LMFDB - Embedded newform 65.5.g.a.34.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,5,Mod(34,65)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("65.34");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	65.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.71904760045$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			34.13
Character	$\chi$	$=$	65.34
Dual form			65.5.g.a.44.13

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0630863 + 0.0630863i) q^{2} -12.3873i q^{3} +15.9920i q^{4} +(-17.7387 + 17.6164i) q^{5} +(0.781468 + 0.781468i) q^{6} +(-27.4701 - 27.4701i) q^{7} +(-2.01826 - 2.01826i) q^{8} -72.4449 q^{9} +O(q^{10})$	\(q+(-0.0630863 + 0.0630863i) q^{2} -12.3873i q^{3} +15.9920i q^{4} +(-17.7387 + 17.6164i) q^{5} +(0.781468 + 0.781468i) q^{6} +(-27.4701 - 27.4701i) q^{7} +(-2.01826 - 2.01826i) q^{8} -72.4449 q^{9} +(0.00771715 - 2.23042i) q^{10} +(-136.513 + 136.513i) q^{11} +198.098 q^{12} +(23.3368 + 167.381i) q^{13} +3.46597 q^{14} +(218.219 + 219.735i) q^{15} -255.618 q^{16} +102.058 q^{17} +(4.57028 - 4.57028i) q^{18} +(145.830 + 145.830i) q^{19} +(-281.722 - 283.678i) q^{20} +(-340.279 + 340.279i) q^{21} -17.2242i q^{22} -848.743 q^{23} +(-25.0007 + 25.0007i) q^{24} +(4.32488 - 624.985i) q^{25} +(-12.0317 - 9.08721i) q^{26} -105.975i q^{27} +(439.302 - 439.302i) q^{28} +632.151 q^{29} +(-27.6289 - 0.0955945i) q^{30} +(-806.336 - 806.336i) q^{31} +(48.4181 - 48.4181i) q^{32} +(1691.03 + 1691.03i) q^{33} +(-6.43846 + 6.43846i) q^{34} +(971.207 + 3.36033i) q^{35} -1158.54i q^{36} +(-314.960 - 314.960i) q^{37} -18.3997 q^{38} +(2073.40 - 289.080i) q^{39} +(71.3558 + 0.246887i) q^{40} +(1672.29 + 1672.29i) q^{41} -42.9339i q^{42} -1100.32 q^{43} +(-2183.12 - 2183.12i) q^{44} +(1285.08 - 1276.22i) q^{45} +(53.5440 - 53.5440i) q^{46} +(-1366.99 - 1366.99i) q^{47} +3166.41i q^{48} -891.792i q^{49} +(39.1551 + 39.7008i) q^{50} -1264.22i q^{51} +(-2676.76 + 373.204i) q^{52} +1024.33i q^{53} +(6.68557 + 6.68557i) q^{54} +(16.6992 - 4826.44i) q^{55} +110.883i q^{56} +(1806.44 - 1806.44i) q^{57} +(-39.8801 + 39.8801i) q^{58} +(-4449.90 + 4449.90i) q^{59} +(-3514.01 + 3489.77i) q^{60} +5750.05 q^{61} +101.737 q^{62} +(1990.06 + 1990.06i) q^{63} -4083.78i q^{64} +(-3362.62 - 2558.01i) q^{65} -213.361 q^{66} +(-1850.61 + 1850.61i) q^{67} +1632.12i q^{68} +10513.6i q^{69} +(-61.4819 + 61.0579i) q^{70} +(2832.57 + 2832.57i) q^{71} +(146.212 + 146.212i) q^{72} +(4636.26 + 4636.26i) q^{73} +39.7393 q^{74} +(-7741.87 - 53.5736i) q^{75} +(-2332.12 + 2332.12i) q^{76} +7500.04 q^{77} +(-112.566 + 149.040i) q^{78} +4185.92 q^{79} +(4534.34 - 4503.07i) q^{80} -7180.78 q^{81} -210.998 q^{82} +(-3093.93 + 3093.93i) q^{83} +(-5441.76 - 5441.76i) q^{84} +(-1810.38 + 1797.89i) q^{85} +(69.4152 - 69.4152i) q^{86} -7830.64i q^{87} +551.037 q^{88} +(-1489.20 + 1489.20i) q^{89} +(-0.559068 + 161.583i) q^{90} +(3956.90 - 5239.03i) q^{91} -13573.1i q^{92} +(-9988.31 + 9988.31i) q^{93} +172.476 q^{94} +(-5155.83 - 17.8389i) q^{95} +(-599.769 - 599.769i) q^{96} +(-1580.20 + 1580.20i) q^{97} +(56.2598 + 56.2598i) q^{98} +(9889.67 - 9889.67i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9}+O(q^{10}) $ 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9	$ 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9} + 8 q^{11} + 424 q^{14} - 508 q^{15} - 3128 q^{16} + 268 q^{19} + 2116 q^{20} - 668 q^{21} + 2032 q^{24} + 1100 q^{26} - 3704 q^{29} - 1660 q^{31} + 1252 q^{34} + 6692 q^{35} + 7408 q^{39} + 3644 q^{40} + 5960 q^{41} + 1444 q^{44} - 8674 q^{45} + 17620 q^{46} - 3928 q^{50} - 30588 q^{54} + 14784 q^{55} - 5548 q^{59} - 13976 q^{60} - 20008 q^{61} - 15614 q^{65} + 24752 q^{66} + 26908 q^{70} - 16360 q^{71} - 7304 q^{74} - 5760 q^{76} - 9536 q^{79} - 62348 q^{80} - 36516 q^{81} + 66564 q^{84} - 11604 q^{85} - 5264 q^{86} - 940 q^{89} + 37644 q^{91} + 55448 q^{94} - 61644 q^{96} + 16140 q^{99}+O(q^{100}) $ 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9 + 8 * q^11 + 424 * q^14 - 508 * q^15 - 3128 * q^16 + 268 * q^19 + 2116 * q^20 - 668 * q^21 + 2032 * q^24 + 1100 * q^26 - 3704 * q^29 - 1660 * q^31 + 1252 * q^34 + 6692 * q^35 + 7408 * q^39 + 3644 * q^40 + 5960 * q^41 + 1444 * q^44 - 8674 * q^45 + 17620 * q^46 - 3928 * q^50 - 30588 * q^54 + 14784 * q^55 - 5548 * q^59 - 13976 * q^60 - 20008 * q^61 - 15614 * q^65 + 24752 * q^66 + 26908 * q^70 - 16360 * q^71 - 7304 * q^74 - 5760 * q^76 - 9536 * q^79 - 62348 * q^80 - 36516 * q^81 + 66564 * q^84 - 11604 * q^85 - 5264 * q^86 - 940 * q^89 + 37644 * q^91 + 55448 * q^94 - 61644 * q^96 + 16140 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.0630863	+	0.0630863i	−0.0157716	+	0.0157716i	−0.714949	−	0.699177i	$-0.753550\pi$
$2$	−0.0630863	+	0.0630863i	−0.0157716	+	0.0157716i	0.699177	+	0.714949i	$0.253550\pi$
$3$		−	12.3873i		−	1.37637i	−0.725538	−	0.688183i	$-0.758409\pi$
$3$		−	12.3873i		−	1.37637i	0.725538	−	0.688183i	$-0.241591\pi$
$4$			15.9920i			0.999503i
$5$	−17.7387	+	17.6164i	−0.709549	+	0.704656i
$5$	−17.7387	+	17.6164i	−0.709549	+	0.704656i
$6$	0.781468	+	0.781468i	0.0217074	+	0.0217074i
$7$	−27.4701	−	27.4701i	−0.560613	−	0.560613i	0.368868	−	0.929482i	$-0.379745\pi$
$7$	−27.4701	−	27.4701i	−0.560613	−	0.560613i	−0.929482	+	0.368868i	$0.879745\pi$
$8$	−2.01826	−	2.01826i	−0.0315353	−	0.0315353i
$9$	−72.4449			−0.894381
$10$	0.00771715	−	2.23042i	7.71715e−5	−	0.0223042i
$11$	−136.513	+	136.513i	−1.12821	+	1.12821i	−0.137738	+	0.990469i	$0.543983\pi$
$11$	−136.513	+	136.513i	−1.12821	+	1.12821i	−0.990469	+	0.137738i	$0.956017\pi$
$12$	198.098			1.37568
$13$	23.3368	+	167.381i	0.138088	+	0.990420i
$13$	23.3368	+	167.381i	0.138088	+	0.990420i
$14$	3.46597			0.0176835
$15$	218.219	+	219.735i	0.969864	+	0.976599i
$16$	−255.618			−0.998508
$17$	102.058			0.353142			0.176571	−	0.984288i	$-0.443499\pi$
$17$	102.058			0.353142			0.176571	+	0.984288i	$0.443499\pi$
$18$	4.57028	−	4.57028i	0.0141058	−	0.0141058i
$19$	145.830	+	145.830i	0.403961	+	0.403961i	0.879626	−	0.475666i	$-0.157793\pi$
$19$	145.830	+	145.830i	0.403961	+	0.403961i	−0.475666	+	0.879626i	$0.657793\pi$
$20$	−281.722	−	283.678i	−0.704305	−	0.709196i
$21$	−340.279	+	340.279i	−0.771609	+	0.771609i
$22$		−	17.2242i		−	0.0355872i
$23$	−848.743			−1.60443			−0.802215	−	0.597036i	$-0.796345\pi$
$23$	−848.743			−1.60443			−0.802215	+	0.597036i	$0.796345\pi$
$24$	−25.0007	+	25.0007i	−0.0434041	+	0.0434041i
$25$	4.32488	−	624.985i	0.00691981	−	0.999976i
$26$	−12.0317	−	9.08721i	−0.0177983	−	0.0134426i
$27$		−	105.975i		−	0.145370i
$28$	439.302	−	439.302i	0.560335	−	0.560335i
$29$	632.151			0.751666			0.375833	−	0.926687i	$-0.377357\pi$
$29$	632.151			0.751666			0.375833	+	0.926687i	$0.377357\pi$
$30$	−27.6289	−	0.0955945i	−0.0306988	−	0.000106216i
$31$	−806.336	−	806.336i	−0.839059	−	0.839059i	0.149676	−	0.988735i	$-0.452177\pi$
$31$	−806.336	−	806.336i	−0.839059	−	0.839059i	−0.988735	+	0.149676i	$0.952177\pi$
$32$	48.4181	−	48.4181i	0.0472833	−	0.0472833i
$33$	1691.03	+	1691.03i	1.55282	+	1.55282i
$34$	−6.43846	+	6.43846i	−0.00556960	+	0.00556960i
$35$	971.207	+	3.36033i	0.792822	+	0.00274312i
$36$		−	1158.54i		−	0.893936i
$37$	−314.960	−	314.960i	−0.230065	−	0.230065i	0.582655	−	0.812720i	$-0.302014\pi$
$37$	−314.960	−	314.960i	−0.230065	−	0.230065i	−0.812720	+	0.582655i	$0.802014\pi$
$38$	−18.3997			−0.0127422
$39$	2073.40	−	289.080i	1.36318	−	0.190059i
$40$	71.3558	+	0.246887i	0.0445974	+	0.000154305i
$41$	1672.29	+	1672.29i	0.994821	+	0.994821i	0.999987	−	0.00516607i	$-0.00164442\pi$
$41$	1672.29	+	1672.29i	0.994821	+	0.994821i	−0.00516607	+	0.999987i	$0.501644\pi$
$42$		−	42.9339i		−	0.0243390i
$43$	−1100.32			−0.595090			−0.297545	−	0.954708i	$-0.596168\pi$
$43$	−1100.32			−0.595090			−0.297545	+	0.954708i	$0.596168\pi$
$44$	−2183.12	−	2183.12i	−1.12765	−	1.12765i
$45$	1285.08	−	1276.22i	0.634607	−	0.630231i
$46$	53.5440	−	53.5440i	0.0253044	−	0.0253044i
$47$	−1366.99	−	1366.99i	−0.618827	−	0.618827i	0.326404	−	0.945230i	$-0.394163\pi$
$47$	−1366.99	−	1366.99i	−0.618827	−	0.618827i	−0.945230	+	0.326404i	$0.894163\pi$
$48$			3166.41i			1.37431i
$49$		−	891.792i		−	0.371425i
$50$	39.1551	+	39.7008i	0.0156621	+	0.0158803i
$51$		−	1264.22i		−	0.486052i
$52$	−2676.76	+	373.204i	−0.989927	+	0.138019i
$53$			1024.33i			0.364660i	0.983237	+	0.182330i	$0.0583640\pi$
$53$			1024.33i			0.364660i	−0.983237	+	0.182330i	$0.941636\pi$
$54$	6.68557	+	6.68557i	0.00229272	+	0.00229272i
$55$	16.6992	−	4826.44i	0.00552040	−	1.59552i
$56$			110.883i			0.0353582i
$57$	1806.44	−	1806.44i	0.555997	−	0.555997i
$58$	−39.8801	+	39.8801i	−0.0118550	+	0.0118550i
