LMFDB - Embedded newform 110.5.h.a.51.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,5,Mod(41,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("110.41");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	110.h (of order $10$, degree $4$, 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:	$11.3706959392$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			51.4
Character	$\chi$	$=$	110.51
Dual form			110.5.h.a.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.66251 + 2.28825i) q^{2} +(4.89398 - 15.0621i) q^{3} +(-2.47214 - 7.60845i) q^{4} +(-9.04508 + 6.57164i) q^{5} +(26.3296 + 36.2396i) q^{6} +(-75.4276 + 24.5079i) q^{7} +(21.5200 + 6.99226i) q^{8} +(-137.386 - 99.8171i) q^{9} -31.6228i q^{10} +(116.546 + 32.5265i) q^{11} -126.698 q^{12} +(-109.181 + 150.275i) q^{13} +(69.3189 - 213.342i) q^{14} +(54.7164 + 168.400i) q^{15} +(-51.7771 + 37.6183i) q^{16} +(199.384 + 274.428i) q^{17} +(456.812 - 148.427i) q^{18} +(7.65733 + 2.48802i) q^{19} +(72.3607 + 52.5731i) q^{20} +1256.04i q^{21} +(-268.188 + 212.611i) q^{22} +473.434 q^{23} +(210.637 - 289.916i) q^{24} +(38.6271 - 118.882i) q^{25} +(-162.352 - 499.668i) q^{26} +(-1138.00 + 826.808i) q^{27} +(372.935 + 513.301i) q^{28} +(-1312.91 + 426.591i) q^{29} +(-476.307 - 154.761i) q^{30} +(-1342.21 - 975.170i) q^{31} -181.019i q^{32} +(1060.29 - 1596.25i) q^{33} -959.436 q^{34} +(521.192 - 717.359i) q^{35} +(-419.816 + 1292.06i) q^{36} +(124.180 + 382.188i) q^{37} +(-18.4236 + 13.3855i) q^{38} +(1729.14 + 2379.95i) q^{39} +(-240.600 + 78.1758i) q^{40} +(-2871.98 - 933.163i) q^{41} +(-2874.13 - 2088.18i) q^{42} +2574.67i q^{43} +(-40.6421 - 967.146i) q^{44} +1898.63 q^{45} +(-787.088 + 1083.33i) q^{46} +(-705.352 + 2170.85i) q^{47} +(313.215 + 963.977i) q^{48} +(3146.24 - 2285.88i) q^{49} +(207.813 + 286.031i) q^{50} +(5109.26 - 1660.10i) q^{51} +(1413.27 + 459.201i) q^{52} +(-2648.05 - 1923.92i) q^{53} -3978.61i q^{54} +(-1267.92 + 471.695i) q^{55} -1794.56 q^{56} +(74.9497 - 103.159i) q^{57} +(1206.58 - 3713.48i) q^{58} +(218.082 + 671.187i) q^{59} +(1146.00 - 832.614i) q^{60} +(338.369 + 465.725i) q^{61} +(4462.86 - 1450.07i) q^{62} +(12809.0 + 4161.91i) q^{63} +(414.217 + 300.946i) q^{64} -2076.75i q^{65} +(1889.87 + 5079.99i) q^{66} -1985.60 q^{67} +(1595.07 - 2195.43i) q^{68} +(2316.98 - 7130.93i) q^{69} +(775.009 + 2385.23i) q^{70} +(-1710.82 + 1242.99i) q^{71} +(-2258.60 - 3108.70i) q^{72} +(1025.58 - 333.230i) q^{73} +(-1080.99 - 351.235i) q^{74} +(-1601.58 - 1163.61i) q^{75} -64.4112i q^{76} +(-9587.96 + 402.912i) q^{77} -8320.61 q^{78} +(2287.68 - 3148.72i) q^{79} +(221.115 - 680.521i) q^{80} +(2633.49 + 8105.05i) q^{81} +(6910.00 - 5020.41i) q^{82} +(-5341.44 - 7351.87i) q^{83} +(9556.54 - 3105.11i) q^{84} +(-3606.89 - 1171.95i) q^{85} +(-5891.47 - 4280.41i) q^{86} +21863.0i q^{87} +(2280.64 + 1514.89i) q^{88} -593.105 q^{89} +(-3156.49 + 4344.54i) q^{90} +(4552.36 - 14010.7i) q^{91} +(-1170.39 - 3602.10i) q^{92} +(-21256.9 + 15444.0i) q^{93} +(-3794.79 - 5223.07i) q^{94} +(-85.6116 + 27.8169i) q^{95} +(-2726.54 - 885.906i) q^{96} +(-79.0172 - 57.4093i) q^{97} +10999.7i q^{98} +(-12765.2 - 16102.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 18 q^{3} + 64 q^{4} - 200 q^{5} + 80 q^{6} - 60 q^{7} - 262 q^{9} - 258 q^{11} - 96 q^{12} - 570 q^{13} - 48 q^{14} + 150 q^{15} - 512 q^{16} + 150 q^{17} - 480 q^{18} - 1020 q^{19} + 1600 q^{20}+ \cdots + 65268 q^{99}+O(q^{100}) $ 32 * q - 18 * q^3 + 64 * q^4 - 200 * q^5 + 80 * q^6 - 60 * q^7 - 262 * q^9 - 258 * q^11 - 96 * q^12 - 570 * q^13 - 48 * q^14 + 150 * q^15 - 512 * q^16 + 150 * q^17 - 480 * q^18 - 1020 * q^19 + 1600 * q^20 - 480 * q^22 - 1536 * q^23 + 640 * q^24 - 1000 * q^25 + 448 * q^26 - 4194 * q^27 + 960 * q^28 - 4130 * q^29 - 800 * q^30 - 1936 * q^31 - 5852 * q^33 - 768 * q^34 + 1856 * q^36 + 2728 * q^37 - 1360 * q^38 + 7990 * q^39 - 4490 * q^41 - 2592 * q^42 + 1024 * q^44 + 300 * q^45 + 640 * q^46 - 2732 * q^47 - 1152 * q^48 + 3832 * q^49 + 12080 * q^51 + 5520 * q^52 + 1222 * q^53 - 550 * q^55 + 2304 * q^56 + 14580 * q^57 - 3104 * q^58 - 8340 * q^59 - 300 * q^61 + 11680 * q^62 + 32020 * q^63 + 4096 * q^64 + 29696 * q^66 - 9264 * q^67 + 1200 * q^68 - 25466 * q^69 - 1200 * q^70 - 7144 * q^71 - 20480 * q^72 - 7070 * q^73 + 19840 * q^74 + 1500 * q^75 + 34480 * q^77 - 5696 * q^78 + 57050 * q^79 + 12800 * q^80 - 63694 * q^81 + 13312 * q^82 + 580 * q^83 + 29520 * q^84 + 9750 * q^85 - 13360 * q^86 + 9600 * q^88 + 14368 * q^89 + 17600 * q^90 - 40158 * q^91 - 25712 * q^92 - 103942 * q^93 - 67600 * q^94 + 5700 * q^95 - 31458 * q^97 + 65268 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−1.66251	+	2.28825i	−0.415627	+	0.572061i
$2$	−1.66251	+	2.28825i	−0.415627	+	0.572061i
$3$	4.89398	−	15.0621i	0.543776	−	1.67357i	−0.180106	−	0.983647i	$-0.557644\pi$
$3$	4.89398	−	15.0621i	0.543776	−	1.67357i	0.723882	−	0.689923i	$-0.242356\pi$
$4$	−2.47214	−	7.60845i	−0.154508	−	0.475528i
$5$	−9.04508	+	6.57164i	−0.361803	+	0.262866i
$5$	−9.04508	+	6.57164i	−0.361803	+	0.262866i
$6$	26.3296	+	36.2396i	0.731377	+	1.00665i
$7$	−75.4276	+	24.5079i	−1.53934	+	0.500162i	−0.951194	−	0.308593i	$-0.900142\pi$
$7$	−75.4276	+	24.5079i	−1.53934	+	0.500162i	−0.588146	+	0.808755i	$0.700142\pi$
$8$	21.5200	+	6.99226i	0.336249	+	0.109254i
$9$	−137.386	−	99.8171i	−1.69613	−	1.23231i
$10$		−	31.6228i		−	0.316228i
$11$	116.546	+	32.5265i	0.963192	+	0.268814i
$11$	116.546	+	32.5265i	0.963192	+	0.268814i
$12$	−126.698			−0.879848
$13$	−109.181	+	150.275i	−0.646044	+	0.889203i	−0.998920	−	0.0464667i	$-0.985204\pi$
$13$	−109.181	+	150.275i	−0.646044	+	0.889203i	0.352876	+	0.935670i	$0.385204\pi$
$14$	69.3189	−	213.342i	0.353668	−	1.08848i
$15$	54.7164	+	168.400i	0.243184	+	0.748444i
$16$	−51.7771	+	37.6183i	−0.202254	+	0.146946i
$17$	199.384	+	274.428i	0.689909	+	0.949579i	0.999999	−	0.00112843i	$-0.000359191\pi$
$17$	199.384	+	274.428i	0.689909	+	0.949579i	−0.310090	+	0.950707i	$0.600359\pi$
$18$	456.812	−	148.427i	1.40991	−	0.458109i
$19$	7.65733	+	2.48802i	0.0212114	+	0.00689202i	0.319604	−	0.947551i	$-0.396450\pi$
$19$	7.65733	+	2.48802i	0.0212114	+	0.00689202i	−0.298392	+	0.954443i	$0.596450\pi$
$20$	72.3607	+	52.5731i	0.180902	+	0.131433i
$21$			1256.04i			2.84817i
$22$	−268.188	+	212.611i	−0.554107	+	0.439279i
$23$	473.434			0.894960			0.447480	−	0.894294i	$-0.352321\pi$
$23$	473.434			0.894960			0.447480	+	0.894294i	$0.352321\pi$
$24$	210.637	−	289.916i	0.365689	−	0.503327i
$25$	38.6271	−	118.882i	0.0618034	−	0.190211i
$26$	−162.352	−	499.668i	−0.240166	−	0.739154i
$27$	−1138.00	+	826.808i	−1.56105	+	1.13417i
$28$	372.935	+	513.301i	0.475682	+	0.654720i
$29$	−1312.91	+	426.591i	−1.56113	+	0.507243i	−0.957110	−	0.289724i	$-0.906436\pi$
$29$	−1312.91	+	426.591i	−1.56113	+	0.507243i	−0.604023	+	0.796967i	$0.706436\pi$
$30$	−476.307	−	154.761i	−0.529229	−	0.171957i
$31$	−1342.21	−	975.170i	−1.39668	−	1.01474i	−0.995095	−	0.0989211i	$-0.968461\pi$
$31$	−1342.21	−	975.170i	−1.39668	−	1.01474i	−0.401581	−	0.915824i	$-0.631539\pi$
$32$		−	181.019i		−	0.176777i
$33$	1060.29	−	1596.25i	0.973640	−	1.46580i
$34$	−959.436			−0.829962
$35$	521.192	−	717.359i	0.425463	−	0.585600i
$36$	−419.816	+	1292.06i	−0.323932	+	0.996960i
$37$	124.180	+	382.188i	0.0907089	+	0.279173i	0.986112	−	0.166084i	$-0.0531123\pi$
$37$	124.180	+	382.188i	0.0907089	+	0.279173i	−0.895403	+	0.445257i	$0.853112\pi$
$38$	−18.4236	+	13.3855i	−0.0127587	+	0.00926974i
$39$	1729.14	+	2379.95i	1.13684	+	1.56473i
$40$	−240.600	+	78.1758i	−0.150375	+	0.0488599i
$41$	−2871.98	−	933.163i	−1.70850	−	0.555124i	−0.718414	−	0.695616i	$-0.755131\pi$
$41$	−2871.98	−	933.163i	−1.70850	−	0.555124i	−0.990082	+	0.140492i	$0.955131\pi$
$42$	−2874.13	−	2088.18i	−1.62933	−	1.18378i
$43$			2574.67i			1.39247i	0.717816	+	0.696233i	$0.245142\pi$
$43$			2574.67i			1.39247i	−0.717816	+	0.696233i	$0.754858\pi$
$44$	−40.6421	−	967.146i	−0.0209928	−	0.499559i
$45$	1898.63			0.937597
$46$	−787.088	+	1083.33i	−0.371970	+	0.511972i
$47$	−705.352	+	2170.85i	−0.319308	+	0.982730i	0.654636	+	0.755944i	$0.272822\pi$
$47$	−705.352	+	2170.85i	−0.319308	+	0.982730i	−0.973945	+	0.226786i	$0.927178\pi$
$48$	313.215	+	963.977i	0.135944	+	0.418393i
$49$	3146.24	−	2285.88i	1.31039	−	0.952052i
$50$	207.813	+	286.031i	0.0831254	+	0.114412i
$51$	5109.26	−	1660.10i	1.96434	−	0.638254i
$52$	1413.27	+	459.201i	0.522661	+	0.169823i
$53$	−2648.05	−	1923.92i	−0.942702	−	0.684913i	0.00636735	−	0.999980i	$-0.497973\pi$
$53$	−2648.05	−	1923.92i	−0.942702	−	0.684913i	−0.949070	+	0.315066i	$0.897973\pi$
$54$		−	3978.61i		−	1.36441i
$55$	−1267.92	+	471.695i	−0.419148	+	0.155932i
$56$	−1794.56			−0.572246
$57$	74.9497	−	103.159i	0.0230686	−	0.0317511i
$58$	1206.58	−	3713.48i	0.358675	−	1.10389i
$59$	218.082	+	671.187i	0.0626492	+	0.192814i	0.977482	−	0.211018i	$-0.0676779\pi$
$59$	218.082	+	671.187i	0.0626492	+	0.192814i	−0.914833	+	0.403832i	$0.867678\pi$
$60$	1146.00	−	832.614i	0.318332	−	0.231282i
$61$	338.369	+	465.725i	0.0909350	+	0.125161i	0.852060	−	0.523443i	$-0.175353\pi$
