LMFDB - Embedded newform 42.5.g.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,5,Mod(19,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("42.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	42.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.34153844952$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	42.31
Dual form			42.5.g.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 - 2.44949i) q^{2} +(-4.50000 - 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(-12.2574 + 7.07679i) q^{5} +14.6969i q^{6} +(12.1985 + 47.4573i) q^{7} +22.6274 q^{8} +(13.5000 + 23.3827i) q^{9} +(34.6690 + 20.0162i) q^{10} +(-32.0147 + 55.4511i) q^{11} +(36.0000 - 20.7846i) q^{12} +228.919i q^{13} +(98.9949 - 96.9948i) q^{14} +73.5442 q^{15} +(-32.0000 - 55.4256i) q^{16} +(-195.250 - 112.728i) q^{17} +(38.1838 - 66.1362i) q^{18} +(-255.250 + 147.369i) q^{19} -113.229i q^{20} +(68.4045 - 245.251i) q^{21} +181.103 q^{22} +(-354.749 - 614.444i) q^{23} +(-101.823 - 58.7878i) q^{24} +(-212.338 + 367.780i) q^{25} +(560.735 - 323.741i) q^{26} -140.296i q^{27} +(-377.588 - 105.316i) q^{28} +740.397 q^{29} +(-104.007 - 180.146i) q^{30} +(-577.390 - 333.356i) q^{31} +(-90.5097 + 156.767i) q^{32} +(288.132 - 166.353i) q^{33} +637.683i q^{34} +(-485.367 - 495.375i) q^{35} -216.000 q^{36} +(416.882 + 722.061i) q^{37} +(721.955 + 416.821i) q^{38} +(594.749 - 1030.14i) q^{39} +(-277.352 + 160.129i) q^{40} +2817.60i q^{41} +(-697.477 + 179.280i) q^{42} +3066.41 q^{43} +(-256.118 - 443.609i) q^{44} +(-330.949 - 191.073i) q^{45} +(-1003.38 + 1737.91i) q^{46} +(-531.502 + 306.863i) q^{47} +332.554i q^{48} +(-2103.39 + 1157.81i) q^{49} +1201.17 q^{50} +(585.749 + 1014.55i) q^{51} +(-1586.00 - 915.677i) q^{52} +(576.300 - 998.181i) q^{53} +(-343.654 + 198.409i) q^{54} -906.246i q^{55} +(276.020 + 1073.84i) q^{56} +1531.50 q^{57} +(-1047.08 - 1813.59i) q^{58} +(-3024.67 - 1746.30i) q^{59} +(-294.177 + 509.529i) q^{60} +(1967.79 - 1136.11i) q^{61} +1885.75i q^{62} +(-945.000 + 925.907i) q^{63} +512.000 q^{64} +(-1620.01 - 2805.94i) q^{65} +(-814.962 - 470.518i) q^{66} +(4337.31 - 7512.44i) q^{67} +(1562.00 - 901.820i) q^{68} +3686.66i q^{69} +(-527.005 + 1889.47i) q^{70} -353.591 q^{71} +(305.470 + 529.090i) q^{72} +(3524.68 + 2034.97i) q^{73} +(1179.12 - 2042.30i) q^{74} +(1911.04 - 1103.34i) q^{75} -2357.90i q^{76} +(-3022.09 - 842.913i) q^{77} -3364.41 q^{78} +(-3236.41 - 5605.63i) q^{79} +(784.471 + 452.915i) q^{80} +(-364.500 + 631.333i) q^{81} +(6901.69 - 3984.69i) q^{82} +8225.83i q^{83} +(1425.53 + 1454.92i) q^{84} +3191.00 q^{85} +(-4336.55 - 7511.13i) q^{86} +(-3331.79 - 1923.61i) q^{87} +(-724.410 + 1254.72i) q^{88} +(-13456.5 + 7769.13i) q^{89} +1080.87i q^{90} +(-10863.9 + 2792.47i) q^{91} +5675.99 q^{92} +(1732.17 + 3000.21i) q^{93} +(1503.32 + 867.939i) q^{94} +(2085.79 - 3612.70i) q^{95} +(814.587 - 470.302i) q^{96} -1558.61i q^{97} +(5810.70 + 3514.84i) q^{98} -1728.79 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 18 q^{3} - 16 q^{4} - 66 q^{5} - 70 q^{7} + 54 q^{9} - 48 q^{10} - 162 q^{11} + 144 q^{12} + 396 q^{15} - 128 q^{16} - 204 q^{17} - 444 q^{19} + 630 q^{21} - 192 q^{22} + 312 q^{23} - 476 q^{25} + 1632 q^{26}+ \cdots - 8748 q^{99}+O(q^{100}) $ 4 * q - 18 * q^3 - 16 * q^4 - 66 * q^5 - 70 * q^7 + 54 * q^9 - 48 * q^10 - 162 * q^11 + 144 * q^12 + 396 * q^15 - 128 * q^16 - 204 * q^17 - 444 * q^19 + 630 * q^21 - 192 * q^22 + 312 * q^23 - 476 * q^25 + 1632 * q^26 - 560 * q^28 + 2724 * q^29 + 144 * q^30 - 3786 * q^31 + 1458 * q^33 + 672 * q^35 - 864 * q^36 + 1396 * q^37 + 1632 * q^38 + 648 * q^39 + 384 * q^40 - 1008 * q^42 - 632 * q^43 - 1296 * q^44 - 1782 * q^45 - 4896 * q^46 - 7896 * q^47 - 98 * q^49 + 2112 * q^50 + 612 * q^51 - 1728 * q^52 - 1038 * q^53 + 2688 * q^56 + 2664 * q^57 - 336 * q^58 - 966 * q^59 - 1584 * q^60 + 5088 * q^61 - 3780 * q^63 + 2048 * q^64 - 744 * q^65 + 864 * q^66 + 14600 * q^67 + 1632 * q^68 + 5376 * q^70 - 9696 * q^71 + 22584 * q^73 + 768 * q^74 + 4284 * q^75 - 3654 * q^77 - 9792 * q^78 + 3974 * q^79 + 4224 * q^80 - 1458 * q^81 + 18816 * q^82 + 1224 * q^85 - 18240 * q^86 - 12258 * q^87 + 768 * q^88 - 33156 * q^89 - 18984 * q^91 - 4992 * q^92 + 11358 * q^93 - 16320 * q^94 + 3252 * q^95 + 23520 * q^98 - 8748 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.41421	−	2.44949i	−0.353553	−	0.612372i
$2$	−1.41421	−	2.44949i	−0.353553	−	0.612372i
$3$	−4.50000	−	2.59808i	−0.500000	−	0.288675i
$3$	−4.50000	−	2.59808i	−0.500000	−	0.288675i
$4$	−4.00000	+	6.92820i	−0.250000	+	0.433013i
$5$	−12.2574	+	7.07679i	−0.490294	+	0.283072i	−0.724697	−	0.689068i	$-0.758020\pi$
$5$	−12.2574	+	7.07679i	−0.490294	+	0.283072i	0.234402	+	0.972140i	$0.424687\pi$
$6$			14.6969i			0.408248i
$7$	12.1985	+	47.4573i	0.248949	+	0.968517i
$7$	12.1985	+	47.4573i	0.248949	+	0.968517i
$8$	22.6274			0.353553
$9$	13.5000	+	23.3827i	0.166667	+	0.288675i
$10$	34.6690	+	20.0162i	0.346690	+	0.200162i
$11$	−32.0147	+	55.4511i	−0.264584	+	0.458274i	−0.967455	−	0.253044i	$-0.918568\pi$
$11$	−32.0147	+	55.4511i	−0.264584	+	0.458274i	0.702870	+	0.711318i	$0.251901\pi$
$12$	36.0000	−	20.7846i	0.250000	−	0.144338i
$13$			228.919i			1.35455i	0.735729	+	0.677276i	$0.236839\pi$
$13$			228.919i			1.35455i	−0.735729	+	0.677276i	$0.763161\pi$
$14$	98.9949	−	96.9948i	0.505076	−	0.494872i
$15$	73.5442			0.326863
$16$	−32.0000	−	55.4256i	−0.125000	−	0.216506i
$17$	−195.250	−	112.728i	−0.675605	−	0.390061i	0.122592	−	0.992457i	$-0.460879\pi$
$17$	−195.250	−	112.728i	−0.675605	−	0.390061i	−0.798197	+	0.602397i	$0.794213\pi$
$18$	38.1838	−	66.1362i	0.117851	−	0.204124i
$19$	−255.250	+	147.369i	−0.707063	+	0.408223i	−0.809973	−	0.586468i	$-0.800518\pi$
$19$	−255.250	+	147.369i	−0.707063	+	0.408223i	0.102910	+	0.994691i	$0.467185\pi$
$20$		−	113.229i		−	0.283072i
$21$	68.4045	−	245.251i	0.155112	−	0.556124i
$22$	181.103			0.374179
$23$	−354.749	−	614.444i	−0.670604	−	1.16152i	−0.977733	−	0.209852i	$-0.932702\pi$
$23$	−354.749	−	614.444i	−0.670604	−	1.16152i	0.307129	−	0.951668i	$-0.400632\pi$
$24$	−101.823	−	58.7878i	−0.176777	−	0.102062i
$25$	−212.338	+	367.780i	−0.339741	+	0.588449i
$26$	560.735	−	323.741i	0.829490	−	0.478906i
$27$		−	140.296i		−	0.192450i
$28$	−377.588	−	105.316i	−0.481617	−	0.134331i
$29$	740.397			0.880377			0.440188	−	0.897905i	$-0.354912\pi$
$29$	740.397			0.880377			0.440188	+	0.897905i	$0.354912\pi$
$30$	−104.007	−	180.146i	−0.115563	−	0.200162i
$31$	−577.390	−	333.356i	−0.600822	−	0.346885i	0.168543	−	0.985694i	$-0.446094\pi$
$31$	−577.390	−	333.356i	−0.600822	−	0.346885i	−0.769365	+	0.638809i	$0.779427\pi$
$32$	−90.5097	+	156.767i	−0.0883883	+	0.153093i
$33$	288.132	−	166.353i	0.264584	−	0.152758i
$34$			637.683i			0.551629i
$35$	−485.367	−	495.375i	−0.396218	−	0.404388i
$36$	−216.000			−0.166667
$37$	416.882	+	722.061i	0.304516	+	0.527437i	0.977153	−	0.212535i	$-0.0681720\pi$
$37$	416.882	+	722.061i	0.304516	+	0.527437i	−0.672638	+	0.739972i	$0.734839\pi$
$38$	721.955	+	416.821i	0.499969	+	0.288657i
$39$	594.749	−	1030.14i	0.391025	−	0.677276i
$40$	−277.352	+	160.129i	−0.173345	+	0.100081i
$41$			2817.60i			1.67615i	0.545558	+	0.838073i	$0.316318\pi$
$41$			2817.60i			1.67615i	−0.545558	+	0.838073i	$0.683682\pi$
$42$	−697.477	+	179.280i	−0.395395	+	0.101633i
$43$	3066.41			1.65841			0.829207	−	0.558942i	$-0.188793\pi$
$43$	3066.41			1.65841			0.829207	+	0.558942i	$0.188793\pi$
$44$	−256.118	−	443.609i	−0.132292	−	0.229137i
$45$	−330.949	−	191.073i	−0.163431	−	0.0943572i
$46$	−1003.38	+	1737.91i	−0.474188	+	0.821318i
$47$	−531.502	+	306.863i	−0.240608	+	0.138915i	−0.615456	−	0.788171i	$-0.711028\pi$
$47$	−531.502	+	306.863i	−0.240608	+	0.138915i	0.374848	+	0.927086i	$0.377695\pi$
$48$			332.554i			0.144338i
$49$	−2103.39	+	1157.81i	−0.876049	+	0.482222i
$50$	1201.17			0.480466
$51$	585.749	+	1014.55i	0.225202	+	0.390061i
$52$	−1586.00	−	915.677i	−0.586538	−	0.338638i
$53$	576.300	−	998.181i	0.205162	−	0.355351i	−0.745022	−	0.667040i	$-0.767561\pi$
$53$	576.300	−	998.181i	0.205162	−	0.355351i	0.950184	+	0.311688i	$0.100895\pi$
$54$	−343.654	+	198.409i	−0.117851	+	0.0680414i
$55$		−	906.246i		−	0.299585i
$56$	276.020	+	1073.84i	0.0880166	+	0.342422i
$57$	1531.50			0.471375
$58$	−1047.08	−	1813.59i	−0.311260	−	0.539119i
$59$	−3024.67	−	1746.30i	−0.868909	−	0.501665i	−0.00192348	−	0.999998i	$-0.500612\pi$
$59$	−3024.67	−	1746.30i	−0.868909	−	0.501665i	−0.866986	+	0.498333i	$0.833946\pi$
$60$	−294.177	+	509.529i	−0.0817157	+	0.141536i
$61$	1967.79	−	1136.11i	0.528834	−	0.305323i	−0.211707	−	0.977333i	$-0.567902\pi$
$61$	1967.79	−	1136.11i	0.528834	−	0.305323i	0.740542	+	0.672010i	$0.234569\pi$
$62$			1885.75i			0.490569i
$63$	−945.000	+	925.907i	−0.238095	+	0.233285i
$64$	512.000			0.125000
$65$	−1620.01	−	2805.94i	−0.383435	−	0.664129i
