LMFDB - Embedded newform 63.4.h.a.25.7

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.7
Character	$\chi$	$=$	63.25
Dual form			63.4.h.a.58.7

$q$-expansion

$f(q)$	$=$	$q-2.65476 q^{2} +(-0.794408 + 5.13507i) q^{3} -0.952261 q^{4} +(-3.67781 + 6.37015i) q^{5} +(2.10896 - 13.6324i) q^{6} +(-1.32557 - 18.4728i) q^{7} +23.7661 q^{8} +(-25.7378 - 8.15868i) q^{9} +O(q^{10})$	\(q-2.65476 q^{2} +(-0.794408 + 5.13507i) q^{3} -0.952261 q^{4} +(-3.67781 + 6.37015i) q^{5} +(2.10896 - 13.6324i) q^{6} +(-1.32557 - 18.4728i) q^{7} +23.7661 q^{8} +(-25.7378 - 8.15868i) q^{9} +(9.76368 - 16.9112i) q^{10} +(-5.67162 - 9.82353i) q^{11} +(0.756484 - 4.88992i) q^{12} +(-30.2941 - 52.4710i) q^{13} +(3.51906 + 49.0407i) q^{14} +(-29.7895 - 23.9463i) q^{15} -55.4751 q^{16} +(-5.29282 + 9.16743i) q^{17} +(68.3277 + 21.6593i) q^{18} +(-41.6545 - 72.1477i) q^{19} +(3.50223 - 6.06604i) q^{20} +(95.9119 + 7.86803i) q^{21} +(15.0568 + 26.0791i) q^{22} +(-43.8117 + 75.8840i) q^{23} +(-18.8800 + 122.040i) q^{24} +(35.4475 + 61.3968i) q^{25} +(80.4236 + 139.298i) q^{26} +(62.3417 - 125.684i) q^{27} +(1.26229 + 17.5909i) q^{28} +(-67.6917 + 117.246i) q^{29} +(79.0838 + 63.5716i) q^{30} +53.5029 q^{31} -42.8557 q^{32} +(54.9501 - 21.3202i) q^{33} +(14.0511 - 24.3373i) q^{34} +(122.549 + 59.4952i) q^{35} +(24.5091 + 7.76919i) q^{36} +(-149.868 - 259.578i) q^{37} +(110.583 + 191.535i) q^{38} +(293.508 - 113.879i) q^{39} +(-87.4071 + 151.393i) q^{40} +(-194.038 - 336.083i) q^{41} +(-254.623 - 20.8877i) q^{42} +(-215.569 + 373.377i) q^{43} +(5.40086 + 9.35456i) q^{44} +(146.631 - 133.948i) q^{45} +(116.309 - 201.454i) q^{46} -511.164 q^{47} +(44.0699 - 284.868i) q^{48} +(-339.486 + 48.9738i) q^{49} +(-94.1045 - 162.994i) q^{50} +(-42.8707 - 34.4617i) q^{51} +(28.8479 + 49.9660i) q^{52} +(116.232 - 201.320i) q^{53} +(-165.502 + 333.661i) q^{54} +83.4364 q^{55} +(-31.5036 - 439.025i) q^{56} +(403.574 - 156.584i) q^{57} +(179.705 - 311.259i) q^{58} +62.3632 q^{59} +(28.3673 + 22.8031i) q^{60} +340.029 q^{61} -142.037 q^{62} +(-116.596 + 486.264i) q^{63} +557.572 q^{64} +445.664 q^{65} +(-145.879 + 56.6001i) q^{66} -549.199 q^{67} +(5.04014 - 8.72978i) q^{68} +(-354.865 - 285.259i) q^{69} +(-325.339 - 157.945i) q^{70} +505.089 q^{71} +(-611.687 - 193.900i) q^{72} +(-99.1981 + 171.816i) q^{73} +(397.862 + 689.117i) q^{74} +(-343.437 + 133.251i) q^{75} +(39.6659 + 68.7034i) q^{76} +(-173.950 + 117.792i) q^{77} +(-779.192 + 302.321i) q^{78} +1177.84 q^{79} +(204.027 - 353.385i) q^{80} +(595.872 + 419.974i) q^{81} +(515.123 + 892.219i) q^{82} +(-722.688 + 1251.73i) q^{83} +(-91.3331 - 7.49242i) q^{84} +(-38.9319 - 67.4320i) q^{85} +(572.284 - 991.225i) q^{86} +(-548.289 - 440.742i) q^{87} +(-134.792 - 233.467i) q^{88} +(-507.365 - 878.783i) q^{89} +(-389.269 + 355.599i) q^{90} +(-929.126 + 629.170i) q^{91} +(41.7201 - 72.2614i) q^{92} +(-42.5031 + 274.741i) q^{93} +1357.02 q^{94} +612.788 q^{95} +(34.0449 - 220.067i) q^{96} +(551.029 - 954.410i) q^{97} +(901.252 - 130.014i) q^{98} +(65.8281 + 299.109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} + O(q^{10}) $	\( 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} - 18q^{10} + 5q^{11} - 62q^{12} - 14q^{13} - 52q^{14} + 119q^{15} + 494q^{16} - 162q^{17} - 188q^{18} + 58q^{19} - 362q^{20} - 59q^{21} - 18q^{22} - 93q^{23} + 30q^{24} - 349q^{25} - 266q^{26} + 272q^{27} - 172q^{28} + 248q^{29} + 85q^{30} - 122q^{31} + 326q^{32} + 77q^{33} + 6q^{34} + 289q^{35} - 806q^{36} - 86q^{37} - 761q^{38} - 256q^{39} - 18q^{40} - 692q^{41} - 364q^{42} - 86q^{43} - 443q^{44} + 527q^{45} - 270q^{46} + 2010q^{47} - 1013q^{48} + 317q^{49} + 239q^{50} + 1209q^{51} - 335q^{52} + 258q^{53} + 577q^{54} - 870q^{55} - 1752q^{56} + 566q^{57} + 237q^{58} + 3330q^{59} + 1669q^{60} - 878q^{61} + 1812q^{62} + 2872q^{63} + 872q^{64} + 1226q^{65} + 1330q^{66} - 590q^{67} - 1374q^{68} + 1389q^{69} + 1251q^{70} + 636q^{71} - 5970q^{72} - 338q^{73} + 1119q^{74} + 2737q^{75} + 1006q^{76} + 2269q^{77} + 157q^{78} - 266q^{79} - 4817q^{80} - 505q^{81} + 6q^{82} - 1356q^{83} - 6013q^{84} + 483q^{85} - 3343q^{86} - 5755q^{87} + 369q^{88} - 2200q^{89} + 2665q^{90} + 1552q^{91} - 396q^{92} - 129q^{93} + 2382q^{94} - 6166q^{95} - 5941q^{96} - 266q^{97} + 3601q^{98} - 5395q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.65476			−0.938599			−0.469299	−	0.883039i	$-0.655493\pi$
$2$	−2.65476			−0.938599			−0.469299	+	0.883039i	$0.655493\pi$
$3$	−0.794408	+	5.13507i	−0.152884	+	0.988244i
$3$	−0.794408	+	5.13507i	−0.152884	+	0.988244i
$4$	−0.952261			−0.119033
$5$	−3.67781	+	6.37015i	−0.328953	+	0.569763i	−0.982304	−	0.187292i	$-0.940029\pi$
$5$	−3.67781	+	6.37015i	−0.328953	+	0.569763i	0.653351	+	0.757055i	$0.273362\pi$
$6$	2.10896	−	13.6324i	0.143497	−	0.927565i
$7$	−1.32557	−	18.4728i	−0.0715740	−	0.997435i
$7$	−1.32557	−	18.4728i	−0.0715740	−	0.997435i
$8$	23.7661			1.05032
$9$	−25.7378	−	8.15868i	−0.953253	−	0.302173i
$10$	9.76368	−	16.9112i	0.308755	−	0.534779i
$11$	−5.67162	−	9.82353i	−0.155460	−	0.269264i	0.777767	−	0.628553i	$-0.216353\pi$
$11$	−5.67162	−	9.82353i	−0.155460	−	0.269264i	−0.933226	+	0.359289i	$0.883019\pi$
$12$	0.756484	−	4.88992i	0.0181982	−	0.117633i
$13$	−30.2941	−	52.4710i	−0.646314	−	1.11945i	−0.983996	−	0.178188i	$-0.942976\pi$
$13$	−30.2941	−	52.4710i	−0.646314	−	1.11945i	0.337683	−	0.941260i	$-0.390357\pi$
$14$	3.51906	+	49.0407i	0.0671792	+	0.936191i
$15$	−29.7895	−	23.9463i	−0.512774	−	0.412194i
$16$	−55.4751			−0.866799
$17$	−5.29282	+	9.16743i	−0.0755116	+	0.130790i	−0.901309	−	0.433178i	$-0.857392\pi$
$17$	−5.29282	+	9.16743i	−0.0755116	+	0.130790i	0.825797	+	0.563967i	$0.190726\pi$
$18$	68.3277	+	21.6593i	0.894722	+	0.283620i
$19$	−41.6545	−	72.1477i	−0.502958	−	0.871148i	−0.999994	−	0.00341841i	$-0.998912\pi$
$19$	−41.6545	−	72.1477i	−0.502958	−	0.871148i	0.497037	−	0.867730i	$-0.334421\pi$
$20$	3.50223	−	6.06604i	0.0391561	−	0.0678204i
$21$	95.9119	+	7.86803i	0.996652	+	0.0817593i
$22$	15.0568	+	26.0791i	0.145914	+	0.252731i
$23$	−43.8117	+	75.8840i	−0.397190	+	0.687953i	−0.993378	−	0.114892i	$-0.963348\pi$
$23$	−43.8117	+	75.8840i	−0.397190	+	0.687953i	0.596188	+	0.802845i	$0.296681\pi$
$24$	−18.8800	+	122.040i	−0.160577	+	1.03798i
$25$	35.4475	+	61.3968i	0.283580	+	0.491175i
$26$	80.4236	+	139.298i	0.606629	+	1.05071i
$27$	62.3417	−	125.684i	0.444358	−	0.895849i
$28$	1.26229	+	17.5909i	0.00851964	+	0.118727i
$29$	−67.6917	+	117.246i	−0.433450	+	0.750757i	−0.997168	−	0.0752104i	$-0.976037\pi$
$29$	−67.6917	+	117.246i	−0.433450	+	0.750757i	0.563718	+	0.825967i	$0.309370\pi$
$30$	79.0838	+	63.5716i	0.481289	+	0.386884i
$31$	53.5029			0.309981			0.154990	−	0.987916i	$-0.450465\pi$
$31$	53.5029			0.309981			0.154990	+	0.987916i	$0.450465\pi$
$32$	−42.8557			−0.236746
$33$	54.9501	−	21.3202i	0.289866	−	0.112466i
$34$	14.0511	−	24.3373i	0.0708751	−	0.122759i
$35$	122.549	+	59.4952i	0.591846	+	0.287329i
$36$	24.5091	+	7.76919i	0.113468	+	0.0359685i
$37$	−149.868	−	259.578i	−0.665894	−	1.15336i	−0.979042	−	0.203658i	$-0.934717\pi$
$37$	−149.868	−	259.578i	−0.665894	−	1.15336i	0.313148	−	0.949704i	$-0.398616\pi$
$38$	110.583	+	191.535i	0.472075	+	0.817658i
$39$	293.508	−	113.879i	1.20510	−	0.467570i
