LMFDB - Embedded newform 63.4.o.a.20.6

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			20.6
Character	$\chi$	$=$	63.20
Dual form			63.4.o.a.41.6

$q$-expansion

$f(q)$	$=$	$q+(-3.28475 - 1.89645i) q^{2} +(4.97559 - 1.49782i) q^{3} +(3.19307 + 5.53055i) q^{4} +(9.97590 + 17.2788i) q^{5} +(-19.1841 - 4.51602i) q^{6} +(-13.5672 + 12.6068i) q^{7} +6.12125i q^{8} +(22.5131 - 14.9051i) q^{9} +O(q^{10})$	\(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} +(-13.5672 + 12.6068i) 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} +(68.4731 - 15.6805i) 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} +(-48.6223 + 83.0474i) 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} +(317.208 - 180.580i) 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} +(25.1387 - 342.078i) 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} +(-77.1691 - 83.0483i) 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} +(-117.535 + 486.038i) 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} +(954.021 + 1026.70i) 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} +(-649.711 + 148.786i) 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} +(-614.552 - 3.73248i) 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	$0.184223\pi$
$5$	9.97590	+	17.2788i	0.892272	+	1.54546i	0.0551264	+	0.998479i	$0.482444\pi$
$6$	−19.1841	−	4.51602i	−1.30532	−	0.307276i
$7$	−13.5672	+	12.6068i	−0.732561	+	0.680702i
$7$	−13.5672	+	12.6068i	−0.732561	+	0.680702i
$8$			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	−0.568747	−	0.822512i	$-0.692572\pi$
$13$	−6.59980	+	3.81040i	−0.140804	+	0.0812934i	0.427943	+	0.903806i	$0.359238\pi$
$14$	68.4731	−	15.6805i	1.30716	−	0.299343i
$15$	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	$-0.451046\pi$
$17$	21.4747			0.306375			0.153187	+	0.988197i	$0.451046\pi$
$18$	−102.217	+	6.26447i	−1.33848	+	0.0820306i
$19$		−	97.3022i		−	1.17488i	−0.809269	−	0.587438i	$-0.800136\pi$
$19$		−	97.3022i		−	1.17488i	0.809269	−	0.587438i	$-0.199864\pi$
$20$	−63.7074	+	110.345i	−0.712271	+	1.23369i
$21$	−48.6223	+	83.0474i	−0.505250	+	0.862973i
$22$	−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	−0.666558	−	0.745453i	$-0.732233\pi$
$31$	−61.1449	+	35.3020i	−0.354256	+	0.204530i	0.312302	+	0.949983i	$0.398900\pi$
$32$	−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	0.851771	−	0.523914i	$-0.175529\pi$
$41$	−7.30794	−	12.6577i	−0.0278368	−	0.0482147i	−0.879608	+	0.475699i	$0.842195\pi$
$42$	317.208	−	180.580i	1.16539	−	0.663432i
$43$	−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	$-0.573316\pi$
$47$	234.897	−	406.853i	0.729005	−	1.26267i	0.957304	−	0.289083i	$-0.0933503\pi$
$48$	88.4728	−	375.834i	0.266041	−	1.13015i
$49$	25.1387	−	342.078i	0.0732907	−	0.997311i
$50$	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
$56$	−77.1691	−	83.0483i	−0.184146	−	0.198175i
$57$	−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	$-0.994996\pi$
$59$	−232.735	−	403.109i	−0.513551	−	0.889497i	0.486325	−	0.873778i	$-0.338337\pi$
$60$	−151.706	+	644.452i	−0.326420	+	1.38664i
$61$	−542.558	−	313.246i	−1.13881	−	0.657492i	−0.192674	−	0.981263i	$-0.561716\pi$
$61$	−542.558	−	313.246i	−1.13881	−	0.657492i	−0.946136	+	0.323771i	$0.895049\pi$
$62$	267.794			0.548547
$63$	−117.535	+	486.038i	−0.235048	+	0.971984i
$64$	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
$70$	954.021	+	1026.70i	1.62896	+	1.75306i
$71$		−	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	$-0.807828\pi$
$73$		−	708.180i		−	1.13543i	0.823226	−	0.567714i	$-0.192172\pi$
$74$	−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
$77$	−649.711	+	148.786i	−0.961577	+	0.220204i
$78$	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	−0.967632	−	0.252364i	$-0.918792\pi$