$61$	338.369	+	465.725i	0.0909350	+	0.125161i	−0.761125	+	0.648605i	$0.775353\pi$
$62$	4462.86	−	1450.07i	1.16099	−	0.377229i
$63$	12809.0	+	4161.91i	3.22727	+	1.04860i
$64$	414.217	+	300.946i	0.101127	+	0.0734732i
$65$		−	2076.75i		−	0.491540i
$66$	1889.87	+	5079.99i	0.433854	+	1.16621i
$67$	−1985.60			−0.442326			−0.221163	−	0.975237i	$-0.570985\pi$
$67$	−1985.60			−0.442326			−0.221163	+	0.975237i	$0.570985\pi$
$68$	1595.07	−	2195.43i	0.344955	−	0.474789i
$69$	2316.98	−	7130.93i	0.486658	−	1.49778i
$70$	775.009	+	2385.23i	0.158165	+	0.486782i
$71$	−1710.82	+	1242.99i	−0.339382	+	0.246575i	−0.744401	−	0.667733i	$-0.767265\pi$
$71$	−1710.82	+	1242.99i	−0.339382	+	0.246575i	0.405019	+	0.914308i	$0.367265\pi$
$72$	−2258.60	−	3108.70i	−0.435687	−	0.599672i
$73$	1025.58	−	333.230i	0.192452	−	0.0625315i	−0.211205	−	0.977442i	$-0.567739\pi$
$73$	1025.58	−	333.230i	0.192452	−	0.0625315i	0.403657	+	0.914910i	$0.367739\pi$
$74$	−1080.99	−	351.235i	−0.197405	−	0.0641409i
$75$	−1601.58	−	1163.61i	−0.284725	−	0.206865i
$76$		−	64.4112i		−	0.0111515i
$77$	−9587.96	+	402.912i	−1.61713	+	0.0679561i
$78$	−8320.61			−1.36762
$79$	2287.68	−	3148.72i	0.366557	−	0.504522i	−0.585404	−	0.810741i	$-0.699064\pi$
$79$	2287.68	−	3148.72i	0.366557	−	0.504522i	0.951961	+	0.306220i	$0.0990642\pi$
$80$	221.115	−	680.521i	0.0345492	−	0.106331i
$81$	2633.49	+	8105.05i	0.401385	+	1.23534i
$82$	6910.00	−	5020.41i	1.02766	−	0.746640i
$83$	−5341.44	−	7351.87i	−0.775358	−	1.06719i	−0.995779	−	0.0917844i	$-0.970743\pi$
$83$	−5341.44	−	7351.87i	−0.775358	−	1.06719i	0.220420	−	0.975405i	$-0.429257\pi$
$84$	9556.54	−	3105.11i	1.35439	−	0.440066i
$85$	−3606.89	−	1171.95i	−0.499223	−	0.162207i
$86$	−5891.47	−	4280.41i	−0.796576	−	0.578746i
$87$			21863.0i			2.88849i
$88$	2280.64	+	1514.89i	0.294504	+	0.195621i
$89$	−593.105			−0.0748776			−0.0374388	−	0.999299i	$-0.511920\pi$
$89$	−593.105			−0.0748776			−0.0374388	+	0.999299i	$0.511920\pi$
$90$	−3156.49	+	4344.54i	−0.389691	+	0.536363i
$91$	4552.36	−	14010.7i	0.549736	−	1.69191i
$92$	−1170.39	−	3602.10i	−0.138279	−	0.425579i
$93$	−21256.9	+	15444.0i	−2.45773	+	1.78564i
$94$	−3794.79	−	5223.07i	−0.429469	−	0.591113i
$95$	−85.6116	+	27.8169i	−0.00948605	+	0.00308220i
$96$	−2726.54	−	885.906i	−0.295848	−	0.0961269i
$97$	−79.0172	−	57.4093i	−0.00839804	−	0.00610154i	0.583578	−	0.812057i	$-0.301652\pi$
$97$	−79.0172	−	57.4093i	−0.00839804	−	0.00610154i	−0.591976	+	0.805955i	$0.701652\pi$
$98$			10999.7i			1.14532i
$99$	−12765.2	−	16102.0i	−1.30244	−	1.64289i
$100$	−1000.00			−0.100000
$101$	3849.12	−	5297.86i	0.377328	−	0.519347i	−0.577546	−	0.816358i	$-0.695990\pi$
$101$	3849.12	−	5297.86i	0.377328	−	0.519347i	0.954874	+	0.297011i	$0.0959898\pi$
$102$	−4695.47	+	14451.2i	−0.451314	+	1.38900i
$103$	4639.97	+	14280.4i	0.437362	+	1.34606i	0.890647	+	0.454696i	$0.150252\pi$
$103$	4639.97	+	14280.4i	0.437362	+	1.34606i	−0.453285	+	0.891366i	$0.649748\pi$
$104$	−3400.34	+	2470.49i	−0.314381	+	0.228411i
$105$	−8254.26	−	11361.0i	−0.748686	−	1.03048i
$106$	8804.81	−	2860.86i	0.783625	−	0.254615i
$107$	8188.80	+	2660.70i	0.715242	+	0.232396i	0.643959	−	0.765060i	$-0.277291\pi$
$107$	8188.80	+	2660.70i	0.715242	+	0.232396i	0.0712828	+	0.997456i	$0.477291\pi$
$108$	9104.03	+	6614.47i	0.780524	+	0.567084i
$109$		−	6056.07i		−	0.509728i	−0.966977	−	0.254864i	$-0.917969\pi$
$109$		−	6056.07i		−	0.509728i	0.966977	−	0.254864i	$-0.0820306\pi$
$110$	1028.58	−	3685.52i	0.0850064	−	0.304588i
$111$	6364.31			0.516541
$112$	2983.48	−	4106.41i	0.237841	−	0.327360i
$113$	2258.58	−	6951.20i	0.176880	−	0.544381i	−0.822834	−	0.568281i	$-0.807608\pi$
$113$	2258.58	−	6951.20i	0.176880	−	0.544381i	0.999714	+	0.0239005i	$0.00760850\pi$
$114$	111.450	+	343.007i	0.00857569	+	0.0263933i
$115$	−4282.25	+	3111.24i	−0.323800	+	0.235254i
$116$	6491.40	+	8934.64i	0.482417	+	0.663989i
$117$	30000.1	−	9747.63i	2.19155	−	0.712077i
$118$	−1898.40	−	616.828i	−0.136340	−	0.0442997i
$119$	−21764.7	−	15813.0i	−1.53695	−	1.11666i
$120$			4006.55i			0.278232i
$121$	12525.1	+	7581.68i	0.855478	+	0.517839i
$122$	−1628.23			−0.109395
$123$	−28110.9	+	38691.3i	−1.85808	+	2.55742i
$124$	−4101.42	+	12622.9i	−0.266741	+	0.820946i
$125$	431.864	+	1329.14i	0.0276393	+	0.0850651i
$126$	−30818.6	+	22391.0i	−1.94121	+	1.41037i
$127$	4179.71	+	5752.88i	0.259142	+	0.356679i	0.918687	−	0.394987i	$-0.129251\pi$
$127$	4179.71	+	5752.88i	0.259142	+	0.356679i	−0.659544	+	0.751666i	$0.729251\pi$
$128$	−1377.28	+	447.504i	−0.0840623	+	0.0273135i
$129$	38780.0	+	12600.4i	2.33039	+	0.757189i
$130$	4752.12	+	3452.62i	0.281191	+	0.204297i
$131$		−	4271.99i		−	0.248936i	−0.992224	−	0.124468i	$-0.960278\pi$
$131$		−	4271.99i		−	0.248936i	0.992224	−	0.124468i	$-0.0397224\pi$
$132$	−14766.2	−	4121.04i	−0.847463	−	0.236515i
$133$	−638.551			−0.0360987
$134$	3301.08	−	4543.55i	0.183843	−	0.253038i
$135$	4859.86	−	14957.1i	0.266659	−	0.820691i
$136$	2371.86	+	7299.83i	0.128236	+	0.394671i
$137$	4256.22	−	3092.33i	0.226769	−	0.164757i	−0.468600	−	0.883411i	$-0.655241\pi$
$137$	4256.22	−	3092.33i	0.226769	−	0.164757i	0.695368	+	0.718654i	$0.255241\pi$
$138$	12465.3	+	17157.0i	0.654554	+	0.900916i
$139$	−7985.47	+	2594.64i	−0.413305	+	0.134291i	−0.508286	−	0.861188i	$-0.669721\pi$
$139$	−7985.47	+	2594.64i	−0.413305	+	0.134291i	0.0949814	+	0.995479i	$0.469721\pi$
$140$	−6746.45	−	2192.06i	−0.344207	−	0.111840i
$141$	29245.7	+	21248.2i	1.47104	+	1.06877i
$142$		−	5981.26i		−	0.296631i
$143$	−17612.6	+	13962.7i	−0.861295	+	0.682808i
$144$	10868.4			0.524133
$145$	9072.00	−	12486.5i	0.431487	−	0.593890i
$146$	−942.518	+	2900.77i	−0.0442164	+	0.136084i
$147$	−19032.5	−	58576.1i	−0.880769	−	2.71073i
$148$	2600.87	−	1889.64i	0.118739	−	0.0862693i
$149$	−9698.99	−	13349.5i	−0.436872	−	0.601302i	0.532642	−	0.846341i	$-0.321199\pi$
$149$	−9698.99	−	13349.5i	−0.436872	−	0.601302i	−0.969513	+	0.245039i	$0.921199\pi$
$150$	5325.27	−	1730.28i	0.236679	−	0.0769015i
$151$	−6137.80	−	1994.29i	−0.269190	−	0.0874651i	0.171312	−	0.985217i	$-0.445199\pi$
$151$	−6137.80	−	1994.29i	−0.269190	−	0.0874651i	−0.440502	+	0.897752i	$0.645199\pi$
$152$	147.389	+	107.084i	0.00637935	+	0.00463487i
$153$		−	57604.6i		−	2.46079i
$154$	15018.1	−	22609.5i	0.633248	−	0.953342i
$155$	18548.8			0.772064
$156$	13833.1	−	19039.6i	0.568421	−	0.782364i
$157$	2488.58	−	7659.06i	0.100961	−	0.310725i	−0.887801	−	0.460228i	$-0.847768\pi$
$157$	2488.58	−	7659.06i	0.100961	−	0.310725i	0.988761	+	0.149504i	$0.0477675\pi$
$158$	3401.76	+	10469.5i	0.136267	+	0.419386i
$159$	−41937.9	+	30469.7i	−1.65887	+	1.20524i
$160$	1189.59	+	1637.34i	0.0464685	+	0.0639584i
$161$	−35710.0	+	11602.9i	−1.37765	+	0.447625i
$162$	−22924.5	−	7448.63i	−0.873515	−	0.283822i
$163$	−24463.6	−	17773.9i	−0.920758	−	0.668970i	0.0229546	−	0.999737i	$-0.492693\pi$
$163$	−24463.6	−	17773.9i	−0.920758	−	0.668970i	−0.943713	+	0.330767i	$0.892693\pi$
$164$			24158.2i			0.898209i
$165$	899.541	+	21406.1i	0.0330410	+	0.786266i
$166$	25703.1			0.932758
$167$	−19175.6	+	26392.9i	−0.687567	+	0.946355i	−0.999994	−	0.00358666i	$-0.998858\pi$
$167$	−19175.6	+	26392.9i	−0.687567	+	0.946355i	0.312426	+	0.949942i	$0.398858\pi$
$168$	−8782.57	+	27030.0i	−0.311174	+	0.957695i
$169$	−1836.27	−	5651.45i	−0.0642928	−	0.197873i
$170$	8678.18	−	6305.07i	0.300283	−	0.218168i
$171$	−803.667	−	1106.15i	−0.0274842	−	0.0378288i
$172$	19589.2	−	6364.93i	0.662157	−	0.215148i
$173$	20432.8	+	6639.01i	0.682709	+	0.221825i	0.629781	−	0.776773i	$-0.283145\pi$
$173$	20432.8	+	6639.01i	0.682709	+	0.221825i	0.0529278	+	0.998598i	$0.483145\pi$
$174$	−50027.9	−	36347.4i	−1.65240	−	1.20054i
$175$			9913.66i			0.323711i
$176$	−7258.01	+	2700.14i	−0.234311	+	0.0871688i
$177$	11176.8			0.356756
$178$	986.042	−	1357.17i	0.0311211	−	0.0428346i
$179$	−6223.61	+	19154.3i	−0.194239	+	0.597806i	0.805746	+	0.592262i	$0.201765\pi$
$179$	−6223.61	+	19154.3i	−0.194239	+	0.597806i	−0.999985	+	0.00554457i	$0.998235\pi$
$180$	−4693.68	−	14445.7i	−0.144867	−	0.445854i
$181$	−29614.9	+	21516.5i	−0.903967	+	0.656771i	−0.939482	−	0.342598i	$-0.888693\pi$
$181$	−29614.9	+	21516.5i	−0.903967	+	0.656771i	0.0355146	+	0.999369i	$0.488693\pi$
$182$	24491.7	+	33709.9i	0.739393	+	1.01769i
$183$	8670.79	−	2817.31i	0.258914	−	0.0841264i
$184$	10188.3	+	3310.37i	0.300930	+	0.0977780i
$185$	−3634.83	−	2640.86i	−0.106204	−	0.0771616i
$186$		−	74316.7i		−	2.14813i
$187$	14311.3	+	38468.8i	0.409255	+	1.10008i
$188$	18260.5			0.516652
$189$	65573.6	−	90254.3i	1.83572	−	2.52665i
$190$	78.6780	−	242.146i	0.00217945	−	0.00670765i
$191$	9645.48	+	29685.7i	0.264397	+	0.813731i	0.991832	+	0.127554i	$0.0407126\pi$
$191$	9645.48	+	29685.7i	0.264397	+	0.813731i	−0.727434	+	0.686177i	$0.759287\pi$
$192$	6560.06	−	4766.16i	0.177953	−	0.129290i
$193$	−8084.08	−	11126.8i	−0.217028	−	0.298713i	0.686597	−	0.727039i	$-0.259104\pi$
$193$	−8084.08	−	11126.8i	−0.217028	−	0.298713i	−0.903625	+	0.428325i	$0.859104\pi$
$194$	262.733	−	85.3673i	0.00698091	−	0.00226823i
$195$	−31280.4	−	10163.6i	−0.822626	−	0.267287i
$196$	−25169.9	−	18287.0i	−0.655194	−	0.476026i
