LMFDB - Embedded newform 27.6.e.a.25.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,6,Mod(4,27)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("27.4"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.33036313495$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.12
Character	$\chi$	$=$	27.25
Dual form			27.6.e.a.13.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40309 - 7.95730i) q^{2} +(-9.89503 - 12.0453i) q^{3} +(-31.2798 - 11.3849i) q^{4} +(15.2280 - 12.7778i) q^{5} +(-109.731 + 61.8372i) q^{6} +(-70.6933 + 25.7303i) q^{7} +(-5.20070 + 9.00788i) q^{8} +(-47.1768 + 238.376i) q^{9} +(-80.3108 - 139.102i) q^{10} +(144.573 + 121.311i) q^{11} +(172.380 + 489.428i) q^{12} +(-145.413 - 824.679i) q^{13} +(105.555 + 598.630i) q^{14} +(-304.594 - 56.9886i) q^{15} +(-751.604 - 630.671i) q^{16} +(-465.095 - 805.567i) q^{17} +(1830.64 + 709.863i) q^{18} +(1078.70 - 1868.37i) q^{19} +(-621.804 + 226.318i) q^{20} +(1009.44 + 596.918i) q^{21} +(1168.16 - 980.203i) q^{22} +(2223.04 + 809.122i) q^{23} +(159.963 - 26.4894i) q^{24} +(-474.031 + 2688.36i) q^{25} -6766.25 q^{26} +(3338.12 - 1790.49i) q^{27} +2504.21 q^{28} +(-17.6525 + 100.112i) q^{29} +(-880.847 + 2343.79i) q^{30} +(5477.24 + 1993.55i) q^{31} +(-6327.98 + 5309.80i) q^{32} +(30.6709 - 2941.80i) q^{33} +(-7062.71 + 2570.62i) q^{34} +(-747.743 + 1295.13i) q^{35} +(4189.58 - 6919.27i) q^{36} +(-5390.69 - 9336.95i) q^{37} +(-13353.7 - 11205.0i) q^{38} +(-8494.61 + 9911.76i) q^{39} +(35.9047 + 203.626i) q^{40} +(2497.97 + 14166.7i) q^{41} +(6166.19 - 7194.89i) q^{42} +(512.502 + 430.040i) q^{43} +(-3141.11 - 5440.55i) q^{44} +(2327.52 + 4232.82i) q^{45} +(9557.55 - 16554.2i) q^{46} +(26728.7 - 9728.44i) q^{47} +(-159.451 + 15293.8i) q^{48} +(-8539.41 + 7165.41i) q^{49} +(20727.0 + 7544.01i) q^{50} +(-5101.15 + 13573.3i) q^{51} +(-4840.41 + 27451.3i) q^{52} +25335.8 q^{53} +(-9563.76 - 29074.7i) q^{54} +3751.66 q^{55} +(135.880 - 770.613i) q^{56} +(-33178.8 + 5494.30i) q^{57} +(771.857 + 280.933i) q^{58} +(11752.3 - 9861.37i) q^{59} +(8878.84 + 5250.37i) q^{60} +(-8422.09 + 3065.39i) q^{61} +(23548.3 - 40786.9i) q^{62} +(-2798.41 - 18065.5i) q^{63} +(17674.6 + 30613.3i) q^{64} +(-12752.0 - 10700.2i) q^{65} +(-23365.8 - 4371.66i) q^{66} +(-10635.1 - 60314.5i) q^{67} +(5376.75 + 30493.1i) q^{68} +(-12251.0 - 34783.4i) q^{69} +(9256.58 + 7767.19i) q^{70} +(-2552.14 - 4420.44i) q^{71} +(-1901.91 - 1664.69i) q^{72} +(-17695.8 + 30650.1i) q^{73} +(-81860.5 + 29794.8i) q^{74} +(37072.6 - 20891.6i) q^{75} +(-55012.9 + 46161.3i) q^{76} +(-13341.7 - 4856.00i) q^{77} +(66952.2 + 81501.2i) q^{78} +(-9551.12 + 54167.1i) q^{79} -19504.0 q^{80} +(-54597.7 - 22491.7i) q^{81} +116233. q^{82} +(-16596.8 + 94125.4i) q^{83} +(-24779.3 - 30163.9i) q^{84} +(-17375.9 - 6324.30i) q^{85} +(4141.04 - 3474.75i) q^{86} +(1380.55 - 777.986i) q^{87} +(-1844.64 + 671.394i) q^{88} +(50371.1 - 87245.3i) q^{89} +(36947.5 - 12581.8i) q^{90} +(31499.0 + 54557.8i) q^{91} +(-60324.6 - 50618.4i) q^{92} +(-30184.6 - 85701.0i) q^{93} +(-39909.5 - 226338. i) q^{94} +(-7447.18 - 42235.0i) q^{95} +(126573. + 23681.5i) q^{96} +(71726.7 + 60185.8i) q^{97} +(45035.8 + 78004.3i) q^{98} +(-35738.3 + 28739.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 93 q^{5} - 126 q^{6} - 6 q^{7} + 573 q^{8} + 324 q^{9} - 3 q^{10} + 111 q^{11} - 2769 q^{12} - 6 q^{13} - 1641 q^{14} + 1989 q^{15} + 90 q^{16} + 3465 q^{17} - 99 q^{18}+ \cdots - 28323 q^{99}+O(q^{100}) $ 84 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 93 * q^5 - 126 * q^6 - 6 * q^7 + 573 * q^8 + 324 * q^9 - 3 * q^10 + 111 * q^11 - 2769 * q^12 - 6 * q^13 - 1641 * q^14 + 1989 * q^15 + 90 * q^16 + 3465 * q^17 - 99 * q^18 - 3 * q^19 + 9987 * q^20 + 5424 * q^21 - 2850 * q^22 - 7716 * q^23 - 18486 * q^24 + 4953 * q^25 - 7806 * q^26 - 8109 * q^27 - 12 * q^28 - 20418 * q^29 - 6453 * q^30 - 6657 * q^31 + 51192 * q^32 + 50634 * q^33 - 11394 * q^34 + 35868 * q^35 - 3600 * q^36 - 3 * q^37 - 44076 * q^38 - 13971 * q^39 + 12441 * q^40 - 79077 * q^41 - 64422 * q^42 - 9465 * q^43 + 110757 * q^44 + 92493 * q^45 - 3 * q^46 + 103557 * q^47 + 134049 * q^48 + 5484 * q^49 - 105513 * q^50 - 124866 * q^51 + 68625 * q^52 - 206406 * q^53 - 350946 * q^54 - 12 * q^55 - 147237 * q^56 + 67767 * q^57 - 9753 * q^58 + 116484 * q^59 + 241290 * q^60 - 70116 * q^61 + 246066 * q^62 + 135981 * q^63 - 86019 * q^64 - 19815 * q^65 - 32931 * q^66 + 48117 * q^67 - 48105 * q^68 + 25263 * q^69 + 270111 * q^70 + 279531 * q^71 + 441684 * q^72 - 27012 * q^73 + 233691 * q^74 + 18399 * q^75 - 125670 * q^76 - 345135 * q^77 - 520974 * q^78 - 216186 * q^79 - 924114 * q^80 - 428616 * q^81 - 12 * q^82 - 370401 * q^83 - 522390 * q^84 - 43731 * q^85 + 116682 * q^86 + 304173 * q^87 + 371418 * q^88 + 154827 * q^89 + 327366 * q^90 - 91002 * q^91 + 1279059 * q^92 + 890079 * q^93 + 11667 * q^94 + 1087671 * q^95 + 1165698 * q^96 - 420621 * q^97 + 463410 * q^98 - 28323 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	1.40309	−	7.95730i	0.248033	−	1.40667i	−0.565309	−	0.824879i	$-0.691243\pi$
$2$	1.40309	−	7.95730i	0.248033	−	1.40667i	0.813342	−	0.581786i	$-0.197646\pi$
$3$	−9.89503	−	12.0453i	−0.634766	−	0.772704i
$3$	−9.89503	−	12.0453i	−0.634766	−	0.772704i
$4$	−31.2798	−	11.3849i	−0.977495	−	0.355779i
$5$	15.2280	−	12.7778i	0.272407	−	0.228577i	−0.496342	−	0.868127i	$-0.665324\pi$
$5$	15.2280	−	12.7778i	0.272407	−	0.228577i	0.768749	+	0.639550i	$0.220879\pi$
$6$	−109.731	+	61.8372i	−1.24438	+	0.701248i
$7$	−70.6933	+	25.7303i	−0.545297	+	0.198472i	−0.599956	−	0.800033i	$-0.704815\pi$
$7$	−70.6933	+	25.7303i	−0.545297	+	0.198472i	0.0546585	+	0.998505i	$0.482593\pi$
$8$	−5.20070	+	9.00788i	−0.0287301	+	0.0497620i
$9$	−47.1768	+	238.376i	−0.194143	+	0.980973i
$10$	−80.3108	−	139.102i	−0.253965	−	0.439880i
$11$	144.573	+	121.311i	0.360252	+	0.302287i	0.804891	−	0.593423i	$-0.202224\pi$
$11$	144.573	+	121.311i	0.360252	+	0.302287i	−0.444639	+	0.895710i	$0.646668\pi$
$12$	172.380	+	489.428i	0.345569	+	0.981150i
$13$	−145.413	−	824.679i	−0.238641	−	1.35340i	−0.834808	−	0.550541i	$-0.814422\pi$
$13$	−145.413	−	824.679i	−0.238641	−	1.35340i	0.596167	−	0.802860i	$-0.296690\pi$
$14$	105.555	+	598.630i	0.143932	+	0.816279i
$15$	−304.594	−	56.9886i	−0.349537	−	0.0653973i
$16$	−751.604	−	630.671i	−0.733988	−	0.615889i
$17$	−465.095	−	805.567i	−0.390318	−	0.676051i	0.602173	−	0.798366i	$-0.294302\pi$
$17$	−465.095	−	805.567i	−0.390318	−	0.676051i	−0.992491	+	0.122314i	$0.960968\pi$
$18$	1830.64	+	709.863i	1.33175	+	0.516408i
$19$	1078.70	−	1868.37i	0.685517	−	1.18735i	−0.287758	−	0.957703i	$-0.592910\pi$
$19$	1078.70	−	1868.37i	0.685517	−	1.18735i	0.973274	−	0.229646i	$-0.0737569\pi$
$20$	−621.804	+	226.318i	−0.347599	+	0.126516i
$21$	1009.44	+	596.918i	0.499497	+	0.295370i
$22$	1168.16	−	980.203i	0.514571	−	0.431777i
$23$	2223.04	+	809.122i	0.876251	+	0.318929i	0.740696	−	0.671841i	$-0.234496\pi$
$23$	2223.04	+	809.122i	0.876251	+	0.318929i	0.135555	+	0.990770i	$0.456718\pi$
$24$	159.963	−	26.4894i	0.0566882	−	0.00938738i
$25$	−474.031	+	2688.36i	−0.151690	+	0.860276i
$26$	−6766.25			−1.96297
$27$	3338.12	−	1790.49i	0.881238	−	0.472674i
$28$	2504.21			0.603637
$29$	−17.6525	+	100.112i	−0.00389773	+	0.0221051i	−0.986695	−	0.162585i	$-0.948017\pi$
$29$	−17.6525	+	100.112i	−0.00389773	+	0.0221051i	0.982797	+	0.184690i	$0.0591280\pi$
$30$	−880.847	+	2343.79i	−0.178689	+	0.475461i
$31$	5477.24	+	1993.55i	1.02366	+	0.372583i	0.798665	−	0.601776i	$-0.205540\pi$
$31$	5477.24	+	1993.55i	1.02366	+	0.372583i	0.224999	+	0.974359i	$0.427762\pi$
$32$	−6327.98	+	5309.80i	−1.09242	+	0.916650i
$33$	30.6709	−	2941.80i	0.00490276	−	0.470250i
$34$	−7062.71	+	2570.62i	−1.04779	+	0.381364i
$35$	−747.743	+	1295.13i	−0.103177	+	0.178707i
$36$	4189.58	−	6919.27i	0.538783	−	0.889824i
$37$	−5390.69	−	9336.95i	−0.647351	−	1.12125i	−0.983753	−	0.179527i	$-0.942543\pi$
$37$	−5390.69	−	9336.95i	−0.647351	−	1.12125i	0.336402	−	0.941718i	$-0.390790\pi$
$38$	−13353.7	−	11205.0i	−1.50017	−	1.25879i
$39$	−8494.61	+	9911.76i	−0.894297	+	1.04349i
$40$	35.9047	+	203.626i	0.00354815	+	0.0201225i
$41$	2497.97	+	14166.7i	0.232074	+	1.31616i	0.848689	+	0.528893i	$0.177393\pi$
$41$	2497.97	+	14166.7i	0.232074	+	1.31616i	−0.616615	+	0.787265i	$0.711496\pi$
$42$	6166.19	−	7194.89i	0.539379	−	0.629363i
$43$	512.502	+	430.040i	0.0422692	+	0.0354681i	0.663678	−	0.748019i	$-0.268995\pi$
$43$	512.502	+	430.040i	0.0422692	+	0.0354681i	−0.621408	+	0.783487i	$0.713439\pi$
$44$	−3141.11	−	5440.55i	−0.244597	−	0.423654i
$45$	2327.52	+	4232.82i	0.171342	+	0.311601i
$46$	9557.55	−	16554.2i	0.665966	−	1.15349i
$47$	26728.7	−	9728.44i	1.76495	−	0.642390i	0.764952	−	0.644087i	$-0.222763\pi$
$47$	26728.7	−	9728.44i	1.76495	−	0.642390i	0.999999	+	0.00169735i	$0.000540285\pi$
$48$	−159.451	+	15293.8i	−0.00998904	+	0.958102i
$49$	−8539.41	+	7165.41i	−0.508086	+	0.426335i
$50$	20727.0	+	7544.01i	1.17250	+	0.426754i
$51$	−5101.15	+	13573.3i	−0.274626	+	0.730735i
$52$	−4840.41	+	27451.3i	−0.248241	+	1.40785i
$53$	25335.8			1.23892			0.619461	−	0.785027i	$-0.287351\pi$
$53$	25335.8			1.23892			0.619461	+	0.785027i	$0.287351\pi$
$54$	−9563.76	−	29074.7i	−0.446318	−	1.35685i
$55$	3751.66			0.167231
$56$	135.880	−	770.613i	0.00579008	−	0.0328372i
$57$	−33178.8	+	5494.30i	−1.35261	+	0.223988i
$58$	771.857	+	280.933i	0.0301277	+	0.0109656i
$59$	11752.3	−	9861.37i	0.439535	−	0.368814i	−0.396000	−	0.918250i	$-0.629602\pi$
$59$	11752.3	−	9861.37i	0.439535	−	0.368814i	0.835535	+	0.549437i	$0.185158\pi$
$60$	8878.84	+	5250.37i	0.318404	+	0.188283i
$61$	−8422.09	+	3065.39i	−0.289798	+	0.105478i	−0.482829	−	0.875715i	$-0.660391\pi$
$61$	−8422.09	+	3065.39i	−0.289798	+	0.105478i	0.193031	+	0.981193i	$0.438168\pi$
$62$	23548.3	−	40786.9i	0.778002	−	1.34754i
