LMFDB - Embedded newform 35.5.i.a.19.4

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			19.4
Character	$\chi$	$=$	35.19
Dual form			35.5.i.a.24.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.03096 - 2.32728i) q^{2} +(7.86751 + 13.6269i) q^{3} +(2.83245 + 4.90594i) q^{4} +(-24.7840 - 3.27931i) q^{5} -73.2395i q^{6} +(-45.1600 - 19.0150i) q^{7} +48.1053i q^{8} +(-83.2953 + 144.272i) q^{9} +O(q^{10})$	\(q+(-4.03096 - 2.32728i) q^{2} +(7.86751 + 13.6269i) q^{3} +(2.83245 + 4.90594i) q^{4} +(-24.7840 - 3.27931i) q^{5} -73.2395i q^{6} +(-45.1600 - 19.0150i) q^{7} +48.1053i q^{8} +(-83.2953 + 144.272i) q^{9} +(92.2715 + 70.8980i) 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} +(603.492 + 162.549i) q^{25} +(995.742 + 574.892i) q^{26} -1346.77 q^{27} +(-34.6268 - 275.411i) q^{28} +1094.49 q^{29} +(-240.175 + 1815.17i) q^{30} +(-502.352 + 290.033i) q^{31} +(-601.362 + 347.196i) q^{32} +(-333.928 + 578.380i) q^{33} -1417.19i q^{34} +(1056.89 + 619.362i) q^{35} -943.718 q^{36} +(-362.484 - 209.280i) q^{37} +(28.3665 + 49.1323i) q^{38} +(-1943.46 - 3366.17i) q^{39} +(157.752 - 1192.24i) q^{40} +1149.43i q^{41} +(-1392.65 + 3307.50i) q^{42} -354.717i q^{43} +(-120.220 + 208.227i) q^{44} +(2537.50 - 3302.48i) 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} +(1357.73 - 1767.05i) q^{60} +(165.555 + 95.5833i) q^{61} +2699.95 q^{62} +(6504.95 - 4931.45i) q^{63} -1800.67 q^{64} +(6122.22 + 810.065i) q^{65} +(2692.10 - 1554.29i) q^{66} +(1485.00 - 857.362i) q^{67} +(-862.404 + 1493.73i) q^{68} +583.540i q^{69} +(-2818.86 - 4956.30i) q^{70} -1021.27 q^{71} +(-6940.24 - 4006.95i) q^{72} +(-3355.88 - 5812.56i) q^{73} +(974.106 + 1687.20i) q^{74} +(2532.94 + 9502.60i) q^{75} -69.0477i q^{76} +(-259.439 - 2063.51i) q^{77} +18091.9i q^{78} +(276.955 - 479.700i) q^{79} +(-4791.17 + 6235.56i) 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} +(241.628 + 185.658i) 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	−0.0972115	−	0.995264i	$-0.530992\pi$
$2$	−4.03096	−	2.32728i	−1.00774	−	0.581820i	−0.910529	+	0.413444i	$0.864326\pi$
$3$	7.86751	+	13.6269i	0.874167	+	1.51410i	0.857647	+	0.514239i	$0.171926\pi$
$3$	7.86751	+	13.6269i	0.874167	+	1.51410i	0.0165205	+	0.999864i	$0.494741\pi$
$4$	2.83245	+	4.90594i	0.177028	+	0.306621i
$5$	−24.7840	−	3.27931i	−0.991360	−	0.131172i
$5$	−24.7840	−	3.27931i	−0.991360	−	0.131172i
$6$		−	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
$10$	92.2715	+	70.8980i	0.922715	+	0.708980i
$11$	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	$-0.760870\pi$
$13$	−247.023			−1.46168			−0.730838	+	0.682551i	$0.760870\pi$
$14$	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	$0.00993044\pi$
$17$	152.237	+	263.681i	0.526770	+	0.912393i	−0.472743	+	0.881200i	$0.656736\pi$
$18$	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	0.530049	−	0.847967i	$-0.322174\pi$
$23$	32.1169	+	18.5427i	0.0607126	+	0.0350524i	−0.469336	+	0.883019i	$0.655507\pi$
$24$	−655.528	+	378.469i	−1.13807	+	0.657064i
$25$	603.492	+	162.549i	0.965588	+	0.260078i
$26$	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	$0.274471\pi$
$30$	−240.175	+	1815.17i	−0.266861	+	2.01685i
$31$	−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
$35$	1056.89	+	619.362i	0.862767	+	0.505602i
$36$	−943.718			−0.728178
$37$	−362.484	−	209.280i	−0.264780	−	0.152871i	0.361733	−	0.932282i	$-0.382185\pi$
$37$	−362.484	−	209.280i	−0.264780	−	0.152871i	−0.626513	+	0.779411i	$0.715518\pi$
$38$	28.3665	+	49.1323i	0.0196444	+	0.0340251i
$39$	−1943.46	−	3366.17i	−1.27775	−	2.21313i
$40$	157.752	−	1192.24i	0.0985952	−	0.745151i
$41$			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	$-0.969420\pi$
$43$		−	354.717i		−	0.191843i	0.995389	−	0.0959214i	$-0.0305798\pi$
$44$	−120.220	+	208.227i	−0.0620972	+	0.107555i
$45$	2537.50	−	3302.48i	1.25309	−	1.63085i
$46$	−86.3081	−	149.490i	−0.0407883	−	0.0706475i
$47$	−426.210	+	738.218i	−0.192943	+	0.334186i	−0.946224	−	0.323512i	$-0.895136\pi$
$47$	−426.210	+	738.218i	−0.192943	+	0.334186i	0.753282	+	0.657698i	$0.228470\pi$
$48$	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	−0.922169	−	0.386787i	$-0.873585\pi$
$53$	−2944.64	+	1700.09i	−1.04829	+	0.605229i	−0.126118	+	0.992015i	$0.540252\pi$
$54$	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	$0.593447\pi$
$60$	1357.73	−	1767.05i	0.377148	−	0.490846i
$61$	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
$65$	6122.22	+	810.065i	1.44905	+	0.191731i
$66$	2692.10	−	1554.29i	0.618022	−	0.356815i