$66$	−814.962	−	470.518i	−0.187089	−	0.108016i
$67$	4337.31	−	7512.44i	0.966208	−	1.67352i	0.259874	−	0.965642i	$-0.416319\pi$
$67$	4337.31	−	7512.44i	0.966208	−	1.67352i	0.706334	−	0.707879i	$-0.250348\pi$
$68$	1562.00	−	901.820i	0.337802	−	0.195030i
$69$			3686.66i			0.774346i
$70$	−527.005	+	1889.47i	−0.107552	+	0.385606i
$71$	−353.591			−0.0701431			−0.0350715	−	0.999385i	$-0.511166\pi$
$71$	−353.591			−0.0701431			−0.0350715	+	0.999385i	$0.511166\pi$
$72$	305.470	+	529.090i	0.0589256	+	0.102062i
$73$	3524.68	+	2034.97i	0.661415	+	0.381868i	0.792816	−	0.609461i	$-0.208614\pi$
$73$	3524.68	+	2034.97i	0.661415	+	0.381868i	−0.131401	+	0.991329i	$0.541948\pi$
$74$	1179.12	−	2042.30i	0.215325	−	0.372954i
$75$	1911.04	−	1103.34i	0.339741	−	0.196150i
$76$		−	2357.90i		−	0.408223i
$77$	−3022.09	−	842.913i	−0.509714	−	0.142168i
$78$	−3364.41			−0.552993
$79$	−3236.41	−	5605.63i	−0.518573	−	0.898194i	−0.999767	−	0.0215805i	$-0.993130\pi$
$79$	−3236.41	−	5605.63i	−0.518573	−	0.898194i	0.481194	−	0.876614i	$-0.340203\pi$
$80$	784.471	+	452.915i	0.122574	+	0.0707679i
$81$	−364.500	+	631.333i	−0.0555556	+	0.0962250i
$82$	6901.69	−	3984.69i	1.02643	−	0.592607i
$83$			8225.83i			1.19405i	0.802222	+	0.597026i	$0.203651\pi$
$83$			8225.83i			1.19405i	−0.802222	+	0.597026i	$0.796349\pi$
$84$	1425.53	+	1454.92i	0.202031	+	0.206197i
$85$	3191.00			0.441660
$86$	−4336.55	−	7511.13i	−0.586338	−	1.01557i
$87$	−3331.79	−	1923.61i	−0.440188	−	0.254143i
$88$	−724.410	+	1254.72i	−0.0935447	+	0.162024i
$89$	−13456.5	+	7769.13i	−1.69884	+	0.980828i	−0.751983	+	0.659183i	$0.770902\pi$
$89$	−13456.5	+	7769.13i	−1.69884	+	0.980828i	−0.946860	+	0.321645i	$0.895764\pi$
$90$			1080.87i			0.133441i
$91$	−10863.9	+	2792.47i	−1.31191	+	0.337214i
$92$	5675.99			0.670604
$93$	1732.17	+	3000.21i	0.200274	+	0.346885i
$94$	1503.32	+	867.939i	0.170135	+	0.0982276i
$95$	2085.79	−	3612.70i	0.231113	−	0.400299i
$96$	814.587	−	470.302i	0.0883883	−	0.0510310i
$97$		−	1558.61i		−	0.165651i	−0.996564	−	0.0828254i	$-0.973606\pi$
$97$		−	1558.61i		−	0.165651i	0.996564	−	0.0828254i	$-0.0263944\pi$
$98$	5810.70	+	3514.84i	0.605030	+	0.365977i
$99$	−1728.79			−0.176390
$100$	−1698.70	−	2942.24i	−0.169870	−	0.294224i
$101$	13627.2	+	7867.66i	1.33587	+	0.771264i	0.986192	−	0.165607i	$-0.0529583\pi$
$101$	13627.2	+	7867.66i	1.33587	+	0.771264i	0.349676	+	0.936871i	$0.386292\pi$
$102$	1656.75	−	2869.57i	0.159242	−	0.275814i
$103$	29.2099	−	16.8644i	0.00275332	−	0.00158963i	−0.498623	−	0.866819i	$-0.666161\pi$
$103$	29.2099	−	16.8644i	0.00275332	−	0.00158963i	0.501376	+	0.865229i	$0.332827\pi$
$104$			5179.85i			0.478906i
$105$	897.127	+	3490.21i	0.0813721	+	0.316572i
$106$	−3260.05			−0.290143
$107$	2723.23	+	4716.78i	0.237858	+	0.411981i	0.960099	−	0.279659i	$-0.0902215\pi$
$107$	2723.23	+	4716.78i	0.237858	+	0.411981i	−0.722242	+	0.691641i	$0.756888\pi$
$108$	972.000	+	561.184i	0.0833333	+	0.0481125i
$109$	−8348.89	+	14460.7i	−0.702709	+	1.21713i	0.264803	+	0.964303i	$0.414693\pi$
$109$	−8348.89	+	14460.7i	−0.702709	+	1.21713i	−0.967512	+	0.252825i	$0.918640\pi$
$110$	−2219.84	+	1281.62i	−0.183458	+	0.105919i
$111$		−	4332.37i		−	0.351625i
$112$	2240.00	−	2194.74i	0.178571	−	0.174964i
$113$	9455.64			0.740515			0.370258	−	0.928929i	$-0.379269\pi$
$113$	9455.64			0.740515			0.370258	+	0.928929i	$0.379269\pi$
$114$	−2165.87	−	3751.39i	−0.166656	−	0.288657i
$115$	8696.58	+	5020.97i	0.657586	+	0.379658i
$116$	−2961.59	+	5129.62i	−0.220094	+	0.381214i
$117$	−5352.74	+	3090.41i	−0.391025	+	0.225759i
$118$			9878.54i			0.709461i
$119$	2967.99	−	10641.1i	0.209589	−	0.751440i
$120$	1664.11			0.115563
$121$	5270.62	+	9128.97i	0.359990	+	0.623521i
$122$	−5565.76	−	3213.39i	−0.373942	−	0.215896i
$123$	7320.35	−	12679.2i	0.483862	−	0.838073i
$124$	4619.12	−	2666.85i	0.300411	−	0.173442i
$125$		−	14856.7i		−	0.950827i
$126$	3604.43	+	1005.34i	0.227037	+	0.0633244i
$127$	−2380.07			−0.147564			−0.0737822	−	0.997274i	$-0.523507\pi$
$127$	−2380.07			−0.147564			−0.0737822	+	0.997274i	$0.523507\pi$
$128$	−724.077	−	1254.14i	−0.0441942	−	0.0765466i
$129$	−13798.8	−	7966.76i	−0.829207	−	0.478743i
$130$	−4582.09	+	7936.41i	−0.271129	+	0.469610i
$131$	−3758.37	+	2169.90i	−0.219006	+	0.126443i	−0.605490	−	0.795853i	$-0.707023\pi$
$131$	−3758.37	+	2169.90i	−0.219006	+	0.126443i	0.386484	+	0.922296i	$0.373690\pi$
$132$			2661.65i			0.152758i
$133$	−10107.4	−	10315.8i	−0.571393	−	0.583176i
$134$	−24535.5			−1.36642
$135$	992.846	+	1719.66i	0.0544772	+	0.0943572i
$136$	−4418.00	−	2550.73i	−0.238862	−	0.137907i
$137$	15379.6	−	26638.2i	0.819414	−	1.41927i	−0.0867001	−	0.996234i	$-0.527632\pi$
$137$	15379.6	−	26638.2i	0.819414	−	1.41927i	0.906114	−	0.423033i	$-0.139034\pi$
$138$	9030.44	−	5213.73i	0.474188	−	0.273773i
$139$		−	27186.6i		−	1.40710i	−0.710644	−	0.703551i	$-0.751596\pi$
$139$		−	27186.6i		−	1.40710i	0.710644	−	0.703551i	$-0.248404\pi$
$140$	5373.53	−	1381.22i	0.274160	−	0.0704703i
$141$	3189.01			0.160405
$142$	500.054	+	866.118i	0.0247993	+	0.0429537i
$143$	−12693.8	−	7328.78i	−0.620755	−	0.358393i
$144$	864.000	−	1496.49i	0.0416667	−	0.0721688i
$145$	−9075.31	+	5239.63i	−0.431644	+	0.249210i
$146$		−	11511.6i		−	0.540043i
$147$	12473.4	+	254.611i	0.577230	+	0.0117827i
$148$	−6670.12			−0.304516
$149$	2913.46	+	5046.26i	0.131231	+	0.227299i	0.924151	−	0.382027i	$-0.124774\pi$
$149$	2913.46	+	5046.26i	0.131231	+	0.227299i	−0.792920	+	0.609325i	$0.791440\pi$
$150$	−5405.25	−	3120.72i	−0.240233	−	0.138699i
$151$	−12593.4	+	21812.4i	−0.552317	+	0.956642i	0.445789	+	0.895138i	$0.352923\pi$
$151$	−12593.4	+	21812.4i	−0.552317	+	0.956642i	−0.998107	+	0.0615039i	$0.980410\pi$
$152$	−5775.64	+	3334.57i	−0.249985	+	0.144329i
$153$		−	6087.29i		−	0.260040i
$154$	2209.18	+	8594.64i	0.0931513	+	0.362399i
$155$	9436.37			0.392773
$156$	4757.99	+	8241.09i	0.195513	+	0.338638i
$157$	20694.6	+	11948.0i	0.839571	+	0.484726i	0.857118	−	0.515120i	$-0.172253\pi$
$157$	20694.6	+	11948.0i	0.839571	+	0.484726i	−0.0175475	+	0.999846i	$0.505586\pi$
$158$	−9153.96	+	15855.1i	−0.366686	+	0.635119i
$159$	−5186.70	+	2994.54i	−0.205162	+	0.118450i
$160$		−	2562.07i		−	0.100081i
$161$	24832.5	−	24330.7i	0.958005	−	0.938650i
$162$	2061.92			0.0785674
$163$	21293.0	+	36880.5i	0.801422	+	1.38810i	0.918680	+	0.395001i	$0.129256\pi$
$163$	21293.0	+	36880.5i	0.801422	+	1.38810i	−0.117259	+	0.993101i	$0.537411\pi$
$164$	−19520.9	−	11270.4i	−0.725793	−	0.419037i
$165$	−2354.50	+	4078.11i	−0.0864828	+	0.149793i
$166$	20149.1	−	11633.1i	0.731205	−	0.422161i
$167$			26356.3i			0.945043i	0.881319	+	0.472521i	$0.156656\pi$
$167$			26356.3i			0.945043i	−0.881319	+	0.472521i	$0.843344\pi$
$168$	1547.82	−	5549.39i	0.0548405	−	0.196619i
$169$	−23843.0			−0.834809
$170$	−4512.75	−	7816.31i	−0.156150	−	0.270461i
$171$	−6891.74	−	3978.95i	−0.235688	−	0.136074i
$172$	−12265.6	+	21244.7i	−0.414603	+	0.718114i
$173$	24265.3	−	14009.6i	0.810763	−	0.468094i	−0.0364578	−	0.999335i	$-0.511607\pi$
$173$	24265.3	−	14009.6i	0.810763	−	0.468094i	0.847221	+	0.531241i	$0.178274\pi$
$174$			10881.6i			0.359412i
$175$	−20044.1	−	5590.63i	−0.654500	−	0.182551i
$176$	4097.88			0.132292
$177$	9074.02	+	15716.7i	0.289636	+	0.501665i
$178$	38060.8	+	21974.4i	1.20126	+	0.693550i
$179$	−12699.2	+	21995.7i	−0.396343	+	0.686487i	−0.993272	−	0.115808i	$-0.963054\pi$
$179$	−12699.2	+	21995.7i	−0.396343	+	0.686487i	0.596928	+	0.802295i	$0.296388\pi$
$180$	2647.59	−	1528.59i	0.0817157	−	0.0471786i
$181$		−	44097.2i		−	1.34603i	−0.739630	−	0.673014i	$-0.764999\pi$
$181$		−	44097.2i		−	1.34603i	0.739630	−	0.673014i	$-0.235001\pi$
$182$	22204.0	+	22661.8i	0.670329	+	0.684152i
$183$	−11806.8			−0.352556
$184$	−8027.06	−	13903.3i	−0.237094	−	0.410659i
$185$	−10219.8	−	5900.38i	−0.298605	−	0.172400i
$186$	4899.32	−	8485.87i	0.141615	−	0.245285i
$187$	12501.7	−	7217.88i	0.357509	−	0.206408i
$188$		−	4909.81i		−	0.138915i
$189$	6658.08	−	1711.40i	0.186391	−	0.0479102i
$190$	−11799.0			−0.326843
$191$	32279.6	+	55909.8i	0.884832	+	1.53257i	0.845906	+	0.533332i	$0.179060\pi$
$191$	32279.6	+	55909.8i	0.884832	+	1.53257i	0.0389256	+	0.999242i	$0.487606\pi$
$192$	−2304.00	−	1330.22i	−0.0625000	−	0.0360844i
$193$	−18337.3	+	31761.1i	−0.492290	+	0.852670i	−0.999961	−	0.00888055i	$-0.997173\pi$
$193$	−18337.3	+	31761.1i	−0.492290	+	0.852670i	0.507671	+	0.861551i	$0.330507\pi$
$194$	−3817.80	+	2204.20i	−0.101440	+	0.0585664i
$195$			16835.7i			0.442753i
$196$	392.000	−	19204.0i	0.0102041	−	0.499896i
$197$	−73147.0			−1.88480			−0.942398	−	0.334494i	$-0.891434\pi$
$197$	−73147.0			−1.88480			−0.942398	+	0.334494i	$0.891434\pi$
$198$	2444.89	+	4234.67i	0.0623632	+	0.108016i
$199$	−1213.33	−	700.514i	−0.0306387	−	0.0176893i	0.484602	−	0.874735i	$-0.338964\pi$
$199$	−1213.33	−	700.514i	−0.0306387	−	0.0176893i	−0.515241	+	0.857045i	$0.672298\pi$
