LMFDB - Embedded newform 63.4.o.a.20.5

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			20.5
Character	$\chi$	$=$	63.20
Dual form			63.4.o.a.41.5

$q$-expansion

$f(q)$	$=$	$q+(-3.28475 - 1.89645i) q^{2} +(-4.97559 + 1.49782i) q^{3} +(3.19307 + 5.53055i) q^{4} +(-9.97590 - 17.2788i) q^{5} +(19.1841 + 4.51602i) q^{6} +(-4.13417 + 18.0529i) q^{7} +6.12125i q^{8} +(22.5131 - 14.9051i) q^{9} +O(q^{10})$	\(q+(-3.28475 - 1.89645i) q^{2} +(-4.97559 + 1.49782i) q^{3} +(3.19307 + 5.53055i) q^{4} +(-9.97590 - 17.2788i) q^{5} +(19.1841 + 4.51602i) q^{6} +(-4.13417 + 18.0529i) q^{7} +6.12125i q^{8} +(22.5131 - 14.9051i) q^{9} +75.6753i q^{10} +(31.1676 + 17.9946i) q^{11} +(-24.1712 - 22.7352i) q^{12} +(6.59980 - 3.81040i) q^{13} +(47.8163 - 51.4592i) q^{14} +(75.5165 + 71.0301i) q^{15} +(37.1532 - 64.3512i) q^{16} -21.4747 q^{17} +(-102.217 + 6.26447i) q^{18} +97.3022i q^{19} +(63.7074 - 110.345i) q^{20} +(-6.47004 - 96.0163i) q^{21} +(-68.2518 - 118.216i) q^{22} +(-35.6964 + 20.6094i) q^{23} +(-9.16851 - 30.4568i) q^{24} +(-136.537 + 236.489i) q^{25} -28.9050 q^{26} +(-89.6909 + 107.882i) q^{27} +(-113.043 + 34.7800i) q^{28} +(-51.8612 - 29.9421i) q^{29} +(-113.348 - 376.530i) q^{30} +(61.1449 - 35.3020i) q^{31} +(-201.669 + 116.434i) q^{32} +(-182.030 - 42.8505i) q^{33} +(70.5390 + 40.7257i) q^{34} +(353.175 - 108.661i) q^{35} +(154.319 + 76.9169i) q^{36} +355.309 q^{37} +(184.529 - 319.614i) q^{38} +(-27.1307 + 28.8443i) q^{39} +(105.768 - 61.0649i) q^{40} +(7.30794 + 12.6577i) q^{41} +(-160.838 + 327.660i) q^{42} +(-48.8575 + 84.6237i) q^{43} +229.832i q^{44} +(-482.130 - 240.307i) q^{45} +156.339 q^{46} +(-234.897 + 406.853i) q^{47} +(-88.4728 + 375.834i) q^{48} +(-308.817 - 149.268i) q^{49} +(896.982 - 517.873i) q^{50} +(106.849 - 32.1651i) q^{51} +(42.1472 + 24.3337i) q^{52} +710.531i q^{53} +(499.206 - 184.271i) q^{54} -718.049i q^{55} +(-110.506 - 25.3063i) q^{56} +(-145.741 - 484.136i) q^{57} +(113.568 + 196.705i) q^{58} +(232.735 + 403.109i) q^{59} +(-151.706 + 644.452i) q^{60} +(542.558 + 313.246i) q^{61} -267.794 q^{62} +(176.007 + 468.047i) q^{63} +288.792 q^{64} +(-131.678 - 76.0243i) q^{65} +(516.659 + 485.964i) q^{66} +(-262.327 - 454.364i) q^{67} +(-68.5700 - 118.767i) q^{68} +(146.742 - 156.011i) q^{69} +(-1366.16 - 312.855i) q^{70} -115.729i q^{71} +(91.2376 + 137.808i) q^{72} +708.180i q^{73} +(-1167.10 - 673.827i) q^{74} +(325.136 - 1381.18i) q^{75} +(-538.135 + 310.692i) q^{76} +(-453.708 + 488.273i) q^{77} +(143.819 - 43.2944i) q^{78} +(128.747 - 222.997i) q^{79} -1482.55 q^{80} +(284.678 - 671.118i) q^{81} -55.4366i q^{82} +(200.583 - 347.420i) q^{83} +(510.364 - 342.369i) q^{84} +(214.229 + 371.056i) q^{85} +(320.970 - 185.312i) q^{86} +(302.888 + 71.3010i) q^{87} +(-110.149 + 190.784i) q^{88} -977.834 q^{89} +(1127.95 + 1703.68i) q^{90} +(41.5042 + 134.899i) q^{91} +(-227.962 - 131.614i) q^{92} +(-251.356 + 267.233i) q^{93} +(1543.16 - 890.942i) q^{94} +(1681.26 - 970.677i) q^{95} +(829.026 - 881.389i) q^{96} +(-521.193 - 300.911i) q^{97} +(731.308 + 1075.97i) q^{98} +(969.889 - 59.4408i) 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 $

$2$	−3.28475	−	1.89645i	−1.16134	−	0.670497i	−0.209712	−	0.977763i	$-0.567253\pi$
$2$	−3.28475	−	1.89645i	−1.16134	−	0.670497i	−0.951624	+	0.307266i	$0.900586\pi$
$3$	−4.97559	+	1.49782i	−0.957554	+	0.288255i
$3$	−4.97559	+	1.49782i	−0.957554	+	0.288255i
$4$	3.19307	+	5.53055i	0.399133	+	0.691319i
$5$	−9.97590	−	17.2788i	−0.892272	−	1.54546i	−0.837145	−	0.546981i	$-0.815777\pi$
$5$	−9.97590	−	17.2788i	−0.892272	−	1.54546i	−0.0551264	−	0.998479i	$-0.517556\pi$
$6$	19.1841	+	4.51602i	1.30532	+	0.307276i
$7$	−4.13417	+	18.0529i	−0.223224	+	0.974767i
$7$	−4.13417	+	18.0529i	−0.223224	+	0.974767i
$8$			6.12125i			0.270523i
$9$	22.5131	−	14.9051i	0.833818	−	0.552040i
$10$			75.6753i			2.39306i
$11$	31.1676	+	17.9946i	0.854307	+	0.493234i	0.862102	−	0.506735i	$-0.169148\pi$
$11$	31.1676	+	17.9946i	0.854307	+	0.493234i	−0.00779501	+	0.999970i	$0.502481\pi$
$12$	−24.1712	−	22.7352i	−0.581468	−	0.546923i
$13$	6.59980	−	3.81040i	0.140804	−	0.0812934i	−0.427943	−	0.903806i	$-0.640762\pi$
$13$	6.59980	−	3.81040i	0.140804	−	0.0812934i	0.568747	+	0.822512i	$0.307428\pi$
$14$	47.8163	−	51.4592i	0.912817	−	0.982360i
$15$	75.5165	+	71.0301i	1.29988	+	1.22266i
$16$	37.1532	−	64.3512i	0.580519	−	1.00549i
$17$	−21.4747			−0.306375			−0.153187	−	0.988197i	$-0.548954\pi$
$17$	−21.4747			−0.306375			−0.153187	+	0.988197i	$0.548954\pi$
$18$	−102.217	+	6.26447i	−1.33848	+	0.0820306i
$19$			97.3022i			1.17488i	0.809269	+	0.587438i	$0.199864\pi$
$19$			97.3022i			1.17488i	−0.809269	+	0.587438i	$0.800136\pi$
$20$	63.7074	−	110.345i	0.712271	−	1.23369i
$21$	−6.47004	−	96.0163i	−0.0672323	−	0.997737i
$22$	−68.2518	−	118.216i	−0.661424	−	1.14562i
$23$	−35.6964	+	20.6094i	−0.323618	+	0.186841i	−0.653004	−	0.757354i	$-0.726492\pi$
$23$	−35.6964	+	20.6094i	−0.323618	+	0.186841i	0.329386	+	0.944195i	$0.393158\pi$
$24$	−9.16851	−	30.4568i	−0.0779798	−	0.259041i
$25$	−136.537	+	236.489i	−1.09230	+	1.89191i
$26$	−28.9050			−0.218028
$27$	−89.6909	+	107.882i	−0.639297	+	0.768960i
$28$	−113.043	+	34.7800i	−0.762971	+	0.234743i
$29$	−51.8612	−	29.9421i	−0.332082	−	0.191728i	0.324683	−	0.945823i	$-0.394742\pi$
$29$	−51.8612	−	29.9421i	−0.332082	−	0.191728i	−0.656765	+	0.754095i	$0.728076\pi$
$30$	−113.348	−	376.530i	−0.689813	−	2.29149i
$31$	61.1449	−	35.3020i	0.354256	−	0.204530i	−0.312302	−	0.949983i	$-0.601100\pi$
$31$	61.1449	−	35.3020i	0.354256	−	0.204530i	0.666558	+	0.745453i	$0.267767\pi$
$32$	−201.669	+	116.434i	−1.11407	+	0.643211i
$33$	−182.030	−	42.8505i	−0.960222	−	0.226040i
$34$	70.5390	+	40.7257i	0.355804	+	0.205423i
$35$	353.175	−	108.661i	1.70564	−	0.524773i
$36$	154.319	+	76.9169i	0.714440	+	0.356097i
$37$	355.309			1.57872			0.789358	−	0.613933i	$-0.210414\pi$
$37$	355.309			1.57872			0.789358	+	0.613933i	$0.210414\pi$
$38$	184.529	−	319.614i	0.787752	−	1.36443i
$39$	−27.1307	+	28.8443i	−0.111394	+	0.118430i
$40$	105.768	−	61.0649i	0.418083	−	0.241380i
$41$	7.30794	+	12.6577i	0.0278368	+	0.0482147i	0.879608	−	0.475699i	$-0.157805\pi$
$41$	7.30794	+	12.6577i	0.0278368	+	0.0482147i	−0.851771	+	0.523914i	$0.824471\pi$
$42$	−160.838	+	327.660i	−0.590901	+	1.20379i
$43$	−48.8575	+	84.6237i	−0.173272	+	0.300116i	−0.939562	−	0.342379i	$-0.888767\pi$
$43$	−48.8575	+	84.6237i	−0.173272	+	0.300116i	0.766290	+	0.642495i	$0.222101\pi$
$44$			229.832i			0.787465i
$45$	−482.130	−	240.307i	−1.59715	−	0.796063i
$46$	156.339			0.501106
$47$	−234.897	+	406.853i	−0.729005	+	1.26267i	0.228299	+	0.973591i	$0.426684\pi$
$47$	−234.897	+	406.853i	−0.729005	+	1.26267i	−0.957304	+	0.289083i	$0.906650\pi$
$48$	−88.4728	+	375.834i	−0.266041	+	1.13015i
$49$	−308.817	−	149.268i	−0.900342	−	0.435184i
$50$	896.982	−	517.873i	2.53705	−	1.46477i
$51$	106.849	−	32.1651i	0.293370	−	0.0883141i
$52$	42.1472	+	24.3337i	0.112399	+	0.0648938i
