LMFDB - Embedded newform 84.6.e.a.71.39

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,6,Mod(71,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("84.71");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	84.e (of order $2$, degree $1$, 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:	$13.4722408643$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.39
Character	$\chi$	$=$	84.71
Dual form			84.6.e.a.71.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.82774 - 4.89937i) q^{2} +(-13.5680 - 7.67518i) q^{3} +(-16.0077 - 27.7084i) q^{4} +64.9508i q^{5} +(-75.9705 + 44.7714i) q^{6} +49.0000i q^{7} +(-181.019 + 0.0757033i) q^{8} +(125.183 + 208.274i) q^{9} +(318.218 + 183.664i) q^{10} +720.274 q^{11} +(4.52680 + 498.810i) q^{12} -598.221 q^{13} +(240.069 + 138.559i) q^{14} +(498.509 - 881.254i) q^{15} +(-511.505 + 887.095i) q^{16} -186.186i q^{17} +(1374.40 - 24.3730i) q^{18} +489.476i q^{19} +(1799.68 - 1039.71i) q^{20} +(376.084 - 664.834i) q^{21} +(2036.75 - 3528.89i) q^{22} +2817.60 q^{23} +(2456.66 + 1388.33i) q^{24} -1093.60 q^{25} +(-1691.62 + 2930.91i) q^{26} +(-99.9478 - 3786.68i) q^{27} +(1357.71 - 784.379i) q^{28} +8215.09i q^{29} +(-2907.94 - 4934.34i) q^{30} +2487.97i q^{31} +(2899.81 + 5014.54i) q^{32} +(-9772.71 - 5528.24i) q^{33} +(-912.196 - 526.487i) q^{34} -3182.59 q^{35} +(3767.04 - 6802.62i) q^{36} +8549.11 q^{37} +(2398.13 + 1384.11i) q^{38} +(8116.69 + 4591.46i) q^{39} +(-4.91698 - 11757.3i) q^{40} +15568.3i q^{41} +(-2193.80 - 3722.56i) q^{42} +5087.01i q^{43} +(-11530.0 - 19957.6i) q^{44} +(-13527.6 + 8130.74i) q^{45} +(7967.46 - 13804.5i) q^{46} -6331.13 q^{47} +(13748.7 - 8110.25i) q^{48} -2401.00 q^{49} +(-3092.43 + 5357.96i) q^{50} +(-1429.01 + 2526.18i) q^{51} +(9576.16 + 16575.7i) q^{52} +3826.91i q^{53} +(-18835.0 - 10218.1i) q^{54} +46782.4i q^{55} +(-3.70946 - 8869.95i) q^{56} +(3756.82 - 6641.23i) q^{57} +(40248.8 + 23230.2i) q^{58} +31508.5 q^{59} +(-32398.1 + 294.019i) q^{60} -44614.0 q^{61} +(12189.5 + 7035.34i) q^{62} +(-10205.4 + 6133.98i) q^{63} +(32768.0 - 27.4075i) q^{64} -38854.9i q^{65} +(-54719.6 + 32247.7i) q^{66} +7746.79i q^{67} +(-5158.91 + 2980.42i) q^{68} +(-38229.4 - 21625.6i) q^{69} +(-8999.54 + 15592.7i) q^{70} -83647.6 q^{71} +(-22676.3 - 37692.2i) q^{72} -7542.09 q^{73} +(24174.7 - 41885.3i) q^{74} +(14838.0 + 8393.59i) q^{75} +(13562.6 - 7835.39i) q^{76} +35293.4i q^{77} +(45447.2 - 26783.2i) q^{78} -68196.2i q^{79} +(-57617.5 - 33222.7i) q^{80} +(-27707.3 + 52144.9i) q^{81} +(76274.7 + 44023.0i) q^{82} +15551.4 q^{83} +(-24441.7 + 221.813i) q^{84} +12092.9 q^{85} +(24923.2 + 14384.8i) q^{86} +(63052.3 - 111463. i) q^{87} +(-130384. + 54.5271i) q^{88} -14099.4i q^{89} +(1583.05 + 89268.3i) q^{90} -29312.8i q^{91} +(-45103.4 - 78071.2i) q^{92} +(19095.6 - 33756.8i) q^{93} +(-17902.8 + 31018.5i) q^{94} -31791.8 q^{95} +(-857.201 - 90293.9i) q^{96} +159911. q^{97} +(-6789.41 + 11763.4i) q^{98} +(90166.3 + 150015. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 20 q^{4} - 114 q^{6} + 44 q^{9} + 668 q^{10} + 786 q^{12} - 3004 q^{16} - 3320 q^{18} + 7120 q^{22} + 16466 q^{24} - 37500 q^{25} - 7448 q^{28} - 35236 q^{30} - 9424 q^{33} + 43360 q^{34} + 50524 q^{36}+ \cdots + 232584 q^{97}+O(q^{100}) $ 60 * q - 20 * q^4 - 114 * q^6 + 44 * q^9 + 668 * q^10 + 786 * q^12 - 3004 * q^16 - 3320 * q^18 + 7120 * q^22 + 16466 * q^24 - 37500 * q^25 - 7448 * q^28 - 35236 * q^30 - 9424 * q^33 + 43360 * q^34 + 50524 * q^36 - 15056 * q^37 - 35468 * q^40 - 20090 * q^42 + 36024 * q^45 + 124416 * q^46 + 88654 * q^48 - 144060 * q^49 - 140108 * q^52 + 19486 * q^54 - 65072 * q^57 + 115616 * q^58 + 164908 * q^60 - 169424 * q^61 + 20116 * q^64 - 98484 * q^66 + 142536 * q^69 + 35868 * q^70 + 121312 * q^72 + 107256 * q^73 + 214836 * q^76 + 263708 * q^78 - 114932 * q^81 - 479624 * q^82 + 40474 * q^84 - 383992 * q^85 - 107320 * q^88 + 423760 * q^90 + 545208 * q^93 - 448512 * q^94 - 751618 * q^96 + 232584 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	2.82774	−	4.89937i	0.499879	−	0.866095i
$2$	2.82774	−	4.89937i	0.499879	−	0.866095i
$3$	−13.5680	−	7.67518i	−0.870390	−	0.492363i
$3$	−13.5680	−	7.67518i	−0.870390	−	0.492363i
$4$	−16.0077	−	27.7084i	−0.500241	−	0.865886i
$5$			64.9508i			1.16187i	0.813948	+	0.580937i	$0.197314\pi$
$5$			64.9508i			1.16187i	−0.813948	+	0.580937i	$0.802686\pi$
$6$	−75.9705	+	44.7714i	−0.861523	+	0.507718i
$7$			49.0000i			0.377964i
$7$			49.0000i			0.377964i
$8$	−181.019	+	0.0757033i	−1.00000	+	0.000418205i
$9$	125.183	+	208.274i	0.515157	+	0.857096i
$10$	318.218	+	183.664i	1.00629	+	0.580797i
$11$	720.274			1.79480			0.897400	−	0.441217i	$-0.145453\pi$
$11$	720.274			1.79480			0.897400	+	0.441217i	$0.145453\pi$
$12$	4.52680	+	498.810i	0.00907483	+	0.999959i
$13$	−598.221			−0.981756			−0.490878	−	0.871228i	$-0.663324\pi$
$13$	−598.221			−0.981756			−0.490878	+	0.871228i	$0.663324\pi$
$14$	240.069	+	138.559i	0.327353	+	0.188937i
$15$	498.509	−	881.254i	0.572064	−	1.01128i
$16$	−511.505	+	887.095i	−0.499517	+	0.866304i
$17$		−	186.186i		−	0.156252i	−0.996943	−	0.0781259i	$-0.975106\pi$
$17$		−	186.186i		−	0.156252i	0.996943	−	0.0781259i	$-0.0248936\pi$
$18$	1374.40	−	24.3730i	0.999843	−	0.0177308i
$19$			489.476i			0.311062i	0.987831	+	0.155531i	$0.0497089\pi$
$19$			489.476i			0.311062i	−0.987831	+	0.155531i	$0.950291\pi$
$20$	1799.68	−	1039.71i	1.00605	−	0.581218i
$21$	376.084	−	664.834i	0.186096	−	0.328976i
$22$	2036.75	−	3528.89i	0.897184	−	1.55447i
$23$	2817.60			1.11061			0.555304	−	0.831648i	$-0.312602\pi$
$23$	2817.60			1.11061			0.555304	+	0.831648i	$0.312602\pi$
$24$	2456.66	+	1388.33i	0.870596	+	0.491999i
$25$	−1093.60			−0.349952
$26$	−1691.62	+	2930.91i	−0.490759	+	0.850294i
$27$	−99.9478	−	3786.68i	−0.0263854	−	0.999652i
$28$	1357.71	−	784.379i	0.327274	−	0.189073i
$29$			8215.09i			1.81392i	0.421220	+	0.906958i	$0.361602\pi$
$29$			8215.09i			1.81392i	−0.421220	+	0.906958i	$0.638398\pi$
$30$	−2907.94	−	4934.34i	−0.589905	−	1.00098i
$31$			2487.97i			0.464987i	0.972598	+	0.232493i	$0.0746884\pi$
$31$			2487.97i			0.464987i	−0.972598	+	0.232493i	$0.925312\pi$
$32$	2899.81	+	5014.54i	0.500604	+	0.865677i
$33$	−9772.71	−	5528.24i	−1.56218	−	0.883694i
$34$	−912.196	−	526.487i	−0.135329	−	0.0781071i
$35$	−3182.59			−0.439147
$36$	3767.04	−	6802.62i	0.484444	−	0.874822i
$37$	8549.11			1.02664			0.513318	−	0.858199i	$-0.328416\pi$
$37$	8549.11			1.02664			0.513318	+	0.858199i	$0.328416\pi$
$38$	2398.13	+	1384.11i	0.269409	+	0.155494i
$39$	8116.69	+	4591.46i	0.854510	+	0.483380i
$40$	−4.91698	−	11757.3i	−0.000485902	−	1.16187i
$41$			15568.3i			1.44637i	0.690653	+	0.723186i	$0.257323\pi$
$41$			15568.3i			1.44637i	−0.690653	+	0.723186i	$0.742677\pi$
$42$	−2193.80	−	3722.56i	−0.191900	−	0.325625i
$43$			5087.01i			0.419557i	0.977749	+	0.209779i	$0.0672743\pi$
$43$			5087.01i			0.419557i	−0.977749	+	0.209779i	$0.932726\pi$
$44$	−11530.0	−	19957.6i	−0.897834	−	1.55409i
$45$	−13527.6	+	8130.74i	−0.995838	+	0.598548i
$46$	7967.46	−	13804.5i	0.555169	−	0.961891i
$47$	−6331.13			−0.418058			−0.209029	−	0.977909i	$-0.567030\pi$
$47$	−6331.13			−0.418058			−0.209029	+	0.977909i	$0.567030\pi$
$48$	13748.7	−	8110.25i	0.861311	−	0.508079i
$49$	−2401.00			−0.142857
$50$	−3092.43	+	5357.96i	−0.174934	+	0.303092i
$51$	−1429.01	+	2526.18i	−0.0769326	+	0.136000i
$52$	9576.16	+	16575.7i	0.491115	+	0.850089i
$53$			3826.91i			0.187137i	0.995613	+	0.0935684i	$0.0298274\pi$
$53$			3826.91i			0.187137i	−0.995613	+	0.0935684i	$0.970173\pi$
$54$	−18835.0	−	10218.1i	−0.878983	−	0.476853i
$55$			46782.4i			2.08533i
$56$	−3.70946	−	8869.95i	−0.000158067	−	0.377964i
$57$	3756.82	−	6641.23i	0.153156	−	0.270745i
$58$	40248.8	+	23230.2i	1.57102	+	0.906739i
$59$	31508.5			1.17841			0.589207	−	0.807982i	$-0.299440\pi$
$59$	31508.5			1.17841			0.589207	+	0.807982i	$0.299440\pi$
$60$	−32398.1	+	294.019i	−1.16183	+	0.0105438i
$61$	−44614.0			−1.53513			−0.767567	−	0.640969i	$-0.778533\pi$
$61$	−44614.0			−1.53513			−0.767567	+	0.640969i	$0.778533\pi$
$62$	12189.5	+	7035.34i	0.402723	+	0.232437i
$63$	−10205.4	+	6133.98i	−0.323952	+	0.194711i
$64$	32768.0	−	27.4075i	1.00000	−	0.000836411i
$65$		−	38854.9i		−	1.14068i
$66$	−54719.6	+	32247.7i	−1.54626	+	0.911253i
$67$			7746.79i			0.210831i	0.994428	+	0.105416i	$0.0336173\pi$
$67$			7746.79i			0.210831i	−0.994428	+	0.105416i	$0.966383\pi$
$68$	−5158.91	+	2980.42i	−0.135296	+	0.0781637i
$69$	−38229.4	−	21625.6i	−0.966661	−	0.546822i
$70$	−8999.54	+	15592.7i	−0.219521	+	0.380343i
