LMFDB - Embedded newform 35.5.i.a.19.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(19,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("35.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.i (of order $6$, 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:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.11
Character	$\chi$	$=$	35.19
Dual form			35.5.i.a.24.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.03096 + 2.32728i) q^{2} +(-7.86751 - 13.6269i) q^{3} +(2.83245 + 4.90594i) q^{4} +(-15.2320 - 19.8239i) q^{5} -73.2395i q^{6} +(45.1600 + 19.0150i) q^{7} -48.1053i q^{8} +(-83.2953 + 144.272i) q^{9} +O(q^{10})$	\(q+(4.03096 + 2.32728i) q^{2} +(-7.86751 - 13.6269i) q^{3} +(2.83245 + 4.90594i) q^{4} +(-15.2320 - 19.8239i) q^{5} -73.2395i q^{6} +(45.1600 + 19.0150i) q^{7} -48.1053i q^{8} +(-83.2953 + 144.272i) q^{9} +(-15.2637 - 115.358i) q^{10} +(21.2220 + 36.7575i) q^{11} +(44.5686 - 77.1950i) q^{12} +247.023 q^{13} +(137.785 + 181.749i) q^{14} +(-150.301 + 363.529i) q^{15} +(157.274 - 272.406i) q^{16} +(-152.237 - 263.681i) q^{17} +(-671.521 + 387.703i) q^{18} +(-10.5557 - 6.09436i) q^{19} +(54.1112 - 130.877i) q^{20} +(-96.1806 - 764.993i) q^{21} +197.558i q^{22} +(-32.1169 - 18.5427i) q^{23} +(-655.528 + 378.469i) q^{24} +(-160.975 + 603.914i) q^{25} +(995.742 + 574.892i) q^{26} +1346.77 q^{27} +(34.6268 + 275.411i) q^{28} +1094.49 q^{29} +(-1451.89 + 1115.58i) q^{30} +(-502.352 + 290.033i) q^{31} +(601.362 - 347.196i) q^{32} +(333.928 - 578.380i) q^{33} -1417.19i q^{34} +(-310.924 - 1184.88i) q^{35} -943.718 q^{36} +(362.484 + 209.280i) q^{37} +(-28.3665 - 49.1323i) q^{38} +(-1943.46 - 3366.17i) q^{39} +(-953.636 + 732.739i) q^{40} +1149.43i q^{41} +(1392.65 - 3307.50i) q^{42} +354.717i q^{43} +(-120.220 + 208.227i) q^{44} +(4128.78 - 546.302i) q^{45} +(-86.3081 - 149.490i) q^{46} +(426.210 - 738.218i) q^{47} -4949.41 q^{48} +(1677.86 + 1717.44i) q^{49} +(-2054.36 + 2059.72i) q^{50} +(-2395.44 + 4149.03i) q^{51} +(699.680 + 1211.88i) q^{52} +(2944.64 - 1700.09i) q^{53} +(5428.78 + 3134.31i) q^{54} +(405.426 - 980.591i) q^{55} +(914.724 - 2172.44i) q^{56} +191.790i q^{57} +(4411.87 + 2547.19i) q^{58} +(-4396.62 + 2538.39i) q^{59} +(-2209.17 + 292.308i) q^{60} +(165.555 + 95.5833i) q^{61} -2699.95 q^{62} +(-6504.95 + 4931.45i) q^{63} -1800.67 q^{64} +(-3762.65 - 4896.97i) q^{65} +(2692.10 - 1554.29i) q^{66} +(-1485.00 + 857.362i) q^{67} +(862.404 - 1493.73i) q^{68} +583.540i q^{69} +(1504.23 - 5499.83i) q^{70} -1021.27 q^{71} +(6940.24 + 4006.95i) q^{72} +(3355.88 + 5812.56i) q^{73} +(974.106 + 1687.20i) q^{74} +(9495.96 - 2557.71i) q^{75} -69.0477i q^{76} +(259.439 + 2063.51i) q^{77} -18091.9i q^{78} +(276.955 - 479.700i) q^{79} +(-7795.74 + 1031.50i) q^{80} +(-3848.81 - 6666.33i) q^{81} +(-2675.05 + 4633.33i) q^{82} -5185.78 q^{83} +(3480.58 - 2638.66i) q^{84} +(-2908.34 + 7034.31i) q^{85} +(-825.526 + 1429.85i) q^{86} +(-8610.94 - 14914.6i) q^{87} +(1768.23 - 1020.89i) q^{88} +(-8123.42 - 4690.06i) q^{89} +(17914.4 + 7406.70i) q^{90} +(11155.6 + 4697.15i) q^{91} -210.085i q^{92} +(7904.52 + 4563.68i) q^{93} +(3436.08 - 1983.82i) q^{94} +(39.9706 + 302.085i) q^{95} +(-9462.43 - 5463.14i) q^{96} -333.185 q^{97} +(2766.42 + 10827.8i) q^{98} -7070.76 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9}+O(q^{10}) $ 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9	$ 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9} + 390 q^{10} + 34 q^{11} - 258 q^{14} + 60 q^{15} - 206 q^{16} + 366 q^{19} - 1116 q^{21} - 288 q^{24} + 40 q^{25} + 474 q^{26} + 856 q^{29} - 1620 q^{30} - 5520 q^{31} - 2620 q^{35} + 11892 q^{36} + 1656 q^{39} + 6510 q^{40} - 1082 q^{44} + 7920 q^{45} - 5442 q^{46} + 8356 q^{49} - 15960 q^{50} - 2976 q^{51} + 4392 q^{54} + 11640 q^{56} - 13920 q^{59} - 5700 q^{60} - 24960 q^{61} - 45596 q^{64} + 5290 q^{65} + 10332 q^{66} - 26400 q^{70} + 38272 q^{71} + 31806 q^{74} + 41310 q^{75} + 22028 q^{79} + 48000 q^{80} - 29238 q^{81} + 62784 q^{84} - 33820 q^{85} - 21180 q^{86} - 12516 q^{89} + 4448 q^{91} - 89418 q^{94} - 28890 q^{95} - 27900 q^{96} - 3108 q^{99}+O(q^{100}) $ 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9 + 390 * q^10 + 34 * q^11 - 258 * q^14 + 60 * q^15 - 206 * q^16 + 366 * q^19 - 1116 * q^21 - 288 * q^24 + 40 * q^25 + 474 * q^26 + 856 * q^29 - 1620 * q^30 - 5520 * q^31 - 2620 * q^35 + 11892 * q^36 + 1656 * q^39 + 6510 * q^40 - 1082 * q^44 + 7920 * q^45 - 5442 * q^46 + 8356 * q^49 - 15960 * q^50 - 2976 * q^51 + 4392 * q^54 + 11640 * q^56 - 13920 * q^59 - 5700 * q^60 - 24960 * q^61 - 45596 * q^64 + 5290 * q^65 + 10332 * q^66 - 26400 * q^70 + 38272 * q^71 + 31806 * q^74 + 41310 * q^75 + 22028 * q^79 + 48000 * q^80 - 29238 * q^81 + 62784 * q^84 - 33820 * q^85 - 21180 * q^86 - 12516 * q^89 + 4448 * q^91 - 89418 * q^94 - 28890 * q^95 - 27900 * q^96 - 3108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	4.03096	+	2.32728i	1.00774	+	0.581820i	0.910529	−	0.413444i	$-0.135674\pi$
$2$	4.03096	+	2.32728i	1.00774	+	0.581820i	0.0972115	+	0.995264i	$0.469008\pi$
$3$	−7.86751	−	13.6269i	−0.874167	−	1.51410i	−0.857647	−	0.514239i	$-0.828074\pi$
$3$	−7.86751	−	13.6269i	−0.874167	−	1.51410i	−0.0165205	−	0.999864i	$-0.505259\pi$
$4$	2.83245	+	4.90594i	0.177028	+	0.306621i
$5$	−15.2320	−	19.8239i	−0.609278	−	0.792956i
$5$	−15.2320	−	19.8239i	−0.609278	−	0.792956i
$6$		−	73.2395i		−	2.03443i
$7$	45.1600	+	19.0150i	0.921633	+	0.388062i
$7$	45.1600	+	19.0150i	0.921633	+	0.388062i
$8$		−	48.1053i		−	0.751646i
$9$	−83.2953	+	144.272i	−1.02834	+	1.78113i
$10$	−15.2637	−	115.358i	−0.152637	−	1.15358i
$11$	21.2220	+	36.7575i	0.175388	+	0.303781i	0.940296	−	0.340359i	$-0.110549\pi$
$11$	21.2220	+	36.7575i	0.175388	+	0.303781i	−0.764907	+	0.644140i	$0.777215\pi$
$12$	44.5686	−	77.1950i	0.309504	−	0.536077i
$13$	247.023			1.46168			0.730838	−	0.682551i	$-0.239130\pi$
$13$	247.023			1.46168			0.730838	+	0.682551i	$0.239130\pi$
$14$	137.785	+	181.749i	0.702986	+	0.927290i
$15$	−150.301	+	363.529i	−0.668006	+	1.61569i
$16$	157.274	−	272.406i	0.614350	−	1.06409i
$17$	−152.237	−	263.681i	−0.526770	−	0.912393i	−0.999513	−	0.0311923i	$-0.990070\pi$
$17$	−152.237	−	263.681i	−0.526770	−	0.912393i	0.472743	−	0.881200i	$-0.343264\pi$
$18$	−671.521	+	387.703i	−2.07260	+	1.19661i
$19$	−10.5557	−	6.09436i	−0.0292403	−	0.0168819i	0.485309	−	0.874343i	$-0.338707\pi$
$19$	−10.5557	−	6.09436i	−0.0292403	−	0.0168819i	−0.514549	+	0.857461i	$0.672041\pi$
$20$	54.1112	−	130.877i	0.135278	−	0.327193i
$21$	−96.1806	−	764.993i	−0.218097	−	1.73468i
$22$			197.558i			0.408177i
$23$	−32.1169	−	18.5427i	−0.0607126	−	0.0350524i	0.469336	−	0.883019i	$-0.344493\pi$
$23$	−32.1169	−	18.5427i	−0.0607126	−	0.0350524i	−0.530049	+	0.847967i	$0.677826\pi$
$24$	−655.528	+	378.469i	−1.13807	+	0.657064i
$25$	−160.975	+	603.914i	−0.257560	+	0.966262i
$26$	995.742	+	574.892i	1.47299	+	0.850431i
$27$	1346.77			1.84742
$28$	34.6268	+	275.411i	0.0441668	+	0.351290i
$29$	1094.49			1.30142			0.650710	−	0.759326i	$-0.274471\pi$
$29$	1094.49			1.30142			0.650710	+	0.759326i	$0.274471\pi$
$30$	−1451.89	+	1115.58i	−1.61321	+	1.23953i
$31$	−502.352	+	290.033i	−0.522739	+	0.301803i	−0.738055	−	0.674741i	$-0.764255\pi$
$31$	−502.352	+	290.033i	−0.522739	+	0.301803i	0.215316	+	0.976545i	$0.430922\pi$
$32$	601.362	−	347.196i	0.587267	−	0.339059i
$33$	333.928	−	578.380i	0.306637	−	0.531111i
$34$		−	1417.19i		−	1.22594i
$35$	−310.924	−	1184.88i	−0.253815	−	0.967253i
$36$	−943.718			−0.728178
$37$	362.484	+	209.280i	0.264780	+	0.152871i	0.626513	−	0.779411i	$-0.284482\pi$
$37$	362.484	+	209.280i	0.264780	+	0.152871i	−0.361733	+	0.932282i	$0.617815\pi$
$38$	−28.3665	−	49.1323i	−0.0196444	−	0.0340251i
$39$	−1943.46	−	3366.17i	−1.27775	−	2.21313i
$40$	−953.636	+	732.739i	−0.596022	+	0.457962i
$41$			1149.43i			0.683780i	0.939740	+	0.341890i	$0.111067\pi$
$41$			1149.43i			0.683780i	−0.939740	+	0.341890i	$0.888933\pi$
$42$	1392.65	−	3307.50i	0.789485	−	1.87500i
$43$			354.717i			0.191843i	0.995389	+	0.0959214i	$0.0305798\pi$
$43$			354.717i			0.191843i	−0.995389	+	0.0959214i	$0.969420\pi$
$44$	−120.220	+	208.227i	−0.0620972	+	0.107555i
$45$	4128.78	−	546.302i	2.03890	−	0.269779i
$46$	−86.3081	−	149.490i	−0.0407883	−	0.0706475i
$47$	426.210	−	738.218i	0.192943	−	0.334186i	−0.753282	−	0.657698i	$-0.771530\pi$
$47$	426.210	−	738.218i	0.192943	−	0.334186i	0.946224	+	0.323512i	$0.104864\pi$
$48$	−4949.41			−2.14818
$49$	1677.86	+	1717.44i	0.698816	+	0.715301i
$50$	−2054.36	+	2059.72i	−0.821744	+	0.823889i
$51$	−2395.44	+	4149.03i	−0.920971	+	1.59517i
$52$	699.680	+	1211.88i	0.258757	+	0.448181i
$53$	2944.64	−	1700.09i	1.04829	−	0.605229i	0.126118	−	0.992015i	$-0.459748\pi$
$53$	2944.64	−	1700.09i	1.04829	−	0.605229i	0.922169	+	0.386787i	$0.126415\pi$
$54$	5428.78	+	3134.31i	1.86172	+	1.07487i
$55$	405.426	−	980.591i	0.134025	−	0.324162i
$56$	914.724	−	2172.44i	0.291685	−	0.692742i
$57$			191.790i			0.0590303i
$58$	4411.87	+	2547.19i	1.31149	+	0.757191i
$59$	−4396.62	+	2538.39i	−1.26303	+	0.729213i	−0.973660	−	0.228003i	$-0.926780\pi$