$200$	−4804.66	+	8321.92i	−0.120117	+	0.208048i
$201$	−39035.8	+	22537.3i	−0.966208	+	0.557840i
$202$		−	44506.2i		−	1.09073i
$203$	9031.72	+	35137.3i	0.219169	+	0.852660i
$204$	−9371.99			−0.225202
$205$	−19939.6	−	34536.4i	−0.474469	−	0.821805i
$206$	−82.6182	−	47.6996i	−0.00194689	−	0.00112404i
$207$	9578.23	−	16590.0i	0.223535	−	0.387173i
$208$	12688.0	−	7325.41i	0.293269	−	0.169319i
$209$		−	18871.8i		−	0.432038i
$210$	7280.50	−	7133.40i	0.165091	−	0.161755i
$211$	58231.7			1.30796			0.653980	−	0.756512i	$-0.273098\pi$
$211$	58231.7			1.30796			0.653980	+	0.756512i	$0.273098\pi$
$212$	4610.40	+	7985.45i	0.102581	+	0.177676i
$213$	1591.16	+	918.657i	0.0350715	+	0.0202486i
$214$	7702.46	−	13341.1i	0.168191	−	0.291315i
$215$	−37586.1	+	21700.3i	−0.813111	+	0.469450i
$216$		−	3174.54i		−	0.0680414i
$217$	8776.92	−	31467.8i	0.186390	−	0.668263i
$218$	47228.4			0.993781
$219$	−10574.0	−	18314.8i	−0.220472	−	0.381868i
$220$	6278.65	+	3624.98i	0.129724	+	0.0748963i
$221$	25805.5	−	44696.4i	0.528357	−	0.915141i
$222$	−10612.1	+	6126.89i	−0.215325	+	0.124318i
$223$		−	61050.9i		−	1.22767i	−0.789434	−	0.613836i	$-0.789626\pi$
$223$		−	61050.9i		−	1.22767i	0.789434	−	0.613836i	$-0.210374\pi$
$224$	−8543.84	−	2383.02i	−0.170277	−	0.0474933i
$225$	−11466.3			−0.226494
$226$	−13372.3	−	23161.5i	−0.261812	−	0.453471i
$227$	21645.2	+	12496.8i	0.420058	+	0.242520i	0.695102	−	0.718911i	$-0.255359\pi$
$227$	21645.2	+	12496.8i	0.420058	+	0.242520i	−0.275044	+	0.961432i	$0.588693\pi$
$228$	−6125.99	+	10610.5i	−0.117844	+	0.204112i
$229$	−16392.9	+	9464.44i	−0.312597	+	0.180478i	−0.648088	−	0.761565i	$-0.724431\pi$
$229$	−16392.9	+	9464.44i	−0.312597	+	0.180478i	0.335491	+	0.942043i	$0.391098\pi$
$230$		−	28402.9i		−	0.536917i
$231$	11409.5	+	11644.7i	0.213817	+	0.218226i
$232$	16753.3			0.311260
$233$	−3342.37	−	5789.15i	−0.0615662	−	0.106636i	0.833599	−	0.552369i	$-0.186276\pi$
$233$	−3342.37	−	5789.15i	−0.0615662	−	0.106636i	−0.895166	+	0.445734i	$0.852943\pi$
$234$	15139.8	+	8740.99i	0.276497	+	0.159635i
$235$	4343.21	−	7522.66i	0.0786457	−	0.136218i
$236$	24197.4	−	13970.4i	0.434455	−	0.250832i
$237$			33633.8i			0.598796i
$238$	−30262.7	+	7778.77i	−0.534262	+	0.137327i
$239$	−96461.0			−1.68871			−0.844356	−	0.535782i	$-0.820017\pi$
$239$	−96461.0			−1.68871			−0.844356	+	0.535782i	$0.820017\pi$
$240$	−2353.41	−	4076.23i	−0.0408579	−	0.0707679i
$241$	47371.8	+	27350.1i	0.815616	+	0.470896i	0.848902	−	0.528550i	$-0.177264\pi$
$241$	47371.8	+	27350.1i	0.815616	+	0.470896i	−0.0332863	+	0.999446i	$0.510597\pi$
$242$	14907.6	−	25820.6i	0.254551	−	0.440896i
$243$	3280.50	−	1894.00i	0.0555556	−	0.0320750i
$244$			18177.7i			0.305323i
$245$	17588.4	−	29077.0i	0.293019	−	0.484415i
$246$	−41410.1			−0.684284
$247$	−33735.5	−	58431.6i	−0.552959	−	0.957753i
$248$	−13064.9	−	7542.99i	−0.212423	−	0.122642i
$249$	21371.3	−	37016.2i	0.344693	−	0.597026i
$250$	−36391.3	+	21010.5i	−0.582260	+	0.336168i
$251$			108137.i			1.71643i	0.513286	+	0.858217i	$0.328428\pi$
$251$			108137.i			1.71643i	−0.513286	+	0.858217i	$0.671572\pi$
$252$	−2634.87	−	10250.8i	−0.0414914	−	0.161419i
$253$	45428.8			0.709725
$254$	3365.92	+	5829.95i	0.0521719	+	0.0903643i
$255$	−14359.5	−	8290.45i	−0.220830	−	0.127496i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	31078.3	−	17943.0i	0.470533	−	0.271663i	−0.245930	−	0.969288i	$-0.579093\pi$
$257$	31078.3	−	17943.0i	0.470533	−	0.271663i	0.716463	+	0.697625i	$0.245760\pi$
$258$			45066.8i			0.677045i
$259$	−29181.8	+	28592.2i	−0.435023	+	0.426233i
$260$	25920.2			0.383435
$261$	9995.36	+	17312.5i	0.146729	+	0.254143i
$262$	10630.3	+	6137.39i	0.154861	+	0.0894090i
$263$	32715.8	−	56665.4i	0.472984	−	0.819232i	−0.526538	−	0.850151i	$-0.676510\pi$
$263$	32715.8	−	56665.4i	0.472984	−	0.819232i	0.999522	+	0.0309199i	$0.00984367\pi$
$264$	6519.69	−	3764.15i	0.0935447	−	0.0540081i
$265$			16313.4i			0.232302i
$266$	−10974.5	+	39346.7i	−0.155103	+	0.556089i
$267$	80739.2			1.13256
$268$	34698.5	+	60099.5i	0.483104	+	0.836761i
$269$	−59938.7	−	34605.6i	−0.828329	−	0.478236i	0.0249511	−	0.999689i	$-0.492057\pi$
$269$	−59938.7	−	34605.6i	−0.828329	−	0.478236i	−0.853280	+	0.521453i	$0.825390\pi$
$270$	2808.19	−	4863.93i	0.0385212	−	0.0667206i
$271$	5672.94	−	3275.27i	0.0772449	−	0.0445973i	−0.460880	−	0.887462i	$-0.652466\pi$
$271$	5672.94	−	3275.27i	0.0772449	−	0.0445973i	0.538125	+	0.842865i	$0.319133\pi$
$272$			14429.1i			0.195030i
$273$	56142.5	+	15659.1i	0.753298	+	0.210108i
$274$	−87000.1			−1.15883
$275$	−13595.9	−	23548.8i	−0.179780	−	0.311389i
$276$	−25542.0	−	14746.7i	−0.335302	−	0.193587i
$277$	−39551.6	+	68505.4i	−0.515471	+	0.892823i	0.484367	+	0.874865i	$0.339050\pi$
$277$	−39551.6	+	68505.4i	−0.515471	+	0.892823i	−0.999839	+	0.0179578i	$0.994284\pi$
$278$	−66593.4	+	38447.7i	−0.861671	+	0.497486i
$279$		−	18001.2i		−	0.231257i
$280$	−10982.6	−	11209.1i	−0.140084	−	0.142973i
$281$	34363.1			0.435191			0.217596	−	0.976039i	$-0.430179\pi$
$281$	34363.1			0.435191			0.217596	+	0.976039i	$0.430179\pi$
$282$	−4509.95	−	7811.45i	−0.0567118	−	0.0982276i
$283$	79598.4	+	45956.1i	0.993874	+	0.573813i	0.906430	−	0.422356i	$-0.138797\pi$
$283$	79598.4	+	45956.1i	0.993874	+	0.573813i	0.0874439	+	0.996169i	$0.472130\pi$
$284$	1414.37	−	2449.75i	0.0175358	−	0.0303729i
$285$	−18772.1	+	10838.1i	−0.231113	+	0.133433i
$286$			41457.8i			0.506844i
$287$	−133716.	+	34370.5i	−1.62338	+	0.417274i
$288$	−4887.52			−0.0589256
$289$	−16345.5	−	28311.3i	−0.195705	−	0.338972i
$290$	25668.9	+	14819.9i	0.305218	+	0.176218i
$291$	−4049.38	+	7013.74i	−0.0478193	+	0.0828254i
$292$	−28197.4	+	16279.8i	−0.330707	+	0.190934i
$293$		−	23218.2i		−	0.270453i	−0.990815	−	0.135227i	$-0.956824\pi$
$293$		−	23218.2i		−	0.270453i	0.990815	−	0.135227i	$-0.0431763\pi$
$294$	−17016.3	−	30913.5i	−0.196866	−	0.357646i
$295$	49432.7			0.568028
$296$	9432.97	+	16338.4i	0.107663	+	0.186477i
$297$	7779.58	+	4491.54i	0.0881948	+	0.0509193i
$298$	8240.51	−	14273.0i	0.0927943	−	0.160724i
$299$	140658.	−	81208.9i	1.57334	−	0.908367i
$300$			17653.5i			0.196150i
$301$	37405.5	+	145523.i	0.412860	+	1.60620i
$302$	71239.0			0.781095
$303$	−40881.6	−	70808.9i	−0.445289	−	0.771264i
$304$	16336.0	+	9431.59i	0.176766	+	0.102056i
$305$	−16080.0	+	27851.3i	−0.172856	+	0.299396i
$306$	−14910.7	+	8608.72i	−0.159242	+	0.0919382i
$307$			66385.9i			0.704367i	0.935931	+	0.352183i	$0.114561\pi$
$307$			66385.9i			0.704367i	−0.935931	+	0.352183i	$0.885439\pi$
$308$	17928.2	−	17566.0i	0.188989	−	0.185171i
$309$	−175.260			−0.00183555
$310$	−13345.0	−	23114.3i	−0.138866	−	0.240523i
$311$	−82879.0	−	47850.2i	−0.856888	−	0.494724i	0.00608108	−	0.999982i	$-0.498064\pi$
$311$	−82879.0	−	47850.2i	−0.856888	−	0.494724i	−0.862969	+	0.505257i	$0.831398\pi$
$312$	13457.6	−	23309.3i	0.138248	−	0.239453i
$313$	41486.1	−	23952.0i	0.423461	−	0.244486i	−0.273096	−	0.961987i	$-0.588048\pi$
$313$	41486.1	−	23952.0i	0.423461	−	0.244486i	0.696557	+	0.717501i	$0.254714\pi$
$314$		−	67588.2i		−	0.685507i
$315$	5030.75	−	18036.7i	0.0507005	−	0.181776i
$316$	51782.6			0.518573
$317$	17064.1	+	29555.9i	0.169811	+	0.294121i	0.938353	−	0.345678i	$-0.112351\pi$
$317$	17064.1	+	29555.9i	0.169811	+	0.294121i	−0.768543	+	0.639799i	$0.779018\pi$
$318$	14670.2	+	8469.85i	0.145071	+	0.0837571i
$319$	−23703.6	+	41055.8i	−0.232934	+	0.403454i
$320$	−6275.77	+	3623.32i	−0.0612868	+	0.0353839i
$321$		−	28300.7i		−	0.274654i
$322$	−94716.3	−	26418.0i	−0.913509	−	0.254793i
$323$	66450.0			0.636927
$324$	−2916.00	−	5050.66i	−0.0277778	−	0.0481125i
$325$	−84192.0	−	48608.3i	−0.797084	−	0.460196i
$326$	60225.6	−	104314.i	0.566691	−	0.981537i
$327$	75140.0	−	43382.1i	0.702709	−	0.405709i
$328$			63755.1i			0.592607i
$329$	−21046.4	−	21480.4i	−0.194440	−	0.198450i
$330$	13319.0			0.122305
$331$	−66642.6	−	115428.i	−0.608270	−	1.05355i	−0.991526	−	0.129912i	$-0.958531\pi$
$331$	−66642.6	−	115428.i	−0.608270	−	1.05355i	0.383256	−	0.923642i	$-0.374803\pi$
$332$	−56990.2	−	32903.3i	−0.517040	−	0.298513i
$333$	−11255.8	+	19495.7i	−0.101505	+	0.175812i
$334$	64559.5	−	37273.4i	0.578718	−	0.334123i
$335$			122777.i			1.09402i
$336$	−15782.1	+	4056.65i	−0.139793	+	0.0359326i
$337$	−49734.4			−0.437922			−0.218961	−	0.975734i	$-0.570267\pi$
$337$	−49734.4			−0.437922			−0.218961	+	0.975734i	$0.570267\pi$
$338$	33719.0	+	58403.1i	0.295149	+	0.511214i
$339$	−42550.4	−	24566.5i	−0.370258	−	0.213768i
$340$	−12764.0	+	22107.9i	−0.110415	+	0.191245i
$341$	36970.0	−	21344.6i	0.317936	−	0.183561i
$342$			22508.3i			0.192438i
$343$	−80605.0	−	85697.8i	−0.685131	−	0.728420i
$344$	69384.9			0.586338
$345$	−26089.7	−	45188.8i	−0.219195	−	0.379658i
$346$	−68632.7	−	39625.1i	−0.573296	−	0.330993i
$347$	−9384.77	+	16254.9i	−0.0779408	+	0.134997i	−0.902361	−	0.430980i	$-0.858168\pi$
