50i	0.619394	+	1.07282i	−0.370202	+	0.928951i	$0.620712\pi$
$194$	531.379	+	920.376i	0.196654	+	0.340614i
$195$	−746.830	+	345.906i	−0.274265	+	0.127030i
$196$	−2261.23	+	1207.24i	−0.824063	+	0.439957i
$197$			501.482i			0.181366i	0.995880	+	0.0906830i	$0.0289050\pi$
$197$			501.482i			0.181366i	−0.995880	+	0.0906830i	$0.971095\pi$
$198$	3.21437	−	3.79079i	0.00115371	−	0.00136060i
$199$			4067.59i			1.44896i	0.689294	+	0.724482i	$0.257921\pi$
$199$			4067.59i			1.44896i	−0.689294	+	0.724482i	$0.742079\pi$
$200$	−24.6633	−	14.2393i	−0.00871978	−	0.00503437i
$201$	1918.44	+	172.837i	0.673215	+	0.0606518i
$202$	985.229	−	568.822i	0.343171	−	0.198130i
$203$	5151.58	−	1289.08i	1.78113	−	0.445692i
$204$	−3580.77	−	322.602i	−1.22894	−	0.110719i
$205$	589.213	−	1020.55i	0.200744	−	0.347698i
$206$	−72.7943			−0.0246205
$207$	2444.42	+	2072.73i	0.820767	+	0.695965i
$208$		−	739.062i		−	0.246369i
$209$	16.4987	−	28.5766i	0.00546048	−	0.00945783i
$210$	763.636	−	119.590i	0.250933	−	0.0392976i
$211$	−2456.95	−	4255.56i	−0.801628	−	1.38846i	−0.918544	−	0.395319i	$-0.870634\pi$
$211$	−2456.95	−	4255.56i	−0.801628	−	1.38846i	0.116916	−	0.993142i	$-0.462699\pi$
$212$	−2713.58	+	1566.68i	−0.879100	+	0.507549i
$213$	111.160	+	78.2635i	0.0357583	+	0.0251762i
$214$	200.821	−	347.832i	0.0641487	−	0.111109i
$215$	477.150			0.151355
$216$	419.574	−	1518.69i	0.132169	−	0.478396i
$217$	1259.03	−	4404.87i	0.393865	−	1.37798i
$218$	−251.800	−	145.377i	−0.0782296	−	0.0451659i
$219$	−3095.39	−	2179.35i	−0.955100	−	0.672452i
$220$	−18.1649	+	10.4875i	−0.00556672	+	0.00321394i
$221$	1147.66	−	662.599i	0.349320	−	0.201680i
$222$	−645.461	+	298.956i	−0.195137	+	0.0903810i
$223$	−1033.31	−	596.580i	−0.310293	−	0.179148i	0.336765	−	0.941589i	$-0.390667\pi$
$223$	−1033.31	−	596.580i	−0.310293	−	0.179148i	−0.647058	+	0.762441i	$0.724001\pi$
$224$	−648.027	+	2267.20i	−0.193295	+	0.676265i
$225$	−67.3657	−	12.2376i	−0.0199602	−	0.00362597i
$226$	−517.443			−0.152300
$227$	2804.31	−	4857.22i	0.819951	−	1.42020i	−0.0857665	−	0.996315i	$-0.527334\pi$
$227$	2804.31	−	4857.22i	0.819951	−	1.42020i	0.905718	−	0.423882i	$-0.139333\pi$
$228$	453.330	−	5031.81i	0.131678	−	1.46158i
$229$	−4618.56	+	2666.53i	−1.33276	+	0.769472i	−0.985722	−	0.168378i	$-0.946147\pi$
$229$	−4618.56	+	2666.53i	−1.33276	+	0.769472i	−0.347042	+	0.937850i	$0.612814\pi$
$230$	476.694	+	825.658i	0.136662	+	0.236706i
$231$	−8.78631	+	22.7709i	−0.00250258	+	0.00648579i
$232$	1610.08	−	2788.73i	0.455632	−	0.789179i
$233$		−	111.828i		−	0.0314424i	−0.999876	−	0.0157212i	$-0.994996\pi$
$233$		−	111.828i		−	0.0314424i	0.999876	−	0.0157212i	$-0.00500442\pi$
$234$	94.5698	+	264.066i	0.0264197	+	0.0737715i
$235$	1524.54			0.423192
$236$	−1625.87	+	2816.09i	−0.448455	+	0.776746i
$237$	−212.607	−	459.029i	−0.0582713	−	0.125811i
$238$	−1207.30	+	302.102i	−0.328814	+	0.0822789i
$239$	4132.66	−	2385.99i	1.11849	−	0.645762i	0.177477	−	0.984125i	$-0.443206\pi$
$239$	4132.66	−	2385.99i	1.11849	−	0.645762i	0.941016	+	0.338363i	$0.109873\pi$
$240$	−1709.30	+	2427.76i	−0.459728	+	0.652963i
$241$	4621.37	+	2668.15i	1.23522	+	0.713156i	0.968114	−	0.250510i	$-0.0805984\pi$
$241$	4621.37	+	2668.15i	1.23522	+	0.713156i	0.267109	+	0.963666i	$0.413932\pi$
$242$		−	965.987i		−	0.256595i
$243$	−281.371	−	3777.53i	−0.0742797	−	0.997237i
$244$			1410.93i			0.370186i
$245$	−3348.43	+	1787.68i	−0.873156	+	0.466167i
$246$	−328.375	−	231.198i	−0.0851075	−	0.0599212i
$247$	931.104	+	1612.72i	0.239857	+	0.415445i
$248$	−1389.00	−	2405.83i	−0.355653	−	0.616008i
$249$	1752.99	+	3784.79i	0.446149	+	0.963258i
$250$	−887.119	−	512.178i	−0.224425	−	0.129572i
$251$	3081.73			0.774970			0.387485	−	0.921876i	$-0.373344\pi$
$251$	3081.73			0.774970			0.387485	+	0.921876i	$0.373344\pi$
$252$	244.574	+	3728.95i	0.0611377	+	0.932150i
$253$	−30.1052			−0.00748101
$254$	64.2194	+	37.0771i	0.0158641	+	0.00915915i
$255$	−5302.41	−	477.709i	−1.30216	−	0.117315i
$256$	−828.589	−	1435.16i	−0.202292	−	0.350381i
$257$	1067.55	+	1849.05i	0.259113	+	0.448797i	0.966005	−	0.258525i	$-0.0832365\pi$
$257$	1067.55	+	1849.05i	0.259113	+	0.448797i	−0.706892	+	0.707322i	$0.749903\pi$
$258$	14.5909	−	161.954i	0.00352088	−	0.0390807i
$259$	2510.74	−	2428.71i	0.602354	−	0.582675i
$260$		−	1183.72i		−	0.282352i
$261$	1383.74	−	7617.20i	0.328166	−	1.80649i
$262$			343.189i			0.0809248i
$263$	−1429.14	−	825.115i	−0.335075	−	0.193455i	0.323017	−	0.946393i	$-0.395303\pi$
$263$	−1429.14	−	825.115i	−0.335075	−	0.193455i	−0.658092	+	0.752938i	$0.728636\pi$
$264$	6.22015	+	13.4296i	0.00145009	+	0.00313082i
$265$	−4018.27	+	2319.95i	−0.931473	+	0.537786i
$266$	−424.523	−	1696.54i	−0.0978541	−	0.391058i
$267$	−707.812	+	1005.32i	−0.162238	+	0.230430i
$268$	−1385.16	+	2399.16i	−0.315716	+	0.546837i
$269$	5477.73			1.24157			0.620787	−	0.783979i	$-0.286813\pi$
$269$	5477.73			1.24157			0.620787	+	0.783979i	$0.286813\pi$
$270$	300.077	−	1086.16i	0.0676374	−	0.244820i
$271$			3607.16i			0.808558i	0.914636	+	0.404279i	$0.132477\pi$
