LMFDB - Embedded newform 195.6.bb.a.166.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,6,Mod(121,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("195.121");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	195.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$31.2748448635$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			166.16
Character	$\chi$	$=$	195.166
Dual form			195.6.bb.a.121.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.51954 - 2.60936i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-2.38250 + 4.12662i) q^{4} +25.0000i q^{5} +(40.6759 + 23.4842i) q^{6} +(51.9425 + 29.9890i) q^{7} +191.866i q^{8} +(-40.5000 + 70.1481i) q^{9} +(65.2339 + 112.989i) q^{10} +(144.118 - 83.2065i) q^{11} -42.8850 q^{12} +(-603.169 + 86.4908i) q^{13} +313.008 q^{14} +(-194.856 + 112.500i) q^{15} +(424.407 + 735.095i) q^{16} +(-192.295 + 333.064i) q^{17} +422.716i q^{18} +(-1121.56 - 647.531i) q^{19} +(-103.165 - 59.5626i) q^{20} +539.803i q^{21} +(434.231 - 752.111i) q^{22} +(-990.719 - 1715.97i) q^{23} +(-1495.45 + 863.398i) q^{24} -625.000 q^{25} +(-2500.36 + 1964.78i) q^{26} -729.000 q^{27} +(-247.506 + 142.898i) q^{28} +(637.665 + 1104.47i) q^{29} +(-587.106 + 1016.90i) q^{30} +9337.36i q^{31} +(-1480.90 - 854.997i) q^{32} +(1297.06 + 748.859i) q^{33} +2007.06i q^{34} +(-749.726 + 1298.56i) q^{35} +(-192.983 - 334.256i) q^{36} +(-2352.11 + 1357.99i) q^{37} -6758.57 q^{38} +(-3388.39 - 4312.03i) q^{39} -4796.65 q^{40} +(-3703.17 + 2138.03i) q^{41} +(1408.54 + 2439.66i) q^{42} +(-3226.35 + 5588.21i) q^{43} +792.959i q^{44} +(-1753.70 - 1012.50i) q^{45} +(-8955.19 - 5170.28i) q^{46} +12003.9i q^{47} +(-3819.67 + 6615.85i) q^{48} +(-6604.82 - 11439.9i) q^{49} +(-2824.71 + 1630.85i) q^{50} -3461.30 q^{51} +(1080.14 - 2695.11i) q^{52} +8751.13 q^{53} +(-3294.75 + 1902.22i) q^{54} +(2080.16 + 3602.95i) q^{55} +(-5753.88 + 9966.01i) q^{56} -11655.6i q^{57} +(5763.91 + 3327.79i) q^{58} +(11693.8 + 6751.41i) q^{59} -1072.13i q^{60} +(-6052.99 + 10484.1i) q^{61} +(24364.5 + 42200.6i) q^{62} +(-4207.34 + 2429.11i) q^{63} -36086.0 q^{64} +(-2162.27 - 15079.2i) q^{65} +7816.16 q^{66} +(30125.7 - 17393.1i) q^{67} +(-916.285 - 1587.05i) q^{68} +(8916.47 - 15443.8i) q^{69} +7825.21i q^{70} +(21774.3 + 12571.4i) q^{71} +(-13459.0 - 7770.58i) q^{72} +12638.3i q^{73} +(-7086.98 + 12275.0i) q^{74} +(-2812.50 - 4871.39i) q^{75} +(5344.23 - 3085.49i) q^{76} +9981.13 q^{77} +(-26565.6 - 10646.9i) q^{78} +38441.1 q^{79} +(-18377.4 + 10610.2i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-11157.7 + 19325.8i) q^{82} +51744.5i q^{83} +(-2227.56 - 1286.08i) q^{84} +(-8326.60 - 4807.37i) q^{85} +33674.8i q^{86} +(-5738.99 + 9940.22i) q^{87} +(15964.5 + 27651.3i) q^{88} +(2134.33 - 1232.26i) q^{89} -10567.9 q^{90} +(-33923.9 - 13595.9i) q^{91} +9441.56 q^{92} +(-72777.5 + 42018.1i) q^{93} +(31322.5 + 54252.1i) q^{94} +(16188.3 - 28038.9i) q^{95} -15389.9i q^{96} +(-47857.9 - 27630.8i) q^{97} +(-59701.5 - 34468.7i) q^{98} +13479.5i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 198 q^{3} + 320 q^{4} - 858 q^{7} - 1782 q^{9} - 504 q^{11} + 5760 q^{12} - 1066 q^{13} + 2708 q^{14} - 3508 q^{16} + 1380 q^{17} + 7560 q^{19} + 5700 q^{20} + 1986 q^{22} - 3188 q^{23} - 27500 q^{25}+ \cdots + 408840 q^{98}+O(q^{100}) $ 44 * q + 198 * q^3 + 320 * q^4 - 858 * q^7 - 1782 * q^9 - 504 * q^11 + 5760 * q^12 - 1066 * q^13 + 2708 * q^14 - 3508 * q^16 + 1380 * q^17 + 7560 * q^19 + 5700 * q^20 + 1986 * q^22 - 3188 * q^23 - 27500 * q^25 - 9892 * q^26 - 32076 * q^27 - 50652 * q^28 + 7804 * q^29 + 53040 * q^32 - 4536 * q^33 + 5500 * q^35 + 25920 * q^36 - 30852 * q^37 + 10752 * q^38 - 14760 * q^39 - 69084 * q^41 + 12186 * q^42 + 47754 * q^43 - 118938 * q^46 + 31572 * q^48 - 6424 * q^49 + 24840 * q^51 - 53998 * q^52 - 12208 * q^53 - 20000 * q^55 + 78194 * q^56 + 113862 * q^58 + 165780 * q^59 + 70158 * q^61 - 91292 * q^62 + 69498 * q^63 + 138152 * q^64 - 41300 * q^65 + 35748 * q^66 - 128586 * q^67 - 83136 * q^68 + 28692 * q^69 + 61692 * q^71 + 199966 * q^74 - 123750 * q^75 + 107346 * q^76 + 44120 * q^77 - 2070 * q^78 - 623476 * q^79 + 207000 * q^80 - 144342 * q^81 + 302968 * q^82 - 455868 * q^84 - 70236 * q^87 - 227398 * q^88 + 569928 * q^89 + 256314 * q^91 - 9464 * q^92 + 69282 * q^93 + 199660 * q^94 - 82300 * q^95 - 502962 * q^97 + 408840 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$	4.51954	−	2.60936i	0.798949	−	0.461274i	−0.0441542	−	0.999025i	$-0.514059\pi$
$2$	4.51954	−	2.60936i	0.798949	−	0.461274i	0.843104	+	0.537751i	$0.180726\pi$
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$4$	−2.38250	+	4.12662i	−0.0744532	+	0.128957i
$5$			25.0000i			0.447214i
$5$			25.0000i			0.447214i
$6$	40.6759	+	23.4842i	0.461274	+	0.266316i
$7$	51.9425	+	29.9890i	0.400662	+	0.231322i	0.686770	−	0.726875i	$-0.259028\pi$
$7$	51.9425	+	29.9890i	0.400662	+	0.231322i	−0.286108	+	0.958197i	$0.592362\pi$
$8$			191.866i			1.05992i
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	65.2339	+	112.989i	0.206288	+	0.357301i
$11$	144.118	−	83.2065i	0.359117	−	0.207336i	−0.309576	−	0.950875i	$-0.600187\pi$
$11$	144.118	−	83.2065i	0.359117	−	0.207336i	0.668693	+	0.743538i	$0.266854\pi$
$12$	−42.8850			−0.0859711
$13$	−603.169	+	86.4908i	−0.989875	+	0.141942i
$13$	−603.169	+	86.4908i	−0.989875	+	0.141942i
$14$	313.008			0.426811
$15$	−194.856	+	112.500i	−0.223607	+	0.129099i
$16$	424.407	+	735.095i	0.414460	+	0.717866i
$17$	−192.295	+	333.064i	−0.161378	+	0.279515i	−0.935363	−	0.353689i	$-0.884927\pi$
$17$	−192.295	+	333.064i	−0.161378	+	0.279515i	0.773985	+	0.633204i	$0.218261\pi$
$18$			422.716i			0.307516i
$19$	−1121.56	−	647.531i	−0.712750	−	0.411507i	0.0993282	−	0.995055i	$-0.468331\pi$
$19$	−1121.56	−	647.531i	−0.712750	−	0.411507i	−0.812079	+	0.583548i	$0.801664\pi$
$20$	−103.165	−	59.5626i	−0.0576712	−	0.0332965i
$21$			539.803i			0.267108i
$22$	434.231	−	752.111i	0.191278	−	0.331303i
$23$	−990.719	−	1715.97i	−0.390509	−	0.676381i	0.602008	−	0.798490i	$-0.294368\pi$
$23$	−990.719	−	1715.97i	−0.390509	−	0.676381i	−0.992517	+	0.122109i	$0.961034\pi$
$24$	−1495.45	+	863.398i	−0.529960	+	0.305973i
$25$	−625.000			−0.200000
$26$	−2500.36	+	1964.78i	−0.725386	+	0.570008i
$27$	−729.000			−0.192450
$28$	−247.506	+	142.898i	−0.0596611	+	0.0344454i
$29$	637.665	+	1104.47i	0.140798	+	0.243870i	0.927798	−	0.373084i	$-0.121700\pi$
$29$	637.665	+	1104.47i	0.140798	+	0.243870i	−0.786999	+	0.616954i	$0.788366\pi$
$30$	−587.106	+	1016.90i	−0.119100	+	0.206288i
$31$			9337.36i			1.74510i	0.488527	+	0.872549i	$0.337534\pi$
$31$			9337.36i			1.74510i	−0.488527	+	0.872549i	$0.662466\pi$
$32$	−1480.90	−	854.997i	−0.255653	−	0.147601i
$33$	1297.06	+	748.859i	0.207336	+	0.119706i
$34$			2007.06i			0.297758i
$35$	−749.726	+	1298.56i	−0.103450	+	0.179181i
$36$	−192.983	−	334.256i	−0.0248177	−	0.0429856i
$37$	−2352.11	+	1357.99i	−0.282458	+	0.163077i	−0.634536	−	0.772894i	$-0.718809\pi$
$37$	−2352.11	+	1357.99i	−0.282458	+	0.163077i	0.352078	+	0.935971i	$0.385475\pi$
$38$	−6758.57			−0.759269
$39$	−3388.39	−	4312.03i	−0.356723	−	0.453962i
$40$	−4796.65			−0.474011
$41$	−3703.17	+	2138.03i	−0.344044	+	0.198634i	−0.662059	−	0.749452i	$-0.730317\pi$
$41$	−3703.17	+	2138.03i	−0.344044	+	0.198634i	0.318015	+	0.948086i	$0.396984\pi$
$42$	1408.54	+	2439.66i	0.123210	+	0.213406i
$43$	−3226.35	+	5588.21i	−0.266098	+	0.460894i	−0.967851	−	0.251526i	$-0.919068\pi$
$43$	−3226.35	+	5588.21i	−0.266098	+	0.460894i	0.701753	+	0.712420i	$0.252401\pi$
$44$			792.959i			0.0617475i
$45$	−1753.70	−	1012.50i	−0.129099	−	0.0745356i
$46$	−8955.19	−	5170.28i	−0.623993	−	0.360263i
$47$			12003.9i			0.792644i	0.918112	+	0.396322i	$0.129714\pi$
$47$			12003.9i			0.792644i	−0.918112	+	0.396322i	$0.870286\pi$
$48$	−3819.67	+	6615.85i	−0.239289	+	0.414460i
$49$	−6604.82	−	11439.9i	−0.392980	−	0.680661i
$50$	−2824.71	+	1630.85i	−0.159790	+	0.0922547i
$51$	−3461.30			−0.186343
$52$	1080.14	−	2695.11i	0.0553950	−	0.138219i
$53$	8751.13			0.427932			0.213966	−	0.976841i	$-0.431362\pi$
$53$	8751.13			0.427932			0.213966	+	0.976841i	$0.431362\pi$
$54$	−3294.75	+	1902.22i	−0.153758	+	0.0887722i
$55$	2080.16	+	3602.95i	0.0927237	+	0.160602i
$56$	−5753.88	+	9966.01i	−0.245183	+	0.424670i
$57$		−	11655.6i		−	0.475167i
$58$	5763.91	+	3327.79i	0.224982	+	0.129893i
$59$	11693.8	+	6751.41i	0.437346	+	0.252502i	0.702471	−	0.711712i	$-0.252080\pi$
$59$	11693.8	+	6751.41i	0.437346	+	0.252502i	−0.265125	+	0.964214i	$0.585413\pi$
$60$		−	1072.13i		−	0.0384475i
$61$	−6052.99	+	10484.1i	−0.208279	+	0.360750i	−0.951172	−	0.308660i	$-0.900120\pi$
$61$	−6052.99	+	10484.1i	−0.208279	+	0.360750i	0.742894	+	0.669410i	$0.233453\pi$
$62$	24364.5	+	42200.6i	0.804968	+	1.39424i
$63$	−4207.34	+	2429.11i	−0.133554	+	0.0771074i
$64$	−36086.0			−1.10126
$65$	−2162.27	−	15079.2i	−0.0634785	−	0.442686i
$66$	7816.16			0.220868
$67$	30125.7	−	17393.1i	0.819880	−	0.473358i	−0.0304952	−	0.999535i	$-0.509708\pi$
