LMFDB - Embedded newform 18.6.c.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,6,Mod(7,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("18.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	18.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.88690875663$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			13.2
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	18.13
Dual form			18.6.c.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00000 + 3.46410i) q^{2} +(14.6969 + 5.19615i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(1.19694 - 2.07316i) q^{5} +(11.3939 + 61.3040i) q^{6} +(25.8485 + 44.7709i) q^{7} -64.0000 q^{8} +(189.000 + 152.735i) q^{9} +9.57551 q^{10} +(-335.484 - 581.076i) q^{11} +(-189.576 + 162.078i) q^{12} +(423.469 - 733.470i) q^{13} +(-103.394 + 179.083i) q^{14} +(28.3638 - 24.2496i) q^{15} +(-128.000 - 221.703i) q^{16} -1135.51 q^{17} +(-151.090 + 960.185i) q^{18} +1002.42 q^{19} +(19.1510 + 33.1705i) q^{20} +(147.257 + 792.307i) q^{21} +(1341.94 - 2324.30i) q^{22} +(-1200.79 + 2079.83i) q^{23} +(-940.604 - 332.554i) q^{24} +(1559.63 + 2701.37i) q^{25} +3387.76 q^{26} +(1984.09 + 3226.81i) q^{27} -827.151 q^{28} +(-1884.71 - 3264.41i) q^{29} +(140.731 + 49.7558i) q^{30} +(-2017.08 + 3493.69i) q^{31} +(512.000 - 886.810i) q^{32} +(-1911.23 - 10283.3i) q^{33} +(-2271.02 - 3933.53i) q^{34} +123.756 q^{35} +(-3628.36 + 1396.98i) q^{36} -14537.7 q^{37} +(2004.84 + 3472.49i) q^{38} +(10034.9 - 8579.36i) q^{39} +(-76.6041 + 132.682i) q^{40} +(3941.38 - 6826.67i) q^{41} +(-2450.12 + 2094.73i) q^{42} +(10176.5 + 17626.3i) q^{43} +10735.5 q^{44} +(542.865 - 209.012i) q^{45} -9606.31 q^{46} +(8068.27 + 13974.7i) q^{47} +(-729.208 - 3923.46i) q^{48} +(7067.21 - 12240.8i) q^{49} +(-6238.54 + 10805.5i) q^{50} +(-16688.6 - 5900.29i) q^{51} +(6775.51 + 11735.5i) q^{52} -5549.94 q^{53} +(-7209.83 + 13326.7i) q^{54} -1606.22 q^{55} +(-1654.30 - 2865.34i) q^{56} +(14732.5 + 5208.73i) q^{57} +(7538.84 - 13057.7i) q^{58} +(3206.13 - 5553.17i) q^{59} +(109.102 + 587.017i) q^{60} +(-4440.22 - 7690.68i) q^{61} -16136.7 q^{62} +(-1952.72 + 12409.7i) q^{63} +4096.00 q^{64} +(-1013.73 - 1755.84i) q^{65} +(31799.8 - 27187.2i) q^{66} +(21468.8 - 37185.0i) q^{67} +(9084.10 - 15734.1i) q^{68} +(-28455.0 + 24327.6i) q^{69} +(247.512 + 428.704i) q^{70} -63349.1 q^{71} +(-12096.0 - 9775.04i) q^{72} -12807.7 q^{73} +(-29075.3 - 50360.0i) q^{74} +(8885.14 + 47805.9i) q^{75} +(-8019.36 + 13889.9i) q^{76} +(17343.5 - 30039.8i) q^{77} +(49789.6 + 17603.3i) q^{78} +(1463.87 + 2535.49i) q^{79} -612.832 q^{80} +(12393.0 + 57733.9i) q^{81} +31531.0 q^{82} +(23770.7 + 41172.1i) q^{83} +(-12156.6 - 4298.00i) q^{84} +(-1359.14 + 2354.10i) q^{85} +(-40706.2 + 70505.1i) q^{86} +(-10737.1 - 57770.1i) q^{87} +(21471.0 + 37188.8i) q^{88} +84795.6 q^{89} +(1809.77 + 1462.52i) q^{90} +43784.1 q^{91} +(-19212.6 - 33277.2i) q^{92} +(-47798.7 + 40865.5i) q^{93} +(-32273.1 + 55898.6i) q^{94} +(1199.84 - 2078.18i) q^{95} +(12132.8 - 10373.0i) q^{96} +(-55874.3 - 96777.2i) q^{97} +56537.7 q^{98} +(25344.1 - 161063. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} - 32 q^{4} - 54 q^{5} - 72 q^{6} + 74 q^{7} - 256 q^{8} + 756 q^{9} - 432 q^{10} - 78 q^{11} - 288 q^{12} + 1106 q^{13} - 296 q^{14} + 378 q^{15} - 512 q^{16} + 984 q^{17} + 1512 q^{18} - 3280 q^{19}+ \cdots + 319626 q^{99}+O(q^{100}) $ 4 * q + 8 * q^2 - 32 * q^4 - 54 * q^5 - 72 * q^6 + 74 * q^7 - 256 * q^8 + 756 * q^9 - 432 * q^10 - 78 * q^11 - 288 * q^12 + 1106 * q^13 - 296 * q^14 + 378 * q^15 - 512 * q^16 + 984 * q^17 + 1512 * q^18 - 3280 * q^19 - 864 * q^20 - 234 * q^21 + 312 * q^22 - 5538 * q^23 + 3064 * q^25 + 8848 * q^26 - 2368 * q^28 - 3894 * q^29 + 6912 * q^30 + 4718 * q^31 + 2048 * q^32 - 17874 * q^33 + 1968 * q^34 - 2268 * q^35 - 6048 * q^36 - 9592 * q^37 - 6560 * q^38 + 18594 * q^39 + 3456 * q^40 + 15354 * q^41 - 4392 * q^42 + 32858 * q^43 + 2496 * q^44 + 5346 * q^45 - 44304 * q^46 + 24954 * q^47 + 4608 * q^48 + 30444 * q^49 - 12256 * q^50 - 81216 * q^51 + 17696 * q^52 - 32664 * q^53 - 44712 * q^54 - 70092 * q^55 - 4736 * q^56 + 107136 * q^57 + 15576 * q^58 + 21966 * q^59 + 21600 * q^60 + 3050 * q^61 + 37744 * q^62 + 6210 * q^63 + 16384 * q^64 + 12582 * q^65 + 77112 * q^66 + 36758 * q^67 - 7872 * q^68 - 39042 * q^69 - 4536 * q^70 - 147696 * q^71 - 48384 * q^72 - 102376 * q^73 - 19184 * q^74 + 19080 * q^75 + 26240 * q^76 + 21462 * q^77 + 69120 * q^78 - 14926 * q^79 + 27648 * q^80 + 49572 * q^81 + 122832 * q^82 + 90762 * q^83 - 13824 * q^84 - 94500 * q^85 - 131432 * q^86 - 18522 * q^87 + 4992 * q^88 - 18600 * q^89 - 81648 * q^90 + 99124 * q^91 - 88608 * q^92 - 145458 * q^93 - 99816 * q^94 + 151416 * q^95 + 18432 * q^96 - 30262 * q^97 + 243552 * q^98 + 319626 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$3$	14.6969	+	5.19615i	0.942809	+	0.333333i
$3$	14.6969	+	5.19615i	0.942809	+	0.333333i
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	1.19694	−	2.07316i	0.0214115	−	0.0370858i	−0.855121	−	0.518428i	$-0.826517\pi$
$5$	1.19694	−	2.07316i	0.0214115	−	0.0370858i	0.876533	+	0.481342i	$0.159851\pi$
$6$	11.3939	+	61.3040i	0.129209	+	0.695201i
$7$	25.8485	+	44.7709i	0.199384	+	0.345343i	0.948329	−	0.317289i	$-0.102773\pi$
$7$	25.8485	+	44.7709i	0.199384	+	0.345343i	−0.748945	+	0.662632i	$0.769439\pi$
$8$	−64.0000			−0.353553
$9$	189.000	+	152.735i	0.777778	+	0.628539i
$10$	9.57551			0.0302804
$11$	−335.484	−	581.076i	−0.835969	−	1.44794i	−0.893239	−	0.449583i	$-0.851573\pi$
$11$	−335.484	−	581.076i	−0.835969	−	1.44794i	0.0572695	−	0.998359i	$-0.481761\pi$
$12$	−189.576	+	162.078i	−0.380040	+	0.324915i
$13$	423.469	−	733.470i	0.694966	−	1.20372i	−0.275226	−	0.961380i	$-0.588753\pi$
$13$	423.469	−	733.470i	0.694966	−	1.20372i	0.970192	−	0.242337i	$-0.0779140\pi$
$14$	−103.394	+	179.083i	−0.140986	+	0.244194i
$15$	28.3638	−	24.2496i	0.0325489	−	0.0278276i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	−1135.51			−0.952949			−0.476474	−	0.879188i	$-0.658085\pi$
$17$	−1135.51			−0.952949			−0.476474	+	0.879188i	$0.658085\pi$
$18$	−151.090	+	960.185i	−0.109914	+	0.698512i
$19$	1002.42			0.637039			0.318519	−	0.947916i	$-0.396814\pi$
$19$	1002.42			0.637039			0.318519	+	0.947916i	$0.396814\pi$
$20$	19.1510	+	33.1705i	0.0107057	+	0.0185429i
$21$	147.257	+	792.307i	0.0728665	+	0.392054i
$22$	1341.94	−	2324.30i	0.591120	−	1.02385i
$23$	−1200.79	+	2079.83i	−0.473311	+	0.819799i	−0.999533	−	0.0305480i	$-0.990275\pi$
$23$	−1200.79	+	2079.83i	−0.473311	+	0.819799i	0.526222	+	0.850347i	$0.323608\pi$
$24$	−940.604	−	332.554i	−0.333333	−	0.117851i
$25$	1559.63	+	2701.37i	0.499083	+	0.864437i
$26$	3387.76			0.982831
$27$	1984.09	+	3226.81i	0.523783	+	0.851852i
$28$	−827.151			−0.199384
$29$	−1884.71	−	3264.41i	−0.416150	−	0.720792i	0.579399	−	0.815044i	$-0.303287\pi$
$29$	−1884.71	−	3264.41i	−0.416150	−	0.720792i	−0.995548	+	0.0942518i	$0.969954\pi$
$30$	140.731	+	49.7558i	0.0285486	+	0.0100935i
$31$	−2017.08	+	3493.69i	−0.376981	+	0.652951i	−0.990621	−	0.136635i	$-0.956371\pi$
$31$	−2017.08	+	3493.69i	−0.376981	+	0.652951i	0.613640	+	0.789586i	$0.289705\pi$
$32$	512.000	−	886.810i	0.0883883	−	0.153093i
$33$	−1911.23	−	10283.3i	−0.305512	−	1.64379i
$34$	−2271.02	−	3933.53i	−0.336918	−	0.583559i
$35$	123.756			0.0170764
$36$	−3628.36	+	1396.98i	−0.466610	+	0.179653i
$37$	−14537.7			−1.74578			−0.872892	−	0.487913i	$-0.837758\pi$
$37$	−14537.7			−1.74578			−0.872892	+	0.487913i	$0.837758\pi$
$38$	2004.84	+	3472.49i	0.225227	+	0.390105i
$39$	10034.9	−	8579.36i	1.05646	−	0.903220i
$40$	−76.6041	+	132.682i	−0.00757010	+	0.0131118i
$41$	3941.38	−	6826.67i	0.366175	−	0.634233i	−0.622789	−	0.782390i	$-0.714001\pi$
$41$	3941.38	−	6826.67i	0.366175	−	0.634233i	0.988964	+	0.148156i	$0.0473339\pi$
$42$	−2450.12	+	2094.73i	−0.214321	+	0.183233i
$43$	10176.5	+	17626.3i	0.839323	+	1.45375i	0.890462	+	0.455058i	$0.150382\pi$
$43$	10176.5	+	17626.3i	0.839323	+	1.45375i	−0.0511388	+	0.998692i	$0.516285\pi$
$44$	10735.5			0.835969
$45$	542.865	−	209.012i	0.0399633	−	0.0153865i
$46$	−9606.31			−0.669363
$47$	8068.27	+	13974.7i	0.532765	+	0.922776i	0.999268	+	0.0382565i	$0.0121804\pi$
$47$	8068.27	+	13974.7i	0.532765	+	0.922776i	−0.466503	+	0.884520i	$0.654486\pi$
$48$	−729.208	−	3923.46i	−0.0456823	−	0.245791i
$49$	7067.21	−	12240.8i	0.420492	−	0.728314i
$50$	−6238.54	+	10805.5i	−0.352905	+	0.611249i
$51$	−16688.6	−	5900.29i	−0.898449	−	0.317650i
$52$	6775.51	+	11735.5i	0.347483	+	0.601858i
$53$	−5549.94			−0.271393			−0.135697	−	0.990750i	$-0.543327\pi$
$53$	−5549.94			−0.271393			−0.135697	+	0.990750i	$0.543327\pi$
$54$	−7209.83	+	13326.7i	−0.336465	+	0.621925i
$55$	−1606.22			−0.0715974
$56$	−1654.30	−	2865.34i	−0.0704928	−	0.122097i
$57$	14732.5	+	5208.73i	0.600606	+	0.212346i
$58$	7538.84	−	13057.7i	0.294262	−	0.509677i
$59$	3206.13	−	5553.17i	0.119909	−	0.207688i	−0.799823	−	0.600236i	$-0.795073\pi$
$59$	3206.13	−	5553.17i	0.119909	−	0.207688i	0.919731	+	0.392549i	$0.128406\pi$
$60$	109.102	+	587.017i	0.00391251	+	0.0210510i
$61$	−4440.22	−	7690.68i	−0.152785	−	0.264631i	0.779466	−	0.626445i	$-0.215491\pi$
$61$	−4440.22	−	7690.68i	−0.152785	−	0.264631i	−0.932250	+	0.361814i	$0.882157\pi$
$62$	−16136.7			−0.533132