$67$	1485.00	−	857.362i	0.330808	−	0.190992i	−0.325392	−	0.945579i	$-0.605496\pi$
$67$	1485.00	−	857.362i	0.330808	−	0.190992i	0.656200	+	0.754587i	$0.272163\pi$
$68$	−862.404	+	1493.73i	−0.186506	+	0.323038i
$69$			583.540i			0.122567i
$70$	−2818.86	−	4956.30i	−0.575277	−	1.01149i
$71$	−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	$-0.949828\pi$
$73$	−3355.88	−	5812.56i	−0.629739	−	1.09074i	0.357865	−	0.933773i	$-0.383505\pi$
$74$	974.106	+	1687.20i	0.177886	+	0.308108i
$75$	2532.94	+	9502.60i	0.450301	+	1.68935i
$76$		−	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	$0.152536\pi$
$80$	−4791.17	+	6235.56i	−0.748621	+	0.974306i
$81$	−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	$-0.377168\pi$
$83$	5185.78			0.752763			0.376381	+	0.926465i	$0.377168\pi$
$84$	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
$95$	241.628	+	185.658i	0.0267732	+	0.0205715i
$96$	−9462.43	−	5463.14i	−1.02674	−	0.592788i
$97$	333.185			0.0354113			0.0177056	−	0.999843i	$-0.494364\pi$
$97$	333.185			0.0354113			0.0177056	+	0.999843i	$0.494364\pi$
$98$	−2766.42	−	10827.8i	−0.288049	−	1.12742i
$99$	−7070.76			−0.721433
$100$	911.905	+	3421.11i	0.0911905	+	0.342111i
$101$	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	$0.429563\pi$
$103$	−7799.39	+	13508.9i	−0.735167	+	1.27335i	−0.954650	+	0.297730i	$0.903770\pi$
$104$		−	11883.1i		−	1.09866i
$105$	−124.911	+	19275.0i	−0.0113298	+	1.74830i
$106$	15826.3			1.40854
$107$	4460.99	+	2575.55i	0.389640	+	0.224959i	0.682004	−	0.731348i	$-0.261109\pi$
$107$	4460.99	+	2575.55i	0.389640	+	0.224959i	−0.292364	+	0.956307i	$0.594442\pi$
$108$	−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	$0.546442\pi$
$110$	−647.853	+	4896.27i	−0.0535415	+	0.404650i
$111$		−	6586.05i		−	0.534539i
$112$	−12282.3	+	9311.30i	−0.979137	+	0.742291i
$113$		−	3398.92i		−	0.266185i	−0.991104	−	0.133092i	$-0.957509\pi$
$113$		−	3398.92i		−	0.266185i	0.991104	−	0.133092i	$-0.0424907\pi$
$114$	−446.348	+	773.097i	−0.0343450	+	0.0594873i
$115$	−735.179	−	564.884i	−0.0555901	−	0.0427133i
$116$	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	$-0.776839\pi$
$127$		−	20807.8i		−	1.29009i	0.764145	−	0.645044i	$-0.223161\pi$
$128$	16880.2	+	9745.79i	1.03029	+	0.594836i
$129$	4833.71	−	2790.74i	0.290470	−	0.167703i
$130$	−22793.2	−	17513.5i	−1.34871	−	1.03630i
$131$	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
$135$	33378.4	+	4416.48i	1.83146	+	0.242331i
$136$	−12684.5	+	7323.39i	−0.685796	+	0.395945i
$137$	−21398.2	+	12354.2i	−1.14008	+	0.658226i	−0.946451	−	0.322849i	$-0.895359\pi$
$137$	−21398.2	+	12354.2i	−1.14008	+	0.658226i	−0.193630	+	0.981075i	$0.562026\pi$
$138$	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	$0.742320\pi$
$140$	−44.9701	+	6939.35i	−0.00229440	+	0.354048i
$141$	−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
$145$	−27125.9	−	3589.18i	−1.29017	−	0.170710i
$146$			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	$0.0685445\pi$
$150$	11905.0	−	44199.5i	0.529111	−	1.96442i
$151$	−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	$0.0342585\pi$
$157$	14546.2	+	25194.8i	0.590134	+	1.02214i	−0.404080	+	0.914724i	$0.632408\pi$
$158$	−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	0.496940	−	0.867785i	$-0.334457\pi$
$163$	−162.453	−	93.7920i	−0.00611437	−	0.00353013i	−0.503054	+	0.864255i	$0.667790\pi$
$164$	−5639.05	+	3255.71i	−0.209661	+	0.121048i
$165$	10172.8	−	13239.5i	0.373655	−	0.486300i
$166$	−20903.7	−	12068.8i	−0.758590	−	0.437972i
$167$	24709.4			0.885992			0.442996	−	0.896524i	$-0.353916\pi$
$167$	24709.4			0.885992			0.442996	+	0.896524i	$0.353916\pi$
$168$	36800.3	−	4626.80i	1.30386	−	0.163931i
$169$	32459.5			1.13650
$170$	−4647.39	+	35123.6i	−0.160810	+	1.21535i
$171$	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	$-0.592257\pi$
$173$	20561.5	−	35613.6i	0.687009	−	1.18993i	0.972801	−	0.231643i	$-0.0744101\pi$
$174$		−	80160.2i		−	2.64765i
$175$	−24162.9	−	18816.1i	−0.788991	−	0.614404i
$176$	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	$0.893177\pi$
$180$	23389.1	+	3094.74i	0.721886	+	0.0955168i
$181$			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
$185$	8297.50	+	6375.49i	0.242440	+	0.186282i
$186$	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	0.431258	−	0.902228i	$-0.358070\pi$
$193$	53200.5	−	30715.3i	1.42824	−	0.824595i	0.996982	+	0.0776335i	$0.0247364\pi$
$194$	−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	$0.172113\pi$
$197$			39953.3i			1.02949i	−0.857344	+	0.514743i	$0.827887\pi$
$198$	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	$0.962522\pi$