$53$			710.531i			1.84149i	0.390167	+	0.920744i	$0.372417\pi$
$53$			710.531i			1.84149i	−0.390167	+	0.920744i	$0.627583\pi$
$54$	499.206	−	184.271i	1.25802	−	0.464374i
$55$		−	718.049i		−	1.76040i
$56$	−110.506	−	25.3063i	−0.263697	−	0.0603874i
$57$	−145.741	−	484.136i	−0.338664	−	1.12501i
$58$	113.568	+	196.705i	0.257106	+	0.445321i
$59$	232.735	+	403.109i	0.513551	+	0.889497i	0.999876	+	0.0157191i	$0.00500375\pi$
$59$	232.735	+	403.109i	0.513551	+	0.889497i	−0.486325	+	0.873778i	$0.661663\pi$
$60$	−151.706	+	644.452i	−0.326420	+	1.38664i
$61$	542.558	+	313.246i	1.13881	+	0.657492i	0.946136	−	0.323771i	$-0.104951\pi$
$61$	542.558	+	313.246i	1.13881	+	0.657492i	0.192674	+	0.981263i	$0.438284\pi$
$62$	−267.794			−0.548547
$63$	176.007	+	468.047i	0.351982	+	0.936007i
$64$	288.792			0.564047
$65$	−131.678	−	76.0243i	−0.251271	−	0.145072i
$66$	516.659	+	485.964i	0.963580	+	0.906334i
$67$	−262.327	−	454.364i	−0.478334	−	0.828498i	0.521358	−	0.853338i	$-0.325426\pi$
$67$	−262.327	−	454.364i	−0.478334	−	0.828498i	−0.999691	+	0.0248401i	$0.992092\pi$
$68$	−68.5700	−	118.767i	−0.122284	−	0.211803i
$69$	146.742	−	156.011i	0.256024	−	0.272195i
$70$	−1366.16	−	312.855i	−2.33268	−	0.534190i
$71$		−	115.729i		−	0.193443i	−0.995311	−	0.0967216i	$-0.969164\pi$
$71$		−	115.729i		−	0.193443i	0.995311	−	0.0967216i	$-0.0308356\pi$
$72$	91.2376	+	137.808i	0.149340	+	0.225567i
$73$			708.180i			1.13543i	0.823226	+	0.567714i	$0.192172\pi$
$73$			708.180i			1.13543i	−0.823226	+	0.567714i	$0.807828\pi$
$74$	−1167.10	−	673.827i	−1.83342	−	1.05852i
$75$	325.136	−	1381.18i	0.500579	−	2.12647i
$76$	−538.135	+	310.692i	−0.812215	+	0.468933i
$77$	−453.708	+	488.273i	−0.671491	+	0.722648i
$78$	143.819	−	43.2944i	0.208774	−	0.0628477i
$79$	128.747	−	222.997i	0.183357	−	0.317584i	−0.759665	−	0.650315i	$-0.774637\pi$
$79$	128.747	−	222.997i	0.183357	−	0.317584i	0.943022	+	0.332731i	$0.107970\pi$
$80$	−1482.55			−2.07192
$81$	284.678	−	671.118i	0.390504	−	0.920601i
$82$		−	55.4366i		−	0.0746579i
$83$	200.583	−	347.420i	0.265263	−	0.459449i	−0.702370	−	0.711812i	$-0.747875\pi$
$83$	200.583	−	347.420i	0.265263	−	0.459449i	0.967632	+	0.252364i	$0.0812079\pi$
$84$	510.364	−	342.369i	0.662920	−	0.444709i
$85$	214.229	+	371.056i	0.273370	+	0.473490i
$86$	320.970	−	185.312i	0.402454	−	0.232357i
$87$	302.888	+	71.3010i	0.373253	+	0.0878652i
$88$	−110.149	+	190.784i	−0.133431	+	0.231110i
$89$	−977.834			−1.16461			−0.582304	−	0.812971i	$-0.697849\pi$
$89$	−977.834			−1.16461			−0.582304	+	0.812971i	$0.697849\pi$
$90$	1127.95	+	1703.68i	1.32107	+	1.99538i
$91$	41.5042	+	134.899i	0.0478112	+	0.155398i
$92$	−227.962	−	131.614i	−0.258334	−	0.149149i
$93$	−251.356	+	267.233i	−0.280263	+	0.297965i
$94$	1543.16	−	890.942i	1.69324	−	0.977592i
$95$	1681.26	−	970.677i	1.81573	−	1.04831i
$96$	829.026	−	881.389i	0.881376	−	0.937046i
$97$	−521.193	−	300.911i	−0.545558	−	0.314978i	0.201770	−	0.979433i	$-0.435330\pi$
$97$	−521.193	−	300.911i	−0.545558	−	0.314978i	−0.747328	+	0.664455i	$0.768664\pi$
$98$	731.308	+	1075.97i	0.753809	+	1.10907i
$99$	969.889	−	59.4408i	0.984621	−	0.0603437i
$100$	−1743.89			−1.74389
$101$	212.644	−	368.310i	0.209494	−	0.362853i	−0.742062	−	0.670332i	$-0.766152\pi$
$101$	212.644	−	368.310i	0.209494	−	0.362853i	0.951555	+	0.307478i	$0.0994851\pi$
$102$	−411.973	−	96.9800i	−0.399916	−	0.0941417i
$103$	−657.161	+	379.412i	−0.628660	+	0.362957i	−0.780233	−	0.625489i	$-0.784899\pi$
$103$	−657.161	+	379.412i	−0.628660	+	0.362957i	0.151573	+	0.988446i	$0.451566\pi$
$104$	23.3244	+	40.3990i	0.0219918	+	0.0380909i
$105$	−1594.50	+	1069.64i	−1.48197	+	0.994158i
$106$	1347.49	−	2333.92i	1.23471	−	2.13859i
$107$		−	866.455i		−	0.782835i	−0.920213	−	0.391418i	$-0.871985\pi$
$107$		−	866.455i		−	0.782835i	0.920213	−	0.391418i	$-0.128015\pi$
$108$	−883.037	−	151.566i	−0.786761	−	0.135041i
$109$	−94.9205			−0.0834104			−0.0417052	−	0.999130i	$-0.513279\pi$
$109$	−94.9205			−0.0834104			−0.0417052	+	0.999130i	$0.513279\pi$
$110$	−1361.75	+	2358.61i	−1.18034	+	2.04441i
$111$	−1767.87	+	532.189i	−1.51170	+	0.455073i
$112$	1008.13	+	936.763i	0.850530	+	0.790320i
$113$	−1432.66	+	827.148i	−1.19269	+	0.688597i	−0.958915	−	0.283694i	$-0.908440\pi$
$113$	−1432.66	+	827.148i	−1.19269	+	0.688597i	−0.233771	+	0.972292i	$0.575107\pi$
$114$	−439.419	+	1866.66i	−0.361012	+	1.53358i
$115$	712.208	+	411.194i	0.577511	+	0.333426i
$116$		−	382.428i		−	0.306100i
$117$	91.7877	−	184.154i	0.0725280	−	0.145513i
$118$		−	1765.48i		−	1.37734i
$119$	88.7800	−	387.681i	0.0683903	−	0.298644i
$120$	−434.792	+	462.255i	−0.330758	+	0.351649i
$121$	−17.8889	−	30.9845i	−0.0134402	−	0.0232791i
$122$	−1188.11	−	2057.87i	−0.881693	−	1.52714i
$123$	−55.3203	−	52.0337i	−0.0405534	−	0.0381441i
$124$	390.479	+	225.443i	0.282791	+	0.163269i
$125$	2954.35			2.11396
$126$	309.489	−	1871.21i	0.218821	−	1.32302i
$127$	−280.600			−0.196057			−0.0980284	−	0.995184i	$-0.531254\pi$
$127$	−280.600			−0.196057			−0.0980284	+	0.995184i	$0.531254\pi$
$128$	664.740	+	383.788i	0.459026	+	0.265019i
$129$	116.344	−	494.233i	0.0794073	−	0.337324i
$130$	288.353	+	499.442i	0.194540	+	0.336954i
$131$	1095.66	+	1897.74i	0.730751	+	1.26570i	0.956563	+	0.291527i	$0.0941632\pi$
$131$	1095.66	+	1897.74i	0.730751	+	1.26570i	−0.225812	+	0.974171i	$0.572503\pi$
$132$	−344.246	−	1143.55i	−0.226991	−	0.754040i
$133$	−1756.59	−	402.264i	−1.14523	−	0.262261i
$134$			1989.96i			1.28289i
$135$	2758.82	+	473.527i	1.75882	+	0.301887i
$136$		−	131.452i		−	0.0828815i
$137$	985.315	+	568.872i	0.614461	+	0.354759i	0.774709	−	0.632318i	$-0.217896\pi$
$137$	985.315	+	568.872i	0.614461	+	0.354759i	−0.160248	+	0.987077i	$0.551230\pi$
$138$	−777.878	+	234.167i	−0.479836	+	0.144446i
$139$	−1842.29	+	1063.64i	−1.12418	+	0.649044i	−0.942464	−	0.334308i	$-0.891498\pi$
$139$	−1842.29	+	1063.64i	−1.12418	+	0.649044i	−0.181713	+	0.983352i	$0.558164\pi$
$140$	1728.67	+	1606.29i	1.04356	+	0.969688i
$141$	559.359	−	2376.17i	0.334089	−	1.41922i
$142$	−219.474	+	380.140i	−0.129703	+	0.224652i
$143$	274.266			0.160387
$144$	−122.727	−	2002.51i	−0.0710223	−	1.15886i
$145$			1194.80i			0.684293i
$146$	1343.03	−	2326.20i	0.761301	−	1.31861i
$147$	1760.13	+	280.145i	0.987569	+	0.157183i
$148$	1134.53	+	1965.06i	0.630118	+	1.09140i
$149$	−362.688	+	209.398i	−0.199413	+	0.115131i	−0.596382	−	0.802701i	$-0.703395\pi$
$149$	−362.688	+	209.398i	−0.199413	+	0.115131i	0.396969	+	0.917832i	$0.370062\pi$
$150$	−3687.34	+	3920.24i	−2.00713	+	2.13391i
$151$	475.546	−	823.669i	0.256287	−	0.443902i	−0.708957	−	0.705252i	$-0.750834\pi$
$151$	475.546	−	823.669i	0.256287	−	0.443902i	0.965244	+	0.261349i	$0.0841674\pi$
$152$	−595.611			−0.317832
$153$	−483.461	+	320.081i	−0.255461	+	0.169131i
$154$	2416.30	−	743.422i	1.26436	−	0.389004i
$155$	−1219.95	−	704.339i	−0.632186	−	0.364993i
$156$	−246.155	−	57.9458i	−0.126334	−	0.0297396i