$59$	−4449.90	+	4449.90i	−1.27834	+	1.27834i	−0.336745	+	0.941596i	$0.609326\pi$
$59$	−4449.90	+	4449.90i	−1.27834	+	1.27834i	−0.941596	+	0.336745i	$0.890674\pi$
$60$	−3514.01	+	3489.77i	−0.976113	+	0.969381i
$61$	5750.05			1.54530			0.772648	−	0.634835i	$-0.218932\pi$
$61$	5750.05			1.54530			0.772648	+	0.634835i	$0.218932\pi$
$62$	101.737			0.0264666
$63$	1990.06	+	1990.06i	0.501402	+	0.501402i
$64$		−	4083.78i		−	0.997016i
$65$	−3362.62	−	2558.01i	−0.795886	−	0.605447i
$66$	−213.361			−0.0489810
$67$	−1850.61	+	1850.61i	−0.412253	+	0.412253i	−0.882523	−	0.470270i	$-0.844157\pi$
$67$	−1850.61	+	1850.61i	−0.412253	+	0.412253i	0.470270	+	0.882523i	$0.344157\pi$
$68$			1632.12i			0.352966i
$69$			10513.6i			2.20828i
$70$	−61.4819	+	61.0579i	−0.0125473	+	0.0124608i
$71$	2832.57	+	2832.57i	0.561907	+	0.561907i	0.929849	−	0.367942i	$-0.119938\pi$
$71$	2832.57	+	2832.57i	0.561907	+	0.561907i	−0.367942	+	0.929849i	$0.619938\pi$
$72$	146.212	+	146.212i	0.0282046	+	0.0282046i
$73$	4636.26	+	4636.26i	0.870005	+	0.870005i	0.992473	−	0.122467i	$-0.0390806\pi$
$73$	4636.26	+	4636.26i	0.870005	+	0.870005i	−0.122467	+	0.992473i	$0.539081\pi$
$74$	39.7393			0.00725699
$75$	−7741.87	−	53.5736i	−1.37633	−	0.00952419i
$76$	−2332.12	+	2332.12i	−0.403760	+	0.403760i
$77$	7500.04			1.26498
$78$	−112.566	+	149.040i	−0.0185019	+	0.0244970i
$79$	4185.92			0.670713			0.335356	−	0.942091i	$-0.391143\pi$
$79$	4185.92			0.670713			0.335356	+	0.942091i	$0.391143\pi$
$80$	4534.34	−	4503.07i	0.708490	−	0.703605i
$81$	−7180.78			−1.09446
$82$	−210.998			−0.0313798
$83$	−3093.93	+	3093.93i	−0.449112	+	0.449112i	−0.895059	−	0.445947i	$-0.852867\pi$
$83$	−3093.93	+	3093.93i	−0.449112	+	0.449112i	0.445947	+	0.895059i	$0.352867\pi$
$84$	−5441.76	−	5441.76i	−0.771225	−	0.771225i
$85$	−1810.38	+	1797.89i	−0.250572	+	0.248844i
$86$	69.4152	−	69.4152i	0.00938550	−	0.00938550i
$87$		−	7830.64i		−	1.03457i
$88$	551.037			0.0711567
$89$	−1489.20	+	1489.20i	−0.188007	+	0.188007i	−0.794834	−	0.606827i	$-0.792442\pi$
$89$	−1489.20	+	1489.20i	−0.188007	+	0.188007i	0.606827	+	0.794834i	$0.292442\pi$
$90$	−0.559068	+	161.583i	−6.90207e−5	+	0.0199485i
$91$	3956.90	−	5239.03i	0.477829	−	0.632657i
$92$		−	13573.1i		−	1.60363i
$93$	−9988.31	+	9988.31i	−1.15485	+	1.15485i
$94$	172.476			0.0195197
$95$	−5155.83	−	17.8389i	−0.571283	−	0.00197661i
$96$	−599.769	−	599.769i	−0.0650791	−	0.0650791i
$97$	−1580.20	+	1580.20i	−0.167946	+	0.167946i	−0.786076	−	0.618130i	$-0.787890\pi$
$97$	−1580.20	+	1580.20i	−0.167946	+	0.167946i	0.618130	+	0.786076i	$0.287890\pi$
$98$	56.2598	+	56.2598i	0.00585796	+	0.00585796i
$99$	9889.67	−	9889.67i	1.00905	−	1.00905i
$100$	9994.79	+	69.1637i	0.999479	+	0.00691637i
$101$		−	2359.28i		−	0.231279i	−0.993291	−	0.115640i	$-0.963108\pi$
$101$		−	2359.28i		−	0.231279i	0.993291	−	0.115640i	$-0.0368918\pi$
$102$	79.7551	+	79.7551i	0.00766581	+	0.00766581i
$103$	2367.51			0.223161			0.111580	−	0.993755i	$-0.464409\pi$
$103$	2367.51			0.223161			0.111580	+	0.993755i	$0.464409\pi$
$104$	290.718	−	384.918i	0.0268785	−	0.0355878i
$105$	41.6253	−	12030.6i	0.00377554	−	1.09121i
$106$	−64.6212	−	64.6212i	−0.00575127	−	0.00575127i
$107$			14310.1i			1.24990i	0.780665	+	0.624950i	$0.214881\pi$
$107$			14310.1i			1.24990i	−0.780665	+	0.624950i	$0.785119\pi$
$108$	1694.76			0.145298
$109$	2202.81	+	2202.81i	0.185406	+	0.185406i	0.793707	−	0.608301i	$-0.208149\pi$
$109$	2202.81	+	2202.81i	0.185406	+	0.185406i	−0.608301	+	0.793707i	$0.708149\pi$
$110$	303.428	+	305.535i	0.0250767	+	0.0252509i
$111$	−3901.49	+	3901.49i	−0.316654	+	0.316654i
$112$	7021.84	+	7021.84i	0.559777	+	0.559777i
$113$			15981.9i			1.25162i	0.779976	+	0.625809i	$0.215231\pi$
$113$			15981.9i			1.25162i	−0.779976	+	0.625809i	$0.784769\pi$
$114$			227.923i			0.0175379i
$115$	15055.6	−	14951.8i	1.13842	−	1.13057i
$116$			10109.4i			0.751292i
$117$	−1690.63	−	12125.9i	−0.123503	−	0.885813i
$118$		−	561.456i		−	0.0403229i
$119$	−2803.54	−	2803.54i	−0.197976	−	0.197976i
$120$	3.05826	−	883.905i	0.000212379	−	0.0613823i
$121$		−	22630.6i		−	1.54570i
$122$	−362.749	+	362.749i	−0.0243717	+	0.0243717i
$123$	20715.2	−	20715.2i	1.36924	−	1.36924i
$124$	12895.0	−	12895.0i	0.838642	−	0.838642i
$125$	10933.3	+	11162.6i	0.699729	+	0.714408i
$126$	−251.092			−0.0158158
$127$	11015.9			0.682987			0.341494	−	0.939884i	$-0.389067\pi$
$127$	11015.9			0.682987			0.341494	+	0.939884i	$0.389067\pi$
$128$	1032.32	+	1032.32i	0.0630078	+	0.0630078i
$129$			13630.0i			0.819061i
$130$	373.511	−	50.7593i	0.0221012	−	0.00300351i
$131$	−23637.6			−1.37740			−0.688700	−	0.725046i	$-0.741818\pi$
$131$	−23637.6			−1.37740			−0.688700	+	0.725046i	$0.741818\pi$
$132$	−27043.0	+	27043.0i	−1.55205	+	1.55205i
$133$		−	8011.91i		−	0.452932i
$134$		−	233.496i		−	0.0130038i
$135$	1866.90	+	1879.86i	0.102436	+	0.103147i
$136$	−205.979	−	205.979i	−0.0111364	−	0.0111364i
$137$	−12993.2	−	12993.2i	−0.692267	−	0.692267i	0.270463	−	0.962730i	$-0.412823\pi$
$137$	−12993.2	−	12993.2i	−0.692267	−	0.692267i	−0.962730	+	0.270463i	$0.912823\pi$
$138$	−663.265	−	663.265i	−0.0348281	−	0.0348281i
$139$	−22072.8			−1.14242			−0.571211	−	0.820803i	$-0.693526\pi$
$139$	−22072.8			−1.14242			−0.571211	+	0.820803i	$0.693526\pi$
$140$	−53.7385	+	15531.6i	−0.00274176	+	0.792428i
$141$	−16933.3	+	16933.3i	−0.851732	+	0.851732i
$142$	−357.393			−0.0177243
$143$	−26035.5	−	19663.9i	−1.27319	−	0.961607i
$144$	18518.2			0.893046
$145$	−11213.6	+	11136.2i	−0.533344	+	0.529666i
$146$	−584.969			−0.0274427
$147$	−11046.9			−0.511217
$148$	5036.85	−	5036.85i	0.229951	−	0.229951i
$149$	1744.22	+	1744.22i	0.0785648	+	0.0785648i	0.745297	−	0.666732i	$-0.232308\pi$
$149$	1744.22	+	1744.22i	0.0785648	+	0.0785648i	−0.666732	+	0.745297i	$0.732308\pi$
$150$	491.785	−	485.026i	0.0218571	−	0.0215567i
$151$	12785.9	−	12785.9i	0.560763	−	0.560763i	−0.368761	−	0.929524i	$-0.620218\pi$
$151$	12785.9	−	12785.9i	0.560763	−	0.560763i	0.929524	+	0.368761i	$0.120218\pi$
$152$		−	588.645i		−	0.0254780i
$153$	−7393.58			−0.315843
$154$	−473.150	+	473.150i	−0.0199507	+	0.0199507i
$155$	28508.1	+	98.6366i	1.18660	+	0.00410558i
$156$	4622.98	+	33157.8i	0.189965	+	1.36250i
$157$		−	30214.0i		−	1.22577i	−0.790172	−	0.612886i	$-0.790009\pi$
$157$		−	30214.0i		−	1.22577i	0.790172	−	0.612886i	$-0.209991\pi$
$158$	−264.074	+	264.074i	−0.0105782	+	0.0105782i
$159$	12688.7			0.501906
$160$	−5.92284	+	1711.83i	−0.000231361	+	0.0668683i
$161$	23315.0	+	23315.0i	0.899465	+	0.899465i
$162$	453.008	−	453.008i	0.0172614	−	0.0172614i
$163$	25500.7	+	25500.7i	0.959790	+	0.959790i	0.999222	−	0.0394319i	$-0.0125548\pi$
$163$	25500.7	+	25500.7i	0.959790	+	0.959790i	−0.0394319	+	0.999222i	$0.512555\pi$
$164$	−26743.4	+	26743.4i	−0.994326	+	0.994326i
$165$	−59786.4	−	206.858i	−2.19601	−	0.00759809i
$166$		−	390.369i		−	0.0141664i
$167$	25001.7	+	25001.7i	0.896472	+	0.896472i	0.995122	−	0.0986503i	$-0.0314525\pi$
$167$	25001.7	+	25001.7i	0.896472	+	0.896472i	−0.0986503	+	0.995122i	$0.531453\pi$
$168$	1373.54			0.0486658
$169$	−27471.8	+	7812.29i	−0.961863	+	0.273530i
$170$	0.787597	−	227.633i	2.72525e−5	−	0.00787656i
$171$	−10564.6	−	10564.6i	−0.361295	−	0.361295i
$172$		−	17596.4i		−	0.594794i
$173$	−27905.1			−0.932375			−0.466188	−	0.884686i	$-0.654373\pi$
$173$	−27905.1			−0.932375			−0.466188	+	0.884686i	$0.654373\pi$
$174$	494.006	+	494.006i	0.0163167	+	0.0163167i
$175$	−17287.2	+	17049.6i	−0.564479	+	0.556721i
$176$	34895.2	−	34895.2i	1.12652	−	1.12652i
$177$	55122.2	+	55122.2i	1.75946	+	1.75946i
$178$		−	187.896i		−	0.00593032i
$179$			10888.3i			0.339825i	0.985459	+	0.169913i	$0.0543485\pi$
$179$			10888.3i			0.339825i	−0.985459	+	0.169913i	$0.945651\pi$
$180$	20409.3	+	20551.0i	0.629917	+	0.634292i
$181$		−	22079.3i		−	0.673951i	−0.941513	−	0.336976i	$-0.890596\pi$
$181$		−	22079.3i		−	0.673951i	0.941513	−	0.336976i	$-0.109404\pi$
$182$	80.8848	+	580.137i	0.00244188	+	0.0175141i
$183$		−	71227.5i		−	2.12689i
$184$	1712.98	+	1712.98i	0.0505962	+	0.0505962i
$185$	11135.4	+	38.5280i	0.325360	+	0.00112573i
$186$		−	1260.25i		−	0.0364277i
$187$	−13932.3	+	13932.3i	−0.398417	+	0.398417i
$188$	21860.9	−	21860.9i	0.618519	−	0.618519i
$189$	−2911.14	+	2911.14i	−0.0814966	+	0.0814966i
$190$	326.388	−	324.137i	0.00904121	−	0.00897886i
$191$	−8766.27			−0.240297			−0.120148	−	0.992756i	$-0.538337\pi$
$191$	−8766.27			−0.240297			−0.120148	+	0.992756i	$0.538337\pi$
$192$	−50586.9			−1.37226
$193$	−29679.4	−	29679.4i	−0.796783	−	0.796783i	0.185804	−	0.982587i	$-0.440511\pi$
$193$	−29679.4	−	29679.4i	−0.796783	−	0.796783i	−0.982587	+	0.185804i	$0.940511\pi$
$194$		−	199.378i		−	0.00529753i