$200$	−7819.46	+	29031.2i	−0.195487	+	0.725780i
$201$	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
$205$	3769.35	−	28487.6i	0.0896930	−	0.677872i
$206$	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
$210$	45361.8	−	77406.1i	1.02861	−	1.75524i
$211$	−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
$215$	−1163.23	+	8791.31i	−0.0251645	+	0.190185i
$216$		−	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
$220$	3662.38	−	4766.47i	0.0756689	−	0.0984807i
$221$	−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	$-0.499214\pi$
$223$	245.690			0.00494058			0.00247029	+	0.999997i	$0.499214\pi$
$224$	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	$0.104750\pi$
$227$	38803.7	+	67210.0i	0.753046	+	1.30431i	−0.193294	+	0.981141i	$0.561917\pi$
$228$	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	0.773766	−	0.633471i	$-0.218371\pi$
$233$	33227.4	+	19183.9i	0.612047	+	0.353365i	−0.161719	+	0.986837i	$0.551704\pi$
$234$	−165881.	+	95771.6i	−3.02946	+	1.74906i
$235$	12984.0	−	16898.3i	0.235112	−	0.305990i
$236$	−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	$0.544005\pi$
$240$	−122666.	−	16230.6i	−2.12962	−	0.281782i
$241$	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
$245$	−35952.0	−	48067.2i	−0.598950	−	0.800786i
$246$	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
$250$	44160.8	+	57785.0i	0.706572	+	0.924560i
$251$			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
$255$	72974.6	−	94974.1i	1.12225	−	1.46058i
$256$	−30957.0	−	53619.1i	−0.472366	−	0.818163i
$257$	17844.1	−	30906.9i	0.270165	−	0.467939i	−0.698739	−	0.715376i	$-0.746255\pi$
$257$	17844.1	−	30906.9i	0.270165	−	0.467939i	0.968904	+	0.247438i	$0.0795886\pi$
$258$	−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	−0.412895	−	0.910779i	$-0.635482\pi$
$263$	11718.3	−	6765.57i	0.169416	−	0.0978122i	0.582310	+	0.812967i	$0.302149\pi$
$264$	−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	$0.236478\pi$
$270$	−124269.	−	95483.4i	−1.70464	−	1.30979i
$271$	−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
$275$	6832.40	+	25632.5i	0.0903458	+	0.338942i
$276$	−2862.81	+	1652.85i	−0.0375816	+	0.0216977i
$277$	46200.6	−	26673.9i	0.602127	−	0.347638i	−0.167751	−	0.985829i	$-0.553650\pi$
$277$	46200.6	−	26673.9i	0.602127	−	0.347638i	0.769878	+	0.638191i	$0.220317\pi$
$278$	65106.1	−	112767.i	0.842427	−	1.45913i
$279$		−	96633.6i		−	1.24142i
$280$	−29794.6	+	50842.0i	−0.380033	+	0.648495i
$281$	−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	0.680611	−	0.732645i	$-0.261714\pi$
$283$	−23560.8	−	40808.6i	−0.294183	−	0.509540i	−0.974795	+	0.223104i	$0.928381\pi$
$284$	−2892.70	−	5010.30i	−0.0358646	−	0.0621194i
$285$	−628.937	+	4753.31i	−0.00774315	+	0.0585203i
$286$			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
$290$	100991.	+	77597.4i	1.20084	+	0.922681i
$291$	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	$-0.879640\pi$
$293$	−159569.			−1.85872			−0.929359	+	0.369177i	$0.879640\pi$
$294$	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
$305$	−3789.67	−	2911.84i	−0.0407382	−	0.0313017i
$306$	204460.	+	118045.i	2.18356	+	1.26068i
$307$	−35369.2			−0.375274			−0.187637	−	0.982238i	$-0.560083\pi$
$307$	−35369.2			−0.375274			−0.187637	+	0.982238i	$0.560083\pi$
$308$	9388.59	−	7117.57i	0.0989690	−	0.0750292i
$309$	−245447.			−2.57064
$310$	−66915.5	−	8853.97i	−0.696312	−	0.0921329i
$311$	−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	−0.956412	−	0.292020i	$-0.905673\pi$
$313$	−22073.3	+	38232.1i	−0.225309	+	0.390247i	0.731103	+	0.682267i	$0.239006\pi$
$314$		−	135412.i		−	1.37341i
$315$	−177390.	+	100889.i	−1.78776	+	1.01677i
$316$	3137.84			0.0314236
$317$	141333.	+	81598.8i	1.40645	+	0.812017i	0.995044	−	0.0994330i	$-0.0317029\pi$
$317$	141333.	+	81598.8i	1.40645	+	0.812017i	0.411411	+	0.911450i	$0.365036\pi$
$318$	124514.	+	215664.i	1.23130	+	2.13267i
$319$	23227.3	+	40230.9i	0.228254	+	0.395347i
$320$	44627.7	+	5904.95i	0.435818	+	0.0576655i
$321$			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
$325$	−149077.	−	40153.3i	−1.41138	−	0.380150i
$326$	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	$-0.911194\pi$
$337$		−	62550.8i		−	0.550773i	0.961334	−	0.275387i	$-0.0888059\pi$
$338$	−130843.	−	75542.2i	−1.14529	−	0.661235i
$339$	46316.8	−	26741.0i	0.403031	−	0.232690i
$340$	26272.2	−	34192.4i	0.227268	−	0.295782i
$341$	−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
$345$	1913.61	−	14462.5i	0.0160774	−	0.121508i
$346$	−165765.	+	95704.6i	−1.38465	+	0.799431i
