LMFDB - Embedded newform 27.6.e.a.4.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,6,Mod(4,27)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$4.33036313495$
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			4.10
Character	$\chi$	$=$	27.4
Dual form			27.6.e.a.7.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.64663 + 1.69124i) q^{2} +(-11.1566 - 10.8872i) q^{3} +(-5.78253 - 4.85212i) q^{4} +(9.66519 - 54.8140i) q^{5} +(-33.4278 - 69.4570i) q^{6} +(60.6928 - 50.9273i) q^{7} +(-97.7806 - 169.361i) q^{8} +(5.93943 + 242.927i) q^{9} +O(q^{10})$	\(q+(4.64663 + 1.69124i) q^{2} +(-11.1566 - 10.8872i) q^{3} +(-5.78253 - 4.85212i) q^{4} +(9.66519 - 54.8140i) q^{5} +(-33.4278 - 69.4570i) q^{6} +(60.6928 - 50.9273i) q^{7} +(-97.7806 - 169.361i) q^{8} +(5.93943 + 242.927i) q^{9} +(137.614 - 238.354i) q^{10} +(30.3601 + 172.181i) q^{11} +(11.6876 + 117.088i) q^{12} +(162.354 - 59.0920i) q^{13} +(368.147 - 133.995i) q^{14} +(-704.600 + 506.312i) q^{15} +(-125.976 - 714.444i) q^{16} +(263.395 - 456.213i) q^{17} +(-383.249 + 1138.84i) q^{18} +(-343.270 - 594.561i) q^{19} +(-321.853 + 270.067i) q^{20} +(-1231.58 - 92.5967i) q^{21} +(-150.126 + 851.406i) q^{22} +(3501.96 + 2938.49i) q^{23} +(-752.961 + 2954.05i) q^{24} +(25.3785 + 9.23702i) q^{25} +854.338 q^{26} +(2578.53 - 2774.91i) q^{27} -598.063 q^{28} +(4147.67 + 1509.63i) q^{29} +(-4130.31 + 1161.00i) q^{30} +(-8175.51 - 6860.06i) q^{31} +(-463.753 + 2630.08i) q^{32} +(1535.84 - 2251.49i) q^{33} +(1995.46 - 1674.39i) q^{34} +(-2204.92 - 3819.04i) q^{35} +(1144.37 - 1433.55i) q^{36} +(7714.90 - 13362.6i) q^{37} +(-589.506 - 3343.25i) q^{38} +(-2454.66 - 1108.31i) q^{39} +(-10228.4 + 3722.84i) q^{40} +(5165.96 - 1880.26i) q^{41} +(-5566.09 - 2513.15i) q^{42} +(1242.19 + 7044.79i) q^{43} +(659.882 - 1142.95i) q^{44} +(13373.2 + 2022.38i) q^{45} +(11302.6 + 19576.7i) q^{46} +(-1340.96 + 1125.20i) q^{47} +(-6372.81 + 9342.29i) q^{48} +(-1828.48 + 10369.8i) q^{49} +(102.303 + 85.8421i) q^{50} +(-7905.45 + 2222.16i) q^{51} +(-1225.54 - 446.059i) q^{52} -23678.4 q^{53} +(16674.5 - 8533.07i) q^{54} +9731.35 q^{55} +(-14559.7 - 5299.29i) q^{56} +(-2643.36 + 10370.5i) q^{57} +(16719.6 + 14029.4i) q^{58} +(-6413.00 + 36369.9i) q^{59} +(6531.05 + 491.039i) q^{60} +(33541.7 - 28144.8i) q^{61} +(-26386.6 - 45702.9i) q^{62} +(12732.1 + 14441.5i) q^{63} +(-18210.4 + 31541.4i) q^{64} +(-1669.89 - 9470.42i) q^{65} +(10944.3 - 7864.35i) q^{66} +(-39499.8 + 14376.8i) q^{67} +(-3736.68 + 1360.04i) q^{68} +(-7078.12 - 70910.0i) q^{69} +(-3786.57 - 21474.7i) q^{70} +(-12558.4 + 21751.8i) q^{71} +(40561.7 - 24759.5i) q^{72} +(20511.6 + 35527.1i) q^{73} +(58447.6 - 49043.4i) q^{74} +(-182.573 - 379.354i) q^{75} +(-899.911 + 5103.65i) q^{76} +(10611.3 + 8903.97i) q^{77} +(-9531.51 - 9301.31i) q^{78} +(-66682.8 - 24270.6i) q^{79} -40379.1 q^{80} +(-58978.4 + 2885.70i) q^{81} +27184.3 q^{82} +(59133.9 + 21523.0i) q^{83} +(6672.35 + 6511.21i) q^{84} +(-22461.1 - 18847.1i) q^{85} +(-6142.42 + 34835.4i) q^{86} +(-29838.3 - 61998.7i) q^{87} +(26192.1 - 21977.7i) q^{88} +(35695.2 + 61825.9i) q^{89} +(58720.2 + 32014.5i) q^{90} +(6844.32 - 11854.7i) q^{91} +(-5992.27 - 33983.8i) q^{92} +(16524.2 + 165543. i) q^{93} +(-8133.90 + 2960.50i) q^{94} +(-35908.0 + 13069.5i) q^{95} +(33808.0 - 24293.7i) q^{96} +(-6073.03 - 34441.8i) q^{97} +(-26034.1 + 45092.3i) q^{98} +(-41647.1 + 8397.95i) 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}+O(q^{10}) $ 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	\( 84 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 93 q^{5} - 126 q^{6} - 6 q^{7} + 573 q^{8} + 324 q^{9} - 3 q^{10} + 111 q^{11} - 2769 q^{12} - 6 q^{13} - 1641 q^{14} + 1989 q^{15} + 90 q^{16} + 3465 q^{17} - 99 q^{18} - 3 q^{19} + 9987 q^{20} + 5424 q^{21} - 2850 q^{22} - 7716 q^{23} - 18486 q^{24} + 4953 q^{25} - 7806 q^{26} - 8109 q^{27} - 12 q^{28} - 20418 q^{29} - 6453 q^{30} - 6657 q^{31} + 51192 q^{32} + 50634 q^{33} - 11394 q^{34} + 35868 q^{35} - 3600 q^{36} - 3 q^{37} - 44076 q^{38} - 13971 q^{39} + 12441 q^{40} - 79077 q^{41} - 64422 q^{42} - 9465 q^{43} + 110757 q^{44} + 92493 q^{45} - 3 q^{46} + 103557 q^{47} + 134049 q^{48} + 5484 q^{49} - 105513 