LMFDB - Embedded newform 70.4.i.a.39.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [70,4,Mod(9,70)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(70, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("70.9"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	70.i (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.13013370040$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			39.10
Character	$\chi$	$=$	70.39
Dual form			70.4.i.a.9.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 - 1.00000i) q^{2} +(2.65661 + 1.53379i) q^{3} +(2.00000 - 3.46410i) q^{4} +(10.0503 + 4.89820i) q^{5} +6.13518 q^{6} +(-1.78031 + 18.4345i) q^{7} -8.00000i q^{8} +(-8.79495 - 15.2333i) q^{9} +(22.3058 - 1.56633i) q^{10} +(24.7508 - 42.8697i) q^{11} +(10.6264 - 6.13518i) q^{12} +44.6154i q^{13} +(15.3509 + 33.7098i) q^{14} +(19.1868 + 28.4276i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-34.0272 - 19.6456i) q^{17} +(-30.4666 - 17.5899i) q^{18} +(-28.1578 - 48.7708i) q^{19} +(37.0684 - 25.0187i) q^{20} +(-33.0043 + 46.2426i) q^{21} -99.0033i q^{22} +(-79.3801 + 45.8301i) q^{23} +(12.2704 - 21.2529i) q^{24} +(77.0153 + 98.4563i) q^{25} +(44.6154 + 77.2761i) q^{26} -136.783i q^{27} +(60.2983 + 43.0362i) q^{28} -281.845 q^{29} +(61.6601 + 30.0513i) q^{30} +(-35.2827 + 61.1114i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(131.507 - 75.9254i) q^{33} -78.5824 q^{34} +(-108.188 + 176.551i) q^{35} -70.3596 q^{36} +(-170.684 + 98.5446i) q^{37} +(-97.5416 - 56.3157i) q^{38} +(-68.4308 + 118.526i) q^{39} +(39.1856 - 80.4020i) q^{40} +399.021 q^{41} +(-10.9225 + 113.099i) q^{42} -203.567i q^{43} +(-99.0033 - 171.479i) q^{44} +(-13.7758 - 196.178i) q^{45} +(-91.6603 + 158.760i) q^{46} +(-59.3217 + 34.2494i) q^{47} -49.0814i q^{48} +(-336.661 - 65.6384i) q^{49} +(231.851 + 93.5161i) q^{50} +(-60.2646 - 104.381i) q^{51} +(154.552 + 89.2307i) q^{52} +(534.758 + 308.743i) q^{53} +(-136.783 - 236.916i) q^{54} +(458.736 - 309.617i) q^{55} +(147.476 + 14.2425i) q^{56} -172.753i q^{57} +(-488.169 + 281.845i) q^{58} +(240.256 - 416.136i) q^{59} +(136.850 - 9.60969i) q^{60} +(11.7487 + 20.3493i) q^{61} +141.131i q^{62} +(296.476 - 135.010i) q^{63} -64.0000 q^{64} +(-218.535 + 448.396i) q^{65} +(151.851 - 263.013i) q^{66} +(218.346 + 126.062i) q^{67} +(-136.109 + 78.5824i) q^{68} -281.176 q^{69} +(-10.8368 + 413.984i) q^{70} +835.640 q^{71} +(-121.866 + 70.3596i) q^{72} +(223.249 + 128.893i) q^{73} +(-197.089 + 341.369i) q^{74} +(53.5878 + 379.686i) q^{75} -225.263 q^{76} +(746.216 + 532.590i) q^{77} +273.723i q^{78} +(-386.850 - 670.044i) q^{79} +(-12.5306 - 178.446i) q^{80} +(-27.6658 + 47.9185i) q^{81} +(691.125 - 399.021i) q^{82} -1341.21i q^{83} +(94.1805 + 206.816i) q^{84} +(-245.754 - 364.115i) q^{85} +(-203.567 - 352.588i) q^{86} +(-748.752 - 432.292i) q^{87} +(-342.957 - 198.007i) q^{88} +(650.558 + 1126.80i) q^{89} +(-220.038 - 326.014i) q^{90} +(-822.462 - 79.4293i) q^{91} +366.641i q^{92} +(-187.465 + 108.233i) q^{93} +(-68.4988 + 118.643i) q^{94} +(-44.1043 - 628.082i) q^{95} +(-49.0814 - 85.0115i) q^{96} +323.729i q^{97} +(-648.752 + 222.972i) q^{98} -870.729 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 48 q^{4} - 8 q^{5} + 56 q^{6} + 62 q^{9} + 12 q^{10} - 62 q^{11} - 84 q^{14} + 172 q^{15} - 192 q^{16} + 186 q^{19} - 64 q^{20} + 350 q^{21} + 112 q^{24} + 126 q^{25} - 236 q^{26} - 676 q^{29} + 28 q^{30}+ \cdots - 17092 q^{99}+O(q^{100}) $ 24 * q + 48 * q^4 - 8 * q^5 + 56 * q^6 + 62 * q^9 + 12 * q^10 - 62 * q^11 - 84 * q^14 + 172 * q^15 - 192 * q^16 + 186 * q^19 - 64 * q^20 + 350 * q^21 + 112 * q^24 + 126 * q^25 - 236 * q^26 - 676 * q^29 + 28 * q^30 - 652 * q^31 - 544 * q^34 - 1344 * q^35 + 496 * q^36 - 868 * q^39 - 48 * q^40 + 792 * q^41 + 248 * q^44 + 664 * q^45 + 376 * q^46 + 1602 * q^49 + 320 * q^50 - 1448 * q^51 + 1540 * q^54 + 596 * q^55 - 144 * q^56 + 1336 * q^59 + 344 * q^60 - 314 * q^61 - 1536 * q^64 + 1862 * q^65 - 1600 * q^66 + 180 * q^69 - 484 * q^70 + 4432 * q^71 - 1012 * q^74 - 4550 * q^75 + 1488 * q^76 - 1772 * q^79 - 128 * q^80 + 1228 * q^81 + 784 * q^84 + 4564 * q^85 + 396 * q^86 + 6094 * q^89 + 200 * q^90 - 4364 * q^91 + 3604 * q^94 + 1166 * q^95 - 448 * q^96 - 17092 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	2.65661	+	1.53379i	0.511265	+	0.295179i	0.733353	−	0.679848i	$-0.237954\pi$
$3$	2.65661	+	1.53379i	0.511265	+	0.295179i	−0.222089	+	0.975027i	$0.571287\pi$
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	10.0503	+	4.89820i	0.898922	+	0.438108i
$5$	10.0503	+	4.89820i	0.898922	+	0.438108i
$6$	6.13518			0.417446
$7$	−1.78031	+	18.4345i	−0.0961279	+	0.995369i
$7$	−1.78031	+	18.4345i	−0.0961279	+	0.995369i
$8$		−	8.00000i		−	0.353553i
$9$	−8.79495	−	15.2333i	−0.325739	−	0.564196i
$10$	22.3058	−	1.56633i	0.705370	−	0.0495316i
$11$	24.7508	−	42.8697i	0.678423	−	1.17506i	−0.297033	−	0.954867i	$-0.595997\pi$
$11$	24.7508	−	42.8697i	0.678423	−	1.17506i	0.975456	−	0.220196i	$-0.0706696\pi$
$12$	10.6264	−	6.13518i	0.255632	−	0.147589i
$13$			44.6154i			0.951852i	0.879485	+	0.475926i	$0.157887\pi$
$13$			44.6154i			0.951852i	−0.879485	+	0.475926i	$0.842113\pi$
$14$	15.3509	+	33.7098i	0.293050	+	0.643523i
$15$	19.1868	+	28.4276i	0.330267	+	0.489332i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−34.0272	−	19.6456i	−0.485459	−	0.280280i	0.237230	−	0.971454i	$-0.423761\pi$
$17$	−34.0272	−	19.6456i	−0.485459	−	0.280280i	−0.722689	+	0.691174i	$0.757094\pi$
$18$	−30.4666	−	17.5899i	−0.398947	−	0.230332i
$19$	−28.1578	−	48.7708i	−0.339992	−	0.588884i	0.644439	−	0.764656i	$-0.277091\pi$
$19$	−28.1578	−	48.7708i	−0.339992	−	0.588884i	−0.984431	+	0.175772i	$0.943758\pi$
$20$	37.0684	−	25.0187i	0.414437	−	0.279718i
$21$	−33.0043	+	46.2426i	−0.342959	+	0.480522i
$22$		−	99.0033i		−	0.959435i
$23$	−79.3801	+	45.8301i	−0.719648	+	0.415489i	−0.814623	−	0.579991i	$-0.803056\pi$
$23$	−79.3801	+	45.8301i	−0.719648	+	0.415489i	0.0949751	+	0.995480i	$0.469723\pi$
$24$	12.2704	−	21.2529i	0.104362	−	0.180759i
$25$	77.0153	+	98.4563i	0.616122	+	0.787651i
$26$	44.6154	+	77.2761i	0.336530	+	0.582888i
$27$		−	136.783i		−	0.974963i
$28$	60.2983	+	43.0362i	0.406975	+	0.290467i
$29$	−281.845			−1.80473			−0.902367	−	0.430969i	$-0.858172\pi$
$29$	−281.845			−1.80473			−0.902367	+	0.430969i	$0.858172\pi$
$30$	61.6601	+	30.0513i	0.375252	+	0.182887i
$31$	−35.2827	+	61.1114i	−0.204418	+	0.354063i	−0.949947	−	0.312411i	$-0.898864\pi$
$31$	−35.2827	+	61.1114i	−0.204418	+	0.354063i	0.745529	+	0.666473i	$0.232197\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	131.507	−	75.9254i	0.693708	−	0.400512i
$34$	−78.5824			−0.396376
$35$	−108.188	+	176.551i	−0.522491	+	0.852645i
$36$	−70.3596			−0.325739
$37$	−170.684	+	98.5446i	−0.758387	+	0.437855i	−0.828716	−	0.559669i	$-0.810928\pi$
$37$	−170.684	+	98.5446i	−0.758387	+	0.437855i	0.0703292	+	0.997524i	$0.477595\pi$
$38$	−97.5416	−	56.3157i	−0.416404	−	0.240411i
$39$	−68.4308	+	118.526i	−0.280967	+	0.486649i
$40$	39.1856	−	80.4020i	0.154895	−	0.317817i
$41$	399.021			1.51992			0.759959	−	0.649971i	$-0.225219\pi$
$41$	399.021			1.51992			0.759959	+	0.649971i	$0.225219\pi$
$42$	−10.9225	+	113.099i	−0.0401282	+	0.415513i
$43$		−	203.567i		−	0.721946i	−0.932576	−	0.360973i	$-0.882445\pi$
$43$		−	203.567i		−	0.721946i	0.932576	−	0.360973i	$-0.117555\pi$
$44$	−99.0033	−	171.479i	−0.339211	−	0.587531i
$45$	−13.7758	−	196.178i	−0.0456348	−	0.649877i
$46$	−91.6603	+	158.760i	−0.293795	+	0.508868i
$47$	−59.3217	+	34.2494i	−0.184106	+	0.106293i	−0.589220	−	0.807972i	$-0.700565\pi$
$47$	−59.3217	+	34.2494i	−0.184106	+	0.106293i	0.405115	+	0.914266i	$0.367232\pi$
$48$		−	49.0814i		−	0.147589i
$49$	−336.661	−	65.6384i	−0.981519	−	0.191365i
$50$	231.851	+	93.5161i	0.655773	+	0.264503i
$51$	−60.2646	−	104.381i	−0.165465	−	0.286595i
$52$	154.552	+	89.2307i	0.412164	+	0.237963i
$53$	534.758	+	308.743i	1.38594	+	0.800172i	0.992855	−	0.119331i	$-0.0380750\pi$
$53$	534.758	+	308.743i	1.38594	+	0.800172i	0.393084	+	0.919503i	$0.371408\pi$
$54$	−136.783	−	236.916i	−0.344701	−	0.597040i
$55$	458.736	−	309.617i	1.12465	−	0.759068i
$56$	147.476	+	14.2425i	0.351916	+	0.0339863i
$57$		−	172.753i		−	0.401434i
$58$	−488.169	+	281.845i	−1.10517	+	0.638070i
$59$	240.256	−	416.136i	0.530147	−	0.918242i	−0.469234	−	0.883074i	$-0.655470\pi$
$59$	240.256	−	416.136i	0.530147	−	0.918242i	0.999381	−	0.0351685i	$-0.0111968\pi$
$60$	136.850	−	9.60969i	0.294454	−	0.0206768i
$61$	11.7487	+	20.3493i	0.0246601	+	0.0427125i	0.878092	−	0.478492i	$-0.158816\pi$
$61$	11.7487	+	20.3493i	0.0246601	+	0.0427125i	−0.853432	+	0.521204i	$0.825483\pi$
$62$			141.131i			0.289091i
$63$	296.476	−	135.010i	0.592896	−	0.269995i
$64$	−64.0000			−0.125000
$65$	−218.535	+	448.396i	−0.417014	+	0.855641i
$66$	151.851	−	263.013i	0.283205	−	0.490525i
$67$	218.346	+	126.062i	0.398137	+	0.229865i	0.685680	−	0.727903i	$-0.259505\pi$
$67$	218.346	+	126.062i	0.398137	+	0.229865i	−0.287543	+	0.957768i	$0.592838\pi$