$347$	−127193.	+	73435.2i	−1.05634	+	0.609881i	−0.924419	−	0.381379i	$-0.875449\pi$
$347$	−127193.	+	73435.2i	−1.05634	+	0.609881i	−0.131926	+	0.991260i	$0.542116\pi$
$348$	−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	$-0.200180\pi$
$350$	53609.3	+	132081.i	0.437627	+	1.07821i
$351$	332684.			2.70033
$352$	−25524.1	−	14736.4i	−0.205999	−	0.118934i
$353$	−12842.2	−	22243.3i	−0.103060	−	0.178505i	0.809884	−	0.586590i	$-0.199530\pi$
$353$	−12842.2	−	22243.3i	−0.103060	−	0.178505i	−0.912944	+	0.408085i	$0.866197\pi$
$354$	185910.	+	322006.i	1.48353	+	2.56956i
$355$	25311.2	+	3349.07i	0.200843	+	0.0265746i
$356$		−	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	$0.944371\pi$
$360$	158867.	+	122067.i	1.22582	+	0.941878i
$361$	−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	0.764843	−	0.644217i	$-0.222817\pi$
$367$	−23636.1	−	40939.0i	−0.175487	−	0.303952i	−0.940330	+	0.340265i	$0.889483\pi$
$368$	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	0.459058	−	0.888407i	$-0.348187\pi$
$373$	−11241.1	−	6490.06i	−0.0807963	−	0.0466478i	−0.539854	+	0.841759i	$0.681521\pi$
$374$	52092.3	−	30075.5i	0.372418	−	0.215015i
$375$	−31614.4	−	243819.i	−0.224814	−	1.73382i
$376$	−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	$0.604053\pi$
$380$	−226.429	+	1711.28i	−0.00156807	+	0.0118510i
$381$	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	−0.589675	−	0.807640i	$-0.700744\pi$
$383$	59350.3	−	102798.i	0.404599	−	0.700787i	0.994275	+	0.106854i	$0.0340776\pi$
$384$			306700.i			2.07995i
$385$	−336.937	+	51992.7i	−0.00227314	+	0.350769i
$386$	−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	$0.499139\pi$
$390$	59328.8	−	448388.i	0.390064	−	2.94798i
$391$			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
$395$	−8437.13	+	10980.7i	−0.0540755	+	0.0703776i
$396$	−20027.6	−	34688.7i	−0.127714	−	0.221207i
$397$	64554.8	−	111812.i	0.409588	−	0.709428i	−0.585255	−	0.810849i	$-0.699006\pi$
$397$	64554.8	−	111812.i	0.409588	−	0.709428i	0.994844	+	0.101422i	$0.0323391\pi$
$398$	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	$0.581392\pi$
$410$	−81492.6	+	106060.i	−0.484786	+	0.630934i
$411$	−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
$415$	−128524.	−	17005.8i	−0.746259	−	0.0987417i
$416$	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	$0.888022\pi$
$420$	−94915.7	+	53982.6i	−0.538071	+	0.306024i
$421$	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
$425$	49012.5	+	183876.i	0.271349	+	1.01800i
$426$			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
$430$	25148.8	−	32730.3i	0.136013	−	0.177016i
$431$	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	$-0.426274\pi$
$433$	86077.3			0.459106			0.229553	+	0.973296i	$0.426274\pi$
$434$	−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	0.253398	−	0.967362i	$-0.418452\pi$
$443$	−89816.0	−	51855.3i	−0.457663	−	0.264232i	−0.711061	+	0.703130i	$0.751785\pi$
$444$	32310.8	−	18654.6i	0.163901	−	0.0946283i
$445$	185951.	+	142878.i	0.939026	+	0.721513i
$446$	−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	$0.401366\pi$
$450$	468278.	−	124821.i	2.31249	−	0.616399i
$451$	−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
$455$	−261076.	−	152997.i	−1.26109	−	0.739026i
$456$	9226.10			0.0443699
$457$	71816.8	+	41463.5i	0.343870	+	0.198533i	0.661982	−	0.749520i	$-0.269716\pi$
$457$	71816.8	+	41463.5i	0.343870	+	0.198533i	−0.318112	+	0.948053i	$0.603049\pi$
$458$	−200353.	−	347021.i	−0.955135	−	1.65434i
$459$	−205028.	−	355118.i	−0.973167	−	1.68557i
$460$	688.934	−	5206.75i	0.00325583	−	0.0246065i
$461$			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	$0.441621\pi$
$463$			421547.i			1.96646i	−0.182378	+	0.983229i	$0.558379\pi$
$464$	172135.	−	298147.i	0.799527	−	1.38482i
$465$	180940.	+	139027.i	0.836812	+	0.642976i
$466$	−89292.3	−	154659.i	−0.411190	−	0.712202i
$467$	14660.4	−	25392.6i	0.0672223	−	0.116432i	−0.830455	−	0.557085i	$-0.811920\pi$
$467$	14660.4	−	25392.6i	0.0672223	−	0.116432i	0.897678	+	0.440653i	$0.145253\pi$
$468$	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	$0.415026\pi$
$480$	216602.	+	166429.i	0.940111	+	0.722346i
$481$	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
$485$	−8257.64	−	1092.62i	−0.0351053	−	0.00464498i
$486$	−48507.0	+	28005.5i	−0.205368	+	0.118569i
$487$	−182358.	+	105284.i	−0.768895	+	0.443922i	−0.832480	−	0.554055i	$-0.813080\pi$
$487$	−182358.	+	105284.i	−0.768895	+	0.443922i	0.0635854	+	0.997976i	$0.479746\pi$
$488$	−4598.06	+	7964.08i	−0.0193079	+	0.0334423i