$63$	−1952.72	+	12409.7i	−0.0619853	+	0.393920i
$64$	4096.00			0.125000
$65$	−1013.73	−	1755.84i	−0.0297605	−	0.0515467i
$66$	31799.8	−	27187.2i	0.898596	−	0.768254i
$67$	21468.8	−	37185.0i	0.584279	−	1.01200i	−0.410685	−	0.911777i	$-0.634711\pi$
$67$	21468.8	−	37185.0i	0.584279	−	1.01200i	0.994965	−	0.100225i	$-0.0319561\pi$
$68$	9084.10	−	15734.1i	0.238237	−	0.412639i
$69$	−28455.0	+	24327.6i	−0.719509	+	0.615144i
$70$	247.512	+	428.704i	0.00603742	+	0.0104571i
$71$	−63349.1			−1.49140			−0.745701	−	0.666281i	$-0.767885\pi$
$71$	−63349.1			−1.49140			−0.745701	+	0.666281i	$0.767885\pi$
$72$	−12096.0	−	9775.04i	−0.274986	−	0.222222i
$73$	−12807.7			−0.281295			−0.140648	−	0.990060i	$-0.544919\pi$
$73$	−12807.7			−0.281295			−0.140648	+	0.990060i	$0.544919\pi$
$74$	−29075.3	−	50360.0i	−0.617228	−	1.06907i
$75$	8885.14	+	47805.9i	0.182394	+	0.981360i
$76$	−8019.36	+	13889.9i	−0.159260	+	0.275846i
$77$	17343.5	−	30039.8i	0.333357	−	0.577392i
$78$	49789.6	+	17603.3i	0.926622	+	0.327610i
$79$	1463.87	+	2535.49i	0.0263897	+	0.0457083i	0.878919	−	0.476972i	$-0.158266\pi$
$79$	1463.87	+	2535.49i	0.0263897	+	0.0457083i	−0.852529	+	0.522680i	$0.824932\pi$
$80$	−612.832			−0.0107057
$81$	12393.0	+	57733.9i	0.209877	+	0.977728i
$82$	31531.0			0.517849
$83$	23770.7	+	41172.1i	0.378745	+	0.656006i	0.990880	−	0.134747i	$-0.0430223\pi$
$83$	23770.7	+	41172.1i	0.378745	+	0.656006i	−0.612135	+	0.790753i	$0.709689\pi$
$84$	−12156.6	−	4298.00i	−0.187981	−	0.0664612i
$85$	−1359.14	+	2354.10i	−0.0204040	+	0.0353408i
$86$	−40706.2	+	70505.1i	−0.593491	+	1.02796i
$87$	−10737.1	−	57770.1i	−0.152086	−	0.818286i
$88$	21471.0	+	37188.8i	0.295560	+	0.511925i
$89$	84795.6			1.13474			0.567372	−	0.823461i	$-0.307960\pi$
$89$	84795.6			1.13474			0.567372	+	0.823461i	$0.307960\pi$
$90$	1809.77	+	1462.52i	0.0235514	+	0.0190324i
$91$	43784.1			0.554260
$92$	−19212.6	−	33277.2i	−0.236656	−	0.409900i
$93$	−47798.7	+	40865.5i	−0.573072	+	0.489947i
$94$	−32273.1	+	55898.6i	−0.376722	+	0.652501i
$95$	1199.84	−	2078.18i	0.0136399	−	0.0236251i
$96$	12132.8	−	10373.0i	0.134364	−	0.114875i
$97$	−55874.3	−	96777.2i	−0.602952	−	1.04434i	−0.992371	−	0.123284i	$-0.960658\pi$
$97$	−55874.3	−	96777.2i	−0.602952	−	1.04434i	0.389419	−	0.921061i	$-0.372676\pi$
$98$	56537.7			0.594666
$99$	25344.1	−	161063.i	0.259890	−	1.65162i
$100$	−49908.3			−0.499083
$101$	47291.0	+	81910.3i	0.461291	+	0.798979i	0.999026	−	0.0441351i	$-0.0140532\pi$
$101$	47291.0	+	81910.3i	0.461291	+	0.798979i	−0.537735	+	0.843114i	$0.680720\pi$
$102$	−12937.9	−	69611.4i	−0.123130	−	0.662491i
$103$	−19556.5	+	33872.9i	−0.181635	+	0.314601i	−0.942437	−	0.334383i	$-0.891472\pi$
$103$	−19556.5	+	33872.9i	−0.181635	+	0.314601i	0.760803	+	0.648983i	$0.224806\pi$
$104$	−27102.0	+	46942.1i	−0.245708	+	0.425578i
$105$	1818.84	+	643.056i	0.0160998	+	0.00569214i
$106$	−11099.9	−	19225.6i	−0.0959520	−	0.166194i
$107$	6691.62			0.0565030			0.0282515	−	0.999601i	$-0.491006\pi$
$107$	6691.62			0.0565030			0.0282515	+	0.999601i	$0.491006\pi$
$108$	−60584.7	+	1677.83i	−0.499808	+	0.0138416i
$109$	−34661.9			−0.279438			−0.139719	−	0.990191i	$-0.544620\pi$
$109$	−34661.9			−0.279438			−0.139719	+	0.990191i	$0.544620\pi$
$110$	−3212.43	−	5564.09i	−0.0253135	−	0.0438443i
$111$	−213659.	−	75540.0i	−1.64594	−	0.581928i
$112$	6617.21	−	11461.3i	0.0498459	−	0.0863357i
$113$	47363.9	−	82036.6i	0.348940	−	0.604382i	−0.637121	−	0.770764i	$-0.719875\pi$
$113$	47363.9	−	82036.6i	0.348940	−	0.604382i	0.986061	+	0.166381i	$0.0532083\pi$
$114$	11421.5	+	61452.4i	0.0823113	+	0.442870i
$115$	2874.54	+	4978.85i	0.0202686	+	0.0351062i
$116$	60310.7			0.416150
$117$	192062.	−	73947.3i	1.29711	−	0.499410i
$118$	25649.0			0.169576
$119$	−29351.3	−	50837.9i	−0.190002	−	0.329094i
$120$	−1815.28	+	1551.97i	−0.0115078	+	0.00983856i
$121$	−144574.	+	250409.i	−0.897689	+	1.55484i
$122$	17760.9	−	30762.7i	0.108035	−	0.187122i
$123$	93398.6	−	79851.1i	0.556644	−	0.475903i
$124$	−32273.3	−	55899.1i	−0.188491	−	0.326475i
$125$	14948.0			0.0855674
$126$	−46893.8	+	18054.9i	−0.263141	+	0.101314i
$127$	156622.			0.861673			0.430837	−	0.902430i	$-0.358219\pi$
$127$	156622.			0.861673			0.430837	+	0.902430i	$0.358219\pi$
$128$	8192.00	+	14189.0i	0.0441942	+	0.0765466i
$129$	57975.1	+	311931.i	0.306738	+	1.65038i
$130$	4054.93	−	7023.35i	0.0210439	−	0.0364490i
$131$	−87709.2	+	151917.i	−0.446547	+	0.773441i	−0.998159	−	0.0606596i	$-0.980680\pi$
$131$	−87709.2	+	151917.i	−0.446547	+	0.773441i	0.551612	+	0.834101i	$0.314013\pi$
$132$	157779.	+	55783.3i	0.788159	+	0.278656i
$133$	25911.0	+	44879.2i	0.127015	+	0.219997i
$134$	171750.			0.826296
$135$	9064.52	−	251.032i	0.0428066	−	0.00118548i
$136$	72672.8			0.336918
$137$	−35875.3	−	62137.9i	−0.163303	−	0.282849i	0.772748	−	0.634713i	$-0.218882\pi$
$137$	−35875.3	−	62137.9i	−0.163303	−	0.282849i	−0.936051	+	0.351863i	$0.885548\pi$
$138$	−141183.	−	49915.8i	−0.631082	−	0.223121i
$139$	−23800.6	+	41223.8i	−0.104484	+	0.180972i	−0.913527	−	0.406777i	$-0.866653\pi$
$139$	−23800.6	+	41223.8i	−0.104484	+	0.180972i	0.809043	+	0.587749i	$0.199986\pi$
$140$	−990.049	+	1714.81i	−0.00426910	+	0.00739430i
$141$	45964.4	+	247309.i	0.194704	+	1.04759i
$142$	−126698.	−	219448.i	−0.527290	−	0.913293i
$143$	−568269.			−2.32388
$144$	9669.75	−	61451.9i	0.0388605	−	0.246961i
$145$	−9023.53			−0.0356415
$146$	−25615.3	−	44367.0i	−0.0994530	−	0.172258i
$147$	167471.	−	143180.i	0.639215	−	0.546497i
$148$	116301.	−	201440.i	0.436446	−	0.755947i
$149$	136540.	−	236494.i	0.503840	−	0.872677i	−0.496150	−	0.868237i	$-0.665253\pi$
$149$	136540.	−	236494.i	0.503840	−	0.872677i	0.999990	−	0.00444010i	$-0.00141333\pi$
$150$	−147834.	+	126391.i	−0.536472	+	0.458657i
$151$	8638.27	+	14961.9i	0.0308308	+	0.0534005i	0.881029	−	0.473062i	$-0.156851\pi$
$151$	8638.27	+	14961.9i	0.0308308	+	0.0534005i	−0.850198	+	0.526463i	$0.823518\pi$
$152$	−64154.9			−0.225227
$153$	−214612.	−	173433.i	−0.741182	−	0.598966i
$154$	138748.			0.471439
$155$	4828.65	+	8363.47i	0.0161435	+	0.0279613i
$156$	38599.7	+	207683.i	0.126991	+	0.683265i
$157$	194609.	−	337073.i	0.630107	−	1.09138i	−0.357423	−	0.933943i	$-0.616344\pi$
$157$	194609.	−	337073.i	0.630107	−	1.09138i	0.987529	−	0.157434i	$-0.0503222\pi$
$158$	−5855.47	+	10142.0i	−0.0186603	+	0.0323206i
$159$	−81567.2	−	28838.4i	−0.255872	−	0.0904644i
$160$	−1225.66	−	2122.91i	−0.00378505	−	0.00655590i
$161$	−124154.			−0.377482
$162$	−175210.	+	158398.i	−0.524531	+	0.474202i
$163$	608055.			1.79256			0.896280	−	0.443489i	$-0.146260\pi$
$163$	608055.			1.79256			0.896280	+	0.443489i	$0.146260\pi$
$164$	63062.1	+	109227.i	0.183087	+	0.317117i
$165$	−23606.5	−	8346.14i	−0.0675027	−	0.0238658i
$166$	−95082.9	+	164688.i	−0.267813	+	0.463866i
$167$	−24979.3	+	43265.4i	−0.0693089	+	0.120047i	−0.898597	−	0.438774i	$-0.855413\pi$
$167$	−24979.3	+	43265.4i	−0.0693089	+	0.120047i	0.829288	+	0.558821i	$0.188746\pi$
$168$	−9424.46	−	50707.7i	−0.0257622	−	0.138612i
$169$	−173006.	−	299655.i	−0.465956	−	0.807059i
$170$	−10873.1			−0.0288557
$171$	189457.	+	153105.i	0.495475	+	0.400404i
$172$	−325649.			−0.839323
$173$	−93398.2	−	161770.i	−0.237259	−	0.410945i	0.722668	−	0.691196i	$-0.242916\pi$
$173$	−93398.2	−	161770.i	−0.237259	−	0.410945i	−0.959927	+	0.280251i	$0.909582\pi$
$174$	178647.	−	152735.i	0.447326	−	0.382441i
$175$	−80628.3	+	139652.i	−0.199018	+	0.344709i
$176$	−85883.9	+	148755.i	−0.208992	+	0.361985i
$177$	75975.4	−	64955.1i	0.182280	−	0.155840i
$178$	169591.	+	293740.i	0.401193	+	0.694886i
$179$	364514.			0.850319			0.425159	−	0.905119i	$-0.360218\pi$
$179$	364514.			0.850319			0.425159	+	0.905119i	$0.360218\pi$
$180$	−1446.76	+	9194.26i	−0.00332825	+	0.0211512i
$181$	−679166.			−1.54092			−0.770459	−	0.637489i	$-0.779973\pi$
$181$	−679166.			−1.54092			−0.770459	+	0.637489i	$0.779973\pi$
$182$	87568.3	+	151673.i	0.195960	+	0.339413i
$183$	−25295.6	−	136101.i	−0.0558365	−	0.300424i
$184$	76850.4	−	133109.i	0.167341	−	0.289843i
$185$	−17400.7	+	30138.9i	−0.0373798	+	0.0647438i
$186$	−237160.	−	83848.6i	−0.502642	−	0.177711i
$187$	380946.	+	659818.i	0.796636	+	1.37981i
$188$	−258185.			−0.532765
$189$	−93181.5	+	172237.i	−0.189747	+	0.350730i
$190$	9598.68			0.0192898
$191$	383947.	+	665015.i	0.761531	+	1.31901i	0.942061	+	0.335440i	$0.108885\pi$
$191$	383947.	+	665015.i	0.761531	+	1.31901i	−0.180531	+	0.983569i	$0.557782\pi$
$192$	60198.7	+	21283.4i	0.117851	+	0.0416667i
$193$	−23647.4	+	40958.4i	−0.0456972	+	0.0791498i	−0.887969	−	0.459903i	$-0.847884\pi$
$193$	−23647.4	+	40958.4i	−0.0456972	+	0.0791498i	0.842272	+	0.539053i	$0.181218\pi$
$194$	223497.	−	387109.i	0.426352	−	0.738463i
$195$	−5775.18	−	31073.0i	−0.0108762	−	0.0585189i
$196$	113075.	+	195852.i	0.210246	+	0.364157i
$197$	817588.			1.50096			0.750479	−	0.660894i	$-0.229823\pi$
$197$	817588.			1.50096			0.750479	+	0.660894i	$0.229823\pi$
$198$	608629.	−	234332.i	1.10329	−	0.424785i
$199$	−965334.			−1.72800			−0.864002	−	0.503488i	$-0.832050\pi$
$199$	−965334.			−1.72800			−0.864002	+	0.503488i	$0.832050\pi$
$200$	−99816.6	−	172887.i	−0.176453	−	0.305625i
$201$	508745.	−	434951.i	0.888198	−	0.759365i
$202$	−189164.	+	327641.i	−0.326182	+	0.564963i
$203$	97433.7	−	168760.i	0.165947	−	0.287429i
$204$	215265.	−	184041.i	0.362158	−	0.309627i