$68$	−136.109	+	78.5824i	−0.242729	+	0.140140i
$69$	−281.176			−0.490574
$70$	−10.8368	+	413.984i	−0.0185035	+	0.706865i
$71$	835.640			1.39679			0.698396	−	0.715711i	$-0.253897\pi$
$71$	835.640			1.39679			0.698396	+	0.715711i	$0.253897\pi$
$72$	−121.866	+	70.3596i	−0.199473	+	0.115166i
$73$	223.249	+	128.893i	0.357936	+	0.206654i	0.668175	−	0.744004i	$-0.267076\pi$
$73$	223.249	+	128.893i	0.357936	+	0.206654i	−0.310239	+	0.950659i	$0.600409\pi$
$74$	−197.089	+	341.369i	−0.309610	+	0.536261i
$75$	53.5878	+	379.686i	0.0825039	+	0.584564i
$76$	−225.263			−0.339992
$77$	746.216	+	532.590i	1.10441	+	0.788237i
$78$			273.723i			0.397347i
$79$	−386.850	−	670.044i	−0.550937	−	0.954251i	−0.998207	−	0.0598520i	$-0.980937\pi$
$79$	−386.850	−	670.044i	−0.550937	−	0.954251i	0.447270	−	0.894399i	$-0.352396\pi$
$80$	−12.5306	−	178.446i	−0.0175121	−	0.249386i
$81$	−27.6658	+	47.9185i	−0.0379503	+	0.0657318i
$82$	691.125	−	399.021i	0.930756	−	0.537372i
$83$		−	1341.21i		−	1.77369i	−0.462065	−	0.886846i	$-0.652891\pi$
$83$		−	1341.21i		−	1.77369i	0.462065	−	0.886846i	$-0.347109\pi$
$84$	94.1805	+	206.816i	0.122333	+	0.268636i
$85$	−245.754	−	364.115i	−0.313597	−	0.464633i
$86$	−203.567	−	352.588i	−0.255246	−	0.442100i
$87$	−748.752	−	432.292i	−0.922697	−	0.532719i
$88$	−342.957	−	198.007i	−0.415448	−	0.239859i
$89$	650.558	+	1126.80i	0.774821	+	1.34203i	0.934895	+	0.354924i	$0.115493\pi$
$89$	650.558	+	1126.80i	0.774821	+	1.34203i	−0.160075	+	0.987105i	$0.551173\pi$
$90$	−220.038	−	326.014i	−0.257712	−	0.381833i
$91$	−822.462	−	79.4293i	−0.947444	−	0.0914995i
$92$			366.641i			0.415489i
$93$	−187.465	+	108.233i	−0.209024	+	0.120680i
$94$	−68.4988	+	118.643i	−0.0751608	+	0.130182i
$95$	−44.1043	−	628.082i	−0.0476317	−	0.678314i
$96$	−49.0814	−	85.0115i	−0.0521808	−	0.0903797i
$97$			323.729i			0.338862i	0.985542	+	0.169431i	$0.0541931\pi$
$97$			323.729i			0.338862i	−0.985542	+	0.169431i	$0.945807\pi$
$98$	−648.752	+	222.972i	−0.668713	+	0.229832i
$99$	−870.729			−0.883955
$100$	495.093	−	69.8761i	0.495093	−	0.0698761i
$101$	−590.509	+	1022.79i	−0.581761	+	1.00764i	0.413510	+	0.910500i	$0.364303\pi$
$101$	−590.509	+	1022.79i	−0.581761	+	1.00764i	−0.995271	+	0.0971395i	$0.969031\pi$
$102$	−208.763	−	120.529i	−0.202653	−	0.117002i
$103$	−633.967	+	366.021i	−0.606472	+	0.350147i	−0.771583	−	0.636128i	$-0.780535\pi$
$103$	−633.967	+	366.021i	−0.606472	+	0.350147i	0.165111	+	0.986275i	$0.447202\pi$
$104$	356.923			0.336530
$105$	−558.208	+	303.088i	−0.518814	+	0.281699i
$106$	1234.97			1.13161
$107$	−1158.78	+	669.021i	−1.04695	+	0.604455i	−0.921793	−	0.387682i	$-0.873276\pi$
$107$	−1158.78	+	669.021i	−1.04695	+	0.604455i	−0.125154	+	0.992137i	$0.539942\pi$
$108$	−473.832	−	273.567i	−0.422171	−	0.243741i
$109$	−25.8786	+	44.8230i	−0.0227405	+	0.0393877i	−0.877172	−	0.480177i	$-0.840572\pi$
$109$	−25.8786	+	44.8230i	−0.0227405	+	0.0393877i	0.854431	+	0.519565i	$0.173906\pi$
$110$	484.938	−	995.008i	0.420336	−	0.862457i
$111$	−604.589			−0.516982
$112$	269.678	−	122.807i	0.227520	−	0.103609i
$113$			471.803i			0.392774i	0.980526	+	0.196387i	$0.0629209\pi$
$113$			471.803i			0.392774i	−0.980526	+	0.196387i	$0.937079\pi$
$114$	−172.753	−	299.218i	−0.141928	−	0.245827i
$115$	−1022.28	+	71.7849i	−0.828937	+	0.0582085i
$116$	−563.690	+	976.339i	−0.451183	+	0.781472i
$117$	679.639	−	392.390i	0.537031	−	0.310055i
$118$		−	961.025i		−	0.749742i
$119$	422.736	−	592.298i	0.325648	−	0.456268i
$120$	227.421	−	153.494i	0.173005	−	0.116767i
$121$	−559.706	−	969.439i	−0.420515	−	0.728354i
$122$	40.6987	+	23.4974i	0.0302023	+	0.0174373i
$123$	1060.04	+	612.017i	0.777081	+	0.448648i
$124$	141.131	+	244.446i	0.102209	+	0.177031i
$125$	291.765	+	1366.75i	0.208770	+	0.977965i
$126$	378.501	−	530.321i	0.267615	−	0.374958i
$127$		−	202.294i		−	0.141344i	−0.997500	−	0.0706721i	$-0.977486\pi$
$127$		−	202.294i		−	0.141344i	0.997500	−	0.0706721i	$-0.0225144\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	312.230	−	540.798i	0.213103	−	0.369106i
$130$	69.8822	+	995.179i	0.0471467	+	0.671408i
$131$	584.478	+	1012.35i	0.389817	+	0.675184i	0.992425	−	0.122854i	$-0.0392048\pi$
$131$	584.478	+	1012.35i	0.389817	+	0.675184i	−0.602607	+	0.798038i	$0.705871\pi$
$132$		−	607.403i		−	0.400512i
$133$	949.195	−	432.248i	0.618839	−	0.281810i
$134$	504.248			0.325078
$135$	669.993	−	1374.71i	0.427139	−	0.876416i
$136$	−157.165	+	272.217i	−0.0990939	+	0.171636i
$137$	127.061	+	73.3588i	0.0792377	+	0.0457479i	0.539095	−	0.842245i	$-0.318766\pi$
$137$	127.061	+	73.3588i	0.0792377	+	0.0457479i	−0.459858	+	0.887993i	$0.652100\pi$
$138$	−487.011	+	281.176i	−0.300414	+	0.173444i
$139$	2505.64			1.52896			0.764479	−	0.644648i	$-0.222996\pi$
$139$	2505.64			1.52896			0.764479	+	0.644648i	$0.222996\pi$
$140$	395.214	+	727.878i	0.238583	+	0.439406i
$141$	−210.126			−0.125502
$142$	1447.37	−	835.640i	0.855357	−	0.493841i
$143$	1912.65	+	1104.27i	1.11849	+	0.645758i
$144$	−140.719	+	243.733i	−0.0814347	+	0.141049i
$145$	−2832.61	−	1380.53i	−1.62231	−	0.790669i
$146$	515.571			0.292253
$147$	−793.701	−	690.744i	−0.445329	−	0.387562i
$148$			788.357i			0.437855i
$149$	1054.09	+	1825.74i	0.579559	+	1.00383i	0.995530	+	0.0944481i	$0.0301087\pi$
$149$	1054.09	+	1825.74i	0.579559	+	1.00383i	−0.415970	+	0.909378i	$0.636558\pi$
$150$	472.503	+	604.047i	0.257198	+	0.328802i
$151$	1107.75	−	1918.68i	0.597004	−	1.03404i	−0.396256	−	0.918140i	$-0.629691\pi$
$151$	1107.75	−	1918.68i	0.597004	−	1.03404i	0.993261	−	0.115902i	$-0.0369758\pi$
$152$	−390.166	+	225.263i	−0.208202	+	0.120205i
$153$			691.128i			0.365192i
$154$	1825.07	+	176.257i	0.954992	+	0.0922285i
$155$	−653.936	+	441.364i	−0.338874	+	0.228717i
$156$	273.723	+	474.103i	0.140483	+	0.243324i
$157$	−1958.97	−	1131.01i	−0.995816	−	0.574935i	−0.0888082	−	0.996049i	$-0.528306\pi$
$157$	−1958.97	−	1131.01i	−0.995816	−	0.574935i	−0.907008	+	0.421114i	$0.861639\pi$
$158$	−1340.09	−	773.700i	−0.674757	−	0.389571i
$159$	947.097	+	1640.42i	0.472388	+	0.818200i
$160$	−200.150	−	296.547i	−0.0988951	−	0.146526i
$161$	−703.534	−	1544.92i	−0.344387	−	0.756255i
$162$			110.663i			0.0536698i
$163$	75.9641	−	43.8579i	0.0365029	−	0.0210750i	−0.481638	−	0.876371i	$-0.659958\pi$
$163$	75.9641	−	43.8579i	0.0365029	−	0.0210750i	0.518140	+	0.855296i	$0.326624\pi$
$164$	798.043	−	1382.25i	0.379980	−	0.658144i
$165$	1693.57	−	118.924i	0.799057	−	0.0561103i
$166$	−1341.21	−	2323.04i	−0.627095	−	1.08616i
$167$			1851.38i			0.857868i	0.903336	+	0.428934i	$0.141111\pi$
$167$			1851.38i			0.857868i	−0.903336	+	0.428934i	$0.858889\pi$
$168$	369.941	+	264.035i	0.169890	+	0.121254i
$169$	206.469			0.0939779
$170$	−789.773	−	384.912i	−0.356311	−	0.173655i
$171$	−495.293	+	857.873i	−0.221497	+	0.383645i
$172$	−705.177	−	407.134i	−0.312612	−	0.180486i
$173$	1595.29	−	921.039i	0.701083	−	0.404771i	−0.106668	−	0.994295i	$-0.534018\pi$
$173$	1595.29	−	921.039i	0.701083	−	0.404771i	0.807751	+	0.589524i	$0.200685\pi$
$174$	−1729.17			−0.753379
$175$	−1952.10	+	1244.45i	−0.843229	+	0.537554i
$176$	−792.026			−0.339211
$177$	1276.53	−	737.008i	0.542092	−	0.312977i
$178$	2253.60	+	1301.12i	0.948958	+	0.547881i
$179$	374.266	−	648.248i	0.156279	−	0.270683i	−0.777245	−	0.629198i	$-0.783383\pi$
$179$	374.266	−	648.248i	0.156279	−	0.270683i	0.933524	+	0.358515i	$0.116717\pi$
$180$	−707.132	−	344.635i	−0.292814	−	0.142709i
$181$	−1393.90			−0.572418			−0.286209	−	0.958167i	$-0.592395\pi$
$181$	−1393.90			−0.572418			−0.286209	+	0.958167i	$0.592395\pi$
$182$	−1503.97	+	684.886i	−0.612539	+	0.278940i
$183$			72.0803i			0.0291166i
$184$	366.641	+	635.041i	0.146898	+	0.254434i
$185$	−2198.11	+	154.353i	−0.873559	+	0.0613419i
$186$	−216.466	+	374.930i	−0.0853335	+	0.147802i
$187$	−1684.40	+	972.489i	−0.658693	+	0.380297i
$188$			273.995i			0.106293i
$189$	2521.53	+	243.518i	0.970448	+	0.0937211i
$190$	−704.473	−	1043.77i	−0.268989	−	0.398541i
$191$	479.087	+	829.803i	0.181495	+	0.314358i	0.942390	−	0.334517i	$-0.108573\pi$
$191$	479.087	+	829.803i	0.181495	+	0.314358i	−0.760895	+	0.648875i	$0.775240\pi$
$192$	−170.023	−	98.1629i	−0.0639081	−	0.0368974i
$193$	−3963.83	−	2288.52i	−1.47836	−	0.853530i	−0.478656	−	0.878002i	$-0.658876\pi$
$193$	−3963.83	−	2288.52i	−1.47836	−	0.853530i	−0.999700	+	0.0244729i	$0.992209\pi$
$194$	323.729	+	560.714i	0.119806	+	0.207510i
$195$	−1268.31	+	856.025i	−0.465772	+	0.314365i
$196$	−900.700	+	1034.95i	−0.328243	+	0.377169i
$197$		−	3429.27i		−	1.24023i	−0.784511	−	0.620115i	$-0.787086\pi$
$197$		−	3429.27i		−	1.24023i	0.784511	−	0.620115i	$-0.212914\pi$
$198$	−1508.15	+	870.729i	−0.541309	+	0.312525i
$199$	−73.0079	+	126.453i	−0.0260070	+	0.0450454i	−0.878736	−	0.477308i	$-0.841613\pi$
$199$	−73.0079	+	126.453i	−0.0260070	+	0.0450454i	0.852729	+	0.522354i	$0.174946\pi$
$200$	787.651	−	616.122i	0.278477	−	0.217832i
$201$	386.707	+	669.795i	0.135702	+	0.235043i
$202$			2362.04i			0.822734i