$71$	−83647.6			−1.96928			−0.984640	−	0.174598i	$-0.944137\pi$
$71$	−83647.6			−1.96928			−0.984640	+	0.174598i	$0.944137\pi$
$72$	−22676.3	−	37692.2i	−0.515516	−	0.856880i
$73$	−7542.09			−0.165647			−0.0828237	−	0.996564i	$-0.526394\pi$
$73$	−7542.09			−0.165647			−0.0828237	+	0.996564i	$0.526394\pi$
$74$	24174.7	−	41885.3i	0.513194	−	0.889164i
$75$	14838.0	+	8393.59i	0.304595	+	0.172304i
$76$	13562.6	−	7835.39i	0.269344	−	0.155606i
$77$			35293.4i			0.678371i
$78$	45447.2	−	26783.2i	0.845805	−	0.498455i
$79$		−	68196.2i		−	1.22940i	−0.788761	−	0.614699i	$-0.789277\pi$
$79$		−	68196.2i		−	1.22940i	0.788761	−	0.614699i	$-0.210723\pi$
$80$	−57617.5	−	33222.7i	−1.00654	−	0.580376i
$81$	−27707.3	+	52144.9i	−0.469226	+	0.883078i
$82$	76274.7	+	44023.0i	1.25270	+	0.723012i
$83$	15551.4			0.247785			0.123893	−	0.992296i	$-0.460462\pi$
$83$	15551.4			0.247785			0.123893	+	0.992296i	$0.460462\pi$
$84$	−24441.7	+	221.813i	−0.377949	+	0.00342996i
$85$	12092.9			0.181545
$86$	24923.2	+	14384.8i	0.363377	+	0.209728i
$87$	63052.3	−	111463.i	0.893106	−	1.57881i
$88$	−130384.	+	54.5271i	−1.79480	+	0.000750595i
$89$		−	14099.4i		−	0.188680i	−0.995540	−	0.0943400i	$-0.969926\pi$
$89$		−	14099.4i		−	0.188680i	0.995540	−	0.0943400i	$-0.0300741\pi$
$90$	1583.05	+	89268.3i	0.0206009	+	1.16169i
$91$		−	29312.8i		−	0.371069i
$92$	−45103.4	−	78071.2i	−0.555572	−	0.961659i
$93$	19095.6	−	33756.8i	0.228942	−	0.404720i
$94$	−17902.8	+	31018.5i	−0.208978	+	0.362078i
$95$	−31791.8			−0.361415
$96$	−857.201	−	90293.9i	−0.00949302	−	0.999955i
$97$	159911.			1.72563			0.862817	−	0.505517i	$-0.168698\pi$
$97$	159911.			1.72563			0.862817	+	0.505517i	$0.168698\pi$
$98$	−6789.41	+	11763.4i	−0.0714113	+	0.123728i
$99$	90166.3	+	150015.i	0.924605	+	1.53832i
$100$	17506.1	+	30301.9i	0.175061	+	0.303019i
$101$			95605.7i			0.932567i	0.884635	+	0.466284i	$0.154407\pi$
$101$			95605.7i			0.932567i	−0.884635	+	0.466284i	$0.845593\pi$
$102$	8335.82	+	14144.7i	0.0793319	+	0.134615i
$103$			13359.9i			0.124083i	0.998074	+	0.0620414i	$0.0197611\pi$
$103$			13359.9i			0.124083i	−0.998074	+	0.0620414i	$0.980239\pi$
$104$	108290.	−	45.2873i	0.981756	−	0.000410576i
$105$	43181.5	+	24426.9i	0.382229	+	0.216220i
$106$	18749.5	+	10821.5i	0.162078	+	0.0935458i
$107$	−8555.00			−0.0722372			−0.0361186	−	0.999348i	$-0.511499\pi$
$107$	−8555.00			−0.0722372			−0.0361186	+	0.999348i	$0.511499\pi$
$108$	−103323.	+	63385.5i	−0.852385	+	0.522914i
$109$	19313.4			0.155702			0.0778509	−	0.996965i	$-0.475194\pi$
$109$	19313.4			0.155702			0.0778509	+	0.996965i	$0.475194\pi$
$110$	229204.	+	132289.i	1.80610	+	1.04242i
$111$	−115995.	−	65615.9i	−0.893573	−	0.505477i
$112$	−43467.7	−	25063.8i	−0.327432	−	0.188800i
$113$		−	113139.i		−	0.833522i	−0.909016	−	0.416761i	$-0.863165\pi$
$113$		−	113139.i		−	0.833522i	0.909016	−	0.416761i	$-0.136835\pi$
$114$	−21914.5	−	37185.7i	−0.157932	−	0.267987i
$115$			183006.i			1.29039i
$116$	227627.	−	131505.i	1.57064	−	0.907396i
$117$	−74887.3	−	124594.i	−0.505759	−	0.841459i
$118$	89098.0	−	154372.i	0.589065	−	1.02062i
$119$	9123.12			0.0590577
$120$	−90173.0	+	159562.i	−0.571641	+	1.01152i
$121$	357744.			2.22131
$122$	−126157.	+	218580.i	−0.767382	+	1.32957i
$123$	119489.	−	211231.i	0.712140	−	1.25891i
$124$	68937.5	−	39826.7i	0.402625	−	0.232606i
$125$			131941.i			0.755274i
$126$	1194.28	+	67345.6i	0.00670161	+	0.377905i
$127$		−	55036.9i		−	0.302792i	−0.988473	−	0.151396i	$-0.951623\pi$
$127$		−	55036.9i		−	0.302792i	0.988473	−	0.151396i	$-0.0483769\pi$
$128$	92525.2	−	160620.i	0.499155	−	0.866513i
$129$	39043.7	−	69020.7i	0.206575	−	0.365178i
$130$	−190365.	−	109872.i	−0.987935	−	0.570201i
$131$	−101471.			−0.516611			−0.258305	−	0.966063i	$-0.583164\pi$
$131$	−101471.			−0.516611			−0.258305	+	0.966063i	$0.583164\pi$
$132$	3260.54	+	359280.i	0.0162875	+	1.79473i
$133$	−23984.3			−0.117570
$134$	37954.4	+	21905.9i	0.182600	+	0.105390i
$135$	245948.	−	6491.68i	1.16147	−	0.0306565i
$136$	14.0949	+	33703.3i	6.53454e−5	+	0.156252i
$137$		−	301854.i		−	1.37403i	−0.726644	−	0.687015i	$-0.758921\pi$
$137$		−	301854.i		−	1.37403i	0.726644	−	0.687015i	$-0.241079\pi$
$138$	−214055.	+	126148.i	−0.956814	+	0.563876i
$139$		−	160398.i		−	0.704147i	−0.935972	−	0.352073i	$-0.885477\pi$
$139$		−	160398.i		−	0.704147i	0.935972	−	0.352073i	$-0.114523\pi$
$140$	50946.0	+	88184.2i	0.219680	+	0.380251i
$141$	85900.9	+	48592.5i	0.363873	+	0.205836i
$142$	−236534.	+	409821.i	−0.984402	+	1.70558i
$143$	−430883.			−1.76206
$144$	−248791.	+	4516.03i	−0.999835	+	0.0181489i
$145$	−533576.			−2.10754
$146$	−21327.1	+	36951.5i	−0.0828037	+	0.143466i
$147$	32576.9	+	18428.1i	0.124341	+	0.0703376i
$148$	−136852.	−	236882.i	−0.513566	−	0.888949i
$149$			336852.i			1.24301i	0.783411	+	0.621504i	$0.213478\pi$
$149$			336852.i			1.24301i	−0.783411	+	0.621504i	$0.786522\pi$
$150$	83081.5	−	48962.1i	0.301492	−	0.177677i
$151$		−	130840.i		−	0.466978i	−0.972359	−	0.233489i	$-0.924986\pi$
$151$		−	130840.i		−	0.466978i	0.972359	−	0.233489i	$-0.0750143\pi$
$152$	−37.0549	−	88604.6i	−0.000130088	−	0.311062i
$153$	38777.8	−	23307.4i	0.133923	−	0.0804943i
$154$	172916.	+	99800.8i	0.587534	+	0.339104i
$155$	−161595.			−0.540256
$156$	−2708.03	−	298399.i	−0.00890927	−	0.981715i
$157$	441607.			1.42984			0.714919	−	0.699207i	$-0.246464\pi$
$157$	441607.			1.42984			0.714919	+	0.699207i	$0.246464\pi$
$158$	−334119.	−	192842.i	−1.06478	−	0.614551i
$159$	29372.3	−	51923.7i	0.0921392	−	0.162882i
$160$	−325698.	+	188345.i	−1.00581	+	0.581638i
$161$			138063.i			0.419770i
$162$	177128.	+	283201.i	0.530273	+	0.847827i
$163$		−	125661.i		−	0.370451i	−0.982696	−	0.185226i	$-0.940698\pi$
$163$		−	125661.i		−	0.370451i	0.982696	−	0.185226i	$-0.0593016\pi$
$164$	431371.	−	249212.i	1.25239	−	0.723536i
$165$	359063.	−	634745.i	1.02674	−	1.81505i
$166$	43975.5	−	76192.3i	0.123863	−	0.214605i
$167$	−384584.			−1.06709			−0.533544	−	0.845772i	$-0.679140\pi$
$167$	−384584.			−1.06709			−0.533544	+	0.845772i	$0.679140\pi$
$168$	−68028.1	+	120376.i	−0.185958	+	0.329054i
$169$	−13424.4			−0.0361557
$170$	34195.7	−	59247.8i	0.0907506	−	0.157235i
$171$	−101945.	+	61274.2i	−0.266610	+	0.160246i
$172$	140953.	−	81431.4i	0.363289	−	0.209880i
$173$		−	291106.i		−	0.739497i	−0.929132	−	0.369748i	$-0.879444\pi$
$173$		−	291106.i		−	0.739497i	0.929132	−	0.369748i	$-0.120556\pi$
$174$	−367801.	−	624105.i	−0.920959	−	1.56273i
$175$		−	53586.5i		−	0.132270i
$176$	−368424.	+	638952.i	−0.896534	+	1.55484i
$177$	−427509.	−	241834.i	−1.02568	−	0.580208i
$178$	−69078.2	−	39869.5i	−0.163415	−	0.0943172i
$179$	730752.			1.70466			0.852329	−	0.523006i	$-0.175189\pi$
$179$	730752.			1.70466			0.852329	+	0.523006i	$0.175189\pi$
$180$	441835.	+	244672.i	1.01643	+	0.562863i
$181$	−315322.			−0.715414			−0.357707	−	0.933834i	$-0.616441\pi$
$181$	−315322.			−0.715414			−0.357707	+	0.933834i	$0.616441\pi$
$182$	−143615.	−	82889.2i	−0.321381	−	0.185490i
$183$	605324.	+	342420.i	1.33616	+	0.755843i
$184$	−510041.	+	213.302i	−1.11061	+	0.000464462i
$185$			555271.i			1.19282i
$186$	−111390.	−	189012.i	−0.236082	−	0.400597i
$187$		−	134105.i		−	0.280441i
$188$	101347.	+	175425.i	0.209130	+	0.361990i
$189$	185547.	−	4897.44i	0.377833	−	0.00997274i
$190$	−89899.2	+	155760.i	−0.180664	+	0.313020i
$191$	−588590.			−1.16743			−0.583713	−	0.811960i	$-0.698401\pi$
$191$	−588590.			−1.16743			−0.583713	+	0.811960i	$0.698401\pi$
$192$	−444808.	−	251128.i	−0.870801	−	0.491635i
$193$	−796389.			−1.53898			−0.769488	−	0.638661i	$-0.779489\pi$
$193$	−796389.			−1.53898			−0.769488	+	0.638661i	$0.779489\pi$
$194$	452187.	−	783463.i	0.862608	−	1.49456i
$195$	−298219.	+	527185.i	−0.561627	+	0.992834i
$196$	38434.5	+	66527.8i	0.0714631	+	0.123698i
$197$			532104.i			0.976856i	0.872604	+	0.488428i	$0.162430\pi$
$197$			532104.i			0.976856i	−0.872604	+	0.488428i	$0.837570\pi$
$198$	989945.	−	17555.3i	1.79452	−	0.0318232i
$199$			564156.i			1.00987i	0.863157	+	0.504936i	$0.168484\pi$
$199$			564156.i			1.00987i	−0.863157	+	0.504936i	$0.831516\pi$
$200$	197963.	−	82.7892i	0.349952	−	0.000146352i
$201$	59458.0	−	105109.i	0.103805	−	0.183505i
$202$	468408.	+	270348.i	0.807692	+	0.466171i
$203$	−402539.			−0.685596
$204$	92871.6	−	842.829i	0.156245	−	0.00141796i
$205$	−1.01117e6			−1.68050
$206$	65455.3	+	37778.5i	0.107467	+	0.0620264i
$207$	352717.	+	586834.i	0.572137	+	0.951897i
$208$	305993.	−	530679.i	0.490404	−	0.850499i
$209$			352557.i			0.558295i
$210$	241783.	−	142489.i	0.378336	−	0.222963i
$211$			797229.i			1.23276i	0.787451	+	0.616378i	$0.211400\pi$