$347$	−9384.77	+	16254.9i	−0.0779408	+	0.134997i	0.824421	+	0.565978i	$0.191501\pi$
$348$	26654.3	−	15388.9i	0.220094	−	0.127071i
$349$			4574.17i			0.0375545i	0.999824	+	0.0187772i	$0.00597733\pi$
$349$			4574.17i			0.0375545i	−0.999824	+	0.0187772i	$0.994023\pi$
$350$	14652.4	+	57004.1i	0.119611	+	0.465340i
$351$	32116.5			0.260683
$352$	−5795.28	−	10037.7i	−0.0467724	−	0.0810121i
$353$	52734.9	+	30446.5i	0.423203	+	0.244336i	0.696447	−	0.717608i	$-0.254763\pi$
$353$	52734.9	+	30446.5i	0.423203	+	0.244336i	−0.273244	+	0.961945i	$0.588097\pi$
$354$	25665.2	−	44453.4i	0.204804	−	0.354731i
$355$	4334.10	−	2502.29i	0.0343908	−	0.0198555i
$356$		−	124306.i		−	0.980828i
$357$	−41002.5	+	40174.0i	−0.321717	+	0.315217i
$358$	71837.7			0.560514
$359$	−116059.	−	201020.i	−0.900513	−	1.55973i	−0.826830	−	0.562452i	$-0.809858\pi$
$359$	−116059.	−	201020.i	−0.900513	−	1.55973i	−0.0736826	−	0.997282i	$-0.523475\pi$
$360$	−7488.51	−	4323.50i	−0.0577817	−	0.0333603i
$361$	−21725.5	+	37629.7i	−0.166708	+	0.288746i
$362$	−108016.	+	62362.9i	−0.824271	+	0.475893i
$363$		−	54773.8i		−	0.415681i
$364$	24108.8	−	86437.1i	0.181959	−	0.652375i
$365$	−57604.4			−0.432384
$366$	16697.3	+	28920.5i	0.124647	+	0.215896i
$367$	−125329.	−	72358.9i	−0.930509	−	0.537229i	−0.0435362	−	0.999052i	$-0.513862\pi$
$367$	−125329.	−	72358.9i	−0.930509	−	0.537229i	−0.886972	+	0.461822i	$0.847196\pi$
$368$	−22704.0	+	39324.4i	−0.167651	+	0.290380i
$369$	−65883.1	+	38037.6i	−0.483862	+	0.279358i
$370$			33377.6i			0.243810i
$371$	54401.0	+	15173.4i	0.395238	+	0.110239i
$372$	−27714.7			−0.200274
$373$	74441.6	+	128937.i	0.535054	+	0.926741i	0.999161	+	0.0409616i	$0.0130421\pi$
$373$	74441.6	+	128937.i	0.535054	+	0.926741i	−0.464107	+	0.885779i	$0.653625\pi$
$374$	−35360.2	−	20415.2i	−0.252797	−	0.145952i
$375$	−38598.8	+	66855.0i	−0.274480	+	0.475414i
$376$	−12026.5	+	6943.52i	−0.0850676	+	0.0491138i
$377$			169491.i			1.19252i
$378$	−13608.0	−	13888.6i	−0.0952381	−	0.0972020i
$379$	140667.			0.979299			0.489649	−	0.871919i	$-0.337125\pi$
$379$	140667.			0.979299			0.489649	+	0.871919i	$0.337125\pi$
$380$	16686.3	+	28901.6i	0.115556	+	0.200149i
$381$	10710.3	+	6183.59i	0.0737822	+	0.0425982i
$382$	91300.4	−	158137.i	0.625671	−	1.08369i
$383$	25393.9	−	14661.2i	0.173114	−	0.0999473i	−0.410939	−	0.911663i	$-0.634799\pi$
$383$	25393.9	−	14661.2i	0.173114	−	0.0999473i	0.584053	+	0.811715i	$0.301466\pi$
$384$			7524.83i			0.0510310i
$385$	43008.0	−	11054.8i	0.290153	−	0.0745814i
$386$	103731.			0.696202
$387$	41396.5	+	71700.8i	0.276402	+	0.478743i
$388$	10798.4	+	6234.43i	0.0717289	+	0.0414127i
$389$	−66209.9	+	114679.i	−0.437546	+	0.757852i	−0.997500	−	0.0706723i	$-0.977486\pi$
$389$	−66209.9	+	114679.i	−0.437546	+	0.757852i	0.559954	+	0.828524i	$0.310819\pi$
$390$	41238.8	−	23809.2i	0.271129	−	0.156537i
$391$			159960.i			1.04630i
$392$	−47594.4	+	26198.4i	−0.309730	+	0.170491i
$393$	22550.2			0.146004
$394$	103446.	+	179173.i	0.666376	+	1.15420i
$395$	79339.7	+	45806.8i	0.508507	+	0.293586i
$396$	6915.18	−	11977.4i	0.0440974	−	0.0763790i
$397$	29642.0	−	17113.8i	0.188073	−	0.108584i	−0.403007	−	0.915197i	$-0.632035\pi$
$397$	29642.0	−	17113.8i	0.188073	−	0.108584i	0.591080	+	0.806613i	$0.298702\pi$
$398$			3962.70i			0.0250164i
$399$	18682.0	+	72680.8i	0.117348	+	0.456535i
$400$	27179.3			0.169870
$401$	89540.6	+	155089.i	0.556841	+	0.964477i	0.997758	+	0.0669288i	$0.0213200\pi$
$401$	89540.6	+	155089.i	0.556841	+	0.964477i	−0.440917	+	0.897548i	$0.645347\pi$
$402$	110410.	+	63745.1i	0.683212	+	0.394453i
$403$	76311.7	−	132176.i	0.469873	−	0.813845i
$404$	−109018.	+	62941.3i	−0.667934	+	0.385632i
$405$		−	10318.0i		−	0.0629048i
$406$	73295.6	−	71814.7i	0.444657	−	0.435674i
$407$	−53385.5			−0.322281
$408$	13254.0	+	22956.6i	0.0796208	+	0.137907i
$409$	43099.3	+	24883.4i	0.257646	+	0.148752i	0.623260	−	0.782014i	$-0.285808\pi$
$409$	43099.3	+	24883.4i	0.257646	+	0.148752i	−0.365614	+	0.930767i	$0.619141\pi$
$410$	−56397.6	+	97683.6i	−0.335501	+	0.581104i
$411$	−138416.	+	79914.7i	−0.819414	+	0.473089i
$412$			269.830i			0.00158963i
$413$	45978.1	−	164845.i	0.269557	−	0.966442i
$414$	−54182.7			−0.316126
$415$	−58212.4	−	100827.i	−0.338002	−	0.585437i
$416$	−35887.0	−	20719.4i	−0.207372	−	0.119727i
$417$	−70633.0	+	122340.i	−0.406196	+	0.703551i
$418$	−46226.4	+	26688.8i	−0.264568	+	0.152748i
$419$			43951.2i			0.250347i	0.992135	+	0.125174i	$0.0399488\pi$
$419$			43951.2i			0.250347i	−0.992135	+	0.125174i	$0.960051\pi$
$420$	−27769.4	−	7745.35i	−0.157423	−	0.0439079i
$421$	−218257.			−1.23141			−0.615707	−	0.787975i	$-0.711129\pi$
$421$	−218257.			−1.23141			−0.615707	+	0.787975i	$0.711129\pi$
$422$	−82352.0	−	142638.i	−0.462433	−	0.800958i
$423$	−14350.6	−	8285.30i	−0.0802025	−	0.0463050i
$424$	13040.2	−	22586.3i	0.0725357	−	0.125636i
$425$	82917.9	−	47872.7i	0.459061	−	0.265039i
$426$		−	5196.71i		−	0.0286358i
$427$	77920.6	+	79527.4i	0.427363	+	0.436175i
$428$	−43571.7			−0.237858
$429$	38081.5	+	65959.0i	0.206918	+	0.358393i
$430$	106309.	+	61377.8i	0.574956	+	0.331951i
$431$	38369.8	−	66458.5i	0.206555	−	0.357763i	−0.744072	−	0.668099i	$-0.767108\pi$
$431$	38369.8	−	66458.5i	0.206555	−	0.357763i	0.950627	+	0.310336i	$0.100442\pi$
$432$	−7776.00	+	4489.48i	−0.0416667	+	0.0240563i
$433$		−	216713.i		−	1.15587i	−0.816083	−	0.577935i	$-0.803859\pi$
$433$		−	216713.i		−	1.15587i	0.816083	−	0.577935i	$-0.196141\pi$
$434$	−89492.6	+	23003.3i	−0.475125	+	0.122127i
$435$	54451.9			0.287763
$436$	−66791.1	−	115686.i	−0.351354	−	0.608564i
$437$	181099.	+	104558.i	0.948318	+	0.547512i
$438$	−29907.9	+	51802.0i	−0.155897	+	0.270021i
$439$	20578.6	−	11881.0i	0.106779	−	0.0616489i	−0.445659	−	0.895203i	$-0.647031\pi$
$439$	20578.6	−	11881.0i	0.106779	−	0.0616489i	0.552438	+	0.833554i	$0.313697\pi$
$440$		−	20506.0i		−	0.105919i
$441$	−55468.6	−	33552.5i	−0.285214	−	0.172523i
$442$	−145978.			−0.747210
$443$	−87432.4	−	151437.i	−0.445517	−	0.771659i	0.552571	−	0.833466i	$-0.313647\pi$
$443$	−87432.4	−	151437.i	−0.445517	−	0.771659i	−0.998088	+	0.0618072i	$0.980314\pi$
$444$	30015.5	+	17329.5i	0.152258	+	0.0879062i
$445$	109961.	−	190458.i	0.555289	−	0.961788i
$446$	−149544.	+	86339.0i	−0.751793	+	0.434048i
$447$		−	30277.6i		−	0.151532i
$448$	6245.62	+	24298.1i	0.0311186	+	0.121065i
$449$	−195154.			−0.968023			−0.484011	−	0.875062i	$-0.660821\pi$
$449$	−195154.			−0.968023			−0.484011	+	0.875062i	$0.660821\pi$
$450$	16215.7	+	28086.5i	0.0800777	+	0.138699i
$451$	−156239.	−	90204.7i	−0.768134	−	0.443482i
$452$	−37822.6	+	65510.6i	−0.185129	+	0.320653i
$453$	113340.	−	65437.2i	0.552317	−	0.318881i
$454$		−	70692.8i		−	0.342976i
$455$	113401.	−	111110.i	0.547764	−	0.536697i
$456$	34653.9			0.166656
$457$	−29236.1	−	50638.5i	−0.139987	−	0.242464i	0.787505	−	0.616309i	$-0.211373\pi$
$457$	−29236.1	−	50638.5i	−0.139987	−	0.242464i	−0.927491	+	0.373844i	$0.878039\pi$
$458$	46366.1	+	26769.5i	0.221039	+	0.127617i
$459$	−15815.2	+	27392.8i	−0.0750672	+	0.130020i
$460$	−69572.6	+	40167.8i	−0.328793	+	0.189829i
$461$		−	307243.i		−	1.44571i	−0.691002	−	0.722853i	$-0.742831\pi$
$461$		−	307243.i		−	1.44571i	0.691002	−	0.722853i	$-0.257169\pi$
$462$	12388.2	−	44415.5i	0.0580398	−	0.208090i
$463$	−17772.2			−0.0829049			−0.0414524	−	0.999140i	$-0.513199\pi$
$463$	−17772.2			−0.0829049			−0.0414524	+	0.999140i	$0.513199\pi$
$464$	−23692.7	−	41037.0i	−0.110047	−	0.190607i
$465$	−42463.7	−	24516.4i	−0.196387	−	0.113384i
$466$	−9453.65	+	16374.2i	−0.0435339	+	0.0754029i
$467$	56261.4	−	32482.5i	0.257974	−	0.148942i	−0.365436	−	0.930837i	$-0.619080\pi$
$467$	56261.4	−	32482.5i	0.257974	−	0.148942i	0.623410	+	0.781895i	$0.285747\pi$
$468$		−	49446.5i		−	0.225759i
$469$	409429.	+	114197.i	1.86137	+	0.519168i
$470$	−24568.9			−0.111222
$471$	−62083.7	−	107532.i	−0.279857	−	0.484726i
$472$	−68440.5	−	39514.2i	−0.307206	−	0.177365i
$473$	−98170.2	+	170036.i	−0.438790	+	0.760007i
$474$	82385.6	−	47565.4i	0.366686	−	0.211706i
$475$		−	125168.i		−	0.554760i
$476$	61852.0	+	63127.4i	0.272986	+	0.278615i
$477$	31120.2			0.136775
$478$	136416.	+	236280.i	0.597050	+	1.03412i
$479$	182677.	+	105468.i	0.796181	+	0.459675i	0.842134	−	0.539268i	$-0.181299\pi$
$479$	182677.	+	105468.i	0.796181	+	0.459675i	−0.0459530	+	0.998944i	$0.514632\pi$
$480$	−6656.46	+	11529.3i	−0.0288909	+	0.0500405i
$481$	−165294.	+	95432.3i	−0.714440	+	0.412482i
$482$		−	154716.i		−	0.665948i
$483$	−174959.	+	44971.7i	−0.749967	+	0.192773i
$484$	−84329.8			−0.359990
$485$	11029.9	+	19104.4i	0.0468910	+	0.0812177i
$486$	−9278.66	−	5357.03i	−0.0392837	−	0.0226805i
$487$	114444.	−	198223.i	0.482542	−	0.835787i	−0.517257	−	0.855830i	$-0.673047\pi$
$487$	114444.	−	198223.i	0.482542	−	0.835787i	0.999799	+	0.0200431i	$0.00638033\pi$