$489$		−	2951.64i		−	0.0123437i
$490$	33055.4	+	277427.i	0.137674	+	1.15547i
$491$	−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
$495$	175242.	+	23187.2i	0.715199	+	0.0946320i
$496$			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	$0.118135\pi$
$500$	−11381.8	−	87779.1i	−0.0455271	−	0.351116i
$501$	194402.	+	336713.i	0.774505	+	1.34148i
$502$	111230.	−	192655.i	0.441380	−	0.764493i
$503$	−68106.8			−0.269187			−0.134594	−	0.990901i	$-0.542973\pi$
$503$	−68106.8			−0.269187			−0.134594	+	0.990901i	$0.542973\pi$
$504$	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
$515$	237600.	−	309229.i	0.895843	−	1.16591i
$516$	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
$520$	−38968.5	+	294511.i	−0.144114	+	1.08917i
$521$	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	−0.859010	−	0.511959i	$-0.828920\pi$
$523$	3792.47	−	6568.74i	0.0138649	−	0.0240148i	0.872875	+	0.487945i	$0.162253\pi$
$524$			148162.i			0.539604i
$525$	66304.4	−	477301.i	0.240560	−	1.73171i
$526$	−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
$530$	−392239.	−	51899.3i	−1.39637	−	0.184761i
$531$		−	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
$535$	−102115.	−	78461.4i	−0.356765	−	0.274125i
$536$	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	$0.127254\pi$
$547$			232914.i			0.778431i	−0.921147	+	0.389216i	$0.872746\pi$
$548$	−121218.	−	69985.4i	−0.403652	−	0.233049i
$549$	−27579.9	+	15923.3i	−0.0915058	+	0.0528309i
$550$	32112.7	−	119224.i	0.106158	−	0.394131i
$551$	−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
$555$	−21597.7	+	163229.i	−0.0701167	+	0.529920i
$556$	−137245.	+	79238.3i	−0.443963	+	0.256322i
$557$	394668.	−	227862.i	1.27210	−	0.734447i	0.296717	−	0.954965i	$-0.404108\pi$
$557$	394668.	−	227862.i	1.27210	−	0.734447i	0.975383	+	0.220518i	$0.0707748\pi$
$558$	−224893.	+	389527.i	−0.722284	+	1.25103i
$559$			87623.4i			0.280412i
$560$	334939.	−	190494.i	1.06804	−	0.607442i
$561$	−203344.			−0.646109
$562$	439860.	+	253953.i	1.39265	+	0.804046i
$563$	4036.10	+	6990.74i	0.0127334	+	0.0220550i	0.872322	−	0.488932i	$-0.162613\pi$
$563$	4036.10	+	6990.74i	0.0127334	+	0.0220550i	−0.859588	+	0.510987i	$0.829280\pi$
$564$	−37991.2	−	65802.6i	−0.119433	−	0.206864i
$565$	−11146.1	+	84238.7i	−0.0349161	+	0.263885i
$566$			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	$0.938407\pi$
$570$	13597.5	−	17696.7i	0.0418513	−	0.0544682i
$571$	−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	0.968841	−	0.247683i	$-0.0796692\pi$
$577$	89864.4	+	155650.i	0.269920	+	0.467516i	−0.698921	+	0.715199i	$0.746336\pi$
$578$	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
$585$	−626822.	+	815789.i	−1.83161	+	2.38378i
$586$	643217.	+	371362.i	1.87311	+	1.08144i
$587$	166789.			0.484050			0.242025	−	0.970270i	$-0.422188\pi$
$587$	166789.			0.484050			0.242025	+	0.970270i	$0.422188\pi$
$588$	−207357.	+	52978.5i	−0.599743	+	0.153230i
$589$	7070.26			0.0203800
$590$	−585650.	−	77490.6i	−1.68242	−	0.222610i
$591$	−544441.	+	314333.i	−1.55875	+	0.899943i
$592$	−114018.	+	65828.5i	−0.325335	+	0.187832i
$593$	−159004.	+	275403.i	−0.452167	+	0.783177i	−0.998520	−	0.0543780i	$-0.982682\pi$
$593$	−159004.	+	275403.i	−0.452167	+	0.783177i	0.546353	+	0.837555i	$0.316016\pi$
$594$			266065.i			0.754075i
$595$	−2417.03	+	372972.i	−0.00682728	+	1.05352i
$596$	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	$0.803709\pi$
$600$	−457126.	+	121848.i	−1.26979	+	0.338467i
$601$			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
$605$	−195571.	+	254529.i	−0.534310	+	0.695388i
$606$	−99719.8	−	172720.i	−0.271541	−	0.470324i
$607$	74923.8	−	129772.i	0.203349	−	0.352211i	−0.746256	−	0.665659i	$-0.768151\pi$
$607$	74923.8	−	129772.i	0.203349	−	0.352211i	0.949605	+	0.313448i	$0.101484\pi$
$608$	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	−0.190449	−	0.981697i	$-0.560995\pi$
$613$	212122.	−	122469.i	0.564500	−	0.325914i	0.754950	+	0.655783i	$0.227661\pi$
$614$	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	$-0.863464\pi$
$617$		−	316663.i		−	0.831816i	0.909407	−	0.415908i	$-0.136536\pi$
$618$	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	$0.319019\pi$
$620$	65141.6	+	50052.4i	0.169463	+	0.130209i
$621$	−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
$625$	337781.	+	196194.i	0.864719	+	0.502256i
$626$	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
$630$	949852.	+	6155.48i	2.39318	+	0.0155089i
$631$	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
$635$	−68235.3	+	515701.i	−0.169224	+	1.27894i