$83$	−200.583	+	347.420i	−0.265263	+	0.459449i	0.702370	+	0.711812i	$0.252125\pi$
$84$	−614.552	−	3.73248i	−0.798252	−	0.00484817i
$85$	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	$-0.302151\pi$
$89$	977.834			1.16461			0.582304	+	0.812971i	$0.302151\pi$
$90$	−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	0.747328	−	0.664455i	$-0.231336\pi$
$97$	521.193	+	300.911i	0.545558	+	0.314978i	−0.201770	+	0.979433i	$0.564670\pi$
$98$	−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	−0.951555	−	0.307478i	$-0.900515\pi$
$101$	−212.644	+	368.310i	−0.209494	+	0.362853i	0.742062	+	0.670332i	$0.233848\pi$
$102$	−411.973	−	96.9800i	−0.399916	−	0.0941417i
$103$	657.161	−	379.412i	0.628660	−	0.362957i	−0.151573	−	0.988446i	$-0.548434\pi$
$103$	657.161	−	379.412i	0.628660	−	0.362957i	0.780233	+	0.625489i	$0.215101\pi$
$104$	−23.3244	−	40.3990i	−0.0219918	−	0.0380909i
$105$	−1920.01	−	11.6611i	−1.78451	−	0.0108382i
$106$	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
$112$	307.195	+	1341.45i	0.259172	+	1.13174i
$113$	−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
$119$	−291.351	+	270.726i	−0.224438	+	0.208550i
$120$	−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
$126$	1307.82	−	1373.61i	0.924682	−	0.971200i
$127$	−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	$-0.905837\pi$
$131$	−1095.66	−	1897.74i	−0.730751	−	1.26570i	0.225812	−	0.974171i	$-0.427497\pi$
$132$	344.246	+	1143.55i	0.226991	+	0.754040i
$133$	1226.67	+	1320.12i	0.799741	+	0.860669i
$134$			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	0.181713	−	0.983352i	$-0.441836\pi$
$139$	1842.29	−	1063.64i	1.12418	−	0.649044i	0.942464	+	0.334308i	$0.108502\pi$
$140$	−526.755	−	2300.21i	−0.317992	−	1.38860i
$141$	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
$147$	−387.290	−	1739.69i	−0.217300	−	0.976105i
$148$	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	−0.895663	−	0.444734i	$-0.853298\pi$
$157$	−1885.26	+	1088.45i	−0.958343	+	0.553300i	−0.0626806	+	0.998034i	$0.519965\pi$
$158$	−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	0.893134	−	0.449791i	$-0.148501\pi$
$167$	123.092	+	213.202i	0.0570370	+	0.0987909i	−0.836097	+	0.548582i	$0.815168\pi$
$168$	−508.353	−	297.629i	−0.233454	−	0.136682i
$169$	−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	$0.505169\pi$
$173$	−1988.82	+	3444.74i	−0.874031	+	1.51387i	−0.857792	+	0.513998i	$0.828164\pi$
$174$	859.694	+	808.620i	0.374559	+	0.352306i
$175$	−1128.94	−	4929.80i	−0.487655	−	2.12947i
$176$	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	$-0.951718\pi$
$181$		−	735.896i		−	0.302203i	0.988518	−	0.151101i	$-0.0482820\pi$
$182$	−392.160	+	364.398i	−0.159719	+	0.148412i
$183$	−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
$189$	143.189	+	2594.37i	0.0551083	+	0.998480i
$190$	−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
$196$	1972.15	−	953.245i	0.718713	−	0.347393i
$197$			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	$-0.703796\pi$
$199$		−	4502.53i		−	1.60390i	0.597391	−	0.801950i	$-0.296204\pi$
$200$	−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
$203$	1081.09	−	247.572i	0.373780	−	0.0855967i
$204$	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
$210$	6284.64	+	3679.51i	2.06515	+	1.20910i
$211$	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	0.786255	−	0.617903i	$-0.212017\pi$
$223$	2145.46	+	1238.68i	0.644263	+	0.371965i	−0.141992	+	0.989868i	$0.545351\pi$
$224$	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	−0.878048	−	0.478573i	$-0.841154\pi$
$227$	−84.0252	+	145.536i	−0.0245681	+	0.0425531i	0.853480	+	0.521126i	$0.174488\pi$
$228$	2212.18	−	2351.91i	0.642567	−	0.683153i