$203$	501.772	−	5195.67i	0.173485	−	1.79638i
$204$	−482.117			−0.165465
$205$	4010.27	+	1954.49i	1.36629	+	0.665889i
$206$	−732.042	+	1267.93i	−0.247591	+	0.428840i
$207$	1396.29	+	806.147i	0.468835	+	0.270682i
$208$	618.209	−	356.923i	0.206082	−	0.118981i
$209$	−2787.72			−0.922634
$210$	−663.755	+	1083.17i	−0.218112	+	0.355933i
$211$	−705.410			−0.230154			−0.115077	−	0.993357i	$-0.536711\pi$
$211$	−705.410			−0.230154			−0.115077	+	0.993357i	$0.536711\pi$
$212$	2139.03	−	1234.97i	0.692969	−	0.400086i
$213$	2219.97	+	1281.70i	0.714131	+	0.412304i
$214$	−1338.04	+	2317.56i	−0.427414	+	0.740303i
$215$	997.112	−	2045.90i	0.316290	−	0.648973i
$216$	−1094.27			−0.344701
$217$	−1063.74	−	759.216i	−0.332773	−	0.237507i
$218$			103.514i			0.0321600i
$219$	395.390	+	684.836i	0.122000	+	0.211310i
$220$	−155.071	−	2208.34i	−0.0475223	−	0.676756i
$221$	876.496	−	1518.13i	0.266785	−	0.462085i
$222$	−1047.18	+	604.589i	−0.316586	+	0.182781i
$223$			2232.07i			0.670271i	0.942170	+	0.335135i	$0.108782\pi$
$223$			2232.07i			0.670271i	−0.942170	+	0.335135i	$0.891218\pi$
$224$	344.289	−	482.387i	0.102696	−	0.143888i
$225$	822.469	−	2039.11i	0.243694	−	0.604182i
$226$	471.803	+	817.186i	0.138867	+	0.240524i
$227$	4732.79	+	2732.48i	1.38382	+	0.798947i	0.992609	−	0.121355i	$-0.0387239\pi$
$227$	4732.79	+	2732.48i	1.38382	+	0.798947i	0.391208	+	0.920302i	$0.372057\pi$
$228$	−598.435	−	345.507i	−0.173826	−	0.100359i
$229$	971.944	+	1683.46i	0.280471	+	0.485790i	0.971501	−	0.237036i	$-0.0761760\pi$
$229$	971.944	+	1683.46i	0.280471	+	0.485790i	−0.691030	+	0.722826i	$0.742843\pi$
$230$	−1698.85	+	1146.61i	−0.487038	+	0.328719i
$231$	1165.52	+	2559.43i	0.331973	+	0.728996i
$232$			2254.76i			0.638070i
$233$	−2864.16	+	1653.62i	−0.805311	+	0.464946i	−0.845325	−	0.534253i	$-0.820593\pi$
$233$	−2864.16	+	1653.62i	−0.805311	+	0.464946i	0.0400141	+	0.999199i	$0.487260\pi$
$234$	784.780	−	1359.28i	0.219242	−	0.379738i
$235$	−763.959	+	53.6457i	−0.212065	+	0.0148913i
$236$	−961.025	−	1664.54i	−0.265074	−	0.459121i
$237$		−	2373.39i		−	0.650500i
$238$	139.901	−	1448.63i	0.0381028	−	0.394540i
$239$	−6107.99			−1.65311			−0.826554	−	0.562857i	$-0.809702\pi$
$239$	−6107.99			−1.65311			−0.826554	+	0.562857i	$0.809702\pi$
$240$	240.411	−	493.281i	0.0646602	−	0.132671i
$241$	1981.30	−	3431.71i	0.529571	−	0.917245i	−0.469834	−	0.882755i	$-0.655686\pi$
$241$	1981.30	−	3431.71i	0.529571	−	0.917245i	0.999405	−	0.0344896i	$-0.0109805\pi$
$242$	−1938.88	−	1119.41i	−0.515024	−	0.297349i
$243$	−3345.36	+	1931.44i	−0.883148	+	0.509886i
$244$	93.9895			0.0246601
$245$	−3062.02	−	2308.71i	−0.798470	−	0.602034i
$246$	2448.07			0.634484
$247$	2175.93	−	1256.27i	0.560530	−	0.323622i
$248$	488.892	+	282.262i	0.125180	+	0.0722727i
$249$	2057.13	−	3563.06i	0.523556	−	0.906826i
$250$	1872.10	+	2075.51i	0.473608	+	0.525067i
$251$	−3.92299			−0.000986522			−0.000493261	−	1.00000i	$-0.500157\pi$
$251$	−3.92299			−0.000986522			−0.000493261		1.00000i	$0.500157\pi$
$252$	125.262	−	1297.04i	0.0313126	−	0.324230i
$253$			4537.33i			1.12751i
$254$	−202.294	−	350.384i	−0.0499727	−	0.0865553i
$255$	−94.3940	−	1344.25i	−0.0231811	−	0.330118i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−190.175	+	109.797i	−0.0461586	+	0.0266497i	−0.522902	−	0.852393i	$-0.675151\pi$
$257$	−190.175	+	109.797i	−0.0461586	+	0.0266497i	0.476743	+	0.879043i	$0.341817\pi$
$258$		−	1248.92i		−	0.301373i
$259$	−1512.75	−	3321.92i	−0.362925	−	0.796965i
$260$	1116.22	+	1653.82i	0.266250	+	0.394483i
$261$	2478.81	+	4293.42i	0.587872	+	1.01822i
$262$	2024.69	+	1168.96i	0.477427	+	0.275643i
$263$	−4735.18	−	2733.86i	−1.11020	−	0.640977i	−0.171322	−	0.985215i	$-0.554804\pi$
$263$	−4735.18	−	2733.86i	−1.11020	−	0.640977i	−0.938882	+	0.344238i	$0.888137\pi$
$264$	−607.403	−	1052.05i	−0.141602	−	0.245263i
$265$	3862.17	+	5722.30i	0.895289	+	1.32648i
$266$	1211.81	−	1697.87i	0.279325	−	0.391365i
$267$			3991.29i			0.914843i
$268$	873.383	−	504.248i	0.199069	−	0.114932i
$269$	−145.866	+	252.647i	−0.0330616	+	0.0572644i	−0.882083	−	0.471094i	$-0.843859\pi$
$269$	−145.866	+	252.647i	−0.0330616	+	0.0572644i	0.849021	+	0.528359i	$0.177192\pi$
$270$	−214.247	−	3051.06i	−0.0482914	−	0.687709i
$271$	−1330.51	−	2304.51i	−0.298239	−	0.516565i	0.677494	−	0.735528i	$-0.263066\pi$
$271$	−1330.51	−	2304.51i	−0.298239	−	0.516565i	−0.975733	+	0.218963i	$0.929733\pi$
$272$			628.659i			0.140140i
$273$	−2063.13	−	1472.50i	−0.457386	−	0.326446i
$274$	293.435			0.0646973
$275$	6126.98	−	864.746i	1.34353	−	0.189622i
$276$	−562.352	+	974.023i	−0.122644	+	0.212425i
$277$	3899.41	+	2251.33i	0.845824	+	0.488336i	0.859240	−	0.511574i	$-0.170937\pi$
$277$	3899.41	+	2251.33i	0.845824	+	0.488336i	−0.0134159	+	0.999910i	$0.504271\pi$
$278$	4339.89	−	2505.64i	0.936292	−	0.540568i
$279$	1241.24			0.266348
$280$	1412.41	+	865.507i	0.301455	+	0.184728i
$281$	−462.388			−0.0981628			−0.0490814	−	0.998795i	$-0.515629\pi$
$281$	−462.388			−0.0981628			−0.0490814	+	0.998795i	$0.515629\pi$
$282$	−363.949	+	210.126i	−0.0768542	+	0.0443718i
$283$	6188.37	+	3572.86i	1.29986	+	0.750474i	0.980380	−	0.197118i	$-0.0631584\pi$
$283$	6188.37	+	3572.86i	1.29986	+	0.750474i	0.319480	+	0.947593i	$0.396492\pi$
$284$	1671.28	−	2894.74i	0.349198	−	0.604829i
$285$	846.181	−	1736.22i	0.175872	−	0.360858i
$286$	4417.07			0.913240
$287$	−710.383	+	7355.75i	−0.146107	+	1.51288i
$288$			562.877i			0.115166i
$289$	−1684.60	−	2917.81i	−0.342886	−	0.593897i
$290$	−6286.76	+	441.461i	−1.27300	+	0.0893913i
$291$	−496.533	+	860.021i	−0.100025	+	0.173248i
$292$	892.996	−	515.571i	0.178968	−	0.103327i
$293$		−	8656.21i		−	1.72594i	−0.505254	−	0.862971i	$-0.668601\pi$
$293$		−	8656.21i		−	1.72594i	0.505254	−	0.862971i	$-0.331399\pi$
$294$	−2065.48	−	402.703i	−0.409731	−	0.0798848i
$295$	4452.95	−	3005.45i	0.878851	−	0.593166i
$296$	788.357	+	1365.47i	0.154805	+	0.268130i
$297$	−5863.86	−	3385.50i	−1.14564	−	0.661437i
$298$	3651.47	+	2108.18i	0.709812	+	0.409810i
$299$	−2044.73	−	3541.57i	−0.395484	−	0.684998i
$300$	1422.45	+	573.738i	0.273750	+	0.110416i
$301$	3752.65	+	362.413i	0.718603	+	0.0693991i
$302$		−	4431.01i		−	0.844291i
$303$	−3137.50	+	1811.44i	−0.594868	+	0.343447i
$304$	−450.525	+	780.333i	−0.0849981	+	0.147221i
$305$	18.4023	+	262.063i	0.00345479	+	0.0491990i
$306$	691.128	+	1197.07i	0.129115	+	0.223634i
$307$			4296.26i			0.798699i	0.916799	+	0.399349i	$0.130764\pi$
$307$			4296.26i			0.798699i	−0.916799	+	0.399349i	$0.869236\pi$
$308$	3337.38	−	1519.79i	0.617418	−	0.281162i
$309$	−2245.60			−0.413424
$310$	−691.287	+	1418.40i	−0.126653	+	0.259870i
$311$	−1967.56	+	3407.92i	−0.358747	+	0.621368i	−0.987752	−	0.156034i	$-0.950129\pi$
$311$	−1967.56	+	3407.92i	−0.358747	+	0.621368i	0.629005	+	0.777401i	$0.283463\pi$
$312$	948.205	+	547.446i	0.172056	+	0.0993367i
$313$	−9092.34	+	5249.47i	−1.64195	+	0.947979i	−0.661807	+	0.749674i	$0.730210\pi$
$313$	−9092.34	+	5249.47i	−1.64195	+	0.947979i	−0.980140	+	0.198304i	$0.936457\pi$
$314$	−4524.05			−0.813080
$315$	3640.97	+	95.3092i	0.651254	+	0.0170478i
$316$	−3094.80			−0.550937
$317$	4977.20	−	2873.59i	0.881853	−	0.509138i	0.0105840	−	0.999944i	$-0.496631\pi$
$317$	4977.20	−	2873.59i	0.881853	−	0.509138i	0.871269	+	0.490806i	$0.163298\pi$
$318$	3280.84	+	1894.19i	0.578554	+	0.334029i
$319$	−6975.89	+	12082.6i	−1.22437	+	2.12068i
$320$	−643.216	−	313.485i	−0.112365	−	0.0547635i
$321$	−4104.56			−0.713690
$322$	−2763.48	−	1972.35i	−0.478270	−	0.341351i
$323$			2212.71i			0.381172i
$324$	110.663	+	191.674i	0.0189751	+	0.0328659i
$325$	−4392.66	+	3436.06i	−0.749727	+	0.586457i
$326$	87.7158	−	151.928i	0.0149022	−	0.0258114i
$327$	−137.499	+	79.3848i	−0.0232529	+	0.0134250i
$328$		−	3192.17i		−	0.537372i
$329$	−525.759	−	1154.54i	−0.0881035	−	0.193471i
$330$	2814.43	−	1899.55i	0.469483	−	0.316870i
$331$	−4704.04	−	8147.64i	−0.781141	−	1.35298i	−0.931277	−	0.364311i	$-0.881305\pi$
$331$	−4704.04	−	8147.64i	−0.781141	−	1.35298i	0.150136	−	0.988665i	$-0.452029\pi$
$332$	−4646.07	−	2682.41i	−0.768031	−	0.443423i
$333$	3002.32	+	1733.39i	0.494072	+	0.285253i
$334$	1851.38	+	3206.68i	0.303302	+	0.525335i
$335$	1576.95	+	2336.46i	0.257189	+	0.381058i
$336$	904.791	+	87.3803i	0.146906	+	0.0141875i
$337$		−	4501.95i		−	0.727706i	−0.931456	−	0.363853i	$-0.881461\pi$
$337$		−	4501.95i		−	0.727706i	0.931456	−	0.363853i	$-0.118539\pi$
$338$	357.615	−	206.469i	0.0575495	−	0.0332262i
$339$	−723.649	+	1253.40i	−0.115939	+	0.200812i
$340$	−1752.84	+	123.086i	−0.279591	+	0.0196331i
$341$	1746.55	+	3025.12i	0.277364	+	0.480408i
$342$			1981.17i			0.313244i
$343$	1809.37	−	6089.32i	0.284831	−	0.958578i
$344$	−1628.54			−0.255246
$345$	−2825.89	−	1377.26i	−0.440988	−	0.214925i
$346$	1842.08	−	3190.57i	0.286216	−	0.495741i
$347$	−4324.38	−	2496.68i	−0.669005	−	0.386250i	0.126695	−	0.991942i	$-0.459563\pi$
$347$	−4324.38	−	2496.68i	−0.669005	−	0.386250i	−0.795700	+	0.605692i	$0.792897\pi$
