LMFDB - Embedded newform 43.6.c.a.36.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,6,Mod(6,43)]

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([4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("43.6");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	43.c (of order $3$, 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:	$6.89650425196$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			36.12
Character	$\chi$	$=$	43.36
Dual form			43.6.c.a.6.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.36550 q^{2} +(0.424863 + 0.735884i) q^{3} -12.9424 q^{4} +(-30.5339 - 52.8863i) q^{5} +(1.85474 + 3.21250i) q^{6} +(93.7016 - 162.296i) q^{7} -196.196 q^{8} +(121.139 - 209.819i) q^{9} +O(q^{10})$	\(q+4.36550 q^{2} +(0.424863 + 0.735884i) q^{3} -12.9424 q^{4} +(-30.5339 - 52.8863i) q^{5} +(1.85474 + 3.21250i) q^{6} +(93.7016 - 162.296i) q^{7} -196.196 q^{8} +(121.139 - 209.819i) q^{9} +(-133.296 - 230.875i) q^{10} +227.558 q^{11} +(-5.49874 - 9.52410i) q^{12} +(-266.361 + 461.350i) q^{13} +(409.055 - 708.503i) q^{14} +(25.9454 - 44.9388i) q^{15} -442.338 q^{16} +(-497.997 + 862.557i) q^{17} +(528.832 - 915.965i) q^{18} +(-1040.23 - 1801.72i) q^{19} +(395.182 + 684.475i) q^{20} +159.241 q^{21} +993.406 q^{22} +(574.238 + 994.609i) q^{23} +(-83.3564 - 144.378i) q^{24} +(-302.137 + 523.317i) q^{25} +(-1162.80 + 2014.02i) q^{26} +412.353 q^{27} +(-1212.72 + 2100.50i) q^{28} +(2126.57 - 3683.33i) q^{29} +(113.265 - 196.180i) q^{30} +(369.739 + 640.406i) q^{31} +4347.25 q^{32} +(96.6811 + 167.457i) q^{33} +(-2174.01 + 3765.49i) q^{34} -11444.3 q^{35} +(-1567.83 + 2715.56i) q^{36} +(8284.34 + 14348.9i) q^{37} +(-4541.11 - 7865.43i) q^{38} -452.667 q^{39} +(5990.63 + 10376.1i) q^{40} +8487.64 q^{41} +695.169 q^{42} +(9259.50 - 7827.52i) q^{43} -2945.15 q^{44} -14795.4 q^{45} +(2506.84 + 4341.97i) q^{46} +8271.90 q^{47} +(-187.933 - 325.509i) q^{48} +(-9156.50 - 15859.5i) q^{49} +(-1318.98 + 2284.54i) q^{50} -846.323 q^{51} +(3447.34 - 5970.97i) q^{52} +(-14039.9 - 24317.9i) q^{53} +1800.13 q^{54} +(-6948.24 - 12034.7i) q^{55} +(-18383.9 + 31841.8i) q^{56} +(883.906 - 1530.97i) q^{57} +(9283.54 - 16079.6i) q^{58} +8728.07 q^{59} +(-335.796 + 581.616i) q^{60} +(20730.1 - 35905.5i) q^{61} +(1614.09 + 2795.69i) q^{62} +(-22701.8 - 39320.7i) q^{63} +33132.7 q^{64} +32532.1 q^{65} +(422.061 + 731.032i) q^{66} +(-21098.2 - 36543.1i) q^{67} +(6445.28 - 11163.6i) q^{68} +(-487.945 + 845.145i) q^{69} -49960.1 q^{70} +(-7145.46 + 12376.3i) q^{71} +(-23767.0 + 41165.6i) q^{72} +(-39706.8 + 68774.1i) q^{73} +(36165.3 + 62640.2i) q^{74} -513.467 q^{75} +(13463.0 + 23318.6i) q^{76} +(21322.6 - 36931.8i) q^{77} -1976.12 q^{78} +(-25368.9 + 43940.3i) q^{79} +(13506.3 + 23393.6i) q^{80} +(-29261.6 - 50682.5i) q^{81} +37052.8 q^{82} +(36303.0 + 62878.6i) q^{83} -2060.97 q^{84} +60823.2 q^{85} +(40422.4 - 34171.0i) q^{86} +3614.00 q^{87} -44646.1 q^{88} +(22812.5 + 39512.3i) q^{89} -64589.2 q^{90} +(49916.8 + 86458.5i) q^{91} +(-7432.01 - 12872.6i) q^{92} +(-314.176 + 544.169i) q^{93} +36111.0 q^{94} +(-63524.3 + 110027. i) q^{95} +(1846.98 + 3199.07i) q^{96} -104823. q^{97} +(-39972.7 - 69234.7i) q^{98} +(27566.2 - 47746.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9}+O(q^{10}) $ 34 * q - 14 * q^2 - 14 * q^3 + 454 * q^4 + 71 * q^5 + 15 * q^6 + 225 * q^7 - 936 * q^8 - 1011 * q^9	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9} - 317 q^{10} + 1326 q^{11} - 648 q^{12} + 1006 q^{13} - 1272 q^{14} + 683 q^{15} + 3574 q^{16} + 200 q^{17} + 1861 q^{18} + 3361 q^{19} + 3825 q^{20} - 1320 q^{21} - 8768 q^{22} + 560 q^{23} - 7382 q^{24} - 3232 q^{25} - 3201 q^{26} - 122 q^{27} + 13934 q^{28} + 8887 q^{29} - 19449 q^{30} - 6749 q^{31} - 19086 q^{32} + 7106 q^{33} + 8423 q^{34} + 31118 q^{35} - 14112 q^{36} - 4514 q^{37} + 7072 q^{38} - 5404 q^{39} - 18519 q^{40} - 28996 q^{41} + 58118 q^{42} - 14998 q^{43} + 71050 q^{44} - 92096 q^{45} + 20052 q^{46} - 10742 q^{47} + 32927 q^{48} + 7472 q^{49} + 20362 q^{50} + 20250 q^{51} + 59532 q^{52} - 50572 q^{53} - 230084 q^{54} + 38544 q^{55} - 40355 q^{56} - 18087 q^{57} - 33436 q^{58} + 112654 q^{59} + 134093 q^{60} - 20120 q^{61} - 31491 q^{62} + 188227 q^{63} + 125164 q^{64} - 36578 q^{65} + 8803 q^{66} - 73824 q^{67} - 128456 q^{68} + 8005 q^{69} - 141610 q^{70} + 142842 q^{71} + 98466 q^{72} - 91624 q^{73} - 99720 q^{74} + 298358 q^{75} + 258288 q^{76} + 68051 q^{77} - 201116 q^{78} + 99734 q^{79} - 31261 q^{80} - 28441 q^{81} - 147772 q^{82} - 47340 q^{83} - 624232 q^{84} - 71734 q^{85} - 115526 q^{86} - 215924 q^{87} - 720684 q^{88} + 60402 q^{89} + 676108 q^{90} + 164172 q^{91} + 78997 q^{92} - 40793 q^{93} - 341874 q^{94} + 123541 q^{95} - 442140 q^{96} + 318476 q^{97} + 217473 q^{98} - 134770 q^{99}+O(q^{100}) \) 34 * q - 14 * q^2 - 14 * q^3 + 454 * q^4 + 71 * q^5 + 15 * q^6 + 225 * q^7 - 936 * q^8 - 1011 * q^9 - 317 * q^10 + 1326 * q^11 - 648 * q^12 + 1006 * q^13 - 1272 * q^14 + 683 * q^15 + 3574 * q^16 + 200 * q^17 + 1861 * q^18 + 3361 * q^19 + 3825 * q^20 - 1320 * q^21 - 8768 * q^22 + 560 * q^23 - 7382 * q^24 - 3232 * q^25 - 3201 * q^26 - 122 * q^27 + 13934 * q^28 + 8887 * q^29 - 19449 * q^30 - 6749 * q^31 - 19086 * q^32 + 7106 * q^33 + 8423 * q^34 + 31118 * q^35 - 14112 * q^36 - 4514 * q^37 + 7072 * q^38 - 5404 * q^39 - 18519 * q^40 - 28996 * q^41 + 58118 * q^42 - 14998 * q^43 + 71050 * q^44 - 92096 * q^45 + 20052 * q^46 - 10742 * q^47 + 32927 * q^48 + 7472 * q^49 + 20362 * q^50 + 20250 * q^51 + 59532 * q^52 - 50572 * q^53 - 230084 * q^54 + 38544 * q^55 - 40355 * q^56 - 18087 * q^57 - 33436 * q^58 + 112654 * q^59 + 134093 * q^60 - 20120 * q^61 - 31491 * q^62 + 188227 * q^63 + 125164 * q^64 - 36578 * q^65 + 8803 * q^66 - 73824 * q^67 - 128456 * q^68 + 8005 * q^69 - 141610 * q^70 + 142842 * q^71 + 98466 * q^72 - 91624 * q^73 - 99720 * q^74 + 298358 * q^75 + 258288 * q^76 + 68051 * q^77 - 201116 * q^78 + 99734 * q^79 - 31261 * q^80 - 28441 * q^81 - 147772 * q^82 - 47340 * q^83 - 624232 * q^84 - 71734 * q^85 - 115526 * q^86 - 215924 * q^87 - 720684 * q^88 + 60402 * q^89 + 676108 * q^90 + 164172 * q^91 + 78997 * q^92 - 40793 * q^93 - 341874 * q^94 + 123541 * q^95 - 442140 * q^96 + 318476 * q^97 + 217473 * q^98 - 134770 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	4.36550			0.771719			0.385859	−	0.922558i	$-0.373905\pi$
$2$	4.36550			0.771719			0.385859	+	0.922558i	$0.373905\pi$
$3$	0.424863	+	0.735884i	0.0272550	+	0.0472070i	0.879331	−	0.476211i	$-0.157990\pi$
$3$	0.424863	+	0.735884i	0.0272550	+	0.0472070i	−0.852076	+	0.523418i	$0.824657\pi$
$4$	−12.9424			−0.404450
$5$	−30.5339	−	52.8863i	−0.546207	−	0.946058i	−0.998530	−	0.0542039i	$-0.982738\pi$
$5$	−30.5339	−	52.8863i	−0.546207	−	0.946058i	0.452323	−	0.891854i	$-0.350595\pi$
$6$	1.85474	+	3.21250i	0.0210332	+	0.0364305i
$7$	93.7016	−	162.296i	0.722773	−	1.25188i	−0.237111	−	0.971483i	$-0.576200\pi$
$7$	93.7016	−	162.296i	0.722773	−	1.25188i	0.959884	−	0.280397i	$-0.0904663\pi$
$8$	−196.196			−1.08384
$9$	121.139	−	209.819i	0.498514	−	0.863452i
$10$	−133.296	−	230.875i	−0.421518	−	0.730091i
$11$	227.558			0.567037			0.283518	−	0.958967i	$-0.408498\pi$
$11$	227.558			0.567037			0.283518	+	0.958967i	$0.408498\pi$
$12$	−5.49874	−	9.52410i	−0.0110233	−	0.0190929i
$13$	−266.361	+	461.350i	−0.437131	+	0.757133i	−0.997467	−	0.0711325i	$-0.977339\pi$
$13$	−266.361	+	461.350i	−0.437131	+	0.757133i	0.560336	+	0.828265i	$0.310672\pi$
$14$	409.055	−	708.503i	0.557778	−	0.966100i
$15$	25.9454	−	44.9388i	0.0297737	−	0.0515696i
$16$	−442.338			−0.431970
$17$	−497.997	+	862.557i	−0.417931	+	0.723878i	−0.995731	−	0.0923003i	$-0.970578\pi$
$17$	−497.997	+	862.557i	−0.417931	+	0.723878i	0.577800	+	0.816178i	$0.303911\pi$
$18$	528.832	−	915.965i	0.384713	−	0.666342i
$19$	−1040.23	−	1801.72i	−0.661064	−	1.14500i	−0.980336	−	0.197333i	$-0.936772\pi$
$19$	−1040.23	−	1801.72i	−0.661064	−	1.14500i	0.319273	−	0.947663i	$-0.396561\pi$
$20$	395.182	+	684.475i	0.220913	+	0.382633i
$21$	159.241			0.0787966
$22$	993.406			0.437593
$23$	574.238	+	994.609i	0.226346	+	0.392042i	0.956722	−	0.291002i	$-0.0939888\pi$
$23$	574.238	+	994.609i	0.226346	+	0.392042i	−0.730377	+	0.683045i	$0.760655\pi$
$24$	−83.3564	−	144.378i	−0.0295400	−	0.0511648i
$25$	−302.137	+	523.317i	−0.0966839	+	0.167461i
$26$	−1162.80	+	2014.02i	−0.337342	+	0.584294i
$27$	412.353			0.108858
$28$	−1212.72	+	2100.50i	−0.292326	+	0.506323i
$29$	2126.57	−	3683.33i	0.469553	−	0.813290i	−0.529841	−	0.848097i	$-0.677748\pi$
$29$	2126.57	−	3683.33i	0.469553	−	0.813290i	0.999394	+	0.0348074i	$0.0110818\pi$
$30$	113.265	−	196.180i	0.0229769	−	0.0397972i
$31$	369.739	+	640.406i	0.0691020	+	0.119688i	0.898506	−	0.438961i	$-0.144653\pi$
$31$	369.739	+	640.406i	0.0691020	+	0.119688i	−0.829404	+	0.558649i	$0.811320\pi$
$32$	4347.25			0.750481
$33$	96.6811	+	167.457i	0.0154546	+	0.0267681i
$34$	−2174.01	+	3765.49i	−0.322525	+	0.558630i
$35$	−11444.3			−1.57914
$36$	−1567.83	+	2715.56i	−0.201624	+	0.349223i
$37$	8284.34	+	14348.9i	0.994841	+	1.72312i	0.585272	+	0.810837i	$0.300988\pi$
$37$	8284.34	+	14348.9i	0.994841	+	1.72312i	0.409569	+	0.912279i	$0.365679\pi$
$38$	−4541.11	−	7865.43i	−0.510156	−	0.883615i
$39$	−452.667			−0.0476559
$40$	5990.63	+	10376.1i	0.592001	+	1.02538i