$271$			3607.16i			0.808558i	−0.914636	+	0.404279i	$0.867523\pi$
$272$	2390.31	−	4140.15i	0.532846	−	0.922916i
$273$	−864.981	−	1071.96i	−0.191762	−	0.237649i
$274$	950.577	+	1646.45i	0.209586	+	0.363013i
$275$	0.556988	−	0.321577i	0.000122137	−	7.05158e-5i
$276$	−4182.52	+	1937.20i	−0.912167	+	0.422485i
$277$	−1488.99	+	2579.00i	−0.322977	+	0.559413i	−0.981101	−	0.193497i	$-0.938017\pi$
$277$	−1488.99	+	2579.00i	−0.322977	+	0.559413i	0.658124	+	0.752910i	$0.271350\pi$
$278$	901.707			0.194535
$279$	−5094.05	−	4319.47i	−1.09309	−	0.926881i
$280$	−632.554	+	2213.06i	−0.135008	+	0.472342i
$281$	−4936.36	−	2850.01i	−1.04797	−	0.605043i	−0.125886	−	0.992045i	$-0.540177\pi$
$281$	−4936.36	−	2850.01i	−1.04797	−	0.605043i	−0.922079	+	0.387002i	$0.873511\pi$
$282$	46.6192	−	517.458i	0.00984445	−	0.109270i
$283$	476.719	−	275.234i	0.100134	−	0.0578125i	−0.449097	−	0.893483i	$-0.648254\pi$
$283$	476.719	−	275.234i	0.100134	−	0.0578125i	0.549231	+	0.835671i	$0.314921\pi$
$284$	−169.327	+	97.7611i	−0.0353793	+	0.0204262i
$285$	671.291	−	7451.11i	0.139522	−	1.54865i
$286$	−2.28178	−	1.31739i	−0.000471763	−	0.000272373i
$287$	1896.23	+	541.996i	0.390004	+	0.111474i
$288$	2621.92	+	2223.24i	0.536452	+	0.454881i
$289$	3659.06			0.744771
$290$	1151.52	−	1994.49i	0.233170	−	0.403863i
$291$	−6903.98	+	3197.69i	−1.39078	+	0.644164i
$292$	4715.14	−	2722.29i	0.944976	−	0.545582i
$293$	3915.00	+	6780.98i	0.780603	+	1.35204i	0.931591	+	0.363508i	$0.118421\pi$
$293$	3915.00	+	6780.98i	0.780603	+	1.35204i	−0.150988	+	0.988536i	$0.548246\pi$
$294$	504.382	+	1191.19i	0.100055	+	0.236297i
$295$	−2407.59	+	4170.08i	−0.475171	+	0.823021i
$296$		−	2118.22i		−	0.415943i
$297$	24.9648	+	25.3548i	0.00487746	+	0.00495366i
$298$	816.195			0.158661
$299$	849.492	−	1471.36i	0.164306	−	0.284586i
$300$	56.6897	−	80.5177i	0.0109099	−	0.0154956i
$301$	193.842	+	774.658i	0.0371192	+	0.148341i
$302$	298.940	−	172.593i	0.0569604	−	0.0328861i
$303$	3423.01	+	7390.46i	0.648999	+	1.40122i
$304$	5817.86	+	3358.94i	1.09762	+	0.633712i
$305$			2089.30i			0.392240i
$306$	−324.287	+	1785.13i	−0.0605825	+	0.333494i
$307$			5845.06i			1.08663i	0.839529	+	0.543315i	$0.182831\pi$
$307$			5845.06i			1.08663i	−0.839529	+	0.543315i	$0.817169\pi$
$308$	−24.4060	−	25.2303i	−0.00451514	−	0.00466764i
$309$	46.7627	−	519.050i	0.00860917	−	0.0955591i
$310$	−993.407	−	1720.63i	−0.182006	−	0.315243i
$311$	−2909.85	−	5040.01i	−0.530554	−	0.918947i	−0.999364	−	0.0356482i	$-0.988650\pi$
$311$	−2909.85	−	5040.01i	−0.530554	−	0.918947i	0.468810	−	0.883299i	$-0.344683\pi$
$312$	−831.878	−	74.9462i	−0.150948	−	0.0135993i
$313$	−5754.23	−	3322.21i	−1.03913	−	0.599943i	−0.119545	−	0.992829i	$-0.538143\pi$
$313$	−5754.23	−	3322.21i	−1.03913	−	0.599943i	−0.919587	+	0.392886i	$0.871477\pi$
$314$	1403.19			0.252187
$315$	362.165	+	5521.83i	0.0647800	+	0.987682i
$316$	727.561			0.129521
$317$	5206.82	+	3006.16i	0.922536	+	0.532626i	0.884443	−	0.466648i	$-0.154538\pi$
$317$	5206.82	+	3006.16i	0.922536	+	0.532626i	0.0380927	+	0.999274i	$0.487872\pi$
$318$	664.559	+	1434.82i	0.117191	+	0.253021i
$319$	36.3615	+	62.9800i	0.00638198	+	0.0110539i
$320$	−1774.33	−	3073.22i	−0.309962	−	0.536870i
$321$	2351.16	+	1655.37i	0.408814	+	0.287831i
$322$	−1146.81	+	1109.34i	−0.198475	+	0.191991i
$323$			12045.7i			2.07505i
$324$	5099.89	+	1916.13i	0.874468	+	0.328554i
$325$			36.2964i			0.00619496i
$326$	−467.221	−	269.750i	−0.0793772	−	0.0458285i
$327$	1198.35	−	1702.04i	0.202657	−	0.287838i
$328$	1035.68	−	597.947i	0.174346	−	0.100659i
$329$	619.344	+	2475.11i	0.103786	+	0.414763i
$330$	4.44861	+	9.60479i	0.000742085	+	0.00160220i
$331$	1371.24	−	2375.06i	0.227705	−	0.394397i	−0.729422	−	0.684064i	$-0.760211\pi$
$331$	1371.24	−	2375.06i	0.227705	−	0.394397i	0.957128	+	0.289667i	$0.0935444\pi$
$332$	−5998.89			−0.991662
$333$	−1717.02	−	4794.42i	−0.282560	−	0.788988i
$334$		−	2629.70i		−	0.430811i
$335$	−2051.14	+	3552.68i	−0.334525	+	0.579414i
$336$	−4635.89	−	1788.79i	−0.752704	−	0.290436i
$337$	1953.27	+	3383.16i	0.315731	+	0.546862i	0.979593	−	0.200993i	$-0.0644169\pi$
$337$	1953.27	+	3383.16i	0.315731	+	0.546862i	−0.663862	+	0.747856i	$0.731084\pi$
$338$	−1252.17	+	722.940i	−0.201506	+	0.116339i
$339$	332.402	−	3689.56i	0.0532555	−	0.591119i
$340$	3828.47	−	6631.10i	0.610670	−	1.05771i
$341$	62.7377			0.00996316
$342$	−2508.52	−	455.698i	−0.396624	−	0.0720506i
$343$	−4262.62	−	4709.96i	−0.671019	−	0.741440i
$344$	419.350	+	242.112i	0.0657262	+	0.0379471i
$345$	−6193.48	+	2868.61i	−0.966509	+	0.447654i
$346$	−2072.36	+	1196.48i	−0.321996	+	0.185904i
$347$	−509.871	+	294.374i	−0.0788799	+	0.0455413i	−0.538921	−	0.842356i	$-0.681168\pi$
$347$	−509.871	+	294.374i	−0.0788799	+	0.0455413i	0.460041	+	0.887898i	$0.347835\pi$
$348$	9104.33	+	6410.04i	1.40242	+	0.987397i
$349$	−6360.33	−	3672.14i	−0.975532	−	0.563224i	−0.0746138	−	0.997213i	$-0.523772\pi$
$349$	−6360.33	−	3672.14i	−0.975532	−	0.563224i	−0.900918	+	0.433989i	$0.857106\pi$
$350$	9.36780	−	32.7743i	0.00143066	−	0.00500532i