$67$	30125.7	−	17393.1i	0.819880	−	0.473358i	0.850375	+	0.526177i	$0.176375\pi$
$68$	−916.285	−	1587.05i	−0.0240302	−	0.0416216i
$69$	8916.47	−	15443.8i	0.225460	−	0.390509i
$70$			7825.21i			0.190876i
$71$	21774.3	+	12571.4i	0.512623	+	0.295963i	0.733911	−	0.679245i	$-0.237693\pi$
$71$	21774.3	+	12571.4i	0.512623	+	0.295963i	−0.221288	+	0.975208i	$0.571026\pi$
$72$	−13459.0	−	7770.58i	−0.305973	−	0.176653i
$73$			12638.3i			0.277575i	0.990322	+	0.138787i	$0.0443205\pi$
$73$			12638.3i			0.277575i	−0.990322	+	0.138787i	$0.955680\pi$
$74$	−7086.98	+	12275.0i	−0.150446	+	0.260581i
$75$	−2812.50	−	4871.39i	−0.0577350	−	0.100000i
$76$	5344.23	−	3085.49i	0.106133	−	0.0612760i
$77$	9981.13			0.191846
$78$	−26565.6	−	10646.9i	−0.494405	−	0.198146i
$79$	38441.1			0.692992			0.346496	−	0.938051i	$-0.387371\pi$
$79$	38441.1			0.692992			0.346496	+	0.938051i	$0.387371\pi$
$80$	−18377.4	+	10610.2i	−0.321040	+	0.185352i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	−11157.7	+	19325.8i	−0.183249	+	0.317397i
$83$			51744.5i			0.824459i	0.911080	+	0.412230i	$0.135250\pi$
$83$			51744.5i			0.824459i	−0.911080	+	0.412230i	$0.864750\pi$
$84$	−2227.56	−	1286.08i	−0.0344454	−	0.0198870i
$85$	−8326.60	−	4807.37i	−0.125003	−	0.0721705i
$86$			33674.8i			0.490975i
$87$	−5738.99	+	9940.22i	−0.0812900	+	0.140798i
$88$	15964.5	+	27651.3i	0.219760	+	0.380636i
$89$	2134.33	−	1232.26i	0.0285618	−	0.0164902i	−0.485651	−	0.874153i	$-0.661417\pi$
$89$	2134.33	−	1232.26i	0.0285618	−	0.0164902i	0.514213	+	0.857663i	$0.328084\pi$
$90$	−10567.9			−0.137525
$91$	−33923.9	−	13595.9i	−0.429439	−	0.172109i
$92$	9441.56			0.116298
$93$	−72777.5	+	42018.1i	−0.872549	+	0.503766i
$94$	31322.5	+	54252.1i	0.365626	+	0.633282i
$95$	16188.3	−	28038.9i	0.184031	−	0.318752i
$96$		−	15389.9i		−	0.170435i
$97$	−47857.9	−	27630.8i	−0.516445	−	0.298170i	0.219034	−	0.975717i	$-0.429710\pi$
$97$	−47857.9	−	27630.8i	−0.516445	−	0.298170i	−0.735479	+	0.677547i	$0.763043\pi$
$98$	−59701.5	−	34468.7i	−0.627942	−	0.362543i
$99$			13479.5i			0.138224i
$100$	1489.06	−	2579.13i	0.0148906	−	0.0257913i
$101$	54032.2	+	93586.5i	0.527047	+	0.912872i	0.999503	+	0.0315179i	$0.0100341\pi$
$101$	54032.2	+	93586.5i	0.527047	+	0.912872i	−0.472456	+	0.881354i	$0.656633\pi$
$102$	−15643.5	+	9031.78i	−0.148879	+	0.0859553i
$103$	189283.			1.75800			0.879001	−	0.476821i	$-0.158211\pi$
$103$	189283.			1.75800			0.879001	+	0.476821i	$0.158211\pi$
$104$	−16594.7	−	115728.i	−0.150447	−	1.04919i
$105$	−13495.1			−0.119454
$106$	39551.1	−	22834.8i	0.341896	−	0.197394i
$107$	−4400.02	−	7621.05i	−0.0371531	−	0.0643510i	0.846851	−	0.531830i	$-0.178496\pi$
$107$	−4400.02	−	7621.05i	−0.0371531	−	0.0643510i	−0.884004	+	0.467479i	$0.845162\pi$
$108$	1736.84	−	3008.30i	0.0143285	−	0.0248177i
$109$		−	109262.i		−	0.880852i	−0.897789	−	0.440426i	$-0.854827\pi$
$109$		−	109262.i		−	0.880852i	0.897789	−	0.440426i	$-0.145173\pi$
$110$	18802.8	+	10855.8i	0.148163	+	0.0855420i
$111$	−21169.0	−	12221.9i	−0.163077	−	0.0941526i
$112$			50910.3i			0.383495i
$113$	22817.2	−	39520.6i	0.168100	−	0.291157i	−0.769652	−	0.638464i	$-0.779570\pi$
$113$	22817.2	−	39520.6i	0.168100	−	0.291157i	0.937752	+	0.347306i	$0.112904\pi$
$114$	−30413.5	−	52677.8i	−0.219182	−	0.379634i
$115$	42899.4	−	24768.0i	0.302487	−	0.174641i
$116$	−6076.95			−0.0419316
$117$	18361.2	−	45814.0i	0.124004	−	0.309409i
$118$	70467.4			0.465890
$119$	−19976.5	+	11533.5i	−0.129316	+	0.0746607i
$120$	−21584.9	−	37386.2i	−0.136835	−	0.237005i
$121$	−66678.8	+	115491.i	−0.414023	+	0.717109i
$122$			63177.7i			0.384294i
$123$	−33328.5	−	19242.2i	−0.198634	−	0.114681i
$124$	−38531.7	−	22246.3i	−0.225042	−	0.129928i
$125$		−	15625.0i		−	0.0894427i
$126$	−12676.8	+	21956.9i	−0.0711352	+	0.123210i
$127$	538.345	+	932.441i	0.00296177	+	0.00512994i	0.867502	−	0.497433i	$-0.165724\pi$
$127$	538.345	+	932.441i	0.00296177	+	0.00512994i	−0.864541	+	0.502563i	$0.832391\pi$
$128$	−115704.	+	66801.5i	−0.624197	+	0.360380i
$129$	−58074.4			−0.307263
$130$	−49119.5	−	62509.0i	−0.254915	−	0.324402i
$131$	−27169.4			−0.138325			−0.0691626	−	0.997605i	$-0.522033\pi$
$131$	−27169.4			−0.138325			−0.0691626	+	0.997605i	$0.522033\pi$
$132$	−6180.50	+	3568.32i	−0.0308737	+	0.0178250i
$133$	−38837.7	−	67268.8i	−0.190381	−	0.329750i
$134$	90769.6	−	157218.i	0.436695	−	0.756378i
$135$		−	18225.0i		−	0.0860663i
$136$	−63903.7	−	36894.8i	−0.296264	−	0.171048i
$137$	110342.	+	63705.8i	0.502271	+	0.289986i	0.729651	−	0.683820i	$-0.239683\pi$
$137$	110342.	+	63705.8i	0.502271	+	0.289986i	−0.227380	+	0.973806i	$0.573016\pi$
$138$		−	93065.0i		−	0.415996i
$139$	133572.	−	231353.i	0.586378	−	1.01564i	−0.408324	−	0.912837i	$-0.633887\pi$
$139$	133572.	−	231353.i	0.586378	−	1.01564i	0.994702	−	0.102800i	$-0.0327801\pi$
$140$	−3572.45	−	6187.66i	−0.0154044	−	0.0266813i
$141$	−93561.2	+	54017.6i	−0.396322	+	0.228817i
$142$	131213.			0.546080
$143$	−79730.8	+	62652.4i	−0.326051	+	0.256211i
$144$	−68754.0			−0.276307
$145$	−27611.7	+	15941.6i	−0.109062	+	0.0629670i
$146$	32977.7	+	57119.1i	0.128038	+	0.221768i
$147$	59443.3	−	102959.i	0.226887	−	0.392980i
$148$		−	12941.7i		−	0.0485664i
$149$	−297875.	−	171978.i	−1.09918	−	0.634611i	−0.163173	−	0.986598i	$-0.552173\pi$
$149$	−297875.	−	171978.i	−1.09918	−	0.634611i	−0.936005	+	0.351987i	$0.885506\pi$
$150$	−25422.4	−	14677.6i	−0.0922547	−	0.0532633i
$151$			399.575i			0.00142612i	1.00000		0.000713060i	$0.000226974\pi$
$151$			399.575i			0.00142612i	−1.00000		0.000713060i	$0.999773\pi$
$152$	124239.	−	215189.i	0.436164	−	0.755459i
$153$	−15575.9	−	26978.2i	−0.0537927	−	0.0931717i
$154$	45110.1	−	26044.3i	0.153275	−	0.0884936i
$155$	−233434.			−0.780431
$156$	25866.9	−	3709.16i	0.0851007	−	0.0122029i
$157$	354487.			1.14776			0.573879	−	0.818940i	$-0.305438\pi$
$157$	354487.			1.14776			0.573879	+	0.818940i	$0.305438\pi$
$158$	173736.	−	100307.i	0.553666	−	0.319659i
$159$	39380.1	+	68208.3i	0.123533	+	0.213966i
$160$	21374.9	−	37022.4i	0.0660092	−	0.114331i
$161$		−	118843.i		−	0.361333i
$162$	−29652.7	−	17120.0i	−0.0887722	−	0.0512526i
$163$	294303.	+	169916.i	0.867611	+	0.500916i	0.866554	−	0.499084i	$-0.166330\pi$
$163$	294303.	+	169916.i	0.867611	+	0.500916i	0.00105751	+	0.999999i	$0.499663\pi$
$164$		−	20375.4i		−	0.0591557i
$165$	−18721.5	+	32426.5i	−0.0535340	+	0.0927237i
$166$	135020.	+	233861.i	0.380301	+	0.658701i
$167$	182387.	−	105301.i	0.506061	−	0.292175i	−0.225152	−	0.974324i	$-0.572288\pi$
$167$	182387.	−	105301.i	0.506061	−	0.292175i	0.731213	+	0.682149i	$0.238955\pi$
$168$	−103570.			−0.283113
$169$	356332.	−	104337.i	0.959705	−	0.281010i
$170$	−50176.5			−0.133161
$171$	90846.1	−	52450.0i	0.237583	−	0.137169i
$172$	−15373.6	−	26627.8i	−0.0396236	−	0.0686301i
$173$	−76009.6	+	131653.i	−0.193087	+	0.334437i	−0.946272	−	0.323372i	$-0.895183\pi$
$173$	−76009.6	+	131653.i	−0.193087	+	0.334437i	0.753185	+	0.657809i	$0.228517\pi$
$174$			59900.3i			0.149988i
$175$	−32464.1	−	18743.1i	−0.0801324	−	0.0462644i
$176$	122329.	+	70626.9i	0.297680	+	0.171865i
$177$			121525.i			0.291564i
$178$	6430.79	−	11138.5i	0.0152130	−	0.0263497i
$179$	−152608.	−	264325.i	−0.355996	−	0.616603i	0.631292	−	0.775545i	$-0.282525\pi$
$179$	−152608.	−	264325.i	−0.355996	−	0.616603i	−0.987288	+	0.158942i	$0.949192\pi$
$180$	8356.40	−	4824.57i	0.0192237	−	0.0110988i
$181$	877478.			1.99086			0.995428	−	0.0955129i	$-0.0304491\pi$
$181$	877478.			1.99086			0.995428	+	0.0955129i	$0.0304491\pi$
$182$	−188797.	+	27072.4i	−0.422490	+	0.0605826i
$183$	−108954.			−0.240500
$184$	329237.	−	190085.i	0.716910	−	0.413908i
$185$	−33949.8	−	58802.8i	−0.0729303	−	0.126319i
$186$	−219281.	+	379805.i	−0.464748	+	0.804968i
$187$			64000.7i			0.133838i
$188$	−49535.5	−	28599.3i	−0.102217	−	0.0590149i
$189$	−37866.1	−	21862.0i	−0.0771074	−	0.0445180i
$190$		−	168964.i		−	0.339555i
$191$	−67180.3	+	116360.i	−0.133247	+	0.230791i	−0.924927	−	0.380146i	$-0.875874\pi$
$191$	−67180.3	+	116360.i	−0.133247	+	0.230791i	0.791679	+	0.610937i	$0.209207\pi$
$192$	−162387.	−	281263.i	−0.317906	−	0.550629i
$193$	67321.2	−	38867.9i	0.130094	−	0.0751100i	−0.433540	−	0.901134i	$-0.642736\pi$
$193$	67321.2	−	38867.9i	0.130094	−	0.0751100i	0.563635	+	0.826024i	$0.309403\pi$
$194$	−288394.			−0.550152
$195$	107801.	−	84709.7i	0.203018	−	0.159532i
$196$	62944.0			0.117034
$197$	−90820.3	+	52435.1i	−0.166731	+	0.0962624i	−0.581044	−	0.813872i	$-0.697355\pi$
$197$	−90820.3	+	52435.1i	−0.166731	+	0.0962624i	0.414312	+	0.910135i	$0.364022\pi$
$198$	35172.7	+	60921.0i	0.0637592	+	0.110434i
$199$	−107055.	+	185424.i	−0.191634	+	0.331920i	−0.945792	−	0.324773i	$-0.894712\pi$
$199$	−107055.	+	185424.i	−0.191634	+	0.331920i	0.754158	+	0.656693i	$0.228045\pi$
$200$		−	119916.i		−	0.211984i
$201$	271131.	+	156538.i	0.473358	+	0.273293i
$202$	488401.	+	281979.i	0.842168	+	0.486226i
$203$			76491.8i			0.130279i
$204$	8246.56	−	14283.5i	0.0138739	−	0.0240302i