$488$	44526.1	−	25707.1i	0.186971	−	0.107948i
$489$		−	221283.i		−	0.925402i
$490$	−96097.7	−	1961.59i	−0.400240	−	0.00816987i
$491$	140350.			0.582169			0.291085	−	0.956697i	$-0.405984\pi$
$491$	140350.			0.582169			0.291085	+	0.956697i	$0.405984\pi$
$492$	58562.8	+	101434.i	0.241931	+	0.419037i
$493$	−144562.	−	83463.1i	−0.594787	−	0.343400i
$494$	−95418.3	+	165269.i	−0.391001	+	0.677234i
$495$	21190.5	−	12234.3i	0.0864828	−	0.0499309i
$496$			42669.6i			0.173442i
$497$	−4313.28	−	16780.5i	−0.0174620	−	0.0679348i
$498$	−120894.			−0.487470
$499$	172663.	+	299062.i	0.693424	+	1.20105i	0.970709	+	0.240258i	$0.0772322\pi$
$499$	172663.	+	299062.i	0.693424	+	1.20105i	−0.277285	+	0.960788i	$0.589434\pi$
$500$	102930.	+	59426.7i	0.411720	+	0.237707i
$501$	68475.7	−	118603.i	0.272810	−	0.472521i
$502$	264881.	−	152929.i	1.05110	−	0.606851i
$503$			58979.0i			0.233110i	0.993184	+	0.116555i	$0.0371851\pi$
$503$			58979.0i			0.233110i	−0.993184	+	0.116555i	$0.962815\pi$
$504$	−21382.9	+	20950.9i	−0.0841794	+	0.0824786i
$505$	−222711.			−0.873291
$506$	−64246.0	−	111277.i	−0.250926	−	0.434616i
$507$	107293.	+	61945.9i	0.417404	+	0.240988i
$508$	9520.26	−	16489.6i	0.0368911	−	0.0638972i
$509$	20653.6	−	11924.3i	0.0797186	−	0.0460255i	−0.459611	−	0.888120i	$-0.652011\pi$
$509$	20653.6	−	11924.3i	0.0797186	−	0.0460255i	0.539329	+	0.842095i	$0.318678\pi$
$510$			46897.9i			0.180307i
$511$	−53578.7	+	192095.i	−0.205187	+	0.735657i
$512$	11585.2			0.0441942
$513$	20675.2	+	35810.6i	0.0785626	+	0.136074i
$514$	−87902.6	−	50750.6i	−0.332717	−	0.192094i
$515$	−238.691	+	413.425i	−0.000899957	+	0.00155877i
$516$	110391.	−	63734.1i	0.414603	−	0.239371i
$517$		−	39296.5i		−	0.147019i
$518$	111305.	+	31045.0i	0.414817	+	0.115700i
$519$	−145592.			−0.540509
$520$	−36656.7	−	63491.3i	−0.135565	−	0.234805i
$521$	417171.	+	240854.i	1.53688	+	0.887315i	0.999019	+	0.0442788i	$0.0140990\pi$
$521$	417171.	+	240854.i	1.53688	+	0.887315i	0.537856	+	0.843037i	$0.319234\pi$
$522$	28271.1	−	48967.1i	0.103753	−	0.179706i
$523$	−399593.	+	230705.i	−1.46088	+	0.843438i	−0.999052	−	0.0435320i	$-0.986139\pi$
$523$	−399593.	+	230705.i	−1.46088	+	0.843438i	−0.461826	+	0.886970i	$0.652806\pi$
$524$		−	34718.3i		−	0.126443i
$525$	75673.4	+	77233.9i	0.274552	+	0.280214i
$526$	−185068.			−0.668900
$527$	75156.9	+	130176.i	0.270612	+	0.468714i
$528$	−18440.5	−	10646.6i	−0.0661461	−	0.0381895i
$529$	−111774.	+	193598.i	−0.399419	+	0.691813i
$530$	39959.6	−	23070.7i	0.142255	−	0.0821312i
$531$		−	94299.9i		−	0.334443i
$532$	111899.	−	28762.8i	0.395371	−	0.101627i
$533$	−645003.			−2.27043
$534$	−114182.	−	197770.i	−0.400421	−	0.693550i
$535$	−66759.3	−	38543.5i	−0.233240	−	0.134661i
$536$	98142.1	−	169987.i	0.341606	−	0.591679i
$537$	114293.	−	65987.2i	0.396343	−	0.228829i
$538$			195759.i			0.676328i
$539$	3137.44	−	153703.i	0.0107994	−	0.529059i
$540$	−15885.5			−0.0544772
$541$	254098.	+	440111.i	0.868174	+	1.50372i	0.863861	+	0.503731i	$0.168040\pi$
$541$	254098.	+	440111.i	0.868174	+	1.50372i	0.00431302	+	0.999991i	$0.498627\pi$
$542$	−16045.5	−	9263.87i	−0.0546204	−	0.0315351i
$543$	−114568.	+	198438.i	−0.388565	+	0.673014i
$544$	35344.0	−	20405.9i	0.119431	−	0.0689536i
$545$		−	236333.i		−	0.795668i
$546$	−41040.7	−	159666.i	−0.137667	−	0.535583i
$547$	40170.8			0.134257			0.0671283	−	0.997744i	$-0.478616\pi$
$547$	40170.8			0.134257			0.0671283	+	0.997744i	$0.478616\pi$
$548$	123037.	+	213106.i	0.409707	+	0.709634i
$549$	53130.4	+	30674.9i	0.176278	+	0.101774i
$550$	−38455.0	+	66606.0i	−0.127124	+	0.220185i
$551$	−188986.	+	109111.i	−0.622482	+	0.359390i
$552$			83419.7i			0.273773i
$553$	226549.	−	221972.i	0.740818	−	0.725851i
$554$	223738.			0.728987
$555$	30659.3	+	53103.4i	0.0995350	+	0.172400i
$556$	188355.	+	108747.i	0.609293	+	0.351776i
$557$	39230.2	−	67948.7i	0.126447	−	0.219013i	−0.795850	−	0.605493i	$-0.792976\pi$
$557$	39230.2	−	67948.7i	0.126447	−	0.219013i	0.922298	+	0.386480i	$0.126309\pi$
$558$	−44093.9	+	25457.6i	−0.141615	+	0.0817616i
$559$			701959.i			2.24641i
$560$	−11924.8	+	42753.8i	−0.0380254	+	0.136332i
$561$	−75010.4			−0.238339
$562$	−48596.8	−	84172.2i	−0.153863	−	0.266499i
$563$	−355612.	−	205312.i	−1.12191	−	0.647737i	−0.180024	−	0.983662i	$-0.557618\pi$
$563$	−355612.	−	205312.i	−1.12191	−	0.647737i	−0.941889	+	0.335926i	$0.890951\pi$
$564$	−12756.1	+	22094.1i	−0.0401013	+	0.0694574i
$565$	−115901.	+	66915.6i	−0.363071	+	0.209619i
$566$		−	259967.i		−	0.811495i
$567$	−34407.7	−	9596.89i	−0.107026	−	0.0298514i
$568$	−8000.86			−0.0247993
$569$	74404.3	+	128872.i	0.229812	+	0.398047i	0.957752	−	0.287594i	$-0.0928554\pi$
$569$	74404.3	+	128872.i	0.229812	+	0.398047i	−0.727940	+	0.685641i	$0.759522\pi$
$570$	53095.6	+	30654.8i	0.163421	+	0.0943514i
$571$	−36146.3	+	62607.3i	−0.110864	+	0.192023i	−0.916119	−	0.400906i	$-0.868695\pi$
$571$	−36146.3	+	62607.3i	−0.110864	+	0.192023i	0.805255	+	0.592929i	$0.202029\pi$
$572$	101551.	−	58630.3i	0.310378	−	0.179197i
$573$		−	335459.i		−	1.02172i
$574$	273293.	+	278928.i	0.829477	+	0.846582i
$575$	301307.			0.911326
$576$	6912.00	+	11971.9i	0.0208333	+	0.0360844i
$577$	−482666.	−	278667.i	−1.44976	−	0.837018i	−0.451290	−	0.892377i	$-0.649036\pi$
$577$	−482666.	−	278667.i	−1.44976	−	0.837018i	−0.998466	+	0.0553596i	$0.982369\pi$
$578$	−46232.1	+	80076.3i	−0.138385	+	0.239689i
$579$	165036.	−	95283.4i	0.492290	−	0.284223i
$580$		−	83834.1i		−	0.249210i
$581$	−390376.	+	100343.i	−1.15646	+	0.297258i
$582$	22906.8			0.0676267
$583$	36900.2	+	63913.0i	0.108565	+	0.188041i
$584$	79754.4	+	46046.2i	0.233845	+	0.135011i
$585$	43740.3	−	75760.5i	0.127812	−	0.221376i
$586$	−56872.6	+	32835.4i	−0.165618	+	0.0956197i
$587$			308119.i			0.894217i	0.894480	+	0.447109i	$0.147546\pi$
$587$			308119.i			0.894217i	−0.894480	+	0.447109i	$0.852454\pi$
$588$	−51657.5	+	85399.6i	−0.149410	+	0.247002i
$589$	196505.			0.566426
$590$	−69908.3	−	121085.i	−0.200828	−	0.347845i
$591$	329162.	+	190042.i	0.942398	+	0.544094i
$592$	26680.5	−	46211.9i	0.0761290	−	0.131859i
$593$	−200805.	+	115935.i	−0.571038	+	0.329689i	−0.757564	−	0.652761i	$-0.773611\pi$
$593$	−200805.	+	115935.i	−0.571038	+	0.329689i	0.186526	+	0.982450i	$0.440277\pi$
$594$		−	25408.0i		−	0.0720108i
$595$	38925.3	+	151436.i	0.109951	+	0.427755i
$596$	−46615.3			−0.131231
$597$	3639.98	+	6304.62i	0.0102129	+	0.0176893i
$598$	−397841.	−	229693.i	−1.11252	−	0.642312i
$599$	167042.	−	289325.i	0.465555	−	0.806365i	−0.533671	−	0.845692i	$-0.679188\pi$
$599$	167042.	−	289325.i	0.465555	−	0.806365i	0.999226	+	0.0393269i	$0.0125214\pi$
$600$	43242.0	−	24965.8i	0.120117	−	0.0693493i
$601$		−	645072.i		−	1.78591i	−0.450147	−	0.892955i	$-0.648628\pi$
$601$		−	645072.i		−	1.78591i	0.450147	−	0.892955i	$-0.351372\pi$
$602$	303559.	−	297426.i	0.837625	−	0.820702i
$603$	234215.			0.644139
$604$	−100747.	−	174499.i	−0.276159	−	0.478321i
$605$	−129208.	−	74598.1i	−0.353002	−	0.203806i
$606$	−115631.	+	200278.i	−0.314867	+	0.545366i
$607$	120643.	−	69653.0i	0.327433	−	0.189044i	−0.327268	−	0.944932i	$-0.606128\pi$
$607$	120643.	−	69653.0i	0.327433	−	0.189044i	0.654701	+	0.755888i	$0.272795\pi$
$608$		−	53353.1i		−	0.144329i
$609$	50646.5	−	181583.i	0.136557	−	0.489598i
$610$	90962.0			0.244456
$611$	−70246.8	−	121671.i	−0.188167	−	0.325915i
$612$	42174.0	+	24349.1i	0.112601	+	0.0650101i
$613$	203665.	−	352759.i	0.541997	−	0.938765i	−0.456793	−	0.889573i	$-0.651002\pi$
$613$	203665.	−	352759.i	0.541997	−	0.938765i	0.998789	−	0.0491924i	$-0.0156647\pi$
$614$	162611.	−	93883.8i	0.431335	−	0.249031i
$615$			207218.i			0.547870i
$616$	−68382.1	−	19072.9i	−0.180211	−	0.0502639i
$617$	276504.			0.726325			0.363163	−	0.931726i	$-0.381697\pi$
$617$	276504.			0.726325			0.363163	+	0.931726i	$0.381697\pi$
$618$	247.855	+	429.297i	0.000648963	+	0.00112404i
$619$	193904.	+	111950.i	0.506064	+	0.292176i	0.731214	−	0.682148i	$-0.238954\pi$
$619$	193904.	+	111950.i	0.506064	+	0.292176i	−0.225150	+	0.974324i	$0.572287\pi$
$620$	−37745.5	+	65377.1i	−0.0981933	+	0.170076i
$621$	−86204.1	+	49770.0i	−0.223535	+	0.129058i
$622$			270682.i			0.699646i
$623$	−532852.	−	543839.i	−1.37287	−	1.40118i
$624$	−76127.9			−0.195513
$625$	−27573.7	−	47759.1i	−0.0705888	−	0.122263i
$626$	−117340.	−	67746.5i	−0.299432	−	0.172877i
$627$	−49030.5	+	84923.3i	−0.124719	+	0.216019i
$628$	−165557.	+	95584.2i	−0.419785	+	0.242363i
$629$		−	187976.i		−	0.475119i
$630$	−51295.4	+	13185.0i	−0.129240	+	0.0332200i
$631$	299528.			0.752278			0.376139	−	0.926563i	$-0.377251\pi$
$631$	299528.			0.752278			0.376139	+	0.926563i	$0.377251\pi$
$632$	−73231.7	−	126841.i	−0.183343	−	0.317560i
$633$	−262042.	−	151290.i	−0.653980	−	0.377575i
$634$	48264.6	−	83596.7i	0.120074	−	0.207975i
$635$	29173.3	−	16843.2i	0.0723500	−	0.0417713i
$636$		−	47912.7i		−	0.118450i
