LMFDB - Embedded newform 43.5.d.a.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,5,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	43.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.44490841261$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.5
Character	$\chi$	$=$	43.37
Dual form			43.5.d.a.7.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.98081i q^{2} +(-1.27161 - 0.734162i) q^{3} +7.11478 q^{4} +(26.8620 + 15.5088i) q^{5} +(-2.18840 + 3.79041i) q^{6} +(15.5504 - 8.97804i) q^{7} -68.9007i q^{8} +(-39.4220 - 68.2809i) q^{9} +O(q^{10})$	\(q-2.98081i q^{2} +(-1.27161 - 0.734162i) q^{3} +7.11478 q^{4} +(26.8620 + 15.5088i) q^{5} +(-2.18840 + 3.79041i) q^{6} +(15.5504 - 8.97804i) q^{7} -68.9007i q^{8} +(-39.4220 - 68.2809i) q^{9} +(46.2288 - 80.0706i) q^{10} +38.7980 q^{11} +(-9.04719 - 5.22340i) q^{12} +(29.5583 + 51.1965i) q^{13} +(-26.7618 - 46.3528i) q^{14} +(-22.7719 - 39.4422i) q^{15} -91.5435 q^{16} +(7.85783 + 13.6102i) q^{17} +(-203.532 + 117.509i) q^{18} +(143.154 + 82.6503i) q^{19} +(191.118 + 110.342i) q^{20} -26.3653 q^{21} -115.649i q^{22} +(-212.919 + 368.786i) q^{23} +(-50.5843 + 87.6145i) q^{24} +(168.546 + 291.931i) q^{25} +(152.607 - 88.1076i) q^{26} +234.703i q^{27} +(110.638 - 63.8768i) q^{28} +(-251.682 + 145.309i) q^{29} +(-117.570 + 67.8788i) q^{30} +(-904.977 + 1567.47i) q^{31} -829.538i q^{32} +(-49.3357 - 28.4840i) q^{33} +(40.5693 - 23.4227i) q^{34} +556.955 q^{35} +(-280.479 - 485.804i) q^{36} +(-1167.27 - 673.925i) q^{37} +(246.365 - 426.716i) q^{38} -86.8023i q^{39} +(1068.57 - 1850.81i) q^{40} +923.580 q^{41} +78.5900i q^{42} +(-1509.18 + 1068.25i) q^{43} +276.039 q^{44} -2445.55i q^{45} +(1099.28 + 634.670i) q^{46} +1847.06 q^{47} +(116.407 + 67.2077i) q^{48} +(-1039.29 + 1800.10i) q^{49} +(870.190 - 502.405i) q^{50} -23.0757i q^{51} +(210.301 + 364.252i) q^{52} +(2128.96 - 3687.46i) q^{53} +699.604 q^{54} +(1042.19 + 601.711i) q^{55} +(-618.594 - 1071.44i) q^{56} +(-121.357 - 210.197i) q^{57} +(433.138 + 750.217i) q^{58} -3005.34 q^{59} +(-162.017 - 280.622i) q^{60} +(-2156.94 + 1245.31i) q^{61} +(4672.32 + 2697.56i) q^{62} +(-1226.06 - 707.865i) q^{63} -3937.39 q^{64} +1833.66i q^{65} +(-84.9053 + 147.060i) q^{66} +(-1950.13 + 3377.72i) q^{67} +(55.9067 + 96.8333i) q^{68} +(541.497 - 312.633i) q^{69} -1660.18i q^{70} +(-269.006 + 155.310i) q^{71} +(-4704.61 + 2716.21i) q^{72} +(1594.06 - 920.330i) q^{73} +(-2008.84 + 3479.42i) q^{74} -494.961i q^{75} +(1018.51 + 588.038i) q^{76} +(603.325 - 348.330i) q^{77} -258.741 q^{78} +(-1812.66 - 3139.62i) q^{79} +(-2459.05 - 1419.73i) q^{80} +(-3020.87 + 5232.31i) q^{81} -2753.01i q^{82} +(2244.46 - 3887.51i) q^{83} -187.583 q^{84} +487.462i q^{85} +(3184.26 + 4498.59i) q^{86} +426.721 q^{87} -2673.21i q^{88} +(11516.0 + 6648.75i) q^{89} -7289.73 q^{90} +(919.288 + 530.751i) q^{91} +(-1514.87 + 2623.83i) q^{92} +(2301.55 - 1328.80i) q^{93} -5505.73i q^{94} +(2563.61 + 4440.31i) q^{95} +(-609.015 + 1054.85i) q^{96} +9109.89 q^{97} +(5365.76 + 3097.92i) q^{98} +(-1529.49 - 2649.16i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 6 q^{3} - 234 q^{4} - 3 q^{5} + 15 q^{6} + 129 q^{7} + 534 q^{9}+O(q^{10}) $ 28 * q + 6 * q^3 - 234 * q^4 - 3 * q^5 + 15 * q^6 + 129 * q^7 + 534 * q^9	\( 28 q + 6 q^{3} - 234 q^{4} - 3 q^{5} + 15 q^{6} + 129 q^{7} + 534 q^{9} + 91 q^{10} - 376 q^{11} - 1026 q^{12} - 198 q^{13} + 78 q^{14} - 289 q^{15} + 806 q^{16} + 23 q^{17} - 435 q^{18} - 438 q^{19} + 177 q^{20} + 1684 q^{21} - 214 q^{23} + 1450 q^{24} + 463 q^{25} + 45 q^{26} - 3828 q^{28} + 1725 q^{29} + 8127 q^{30} + 2135 q^{31} - 474 q^{33} + 201 q^{34} - 6882 q^{35} - 12052 q^{36} + 1638 q^{37} - 2124 q^{38} - 6721 q^{40} + 3014 q^{41} + 157 q^{43} + 17162 q^{44} - 6240 q^{46} - 3670 q^{47} + 11547 q^{48} + 3085 q^{49} + 9738 q^{50} + 13746 q^{52} + 1208 q^{53} - 32416 q^{54} - 11202 q^{55} - 16245 q^{56} + 6207 q^{57} - 5756 q^{58} - 8716 q^{59} - 281 q^{60} + 8382 q^{61} - 25191 q^{62} + 23625 q^{63} + 17564 q^{64} - 21909 q^{66} - 9295 q^{67} + 6758 q^{68} + 30663 q^{69} + 24828 q^{71} + 46194 q^{72} + 5307 q^{73} + 13866 q^{74} + 5178 q^{76} - 27645 q^{77} - 10592 q^{78} - 24914 q^{79} - 13683 q^{80} - 43222 q^{81} + 7010 q^{83} - 21568 q^{84} + 15366 q^{86} + 57084 q^{87} - 80787 q^{89} + 114772 q^{90} - 24438 q^{91} + 22049 q^{92} - 39723 q^{93} + 29955 q^{95} + 1378 q^{96} - 12210 q^{97} + 28845 q^{98} - 49211 q^{99}+O(q^{100}) \) 28 * q + 6 * q^3 - 234 * q^4 - 3 * q^5 + 15 * q^6 + 129 * q^7 + 534 * q^9 + 91 * q^10 - 376 * q^11 - 1026 * q^12 - 198 * q^13 + 78 * q^14 - 289 * q^15 + 806 * q^16 + 23 * q^17 - 435 * q^18 - 438 * q^19 + 177 * q^20 + 1684 * q^21 - 214 * q^23 + 1450 * q^24 + 463 * q^25 + 45 * q^26 - 3828 * q^28 + 1725 * q^29 + 8127 * q^30 + 2135 * q^31 - 474 * q^33 + 201 * q^34 - 6882 * q^35 - 12052 * q^36 + 1638 * q^37 - 2124 * q^38 - 6721 * q^40 + 3014 * q^41 + 157 * q^43 + 17162 * q^44 - 6240 * q^46 - 3670 * q^47 + 11547 * q^48 + 3085 * q^49 + 9738 * q^50 + 13746 * q^52 + 1208 * q^53 - 32416 * q^54 - 11202 * q^55 - 16245 * q^56 + 6207 * q^57 - 5756 * q^58 - 8716 * q^59 - 281 * q^60 + 8382 * q^61 - 25191 * q^62 + 23625 * q^63 + 17564 * q^64 - 21909 * q^66 - 9295 * q^67 + 6758 * q^68 + 30663 * q^69 + 24828 * q^71 + 46194 * q^72 + 5307 * q^73 + 13866 * q^74 + 5178 * q^76 - 27645 * q^77 - 10592 * q^78 - 24914 * q^79 - 13683 * q^80 - 43222 * q^81 + 7010 * q^83 - 21568 * q^84 + 15366 * q^86 + 57084 * q^87 - 80787 * q^89 + 114772 * q^90 - 24438 * q^91 + 22049 * q^92 - 39723 * q^93 + 29955 * q^95 + 1378 * q^96 - 12210 * q^97 + 28845 * q^98 - 49211 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	2.98081i		−	0.745202i	−0.927992	−	0.372601i	$-0.878466\pi$
$2$		−	2.98081i		−	0.745202i	0.927992	−	0.372601i	$-0.121534\pi$
$3$	−1.27161	−	0.734162i	−0.141289	−	0.0815735i	0.427689	−	0.903926i	$-0.359328\pi$
$3$	−1.27161	−	0.734162i	−0.141289	−	0.0815735i	−0.568978	+	0.822352i	$0.692661\pi$
$4$	7.11478			0.444674
$5$	26.8620	+	15.5088i	1.07448	+	0.620352i	0.929403	−	0.369068i	$-0.120323\pi$
$5$	26.8620	+	15.5088i	1.07448	+	0.620352i	0.145079	+	0.989420i	$0.453656\pi$
$6$	−2.18840	+	3.79041i	−0.0607888	+	0.105289i
$7$	15.5504	−	8.97804i	0.317356	−	0.183225i	−0.332858	−	0.942977i	$-0.608013\pi$
$7$	15.5504	−	8.97804i	0.317356	−	0.183225i	0.650213	+	0.759752i	$0.274680\pi$
$8$		−	68.9007i		−	1.07657i
$9$	−39.4220	−	68.2809i	−0.486692	−	0.842974i
$10$	46.2288	−	80.0706i	0.462288	−	0.800706i
$11$	38.7980			0.320645			0.160322	−	0.987065i	$-0.448747\pi$
$11$	38.7980			0.320645			0.160322	+	0.987065i	$0.448747\pi$
$12$	−9.04719	−	5.22340i	−0.0628277	−	0.0362736i
$13$	29.5583	+	51.1965i	0.174901	+	0.302938i	0.940127	−	0.340824i	$-0.110706\pi$
$13$	29.5583	+	51.1965i	0.174901	+	0.302938i	−0.765226	+	0.643762i	$0.777373\pi$
$14$	−26.7618	−	46.3528i	−0.136540	−	0.236494i
$15$	−22.7719	−	39.4422i	−0.101209	−	0.175299i
$16$	−91.5435			−0.357592
$17$	7.85783	+	13.6102i	0.0271897	+	0.0470940i	0.879300	−	0.476268i	$-0.158011\pi$
$17$	7.85783	+	13.6102i	0.0271897	+	0.0470940i	−0.852110	+	0.523362i	$0.824678\pi$
$18$	−203.532	+	117.509i	−0.628186	+	0.362684i
$19$	143.154	+	82.6503i	0.396550	+	0.228948i	0.684994	−	0.728549i	$-0.259805\pi$
$19$	143.154	+	82.6503i	0.396550	+	0.228948i	−0.288444	+	0.957497i	$0.593138\pi$
$20$	191.118	+	110.342i	0.477794	+	0.275854i
$21$	−26.3653			−0.0597853
$22$		−	115.649i		−	0.238945i
$23$	−212.919	+	368.786i	−0.402493	+	0.697138i	−0.994026	−	0.109143i	$-0.965189\pi$
$23$	−212.919	+	368.786i	−0.402493	+	0.697138i	0.591533	+	0.806280i	$0.298523\pi$
$24$	−50.5843	+	87.6145i	−0.0878199	+	0.152109i
$25$	168.546	+	291.931i	0.269674	+	0.467089i
$26$	152.607	−	88.1076i	0.225750	−	0.130337i
$27$			234.703i			0.321952i
$28$	110.638	−	63.8768i	0.141120	−	0.0814755i
$29$	−251.682	+	145.309i	−0.299266	+	0.172781i	−0.642113	−	0.766610i	$-0.721942\pi$
$29$	−251.682	+	145.309i	−0.299266	+	0.172781i	0.342847	+	0.939391i	$0.388609\pi$
$30$	−117.570	+	67.8788i	−0.130633	+	0.0754209i
$31$	−904.977	+	1567.47i	−0.941704	+	1.63108i	−0.179484	+	0.983761i	$0.557443\pi$
$31$	−904.977	+	1567.47i	−0.941704	+	1.63108i	−0.762220	+	0.647318i	$0.775891\pi$
$32$		−	829.538i		−	0.810096i
$33$	−49.3357	−	28.4840i	−0.0453037	−	0.0261561i
$34$	40.5693	−	23.4227i	0.0350945	−	0.0202618i
$35$	556.955			0.454657
$36$	−280.479	−	485.804i	−0.216419	−	0.374849i
$37$	−1167.27	−	673.925i	−0.852647	−	0.492276i	0.00889642	−	0.999960i	$-0.497168\pi$
$37$	−1167.27	−	673.925i	−0.852647	−	0.492276i	−0.861543	+	0.507685i	$0.830501\pi$
$38$	246.365	−	426.716i	0.170613	−	0.295510i
$39$		−	86.8023i		−	0.0570692i
$40$	1068.57	−	1850.81i	0.667855	−	1.15676i
$41$	923.580			0.549423			0.274711	−	0.961527i	$-0.411418\pi$
$41$	923.580			0.549423			0.274711	+	0.961527i	$0.411418\pi$
$42$			78.5900i			0.0445522i
$43$	−1509.18	+	1068.25i	−0.816216	+	0.577746i
$43$	−1509.18	+	1068.25i	−0.816216	+	0.577746i
$44$	276.039			0.142582
$45$		−	2445.55i		−	1.20768i
$46$	1099.28	+	634.670i	0.519509	+	0.299938i