$59$	−4396.62	+	2538.39i	−1.26303	+	0.729213i	−0.289374	+	0.957216i	$0.593447\pi$
$60$	−2209.17	+	292.308i	−0.613660	+	0.0811968i
$61$	165.555	+	95.5833i	0.0444921	+	0.0256875i	0.522081	−	0.852896i	$-0.325156\pi$
$61$	165.555	+	95.5833i	0.0444921	+	0.0256875i	−0.477589	+	0.878583i	$0.658489\pi$
$62$	−2699.95			−0.702380
$63$	−6504.95	+	4931.45i	−1.63894	+	1.24249i
$64$	−1800.67			−0.439616
$65$	−3762.65	−	4896.97i	−0.890567	−	1.15905i
$66$	2692.10	−	1554.29i	0.618022	−	0.356815i
$67$	−1485.00	+	857.362i	−0.330808	+	0.190992i	−0.656200	−	0.754587i	$-0.727837\pi$
$67$	−1485.00	+	857.362i	−0.330808	+	0.190992i	0.325392	+	0.945579i	$0.394504\pi$
$68$	862.404	−	1493.73i	0.186506	−	0.323038i
$69$			583.540i			0.122567i
$70$	1504.23	−	5499.83i	0.306987	−	1.12241i
$71$	−1021.27			−0.202593			−0.101297	−	0.994856i	$-0.532299\pi$
$71$	−1021.27			−0.202593			−0.101297	+	0.994856i	$0.532299\pi$
$72$	6940.24	+	4006.95i	1.33878	+	0.772946i
$73$	3355.88	+	5812.56i	0.629739	+	1.09074i	0.987604	+	0.156967i	$0.0501716\pi$
$73$	3355.88	+	5812.56i	0.629739	+	1.09074i	−0.357865	+	0.933773i	$0.616495\pi$
$74$	974.106	+	1687.20i	0.177886	+	0.308108i
$75$	9495.96	−	2557.71i	1.68817	−	0.454703i
$76$		−	69.0477i		−	0.0119542i
$77$	259.439	+	2063.51i	0.0437577	+	0.348036i
$78$		−	18091.9i		−	2.97368i
$79$	276.955	−	479.700i	0.0443767	−	0.0768627i	−0.842984	−	0.537939i	$-0.819203\pi$
$79$	276.955	−	479.700i	0.0443767	−	0.0768627i	0.887361	+	0.461076i	$0.152536\pi$
$80$	−7795.74	+	1031.50i	−1.21808	+	0.161172i
$81$	−3848.81	−	6666.33i	−0.586619	−	1.01605i
$82$	−2675.05	+	4633.33i	−0.397836	+	0.689073i
$83$	−5185.78			−0.752763			−0.376381	−	0.926465i	$-0.622832\pi$
$83$	−5185.78			−0.752763			−0.376381	+	0.926465i	$0.622832\pi$
$84$	3480.58	−	2638.66i	0.493280	−	0.373959i
$85$	−2908.34	+	7034.31i	−0.402538	+	0.973607i
$86$	−825.526	+	1429.85i	−0.111618	+	0.193328i
$87$	−8610.94	−	14914.6i	−1.13766	−	1.97048i
$88$	1768.23	−	1020.89i	0.228336	−	0.131830i
$89$	−8123.42	−	4690.06i	−1.02555	−	0.592104i	−0.109847	−	0.993949i	$-0.535036\pi$
$89$	−8123.42	−	4690.06i	−1.02555	−	0.592104i	−0.915708	+	0.401844i	$0.868369\pi$
$90$	17914.4	+	7406.70i	2.21165	+	0.914407i
$91$	11155.6	+	4697.15i	1.34713	+	0.567221i
$92$		−	210.085i		−	0.0248210i
$93$	7904.52	+	4563.68i	0.913923	+	0.527653i
$94$	3436.08	−	1983.82i	0.388872	−	0.224516i
$95$	39.9706	+	302.085i	0.00442887	+	0.0334720i
$96$	−9462.43	−	5463.14i	−1.02674	−	0.592788i
$97$	−333.185			−0.0354113			−0.0177056	−	0.999843i	$-0.505636\pi$
$97$	−333.185			−0.0354113			−0.0177056	+	0.999843i	$0.505636\pi$
$98$	2766.42	+	10827.8i	0.288049	+	1.12742i
$99$	−7070.76			−0.721433
$100$	−3418.72	+	920.821i	−0.341872	+	0.0920821i
$101$	2358.29	−	1361.56i	0.231182	−	0.133473i	−0.379935	−	0.925013i	$-0.624054\pi$
$101$	2358.29	−	1361.56i	0.231182	−	0.133473i	0.611117	+	0.791540i	$0.290720\pi$
$102$	−19311.9	+	11149.7i	−1.85620	+	1.07168i
$103$	7799.39	−	13508.9i	0.735167	−	1.27335i	−0.219483	−	0.975616i	$-0.570437\pi$
$103$	7799.39	−	13508.9i	0.735167	−	1.27335i	0.954650	−	0.297730i	$-0.0962297\pi$
$104$		−	11883.1i		−	1.09866i
$105$	−13700.1	+	13559.0i	−1.24264	+	1.22984i
$106$	15826.3			1.40854
$107$	−4460.99	−	2575.55i	−0.389640	−	0.224959i	0.292364	−	0.956307i	$-0.405558\pi$
$107$	−4460.99	−	2575.55i	−0.389640	−	0.224959i	−0.682004	+	0.731348i	$0.738891\pi$
$108$	3814.66	+	6607.18i	0.327045	+	0.566459i
$109$	9316.28	+	16136.3i	0.784132	+	1.35816i	0.929516	+	0.368782i	$0.120225\pi$
$109$	9316.28	+	16136.3i	0.784132	+	1.35816i	−0.145384	+	0.989375i	$0.546442\pi$
$110$	3916.36	−	3009.19i	0.323666	−	0.248693i
$111$		−	6586.05i		−	0.534539i
$112$	12282.3	−	9311.30i	0.979137	−	0.742291i
$113$			3398.92i			0.266185i	0.991104	+	0.133092i	$0.0424907\pi$
$113$			3398.92i			0.266185i	−0.991104	+	0.133092i	$0.957509\pi$
$114$	−446.348	+	773.097i	−0.0343450	+	0.0594873i
$115$	121.615	+	919.125i	0.00919581	+	0.0694991i
$116$	3100.10	+	5369.52i	0.230388	+	0.399043i
$117$	−20575.9	+	35638.5i	−1.50310	+	2.60344i
$118$	−23630.2			−1.69708
$119$	−1861.10	−	14802.6i	−0.131424	−	1.04531i
$120$	17487.7	+	7230.30i	1.21442	+	0.502104i
$121$	6419.76	−	11119.3i	0.438478	−	0.759466i
$122$	444.898	+	770.585i	0.0298910	+	0.0517727i
$123$	15663.2	−	9043.18i	1.03531	−	0.597738i
$124$	−2845.77	−	1643.01i	−0.185079	−	0.106855i
$125$	14423.9	−	6007.64i	0.923129	−	0.384489i
$126$	−37698.1	+	4739.68i	−2.37453	+	0.298544i
$127$			20807.8i			1.29009i	0.764145	+	0.645044i	$0.223161\pi$
$127$			20807.8i			1.29009i	−0.764145	+	0.645044i	$0.776839\pi$
$128$	−16880.2	−	9745.79i	−1.03029	−	0.594836i
$129$	4833.71	−	2790.74i	0.290470	−	0.167703i
$130$	−3770.49	−	28496.2i	−0.223106	−	1.68617i
$131$	22650.4	+	13077.2i	1.31988	+	0.762032i	0.983709	−	0.179770i	$-0.0575353\pi$
$131$	22650.4	+	13077.2i	1.31988	+	0.762032i	0.336169	+	0.941802i	$0.390869\pi$
$132$	3783.33			0.217133
$133$	−360.813	−	475.939i	−0.0203976	−	0.0269059i
$134$	−7981.28			−0.444491
$135$	−20514.0	−	26698.3i	−1.12559	−	1.46493i
$136$	−12684.5	+	7323.39i	−0.685796	+	0.395945i
$137$	21398.2	−	12354.2i	1.14008	−	0.658226i	0.193630	−	0.981075i	$-0.437974\pi$
$137$	21398.2	−	12354.2i	1.14008	−	0.658226i	0.946451	+	0.322849i	$0.104641\pi$
$138$	−1358.06	+	2352.23i	−0.0713117	+	0.123515i
$139$			27975.2i			1.44792i	0.689843	+	0.723959i	$0.257680\pi$
$139$			27975.2i			1.44792i	−0.689843	+	0.723959i	$0.742320\pi$
$140$	4932.30	−	4881.49i	0.251648	−	0.249056i
$141$	−13412.8			−0.674657
$142$	−4116.71	−	2376.78i	−0.204161	−	0.117873i
$143$	5242.32	+	9079.96i	0.256361	+	0.444029i
$144$	26200.3	+	45380.3i	1.26352	+	2.18848i
$145$	−16671.3	−	21697.1i	−0.792927	−	1.03197i
$146$			31240.3i			1.46558i
$147$	10202.8	−	36376.0i	0.472157	−	1.68337i
$148$			2371.10i			0.108250i
$149$	6735.81	−	11666.8i	0.303401	−	0.525506i	−0.673503	−	0.739185i	$-0.735211\pi$
$149$	6735.81	−	11666.8i	0.303401	−	0.525506i	0.976904	+	0.213678i	$0.0685445\pi$
$150$	44230.4	+	11789.7i	1.96579	+	0.523987i
$151$	−5571.47	−	9650.07i	−0.244352	−	0.423230i	0.717597	−	0.696458i	$-0.245242\pi$
$151$	−5571.47	−	9650.07i	−0.244352	−	0.423230i	−0.961949	+	0.273228i	$0.911909\pi$
$152$	−293.171	+	507.787i	−0.0126892	+	0.0219783i
$153$	50722.4			2.16679
$154$	−3756.56	+	8921.71i	−0.158398	+	0.376189i
$155$	13401.4	+	5540.81i	0.557810	+	0.230627i
$156$	11009.5	−	19069.0i	0.452395	−	0.783570i
$157$	−14546.2	−	25194.8i	−0.590134	−	1.02214i	−0.994214	−	0.107418i	$-0.965742\pi$
$157$	−14546.2	−	25194.8i	−0.590134	−	1.02214i	0.404080	−	0.914724i	$-0.367592\pi$
$158$	2232.79	−	1289.10i	0.0894404	−	0.0516385i
$159$	−46333.9	−	26750.9i	−1.83276	−	1.05814i
$160$	−16042.7	−	6632.86i	−0.626668	−	0.259096i
$161$	−1097.81	−	1448.09i	−0.0423522	−	0.0558657i
$162$		−	35829.0i		−	1.36522i
$163$	162.453	+	93.7920i	0.00611437	+	0.00353013i	0.503054	−	0.864255i	$-0.332210\pi$
$163$	162.453	+	93.7920i	0.00611437	+	0.00353013i	−0.496940	+	0.867785i	$0.665543\pi$
$164$	−5639.05	+	3255.71i	−0.209661	+	0.121048i
$165$	−16552.1	+	2190.11i	−0.607975	+	0.0804446i
$166$	−20903.7	−	12068.8i	−0.758590	−	0.437972i
$167$	−24709.4			−0.885992			−0.442996	−	0.896524i	$-0.646084\pi$
$167$	−24709.4			−0.885992			−0.442996	+	0.896524i	$0.646084\pi$
$168$	−36800.3	+	4626.80i	−1.30386	+	0.163931i
$169$	32459.5			1.13650
$170$	−28094.2	+	21586.5i	−0.972117	+	0.746939i
$171$	1758.49	−	1015.26i	0.0601377	−	0.0347205i
$172$	−1740.22	+	1004.72i	−0.0588231	+	0.0339615i
$173$	−20561.5	+	35613.6i	−0.687009	+	1.18993i	0.285792	+	0.958292i	$0.407743\pi$
$173$	−20561.5	+	35613.6i	−0.687009	+	1.18993i	−0.972801	+	0.231643i	$0.925590\pi$
$174$		−	80160.2i		−	2.64765i
$175$	−18753.1	+	24211.8i	−0.612345	+	0.790591i
$176$	13350.6			0.430999
$177$	69180.9	+	39941.6i	2.20821	+	1.27491i
$178$	−21830.1	−	37810.9i	−0.688996	−	1.19338i
$179$	−5988.39	−	10372.2i	−0.186898	−	0.323716i	0.757317	−	0.653048i	$-0.226510\pi$
$179$	−5988.39	−	10372.2i	−0.186898	−	0.323716i	−0.944214	+	0.329332i	$0.893177\pi$
$180$	14374.7	+	18708.2i	0.443663	+	0.577413i
$181$			9776.20i			0.298410i	0.988806	+	0.149205i	$0.0476714\pi$
$181$			9776.20i			0.298410i	−0.988806	+	0.149205i	$0.952329\pi$
$182$	34036.1	+	44896.2i	1.02754	+	1.35540i
$183$		−	3008.01i		−	0.0898208i
$184$	−892.004	+	1545.00i	−0.0263470	+	0.0456343i
$185$	−1372.59	−	10373.6i	−0.0401048	−	0.303100i
$186$	21241.9	+	36792.0i	0.613998	+	1.06348i
$187$	6461.52	−	11191.7i	0.184778	−	0.320046i
$188$	4828.87			0.136625
$189$	60820.2	+	25608.9i	1.70265	+	0.716914i
$190$	−541.916	+	1310.72i	−0.0150115	+	0.0363079i
$191$	−5536.64	+	9589.74i	−0.151768	+	0.262869i	−0.931877	−	0.362773i	$-0.881830\pi$
$191$	−5536.64	+	9589.74i	−0.151768	+	0.262869i	0.780110	+	0.625643i	$0.215163\pi$
$192$	14166.8	+	24537.6i	0.384298	+	0.665624i
$193$	−53200.5	+	30715.3i	−1.42824	+	0.824595i	−0.996982	−	0.0776335i	$-0.975264\pi$
$193$	−53200.5	+	30715.3i	−1.42824	+	0.824595i	−0.431258	+	0.902228i	$0.641930\pi$
$194$	−1343.05	−	775.413i	−0.0356854	−	0.0206030i
$195$	−37127.9	+	89800.2i	−0.976408	+	2.36161i
$196$	−3673.21	+	13096.0i	−0.0956167	+	0.340900i