$229$	989.455	−	571.262i	0.285524	−	0.164847i	−0.350397	−	0.936601i	$-0.613953\pi$
$229$	989.455	−	571.262i	0.285524	−	0.164847i	0.635922	+	0.771754i	$0.280620\pi$
$230$	1559.62	+	2701.34i	0.447123	+	0.774439i
$231$	−3009.84	+	1713.45i	−0.857286	+	0.488037i
$232$	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
$238$	1470.44	−	336.734i	0.400480	−	0.0917111i
$239$	−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	0.738836	−	0.673886i	$-0.235376\pi$
$241$	1962.89	+	1133.28i	0.524651	+	0.302907i	−0.214184	+	0.976793i	$0.568709\pi$
$242$			135.702i			0.0360464i
$243$	411.228	−	3765.61i	0.108561	−	0.994090i
$244$		−	4000.86i		−	1.04971i
$245$	6161.46	−	2978.17i	1.60670	−	0.776604i
$246$	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	$-0.487360\pi$
$251$	315.743			0.0794004			0.0397002	+	0.999212i	$0.487360\pi$
$252$	−3063.35	+	901.916i	−0.765767	+	0.225458i
$253$	−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	0.502939	−	0.864322i	$-0.332252\pi$
$257$	−2047.88	−	3547.03i	−0.497055	−	0.860924i	−0.999994	+	0.00339730i	$0.998919\pi$
$258$	1319.45	−	1402.79i	0.318393	−	0.338504i
$259$	−4820.56	+	4479.30i	−1.15651	+	1.07463i
$260$		−	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
$266$	−1525.75	−	6662.58i	−0.351691	−	1.53575i
$267$	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	$-0.285499\pi$
$269$	5506.26			1.24804			0.624019	+	0.781409i	$0.285499\pi$
$270$	−8164.01	−	6787.38i	−1.84017	−	1.52988i
$271$			7622.48i			1.70861i	0.519774	+	0.854304i	$0.326016\pi$
$271$			7622.48i			1.70861i	−0.519774	+	0.854304i	$0.673984\pi$
$272$	797.852	−	1381.92i	0.177856	−	0.308056i
$273$	4.45410	−	733.367i	0.000987451	−	0.162584i
$274$	−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	−0.276750	−	0.960942i	$-0.589257\pi$
$283$	1985.61	−	1146.39i	0.417075	−	0.240799i	0.693825	+	0.720143i	$0.255924\pi$
$284$	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	0.837514	−	0.546416i	$-0.184008\pi$
$293$	−273.105	−	473.031i	−0.0544537	−	0.0943166i	−0.891967	+	0.452100i	$0.850675\pi$
$294$	−2027.09	+	6448.94i	−0.402117	+	1.27928i
$295$	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
$301$	−403.971	−	1764.04i	−0.0773572	−	0.337800i
$302$	−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	$0.195261\pi$
$307$			6193.21i			1.15135i	−0.817677	+	0.575677i	$0.804739\pi$
$308$	−2897.44	−	3118.18i	−0.536028	−	0.576866i
$309$	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	0.570706	−	0.821155i	$-0.306670\pi$
$311$	−2335.25	−	4044.78i	−0.425788	−	0.737486i	−0.996494	+	0.0836685i	$0.973336\pi$
$312$	−176.563	−	166.073i	−0.0320382	−	0.0301348i
$313$	2218.64	+	1280.93i	0.400655	+	0.231318i	0.686767	−	0.726878i	$-0.259029\pi$
$313$	2218.64	+	1280.93i	0.400655	+	0.231318i	−0.286112	+	0.958196i	$0.592363\pi$
$314$	8256.81			1.48394
$315$	−9570.65	+	2817.80i	−1.71189	+	0.504016i
$316$	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
$322$	−2121.08	+	1970.93i	−0.367091	+	0.341104i
$323$		−	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
$329$	1942.21	+	8481.16i	0.325463	+	1.42122i
$330$	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
$336$	3537.73	+	6214.38i	0.574401	+	1.00899i
$337$	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	−0.0697122	−	0.997567i	$-0.522208\pi$
$349$	−6314.40	−	3645.62i	−0.968487	−	0.559156i	−0.898775	+	0.438411i	$0.855541\pi$
$350$	−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	$0.439390\pi$
$353$	−5012.28	+	8681.52i	−0.755741	+	1.30898i	−0.945005	+	0.327056i	$0.893943\pi$
$354$	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
$357$	−1044.15	+	1783.42i	−0.154796	+	0.264393i
$358$	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