q^{50} - 124866 q^{51} + 68625 q^{52} - 206406 q^{53} - 350946 q^{54} - 12 q^{55} - 147237 q^{56} + 67767 q^{57} - 9753 q^{58} + 116484 q^{59} + 241290 q^{60} - 70116 q^{61} + 246066 q^{62} + 135981 q^{63} - 86019 q^{64} - 19815 q^{65} - 32931 q^{66} + 48117 q^{67} - 48105 q^{68} + 25263 q^{69} + 270111 q^{70} + 279531 q^{71} + 441684 q^{72} - 27012 q^{73} + 233691 q^{74} + 18399 q^{75} - 125670 q^{76} - 345135 q^{77} - 520974 q^{78} - 216186 q^{79} - 924114 q^{80} - 428616 q^{81} - 12 q^{82} - 370401 q^{83} - 522390 q^{84} - 43731 q^{85} + 116682 q^{86} + 304173 q^{87} + 371418 q^{88} + 154827 q^{89} + 327366 q^{90} - 91002 q^{91} + 1279059 q^{92} + 890079 q^{93} + 11667 q^{94} + 1087671 q^{95} + 1165698 q^{96} - 420621 q^{97} + 463410 q^{98} - 28323 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	4.64663	+	1.69124i	0.821416	+	0.298971i	0.718331	−	0.695702i	$-0.244906\pi$
$2$	4.64663	+	1.69124i	0.821416	+	0.298971i	0.103085	+	0.994673i	$0.467129\pi$
$3$	−11.1566	−	10.8872i	−0.715696	−	0.698412i
$3$	−11.1566	−	10.8872i	−0.715696	−	0.698412i
$4$	−5.78253	−	4.85212i	−0.180704	−	0.151629i
$5$	9.66519	−	54.8140i	0.172896	−	0.980543i	−0.767648	−	0.640872i	$-0.778573\pi$
$5$	9.66519	−	54.8140i	0.172896	−	0.980543i	0.940544	−	0.339671i	$-0.110316\pi$
$6$	−33.4278	−	69.4570i	−0.379079	−	0.787659i
$7$	60.6928	−	50.9273i	0.468158	−	0.392831i	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	60.6928	−	50.9273i	0.468158	−	0.392831i	0.846122	+	0.532989i	$0.178931\pi$
$8$	−97.7806	−	169.361i	−0.540167	−	0.935596i
$9$	5.93943	+	242.927i	0.0244421	+	0.999701i
$10$	137.614	−	238.354i	0.435174	−	0.753743i
$11$	30.3601	+	172.181i	0.0756522	+	0.429045i	0.998985	+	0.0450441i	$0.0143428\pi$
$11$	30.3601	+	172.181i	0.0756522	+	0.429045i	−0.923333	+	0.384001i	$0.874546\pi$
$12$	11.6876	+	117.088i	0.0234299	+	0.234726i
$13$	162.354	−	59.0920i	0.266443	−	0.0969774i	−0.205344	−	0.978690i	$-0.565831\pi$
$13$	162.354	−	59.0920i	0.266443	−	0.0969774i	0.471787	+	0.881712i	$0.343609\pi$
$14$	368.147	−	133.995i	0.501997	−	0.182712i
$15$	−704.600	+	506.312i	−0.808564	+	0.581018i
$16$	−125.976	−	714.444i	−0.123023	−	0.697699i
$17$	263.395	−	456.213i	0.221047	−	0.382865i	−0.734079	−	0.679064i	$-0.762386\pi$
$17$	263.395	−	456.213i	0.221047	−	0.382865i	0.955126	+	0.296199i	$0.0957193\pi$
$18$	−383.249	+	1138.84i	−0.278804	+	0.828478i
$19$	−343.270	−	594.561i	−0.218148	−	0.377844i	0.736094	−	0.676880i	$-0.236668\pi$
$19$	−343.270	−	594.561i	−0.218148	−	0.377844i	−0.954242	+	0.299036i	$0.903335\pi$
$20$	−321.853	+	270.067i	−0.179921	+	0.150972i
$21$	−1231.58	−	92.5967i	−0.609416	−	0.0458192i
$22$	−150.126	+	851.406i	−0.0661300	+	0.375042i
$23$	3501.96	+	2938.49i	1.38036	+	1.15826i	0.969080	+	0.246748i	$0.0793620\pi$
$23$	3501.96	+	2938.49i	1.38036	+	1.15826i	0.411278	+	0.911510i	$0.365082\pi$
$24$	−752.961	+	2954.05i	−0.266836	+	1.04686i
$25$	25.3785	+	9.23702i	0.00812112	+	0.00295585i
$26$	854.338			0.247854
$27$	2578.53	−	2774.91i	0.680710	−	0.732553i
$28$	−598.063			−0.144162
$29$	4147.67	+	1509.63i	0.915818	+	0.333330i	0.756573	−	0.653909i	$-0.226872\pi$
$29$	4147.67	+	1509.63i	0.915818	+	0.333330i	0.159245	+	0.987239i	$0.449094\pi$
$30$	−4130.31	+	1161.00i	−0.837875	+	0.235520i
$31$	−8175.51	−	6860.06i	−1.52795	−	1.28211i	−0.811168	−	0.584814i	$-0.801168\pi$
$31$	−8175.51	−	6860.06i	−1.52795	−	1.28211i	−0.716787	−	0.697292i	$-0.754388\pi$
$32$	−463.753	+	2630.08i	−0.0800594	+	0.454039i
$33$	1535.84	−	2251.49i	0.245506	−	0.359902i
$34$	1995.46	−	1674.39i	0.296037	−	0.248404i
$35$	−2204.92	−	3819.04i	−0.304245	−	0.526968i
$36$	1144.37	−	1433.55i	0.147167	−	0.184356i
$37$	7714.90	−	13362.6i	0.926459	−	1.60467i	0.137261	−	0.990535i	$-0.456170\pi$
$37$	7714.90	−	13362.6i	0.926459	−	1.60467i	0.789198	−	0.614139i	$-0.210497\pi$
$38$	−589.506	−	3343.25i	−0.0662261	−	0.375587i
$39$	−2454.66	−	1108.31i	−0.258423	−	0.116681i
$40$	−10228.4	+	3722.84i	−1.01079	+	0.367896i
$41$	5165.96	−	1880.26i	0.479945	−	0.174686i	−0.0907070	−	0.995878i	$-0.528913\pi$
$41$	5165.96	−	1880.26i	0.479945	−	0.174686i	0.570652	+	0.821192i	$0.306690\pi$
$42$	−5566.09	−	2513.15i	−0.486886	−	0.219834i
$43$	1242.19	+	7044.79i	0.102451	+	0.581028i	0.992208	+	0.124593i	$0.0397627\pi$