$157$	1885.26	−	1088.45i	0.958343	−	0.553300i	0.0626806	−	0.998034i	$-0.480035\pi$
$157$	1885.26	−	1088.45i	0.958343	−	0.553300i	0.895663	+	0.444734i	$0.146702\pi$
$158$	−845.807	+	488.327i	−0.425878	+	0.245881i
$159$	−1064.25	−	3535.31i	−0.530819	−	1.76332i
$160$	4023.66	+	2323.06i	1.98811	+	1.14784i
$161$	−224.484	−	729.628i	−0.109887	−	0.357160i
$162$	−2207.84	+	1664.58i	−1.07077	+	0.807294i
$163$	−382.330			−0.183720			−0.0918601	−	0.995772i	$-0.529281\pi$
$163$	−382.330			−0.183720			−0.0918601	+	0.995772i	$0.529281\pi$
$164$	−46.6695	+	80.8339i	−0.0222212	+	0.0384882i
$165$	1075.51	+	3572.72i	0.507443	+	1.68567i
$166$	−1317.73	+	760.792i	−0.616118	+	0.355716i
$167$	−123.092	−	213.202i	−0.0570370	−	0.0987909i	0.836097	−	0.548582i	$-0.184832\pi$
$167$	−123.092	−	213.202i	−0.0570370	−	0.0987909i	−0.893134	+	0.449791i	$0.851499\pi$
$168$	587.740	−	39.6047i	0.269911	−	0.0181879i
$169$	−1069.46	+	1852.36i	−0.486783	+	0.843132i
$170$		−	1625.10i		−	0.733174i
$171$	1450.30	+	2190.57i	0.648579	+	0.979633i
$172$	−624.021			−0.276635
$173$	1988.82	−	3444.74i	0.874031	−	1.51387i	0.0162391	−	0.999868i	$-0.494831\pi$
$173$	1988.82	−	3444.74i	0.874031	−	1.51387i	0.857792	−	0.513998i	$-0.171836\pi$
$174$	−859.694	−	808.620i	−0.374559	−	0.352306i
$175$	−3704.86	−	3442.59i	−1.60035	−	1.48706i
$176$	2315.95	−	1337.11i	0.991882	−	0.572663i
$177$	−1761.78	−	1657.11i	−0.748155	−	0.703707i
$178$	3211.94	+	1854.42i	1.35250	+	0.780867i
$179$			1454.87i			0.607498i	0.952752	+	0.303749i	$0.0982384\pi$
$179$			1454.87i			0.607498i	−0.952752	+	0.303749i	$0.901762\pi$
$180$	−210.442	−	3433.76i	−0.0871413	−	1.42187i
$181$			735.896i			0.302203i	0.988518	+	0.151101i	$0.0482820\pi$
$181$			735.896i			0.302203i	−0.988518	+	0.151101i	$0.951718\pi$
$182$	119.498	−	521.820i	0.0486692	−	0.212527i
$183$	−3168.73	−	745.931i	−1.28000	−	0.301316i
$184$	−126.155	−	218.507i	−0.0505449	−	0.0875463i
$185$	−3544.53	−	6139.31i	−1.40864	−	2.43984i
$186$	1332.44	−	401.107i	0.525263	−	0.158122i
$187$	−669.313	−	386.428i	−0.261738	−	0.151115i
$188$	−3000.17			−1.16388
$189$	−1576.79	−	2065.19i	−0.606850	−	0.794816i
$190$	−7363.38			−2.81155
$191$	2390.26	+	1380.02i	0.905515	+	0.522799i	0.878985	−	0.476849i	$-0.158221\pi$
$191$	2390.26	+	1380.02i	0.905515	+	0.522799i	0.0265297	+	0.999648i	$0.491554\pi$
$192$	−1436.91	+	432.558i	−0.540105	+	0.162589i
$193$	−616.442	−	1067.71i	−0.229909	−	0.398214i	0.727872	−	0.685713i	$-0.240510\pi$
$193$	−616.442	−	1067.71i	−0.229909	−	0.398214i	−0.957781	+	0.287499i	$0.907176\pi$
$194$	1141.33	+	1976.84i	0.422384	+	0.731590i
$195$	769.047	+	181.037i	0.282424	+	0.0664836i
$196$	−160.539	−	2184.55i	−0.0585055	−	0.796120i
$197$			497.068i			0.179770i	0.995952	+	0.0898849i	$0.0286499\pi$
$197$			497.068i			0.179770i	−0.995952	+	0.0898849i	$0.971350\pi$
$198$	−3298.57	−	1644.10i	−1.18394	−	0.590106i
$199$			4502.53i			1.60390i	0.597391	+	0.801950i	$0.296204\pi$
$199$			4502.53i			1.60390i	−0.597391	+	0.801950i	$0.703796\pi$
$200$	−1447.61	−	835.778i	−0.511807	−	0.295492i
$201$	1985.79	+	1867.81i	0.696849	+	0.655449i
$202$	−1396.96	+	806.538i	−0.486585	+	0.280930i
$203$	754.946	−	812.462i	0.261019	−	0.280905i
$204$	519.068	+	488.230i	0.178147	+	0.167563i
$205$	145.807	−	252.544i	0.0496759	−	0.0860413i
$206$	2878.15			0.973447
$207$	−496.453	+	996.038i	−0.166695	+	0.334442i
$208$		−	566.274i		−	0.188769i
$209$	−1750.91	+	3032.67i	−0.579489	+	1.00371i
$210$	7266.07	−	489.622i	2.38765	−	0.160891i
$211$	1714.83	+	2970.17i	0.559495	+	0.969074i	0.997539	+	0.0701201i	$0.0223383\pi$
$211$	1714.83	+	2970.17i	0.559495	+	0.969074i	−0.438043	+	0.898954i	$0.644328\pi$
$212$	−3929.63	+	2268.77i	−1.27306	+	0.734999i
$213$	173.340	+	575.819i	0.0557610	+	0.185232i
$214$	−1643.19	+	2846.09i	−0.524889	+	0.909134i
$215$	1949.59			0.618424
$216$	−660.373	−	549.020i	−0.208022	−	0.172945i
$217$	384.522	+	1249.79i	0.120290	+	0.390974i
$218$	311.790	+	180.012i	0.0968675	+	0.0559265i
$219$	−1060.72	−	3523.62i	−0.327293	−	1.08723i
$220$	3971.21	−	2292.78i	1.21700	−	0.702632i
$221$	−141.729	+	81.8270i	−0.0431389	+	0.0249063i
$222$	6816.30	+	1604.58i	2.06072	+	0.485102i
$223$	−2145.46	−	1238.68i	−0.644263	−	0.371965i	0.141992	−	0.989868i	$-0.454649\pi$
$223$	−2145.46	−	1238.68i	−0.644263	−	0.371965i	−0.786255	+	0.617903i	$0.787983\pi$
$224$	−1268.23	−	4122.07i	−0.378292	−	1.22954i
$225$	451.018	+	7359.20i	0.133635	+	2.18050i
$226$	6274.59			1.84681
$227$	84.0252	−	145.536i	0.0245681	−	0.0425531i	−0.853480	−	0.521126i	$-0.825512\pi$
$227$	84.0252	−	145.536i	0.0245681	−	0.0425531i	0.878048	+	0.478573i	$0.158846\pi$
$228$	2212.18	−	2351.91i	0.642567	−	0.683153i
$229$	−989.455	+	571.262i	−0.285524	+	0.164847i	−0.635922	−	0.771754i	$-0.719380\pi$
$229$	−989.455	+	571.262i	−0.285524	+	0.164847i	0.350397	+	0.936601i	$0.386047\pi$
$230$	−1559.62	−	2701.34i	−0.447123	−	0.774439i
$231$	1526.12	−	3109.02i	0.434681	−	0.885535i
$232$	183.283	−	317.455i	0.0518669	−	0.0898361i
$233$		−	2181.50i		−	0.613370i	−0.951811	−	0.306685i	$-0.900780\pi$
$233$		−	2181.50i		−	0.613370i	0.951811	−	0.306685i	$-0.0992198\pi$
$234$	−650.740	+	430.831i	−0.181796	+	0.120360i
$235$	9373.23			2.60188
$236$	−1486.28	+	2574.31i	−0.409951	+	0.710056i
$237$	−306.586	+	1302.38i	−0.0840291	+	0.356957i
$238$	−1026.84	+	1105.07i	−0.279664	+	0.300970i
$239$	−1654.14	+	955.020i	−0.447689	+	0.258473i	−0.706854	−	0.707360i	$-0.749886\pi$
$239$	−1654.14	+	955.020i	−0.447689	+	0.258473i	0.259165	+	0.965833i	$0.416553\pi$
$240$	7376.55	−	2220.58i	1.98398	−	0.597242i
$241$	−1962.89	−	1133.28i	−0.524651	−	0.302907i	0.214184	−	0.976793i	$-0.431291\pi$
$241$	−1962.89	−	1133.28i	−0.524651	−	0.302907i	−0.738836	+	0.673886i	$0.764624\pi$
$242$			135.702i			0.0360464i
$243$	−411.228	+	3765.61i	−0.108561	+	0.994090i
$244$			4000.86i			1.04971i
$245$	501.563	+	6825.06i	0.130791	+	1.77974i
$246$	83.0340	+	275.830i	0.0215205	+	0.0714890i
$247$	370.760	+	642.176i	0.0955098	+	0.165428i
$248$	216.092	+	374.283i	0.0553302	+	0.0958346i
$249$	−477.647	+	2029.06i	−0.121565	+	0.516410i
$250$	−9704.31	−	5602.79i	−2.45502	−	1.41741i
$251$	−315.743			−0.0794004			−0.0397002	−	0.999212i	$-0.512640\pi$
$251$	−315.743			−0.0794004			−0.0397002	+	0.999212i	$0.512640\pi$
$252$	−2026.56	+	2467.92i	−0.506592	+	0.616923i
$253$	−1483.43			−0.368626
$254$	921.702	+	532.145i	0.227688	+	0.131456i
$255$	−1621.69	−	1525.35i	−0.398252	−	0.374592i
$256$	−2610.84	−	4522.11i	−0.637412	−	1.10403i
$257$	2047.88	+	3547.03i	0.497055	+	0.860924i	0.999994	−	0.00339730i	$-0.00108139\pi$
$257$	2047.88	+	3547.03i	0.497055	+	0.860924i	−0.502939	+	0.864322i	$0.667748\pi$
$258$	−1319.45	+	1402.79i	−0.318393	+	0.338504i
$259$	−1468.91	+	6414.38i	−0.352408	+	1.53888i
$260$		−	971.003i		−	0.231612i
$261$	−1613.85	+	98.9065i	−0.382738	+	0.0234566i
$262$		−	8311.48i		−	1.95987i
$263$	4270.21	+	2465.41i	1.00119	+	0.578036i	0.908600	−	0.417668i	$-0.137153\pi$
$263$	4270.21	+	2465.41i	1.00119	+	0.578036i	0.0925883	+	0.995704i	$0.470486\pi$