$205$	−53450.6	−	92579.2i	−0.0888318	−	0.153861i
$206$	855473.	−	493908.i	1.40455	−	0.810920i
$207$	160496.			0.260339
$208$	−319568.	−	406679.i	−0.512159	−	0.651768i
$209$	−215515.			−0.341281
$210$	−60991.5	+	35213.5i	−0.0954379	+	0.0551011i
$211$	616088.	+	1.06710e6i	0.952657	+	1.65005i	0.739641	+	0.673001i	$0.234995\pi$
$211$	616088.	+	1.06710e6i	0.952657	+	1.65005i	0.213016	+	0.977049i	$0.431671\pi$
$212$	−20849.6	+	36112.5i	−0.0318609	+	0.0551847i
$213$			226285.i			0.341749i
$214$	−39772.1	−	22962.4i	−0.0593669	−	0.0342755i
$215$	−139705.	−	80658.8i	−0.206118	−	0.119002i
$216$		−	139870.i		−	0.203982i
$217$	−280018.	+	485006.i	−0.403680	+	0.699194i
$218$	−285104.	−	493814.i	−0.406314	−	0.703756i
$219$	−98505.4	+	56872.1i	−0.138787	+	0.0801289i
$220$	−19824.0			−0.0276143
$221$	87179.1	−	217525.i	0.120069	−	0.299591i
$222$	−127566.			−0.173720
$223$	−266218.	+	153701.i	−0.358489	+	0.206973i	−0.668418	−	0.743786i	$-0.733028\pi$
$223$	−266218.	+	153701.i	−0.358489	+	0.206973i	0.309929	+	0.950760i	$0.399695\pi$
$224$	−51281.0	−	88821.4i	−0.0682868	−	0.118276i
$225$	25312.5	−	43842.5i	0.0333333	−	0.0577350i
$226$		−	238153.i		−	0.310160i
$227$	−1.03194e6	−	595789.i	−1.32919	−	0.767411i	−0.344019	−	0.938963i	$-0.611788\pi$
$227$	−1.03194e6	−	595789.i	−1.32919	−	0.767411i	−0.985175	+	0.171552i	$0.945122\pi$
$228$	48098.0	+	27769.4i	0.0612760	+	0.0353777i
$229$		−	298650.i		−	0.376334i	−0.982137	−	0.188167i	$-0.939745\pi$
$229$		−	298650.i		−	0.376334i	0.982137	−	0.188167i	$-0.0602546\pi$
$230$	129257.	−	223880.i	0.161114	−	0.279058i
$231$	44915.1	+	77795.2i	0.0553812	+	0.0959231i
$232$	−211910.	+	122346.i	−0.258483	+	0.149235i
$233$	−1.07994e6			−1.30319			−0.651597	−	0.758566i	$-0.725901\pi$
$233$	−1.07994e6			−1.30319			−0.651597	+	0.758566i	$0.725901\pi$
$234$	−36561.0	−	254969.i	−0.0436495	−	0.304402i
$235$	−300098.			−0.354481
$236$	−55721.0	+	32170.5i	−0.0651236	+	0.0375992i
$237$	172985.	+	299619.i	0.200050	+	0.346496i
$238$	−60189.8	+	104252.i	−0.0688780	+	0.119300i
$239$			1.33861e6i			1.51586i	0.652339	+	0.757928i	$0.273788\pi$
$239$			1.33861e6i			1.51586i	−0.652339	+	0.757928i	$0.726212\pi$
$240$	−165396.	−	95491.6i	−0.185352	−	0.107013i
$241$	919850.	+	531076.i	1.02017	+	0.588998i	0.914154	−	0.405366i	$-0.132856\pi$
$241$	919850.	+	531076.i	1.02017	+	0.588998i	0.106020	+	0.994364i	$0.466189\pi$
$242$			695956.i			0.763912i
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$	−28842.5	−	49956.7i	−0.0310141	−	0.0537179i
$245$	285997.	−	165120.i	0.304401	−	0.175746i
$246$	−200839.			−0.211598
$247$	732494.	+	293566.i	0.763944	+	0.306171i
$248$	−1.79152e6			−1.84966
$249$	−403309.	+	232850.i	−0.412230	+	0.238001i
$250$	−40771.2	−	70617.8i	−0.0412576	−	0.0714602i
$251$	−588083.	+	1.01859e6i	−0.589189	+	1.02050i	0.405150	+	0.914250i	$0.367219\pi$
$251$	−588083.	+	1.01859e6i	−0.589189	+	1.02050i	−0.994339	+	0.106255i	$0.966114\pi$
$252$		−	23149.5i		−	0.0229636i
$253$	−285561.	−	164868.i	−0.280477	−	0.161933i
$254$	4866.15	+	2809.47i	0.00473261	+	0.00273237i
$255$		−	86532.6i		−	0.0833353i
$256$	228759.	−	396221.i	0.218161	−	0.377866i
$257$	486030.	+	841828.i	0.459018	+	0.795043i	0.998909	−	0.0466919i	$-0.0148679\pi$
$257$	486030.	+	841828.i	0.459018	+	0.795043i	−0.539891	+	0.841735i	$0.681535\pi$
$258$	−262469.	+	151537.i	−0.245488	+	0.141732i
$259$	−162899.			−0.150893
$260$	67377.7	+	27003.4i	0.0618135	+	0.0247734i
$261$	−103302.			−0.0938656
$262$	−122793.	+	70894.7i	−0.110515	+	0.0638058i
$263$	−403494.	−	698872.i	−0.359706	−	0.623029i	0.628206	−	0.778047i	$-0.283790\pi$
$263$	−403494.	−	698872.i	−0.359706	−	0.623029i	−0.987912	+	0.155018i	$0.950456\pi$
$264$	−143681.	+	248862.i	−0.126879	+	0.219760i
$265$			218778.i			0.191377i
$266$	−351057.	−	202683.i	−0.304210	−	0.175636i
$267$	19209.0	+	11090.3i	0.0164902	+	0.00952062i
$268$			165756.i			0.140972i
$269$	−895225.	+	1.55057e6i	−0.754313	+	1.30651i	0.191403	+	0.981512i	$0.438696\pi$
$269$	−895225.	+	1.55057e6i	−0.754313	+	1.30651i	−0.945715	+	0.324996i	$0.894637\pi$
$270$	−47555.5	−	82368.6i	−0.0397001	−	0.0687626i
$271$	1.06468e6	−	614693.i	0.880635	−	0.508435i	0.00976724	−	0.999952i	$-0.496891\pi$
$271$	1.06468e6	−	614693.i	0.880635	−	0.508435i	0.870868	+	0.491517i	$0.163558\pi$
$272$	−326445.			−0.267539
$273$	−46688.0	−	325592.i	−0.0379139	−	0.264403i
$274$	664925.			0.535053
$275$	−90073.7	+	52004.1i	−0.0718235	+	0.0414673i
$276$	42487.0	+	73589.7i	0.0335725	+	0.0581492i
$277$	−713522.	+	1.23586e6i	−0.558737	+	0.967761i	0.438865	+	0.898553i	$0.355381\pi$
$277$	−713522.	+	1.23586e6i	−0.558737	+	0.967761i	−0.997602	+	0.0692084i	$0.977953\pi$
$278$		−	1.39415e6i		−	1.08192i
$279$	−654997.	−	378163.i	−0.503766	−	0.290850i
$280$	−249150.	−	143847.i	−0.189918	−	0.109649i
$281$			1.36246e6i			1.02934i	0.857389	+	0.514668i	$0.172085\pi$
$281$			1.36246e6i			1.02934i	−0.857389	+	0.514668i	$0.827915\pi$
$282$	−281902.	+	488269.i	−0.211094	+	0.365626i
$283$	−458620.	−	794353.i	−0.340398	−	0.589587i	0.644109	−	0.764934i	$-0.277228\pi$
$283$	−458620.	−	794353.i	−0.340398	−	0.589587i	−0.984507	+	0.175347i	$0.943895\pi$
$284$	−103755.	+	59902.7i	−0.0763328	+	0.0440708i
$285$	291389.			0.212501
$286$	−196864.	+	491206.i	−0.142315	+	0.355099i
$287$	−256469.			−0.183794
$288$	119953.	−	69254.7i	0.0852175	−	0.0492004i
$289$	635974.	+	1.10154e6i	0.447914	+	0.775810i
$290$	−83194.8	+	144098.i	−0.0580900	+	0.100615i
$291$		−	497354.i		−	0.344297i
$292$	−52153.2	−	30110.7i	−0.0357951	−	0.0206663i
$293$	31692.1	+	18297.5i	0.0215666	+	0.0124515i	0.510745	−	0.859733i	$-0.329370\pi$
$293$	31692.1	+	18297.5i	0.0215666	+	0.0124515i	−0.489178	+	0.872184i	$0.662703\pi$
$294$		−	620436.i		−	0.418628i
$295$	−168785.	+	292345.i	−0.112922	+	0.195587i
$296$	−260553.	−	451290.i	−0.172849	−	0.299383i
$297$	−105062.	+	60657.6i	−0.0691122	+	0.0399019i
$298$	−1.79501e6			−1.17092
$299$	745986.	+	949334.i	0.482562	+	0.614103i
$300$	26803.2			0.0171942
$301$	−335170.	+	193510.i	−0.213230	+	0.123109i
$302$	1042.64	+	1805.90i	0.000657832	+	0.00113940i
$303$	−486290.	+	842279.i	−0.304291	+	0.527047i
$304$		−	1.09927e6i		−	0.682213i
$305$	−262102.	−	151325.i	−0.161332	−	0.0931452i
$306$	−140791.	−	81286.0i	−0.0859553	−	0.0496263i
$307$			2.09577e6i			1.26910i	0.772880	+	0.634552i	$0.218815\pi$
$307$			2.09577e6i			1.26910i	−0.772880	+	0.634552i	$0.781185\pi$
$308$	−23780.1	+	41188.3i	−0.0142836	+	0.0247398i
$309$	851775.	+	1.47532e6i	0.507491	+	0.879001i
$310$	−1.05501e6	+	609113.i	−0.623525	+	0.359992i
$311$	729836.			0.427882			0.213941	−	0.976847i	$-0.431370\pi$
$311$	729836.			0.427882			0.213941	+	0.976847i	$0.431370\pi$
$312$	827332.	−	650117.i	0.481164	−	0.378098i
$313$	−2.02399e6			−1.16775			−0.583873	−	0.811845i	$-0.698464\pi$
$313$	−2.02399e6			−1.16775			−0.583873	+	0.811845i	$0.698464\pi$
$314$	1.60212e6	−	924982.i	0.917001	−	0.529431i
$315$	−60727.8	−	105184.i	−0.0344835	−	0.0597271i
$316$	−91586.0	+	158632.i	−0.0515955	+	0.0893660i
$317$		−	170968.i		−	0.0955578i	−0.998858	−	0.0477789i	$-0.984786\pi$
$317$		−	170968.i		−	0.0955578i	0.998858	−	0.0477789i	$-0.0152143\pi$
$318$	355960.	+	205513.i	0.197394	+	0.113965i
$319$	183798.	+	106116.i	0.101126	+	0.0583853i
$320$		−	902151.i		−	0.492498i
$321$	39600.1	−	68589.5i	0.0214503	−	0.0371531i
$322$	−310103.	−	537115.i	−0.166674	−	0.288687i
$323$	431339.	−	249034.i	0.230045	−	0.132816i
$324$	31263.2			0.0165452
$325$	376980.	−	54056.8i	0.197975	−	0.0283884i
$326$	1.77348e6			0.924237
$327$	851613.	−	491679.i	0.440426	−	0.254280i
$328$	−410215.	−	710513.i	−0.210536	−	0.364659i
$329$	−359986.	+	623513.i	−0.183356	+	0.317582i
$330$			195404.i			0.0987754i
$331$	1.32868e6	+	767114.i	0.666578	+	0.384849i	0.794779	−	0.606899i	$-0.207587\pi$
$331$	1.32868e6	+	767114.i	0.666578	+	0.384849i	−0.128201	+	0.991748i	$0.540920\pi$
$332$	−213530.	−	123281.i	−0.106320	−	0.0613836i
$333$		−	219995.i		−	0.108718i
$334$	549537.	−	951826.i	0.269545	−	0.466865i
$335$	434827.	+	753143.i	0.211692	+	0.366661i
$336$	−396806.	+	229096.i	−0.191748	+	0.110706i
$337$	31943.4			0.0153217			0.00766083	−	0.999971i	$-0.497561\pi$
$337$	31943.4			0.0153217			0.00766083	+	0.999971i	$0.497561\pi$
$338$	1.33820e6	−	1.40135e6i	0.637133	−	0.667199i
$339$	410710.			0.194105
$340$	39676.3	−	22907.1i	0.0186137	−	0.0107467i
$341$	776929.	+	1.34568e6i	0.361822	+	0.626695i
$342$	273722.	−	474100.i	0.126545	−	0.219182i
$343$		−	1.80034e6i		−	0.826264i
$344$	−1.07219e6	−	619028.i	−0.488511	−	0.282042i
$345$	386094.	+	222912.i	0.174641	+	0.100829i
$346$			793345.i			0.356264i
$347$	1.41178e6	−	2.44528e6i	0.629424	−	1.09019i	−0.358243	−	0.933628i	$-0.616624\pi$
$347$	1.41178e6	−	2.44528e6i	0.629424	−	1.09019i	0.987667	−	0.156567i	$-0.0500426\pi$
$348$	−27346.3	−	47365.2i	−0.0121046	−	0.0209658i
$349$	850966.	−	491306.i	0.373980	−	0.215918i	−0.301216	−	0.953556i	$-0.597392\pi$
$349$	850966.	−	491306.i	0.373980	−	0.215918i	0.675196	+	0.737638i	$0.264059\pi$