$43$	1242.19	+	7044.79i	0.102451	+	0.581028i	−0.889757	+	0.456435i	$0.849126\pi$
$44$	659.882	−	1142.95i	0.0513848	−	0.0890011i
$45$	13373.2	+	2022.38i	0.984476	+	0.148878i
$46$	11302.6	+	19576.7i	0.787563	+	1.36410i
$47$	−1340.96	+	1125.20i	−0.0885462	+	0.0742991i	−0.685986	−	0.727614i	$-0.740629\pi$
$47$	−1340.96	+	1125.20i	−0.0885462	+	0.0742991i	0.597440	+	0.801914i	$0.296185\pi$
$48$	−6372.81	+	9342.29i	−0.399234	+	0.585262i
$49$	−1828.48	+	10369.8i	−0.108793	+	0.616994i
$50$	102.303	+	85.8421i	0.00578711	+	0.00485596i
$51$	−7905.45	+	2222.16i	−0.425600	+	0.119633i
$52$	−1225.54	−	446.059i	−0.0628519	−	0.0228762i
$53$	−23678.4			−1.15788			−0.578939	−	0.815371i	$-0.696533\pi$
$53$	−23678.4			−1.15788			−0.578939	+	0.815371i	$0.696533\pi$
$54$	16674.5	−	8533.07i	0.778158	−	0.398218i
$55$	9731.35			0.433777
$56$	−14559.7	−	5299.29i	−0.620414	−	0.225812i
$57$	−2643.36	+	10370.5i	−0.107763	+	0.422779i
$58$	16719.6	+	14029.4i	0.652611	+	0.547606i
$59$	−6413.00	+	36369.9i	−0.239845	+	1.36023i	0.592320	+	0.805703i	$0.298212\pi$
$59$	−6413.00	+	36369.9i	−0.239845	+	1.36023i	−0.832165	+	0.554527i	$0.812899\pi$
$60$	6531.05	+	491.039i	0.234210	+	0.0176091i
$61$	33541.7	−	28144.8i	1.15414	−	0.968442i	0.154336	−	0.988018i	$-0.450676\pi$
$61$	33541.7	−	28144.8i	1.15414	−	0.968442i	0.999808	+	0.0195766i	$0.00623183\pi$
$62$	−26386.6	−	45702.9i	−0.871774	−	1.50996i
$63$	12732.1	+	14441.5i	0.404156	+	0.458416i
$64$	−18210.4	+	31541.4i	−0.555738	+	0.962566i
$65$	−1669.89	−	9470.42i	−0.0490235	−	0.278026i
$66$	10944.3	−	7864.35i	0.309263	−	0.222230i
$67$	−39499.8	+	14376.8i	−1.07500	+	0.391268i	−0.818044	−	0.575155i	$-0.804942\pi$
$67$	−39499.8	+	14376.8i	−1.07500	+	0.391268i	−0.256955	+	0.966423i	$0.582719\pi$
$68$	−3736.68	+	1360.04i	−0.0979973	+	0.0356681i
$69$	−7078.12	−	70910.0i	−0.178976	−	1.79302i
$70$	−3786.57	−	21474.7i	−0.0923636	−	0.523820i
$71$	−12558.4	+	21751.8i	−0.295657	+	0.512093i	−0.975137	−	0.221601i	$-0.928872\pi$
$71$	−12558.4	+	21751.8i	−0.295657	+	0.512093i	0.679481	+	0.733693i	$0.262205\pi$
$72$	40561.7	−	24759.5i	0.922114	−	0.562873i
$73$	20511.6	+	35527.1i	0.450497	+	0.780283i	0.998417	−	0.0562477i	$-0.0179136\pi$
$73$	20511.6	+	35527.1i	0.450497	+	0.780283i	−0.547920	+	0.836531i	$0.684580\pi$
$74$	58447.6	−	49043.4i	1.24076	−	1.04112i
$75$	−182.573	−	379.354i	−0.00374786	−	0.00778738i
$76$	−899.911	+	5103.65i	−0.0178717	+	0.101355i
$77$	10611.3	+	8903.97i	0.203959	+	0.171142i
$78$	−9531.51	−	9301.31i	−0.177388	−	0.173104i
$79$	−66682.8	−	24270.6i	−1.20212	−	0.437534i	−0.338153	−	0.941091i	$-0.609802\pi$
$79$	−66682.8	−	24270.6i	−1.20212	−	0.437534i	−0.863962	+	0.503557i	$0.832024\pi$
$80$	−40379.1			−0.705395
$81$	−58978.4	+	2885.70i	−0.998805	+	0.0488696i
$82$	27184.3			0.446461
$83$	59133.9	+	21523.0i	0.942196	+	0.342931i	0.767032	−	0.641608i	$-0.221732\pi$
$83$	59133.9	+	21523.0i	0.942196	+	0.342931i	0.175163	+	0.984539i	$0.443955\pi$
$84$	6672.35	+	6511.21i	0.103176	+	0.100685i
$85$	−22461.1	−	18847.1i	−0.337197	−	0.282942i
$86$	−6142.42	+	34835.4i	−0.0895557	+	0.507896i
$87$	−29838.3	−	61998.7i	−0.422646	−	0.878181i
$88$	26192.1	−	21977.7i	0.360548	−	0.302536i
$89$	35695.2	+	61825.9i	0.477678	+	0.827362i	0.999673	−	0.0255865i	$-0.00814533\pi$
$89$	35695.2	+	61825.9i	0.477678	+	0.827362i	−0.521995	+	0.852949i	$0.674812\pi$
$90$	58720.2	+	32014.5i	0.764154	+	0.416620i
$91$	6844.32	−	11854.7i	0.0866417	−	0.150068i
$92$	−5992.27	−	33983.8i	−0.0738111	−	0.418604i
$93$	16524.2	+	165543.i	0.198113	+	1.98474i
$94$	−8133.90	+	2960.50i	−0.0949466	+	0.0345577i
$95$	−35908.0	+	13069.5i	−0.408209	+	0.148576i
$96$	33808.0	−	24293.7i	0.374404	−	0.269040i
$97$	−6073.03	−	34441.8i	−0.0655354	−	0.371670i	−0.999883	−	0.0153063i	$-0.995128\pi$
$97$	−6073.03	−	34441.8i	−0.0655354	−	0.371670i	0.934347	−	0.356363i	$-0.115983\pi$
$98$	−26034.1	+	45092.3i	−0.273827	+	0.474283i
$99$	−41647.1	+	8397.95i	−0.427067	+	0.0861163i
$100$	−101.933	−	176.553i	−0.00101933	−	0.00176553i
$101$	76822.5	−	64461.7i	0.749351	−	0.628780i	−0.185981	−	0.982553i	$-0.559546\pi$
$101$	76822.5	−	64461.7i	0.749351	−	0.628780i	0.935331	+	0.353774i	$0.115102\pi$
$102$	−40491.9	−	3044.40i	−0.385361	−	0.0289735i