$63$	−2798.41	−	18065.5i	−0.0888300	−	0.573454i
$64$	17674.6	+	30613.3i	0.539386	+	0.934244i
$65$	−12752.0	−	10700.2i	−0.374364	−	0.314128i
$66$	−23365.8	−	4371.66i	−0.660268	−	0.123534i
$67$	−10635.1	−	60314.5i	−0.289437	−	1.64148i	−0.688993	−	0.724768i	$-0.741947\pi$
$67$	−10635.1	−	60314.5i	−0.289437	−	1.64148i	0.399556	−	0.916709i	$-0.369164\pi$
$68$	5376.75	+	30493.1i	0.141009	+	0.799703i
$69$	−12251.0	−	34783.4i	−0.309777	−	0.879528i
$70$	9256.58	+	7767.19i	0.225790	+	0.189461i
$71$	−2552.14	−	4420.44i	−0.0600840	−	0.104068i	0.834419	−	0.551131i	$-0.185804\pi$
$71$	−2552.14	−	4420.44i	−0.0600840	−	0.104068i	−0.894503	+	0.447062i	$0.852470\pi$
$72$	−1901.91	−	1664.69i	−0.0432374	−	0.0378444i
$73$	−17695.8	+	30650.1i	−0.388655	+	0.673170i	−0.992269	−	0.124107i	$-0.960393\pi$
$73$	−17695.8	+	30650.1i	−0.388655	+	0.673170i	0.603614	+	0.797277i	$0.293727\pi$
$74$	−81860.5	+	29794.8i	−1.73778	+	0.632501i
$75$	37072.6	−	20891.6i	0.761026	−	0.428863i
$76$	−55012.9	+	46161.3i	−1.09252	+	0.916735i
$77$	−13341.7	−	4856.00i	−0.256440	−	0.0933365i
$78$	66952.2	+	81501.2i	1.24603	+	1.51680i
$79$	−9551.12	+	54167.1i	−0.172182	+	0.976490i	0.769165	+	0.639050i	$0.220672\pi$
$79$	−9551.12	+	54167.1i	−0.172182	+	0.976490i	−0.941347	+	0.337440i	$0.890439\pi$
$80$	−19504.0			−0.340722
$81$	−54597.7	−	22491.7i	−0.924617	−	0.380898i
$82$	116233.			1.90896
$83$	−16596.8	+	94125.4i	−0.264442	+	1.49972i	0.506178	+	0.862429i	$0.331058\pi$
$83$	−16596.8	+	94125.4i	−0.264442	+	1.49972i	−0.770620	+	0.637295i	$0.780053\pi$
$84$	−24779.3	−	30163.9i	−0.383169	−	0.466433i
$85$	−17375.9	−	6324.30i	−0.260855	−	0.0949435i
$86$	4141.04	−	3474.75i	0.0603759	−	0.0506614i
$87$	1380.55	−	777.986i	0.0195549	−	0.0110198i
$88$	−1844.64	+	671.394i	−0.0253925	+	0.00924211i
$89$	50371.1	−	87245.3i	0.674072	−	1.16753i	−0.302667	−	0.953096i	$-0.597877\pi$
$89$	50371.1	−	87245.3i	0.674072	−	1.16753i	0.976739	−	0.214431i	$-0.0687896\pi$
$90$	36947.5	−	12581.8i	0.480816	−	0.163733i
$91$	31499.0	+	54557.8i	0.398743	+	0.690642i
$92$	−60324.6	−	50618.4i	−0.743062	−	0.623503i
$93$	−30184.6	−	85701.0i	−0.361891	−	1.02749i
$94$	−39909.5	−	226338.i	−0.465861	−	2.64203i
$95$	−7447.18	−	42235.0i	−0.0846609	−	0.480136i
$96$	126573.	+	23681.5i	1.40173	+	0.262259i
$97$	71726.7	+	60185.8i	0.774019	+	0.649479i	0.941735	−	0.336357i	$-0.109195\pi$
$97$	71726.7	+	60185.8i	0.774019	+	0.649479i	−0.167716	+	0.985835i	$0.553639\pi$
$98$	45035.8	+	78004.3i	0.473689	+	0.820453i
$99$	−35738.3	+	28739.8i	−0.366476	+	0.294710i
$100$	45434.4	−	78694.7i	0.454344	−	0.786947i
$101$	−81030.2	+	29492.6i	−0.790394	+	0.287680i	−0.705500	−	0.708710i	$-0.749277\pi$
$101$	−81030.2	+	29492.6i	−0.790394	+	0.287680i	−0.0848941	+	0.996390i	$0.527055\pi$
$102$	100849.	+	59635.9i	0.959783	+	0.567554i
$103$	−91777.0	+	77010.0i	−0.852395	+	0.715244i	−0.960316	−	0.278916i	$-0.910025\pi$
$103$	−91777.0	+	77010.0i	−0.852395	+	0.715244i	0.107921	+	0.994159i	$0.465581\pi$
$104$	8184.86	+	2979.05i	0.0742041	+	0.0270081i
$105$	22999.1	−	3808.57i	0.203581	−	0.0337124i
$106$	35548.3	−	201604.i	0.307294	−	1.74275i
$107$	127097.			1.07319			0.536593	−	0.843841i	$-0.319711\pi$
$107$	127097.			1.07319			0.536593	+	0.843841i	$0.319711\pi$
$108$	−124800.	+	18001.8i	−1.02957	+	0.148510i
$109$	−112941.			−0.910511			−0.455256	−	0.890361i	$-0.650452\pi$
$109$	−112941.			−0.910511			−0.455256	+	0.890361i	$0.650452\pi$
$110$	5263.91	−	29853.1i	0.0414788	−	0.235238i
$111$	−59125.0	+	157322.i	−0.455474	+	1.21194i
$112$	69360.7	+	25245.2i	0.522479	+	0.190167i
$113$	−72005.2	+	60419.5i	−0.530478	+	0.445124i	−0.868267	−	0.496098i	$-0.834766\pi$
$113$	−72005.2	+	60419.5i	−0.530478	+	0.445124i	0.337788	+	0.941222i	$0.390321\pi$
$114$	−2832.94	+	271723.i	−0.0204162	+	1.95823i
$115$	44191.4	−	16084.3i	0.311597	−	0.113412i
$116$	1691.94	−	2930.53i	0.0116745	−	0.0202209i
$117$	203444.	+	4242.63i	1.37398	+	0.0286530i
$118$	−61980.3	−	107353.i	−0.409778	−	0.709757i
$119$	53606.6	+	44981.2i	0.347017	+	0.291182i
$120$	2097.45	−	2447.37i	0.0132965	−	0.0155148i
$121$	−21781.2	−	123528.i	−0.135244	−	0.767009i
$122$	12575.3	+	71318.1i	0.0764926	+	0.433811i
$123$	145924.	−	170268.i	0.869688	−	1.01478i
$124$	−148631.	−	124716.i	−0.868068	−	0.728396i
$125$	58193.5	+	100794.i	0.333119	+	0.576979i
$126$	−147679.	−	3079.70i	−0.828691	−	0.0172815i
$127$	−23373.5	+	40484.0i	−0.128592	+	0.222728i	−0.923131	−	0.384485i	$-0.874379\pi$
$127$	−23373.5	+	40484.0i	−0.128592	+	0.222728i	0.794539	+	0.607213i	$0.207712\pi$
$128$	20001.2	−	7279.84i	0.107902	−	0.0392733i
$129$	108.726	−	10428.5i	0.000575253	−	0.0551756i
$130$	−103037.	+	86457.9i	−0.534728	+	0.448690i
$131$	−113984.	−	41486.6i	−0.580315	−	0.211218i	0.0351492	−	0.999382i	$-0.488809\pi$
$131$	−113984.	−	41486.6i	−0.580315	−	0.211218i	−0.615465	+	0.788165i	$0.711032\pi$
$132$	−34451.6	+	91669.9i	−0.172097	+	0.457922i
$133$	−28183.5	+	159837.i	−0.138155	+	0.783514i
$134$	−494863.			−2.38080
$135$	27954.5	−	69919.5i	0.132013	−	0.330190i
$136$	9675.27			0.0448555
$137$	42054.7	−	238504.i	0.191431	−	1.08566i	−0.725979	−	0.687717i	$-0.758613\pi$
$137$	42054.7	−	238504.i	0.191431	−	1.08566i	0.917410	−	0.397943i	$-0.130276\pi$
$138$	−293972.	+	48680.7i	−1.31404	+	0.217600i
$139$	318192.	+	115813.i	1.39686	+	0.508416i	0.927245	−	0.374456i	$-0.122170\pi$
$139$	318192.	+	115813.i	1.39686	+	0.508416i	0.469615	+	0.882871i	$0.344393\pi$
$140$	38134.2	−	31998.4i	0.164435	−	0.137977i
$141$	−381663.	−	225691.i	−1.61671	−	0.956017i
$142$	−38755.6	+	14105.9i	−0.161292	+	0.0587056i
$143$	79020.1	−	136867.i	0.323145	−	0.559703i
$144$	185795.	−	149412.i	0.746670	−	0.600452i
$145$	1010.41	+	1750.07i	0.00399095	+	0.00691252i
$146$	219063.	+	183816.i	0.850526	+	0.713676i
$147$	170807.	+	31957.4i	0.651947	+	0.121977i
$148$	62319.4	+	353431.i	0.233867	+	1.32632i
$149$	−13321.8	−	75551.7i	−0.0491583	−	0.278791i	0.950313	−	0.311295i	$-0.100763\pi$
$149$	−13321.8	−	75551.7i	−0.0491583	−	0.278791i	−0.999472	+	0.0325045i	$0.989652\pi$
$150$	−114225.	−	324310.i	−0.414507	−	1.17688i
$151$	261998.	+	219842.i	0.935094	+	0.784637i	0.976725	−	0.214496i	$-0.0688109\pi$
$151$	261998.	+	219842.i	0.935094	+	0.784637i	−0.0416308	+	0.999133i	$0.513255\pi$
$152$	11220.0	+	19433.7i	0.0393899	+	0.0682253i
$153$	213970.	−	72863.5i	0.738966	−	0.251641i
$154$	−57360.3	+	99350.9i	−0.194899	+	0.337575i
$155$	108881.	−	39629.3i	0.364017	−	0.132491i
$156$	378555.	−	213328.i	1.24542	−	0.701836i
$157$	−34235.4	+	28726.9i	−0.110847	+	0.0930121i	−0.696527	−	0.717531i	$-0.745272\pi$
$157$	−34235.4	+	28726.9i	−0.110847	+	0.0930121i	0.585679	+	0.810543i	$0.300828\pi$
$158$	417623.	+	152002.i	1.33089	+	0.484404i
$159$	−250698.	−	305176.i	−0.786427	−	0.957321i
$160$	−28514.8	+	161716.i	−0.0880584	+	0.499404i
$161$	−177973.			−0.541116
$162$	−255578.	+	402893.i	−0.765132	+	1.20615i
$163$	−102723.			−0.302831			−0.151415	−	0.988470i	$-0.548383\pi$
$163$	−102723.			−0.302831			−0.151415	+	0.988470i	$0.548383\pi$
$164$	83150.5	−	471570.i	0.241410	−	1.36910i
$165$	−37122.8	−	45189.7i	−0.106153	−	0.129220i
$166$	725697.	+	264132.i	2.04402	+	0.743963i
$167$	−39669.8	+	33286.9i	−0.110070	+	0.0923596i	−0.696162	−	0.717885i	$-0.745110\pi$
$167$	−39669.8	+	33286.9i	−0.110070	+	0.0923596i	0.586092	+	0.810245i	$0.300666\pi$
$168$	−10626.8	+	5988.53i	−0.0290488	+	0.0163699i
$169$	−310049.	+	112849.i	−0.835052	+	0.303934i
$170$	−74704.2	+	129391.i	−0.198254	+	0.343387i
$171$	394485.	+	345281.i	1.03167	+	0.902989i
$172$	−11135.0	−	19286.4i	−0.0286991	−	0.0497084i
$173$	252329.	+	211729.i	0.640991	+	0.537855i	0.904322	−	0.426850i	$-0.140377\pi$
$173$	252329.	+	211729.i	0.640991	+	0.537855i	−0.263332	+	0.964705i	$0.584821\pi$
$174$	−4253.63	−	12077.1i	−0.0106509	−	0.0302404i
$175$	−35661.5	−	202246.i	−0.0880246	−	0.499212i
$176$	−32154.3	−	182356.i	−0.0782452	−	0.443751i
$177$	−235072.	−	43981.3i	−0.563986	−	0.105520i
$178$	−623562.	−	523231.i	−1.47513	−	1.23778i
$179$	162697.	+	281800.i	0.379531	+	0.657367i	0.990994	−	0.133906i	$-0.0427520\pi$
$179$	162697.	+	281800.i	0.379531	+	0.657367i	−0.611463	+	0.791273i	$0.709419\pi$
$180$	−24614.2	−	158901.i	−0.0566246	−	0.365548i
$181$	113357.	−	196341.i	0.257189	−	0.445465i	−0.708299	−	0.705913i	$-0.750537\pi$
$181$	113357.	−	196341.i	0.257189	−	0.445465i	0.965488	+	0.260448i	$0.0838703\pi$
$182$	478329.	−	174097.i	1.07040	−	0.389595i
$183$	120260.	+	71114.2i	0.265457	+	0.156974i
$184$	−18849.9	+	15816.9i	−0.0410453	+	0.0344411i
$185$	−201395.	−	73301.9i	−0.432634	−	0.157466i
$186$	−724300.	+	119942.i	−1.53510	+	0.254207i
$187$	30484.2	−	172885.i	0.0637487	−	0.361537i
$188$	−946825.			−1.95378
$189$	−189913.	+	212466.i	−0.386724	+	0.432649i
$190$	−346526.			−0.696389
$191$	−71114.8	+	403312.i	−0.141051	+	0.799940i	0.829402	+	0.558652i	$0.188681\pi$
$191$	−71114.8	+	403312.i	−0.141051	+	0.799940i	−0.970453	+	0.241289i	$0.922430\pi$
$192$	193855.	−	515815.i	0.379510	−	1.00981i
$193$	−444586.	−	161816.i	−0.859137	−	0.312700i	−0.125377	−	0.992109i	$-0.540014\pi$
$193$	−444586.	−	161816.i	−0.859137	−	0.312700i	−0.733760	+	0.679409i	$0.762236\pi$
$194$	579556.	−	486305.i	1.10558	−	0.927693i
$195$	−2705.30	+	259479.i	−0.00509481	+	0.488670i
$196$	348689.	−	126912.i	0.648333	−	0.235974i
$197$	186041.	−	322233.i	0.341542	−	0.591567i	−0.643178	−	0.765717i	$-0.722384\pi$
$197$	186041.	−	322233.i	0.341542	−	0.591567i	0.984719	+	0.174150i	$0.0557177\pi$
$198$	178547.	+	324705.i	0.323661	+	0.588607i
$199$	−306334.	−	530585.i	−0.548355	−	0.949779i	−0.998387	−	0.0567666i	$-0.981921\pi$
$199$	−306334.	−	530585.i	−0.548355	−	0.949779i	0.450032	−	0.893012i	$-0.351412\pi$
$200$	−21751.2	−	18251.4i	−0.0384510	−	0.0322642i
$201$	−621270.	+	724916.i	−1.08465	+	1.26560i
$202$	120989.	+	686163.i	0.208625	+	1.18317i
$203$	−1328.00	−	7531.48i	−0.00226183	−	0.0128275i