$350$	−195630.			−0.0853623
$351$	439710.	−	63051.8i	0.190502	−	0.0273168i
$352$	−284565.			−0.122412
$353$	2.11683e6	−	1.22215e6i	0.904168	−	0.522022i	0.0256180	−	0.999672i	$-0.491845\pi$
$353$	2.11683e6	−	1.22215e6i	0.904168	−	0.522022i	0.878550	+	0.477650i	$0.158511\pi$
$354$	317103.	+	549239.i	0.134491	+	0.232945i
$355$	−314285.	+	544357.i	−0.132359	+	0.229252i
$356$			11743.4i			0.00491099i
$357$	−179789.	−	103801.i	−0.0746607	−	0.0431054i
$358$	−1.37944e6	−	796418.i	−0.568846	−	0.328423i
$359$			3.34651e6i			1.37043i	0.728342	+	0.685214i	$0.240291\pi$
$359$			3.34651e6i			1.37043i	−0.728342	+	0.685214i	$0.759709\pi$
$360$	194264.	−	336476.i	0.0790018	−	0.136835i
$361$	−399456.	−	691877.i	−0.161325	−	0.279422i
$362$	3.96580e6	−	2.28965e6i	1.59059	−	0.918330i
$363$	−1.20022e6			−0.478073
$364$	136929.	−	107599.i	0.0541678	−	0.0425650i
$365$	−315956.			−0.124135
$366$	−492421.	+	284299.i	−0.192147	+	0.110936i
$367$	−60415.6	−	104643.i	−0.0234144	−	0.0405550i	0.854081	−	0.520140i	$-0.174120\pi$
$367$	−60415.6	−	104643.i	−0.0234144	−	0.0405550i	−0.877495	+	0.479585i	$0.840787\pi$
$368$	840936.	−	1.45654e6i	0.323701	−	0.560666i
$369$		−	346360.i		−	0.132423i
$370$	−306875.	−	177174.i	−0.116535	−	0.0672817i
$371$	454556.	+	262438.i	0.171456	+	0.0989901i
$372$		−	400433.i		−	0.150028i
$373$	2.36847e6	−	4.10230e6i	0.881445	−	1.52671i	0.0317096	−	0.999497i	$-0.489905\pi$
$373$	2.36847e6	−	4.10230e6i	0.881445	−	1.52671i	0.849735	−	0.527210i	$-0.176762\pi$
$374$	167001.	+	289254.i	0.0617361	+	0.106930i
$375$	121785.	−	70312.5i	0.0447214	−	0.0258199i
$376$	−2.30314e6			−0.840139
$377$	−480146.	−	611028.i	−0.173988	−	0.221416i
$378$	−228183.			−0.0821399
$379$	3.14885e6	−	1.81799e6i	1.12604	−	0.650119i	0.183104	−	0.983094i	$-0.441386\pi$
$379$	3.14885e6	−	1.81799e6i	1.12604	−	0.650119i	0.942936	+	0.332974i	$0.108052\pi$
$380$	77137.3	+	133606.i	0.0274034	+	0.0474642i
$381$	−4845.11	+	8391.97i	−0.00170998	+	0.00296177i
$382$			701190.i			0.245854i
$383$	−2.49640e6	−	1.44130e6i	−0.869596	−	0.502061i	−0.00238185	−	0.999997i	$-0.500758\pi$
$383$	−2.49640e6	−	1.44130e6i	−0.869596	−	0.502061i	−0.867214	+	0.497936i	$0.834092\pi$
$384$	−1.04133e6	−	601213.i	−0.360380	−	0.208066i
$385$			249528.i			0.0857962i
$386$	202841.	−	351330.i	0.0692926	−	0.120018i
$387$	−261335.	−	452645.i	−0.0886992	−	0.153631i
$388$	228043.	−	131661.i	0.0769020	−	0.0443994i
$389$	1.85772e6			0.622452			0.311226	−	0.950336i	$-0.399260\pi$
$389$	1.85772e6			0.622452			0.311226	+	0.950336i	$0.399260\pi$
$390$	266171.	−	664139.i	0.0886135	−	0.221105i
$391$	762039.			0.252078
$392$	2.19492e6	−	1.26724e6i	0.721447	−	0.416528i
$393$	−122262.	−	211764.i	−0.0399311	−	0.0691626i
$394$	−273644.	+	473965.i	−0.0888066	+	0.153818i
$395$			961028.i			0.309915i
$396$	−55624.5	−	32114.8i	−0.0178250	−	0.0102912i
$397$	−922605.	−	532666.i	−0.293792	−	0.169621i	0.345859	−	0.938287i	$-0.387588\pi$
$397$	−922605.	−	532666.i	−0.293792	−	0.169621i	−0.639651	+	0.768666i	$0.720921\pi$
$398$			1.11738e6i			0.353584i
$399$	349539.	−	605420.i	0.109917	−	0.190381i
$400$	−265255.	−	459434.i	−0.0828920	−	0.143573i
$401$	1.68649e6	−	973694.i	0.523748	−	0.302386i	−0.214719	−	0.976676i	$-0.568884\pi$
$401$	1.68649e6	−	973694.i	0.523748	−	0.302386i	0.738467	+	0.674290i	$0.235550\pi$
$402$	1.63385e6			0.504252
$403$	−807596.	−	5.63200e6i	−0.247703	−	1.72743i
$404$	−514927.			−0.156961
$405$	142050.	−	82012.5i	0.0430331	−	0.0248452i
$406$	199595.	+	345708.i	0.0600944	+	0.104086i
$407$	−225988.	+	391422.i	−0.0676237	+	0.117128i
$408$		−	664107.i		−	0.197509i
$409$	−2.09310e6	−	1.20845e6i	−0.618704	−	0.357209i	0.157660	−	0.987493i	$-0.449605\pi$
$409$	−2.09310e6	−	1.20845e6i	−0.618704	−	0.357209i	−0.776364	+	0.630285i	$0.782938\pi$
$410$	−483145.	−	278944.i	−0.141944	−	0.0819515i
$411$			1.14670e6i			0.334848i
$412$	−450968.	+	781099.i	−0.130889	+	0.226706i
$413$	404937.	+	701371.i	0.116819	+	0.202336i
$414$	725370.	−	418793.i	0.207998	−	0.120088i
$415$	−1.29361e6			−0.368709
$416$	967180.	+	387623.i	0.274015	+	0.109819i
$417$	2.40429e6			0.677091
$418$	−974030.	+	562357.i	−0.272667	+	0.157424i
$419$	1.71640e6	+	2.97289e6i	0.477621	+	0.827265i	0.999671	−	0.0256506i	$-0.00816573\pi$
$419$	1.71640e6	+	2.97289e6i	0.477621	+	0.827265i	−0.522050	+	0.852915i	$0.674832\pi$
$420$	32152.0	−	55688.9i	0.00889375	−	0.0154044i
$421$		−	6.32471e6i		−	1.73914i	−0.493806	−	0.869572i	$-0.664395\pi$
$421$		−	6.32471e6i		−	1.73914i	0.493806	−	0.869572i	$-0.335605\pi$
$422$	5.56887e6	+	3.21519e6i	1.52225	+	0.878871i
$423$	−842051.	−	486158.i	−0.228817	−	0.132107i
$424$			1.67904e6i			0.453574i
$425$	120184.	−	208165.i	0.0322756	−	0.0559030i
$426$	590458.	+	1.02270e6i	0.157640	+	0.273040i
$427$	−628815.	+	363047.i	−0.166899	+	0.0963591i
$428$	41932.2			0.0110647
$429$	−847116.	−	339504.i	−0.222228	−	0.0890639i
$430$	−841871.			−0.219571
$431$	3.52739e6	−	2.03654e6i	0.914662	−	0.528080i	0.0327339	−	0.999464i	$-0.489579\pi$
$431$	3.52739e6	−	2.03654e6i	0.914662	−	0.528080i	0.881928	+	0.471384i	$0.156245\pi$
$432$	−309393.	−	535884.i	−0.0797629	−	0.138153i
$433$	−1.18073e6	+	2.04508e6i	−0.302643	+	0.524193i	−0.976734	−	0.214455i	$-0.931202\pi$
$433$	−1.18073e6	+	2.04508e6i	−0.302643	+	0.524193i	0.674091	+	0.738649i	$0.264536\pi$
$434$			2.92267e6i			0.744828i
$435$	−248505.	−	143475.i	−0.0629670	−	0.0363540i
$436$	450882.	+	260317.i	0.113592	+	0.0655822i
$437$			2.56609e6i			0.642788i
$438$	−296800.	+	514072.i	−0.0739227	+	0.128038i
$439$	−495600.	−	858404.i	−0.122735	−	0.212584i	0.798110	−	0.602512i	$-0.205833\pi$
$439$	−495600.	−	858404.i	−0.122735	−	0.212584i	−0.920845	+	0.389928i	$0.872500\pi$
$440$	−691284.	+	399113.i	−0.170226	+	0.0982797i
$441$	1.06998e6			0.261987
$442$	−173592.	−	1.21060e6i	−0.0422644	−	0.294743i
$443$	−7.82126e6			−1.89351			−0.946754	−	0.321958i	$-0.895659\pi$
$443$	−7.82126e6			−1.89351			−0.946754	+	0.321958i	$0.895659\pi$
$444$	100870.	−	58237.6i	0.0242832	−	0.0140199i
$445$	30806.4	+	53358.2i	0.00737464	+	0.0127732i
$446$	−802122.	+	1.38932e6i	−0.190943	+	0.330723i
$447$		−	3.09560e6i		−	0.732785i
$448$	−1.87440e6	−	1.08219e6i	−0.441232	−	0.254746i
$449$	6.07750e6	+	3.50884e6i	1.42269	+	0.821388i	0.996528	−	0.0832613i	$-0.0265336\pi$
$449$	6.07750e6	+	3.50884e6i	1.42269	+	0.821388i	0.426157	+	0.904649i	$0.359867\pi$
$450$		−	264197.i		−	0.0615032i
$451$	−355795.	+	616256.i	−0.0823681	+	0.142666i
$452$	108724.	+	188316.i	0.0250311	+	0.0433552i
$453$	−3114.38	+	1798.09i	−0.000713060	+	0.000411686i
$454$	−6.21851e6			−1.41595
$455$	339897.	−	848097.i	0.0769696	−	0.192051i
$456$	2.23631e6			0.503639
$457$	−5.51398e6	+	3.18350e6i	−1.23502	+	0.713041i	−0.968073	−	0.250669i	$-0.919349\pi$
$457$	−5.51398e6	+	3.18350e6i	−1.23502	+	0.713041i	−0.266950	+	0.963710i	$0.586016\pi$
$458$	−779284.	−	1.34976e6i	−0.173593	−	0.300672i
$459$	140183.	−	242804.i	0.0310572	−	0.0537927i
$460$			236039.i			0.0520103i
$461$	−1.20272e6	−	694388.i	−0.263579	−	0.152177i	0.362387	−	0.932028i	$-0.381962\pi$
$461$	−1.20272e6	−	694388.i	−0.263579	−	0.152177i	−0.625966	+	0.779850i	$0.715295\pi$
$462$	405991.	+	234399.i	0.0884936	+	0.0510918i
$463$		−	799163.i		−	0.173254i	−0.996241	−	0.0866269i	$-0.972391\pi$
$463$		−	799163.i		−	0.173254i	0.996241	−	0.0866269i	$-0.0276088\pi$
$464$	−541259.	+	937489.i	−0.116711	+	0.202149i
$465$	−1.05045e6	−	1.81944e6i	−0.225291	−	0.390216i
$466$	−4.88082e6	+	2.81794e6i	−1.04119	+	0.601129i
$467$	−5.06728e6			−1.07518			−0.537592	−	0.843205i	$-0.680666\pi$
$467$	−5.06728e6			−1.07518			−0.537592	+	0.843205i	$0.680666\pi$
$468$	145311.	+	184921.i	0.0306679	+	0.0390277i
$469$	2.08641e6			0.437993
$470$	−1.35630e6	+	783062.i	−0.283212	+	0.163513i
$471$	1.59519e6	+	2.76295e6i	0.331329	+	0.573879i
$472$	−1.29537e6	+	2.24364e6i	−0.267632	+	0.463552i
$473$			1.07381e6i			0.220687i
$474$	1.56363e6	+	902760.i	0.319659	+	0.184555i
$475$	700973.	+	404707.i	0.142550	+	0.0823013i
$476$		−	109914.i		−	0.0222349i
$477$	−354421.	+	613875.i	−0.0713219	+	0.123533i
$478$	3.49290e6	+	6.04988e6i	0.699224	+	1.21109i
$479$	−2.79367e6	+	1.61292e6i	−0.556334	+	0.321200i	−0.751673	−	0.659536i	$-0.770753\pi$
$479$	−2.79367e6	+	1.61292e6i	−0.556334	+	0.321200i	0.195339	+	0.980736i	$0.437419\pi$
$480$	384749.			0.0762209
$481$	1.30127e6	−	1.02253e6i	0.256450	−	0.201519i
$482$	5.54307e6			1.08676
$483$	926288.	−	534792.i	0.180667	−	0.104308i
$484$	−317725.	−	550316.i	−0.0616507	−	0.106782i
$485$	690770.	−	1.19645e6i	0.133346	−	0.230961i
$486$		−	308160.i		−	0.0591814i
$487$	−4.20416e6	−	2.42727e6i	−0.803261	−	0.463763i	0.0413489	−	0.999145i	$-0.486834\pi$
$487$	−4.20416e6	−	2.42727e6i	−0.803261	−	0.463763i	−0.844610	+	0.535382i	$0.820168\pi$
$488$	−2.01154e6	−	1.16136e6i	−0.382366	−	0.220759i
$489$			3.05848e6i			0.578407i
$490$	861716.	−	1.49254e6i	0.162134	−	0.280824i
$491$	−2.82546e6	−	4.89385e6i	−0.528915	−	0.916108i	−0.999431	−	0.0337164i	$-0.989266\pi$