$197$		−	39953.3i		−	1.02949i	−0.857344	−	0.514743i	$-0.827887\pi$
$197$		−	39953.3i		−	1.02949i	0.857344	−	0.514743i	$-0.172113\pi$
$198$	−28502.0	−	16455.6i	−0.727017	−	0.419744i
$199$	−63018.9	+	36384.0i	−1.59135	+	0.918764i	−0.598270	+	0.801295i	$0.704145\pi$
$199$	−63018.9	+	36384.0i	−1.59135	+	0.918764i	−0.993076	+	0.117470i	$0.962522\pi$
$200$	29051.5	+	7743.75i	0.726287	+	0.193594i
$201$	23366.4	+	13490.6i	0.578363	+	0.333918i
$202$	12674.9			0.310629
$203$	49427.4	+	20811.8i	1.19943	+	0.505031i
$204$	−27139.9			−0.652150
$205$	22786.3	−	17508.1i	0.542208	−	0.416612i
$206$	62878.1	−	36302.7i	1.48172	−	0.855469i
$207$	5350.38	−	3089.05i	0.124866	−	0.0720914i
$208$	38850.2	−	67290.6i	0.897981	−	1.55535i
$209$		−	517.337i		−	0.0118435i
$210$	−86780.4	+	22771.9i	−1.96781	+	0.516369i
$211$	−55326.3			−1.24270			−0.621350	−	0.783533i	$-0.713416\pi$
$211$	−55326.3			−1.24270			−0.621350	+	0.783533i	$0.713416\pi$
$212$	16681.1	+	9630.81i	0.371152	+	0.214285i
$213$	8034.87	+	13916.8i	0.177100	+	0.306747i
$214$	−11988.1	−	20763.9i	−0.261771	−	0.453400i
$215$	7031.89	−	5403.04i	0.152123	−	0.116886i
$216$		−	64786.9i		−	1.38861i
$217$	−28201.2	+	3545.67i	−0.598892	+	0.0752971i
$218$			86726.3i			1.82489i
$219$	52804.8	−	91460.6i	1.10100	−	1.90698i
$220$	5959.07	−	788.478i	0.123121	−	0.0162909i
$221$	−37606.0	−	65135.4i	−0.769967	−	1.33362i
$222$	15327.6	−	26548.1i	0.311005	−	0.538677i
$223$	−245.690			−0.00494058			−0.00247029	−	0.999997i	$-0.500786\pi$
$223$	−245.690			−0.00494058			−0.00247029	+	0.999997i	$0.500786\pi$
$224$	33759.5	−	4244.49i	0.672821	−	0.0845920i
$225$	−73719.3	−	73527.3i	−1.45618	−	1.45239i
$226$	−7910.22	+	13700.9i	−0.154872	+	0.268245i
$227$	−38803.7	−	67210.0i	−0.753046	−	1.30431i	−0.946340	−	0.323173i	$-0.895250\pi$
$227$	−38803.7	−	67210.0i	−0.753046	−	1.30431i	0.193294	−	0.981141i	$-0.438083\pi$
$228$	−940.908	+	543.234i	−0.0181000	+	0.0104500i
$229$	74555.2	+	43044.5i	1.42170	+	0.820817i	0.996444	−	0.0842572i	$-0.0268517\pi$
$229$	74555.2	+	43044.5i	1.42170	+	0.820817i	0.425253	+	0.905074i	$0.360185\pi$
$230$	−1648.84	+	3987.99i	−0.0311689	+	0.0753874i
$231$	26078.1	−	19770.0i	0.488711	−	0.370496i
$232$		−	52651.0i		−	0.978207i
$233$	−33227.4	−	19183.9i	−0.612047	−	0.353365i	0.161719	−	0.986837i	$-0.448296\pi$
$233$	−33227.4	−	19183.9i	−0.612047	−	0.353365i	−0.773766	+	0.633471i	$0.781629\pi$
$234$	−165881.	+	95771.6i	−3.02946	+	1.74906i
$235$	−21126.4	+	2795.35i	−0.382551	+	0.0506175i
$236$	−24906.4	−	14379.7i	−0.447184	−	0.258182i
$237$	−8715.78			−0.155171
$238$	26947.9	−	64000.2i	0.475741	−	1.12987i
$239$	−15743.1			−0.275610			−0.137805	−	0.990459i	$-0.544005\pi$
$239$	−15743.1			−0.275610			−0.137805	+	0.990459i	$0.544005\pi$
$240$	75389.2	+	98116.6i	1.30884	+	1.70341i
$241$	63240.2	−	36511.7i	1.08883	−	0.628635i	0.155563	−	0.987826i	$-0.450281\pi$
$241$	63240.2	−	36511.7i	1.08883	−	0.628635i	0.933264	+	0.359191i	$0.116947\pi$
$242$	51755.6	−	29881.1i	0.883745	−	0.510230i
$243$	−6016.80	+	10421.4i	−0.101895	+	0.176487i
$244$			1082.94i			0.0181896i
$245$	8489.29	−	59421.7i	0.141429	−	0.989948i
$246$	84184.0			1.39110
$247$	−2607.51	−	1505.45i	−0.0427398	−	0.0246758i
$248$	13952.1	+	24165.8i	0.226849	+	0.392915i
$249$	40799.2	+	70666.3i	0.658041	+	1.13976i
$250$	72123.7	+	9351.83i	1.15398	+	0.149629i
$251$			47793.8i			0.758620i	0.925270	+	0.379310i	$0.123839\pi$
$251$			47793.8i			0.758620i	−0.925270	+	0.379310i	$0.876161\pi$
$252$	−42618.3	−	17944.8i	−0.671113	−	0.282578i
$253$		−	1574.05i		−	0.0245911i
$254$	−48425.6	+	83875.6i	−0.750598	+	1.30007i
$255$	118737.	−	15710.8i	1.82603	−	0.241612i
$256$	−30957.0	−	53619.1i	−0.472366	−	0.818163i
$257$	−17844.1	+	30906.9i	−0.270165	+	0.467939i	−0.968904	−	0.247438i	$-0.920411\pi$
$257$	−17844.1	+	30906.9i	−0.270165	+	0.467939i	0.698739	+	0.715376i	$0.253745\pi$
$258$	25979.3			0.390291
$259$	12390.3	+	16343.7i	0.184707	+	0.243642i
$260$	13366.7	−	32329.7i	0.197733	−	0.478250i
$261$	−91166.3	+	157905.i	−1.33830	+	2.31800i
$262$	60868.7	+	105428.i	0.886730	+	1.53586i
$263$	−11718.3	+	6765.57i	−0.169416	+	0.0978122i	−0.582310	−	0.812967i	$-0.697851\pi$
$263$	−11718.3	+	6765.57i	−0.169416	+	0.0978122i	0.412895	+	0.910779i	$0.364518\pi$
$264$	−27823.2	−	16063.7i	−0.399208	−	0.230483i
$265$	−78555.0	−	32478.6i	−1.11862	−	0.462493i
$266$	−346.782	−	2758.20i	−0.00490109	−	0.0389819i
$267$			147596.i			2.07039i
$268$	−8412.34	−	4856.87i	−0.117124	−	0.0676218i
$269$	37550.5	−	21679.8i	0.518933	−	0.299606i	−0.217565	−	0.976046i	$-0.569811\pi$
$269$	37550.5	−	21679.8i	0.518933	−	0.299606i	0.736498	+	0.676440i	$0.236478\pi$
$270$	−20556.7	−	155361.i	−0.281985	−	2.13116i
$271$	−9881.32	−	5704.99i	−0.134548	−	0.0776812i	0.431215	−	0.902249i	$-0.358085\pi$
$271$	−9881.32	−	5704.99i	−0.134548	−	0.0776812i	−0.565763	+	0.824568i	$0.691418\pi$
$272$	−95771.2			−1.29449
$273$	−23758.8	−	188971.i	−0.318786	−	2.53554i
$274$	115007.			1.53187
$275$	−25614.6	+	6899.21i	−0.338705	+	0.0912292i
$276$	−2862.81	+	1652.85i	−0.0375816	+	0.0216977i
$277$	−46200.6	+	26673.9i	−0.602127	+	0.347638i	−0.769878	−	0.638191i	$-0.779683\pi$
$277$	−46200.6	+	26673.9i	−0.602127	+	0.347638i	0.167751	+	0.985829i	$0.446350\pi$
$278$	−65106.1	+	112767.i	−0.842427	+	1.45913i
$279$		−	96633.6i		−	1.24142i
$280$	−56999.3	+	14957.1i	−0.727032	+	0.190779i
$281$	−109120.			−1.38195			−0.690975	−	0.722878i	$-0.742819\pi$
$281$	−109120.			−1.38195			−0.690975	+	0.722878i	$0.742819\pi$
$282$	−54066.7	−	31215.4i	−0.679879	−	0.392528i
$283$	23560.8	+	40808.6i	0.294183	+	0.509540i	0.974795	−	0.223104i	$-0.0716191\pi$
$283$	23560.8	+	40808.6i	0.294183	+	0.509540i	−0.680611	+	0.732645i	$0.738286\pi$
$284$	−2892.70	−	5010.30i	−0.0358646	−	0.0621194i
$285$	3802.02	−	2921.33i	0.0468085	−	0.0359659i
$286$			48801.3i			0.596622i
$287$	−21856.5	+	51908.5i	−0.265349	+	0.630194i
$288$			115679.i			1.39467i
$289$	−4591.43	+	7952.60i	−0.0549734	+	0.0952167i
$290$	−16706.1	−	126259.i	−0.198645	−	1.50130i
$291$	2621.33	+	4540.28i	0.0309554	+	0.0536163i
$292$	−19010.7	+	32927.5i	−0.222963	+	0.386183i
$293$	159569.			1.85872			0.929359	−	0.369177i	$-0.120360\pi$
$293$	159569.			1.85872			0.929359	+	0.369177i	$0.120360\pi$
$294$	125784.	−	122885.i	1.45523	−	1.42169i
$295$	117290.	+	48493.6i	1.34777	+	0.557237i
$296$	10067.5	−	17437.4i	0.114905	−	0.199021i
$297$	28581.1	+	49503.9i	0.324016	+	0.561212i
$298$	54303.6	−	31352.2i	0.611499	−	0.353049i
$299$	−7933.63	−	4580.48i	−0.0887421	−	0.0512353i
$300$	39444.8	+	39342.0i	0.438275	+	0.437134i
$301$	−6744.96	+	16019.1i	−0.0744469	+	0.176809i
$302$		−	51865.4i		−	0.568675i
$303$	−37107.7	−	21424.1i	−0.404183	−	0.233355i
$304$	−3320.28	+	1916.96i	−0.0359275	+	0.0207428i
$305$	−626.894	−	4737.87i	−0.00673899	−	0.0509311i
$306$	204460.	+	118045.i	2.18356	+	1.26068i
$307$	35369.2			0.375274			0.187637	−	0.982238i	$-0.439917\pi$
$307$	35369.2			0.375274			0.187637	+	0.982238i	$0.439917\pi$
$308$	−9388.59	+	7117.57i	−0.0989690	+	0.0750292i
$309$	−245447.			−2.57064
$310$	41125.5	+	53523.6i	0.427945	+	0.556957i
$311$	−118276.	+	68286.6i	−1.22286	+	0.706017i	−0.965526	−	0.260307i	$-0.916176\pi$
$311$	−118276.	+	68286.6i	−1.22286	+	0.706017i	−0.257331	+	0.966323i	$0.582843\pi$
$312$	−161931.	+	93490.6i	−1.66349	+	0.960415i
$313$	22073.3	−	38232.1i	0.225309	−	0.390247i	−0.731103	−	0.682267i	$-0.760994\pi$
$313$	22073.3	−	38232.1i	0.225309	−	0.390247i	0.956412	+	0.292020i	$0.0943274\pi$
$314$		−	135412.i		−	1.37341i
$315$	196844.	+	53837.9i	1.98381	+	0.542584i
$316$	3137.84			0.0314236
$317$	−141333.	−	81598.8i	−1.40645	−	0.812017i	−0.411411	−	0.911450i	$-0.634964\pi$
$317$	−141333.	−	81598.8i	−1.40645	−	0.812017i	−0.995044	+	0.0994330i	$0.968297\pi$
$318$	−124514.	−	215664.i	−1.23130	−	2.13267i
$319$	23227.3	+	40230.9i	0.228254	+	0.395347i
$320$	27427.7	+	35696.3i	0.267849	+	0.348596i
$321$			81052.7i			0.786606i
$322$	−1055.12	−	8392.13i	−0.0101763	−	0.0809395i
$323$			3711.13i			0.0355715i
$324$	21803.1	−	37764.0i	0.207696	−	0.359740i
$325$	−39764.5	+	149181.i	−0.376469	+	1.41236i
$326$	436.560	+	756.145i	0.00410780	+	0.00711491i
$327$	146592.	−	253904.i	1.37093	−	2.37451i
$328$	55293.9			0.513960
$329$	33284.9	−	25233.5i	0.307507	−	0.233124i
$330$	−71818.0	−	29693.2i	−0.659486	−	0.272665i
$331$	104688.	−	181324.i	0.955520	−	1.65501i	0.222346	−	0.974968i	$-0.428628\pi$
$331$	104688.	−	181324.i	0.955520	−	1.65501i	0.733174	−	0.680041i	$-0.238038\pi$
$332$	−14688.4	−	25441.1i	−0.133260	−	0.230813i
$333$	−60386.4	+	34864.1i	−0.544566	+	0.314406i
$334$	−99602.8	−	57505.7i	−0.892850	−	0.515487i
$335$	39615.7	+	16379.1i	0.353002	+	0.145949i
$336$	−223515.	−	94113.1i	−1.97983	−	0.833626i
$337$			62550.8i			0.550773i	0.961334	+	0.275387i	$0.0888059\pi$
$337$			62550.8i			0.550773i	−0.961334	+	0.275387i	$0.911194\pi$
$338$	130843.	+	75542.2i	1.14529	+	0.661235i
$339$	46316.8	−	26741.0i	0.403031	−	0.232690i
$340$	−42747.6	+	5656.18i	−0.369789	+	0.0489289i
$341$	−21321.8	−	12310.1i	−0.183364	−	0.105865i
$342$	9451.20			0.0808043
$343$	43114.9	+	109464.i	0.366471	+	0.930429i