$205$	−9435.18	−	16342.2i	−0.0156807	−	0.0271598i
$206$	−156452.			−0.256870
$207$	−544611.	+	209685.i	−0.883407	+	0.340127i
$208$	−216816.			−0.347483
$209$	−336296.	−	582482.i	−0.532545	−	0.922395i
$210$	1410.06	+	7586.74i	0.00220643	+	0.0118715i
$211$	283585.	−	491183.i	0.438507	−	0.759516i	−0.559068	−	0.829122i	$-0.688841\pi$
$211$	283585.	−	491183.i	0.438507	−	0.759516i	0.997575	+	0.0696058i	$0.0221741\pi$
$212$	44399.6	−	76902.3i	0.0678483	−	0.117517i
$213$	−931038.	−	329172.i	−1.40611	−	0.497134i
$214$	13383.2	+	23180.4i	0.0199768	+	0.0346009i
$215$	48722.8			0.0718846
$216$	−126982.	−	206516.i	−0.185185	−	0.301175i
$217$	−208554.			−0.300656
$218$	−69323.8	−	120072.i	−0.0987964	−	0.171120i
$219$	−188233.	−	66550.6i	−0.265208	−	0.0937652i
$220$	12849.7	−	22256.4i	0.0178993	−	0.0310026i
$221$	−480855.	+	832865.i	−0.662267	+	1.14708i
$222$	−165640.	−	891217.i	−0.225571	−	1.21367i
$223$	−103151.	−	178663.i	−0.138903	−	0.240587i	0.788179	−	0.615446i	$-0.211024\pi$
$223$	−103151.	−	178663.i	−0.138903	−	0.240587i	−0.927082	+	0.374860i	$0.877691\pi$
$224$	52937.7			0.0704928
$225$	−117822.	+	748769.i	−0.155157	+	0.986033i
$226$	378911.			0.493476
$227$	70617.9	+	122314.i	0.0909600	+	0.157547i	0.907915	−	0.419154i	$-0.137673\pi$
$227$	70617.9	+	122314.i	0.0909600	+	0.157547i	−0.816955	+	0.576701i	$0.804340\pi$
$228$	−190034.	+	162470.i	−0.242100	+	0.206983i
$229$	147494.	−	255467.i	0.185860	−	0.321919i	−0.758006	−	0.652247i	$-0.773826\pi$
$229$	147494.	−	255467.i	0.185860	−	0.321919i	0.943866	+	0.330329i	$0.107160\pi$
$230$	−11498.2	+	19915.4i	−0.0143321	+	0.0248239i
$231$	410988.	−	351374.i	0.506756	−	0.433251i
$232$	120621.	+	208922.i	0.147131	+	0.254839i
$233$	1.13433e6			1.36883			0.684417	−	0.729091i	$-0.260057\pi$
$233$	1.13433e6			1.36883			0.684417	+	0.729091i	$0.260057\pi$
$234$	640286.	+	517429.i	0.764424	+	0.617748i
$235$	38628.9			0.0456292
$236$	51298.0	+	88850.8i	0.0599543	+	0.103844i
$237$	8339.56	+	44870.5i	0.00964434	+	0.0518907i
$238$	117405.	−	203351.i	0.134352	−	0.232705i
$239$	−272291.	+	471622.i	−0.308347	+	0.534072i	−0.978001	−	0.208601i	$-0.933109\pi$
$239$	−272291.	+	471622.i	−0.308347	+	0.534072i	0.669654	+	0.742673i	$0.266442\pi$
$240$	−9006.76	−	3184.37i	−0.0100935	−	0.00356858i
$241$	182180.	+	315546.i	0.202050	+	0.349961i	0.949189	−	0.314707i	$-0.101906\pi$
$241$	182180.	+	315546.i	0.202050	+	0.349961i	−0.747139	+	0.664668i	$0.768573\pi$
$242$	−1.15659e6			−1.26952
$243$	−117855.	+	912907.i	−0.128036	+	0.991770i
$244$	142087.			0.152785
$245$	−16918.0	−	29302.9i	−0.0180067	−	0.0311886i
$246$	463410.	+	163840.i	0.488233	+	0.172616i
$247$	424494.	−	735246.i	0.442720	−	0.766814i
$248$	129093.	−	223596.i	0.133283	−	0.230853i
$249$	135420.	+	728620.i	0.138416	+	0.744737i
$250$	29896.0	+	51781.4i	0.0302526	+	0.0523991i
$251$	−371240.			−0.371938			−0.185969	−	0.982556i	$-0.559542\pi$
$251$	−371240.			−0.371938			−0.185969	+	0.982556i	$0.559542\pi$
$252$	−156332.	−	126335.i	−0.155076	−	0.125321i
$253$	1.61138e6			1.58269
$254$	313243.	+	542553.i	0.304647	+	0.527665i
$255$	−32207.4	+	27535.7i	−0.0310174	+	0.0265183i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	−132228.	+	229025.i	−0.124879	+	0.216297i	−0.921686	−	0.387938i	$-0.873188\pi$
$257$	−132228.	+	229025.i	−0.124879	+	0.216297i	0.796807	+	0.604234i	$0.206521\pi$
$258$	−964611.	+	824694.i	−0.902201	+	0.771336i
$259$	−375777.	−	650864.i	−0.348081	−	0.602894i
$260$	32439.5			0.0297605
$261$	142380.	−	904836.i	0.129374	−	0.822183i
$262$	−701673.			−0.631512
$263$	−973703.	−	1.68650e6i	−0.868035	−	1.50348i	−0.864002	−	0.503489i	$-0.832049\pi$
$263$	−973703.	−	1.68650e6i	−0.868035	−	1.50348i	−0.00403330	−	0.999992i	$-0.501284\pi$
$264$	122319.	+	658129.i	0.108015	+	0.581167i
$265$	−6642.94	+	11505.9i	−0.00581093	+	0.0100648i
$266$	−103644.	+	179517.i	−0.0898133	+	0.155561i
$267$	1.24624e6	+	440611.i	1.06985	+	0.378248i
$268$	343501.	+	594961.i	0.292140	+	0.506001i
$269$	−1.60697e6			−1.35402			−0.677012	−	0.735972i	$-0.736726\pi$
$269$	−1.60697e6			−1.35402			−0.677012	+	0.735972i	$0.736726\pi$
$270$	18998.6	+	30898.4i	0.0158604	+	0.0257944i
$271$	−201653.			−0.166795			−0.0833974	−	0.996516i	$-0.526577\pi$
$271$	−201653.			−0.166795			−0.0833974	+	0.996516i	$0.526577\pi$
$272$	145346.	+	251746.i	0.119119	+	0.206319i
$273$	643493.	+	227509.i	0.522561	+	0.184753i
$274$	143501.	−	248552.i	0.115473	−	0.200005i
$275$	1.04647e6	−	1.81253e6i	0.834436	−	1.44529i
$276$	−109453.	−	588905.i	−0.0864879	−	0.465342i
$277$	110903.	+	192089.i	0.0868445	+	0.150419i	0.906176	−	0.422901i	$-0.138988\pi$
$277$	110903.	+	192089.i	0.0868445	+	0.150419i	−0.819331	+	0.573321i	$0.805655\pi$
$278$	−190405.			−0.147763
$279$	−914838.	+	352228.i	−0.703613	+	0.270903i
$280$	−7920.39			−0.00603742
$281$	−557032.	−	964807.i	−0.420837	−	0.728911i	0.575185	−	0.818024i	$-0.304930\pi$
$281$	−557032.	−	964807.i	−0.420837	−	0.728911i	−0.996022	+	0.0891126i	$0.971597\pi$
$282$	−764773.	+	653843.i	−0.572677	+	0.489610i
$283$	−521931.	+	904011.i	−0.387389	+	0.670977i	−0.992097	−	0.125470i	$-0.959956\pi$
$283$	−521931.	+	904011.i	−0.387389	+	0.670977i	0.604709	+	0.796447i	$0.293290\pi$
$284$	506793.	−	877791.i	0.372850	−	0.645796i
$285$	28432.4	−	24308.3i	0.0207349	−	0.0177273i
$286$	−1.13654e6	−	1.96854e6i	−0.821616	−	1.42308i
$287$	407514.			0.292037
$288$	232215.	−	89406.7i	0.164972	−	0.0635169i
$289$	−130469.			−0.0918888
$290$	−18047.1	−	31258.4i	−0.0126012	−	0.0218259i
$291$	−318313.	−	1.71266e6i	−0.220354	−	1.18560i
$292$	102461.	−	177468.i	0.0703239	−	0.121805i
$293$	−1.28339e6	+	2.22290e6i	−0.873352	+	1.51269i	−0.0148448	+	0.999890i	$0.504725\pi$
$293$	−1.28339e6	+	2.22290e6i	−0.873352	+	1.51269i	−0.858508	+	0.512801i	$0.828608\pi$
$294$	830931.	+	293779.i	0.560656	+	0.198222i
$295$	−7675.07	−	13293.6i	−0.00513485	−	0.00889381i
$296$	930411.			0.617228
$297$	1.20939e6	−	2.23545e6i	0.795565	−	1.47053i
$298$	1.09232e6			0.712538
$299$	1.01699e6	+	1.76149e6i	0.657871	+	1.13947i
$300$	−733499.	−	259331.i	−0.470540	−	0.166361i
$301$	−526096.	+	911225.i	−0.334695	+	0.579708i
$302$	−34553.1	+	59847.7i	−0.0218007	+	0.0377598i
$303$	269414.	+	1.44956e6i	0.168583	+	0.907048i
$304$	−128310.	−	222239.i	−0.0796298	−	0.137923i
$305$	−21258.7			−0.0130854
$306$	171564.	−	1.09030e6i	0.104743	−	0.665646i
$307$	−1.45132e6			−0.878857			−0.439428	−	0.898278i	$-0.644819\pi$
$307$	−1.45132e6			−0.878857			−0.439428	+	0.898278i	$0.644819\pi$
$308$	277496.	+	480637.i	0.166679	+	0.288696i
$309$	−463430.	+	396210.i	−0.276114	+	0.236064i
$310$	−19314.6	+	33453.9i	−0.0114151	+	0.0197716i
$311$	866527.	−	1.50087e6i	0.508020	−	0.879917i	−0.491936	−	0.870631i	$-0.663711\pi$
$311$	866527.	−	1.50087e6i	0.508020	−	0.879917i	0.999957	−	0.00928608i	$-0.00295589\pi$
$312$	−642235.	+	549079.i	−0.373515	+	0.319336i
$313$	1.24020e6	+	2.14810e6i	0.715538	+	1.23935i	0.962752	+	0.270386i	$0.0871515\pi$
$313$	1.24020e6	+	2.14810e6i	0.715538	+	1.23935i	−0.247214	+	0.968961i	$0.579515\pi$
$314$	1.55687e6			0.891105
$315$	23389.9	+	18901.9i	0.0132817	+	0.0107332i
$316$	−46843.8			−0.0263897
$317$	1.06813e6	+	1.85006e6i	0.597002	+	1.03404i	0.993261	+	0.115899i	$0.0369750\pi$
$317$	1.06813e6	+	1.85006e6i	0.597002	+	1.03404i	−0.396259	+	0.918139i	$0.629692\pi$
$318$	−63235.4	−	340234.i	−0.0350665	−	0.188673i
$319$	−1.26458e6	+	2.19032e6i	−0.695777	+	1.20512i
$320$	4902.66	−	8491.66i	0.00267644	−	0.00463572i
$321$	98346.3	+	34770.7i	0.0532716	+	0.0188343i
$322$	−248308.	−	430083.i	−0.133460	−	0.231160i
$323$	−1.13826e6			−0.607065
$324$	−899128.	−	290148.i	−0.475838	−	0.153553i
$325$	2.64183e6			1.38738
$326$	1.21611e6	+	2.10636e6i	0.633765	+	1.09771i
$327$	−509424.	−	180109.i	−0.263457	−	0.0931461i
$328$	−252248.	+	436907.i	−0.129462	+	0.224235i
$329$	−417105.	+	722447.i	−0.212449	+	0.367973i
$330$	−18301.0	−	98467.4i	−0.00925104	−	0.0497746i
$331$	−1.69411e6	−	2.93428e6i	−0.849906	−	1.47208i	−0.881291	−	0.472573i	$-0.843325\pi$
$331$	−1.69411e6	−	2.93428e6i	−0.849906	−	1.47208i	0.0313853	−	0.999507i	$-0.490008\pi$
$332$	−760663.			−0.378745
$333$	−2.74762e6	−	2.22041e6i	−1.35783	−	1.09729i
$334$	−199834.			−0.0980176
$335$	−51393.6	−	89016.4i	−0.0250206	−	0.0433369i
$336$	156808.	−	134063.i	0.0757738	−	0.0647828i
$337$	−953269.	+	1.65111e6i	−0.457237	+	0.791957i	−0.998814	−	0.0486941i	$-0.984494\pi$
$337$	−953269.	+	1.65111e6i	−0.457237	+	0.791957i	0.541577	+	0.840651i	$0.317827\pi$
$338$	692025.	−	1.19862e6i	0.329481	−	0.570677i
$339$	1.12238e6	−	959577.i	0.530445	−	0.453504i
$340$	−21746.2	−	37665.5i	−0.0102020	−	0.0176704i
$341$	2.70680e6			1.26058
$342$	−151455.	+	962509.i	−0.0700196	+	0.444979i
$343$	1.59958e6			0.734125
$344$	−651299.	−	1.12808e6i	−0.296745	−	0.513978i
$345$	16376.1	+	88110.4i	0.00740734	+	0.0398547i
$346$	373593.	−	647081.i	0.167768	−	0.290582i
$347$	−13788.8	+	23882.9i	−0.00614757	+	0.0106479i	−0.869083	−	0.494667i	$-0.835290\pi$
$347$	−13788.8	+	23882.9i	−0.00614757	+	0.0106479i	0.862935	+	0.505315i	$0.168624\pi$
$348$	886383.	+	313384.i	0.392350	+	0.138717i
$349$	−533175.	−	923486.i	−0.234318	−	0.405851i	0.724756	−	0.689005i	$-0.241952\pi$
$349$	−533175.	−	923486.i	−0.234318	−	0.405851i	−0.959074	+	0.283154i	$0.908619\pi$
$350$	−645027.			−0.281454