$195$	−31686.9	+	41653.7i	−0.833316	+	1.09543i
$196$	14261.6			0.371240
$197$	8401.98	−	8401.98i	0.216496	−	0.216496i	−0.590524	−	0.807020i	$-0.701079\pi$
$197$	8401.98	−	8401.98i	0.216496	−	0.216496i	0.807020	+	0.590524i	$0.201079\pi$
$198$			1247.80i			0.0318285i
$199$		−	64611.3i		−	1.63156i	−0.578364	−	0.815779i	$-0.696309\pi$
$199$		−	64611.3i		−	1.63156i	0.578364	−	0.815779i	$-0.303691\pi$
$200$	−1270.11	+	1252.65i	−0.0317528	+	0.0313163i
$201$	22924.0	+	22924.0i	0.567411	+	0.567411i
$202$	148.838	+	148.838i	0.00364764	+	0.00364764i
$203$	−17365.2	−	17365.2i	−0.421394	−	0.421394i
$204$	20217.5			0.485810
$205$	−59124.1	−	204.566i	−1.40688	−	0.00486773i
$206$	−149.357	+	149.357i	−0.00351959	+	0.00351959i
$207$	61487.1			1.43497
$208$	−5965.32	−	42785.6i	−0.137882	−	0.988942i
$209$	−39815.3			−0.911502
$210$	756.341	+	761.593i	0.0171506	+	0.0172697i
$211$	64702.2			1.45330			0.726648	−	0.687010i	$-0.241077\pi$
$211$	64702.2			1.45330			0.726648	+	0.687010i	$0.241077\pi$
$212$	−16381.1			−0.364479
$213$	35087.9	−	35087.9i	0.773389	−	0.773389i
$214$	−902.771	−	902.771i	−0.0197129	−	0.0197129i
$215$	19518.3	−	19383.7i	0.422245	−	0.419334i
$216$	−213.885	+	213.885i	−0.00458430	+	0.00458430i
$217$			44300.2i			0.940776i
$218$	−277.934			−0.00584829
$219$	57430.7	−	57430.7i	1.19744	−	1.19744i
$220$	77184.6	+	267.055i	1.59472	+	0.00551766i
$221$	2381.71	+	17082.6i	0.0487646	+	0.349759i
$222$		−	492.262i		−	0.00998826i
$223$	−55506.5	+	55506.5i	−1.11618	+	1.11618i	−0.123883	+	0.992297i	$0.539535\pi$
$223$	−55506.5	+	55506.5i	−1.11618	+	1.11618i	−0.992297	+	0.123883i	$0.960465\pi$
$224$	−2660.10			−0.0530153
$225$	−313.316	+	45277.0i	−0.00618895	+	0.894360i
$226$	−1008.24	−	1008.24i	−0.0197400	−	0.0197400i
$227$	34538.9	−	34538.9i	0.670282	−	0.670282i	−0.287499	−	0.957781i	$-0.592824\pi$
$227$	34538.9	−	34538.9i	0.670282	−	0.670282i	0.957781	+	0.287499i	$0.0928239\pi$
$228$	28888.6	+	28888.6i	0.555721	+	0.555721i
$229$	10751.3	−	10751.3i	0.205017	−	0.205017i	−0.597129	−	0.802145i	$-0.703692\pi$
$229$	10751.3	−	10751.3i	0.205017	−	0.205017i	0.802145	+	0.597129i	$0.203692\pi$
$230$	−6.54988	+	1893.06i	−0.000123816	+	0.0357856i
$231$		−	92905.2i		−	1.74107i
$232$	−1275.84	−	1275.84i	−0.0237040	−	0.0237040i
$233$	−40197.1			−0.740427			−0.370214	−	0.928947i	$-0.620716\pi$
$233$	−40197.1			−0.740427			−0.370214	+	0.928947i	$0.620716\pi$
$234$	871.633	+	658.322i	0.0159185	+	0.0120228i
$235$	48330.0	+	167.219i	0.875148	+	0.00302797i
$236$	−71163.0	−	71163.0i	−1.27770	−	1.27770i
$237$		−	51852.2i		−	0.923146i
$238$	353.730			0.00624479
$239$	−19634.6	−	19634.6i	−0.343738	−	0.343738i	0.514033	−	0.857771i	$-0.328151\pi$
$239$	−19634.6	−	19634.6i	−0.343738	−	0.343738i	−0.857771	+	0.514033i	$0.828151\pi$
$240$	−55780.8	−	56168.1i	−0.968417	−	0.975141i
$241$	−72388.0	+	72388.0i	−1.24633	+	1.24633i	−0.288999	+	0.957329i	$0.593322\pi$
$241$	−72388.0	+	72388.0i	−1.24633	+	1.24633i	−0.957329	+	0.288999i	$0.906678\pi$
$242$	1427.68	+	1427.68i	0.0243782	+	0.0243782i
$243$			80366.4i			1.36101i
$244$			91955.0i			1.54453i
$245$	15710.2	+	15819.3i	0.261727	+	0.263544i
$246$			2613.69i			0.0431900i
$247$	−21005.9	+	27812.3i	−0.344309	+	0.455873i
$248$			3254.79i			0.0529200i
$249$	38325.4	+	38325.4i	0.618142	+	0.618142i
$250$	−1393.95	−	14.4694i	−0.0223032	−	0.000231511i
$251$			61857.8i			0.981854i	0.871201	+	0.490927i	$0.163342\pi$
$251$			61857.8i			0.981854i	−0.871201	+	0.490927i	$0.836658\pi$
$252$	−31825.2	+	31825.2i	−0.501153	+	0.501153i
$253$	115865.	−	115865.i	1.81013	−	1.81013i
$254$	−694.952	+	694.952i	−0.0107718	+	0.0107718i
$255$	22271.0	+	22425.7i	0.342500	+	0.344878i
$256$	65210.2			0.995029
$257$	−59585.4			−0.902140			−0.451070	−	0.892489i	$-0.648957\pi$
$257$	−59585.4			−0.902140			−0.451070	+	0.892489i	$0.648957\pi$
$258$	−859.865	−	859.865i	−0.0129179	−	0.0129179i
$259$			17303.9i			0.257956i
$260$	40907.9	−	53775.1i	0.605146	−	0.795490i
$261$	−45796.1			−0.672276
$262$	1491.21	−	1491.21i	0.0217238	−	0.0217238i
$263$			21043.6i			0.304234i	0.988362	+	0.152117i	$0.0486091\pi$
$263$			21043.6i			0.304234i	−0.988362	+	0.152117i	$0.951391\pi$
$264$		−	6825.86i		−	0.0979376i
$265$	−18045.0	−	18170.3i	−0.256960	−	0.258744i
$266$	505.441	+	505.441i	0.00714344	+	0.00714344i
$267$	18447.2	+	18447.2i	0.258766	+	0.258766i
$268$	−29595.0	−	29595.0i	−0.412048	−	0.412048i
$269$	35675.8			0.493025			0.246513	−	0.969140i	$-0.420715\pi$
$269$	35675.8			0.493025			0.246513	+	0.969140i	$0.420715\pi$
$270$	−236.369	−	0.817825i	−0.00324237	−	1.12184e-5i
$271$	−78213.4	+	78213.4i	−1.06498	+	1.06498i	−0.0672465	+	0.997736i	$0.521421\pi$
$271$	−78213.4	+	78213.4i	−1.06498	+	1.06498i	−0.997736	+	0.0672465i	$0.978579\pi$
$272$	−26087.9			−0.352615
$273$	−64897.4	−	49015.3i	−0.870767	−	0.657667i
$274$	1639.38			0.0218363
$275$	84728.2	+	85909.0i	1.12037	+	1.13599i
$276$	−168134.			−2.20718
$277$	−19619.9			−0.255704			−0.127852	−	0.991793i	$-0.540808\pi$
$277$	−19619.9			−0.255704			−0.127852	+	0.991793i	$0.540808\pi$
$278$	1392.49	−	1392.49i	0.0180178	−	0.0180178i
$279$	58414.9	+	58414.9i	0.750439	+	0.750439i
$280$	−1953.37	−	1966.93i	−0.0249154	−	0.0250884i
$281$	6192.70	−	6192.70i	0.0784273	−	0.0784273i	−0.666805	−	0.745232i	$-0.732339\pi$
$281$	6192.70	−	6192.70i	0.0784273	−	0.0784273i	0.745232	+	0.666805i	$0.232339\pi$
$282$		−	2136.51i		−	0.0268663i
$283$	50558.5			0.631279			0.315639	−	0.948879i	$-0.397781\pi$
$283$	50558.5			0.631279			0.315639	+	0.948879i	$0.397781\pi$
$284$	−45298.6	+	45298.6i	−0.561627	+	0.561627i
$285$	−220.976	+	63866.8i	−0.00272054	+	0.786294i
$286$	2883.00	−	401.959i	0.0352463	−	0.00491416i
$287$		−	91876.0i		−	1.11542i
$288$	−3507.64	+	3507.64i	−0.0422893	+	0.0422893i
$289$	−73105.2			−0.875291
$290$	4.87840	−	1409.96i	5.80072e−5	−	0.0167653i
$291$	19574.4	+	19574.4i	0.231155	+	0.231155i
$292$	−74143.2	+	74143.2i	−0.869573	+	0.869573i
$293$	56399.1	+	56399.1i	0.656957	+	0.656957i	0.954659	−	0.297702i	$-0.0962202\pi$
$293$	56399.1	+	56399.1i	0.656957	+	0.656957i	−0.297702	+	0.954659i	$0.596220\pi$
$294$	696.907	−	696.907i	0.00806269	−	0.00806269i
$295$	544.343	−	157327.i	0.00625502	−	1.80784i
$296$			1271.34i			0.0145104i
$297$	14467.0	+	14467.0i	0.164008	+	0.164008i
$298$	−220.072			−0.00247818
$299$	−19807.0	−	142063.i	−0.221552	−	1.58906i
$300$	856.751	−	123808.i	0.00951945	−	1.37565i
$301$	30225.9	+	30225.9i	0.333615	+	0.333615i
$302$			1613.24i			0.0176882i
$303$	−29225.1			−0.318325
$304$	−37276.7	−	37276.7i	−0.403358	−	0.403358i
$305$	−101999.	+	101295.i	−1.09646	+	1.08890i
$306$	466.433	−	466.433i	0.00498135	−	0.00498135i
$307$	40098.8	+	40098.8i	0.425456	+	0.425456i	0.887077	−	0.461621i	$-0.152732\pi$
$307$	40098.8	+	40098.8i	0.425456	+	0.425456i	−0.461621	+	0.887077i	$0.652732\pi$
$308$			119941.i			1.26435i
$309$		−	29327.0i		−	0.307151i
$310$	−1804.69	+	1792.25i	−0.0187793	+	0.0186498i
$311$		−	69925.5i		−	0.722961i	−0.932380	−	0.361481i	$-0.882271\pi$
$311$		−	69925.5i		−	0.722961i	0.932380	−	0.361481i	$-0.117729\pi$
$312$	−4768.09	−	3601.21i	−0.0489818	−	0.0369947i
$313$			163724.i			1.67118i	0.549355	+	0.835589i	$0.314874\pi$
$313$			163724.i			1.67118i	−0.549355	+	0.835589i	$0.685126\pi$
$314$	1906.09	+	1906.09i	0.0193323	+	0.0193323i
$315$	−70359.0	−	243.438i	−0.709085	−	0.00245340i
$316$			66941.4i			0.670379i
$317$	86879.5	−	86879.5i	0.864568	−	0.864568i	−0.127297	−	0.991865i	$-0.540630\pi$
$317$	86879.5	−	86879.5i	0.864568	−	0.864568i	0.991865	+	0.127297i	$0.0406301\pi$
$318$	−800.482	+	800.482i	−0.00791584	+	0.00791584i
$319$	−86296.9	+	86296.9i	−0.848035	+	0.848035i
$320$	71941.5	+	72441.0i	0.702554	+	0.707432i
$321$	177263.			1.72032
$322$	−2941.72			−0.0283719
$323$	14883.1	+	14883.1i	0.142655	+	0.142655i
$324$		−	114835.i		−	1.09392i
$325$	104712.	−	13861.3i	0.991352	−	0.131231i
$326$	−3217.48			−0.0302748
$327$	27286.8	−	27286.8i	0.255186	−	0.255186i
$328$		−	6750.24i		−	0.0627439i
$329$			75102.5i			0.693845i
$330$	3784.75	−	3758.65i	0.0347544	−	0.0345147i
$331$	−61728.3	−	61728.3i	−0.563415	−	0.563415i	0.366861	−	0.930276i	$-0.380433\pi$
$331$	−61728.3	−	61728.3i	−0.563415	−	0.563415i	−0.930276	+	0.366861i	$0.880433\pi$
$332$	−49478.3	−	49478.3i	−0.448888	−	0.448888i
$333$	22817.2	+	22817.2i	0.205766	+	0.205766i
$334$	−3154.53			−0.0282775
$335$	226.379	−	65428.4i	0.00201719	−	0.583011i
$336$	86981.6	−	86981.6i	0.770457	−	0.770457i
$337$	167234.			1.47253			0.736267	−	0.676691i	$-0.236587\pi$
$337$	167234.			1.47253			0.736267	+	0.676691i	$0.236587\pi$
$338$	1240.24	−	2225.94i	0.0108561	−	0.0194841i
$339$	197972.			1.72268