$197$			6804.30i			0.175328i	0.996150	+	0.0876639i	$0.0279402\pi$
$197$			6804.30i			0.175328i	−0.996150	+	0.0876639i	$0.972060\pi$
$198$	58067.6	−	2440.15i	1.48116	−	0.0622425i
$199$	42627.8			1.07643			0.538216	−	0.842807i	$-0.319099\pi$
$199$	42627.8			1.07643			0.538216	+	0.842807i	$0.319099\pi$
$200$	1662.51	−	2288.25i	0.0415627	−	0.0572061i
$201$	−9717.51	+	29907.4i	−0.240527	+	0.740265i
$202$	5723.61	+	17615.5i	0.140271	+	0.431709i
$203$	88575.0	−	64353.5i	2.14941	−	1.56164i
$204$	−25261.6	−	34769.5i	−0.607015	−	0.835485i
$205$	32109.7	−	10433.1i	0.764062	−	0.248259i
$206$	−40391.0	−	13123.8i	−0.951810	−	0.309262i
$207$	−65043.4	−	47256.8i	−1.51797	−	1.10287i
$208$		−	11888.0i		−	0.274779i
$209$	811.507	+	539.035i	0.0185780	+	0.0123403i
$210$	39719.6			0.900670
$211$	34454.8	−	47422.9i	0.773899	−	1.06518i	−0.222030	−	0.975040i	$-0.571268\pi$
$211$	34454.8	−	47422.9i	0.773899	−	1.06518i	0.995929	−	0.0901411i	$-0.0287318\pi$
$212$	−8091.72	+	24903.8i	−0.180040	+	0.554106i
$213$	10349.3	+	31851.8i	0.228113	+	0.702061i
$214$	−19702.3	+	14314.6i	−0.430219	+	0.312572i
$215$	−16919.8	−	23288.1i	−0.366031	−	0.503799i
$216$	−30271.0	+	9835.66i	−0.648813	+	0.210812i
$217$	125139.	+	40660.1i	2.65750	+	0.863473i
$218$	13857.8	+	10068.3i	0.291595	+	0.211856i
$219$		−	17078.2i		−	0.356085i
$220$	6723.35	+	8480.84i	0.138912	+	0.175224i
$221$	−63008.8			−1.29008
$222$	−10580.7	+	14563.1i	−0.214689	+	0.295493i
$223$	−5698.33	+	17537.7i	−0.114588	+	0.352665i	−0.991861	−	0.127327i	$-0.959360\pi$
$223$	−5698.33	+	17537.7i	−0.114588	+	0.352665i	0.877273	+	0.479992i	$0.159360\pi$
$224$	4436.41	+	13653.9i	0.0884169	+	0.272119i
$225$	−17173.3	+	12477.1i	−0.339226	+	0.246462i
$226$	12151.1	+	16724.6i	0.237903	+	0.327446i
$227$	6106.78	−	1984.21i	0.118511	−	0.0385067i	−0.249161	−	0.968462i	$-0.580155\pi$
$227$	6106.78	−	1984.21i	0.118511	−	0.0385067i	0.367672	+	0.929955i	$0.380155\pi$
$228$	−970.170	−	315.227i	−0.0186628	−	0.00606393i
$229$	82077.4	+	59632.7i	1.56514	+	1.13714i	0.931633	+	0.363401i	$0.118384\pi$
$229$	82077.4	+	59632.7i	1.56514	+	1.13714i	0.633505	+	0.773739i	$0.281616\pi$
$230$		−	14971.3i		−	0.283011i
$231$	−40854.6	+	146387.i	−0.765627	+	2.74333i
$232$	−31236.7			−0.580348
$233$	−35041.2	+	48230.0i	−0.645456	+	0.888394i	−0.998892	−	0.0470645i	$-0.985013\pi$
$233$	−35041.2	+	48230.0i	−0.645456	+	0.888394i	0.353436	+	0.935459i	$0.385013\pi$
$234$	−27570.4	+	84853.1i	−0.503515	+	1.54966i
$235$	−7886.08	−	24270.8i	−0.142799	−	0.439490i
$236$	4567.56	−	3318.53i	0.0820088	−	0.0595829i
$237$	−36230.6	−	49867.1i	−0.645028	−	0.887805i
$238$	72368.0	−	23513.8i	1.27759	−	0.415115i
$239$	−99182.8	−	32226.5i	−1.73636	−	0.564179i	−0.742019	−	0.670379i	$-0.766132\pi$
$239$	−99182.8	−	32226.5i	−1.73636	−	0.564179i	−0.994345	+	0.106200i	$0.966132\pi$
$240$	−9167.96	−	6660.91i	−0.159166	−	0.115641i
$241$		−	51292.2i		−	0.883116i	−0.897233	−	0.441558i	$-0.854426\pi$
$241$		−	51292.2i		−	0.883116i	0.897233	−	0.441558i	$-0.145574\pi$
$242$	−38171.7	+	16055.8i	−0.651795	+	0.274158i
$243$	21028.9			0.356127
$244$	2706.95	−	3725.80i	0.0454675	−	0.0625806i
$245$	−13436.1	+	41351.9i	−0.223841	+	0.688912i
$246$	−41800.6	−	128649.i	−0.690737	−	2.12587i
$247$	−1209.93	+	879.063i	−0.0198319	+	0.0144087i
$248$	−22065.6	−	30370.7i	−0.358766	−	0.493800i
$249$	−136876.	+	44473.6i	−2.20764	+	0.717305i
$250$	−3759.38	−	1221.50i	−0.0601501	−	0.0195440i
$251$	55459.4	+	40293.6i	0.880295	+	0.639572i	0.933329	−	0.359021i	$-0.116889\pi$
$251$	55459.4	+	40293.6i	0.880295	+	0.639572i	−0.0530347	+	0.998593i	$0.516889\pi$
$252$		−	107746.i		−	1.69668i
$253$	55177.0	+	15399.1i	0.862019	+	0.240578i
$254$	−20112.8			−0.311749
$255$	−35304.1	+	48591.9i	−0.542931	+	0.747281i
$256$	1265.73	−	3895.53i	0.0193136	−	0.0594410i
$257$	−23012.1	−	70823.9i	−0.348409	−	1.07229i	−0.959733	−	0.280913i	$-0.909363\pi$
$257$	−23012.1	−	70823.9i	−0.348409	−	1.07229i	0.611324	−	0.791380i	$-0.290637\pi$
$258$	−93304.8	+	67789.9i	−1.40173	+	1.01842i
$259$	−18733.3	−	25784.1i	−0.279264	−	0.384373i
$260$	−15800.9	+	5134.02i	−0.233741	+	0.0759470i
$261$	222958.	+	72443.3i	3.27296	+	1.06345i
$262$	9775.36	+	7102.22i	0.142407	+	0.103464i
$263$		−	29697.8i		−	0.429352i	−0.976685	−	0.214676i	$-0.931130\pi$
$263$		−	29697.8i		−	0.429352i	0.976685	−	0.214676i	$-0.0688696\pi$
$264$	33978.9	−	26937.4i	0.487530	−	0.386499i
$265$	36595.2			0.521113
$266$	1061.60	−	1461.16i	0.0150036	−	0.0206507i
$267$	−2902.65	+	8933.43i	−0.0407166	+	0.125313i
$268$	4908.68	+	15107.4i	0.0683432	+	0.210339i
$269$	76848.3	−	55833.6i	1.06201	−	0.771597i	0.0875530	−	0.996160i	$-0.472095\pi$
$269$	76848.3	−	55833.6i	1.06201	−	0.771597i	0.974460	+	0.224562i	$0.0720953\pi$
$270$	26146.0	+	35986.8i	0.358655	+	0.493647i
$271$	−27600.9	+	8968.09i	−0.375825	+	0.122113i	−0.490838	−	0.871251i	$-0.663309\pi$
$271$	−27600.9	+	8968.09i	−0.375825	+	0.122113i	0.115013	+	0.993364i	$0.463309\pi$
$272$	−20647.0	−	6708.63i	−0.279074	−	0.0906767i
$273$	−188752.	−	137137.i	−2.53260	−	1.84004i
$274$			14880.3i			0.198203i
$275$	8368.66	−	12598.9i	0.110660	−	0.166596i
$276$	−59983.2			−0.787429
$277$	−36853.9	+	50725.1i	−0.480313	+	0.661094i	−0.978565	−	0.205938i	$-0.933975\pi$
$277$	−36853.9	+	50725.1i	−0.480313	+	0.661094i	0.498252	+	0.867032i	$0.333975\pi$
$278$	7338.74	−	22586.3i	0.0949580	−	0.292251i
$279$	87062.3	+	267950.i	1.11846	+	3.44228i
$280$	16232.0	−	11793.2i	0.207041	−	0.150424i
$281$	11738.0	+	16156.0i	0.148656	+	0.204608i	0.876851	−	0.480763i	$-0.159640\pi$
$281$	11738.0	+	16156.0i	0.148656	+	0.204608i	−0.728194	+	0.685371i	$0.759640\pi$
$282$	−97242.3	+	31595.9i	−1.22280	+	0.397313i
$283$	−56112.1	−	18231.9i	−0.700622	−	0.227646i	−0.0630203	−	0.998012i	$-0.520073\pi$
$283$	−56112.1	−	18231.9i	−0.700622	−	0.227646i	−0.637601	+	0.770366i	$0.720073\pi$
$284$	13686.6	+	9943.89i	0.169691	+	0.123288i
$285$			1425.63i			0.0175516i
$286$	−2669.08	−	63515.2i	−0.0326309	−	0.776507i
$287$	239497.			2.90761
$288$	−18068.8	+	24869.6i	−0.217844	+	0.299836i
$289$	−9747.56	+	29999.9i	−0.116708	+	0.359190i
$290$	13490.0	+	41517.9i	0.160404	+	0.493674i
$291$	−1251.42	+	909.207i	−0.0147780	+	0.0107368i
$292$	−5070.73	−	6979.27i	−0.0594710	−	0.0818548i
$293$	−139410.	+	45297.1i	−1.62390	+	0.527636i	−0.972857	−	0.231407i	$-0.925667\pi$
$293$	−139410.	+	45297.1i	−1.62390	+	0.527636i	−0.651041	+	0.759043i	$0.725667\pi$
$294$	165678.	+	53832.2i	1.91678	+	0.622798i
$295$	−6383.37	−	4637.79i	−0.0733509	−	0.0532926i
$296$			9092.97i			0.103782i
$297$	−159523.	+	59346.1i	−1.80847	+	0.672790i
$298$	46671.6			0.525557
$299$	−51690.2	+	71145.5i	−0.578184	+	0.795802i
$300$	−4893.98	+	15062.1i	−0.0543776	+	0.167357i
$301$	−63099.8	−	194201.i	−0.696458	−	2.14348i
$302$	14767.6	−	10729.3i	0.161918	−	0.117640i
$303$	−60959.5	−	83903.6i	−0.663982	−	0.913893i
$304$	−490.069	+	159.233i	−0.00530286	+	0.00172300i
$305$	−6121.15	−	1988.88i	−0.0658012	−	0.0213801i
$306$	131814.	+	95768.2i	1.40772	+	1.02277i
$307$			92349.8i			0.979849i	0.871765	+	0.489925i	$0.162976\pi$
$307$			92349.8i			0.979849i	−0.871765	+	0.489925i	$0.837024\pi$
$308$	26768.3	+	71953.5i	0.282175	+	0.758491i
$309$	237801.			2.49056
$310$	−30837.6	+	42444.3i	−0.320890	+	0.441668i
$311$	−40126.6	+	123497.i	−0.414870	+	1.27684i	0.497497	+	0.867465i	$0.334252\pi$
$311$	−40126.6	+	123497.i	−0.414870	+	1.27684i	−0.912367	+	0.409373i	$0.865748\pi$
$312$	20569.7	+	63307.0i	0.211309	+	0.650343i
$313$	48991.0	−	35594.0i	0.500066	−	0.363319i	−0.308976	−	0.951070i	$-0.599986\pi$
$313$	48991.0	−	35594.0i	0.500066	−	0.363319i	0.809042	+	0.587751i	$0.199986\pi$
$314$	13388.5	+	18427.7i	0.135792	+	0.186901i
$315$	−143209.	+	46531.6i	−1.44328	+	0.468950i
$316$	−29612.3	−	9621.63i	−0.296550	−	0.0963551i
$317$	49792.9	+	36176.7i	0.495506	+	0.360006i	0.807298	−	0.590144i	$-0.200929\pi$
$317$	49792.9	+	36176.7i	0.495506	+	0.360006i	−0.311792	+	0.950150i	$0.600929\pi$
$318$		−	146620.i		−	1.44991i
$319$	−166891.	+	7013.19i	−1.64002	+	0.0689182i
$320$	−5724.33			−0.0559017
$321$	80151.8	−	110319.i	0.777863	−	1.07064i
$322$	32817.9	−	101003.i	0.316519	−	0.974144i
$323$	843.965	+	2597.46i	0.00808946	+	0.0248968i
$324$	55156.5	−	40073.6i	0.525420	−	0.381740i
$325$	13647.7	+	18784.4i	0.129209	+	0.177841i
$326$	81341.9	−	26429.6i	0.765384	−	0.248688i
$327$	−91217.4	−	29638.3i	−0.853065	−	0.277178i
$328$	−55280.0	−	40163.2i	−0.513831	−	0.373320i
$329$		−	181029.i		−	1.67246i
$330$	−50477.9	−	33529.4i	−0.463525	−	0.307892i
$331$	161058.			1.47003			0.735013	−	0.678053i	$-0.237176\pi$
$331$	161058.			1.47003			0.735013	+	0.678053i	$0.237176\pi$
$332$	−42731.6	+	58814.9i	−0.387679	+	0.533595i
$333$	21088.2	−	64902.8i	0.190174	−	0.585295i
$334$	−28513.9	−	87756.8i	−0.255602	−	0.786662i
$335$	17960.0	−	13048.7i	0.160035	−	0.116272i
$336$	−47250.1	−	65034.2i	−0.418528	−	0.576054i
$337$	145390.	−	47240.1i	1.28019	−	0.415959i	0.411544	−	0.911390i	$-0.364990\pi$
$337$	145390.	−	47240.1i	1.28019	−	0.415959i	0.868648	+	0.495431i	$0.164990\pi$
$338$	15984.7	+	5193.75i	0.139917	+	0.0454619i
$339$	−93646.4	−	68038.1i	−0.814877	−	0.592043i
$340$			30340.0i			0.262457i