$348$	−2995.01	+	1729.17i	−0.461348	+	0.266360i
$349$	−6675.06			−1.02381			−0.511903	−	0.859044i	$-0.671059\pi$
$349$	−6675.06			−1.02381			−0.511903	+	0.859044i	$0.671059\pi$
$350$	−2136.69	+	4107.56i	−0.326316	+	0.627310i
$351$	6102.65			0.928020
$352$	−1371.83	+	792.026i	−0.207724	+	0.119929i
$353$	2458.93	+	1419.66i	0.370752	+	0.214054i	0.673787	−	0.738926i	$-0.264667\pi$
$353$	2458.93	+	1419.66i	0.370752	+	0.214054i	−0.303035	+	0.952979i	$0.598000\pi$
$354$	1474.02	−	2553.07i	0.221308	−	0.383317i
$355$	8398.40	+	4093.13i	1.25561	+	0.611946i
$356$	5204.47			0.774821
$357$	2031.51	−	925.116i	0.301173	−	0.137149i
$358$		−	1497.06i		−	0.221012i
$359$	−4242.21	−	7347.72i	−0.623663	−	1.08022i	−0.988798	−	0.149262i	$-0.952310\pi$
$359$	−4242.21	−	7347.72i	−0.623663	−	1.08022i	0.365134	−	0.930955i	$-0.381023\pi$
$360$	−1569.42	+	110.206i	−0.229766	+	0.0161344i
$361$	1843.77	−	3193.51i	0.268811	−	0.465594i
$362$	−2414.30	+	1393.90i	−0.350533	+	0.202380i
$363$		−	3433.90i		−	0.496509i
$364$	−1920.07	+	2690.23i	−0.276481	+	0.387380i
$365$	1612.37	+	2388.92i	0.231220	+	0.342581i
$366$	72.0803	+	124.847i	0.0102943	+	0.0178302i
$367$	−9803.17	−	5659.86i	−1.39434	−	0.805020i	−0.400544	−	0.916277i	$-0.631179\pi$
$367$	−9803.17	−	5659.86i	−1.39434	−	0.805020i	−0.993792	+	0.111257i	$0.964512\pi$
$368$	1270.08	+	733.282i	0.179912	+	0.103872i
$369$	−3509.37	−	6078.41i	−0.495096	−	0.857532i
$370$	−3652.89	+	2465.46i	−0.513256	+	0.346414i
$371$	−6643.56	+	9308.34i	−0.929693	+	1.30260i
$372$			865.863i			0.120680i
$373$	−9791.45	+	5653.09i	−1.35920	+	0.784735i	−0.989516	−	0.144423i	$-0.953868\pi$
$373$	−9791.45	+	5653.09i	−1.35920	+	0.784735i	−0.369684	+	0.929157i	$0.620534\pi$
$374$	−1944.98	+	3368.80i	−0.268910	+	0.465766i
$375$	−1321.20	+	4078.42i	−0.181938	+	0.561624i
$376$	273.995	+	474.574i	0.0375804	+	0.0650912i
$377$		−	12574.6i		−	1.71784i
$378$	4610.94	−	2099.75i	0.627411	−	0.285713i
$379$	10626.4			1.44022			0.720109	−	0.693861i	$-0.244092\pi$
$379$	10626.4			1.44022			0.720109	+	0.693861i	$0.244092\pi$
$380$	−2263.95	−	1103.38i	−0.305627	−	0.148953i
$381$	310.278	−	537.417i	0.0417218	−	0.0722644i
$382$	1659.61	+	958.174i	0.222285	+	0.128336i
$383$	6566.96	−	3791.44i	0.876126	−	0.505832i	0.00674681	−	0.999977i	$-0.497852\pi$
$383$	6566.96	−	3791.44i	0.876126	−	0.505832i	0.869379	+	0.494146i	$0.164519\pi$
$384$	−392.651			−0.0521808
$385$	4890.93	+	9007.78i	0.647442	+	1.19241i
$386$	−9154.08			−1.20707
$387$	−3101.00	+	1790.36i	−0.407319	+	0.235166i
$388$	1121.43	+	647.457i	0.146732	+	0.0847156i
$389$	1606.41	−	2782.39i	0.209379	−	0.362655i	−0.742140	−	0.670245i	$-0.766189\pi$
$389$	1606.41	−	2782.39i	0.209379	−	0.362655i	0.951519	+	0.307590i	$0.0995225\pi$
$390$	−1340.75	+	2750.99i	−0.174081	+	0.357184i
$391$	3601.44			0.465813
$392$	−525.107	+	2693.29i	−0.0676579	+	0.347019i
$393$			3585.88i			0.460264i
$394$	−3429.27	−	5939.67i	−0.438488	−	0.759483i
$395$	−605.933	−	8628.98i	−0.0771843	−	1.09917i
$396$	−1741.46	+	3016.29i	−0.220989	+	0.382764i
$397$	11414.9	−	6590.40i	1.44307	−	0.833155i	0.445014	−	0.895524i	$-0.353199\pi$
$397$	11414.9	−	6590.40i	1.44307	−	0.833155i	0.998053	+	0.0623685i	$0.0198654\pi$
$398$			292.031i			0.0367794i
$399$	3184.62	+	307.555i	0.399575	+	0.0385890i
$400$	748.128	−	1854.81i	0.0935161	−	0.231851i
$401$	3597.12	+	6230.39i	0.447959	+	0.775887i	0.998253	−	0.0590837i	$-0.0188179\pi$
$401$	3597.12	+	6230.39i	0.447959	+	0.775887i	−0.550295	+	0.834971i	$0.685485\pi$
$402$	1339.59	+	773.413i	0.166201	+	0.0959561i
$403$	−2726.51	−	1574.15i	−0.337015	−	0.194576i
$404$	2362.04	+	4091.17i	0.290880	+	0.503820i
$405$	−512.762	+	346.081i	−0.0629120	+	0.0424615i
$406$	−4326.57	−	9500.93i	−0.528877	−	1.16139i
$407$			9756.24i			1.18820i
$408$	−835.051	+	482.117i	−0.101326	+	0.0585009i
$409$	−544.577	+	943.234i	−0.0658376	+	0.114034i	−0.897065	−	0.441898i	$-0.854305\pi$
$409$	−544.577	+	943.234i	−0.0658376	+	0.114034i	0.831228	+	0.555932i	$0.187639\pi$
$410$	8900.47	−	624.997i	1.07210	−	0.0752839i
$411$	225.035	+	389.771i	0.0270076	+	0.0467786i
$412$			2928.17i			0.350147i
$413$	7243.53	+	5169.85i	0.863028	+	0.615961i
$414$	3224.59			0.382802
$415$	6569.49	−	13479.5i	0.777069	−	1.59441i
$416$	713.846	−	1236.42i	0.0841326	−	0.145722i
$417$	6656.50	+	3843.13i	0.781703	+	0.451316i
$418$	−4828.47	+	2787.72i	−0.564996	+	0.326200i
$419$	12514.5			1.45913			0.729563	−	0.683914i	$-0.239724\pi$
$419$	12514.5			1.45913			0.729563	+	0.683914i	$0.239724\pi$
$420$	−66.4858	+	2539.86i	−0.00772423	+	0.295078i
$421$	−827.022			−0.0957401			−0.0478701	−	0.998854i	$-0.515243\pi$
$421$	−827.022			−0.0957401			−0.0478701	+	0.998854i	$0.515243\pi$
$422$	−1221.81	+	705.410i	−0.140940	+	0.0813716i
$423$	1043.46	+	602.444i	0.119941	+	0.0692478i
$424$	2469.94	−	4278.07i	0.282903	−	0.490003i
$425$	−686.379	−	4863.20i	−0.0783395	−	0.555059i
$426$	5126.80			0.583085
$427$	−396.046	+	180.353i	−0.0448853	+	0.0204400i
$428$			5352.17i			0.604455i
$429$	3387.44	+	5867.21i	0.381228	+	0.660307i
$430$	−318.852	−	4540.71i	−0.0357591	−	0.509239i
$431$	840.220	−	1455.30i	0.0939025	−	0.162644i	−0.815248	−	0.579113i	$-0.803399\pi$
$431$	840.220	−	1455.30i	0.0939025	−	0.162644i	0.909150	+	0.416469i	$0.136732\pi$
$432$	−1895.33	+	1094.27i	−0.211086	+	0.121870i
$433$		−	7421.56i		−	0.823689i	−0.911254	−	0.411845i	$-0.864885\pi$
$433$		−	7421.56i		−	0.823689i	0.911254	−	0.411845i	$-0.135115\pi$
$434$	−2601.68	−	251.257i	−0.287752	−	0.0277897i
$435$	−5407.69	−	8012.18i	−0.596044	−	0.883114i
$436$	103.514	+	179.292i	0.0113703	+	0.0196939i
$437$	4470.35	+	2580.96i	0.489349	+	0.282526i
$438$	1369.67	+	790.781i	0.149419	+	0.0862671i
$439$	2399.11	+	4155.39i	0.260828	+	0.451767i	0.966462	−	0.256809i	$-0.0826711\pi$
$439$	2399.11	+	4155.39i	0.260828	+	0.451767i	−0.705634	+	0.708576i	$0.749338\pi$
$440$	−2476.93	−	3669.89i	−0.268371	−	0.397625i
$441$	1961.03	+	5705.74i	0.211751	+	0.616104i
$442$		−	3505.98i		−	0.377291i
$443$	−13800.6	+	7967.80i	−1.48011	+	0.854541i	−0.999746	−	0.0225292i	$-0.992828\pi$
$443$	−13800.6	+	7967.80i	−1.48011	+	0.854541i	−0.480362	+	0.877070i	$0.659495\pi$
$444$	−1209.18	+	2094.36i	−0.129246	+	0.223860i
$445$	1018.99	+	14511.2i	0.108550	+	1.54583i
$446$	2232.07	+	3866.06i	0.236977	+	0.410455i
$447$			6467.03i			0.684295i
$448$	113.940	−	1179.81i	0.0120160	−	0.124421i
$449$	9352.06			0.982964			0.491482	−	0.870888i	$-0.336455\pi$
$449$	9352.06			0.982964			0.491482	+	0.870888i	$0.336455\pi$
$450$	−614.557	−	4354.32i	−0.0643789	−	0.456143i
$451$	9876.10	−	17105.9i	1.03115	−	1.78600i
$452$	1634.37	+	943.606i	0.170076	+	0.0981935i
$453$	5885.73	−	3398.13i	0.610455	−	0.352446i
$454$	10929.9			1.12988
$455$	−7876.89	−	4826.87i	−0.811592	−	0.497334i
$456$	−1382.03			−0.141928
$457$	−7428.09	+	4288.61i	−0.760331	+	0.438977i	−0.829415	−	0.558633i	$-0.811326\pi$
$457$	−7428.09	+	4288.61i	−0.760331	+	0.438977i	0.0690835	+	0.997611i	$0.477993\pi$
$458$	3366.91	+	1943.89i	0.343506	+	0.198323i
$459$	−2687.19	+	4654.36i	−0.273262	+	0.473304i
$460$	−1795.88	+	3684.84i	−0.182029	+	0.373492i
$461$	−8463.98			−0.855113			−0.427556	−	0.903989i	$-0.640625\pi$
$461$	−8463.98			−0.855113			−0.427556	+	0.903989i	$0.640625\pi$
$462$	4578.17	+	3267.54i	0.461030	+	0.329047i
$463$		−	4297.74i		−	0.431388i	−0.976461	−	0.215694i	$-0.930799\pi$
$463$		−	4297.74i		−	0.431388i	0.976461	−	0.215694i	$-0.0692014\pi$
$464$	2254.76	+	3905.36i	0.225592	+	0.390736i
$465$	−2414.22	+	169.528i	−0.240767	+	0.0169068i
$466$	−3307.25	+	5728.32i	−0.328767	+	0.569441i
$467$	892.116	−	515.064i	0.0883988	−	0.0510371i	−0.455149	−	0.890415i	$-0.650414\pi$
$467$	892.116	−	515.064i	0.0883988	−	0.0510371i	0.543548	+	0.839378i	$0.317081\pi$
$468$		−	3139.12i		−	0.310055i
$469$	−2712.61	+	3800.66i	−0.267072	+	0.374197i
$470$	−1269.57	+	856.876i	−0.124598	+	0.0840952i
$471$	−3469.49	−	6009.33i	−0.339417	−	0.587888i
$472$	−3329.09	−	1922.05i	−0.324648	−	0.187435i
$473$	−8726.85	−	5038.45i	−0.848332	−	0.489785i
$474$	−2373.39	−	4110.84i	−0.229986	−	0.398348i
$475$	2633.21	−	6528.42i	0.254358	−	0.630619i
$476$	−1206.31	−	2649.00i	−0.116158	−	0.255077i
$477$		−	10861.5i		−	1.04259i
$478$	−10579.3	+	6107.99i	−1.01232	+	0.584462i
$479$	2568.74	−	4449.19i	0.245029	−	0.424402i	−0.717111	−	0.696959i	$-0.754536\pi$
$479$	2568.74	−	4449.19i	0.245029	−	0.424402i	0.962140	+	0.272557i	$0.0878692\pi$
$480$	−76.8775	−	1094.80i	−0.00731034	−	0.104105i
$481$	−4396.60	−	7615.14i	−0.416773	−	0.721872i
$482$		−	7925.20i		−	0.748927i
$483$	500.582	−	5183.34i	0.0471579	−	0.488303i
$484$	−4477.65			−0.420515
$485$	−1585.69	+	3253.55i	−0.148458	+	0.304611i
$486$	−3862.89	+	6690.72i	−0.360544	+	0.624480i
$487$	455.995	+	263.269i	0.0424294	+	0.0244966i	0.521065	−	0.853517i	$-0.325535\pi$
$487$	455.995	+	263.269i	0.0424294	+	0.0244966i	−0.478635	+	0.878014i	$0.658868\pi$
$488$	162.795	−	93.9895i	0.0151012	−	0.00871866i
$489$	269.076			0.0248835
$490$	−7612.29	−	936.792i	−0.701812	−	0.0863673i