$340$	−28752.0	−	28951.7i	−0.248720	−	0.250447i
$341$	220151.			1.89327
$342$	1332.97			0.0113964
$343$	−90453.2	+	90453.2i	−0.768839	+	0.768839i
$344$	2220.73	+	2220.73i	0.0187663	+	0.0187663i
$345$	−185212.	−	186498.i	−1.55608	−	1.56688i
$346$	1760.43	−	1760.43i	0.0147050	−	0.0147050i
$347$		−	194584.i		−	1.61602i	−0.589168	−	0.808011i	$-0.700544\pi$
$347$		−	194584.i		−	1.61602i	0.589168	−	0.808011i	$-0.299456\pi$
$348$	125228.			1.03405
$349$	−73554.9	+	73554.9i	−0.603894	+	0.603894i	−0.941344	−	0.337450i	$-0.890436\pi$
$349$	−73554.9	+	73554.9i	−0.603894	+	0.603894i	0.337450	+	0.941344i	$0.390436\pi$
$350$	14.9899	−	2166.18i	0.000122367	−	0.0176831i
$351$	17738.2	−	2473.12i	0.143978	−	0.0200739i
$352$			13219.4i			0.106691i
$353$	−93482.4	+	93482.4i	−0.750206	+	0.750206i	−0.974517	−	0.224311i	$-0.927987\pi$
$353$	−93482.4	+	93482.4i	−0.750206	+	0.750206i	0.224311	+	0.974517i	$0.427987\pi$
$354$	−6954.91			−0.0554990
$355$	−100146.	−	346.500i	−0.794651	−	0.00274945i
$356$	−23815.4	−	23815.4i	−0.187913	−	0.187913i
$357$	−34728.2	+	34728.2i	−0.272487	+	0.272487i
$358$	−686.905	−	686.905i	−0.00535958	−	0.00535958i
$359$	83018.2	−	83018.2i	0.644146	−	0.644146i	−0.307426	−	0.951572i	$-0.599468\pi$
$359$	83018.2	−	83018.2i	0.644146	−	0.644146i	0.951572	+	0.307426i	$0.0994676\pi$
$360$	−5169.36	−	17.8857i	−0.0398870	−	0.000138007i
$361$		−	87788.3i		−	0.673632i
$362$	1392.90	+	1392.90i	0.0106293	+	0.0106293i
$363$	−280332.			−2.12745
$364$	83782.8	+	63278.9i	0.632342	+	0.477591i
$365$	−163916.	−	567.139i	−1.23037	−	0.00425700i
$366$	4493.48	+	4493.48i	0.0335444	+	0.0335444i
$367$			42520.1i			0.315691i	0.987464	+	0.157846i	$0.0504548\pi$
$367$			42520.1i			0.315691i	−0.987464	+	0.157846i	$0.949545\pi$
$368$	216954.			1.60204
$369$	−121149.	−	121149.i	−0.889749	−	0.889749i
$370$	−704.924	+	700.063i	−0.00514919	+	0.00511368i
$371$	28138.4	−	28138.4i	0.204434	−	0.204434i
$372$	−159734.	−	159734.i	−1.15428	−	1.15428i
$373$			61782.7i			0.444068i	0.975039	+	0.222034i	$0.0712696\pi$
$373$			61782.7i			0.444068i	−0.975039	+	0.222034i	$0.928730\pi$
$374$		−	1757.87i		−	0.0125673i
$375$	138275.	−	135434.i	0.983287	−	0.963083i
$376$			5517.87i			0.0390298i
$377$	14752.4	+	105810.i	0.103796	+	0.744465i
$378$		−	367.306i		−	0.00257066i
$379$	2079.32	+	2079.32i	0.0144758	+	0.0144758i	0.714308	−	0.699832i	$-0.246742\pi$
$379$	2079.32	+	2079.32i	0.0144758	+	0.0144758i	−0.699832	+	0.714308i	$0.746742\pi$
$380$	285.280	−	82452.3i	0.00197563	−	0.570999i
$381$		−	136457.i		−	0.940040i
$382$	553.031	−	553.031i	0.00378986	−	0.00378986i
$383$	95946.1	−	95946.1i	0.654078	−	0.654078i	−0.299894	−	0.953972i	$-0.596951\pi$
$383$	95946.1	−	95946.1i	0.654078	−	0.654078i	0.953972	+	0.299894i	$0.0969514\pi$
$384$	12787.6	−	12787.6i	0.0867218	−	0.0867218i
$385$	−133041.	+	132124.i	−0.897563	+	0.891373i
$386$	3744.72			0.0251330
$387$	79712.6			0.532237
$388$	−25270.6	−	25270.6i	−0.167862	−	0.167862i
$389$			81570.7i			0.539057i	0.962992	+	0.269529i	$0.0868679\pi$
$389$			81570.7i			0.539057i	−0.962992	+	0.269529i	$0.913132\pi$
$390$	−628.771	−	4626.78i	−0.00413393	−	0.0304193i
$391$	−86621.0			−0.566591
$392$	−1799.87	+	1799.87i	−0.0117130	+	0.0117130i
$393$			292805.i			1.89581i
$394$			1060.10i			0.00682896i
$395$	−74252.9	+	73740.8i	−0.475904	+	0.472622i
$396$	158156.	+	158156.i	1.00854	+	1.00854i
$397$	14639.9	+	14639.9i	0.0928876	+	0.0928876i	0.752024	−	0.659136i	$-0.229078\pi$
$397$	14639.9	+	14639.9i	0.0928876	+	0.0928876i	−0.659136	+	0.752024i	$0.729078\pi$
$398$	4076.09	+	4076.09i	0.0257322	+	0.0257322i
$399$	−99245.8			−0.623399
$400$	−1105.52	+	159757.i	−0.00690949	+	0.998484i
$401$	−44235.6	+	44235.6i	−0.275095	+	0.275095i	−0.831147	−	0.556052i	$-0.812316\pi$
$401$	−44235.6	+	44235.6i	−0.275095	+	0.275095i	0.556052	+	0.831147i	$0.312316\pi$
$402$	−2892.38			−0.0178979
$403$	116148.	−	153783.i	0.715157	−	0.946885i
$404$	37729.7			0.231164
$405$	127378.	−	126499.i	0.776576	−	0.771220i
$406$	2191.02			0.0132921
$407$	85992.2			0.519123
$408$	−2551.53	+	2551.53i	−0.0153278	+	0.0153278i
$409$	−147681.	−	147681.i	−0.882829	−	0.882829i	0.110992	−	0.993821i	$-0.464597\pi$
$409$	−147681.	−	147681.i	−0.882829	−	0.882829i	−0.993821	+	0.110992i	$0.964597\pi$
$410$	3742.83	−	3717.02i	0.0222655	−	0.0221119i
$411$	−160950.	+	160950.i	−0.952812	+	0.952812i
$412$			37861.3i			0.223050i
$413$	244478.			1.43331
$414$	−3878.99	+	3878.99i	−0.0226317	+	0.0226317i
$415$	378.471	−	109386.i	0.00219754	−	0.635136i
$416$	9234.20	+	6974.35i	0.0533596	+	0.0403011i
$417$			273422.i			1.57239i
$418$	2511.80	−	2511.80i	0.0143758	−	0.0143758i
$419$	243288.			1.38577			0.692886	−	0.721047i	$-0.256339\pi$
$419$	243288.			1.38577			0.692886	+	0.721047i	$0.256339\pi$
$420$	192394.	+	665.674i	1.09067	+	0.00377366i
$421$	124817.	+	124817.i	0.704221	+	0.704221i	0.965314	−	0.261092i	$-0.0840827\pi$
$421$	124817.	+	124817.i	0.704221	+	0.704221i	−0.261092	+	0.965314i	$0.584083\pi$
$422$	−4081.82	+	4081.82i	−0.0229207	+	0.0229207i
$423$	99031.3	+	99031.3i	0.553467	+	0.553467i
$424$	2067.37	−	2067.37i	0.0114997	−	0.0114997i
$425$	441.389	−	63784.7i	0.00244368	−	0.353133i
$426$			4427.13i			0.0243951i
$427$	−157954.	−	157954.i	−0.866314	−	0.866314i
$428$	−228848.			−1.24928
$429$	−243582.	+	322509.i	−1.32352	+	1.75237i
$430$	−8.49134	+	2454.18i	−4.59240e−5	+	0.0132730i
$431$	−67359.1	−	67359.1i	−0.362611	−	0.362611i	0.502162	−	0.864774i	$-0.332538\pi$
$431$	−67359.1	−	67359.1i	−0.362611	−	0.362611i	−0.864774	+	0.502162i	$0.832538\pi$
$432$			27089.1i			0.145153i
$433$	−185383.			−0.988767			−0.494383	−	0.869244i	$-0.664606\pi$
$433$	−185383.			−0.988767			−0.494383	+	0.869244i	$0.664606\pi$
$434$	−2794.73	−	2794.73i	−0.0148375	−	0.0148375i
$435$	137948.	+	138906.i	0.729014	+	0.734076i
$436$	−35227.4	+	35227.4i	−0.185314	+	0.185314i
$437$	−123772.	−	123772.i	−0.648126	−	0.648126i
$438$			7246.17i			0.0377712i
$439$			162272.i			0.842005i	0.907059	+	0.421003i	$0.138322\pi$
$439$			162272.i			0.842005i	−0.907059	+	0.421003i	$0.861678\pi$
$440$	−9774.70	+	9707.29i	−0.0504892	+	0.0501410i
$441$			64605.7i			0.332196i
$442$	−1227.93	−	927.422i	−0.00628534	−	0.00474715i
$443$			113031.i			0.575955i	0.957637	+	0.287978i	$0.0929828\pi$
$443$			113031.i			0.575955i	−0.957637	+	0.287978i	$0.907017\pi$
$444$	−62392.9	−	62392.9i	−0.316497	−	0.316497i
$445$	182.169	−	52650.9i	0.000919931	−	0.265880i
$446$		−	7003.40i		−	0.0352078i
$447$	21606.1	−	21606.1i	0.108134	−	0.108134i
$448$	−112182.	+	112182.i	−0.558941	+	0.558941i
$449$	104799.	−	104799.i	0.519835	−	0.519835i	−0.397686	−	0.917522i	$-0.630187\pi$
$449$	104799.	−	104799.i	0.519835	−	0.519835i	0.917522	+	0.397686i	$0.130187\pi$
$450$	−2836.59	−	2876.12i	−0.0140078	−	0.0142031i
$451$	−456580.			−2.24473
$452$	−255583.			−1.25100
$453$	−158383.	−	158383.i	−0.771814	−	0.771814i
$454$			4357.87i			0.0211428i
$455$	22102.5	+	162640.i	0.106762	+	0.785606i
$456$	−7291.71			−0.0350671
$457$	187167.	−	187167.i	0.896183	−	0.896183i	−0.0989132	−	0.995096i	$-0.531537\pi$
$457$	187167.	−	187167.i	0.896183	−	0.896183i	0.995096	+	0.0989132i	$0.0315366\pi$
$458$			1356.52i			0.00646687i
$459$		−	10815.6i		−	0.0513364i
$460$	239110.	+	240770.i	1.13001	+	1.13786i
$461$	−120626.	−	120626.i	−0.567596	−	0.567596i	0.363859	−	0.931454i	$-0.381459\pi$
$461$	−120626.	−	120626.i	−0.567596	−	0.567596i	−0.931454	+	0.363859i	$0.881459\pi$
$462$	5861.04	+	5861.04i	0.0274594	+	0.0274594i
$463$	−121784.	−	121784.i	−0.568106	−	0.568106i	0.363491	−	0.931598i	$-0.381585\pi$
$463$	−121784.	−	121784.i	−0.568106	−	0.568106i	−0.931598	+	0.363491i	$0.881585\pi$
$464$	−161589.			−0.750544
$465$	1221.84	−	353138.i	0.00565078	−	1.63320i
$466$	2535.88	−	2535.88i	0.0116777	−	0.0116777i
$467$	−193392.			−0.886756			−0.443378	−	0.896335i	$-0.646220\pi$
$467$	−193392.			−0.886756			−0.443378	+	0.896335i	$0.646220\pi$
$468$	193918.	−	27036.7i	0.885372	−	0.123442i
$469$	101672.			0.462229
$470$	−3059.51	+	3038.41i	−0.0138502	+	0.0137547i
$471$	−374270.			−1.68711
$472$	17962.1			0.0806257
$473$	150208.	−	150208.i	0.671384	−	0.671384i
$474$	3271.16	+	3271.16i	0.0145595	+	0.0145595i
$475$	91772.1	−	90510.7i	0.406746	−	0.401156i
$476$	44834.3	−	44834.3i	0.197878	−	0.197878i
$477$		−	74207.5i		−	0.326145i
$478$	2477.35			0.0108426
$479$	−130475.	+	130475.i	−0.568663	+	0.568663i	−0.931754	−	0.363091i	$-0.881722\pi$
$479$	−130475.	+	130475.i	−0.568663	+	0.568663i	0.363091	+	0.931754i	$0.381722\pi$
$480$	21204.9	+	73.3679i	0.0920352	+	0.000318437i
$481$	45368.1	−	60068.4i	0.196092	−	0.259631i
$482$		−	9133.38i		−	0.0393131i
$483$	288810.	−	288810.i	1.23799	−	1.23799i