$341$	−124710.	−	157310.i	−1.07249	−	1.35284i
$342$	3867.25			0.0330636
$343$	−69364.3	+	95471.8i	−0.589587	+	0.811497i
$344$	−18002.7	+	55406.7i	−0.152132	+	0.468215i
$345$	25904.6	+	79726.2i	0.217640	+	0.669827i
$346$	−49161.4	+	35717.8i	−0.410650	+	0.298355i
$347$	77459.2	+	106613.i	0.643301	+	0.885427i	0.998786	−	0.0492544i	$-0.0156845\pi$
$347$	77459.2	+	106613.i	0.643301	+	0.885427i	−0.355486	+	0.934682i	$0.615685\pi$
$348$	166344.	−	54048.3i	1.37356	−	0.446297i
$349$	−85603.5	−	27814.3i	−0.702814	−	0.228358i	−0.0642580	−	0.997933i	$-0.520468\pi$
$349$	−85603.5	−	27814.3i	−0.702814	−	0.228358i	−0.638556	+	0.769575i	$0.720468\pi$
$350$	−22684.9	−	16481.5i	−0.185183	−	0.134543i
$351$		−	261286.i		−	2.12081i
$352$	5887.92	−	21097.1i	0.0475200	−	0.170270i
$353$	−136929.			−1.09887			−0.549436	−	0.835536i	$-0.685158\pi$
$353$	−136929.			−1.09887			−0.549436	+	0.835536i	$0.685158\pi$
$354$	−18581.5	+	25575.3i	−0.148277	+	0.204086i
$355$	7306.09	−	22485.8i	0.0579733	−	0.178424i
$356$	1466.24	+	4512.61i	0.0115692	+	0.0356064i
$357$	−344694.	+	250435.i	−2.70456	+	1.96498i
$358$	−33483.0	−	46085.4i	−0.261251	−	0.359581i
$359$	182984.	−	59455.2i	1.41979	−	0.461319i	0.504257	−	0.863554i	$-0.331766\pi$
$359$	182984.	−	59455.2i	1.41979	−	0.461319i	0.915537	+	0.402235i	$0.131766\pi$
$360$	40858.5	+	13275.7i	0.315266	+	0.102436i
$361$	−105379.	−	76562.7i	−0.808615	−	0.587493i
$362$		−	103537.i		−	0.790096i
$363$	175494.	−	151550.i	1.33183	−	1.15011i
$364$	−117854.			−0.889491
$365$	−7086.57	+	9753.82i	−0.0531925	+	0.0732131i
$366$	−7968.55	+	24524.7i	−0.0594864	+	0.183080i
$367$	−31877.4	−	98108.5i	−0.236674	−	0.728407i	−0.996895	−	0.0787429i	$-0.974909\pi$
$367$	−31877.4	−	98108.5i	−0.236674	−	0.728407i	0.760221	−	0.649664i	$-0.225091\pi$
$368$	−24513.0	+	17809.8i	−0.181010	+	0.131511i
$369$	301426.	+	414877.i	2.21374	+	3.04696i
$370$	12085.9	−	3926.93i	0.0882823	−	0.0286847i
$371$	246888.	+	80218.6i	1.79371	+	0.582811i
$372$	170055.	+	123552.i	1.22886	+	0.892821i
$373$		−	158342.i		−	1.13809i	−0.822305	−	0.569047i	$-0.807312\pi$
$373$		−	158342.i		−	1.13809i	0.822305	−	0.569047i	$-0.192688\pi$
$374$	−111819.	−	31207.1i	−0.799413	−	0.223105i
$375$	22133.3			0.157392
$376$	−30358.3	+	41784.6i	−0.214734	+	0.295557i
$377$	79239.6	−	243874.i	0.557519	−	1.71587i
$378$	97507.4	+	300097.i	0.682424	+	2.10028i
$379$	−82118.6	+	59662.6i	−0.571693	+	0.415359i	−0.835720	−	0.549156i	$-0.814949\pi$
$379$	−82118.6	+	59662.6i	−0.571693	+	0.415359i	0.264027	+	0.964515i	$0.414949\pi$
$380$	423.287	+	582.604i	0.00293135	+	0.00403466i
$381$	107106.	−	34800.9i	0.737843	−	0.239740i
$382$	−83963.9	−	27281.5i	−0.575395	−	0.186957i
$383$	−121897.	−	88563.2i	−0.830988	−	0.603748i	0.0888508	−	0.996045i	$-0.471681\pi$
$383$	−121897.	−	88563.2i	−0.830988	−	0.603748i	−0.919839	+	0.392297i	$0.871681\pi$
$384$			22934.8i			0.155537i
$385$	84076.2	−	66653.0i	0.567220	−	0.449675i
$386$	38900.6			0.261085
$387$	256996.	−	353725.i	1.71595	−	2.36180i
$388$	−241.455	+	743.122i	−0.00160388	+	0.00493625i
$389$	−27838.1	−	85676.7i	−0.183967	−	0.566192i	0.815962	−	0.578105i	$-0.196208\pi$
$389$	−27838.1	−	85676.7i	−0.183967	−	0.566192i	−0.999929	+	0.0119134i	$0.996208\pi$
$390$	75260.7	−	54680.1i	0.494810	−	0.359501i
$391$	94395.1	+	129924.i	0.617442	+	0.849835i
$392$	83690.4	−	27192.7i	0.544632	−	0.176962i
$393$	−64345.3	−	20907.1i	−0.416612	−	0.135365i
$394$	−15569.9	−	11312.2i	−0.100298	−	0.0728710i
$395$			43514.2i			0.278893i
$396$	−90954.1	+	136930.i	−0.580005	+	0.873186i
$397$	−267884.			−1.69968			−0.849839	−	0.527043i	$-0.823301\pi$
$397$	−267884.			−1.69968			−0.849839	+	0.527043i	$0.823301\pi$
$398$	−70869.0	+	97542.8i	−0.447394	+	0.615785i
$399$	−3125.06	+	9617.94i	−0.0196296	+	0.0604138i
$400$	2472.14	+	7608.45i	0.0154508	+	0.0475528i
$401$	180960.	−	131475.i	1.12537	−	0.817627i	0.140353	−	0.990102i	$-0.455176\pi$
$401$	180960.	−	131475.i	1.12537	−	0.817627i	0.985014	+	0.172475i	$0.0551763\pi$
$402$	−52280.1	−	71957.4i	−0.323507	−	0.445270i
$403$	293088.	−	95230.1i	1.80463	−	0.586359i
$404$	−49824.0	−	16188.8i	−0.305264	−	0.0991864i
$405$	−77083.6	−	56004.5i	−0.469950	−	0.341439i
$406$			309670.i			1.87865i
$407$	2041.54	+	48581.7i	0.0123245	+	0.293281i
$408$	121559.			0.730241
$409$	21795.0	−	29998.3i	0.130290	−	0.179329i	−0.738888	−	0.673828i	$-0.764649\pi$
$409$	21795.0	−	29998.3i	0.130290	−	0.179329i	0.869178	+	0.494500i	$0.164649\pi$
$410$	−29509.2	+	90820.0i	−0.175546	+	0.540274i
$411$	−25747.1	−	79241.6i	−0.152421	−	0.469104i
$412$	97180.9	−	70606.0i	0.572514	−	0.415956i
$413$	−32898.8	−	45281.3i	−0.192877	−	0.265472i
$414$	216270.	−	70270.5i	1.26182	−	0.409989i
$415$	96627.6	+	31396.2i	0.561055	+	0.182298i
$416$	27202.8	+	19764.0i	0.157190	+	0.114206i
$417$			132976.i			0.764719i
$418$	−2582.58	+	960.777i	−0.0147809	+	0.00549883i
$419$	−254975.			−1.45234			−0.726171	−	0.687514i	$-0.758702\pi$
$419$	−254975.			−1.45234			−0.726171	+	0.687514i	$0.758702\pi$
$420$	−66034.1	+	90888.1i	−0.374343	+	0.515239i
$421$	−105341.	+	324206.i	−0.594337	+	1.82918i	−0.0363359	+	0.999340i	$0.511569\pi$
$421$	−105341.	+	324206.i	−0.594337	+	1.82918i	−0.558001	+	0.829840i	$0.688431\pi$
$422$	51234.0	+	157682.i	0.287696	+	0.885436i
$423$	313594.	−	227839.i	1.75262	−	1.27335i
$424$	−43533.4	−	59918.5i	−0.242153	−	0.333296i
$425$	40326.2	−	13102.8i	0.223259	−	0.0725414i
$426$	−90090.5	−	29272.2i	−0.496432	−	0.161301i
$427$	−36936.3	−	26835.8i	−0.202581	−	0.147183i
$428$		−	68881.7i		−	0.376025i
$429$	124113.	+	333617.i	0.674376	+	1.81273i
$430$	81418.2			0.440336
$431$	51918.6	−	71459.8i	0.279491	−	0.384687i	−0.646074	−	0.763275i	$-0.723590\pi$
$431$	51918.6	−	71459.8i	0.279491	−	0.384687i	0.925565	+	0.378588i	$0.123590\pi$
$432$	27819.4	−	85619.4i	0.149067	−	0.458780i
$433$	87917.2	+	270581.i	0.468920	+	1.44319i	0.853985	+	0.520297i	$0.174179\pi$
$433$	87917.2	+	270581.i	0.468920	+	1.44319i	−0.385066	+	0.922889i	$0.625821\pi$
$434$	−301084.	+	218751.i	−1.59849	+	1.16137i
$435$	−143676.	−	197753.i	−0.759285	−	1.04507i
$436$	−46077.3	+	14971.4i	−0.242390	+	0.0787572i
$437$	3625.24	+	1177.91i	0.0189834	+	0.00616808i
$438$	39079.1	+	28392.7i	0.203703	+	0.147999i
$439$			145989.i			0.757517i	0.925496	+	0.378758i	$0.123649\pi$
$439$			145989.i			0.757517i	−0.925496	+	0.378758i	$0.876351\pi$
$440$	−30583.9	+	1285.22i	−0.157974	+	0.00663851i
$441$	−660420.			−3.39581
$442$	104753.	−	144180.i	0.536192	−	0.738005i
$443$	1141.72	−	3513.84i	0.00581769	−	0.0179050i	−0.948106	−	0.317956i	$-0.897004\pi$
$443$	1141.72	−	3513.84i	0.00581769	−	0.0179050i	0.953923	+	0.300051i	$0.0970036\pi$
$444$	−15733.4	−	48422.5i	−0.0798100	−	0.245630i
$445$	5364.69	−	3897.67i	0.0270910	−	0.0196827i
$446$	−30657.0	−	42195.7i	−0.154120	−	0.212128i
$447$	−248539.	+	80755.2i	−1.24388	+	0.404162i
$448$	−38619.0	−	12548.1i	−0.192417	−	0.0625202i
$449$	−134699.	−	97864.7i	−0.668147	−	0.485437i	0.201257	−	0.979538i	$-0.435497\pi$
$449$	−134699.	−	97864.7i	−0.668147	−	0.485437i	−0.869404	+	0.494101i	$0.835497\pi$
$450$		−	60040.1i		−	0.296494i
$451$	−304366.	−	202172.i	−1.49638	−	0.993958i
$452$	−58471.4			−0.286198
$453$	−60076.6	+	82688.3i	−0.292758	+	0.402947i
$454$	−5612.20	+	17272.6i	−0.0272284	+	0.0838003i
$455$	50897.0	+	156645.i	0.245849	+	0.756646i
$456$	2334.23	−	1695.92i	0.0112257	−	0.00815596i
$457$	90738.0	+	124890.i	0.434467	+	0.597992i	0.968971	−	0.247173i	$-0.0795017\pi$
$457$	90738.0	+	124890.i	0.434467	+	0.597992i	−0.534504	+	0.845166i	$0.679502\pi$
$458$	−272909.	+	88673.4i	−1.30103	+	0.422729i
$459$	−453799.	−	147448.i	−2.15396	−	0.699865i
$460$	34258.0	+	24889.9i	0.161900	+	0.117627i
$461$			53007.3i			0.249421i	0.992193	+	0.124711i	$0.0398003\pi$
$461$			53007.3i			0.249421i	−0.992193	+	0.124711i	$0.960200\pi$
$462$	−267048.	−	336855.i	−1.25114	−	1.57819i
$463$	176639.			0.823995			0.411998	−	0.911185i	$-0.364831\pi$
$463$	176639.			0.823995			0.411998	+	0.911185i	$0.364831\pi$
$464$	51931.2	−	71477.1i	0.241208	−	0.331995i
$465$	90777.7	−	279385.i	0.419830	−	1.29210i
$466$	−52106.0	−	160366.i	−0.239947	−	0.738481i
$467$	174511.	−	126789.i	0.800181	−	0.581366i	−0.110786	−	0.993844i	$-0.535337\pi$
$467$	174511.	−	126789.i	0.800181	−	0.581366i	0.910967	+	0.412479i	$0.135337\pi$
$468$	−148329.	−	204157.i	−0.677226	−	0.932121i
$469$	149769.	−	48663.0i	0.680891	−	0.221235i
$470$	68648.3	+	22305.2i	0.310767	+	0.100974i
$471$	−103183.	−	74966.6i	−0.465120	−	0.337929i
$472$			15968.8i			0.0716784i
$473$	−83744.9	+	300068.i	−0.374314	+	1.34121i
$474$	174342.			0.775970
$475$	591.561	−	814.214i	0.00262188	−	0.00360871i
$476$	−66507.1	+	204688.i	−0.293531	+	0.903395i
$477$	171766.	+	528641.i	0.754919	+	2.32340i
$478$	238634.	−	173378.i	1.04442	−	0.758819i
$479$	193242.	+	265975.i	0.842231	+	1.15923i	0.985522	+	0.169550i	$0.0542315\pi$
$479$	193242.	+	265975.i	0.842231	+	1.15923i	−0.143291	+	0.989681i	$0.545768\pi$
$480$	30483.6	−	9904.73i	0.132307	−	0.0429893i
$481$	−70991.7	−	23066.6i	−0.306844	−	0.0996996i
$482$	117369.	+	85273.7i	0.505196	+	0.367047i
$483$			594653.i			2.54900i