$344$	17063.8			0.144198
$345$	11568.0	−	8888.46i	0.0971900	−	0.0746772i
$346$	−165765.	+	95704.6i	−1.38465	+	0.799431i
$347$	127193.	−	73435.2i	1.05634	−	0.609881i	0.131926	−	0.991260i	$-0.457884\pi$
$347$	127193.	−	73435.2i	1.05634	−	0.609881i	0.924419	+	0.381379i	$0.124551\pi$
$348$	48780.0	−	84489.5i	0.402795	−	0.697661i
$349$		−	143297.i		−	1.17648i	−0.808685	−	0.588242i	$-0.799820\pi$
$349$		−	143297.i		−	1.17648i	0.808685	−	0.588242i	$-0.200180\pi$
$350$	−131941.	+	53953.4i	−1.07707	+	0.440436i
$351$	332684.			2.70033
$352$	25524.1	+	14736.4i	0.205999	+	0.118934i
$353$	12842.2	+	22243.3i	0.103060	+	0.178505i	0.912944	−	0.408085i	$-0.133803\pi$
$353$	12842.2	+	22243.3i	0.103060	+	0.178505i	−0.809884	+	0.586590i	$0.800470\pi$
$354$	185910.	+	322006.i	1.48353	+	2.56956i
$355$	15556.0	+	20245.6i	0.123436	+	0.160648i
$356$		−	53137.3i		−	0.419276i
$357$	−187072.	+	141821.i	−1.46782	+	1.11277i
$358$		−	55746.6i		−	0.434963i
$359$	−82866.0	+	143528.i	−0.642965	+	1.11365i	0.341802	+	0.939772i	$0.388963\pi$
$359$	−82866.0	+	143528.i	−0.642965	+	1.11365i	−0.984767	+	0.173876i	$0.944371\pi$
$360$	−26280.1	−	198616.i	−0.202778	−	1.53253i
$361$	−65086.2	−	112733.i	−0.499430	−	0.865038i
$362$	−22751.9	+	39407.5i	−0.173621	+	0.300720i
$363$	−202030.			−1.53321
$364$	8553.61	+	68033.0i	0.0645575	+	0.513472i
$365$	64110.9	−	155063.i	0.481223	−	1.16392i
$366$	7000.47	−	12125.2i	0.0522595	−	0.0905161i
$367$	23636.1	+	40939.0i	0.175487	+	0.303952i	0.940330	−	0.340265i	$-0.110517\pi$
$367$	23636.1	+	40939.0i	0.175487	+	0.303952i	−0.764843	+	0.644217i	$0.777183\pi$
$368$	−10102.3	+	5832.56i	−0.0745975	+	0.0430689i
$369$	−165831.	−	95742.5i	−1.21790	−	0.703156i
$370$	18609.4	−	45010.0i	0.135934	−	0.328780i
$371$	165307.	−	20783.6i	1.20100	−	0.150999i
$372$			51705.5i			0.373638i
$373$	11241.1	+	6490.06i	0.0807963	+	0.0466478i	0.539854	−	0.841759i	$-0.318479\pi$
$373$	11241.1	+	6490.06i	0.0807963	+	0.0466478i	−0.459058	+	0.888407i	$0.651813\pi$
$374$	52092.3	−	30075.5i	0.372418	−	0.215015i
$375$	−195346.	−	149288.i	−1.38913	−	1.06160i
$376$	−35512.2	−	20503.0i	−0.251190	−	0.145025i
$377$	270365.			1.90225
$378$	185565.	+	244774.i	1.29871	+	1.71310i
$379$	−92246.9			−0.642204			−0.321102	−	0.947045i	$-0.604053\pi$
$379$	−92246.9			−0.642204			−0.321102	+	0.947045i	$0.604053\pi$
$380$	−1368.80	+	1051.73i	−0.00947920	+	0.00728346i
$381$	283547.	−	163706.i	1.95333	−	1.12775i
$382$	−44636.0	+	25770.6i	−0.305885	+	0.176603i
$383$	−59350.3	+	102798.i	−0.404599	+	0.700787i	−0.994275	−	0.106854i	$-0.965922\pi$
$383$	−59350.3	+	102798.i	−0.404599	+	0.700787i	0.589675	+	0.807640i	$0.299256\pi$
$384$			306700.i			2.07995i
$385$	36955.0	−	36574.4i	0.249317	−	0.246749i
$386$	−285933.			−1.91906
$387$	−51175.7	−	29546.3i	−0.341698	−	0.197279i
$388$	−943.727	−	1634.58i	−0.00626878	−	0.0108578i
$389$	131252.	+	227335.i	0.867374	+	1.50234i	0.864670	+	0.502340i	$0.167527\pi$
$389$	131252.	+	227335.i	0.867374	+	1.50234i	0.00270360	+	0.999996i	$0.499139\pi$
$390$	−358651.	+	275574.i	−2.35800	+	1.81180i
$391$			11291.5i			0.0738582i
$392$	82618.0	−	80713.9i	0.537653	−	0.525262i
$393$		−	411541.i		−	2.66457i
$394$	92982.5	−	161050.i	0.598975	−	1.03746i
$395$	−13728.1	+	1816.44i	−0.0879865	+	0.0116420i
$396$	−20027.6	−	34688.7i	−0.127714	−	0.221207i
$397$	−64554.8	+	111812.i	−0.409588	+	0.709428i	−0.994844	−	0.101422i	$-0.967661\pi$
$397$	−64554.8	+	111812.i	−0.409588	+	0.709428i	0.585255	+	0.810849i	$0.300994\pi$
$398$	−338703.			−2.13822
$399$	−3646.88	+	8661.22i	−0.0229074	+	0.0544043i
$400$	139193.	+	138830.i	0.869954	+	0.867689i
$401$	79376.2	−	137484.i	0.493630	−	0.854992i	−0.506343	−	0.862332i	$-0.669003\pi$
$401$	79376.2	−	137484.i	0.493630	−	0.854992i	0.999973	+	0.00733998i	$0.00233641\pi$
$402$	62792.8	+	108760.i	0.388560	+	0.673005i
$403$	−124093.	+	71644.9i	−0.764075	+	0.441139i
$404$	13359.4	+	7713.08i	0.0818513	+	0.0472569i
$405$	−73527.8	+	177840.i	−0.448272	+	1.08422i
$406$	150805.	+	198923.i	0.914879	+	1.20679i
$407$			17765.3i			0.107247i
$408$	199591.	+	115234.i	1.19900	+	0.692244i
$409$	−203623.	+	117562.i	−1.21725	+	0.702780i	−0.964329	−	0.264707i	$-0.914725\pi$
$409$	−203623.	+	117562.i	−1.21725	+	0.702780i	−0.252922	+	0.967487i	$0.581392\pi$
$410$	132597.	−	17544.6i	0.788798	−	0.104370i
$411$	−336701.	−	194394.i	−1.99324	−	1.15080i
$412$	88365.4			0.520580
$413$	−246819.	+	31031.9i	−1.44703	+	0.181932i
$414$	28756.3			0.167777
$415$	78989.6	+	102802.i	0.458642	+	0.596908i
$416$	148550.	−	85765.5i	0.858394	−	0.495594i
$417$	381216.	−	220095.i	2.19230	−	1.26572i
$418$	1203.99	−	2085.37i	0.00689079	−	0.0119352i
$419$			120989.i			0.689157i	0.938757	+	0.344579i	$0.111978\pi$
$419$			120989.i			0.689157i	−0.938757	+	0.344579i	$0.888022\pi$
$420$	−105325.	−	28806.9i	−0.597078	−	0.163304i
$421$	182388.			1.02904			0.514519	−	0.857479i	$-0.327970\pi$
$421$	182388.			1.02904			0.514519	+	0.857479i	$0.327970\pi$
$422$	−223018.	−	128760.i	−1.25232	−	0.723027i
$423$	71002.7	+	122980.i	0.396820	+	0.687313i
$424$	−81783.3	−	141653.i	−0.454918	−	0.787941i
$425$	183747.	−	49491.7i	1.01729	−	0.274003i
$426$			74797.5i			0.412162i
$427$	5658.95	+	7464.58i	0.0310370	+	0.0409402i
$428$		−	29180.5i		−	0.159296i
$429$	82487.9	−	142873.i	0.448204	−	0.776312i
$430$	40919.7	−	5414.31i	0.221307	−	0.0292824i
$431$	133916.	+	231949.i	0.720905	+	1.24864i	0.960637	+	0.277805i	$0.0896070\pi$
$431$	133916.	+	231949.i	0.720905	+	1.24864i	−0.239732	+	0.970839i	$0.577060\pi$
$432$	211812.	−	366868.i	1.13496	−	1.96582i
$433$	−86077.3			−0.459106			−0.229553	−	0.973296i	$-0.573726\pi$
$433$	−86077.3			−0.459106			−0.229553	+	0.973296i	$0.573726\pi$
$434$	−121930.	−	51339.6i	−0.647337	−	0.272567i
$435$	−164504.	+	397881.i	−0.869356	+	2.10269i
$436$	−52775.7	+	91410.2i	−0.277627	+	0.480863i
$437$	226.012	+	391.464i	0.00118350	+	0.00204988i
$438$	425709.	−	245783.i	2.21904	−	1.28116i
$439$	157393.	+	90871.0i	0.816689	+	0.471516i	0.849273	−	0.527953i	$-0.177040\pi$
$439$	157393.	+	90871.0i	0.816689	+	0.471516i	−0.0325841	+	0.999469i	$0.510374\pi$
$440$	−47171.7	−	19503.1i	−0.243655	−	0.100739i
$441$	−387536.	+	99012.8i	−1.99267	+	0.509113i
$442$		−	350078.i		−	1.79193i
$443$	89816.0	+	51855.3i	0.457663	+	0.264232i	0.711061	−	0.703130i	$-0.248215\pi$
$443$	89816.0	+	51855.3i	0.457663	+	0.264232i	−0.253398	+	0.967362i	$0.581548\pi$
$444$	32310.8	−	18654.6i	0.163901	−	0.0946283i
$445$	30760.3	+	232477.i	0.155335	+	1.17398i
$446$	−990.369	−	571.790i	−0.00497883	−	0.00287453i
$447$	−211976.			−1.06089
$448$	−81318.2	−	34239.7i	−0.405165	−	0.170598i
$449$	122949.			0.609865			0.304933	−	0.952374i	$-0.401366\pi$
$449$	122949.			0.609865			0.304933	+	0.952374i	$0.401366\pi$
$450$	−126041.	−	467951.i	−0.622426	−	2.31087i
$451$	−42250.3	+	24393.2i	−0.207719	+	0.119927i
$452$	−16674.9	+	9627.24i	−0.0816180	+	0.0471222i
$453$	−87667.1	+	151844.i	−0.427209	+	0.739948i
$454$		−	361228.i		−	1.75255i
$455$	−76805.3	−	292694.i	−0.370995	−	1.41381i
$456$	9226.10			0.0443699
$457$	−71816.8	−	41463.5i	−0.343870	−	0.198533i	0.318112	−	0.948053i	$-0.396951\pi$
$457$	−71816.8	−	41463.5i	−0.343870	−	0.198533i	−0.661982	+	0.749520i	$0.730284\pi$
$458$	200353.	+	347021.i	0.955135	+	1.65434i
$459$	−205028.	−	355118.i	−0.973167	−	1.68557i
$460$	−4164.71	+	3200.01i	−0.0196820	+	0.0151229i
$461$			38947.3i			0.183263i	0.995793	+	0.0916316i	$0.0292082\pi$
$461$			38947.3i			0.183263i	−0.995793	+	0.0916316i	$0.970792\pi$
$462$	151130.	−	19001.2i	0.708056	−	0.0890220i
$463$		−	421547.i		−	1.96646i	−0.182378	−	0.983229i	$-0.558379\pi$
$463$		−	421547.i		−	1.96646i	0.182378	−	0.983229i	$-0.441621\pi$
$464$	172135.	−	298147.i	0.799527	−	1.38482i
$465$	−29931.4	−	226212.i	−0.138427	−	1.04619i
$466$	−89292.3	−	154659.i	−0.411190	−	0.712202i
$467$	−14660.4	+	25392.6i	−0.0672223	+	0.116432i	−0.897678	−	0.440653i	$-0.854747\pi$
$467$	−14660.4	+	25392.6i	−0.0672223	+	0.116432i	0.830455	+	0.557085i	$0.188080\pi$
$468$	−233120.			−1.06436
$469$	−83365.2	+	10481.3i	−0.379000	+	0.0476507i
$470$	−91665.2	−	37899.0i	−0.414963	−	0.171566i
$471$	−228885.	+	396440.i	−1.03175	+	1.78705i
$472$	122110.	+	211501.i	0.548110	+	0.949354i
$473$	−13038.5	+	7527.80i	−0.0582782	+	0.0336470i
$474$	−35133.0	−	20284.0i	−0.156372	−	0.0902813i
$475$	5379.67	−	5393.72i	0.0238434	−	0.0239057i
$476$	67349.4	−	51058.1i	0.297249	−	0.225347i
$477$			566437.i			2.48952i
$478$	−63460.0	−	36638.7i	−0.277744	−	0.160356i
$479$	−100876.	+	58240.8i	−0.439660	+	0.253838i	−0.703453	−	0.710741i	$-0.748360\pi$
$479$	−100876.	+	58240.8i	−0.439660	+	0.253838i	0.263793	+	0.964579i	$0.415026\pi$
$480$	35830.6	+	270797.i	0.155515	+	1.17533i
$481$	89541.9	+	51697.0i	0.387022	+	0.223448i
$482$	339892.			1.46301
$483$	−11096.0	+	26352.7i	−0.0475635	+	0.112962i
$484$	72734.5			0.310491
$485$	5075.05	+	6605.02i	0.0215753	+	0.0280796i
$486$	−48507.0	+	28005.5i	−0.205368	+	0.118569i
$487$	182358.	−	105284.i	0.768895	−	0.443922i	−0.0635854	−	0.997976i	$-0.520254\pi$
$487$	182358.	−	105284.i	0.768895	−	0.443922i	0.832480	+	0.554055i	$0.186920\pi$