$364$	878.590	−	201.200i	0.126513	−	0.0289718i
$365$	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	0.303766	−	0.952747i	$-0.401756\pi$
$367$	−2597.53	−	1499.68i	−0.369455	−	0.213305i	−0.673220	+	0.739442i	$0.735089\pi$
$368$			3062.81i			0.433859i
$369$	−353.188	−	176.039i	−0.0498272	−	0.0248353i
$370$		−	26888.1i		−	3.77797i
$371$	−8957.50	−	9639.92i	−1.25350	−	1.34900i
$372$	−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
$378$	4449.76	−	8793.42i	0.605479	−	1.19652i
$379$	−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	0.989828	−	0.142266i	$-0.0454389\pi$
$383$	2786.12	+	4825.70i	0.371708	+	0.643817i	−0.618120	+	0.786083i	$0.712106\pi$
$384$	3882.32	+	913.914i	0.515935	+	0.121453i
$385$	−9052.28	−	9741.93i	−1.19830	−	1.28960i
$386$			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
$392$	2093.94	+	153.880i	0.269796	+	0.0198269i
$393$	−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	$-0.876668\pi$
$397$		−	5977.49i		−	0.755672i	0.925872	−	0.377836i	$-0.123332\pi$
$398$	−8538.84	+	14789.7i	−1.07541	+	1.86267i
$399$	8080.70	+	4731.06i	1.01389	+	0.593607i
$400$	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	−0.949672	−	0.313245i	$-0.898584\pi$
$409$	−9538.96	+	5507.32i	−1.15323	+	0.665818i	−0.203558	+	0.979063i	$0.565250\pi$
$410$	−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	$-0.927750\pi$
$419$	−5849.85	−	10132.2i	−0.682062	−	1.18137i	0.292289	−	0.956330i	$-0.405583\pi$
$420$	−6066.22	−	10655.9i	−0.704765	−	1.23799i
$421$	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
$427$	11310.0	−	2590.03i	1.28180	−	0.293537i
$428$	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	$0.253749\pi$
$433$			12891.4i			1.43077i	−0.698730	+	0.715385i	$0.746251\pi$
$434$	−3633.23	+	3376.02i	−0.401844	+	0.373397i
$435$	−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	−0.192078	−	0.981380i	$-0.561523\pi$
$439$	−10467.6	−	6043.45i	−1.13802	−	0.657035i	−0.945939	+	0.324345i	$0.894856\pi$
$440$	−4395.36			−0.476228
$441$	−4532.74	−	8075.91i	−0.489444	−	0.872035i
$442$	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
$448$	−3918.10	+	3640.73i	−0.413199	+	0.383947i
$449$			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
$455$	2744.92	−	628.596i	0.282822	−	0.0647671i
$456$	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	−0.974214	−	0.225628i	$-0.927557\pi$
$461$	−2887.34	+	5001.02i	−0.291707	+	0.505251i	0.682506	+	0.730880i	$0.260890\pi$
$462$	13136.1	+	79.7817i	1.32282	+	0.00803416i
$463$	−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	$-0.634360\pi$
$467$	−8268.97			−0.819363			−0.409681	+	0.912229i	$0.634360\pi$
$468$	−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	$-0.588326\pi$
$479$	7295.72	−	12636.6i	0.695929	−	1.20538i	0.969867	−	0.243637i	$-0.0783404\pi$
$480$	−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
$483$	24.0909	−	3966.57i	0.00226951	−	0.373675i
$484$	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
$490$	−25886.8	−	1902.38i	−2.38663	−	0.175389i
$491$	−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
$497$	1458.96	+	1570.12i	0.131677	+	0.141709i
$498$	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	$-0.700182\pi$
$503$	−13272.2			−1.17650			−0.588248	+	0.808681i	$0.700182\pi$
$504$	−2975.16	−	719.461i	−0.262944	−	0.0635860i
$505$	−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	$0.0615935\pi$
$509$	7547.02	+	13071.8i	0.657202	+	1.13831i	−0.324135	+	0.946011i	$0.605073\pi$
$510$	−2434.11	−	8085.85i	−0.211341	−	0.702054i
$511$	8927.86	+	9608.03i	0.772887	+	0.831769i
$512$			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
$518$	24329.1	−	5571.44i	2.06363	−	0.472577i
$519$	−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	$-0.567451\pi$