$351$	−1943.64	+	504.683i	−0.295566	+	0.0767464i
$352$	−32.2913			−0.00488957
$353$	−4370.77	+	7570.40i	−0.659016	+	1.14145i	0.321855	+	0.946789i	$0.395694\pi$
$353$	−4370.77	+	7570.40i	−0.659016	+	1.14145i	−0.980871	+	0.194660i	$0.937640\pi$
$354$	1341.78	+	944.701i	0.201454	+	0.141837i
$355$	−250.740	+	144.765i	−0.0374870	+	0.0216431i
$356$	−884.148	−	1531.39i	−0.131628	−	0.227987i
$357$	−1378.54	−	8802.58i	−0.204369	−	1.30499i
$358$	−996.797	+	1726.50i	−0.147157	+	0.254884i
$359$		−	7817.81i		−	1.14933i	−0.818390	−	0.574663i	$-0.805133\pi$
$359$		−	7817.81i		−	1.14933i	0.818390	−	0.574663i	$-0.194867\pi$
$360$	2559.32	+	2170.16i	0.374689	+	0.317715i
$361$	−10068.0			−1.46785
$362$	267.976	−	464.148i	0.0389075	−	0.0673897i
$363$	6887.85	+	620.545i	0.995918	+	0.0897249i
$364$	1921.79	−	480.887i	0.276728	−	0.0692454i
$365$	6982.19	−	4031.17i	1.00127	−	0.578085i
$366$	709.150	+	63.8892i	0.101278	+	0.00912443i
$367$	−2084.12	−	1203.27i	−0.296431	−	0.171145i	0.344407	−	0.938820i	$-0.388080\pi$
$367$	−2084.12	−	1203.27i	−0.296431	−	0.171145i	−0.640839	+	0.767676i	$0.721413\pi$
$368$		−	6129.05i		−	0.868204i
$369$	1859.47	−	2192.92i	0.262331	−	0.309374i
$370$		−	1514.94i		−	0.212859i
$371$	−5398.87	−	5581.22i	−0.755514	−	0.781031i
$372$	8716.16	−	4037.03i	1.21482	−	0.562662i
$373$	−2185.08	−	3784.67i	−0.303322	−	0.525370i	0.673564	−	0.739129i	$-0.264763\pi$
$373$	−2185.08	−	3784.67i	−0.303322	−	0.525370i	−0.976886	+	0.213759i	$0.931429\pi$
$374$	−8.52152	−	14.7597i	−0.00117817	−	0.00204066i
$375$	4221.90	−	5996.47i	0.581381	−	0.825750i
$376$	1339.86	+	773.570i	0.183772	+	0.106101i
$377$	−4104.12			−0.560671
$378$	1885.29	+	45.9274i	0.256531	+	0.00624934i
$379$	11260.9			1.52620			0.763102	−	0.646278i	$-0.223675\pi$
$379$	11260.9			1.52620			0.763102	+	0.646278i	$0.223675\pi$
$380$	9318.22	+	5379.88i	1.25793	+	0.726268i
$381$	−305.628	+	434.090i	−0.0410965	+	0.0583704i
$382$	−1206.70	−	2090.07i	−0.161624	−	0.279940i
$383$	1486.57	+	2574.82i	0.198330	+	0.343517i	0.947987	−	0.318309i	$-0.103115\pi$
$383$	1486.57	+	2574.82i	0.198330	+	0.343517i	−0.749657	+	0.661826i	$0.769782\pi$
$384$	−5899.83	+	2732.60i	−0.784048	+	0.363144i
$385$	−36.1405	−	37.3611i	−0.00478413	−	0.00494571i
$386$			2410.72i			0.317882i
$387$	1145.42	+	208.077i	0.150452	+	0.0273311i
$388$		−	10942.8i		−	1.43179i
$389$	−5714.27	−	3299.13i	−0.744794	−	0.430007i	0.0790159	−	0.996873i	$-0.474822\pi$
$389$	−5714.27	−	3299.13i	−0.744794	−	0.430007i	−0.823810	+	0.566866i	$0.808156\pi$
$390$	−594.954	−	53.6010i	−0.0772479	−	0.00695947i
$391$	9517.53	−	5494.95i	1.23100	−	0.710720i
$392$	−3849.90	−	127.903i	−0.496044	−	0.0164798i
$393$	−2447.07	−	220.463i	−0.314092	−	0.0282974i
$394$	−181.987	+	315.210i	−0.0232699	+	0.0403047i
$395$	1077.37			0.137237
$396$	−48.1790	+	17.2543i	−0.00611385	+	0.00218955i
$397$			5908.48i			0.746947i	0.927641	+	0.373474i	$0.121833\pi$
$397$			5908.48i			0.746947i	−0.927641	+	0.373474i	$0.878167\pi$
$398$	−1476.12	+	2556.71i	−0.185907	+	0.322001i
$399$	12369.7	−	1937.16i	1.55202	−	0.243056i
$400$	65.4693	+	113.396i	0.00818366	+	0.0141745i
$401$	−4847.53	+	2798.72i	−0.603676	+	0.348532i	−0.770486	−	0.637457i	$-0.779986\pi$
$401$	−4847.53	+	2798.72i	−0.603676	+	0.348532i	0.166811	+	0.985989i	$0.446653\pi$
$402$	1143.13	+	804.835i	0.141826	+	0.0998546i
$403$	−1770.30	+	3066.25i	−0.218821	+	0.379009i
$404$	−11713.9			−1.44254
$405$	7551.93	+	2837.40i	0.926564	+	0.348127i
$406$	3705.87	+	1059.24i	0.453003	+	0.129481i
$407$	41.4283	+	23.9187i	0.00504552	+	0.00291303i
$408$	−4417.70	−	3110.35i	−0.536051	−	0.377415i
$409$	−948.568	+	547.656i	−0.114679	+	0.0662099i	−0.556242	−	0.831020i	$-0.687757\pi$
$409$	−948.568	+	547.656i	−0.114679	+	0.0662099i	0.441563	+	0.897230i	$0.354424\pi$
$410$	740.708	−	427.648i	0.0892219	−	0.0515123i
$411$	−12350.4	+	5720.30i	−1.48224	+	0.686525i
$412$	649.115	+	374.767i	0.0776204	+	0.0448141i
$413$	−7748.24	−	2214.66i	−0.923162	−	0.263865i
$414$	784.269	+	2189.90i	0.0931031	+	0.259971i
$415$	−8883.16			−1.05074
$416$	911.178	−	1578.21i	0.107390	−	0.186005i
$417$	−579.251	+	6429.50i	−0.0680241	+	0.755046i
$418$	20.7408	−	11.9747i	0.00242695	−	0.00140120i
$419$	−6796.78	−	11772.4i	−0.792468	−	1.37260i	−0.924434	−	0.381341i	$-0.875462\pi$
$419$	−6796.78	−	11772.4i	−0.792468	−	1.37260i	0.131966	−	0.991254i	$-0.457871\pi$
$420$	−7425.11	−	2865.03i	−0.862639	−	0.332855i
$421$	2842.13	−	4922.72i	0.329019	−	0.569878i	−0.653298	−	0.757101i	$-0.726615\pi$
$421$	2842.13	−	4922.72i	0.329019	−	0.569878i	0.982318	+	0.187222i	$0.0599485\pi$
$422$		−	3566.49i		−	0.411407i
$423$	3659.72	+	664.825i	0.420666	+	0.0764182i
$424$	−4708.68			−0.539324
$425$	−117.392	+	203.329i	−0.0133984	+	0.0232068i
$426$	41.4685	+	89.5327i	0.00471633	+	0.0101828i
$427$	−3392.00	+	848.778i	−0.384427	+	0.0961949i
$428$	−3581.48	+	2067.77i	−0.404480	+	0.233527i
$429$	10.8592	−	15.4236i	0.00122212	−	0.00173581i
$430$	299.916	+	173.157i	0.0336355	+	0.0194194i
$431$			4806.22i			0.537140i	0.963260	+	0.268570i	$0.0865511\pi$