$47$	1847.06			0.836151			0.418076	−	0.908412i	$-0.362705\pi$
$47$	1847.06			0.836151			0.418076	+	0.908412i	$0.362705\pi$
$48$	116.407	+	67.2077i	0.0505239	+	0.0291700i
$49$	−1039.29	+	1800.10i	−0.432857	+	0.749730i
$50$	870.190	−	502.405i	0.348076	−	0.200962i
$51$		−	23.0757i		−	0.00887184i
$52$	210.301	+	364.252i	0.0777740	+	0.134708i
$53$	2128.96	−	3687.46i	0.757906	−	1.31273i	−0.186010	−	0.982548i	$-0.559556\pi$
$53$	2128.96	−	3687.46i	0.757906	−	1.31273i	0.943917	−	0.330184i	$-0.107111\pi$
$54$	699.604			0.239919
$55$	1042.19	+	601.711i	0.344527	+	0.198913i
$56$	−618.594	−	1071.44i	−0.197256	−	0.341657i
$57$	−121.357	−	210.197i	−0.0373522	−	0.0646959i
$58$	433.138	+	750.217i	0.128757	+	0.223013i
$59$	−3005.34			−0.863357			−0.431678	−	0.902028i	$-0.642078\pi$
$59$	−3005.34			−0.863357			−0.431678	+	0.902028i	$0.642078\pi$
$60$	−162.017	−	280.622i	−0.0450048	−	0.0779506i
$61$	−2156.94	+	1245.31i	−0.579667	+	0.334671i	−0.761001	−	0.648751i	$-0.775292\pi$
$61$	−2156.94	+	1245.31i	−0.579667	+	0.334671i	0.181334	+	0.983422i	$0.441958\pi$
$62$	4672.32	+	2697.56i	1.21548	+	0.701760i
$63$	−1226.06	−	707.865i	−0.308909	−	0.178348i
$64$	−3937.39			−0.961277
$65$			1833.66i			0.434002i
$66$	−84.9053	+	147.060i	−0.0194916	+	0.0337604i
$67$	−1950.13	+	3377.72i	−0.434424	+	0.752445i	−0.997248	−	0.0741319i	$-0.976381\pi$
$67$	−1950.13	+	3377.72i	−0.434424	+	0.752445i	0.562824	+	0.826577i	$0.309715\pi$
$68$	55.9067	+	96.8333i	0.0120906	+	0.0209415i
$69$	541.497	−	312.633i	0.113736	−	0.0656655i
$70$		−	1660.18i		−	0.338811i
$71$	−269.006	+	155.310i	−0.0533635	+	0.0308094i	−0.526444	−	0.850210i	$-0.676475\pi$
$71$	−269.006	+	155.310i	−0.0533635	+	0.0308094i	0.473081	+	0.881019i	$0.343142\pi$
$72$	−4704.61	+	2716.21i	−0.907524	+	0.523959i
$73$	1594.06	−	920.330i	0.299129	−	0.172702i	−0.342923	−	0.939364i	$-0.611417\pi$
$73$	1594.06	−	920.330i	0.299129	−	0.172702i	0.642051	+	0.766662i	$0.278084\pi$
$74$	−2008.84	+	3479.42i	−0.366845	+	0.635394i
$75$		−	494.961i		−	0.0879931i
$76$	1018.51	+	588.038i	0.176335	+	0.101807i
$77$	603.325	−	348.330i	0.101758	−	0.0587502i
$78$	−258.741			−0.0425281
$79$	−1812.66	−	3139.62i	−0.290444	−	0.503063i	0.683471	−	0.729978i	$-0.260470\pi$
$79$	−1812.66	−	3139.62i	−0.290444	−	0.503063i	−0.973915	+	0.226914i	$0.927136\pi$
$80$	−2459.05	−	1419.73i	−0.384226	−	0.221833i
$81$	−3020.87	+	5232.31i	−0.460429	+	0.797486i
$82$		−	2753.01i		−	0.409431i
$83$	2244.46	−	3887.51i	0.325803	−	0.564307i	−0.655872	−	0.754872i	$-0.727699\pi$
$83$	2244.46	−	3887.51i	0.325803	−	0.564307i	0.981675	+	0.190565i	$0.0610321\pi$
$84$	−187.583			−0.0265850
$85$			487.462i			0.0674688i
$86$	3184.26	+	4498.59i	0.430538	+	0.608246i
$87$	426.721			0.0563774
$88$		−	2673.21i		−	0.345198i
$89$	11516.0	+	6648.75i	1.45385	+	0.839383i	0.998697	−	0.0510286i	$-0.0162500\pi$
$89$	11516.0	+	6648.75i	1.45385	+	0.839383i	0.455157	+	0.890411i	$0.349583\pi$
$90$	−7289.73			−0.899967
$91$	919.288	+	530.751i	0.111012	+	0.0640926i
$92$	−1514.87	+	2623.83i	−0.178978	+	0.309999i
$93$	2301.55	−	1328.80i	0.266106	−	0.153636i
$94$		−	5505.73i		−	0.623102i
$95$	2563.61	+	4440.31i	0.284057	+	0.492001i
$96$	−609.015	+	1054.85i	−0.0660824	+	0.114458i
$97$	9109.89			0.968211			0.484105	−	0.875010i	$-0.339145\pi$
$97$	9109.89			0.968211			0.484105	+	0.875010i	$0.339145\pi$
$98$	5365.76	+	3097.92i	0.558701	+	0.322566i
$99$	−1529.49	−	2649.16i	−0.156055	−	0.270295i
$100$	1199.17	+	2077.02i	0.119917	+	0.207702i
$101$	−6165.99	−	10679.8i	−0.604450	−	1.04694i	−0.992138	−	0.125147i	$-0.960060\pi$
$101$	−6165.99	−	10679.8i	−0.604450	−	1.04694i	0.387688	−	0.921790i	$-0.373274\pi$
$102$	−68.7841			−0.00661132
$103$	−4662.56	−	8075.80i	−0.439491	−	0.761221i	0.558159	−	0.829734i	$-0.311508\pi$
$103$	−4662.56	−	8075.80i	−0.439491	−	0.761221i	−0.997650	+	0.0685127i	$0.978175\pi$
$104$	3527.48	−	2036.59i	0.326135	−	0.188294i
$105$	−708.227	−	408.895i	−0.0642382	−	0.0370880i
$106$	−10991.6	−	6346.02i	−0.978251	−	0.564793i
$107$	15071.5			1.31640			0.658201	−	0.752843i	$-0.271318\pi$
$107$	15071.5			1.31640			0.658201	+	0.752843i	$0.271318\pi$
$108$			1669.86i			0.143163i
$109$	7915.51	−	13710.1i	0.666233	−	1.15395i	−0.312717	−	0.949846i	$-0.601239\pi$
$109$	7915.51	−	13710.1i	0.666233	−	1.15395i	0.978950	−	0.204103i	$-0.0654276\pi$
$110$	1793.58	−	3106.58i	0.148230	−	0.256742i
$111$	989.540	+	1713.93i	0.0803133	+	0.139107i
$112$	−1423.54	+	821.881i	−0.113484	+	0.0655198i
$113$		−	16542.8i		−	1.29554i	−0.761834	−	0.647772i	$-0.775701\pi$
$113$		−	16542.8i		−	1.29554i	0.761834	−	0.647772i	$-0.224299\pi$
$114$	−626.557	+	361.743i	−0.0482115	+	0.0278349i
$115$	−11438.9	+	6604.23i	−0.864942	+	0.499375i
$116$	−1790.66	+	1033.84i	−0.133076	+	0.0768312i
$117$	2330.50	−	4036.54i	0.170246	−	0.294874i
$118$			8958.36i			0.643375i
$119$	244.385	+	141.096i	0.0172576	+	0.00996369i
$120$	−2717.59	+	1569.00i	−0.188722	+	0.108959i
$121$	−13135.7			−0.897187
$122$	3712.03	+	6429.43i	0.249397	+	0.431969i
$123$	−1174.43	−	678.057i	−0.0776276	−	0.0448183i
$124$	−6438.71	+	11152.2i	−0.418751	+	0.725298i
$125$		−	8930.20i		−	0.571533i
$126$	−2110.01	+	3654.64i	−0.132906	+	0.230199i
$127$	−1975.43			−0.122477			−0.0612384	−	0.998123i	$-0.519505\pi$
$127$	−1975.43			−0.122477			−0.0612384	+	0.998123i	$0.519505\pi$
$128$		−	1536.00i		−	0.0937502i
$129$	2703.36	−	250.410i	0.162452	−	0.0150478i
$130$	5465.78			0.323419
$131$			25150.8i			1.46558i	0.680454	+	0.732790i	$0.261782\pi$
$131$			25150.8i			1.46558i	−0.680454	+	0.732790i	$0.738218\pi$
$132$	−351.013	−	202.657i	−0.0201454	−	0.0116309i
$133$	2968.15			0.167796
$134$	10068.3	+	5812.96i	0.560723	+	0.323734i
$135$	−3639.96	+	6304.59i	−0.199723	+	0.345931i
$136$	937.750	−	541.410i	0.0507002	−	0.0292717i
$137$		−	4555.78i		−	0.242729i	−0.992608	−	0.121365i	$-0.961273\pi$
$137$		−	4555.78i		−	0.242729i	0.992608	−	0.121365i	$-0.0387270\pi$
$138$	−931.900	−	1614.10i	−0.0489340	−	0.0847563i
$139$	−2633.24	+	4560.90i	−0.136289	+	0.236059i	−0.926089	−	0.377305i	$-0.876851\pi$
$139$	−2633.24	+	4560.90i	−0.136289	+	0.236059i	0.789800	+	0.613364i	$0.210184\pi$
$140$	3962.61			0.202174
$141$	−2348.73	−	1356.04i	−0.118139	−	0.0682078i
$142$	462.951	+	801.854i	0.0229593	+	0.0397666i
$143$	1146.80	+	1986.32i	0.0560811	+	0.0971353i
$144$	3608.83	+	6250.67i	0.174037	+	0.301441i
$145$	−9014.27			−0.428741
$146$	−2743.33	−	4751.58i	−0.128698	−	0.222912i
$147$	2643.13	−	1526.01i	0.122316	−	0.0706193i
$148$	−8304.89	−	4794.83i	−0.379149	−	0.218902i
$149$	11680.4	+	6743.67i	0.526120	+	0.303755i	0.739435	−	0.673228i	$-0.235093\pi$
$149$	11680.4	+	6743.67i	0.526120	+	0.303755i	−0.213315	+	0.976983i	$0.568426\pi$
$150$	−1475.38			−0.0655726
$151$			31450.7i			1.37935i	0.724117	+	0.689677i	$0.242248\pi$
$151$			31450.7i			1.37935i	−0.724117	+	0.689677i	$0.757752\pi$
$152$	5694.66	−	9863.45i	0.246480	−	0.426915i
$153$	619.543	−	1073.08i	0.0264660	−	0.0458405i
$154$	−1038.30	−	1798.40i	−0.0437808	−	0.0758305i
$155$	−48619.1	+	28070.2i	−2.02369	+	1.16838i
$156$		−	617.579i		−	0.0253772i
$157$	21704.0	−	12530.8i	0.880522	−	0.508370i	0.00969138	−	0.999953i	$-0.496915\pi$
$157$	21704.0	−	12530.8i	0.880522	−	0.508370i	0.870830	+	0.491584i	$0.163582\pi$
$158$	−9358.60	+	5403.19i	−0.374884	+	0.216439i
$159$	−5414.39	+	3126.00i	−0.214168	+	0.123650i
$160$	12865.2	−	22283.1i	0.502545	−	0.870433i
$161$			7646.37i			0.294987i
$162$	15596.5	+	9004.65i	0.594288	+	0.343113i
$163$	−1271.22	+	733.937i	−0.0478458	+	0.0276238i	−0.523732	−	0.851883i	$-0.675461\pi$
$163$	−1271.22	+	733.937i	−0.0478458	+	0.0276238i	0.475886	+	0.879507i	$0.342127\pi$
$164$	6571.06			0.244314
$165$	−883.506	−	1530.28i	−0.0324520	−	0.0562085i
$166$	−11587.9	−	6690.30i	−0.420523	−	0.242789i
$167$	6452.32	−	11175.7i	0.231357	−	0.400722i	−0.726851	−	0.686796i	$-0.759017\pi$
$167$	6452.32	−	11175.7i	0.231357	−	0.400722i	0.958208	+	0.286073i	$0.0923501\pi$
$168$			1816.59i			0.0643633i
$169$	12533.1	−	21708.0i	0.438819	−	0.760057i
$170$	1453.03			0.0502779
$171$		−	13033.0i		−	0.445708i
$172$	−10737.5	+	7600.38i	−0.362950	+	0.256908i
$173$	−38722.3			−1.29380			−0.646902	−	0.762573i	$-0.723936\pi$
$173$	−38722.3			−1.29380			−0.646902	+	0.762573i	$0.723936\pi$
$174$		−	1271.97i		−	0.0420126i
$175$	5241.94	+	3026.43i	0.171165	+	0.0988223i
$176$	−3551.70			−0.114660
$177$	3821.61	+	2206.41i	0.121983	+	0.0704270i
$178$	19818.7	−	34326.9i	0.625510	−	1.08342i
$179$	16416.7	−	9478.18i	0.512365	−	0.295814i	−0.221440	−	0.975174i	$-0.571076\pi$
$179$	16416.7	−	9478.18i	0.512365	−	0.295814i	0.733805	+	0.679360i	$0.237742\pi$
$180$		−	17399.6i		−	0.537024i
$181$	−7951.56	−	13772.5i	−0.242714	−	0.420394i	0.718772	−	0.695246i	$-0.244704\pi$
$181$	−7951.56	−	13772.5i	−0.242714	−	0.420394i	−0.961487	+	0.274852i	$0.911371\pi$
$182$	1582.07	−	2740.22i	0.0477620	−	0.0827262i
$183$	3657.04			0.109201
$184$	25409.6	+	14670.2i	0.750520	+	0.433313i
$185$	−20903.6	−	36206.0i	−0.610769	−	1.05788i
$186$	−3960.90	−	6860.47i	−0.114490	−	0.198303i