$521$	−5002.27			−0.420640			−0.210320	+	0.977633i	$0.567451\pi$
$522$	5488.65	+	2735.70i	0.460214	+	0.229384i
$523$			909.042i			0.0760031i	0.999278	+	0.0380016i	$0.0120992\pi$
$523$			909.042i			0.0760031i	−0.999278	+	0.0380016i	$0.987901\pi$
$524$	6997.04	−	12119.2i	0.583334	−	1.01036i
$525$	−13001.1	−	22837.7i	−1.08079	−	1.89851i
$526$	−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
$546$	−1405.43	+	2400.48i	−0.110159	+	0.188152i
$547$	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
$553$	1064.53	+	4648.54i	0.0818596	+	0.357461i
$554$	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
$560$	−20114.0	+	18690.1i	−1.51781	+	1.41036i
$561$	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	0.972675	−	0.232170i	$-0.0745825\pi$
$563$	3810.86	+	6600.60i	0.285273	+	0.494107i	−0.687403	+	0.726277i	$0.741249\pi$
$564$	14927.6	−	4493.70i	1.11448	−	0.335495i
$565$	−28584.2	−	16503.1i	−2.12840	−	1.22883i
$566$	−8696.32			−0.645819
$567$	4598.35	+	12694.1i	0.340586	+	0.940213i
$568$	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
$574$	−698.877	−	752.121i	−0.0508198	−	0.0546915i
$575$		−	11255.8i		−	0.816345i
$576$	6501.60	−	4304.46i	0.470312	−	0.311376i
$577$		−	26192.0i		−	1.88975i	−0.327426	−	0.944877i	$-0.606181\pi$
$577$		−	26192.0i		−	1.88975i	0.327426	−	0.944877i	$-0.393819\pi$
$578$	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
$581$	−1658.49	−	7242.22i	−0.118426	−	0.517139i
$582$	−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	−0.910391	−	0.413750i	$-0.864219\pi$
$587$	−1377.78	+	2386.39i	−0.0968777	+	0.167797i	0.813513	+	0.581547i	$0.197552\pi$
$588$	8384.82	−	7696.88i	0.588068	−	0.539820i
$589$	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	$-0.338352\pi$
$593$	14044.3			0.972567			0.486284	+	0.873801i	$0.338352\pi$
$594$	−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	0.997134	−	0.0756510i	$-0.0241035\pi$
$601$	21071.9	+	12165.9i	1.43019	+	0.825718i	0.433051	+	0.901369i	$0.357437\pi$
$602$	−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	−0.168382	−	0.985722i	$-0.553854\pi$
$607$	8989.19	−	5189.91i	0.601087	−	0.347038i	0.769469	+	0.638684i	$0.220521\pi$
$608$	11329.2	+	19622.8i	0.755693	+	1.30890i
$609$	5008.23	−	2851.09i	0.333241	−	0.189707i
$610$	−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
$616$	−910.753	−	3977.04i	−0.0595703	−	0.260129i
$617$	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	$0.0659436\pi$
$619$	25350.2	+	14635.9i	1.64606	+	0.950352i	0.667441	+	0.744663i	$0.267390\pi$
$620$		−	8996.01i		−	0.582723i
$621$	−978.266	+	5699.48i	−0.0632149	+	0.368297i
$622$			17714.8i			1.14196i
$623$	−13266.5	+	12327.3i	−0.853147	+	0.792751i
$624$	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
$630$	36781.0	+	8894.50i	2.32602	+	0.562485i
$631$	−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
$637$	1137.54	+	2353.43i	0.0707551	+	0.146384i
$638$			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	−0.950263	−	0.311447i	$-0.899186\pi$
$643$	−18843.1	+	10879.1i	−1.15567	+	0.667229i	−0.205411	+	0.978676i	$0.565853\pi$
$644$	4752.04	−	1088.23i	0.290771	−	0.0665874i
$645$	−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	$-0.773569\pi$
$647$	−24932.0			−1.51496			−0.757478	+	0.652860i	$0.773569\pi$
$648$	4108.08	+	1742.58i	0.249044	+	0.105641i
$649$		−	16751.9i		−	1.01320i
$650$	−3946.60	+	6835.72i	−0.238152	+	0.412491i
$651$	41.2657	−	6794.39i	0.00248438	−	0.409053i
$652$	−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	−0.571931	−	0.820302i	$-0.693805\pi$
$661$	−2506.55	+	1447.16i	−0.147494	+	0.0851555i	0.424437	+	0.905457i	$0.360472\pi$
$662$	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
$672$	136.103	−	22409.3i	0.00781292	−	1.28640i