$351$	3.20697e6	−	88813.5i	1.38940	−	0.0384779i
$352$	−687072.			−0.295560
$353$	−1.32674e6	−	2.29799e6i	−0.566696	−	0.981546i	−0.996890	−	0.0788097i	$-0.974888\pi$
$353$	−1.32674e6	−	2.29799e6i	−0.566696	−	0.981546i	0.430194	−	0.902737i	$-0.358445\pi$
$354$	376962.	+	133276.i	0.159878	+	0.0565255i
$355$	−75825.0	+	131333.i	−0.0319331	+	0.0553098i
$356$	−678365.	+	1.17496e6i	−0.283686	+	0.491359i
$357$	−167212.	−	899674.i	−0.0694381	−	0.373607i
$358$	729028.	+	1.26271e6i	0.300633	+	0.520712i
$359$	386007.			0.158073			0.0790367	−	0.996872i	$-0.474816\pi$
$359$	386007.			0.158073			0.0790367	+	0.996872i	$0.474816\pi$
$360$	−34743.4	+	13376.8i	−0.0141291	+	0.00543996i
$361$	−1.47125e6			−0.594182
$362$	−1.35833e6	−	2.35270e6i	−0.544797	−	0.943616i
$363$	−3.42596e6	+	2.92902e6i	−1.36463	+	1.16669i
$364$	−350273.	+	606691.i	−0.138565	+	0.240002i
$365$	−15330.0	+	26552.3i	−0.00602295	+	0.0104321i
$366$	420878.	−	359830.i	0.164230	−	0.140409i
$367$	−673892.	−	1.16721e6i	−0.261171	−	0.452361i	0.705382	−	0.708827i	$-0.250775\pi$
$367$	−673892.	−	1.16721e6i	−0.261171	−	0.452361i	−0.966553	+	0.256466i	$0.917442\pi$
$368$	614804.			0.236656
$369$	1.78759e6	−	688254.i	0.683443	−	0.263137i
$370$	−139206.			−0.0528631
$371$	−143458.	−	248476.i	−0.0541114	−	0.0937237i
$372$	−183859.	−	989242.i	−0.0688856	−	0.370634i
$373$	2.04617e6	−	3.54407e6i	0.761500	−	1.31896i	−0.180578	−	0.983561i	$-0.557797\pi$
$373$	2.04617e6	−	3.54407e6i	0.761500	−	1.31896i	0.942077	−	0.335396i	$-0.108870\pi$
$374$	−1.52379e6	+	2.63927e6i	−0.563307	+	0.975676i
$375$	219690.	+	77672.2i	0.0806737	+	0.0285225i
$376$	−516369.	−	894378.i	−0.188361	−	0.326251i
$377$	−3.19247e6			−1.15684
$378$	−783011.	+	21684.6i	−0.281863	+	0.00780589i
$379$	−683876.			−0.244557			−0.122278	−	0.992496i	$-0.539020\pi$
$379$	−683876.			−0.244557			−0.122278	+	0.992496i	$0.539020\pi$
$380$	19197.4	+	33250.8i	0.00681997	+	0.0118125i
$381$	2.30186e6	+	813830.i	0.812393	+	0.287224i
$382$	−1.53579e6	+	2.66006e6i	−0.538483	+	0.932681i
$383$	2.12093e6	−	3.67355e6i	0.738803	−	1.27964i	−0.214232	−	0.976783i	$-0.568725\pi$
$383$	2.12093e6	−	3.67355e6i	0.738803	−	1.27964i	0.953035	−	0.302861i	$-0.0979418\pi$
$384$	46669.3	+	251101.i	0.0161511	+	0.0869002i
$385$	−41518.2	−	71911.7i	−0.0142754	−	0.0247256i
$386$	−189179.			−0.0646256
$387$	−768786.	+	4.88568e6i	−0.260932	+	1.65824i
$388$	1.78798e6			0.602952
$389$	−1.01046e6	−	1.75017e6i	−0.338567	−	0.586415i	0.645596	−	0.763679i	$-0.276609\pi$
$389$	−1.01046e6	−	1.75017e6i	−0.338567	−	0.586415i	−0.984163	+	0.177264i	$0.943275\pi$
$390$	96089.5	−	82151.7i	0.0319900	−	0.0273499i
$391$	1.36351e6	−	2.36167e6i	0.451041	−	0.781227i
$392$	−452302.	+	783409.i	−0.148666	+	0.257498i
$393$	−2.07844e6	+	1.77696e6i	−0.678822	+	0.580359i
$394$	1.63518e6	+	2.83221e6i	0.530669	+	0.919146i
$395$	7008.64			0.00226017
$396$	2.02901e6	+	1.63969e6i	0.650198	+	0.525440i
$397$	2.77276e6			0.882951			0.441475	−	0.897273i	$-0.354455\pi$
$397$	2.77276e6			0.882951			0.441475	+	0.897273i	$0.354455\pi$
$398$	−1.93067e6	−	3.34401e6i	−0.610942	−	1.05818i
$399$	147614.	+	794225.i	0.0464188	+	0.249753i
$400$	399266.	−	691550.i	0.124771	−	0.216109i
$401$	−1.47738e6	+	2.55889e6i	−0.458808	+	0.794678i	−0.998898	−	0.0469286i	$-0.985057\pi$
$401$	−1.47738e6	+	2.55889e6i	−0.458808	+	0.794678i	0.540090	+	0.841607i	$0.318390\pi$
$402$	2.52420e6	+	892441.i	0.779039	+	0.275432i
$403$	1.70835e6	+	2.95894e6i	0.523978	+	0.907557i
$404$	−1.51331e6			−0.461291
$405$	134525.	+	43411.2i	0.0407536	+	0.0131512i
$406$	779470.			0.234684
$407$	4.87716e6	+	8.44749e6i	1.45942	+	2.52779i
$408$	1.06807e6	+	377619.i	0.317650	+	0.112306i
$409$	1.30179e6	−	2.25476e6i	0.384797	−	0.666488i	−0.606944	−	0.794745i	$-0.707605\pi$
$409$	1.30179e6	−	2.25476e6i	0.384797	−	0.666488i	0.991741	+	0.128256i	$0.0409380\pi$
$410$	37740.7	−	65368.8i	0.0110879	−	0.0192049i
$411$	−204380.	−	1.09965e6i	−0.0596806	−	0.321107i
$412$	−312905.	−	541967.i	−0.0908174	−	0.157300i
$413$	331494.			0.0956313
$414$	−1.81559e6	−	1.46722e6i	−0.520616	−	0.420721i
$415$	113808.			0.0324380
$416$	−433633.	−	751074.i	−0.122854	−	0.212789i
$417$	−564001.	+	482193.i	−0.158833	+	0.135794i
$418$	1.34518e6	−	2.32993e6i	0.376566	−	0.652232i
$419$	310777.	−	538281.i	0.0864796	−	0.149787i	−0.819541	−	0.573020i	$-0.805772\pi$
$419$	310777.	−	538281.i	0.0864796	−	0.149787i	0.906021	+	0.423233i	$0.139105\pi$
$420$	−23461.1	+	20058.1i	−0.00648972	+	0.00554838i
$421$	−1.28480e6	−	2.22533e6i	−0.353288	−	0.611913i	0.633535	−	0.773714i	$-0.281603\pi$
$421$	−1.28480e6	−	2.22533e6i	−0.353288	−	0.611913i	−0.986823	+	0.161801i	$0.948270\pi$
$422$	2.26868e6			0.620142
$423$	−609516.	+	3.87352e6i	−0.165628	+	1.05258i
$424$	355196.			0.0959520
$425$	−1.77098e6	−	3.06743e6i	−0.475601	−	0.823764i
$426$	−721792.	−	3.88355e6i	−0.192703	−	1.03682i
$427$	229546.	−	397585.i	0.0609255	−	0.105526i
$428$	−53532.9	+	92721.8i	−0.0141258	+	0.0244665i
$429$	−8.35182e6	−	2.95281e6i	−2.19098	−	0.774627i
$430$	97445.5	+	168781.i	0.0254150	+	0.0440201i
$431$	−1.69346e6			−0.439118			−0.219559	−	0.975599i	$-0.570462\pi$
$431$	−1.69346e6			−0.439118			−0.219559	+	0.975599i	$0.570462\pi$
$432$	461429.	−	852909.i	0.118958	−	0.219884i
$433$	−6.01185e6			−1.54095			−0.770475	−	0.637471i	$-0.779981\pi$
$433$	−6.01185e6			−1.54095			−0.770475	+	0.637471i	$0.779981\pi$
$434$	−417108.	−	722453.i	−0.106298	−	0.184113i
$435$	−132618.	−	46887.6i	−0.0336032	−	0.0118805i
$436$	277295.	−	480289.i	0.0698596	−	0.121000i
$437$	−1.20369e6	+	2.08486e6i	−0.301518	+	0.522244i
$438$	−145929.	−	785161.i	−0.0363460	−	0.195557i
$439$	1.64565e6	+	2.85034e6i	0.407545	+	0.705888i	0.994614	−	0.103648i	$-0.0330517\pi$
$439$	1.64565e6	+	2.85034e6i	0.407545	+	0.705888i	−0.587069	+	0.809537i	$0.699718\pi$
$440$	102798.			0.0253135
$441$	3.20530e6	−	1.23409e6i	0.784824	−	0.302170i
$442$	−3.84684e6			−0.936587
$443$	−1.34712e6	−	2.33328e6i	−0.326135	−	0.564882i	0.655607	−	0.755102i	$-0.272413\pi$
$443$	−1.34712e6	−	2.33328e6i	−0.326135	−	0.564882i	−0.981741	+	0.190221i	$0.939080\pi$
$444$	2.75599e6	−	2.35623e6i	0.663467	−	0.567231i
$445$	101495.	−	175795.i	0.0242966	−	0.0420829i
$446$	412603.	−	714650.i	0.0982190	−	0.170120i
$447$	3.23557e6	−	2.76625e6i	0.765918	−	0.654821i
$448$	105875.	+	183381.i	0.0249230	+	0.0431678i
$449$	5.22213e6			1.22245			0.611226	−	0.791456i	$-0.290677\pi$
$449$	5.22213e6			1.22245			0.611226	+	0.791456i	$0.290677\pi$
$450$	−2.82946e6	+	1.08939e6i	−0.658676	+	0.253602i
$451$	−5.28908e6			−1.22444
$452$	757822.	+	1.31259e6i	0.174470	+	0.302191i
$453$	49211.7	+	264780.i	0.0112674	+	0.0606234i
$454$	−282472.	+	489255.i	−0.0643184	+	0.111403i
$455$	52406.9	−	90771.5i	0.0118675	−	0.0205552i
$456$	−942881.	−	333359.i	−0.212346	−	0.0750757i
$457$	−62165.7	−	107674.i	−0.0139239	−	0.0241169i	0.858980	−	0.512010i	$-0.171099\pi$
$457$	−62165.7	−	107674.i	−0.0139239	−	0.0241169i	−0.872903	+	0.487893i	$0.837766\pi$
$458$	1.17995e6			0.262845
$459$	−2.25295e6	−	3.66408e6i	−0.499138	−	0.811771i
$460$	−91985.3			−0.0202686
$461$	4.40216e6	+	7.62476e6i	0.964747	+	1.67099i	0.710294	+	0.703905i	$0.248562\pi$
$461$	4.40216e6	+	7.62476e6i	0.964747	+	1.67099i	0.254453	+	0.967085i	$0.418105\pi$
$462$	2.03917e6	+	720956.i	0.444476	+	0.157146i
$463$	893603.	−	1.54777e6i	0.193728	−	0.335547i	−0.752755	−	0.658301i	$-0.771275\pi$
$463$	893603.	−	1.54777e6i	0.193728	−	0.335547i	0.946483	+	0.322754i	$0.104609\pi$
$464$	−482486.	+	835690.i	−0.104037	+	0.180198i
$465$	27508.5	+	148008.i	0.00589977	+	0.0317433i
$466$	2.26867e6	+	3.92944e6i	0.483956	+	0.838236i
$467$	−4.70809e6			−0.998970			−0.499485	−	0.866323i	$-0.666477\pi$
$467$	−4.70809e6			−0.998970			−0.499485	+	0.866323i	$0.666477\pi$
$468$	−511855.	+	3.25287e6i	−0.108027	+	0.686519i
$469$	2.21974e6			0.465983
$470$	77257.8	+	133814.i	0.0161323	+	0.0279420i
$471$	4.61164e6	−	3.94272e6i	0.957863	−	0.818924i
$472$	−205192.	+	355403.i	−0.0423941	+	0.0734288i
$473$	6.82814e6	−	1.18267e7i	1.40330	−	2.43058i
$474$	−138757.	+	118630.i	−0.0283667	+	0.0242521i
$475$	1.56341e6	+	2.70790e6i	0.317935	+	0.550680i
$476$	939240.			0.190002
$477$	−1.04894e6	−	847671.i	−0.211084	−	0.170581i
$478$	−2.17833e6			−0.436068
$479$	786587.	+	1.36241e6i	0.156642	+	0.271312i	0.933656	−	0.358172i	$-0.116600\pi$
$479$	786587.	+	1.36241e6i	0.156642	+	0.271312i	−0.777014	+	0.629484i	$0.783266\pi$
$480$	−6982.54	−	37569.1i	−0.00138328	−	0.00744265i
$481$	−6.15626e6	+	1.06630e7i	−1.21326	+	2.10143i
$482$	−728722.	+	1.26218e6i	−0.142871	+	0.247460i
$483$	−1.82469e6	−	645124.i	−0.355894	−	0.125827i
$484$	−2.31318e6	−	4.00655e6i	−0.448845	−	0.777422i
$485$	−267513.			−0.0516404
$486$	−3.39811e6	+	1.41755e6i	−0.652600	+	0.272238i
$487$	−2.08272e6			−0.397932			−0.198966	−	0.980006i	$-0.563758\pi$
$487$	−2.08272e6			−0.397932			−0.198966	+	0.980006i	$0.563758\pi$
$488$	284174.	+	492204.i	0.0540175	+	0.0935611i
$489$	8.93654e6	+	3.15954e6i	1.69004	+	0.597520i
$490$	67672.2	−	117212.i	0.0127327	−	0.0220536i
$491$	120692.	−	209045.i	0.0225931	−	0.0391324i	−0.854508	−	0.519439i	$-0.826141\pi$
$491$	120692.	−	209045.i	0.0225931	−	0.0391324i	0.877101	+	0.480306i	$0.159474\pi$
$492$	359261.	+	1.93298e6i	0.0669109	+	0.360010i
$493$	2.14011e6	+	3.70678e6i	0.396569	+	0.686878i