$636$		−	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
$640$	−386399.	−	296895.i	−0.943358	−	0.724842i
$641$	−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	$-0.746839\pi$
$643$	−578869.			−1.40010			−0.700049	+	0.714095i	$0.746839\pi$
$644$	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	0.995846	−	0.0910563i	$-0.0290243\pi$
$647$	175425.	+	303844.i	0.419066	+	0.725843i	−0.576780	+	0.816900i	$0.695691\pi$
$648$	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	−0.103482	−	0.994631i	$-0.532998\pi$
$653$	−433487.	−	250274.i	−1.01660	−	0.586934i	−0.913117	+	0.407698i	$0.866332\pi$
$654$	1.18181e6	−	682319.i	2.76308	−	1.59526i
$655$	−518484.	−	398384.i	−1.20852	−	0.928579i
$656$	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	$0.387712\pi$
$660$	93766.0	+	12406.7i	0.215257	+	0.0284819i
$661$	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
$665$	−7381.63	−	12978.9i	−0.0166920	−	0.0293490i
$666$	−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
$670$	197808.	+	26173.1i	0.440651	+	0.0583050i
$671$			8113.86i			0.0180211i
$672$	323442.	+	426644.i	0.716239	+	0.944772i
$673$		−	226218.i		−	0.499457i	−0.968316	−	0.249728i	$-0.919659\pi$
$673$		−	226218.i		−	0.499457i	0.968316	−	0.249728i	$-0.0803413\pi$
$674$	−145573.	+	252140.i	−0.320451	+	0.555037i
$675$	−812766.	−	218916.i	−1.78385	−	0.480474i
$676$	91939.7	+	159244.i	0.201191	+	0.348474i
$677$	101310.	−	175473.i	0.221041	−	0.382855i	−0.734083	−	0.679060i	$-0.762388\pi$
$677$	101310.	−	175473.i	0.221041	−	0.382855i	0.955124	+	0.296205i	$0.0957211\pi$
$678$	−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	−0.663509	−	0.748168i	$-0.730934\pi$
$683$	−162026.	+	93545.9i	−0.347331	+	0.200532i	0.316178	+	0.948700i	$0.397600\pi$
$684$	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
$690$	−41371.8	+	53844.1i	−0.0868974	+	0.113094i
$691$	−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
$695$	91739.4	−	693338.i	0.189927	−	1.43541i
$696$	−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
$700$	23870.8	−	171837.i	0.0487159	−	0.350688i
$701$	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
$705$	332424.	+	43984.9i	0.668827	+	0.0884963i
$706$			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	$0.302787\pi$
$710$	−94234.3	−	72406.2i	−0.186936	−	0.143635i
$711$	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
$725$	660519.	+	177909.i	1.25663	+	0.338471i
$726$	−814375.	−	470180.i	−1.54508	−	0.892053i
$727$	−535853.			−1.01386			−0.506929	−	0.861988i	$-0.669219\pi$
$727$	−535853.			−1.01386			−0.506929	+	0.861988i	$0.669219\pi$
$728$	−225958.	+	536643.i	−0.426349	+	1.01256i
$729$	−434158.			−0.816944
$730$	102446.	−	774258.i	0.192243	−	1.45292i
$731$	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	$0.478784\pi$
$733$	−446381.	+	773154.i	−0.830802	+	1.43899i	−0.897403	+	0.441211i	$0.854549\pi$
$734$			220032.i			0.408407i
$735$	372155.	−	868084.i	0.688890	−	1.60689i
$736$	−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	$0.656250\pi$
$740$	−7775.57	+	58765.3i	−0.0141994	+	0.107314i
$741$			47376.5i			0.0862832i
$742$	−714716.	−	300938.i	−1.29815	−	0.546599i
$743$		−	428933.i		−	0.776984i	−0.921452	−	0.388492i	$-0.872996\pi$
$743$		−	428933.i		−	0.776984i	0.921452	−	0.388492i	$-0.127004\pi$
$744$	219537.	−	380249.i	0.396609	−	0.686946i
$745$	−205199.	+	267060.i	−0.369712	+	0.481168i
$746$	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	$-0.956271\pi$
$757$		−	156953.i		−	0.273892i	0.990579	−	0.136946i	$-0.0437287\pi$
$758$	371844.	+	214684.i	0.647176	+	0.373647i
$759$	−21449.5	+	12383.9i	−0.0372334	+	0.0214967i
$760$	−8931.14	+	11623.6i	−0.0154625	+	0.0201239i
$761$	−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
$765$	1.25710e6	+	166334.i	2.14807	+	0.284223i
$766$	−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	$0.785590\pi$
$770$	122360.	−	208797.i	0.206375	−	0.352162i
$771$	561554.			0.944676
$772$	301375.	+	173999.i	0.505677	+	0.291953i
$773$	423005.	+	732666.i	0.707924	+	1.22616i	0.965626	+	0.259935i	$0.0837012\pi$
$773$	423005.	+	732666.i	0.707924	+	1.22616i	−0.257702	+	0.966224i	$0.582965\pi$
$774$	−137525.	−	238200.i	−0.229562	−	0.397613i
$775$	−350310.	+	93376.0i	−0.583243	+	0.155465i
$776$			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
$780$	−335392.	+	436502.i	−0.551268	+	0.717458i
$781$	−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	0.704168	−	0.710034i	$-0.251320\pi$
$787$	−162785.	−	281951.i	−0.262824	−	0.455224i	−0.966991	+	0.254810i	$0.917987\pi$
$788$	−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