$491$	−1546.87			−0.142178			−0.0710889	−	0.997470i	$-0.522647\pi$
$491$	−1546.87			−0.142178			−0.0710889	+	0.997470i	$0.522647\pi$
$492$	4240.18	−	2448.07i	0.388540	−	0.224324i
$493$	9590.38	+	5537.01i	0.876124	+	0.505830i
$494$	2512.54	−	4351.85i	0.228835	−	0.396355i
$495$	−8751.04	−	4265.00i	−0.794606	−	0.387268i
$496$	1129.05			0.102209
$497$	−1487.70	+	15404.6i	−0.134271	+	1.39032i
$498$		−	8228.54i		−	0.740421i
$499$	4746.42	+	8221.04i	0.425809	+	0.737524i	0.996496	−	0.0836446i	$-0.0266561\pi$
$499$	4746.42	+	8221.04i	0.425809	+	0.737524i	−0.570686	+	0.821168i	$0.693323\pi$
$500$	5318.08	+	1722.79i	0.475664	+	0.154091i
$501$	−2839.64	+	4918.39i	−0.253225	+	0.438598i
$502$	−6.79482	+	3.92299i	−0.000604119	+	0.000348788i
$503$		−	9819.97i		−	0.870479i	−0.900315	−	0.435239i	$-0.856664\pi$
$503$		−	9819.97i		−	0.870479i	0.900315	−	0.435239i	$-0.143336\pi$
$504$	−1080.08	−	2371.81i	−0.0954578	−	0.209620i
$505$	−10944.6	+	7386.89i	−0.964413	+	0.650915i
$506$	4537.33	+	7858.89i	0.398635	+	0.690455i
$507$	548.509	+	316.682i	0.0480476	+	0.0277403i
$508$	−700.768	−	404.589i	−0.0612039	−	0.0353361i
$509$	−1319.03	−	2284.62i	−0.114862	−	0.198947i	0.802863	−	0.596164i	$-0.203309\pi$
$509$	−1319.03	−	2284.62i	−0.114862	−	0.198947i	−0.917725	+	0.397217i	$0.869976\pi$
$510$	−1507.74	−	2233.91i	−0.130910	−	0.193959i
$511$	−2773.53	+	3886.01i	−0.240105	+	0.336413i
$512$			512.000i			0.0441942i
$513$	−6671.04	+	3851.53i	−0.574140	+	0.331480i
$514$	−219.595	+	380.349i	−0.0188442	+	0.0326391i
$515$	−8164.37	+	573.308i	−0.698573	+	0.0490543i
$516$	−1248.92	−	2163.19i	−0.106552	−	0.184553i
$517$			3390.80i			0.288448i
$518$	−5942.08	−	4240.98i	−0.504015	−	0.359726i
$519$	5650.74			0.477919
$520$	3587.17	+	1748.28i	0.302515	+	0.147437i
$521$	−2213.18	+	3833.33i	−0.186106	+	0.322344i	−0.943949	−	0.330093i	$-0.892920\pi$
$521$	−2213.18	+	3833.33i	−0.186106	+	0.322344i	0.757843	+	0.652437i	$0.226253\pi$
$522$	8586.85	+	4957.62i	0.719993	+	0.415688i
$523$	784.415	−	452.882i	0.0655833	−	0.0378645i	−0.466850	−	0.884337i	$-0.654611\pi$
$523$	784.415	−	452.882i	0.0655833	−	0.0378645i	0.532433	+	0.846472i	$0.321278\pi$
$524$	4675.82			0.389817
$525$	−7094.72	+	311.905i	−0.589788	+	0.0259288i
$526$	−10935.4			−0.906478
$527$	2401.14	−	1386.30i	0.198473	−	0.114589i
$528$	−2104.11	−	1214.81i	−0.173427	−	0.100128i
$529$	−1882.70	+	3260.92i	−0.154738	+	0.268014i
$530$	12411.8	+	6049.14i	1.01723	+	0.495769i
$531$	−8452.16			−0.690758
$532$	401.038	−	4152.60i	0.0326827	−	0.338418i
$533$			17802.5i			1.44674i
$534$	3991.29	+	6913.12i	0.323446	+	0.560225i
$535$	−14923.0	+	1047.90i	−1.20594	+	0.0846820i
$536$	1008.50	−	1746.77i	0.0812694	−	0.140763i
$537$	1988.56	−	1148.09i	0.159800	−	0.0922606i
$538$			583.462i			0.0467562i
$539$	−11146.5	+	12807.9i	−0.890751	+	1.02352i
$540$	−3422.15	−	5070.34i	−0.272714	−	0.404061i
$541$	−9810.32	−	16992.0i	−0.779628	−	1.35035i	−0.932157	−	0.362056i	$-0.882075\pi$
$541$	−9810.32	−	16992.0i	−0.779628	−	1.35035i	0.152529	−	0.988299i	$-0.451258\pi$
$542$	−4609.02	−	2661.02i	−0.365267	−	0.210887i
$543$	−3703.05	−	2137.96i	−0.292657	−	0.168966i
$544$	628.659	+	1088.87i	0.0495470	+	0.0858178i
$545$	−479.638	+	323.724i	−0.0376980	+	0.0254437i
$546$	−5045.95	−	487.313i	−0.395507	−	0.0381961i
$547$		−	6717.26i		−	0.525062i	−0.964923	−	0.262531i	$-0.915443\pi$
$547$		−	6717.26i		−	0.525062i	0.964923	−	0.262531i	$-0.0845573\pi$
$548$	508.244	−	293.435i	0.0396188	−	0.0228740i
$549$	206.658	−	357.943i	0.0160655	−	0.0278263i
$550$	9747.50	−	7624.77i	0.755699	−	0.591129i
$551$	7936.14	+	13745.8i	0.613595	+	1.06278i
$552$			2249.41i			0.173444i
$553$	13040.6	−	5938.49i	1.00279	−	0.456655i
$554$	9005.31			0.690612
$555$	−6076.27	−	2961.40i	−0.464727	−	0.226494i
$556$	5011.27	−	8679.78i	0.382240	−	0.662058i
$557$	−11348.4	−	6551.98i	−0.863277	−	0.498413i	0.00183114	−	0.999998i	$-0.499417\pi$
$557$	−11348.4	−	6551.98i	−0.863277	−	0.498413i	−0.865108	+	0.501585i	$0.832750\pi$
$558$	2149.89	−	1241.24i	0.163104	−	0.0941681i
$559$	9082.21			0.687186
$560$	3311.87	+	86.6945i	0.249914	+	0.00654199i
$561$	−5966.40			−0.449022
$562$	−800.879	+	462.388i	−0.0601122	+	0.0347058i
$563$	14418.2	+	8324.35i	1.07932	+	0.623143i	0.930712	−	0.365754i	$-0.119189\pi$
$563$	14418.2	+	8324.35i	1.07932	+	0.623143i	0.148604	+	0.988897i	$0.452522\pi$
$564$	−420.253	+	727.899i	−0.0313756	+	0.0543441i
$565$	−2310.98	+	4741.74i	−0.172078	+	0.353073i
$566$	14291.4			1.06133
$567$	−834.099	−	595.314i	−0.0617793	−	0.0440932i
$568$		−	6685.12i		−	0.493841i
$569$	7348.85	+	12728.6i	0.541441	+	0.937803i	0.998822	+	0.0485321i	$0.0154543\pi$
$569$	7348.85	+	12728.6i	0.541441	+	0.937803i	−0.457381	+	0.889271i	$0.651212\pi$
$570$	−270.588	−	3853.39i	−0.0198837	−	0.283160i
$571$	−1498.89	+	2596.15i	−0.109854	+	0.190272i	−0.915711	−	0.401838i	$-0.868372\pi$
$571$	−1498.89	+	2596.15i	−0.109854	+	0.190272i	0.805857	+	0.592110i	$0.201705\pi$
$572$	7650.58	−	4417.07i	0.559243	−	0.322879i
$573$			2939.28i			0.214294i
$574$	6125.34	+	13450.9i	0.445412	+	0.978102i
$575$	−10625.8	−	4285.85i	−0.770651	−	0.310839i
$576$	562.877	+	974.931i	0.0407173	+	0.0705245i
$577$	4220.38	+	2436.64i	0.304500	+	0.175803i	0.644463	−	0.764636i	$-0.277081\pi$
$577$	4220.38	+	2436.64i	0.304500	+	0.175803i	−0.339963	+	0.940439i	$0.610414\pi$
$578$	−5835.63	−	3369.20i	−0.419948	−	0.242457i
$579$	−7020.24	−	12159.4i	−0.503888	−	0.872759i
$580$	−10447.5	+	7051.39i	−0.747948	+	0.504816i
$581$	24724.4	+	2387.77i	1.76548	+	0.170501i
$582$			1986.13i			0.141457i
$583$	26471.4	−	15283.3i	1.88050	−	1.08571i
$584$	1031.14	−	1785.99i	0.0730634	−	0.126549i
$585$	8752.55	−	614.610i	0.618587	−	0.0434376i
$586$	−8656.21	−	14993.0i	−0.610213	−	1.05692i
$587$			23971.4i			1.68553i	0.538283	+	0.842764i	$0.319073\pi$
$587$			23971.4i			1.68553i	−0.538283	+	0.842764i	$0.680927\pi$
$588$	−3980.21	+	1367.97i	−0.279152	+	0.0959426i
$589$	3973.94			0.278002
$590$	4707.29	−	9658.55i	0.328468	−	0.673960i
$591$	5259.80	−	9110.24i	0.366090	−	0.634086i
$592$	2730.95	+	1576.71i	0.189597	+	0.109464i
$593$	−1352.44	+	780.834i	−0.0936564	+	0.0540726i	−0.546097	−	0.837722i	$-0.683887\pi$
$593$	−1352.44	+	780.834i	−0.0936564	+	0.0540726i	0.452440	+	0.891795i	$0.350554\pi$
$594$	−13542.0			−0.935413
$595$	7149.80	−	3882.11i	0.492627	−	0.267480i
$596$	8432.71			0.579559
$597$	−387.907	+	223.958i	−0.0265929	+	0.0153534i
$598$	−7083.15	−	4089.46i	−0.484367	−	0.279649i
$599$	8700.70	−	15070.1i	0.593491	−	1.02796i	−0.400267	−	0.916398i	$-0.631083\pi$
$599$	8700.70	−	15070.1i	0.593491	−	1.02796i	0.993758	−	0.111557i	$-0.0355839\pi$
$600$	3037.49	−	428.703i	0.206675	−	0.0291695i
$601$	−26823.7			−1.82057			−0.910283	−	0.413987i	$-0.864136\pi$
$601$	−26823.7			−1.82057			−0.910283	+	0.413987i	$0.864136\pi$
$602$	6862.20	−	3124.94i	0.464589	−	0.211566i
$603$		−	4434.84i		−	0.299503i
$604$	−4431.01	−	7674.74i	−0.298502	−	0.517021i
$605$	−876.682	−	12484.7i	−0.0589127	−	0.838965i
$606$	−3622.88	+	6275.01i	−0.242854	+	0.420635i
$607$	−19677.3	+	11360.7i	−1.31578	+	0.759665i	−0.983046	−	0.183357i	$-0.941304\pi$
$607$	−19677.3	+	11360.7i	−1.31578	+	0.759665i	−0.332731	+	0.943022i	$0.607970\pi$
$608$			1802.10i			0.120205i
$609$	9302.10	−	13033.2i	0.618949	−	0.867215i
$610$	293.937	+	435.505i	0.0195101	+	0.0289067i
$611$	−1528.05	−	2646.66i	−0.101176	−	0.175241i
$612$	2394.14	+	1382.26i	0.158133	+	0.0912980i
$613$	19859.3	+	11465.8i	1.30850	+	0.755462i	0.981846	−	0.189682i	$-0.0607457\pi$
$613$	19859.3	+	11465.8i	1.30850	+	0.755462i	0.326653	+	0.945144i	$0.394079\pi$
$614$	4296.26	+	7441.34i	0.282383	+	0.489101i
$615$	7655.93	+	11343.2i	0.501979	+	0.743745i
$616$	4260.72	−	5969.73i	0.278684	−	0.390466i
$617$		−	4299.04i		−	0.280507i	−0.990116	−	0.140253i	$-0.955208\pi$
$617$		−	4299.04i		−	0.280507i	0.990116	−	0.140253i	$-0.0447918\pi$
$618$	−3889.50	+	2245.60i	−0.253169	+	0.146167i
$619$	−2660.95	+	4608.89i	−0.172783	+	0.299268i	−0.939392	−	0.342846i	$-0.888609\pi$
$619$	−2660.95	+	4608.89i	−0.172783	+	0.299268i	0.766609	+	0.642114i	$0.221942\pi$
$620$	221.057	+	3148.03i	0.0143191	+	0.203916i
$621$	6268.81	+	10857.9i	0.405086	+	0.701630i
$622$			7870.25i			0.507345i
$623$	−21930.2	+	9986.65i	−1.41030	+	0.642226i
$624$	2189.79			0.140483
$625$	−3762.29	+	15165.3i	−0.240787	+	0.970578i
$626$	−10498.9	+	18184.7i	−0.670322	+	1.16103i
$627$	−7405.88	−	4275.79i	−0.471710	−	0.272342i
$628$	−7835.89	+	4524.05i	−0.497908	+	0.287467i
$629$	7743.87			0.490888
$630$	6401.65	−	3475.88i	0.404838	−	0.219814i
$631$	19486.3			1.22938			0.614688	−	0.788771i	$-0.289282\pi$
$631$	19486.3			1.22938			0.614688	+	0.788771i	$0.289282\pi$
$632$	−5360.35	+	3094.80i	−0.337379	+	0.194786i
$633$	−1874.00	−	1081.95i	−0.117670	−	0.0679365i
$634$	5747.17	−	9954.40i	0.360015	−	0.623564i
$635$	990.878	−	2033.11i	0.0619241	−	0.127057i
$636$	7576.77			0.472388
$637$	2928.48	−	15020.3i	0.182152	−	0.934261i
$638$			27903.6i			1.73152i
$639$	−7349.41	−	12729.6i	−0.454989	−	0.788065i