$484$	361910.			1.54493
$485$	193.301	−	55868.2i	0.000821771	−	0.237510i
$486$	−5070.01	−	5070.01i	−0.0214653	−	0.0214653i
$487$	−176673.	+	176673.i	−0.744926	+	0.744926i	−0.973522	−	0.228595i	$-0.926587\pi$
$487$	−176673.	+	176673.i	−0.744926	+	0.744926i	0.228595	+	0.973522i	$0.426587\pi$
$488$	−11605.1	−	11605.1i	−0.0487314	−	0.0487314i
$489$	315884.	−	315884.i	1.32102	−	1.32102i
$490$	−1989.07	−	6.88209i	−0.00828435	−	2.86634e-5i
$491$			383831.i			1.59213i	0.605214	+	0.796063i	$0.293088\pi$
$491$			383831.i			1.59213i	−0.605214	+	0.796063i	$0.706912\pi$
$492$	331278.	+	331278.i	1.36856	+	1.36856i
$493$	64516.1			0.265445
$494$	−429.391	−	3079.76i	−0.00175954	−	0.0126201i
$495$	−1209.77	+	349651.i	−0.00493734	+	1.42700i
$496$	206114.	+	206114.i	0.837807	+	0.837807i
$497$		−	155622.i		−	0.630025i
$498$	−4835.62			−0.0194981
$499$	−30738.7	−	30738.7i	−0.123448	−	0.123448i	0.642684	−	0.766132i	$-0.277821\pi$
$499$	−30738.7	−	30738.7i	−0.123448	−	0.123448i	−0.766132	+	0.642684i	$0.777821\pi$
$500$	−178513.	+	174845.i	−0.714053	+	0.699381i
$501$	309703.	−	309703.i	1.23387	−	1.23387i
$502$	−3902.38	−	3902.38i	−0.0154854	−	0.0154854i
$503$		−	66574.3i		−	0.263130i	−0.991308	−	0.131565i	$-0.958000\pi$
$503$		−	66574.3i		−	0.263130i	0.991308	−	0.131565i	$-0.0420002\pi$
$504$		−	8032.93i		−	0.0316237i
$505$	41562.0	+	41850.6i	0.162972	+	0.164104i
$506$			14618.9i			0.0570971i
$507$	96773.1	+	340301.i	0.376477	+	1.32388i
$508$			176167.i			0.682648i
$509$	−188352.	−	188352.i	−0.726999	−	0.726999i	0.243022	−	0.970021i	$-0.421861\pi$
$509$	−188352.	−	188352.i	−0.726999	−	0.726999i	−0.970021	+	0.243022i	$0.921861\pi$
$510$	−2819.75	−	9.75619i	−0.0108410	−	3.75094e-5i
$511$		−	254717.i		−	0.975473i
$512$	−20631.0	+	20631.0i	−0.0787010	+	0.0787010i
$513$	15454.3	−	15454.3i	0.0587239	−	0.0587239i
$514$	3759.02	−	3759.02i	0.0142282	−	0.0142282i
$515$	−41996.6	+	41707.0i	−0.158343	+	0.157251i
$516$	−217971.			−0.818653
$517$	373224.			1.39633
$518$	−1091.64	−	1091.64i	−0.00406836	−	0.00406836i
$519$			345668.i			1.28329i
$520$	1623.90	+	11949.4i	0.00600553	+	0.0441914i
$521$	−44030.7			−0.162211			−0.0811054	−	0.996706i	$-0.525845\pi$
$521$	−44030.7			−0.162211			−0.0811054	+	0.996706i	$0.525845\pi$
$522$	2889.11	−	2889.11i	0.0106028	−	0.0106028i
$523$		−	479903.i		−	1.75449i	−0.480046	−	0.877243i	$-0.659380\pi$
$523$		−	479903.i		−	1.75449i	0.480046	−	0.877243i	$-0.340620\pi$
$524$		−	378013.i		−	1.37672i
$525$	211198.	+	214141.i	0.766251	+	0.776930i
$526$	−1327.56	−	1327.56i	−0.00479825	−	0.00479825i
$527$	−82293.0	−	82293.0i	−0.296307	−	0.296307i
$528$	−432257.	−	432257.i	−1.55051	−	1.55051i
$529$	440524.			1.57419
$530$	2284.69	+	7.90492i	0.00813347	+	2.81414e-5i
$531$	322373.	−	322373.i	1.14332	−	1.14332i
$532$	128127.			0.452706
$533$	−240884.	+	318936.i	−0.847918	+	1.12266i
$534$	−2327.53			−0.00816229
$535$	−252093.	−	253843.i	−0.880750	−	0.886866i
$536$	7470.00			0.0260011
$537$	134877.			0.467724
$538$	−2250.65	+	2250.65i	−0.00777578	+	0.00777578i
$539$	121741.	+	121741.i	0.419044	+	0.419044i
$540$	−30062.8	+	29855.5i	−0.103096	+	0.102385i
$541$	183405.	−	183405.i	0.626636	−	0.626636i	−0.320584	−	0.947220i	$-0.603879\pi$
$541$	183405.	−	183405.i	0.626636	−	0.626636i	0.947220	+	0.320584i	$0.103879\pi$
$542$		−	9868.39i		−	0.0335929i
$543$	−273503.			−0.927603
$544$	4941.46	−	4941.46i	0.0166977	−	0.0166977i
$545$	−77880.6	−	269.463i	−0.262202	−	0.000907205i
$546$	7186.32	−	1001.94i	0.0241058	−	0.00336092i
$547$			428185.i			1.43106i	0.698584	+	0.715529i	$0.253814\pi$
$547$			428185.i			1.43106i	−0.698584	+	0.715529i	$0.746186\pi$
$548$	207787.	−	207787.i	0.691923	−	0.691923i
$549$	−416561.			−1.38208
$550$	−10764.9	−	74.4927i	−0.0355863	−	0.000246257i
$551$	92186.5	+	92186.5i	0.303644	+	0.303644i
$552$	21219.2	−	21219.2i	0.0696388	−	0.0696388i
$553$	−114987.	−	114987.i	−0.376011	−	0.376011i
$554$	1237.75	−	1237.75i	0.00403286	−	0.00403286i
$555$	477.258	−	137938.i	0.00154941	−	0.447814i
$556$		−	352988.i		−	1.14185i
$557$	−316403.	−	316403.i	−1.01983	−	1.01983i	−0.999799	−	0.0200349i	$-0.993622\pi$
$557$	−316403.	−	316403.i	−1.01983	−	1.01983i	−0.0200349	−	0.999799i	$-0.506378\pi$
$558$	−7370.36			−0.0236712
$559$	−25678.0	−	184173.i	−0.0821747	−	0.589389i
$560$	−248258.	−	858.960i	−0.791639	−	0.00273903i
$561$	172583.	+	172583.i	0.548368	+	0.548368i
$562$			781.349i			0.00247384i
$563$	165682.			0.522707			0.261353	−	0.965243i	$-0.415831\pi$
$563$	165682.			0.522707			0.261353	+	0.965243i	$0.415831\pi$
$564$	−270798.	−	270798.i	−0.851308	−	0.851308i
$565$	−281544.	−	283499.i	−0.881960	−	0.888084i
$566$	−3189.55	+	3189.55i	−0.00995625	+	0.00995625i
$567$	197256.	+	197256.i	0.613571	+	0.613571i
$568$		−	11433.7i		−	0.0354398i
$569$			486642.i			1.50309i	0.659681	+	0.751546i	$0.270691\pi$
$569$			486642.i			1.50309i	−0.659681	+	0.751546i	$0.729309\pi$
$570$	−4015.18	−	4043.06i	−0.0123582	−	0.0124440i
$571$			390348.i			1.19724i	0.801035	+	0.598618i	$0.204283\pi$
$571$			390348.i			1.19724i	−0.801035	+	0.598618i	$0.795717\pi$
$572$	314466.	−	416360.i	0.961129	−	1.27256i
$573$			108590.i			0.330736i
$574$	5796.11	+	5796.11i	0.0175919	+	0.0175919i
$575$	−3670.71	+	530452.i	−0.0111024	+	1.60439i
$576$			295849.i			0.891712i
$577$	−225648.	+	225648.i	−0.677767	+	0.677767i	−0.959495	−	0.281727i	$-0.909093\pi$
$577$	−225648.	+	225648.i	−0.677767	+	0.677767i	0.281727	+	0.959495i	$0.409093\pi$
$578$	4611.93	−	4611.93i	0.0138047	−	0.0138047i
$579$	−367647.	+	367647.i	−1.09666	+	1.09666i
$580$	−178091.	−	179328.i	−0.529403	−	0.533079i
$581$	169981.			0.503556
$582$	−2469.75			−0.00729134
$583$	−139835.	−	139835.i	−0.411412	−	0.411412i
$584$		−	18714.3i		−	0.0548717i
$585$	243604.	+	185315.i	0.711825	+	0.541500i
$586$	−7116.02			−0.0207225
$587$	332001.	−	332001.i	0.963525	−	0.963525i	−0.0358330	−	0.999358i	$-0.511408\pi$
$587$	332001.	−	332001.i	0.963525	−	0.963525i	0.999358	+	0.0358330i	$0.0114084\pi$
$588$		−	176662.i		−	0.510962i
$589$		−	235176.i		−	0.677894i
$590$	9890.83	+	9959.51i	0.0284138	+	0.0286111i
$591$	−104078.	−	104078.i	−0.297977	−	0.297977i
$592$	80509.3	+	80509.3i	0.229722	+	0.229722i
$593$	13775.1	+	13775.1i	0.0391728	+	0.0391728i	0.726422	−	0.687249i	$-0.241182\pi$
$593$	13775.1	+	13775.1i	0.0391728	+	0.0391728i	−0.687249	+	0.726422i	$0.741182\pi$
$594$	−1825.33			−0.00517332
$595$	99119.5	+	342.948i	0.279979	+	0.000968712i
$596$	−27893.6	+	27893.6i	−0.0785257	+	0.0785257i
$597$	−800359.			−2.24562
$598$	10211.8	+	7712.71i	0.0285562	+	0.0215677i
$599$	302072.			0.841893			0.420947	−	0.907085i	$-0.361698\pi$
$599$	302072.			0.841893			0.420947	+	0.907085i	$0.361698\pi$
$600$	15517.0	+	15733.2i	0.0431027	+	0.0437034i
$601$	102472.			0.283698			0.141849	−	0.989888i	$-0.454695\pi$
$601$	102472.			0.283698			0.141849	+	0.989888i	$0.454695\pi$
$602$	−3813.68			−0.0105233
$603$	134067.	−	134067.i	0.368712	−	0.368712i
$604$	204473.	+	204473.i	0.560484	+	0.560484i
$605$	398670.	+	401439.i	1.08919	+	1.09675i
$606$	1843.70	−	1843.70i	0.00502048	−	0.00502048i
$607$			333131.i			0.904143i	0.891982	+	0.452072i	$0.149315\pi$
$607$			333131.i			0.904143i	−0.891982	+	0.452072i	$0.850685\pi$
$608$	14121.6			0.0382012
$609$	−215108.	+	215108.i	−0.579992	+	0.579992i
$610$	44.3740	−	12825.0i	0.000119253	−	0.0344666i
$611$	196907.	−	260709.i	0.527446	−	0.698351i
$612$		−	118238.i		−	0.315686i
$613$	−113073.	+	113073.i	−0.300910	+	0.300910i	−0.841370	−	0.540460i	$-0.818250\pi$
$613$	−113073.	+	113073.i	−0.300910	+	0.300910i	0.540460	+	0.841370i	$0.318250\pi$
$614$	−5059.37			−0.0134202
$615$	−2534.02	+	732388.i	−0.00669978	+	1.93638i
$616$	−15137.0	−	15137.0i	−0.0398914	−	0.0398914i
$617$	22302.4	−	22302.4i	0.0585842	−	0.0585842i	−0.677208	−	0.735792i	$-0.736810\pi$
$617$	22302.4	−	22302.4i	0.0585842	−	0.0585842i	0.735792	+	0.677208i	$0.236810\pi$
$618$	1850.13	+	1850.13i	0.00484425	+	0.00484425i
$619$	−111185.	+	111185.i	−0.290179	+	0.290179i	−0.837151	−	0.546972i	$-0.815781\pi$
$619$	−111185.	+	111185.i	−0.290179	+	0.290179i	0.546972	+	0.837151i	$0.315781\pi$
$620$	−1577.40	+	455903.i	−0.00410354	+	1.18601i
$621$			89945.5i			0.233236i
$622$	4411.34	+	4411.34i	0.0114022	+	0.0114022i
$623$	81816.9			0.210798
$624$	−529997.	+	73894.1i	−1.36115	+	0.189776i
$625$	−390588.	−	5405.97i	−0.999904	−	0.0138393i
$626$	−10328.7	−	10328.7i	−0.0263571	−	0.0263571i
$627$			493204.i			1.25456i
$628$	483184.			1.22516
$629$	−32144.1	−	32144.1i	−0.0812458	−	0.0812458i
$630$	4454.04	−	4423.33i	0.0112221	−	0.0111447i
$631$	−82066.0	+	82066.0i	−0.206113	+	0.206113i	−0.802613	−	0.596500i	$-0.796557\pi$