$491$	−2.82546e6	−	4.89385e6i	−0.528915	−	0.916108i	0.470516	−	0.882391i	$-0.344068\pi$
$492$	158811.	−	91689.3i	0.0295779	−	0.0170768i
$493$	−490478.			−0.0908871
$494$	4.07655e6	−	584554.i	0.751581	−	0.107772i
$495$	−336986.			−0.0618158
$496$	−6.86384e6	+	3.96284e6i	−1.25275	+	0.723274i
$497$	754007.	+	1.30598e6i	0.136926	+	0.237162i
$498$	−1.21518e6	+	2.10475e6i	−0.219567	+	0.380301i
$499$		−	1.00718e7i		−	1.81074i	−0.424623	−	0.905370i	$-0.639593\pi$
$499$		−	1.00718e7i		−	1.81074i	0.424623	−	0.905370i	$-0.360407\pi$
$500$	64478.4	+	37226.6i	0.0115342	+	0.00665930i
$501$	1.64148e6	+	947711.i	0.292175	+	0.168687i
$502$			6.13808e6i			1.08711i
$503$	1.50537e6	−	2.60738e6i	0.265292	−	0.459499i	−0.702348	−	0.711834i	$-0.747865\pi$
$503$	1.50537e6	−	2.60738e6i	0.265292	−	0.459499i	0.967640	+	0.252335i	$0.0811984\pi$
$504$	−466064.	−	807247.i	−0.0817277	−	0.141557i
$505$	−2.33966e6	+	1.35081e6i	−0.408249	+	0.235703i
$506$	−1.72080e6			−0.298782
$507$	2.41672e6	+	2.30781e6i	0.417548	+	0.398732i
$508$	−5130.43			−0.000882053
$509$	−8.43937e6	+	4.87247e6i	−1.44383	+	0.833595i	−0.998102	−	0.0615747i	$-0.980388\pi$
$509$	−8.43937e6	+	4.87247e6i	−1.44383	+	0.833595i	−0.445726	+	0.895169i	$0.647054\pi$
$510$	−225794.	−	391087.i	−0.0384404	−	0.0665807i
$511$	−379009.	+	656463.i	−0.0642092	+	0.111214i
$512$		−	6.66295e6i		−	1.12329i
$513$	817615.	+	472050.i	0.137169	+	0.0791945i
$514$	4.39326e6	+	2.53645e6i	0.733465	+	0.423466i
$515$			4.73208e6i			0.786202i
$516$	138362.	−	239651.i	0.0228767	−	0.0396236i
$517$	998804.	+	1.72998e6i	0.164344	+	0.284652i
$518$	−736231.	+	425063.i	−0.120556	+	0.0696032i
$519$	−1.36817e6			−0.222958
$520$	2.89319e6	−	414866.i	0.469211	−	0.0672822i
$521$	134535.			0.0217140			0.0108570	−	0.999941i	$-0.496544\pi$
$521$	134535.			0.0217140			0.0108570	+	0.999941i	$0.496544\pi$
$522$	−466876.	+	269551.i	−0.0749939	+	0.0432977i
$523$	927891.	+	1.60716e6i	0.148335	+	0.256923i	0.930612	−	0.366007i	$-0.119275\pi$
$523$	927891.	+	1.60716e6i	0.148335	+	0.256923i	−0.782277	+	0.622930i	$0.785942\pi$
$524$	64731.1	−	112118.i	0.0102988	−	0.0178380i
$525$		−	337377.i		−	0.0534216i
$526$	−3.64721e6	−	2.10572e6i	−0.574774	−	0.331846i
$527$	−3.10994e6	−	1.79552e6i	−0.487781	−	0.281621i
$528$			1.27128e6i			0.198453i
$529$	1.25513e6	−	2.17394e6i	0.195006	−	0.337760i
$530$	570871.	+	988777.i	0.0882771	+	0.152900i
$531$	−947197.	+	546865.i	−0.145782	+	0.0841673i
$532$	370123.			0.0566980
$533$	2.04872e6	−	1.60988e6i	0.312366	−	0.245457i
$534$	115754.			0.0175664
$535$	190526.	−	110000.i	0.0287786	−	0.0166154i
$536$	3.33714e6	+	5.78010e6i	0.501722	+	0.869008i
$537$	1.37347e6	−	2.37893e6i	0.205534	−	0.355996i
$538$			9.34385e6i			1.39178i
$539$	−1.90374e6	−	1.09913e6i	−0.282252	−	0.162958i
$540$	75207.6	+	43421.1i	0.0110988	+	0.00640791i
$541$			7.51174e6i			1.10344i	0.834031	+	0.551718i	$0.186028\pi$
$541$			7.51174e6i			1.10344i	−0.834031	+	0.551718i	$0.813972\pi$
$542$	3.20791e6	−	5.55626e6i	0.469055	−	0.812427i
$543$	3.94865e6	+	6.83927e6i	0.574711	+	0.995428i
$544$	569537.	−	328823.i	0.0825135	−	0.0476392i
$545$	2.73155e6			0.393929
$546$	−1.06059e6	−	1.34970e6i	−0.152254	−	0.193756i
$547$	−1.27898e7			−1.82766			−0.913829	−	0.406099i	$-0.866889\pi$
$547$	−1.27898e7			−1.82766			−0.913829	+	0.406099i	$0.866889\pi$
$548$	−525779.	+	303559.i	−0.0747914	+	0.0431808i
$549$	−490292.	−	849211.i	−0.0694263	−	0.120250i
$550$	−271395.	+	470069.i	−0.0382555	+	0.0662605i
$551$		−	1.65163e6i		−	0.231758i
$552$	2.96314e6	+	1.71077e6i	0.413908	+	0.238970i
$553$	1.99673e6	+	1.15281e6i	0.277655	+	0.160304i
$554$			7.44733e6i			1.03092i
$555$	305548.	−	529225.i	0.0421063	−	0.0729303i
$556$	636470.	+	1.10240e6i	0.0873155	+	0.151235i
$557$	3.85138e6	−	2.22360e6i	0.525991	−	0.303681i	−0.213391	−	0.976967i	$-0.568451\pi$
$557$	3.85138e6	−	2.22360e6i	0.525991	−	0.303681i	0.739383	+	0.673286i	$0.235118\pi$
$558$	−3.94705e6			−0.536645
$559$	1.46271e6	−	3.64968e6i	0.197983	−	0.493998i
$560$	−1.27276e6			−0.171504
$561$	−498836.	+	288003.i	−0.0669192	+	0.0386358i
$562$	3.55514e6	+	6.15769e6i	0.474806	+	0.822388i
$563$	3.75805e6	−	6.50913e6i	0.499679	−	0.865470i	−0.500321	−	0.865840i	$-0.666785\pi$
$563$	3.75805e6	−	6.50913e6i	0.499679	−	0.865470i	1.00000		0.000370381i	$0.000117896\pi$
$564$		−	514788.i		−	0.0681445i
$565$	988015.	+	570431.i	0.130209	+	0.0751765i
$566$	−4.14550e6	−	2.39341e6i	−0.543922	−	0.314033i
$567$		−	393516.i		−	0.0514049i
$568$	−2.41202e6	+	4.17775e6i	−0.313697	+	0.543339i
$569$	−7.19533e6	−	1.24627e7i	−0.931688	−	1.61373i	−0.780437	−	0.625235i	$-0.785003\pi$
$569$	−7.19533e6	−	1.24627e7i	−0.931688	−	1.61373i	−0.151251	−	0.988495i	$-0.548330\pi$
$570$	1.31695e6	−	760339.i	0.169778	−	0.0980212i
$571$	3.62318e6			0.465050			0.232525	−	0.972590i	$-0.425301\pi$
$571$	3.62318e6			0.465050			0.232525	+	0.972590i	$0.425301\pi$
$572$	−68583.7	−	478288.i	−0.00876457	−	0.0611223i
$573$	−1.20925e6			−0.153861
$574$	−1.15912e6	+	669220.i	−0.146842	+	0.0847792i
$575$	619199.	+	1.07248e6i	0.0781017	+	0.135276i
$576$	1.46148e6	−	2.53137e6i	0.183543	−	0.317906i
$577$		−	3.39602e6i		−	0.424649i	−0.977199	−	0.212325i	$-0.931897\pi$
$577$		−	3.39602e6i		−	0.424649i	0.977199	−	0.212325i	$-0.0681034\pi$
$578$	5.74862e6	+	3.31897e6i	0.715722	+	0.413222i
$579$	605891.	+	349811.i	0.0751100	+	0.0433648i
$580$		−	151924.i		−	0.0187524i
$581$	−1.55177e6	+	2.68774e6i	−0.190716	+	0.330329i
$582$	−1.29777e6	−	2.24781e6i	−0.158815	−	0.275076i
$583$	1.26119e6	−	728151.i	0.153678	−	0.0887258i
$584$	−2.42485e6			−0.294207
$585$	1.14535e6	+	459029.i	0.138372	+	0.0554563i
$586$	190978.			0.0229742
$587$	−8.17357e6	+	4.71901e6i	−0.979076	+	0.565270i	−0.901991	−	0.431755i	$-0.857895\pi$
$587$	−8.17357e6	+	4.71901e6i	−0.979076	+	0.565270i	−0.0770848	+	0.997025i	$0.524561\pi$
$588$	283248.	+	490600.i	0.0337849	+	0.0585172i
$589$	6.04623e6	−	1.04724e7i	0.718119	−	1.24382i
$590$			1.76169e6i			0.208352i
$591$	−817383.	−	471916.i	−0.0962624	−	0.0555771i
$592$	−1.99651e6	−	1.15268e6i	−0.234135	−	0.135178i
$593$		−	7.96111e6i		−	0.929688i	−0.885393	−	0.464844i	$-0.846110\pi$
$593$		−	7.96111e6i		−	0.929688i	0.885393	−	0.464844i	$-0.153890\pi$
$594$	−316555.	+	548289.i	−0.0368114	+	0.0637592i
$595$	−288336.	−	499413.i	−0.0333893	−	0.0578319i
$596$	1.41937e6	−	819476.i	0.163675	−	0.0944976i
$597$	−1.92699e6			−0.221280
$598$	5.84867e6	+	2.34401e6i	0.668812	+	0.268044i
$599$	−1.15336e7			−1.31341			−0.656703	−	0.754149i	$-0.728050\pi$
$599$	−1.15336e7			−1.31341			−0.656703	+	0.754149i	$0.728050\pi$
$600$	934655.	−	539623.i	0.105992	−	0.0611945i
$601$	−302621.	−	524156.i	−0.0341754	−	0.0591935i	0.848432	−	0.529305i	$-0.177547\pi$
$601$	−302621.	−	524156.i	−0.0341754	−	0.0591935i	−0.882607	+	0.470111i	$0.844214\pi$
$602$	−1.00988e6	+	1.74916e6i	−0.113573	+	0.196715i
$603$			2.81768e6i			0.315572i
$604$	−1648.89	−	951.989i	−0.000183908	−	0.000106179i
$605$	−2.88728e6	−	1.66697e6i	−0.320701	−	0.185157i
$606$			5.07562e6i			0.561445i
$607$	537341.	−	930702.i	0.0591941	−	0.102527i	−0.834910	−	0.550387i	$-0.814480\pi$
$607$	537341.	−	930702.i	0.0591941	−	0.102527i	0.894104	+	0.447860i	$0.147814\pi$
$608$	1.10727e6	+	1.91786e6i	0.121478	+	0.210405i
$609$	−596195.	+	344213.i	−0.0651396	+	0.0376084i
$610$	−1.57944e6			−0.171862
$611$	−1.03823e6	−	7.24038e6i	−0.112510	−	0.784618i
$612$	148438.			0.0160202
$613$	4.71726e6	−	2.72351e6i	0.507036	−	0.292737i	−0.224579	−	0.974456i	$-0.572101\pi$
$613$	4.71726e6	−	2.72351e6i	0.507036	−	0.292737i	0.731614	+	0.681719i	$0.238767\pi$
$614$	5.46861e6	+	9.47190e6i	0.585404	+	1.01395i
$615$	481056.	−	833213.i	0.0512870	−	0.0888318i
$616$			1.91504e6i			0.203342i
$617$	−5.81016e6	−	3.35450e6i	−0.614434	−	0.354744i	0.160265	−	0.987074i	$-0.448765\pi$
$617$	−5.81016e6	−	3.35450e6i	−0.614434	−	0.354744i	−0.774699	+	0.632330i	$0.782099\pi$
$618$	7.69926e6	+	4.44517e6i	0.810920	+	0.468185i
$619$		−	4.89152e6i		−	0.513118i	−0.966529	−	0.256559i	$-0.917411\pi$
$619$		−	4.89152e6i		−	0.513118i	0.966529	−	0.256559i	$-0.0825889\pi$
$620$	556157.	−	963292.i	0.0581056	−	0.100642i
$621$	722234.	+	1.25095e6i	0.0751534	+	0.130170i
$622$	3.29852e6	−	1.90440e6i	0.341856	−	0.197371i
$623$	147817.			0.0152582
$624$	1.73169e6	−	4.32084e6i	0.178037	−	0.444229i
$625$	390625.			0.0400000
$626$	−9.14753e6	+	5.28133e6i	−0.932970	+	0.538651i
$627$	−969819.	−	1.67978e6i	−0.0985194	−	0.170641i
$628$	−844565.	+	1.46283e6i	−0.0854543	+	0.148011i
$629$		−	1.04454e6i		−	0.105268i
$630$	−548923.	−	316921.i	−0.0551011	−	0.0318126i
$631$	−4.34348e6	−	2.50771e6i	−0.434275	−	0.250729i	0.266891	−	0.963727i	$-0.414004\pi$
$631$	−4.34348e6	−	2.50771e6i	−0.434275	−	0.250729i	−0.701166	+	0.712998i	$0.747337\pi$
$632$			7.37555e6i			0.734516i
$633$	−5.54479e6	+	9.60386e6i	−0.550017	+	0.952657i
$634$	−446116.	−	772696.i	−0.0440783	−	0.0763459i
$635$	−23311.0	+	13458.6i	−0.00229418	+	0.00132454i
$636$	−375293.			−0.0367898
$637$	4.97326e6	+	6.32892e6i	0.485616	+	0.617989i