$41$	8487.64			0.788546			0.394273	−	0.918993i	$-0.370996\pi$
$41$	8487.64			0.788546			0.394273	+	0.918993i	$0.370996\pi$
$42$	695.169			0.0608089
$43$	9259.50	−	7827.52i	0.763689	−	0.645584i
$43$	9259.50	−	7827.52i	0.763689	−	0.645584i
$44$	−2945.15			−0.229338
$45$	−14795.4			−1.08917
$46$	2506.84	+	4341.97i	0.174675	+	0.302546i
$47$	8271.90			0.546211			0.273106	−	0.961984i	$-0.411949\pi$
$47$	8271.90			0.546211			0.273106	+	0.961984i	$0.411949\pi$
$48$	−187.933	−	325.509i	−0.0117733	−	0.0203920i
$49$	−9156.50	−	15859.5i	−0.544803	−	0.943626i
$50$	−1318.98	+	2284.54i	−0.0746128	+	0.129233i
$51$	−846.323			−0.0455628
$52$	3447.34	−	5970.97i	0.176798	−	0.306222i
$53$	−14039.9	−	24317.9i	−0.686555	−	1.18915i	−0.972946	−	0.231035i	$-0.925789\pi$
$53$	−14039.9	−	24317.9i	−0.686555	−	1.18915i	0.286391	−	0.958113i	$-0.407544\pi$
$54$	1800.13			0.0840077
$55$	−6948.24	−	12034.7i	−0.309719	−	0.536450i
$56$	−18383.9	+	31841.8i	−0.783371	+	1.35684i
$57$	883.906	−	1530.97i	0.0360345	−	0.0624137i
$58$	9283.54	−	16079.6i	0.362363	−	0.627631i
$59$	8728.07			0.326429			0.163214	−	0.986591i	$-0.447814\pi$
$59$	8728.07			0.326429			0.163214	+	0.986591i	$0.447814\pi$
$60$	−335.796	+	581.616i	−0.0120420	+	0.0208573i
$61$	20730.1	−	35905.5i	0.713307	−	1.23548i	−0.250302	−	0.968168i	$-0.580530\pi$
$61$	20730.1	−	35905.5i	0.713307	−	1.23548i	0.963609	−	0.267316i	$-0.0861367\pi$
$62$	1614.09	+	2795.69i	0.0533273	+	0.0923656i
$63$	−22701.8	−	39320.7i	−0.720626	−	1.24816i
$64$	33132.7			1.01113
$65$	32532.1			0.955056
$66$	422.061	+	731.032i	0.0119266	+	0.0206574i
$67$	−21098.2	−	36543.1i	−0.574193	−	0.994531i	−0.996129	−	0.0879051i	$-0.971983\pi$
$67$	−21098.2	−	36543.1i	−0.574193	−	0.994531i	0.421936	−	0.906625i	$-0.361351\pi$
$68$	6445.28	−	11163.6i	0.169032	−	0.292772i
$69$	−487.945	+	845.145i	−0.0123381	+	0.0213702i
$70$	−49960.1			−1.21865
$71$	−7145.46	+	12376.3i	−0.168223	+	0.291370i	−0.937795	−	0.347190i	$-0.887136\pi$
$71$	−7145.46	+	12376.3i	−0.168223	+	0.291370i	0.769572	+	0.638559i	$0.220469\pi$
$72$	−23767.0	+	41165.6i	−0.540310	+	0.935844i
$73$	−39706.8	+	68774.1i	−0.872082	+	1.51049i	−0.0122429	+	0.999925i	$0.503897\pi$
$73$	−39706.8	+	68774.1i	−0.872082	+	1.51049i	−0.859839	+	0.510565i	$0.829436\pi$
$74$	36165.3	+	62640.2i	0.767738	+	1.32976i
$75$	−513.467			−0.0105405
$76$	13463.0	+	23318.6i	0.267367	+	0.463094i
$77$	21322.6	−	36931.8i	0.409839	−	0.709862i
$78$	−1976.12			−0.0367770
$79$	−25368.9	+	43940.3i	−0.457335	+	0.792128i	−0.998819	−	0.0485832i	$-0.984529\pi$
$79$	−25368.9	+	43940.3i	−0.457335	+	0.792128i	0.541484	+	0.840711i	$0.317863\pi$
$80$	13506.3	+	23393.6i	0.235945	+	0.408669i
$81$	−29261.6	−	50682.5i	−0.495547	−	0.858313i
$82$	37052.8			0.608536
$83$	36303.0	+	62878.6i	0.578425	+	1.00186i	0.995660	+	0.0930634i	$0.0296659\pi$
$83$	36303.0	+	62878.6i	0.578425	+	1.00186i	−0.417235	+	0.908799i	$0.637001\pi$
$84$	−2060.97			−0.0318693
$85$	60823.2			0.913108
$86$	40422.4	−	34171.0i	0.589353	−	0.498210i
$87$	3614.00			0.0511906
$88$	−44646.1			−0.614577
$89$	22812.5	+	39512.3i	0.305279	+	0.528759i	0.977323	−	0.211752i	$-0.0679169\pi$
$89$	22812.5	+	39512.3i	0.305279	+	0.528759i	−0.672044	+	0.740511i	$0.734584\pi$
$90$	−64589.2			−0.840531
$91$	49916.8	+	86458.5i	0.631893	+	1.09447i
$92$	−7432.01	−	12872.6i	−0.0915455	−	0.158561i
$93$	−314.176	+	544.169i	−0.00376674	+	0.00652419i
$94$	36111.0			0.421521
$95$	−63524.3	+	110027.i	−0.722155	+	1.25081i
$96$	1846.98	+	3199.07i	0.0204543	+	0.0354279i
$97$	−104823.			−1.13116			−0.565582	−	0.824692i	$-0.691348\pi$
$97$	−104823.			−1.13116			−0.565582	+	0.824692i	$0.691348\pi$
$98$	−39972.7	−	69234.7i	−0.420434	−	0.728214i
$99$	27566.2	−	47746.0i	0.282676	−	0.489609i
$100$	3910.38	−	6772.97i	0.0391038	−	0.0677297i
$101$	32216.9	−	55801.3i	0.314254	−	0.544303i	−0.665025	−	0.746821i	$-0.731579\pi$
$101$	32216.9	−	55801.3i	0.314254	−	0.544303i	0.979279	+	0.202518i	$0.0649124\pi$
$102$	−3694.62			−0.0351617
$103$	2971.91	−	5147.50i	0.0276021	−	0.0478083i	−0.851894	−	0.523714i	$-0.824546\pi$
$103$	2971.91	−	5147.50i	0.0276021	−	0.0478083i	0.879497	+	0.475905i	$0.157880\pi$
$104$	52258.9	−	90515.1i	0.473780	−	0.820611i
$105$	−4862.26	−	8421.68i	−0.0430393	−	0.0745462i
$106$	−61291.3	−	106160.i	−0.529827	−	0.917688i
$107$	70544.3			0.595666			0.297833	−	0.954618i	$-0.403736\pi$
$107$	70544.3			0.595666			0.297833	+	0.954618i	$0.403736\pi$
$108$	−5336.84			−0.0440276
$109$	−80147.6	−	138820.i	−0.646136	−	1.11914i	−0.984038	−	0.177960i	$-0.943050\pi$
$109$	−80147.6	−	138820.i	−0.646136	−	1.11914i	0.337901	−	0.941182i	$-0.390283\pi$
$110$	−30332.6	−	52537.5i	−0.239016	−	0.413988i
$111$	−7039.42	+	12192.6i	−0.0542287	+	0.0939269i
$112$	−41447.8	+	71789.6i	−0.312217	+	0.540775i
$113$	115601.			0.851656			0.425828	−	0.904804i	$-0.359983\pi$
$113$	115601.			0.851656			0.425828	+	0.904804i	$0.359983\pi$
$114$	3858.69	−	6683.45i	0.0278085	−	0.0481658i
$115$	35067.4	−	60738.6i	0.247263	−	0.428272i
$116$	−27522.9	+	47671.1i	−0.189911	+	0.328935i
$117$	64533.3	+	111775.i	0.435832	+	0.754883i
$118$	38102.4			0.251911
$119$	93326.4	+	161646.i	0.604139	+	1.04640i
$120$	−5090.39	+	8816.82i	−0.0322699	+	0.0558932i
$121$	−109268.			−0.678470
$122$	90497.2	−	156746.i	0.550472	−	0.953446i
$123$	3606.08	+	6245.92i	0.0214918	+	0.0372249i
$124$	−4785.30	−	8288.39i	−0.0279483	−	0.0484079i
$125$	−153935.			−0.881176
$126$	−99104.9	−	171655.i	−0.556121	−	0.963229i
$127$	−171900.			−0.945730			−0.472865	−	0.881135i	$-0.656780\pi$
$127$	−171900.			−0.945730			−0.472865	+	0.881135i	$0.656780\pi$
$128$	5529.01			0.0298279
$129$	9694.17	+	3488.30i	0.0512904	+	0.0184561i
$130$	142019.			0.737034
$131$	213882.			1.08892			0.544459	−	0.838787i	$-0.316735\pi$
$131$	213882.			1.08892			0.544459	+	0.838787i	$0.316735\pi$
$132$	−1251.29	−	2167.29i	−0.00625060	−	0.0108263i
$133$	−389883.			−1.91120
$134$	−92104.0	−	159529.i	−0.443115	−	0.767498i
$135$	−12590.7	−	21807.8i	−0.0594589	−	0.102986i
$136$	97705.2	−	169230.i	0.452971	−	0.784568i
$137$	339950.			1.54744			0.773720	−	0.633528i	$-0.218394\pi$
$137$	339950.			1.54744			0.773720	+	0.633528i	$0.218394\pi$
$138$	−2130.12	+	3689.48i	−0.00952154	+	0.0164918i
$139$	144788.	+	250780.i	0.635617	+	1.10092i	0.986384	+	0.164458i	$0.0525876\pi$
$139$	144788.	+	250780.i	0.635617	+	1.10092i	−0.350767	+	0.936463i	$0.614079\pi$
$140$	148117.			0.638681
$141$	3514.42	+	6087.16i	0.0148870	+	0.0257850i
$142$	−31193.5	+	54028.7i	−0.129820	+	0.224856i
$143$	−60612.6	+	104984.i	−0.247869	+	0.429322i
$144$	−53584.3	+	92810.8i	−0.215343	+	0.372986i
$145$	−259730.			−1.02589
$146$	−173340.	+	300234.i	−0.673002	+	1.16567i
$147$	7780.51	−	13476.2i	0.0296972	−	0.0514370i
$148$	−107219.	−	185709.i	−0.402363	−	0.696914i
$149$	43963.9	+	76147.7i	0.162230	+	0.280990i	0.935668	−	0.352881i	$-0.114798\pi$
$149$	43963.9	+	76147.7i	0.162230	+	0.280990i	−0.773438	+	0.633872i	$0.781465\pi$
$150$	−2241.54			−0.00813428
$151$	−58864.2			−0.210092			−0.105046	−	0.994467i	$-0.533499\pi$
$151$	−58864.2			−0.210092			−0.105046	+	0.994467i	$0.533499\pi$
$152$	204088.	+	353491.i	0.716488	+	1.24099i
$153$	120654.	+	208979.i	0.416689	+	0.721727i
$154$	93083.8	−	161226.i	0.316280	−	0.547814i
$155$	22579.1	−	39108.2i	0.0754880	−	0.130749i
$156$	5858.59			0.0192744
$157$	158855.	−	275145.i	0.514342	−	0.890866i	−0.485520	−	0.874226i	$-0.661370\pi$
$157$	158855.	−	275145.i	0.514342	−	0.890866i	0.999862	−	0.0166401i	$-0.00529695\pi$
$158$	−110748.	+	191821.i	−0.352934	+	0.611300i
$159$	11930.1	−	20663.5i	0.0374240	−	0.0648204i
$160$	−132738.	−	229910.i	−0.409918	−	0.709998i
$161$	215228.			0.654387
$162$	−127741.	−	221255.i	−0.382423	−	0.662377i
$163$	102435.	−	177423.i	0.301981	−	0.523047i	−0.674603	−	0.738180i	$-0.735685\pi$
$163$	102435.	−	177423.i	0.301981	−	0.523047i	0.976585	+	0.215133i	$0.0690186\pi$
$164$	−109850.			−0.318927
$165$	5904.10	−	10226.2i	0.0168828	−	0.0292418i
$166$	158481.	+	274497.i	0.446382	+	0.773156i
$167$	199629.	+	345767.i	0.553901	+	0.959384i	0.997988	+	0.0634009i	$0.0201947\pi$
$167$	199629.	+	345767.i	0.553901	+	0.959384i	−0.444087	+	0.895984i	$0.646472\pi$
$168$	−31242.5			−0.0854030
$169$	43750.7	+	75778.4i	0.117833	+	0.204093i
$170$	265524.			0.704662
$171$	−504047.			−1.31820
$172$	−119840.	+	101307.i	−0.308874	+	0.261107i
$173$	−571301.			−1.45127			−0.725637	−	0.688077i	$-0.758455\pi$
$173$	−571301.			−1.45127			−0.725637	+	0.688077i	$0.758455\pi$
$174$	15776.9			0.0395048
$175$	56621.5	+	98071.3i	0.139761	+	0.242073i
$176$	−100658.			−0.244943
$177$	3708.23	+	6422.85i	0.00889680	+	0.0154097i
$178$	99587.8	+	172491.i	0.235590	+	0.408053i
$179$	−103377.	+	179053.i	−0.241151	+	0.417686i	−0.961042	−	0.276401i	$-0.910858\pi$
$179$	−103377.	+	179053.i	−0.241151	+	0.417686i	0.719891	+	0.694087i	$0.244192\pi$
$180$	191488.			0.440514
$181$	49747.6	−	86165.4i	0.112869	−	0.195495i	−0.804057	−	0.594553i	$-0.797329\pi$
$181$	49747.6	−	86165.4i	0.112869	−	0.195495i	0.916926	+	0.399057i	$0.130663\pi$
$182$	217912.	+	377435.i	0.487644	+	0.844624i
$183$	35229.8			0.0777646
$184$	−112663.	−	195138.i	−0.245323	−	0.424911i
$185$	505907.	−	876256.i	1.08678	−	1.88236i
$186$	−1371.54	+	2375.57i	−0.00290687	+	0.00503484i
$187$	−113323.	+	196282.i	−0.236982	+	0.410465i
$188$	−107058.			−0.220915