$431$			4806.22i			0.537140i	−0.963260	+	0.268570i	$0.913449\pi$
$432$	−5161.95	+	5082.54i	−0.574894	+	0.566050i
$433$		−	9621.49i		−	1.06785i	−0.845532	−	0.533925i	$-0.820716\pi$
$433$		−	9621.49i		−	1.06785i	0.845532	−	0.533925i	$-0.179284\pi$
$434$	2389.89	−	2311.81i	0.264328	−	0.255692i
$435$	13481.7	+	9491.99i	1.48597	+	1.04622i
$436$	1496.89	+	2592.68i	0.164422	+	0.284787i
$437$	7721.67	+	13374.3i	0.845257	+	1.46403i
$438$	−1154.75	−	2493.16i	−0.125972	−	0.271981i
$439$	11200.0	+	6466.31i	1.21764	+	0.703007i	0.964413	−	0.264399i	$-0.0851737\pi$
$439$	11200.0	+	6466.31i	1.21764	+	0.703007i	0.253230	+	0.967406i	$0.418507\pi$
$440$	−31.5202			−0.00341516
$441$	−8817.61	+	2831.22i	−0.952123	+	0.305714i
$442$	961.823			0.103505
$443$	11401.0	+	6582.35i	1.22275	+	0.705953i	0.965502	−	0.260394i	$-0.0838524\pi$
$443$	11401.0	+	6582.35i	1.22275	+	0.705953i	0.257244	+	0.966347i	$0.417186\pi$
$444$	7294.76	+	657.205i	0.779716	+	0.0702467i
$445$	−1309.25	−	2267.68i	−0.139470	−	0.241569i
$446$	−432.995	−	749.969i	−0.0459706	−	0.0796235i
$447$	−524.319	+	5819.78i	−0.0554798	+	0.615807i
$448$	4268.59	−	4129.13i	0.450160	−	0.435453i
$449$			7787.86i			0.818557i	0.912410	+	0.409278i	$0.134219\pi$
$449$			7787.86i			0.818557i	−0.912410	+	0.409278i	$0.865781\pi$
$450$	−37.9022	−	32.1389i	−0.00397050	−	0.00336676i
$451$			27.0077i			0.00281983i
$452$	4614.09	+	2663.95i	0.480152	+	0.277216i
$453$	1038.61	+	2242.42i	0.107723	+	0.232579i
$454$	3525.34	−	2035.36i	0.364433	−	0.210406i
$455$	2845.78	−	712.098i	0.293214	−	0.0733707i
$456$	4370.75	−	6207.88i	0.448858	−	0.637524i
$457$	−2408.56	+	4171.76i	−0.246538	+	0.427017i	−0.962563	−	0.271058i	$-0.912626\pi$
$457$	−2408.56	+	4171.76i	−0.246538	+	0.427017i	0.716025	+	0.698075i	$0.245960\pi$
$458$	−3870.71			−0.394904
$459$	−12520.3	−	3459.05i	−1.27320	−	0.351753i
$460$		−	9816.65i		−	0.995008i
$461$	−25.6446	+	44.4177i	−0.00259086	+	0.00448750i	−0.867318	−	0.497755i	$-0.834158\pi$
$461$	−25.6446	+	44.4177i	−0.00259086	+	0.00448750i	0.864727	+	0.502242i	$0.167491\pi$
$462$	−13.7862	+	11.1243i	−0.00138830	+	0.00112024i
$463$	4787.43	+	8292.07i	0.480542	+	0.832322i	0.999751	−	0.0223247i	$-0.00710677\pi$
$463$	4787.43	+	8292.07i	0.480542	+	0.832322i	−0.519209	+	0.854647i	$0.673773\pi$
$464$	−12822.0	+	7402.77i	−1.28286	+	0.740657i
$465$	12906.9	−	5978.04i	1.28719	−	0.596183i
$466$	40.5820	−	70.2901i	0.00403418	−	0.00698740i
$467$	12806.5			1.26898			0.634492	−	0.772929i	$-0.281209\pi$
$467$	12806.5			1.26898			0.634492	+	0.772929i	$0.281209\pi$
$468$	516.201	−	2841.58i	0.0509859	−	0.280667i
$469$	−6601.09	−	1886.77i	−0.649915	−	0.185764i
$470$	958.262	+	553.253i	0.0940453	+	0.0542971i
$471$	−901.404	+	10005.3i	−0.0881837	+	0.978811i
$472$	−4231.89	+	2443.28i	−0.412688	+	0.238265i
$473$	−9.47047	+	5.46778i	−0.000920619	+	0.000531520i
$474$	32.9452	−	365.681i	0.00319245	−	0.0354352i
$475$	−285.723	−	164.962i	−0.0275998	−	0.0159347i
$476$	12321.0	+	3521.67i	1.18641	+	0.339108i
$477$	−10657.7	+	3816.84i	−1.02302	+	0.366375i
$478$	3463.49			0.331415
$479$	−2542.79	+	4404.24i	−0.242553	+	0.420114i	−0.961441	−	0.275012i	$-0.911318\pi$
$479$	−2542.79	+	4404.24i	−0.242553	+	0.420114i	0.718888	+	0.695126i	$0.244652\pi$
$480$	−6643.21	+	3076.91i	−0.631708	+	0.292586i
$481$	−2338.01	+	1349.85i	−0.221630	+	0.127958i
$482$	1936.53	+	3354.17i	0.183001	+	0.316967i
$483$	−7173.30	−	8889.79i	−0.675769	−	0.837473i
$484$	−4973.19	+	8613.81i	−0.467054	+	0.808961i
$485$		−	16204.1i		−	1.51709i
$486$	1194.00	−	2476.50i	0.111442	−	0.231145i
$487$	16991.3			1.58100			0.790501	−	0.612461i	$-0.209820\pi$
$487$	16991.3			1.58100			0.790501	+	0.612461i	$0.209820\pi$
$488$	−1060.14	+	1836.21i	−0.0983405	+	0.170331i
$489$	2223.56	−	3158.17i	0.205629	−	0.292060i
$490$	−2753.43	−	91.4755i	−0.253851	−	0.00843355i
$491$	8055.59	−	4650.90i	0.740415	−	0.427479i	−0.0818052	−	0.996648i	$-0.526069\pi$
$491$	8055.59	−	4650.90i	0.740415	−	0.427479i	0.822220	+	0.569170i	$0.192735\pi$
$492$	1737.89	+	3752.19i	0.159248	+	0.343825i
$493$	−22990.8	−	13273.8i	−2.10032	−	1.21262i
$494$			1351.58i			0.123098i
$495$	−71.3435	+	25.5502i	−0.00647808	+	0.00231999i
$496$			12772.6i			1.15627i
$497$	−336.890	−	348.268i	−0.0304056	−	0.0314325i
$498$	−271.640	+	3015.11i	−0.0244427	+	0.271306i
$499$	250.332	+	433.588i	0.0224577	+	0.0388979i	0.877036	−	0.480425i	$-0.159518\pi$
$499$	250.332	+	433.588i	0.0224577	+	0.0388979i	−0.854578	+	0.519323i	$0.826184\pi$
$500$	5273.69	+	9134.30i	0.471693	+	0.816997i
$501$	18750.7	+	1689.30i	1.67210	+	0.150644i
$502$	1937.05	+	1118.35i	0.172220	+	0.0994315i
$503$	−3581.09			−0.317441			−0.158721	−	0.987324i	$-0.550737\pi$
$503$	−3581.09			−0.317441			−0.158721	+	0.987324i	$0.550737\pi$
$504$	−2483.55	+	5036.70i	−0.219496	+	0.445144i
$505$	−17345.9			−1.52848
$506$	−18.9228	−	10.9251i	−0.00166249	−	0.000959842i
$507$	−4350.44	−	9392.84i	−0.381085	−	0.822782i
$508$	−381.768	−	661.241i	−0.0333429	−	0.0577516i
$509$	−5085.37	−	8808.13i	−0.442839	−	0.767020i	0.555060	−	0.831811i	$-0.312695\pi$