$484$	26721.2	−	114039.i	0.114068	−	0.486815i
$485$	1091.99			0.00464232
$486$	−34960.8	+	48119.4i	−0.148016	+	0.203727i
$487$	−69972.0	+	215352.i	−0.295030	+	0.908010i	0.688181	+	0.725539i	$0.258409\pi$
$487$	−69972.0	+	215352.i	−0.295030	+	0.908010i	−0.983211	+	0.182471i	$0.941591\pi$
$488$	4025.22	+	12388.3i	0.0169025	+	0.0520204i
$489$	−387437.	+	281489.i	−1.62025	+	1.17718i
$490$	−72285.8	−	99492.9i	−0.301065	−	0.414381i
$491$	−274974.	+	89344.6i	−1.14059	+	0.370600i	−0.817591	−	0.575799i	$-0.804691\pi$
$491$	−274974.	+	89344.6i	−1.14059	+	0.370600i	−0.322999	+	0.946399i	$0.604691\pi$
$492$	363875.	+	118230.i	1.50322	+	0.488425i
$493$	−378842.	−	275245.i	−1.55871	−	1.13247i
$494$		−	4230.06i		−	0.0173337i
$495$	221279.	+	61755.9i	0.903086	+	0.252039i
$496$	106180.			0.431597
$497$	98580.4	−	135684.i	0.399096	−	0.549309i
$498$	125790.	−	387143.i	0.507211	−	1.56104i
$499$	−18146.5	−	55849.2i	−0.0728773	−	0.224293i	0.907983	−	0.419008i	$-0.137622\pi$
$499$	−18146.5	−	55849.2i	−0.0728773	−	0.224293i	−0.980860	+	0.194714i	$0.937622\pi$
$500$	9045.08	−	6571.64i	0.0361803	−	0.0262866i
$501$	303689.	+	417991.i	1.20991	+	1.66530i
$502$	−184404.	+	59916.3i	−0.731748	+	0.237759i
$503$	−241937.	−	78610.2i	−0.956240	−	0.310701i	−0.210991	−	0.977488i	$-0.567669\pi$
$503$	−241937.	−	78610.2i	−0.956240	−	0.310701i	−0.745248	+	0.666787i	$0.767669\pi$
$504$	246549.	+	179128.i	0.970604	+	0.705185i
$505$			73214.6i			0.287088i
$506$	−126969.	+	100657.i	−0.495904	+	0.393137i
$507$	−94109.5			−0.366115
$508$	33437.7	−	46023.0i	0.129571	−	0.178340i
$509$	138608.	−	426592.i	0.534999	−	1.64656i	−0.208652	−	0.977990i	$-0.566908\pi$
$509$	138608.	−	426592.i	0.534999	−	1.64656i	0.743651	−	0.668568i	$-0.233092\pi$
$510$	−52496.9	−	161569.i	−0.201834	−	0.621180i
$511$	−69190.1	+	50269.6i	−0.264973	+	0.192514i
$512$	6809.63	+	9372.65i	0.0259767	+	0.0357538i
$513$	−10771.2	+	3499.77i	−0.0409288	+	0.0132986i
$514$	200320.	+	65088.0i	0.758226	+	0.246363i
$515$	−135814.	−	98674.9i	−0.512072	−	0.372042i
$516$		−	326206.i		−	1.22516i
$517$	−152816.	+	230062.i	−0.571727	+	0.860723i
$518$	90144.7			0.335955
$519$	199995.	−	275270.i	0.742481	−	1.02194i
$520$	14521.2	−	44691.7i	0.0537027	−	0.165280i
$521$	−26747.6	−	82320.5i	−0.0985391	−	0.303272i	0.889621	−	0.456700i	$-0.150969\pi$
$521$	−26747.6	−	82320.5i	−0.0985391	−	0.303272i	−0.988160	+	0.153428i	$0.950969\pi$
$522$	−536437.	+	389744.i	−1.96869	+	1.43034i
$523$	174188.	+	239749.i	0.636817	+	0.876503i	0.998441	−	0.0558208i	$-0.0177776\pi$
$523$	174188.	+	239749.i	0.636817	+	0.876503i	−0.361624	+	0.932324i	$0.617778\pi$
$524$	−32503.2	+	10560.9i	−0.118376	+	0.0384627i
$525$	149321.	+	48517.3i	0.541754	+	0.176027i
$526$	67956.0	+	49372.9i	0.245616	+	0.178450i
$527$		−	562772.i		−	2.02634i
$528$	5149.28	+	122536.i	0.0184705	+	0.439536i
$529$	−55701.2			−0.199046
$530$	−60839.7	+	83738.7i	−0.216589	+	0.298109i
$531$	37034.4	−	113980.i	0.131346	−	0.404241i
$532$	1578.58	+	4858.38i	0.00557756	+	0.0171660i
$533$	453798.	−	329704.i	1.59738	−	1.16057i
$534$	−15616.2	−	21493.9i	−0.0547637	−	0.0753758i
$535$	−91553.6	+	29747.6i	−0.319866	+	0.103931i
$536$	−42730.1	−	13883.8i	−0.148732	−	0.0483259i
$537$	258047.	+	187482.i	0.894849	+	0.650146i
$538$			268672.i			0.928233i
$539$	441034.	−	164074.i	1.51808	−	0.564759i
$540$	−125815.			−0.431463
$541$	112033.	−	154200.i	0.382781	−	0.526853i	−0.573537	−	0.819179i	$-0.694429\pi$
$541$	112033.	−	154200.i	0.382781	−	0.526853i	0.956319	+	0.292326i	$0.0944293\pi$
$542$	25365.6	−	78067.3i	0.0863468	−	0.265748i
$543$	179149.	+	551364.i	0.607596	+	1.86999i
$544$	49676.8	−	36092.3i	0.167863	−	0.121960i
$545$	39798.3	+	54777.7i	0.133990	+	0.184421i
$546$	627604.	−	203921.i	2.10524	−	0.684032i
$547$	450105.	+	146248.i	1.50432	+	0.488782i	0.941273	−	0.337645i	$-0.109630\pi$
$547$	450105.	+	146248.i	1.50432	+	0.488782i	0.563043	+	0.826427i	$0.309630\pi$
$548$	−34049.8	−	24738.6i	−0.113384	−	0.0823785i
$549$		−	97759.3i		−	0.324350i
$550$	14916.3	+	40095.2i	0.0493101	+	0.132546i
$551$	−11114.8			−0.0366098
$552$	99722.6	−	137256.i	0.327277	−	0.450458i
$553$	−95385.6	+	293567.i	−0.311912	+	0.959968i
$554$	−54801.5	−	168662.i	−0.178555	−	0.549537i
$555$	−57565.7	+	41823.9i	−0.186886	+	0.135781i
$556$	39482.3	+	54342.7i	0.127718	+	0.175789i
$557$	283002.	−	91952.9i	0.912177	−	0.296384i	0.184923	−	0.982753i	$-0.440796\pi$
$557$	283002.	−	91952.9i	0.912177	−	0.296384i	0.727254	+	0.686369i	$0.240796\pi$
$558$	−757878.	−	246249.i	−2.43406	−	0.790873i
$559$	−386909.	−	281106.i	−1.23818	−	0.899594i
$560$			56749.1i			0.180960i
$561$	649462.	−	27292.1i	2.06361	−	0.0867185i
$562$	−56483.6			−0.178834
$563$	−167187.	+	230113.i	−0.527455	+	0.725980i	−0.986740	−	0.162309i	$-0.948106\pi$
$563$	−167187.	+	230113.i	−0.527455	+	0.725980i	0.459285	+	0.888289i	$0.348106\pi$
$564$	89366.8	−	275043.i	0.280943	−	0.864653i
$565$	25251.7	+	77716.8i	0.0791032	+	0.243455i
$566$	135006.	−	98087.5i	0.421425	−	0.306183i
$567$	−397276.	−	546803.i	−1.23574	−	1.70085i
$568$	−45508.1	+	14786.5i	−0.141056	+	0.0458319i
$569$	−56742.4	−	18436.7i	−0.175260	−	0.0569455i	0.220072	−	0.975484i	$-0.429371\pi$
$569$	−56742.4	−	18436.7i	−0.175260	−	0.0569455i	−0.395333	+	0.918538i	$0.629371\pi$
$570$	−3262.19	−	2370.12i	−0.0100406	−	0.00729492i
$571$			445717.i			1.36706i	0.729923	+	0.683529i	$0.239556\pi$
$571$			445717.i			1.36706i	−0.729923	+	0.683529i	$0.760444\pi$
$572$	149776.	+	99487.0i	0.457772	+	0.304070i
$573$	494335.			1.50561
$574$	−398165.	+	548027.i	−1.20848	+	1.66333i
$575$	18287.4	−	56282.8i	0.0553116	−	0.170232i
$576$	−26868.2	−	82691.8i	−0.0809830	−	0.249240i
$577$	−107665.	+	78223.6i	−0.323389	+	0.234956i	−0.737620	−	0.675216i	$-0.764050\pi$
$577$	−107665.	+	78223.6i	−0.323389	+	0.234956i	0.414231	+	0.910172i	$0.364050\pi$
$578$	−52441.8	−	72179.9i	−0.156972	−	0.216053i
$579$	−207156.	+	67309.2i	−0.617933	+	0.200779i
$580$	−117430.	−	38155.5i	−0.349080	−	0.113423i
$581$	583072.	+	423626.i	1.72731	+	1.25496i
$582$		−	4375.11i		−	0.0129165i
$583$	−246042.	−	310358.i	−0.723889	−	0.913114i
$584$	24400.4			0.0715437
$585$	−207296.	+	285318.i	−0.605729	+	0.833715i
$586$	128119.	−	394311.i	0.373095	−	1.14827i
$587$	−137518.	−	423238.i	−0.399102	−	1.22831i	−0.925720	−	0.378208i	$-0.876540\pi$
$587$	−137518.	−	423238.i	−0.399102	−	1.22831i	0.526618	−	0.850102i	$-0.323460\pi$
$588$	−398623.	+	289616.i	−1.15294	+	0.837661i
$589$	−7851.48	−	10806.6i	−0.0226319	−	0.0311501i
$590$	21224.8	−	6896.35i	0.0609733	−	0.0198114i
$591$	102487.	+	33300.1i	0.293423	+	0.0953391i
$592$	−20807.0	−	15117.1i	−0.0593697	−	0.0431346i
$593$			511499.i			1.45457i	0.686334	+	0.727286i	$0.259219\pi$
$593$			511499.i			1.45457i	−0.686334	+	0.727286i	$0.740781\pi$
$594$	129410.	−	463692.i	0.366771	−	1.31418i
$595$	300781.			0.849604
$596$	−77591.9	+	106796.i	−0.218436	+	0.300651i
$597$	208620.	−	642065.i	0.585338	−	1.80148i
$598$	−76863.0	−	236560.i	−0.214939	−	0.661513i
$599$	487583.	−	354250.i	1.35892	−	0.987315i	0.360410	−	0.932794i	$-0.382637\pi$
$599$	487583.	−	354250.i	1.35892	−	0.987315i	0.998513	−	0.0545208i	$-0.0173631\pi$
$600$	−26329.6	−	36239.6i	−0.0731377	−	0.100665i
$601$	−454526.	+	147685.i	−1.25837	+	0.408871i	−0.860915	−	0.508749i	$-0.830108\pi$
$601$	−454526.	+	147685.i	−1.25837	+	0.408871i	−0.397460	+	0.917620i	$0.630108\pi$
$602$	549284.	+	178473.i	1.51567	+	0.492470i
$603$	272795.	+	198197.i	0.750243	+	0.545083i
$604$			51629.3i			0.141522i
$605$	−163114.	+	13733.2i	−0.445637	+	0.0375200i
$606$	293338.			0.798772
$607$	80389.5	−	110647.i	0.218183	−	0.300304i	−0.685869	−	0.727725i	$-0.740578\pi$
$607$	80389.5	−	110647.i	0.218183	−	0.300304i	0.904053	+	0.427421i	$0.140578\pi$
$608$	450.379	−	1386.13i	0.00121835	−	0.00374969i
$609$	−535817.	−	1.64907e6i	−1.44471	−	4.44637i
$610$	14727.5	−	10700.2i	0.0395795	−	0.0287562i
$611$	−249214.	−	343014.i	−0.667560	−	0.918817i
$612$	−438282.	+	142407.i	−1.17018	+	0.380213i
$613$	110540.	+	35916.6i	0.294170	+	0.0955815i	0.452384	−	0.891823i	$-0.350574\pi$
$613$	110540.	+	35916.6i	0.294170	+	0.0955815i	−0.158214	+	0.987405i	$0.550574\pi$
$614$	−211319.	−	153532.i	−0.560534	−	0.407252i
$615$		−	534700.i		−	1.41371i
$616$	−209150.	−	58370.9i	−0.551183	−	0.153828i
$617$	−626094.			−1.64463			−0.822317	−	0.569030i	$-0.807319\pi$
$617$	−626094.			−1.64463			−0.822317	+	0.569030i	$0.807319\pi$
$618$	−395346.	+	544147.i	−1.03514	+	1.42475i
$619$	−7784.19	+	23957.3i	−0.0203157	+	0.0625253i	−0.960700	−	0.277587i	$-0.910465\pi$
$619$	−7784.19	+	23957.3i	−0.0203157	+	0.0625253i	0.940385	+	0.340113i	$0.110465\pi$
$620$	−45855.2	−	141128.i	−0.119290	−	0.367138i
$621$	−538770.	+	391439.i	−1.39708	+	1.01504i
$622$	−215881.	−	297134.i	−0.557999	−	0.768019i
$623$	44736.5	−	14535.8i	0.115262	−	0.0374509i
$624$	−179059.	−	58179.9i	−0.459862	−	0.149418i
$625$	−12640.9	−	9184.14i	−0.0323607	−	0.0235114i
$626$			171279.i			0.437074i
$627$	12090.5	−	9585.00i	0.0307546	−	0.0243813i
$628$	−64425.7			−0.163358
$629$	−80123.7	+	110281.i	−0.202516	+	0.278739i
$630$	131611.	−	405058.i	0.331598	−	1.02055i