$264$	262.298	−	1114.25i	0.0611490	−	0.259762i
$265$	12277.1	−	7088.18i	2.84595	−	1.64311i
$266$	5007.09	+	4652.63i	1.15415	+	1.07245i
$267$	4865.30	−	1464.62i	1.11518	−	0.335705i
$268$	1675.26	−	2901.63i	0.381838	−	0.661362i
$269$	−5506.26			−1.24804			−0.624019	−	0.781409i	$-0.714501\pi$
$269$	−5506.26			−1.24804			−0.624019	+	0.781409i	$0.714501\pi$
$270$	−8164.01	−	6787.38i	−1.84017	−	1.52988i
$271$		−	7622.48i		−	1.70861i	−0.519774	−	0.854304i	$-0.673984\pi$
$271$		−	7622.48i		−	1.70861i	0.519774	−	0.854304i	$-0.326016\pi$
$272$	−797.852	+	1381.92i	−0.177856	+	0.308056i
$273$	−408.562	−	609.036i	−0.0905761	−	0.135020i
$274$	−2157.68	−	3737.21i	−0.475730	−	0.823989i
$275$	−8511.06	+	4913.86i	−1.86631	+	1.07752i
$276$	1331.38	+	313.412i	0.290361	+	0.0683522i
$277$	−1811.14	+	3136.99i	−0.392856	+	0.680446i	−0.992825	−	0.119577i	$-0.961846\pi$
$277$	−1811.14	+	3136.99i	−0.392856	+	0.680446i	0.599969	+	0.800023i	$0.295179\pi$
$278$	8068.60			1.74073
$279$	850.381	−	1706.13i	0.182477	−	0.366104i
$280$	665.140	+	2161.87i	0.141963	+	0.461416i
$281$	−1888.83	−	1090.51i	−0.400989	−	0.231511i	0.285922	−	0.958253i	$-0.407700\pi$
$281$	−1888.83	−	1090.51i	−0.400989	−	0.231511i	−0.686911	+	0.726742i	$0.741034\pi$
$282$	−6343.65	+	6744.33i	−1.33957	+	1.42418i
$283$	−1985.61	+	1146.39i	−0.417075	+	0.240799i	−0.693825	−	0.720143i	$-0.744076\pi$
$283$	−1985.61	+	1146.39i	−0.417075	+	0.240799i	0.276750	+	0.960942i	$0.410743\pi$
$284$	640.043	−	369.529i	0.133731	−	0.0772096i
$285$	−6911.38	+	7347.92i	−1.43647	+	1.52720i
$286$	−900.897	−	520.133i	−0.186263	−	0.107539i
$287$	−258.721	+	79.6005i	−0.0532120	+	0.0163717i
$288$	−2804.74	+	5627.17i	−0.573856	+	1.15133i
$289$	−4451.84			−0.906134
$290$	2265.88	−	3924.61i	0.458817	−	0.794694i
$291$	3043.95	+	716.558i	0.613195	+	0.144348i
$292$	−3916.63	+	2261.27i	−0.784943	+	0.453187i
$293$	273.105	+	473.031i	0.0544537	+	0.0943166i	0.891967	−	0.452100i	$-0.149325\pi$
$293$	273.105	+	473.031i	0.0544537	+	0.0943166i	−0.837514	+	0.546416i	$0.815992\pi$
$294$	−5250.29	−	4258.20i	−1.04151	−	0.844705i
$295$	4643.48	−	8042.75i	0.916455	−	1.58735i
$296$			2174.94i			0.427080i
$297$	−4736.74	+	1748.47i	−0.925433	+	0.341604i
$298$	1588.45			0.308780
$299$	−157.060	+	272.035i	−0.0303779	+	0.0526161i
$300$	8676.89	−	2612.03i	1.66987	−	0.502685i
$301$	−1325.72	−	1231.87i	−0.253865	−	0.235893i
$302$	−3124.10	+	1803.70i	−0.595271	+	0.343680i
$303$	−506.368	+	2151.06i	−0.0960069	+	0.407839i
$304$	6261.52	+	3615.09i	1.18132	+	0.682038i
$305$		−	12499.6i		−	2.34665i
$306$	2195.07	−	134.528i	0.410078	−	0.0251321i
$307$		−	6193.21i		−	1.15135i	−0.817677	−	0.575677i	$-0.804739\pi$
$307$		−	6193.21i		−	1.15135i	0.817677	−	0.575677i	$-0.195261\pi$
$308$	−4149.14	−	950.165i	−0.767595	−	0.175781i
$309$	2701.48	−	2872.11i	0.497351	−	0.528765i
$310$	2671.49	+	4627.16i	0.489453	+	0.847758i
$311$	2335.25	+	4044.78i	0.425788	+	0.737486i	0.996494	−	0.0836685i	$-0.0266637\pi$
$311$	2335.25	+	4044.78i	0.425788	+	0.737486i	−0.570706	+	0.821155i	$0.693330\pi$
$312$	−176.563	−	166.073i	−0.0320382	−	0.0301348i
$313$	−2218.64	−	1280.93i	−0.400655	−	0.231318i	0.286112	−	0.958196i	$-0.407637\pi$
$313$	−2218.64	−	1280.93i	−0.400655	−	0.231318i	−0.686767	+	0.726878i	$0.740971\pi$
$314$	−8256.81			−1.48394
$315$	6331.45	−	7710.38i	1.13250	−	1.37915i
$316$	1644.40			0.292736
$317$	2351.36	+	1357.56i	0.416611	+	0.240530i	0.693626	−	0.720335i	$-0.256012\pi$
$317$	2351.36	+	1357.56i	0.416611	+	0.240530i	−0.277015	+	0.960865i	$0.589345\pi$
$318$	−3208.77	+	13630.9i	−0.565845	+	2.40372i
$319$	−1077.59	−	1866.44i	−0.189133	−	0.327589i
$320$	−2880.96	−	4989.97i	−0.503283	−	0.871712i
$321$	1297.79	+	4311.13i	0.225656	+	0.749607i
$322$	−646.331	+	2822.37i	−0.111859	+	0.488462i
$323$		−	2089.53i		−	0.359953i
$324$	4620.65	−	568.500i	0.792292	−	0.0974794i
$325$			2081.04i			0.355186i
$326$	1255.86	+	725.070i	0.213361	+	0.123184i
$327$	472.286	−	142.174i	0.0798700	−	0.0240435i
$328$	−77.4810	+	44.7337i	−0.0130432	+	0.00753050i
$329$	−6373.79	−	5922.58i	−1.06808	−	0.992470i
$330$	3242.72	−	13775.2i	0.540927	−	2.29787i
$331$	−2272.97	+	3936.89i	−0.377443	+	0.653750i	−0.990689	−	0.136142i	$-0.956530\pi$
$331$	−2272.97	+	3936.89i	−0.377443	+	0.653750i	0.613247	+	0.789891i	$0.289863\pi$
$332$	2561.90			0.423501
$333$	7999.11	−	5295.91i	1.31636	−	0.871514i
$334$			933.756i			0.152973i
$335$	−5233.90	+	9065.38i	−0.853607	+	1.47849i
$336$	−6419.15	−	3150.96i	−1.04224	−	0.511604i
$337$	3627.36	+	6282.78i	0.586336	+	1.01556i	0.994707	+	0.102747i	$0.0327634\pi$
$337$	3627.36	+	6282.78i	0.586336	+	1.01556i	−0.408372	+	0.912816i	$0.633903\pi$
$338$	7025.83	−	4056.37i	1.13064	−	0.652773i
$339$	5889.43	−	6261.42i	0.943569	−	1.00317i
$340$	−1368.10	+	2369.61i	−0.218222	+	0.377971i
$341$	2540.98			0.403525
$342$	−609.547	−	9945.91i	−0.0963759	−	1.57255i
$343$	3971.43	−	4957.96i	0.625181	−	0.780480i
$344$	−518.003	−	299.069i	−0.0811885	−	0.0468742i
$345$	−4159.55	−	979.175i	−0.649110	−	0.152803i
$346$	−13065.6	+	7543.41i	−2.03009	+	1.17207i
$347$	−7611.25	+	4394.36i	−1.17750	+	0.679832i	−0.955436	−	0.295200i	$-0.904614\pi$
$347$	−7611.25	+	4394.36i	−1.17750	+	0.679832i	−0.222067	+	0.975031i	$0.571280\pi$
$348$	572.808	+	1902.81i	0.0882349	+	0.293107i
$349$	6314.40	+	3645.62i	0.968487	+	0.559156i	0.898775	−	0.438411i	$-0.144459\pi$
$349$	6314.40	+	3645.62i	0.968487	+	0.559156i	0.0697122	+	0.997567i	$0.477792\pi$
$350$	5640.84	+	18334.1i	0.861474	+	2.80000i
$351$	−180.868	+	1053.76i	−0.0275044	+	0.160244i
$352$	−8380.70			−1.26901
$353$	5012.28	−	8681.52i	0.755741	−	1.30898i	−0.189264	−	0.981926i	$-0.560610\pi$
$353$	5012.28	−	8681.52i	0.755741	−	1.30898i	0.945005	−	0.327056i	$-0.106057\pi$
$354$	2644.37	+	8784.34i	0.397025	+	1.31888i
$355$	−1999.65	+	1154.50i	−0.298959	+	0.172604i
$356$	−3122.29	−	5407.96i	−0.464834	−	0.805116i
$357$	138.942	+	2061.92i	0.0205983	+	0.305682i
$358$	2759.09	−	4778.89i	0.407326	−	0.705509i
$359$		−	11205.2i		−	1.64732i	−0.567083	−	0.823660i	$-0.691928\pi$
$359$		−	11205.2i		−	1.64732i	0.567083	−	0.823660i	$-0.308072\pi$
$360$	1470.98	−	2951.23i	0.215354	−	0.432066i
$361$	−2608.72			−0.380336
$362$	1395.59	−	2417.24i	0.202626	−	0.350959i
$363$	135.417	+	127.372i	0.0195800	+	0.0184168i
$364$	−613.539	+	660.282i	−0.0883467	+	0.0950773i
$365$	12236.5	−	7064.73i	1.75476	−	1.01311i
$366$	8993.88	+	8459.55i	1.28447	+	1.20816i
$367$	2597.53	+	1499.68i	0.369455	+	0.213305i	0.673220	−	0.739442i	$-0.264911\pi$
$367$	2597.53	+	1499.68i	0.369455	+	0.213305i	−0.303766	+	0.952747i	$0.598244\pi$
$368$			3062.81i			0.433859i
$369$	353.188	+	176.039i	0.0498272	+	0.0248353i
$370$			26888.1i			3.77797i
$371$	−12827.2	−	2937.46i	−1.79502	−	0.411065i
$372$	−2280.54	−	536.848i	−0.317851	−	0.0748233i
$373$	−2052.54	−	3555.11i	−0.284924	−	0.493503i	0.687667	−	0.726026i	$-0.258635\pi$
$373$	−2052.54	−	3555.11i	−0.284924	−	0.493503i	−0.972591	+	0.232524i	$0.925302\pi$