$40$	−87.4071	+	151.393i	−0.345507	+	0.598435i
$41$	−194.038	−	336.083i	−0.739112	−	1.28018i	−0.952896	−	0.303298i	$-0.901912\pi$
$41$	−194.038	−	336.083i	−0.739112	−	1.28018i	0.213784	−	0.976881i	$-0.431421\pi$
$42$	−254.623	−	20.8877i	−0.935456	−	0.0767392i
$43$	−215.569	+	373.377i	−0.764511	+	1.32417i	0.175993	+	0.984391i	$0.443686\pi$
$43$	−215.569	+	373.377i	−0.764511	+	1.32417i	−0.940505	+	0.339781i	$0.889647\pi$
$44$	5.40086	+	9.35456i	0.0185048	+	0.0320512i
$45$	146.631	−	133.948i	0.485743	−	0.443728i
$46$	116.309	−	201.454i	0.372802	−	0.645712i
$47$	−511.164			−1.58640			−0.793202	−	0.608959i	$-0.791588\pi$
$47$	−511.164			−1.58640			−0.793202	+	0.608959i	$0.791588\pi$
$48$	44.0699	−	284.868i	0.132520	−	0.856609i
$49$	−339.486	+	48.9738i	−0.989754	+	0.142781i
$50$	−94.1045	−	162.994i	−0.266168	−	0.461016i
$51$	−42.8707	−	34.4617i	−0.117708	−	0.0946195i
$52$	28.8479	+	49.9660i	0.0769324	+	0.133251i
$53$	116.232	−	201.320i	0.301240	−	0.521762i	−0.675177	−	0.737655i	$-0.735933\pi$
$53$	116.232	−	201.320i	0.301240	−	0.521762i	0.976417	+	0.215893i	$0.0692663\pi$
$54$	−165.502	+	333.661i	−0.417074	+	0.840843i
$55$	83.4364			0.204556
$56$	−31.5036	−	439.025i	−0.0751758	−	1.04763i
$57$	403.574	−	156.584i	0.937801	−	0.363860i
$58$	179.705	−	311.259i	0.406835	−	0.704659i
$59$	62.3632			0.137610			0.0688050	−	0.997630i	$-0.478081\pi$
$59$	62.3632			0.137610			0.0688050	+	0.997630i	$0.478081\pi$
$60$	28.3673	+	22.8031i	0.0610368	+	0.0490645i
$61$	340.029			0.713710			0.356855	−	0.934160i	$-0.383849\pi$
$61$	340.029			0.713710			0.356855	+	0.934160i	$0.383849\pi$
$62$	−142.037			−0.290948
$63$	−116.596	+	486.264i	−0.233170	+	0.972436i
$64$	557.572			1.08901
$65$	445.664			0.850427
$66$	−145.879	+	56.6001i	−0.272068	+	0.105560i
$67$	−549.199			−1.00142			−0.500711	−	0.865614i	$-0.666928\pi$
$67$	−549.199			−1.00142			−0.500711	+	0.865614i	$0.666928\pi$
$68$	5.04014	−	8.72978i	0.00898834	−	0.0155683i
$69$	−354.865	−	285.259i	−0.619142	−	0.497697i
$70$	−325.339	−	157.945i	−0.555506	−	0.269687i
$71$	505.089			0.844269			0.422134	−	0.906533i	$-0.361281\pi$
$71$	505.089			0.844269			0.422134	+	0.906533i	$0.361281\pi$
$72$	−611.687	−	193.900i	−1.00122	−	0.317379i
$73$	−99.1981	+	171.816i	−0.159045	+	0.275473i	−0.934524	−	0.355899i	$-0.884175\pi$
$73$	−99.1981	+	171.816i	−0.159045	+	0.275473i	0.775480	+	0.631372i	$0.217508\pi$
$74$	397.862	+	689.117i	0.625007	+	1.08254i
$75$	−343.437	+	133.251i	−0.528755	+	0.205153i
$76$	39.6659	+	68.7034i	0.0598683	+	0.103695i
$77$	−173.950	+	117.792i	−0.257447	+	0.174333i
$78$	−779.192	+	302.321i	−1.13110	+	0.438861i
$79$	1177.84			1.67744			0.838720	−	0.544562i	$-0.183304\pi$
$79$	1177.84			1.67744			0.838720	+	0.544562i	$0.183304\pi$
$80$	204.027	−	353.385i	0.285136	−	0.493870i
$81$	595.872	+	419.974i	0.817382	+	0.576095i
$82$	515.123	+	892.219i	0.693730	+	1.20157i
$83$	−722.688	+	1251.73i	−0.955726	+	1.65537i	−0.223028	+	0.974812i	$0.571594\pi$
$83$	−722.688	+	1251.73i	−0.955726	+	1.65537i	−0.732698	+	0.680554i	$0.761739\pi$
$84$	−91.3331	−	7.49242i	−0.118634	−	0.00973202i
$85$	−38.9319	−	67.4320i	−0.0496795	−	0.0860474i
$86$	572.284	−	991.225i	0.717569	−	1.24287i
$87$	−548.289	−	440.742i	−0.675664	−	0.543133i
$88$	−134.792	−	233.467i	−0.163283	−	0.282814i
$89$	−507.365	−	878.783i	−0.604277	−	1.04664i	−0.992165	−	0.124932i	$-0.960129\pi$
$89$	−507.365	−	878.783i	−0.604277	−	1.04664i	0.387889	−	0.921706i	$-0.373204\pi$
$90$	−389.269	+	355.599i	−0.455917	+	0.416482i
$91$	−929.126	+	629.170i	−1.07032	+	0.724779i
$92$	41.7201	−	72.2614i	0.0472785	−	0.0818888i
$93$	−42.5031	+	274.741i	−0.0473911	+	0.306337i
$94$	1357.02			1.48900
$95$	612.788			0.661797
$96$	34.0449	−	220.067i	0.0361947	−	0.233963i
$97$	551.029	−	954.410i	0.576789	−	0.999028i	−0.419056	−	0.907960i	$-0.637639\pi$
$97$	551.029	−	954.410i	0.576789	−	0.999028i	0.995845	−	0.0910671i	$-0.0290278\pi$
$98$	901.252	−	130.014i	0.928982	−	0.134014i
$99$	65.8281	+	299.109i	0.0668280	+	0.303653i
$100$	−33.7552	−	58.4658i	−0.0337552	−	0.0584658i
$101$	−200.936	−	348.032i	−0.197960	−	0.342876i	0.749907	−	0.661543i	$-0.230098\pi$
$101$	−200.936	−	348.032i	−0.197960	−	0.342876i	−0.947867	+	0.318667i	$0.896765\pi$
$102$	113.811	+	91.4873i	0.110480	+	0.0888098i
$103$	−14.1227	+	24.4612i	−0.0135102	+	0.0234003i	−0.872701	−	0.488254i	$-0.837634\pi$
$103$	−14.1227	+	24.4612i	−0.0135102	+	0.0234003i	0.859191	+	0.511655i	$0.170967\pi$
$104$	−719.973	−	1247.03i	−0.678838	−	1.17578i
$105$	−402.866	+	582.036i	−0.374435	+	0.540961i
$106$	−308.568	+	534.455i	−0.282743	+	0.489725i
$107$	837.694	+	1450.93i	0.756850	+	1.31090i	0.944449	+	0.328657i	$0.106596\pi$
$107$	837.694	+	1450.93i	0.756850	+	1.31090i	−0.187600	+	0.982246i	$0.560071\pi$
$108$	−59.3656	+	119.684i	−0.0528931	+	0.106635i
$109$	−197.497	+	342.074i	−0.173548	+	0.300594i	−0.939658	−	0.342116i	$-0.888857\pi$
$109$	−197.497	+	342.074i	−0.173548	+	0.300594i	0.766110	+	0.642710i	$0.222190\pi$
$110$	−221.504			−0.191996
$111$	1452.01	−	563.369i	1.24161	−	0.481735i
$112$	73.5361	+	1024.78i	0.0620402	+	0.864576i
$113$	−94.3578	−	163.433i	−0.0785525	−	0.136057i	0.824073	−	0.566483i	$-0.191697\pi$
$113$	−94.3578	−	163.433i	−0.0785525	−	0.136057i	−0.902626	+	0.430426i	$0.858363\pi$
$114$	−1071.39	+	415.692i	−0.880219	+	0.341519i
$115$	−322.262	−	558.174i	−0.261314	−	0.452608i
$116$	64.4602	−	111.648i	0.0515946	−	0.0893645i
$117$	351.611	+	1597.65i	0.277833	+	1.26242i
$118$	−165.559			−0.129161
$119$	176.364	+	85.6209i	0.135859	+	0.0659568i
$120$	−707.979	−	569.109i	−0.538578	−	0.432936i
$121$	601.165	−	1041.25i	0.451665	−	0.782306i
$122$	−902.695			−0.669887
$123$	1879.95	−	729.409i	1.37813	−	0.534704i
$124$	−50.9487			−0.0368978
$125$	−1440.93			−1.03104
$126$	309.534	−	1290.91i	0.218853	−	0.912727i
$127$	340.864			0.238164			0.119082	−	0.992884i	$-0.462005\pi$
$127$	340.864			0.238164			0.119082	+	0.992884i	$0.462005\pi$
$128$	−1137.37			−0.785396
$129$	−1746.06	−	1403.58i	−1.19172	−	0.957969i
$130$	−1183.13			−0.798210
$131$	449.959	−	779.351i	0.300100	−	0.519788i	−0.676059	−	0.736848i	$-0.736313\pi$
$131$	449.959	−	779.351i	0.300100	−	0.519788i	0.976158	+	0.217060i	$0.0696467\pi$
$132$	−52.3268	+	20.3024i	−0.0345035	+	0.0133871i
$133$	−1277.55	+	865.110i	−0.832915	+	0.564019i
$134$	1457.99			0.939934
$135$	571.346	+	859.368i	0.364249	+	0.547871i
$136$	−125.790	+	217.874i	−0.0793115	+	0.137372i
$137$	36.6587	+	63.4947i	0.0228610	+	0.0395965i	0.877230	−	0.480071i	$-0.159389\pi$
$137$	36.6587	+	63.4947i	0.0228610	+	0.0395965i	−0.854369	+	0.519668i	$0.826056\pi$
$138$	942.082	+	757.293i	0.581125	+	0.467138i
$139$	744.772	+	1289.98i	0.454466	+	0.787158i	0.998657	−	0.0518033i	$-0.0164969\pi$
$139$	744.772	+	1289.98i	0.454466	+	0.787158i	−0.544192	+	0.838961i	$0.683164\pi$
$140$	−116.699	−	56.6549i	−0.0704490	−	0.0342015i
$141$	406.073	−	2624.86i	0.242536	−	1.56775i
$142$	−1340.89			−0.792429
$143$	−343.633	+	595.190i	−0.200951	+	0.348058i
$144$	1427.81	+	452.604i	0.826278	+	0.261923i
$145$	−497.914	−	862.413i	−0.285169	−	0.493927i
$146$	263.347	−	456.130i	0.149279	−	0.258559i
$147$	18.2064	−	1782.19i	0.0102153	−	0.999948i
$148$	142.713	+	247.186i	0.0792631	+	0.137288i