$631$	160364.	+	493548.i	0.402760	+	1.23957i	0.922751	+	0.385397i	$0.125936\pi$
$631$	160364.	+	493548.i	0.402760	+	1.23957i	−0.519990	+	0.854172i	$0.674064\pi$
$632$	71247.4	−	51764.3i	0.178375	−	0.129597i
$633$	−545669.	−	751049.i	−1.36183	−	1.87439i
$634$	−165562.	+	53794.4i	−0.411891	+	0.133832i
$635$	−75611.6	−	24567.7i	−0.187517	−	0.0609280i
$636$	335503.	+	243757.i	0.829435	+	0.602620i
$637$			722378.i			1.78027i
$638$	261409.	−	393546.i	0.642213	−	0.966839i
$639$	359115.			0.879492
$640$	9516.75	−	13098.7i	0.0232343	−	0.0319792i
$641$	−147680.	+	454514.i	−0.359424	+	1.10619i	0.593976	+	0.804483i	$0.297557\pi$
$641$	−147680.	+	454514.i	−0.359424	+	1.10619i	−0.953400	+	0.301710i	$0.902443\pi$
$642$	119185.	+	366814.i	0.289169	+	0.889970i
$643$	−386078.	+	280502.i	−0.933798	+	0.678444i	−0.946920	−	0.321470i	$-0.895823\pi$
$643$	−386078.	+	280502.i	−0.933798	+	0.678444i	0.0131219	+	0.999914i	$0.495823\pi$
$644$	176560.	+	243014.i	0.425717	+	0.585949i
$645$	−433574.	+	140877.i	−1.04218	+	0.338625i
$646$	−7346.72	−	2387.09i	−0.0176047	−	0.00572011i
$647$	286054.	+	207831.i	0.683345	+	0.496479i	0.874466	−	0.485087i	$-0.161212\pi$
$647$	286054.	+	207831.i	0.683345	+	0.496479i	−0.191121	+	0.981567i	$0.561212\pi$
$648$			192834.i			0.459234i
$649$	3585.28	+	85317.7i	0.00851204	+	0.202558i
$650$	−65672.8			−0.155438
$651$	1.22485e6	−	1.68587e6i	2.89016	−	3.97797i
$652$	−74754.2	+	230070.i	−0.175849	+	0.541208i
$653$	−69709.4	−	214544.i	−0.163480	−	0.503140i	0.835441	−	0.549580i	$-0.185212\pi$
$653$	−69709.4	−	214544.i	−0.163480	−	0.503140i	−0.998921	+	0.0464400i	$0.985212\pi$
$654$	219469.	−	159454.i	0.513119	−	0.372803i
$655$	28074.0	+	38640.5i	0.0654367	+	0.0900659i
$656$	183807.	−	59722.4i	0.427124	−	0.138781i
$657$	−174163.	−	56588.8i	−0.403482	−	0.131099i
$658$	414238.	+	300962.i	0.956750	+	0.695120i
$659$			524030.i			1.20666i	0.797491	+	0.603331i	$0.206160\pi$
$659$			524030.i			1.20666i	−0.797491	+	0.603331i	$0.793840\pi$
$660$	160643.	−	59762.9i	0.368787	−	0.137197i
$661$	−322127.			−0.737265			−0.368633	−	0.929575i	$-0.620174\pi$
$661$	−322127.			−0.737265			−0.368633	+	0.929575i	$0.620174\pi$
$662$	−267759.	+	368539.i	−0.610983	+	0.840945i
$663$	−308364.	+	949047.i	−0.701515	+	2.15904i
$664$	−63541.5	−	195561.i	−0.144119	−	0.443553i
$665$	5775.74	−	4196.32i	0.0130606	−	0.00948912i
$666$	113454.	+	156156.i	0.255783	+	0.352056i
$667$	−621578.	+	201963.i	−1.39715	+	0.453962i
$668$	248214.	+	80649.5i	0.556254	+	0.180738i
$669$	236267.	+	171658.i	0.527899	+	0.383541i
$670$			62790.3i			0.139876i
$671$	24287.3	+	65284.5i	0.0539428	+	0.144999i
$672$	227368.			0.503490
$673$	−75463.9	+	103867.i	−0.166613	+	0.229323i	−0.884157	−	0.467190i	$-0.845266\pi$
$673$	−75463.9	+	103867.i	−0.166613	+	0.229323i	0.717544	+	0.696513i	$0.245266\pi$
$674$	−133615.	+	411225.i	−0.294128	+	0.905232i
$675$	54334.8	+	167225.i	0.119253	+	0.367024i
$676$	−38459.3	+	27942.3i	−0.0841603	+	0.0611461i
$677$	−52364.9	−	72074.1i	−0.114252	−	0.157254i	0.748061	−	0.663630i	$-0.230985\pi$
$677$	−52364.9	−	72074.1i	−0.114252	−	0.157254i	−0.862313	+	0.506376i	$0.830985\pi$
$678$	311376.	−	101172.i	0.677369	−	0.220091i
$679$	7367.06	+	2393.70i	0.0159792	+	0.00519196i
$680$	−69425.5	−	50440.6i	−0.150142	−	0.109084i
$681$		−	101692.i		−	0.219276i
$682$	567295.	−	23839.2i	1.21966	−	0.0512535i
$683$	535111.			1.14710			0.573552	−	0.819169i	$-0.305565\pi$
$683$	535111.			1.14710			0.573552	+	0.819169i	$0.305565\pi$
$684$	−6429.34	+	8849.22i	−0.0137421	+	0.0189144i
$685$	−18176.2	+	55940.7i	−0.0387367	+	0.119219i
$686$	−103144.	−	317445.i	−0.219178	−	0.674560i
$687$	1.29988e6	−	944419.i	2.75417	−	2.00102i
$688$	−96854.5	−	133309.i	−0.204618	−	0.281632i
$689$	578236.	−	187880.i	1.21805	−	0.395770i
$690$	−225500.	−	73269.3i	−0.473639	−	0.153895i
$691$	145982.	+	106062.i	0.305733	+	0.222128i	0.730063	−	0.683380i	$-0.239491\pi$
$691$	145982.	+	106062.i	0.305733	+	0.222128i	−0.424331	+	0.905507i	$0.639491\pi$
$692$		−	171874.i		−	0.358921i
$693$	1.35747e6	+	901688.i	2.82660	+	1.87754i
$694$	−372734.			−0.773892
$695$	55178.2	−	75946.3i	0.114235	−	0.157231i
$696$	−152872.	+	470491.i	−0.315579	+	0.971253i
$697$	−316540.	−	974210.i	−0.651573	−	2.00534i
$698$	205962.	−	149640.i	0.422743	−	0.307141i
$699$	554956.	+	763832.i	1.13581	+	1.56330i
$700$	75427.6	−	24507.9i	0.153934	−	0.0500162i
$701$	−320482.	−	104131.i	−0.652181	−	0.211907i	−0.0358055	−	0.999359i	$-0.511400\pi$
$701$	−320482.	−	104131.i	−0.652181	−	0.211907i	−0.616376	+	0.787452i	$0.711400\pi$
$702$	597887.	+	434390.i	1.21323	+	0.881466i
$703$			3235.50i			0.00654683i
$704$	38486.7	+	48547.1i	0.0776543	+	0.0979531i
$705$	−404165.			−0.813169
$706$	227646.	−	313328.i	0.456721	−	0.628623i
$707$	−160490.	+	493939.i	−0.321078	+	0.988176i
$708$	−27630.6	−	85038.1i	−0.0551218	−	0.169647i
$709$	574225.	−	417199.i	1.14232	−	0.829948i	0.154883	−	0.987933i	$-0.450500\pi$
$709$	574225.	−	417199.i	1.14232	−	0.829948i	0.987441	+	0.157985i	$0.0504998\pi$
$710$	39306.7	+	54101.0i	0.0779739	+	0.107322i
$711$	−628592.	+	204242.i	−1.24345	+	0.404023i
$712$	−12763.6	−	4147.14i	−0.0251775	−	0.00818067i
$713$	−635446.	−	461679.i	−1.24997	−	0.908156i
$714$		−	1.20509e6i		−	2.36387i
$715$	67549.5	−	242038.i	0.132133	−	0.473447i
$716$	161120.			0.314285
$717$	−970798.	+	1.33619e6i	−1.88839	+	2.59914i
$718$	−168165.	+	517558.i	−0.326202	+	1.00395i
$719$	9151.06	+	28164.1i	0.0177016	+	0.0544800i	0.959517	−	0.281650i	$-0.0908818\pi$
$719$	9151.06	+	28164.1i	0.0177016	+	0.0544800i	−0.941816	+	0.336130i	$0.890882\pi$
$720$	−98305.7	+	71423.3i	−0.189633	+	0.137776i
$721$	−699965.	−	963419.i	−1.34650	−	1.85329i
$722$	350388.	−	113848.i	0.672164	−	0.218399i
$723$	−772571.	−	251023.i	−1.47796	−	0.480217i
$724$	236919.	+	172132.i	0.451984	+	0.328385i
$725$			172560.i			0.328294i
$726$	55022.9	+	653525.i	0.104393	+	1.23991i
$727$	−200557.			−0.379463			−0.189732	−	0.981836i	$-0.560762\pi$
$727$	−200557.			−0.379463			−0.189732	+	0.981836i	$0.560762\pi$
$728$	195933.	−	269679.i	0.369696	−	0.508844i
$729$	−110397.	+	339768.i	−0.207732	+	0.639334i
$730$	−10537.7	−	32431.6i	−0.0197742	−	0.0608587i
$731$	−706562.	+	513347.i	−1.32226	+	0.960675i
$732$	−42870.7	−	59006.5i	−0.0800090	−	0.110123i
$733$	89057.4	−	28936.5i	0.165753	−	0.0538565i	−0.224965	−	0.974367i	$-0.572227\pi$
$733$	89057.4	−	28936.5i	0.165753	−	0.0538565i	0.390718	+	0.920510i	$0.372227\pi$
$734$	277493.	+	90162.8i	0.515062	+	0.167354i
$735$	557092.	+	404751.i	1.03122	+	0.749227i
$736$		−	85700.7i		−	0.158208i
$737$	−231415.	−	64584.7i	−0.426045	−	0.118903i
$738$	−1.45046e6			−2.66314
$739$	−150274.	+	206835.i	−0.275167	+	0.378735i	−0.924126	−	0.382089i	$-0.875205\pi$
$739$	−150274.	+	206835.i	−0.275167	+	0.378735i	0.648959	+	0.760824i	$0.275205\pi$
$740$	−11107.0	+	34183.9i	−0.0202831	+	0.0624250i
$741$	7319.20	+	22526.2i	0.0133299	+	0.0410253i
$742$	−594012.	+	431575.i	−1.07892	+	0.783878i
$743$	−390015.	−	536809.i	−0.706486	−	0.972394i	−0.999866	−	0.0163980i	$-0.994780\pi$
$743$	−390015.	−	536809.i	−0.706486	−	0.972394i	0.293380	−	0.955996i	$-0.405220\pi$
$744$	−565435.	+	183721.i	−1.02150	+	0.331905i
$745$	175456.	+	57009.2i	0.316123	+	0.102715i
$746$	362325.	+	263245.i	0.651060	+	0.473023i
$747$			1.54321e6i			2.76557i
$748$	257309.	−	203987.i	0.459888	−	0.364585i
$749$	−682870.			−1.21724
$750$	−36796.7	+	50646.3i	−0.0654164	+	0.0900379i
$751$	145739.	−	448538.i	0.258402	−	0.795279i	−0.734739	−	0.678350i	$-0.762695\pi$
$751$	145739.	−	448538.i	0.258402	−	0.795279i	0.993140	−	0.116928i	$-0.0373048\pi$
$752$	−45142.5	−	138934.i	−0.0798271	−	0.245682i
$753$	878326.	−	638141.i	1.54905	−	1.12545i
$754$	426308.	+	586763.i	0.749861	+	1.03210i
$755$	68622.7	−	22296.9i	0.120385	−	0.0391156i
$756$	−848802.	−	275793.i	−1.48512	−	0.482546i
$757$	−296813.	−	215647.i	−0.517954	−	0.376315i	0.297879	−	0.954604i	$-0.403721\pi$
$757$	−296813.	−	215647.i	−0.517954	−	0.376315i	−0.815833	+	0.578288i	$0.803721\pi$
$758$		−	287097.i		−	0.499678i
$759$	501979.	−	755720.i	0.871369	−	1.31183i
$760$	−2036.86			−0.00352642
$761$	−598122.	+	823245.i	−1.03281	+	1.42154i	−0.129995	+	0.991515i	$0.541496\pi$
$761$	−598122.	+	823245.i	−1.03281	+	1.42154i	−0.902816	+	0.430027i	$0.858504\pi$
$762$	−98431.7	+	302942.i	−0.169522	+	0.521734i
$763$	148422.	+	456795.i	0.254946	+	0.784644i
$764$	202017.	−	146774.i	0.346100	−	0.251457i
$765$	378557.	+	521039.i	0.646857	+	0.890322i
$766$	405309.	−	131693.i	0.690762	−	0.224442i
$767$	−124673.	−	40508.8i	−0.211925	−	0.0688587i
$768$	−52480.5	−	38129.3i	−0.0889765	−	0.0646452i
$769$		−	1.10968e6i		−	1.87648i	−0.345983	−	0.938241i	$-0.612454\pi$
$769$		−	1.10968e6i		−	1.87648i	0.345983	−	0.938241i	$-0.387546\pi$
$770$	12741.2	+	303198.i	0.0214896	+	0.511381i
$771$	−1.17938e6			−1.98402
$772$	−64672.6	+	89014.2i	−0.108514	+	0.149357i
$773$	109830.	−	338023.i	0.183807	−	0.565701i	−0.816118	−	0.577885i	$-0.803878\pi$
$773$	109830.	−	338023.i	0.183807	−	0.565701i	0.999926	+	0.0121836i	$0.00387827\pi$
$774$	382151.	+	1.17614e6i	0.637901	+	1.96326i
$775$	−167776.	+	121896.i	−0.279335	+	0.202949i