$187$	304.868	+	528.047i	0.00871824	+	0.0151004i
$188$	13141.4			0.371815
$189$	2107.17	+	3649.73i	0.0589897	+	0.102173i
$190$	13235.7	−	7641.65i	0.366640	−	0.211680i
$191$	−48913.1	−	28240.0i	−1.34078	−	0.774101i	−0.353861	−	0.935298i	$-0.615131\pi$
$191$	−48913.1	−	28240.0i	−1.34078	−	0.774101i	−0.986922	+	0.161197i	$0.948465\pi$
$192$	5006.81	+	2890.68i	0.135818	+	0.0784147i
$193$	65667.2			1.76293			0.881463	−	0.472253i	$-0.156559\pi$
$193$	65667.2			1.76293			0.881463	+	0.472253i	$0.156559\pi$
$194$		−	27154.9i		−	0.721513i
$195$	1346.20	−	2331.69i	0.0354030	−	0.0613198i
$196$	−7394.32	+	12807.3i	−0.192480	+	0.333385i
$197$	19781.3	+	34262.3i	0.509710	+	0.882844i	0.999937	+	0.0112487i	$0.00358065\pi$
$197$	19781.3	+	34262.3i	0.509710	+	0.882844i	−0.490227	+	0.871595i	$0.663086\pi$
$198$	−7896.65	+	4559.13i	−0.201425	+	0.116293i
$199$			72484.2i			1.83036i	0.403042	+	0.915181i	$0.367953\pi$
$199$			72484.2i			1.83036i	−0.403042	+	0.915181i	$0.632047\pi$
$200$	20114.3	−	11613.0i	0.502856	−	0.290324i
$201$	4959.59	−	2863.42i	0.122759	−	0.0708750i
$202$	−31834.5	+	18379.6i	−0.780180	+	0.450437i
$203$	−2609.18	+	4519.23i	−0.0633157	+	0.109666i
$204$		−	164.178i		−	0.00394507i
$205$	24809.2	+	14323.6i	0.590345	+	0.340836i
$206$	−24072.4	+	13898.2i	−0.567264	+	0.327510i
$207$	33574.7			0.783559
$208$	−2705.87	−	4686.70i	−0.0625432	−	0.108328i
$209$	5554.11	+	3206.66i	0.127152	+	0.0734110i
$210$	−1218.84	+	2111.09i	−0.0276380	+	0.0478705i
$211$			42931.4i			0.964296i	0.876090	+	0.482148i	$0.160143\pi$
$211$			42931.4i			0.964296i	−0.876090	+	0.482148i	$0.839857\pi$
$212$	15147.1	−	26235.5i	0.337021	−	0.583737i
$213$	456.092			0.0100529
$214$		−	44925.2i		−	0.980985i
$215$	−57107.1	+	5289.80i	−1.23542	+	0.114436i
$216$	16171.2			0.346605
$217$			32499.7i			0.690176i
$218$	−40867.1	−	23594.6i	−0.859925	−	0.496478i
$219$	−2702.68			−0.0563517
$220$	7414.98	+	4281.04i	0.153202	+	0.0884512i
$221$	−464.528	+	804.586i	−0.00951103	+	0.0164736i
$222$	5108.91	−	2949.63i	0.103663	−	0.0598497i
$223$		−	31064.5i		−	0.624676i	−0.949971	−	0.312338i	$-0.898888\pi$
$223$		−	31064.5i		−	0.624676i	0.949971	−	0.312338i	$-0.101112\pi$
$224$	−7447.63	−	12899.7i	−0.148430	−	0.257088i
$225$	13288.9	−	23017.0i	0.262496	−	0.454657i
$226$	−49311.0			−0.965443
$227$	12012.2	+	6935.26i	0.233116	+	0.134589i	0.612009	−	0.790851i	$-0.290362\pi$
$227$	12012.2	+	6935.26i	0.233116	+	0.134589i	−0.378893	+	0.925441i	$0.623695\pi$
$228$	−863.430	−	1495.51i	−0.0166095	−	0.0287686i
$229$	−4647.57	−	8049.82i	−0.0886247	−	0.153502i	0.818305	−	0.574784i	$-0.194914\pi$
$229$	−4647.57	−	8049.82i	−0.0886247	−	0.153502i	−0.906930	+	0.421281i	$0.861581\pi$
$230$	19685.9	+	34097.0i	0.372135	+	0.644557i
$231$	−1022.92			−0.0191698
$232$	10011.9	+	17341.1i	0.186012	+	0.322182i
$233$	−73343.6	+	42344.9i	−1.35098	+	0.779991i	−0.988387	−	0.151955i	$-0.951443\pi$
$233$	−73343.6	+	42344.9i	−1.35098	+	0.779991i	−0.362597	+	0.931946i	$0.618110\pi$
$234$	−12032.1	−	6946.76i	−0.219741	−	0.126868i
$235$	49615.8	+	28645.7i	0.898430	+	0.518709i
$236$	−21382.4			−0.383912
$237$			5323.14i			0.0947700i
$238$	420.580	−	728.465i	0.00742496	−	0.0128604i
$239$	−404.141	+	699.992i	−0.00707517	+	0.0122545i	−0.869541	−	0.493860i	$-0.835585\pi$
$239$	−404.141	+	699.992i	−0.00707517	+	0.0122545i	0.862466	+	0.506115i	$0.168919\pi$
$240$	2084.62	+	3610.67i	0.0361914	+	0.0626853i
$241$	−55211.3	+	31876.3i	−0.950591	+	0.548824i	−0.893265	−	0.449531i	$-0.851591\pi$
$241$	−55211.3	+	31876.3i	−0.950591	+	0.548824i	−0.0573269	+	0.998355i	$0.518258\pi$
$242$			39155.1i			0.668586i
$243$	24146.7	−	13941.1i	0.408926	−	0.236093i
$244$	−15346.2	+	8860.11i	−0.257763	+	0.148819i
$245$	−55834.9	+	32236.3i	−0.930194	+	0.537048i
$246$	−2021.16	+	3500.75i	−0.0333987	+	0.0578483i
$247$			9772.01i			0.160173i
$248$	108000.	+	62353.6i	1.75598	+	1.01381i
$249$	−5708.13	+	3295.59i	−0.0920651	+	0.0531538i
$250$	−26619.2			−0.425907
$251$	−44994.1	−	77932.0i	−0.714180	−	1.23700i	−0.963275	−	0.268518i	$-0.913466\pi$
$251$	−44994.1	−	77932.0i	−0.714180	−	1.23700i	0.249094	−	0.968479i	$-0.419867\pi$
$252$	−8723.13	−	5036.30i	−0.137363	−	0.0793068i
$253$	−8260.81	+	14308.1i	−0.129057	+	0.223533i
$254$			5888.37i			0.0912699i
$255$	357.876	−	619.860i	0.00550367	−	0.00953264i
$256$	−67576.8			−1.03114
$257$		−	105051.i		−	1.59050i	−0.606284	−	0.795248i	$-0.707340\pi$
$257$		−	105051.i		−	1.59050i	0.606284	−	0.795248i	$-0.292660\pi$
$258$	−746.426	−	8058.19i	−0.0112137	−	0.121059i
$259$	−24202.1			−0.360789
$260$			13046.1i			0.192989i
$261$	19843.7	+	11456.7i	0.291300	+	0.168182i
$262$	74969.8			1.09215
$263$	40126.5	+	23167.1i	0.580123	+	0.334934i	0.761182	−	0.648538i	$-0.224619\pi$
$263$	40126.5	+	23167.1i	0.580123	+	0.334934i	−0.181059	+	0.983472i	$0.557953\pi$
$264$	−1962.57	+	3399.27i	−0.0281590	+	0.0487728i
$265$	114376.	−	66035.2i	1.62871	−	0.940338i
$266$		−	8847.49i		−	0.125042i
$267$	−9762.52	−	16909.2i	−0.136943	−	0.237192i
$268$	−13874.7	+	24031.8i	−0.193177	+	0.334592i
$269$	1725.50			0.0238457			0.0119229	−	0.999929i	$-0.496205\pi$
$269$	1725.50			0.0238457			0.0119229	+	0.999929i	$0.496205\pi$
$270$	18792.8	+	10850.0i	0.257789	+	0.148834i
$271$	−55532.6	−	96185.3i	−0.756153	−	1.30970i	−0.944799	−	0.327650i	$-0.893743\pi$
$271$	−55532.6	−	96185.3i	−0.756153	−	1.30970i	0.188646	−	0.982045i	$-0.439590\pi$
$272$	−719.333	−	1245.92i	−0.00972282	−	0.0168404i
$273$	−779.314	−	1349.81i	−0.0104565	−	0.0181112i
$274$	−13579.9			−0.180882
$275$	6539.26	+	11326.3i	0.0864696	+	0.149770i
$276$	3852.63	−	2224.32i	0.0505754	−	0.0291997i
$277$	38947.2	+	22486.2i	0.507594	+	0.293060i	0.731844	−	0.681472i	$-0.238660\pi$
$277$	38947.2	+	22486.2i	0.507594	+	0.293060i	−0.224250	+	0.974532i	$0.571993\pi$
$278$	13595.2	+	7849.17i	0.175912	+	0.101563i
$279$	142704.			1.83328
$280$		−	38374.6i		−	0.489472i
$281$	49822.3	−	86294.8i	0.630974	−	1.09288i	−0.356379	−	0.934342i	$-0.615989\pi$
$281$	49822.3	−	86294.8i	0.630974	−	1.09288i	0.987353	−	0.158538i	$-0.0506779\pi$
$282$	−4042.09	+	7001.11i	−0.0508286	+	0.0880377i
$283$	25832.5	+	44743.2i	0.322548	+	0.558669i	0.981013	−	0.193942i	$-0.0621274\pi$
$283$	25832.5	+	44743.2i	0.322548	+	0.558669i	−0.658465	+	0.752611i	$0.728794\pi$
$284$	−1913.91	+	1105.00i	−0.0237294	+	0.0137001i
$285$		−	7528.43i		−	0.0926861i
$286$	5920.84	−	3418.40i	0.0723855	−	0.0417918i
$287$	14362.1	−	8291.94i	0.174362	−	0.100668i
$288$	−56641.6	+	32702.1i	−0.682890	+	0.394267i
$289$	41637.0	−	72117.4i	0.498521	−	0.863464i
$290$			26869.8i			0.319498i
$291$	−11584.2	−	6688.13i	−0.136798	−	0.0789803i
$292$	11341.4	−	6547.94i	0.133015	−	0.0767961i
$293$	−68979.9			−0.803503			−0.401752	−	0.915749i	$-0.631598\pi$
$293$	−68979.9			−0.803503			−0.401752	+	0.915749i	$0.631598\pi$
$294$	−4548.75	−	7878.67i	−0.0526257	−	0.0911503i
$295$	−80729.7	−	46609.3i	−0.927661	−	0.535585i
$296$	−46434.0	+	80426.0i	−0.529971	+	0.917937i
$297$			9105.99i			0.103232i
$298$	20101.6	−	34817.0i	0.226359	−	0.392066i
$299$	−25174.0			−0.281586
$300$		−	3521.54i		−	0.0391282i
$301$	−13877.6	+	30161.3i	−0.153173	+	0.332902i
$302$	93748.4			1.02790
$303$			18107.3i			0.197228i
$304$	−13104.9	−	7566.09i	−0.141803	−	0.0818699i
$305$	−77253.1			−0.830456
$306$	−3198.65	−	1846.74i	−0.0341604	−	0.0197225i
$307$	54485.4	−	94371.5i	0.578101	−	1.00130i	−0.417596	−	0.908633i	$-0.637127\pi$
$307$	54485.4	−	94371.5i	0.578101	−	1.00130i	0.995697	−	0.0926672i	$-0.0295393\pi$
$308$	4292.52	−	2478.29i	0.0452492	−	0.0261247i
$309$			13692.3i			0.143403i
$310$	83672.0	+	144924.i	0.870677	+	1.50806i
$311$	22721.8	−	39355.4i	0.234921	−	0.406896i	−0.724328	−	0.689455i	$-0.757850\pi$
$311$	22721.8	−	39355.4i	0.234921	−	0.406896i	0.959250	+	0.282559i	$0.0911834\pi$
$312$	−5980.74			−0.0614392
$313$	78576.1	+	45365.9i	0.802050	+	0.463064i	0.844188	−	0.536048i	$-0.180083\pi$
$313$	78576.1	+	45365.9i	0.802050	+	0.463064i	−0.0421373	+	0.999112i	$0.513417\pi$
$314$	−37351.9	−	64695.4i	−0.378838	−	0.656167i
$315$	−21956.3	−	38029.4i	−0.221278	−	0.383264i
$316$	−12896.7	−	22337.7i	−0.129153	−	0.223699i
$317$	−84013.0			−0.836042			−0.418021	−	0.908437i	$-0.637276\pi$
$317$	−84013.0			−0.836042			−0.418021	+	0.908437i	$0.637276\pi$
$318$	9318.01	+	16139.3i	0.0921444	+	0.159599i
$319$	−9764.77	+	5637.69i	−0.0959579	+	0.0554013i
$320$	−105766.	−	61064.2i	−1.03287	−	0.596330i
$321$	−19165.0	−	11064.9i	−0.185994	−	0.107383i
$322$	22792.4			0.219825
$323$			2597.81i			0.0249001i
$324$	−21492.8	+	37226.7i	−0.204741	+	0.354621i
$325$	−9963.89	+	17258.0i	−0.0943327	+	0.163389i
$326$	2187.73	+	3789.25i	0.0205853	+	0.0356548i
$327$	−20130.8	+	11622.5i	−0.188263	+	0.108694i
$328$		−	63635.3i		−	0.591494i
$329$	28722.5	−	16583.0i	0.265357	−	0.153204i
$330$	−4561.46	+	2633.56i	−0.0418867	+	0.0241833i
$331$	−251.465	+	145.183i	−0.00229521	+	0.00132514i	−0.501147	−	0.865362i	$-0.667088\pi$
$331$	−251.465	+	145.183i	−0.00229521	+	0.00132514i	0.498852	+	0.866687i	$0.333755\pi$
$332$	15968.8	−	27658.8i	0.144876	−	0.250933i