$494$	3.39595e6			0.626101
$495$	−303575.	−	245325.i	−0.0556869	−	0.0450018i
$496$	1.03275e6			0.188491
$497$	−1.63748e6	−	2.83619e6i	−0.297361	−	0.515045i
$498$	−2.25317e6	+	1.92635e6i	−0.407119	+	0.348066i
$499$	346655.	−	600424.i	0.0623227	−	0.107946i	−0.833181	−	0.553001i	$-0.813483\pi$
$499$	346655.	−	600424.i	0.0623227	−	0.107946i	0.895503	+	0.445055i	$0.146816\pi$
$500$	−119584.	+	207126.i	−0.0213919	+	0.0370518i
$501$	−591933.	+	506073.i	−0.105361	+	0.0900780i
$502$	−742480.	−	1.28601e6i	−0.131500	−	0.227765i
$503$	−1.94784e6			−0.343268			−0.171634	−	0.985161i	$-0.554905\pi$
$503$	−1.94784e6			−0.343268			−0.171634	+	0.985161i	$0.554905\pi$
$504$	124974.	−	794218.i	0.0219151	−	0.139272i
$505$	226417.			0.0395077
$506$	3.22276e6	+	5.58199e6i	0.559567	+	0.969199i
$507$	−985605.	−	5.30298e6i	−0.170288	−	0.916221i
$508$	−1.25297e6	+	2.17021e6i	−0.215418	+	0.373115i
$509$	−5.46581e6	+	9.46706e6i	−0.935104	+	1.61965i	−0.160655	+	0.987011i	$0.551361\pi$
$509$	−5.46581e6	+	9.46706e6i	−0.935104	+	1.61965i	−0.774449	+	0.632637i	$0.781973\pi$
$510$	−159801.	−	56498.3i	−0.0272054	−	0.00961856i
$511$	−331058.	−	573410.i	−0.0560857	−	0.0971434i
$512$	−262144.			−0.0441942
$513$	1.98889e6	+	3.23462e6i	0.333670	+	0.542663i
$514$	−1.05782e6			−0.176606
$515$	46816.0	+	81087.6i	0.00777814	+	0.0134721i
$516$	−4.78605e6	−	1.69212e6i	−0.791321	−	0.279774i
$517$	5.41355e6	−	9.37655e6i	0.890750	−	1.54282i
$518$	1.50311e6	−	2.60346e6i	0.246130	−	0.426310i
$519$	−532084.	−	2.86284e6i	−0.0867085	−	0.466529i
$520$	64878.9	+	112374.i	0.0105219	+	0.0182245i
$521$	−1.76332e6			−0.284602			−0.142301	−	0.989823i	$-0.545450\pi$
$521$	−1.76332e6			−0.284602			−0.142301	+	0.989823i	$0.545450\pi$
$522$	3.41920e6	−	1.31645e6i	0.549223	−	0.211460i
$523$	7.05362e6			1.12761			0.563804	−	0.825909i	$-0.309337\pi$
$523$	7.05362e6			1.12761			0.563804	+	0.825909i	$0.309337\pi$
$524$	−1.40335e6	−	2.43067e6i	−0.223273	−	0.386721i
$525$	−1.91064e6	+	1.63351e6i	−0.302539	+	0.258656i
$526$	3.89481e6	−	6.74601e6i	0.613793	−	1.06312i
$527$	2.29042e6	−	3.96713e6i	0.359244	−	0.622229i
$528$	−2.03519e6	+	1.73998e6i	−0.317702	+	0.271619i
$529$	334387.	+	579175.i	0.0519529	+	0.0899850i
$530$	−53143.5			−0.00821790
$531$	1.45412e6	−	559862.i	0.223802	−	0.0861677i
$532$	−829153.			−0.127015
$533$	−3.33811e6	−	5.78177e6i	−0.508958	−	0.881542i
$534$	966150.	+	5.19831e6i	0.146619	+	0.788876i
$535$	8009.45	−	13872.8i	0.00120981	−	0.00209546i
$536$	−1.37400e6	+	2.37984e6i	−0.206574	+	0.357797i
$537$	5.35724e6	+	1.89407e6i	0.801688	+	0.283440i
$538$	−3.21394e6	−	5.56670e6i	−0.478720	−	0.829167i
$539$	−9.48375e6			−1.40607
$540$	−69037.7	+	127610.i	−0.0101883	+	0.0188322i
$541$	−7.53297e6			−1.10655			−0.553277	−	0.832997i	$-0.686623\pi$
$541$	−7.53297e6			−1.10655			−0.553277	+	0.832997i	$0.686623\pi$
$542$	−403307.	−	698548.i	−0.0589708	−	0.102140i
$543$	−9.98166e6	−	3.52905e6i	−1.45279	−	0.513639i
$544$	−581382.	+	1.00698e6i	−0.0842296	+	0.145890i
$545$	−41488.2	+	71859.6i	−0.00598319	+	0.0103632i
$546$	498871.	+	2.68414e6i	0.0716155	+	0.385322i
$547$	−2.32849e6	−	4.03306e6i	−0.332740	−	0.576323i	0.650308	−	0.759671i	$-0.274640\pi$
$547$	−2.32849e6	−	4.03306e6i	−0.332740	−	0.576323i	−0.983048	+	0.183348i	$0.941307\pi$
$548$	1.14801e6			0.163303
$549$	335436.	−	2.13172e6i	0.0474983	−	0.301855i
$550$	8.37172e6			1.18007
$551$	−1.88927e6	−	3.27231e6i	−0.265104	−	0.459173i
$552$	1.82112e6	−	1.55697e6i	0.254385	−	0.217486i
$553$	−75677.5	+	131077.i	−0.0105233	+	0.0182270i
$554$	−443611.	+	768356.i	−0.0614084	+	0.106362i
$555$	−412343.	+	352533.i	−0.0568233	+	0.0485811i
$556$	−380810.	−	659582.i	−0.0522421	−	0.0904860i
$557$	8.59105e6			1.17330			0.586649	−	0.809842i	$-0.300447\pi$
$557$	8.59105e6			1.17330			0.586649	+	0.809842i	$0.300447\pi$
$558$	−3.04983e6	−	2.46464e6i	−0.414658	−	0.335094i
$559$	1.72378e7			2.33320
$560$	−15840.8	−	27437.0i	−0.00213455	−	0.00369715i
$561$	2.17023e6	+	1.16768e7i	0.291138	+	1.56645i
$562$	2.22813e6	−	3.85923e6i	0.297577	−	0.515418i
$563$	−5.45579e6	+	9.44970e6i	−0.725415	+	1.25646i	0.233388	+	0.972384i	$0.425019\pi$
$563$	−5.45579e6	+	9.44970e6i	−0.725415	+	1.25646i	−0.958803	+	0.284072i	$0.908315\pi$
$564$	−3.79452e6	−	1.34157e6i	−0.502296	−	0.177588i
$565$	−113383.	−	196386.i	−0.0149427	−	0.0258814i
$566$	−4.17545e6			−0.547850
$567$	−2.26445e6	+	2.04718e6i	−0.295805	+	0.267422i
$568$	4.05434e6			0.527290
$569$	−2.29345e6	−	3.97238e6i	−0.296968	−	0.514363i	0.678473	−	0.734625i	$-0.262642\pi$
$569$	−2.29345e6	−	3.97238e6i	−0.296968	−	0.514363i	−0.975441	+	0.220262i	$0.929309\pi$
$570$	141071.	+	49876.2i	0.0181866	+	0.00642993i
$571$	−3.02168e6	+	5.23371e6i	−0.387846	+	0.671768i	−0.992160	−	0.124978i	$-0.960114\pi$
$571$	−3.02168e6	+	5.23371e6i	−0.387846	+	0.671768i	0.604314	+	0.796746i	$0.293447\pi$
$572$	4.54615e6	−	7.87417e6i	0.580970	−	1.00627i
$573$	2.18732e6	+	1.17687e7i	0.278308	+	1.49742i
$574$	815029.	+	1.41167e6i	0.103251	+	0.178836i
$575$	−7.49116e6			−0.944887
$576$	774144.	+	625603.i	0.0972222	+	0.0785674i
$577$	−3.84995e6			−0.481411			−0.240705	−	0.970598i	$-0.577379\pi$
$577$	−3.84995e6			−0.481411			−0.240705	+	0.970598i	$0.577379\pi$
$578$	−260938.	−	451958.i	−0.0324876	−	0.0562702i
$579$	−560370.	+	479088.i	−0.0694670	+	0.0593908i
$580$	72188.2	−	125034.i	0.00891038	−	0.0154332i
$581$	−1.22887e6	+	2.12847e6i	−0.151031	+	0.261594i
$582$	5.29620e6	−	4.52799e6i	0.648123	−	0.554112i
$583$	1.86192e6	+	3.22494e6i	0.226876	+	0.392961i
$584$	819690.			0.0994530
$585$	76582.4	−	486686.i	0.00925208	−	0.0587976i
$586$	−1.02671e7			−1.23511
$587$	256984.	+	445109.i	0.0307830	+	0.0533177i	0.881006	−	0.473104i	$-0.156867\pi$
$587$	256984.	+	445109.i	0.0307830	+	0.0533177i	−0.850223	+	0.526422i	$0.823533\pi$
$588$	644184.	+	3.46599e6i	0.0768363	+	0.413413i
$589$	−2.02197e6	+	3.50215e6i	−0.240152	+	0.415955i
$590$	30700.3	−	53174.5i	0.00363088	−	0.00628888i
$591$	1.20160e7	+	4.24831e6i	1.41512	+	0.500320i
$592$	1.86082e6	+	3.22304e6i	0.218223	+	0.377973i
$593$	6.84103e6			0.798886			0.399443	−	0.916758i	$-0.369204\pi$
$593$	6.84103e6			0.798886			0.399443	+	0.916758i	$0.369204\pi$
$594$	1.01626e7	−	281442.i	1.18179	−	0.0327283i
$595$	−140527.			−0.0162729
$596$	2.18463e6	+	3.78390e6i	0.251920	+	0.436339i
$597$	−1.41874e7	−	5.01602e6i	−1.62918	−	0.576001i
$598$	−4.06798e6	+	7.04594e6i	−0.465185	+	0.805724i
$599$	−544385.	+	942903.i	−0.0619925	+	0.107374i	−0.895356	−	0.445351i	$-0.853079\pi$
$599$	−544385.	+	942903.i	−0.0619925	+	0.107374i	0.833363	+	0.552725i	$0.186412\pi$
$600$	−568649.	−	3.05958e6i	−0.0644861	−	0.346963i
$601$	−5.05171e6	−	8.74982e6i	−0.570495	−	0.988127i	−0.996515	−	0.0834130i	$-0.973418\pi$
$601$	−5.05171e6	−	8.74982e6i	−0.570495	−	0.988127i	0.426020	−	0.904714i	$-0.359915\pi$
$602$	−4.20877e6			−0.473330
$603$	9.73706e6	−	3.74893e6i	1.09052	−	0.419870i
$604$	−276425.			−0.0308308
$605$	346092.	+	599449.i	0.0384417	+	0.0665830i
$606$	−4.48260e6	+	3.83240e6i	−0.495848	+	0.423925i
$607$	−1.79621e6	+	3.11112e6i	−0.197872	+	0.342725i	−0.947838	−	0.318752i	$-0.896736\pi$
$607$	−1.79621e6	+	3.11112e6i	−0.197872	+	0.342725i	0.749966	+	0.661476i	$0.230070\pi$
$608$	513239.	−	888956.i	0.0563068	−	0.0975262i
$609$	2.30888e6	−	1.97398e6i	0.252266	−	0.215675i
$610$	−42517.3	−	73642.2i	−0.00462638	−	0.00801313i
$611$	1.36667e7			1.48101
$612$	4.12005e6	−	1.58629e6i	0.444655	−	0.171200i
$613$	8.58164e6			0.922400			0.461200	−	0.887296i	$-0.347419\pi$
$613$	8.58164e6			0.922400			0.461200	+	0.887296i	$0.347419\pi$
$614$	−2.90265e6	−	5.02753e6i	−0.310723	−	0.538188i
$615$	−53751.6	−	289207.i	−0.00573065	−	0.0308334i
$616$	−1.10998e6	+	1.92255e6i	−0.117860	+	0.204139i
$617$	2.65301e6	−	4.59515e6i	0.280560	−	0.485944i	−0.690963	−	0.722890i	$-0.742813\pi$
$617$	2.65301e6	−	4.59515e6i	0.280560	−	0.485944i	0.971523	+	0.236946i	$0.0761465\pi$
$618$	−2.29937e6	−	812951.i	−0.242180	−	0.0856235i
$619$	−4.28264e6	−	7.41775e6i	−0.449247	−	0.778119i	0.549090	−	0.835763i	$-0.314974\pi$
$619$	−4.28264e6	−	7.41775e6i	−0.449247	−	0.778119i	−0.998337	+	0.0576445i	$0.981641\pi$
$620$	−154517.			−0.0161435
$621$	−9.09367e6	+	251839.i	−0.946260	+	0.0262056i
$622$	6.93222e6			0.718449
$623$	2.19184e6	+	3.79637e6i	0.226250	+	0.391876i
$624$	−3.18654e6	−	1.12661e6i	−0.327610	−	0.115828i
$625$	−4.85597e6	+	8.41078e6i	−0.497251	+	0.861264i
$626$	−4.96082e6	+	8.59239e6i	−0.505961	+	0.876351i
$627$	−1.91586e6	−	1.03081e7i	−0.194623	−	1.04716i
$628$	3.11375e6	+	5.39317e6i	0.315053	+	0.545688i
$629$	1.65077e7			1.66364
$630$	−18698.3	+	118829.i	−0.00187694	+	0.0119281i
$631$	−8.97840e6			−0.897688			−0.448844	−	0.893610i	$-0.648164\pi$
$631$	−8.97840e6			−0.897688			−0.448844	+	0.893610i	$0.648164\pi$
$632$	−93687.5	−	162272.i	−0.00933016	−	0.0161603i
$633$	6.72009e6	−	5.74534e6i	0.666600	−	0.569910i
$634$	−4.27252e6	+	7.40022e6i	−0.422144	+	0.731176i
$635$	187467.	−	324702.i	0.0184497	−	0.0319558i
$636$	1.05213e6	−	899521.i	0.103140	−	0.0881797i
$637$	−5.98550e6	−	1.03672e7i	−0.584456	−	1.01231i
$638$	−1.01166e7			−0.983977
$639$	−1.19730e7	−	9.67563e6i	−1.15998	−	0.937404i
$640$	39221.3			0.00378505
$641$	−4.13865e6	−	7.16835e6i	−0.397844	−	0.689087i	0.595615	−	0.803270i	$-0.296908\pi$