$776$	−1299.03	−	1787.95i	−0.00215722	−	0.00296916i
$777$	−480045.	+	155976.i	−0.795133	+	0.258354i
$778$	242330.	+	78737.9i	0.400358	+	0.130084i
$779$	−19670.0	−	14291.1i	−0.0324137	−	0.0235500i
$780$			263121.i			0.432480i
$781$	−239820.	+	89218.3i	−0.393173	+	0.146269i
$782$	−454230.			−0.742783
$783$	1.14139e6	−	1.57099e6i	1.86170	−	2.56242i
$784$	−76912.4	+	236712.i	−0.125131	+	0.385113i
$785$	27823.2	+	85630.9i	0.0451510	+	0.138960i
$786$	154815.	−	112480.i	0.250592	−	0.182066i
$787$	70476.9	+	97003.1i	0.113788	+	0.156616i	0.862112	−	0.506717i	$-0.169141\pi$
$787$	70476.9	+	97003.1i	0.113788	+	0.156616i	−0.748324	+	0.663333i	$0.769141\pi$
$788$	51770.2	−	16821.1i	0.0833733	−	0.0270896i
$789$	−447313.	−	145341.i	−0.718551	−	0.233471i
$790$	−99571.3	−	72342.8i	−0.159544	−	0.115915i
$791$			579666.i			0.926456i
$792$	−162117.	−	435772.i	−0.258450	−	0.694718i
$793$	−106931.			−0.170042
$794$	445360.	−	612985.i	0.706432	−	0.972320i
$795$	179096.	−	551201.i	0.283369	−	0.872119i
$796$	−105382.	−	324331.i	−0.166318	−	0.511874i
$797$	743265.	−	540014.i	1.17011	−	0.850135i	0.179089	−	0.983833i	$-0.442685\pi$
$797$	743265.	−	540014.i	1.17011	−	0.850135i	0.991022	+	0.133698i	$0.0426851\pi$
$798$	−16812.8	−	23140.8i	−0.0264018	−	0.0363390i
$799$	−736379.	+	239264.i	−1.15347	+	0.374786i
$800$	−21520.0	−	6992.26i	−0.0336249	−	0.0109254i
$801$	81484.6	+	59202.0i	0.127002	+	0.0922724i
$802$			632660.i			0.983607i
$803$	130366.	−	5478.33i	0.202178	−	0.00849605i
$804$	251572.			0.389180
$805$	246750.	−	339622.i	0.380773	−	0.524088i
$806$	−269351.	+	828978.i	−0.414619	+	1.27607i
$807$	−464878.	−	1.43075e6i	−0.713826	−	2.19693i
$808$	119877.	−	87095.6i	0.183617	−	0.133405i
$809$	−236470.	−	325474.i	−0.361310	−	0.497300i	0.589203	−	0.807985i	$-0.299442\pi$
$809$	−236470.	−	325474.i	−0.361310	−	0.497300i	−0.950513	+	0.310684i	$0.899442\pi$
$810$	256304.	−	83278.3i	0.390648	−	0.126929i
$811$	−10379.5	−	3372.50i	−0.0157810	−	0.00512755i	0.301116	−	0.953588i	$-0.402641\pi$
$811$	−10379.5	−	3372.50i	−0.0157810	−	0.00512755i	−0.316897	+	0.948460i	$0.602641\pi$
$812$	−708600.	−	514828.i	−1.07471	−	0.780819i
$813$			459619.i			0.695371i
$814$	−114561.	−	76096.0i	−0.172897	−	0.114845i
$815$	338079.			0.508982
$816$	−202092.	+	278156.i	−0.303508	+	0.417743i
$817$	−6405.82	+	19715.1i	−0.00959689	+	0.0295362i
$818$	32409.1	+	99744.8i	0.0484351	+	0.149068i
$819$	−2.02394e6	+	1.47048e6i	−3.01738	+	2.19226i
$820$	−158759.	−	218513.i	−0.236108	−	0.324975i
$821$	115263.	−	37451.3i	0.171004	−	0.0555624i	−0.222264	−	0.974987i	$-0.571345\pi$
$821$	115263.	−	37451.3i	0.171004	−	0.0555624i	0.393267	+	0.919424i	$0.371345\pi$
$822$	224129.	+	72823.9i	0.331707	+	0.107778i
$823$	523952.	+	380674.i	0.773557	+	0.562022i	0.903038	−	0.429560i	$-0.141331\pi$
$823$	523952.	+	380674.i	0.773557	+	0.562022i	−0.129482	+	0.991582i	$0.541331\pi$
$824$			339757.i			0.500396i
$825$	−148810.	−	187708.i	−0.218637	−	0.275788i
$826$	158309.			0.232031
$827$	31437.7	−	43270.3i	0.0459663	−	0.0632672i	−0.785415	−	0.618969i	$-0.787550\pi$
$827$	31437.7	−	43270.3i	0.0459663	−	0.0632672i	0.831381	+	0.555702i	$0.187550\pi$
$828$	−198755.	+	611705.i	−0.289906	+	0.892239i
$829$	13213.4	+	40666.8i	0.0192268	+	0.0591740i	0.960210	−	0.279280i	$-0.0900959\pi$
$829$	13213.4	+	40666.8i	0.0192268	+	0.0591740i	−0.940983	+	0.338454i	$0.890096\pi$
$830$	−232486.	+	168911.i	−0.337475	+	0.245190i
$831$	583665.	+	803347.i	0.845205	+	1.16332i
$832$	−90449.6	+	29388.8i	−0.130665	+	0.0424557i
$833$	1.25462e6	+	407650.i	1.80810	+	0.587486i
$834$	−304282.	−	221074.i	−0.437466	−	0.317838i
$835$		−	364741.i		−	0.523132i
$836$	2095.07	−	7506.88i	0.00299768	−	0.0107411i
$837$	2.33371e6			3.33117
$838$	423897.	−	583444.i	0.603632	−	0.830829i
$839$	114652.	−	352863.i	0.162876	−	0.501282i	−0.835997	−	0.548734i	$-0.815110\pi$
$839$	114652.	−	352863.i	0.162876	−	0.501282i	0.998874	+	0.0474520i	$0.0151101\pi$
$840$	−98192.1	−	302204.i	−0.139161	−	0.428294i
$841$	969557.	−	704425.i	1.37082	−	0.995962i
$842$	−566732.	−	780040.i	−0.799381	−	1.10025i
$843$	300790.	−	97732.7i	0.423261	−	0.137526i
$844$	−445992.	−	144912.i	−0.626098	−	0.203431i
$845$	53748.4	+	39050.5i	0.0752753	+	0.0546907i
$846$			1.09636e6i			1.53184i
$847$	−1.13055e6	−	264905.i	−1.57587	−	0.369252i
$848$	209483.			0.291311
$849$	−549223.	+	755941.i	−0.761963	+	1.04875i
$850$	−37060.3	+	114060.i	−0.0512945	+	0.157868i
$851$	58791.3	+	180941.i	0.0811809	+	0.249849i
$852$	216758.	−	157484.i	0.298604	−	0.216949i
$853$	520557.	+	716485.i	0.715434	+	0.984711i	0.999663	+	0.0259545i	$0.00826250\pi$
$853$	520557.	+	716485.i	0.715434	+	0.984711i	−0.284229	+	0.958757i	$0.591737\pi$
$854$	122814.	−	39904.7i	0.168396	−	0.0547152i
$855$	14538.5	+	4723.84i	0.0198878	+	0.00646193i
$856$	157618.	+	114516.i	0.215109	+	0.156286i
$857$		−	534294.i		−	0.727476i	−0.931501	−	0.363738i	$-0.881500\pi$
$857$		−	534294.i		−	0.727476i	0.931501	−	0.363738i	$-0.118500\pi$
$858$	−969736.	−	270640.i	−1.31728	−	0.367636i
$859$	724471.			0.981827			0.490914	−	0.871208i	$-0.336663\pi$
$859$	724471.			0.981827			0.490914	+	0.871208i	$0.336663\pi$
$860$	−135358.	+	186305.i	−0.183016	+	0.251899i
$861$	1.17209e6	−	3.60733e6i	1.58109	−	4.86608i
$862$	77202.5	+	237605.i	0.103900	+	0.319772i
$863$	−201547.	+	146432.i	−0.270616	+	0.196614i	−0.714814	−	0.699314i	$-0.753489\pi$
$863$	−201547.	+	146432.i	−0.270616	+	0.196614i	0.444198	+	0.895929i	$0.353489\pi$
$864$	149668.	+	206001.i	0.200494	+	0.275957i
$865$	−228446.	+	74226.4i	−0.305317	+	0.0992034i
$866$	−765320.	−	248668.i	−1.02049	−	0.331576i
$867$	404158.	+	293638.i	0.537667	+	0.390638i
$868$		−	1.05263e6i		−	1.39713i
$869$	369037.	−	292561.i	0.488687	−	0.387416i
$870$	691369.			0.913422
$871$	216791.	−	298387.i	0.285762	−	0.393318i
$872$	42345.6	−	130326.i	0.0556898	−	0.171396i
$873$	5125.46	+	15774.5i	0.00672518	+	0.0206980i
$874$	−8722.35	+	6337.16i	−0.0114185	+	0.00829605i
$875$	−65149.0	−	89669.9i	−0.0850926	−	0.117120i
$876$	−129939.	+	42219.7i	−0.169329	+	0.0550182i
$877$	261333.	+	84912.3i	0.339778	+	0.110401i	0.473936	−	0.880559i	$-0.342833\pi$
$877$	261333.	+	84912.3i	0.339778	+	0.110401i	−0.134158	+	0.990960i	$0.542833\pi$
$878$	−334060.	−	242708.i	−0.433346	−	0.314844i
$879$			2.32150e6i			3.00462i
$880$	47905.0	−	72120.1i	0.0618608	−	0.0931302i
$881$	−264167.			−0.340351			−0.170175	−	0.985414i	$-0.554433\pi$
$881$	−264167.			−0.340351			−0.170175	+	0.985414i	$0.554433\pi$
$882$	1.09795e6	−	1.51120e6i	1.41139	−	1.94261i
$883$	−79926.4	+	245988.i	−0.102511	+	0.315495i	−0.989138	−	0.146989i	$-0.953042\pi$
$883$	−79926.4	+	245988.i	−0.102511	+	0.315495i	0.886627	+	0.462484i	$0.153042\pi$
$884$	155766.	+	479400.i	0.199328	+	0.613470i
$885$	−101095.	+	73449.9i	−0.129075	+	0.0937787i
$886$	6142.42	+	8454.32i	0.00782478	+	0.0107699i
$887$	−300034.	+	97487.1i	−0.381350	+	0.123908i	−0.493418	−	0.869792i	$-0.664253\pi$
$887$	−300034.	+	97487.1i	−0.381350	+	0.123908i	0.112068	+	0.993701i	$0.464253\pi$
$888$	136960.	+	44500.9i	0.173687	+	0.0564342i
$889$	−456257.	−	331490.i	−0.577305	−	0.419437i
$890$			18755.6i			0.0236784i
$891$	43294.8	+	1.03027e6i	0.0545356	+	1.29777i
$892$	147522.			0.185407
$893$	−10802.2	+	14868.0i	−0.0135460	+	0.0186444i
$894$	228410.	−	702974.i	0.285786	−	0.879558i
$895$	−69582.1	−	214152.i	−0.0868664	−	0.267347i
$896$	92917.3	−	67508.4i	0.115739	−	0.0840895i
$897$	818632.	+	1.12675e6i	1.01743	+	1.40037i
$898$	447877.	−	145524.i	0.555400	−	0.180460i
$899$	2.17820e6	+	707739.i	2.69512	+	0.875697i
$900$	137386.	+	99817.1i	0.169613	+	0.123231i
$901$		−	1.11030e6i		−	1.36770i
$902$	968630.	−	360352.i	1.19054	−	0.442908i
$903$	−3.23389e6			−3.96598
$904$	97209.1	−	133797.i	0.118952	−	0.163723i
$905$	126471.	−	389237.i	0.154416	−	0.475244i
$906$	−89333.4	−	274940.i	−0.108832	−	0.334951i
$907$	83861.2	−	60928.7i	0.101940	−	0.0740641i	−0.535647	−	0.844442i	$-0.679932\pi$
$907$	83861.2	−	60928.7i	0.101940	−	0.0740641i	0.637588	+	0.770378i	$0.279932\pi$
$908$	−30193.6	−	41557.9i	−0.0366221	−	0.0504060i
$909$	−1.05763e6	+	343646.i	−1.27999	+	0.415895i
$910$	−443058.	−	143958.i	−0.535030	−	0.173842i
$911$	−1.10533e6	−	803071.i	−1.33185	−	0.967647i	−0.999702	−	0.0244211i	$-0.992226\pi$
$911$	−1.10533e6	−	803071.i	−1.33185	−	0.967647i	−0.332151	−	0.943226i	$-0.607774\pi$
$912$			8160.77i			0.00981164i
$913$	−383395.	−	1.03057e6i	−0.459944	−	1.23634i
$914$	−436632.			−0.522664
$915$	−59913.7	+	82464.1i	−0.0715622	+	0.0984969i
$916$	250806.	−	771902.i	0.298915	−	0.919965i
$917$	104698.	+	322226.i	0.124508	+	0.383197i
$918$	1.09184e6	−	793270.i	1.29561	−	0.941316i
$919$	555794.	+	764984.i	0.658086	+	0.905778i	0.999416	−	0.0341659i	$-0.0108775\pi$
$919$	555794.	+	764984.i	0.658086	+	0.905778i	−0.341330	+	0.939943i	$0.610877\pi$
$920$	−113908.	+	37011.1i	−0.134580	+	0.0437277i
$921$	1.39099e6	+	451959.i	1.63985	+	0.532819i
$922$	−121294.	−	88125.0i	−0.142684	−	0.103666i
$923$		−	392806.i		−	0.461078i
$924$	1.21478e6	−	51048.2i	1.42283	−	0.0597911i
$925$	50232.1			0.0587080
$926$	−293664.	+	404194.i	−0.342475	+	0.471376i