$204$	314094.	−	366494.i	0.528426	−	0.616583i
$205$	219058.	+	183812.i	0.364062	+	0.305484i
$206$	484021.	+	838349.i	0.794687	+	1.37644i
$207$	−297752.	+	491750.i	−0.482979	+	0.797661i
$208$	−410808.	+	711540.i	−0.658386	+	1.14036i
$209$	382606.	−	139257.i	0.605879	−	0.220522i
$210$	1963.76	−	188355.i	0.00307284	−	0.294732i
$211$	337586.	−	283268.i	0.522010	−	0.438018i	−0.343322	−	0.939218i	$-0.611552\pi$
$211$	337586.	−	283268.i	0.522010	−	0.438018i	0.865332	+	0.501200i	$0.167108\pi$
$212$	−792498.	−	288446.i	−1.21104	−	0.440783i
$213$	−27991.8	+	74481.5i	−0.0422749	+	0.112486i
$214$	178328.	−	1.01135e6i	0.266186	−	1.50961i
$215$	13299.4			0.0196216
$216$	−1232.11	+	39381.2i	−0.00179686	+	0.0574321i
$217$	−438499.			−0.632148
$218$	−158466.	+	898705.i	−0.225837	+	1.28078i
$219$	544289.	−	90132.5i	0.766866	−	0.126990i
$220$	−117351.	−	42712.4i	−0.163467	−	0.0594973i
$221$	−596704.	+	500694.i	−0.821822	+	0.689591i
$222$	1.16890e6	+	691211.i	1.59182	+	0.941300i
$223$	919313.	−	334602.i	1.23794	−	0.450575i	0.361633	−	0.932320i	$-0.382219\pi$
$223$	919313.	−	334602.i	1.23794	−	0.450575i	0.876311	+	0.481746i	$0.159997\pi$
$224$	310723.	−	538188.i	0.413765	−	0.716662i
$225$	−618479.	−	239826.i	−0.814458	−	0.315820i
$226$	379747.	+	657741.i	0.494565	+	0.856611i
$227$	−843674.	−	707927.i	−1.08670	−	0.911851i	−0.0902415	−	0.995920i	$-0.528764\pi$
$227$	−843674.	−	707927.i	−1.08670	−	0.911851i	−0.996460	+	0.0840691i	$0.973208\pi$
$228$	1.10038e6	+	205877.i	1.40186	+	0.262284i
$229$	−16503.5	−	93596.0i	−0.0207964	−	0.117942i	0.972642	−	0.232308i	$-0.0746276\pi$
$229$	−16503.5	−	93596.0i	−0.0207964	−	0.117942i	−0.993439	+	0.114366i	$0.963516\pi$
$230$	−65983.7	−	374212.i	−0.0822464	−	0.466442i
$231$	73525.2	+	208755.i	0.0906580	+	0.257399i
$232$	−809.995	−	679.667i	−0.000988012	−	0.000829041i
$233$	538472.	+	932660.i	0.649790	+	1.12547i	0.983173	+	0.182678i	$0.0584766\pi$
$233$	538472.	+	932660.i	0.649790	+	1.12547i	−0.333383	+	0.942792i	$0.608190\pi$
$234$	319210.	−	1.61291e6i	0.381098	−	1.92562i
$235$	282716.	−	489679.i	0.333950	−	0.578418i
$236$	−479881.	+	174663.i	−0.560859	+	0.204136i
$237$	746966.	−	420939.i	0.863833	−	0.486798i
$238$	433144.	−	363451.i	0.495667	−	0.415914i
$239$	−1.18171e6	−	430108.i	−1.33819	−	0.487061i	−0.428947	−	0.903330i	$-0.641115\pi$
$239$	−1.18171e6	−	430108.i	−1.33819	−	0.487061i	−0.909241	+	0.416269i	$0.863337\pi$
$240$	192993.	+	234931.i	0.216279	+	0.263277i
$241$	112260.	−	636660.i	0.124504	−	0.706098i	−0.857097	−	0.515155i	$-0.827734\pi$
$241$	112260.	−	636660.i	0.124504	−	0.706098i	0.981601	−	0.190943i	$-0.0611546\pi$
$242$	−1.01351e6			−1.11247
$243$	269328.	+	880200.i	0.292594	+	0.956237i
$244$	298341.			0.320803
$245$	−38479.9	+	218230.i	−0.0409561	+	0.232273i
$246$	−1.15013e6	−	1.40006e6i	−1.21174	−	1.47506i
$247$	−1.69766e6	−	617898.i	−1.77055	−	0.644428i
$248$	−46443.1	+	38970.4i	−0.0479504	+	0.0402352i
$249$	1.29799e6	−	731460.i	1.32670	−	0.747640i
$250$	883699.	−	321640.i	0.894240	−	0.325477i
$251$	23452.5	−	40620.9i	0.0234966	−	0.0406973i	−0.854038	−	0.520211i	$-0.825853\pi$
$251$	23452.5	−	40620.9i	0.0234966	−	0.0406973i	0.877535	+	0.479513i	$0.159187\pi$
$252$	−118141.	+	596945.i	−0.117192	+	0.592152i
$253$	223237.	+	386658.i	0.219263	+	0.379774i
$254$	289349.	+	242792.i	0.281408	+	0.236130i
$255$	95756.9	+	271876.i	0.0922188	+	0.261831i
$256$	166562.	+	944620.i	0.158846	+	0.900860i
$257$	−105778.	−	599898.i	−0.0998995	−	0.566558i	−0.993135	−	0.116970i	$-0.962682\pi$
$257$	−105778.	−	599898.i	−0.0998995	−	0.566558i	0.893236	−	0.449588i	$-0.148429\pi$
$258$	−82830.0	−	15497.2i	−0.0774709	−	0.0144945i
$259$	621328.	+	521356.i	0.575535	+	0.482931i
$260$	277058.	+	479879.i	0.254178	+	0.440249i
$261$	−23031.7	−	8930.93i	−0.0209278	−	0.00811513i
$262$	−490050.	+	848792.i	−0.441050	+	0.763921i
$263$	−767893.	+	279490.i	−0.684560	+	0.249159i	−0.660804	−	0.750558i	$-0.729785\pi$
$263$	−767893.	+	279490.i	−0.684560	+	0.249159i	−0.0237556	+	0.999718i	$0.507562\pi$
$264$	26339.9	+	15575.7i	0.0232597	+	0.0137543i
$265$	385814.	−	323736.i	0.337491	−	0.283189i
$266$	1.23232e6	+	448529.i	1.06788	+	0.388675i
$267$	−1.54932e6	+	256562.i	−1.33003	+	0.220249i
$268$	−354013.	+	2.00771e6i	−0.301080	+	1.70751i
$269$	1.06427e6			0.896753			0.448376	−	0.893845i	$-0.352002\pi$
$269$	1.06427e6			0.896753			0.448376	+	0.893845i	$0.352002\pi$
$270$	−517148.	−	320546.i	−0.431723	−	0.267596i
$271$	1.32722e6			1.09779			0.548894	−	0.835892i	$-0.315049\pi$
$271$	1.32722e6			1.09779			0.548894	+	0.835892i	$0.315049\pi$
$272$	−158481.	+	898789.i	−0.129884	+	0.736607i
$273$	345480.	−	919264.i	0.280554	−	0.746507i
$274$	−1.83884e6	−	669283.i	−1.47968	−	0.538559i
$275$	−394661.	+	331160.i	−0.314697	+	0.264062i
$276$	−12797.7	+	1.22750e6i	−0.0101125	+	0.969946i
$277$	−1.75176e6	+	637590.i	−1.37175	+	0.499278i	−0.919668	−	0.392697i	$-0.871542\pi$
$277$	−1.75176e6	+	637590.i	−1.37175	+	0.499278i	−0.452086	+	0.891974i	$0.649320\pi$
$278$	1.36801e6	−	2.36946e6i	1.06164	−	1.83881i
$279$	−733614.	+	1.21160e6i	−0.564231	+	0.931852i
$280$	−7777.57	−	13471.2i	−0.00592856	−	0.0102686i
$281$	−347433.	−	291531.i	−0.262485	−	0.220251i	0.502041	−	0.864844i	$-0.332583\pi$
$281$	−347433.	−	291531.i	−0.262485	−	0.220251i	−0.764526	+	0.644592i	$0.777027\pi$
$282$	−2.33139e6	+	2.72034e6i	−1.74579	+	2.03704i
$283$	27335.0	+	155025.i	0.0202887	+	0.115063i	0.993270	−	0.115820i	$-0.0369497\pi$
$283$	27335.0	+	155025.i	0.0202887	+	0.115063i	−0.972982	+	0.230883i	$0.925839\pi$
$284$	29504.2	+	167326.i	0.0217064	+	0.123103i
$285$	−435042.	+	507620.i	−0.317263	+	0.370192i
$286$	−978218.	−	820823.i	−0.707165	−	0.593382i
$287$	−541102.	−	937216.i	−0.387770	−	0.671637i
$288$	−967199.	−	1.75894e6i	−0.687123	−	1.24960i
$289$	277303.	−	480302.i	0.195303	−	0.338275i
$290$	15343.6	−	5584.60i	0.0107135	−	0.00389939i
$291$	15216.6	−	1.45951e6i	0.0105338	−	1.01035i
$292$	902472.	−	757264.i	0.619408	−	0.519745i
$293$	2.65866e6	+	967672.i	1.80923	+	0.658505i	0.997191	+	0.0748978i	$0.0238631\pi$
$293$	2.65866e6	+	967672.i	1.80923	+	0.658505i	0.812036	+	0.583607i	$0.198359\pi$
$294$	493952.	−	1.31432e6i	0.333286	−	0.886817i
$295$	52957.7	−	300338.i	0.0354303	−	0.200935i
$296$	112141.			0.0743938
$297$	699810.	+	146096.i	0.460351	+	0.0961053i
$298$	−619879.			−0.404358
$299$	344006.	−	1.95095e6i	0.222530	−	1.26203i
$300$	−1.39747e6	+	231417.i	−0.896479	+	0.148454i
$301$	−47295.5	−	17214.2i	−0.0300887	−	0.0109514i
$302$	2.11696e6	−	1.77634e6i	1.33566	−	1.12075i
$303$	1.15704e6	+	684200.i	0.724007	+	0.428131i
$304$	−1.98908e6	+	723967.i	−1.23444	+	0.449298i
$305$	−89082.8	+	154296.i	−0.0548333	+	0.0949740i
$306$	−279579.	−	1.80486e6i	−0.170687	−	1.10189i
$307$	62247.4	+	107816.i	0.0376943	+	0.0652884i	0.884257	−	0.467000i	$-0.154665\pi$
$307$	62247.4	+	107816.i	0.0376943	+	0.0652884i	−0.846563	+	0.532289i	$0.821332\pi$
$308$	362042.	+	303789.i	0.217462	+	0.182472i
$309$	1.83574e6	+	343461.i	1.09374	+	0.204636i
$310$	−162574.	−	922000.i	−0.0960828	−	0.544913i
$311$	350085.	+	1.98543e6i	0.205245	+	1.16400i	0.897054	+	0.441921i	$0.145703\pi$
$311$	350085.	+	1.98543e6i	0.205245	+	1.16400i	−0.691809	+	0.722081i	$0.743186\pi$
$312$	−45106.0	−	128067.i	−0.0262330	−	0.0744816i
$313$	1.80229e6	+	1.51230e6i	1.03983	+	0.872525i	0.991988	−	0.126330i	$-0.0403198\pi$
$313$	1.80229e6	+	1.51230e6i	1.03983	+	0.872525i	0.0478464	+	0.998855i	$0.484764\pi$
$314$	180553.	+	312727.i	0.103343	+	0.178995i
$315$	−273452.	−	239344.i	−0.155276	−	0.135909i
$316$	915446.	−	1.58560e6i	0.515721	−	0.893255i
$317$	527136.	−	191862.i	0.294628	−	0.107236i	−0.190477	−	0.981692i	$-0.561003\pi$
$317$	527136.	−	191862.i	0.294628	−	0.107236i	0.485105	+	0.874456i	$0.338781\pi$
$318$	−2.78013e6	+	1.56669e6i	−1.54169	+	0.868792i
$319$	−14696.9	+	12332.1i	−0.00808626	+	0.00678518i
$320$	660321.	+	240337.i	0.360479	+	0.131204i
$321$	−1.25763e6	−	1.53091e6i	−0.681223	−	0.829256i
$322$	−249712.	+	1.41619e6i	−0.134215	+	0.761169i
$323$	−2.00680e6			−1.07028
$324$	1.45174e6	+	1.32513e6i	0.768292	+	0.701285i
$325$	2.28597e6			1.20050
$326$	−144130.	+	817400.i	−0.0751121	+	0.425982i
$327$	1.11755e6	+	1.36040e6i	0.577962	+	0.703556i
$328$	−140603.	−	51175.2i	−0.0721621	−	0.0262649i
$329$	−1.63922e6	+	1.37547e6i	−0.834927	+	0.700587i
$330$	−411675.	+	231992.i	−0.208099	+	0.117270i
$331$	−1.76678e6	+	643055.i	−0.886365	+	0.322610i	−0.744775	−	0.667315i	$-0.767443\pi$
$331$	−1.76678e6	+	643055.i	−0.886365	+	0.322610i	−0.141589	+	0.989926i	$0.545221\pi$
$332$	1.59076e6	−	2.75527e6i	0.792061	−	1.37189i
$333$	2.48002e6	−	844526.i	1.22559	−	0.417352i
$334$	209214.	+	362369.i	0.102618	+	0.177740i
$335$	−932640.	−	782578.i	−0.454048	−	0.380992i
$336$	−382241.	−	1.08527e6i	−0.184709	−	0.524433i
$337$	693819.	+	3.93484e6i	0.332791	+	1.88735i	0.448038	+	0.894015i	$0.352123\pi$
$337$	693819.	+	3.93484e6i	0.332791	+	1.88735i	−0.115247	+	0.993337i	$0.536766\pi$
$338$	462945.	+	2.62549e6i	0.220413	+	1.25002i
$339$	1.44026e6	+	269469.i	0.680679	+	0.127353i
$340$	471512.	+	395646.i	0.221205	+	0.185613i
$341$	550022.	+	952665.i	0.256150	+	0.443664i
$342$	3.30100e6	−	2.65458e6i	1.52609	−	1.22724i
$343$	1.05151e6	−	1.82127e6i	0.482589	−	0.835869i
$344$	−6539.12	+	2380.04i	−0.00297936	+	0.00108440i
$345$	−631015.	−	373142.i	−0.285425	−	0.168782i
$346$	2.03883e6	−	1.71078e6i	0.915569	−	0.768254i
$347$	−1.26492e6	−	460394.i	−0.563949	−	0.205261i	0.0442843	−	0.999019i	$-0.485899\pi$
$347$	−1.26492e6	−	460394.i	−0.563949	−	0.205261i	−0.608233	+	0.793758i	$0.708121\pi$
$348$	−52040.8	+	8617.78i	−0.0230354	+	0.00381458i
$349$	−457946.	+	2.59714e6i	−0.201257	+	1.14138i	0.701966	+	0.712211i	$0.252306\pi$
$349$	−457946.	+	2.59714e6i	−0.201257	+	1.14138i	−0.903222	+	0.429173i	$0.858805\pi$
$350$	−1.65937e6			−0.724058