$149$	−726.774	+	1258.81i	−0.399595	+	0.692119i	−0.993676	−	0.112287i	$-0.964183\pi$
$149$	−726.774	+	1258.81i	−0.399595	+	0.692119i	0.594081	+	0.804405i	$0.297516\pi$
$150$	911.741	−	353.749i	0.496289	−	0.192557i
$151$	−1020.96	−	1768.36i	−0.550230	−	0.953026i	−0.998258	−	0.0590065i	$-0.981207\pi$
$151$	−1020.96	−	1768.36i	−0.550230	−	0.953026i	0.448028	−	0.894020i	$-0.352127\pi$
$152$	−989.964	−	1714.67i	−0.528268	−	0.914986i
$153$	211.020	−	192.767i	0.111503	−	0.101858i
$154$	461.794	−	312.710i	0.241639	−	0.163629i
$155$	−196.773	+	340.821i	−0.101969	+	0.176616i
$156$	−279.496	+	108.442i	−0.143446	+	0.0556561i
$157$	−97.1388			−0.0493791			−0.0246896	−	0.999695i	$-0.507860\pi$
$157$	−97.1388			−0.0493791			−0.0246896	+	0.999695i	$0.507860\pi$
$158$	−3126.89			−1.57444
$159$	941.455	+	756.789i	0.469574	+	0.377467i
$160$	157.615	−	272.997i	0.0778784	−	0.134889i
$161$	1459.86	+	708.733i	0.714617	+	0.346932i
$162$	−1581.90	−	1114.93i	−0.767194	−	0.540722i
$163$	−972.103	−	1683.73i	−0.467122	−	0.809080i	0.532172	−	0.846636i	$-0.321376\pi$
$163$	−972.103	−	1683.73i	−0.467122	−	0.809080i	−0.999295	+	0.0375565i	$0.988043\pi$
$164$	184.774	+	320.039i	0.0879784	+	0.152383i
$165$	−66.2826	+	428.452i	−0.0312733	+	0.202151i
$166$	1918.56	−	3323.04i	0.897043	−	1.55372i
$167$	1790.86	+	3101.86i	0.829825	+	1.43730i	0.898175	+	0.439638i	$0.144893\pi$
$167$	1790.86	+	3101.86i	0.829825	+	1.43730i	−0.0683496	+	0.997661i	$0.521773\pi$
$168$	2279.45	+	186.992i	1.04681	+	0.0858736i
$169$	−736.967	+	1276.46i	−0.335443	+	0.581004i
$170$	103.355	+	179.016i	0.0466291	+	0.0807640i
$171$	483.466	+	2196.77i	0.216208	+	0.982405i
$172$	205.278	−	355.552i	0.0910018	−	0.157620i
$173$	−398.433			−0.175100			−0.0875501	−	0.996160i	$-0.527904\pi$
$173$	−398.433			−0.175100			−0.0875501	+	0.996160i	$0.527904\pi$
$174$	1455.57	+	1170.06i	0.634177	+	0.509784i
$175$	1087.18	−	736.199i	0.469618	−	0.318008i
$176$	314.634	+	544.961i	0.134752	+	0.233398i
$177$	−49.5418	+	320.239i	−0.0210384	+	0.135992i
$178$	1346.93	+	2332.96i	0.567173	+	0.982373i
$179$	−2119.43	+	3670.96i	−0.884993	+	1.53285i	−0.0392708	+	0.999229i	$0.512503\pi$
$179$	−2119.43	+	3670.96i	−0.884993	+	1.53285i	−0.845722	+	0.533624i	$0.820830\pi$
$180$	−139.631	+	127.553i	−0.0578192	+	0.0528181i
$181$	−1047.33			−0.430096			−0.215048	−	0.976603i	$-0.568991\pi$
$181$	−1047.33			−0.430096			−0.215048	+	0.976603i	$0.568991\pi$
$182$	2466.61	−	1670.29i	1.00460	−	0.680277i
$183$	−270.122	+	1746.07i	−0.109115	+	0.705319i
$184$	−1041.23	+	1803.47i	−0.417177	+	0.722572i
$185$	2204.73			0.876191
$186$	112.836	−	729.371i	0.0444812	−	0.287527i
$187$	120.075			0.0469560
$188$	486.762			0.188834
$189$	−2404.37	−	985.021i	−0.925356	−	0.379099i
$190$	−1626.80			−0.621162
$191$	56.6430			0.0214583			0.0107292	−	0.999942i	$-0.496585\pi$
$191$	56.6430			0.0214583			0.0107292	+	0.999942i	$0.496585\pi$
$192$	−442.940	+	2863.17i	−0.166492	+	1.07621i
$193$	−4931.96			−1.83943			−0.919716	−	0.392584i	$-0.871581\pi$
$193$	−4931.96			−1.83943			−0.919716	+	0.392584i	$0.871581\pi$
$194$	−1462.85	+	2533.73i	−0.541373	+	0.937686i
$195$	−354.039	+	2288.51i	−0.130017	+	0.840430i
$196$	323.279	−	46.6358i	0.117813	−	0.0169956i
$197$	1854.91			0.670846			0.335423	−	0.942068i	$-0.391121\pi$
$197$	1854.91			0.670846			0.335423	+	0.942068i	$0.391121\pi$
$198$	−174.758	−	794.063i	−0.0627247	−	0.285008i
$199$	785.414	−	1360.38i	0.279782	−	0.484596i	−0.691549	−	0.722330i	$-0.743071\pi$
$199$	785.414	−	1360.38i	0.279782	−	0.484596i	0.971330	+	0.237734i	$0.0764046\pi$
$200$	842.448	+	1459.16i	0.297850	+	0.515892i
$201$	436.288	−	2820.17i	0.153101	−	0.989650i
$202$	533.438	+	923.941i	0.185805	+	0.321823i
$203$	2255.58	+	1095.04i	0.779855	+	0.378603i
$204$	40.8241	+	32.8165i	0.0140111	+	0.0112628i
$205$	2854.53			0.972532
$206$	37.4922	−	64.9385i	0.0126806	−	0.0219635i
$207$	1746.73	−	1595.65i	0.586503	−	0.535773i
$208$	1680.57	+	2910.83i	0.560224	+	0.970336i
$209$	−472.497	+	818.388i	−0.156379	+	0.270857i
$210$	1069.51	−	1545.16i	0.351444	−	0.507745i
$211$	542.645	+	939.888i	0.177048	+	0.306657i	0.940868	−	0.338773i	$-0.110012\pi$
$211$	542.645	+	939.888i	0.177048	+	0.306657i	−0.763820	+	0.645429i	$0.776678\pi$
$212$	−110.683	+	191.709i	−0.0358573	+	0.0621067i
$213$	−401.247	+	2593.67i	−0.129075	+	0.834344i
$214$	−2223.87	−	3851.86i	−0.710378	−	1.23041i
$215$	−1585.64	−	2746.41i	−0.502977	−	0.871181i
$216$	1481.62	−	2987.02i	0.466719	−	0.940931i
$217$	−70.9218	−	988.346i	−0.0221866	−	0.309186i
$218$	524.306	−	908.124i	0.162892	−	0.282137i
$219$	−803.483	−	645.881i	−0.247919	−	0.199290i
$220$	−79.4532			−0.0243488
$221$	641.365			0.195217
$222$	−3854.73	+	1495.61i	−1.16537	+	0.452156i
$223$	2030.15	−	3516.32i	0.609636	−	1.05592i	−0.381664	−	0.924301i	$-0.624649\pi$
$223$	2030.15	−	3516.32i	0.609636	−	1.05592i	0.991300	−	0.131620i	$-0.0420178\pi$
$224$	56.8081	+	791.663i	0.0169449	+	0.236139i
$225$	−411.424	−	1869.43i	−0.121903	−	0.553904i
$226$	250.497	+	433.874i	0.0737293	+	0.127703i
$227$	−2564.59	−	4441.99i	−0.749857	−	1.29879i	−0.947891	−	0.318596i	$-0.896789\pi$
$227$	−2564.59	−	4441.99i	−0.749857	−	1.29879i	0.198033	−	0.980195i	$-0.436545\pi$
$228$	−384.307	+	149.109i	−0.111629	+	0.0433112i
$229$	2749.25	−	4761.84i	0.793343	−	1.37411i	−0.130543	−	0.991443i	$-0.541672\pi$
$229$	2749.25	−	4761.84i	0.793343	−	1.37411i	0.923886	−	0.382668i	$-0.124995\pi$
$230$	855.527	+	1481.82i	0.245269	+	0.424818i
$231$	−466.684	−	986.818i	−0.132924	−	0.281073i
$232$	−1608.77	+	2786.47i	−0.455262	+	0.788537i
$233$	−2344.75	−	4061.23i	−0.659270	−	1.14189i	−0.980805	−	0.194991i	$-0.937532\pi$
$233$	−2344.75	−	4061.23i	−0.659270	−	1.14189i	0.321536	−	0.946898i	$-0.395801\pi$
$234$	−933.442	−	4241.37i	−0.260774	−	1.18490i
$235$	1879.96	−	3256.19i	0.521852	−	0.903875i
$236$	−59.3860			−0.0163801
$237$	−935.689	+	6048.31i	−0.256454	+	1.65772i
$238$	−468.203	−	227.303i	−0.127517	−	0.0619069i
$239$	−2236.53	−	3873.78i	−0.605309	−	1.04843i	−0.992003	−	0.126218i	$-0.959716\pi$
$239$	−2236.53	−	3873.78i	−0.605309	−	1.04843i	0.386693	−	0.922208i	$-0.373617\pi$
$240$	1652.57	+	1328.42i	0.444471	+	0.357289i
$241$	429.795	+	744.427i	0.114878	+	0.198974i	0.917731	−	0.397203i	$-0.130019\pi$
$241$	429.795	+	744.427i	0.114878	+	0.198974i	−0.802853	+	0.596177i	$0.796686\pi$
$242$	−1595.95	+	2764.26i	−0.423932	+	0.734271i
$243$	−2629.96	+	2726.21i	−0.694288	+	0.719698i
$244$	−323.797			−0.0849547
$245$	936.592	−	2342.69i	0.244231	−	0.610894i
$246$	−4990.82	+	1936.40i	−1.29351	+	0.501873i
$247$	−2523.77	+	4371.30i	−0.650137	+	1.12607i
$248$	1271.55			0.325580
$249$	−5853.62	−	4705.44i	−1.48979	−	1.19757i
$250$	3825.31			0.967736
$251$	−1788.58			−0.449778			−0.224889	−	0.974384i	$-0.572202\pi$
$251$	−1788.58			−0.449778			−0.224889	+	0.974384i	$0.572202\pi$
$252$	111.030	−	463.050i	0.0277549	−	0.115752i
$253$	993.932			0.246988
$254$	−904.911			−0.223540
$255$	377.196	−	146.349i	0.0926311	−	0.0359402i
$256$	−1441.13			−0.351837
$257$	869.979	−	1506.85i	0.211159	−	0.365738i	−0.740919	−	0.671595i	$-0.765610\pi$
$257$	869.979	−	1506.85i	0.211159	−	0.365738i	0.952077	+	0.305857i	$0.0989429\pi$
$258$	4635.38	+	3726.15i	1.11855	+	0.899148i
$259$	−4596.47	+	3112.56i	−1.10274	+	0.746737i
$260$	−424.388			−0.101229