$103$	−2635.34	+	14945.8i	−0.0244762	+	0.138811i	−0.994597	−	0.103811i	$-0.966896\pi$
$103$	−2635.34	+	14945.8i	−0.0244762	+	0.138811i	0.970121	+	0.242622i	$0.0780075\pi$
$104$	−25883.0	−	21718.4i	−0.234656	−	0.196899i
$105$	−16979.0	+	66612.8i	−0.150293	+	0.589637i
$106$	−110025.	−	40045.8i	−0.951100	−	0.346172i
$107$	78739.5			0.664864			0.332432	−	0.943127i	$-0.392131\pi$
$107$	78739.5			0.664864			0.332432	+	0.943127i	$0.392131\pi$
$108$	−28374.6	+	3534.67i	−0.234083	+	0.0291601i
$109$	105803.			0.852964			0.426482	−	0.904496i	$-0.359753\pi$
$109$	105803.			0.852964			0.426482	+	0.904496i	$0.359753\pi$
$110$	45218.0	+	16458.0i	0.356311	+	0.129687i
$111$	−231553.	+	65087.8i	−1.78379	+	0.501409i
$112$	−44030.5	−	36946.0i	−0.331672	−	0.278306i
$113$	−19731.4	+	111902.i	−0.145365	+	0.824408i	0.821708	+	0.569909i	$0.193022\pi$
$113$	−19731.4	+	111902.i	−0.145365	+	0.824408i	−0.967073	+	0.254499i	$0.918089\pi$
$114$	−29821.7	+	43717.4i	−0.214916	+	0.315059i
$115$	194918.	−	163555.i	1.37438	−	1.15324i
$116$	−16659.1	−	28854.4i	−0.114949	−	0.199098i
$117$	15319.4	+	39089.3i	0.103461	+	0.263993i
$118$	−91308.9	+	158152.i	−0.603682	+	1.04561i
$119$	−7247.53	−	41102.8i	−0.0469162	−	0.266075i
$120$	154646.	+	69824.3i	0.980358	+	0.442643i
$121$	122614.	−	44627.8i	0.761336	−	0.277104i
$122$	203455.	−	74051.6i	1.23757	−	0.450438i
$123$	−78105.2	−	35265.4i	−0.465497	−	0.210177i
$124$	13989.3	+	79337.0i	0.0817034	+	0.463363i
$125$	87719.8	−	151935.i	0.502137	−	0.869727i
$126$	34737.5	+	88637.1i	0.194927	+	0.497381i
$127$	−91094.0	−	157780.i	−0.501165	−	0.868043i	−0.999999	−	0.00134563i	$-0.999572\pi$
$127$	−91094.0	−	157780.i	−0.501165	−	0.868043i	0.498834	−	0.866697i	$-0.333762\pi$
$128$	−72494.2	+	60829.9i	−0.391091	+	0.328165i
$129$	62839.2	−	92119.8i	0.332473	−	0.487393i
$130$	8257.34	−	46829.7i	0.0428530	−	0.243032i
$131$	−88312.2	−	74102.7i	−0.449617	−	0.377273i	0.389677	−	0.920952i	$-0.372587\pi$
$131$	−88312.2	−	74102.7i	−0.449617	−	0.377273i	−0.839294	+	0.543678i	$0.817031\pi$
$132$	−19805.5	+	5567.19i	−0.0989353	+	0.0278100i
$133$	−51113.4	−	18603.7i	−0.250556	−	0.0911951i
$134$	−207856.			−0.999999
$135$	−127182.	−	168159.i	−0.600608	−	0.794121i
$136$	−103020.			−0.477609
$137$	−106354.	−	38709.6i	−0.484118	−	0.176205i	0.0884191	−	0.996083i	$-0.471819\pi$
$137$	−106354.	−	38709.6i	−0.484118	−	0.176205i	−0.572537	+	0.819879i	$0.694041\pi$
$138$	87036.1	−	341463.i	0.389047	−	1.52632i
$139$	−26623.6	−	22339.8i	−0.116877	−	0.0980715i	0.582476	−	0.812848i	$-0.302084\pi$
$139$	−26623.6	−	22339.8i	−0.116877	−	0.0980715i	−0.699353	+	0.714776i	$0.746528\pi$
$140$	−5780.39	+	32782.2i	−0.0249251	+	0.141357i
$141$	27210.7	+	2045.85i	0.115264	+	0.00866614i
$142$	−95141.5	+	79833.2i	−0.395958	+	0.332248i
$143$	15103.6	+	26160.2i	0.0617647	+	0.106980i
$144$	172810.	−	34846.4i	0.694484	−	0.140040i
$145$	122837.	−	212760.i	0.485186	−	0.840367i
$146$	35225.0	+	199771.i	0.136763	+	0.775622i
$147$	133298.	−	95785.0i	0.508779	−	0.365598i
$148$	−109449.	+	39836.0i	−0.410729	+	0.149493i
$149$	299028.	−	108837.i	1.10343	−	0.401616i	0.274852	−	0.961487i	$-0.411371\pi$
$149$	299028.	−	108837.i	1.10343	−	0.401616i	0.828580	+	0.559870i	$0.189149\pi$
$150$	−206.773	−	2071.49i	−0.000750352	−	0.00751718i
$151$	93234.6	+	528760.i	0.332763	+	1.88719i	0.448290	+	0.893888i	$0.352033\pi$
$151$	93234.6	+	528760.i	0.332763	+	1.88719i	−0.115527	+	0.993304i	$0.536856\pi$
$152$	−67130.3	+	116273.i	−0.235673	+	0.408197i
$153$	112391.	+	61276.1i	0.388153	+	0.211623i
$154$	34248.2	+	59319.7i	0.116369	+	0.201557i
$155$	−455046.	+	381829.i	−1.52134	+	1.27655i
$156$	8816.52	+	18319.1i	0.0290059	+	0.0602689i
$157$	−55821.4	+	316579.i	−0.180739	+	1.02502i	0.750570	+	0.660791i	$0.229779\pi$
$157$	−55821.4	+	316579.i	−0.180739	+	1.02502i	−0.931309	+	0.364230i	$0.881332\pi$
$158$	−268803.	−	225553.i	−0.856627	−	0.718795i
$159$	264171.	+	257791.i	0.828689	+	0.808676i
$160$	139683.	+	50840.4i	0.431363	+	0.157003i
$161$	362193.			1.10122
$162$	−278931.	−	86337.6i	−0.835045	−	0.258471i
$163$	−107839.			−0.317911			−0.158956	−	0.987286i	$-0.550813\pi$
$163$	−107839.			−0.317911			−0.158956	+	0.987286i	$0.550813\pi$
$164$	−38995.5	−	14193.2i	−0.113215	−	0.0412070i