$638$	1.10758e6			0.107726
$639$	−1.76372e6	+	1.01828e6i	−0.170874	+	0.0986543i
$640$	−1.67004e6	−	2.89259e6i	−0.161167	−	0.279150i
$641$	2.33486e6	−	4.04409e6i	0.224448	−	0.388755i	−0.731706	−	0.681620i	$-0.761276\pi$
$641$	2.33486e6	−	4.04409e6i	0.224448	−	0.388755i	0.956154	+	0.292866i	$0.0946089\pi$
$642$		−	413324.i		−	0.0395779i
$643$	1.25679e7	+	7.25609e6i	1.19877	+	0.692110i	0.960281	−	0.279035i	$-0.0900146\pi$
$643$	1.25679e7	+	7.25609e6i	1.19877	+	0.692110i	0.238489	+	0.971145i	$0.423348\pi$
$644$	490418.	+	283143.i	0.0465964	+	0.0269024i
$645$		−	1.45186e6i		−	0.137412i
$646$	1.29964e6	−	2.25103e6i	0.122529	−	0.212227i
$647$	−3.81368e6	−	6.60549e6i	−0.358166	−	0.620361i	0.629489	−	0.777010i	$-0.283264\pi$
$647$	−3.81368e6	−	6.60549e6i	−0.358166	−	0.620361i	−0.987654	+	0.156648i	$0.949931\pi$
$648$	1.09018e6	−	629417.i	0.101991	−	0.0588845i
$649$	2.24705e6			0.209411
$650$	1.56272e6	−	1.22799e6i	0.145077	−	0.114002i
$651$	−5.04033e6			−0.466129
$652$	−1.40235e6	+	809649.i	−0.129193	+	0.0745895i
$653$	8.85402e6	+	1.53356e7i	0.812564	+	1.40740i	0.911064	+	0.412265i	$0.135262\pi$
$653$	8.85402e6	+	1.53356e7i	0.812564	+	1.40740i	−0.0985004	+	0.995137i	$0.531405\pi$
$654$	2.56593e6	−	4.44433e6i	0.234585	−	0.406314i
$655$		−	679235.i		−	0.0618610i
$656$	−3.14330e6	−	1.81479e6i	−0.285185	−	0.164652i
$657$	−886549.	−	511849.i	−0.0801289	−	0.0462625i
$658$			3.75732e6i			0.338309i
$659$	−256484.	+	444243.i	−0.0230063	+	0.0398480i	−0.877299	−	0.479944i	$-0.840657\pi$
$659$	−256484.	+	444243.i	−0.0230063	+	0.0398480i	0.854293	+	0.519792i	$0.173990\pi$
$660$	−89207.9	−	154513.i	−0.00797156	−	0.0138071i
$661$	1.61427e7	−	9.32002e6i	1.43706	−	0.829685i	0.439412	−	0.898286i	$-0.355187\pi$
$661$	1.61427e7	−	9.32002e6i	1.43706	−	0.829685i	0.997644	+	0.0686013i	$0.0218536\pi$
$662$	8.00670e6			0.710082
$663$	2.08775e6	−	299371.i	0.184457	−	0.0264500i
$664$	−9.92802e6			−0.873861
$665$	1.68172e6	−	970942.i	0.147469	−	0.0851411i
$666$	−574045.	−	994275.i	−0.0501488	−	0.0868602i
$667$	1.26349e6	−	2.18843e6i	0.109966	−	0.190467i
$668$			1.00352e6i			0.0870133i
$669$	−2.39596e6	−	1.38331e6i	−0.206973	−	0.119496i
$670$	3.93044e6	+	2.26924e6i	0.338263	+	0.195296i
$671$			2.01459e6i			0.172735i
$672$	461529.	−	799392.i	0.0394254	−	0.0682868i
$673$	3.16996e6	+	5.49053e6i	0.269784	+	0.467280i	0.968806	−	0.247821i	$-0.0797143\pi$
$673$	3.16996e6	+	5.49053e6i	0.269784	+	0.467280i	−0.699022	+	0.715100i	$0.746381\pi$
$674$	144369.	−	83351.7i	0.0122412	−	0.00706748i
$675$	455625.			0.0384900
$676$	−418402.	+	1.71903e6i	−0.0352150	+	0.144682i
$677$	−8.47267e6			−0.710475			−0.355237	−	0.934776i	$-0.615600\pi$
$677$	−8.47267e6			−0.710475			−0.355237	+	0.934776i	$0.615600\pi$
$678$	1.85622e6	−	1.07169e6i	0.155080	−	0.0895354i
$679$	−1.65724e6	−	2.87043e6i	−0.137947	−	0.238931i
$680$	922370.	−	1.59759e6i	0.0764950	−	0.132493i
$681$		−	1.07242e7i		−	0.886129i
$682$	7.02272e6	+	4.05457e6i	0.578156	+	0.333798i
$683$	806023.	+	465357.i	0.0661143	+	0.0381711i	0.532693	−	0.846309i	$-0.321180\pi$
$683$	806023.	+	465357.i	0.0661143	+	0.0381711i	−0.466578	+	0.884480i	$0.654513\pi$
$684$			499849.i			0.0408506i
$685$	−1.59265e6	+	2.75854e6i	−0.129686	+	0.224623i
$686$	−4.69773e6	−	8.13671e6i	−0.381134	−	0.660144i
$687$	2.32775e6	−	1.34392e6i	0.188167	−	0.108638i
$688$	−5.47715e6			−0.441147
$689$	−5.27841e6	+	756892.i	−0.423599	+	0.0607416i
$690$	2.32663e6			0.186039
$691$	2.89151e6	−	1.66942e6i	0.230372	−	0.133006i	−0.380371	−	0.924834i	$-0.624204\pi$
$691$	2.89151e6	−	1.66942e6i	0.230372	−	0.133006i	0.610744	+	0.791828i	$0.290871\pi$
$692$	−362186.	−	627325.i	−0.0287519	−	0.0497998i
$693$	−404236.	+	700157.i	−0.0319744	+	0.0553812i
$694$		−	1.47354e7i		−	1.16135i
$695$	5.78383e6	+	3.33930e6i	0.454207	+	0.262236i
$696$	−1.90719e6	−	1.10112e6i	−0.149235	−	0.0861609i
$697$		−	1.64452e6i		−	0.128221i
$698$	2.56399e6	−	4.44095e6i	0.199194	−	0.345015i
$699$	−4.85972e6	−	8.41728e6i	−0.376200	−	0.651597i
$700$	154691.	−	89311.2i	0.0119322	−	0.00688907i
$701$	−7.31359e6			−0.562128			−0.281064	−	0.959689i	$-0.590687\pi$
$701$	−7.31359e6			−0.562128			−0.281064	+	0.959689i	$0.590687\pi$
$702$	1.82276e6	−	1.43233e6i	0.139601	−	0.109698i
$703$	3.51737e6			0.268429
$704$	−5.20065e6	+	3.00259e6i	−0.395481	+	0.228331i
$705$	−1.35044e6	−	2.33903e6i	−0.102330	−	0.177241i
$706$	6.37807e6	−	1.10471e7i	0.481590	−	0.834138i
$707$			6.48149e6i			0.487671i
$708$	−501489.	−	289535.i	−0.0375992	−	0.0217079i
$709$	4.35669e6	+	2.51534e6i	0.325492	+	0.187923i	0.653838	−	0.756634i	$-0.273158\pi$
$709$	4.35669e6	+	2.51534e6i	0.325492	+	0.187923i	−0.328346	+	0.944558i	$0.606491\pi$
$710$			3.28032e6i			0.244214i
$711$	−1.55687e6	+	2.69657e6i	−0.115499	+	0.200050i
$712$	236428.	+	409505.i	0.0174783	+	0.0302733i
$713$	1.60227e7	−	9.25069e6i	1.18035	−	0.681476i
$714$	−1.08342e6			−0.0795335
$715$	−1.56631e6	−	1.99327e6i	−0.114581	−	0.145815i
$716$	1.45436e6			0.106020
$717$	−1.04334e7	+	6.02372e6i	−0.757928	+	0.437590i
$718$	8.73225e6	+	1.51247e7i	0.632143	+	1.09490i
$719$	−5.16627e6	+	8.94823e6i	−0.372696	+	0.645528i	−0.989979	−	0.141213i	$-0.954900\pi$
$719$	−5.16627e6	+	8.94823e6i	−0.372696	+	0.645528i	0.617283	+	0.786741i	$0.288233\pi$
$720$		−	1.71885e6i		−	0.123568i
$721$	9.83185e6	+	5.67642e6i	0.704364	+	0.406665i
$722$	−3.61071e6	−	2.08465e6i	−0.257780	−	0.148830i
$723$			9.55936e6i			0.680116i
$724$	−2.09059e6	+	3.62102e6i	−0.148226	+	0.256734i
$725$	−398541.	−	690293.i	−0.0281597	−	0.0487740i
$726$	−5.42444e6	+	3.13180e6i	−0.381956	+	0.220522i
$727$	−2.49303e7			−1.74941			−0.874706	−	0.484654i	$-0.838945\pi$
$727$	−2.49303e7			−1.74941			−0.874706	+	0.484654i	$0.838945\pi$
$728$	2.60859e6	−	6.50884e6i	0.182422	−	0.455172i
$729$	531441.			0.0370370
$730$	−1.42798e6	+	824443.i	−0.0991777	+	0.0572603i
$731$	−1.24082e6	−	2.14916e6i	−0.0858847	−	0.148757i
$732$	259583.	−	449610.i	0.0179060	−	0.0310141i
$733$			7.08686e6i			0.487185i	0.969878	+	0.243593i	$0.0783260\pi$
$733$			7.08686e6i			0.487185i	−0.969878	+	0.243593i	$0.921674\pi$
$734$	−546101.	−	315292.i	−0.0374139	−	0.0216009i
$735$	2.57397e6	+	1.48608e6i	0.175746	+	0.101467i
$736$			3.38824e6i			0.230558i
$737$	2.89444e6	−	5.01331e6i	0.196289	−	0.339982i
$738$	−903778.	−	1.56539e6i	−0.0610830	−	0.105799i
$739$	2.32084e6	−	1.33994e6i	0.156327	−	0.0902553i	−0.419796	−	0.907619i	$-0.637898\pi$
$739$	2.32084e6	−	1.33994e6i	0.156327	−	0.0902553i	0.576123	+	0.817363i	$0.304565\pi$
$740$	323542.			0.0217196
$741$	1.00810e6	+	7.03027e6i	0.0674463	+	0.470356i
$742$	2.73918e6			0.182646
$743$	−1.18974e7	+	6.86897e6i	−0.790643	+	0.456478i	−0.840189	−	0.542294i	$-0.817556\pi$
$743$	−1.18974e7	+	6.86897e6i	−0.790643	+	0.456478i	0.0495461	+	0.998772i	$0.484223\pi$
$744$	−8.06185e6	−	1.39635e7i	−0.533952	−	0.924832i
$745$	4.29945e6	−	7.44687e6i	0.283806	−	0.491567i
$746$		−	2.47207e7i		−	1.62635i
$747$	−3.62978e6	−	2.09565e6i	−0.238001	−	0.137410i
$748$	−264106.	−	152482.i	−0.0172594	−	0.00996469i
$749$		−	527809.i		−	0.0343773i
$750$	366941.	−	635560.i	0.0238201	−	0.0412576i
$751$	−2.59564e6	−	4.49579e6i	−0.167937	−	0.290875i	0.769758	−	0.638336i	$-0.220377\pi$
$751$	−2.59564e6	−	4.49579e6i	−0.167937	−	0.290875i	−0.937694	+	0.347462i	$0.887044\pi$
$752$	−8.82401e6	+	5.09455e6i	−0.569012	+	0.328519i
$753$	−1.05855e7			−0.680337
$754$	−3.76443e6	−	1.50870e6i	−0.241141	−	0.0966436i
$755$	−9989.38			−0.000637781
$756$	180432.	−	104173.i	0.0114818	−	0.00662901i
$757$	−3.81097e6	−	6.60080e6i	−0.241711	−	0.418656i	0.719491	−	0.694502i	$-0.244375\pi$
$757$	−3.81097e6	−	6.60080e6i	−0.241711	−	0.418656i	−0.961202	+	0.275846i	$0.911042\pi$
$758$	9.48756e6	−	1.64329e7i	0.599766	−	1.03882i
$759$		−	2.96763e6i		−	0.186985i
$760$	5.37972e6	+	3.10598e6i	0.337851	+	0.195059i
$761$	1.01723e7	+	5.87296e6i	0.636731	+	0.367617i	0.783354	−	0.621576i	$-0.213507\pi$
$761$	1.01723e7	+	5.87296e6i	0.636731	+	0.367617i	−0.146623	+	0.989192i	$0.546840\pi$
$762$			50570.5i			0.00315507i
$763$	3.27666e6	−	5.67534e6i	0.203761	−	0.352924i
$764$	−320114.	−	554455.i	−0.0198414	−	0.0343663i
$765$	674455.	−	389397.i	0.0416677	−	0.0240568i
$766$	−1.50434e7			−0.926351
$767$	−7.63726e6	−	3.06084e6i	−0.468759	−	0.187867i
$768$	4.11765e6			0.251911
$769$	1.92883e7	−	1.11361e7i	1.17619	−	0.679074i	0.221060	−	0.975260i	$-0.429048\pi$
$769$	1.92883e7	−	1.11361e7i	1.17619	−	0.679074i	0.955130	+	0.296186i	$0.0957149\pi$
$770$	651109.	+	1.12775e6i	0.0395755	+	0.0685468i
$771$	−4.37427e6	+	7.57645e6i	−0.265014	+	0.459018i
$772$			370412.i			0.0223687i
$773$	1.65192e7	+	9.53738e6i	0.994354	+	0.574090i	0.906573	−	0.422049i	$-0.138689\pi$
$773$	1.65192e7	+	9.53738e6i	0.994354	+	0.574090i	0.0877810	+	0.996140i	$0.472022\pi$
$774$	−2.36223e6	−	1.36383e6i	−0.141732	−	0.0818292i
$775$		−	5.83585e6i		−	0.349020i
$776$	5.30141e6	−	9.18231e6i	0.316036	−	0.547391i
$777$	−733048.	−	1.26968e6i	−0.0435592	−	0.0754467i
$778$	8.39603e6	−	4.84745e6i	0.497308	−	0.287121i