$351$	−1.96198e6	−	2.49252e6i	−0.850017	−	1.07987i
$352$	−1.55900e6			−0.670638
$353$	780431.	−	4.42604e6i	0.333348	−	1.89051i	−0.109624	−	0.993973i	$-0.534965\pi$
$353$	780431.	−	4.42604e6i	0.333348	−	1.89051i	0.442972	−	0.896536i	$-0.353924\pi$
$354$	−679799.	+	1.80883e6i	−0.288319	+	0.767167i
$355$	−95347.6	−	34703.7i	−0.0401549	−	0.0146152i
$356$	−2.56888e6	+	2.15555e6i	−1.07428	+	0.901431i
$357$	11372.5	−	1.09080e6i	0.00472264	−	0.452974i
$358$	2.47064e6	−	899240.i	1.01883	−	0.370824i
$359$	−525561.	+	910298.i	−0.215222	+	0.372776i	−0.953341	−	0.301895i	$-0.902381\pi$
$359$	−525561.	+	910298.i	−0.215222	+	0.372776i	0.738119	+	0.674670i	$0.235714\pi$
$360$	−50233.5	−	1047.57i	−0.0204285	−	0.000426017i
$361$	−1.08915e6	−	1.88647e6i	−0.439866	−	0.761870i
$362$	−1.40329e6	−	1.17750e6i	−0.562829	−	0.472269i
$363$	−1.27240e6	+	1.48467e6i	−0.506822	+	0.591375i
$364$	−364145.	−	2.06517e6i	−0.144053	−	0.816963i
$365$	122169.	+	692855.i	0.0479986	+	0.272214i
$366$	734613.	−	857168.i	0.286653	−	0.334475i
$367$	−1.31221e6	−	1.10107e6i	−0.508555	−	0.426728i	0.352066	−	0.935975i	$-0.385479\pi$
$367$	−1.31221e6	−	1.10107e6i	−0.508555	−	0.426728i	−0.860620	+	0.509247i	$0.829924\pi$
$368$	−1.16056e6	−	2.01015e6i	−0.446733	−	0.773764i
$369$	−3.49485e6	−	72881.5i	−1.33617	−	0.0278645i
$370$	−865861.	+	1.49971e6i	−0.328809	+	0.569514i
$371$	−1.79107e6	+	651896.i	−0.675581	+	0.245892i
$372$	−31531.6	+	3.02436e6i	−0.0118138	+	1.13312i
$373$	−3.67690e6	+	3.08529e6i	−1.36839	+	1.14822i	−0.395100	+	0.918638i	$0.629290\pi$
$373$	−3.67690e6	+	3.08529e6i	−1.36839	+	1.14822i	−0.973290	+	0.229577i	$0.926266\pi$
$374$	−1.33292e6	−	485145.i	−0.492750	−	0.179346i
$375$	638265.	−	1.69832e6i	0.234381	−	0.623649i
$376$	−51375.2	+	291363.i	−0.0187406	+	0.106283i
$377$	85127.5			0.0308473
$378$	1.42419e6	+	1.80931e6i	0.512672	+	0.651302i
$379$	1.68242e6			0.601640			0.300820	−	0.953681i	$-0.402740\pi$
$379$	1.68242e6			0.601640			0.300820	+	0.953681i	$0.402740\pi$
$380$	−247896.	+	1.40589e6i	−0.0880666	+	0.499450i
$381$	718922.	−	119051.i	0.253729	−	0.0420166i
$382$	3.10949e6	+	1.13176e6i	1.09026	+	0.396823i
$383$	374234.	−	314020.i	0.130361	−	0.109386i	−0.575276	−	0.817959i	$-0.695105\pi$
$383$	374234.	−	314020.i	0.130361	−	0.109386i	0.705637	+	0.708574i	$0.250661\pi$
$384$	−285600.	−	168886.i	−0.0988395	−	0.0584473i
$385$	−265217.	+	96531.2i	−0.0911906	+	0.0331907i
$386$	−1.91141e6	+	3.31066e6i	−0.652959	+	1.13096i
$387$	−126690.	+	101880.i	−0.0429995	+	0.0345791i
$388$	−1.55839e6	−	2.69921e6i	−0.525528	−	0.910242i
$389$	1.69918e6	+	1.42578e6i	0.569333	+	0.477727i	0.881424	−	0.472325i	$-0.156585\pi$
$389$	1.69918e6	+	1.42578e6i	0.569333	+	0.477727i	−0.312092	+	0.950052i	$0.601030\pi$
$390$	2.06096e6	+	385599.i	0.686132	+	0.128373i
$391$	−382123.	−	2.16713e6i	−0.126404	−	0.716874i
$392$	−20134.3	−	114187.i	−0.00661791	−	0.0375320i
$393$	628153.	+	1.78347e6i	0.205156	+	0.582486i
$394$	−2.30307e6	−	1.93251e6i	−0.747424	−	0.627163i
$395$	546693.	+	946900.i	0.176299	+	0.305360i
$396$	1.44509e6	−	492098.i	0.463080	−	0.157693i
$397$	572491.	−	991584.i	0.182303	−	0.315757i	−0.760362	−	0.649500i	$-0.774978\pi$
$397$	572491.	−	991584.i	0.182303	−	0.315757i	0.942664	+	0.333743i	$0.108312\pi$
$398$	−4.65184e6	+	1.69313e6i	−1.47203	+	0.535775i
$399$	2.20415e6	−	1.24211e6i	0.693121	−	0.390596i
$400$	2.05175e6	−	1.72163e6i	0.641173	−	0.538008i
$401$	2.21375e6	+	805740.i	0.687493	+	0.250227i	0.662061	−	0.749450i	$-0.269682\pi$
$401$	2.21375e6	+	805740.i	0.687493	+	0.250227i	0.0254313	+	0.999677i	$0.491904\pi$
$402$	4.89668e6	+	5.96075e6i	1.51125	+	1.83965i
$403$	847577.	−	4.80685e6i	0.259966	−	1.47434i
$404$	2.87038e6			0.874956
$405$	−1.11881e6	+	355136.i	−0.338937	+	0.107586i
$406$	−61793.6			−0.0186049
$407$	353328.	−	2.00382e6i	0.105729	−	0.599617i
$408$	−95737.1	−	116541.i	−0.0284728	−	0.0346600i
$409$	−3.97038e6	−	1.44510e6i	−1.17361	−	0.427159i	−0.319670	−	0.947529i	$-0.603572\pi$
$409$	−3.97038e6	−	1.44510e6i	−1.17361	−	0.427159i	−0.853941	+	0.520370i	$0.825794\pi$
$410$	1.77000e6	−	1.48521e6i	0.520013	−	0.436343i
$411$	−3.28897e6	+	1.85344e6i	−0.960408	+	0.541221i
$412$	3.74752e6	−	1.36399e6i	1.08768	−	0.395883i
$413$	−577075.	+	999523.i	−0.166478	+	0.288349i
$414$	3.49523e6	+	3.05927e6i	1.00225	+	0.877236i
$415$	949981.	+	1.64541e6i	0.270766	+	0.468981i
$416$	5.29905e6	+	4.44643e6i	1.50129	+	1.25973i
$417$	−1.75353e6	−	4.97868e6i	−0.493825	−	1.40208i
$418$	−571282.	−	3.23990e6i	−0.159923	−	0.906966i
$419$	−343665.	−	1.94902e6i	−0.0956314	−	0.542353i	−0.994552	−	0.104241i	$-0.966759\pi$
$419$	−343665.	−	1.94902e6i	−0.0956314	−	0.542353i	0.898921	−	0.438112i	$-0.144353\pi$
$420$	−762768.	−	142711.i	−0.210994	−	0.0394762i
$421$	1.60683e6	+	1.34829e6i	0.441839	+	0.370747i	0.836397	−	0.548124i	$-0.184658\pi$
$421$	1.60683e6	+	1.34829e6i	0.441839	+	0.370747i	−0.394558	+	0.918871i	$0.629102\pi$
$422$	−1.78039e6	−	3.08372e6i	−0.486669	−	0.842936i
$423$	1.05806e6	+	6.83044e6i	0.287514	+	1.85609i
$424$	−131764.	+	228222.i	−0.0355944	+	0.0616513i
$425$	2.38613e6	−	868479.i	0.640798	−	0.233231i
$426$	553397.	+	327243.i	0.147745	+	0.0873669i
$427$	516513.	−	433405.i	0.137092	−	0.115034i
$428$	−3.97557e6	−	1.44699e6i	−1.04903	−	0.381817i
$429$	−2.43050e6	+	402483.i	−0.637607	+	0.105586i
$430$	18660.2	−	105827.i	0.00486681	−	0.0276010i
$431$	4.31651e6			1.11928			0.559641	−	0.828735i	$-0.310939\pi$
$431$	4.31651e6			1.11928			0.559641	+	0.828735i	$0.310939\pi$
$432$	−3.63815e6	−	759521.i	−0.937933	−	0.195808i
$433$	−4.01768e6			−1.02981			−0.514903	−	0.857249i	$-0.672172\pi$
$433$	−4.01768e6			−1.02981			−0.514903	+	0.857249i	$0.672172\pi$
$434$	−615252.	+	3.48927e6i	−0.156794	+	0.889221i
$435$	11082.1	−	29487.6i	0.00280802	−	0.00747166i
$436$	3.53277e6	+	1.28582e6i	0.890020	+	0.323941i
$437$	3.90974e6	−	3.28066e6i	0.979365	−	0.821785i
$438$	46473.7	−	4.45754e6i	0.0115750	−	1.11022i
$439$	−4.80362e6	+	1.74838e6i	−1.18962	+	0.432986i	−0.859589	−	0.510985i	$-0.829281\pi$
$439$	−4.80362e6	+	1.74838e6i	−1.18962	+	0.432986i	−0.330029	+	0.943971i	$0.607058\pi$
$440$	−19511.3	+	33794.5i	−0.00480456	+	0.00832175i
$441$	−1.30520e6	−	2.37364e6i	−0.319582	−	0.581189i
$442$	3.14694e6	+	5.45067e6i	0.766184	+	1.32707i
$443$	−1.89927e6	−	1.59367e6i	−0.459808	−	0.385825i	0.383252	−	0.923644i	$-0.374804\pi$
$443$	−1.89927e6	−	1.59367e6i	−0.459808	−	0.385825i	−0.843060	+	0.537819i	$0.819248\pi$
$444$	3.64051e6	−	4.24786e6i	0.876406	−	1.02262i
$445$	−347753.	−	1.97221e6i	−0.0832475	−	0.472120i
$446$	−1.37266e6	−	7.78472e6i	−0.326757	−	1.85313i
$447$	−778220.	+	908051.i	−0.184219	+	0.214952i
$448$	−2.03717e6	−	1.70939e6i	−0.479547	−	0.402388i
$449$	1.88192e6	+	3.25958e6i	0.440540	+	0.763038i	0.997730	−	0.0673475i	$-0.0214536\pi$
$449$	1.88192e6	+	3.25958e6i	0.440540	+	0.763038i	−0.557189	+	0.830385i	$0.688120\pi$
$450$	−2.77615e6	+	4.58493e6i	−0.646266	+	1.06734i
$451$	−1.35744e6	+	2.35115e6i	−0.314253	+	0.544301i
$452$	2.94018e6	−	1.07014e6i	0.676906	−	0.246373i
$453$	55582.2	−	5.33118e6i	0.0127259	−	1.22061i
$454$	−6.81694e6	+	5.72009e6i	−1.55221	+	1.30246i
$455$	1.17680e6	+	428319.i	0.266485	+	0.0969927i
$456$	123061.	−	327445.i	0.0277146	−	0.0737439i
$457$	795942.	−	4.51401e6i	0.178275	−	1.01105i	−0.756020	−	0.654549i	$-0.772859\pi$
$457$	795942.	−	4.51401e6i	0.178275	−	1.01105i	0.934295	−	0.356500i	$-0.116030\pi$
$458$	−767927.			−0.171063
$459$	−2.99490e6	−	1.85634e6i	−0.663515	−	0.411268i
$460$	−1.56542e6			−0.344934
$461$	−1.21990e6	+	6.91840e6i	−0.267345	+	1.51619i	0.494928	+	0.868934i	$0.335194\pi$
$461$	−1.21990e6	+	6.91840e6i	−0.267345	+	1.51619i	−0.762273	+	0.647256i	$0.775917\pi$
$462$	1.76429e6	−	292160.i	0.384561	−	0.0636820i
$463$	6.55566e6	+	2.38607e6i	1.42123	+	0.517285i	0.934404	−	0.356214i	$-0.115933\pi$
$463$	6.55566e6	+	2.38607e6i	1.42123	+	0.517285i	0.486825	+	0.873499i	$0.338155\pi$
$464$	76405.7	−	64112.0i	0.0164752	−	0.0138243i
$465$	−1.55472e6	−	919364.i	−0.333442	−	0.197176i
$466$	8.17698e6	−	2.97618e6i	1.74433	−	0.634884i
$467$	311260.	−	539118.i	0.0660437	−	0.114391i	−0.831113	−	0.556104i	$-0.812296\pi$
$467$	311260.	−	539118.i	0.0660437	−	0.114391i	0.897156	+	0.441713i	$0.145629\pi$
$468$	−6.31540e6	−	2.44891e6i	−1.33286	−	0.516842i
$469$	2.30374e6	+	3.99019e6i	0.483616	+	0.837648i
$470$	−3.49985e6	−	2.93672e6i	−0.730810	−	0.613223i
$471$	684783.	+	128121.i	0.142233	+	0.0266114i
$472$	27709.7	+	157150.i	0.00572502	+	0.0324682i
$473$	21925.3	+	124345.i	0.00450602	+	0.0255549i
$474$	−2.30148e6	−	6.53445e6i	−0.470502	−	1.33587i
$475$	4.51151e6	+	3.78561e6i	0.917462	+	0.769842i
$476$	−1.16470e6	−	2.01731e6i	−0.235611	−	0.408090i
$477$	−1.19526e6	+	6.03945e6i	−0.240528	+	1.21535i
$478$	−5.08055e6	+	8.79976e6i	−1.01705	+	1.76158i
$479$	2.67506e6	−	973643.i	0.532715	−	0.193892i	−0.0616352	−	0.998099i	$-0.519632\pi$
$479$	2.67506e6	−	973643.i	0.532715	−	0.193892i	0.594350	+	0.804206i	$0.297409\pi$
$480$	2.23006e6	−	1.25671e6i	0.441788	−	0.248962i
$481$	−6.91611e6	+	5.80330e6i	−1.36301	+	1.14370i
$482$	−4.90859e6	−	1.78658e6i	−0.962363	−	0.350271i
$483$	1.76105e6	+	2.14374e6i	0.343482	+	0.418122i
$484$	−725038.	+	4.11190e6i	−0.140685	+	0.797864i
$485$	1.86130e6			0.359304
$486$	7.38190e6	−	908125.i	1.41768	−	0.174403i
$487$	3.37660e6			0.645146			0.322573	−	0.946545i	$-0.395452\pi$
$487$	3.37660e6			0.645146			0.322573	+	0.946545i	$0.395452\pi$
$488$	16188.1	−	91807.4i	0.00307714	−	0.0174513i
$489$	1.01645e6	+	1.23733e6i	0.192227	+	0.233999i
$490$	1.68253e6	+	612392.i	0.316573	+	0.115223i
$491$	−5.30712e6	+	4.45321e6i	−0.993472	+	0.833622i	−0.986067	−	0.166351i	$-0.946802\pi$
$491$	−5.30712e6	+	4.45321e6i	−0.993472	+	0.833622i	−0.00740519	+	0.999973i	$0.502357\pi$
$492$	−6.50296e6	+	3.66463e6i	−1.21115	+	0.682523i