$333$			106270.i			0.958346i
$334$	−33312.8	−	19233.1i	−0.298619	−	0.172408i
$335$	−104769.	+	60488.4i	−0.933562	+	0.538992i
$336$	2413.57			0.0213787
$337$	−61054.3	−	105749.i	−0.537597	−	0.931145i	−0.999033	−	0.0439713i	$-0.985999\pi$
$337$	−61054.3	−	105749.i	−0.537597	−	0.931145i	0.461436	−	0.887173i	$-0.347334\pi$
$338$	−64707.4	−	37358.8i	−0.566396	−	0.327009i
$339$	−12145.1	+	21035.9i	−0.105682	+	0.183047i
$340$			3468.19i			0.0300016i
$341$	−35111.3	+	60814.6i	−0.301952	+	0.522997i
$342$	−38848.8			−0.332143
$343$			80435.7i			0.683692i
$344$	73603.4	+	103984.i	0.621987	+	0.878717i
$345$	19394.3			0.162943
$346$			115424.i			0.964145i
$347$	157834.	+	91125.3i	1.31081	+	0.756798i	0.982231	−	0.187677i	$-0.0600959\pi$
$347$	157834.	+	91125.3i	1.31081	+	0.756798i	0.328582	+	0.944475i	$0.393429\pi$
$348$	3036.02			0.0250696
$349$	61252.2	+	35364.0i	0.502887	+	0.290342i	0.729905	−	0.683548i	$-0.239564\pi$
$349$	61252.2	+	35364.0i	0.502887	+	0.290342i	−0.227018	+	0.973891i	$0.572898\pi$
$350$	9021.22	−	15625.2i	0.0736426	−	0.127553i
$351$	−12016.0	+	6937.41i	−0.0975313	+	0.0563097i
$352$		−	32184.4i		−	0.259753i
$353$	109426.	+	189531.i	0.878152	+	1.52100i	0.853366	+	0.521312i	$0.174557\pi$
$353$	109426.	+	189531.i	0.878152	+	1.52100i	0.0247860	+	0.999693i	$0.492110\pi$
$354$	6576.88	−	11391.5i	0.0524824	−	0.0909022i
$355$	−9634.72			−0.0764509
$356$	81933.6	+	47304.4i	0.646490	+	0.373251i
$357$	−207.174	−	358.836i	−0.00162555	−	0.00281553i
$358$	−28252.6	−	48935.0i	−0.220441	−	0.381816i
$359$	84028.5	+	145542.i	0.651985	+	1.12927i	0.982641	+	0.185519i	$0.0593968\pi$
$359$	84028.5	+	145542.i	0.651985	+	1.12927i	−0.330656	+	0.943751i	$0.607270\pi$
$360$	−168500.			−1.30016
$361$	−51498.4	−	89197.8i	−0.395166	−	0.684447i
$362$	−41053.2	+	23702.1i	−0.313278	+	0.180871i
$363$	16703.4	+	9643.74i	0.126763	+	0.0731867i
$364$	6540.53	+	3776.18i	0.0493640	+	0.0285003i
$365$	57092.9			0.428545
$366$		−	10900.9i		−	0.0813769i
$367$	88583.7	−	153431.i	0.657690	−	1.13915i	−0.323522	−	0.946221i	$-0.604867\pi$
$367$	88583.7	−	153431.i	0.657690	−	1.13915i	0.981212	−	0.192933i	$-0.0617999\pi$
$368$	19491.3	−	33759.9i	0.143928	−	0.249291i
$369$	−36409.4	−	63062.9i	−0.267399	−	0.463149i
$370$	−107923.	+	62309.5i	−0.788336	+	0.455146i
$371$		−	76455.5i		−	0.555470i
$372$	16375.0	−	9454.11i	0.118330	−	0.0683180i
$373$	−113524.	+	65543.3i	−0.815965	+	0.471097i	−0.849023	−	0.528356i	$-0.822809\pi$
$373$	−113524.	+	65543.3i	−0.815965	+	0.471097i	0.0330583	+	0.999453i	$0.489475\pi$
$374$	1574.01	−	908.753i	0.0112529	−	0.00649685i
$375$	−6556.21	+	11355.7i	−0.0466219	+	0.0807515i
$376$		−	127264.i		−	0.900179i
$377$	−14878.6	−	8590.17i	−0.104684	−	0.0604392i
$378$	10879.1	−	6281.07i	0.0761396	−	0.0439592i
$379$	−114722.			−0.798669			−0.399334	−	0.916805i	$-0.630759\pi$
$379$	−114722.			−0.798669			−0.399334	+	0.916805i	$0.630759\pi$
$380$	18239.6	+	31591.8i	0.126313	+	0.218780i
$381$	2511.96	+	1450.28i	0.0173047	+	0.00999086i
$382$	−84178.0	+	145801.i	−0.576862	+	0.999154i
$383$		−	222245.i		−	1.51507i	−0.652792	−	0.757537i	$-0.726402\pi$
$383$		−	222245.i		−	1.51507i	0.652792	−	0.757537i	$-0.273598\pi$
$384$	−1127.67	+	1953.19i	−0.00764753	+	0.0132459i
$385$	21608.7			0.145783
$386$		−	195741.i		−	1.31374i
$387$	132436.	+	60935.8i	0.884271	+	0.406865i
$388$	64814.9			0.430538
$389$			176795.i			1.16835i	0.811629	+	0.584173i	$0.198581\pi$
$389$			176795.i			1.16835i	−0.811629	+	0.584173i	$0.801419\pi$
$390$	−6950.31	−	4012.77i	−0.0456957	−	0.0263824i
$391$	−6692.31			−0.0437746
$392$	124028.	+	71607.8i	0.807140	+	0.466003i
$393$	18464.8	−	31981.9i	0.119553	−	0.207071i
$394$	102129.	−	58964.4i	0.657897	−	0.379837i
$395$		−	112449.i		−	0.720710i
$396$	−10882.0	−	18848.2i	−0.0693935	−	0.120193i
$397$	44553.3	−	77168.5i	0.282682	−	0.489620i	−0.689362	−	0.724417i	$-0.742109\pi$
$397$	44553.3	−	77168.5i	0.282682	−	0.489620i	0.972044	+	0.234797i	$0.0754425\pi$
$398$	216062.			1.36399
$399$	−3774.31	−	2179.10i	−0.0237079	−	0.0136877i
$400$	−15429.3	−	26724.4i	−0.0964333	−	0.167027i
$401$	10908.5	+	18894.0i	0.0678383	+	0.117499i	0.897950	−	0.440098i	$-0.145056\pi$
$401$	10908.5	+	18894.0i	0.0678383	+	0.117499i	−0.830111	+	0.557598i	$0.811723\pi$
$402$	−8535.31	−	14783.6i	−0.0528162	−	0.0914803i
$403$	−106998.			−0.658820
$404$	−43869.7	−	75984.5i	−0.268783	−	0.465546i
$405$	−162294.	+	93700.3i	−0.989445	+	0.571256i
$406$	13471.0	+	7777.46i	0.0817234	+	0.0471830i
$407$	−45287.9	−	26147.0i	−0.273396	−	0.157846i
$408$	−1589.93			−0.00955120
$409$		−	7905.64i		−	0.0472596i	−0.999721	−	0.0236298i	$-0.992478\pi$
$409$		−	7905.64i		−	0.0472596i	0.999721	−	0.0236298i	$-0.00752230\pi$
$410$	42696.0	−	73951.6i	0.253992	−	0.439926i
$411$	−3344.68	+	5793.16i	−0.0198003	+	0.0342951i
$412$	−33173.1	−	57457.5i	−0.195430	−	0.338495i
$413$	−46734.4	+	26982.1i	−0.273991	+	0.158189i
$414$		−	100080.i		−	0.583910i
$415$	120581.	−	69617.7i	0.700139	−	0.404225i
$416$	42469.4	−	24519.7i	0.245409	−	0.141687i
$417$	6696.87	−	3866.44i	0.0385123	−	0.0222351i
$418$	9558.45	−	16555.7i	0.0547060	−	0.0947536i
$419$		−	158457.i		−	0.902575i	−0.892379	−	0.451288i	$-0.850965\pi$
$419$		−	158457.i		−	0.902575i	0.892379	−	0.451288i	$-0.149035\pi$
$420$	−5038.88	−	2909.20i	−0.0285651	−	0.0164920i
$421$	−257038.	+	148401.i	−1.45022	+	0.837284i	−0.998493	−	0.0548726i	$-0.982525\pi$
$421$	−257038.	+	148401.i	−1.45022	+	0.837284i	−0.451726	+	0.892157i	$0.649191\pi$
$422$	127970.			0.718595
$423$	−72814.8	−	126119.i	−0.406948	−	0.704854i
$424$	−254069.	−	146687.i	−1.41325	−	0.815942i
$425$	−2648.82	+	4587.89i	−0.0146647	+	0.0254001i
$426$		−	1359.52i		−	0.00749147i
$427$	−22360.9	+	38730.2i	−0.122640	+	0.212419i
$428$	107230.			0.585369
$429$		−	3367.75i		−	0.0182989i
$430$	15767.9	+	170225.i	0.0852779	+	0.920635i
$431$	299290.			1.61115			0.805577	−	0.592491i	$-0.201855\pi$
$431$	299290.			1.61115			0.805577	+	0.592491i	$0.201855\pi$
$432$		−	21485.5i		−	0.115127i
$433$	−209276.	−	120826.i	−1.11621	−	0.644442i	−0.175776	−	0.984430i	$-0.556243\pi$
$433$	−209276.	−	120826.i	−1.11621	−	0.644442i	−0.940430	+	0.339989i	$0.889577\pi$
$434$	96875.4			0.514321
$435$	11462.6	+	6617.93i	0.0605765	+	0.0349739i
$436$	56317.1	−	97544.1i	0.296256	−	0.513131i
$437$	−60960.5	+	35195.6i	−0.319217	+	0.184300i
$438$			8056.18i			0.0419934i
$439$	138797.	+	240403.i	0.720195	+	1.24741i	0.960921	+	0.276821i	$0.0892811\pi$
$439$	138797.	+	240403.i	0.720195	+	1.24741i	−0.240726	+	0.970593i	$0.577386\pi$
$440$	41458.3	−	71807.9i	0.214144	−	0.370909i
$441$	163884.			0.842671
$442$	2398.32	+	1384.67i	0.0122762	+	0.00708764i
$443$	34551.1	+	59844.2i	0.176057	+	0.304940i	0.940527	−	0.339720i	$-0.110332\pi$
$443$	34551.1	+	59844.2i	0.176057	+	0.304940i	−0.764469	+	0.644660i	$0.776999\pi$
$444$	7040.36	+	12194.3i	0.0357132	+	0.0618571i
$445$	206228.	+	357198.i	1.04143	+	1.80380i
$446$	−92597.4			−0.465510
$447$	−9901.89	−	17150.6i	−0.0495568	−	0.0858349i
$448$	−61228.1	+	35350.0i	−0.305067	+	0.176130i
$449$	−10661.3	−	6155.32i	−0.0528833	−	0.0305322i	0.473325	−	0.880888i	$-0.343054\pi$
$449$	−10661.3	−	6155.32i	−0.0528833	−	0.0305322i	−0.526209	+	0.850356i	$0.676387\pi$
$450$	−68609.3	−	39611.6i	−0.338811	−	0.195613i
$451$	35833.0			0.176169
$452$		−	117698.i		−	0.576095i
$453$	23089.9	−	39992.8i	0.112519	−	0.194888i
$454$	20672.7	−	35806.1i	0.100296	−	0.173718i
$455$	16462.6	+	28514.1i	0.0795201	+	0.137733i
$456$	−14482.7	+	8361.61i	−0.0696499	+	0.0402124i
$457$			259955.i			1.24470i	0.782739	+	0.622350i	$0.213822\pi$
$457$			259955.i			1.24470i	−0.782739	+	0.622350i	$0.786178\pi$
$458$	−23995.0	+	13853.5i	−0.114390	+	0.0660433i
$459$	−3194.34	+	1844.25i	−0.0151620	+	0.00875377i
$460$	−81384.9	+	46987.6i	−0.384617	+	0.222059i
$461$	−151546.	+	262486.i	−0.713088	+	1.23510i	0.250605	+	0.968089i	$0.419371\pi$
$461$	−151546.	+	262486.i	−0.713088	+	1.23510i	−0.963692	+	0.267015i	$0.913963\pi$
$462$			3049.13i			0.0142854i
$463$	−133486.	−	77068.1i	−0.622692	−	0.359511i	0.155224	−	0.987879i	$-0.450390\pi$
$463$	−133486.	−	77068.1i	−0.622692	−	0.359511i	−0.777916	+	0.628368i	$0.783723\pi$
$464$	23039.9	−	13302.1i	0.107015	−	0.0617851i
$465$	82432.4			0.381234
$466$	126222.	+	218623.i	0.581251	+	1.00676i
$467$	−260551.	−	150429.i	−1.19470	−	0.689761i	−0.235332	−	0.971915i	$-0.575618\pi$
$467$	−260551.	−	150429.i	−1.19470	−	0.689761i	−0.959369	+	0.282154i	$0.908951\pi$
$468$	16581.0	−	28719.1i	0.0757038	−	0.131123i
$469$			70033.4i			0.318390i
$470$	85387.3	−	147895.i	0.386543	−	0.669512i
$471$	−36798.5			−0.165878
$472$			207070.i			0.929467i
$473$	−58553.3	+	41446.1i	−0.261715	+	0.185251i
$474$	15867.3			0.0706228
$475$			55721.6i			0.246966i
$476$	1738.75	+	1003.87i	0.00767401	+	0.00443059i
$477$	−335711.			−1.47547
$478$	2086.54	+	1204.67i	0.00913212	+	0.00527243i
$479$	88551.3	−	153375.i	0.385944	−	0.668474i	−0.605956	−	0.795498i	$-0.707209\pi$
$479$	88551.3	−	153375.i	0.385944	−	0.668474i	0.991900	+	0.127024i	$0.0405426\pi$