$165$	−108569.	−	105947.i	−0.310452	−	0.302955i
$166$	238373.	+	200019.i	0.671408	+	0.563378i
$167$	−58111.5	+	329567.i	−0.161239	+	0.914434i	0.791618	+	0.611016i	$0.209239\pi$
$167$	−58111.5	+	329567.i	−0.161239	+	0.914434i	−0.952858	+	0.303418i	$0.901872\pi$
$168$	104742.	+	217636.i	0.286318	+	0.594918i
$169$	−261560.	+	219475.i	−0.704457	+	0.591110i
$170$	−72493.5	−	125562.i	−0.192388	−	0.333225i
$171$	142396.	−	86921.0i	0.372399	−	0.227318i
$172$	26999.2	−	46763.9i	0.0695872	−	0.120529i
$173$	−8344.79	−	47325.7i	−0.0211983	−	0.120221i	0.972372	−	0.233435i	$-0.0749966\pi$
$173$	−8344.79	−	47325.7i	−0.0211983	−	0.120221i	−0.993571	+	0.113214i	$0.963886\pi$
$174$	−33793.3	−	338549.i	−0.0846171	−	0.847711i
$175$	2010.71	−	731.838i	0.00496311	−	0.00180643i
$176$	119189.	−	43381.2i	0.290037	−	0.105565i
$177$	467513.	−	335945.i	1.12166	−	0.806001i
$178$	61300.3	+	347651.i	0.145015	+	0.822420i
$179$	174243.	−	301798.i	0.406465	−	0.704019i	−0.588025	−	0.808842i	$-0.700094\pi$
$179$	174243.	−	301798.i	0.406465	−	0.704019i	0.994491	+	0.104824i	$0.0334278\pi$
$180$	−67518.3	−	76582.9i	−0.155325	−	0.176178i
$181$	−63151.2	−	109381.i	−0.143280	−	0.248168i	0.785450	−	0.618925i	$-0.212432\pi$
$181$	−63151.2	−	109381.i	−0.143280	−	0.248168i	−0.928730	+	0.370757i	$0.879098\pi$
$182$	51852.2	−	43509.1i	0.116035	−	0.0973648i
$183$	−680628.	−	51173.3i	−1.50239	−	0.112958i
$184$	155242.	−	880424.i	0.338038	−	1.91711i
$185$	−657892.	−	552037.i	−1.41327	−	1.18587i
$186$	−203190.	+	797164.i	−0.430646	+	1.68953i
$187$	86547.7	+	31500.8i	0.180989	+	0.0658745i
$188$	13213.7			0.0272665
$189$	15179.4	−	299734.i	0.0309101	−	0.610354i
$190$	−188955.			−0.379729
$191$	−611053.	−	222405.i	−1.21198	−	0.441125i	−0.344590	−	0.938753i	$-0.611982\pi$
$191$	−611053.	−	222405.i	−1.21198	−	0.441125i	−0.867390	+	0.497629i	$0.834204\pi$
$192$	546562.	−	153635.i	1.07001	−	0.300771i
$193$	112492.	+	94392.1i	0.217385	+	0.182407i	0.744977	−	0.667090i	$-0.232461\pi$
$193$	112492.	+	94392.1i	0.217385	+	0.182407i	−0.527592	+	0.849498i	$0.676905\pi$
$194$	30030.1	−	170309.i	0.0572866	−	0.324888i
$195$	−84475.6	+	123838.i	−0.159091	+	0.233221i
$196$	60888.8	−	51091.8i	0.113213	−	0.0949972i
$197$	291030.	+	504079.i	0.534284	+	0.925407i	0.999198	+	0.0400512i	$0.0127521\pi$
$197$	291030.	+	504079.i	0.534284	+	0.925407i	−0.464913	+	0.885356i	$0.653915\pi$
$198$	−207721.	−	31412.8i	−0.376546	−	0.0569434i
$199$	349885.	−	606018.i	0.626314	−	1.08481i	−0.361971	−	0.932189i	$-0.617896\pi$
$199$	349885.	−	606018.i	0.626314	−	1.08481i	0.988285	−	0.152619i	$-0.0487707\pi$
$200$	−917.135	−	5201.33i	−0.00162128	−	0.00919475i
$201$	597206.	+	269645.i	1.04264	+	0.470763i
$202$	465986.	−	169605.i	0.803515	−	0.292456i
$203$	328615.	−	119606.i	0.559690	−	0.203710i
$204$	56495.7	+	25508.4i	0.0950473	+	0.0429149i
$205$	−53134.4	−	301340.i	−0.0883062	−	0.500809i
$206$	−37522.3	+	64990.5i	−0.0616057	+	0.106704i
$207$	−693041.	+	868175.i	−1.12417	+	1.40826i
$208$	−62670.7	−	108549.i	−0.100440	−	0.173967i
$209$	91950.1	−	77155.3i	0.145608	−	0.122180i
$210$	−191553.	+	280810.i	−0.299738	+	0.439404i
$211$	−28592.5	+	162156.i	−0.0442126	+	0.250742i	−0.998901	−	0.0468641i	$-0.985077\pi$
$211$	−28592.5	+	162156.i	−0.0442126	+	0.250742i	0.954689	+	0.297607i	$0.0961883\pi$
$212$	136921.	+	114890.i	0.209233	+	0.175568i
$213$	376924.	−	105950.i	0.569252	−	0.160013i
$214$	365873.	+	133167.i	0.546130	+	0.198775i
$215$	398159.			0.587436
$216$	−722091.	−	165370.i	−1.05307	−	0.241169i
$217$	−845559.			−1.21897
$218$	491626.	+	178937.i	0.700638	+	0.255012i
$219$	157950.	−	619674.i	0.222540	−	0.873078i
$220$	−56271.8	−	47217.6i	−0.0783852	−	0.0657730i
$221$	15804.6	−	89632.5i	0.0217673	−	0.123448i
$222$	−1.18602e6	−	89171.3i	−1.61514	−	0.121435i
$223$	−605116.	+	507752.i	−0.814847	+	0.683738i	−0.951759	−	0.306845i	$-0.900727\pi$
$223$	−605116.	+	507752.i	−0.814847	+	0.683738i	0.136912	+	0.990583i	$0.456282\pi$
$224$	105796.	+	183244.i	0.140880	+	0.244012i
$225$	−2093.19	+	6220.00i	−0.00275647	+	0.00819094i
$226$	−280937.	+	486597.i	−0.365879	+	0.633722i
$227$	203576.	+	1.15453e6i	0.262217	+	1.48711i	0.776844	+	0.629693i	$0.216819\pi$