$189$	38638.2	−	66923.3i	0.0786796	−	0.136277i
$190$	−277315.	+	480324.i	−0.557301	+	0.965273i
$191$	230622.	+	399449.i	0.457422	+	0.792278i	0.998824	−	0.0484856i	$-0.0154395\pi$
$191$	230622.	+	399449.i	0.457422	+	0.792278i	−0.541402	+	0.840764i	$0.682106\pi$
$192$	14076.9	+	24381.8i	0.0275583	+	0.0477324i
$193$	348735.			0.673910			0.336955	−	0.941521i	$-0.390603\pi$
$193$	348735.			0.673910			0.336955	+	0.941521i	$0.390603\pi$
$194$	−457603.			−0.872941
$195$	13821.7	+	23939.8i	0.0260300	+	0.0450853i
$196$	118507.	+	205260.i	0.220345	+	0.381649i
$197$	351170.	−	608245.i	0.644692	−	1.11664i	−0.339680	−	0.940541i	$-0.610319\pi$
$197$	351170.	−	608245.i	0.644692	−	1.11664i	0.984373	−	0.176099i	$-0.0563478\pi$
$198$	120340.	−	208435.i	0.218146	−	0.377841i
$199$	−405599.			−0.726047			−0.363023	−	0.931780i	$-0.618255\pi$
$199$	−405599.			−0.726047			−0.363023	+	0.931780i	$0.618255\pi$
$200$	59278.1	−	102673.i	0.104790	−	0.181501i
$201$	17927.6	−	31051.6i	0.0312992	−	0.0542118i
$202$	140643.	−	243601.i	0.242516	−	0.420049i
$203$	−398526.	−	690267.i	−0.678761	−	1.17565i
$204$	10953.4			0.0184279
$205$	−259161.	−	448879.i	−0.430709	−	0.746011i
$206$	12973.9	−	22471.4i	0.0213011	−	0.0368946i
$207$	278250.			0.451346
$208$	117821.	−	204072.i	0.188828	−	0.327059i
$209$	−236712.	−	409997.i	−0.374847	−	0.649255i
$210$	−21226.2	−	36764.9i	−0.0332142	−	0.0575287i
$211$	−289100.			−0.447035			−0.223518	−	0.974700i	$-0.571754\pi$
$211$	−289100.			−0.447035			−0.223518	+	0.974700i	$0.571754\pi$
$212$	181710.	+	314731.i	0.277677	+	0.480951i
$213$	−12143.4			−0.0183396
$214$	307961.			0.459687
$215$	−696697.	−	250696.i	−1.02789	−	0.369871i
$216$	−80902.1			−0.117985
$217$	138580.			0.199780
$218$	−349884.	−	606018.i	−0.498636	−	0.863662i
$219$	−67479.7			−0.0950743
$220$	89926.9	+	155758.i	0.125266	+	0.216967i
$221$	−265294.	−	459502.i	−0.365381	−	0.632859i
$222$	−30730.6	+	53227.0i	−0.0418493	+	0.0724852i
$223$	−848271.			−1.14228			−0.571140	−	0.820853i	$-0.693499\pi$
$223$	−848271.			−1.14228			−0.571140	+	0.820853i	$0.693499\pi$
$224$	407344.	−	705541.i	0.542428	−	0.939512i
$225$	73201.2	+	126788.i	0.0963966	+	0.166964i
$226$	504655.			0.657239
$227$	617857.	+	1.07016e6i	0.795835	+	1.37843i	0.922307	+	0.386457i	$0.126301\pi$
$227$	617857.	+	1.07016e6i	0.795835	+	1.37843i	−0.126472	+	0.991970i	$0.540365\pi$
$228$	−11439.9	+	19814.4i	−0.0145742	+	0.0252432i
$229$	−3190.49	+	5526.09i	−0.00402039	+	0.00696353i	−0.868029	−	0.496514i	$-0.834613\pi$
$229$	−3190.49	+	5526.09i	−0.00402039	+	0.00696353i	0.864008	+	0.503478i	$0.167946\pi$
$230$	153087.	−	265154.i	0.190818	−	0.330506i
$231$	36236.7			0.0446806
$232$	−417225.	+	722654.i	−0.508921	+	0.881476i
$233$	716746.	−	1.24144e6i	0.864919	−	1.49808i	−0.00220787	−	0.999998i	$-0.500703\pi$
$233$	716746.	−	1.24144e6i	0.864919	−	1.49808i	0.867127	−	0.498087i	$-0.165964\pi$
$234$	281720.	+	487954.i	0.336340	+	0.582558i
$235$	−252573.	−	437470.i	−0.298344	−	0.516747i
$236$	−112962.			−0.132024
$237$	−43113.3			−0.0498586
$238$	407416.	+	705666.i	0.466226	+	0.807526i
$239$	831921.	+	1.44093e6i	0.942079	+	1.63173i	0.761496	+	0.648170i	$0.224465\pi$
$239$	831921.	+	1.44093e6i	0.942079	+	1.63173i	0.180584	+	0.983560i	$0.442201\pi$
$240$	−11476.6	+	19878.1i	−0.0128614	+	0.0222765i
$241$	206523.	−	357709.i	0.229048	−	0.396722i	−0.728478	−	0.685069i	$-0.759772\pi$
$241$	206523.	−	357709.i	0.229048	−	0.396722i	0.957526	+	0.288346i	$0.0931055\pi$
$242$	−477010.			−0.523588
$243$	74965.2	−	129844.i	0.0814412	−	0.141060i
$244$	−268297.	+	464704.i	−0.288497	+	0.499691i
$245$	−559167.	+	968506.i	−0.595150	+	1.03083i
$246$	15742.4	+	27266.6i	0.0165856	+	0.0287272i
$247$	1.10830e6			1.15589
$248$	−72541.3	−	125645.i	−0.0748955	−	0.129723i
$249$	−30847.6	+	53429.6i	−0.0315299	+	0.0546114i
$250$	−672004.			−0.680020
$251$	−847355.	+	1.46766e6i	−0.848948	+	1.47042i	0.0332009	+	0.999449i	$0.489430\pi$
$251$	−847355.	+	1.46766e6i	−0.848948	+	1.47042i	−0.882148	+	0.470972i	$0.843903\pi$
$252$	293816.	+	508905.i	0.291457	+	0.504818i
$253$	130673.	+	226332.i	0.128346	+	0.222302i
$254$	−750431.			−0.729838
$255$	25841.5	+	44758.8i	0.0248867	+	0.0431051i
$256$	−1.03611e6			−0.988112
$257$	−423541.			−0.400003			−0.200001	−	0.979796i	$-0.564095\pi$
$257$	−423541.			−0.400003			−0.200001	+	0.979796i	$0.564095\pi$
$258$	42319.9	+	15228.2i	0.0395818	+	0.0142429i
$259$	3.10503e6			2.87618
$260$	−421043.			−0.386272
$261$	−515221.	−	892389.i	−0.468158	−	0.810873i
$262$	933700.			0.840339
$263$	245923.	+	425951.i	0.219235	+	0.379726i	0.954574	−	0.297973i	$-0.0963105\pi$
$263$	245923.	+	425951.i	0.219235	+	0.379726i	−0.735339	+	0.677699i	$0.762977\pi$
$264$	−18968.5	−	32854.3i	−0.0167503	−	0.0290123i
$265$	−857387.	+	1.48504e6i	−0.750002	+	1.29904i
$266$	−1.70204e6			−1.47491
$267$	−19384.3	+	33574.7i	−0.0166407	+	0.0288226i
$268$	273061.	+	472955.i	0.232232	+	0.402238i
$269$	−1.50648e6			−1.26935			−0.634675	−	0.772779i	$-0.718866\pi$
$269$	−1.50648e6			−1.26935			−0.634675	+	0.772779i	$0.718866\pi$
$270$	−54964.9	−	95202.0i	−0.0458856	−	0.0794762i
$271$	841293.	−	1.45716e6i	0.695864	−	1.20527i	−0.274025	−	0.961723i	$-0.588355\pi$
$271$	841293.	−	1.45716e6i	0.695864	−	1.20527i	0.969889	−	0.243549i	$-0.0783116\pi$
$272$	220283.	−	381541.i	0.180534	−	0.312694i
$273$	−42415.6	+	73466.0i	−0.0344444	+	0.0596595i
$274$	1.48405e6			1.19419
$275$	−68753.8	+	119085.i	−0.0548233	+	0.0949567i
$276$	6315.17	−	10938.2i	0.00499014	−	0.00864317i
$277$	−273684.	−	474035.i	−0.214314	−	0.371203i	0.738746	−	0.673984i	$-0.235418\pi$
$277$	−273684.	−	474035.i	−0.214314	−	0.371203i	−0.953060	+	0.302781i	$0.902085\pi$
$278$	632072.	+	1.09478e6i	0.490518	+	0.849602i
$279$	179159.			0.137793
$280$	2.24533e6			1.71153
$281$	−15157.9	−	26254.3i	−0.0114518	−	0.0198351i	0.860243	−	0.509885i	$-0.170312\pi$
$281$	−15157.9	−	26254.3i	−0.0114518	−	0.0198351i	−0.871695	+	0.490050i	$0.836979\pi$
$282$	15342.2	+	26573.5i	0.0114886	+	0.0198988i
$283$	−794499.	+	1.37611e6i	−0.589695	+	1.02138i	0.404578	+	0.914504i	$0.367419\pi$
$283$	−794499.	+	1.37611e6i	−0.589695	+	1.02138i	−0.994272	+	0.106877i	$0.965915\pi$
$284$	92479.3	−	160179.i	0.0680376	−	0.117845i
$285$	−107956.			−0.0787293
$286$	−264604.	+	458308.i	−0.191285	+	0.331316i
$287$	795306.	−	1.37751e6i	0.569940	−	0.987166i
$288$	526621.	−	912135.i	0.374125	−	0.648004i
$289$	213926.	+	370530.i	0.150667	+	0.260963i
$290$	−1.13385e6			−0.791700
$291$	−44535.2	−	77137.3i	−0.0308298	−	0.0533988i
$292$	513901.	−	890102.i	0.352713	−	0.610918i
$293$	−414223.			−0.281881			−0.140940	−	0.990018i	$-0.545013\pi$
$293$	−414223.			−0.281881			−0.140940	+	0.990018i	$0.545013\pi$
$294$	33965.8	−	58830.5i	0.0229179	−	0.0396949i
$295$	−266502.	−	461595.i	−0.178298	−	0.308821i
$296$	−1.62536e6	−	2.81520e6i	−1.07825	−	1.86758i
$297$	93834.4			0.0617264
$298$	191924.	+	332423.i	0.125196	+	0.216845i
$299$	−611817.			−0.395771
$300$	6645.50			0.00426309
$301$	−402745.	−	2.23623e6i	−0.256220	−	1.42266i
$302$	−256972.			−0.162132
$303$	54751.1			0.0342599
$304$	460131.	+	796970.i	0.285560	+	0.494605i
$305$	−2.53188e6			−1.55845
$306$	526714.	+	912296.i	0.321567	+	0.556971i
$307$	−1.00547e6	−	1.74152e6i	−0.608867	−	1.05459i	−0.991427	−	0.130658i	$-0.958291\pi$
$307$	−1.00547e6	−	1.74152e6i	−0.608867	−	1.05459i	0.382561	−	0.923930i	$-0.375042\pi$
$308$	−275965.	+	477986.i	−0.165759	+	0.287104i
$309$	5050.62			0.00300918
$310$	98569.2	−	170727.i	0.0582555	−	0.100901i
$311$	−901562.	−	1.56155e6i	−0.528561	−	0.915494i	−0.999445	−	0.0332991i	$-0.989399\pi$
$311$	−901562.	−	1.56155e6i	−0.528561	−	0.915494i	0.470885	−	0.882195i	$-0.343935\pi$
$312$	88811.5			0.0516514
$313$	345410.	+	598267.i	0.199285	+	0.345171i	0.948297	−	0.317385i	$-0.102805\pi$
$313$	345410.	+	598267.i	0.199285	+	0.345171i	−0.749012	+	0.662556i	$0.769472\pi$
$314$	693481.	−	1.20115e6i	0.396927	−	0.687498i
$315$	−1.38635e6	+	2.40123e6i	−0.787221	+	1.36351i
$316$	328335.	−	568693.i	0.184969	−	0.320376i
$317$	3.03303e6			1.69523			0.847614	−	0.530613i	$-0.178038\pi$
$317$	3.03303e6			1.69523			0.847614	+	0.530613i	$0.178038\pi$
$318$	52080.8	−	90206.6i	0.0288808	−	0.0500231i
$319$	483919.	−	838172.i	0.266254	−	0.461165i
$320$	−1.01167e6	−	1.75227e6i	−0.552287	−	0.956588i
$321$	29971.7	+	51912.5i	0.0162349	+	0.0281196i
$322$	939579.			0.505002
$323$	2.07212e6			1.10512
$324$	378715.	+	655954.i	0.200424	+	0.347145i
$325$	−160955.	−	278782.i	−0.0845270	−	0.146405i
$326$	447181.	−	774540.i	0.233045	−	0.403645i
$327$	68103.5	−	117959.i	0.0352209	−	0.0610043i
$328$	−1.66524e6			−0.854659
$329$	775090.	−	1.34250e6i	0.394787	−	0.683791i
$330$	25774.4	−	44642.5i	0.0130288	−	0.0225665i
$331$	−709993.	+	1.22974e6i	−0.356192	+	0.616943i	−0.987321	−	0.158735i	$-0.949258\pi$
$331$	−709993.	+	1.22974e6i	−0.356192	+	0.616943i	0.631129	+	0.775678i	$0.282592\pi$
$332$	−469848.	−	813800.i	−0.233944	−	0.405203i
$333$	4.01423e6			1.98377
$334$	871480.	+	1.50945e6i	0.427456	+	0.740375i
$335$	−1.28842e6	+	2.23160e6i	−0.627256	+	1.08644i
$336$	−70438.5			−0.0340378
$337$	−906569.	+	1.57022e6i	−0.434837	+	0.753159i	−0.997282	−	0.0736750i	$-0.976527\pi$
$337$	−906569.	+	1.57022e6i	−0.434837	+	0.753159i	0.562446	+	0.826834i	$0.309861\pi$
$338$	190994.	+	330811.i	0.0909341	+	0.157503i
$339$	49114.4	+	85068.7i	0.0232119	+	0.0402041i