$488$	4598.06	−	7964.08i	0.0193079	−	0.0334423i
$489$		−	2951.64i		−	0.0123437i
$490$	172511.	−	219770.i	0.718495	−	0.915325i
$491$	−198076.			−0.821618			−0.410809	−	0.911721i	$-0.634754\pi$
$491$	−198076.			−0.821618			−0.410809	+	0.911721i	$0.634754\pi$
$492$	88730.6	+	51228.6i	0.366558	+	0.211633i
$493$	−166622.	−	288598.i	−0.685549	−	1.18741i
$494$	−7007.19	−	12136.8i	−0.0287137	−	0.0497337i
$495$	107702.	+	140170.i	0.439553	+	0.572065i
$496$			182458.i			0.741652i
$497$	−46120.7	−	19419.5i	−0.186717	−	0.0786187i
$498$			379804.i			1.53144i
$499$	37817.6	−	65501.9i	0.151877	−	0.263059i	−0.780040	−	0.625729i	$-0.784802\pi$
$499$	37817.6	−	65501.9i	0.151877	−	0.263059i	0.931918	+	0.362670i	$0.118135\pi$
$500$	70328.1	+	53746.5i	0.281312	+	0.214986i
$501$	194402.	+	336713.i	0.774505	+	1.34148i
$502$	−111230.	+	192655.i	−0.441380	+	0.764493i
$503$	68106.8			0.269187			0.134594	−	0.990901i	$-0.457027\pi$
$503$	68106.8			0.269187			0.134594	+	0.990901i	$0.457027\pi$
$504$	237229.	+	312923.i	0.933915	+	1.23190i
$505$	−62912.7	−	26011.3i	−0.246692	−	0.101995i
$506$	3663.26	−	6344.95i	0.0143076	−	0.0247815i
$507$	−255375.	−	442323.i	−0.993488	−	1.72077i
$508$	−102082.	+	58937.1i	−0.395568	+	0.228382i
$509$	−79228.5	−	45742.6i	−0.305806	−	0.176557i	0.339242	−	0.940699i	$-0.389829\pi$
$509$	−79228.5	−	45742.6i	−0.305806	−	0.176557i	−0.645048	+	0.764142i	$0.723163\pi$
$510$	515189.	+	213005.i	1.98074	+	0.818935i
$511$	41025.8	+	326307.i	0.157114	+	1.24964i
$512$			23683.2i			0.0903442i
$513$	−14216.2	−	8207.70i	−0.0540191	−	0.0311879i
$514$	−143858.	+	83056.4i	−0.544512	+	0.314374i
$515$	−386600.	+	51153.2i	−1.45763	+	0.192867i
$516$	27382.4	+	15809.3i	0.102842	+	0.0593761i
$517$	36180.1			0.135359
$518$	11908.5	+	94716.7i	0.0443810	+	0.352994i
$519$	647071.			2.40224
$520$	−235570.	+	181003.i	−0.871192	+	0.669391i
$521$	158501.	−	91510.4i	0.583923	−	0.337128i	−0.178768	−	0.983891i	$-0.557211\pi$
$521$	158501.	−	91510.4i	0.583923	−	0.337128i	0.762691	+	0.646763i	$0.223878\pi$
$522$	−734976.	+	424338.i	−2.69732	+	1.55730i
$523$	−3792.47	+	6568.74i	−0.0138649	+	0.0240148i	−0.872875	−	0.487945i	$-0.837747\pi$
$523$	−3792.47	+	6568.74i	−0.0138649	+	0.0240148i	0.859010	+	0.511959i	$0.171080\pi$
$524$			148162.i			0.539604i
$525$	477473.	+	65059.8i	1.73233	+	0.236045i
$526$	−62981.5			−0.227636
$527$	152953.	+	88307.3i	0.550726	+	0.317962i
$528$	−105036.	−	181928.i	−0.376765	−	0.652576i
$529$	−139233.	−	241158.i	−0.497543	−	0.861769i
$530$	−241066.	−	313739.i	−0.858190	−	1.11691i
$531$		−	845744.i		−	2.99951i
$532$	1312.94	−	3118.20i	0.00463899	−	0.0110174i
$533$			283937.i			0.999464i
$534$	−343498.	+	594955.i	−1.20460	+	2.08642i
$535$	16892.1	+	127665.i	0.0590167	+	0.446030i
$536$	41243.7	+	71436.2i	0.143558	+	0.248650i
$537$	−94227.3	+	163207.i	−0.326760	+	0.565964i
$538$	201820.			0.697267
$539$	−27521.4	+	98121.3i	−0.0947310	+	0.337742i
$540$	72875.4	−	176262.i	0.249916	−	0.604464i
$541$	131921.	−	228494.i	0.450733	−	0.780693i	−0.547699	−	0.836676i	$-0.684496\pi$
$541$	131921.	−	228494.i	0.450733	−	0.780693i	0.998432	+	0.0559830i	$0.0178293\pi$
$542$	−26554.2	−	45993.2i	−0.0903929	−	0.156565i
$543$	133219.	−	76914.3i	0.451823	−	0.260860i
$544$	−183098.	−	105712.i	−0.618709	−	0.357212i
$545$	177979.	−	430472.i	0.599204	−	1.44928i
$546$	344017.	−	817029.i	1.15397	−	2.74064i
$547$		−	232914.i		−	0.778431i	−0.921147	−	0.389216i	$-0.872746\pi$
$547$		−	232914.i		−	0.778431i	0.921147	−	0.389216i	$-0.127254\pi$
$548$	121218.	+	69985.4i	0.403652	+	0.233049i
$549$	−27579.9	+	15923.3i	−0.0915058	+	0.0528309i
$550$	−119308.	−	31801.8i	−0.394406	−	0.105130i
$551$	−11553.2	−	6670.24i	−0.0380539	−	0.0219704i
$552$	28071.4			0.0921268
$553$	21628.8	−	16397.0i	0.0707265	−	0.0536183i
$554$	−248311.			−0.809051
$555$	−130561.	+	100318.i	−0.423866	+	0.325683i
$556$	−137245.	+	79238.3i	−0.443963	+	0.256322i
$557$	−394668.	+	227862.i	−1.27210	+	0.734447i	−0.975383	−	0.220518i	$-0.929225\pi$
$557$	−394668.	+	227862.i	−1.27210	+	0.734447i	−0.296717	+	0.954965i	$0.595892\pi$
$558$	224893.	−	389527.i	0.722284	−	1.25103i
$559$			87623.4i			0.280412i
$560$	−371670.	−	101654.i	−1.18517	−	0.324151i
$561$	−203344.			−0.646109
$562$	−439860.	−	253953.i	−1.39265	−	0.804046i
$563$	−4036.10	−	6990.74i	−0.0127334	−	0.0220550i	0.859588	−	0.510987i	$-0.170720\pi$
$563$	−4036.10	−	6990.74i	−0.0127334	−	0.0220550i	−0.872322	+	0.488932i	$0.837387\pi$
$564$	−37991.2	−	65802.6i	−0.119433	−	0.206864i
$565$	67379.8	−	51772.1i	0.211073	−	0.162181i
$566$			219330.i			0.684646i
$567$	−47051.8	−	374237.i	−0.146356	−	1.16407i
$568$			49128.6i			0.152278i
$569$	−212776.	+	368539.i	−0.657200	+	1.13830i	0.324137	+	0.946010i	$0.394926\pi$
$569$	−212776.	+	368539.i	−0.657200	+	1.13830i	−0.981337	+	0.192294i	$0.938407\pi$
$570$	22124.5	−	2927.42i	0.0680965	−	0.00901023i
$571$	−129907.	−	225006.i	−0.398438	−	0.690114i	0.595096	−	0.803655i	$-0.297114\pi$
$571$	−129907.	−	225006.i	−0.398438	−	0.690114i	−0.993533	+	0.113540i	$0.963781\pi$
$572$	−29697.2	+	51437.0i	−0.0907659	+	0.157211i
$573$	174238.			0.530682
$574$	−208908.	+	158375.i	−0.634062	+	0.480687i
$575$	16368.2	−	16411.0i	0.0495069	−	0.0496362i
$576$	149987.	−	259785.i	0.452074	−	0.783015i
$577$	−89864.4	−	155650.i	−0.269920	−	0.467516i	0.698921	−	0.715199i	$-0.253664\pi$
$577$	−89864.4	−	155650.i	−0.269920	−	0.467516i	−0.968841	+	0.247683i	$0.920331\pi$
$578$	−37015.8	+	21371.1i	−0.110798	+	0.0639692i
$579$	837111.	+	483306.i	2.49704	+	1.44167i
$580$	59224.4	−	143244.i	0.176054	−	0.425816i
$581$	−234190.	−	98607.8i	−0.693771	−	0.292118i
$582$			24402.3i			0.0720418i
$583$	124982.	+	72158.4i	0.367714	+	0.212300i
$584$	279615.	−	161436.i	0.819851	−	0.473341i
$585$	1.01990e6	−	134949.i	2.98022	−	0.394329i
$586$	643217.	+	371362.i	1.87311	+	1.08144i
$587$	−166789.			−0.484050			−0.242025	−	0.970270i	$-0.577812\pi$
$587$	−166789.			−0.484050			−0.242025	+	0.970270i	$0.577812\pi$
$588$	207357.	−	52978.5i	0.599743	−	0.153230i
$589$	7070.26			0.0203800
$590$	359934.	+	468442.i	1.03400	+	1.34571i
$591$	−544441.	+	314333.i	−1.55875	+	0.899943i
$592$	114018.	−	65828.5i	0.325335	−	0.187832i
$593$	159004.	−	275403.i	0.452167	−	0.783177i	−0.546353	−	0.837555i	$-0.683984\pi$
$593$	159004.	−	275403.i	0.452167	−	0.783177i	0.998520	+	0.0543780i	$0.0173176\pi$
$594$			266065.i			0.754075i
$595$	−265098.	+	262368.i	−0.748812	+	0.741099i
$596$	76315.3			0.214842
$597$	991603.	+	572503.i	2.78221	+	1.60631i
$598$	−21320.1	−	36927.5i	−0.0596193	−	0.103264i
$599$	33345.0	+	57755.3i	0.0929346	+	0.160967i	0.908745	−	0.417352i	$-0.137042\pi$
$599$	33345.0	+	57755.3i	0.0929346	+	0.160967i	−0.815810	+	0.578320i	$0.803709\pi$
$600$	−123039.	−	456806.i	−0.341776	−	1.26891i
$601$			274568.i			0.760154i	0.924955	+	0.380077i	$0.124103\pi$
$601$			274568.i			0.760154i	−0.924955	+	0.380077i	$0.875897\pi$
$602$	−64469.5	+	48874.8i	−0.177894	+	0.134863i
$603$		−	285657.i		−	0.785616i
$604$	31561.8	−	54666.6i	0.0865142	−	0.149847i
$605$	−318214.	+	42104.7i	−0.869379	+	0.115032i
$606$	−99719.8	−	172720.i	−0.271541	−	0.470324i
$607$	−74923.8	+	129772.i	−0.203349	+	0.352211i	−0.949605	−	0.313448i	$-0.898516\pi$
$607$	−74923.8	+	129772.i	−0.203349	+	0.352211i	0.746256	+	0.665659i	$0.231849\pi$
$608$	−8463.75			−0.0228958
$609$	−105269.	−	837280.i	−0.283835	−	2.25754i
$610$	8499.35	−	20557.1i	0.0228416	−	0.0552463i
$611$	105284.	−	182357.i	0.282020	−	0.488472i
$612$	143668.	+	248841.i	0.383582	+	0.664384i
$613$	−212122.	+	122469.i	−0.564500	+	0.325914i	−0.754950	−	0.655783i	$-0.772339\pi$
$613$	−212122.	+	122469.i	−0.564500	+	0.325914i	0.190449	+	0.981697i	$0.439005\pi$
$614$	142572.	+	82313.9i	0.378179	+	0.218342i
$615$	−417853.	−	172761.i	−1.10477	−	0.456769i
$616$	99265.7	−	12480.4i	0.261600	−	0.0328903i
$617$			316663.i			0.831816i	0.909407	+	0.415908i	$0.136536\pi$
$617$			316663.i			0.831816i	−0.909407	+	0.415908i	$0.863464\pi$
$618$	−989388.	−	571223.i	−2.59054	−	1.49565i
$619$	29834.0	−	17224.7i	0.0778630	−	0.0449542i	−0.460563	−	0.887627i	$-0.652352\pi$
$619$	29834.0	−	17224.7i	0.0778630	−	0.0449542i	0.538426	+	0.842673i	$0.319019\pi$
$620$	10775.9	+	81440.5i	0.0280329	+	0.211864i
$621$	−43254.2	−	24972.8i	−0.112162	−	0.0647566i
$622$	−635688.			−1.64310
$623$	−277672.	−	366270.i	−0.715412	−	0.943682i
$624$	−1.22262e6			−3.13994
$625$	−338799.	−	194430.i	−0.867326	−	0.497740i
$626$	177954.	−	102742.i	0.454107	−	0.262179i
$627$	−7049.71	+	4070.15i	−0.0179323	+	0.0103532i
$628$	82402.7	−	142726.i	0.208940	−	0.361895i
$629$		−	127440.i		−	0.322111i
$630$	668175.	+	675129.i	1.68348	+	1.70101i
$631$	70700.7			0.177568			0.0887840	−	0.996051i	$-0.471702\pi$
$631$	70700.7			0.177568			0.0887840	+	0.996051i	$0.471702\pi$
$632$	−23076.1	−	13323.0i	−0.0577735	−	0.0333556i
$633$	435280.	+	753927.i	1.08633	+	1.88158i
$634$	−379806.	−	657843.i	−0.944895	−	1.63661i
$635$	412493.	−	316944.i	1.02298	−	0.786023i
$636$		−	303082.i		−	0.749283i
$637$	414470.	+	424247.i	1.02144	+	1.04554i
$638$			216226.i			0.531209i
$639$	85067.2	−	147341.i	0.208334	−	0.360845i