$227$	203576.	+	1.15453e6i	0.262217	+	1.48711i	−0.514627	+	0.857414i	$0.672069\pi$
$228$	65604.2	−	47141.9i	0.0835785	−	0.0600579i
$229$	188581.	−	68638.0i	0.237635	−	0.0864920i	−0.220458	−	0.975397i	$-0.570755\pi$
$229$	188581.	−	68638.0i	0.237635	−	0.0864920i	0.458093	+	0.888905i	$0.348533\pi$
$230$	1.18232e6	−	430330.i	1.47372	−	0.536392i
$231$	−21447.5	−	214865.i	−0.0264452	−	0.264933i
$232$	−149890.	−	850066.i	−0.182832	−	1.03689i
$233$	−293226.	+	507882.i	−0.353844	+	0.612877i	−0.986920	−	0.161214i	$-0.948459\pi$
$233$	−293226.	+	507882.i	−0.353844	+	0.612877i	0.633075	+	0.774090i	$0.281792\pi$
$234$	5074.28	+	207542.i	0.00605808	+	0.247780i
$235$	48715.9	+	84378.5i	0.0575442	+	0.0996694i
$236$	213554.	−	179193.i	0.249591	−	0.209432i
$237$	479716.	+	996763.i	0.554770	+	1.15271i
$238$	35837.9	−	203247.i	0.0410110	−	0.232585i
$239$	−969698.	−	813673.i	−1.09810	−	0.921415i	−0.100804	−	0.994906i	$-0.532141\pi$
$239$	−969698.	−	813673.i	−1.09810	−	0.921415i	−0.997296	+	0.0734913i	$0.976586\pi$
$240$	450494.	+	439614.i	0.504848	+	0.492656i
$241$	−730630.	−	265928.i	−0.810317	−	0.294931i	−0.0965623	−	0.995327i	$-0.530785\pi$
$241$	−730630.	−	265928.i	−0.810317	−	0.294931i	−0.713755	+	0.700396i	$0.753007\pi$
$242$	645218.			0.708220
$243$	689416.	+	609913.i	0.748972	+	0.662601i
$244$	−330517.			−0.355402
$245$	550739.	+	200453.i	0.586180	+	0.213352i
$246$	−303284.	−	295960.i	−0.319530	−	0.311813i
$247$	−90865.1	−	76244.8i	−0.0947664	−	0.0795185i
$248$	−362421.	+	2.05539e6i	−0.374183	+	2.12210i
$249$	−425409.	−	883923.i	−0.434819	−	0.903475i
$250$	664559.	−	557631.i	0.672487	−	0.564283i
$251$	19661.3	+	34054.3i	0.0196982	+	0.0341183i	0.875706	−	0.482844i	$-0.160396\pi$
$251$	19661.3	+	34054.3i	0.0196982	+	0.0341183i	−0.856008	+	0.516962i	$0.827063\pi$
$252$	−3552.16	−	145286.i	−0.00352363	−	0.144119i
$253$	−399632.	+	692183.i	−0.392517	+	0.679860i
$254$	−156438.	−	887204.i	−0.152145	−	0.862858i
$255$	45398.1	+	454807.i	0.0437207	+	0.438003i
$256$	655449.	−	238564.i	0.625085	−	0.227512i
$257$	−102923.	+	37460.9i	−0.0972030	+	0.0353790i	−0.390164	−	0.920745i	$-0.627582\pi$
$257$	−102923.	+	37460.9i	−0.0972030	+	0.0353790i	0.292961	+	0.956124i	$0.405359\pi$
$258$	447787.	−	321771.i	0.418815	−	0.300952i
$259$	−212282.	−	1.20391e6i	−0.196637	−	1.11518i
$260$	−36295.4	+	62865.4i	−0.0332980	+	0.0576738i
$261$	−342095.	+	1.01655e6i	−0.310846	+	0.923692i
$262$	−285029.	−	493685.i	−0.256529	−	0.444321i
$263$	−2656.58	+	2229.13i	−0.00236828	+	0.00198722i	−0.643971	−	0.765050i	$-0.722714\pi$
$263$	−2656.58	+	2229.13i	−0.00236828	+	0.00198722i	0.641603	+	0.767037i	$0.278270\pi$
$264$	−531490.	−	39960.2i	−0.469337	−	0.0352873i
$265$	−228856.	+	1.29791e6i	−0.200193	+	1.13535i
$266$	−206042.	−	172889.i	−0.178546	−	0.149818i
$267$	274872.	−	1.07839e6i	0.235967	−	0.925756i
$268$	298167.	+	108524.i	0.253584	+	0.0922971i
$269$	−191888.			−0.161684			−0.0808421	−	0.996727i	$-0.525761\pi$
$269$	−191888.			−0.161684			−0.0808421	+	0.996727i	$0.525761\pi$
$270$	−306570.	−	996469.i	−0.255930	−	0.831868i
$271$	2.10473e6			1.74090			0.870449	−	0.492259i	$-0.163829\pi$
$271$	2.10473e6			1.74090			0.870449	+	0.492259i	$0.163829\pi$
$272$	−359120.	−	130709.i	−0.294318	−	0.107123i
$273$	−205424.	+	57743.1i	−0.166818	+	0.0468914i
$274$	−428719.	−	359738.i	−0.344982	−	0.289474i
$275$	−819.943	+	4650.13i	−0.000653810	+	0.00370794i
$276$	−303134.	+	444383.i	−0.239531	+	0.351144i
$277$	−913209.	+	766273.i	−0.715107	+	0.600046i	−0.926027	−	0.377458i	$-0.876798\pi$
$277$	−913209.	+	766273.i	−0.715107	+	0.600046i	0.210920	+	0.977503i	$0.432354\pi$
$278$	−85928.0	−	148832.i	−0.0666841	−	0.115500i
$279$	1.61794e6	−	2.02680e6i	1.24438	−	1.55884i
$280$	−431198.	+	746856.i	−0.328686	+	0.569301i
$281$	−355898.	−	2.01840e6i	−0.268881	−	1.52490i	−0.757753	−	0.652542i	$-0.773703\pi$
$281$	−355898.	−	2.01840e6i	−0.268881	−	1.52490i	0.488872	−	0.872355i	$-0.337408\pi$
$282$	122978.	+	55526.0i	0.0920884	+	0.0415790i
$283$	−334139.	+	121617.i	−0.248005	+	0.0902665i	−0.463032	−	0.886342i	$-0.653238\pi$
$283$	−334139.	+	121617.i	−0.248005	+	0.0902665i	0.215027	+	0.976608i	$0.431016\pi$
$284$	178161.	−	64845.4i	0.131074	−	0.0477071i
$285$	542901.	+	245126.i	0.395921	+	0.178763i