$211$			797229.i			1.23276i	−0.787451	+	0.616378i	$0.788600\pi$
$212$	106037.	−	61260.2i	0.162039	−	0.0936136i
$213$	1.13493e6	+	642010.i	1.71404	+	0.969601i
$214$	−24191.4	+	41914.1i	−0.0361099	+	0.0625642i
$215$	−330405.			−0.487473
$216$	18379.1	+	685454.i	0.0268035	+	0.999641i
$217$	−121910.			−0.175748
$218$	54613.5	−	94623.8i	0.0778321	−	0.134853i
$219$	102331.	+	57886.9i	0.144178	+	0.0815586i
$220$	1.29626e6	−	748879.i	1.80566	−	1.04317i
$221$			111381.i			0.153401i
$222$	−649480.	+	382756.i	−0.884470	+	0.521242i
$223$		−	829017.i		−	1.11635i	−0.829722	−	0.558176i	$-0.811501\pi$
$223$		−	829017.i		−	1.11635i	0.829722	−	0.558176i	$-0.188499\pi$
$224$	−245712.	+	142090.i	−0.327195	+	0.189210i
$225$	−136901.	−	227769.i	−0.180281	−	0.299943i
$226$	−554311.	−	319929.i	−0.721909	−	0.416660i
$227$	718262.			0.925163			0.462581	−	0.886577i	$-0.346923\pi$
$227$	718262.			0.925163			0.462581	+	0.886577i	$0.346923\pi$
$228$	−244155.	+	2215.76i	−0.311049	+	0.00282284i
$229$	551880.			0.695435			0.347717	−	0.937599i	$-0.386957\pi$
$229$	551880.			0.695435			0.347717	+	0.937599i	$0.386957\pi$
$230$	896613.	+	517493.i	1.11760	+	0.645037i
$231$	270884.	−	478863.i	0.334005	−	0.590447i
$232$	−621.909	−	1.48709e6i	−0.000758590	−	1.81392i
$233$		−	361283.i		−	0.435971i	−0.975952	−	0.217986i	$-0.930051\pi$
$233$		−	361283.i		−	0.435971i	0.975952	−	0.217986i	$-0.0699486\pi$
$234$	−822195.	+	14580.5i	−0.981601	+	0.0174073i
$235$		−	411211.i		−	0.485731i
$236$	−504380.	−	873049.i	−0.589492	−	1.02037i
$237$	−523419.	+	925289.i	−0.605311	+	1.07006i
$238$	25797.9	−	44697.6i	0.0295217	−	0.0511495i
$239$	542842.			0.614722			0.307361	−	0.951593i	$-0.400554\pi$
$239$	542842.			0.614722			0.307361	+	0.951593i	$0.400554\pi$
$240$	526767.	+	892991.i	0.590324	+	1.00073i
$241$	−1.09992e6			−1.21988			−0.609940	−	0.792448i	$-0.708806\pi$
$241$	−1.09992e6			−1.21988			−0.609940	+	0.792448i	$0.708806\pi$
$242$	1.01161e6	−	1.75272e6i	1.11039	−	1.92387i
$243$	776155.	−	494845.i	0.843205	−	0.537593i
$244$	714168.	+	1.23618e6i	0.767937	+	1.32925i
$245$		−	155947.i		−	0.165982i
$246$	−697013.	−	1.18273e6i	−0.734350	−	1.24608i
$247$		−	292815.i		−	0.305387i
$248$	−188.347	−	450370.i	−0.000194460	−	0.464987i
$249$	−211002.	−	119360.i	−0.215670	−	0.122000i
$250$	646428.	+	373095.i	0.654139	+	0.377546i
$251$	1.14192e6			1.14406			0.572031	−	0.820232i	$-0.306156\pi$
$251$	1.14192e6			1.14406			0.572031	+	0.820232i	$0.306156\pi$
$252$	333328.	+	184585.i	0.330652	+	0.183103i
$253$	2.02945e6			1.99332
$254$	−269646.	−	155630.i	−0.262247	−	0.151359i
$255$	−164077.	−	92815.5i	−0.158015	−	0.0893861i
$256$	−525300.	−	907508.i	−0.500965	−	0.865467i
$257$			562917.i			0.531633i	0.964024	+	0.265816i	$0.0856415\pi$
$257$			562917.i			0.531633i	−0.964024	+	0.265816i	$0.914359\pi$
$258$	−227753.	−	386463.i	−0.213017	−	0.361458i
$259$			418906.i			0.388032i
$260$	−1.07661e6	+	621979.i	−0.987696	+	0.570614i
$261$	−1.71099e6	+	1.02839e6i	−1.55470	+	0.934452i
$262$	−286934.	+	497144.i	−0.258243	+	0.447434i
$263$	235877.			0.210279			0.105140	−	0.994457i	$-0.466471\pi$
$263$	235877.			0.210279			0.105140	+	0.994457i	$0.466471\pi$
$264$	1.76947e6	+	999978.i	1.56255	+	0.883040i
$265$	−248561.			−0.217429
$266$	−67821.5	+	117508.i	−0.0587710	+	0.101827i
$267$	−108215.	+	191301.i	−0.0928990	+	0.164225i
$268$	214651.	−	124008.i	0.182556	−	0.105466i
$269$		−	1.28468e6i		−	1.08246i	−0.840873	−	0.541232i	$-0.817958\pi$
$269$		−	1.28468e6i		−	1.08246i	0.840873	−	0.541232i	$-0.182042\pi$
$270$	663671.	−	1.22335e6i	0.554043	−	1.02127i
$271$		−	1.94474e6i		−	1.60856i	−0.594247	−	0.804282i	$-0.702550\pi$
$271$		−	1.94474e6i		−	1.60856i	0.594247	−	0.804282i	$-0.297450\pi$
$272$	165165.	+	95235.3i	0.135362	+	0.0780505i
$273$	−224981.	+	397718.i	−0.182701	+	0.322975i
$274$	−1.47890e6	−	853567.i	−1.19004	−	0.686849i
$275$	−787693.			−0.628095
$276$	12754.7	+	1.40545e6i	0.0100786	+	1.11056i
$277$	−573507.			−0.449096			−0.224548	−	0.974463i	$-0.572091\pi$
$277$	−573507.			−0.449096			−0.224548	+	0.974463i	$0.572091\pi$
$278$	−785852.	−	453566.i	−0.609858	−	0.351988i
$279$	−518180.	+	311452.i	−0.398538	+	0.239541i
$280$	576110.	−	240.932i	0.439147	−	0.000183654i
$281$		−	1.07722e6i		−	0.813839i	−0.913464	−	0.406920i	$-0.866603\pi$
$281$		−	1.07722e6i		−	0.813839i	0.913464	−	0.406920i	$-0.133397\pi$
$282$	480979.	−	283454.i	0.360166	−	0.212256i
$283$			1.71527e6i			1.27311i	0.771232	+	0.636554i	$0.219641\pi$
$283$			1.71527e6i			1.27311i	−0.771232	+	0.636554i	$0.780359\pi$
$284$	1.33901e6	+	2.31774e6i	0.985115	+	1.70517i
$285$	431353.	+	244008.i	0.314572	+	0.177948i
$286$	−1.21843e6	+	2.11106e6i	−0.880815	+	1.52611i
$287$	−762844.			−0.546677
$288$	−681392.	+	1.23169e6i	−0.484078	+	0.875025i
$289$	1.38519e6			0.975585
$290$	−1.50882e6	+	2.61419e6i	−1.05352	+	1.82533i
$291$	−2.16968e6	−	1.22734e6i	−1.50197	−	0.849638i
$292$	120732.	+	208979.i	0.0828637	+	0.143432i
$293$			1.55108e6i			1.05552i	0.849394	+	0.527759i	$0.176967\pi$
$293$			1.55108e6i			1.05552i	−0.849394	+	0.527759i	$0.823033\pi$
$294$	182405.	−	107496.i	0.123075	−	0.0725312i
$295$			2.04650e6i			1.36917i
$296$	−1.54755e6	+	647.195i	−1.02664	+	0.000429345i
$297$	−71989.8	−	2.72745e6i	−0.0473565	−	1.79418i
$298$	1.65037e6	+	952532.i	1.07656	+	0.621354i
$299$	−1.68555e6			−1.09034
$300$	−4950.52	−	545499.i	−0.00317576	−	0.349938i
$301$	−249263.			−0.158578
$302$	−641032.	−	369981.i	−0.404448	−	0.233433i
$303$	733791.	−	1.29718e6i	0.459162	−	0.811697i
$304$	−434212.	−	250370.i	−0.269474	−	0.155381i
$305$		−	2.89771e6i		−	1.78363i
$306$	−4537.92	−	255894.i	−0.00277047	−	0.156227i
$307$		−	1.80336e6i		−	1.09204i	−0.837773	−	0.546018i	$-0.816143\pi$
$307$		−	1.80336e6i		−	1.09204i	0.837773	−	0.546018i	$-0.183857\pi$
$308$	977923.	−	564968.i	0.587392	−	0.339349i
$309$	102540.	−	181268.i	0.0610938	−	0.108000i
$310$	−456951.	+	791716.i	−0.270063	+	0.467913i
$311$	1.87095e6			1.09689			0.548444	−	0.836187i	$-0.315220\pi$
$311$	1.87095e6			1.09689			0.548444	+	0.836187i	$0.315220\pi$
$312$	−1.46962e6	−	830528.i	−0.854712	−	0.483023i
$313$	68930.7			0.0397697			0.0198848	−	0.999802i	$-0.493670\pi$
$313$	68930.7			0.0397697			0.0198848	+	0.999802i	$0.493670\pi$
$314$	1.24875e6	−	2.16360e6i	0.714746	−	1.23838i
$315$	−398406.	−	662851.i	−0.226230	−	0.376391i
$316$	−1.88961e6	+	1.09167e6i	−1.06452	+	0.614996i
$317$			97626.4i			0.0545656i	0.999628	+	0.0272828i	$0.00868546\pi$
$317$			97626.4i			0.0545656i	−0.999628	+	0.0272828i	$0.991315\pi$
$318$	−171336.	−	290733.i	−0.0950128	−	0.161223i
$319$			5.91712e6i			3.25562i
$320$	1780.14	+	2.12831e6i	0.000971804	+	1.16187i
$321$	116075.	+	65661.2i	0.0628745	+	0.0355669i
$322$	676420.	+	390406.i	0.363561	+	0.209834i
$323$	91133.7			0.0486041
$324$	1.88838e6	−	66996.5i	0.999371	−	0.0354560i
$325$	654216.			0.343568
$326$	−615660.	−	355337.i	−0.320846	−	0.185181i
$327$	−262046.	−	148234.i	−0.135521	−	0.0766618i
$328$	−1178.57	−	2.81815e6i	−0.000604881	−	1.44637i
$329$		−	310225.i		−	0.158011i
$330$	−2.09451e6	−	3.55408e6i	−1.05876	−	1.79656i
$331$		−	881905.i		−	0.442438i	−0.975224	−	0.221219i	$-0.928997\pi$
$331$		−	881905.i		−	0.442438i	0.975224	−	0.221219i	$-0.0710035\pi$
$332$	−248943.	−	430905.i	−0.123952	−	0.214554i
$333$	1.07020e6	+	1.78056e6i	0.528879	+	0.879925i
$334$	−1.08751e6	+	1.88422e6i	−0.533415	+	0.924200i
$335$	−503160.			−0.244959
$336$	397402.	+	673688.i	0.192036	+	0.325545i
$337$	2.80428e6			1.34507			0.672537	−	0.740064i	$-0.265205\pi$
$337$	2.80428e6			1.34507			0.672537	+	0.740064i	$0.265205\pi$
$338$	−37960.7	+	65771.0i	−0.0180735	+	0.0313143i
$339$	−868364.	+	1.53508e6i	−0.410395	+	0.725489i
$340$	−193580.	−	335075.i	−0.0908164	−	0.157197i
$341$			1.79202e6i			0.834559i
$342$	11930.0	+	672735.i	0.00551538	+	0.311013i
$343$		−	117649.i		−	0.0539949i
$344$	−385.103	−	920847.i	−0.000175461	−	0.419557i
$345$	1.40460e6	−	2.48303e6i	0.635338	−	1.12314i
$346$	−1.42624e6	−	823174.i	−0.640475	−	0.369659i
$347$	743525.			0.331491			0.165746	−	0.986169i	$-0.446997\pi$
$347$	743525.			0.331491			0.165746	+	0.986169i	$0.446997\pi$
$348$	−4.09777e6	+	37188.1i	−1.81384	+	0.0164610i
$349$	2.73787e6			1.20323			0.601615	−	0.798786i	$-0.294524\pi$
$349$	2.73787e6			1.20323			0.601615	+	0.798786i	$0.294524\pi$
$350$	−262540.	−	151529.i	−0.114558	−	0.0661188i
$351$	59790.9	+	2.26527e6i	0.0259040	+	0.981414i
$352$	2.08866e6	+	3.61184e6i	0.898484	+	1.55372i
$353$			531128.i			0.226862i	0.993546	+	0.113431i	$0.0361842\pi$
$353$			531128.i			0.226862i	−0.993546	+	0.113431i	$0.963816\pi$