$261$	2698.81	−	2465.37i	0.640046	−	0.584684i
$262$	−1194.53	+	2068.99i	−0.281673	+	0.487872i
$263$	1257.77	+	2178.53i	0.294896	+	0.510774i	0.974961	−	0.222378i	$-0.0713818\pi$
$263$	1257.77	+	2178.53i	0.294896	+	0.510774i	−0.680065	+	0.733152i	$0.738048\pi$
$264$	1305.95	−	506.699i	0.304453	−	0.118126i
$265$	854.958	+	1480.83i	0.198187	+	0.343270i
$266$	3391.59	−	2296.66i	0.781773	−	0.529388i
$267$	4915.66	−	1907.24i	1.12672	−	0.437159i
$268$	522.980			0.119202
$269$	993.225	−	1720.32i	0.225123	−	0.389924i	−0.731234	−	0.682127i	$-0.761055\pi$
$269$	993.225	−	1720.32i	0.225123	−	0.389924i	0.956356	+	0.292203i	$0.0943884\pi$
$270$	−1516.78	−	2281.41i	−0.341884	−	0.514231i
$271$	2220.71	+	3846.38i	0.497780	+	0.862180i	0.999997	−	0.00256147i	$-0.000815341\pi$
$271$	2220.71	+	3846.38i	0.497780	+	0.862180i	−0.502217	+	0.864742i	$0.667482\pi$
$272$	293.620	−	508.564i	0.0654533	−	0.113368i
$273$	−2492.72	−	5270.94i	−0.552625	−	1.16854i
$274$	−97.3199	−	168.563i	−0.0214573	−	0.0371652i
$275$	402.089	−	696.439i	0.0881705	−	0.152716i
$276$	337.924	+	271.641i	0.0736980	+	0.0592422i
$277$	4222.69	+	7313.92i	0.915946	+	1.58646i	0.805511	+	0.592581i	$0.201891\pi$
$277$	4222.69	+	7313.92i	0.915946	+	1.58646i	0.110435	+	0.993883i	$0.464776\pi$
$278$	−1977.19	−	3424.59i	−0.426561	−	0.738825i
$279$	−1377.05	−	436.513i	−0.295490	−	0.0936679i
$280$	2912.52	+	1413.97i	0.621630	+	0.301788i
$281$	3944.00	−	6831.21i	0.837293	−	1.45023i	−0.0548575	−	0.998494i	$-0.517470\pi$
$281$	3944.00	−	6831.21i	0.837293	−	1.45023i	0.892150	−	0.451739i	$-0.149196\pi$
$282$	−1078.03	+	6968.38i	−0.227644	+	1.47149i
$283$	−7135.85			−1.49888			−0.749438	−	0.662074i	$-0.769676\pi$
$283$	−7135.85			−1.49888			−0.749438	+	0.662074i	$0.769676\pi$
$284$	−480.977			−0.100495
$285$	−486.804	+	3146.71i	−0.101178	+	0.654017i
$286$	912.263	−	1580.09i	0.188613	−	0.326687i
$287$	−5951.17	+	4029.91i	−1.22400	+	0.828844i
$288$	1103.01	+	349.646i	0.225679	+	0.0715385i
$289$	2400.47	+	4157.74i	0.488596	+	0.846273i
$290$	1321.84	+	2289.50i	0.267659	+	0.463600i
$291$	4463.22	+	3587.76i	0.899101	+	0.722743i
$292$	94.4624	−	163.614i	0.0189315	−	0.0327903i
$293$	−2502.16	−	4333.86i	−0.498900	−	0.864119i	0.501100	−	0.865390i	$-0.332929\pi$
$293$	−2502.16	−	4333.86i	−0.498900	−	0.864119i	−0.999999	+	0.00127016i	$0.999596\pi$
$294$	−48.3337	+	4731.28i	−0.00958802	+	0.938550i
$295$	−229.360	+	397.263i	−0.0452672	+	0.0784052i
$296$	−3561.76	−	6169.16i	−0.699403	−	1.21140i
$297$	−1588.24	+	100.417i	−0.310300	+	0.0196187i
$298$	1929.41	−	3341.83i	0.375059	−	0.649622i
$299$	5308.94			1.02684
$300$	327.041	−	126.890i	0.0629391	−	0.0244199i
$301$	7183.05	+	3487.22i	1.37550	+	0.667774i
$302$	2710.41	+	4694.56i	0.516445	+	0.894509i
$303$	1946.79	−	755.342i	0.369110	−	0.143212i
$304$	2310.79	+	4002.40i	0.435963	+	0.755110i
$305$	−1250.56	+	2166.04i	−0.234777	+	0.406646i
$306$	−560.206	+	511.751i	−0.104656	+	0.0956040i
$307$	−5233.06			−0.972855			−0.486428	−	0.873721i	$-0.661700\pi$
$307$	−5233.06			−0.972855			−0.486428	+	0.873721i	$0.661700\pi$
$308$	165.645	−	112.169i	0.0306445	−	0.0207513i
$309$	−114.391	−	91.9530i	−0.0210597	−	0.0169289i
$310$	522.385	−	904.798i	0.0957081	−	0.165771i
$311$	2411.03			0.439604			0.219802	−	0.975544i	$-0.429459\pi$
$311$	2411.03			0.439604			0.219802	+	0.975544i	$0.429459\pi$
$312$	6975.53	−	2706.46i	1.26574	−	0.491099i
$313$	1589.21			0.286989			0.143495	−	0.989651i	$-0.454166\pi$
$313$	1589.21			0.286989			0.143495	+	0.989651i	$0.454166\pi$
$314$	257.880			0.0463472
$315$	−2668.75	−	2531.12i	−0.477356	−	0.452738i
$316$	−1121.61			−0.199670
$317$	−3517.51			−0.623227			−0.311614	−	0.950209i	$-0.600869\pi$
$317$	−3517.51			−0.623227			−0.311614	+	0.950209i	$0.600869\pi$
$318$	−2499.33	−	2009.09i	−0.440741	−	0.354290i
$319$	1535.69			0.269536
$320$	−2050.64	+	3551.82i	−0.358233	+	0.620477i
$321$	−8116.09	+	3148.98i	−1.41120	+	0.547536i
$322$	−3875.58	−	1881.51i	−0.670739	−	0.325630i
$323$	881.878			0.151916
$324$	−567.425	−	399.924i	−0.0972951	−	0.0685741i
$325$	2147.70	−	3719.93i	0.366563	−	0.634906i
$326$	2580.70	+	4469.90i	0.438440	+	0.759401i
$327$	−1599.68	−	1285.90i	−0.270528	−	0.217464i
$328$	−4611.52	−	7987.38i	−0.776306	−	1.34460i
$329$	677.584	+	9442.62i	0.113545	+	1.58234i
$330$	175.964	−	1137.44i	0.0293531	−	0.189739i
$331$	2764.96			0.459141			0.229571	−	0.973292i	$-0.426268\pi$
$331$	2764.96			0.459141			0.229571	+	0.973292i	$0.426268\pi$
$332$	688.187	−	1191.97i	0.113763	−	0.197042i
$333$	1739.45	+	7903.70i	0.286250	+	1.30066i
$334$	−4754.30	−	8234.68i	−0.778873	−	1.34905i
$335$	2019.85	−	3498.48i	0.329421	−	0.570574i
$336$	−5320.72	−	436.480i	−0.863897	−	0.0708689i
$337$	1746.39	+	3024.83i	0.282290	+	0.488941i	0.971948	−	0.235194i	$-0.0755726\pi$
$337$	1746.39	+	3024.83i	0.282290	+	0.488941i	−0.689658	+	0.724135i	$0.742239\pi$
$338$	1956.47	−	3388.70i	0.314846	−	0.545329i
$339$	914.196	−	354.702i	0.146467	−	0.0568282i
$340$	37.0733	+	64.2129i	0.00591348	+	0.0102424i
$341$	−303.448	−	525.587i	−0.0481895	−	0.0834667i
$342$	−1283.49	−	5831.89i	−0.202933	−	0.922084i
$343$	1354.69	+	6206.32i	0.213255	+	0.976997i
$344$	−5123.23	+	8873.70i	−0.802983	+	1.39081i
$345$	3122.27	−	1211.42i	0.487238	−	0.189045i
$346$	1057.74			0.164349
$347$	2057.15			0.318252			0.159126	−	0.987258i	$-0.449132\pi$
$347$	2057.15			0.318252			0.159126	+	0.987258i	$0.449132\pi$
$348$	522.114	+	419.702i	0.0804260	+	0.0646505i
$349$	992.838	−	1719.65i	0.152279	−	0.263755i	−0.779786	−	0.626046i	$-0.784672\pi$
$349$	992.838	−	1719.65i	0.152279	−	0.263755i	0.932065	+	0.362291i	$0.118005\pi$
$350$	−2886.20	+	1954.43i	−0.440783	+	0.298482i
$351$	−8483.36	+	536.361i	−1.29005	+	0.0815636i
$352$	243.061	+	420.994i	0.0368045	+	0.0637473i
$353$	−6160.41	−	10670.1i	−0.928854	−	1.60882i	−0.785243	−	0.619188i	$-0.787462\pi$
$353$	−6160.41	−	10670.1i	−0.928854	−	1.60882i	−0.143611	−	0.989634i	$-0.545871\pi$
$354$	131.522	−	850.157i	0.0197466	−	0.127642i
$355$	−1857.62	+	3217.49i	−0.277725	+	0.481033i
$356$	483.144	+	836.830i	0.0719286	+	0.124584i
$357$	−579.774	+	837.621i	−0.0859521	+	0.124178i
$358$	5626.58	−	9745.52i	0.830653	−	1.43873i
$359$	6436.37	+	11148.1i	0.946236	+	1.63893i	0.753257	+	0.657726i	$0.228482\pi$
$359$	6436.37	+	11148.1i	0.946236	+	1.63893i	0.192979	+	0.981203i	$0.438185\pi$
$360$	3484.84	−	3183.41i	0.510186	−	0.466057i
$361$	−40.6911	+	70.4791i	−0.00593252	+	0.0102754i
$362$	2780.41			0.403688
$363$	4869.31	+	3914.20i	0.704057	+	0.565957i
$364$	884.770	−	599.134i	0.127403	−	0.0862724i
$365$	−729.662	−	1263.81i	−0.104636	−	0.181236i
$366$	717.109	−	4635.40i	0.102415	−	0.662012i
$367$	−5401.34	−	9355.39i	−0.768250	−	1.33065i	−0.938511	−	0.345248i	$-0.887795\pi$
$367$	−5401.34	−	9355.39i	−0.768250	−	1.33065i	0.170262	−	0.985399i	$-0.445539\pi$
$368$	2430.46	−	4209.68i	0.344284	−	0.596317i
$369$	2252.11	+	10233.1i	0.317725	+	1.44367i
$370$	−5853.04			−0.822392
$371$	−3873.01	−	1880.26i	−0.541985	−	0.263122i
$372$	40.4741	−	261.625i	0.00564108	−	0.0364640i
$373$	641.645	−	1111.36i	0.0890700	−	0.154274i	−0.818048	−	0.575150i	$-0.804944\pi$
$373$	641.645	−	1111.36i	0.0890700	−	0.154274i	0.907118	+	0.420876i	$0.138277\pi$
$374$	−318.771			−0.0440729