$509$	−5085.37	−	8808.13i	−0.442839	−	0.767020i	−0.997899	+	0.0647904i	$0.979362\pi$
$510$	−3159.51	−	2224.50i	−0.274325	−	0.193142i
$511$	9381.15	+	9697.99i	0.812128	+	0.839557i
$512$		−	11213.1i		−	0.967882i
$513$	4860.76	−	17594.0i	0.418338	−	1.51421i
$514$			1549.65i			0.132981i
$515$	961.210	+	554.955i	0.0822446	+	0.0474839i
$516$	−963.895	+	1369.04i	−0.0822348	+	0.116800i
$517$	−30.2591	+	17.4701i	−0.00257407	+	0.00148614i
$518$	2459.52	−	615.443i	0.208620	−	0.0522027i
$519$	−7200.05	−	15545.3i	−0.608954	−	1.31476i
$520$	889.422	−	1540.52i	0.0750072	−	0.129916i
$521$	−389.899			−0.0327865			−0.0163933	−	0.999866i	$-0.505218\pi$
$521$	−389.899			−0.0327865			−0.0163933	+	0.999866i	$0.505218\pi$
$522$	3634.02	−	4285.69i	0.304707	−	0.359348i
$523$			14306.4i			1.19613i	0.801448	+	0.598065i	$0.204063\pi$
$523$			14306.4i			1.19613i	−0.801448	+	0.598065i	$0.795937\pi$
$524$	1766.84	−	3060.25i	0.147299	−	0.255130i
$525$	227.675	+	87.8500i	0.0189268	+	0.00730302i
$526$	−598.865	−	1037.26i	−0.0496421	−	0.0859827i
$527$	−19834.1	+	11451.2i	−1.63944	+	0.946532i
$528$	6.10589	−	67.7734i	0.000503266	−	0.00558609i
$529$	961.351	−	1665.11i	0.0790130	−	0.136854i
$530$	−3367.62			−0.276000
$531$	−7598.02	+	8960.53i	−0.620953	+	0.732305i
$532$	−4948.76	+	17313.8i	−0.403301	+	1.41099i
$533$	−1319.98	−	762.090i	−0.107269	−	0.0619320i
$534$	−809.730	+	375.039i	−0.0656188	+	0.0303924i
$535$	−5303.46	+	3061.96i	−0.428577	+	0.247439i
$536$	−3605.35	+	2081.55i	−0.290536	+	0.167741i
$537$	−11670.3	−	8216.63i	−0.937820	−	0.660286i
$538$	3443.07	+	1987.86i	0.275913	+	0.159299i
$539$	45.9740	−	73.8523i	0.00367392	−	0.00590175i
$540$	−8267.67	+	8140.49i	−0.658859	+	0.648724i
$541$	21775.6			1.73051			0.865257	−	0.501328i	$-0.167155\pi$
$541$	21775.6			1.73051			0.865257	+	0.501328i	$0.167155\pi$
$542$	−1309.03	+	2267.30i	−0.103741	+	0.179685i
$543$	3137.40	+	2208.93i	0.247954	+	0.174575i
$544$	10208.6	−	5893.96i	0.804581	−	0.464525i
$545$	2216.59	+	3839.25i	0.174217	+	0.301753i
$546$	−154.678	−	987.689i	−0.0121238	−	0.0774161i
$547$	8960.85	−	15520.7i	0.700436	−	1.21319i	−0.267878	−	0.963453i	$-0.586322\pi$
$547$	8960.85	−	15520.7i	0.700436	−	1.21319i	0.968314	−	0.249738i	$-0.0803444\pi$
$548$		−	19575.4i		−	1.52595i
$549$	−911.107	+	5015.46i	−0.0708290	+	0.389899i
$550$	0.466799			3.61897e−5
$551$	18652.7	−	32307.4i	1.44216	−	2.49790i
$552$	−6898.78	−	621.530i	−0.531941	−	0.0479240i
$553$	437.682	+	1749.12i	0.0336566	+	0.134503i
$554$	−1871.83	+	1080.70i	−0.143550	+	0.0828783i
$555$	10802.1	+	973.189i	0.826168	+	0.0744317i
$556$	−8040.62	−	4642.25i	−0.613306	−	0.354092i
$557$		−	19309.8i		−	1.46891i	−0.678657	−	0.734455i	$-0.737438\pi$
$557$		−	19309.8i		−	1.46891i	0.678657	−	0.734455i	$-0.262562\pi$
$558$	−1634.38	−	4563.65i	−0.123994	−	0.346227i
$559$		−	617.148i		−	0.0466951i
$560$	7606.28	−	7357.77i	0.573971	−	0.555219i
$561$	110.716	−	51.2801i	0.00833235	−	0.00385926i
$562$	−2068.52	−	3582.78i	−0.155259	−	0.268916i
$563$	3232.24	+	5598.41i	0.241959	+	0.419085i	0.961272	−	0.275601i	$-0.0888768\pi$
$563$	3232.24	+	5598.41i	0.241959	+	0.419085i	−0.719313	+	0.694686i	$0.755543\pi$
$564$	−3079.74	+	4374.23i	−0.229930	+	0.326575i
$565$	6832.55	+	3944.78i	0.508757	+	0.293731i
$566$	399.527			0.0296702
$567$	−1538.58	+	13413.3i	−0.113958	+	0.993486i
$568$	−293.821			−0.0217050
$569$	17286.9	+	9980.61i	1.27365	+	0.735341i	0.975673	−	0.219233i	$-0.0703555\pi$
$569$	17286.9	+	9980.61i	1.27365	+	0.735341i	0.297975	+	0.954574i	$0.403689\pi$
$570$	3125.94	−	4439.84i	0.229704	−	0.326253i
$571$	6257.56	+	10838.4i	0.458617	+	0.794349i	0.998888	−	0.0471426i	$-0.0150115\pi$
$571$	6257.56	+	10838.4i	0.458617	+	0.794349i	−0.540271	+	0.841491i	$0.681678\pi$
$572$	13.5646	+	23.4945i	0.000991545	+	0.00171741i
$573$	15678.1	−	7261.58i	1.14304	−	0.529419i
$574$	995.203	+	1028.82i	0.0723675	+	0.0748117i
$575$			301.007i			0.0218310i
$576$	−2919.17	−	8151.15i	−0.211166	−	0.589638i
$577$		−	547.118i		−	0.0394746i	−0.999805	−	0.0197373i	$-0.993717\pi$
$577$		−	547.118i		−	0.0394746i	0.999805	−	0.0197373i	$-0.00628298\pi$
$578$	2299.93	+	1327.87i	0.165509	+	0.0955569i
$579$	−17189.4	−	1548.64i	−1.23379	−	0.111156i
$580$	−20536.4	+	11856.7i	−1.47022	+	0.848832i
$581$	−3608.77	−	14421.9i	−0.257689	−	1.02981i
$582$	−5499.98	−	495.508i	−0.391721	−	0.0352912i
$583$	53.1697	−	92.0926i	0.00377712	−	0.00654217i
$584$	8181.85			0.579739
$585$	764.391	−	4207.81i	0.0540234	−	0.297387i
$586$			5682.98i			0.400617i
$587$	902.414	−	1563.03i	0.0634525	−	0.109903i	−0.832554	−	0.553944i	$-0.813122\pi$
$587$	902.414	−	1563.03i	0.0634525	−	0.109903i	0.896006	+	0.444041i	$0.146456\pi$
$588$	1634.95	−	13218.6i	0.114667	−	0.927088i
$589$	−16091.6	−	27871.4i	−1.12571	−	1.94978i
$590$	−3026.62	+	1747.42i	−0.211193	+	0.121933i
$591$	−2130.66	−	1500.12i	−0.148297	−	0.104411i
$592$	−4869.55	+	8434.31i	−0.338070	+	0.585554i
$593$	20359.7			1.40990			0.704951	−	0.709256i	$-0.250969\pi$
$593$	20359.7			1.40990			0.704951	+	0.709256i	$0.250969\pi$