$354$	−2.39372e6	+	1.41068e6i	−1.01523	+	0.598303i
$355$		−	5.43297e6i		−	2.28806i
$356$	−390671.	+	225699.i	−0.163375	+	0.0943855i
$357$	−123783.	−	70021.6i	−0.0514032	−	0.0290778i
$358$	2.06638e6	−	3.58023e6i	0.852123	−	1.47640i
$359$	−237354.			−0.0971986			−0.0485993	−	0.998818i	$-0.515476\pi$
$359$	−237354.			−0.0971986			−0.0485993	+	0.998818i	$0.515476\pi$
$360$	2.44814e6	−	1.47285e6i	0.995587	−	0.598964i
$361$	2.23651e6			0.903240
$362$	−891649.	+	1.54488e6i	−0.357621	+	0.619617i
$363$	−4.85389e6	−	2.74575e6i	−1.93341	−	1.09369i
$364$	−812210.	+	469232.i	−0.321303	+	0.185624i
$365$		−	489864.i		−	0.192461i
$366$	3.38935e6	−	1.99743e6i	1.32255	−	0.779416i
$367$		−	3.71616e6i		−	1.44022i	−0.693859	−	0.720111i	$-0.744091\pi$
$367$		−	3.71616e6i		−	1.44022i	0.693859	−	0.720111i	$-0.255909\pi$
$368$	−1.44122e6	+	2.49948e6i	−0.554767	+	0.962123i
$369$	−3.24247e6	+	1.94888e6i	−1.23968	+	0.745109i
$370$	2.72048e6	+	1.57016e6i	1.03310	+	0.596267i
$371$	−187519.			−0.0707310
$372$	−1.24102e6	+	11262.5i	−0.464968	+	0.00421968i
$373$	−1.53507e6			−0.571291			−0.285645	−	0.958335i	$-0.592208\pi$
$373$	−1.53507e6			−0.571291			−0.285645	+	0.958335i	$0.592208\pi$
$374$	−657031.	−	379215.i	−0.242889	−	0.140187i
$375$	1.01267e6	−	1.79018e6i	0.371869	−	0.657383i
$376$	1.14606e6	−	479.287i	0.418058	−	0.000174834i
$377$		−	4.91444e6i		−	1.78082i
$378$	500685.	−	922913.i	0.180233	−	0.332224i
$379$			1.34810e6i			0.482084i	0.970515	+	0.241042i	$0.0774892\pi$
$379$			1.34810e6i			0.482084i	−0.970515	+	0.241042i	$0.922511\pi$
$380$	508915.	+	880899.i	0.180795	+	0.312944i
$381$	−422418.	+	746742.i	−0.149084	+	0.263547i
$382$	−1.66438e6	+	2.88372e6i	−0.583572	+	1.01110i
$383$	1.96799e6			0.685528			0.342764	−	0.939421i	$-0.388637\pi$
$383$	1.96799e6			0.685528			0.342764	+	0.939421i	$0.388637\pi$
$384$	−2.48817e6	+	1.46915e6i	−0.861098	+	0.508439i
$385$	−2.29234e6			−0.788182
$386$	−2.25198e6	+	3.90181e6i	−0.769302	+	1.33290i
$387$	−1.05949e6	+	636808.i	−0.359601	+	0.216138i
$388$	−2.55981e6	−	4.43087e6i	−0.863233	−	1.49420i
$389$			3.46309e6i			1.16035i	0.814491	+	0.580176i	$0.197016\pi$
$389$			3.46309e6i			1.16035i	−0.814491	+	0.580176i	$0.802984\pi$
$390$	1.73959e6	+	2.95183e6i	0.579143	+	0.982720i
$391$		−	524599.i		−	0.173534i
$392$	434627.	−	181.764i	0.142857	−	5.97436e-5i
$393$	1.37676e6	+	778808.i	0.449653	+	0.254360i
$394$	2.60697e6	+	1.50465e6i	0.846050	+	0.488310i
$395$	4.42940e6			1.42841
$396$	2.71330e6	−	4.89975e6i	0.869481	−	1.57013i
$397$	1.27685e6			0.406596			0.203298	−	0.979117i	$-0.434834\pi$
$397$	1.27685e6			0.406596			0.203298	+	0.979117i	$0.434834\pi$
$398$	2.76401e6	+	1.59529e6i	0.874645	+	0.504814i
$399$	325420.	+	184084.i	0.102332	+	0.0578874i
$400$	559383.	−	970129.i	0.174807	−	0.303165i
$401$		−	2.02569e6i		−	0.629088i	−0.949243	−	0.314544i	$-0.898148\pi$
$401$		−	2.02569e6i		−	0.629088i	0.949243	−	0.314544i	$-0.101852\pi$
$402$	−346835.	−	588528.i	−0.107043	−	0.181636i
$403$		−	1.48836e6i		−	0.456503i
$404$	2.64908e6	−	1.53043e6i	0.807497	−	0.466509i
$405$	−3.38685e6	−	1.79961e6i	−1.02603	−	0.545182i
$406$	−1.13828e6	+	1.97219e6i	−0.342715	+	0.593791i
$407$	6.15770e6			1.84261
$408$	258488.	−	457396.i	0.0768758	−	0.136032i
$409$	−1.79594e6			−0.530863			−0.265432	−	0.964130i	$-0.585514\pi$
$409$	−1.79594e6			−0.530863			−0.265432	+	0.964130i	$0.585514\pi$
$410$	−2.85933e6	+	4.95410e6i	−0.840049	+	1.45548i
$411$	−2.31679e6	+	4.09557e6i	−0.676521	+	1.19594i
$412$	370182.	−	213862.i	0.107442	−	0.0620713i
$413$			1.54392e6i			0.445399i
$414$	3.87251e6	−	68673.5i	1.11043	−	0.0196919i
$415$			1.01008e6i			0.287895i
$416$	−1.73473e6	−	2.99980e6i	−0.491470	−	0.849883i
$417$	−1.23109e6	+	2.17629e6i	−0.346696	+	0.612882i
$418$	1.72731e6	+	996941.i	0.483536	+	0.279080i
$419$	960650.			0.267319			0.133660	−	0.991027i	$-0.457327\pi$
$419$	960650.			0.267319			0.133660	+	0.991027i	$0.457327\pi$
$420$	−14407.0	−	1.58751e6i	−0.00398519	−	0.439129i
$421$	1.37453e6			0.377963			0.188981	−	0.981981i	$-0.439481\pi$
$421$	1.37453e6			0.377963			0.188981	+	0.981981i	$0.439481\pi$
$422$	3.90592e6	+	2.25436e6i	1.06768	+	0.616229i
$423$	−792551.	−	1.31861e6i	−0.215365	−	0.358315i
$424$	−289.710	−	692746.i	−7.82616e−5	−	0.187137i
$425$			203614.i			0.0546807i
$426$	6.35475e6	−	3.74502e6i	1.69658	−	0.999839i
$427$		−	2.18608e6i		−	0.580226i
$428$	136946.	+	237045.i	0.0361360	+	0.0625491i
$429$	5.84624e6	+	3.30711e6i	1.53368	+	0.867571i
$430$	−934301.	+	1.61878e6i	−0.243678	+	0.422198i
$431$	−2.50758e6			−0.650223			−0.325112	−	0.945676i	$-0.605402\pi$
$431$	−2.50758e6			−0.650223			−0.325112	+	0.945676i	$0.605402\pi$
$432$	3.41027e6	+	1.84824e6i	0.879182	+	0.476485i
$433$	−4.88530e6			−1.25219			−0.626097	−	0.779745i	$-0.715349\pi$
$433$	−4.88530e6			−1.25219			−0.626097	+	0.779745i	$0.715349\pi$
$434$	−344732.	+	597285.i	−0.0878530	+	0.152215i
$435$	7.23958e6	+	4.09529e6i	1.83438	+	1.03768i
$436$	−309164.	−	535144.i	−0.0778885	−	0.134820i
$437$			1.37915e6i			0.345468i
$438$	572976.	−	337670.i	0.142709	−	0.0841022i
$439$		−	129428.i		−	0.0320528i	−0.999872	−	0.0160264i	$-0.994898\pi$
$439$		−	129428.i		−	0.0320528i	0.999872	−	0.0160264i	$-0.00510158\pi$
$440$	−3541.58	−	8.46851e6i	−0.000872098	−	2.08533i
$441$	−300565.	−	500066.i	−0.0735939	−	0.122442i
$442$	545695.	+	314956.i	0.132860	+	0.0766821i
$443$	584552.			0.141519			0.0707593	−	0.997493i	$-0.477458\pi$
$443$	584552.			0.141519			0.0707593	+	0.997493i	$0.477458\pi$
$444$	38700.1	+	4.26438e6i	0.00931655	+	1.02659i
$445$	915767.			0.219222
$446$	−4.06167e6	−	2.34425e6i	−0.966868	−	0.558042i
$447$	2.58540e6	−	4.57043e6i	0.612011	−	1.08190i
$448$	1342.97	+	1.60563e6i	0.000316134	+	0.377964i
$449$		−	7.46140e6i		−	1.74664i	−0.487144	−	0.873322i	$-0.661961\pi$
$449$		−	7.46140e6i		−	1.74664i	0.487144	−	0.873322i	$-0.338039\pi$
$450$	−1.50305e6	+	26654.4i	−0.349897	+	0.00620493i
$451$			1.12134e7i			2.59595i
$452$	−3.13490e6	+	1.81110e6i	−0.721735	+	0.416962i
$453$	−1.00422e6	+	1.77524e6i	−0.229923	+	0.406453i
$454$	2.03106e6	−	3.51903e6i	0.462470	−	0.801279i
$455$	1.90389e6			0.431135
$456$	−679553.	+	1.20247e6i	−0.153042	+	0.270809i
$457$	−6.26840e6			−1.40400			−0.701999	−	0.712178i	$-0.747709\pi$
$457$	−6.26840e6			−1.40400			−0.701999	+	0.712178i	$0.747709\pi$
$458$	1.56058e6	−	2.70387e6i	0.347633	−	0.602312i
$459$	−705027.	+	18608.9i	−0.156197	+	0.00412277i
$460$	5.07078e6	−	2.92950e6i	1.11733	−	0.645505i
$461$		−	652152.i		−	0.142921i	−0.997443	−	0.0714605i	$-0.977234\pi$
$461$		−	652152.i		−	0.142921i	0.997443	−	0.0714605i	$-0.0227660\pi$
$462$	−1.58014e6	−	2.68126e6i	−0.344421	−	0.584432i
$463$			2.41902e6i			0.524429i	0.965010	+	0.262214i	$0.0844528\pi$
$463$			2.41902e6i			0.524429i	−0.965010	+	0.262214i	$0.915547\pi$
$464$	−7.28757e6	−	4.20206e6i	−1.57140	−	0.906082i
$465$	2.19253e6	+	1.24027e6i	0.470234	+	0.266002i
$466$	−1.77006e6	−	1.02162e6i	−0.377593	−	0.217933i
$467$	−2.68809e6			−0.570363			−0.285182	−	0.958473i	$-0.592054\pi$
$467$	−2.68809e6			−0.570363			−0.285182	+	0.958473i	$0.592054\pi$
$468$	−2.25352e6	+	4.06947e6i	−0.475606	+	0.858862i
$469$	−379593.			−0.0796867
$470$	−2.01468e6	−	1.16280e6i	−0.420689	−	0.242807i
$471$	−5.99174e6	−	3.38941e6i	−1.24452	−	0.703999i
$472$	−5.70365e6	+	2385.30i	−1.17841	+	0.000492819i
$473$			3.66404e6i			0.753022i
$474$	3.05324e6	+	5.18090e6i	0.624188	+	1.05916i
$475$		−	535291.i		−	0.108857i
$476$	−146040.	−	252787.i	−0.0295431	−	0.0511372i
$477$	−797048.	+	479065.i	−0.160394	+	0.0964049i
$478$	1.53502e6	−	2.65959e6i	0.307287	−	0.532408i
$479$	−5.26759e6			−1.04899			−0.524497	−	0.851412i	$-0.675747\pi$
$479$	−5.26759e6			−1.04899			−0.524497	+	0.851412i	$0.675747\pi$
$480$	5.86466e6	−	55675.8i	1.16182	−	0.0110297i
$481$	−5.11426e6			−1.00791
$482$	−3.11028e6	+	5.38890e6i	−0.609793	+	1.05653i
$483$	1.05966e6	−	1.87324e6i	0.206679	−	0.365364i
$484$	−5.72667e6	−	9.91250e6i	−1.11119	−	1.92340i
$485$			1.03863e7i			2.00497i
$486$	−229661.	−	5.20197e6i	−0.0441059	−	0.999027i
$487$			3.71875e6i			0.710517i	0.934768	+	0.355259i	$0.115607\pi$
$487$			3.71875e6i			0.710517i	−0.934768	+	0.355259i	$0.884393\pi$
$488$	8.07599e6	−	3377.42i	1.53513	−	0.000642001i
$489$	−964470.	+	1.70497e6i	−0.182397	+	0.322437i
$490$	−764042.	−	440978.i	−0.143756	−	0.0829710i
$491$	−2.91679e6			−0.546011			−0.273006	−	0.962012i	$-0.588018\pi$
$491$	−2.91679e6			−0.546011			−0.273006	+	0.962012i	$0.588018\pi$
$492$	−7.76560e6	+	70474.4i	−1.44631	+	0.0131256i
$493$	1.52954e6			0.283428