$480$	−32718.8	+	18890.2i	−0.142009	+	0.0819887i
$481$		−	79680.4i		−	0.344398i
$482$	95017.0	+	164574.i	0.408985	+	0.708383i
$483$	5613.67	−	9723.16i	0.0240631	−	0.0416786i
$484$	−93457.7			−0.398955
$485$	244710.	+	141284.i	1.04032	+	0.600632i
$486$	−41555.7	−	71976.6i	−0.175937	−	0.304732i
$487$	−142874.	−	247465.i	−0.602413	−	1.04341i	−0.992455	−	0.122613i	$-0.960873\pi$
$487$	−142874.	−	247465.i	−0.602413	−	1.04341i	0.390041	−	0.920797i	$-0.372461\pi$
$488$	85802.8	+	148615.i	0.360298	+	0.624054i
$489$	2155.31			0.00901349
$490$	96090.2	+	166433.i	0.400209	+	0.693183i
$491$	−189932.	+	109658.i	−0.787837	+	0.454858i	−0.839200	−	0.543822i	$-0.816977\pi$
$491$	−189932.	+	109658.i	−0.787837	+	0.454858i	0.0513638	+	0.998680i	$0.483643\pi$
$492$	−8355.80	−	4824.22i	−0.0345190	−	0.0199295i
$493$	−3955.35	−	2283.62i	−0.0162739	−	0.00939574i
$494$	29128.5			0.119361
$495$		−	94882.6i		−	0.387236i
$496$	82844.8	−	143491.i	0.336745	−	0.583260i
$497$	−2788.77	+	4830.28i	−0.0112901	+	0.0195551i
$498$	9823.52	+	17014.8i	0.0396103	+	0.0686071i
$499$	129236.	−	74614.3i	0.519017	−	0.299655i	−0.217515	−	0.976057i	$-0.569795\pi$
$499$	129236.	−	74614.3i	0.519017	−	0.299655i	0.736532	+	0.676402i	$0.236462\pi$
$500$		−	63536.4i		−	0.254145i
$501$	−16409.6	+	9474.09i	−0.0653767	+	0.0377452i
$502$	−232300.	+	134119.i	−0.921813	+	0.532209i
$503$	−280032.	+	161676.i	−1.10681	+	0.639014i	−0.938000	−	0.346635i	$-0.887324\pi$
$503$	−280032.	+	161676.i	−1.10681	+	0.639014i	−0.168805	+	0.985649i	$0.553991\pi$
$504$	−48772.4	+	84476.3i	−0.192005	+	0.332563i
$505$		−	382509.i		−	1.49989i
$506$	42649.9	+	24623.9i	0.166578	+	0.0961736i
$507$	−31874.3	+	18402.7i	−0.124001	+	0.0715920i
$508$	−14054.7			−0.0544622
$509$	−109030.	−	188846.i	−0.420834	−	0.728907i	0.575187	−	0.818022i	$-0.304929\pi$
$509$	−109030.	−	188846.i	−0.420834	−	0.728907i	−0.996021	+	0.0891154i	$0.971596\pi$
$510$	−1847.68	−	1066.76i	−0.00710374	−	0.00410135i
$511$	16525.5	−	28623.0i	0.0632868	−	0.109616i
$512$			176857.i			0.674657i
$513$	−19398.2	+	33598.7i	−0.0737102	+	0.127670i
$514$	−313136.			−1.18524
$515$		−	289243.i		−	1.09056i
$516$	19233.8	−	1781.61i	0.0722379	−	0.00669136i
$517$	71662.2			0.268107
$518$			72141.9i			0.268861i
$519$	49239.4	+	28428.4i	0.182801	+	0.105540i
$520$	126340.			0.467235
$521$	−72348.0	−	41770.2i	−0.266533	−	0.153883i	0.360778	−	0.932652i	$-0.382511\pi$
$521$	−72348.0	−	41770.2i	−0.266533	−	0.153883i	−0.627311	+	0.778769i	$0.715845\pi$
$522$	34150.3	−	59150.1i	0.125330	−	0.217077i
$523$	214473.	−	123826.i	0.784097	−	0.452698i	−0.0537835	−	0.998553i	$-0.517128\pi$
$523$	214473.	−	123826.i	0.784097	−	0.452698i	0.837880	+	0.545854i	$0.183795\pi$
$524$			178943.i			0.651705i
$525$	−4443.78	−	7696.85i	−0.0161226	−	0.0279251i
$526$	69056.6	−	119610.i	0.249594	−	0.432309i
$527$	−28444.6			−0.102419
$528$	4516.36	+	2607.52i	0.0162002	+	0.00935320i
$529$	49251.9	+	85306.7i	0.175999	+	0.304840i
$530$	−196838.	−	340934.i	−0.700742	−	1.21372i
$531$	118477.	+	205208.i	0.420188	+	0.727788i
$532$	21117.7			0.0746146
$533$	27299.4	+	47284.0i	0.0960947	+	0.166441i
$534$	−50403.0	+	29100.2i	−0.176756	+	0.102050i
$535$	404851.	+	233741.i	1.41445	+	0.816633i
$536$	232728.	+	134365.i	0.810062	+	0.467690i
$537$	−27834.1			−0.0965224
$538$		−	5143.39i		−	0.0177699i
$539$	−40322.3	+	69840.4i	−0.138793	+	0.240397i
$540$	−25897.5	+	44855.8i	−0.0888117	+	0.153826i
$541$	−33920.5	−	58752.1i	−0.115896	−	0.200738i	0.802242	−	0.597000i	$-0.203641\pi$
$541$	−33920.5	−	58752.1i	−0.115896	−	0.200738i	−0.918138	+	0.396262i	$0.870307\pi$
$542$	−286710.	+	165532.i	−0.975988	+	0.563487i
$543$			23350.9i			0.0791962i
$544$	11290.1	−	6518.37i	0.0381506	−	0.0220263i
$545$	425254.	−	245520.i	1.43171	−	0.826598i
$546$	−4023.53	+	2322.99i	−0.0134965	+	0.00779223i
$547$	272146.	−	471370.i	0.909551	−	1.57539i	0.0948610	−	0.995491i	$-0.469759\pi$
$547$	272146.	−	471370.i	0.909551	−	1.57539i	0.814690	−	0.579897i	$-0.196907\pi$
$548$		−	32413.4i		−	0.107935i
$549$	170062.	+	98185.3i	0.564238	+	0.325763i
$550$	33761.6	−	19492.3i	0.111609	−	0.0644373i
$551$	−48039.3			−0.158232
$552$	−21540.7	−	37309.5i	−0.0706937	−	0.122445i
$553$	−56375.2	−	32548.2i	−0.184348	−	0.106433i
$554$	67027.0	−	116094.i	0.218389	−	0.378260i
$555$			61386.4i			0.199290i
$556$	−18734.9	+	32449.8i	−0.0606040	+	0.104969i
$557$	178656.			0.575846			0.287923	−	0.957654i	$-0.407035\pi$
$557$	178656.			0.575846			0.287923	+	0.957654i	$0.407035\pi$
$558$		−	425374.i		−	1.36616i
$559$	−99299.7	−	45689.2i	−0.317778	−	0.146214i
$560$	−50985.6			−0.162582
$561$		−	895.289i		−	0.00284471i
$562$	−257228.	−	148511.i	−0.814416	−	0.470203i
$563$	−120250.			−0.379375			−0.189687	−	0.981845i	$-0.560747\pi$
$563$	−120250.			−0.379375			−0.189687	+	0.981845i	$0.560747\pi$
$564$	−16710.7	−	9647.92i	−0.0525335	−	0.0303302i
$565$	256559.	−	444374.i	0.803694	−	1.39204i
$566$	133371.	−	77001.8i	0.416321	−	0.240363i
$567$			108486.i			0.337449i
$568$	10701.0	+	18534.7i	0.0331686	+	0.0574498i
$569$	141399.	−	244910.i	0.436738	−	0.756453i	−0.560698	−	0.828021i	$-0.689467\pi$
$569$	141399.	−	244910.i	0.436738	−	0.756453i	0.997436	+	0.0715681i	$0.0228003\pi$
$570$	−22440.8			−0.0690699
$571$	515078.	+	297381.i	1.57980	+	0.912096i	0.994887	+	0.100997i	$0.0322033\pi$
$571$	515078.	+	297381.i	1.57980	+	0.912096i	0.584909	+	0.811099i	$0.301130\pi$
$572$	8159.25	+	14132.2i	0.0249378	+	0.0431935i
$573$	41465.4	+	71820.2i	0.126292	+	0.218745i
$574$	−24716.7	−	42810.5i	−0.0750181	−	0.129935i
$575$	−143547.			−0.434168
$576$	155220.	+	268849.i	0.467845	+	0.810332i
$577$	−176239.	+	101751.i	−0.529358	+	0.305625i	−0.740755	−	0.671775i	$-0.765532\pi$
$577$	−176239.	+	101751.i	−0.529358	+	0.305625i	0.211397	+	0.977400i	$0.432199\pi$
$578$	−214968.	−	124112.i	−0.643456	−	0.371499i
$579$	−83502.8	−	48210.4i	−0.249083	−	0.143808i
$580$	−64134.5			−0.190650
$581$		−	80603.3i		−	0.238781i
$582$	−19936.0	+	34530.3i	−0.0588563	+	0.101942i
$583$	82599.3	−	143066.i	0.243019	−	0.420920i
$584$	−63411.4	−	109832.i	−0.185927	−	0.322034i
$585$	125204.	−	72286.4i	0.365852	−	0.211225i
$586$			205616.i			0.598772i
$587$	−418189.	+	241441.i	−1.21366	+	0.700705i	−0.963554	−	0.267514i	$-0.913798\pi$
$587$	−418189.	+	241441.i	−1.21366	+	0.700705i	−0.250103	+	0.968219i	$0.580465\pi$
$588$	18805.3	−	10857.2i	0.0543908	−	0.0314026i
$589$	−259103.	+	149593.i	−0.746865	+	0.431203i
$590$	−138933.	+	240640.i	−0.399119	+	0.691295i
$591$		−	58090.8i		−	0.166315i
$592$	106856.	+	61693.5i	0.304899	+	0.176034i
$593$	315289.	−	182032.i	0.896602	−	0.517653i	0.0205055	−	0.999790i	$-0.493472\pi$
$593$	315289.	−	182032.i	0.896602	−	0.517653i	0.876096	+	0.482137i	$0.160139\pi$
$594$	27143.2			0.0769287
$595$	4376.46	+	7580.24i	0.0123620	+	0.0214116i
$596$	83103.4	+	47979.7i	0.233952	+	0.135072i
$597$	53215.1	−	92171.3i	0.149309	−	0.258611i
$598$			75039.0i			0.209838i
$599$	−313454.	+	542919.i	−0.873616	+	1.51315i	−0.0153857	+	0.999882i	$0.504898\pi$
$599$	−313454.	+	542919.i	−0.873616	+	1.51315i	−0.858230	+	0.513265i	$0.828436\pi$
$600$	−34103.2			−0.0947311
$601$			171752.i			0.475503i	0.971326	+	0.237752i	$0.0764105\pi$
$601$			171752.i			0.475503i	−0.971326	+	0.237752i	$0.923590\pi$
$602$	89905.1	+	41366.6i	0.248080	+	0.114145i
$603$	307512.			0.845722
$604$			223764.i			0.613362i
$605$	−352852.	−	203719.i	−0.964011	−	0.556572i
$606$	53974.5			0.146975
$607$	−141604.	−	81755.3i	−0.384325	−	0.221890i	0.295373	−	0.955382i	$-0.404556\pi$
$607$	−141604.	−	81755.3i	−0.384325	−	0.221890i	−0.679698	+	0.733492i	$0.737889\pi$
$608$	68561.6	−	118752.i	0.185470	−	0.321243i
$609$	6635.69	−	3831.12i	0.0178917	−	0.0103298i
$610$			230277.i			0.618857i
$611$	54595.9	+	94562.9i	0.146244	+	0.253302i
$612$	4407.91	−	7634.72i	0.0117687	−	0.0203841i
$613$	−698661.			−1.85928			−0.929642	−	0.368463i	$-0.879884\pi$
$613$	−698661.			−1.85928			−0.929642	+	0.368463i	$0.879884\pi$
$614$	−281303.	−	162411.i	−0.746171	−	0.430802i
$615$	−21031.7	−	36428.0i	−0.0556063	−	0.0963130i
$616$	−24000.2	−	41569.5i	−0.0632489	−	0.109550i
$617$	−46335.5	−	80255.4i	−0.121715	−	0.210816i	0.798729	−	0.601691i	$-0.205506\pi$
$617$	−46335.5	−	80255.4i	−0.121715	−	0.210816i	−0.920444	+	0.390875i	$0.872173\pi$
$618$	40814.1			0.106865
$619$	126450.	+	219018.i	0.330018	+	0.571607i	0.982515	−	0.186184i	$-0.0596120\pi$
$619$	126450.	+	219018.i	0.330018	+	0.571607i	−0.652497	+	0.757791i	$0.726279\pi$
$620$	−345914.	+	199714.i	−0.899880	+	0.519546i
$621$	−86555.0	−	49972.6i	−0.224445	−	0.129583i
$622$	−117311.	−	67729.5i	−0.303220	−	0.175064i
$623$	238771.			0.615185
$624$			7946.18i			0.0204075i
$625$	243838.	−	422340.i	0.624226	−	1.08119i
$626$	135227.	−	234220.i	0.345076	−	0.597690i
$627$	−4708.42	−	8155.22i	−0.0119768	−	0.0207444i
$628$	154419.	−	89153.9i	0.391545	−	0.226059i
$629$		−	21182.4i		−	0.0535394i
$630$	−113358.	+	65447.5i	−0.285609	+	0.164897i
$631$	348428.	−	201165.i	0.875093	−	0.505235i	0.00605596	−	0.999982i	$-0.498072\pi$