$340$	−787198.			−0.369306
$341$	84137.1	+	145730.i	0.0391834	+	0.0678676i
$342$	−2.20042e6			−1.01728
$343$	−282228.			−0.129528
$344$	−1.81668e6	+	1.53573e6i	−0.827717	+	0.699711i
$345$	59595.4			0.0269566
$346$	−2.49401e6			−1.11998
$347$	1.44905e6	+	2.50983e6i	0.646041	+	1.11898i	0.984060	+	0.177837i	$0.0569099\pi$
$347$	1.44905e6	+	2.50983e6i	0.646041	+	1.11898i	−0.338019	+	0.941139i	$0.609757\pi$
$348$	−46773.8			−0.0207040
$349$	−870184.	−	1.50720e6i	−0.382426	−	0.662381i	0.608982	−	0.793184i	$-0.291578\pi$
$349$	−870184.	−	1.50720e6i	−0.382426	−	0.662381i	−0.991408	+	0.130802i	$0.958245\pi$
$350$	247181.	+	428130.i	0.107856	+	0.186813i
$351$	−109835.	+	190239.i	−0.0475851	+	0.0824199i
$352$	989253.			0.425550
$353$	−2979.14	+	5160.02i	−0.00127249	+	0.00220402i	−0.866661	−	0.498898i	$-0.833738\pi$
$353$	−2979.14	+	5160.02i	−0.00127249	+	0.00220402i	0.865388	+	0.501102i	$0.167072\pi$
$354$	16188.3	+	28039.0i	0.00686583	+	0.0118920i
$355$	872714.			0.367537
$356$	−295248.	−	511384.i	−0.123470	−	0.213857i
$357$	−79301.8	+	137355.i	−0.0329316	+	0.0570392i
$358$	−451290.	+	781658.i	−0.186101	+	0.322336i
$359$	112246.	−	194415.i	0.0459657	−	0.0796149i	−0.842127	−	0.539279i	$-0.818697\pi$
$359$	112246.	−	194415.i	0.0459657	−	0.0796149i	0.888093	+	0.459664i	$0.152030\pi$
$360$	2.90280e6			1.18048
$361$	−926088.	+	1.60403e6i	−0.374011	+	0.647806i
$362$	217173.	−	376155.i	0.0871034	−	0.150868i
$363$	−46424.0	−	80408.7i	−0.0184917	−	0.0320285i
$364$	−646043.	−	1.11898e6i	−0.255569	−	0.442659i
$365$	4.84961e6			1.90535
$366$	153796.			0.0600124
$367$	2.15113e6	+	3.72587e6i	0.833685	+	1.44398i	0.895097	+	0.445872i	$0.147106\pi$
$367$	2.15113e6	+	3.72587e6i	0.833685	+	1.44398i	−0.0614120	+	0.998113i	$0.519560\pi$
$368$	−254007.	−	439953.i	−0.0977746	−	0.169351i
$369$	1.02818e6	−	1.78087e6i	0.393102	−	0.680872i
$370$	2.20854e6	−	3.82530e6i	0.838687	−	1.45265i
$371$	−5.26226e6			−1.98489
$372$	4066.19	−	7042.86i	0.00152346	−	0.00263871i
$373$	−1.56011e6	+	2.70219e6i	−0.580609	+	1.00564i	0.414799	+	0.909913i	$0.363852\pi$
$373$	−1.56011e6	+	2.70219e6i	−0.580609	+	1.00564i	−0.995407	+	0.0957304i	$0.969481\pi$
$374$	−494714.	+	856870.i	−0.182884	+	0.316764i
$375$	−65401.3	−	113278.i	−0.0240164	−	0.0415977i
$376$	−1.62291e6			−0.592006
$377$	1.13287e6	+	1.96219e6i	0.410512	+	0.711028i
$378$	168675.	−	292154.i	0.0607185	−	0.105168i
$379$	−4.12331e6			−1.47451			−0.737255	−	0.675614i	$-0.763878\pi$
$379$	−4.12331e6			−1.47451			−0.737255	+	0.675614i	$0.763878\pi$
$380$	822156.	−	1.42402e6i	0.292076	−	0.505890i
$381$	−73034.0	−	126499.i	−0.0257758	−	0.0446451i
$382$	1.00678e6	+	1.74379e6i	0.353001	+	0.611416i
$383$	−1.12528e6			−0.391979			−0.195990	−	0.980606i	$-0.562792\pi$
$383$	−1.12528e6			−0.391979			−0.195990	+	0.980606i	$0.562792\pi$
$384$	2349.07	+	4068.71i	0.000812958	+	0.00140808i
$385$	−2.60425e6			−0.895427
$386$	1.52240e6			0.520069
$387$	−520675.	−	2.89104e6i	−0.176721	−	0.981242i
$388$	1.35666e6			0.457499
$389$	1.57279e6			0.526983			0.263491	−	0.964662i	$-0.415126\pi$
$389$	1.57279e6			0.526983			0.263491	+	0.964662i	$0.415126\pi$
$390$	60338.6	+	104509.i	0.0200878	+	0.0347932i
$391$	−1.14388e6			−0.378388
$392$	1.79647e6	+	3.11158e6i	0.590479	+	1.02274i
$393$	90870.3	+	157392.i	0.0296784	+	0.0514045i
$394$	1.53304e6	−	2.65529e6i	0.497521	−	0.861732i
$395$	3.09845e6			0.999199
$396$	−356773.	+	617948.i	−0.114328	+	0.198022i
$397$	696834.	+	1.20695e6i	0.221898	+	0.384338i	0.955384	−	0.295366i	$-0.0954415\pi$
$397$	696834.	+	1.20695e6i	0.221898	+	0.384338i	−0.733486	+	0.679704i	$0.762108\pi$
$398$	−1.77064e6			−0.560304
$399$	−165647.	−	286909.i	−0.0520896	−	0.0902219i
$400$	133647.	−	231483.i	0.0417646	−	0.0723384i
$401$	−356158.	+	616884.i	−0.110607	+	0.191577i	−0.916015	−	0.401144i	$-0.868613\pi$
$401$	−356158.	+	616884.i	−0.110607	+	0.191577i	0.805408	+	0.592720i	$0.201946\pi$
$402$	78263.2	−	135556.i	0.0241542	−	0.0418363i
$403$	−393935.			−0.120826
$404$	−416964.	+	722203.i	−0.127100	+	0.220143i
$405$	−1.78694e6	+	3.09507e6i	−0.541343	+	0.937633i
$406$	−1.73977e6	−	3.01336e6i	−0.523812	−	0.907270i
$407$	1.88517e6	+	3.26521e6i	0.564111	+	0.977070i
$408$	166045.			0.0493828
$409$	−617135.			−0.182420			−0.0912100	−	0.995832i	$-0.529073\pi$
$409$	−617135.			−0.182420			−0.0912100	+	0.995832i	$0.529073\pi$
$410$	−1.13137e6	−	1.95958e6i	−0.332387	−	0.575711i
$411$	144432.	+	250164.i	0.0421754	+	0.0730499i
$412$	−38463.6	+	66621.0i	−0.0111637	+	0.0193361i
$413$	817835.	−	1.41653e6i	0.235934	−	0.408650i
$414$	1.21470e6			0.348312
$415$	2.21694e6	−	3.83986e6i	0.631880	−	1.09445i
$416$	−1.15794e6	+	2.00560e6i	−0.328058	+	0.568214i
$417$	−123030.	+	213094.i	−0.0346474	+	0.0600111i
$418$	−1.03337e6	−	1.78984e6i	−0.289277	−	0.501042i
$419$	1.98216e6			0.551575			0.275788	−	0.961219i	$-0.411061\pi$
$419$	1.98216e6			0.551575			0.275788	+	0.961219i	$0.411061\pi$
$420$	62929.3	+	108997.i	0.0174072	+	0.0301502i
$421$	271063.	−	469495.i	0.0745359	−	0.129100i	−0.826348	−	0.563159i	$-0.809586\pi$
$421$	271063.	−	469495.i	0.0745359	−	0.129100i	0.900884	+	0.434059i	$0.142919\pi$
$422$	−1.26207e6			−0.344986
$423$	1.00205e6	−	1.73560e6i	0.272294	−	0.471627i
$424$	2.75458e6	+	4.77107e6i	0.744116	+	1.28885i
$425$	−300927.	−	521221.i	−0.0808144	−	0.139975i
$426$	−53011.8			−0.0141530
$427$	−3.88488e6	−	6.72882e6i	−1.03112	−	1.78595i
$428$	−913013.			−0.240917
$429$	−103008.			−0.0270227
$430$	−3.04143e6	−	1.09441e6i	−0.793244	−	0.285437i
$431$	−4.50685e6			−1.16864			−0.584319	−	0.811524i	$-0.698638\pi$
$431$	−4.50685e6			−1.16864			−0.584319	+	0.811524i	$0.698638\pi$
$432$	−182399.			−0.0470234
$433$	2.71194e6	+	4.69722e6i	0.695121	+	1.20398i	0.970140	+	0.242546i	$0.0779824\pi$
$433$	2.71194e6	+	4.69722e6i	0.695121	+	1.20398i	−0.275019	+	0.961439i	$0.588684\pi$
$434$	604973.			0.154174
$435$	−110350.	−	191131.i	−0.0279607	−	0.0484293i
$436$	1.03730e6	+	1.79666e6i	0.261330	+	0.452636i
$437$	1.19467e6	−	2.06924e6i	0.299258	−	0.518330i
$438$	−294583.			−0.0733706
$439$	−1.67647e6	+	2.90373e6i	−0.415178	+	0.719110i	−0.995447	−	0.0953151i	$-0.969614\pi$
$439$	−1.67647e6	+	2.90373e6i	−0.415178	+	0.719110i	0.580269	+	0.814425i	$0.302947\pi$
$440$	1.36322e6	+	2.36116e6i	0.335686	+	0.581426i
$441$	−4.43683e6			−1.08637
$442$	−1.15814e6	−	2.00596e6i	−0.281972	−	0.488389i
$443$	3.71963e6	−	6.44259e6i	0.900514	−	1.55974i	0.0736847	−	0.997282i	$-0.476524\pi$
$443$	3.71963e6	−	6.44259e6i	0.900514	−	1.55974i	0.826829	−	0.562454i	$-0.190143\pi$
$444$	91107.0	−	157802.i	0.0219328	−	0.0379887i
$445$	1.39311e6	−	2.41293e6i	0.333491	−	0.577624i
$446$	−3.70313e6			−0.881519
$447$	−37357.2	+	64704.6i	−0.00884313	+	0.0153167i
$448$	3.10459e6	−	5.37731e6i	0.730818	−	1.26581i
$449$	2.18698e6	+	3.78796e6i	0.511952	+	0.886726i	0.999904	+	0.0138560i	$0.00441063\pi$
$449$	2.18698e6	+	3.78796e6i	0.511952	+	0.886726i	−0.487952	+	0.872870i	$0.662256\pi$
$450$	319560.	+	553494.i	0.0743911	+	0.128849i
$451$	1.93143e6			0.447135
$452$	−1.49615e6			−0.344452
$453$	−25009.2	−	43317.2i	−0.00572604	−	0.00991780i
$454$	2.69725e6	+	4.67178e6i	0.614161	+	1.06376i
$455$	3.04831e6	−	5.27983e6i	0.690289	−	1.19562i
$456$	−173419.	+	300370.i	−0.0390557	+	0.0676465i
$457$	3.86721e6			0.866177			0.433089	−	0.901351i	$-0.357424\pi$
$457$	3.86721e6			0.866177			0.433089	+	0.901351i	$0.357424\pi$
$458$	−13928.1	+	24124.2i	−0.00310261	+	0.00537388i
$459$	−205351.	+	355678.i	−0.0454951	+	0.0787999i
$460$	−453857.	+	786103.i	−0.100006	+	0.173215i
$461$	−1.47161e6	−	2.54890e6i	−0.322507	−	0.558599i	0.658498	−	0.752583i	$-0.271192\pi$
$461$	−1.47161e6	−	2.54890e6i	−0.322507	−	0.558599i	−0.981005	+	0.193984i	$0.937859\pi$
$462$	158191.			0.0344809
$463$	−3.22970e6	−	5.59400e6i	−0.700180	−	1.21275i	−0.968403	−	0.249390i	$-0.919770\pi$
$463$	−3.22970e6	−	5.59400e6i	−0.700180	−	1.21275i	0.268224	−	0.963357i	$-0.413563\pi$
$464$	−940662.	+	1.62927e6i	−0.202833	+	0.351317i
$465$	38372.1			0.00822969
$466$	3.12896e6	−	5.41951e6i	0.667475	−	1.15610i
$467$	3.74977e6	+	6.49479e6i	0.795632	+	1.37807i	0.922437	+	0.386147i	$0.126194\pi$
$467$	3.74977e6	+	6.49479e6i	0.795632	+	1.37807i	−0.126806	+	0.991928i	$0.540473\pi$
$468$	−835215.	−	1.44664e6i	−0.176272	−	0.305312i
$469$	−7.90773e6			−1.66004
$470$	−1.10261e6	−	1.90977e6i	−0.230238	−	0.398784i
$471$	269966.			0.0560734
$472$	−1.71241e6			−0.353797
$473$	2.10708e6	−	1.78122e6i	0.433040	−	0.366070i
$474$	−188211.			−0.0384768
$475$	1.25716e6			0.255657
$476$	−1.20787e6	−	2.09209e6i	−0.244344	−	0.423216i
$477$	−6.80313e6			−1.36903
$478$	3.63175e6	+	6.29038e6i	0.727021	+	1.25924i
$479$	−2.23566e6	−	3.87228e6i	−0.445213	−	0.771131i	0.552854	−	0.833278i	$-0.313539\pi$
$479$	−2.23566e6	−	3.87228e6i	−0.445213	−	0.771131i	−0.998067	+	0.0621470i	$0.980205\pi$
$480$	112791.	−	195360.i	0.0223446	−	0.0387020i
$481$	−8.82649e6			−1.73950
$482$	901577.	−	1.56158e6i	0.176761	−	0.306158i
$483$	91442.4	+	158383.i	0.0178353	+	0.0308916i
$484$	1.41419e6			0.274407
$485$	3.20064e6	+	5.54367e6i	0.617849	+	1.07015i
$486$	327261.	−	566832.i	0.0628497	−	0.108859i
$487$	3.41494e6	−	5.91485e6i	0.652470	−	1.13011i	−0.330051	−	0.943963i	$-0.607066\pi$
$487$	3.41494e6	−	5.91485e6i	0.652470	−	1.13011i	0.982522	−	0.186149i	$-0.0596007\pi$
$488$	−4.06716e6	+	7.04453e6i	−0.773111	+	1.33907i