$640$	−1427.57	+	100.245i	−0.0881712	+	0.00619145i
$641$	14287.3	−	24746.4i	0.880368	−	1.52484i	0.0294367	−	0.999567i	$-0.490629\pi$
$641$	14287.3	−	24746.4i	0.880368	−	1.52484i	0.850932	−	0.525276i	$-0.176038\pi$
$642$	−7109.31	+	4104.56i	−0.437044	+	0.252327i
$643$		−	6347.10i		−	0.389277i	−0.980875	−	0.194639i	$-0.937647\pi$
$643$		−	6347.10i		−	0.389277i	0.980875	−	0.194639i	$-0.0623534\pi$
$644$	−6758.84	−	652.736i	−0.413565	−	0.0399401i
$645$	5786.93	−	3905.80i	0.353271	−	0.238435i
$646$	2212.71	+	3832.53i	0.134765	+	0.233419i
$647$	−2294.70	−	1324.85i	−0.139434	−	0.0805024i	0.428660	−	0.903466i	$-0.358986\pi$
$647$	−2294.70	−	1324.85i	−0.139434	−	0.0805024i	−0.568094	+	0.822963i	$0.692319\pi$
$648$	383.348	+	221.326i	0.0232397	+	0.0134175i
$649$	−11893.1	−	20599.4i	−0.719328	−	1.24591i
$650$	−4172.25	+	10344.1i	−0.251768	+	0.624199i
$651$	−1661.47	−	3648.51i	−0.100028	−	0.219656i
$652$		−	350.863i		−	0.0210750i
$653$	6115.54	−	3530.81i	0.366493	−	0.211595i	−0.305432	−	0.952214i	$-0.598801\pi$
$653$	6115.54	−	3530.81i	0.366493	−	0.211595i	0.671925	+	0.740619i	$0.265468\pi$
$654$	−158.770	+	274.997i	−0.00949294	+	0.0164423i
$655$	915.483	+	13037.2i	0.0546120	+	0.777720i
$656$	−3192.17	−	5529.00i	−0.189990	−	0.329072i
$657$		−	4534.42i		−	0.269261i
$658$	−2065.18	−	1473.96i	−0.122354	−	0.0873269i
$659$	−11227.0			−0.663646			−0.331823	−	0.943342i	$-0.607664\pi$
$659$	−11227.0			−0.663646			−0.331823	+	0.943342i	$0.607664\pi$
$660$	2975.18	−	6104.55i	0.175468	−	0.360029i
$661$	−14375.0	+	24898.2i	−0.845873	+	1.46509i	0.0389881	+	0.999240i	$0.487587\pi$
$661$	−14375.0	+	24898.2i	−0.845873	+	1.46509i	−0.884861	+	0.465855i	$0.845747\pi$
$662$	−16295.3	−	9408.09i	−0.956698	−	0.552350i
$663$	4657.01	−	2688.73i	0.272796	−	0.157499i
$664$	−10729.6			−0.627095
$665$	11656.9	+	305.141i	0.679752	+	0.0177938i
$666$	6933.56			0.403408
$667$	22372.9	−	12917.0i	1.29877	−	0.749847i
$668$	6413.36	+	3702.76i	0.371468	+	0.214467i
$669$	−3423.54	+	5929.74i	−0.197850	+	0.342686i
$670$	5067.82	+	2469.91i	0.292220	+	0.142419i
$671$	1163.16			0.0669199
$672$	1654.52	−	753.444i	0.0949772	−	0.0432511i
$673$		−	4440.57i		−	0.254341i	−0.991881	−	0.127170i	$-0.959411\pi$
$673$		−	4440.57i		−	0.254341i	0.991881	−	0.127170i	$-0.0405895\pi$
$674$	−4501.95	−	7797.61i	−0.257283	−	0.445627i
$675$	13467.2	−	10534.4i	0.767930	−	0.600696i
$676$	412.939	−	715.231i	0.0234945	−	0.0406936i
$677$	14124.7	−	8154.92i	0.801857	−	0.462953i	−0.0422629	−	0.999107i	$-0.513457\pi$
$677$	14124.7	−	8154.92i	0.801857	−	0.462953i	0.844120	+	0.536154i	$0.180123\pi$
$678$			2894.59i			0.163962i
$679$	−5967.77	−	576.338i	−0.337293	−	0.0325741i
$680$	−2912.92	+	1966.03i	−0.164273	+	0.110873i
$681$	8382.13	+	14518.3i	0.471665	+	0.816948i
$682$	6050.23	+	3493.10i	0.339700	+	0.196126i
$683$	−4214.46	−	2433.22i	−0.236108	−	0.136317i	0.377279	−	0.926100i	$-0.376860\pi$
$683$	−4214.46	−	2433.22i	−0.236108	−	0.136317i	−0.613387	+	0.789783i	$0.710193\pi$
$684$	1981.17	+	3431.49i	0.110749	+	0.191822i
$685$	917.671	+	1359.65i	0.0511860	+	0.0758385i
$686$	−2955.39	−	12356.4i	−0.164486	−	0.687709i
$687$			5963.05i			0.331157i
$688$	−2820.71	+	1628.54i	−0.156306	+	0.0902432i
$689$	−13774.7	+	23858.4i	−0.761645	+	1.31921i
$690$	−6271.85	+	440.413i	−0.346036	+	0.0242989i
$691$	7513.56	+	13013.9i	0.413646	+	0.716455i	0.995285	−	0.0969914i	$-0.0309219\pi$
$691$	7513.56	+	13013.9i	0.413646	+	0.716455i	−0.581640	+	0.813447i	$0.697589\pi$
$692$		−	7368.31i		−	0.404771i
$693$	1550.17	−	16051.4i	0.0849727	−	0.879861i
$694$	−9986.72			−0.546240
$695$	25182.3	+	12273.1i	1.37441	+	0.669849i
$696$	−3458.34	+	5990.01i	−0.188345	+	0.326223i
$697$	−13577.6	−	7839.01i	−0.737858	−	0.426003i
$698$	−11561.5	+	6675.06i	−0.626950	+	0.361970i
$699$	−10145.3			−0.548970
$700$	406.710	+	9251.19i	0.0219603	+	0.499518i
$701$	−10821.8			−0.583073			−0.291536	−	0.956560i	$-0.594166\pi$
$701$	−10821.8			−0.583073			−0.291536	+	0.956560i	$0.594166\pi$
$702$	10570.1	−	6102.65i	0.568294	−	0.328105i
$703$	9612.20	+	5549.61i	0.515691	+	0.297735i
$704$	−1584.05	+	2743.66i	−0.0848029	+	0.146883i
$705$	−2111.82	−	1029.24i	−0.112817	−	0.0549836i
$706$	5678.64			0.302718
$707$	−17803.3	−	12706.6i	−0.947049	−	0.675929i
$708$		−	5896.06i		−	0.312977i
$709$	10251.4	+	17755.9i	0.543016	+	0.940532i	0.998729	+	0.0504047i	$0.0160511\pi$
$709$	10251.4	+	17755.9i	0.543016	+	0.940532i	−0.455713	+	0.890127i	$0.650616\pi$
$710$	18639.6	−	1308.88i	0.985255	−	0.0691853i
$711$	−6804.65	+	11786.0i	−0.358923	+	0.621673i
$712$	9014.40	−	5204.47i	0.474479	−	0.273940i
$713$		−	6468.05i		−	0.339734i
$714$	2593.56	−	3633.86i	0.135940	−	0.190467i
$715$	13813.7	+	20466.7i	0.722520	+	1.07050i
$716$	−1497.06	−	2592.99i	−0.0781396	−	0.135342i
$717$	−16226.5	−	9368.40i	−0.845176	−	0.487963i
$718$	−14695.4	−	8484.41i	−0.763828	−	0.440997i
$719$	136.829	+	236.995i	0.00709717	+	0.0122927i	0.869552	−	0.493841i	$-0.164408\pi$
$719$	136.829	+	236.995i	0.00709717	+	0.0122927i	−0.862455	+	0.506134i	$0.831074\pi$
$720$	−2608.11	+	1760.31i	−0.134998	+	0.0911149i
$721$	−5618.75	−	12338.5i	−0.290226	−	0.637322i
$722$		−	7375.09i		−	0.380156i
$723$	10527.1	−	6077.81i	0.541503	−	0.312637i
$724$	−2787.80	+	4828.61i	−0.143105	+	0.247864i
$725$	−21706.4	−	27749.4i	−1.11194	−	1.42150i
$726$	−3433.90	−	5947.68i	−0.175542	−	0.304049i
$727$		−	1244.59i		−	0.0634931i	−0.999496	−	0.0317465i	$-0.989893\pi$
$727$		−	1244.59i		−	0.0634931i	0.999496	−	0.0317465i	$-0.0101069\pi$
$728$	−635.435	+	6579.69i	−0.0323500	+	0.334972i
$729$	−10355.8			−0.526129
$730$	5181.63	+	2525.37i	0.262713	+	0.128039i
$731$	−3999.20	+	6926.81i	−0.202347	+	0.350475i
$732$	249.694	+	144.161i	0.0126078	+	0.00727914i
$733$	−13556.1	+	7826.61i	−0.683091	+	0.394383i	−0.801019	−	0.598640i	$-0.795708\pi$
$733$	−13556.1	+	7826.61i	−0.683091	+	0.394383i	0.117928	+	0.993022i	$0.462375\pi$
$734$	−22639.5			−1.13847
$735$	−4593.50	−	10829.9i	−0.230522	−	0.543491i
$736$	2933.13			0.146898
$737$	10808.5	−	6240.28i	0.540211	−	0.311891i
$738$	−12156.8	−	7018.74i	−0.606367	−	0.350086i
$739$	−2683.14	+	4647.34i	−0.133560	+	0.231333i	−0.925047	−	0.379854i	$-0.875974\pi$
$739$	−2683.14	+	4647.34i	−0.133560	+	0.231333i	0.791486	+	0.611187i	$0.209308\pi$
$740$	−3861.53	+	7923.19i	−0.191828	+	0.393598i
$741$	7707.46			0.382106
$742$	−2198.64	+	22766.1i	−0.108780	+	1.12637i
$743$			7927.48i			0.391428i	0.980661	+	0.195714i	$0.0627024\pi$
$743$			7927.48i			0.391428i	−0.980661	+	0.195714i	$0.937298\pi$
$744$	865.863	+	1499.72i	0.0426668	+	0.0739010i
$745$	1651.05	+	23512.3i	0.0811942	+	1.15627i
$746$	−11306.2	+	19582.9i	−0.554891	+	0.961100i
$747$	−20431.0	+	11795.8i	−1.00071	+	0.577760i
$748$			7779.91i			0.380297i
$749$	−10270.1	−	22552.6i	−0.501015	−	1.10020i
$750$	1790.03	+	8385.24i	0.0871501	+	0.408248i
$751$	−3693.26	−	6396.92i	−0.179453	−	0.310821i	0.762240	−	0.647294i	$-0.224099\pi$
$751$	−3693.26	−	6396.92i	−0.179453	−	0.310821i	−0.941693	+	0.336473i	$0.890766\pi$
$752$	949.148	+	547.991i	0.0460264	+	0.0265734i
$753$	−10.4219	−	6.01707i	−0.000504374	−	0.000291201i
$754$	−12574.6	−	21779.9i	−0.607348	−	1.05196i
$755$	20531.3	−	13857.3i	0.989683	−	0.667970i
$756$	5886.64	−	8247.82i	0.283194	−	0.396786i
$757$			13406.0i			0.643659i	0.946798	+	0.321829i	$0.104298\pi$
$757$			13406.0i			0.643659i	−0.946798	+	0.321829i	$0.895702\pi$
$758$	18405.5	−	10626.4i	0.881949	−	0.509194i
$759$	−6959.34	+	12053.9i	−0.332817	+	0.576456i
$760$	−5024.65	+	352.835i	−0.239820	+	0.0168403i
$761$	12942.5	+	22417.0i	0.616510	+	1.06783i	0.990117	+	0.140240i	$0.0447875\pi$
$761$	12942.5	+	22417.0i	0.616510	+	1.06783i	−0.373607	+	0.927587i	$0.621879\pi$
$762$		−	1241.11i		−	0.0590036i
$763$	−780.217	−	556.857i	−0.0370193	−	0.0264215i
$764$	3832.69			0.181495
$765$	−3385.28	+	6946.01i	−0.159994	+	0.328279i
$766$	7582.88	−	13133.9i	0.357677	−	0.619515i
$767$	18566.1	+	10719.1i	0.874031	+	0.504622i
$768$	−680.092	+	392.651i	−0.0319541	+	0.0184487i
$769$	−11600.6			−0.543991			−0.271996	−	0.962299i	$-0.587684\pi$
$769$	−11600.6			−0.543991			−0.271996	+	0.962299i	$0.587684\pi$
$770$	17479.1	+	10711.0i	0.818057	+	0.501296i
$771$	−673.626			−0.0314657
$772$	−15855.3	+	9154.08i	−0.739178	+	0.426765i
$773$	−24462.9	−	14123.7i	−1.13825	−	0.657170i	−0.192255	−	0.981345i	$-0.561580\pi$
$773$	−24462.9	−	14123.7i	−1.13825	−	0.657170i	−0.945997	+	0.324175i	$0.894913\pi$
$774$	−3580.72	+	6201.99i	−0.166287	+	0.288018i
$775$	−8734.12	+	1232.71i	−0.404824	+	0.0571358i
$776$	2589.83			0.119806
$777$	1076.36	−	11145.3i	0.0496964	−	0.514588i
$778$		−	6425.65i		−	0.296106i
$779$	−11235.6	−	19460.6i	−0.516760	−	0.895055i
$780$	428.740	+	6105.60i	0.0196812	+	0.280276i
$781$	20682.8	−	35823.6i	0.947616	−	1.64132i
$782$	6237.88	−	3601.44i	0.285251	−	0.164690i
$783$			38551.7i			1.75955i
$784$	1783.78	+	5190.02i	0.0812580	+	0.236426i
$785$	−14148.3	−	20962.4i	−0.643277	−	0.953097i
$786$	3585.88	+	6210.92i	0.162728	+	0.281853i