$795$	1.06061e6	+	814937.i	1.67812	+	1.28941i
$796$	−356995.	−	206111.i	−0.563425	−	0.325294i
$797$	−34880.5			−0.0549119			−0.0274560	−	0.999623i	$-0.508741\pi$
$797$	−34880.5			−0.0549119			−0.0274560	+	0.999623i	$0.508741\pi$
$798$	34857.5	−	26425.8i	0.0547382	−	0.0414975i
$799$	−259539.			−0.406546
$800$	−419353.	+	111780.i	−0.655240	+	0.174656i
$801$	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
$805$	22459.4	+	39489.6i	0.0346582	+	0.0609384i
$806$	−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	$0.878789\pi$
$810$	117494.	−	887985.i	0.179080	−	1.35343i
$811$		−	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
$815$	3718.65	+	2857.27i	0.00559848	+	0.00430166i
$816$	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	0.285891	−	0.958262i	$-0.407711\pi$
$823$	852565.	−	492228.i	1.25872	−	0.726720i	0.972825	+	0.231542i	$0.0743772\pi$
$824$	−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	$-0.970960\pi$
$827$		−	124621.i		−	0.182213i	0.995841	−	0.0911064i	$-0.0290403\pi$
$828$	−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	$0.337113\pi$
$830$	478500.	+	367662.i	0.694585	+	0.533694i
$831$	726967.	+	419715.i	1.05272	+	0.607788i
$832$	444807.			0.642576
$833$	−197425.	+	703877.i	−0.284520	+	1.01439i
$834$	2.04889e6			2.94569
$835$	−612398.	−	81029.9i	−0.878337	−	0.116218i
$836$	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	$-0.292822\pi$
$840$	−927230.	−	6008.87i	−1.31410	−	0.00851598i
$841$	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
$845$	−804475.	−	106445.i	−1.12668	−	0.149077i
$846$			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
$850$	230362.	−	855261.i	0.318840	−	1.18375i
$851$	−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	$-0.481541\pi$
$853$	84342.4			0.115917			0.0579586	+	0.998319i	$0.481541\pi$
$854$	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	0.632626	−	0.774457i	$-0.281977\pi$
$857$	−260279.	−	450816.i	−0.354387	−	0.613816i	−0.987013	+	0.160642i	$0.948644\pi$
$858$	−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	0.786803	−	0.617204i	$-0.211735\pi$
$863$	480890.	+	277642.i	0.645691	+	0.372790i	−0.141113	+	0.989994i	$0.545068\pi$
$864$	809896.	−	467594.i	1.08493	−	0.626385i
$865$	−626384.	+	815218.i	−0.837160	+	1.08954i
$866$	−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
$870$	−262870.	+	1.98669e6i	−0.347298	+	2.62477i
$871$	−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
$875$	537148.	+	545576.i	0.701581	+	0.712589i
$876$	598267.			0.779627
$877$	1.13396e6	+	654695.i	1.47435	+	0.851216i	0.999582	−	0.0288957i	$-0.00919908\pi$
$877$	1.13396e6	+	654695.i	1.47435	+	0.851216i	0.474767	+	0.880112i	$0.342532\pi$
$878$	−422964.	−	732595.i	−0.548674	−	0.950332i
$879$	−1.25541e6	−	2.17444e6i	−1.62483	−	2.81429i
$880$	−330882.	−	43780.8i	−0.427275	−	0.0565351i
$881$		−	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	$0.253194\pi$
$883$			1.11366e6i			1.42833i	−0.699975	+	0.714167i	$0.746806\pi$
$884$	213034.	−	368985.i	0.272611	−	0.472177i
$885$	1.58360e6	+	1.21678e6i	2.02189	+	1.55355i
$886$	241363.	+	418054.i	0.307471	+	0.532555i
$887$	208559.	−	361236.i	0.265083	−	0.459138i	−0.702502	−	0.711682i	$-0.747934\pi$
$887$	208559.	−	361236.i	0.265083	−	0.459138i	0.967585	+	0.252544i	$0.0812671\pi$
$888$	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
$900$	−569527.	−	153400.i	−0.703119	−	0.189383i
$901$	−896563.	−	517631.i	−1.10441	−	0.637633i
$902$	227079.			0.279103
$903$	−271356.	+	34116.9i	−0.332786	+	0.0418403i
$904$	163506.			0.200077
$905$	32059.2	−	242293.i	0.0391431	−	0.295831i
$906$	−706766.	+	408052.i	−0.861032	+	0.497117i
$907$	−969958.	+	560006.i	−1.17907	+	0.680735i	−0.955799	−	0.294022i	$-0.905006\pi$
$907$	−969958.	+	560006.i	−1.17907	+	0.680735i	−0.223268	+	0.974757i	$0.571673\pi$
$908$	−219819.	+	380737.i	−0.266620	+	0.461800i
$909$			453646.i			0.549021i
$910$	696323.	+	1.22432e6i	0.840868	+	1.47847i
$911$	−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
$915$	9864.19	−	74550.4i	0.0117820	−	0.0890447i
$916$			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	$-0.0406463\pi$
$920$	27173.9	−	35366.0i	0.0321053	−	0.0417840i
$921$	−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
$935$	196843.	−	256185.i	0.225163	−	0.293042i
$936$	1.71440e6	+	989810.i	1.95686	+	1.12980i
$937$	739900.			0.842741			0.421370	−	0.906889i	$-0.361549\pi$
$937$	739900.			0.842741			0.421370	+	0.906889i	$0.361549\pi$
$938$	360435.	+	151764.i	0.409658	+	0.172490i
$939$	−694649.			−0.787833
$940$	119679.	+	15835.4i	0.135444	+	0.0179214i