$637$	−265046.	−	481507.i	−0.653194	−	1.18665i
$638$	134088.			0.329418
$639$	−4773.48	−	8267.92i	−0.0116905	−	0.0202486i
$640$	17750.6	+	10248.3i	0.0433363	+	0.0250202i
$641$	−288942.	+	500462.i	−0.703226	+	1.21802i	0.264102	+	0.964495i	$0.414924\pi$
$641$	−288942.	+	500462.i	−0.703226	+	1.21802i	−0.967328	+	0.253528i	$0.918409\pi$
$642$	−69322.2	+	40023.2i	−0.168191	+	0.0971050i
$643$			135320.i			0.327295i	0.986519	+	0.163647i	$0.0523259\pi$
$643$			135320.i			0.327295i	−0.986519	+	0.163647i	$0.947674\pi$
$644$	69238.5	+	269367.i	0.166946	+	0.649491i
$645$	225516.			0.542074
$646$	−93974.4	−	162768.i	−0.225188	−	0.390037i
$647$	188880.	+	109050.i	0.451209	+	0.260506i	0.708341	−	0.705871i	$-0.249444\pi$
$647$	188880.	+	109050.i	0.451209	+	0.260506i	−0.257132	+	0.966376i	$0.582777\pi$
$648$	−8247.69	+	14285.4i	−0.0196419	+	0.0340207i
$649$	193668.	−	111814.i	0.459800	−	0.265465i
$650$			274970.i			0.650816i
$651$	−121252.	+	118802.i	−0.286106	+	0.280325i
$652$	−340688.			−0.801422
$653$	−72127.2	−	124928.i	−0.169150	−	0.292977i	0.768971	−	0.639284i	$-0.220769\pi$
$653$	−72127.2	−	124928.i	−0.169150	−	0.292977i	−0.938121	+	0.346307i	$0.887436\pi$
$654$	−212528.	−	122703.i	−0.496890	−	0.286880i
$655$	30711.8	−	53194.4i	0.0715851	−	0.123989i
$656$	156167.	−	90163.3i	0.362896	−	0.209518i
$657$			109889.i			0.254579i
$658$	−22851.9	+	81930.8i	−0.0527802	+	0.189232i
$659$	−159392.			−0.367024			−0.183512	−	0.983017i	$-0.558747\pi$
$659$	−159392.			−0.367024			−0.183512	+	0.983017i	$0.558747\pi$
$660$	−18836.0	−	32624.8i	−0.0432414	−	0.0748963i
$661$	305674.	+	176481.i	0.699609	+	0.403919i	0.807202	−	0.590276i	$-0.200981\pi$
$661$	305674.	+	176481.i	0.699609	+	0.403919i	−0.107593	+	0.994195i	$0.534314\pi$
$662$	−188494.	+	326481.i	−0.430112	+	0.744975i
$663$	−232249.	+	134089.i	−0.528357	+	0.305047i
$664$			186129.i			0.422161i
$665$	196892.	+	54916.7i	0.445231	+	0.124183i
$666$	63672.5			0.143550
$667$	−262655.	−	454932.i	−0.590384	−	1.02258i
$668$	−182602.	−	105425.i	−0.409216	−	0.236261i
$669$	−158615.	+	274729.i	−0.354398	+	0.613836i
$670$	300741.	−	173633.i	0.669950	−	0.386796i
$671$			145488.i			0.323135i
$672$	32256.0	+	32921.1i	0.0714286	+	0.0729015i
$673$	504858.			1.11465			0.557326	−	0.830294i	$-0.311827\pi$
$673$	504858.			1.11465			0.557326	+	0.830294i	$0.311827\pi$
$674$	70335.1	+	121824.i	0.154829	+	0.268172i
$675$	51598.2	+	29790.2i	0.113247	+	0.0653832i
$676$	95371.9	−	165189.i	0.208702	−	0.361483i
$677$	−169486.	+	97853.0i	−0.369792	+	0.213500i	−0.673368	−	0.739308i	$-0.735153\pi$
$677$	−169486.	+	97853.0i	−0.369792	+	0.213500i	0.303576	+	0.952807i	$0.401820\pi$
$678$			138969.i			0.302314i
$679$	73967.4	−	19012.7i	0.160436	−	0.0412385i
$680$	72204.0			0.156150
$681$	−64935.5	−	112472.i	−0.140019	−	0.242520i
$682$	−104567.	−	60371.7i	−0.224815	−	0.129797i
$683$	117221.	−	203032.i	0.251283	−	0.435235i	−0.712596	−	0.701574i	$-0.752481\pi$
$683$	117221.	−	203032.i	0.251283	−	0.435235i	0.963879	+	0.266340i	$0.0858142\pi$
$684$	55134.0	−	31831.6i	0.117844	−	0.0680372i
$685$			435352.i			0.927812i
$686$	−95923.3	+	318636.i	−0.203834	+	0.677091i
$687$	98357.4			0.208398
$688$	−98125.0	−	169958.i	−0.207302	−	0.359057i
$689$	228503.	+	131926.i	0.481341	+	0.277902i
$690$	−73792.9	+	127813.i	−0.154995	+	0.268459i
$691$	−77344.0	+	44654.6i	−0.161983	+	0.0935212i	−0.578800	−	0.815469i	$-0.696479\pi$
$691$	−77344.0	+	44654.6i	−0.161983	+	0.0935212i	0.416817	+	0.908990i	$0.363146\pi$
$692$			224153.i			0.468094i
$693$	−21088.7	−	82044.0i	−0.0439120	−	0.170836i
$694$	53088.3			0.110225
$695$	192394.	+	333236.i	0.398311	+	0.689895i
$696$	−75389.7	−	43526.3i	−0.155630	−	0.0898531i
$697$	317621.	−	550136.i	0.653799	−	1.13241i
$698$	11204.4	−	6468.85i	0.0229973	−	0.0132775i
$699$			34734.9i			0.0710905i
$700$	118909.	−	116507.i	0.242672	−	0.237769i
$701$	122213.			0.248704			0.124352	−	0.992238i	$-0.460315\pi$
$701$	122213.			0.248704			0.124352	+	0.992238i	$0.460315\pi$
$702$	−45419.5	−	78669.0i	−0.0921655	−	0.159635i
$703$	−212818.	−	122871.i	−0.430624	−	0.248621i
$704$	−16391.5	+	28391.0i	−0.0330731	+	0.0572842i
$705$	−39088.9	+	22568.0i	−0.0786457	+	0.0454061i
$706$		−	172231.i		−	0.345544i
$707$	−207147.	+	742683.i	−0.414419	+	1.48582i
$708$	−145184.			−0.289636
$709$	−42009.9	−	72763.3i	−0.0835717	−	0.144750i	0.821210	−	0.570626i	$-0.193299\pi$
$709$	−42009.9	−	72763.3i	−0.0835717	−	0.144750i	−0.904782	+	0.425876i	$0.859966\pi$
$710$	−12258.7	−	7077.55i	−0.0243179	−	0.0140400i
$711$	87383.1	−	151352.i	0.172858	−	0.299398i
$712$	−304487.	+	175795.i	−0.600632	+	0.346775i
$713$			473032.i			0.930489i
$714$	156392.	+	43620.4i	0.306774	+	0.0855645i
$715$	207457.			0.405804
$716$	−101594.	−	175966.i	−0.198172	−	0.343243i
$717$	434074.	+	250613.i	0.844356	+	0.487489i
$718$	−328264.	+	568570.i	−0.636759	+	1.10290i
$719$	657416.	−	379560.i	1.27169	−	0.734213i	0.296388	−	0.955068i	$-0.404218\pi$
$719$	657416.	−	379560.i	1.27169	−	0.734213i	0.975307	+	0.220855i	$0.0708846\pi$
$720$			24457.4i			0.0471786i
$721$	1156.65	+	1180.51i	0.00222502	+	0.00227090i
$722$	122898.			0.235760
$723$	−142115.	−	246151.i	−0.271872	−	0.470896i
$724$	305515.	+	176389.i	0.582847	+	0.336507i
$725$	−157214.	+	272303.i	−0.299100	+	0.518057i
$726$	−134168.	+	77461.9i	−0.254551	+	0.146965i
$727$		−	92384.1i		−	0.174795i	−0.996174	−	0.0873974i	$-0.972145\pi$
$727$		−	92384.1i		−	0.174795i	0.996174	−	0.0873974i	$-0.0278550\pi$
$728$	−245822.	+	63186.3i	−0.463829	+	0.119223i
$729$	−19683.0			−0.0370370
$730$	81464.9	+	141101.i	0.152871	+	0.264780i
$731$	−598715.	−	345668.i	−1.12043	−	0.646882i
$732$	47227.0	−	81799.6i	0.0881391	−	0.152661i
$733$	2903.50	−	1676.34i	0.00540399	−	0.00312000i	−0.497296	−	0.867581i	$-0.665674\pi$
$733$	2903.50	−	1676.34i	0.00540399	−	0.00312000i	0.502700	+	0.864461i	$0.332340\pi$
$734$			409324.i			0.759757i
$735$	−154692.	+	85150.5i	−0.286348	+	0.157620i
$736$	128433.			0.237094
$737$	277715.	+	481017.i	0.511287	+	0.885575i
$738$	186346.	+	107587.i	0.342142	+	0.197536i
$739$	13592.8	−	23543.4i	0.0248897	−	0.0431103i	−0.853312	−	0.521400i	$-0.825410\pi$
$739$	13592.8	−	23543.4i	0.0248897	−	0.0431103i	0.878202	+	0.478290i	$0.158743\pi$
$740$	81758.0	−	47203.0i	0.149302	−	0.0861998i
$741$			350589.i			0.638502i
$742$	−39767.6	−	154713.i	−0.0722307	−	0.281008i
$743$	773801.			1.40169			0.700845	−	0.713314i	$-0.252807\pi$
$743$	773801.			1.40169			0.700845	+	0.713314i	$0.252807\pi$
$744$	39194.6	+	67887.0i	0.0708076	+	0.122642i
$745$	−71422.6	−	41235.9i	−0.128684	−	0.0742955i
$746$	210553.	−	364688.i	0.378340	−	0.655305i
$747$	−192342.	+	111049.i	−0.344693	+	0.199009i
$748$			115486.i			0.206408i
$749$	−190626.	+	186775.i	−0.339797	+	0.332931i
$750$	218348.			0.388174
$751$	−98922.2	−	171338.i	−0.175394	−	0.303791i	0.764904	−	0.644145i	$-0.222786\pi$
$751$	−98922.2	−	171338.i	−0.175394	−	0.303791i	−0.940297	+	0.340354i	$0.889453\pi$
$752$	34016.1	+	19639.2i	0.0601519	+	0.0347287i
$753$	280948.	−	486617.i	0.495492	−	0.858217i
$754$	415167.	−	239697.i	0.730264	−	0.421618i
$755$		−	356483.i		−	0.625381i
$756$	−14775.4	+	52974.1i	−0.0258521	+	0.0926873i
$757$	−770706.			−1.34492			−0.672461	−	0.740132i	$-0.734763\pi$
$757$	−770706.			−1.34492			−0.672461	+	0.740132i	$0.734763\pi$
$758$	−198934.	−	344564.i	−0.346234	−	0.599696i
$759$	−204430.	−	118027.i	−0.354863	−	0.204880i
$760$	47196.1	−	81746.0i	0.0817107	−	0.141527i
$761$	−131757.	+	76069.9i	−0.227512	+	0.131354i	−0.609424	−	0.792845i	$-0.708599\pi$
$761$	−131757.	+	76069.9i	−0.227512	+	0.131354i	0.381912	+	0.924199i	$0.375266\pi$
$762$		−	34979.7i		−	0.0602429i
$763$	−788109.	−	219817.i	−1.35375	−	0.377583i
$764$	−516473.			−0.884832
$765$	43078.4	+	74614.0i	0.0736100	+	0.127496i
$766$	−71824.8	−	41468.0i	−0.122410	−	0.0706734i
$767$	399760.	−	692405.i	0.679531	−	1.17698i
$768$	18432.0	−	10641.7i	0.0312500	−	0.0180422i
$769$			961897.i			1.62658i	0.581857	+	0.813291i	$0.302326\pi$
$769$			961897.i			1.62658i	−0.581857	+	0.813291i	$0.697674\pi$
$770$	−87901.2	−	89713.7i	−0.148256	−	0.151313i
$771$	−186470.			−0.313689
$772$	−146698.	−	254089.i	−0.246145	−	0.426335i
$773$	−130829.	−	75534.4i	−0.218951	−	0.126411i	0.386514	−	0.922284i	$-0.373679\pi$
$773$	−130829.	−	75534.4i	−0.218951	−	0.126411i	−0.605464	+	0.795872i	$0.707013\pi$
$774$	117087.	−	202801.i	0.195446	−	0.338522i
$775$	245204.	−	141569.i	0.408248	−	0.235702i
$776$		−	35267.3i		−	0.0585664i
$777$	205603.	−	52848.3i	0.340554	−	0.0875365i
$778$	374540.			0.618783
$779$	−415226.	−	719192.i	−0.684242	−	1.18514i
$780$	−116641.	−	67342.7i	−0.191717	−	0.110688i
$781$	11320.1	−	19607.0i	0.0185588	−	0.0321447i
$782$	391821.	−	226218.i	0.640728	−	0.369924i
$783$		−	103875.i		−	0.169429i
$784$	131481.	+	79531.9i	0.213910	+	0.129392i
$785$	−338215.			−0.548849