$374$	1465.68	+	2538.64i	0.202644	+	0.350989i
$375$	−14699.7	+	4425.08i	−2.02423	+	0.609360i
$376$	−2490.45	−	1437.86i	−0.341583	−	0.197213i
$377$	−456.365			−0.0623449
$378$	1262.84	+	9773.94i	0.171834	+	1.32994i
$379$	−2051.20			−0.278002			−0.139001	−	0.990292i	$-0.544389\pi$
$379$	−2051.20			−0.278002			−0.139001	+	0.990292i	$0.544389\pi$
$380$	10736.8	+	6198.87i	1.44943	+	0.836830i
$381$	1396.15	−	420.288i	0.187735	−	0.0565144i
$382$	−5234.28	−	9066.04i	−0.701071	−	1.21429i
$383$	−2786.12	−	4825.70i	−0.371708	−	0.643817i	0.618120	−	0.786083i	$-0.287894\pi$
$383$	−2786.12	−	4825.70i	−0.371708	−	0.643817i	−0.989828	+	0.142266i	$0.954561\pi$
$384$	−3882.32	−	913.914i	−0.515935	−	0.121453i
$385$	12962.9	+	2968.54i	1.71598	+	0.392963i
$386$			4676.21i			0.616614i
$387$	161.389	+	2633.37i	0.0211986	+	0.345895i
$388$		−	3843.31i		−	0.502873i
$389$	1483.30	+	856.385i	0.193333	+	0.111621i	0.593542	−	0.804803i	$-0.297729\pi$
$389$	1483.30	+	856.385i	0.193333	+	0.111621i	−0.400209	+	0.916424i	$0.631063\pi$
$390$	−2182.80	−	2053.12i	−0.283411	−	0.266574i
$391$	766.569	−	442.579i	0.0991485	−	0.0572434i
$392$	913.706	−	1890.35i	0.117727	−	0.243563i
$393$	−8294.04	−	7801.29i	−1.06458	−	1.00133i
$394$	942.667	−	1632.75i	0.120535	−	0.208773i
$395$	−5137.48			−0.654417
$396$	3425.66	+	5174.22i	0.434712	+	0.656602i
$397$			5977.49i			0.755672i	0.925872	+	0.377836i	$0.123332\pi$
$397$			5977.49i			0.755672i	−0.925872	+	0.377836i	$0.876668\pi$
$398$	8538.84	−	14789.7i	1.07541	−	1.86267i
$399$	9342.60	−	629.550i	1.17222	−	0.0789897i
$400$	10145.6	+	17572.7i	1.26820	+	2.19658i
$401$	2620.36	−	1512.86i	0.326320	−	0.188401i	−0.327886	−	0.944717i	$-0.606336\pi$
$401$	2620.36	−	1512.86i	0.326320	−	0.188401i	0.654206	+	0.756316i	$0.273003\pi$
$402$	−2980.60	−	9901.25i	−0.369798	−	1.22843i
$403$	269.030	−	465.973i	0.0332539	−	0.0575974i
$404$	2715.94			0.334463
$405$	−14436.0	+	1776.13i	−1.77119	+	0.217917i
$406$	−4020.61	+	1237.02i	−0.491476	+	0.151212i
$407$	11074.1	+	6393.65i	1.34871	+	0.778676i
$408$	196.891	+	654.050i	0.0238910	+	0.0793635i
$409$	9538.96	−	5507.32i	1.15323	−	0.665818i	0.203558	−	0.979063i	$-0.434750\pi$
$409$	9538.96	−	5507.32i	1.15323	−	0.665818i	0.949672	+	0.313245i	$0.101416\pi$
$410$	−957.877	+	553.030i	−0.115381	+	0.0666152i
$411$	−5754.59	−	1354.65i	−0.690640	−	0.162579i
$412$	−4196.72	−	2422.98i	−0.501838	−	0.289736i
$413$	−8239.47	+	2535.03i	−0.981690	+	0.302035i
$414$	3519.67	−	2330.24i	0.417831	−	0.276630i
$415$	−8003.98			−0.946746
$416$	−887.316	+	1536.88i	−0.104578	+	0.181134i
$417$	7573.32	−	8051.67i	0.889370	−	0.945544i
$418$	11502.6	−	6641.05i	1.34596	−	0.777092i
$419$	5849.85	+	10132.2i	0.682062	+	1.18137i	0.974351	+	0.225036i	$0.0722499\pi$
$419$	5849.85	+	10132.2i	0.682062	+	1.18137i	−0.292289	+	0.956330i	$0.594417\pi$
$420$	−11007.1	−	5403.02i	−1.27879	−	0.627715i
$421$	3481.75	−	6030.57i	0.403064	−	0.698128i	−0.591030	−	0.806650i	$-0.701278\pi$
$421$	3481.75	−	6030.57i	0.403064	−	0.698128i	0.994094	+	0.108522i	$0.0346117\pi$
$422$		−	13008.3i		−	1.50056i
$423$	775.925	+	12660.7i	0.0891886	+	1.45528i
$424$	−4349.33			−0.498166
$425$	2932.09	−	5078.53i	0.334652	−	0.579635i
$426$	522.633	−	2220.15i	0.0594405	−	0.252504i
$427$	−7898.04	+	8499.75i	−0.895112	+	0.963306i
$428$	4791.98	−	2766.65i	0.541189	−	0.312456i
$429$	−1364.64	+	410.801i	−0.153579	+	0.0462323i
$430$	−6403.93	−	3697.31i	−0.718197	−	0.414651i
$431$			12686.3i			1.41781i	0.705305	+	0.708904i	$0.250810\pi$
$431$			12686.3i			1.41781i	−0.705305	+	0.708904i	$0.749190\pi$
$432$	3610.04	+	9779.88i	0.402056	+	1.08920i
$433$		−	12891.4i		−	1.43077i	−0.698730	−	0.715385i	$-0.746251\pi$
$433$		−	12891.4i		−	1.43077i	0.698730	−	0.715385i	$-0.253749\pi$
$434$	1107.11	−	4834.48i	0.122449	−	0.534706i
$435$	−1789.59	−	5944.83i	−0.197251	−	0.655248i
$436$	−303.088	−	524.963i	−0.0332919	−	0.0576632i
$437$	−2005.34	−	3473.34i	−0.219515	−	0.380212i
$438$	−3198.15	+	13585.8i	−0.348890	+	1.48209i
$439$	10467.6	+	6043.45i	1.13802	+	0.657035i	0.945939	−	0.324345i	$-0.105144\pi$
$439$	10467.6	+	6043.45i	1.13802	+	0.657035i	0.192078	+	0.981380i	$0.438477\pi$
$440$	4395.36			0.476228
$441$	−9177.28	+	1242.46i	−0.990960	+	0.134160i
$442$	620.724			0.0667983
$443$	−8703.97	−	5025.24i	−0.933495	−	0.538953i	−0.0455796	−	0.998961i	$-0.514513\pi$
$443$	−8703.97	−	5025.24i	−0.933495	−	0.538953i	−0.887915	+	0.460007i	$0.847847\pi$
$444$	−8588.24	−	8078.01i	−0.917973	−	0.863436i
$445$	9754.77	+	16895.8i	1.03915	+	1.79986i
$446$	4698.20	+	8137.53i	0.498803	+	0.863953i
$447$	1490.95	−	1585.12i	0.157761	−	0.167726i
$448$	−1193.92	+	5213.54i	−0.125909	+	0.549814i
$449$			10044.6i			1.05575i	0.849321	+	0.527877i	$0.177012\pi$
$449$			10044.6i			1.05575i	−0.849321	+	0.527877i	$0.822988\pi$
$450$	12474.9	−	25028.5i	1.30683	−	2.62190i
$451$			526.014i			0.0549202i
$452$	−9149.17	−	5282.27i	−0.952081	−	0.549684i
$453$	−1132.42	+	4810.53i	−0.117452	+	0.498937i
$454$	−552.004	+	318.700i	−0.0570635	+	0.0329456i
$455$	1916.84	−	2062.88i	0.197501	−	0.212548i
$456$	2963.52	−	892.117i	0.304341	−	0.0916166i
$457$	7705.51	−	13346.3i	0.788727	−	1.36612i	−0.138020	−	0.990430i	$-0.544074\pi$
$457$	7705.51	−	13346.3i	0.788727	−	1.36612i	0.926747	−	0.375686i	$-0.122593\pi$
$458$	4333.49			0.442119
$459$	1926.08	−	2316.73i	0.195864	−	0.235590i
$460$			5251.88i			0.532326i
$461$	2887.34	−	5001.02i	0.291707	−	0.505251i	−0.682506	−	0.730880i	$-0.739110\pi$
$461$	2887.34	−	5001.02i	0.291707	−	0.505251i	0.974214	+	0.225628i	$0.0724434\pi$
$462$	−10909.0	+	7318.15i	−1.09856	+	0.736951i
$463$	−4764.84	−	8252.94i	−0.478274	−	0.828395i	0.521416	−	0.853303i	$-0.325404\pi$
$463$	−4764.84	−	8252.94i	−0.478274	−	0.828395i	−0.999690	+	0.0249078i	$0.992071\pi$
$464$	−3853.62	+	2224.89i	−0.385560	+	0.222603i
$465$	7124.95	+	1677.24i	0.710563	+	0.167269i
$466$	−4137.12	+	7165.70i	−0.411263	+	0.712328i
$467$	8268.97			0.819363			0.409681	−	0.912229i	$-0.365640\pi$
$467$	8268.97			0.819363			0.409681	+	0.912229i	$0.365640\pi$
$468$	1311.56	−	80.3806i	0.129545	−	0.00793930i
$469$	9287.11	−	2857.35i	0.914368	−	0.281323i
$470$	−30788.8	−	17775.9i	−3.02166	−	1.74456i
$471$	−7749.97	+	8239.48i	−0.758174	+	0.806062i
$472$	−2467.53	+	1424.63i	−0.240630	+	0.138928i
$473$	−3045.54	+	1758.34i	−0.296055	+	0.170928i
$474$	3476.97	−	3696.58i	0.336925	−	0.358206i
$475$	−23010.9	−	13285.4i	−2.22277	−	1.28332i
$476$	2427.57	−	746.888i	0.233755	−	0.0719192i
$477$	10590.5	+	15996.2i	1.01657	+	1.53547i
$478$	7244.60			0.693222
$479$	−7295.72	+	12636.6i	−0.695929	+	1.20538i	0.273938	+	0.961747i	$0.411674\pi$
$479$	−7295.72	+	12636.6i	−0.695929	+	1.20538i	−0.969867	+	0.243637i	$0.921660\pi$
$480$	−23499.6	−	5531.89i	−2.23459	−	0.526032i
$481$	2344.97	−	1353.87i	0.222290	−	0.128339i
$482$	4298.41	+	7445.06i	0.406197	+	0.703554i
$483$	2209.79	+	3294.10i	0.208176	+	0.310324i
$484$	114.241	−	197.871i	0.0107288	−	0.0185829i