$375$	1144.68	−	7399.26i	0.157630	−	1.01892i
$376$	−12148.4			−1.66624
$377$	8202.65			1.12058
$378$	6383.02	+	2614.99i	0.868538	+	0.355822i
$379$	1490.02			0.201945			0.100973	−	0.994889i	$-0.467805\pi$
$379$	1490.02			0.201945			0.100973	+	0.994889i	$0.467805\pi$
$380$	−583.534			−0.0787755
$381$	−270.785	+	1750.36i	−0.0364114	+	0.235364i
$382$	−150.373			−0.0201408
$383$	−2757.11	+	4775.45i	−0.367837	+	0.637112i	−0.989227	−	0.146389i	$-0.953235\pi$
$383$	−2757.11	+	4775.45i	−0.367837	+	0.637112i	0.621390	+	0.783501i	$0.286568\pi$
$384$	903.540	−	5840.49i	0.120074	−	0.776163i
$385$	−110.601	−	1541.30i	−0.0146409	−	0.204031i
$386$	13093.2			1.72649
$387$	8594.54	−	7851.15i	1.12890	−	1.03126i
$388$	−524.723	+	908.847i	−0.0686567	+	0.118917i
$389$	682.473	+	1182.08i	0.0889531	+	0.154071i	0.907069	−	0.420982i	$-0.138315\pi$
$389$	682.473	+	1182.08i	0.0889531	+	0.154071i	−0.818116	+	0.575054i	$0.804981\pi$
$390$	939.888	−	6075.45i	0.122033	−	0.788826i
$391$	−463.774	−	803.281i	−0.0599849	−	0.103897i
$392$	−8068.25	+	1163.92i	−1.03956	+	0.149966i
$393$	3644.57	+	2929.69i	0.467797	+	0.376039i
$394$	−4924.33			−0.629655
$395$	−4331.88	+	7503.04i	−0.551799	+	0.955744i
$396$	−62.6855	−	284.830i	−0.00795471	−	0.0361446i
$397$	3119.14	+	5402.51i	0.394321	+	0.682984i	0.993014	−	0.117995i	$-0.0376466\pi$
$397$	3119.14	+	5402.51i	0.394321	+	0.682984i	−0.598694	+	0.800978i	$0.704313\pi$
$398$	−2085.09	+	3611.47i	−0.262603	+	0.454841i
$399$	−3427.50	−	7247.56i	−0.430049	−	0.909353i
$400$	−1966.45	−	3406.00i	−0.245807	−	0.425750i
$401$	−191.520	+	331.722i	−0.0238505	+	0.0413102i	−0.877704	−	0.479203i	$-0.840926\pi$
$401$	−191.520	+	331.722i	−0.0238505	+	0.0413102i	0.853854	+	0.520513i	$0.174259\pi$
$402$	−1158.24	+	7486.88i	−0.143701	+	0.928884i
$403$	−1620.82	−	2807.35i	−0.200345	−	0.347007i
$404$	191.344	+	331.417i	0.0235636	+	0.0408134i
$405$	−4866.79	+	2251.21i	−0.597118	+	0.276206i
$406$	−5988.02	−	2907.06i	−0.731971	−	0.355357i
$407$	−1699.98	+	2944.46i	−0.207039	+	0.358603i
$408$	−1018.87	−	819.019i	−0.123631	−	0.0993810i
$409$	9835.18			1.18904			0.594521	−	0.804080i	$-0.297342\pi$
$409$	9835.18			1.18904			0.594521	+	0.804080i	$0.297342\pi$
$410$	−7578.09			−0.912818
$411$	−355.171	+	137.804i	−0.0426260	+	0.0165386i
$412$	13.4485	−	23.2934i	0.00160815	−	0.00278540i
$413$	−82.6667	−	1152.02i	−0.00984930	−	0.137257i
$414$	−4637.15	+	4236.05i	−0.550491	+	0.502876i
$415$	−5315.81	−	9207.25i	−0.628778	−	1.08908i
$416$	1298.27	+	2248.68i	0.153012	+	0.265025i
$417$	−7215.80	+	2799.68i	−0.847385	+	0.328779i
$418$	1254.36	−	2172.62i	0.146777	−	0.254226i
$419$	−3138.73	−	5436.44i	−0.365959	−	0.633860i	0.622970	−	0.782245i	$-0.285926\pi$
$419$	−3138.73	−	5436.44i	−0.365959	−	0.633860i	−0.988930	+	0.148386i	$0.952592\pi$
$420$	383.633	−	554.250i	0.0445700	−	0.0643920i
$421$	−6522.30	+	11297.0i	−0.755054	+	1.30779i	0.190294	+	0.981727i	$0.439056\pi$
$421$	−6522.30	+	11297.0i	−0.755054	+	1.30779i	−0.945348	+	0.326064i	$0.894277\pi$
$422$	−1440.59	−	2495.18i	−0.166177	−	0.287828i
$423$	13156.3	+	4170.43i	1.51224	+	0.479369i
$424$	2762.38	−	4784.58i	0.316399	−	0.548019i
$425$	−750.468			−0.0856542
$426$	1065.21	−	6885.56i	0.121150	−	0.783114i
$427$	−450.732	−	6281.28i	−0.0510830	−	0.711879i
$428$	−797.703	−	1381.66i	−0.0900898	−	0.156040i
$429$	−2783.36	−	2237.40i	−0.313244	−	0.251802i
$430$	4209.50	+	7291.07i	0.472093	+	0.817689i
$431$	4874.53	−	8442.93i	0.544774	−	0.943577i	−0.453847	−	0.891080i	$-0.649949\pi$
$431$	4874.53	−	8442.93i	0.544774	−	0.943577i	0.998621	−	0.0524973i	$-0.0167181\pi$
$432$	−3458.41	+	6972.34i	−0.385169	+	0.776521i
$433$	−322.352			−0.0357765			−0.0178883	−	0.999840i	$-0.505694\pi$
$433$	−322.352			−0.0357765			−0.0178883	+	0.999840i	$0.505694\pi$
$434$	188.280	+	2623.82i	0.0208243	+	0.290201i
$435$	4824.09	−	1871.71i	0.531719	−	0.206303i
$436$	188.068	−	325.744i	0.0206579	−	0.0357805i
$437$	7299.81			0.799078
$438$	2133.05	+	1714.66i	0.232697	+	0.187054i
$439$	−3104.99			−0.337569			−0.168785	−	0.985653i	$-0.553984\pi$
$439$	−3104.99			−0.337569			−0.168785	+	0.985653i	$0.553984\pi$
$440$	1982.96			0.214850
$441$	9137.19	+	1509.28i	0.986631	+	0.162971i
$442$	−1702.67			−0.183230
$443$	−2399.30			−0.257324			−0.128662	−	0.991689i	$-0.541068\pi$
$443$	−2399.30			−0.257324			−0.128662	+	0.991689i	$0.541068\pi$
$444$	−1382.69	+	536.474i	−0.147792	+	0.0573422i
$445$	7463.97			0.795114
$446$	−5389.56	+	9334.98i	−0.572204	+	0.991086i
$447$	−5886.72	−	4732.04i	−0.622891	−	0.500711i
$448$	−739.100	−	10299.9i	−0.0779447	−	1.08622i
$449$	−9003.79			−0.946358			−0.473179	−	0.880966i	$-0.656894\pi$
$449$	−9003.79			−0.946358			−0.473179	+	0.880966i	$0.656894\pi$
$450$	1092.23	+	4962.87i	0.114418	+	0.519894i
$451$	−2201.01	+	3812.27i	−0.229804	+	0.398033i
$452$	89.8532	+	155.630i	0.00935031	+	0.0161952i
$453$	9891.70	−	3837.91i	1.02594	−	0.398059i
$454$	6808.36	+	11792.4i	0.703815	+	1.21904i
$455$	−590.758	−	8232.64i	−0.0608685	−	0.848246i
$456$	9591.37	−	3721.38i	0.984993	−	0.382171i
$457$	−6734.97			−0.689384			−0.344692	−	0.938716i	$-0.612017\pi$
$457$	−6734.97			−0.689384			−0.344692	+	0.938716i	$0.612017\pi$
$458$	−7298.60	+	12641.5i	−0.744631	+	1.28974i
$459$	822.237	+	1236.74i	0.0836138	+	0.125765i
$460$	306.877	+	531.527i	0.0311048	+	0.0538751i
$461$	1082.44	−	1874.84i	0.109358	−	0.189414i	−0.806152	−	0.591708i	$-0.798454\pi$
$461$	1082.44	−	1874.84i	0.109358	−	0.189414i	0.915510	+	0.402294i	$0.131787\pi$
$462$	1238.93	+	2619.76i	0.124763	+	0.263815i
$463$	−1458.61	−	2526.39i	−0.146409	−	0.253589i	0.783488	−	0.621406i	$-0.213438\pi$
$463$	−1458.61	−	2526.39i	−0.146409	−	0.253589i	−0.929898	+	0.367818i	$0.880105\pi$
$464$	3755.21	−	6504.21i	0.375714	−	0.650755i
$465$	−1593.82	−	1281.20i	−0.158950	−	0.127772i
$466$	6224.75	+	10781.6i	0.618789	+	1.07177i
$467$	870.004	+	1506.89i	0.0862077	+	0.149316i	0.905905	−	0.423481i	$-0.139192\pi$
$467$	870.004	+	1506.89i	0.0862077	+	0.149316i	−0.819698	+	0.572797i	$0.805858\pi$
$468$	−334.825	−	1521.38i	−0.0330712	−	0.150269i
$469$	728.001	+	10145.2i	0.0716758	+	0.998854i
$470$	−4990.85	+	8644.40i	−0.489810	+	0.848376i
$471$	77.1679	−	498.814i	0.00754928	−	0.0487986i
$472$	1482.13			0.144535
$473$	4890.50			0.475403
$474$	2484.03	−	16056.8i	0.240707	−	1.55593i
$475$	2953.09	−	5114.91i	0.285257	−	0.494080i
$476$	−167.944	−	81.5334i	−0.0161717	−	0.00785100i
$477$	−4634.06	+	4233.23i	−0.444820	+	0.406345i
$478$	5937.44	+	10283.9i	0.568142	+	0.984052i
$479$	5616.37	+	9727.83i	0.535738	+	0.927925i	0.999127	+	0.0417702i	$0.0132997\pi$
$479$	5616.37	+	9727.83i	0.535738	+	0.927925i	−0.463390	+	0.886155i	$0.653367\pi$
$480$	1276.65	+	1026.23i	0.121397	+	0.0975853i
$481$	−9080.21	+	15727.4i	−0.860752	+	1.49087i
$482$	−1141.00	−	1976.27i	−0.107824	−	0.186757i
$483$	−4799.12	+	6933.47i	−0.452107	+	0.653176i
$484$	−572.466	+	991.541i	−0.0537628	+	0.0931199i
$485$	4053.16	+	7020.27i	0.379473	+	0.657266i
$486$	6981.90	−	7237.43i	0.651657	−	0.675507i
$487$	−825.982	+	1430.64i	−0.0768558	+	0.133118i	−0.901892	−	0.431962i	$-0.857821\pi$
$487$	−825.982	+	1430.64i	−0.0768558	+	0.133118i	0.825036	+	0.565080i	$0.191155\pi$
$488$	8081.17			0.749625
$489$	9418.32	−	3654.24i	0.870984	−	0.337936i
$490$	−2486.43	+	6219.28i	−0.229235	+	0.573384i