$594$	6.49060	+	24.9967i	0.000448338	+	0.00172664i
$595$	18244.9	+	5214.89i	1.25709	+	0.359311i
$596$	−7278.10	−	4202.01i	−0.500206	−	0.288794i
$597$	−17282.1	−	12167.7i	−1.18477	−	0.834155i
$598$	1067.91	−	616.557i	0.0730268	−	0.0421620i
$599$	−3739.33	+	2158.90i	−0.255067	+	0.147263i	−0.622082	−	0.782952i	$-0.713713\pi$
$599$	−3739.33	+	2158.90i	−0.255067	+	0.147263i	0.367015	+	0.930215i	$0.380380\pi$
$600$	134.276	−	62.1922i	0.00913634	−	0.00423164i
$601$	6928.17	+	3999.98i	0.470227	+	0.271485i	0.716335	−	0.697757i	$-0.245818\pi$
$601$	6928.17	+	3999.98i	0.470227	+	0.271485i	−0.246108	+	0.969242i	$0.579152\pi$
$602$	−159.281	+	557.262i	−0.0107837	+	0.0377281i
$603$	−6473.11	+	7633.90i	−0.437157	+	0.515549i
$604$	−3554.24			−0.239437
$605$	−7364.30	+	12755.3i	−0.494878	+	0.857154i
$606$	−530.423	+	5887.53i	−0.0355561	+	0.394661i
$607$	−3079.67	+	1778.05i	−0.205931	+	0.118894i	−0.599419	−	0.800435i	$-0.704602\pi$
$607$	−3079.67	+	1778.05i	−0.205931	+	0.118894i	0.393488	+	0.919330i	$0.371268\pi$
$608$	8282.37	+	14345.5i	0.552458	+	0.956886i
$609$	−9933.40	+	25743.8i	−0.660955	+	1.71296i
$610$	−758.204	+	1313.25i	−0.0503258	+	0.0871669i
$611$		−	1971.85i		−	0.130560i
$612$	12082.1	−	14248.7i	0.798022	−	0.941127i
$613$	−7113.75			−0.468714			−0.234357	−	0.972151i	$-0.575298\pi$
$613$	−7113.75			−0.468714			−0.234357	+	0.972151i	$0.575298\pi$
$614$	−2121.16	+	3673.96i	−0.139419	+	0.241480i
$615$	2573.46	+	5556.25i	0.168735	+	0.364308i
$616$	−12.8051	−	51.1734i	−0.000837551	−	0.00334714i
$617$	790.942	−	456.650i	0.0516080	−	0.0297959i	−0.473974	−	0.880539i	$-0.657181\pi$
$617$	790.942	−	456.650i	0.0516080	−	0.0297959i	0.525582	+	0.850743i	$0.323848\pi$
$618$	217.755	−	309.283i	0.0141738	−	0.0201314i
$619$	−819.836	−	473.333i	−0.0532342	−	0.0307348i	0.473147	−	0.880984i	$-0.343118\pi$
$619$	−819.836	−	473.333i	−0.0532342	−	0.0307348i	−0.526381	+	0.850249i	$0.676451\pi$
$620$			20457.4i			1.32514i
$621$	−16118.6	+	4185.35i	−1.04158	+	0.270454i
$622$		−	4223.91i		−	0.272288i
$623$	3149.72	−	3046.82i	0.202554	−	0.195936i
$624$	3140.07	+	2210.81i	0.201448	+	0.141832i
$625$	7650.79	+	13251.6i	0.489651	+	0.848100i
$626$	−2411.24	−	4176.39i	−0.153950	−	0.266649i
$627$	72.0603	+	155.582i	0.00458981	+	0.00990964i
$628$	−12512.4	−	7224.06i	−0.795065	−	0.459031i
$629$	−17463.0			−1.10699
$630$	−1776.22	+	3602.22i	−0.112327	+	0.227803i
$631$	3209.46			0.202482			0.101241	−	0.994862i	$-0.467719\pi$
$631$	3209.46			0.202482			0.101241	+	0.994862i	$0.467719\pi$
$632$	946.863	+	546.671i	0.0595952	+	0.0344073i
$633$	25430.4	+	2291.09i	1.59679	+	0.143859i
$634$	2181.85	+	3779.08i	0.136676	+	0.236730i
$635$	−565.322	−	979.167i	−0.0353293	−	0.0611922i
$636$	1460.92	−	16215.8i	0.0910840	−	1.01100i
$637$	2312.20	+	4330.87i	0.143819	+	0.269380i
$638$			52.7820i			0.00327533i
$639$	−665.040	+	238.170i	−0.0411715	+	0.0147447i
$640$		−	13847.3i		−	0.855253i
$641$	12387.1	+	7151.71i	0.763279	+	0.440679i	0.830472	−	0.557061i	$-0.188071\pi$
$641$	12387.1	+	7151.71i	0.763279	+	0.440679i	−0.0671928	+	0.997740i	$0.521404\pi$
$642$	877.111	+	1893.73i	0.0539202	+	0.116417i
$643$	−844.276	+	487.443i	−0.0517807	+	0.0298956i	−0.525667	−	0.850691i	$-0.676184\pi$
$643$	−844.276	+	487.443i	−0.0517807	+	0.0298956i	0.473886	+	0.880586i	$0.342851\pi$
$644$	15937.4	−	3988.01i	0.975190	−	0.244021i
$645$	−1427.34	+	2027.28i	−0.0871339	+	0.123758i
$646$	−4371.36	+	7571.43i	−0.266237	+	0.461136i
$647$	−12668.5			−0.769783			−0.384891	−	0.922962i	$-0.625761\pi$
$647$	−12668.5			−0.769783			−0.384891	+	0.922962i	$0.625761\pi$
$648$	5197.38	+	6325.62i	0.315081	+	0.383478i
$649$		−	110.357i		−	0.00667470i
$650$	−13.1719	+	22.8144i	−0.000794836	+	0.00137670i
$651$	14948.8	+	18525.9i	0.899985	+	1.11534i
$652$	2777.51	+	4810.78i	0.166834	+	0.288964i
$653$	−13746.7	+	7936.65i	−0.823812	+	0.475628i	−0.851729	−	0.523982i	$-0.824446\pi$
$653$	−13746.7	+	7936.65i	−0.823812	+	0.475628i	0.0279172	+	0.999610i	$0.491113\pi$
$654$	1370.90	−	634.952i	0.0819668	−	0.0379642i
$655$	2616.34	−	4531.63i	0.156074	−	0.270329i
$656$	−5498.45			−0.327254
$657$	18518.9	−	6632.18i	1.09968	−	0.393829i
$658$	−508.918	+	1780.50i	−0.0301515	+	0.105488i
$659$	−26410.9	−	15248.4i	−1.56119	−	0.901353i	−0.997137	−	0.0756145i	$-0.975908\pi$
$659$	−26410.9	−	15248.4i	−1.56119	−	0.901353i	−0.564053	−	0.825739i	$-0.690759\pi$
$660$	9.77954	−	108.550i	0.000576770	−	0.00640196i
$661$	14464.7	−	8351.23i	0.851155	−	0.491415i	−0.00988528	−	0.999951i	$-0.503147\pi$
$661$	14464.7	−	8351.23i	0.851155	−	0.491415i	0.861040	+	0.508536i	$0.169813\pi$
$662$	1723.81	−	995.243i	0.101205	−	0.0584308i
$663$	−617.870	+	6858.16i	−0.0361932	+	0.401733i
$664$	−7807.08	−	4507.42i	−0.456285	−	0.263436i
$665$	−7328.13	+	25638.3i	−0.427327	+	1.49505i
$666$	660.638	−	3636.67i	0.0384372	−	0.211589i
$667$	−34035.5			−1.97580
$668$	−13538.5	+	23449.3i	−0.784160	+	1.35821i
$669$	5625.71	−	2605.64i	0.325116	−	0.150583i
$670$	−2578.52	+	1488.71i	−0.148682	+	0.0858416i
$671$	−23.9418	−	41.4685i	−0.00137744	−	0.00238580i