$779$	5.53776e6			0.326957
$780$	92729.1	+	646673.i	0.00545732	+	0.0380582i
$781$	4.18409e6			0.245456
$782$	3.44407e6	−	1.98843e6i	0.201398	−	0.116277i
$783$	−464858.	−	805157.i	−0.0270967	−	0.0469328i
$784$	5.60626e6	−	9.71033e6i	0.325749	−	0.564214i
$785$			8.86217e6i			0.513293i
$786$	−1.10514e6	−	638052.i	−0.0638058	−	0.0368383i
$787$	1.20781e7	+	6.97327e6i	0.695121	+	0.401328i	0.805528	−	0.592558i	$-0.201882\pi$
$787$	1.20781e7	+	6.97327e6i	0.695121	+	0.401328i	−0.110407	+	0.993886i	$0.535215\pi$
$788$		−	499707.i		−	0.0286682i
$789$	3.63145e6	−	6.28985e6i	0.207676	−	0.359706i
$790$	2.50767e6	+	4.34340e6i	0.142956	+	0.247607i
$791$	2.37037e6	−	1.36853e6i	0.134702	−	0.0777704i
$792$	−2.58625e6			−0.146507
$793$	2.74420e6	−	6.84720e6i	0.154964	−	0.386661i
$794$	−5.55967e6			−0.312966
$795$	−1.70521e6	+	984502.i	−0.0956884	+	0.0552457i
$796$	−510117.	−	883548.i	−0.0285356	−	0.0494251i
$797$	1.63419e7	−	2.83050e7i	0.911290	−	1.57840i	0.0990448	−	0.995083i	$-0.468421\pi$
$797$	1.63419e7	−	2.83050e7i	0.911290	−	1.57840i	0.812245	−	0.583317i	$-0.198245\pi$
$798$		−	3.64829e6i		−	0.202807i
$799$	−3.99807e6	−	2.30829e6i	−0.221556	−	0.127915i
$800$	925561.	+	534373.i	0.0511305	+	0.0295202i
$801$			199625.i			0.0109935i
$802$	5.08143e6	−	8.80130e6i	0.278965	−	0.483182i
$803$	1.05159e6	+	1.82140e6i	0.0575514	+	0.0996819i
$804$	−1.29194e6	+	745903.i	−0.0704860	+	0.0406951i
$805$	2.97107e6			0.161593
$806$	−1.83459e7	−	2.33467e7i	−0.994719	−	1.26587i
$807$	−1.61140e7			−0.871005
$808$	−1.79561e7	+	1.03669e7i	−0.967572	+	0.558628i
$809$	9.71774e6	+	1.68316e7i	0.522028	+	0.904179i	0.999672	+	0.0256256i	$0.00815779\pi$
$809$	9.71774e6	+	1.68316e7i	0.522028	+	0.904179i	−0.477643	+	0.878554i	$0.658509\pi$
$810$	428000.	−	741318.i	0.0229209	−	0.0397001i
$811$		−	151625.i		−	0.00809503i	−0.999992	−	0.00404751i	$-0.998712\pi$
$811$		−	151625.i		−	0.00809503i	0.999992	−	0.00404751i	$-0.00128837\pi$
$812$	−315652.	−	182242.i	−0.0168004	−	0.00969970i
$813$	9.58212e6	+	5.53224e6i	0.508435	+	0.293545i
$814$			2.35873e6i			0.124772i
$815$	−4.24789e6	+	7.35757e6i	−0.224016	+	0.388008i
$816$	−1.46900e6	−	2.54439e6i	−0.0772320	−	0.133770i
$817$	7.23708e6	−	4.17833e6i	0.379322	−	0.219002i
$818$	−1.26132e7			−0.659084
$819$	2.32764e6	−	1.82906e6i	0.121257	−	0.0952836i
$820$	509385.			0.0264552
$821$	−1.13403e6	+	654735.i	−0.0587176	+	0.0339006i	−0.529071	−	0.848577i	$-0.677460\pi$
$821$	−1.13403e6	+	654735.i	−0.0587176	+	0.0339006i	0.470354	+	0.882478i	$0.344126\pi$
$822$	2.99216e6	+	5.18258e6i	0.154456	+	0.267526i
$823$	3.30306e6	−	5.72107e6i	0.169988	−	0.294427i	−0.768428	−	0.639937i	$-0.778961\pi$
$823$	3.30306e6	−	5.72107e6i	0.169988	−	0.294427i	0.938415	+	0.345510i	$0.112294\pi$
$824$			3.63170e7i			1.86334i
$825$	−810663.	−	468037.i	−0.0414673	−	0.0239412i
$826$	3.66026e6	+	2.11325e6i	0.186664	+	0.107771i
$827$			2.30238e7i			1.17062i	0.810811	+	0.585308i	$0.199026\pi$
$827$			2.30238e7i			1.17062i	−0.810811	+	0.585308i	$0.800974\pi$
$828$	−382383.	+	662307.i	−0.0193831	+	0.0335725i
$829$	−7.29332e6	−	1.26324e7i	−0.368586	−	0.638410i	0.620759	−	0.784002i	$-0.286825\pi$
$829$	−7.29332e6	−	1.26324e7i	−0.368586	−	0.638410i	−0.989345	+	0.145592i	$0.953491\pi$
$830$	−5.84654e6	+	3.37550e6i	−0.294580	+	0.170076i
$831$	−1.28434e7			−0.645174
$832$	2.17660e7	−	3.12111e6i	1.09011	−	0.156315i
$833$	5.08028e6			0.253674
$834$	1.08663e7	−	6.27366e6i	0.540962	−	0.312324i
$835$	2.63253e6	+	4.55968e6i	0.130664	+	0.226317i
$836$	513466.	−	889349.i	0.0254095	−	0.0440105i
$837$		−	6.80693e6i		−	0.335844i
$838$	1.55147e7	+	8.95741e6i	0.763191	+	0.440628i
$839$	1.31511e7	+	7.59280e6i	0.644997	+	0.372389i	0.786537	−	0.617543i	$-0.211872\pi$
$839$	1.31511e7	+	7.59280e6i	0.644997	+	0.372389i	−0.141540	+	0.989933i	$0.545205\pi$
$840$		−	2.58925e6i		−	0.126612i
$841$	9.44234e6	−	1.63546e7i	0.460352	−	0.797352i
$842$	−1.65034e7	−	2.85848e7i	−0.802221	−	1.38949i
$843$	−1.06193e7	+	6.13106e6i	−0.514668	+	0.297144i
$844$	−5.87132e6			−0.283713
$845$	2.60843e6	+	8.90829e6i	0.125672	+	0.429193i
$846$	−5.07424e6			−0.243750
$847$	−6.92694e6	+	3.99927e6i	−0.331767	+	0.191546i
$848$	3.71404e6	+	6.43291e6i	0.177361	+	0.307198i
$849$	4.12758e6	−	7.14918e6i	0.196529	−	0.340398i
$850$		−	1.25441e6i		−	0.0595516i
$851$	4.66056e6	+	2.69078e6i	0.220604	+	0.127366i
$852$	−933791.	−	539124.i	−0.0440708	−	0.0254443i
$853$			1.91131e7i			0.899412i	0.893177	+	0.449706i	$0.148471\pi$
$853$			1.91131e7i			0.899412i	−0.893177	+	0.449706i	$0.851529\pi$
$854$	−1.89464e6	+	3.28161e6i	−0.0888958	+	0.153972i
$855$	1.31125e6	+	2.27115e6i	0.0613438	+	0.106251i
$856$	1.46222e6	−	844214.i	0.0682070	−	0.0393793i
$857$	−694424.			−0.0322978			−0.0161489	−	0.999870i	$-0.505141\pi$
$857$	−694424.			−0.0322978			−0.0161489	+	0.999870i	$0.505141\pi$
$858$	−4.71446e6	+	676026.i	−0.218632	+	0.0313506i
$859$	3.06363e7			1.41662			0.708310	−	0.705902i	$-0.249458\pi$
$859$	3.06363e7			1.41662			0.708310	+	0.705902i	$0.249458\pi$
$860$	665696.	−	384340.i	0.0306923	−	0.0177202i
$861$	−1.15411e6	−	1.99898e6i	−0.0530567	−	0.0918968i
$862$	1.06281e7	−	1.84085e7i	0.487179	−	0.843819i
$863$		−	1.30948e6i		−	0.0598511i	−0.999552	−	0.0299255i	$-0.990473\pi$
$863$		−	1.30948e6i		−	0.0598511i	0.999552	−	0.0299255i	$-0.00952702\pi$
$864$	1.07957e6	+	623293.i	0.0492004	+	0.0284058i
$865$	−3.29131e6	−	1.90024e6i	−0.149565	−	0.0863512i
$866$			1.23238e7i			0.558405i
$867$	−5.72377e6	+	9.91385e6i	−0.258603	+	0.447914i
$868$	−1.33429e6	−	2.31106e6i	−0.0601105	−	0.104114i
$869$	5.54005e6	−	3.19855e6i	0.248865	−	0.143683i
$870$	−1.49751e6			−0.0670765
$871$	−1.66665e7	+	1.30966e7i	−0.744389	+	0.584941i
$872$	2.09637e7			0.933633
$873$	3.87649e6	−	2.23809e6i	0.172148	−	0.0993900i
$874$	6.69584e6	+	1.15975e7i	0.296501	+	0.513555i
$875$	468579.	−	811602.i	0.0206901	−	0.0358363i
$876$		−	541992.i		−	0.0238634i
$877$	3.04731e7	+	1.75936e7i	1.33788	+	0.772426i	0.986493	−	0.163804i	$-0.0523764\pi$
$877$	3.04731e7	+	1.75936e7i	1.33788	+	0.772426i	0.351388	+	0.936230i	$0.385710\pi$
$878$	−4.47977e6	−	2.58639e6i	−0.196119	−	0.113229i
$879$			329354.i			0.0143778i
$880$	−1.76567e6	+	3.05824e6i	−0.0768606	+	0.133126i
$881$	−2.41552e6	−	4.18380e6i	−0.104850	−	0.181606i	0.808827	−	0.588047i	$-0.200103\pi$
$881$	−2.41552e6	−	4.18380e6i	−0.104850	−	0.181606i	−0.913677	+	0.406441i	$0.866770\pi$
$882$	4.83582e6	−	2.79196e6i	0.209314	−	0.120848i
$883$	−4.01230e7			−1.73178			−0.865888	−	0.500238i	$-0.833246\pi$
$883$	−4.01230e7			−1.73178			−0.865888	+	0.500238i	$0.833246\pi$
$884$	689940.	+	878009.i	0.0296948	+	0.0377893i
$885$	−3.03814e6			−0.130391
$886$	−3.53485e7	+	2.04085e7i	−1.51282	+	0.873425i
$887$	653107.	+	1.13122e6i	0.0278725	+	0.0482765i	0.879625	−	0.475667i	$-0.157793\pi$
$887$	653107.	+	1.13122e6i	0.0278725	+	0.0482765i	−0.851753	+	0.523944i	$0.824460\pi$
$888$	2.34497e6	−	4.06161e6i	0.0997943	−	0.172849i
$889$			64577.8i			0.00274049i
$890$	278461.	+	160770.i	0.0117839	+	0.00680345i
$891$	−945558.	−	545918.i	−0.0399019	−	0.0230374i
$892$		−	1.46477e6i		−	0.0616394i
$893$	7.77291e6	−	1.34631e7i	0.326178	−	0.564957i
$894$	−8.07754e6	−	1.39907e7i	−0.338014	−	0.585458i
$895$	6.60813e6	−	3.81520e6i	0.275753	−	0.159206i
$896$	−8.01325e6			−0.333456
$897$	−4.04239e6	+	1.00864e7i	−0.167748	+	0.418557i
$898$	3.66233e7			1.51554
$899$	−1.03128e7	+	5.95411e6i	−0.425577	+	0.245707i
$900$	120614.	+	208910.i	0.00496355	+	0.00859711i
$901$	−1.68279e6	+	2.91469e6i	−0.0690588	+	0.119613i
$902$			3.71359e6i			0.151977i
$903$	−3.01653e6	−	1.74159e6i	−0.123109	−	0.0710767i
$904$	7.58266e6	+	4.37785e6i	0.308603	+	0.178172i
$905$			2.19370e7i			0.890338i
$906$	−9383.72	+	16253.1i	−0.000379799	+	0.000657832i
$907$	5.75673e6	+	9.97095e6i	0.232358	+	0.402456i	0.958502	−	0.285087i	$-0.0920225\pi$
$907$	5.75673e6	+	9.97095e6i	0.232358	+	0.402456i	−0.726143	+	0.687543i	$0.758689\pi$
$908$	4.91718e6	−	2.83894e6i	0.197926	−	0.114272i
$909$	−8.75322e6			−0.351365
$910$	−676809.	−	4.71992e6i	−0.0270933	−	0.188943i
$911$	−2.93959e7			−1.17352			−0.586760	−	0.809761i	$-0.699597\pi$
$911$	−2.93959e7			−1.17352			−0.586760	+	0.809761i	$0.699597\pi$
$912$	8.56795e6	−	4.94671e6i	0.341106	−	0.196938i
$913$	4.30548e6	+	7.45731e6i	0.170940	+	0.296078i
$914$	−1.66138e7	+	2.87759e7i	−0.657814	+	1.13937i
$915$		−	2.72384e6i		−	0.107555i
$916$	1.23241e6	+	711534.i	0.0485308	+	0.0280193i
$917$	−1.41125e6	−	814784.i	−0.0554217	−	0.0319977i
$918$		−	1.46315e6i		−	0.0573036i
$919$	−2.02023e7	+	3.49914e7i	−0.789063	+	1.36670i	0.137479	+	0.990505i	$0.456100\pi$
$919$	−2.02023e7	+	3.49914e7i	−0.789063	+	1.36670i	−0.926542	+	0.376192i	$0.877233\pi$
$920$	4.75213e6	+	8.23094e6i	0.185105	+	0.320612i
$921$	−1.63349e7	+	9.43095e6i	−0.634552	+	0.366359i
$922$	−7.24763e6			−0.280782
$923$	−1.42209e7	−	5.69939e6i	−0.549442	−	0.220203i
$924$	−428041.			−0.0164932
$925$	1.47007e6	−	848745.i	0.0564916	−	0.0326154i
$926$	−2.08530e6	−	3.61185e6i	−0.0799174	−	0.138421i