$491$	−7910.90	−	13702.1i	−0.727116	−	1.25940i	−0.958097	−	0.286443i	$-0.907527\pi$
$491$	−7910.90	−	13702.1i	−0.727116	−	1.25940i	0.230982	−	0.972958i	$-0.425806\pi$
$492$	−1790.21	+	694.588i	−0.164042	+	0.0636472i
$493$	−716.560	−	1241.12i	−0.0654609	−	0.113382i
$494$	6700.00	−	11604.7i	0.610217	−	1.05693i
$495$	−2147.47	−	680.731i	−0.194993	−	0.0618113i
$496$	−2968.08			−0.268691
$497$	−669.531	−	9330.39i	−0.0604277	−	0.842103i
$498$	15539.9	+	12491.8i	1.39832	+	1.12404i
$499$	7054.82	−	12219.3i	0.632900	−	1.09622i	−0.354056	−	0.935224i	$-0.615198\pi$
$499$	7054.82	−	12219.3i	0.632900	−	1.09622i	0.986956	−	0.160991i	$-0.0514690\pi$
$500$	1372.14			0.122728
$501$	−17350.9	+	6732.04i	−1.54727	+	0.600330i
$502$	4748.25			0.422161
$503$	−12196.8			−1.08117			−0.540585	−	0.841289i	$-0.681797\pi$
$503$	−12196.8			−1.08117			−0.540585	+	0.841289i	$0.681797\pi$
$504$	−2771.03	+	11556.6i	−0.244904	+	1.02137i
$505$	2956.02			0.260478
$506$	−2638.65			−0.231823
$507$	−5969.28	−	4798.41i	−0.522890	−	0.420325i
$508$	−324.591			−0.0283492
$509$	−279.226	+	483.634i	−0.0243153	+	0.0421153i	−0.877927	−	0.478795i	$-0.841074\pi$
$509$	−279.226	+	483.634i	−0.0243153	+	0.0421153i	0.853612	+	0.520910i	$0.174407\pi$
$510$	−1001.36	+	388.522i	−0.0869434	+	0.0337334i
$511$	3305.41	+	1604.71i	0.286150	+	0.138920i
$512$	12924.8			1.11563
$513$	−11664.6	+	737.498i	−1.00391	+	0.0634724i
$514$	−2309.58	+	4000.32i	−0.198193	+	0.343281i
$515$	−103.881	−	179.927i	−0.00888842	−	0.0153952i
$516$	1662.71	+	1336.57i	0.141854	+	0.114029i
$517$	2899.13	+	5021.44i	0.246622	+	0.427162i
$518$	12202.5	−	8263.08i	1.03503	−	0.700886i
$519$	316.519	−	2045.98i	0.0267700	−	0.173042i
$520$	10591.7			0.893223
$521$	5208.33	−	9021.10i	0.437968	−	0.758583i	−0.559565	−	0.828787i	$-0.689032\pi$
$521$	5208.33	−	9021.10i	0.437968	−	0.758583i	0.997533	+	0.0702040i	$0.0223650\pi$
$522$	−7164.68	+	6544.96i	−0.600746	+	0.548784i
$523$	−4310.74	−	7466.43i	−0.360412	−	0.624252i	0.627616	−	0.778523i	$-0.284031\pi$
$523$	−4310.74	−	7466.43i	−0.360412	−	0.624252i	−0.988029	+	0.154270i	$0.950697\pi$
$524$	−428.478	+	742.145i	−0.0357216	+	0.0618717i
$525$	2916.76	+	6167.59i	0.242472	+	0.512716i
$526$	−3339.08	−	5783.46i	−0.276789	−	0.479412i
$527$	−283.181	+	490.484i	−0.0234071	+	0.0405423i
$528$	−3048.36	+	1182.74i	−0.251256	+	0.0974854i
$529$	2244.57	+	3887.72i	0.184480	+	0.319530i
$530$	−2269.71	−	3931.25i	−0.186018	−	0.322193i
$531$	−1605.09	−	508.801i	−0.131177	−	0.0415821i
$532$	1216.56	−	823.810i	0.0991440	−	0.0671366i
$533$	−11756.4	+	20362.7i	−0.955396	+	1.65479i
$534$	−13049.9	+	5063.27i	−1.05754	+	0.410317i
$535$	−12323.5			−0.995872
$536$	−13052.3			−1.05182
$537$	−17166.9	−	13799.7i	−1.37953	−	1.10894i
$538$	−2636.77	+	4567.02i	−0.211300	+	0.365982i
$539$	2406.53	+	3057.19i	0.192313	+	0.244309i
$540$	−544.070	−	818.342i	−0.0433575	−	0.0652145i
$541$	−5922.96	−	10258.9i	−0.470699	−	0.815274i	0.528740	−	0.848784i	$-0.322665\pi$
$541$	−5922.96	−	10258.9i	−0.470699	−	0.815274i	−0.999438	+	0.0335100i	$0.989331\pi$
$542$	−5895.44	−	10211.2i	−0.467216	−	0.809241i
$543$	832.008	−	5378.11i	0.0657548	−	0.425040i
$544$	226.827	−	392.876i	0.0178771	−	0.0309640i
$545$	−1452.71	−	2516.16i	−0.114178	−	0.197763i
$546$	6617.58	+	13993.1i	0.518693	+	1.09679i
$547$	6313.20	−	10934.8i	0.493479	−	0.854730i	−0.506493	−	0.862244i	$-0.669058\pi$
$547$	6313.20	−	10934.8i	0.493479	−	0.854730i	0.999972	+	0.00751393i	$0.00239178\pi$
$548$	−34.9086	−	60.4635i	−0.00272121	−	0.00471327i
$549$	−8751.62	−	2774.19i	−0.680346	−	0.215664i
$550$	−1067.45	+	1848.88i	−0.0827567	+	0.143339i
$551$	11278.7			0.872027
$552$	−8433.76	−	6779.49i	−0.650298	−	0.522743i
$553$	−1561.31	−	21758.0i	−0.120061	−	1.67314i
$554$	−11210.2	−	19416.7i	−0.859705	−	1.48905i
$555$	−1751.46	+	11321.5i	−0.133956	+	0.865891i
$556$	−709.217	−	1228.40i	−0.0540962	−	0.0936974i
$557$	10649.8	−	18446.0i	0.810136	−	1.40320i	−0.102633	−	0.994719i	$-0.532727\pi$
$557$	10649.8	−	18446.0i	0.810136	−	1.40320i	0.912769	−	0.408477i	$-0.133940\pi$
$558$	3655.73	+	1158.84i	0.277347	+	0.0879166i
$559$	26121.9			1.97646
$560$	−6798.44	−	3300.50i	−0.513012	−	0.249056i
$561$	−95.3889	+	616.595i	−0.00717883	+	0.0464040i
$562$	−10470.4	+	18135.2i	−0.785882	+	1.36119i
$563$	2526.22			0.189107			0.0945536	−	0.995520i	$-0.469858\pi$
$563$	2526.22			0.189107			0.0945536	+	0.995520i	$0.469858\pi$
$564$	−386.688	+	2499.55i	−0.0288697	+	0.186614i
$565$	1388.12			0.103360
$566$	18944.0			1.40684
$567$	6968.20	−	11564.1i	0.516115	−	0.856520i
$568$	12004.0			0.886754
$569$	−470.986			−0.0347008			−0.0173504	−	0.999849i	$-0.505523\pi$
$569$	−470.986			−0.0347008			−0.0173504	+	0.999849i	$0.505523\pi$
$570$	1292.35	−	8353.75i	0.0949658	−	0.613860i
$571$	−10616.2			−0.778060			−0.389030	−	0.921225i	$-0.627190\pi$
$571$	−10616.2			−0.778060			−0.389030	+	0.921225i	$0.627190\pi$
$572$	327.228	−	566.776i	0.0239198	−	0.0414303i
$573$	−44.9977	+	290.866i	−0.00328064	+	0.0212061i
$574$	15798.9	−	10698.4i	1.14884	−	0.777952i
$575$	−6212.05			−0.450540
$576$	−14350.7	−	4549.06i	−1.03810	−	0.329069i
$577$	10567.4	−	18303.2i	0.762434	−	1.32057i	−0.179158	−	0.983820i	$-0.557337\pi$
$577$	10567.4	−	18303.2i	0.762434	−	1.32057i	0.941592	−	0.336755i	$-0.109329\pi$
$578$	−6372.67	−	11037.8i	−0.458596	−	0.794311i
$579$	3917.99	−	25326.0i	0.281220	−	1.81781i
$580$	474.144	+	821.242i	0.0339444	+	0.0587935i
$581$	24080.9	+	11690.8i	1.71953	+	0.834794i
$582$	−11848.8	−	9524.64i	−0.843895	−	0.678366i
$583$	−2636.89			−0.187322
$584$	−2357.55	+	4083.40i	−0.167048	+	0.289336i
$585$	−11470.4	−	3636.03i	−0.810672	−	0.256976i
$586$	6642.62	+	11505.4i	0.468266	+	0.811061i
$587$	−6558.36	+	11359.4i	−0.461146	+	0.798727i	−0.999018	−	0.0442985i	$-0.985895\pi$
$587$	−6558.36	+	11359.4i	−0.461146	+	0.798727i	0.537873	+	0.843026i	$0.319228\pi$
$588$	−17.3373	+	1697.11i	−0.00121595	+	0.119026i
$589$	−2228.64	−	3860.11i	−0.155907	−	0.270039i
$590$	608.894	−	1054.64i	0.0424878	−	0.0735910i
$591$	−1473.55	+	9525.07i	−0.102562	+	0.662959i
$592$	8313.92	+	14400.1i	0.577196	+	0.999733i
$593$	−6711.80	−	11625.2i	−0.464790	−	0.805040i	0.534402	−	0.845231i	$-0.320537\pi$
$593$	−6711.80	−	11625.2i	−0.464790	−	0.805040i	−0.999192	+	0.0401902i	$0.987204\pi$
$594$	4216.39	−	266.582i	0.291247	−	0.0184141i
$595$	−1194.05	+	808.566i	−0.0822710	+	0.0557109i
$596$	692.078	−	1198.71i	0.0475648	−	0.0823847i
$597$	6361.69	+	5113.85i	0.436125	+	0.350580i
$598$	−14094.0			−0.963788
$599$	10034.0			0.684441			0.342220	−	0.939620i	$-0.388821\pi$
$599$	10034.0			0.684441			0.342220	+	0.939620i	$0.388821\pi$
$600$	−8162.15	+	3166.86i	−0.555364	+	0.215477i
$601$	−6335.96	+	10974.2i	−0.430032	+	0.744837i	−0.996876	−	0.0789886i	$-0.974831\pi$
$601$	−6335.96	+	10974.2i	−0.430032	+	0.744837i	0.566844	+	0.823825i	$0.308164\pi$
$602$	−19069.3	−	9257.73i	−1.29104	−	0.626772i
$603$	14135.2	+	4480.74i	0.954609	+	0.302603i
$604$	972.222	+	1683.94i	0.0654953	+	0.113441i
$605$	4421.94	+	7659.03i	0.297153	+	0.514684i
$606$	−5168.27	+	2005.25i	−0.346446	+	0.134419i
$607$	4986.25	−	8636.44i	0.333420	−	0.577500i	−0.649760	−	0.760139i	$-0.725131\pi$
$607$	4986.25	−	8636.44i	0.333420	−	0.577500i	0.983180	+	0.182639i	$0.0584641\pi$