$494$	−1.43461e6	−	828005.i	−0.264494	−	0.152657i
$495$	−9.74356e6	+	5.85637e6i	−1.78733	+	1.07427i
$496$	−2.20706e6	−	1.27261e6i	−0.402820	−	0.232269i
$497$		−	4.09873e6i		−	0.744318i
$498$	−1.18145e6	+	696260.i	−0.213473	+	0.125805i
$499$			1.37929e6i			0.247972i	0.992284	+	0.123986i	$0.0395678\pi$
$499$			1.37929e6i			0.247972i	−0.992284	+	0.123986i	$0.960432\pi$
$500$	3.65586e6	−	2.11207e6i	0.653981	−	0.377819i
$501$	5.21805e6	+	2.95175e6i	0.928783	+	0.525395i
$502$	3.22904e6	−	5.59467e6i	0.571893	−	0.990866i
$503$	4.77170e6			0.840916			0.420458	−	0.907312i	$-0.361869\pi$
$503$	4.77170e6			0.840916			0.420458	+	0.907312i	$0.361869\pi$
$504$	1.84692e6	−	1.11114e6i	0.323870	−	0.194847i
$505$	−6.20966e6			−1.08353
$506$	5.73876e6	−	9.94303e6i	0.996419	−	1.72640i
$507$	182142.	+	103034.i	0.0314696	+	0.0178017i
$508$	−1.52498e6	+	881015.i	−0.262183	+	0.151469i
$509$			1.24482e6i			0.212967i	0.994314	+	0.106483i	$0.0339591\pi$
$509$			1.24482e6i			0.212967i	−0.994314	+	0.106483i	$0.966041\pi$
$510$	−918707.	+	541418.i	−0.156405	+	0.0921738i
$511$		−	369562.i		−	0.0626088i
$512$	−5.93164e6	+	7441.93i	−0.999999	+	0.00125462i
$513$	1.85349e6	−	48922.0i	0.310954	−	0.00820750i
$514$	2.75794e6	+	1.59179e6i	0.460444	+	0.265752i
$515$	−867738.			−0.144169
$516$	−2.53745e6	+	23027.9i	−0.419540	+	0.00380741i
$517$	−4.56015e6			−0.750330
$518$	2.05238e6	+	1.18456e6i	0.336072	+	0.193969i
$519$	−2.23429e6	+	3.94974e6i	−0.364101	+	0.643651i
$520$	2941.44	+	7.03349e6i	0.000477037	+	1.14068i
$521$		−	7.79457e6i		−	1.25805i	−0.777385	−	0.629025i	$-0.783454\pi$
$521$		−	7.79457e6i		−	1.25805i	0.777385	−	0.629025i	$-0.216546\pi$
$522$	200226.	+	1.12908e7i	0.0321622	+	1.81363i
$523$		−	6.23823e6i		−	0.997257i	−0.866816	−	0.498628i	$-0.833837\pi$
$523$		−	6.23823e6i		−	0.997257i	0.866816	−	0.498628i	$-0.166163\pi$
$524$	1.62432e6	+	2.81159e6i	0.258430	+	0.447326i
$525$	−411286.	+	727063.i	−0.0651247	+	0.115126i
$526$	667000.	−	1.15565e6i	0.105114	−	0.182122i
$527$	463225.			0.0726550
$528$	9.90287e6	−	5.84160e6i	1.54588	−	0.911900i
$529$	1.50255e6			0.233448
$530$	−702867.	+	1.21779e6i	−0.108688	+	0.188315i
$531$	3.94434e6	+	6.56241e6i	0.607069	+	1.01001i
$532$	383934.	+	664566.i	0.0588136	+	0.101803i
$533$		−	9.31326e6i		−	1.41998i
$534$	631250.	+	1.07114e6i	0.0957963	+	0.162552i
$535$		−	555654.i		−	0.0839305i
$536$	−586.457	−	1.40232e6i	−8.81707e−5	−	0.210831i
$537$	−9.91487e6	−	5.60865e6i	−1.48372	−	0.839311i
$538$	−6.29412e6	−	3.63274e6i	−0.937517	−	0.541101i
$539$	−1.72938e6			−0.256400
$540$	−4.11693e6	−	6.71088e6i	−0.607560	−	0.990365i
$541$	2.62854e6			0.386119			0.193060	−	0.981187i	$-0.438159\pi$
$541$	2.62854e6			0.386119			0.193060	+	0.981187i	$0.438159\pi$
$542$	−9.52801e6	−	5.49923e6i	−1.39317	−	0.804088i
$543$	4.27830e6	+	2.42015e6i	0.622689	+	0.352244i
$544$	933637.	−	539904.i	0.135264	−	0.0782202i
$545$			1.25442e6i			0.180906i
$546$	1.31238e6	+	2.22691e6i	0.188398	+	0.319684i
$547$		−	7.51145e6i		−	1.07338i	−0.843778	−	0.536692i	$-0.819674\pi$
$547$		−	7.51145e6i		−	1.07338i	0.843778	−	0.536692i	$-0.180326\pi$
$548$	−8.36389e6	+	4.83200e6i	−1.18975	+	0.687346i
$549$	−5.58492e6	−	9.29194e6i	−0.790835	−	1.31576i
$550$	−2.22739e6	+	3.85920e6i	−0.313972	+	0.543990i
$551$	−4.02109e6			−0.564241
$552$	6.92189e6	+	3.91176e6i	0.966890	+	0.546418i
$553$	3.34162e6			0.464669
$554$	−1.62173e6	+	2.80982e6i	−0.224494	+	0.388960i
$555$	4.26180e6	−	7.53394e6i	0.587301	−	1.03822i
$556$	−4.44438e6	+	2.56762e6i	−0.609711	+	0.352243i
$557$			1.36014e6i			0.185757i	0.995677	+	0.0928785i	$0.0296068\pi$
$557$			1.36014e6i			0.185757i	−0.995677	+	0.0928785i	$0.970393\pi$
$558$	60639.3	+	3.41946e6i	0.00824458	+	0.464914i
$559$		−	3.04316e6i		−	0.411903i
$560$	1.62791e6	−	2.82326e6i	0.219362	−	0.380435i
$561$	−1.02928e6	+	1.81954e6i	−0.138079	+	0.244093i
$562$	−5.27770e6	−	3.04610e6i	−0.704862	−	0.406821i
$563$	8.89612e6			1.18285			0.591425	−	0.806360i	$-0.298566\pi$
$563$	8.89612e6			1.18285			0.591425	+	0.806360i	$0.298566\pi$
$564$	−28659.8	−	3.15803e6i	−0.00379380	−	0.418041i
$565$	7.34848e6			0.968448
$566$	8.40373e6	+	4.85033e6i	1.10263	+	0.636400i
$567$	−2.55510e6	−	1.35766e6i	−0.333772	−	0.177351i
$568$	1.51418e7	−	6332.39i	1.96928	−	0.000823563i
$569$			5.45259e6i			0.706029i	0.935618	+	0.353014i	$0.114843\pi$
$569$			5.45259e6i			0.706029i	−0.935618	+	0.353014i	$0.885157\pi$
$570$	2.41524e6	−	1.42337e6i	0.311368	−	0.183497i
$571$			1.35505e6i			0.173926i	0.996212	+	0.0869629i	$0.0277162\pi$
$571$			1.35505e6i			0.173926i	−0.996212	+	0.0869629i	$0.972284\pi$
$572$	6.89746e6	+	1.19391e7i	0.881453	+	1.52574i
$573$	7.98600e6	+	4.51753e6i	1.01612	+	0.574797i
$574$	−2.15713e6	+	3.73746e6i	−0.273273	+	0.473475i
$575$	−3.08134e6			−0.388660
$576$	4.10771e6	+	6.82130e6i	0.515874	+	0.856665i
$577$	1.22098e7			1.52675			0.763376	−	0.645954i	$-0.223540\pi$
$577$	1.22098e7			1.52675			0.763376	+	0.645954i	$0.223540\pi$
$578$	3.91697e6	−	6.78657e6i	0.487675	−	0.844950i
$579$	1.08054e7	+	6.11243e6i	1.33951	+	0.757735i
$580$	8.54134e6	+	1.47845e7i	1.05428	+	1.82489i
$581$			762020.i			0.0936540i
$582$	−1.21485e7	+	7.15944e6i	−1.48667	+	0.876136i
$583$			2.75643e6i			0.335873i
$584$	1.36526e6	−	570.961i	0.165647	−	6.92746e-5i
$585$	8.09248e6	−	4.86398e6i	0.977669	−	0.587628i
$586$	7.59932e6	+	4.38606e6i	0.914178	+	0.527631i
$587$	−1.17760e7			−1.41060			−0.705298	−	0.708911i	$-0.749187\pi$
$587$	−1.17760e7			−1.41060			−0.705298	+	0.708911i	$0.749187\pi$
$588$	−10868.9	−	1.19764e6i	−0.00129640	−	0.142851i
$589$	−1.21780e6			−0.144640
$590$	1.00266e7	+	5.78699e6i	1.18583	+	0.684419i
$591$	4.08399e6	−	7.21960e6i	0.480968	−	0.850246i
$592$	−4.37291e6	+	7.58387e6i	−0.512822	+	0.889379i
$593$			5.59902e6i			0.653845i	0.945051	+	0.326923i	$0.106012\pi$
$593$			5.59902e6i			0.653845i	−0.945051	+	0.326923i	$0.893988\pi$
$594$	−1.35663e7	−	7.35982e6i	−1.57760	−	0.855856i
$595$			592554.i			0.0686176i
$596$	9.33363e6	−	5.39224e6i	1.07630	−	0.621804i
$597$	4.33000e6	−	7.65449e6i	0.497224	−	0.878982i
$598$	−4.76631e6	+	8.25814e6i	−0.545041	+	0.944342i
$599$	2.05696e6			0.234239			0.117120	−	0.993118i	$-0.462634\pi$
$599$	2.05696e6			0.234239			0.117120	+	0.993118i	$0.462634\pi$
$600$	−2.68660e6	−	1.51828e6i	−0.304667	−	0.172176i
$601$	−1.14296e7			−1.29076			−0.645379	−	0.763862i	$-0.723301\pi$
$601$	−1.14296e7			−1.29076			−0.645379	+	0.763862i	$0.723301\pi$
$602$	−704853.	+	1.22123e6i	−0.0792697	+	0.137343i
$603$	−1.61346e6	+	969768.i	−0.180702	+	0.108611i
$604$	−3.62535e6	+	2.09444e6i	−0.404350	+	0.233602i
$605$			2.32358e7i			2.58088i
$606$	−4.28040e6	−	7.26321e6i	−0.473482	−	0.803428i
$607$		−	1.70632e7i		−	1.87970i	−0.341587	−	0.939850i	$-0.610964\pi$
$607$		−	1.70632e7i		−	1.87970i	0.341587	−	0.939850i	$-0.389036\pi$
$608$	−2.45449e6	+	1.41938e6i	−0.269279	+	0.155719i
$609$	5.46167e6	+	3.08956e6i	0.596736	+	0.337562i
$610$	−1.41970e7	−	8.19399e6i	−1.54480	−	0.891601i
$611$	3.78741e6			0.410431
$612$	−1.26655e6	−	701370.i	−0.136693	−	0.0756953i
$613$	323335.			0.0347537			0.0173769	−	0.999849i	$-0.494468\pi$
$613$	323335.			0.0347537			0.0173769	+	0.999849i	$0.494468\pi$
$614$	−8.83535e6	−	5.09945e6i	−0.945807	−	0.545886i
$615$	1.37196e7	+	7.76091e6i	1.46269	+	0.827418i
$616$	−2671.83	−	6.38880e6i	−0.000283698	−	0.678371i
$617$			1.07810e7i			1.14011i	0.821607	+	0.570055i	$0.193078\pi$
$617$			1.07810e7i			1.14011i	−0.821607	+	0.570055i	$0.806922\pi$
$618$	−598144.	−	1.01496e6i	−0.0629991	−	0.106900i
$619$		−	9.28241e6i		−	0.973720i	−0.873480	−	0.486860i	$-0.838142\pi$
$619$		−	9.28241e6i		−	0.973720i	0.873480	−	0.486860i	$-0.161858\pi$
$620$	2.58678e6	+	4.47754e6i	0.270259	+	0.467800i
$621$	−281613.	−	1.06694e7i	−0.0293038	−	1.11022i
$622$	5.29058e6	−	9.16650e6i	0.548312	−	0.950009i
$623$	690871.			0.0713143
$624$	−8.22479e6	+	4.85172e6i	−0.845597	+	0.498809i
$625$	−1.19872e7			−1.22749
$626$	194918.	−	337717.i	0.0198800	−	0.0344443i
$627$	2.70594e6	−	4.78351e6i	0.274884	−	0.485934i
$628$	−7.06912e6	−	1.22362e7i	−0.715264	−	1.23808i
$629$		−	1.59173e6i		−	0.160414i
$630$	−4.37415e6	+	77569.2i	−0.439078	+	0.00778642i
$631$			1.10028e7i			1.10009i	0.835135	+	0.550046i	$0.185390\pi$
$631$			1.10028e7i			1.10009i	−0.835135	+	0.550046i	$0.814610\pi$
$632$	5162.68	+	1.23448e7i	0.000514141	+	1.22940i
$633$	6.11887e6	−	1.08168e7i	0.606963	−	1.07298i
$634$	478308.	+	276062.i	0.0472590	+	0.0272762i
$635$	3.57469e6			0.351806
$636$	−1.90890e6	+	17323.7i	−0.187129	+	0.00169824i
$637$	1.43633e6			0.140251
$638$	2.89902e7	+	1.67321e7i	2.81968	+	1.62742i