$787$	9097.82	+	5252.63i	0.412074	+	0.237911i	0.691680	−	0.722204i	$-0.256871\pi$
$787$	9097.82	+	5252.63i	0.412074	+	0.237911i	−0.279606	+	0.960115i	$0.590204\pi$
$788$	−11879.3	−	6858.54i	−0.537036	−	0.310058i
$789$	−8386.36	−	14525.6i	−0.378406	−	0.655418i
$790$	−9678.49	−	14339.9i	−0.435880	−	0.645811i
$791$	−8697.45	−	839.957i	−0.390955	−	0.0377566i
$792$			6965.83i			0.312525i
$793$	−907.893	+	524.172i	−0.0406560	+	0.0234728i
$794$	13180.8	−	22829.8i	0.589130	−	1.02040i
$795$	1483.46	+	21125.7i	0.0661798	+	0.942455i
$796$	292.031	+	505.813i	0.0130035	+	0.0225227i
$797$			2165.99i			0.0962651i	0.998841	+	0.0481325i	$0.0153270\pi$
$797$			2165.99i			0.0962651i	−0.998841	+	0.0481325i	$0.984673\pi$
$798$	5823.48	−	2651.92i	0.258332	−	0.117640i
$799$	2691.40			0.119168
$800$	−559.009	−	3960.75i	−0.0247049	−	0.175042i
$801$	11443.3	−	19820.3i	0.504778	−	0.874302i
$802$	12460.8	+	7194.23i	0.548635	+	0.316755i
$803$	11051.2	−	6380.41i	0.485664	−	0.280398i
$804$	3093.65			0.135702
$805$	496.653	−	18972.9i	0.0217450	−	0.830693i
$806$	−6296.60			−0.275172
$807$	−775.016	+	447.456i	−0.0338065	+	0.0195182i
$808$	8182.33	+	4724.07i	0.356254	+	0.205683i
$809$	2674.33	−	4632.08i	0.116223	−	0.201304i	−0.802045	−	0.597264i	$-0.796255\pi$
$809$	2674.33	−	4632.08i	0.116223	−	0.201304i	0.918268	+	0.395959i	$0.129588\pi$
$810$	−542.050	+	1112.19i	−0.0235132	+	0.0482450i
$811$	−33841.2			−1.46526			−0.732629	−	0.680628i	$-0.761707\pi$
$811$	−33841.2			−1.46526			−0.732629	+	0.680628i	$0.761707\pi$
$812$	−16994.8	−	12129.5i	−0.734482	−	0.524215i
$813$		−	8162.92i		−	0.352135i
$814$	9756.24	+	16898.3i	0.420093	+	0.727623i
$815$	978.284	−	68.6958i	0.0420464	−	0.00295253i
$816$	−964.234	+	1670.10i	−0.0413664	+	0.0716486i
$817$	−9928.13	+	5732.01i	−0.425142	+	0.245456i
$818$			2178.31i			0.0931084i
$819$	6023.54	+	13227.4i	0.256996	+	0.564349i
$820$	14791.1	−	9983.00i	0.629910	−	0.425148i
$821$	−7290.73	−	12627.9i	−0.309925	−	0.536806i	0.668421	−	0.743783i	$-0.266971\pi$
$821$	−7290.73	−	12627.9i	−0.309925	−	0.536806i	−0.978346	+	0.206978i	$0.933637\pi$
$822$	779.543	+	450.069i	0.0330775	+	0.0190973i
$823$	2665.86	+	1539.13i	0.112911	+	0.0651894i	0.555392	−	0.831589i	$-0.312568\pi$
$823$	2665.86	+	1539.13i	0.112911	+	0.0651894i	−0.442481	+	0.896778i	$0.645902\pi$
$824$	2928.17	+	5071.74i	0.123796	+	0.214420i
$825$	17603.3	+	7100.24i	0.742873	+	0.299635i
$826$	17716.0	+	1710.93i	0.746270	+	0.0720711i
$827$			40275.0i			1.69347i	0.532017	+	0.846734i	$0.321434\pi$
$827$			40275.0i			1.69347i	−0.532017	+	0.846734i	$0.678566\pi$
$828$	5585.15	−	3224.59i	0.234417	−	0.135341i
$829$	14593.5	−	25276.6i	0.611402	−	1.05898i	−0.379603	−	0.925150i	$-0.623939\pi$
$829$	14593.5	−	25276.6i	0.611402	−	1.05898i	0.991004	−	0.133829i	$-0.0427274\pi$
$830$	−2100.76	−	29916.6i	−0.0878537	−	1.25111i
$831$	6906.15	+	11961.8i	0.288293	+	0.499339i
$832$		−	2855.38i		−	0.118981i
$833$	10166.1	+	8847.39i	0.422851	+	0.368000i
$834$	15372.5			0.638258
$835$	−9068.42	+	18606.8i	−0.375839	+	0.771157i
$836$	−5575.44	+	9656.94i	−0.230659	+	0.399512i
$837$	8359.04	+	4826.09i	0.345198	+	0.199300i
$838$	21675.8	−	12514.5i	0.893528	−	0.515879i
$839$	−9396.07			−0.386637			−0.193318	−	0.981136i	$-0.561925\pi$
$839$	−9396.07			−0.386637			−0.193318	+	0.981136i	$0.561925\pi$
$840$	2424.71	+	4465.66i	0.0995957	+	0.183428i
$841$	55047.5			2.25706
$842$	−1432.44	+	827.022i	−0.0586286	+	0.0338493i
$843$	−1228.38	−	709.208i	−0.0501872	−	0.0289756i
$844$	−1410.82	+	2443.61i	−0.0575384	+	0.0996595i
$845$	2075.07	+	1011.33i	0.0844788	+	0.0411725i
$846$	2409.77			0.0979312
$847$	18867.6	−	8591.99i	0.765404	−	0.348553i
$848$		−	9879.77i		−	0.400086i
$849$	10960.1	+	18983.4i	0.443049	+	0.767383i
$850$	−6052.05	−	7736.93i	−0.244216	−	0.312205i
$851$	9032.63	−	15645.0i	0.363848	−	0.630203i
$852$	8879.88	−	5126.80i	0.357065	−	0.206152i
$853$			20167.0i			0.809502i	0.914427	+	0.404751i	$0.132642\pi$
$853$			20167.0i			0.809502i	−0.914427	+	0.404751i	$0.867358\pi$
$854$	−505.619	+	708.426i	−0.0202599	+	0.0283862i
$855$	−9179.86	+	6195.80i	−0.367187	+	0.247827i
$856$	5352.17	+	9270.23i	0.213707	+	0.370152i
$857$	36788.3	+	21239.7i	1.46635	+	0.846599i	0.999292	−	0.0376269i	$-0.0119799\pi$
$857$	36788.3	+	21239.7i	1.46635	+	0.846599i	0.467060	+	0.884226i	$0.345313\pi$
$858$	11734.4	+	6774.87i	0.466908	+	0.269569i
$859$	10521.8	+	18224.4i	0.417929	+	0.723873i	0.995731	−	0.0923032i	$-0.0294229\pi$
$859$	10521.8	+	18224.4i	0.417929	+	0.723873i	−0.577802	+	0.816177i	$0.696090\pi$
$860$	−5092.98	−	7545.90i	−0.201941	−	0.299201i
$861$	−13169.4	+	18451.8i	−0.521269	+	0.730355i
$862$		−	3360.88i		−	0.132798i
$863$	−7318.91	+	4225.57i	−0.288689	+	0.166675i	−0.637350	−	0.770574i	$-0.719970\pi$
$863$	−7318.91	+	4225.57i	−0.288689	+	0.166675i	0.348662	+	0.937249i	$0.386636\pi$
$864$	−2188.54	+	3790.66i	−0.0861754	+	0.149260i
$865$	20544.5	−	1442.65i	0.807553	−	0.0567069i
$866$	−7421.56	−	12854.5i	−0.291218	−	0.504405i
$867$		−	10335.3i		−	0.404851i
$868$	−4757.49	+	2166.49i	−0.186037	+	0.0847181i
$869$	−38299.4			−1.49507
$870$	−17378.6	−	8469.81i	−0.677229	−	0.330061i
$871$	−5624.30	+	9741.58i	−0.218797	+	0.378968i
$872$	358.584	+	207.028i	0.0139257	+	0.00803999i
$873$	4931.45	−	2847.18i	0.191185	−	0.110381i
$874$	10323.8			0.399552
$875$	−25714.7	+	2945.29i	−0.993504	+	0.113793i
$876$	3163.12			0.122000
$877$	−29818.1	+	17215.5i	−1.14810	+	0.662856i	−0.948424	−	0.317005i	$-0.897323\pi$
$877$	−29818.1	+	17215.5i	−1.14810	+	0.662856i	−0.199677	+	0.979862i	$0.563989\pi$
$878$	8310.78	+	4798.23i	0.319448	+	0.184433i
$879$	13276.8	−	22996.2i	0.509462	−	0.882414i
$880$	−7960.07	−	3879.50i	−0.304925	−	0.148611i
$881$	−11602.4			−0.443695			−0.221848	−	0.975081i	$-0.571209\pi$
$881$	−11602.4			−0.443695			−0.221848	+	0.975081i	$0.571209\pi$
$882$	9102.34	+	7921.61i	0.347496	+	0.302420i
$883$		−	37934.8i		−	1.44576i	−0.690974	−	0.722880i	$-0.742818\pi$
$883$		−	37934.8i		−	1.44576i	0.690974	−	0.722880i	$-0.257182\pi$
$884$	−3505.98	−	6072.54i	−0.133392	−	0.231043i
$885$	16439.5	−	1154.39i	0.624416	−	0.0438469i
$886$	−15935.6	+	27601.3i	−0.604252	+	1.04659i
$887$	22028.5	−	12718.1i	0.833871	−	0.481436i	−0.0213052	−	0.999773i	$-0.506782\pi$
$887$	22028.5	−	12718.1i	0.833871	−	0.481436i	0.855176	+	0.518337i	$0.173449\pi$
$888$			4836.71i			0.182781i
$889$	3729.19	+	360.147i	0.140690	+	0.0135871i
$890$	16276.1	+	24115.1i	0.613008	+	0.908249i
$891$	1369.50	+	2372.04i	0.0514927	+	0.0891879i
$892$	7732.12	+	4464.14i	0.290236	+	0.167568i
$893$	3340.74	+	1928.78i	0.125189	+	0.0722779i
$894$	6467.03	+	11201.2i	0.241935	+	0.419043i
$895$	6936.72	−	4681.83i	0.259071	−	0.174856i
$896$	−982.457	−	2157.43i	−0.0366313	−	0.0804404i
$897$		−	12544.8i		−	0.466954i
$898$	16198.2	−	9352.06i	0.601940	−	0.347530i
$899$	9944.25	−	17223.9i	0.368920	−	0.638988i
$900$	−5418.76	−	6927.34i	−0.200695	−	0.256568i
$901$	−12130.9	−	21011.3i	−0.448544	−	0.776901i
$902$		−	39504.4i		−	1.45826i
$903$	9413.47	+	6718.59i	0.346911	+	0.247598i
$904$	3774.42			0.138867
$905$	−14009.0	−	6827.60i	−0.514560	−	0.250781i
$906$	6796.26	−	11771.5i	0.249217	−	0.431657i
$907$	−5223.74	−	3015.93i	−0.191236	−	0.110410i	0.401325	−	0.915936i	$-0.368550\pi$
$907$	−5223.74	−	3015.93i	−0.191236	−	0.110410i	−0.592561	+	0.805525i	$0.701883\pi$
$908$	18931.2	−	10929.9i	0.691909	−	0.399474i
$909$	20774.0			0.758008
$910$	−18470.0	−	483.489i	−0.672830	−	0.0176126i
$911$	−21631.5			−0.786699			−0.393349	−	0.919389i	$-0.628684\pi$
$911$	−21631.5			−0.786699			−0.393349	+	0.919389i	$0.628684\pi$
$912$	−2393.74	+	1382.03i	−0.0869130	+	0.0501793i
$913$	−57497.0	−	33195.9i	−2.08420	−	1.20331i
$914$	−8577.22	+	14856.2i	−0.310404	+	0.537635i
$915$	−353.064	+	724.426i	−0.0127562	+	0.0261735i
$916$	7775.56			0.280471
$917$	−19702.6	+	8972.26i	−0.709529	+	0.323108i
$918$			10748.8i			0.386451i
$919$	−14122.3	−	24460.6i	−0.506913	−	0.877999i	−0.999968	−	0.00800113i	$-0.997453\pi$
$919$	−14122.3	−	24460.6i	−0.506913	−	0.877999i	0.493055	−	0.869998i	$-0.335880\pi$
$920$	574.279	+	8178.21i	0.0205798	+	0.293073i
$921$	−6589.58	+	11413.5i	−0.235759	+	0.408347i
$922$	−14660.0	+	8463.98i	−0.523647	+	0.302328i
$923$			37282.4i			1.32954i
$924$	11197.2	+	1081.37i	0.398658	+	0.0385004i
$925$	−22847.6	−	9215.50i	−0.812136	−	0.327572i
$926$	−4297.74	−	7443.90i	−0.152519	−	0.264170i
$927$	11151.4	+	6438.27i	0.395103	+	0.228113i
$928$	7810.71	+	4509.52i	0.276292	+	0.159517i
$929$	22472.1	+	38922.8i	0.793633	+	1.37461i	0.923703	+	0.383109i	$0.125146\pi$
$929$	22472.1	+	38922.8i	0.793633	+	1.37461i	−0.130070	+	0.991505i	$0.541520\pi$
$930$	−4012.02	+	2707.85i	−0.141462	+	0.0954772i
$931$	6278.41	+	18267.5i	0.221017	+	0.643063i
$932$			13229.0i			0.464946i
$933$	−10454.1	+	6035.68i	−0.366829	+	0.211789i
$934$	1030.13	−	1784.23i	0.0360886	−	0.0625074i
$935$	−21692.1	+	1523.23i	−0.758725	+	0.0532782i
$936$	−3139.12	−	5437.11i	−0.109621	−	0.189869i