$493$	88857.4	−	32341.4i	0.0164655	−	0.00599297i
$494$	−7.29877e6	+	1.26418e7i	−1.34565	+	2.33074i
$495$	−176991.	+	894308.i	−0.0324668	+	0.164049i
$496$	−2.85944e6	−	4.95269e6i	−0.521887	−	0.903935i
$497$	294158.	+	246828.i	0.0534183	+	0.0448233i
$498$	−3.99925e6	−	1.13548e7i	−0.722613	−	2.05167i
$499$	−445945.	−	2.52908e6i	−0.0801734	−	0.454686i	−0.998294	−	0.0583852i	$-0.981405\pi$
$499$	−445945.	−	2.52908e6i	−0.0801734	−	0.454686i	0.918121	−	0.396301i	$-0.129706\pi$
$500$	−672749.	−	3.81535e6i	−0.120345	−	0.682510i
$501$	793483.	+	148458.i	0.141235	+	0.0264247i
$502$	−290327.	−	243613.i	−0.0514195	−	0.0431461i
$503$	−1.32401e6	−	2.29325e6i	−0.233330	−	0.404139i	0.725456	−	0.688268i	$-0.241629\pi$
$503$	−1.32401e6	−	2.29325e6i	−0.233330	−	0.404139i	−0.958786	+	0.284129i	$0.908295\pi$
$504$	177286.	+	68745.6i	0.0310883	+	0.0120550i
$505$	−857079.	+	1.48450e6i	−0.149552	+	0.259032i
$506$	3.38997e6	−	1.23385e6i	0.588600	−	0.214233i
$507$	4.42724e6	+	2.61798e6i	0.764914	+	0.452321i
$508$	1.19203e6	−	1.00023e6i	0.204940	−	0.171965i
$509$	−1.24319e6	−	452483.i	−0.212687	−	0.0774119i	0.233479	−	0.972362i	$-0.424989\pi$
$509$	−1.24319e6	−	452483.i	−0.212687	−	0.0774119i	−0.446167	+	0.894950i	$0.647211\pi$
$510$	2.29775e6	−	380501.i	0.391181	−	0.0647784i
$511$	462343.	−	2.62208e6i	0.0783271	−	0.444215i
$512$	8.43144e6			1.42143
$513$	255557.	−	8.16825e6i	0.0428741	−	1.37036i
$514$	−4.92198e6			−0.821736
$515$	−413561.	+	2.34542e6i	−0.0687102	+	0.389675i
$516$	−122128.	+	324963.i	−0.0201926	+	0.0537291i
$517$	5.04442e6	+	1.83602e6i	0.830013	+	0.302100i
$518$	5.02036e6	−	4.21259e6i	0.822074	−	0.689802i
$519$	53530.9	−	5.13443e6i	0.00872341	−	0.836708i
$520$	162705.	−	59219.8i	0.0263871	−	0.00960414i
$521$	1.65240e6	−	2.86205e6i	0.266699	−	0.461937i	−0.701308	−	0.712858i	$-0.747400\pi$
$521$	1.65240e6	−	2.86205e6i	0.266699	−	0.461937i	0.968007	+	0.250921i	$0.0807336\pi$
$522$	−103381.	+	170739.i	−0.0166061	+	0.0274256i
$523$	−3.50814e6	−	6.07627e6i	−0.560819	−	0.971366i	−0.997425	−	0.0717138i	$-0.977153\pi$
$523$	−3.50814e6	−	6.07627e6i	−0.560819	−	0.971366i	0.436607	−	0.899653i	$-0.356180\pi$
$524$	3.09306e6	+	2.59539e6i	0.492108	+	0.412928i
$525$	−2.08324e6	+	2.43078e6i	−0.329868	+	0.384900i
$526$	1.14657e6	+	6.50250e6i	0.180690	+	1.02475i
$527$	−941493.	−	5.33947e6i	−0.147669	−	0.837475i
$528$	−1.87836e6	+	2.19173e6i	−0.293220	+	0.342138i
$529$	−643277.	−	539774.i	−0.0999445	−	0.0838634i
$530$	−2.03473e6	−	3.52426e6i	−0.314643	−	0.544978i
$531$	1.79628e6	+	3.26670e6i	0.276464	+	0.502775i
$532$	2.70130e6	−	4.67879e6i	0.413803	−	0.716728i
$533$	1.13197e7	−	4.12004e6i	1.72591	−	0.628179i
$534$	−132287.	+	1.26884e7i	−0.0200754	+	1.92554i
$535$	1.93543e6	−	1.62402e6i	0.292344	−	0.245305i
$536$	598616.	+	217878.i	0.0899987	+	0.0327568i
$537$	1.78446e6	−	4.74815e6i	0.267037	−	0.710540i
$538$	1.49327e6	−	8.46875e6i	0.222424	−	1.26143i
$539$	−2.10382e6			−0.311915
$540$	−1.67044e6	+	1.86881e6i	−0.246517	+	0.275791i
$541$	−5.60437e6			−0.823254			−0.411627	−	0.911352i	$-0.635039\pi$
$541$	−5.60437e6			−0.823254			−0.411627	+	0.911352i	$0.635039\pi$
$542$	1.86220e6	−	1.05611e7i	0.272288	−	1.54422i
$543$	−3.48665e6	+	577377.i	−0.507468	+	0.0840350i
$544$	7.22051e6	+	2.62805e6i	1.04609	+	0.380747i
$545$	−1.71987e6	+	1.44314e6i	−0.248030	+	0.208122i
$546$	−6.83012e6	−	4.03890e6i	−0.980499	−	0.579804i
$547$	1.28768e6	−	468679.i	0.184010	−	0.0669741i	−0.248372	−	0.968665i	$-0.579896\pi$
$547$	1.28768e6	−	468679.i	0.184010	−	0.0669741i	0.432382	+	0.901691i	$0.357673\pi$
$548$	−4.03081e6	+	6.98157e6i	−0.573378	+	0.993120i
$549$	−333390.	−	2.15224e6i	−0.0472087	−	0.304762i
$550$	2.08140e6	+	3.60508e6i	0.293392	+	0.508169i
$551$	168005.	+	140973.i	0.0235745	+	0.0197814i
$552$	377039.	+	70542.8i	0.0526670	+	0.00985382i
$553$	−718534.	−	4.07501e6i	−0.0999158	−	0.566651i
$554$	2.61562e6	+	1.48339e7i	0.362076	+	2.05344i
$555$	1.10987e6	+	3.15119e6i	0.152947	+	0.434252i
$556$	−8.63449e6	−	7.24520e6i	−1.18454	−	0.993947i
$557$	−1.07251e6	−	1.85765e6i	−0.146476	−	0.253703i	0.783447	−	0.621459i	$-0.213460\pi$
$557$	−1.07251e6	−	1.85765e6i	−0.146476	−	0.253703i	−0.929922	+	0.367756i	$0.880126\pi$
$558$	8.61170e6	+	7.53756e6i	1.17086	+	1.02481i
$559$	280120.	−	485183.i	0.0379154	−	0.0656714i
$560$	1.37881e6	−	501844.i	0.185795	−	0.0676237i
$561$	−2.38409e6	+	1.34351e6i	−0.319827	+	0.180233i
$562$	−2.80728e6	+	2.35558e6i	−0.374925	+	0.314599i
$563$	1.21476e7	+	4.42136e6i	1.61517	+	0.587874i	0.982454	−	0.186508i	$-0.0597169\pi$
$563$	1.21476e7	+	4.42136e6i	1.61517	+	0.587874i	0.632718	+	0.774382i	$0.281939\pi$
$564$	9.36887e6	+	1.14048e7i	1.24019	+	1.50969i
$565$	−324466.	+	1.84014e6i	−0.0427611	+	0.242510i
$566$	1.27193e6			0.166887
$567$	4.43841e6	+	185198.i	0.579789	+	0.0241924i
$568$	53091.7			0.00690487
$569$	328849.	−	1.86499e6i	0.0425809	−	0.241489i	−0.956087	−	0.293082i	$-0.905319\pi$
$569$	328849.	−	1.86499e6i	0.0425809	−	0.241489i	0.998668	+	0.0515938i	$0.0164301\pi$
$570$	3.42888e6	+	4.17400e6i	0.442044	+	0.538102i
$571$	5.20969e6	+	1.89617e6i	0.668686	+	0.243382i	0.653982	−	0.756510i	$-0.273097\pi$
$571$	5.20969e6	+	1.89617e6i	0.668686	+	0.243382i	0.0147037	+	0.999892i	$0.495319\pi$
$572$	−4.02995e6	+	3.38153e6i	−0.515003	+	0.432139i
$573$	5.56168e6	−	3.13419e6i	0.707652	−	0.398785i
$574$	−8.21692e6	+	2.99071e6i	−1.04095	+	0.378874i
$575$	−3.22900e6	+	5.59280e6i	−0.407286	+	0.705439i
$576$	−8.13133e6	+	2.76897e6i	−1.02119	+	0.347746i
$577$	−3.95063e6	−	6.84269e6i	−0.494000	−	0.855633i	0.505976	−	0.862547i	$-0.331132\pi$
$577$	−3.95063e6	−	6.84269e6i	−0.494000	−	0.855633i	−0.999976	+	0.00691467i	$0.997799\pi$
$578$	−3.43283e6	−	2.88049e6i	−0.427398	−	0.358630i
$579$	2.45007e6	+	6.95633e6i	0.303727	+	0.862351i
$580$	−11680.9	−	66245.4i	−0.00144180	−	0.00817685i
$581$	−1.24859e6	−	7.08108e6i	−0.153454	−	0.870280i
$582$	−1.15924e7	−	2.16890e6i	−1.41862	−	0.265419i
$583$	3.66287e6	+	3.07352e6i	0.446324	+	0.374511i
$584$	−184062.	−	318804.i	−0.0223322	−	0.0386805i
$585$	3.15226e6	−	2.53497e6i	0.380832	−	0.306255i
$586$	1.14304e7	−	1.97980e7i	1.37504	−	2.38165i
$587$	−1.45319e7	+	5.28919e6i	−1.74072	+	0.633569i	−0.999298	−	0.0374727i	$-0.988069\pi$
$587$	−1.45319e7	+	5.28919e6i	−1.74072	+	0.633569i	−0.741419	+	0.671042i	$0.765847\pi$
$588$	−4.97898e6	−	2.94425e6i	−0.593878	−	0.351181i
$589$	9.63300e6	−	8.08305e6i	1.14412	−	0.960035i
$590$	−2.31558e6	−	842801.i	−0.273860	−	0.0996771i
$591$	−5.72226e6	+	947588.i	−0.673905	+	0.111597i
$592$	−1.83688e6	+	1.04174e7i	−0.215415	+	1.22168i
$593$	−6.33686e6			−0.740009			−0.370005	−	0.929030i	$-0.620644\pi$
$593$	−6.33686e6			−0.740009			−0.370005	+	0.929030i	$0.620644\pi$
$594$	2.14442e6	−	5.36361e6i	0.249370	−	0.623722i
$595$	1.39108e6			0.161087
$596$	−443447.	+	2.51491e6i	−0.0511359	+	0.290006i
$597$	−3.35986e6	+	8.94002e6i	−0.385821	+	1.02660i
$598$	−1.50417e7	−	5.47472e6i	−1.72006	−	0.626050i
$599$	−5.69469e6	+	4.77841e6i	−0.648490	+	0.544147i	−0.906612	−	0.421965i	$-0.861341\pi$
$599$	−5.69469e6	+	4.77841e6i	−0.648490	+	0.544147i	0.258123	+	0.966112i	$0.416896\pi$
$600$	−4614.45	+	442596.i	−0.000523289	+	0.0501914i
$601$	−1.05116e7	+	3.82591e6i	−1.18709	+	0.432065i	−0.858700	−	0.512478i	$-0.828727\pi$
$601$	−1.05116e7	+	3.82591e6i	−1.18709	+	0.432065i	−0.328388	+	0.944543i	$0.606505\pi$
$602$	−203338.	+	352192.i	−0.0228679	+	0.0396085i
$603$	1.48793e7	+	310293.i	1.66644	+	0.0347519i
$604$	−5.69236e6	−	9.85945e6i	−0.634892	−	1.09967i
$605$	−1.91010e6	−	1.60276e6i	−0.212162	−	0.178025i
$606$	7.06782e6	−	8.24694e6i	0.781815	−	0.912245i
$607$	−39412.6	−	223520.i	−0.00434174	−	0.0246232i	0.982560	−	0.185946i	$-0.0595350\pi$
$607$	−39412.6	−	223520.i	−0.00434174	−	0.0246232i	−0.986902	+	0.161323i	$0.948424\pi$
$608$	3.09466e6	+	1.75507e7i	0.339511	+	1.92546i
$609$	−77578.1	+	90520.4i	−0.00847609	+	0.00989016i
$610$	1.10279e6	+	925349.i	0.119996	+	0.100689i
$611$	−1.19095e7	−	2.06279e7i	−1.29060	−	2.23539i
$612$	−7.52249e6	−	156874.i	−0.811863	−	0.0169306i
$613$	−4.90647e6	+	8.49826e6i	−0.527373	+	0.913438i	0.472118	+	0.881536i	$0.343490\pi$
$613$	−4.90647e6	+	8.49826e6i	−0.527373	+	0.913438i	−0.999491	+	0.0319019i	$0.989844\pi$
$614$	945260.	−	344047.i	0.101188	−	0.0368295i
$615$	46472.7	−	4.45744e6i	0.00495461	−	0.475223i
$616$	113129.	−	94926.2i	0.0120122	−	0.0100794i
$617$	−9.61915e6	−	3.50109e6i	−1.01724	−	0.370246i	−0.221032	−	0.975267i	$-0.570942\pi$
$617$	−9.61915e6	−	3.50109e6i	−1.01724	−	0.370246i	−0.796209	+	0.605021i	$0.793165\pi$
$618$	5.30873e6	−	1.41256e7i	0.559139	−	1.48777i
$619$	470254.	−	2.66694e6i	0.0493294	−	0.279761i	−0.950158	−	0.311768i	$-0.899079\pi$
$619$	470254.	−	2.66694e6i	0.0493294	−	0.279761i	0.999488	+	0.0320071i	$0.0101899\pi$
$620$	−3.85695e6			−0.402962
$621$	8.86952e6	−	1.27938e6i	0.922935	−	0.133128i
$622$	1.62899e7			1.68827
$623$	−1.31606e6	+	7.46372e6i	−0.135848	+	0.770434i
$624$	1.26356e7	−	2.09242e6i	1.29908	−	0.215123i
$625$	−5.84217e6	−	2.12637e6i	−0.598238	−	0.217741i
$626$	1.45626e7	−	1.22195e7i	1.48526	−	1.24628i
$627$	−5.46329e6	−	3.23064e6i	−0.554990	−	0.328185i
$628$	1.39793e6	−	508805.i	0.141445	−	0.0514816i
$629$	−5.01436e6	+	8.68513e6i	−0.505346	+	0.875285i
$630$	−2.28821e6	+	1.84012e6i	−0.229691	+	0.184712i
$631$	6.63331e6	+	1.14892e7i	0.663219	+	1.14873i	0.979765	+	0.200151i	$0.0641434\pi$
$631$	6.63331e6	+	1.14892e7i	0.663219	+	1.14873i	−0.316546	+	0.948577i	$0.602523\pi$
$632$	−438258.	−	367742.i	−0.0436453	−	0.0366228i
$633$	−6.75247e6	−	1.26336e6i	−0.669812	−	0.125320i
$634$	−787084.	−	4.46378e6i	−0.0777675	−	0.441041i
$635$	161366.	+	915154.i	0.0158810	+	0.0900658i
$636$	4.36739e6	+	1.24000e7i	0.428133	+	1.21557i
$637$	7.15091e6	+	6.00032e6i	0.698253	+	0.585904i
$638$	77509.5	+	134250.i	0.00753882	+	0.0130576i
$639$	1.17413e6	−	399828.i	0.113753	−	0.0387366i