$631$	348428.	−	201165.i	0.875093	−	0.505235i	0.869038	+	0.494746i	$0.164739\pi$
$632$	−216322.	+	124894.i	−0.541585	+	0.312684i
$633$	31518.6	−	54591.8i	0.0786610	−	0.136245i
$634$			250427.i			0.623020i
$635$	−53064.0	−	30636.5i	−0.131599	−	0.0759787i
$636$	−38522.2	+	22240.8i	−0.0952350	+	0.0549840i
$637$	−122879.			−0.302829
$638$	16804.9	+	29106.9i	0.0412852	+	0.0715080i
$639$	21209.5	+	12245.3i	0.0519431	+	0.0299894i
$640$	23821.6	−	41260.2i	0.0581581	−	0.100733i
$641$			292847.i			0.712730i	0.934347	+	0.356365i	$0.115984\pi$
$641$			292847.i			0.712730i	−0.934347	+	0.356365i	$0.884016\pi$
$642$	−32982.4	+	57127.1i	−0.0800224	+	0.138603i
$643$	−653871.			−1.58150			−0.790751	−	0.612138i	$-0.790310\pi$
$643$	−653871.			−1.58150			−0.790751	+	0.612138i	$0.790310\pi$
$644$			54402.2i			0.131173i
$645$	76501.3	+	35199.3i	0.183886	+	0.0846086i
$646$	7743.57			0.0185556
$647$			281679.i			0.672894i	0.941702	+	0.336447i	$0.109225\pi$
$647$			281679.i			0.672894i	−0.941702	+	0.336447i	$0.890775\pi$
$648$	360510.	+	208140.i	0.858553	+	0.495686i
$649$	−116601.			−0.276831
$650$	51442.7	+	29700.5i	0.121758	+	0.0702969i
$651$	23860.0	−	41326.8i	0.0563001	−	0.0975146i
$652$	−9044.42	+	5221.80i	−0.0212758	+	0.0122836i
$653$			85425.3i			0.200337i	0.994971	+	0.100168i	$0.0319381\pi$
$653$			85425.3i			0.200337i	−0.994971	+	0.100168i	$0.968062\pi$
$654$	34644.5	+	60006.1i	0.0809989	+	0.140294i
$655$	−390059.	+	675603.i	−0.909177	+	1.57474i
$656$	−84547.7			−0.196469
$657$	−125682.	−	72562.5i	−0.291167	−	0.168105i
$658$	−49430.6	−	85616.4i	−0.114168	−	0.197745i
$659$	30169.2	+	52254.6i	0.0694694	+	0.120324i	0.898668	−	0.438630i	$-0.144536\pi$
$659$	30169.2	+	52254.6i	0.0694694	+	0.120324i	−0.829198	+	0.558954i	$0.811203\pi$
$660$	−6285.95	−	10887.6i	−0.0144305	−	0.0249944i
$661$	632433.			1.44748			0.723738	−	0.690074i	$-0.242422\pi$
$661$	632433.			1.44748			0.723738	+	0.690074i	$0.242422\pi$
$662$	432.764	+	749.570i	0.000987496	+	0.00171039i
$663$	1181.39	−	682.077i	0.00268762	−	0.00155170i
$664$	−267853.	−	154645.i	−0.607519	−	0.350751i
$665$	79730.6	+	46032.5i	0.180294	+	0.104093i
$666$	316771.			0.714161
$667$		−	123756.i		−	0.278172i
$668$	45906.8	−	79513.0i	0.102878	−	0.178191i
$669$	−22806.4	+	39501.8i	−0.0509570	+	0.0882602i
$670$	180304.	+	312296.i	0.401658	+	0.695692i
$671$	−83685.0	+	48315.5i	−0.185867	+	0.107310i
$672$			21871.0i			0.0484318i
$673$	289747.	−	167285.i	0.639718	−	0.369341i	−0.144788	−	0.989463i	$-0.546250\pi$
$673$	289747.	−	167285.i	0.639718	−	0.369341i	0.784506	+	0.620121i	$0.212917\pi$
$674$	−315218.	+	181991.i	−0.693891	+	0.400618i
$675$	−68517.0	+	39558.3i	−0.150380	+	0.0868220i
$676$	89170.3	−	154448.i	0.195131	−	0.337977i
$677$			192583.i			0.420186i	0.977681	+	0.210093i	$0.0673766\pi$
$677$			192583.i			0.420186i	−0.977681	+	0.210093i	$0.932623\pi$
$678$	62704.1	+	36202.2i	0.136407	+	0.0787546i
$679$	141663.	−	81789.0i	0.307267	−	0.177401i
$680$	33586.5			0.0726352
$681$	−10183.2	−	17637.8i	−0.0219579	−	0.0380321i
$682$	181277.	+	104660.i	0.389738	+	0.225015i
$683$	30297.5	−	52476.8i	0.0649479	−	0.112493i	−0.831723	−	0.555191i	$-0.812645\pi$
$683$	30297.5	−	52476.8i	0.0649479	−	0.112493i	0.896671	+	0.442698i	$0.145979\pi$
$684$		−	92726.6i		−	0.198195i
$685$	70654.8	−	122378.i	0.150578	−	0.260808i
$686$	239763.			0.509489
$687$			13648.3i			0.0289177i
$688$	138156.	−	97791.6i	0.291872	−	0.206597i
$689$	251714.			0.530235
$690$		−	57810.6i		−	0.121425i
$691$	−204340.	−	117976.i	−0.427954	−	0.247080i	0.270520	−	0.962714i	$-0.412804\pi$
$691$	−204340.	−	117976.i	−0.427954	−	0.247080i	−0.698475	+	0.715635i	$0.746138\pi$
$692$	−275500.			−0.575320
$693$	−47568.6	−	27463.7i	−0.0990498	−	0.0571864i
$694$	271627.	−	470472.i	0.563968	−	0.976821i
$695$	−141468.	+	81676.7i	−0.292880	+	0.169094i
$696$		−	29401.4i		−	0.0606945i
$697$	7257.33	+	12570.1i	0.0149387	+	0.0258745i
$698$	105413.	−	182581.i	0.216364	−	0.374753i
$699$	124352.			0.254506
$700$	37295.2	+	21532.4i	0.0761127	+	0.0439437i
$701$	26655.3	+	46168.4i	0.0542436	+	0.0939526i	0.891872	−	0.452288i	$-0.149392\pi$
$701$	26655.3	+	46168.4i	0.0542436	+	0.0939526i	−0.837629	+	0.546240i	$0.816059\pi$
$702$	20679.1	+	35817.3i	0.0419621	+	0.0726805i
$703$	−111400.	−	192951.i	−0.225411	−	0.390424i
$704$	−152763.			−0.308228
$705$	−42061.1	−	72852.0i	−0.0846258	−	0.146576i
$706$	564955.	−	326177.i	1.13346	−	0.654401i
$707$	−191768.	−	110717.i	−0.383651	−	0.221501i
$708$	27189.9	+	15698.1i	0.0542427	+	0.0313170i
$709$	−455800.			−0.906739			−0.453369	−	0.891323i	$-0.649778\pi$
$709$	−455800.			−0.906739			−0.453369	+	0.891323i	$0.649778\pi$
$710$			28719.3i			0.0569713i
$711$	−142917.	+	247540.i	−0.282713	+	0.489673i
$712$	458104.	−	793459.i	0.903658	−	1.56518i
$713$	−385373.	−	667486.i	−0.758058	−	1.31299i
$714$	−1069.62	+	617.547i	−0.00209814	+	0.00121136i
$715$			71142.2i			0.139160i
$716$	116801.	−	67435.1i	0.227835	−	0.131541i
$717$	1027.81	−	593.409i	0.00199929	−	0.00115429i
$718$	433832.	−	250473.i	0.841535	−	0.485861i
$719$	117828.	−	204083.i	0.227923	−	0.394775i	−0.729269	−	0.684227i	$-0.760140\pi$
$719$	117828.	−	204083.i	0.227923	−	0.394775i	0.957193	+	0.289452i	$0.0934731\pi$
$720$			223875.i			0.431857i
$721$	−145010.	−	83721.4i	−0.278950	−	0.161052i
$722$	−265882.	+	153507.i	−0.510051	+	0.294478i
$723$	93609.3			0.179078
$724$	−56573.6	−	97988.4i	−0.107929	−	0.186938i
$725$	−84840.3	−	48982.6i	−0.161408	−	0.0931892i
$726$	28746.1	−	49789.8i	0.0545389	−	0.0944641i
$727$		−	47101.9i		−	0.0891189i	−0.999007	−	0.0445594i	$-0.985812\pi$
$727$		−	47101.9i		−	0.0891189i	0.999007	−	0.0445594i	$-0.0141884\pi$
$728$	36569.2	−	63339.6i	0.0690005	−	0.119512i
$729$	448441.			0.843822
$730$		−	170183.i		−	0.319353i
$731$	−26398.0	−	12146.1i	−0.0494011	−	0.0227301i
$732$	26019.0			0.0485589
$733$			602541.i			1.12145i	0.828003	+	0.560723i	$0.189477\pi$
$733$			602541.i			1.12145i	−0.828003	+	0.560723i	$0.810523\pi$
$734$	−457350.	−	264051.i	−0.848900	−	0.490112i
$735$	94666.6			0.175235
$736$	305922.	+	176624.i	0.564748	+	0.326058i
$737$	−75661.1	+	131049.i	−0.139296	+	0.241267i
$738$	−187978.	+	108529.i	−0.345140	+	0.199267i
$739$		−	547633.i		−	1.00277i	−0.865225	−	0.501384i	$-0.832824\pi$
$739$		−	547633.i		−	1.00277i	0.865225	−	0.501384i	$-0.167176\pi$
$740$	−148724.	−	257598.i	−0.271593	−	0.470413i
$741$	7174.23	−	12426.1i	0.0130659	−	0.0226308i
$742$	−227899.			−0.413938
$743$	−410747.	−	237145.i	−0.744042	−	0.429573i	0.0794954	−	0.996835i	$-0.474669\pi$
$743$	−410747.	−	237145.i	−0.744042	−	0.429573i	−0.823537	+	0.567263i	$0.808002\pi$
$744$	−91555.2	−	158578.i	−0.165401	−	0.286482i
$745$	209173.	+	362298.i	0.376871	+	0.652759i
$746$	195372.	+	338394.i	0.351063	+	0.608059i
$747$	−353924.			−0.634262
$748$	2169.07	+	3756.94i	0.00387677	+	0.00671476i
$749$	234368.	−	135312.i	0.417767	−	0.241198i
$750$	33849.1	+	19542.8i	0.0601762	+	0.0347428i
$751$	561176.	+	323995.i	0.994992	+	0.574459i	0.906763	−	0.421642i	$-0.138546\pi$
$751$	561176.	+	323995.i	0.994992	+	0.574459i	0.0882290	+	0.996100i	$0.471879\pi$
$752$	−169086.			−0.299001
$753$			132132.i			0.233033i
$754$	−25605.6	+	44350.3i	−0.0450395	+	0.0780106i
$755$	−487762.	+	844829.i	−0.855686	+	1.48209i
$756$	14992.0	+	25967.0i	0.0262312	+	0.0454337i
$757$	−123212.	+	71136.7i	−0.215012	+	0.124137i	−0.603638	−	0.797258i	$-0.706283\pi$
$757$	−123212.	+	71136.7i	−0.215012	+	0.124137i	0.388627	+	0.921395i	$0.372950\pi$
$758$			341963.i			0.595170i
$759$	21009.0	−	12129.5i	0.0364688	−	0.0210553i
$760$	305941.	−	176635.i	0.529676	−	0.305808i
$761$	466966.	−	269603.i	0.806335	−	0.465538i	−0.0393464	−	0.999226i	$-0.512528\pi$
$761$	466966.	−	269603.i	0.806335	−	0.465538i	0.845682	+	0.533688i	$0.179194\pi$
$762$	4323.02	−	7487.68i	0.00744521	−	0.0128955i
$763$		−	284263.i		−	0.488283i
$764$	−348006.	−	200921.i	−0.596211	−	0.344222i
$765$	33284.4	−	19216.7i	0.0568745	−	0.0328365i
$766$	−662469.			−1.12904
$767$	−88832.9	−	153863.i	−0.151002	−	0.261543i
$768$	85931.0	+	49612.3i	0.145689	+	0.0841137i
$769$	−331783.	+	574665.i	−0.561050	+	0.971767i	0.436355	+	0.899774i	$0.356269\pi$
$769$	−331783.	+	574665.i	−0.561050	+	0.971767i	−0.997405	+	0.0719925i	$0.977064\pi$
$770$		−	64411.5i		−	0.108638i
$771$	−77124.2	+	133583.i	−0.129742	+	0.224720i
$772$	467208.			0.783927
$773$			469528.i			0.785782i	0.919585	+	0.392891i	$0.128525\pi$
$773$			469528.i			0.785782i	−0.919585	+	0.392891i	$0.871475\pi$
$774$	181638.	−	394768.i	0.303197	−	0.658961i
$775$	−610123.			−1.01581
$776$		−	627678.i		−	1.04235i
$777$	30775.5	+	17768.3i	0.0509757	+	0.0294309i
$778$	526993.			0.870653
$779$	132215.	+	76334.1i	0.217873	+	0.125789i
$780$	9577.91	−	16589.4i	0.0157428	−	0.0272673i
$781$	−10436.9	+	6025.73i	−0.0171107	+	0.00987888i
$782$			19948.5i			0.0326210i
$783$	−34104.4	−	59070.5i	−0.0556271	−	0.0963490i
$784$	95140.2	−	164788.i	0.154786	−	0.268097i
$785$	777351.			1.26147
$786$	−95332.0	−	55040.0i	−0.154310	−	0.0890908i