$937$			3777.71i			0.131710i	0.997829	+	0.0658551i	$0.0209775\pi$
$937$			3777.71i			0.131710i	−0.997829	+	0.0658551i	$0.979022\pi$
$938$	−897.720	+	9295.56i	−0.0312490	+	0.323572i
$939$	−32206.4			−1.11929
$940$	−1342.08	+	2753.72i	−0.0465680	+	0.0955495i
$941$	176.423	−	305.573i	0.00611182	−	0.0105860i	−0.862953	−	0.505284i	$-0.831388\pi$
$941$	176.423	−	305.573i	0.00611182	−	0.0105860i	0.869065	+	0.494698i	$0.164721\pi$
$942$	−12018.7	−	6938.97i	−0.415699	−	0.240004i
$943$	−31674.4	+	18287.2i	−1.09381	+	0.631509i
$944$	−7688.20			−0.265074
$945$	24149.3	+	14798.4i	0.831297	+	0.509409i
$946$	−20153.8			−0.692660
$947$	11721.5	−	6767.42i	0.402215	−	0.232219i	−0.285224	−	0.958461i	$-0.592068\pi$
$947$	11721.5	−	6767.42i	0.402215	−	0.232219i	0.687439	+	0.726242i	$0.258735\pi$
$948$	−8221.68	−	4746.79i	−0.281675	−	0.162625i
$949$	−5750.60	+	9960.34i	−0.196704	+	0.340702i
$950$	−1967.56	−	13940.8i	−0.0671959	−	0.476103i
$951$	17630.0			0.601147
$952$	−4738.39	−	3381.89i	−0.161315	−	0.115134i
$953$		−	51886.1i		−	1.76365i	−0.471579	−	0.881824i	$-0.656316\pi$
$953$		−	51886.1i		−	1.76365i	0.471579	−	0.881824i	$-0.343684\pi$
$954$	−10861.5	−	18812.7i	−0.368610	−	0.638452i
$955$	750.406	+	10686.4i	0.0254268	+	0.362098i
$956$	−12216.0	+	21158.7i	−0.413277	+	0.715817i
$957$	−37064.4	+	21399.2i	−1.25196	+	0.722818i
$958$		−	10275.0i		−	0.346523i
$959$	−1578.54	+	2211.71i	−0.0531530	+	0.0744731i
$960$	−1227.95	−	1819.37i	−0.0412834	−	0.0611665i
$961$	12405.8	+	21487.4i	0.416426	+	0.721272i
$962$	−15230.3	−	8793.21i	−0.510441	−	0.294703i
$963$	20382.8	+	11768.0i	0.682063	+	0.393789i
$964$	−7925.20	−	13726.8i	−0.264786	−	0.458622i
$965$	−28627.9	−	42415.8i	−0.954989	−	1.41494i
$966$	−4316.31	−	9478.39i	−0.143763	−	0.315696i
$967$		−	45517.8i		−	1.51371i	−0.653585	−	0.756853i	$-0.726736\pi$
$967$		−	45517.8i		−	1.51371i	0.653585	−	0.756853i	$-0.273264\pi$
$968$	−7755.51	+	4477.65i	−0.257512	+	0.148675i
$969$	−3393.84	+	5878.31i	−0.112514	+	0.194880i
$970$	507.064	+	7221.01i	0.0167844	+	0.239023i
$971$	−11699.1	−	20263.5i	−0.386656	−	0.669708i	0.605341	−	0.795966i	$-0.293037\pi$
$971$	−11699.1	−	20263.5i	−0.386656	−	0.669708i	−0.991997	+	0.126258i	$0.959703\pi$
$972$			15451.6i			0.509886i
$973$	−4460.82	+	46190.1i	−0.146976	+	1.52188i
$974$	1053.07			0.0346434
$975$	−16939.8	+	2390.84i	−0.556419	+	0.0785315i
$976$	187.979	−	325.589i	0.00616502	−	0.0106781i
$977$	29725.3	+	17161.9i	0.973386	+	0.561985i	0.900267	−	0.435339i	$-0.143371\pi$
$977$	29725.3	+	17161.9i	0.973386	+	0.561985i	0.0731191	+	0.997323i	$0.476705\pi$
$978$	466.054	−	269.076i	0.0152380	−	0.00879766i
$979$	64407.4			2.10262
$980$	−14121.7	+	5989.72i	−0.460306	+	0.195239i
$981$	910.402			0.0296299
$982$	−2679.26	+	1546.87i	−0.0870658	+	0.0502675i
$983$	−32178.9	−	18578.5i	−1.04410	−	0.602809i	−0.123106	−	0.992394i	$-0.539285\pi$
$983$	−32178.9	−	18578.5i	−1.04410	−	0.602809i	−0.920991	+	0.389584i	$0.872619\pi$
$984$	4896.13	−	8480.35i	0.158621	−	0.274740i
$985$	16797.3	−	34465.1i	0.543355	−	1.11487i
$986$	22148.0			0.715352
$987$	374.091	−	3873.57i	0.0120643	−	0.124921i
$988$		−	10050.2i		−	0.323622i
$989$	9329.50	+	16159.2i	0.299961	+	0.519547i
$990$	−19422.3	+	1363.84i	−0.623515	+	0.0437837i
$991$	5271.25	−	9130.08i	0.168968	−	0.292660i	−0.769090	−	0.639141i	$-0.779290\pi$
$991$	5271.25	−	9130.08i	0.168968	−	0.292660i	0.938057	+	0.346481i	$0.112623\pi$
$992$	1955.57	−	1129.05i	0.0625900	−	0.0361364i
$993$		−	28860.2i		−	0.922306i
$994$	12827.8	+	28169.3i	0.409330	+	0.898868i
$995$	−1353.14	+	913.281i	−0.0431130	+	0.0290985i
$996$	−8228.54	−	14252.2i	−0.261778	−	0.453413i
$997$	−31398.6	−	18128.0i	−0.997394	−	0.575846i	−0.0899181	−	0.995949i	$-0.528661\pi$
$997$	−31398.6	−	18128.0i	−0.997394	−	0.575846i	−0.907476	+	0.420103i	$0.861994\pi$
$998$	16442.1	+	9492.84i	0.521508	+	0.301093i
$999$	13479.3	+	23346.8i	0.426892	+	0.739399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.4.i.a.39.10	yes	24
5.2	odd	4		350.4.e.o.151.4		12
5.3	odd	4		350.4.e.n.151.3		12
5.4	even	2	inner	70.4.i.a.39.3	yes	24
7.2	even	3	inner	70.4.i.a.9.3	✓	24
7.3	odd	6		490.4.c.e.99.10		12
7.4	even	3		490.4.c.f.99.9		12
35.2	odd	12		350.4.e.o.51.4		12
35.3	even	12		2450.4.a.cx.1.3		6
35.4	even	6		490.4.c.f.99.4		12
35.9	even	6	inner	70.4.i.a.9.10	yes	24
35.17	even	12		2450.4.a.cw.1.4		6
35.18	odd	12		2450.4.a.cy.1.4		6
35.23	odd	12		350.4.e.n.51.3		12
35.24	odd	6		490.4.c.e.99.3		12
35.32	odd	12		2450.4.a.cv.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.i.a.9.3	✓	24	7.2	even	3	inner
70.4.i.a.9.10	yes	24	35.9	even	6	inner
70.4.i.a.39.3	yes	24	5.4	even	2	inner
70.4.i.a.39.10	yes	24	1.1	even	1	trivial
350.4.e.n.51.3		12	35.23	odd	12
350.4.e.n.151.3		12	5.3	odd	4
350.4.e.o.51.4		12	35.2	odd	12
350.4.e.o.151.4		12	5.2	odd	4
490.4.c.e.99.3		12	35.24	odd	6
490.4.c.e.99.10		12	7.3	odd	6
490.4.c.f.99.4		12	35.4	even	6
490.4.c.f.99.9		12	7.4	even	3
2450.4.a.cv.1.3		6	35.32	odd	12
2450.4.a.cw.1.4		6	35.17	even	12
2450.4.a.cx.1.3		6	35.3	even	12
2450.4.a.cy.1.4		6	35.18	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	70.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(2.65661 + 1.53379i) q^{3} +(2.00000 - 3.46410i) q^{4} +(10.0503 + 4.89820i) q^{5} +6.13518 q^{6} +(-1.78031 + 18.4345i) q^{7} -8.00000i q^{8} +(-8.79495 - 15.2333i) q^{9} +(22.3058 - 1.56633i) q^{10} +(24.7508 - 42.8697i) q^{11} +(10.6264 - 6.13518i) q^{12} +44.6154i q^{13} +(15.3509 + 33.7098i) q^{14} +(19.1868 + 28.4276i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-34.0272 - 19.6456i) q^{17} +(-30.4666 - 17.5899i) q^{18} +(-28.1578 - 48.7708i) q^{19} +(37.0684 - 25.0187i) q^{20} +(-33.0043 + 46.2426i) q^{21} -99.0033i q^{22} +(-79.3801 + 45.8301i) q^{23} +(12.2704 - 21.2529i) q^{24} +(77.0153 + 98.4563i) q^{25} +(44.6154 + 77.2761i) q^{26} -136.783i q^{27} +(60.2983 + 43.0362i) q^{28} -281.845 q^{29} +(61.6601 + 30.0513i) q^{30} +(-35.2827 + 61.1114i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(131.507 - 75.9254i) q^{33} -78.5824 q^{34} +(-108.188 + 176.551i) q^{35} -70.3596 q^{36} +(-170.684 + 98.5446i) q^{37} +(-97.5416 - 56.3157i) q^{38} +(-68.4308 + 118.526i) q^{39} +(39.1856 - 80.4020i) q^{40} +399.021 q^{41} +(-10.9225 + 113.099i) q^{42} -203.567i q^{43} +(-99.0033 - 171.479i) q^{44} +(-13.7758 - 196.178i) q^{45} +(-91.6603 + 158.760i) q^{46} +(-59.3217 + 34.2494i) q^{47} -49.0814i q^{48} +(-336.661 - 65.6384i) q^{49} +(231.851 + 93.5161i) q^{50} +(-60.2646 - 104.381i) q^{51} +(154.552 + 89.2307i) q^{52} +(534.758 + 308.743i) q^{53} +(-136.783 - 236.916i) q^{54} +(458.736 - 309.617i) q^{55} +(147.476 + 14.2425i) q^{56} -172.753i q^{57} +(-488.169 + 281.845i) q^{58} +(240.256 - 416.136i) q^{59} +(136.850 - 9.60969i) q^{60} +(11.7487 + 20.3493i) q^{61} +141.131i q^{62} +(296.476 - 135.010i) q^{63} -64.0000 q^{64} +(-218.535 + 448.396i) q^{65} +(151.851 - 263.013i) q^{66} +(218.346 + 126.062i) q^{67} +(-136.109 + 78.5824i) q^{68} -281.176 q^{69} +(-10.8368 + 413.984i) q^{70} +835.640 q^{71} +(-121.866 + 70.3596i) q^{72} +(223.249 + 128.893i) q^{73} +(-197.089 + 341.369i) q^{74} +(53.5878 + 379.686i) q^{75} -225.263 q^{76} +(746.216 + 532.590i) q^{77} +273.723i q^{78} +(-386.850 - 670.044i) q^{79} +(-12.5306 - 178.446i) q^{80} +(-27.6658 + 47.9185i) q^{81} +(691.125 - 399.021i) q^{82} -1341.21i q^{83} +(94.1805 + 206.816i) q^{84} +(-245.754 - 364.115i) q^{85} +(-203.567 - 352.588i) q^{86} +(-748.752 - 432.292i) q^{87} +(-342.957 - 198.007i) q^{88} +(650.558 + 1126.80i) q^{89} +(-220.038 - 326.014i) q^{90} +(-822.462 - 79.4293i) q^{91} +366.641i q^{92} +(-187.465 + 108.233i) q^{93} +(-68.4988 + 118.643i) q^{94} +(-44.1043 - 628.082i) q^{95} +(-49.0814 - 85.0115i) q^{96} +323.729i q^{97} +(-648.752 + 222.972i) q^{98} -870.729 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 48 q^{4} - 8 q^{5} + 56 q^{6} + 62 q^{9} + 12 q^{10} - 62 q^{11} - 84 q^{14} + 172 q^{15} - 192 q^{16} + 186 q^{19} - 64 q^{20} + 350 q^{21} + 112 q^{24} + 126 q^{25} - 236 q^{26} - 676 q^{29} + 28 q^{30}+ \cdots - 17092 q^{99}+O(q^{100}) \) 24 * q + 48 * q^4 - 8 * q^5 + 56 * q^6 + 62 * q^9 + 12 * q^10 - 62 * q^11 - 84 * q^14 + 172 * q^15 - 192 * q^16 + 186 * q^19 - 64 * q^20 + 350 * q^21 + 112 * q^24 + 126 * q^25 - 236 * q^26 - 676 * q^29 + 28 * q^30 - 652 * q^31 - 544 * q^34 - 1344 * q^35 + 496 * q^36 - 868 * q^39 - 48 * q^40 + 792 * q^41 + 248 * q^44 + 664 * q^45 + 376 * q^46 + 1602 * q^49 + 320 * q^50 - 1448 * q^51 + 1540 * q^54 + 596 * q^55 - 144 * q^56 + 1336 * q^59 + 344 * q^60 - 314 * q^61 - 1536 * q^64 + 1862 * q^65 - 1600 * q^66 + 180 * q^69 - 484 * q^70 + 4432 * q^71 - 1012 * q^74 - 4550 * q^75 + 1488 * q^76 - 1772 * q^79 - 128 * q^80 + 1228 * q^81 + 784 * q^84 + 4564 * q^85 + 396 * q^86 + 6094 * q^89 + 200 * q^90 - 4364 * q^91 + 3604 * q^94 + 1166 * q^95 - 448 * q^96 - 17092 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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