$640$	211558.	−	366430.i	0.0204164	−	0.0353623i
$641$	−1.54658e7	+	5.62908e6i	−1.48671	+	0.541118i	−0.952581	−	0.304284i	$-0.901583\pi$
$641$	−1.54658e7	+	5.62908e6i	−1.48671	+	0.541118i	−0.534129	+	0.845403i	$0.679360\pi$
$642$	−1.39465e7	+	7.85931e6i	−1.33545	+	0.752570i
$643$	6.81488e6	−	5.71836e6i	0.650026	−	0.545437i	−0.257053	−	0.966397i	$-0.582751\pi$
$643$	6.81488e6	−	5.71836e6i	0.650026	−	0.545437i	0.907079	+	0.420961i	$0.138307\pi$
$644$	5.56698e6	+	2.02621e6i	0.528938	+	0.192518i
$645$	−131598.	−	160194.i	−0.0124551	−	0.0151617i
$646$	−2.81571e6	+	1.59687e7i	−0.265464	+	1.50552i
$647$	8.09399e6			0.760154			0.380077	−	0.924955i	$-0.375897\pi$
$647$	8.09399e6			0.760154			0.380077	+	0.924955i	$0.375897\pi$
$648$	486549.	−	374837.i	0.0455186	−	0.0350675i
$649$	2.89537e6			0.269831
$650$	3.20741e6	−	1.81901e7i	0.297763	−	1.68870i
$651$	4.33896e6	+	5.28183e6i	0.401267	+	0.488464i
$652$	3.21317e6	+	1.16950e6i	0.296015	+	0.107741i
$653$	−6.97748e6	+	5.85480e6i	−0.640348	+	0.537315i	−0.904125	−	0.427268i	$-0.859476\pi$
$653$	−6.97748e6	+	5.85480e6i	−0.640348	+	0.537315i	0.263777	+	0.964584i	$0.415032\pi$
$654$	1.23932e7	−	6.98395e6i	1.13302	−	0.638494i
$655$	−2.26585e6	+	824703.i	−0.206361	+	0.0751094i
$656$	7.05702e6	−	1.22231e7i	0.640268	−	1.10898i
$657$	−6.47143e6	−	5.66425e6i	−0.584907	−	0.511951i
$658$	8.64507e6	+	1.49737e7i	0.778402	+	1.34823i
$659$	6.90678e6	+	5.79548e6i	0.619530	+	0.519847i	0.897656	−	0.440697i	$-0.145269\pi$
$659$	6.90678e6	+	5.79548e6i	0.619530	+	0.519847i	−0.278126	+	0.960545i	$0.589713\pi$
$660$	646713.	+	1.83617e6i	0.0577898	+	0.164079i
$661$	1.78471e6	+	1.01216e7i	0.158878	+	0.901044i	0.955154	+	0.296110i	$0.0956895\pi$
$661$	1.78471e6	+	1.01216e7i	0.158878	+	0.901044i	−0.796275	+	0.604934i	$0.793199\pi$
$662$	2.63804e6	+	1.49611e7i	0.233957	+	1.32684i
$663$	1.19354e7	+	2.23307e6i	1.05451	+	0.197296i
$664$	−761555.	−	639020.i	−0.0670318	−	0.0562464i
$665$	1.61318e6	+	2.79412e6i	0.141459	+	0.245014i
$666$	−3.24046e6	−	2.09192e7i	−0.283088	−	1.82751i
$667$	−120245.	+	208271.i	−0.0104654	+	0.0181265i
$668$	1.61983e6	−	589571.i	0.140452	−	0.0511205i
$669$	−1.31270e7	−	7.76246e6i	−1.13397	−	0.670555i
$670$	−7.53578e6	+	6.32327e6i	−0.648547	+	0.544195i
$671$	−1.58948e6	−	578522.i	−0.136285	−	0.0496037i
$672$	−9.55723e6	+	1.58265e6i	−0.816411	+	0.135195i
$673$	584432.	−	3.31448e6i	0.0497389	−	0.282083i	−0.949786	−	0.312900i	$-0.898700\pi$
$673$	584432.	−	3.31448e6i	0.0497389	−	0.282083i	0.999525	+	0.0308164i	$0.00981072\pi$
$674$	3.22842e7			2.73742
$675$	3.23110e6	+	9.82283e6i	0.272955	+	0.829807i
$676$	1.09831e7			0.924392
$677$	−1.36986e6	+	7.76886e6i	−0.114869	+	0.651457i	0.871945	+	0.489603i	$0.162858\pi$
$677$	−1.36986e6	+	7.76886e6i	−0.114869	+	0.651457i	−0.986815	+	0.161854i	$0.948253\pi$
$678$	4.16506e6	−	1.10825e7i	0.347974	−	0.925900i
$679$	−6.61920e6	−	2.40919e6i	−0.550974	−	0.200538i
$680$	147335.	−	123629.i	0.0122190	−	0.0102529i
$681$	−178983.	+	1.71672e7i	−0.0147892	+	1.41851i
$682$	8.35237e6	−	3.04002e6i	0.687621	−	0.250273i
$683$	5.56506e6	−	9.63896e6i	0.456476	−	0.790640i	−0.542296	−	0.840188i	$-0.682445\pi$
$683$	5.56506e6	−	9.63896e6i	0.456476	−	0.790640i	0.998772	+	0.0495481i	$0.0157781\pi$
$684$	−8.40844e6	−	1.52915e7i	−0.687187	−	1.24971i
$685$	−2.40715e6	−	4.16931e6i	−0.196009	−	0.339498i
$686$	−1.30170e7	−	1.09226e7i	−1.05609	−	0.886165i
$687$	−964085.	+	1.12492e6i	−0.0779334	+	0.0909350i
$688$	−113985.	−	646440.i	−0.00918070	−	0.0520663i
$689$	−3.68415e6	−	2.08939e7i	−0.295658	−	1.67676i
$690$	−3.85457e6	+	4.49763e6i	−0.308215	+	0.359634i
$691$	−5.40132e6	−	4.53224e6i	−0.430333	−	0.361092i	0.401744	−	0.915752i	$-0.368404\pi$
$691$	−5.40132e6	−	4.53224e6i	−0.430333	−	0.361092i	−0.832077	+	0.554660i	$0.812848\pi$
$692$	−5.48228e6	−	9.49559e6i	−0.435207	−	0.753801i
$693$	1.78698e6	−	2.95127e6i	0.141347	−	0.233440i
$694$	−5.43829e6	+	9.41939e6i	−0.428611	+	0.742376i
$695$	6.32528e6	−	2.30221e6i	0.496727	−	0.180794i
$696$	−171.838	+	16481.9i	−1.34461e−5	+	0.00128969i
$697$	1.02504e7	−	8.60112e6i	0.799207	−	0.670614i
$698$	2.00237e7	+	7.28802e6i	1.55563	+	0.566202i
$699$	5.90595e6	−	1.57147e7i	0.457190	−	1.21651i
$700$	−1.18707e6	+	6.73223e6i	−0.0915657	+	0.519295i
$701$	7.27260e6			0.558978			0.279489	−	0.960149i	$-0.409835\pi$
$701$	7.27260e6			0.558978			0.279489	+	0.960149i	$0.409835\pi$
$702$	−2.25866e7	+	1.21149e7i	−1.72985	+	0.927846i
$703$	−2.32598e7			−1.77508
$704$	−1.15847e6	+	6.57000e6i	−0.0880952	+	0.499613i
$705$	−8.69580e6	+	1.44000e6i	−0.658926	+	0.109116i
$706$	−3.41243e7	−	1.24202e7i	−2.57663	−	0.937817i
$707$	4.96944e6	−	4.16986e6i	0.373903	−	0.313742i
$708$	6.85230e6	+	4.05201e6i	0.513752	+	0.303800i
$709$	1.85022e7	−	6.73425e6i	1.38232	−	0.503122i	0.459437	−	0.888210i	$-0.348051\pi$
$709$	1.85022e7	−	6.73425e6i	1.38232	−	0.503122i	0.922880	+	0.385088i	$0.125829\pi$
$710$	−409929.	+	710017.i	−0.0305184	+	0.0528595i
$711$	−1.24616e7	−	4.83219e6i	−0.924483	−	0.358484i
$712$	523930.	+	907474.i	0.0387323	+	0.0670863i
$713$	1.05631e7	+	8.86351e6i	0.778159	+	0.652953i
$714$	−8.66383e6	−	1.62098e6i	−0.636011	−	0.118996i
$715$	−545541.	−	3.09392e6i	−0.0399082	−	0.226331i
$716$	−1.88087e6	−	1.06669e7i	−0.137112	−	0.777602i
$717$	6.51231e6	+	1.84900e7i	0.473083	+	1.34319i
$718$	6.50611e6	+	5.45927e6i	0.470988	+	0.395206i
$719$	3.97787e6	+	6.88987e6i	0.286965	+	0.497037i	0.973084	−	0.230452i	$-0.0740205\pi$
$719$	3.97787e6	+	6.88987e6i	0.286965	+	0.497037i	−0.686119	+	0.727489i	$0.740687\pi$
$720$	920138.	−	4.64931e6i	0.0661488	−	0.334239i
$721$	4.50653e6	−	7.80554e6i	0.322853	−	0.559197i
$722$	−1.65393e7	+	6.01983e6i	−1.18080	+	0.429775i
$723$	−8.77956e6	+	4.94757e6i	−0.624636	+	0.352003i
$724$	−5.78112e6	+	4.85093e6i	−0.409888	+	0.343937i
$725$	−260771.	−	94912.7i	−0.0184253	−	0.00670624i
$726$	1.00287e7	+	1.22080e7i	0.706158	+	0.859610i
$727$	1.10525e6	−	6.26818e6i	0.0775575	−	0.439850i	−0.921158	−	0.389188i	$-0.872756\pi$
$727$	1.10525e6	−	6.26818e6i	0.0775575	−	0.439850i	0.998716	−	0.0506624i	$-0.0161333\pi$
$728$	−655267.			−0.0458236
$729$	7.93723e6	−	1.19537e7i	0.553159	−	0.833076i
$730$	5.68467e6			0.394819
$731$	108064.	−	612864.i	0.00747979	−	0.0424200i
$732$	−2.95209e6	−	3.59359e6i	−0.203635	−	0.247886i
$733$	−2.40900e7	−	8.76803e6i	−1.65606	−	0.602757i	−0.666324	−	0.745662i	$-0.732133\pi$
$733$	−2.40900e7	−	8.76803e6i	−1.65606	−	0.602757i	−0.989736	+	0.142906i	$0.954355\pi$
$734$	−1.06027e7	+	8.89674e6i	−0.726402	+	0.609524i
$735$	3.00940e6	−	1.69589e6i	0.205476	−	0.115792i
$736$	−1.83637e7	+	6.68382e6i	−1.24958	+	0.454810i
$737$	5.77929e6	−	1.00100e7i	0.391927	−	0.678838i
$738$	−5.48351e6	+	2.77073e7i	−0.370611	+	1.87263i
$739$	3.31109e6	+	5.73498e6i	0.223028	+	0.386296i	0.955726	−	0.294258i	$-0.0950724\pi$
$739$	3.31109e6	+	5.73498e6i	0.223028	+	0.386296i	−0.732698	+	0.680554i	$0.761739\pi$
$740$	5.46508e6	+	4.58574e6i	0.366874	+	0.307844i
$741$	9.35566e6	+	2.65629e7i	0.625935	+	1.77717i
$742$	2.67431e6	+	1.51667e7i	0.178321	+	1.01131i
$743$	−62505.3	−	354485.i	−0.00415379	−	0.0235573i	0.982660	−	0.185414i	$-0.0593627\pi$
$743$	−62505.3	−	354485.i	−0.00415379	−	0.0235573i	−0.986814	+	0.161857i	$0.948252\pi$
$744$	928965.	+	173806.i	0.0615272	+	0.0115115i
$745$	−1.16825e6	−	980279.i	−0.0771162	−	0.0647081i
$746$	1.93915e7	+	3.35871e7i	1.27575	+	2.20966i
$747$	−2.16543e7	−	8.39683e6i	−1.41985	−	0.550572i
$748$	−2.92182e6	+	5.06074e6i	−0.190941	+	0.330720i
$749$	−8.98490e6	+	3.27024e6i	−0.585206	+	0.212997i
$750$	−1.26185e7	−	7.46175e6i	−0.819131	−	0.484381i
$751$	3.97959e6	−	3.33927e6i	0.257477	−	0.216049i	−0.504907	−	0.863174i	$-0.668473\pi$
$751$	3.97959e6	−	3.33927e6i	0.257477	−	0.216049i	0.762384	+	0.647125i	$0.224029\pi$
$752$	−2.62248e7	−	9.54505e6i	−1.69109	−	0.615508i
$753$	−721353.	+	119454.i	−0.0463618	+	0.00767736i
$754$	119441.	−	677385.i	0.00765114	−	0.0433918i
$755$	6.79881e6			0.434076
$756$	8.35937e6	−	4.48376e6i	0.531948	−	0.285323i
$757$	6.85707e6			0.434909			0.217455	−	0.976070i	$-0.430225\pi$
$757$	6.85707e6			0.434909			0.217455	+	0.976070i	$0.430225\pi$
$758$	2.36058e6	−	1.33875e7i	0.149227	−	0.846307i
$759$	2.44846e6	−	6.51494e6i	0.154273	−	0.410493i
$760$	419179.	+	152569.i	0.0263248	+	0.00958145i
$761$	8.70747e6	−	7.30643e6i	0.545042	−	0.457345i	−0.328216	−	0.944603i	$-0.606447\pi$
$761$	8.70747e6	−	7.30643e6i	0.545042	−	0.457345i	0.873258	+	0.487258i	$0.162003\pi$
$762$	61384.6	−	5.88772e6i	0.00382976	−	0.367333i
$763$	7.98417e6	−	2.90600e6i	0.496499	−	0.180711i
$764$	6.81613e6	−	1.18059e7i	0.422479	−	0.731754i
$765$	2.32730e6	−	3.84364e6i	0.143780	−	0.237459i
$766$	−1.97367e6	−	3.41849e6i	−0.121535	−	0.210505i
$767$	−9.84140e6	−	8.25792e6i	−0.604044	−	0.506853i
$768$	9.73006e6	−	1.13533e7i	0.595268	−	0.694576i
$769$	718369.	+	4.07407e6i	0.0438058	+	0.248435i	0.998845	−	0.0480437i	$-0.0152987\pi$
$769$	718369.	+	4.07407e6i	0.0438058	+	0.248435i	−0.955039	+	0.296479i	$0.904188\pi$
$770$	396005.	+	2.24586e6i	0.0240699	+	0.136507i
$771$	−6.17925e6	+	7.21013e6i	−0.374369	+	0.436825i
$772$	1.20643e7	+	1.01232e7i	0.728550	+	0.611326i
$773$	774280.	+	1.34109e6i	0.0466068	+	0.0807254i	0.888388	−	0.459094i	$-0.151826\pi$
$773$	774280.	+	1.34109e6i	0.0466068	+	0.0807254i	−0.841781	+	0.539819i	$0.818493\pi$
$774$	632937.	+	1.15105e6i	0.0379759	+	0.0690627i
$775$	−7.95577e6	+	1.37798e7i	−0.475804	+	0.824116i
$776$	−915176.	+	333097.i	−0.0545570	+	0.0198571i
$777$	131813.	−	1.26429e7i	0.00783260	−	0.751266i
$778$	1.37295e7	−	1.15204e7i	0.813215	−	0.682369i
$779$	2.91631e7	+	1.06145e7i	1.72183	+	0.626695i
$780$	3.03877e6	−	8.08566e6i	0.178839	−	0.475860i
$781$	167278.	−	948680.i	0.00981321	−	0.0556535i
$782$	−1.77807e7			−1.03975
$783$	120324.	+	365794.i	0.00701368	+	0.0213222i
$784$	1.09373e7			0.635505