$485$			12007.4i			1.12418i
$486$	8492.08	−	11589.2i	0.792610	−	1.08168i
$487$	−14380.5			−1.33807			−0.669036	−	0.743230i	$-0.733293\pi$
$487$	−14380.5			−1.33807			−0.669036	+	0.743230i	$0.733293\pi$
$488$	−1917.45	+	3321.13i	−0.177867	+	0.308075i
$489$	1902.32	−	572.661i	0.175922	−	0.0529583i
$490$	11295.9	−	23369.8i	1.04142	−	2.15457i
$491$	−512.614	+	295.958i	−0.0471160	+	0.0272024i	−0.523373	−	0.852104i	$-0.675327\pi$
$491$	−512.614	+	295.958i	−0.0471160	+	0.0272024i	0.476257	+	0.879306i	$0.341993\pi$
$492$	111.134	−	472.099i	0.0101835	−	0.0432599i
$493$	1113.70	+	642.997i	0.101742	+	0.0587406i
$494$		−	2812.52i		−	0.256156i
$495$	−10702.6	−	16165.5i	−0.971808	−	1.46785i
$496$		−	5246.33i		−	0.474934i
$497$	2089.24	+	478.442i	0.188562	+	0.0431812i
$498$	5416.96	−	5759.11i	0.487429	−	0.518217i
$499$	2075.90	+	3595.56i	0.186232	+	0.322564i	0.943991	−	0.329971i	$-0.107039\pi$
$499$	2075.90	+	3595.56i	0.186232	+	0.322564i	−0.757759	+	0.652535i	$0.773706\pi$
$500$	9433.44	+	16339.2i	0.843752	+	1.46142i
$501$	931.796	+	876.438i	0.0830930	+	0.0781564i
$502$	1037.14	+	598.791i	0.0922105	+	0.0532378i
$503$	13272.2			1.17650			0.588248	−	0.808681i	$-0.299818\pi$
$503$	13272.2			1.17650			0.588248	+	0.808681i	$0.299818\pi$
$504$	−2865.03	+	1077.38i	−0.253212	+	0.0952192i
$505$	−8485.25			−0.747701
$506$	4872.69	+	2813.25i	0.428098	+	0.247163i
$507$	2546.71	−	10818.5i	0.223083	−	0.947662i
$508$	−895.974	−	1551.87i	−0.0782528	−	0.135538i
$509$	−7547.02	−	13071.8i	−0.657202	−	1.13831i	−0.981337	−	0.192296i	$-0.938407\pi$
$509$	−7547.02	−	13071.8i	−0.657202	−	1.13831i	0.324135	−	0.946011i	$-0.394927\pi$
$510$	2434.11	+	8085.85i	0.211341	+	0.702054i
$511$	−12784.7	−	2927.74i	−1.10678	−	0.253455i
$512$			13664.7i			1.17949i
$513$	−10497.2	−	8727.12i	−0.903433	−	0.751095i
$514$		−	15534.8i		−	1.33310i
$515$	13111.5	+	7569.95i	1.12187	+	0.647713i
$516$	3104.88	−	934.671i	0.264893	−	0.0797414i
$517$	−14642.3	+	8453.75i	−1.24559	+	0.719140i
$518$	16989.6	−	18283.9i	1.44108	−	1.55087i
$519$	−4735.98	+	20118.5i	−0.400552	+	1.70155i
$520$	465.364	−	806.033i	0.0392453	−	0.0679748i
$521$	5002.27			0.420640			0.210320	−	0.977633i	$-0.432549\pi$
$521$	5002.27			0.420640			0.210320	+	0.977633i	$0.432549\pi$
$522$	5488.65	+	2735.70i	0.460214	+	0.229384i
$523$		−	909.042i		−	0.0760031i	−0.999278	−	0.0380016i	$-0.987901\pi$
$523$		−	909.042i		−	0.0760031i	0.999278	−	0.0380016i	$-0.0120992\pi$
$524$	−6997.04	+	12119.2i	−0.583334	+	1.01036i
$525$	23590.2	+	11579.7i	1.96107	+	0.962628i
$526$	−9351.05	−	16196.5i	−0.775143	−	1.34259i
$527$	−1313.07	+	758.099i	−0.108535	+	0.0626628i
$528$	−9520.47	+	10121.8i	−0.784707	+	0.834271i
$529$	−5234.01	+	9065.57i	−0.430181	+	0.745095i
$530$	−53769.6			−4.40680
$531$	11248.0	+	5606.29i	0.919246	+	0.458178i
$532$	−3384.17	−	10999.4i	−0.275794	−	0.896398i
$533$	96.4619	+	55.6923i	0.00783908	+	0.00452589i
$534$	−18758.9	−	4415.92i	−1.52018	−	0.357856i
$535$	−14971.3	+	8643.67i	−1.20984	+	0.698502i
$536$	2781.27	−	1605.77i	0.224128	−	0.129400i
$537$	−2179.13	−	7238.84i	−0.175114	−	0.581712i
$538$	18086.7	+	10442.4i	1.44939	+	0.836807i
$539$	−6939.06	−	10209.4i	−0.554520	−	0.815860i
$540$	6190.22	+	16769.8i	0.493305	+	1.33640i
$541$	21816.1			1.73373			0.866865	−	0.498544i	$-0.166132\pi$
$541$	21816.1			1.73373			0.866865	+	0.498544i	$0.166132\pi$
$542$	−14455.7	+	25038.0i	−1.14562	+	1.98427i
$543$	−1102.24	−	3661.52i	−0.0871116	−	0.289376i
$544$	4330.77	−	2500.37i	0.341324	−	0.197063i
$545$	946.918	+	1640.11i	0.0744248	+	0.128907i
$546$	187.016	+	2775.35i	0.0146585	+	0.217535i
$547$	3976.21	−	6887.00i	0.310805	−	0.538330i	−0.667732	−	0.744402i	$-0.732735\pi$
$547$	3976.21	−	6887.00i	0.310805	−	0.538330i	0.978537	+	0.206072i	$0.0660680\pi$
$548$			7265.78i			0.566385i
$549$	16883.6	−	1034.73i	1.31252	−	0.0804395i
$550$	37275.6			2.88989
$551$	2913.43	−	5046.21i	0.225257	−	0.390156i
$552$	954.979	+	898.244i	0.0736352	+	0.0692605i
$553$	3493.49	+	3246.18i	0.268640	+	0.249623i
$554$	11898.3	−	6869.49i	0.912474	−	0.526817i
$555$	26831.7	+	25237.6i	2.05215	+	1.93023i
$556$	−11765.1	−	6792.57i	−0.897393	−	0.518110i
$557$		−	16793.7i		−	1.27750i	−0.769413	−	0.638752i	$-0.779451\pi$
$557$		−	16793.7i		−	1.27750i	0.769413	−	0.638752i	$-0.220549\pi$
$558$	−6028.88	+	3991.50i	−0.457389	+	0.302820i
$559$			744.667i			0.0563436i
$560$	6129.10	−	26764.3i	0.462503	−	2.01964i
$561$	3909.03	+	920.200i	0.294188	+	0.0692529i
$562$	4136.22	+	7164.14i	0.310455	+	0.537724i
$563$	−3810.86	−	6600.60i	−0.285273	−	0.494107i	0.687403	−	0.726277i	$-0.258751\pi$
$563$	−3810.86	−	6600.60i	−0.285273	−	0.494107i	−0.972675	+	0.232170i	$0.925418\pi$
$564$	14927.6	−	4493.70i	1.11448	−	0.335495i
$565$	28584.2	+	16503.1i	2.12840	+	1.22883i
$566$	8696.32			0.645819
$567$	10938.7	+	7913.79i	0.810201	+	0.586151i
$568$	708.403			0.0523309
$569$	−2201.40	−	1270.98i	−0.162193	−	0.0936420i	0.416707	−	0.909041i	$-0.363184\pi$
$569$	−2201.40	−	1270.98i	−0.162193	−	0.0936420i	−0.578899	+	0.815399i	$0.696518\pi$
$570$	36637.2	−	11029.0i	2.69221	−	0.810445i
$571$	−2123.22	−	3677.53i	−0.155611	−	0.269527i	0.777670	−	0.628673i	$-0.216401\pi$
$571$	−2123.22	−	3677.53i	−0.155611	−	0.269527i	−0.933281	+	0.359146i	$0.883068\pi$
$572$	875.751	+	1516.84i	0.0640157	+	0.110878i
$573$	−13960.0	−	3286.24i	−1.01778	−	0.239589i
$574$	1000.79	+	229.185i	0.0727741	+	0.0166655i
$575$		−	11255.8i		−	0.816345i
$576$	6501.60	−	4304.46i	0.470312	−	0.311376i
$577$			26192.0i			1.88975i	0.327426	+	0.944877i	$0.393819\pi$
$577$			26192.0i			1.88975i	−0.327426	+	0.944877i	$0.606181\pi$
$578$	14623.2	+	8442.70i	1.05233	+	0.607561i
$579$	4666.40	+	4389.17i	0.334938	+	0.315039i
$580$	−6607.89	+	3815.07i	−0.473065	+	0.273124i
$581$	5442.70	+	5057.40i	0.388642	+	0.361130i
$582$	−8639.72	−	8126.43i	−0.615340	−	0.578783i
$583$	−12785.7	+	22145.5i	−0.908285	+	1.57320i
$584$	−4334.94			−0.307160
$585$	−4097.63	+	251.128i	−0.289600	+	0.0177485i
$586$		−	2071.72i		−	0.146044i
$587$	1377.78	−	2386.39i	0.0968777	−	0.167797i	−0.813513	−	0.581547i	$-0.802448\pi$
$587$	1377.78	−	2386.39i	0.0968777	−	0.167797i	0.910391	+	0.413750i	$0.135781\pi$
$588$	4070.84	+	10629.0i	0.285508	+	0.745463i
$589$	3434.97	+	5949.53i	0.240298	+	0.416208i
$590$	−30505.4	+	17612.3i	−2.12862	+	1.22896i
$591$	−744.518	−	2473.21i	−0.0518196	−	0.172139i
$592$	13200.9	−	22864.6i	0.916474	−	1.58738i
$593$	−14044.3			−0.972567			−0.486284	−	0.873801i	$-0.661648\pi$
$593$	−14044.3			−0.972567			−0.486284	+	0.873801i	$0.661648\pi$
$594$	18874.9	+	3239.71i	1.30378	+	0.223783i
$595$	−7584.31	+	2333.46i	−0.522565	+	0.160777i
$596$	−2316.17	−	1337.24i	−0.159185	−	0.0919053i
$597$	−6743.98	−	22402.8i	−0.462333	−	1.53582i
$598$	1031.80	−	595.713i	0.0705579	−	0.0407366i
$599$	−10357.8	+	5980.08i	−0.706524	+	0.407912i	−0.809773	−	0.586744i	$-0.800410\pi$
$599$	−10357.8	+	5980.08i	−0.706524	+	0.407912i	0.103248	+	0.994656i	$0.467076\pi$