$941$	−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
$945$	−1.42339e6	−	834139.i	−1.59389	−	0.934060i
$946$	−70077.1			−0.0783058
$947$	1.03060e6	+	595020.i	1.14919	+	0.663486i	0.948690	−	0.316208i	$-0.102410\pi$
$947$	1.03060e6	+	595020.i	1.14919	+	0.663486i	0.200501	+	0.979694i	$0.435743\pi$
$948$	24687.0	+	42759.1i	0.0274695	+	0.0475786i
$949$	828980.	+	1.43584e6i	0.920475	+	1.59431i
$950$	9132.59	+	34261.9i	0.0101192	+	0.0379633i
$951$			2.56792e6i			2.83936i
$952$	712086.	−	89528.7i	0.785704	−	0.0987844i
$953$		−	230956.i		−	0.254298i	−0.991884	−	0.127149i	$-0.959417\pi$
$953$		−	230956.i		−	0.254298i	0.991884	−	0.127149i	$-0.0405826\pi$
$954$	−1.31826e6	+	2.28329e6i	−1.44845	+	2.50879i
$955$	168668.	−	219516.i	0.184938	−	0.240690i
$956$	−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	$0.206097\pi$
$967$			1.12804e6i			1.20635i	−0.797610	+	0.603173i	$0.793903\pi$
$968$	534900.	+	308825.i	0.570850	+	0.329580i
$969$	50571.3	−	29197.4i	0.0538588	−	0.0310954i
$970$	30743.4	+	23622.1i	0.0326745	+	0.0251059i
$971$	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
$975$	−625695.	−	2.34736e6i	−0.658193	−	2.46928i
$976$	52074.9	−	30065.5i	0.0546674	−	0.0315623i
$977$	−569827.	+	328990.i	−0.596972	+	0.344662i	−0.767850	−	0.640630i	$-0.778673\pi$
$977$	−569827.	+	328990.i	−0.596972	+	0.344662i	0.170877	+	0.985292i	$0.445340\pi$
$978$	−6869.28	+	11897.9i	−0.00718181	+	0.0124393i
$979$		−	398129.i		−	0.415392i
$980$	133983.	−	312526.i	0.139507	−	0.325412i
$981$	−3.10401e6			−3.22541
$982$	798439.	+	460979.i	0.827978	+	0.478033i
$983$	135356.	+	234444.i	0.140078	+	0.242623i	0.927526	−	0.373759i	$-0.121931\pi$
$983$	135356.	+	234444.i	0.140078	+	0.242623i	−0.787448	+	0.616382i	$0.788598\pi$
$984$	−435025.	−	753486.i	−0.449287	−	0.778189i
$985$	131019.	−	990203.i	0.135040	−	1.02059i
$986$		−	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
$990$	−652430.	−	501303.i	−0.665677	−	0.511481i
$991$	−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	0.997619	−	0.0689671i	$-0.0219704\pi$
$997$	436452.	+	755956.i	0.439082	+	0.760513i	−0.558537	+	0.829480i	$0.688637\pi$
$998$	−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.19.4	✓	28
5.2	odd	4		175.5.i.e.26.11		28
5.3	odd	4		175.5.i.e.26.4		28
5.4	even	2	inner	35.5.i.a.19.11	yes	28
7.2	even	3		245.5.c.a.244.28		28
7.3	odd	6	inner	35.5.i.a.24.11	yes	28
7.5	odd	6		245.5.c.a.244.2		28
35.3	even	12		175.5.i.e.101.4		28
35.9	even	6		245.5.c.a.244.1		28
35.17	even	12		175.5.i.e.101.11		28
35.19	odd	6		245.5.c.a.244.27		28
35.24	odd	6	inner	35.5.i.a.24.4	yes	28

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

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)

\(f(q)\)	\(=\)	\(q+(-4.03096 - 2.32728i) q^{2} +(7.86751 + 13.6269i) q^{3} +(2.83245 + 4.90594i) q^{4} +(-24.7840 - 3.27931i) q^{5} -73.2395i q^{6} +(-45.1600 - 19.0150i) q^{7} +48.1053i q^{8} +(-83.2953 + 144.272i) q^{9} +O(q^{10})\)	\(q+(-4.03096 - 2.32728i) q^{2} +(7.86751 + 13.6269i) q^{3} +(2.83245 + 4.90594i) q^{4} +(-24.7840 - 3.27931i) q^{5} -73.2395i q^{6} +(-45.1600 - 19.0150i) q^{7} +48.1053i q^{8} +(-83.2953 + 144.272i) q^{9} +(92.2715 + 70.8980i) 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} +(603.492 + 162.549i) q^{25} +(995.742 + 574.892i) q^{26} -1346.77 q^{27} +(-34.6268 - 275.411i) q^{28} +1094.49 q^{29} +(-240.175 + 1815.17i) q^{30} +(-502.352 + 290.033i) q^{31} +(-601.362 + 347.196i) q^{32} +(-333.928 + 578.380i) q^{33} -1417.19i q^{34} +(1056.89 + 619.362i) q^{35} -943.718 q^{36} +(-362.484 - 209.280i) q^{37} +(28.3665 + 49.1323i) q^{38} +(-1943.46 - 3366.17i) q^{39} +(157.752 - 1192.24i) q^{40} +1149.43i q^{41} +(-1392.65 + 3307.50i) q^{42} -354.717i q^{43} +(-120.220 + 208.227i) q^{44} +(2537.50 - 3302.48i) 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} +(1357.73 - 1767.05i) q^{60} +(165.555 + 95.5833i) q^{61} +2699.95 q^{62} +(6504.95 - 4931.45i) q^{63} -1800.67 q^{64} +(6122.22 + 810.065i) q^{65} +(2692.10 - 1554.29i) q^{66} +(1485.00 - 857.362i) q^{67} +(-862.404 + 1493.73i) q^{68} +583.540i q^{69} +(-2818.86 - 4956.30i) q^{70} -1021.27 q^{71} +(-6940.24 - 4006.95i) q^{72} +(-3355.88 - 5812.56i) q^{73} +(974.106 + 1687.20i) q^{74} +(2532.94 + 9502.60i) q^{75} -69.0477i q^{76} +(-259.439 - 2063.51i) q^{77} +18091.9i q^{78} +(276.955 - 479.700i) q^{79} +(-4791.17 + 6235.56i) 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} +(241.628 + 185.658i) 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

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