$927$	−7.66597e6	+	1.32779e7i	−0.293000	+	0.507491i
$928$		−	2.18081e6i		−	0.0831280i
$929$	4.33856e7	+	2.50487e7i	1.64933	+	0.952239i	0.977340	+	0.211674i	$0.0678917\pi$
$929$	4.33856e7	+	2.50487e7i	1.64933	+	0.952239i	0.671986	+	0.740564i	$0.265442\pi$
$930$	−9.49513e6	−	5.48201e6i	−0.359992	−	0.207842i
$931$			1.71073e7i			0.646856i
$932$	2.57295e6	−	4.45649e6i	0.0970269	−	0.168056i
$933$	3.28426e6	+	5.68851e6i	0.123519	+	0.213941i
$934$	−2.29018e7	+	1.32223e7i	−0.859017	+	0.495954i
$935$	−1.60002e6			−0.0598543
$936$	8.79015e6	+	3.52289e6i	0.327949	+	0.131434i
$937$	−1.74797e7			−0.650408			−0.325204	−	0.945644i	$-0.605433\pi$
$937$	−1.74797e7			−0.650408			−0.325204	+	0.945644i	$0.605433\pi$
$938$	9.42960e6	−	5.44418e6i	0.349934	−	0.202035i
$939$	−9.10798e6	−	1.57755e7i	−0.337099	−	0.583873i
$940$	714983.	−	1.23839e6i	0.0263922	−	0.0457127i
$941$			2.44440e7i			0.899907i	0.893052	+	0.449954i	$0.148560\pi$
$941$			2.44440e7i			0.899907i	−0.893052	+	0.449954i	$0.851440\pi$
$942$	1.44190e7	+	8.32484e6i	0.529431	+	0.305667i
$943$	7.33760e6	+	4.23636e6i	0.268704	+	0.155136i
$944$			1.14614e7i			0.418608i
$945$	546550.	−	946653.i	0.0199090	−	0.0344835i
$946$	2.80197e6	+	4.85315e6i	0.101797	+	0.176318i
$947$	−4.15382e7	+	2.39821e7i	−1.50513	+	0.868986i	−0.505145	+	0.863035i	$0.668561\pi$
$947$	−4.15382e7	+	2.39821e7i	−1.50513	+	0.868986i	−0.999982	+	0.00595105i	$0.998106\pi$
$948$	−1.64855e6			−0.0595773
$949$	−1.09309e6	−	7.62300e6i	−0.0393996	−	0.274764i
$950$	4.22410e6			0.151854
$951$	1.33256e6	−	769355.i	0.0477789	−	0.0275852i
$952$	−2.21288e6	−	3.83282e6i	−0.0791344	−	0.137065i
$953$	2.01944e7	−	3.49778e7i	0.720277	−	1.24756i	−0.240612	−	0.970621i	$-0.577348\pi$
$953$	2.01944e7	−	3.49778e7i	0.720277	−	1.24756i	0.960889	−	0.276934i	$-0.0893185\pi$
$954$			3.69924e6i			0.131596i
$955$	−2.90899e6	−	1.67951e6i	−0.103213	−	0.0595900i
$956$	−5.52391e6	−	3.18923e6i	−0.195480	−	0.112860i
$957$			1.91008e6i			0.0674175i
$958$	−8.41739e6	+	1.45794e7i	−0.296322	+	0.513245i
$959$	3.82095e6	+	6.61808e6i	0.134161	+	0.232373i
$960$	7.03157e6	−	4.05968e6i	0.246249	−	0.142172i
$961$	−5.85571e7			−2.04537
$962$	3.21297e6	−	8.01685e6i	0.111936	−	0.279297i
$963$	712802.			0.0247687
$964$	−4.38309e6	+	2.53058e6i	−0.151910	+	0.0877055i
$965$	971698.	+	1.68303e6i	0.0335902	+	0.0581800i
$966$	2.79093e6	−	4.83403e6i	0.0962290	−	0.166674i
$967$		−	4.79161e7i		−	1.64784i	−0.566706	−	0.823920i	$-0.691782\pi$
$967$		−	4.79161e7i		−	1.64784i	0.566706	−	0.823920i	$-0.308218\pi$
$968$	−2.21588e7	−	1.27934e7i	−0.760079	−	0.438832i
$969$	3.88205e6	+	2.24130e6i	0.132816	+	0.0766816i
$970$		−	7.20986e6i		−	0.246035i
$971$	1.18520e7	−	2.05282e7i	0.403406	−	0.698720i	−0.590728	−	0.806871i	$-0.701159\pi$
$971$	1.18520e7	−	2.05282e7i	0.403406	−	0.698720i	0.994135	+	0.108150i	$0.0344928\pi$
$972$	140684.	+	243672.i	0.00477617	+	0.00827258i
$973$	1.38761e7	−	8.01138e6i	0.469879	−	0.271285i
$974$	−2.53345e7			−0.855687
$975$	2.11774e6	+	2.69502e6i	0.0713447	+	0.0907925i
$976$	−1.02757e7			−0.345293
$977$	−2.09892e7	+	1.21181e7i	−0.703493	+	0.406162i	−0.808647	−	0.588294i	$-0.799800\pi$
$977$	−2.09892e7	+	1.21181e7i	−0.703493	+	0.406162i	0.105154	+	0.994456i	$0.466467\pi$
$978$	7.98068e6	+	1.38229e7i	0.266804	+	0.462118i
$979$	205063.	−	355180.i	0.00683804	−	0.0118438i
$980$			1.57360e6i			0.0523394i
$981$	7.66452e6	+	4.42511e6i	0.254280	+	0.146809i
$982$	−2.55396e7	−	1.47453e7i	−0.845153	−	0.487949i
$983$			3.71789e6i			0.122719i	0.998116	+	0.0613597i	$0.0195437\pi$
$983$			3.71789e6i			0.122719i	−0.998116	+	0.0613597i	$0.980456\pi$
$984$	3.69193e6	−	6.39461e6i	0.121553	−	0.210536i
$985$	−1.31088e6	−	2.27051e6i	−0.0430499	−	0.0745645i
$986$	−2.21674e6	+	1.27983e6i	−0.0726142	+	0.0419238i
$987$	−6.47974e6			−0.211721
$988$	−2.95660e6	+	2.32330e6i	−0.0963608	+	0.0757203i
$989$	1.27856e7			0.415654
$990$	−1.52302e6	+	879318.i	−0.0493877	+	0.0285140i
$991$	−8.13116e6	−	1.40836e7i	−0.263008	−	0.455543i	0.704032	−	0.710168i	$-0.251381\pi$
$991$	−8.13116e6	−	1.40836e7i	−0.263008	−	0.455543i	−0.967040	+	0.254626i	$0.918048\pi$
$992$	7.98341e6	−	1.38277e7i	0.257578	−	0.446139i
$993$			1.38081e7i			0.444385i
$994$	6.81553e6	+	3.93495e6i	0.218793	+	0.126320i
$995$	−4.63561e6	−	2.67637e6i	−0.148439	−	0.0857015i
$996$		−	2.21907e6i		−	0.0708797i
$997$	1.07275e6	−	1.85806e6i	0.0341791	−	0.0592000i	−0.848430	−	0.529308i	$-0.822452\pi$
$997$	1.07275e6	−	1.85806e6i	0.0341791	−	0.0592000i	0.882609	+	0.470108i	$0.155785\pi$
$998$	−2.62810e7	−	4.55200e7i	−0.835247	−	1.44669i
$999$	1.71469e6	−	989976.i	0.0543590	−	0.0313842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.6.bb.a.166.16	yes	44
13.4	even	6	inner	195.6.bb.a.121.16	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.6.bb.a.121.16	✓	44	13.4	even	6	inner
195.6.bb.a.166.16	yes	44	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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	195.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.51954 - 2.60936i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-2.38250 + 4.12662i) q^{4} +25.0000i q^{5} +(40.6759 + 23.4842i) q^{6} +(51.9425 + 29.9890i) q^{7} +191.866i q^{8} +(-40.5000 + 70.1481i) q^{9} +(65.2339 + 112.989i) q^{10} +(144.118 - 83.2065i) q^{11} -42.8850 q^{12} +(-603.169 + 86.4908i) q^{13} +313.008 q^{14} +(-194.856 + 112.500i) q^{15} +(424.407 + 735.095i) q^{16} +(-192.295 + 333.064i) q^{17} +422.716i q^{18} +(-1121.56 - 647.531i) q^{19} +(-103.165 - 59.5626i) q^{20} +539.803i q^{21} +(434.231 - 752.111i) q^{22} +(-990.719 - 1715.97i) q^{23} +(-1495.45 + 863.398i) q^{24} -625.000 q^{25} +(-2500.36 + 1964.78i) q^{26} -729.000 q^{27} +(-247.506 + 142.898i) q^{28} +(637.665 + 1104.47i) q^{29} +(-587.106 + 1016.90i) q^{30} +9337.36i q^{31} +(-1480.90 - 854.997i) q^{32} +(1297.06 + 748.859i) q^{33} +2007.06i q^{34} +(-749.726 + 1298.56i) q^{35} +(-192.983 - 334.256i) q^{36} +(-2352.11 + 1357.99i) q^{37} -6758.57 q^{38} +(-3388.39 - 4312.03i) q^{39} -4796.65 q^{40} +(-3703.17 + 2138.03i) q^{41} +(1408.54 + 2439.66i) q^{42} +(-3226.35 + 5588.21i) q^{43} +792.959i q^{44} +(-1753.70 - 1012.50i) q^{45} +(-8955.19 - 5170.28i) q^{46} +12003.9i q^{47} +(-3819.67 + 6615.85i) q^{48} +(-6604.82 - 11439.9i) q^{49} +(-2824.71 + 1630.85i) q^{50} -3461.30 q^{51} +(1080.14 - 2695.11i) q^{52} +8751.13 q^{53} +(-3294.75 + 1902.22i) q^{54} +(2080.16 + 3602.95i) q^{55} +(-5753.88 + 9966.01i) q^{56} -11655.6i q^{57} +(5763.91 + 3327.79i) q^{58} +(11693.8 + 6751.41i) q^{59} -1072.13i q^{60} +(-6052.99 + 10484.1i) q^{61} +(24364.5 + 42200.6i) q^{62} +(-4207.34 + 2429.11i) q^{63} -36086.0 q^{64} +(-2162.27 - 15079.2i) q^{65} +7816.16 q^{66} +(30125.7 - 17393.1i) q^{67} +(-916.285 - 1587.05i) q^{68} +(8916.47 - 15443.8i) q^{69} +7825.21i q^{70} +(21774.3 + 12571.4i) q^{71} +(-13459.0 - 7770.58i) q^{72} +12638.3i q^{73} +(-7086.98 + 12275.0i) q^{74} +(-2812.50 - 4871.39i) q^{75} +(5344.23 - 3085.49i) q^{76} +9981.13 q^{77} +(-26565.6 - 10646.9i) q^{78} +38441.1 q^{79} +(-18377.4 + 10610.2i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-11157.7 + 19325.8i) q^{82} +51744.5i q^{83} +(-2227.56 - 1286.08i) q^{84} +(-8326.60 - 4807.37i) q^{85} +33674.8i q^{86} +(-5738.99 + 9940.22i) q^{87} +(15964.5 + 27651.3i) q^{88} +(2134.33 - 1232.26i) q^{89} -10567.9 q^{90} +(-33923.9 - 13595.9i) q^{91} +9441.56 q^{92} +(-72777.5 + 42018.1i) q^{93} +(31322.5 + 54252.1i) q^{94} +(16188.3 - 28038.9i) q^{95} -15389.9i q^{96} +(-47857.9 - 27630.8i) q^{97} +(-59701.5 - 34468.7i) q^{98} +13479.5i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 198 q^{3} + 320 q^{4} - 858 q^{7} - 1782 q^{9} - 504 q^{11} + 5760 q^{12} - 1066 q^{13} + 2708 q^{14} - 3508 q^{16} + 1380 q^{17} + 7560 q^{19} + 5700 q^{20} + 1986 q^{22} - 3188 q^{23} - 27500 q^{25}+ \cdots + 408840 q^{98}+O(q^{100}) \) 44 * q + 198 * q^3 + 320 * q^4 - 858 * q^7 - 1782 * q^9 - 504 * q^11 + 5760 * q^12 - 1066 * q^13 + 2708 * q^14 - 3508 * q^16 + 1380 * q^17 + 7560 * q^19 + 5700 * q^20 + 1986 * q^22 - 3188 * q^23 - 27500 * q^25 - 9892 * q^26 - 32076 * q^27 - 50652 * q^28 + 7804 * q^29 + 53040 * q^32 - 4536 * q^33 + 5500 * q^35 + 25920 * q^36 - 30852 * q^37 + 10752 * q^38 - 14760 * q^39 - 69084 * q^41 + 12186 * q^42 + 47754 * q^43 - 118938 * q^46 + 31572 * q^48 - 6424 * q^49 + 24840 * q^51 - 53998 * q^52 - 12208 * q^53 - 20000 * q^55 + 78194 * q^56 + 113862 * q^58 + 165780 * q^59 + 70158 * q^61 - 91292 * q^62 + 69498 * q^63 + 138152 * q^64 - 41300 * q^65 + 35748 * q^66 - 128586 * q^67 - 83136 * q^68 + 28692 * q^69 + 61692 * q^71 + 199966 * q^74 - 123750 * q^75 + 107346 * q^76 + 44120 * q^77 - 2070 * q^78 - 623476 * q^79 + 207000 * q^80 - 144342 * q^81 + 302968 * q^82 - 455868 * q^84 - 70236 * q^87 - 227398 * q^88 + 569928 * q^89 + 256314 * q^91 - 9464 * q^92 + 69282 * q^93 + 199660 * q^94 - 82300 * q^95 - 502962 * q^97 + 408840 * q^98

Introduction

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