$786$	−31890.8	−	55236.5i	−0.0516203	−	0.0894090i
$787$	−172244.	−	99445.4i	−0.278097	−	0.160559i	0.354465	−	0.935069i	$-0.384663\pi$
$787$	−172244.	−	99445.4i	−0.278097	−	0.160559i	−0.632561	+	0.774510i	$0.717996\pi$
$788$	292588.	−	506777.i	0.471199	−	0.816140i
$789$	−294442.	+	169996.i	−0.472984	+	0.273077i
$790$		−	259123.i		−	0.415194i
$791$	115344.	+	448739.i	0.184350	+	0.717202i
$792$	−39118.2			−0.0623632
$793$	260076.	+	450465.i	0.413575	+	0.716333i
$794$	−83840.2	−	48405.1i	−0.132988	−	0.0767804i
$795$	42383.5	−	73410.4i	0.0670599	−	0.116151i
$796$	9706.60	−	5604.11i	0.0153194	−	0.00884465i
$797$		−	990756.i		−	1.55973i	−0.625947	−	0.779866i	$-0.715287\pi$
$797$		−	990756.i		−	1.55973i	0.625947	−	0.779866i	$-0.284713\pi$
$798$	151611.	−	148547.i	0.238081	−	0.233270i
$799$	138368.			0.216741
$800$	−38437.3	−	66575.4i	−0.0600583	−	0.104024i
$801$	−363326.	−	209767.i	−0.566281	−	0.326943i
$802$	253259.	−	438657.i	0.393746	−	0.681988i
$803$	−225683.	+	130298.i	−0.350000	+	0.202073i
$804$		−	360597.i		−	0.557840i
$805$	−132197.	+	473965.i	−0.204000	+	0.731399i
$806$	−431684.			−0.664501
$807$	179816.	+	311451.i	0.276110	+	0.478236i
$808$	308348.	+	178025.i	0.472301	+	0.272683i
$809$	46144.3	−	79924.3i	0.0705052	−	0.122119i	−0.828618	−	0.559815i	$-0.810872\pi$
$809$	46144.3	−	79924.3i	0.0705052	−	0.122119i	0.899123	+	0.437696i	$0.144206\pi$
$810$	−25273.7	+	14591.8i	−0.0385212	+	0.0222402i
$811$		−	617125.i		−	0.938277i	−0.883125	−	0.469139i	$-0.844564\pi$
$811$		−	617125.i		−	0.938277i	0.883125	−	0.469139i	$-0.155436\pi$
$812$	−279565.	−	77975.4i	−0.424005	−	0.118262i
$813$	−34037.6			−0.0514966
$814$	75498.5	+	130767.i	0.113943	+	0.197356i
$815$	−521991.	−	301372.i	−0.785865	−	0.453719i
$816$	37488.0	−	64931.0i	0.0563004	−	0.0975152i
$817$	−782700.	+	451892.i	−1.17260	+	0.677003i
$818$		−	140762.i		−	0.210367i
$819$	−211958.	−	216329.i	−0.315996	−	0.322512i
$820$	319033.			0.474469
$821$	−153533.	−	265927.i	−0.227780	−	0.394526i	0.729370	−	0.684119i	$-0.239813\pi$
$821$	−153533.	−	265927.i	−0.227780	−	0.394526i	−0.957150	+	0.289593i	$0.906480\pi$
$822$	391500.	+	226033.i	0.579413	+	0.334524i
$823$	−423429.	+	733401.i	−0.625146	+	1.08278i	0.363367	+	0.931646i	$0.381627\pi$
$823$	−423429.	+	733401.i	−0.625146	+	1.08278i	−0.988513	+	0.151138i	$0.951706\pi$
$824$	660.946	−	381.597i	0.000973445	−	0.000562019i
$825$			141293.i			0.207592i
$826$	−468809.	+	120503.i	−0.687125	+	0.176619i
$827$	294059.			0.429956			0.214978	−	0.976619i	$-0.431032\pi$
$827$	294059.			0.429956			0.214978	+	0.976619i	$0.431032\pi$
$828$	76625.9	+	132720.i	0.111767	+	0.193587i
$829$	895803.	+	517192.i	1.30348	+	0.752563i	0.980999	−	0.194013i	$-0.0621506\pi$
$829$	895803.	+	517192.i	1.30348	+	0.752563i	0.322479	+	0.946577i	$0.395484\pi$
$830$	−164650.	+	285182.i	−0.239004	+	0.413967i
$831$	355964.	−	205516.i	0.515471	−	0.297608i
$832$			117207.i			0.169319i
$833$	541205.	+	11047.3i	0.779959	+	0.0159208i
$834$	399560.			0.574447
$835$	−186518.	−	323059.i	−0.267515	−	0.463349i
$836$	130748.	+	75487.4i	0.187078	+	0.108009i
$837$	−46768.6	+	81005.6i	−0.0667580	+	0.115628i
$838$	107658.	−	62156.4i	0.153306	−	0.0885111i
$839$			307258.i			0.436495i	0.975893	+	0.218248i	$0.0700340\pi$
$839$			307258.i			0.436495i	−0.975893	+	0.218248i	$0.929966\pi$
$840$	20299.7	+	78974.4i	0.0287694	+	0.111925i
$841$	−159093.			−0.224937
$842$	308662.	+	534618.i	0.435370	+	0.754084i
$843$	−154634.	−	89278.1i	−0.217596	−	0.125629i
$844$	−232927.	+	403441.i	−0.326990	+	0.566363i
$845$	292252.	−	168732.i	0.409302	−	0.236311i
$846$			46868.7i			0.0654851i
$847$	−368943.	+	361489.i	−0.514272	+	0.503881i
$848$	−73766.4			−0.102581
$849$	−238795.	−	413605.i	−0.331291	−	0.573813i
$850$	−234527.	−	135404.i	−0.324605	−	0.187411i
$851$	295777.	−	512302.i	0.408419	−	0.707402i
$852$	−12729.3	+	7349.26i	−0.0175358	+	0.0101243i
$853$			70737.4i			0.0972190i	0.998818	+	0.0486095i	$0.0154790\pi$
$853$			70737.4i			0.0972190i	−0.998818	+	0.0486095i	$0.984521\pi$
$854$	84605.2	−	303335.i	0.116006	−	0.415916i
$855$	112633.			0.154075
$856$	61619.7	+	106728.i	0.0840954	+	0.145657i
$857$	285670.	+	164932.i	0.388958	+	0.224565i	0.681709	−	0.731624i	$-0.261237\pi$
$857$	285670.	+	164932.i	0.388958	+	0.224565i	−0.292751	+	0.956189i	$0.594571\pi$
$858$	107711.	−	186560.i	0.146313	−	0.253422i
$859$	−60589.3	+	34981.2i	−0.0821125	+	0.0474077i	−0.540494	−	0.841348i	$-0.681763\pi$
$859$	−60589.3	+	34981.2i	−0.0821125	+	0.0474077i	0.458382	+	0.888756i	$0.348429\pi$
$860$		−	347205.i		−	0.469450i
$861$	691018.	+	192737.i	0.932145	+	0.259991i
$862$	−217052.			−0.292113
$863$	386112.	+	668765.i	0.518431	+	0.897949i	0.999771	+	0.0214151i	$0.00681715\pi$
$863$	386112.	+	668765.i	0.518431	+	0.897949i	−0.481339	+	0.876534i	$0.659850\pi$
$864$	21993.8	+	12698.2i	0.0294628	+	0.0170103i
$865$	−198286.	+	343441.i	−0.265008	+	0.459008i
$866$	−530836.	+	306478.i	−0.707823	+	0.408662i
$867$			169868.i			0.225981i
$868$	182908.	+	186680.i	0.242769	+	0.247775i
$869$	414451.			0.548825
$870$	−77006.6	−	133379.i	−0.101739	−	0.176218i
$871$	1.71974e6	+	992893.i	2.26687	+	1.30878i
$872$	−188914.	+	327208.i	−0.248445	+	0.430320i
$873$	36444.4	−	21041.2i	0.0478193	−	0.0276085i
$874$		−	591468.i		−	0.774299i
$875$	705058.	−	181229.i	0.920892	−	0.236707i
$876$	169185.			0.220472
$877$	−121260.	−	210028.i	−0.157659	−	0.273073i	0.776365	−	0.630283i	$-0.217061\pi$
$877$	−121260.	−	210028.i	−0.157659	−	0.273073i	−0.934024	+	0.357211i	$0.883728\pi$
$878$	−58204.9	−	33604.6i	−0.0755042	−	0.0435923i
$879$	−60322.5	+	104482.i	−0.0780732	+	0.135227i
$880$	−50229.2	+	28999.9i	−0.0648621	+	0.0374482i
$881$			646528.i			0.832982i	0.909140	+	0.416491i	$0.136740\pi$
$881$			646528.i			0.832982i	−0.909140	+	0.416491i	$0.863260\pi$
$882$	−3742.01	+	183320.i	−0.00481025	+	0.235653i
$883$	−461877.			−0.592387			−0.296193	−	0.955128i	$-0.595717\pi$
$883$	−461877.			−0.592387			−0.296193	+	0.955128i	$0.595717\pi$
$884$	206444.	+	357571.i	0.264179	+	0.457571i
$885$	−222447.	−	128430.i	−0.284014	−	0.163976i
$886$	−247296.	+	428329.i	−0.315028	+	0.545645i
$887$	−186391.	+	107613.i	−0.236907	+	0.136778i	−0.613754	−	0.789497i	$-0.710342\pi$
$887$	−186391.	+	107613.i	−0.236907	+	0.136778i	0.376847	+	0.926275i	$0.377008\pi$
$888$		−	98030.3i		−	0.124318i
$889$	−29033.2	−	112952.i	−0.0367359	−	0.142919i
$890$	−622034.			−0.785297
$891$	−23338.7	−	40423.9i	−0.0293983	−	0.0509193i
$892$	422973.	+	244204.i	0.531598	+	0.306918i
$893$	90443.9	−	156653.i	0.113417	−	0.196443i
$894$	−74164.6	+	42818.9i	−0.0927943	+	0.0535748i
$895$		−	359479.i		−	0.448774i
$896$	50685.4	−	49661.4i	0.0631345	−	0.0618590i
$897$	−843948.			−1.04889
$898$	275990.	+	478029.i	0.342248	+	0.592791i
$899$	−427498.	−	246816.i	−0.528950	−	0.305389i
$900$	45865.0	−	79440.6i	0.0566235	−	0.0980748i
$901$	−225045.	+	129930.i	−0.277217	+	0.160051i
$902$			510275.i			0.627179i
$903$	209756.	−	752038.i	0.257240	−	0.922283i
$904$	213957.			0.261812
$905$	312067.	+	540516.i	0.381022	+	0.659950i
$906$	−320575.	−	185084.i	−0.390547	−	0.225483i
$907$	−549134.	+	951128.i	−0.667519	+	1.15618i	0.311076	+	0.950385i	$0.399311\pi$
$907$	−549134.	+	951128.i	−0.667519	+	1.15618i	−0.978596	+	0.205793i	$0.934023\pi$
$908$	−173161.	+	99974.7i	−0.210029	+	0.121260i
$909$			424854.i			0.514176i
$910$	−432535.	−	120641.i	−0.522322	−	0.145685i
$911$	−1.32312e6			−1.59427			−0.797133	−	0.603803i	$-0.793651\pi$
$911$	−1.32312e6			−1.59427			−0.797133	+	0.603803i	$0.793651\pi$
$912$	−49008.0	−	84884.3i	−0.0589219	−	0.102056i
$913$	−456131.	−	263348.i	−0.547203	−	0.315928i
$914$	−82692.2	+	143227.i	−0.0989857	+	0.171448i
$915$	144720.	−	83553.9i	0.172856	−	0.0997987i
$916$		−	151431.i		−	0.180478i
$917$	−148824.	−	151893.i	−0.176984	−	0.180633i
$918$	89464.5			0.106161
$919$	−258264.	−	447326.i	−0.305797	−	0.529656i	0.671642	−	0.740876i	$-0.265589\pi$
$919$	−258264.	−	447326.i	−0.305797	−	0.529656i	−0.977438	+	0.211221i	$0.932256\pi$
$920$	196781.	+	113612.i	0.232492	+	0.134229i
$921$	172476.	−	298736.i	0.203333	−	0.352183i
$922$	−752588.	+	434507.i	−0.885310	+	0.511134i
$923$		−	80943.8i		−	0.0950124i
$924$	−126315.	+	32468.1i	−0.147949	+	0.0380289i
$925$	−354080.			−0.413826
$926$	25133.7	+	43532.9i	0.0293113	+	0.0507687i
$927$	788.669	+	455.338i	0.000917773	+	0.000529876i
$928$	−67013.1	+	116070.i	−0.0778151	+	0.134780i
$929$	1.07335e6	−	619697.i	1.24368	−	0.718039i	0.273838	−	0.961776i	$-0.411707\pi$
$929$	1.07335e6	−	619697.i	1.24368	−	0.718039i	0.969841	+	0.243737i	$0.0783734\pi$
$930$			138686.i			0.160349i
$931$	366265.	−	605506.i	0.422568	−	0.698585i
$932$	53477.9			0.0615662
$933$	248637.	+	430652.i	0.285629	+	0.494724i
$934$	−159131.	−	91874.5i	−0.182415	−	0.105318i
$935$	−102159.	+	176944.i	−0.116856	+	0.202401i
$936$	−121119.	+	69928.0i	−0.138248	+	0.0798177i