$641$	−4.13865e6	−	7.16835e6i	−0.397844	−	0.689087i	−0.993460	+	0.114183i	$0.963575\pi$
$642$	76243.5	+	410223.i	0.00730071	+	0.0392810i
$643$	2.09217e6	−	3.62374e6i	0.199558	−	0.345644i	−0.748827	−	0.662765i	$-0.769383\pi$
$643$	2.09217e6	−	3.62374e6i	0.199558	−	0.345644i	0.948385	+	0.317121i	$0.102716\pi$
$644$	993233.	−	1.72033e6i	0.0943706	−	0.163455i
$645$	716076.	+	253171.i	0.0677735	+	0.0239615i
$646$	−2.27652e6	−	3.94305e6i	−0.214630	−	0.371750i
$647$	−2.56671e6			−0.241055			−0.120527	−	0.992710i	$-0.538459\pi$
$647$	−2.56671e6			−0.241055			−0.120527	+	0.992710i	$0.538459\pi$
$648$	−793152.	−	3.69497e6i	−0.0742026	−	0.345679i
$649$	−4.30242e6			−0.400960
$650$	5.28366e6	+	9.15157e6i	0.490514	+	0.849595i
$651$	−3.06511e6	−	1.08368e6i	−0.283461	−	0.100219i
$652$	−4.86444e6	+	8.42545e6i	−0.448140	+	0.776201i
$653$	983421.	−	1.70333e6i	0.0902519	−	0.156321i	−0.817365	−	0.576120i	$-0.804566\pi$
$653$	983421.	−	1.70333e6i	0.0902519	−	0.156321i	0.907617	+	0.419799i	$0.137899\pi$
$654$	−394933.	−	2.12491e6i	−0.0361060	−	0.194266i
$655$	209965.	+	363670.i	0.0191224	+	0.0331211i
$656$	−2.01799e6			−0.183087
$657$	−2.42065e6	−	1.95618e6i	−0.218785	−	0.176805i
$658$	−3.33684e6			−0.300449
$659$	3.66017e6	+	6.33961e6i	0.328313	+	0.568655i	0.982177	−	0.187957i	$-0.0601866\pi$
$659$	3.66017e6	+	6.33961e6i	0.328313	+	0.568655i	−0.653864	+	0.756612i	$0.726853\pi$
$660$	304499.	−	260331.i	0.0272099	−	0.0232631i
$661$	4.17464e6	−	7.23068e6i	0.371634	−	0.643688i	−0.618183	−	0.786034i	$-0.712131\pi$
$661$	4.17464e6	−	7.23068e6i	0.371634	−	0.643688i	0.989817	+	0.142346i	$0.0454645\pi$
$662$	6.77643e6	−	1.17371e7i	0.600974	−	1.04092i
$663$	−1.13948e7	+	9.74197e6i	−1.00675	+	0.860722i
$664$	−1.52133e6	−	2.63501e6i	−0.133907	−	0.231933i
$665$	124056.			0.0108783
$666$	2.19649e6	−	1.39589e7i	0.191886	−	1.21945i
$667$	9.05255e6			0.787873
$668$	−399669.	−	692247.i	−0.0346545	−	0.0600233i
$669$	−587644.	−	3.16178e6i	−0.0507632	−	0.273128i
$670$	205575.	−	356066.i	0.0176922	−	0.0306438i
$671$	−2.97924e6	+	5.16020e6i	−0.255446	+	0.442446i
$672$	778022.	+	275072.i	0.0664612	+	0.0234976i
$673$	777542.	+	1.34674e6i	0.0661738	+	0.114616i	0.897214	−	0.441596i	$-0.145587\pi$
$673$	777542.	+	1.34674e6i	0.0661738	+	0.114616i	−0.831040	+	0.556212i	$0.812254\pi$
$674$	−7.62616e6			−0.646630
$675$	−5.62235e6	+	1.03924e7i	−0.474961	+	0.877922i
$676$	5.53620e6			0.465956
$677$	8.74320e6	+	1.51437e7i	0.733160	+	1.26987i	0.955526	+	0.294907i	$0.0952888\pi$
$677$	8.74320e6	+	1.51437e7i	0.733160	+	1.26987i	−0.222366	+	0.974963i	$0.571378\pi$
$678$	5.56883e6	+	1.96888e6i	0.465254	+	0.164492i
$679$	2.88853e6	−	5.00308e6i	0.240438	−	0.416451i
$680$	86984.8	−	150662.i	0.00721392	−	0.0124949i
$681$	402306.	+	2.16458e6i	0.0332421	+	0.178857i
$682$	5.41360e6	+	9.37663e6i	0.445682	+	0.771944i
$683$	1.78944e7			1.46779			0.733897	−	0.679260i	$-0.237699\pi$
$683$	1.78944e7			1.46779			0.733897	+	0.679260i	$0.237699\pi$
$684$	−3.63714e6	+	1.40036e6i	−0.297249	+	0.114446i
$685$	−171762.			−0.0139863
$686$	3.19915e6	+	5.54110e6i	0.259552	+	0.449558i
$687$	3.49516e6	−	2.98818e6i	0.282537	−	0.241555i
$688$	2.60519e6	−	4.51233e6i	0.209831	−	0.363437i
$689$	−2.35023e6	+	4.07072e6i	−0.188609	+	0.326681i
$690$	−272471.	+	232949.i	−0.0217870	+	0.0186268i
$691$	1.08189e7	+	1.87389e7i	0.861960	+	1.49296i	0.870034	+	0.492992i	$0.164097\pi$
$691$	1.08189e7	+	1.87389e7i	0.861960	+	1.49296i	−0.00807386	+	0.999967i	$0.502570\pi$
$692$	2.98874e6			0.237259
$693$	7.86606e6	−	3.02857e6i	0.622191	−	0.239554i
$694$	−110311.			−0.00869397
$695$	56975.7	+	98684.8i	0.00447433	+	0.00774976i
$696$	687173.	+	3.69729e6i	0.0537704	+	0.289308i
$697$	−4.47548e6	+	7.75176e6i	−0.348946	+	0.604392i
$698$	2.13270e6	−	3.69394e6i	0.165688	−	0.286980i
$699$	1.66712e7	+	5.89417e6i	1.29055	+	0.456278i
$700$	−1.29005e6	−	2.23444e6i	−0.0995091	−	0.172355i
$701$	−1.77842e7			−1.36691			−0.683455	−	0.729993i	$-0.739523\pi$
$701$	−1.77842e7			−1.36691			−0.683455	+	0.729993i	$0.739523\pi$
$702$	6.72160e6	+	1.09316e7i	0.514790	+	0.837226i
$703$	−1.45729e7			−1.11213
$704$	−1.37414e6	−	2.38009e6i	−0.104496	−	0.180993i
$705$	567726.	+	200722.i	0.0430196	+	0.0152097i
$706$	5.30697e6	−	9.19195e6i	0.400715	−	0.694058i
$707$	−2.44480e6	+	4.23451e6i	−0.183948	+	0.318607i
$708$	292242.	+	1.57239e6i	0.0219108	+	0.117890i
$709$	−3.47018e6	−	6.01052e6i	−0.259260	−	0.449052i	0.706784	−	0.707430i	$-0.250145\pi$
$709$	−3.47018e6	−	6.01052e6i	−0.259260	−	0.449052i	−0.966044	+	0.258378i	$0.916812\pi$
$710$	−606600.			−0.0451603
$711$	−110588.	+	702792.i	−0.00820414	+	0.0521378i
$712$	−5.42692e6			−0.401193
$713$	−4.84418e6	−	8.39037e6i	−0.356859	−	0.618098i
$714$	2.78214e6	−	2.37859e6i	0.204236	−	0.174612i
$715$	−680183.	+	1.17811e6i	−0.0497578	+	0.0861830i
$716$	−2.91611e6	+	5.05085e6i	−0.212580	+	0.368199i
$717$	−6.45247e6	+	5.51654e6i	−0.468736	+	0.400746i
$718$	772013.	+	1.33717e6i	0.0558874	+	0.0967998i
$719$	−5.54667e6			−0.400138			−0.200069	−	0.979782i	$-0.564117\pi$
$719$	−5.54667e6			−0.400138			−0.200069	+	0.979782i	$0.564117\pi$
$720$	−115825.	−	93601.0i	−0.00832669	−	0.00672898i
$721$	−2.02203e6			−0.144860
$722$	−2.94250e6	−	5.09657e6i	−0.210075	−	0.363860i
$723$	1.03787e6	+	5.58420e6i	0.0738410	+	0.397297i
$724$	5.43333e6	−	9.41080e6i	0.385230	−	0.667237i
$725$	5.87892e6	−	1.01826e7i	0.415387	−	0.719471i
$726$	−1.69983e7	−	6.00982e6i	−1.19692	−	0.423175i
$727$	2.49481e6	+	4.32114e6i	0.175066	+	0.303223i	0.940184	−	0.340667i	$-0.110653\pi$
$727$	2.49481e6	+	4.32114e6i	0.175066	+	0.303223i	−0.765118	+	0.643890i	$0.777320\pi$
$728$	−2.80219e6			−0.195960
$729$	−6.47571e6	+	1.28045e7i	−0.451303	+	0.892371i
$730$	−122640.			−0.00851774
$731$	−1.15556e7	−	2.00149e7i	−0.799832	−	1.38535i
$732$	2.08824e6	+	738305.i	0.144047	+	0.0509282i
$733$	1.12432e7	−	1.94739e7i	0.772914	−	1.33873i	−0.163045	−	0.986619i	$-0.552132\pi$
$733$	1.12432e7	−	1.94739e7i	0.772914	−	1.33873i	0.935959	−	0.352108i	$-0.114535\pi$
$734$	2.69557e6	−	4.66886e6i	0.184676	−	0.319868i
$735$	−96381.0	−	518572.i	−0.00658072	−	0.0354071i
$736$	1.22961e6	+	2.12974e6i	0.0836704	+	0.144921i
$737$	−2.88098e7			−1.95376
$738$	5.95936e6	+	4.81589e6i	0.402772	+	0.325489i
$739$	9.61700e6			0.647781			0.323891	−	0.946095i	$-0.395009\pi$
$739$	9.61700e6			0.647781			0.323891	+	0.946095i	$0.395009\pi$
$740$	−278411.	−	482222.i	−0.0186899	−	0.0323719i
$741$	1.00592e7	−	8.60012e6i	0.673006	−	0.575386i
$742$	573830.	−	993903.i	0.0382625	−	0.0662727i
$743$	−4.41865e6	+	7.65333e6i	−0.293642	+	0.508602i	−0.974668	−	0.223657i	$-0.928201\pi$
$743$	−4.41865e6	+	7.65333e6i	−0.293642	+	0.508602i	0.681026	+	0.732259i	$0.261534\pi$
$744$	3.05912e6	−	2.61539e6i	0.202611	−	0.173223i
$745$	−326859.	−	566136.i	−0.0215759	−	0.0373706i
$746$	1.63694e7			1.07692
$747$	−1.79576e6	+	1.14122e7i	−0.117746	+	0.748283i
$748$	−1.21903e7			−0.796636
$749$	172968.	+	299589.i	0.0112658	+	0.0195129i
$750$	170316.	+	916373.i	0.0110561	+	0.0594866i
$751$	−2.29253e6	+	3.97078e6i	−0.148325	+	0.256907i	−0.930609	−	0.366016i	$-0.880722\pi$
$751$	−2.29253e6	+	3.97078e6i	−0.148325	+	0.256907i	0.782283	+	0.622923i	$0.214055\pi$
$752$	2.06548e6	−	3.57751e6i	0.133191	−	0.230694i
$753$	−5.45609e6	−	1.92902e6i	−0.350666	−	0.123979i
$754$	−6.38494e6	−	1.10590e7i	−0.409005	−	0.708417i
$755$	41357.9			0.00264053
$756$	−1.64114e6	−	2.66906e6i	−0.104434	−	0.169845i
$757$	6.18063e6			0.392006			0.196003	−	0.980603i	$-0.437204\pi$
$757$	6.18063e6			0.392006			0.196003	+	0.980603i	$0.437204\pi$
$758$	−1.36775e6	−	2.36902e6i	−0.0864638	−	0.149760i
$759$	2.36824e7	+	8.37299e6i	1.49218	+	0.527565i
$760$	−76789.5	+	133003.i	−0.00482245	+	0.00835273i
$761$	9.54035e6	−	1.65244e7i	0.597177	−	1.03434i	−0.396059	−	0.918225i	$-0.629622\pi$
$761$	9.54035e6	−	1.65244e7i	0.597177	−	1.03434i	0.993236	−	0.116115i	$-0.0370442\pi$
$762$	1.78453e6	+	9.60153e6i	0.111336	+	0.599036i
$763$	−895957.	−	1.55184e6i	−0.0557155	−	0.0965020i
$764$	−1.22863e7			−0.761531
$765$	−616430.	+	237336.i	−0.0380829	+	0.0146626i
$766$	1.69674e7			1.04482
$767$	−2.71539e6	−	4.70320e6i	−0.166665	−	0.288672i
$768$	−776501.	+	663870.i	−0.0475050	+	0.0406144i
$769$	−1.79090e6	+	3.10193e6i	−0.109208	+	0.189154i	−0.915450	−	0.402432i	$-0.868165\pi$
$769$	−1.79090e6	+	3.10193e6i	−0.109208	+	0.189154i	0.806241	+	0.591587i	$0.201498\pi$
$770$	166073.	−	287647.i	0.0100942	−	0.0174837i
$771$	−3.13339e6	+	2.67889e6i	−0.189836	+	0.162300i
$772$	−378358.	−	655335.i	−0.0228486	−	0.0395749i
$773$	−1.20939e7			−0.727980			−0.363990	−	0.931403i	$-0.618586\pi$
$773$	−1.20939e7			−0.727980			−0.363990	+	0.931403i	$0.618586\pi$
$774$	−1.84621e7	+	7.10821e6i	−1.10772	+	0.426489i
$775$	−1.25837e7			−0.752580
$776$	3.57596e6	+	6.19374e6i	0.213176	+	0.369231i
$777$	−2.14078e6	−	1.15183e7i	−0.127209	−	0.684441i
$778$	4.04183e6	−	7.00066e6i	0.239403	−	0.414658i
$779$	3.95092e6	−	6.84319e6i	0.233268	−	0.404031i
$780$	476761.	+	168560.i	0.0280585	+	0.00992017i
$781$	2.12526e7	+	3.68106e7i	1.24677	+	2.15946i
$782$	1.09081e7			0.637869
$783$	6.79422e6	−	1.25585e7i	0.396036	−	0.732037i
$784$	−3.61841e6			−0.210246
$785$	−465870.	−	806911.i	−0.0269830	−	0.0467360i
$786$	−1.03124e7	−	3.64600e6i	−0.595395	−	0.210504i
$787$	1.39647e7	−	2.41876e7i	0.803701	−	1.39205i	−0.113463	−	0.993542i	$-0.536194\pi$