$672$	−7694.19	−	9535.33i	−0.441681	−	0.547371i
$673$	−12445.2	+	21555.7i	−0.712820	+	1.23464i	0.250975	+	0.967994i	$0.419249\pi$
$673$	−12445.2	+	21555.7i	−0.712820	+	1.23464i	−0.963794	+	0.266646i	$0.914084\pi$
$674$			2835.35i			0.162038i
$675$	253.511	−	249.611i	0.0144557	−	0.0142334i
$676$	14887.6			0.847043
$677$	−756.276	+	1309.91i	−0.0429336	+	0.0743632i	−0.886694	−	0.462357i	$-0.847004\pi$
$677$	−756.276	+	1309.91i	−0.0429336	+	0.0743632i	0.843760	+	0.536721i	$0.180337\pi$
$678$	1547.87	−	2198.47i	0.0876776	−	0.124531i
$679$	26307.5	−	6582.90i	1.48688	−	0.372060i
$680$	9964.90	−	5753.23i	0.561965	−	0.324451i
$681$	12248.2	+	26444.5i	0.689210	+	1.48804i
$682$	39.4342	+	22.7674i	0.00221410	+	0.00127831i
$683$			2180.44i			0.122156i	0.998133	+	0.0610778i	$0.0194538\pi$
$683$			2180.44i			0.122156i	−0.998133	+	0.0610778i	$0.980546\pi$
$684$	20022.7	+	16978.1i	1.11928	+	0.949086i
$685$		−	28987.3i		−	1.61686i
$686$	−970.066	−	4507.37i	−0.0539902	−	0.250863i
$687$	2486.52	−	27599.6i	0.138088	−	1.53274i
$688$	−1113.17	−	1928.08i	−0.0616852	−	0.106842i
$689$	3000.63	+	5197.24i	0.165914	+	0.287372i
$690$	−4933.97	−	444.514i	−0.272222	−	0.0245252i
$691$	24166.2	+	13952.4i	1.33043	+	0.768124i	0.985365	−	0.170455i	$-0.0545237\pi$
$691$	24166.2	+	13952.4i	1.33043	+	0.768124i	0.345064	+	0.938579i	$0.387857\pi$
$692$	24639.2			1.35353
$693$	−70.4642	−	105.447i	−0.00386250	−	0.00578009i
$694$	−427.311			−0.0233725
$695$	−11906.6	−	6874.25i	−0.649844	−	0.375187i
$696$	7032.22	+	15182.9i	0.382982	+	0.826879i
$697$	−4929.59	−	8538.30i	−0.267893	−	0.464004i
$698$	−2665.22	−	4616.30i	−0.144527	−	0.250329i
$699$	475.125	+	334.519i	0.0257094	+	0.0181011i
$700$	−252.266	+	244.024i	−0.0136211	+	0.0131761i
$701$			15696.6i			0.845722i	0.906195	+	0.422861i	$0.138974\pi$
$701$			15696.6i			0.845722i	−0.906195	+	0.422861i	$0.861026\pi$
$702$	−1404.84	−	388.120i	−0.0755302	−	0.0208670i
$703$		−	24539.6i		−	1.31654i
$704$	70.4336	+	40.6648i	0.00377069	+	0.00217701i
$705$	−4560.48	+	6477.36i	−0.243628	+	0.346030i
$706$	−5494.56	+	3172.29i	−0.292904	+	0.169108i
$707$	−7046.76	−	28161.2i	−0.374852	−	1.49804i
$708$	−7101.21	−	15331.9i	−0.376949	−	0.813853i
$709$	9253.46	−	16027.5i	0.490157	−	0.848976i	−0.509779	−	0.860305i	$-0.670273\pi$
$709$	9253.46	−	16027.5i	0.490157	−	0.848976i	0.999936	+	0.0113291i	$0.00360624\pi$
$710$	−210.139			−0.0111076
$711$	2586.28	+	469.823i	0.136418	+	0.0247816i
$712$		−	2657.31i		−	0.139869i
$713$	−14681.1	+	25428.5i	−0.771126	+	1.33563i
$714$	2327.95	−	6033.20i	0.122019	−	0.316228i
$715$	20.0864	+	34.7907i	0.00105062	+	0.00181972i
$716$	17777.1	−	10263.6i	0.927879	−	0.535711i
$717$	−2224.93	+	24696.0i	−0.115888	+	1.28631i
$718$	2837.06	−	4913.94i	0.147463	−	0.255413i
$719$	−12998.8			−0.674232			−0.337116	−	0.941463i	$-0.609451\pi$
$719$	−12998.8			−0.674232			−0.337116	+	0.941463i	$0.609451\pi$
$720$	−5201.72	−	14524.7i	−0.269245	−	0.751810i
$721$	−510.483	+	1785.98i	−0.0263681	+	0.0922517i
$722$	−6328.32	−	3653.66i	−0.326199	−	0.188331i
$723$	−25160.5	+	11653.5i	−1.29423	+	0.599444i
$724$	−4779.14	+	2759.24i	−0.245325	+	0.141639i
$725$	629.705	−	363.561i	0.0322575	−	0.0186239i
$726$	4104.21	+	2889.63i	0.209809	+	0.147719i
$727$	−1646.14	−	950.399i	−0.0839779	−	0.0484846i	0.457423	−	0.889249i	$-0.348773\pi$
$727$	−1646.14	−	950.399i	−0.0839779	−	0.0484846i	−0.541401	+	0.840765i	$0.682106\pi$
$728$	2862.38	+	818.148i	0.145724	+	0.0416519i
$729$	16891.4	+	10104.6i	0.858171	+	0.513364i
$730$	5851.61			0.296682
$731$	1996.01	−	3457.20i	0.100992	−	0.174923i
$732$	−5994.64	−	4220.62i	−0.302689	−	0.213113i
$733$	−4804.26	+	2773.74i	−0.242087	+	0.139769i	−0.616135	−	0.787640i	$-0.711303\pi$
$733$	−4804.26	+	2773.74i	−0.242087	+	0.139769i	0.374049	+	0.927409i	$0.377969\pi$
$734$	−873.327	−	1512.65i	−0.0439170	−	0.0760665i
$735$	2421.04	−	19574.2i	0.121498	−	0.982319i
$736$	7556.41	−	13088.1i	0.378442	−	0.655480i
$737$		−	94.0181i		−	0.00469905i
$738$	1964.59	−	703.577i	0.0979913	−	0.0350936i
$739$	−15681.5			−0.780586			−0.390293	−	0.920691i	$-0.627626\pi$
$739$	−15681.5			−0.780586			−0.390293	+	0.920691i	$0.627626\pi$
$740$	−7799.36	+	13508.9i	−0.387446	+	0.671076i
$741$	−9637.29	−	868.249i	−0.477780	−	0.0430445i
$742$	−1368.09	−	5467.35i	−0.0676876	−	0.270503i
$743$	15659.4	−	9040.97i	0.773201	−	0.446408i	−0.0608145	−	0.998149i	$-0.519370\pi$
$743$	15659.4	−	9040.97i	0.773201	−	0.446408i	0.834015	+	0.551741i	$0.186036\pi$
$744$	14376.7	+	1295.24i	0.708436	+	0.0638249i
$745$	−10777.4	−	6222.35i	−0.530006	−	0.305999i
$746$		−	3171.84i		−	0.155669i
$747$	−21324.4	−	3873.78i	−1.04447	−	0.189738i
$748$			175.485i			0.00857804i
$749$	−7125.64	−	7366.30i	−0.347617	−	0.359358i
$750$	4829.81	−	2237.00i	0.235146	−	0.108912i
$751$	−11091.4	−	19210.8i	−0.538921	−	0.933438i	−0.998962	−	0.0455407i	$-0.985499\pi$
$751$	−11091.4	−	19210.8i	−0.538921	−	0.933438i	0.460042	−	0.887897i	$-0.347834\pi$
$752$	−3556.70	−	6160.39i	−0.172473	−	0.298732i
$753$	−9218.63	+	13093.4i	−0.446143	+	0.633667i