$286$	25937.8	+	147100.i	0.0187507	+	0.106341i
$287$	217780.	−	377207.i	0.156068	−	0.270318i
$288$	−641672.	−	97037.2i	−0.455860	−	0.0689378i
$289$	571175.	+	989304.i	0.402277	+	0.696763i
$290$	930604.	−	780869.i	0.649785	−	0.545235i
$291$	−307220.	+	450372.i	−0.212675	+	0.311773i
$292$	53772.8	−	304961.i	0.0369067	−	0.209308i
$293$	−1.62834e6	−	1.36634e6i	−1.10809	−	0.929798i	−0.110148	−	0.993915i	$-0.535132\pi$
$293$	−1.62834e6	−	1.36634e6i	−1.10809	−	0.929798i	−0.997942	+	0.0641175i	$0.979577\pi$
$294$	781379.	−	219640.i	0.527222	−	0.148198i
$295$	1.93160e6	+	703045.i	1.29230	+	0.470357i
$296$	−3.01747e6			−2.00177
$297$	556070.	+	359726.i	0.365795	+	0.236636i
$298$	1.57354e6			1.02645
$299$	742199.	+	270138.i	0.480112	+	0.174746i
$300$	−784.935	+	3079.49i	−0.000503536	+	0.00197549i
$301$	434164.	+	364307.i	0.276209	+	0.231767i
$302$	−461030.	+	2.61463e6i	−0.290879	+	1.64966i
$303$	−1.55888e6	−	117205.i	−0.975454	−	0.0733399i
$304$	−381537.	+	320147.i	−0.236784	+	0.198685i
$305$	−1.21854e6	−	2.11058e6i	−0.750052	−	1.29913i
$306$	418607.	+	474807.i	0.255566	+	0.289877i
$307$	765940.	−	1.32665e6i	0.463820	−	0.803359i	−0.535328	−	0.844644i	$-0.679812\pi$
$307$	765940.	−	1.32665e6i	0.463820	−	0.803359i	0.999147	+	0.0412854i	$0.0131453\pi$
$308$	−18157.2	−	102975.i	−0.0109062	−	0.0618521i
$309$	192119.	−	138053.i	0.114465	−	0.0822524i
$310$	−2.76019e6	+	1.00463e6i	−1.63130	+	0.593746i
$311$	1.27935e6	−	465644.i	0.750044	−	0.272994i	0.0614200	−	0.998112i	$-0.480437\pi$
$311$	1.27935e6	−	465644.i	0.750044	−	0.272994i	0.688624	+	0.725118i	$0.258215\pi$
$312$	52314.3	+	524096.i	0.0304252	+	0.304806i
$313$	−146004.	−	828032.i	−0.0842374	−	0.477734i	−0.997519	−	0.0704043i	$-0.977571\pi$
$313$	−146004.	−	828032.i	−0.0842374	−	0.477734i	0.913281	−	0.407330i	$-0.133540\pi$
$314$	−794790.	+	1.37662e6i	−0.454913	+	0.787932i
$315$	914653.	−	558319.i	0.519374	−	0.317034i
$316$	267832.	+	463898.i	0.150884	+	0.261339i
$317$	−829886.	+	696357.i	−0.463842	+	0.389210i	−0.844542	−	0.535489i	$-0.820127\pi$
$317$	−829886.	+	696357.i	−0.463842	+	0.389210i	0.380700	+	0.924699i	$0.375683\pi$
$318$	791519.	+	1.64463e6i	0.438928	+	0.912014i
$319$	−134005.	+	759981.i	−0.0737301	+	0.418144i
$320$	1.55290e6	+	1.30304e6i	0.847753	+	0.711349i
$321$	−878465.	−	857249.i	−0.475841	−	0.464349i
$322$	1.68298e6	+	612554.i	0.904563	+	0.329234i
$323$	−361662.			−0.192884
$324$	355046.	+	269484.i	0.187898	+	0.142617i
$325$	4666.14			0.00245047
$326$	−501087.	−	182381.i	−0.261137	−	0.0950463i
$327$	−1.18040e6	−	1.15189e6i	−0.610463	−	0.595720i
$328$	−823573.	−	691060.i	−0.422686	−	0.354676i
$329$	−24083.2	+	136583.i	−0.0122666	+	0.0695674i
$330$	−325298.	−	675911.i	−0.164436	−	0.341668i
$331$	291525.	−	244618.i	0.146253	−	0.122721i	−0.566726	−	0.823907i	$-0.691790\pi$
$331$	291525.	−	244618.i	0.146253	−	0.122721i	0.712979	+	0.701186i	$0.247346\pi$
$332$	−237511.	−	411382.i	−0.118260	−	0.204833i
$333$	3.29196e6	+	1.79479e6i	1.62684	+	0.886960i
$334$	−827397.	+	1.43309e6i	−0.405834	+	0.702924i
$335$	406275.	+	2.30410e6i	0.197792	+	1.12173i
$336$	88993.9	+	891559.i	0.0430043	+	0.430826i
$337$	−2.07223e6	+	754229.i	−0.993945	+	0.361767i	−0.787247	−	0.616638i	$-0.788494\pi$
$337$	−2.07223e6	+	754229.i	−0.993945	+	0.361767i	−0.206699	+	0.978405i	$0.566272\pi$
$338$	−1.58656e6	+	577459.i	−0.755377	+	0.274935i
$339$	1.43843e6	−	1.03363e6i	0.679814	−	0.488501i
$340$	38433.6	+	217968.i	0.0180307	+	0.102257i
$341$	932961.	−	1.61594e6i	0.434488	−	0.752555i
$342$	808667.	−	163064.i	0.373856	−	0.0753864i
$343$	1.08293e6	+	1.87569e6i	0.497010	+	0.860847i
$344$	1.07165e6	−	899222.i	0.488267	−	0.409705i
$345$	−3.95527e6	−	297379.i	−1.78908	−	0.134512i
$346$	41263.7	−	234018.i	0.0185301	−	0.105089i
$347$	2.85458e6	+	2.39528e6i	1.27268	+	1.06790i	0.994209	+	0.107460i	$0.0342717\pi$
$347$	2.85458e6	+	2.39528e6i	1.27268	+	1.06790i	0.278470	+	0.960445i	$0.410173\pi$
$348$	−128284.	+	503288.i	−0.0567837	+	0.222776i
$349$	−2.71325e6	−	987543.i	−1.19241	−	0.434003i	−0.331843	−	0.943335i	$-0.607670\pi$
$349$	−2.71325e6	−	987543.i	−1.19241	−	0.434003i	−0.860570	+	0.509332i	$0.829893\pi$
$350$	10580.7			0.00461685
$351$	254659.	−	602888.i	0.110329	−	0.261197i
$352$	−466928.			−0.200860