$640$	63918.9	+	483079.i	0.156052	+	1.17939i
$641$	−45782.4	−	79297.5i	−0.111425	−	0.192994i	0.804920	−	0.593383i	$-0.202208\pi$
$641$	−45782.4	−	79297.5i	−0.111425	−	0.192994i	−0.916345	+	0.400390i	$0.868875\pi$
$642$	−188632.	+	326721.i	−0.457663	+	0.792696i
$643$	578869.			1.40010			0.700049	−	0.714095i	$-0.253161\pi$
$643$	578869.			1.40010			0.700049	+	0.714095i	$0.253161\pi$
$644$	3994.77	−	9487.45i	0.00963209	−	0.0228759i
$645$	−128950.	−	53314.5i	−0.309958	−	0.128152i
$646$	−8636.84	+	14959.4i	−0.0206962	+	0.0358468i
$647$	−175425.	−	303844.i	−0.419066	−	0.725843i	0.576780	−	0.816900i	$-0.304309\pi$
$647$	−175425.	−	303844.i	−0.419066	−	0.725843i	−0.995846	+	0.0910563i	$0.970976\pi$
$648$	−320686.	+	185148.i	−0.763712	+	0.440930i
$649$	−186610.	−	107739.i	−0.443042	−	0.255791i
$650$	−507474.	+	508799.i	−1.20112	+	1.20426i
$651$	270190.	+	356400.i	0.637539	+	0.840962i
$652$			1062.64i			0.00249973i
$653$	433487.	+	250274.i	1.01660	+	0.586934i	0.913117	−	0.407698i	$-0.133668\pi$
$653$	433487.	+	250274.i	1.01660	+	0.586934i	0.103482	+	0.994631i	$0.467002\pi$
$654$	1.18181e6	−	682319.i	2.76308	−	1.59526i
$655$	−85768.6	−	648212.i	−0.199915	−	1.51090i
$656$	313113.	+	180776.i	0.727600	+	0.420080i
$657$	−1.11812e6			−2.59034
$658$	192896.	−	24252.3i	0.445524	−	0.0560145i
$659$	300083.			0.690987			0.345494	−	0.938421i	$-0.387712\pi$
$659$	300083.			0.690987			0.345494	+	0.938421i	$0.387712\pi$
$660$	−57627.5	−	75000.4i	−0.132295	−	0.172177i
$661$	127498.	−	73610.9i	0.291810	−	0.168476i	−0.346948	−	0.937884i	$-0.612782\pi$
$661$	127498.	−	73610.9i	0.291810	−	0.168476i	0.638758	+	0.769408i	$0.279449\pi$
$662$	843985.	−	487275.i	1.92583	−	1.11188i
$663$	−591730.	+	1.02491e6i	−1.34616	+	2.33162i
$664$			249464.i			0.565811i
$665$	−3939.08	+	14402.2i	−0.00890741	+	0.0325676i
$666$	−324554.			−0.731709
$667$	−35151.8	−	20294.9i	−0.0790125	−	0.0456179i
$668$	−69988.1	−	121223.i	−0.156845	−	0.271664i
$669$	1932.97	+	3348.00i	0.00431890	+	0.00748055i
$670$	121571.	+	158220.i	0.270819	+	0.352462i
$671$			8113.86i			0.0180211i
$672$	−323442.	−	426644.i	−0.716239	−	0.944772i
$673$			226218.i			0.499457i	0.968316	+	0.249728i	$0.0803413\pi$
$673$			226218.i			0.499457i	−0.968316	+	0.249728i	$0.919659\pi$
$674$	−145573.	+	252140.i	−0.320451	+	0.555037i
$675$	−216796.	+	813334.i	−0.475821	+	1.78509i
$676$	91939.7	+	159244.i	0.201191	+	0.348474i
$677$	−101310.	+	175473.i	−0.221041	+	0.382855i	−0.955124	−	0.296205i	$-0.904279\pi$
$677$	−101310.	+	175473.i	−0.221041	+	0.382855i	0.734083	+	0.679060i	$0.237612\pi$
$678$	248935.			0.541535
$679$	−15046.6	−	6335.51i	−0.0326362	−	0.0137418i
$680$	338388.	+	139906.i	0.731808	+	0.302566i
$681$	−610577.	+	1.05755e6i	−1.31658	+	2.28038i
$682$	−57298.2	−	99243.5i	−0.123189	−	0.213370i
$683$	162026.	−	93545.9i	0.347331	−	0.200532i	−0.316178	−	0.948700i	$-0.602400\pi$
$683$	162026.	−	93545.9i	0.347331	−	0.200532i	0.663509	+	0.748168i	$0.269066\pi$
$684$	9961.64	+	5751.35i	0.0212921	+	0.0122930i
$685$	−570845.	−	236016.i	−1.21657	−	0.502991i
$686$	−80958.6	+	541586.i	−0.172034	+	1.15085i
$687$		−	1.35461e6i		−	2.87013i
$688$	96627.1	+	55787.7i	0.204137	+	0.117859i
$689$	727394.	−	419961.i	1.53226	−	0.884648i
$690$	67316.3	−	8907.00i	0.141391	−	0.0187082i
$691$	−552053.	−	318728.i	−1.15618	−	0.667520i	−0.205793	−	0.978596i	$-0.565977\pi$
$691$	−552053.	−	318728.i	−1.15618	−	0.667520i	−0.950385	+	0.311076i	$0.899311\pi$
$692$	−232957.			−0.486479
$693$	−319316.	−	134451.i	−0.664896	−	0.279960i
$694$	683616.			1.41936
$695$	554579.	−	426118.i	1.14814	−	0.882186i
$696$	−717471.	+	414232.i	−1.48111	+	0.855117i
$697$	303084.	−	174986.i	0.623876	−	0.360195i
$698$	333492.	−	577625.i	0.684501	−	1.18559i
$699$			603716.i			1.23560i
$700$	−171899.	−	23422.7i	−0.350814	−	0.0478015i
$701$	555633.			1.13071			0.565356	−	0.824847i	$-0.308739\pi$
$701$	555633.			1.13071			0.565356	+	0.824847i	$0.308739\pi$
$702$	1.34104e6	+	774247.i	2.72124	+	1.57111i
$703$	−2550.85	−	4418.21i	−0.00516149	−	0.00893996i
$704$	−38213.7	−	66188.1i	−0.0771034	−	0.133547i
$705$	204304.	+	265895.i	0.411054	+	0.534973i
$706$			119549.i			0.239849i
$707$	132390.	−	16645.1i	0.264861	−	0.0333002i
$708$			452530.i			0.902777i
$709$	−208472.	+	361083.i	−0.414719	+	0.718315i	−0.995399	−	0.0958171i	$-0.969454\pi$
$709$	−208472.	+	361083.i	−0.414719	+	0.718315i	0.580680	+	0.814132i	$0.302787\pi$
$710$	15588.4	+	117812.i	0.0309233	+	0.233708i
$711$	46138.1	+	79913.6i	0.0912684	+	0.158082i
$712$	−225617.	+	390780.i	−0.445053	+	0.770854i
$713$	21512.0			0.0423157
$714$	−1.08414e6	+	136306.i	−2.12661	+	0.267373i
$715$	100150.	−	242229.i	0.195901	−	0.473820i
$716$	33923.6	−	58757.3i	0.0661722	−	0.114614i
$717$	123859.	+	214531.i	0.240930	+	0.417302i
$718$	−668060.	+	385704.i	−1.29588	+	0.748179i
$719$	−739037.	−	426683.i	−1.42958	−	0.825369i	−0.432493	−	0.901637i	$-0.642366\pi$
$719$	−739037.	−	426683.i	−1.42958	−	0.825369i	−0.997087	+	0.0762684i	$0.975699\pi$
$720$	500533.	−	1.21062e6i	0.965533	−	2.33531i
$721$	609093.	−	461758.i	1.17169	−	0.888269i
$722$		−	605895.i		−	1.16231i
$723$	−995085.	−	574513.i	−1.90363	−	1.09906i
$724$	−47961.4	+	27690.6i	−0.0914987	+	0.0528268i
$725$	−176186.	+	660980.i	−0.335193	+	1.25751i
$726$	−814375.	−	470180.i	−1.54508	−	0.892053i
$727$	535853.			1.01386			0.506929	−	0.861988i	$-0.330781\pi$
$727$	535853.			1.01386			0.506929	+	0.861988i	$0.330781\pi$
$728$	225958.	−	536643.i	0.426349	−	1.01256i
$729$	−434158.			−0.816944
$730$	619304.	−	475850.i	1.16214	−	0.892945i
$731$	93532.4	−	54001.0i	0.175036	−	0.101057i
$732$	14757.1	−	8520.02i	0.0275410	−	0.0159008i
$733$	446381.	−	773154.i	0.830802	−	1.43899i	−0.0666014	−	0.997780i	$-0.521216\pi$
$733$	446381.	−	773154.i	0.830802	−	1.43899i	0.897403	−	0.441211i	$-0.145451\pi$
$734$			220032.i			0.408407i
$735$	−876524.	+	351817.i	−1.62252	+	0.651242i
$736$	−25751.9			−0.0475393
$737$	−63029.0	−	36389.8i	−0.116039	−	0.0669954i
$738$	−445639.	−	771869.i	−0.818220	−	1.41720i
$739$	288389.	+	499504.i	0.528068	+	0.914640i	0.999465	+	0.0327191i	$0.0104167\pi$
$739$	288389.	+	499504.i	0.528068	+	0.914640i	−0.471397	+	0.881921i	$0.656250\pi$
$740$	47004.4	−	36116.5i	0.0858372	−	0.0659541i
$741$			47376.5i			0.0862832i
$742$	714716.	+	300938.i	1.29815	+	0.546599i
$743$			428933.i			0.776984i	0.921452	+	0.388492i	$0.127004\pi$
$743$			428933.i			0.776984i	−0.921452	+	0.388492i	$0.872996\pi$
$744$	219537.	−	380249.i	0.396609	−	0.686946i
$745$	−333880.	+	44177.6i	−0.601559	+	0.0795957i
$746$	30208.3	+	52322.4i	0.0542812	+	0.0940177i
$747$	431952.	−	748162.i	0.774094	−	1.34077i
$748$	73207.6			0.130844
$749$	−152484.	−	201138.i	−0.271807	−	0.358534i
$750$	−439997.	−	1.05640e6i	−0.782217	−	1.87804i
$751$	121543.	−	210519.i	0.215502	−	0.373260i	−0.737926	−	0.674882i	$-0.764195\pi$
$751$	121543.	−	210519.i	0.215502	−	0.373260i	0.953428	+	0.301622i	$0.0975280\pi$
$752$	−134063.	−	232204.i	−0.237069	−	0.410615i
$753$	651283.	−	376018.i	1.14863	−	0.663161i
$754$	1.08983e6	+	629215.i	1.91698	+	1.10677i
$755$	−106438.	+	257438.i	−0.186725	+	0.451625i
$756$	46634.3	+	370916.i	0.0815947	+	0.648981i
$757$			156953.i			0.273892i	0.990579	+	0.136946i	$0.0437287\pi$
$757$			156953.i			0.273892i	−0.990579	+	0.136946i	$0.956271\pi$
$758$	−371844.	−	214684.i	−0.647176	−	0.373647i
$759$	−21449.5	+	12383.9i	−0.0372334	+	0.0214967i
$760$	14531.9	−	1922.80i	0.0251591	−	0.00332894i
$761$	−368455.	−	212727.i	−0.636231	−	0.367328i	0.146930	−	0.989147i	$-0.453061\pi$
$761$	−368455.	−	212727.i	−0.636231	−	0.367328i	−0.783161	+	0.621819i	$0.786394\pi$
$762$	1.52396e6			2.62459
$763$	113892.	+	905863.i	0.195634	+	1.55601i
$764$	−62728.9			−0.107469
$765$	−772601.	−	1.00552e6i	−1.32018	−	1.71817i
$766$	−478478.	+	276249.i	−0.815463	+	0.470808i
$767$	−1.08607e6	+	627041.i	−1.84615	+	1.06587i
$768$	−487109.	+	843697.i	−0.825855	+	1.43042i
$769$			737777.i			1.24759i	0.781587	+	0.623796i	$0.214410\pi$
$769$			737777.i			1.24759i	−0.781587	+	0.623796i	$0.785590\pi$
$770$	234083.	−	61425.3i	0.394810	−	0.103601i
$771$	561554.			0.944676
$772$	−301375.	−	173999.i	−0.505677	−	0.291953i
$773$	−423005.	−	732666.i	−0.707924	−	1.22616i	−0.965626	−	0.259935i	$-0.916299\pi$
$773$	−423005.	−	732666.i	−0.707924	−	1.22616i	0.257702	−	0.966224i	$-0.417035\pi$
$774$	−137525.	−	238200.i	−0.229562	−	0.397613i
$775$	−94289.0	−	350065.i	−0.156985	−	0.582835i
$776$			16028.0i			0.0266167i
$777$	125234.	−	297426.i	0.207434	−	0.492649i
$778$			1.22184e6i			2.01862i
$779$	7005.06	−	12133.1i	0.0115435	−	0.0199939i
$780$	−545717.	+	72206.9i	−0.896971	+	0.118683i
$781$	−21673.4	−	37539.4i	−0.0355324	−	0.0615440i
$782$	−26278.5	+	45515.7i	−0.0429722	+	0.0744300i
$783$	1.47403e6			2.40427
$784$	731723.	−	186950.i	1.19046	−	0.304155i
$785$	−277892.	+	672129.i	−0.450958	+	1.09072i
$786$	957770.	−	1.65891e6i	1.55030	−	2.68520i
$787$	162785.	+	281951.i	0.262824	+	0.455224i	0.966991	−	0.254810i	$-0.0820130\pi$
$787$	162785.	+	281951.i	0.262824	+	0.455224i	−0.704168	+	0.710034i	$0.748680\pi$
$788$	196009.	−	113166.i	0.315662	−	0.182248i