$489$	174084.			0.0329220
$490$	−2.44104e6	+	4.22801e6i	−0.459288	+	0.795511i
$491$	4.08976e6	−	7.08367e6i	0.765586	−	1.32603i	−0.174350	−	0.984684i	$-0.555782\pi$
$491$	4.08976e6	−	7.08367e6i	0.765586	−	1.32603i	0.939936	−	0.341350i	$-0.110884\pi$
$492$	−46671.3	−	80837.1i	−0.00869236	−	0.0150556i
$493$	2.11805e6	+	3.66857e6i	0.392482	+	0.679798i
$494$	4.83828e6			0.892019
$495$	−3.36681e6			−0.617598
$496$	−163549.	−	283276.i	−0.0298500	−	0.0517017i
$497$	1.33908e6	+	2.31936e6i	0.243173	+	0.421189i
$498$	−134665.	+	233247.i	−0.0243322	+	0.0421447i
$499$	1.84543e6	−	3.19637e6i	0.331777	−	0.574654i	−0.651084	−	0.759006i	$-0.725685\pi$
$499$	1.84543e6	−	3.19637e6i	0.331777	−	0.574654i	0.982860	+	0.184352i	$0.0590187\pi$
$500$	1.99229e6			0.356392
$501$	−169630.	+	293807.i	−0.0301931	+	0.0522960i
$502$	−3.69913e6	+	6.40708e6i	−0.655149	+	1.13475i
$503$	−2.19122e6	+	3.79531e6i	−0.386160	+	0.668848i	−0.991929	−	0.126792i	$-0.959532\pi$
$503$	−2.19122e6	+	3.79531e6i	−0.386160	+	0.668848i	0.605770	+	0.795640i	$0.292865\pi$
$504$	4.45401e6	+	7.71458e6i	0.781043	+	1.35281i
$505$	−3.93483e6			−0.686590
$506$	570452.	+	988051.i	0.0990473	+	0.171555i
$507$	−37176.1	+	64390.8i	−0.00642308	+	0.0111251i
$508$	2.22480e6			0.382500
$509$	1.58121e6	−	2.73874e6i	0.270518	−	0.468551i	−0.698477	−	0.715633i	$-0.746138\pi$
$509$	1.58121e6	−	2.73874e6i	0.270518	−	0.468551i	0.968995	+	0.247082i	$0.0794718\pi$
$510$	112811.	+	195395.i	0.0192056	+	0.0332650i
$511$	7.44118e6	+	1.28885e7i	1.26064	+	2.18348i
$512$	−4.70007e6			−0.792373
$513$	−428940.	−	742946.i	−0.0719620	−	0.124642i
$514$	−1.84897e6			−0.308690
$515$	−362976.			−0.0603059
$516$	−125466.	−	45146.9i	−0.0207444	−	0.00746456i
$517$	1.88234e6			0.309722
$518$	1.35550e7			2.21960
$519$	−242725.	−	420411.i	−0.0395544	−	0.0685103i
$520$	−6.38267e6			−1.03513
$521$	1.59237e6	+	2.75806e6i	0.257010	+	0.445154i	0.965439	−	0.260627i	$-0.0839294\pi$
$521$	1.59237e6	+	2.75806e6i	0.257010	+	0.445154i	−0.708430	+	0.705781i	$0.750596\pi$
$522$	−2.24920e6	−	3.89572e6i	−0.361286	−	0.625766i
$523$	−21079.2	+	36510.2i	−0.00336977	+	0.00583661i	−0.867705	−	0.497079i	$-0.834406\pi$
$523$	−21079.2	+	36510.2i	−0.00336977	+	0.00583661i	0.864336	+	0.502915i	$0.167739\pi$
$524$	−2.76814e6			−0.440413
$525$	−48112.7	+	83333.7i	−0.00761837	+	0.0131954i
$526$	1.07358e6	+	1.85949e6i	0.169188	+	0.293042i
$527$	−736515.			−0.115520
$528$	−42765.7	−	74072.4i	−0.00667591	−	0.0115630i
$529$	2.55867e6	−	4.43175e6i	0.397535	−	0.688551i
$530$	−3.74292e6	+	6.48294e6i	−0.578791	+	1.00249i
$531$	1.05731e6	−	1.83131e6i	0.162729	−	0.281856i
$532$	5.04602e6			0.772984
$533$	−2.26077e6	+	3.91577e6i	−0.344698	+	0.597034i
$534$	−84622.4	+	146570.i	−0.0128420	+	0.0222430i
$535$	−2.15399e6	−	3.73083e6i	−0.325357	−	0.563535i
$536$	4.13938e6	+	7.16961e6i	0.622333	+	1.07791i
$537$	−175683.			−0.0262903
$538$	−6.57652e6			−0.979582
$539$	−2.08364e6	−	3.60897e6i	−0.308923	−	0.535070i
$540$	162954.	+	282245.i	0.0240482	+	0.0416526i
$541$	3.67365e6	−	6.36296e6i	0.539641	−	0.934686i	−0.459282	−	0.888291i	$-0.651893\pi$
$541$	3.67365e6	−	6.36296e6i	0.539641	−	0.934686i	0.998923	−	0.0463955i	$-0.0147734\pi$
$542$	3.67267e6	−	6.36125e6i	0.537011	−	0.930131i
$543$	84543.7			0.0123050
$544$	−2.16492e6	+	3.74975e6i	−0.313649	+	0.543257i
$545$	−4.89444e6	+	8.47741e6i	−0.705848	+	1.22257i
$546$	−185165.	+	320716.i	−0.0265814	+	0.0460404i
$547$	1.09198e6	+	1.89136e6i	0.156044	+	0.270275i	0.933439	−	0.358737i	$-0.116793\pi$
$547$	1.09198e6	+	1.89136e6i	0.156044	+	0.270275i	−0.777395	+	0.629013i	$0.783459\pi$
$548$	−4.39977e6			−0.625862
$549$	−5.02244e6	−	8.69912e6i	−0.711187	−	1.23181i
$550$	−300145.	+	519866.i	−0.0423082	+	0.0732799i
$551$	−8.84845e6			−1.24162
$552$	95732.8	−	165814.i	0.0133725	−	0.0231619i
$553$	4.75422e6	+	8.23456e6i	0.661099	+	1.14506i
$554$	−1.19477e6	−	2.06940e6i	−0.165390	−	0.286464i
$555$	859764.			0.118480
$556$	−1.87390e6	−	3.24570e6i	−0.257075	−	0.445267i
$557$	8.33597e6			1.13846			0.569230	−	0.822178i	$-0.307241\pi$
$557$	8.33597e6			1.13846			0.569230	+	0.822178i	$0.307241\pi$
$558$	782119.			0.106338
$559$	1.14486e6	+	6.35681e6i	0.154961	+	0.860419i
$560$	5.06225e6			0.682140
$561$	−192588.			−0.0258358
$562$	−66171.9	−	114613.i	−0.00883757	−	0.0153071i
$563$	9.33454e6			1.24114			0.620571	−	0.784150i	$-0.286901\pi$
$563$	9.33454e6			1.24114			0.620571	+	0.784150i	$0.286901\pi$
$564$	−45485.0	−	78782.4i	−0.00602103	−	0.0104287i
$565$	−3.52974e6	−	6.11368e6i	−0.465180	−	0.805716i
$566$	−3.46839e6	+	6.00742e6i	−0.455078	+	0.788219i
$567$	−1.09674e7			−1.43267
$568$	1.40191e6	−	2.42818e6i	0.182326	−	0.315799i
$569$	−1.91530e6	−	3.31740e6i	−0.248002	−	0.429553i	0.714969	−	0.699156i	$-0.246441\pi$
$569$	−1.91530e6	−	3.31740e6i	−0.248002	−	0.429553i	−0.962971	+	0.269603i	$0.913107\pi$
$570$	−471284.			−0.0607569
$571$	−7.28871e6	−	1.26244e7i	−0.935536	−	1.62040i	−0.773676	−	0.633582i	$-0.781584\pi$
$571$	−7.28871e6	−	1.26244e7i	−0.935536	−	1.62040i	−0.161860	−	0.986814i	$-0.551749\pi$
$572$	784472.	−	1.35874e6i	0.100251	−	0.173639i
$573$	−195965.	+	339422.i	−0.0249341	+	0.0431870i
$574$	3.47191e6	−	6.01352e6i	0.439834	−	0.761814i
$575$	−693994.			−0.0875359
$576$	4.01367e6	−	6.95187e6i	0.504063	−	0.873063i
$577$	−4.73153e6	+	8.19524e6i	−0.591646	+	1.02476i	0.402365	+	0.915479i	$0.368188\pi$
$577$	−4.73153e6	+	8.19524e6i	−0.591646	+	1.02476i	−0.994011	+	0.109281i	$0.965145\pi$
$578$	933892.	+	1.61755e6i	0.116273	+	0.201390i
$579$	148164.	+	256628.i	0.0183674	+	0.0318133i
$580$	3.36153e6			0.414922
$581$	1.36066e7			1.67228
$582$	−194419.	−	336743.i	−0.0237920	−	0.0412089i
$583$	−3.19490e6	−	5.53373e6i	−0.389302	−	0.674290i
$584$	7.79031e6	−	1.34932e7i	0.945198	−	1.63713i
$585$	3.94090e6	−	6.82585e6i	0.476109	−	0.824645i
$586$	−1.80829e6			−0.217533
$587$	360633.	−	624635.i	0.0431987	−	0.0748223i	−0.843618	−	0.536944i	$-0.819578\pi$
$587$	360633.	−	624635.i	0.0431987	−	0.0748223i	0.886816	+	0.462122i	$0.152912\pi$
$588$	−100698.	+	174415.i	−0.0120110	+	0.0208037i
$589$	769223.	−	1.33233e6i	0.0913616	−	0.158243i
$590$	−1.16342e6	−	2.01509e6i	−0.137596	−	0.238323i
$591$	596797.			0.0702843
$592$	−3.66448e6	−	6.34706e6i	−0.429742	−	0.744335i
$593$	−5.58315e6	+	9.67029e6i	−0.651992	+	1.12928i	0.330647	+	0.943755i	$0.392733\pi$
$593$	−5.58315e6	+	9.67029e6i	−0.651992	+	1.12928i	−0.982639	+	0.185529i	$0.940600\pi$
$594$	409634.			0.0476354
$595$	5.69923e6	−	9.87136e6i	0.659970	−	1.14310i
$596$	−568998.	−	985533.i	−0.0656138	−	0.113646i
$597$	−172324.	−	298474.i	−0.0197884	−	0.0342745i
$598$	−2.67089e6			−0.305424
$599$	−2.27539e6	−	3.94109e6i	−0.259112	−	0.448796i	0.706892	−	0.707322i	$-0.250097\pi$
$599$	−2.27539e6	−	3.94109e6i	−0.259112	−	0.448796i	−0.966004	+	0.258526i	$0.916763\pi$
$600$	100740.			0.0114242
$601$	8.68908e6			0.981268			0.490634	−	0.871366i	$-0.336765\pi$
$601$	8.68908e6			0.981268			0.490634	+	0.871366i	$0.336765\pi$
$602$	−1.75818e6	−	9.76227e6i	−0.197730	−	1.09789i
$603$	−1.02232e7			−1.14497
$604$	761844.			0.0849716
$605$	3.33638e6	+	5.77879e6i	0.370585	+	0.641872i
$606$	239016.			0.0264390
$607$	7.75543e6	+	1.34328e7i	0.854347	+	1.47977i	0.877249	+	0.480035i	$0.159376\pi$
$607$	7.75543e6	+	1.34328e7i	0.854347	+	1.47977i	−0.0229025	+	0.999738i	$0.507291\pi$
$608$	−4.52212e6	−	7.83254e6i	−0.496116	−	0.859298i
$609$	338638.	−	586538.i	0.0369992	−	0.0640845i
$610$	−1.10529e7			−1.20269
$611$	−2.20331e6	+	3.81624e6i	−0.238766	+	0.413554i
$612$	−1.56155e6	−	2.70468e6i	−0.168530	−	0.291902i
$613$	−4.37654e6			−0.470414			−0.235207	−	0.971945i	$-0.575577\pi$
$613$	−4.37654e6			−0.470414			−0.235207	+	0.971945i	$0.575577\pi$
$614$	−4.38937e6	−	7.60262e6i	−0.469874	−	0.813846i
$615$	220215.	−	381424.i	0.0234779	−	0.0406650i
$616$	−4.18341e6	+	7.24588e6i	−0.444200	+	0.769377i
$617$	315752.	−	546899.i	0.0333913	−	0.0578355i	−0.848847	−	0.528639i	$-0.822703\pi$
$617$	315752.	−	546899.i	0.0333913	−	0.0578355i	0.882238	+	0.470803i	$0.156036\pi$
$618$	22048.5			0.00232224
$619$	−6.46582e6	+	1.11991e7i	−0.678261	+	1.17478i	0.297243	+	0.954802i	$0.403933\pi$
$619$	−6.46582e6	+	1.11991e7i	−0.678261	+	1.17478i	−0.975504	+	0.219981i	$0.929401\pi$
$620$	−292228.	+	506153.i	−0.0305311	+	0.0528814i
$621$	236789.	+	410130.i	0.0246395	+	0.0426769i
$622$	−3.93577e6	−	6.81696e6i	−0.407900	−	0.706504i
$623$	8.55026e6			0.882591
$624$	200232.			0.0205860
$625$	5.64442e6	+	9.77642e6i	0.577988	+	1.00111i
$626$	1.50789e6	+	2.61174e6i	0.153792	+	0.266375i
$627$	201140.	−	348385.i	0.0204329	−	0.0353908i
$628$	−2.05596e6	+	3.56103e6i	−0.208025	+	0.360310i
$629$	−1.65023e7			−1.66310
$630$	−6.05212e6	+	1.04826e7i	−0.607514	+	1.05224i
$631$	526104.	−	911240.i	0.0526016	−	0.0911086i	−0.838526	−	0.544862i	$-0.816582\pi$
$631$	526104.	−	911240.i	0.0526016	−	0.0911086i	0.891127	+	0.453754i	$0.149915\pi$
$632$	4.97729e6	−	8.62092e6i	0.495679	−	0.858540i
$633$	−122828.	−	212744.i	−0.0121839	−	0.0211032i
$634$	1.32407e7			1.30824
$635$	5.24878e6	+	9.09116e6i	0.516564	+	0.894716i
$636$	−154404.	+	267435.i	−0.0151362	+	0.0262166i
$637$	9.75572e6			0.952600
$638$	2.11255e6	−	3.65904e6i	0.205473	−	0.355890i
$639$	1.73119e6	+	2.99850e6i	0.167723	+	0.290504i
$640$	−168822.	−	292409.i	−0.0162922	−	0.0282189i