$927$	787956.	−	2.42508e6i	0.916943	−	2.82206i
$928$	77221.3	+	237663.i	0.0896687	+	0.275972i
$929$	−591734.	+	429920.i	−0.685639	+	0.498146i	−0.875223	−	0.483719i	$-0.839286\pi$
$929$	−591734.	+	429920.i	−0.685639	+	0.498146i	0.189585	+	0.981864i	$0.439286\pi$
$930$	488383.	+	672201.i	0.564670	+	0.777201i
$931$	29779.1	−	9675.82i	0.0343568	−	0.0111632i
$932$	453583.	+	147378.i	0.522185	+	0.169668i
$933$	1.66375e6	+	1.20879e6i	1.91128	+	1.38863i
$934$			610112.i			0.699384i
$935$	−382250.	−	253906.i	−0.437244	−	0.290435i
$936$	713759.			0.814704
$937$	−765154.	+	1.05314e6i	−0.871505	+	1.19952i	0.107197	+	0.994238i	$0.465812\pi$
$937$	−765154.	+	1.05314e6i	−0.871505	+	1.19952i	−0.978702	+	0.205286i	$0.934188\pi$
$938$	−137640.	+	423612.i	−0.156437	+	0.481462i
$939$	−296361.	−	912105.i	−0.336116	−	1.03446i
$940$	−165168.	+	120002.i	−0.186926	+	0.135810i
$941$	−268909.	−	370121.i	−0.303687	−	0.417989i	0.629713	−	0.776828i	$-0.283173\pi$
$941$	−268909.	−	370121.i	−0.303687	−	0.417989i	−0.933399	+	0.358839i	$0.883173\pi$
$942$	343084.	−	111475.i	0.386633	−	0.125625i
$943$	−1.35969e6	−	441791.i	−1.52904	−	0.496814i
$944$	−36540.5	−	26548.2i	−0.0410044	−	0.0297915i
$945$			1.24728e6i			1.39670i
$946$	−547403.	−	690494.i	−0.611680	−	0.771574i
$947$	1.27039e6			1.41656			0.708282	−	0.705930i	$-0.249471\pi$
$947$	1.27039e6			1.41656			0.708282	+	0.705930i	$0.249471\pi$
$948$	−289845.	+	398937.i	−0.322514	+	0.443903i
$949$	−61897.7	+	190502.i	−0.0687294	+	0.211527i
$950$	879.647	+	2707.28i	0.000974678	+	0.00299975i
$951$	788584.	−	572940.i	0.871940	−	0.633502i
$952$	−357807.	−	492479.i	−0.394798	−	0.543393i
$953$	−409152.	+	132942.i	−0.450505	+	0.146378i	−0.525477	−	0.850808i	$-0.676113\pi$
$953$	−409152.	+	132942.i	−0.450505	+	0.146378i	0.0749724	+	0.997186i	$0.476113\pi$
$954$	−1.49522e6	−	485828.i	−1.64289	−	0.533809i
$955$	−282328.	−	205123.i	−0.309562	−	0.224910i
$956$			834296.i			0.912860i
$957$	−711126.	+	2.54805e6i	−0.776467	+	2.78217i
$958$	−929883.			−1.01321
$959$	−245250.	+	337558.i	−0.266669	+	0.367038i
$960$	−28014.8	+	86220.7i	−0.0303980	+	0.0935554i
$961$	565177.	+	1.73944e6i	0.611981	+	1.88348i
$962$	170806.	−	124098.i	0.184567	−	0.134096i
$963$	−859447.	−	1.18293e6i	−0.926758	−	1.27557i
$964$	−390255.	+	126801.i	−0.419946	+	0.136449i
$965$	146242.	+	47517.0i	0.157043	+	0.0510264i
$966$	−1.36071e6	−	988616.i	−1.45818	−	1.05943i
$967$			266832.i			0.285354i	0.989769	+	0.142677i	$0.0455711\pi$
$967$			266832.i			0.285354i	−0.989769	+	0.142677i	$0.954429\pi$
$968$	216526.	+	250736.i	0.231078	+	0.267587i
$969$	43253.6			0.0460654
$970$	−1815.44	+	2498.74i	−0.00192947	+	0.00265569i
$971$	−426622.	+	1.31301e6i	−0.452486	+	1.39261i	0.421576	+	0.906793i	$0.361477\pi$
$971$	−426622.	+	1.31301e6i	−0.452486	+	1.39261i	−0.874062	+	0.485815i	$0.838523\pi$
$972$	−51986.4	−	159998.i	−0.0550246	−	0.169348i
$973$	538736.	−	391414.i	0.569050	−	0.413439i
$974$	−376449.	−	518137.i	−0.396815	−	0.546169i
$975$	349725.	−	113633.i	0.367890	−	0.119535i
$976$	−35039.5	−	11385.0i	−0.0367840	−	0.0119518i
$977$	−77747.2	−	56486.7i	−0.0814509	−	0.0591775i	0.546315	−	0.837580i	$-0.316030\pi$
$977$	−77747.2	−	56486.7i	−0.0814509	−	0.0591775i	−0.627765	+	0.778403i	$0.716030\pi$
$978$		−	1.35453e6i		−	1.41615i
$979$	−69124.2	−	19291.6i	−0.0721215	−	0.0201281i
$980$	347840.			0.362182
$981$	−604500.	+	832022.i	−0.628142	+	0.864564i
$982$	252705.	−	777745.i	0.262054	−	0.806519i
$983$	21031.5	+	64728.4i	0.0217653	+	0.0669866i	0.961349	−	0.275332i	$-0.0887878\pi$
$983$	21031.5	+	64728.4i	0.0217653	+	0.0669866i	−0.939584	+	0.342319i	$0.888788\pi$
$984$	−875484.	+	636076.i	−0.904186	+	0.656930i
$985$	−44715.4	−	61545.5i	−0.0460876	−	0.0634342i
$986$	1.25966e6	−	409287.i	1.29568	−	0.420992i
$987$	−2.72668e6	−	885952.i	−2.79898	−	0.909444i
$988$	9679.41	+	7032.50i	0.00991597	+	0.00720437i
$989$			1.21894e6i			1.24620i
$990$	−509190.	+	403670.i	−0.519529	+	0.411867i
$991$	336596.			0.342738			0.171369	−	0.985207i	$-0.445181\pi$
$991$	336596.			0.342738			0.171369	+	0.985207i	$0.445181\pi$
$992$	−176525.	+	242965.i	−0.179383	+	0.246900i
$993$	788213.	−	2.42587e6i	0.799365	−	2.46019i
$994$	146588.	+	451152.i	0.148363	+	0.456615i
$995$	−385572.	+	280134.i	−0.389457	+	0.282957i
$996$	676751.	+	931468.i	0.682198	+	0.938965i
$997$	920987.	−	299247.i	0.926538	−	0.301050i	0.193392	−	0.981122i	$-0.438051\pi$
$997$	920987.	−	299247.i	0.926538	−	0.301050i	0.733146	+	0.680071i	$0.238051\pi$
$998$	157966.	+	51326.1i	0.158599	+	0.0515320i
$999$	−457314.	−	332258.i	−0.458230	−	0.332924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.5.h.a.51.4	yes	32
11.8	odd	10	inner	110.5.h.a.41.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.5.h.a.41.4	✓	32	11.8	odd	10	inner
110.5.h.a.51.4	yes	32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	110.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.66251 + 2.28825i) q^{2} +(4.89398 - 15.0621i) q^{3} +(-2.47214 - 7.60845i) q^{4} +(-9.04508 + 6.57164i) q^{5} +(26.3296 + 36.2396i) q^{6} +(-75.4276 + 24.5079i) q^{7} +(21.5200 + 6.99226i) q^{8} +(-137.386 - 99.8171i) q^{9} -31.6228i q^{10} +(116.546 + 32.5265i) q^{11} -126.698 q^{12} +(-109.181 + 150.275i) q^{13} +(69.3189 - 213.342i) q^{14} +(54.7164 + 168.400i) q^{15} +(-51.7771 + 37.6183i) q^{16} +(199.384 + 274.428i) q^{17} +(456.812 - 148.427i) q^{18} +(7.65733 + 2.48802i) q^{19} +(72.3607 + 52.5731i) q^{20} +1256.04i q^{21} +(-268.188 + 212.611i) q^{22} +473.434 q^{23} +(210.637 - 289.916i) q^{24} +(38.6271 - 118.882i) q^{25} +(-162.352 - 499.668i) q^{26} +(-1138.00 + 826.808i) q^{27} +(372.935 + 513.301i) q^{28} +(-1312.91 + 426.591i) q^{29} +(-476.307 - 154.761i) q^{30} +(-1342.21 - 975.170i) q^{31} -181.019i q^{32} +(1060.29 - 1596.25i) q^{33} -959.436 q^{34} +(521.192 - 717.359i) q^{35} +(-419.816 + 1292.06i) q^{36} +(124.180 + 382.188i) q^{37} +(-18.4236 + 13.3855i) q^{38} +(1729.14 + 2379.95i) q^{39} +(-240.600 + 78.1758i) q^{40} +(-2871.98 - 933.163i) q^{41} +(-2874.13 - 2088.18i) q^{42} +2574.67i q^{43} +(-40.6421 - 967.146i) q^{44} +1898.63 q^{45} +(-787.088 + 1083.33i) q^{46} +(-705.352 + 2170.85i) q^{47} +(313.215 + 963.977i) q^{48} +(3146.24 - 2285.88i) q^{49} +(207.813 + 286.031i) q^{50} +(5109.26 - 1660.10i) q^{51} +(1413.27 + 459.201i) q^{52} +(-2648.05 - 1923.92i) q^{53} -3978.61i q^{54} +(-1267.92 + 471.695i) q^{55} -1794.56 q^{56} +(74.9497 - 103.159i) q^{57} +(1206.58 - 3713.48i) q^{58} +(218.082 + 671.187i) q^{59} +(1146.00 - 832.614i) q^{60} +(338.369 + 465.725i) q^{61} +(4462.86 - 1450.07i) q^{62} +(12809.0 + 4161.91i) q^{63} +(414.217 + 300.946i) q^{64} -2076.75i q^{65} +(1889.87 + 5079.99i) q^{66} -1985.60 q^{67} +(1595.07 - 2195.43i) q^{68} +(2316.98 - 7130.93i) q^{69} +(775.009 + 2385.23i) q^{70} +(-1710.82 + 1242.99i) q^{71} +(-2258.60 - 3108.70i) q^{72} +(1025.58 - 333.230i) q^{73} +(-1080.99 - 351.235i) q^{74} +(-1601.58 - 1163.61i) q^{75} -64.4112i q^{76} +(-9587.96 + 402.912i) q^{77} -8320.61 q^{78} +(2287.68 - 3148.72i) q^{79} +(221.115 - 680.521i) q^{80} +(2633.49 + 8105.05i) q^{81} +(6910.00 - 5020.41i) q^{82} +(-5341.44 - 7351.87i) q^{83} +(9556.54 - 3105.11i) q^{84} +(-3606.89 - 1171.95i) q^{85} +(-5891.47 - 4280.41i) q^{86} +21863.0i q^{87} +(2280.64 + 1514.89i) q^{88} -593.105 q^{89} +(-3156.49 + 4344.54i) q^{90} +(4552.36 - 14010.7i) q^{91} +(-1170.39 - 3602.10i) q^{92} +(-21256.9 + 15444.0i) q^{93} +(-3794.79 - 5223.07i) q^{94} +(-85.6116 + 27.8169i) q^{95} +(-2726.54 - 885.906i) q^{96} +(-79.0172 - 57.4093i) q^{97} +10999.7i q^{98} +(-12765.2 - 16102.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 18 q^{3} + 64 q^{4} - 200 q^{5} + 80 q^{6} - 60 q^{7} - 262 q^{9} - 258 q^{11} - 96 q^{12} - 570 q^{13} - 48 q^{14} + 150 q^{15} - 512 q^{16} + 150 q^{17} - 480 q^{18} - 1020 q^{19} + 1600 q^{20}+ \cdots + 65268 q^{99}+O(q^{100}) \) 32 * q - 18 * q^3 + 64 * q^4 - 200 * q^5 + 80 * q^6 - 60 * q^7 - 262 * q^9 - 258 * q^11 - 96 * q^12 - 570 * q^13 - 48 * q^14 + 150 * q^15 - 512 * q^16 + 150 * q^17 - 480 * q^18 - 1020 * q^19 + 1600 * q^20 - 480 * q^22 - 1536 * q^23 + 640 * q^24 - 1000 * q^25 + 448 * q^26 - 4194 * q^27 + 960 * q^28 - 4130 * q^29 - 800 * q^30 - 1936 * q^31 - 5852 * q^33 - 768 * q^34 + 1856 * q^36 + 2728 * q^37 - 1360 * q^38 + 7990 * q^39 - 4490 * q^41 - 2592 * q^42 + 1024 * q^44 + 300 * q^45 + 640 * q^46 - 2732 * q^47 - 1152 * q^48 + 3832 * q^49 + 12080 * q^51 + 5520 * q^52 + 1222 * q^53 - 550 * q^55 + 2304 * q^56 + 14580 * q^57 - 3104 * q^58 - 8340 * q^59 - 300 * q^61 + 11680 * q^62 + 32020 * q^63 + 4096 * q^64 + 29696 * q^66 - 9264 * q^67 + 1200 * q^68 - 25466 * q^69 - 1200 * q^70 - 7144 * q^71 - 20480 * q^72 - 7070 * q^73 + 19840 * q^74 + 1500 * q^75 + 34480 * q^77 - 5696 * q^78 + 57050 * q^79 + 12800 * q^80 - 63694 * q^81 + 13312 * q^82 + 580 * q^83 + 29520 * q^84 + 9750 * q^85 - 13360 * q^86 + 9600 * q^88 + 14368 * q^89 + 17600 * q^90 - 40158 * q^91 - 25712 * q^92 - 103942 * q^93 - 67600 * q^94 + 5700 * q^95 - 31458 * q^97 + 65268 * q^99

Introduction

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