$785$	−154270.	+	874907.i	−0.00893525	+	0.0506743i
$786$	1.50730e7	−	2.49604e6i	0.870248	−	0.144110i
$787$	2.21710e7	+	8.06958e6i	1.27599	+	0.464423i	0.889105	−	0.457704i	$-0.151328\pi$
$787$	2.21710e7	+	8.06958e6i	1.27599	+	0.464423i	0.386888	+	0.922127i	$0.373550\pi$
$788$	−9.48793e6	+	7.96132e6i	−0.544322	+	0.456740i
$789$	1.09649e7	+	6.48391e6i	0.627062	+	0.370804i
$790$	8.30183e6	−	3.02162e6i	0.473267	−	0.172255i
$791$	3.53568e6	−	6.12397e6i	0.200924	−	0.348010i
$792$	−73020.4	−	471393.i	−0.00413648	−	0.0267036i
$793$	3.75265e6	+	6.49977e6i	0.211912	+	0.367042i
$794$	−7.08708e6	−	5.94677e6i	−0.398948	−	0.334757i
$795$	−7.71712e6	−	1.44385e6i	−0.433049	−	0.0810222i
$796$	3.54139e6	+	2.00842e7i	0.198103	+	1.12350i
$797$	1.77651e6	+	1.00751e7i	0.0990652	+	0.561827i	0.993426	+	0.114480i	$0.0365201\pi$
$797$	1.77651e6	+	1.00751e7i	0.0990652	+	0.561827i	−0.894360	+	0.447347i	$0.852369\pi$
$798$	−6.79123e6	−	1.92819e7i	−0.377521	−	1.07187i
$799$	−2.02683e7	−	1.70071e7i	−1.12318	−	0.942461i
$800$	−1.12750e7	−	1.95289e7i	−0.622863	−	1.07883i
$801$	1.84209e7	+	1.61232e7i	1.01445	+	0.887914i
$802$	9.51760e6	−	1.64850e7i	0.522506	−	0.905007i
$803$	−6.27655e6	+	2.28448e6i	−0.343504	+	0.125025i
$804$	2.76863e7	−	1.56021e7i	1.51052	−	0.851224i
$805$	−2.71018e6	+	2.27411e6i	−0.147404	+	0.123686i
$806$	−3.70603e7	−	1.34889e7i	−2.00942	−	0.731371i
$807$	−1.05310e7	−	1.28195e7i	−0.569229	−	0.692925i
$808$	155748.	−	883293.i	0.00839257	−	0.0475966i
$809$	−2.67937e7			−1.43933			−0.719667	−	0.694319i	$-0.755706\pi$
$809$	−2.67937e7			−1.43933			−0.719667	+	0.694319i	$0.755706\pi$
$810$	1.25614e6	+	9.40099e6i	0.0672706	+	0.503456i
$811$	−3.77636e6			−0.201614			−0.100807	−	0.994906i	$-0.532142\pi$
$811$	−3.77636e6			−0.201614			−0.100807	+	0.994906i	$0.532142\pi$
$812$	−44205.7	+	250703.i	−0.00235281	+	0.0133435i
$813$	−1.31329e7	−	1.59867e7i	−0.696839	−	0.848266i
$814$	−1.54493e7	−	5.62308e6i	−0.817236	−	0.297450i
$815$	−1.56427e6	+	1.31258e6i	−0.0824933	+	0.0692201i
$816$	1.23943e7	−	6.98460e6i	0.651625	−	0.367212i
$817$	1.35631e6	−	493657.i	0.0710893	−	0.0258744i
$818$	−1.70699e7	+	2.95659e7i	−0.891965	+	1.54493i
$819$	−1.44913e7	+	4.93475e6i	−0.754915	+	0.257072i
$820$	−4.75942e6	−	8.24356e6i	−0.247184	−	0.428134i
$821$	1.97495e7	+	1.65718e7i	1.02258	+	0.858050i	0.989950	−	0.141418i	$-0.0451661\pi$
$821$	1.97495e7	+	1.65718e7i	1.02258	+	0.858050i	0.0326337	+	0.999467i	$0.489611\pi$
$822$	1.01337e7	+	2.87719e7i	0.523104	+	1.48521i
$823$	−2.15299e6	−	1.22102e7i	−0.110801	−	0.628383i	−0.988744	−	0.149618i	$-0.952196\pi$
$823$	−2.15299e6	−	1.22102e7i	−0.110801	−	0.628383i	0.877943	−	0.478765i	$-0.158915\pi$
$824$	−216392.	−	1.22722e6i	−0.0111026	−	0.0629659i
$825$	7.89409e6	+	1.47696e6i	0.403801	+	0.0755499i
$826$	7.14382e6	+	5.99438e6i	0.364318	+	0.305699i
$827$	638693.	+	1.10625e6i	0.0324734	+	0.0562456i	0.881805	−	0.471613i	$-0.156328\pi$
$827$	638693.	+	1.10625e6i	0.0324734	+	0.0562456i	−0.849332	+	0.527859i	$0.822995\pi$
$828$	1.49122e7	−	1.19920e7i	0.755900	−	0.607875i
$829$	7.89038e6	−	1.36665e7i	0.398760	−	0.690673i	−0.594813	−	0.803864i	$-0.702774\pi$
$829$	7.89038e6	−	1.36665e7i	0.398760	−	0.690673i	0.993573	+	0.113191i	$0.0361073\pi$
$830$	1.44260e7	−	5.25062e6i	0.726858	−	0.264555i
$831$	2.50137e7	+	1.47915e7i	1.25654	+	0.743035i
$832$	2.26760e7	−	1.90275e7i	1.13569	−	0.952955i
$833$	9.74385e6	+	3.54647e6i	0.486540	+	0.177086i
$834$	−4.20772e7	+	6.96785e6i	−2.09475	+	0.346883i
$835$	−178758.	+	1.01379e6i	−0.00887257	+	0.0503189i
$836$	−1.35533e7			−0.670701
$837$	2.18531e7	−	3.15219e6i	1.07820	−	0.155525i
$838$	−1.59912e7			−0.786629
$839$	−6.36209e6	+	3.60812e7i	−0.312029	+	1.76960i	0.276388	+	0.961046i	$0.410863\pi$
$839$	−6.36209e6	+	3.60812e7i	−0.312029	+	1.76960i	−0.588417	+	0.808558i	$0.700249\pi$
$840$	−85304.3	+	226980.i	−0.00417131	+	0.0110992i
$841$	1.92645e7	+	7.01169e6i	0.939219	+	0.341848i
$842$	1.29833e7	−	1.08942e7i	0.631108	−	0.529562i
$843$	−73707.0	+	7.06963e6i	−0.00357223	+	0.342632i
$844$	−1.37846e7	+	5.01719e6i	−0.666099	+	0.242440i
$845$	−3.27947e6	+	5.68022e6i	−0.158002	+	0.273667i
$846$	5.58364e7	+	1.16441e6i	2.68220	+	0.0559347i
$847$	4.71818e6	+	8.17214e6i	0.225978	+	0.391406i
$848$	−1.90425e7	−	1.59785e7i	−0.909355	−	0.763039i
$849$	1.59683e6	−	1.86323e6i	0.0760308	−	0.0887150i
$850$	−3.56281e6	−	2.02057e7i	−0.169139	−	0.959237i
$851$	−4.42901e6	−	2.51182e7i	−0.209644	−	1.18895i
$852$	1.72355e6	−	2.01108e6i	0.0813437	−	0.0949142i
$853$	4.67099e6	+	3.91942e6i	0.219804	+	0.184438i	0.746040	−	0.665901i	$-0.231953\pi$
$853$	4.67099e6	+	3.91942e6i	0.219804	+	0.184438i	−0.526236	+	0.850339i	$0.676397\pi$
$854$	−2.72403e6	−	4.71815e6i	−0.127811	−	0.221374i
$855$	1.04192e7	+	217282.i	0.487436	+	0.0101650i
$856$	−660993.	+	1.14487e6i	−0.0308327	+	0.0534039i
$857$	3.17840e7	−	1.15684e7i	1.47828	−	0.538050i	0.527945	−	0.849278i	$-0.322963\pi$
$857$	3.17840e7	−	1.15684e7i	1.47828	−	0.538050i	0.950335	+	0.311228i	$0.100740\pi$
$858$	−207527.	+	1.99050e7i	−0.00962399	+	0.923088i
$859$	3.51837e6	−	2.95227e6i	0.162689	−	0.136513i	−0.557809	−	0.829970i	$-0.688358\pi$
$859$	3.51837e6	−	2.95227e6i	0.162689	−	0.136513i	0.720498	+	0.693457i	$0.243913\pi$
$860$	−416002.	−	151412.i	−0.0191800	−	0.00698096i
$861$	−5.93479e6	+	1.57915e7i	−0.272833	+	0.725964i
$862$	6.05644e6	−	3.43478e7i	0.277619	−	1.57446i
$863$	−4.00578e7			−1.83088			−0.915441	−	0.402451i	$-0.868158\pi$
$863$	−4.00578e7			−1.83088			−0.915441	+	0.402451i	$0.868158\pi$
$864$	−1.16164e7	+	2.90549e7i	−0.529406	+	1.32414i
$865$	6.54791e6			0.297552
$866$	−5.63715e6	+	3.19699e7i	−0.255426	+	1.44859i
$867$	−8.52929e6	+	1.41242e6i	−0.385359	+	0.0638141i
$868$	1.37162e7	+	4.99228e6i	0.617922	+	0.224905i
$869$	−7.95192e6	+	6.67246e6i	−0.357209	+	0.299734i
$870$	−219093.	−	129557.i	−0.00981364	−	0.00580316i
$871$	−4.81936e7	+	1.75410e7i	−2.15251	+	0.783448i
$872$	587372.	−	1.01736e6i	0.0261591	−	0.0453088i
$873$	−1.77307e7	+	1.42586e7i	−0.787392	+	0.633200i
$874$	−2.06195e7	−	3.57141e7i	−0.913061	−	1.58147i
$875$	−6.70735e6	−	5.62813e6i	−0.296163	−	0.248510i
$876$	−1.80514e7	−	3.37736e6i	−0.794788	−	0.148702i
$877$	4.86976e6	+	2.76178e7i	0.213800	+	1.21252i	0.882976	+	0.469418i	$0.155536\pi$
$877$	4.86976e6	+	2.76178e7i	0.213800	+	1.21252i	−0.669176	+	0.743104i	$0.733353\pi$
$878$	7.17245e6	+	4.06770e7i	0.314001	+	1.78079i
$879$	−1.46516e7	−	4.15994e7i	−0.639607	−	1.81599i
$880$	−2.81976e6	−	2.36606e6i	−0.122746	−	0.102996i
$881$	4.53807e6	+	7.86017e6i	0.196984	+	0.341187i	0.947549	−	0.319610i	$-0.103552\pi$
$881$	4.53807e6	+	7.86017e6i	0.196984	+	0.341187i	−0.750565	+	0.660797i	$0.770219\pi$
$882$	−2.07190e7	+	7.05549e6i	−0.896806	+	0.305391i
$883$	−1.36576e7	+	2.36557e7i	−0.589486	+	1.02102i	0.404814	+	0.914399i	$0.367336\pi$
$883$	−1.36576e7	+	2.36557e7i	−0.589486	+	1.02102i	−0.994300	+	0.106620i	$0.965997\pi$
$884$	2.43651e7	−	8.86819e6i	1.04867	−	0.381684i
$885$	−4.14167e6	+	2.33397e6i	−0.177753	+	0.100170i
$886$	−1.53462e7	+	1.28770e7i	−0.656774	+	0.551099i
$887$	3.46203e7	+	1.26008e7i	1.47748	+	0.537759i	0.950120	−	0.311883i	$-0.100960\pi$
$887$	3.46203e7	+	1.26008e7i	1.47748	+	0.537759i	0.527360	+	0.849642i	$0.323182\pi$
$888$	−1.10964e6	−	1.35077e6i	−0.0472227	−	0.0574844i
$889$	610683.	−	3.46336e6i	0.0259156	−	0.146975i
$890$	−1.61814e7			−0.684763
$891$	−5.16487e6	−	9.87502e6i	−0.217954	−	0.416719i
$892$	−3.25654e7			−1.37039
$893$	1.06560e7	−	6.04331e7i	0.447162	−	2.53598i
$894$	6.13372e6	+	7.46661e6i	0.256673	+	0.312449i
$895$	6.07834e6	+	2.21234e6i	0.253646	+	0.0923195i
$896$	−1.22664e6	+	1.02927e6i	−0.0510443	+	0.0428312i
$897$	−2.69037e7	+	1.51611e7i	−1.11643	+	0.629144i
$898$	2.85780e7	−	1.04015e7i	1.18261	−	0.430434i
$899$	−296266.	+	513148.i	−0.0122260	+	0.0211760i
$900$	1.66155e7	+	1.45431e7i	0.683766	+	0.598480i
$901$	−1.17835e7	−	2.04097e7i	−0.483574	−	0.837575i
$902$	1.68042e7	+	1.41004e7i	0.687705	+	0.577053i
$903$	260641.	+	740022.i	0.0106371	+	0.0302013i
$904$	−169774.	−	962838.i	−0.00690957	−	0.0391861i
$905$	−782599.	−	4.43834e6i	−0.0317627	−	0.180135i
$906$	−4.23438e7	−	7.92239e6i	−1.71384	−	0.320653i
$907$	−2.97699e7	−	2.49799e7i	−1.20160	−	1.00826i	−0.999583	−	0.0288777i	$-0.990807\pi$
$907$	−2.97699e7	−	2.49799e7i	−1.20160	−	1.00826i	−0.202015	−	0.979382i	$-0.564749\pi$
$908$	1.83303e7	+	3.17490e7i	0.737827	+	1.27795i
$909$	−3.20759e6	−	2.07071e7i	−0.128757	−	0.831206i
$910$	5.05941e6	−	8.76316e6i	0.202533	−	0.350798i
$911$	2.87284e7	−	1.04563e7i	1.14688	−	0.417428i	0.302483	−	0.953155i	$-0.402184\pi$
$911$	2.87284e7	−	1.04563e7i	1.14688	−	0.417428i	0.844392	+	0.535726i	$0.179962\pi$
$912$	2.84024e7	+	1.67954e7i	1.13075	+	0.668655i
$913$	−1.38179e7	+	1.15946e7i	−0.548613	+	0.460341i
$914$	−3.48026e7	−	1.26671e7i	−1.37799	−	0.501547i
$915$	2.74001e6	−	453737.i	0.108193	−	0.0179164i
$916$	−549357.	+	3.11556e6i	−0.0216329	+	0.122687i
$917$	9.12534e6			0.358365
$918$	−1.89735e7	+	2.12267e7i	−0.743091	+	0.831335i
$919$	−4.08434e6			−0.159527			−0.0797633	−	0.996814i	$-0.525416\pi$
$919$	−4.08434e6			−0.159527			−0.0797633	+	0.996814i	$0.525416\pi$
$920$	−84940.3	+	481721.i	−0.00330860	+	0.0187640i
$921$	682728.	−	1.81663e6i	0.0265215	−	0.0705694i
$922$	5.33402e7	+	1.94142e7i	2.06646	+	0.752130i
$923$	−3.27433e6	+	2.74749e6i	−0.126508	+	0.106153i
$924$	76806.3	−	7.36690e6i	0.00295949	−	0.283860i
$925$	2.76564e7	−	1.00661e7i	1.06278	−	0.386819i
$926$	2.81848e7	−	4.88175e7i	1.08016	−	1.87089i
$927$	−1.40276e7	−	2.55106e7i	−0.536149	−	0.975036i
$928$	−419872.	−	727240.i	−0.0160047	−	0.0277209i
$929$	−1.82066e7	−	1.52772e7i	−0.692134	−	0.580769i	0.227390	−	0.973804i	$-0.426981\pi$
$929$	−1.82066e7	−	1.52772e7i	−0.692134	−	0.580769i	−0.919524	+	0.393035i	$0.871425\pi$
$930$	−9.49707e6	+	1.10815e7i	−0.360066	+	0.420136i