$600$	8454.56	+	1990.24i	0.575260	+	0.135418i
$601$	−21071.9	−	12165.9i	−1.43019	−	0.825718i	−0.433051	−	0.901369i	$-0.642563\pi$
$601$	−21071.9	−	12165.9i	−1.43019	−	0.825718i	−0.997134	+	0.0756510i	$0.975897\pi$
$602$	2018.48	+	6560.56i	0.136656	+	0.444167i
$603$	−12678.1	−	6319.13i	−0.856207	−	0.426757i
$604$	6073.80			0.409171
$605$	−356.915	+	618.196i	−0.0239846	+	0.0415425i
$606$	5742.68	−	6105.40i	0.384951	−	0.409266i
$607$	−8989.19	+	5189.91i	−0.601087	+	0.347038i	−0.769469	−	0.638684i	$-0.779479\pi$
$607$	−8989.19	+	5189.91i	−0.601087	+	0.347038i	0.168382	+	0.985722i	$0.446146\pi$
$608$	−11329.2	−	19622.8i	−0.755693	−	1.30890i
$609$	−2539.39	+	5173.25i	−0.168967	+	0.344221i
$610$	−23705.0	+	41058.2i	−1.57342	+	2.72524i
$611$			3580.20i			0.237053i
$612$	−3313.95	−	1651.77i	−0.218886	−	0.109099i
$613$	−7728.54			−0.509222			−0.254611	−	0.967044i	$-0.581947\pi$
$613$	−7728.54			−0.509222			−0.254611	+	0.967044i	$0.581947\pi$
$614$	−11745.1	+	20343.2i	−0.771979	+	1.33711i
$615$	−347.209	+	1474.95i	−0.0227655	+	0.0967085i
$616$	−2988.84	−	2777.25i	−0.195493	−	0.181654i
$617$	6665.11	−	3848.10i	0.434890	−	0.251084i	−0.266538	−	0.963825i	$-0.585880\pi$
$617$	6665.11	−	3848.10i	0.434890	−	0.251084i	0.701428	+	0.712741i	$0.252546\pi$
$618$	−14320.5	+	4310.94i	−0.932127	+	0.280601i
$619$	−25350.2	−	14635.9i	−1.64606	−	0.950352i	−0.978617	−	0.205689i	$-0.934056\pi$
$619$	−25350.2	−	14635.9i	−1.64606	−	0.950352i	−0.667441	−	0.744663i	$-0.732610\pi$
$620$		−	8996.01i		−	0.582723i
$621$	978.266	−	5699.48i	0.0632149	−	0.368297i
$622$		−	17714.8i		−	1.14196i
$623$	4042.54	−	17652.8i	0.259969	−	1.13522i
$624$	848.175	+	2817.55i	0.0544138	+	0.180757i
$625$	−12405.2	−	21486.4i	−0.793931	−	1.37513i
$626$	4858.46	+	8415.10i	0.310197	+	0.537276i
$627$	4169.45	−	17711.9i	0.265569	−	1.12814i
$628$	12039.5	+	6951.01i	0.765014	+	0.441681i
$629$	−7630.15			−0.483679
$630$	−35419.6	+	13319.4i	−2.23992	+	0.842314i
$631$	−16177.9			−1.02065			−0.510326	−	0.859981i	$-0.670475\pi$
$631$	−16177.9			−1.02065			−0.510326	+	0.859981i	$0.670475\pi$
$632$	1365.02	+	788.094i	0.0859138	+	0.0496024i
$633$	−12981.0	−	12209.8i	−0.815087	−	0.766663i
$634$	−5149.09	−	8918.49i	−0.322550	−	0.558673i
$635$	2799.24	+	4848.42i	0.174936	+	0.302998i
$636$	16154.0	−	17174.4i	1.00715	−	1.07077i
$637$	−2606.90	+	191.577i	−0.162150	+	0.0119161i
$638$			8174.41i			0.507254i
$639$	−1724.94	−	2605.41i	−0.106788	−	0.161296i
$640$		−	15314.5i		−	0.945875i
$641$	−23508.3	−	13572.5i	−1.44855	−	0.836321i	−0.450155	−	0.892951i	$-0.648631\pi$
$641$	−23508.3	−	13572.5i	−1.44855	−	0.836321i	−0.998395	+	0.0566298i	$0.981965\pi$
$642$	3912.93	−	16622.2i	0.240547	−	1.02185i
$643$	18843.1	−	10879.1i	1.15567	−	0.667229i	0.205411	−	0.978676i	$-0.434147\pi$
$643$	18843.1	−	10879.1i	1.15567	−	0.667229i	0.950263	+	0.311447i	$0.100814\pi$
$644$	3318.46	−	3571.27i	0.203052	−	0.218522i
$645$	−9700.38	+	2920.13i	−0.592174	+	0.178264i
$646$	−3962.70	+	6863.60i	−0.241347	+	0.418026i
$647$	24932.0			1.51496			0.757478	−	0.652860i	$-0.226431\pi$
$647$	24932.0			1.51496			0.757478	+	0.652860i	$0.226431\pi$
$648$	4108.08	+	1742.58i	0.249044	+	0.105641i
$649$			16751.9i			1.01320i
$650$	3946.60	−	6835.72i	0.238152	−	0.412491i
$651$	−3785.18	−	5642.50i	−0.227885	−	0.339704i
$652$	−1220.80	−	2114.50i	−0.0733288	−	0.127009i
$653$	838.558	−	484.142i	0.0502531	−	0.0290137i	−0.474663	−	0.880168i	$-0.657430\pi$
$653$	838.558	−	484.142i	0.0502531	−	0.0290137i	0.524916	+	0.851154i	$0.324097\pi$
$654$	−1820.97	−	428.663i	−0.108877	−	0.0256300i
$655$	21860.4	−	37863.3i	1.30406	−	2.25869i
$656$	1086.05			0.0646391
$657$	10555.5	+	15943.3i	0.626801	+	0.946739i
$658$	9704.44	+	31541.8i	0.574952	+	1.86874i
$659$	−3413.73	−	1970.92i	−0.201791	−	0.116504i	0.395700	−	0.918380i	$-0.370502\pi$
$659$	−3413.73	−	1970.92i	−0.201791	−	0.116504i	−0.597491	+	0.801876i	$0.703835\pi$
$660$	−16325.0	+	17356.1i	−0.962801	+	1.02361i
$661$	2506.55	−	1447.16i	0.147494	−	0.0851555i	−0.424437	−	0.905457i	$-0.639528\pi$
$661$	2506.55	−	1447.16i	0.147494	−	0.0851555i	0.571931	+	0.820302i	$0.306195\pi$
$662$	14932.3	−	8621.15i	0.876675	−	0.506149i
$663$	582.622	−	619.422i	0.0341284	−	0.0362841i
$664$	2126.64	+	1227.82i	0.124292	+	0.0717598i
$665$	10572.9	+	34364.7i	0.616543	+	2.00392i
$666$	−36318.5	+	2225.83i	−2.11308	+	0.129503i
$667$	2468.35			0.143291
$668$	786.084	−	1361.54i	0.0455307	−	0.0788615i
$669$	12530.3	+	2949.67i	0.724137	+	0.170465i
$670$	34384.1	−	19851.7i	1.98265	−	1.14468i
$671$	11273.5	+	19526.2i	0.648595	+	1.12340i
$672$	12484.3	+	18610.2i	0.716657	+	1.06831i
$673$	−6948.10	+	12034.5i	−0.397964	+	0.689293i	−0.993475	−	0.114054i	$-0.963616\pi$
$673$	−6948.10	+	12034.5i	−0.397964	+	0.689293i	0.595511	+	0.803347i	$0.296950\pi$
$674$		−	27516.5i		−	1.57255i
$675$	−13266.8	−	35940.9i	−0.756504	−	2.04943i
$676$	−13659.4			−0.777165
$677$	4561.28	−	7900.37i	0.258943	−	0.448502i	−0.707016	−	0.707197i	$-0.749959\pi$
$677$	4561.28	−	7900.37i	0.258943	−	0.448502i	0.965959	+	0.258695i	$0.0832926\pi$
$678$	−31219.8	+	9398.19i	−1.76842	+	0.532353i
$679$	7587.03	−	8165.05i	0.428812	−	0.461481i
$680$	−2271.32	+	1311.35i	−0.128090	+	0.0739529i
$681$	−200.089	+	849.982i	−0.0112591	+	0.0478288i
$682$	−8346.50	−	4818.85i	−0.468628	−	0.270562i
$683$		−	5500.02i		−	0.308129i	−0.988061	−	0.154065i	$-0.950764\pi$
$683$		−	5500.02i		−	0.308129i	0.988061	−	0.154065i	$-0.0492364\pi$
$684$	−7484.19	+	15015.6i	−0.418370	+	0.839379i
$685$		−	22700.0i		−	1.26617i
$686$	−22447.7	+	8754.04i	−1.24935	+	0.487217i
$687$	4067.48	−	4324.39i	0.225886	−	0.240154i
$688$	3630.43	+	6288.08i	0.201175	+	0.348446i
$689$	2707.41	+	4689.36i	0.149701	+	0.259290i
$690$	11806.1	+	11104.7i	0.651380	+	0.612682i
$691$	9079.68	+	5242.16i	0.499866	+	0.288598i	0.728658	−	0.684877i	$-0.240144\pi$
$691$	9079.68	+	5242.16i	0.499866	+	0.288598i	−0.228792	+	0.973475i	$0.573478\pi$
$692$	25401.8			1.39542
$693$	−2936.61	+	17755.1i	−0.160970	+	0.973246i
$694$	33334.8			1.82330
$695$	36756.9	+	21221.6i	2.00614	+	1.15825i
$696$	−436.451	+	1854.05i	−0.0237696	+	0.100974i
$697$	−156.935	−	271.820i	−0.00852849	−	0.0147718i
$698$	−13827.5	−	23949.9i	−0.749825	−	1.29874i
$699$	3267.50	+	10854.3i	0.176807	+	0.587334i
$700$	7209.54	−	31482.3i	0.389279	−	1.69989i
$701$			15162.7i			0.816955i	0.912768	+	0.408477i	$0.133940\pi$
$701$			15162.7i			0.816955i	−0.912768	+	0.408477i	$0.866060\pi$
$702$	2592.51	−	3118.33i	0.139385	−	0.167655i
$703$			34572.4i			1.85480i
$704$	9000.94	+	5196.69i	0.481869	+	0.278207i
$705$	−46637.4	+	14039.4i	−2.49144	+	0.750006i
$706$	−32928.2	+	19011.1i	−1.75534	+	1.01345i
$707$	5769.97	+	5361.50i	0.306934	+	0.285205i
$708$	3539.27	−	15034.9i	0.187873	−	0.798087i
$709$	1871.41	−	3241.38i	0.0991289	−	0.171696i	−0.812195	−	0.583385i	$-0.801728\pi$
$709$	1871.41	−	3241.38i	0.0991289	−	0.171696i	0.911324	+	0.411689i	$0.135061\pi$
$710$	8757.80			0.462922
$711$	−425.286	−	6939.34i	−0.0224324	−	0.366027i