$639$	−1.04713e7	−	1.74216e7i	−1.01449	−	1.68786i
$640$	1.04324e7	+	6.00958e6i	1.00678	+	0.579955i
$641$		−	1.44073e7i		−	1.38496i	−0.721439	−	0.692478i	$-0.756519\pi$
$641$		−	1.44073e7i		−	1.38496i	0.721439	−	0.692478i	$-0.243481\pi$
$642$	649928.	−	383020.i	0.0622340	−	0.0366761i
$643$		−	1.24851e7i		−	1.19087i	−0.803405	−	0.595433i	$-0.796980\pi$
$643$		−	1.24851e7i		−	1.19087i	0.803405	−	0.595433i	$-0.203020\pi$
$644$	3.82549e6	−	2.21007e6i	0.363473	−	0.209986i
$645$	4.48295e6	+	2.53592e6i	0.424292	+	0.240014i
$646$	257703.	−	446498.i	0.0242962	−	0.0420957i
$647$	−4.12907e6			−0.387785			−0.193893	−	0.981023i	$-0.562111\pi$
$647$	−4.12907e6			−0.387785			−0.193893	+	0.981023i	$0.562111\pi$
$648$	5.01161e6	−	9.44133e6i	0.468857	−	0.883274i
$649$	2.26948e7			2.11502
$650$	1.84995e6	−	3.20525e6i	0.171742	−	0.297562i
$651$	1.65409e6	+	935685.i	0.152970	+	0.0865321i
$652$	−3.48186e6	+	2.01155e6i	−0.320769	+	0.185315i
$653$		−	1.16320e7i		−	1.06751i	−0.845640	−	0.533753i	$-0.820781\pi$
$653$		−	1.16320e7i		−	1.06751i	0.845640	−	0.533753i	$-0.179219\pi$
$654$	−1.46725e6	+	864691.i	−0.134141	+	0.0790527i
$655$		−	6.59062e6i		−	0.600237i
$656$	−1.38105e7	−	7.96325e6i	−1.25300	−	0.722488i
$657$	−944143.	−	1.57082e6i	−0.0853344	−	0.141976i
$658$	−1.51991e6	−	877237.i	−0.136853	−	0.0789864i
$659$	−7.08392e6			−0.635419			−0.317710	−	0.948188i	$-0.602914\pi$
$659$	−7.08392e6			−0.635419			−0.317710	+	0.948188i	$0.602914\pi$
$660$	−2.33355e7	+	211775.i	−2.08525	+	0.0189241i
$661$	1.30268e6			0.115967			0.0579834	−	0.998318i	$-0.481533\pi$
$661$	1.30268e6			0.115967			0.0579834	+	0.998318i	$0.481533\pi$
$662$	−4.32078e6	−	2.49380e6i	−0.383193	−	0.221165i
$663$	854866.	−	1.51122e6i	0.0755291	−	0.133519i
$664$	−2.81511e6	+	1177.29i	−0.247785	+	0.000103625i
$665$		−	1.55780e6i		−	0.136602i
$666$	1.17499e7	−	208367.i	1.02647	−	0.0182031i
$667$			2.31469e7i			2.01455i
$668$	6.15632e6	+	1.06562e7i	0.533802	+	0.923977i
$669$	−6.36286e6	+	1.12481e7i	−0.549651	+	0.971662i
$670$	−1.42281e6	+	2.46517e6i	−0.122450	+	0.212158i
$671$	−3.21343e7			−2.75526
$672$	4.42440e6	−	42002.8i	0.377947	−	0.00358802i
$673$	9.83732e6			0.837219			0.418610	−	0.908166i	$-0.362518\pi$
$673$	9.83732e6			0.837219			0.418610	+	0.908166i	$0.362518\pi$
$674$	7.92978e6	−	1.37392e7i	0.672375	−	1.16496i
$675$	109303.	+	4.14111e6i	0.00923364	+	0.349831i
$676$	214893.	+	371967.i	0.0180866	+	0.0313067i
$677$		−	9.05446e6i		−	0.759261i	−0.925138	−	0.379630i	$-0.876051\pi$
$677$		−	9.05446e6i		−	0.759261i	0.925138	−	0.379630i	$-0.123949\pi$
$678$	5.06540e6	+	8.59524e6i	0.423194	+	0.718098i
$679$			7.83563e6i			0.652228i
$680$	−2.18906e6	+	915.475i	−0.181545	+	7.59231e-5i
$681$	−9.74540e6	−	5.51279e6i	−0.805253	−	0.455516i
$682$	8.77977e6	+	5.06737e6i	0.722807	+	0.417179i
$683$	−1.62228e7			−1.33068			−0.665342	−	0.746539i	$-0.731714\pi$
$683$	−1.62228e7			−1.33068			−0.665342	+	0.746539i	$0.731714\pi$
$684$	3.32972e6	+	1.84387e6i	0.272124	+	0.150692i
$685$	1.96057e7			1.59645
$686$	−576406.	−	332681.i	−0.0467647	−	0.0269909i
$687$	−7.48793e6	−	4.23578e6i	−0.605299	−	0.342406i
$688$	−4.51266e6	−	2.60203e6i	−0.363464	−	0.209576i
$689$		−	2.28934e6i		−	0.183723i
$690$	−8.19342e6	−	1.39030e7i	−0.655153	−	1.11170i
$691$			2.47072e7i			1.96847i	0.176861	+	0.984236i	$0.443406\pi$
$691$			2.47072e7i			1.96847i	−0.176861	+	0.984236i	$0.556594\pi$
$692$	−8.06608e6	+	4.65995e6i	−0.640320	+	0.369927i
$693$	−7.35072e6	+	4.41815e6i	−0.581429	+	0.349468i
$694$	2.10250e6	−	3.64281e6i	0.165706	−	0.287103i
$695$	1.04180e7			0.818130
$696$	−1.14052e7	+	2.01817e7i	−0.892445	+	1.57919i
$697$	2.89859e6			0.225998
$698$	7.74199e6	−	1.34138e7i	0.601470	−	1.04211i
$699$	−2.77291e6	+	4.90190e6i	−0.214656	+	0.379465i
$700$	−1.48479e6	+	857798.i	−0.114530	+	0.0661667i
$701$			4.90589e6i			0.377071i	0.982066	+	0.188535i	$0.0603740\pi$
$701$			4.90589e6i			0.377071i	−0.982066	+	0.188535i	$0.939626\pi$
$702$	1.12675e7	+	6.11267e6i	0.862947	+	0.468153i
$703$			4.18458e6i			0.319348i
$704$	2.36019e7	−	19740.9i	1.79480	−	0.00150119i
$705$	−3.15612e6	+	5.57933e6i	−0.239156	+	0.422775i
$706$	2.60220e6	+	1.50189e6i	0.196484	+	0.113404i
$707$	−4.68468e6			−0.352477
$708$	142633.	+	1.57168e7i	0.0106939	+	1.17837i
$709$	−5.20657e6			−0.388988			−0.194494	−	0.980904i	$-0.562306\pi$
$709$	−5.20657e6			−0.388988			−0.194494	+	0.980904i	$0.562306\pi$
$710$	−2.66182e7	−	1.53631e7i	−1.98167	−	1.14375i
$711$	1.42035e7	−	8.53703e6i	1.05371	−	0.633334i
$712$	1067.37	+	2.55226e6i	7.89070e−5	+	0.188680i
$713$			7.01011e6i			0.516418i
$714$	−693088.	+	408455.i	−0.0508795	+	0.0299847i
$715$		−	2.79862e7i		−	2.04729i
$716$	−1.16977e7	−	2.02479e7i	−0.852741	−	1.47604i
$717$	−7.36530e6	−	4.16641e6i	−0.535048	−	0.302666i
$718$	−671176.	+	1.16288e6i	−0.0485876	+	0.0841832i
$719$	1.65487e7			1.19383			0.596915	−	0.802304i	$-0.296393\pi$
$719$	1.65487e7			1.19383			0.596915	+	0.802304i	$0.296393\pi$
$720$	−293320.	−	1.61592e7i	−0.0210868	−	1.16168i
$721$	−654637.			−0.0468989
$722$	6.32428e6	−	1.09575e7i	0.451511	−	0.782292i
$723$	1.49237e7	+	8.44206e6i	1.06177	+	0.600624i
$724$	5.04758e6	+	8.73705e6i	0.357880	+	0.619467i
$725$		−	8.98403e6i		−	0.634785i
$726$	−2.71780e7	+	1.60167e7i	−1.91371	+	1.12780i
$727$			1.60207e7i			1.12421i	0.827067	+	0.562104i	$0.190008\pi$
$727$			1.60207e7i			1.12421i	−0.827067	+	0.562104i	$0.809992\pi$
$728$	2219.08	+	5.30619e6i	0.000155183	+	0.371069i
$729$	−1.43289e7	+	756940.i	−0.998608	+	0.0527524i
$730$	−2.40003e6	−	1.38521e6i	−0.166690	−	0.0962075i
$731$	947131.			0.0655566
$732$	−201959.	−	2.22539e7i	−0.0139311	−	1.53507i
$733$	−6.17287e6			−0.424353			−0.212176	−	0.977231i	$-0.568055\pi$
$733$	−6.17287e6			−0.424353			−0.212176	+	0.977231i	$0.568055\pi$
$734$	−1.82069e7	−	1.05083e7i	−1.24737	−	0.719937i
$735$	−1.19692e6	+	2.11589e6i	−0.0817234	+	0.144469i
$736$	8.17050e6	+	1.41290e7i	0.555974	+	0.961427i
$737$			5.57982e6i			0.378400i
$738$	379445.	+	2.13970e7i	0.0256453	+	1.44615i
$739$			4.37154e6i			0.294458i	0.989102	+	0.147229i	$0.0470355\pi$
$739$			4.37154e6i			0.294458i	−0.989102	+	0.147229i	$0.952965\pi$
$740$	1.53856e7	−	8.88862e6i	1.03285	−	0.596699i
$741$	−2.24741e6	+	3.97292e6i	−0.150361	+	0.265806i
$742$	−530255.	+	918725.i	−0.0353570	+	0.0612598i
$743$	8.92383e6			0.593033			0.296517	−	0.955028i	$-0.404175\pi$
$743$	8.92383e6			0.593033			0.296517	+	0.955028i	$0.404175\pi$
$744$	−3.45412e6	+	6.11209e6i	−0.228773	+	0.404815i
$745$	−2.18788e7			−1.44422
$746$	−4.34079e6	+	7.52090e6i	−0.285576	+	0.494792i
$747$	1.94678e6	+	3.23896e6i	0.127648	+	0.212376i
$748$	−3.71583e6	+	2.14672e6i	−0.242830	+	0.140288i
$749$		−	419195.i		−	0.0273031i
$750$	−5.90718e6	−	1.00236e7i	−0.383466	−	0.650686i
$751$			1.88311e6i			0.121836i	0.998143	+	0.0609179i	$0.0194028\pi$
$751$			1.88311e6i			0.121836i	−0.998143	+	0.0609179i	$0.980597\pi$
$752$	3.23841e6	−	5.61631e6i	0.208827	−	0.362165i
$753$	−1.54935e7	−	8.76440e6i	−0.995780	−	0.563294i
$754$	−2.40777e7	−	1.38968e7i	−1.54236	−	0.890196i
$755$	8.49813e6			0.542570
$756$	−3.10589e6	−	5.06281e6i	−0.197643	−	0.322171i
$757$	2.21895e7			1.40737			0.703683	−	0.710514i	$-0.251538\pi$
$757$	2.21895e7			1.40737			0.703683	+	0.710514i	$0.251538\pi$
$758$	6.60482e6	+	3.81207e6i	0.417531	+	0.240984i
$759$	−2.75356e7	−	1.55764e7i	−1.73496	−	0.981437i
$760$	5.75494e6	−	2406.75i	0.361415	−	0.000151146i
$761$		−	1.99007e6i		−	0.124568i	−0.998058	−	0.0622841i	$-0.980162\pi$
$761$		−	1.99007e6i		−	0.124568i	0.998058	−	0.0622841i	$-0.0198385\pi$
$762$	2.46408e6	+	4.18118e6i	0.153733	+	0.260862i
$763$			946359.i			0.0588497i
$764$	9.42198e6	+	1.63088e7i	0.583995	+	1.01086i
$765$	1.51383e6	+	2.51865e6i	0.0935243	+	0.155601i
$766$	5.56497e6	−	9.64191e6i	0.342681	−	0.593733i
$767$	−1.88491e7			−1.15691
$768$	162005.	+	1.63449e7i	0.00991121	+	0.999951i
$769$	2.38499e7			1.45436			0.727179	−	0.686448i	$-0.240831\pi$
$769$	2.38499e7			1.45436			0.727179	+	0.686448i	$0.240831\pi$
$770$	−6.48214e6	+	1.12310e7i	−0.393996	+	0.682641i
$771$	4.32049e6	−	7.63768e6i	0.261756	−	0.462728i
$772$	1.27484e7	+	2.20666e7i	0.769860	+	1.33258i
$773$			2.20179e7i			1.32534i	0.748911	+	0.662670i	$0.230577\pi$
$773$			2.20179e7i			1.32534i	−0.748911	+	0.662670i	$0.769423\pi$
$774$	123986.	+	6.99158e6i	0.00743908	+	0.419491i
$775$		−	2.72085e6i		−	0.162723i
$776$	−2.89469e7	+	12105.8i	−1.72563	+	0.000721669i
$777$	3.21518e6	−	5.68373e6i	0.191053	−	0.337739i
$778$	1.69670e7	+	9.79273e6i	1.00497	+	0.580036i
$779$	−7.62028e6			−0.449912
$780$	1.93812e7	−	175889.i	1.14063	−	0.0103515i