$931$	4.17615e6	+	2.36841e7i	0.157907	+	0.895536i
$932$	−6.22503e6	−	3.53039e7i	−0.234748	−	1.33132i
$933$	2.04509e7	−	2.38628e7i	0.769147	−	0.897463i
$934$	−3.85320e6	−	3.23322e6i	−0.144529	−	0.121274i
$935$	−1.74488e6	−	3.02222e6i	−0.0652733	−	0.113057i
$936$	−1.09627e6	+	1.81054e6i	−0.0409004	+	0.0675488i
$937$	6.24788e6	−	1.08216e7i	0.232479	−	0.402665i	−0.726058	−	0.687633i	$-0.758650\pi$
$937$	6.24788e6	−	1.08216e7i	0.232479	−	0.402665i	0.958537	+	0.284968i	$0.0919830\pi$
$938$	3.49835e7	−	1.27330e7i	1.29824	−	0.472522i
$939$	382352.	−	3.66734e7i	0.0141514	−	1.35733i
$940$	−1.44183e7	+	1.20984e7i	−0.532223	+	0.446588i
$941$	−6.24655e6	−	2.27356e6i	−0.229967	−	0.0837012i	0.224466	−	0.974482i	$-0.427936\pi$
$941$	−6.24655e6	−	2.27356e6i	−0.229967	−	0.0837012i	−0.454434	+	0.890781i	$0.650158\pi$
$942$	1.98030e6	−	5.26926e6i	0.0727118	−	0.193474i
$943$	−5.90947e6	+	3.35143e7i	−0.216406	+	1.22730i
$944$	−1.50524e7			−0.549762
$945$	−177149.	+	5.66212e6i	−0.00645296	+	0.206253i
$946$	1.02021e6			0.0370648
$947$	751796.	−	4.26365e6i	0.0272411	−	0.154492i	−0.968153	−	0.250359i	$-0.919451\pi$
$947$	751796.	−	4.26365e6i	0.0272411	−	0.154492i	0.995394	+	0.0958671i	$0.0305624\pi$
$948$	−2.81573e7	+	4.66276e6i	−1.01758	+	0.168509i
$949$	2.78497e7	+	1.01365e7i	1.00382	+	0.365360i
$950$	3.64533e7	−	3.05879e7i	1.31047	−	1.09962i
$951$	−7.52705e6	−	4.45101e6i	−0.269882	−	0.159591i
$952$	−683977.	+	248947.i	−0.0244596	+	0.00890257i
$953$	−2.03268e7	+	3.52070e7i	−0.724997	+	1.25573i	0.233978	+	0.972242i	$0.424826\pi$
$953$	−2.03268e7	+	3.52070e7i	−0.724997	+	1.25573i	−0.958975	+	0.283490i	$0.908508\pi$
$954$	4.63807e7	+	1.79849e7i	1.64993	+	0.639790i
$955$	4.07051e6	+	7.05033e6i	0.144424	+	0.250150i
$956$	3.20670e7	+	2.69074e7i	1.13479	+	0.952198i
$957$	293970.	+	55000.8i	0.0103758	+	0.00194128i
$958$	−3.99422e6	−	2.26524e7i	−0.140611	−	0.797443i
$959$	3.16378e6	+	1.79427e7i	0.111086	+	0.630001i
$960$	−3.63897e6	−	1.03319e7i	−0.127438	−	0.361827i
$961$	4.09468e6	+	3.43584e6i	0.143025	+	0.120012i
$962$	3.64747e7	+	6.31761e7i	1.27073	+	2.20097i
$963$	−5.99602e6	+	3.02969e7i	−0.208352	+	1.05277i
$964$	−1.07598e7	+	1.86365e7i	−0.372917	+	0.645911i
$965$	−8.83782e6	+	3.21671e6i	−0.305511	+	0.111197i
$966$	1.95293e7	−	1.10054e7i	0.673353	−	0.379456i
$967$	−2.24271e7	+	1.88186e7i	−0.771271	+	0.647173i	−0.941034	−	0.338312i	$-0.890144\pi$
$967$	−2.24271e7	+	1.88186e7i	−0.771271	+	0.647173i	0.169763	+	0.985485i	$0.445700\pi$
$968$	1.22600e6	+	446227.i	0.0420535	+	0.0153062i
$969$	1.98573e7	+	2.41724e7i	0.679377	+	0.827009i
$970$	2.61157e6	−	1.48109e7i	0.0891193	−	0.505420i
$971$	2.51690e6			0.0856677			0.0428338	−	0.999082i	$-0.486361\pi$
$971$	2.51690e6			0.0856677			0.0428338	+	0.999082i	$0.486361\pi$
$972$	1.59648e6	−	3.05988e7i	0.0541999	−	1.03881i
$973$	−2.54740e7			−0.862610
$974$	4.73767e6	−	2.68687e7i	0.160017	−	0.907504i
$975$	−2.26197e7	−	2.75351e7i	−0.762036	−	0.927630i
$976$	8.26333e6	+	3.00761e6i	0.277671	+	0.101064i
$977$	−2.23206e7	+	1.87292e7i	−0.748118	+	0.627746i	−0.935005	−	0.354636i	$-0.884605\pi$
$977$	−2.23206e7	+	1.87292e7i	−0.748118	+	0.627746i	0.186886	+	0.982382i	$0.440160\pi$
$978$	1.12720e7	−	6.35212e6i	0.376836	−	0.212359i
$979$	1.78662e7	−	6.50275e6i	0.595764	−	0.216840i
$980$	3.68818e6	−	6.38811e6i	0.122672	−	0.212475i
$981$	5.32819e6	−	2.69225e7i	0.176769	−	0.893187i
$982$	2.79891e7	+	4.84786e7i	0.926213	+	1.60425i
$983$	−3.82122e6	−	3.20638e6i	−0.126130	−	0.105836i	0.577541	−	0.816362i	$-0.304012\pi$
$983$	−3.82122e6	−	3.20638e6i	−0.126130	−	0.105836i	−0.703671	+	0.710526i	$0.748457\pi$
$984$	774850.	+	2.19998e6i	0.0255111	+	0.0724320i
$985$	−1.28440e6	−	7.28417e6i	−0.0421802	−	0.239216i
$986$	−132676.	−	752443.i	−0.00434610	−	0.0246480i
$987$	3.27881e7	+	6.13455e6i	1.07133	+	0.200442i
$988$	4.60678e7	+	3.86555e7i	1.50143	+	1.25985i
$989$	791359.	+	1.37067e6i	0.0257266	+	0.0445598i
$990$	6.86794e6	+	2.66316e6i	0.222709	+	0.0863595i
$991$	−5.96337e6	+	1.03289e7i	−0.192889	+	0.334094i	−0.946207	−	0.323563i	$-0.895119\pi$
$991$	−5.96337e6	+	1.03289e7i	−0.192889	+	0.334094i	0.753317	+	0.657657i	$0.228452\pi$
$992$	−4.52452e7	+	1.64679e7i	−1.45980	+	0.531324i
$993$	2.52281e7	+	1.49183e7i	0.811917	+	0.480115i
$994$	2.37682e6	−	1.99438e6i	0.0763009	−	0.0640240i
$995$	−1.14446e7	−	4.16549e6i	−0.366473	−	0.133385i
$996$	−4.89286e7	+	8.10241e6i	−1.56284	+	0.258801i
$997$	−350452.	+	1.98751e6i	−0.0111658	+	0.0633245i	−0.989882	−	0.141896i	$-0.954680\pi$
$997$	−350452.	+	1.98751e6i	−0.0111658	+	0.0633245i	0.978716	+	0.205221i	$0.0657912\pi$
$998$	−2.07504e7			−0.659477
$999$	−3.47125e7	−	2.15159e7i	−1.10045	−	0.682097i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.6.e.a.25.12	yes	84
3.2	odd	2		81.6.e.a.73.3		84
27.11	odd	18		729.6.a.e.1.8		42
27.13	even	9	inner	27.6.e.a.13.12	✓	84
27.14	odd	18		81.6.e.a.10.3		84
27.16	even	9		729.6.a.c.1.35		42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.6.e.a.13.12	✓	84	27.13	even	9	inner
27.6.e.a.25.12	yes	84	1.1	even	1	trivial
81.6.e.a.10.3		84	27.14	odd	18
81.6.e.a.73.3		84	3.2	odd	2
729.6.a.c.1.35		42	27.16	even	9
729.6.a.e.1.8		42	27.11	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40309 - 7.95730i) q^{2} +(-9.89503 - 12.0453i) q^{3} +(-31.2798 - 11.3849i) q^{4} +(15.2280 - 12.7778i) q^{5} +(-109.731 + 61.8372i) q^{6} +(-70.6933 + 25.7303i) q^{7} +(-5.20070 + 9.00788i) q^{8} +(-47.1768 + 238.376i) q^{9} +(-80.3108 - 139.102i) q^{10} +(144.573 + 121.311i) q^{11} +(172.380 + 489.428i) q^{12} +(-145.413 - 824.679i) q^{13} +(105.555 + 598.630i) q^{14} +(-304.594 - 56.9886i) q^{15} +(-751.604 - 630.671i) q^{16} +(-465.095 - 805.567i) q^{17} +(1830.64 + 709.863i) q^{18} +(1078.70 - 1868.37i) q^{19} +(-621.804 + 226.318i) q^{20} +(1009.44 + 596.918i) q^{21} +(1168.16 - 980.203i) q^{22} +(2223.04 + 809.122i) q^{23} +(159.963 - 26.4894i) q^{24} +(-474.031 + 2688.36i) q^{25} -6766.25 q^{26} +(3338.12 - 1790.49i) q^{27} +2504.21 q^{28} +(-17.6525 + 100.112i) q^{29} +(-880.847 + 2343.79i) q^{30} +(5477.24 + 1993.55i) q^{31} +(-6327.98 + 5309.80i) q^{32} +(30.6709 - 2941.80i) q^{33} +(-7062.71 + 2570.62i) q^{34} +(-747.743 + 1295.13i) q^{35} +(4189.58 - 6919.27i) q^{36} +(-5390.69 - 9336.95i) q^{37} +(-13353.7 - 11205.0i) q^{38} +(-8494.61 + 9911.76i) q^{39} +(35.9047 + 203.626i) q^{40} +(2497.97 + 14166.7i) q^{41} +(6166.19 - 7194.89i) q^{42} +(512.502 + 430.040i) q^{43} +(-3141.11 - 5440.55i) q^{44} +(2327.52 + 4232.82i) q^{45} +(9557.55 - 16554.2i) q^{46} +(26728.7 - 9728.44i) q^{47} +(-159.451 + 15293.8i) q^{48} +(-8539.41 + 7165.41i) q^{49} +(20727.0 + 7544.01i) q^{50} +(-5101.15 + 13573.3i) q^{51} +(-4840.41 + 27451.3i) q^{52} +25335.8 q^{53} +(-9563.76 - 29074.7i) q^{54} +3751.66 q^{55} +(135.880 - 770.613i) q^{56} +(-33178.8 + 5494.30i) q^{57} +(771.857 + 280.933i) q^{58} +(11752.3 - 9861.37i) q^{59} +(8878.84 + 5250.37i) q^{60} +(-8422.09 + 3065.39i) q^{61} +(23548.3 - 40786.9i) q^{62} +(-2798.41 - 18065.5i) q^{63} +(17674.6 + 30613.3i) q^{64} +(-12752.0 - 10700.2i) q^{65} +(-23365.8 - 4371.66i) q^{66} +(-10635.1 - 60314.5i) q^{67} +(5376.75 + 30493.1i) q^{68} +(-12251.0 - 34783.4i) q^{69} +(9256.58 + 7767.19i) q^{70} +(-2552.14 - 4420.44i) q^{71} +(-1901.91 - 1664.69i) q^{72} +(-17695.8 + 30650.1i) q^{73} +(-81860.5 + 29794.8i) q^{74} +(37072.6 - 20891.6i) q^{75} +(-55012.9 + 46161.3i) q^{76} +(-13341.7 - 4856.00i) q^{77} +(66952.2 + 81501.2i) q^{78} +(-9551.12 + 54167.1i) q^{79} -19504.0 q^{80} +(-54597.7 - 22491.7i) q^{81} +116233. q^{82} +(-16596.8 + 94125.4i) q^{83} +(-24779.3 - 30163.9i) q^{84} +(-17375.9 - 6324.30i) q^{85} +(4141.04 - 3474.75i) q^{86} +(1380.55 - 777.986i) q^{87} +(-1844.64 + 671.394i) q^{88} +(50371.1 - 87245.3i) q^{89} +(36947.5 - 12581.8i) q^{90} +(31499.0 + 54557.8i) q^{91} +(-60324.6 - 50618.4i) q^{92} +(-30184.6 - 85701.0i) q^{93} +(-39909.5 - 226338. i) q^{94} +(-7447.18 - 42235.0i) q^{95} +(126573. + 23681.5i) q^{96} +(71726.7 + 60185.8i) q^{97} +(45035.8 + 78004.3i) q^{98} +(-35738.3 + 28739.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 93 q^{5} - 126 q^{6} - 6 q^{7} + 573 q^{8} + 324 q^{9} - 3 q^{10} + 111 q^{11} - 2769 q^{12} - 6 q^{13} - 1641 q^{14} + 1989 q^{15} + 90 q^{16} + 3465 q^{17} - 99 q^{18}+ \cdots - 28323 q^{99}+O(q^{100}) \) 84 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 93 * q^5 - 126 * q^6 - 6 * q^7 + 573 * q^8 + 324 * q^9 - 3 * q^10 + 111 * q^11 - 2769 * q^12 - 6 * q^13 - 1641 * q^14 + 1989 * q^15 + 90 * q^16 + 3465 * q^17 - 99 * q^18 - 3 * q^19 + 9987 * q^20 + 5424 * q^21 - 2850 * q^22 - 7716 * q^23 - 18486 * q^24 + 4953 * q^25 - 7806 * q^26 - 8109 * q^27 - 12 * q^28 - 20418 * q^29 - 6453 * q^30 - 6657 * q^31 + 51192 * q^32 + 50634 * q^33 - 11394 * q^34 + 35868 * q^35 - 3600 * q^36 - 3 * q^37 - 44076 * q^38 - 13971 * q^39 + 12441 * q^40 - 79077 * q^41 - 64422 * q^42 - 9465 * q^43 + 110757 * q^44 + 92493 * q^45 - 3 * q^46 + 103557 * q^47 + 134049 * q^48 + 5484 * q^49 - 105513 * q^50 - 124866 * q^51 + 68625 * q^52 - 206406 * q^53 - 350946 * q^54 - 12 * q^55 - 147237 * q^56 + 67767 * q^57 - 9753 * q^58 + 116484 * q^59 + 241290 * q^60 - 70116 * q^61 + 246066 * q^62 + 135981 * q^63 - 86019 * q^64 - 19815 * q^65 - 32931 * q^66 + 48117 * q^67 - 48105 * q^68 + 25263 * q^69 + 270111 * q^70 + 279531 * q^71 + 441684 * q^72 - 27012 * q^73 + 233691 * q^74 + 18399 * q^75 - 125670 * q^76 - 345135 * q^77 - 520974 * q^78 - 216186 * q^79 - 924114 * q^80 - 428616 * q^81 - 12 * q^82 - 370401 * q^83 - 522390 * q^84 - 43731 * q^85 + 116682 * q^86 + 304173 * q^87 + 371418 * q^88 + 154827 * q^89 + 327366 * q^90 - 91002 * q^91 + 1279059 * q^92 + 890079 * q^93 + 11667 * q^94 + 1087671 * q^95 + 1165698 * q^96 - 420621 * q^97 + 463410 * q^98 - 28323 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more