$673$	−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	−0.965959	−	0.258695i	$-0.916707\pi$
$677$	−4561.28	+	7900.37i	−0.258943	+	0.448502i	0.707016	+	0.707197i	$0.250041\pi$
$678$	31219.8	−	9398.19i	1.76842	−	0.532353i
$679$	−10864.7	+	2488.04i	−0.614060	+	0.140622i
$680$	−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
$686$	−3642.63	−	23817.3i	−0.202735	−	1.32558i
$687$	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	0.228792	−	0.973475i	$-0.426522\pi$
$691$	−9079.68	−	5242.16i	−0.499866	−	0.288598i	−0.728658	+	0.684877i	$0.759856\pi$
$692$	−25401.8			−1.39542
$693$	−12409.3	+	13033.6i	−0.680219	+	0.714438i
$694$	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
$700$	23659.7	−	21984.8i	1.27751	−	1.18707i
$701$			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
$707$	−1758.21	−	7677.69i	−0.0935282	−	0.408415i
$708$	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
$714$	6811.93	−	3877.90i	0.357045	−	0.203259i
$715$	−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	$-0.717738\pi$
$719$	−24366.5			−1.26386			−0.631931	+	0.775024i	$0.717738\pi$
$720$	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	−0.120153	−	0.992755i	$-0.538339\pi$
$727$	−20385.8	−	11769.7i	−1.03998	−	0.600433i	−0.919828	+	0.392322i	$0.871672\pi$
$728$	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	−0.767930	−	0.640534i	$-0.778713\pi$
$733$	−11851.1	+	6842.23i	−0.597176	+	0.344780i	0.170754	+	0.985314i	$0.445380\pi$
$734$	5688.16	+	9852.18i	0.286040	+	0.495437i
$735$	26196.2	−	24046.9i	1.31464	−	1.20678i
$736$	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
$742$	11141.5	+	48652.2i	0.551236	+	2.40712i
$743$	−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
$749$	10923.2	+	11755.4i	0.532877	+	0.573474i
$750$	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
$756$	−13891.1	+	9075.92i	−0.668273	+	0.436624i
$757$	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	0.916933	−	0.399042i	$-0.130657\pi$
$761$	2369.82	+	4104.66i	0.112886	+	0.195524i	−0.804047	+	0.594566i	$0.797324\pi$
$762$	5383.07	+	1267.19i	0.255916	+	0.0602436i
$763$	1287.81	−	1196.64i	0.0611032	−	0.0567776i
$764$			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	−0.0161222	−	0.999870i	$-0.505132\pi$
$769$	17949.9	−	10363.4i	0.841730	−	0.485973i	0.857852	+	0.513897i	$0.171799\pi$
$770$	11259.4	+	49167.1i	0.526962	+	2.30111i
$771$	−15502.2	−	14581.2i	−0.724123	−	0.681103i
$772$	3936.68	−	6818.53i	0.183529	−	0.317881i
$773$	10493.9			0.488279			0.244139	−

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)

\(f(q)\)	\(=\)	\(q+(-3.28475 - 1.89645i) q^{2} +(4.97559 - 1.49782i) q^{3} +(3.19307 + 5.53055i) q^{4} +(9.97590 + 17.2788i) q^{5} +(-19.1841 - 4.51602i) q^{6} +(-13.5672 + 12.6068i) q^{7} +6.12125i q^{8} +(22.5131 - 14.9051i) q^{9} +O(q^{10})\)	\(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} +(-13.5672 + 12.6068i) 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} +(68.4731 - 15.6805i) 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} +(-48.6223 + 83.0474i) 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} +(317.208 - 180.580i) 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} +(25.1387 - 342.078i) 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} +(-77.1691 - 83.0483i) 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} +(-117.535 + 486.038i) 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} +(954.021 + 1026.70i) 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} +(-649.711 + 148.786i) 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} +(-614.552 - 3.73248i) 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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