$789$	184388.	+	106456.i	0.296195	+	0.171009i
$790$	−59564.8	−	24627.1i	−0.0954412	−	0.0394602i
$791$	−64630.5	+	153495.i	−0.103296	+	0.245325i
$792$			340141.i			0.542262i
$793$	40895.9	+	23611.3i	0.0650330	+	0.0375468i
$794$	−520436.	+	300474.i	−0.825518	+	0.476613i
$795$	175449.	+	1.32599e6i	0.277598	+	2.09800i
$796$	−356995.	−	206111.i	−0.563425	−	0.325294i
$797$	34880.5			0.0549119			0.0274560	−	0.999623i	$-0.491259\pi$
$797$	34880.5			0.0549119			0.0274560	+	0.999623i	$0.491259\pi$
$798$	−34857.5	+	26425.8i	−0.0547382	+	0.0414975i
$799$	−259539.			−0.406546
$800$	112873.	+	419060.i	0.176363	+	0.654782i
$801$	1.35329e6	−	781320.i	2.10923	−	1.21777i
$802$	639925.	−	369461.i	0.994902	−	0.574407i
$803$	−142437.	+	246708.i	−0.220898	+	0.382606i
$804$			152846.i			0.236451i
$805$	−11985.1	+	43820.2i	−0.0184948	+	0.0676212i
$806$	−666950.			−1.02665
$807$	−590858.	−	341132.i	−0.907269	−	0.523812i
$808$	−65498.2	−	113446.i	−0.100324	−	0.173767i
$809$	−93144.6	−	161331.i	−0.142318	−	0.246503i	0.786051	−	0.618162i	$-0.212122\pi$
$809$	−93144.6	−	161331.i	−0.142318	−	0.246503i	−0.928369	+	0.371659i	$0.878789\pi$
$810$	−710270.	+	545745.i	−1.08256	+	0.831802i
$811$		−	1.27617e6i		−	1.94030i	−0.242510	−	0.970149i	$-0.577971\pi$
$811$		−	1.27617e6i		−	1.94030i	0.242510	−	0.970149i	$-0.422029\pi$
$812$	37898.8	+	301436.i	0.0574795	+	0.457176i
$813$			179536.i			0.271626i
$814$	−41344.9	+	71611.4i	−0.0623983	+	0.108077i
$815$	−615.146	−	4649.08i	−0.000926111	−	0.00699926i
$816$	753480.	+	1.30507e6i	1.13160	+	1.95998i
$817$	2161.77	−	3744.30i	0.00323867	−	0.00560954i
$818$	−1.09440e6			−1.63556
$819$	−1.60687e6	+	1.21818e6i	−2.39560	+	1.81612i
$820$	150435.	+	62197.3i	0.223728	+	0.0925004i
$821$	−584760.	+	1.01283e6i	−0.867544	+	1.50263i	−0.00304500	+	0.999995i	$0.500969\pi$
$821$	−584760.	+	1.01283e6i	−0.867544	+	1.50263i	−0.864499	+	0.502635i	$0.832364\pi$
$822$	−904819.	−	1.56719e6i	−1.33911	−	2.31942i
$823$	−852565.	+	492228.i	−1.25872	+	0.726720i	−0.972825	−	0.231542i	$-0.925623\pi$
$823$	−852565.	+	492228.i	−1.25872	+	0.726720i	−0.285891	+	0.958262i	$0.592289\pi$
$824$	−649852.	−	375192.i	−0.957106	−	0.552585i
$825$	295538.	+	294768.i	0.434215	+	0.433085i
$826$	−1.06714e6	−	449328.i	−1.56409	−	0.658572i
$827$			124621.i			0.182213i	0.995841	+	0.0911064i	$0.0290403\pi$
$827$			124621.i			0.182213i	−0.995841	+	0.0911064i	$0.970960\pi$
$828$	30309.3	+	17499.1i	0.0442095	+	0.0255244i
$829$	−14134.6	+	8160.64i	−0.0205672	+	0.0118745i	−0.510248	−	0.860027i	$-0.670447\pi$
$829$	−14134.6	+	8160.64i	−0.0205672	+	0.0118745i	0.489681	+	0.871902i	$0.337113\pi$
$830$	79154.4	+	598224.i	0.114900	+	0.868376i
$831$	726967.	+	419715.i	1.05272	+	0.607788i
$832$	−444807.			−0.642576
$833$	197425.	−	703877.i	0.284520	−	1.01439i
$834$	2.04889e6			2.94569
$835$	376373.	+	489837.i	0.539816	+	0.702553i
$836$	2538.02	−	1465.33i	0.00363147	−	0.00209663i
$837$	−676553.	+	390608.i	−0.965719	+	0.557558i
$838$	−281575.	+	487703.i	−0.400965	+	0.694492i
$839$		−	1.12002e6i		−	1.59112i	−0.605878	−	0.795558i	$-0.707178\pi$
$839$		−	1.12002e6i		−	1.59112i	0.605878	−	0.795558i	$-0.292822\pi$
$840$	652261.	+	659050.i	0.924407	+	0.934027i
$841$	490636.			0.693693
$842$	735199.	+	424467.i	1.03700	+	0.598715i
$843$	858504.	+	1.48697e6i	1.20806	+	2.09241i
$844$	−156709.	−	271427.i	−0.219993	−	0.381038i
$845$	−494421.	−	643473.i	−0.692442	−	0.901192i
$846$			660972.i			0.923511i
$847$	501351.	−	380078.i	0.698836	−	0.529793i
$848$		−	1.06952e6i		−	1.48729i
$849$	370730.	−	642123.i	0.514331	−	0.890847i
$850$	855859.	+	228131.i	1.18458	+	0.315753i
$851$	−7761.25	−	13442.9i	−0.0107170	−	0.0185624i
$852$	−45516.7	+	78837.2i	−0.0627034	+	0.108605i
$853$	−84342.4			−0.115917			−0.0579586	−	0.998319i	$-0.518459\pi$
$853$	−84342.4			−0.115917			−0.0579586	+	0.998319i	$0.518459\pi$
$854$	5438.89	+	43259.4i	0.00745752	+	0.0593150i
$855$	−46911.7	−	19395.6i	−0.0641725	−	0.0265321i
$856$	−123898.	+	214597.i	−0.169089	+	0.292871i
$857$	260279.	+	450816.i	0.354387	+	0.613816i	0.987013	−	0.160642i	$-0.0513563\pi$
$857$	260279.	+	450816.i	0.354387	+	0.613816i	−0.632626	+	0.774457i	$0.718023\pi$
$858$	665012.	−	383945.i	0.903347	−	0.521548i
$859$	400501.	+	231230.i	0.542772	+	0.313370i	0.746202	−	0.665720i	$-0.231875\pi$
$859$	400501.	+	231230.i	0.542772	+	0.313370i	−0.203429	+	0.979090i	$0.565209\pi$
$860$	46424.4	+	19194.2i	0.0627697	+	0.0259521i
$861$	879309.	−	110553.i	1.18614	−	0.149130i
$862$			1.24664e6i			1.67775i
$863$	−480890.	−	277642.i	−0.645691	−	0.372790i	0.141113	−	0.989994i	$-0.454932\pi$
$863$	−480890.	−	277642.i	−0.645691	−	0.372790i	−0.786803	+	0.617204i	$0.788265\pi$
$864$	809896.	−	467594.i	1.08493	−	0.626385i
$865$	1.01919e6	−	134855.i	1.36215	−	0.180233i
$866$	−346975.	−	200326.i	−0.462660	−	0.267117i
$867$	144493.			0.192224
$868$	−97273.3	−	128311.i	−0.129108	−	0.170303i
$869$	23510.1			0.0311326
$870$	−1.58909e6	+	1.22100e6i	−2.09947	+	1.61315i
$871$	−366828.	+	211788.i	−0.483533	+	0.279168i
$872$	776240.	−	448163.i	1.02085	−	0.589390i
$873$	27752.7	−	48069.1i	0.0364147	−	0.0630722i
$874$			2103.97i			0.00275433i
$875$	765619.	+	2965.45i	0.999992	+	0.00387324i
$876$	598267.			0.779627
$877$	−1.13396e6	−	654695.i	−1.47435	−	0.851216i	−0.474767	−	0.880112i	$-0.657468\pi$
$877$	−1.13396e6	−	654695.i	−1.47435	−	0.851216i	−0.999582	+	0.0288957i	$0.990801\pi$
$878$	422964.	+	732595.i	0.548674	+	0.950332i
$879$	−1.25541e6	−	2.17444e6i	−1.62483	−	2.81429i
$880$	−203356.	−	264661.i	−0.262598	−	0.341763i
$881$		−	361213.i		−	0.465384i	−0.972550	−	0.232692i	$-0.925247\pi$
$881$		−	361213.i		−	0.465384i	0.972550	−	0.232692i	$-0.0747534\pi$
$882$	−1.79257e6	−	502786.i	−2.30430	−	0.646318i
$883$		−	1.11366e6i		−	1.42833i	−0.699975	−	0.714167i	$-0.746806\pi$
$883$		−	1.11366e6i		−	1.42833i	0.699975	−	0.714167i	$-0.253194\pi$
$884$	213034.	−	368985.i	0.272611	−	0.472177i
$885$	−261962.	−	1.97982e6i	−0.334466	−	2.52779i
$886$	241363.	+	418054.i	0.307471	+	0.532555i
$887$	−208559.	+	361236.i	−0.265083	+	0.459138i	−0.967585	−	0.252544i	$-0.918733\pi$
$887$	−208559.	+	361236.i	−0.265083	+	0.459138i	0.702502	+	0.711682i	$0.252066\pi$
$888$	−316824.			−0.401784
$889$	−395662.	+	939682.i	−0.500634	+	1.18899i
$890$	−417044.	+	1.00869e6i	−0.526505	+	1.27344i
$891$	163358.	−	282945.i	0.205772	−	0.356407i
$892$	−695.905	−	1205.34i	−0.000874621	−	0.00151489i
$893$	−8997.92	+	5194.95i	−0.0112834	+	0.00651447i
$894$	−854468.	−	493327.i	−1.06911	−	0.617249i
$895$	−114402.	+	276702.i	−0.142820	+	0.345435i
$896$	−576994.	−	761098.i	−0.718713	−	0.948036i
$897$			144148.i			0.179153i
$898$	495605.	+	286138.i	0.614586	+	0.354831i
$899$	−549821.	+	317439.i	−0.680303	+	0.392773i
$900$	151915.	−	569925.i	0.187549	−	0.703611i
$901$	−896563.	−	517631.i	−1.10441	−	0.637633i
$902$	−227079.			−0.279103
$903$	271356.	−	34116.9i	0.332786	−	0.0418403i
$904$	163506.			0.200077
$905$	193802.	−	148911.i	0.236626	−	0.181815i
$906$	−706766.	+	408052.i	−0.861032	+	0.497117i
$907$	969958.	−	560006.i	1.17907	−	0.680735i	0.223268	−	0.974757i	$-0.428327\pi$
$907$	969958.	−	560006.i	1.17907	−	0.680735i	0.955799	+	0.294022i	$0.0949940\pi$
$908$	219819.	−	380737.i	0.266620	−	0.461800i
$909$			453646.i			0.549021i
$910$	371581.	−	1.35859e6i	0.448715	−	1.64061i
$911$	−878004.			−1.05794			−0.528968	−	0.848642i	$-0.677421\pi$
$911$	−878004.			−1.05794			−0.528968	+	0.848642i	$0.677421\pi$
$912$	52244.6	+	30163.4i	0.0628133	+	0.0362653i
$913$	−110052.	−	190616.i	−0.132026	−	0.228675i
$914$	−192994.	−	334275.i	−0.231021	−	0.400140i
$915$	−59630.5	+	45817.9i	−0.0712240	+	0.0547259i
$916$			487685.i			0.581230i
$917$	774230.	+	1.02127e6i	0.920728	+	1.21451i
$918$		−	1.90863e6i		−	2.26483i
$919$	511986.	−	886785.i	0.606215	−	1.05000i	−0.385643	−	0.922648i	$-0.626020\pi$
$919$	511986.	−	886785.i	0.606215	−	1.05000i	0.991858	−	0.127347i	$-0.0406463\pi$
$920$	44214.8	−	5850.31i	0.0522387	−	0.00691200i
$921$	−278267.	−	481973.i	−0.328052	−	0.568203i
$922$	−90641.2	+	156995.i	−0.106626	+	0.184682i
$923$	−252278.			−0.296126
$924$	170855.	+	71940.1i	0.200117	+	0.0842611i
$925$	−184738.	+	185220.i	−0.215910	+	0.216474i
$926$	981058.	−	1.69924e6i	1.14412	−	1.98168i
$927$	1.29931e6	+	2.25046e6i	1.51200	+	2.61886i
$928$	658187.	−	380004.i	0.764281	−	0.441258i
$929$	735341.	+	424549.i	0.852034	+	0.491922i	0.861337	−	0.508034i	$-0.169628\pi$
$929$	735341.	+	424549.i	0.852034	+	0.491922i	−0.00930233	+	0.999957i	$0.502961\pi$
$930$	405806.	−	981512.i	0.469194	−	1.13483i
$931$	−7244.33	−	28354.3i	−0.00835794	−	0.0327129i
$932$		−	217349.i		−	0.250222i
$933$	1.86107e6	+	1.07449e6i	2.13796	+	1.23435i
$934$	−118191.	+	68237.8i	−0.135485	+	0.0782225i
$935$	−320284.	+	42378.6i	−0.366364	+	0.0484756i
$936$	1.71440e6	+	989810.i	1.95686	+	1.12980i
$937$	−739900.			−0.842741			−0.421370	−	0.906889i	$-0.638451\pi$
$937$	−739900.			−0.842741			−0.421370	+	0.906889i	$0.638451\pi$
$938$	−360435.	−	151764.i	−0.409658	−	0.172490i
$939$	−694649.			−0.787833
$940$	−73553.2	−	95727.1i	−0.0832426	−	0.108338i