$641$	1.00920e7			0.970139			0.485069	−	0.874476i	$-0.338794\pi$
$641$	1.00920e7			0.970139			0.485069	+	0.874476i	$0.338794\pi$
$642$	130841.	+	226624.i	0.0125287	+	0.0217004i
$643$	−1.49819e6			−0.142902			−0.0714510	−	0.997444i	$-0.522763\pi$
$643$	−1.49819e6			−0.142902			−0.0714510	+	0.997444i	$0.522763\pi$
$644$	−2.78557e6			−0.264667
$645$	−111518.	−	619199.i	−0.0105547	−	0.0586045i
$646$	9.04584e6			0.852840
$647$	65101.5			0.00611407			0.00305703	−	0.999995i	$-0.499027\pi$
$647$	65101.5			0.00611407			0.00305703	+	0.999995i	$0.499027\pi$
$648$	5.74101e6	+	9.94372e6i	0.537094	+	0.930275i
$649$	1.98615e6			0.185097
$650$	−702648.	−	1.21702e6i	−0.0652311	−	0.112984i
$651$	58877.7	+	101979.i	0.00544500	+	0.00943102i
$652$	−1.32576e6	+	2.29628e6i	−0.122136	+	0.211546i
$653$	−1.02603e7			−0.941626			−0.470813	−	0.882233i	$-0.656039\pi$
$653$	−1.02603e7			−0.941626			−0.470813	+	0.882233i	$0.656039\pi$
$654$	297306.	−	514949.i	0.0271806	−	0.0470782i
$655$	−6.53064e6	−	1.13114e7i	−0.594774	−	1.03018i
$656$	−3.75440e6			−0.340629
$657$	9.62007e6	+	1.66625e7i	0.869491	+	1.50600i
$658$	3.38366e6	−	5.86067e6i	0.304664	−	0.527694i
$659$	−1.08022e7	+	1.87100e7i	−0.968948	+	1.67827i	−0.270338	+	0.962766i	$0.587135\pi$
$659$	−1.08022e7	+	1.87100e7i	−0.968948	+	1.67827i	−0.698611	+	0.715502i	$0.746198\pi$
$660$	−76413.2	+	132352.i	−0.00682824	+	0.0118269i
$661$	8.27281e6			0.736461			0.368230	−	0.929735i	$-0.379964\pi$
$661$	8.27281e6			0.736461			0.368230	+	0.929735i	$0.379964\pi$
$662$	−3.09948e6	+	5.36845e6i	−0.274880	+	0.476106i
$663$	225427.	−	390451.i	0.0199169	−	0.0344971i
$664$	−7.12251e6	−	1.23365e7i	−0.626921	−	1.08586i
$665$	1.19047e7	+	2.06195e7i	1.04391	+	1.80810i
$666$	1.75241e7			1.53091
$667$	4.88463e6			0.425125
$668$	−2.58368e6	−	4.47506e6i	−0.224025	−	0.388023i
$669$	−360399.	−	624229.i	−0.0311328	−	0.0539236i
$670$	−5.62459e6	+	9.74208e6i	−0.484065	+	0.838425i
$671$	4.71730e6	−	8.17061e6i	0.404471	−	0.700564i
$672$	692262.			0.0591354
$673$	−4.93783e6	+	8.55257e6i	−0.420241	+	0.727879i	−0.995963	−	0.0897669i	$-0.971388\pi$
$673$	−4.93783e6	+	8.55257e6i	−0.420241	+	0.727879i	0.575722	+	0.817646i	$0.304721\pi$
$674$	−3.95763e6	+	6.85482e6i	−0.335572	+	0.581227i
$675$	−124587.	+	215791.i	−0.0105248	+	0.0182295i
$676$	−566238.	−	980753.i	−0.0476576	−	0.0825454i
$677$	−1.89768e7			−1.59130			−0.795649	−	0.605757i	$-0.792870\pi$
$677$	−1.89768e7			−1.59130			−0.795649	+	0.605757i	$0.792870\pi$
$678$	214409.	+	371367.i	0.0179130	+	0.0310263i
$679$	−9.82205e6	+	1.70123e7i	−0.817575	+	1.41608i
$680$	−1.19333e7			−0.989663
$681$	−525009.	+	909342.i	−0.0433809	+	0.0751380i
$682$	367301.	+	636183.i	0.0302385	+	0.0523747i
$683$	−8.19754e6	−	1.41986e7i	−0.672407	−	1.16464i	−0.977220	−	0.212230i	$-0.931927\pi$
$683$	−8.19754e6	−	1.41986e7i	−0.672407	−	1.16464i	0.304813	−	0.952412i	$-0.401406\pi$
$684$	6.52358e6			0.533146
$685$	−1.03800e7	−	1.79787e7i	−0.845222	−	1.46397i
$686$	−1.23207e6			−0.0999595
$687$	−5422.08			−0.000438303
$688$	−4.09583e6	+	3.46241e6i	−0.329891	+	0.278873i
$689$	1.49587e7			1.20046
$690$	260164.			0.0208029
$691$	3.09629e6	+	5.36293e6i	0.246687	+	0.427274i	0.962605	−	0.270910i	$-0.0873247\pi$
$691$	3.09629e6	+	5.36293e6i	0.246687	+	0.427274i	−0.715918	+	0.698185i	$0.753991\pi$
$692$	7.39400e6			0.586968
$693$	−5.16599e6	−	8.94776e6i	−0.408621	−	0.707753i
$694$	6.32584e6	+	1.09567e7i	0.498562	+	0.863535i
$695$	8.84188e6	−	1.53146e7i	0.694357	−	1.20266i
$696$	−709053.			−0.0554824
$697$	−4.22682e6	+	7.32107e6i	−0.329558	+	0.570811i
$698$	−3.79879e6	−	6.57970e6i	−0.295125	−	0.511172i
$699$	1.21808e6			0.0942934
$700$	−732818.	−	1.26928e6i	−0.0565263	−	0.0979065i
$701$	−7.45084e6	+	1.29052e7i	−0.572677	+	0.991906i	0.423612	+	0.905844i	$0.360762\pi$
$701$	−7.45084e6	+	1.29052e7i	−0.572677	+	0.991906i	−0.996290	+	0.0860628i	$0.972571\pi$
$702$	−479483.	+	830489.i	−0.0367224	+	0.0636050i
$703$	1.72352e7	−	2.98522e7i	1.31531	−	2.27818i
$704$	7.53963e6			0.573348
$705$	214618.	−	371729.i	0.0162627	−	0.0281679i
$706$	−13005.4	+	22526.1i	−0.000982005	+	0.00170088i
$707$	−6.03755e6	−	1.04574e7i	−0.454268	−	0.786816i
$708$	−47993.4	−	83127.1i	−0.00359831	−	0.00623246i
$709$	1.80621e6			0.134943			0.0674717	−	0.997721i	$-0.478507\pi$
$709$	1.80621e6			0.134943			0.0674717	+	0.997721i	$0.478507\pi$
$710$	3.80984e6			0.283635
$711$	6.14634e6	+	1.06458e7i	0.455976	+	0.789774i
$712$	−4.47572e6	−	7.75217e6i	−0.330874	−	0.573090i
$713$	−424636.	+	735491.i	−0.0312819	+	0.0541818i
$714$	−346192.	+	599622.i	−0.0254139	+	0.0440182i
$715$	7.40295e6			0.541551
$716$	1.33794e6	−	2.31738e6i	0.0975336	−	0.168933i
$717$	−706905.	+	1.22440e6i	−0.0513527	+	0.0889455i
$718$	490009.	−	848721.i	0.0354726	−	0.0614403i
$719$	−4.91633e6	−	8.51534e6i	−0.354666	−	0.614299i	0.632395	−	0.774646i	$-0.282072\pi$
$719$	−4.91633e6	−	8.51534e6i	−0.354666	−	0.614299i	−0.987061	+	0.160347i	$0.948739\pi$
$720$	6.54455e6			0.470488
$721$	−556946.	−	964659.i	−0.0399002	−	0.0691091i
$722$	−4.04284e6	+	7.00240e6i	−0.288631	+	0.499924i
$723$	350976.			0.0249708
$724$	−643854.	+	1.11519e6i	−0.0456500	+	0.0790681i
$725$	1.28503e6	+	2.22574e6i	0.0907964	+	0.157264i
$726$	−202664.	−	351024.i	−0.0142704	−	0.0247170i
$727$	−257638.			−0.0180790			−0.00903950	−	0.999959i	$-0.502877\pi$
$727$	−257638.			−0.0180790			−0.00903950	+	0.999959i	$0.502877\pi$
$728$	−9.79349e6	−	1.69628e7i	−0.684871	−	1.18623i
$729$	−1.40937e7			−0.982216
$730$	2.11710e7			1.47039
$731$	2.14047e6	+	1.18849e7i	0.148155	+	0.822628i
$732$	−455958.			−0.0314519
$733$	−1.73566e7			−1.19317			−0.596587	−	0.802548i	$-0.703477\pi$
$733$	−1.73566e7			−1.19317			−0.596587	+	0.802548i	$0.703477\pi$
$734$	9.39077e6	+	1.62653e7i	0.643370	+	1.11435i
$735$	−950277.			−0.0648832
$736$	2.49636e6	+	4.32381e6i	0.169868	+	0.294220i
$737$	−4.80106e6	−	8.31568e6i	−0.325588	−	0.563935i
$738$	4.48854e6	−	7.77438e6i	0.303364	−	0.525442i
$739$	−5.41470e6			−0.364723			−0.182361	−	0.983232i	$-0.558374\pi$
$739$	−5.41470e6			−0.364723			−0.182361	+	0.983232i	$0.558374\pi$
$740$	−6.54764e6	+	1.13409e7i	−0.439547	+	0.761318i
$741$	470875.	+	815580.i	0.0315036	+	0.0545659i
$742$	−2.29724e7			−1.53178
$743$	−42076.7	−	72879.0i	−0.00279621	−	0.00484318i	0.864624	−	0.502420i	$-0.167557\pi$
$743$	−42076.7	−	72879.0i	−0.00279621	−	0.00484318i	−0.867420	+	0.497576i	$0.834223\pi$
$744$	61640.2	−	106764.i	0.00408255	−	0.00707118i
$745$	2.68478e6	−	4.65017e6i	0.177222	−	0.306957i
$746$	−6.81067e6	+	1.17964e7i	−0.448067	+	0.776074i
$747$	1.75908e7			1.15341
$748$	1.46668e6	−	2.54036e6i	0.0958475	−	0.166013i
$749$	6.61012e6	−	1.14491e7i	0.430531	−	0.745702i
$750$	−285510.	−	494517.i	−0.0185339	−	0.0321017i
$751$	1.47060e7	+	2.54715e7i	0.951469	+	1.64799i	0.742250	+	0.670123i	$0.233759\pi$
$751$	1.47060e7	+	2.54715e7i	0.951469	+	1.64799i	0.209219	+	0.977869i	$0.432908\pi$
$752$	−3.65897e6			−0.235947
$753$	−1.44004e6			−0.0925521
$754$	4.94554e6	+	8.56592e6i	0.316800	+	0.548714i
$755$	1.79735e6	+	3.11311e6i	0.114754	+	0.198759i
$756$	−500071.	+	866148.i	−0.0318219	+	0.0551172i
$757$	1.28831e7	−	2.23142e7i	0.817113	−	1.41528i	−0.0906882	−	0.995879i	$-0.528907\pi$
$757$	1.28831e7	−	2.23142e7i	0.817113	−	1.41528i	0.907801	−	0.419401i	$-0.137760\pi$
$758$	−1.80003e7			−1.13791
$759$	−111036.	+	192320.i	−0.00699615	+	0.0121177i
$760$	1.24632e7	−	2.15869e7i	0.782701	−	1.35568i
$761$	9.62848e6	−	1.66770e7i	0.602693	−	1.04390i	−0.389718	−	0.920934i	$-0.627428\pi$
$761$	9.62848e6	−	1.66770e7i	0.602693	−	1.04390i	0.992411	−	0.122961i	$-0.0392390\pi$
$762$	−318830.	−	552230.i	−0.0198917	−	0.0344534i
$763$	−3.00398e7			−1.86804
$764$	−2.98480e6	−	5.16983e6i	−0.185004	−	0.320437i
$765$	7.36806e6	−	1.27619e7i	0.455197	−	0.788425i
$766$	−4.91241e6			−0.302498
$767$	−2.32481e6	+	4.02670e6i	−0.142692	+	0.247150i
$768$	−440205.	−	762457.i	−0.0269310	−	0.0466458i
$769$	−7.79558e6	−	1.35023e7i	−0.475371	−	0.823366i	0.524231	−	0.851576i	$-0.324353\pi$
$769$	−7.79558e6	−	1.35023e7i	−0.475371	−	0.823366i	−0.999602	+	0.0282095i	$0.991019\pi$
$770$	−1.13688e7			−0.691018
$771$	−179947.	−	311677.i	−0.0109021	−	0.0188829i
$772$	−4.51346e6			−0.272563
$773$	1.30934e7			0.788144			0.394072	−	0.919080i	$-0.371066\pi$
$773$	1.30934e7			0.788144			0.394072	+	0.919080i	$0.371066\pi$
$774$	−2.27301e6	−	1.26208e7i	−0.136379	−	0.757243i
$775$	−446847.			−0.0267242
$776$	2.05658e7			1.22600
$777$	1.31921e6	+	2.28494e6i	0.0783902	+	0.135776i
$778$	6.86601e6			0.406683
$779$	−8.82906e6	−	1.52924e7i	−0.521280	−	0.902883i
$780$	−178886.	−	309839.i	−0.0105278	−	0.0182347i
$781$	−1.62601e6	+	2.81633e6i	−0.0953883	+	0.165217i
$782$	−4.99359e6			−0.292009
$783$	876898.	−	1.51883e6i	0.0511145	−	0.0885330i
$784$	4.05026e6	+	7.01526e6i	0.235339	+	0.407618i
$785$	−1.94018e7			−1.12375
$786$	396695.	+	687095.i	0.0229034	+	0.0396699i
$787$	−2.39735e6	+	4.15234e6i	−0.137973	+	0.238977i	−0.926729	−	0.375730i	$-0.877392\pi$
$787$	−2.39735e6	+	4.15234e6i	−0.137973	+	0.238977i	0.788756	+	0.614706i	$0.210725\pi$
$788$	−4.54499e6	+	7.87215e6i	−0.260746	+	0.451625i
$789$	−208967.	+	361942.i	−0.0119505	+	0.0206988i
$790$	1.35263e7			0.771101
$791$	1.08320e7	−	1.87615e7i	0.615554	−	1.06617i
$792$	−5.40838e6	+	9.36759e6i	−0.306376	+	0.530658i
$793$	1.10433e7	+	1.91276e7i	0.623617	+	1.08014i