$787$	583199.	+	1.01013e6i	0.941602	+	1.63090i	0.762416	+	0.647087i	$0.224013\pi$
$787$	583199.	+	1.01013e6i	0.941602	+	1.63090i	0.179186	+	0.983815i	$0.442654\pi$
$788$	140740.	+	243769.i	0.226655	+	0.392577i
$789$	−34016.7	−	58918.7i	−0.0546435	−	0.0946453i
$790$	−335188.			−0.537074
$791$	−148522.	−	257248.i	−0.237377	−	0.411148i
$792$	−182529.	+	105383.i	−0.290993	+	0.168005i
$793$	−127511.	−	73618.5i	−0.202769	−	0.117069i
$794$	−230025.	−	132805.i	−0.364866	−	0.210655i
$795$	−193922.			−0.306827
$796$			515709.i			0.813914i
$797$	−138478.	+	239851.i	−0.218004	+	0.377593i	−0.954198	−	0.299177i	$-0.903288\pi$
$797$	−138478.	+	239851.i	−0.218004	+	0.377593i	0.736194	+	0.676771i	$0.236621\pi$
$798$	−6495.48	+	11250.5i	−0.0102001	+	0.0176671i
$799$	14513.9	+	25138.8i	0.0227347	+	0.0393777i
$800$	242168.	−	139816.i	0.378387	−	0.218462i
$801$		−	1.04843e6i		−	1.63408i
$802$	56319.4	−	32516.0i	0.0875608	−	0.0505532i
$803$	61846.2	−	35706.9i	0.0959141	−	0.0553760i
$804$	35286.4	−	20372.6i	0.0545877	−	0.0315162i
$805$	−118586.	+	205397.i	−0.182996	+	0.316959i
$806$			318942.i			0.490954i
$807$	−2194.16	−	1266.80i	−0.00336915	−	0.00194518i
$808$	−735847.	+	424841.i	−1.12711	+	0.650735i
$809$	815882.			1.24661			0.623305	−	0.781979i	$-0.285790\pi$
$809$	815882.			1.24661			0.623305	+	0.781979i	$0.285790\pi$
$810$	279303.	+	483766.i	0.425701	+	0.737337i
$811$	126639.	+	73115.0i	0.192542	+	0.111164i	0.593172	−	0.805076i	$-0.297875\pi$
$811$	126639.	+	73115.0i	0.192542	+	0.111164i	−0.400630	+	0.916240i	$0.631209\pi$
$812$	−18563.7	+	32153.3i	−0.0281548	+	0.0487656i
$813$			163080.i			0.246728i
$814$	−77939.1	+	134994.i	−0.117627	+	0.203736i
$815$	−45530.0			−0.0685460
$816$			2112.43i			0.00317250i
$817$	−304338.	+	28190.6i	−0.455944	+	0.0422339i
$818$	−23565.2			−0.0352180
$819$		−	83693.1i		−	0.124773i
$820$	176512.	+	101909.i	0.262511	+	0.151561i
$821$	−488338.			−0.724493			−0.362247	−	0.932082i	$-0.617990\pi$
$821$	−488338.			−0.724493			−0.362247	+	0.932082i	$0.617990\pi$
$822$	17268.3	+	9969.85i	0.0255568	+	0.0147552i
$823$	−600718.	+	1.04047e6i	−0.886892	+	1.53614i	−0.0433631	+	0.999059i	$0.513807\pi$
$823$	−600718.	+	1.04047e6i	−0.886892	+	1.53614i	−0.843529	+	0.537083i	$0.819526\pi$
$824$	−556428.	+	321254.i	−0.819511	+	0.473145i
$825$		−	19203.5i		−	0.0282145i
$826$	80428.5	+	139306.i	0.117883	+	0.204179i
$827$	−170129.	+	294672.i	−0.248752	+	0.430851i	−0.963180	−	0.268858i	$-0.913354\pi$
$827$	−170129.	+	294672.i	−0.248752	+	0.430851i	0.714428	+	0.699709i	$0.246687\pi$
$828$	238877.			0.348428
$829$	510890.	+	294963.i	0.743393	+	0.429198i	0.823302	−	0.567604i	$-0.192130\pi$
$829$	510890.	+	294963.i	0.743393	+	0.429198i	−0.0799086	+	0.996802i	$0.525463\pi$
$830$	−207517.	−	359430.i	−0.301230	−	0.521745i
$831$	−33017.0	−	57187.0i	−0.0478118	−	0.0828124i
$832$	−116383.	−	201581.i	−0.168128	−	0.291207i
$833$	−32666.2			−0.0470770
$834$	−11525.1	−	19962.1i	−0.0165697	−	0.0286995i
$835$	346645.	−	200136.i	0.497178	−	0.287046i
$836$	39516.2	+	22814.7i	0.0565409	+	0.0326439i
$837$	−367889.	−	212401.i	−0.525128	−	0.303183i
$838$	−472330.			−0.672601
$839$		−	105787.i		−	0.150282i	−0.997173	−	0.0751412i	$-0.976059\pi$
$839$		−	105787.i		−	0.150282i	0.997173	−	0.0751412i	$-0.0239408\pi$
$840$	−28173.2	+	48797.3i	−0.0399279	+	0.0691572i
$841$	−311411.	+	539380.i	−0.440293	+	0.762611i
$842$	442355.	+	766182.i	0.623946	+	1.08071i
$843$	−126709.	+	73155.3i	−0.178300	+	0.102942i
$844$			305448.i			0.428797i
$845$	673330.	−	388747.i	0.943006	−	0.544445i
$846$	−375936.	+	217047.i	−0.525259	+	0.303258i
$847$	−204266.	+	117933.i	−0.284727	+	0.164387i
$848$	−194892.	+	337563.i	−0.271021	+	0.469422i
$849$		−	75860.9i		−	0.105245i
$850$	13675.6	+	7895.62i	0.0189282	+	0.0109282i
$851$	497068.	−	286982.i	0.686368	−	0.396275i
$852$	3244.99			0.00447028
$853$	18617.7	+	32246.7i	0.0255874	+	0.0443188i	0.878536	−	0.477677i	$-0.158521\pi$
$853$	18617.7	+	32246.7i	0.0255874	+	0.0443188i	−0.852948	+	0.521996i	$0.825188\pi$
$854$	115447.	+	66653.5i	0.158295	+	0.0913919i
$855$	202126.	−	350092.i	0.276496	−	0.478906i
$856$		−	1.03844e6i		−	1.41720i
$857$	718183.	−	1.24393e6i	0.977853	−	1.69369i	0.307673	−	0.951492i	$-0.400450\pi$
$857$	718183.	−	1.24393e6i	0.977853	−	1.69369i	0.670180	−	0.742199i	$-0.266217\pi$
$858$	−10038.6			−0.0136364
$859$			688513.i			0.933095i	0.884496	+	0.466548i	$0.154502\pi$
$859$			688513.i			0.933095i	−0.884496	+	0.466548i	$0.845498\pi$
$860$	−406304.	+	37635.8i	−0.549357	+	0.0508866i
$861$	−24350.5			−0.0328474
$862$		−	892126.i		−	1.20064i
$863$	860230.	+	496654.i	1.15503	+	0.666856i	0.950108	−	0.311922i	$-0.100973\pi$
$863$	860230.	+	496654.i	1.15503	+	0.666856i	0.204921	+	0.978778i	$0.434306\pi$
$864$	194695.			0.260812
$865$	−1.04016e6	−	600536.i	−1.39017	−	0.802614i
$866$	−360158.	+	623813.i	−0.480239	+	0.831799i
$867$	−105892.	+	61136.6i	−0.140872	+	0.0813323i
$868$			231228.i			0.306903i
$869$	−70327.5	−	121811.i	−0.0931292	−	0.161304i
$870$	19726.8	−	34167.8i	0.0260626	−	0.0451418i
$871$	−230570.			−0.303925
$872$	−944634.	−	545385.i	−1.24231	−	0.717249i
$873$	−359130.	−	622032.i	−0.471220	−	0.816177i
$874$	104911.	+	181712.i	0.137341	+	0.237881i
$875$	−80175.7	−	138868.i	−0.104719	−	0.181379i
$876$	−19229.0			−0.0250581
$877$	−712174.	−	1.23352e6i	−0.925949	−	1.60379i	−0.790028	−	0.613071i	$-0.789934\pi$
$877$	−712174.	−	1.23352e6i	−0.925949	−	1.60379i	−0.135921	−	0.990720i	$-0.543399\pi$
$878$	716595.	−	413727.i	0.929576	−	0.536691i
$879$	87715.2	+	50642.4i	0.113527	+	0.0655446i
$880$	−95406.0	−	55082.7i	−0.123200	−	0.0711295i
$881$	813391.			1.04797			0.523984	−	0.851728i	$-0.324445\pi$
$881$	813391.			1.04797			0.523984	+	0.851728i	$0.324445\pi$
$882$		−	488506.i		−	0.627961i
$883$	−397588.	+	688643.i	−0.509932	+	0.883228i	0.490002	+	0.871721i	$0.336996\pi$
$883$	−397588.	+	688643.i	−0.509932	+	0.883228i	−0.999934	+	0.0115067i	$0.996337\pi$
$884$	−3305.01	+	5724.45i	−0.00422930	+	0.00732537i
$885$	68437.6	+	118537.i	0.0873792	+	0.151345i
$886$	178384.	−	102990.i	0.227242	−	0.131198i
$887$		−	292045.i		−	0.371195i	−0.982626	−	0.185597i	$-0.940578\pi$
$887$		−	292045.i		−	0.371195i	0.982626	−	0.185597i	$-0.0594220\pi$
$888$	118091.	−	68180.1i	0.149759	−	0.0864632i
$889$	−30718.7	+	17735.5i	−0.0388687	+	0.0224408i
$890$	1.06474e6	−	614728.i	1.34420	−	0.776073i
$891$	−117204.	+	203003.i	−0.147634	+	0.255710i
$892$		−	221017.i		−	0.277777i
$893$	264415.	+	152660.i	0.331576	+	0.191435i
$894$	−51122.6	+	29515.7i	−0.0639643	+	0.0369298i
$895$	587981.			0.734036
$896$	−13790.3	−	23885.5i	−0.0171774	−	0.0297521i
$897$	32011.4	+	18481.8i	0.0397851	+	0.0229699i
$898$	−18347.8	+	31779.4i	−0.0227526	+	0.0394087i
$899$		−	526005.i		−	0.650834i
$900$	94547.4	−	163761.i	0.116725	−	0.202174i
$901$	66916.0			0.0824290
$902$		−	106811.i		−	0.131282i
$903$	39790.1	−	28164.8i	0.0487978	−	0.0345407i
$904$	−1.13981e6			−1.39475
$905$		−	493277.i		−	0.602274i
$906$	−119211.	−	68826.5i	−0.145231	−	0.0838492i
$907$	1.04609e6			1.27161			0.635804	−	0.771851i	$-0.280669\pi$
$907$	1.04609e6			1.27161			0.635804	+	0.771851i	$0.280669\pi$
$908$	85464.3	+	49342.8i	0.103660	+	0.0598484i
$909$	−486152.	+	842039.i	−0.588361	+	1.01907i
$910$	84995.2	−	49072.0i	0.102639	−	0.0592585i
$911$		−	944697.i		−	1.13830i	−0.822235	−	0.569149i	$-0.807273\pi$
$911$		−	944697.i		−	1.13830i	0.822235	−	0.569149i	$-0.192727\pi$
$912$	11109.5	+	19242.2i	0.0133568	+	0.0231347i
$913$	87080.4	−	150828.i	0.104467	−	0.180942i
$914$	774875.			0.927554
$915$	98235.5	+	56716.3i	0.117335	+	0.0677432i
$916$	−33066.4	−	57272.7i	−0.0394091	−	0.0682585i
$917$	225805.	+	391106.i	0.268531	+	0.465110i
$918$	5497.37	+	9521.72i	0.00652333	+	0.0112987i
$919$	407718.			0.482758			0.241379	−	0.970431i	$-0.422400\pi$
$919$	407718.			0.482758			0.241379	+	0.970431i	$0.422400\pi$
$920$	455036.	+	788146.i	0.537614	+	0.931174i
$921$	−138568.	+	80002.2i	−0.163359	+	0.0943154i
$922$	782419.	+	451730.i	0.920402	+	0.531394i
$923$	−15902.7	−	9181.42i	−0.0186667	−	0.0107772i
$924$	−7277.86			−0.00852432
$925$		−	454351.i		−	0.531016i
$926$	−229725.	+	397896.i	−0.267909	+	0.464032i
$927$	−367615.	+	636728.i	−0.427793	+	0.740960i
$928$	120539.	+	208780.i	0.139969	+	0.242434i
$929$	910030.	−	525406.i	1.05445	−	0.608785i	0.130555	−	0.991441i	$-0.458324\pi$
$929$	910030.	−	525406.i	1.05445	−	0.608785i	0.923891	+	0.382656i	$0.124991\pi$
$930$		−	245715.i		−	0.284097i
$931$	−297558.	+	171795.i	−0.343299	+	0.198204i
$932$	−521823.	+	301275.i	−0.600747	+	0.346841i
$933$	−57786.4	+	33363.0i	−0.0663838	+	0.0383267i
$934$	−448401.	+	776653.i	−0.514011	+	0.890294i
$935$			18912.6i			0.0216335i
$936$	−278120.	−	160573.i	−0.317454	−	0.183282i
$937$	826712.	−	477303.i	0.941619	−	0.543644i	0.0511517	−	0.998691i	$-0.483711\pi$
$937$	826712.	−	477303.i	0.941619	−	0.543644i	0.890468	+	0.455047i	$0.150377\pi$
$938$	208756.			0.237265
$939$	−66611.8	−	115375.i	−0.0755475	−	0.130852i
$940$	353005.	+	203808.i	0.399508	+	0.230656i