$941$	−465455.	+	268730.i	−0.525652	+	0.303485i	−0.739244	−	0.673438i	$-0.764817\pi$
$941$	−465455.	+	268730.i	−0.525652	+	0.303485i	0.213592	+	0.976923i	$0.431484\pi$
$942$	−1.84525e6	+	1.06536e6i	−2.07948	+	1.20059i
$943$	21313.6	−	36916.3i	0.0239681	−	0.0415140i
$944$			1.59689e6i			1.79197i
$945$	−418743.	−	1.59577e6i	−0.468904	−	1.78692i
$946$	−70077.1			−0.0783058
$947$	−1.03060e6	−	595020.i	−1.14919	−	0.663486i	−0.200501	−	0.979694i	$-0.564257\pi$
$947$	−1.03060e6	−	595020.i	−1.14919	−	0.663486i	−0.948690	+	0.316208i	$0.897590\pi$
$948$	−24687.0	−	42759.1i	−0.0274695	−	0.0475786i
$949$	828980.	+	1.43584e6i	0.920475	+	1.59431i
$950$	34238.0	−	9221.88i	0.0379368	−	0.0102182i
$951$			2.56792e6i			2.83936i
$952$	−712086.	+	89528.7i	−0.785704	+	0.0987844i
$953$			230956.i			0.254298i	0.991884	+	0.127149i	$0.0405826\pi$
$953$			230956.i			0.254298i	−0.991884	+	0.127149i	$0.959417\pi$
$954$	−1.31826e6	+	2.28329e6i	−1.44845	+	2.50879i
$955$	274440.	−	36312.7i	0.300913	−	0.0398155i
$956$	−44591.6	−	77234.9i	−0.0487907	−	0.0845080i
$957$	365482.	−	633033.i	0.399064	−	0.691199i
$958$	−542170.			−0.590751
$959$	1.20126e6	−	151031.i	1.30617	−	0.164221i
$960$	270643.	−	654596.i	0.293666	−	0.710282i
$961$	−293522.	+	508395.i	−0.317829	+	0.550497i
$962$	240627.	+	416778.i	0.260012	+	0.450354i
$963$	743159.	−	429063.i	0.801363	−	0.462667i
$964$	358249.	+	206835.i	0.385506	+	0.222572i
$965$	1.41925e6	+	586788.i	1.52406	+	0.630124i
$966$	−106058.	+	80403.2i	−0.113655	+	0.0861626i
$967$		−	1.12804e6i		−	1.20635i	−0.797610	−	0.603173i	$-0.793903\pi$
$967$		−	1.12804e6i		−	1.20635i	0.797610	−	0.603173i	$-0.206097\pi$
$968$	−534900.	−	308825.i	−0.570850	−	0.329580i
$969$	50571.3	−	29197.4i	0.0538588	−	0.0310954i
$970$	5085.64	+	38435.7i	0.00540508	+	0.0408499i
$971$	1.27656e6	+	737020.i	1.35395	+	0.781701i	0.988800	−	0.149249i	$-0.0476856\pi$
$971$	1.27656e6	+	737020.i	1.35395	+	0.781701i	0.365146	+	0.930950i	$0.381019\pi$
$972$	−68169.0			−0.0721530
$973$	−531950.	+	1.26336e6i	−0.561882	+	1.33445i
$974$	980105.			1.03313
$975$	2.34572e6	−	631813.i	2.46756	−	0.664629i
$976$	52074.9	−	30065.5i	0.0546674	−	0.0315623i
$977$	569827.	−	328990.i	0.596972	−	0.344662i	−0.170877	−	0.985292i	$-0.554660\pi$
$977$	569827.	−	328990.i	0.596972	−	0.344662i	0.767850	+	0.640630i	$0.221327\pi$
$978$	6869.28	−	11897.9i	0.00718181	−	0.0124393i
$979$		−	398129.i		−	0.415392i
$980$	315565.	−	126661.i	0.328576	−	0.131883i
$981$	−3.10401e6			−3.22541
$982$	−798439.	−	460979.i	−0.827978	−	0.478033i
$983$	−135356.	−	234444.i	−0.140078	−	0.242623i	0.787448	−	0.616382i	$-0.211402\pi$
$983$	−135356.	−	234444.i	−0.140078	−	0.242623i	−0.927526	+	0.373759i	$0.878069\pi$
$984$	−435025.	−	753486.i	−0.449287	−	0.778189i
$985$	−792031.	+	608568.i	−0.816338	+	0.627244i
$986$		−	1.55110e6i		−	1.59546i
$987$	−605725.	−	255046.i	−0.621786	−	0.261809i
$988$		−	17056.4i		−	0.0174732i
$989$	6577.43	−	11392.4i	0.00672455	−	0.0116473i
$990$	107926.	+	815672.i	0.110118	+	0.832234i
$991$	−290534.	−	503220.i	−0.295835	−	0.512402i	0.679343	−	0.733820i	$-0.262265\pi$
$991$	−290534.	−	503220.i	−0.295835	−	0.512402i	−0.975179	+	0.221418i	$0.928931\pi$
$992$	−201397.	+	348829.i	−0.204658	+	0.354478i
$993$	−3.29453e6			−3.34114
$994$	−140716.	−	185615.i	−0.142420	−	0.187863i
$995$	1.68117e6	+	695082.i	1.69811	+	0.702085i
$996$	−231123.	+	400317.i	−0.232983	+	0.403539i
$997$	−436452.	−	755956.i	−0.439082	−	0.760513i	0.558537	−	0.829480i	$-0.311363\pi$
$997$	−436452.	−	755956.i	−0.439082	−	0.760513i	−0.997619	+	0.0689671i	$0.978030\pi$
$998$	304882.	−	176024.i	0.306106	−	0.176730i
$999$	488183.	+	281852.i	0.489160	+	0.282417i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.i.a.19.11	yes	28
5.2	odd	4		175.5.i.e.26.4		28
5.3	odd	4		175.5.i.e.26.11		28
5.4	even	2	inner	35.5.i.a.19.4	✓	28
7.2	even	3		245.5.c.a.244.1		28
7.3	odd	6	inner	35.5.i.a.24.4	yes	28
7.5	odd	6		245.5.c.a.244.27		28
35.3	even	12		175.5.i.e.101.11		28
35.9	even	6		245.5.c.a.244.28		28
35.17	even	12		175.5.i.e.101.4		28
35.19	odd	6		245.5.c.a.244.2		28
35.24	odd	6	inner	35.5.i.a.24.11	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.i.a.19.4	✓	28	5.4	even	2	inner
35.5.i.a.19.11	yes	28	1.1	even	1	trivial
35.5.i.a.24.4	yes	28	7.3	odd	6	inner
35.5.i.a.24.11	yes	28	35.24	odd	6	inner
175.5.i.e.26.4		28	5.2	odd	4
175.5.i.e.26.11		28	5.3	odd	4
175.5.i.e.101.4		28	35.17	even	12
175.5.i.e.101.11		28	35.3	even	12
245.5.c.a.244.1		28	7.2	even	3
245.5.c.a.244.2		28	35.19	odd	6
245.5.c.a.244.27		28	7.5	odd	6
245.5.c.a.244.28		28	35.9	even	6

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.03096 + 2.32728i) q^{2} +(-7.86751 - 13.6269i) q^{3} +(2.83245 + 4.90594i) q^{4} +(-15.2320 - 19.8239i) q^{5} -73.2395i q^{6} +(45.1600 + 19.0150i) q^{7} -48.1053i q^{8} +(-83.2953 + 144.272i) q^{9} +O(q^{10})\)	\(q+(4.03096 + 2.32728i) q^{2} +(-7.86751 - 13.6269i) q^{3} +(2.83245 + 4.90594i) q^{4} +(-15.2320 - 19.8239i) q^{5} -73.2395i q^{6} +(45.1600 + 19.0150i) q^{7} -48.1053i q^{8} +(-83.2953 + 144.272i) q^{9} +(-15.2637 - 115.358i) q^{10} +(21.2220 + 36.7575i) q^{11} +(44.5686 - 77.1950i) q^{12} +247.023 q^{13} +(137.785 + 181.749i) q^{14} +(-150.301 + 363.529i) q^{15} +(157.274 - 272.406i) q^{16} +(-152.237 - 263.681i) q^{17} +(-671.521 + 387.703i) q^{18} +(-10.5557 - 6.09436i) q^{19} +(54.1112 - 130.877i) q^{20} +(-96.1806 - 764.993i) q^{21} +197.558i q^{22} +(-32.1169 - 18.5427i) q^{23} +(-655.528 + 378.469i) q^{24} +(-160.975 + 603.914i) q^{25} +(995.742 + 574.892i) q^{26} +1346.77 q^{27} +(34.6268 + 275.411i) q^{28} +1094.49 q^{29} +(-1451.89 + 1115.58i) q^{30} +(-502.352 + 290.033i) q^{31} +(601.362 - 347.196i) q^{32} +(333.928 - 578.380i) q^{33} -1417.19i q^{34} +(-310.924 - 1184.88i) q^{35} -943.718 q^{36} +(362.484 + 209.280i) q^{37} +(-28.3665 - 49.1323i) q^{38} +(-1943.46 - 3366.17i) q^{39} +(-953.636 + 732.739i) q^{40} +1149.43i q^{41} +(1392.65 - 3307.50i) q^{42} +354.717i q^{43} +(-120.220 + 208.227i) q^{44} +(4128.78 - 546.302i) q^{45} +(-86.3081 - 149.490i) q^{46} +(426.210 - 738.218i) q^{47} -4949.41 q^{48} +(1677.86 + 1717.44i) q^{49} +(-2054.36 + 2059.72i) q^{50} +(-2395.44 + 4149.03i) q^{51} +(699.680 + 1211.88i) q^{52} +(2944.64 - 1700.09i) q^{53} +(5428.78 + 3134.31i) q^{54} +(405.426 - 980.591i) q^{55} +(914.724 - 2172.44i) q^{56} +191.790i q^{57} +(4411.87 + 2547.19i) q^{58} +(-4396.62 + 2538.39i) q^{59} +(-2209.17 + 292.308i) q^{60} +(165.555 + 95.5833i) q^{61} -2699.95 q^{62} +(-6504.95 + 4931.45i) q^{63} -1800.67 q^{64} +(-3762.65 - 4896.97i) q^{65} +(2692.10 - 1554.29i) q^{66} +(-1485.00 + 857.362i) q^{67} +(862.404 - 1493.73i) q^{68} +583.540i q^{69} +(1504.23 - 5499.83i) q^{70} -1021.27 q^{71} +(6940.24 + 4006.95i) q^{72} +(3355.88 + 5812.56i) q^{73} +(974.106 + 1687.20i) q^{74} +(9495.96 - 2557.71i) q^{75} -69.0477i q^{76} +(259.439 + 2063.51i) q^{77} -18091.9i q^{78} +(276.955 - 479.700i) q^{79} +(-7795.74 + 1031.50i) q^{80} +(-3848.81 - 6666.33i) q^{81} +(-2675.05 + 4633.33i) q^{82} -5185.78 q^{83} +(3480.58 - 2638.66i) q^{84} +(-2908.34 + 7034.31i) q^{85} +(-825.526 + 1429.85i) q^{86} +(-8610.94 - 14914.6i) q^{87} +(1768.23 - 1020.89i) q^{88} +(-8123.42 - 4690.06i) q^{89} +(17914.4 + 7406.70i) q^{90} +(11155.6 + 4697.15i) q^{91} -210.085i q^{92} +(7904.52 + 4563.68i) q^{93} +(3436.08 - 1983.82i) q^{94} +(39.9706 + 302.085i) q^{95} +(-9462.43 - 5463.14i) q^{96} -333.185 q^{97} +(2766.42 + 10827.8i) q^{98} -7070.76 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9}+O(q^{10}) \) 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9	\( 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9} + 390 q^{10} + 34 q^{11} - 258 q^{14} + 60 q^{15} - 206 q^{16} + 366 q^{19} - 1116 q^{21} - 288 q^{24} + 40 q^{25} + 474 q^{26} + 856 q^{29} - 1620 q^{30} - 5520 q^{31} - 2620 q^{35} + 11892 q^{36} + 1656 q^{39} + 6510 q^{40} - 1082 q^{44} + 7920 q^{45} - 5442 q^{46} + 8356 q^{49} - 15960 q^{50} - 2976 q^{51} + 4392 q^{54} + 11640 q^{56} - 13920 q^{59} - 5700 q^{60} - 24960 q^{61} - 45596 q^{64} + 5290 q^{65} + 10332 q^{66} - 26400 q^{70} + 38272 q^{71} + 31806 q^{74} + 41310 q^{75} + 22028 q^{79} + 48000 q^{80} - 29238 q^{81} + 62784 q^{84} - 33820 q^{85} - 21180 q^{86} - 12516 q^{89} + 4448 q^{91} - 89418 q^{94} - 28890 q^{95} - 27900 q^{96} - 3108 q^{99}+O(q^{100}) \) 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9 + 390 * q^10 + 34 * q^11 - 258 * q^14 + 60 * q^15 - 206 * q^16 + 366 * q^19 - 1116 * q^21 - 288 * q^24 + 40 * q^25 + 474 * q^26 + 856 * q^29 - 1620 * q^30 - 5520 * q^31 - 2620 * q^35 + 11892 * q^36 + 1656 * q^39 + 6510 * q^40 - 1082 * q^44 + 7920 * q^45 - 5442 * q^46 + 8356 * q^49 - 15960 * q^50 - 2976 * q^51 + 4392 * q^54 + 11640 * q^56 - 13920 * q^59 - 5700 * q^60 - 24960 * q^61 - 45596 * q^64 + 5290 * q^65 + 10332 * q^66 - 26400 * q^70 + 38272 * q^71 + 31806 * q^74 + 41310 * q^75 + 22028 * q^79 + 48000 * q^80 - 29238 * q^81 + 62784 * q^84 - 33820 * q^85 - 21180 * q^86 - 12516 * q^89 + 4448 * q^91 - 89418 * q^94 - 28890 * q^95 - 27900 * q^96 - 3108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more