$794$	3.04203e6	+	5.26895e6i	0.171243	+	0.296601i
$795$	−1.45709e6			−0.0817651
$796$	5.24943e6			0.293649
$797$	−1.59843e7	−	2.76856e7i	−0.891349	−	1.54386i	−0.838259	−	0.545272i	$-0.816426\pi$
$797$	−1.59843e7	−	2.76856e7i	−0.891349	−	1.54386i	−0.0530902	−	0.998590i	$-0.516907\pi$
$798$	−723132.	−	1.25250e6i	−0.0401985	−	0.0696259i
$799$	−4.11938e6	+	7.13498e6i	−0.228279	+	0.395390i
$800$	−1.31347e6	+	2.27499e6i	−0.0725594	+	0.125677i
$801$	1.10539e7			0.608744
$802$	−1.55481e6	+	2.69301e6i	−0.0853574	+	0.147843i
$803$	−9.03561e6	+	1.56501e7i	−0.494502	+	0.856503i
$804$	−232027.	+	401882.i	−0.0126590	+	0.0219260i
$805$	−6.57175e6	−	1.13826e7i	−0.357430	−	0.619088i
$806$	−1.71972e6			−0.0932440
$807$	−640046.	−	1.10859e6i	−0.0345961	−	0.0599222i
$808$	−6.32083e6	+	1.09480e7i	−0.340601	+	0.589938i
$809$	3.04531e7			1.63591			0.817957	−	0.575279i	$-0.195107\pi$
$809$	3.04531e7			1.63591			0.817957	+	0.575279i	$0.195107\pi$
$810$	−7.80089e6	+	1.35115e7i	−0.417764	+	0.723589i
$811$	1.69647e7	+	2.93837e7i	0.905721	+	1.56875i	0.819947	+	0.572440i	$0.194003\pi$
$811$	1.69647e7	+	2.93837e7i	0.905721	+	1.56875i	0.0857738	+	0.996315i	$0.472664\pi$
$812$	5.15788e6	+	8.93371e6i	0.274525	+	0.475491i
$813$	1.42974e6			0.0758630
$814$	8.22972e6	+	1.42543e7i	0.435336	+	0.754023i
$815$	−1.25110e7			−0.659777
$816$	374360.			0.0196818
$817$	−2.37350e7	−	8.54067e6i	−1.24404	−	0.447648i
$818$	−2.69411e6			−0.140777
$819$	2.41875e7			1.26003
$820$	3.35416e6	+	5.80957e6i	0.174200	+	0.301724i
$821$	−1.74733e7			−0.904725			−0.452363	−	0.891834i	$-0.649419\pi$
$821$	−1.74733e7			−0.904725			−0.452363	+	0.891834i	$0.649419\pi$
$822$	630519.	+	1.09209e6i	0.0325476	+	0.0563740i
$823$	−165489.	−	286636.i	−0.00851667	−	0.0147513i	0.861736	−	0.507358i	$-0.169378\pi$
$823$	−165489.	−	286636.i	−0.00851667	−	0.0147513i	−0.870252	+	0.492606i	$0.836044\pi$
$824$	−583077.	+	1.00992e6i	−0.0299163	+	0.0518166i
$825$	−116844.			−0.00597683
$826$	3.57026e6	−	6.18387e6i	0.182075	−	0.315363i
$827$	−3.76117e6	−	6.51454e6i	−0.191232	−	0.331223i	0.754427	−	0.656384i	$-0.227915\pi$
$827$	−3.76117e6	−	6.51454e6i	−0.191232	−	0.331223i	−0.945659	+	0.325161i	$0.894581\pi$
$828$	−3.60123e6			−0.182547
$829$	−1.67457e7	−	2.90044e7i	−0.846285	−	1.46581i	−0.884501	−	0.466539i	$-0.845501\pi$
$829$	−1.67457e7	−	2.90044e7i	−0.846285	−	1.46581i	0.0382160	−	0.999270i	$-0.487832\pi$
$830$	9.67807e6	−	1.67629e7i	0.487634	−	0.844606i
$831$	232557.	−	402800.i	0.0116822	−	0.0202342i
$832$	−8.82525e6	+	1.52858e7i	−0.441996	+	0.765560i
$833$	1.82396e7			0.910760
$834$	−537088.	+	930264.i	−0.0267381	+	0.0463117i
$835$	1.21909e7	−	2.11152e7i	0.605089	−	1.04804i
$836$	3.06362e6	+	5.30635e6i	0.151607	+	0.262591i
$837$	152463.	+	264073.i	0.00752230	+	0.0130290i
$838$	8.65314e6			0.425661
$839$	−2.36393e6			−0.115939			−0.0579695	−	0.998318i	$-0.518463\pi$
$839$	−2.36393e6			−0.115939			−0.0579695	+	0.998318i	$0.518463\pi$
$840$	953956.	+	1.65230e6i	0.0466477	+	0.0807962i
$841$	1.21098e6	+	2.09748e6i	0.0590401	+	0.102260i
$842$	1.18333e6	−	2.04958e6i	0.0575208	−	0.0996289i
$843$	12880.1	−	22308.9i	0.000624237	−	0.00108121i
$844$	3.74165e6			0.180803
$845$	2.67176e6	−	4.62762e6i	0.128723	−	0.222954i
$846$	4.37445e6	−	7.57676e6i	0.210134	−	0.363964i
$847$	−1.02386e7	+	1.77338e7i	−0.490380	+	0.849362i
$848$	6.21039e6	+	1.07567e7i	0.296571	+	0.513677i
$849$	−1.35021e6			−0.0642884
$850$	−1.31370e6	−	2.27539e6i	−0.0623660	−	0.108021i
$851$	−9.51437e6	+	1.64794e7i	−0.450356	+	0.780040i
$852$	157164.			0.00741745
$853$	1.28880e7	−	2.23226e7i	0.606473	−	1.05044i	−0.385344	−	0.922773i	$-0.625917\pi$
$853$	1.28880e7	−	2.23226e7i	0.606473	−	1.05044i	0.991817	−	0.127669i	$-0.0407496\pi$
$854$	−1.69595e7	−	2.93747e7i	−0.795733	−	1.37825i
$855$	1.53905e7	+	2.66572e7i	0.720009	+	1.24709i
$856$	−1.38405e7			−0.645607
$857$	−1.18789e7	−	2.05749e7i	−0.552491	−	0.956942i	−0.998094	−	0.0617117i	$-0.980344\pi$
$857$	−1.18789e7	−	2.05749e7i	−0.552491	−	0.956942i	0.445603	−	0.895231i	$-0.352989\pi$
$858$	−449682.			−0.0208539
$859$	−3.37108e7			−1.55878			−0.779392	−	0.626537i	$-0.784472\pi$
$859$	−3.37108e7			−1.55878			−0.779392	+	0.626537i	$0.784472\pi$
$860$	9.01693e6	+	3.24460e6i	0.415731	+	0.149594i
$861$	1.35158e6			0.0621348
$862$	−1.96747e7			−0.901860
$863$	324797.	+	562566.i	0.0148452	+	0.0257126i	0.873353	−	0.487089i	$-0.161941\pi$
$863$	324797.	+	562566.i	0.0148452	+	0.0257126i	−0.858507	+	0.512801i	$0.828608\pi$
$864$	1.79260e6			0.0816958
$865$	1.74440e7	+	3.02140e7i	0.792696	+	1.37299i
$866$	1.18390e7	+	2.05057e7i	0.536438	+	0.929138i
$867$	−181778.	+	314849.i	−0.00821285	+	0.0142251i
$868$	−1.79356e6			−0.0808011
$869$	−5.77292e6	+	9.99898e6i	−0.259326	+	0.449165i
$870$	−481731.	−	834383.i	−0.0215778	−	0.0373738i
$871$	2.24789e7			1.00399
$872$	1.57246e7	+	2.72359e7i	0.700309	+	1.21297i
$873$	−1.26981e7	+	2.19938e7i	−0.563901	+	0.976706i
$874$	5.21535e6	−	9.03325e6i	0.230943	−	0.400005i
$875$	−1.44240e7	+	2.49831e7i	−0.636891	+	1.10313i
$876$	873349.			0.0384528
$877$	1.31461e6	−	2.27696e6i	0.0577160	−	0.0999671i	−0.835724	−	0.549150i	$-0.814952\pi$
$877$	1.31461e6	−	2.27696e6i	0.0577160	−	0.0999671i	0.893440	+	0.449183i	$0.148285\pi$
$878$	−7.31863e6	+	1.26762e7i	−0.320401	+	0.554951i
$879$	−175988.	−	304820.i	−0.00768265	−	0.0133067i
$880$	3.07347e6	+	5.32341e6i	0.133790	+	0.231730i
$881$	997781.			0.0433107			0.0216554	−	0.999765i	$-0.493106\pi$
$881$	997781.			0.0433107			0.0216554	+	0.999765i	$0.493106\pi$
$882$	−1.93690e7			−0.838370
$883$	1.20788e7	+	2.09211e7i	0.521342	+	0.902990i	0.999692	+	0.0248210i	$0.00790158\pi$
$883$	1.20788e7	+	2.09211e7i	0.521342	+	0.902990i	−0.478350	+	0.878169i	$0.658765\pi$
$884$	3.43354e6	+	5.94706e6i	0.147778	+	0.255960i
$885$	226454.	−	392229.i	0.00971899	−	0.0168338i
$886$	1.62380e7	−	2.81251e7i	0.694943	−	1.20368i
$887$	−2.64527e7			−1.12891			−0.564456	−	0.825463i	$-0.690914\pi$
$887$	−2.64527e7			−1.12891			−0.564456	+	0.825463i	$0.690914\pi$
$888$	1.38111e6	−	2.39215e6i	0.0587753	−	0.101802i
$889$	−1.61073e7	+	2.78987e7i	−0.683548	+	1.18394i
$890$	6.08161e6	−	1.05337e7i	0.257361	−	0.445763i
$891$	−6.65872e6	−	1.15332e7i	−0.280994	−	0.486695i
$892$	1.09787e7			0.461995
$893$	−8.60464e6	−	1.49037e7i	−0.361080	−	0.625410i
$894$	−163083.	+	282468.i	−0.00682441	+	0.0118202i
$895$	1.26260e7			0.526874
$896$	518078.	−	897337.i	0.0215588	−	0.0373409i
$897$	−259938.	−	450227.i	−0.0107867	−	0.0186831i
$898$	9.54726e6	+	1.65363e7i	0.395083	+	0.684303i
$899$	3.14510e6			0.129788
$900$	−947399.	−	1.64094e6i	−0.0389876	−	0.0675285i
$901$	2.79674e7			1.14773
$902$	8.43167e6			0.345062
$903$	1.47450e6	−	1.24647e6i	0.0601761	−	0.0508699i
$904$	−2.26804e7			−0.923059
$905$	−6.07596e6			−0.246600
$906$	−109178.	−	189101.i	−0.00441890	−	0.00765375i
$907$	4.07350e7			1.64418			0.822091	−	0.569357i	$-0.192808\pi$
$907$	4.07350e7			1.64418			0.822091	+	0.569357i	$0.192808\pi$
$908$	−7.99655e6	−	1.38504e7i	−0.321875	−	0.557505i
$909$	−7.80545e6	−	1.35194e7i	−0.313320	−	0.542686i
$910$	1.33074e7	−	2.30491e7i	0.532709	−	0.922679i
$911$	9.93922e6			0.396786			0.198393	−	0.980123i	$-0.436428\pi$
$911$	9.93922e6			0.396786			0.198393	+	0.980123i	$0.436428\pi$
$912$	−390985.	+	677206.i	−0.0155659	+	0.0269609i
$913$	8.26105e6	+	1.43086e7i	0.327988	+	0.568092i
$914$	1.68823e7			0.668445
$915$	−1.07570e6	−	1.86317e6i	−0.0424756	−	0.0735698i
$916$	41292.6	−	71520.8i	0.00162605	−	0.00281640i
$917$	2.00411e7	−	3.47121e7i	0.787041	−	1.36319i
$918$	−896459.	+	1.55271e6i	−0.0351094	+	0.0608113i
$919$	−2.27558e7			−0.888800			−0.444400	−	0.895828i	$-0.646583\pi$
$919$	−2.27558e7			−0.888800			−0.444400	+	0.895828i	$0.646583\pi$
$920$	−6.88009e6	+	1.19167e7i	−0.267994	+	0.464179i
$921$	854372.	−	1.47982e6i	0.0331893	−	0.0574855i
$922$	−6.42430e6	−	1.11272e7i	−0.248885	−	0.431081i
$923$	−3.80653e6	−	6.59311e6i	−0.147070	−	0.254734i
$924$	−468990.			−0.0180711
$925$	−1.00120e7			−0.384741
$926$	−1.40993e7	−	2.44206e7i	−0.540342	−	0.935899i
$927$	−720029.	−	1.24713e6i	−0.0275201	−	0.0476663i
$928$	9.24473e6	−	1.60123e7i	0.352390	−	0.610358i
$929$	−1.80784e7	+	3.13128e7i	−0.687260	+	1.19037i	0.285460	+	0.958391i	$0.407854\pi$
$929$	−1.80784e7	+	3.13128e7i	−0.687260	+	1.19037i	−0.972721	+	0.231980i	$0.925480\pi$
$930$	167513.			0.00635100
$931$	−1.90496e7	+	3.29949e7i	−0.720299	+	1.24759i
$932$	−9.27641e6	+	1.60672e7i	−0.349817	+	0.605900i
$933$	766081.	−	1.32689e6i	0.0288118	−	0.0499035i
$934$	1.63696e7	+	2.83530e7i	0.614004	+	1.06349i
$935$	1.38408e7			0.517765
$936$	−1.26612e7	−	2.19298e7i	−0.472372	−	0.818173i
$937$	1.36389e7	−	2.36232e7i	0.507493	−	0.879003i	−0.492470	−	0.870330i	$-0.663906\pi$
$937$	1.36389e7	−	2.36232e7i	0.507493	−	0.879003i	0.999962	−	0.00867345i	$-0.00276088\pi$
$938$	−3.45212e7			−1.28109
$939$	−293504.	+	508363.i	−0.0108630	+	0.0188153i
$940$	3.26890e6	+	5.66190e6i	0.120665	+	0.208998i
$941$	6.01275e6	+	1.04144e7i	0.221360	+	0.383407i	0.955221	−	0.295893i	$-0.0956171\pi$
$941$	6.01275e6	+	1.04144e7i	0.221360	+	0.383407i	−0.733861	+	0.679299i	$0.762284\pi$
$942$	1.17854e6			0.0432729
$943$	4.87392e6	+	8.44188e6i	0.178484	+	0.309143i
$944$	−3.86076e6			−0.141008
$945$	−4.71910e6			−0.171901
$946$	9.19845e6	−	7.77591e6i	0.334185	−	0.282503i
$947$	−2.26189e6			−0.0819588			−0.0409794	−	0.999160i	$-0.513048\pi$