$787$	1.39647e7	−	2.41876e7i	0.803701	−	1.39205i	0.917164	−	0.398509i	$-0.130472\pi$
$788$	−6.54070e6	+	1.13288e7i	−0.375240	+	0.649934i
$789$	−5.54713e6	−	2.98459e7i	−0.317231	−	1.70684i
$790$	14017.3	+	24278.6i	0.000799090	+	0.00138407i
$791$	4.89713e6			0.278292
$792$	−1.62202e6	+	1.03081e7i	−0.0918849	+	0.583934i
$793$	−7.52118e6			−0.424720
$794$	5.54552e6	+	9.60513e6i	0.312170	+	0.540695i
$795$	−157417.	+	134584.i	−0.00883354	+	0.00755224i
$796$	7.72267e6	−	1.33761e7i	0.432001	−	0.748248i
$797$	−1.72798e7	+	2.99294e7i	−0.963590	+	1.66899i	−0.250234	+	0.968185i	$0.580507\pi$
$797$	−1.72798e7	+	2.99294e7i	−0.963590	+	1.66899i	−0.713356	+	0.700801i	$0.752826\pi$
$798$	−2.45605e6	+	2.09980e6i	−0.136531	+	0.116727i
$799$	−9.16162e6	−	1.58684e7i	−0.507698	−	0.879358i
$800$	3.19413e6			0.176453
$801$	1.60264e7	+	1.29513e7i	0.882579	+	0.713232i
$802$	−1.18190e7			−0.648852
$803$	4.29677e6	+	7.44222e6i	0.235154	+	0.407299i
$804$	1.95690e6	+	1.05290e7i	0.106765	+	0.574442i
$805$	−148605.	+	257391.i	−0.00808246	+	0.0139992i
$806$	−6.83339e6	+	1.18358e7i	−0.370509	+	0.641740i
$807$	−2.36175e7	−	8.35005e6i	−1.27659	−	0.451342i
$808$	−3.02662e6	−	5.24226e6i	−0.163091	−	0.282482i
$809$	3.05356e7			1.64034			0.820172	−	0.572117i	$-0.193878\pi$
$809$	3.05356e7			1.64034			0.820172	+	0.572117i	$0.193878\pi$
$810$	118669.	+	552831.i	0.00635515	+	0.0296060i
$811$	−8.40877e6			−0.448932			−0.224466	−	0.974482i	$-0.572064\pi$
$811$	−8.40877e6			−0.448932			−0.224466	+	0.974482i	$0.572064\pi$
$812$	1.55894e6	+	2.70016e6i	0.0829735	+	0.143714i
$813$	−2.96369e6	−	1.04782e6i	−0.157256	−	0.0555982i
$814$	−1.95086e7	+	3.37899e7i	−1.03197	+	1.78742i
$815$	727804.	−	1.26059e6i	0.0383814	−	0.0664785i
$816$	828025.	+	4.45513e6i	0.0435329	+	0.234226i
$817$	1.02012e7	+	1.76689e7i	0.534681	+	0.926095i
$818$	1.04143e7			0.544185
$819$	8.27520e6	+	6.68737e6i	0.431091	+	0.348374i
$820$	301926.			0.0156807
$821$	3.42609e6	+	5.93417e6i	0.177395	+	0.307257i	0.940988	−	0.338441i	$-0.109900\pi$
$821$	3.42609e6	+	5.93417e6i	0.177395	+	0.307257i	−0.763592	+	0.645698i	$0.776566\pi$
$822$	3.40054e6	−	2.90729e6i	0.175537	−	0.150075i
$823$	−1.08546e7	+	1.88007e7i	−0.558615	+	0.967550i	0.438997	+	0.898488i	$0.355334\pi$
$823$	−1.08546e7	+	1.88007e7i	−0.558615	+	0.967550i	−0.997612	+	0.0690616i	$0.978000\pi$
$824$	1.25162e6	−	2.16787e6i	0.0642176	−	0.111228i
$825$	2.47980e7	−	2.12011e7i	1.26848	−	1.08448i
$826$	662988.	+	1.14833e6i	0.0338108	+	0.0585620i
$827$	1.01720e7			0.517180			0.258590	−	0.965987i	$-0.416742\pi$
$827$	1.01720e7			0.517180			0.258590	+	0.965987i	$0.416742\pi$
$828$	1.45141e6	−	9.22383e6i	0.0735725	−	0.467558i
$829$	1.34139e7			0.677904			0.338952	−	0.940804i	$-0.389928\pi$
$829$	1.34139e7			0.677904			0.338952	+	0.940804i	$0.389928\pi$
$830$	227617.	+	394244.i	0.0114686	+	0.0198641i
$831$	631806.	+	3.39939e6i	0.0317381	+	0.170765i
$832$	1.73453e6	−	3.00430e6i	0.0868708	−	0.150465i
$833$	−8.02491e6	+	1.38995e7i	−0.400708	+	0.694046i
$834$	−2.79837e6	−	989372.i	−0.139312	−	0.0492544i
$835$	59797.4	+	103572.i	0.00296801	+	0.00514075i
$836$	1.07615e7			0.532545
$837$	−1.52756e7	+	423040.i	−0.753674	+	0.0208722i
$838$	2.48622e6			0.122301
$839$	−7.36884e6	−	1.27632e7i	−0.361405	−	0.625972i	0.626787	−	0.779191i	$-0.284370\pi$
$839$	−7.36884e6	−	1.27632e7i	−0.361405	−	0.625972i	−0.988192	+	0.153218i	$0.951036\pi$
$840$	−116405.	−	41155.6i	−0.00569214	−	0.00201247i
$841$	3.15131e6	−	5.45823e6i	0.153639	−	0.266110i
$842$	5.13919e6	−	8.90134e6i	0.249813	−	0.432688i
$843$	−3.17337e6	−	1.70741e7i	−0.153799	−	0.827503i
$844$	4.53735e6	+	7.85893e6i	0.219253	+	0.379758i
$845$	−828311.			−0.0399072
$846$	−1.46373e7	+	5.63561e6i	−0.703129	+	0.270717i
$847$	−1.49480e7			−0.715939
$848$	710393.	+	1.23044e6i	0.0339242	+	0.0587584i
$849$	−1.23682e7	+	1.05742e7i	−0.588893	+	0.503474i
$850$	7.08394e6	−	1.22697e7i	0.336300	−	0.582489i
$851$	1.74567e7	−	3.02358e7i	0.826299	−	1.43119i
$852$	1.20094e7	−	1.02675e7i	0.566792	−	0.484579i
$853$	1.89932e6	+	3.28972e6i	0.0893770	+	0.154805i	0.907248	−	0.420596i	$-0.138179\pi$
$853$	1.89932e6	+	3.28972e6i	0.0893770	+	0.154805i	−0.817871	+	0.575402i	$0.804846\pi$
$854$	1.83636e6			0.0861617
$855$	544179.	−	209518.i	0.0254581	−	0.00980182i
$856$	−428264.			−0.0199768
$857$	1.28902e7	+	2.23264e7i	0.599524	+	1.03841i	0.992891	+	0.119024i	$0.0379766\pi$
$857$	1.28902e7	+	2.23264e7i	0.599524	+	1.03841i	−0.393368	+	0.919381i	$0.628690\pi$
$858$	−6.47479e6	−	3.48372e7i	−0.300267	−	1.61557i
$859$	−1.26927e7	+	2.19843e7i	−0.586908	+	1.01655i	0.407727	+	0.913104i	$0.366322\pi$
$859$	−1.26927e7	+	2.19843e7i	−0.586908	+	1.01655i	−0.994635	+	0.103450i	$0.967012\pi$
$860$	−389782.	+	675123.i	−0.0179712	+	0.0311269i
$861$	5.98921e6	+	2.11751e6i	0.275335	+	0.0973457i
$862$	−3.38691e6	−	5.86630e6i	−0.155251	−	0.268903i
$863$	−942373.			−0.0430721			−0.0215360	−	0.999768i	$-0.506856\pi$
$863$	−942373.			−0.0430721			−0.0215360	+	0.999768i	$0.506856\pi$
$864$	3.87742e6	−	107381.i	0.176709	−	0.00489376i
$865$	−447167.			−0.0203203
$866$	−1.20237e7	−	2.08257e7i	−0.544808	−	0.943635i
$867$	−1.91750e6	−	677937.i	−0.0866336	−	0.0306296i
$868$	1.66843e6	−	2.88981e6i	0.0751639	−	0.130188i
$869$	982209.	−	1.70124e6i	0.0441219	−	0.0764214i
$870$	−102813.	−	553178.i	−0.00460521	−	0.0247780i
$871$	−1.81828e7	−	3.14935e7i	−0.812109	−	1.40661i
$872$	2.21836e6			0.0987964
$873$	4.22102e6	−	2.68249e7i	0.187448	−	1.19125i
$874$	−9.62956e6			−0.426410
$875$	386383.	+	669235.i	0.0170608	+	0.0295501i
$876$	2.42802e6	−	2.07583e6i	0.106903	−	0.0913971i
$877$	−1.37781e7	+	2.38643e7i	−0.604908	+	1.04773i	0.387158	+	0.922013i	$0.373457\pi$
$877$	−1.37781e7	+	2.38643e7i	−0.604908	+	1.04773i	−0.992066	+	0.125718i	$0.959877\pi$
$878$	−6.58259e6	+	1.14014e7i	−0.288178	+	0.499139i
$879$	−3.04124e7	+	2.60011e7i	−1.32763	+	1.13506i
$880$	205596.	+	356102.i	0.00894967	+	0.0155013i
$881$	−3.45871e7			−1.50132			−0.750662	−	0.660686i	$-0.770265\pi$
$881$	−3.45871e7			−1.50132			−0.750662	+	0.660686i	$0.770265\pi$
$882$	1.06856e7	+	8.63529e6i	0.462518	+	0.373771i
$883$	−2.90981e7			−1.25592			−0.627962	−	0.778244i	$-0.716111\pi$
$883$	−2.90981e7			−1.25592			−0.627962	+	0.778244i	$0.716111\pi$
$884$	−7.69367e6	−	1.33258e7i	−0.331134	−	0.573540i
$885$	−43724.4	−	235256.i	−0.00187657	−	0.0100968i
$886$	5.38848e6	−	9.33312e6i	0.230612	−	0.399432i
$887$	1.60399e7	−	2.77819e7i	0.684529	−	1.18564i	−0.289056	−	0.957312i	$-0.593341\pi$
$887$	1.60399e7	−	2.77819e7i	0.684529	−	1.18564i	0.973585	−	0.228326i	$-0.0733252\pi$
$888$	1.36742e7	+	4.83456e6i	0.581928	+	0.205743i
$889$	4.04843e6	+	7.01209e6i	0.171804	+	0.297573i
$890$	811961.			0.0343605
$891$	2.93901e7	−	2.65701e7i	1.24024	−	1.12124i
$892$	3.30083e6			0.138903
$893$	8.08780e6	+	1.40085e7i	0.339392	+	0.587844i
$894$	1.60537e7	+	5.67584e6i	0.671787	+	0.237513i
$895$	436301.	−	755695.i	0.0182066	−	0.0315347i
$896$	−423501.	+	733526.i	−0.0176232	+	0.0305243i
$897$	5.79375e6	+	3.11729e7i	0.240425	+	1.29359i
$898$	1.04443e7	+	1.80900e7i	0.432202	+	0.748596i
$899$	1.52065e7			0.627523
$900$	−9.43267e6	−	7.62275e6i	−0.388176	−	0.313693i
$901$	6.30203e6			0.258624
$902$	−1.05782e7	−	1.83219e7i	−0.432906	−	0.749816i
$903$	−1.24669e7	+	1.06585e7i	−0.508789	+	0.434989i
$904$	−3.03129e6	+	5.25034e6i	−0.123369	+	0.213681i
$905$	−812920.	+	1.40802e6i	−0.0329934	+	0.0571462i
$906$	−818803.	+	700035.i	−0.0331405	+	0.0283334i
$907$	−1.33468e6	−	2.31173e6i	−0.0538713	−	0.0933079i	0.837832	−	0.545928i	$-0.183823\pi$
$907$	−1.33468e6	−	2.31173e6i	−0.0538713	−	0.0933079i	−0.891704	+	0.452620i	$0.850489\pi$
$908$	−2.25977e6			−0.0909600
$909$	−3.57259e6	+	2.27040e7i	−0.143408	+	0.911367i
$910$	419255.			0.0167832
$911$	−1.90235e6	−	3.29497e6i	−0.0759442	−	0.131539i	0.825552	−	0.564326i	$-0.190864\pi$
$911$	−1.90235e6	−	3.29497e6i	−0.0759442	−	0.131539i	−0.901496	+	0.432786i	$0.857530\pi$
$912$	−730973.	−	3.93295e6i	−0.0291014	−	0.156578i
$913$	1.59494e7	−	2.76252e7i	0.633239	−	1.09680i
$914$	248663.	−	430697.i	0.00984567	−	0.0170532i
$915$	−312437.	−	110463.i	−0.0123370	−	0.00436179i
$916$	2.35990e6	+	4.08747e6i	0.0929299	+	0.160959i
$917$	−9.06859e6			−0.356136
$918$	8.18685e6	−	1.51326e7i	0.320634	−	0.592663i
$919$	3.24011e7			1.26552			0.632762	−	0.774346i	$-0.281921\pi$
$919$	3.24011e7			1.26552			0.632762	+	0.774346i	$0.281921\pi$
$920$	−183971.	−	318646.i	−0.00716603	−	0.0124119i
$921$	−2.13300e7	−	7.54129e6i	−0.828594	−	0.292952i
$922$	−1.76086e7	+	3.04990e7i	−0.682179	+	1.18157i
$923$	−2.68264e7	+	4.64647e7i	−1.03647	+	1.79522i
$924$	1.58088e6	+	8.50581e6i	0.0609142	+	0.327745i
$925$	−2.26735e7	−	3.92716e7i	−0.871291	−	1.50912i
$926$	7.14882e6			0.273973
$927$	−8.86977e6	+	3.41501e6i	−0.339011	+	0.130525i
$928$	−3.85989e6			−0.147131
$929$	1.47138e7	+	2.54851e7i	0.559353	+	0.968829i	0.997551	+	0.0699497i	$0.0222839\pi$
$929$	1.47138e7	+	2.54851e7i	0.559353	+	0.968829i	−0.438197	+	0.898879i	$0.644383\pi$
$930$	−457697.	+	391308.i	−0.0173528	+	0.0148358i
$931$	7.08432e6	−	1.22704e7i	0.267870	−	0.463964i
$932$	−9.07466e6	+	1.57178e7i	−0.342209	+	0.592723i
$933$	2.05340e7	−	1.75556e7i	0.772272	−	0.660254i
$934$	−9.41617e6	−	1.63093e7i	−0.353189	−	0.611741i
$935$	1.82388e6			0.0682286