$608$	1785.13	+	3091.94i	0.119073	+	0.206241i
$609$	−7414.94	+	10712.6i	−0.493380	+	0.712805i
$610$	3319.94	−	5750.30i	0.220361	−	0.381677i
$611$	15485.3	+	26821.3i	1.02531	+	1.77590i
$612$	−200.946	+	183.565i	−0.0132725	+	0.0121245i
$613$	−14113.2	+	24444.7i	−0.929895	+	1.61063i	−0.146403	+	0.989225i	$0.546770\pi$
$613$	−14113.2	+	24444.7i	−0.929895	+	1.61063i	−0.783493	+	0.621401i	$0.786564\pi$
$614$	13892.5			0.913121
$615$	−2267.66	+	14658.2i	−0.148685	+	0.961099i
$616$	−4134.10	+	2799.46i	−0.270402	+	0.183106i
$617$	98.5457	+	170.686i	0.00642999	+	0.0111371i	0.869222	−	0.494421i	$-0.164620\pi$
$617$	98.5457	+	170.686i	0.00642999	+	0.0111371i	−0.862793	+	0.505558i	$0.831287\pi$
$618$	303.679	+	244.113i	0.0197666	+	0.0158894i
$619$	−6575.78	−	11389.6i	−0.426983	−	0.739557i	0.569620	−	0.821908i	$-0.307090\pi$
$619$	−6575.78	−	11389.6i	−0.426983	−	0.739557i	−0.996603	+	0.0823513i	$0.973757\pi$
$620$	187.379	−	324.551i	0.0121376	−	0.0210230i
$621$	6806.13	+	10237.2i	0.439808	+	0.661520i
$622$	−6400.70			−0.412612
$623$	−15561.0	+	10537.3i	−1.00070	+	0.677639i
$624$	−16282.4	+	6317.45i	−1.04458	+	0.405289i
$625$	868.516	−	1504.31i	0.0555850	−	0.0962761i
$626$	−4218.98			−0.269368
$627$	−3827.12	−	3076.44i	−0.243765	−	0.195951i
$628$	92.5015			0.00587772
$629$	3172.89			0.201131
$630$	7084.89	+	6719.50i	0.448046	+	0.424939i
$631$	−342.571			−0.0216126			−0.0108063	−	0.999942i	$-0.503440\pi$
$631$	−342.571			−0.0216126			−0.0108063	+	0.999942i	$0.503440\pi$
$632$	27992.7			1.76185
$633$	−5257.47	+	2039.86i	−0.330120	+	0.128084i
$634$	9338.13			0.584960
$635$	−1253.63	+	2171.35i	−0.0783446	+	0.135697i
$636$	−896.510	−	720.661i	−0.0558946	−	0.0449309i
$637$	12854.1	+	16329.5i	0.799527	+	1.01570i
$638$	−4076.88			−0.252986
$639$	−12999.9	−	4120.86i	−0.804802	−	0.255116i
$640$	4183.04	−	7245.24i	0.258358	−	0.447490i
$641$	−9596.99	−	16622.5i	−0.591355	−	1.02426i	−0.994050	−	0.108923i	$-0.965260\pi$
$641$	−9596.99	−	16622.5i	−0.591355	−	1.02426i	0.402695	−	0.915334i	$-0.368073\pi$
$642$	21546.2	−	8359.79i	1.32455	−	0.513917i
$643$	4980.89	+	8627.15i	0.305485	+	0.529116i	0.977369	−	0.211540i	$-0.0678480\pi$
$643$	4980.89	+	8627.15i	0.305485	+	0.529116i	−0.671884	+	0.740656i	$0.734515\pi$
$644$	−1390.17	−	674.899i	−0.0850627	−	0.0412962i
$645$	15362.7	−	5960.61i	0.937837	−	0.363874i
$646$	−2341.17			−0.142589
$647$	−10665.4	+	18472.9i	−0.648065	+	1.12248i	0.335519	+	0.942033i	$0.391088\pi$
$647$	−10665.4	+	18472.9i	−0.648065	+	1.12248i	−0.983584	+	0.180449i	$0.942245\pi$
$648$	14161.5	+	9981.13i	0.858515	+	0.605086i
$649$	−353.700	−	612.627i	−0.0213928	−	0.0370535i
$650$	−5701.63	+	9875.50i	−0.344056	+	0.595922i
$651$	5131.56	+	420.962i	0.308943	+	0.0253438i
$652$	925.695	+	1603.35i	0.0556028	+	0.0963068i
$653$	−3410.51	+	5907.17i	−0.204385	+	0.354005i	−0.949937	−	0.312443i	$-0.898853\pi$
$653$	−3410.51	+	5907.17i	−0.204385	+	0.354005i	0.745552	+	0.666448i	$0.232186\pi$
$654$	4246.77	+	3413.77i	0.253917	+	0.204111i
$655$	3309.72	+	5732.60i	0.197437	+	0.341972i
$656$	10764.3	+	18644.2i	0.640661	+	1.10966i
$657$	3954.94	−	3612.85i	0.234850	−	0.214537i
$658$	−1798.82	−	25067.9i	−0.106573	−	1.48518i
$659$	−3066.00	+	5310.47i	−0.181236	+	0.313910i	−0.942302	−	0.334765i	$-0.891343\pi$
$659$	−3066.00	+	5310.47i	−0.181236	+	0.313910i	0.761066	+	0.648675i	$0.224676\pi$
$660$	63.1183	−	407.998i	0.00372254	−	0.0240626i
$661$	17153.8			1.00939			0.504695	−	0.863297i	$-0.331605\pi$
$661$	17153.8			1.00939			0.504695	+	0.863297i	$0.331605\pi$
$662$	−7340.29			−0.430949
$663$	−509.506	+	3293.45i	−0.0298455	+	0.192922i
$664$	−17175.5	+	29748.8i	−1.00382	+	1.73867i
$665$	−812.293	−	11319.9i	−0.0473675	−	0.660100i
$666$	−4617.82	−	20982.4i	−0.268674	−	1.22080i
$667$	−5931.38	−	10273.4i	−0.344324	−	0.596386i
$668$	−1705.36	−	2953.78i	−0.0987762	−	0.171085i
$669$	16443.8	+	13218.4i	0.950304	+	0.763903i
$670$	−5362.20	+	9287.61i	−0.309194	+	0.535540i
$671$	−1928.52	−	3340.29i	−0.110953	−	0.192176i
$672$	−4110.37	−	337.190i	−0.235954	−	0.0193562i
$673$	4616.02	−	7995.19i	0.264390	−	0.457937i	−0.703013	−	0.711177i	$-0.748163\pi$
$673$	4616.02	−	7995.19i	0.264390	−	0.457937i	0.967404	+	0.253239i	$0.0814960\pi$
$674$	−4636.24	−	8030.20i	−0.264957	−	0.458919i
$675$	9926.47	−	627.602i	0.566030	−	0.0357873i
$676$	701.785	−	1215.53i	0.0399286	−	0.0691583i
$677$	25076.6			1.42359			0.711797	−	0.702385i	$-0.247882\pi$
$677$	25076.6			1.42359			0.711797	+	0.702385i	$0.247882\pi$
$678$	−2426.97	+	941.647i	−0.137474	+	0.0533388i
$679$	−18361.0	−	8913.89i	−1.03775	−	0.503805i
$680$	−925.259	−	1602.60i	−0.0521795	−	0.0903776i
$681$	24847.3	−	9640.57i	1.39816	−	0.542478i
$682$	805.581	+	1395.31i	0.0452306	+	0.0783417i
$683$	−1958.77	+	3392.69i	−0.109737	+	0.190070i	−0.915664	−	0.401945i	$-0.868334\pi$
$683$	−1958.77	+	3392.69i	−0.109737	+	0.190070i	0.805927	+	0.592015i	$0.201668\pi$
$684$	−460.386	−	2091.90i	−0.0257358	−	0.116938i
$685$	−539.294			−0.0300808
$686$	−3596.38	−	16476.3i	−0.200161	−	0.917008i
$687$	22268.4	+	17900.4i	1.23667	+	0.994096i
$688$	11958.7	−	20713.1i	0.662677	−	1.14779i
$689$	−14084.6			−0.778781
$690$	−8288.86	+	3216.02i	−0.457321	+	0.177437i
$691$	−31924.9			−1.75757			−0.878784	−	0.477220i	$-0.841644\pi$
$691$	−31924.9			−1.75757			−0.878784	+	0.477220i	$0.841644\pi$
$692$	379.412			0.0208426
$693$	5438.11	−	1612.52i	0.298091	−	0.0883902i
$694$	−5461.22			−0.298711
$695$	−10956.5			−0.597991
$696$	−13030.7	−	10474.7i	−0.709665	−	0.570465i
$697$	4108.02			0.223246
$698$	−2635.75	+	4565.25i	−0.142929	+	0.247560i
$699$	22717.4	−	8814.18i	1.22926	−	0.476943i
$700$	−1035.28	+	701.053i	−0.0558998	+	0.0378533i
$701$	−8392.31			−0.452173			−0.226087	−	0.974107i	$-0.572593\pi$
$701$	−8392.31			−0.452173			−0.226087	+	0.974107i	$0.572593\pi$
$702$	22521.3	−	1423.91i	1.21084	−	0.0765555i
$703$	−12485.3	+	21625.2i	−0.669833	+	1.16018i
$704$	−3162.34	−	5477.33i	−0.169297	−	0.293231i
$705$	15227.3	+	12240.5i	0.813466	+	0.653905i
$706$	16354.4	+	28326.6i	0.871821	+	1.51004i
$707$	−6162.76	+	4173.19i	−0.327828	+	0.221993i
$708$	47.1767	−	304.951i	0.00250425	−	0.0161875i
$709$	1541.97			0.0816784			0.0408392	−	0.999166i	$-0.486997\pi$
$709$	1541.97			0.0816784			0.0408392	+	0.999166i	$0.486997\pi$
$710$	4931.53	−	8541.67i	0.260672	−	0.451497i
$711$	−30315.2	−	9609.65i	−1.59903	−	0.506878i
$712$	−12058.1	−	20885.2i	−0.634685	−	1.09931i
$713$	−2344.05	+	4060.02i	−0.123121	+	0.213252i
$714$	1539.16	−	2223.68i	0.0806745	−	0.116554i
$715$	−2527.63	−	4377.99i	−0.132207	−	0.228990i
$716$	2018.25	−	3495.71i	0.105343	−	0.182459i
$717$	21668.8	−	8407.35i	1.12864	−	0.437906i
$718$	−17087.0	−	29595.6i	−0.888136	−	1.53830i
$719$	−12510.3	−	21668.5i	−0.648896	−	1.12392i	−0.983387	−	0.181521i	$-0.941898\pi$
$719$	−12510.3	−	21668.5i	−0.648896	−	1.12392i	0.334492	−	0.942399i	$-0.391435\pi$
$720$	−8134.36	+	7430.76i	−0.421041	+	0.384623i
$721$	470.586	+	228.460i	0.0243073	+	0.0118007i
$722$	108.025	−	187.105i	0.00556825	−	0.00964450i
$723$	−4164.12	+	1615.65i	−0.214198	+	0.0831073i
$724$	997.331			0.0511955
$725$	−9598.01			−0.491670
$726$	−12926.8	−	10391.3i	−0.660827	−	0.531206i
$727$	−712.918	+	1234.81i	−0.0363695	+	0.0629939i	−0.883637	−	0.468172i	$-0.844913\pi$