$781$	−6.02492e7			−3.53447
$782$	−2.57021e6	−	1.48343e6i	−0.150297	−	0.0867463i
$783$	3.11079e7	−	821080.i	1.81329	−	0.0478609i
$784$	1.22812e6	−	2.12992e6i	0.0713596	−	0.123758i
$785$			2.86827e7i			1.66129i
$786$	7.70880e6	−	4.54300e6i	0.445072	−	0.262293i
$787$			9.48459e6i			0.545861i	0.962034	+	0.272930i	$0.0879929\pi$
$787$			9.48459e6i			0.545861i	−0.962034	+	0.272930i	$0.912007\pi$
$788$	1.47437e7	−	8.51777e6i	0.845846	−	0.488664i
$789$	−3.20039e6	−	1.81040e6i	−0.183025	−	0.103534i
$790$	1.25252e7	−	2.17013e7i	0.714031	−	1.23714i
$791$	5.54382e6			0.315042
$792$	−1.63332e7	−	2.71487e7i	−0.925248	−	1.53793i
$793$	2.66890e7			1.50713
$794$	3.61060e6	−	6.25576e6i	0.203249	−	0.352151i
$795$	3.37249e6	+	1.90775e6i	0.189248	+	0.107054i
$796$	1.56318e7	−	9.03085e6i	0.874434	−	0.505180i
$797$		−	2.28383e7i		−	1.27355i	−0.771048	−	0.636777i	$-0.780267\pi$
$797$		−	2.28383e7i		−	1.27355i	0.771048	−	0.636777i	$-0.219733\pi$
$798$	1.82210e6	−	1.07381e6i	0.101290	−	0.0596927i
$799$			1.17877e6i			0.0653223i
$800$	−3.17123e6	−	5.48390e6i	−0.175187	−	0.302946i
$801$	2.93654e6	−	1.76501e6i	0.161717	−	0.0971998i
$802$	−9.92460e6	−	5.72812e6i	−0.544850	−	0.314468i
$803$	−5.43237e6			−0.297304
$804$	−3.86418e6	+	35068.2i	−0.210822	+	0.00191326i
$805$	−8.96727e6			−0.487720
$806$	−7.29201e6	−	4.20869e6i	−0.395375	−	0.228197i
$807$	−9.86014e6	+	1.74306e7i	−0.532965	+	0.942166i
$808$	−7237.66	−	1.73065e7i	−0.000390005	−	0.932567i
$809$		−	2.52134e7i		−	1.35444i	−0.735780	−	0.677221i	$-0.763184\pi$
$809$		−	2.52134e7i		−	1.35444i	0.735780	−	0.677221i	$-0.236816\pi$
$810$	−1.83941e7	+	1.15046e7i	−0.985068	+	0.616111i
$811$			5.71394e6i			0.305059i	0.988299	+	0.152529i	$0.0487419\pi$
$811$			5.71394e6i			0.305059i	−0.988299	+	0.152529i	$0.951258\pi$
$812$	6.44374e6	+	1.11537e7i	0.342964	+	0.593648i
$813$	−1.49262e7	+	2.63863e7i	−0.791998	+	1.40008i
$814$	1.74124e7	−	3.01689e7i	0.921081	−	1.59587i
$815$	8.16177e6			0.430418
$816$	−1.51002e6	−	2.55983e6i	−0.0793882	−	0.134581i
$817$	−2.48997e6			−0.130508
$818$	−5.07845e6	+	8.79897e6i	−0.265368	+	0.459778i
$819$	6.10511e6	−	3.66948e6i	0.318041	−	0.191159i
$820$	1.61865e7	+	2.80178e7i	0.840658	+	1.45512i
$821$			6.54942e6i			0.339113i	0.985520	+	0.169557i	$0.0542335\pi$
$821$			6.54942e6i			0.339113i	−0.985520	+	0.169557i	$0.945766\pi$
$822$	1.35145e7	+	2.29320e7i	0.697620	+	1.18376i
$823$			1.34954e7i			0.694523i	0.937768	+	0.347261i	$0.112888\pi$
$823$			1.34954e7i			0.694523i	−0.937768	+	0.347261i	$0.887112\pi$
$824$	−1011.39	−	2.41841e6i	−5.18921e−5	−	0.124083i
$825$	1.06874e7	+	6.04569e6i	0.546688	+	0.309251i
$826$	7.56423e6	+	4.36580e6i	0.385758	+	0.222646i
$827$	−1.15713e7			−0.588326			−0.294163	−	0.955755i	$-0.595041\pi$
$827$	−1.15713e7			−0.588326			−0.294163	+	0.955755i	$0.595041\pi$
$828$	1.06140e7	−	1.91671e7i	0.538027	−	0.971584i
$829$	−2.69670e7			−1.36285			−0.681423	−	0.731890i	$-0.738638\pi$
$829$	−2.69670e7			−1.36285			−0.681423	+	0.731890i	$0.738638\pi$
$830$	4.94875e6	+	2.85624e6i	0.249345	+	0.143913i
$831$	7.78136e6	+	4.40177e6i	0.390889	+	0.221118i
$832$	−1.96025e7	+	16395.8i	−0.981755	+	0.000821151i
$833$			447033.i			0.0223217i
$834$	7.18127e6	+	1.21856e7i	0.357508	+	0.606639i
$835$		−	2.49790e7i		−	1.23982i
$836$	9.76877e6	−	5.64363e6i	0.483420	−	0.279282i
$837$	9.42113e6	−	248667.i	0.464825	−	0.0122689i
$838$	2.71647e6	−	4.70658e6i	0.133627	−	0.231524i
$839$	−2.11117e6			−0.103542			−0.0517712	−	0.998659i	$-0.516487\pi$
$839$	−2.11117e6			−0.103542			−0.0517712	+	0.998659i	$0.516487\pi$
$840$	−7.81853e6	−	4.41848e6i	−0.382320	−	0.216060i
$841$	−4.69765e7			−2.29029
$842$	3.88682e6	−	6.73434e6i	0.188936	−	0.327352i
$843$	−8.26786e6	+	1.46158e7i	−0.400704	+	0.708358i
$844$	2.20899e7	−	1.27618e7i	1.06743	−	0.616675i
$845$		−	871922.i		−	0.0420084i
$846$	−8.70150e6	+	154309.i	−0.417992	+	0.00741249i
$847$			1.75295e7i			0.839576i
$848$	−3.39484e6	−	1.95749e6i	−0.162117	−	0.0934780i
$849$	1.31650e7	−	2.32728e7i	0.626831	−	1.10810i
$850$	997579.	+	575767.i	0.0473587	+	0.0273338i
$851$	2.40880e7			1.14019
$852$	−378656.	−	4.17242e7i	−0.0178709	−	1.96920i
$853$	7.19963e6			0.338795			0.169398	−	0.985548i	$-0.445818\pi$
$853$	7.19963e6			0.338795			0.169398	+	0.985548i	$0.445818\pi$
$854$	−1.07104e7	−	6.18169e6i	−0.502531	−	0.290043i
$855$	−3.97980e6	−	6.62142e6i	−0.186186	−	0.309767i
$856$	1.54862e6	−	647.642i	0.0722372	−	3.02100e-5i
$857$			4.23345e7i			1.96899i	0.175423	+	0.984493i	$0.443871\pi$
$857$			4.23345e7i			1.96899i	−0.175423	+	0.984493i	$0.556129\pi$
$858$	3.27344e7	−	1.92913e7i	1.51805	−	0.894628i
$859$		−	3.77175e7i		−	1.74405i	−0.489459	−	0.872026i	$-0.662806\pi$
$859$		−	3.77175e7i		−	1.74405i	0.489459	−	0.872026i	$-0.337194\pi$
$860$	5.28903e6	+	9.15498e6i	0.243854	+	0.422096i
$861$	1.03503e7	+	5.85497e6i	0.475823	+	0.269164i
$862$	−7.09081e6	+	1.22856e7i	−0.325033	+	0.563155i
$863$	3.86956e7			1.76862			0.884309	−	0.466901i	$-0.154630\pi$
$863$	3.86956e7			1.76862			0.884309	+	0.466901i	$0.154630\pi$
$864$	1.86986e7	−	1.14818e7i	0.852167	−	0.523270i
$865$	1.89076e7			0.859203
$866$	−1.38144e7	+	2.39349e7i	−0.625946	+	1.08452i
$867$	−1.87943e7	−	1.06316e7i	−0.849140	−	0.480342i
$868$	1.95151e6	+	3.37794e6i	0.0879167	+	0.152178i
$869$		−	4.91200e7i		−	2.20653i
$870$	4.05361e7	−	2.38890e7i	1.81570	−	1.07004i
$871$		−	4.63429e6i		−	0.206985i
$872$	−3.49611e6	+	1462.09i	−0.155702	+	6.51153e-5i
$873$	2.00182e7	+	3.33053e7i	0.888973	+	1.47903i
$874$	6.75697e6	+	3.89988e6i	0.299208	+	0.172692i
$875$	−6.46510e6			−0.285467
$876$	−34141.6	−	3.76207e6i	−0.00150322	−	0.165641i
$877$	3.61986e6			0.158925			0.0794626	−	0.996838i	$-0.474680\pi$
$877$	3.61986e6			0.158925			0.0794626	+	0.996838i	$0.474680\pi$
$878$	−634115.	−	365988.i	−0.0277608	−	0.0160225i
$879$	1.19048e7	−	2.10451e7i	0.519698	−	0.918712i
$880$	−4.15004e7	−	2.39294e7i	−1.80653	−	1.04166i
$881$			3.90563e7i			1.69532i	0.530542	+	0.847659i	$0.321989\pi$
$881$			3.90563e7i			1.69532i	−0.530542	+	0.847659i	$0.678011\pi$
$882$	−3.29993e6	+	58519.6i	−0.142835	+	0.00253297i
$883$		−	3.53383e7i		−	1.52526i	−0.646834	−	0.762631i	$-0.723907\pi$
$883$		−	3.53383e7i		−	1.52526i	0.646834	−	0.762631i	$-0.276093\pi$
$884$	3.08617e6	−	1.78295e6i	0.132828	−	0.0767376i
$885$	1.57073e7	−	2.77670e7i	0.674129	−	1.19171i
$886$	1.65296e6	−	2.86394e6i	0.0707422	−	0.122569i
$887$	3.44126e7			1.46862			0.734309	−	0.678816i	$-0.237506\pi$
$887$	3.44126e7			1.46862			0.734309	+	0.678816i	$0.237506\pi$
$888$	2.10022e7	+	1.18690e7i	0.893785	+	0.505104i
$889$	2.69681e6			0.114445
$890$	2.58955e6	−	4.48668e6i	0.109585	−	0.189867i
$891$	−1.99569e7	+	3.75586e7i	−0.842167	+	1.58495i
$892$	−2.29707e7	+	1.32707e7i	−0.966634	+	0.558446i
$893$		−	3.09893e6i		−	0.130042i
$894$	−1.50814e7	−	2.55909e7i	−0.631098	−	1.07088i
$895$			4.74629e7i			1.98060i
$896$	7.87039e6	+	4.53374e6i	0.327511	+	0.188663i
$897$	2.28696e7	+	1.29369e7i	0.949025	+	0.536846i
$898$	−3.65562e7	−	2.10989e7i	−1.51276	−	0.873111i
$899$	−2.04389e7			−0.843447
$900$	−4.11964e6	+	7.43935e6i	−0.169532	+	0.306146i
$901$	712519.			0.0292405
$902$	5.49387e7	+	3.17087e7i	2.24834	+	1.29766i
$903$	3.38201e6	+	1.91314e6i	0.138024	+	0.0780778i
$904$	8565.00	+	2.04804e7i	0.000348583	+	0.833522i
$905$		−	2.04804e7i		−	0.831221i
$906$	5.85787e6	+	9.93995e6i	0.237093	+	0.402313i
$907$		−	2.08628e7i		−	0.842082i	−0.907042	−	0.421041i	$-0.861665\pi$
$907$		−	2.08628e7i		−	0.842082i	0.907042	−	0.421041i	$-0.138335\pi$
$908$	−1.14977e7	−	1.99019e7i	−0.462805	−	0.801086i
$909$	−1.99122e7	+	1.19682e7i	−0.799300	+	0.480419i
$910$	5.38372e6	−	9.32788e6i	0.215516	−	0.373404i
$911$	−3.67925e7			−1.46880			−0.734401	−	0.678716i	$-0.762537\pi$
$911$	−3.67925e7			−1.46880			−0.734401	+	0.678716i	$0.762537\pi$
$912$	3.96977e6	+	6.72968e6i	0.158044	+	0.267921i
$913$	1.12013e7			0.444725
$914$	−1.77254e7	+	3.07112e7i	−0.701829	+	1.21600i
$915$	−2.22405e7	+	3.93162e7i	−0.878195	+	1.55246i
$916$	−8.83435e6	−	1.52917e7i	−0.347885	−	0.602167i
$917$		−	4.97208e6i		−	0.195261i
$918$	−1.90246e6	+	3.50681e6i	−0.0745092	+	0.137343i
$919$			4.68525e6i			0.182997i	0.995805	+	0.0914985i	$0.0291657\pi$
$919$			4.68525e6i			0.182997i	−0.995805	+	0.0914985i	$0.970834\pi$
$920$	−13854.1	−	3.31275e7i	−0.000539646	−	1.29039i
$921$	−1.38411e7	+	2.44681e7i	−0.537678	+	0.950497i
$922$	−3.19513e6	−	1.84412e6i	−0.123783	−	0.0714433i
$923$	5.00397e7			1.93335
$924$	−1.76047e7	+	159767.i	−0.678343	+	0.00615610i
$925$	−9.34931e6			−0.359274
$926$	1.18517e7	+	6.84036e6i	0.454205	+	0.262151i