$937$		−	1.15260e6i		−	1.31281i	−0.754411	−	0.656403i	$-0.772077\pi$
$937$		−	1.15260e6i		−	1.31281i	0.754411	−	0.656403i	$-0.227923\pi$
$938$	−299296.	−	1.16439e6i	−0.340170	−	1.32340i
$939$	−248917.			−0.282308
$940$	34745.7	+	60181.3i	0.0393228	+	0.0681092i
$941$	93104.2	+	53753.7i	0.105145	+	0.0607057i	0.551650	−	0.834075i	$-0.313998\pi$
$941$	93104.2	+	53753.7i	0.105145	+	0.0607057i	−0.446505	+	0.894781i	$0.647332\pi$
$942$	−175599.	+	304147.i	−0.197889	+	0.342753i
$943$	1.73126e6	−	999543.i	1.94688	−	1.12403i
$944$			223526.i			0.250832i
$945$	−69499.2	+	68095.1i	−0.0778245	+	0.0762521i
$946$	555334.			0.620543
$947$	206307.	+	357335.i	0.230046	+	0.398451i	0.957821	−	0.287364i	$-0.0927790\pi$
$947$	206307.	+	357335.i	0.230046	+	0.398451i	−0.727775	+	0.685815i	$0.759446\pi$
$948$	−233022.	−	134535.i	−0.259286	−	0.149699i
$949$	−465845.	+	806867.i	−0.517260	+	0.895920i
$950$	−306597.	+	177014.i	−0.339720	+	0.196137i
$951$		−	177335.i		−	0.196080i
$952$	67158.0	−	240781.i	0.0741010	−	0.265674i
$953$	1.43052e6			1.57510			0.787550	−	0.616251i	$-0.211349\pi$
$953$	1.43052e6			1.57510			0.787550	+	0.616251i	$0.211349\pi$
$954$	−44010.6	−	76228.6i	−0.0483572	−	0.0837571i
$955$	−791324.	−	456871.i	−0.867656	−	0.500942i
$956$	385844.	−	668301.i	0.422178	−	0.731234i
$957$	213332.	−	123168.i	0.232934	−	0.134485i
$958$		−	596619.i		−	0.650079i
$959$	1.45179e6	+	404928.i	1.57858	+	0.440292i
$960$	37654.6			0.0408579
$961$	−239507.	−	414839.i	−0.259342	−	0.449193i
$962$	467521.	+	269923.i	0.505186	+	0.291669i
$963$	−73527.3	+	127353.i	−0.0792859	+	0.137327i
$964$	−378974.	+	218801.i	−0.407808	+	0.235448i
$965$		−	519077.i		−	0.557413i
$966$	357587.	+	364961.i	0.383202	+	0.391104i
$967$	−344533.			−0.368449			−0.184225	−	0.982884i	$-0.558977\pi$
$967$	−344533.			−0.368449			−0.184225	+	0.982884i	$0.558977\pi$
$968$	119260.	+	206565.i	0.127276	+	0.220448i
$969$	−299025.	−	172642.i	−0.318463	−	0.183865i
$970$	31197.4	−	54035.5i	0.0331570	−	0.0574296i
$971$	−1.25848e6	+	726581.i	−1.33477	+	0.770630i	−0.986027	−	0.166588i	$-0.946725\pi$
$971$	−1.25848e6	+	726581.i	−1.33477	+	0.770630i	−0.348744	+	0.937218i	$0.613392\pi$
$972$			30304.0i			0.0320750i
$973$	1.29020e6	−	331636.i	1.36280	−	0.350296i
$974$	−647393.			−0.682417
$975$	252576.	+	437474.i	0.265695	+	0.460196i
$976$	−125939.	−	72710.8i	−0.132209	−	0.0763307i
$977$	−772853.	+	1.33862e6i	−0.809669	+	1.40239i	0.103424	+	0.994637i	$0.467020\pi$
$977$	−772853.	+	1.33862e6i	−0.809669	+	1.40239i	−0.913093	+	0.407751i	$0.866313\pi$
$978$	−542031.	+	312941.i	−0.566691	+	0.327179i
$979$		−	994907.i		−	1.03805i
$980$	131098.	+	238164.i	0.136503	+	0.247985i
$981$	−450840.			−0.468473
$982$	−198485.	−	343786.i	−0.205828	−	0.356504i
$983$	116280.	+	67134.0i	0.120336	+	0.0694761i	0.558960	−	0.829195i	$-0.311201\pi$
$983$	116280.	+	67134.0i	0.120336	+	0.0694761i	−0.438624	+	0.898671i	$0.644534\pi$
$984$	165641.	−	286898.i	0.171071	−	0.296304i
$985$	896589.	−	517646.i	0.924105	−	0.533532i
$986$			472139.i			0.485641i
$987$	38901.1	+	151342.i	0.0399326	+	0.155355i
$988$	539768.			0.552959
$989$	−1.08781e6	−	1.88414e6i	−1.11214	−	1.92628i
$990$	−59935.7	−	34603.9i	−0.0611526	−	0.0353065i
$991$	395596.	−	685192.i	0.402814	−	0.697694i	−0.591251	−	0.806488i	$-0.701366\pi$
$991$	395596.	−	685192.i	0.402814	−	0.697694i	0.994064	+	0.108794i	$0.0346990\pi$
$992$	104519.	−	60344.0i	0.106211	−	0.0613212i
$993$			692571.i			0.702369i
$994$	−35003.8	+	34296.5i	−0.0354276	+	0.0347118i
$995$	19829.5			0.0200293
$996$	170971.	+	296130.i	0.172347	+	0.298513i
$997$	582624.	+	336378.i	0.586136	+	0.338406i	0.763568	−	0.645727i	$-0.223446\pi$
$997$	582624.	+	336378.i	0.586136	+	0.338406i	−0.177432	+	0.984133i	$0.556779\pi$
$998$	488366.	−	845874.i	0.490325	−	0.849268i
$999$	101302.	−	58487.0i	0.101505	−	0.0586041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.5.g.a.31.1	yes	4
3.2	odd	2		126.5.n.b.73.2		4
4.3	odd	2		336.5.bh.d.241.2		4
7.2	even	3		294.5.g.c.19.1		4
7.3	odd	6		294.5.c.a.97.3		4
7.4	even	3		294.5.c.a.97.4		4
7.5	odd	6	inner	42.5.g.a.19.1	✓	4
7.6	odd	2		294.5.g.c.31.1		4
21.5	even	6		126.5.n.b.19.2		4
21.11	odd	6		882.5.c.a.685.2		4
21.17	even	6		882.5.c.a.685.1		4
28.19	even	6		336.5.bh.d.145.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.5.g.a.19.1	✓	4	7.5	odd	6	inner
42.5.g.a.31.1	yes	4	1.1	even	1	trivial
126.5.n.b.19.2		4	21.5	even	6
126.5.n.b.73.2		4	3.2	odd	2
294.5.c.a.97.3		4	7.3	odd	6
294.5.c.a.97.4		4	7.4	even	3
294.5.g.c.19.1		4	7.2	even	3
294.5.g.c.31.1		4	7.6	odd	2
336.5.bh.d.145.2		4	28.19	even	6
336.5.bh.d.241.2		4	4.3	odd	2
882.5.c.a.685.1		4	21.17	even	6
882.5.c.a.685.2		4	21.11	odd	6

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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	42.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 2.44949i) q^{2} +(-4.50000 - 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(-12.2574 + 7.07679i) q^{5} +14.6969i q^{6} +(12.1985 + 47.4573i) q^{7} +22.6274 q^{8} +(13.5000 + 23.3827i) q^{9} +(34.6690 + 20.0162i) q^{10} +(-32.0147 + 55.4511i) q^{11} +(36.0000 - 20.7846i) q^{12} +228.919i q^{13} +(98.9949 - 96.9948i) q^{14} +73.5442 q^{15} +(-32.0000 - 55.4256i) q^{16} +(-195.250 - 112.728i) q^{17} +(38.1838 - 66.1362i) q^{18} +(-255.250 + 147.369i) q^{19} -113.229i q^{20} +(68.4045 - 245.251i) q^{21} +181.103 q^{22} +(-354.749 - 614.444i) q^{23} +(-101.823 - 58.7878i) q^{24} +(-212.338 + 367.780i) q^{25} +(560.735 - 323.741i) q^{26} -140.296i q^{27} +(-377.588 - 105.316i) q^{28} +740.397 q^{29} +(-104.007 - 180.146i) q^{30} +(-577.390 - 333.356i) q^{31} +(-90.5097 + 156.767i) q^{32} +(288.132 - 166.353i) q^{33} +637.683i q^{34} +(-485.367 - 495.375i) q^{35} -216.000 q^{36} +(416.882 + 722.061i) q^{37} +(721.955 + 416.821i) q^{38} +(594.749 - 1030.14i) q^{39} +(-277.352 + 160.129i) q^{40} +2817.60i q^{41} +(-697.477 + 179.280i) q^{42} +3066.41 q^{43} +(-256.118 - 443.609i) q^{44} +(-330.949 - 191.073i) q^{45} +(-1003.38 + 1737.91i) q^{46} +(-531.502 + 306.863i) q^{47} +332.554i q^{48} +(-2103.39 + 1157.81i) q^{49} +1201.17 q^{50} +(585.749 + 1014.55i) q^{51} +(-1586.00 - 915.677i) q^{52} +(576.300 - 998.181i) q^{53} +(-343.654 + 198.409i) q^{54} -906.246i q^{55} +(276.020 + 1073.84i) q^{56} +1531.50 q^{57} +(-1047.08 - 1813.59i) q^{58} +(-3024.67 - 1746.30i) q^{59} +(-294.177 + 509.529i) q^{60} +(1967.79 - 1136.11i) q^{61} +1885.75i q^{62} +(-945.000 + 925.907i) q^{63} +512.000 q^{64} +(-1620.01 - 2805.94i) q^{65} +(-814.962 - 470.518i) q^{66} +(4337.31 - 7512.44i) q^{67} +(1562.00 - 901.820i) q^{68} +3686.66i q^{69} +(-527.005 + 1889.47i) q^{70} -353.591 q^{71} +(305.470 + 529.090i) q^{72} +(3524.68 + 2034.97i) q^{73} +(1179.12 - 2042.30i) q^{74} +(1911.04 - 1103.34i) q^{75} -2357.90i q^{76} +(-3022.09 - 842.913i) q^{77} -3364.41 q^{78} +(-3236.41 - 5605.63i) q^{79} +(784.471 + 452.915i) q^{80} +(-364.500 + 631.333i) q^{81} +(6901.69 - 3984.69i) q^{82} +8225.83i q^{83} +(1425.53 + 1454.92i) q^{84} +3191.00 q^{85} +(-4336.55 - 7511.13i) q^{86} +(-3331.79 - 1923.61i) q^{87} +(-724.410 + 1254.72i) q^{88} +(-13456.5 + 7769.13i) q^{89} +1080.87i q^{90} +(-10863.9 + 2792.47i) q^{91} +5675.99 q^{92} +(1732.17 + 3000.21i) q^{93} +(1503.32 + 867.939i) q^{94} +(2085.79 - 3612.70i) q^{95} +(814.587 - 470.302i) q^{96} -1558.61i q^{97} +(5810.70 + 3514.84i) q^{98} -1728.79 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 18 q^{3} - 16 q^{4} - 66 q^{5} - 70 q^{7} + 54 q^{9} - 48 q^{10} - 162 q^{11} + 144 q^{12} + 396 q^{15} - 128 q^{16} - 204 q^{17} - 444 q^{19} + 630 q^{21} - 192 q^{22} + 312 q^{23} - 476 q^{25} + 1632 q^{26}+ \cdots - 8748 q^{99}+O(q^{100}) \) 4 * q - 18 * q^3 - 16 * q^4 - 66 * q^5 - 70 * q^7 + 54 * q^9 - 48 * q^10 - 162 * q^11 + 144 * q^12 + 396 * q^15 - 128 * q^16 - 204 * q^17 - 444 * q^19 + 630 * q^21 - 192 * q^22 + 312 * q^23 - 476 * q^25 + 1632 * q^26 - 560 * q^28 + 2724 * q^29 + 144 * q^30 - 3786 * q^31 + 1458 * q^33 + 672 * q^35 - 864 * q^36 + 1396 * q^37 + 1632 * q^38 + 648 * q^39 + 384 * q^40 - 1008 * q^42 - 632 * q^43 - 1296 * q^44 - 1782 * q^45 - 4896 * q^46 - 7896 * q^47 - 98 * q^49 + 2112 * q^50 + 612 * q^51 - 1728 * q^52 - 1038 * q^53 + 2688 * q^56 + 2664 * q^57 - 336 * q^58 - 966 * q^59 - 1584 * q^60 + 5088 * q^61 - 3780 * q^63 + 2048 * q^64 - 744 * q^65 + 864 * q^66 + 14600 * q^67 + 1632 * q^68 + 5376 * q^70 - 9696 * q^71 + 22584 * q^73 + 768 * q^74 + 4284 * q^75 - 3654 * q^77 - 9792 * q^78 + 3974 * q^79 + 4224 * q^80 - 1458 * q^81 + 18816 * q^82 + 1224 * q^85 - 18240 * q^86 - 12258 * q^87 + 768 * q^88 - 33156 * q^89 - 18984 * q^91 - 4992 * q^92 + 11358 * q^93 - 16320 * q^94 + 3252 * q^95 + 23520 * q^98 - 8748 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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