$631$	−82066.0	+	82066.0i	−0.206113	+	0.206113i	0.596500	+	0.802613i	$0.296557\pi$
$632$	−8448.27	−	8448.27i	−0.0211511	−	0.0211511i
$633$		−	801484.i		−	2.00026i
$634$			10961.8i			0.0272712i
$635$	−195408.	+	194061.i	−0.484613	+	0.481271i
$636$			202918.i			0.501656i
$637$	149269.	−	20811.6i	0.367867	−	0.0512893i
$638$		−	10888.3i		−	0.0267497i
$639$	−205205.	−	205205.i	−0.502559	−	0.502559i
$640$	−36497.8	−	126.281i	−0.0891060	−	0.000308302i
$641$			715993.i			1.74258i	0.490769	+	0.871289i	$0.336716\pi$
$641$			715993.i			1.74258i	−0.490769	+	0.871289i	$0.663284\pi$
$642$	−11182.9	+	11182.9i	−0.0271321	+	0.0271321i
$643$	112187.	−	112187.i	0.271345	−	0.271345i	−0.558297	−	0.829641i	$-0.688545\pi$
$643$	112187.	−	112187.i	0.271345	−	0.271345i	0.829641	+	0.558297i	$0.188545\pi$
$644$	−372855.	+	372855.i	−0.899017	+	0.899017i
$645$	−240111.	−	241779.i	−0.577156	−	0.581164i
$646$	−1877.84			−0.00449980
$647$	437902.			1.04609			0.523044	−	0.852306i	$-0.324796\pi$
$647$	437902.			1.04609			0.523044	+	0.852306i	$0.324796\pi$
$648$	14492.7	+	14492.7i	0.0345142	+	0.0345142i
$649$		−	1.21494e6i		−	2.88447i
$650$	−5731.40	+	7480.32i	−0.0135655	+	0.0177049i
$651$	548759.			1.29485
$652$	−407808.	+	407808.i	−0.959313	+	0.959313i
$653$			553410.i			1.29784i	0.760857	+	0.648920i	$0.224779\pi$
$653$			553410.i			1.29784i	−0.760857	+	0.648920i	$0.775221\pi$
$654$			3442.85i			0.00804938i
$655$	419301.	−	416409.i	0.977334	−	0.970594i
$656$	−427468.	−	427468.i	−0.993336	−	0.993336i
$657$	−335873.	−	335873.i	−0.778116	−	0.778116i
$658$	−4737.94	−	4737.94i	−0.0109430	−	0.0109430i
$659$	467856.			1.07731			0.538655	−	0.842526i	$-0.318932\pi$
$659$	467856.			1.07731			0.538655	+	0.842526i	$0.318932\pi$
$660$	3308.08	−	956107.i	0.00759431	−	2.19492i
$661$	203544.	−	203544.i	0.465859	−	0.465859i	−0.434711	−	0.900570i	$-0.643150\pi$
$661$	203544.	−	203544.i	0.465859	−	0.465859i	0.900570	+	0.434711i	$0.143150\pi$
$662$	7788.42			0.0177719
$663$	211607.	−	29503.0i	0.481396	−	0.0671179i
$664$	12488.7			0.0283258
$665$	141141.	+	142121.i	0.319161	+	0.321377i
$666$	−2878.90			−0.00649051
$667$	−536534.			−1.20600
$668$	−399828.	+	399828.i	−0.896026	+	0.896026i
$669$	687575.	+	687575.i	1.53627	+	1.53627i
$670$	4113.35	+	4141.91i	0.00916318	+	0.00922681i
$671$	−784956.	+	784956.i	−1.74341	+	1.74341i
$672$			32951.4i			0.0729685i
$673$	188027.			0.415135			0.207568	−	0.978221i	$-0.433445\pi$
$673$	188027.			0.415135			0.207568	+	0.978221i	$0.433445\pi$
$674$	−10550.2	+	10550.2i	−0.0232242	+	0.0232242i
$675$	−66232.8	−	458.329i	−0.145367	−	0.00100594i
$676$	−124934.	−	439330.i	−0.273394	−	0.961385i
$677$		−	319169.i		−	0.696376i	−0.937425	−	0.348188i	$-0.886797\pi$
$677$		−	319169.i		−	0.696376i	0.937425	−	0.348188i	$-0.113203\pi$
$678$	−12489.3	+	12489.3i	−0.0271694	+	0.0271694i
$679$	86816.4			0.188305
$680$	7282.43	+	25.1968i	0.0157492	+	5.44914e-5i
$681$	−427844.	−	427844.i	−0.922552	−	0.922552i
$682$	−13888.5	+	13888.5i	−0.0298598	+	0.0298598i
$683$	−517231.	−	517231.i	−1.10877	−	1.10877i	−0.993312	−	0.115461i	$-0.963165\pi$
$683$	−517231.	−	517231.i	−1.10877	−	1.10877i	−0.115461	−	0.993312i	$-0.536835\pi$
$684$	168950.	−	168950.i	0.361115	−	0.361115i
$685$	459375.	+	1589.41i	0.979008	+	0.00338732i
$686$		−	11412.7i		−	0.0242516i
$687$	−133179.	−	133179.i	−0.282178	−	0.282178i
$688$	281262.			0.594202
$689$	−171454.	+	23904.7i	−0.361167	+	0.0503552i
$690$	23449.8	+	81.1352i	0.0492540	+	0.000170416i
$691$	259438.	+	259438.i	0.543348	+	0.543348i	0.924509	−	0.381161i	$-0.124476\pi$
$691$	259438.	+	259438.i	0.543348	+	0.543348i	−0.381161	+	0.924509i	$0.624476\pi$
$692$		−	446259.i		−	0.931912i
$693$	−543340.			−1.13137
$694$	12275.6	+	12275.6i	0.0254872	+	0.0254872i
$695$	391543.	−	388842.i	0.810605	−	0.805015i
$696$	−15804.3	+	15804.3i	−0.0326254	+	0.0326254i
$697$	170671.	+	170671.i	0.351313	+	0.351313i
$698$		−	9280.61i		−	0.0190487i
$699$			497932.i			1.01910i
$700$	−272657.	−	276457.i	−0.556444	−	0.564199i
$701$		−	906215.i		−	1.84415i	−0.387015	−	0.922073i	$-0.626494\pi$
$701$		−	906215.i		−	1.84415i	0.387015	−	0.922073i	$-0.373506\pi$
$702$	−963.017	+	1275.06i	−0.00195416	+	0.00258735i
$703$		−	91861.0i		−	0.185875i
$704$	557489.	+	557489.i	1.12484	+	1.12484i
$705$	2071.40	−	598678.i	0.00416759	−	1.20452i
$706$		−	11794.9i		−	0.0236639i
$707$	−64809.6	+	64809.6i	−0.129658	+	0.129658i
$708$	−881517.	+	881517.i	−1.75859	+	1.75859i
$709$	262482.	−	262482.i	0.522164	−	0.522164i	−0.396060	−	0.918225i	$-0.629623\pi$
$709$	262482.	−	262482.i	0.522164	−	0.522164i	0.918225	+	0.396060i	$0.129623\pi$
$710$	6339.69	−	6295.98i	0.0125763	−	0.0124895i
$711$	−303248.			−0.599873
$712$	6011.19			0.0118577
$713$	684372.	+	684372.i	1.34621	+	1.34621i
$714$		−	4381.75i		−	0.00859511i
$715$	808243.	−	109839.i	1.58099	−	0.214854i
$716$	−174127.			−0.339656
$717$	−243220.	+	243220.i	−0.473109	+	0.473109i
$718$			10474.6i			0.0203184i
$719$		−	844996.i		−	1.63454i	−0.576252	−	0.817272i	$-0.695485\pi$
$719$		−	844996.i		−	1.63454i	0.576252	−	0.817272i	$-0.304515\pi$
$720$	−328489.	+	326224.i	−0.633660	+	0.629291i
$721$	−65035.7	−	65035.7i	−0.125107	−	0.125107i
$722$	5538.24	+	5538.24i	0.0106242	+	0.0106242i
$723$	896691.	+	896691.i	1.71540	+	1.71540i
$724$	353093.			0.673616
$725$	2733.98	−	395085.i	0.00520139	−	0.751648i
$726$	17685.1	−	17685.1i	0.0335532	−	0.0335532i
$727$	152914.			0.289320			0.144660	−	0.989481i	$-0.453791\pi$
$727$	152914.			0.289320			0.144660	+	0.989481i	$0.453791\pi$
$728$	−18559.8	+	2587.67i	−0.0350195	+	0.00488254i
$729$	413878.			0.778785
$730$	10376.6	−	10305.0i	0.0194719	−	0.0193377i
$731$	−112297.			−0.210151
$732$	1.13907e6			2.12583
$733$	58648.4	−	58648.4i	0.109156	−	0.109156i	−0.650419	−	0.759575i	$-0.725407\pi$
$733$	58648.4	−	58648.4i	0.109156	−	0.109156i	0.759575	+	0.650419i	$0.225407\pi$
$734$	−2682.44	−	2682.44i	−0.00497894	−	0.00497894i
$735$	195958.	−	194606.i	0.362733	−	0.360232i
$736$	−41094.6	+	41094.6i	−0.0758628	+	0.0758628i
$737$		−	505264.i		−	0.930214i
$738$	15285.7			0.0280655
$739$	−274014.	+	274014.i	−0.501747	+	0.501747i	−0.911980	−	0.410234i	$-0.865447\pi$
$739$	−274014.	+	274014.i	−0.501747	+	0.501747i	0.410234	+	0.911980i	$0.365447\pi$
$740$	−616.142	+	178078.i	−0.00112517	+	0.325198i
$741$	344519.	+	260206.i	0.627447	+	0.473894i
$742$			3550.30i			0.00644848i
$743$	−93475.7	+	93475.7i	−0.169325	+	0.169325i	−0.786683	−	0.617358i	$-0.788203\pi$
$743$	−93475.7	+	93475.7i	−0.169325	+	0.169325i	0.617358	+	0.786683i	$0.288203\pi$
$744$	40318.0			0.0728372
$745$	−61667.0	−	213.365i	−0.111107	−	0.000384423i
$746$	−3897.64	−	3897.64i	−0.00700365	−	0.00700365i
$747$	224139.	−	224139.i	0.401677	−	0.401677i
$748$	−222805.	−	222805.i	−0.398219	−	0.398219i
$749$	393099.	−	393099.i	0.700711	−	0.700711i
$750$	−179.237	+	17267.2i	−0.000318643	+	0.0306973i
$751$		−	385289.i		−	0.683136i	−0.939857	−	0.341568i	$-0.889042\pi$
$751$		−	385289.i		−	0.683136i	0.939857	−	0.341568i	$-0.110958\pi$
$752$	349427.	+	349427.i	0.617903	+	0.617903i
$753$	766250.			1.35139
$754$	−7605.84	−	5744.49i	−0.0133784	−	0.0101044i
$755$	−1564.07	+	452049.i	−0.00274385	+	0.793033i
$756$	−46555.0	−	46555.0i	−0.0814560	−	0.0814560i
$757$			409594.i			0.714762i	0.933959	+	0.357381i	$0.116330\pi$
$757$			409594.i			0.714762i	−0.933959	+	0.357381i	$0.883670\pi$
$758$	−262.353			−0.000456613
$759$	−1.43525e6	−	1.43525e6i	−2.49140	−	2.49140i
$760$	10369.8	+	10441.8i	0.0179533	+	0.0180779i
$761$	−337467.	+	337467.i	−0.582723	+	0.582723i	−0.935651	−	0.352928i	$-0.885186\pi$
$761$	−337467.	+	337467.i	−0.582723	+	0.582723i	0.352928	+	0.935651i	$0.385186\pi$
$762$	8608.57	+	8608.57i	0.0148259	+	0.0148259i
$763$		−	121023.i		−	0.207882i
$764$		−	140191.i		−	0.240177i
$765$	131153.	−	130248.i	0.224106	−	0.222561i
$766$			12105.8i			0.0206317i
$767$	−848676.	−	640983.i	−1.44262	−	1.08957i
$768$		−	807778.i		−	1.36952i
$769$	−106824.	−	106824.i	−0.180641	−	0.180641i	0.610994	−	0.791635i	$-0.290770\pi$
$769$	−106824.	−	106824.i	−0.180641	−	0.180641i	−0.791635	+	0.610994i	$0.790770\pi$
$770$	57.8789	−	16728.3i	9.76201e−5	−	0.0282143i
$771$			738102.i			1.24167i
$772$	474633.	−	474633.i	0.796386	−	0.796386i
$773$	−415649.	+	415649.i	−0.695613	+	0.695613i	−0.963461	−	0.267848i	$-0.913688\pi$
$773$	−415649.	+	415649.i	−0.695613	+	0.695613i	0.267848	+	0.963461i	$0.413688\pi$
$774$	−5028.77	+	5028.77i	−0.00839421	+	0.00839421i
$775$	−507435.	+	500461.i	−0.844845	+	0.833233i
$776$	6378.51			0.0105924
$777$	214349.			0.355041
$778$	−5145.99	−	5145.99i	−0.00850178	−	0.00850178i
$779$			487740.i			0.803737i
$780$	−666127.	−	506737.i	−1.09488	−	0.832902i