$927$	−2.78253e6	+	1.67244e6i	−0.106351	+	0.0639221i
$928$	−4.11949e7	+	2.38222e7i	−1.57027	+	0.908053i
$929$			4.44992e7i			1.69166i	0.533453	+	0.845830i	$0.320894\pi$
$929$			4.44992e7i			1.69166i	−0.533453	+	0.845830i	$0.679106\pi$
$930$	1.22765e7	−	7.23486e6i	0.465443	−	0.274298i
$931$		−	1.17523e6i		−	0.0444375i
$932$	−1.00106e7	+	5.78332e6i	−0.377502	+	0.218091i
$933$	−2.53852e7	−	1.43599e7i	−0.954720	−	0.540067i
$934$	−7.60123e6	+	1.31700e7i	−0.285113	+	0.493989i
$935$	8.71023e6			0.325837
$936$	1.35655e7	+	2.25483e7i	0.506110	+	0.841247i
$937$	6.27601e6			0.233526			0.116763	−	0.993160i	$-0.462748\pi$
$937$	6.27601e6			0.233526			0.116763	+	0.993160i	$0.462748\pi$
$938$	−1.07339e6	+	1.85977e6i	−0.0398337	+	0.0690162i
$939$	−935254.	−	529056.i	−0.0346151	−	0.0195811i
$940$	−1.13940e7	+	6.58256e6i	−0.420587	+	0.242983i
$941$			3.62021e7i			1.33279i	0.745601	+	0.666393i	$0.232162\pi$
$941$			3.62021e7i			1.33279i	−0.745601	+	0.666393i	$0.767838\pi$
$942$	−3.35491e7	+	1.97714e7i	−1.23184	+	0.725955i
$943$			4.38652e7i			1.60635i
$944$	−1.61168e7	+	2.79511e7i	−0.588638	+	1.02087i
$945$	318093.	+	1.20514e7i	0.0115871	+	0.438994i
$946$	1.79515e7	+	1.03610e7i	0.652189	+	0.376420i
$947$	−2.68397e7			−0.972528			−0.486264	−	0.873812i	$-0.661641\pi$
$947$	−2.68397e7			−0.972528			−0.486264	+	0.873812i	$0.661641\pi$
$948$	3.40170e7	−	308711.i	1.22935	−	0.0111566i
$949$	4.51184e6			0.162625
$950$	−2.62259e6	−	1.51367e6i	−0.0942805	−	0.0544154i
$951$	749300.	−	1.32460e6i	0.0268661	−	0.0474933i
$952$	−1.65146e6	+	690.650i	−0.0590576	+	2.46982e-5i
$953$		−	3.69459e7i		−	1.31775i	−0.752251	−	0.658876i	$-0.771032\pi$
$953$		−	3.69459e7i		−	1.31775i	0.752251	−	0.658876i	$-0.228968\pi$
$954$	93273.4	+	5.25971e6i	0.00331808	+	0.187107i
$955$		−	3.82293e7i		−	1.35640i
$956$	−8.68967e6	−	1.50413e7i	−0.307509	−	0.532279i
$957$	4.54150e7	−	8.02837e7i	1.60295	−	2.83366i
$958$	−1.48954e7	+	2.58079e7i	−0.524371	+	0.908529i
$959$	1.47909e7			0.519334
$960$	1.63110e7	−	2.88906e7i	0.571218	−	1.01176i
$961$	2.24392e7			0.783787
$962$	−1.44618e7	+	2.50567e7i	−0.503831	+	0.872942i
$963$	−1.07094e6	−	1.78179e6i	−0.0372135	−	0.0619142i
$964$	1.76072e7	+	3.04769e7i	0.610234	+	1.05628i
$965$		−	5.17261e7i		−	1.78810i
$966$	−6.18126e6	−	1.04887e7i	−0.213125	−	0.361642i
$967$		−	4.88706e7i		−	1.68067i	−0.542071	−	0.840333i	$-0.682360\pi$
$967$		−	4.88706e7i		−	1.68067i	0.542071	−	0.840333i	$-0.317640\pi$
$968$	−6.47586e7	+	27082.4i	−2.22131	+	0.000928964i
$969$	−1.23650e6	−	699467.i	−0.0423045	−	0.0239308i
$970$	5.08865e7	+	2.93699e7i	1.73649	+	1.00224i
$971$	2.82123e7			0.960264			0.480132	−	0.877196i	$-0.340589\pi$
$971$	2.82123e7			0.960264			0.480132	+	0.877196i	$0.340589\pi$
$972$	−2.61358e7	−	1.35846e7i	−0.887300	−	0.461193i
$973$	7.85953e6			0.266143
$974$	1.82195e7	+	1.05157e7i	0.615375	+	0.355173i
$975$	−8.87642e6	−	5.02122e6i	−0.299038	−	0.169160i
$976$	2.28203e7	−	3.95768e7i	0.766825	−	1.32989i
$977$		−	2.22713e7i		−	0.746463i	−0.927738	−	0.373231i	$-0.878250\pi$
$977$		−	2.22713e7i		−	0.746463i	0.927738	−	0.373231i	$-0.121750\pi$
$978$	5.62602e6	+	9.54653e6i	0.188085	+	0.319153i
$979$		−	1.01554e7i		−	0.338643i
$980$	−4.32103e6	+	2.49635e6i	−0.143722	+	0.0830311i
$981$	2.41772e6	+	4.02249e6i	0.0802109	+	0.133451i
$982$	−8.24794e6	+	1.42905e7i	−0.272940	+	0.472898i
$983$	−2.15973e7			−0.712879			−0.356439	−	0.934318i	$-0.616009\pi$
$983$	−2.15973e7			−0.712879			−0.356439	+	0.934318i	$0.616009\pi$
$984$	−2.16139e7	+	3.82459e7i	−0.711614	+	1.25921i
$985$	−3.45605e7			−1.13498
$986$	4.32514e6	−	7.49377e6i	0.141680	−	0.245475i
$987$	−2.38103e6	+	4.20915e6i	−0.0777988	+	0.137531i
$988$	−8.11342e6	+	4.68730e6i	−0.264430	+	0.152767i
$989$			1.43332e7i			0.465963i
$990$	1.14023e6	+	6.42977e7i	0.0369746	+	2.08501i
$991$			7.15417e6i			0.231406i	0.993284	+	0.115703i	$0.0369121\pi$
$991$			7.15417e6i			0.231406i	−0.993284	+	0.115703i	$0.963088\pi$
$992$	−1.24760e7	+	7.21462e6i	−0.402528	+	0.232774i
$993$	−6.76878e6	+	1.19657e7i	−0.217840	+	0.385093i
$994$	−2.00812e7	−	1.15902e7i	−0.644650	−	0.372069i
$995$	−3.66423e7			−1.17334
$996$	70398.3	+	7.75721e6i	0.00224861	+	0.247775i
$997$	−3.20997e6			−0.102274			−0.0511368	−	0.998692i	$-0.516284\pi$
$997$	−3.20997e6			−0.102274			−0.0511368	+	0.998692i	$0.516284\pi$
$998$	6.75764e6	+	3.90027e6i	0.214768	+	0.123956i
$999$	−854464.	−	3.23727e7i	−0.0270882	−	1.02628i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.6.e.a.71.39	yes	60
3.2	odd	2	inner	84.6.e.a.71.22	yes	60
4.3	odd	2	inner	84.6.e.a.71.21	✓	60
12.11	even	2	inner	84.6.e.a.71.40	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.6.e.a.71.21	✓	60	4.3	odd	2	inner
84.6.e.a.71.22	yes	60	3.2	odd	2	inner
84.6.e.a.71.39	yes	60	1.1	even	1	trivial
84.6.e.a.71.40	yes	60	12.11	even	2	inner

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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	84.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.82774 - 4.89937i) q^{2} +(-13.5680 - 7.67518i) q^{3} +(-16.0077 - 27.7084i) q^{4} +64.9508i q^{5} +(-75.9705 + 44.7714i) q^{6} +49.0000i q^{7} +(-181.019 + 0.0757033i) q^{8} +(125.183 + 208.274i) q^{9} +(318.218 + 183.664i) q^{10} +720.274 q^{11} +(4.52680 + 498.810i) q^{12} -598.221 q^{13} +(240.069 + 138.559i) q^{14} +(498.509 - 881.254i) q^{15} +(-511.505 + 887.095i) q^{16} -186.186i q^{17} +(1374.40 - 24.3730i) q^{18} +489.476i q^{19} +(1799.68 - 1039.71i) q^{20} +(376.084 - 664.834i) q^{21} +(2036.75 - 3528.89i) q^{22} +2817.60 q^{23} +(2456.66 + 1388.33i) q^{24} -1093.60 q^{25} +(-1691.62 + 2930.91i) q^{26} +(-99.9478 - 3786.68i) q^{27} +(1357.71 - 784.379i) q^{28} +8215.09i q^{29} +(-2907.94 - 4934.34i) q^{30} +2487.97i q^{31} +(2899.81 + 5014.54i) q^{32} +(-9772.71 - 5528.24i) q^{33} +(-912.196 - 526.487i) q^{34} -3182.59 q^{35} +(3767.04 - 6802.62i) q^{36} +8549.11 q^{37} +(2398.13 + 1384.11i) q^{38} +(8116.69 + 4591.46i) q^{39} +(-4.91698 - 11757.3i) q^{40} +15568.3i q^{41} +(-2193.80 - 3722.56i) q^{42} +5087.01i q^{43} +(-11530.0 - 19957.6i) q^{44} +(-13527.6 + 8130.74i) q^{45} +(7967.46 - 13804.5i) q^{46} -6331.13 q^{47} +(13748.7 - 8110.25i) q^{48} -2401.00 q^{49} +(-3092.43 + 5357.96i) q^{50} +(-1429.01 + 2526.18i) q^{51} +(9576.16 + 16575.7i) q^{52} +3826.91i q^{53} +(-18835.0 - 10218.1i) q^{54} +46782.4i q^{55} +(-3.70946 - 8869.95i) q^{56} +(3756.82 - 6641.23i) q^{57} +(40248.8 + 23230.2i) q^{58} +31508.5 q^{59} +(-32398.1 + 294.019i) q^{60} -44614.0 q^{61} +(12189.5 + 7035.34i) q^{62} +(-10205.4 + 6133.98i) q^{63} +(32768.0 - 27.4075i) q^{64} -38854.9i q^{65} +(-54719.6 + 32247.7i) q^{66} +7746.79i q^{67} +(-5158.91 + 2980.42i) q^{68} +(-38229.4 - 21625.6i) q^{69} +(-8999.54 + 15592.7i) q^{70} -83647.6 q^{71} +(-22676.3 - 37692.2i) q^{72} -7542.09 q^{73} +(24174.7 - 41885.3i) q^{74} +(14838.0 + 8393.59i) q^{75} +(13562.6 - 7835.39i) q^{76} +35293.4i q^{77} +(45447.2 - 26783.2i) q^{78} -68196.2i q^{79} +(-57617.5 - 33222.7i) q^{80} +(-27707.3 + 52144.9i) q^{81} +(76274.7 + 44023.0i) q^{82} +15551.4 q^{83} +(-24441.7 + 221.813i) q^{84} +12092.9 q^{85} +(24923.2 + 14384.8i) q^{86} +(63052.3 - 111463. i) q^{87} +(-130384. + 54.5271i) q^{88} -14099.4i q^{89} +(1583.05 + 89268.3i) q^{90} -29312.8i q^{91} +(-45103.4 - 78071.2i) q^{92} +(19095.6 - 33756.8i) q^{93} +(-17902.8 + 31018.5i) q^{94} -31791.8 q^{95} +(-857.201 - 90293.9i) q^{96} +159911. q^{97} +(-6789.41 + 11763.4i) q^{98} +(90166.3 + 150015. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 20 q^{4} - 114 q^{6} + 44 q^{9} + 668 q^{10} + 786 q^{12} - 3004 q^{16} - 3320 q^{18} + 7120 q^{22} + 16466 q^{24} - 37500 q^{25} - 7448 q^{28} - 35236 q^{30} - 9424 q^{33} + 43360 q^{34} + 50524 q^{36}+ \cdots + 232584 q^{97}+O(q^{100}) \) 60 * q - 20 * q^4 - 114 * q^6 + 44 * q^9 + 668 * q^10 + 786 * q^12 - 3004 * q^16 - 3320 * q^18 + 7120 * q^22 + 16466 * q^24 - 37500 * q^25 - 7448 * q^28 - 35236 * q^30 - 9424 * q^33 + 43360 * q^34 + 50524 * q^36 - 15056 * q^37 - 35468 * q^40 - 20090 * q^42 + 36024 * q^45 + 124416 * q^46 + 88654 * q^48 - 144060 * q^49 - 140108 * q^52 + 19486 * q^54 - 65072 * q^57 + 115616 * q^58 + 164908 * q^60 - 169424 * q^61 + 20116 * q^64 - 98484 * q^66 + 142536 * q^69 + 35868 * q^70 + 121312 * q^72 + 107256 * q^73 + 214836 * q^76 + 263708 * q^78 - 114932 * q^81 - 479624 * q^82 + 40474 * q^84 - 383992 * q^85 - 107320 * q^88 + 423760 * q^90 + 545208 * q^93 - 448512 * q^94 - 751618 * q^96 + 232584 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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