$936$	−1.22920e7	+	4.73263e6i	−0.458599	+	0.176568i
$937$	4.67094e7			1.73802			0.869010	−	0.494794i	$-0.164756\pi$
$937$	4.67094e7			1.73802			0.869010	+	0.494794i	$0.164756\pi$
$938$	4.43948e6	+	7.68941e6i	0.164750	+	0.285355i
$939$	7.06537e6	+	3.80147e7i	0.261499	+	1.40698i
$940$	−309031.	+	535258.i	−0.0114073	+	0.0197580i
$941$	2.19128e7	−	3.79541e7i	0.806722	−	1.39728i	−0.108400	−	0.994107i	$-0.534573\pi$
$941$	2.19128e7	−	3.79541e7i	0.806722	−	1.39728i	0.915122	−	0.403177i	$-0.132094\pi$
$942$	2.28813e7	+	8.08975e6i	0.840142	+	0.297035i
$943$	9.46552e6	+	1.63948e7i	0.346629	+	0.600380i
$944$	−1.64154e6			−0.0599543
$945$	245543.	+	399338.i	0.00894433	+	0.0145466i
$946$	5.46251e7			1.98456
$947$	−7.53955e6	−	1.30589e7i	−0.273194	−	0.473185i	0.696484	−	0.717572i	$-0.254747\pi$
$947$	−7.53955e6	−	1.30589e7i	−0.273194	−	0.473185i	−0.969678	+	0.244387i	$0.921413\pi$
$948$	−688460.	−	243407.i	−0.0248804	−	0.00879656i
$949$	−5.42365e6	+	9.39404e6i	−0.195491	+	0.338600i
$950$	−6.25364e6	+	1.08316e7i	−0.224814	+	0.389390i
$951$	6.08507e6	+	3.27403e7i	0.218180	+	1.17390i
$952$	1.87848e6	+	3.25362e6i	0.0671760	+	0.116352i
$953$	−1.90096e7			−0.678019			−0.339009	−	0.940783i	$-0.610092\pi$
$953$	−1.90096e7			−0.678019			−0.339009	+	0.940783i	$0.610092\pi$
$954$	838540.	−	5.32898e6i	0.0298300	−	0.189571i
$955$	1.83824e6			0.0652220
$956$	−4.35666e6	−	7.54596e6i	−0.154173	−	0.267036i
$957$	−2.99667e7	+	2.56200e7i	−1.05769	+	0.904273i
$958$	−3.14635e6	+	5.44963e6i	−0.110763	+	0.191846i
$959$	1.85465e6	−	3.21234e6i	0.0651200	−	0.112791i
$960$	116178.	−	99326.4i	0.00406861	−	0.00347846i
$961$	6.17732e6	+	1.06994e7i	0.215770	+	0.373725i
$962$	−4.92501e7			−1.71581
$963$	1.26472e6	+	1.02204e6i	0.0439468	+	0.0355144i
$964$	−5.82978e6			−0.202050
$965$	56608.9	+	98049.4i	0.00195689	+	0.00338943i
$966$	−1.41460e6	−	7.61115e6i	−0.0487742	−	0.262426i
$967$	2.07952e7	−	3.60183e7i	0.715149	−	1.23867i	−0.247753	−	0.968823i	$-0.579692\pi$
$967$	2.07952e7	−	3.60183e7i	0.715149	−	1.23867i	0.962902	−	0.269851i	$-0.0869745\pi$
$968$	9.25272e6	−	1.60262e7i	0.317381	−	0.549720i
$969$	−1.67289e7	−	5.91458e6i	−0.572347	−	0.202355i
$970$	−535025.	−	926691.i	−0.0182576	−	0.0316232i
$971$	1.87667e7			0.638763			0.319382	−	0.947626i	$-0.396525\pi$
$971$	1.87667e7			0.638763			0.319382	+	0.947626i	$0.396525\pi$
$972$	−1.17068e7	−	8.93630e6i	−0.397440	−	0.303384i
$973$	−2.46084e6			−0.0833298
$974$	−4.16545e6	−	7.21477e6i	−0.140690	−	0.243683i
$975$	3.88268e7	+	1.37274e7i	1.30804	+	0.462461i
$976$	−1.13670e6	+	1.96881e6i	−0.0381961	+	0.0661577i
$977$	8.03358e6	−	1.39146e7i	0.269260	−	0.466373i	−0.699411	−	0.714720i	$-0.746554\pi$
$977$	8.03358e6	−	1.39146e7i	0.269260	−	0.466373i	0.968671	+	0.248347i	$0.0798874\pi$
$978$	6.92810e6	+	3.72762e7i	0.231615	+	1.24619i
$979$	−2.84476e7	−	4.92726e7i	−0.948612	−	1.64304i
$980$	541377.			0.0180067
$981$	−6.55110e6	−	5.29409e6i	−0.217341	−	0.175638i
$982$	965540.			0.0319515
$983$	2.07596e7	+	3.59566e7i	0.685227	+	1.18685i	0.973365	+	0.229260i	$0.0736305\pi$
$983$	2.07596e7	+	3.59566e7i	0.685227	+	1.18685i	−0.288138	+	0.957589i	$0.593036\pi$
$984$	−5.97751e6	+	5.11047e6i	−0.196803	+	0.168257i
$985$	978602.	−	1.69499e6i	0.0321378	−	0.0556642i
$986$	−8.56045e6	+	1.48271e7i	−0.280417	+	0.485696i
$987$	−9.88411e6	+	8.45041e6i	−0.322957	+	0.276112i
$988$	6.79191e6	+	1.17639e7i	0.221360	+	0.383407i
$989$	−4.88795e7			−1.58904
$990$	242683.	−	1.54226e6i	0.00786957	−	0.0500116i
$991$	2.57716e7			0.833599			0.416800	−	0.908998i	$-0.363152\pi$
$991$	2.57716e7			0.833599			0.416800	+	0.908998i	$0.363152\pi$
$992$	2.06549e6	+	3.57754e6i	0.0666415	+	0.115426i
$993$	−9.65123e6	−	5.19278e7i	−0.310606	−	1.67119i
$994$	6.54991e6	−	1.13448e7i	0.210266	−	0.364192i
$995$	−1.15545e6	+	2.00129e6i	−0.0369991	+	0.0640844i
$996$	−1.11794e7	−	3.95252e6i	−0.357084	−	0.126248i
$997$	−1.09363e7	−	1.89422e7i	−0.348442	−	0.603520i	0.637531	−	0.770425i	$-0.279956\pi$
$997$	−1.09363e7	−	1.89422e7i	−0.348442	−	0.603520i	−0.985973	+	0.166905i	$0.946623\pi$
$998$	2.77324e6			0.0881376
$999$	−2.88440e7	−	4.69103e7i	−0.914412	−	1.48715i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.6.c.a.13.2	yes	4
3.2	odd	2		54.6.c.a.37.1		4
4.3	odd	2		144.6.i.a.49.1		4
9.2	odd	6		54.6.c.a.19.1		4
9.4	even	3		162.6.a.e.1.1		2
9.5	odd	6		162.6.a.f.1.2		2
9.7	even	3	inner	18.6.c.a.7.2	✓	4
12.11	even	2		432.6.i.a.145.1		4
36.7	odd	6		144.6.i.a.97.1		4
36.11	even	6		432.6.i.a.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.6.c.a.7.2	✓	4	9.7	even	3	inner
18.6.c.a.13.2	yes	4	1.1	even	1	trivial
54.6.c.a.19.1		4	9.2	odd	6
54.6.c.a.37.1		4	3.2	odd	2
144.6.i.a.49.1		4	4.3	odd	2
144.6.i.a.97.1		4	36.7	odd	6
162.6.a.e.1.1		2	9.4	even	3
162.6.a.f.1.2		2	9.5	odd	6
432.6.i.a.145.1		4	12.11	even	2
432.6.i.a.289.1		4	36.11	even	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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(14.6969 + 5.19615i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(1.19694 - 2.07316i) q^{5} +(11.3939 + 61.3040i) q^{6} +(25.8485 + 44.7709i) q^{7} -64.0000 q^{8} +(189.000 + 152.735i) q^{9} +9.57551 q^{10} +(-335.484 - 581.076i) q^{11} +(-189.576 + 162.078i) q^{12} +(423.469 - 733.470i) q^{13} +(-103.394 + 179.083i) q^{14} +(28.3638 - 24.2496i) q^{15} +(-128.000 - 221.703i) q^{16} -1135.51 q^{17} +(-151.090 + 960.185i) q^{18} +1002.42 q^{19} +(19.1510 + 33.1705i) q^{20} +(147.257 + 792.307i) q^{21} +(1341.94 - 2324.30i) q^{22} +(-1200.79 + 2079.83i) q^{23} +(-940.604 - 332.554i) q^{24} +(1559.63 + 2701.37i) q^{25} +3387.76 q^{26} +(1984.09 + 3226.81i) q^{27} -827.151 q^{28} +(-1884.71 - 3264.41i) q^{29} +(140.731 + 49.7558i) q^{30} +(-2017.08 + 3493.69i) q^{31} +(512.000 - 886.810i) q^{32} +(-1911.23 - 10283.3i) q^{33} +(-2271.02 - 3933.53i) q^{34} +123.756 q^{35} +(-3628.36 + 1396.98i) q^{36} -14537.7 q^{37} +(2004.84 + 3472.49i) q^{38} +(10034.9 - 8579.36i) q^{39} +(-76.6041 + 132.682i) q^{40} +(3941.38 - 6826.67i) q^{41} +(-2450.12 + 2094.73i) q^{42} +(10176.5 + 17626.3i) q^{43} +10735.5 q^{44} +(542.865 - 209.012i) q^{45} -9606.31 q^{46} +(8068.27 + 13974.7i) q^{47} +(-729.208 - 3923.46i) q^{48} +(7067.21 - 12240.8i) q^{49} +(-6238.54 + 10805.5i) q^{50} +(-16688.6 - 5900.29i) q^{51} +(6775.51 + 11735.5i) q^{52} -5549.94 q^{53} +(-7209.83 + 13326.7i) q^{54} -1606.22 q^{55} +(-1654.30 - 2865.34i) q^{56} +(14732.5 + 5208.73i) q^{57} +(7538.84 - 13057.7i) q^{58} +(3206.13 - 5553.17i) q^{59} +(109.102 + 587.017i) q^{60} +(-4440.22 - 7690.68i) q^{61} -16136.7 q^{62} +(-1952.72 + 12409.7i) q^{63} +4096.00 q^{64} +(-1013.73 - 1755.84i) q^{65} +(31799.8 - 27187.2i) q^{66} +(21468.8 - 37185.0i) q^{67} +(9084.10 - 15734.1i) q^{68} +(-28455.0 + 24327.6i) q^{69} +(247.512 + 428.704i) q^{70} -63349.1 q^{71} +(-12096.0 - 9775.04i) q^{72} -12807.7 q^{73} +(-29075.3 - 50360.0i) q^{74} +(8885.14 + 47805.9i) q^{75} +(-8019.36 + 13889.9i) q^{76} +(17343.5 - 30039.8i) q^{77} +(49789.6 + 17603.3i) q^{78} +(1463.87 + 2535.49i) q^{79} -612.832 q^{80} +(12393.0 + 57733.9i) q^{81} +31531.0 q^{82} +(23770.7 + 41172.1i) q^{83} +(-12156.6 - 4298.00i) q^{84} +(-1359.14 + 2354.10i) q^{85} +(-40706.2 + 70505.1i) q^{86} +(-10737.1 - 57770.1i) q^{87} +(21471.0 + 37188.8i) q^{88} +84795.6 q^{89} +(1809.77 + 1462.52i) q^{90} +43784.1 q^{91} +(-19212.6 - 33277.2i) q^{92} +(-47798.7 + 40865.5i) q^{93} +(-32273.1 + 55898.6i) q^{94} +(1199.84 - 2078.18i) q^{95} +(12132.8 - 10373.0i) q^{96} +(-55874.3 - 96777.2i) q^{97} +56537.7 q^{98} +(25344.1 - 161063. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} - 32 q^{4} - 54 q^{5} - 72 q^{6} + 74 q^{7} - 256 q^{8} + 756 q^{9} - 432 q^{10} - 78 q^{11} - 288 q^{12} + 1106 q^{13} - 296 q^{14} + 378 q^{15} - 512 q^{16} + 984 q^{17} + 1512 q^{18} - 3280 q^{19}+ \cdots + 319626 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 - 32 * q^4 - 54 * q^5 - 72 * q^6 + 74 * q^7 - 256 * q^8 + 756 * q^9 - 432 * q^10 - 78 * q^11 - 288 * q^12 + 1106 * q^13 - 296 * q^14 + 378 * q^15 - 512 * q^16 + 984 * q^17 + 1512 * q^18 - 3280 * q^19 - 864 * q^20 - 234 * q^21 + 312 * q^22 - 5538 * q^23 + 3064 * q^25 + 8848 * q^26 - 2368 * q^28 - 3894 * q^29 + 6912 * q^30 + 4718 * q^31 + 2048 * q^32 - 17874 * q^33 + 1968 * q^34 - 2268 * q^35 - 6048 * q^36 - 9592 * q^37 - 6560 * q^38 + 18594 * q^39 + 3456 * q^40 + 15354 * q^41 - 4392 * q^42 + 32858 * q^43 + 2496 * q^44 + 5346 * q^45 - 44304 * q^46 + 24954 * q^47 + 4608 * q^48 + 30444 * q^49 - 12256 * q^50 - 81216 * q^51 + 17696 * q^52 - 32664 * q^53 - 44712 * q^54 - 70092 * q^55 - 4736 * q^56 + 107136 * q^57 + 15576 * q^58 + 21966 * q^59 + 21600 * q^60 + 3050 * q^61 + 37744 * q^62 + 6210 * q^63 + 16384 * q^64 + 12582 * q^65 + 77112 * q^66 + 36758 * q^67 - 7872 * q^68 - 39042 * q^69 - 4536 * q^70 - 147696 * q^71 - 48384 * q^72 - 102376 * q^73 - 19184 * q^74 + 19080 * q^75 + 26240 * q^76 + 21462 * q^77 + 69120 * q^78 - 14926 * q^79 + 27648 * q^80 + 49572 * q^81 + 122832 * q^82 + 90762 * q^83 - 13824 * q^84 - 94500 * q^85 - 131432 * q^86 - 18522 * q^87 + 4992 * q^88 - 18600 * q^89 - 81648 * q^90 + 99124 * q^91 - 88608 * q^92 - 145458 * q^93 - 99816 * q^94 + 151416 * q^95 + 18432 * q^96 - 30262 * q^97 + 243552 * q^98 + 319626 * q^99

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