$781$	−773366.			−1.26789
$782$	5464.60	−	5464.60i	0.00893603	−	0.00893603i
$783$		−	66992.2i		−	0.109270i
$784$			227958.i			0.370871i
$785$	532263.	+	535959.i	0.863747	+	0.869745i
$786$	−18472.0	−	18472.0i	−0.0298998	−	0.0298998i
$787$	54014.9	+	54014.9i	0.0872096	+	0.0872096i	0.749366	−	0.662156i	$-0.230358\pi$
$787$	54014.9	+	54014.9i	0.0872096	+	0.0872096i	−0.662156	+	0.749366i	$0.730358\pi$
$788$	134365.	+	134365.i	0.216388	+	0.216388i
$789$	260673.			0.418738
$790$	32.3034	−	9336.37i	5.17599e−5	−	0.0149597i
$791$	439024.	−	439024.i	0.701674	−	0.701674i
$792$	−39919.8			−0.0636412
$793$	134188.	+	962448.i	0.213387	+	1.53049i
$794$	−1847.16			−0.00292997
$795$	−225081.	+	223529.i	−0.356127	+	0.353671i
$796$	1.03327e6			1.63075
$797$	−955681.			−1.50451			−0.752257	−	0.658870i	$-0.771035\pi$
$797$	−955681.			−1.50451			−0.752257	+	0.658870i	$0.771035\pi$
$798$	6261.05	−	6261.05i	0.00983198	−	0.00983198i
$799$	−139512.	−	139512.i	−0.218534	−	0.218534i
$800$	−30051.2	−	30470.0i	−0.0469550	−	0.0476094i
$801$	107885.	−	107885.i	0.168150	−	0.168150i
$802$		−	5581.32i		−	0.00867737i
$803$	−1.26582e6			−1.96309
$804$	−366601.	+	366601.i	−0.567129	+	0.567129i
$805$	−824306.	−	2852.05i	−1.27203	−	0.00440115i
$806$	2374.23	+	17028.9i	0.00365471	+	0.0262130i
$807$		−	441926.i		−	0.678582i
$808$	−4761.64	+	4761.64i	−0.00729346	+	0.00729346i
$809$	164792.			0.251791			0.125895	−	0.992044i	$-0.459820\pi$
$809$	164792.			0.251791			0.125895	+	0.992044i	$0.459820\pi$
$810$	−55.4151	+	16016.2i	−8.44614e−5	+	0.0244112i
$811$	575040.	+	575040.i	0.874292	+	0.874292i	0.992937	−	0.118645i	$-0.0378549\pi$
$811$	575040.	+	575040.i	0.874292	+	0.874292i	−0.118645	+	0.992937i	$0.537855\pi$
$812$	277705.	−	277705.i	0.421184	−	0.421184i
$813$	968852.	+	968852.i	1.46581	+	1.46581i
$814$	−5424.93	+	5424.93i	−0.00818738	+	0.00818738i
$815$	−901579.	−	3119.42i	−1.35734	−	0.00469633i
$816$			323158.i			0.485327i
$817$	−160460.	−	160460.i	−0.240393	−	0.240393i
$818$	18633.2			0.0278472
$819$	−286657.	+	379541.i	−0.427361	+	0.565836i
$820$	3271.43	−	945516.i	0.00486531	−	1.40618i
$821$	−164988.	−	164988.i	−0.244774	−	0.244774i	0.574048	−	0.818822i	$-0.305372\pi$
$821$	−164988.	−	164988.i	−0.244774	−	0.244774i	−0.818822	+	0.574048i	$0.805372\pi$
$822$		−	20307.5i		−	0.0300547i
$823$	−677209.			−0.999823			−0.499911	−	0.866077i	$-0.666634\pi$
$823$	−677209.			−0.999823			−0.499911	+	0.866077i	$0.666634\pi$
$824$	−4778.25	−	4778.25i	−0.00703744	−	0.00703744i
$825$	1.06418e6	−	1.04955e6i	1.56353	−	1.54204i
$826$	−15423.2	+	15423.2i	−0.0226055	+	0.0226055i
$827$	−335182.	−	335182.i	−0.490083	−	0.490083i	0.418249	−	0.908332i	$-0.362644\pi$
$827$	−335182.	−	335182.i	−0.490083	−	0.490083i	−0.908332	+	0.418249i	$0.862644\pi$
$828$			983304.i			1.43426i
$829$			1.02593e6i			1.49282i	0.665485	+	0.746411i	$0.268225\pi$
$829$			1.02593e6i			1.49282i	−0.665485	+	0.746411i	$0.731775\pi$
$830$	6876.90	+	6924.65i	0.00998244	+	0.0100518i
$831$			243038.i			0.351943i
$832$	683547.	−	95302.5i	0.987465	−	0.137676i
$833$		−	91014.5i		−	0.131166i
$834$	−17249.1	−	17249.1i	−0.0247991	−	0.0247991i
$835$	−883938.	−	3058.38i	−1.26780	−	0.00438650i
$836$		−	636729.i		−	0.911049i
$837$	−85451.4	+	85451.4i	−0.121974	+	0.121974i
$838$	−15348.1	+	15348.1i	−0.0218558	+	0.0218558i
$839$	−478250.	+	478250.i	−0.679408	+	0.679408i	−0.959866	−	0.280458i	$-0.909514\pi$
$839$	−478250.	+	478250.i	−0.679408	+	0.679408i	0.280458	+	0.959866i	$0.409514\pi$
$840$	−24364.9	+	24196.9i	−0.0345308	+	0.0342927i
$841$	−307666.			−0.434998
$842$	−15748.5			−0.0222134
$843$	−76710.7	−	76710.7i	−0.107945	−	0.107945i
$844$			1.03472e6i			1.45257i
$845$	349690.	−	622534.i	0.489745	−	0.871866i
$846$	−12495.0			−0.0174581
$847$	−621665.	+	621665.i	−0.866541	+	0.866541i
$848$		−	261837.i		−	0.364116i
$849$		−	626282.i		−	0.868870i
$850$	3996.10	+	4051.79i	0.00553093	+	0.00560801i
$851$	267320.	+	267320.i	0.369124	+	0.369124i
$852$	561127.	+	561127.i	0.773004	+	0.773004i
$853$	678438.	+	678438.i	0.932422	+	0.932422i	0.997857	−	0.0654352i	$-0.0208436\pi$
$853$	678438.	+	678438.i	0.932422	+	0.932422i	−0.0654352	+	0.997857i	$0.520844\pi$
$854$	19929.5			0.0273263
$855$	373513.	+	1292.34i	0.510945	+	0.00176784i
$856$	28881.5	−	28881.5i	0.0394160	−	0.0394160i
$857$	868914.			1.18308			0.591541	−	0.806275i	$-0.298520\pi$
$857$	868914.			1.18308			0.591541	+	0.806275i	$0.298520\pi$
$858$	−4979.18	−	35712.6i	−0.00676368	−	0.0485117i
$859$	605786.			0.820981			0.410490	−	0.911865i	$-0.365358\pi$
$859$	605786.			0.820981			0.410490	+	0.911865i	$0.365358\pi$
$860$	309985.	+	312137.i	0.419125	+	0.422035i
$861$	−1.13809e6			−1.53522
$862$	8498.87			0.0114379
$863$	7275.19	−	7275.19i	0.00976838	−	0.00976838i	−0.702206	−	0.711974i	$-0.747801\pi$
$863$	7275.19	−	7275.19i	0.00976838	−	0.00976838i	0.711974	+	0.702206i	$0.247801\pi$
$864$	−5131.11	−	5131.11i	−0.00687359	−	0.00687359i
$865$	495000.	−	491587.i	0.661566	−	0.657004i
$866$	11695.1	−	11695.1i	0.0155944	−	0.0155944i
$867$			905575.i			1.20472i
$868$	−708450.			−0.940308
$869$	−571432.	+	571432.i	−0.756703	+	0.756703i
$870$	−17465.6	−	60.4302i	−0.0230752	−	7.98391e-5i
$871$	−352943.	−	266569.i	−0.465231	−	0.351377i
$872$		−	8891.67i		−	0.0116937i
$873$	114477.	−	114477.i	0.150207	−	0.150207i
$874$	15616.6			0.0204439
$875$	6300.51	−	606976.i	0.00822924	−	0.792784i
$876$	918433.	+	918433.i	1.19685	+	1.19685i
$877$	689720.	−	689720.i	0.896754	−	0.896754i	−0.0983935	−	0.995148i	$-0.531370\pi$
$877$	689720.	−	689720.i	0.896754	−	0.896754i	0.995148	+	0.0983935i	$0.0313704\pi$
$878$	−10237.1	−	10237.1i	−0.0132797	−	0.0132797i
$879$	698632.	−	698632.i	0.904212	−	0.904212i
$880$	−4268.62	+	1.23372e6i	−0.00551216	+	1.59314i
$881$		−	32926.6i		−	0.0424224i	−0.999775	−	0.0212112i	$-0.993248\pi$
$881$		−	32926.6i		−	0.0424224i	0.999775	−	0.0212112i	$-0.00675224\pi$
$882$	−4075.74	−	4075.74i	−0.00523925	−	0.00523925i
$883$	1.38975e6			1.78244			0.891222	−	0.453567i	$-0.149849\pi$
$883$	1.38975e6			1.78244			0.891222	+	0.453567i	$0.149849\pi$
$884$	−273185.	+	38088.4i	−0.349585	+	0.0487404i
$885$	−1.94885e6	−	6742.93i	−2.48824	−	0.00860919i
$886$	−7130.68	−	7130.68i	−0.00908371	−	0.00908371i
$887$			176363.i			0.224160i	0.993699	+	0.112080i	$0.0357514\pi$
$887$			176363.i			0.224160i	−0.993699	+	0.112080i	$0.964249\pi$
$888$	15748.5			0.0199716
$889$	−302607.	−	302607.i	−0.382892	−	0.382892i
$890$	3310.06	+	3333.04i	0.00417884	+	0.00420785i
$891$	980270.	−	980270.i	1.23478	−	1.23478i
$892$	−887662.	−	887662.i	−1.11562	−	1.11562i
$893$		−	398695.i		−	0.499963i
$894$			2726.10i			0.00341088i
$895$	−191813.	−	193145.i	−0.239460	−	0.241123i
$896$		−	56715.8i		−	0.0706461i
$897$	−1.75978e6	+	245355.i	−2.18713	+	0.304937i
$898$			13222.8i			0.0163972i
$899$	−509726.	−	509726.i	−0.630692	−	0.630692i
$900$	−724071.	−	5010.55i	−0.893915	−	0.00618587i
$901$			104541.i			0.128777i
$902$	28803.9	−	28803.9i	0.0354029	−	0.0354029i
$903$	374417.	−	374417.i	0.459176	−	0.459176i
$904$	32255.6	−	32255.6i	0.0394701	−	0.0394701i
$905$	388958.	+	391659.i	0.474904	+	0.478202i
$906$	19983.6			0.0243454
$907$	−863349.			−1.04947			−0.524737	−	0.851264i	$-0.675836\pi$
$907$	−863349.			−1.04947			−0.524737	+	0.851264i	$0.675836\pi$
$908$	552348.	+	552348.i	0.669948	+	0.669948i
$909$			170918.i			0.206852i
$910$	−11654.7	−	8865.99i	−0.0140740	−	0.0107064i
$911$	1.14580e6			1.38061			0.690307	−	0.723517i	$-0.257476\pi$
$911$	1.14580e6			1.38061			0.690307	+	0.723517i	$0.257476\pi$
$912$	−461757.	+	461757.i	−0.555168	+	0.555168i
$913$		−	844724.i		−	1.01338i
$914$			23615.3i			0.0282684i
$915$	1.25477e6	+	1.26348e6i	1.49873	+	1.50913i
$916$	171935.	+	171935.i	0.204915	+	0.204915i
$917$	649326.	+	649326.i	0.772189	+	0.772189i
$918$	682.316	+	682.316i	0.000809655	+	0.000809655i
$919$	−1.32162e6			−1.56486			−0.782430	−	0.622739i	$-0.786020\pi$
$919$	−1.32162e6			−1.56486			−0.782430	+	0.622739i	$0.786020\pi$
$920$	−60562.7	−	209.544i	−0.0715533	−	0.000247571i
$921$	496716.	−	496716.i	0.585583	−	0.585583i
$922$	15219.7			0.0179037
$923$	−408015.	+	540222.i	−0.478931	+	0.634116i
$924$	1.48574e6			1.74020
$925$	−198207.	+	195483.i	−0.231652	+	0.228468i
$926$	15365.9			0.0179199
$927$	−171514.			−0.199591
$928$	30607.6	−	30607.6i	0.0355413	−	0.0355413i
$929$	−862595.	−	862595.i	−0.999483	−	0.999483i	0.000517019	−	1.00000i	$-0.499835\pi$
$929$	−862595.	−	862595.i	−0.999483	−	0.999483i	−1.00000		0.000517019i	$0.999835\pi$
$930$	22201.1	+	22355.3i	0.0256690	+	0.0258472i
$931$	130050.	−	130050.i	0.150041	−	0.150041i
$932$		−	642833.i		−	0.740059i