$727$	−712.918	+	1234.81i	−0.0363695	+	0.0629939i	0.847268	+	0.531166i	$0.178246\pi$
$728$	−22081.7	+	14952.9i	−1.12418	+	0.761252i
$729$	−11910.0	−	15670.7i	−0.605092	−	0.796156i
$730$	1937.08	+	3355.12i	0.0982116	+	0.170107i
$731$	−2281.94	−	3952.43i	−0.115459	−	0.199981i
$732$	257.227	−	1662.72i	0.0129882	−	0.0839560i
$733$	−1294.04	+	2241.34i	−0.0652067	+	0.112941i	−0.896786	−	0.442465i	$-0.854104\pi$
$733$	−1294.04	+	2241.34i	−0.0652067	+	0.112941i	0.831579	+	0.555407i	$0.187437\pi$
$734$	14339.2	+	24836.3i	0.721078	+	1.24894i
$735$	11285.8	+	6670.52i	0.566373	+	0.334756i
$736$	1877.58	−	3252.06i	0.0940333	−	0.162870i
$737$	3114.85	+	5395.07i	0.155681	+	0.269647i
$738$	−5978.82	−	27166.5i	−0.298216	−	1.35503i
$739$	−2281.47	+	3951.62i	−0.113566	+	0.196702i	−0.917206	−	0.398414i	$-0.869561\pi$
$739$	−2281.47	+	3951.62i	−0.113566	+	0.196702i	0.803640	+	0.595116i	$0.202894\pi$
$740$	−2099.48			−0.104295
$741$	−20442.0	−	16432.3i	−1.01344	−	0.814652i
$742$	10281.9	+	4991.64i	0.508706	+	0.246966i
$743$	5519.60	+	9560.23i	0.272536	+	0.472047i	0.969511	−	0.245049i	$-0.0788042\pi$
$743$	5519.60	+	9560.23i	0.272536	+	0.472047i	−0.696974	+	0.717096i	$0.745471\pi$
$744$	−1010.13	+	6529.52i	−0.0497759	+	0.321752i
$745$	−5345.87	−	9259.31i	−0.262896	−	0.455349i
$746$	−1703.41	+	2950.40i	−0.0836010	+	0.144801i
$747$	28812.9	−	26320.7i	1.41126	−	1.28919i
$748$	−114.343			−0.00558930
$749$	25692.2	−	17397.8i	1.25337	−	0.848735i
$750$	−3038.86	+	19643.2i	−0.147951	+	0.956360i
$751$	−9589.06	+	16608.7i	−0.465925	+	0.807006i	−0.999243	−	0.0389093i	$-0.987612\pi$
$751$	−9589.06	+	16608.7i	−0.465925	+	0.807006i	0.533318	+	0.845915i	$0.320945\pi$
$752$	28356.9			1.37509
$753$	1420.86	−	9184.49i	0.0687639	−	0.444491i
$754$	−21776.0			−1.05177
$755$	15019.6			0.723999
$756$	2289.59	+	937.996i	0.110148	+	0.0451251i
$757$	−17087.1			−0.820399			−0.410199	−	0.911996i	$-0.634541\pi$
$757$	−17087.1			−0.820399			−0.410199	+	0.911996i	$0.634541\pi$
$758$	−3955.64			−0.189545
$759$	−789.588	+	5103.91i	−0.0377605	+	0.244085i
$760$	14563.6			0.695101
$761$	−17911.9	+	31024.3i	−0.853228	+	1.47783i	0.0250514	+	0.999686i	$0.492025\pi$
$761$	−17911.9	+	31024.3i	−0.853228	+	1.47783i	−0.878279	+	0.478148i	$0.841308\pi$
$762$	718.869	−	4646.78i	0.0341757	−	0.220912i
$763$	6580.85	+	3194.86i	0.312245	+	0.151588i
$764$	−53.9389			−0.00255424
$765$	451.866	+	2053.19i	0.0213559	+	0.0970368i
$766$	7319.45	−	12677.7i	0.345251	−	0.597993i
$767$	−1889.24	−	3272.26i	−0.0889393	−	0.154047i
$768$	1144.84	−	7400.28i	0.0537903	−	0.347701i
$769$	−15798.1	−	27363.1i	−0.740823	−	1.28314i	−0.952121	−	0.305722i	$-0.901102\pi$
$769$	−15798.1	−	27363.1i	−0.740823	−	1.28314i	0.211297	−	0.977422i	$-0.432231\pi$
$770$	293.618	+	4091.78i	0.0137419	+	0.191503i
$771$	7046.65	+	5664.45i	0.329155	+	0.264592i
$772$	4696.51			0.218952
$773$	−18673.5	+	32343.5i	−0.868875	+	1.50493i

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.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.65476 q^{2} +(-0.794408 + 5.13507i) q^{3} -0.952261 q^{4} +(-3.67781 + 6.37015i) q^{5} +(2.10896 - 13.6324i) q^{6} +(-1.32557 - 18.4728i) q^{7} +23.7661 q^{8} +(-25.7378 - 8.15868i) q^{9} +O(q^{10})\)	\(q-2.65476 q^{2} +(-0.794408 + 5.13507i) q^{3} -0.952261 q^{4} +(-3.67781 + 6.37015i) q^{5} +(2.10896 - 13.6324i) q^{6} +(-1.32557 - 18.4728i) q^{7} +23.7661 q^{8} +(-25.7378 - 8.15868i) q^{9} +(9.76368 - 16.9112i) q^{10} +(-5.67162 - 9.82353i) q^{11} +(0.756484 - 4.88992i) q^{12} +(-30.2941 - 52.4710i) q^{13} +(3.51906 + 49.0407i) q^{14} +(-29.7895 - 23.9463i) q^{15} -55.4751 q^{16} +(-5.29282 + 9.16743i) q^{17} +(68.3277 + 21.6593i) q^{18} +(-41.6545 - 72.1477i) q^{19} +(3.50223 - 6.06604i) q^{20} +(95.9119 + 7.86803i) q^{21} +(15.0568 + 26.0791i) q^{22} +(-43.8117 + 75.8840i) q^{23} +(-18.8800 + 122.040i) q^{24} +(35.4475 + 61.3968i) q^{25} +(80.4236 + 139.298i) q^{26} +(62.3417 - 125.684i) q^{27} +(1.26229 + 17.5909i) q^{28} +(-67.6917 + 117.246i) q^{29} +(79.0838 + 63.5716i) q^{30} +53.5029 q^{31} -42.8557 q^{32} +(54.9501 - 21.3202i) q^{33} +(14.0511 - 24.3373i) q^{34} +(122.549 + 59.4952i) q^{35} +(24.5091 + 7.76919i) q^{36} +(-149.868 - 259.578i) q^{37} +(110.583 + 191.535i) q^{38} +(293.508 - 113.879i) q^{39} +(-87.4071 + 151.393i) q^{40} +(-194.038 - 336.083i) q^{41} +(-254.623 - 20.8877i) q^{42} +(-215.569 + 373.377i) q^{43} +(5.40086 + 9.35456i) q^{44} +(146.631 - 133.948i) q^{45} +(116.309 - 201.454i) q^{46} -511.164 q^{47} +(44.0699 - 284.868i) q^{48} +(-339.486 + 48.9738i) q^{49} +(-94.1045 - 162.994i) q^{50} +(-42.8707 - 34.4617i) q^{51} +(28.8479 + 49.9660i) q^{52} +(116.232 - 201.320i) q^{53} +(-165.502 + 333.661i) q^{54} +83.4364 q^{55} +(-31.5036 - 439.025i) q^{56} +(403.574 - 156.584i) q^{57} +(179.705 - 311.259i) q^{58} +62.3632 q^{59} +(28.3673 + 22.8031i) q^{60} +340.029 q^{61} -142.037 q^{62} +(-116.596 + 486.264i) q^{63} +557.572 q^{64} +445.664 q^{65} +(-145.879 + 56.6001i) q^{66} -549.199 q^{67} +(5.04014 - 8.72978i) q^{68} +(-354.865 - 285.259i) q^{69} +(-325.339 - 157.945i) q^{70} +505.089 q^{71} +(-611.687 - 193.900i) q^{72} +(-99.1981 + 171.816i) q^{73} +(397.862 + 689.117i) q^{74} +(-343.437 + 133.251i) q^{75} +(39.6659 + 68.7034i) q^{76} +(-173.950 + 117.792i) q^{77} +(-779.192 + 302.321i) q^{78} +1177.84 q^{79} +(204.027 - 353.385i) q^{80} +(595.872 + 419.974i) q^{81} +(515.123 + 892.219i) q^{82} +(-722.688 + 1251.73i) q^{83} +(-91.3331 - 7.49242i) q^{84} +(-38.9319 - 67.4320i) q^{85} +(572.284 - 991.225i) q^{86} +(-548.289 - 440.742i) q^{87} +(-134.792 - 233.467i) q^{88} +(-507.365 - 878.783i) q^{89} +(-389.269 + 355.599i) q^{90} +(-929.126 + 629.170i) q^{91} +(41.7201 - 72.2614i) q^{92} +(-42.5031 + 274.741i) q^{93} +1357.02 q^{94} +612.788 q^{95} +(34.0449 - 220.067i) q^{96} +(551.029 - 954.410i) q^{97} +(901.252 - 130.014i) q^{98} +(65.8281 + 299.109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} + O(q^{10}) \)	\( 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} - 18q^{10} + 5q^{11} - 62q^{12} - 14q^{13} - 52q^{14} + 119q^{15} + 494q^{16} - 162q^{17} - 188q^{18} + 58q^{19} - 362q^{20} - 59q^{21} - 18q^{22} - 93q^{23} + 30q^{24} - 349q^{25} - 266q^{26} + 272q^{27} - 172q^{28} + 248q^{29} + 85q^{30} - 122q^{31} + 326q^{32} + 77q^{33} + 6q^{34} + 289q^{35} - 806q^{36} - 86q^{37} - 761q^{38} - 256q^{39} - 18q^{40} - 692q^{41} - 364q^{42} - 86q^{43} - 443q^{44} + 527q^{45} - 270q^{46} + 2010q^{47} - 1013q^{48} + 317q^{49} + 239q^{50} + 1209q^{51} - 335q^{52} + 258q^{53} + 577q^{54} - 870q^{55} - 1752q^{56} + 566q^{57} + 237q^{58} + 3330q^{59} + 1669q^{60} - 878q^{61} + 1812q^{62} + 2872q^{63} + 872q^{64} + 1226q^{65} + 1330q^{66} - 590q^{67} - 1374q^{68} + 1389q^{69} + 1251q^{70} + 636q^{71} - 5970q^{72} - 338q^{73} + 1119q^{74} + 2737q^{75} + 1006q^{76} + 2269q^{77} + 157q^{78} - 266q^{79} - 4817q^{80} - 505q^{81} + 6q^{82} - 1356q^{83} - 6013q^{84} + 483q^{85} - 3343q^{86} - 5755q^{87} + 369q^{88} - 2200q^{89} + 2665q^{90} + 1552q^{91} - 396q^{92} - 129q^{93} + 2382q^{94} - 6166q^{95} - 5941q^{96} - 266q^{97} + 3601q^{98} - 5395q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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