$947$	−2.26189e6			−0.0819588			−0.0409794	+	0.999160i	$0.513048\pi$
$948$	557989.			0.0201653
$949$	−2.11526e7	−	3.66374e7i	−0.762428	−	1.32056i
$950$	5.48815e6			0.197295
$951$	1.28862e6	+	2.23196e6i	0.0462034	+	0.0800266i
$952$	−1.83103e7	−	3.17143e7i	−0.654790	−	1.13413i
$953$	−1.57011e7	+	2.71951e7i	−0.560012	+	0.969969i	0.437483	+	0.899227i	$0.355870\pi$
$953$	−1.57011e7	+	2.71951e7i	−0.560012	+	0.969969i	−0.997495	+	0.0707423i	$0.977463\pi$
$954$	−2.96991e7			−1.05651
$955$	1.40836e7	−	2.43935e7i	0.499694	−	0.865496i
$956$	−1.07671e7	−	1.86491e7i	−0.381024	−	0.659953i
$957$	822396.			0.0290269
$958$	−9.75979e6	−	1.69044e7i	−0.343579	−	0.595096i
$959$	3.18539e7	−	5.51725e7i	1.11845	−	1.93721i
$960$	859643.	−	1.48895e6i	0.0301051	−	0.0521436i
$961$	1.40412e7	−	2.43200e7i	0.490450	−	0.849484i
$962$	−3.85321e7			−1.34241
$963$	8.54567e6	−	1.48015e7i	0.296948	−	0.514329i
$964$	−2.67290e6	+	4.62961e6i	−0.0926383	+	0.160454i
$965$	−1.06482e7	−	1.84433e7i	−0.368094	−	0.637558i
$966$	399192.	+	691421.i	0.0137638	+	0.0238396i
$967$	−2.68404e7			−0.923044			−0.461522	−	0.887129i	$-0.652696\pi$
$967$	−2.68404e7			−0.923044			−0.461522	+	0.887129i	$0.652696\pi$
$968$	2.14380e7			0.735353
$969$	880366.	+	1.52484e6i	0.0301199	+	0.0521692i
$970$	1.39724e7	+	2.42009e7i	0.476806	+	0.825852i
$971$	1.64971e7	−	2.85739e7i	0.561514	−	0.972570i	−0.435851	−	0.900019i	$-0.643553\pi$
$971$	1.64971e7	−	2.85739e7i	0.561514	−	0.972570i	0.997365	−	0.0725513i	$-0.0231141\pi$
$972$	−970230.	+	1.68049e6i	−0.0329389	+	0.0570518i
$973$	5.42675e7			1.83763
$974$	1.49079e7	−	2.58213e7i	0.503524	−	0.872129i
$975$	136767.	−	236888.i	0.00460756	−	0.00798053i
$976$	−9.16969e6	+	1.58824e7i	−0.308127	+	0.533692i
$977$	−2.48337e6	−	4.30133e6i	−0.0832350	−	0.144167i	0.821403	−	0.570349i	$-0.193192\pi$
$977$	−2.48337e6	−	4.30133e6i	−0.0832350	−	0.144167i	−0.904638	+	0.426181i	$0.859859\pi$
$978$	759962.			0.0254065
$979$	5.19117e6	+	8.99136e6i	0.173104	+	0.299826i
$980$	7.23696e6	−	1.25348e7i	0.240708	−	0.416919i
$981$	−3.88360e7			−1.28843
$982$	1.78539e7	−	3.09238e7i	0.590817	−	1.02333i
$983$	7.55947e6	+	1.30934e7i	0.249521	+	0.432183i	0.963393	−	0.268093i	$-0.0863934\pi$
$983$	7.55947e6	+	1.30934e7i	0.249521	+	0.432183i	−0.713872	+	0.700276i	$0.753060\pi$
$984$	−707499.	−	1.22542e6i	−0.0232937	−	0.0403459i
$985$	−4.28904e7			−1.40854
$986$	9.24636e6	+	1.60152e7i	0.302886	+	0.524613i
$987$	1.31723e6			0.0430396
$988$	−1.43441e7			−0.467498
$989$	1.31025e7	+	4.71473e6i	0.425954	+	0.153273i
$990$	−1.46978e7			−0.476612
$991$	−3.35327e6			−0.108464			−0.0542318	−	0.998528i	$-0.517271\pi$
$991$	−3.35327e6			−0.108464			−0.0542318	+	0.998528i	$0.517271\pi$
$992$	1.60735e6	+	2.78400e6i	0.0518597	+	0.0898237i
$993$	−1.20660e6			−0.0388320
$994$	5.84576e6	+	1.01252e7i	0.187662	+	0.325039i
$995$	1.23845e7	+	2.14506e7i	0.396572	+	0.686882i
$996$	399242.	−	691507.i	0.0127523	−	0.0220876i
$997$	4.04469e7			1.28869			0.644344	−	0.764736i	$-0.277131\pi$
$997$	4.04469e7			1.28869			0.644344	+	0.764736i	$0.277131\pi$
$998$	8.05622e6	−	1.39538e7i	0.256038	−	0.443471i
$999$	3.41608e6	+	5.91682e6i	0.108296	+	0.187575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.c.a.36.12	yes	34
43.6	even	3	inner	43.6.c.a.6.12	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.c.a.6.12	✓	34	43.6	even	3	inner
43.6.c.a.36.12	yes	34	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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+4.36550 q^{2} +(0.424863 + 0.735884i) q^{3} -12.9424 q^{4} +(-30.5339 - 52.8863i) q^{5} +(1.85474 + 3.21250i) q^{6} +(93.7016 - 162.296i) q^{7} -196.196 q^{8} +(121.139 - 209.819i) q^{9} +O(q^{10})\)	\(q+4.36550 q^{2} +(0.424863 + 0.735884i) q^{3} -12.9424 q^{4} +(-30.5339 - 52.8863i) q^{5} +(1.85474 + 3.21250i) q^{6} +(93.7016 - 162.296i) q^{7} -196.196 q^{8} +(121.139 - 209.819i) q^{9} +(-133.296 - 230.875i) q^{10} +227.558 q^{11} +(-5.49874 - 9.52410i) q^{12} +(-266.361 + 461.350i) q^{13} +(409.055 - 708.503i) q^{14} +(25.9454 - 44.9388i) q^{15} -442.338 q^{16} +(-497.997 + 862.557i) q^{17} +(528.832 - 915.965i) q^{18} +(-1040.23 - 1801.72i) q^{19} +(395.182 + 684.475i) q^{20} +159.241 q^{21} +993.406 q^{22} +(574.238 + 994.609i) q^{23} +(-83.3564 - 144.378i) q^{24} +(-302.137 + 523.317i) q^{25} +(-1162.80 + 2014.02i) q^{26} +412.353 q^{27} +(-1212.72 + 2100.50i) q^{28} +(2126.57 - 3683.33i) q^{29} +(113.265 - 196.180i) q^{30} +(369.739 + 640.406i) q^{31} +4347.25 q^{32} +(96.6811 + 167.457i) q^{33} +(-2174.01 + 3765.49i) q^{34} -11444.3 q^{35} +(-1567.83 + 2715.56i) q^{36} +(8284.34 + 14348.9i) q^{37} +(-4541.11 - 7865.43i) q^{38} -452.667 q^{39} +(5990.63 + 10376.1i) q^{40} +8487.64 q^{41} +695.169 q^{42} +(9259.50 - 7827.52i) q^{43} -2945.15 q^{44} -14795.4 q^{45} +(2506.84 + 4341.97i) q^{46} +8271.90 q^{47} +(-187.933 - 325.509i) q^{48} +(-9156.50 - 15859.5i) q^{49} +(-1318.98 + 2284.54i) q^{50} -846.323 q^{51} +(3447.34 - 5970.97i) q^{52} +(-14039.9 - 24317.9i) q^{53} +1800.13 q^{54} +(-6948.24 - 12034.7i) q^{55} +(-18383.9 + 31841.8i) q^{56} +(883.906 - 1530.97i) q^{57} +(9283.54 - 16079.6i) q^{58} +8728.07 q^{59} +(-335.796 + 581.616i) q^{60} +(20730.1 - 35905.5i) q^{61} +(1614.09 + 2795.69i) q^{62} +(-22701.8 - 39320.7i) q^{63} +33132.7 q^{64} +32532.1 q^{65} +(422.061 + 731.032i) q^{66} +(-21098.2 - 36543.1i) q^{67} +(6445.28 - 11163.6i) q^{68} +(-487.945 + 845.145i) q^{69} -49960.1 q^{70} +(-7145.46 + 12376.3i) q^{71} +(-23767.0 + 41165.6i) q^{72} +(-39706.8 + 68774.1i) q^{73} +(36165.3 + 62640.2i) q^{74} -513.467 q^{75} +(13463.0 + 23318.6i) q^{76} +(21322.6 - 36931.8i) q^{77} -1976.12 q^{78} +(-25368.9 + 43940.3i) q^{79} +(13506.3 + 23393.6i) q^{80} +(-29261.6 - 50682.5i) q^{81} +37052.8 q^{82} +(36303.0 + 62878.6i) q^{83} -2060.97 q^{84} +60823.2 q^{85} +(40422.4 - 34171.0i) q^{86} +3614.00 q^{87} -44646.1 q^{88} +(22812.5 + 39512.3i) q^{89} -64589.2 q^{90} +(49916.8 + 86458.5i) q^{91} +(-7432.01 - 12872.6i) q^{92} +(-314.176 + 544.169i) q^{93} +36111.0 q^{94} +(-63524.3 + 110027. i) q^{95} +(1846.98 + 3199.07i) q^{96} -104823. q^{97} +(-39972.7 - 69234.7i) q^{98} +(27566.2 - 47746.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9}+O(q^{10}) \) 34 * q - 14 * q^2 - 14 * q^3 + 454 * q^4 + 71 * q^5 + 15 * q^6 + 225 * q^7 - 936 * q^8 - 1011 * q^9	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9} - 317 q^{10} + 1326 q^{11} - 648 q^{12} + 1006 q^{13} - 1272 q^{14} + 683 q^{15} + 3574 q^{16} + 200 q^{17} + 1861 q^{18} + 3361 q^{19} + 3825 q^{20} - 1320 q^{21} - 8768 q^{22} + 560 q^{23} - 7382 q^{24} - 3232 q^{25} - 3201 q^{26} - 122 q^{27} + 13934 q^{28} + 8887 q^{29} - 19449 q^{30} - 6749 q^{31} - 19086 q^{32} + 7106 q^{33} + 8423 q^{34} + 31118 q^{35} - 14112 q^{36} - 4514 q^{37} + 7072 q^{38} - 5404 q^{39} - 18519 q^{40} - 28996 q^{41} + 58118 q^{42} - 14998 q^{43} + 71050 q^{44} - 92096 q^{45} + 20052 q^{46} - 10742 q^{47} + 32927 q^{48} + 7472 q^{49} + 20362 q^{50} + 20250 q^{51} + 59532 q^{52} - 50572 q^{53} - 230084 q^{54} + 38544 q^{55} - 40355 q^{56} - 18087 q^{57} - 33436 q^{58} + 112654 q^{59} + 134093 q^{60} - 20120 q^{61} - 31491 q^{62} + 188227 q^{63} + 125164 q^{64} - 36578 q^{65} + 8803 q^{66} - 73824 q^{67} - 128456 q^{68} + 8005 q^{69} - 141610 q^{70} + 142842 q^{71} + 98466 q^{72} - 91624 q^{73} - 99720 q^{74} + 298358 q^{75} + 258288 q^{76} + 68051 q^{77} - 201116 q^{78} + 99734 q^{79} - 31261 q^{80} - 28441 q^{81} - 147772 q^{82} - 47340 q^{83} - 624232 q^{84} - 71734 q^{85} - 115526 q^{86} - 215924 q^{87} - 720684 q^{88} + 60402 q^{89} + 676108 q^{90} + 164172 q^{91} + 78997 q^{92} - 40793 q^{93} - 341874 q^{94} + 123541 q^{95} - 442140 q^{96} + 318476 q^{97} + 217473 q^{98} - 134770 q^{99}+O(q^{100}) \) 34 * q - 14 * q^2 - 14 * q^3 + 454 * q^4 + 71 * q^5 + 15 * q^6 + 225 * q^7 - 936 * q^8 - 1011 * q^9 - 317 * q^10 + 1326 * q^11 - 648 * q^12 + 1006 * q^13 - 1272 * q^14 + 683 * q^15 + 3574 * q^16 + 200 * q^17 + 1861 * q^18 + 3361 * q^19 + 3825 * q^20 - 1320 * q^21 - 8768 * q^22 + 560 * q^23 - 7382 * q^24 - 3232 * q^25 - 3201 * q^26 - 122 * q^27 + 13934 * q^28 + 8887 * q^29 - 19449 * q^30 - 6749 * q^31 - 19086 * q^32 + 7106 * q^33 + 8423 * q^34 + 31118 * q^35 - 14112 * q^36 - 4514 * q^37 + 7072 * q^38 - 5404 * q^39 - 18519 * q^40 - 28996 * q^41 + 58118 * q^42 - 14998 * q^43 + 71050 * q^44 - 92096 * q^45 + 20052 * q^46 - 10742 * q^47 + 32927 * q^48 + 7472 * q^49 + 20362 * q^50 + 20250 * q^51 + 59532 * q^52 - 50572 * q^53 - 230084 * q^54 + 38544 * q^55 - 40355 * q^56 - 18087 * q^57 - 33436 * q^58 + 112654 * q^59 + 134093 * q^60 - 20120 * q^61 - 31491 * q^62 + 188227 * q^63 + 125164 * q^64 - 36578 * q^65 + 8803 * q^66 - 73824 * q^67 - 128456 * q^68 + 8005 * q^69 - 141610 * q^70 + 142842 * q^71 + 98466 * q^72 - 91624 * q^73 - 99720 * q^74 + 298358 * q^75 + 258288 * q^76 + 68051 * q^77 - 201116 * q^78 + 99734 * q^79 - 31261 * q^80 - 28441 * q^81 - 147772 * q^82 - 47340 * q^83 - 624232 * q^84 - 71734 * q^85 - 115526 * q^86 - 215924 * q^87 - 720684 * q^88 + 60402 * q^89 + 676108 * q^90 + 164172 * q^91 + 78997 * q^92 - 40793 * q^93 - 341874 * q^94 + 123541 * q^95 - 442140 * q^96 + 318476 * q^97 + 217473 * q^98 - 134770 * q^99

Introduction

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