$933$	−866188.			−0.995059
$934$	12200.4	−	12200.4i	0.0139855	−	0.0139855i
$935$	1704.29	−	492577.i	0.00194949	−	0.563444i
$936$	−21061.0	+	27885.3i	−0.0240397	+	0.0318291i
$937$		−	574687.i		−	0.654564i	−0.944927	−	0.327282i	$-0.893867\pi$
$937$		−	574687.i		−	0.654564i	0.944927	−	0.327282i	$-0.106133\pi$
$938$	−6414.14	+	6414.14i	−0.00729008	+	0.00729008i
$939$	2.02809e6			2.30015
$940$	−2674.18	+	772896.i	−0.00302646	+	0.874713i
$941$	375328.	+	375328.i	0.423869	+	0.423869i	0.886533	−	0.462665i	$-0.153107\pi$
$941$	375328.	+	375328.i	0.423869	+	0.423869i	−0.462665	+	0.886533i	$0.653107\pi$
$942$	23611.3	−	23611.3i	0.0266084	−	0.0266084i
$943$	−1.41935e6	−	1.41935e6i	−1.59612	−	1.59612i
$944$	1.13748e6	−	1.13748e6i	1.27643	−	1.27643i
$945$	356.111	−	102924.i	0.000398769	−	0.115253i
$946$			18952.2i			0.0211776i
$947$	−872182.	−	872182.i	−0.972540	−	0.972540i	0.0270933	−	0.999633i	$-0.491375\pi$
$947$	−872182.	−	872182.i	−0.972540	−	0.972540i	−0.999633	+	0.0270933i	$0.991375\pi$
$948$	829222.			0.922686
$949$	−667826.	+	884217.i	−0.741533	+	0.981808i
$950$	−79.5766	+	11499.5i	−8.81735e−5	+	0.0127419i
$951$	−1.07620e6	−	1.07620e6i	−1.18996	−	1.18996i
$952$			11316.5i			0.0124865i
$953$	426284.			0.469368			0.234684	−	0.972072i	$-0.424595\pi$
$953$	426284.			0.469368			0.234684	+	0.972072i	$0.424595\pi$
$954$	4681.48	+	4681.48i	0.00514382	+	0.00514382i
$955$	155502.	−	154430.i	0.170502	−	0.169327i
$956$	313998.	−	313998.i	0.343567	−	0.343567i
$957$	1.06898e6	+	1.06898e6i	1.16721	+	1.16721i
$958$		−	16462.3i		−	0.0179374i
$959$			713846.i			0.776188i
$960$	897348.	−	891160.i	0.973685	−	0.966970i
$961$			376834.i			0.408041i
$962$	927.389	+	6651.60i	0.00100210	+	0.00718746i
$963$		−	1.03669e6i		−	1.11789i
$964$	−1.15763e6	−	1.15763e6i	−1.24571	−	1.24571i
$965$	1.04932e6	+	3630.58i	1.12681	+	0.00389872i
$966$			36439.9i			0.0390501i
$967$	595633.	−	595633.i	0.636980	−	0.636980i	−0.312829	−	0.949809i	$-0.601277\pi$
$967$	595633.	−	595633.i	0.636980	−	0.636980i	0.949809	+	0.312829i	$0.101277\pi$
$968$	−45674.5	+	45674.5i	−0.0487442	+	0.0487442i
$969$	184361.	−	184361.i	0.196346	−	0.196346i
$970$	3512.32	+	3536.71i	0.00373294	+	0.00375886i
$971$	559710.			0.593642			0.296821	−	0.954933i	$-0.404073\pi$
$971$	559710.			0.593642			0.296821	+	0.954933i	$0.404073\pi$
$972$	−1.28522e6			−1.36033
$973$	606340.	+	606340.i	0.640458	+	0.640458i
$974$		−	22291.3i		−	0.0234973i
$975$	−171704.	−	1.29709e6i	−0.180622	−	1.36446i
$976$	−1.46982e6			−1.54299
$977$	677932.	−	677932.i	0.710227	−	0.710227i	−0.256355	−	0.966583i	$-0.582522\pi$
$977$	677932.	−	677932.i	0.710227	−	0.710227i	0.966583	+	0.256355i	$0.0825218\pi$
$978$			39855.9i			0.0416692i
$979$		−	406591.i		−	0.424221i
$980$	−252982.	+	251238.i	−0.263413	+	0.261597i
$981$	−159582.	−	159582.i	−0.165824	−	0.165824i
$982$	−24214.5	−	24214.5i	−0.0251103	−	0.0251103i
$983$	640765.	+	640765.i	0.663119	+	0.663119i	0.956114	−	0.292995i	$-0.0946519\pi$
$983$	640765.	+	640765.i	0.663119	+	0.663119i	−0.292995	+	0.956114i	$0.594652\pi$
$984$	−83617.2			−0.0863585
$985$	−1027.79	+	297053.i	−0.00105933	+	0.306169i
$986$	−4070.08	+	4070.08i	−0.00418648	+	0.00418648i
$987$	930316.			0.954984
$988$	−444776.	−	335928.i	−0.455646	−	0.344137i
$989$	933890.			0.954780
$990$	−21981.8	−	22134.5i	−0.0224282	−	0.0225839i
$991$	−139079.			−0.141616			−0.0708082	−	0.997490i	$-0.522558\pi$
$991$	−139079.			−0.141616			−0.0708082	+	0.997490i	$0.522558\pi$
$992$	−78082.6			−0.0793470
$993$	−764646.	+	764646.i	−0.775465	+	0.775465i
$994$	9817.60	+	9817.60i	0.00993648	+	0.00993648i
$995$	1.13822e6	+	1.14612e6i	1.14969	+	1.15767i
$996$	−612902.	+	612902.i	−0.617834	+	0.617834i
$997$			1.90419e6i			1.91566i	0.287331	+	0.957831i	$0.407232\pi$
$997$			1.90419e6i			1.91566i	−0.287331	+	0.957831i	$0.592768\pi$
$998$	3878.38			0.00389394
$999$	−33377.8	+	33377.8i	−0.0334447	+	0.0334447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.5.g.a.34.13	✓	52
5.4	even	2	inner	65.5.g.a.34.14	yes	52
13.5	odd	4	inner	65.5.g.a.44.14	yes	52
65.44	odd	4	inner	65.5.g.a.44.13	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.5.g.a.34.13	✓	52	1.1	even	1	trivial
65.5.g.a.34.14	yes	52	5.4	even	2	inner
65.5.g.a.44.13	yes	52	65.44	odd	4	inner
65.5.g.a.44.14	yes	52	13.5	odd	4	inner

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	65.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0630863 + 0.0630863i) q^{2} -12.3873i q^{3} +15.9920i q^{4} +(-17.7387 + 17.6164i) q^{5} +(0.781468 + 0.781468i) q^{6} +(-27.4701 - 27.4701i) q^{7} +(-2.01826 - 2.01826i) q^{8} -72.4449 q^{9} +O(q^{10})\)	\(q+(-0.0630863 + 0.0630863i) q^{2} -12.3873i q^{3} +15.9920i q^{4} +(-17.7387 + 17.6164i) q^{5} +(0.781468 + 0.781468i) q^{6} +(-27.4701 - 27.4701i) q^{7} +(-2.01826 - 2.01826i) q^{8} -72.4449 q^{9} +(0.00771715 - 2.23042i) q^{10} +(-136.513 + 136.513i) q^{11} +198.098 q^{12} +(23.3368 + 167.381i) q^{13} +3.46597 q^{14} +(218.219 + 219.735i) q^{15} -255.618 q^{16} +102.058 q^{17} +(4.57028 - 4.57028i) q^{18} +(145.830 + 145.830i) q^{19} +(-281.722 - 283.678i) q^{20} +(-340.279 + 340.279i) q^{21} -17.2242i q^{22} -848.743 q^{23} +(-25.0007 + 25.0007i) q^{24} +(4.32488 - 624.985i) q^{25} +(-12.0317 - 9.08721i) q^{26} -105.975i q^{27} +(439.302 - 439.302i) q^{28} +632.151 q^{29} +(-27.6289 - 0.0955945i) q^{30} +(-806.336 - 806.336i) q^{31} +(48.4181 - 48.4181i) q^{32} +(1691.03 + 1691.03i) q^{33} +(-6.43846 + 6.43846i) q^{34} +(971.207 + 3.36033i) q^{35} -1158.54i q^{36} +(-314.960 - 314.960i) q^{37} -18.3997 q^{38} +(2073.40 - 289.080i) q^{39} +(71.3558 + 0.246887i) q^{40} +(1672.29 + 1672.29i) q^{41} -42.9339i q^{42} -1100.32 q^{43} +(-2183.12 - 2183.12i) q^{44} +(1285.08 - 1276.22i) q^{45} +(53.5440 - 53.5440i) q^{46} +(-1366.99 - 1366.99i) q^{47} +3166.41i q^{48} -891.792i q^{49} +(39.1551 + 39.7008i) q^{50} -1264.22i q^{51} +(-2676.76 + 373.204i) q^{52} +1024.33i q^{53} +(6.68557 + 6.68557i) q^{54} +(16.6992 - 4826.44i) q^{55} +110.883i q^{56} +(1806.44 - 1806.44i) q^{57} +(-39.8801 + 39.8801i) q^{58} +(-4449.90 + 4449.90i) q^{59} +(-3514.01 + 3489.77i) q^{60} +5750.05 q^{61} +101.737 q^{62} +(1990.06 + 1990.06i) q^{63} -4083.78i q^{64} +(-3362.62 - 2558.01i) q^{65} -213.361 q^{66} +(-1850.61 + 1850.61i) q^{67} +1632.12i q^{68} +10513.6i q^{69} +(-61.4819 + 61.0579i) q^{70} +(2832.57 + 2832.57i) q^{71} +(146.212 + 146.212i) q^{72} +(4636.26 + 4636.26i) q^{73} +39.7393 q^{74} +(-7741.87 - 53.5736i) q^{75} +(-2332.12 + 2332.12i) q^{76} +7500.04 q^{77} +(-112.566 + 149.040i) q^{78} +4185.92 q^{79} +(4534.34 - 4503.07i) q^{80} -7180.78 q^{81} -210.998 q^{82} +(-3093.93 + 3093.93i) q^{83} +(-5441.76 - 5441.76i) q^{84} +(-1810.38 + 1797.89i) q^{85} +(69.4152 - 69.4152i) q^{86} -7830.64i q^{87} +551.037 q^{88} +(-1489.20 + 1489.20i) q^{89} +(-0.559068 + 161.583i) q^{90} +(3956.90 - 5239.03i) q^{91} -13573.1i q^{92} +(-9988.31 + 9988.31i) q^{93} +172.476 q^{94} +(-5155.83 - 17.8389i) q^{95} +(-599.769 - 599.769i) q^{96} +(-1580.20 + 1580.20i) q^{97} +(56.2598 + 56.2598i) q^{98} +(9889.67 - 9889.67i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9}+O(q^{10}) \) 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9	\( 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9} + 8 q^{11} + 424 q^{14} - 508 q^{15} - 3128 q^{16} + 268 q^{19} + 2116 q^{20} - 668 q^{21} + 2032 q^{24} + 1100 q^{26} - 3704 q^{29} - 1660 q^{31} + 1252 q^{34} + 6692 q^{35} + 7408 q^{39} + 3644 q^{40} + 5960 q^{41} + 1444 q^{44} - 8674 q^{45} + 17620 q^{46} - 3928 q^{50} - 30588 q^{54} + 14784 q^{55} - 5548 q^{59} - 13976 q^{60} - 20008 q^{61} - 15614 q^{65} + 24752 q^{66} + 26908 q^{70} - 16360 q^{71} - 7304 q^{74} - 5760 q^{76} - 9536 q^{79} - 62348 q^{80} - 36516 q^{81} + 66564 q^{84} - 11604 q^{85} - 5264 q^{86} - 940 q^{89} + 37644 q^{91} + 55448 q^{94} - 61644 q^{96} + 16140 q^{99}+O(q^{100}) \) 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9 + 8 * q^11 + 424 * q^14 - 508 * q^15 - 3128 * q^16 + 268 * q^19 + 2116 * q^20 - 668 * q^21 + 2032 * q^24 + 1100 * q^26 - 3704 * q^29 - 1660 * q^31 + 1252 * q^34 + 6692 * q^35 + 7408 * q^39 + 3644 * q^40 + 5960 * q^41 + 1444 * q^44 - 8674 * q^45 + 17620 * q^46 - 3928 * q^50 - 30588 * q^54 + 14784 * q^55 - 5548 * q^59 - 13976 * q^60 - 20008 * q^61 - 15614 * q^65 + 24752 * q^66 + 26908 * q^70 - 16360 * q^71 - 7304 * q^74 - 5760 * q^76 - 9536 * q^79 - 62348 * q^80 - 36516 * q^81 + 66564 * q^84 - 11604 * q^85 - 5264 * q^86 - 940 * q^89 + 37644 * q^91 + 55448 * q^94 - 61644 * q^96 + 16140 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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