$941$	−281611.	+	487764.i	−0.318031	+	0.550846i	−0.980077	−	0.198617i	$-0.936355\pi$
$941$	−281611.	+	487764.i	−0.318031	+	0.550846i	0.662046	+	0.749463i	$0.269688\pi$
$942$			109689.i			0.123613i
$943$	−196647.	+	340603.i	−0.221139	+	0.383023i
$944$	275120.			0.308729
$945$			130719.i			0.146378i
$946$	123543.	+	174536.i	0.138050	+	0.195031i
$947$	−25524.6			−0.0284616			−0.0142308	−	0.999899i	$-0.504530\pi$
$947$	−25524.6			−0.0284616			−0.0142308	+	0.999899i	$0.504530\pi$
$948$			37872.9i			0.0421417i
$949$	94235.3	+	54406.8i	0.104636	+	0.0604116i
$950$	166096.			0.184039
$951$	106831.	+	61679.1i	0.118124	+	0.0681988i
$952$	9721.61	−	16838.3i	0.0107266	−	0.0185791i
$953$	−102853.	+	59382.5i	−0.113249	+	0.0653841i	−0.555554	−	0.831480i	$-0.687494\pi$
$953$	−102853.	+	59382.5i	−0.113249	+	0.0653841i	0.442306	+	0.896864i	$0.354161\pi$
$954$			1.00069e6i			1.09952i
$955$	−875937.	−	1.51717e6i	−0.960431	−	1.66352i
$956$	−2875.37	+	4980.29i	−0.00314614	+	0.00544927i
$957$	16555.9			0.0180771
$958$	−457182.	−	263954.i	−0.498148	−	0.287606i
$959$	−40902.0	−	70844.3i	−0.0444741	−	0.0770314i
$960$	89662.0	+	155299.i	0.0972895	+	0.168510i
$961$	−1.17621e6	−	2.03725e6i	−1.27361	−	2.20596i
$962$	−237512.			−0.256646
$963$	−594148.	−	1.02909e6i	−0.640681	−	1.10969i
$964$	−392816.	+	226793.i	−0.422703	+	0.244048i
$965$	1.76396e6	+	1.01842e6i	1.89423	+	1.09364i
$966$	−28982.9	−	16733.3i	−0.0310590	−	0.0179319i
$967$	178906.			0.191325			0.0956625	−	0.995414i	$-0.469503\pi$
$967$	178906.			0.191325			0.0956625	+	0.995414i	$0.469503\pi$
$968$			905060.i			0.965888i
$969$	1907.21	−	3303.38i	0.00203119	−	0.00351813i
$970$	421139.	−	729435.i	0.447592	−	0.775252i
$971$	−215488.	−	373236.i	−0.228552	−	0.395863i	0.728827	−	0.684697i	$-0.240066\pi$
$971$	−215488.	−	373236.i	−0.228552	−	0.395863i	−0.957379	+	0.288834i	$0.906732\pi$
$972$	171798.	−	99187.7i	0.181838	−	0.104984i
$973$			94565.2i			0.0998862i
$974$	−737645.	+	425879.i	−0.777552	+	0.448920i
$975$	25340.3	−	14630.2i	0.0266564	−	0.0153901i
$976$	197454.	−	114000.i	0.207284	−	0.119676i
$977$	408393.	−	707357.i	0.427847	−	0.741053i	−0.568834	−	0.822452i	$-0.692605\pi$
$977$	408393.	−	707357.i	0.427847	−	0.741053i	0.996682	+	0.0813989i	$0.0259388\pi$
$978$		−	6424.58i		−	0.00671687i
$979$	446797.	+	257958.i	0.466170	+	0.269144i
$980$	−397253.	+	229354.i	−0.413633	+	0.238811i
$981$	−1.24818e6			−1.29700
$982$	326868.	+	566152.i	0.338961	+	0.587098i
$983$	191869.	+	110776.i	0.198563	+	0.114640i	0.595985	−	0.802996i	$-0.296762\pi$
$983$	191869.	+	110776.i	0.198563	+	0.114640i	−0.397422	+	0.917636i	$0.630095\pi$
$984$	−46718.6	+	80919.0i	−0.0482503	+	0.0835719i
$985$			1.22714e6i			1.26480i
$986$	−6807.05	+	11790.2i	−0.00700173	+	0.0121273i
$987$	−48698.3			−0.0499896
$988$			69525.7i			0.0712248i
$989$	−72623.0	−	784017.i	−0.0742475	−	0.801554i
$990$	−282827.			−0.288569
$991$		−	1.48594e6i		−	1.51305i	−0.653963	−	0.756527i	$-0.726895\pi$
$991$		−	1.48594e6i		−	1.51305i	0.653963	−	0.756527i	$-0.273105\pi$
$992$	1.30027e6	+	750713.i	1.32133	+	0.762870i
$993$	426.353			0.000432385
$994$	14398.2	+	8312.78i	0.0145725	+	0.00841344i
$995$	−1.12414e6	+	1.94707e6i	−1.13547	+	1.96669i
$996$	−40612.0	+	23447.4i	−0.0409389	+	0.0236361i
$997$			437090.i			0.439724i	0.975531	+	0.219862i	$0.0705607\pi$
$997$			437090.i			0.439724i	−0.975531	+	0.219862i	$0.929439\pi$
$998$	−222411.	−	385227.i	−0.223303	−	0.386773i
$999$	158172.	−	273962.i	0.158489	−	0.274511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.5.d.a.37.5	yes	28
43.7	odd	6	inner	43.5.d.a.7.10	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.5.d.a.7.10	✓	28	43.7	odd	6	inner
43.5.d.a.37.5	yes	28	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.98081i q^{2} +(-1.27161 - 0.734162i) q^{3} +7.11478 q^{4} +(26.8620 + 15.5088i) q^{5} +(-2.18840 + 3.79041i) q^{6} +(15.5504 - 8.97804i) q^{7} -68.9007i q^{8} +(-39.4220 - 68.2809i) q^{9} +O(q^{10})\)	\(q-2.98081i q^{2} +(-1.27161 - 0.734162i) q^{3} +7.11478 q^{4} +(26.8620 + 15.5088i) q^{5} +(-2.18840 + 3.79041i) q^{6} +(15.5504 - 8.97804i) q^{7} -68.9007i q^{8} +(-39.4220 - 68.2809i) q^{9} +(46.2288 - 80.0706i) q^{10} +38.7980 q^{11} +(-9.04719 - 5.22340i) q^{12} +(29.5583 + 51.1965i) q^{13} +(-26.7618 - 46.3528i) q^{14} +(-22.7719 - 39.4422i) q^{15} -91.5435 q^{16} +(7.85783 + 13.6102i) q^{17} +(-203.532 + 117.509i) q^{18} +(143.154 + 82.6503i) q^{19} +(191.118 + 110.342i) q^{20} -26.3653 q^{21} -115.649i q^{22} +(-212.919 + 368.786i) q^{23} +(-50.5843 + 87.6145i) q^{24} +(168.546 + 291.931i) q^{25} +(152.607 - 88.1076i) q^{26} +234.703i q^{27} +(110.638 - 63.8768i) q^{28} +(-251.682 + 145.309i) q^{29} +(-117.570 + 67.8788i) q^{30} +(-904.977 + 1567.47i) q^{31} -829.538i q^{32} +(-49.3357 - 28.4840i) q^{33} +(40.5693 - 23.4227i) q^{34} +556.955 q^{35} +(-280.479 - 485.804i) q^{36} +(-1167.27 - 673.925i) q^{37} +(246.365 - 426.716i) q^{38} -86.8023i q^{39} +(1068.57 - 1850.81i) q^{40} +923.580 q^{41} +78.5900i q^{42} +(-1509.18 + 1068.25i) q^{43} +276.039 q^{44} -2445.55i q^{45} +(1099.28 + 634.670i) q^{46} +1847.06 q^{47} +(116.407 + 67.2077i) q^{48} +(-1039.29 + 1800.10i) q^{49} +(870.190 - 502.405i) q^{50} -23.0757i q^{51} +(210.301 + 364.252i) q^{52} +(2128.96 - 3687.46i) q^{53} +699.604 q^{54} +(1042.19 + 601.711i) q^{55} +(-618.594 - 1071.44i) q^{56} +(-121.357 - 210.197i) q^{57} +(433.138 + 750.217i) q^{58} -3005.34 q^{59} +(-162.017 - 280.622i) q^{60} +(-2156.94 + 1245.31i) q^{61} +(4672.32 + 2697.56i) q^{62} +(-1226.06 - 707.865i) q^{63} -3937.39 q^{64} +1833.66i q^{65} +(-84.9053 + 147.060i) q^{66} +(-1950.13 + 3377.72i) q^{67} +(55.9067 + 96.8333i) q^{68} +(541.497 - 312.633i) q^{69} -1660.18i q^{70} +(-269.006 + 155.310i) q^{71} +(-4704.61 + 2716.21i) q^{72} +(1594.06 - 920.330i) q^{73} +(-2008.84 + 3479.42i) q^{74} -494.961i q^{75} +(1018.51 + 588.038i) q^{76} +(603.325 - 348.330i) q^{77} -258.741 q^{78} +(-1812.66 - 3139.62i) q^{79} +(-2459.05 - 1419.73i) q^{80} +(-3020.87 + 5232.31i) q^{81} -2753.01i q^{82} +(2244.46 - 3887.51i) q^{83} -187.583 q^{84} +487.462i q^{85} +(3184.26 + 4498.59i) q^{86} +426.721 q^{87} -2673.21i q^{88} +(11516.0 + 6648.75i) q^{89} -7289.73 q^{90} +(919.288 + 530.751i) q^{91} +(-1514.87 + 2623.83i) q^{92} +(2301.55 - 1328.80i) q^{93} -5505.73i q^{94} +(2563.61 + 4440.31i) q^{95} +(-609.015 + 1054.85i) q^{96} +9109.89 q^{97} +(5365.76 + 3097.92i) q^{98} +(-1529.49 - 2649.16i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{3} - 234 q^{4} - 3 q^{5} + 15 q^{6} + 129 q^{7} + 534 q^{9}+O(q^{10}) \) 28 * q + 6 * q^3 - 234 * q^4 - 3 * q^5 + 15 * q^6 + 129 * q^7 + 534 * q^9	\( 28 q + 6 q^{3} - 234 q^{4} - 3 q^{5} + 15 q^{6} + 129 q^{7} + 534 q^{9} + 91 q^{10} - 376 q^{11} - 1026 q^{12} - 198 q^{13} + 78 q^{14} - 289 q^{15} + 806 q^{16} + 23 q^{17} - 435 q^{18} - 438 q^{19} + 177 q^{20} + 1684 q^{21} - 214 q^{23} + 1450 q^{24} + 463 q^{25} + 45 q^{26} - 3828 q^{28} + 1725 q^{29} + 8127 q^{30} + 2135 q^{31} - 474 q^{33} + 201 q^{34} - 6882 q^{35} - 12052 q^{36} + 1638 q^{37} - 2124 q^{38} - 6721 q^{40} + 3014 q^{41} + 157 q^{43} + 17162 q^{44} - 6240 q^{46} - 3670 q^{47} + 11547 q^{48} + 3085 q^{49} + 9738 q^{50} + 13746 q^{52} + 1208 q^{53} - 32416 q^{54} - 11202 q^{55} - 16245 q^{56} + 6207 q^{57} - 5756 q^{58} - 8716 q^{59} - 281 q^{60} + 8382 q^{61} - 25191 q^{62} + 23625 q^{63} + 17564 q^{64} - 21909 q^{66} - 9295 q^{67} + 6758 q^{68} + 30663 q^{69} + 24828 q^{71} + 46194 q^{72} + 5307 q^{73} + 13866 q^{74} + 5178 q^{76} - 27645 q^{77} - 10592 q^{78} - 24914 q^{79} - 13683 q^{80} - 43222 q^{81} + 7010 q^{83} - 21568 q^{84} + 15366 q^{86} + 57084 q^{87} - 80787 q^{89} + 114772 q^{90} - 24438 q^{91} + 22049 q^{92} - 39723 q^{93} + 29955 q^{95} + 1378 q^{96} - 12210 q^{97} + 28845 q^{98} - 49211 q^{99}+O(q^{100}) \) 28 * q + 6 * q^3 - 234 * q^4 - 3 * q^5 + 15 * q^6 + 129 * q^7 + 534 * q^9 + 91 * q^10 - 376 * q^11 - 1026 * q^12 - 198 * q^13 + 78 * q^14 - 289 * q^15 + 806 * q^16 + 23 * q^17 - 435 * q^18 - 438 * q^19 + 177 * q^20 + 1684 * q^21 - 214 * q^23 + 1450 * q^24 + 463 * q^25 + 45 * q^26 - 3828 * q^28 + 1725 * q^29 + 8127 * q^30 + 2135 * q^31 - 474 * q^33 + 201 * q^34 - 6882 * q^35 - 12052 * q^36 + 1638 * q^37 - 2124 * q^38 - 6721 * q^40 + 3014 * q^41 + 157 * q^43 + 17162 * q^44 - 6240 * q^46 - 3670 * q^47 + 11547 * q^48 + 3085 * q^49 + 9738 * q^50 + 13746 * q^52 + 1208 * q^53 - 32416 * q^54 - 11202 * q^55 - 16245 * q^56 + 6207 * q^57 - 5756 * q^58 - 8716 * q^59 - 281 * q^60 + 8382 * q^61 - 25191 * q^62 + 23625 * q^63 + 17564 * q^64 - 21909 * q^66 - 9295 * q^67 + 6758 * q^68 + 30663 * q^69 + 24828 * q^71 + 46194 * q^72 + 5307 * q^73 + 13866 * q^74 + 5178 * q^76 - 27645 * q^77 - 10592 * q^78 - 24914 * q^79 - 13683 * q^80 - 43222 * q^81 + 7010 * q^83 - 21568 * q^84 + 15366 * q^86 + 57084 * q^87 - 80787 * q^89 + 114772 * q^90 - 24438 * q^91 + 22049 * q^92 - 39723 * q^93 + 29955 * q^95 + 1378 * q^96 - 12210 * q^97 + 28845 * q^98 - 49211 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more