$712$		−	5985.56i		−	0.315054i
$713$	−1455.10	+	2520.31i	−0.0764293	+	0.132379i
$714$	3453.94	−	7036.39i	0.181037	−	0.368810i
$715$	−2736.05	−	4738.98i	−0.143109	−	0.247871i
$716$	−8046.24	+	4645.50i	−0.419975	+	0.242473i
$717$	6799.90	−	7229.40i	0.354180	−	0.376551i
$718$	−21250.1	+	36806.3i	−1.10452	+	1.91309i
$719$	24366.5			1.26386			0.631931	−	0.775024i	$-0.282262\pi$
$719$	24366.5			1.26386			0.631931	+	0.775024i	$0.282262\pi$
$720$	−33376.7	+	22097.5i	−1.72760	+	1.14378i
$721$	−4132.68	−	13432.2i	−0.213466	−	0.693818i
$722$	8569.01	+	4947.32i	0.441697	+	0.255014i
$723$	11464.0	+	2698.67i	0.589696	+	0.138817i
$724$	−4069.91	+	2349.77i	−0.208919	+	0.120619i
$725$	14162.0	−	8176.42i	0.725466	−	0.418848i
$726$	−203.256	−	675.197i	−0.0103906	−	0.0345164i
$727$	20385.8	+	11769.7i	1.03998	+	0.600433i	0.919828	−	0.392322i	$-0.128328\pi$
$727$	20385.8	+	11769.7i	1.03998	+	0.600433i	0.120153	+	0.992755i	$0.461661\pi$
$728$	−825.748	+	254.057i	−0.0420388	+	0.0129340i
$729$	−3594.09	−	19352.1i	−0.182599	−	0.983188i
$730$	−53591.7			−2.71715
$731$	1049.20	−	1817.27i	0.0530862	−	0.0919481i
$732$	−5992.56	−	19906.7i	−0.302584	−	1.00515i
$733$	11851.1	−	6842.23i	0.597176	−	0.344780i	−0.170754	−	0.985314i	$-0.554620\pi$
$733$	11851.1	−	6842.23i	0.597176	−	0.344780i	0.767930	+	0.640534i	$0.221287\pi$
$734$	−5688.16	−	9852.18i	−0.286040	−	0.495437i
$735$	−12718.3	−	33207.5i	−0.638259	−	1.66650i
$736$	4799.24	−	8312.53i	0.240356	−	0.416310i
$737$		−	18881.9i		−	0.943722i
$738$	−826.287	−	1248.05i	−0.0412141	−	0.0622511i
$739$	12978.1			0.646017			0.323009	−	0.946396i	$-0.395306\pi$
$739$	12978.1			0.646017			0.323009	+	0.946396i	$0.395306\pi$
$740$	22635.8	−	39206.4i	1.12447	−	1.94764i
$741$	−2806.62	−	2639.87i	−0.139141	−	0.130875i
$742$	36563.3	+	33974.9i	1.80900	+	1.68094i
$743$	−24571.4	+	14186.3i	−1.21324	+	0.700464i	−0.963463	−	0.267840i	$-0.913690\pi$
$743$	−24571.4	+	14186.3i	−1.21324	+	0.700464i	−0.249775	+	0.968304i	$0.580357\pi$
$744$	−1635.80	−	1538.61i	−0.0806064	−	0.0758176i
$745$	7236.27	+	4177.86i	0.355861	+	0.205456i
$746$			15570.2i			0.764163i
$747$	−662.577	−	10811.2i	−0.0324530	−	0.529532i
$748$		−	4935.56i		−	0.241259i
$749$	15642.1	+	3582.08i	0.763082	+	0.174748i
$750$	56676.7	+	13341.9i	2.75939	+	0.649570i
$751$	13262.7	+	22971.6i	0.644423	+	1.11617i	0.984434	+	0.175752i	$0.0562358\pi$
$751$	13262.7	+	22971.6i	0.644423	+	1.11617i	−0.340011	+	0.940421i	$0.610431\pi$
$752$	17454.3	+	30231.8i	0.846402	+	1.46601i
$753$	1571.01	−	472.925i	0.0760302	−	0.0228876i
$754$	1499.05	+	865.475i	0.0724033	+	0.0418021i
$755$	−18976.0			−0.914711
$756$	6386.83	−	15314.8i	0.307258	−	0.736765i
$757$	15064.7			0.723296			0.361648	−	0.932315i	$-0.382214\pi$
$757$	15064.7			0.723296			0.361648	+	0.932315i	$0.382214\pi$
$758$	6737.68	+	3890.00i	0.322854	+	0.186400i
$759$	7380.94	−	2221.91i	0.352979	−	0.106258i
$760$	5941.75	+	10291.4i	0.283592	+	0.491196i
$761$	−2369.82	−	4104.66i	−0.112886	−	0.195524i	0.804047	−	0.594566i	$-0.202676\pi$
$761$	−2369.82	−	4104.66i	−0.112886	−	0.195524i	−0.916933	+	0.399042i	$0.869343\pi$
$762$	−5383.07	−	1267.19i	−0.255916	−	0.0602436i
$763$	392.418	−	1713.59i	0.0186192	−	0.0813057i
$764$			17626.0i			0.834667i
$765$	10353.6	+	5160.51i	0.489326	+	0.243894i
$766$			21135.0i			0.996917i
$767$	3072.01	+	1773.63i	0.144621	+	0.0834967i
$768$	19763.8	+	18589.6i	0.928599	+	0.873431i
$769$	−17949.9	+	10363.4i	−0.841730	+	0.485973i	−0.857852	−	0.513897i	$-0.828201\pi$
$769$	−17949.9	+	10363.4i	−0.841730	+	0.485973i	0.0161222	+	0.999870i	$0.494868\pi$
$770$	−36950.2	−	34334.5i	−1.72934	−	1.60692i
$771$	−15502.2	−	14581.2i	−0.724123	−	0.681103i
$772$	3936.68	−	6818.53i	0.183529	−	0.317881i
$773$	−10493.9			−0.488279			−0.244139	−	0.969740i	$-0.578505\pi$
$773$	−10493.9			−0.488279			−0.244139	+

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)

\(f(q)\)	\(=\)	\(q+(-3.28475 - 1.89645i) q^{2} +(-4.97559 + 1.49782i) q^{3} +(3.19307 + 5.53055i) q^{4} +(-9.97590 - 17.2788i) q^{5} +(19.1841 + 4.51602i) q^{6} +(-4.13417 + 18.0529i) q^{7} +6.12125i q^{8} +(22.5131 - 14.9051i) q^{9} +O(q^{10})\)	\(q+(-3.28475 - 1.89645i) q^{2} +(-4.97559 + 1.49782i) q^{3} +(3.19307 + 5.53055i) q^{4} +(-9.97590 - 17.2788i) q^{5} +(19.1841 + 4.51602i) q^{6} +(-4.13417 + 18.0529i) q^{7} +6.12125i q^{8} +(22.5131 - 14.9051i) q^{9} +75.6753i q^{10} +(31.1676 + 17.9946i) q^{11} +(-24.1712 - 22.7352i) q^{12} +(6.59980 - 3.81040i) q^{13} +(47.8163 - 51.4592i) q^{14} +(75.5165 + 71.0301i) q^{15} +(37.1532 - 64.3512i) q^{16} -21.4747 q^{17} +(-102.217 + 6.26447i) q^{18} +97.3022i q^{19} +(63.7074 - 110.345i) q^{20} +(-6.47004 - 96.0163i) q^{21} +(-68.2518 - 118.216i) q^{22} +(-35.6964 + 20.6094i) q^{23} +(-9.16851 - 30.4568i) q^{24} +(-136.537 + 236.489i) q^{25} -28.9050 q^{26} +(-89.6909 + 107.882i) q^{27} +(-113.043 + 34.7800i) q^{28} +(-51.8612 - 29.9421i) q^{29} +(-113.348 - 376.530i) q^{30} +(61.1449 - 35.3020i) q^{31} +(-201.669 + 116.434i) q^{32} +(-182.030 - 42.8505i) q^{33} +(70.5390 + 40.7257i) q^{34} +(353.175 - 108.661i) q^{35} +(154.319 + 76.9169i) q^{36} +355.309 q^{37} +(184.529 - 319.614i) q^{38} +(-27.1307 + 28.8443i) q^{39} +(105.768 - 61.0649i) q^{40} +(7.30794 + 12.6577i) q^{41} +(-160.838 + 327.660i) q^{42} +(-48.8575 + 84.6237i) q^{43} +229.832i q^{44} +(-482.130 - 240.307i) q^{45} +156.339 q^{46} +(-234.897 + 406.853i) q^{47} +(-88.4728 + 375.834i) q^{48} +(-308.817 - 149.268i) q^{49} +(896.982 - 517.873i) q^{50} +(106.849 - 32.1651i) q^{51} +(42.1472 + 24.3337i) q^{52} +710.531i q^{53} +(499.206 - 184.271i) q^{54} -718.049i q^{55} +(-110.506 - 25.3063i) q^{56} +(-145.741 - 484.136i) q^{57} +(113.568 + 196.705i) q^{58} +(232.735 + 403.109i) q^{59} +(-151.706 + 644.452i) q^{60} +(542.558 + 313.246i) q^{61} -267.794 q^{62} +(176.007 + 468.047i) q^{63} +288.792 q^{64} +(-131.678 - 76.0243i) q^{65} +(516.659 + 485.964i) q^{66} +(-262.327 - 454.364i) q^{67} +(-68.5700 - 118.767i) q^{68} +(146.742 - 156.011i) q^{69} +(-1366.16 - 312.855i) q^{70} -115.729i q^{71} +(91.2376 + 137.808i) q^{72} +708.180i q^{73} +(-1167.10 - 673.827i) q^{74} +(325.136 - 1381.18i) q^{75} +(-538.135 + 310.692i) q^{76} +(-453.708 + 488.273i) q^{77} +(143.819 - 43.2944i) q^{78} +(128.747 - 222.997i) q^{79} -1482.55 q^{80} +(284.678 - 671.118i) q^{81} -55.4366i q^{82} +(200.583 - 347.420i) q^{83} +(510.364 - 342.369i) q^{84} +(214.229 + 371.056i) q^{85} +(320.970 - 185.312i) q^{86} +(302.888 + 71.3010i) q^{87} +(-110.149 + 190.784i) q^{88} -977.834 q^{89} +(1127.95 + 1703.68i) q^{90} +(41.5042 + 134.899i) q^{91} +(-227.962 - 131.614i) q^{92} +(-251.356 + 267.233i) q^{93} +(1543.16 - 890.942i) q^{94} +(1681.26 - 970.677i) q^{95} +(829.026 - 881.389i) q^{96} +(-521.193 - 300.911i) q^{97} +(731.308 + 1075.97i) q^{98} +(969.889 - 59.4408i) 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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