$754$	−2579.67	−	1489.38i	−0.124597	−	0.0719361i
$755$	−5263.12			−0.253701
$756$	−16574.9	−	10115.6i	−0.797385	−	0.486640i
$757$	−2531.12			−0.121526			−0.0607630	−	0.998152i	$-0.519353\pi$
$757$	−2531.12			−0.121526			−0.0607630	+	0.998152i	$0.519353\pi$
$758$	7078.10	+	4086.54i	0.339166	+	0.195818i
$759$	90.0559	−	127.909i	0.00430675	−	0.00611698i
$760$	8084.62	+	14003.0i	0.385868	+	0.668344i
$761$	−1897.02	−	3285.73i	−0.0903637	−	0.156514i	0.817301	−	0.576212i	$-0.195470\pi$
$761$	−1897.02	−	3285.73i	−0.0903637	−	0.156514i	−0.907664	+	0.419697i	$0.862136\pi$
$762$	−349.635	+	161.939i	−0.0166220	+	0.00769873i
$763$	−5332.57	+	5158.35i	−0.253017	+	0.244751i
$764$			24849.8i			1.17675i
$765$	17891.2	−	21099.5i	0.845564	−	0.997194i
$766$			2157.89i			0.101786i
$767$	5393.59	+	3113.99i	0.253913	+	0.146597i
$768$	8576.22	+	772.654i	0.402953	+	0.0363031i
$769$	−5524.12	+	3189.35i	−0.259044	+	0.149559i	−0.623898	−	0.781506i	$-0.714452\pi$
$769$	−5524.12	+	3189.35i	−0.259044	+	0.149559i	0.364854	+	0.931065i	$0.381119\pi$
$770$	−9.15811	−	36.5989i	−0.000428617	−	0.00171290i
$771$	−11049.6	−	995.485i	−0.516135	−	0.0465000i
$772$	12411.1	−	21496.7i	0.578609	−	1.00218i
$773$	−29728.9			−1.38328

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.628557 + 0.362898i) q^{2} +(-2.99138 + 4.24872i) q^{3} +(-3.73661 - 6.47200i) q^{4} +(-5.53318 - 9.58374i) q^{5} +(-3.42210 + 1.58500i) q^{6} +(13.3114 - 12.8765i) q^{7} -11.2304i q^{8} +(-9.10332 - 25.4191i) q^{9} +O(q^{10})\)	\(q+(0.628557 + 0.362898i) q^{2} +(-2.99138 + 4.24872i) q^{3} +(-3.73661 - 6.47200i) q^{4} +(-5.53318 - 9.58374i) q^{5} +(-3.42210 + 1.58500i) q^{6} +(13.3114 - 12.8765i) q^{7} -11.2304i q^{8} +(-9.10332 - 25.4191i) q^{9} -8.03191i q^{10} +(0.219645 + 0.126812i) q^{11} +(38.6754 + 3.48437i) q^{12} +(-12.3956 + 7.15663i) q^{13} +(13.0399 - 3.26296i) q^{14} +(57.2705 + 5.15965i) q^{15} +(-25.8174 + 44.7170i) q^{16} -92.5854 q^{17} +(3.50257 - 19.2809i) q^{18} -130.104i q^{19} +(-41.3506 + 71.6214i) q^{20} +(14.8894 + 95.0753i) q^{21} +(0.0920395 + 0.159417i) q^{22} +(-102.797 + 59.3500i) q^{23} +(47.7148 + 33.5944i) q^{24} +(1.26793 - 2.19612i) q^{25} -10.3885 q^{26} +(135.230 + 37.3606i) q^{27} +(-133.077 - 38.0370i) q^{28} +(248.320 + 143.368i) q^{29} +(34.1254 + 24.0265i) q^{30} +(214.225 - 123.683i) q^{31} +(-110.262 + 63.6597i) q^{32} +(-1.19583 + 0.553867i) q^{33} +(-58.1952 - 33.5990i) q^{34} +(-197.060 - 56.3252i) q^{35} +(-130.497 + 153.898i) q^{36} +188.615 q^{37} +(47.2144 - 81.7777i) q^{38} +(6.67351 - 74.0738i) q^{39} +(-107.629 + 62.1397i) q^{40} +(53.2437 + 92.2207i) q^{41} +(-25.1438 + 65.1636i) q^{42} +(-21.5586 + 37.3406i) q^{43} -1.89539i q^{44} +(-193.240 + 227.892i) q^{45} -86.1520 q^{46} +(-68.8818 + 119.307i) q^{47} +(-112.761 - 243.457i) q^{48} +(11.3890 - 342.811i) q^{49} +(1.59393 - 0.920258i) q^{50} +(276.958 - 393.370i) q^{51} +(92.6354 + 53.4830i) q^{52} -419.280i q^{53} +(71.4418 + 72.5580i) q^{54} -2.80669i q^{55} +(-144.609 - 149.493i) q^{56} +(552.775 + 389.190i) q^{57} +(104.056 + 180.230i) q^{58} +(-217.560 - 376.825i) q^{59} +(-180.604 - 389.934i) q^{60} +(-163.504 - 94.3989i) q^{61} +179.537 q^{62} +(-448.488 - 221.145i) q^{63} +320.670 q^{64} +(137.175 + 79.1977i) q^{65} +(-0.952645 - 0.0858263i) q^{66} +(-185.350 - 321.035i) q^{67} +(345.956 + 599.213i) q^{68} +(55.3435 - 614.296i) q^{69} +(-103.423 - 106.916i) q^{70} -26.1630i q^{71} +(-285.466 + 102.234i) q^{72} +728.545i q^{73} +(118.555 + 68.4480i) q^{74} +(5.53785 + 11.9565i) q^{75} +(-842.032 + 486.147i) q^{76} +(4.55669 - 1.14022i) q^{77} +(31.0759 - 44.1378i) q^{78} +(-48.6779 + 84.3125i) q^{79} +571.409 q^{80} +(-563.259 + 462.796i) q^{81} +77.2880i q^{82} +(401.359 - 695.174i) q^{83} +(559.691 - 451.623i) q^{84} +(512.291 + 887.315i) q^{85} +(-27.1017 + 15.6471i) q^{86} +(-1351.95 + 626.177i) q^{87} +(1.42415 - 2.46670i) q^{88} +236.618 q^{89} +(-204.164 + 73.1170i) q^{90} +(-72.8512 + 254.878i) q^{91} +(768.227 + 443.536i) q^{92} +(-115.333 + 1280.16i) q^{93} +(-86.5924 + 49.9941i) q^{94} +(-1246.88 + 719.887i) q^{95} +(59.3623 - 658.903i) q^{96} +(1268.09 + 732.133i) q^{97} +(131.564 - 211.343i) q^{98} +(1.22395 - 6.73758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44q - 6q^{2} + 78q^{4} + 5q^{7} + O(q^{10}) \)	\( 44q - 6q^{2} + 78q^{4} + 5q^{7} - 18q^{11} + 204q^{14} + 66q^{15} - 242q^{16} - 210q^{18} - 57q^{21} - 34q^{22} - 102q^{23} - 352q^{25} + 300q^{28} + 246q^{29} - 144q^{30} + 1068q^{32} - 1818q^{36} + 328q^{37} - 798q^{39} - 1158q^{42} - 170q^{43} + 968q^{46} - 79q^{49} + 288q^{50} - 204q^{51} + 1212q^{56} + 324q^{57} - 538q^{58} + 5316q^{60} + 783q^{63} - 808q^{64} + 4350q^{65} - 590q^{67} + 384q^{70} + 4284q^{72} - 5304q^{74} - 2787q^{77} + 612q^{78} - 302q^{79} - 3720q^{81} + 7050q^{84} - 612q^{85} - 13692q^{86} + 1294q^{88} + 210q^{91} - 10194q^{92} - 4266q^{93} + 6336q^{95} + 1014q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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