$353$	−321299.	−	116943.i	−0.137238	−	0.0499504i	0.272488	−	0.962159i	$-0.412153\pi$
$353$	−321299.	−	116943.i	−0.137238	−	0.0499504i	−0.409726	+	0.912209i	$0.634376\pi$
$354$	2.74052e6	−	770340.i	1.16232	−	0.326719i
$355$	1.07092e6	+	898610.i	0.451011	+	0.378443i
$356$	93578.0	−	530707.i	0.0391335	−	0.221937i
$357$	−366635.	+	537473.i	−0.152252	+	0.223196i
$358$	1.32006e6	−	1.10766e6i	0.544358	−	0.456771i
$359$	42214.1	+	73116.9i	0.0172871	+	0.0299421i	0.874540	−	0.484954i	$-0.161164\pi$
$359$	42214.1	+	73116.9i	0.0172871	+	0.0299421i	−0.857252	+	0.514896i	$0.827830\pi$
$360$	−965132.	−	2.46265e6i	−0.392492	−	1.00149i
$361$	1.00238e6	−	1.73618e6i	0.404823	−	0.701174i
$362$	−108451.	−	615057.i	−0.0434974	−	0.246686i
$363$	−1.85383e6	−	837023.i	−0.738418	−	0.333404i
$364$	−97097.9	+	35340.8i	−0.0384111	+	0.0139805i
$365$	2.14563e6	−	780945.i	0.842990	−	0.306823i
$366$	−3.07608e6	−	1.38888e6i	−1.20031	−	0.541955i
$367$	−655783.	−	3.71913e6i	−0.254153	−	1.44137i	−0.798237	−	0.602343i	$-0.794234\pi$
$367$	−655783.	−	3.71913e6i	−0.254153	−	1.44137i	0.544084	−	0.839030i	$-0.316877\pi$
$368$	1.65823e6	−	2.87213e6i	0.638300	−	1.10557i
$369$	487449.	+	1.24379e6i	0.186364	+	0.475532i
$370$	−2.12336e6	−	3.67776e6i	−0.806341	−	1.39662i
$371$	−1.43711e6	+	1.20588e6i	−0.542070	+	0.454850i
$372$	707682.	−	1.03743e6i	0.265144	−	0.388690i
$373$	75549.4	−	428462.i	0.0281164	−	0.159456i	−0.967517	−	0.252806i	$-0.918647\pi$
$373$	75549.4	−	428462.i	0.0281164	−	0.159456i	0.995633	+	0.0933503i	$0.0297576\pi$
$374$	348880.	+	292745.i	0.128972	+	0.108221i
$375$	−2.63280e6	+	740060.i	−0.966805	+	0.271762i
$376$	321684.	+	117083.i	0.117344	+	0.0427096i
$377$	762598.			0.276339
$378$	577454.	−	1.36708e6i	0.207868	−	0.492113i
$379$	−721578.			−0.258039			−0.129020	−	0.991642i	$-0.541183\pi$
$379$	−721578.			−0.258039			−0.129020	+	0.991642i	$0.541183\pi$
$380$	271054.	+	98655.5i	0.0962934	+	0.0350479i
$381$	−701471.	+	2.75204e6i	−0.247570	+	0.971275i
$382$	−2.46320e6	−	2.06687e6i	−0.863656	−	0.724693i
$383$	−115194.	+	653298.i	−0.0401266	+	0.227570i	−0.998276	−	0.0587005i	$-0.981304\pi$
$383$	−115194.	+	653298.i	−0.0401266	+	0.227570i	0.958149	+	0.286270i	$0.0924154\pi$
$384$	1.47105e6	+	110602.i	0.509097	+	0.0382766i
$385$	590623.	−	495591.i	0.203076	−	0.170401i
$386$	363070.	+	628856.i	0.124029	+	0.214824i
$387$	−1.70400e6	+	343603.i	−0.578350	+	0.116622i
$388$	−131998.	+	228628.i	−0.0445132	+	0.0770992i
$389$	22219.4	+	126012.i	0.00744488	+	0.0422220i	0.988304	−	0.152497i	$-0.0487315\pi$
$389$	22219.4	+	126012.i	0.00744488	+	0.0422220i	−0.980859	+	0.194719i	$0.937620\pi$
$390$	−601966.	+	432561.i	−0.200406	+	0.144008i
$391$	2.26298e6	−	823656.i	0.748580	−	0.272461i
$392$	1.93503e6	−	704295.i	0.636024	−	0.231494i
$393$	178495.	+	1.78820e6i	0.0582969	+	0.584031i
$394$	499793.	+	2.83447e6i	0.162200	+	0.919880i
$395$	−1.97487e6	+	3.42057e6i	−0.636862	+	1.10308i
$396$	281573.	+	153515.i	0.0902305	+	0.0491941i
$397$	356265.	+	617070.i	0.113448	+	0.196498i	0.917158	−	0.398523i	$-0.130477\pi$
$397$	356265.	+	617070.i	0.113448	+	0.196498i	−0.803710	+	0.595021i	$0.797144\pi$
$398$	2.65070e6	−	2.22420e6i	0.838791	−	0.703829i
$399$	367710.	+	764034.i	0.115631	+	0.240259i
$400$	3402.26	−	19295.2i	0.00106321	−	0.00602974i
$401$	−1.92754e6	−	1.61740e6i	−0.598607	−	0.502291i	0.292390	−	0.956299i	$-0.405549\pi$
$401$	−1.92754e6	−	1.61740e6i	−0.598607	−	0.502291i	−0.890998	+	0.454008i	$0.849994\pi$
$402$	2.31896e6	+	2.26296e6i	0.715696	+	0.698411i
$403$	−1.73270e6	−	630652.i	−0.531449	−	0.193431i
$404$	−757004.			−0.230752
$405$	−411861.	+	3.26074e6i	−0.124771	+	0.987821i
$406$	1.72923e6			0.520641
$407$	2.53501e6	+	922667.i	0.758565	+	0.276095i
$408$	1.14935e6	+	1.12159e6i	0.341823	+	0.333568i
$409$	258069.	+	216545.i	0.0762828	+	0.0640089i	0.680132	−	0.733090i	$-0.261923\pi$
$409$	258069.	+	216545.i	0.0762828	+	0.0640089i	−0.603849	+	0.797099i	$0.706367\pi$
$410$	262741.	−	1.49008e6i	0.0771913	−	0.437774i
$411$	765108.	+	1.58976e6i	0.223418	+	0.464223i
$412$	87757.6	−	73637.3i	0.0254707	−	0.0213725i
$413$	1.46300e6	+	2.53399e6i	0.422055	+	0.731021i
$414$	−4.68859e6	+	2.86199e6i	−1.34444	+	0.820669i
$415$	1.75130e6	−	3.03334e6i	0.499161	−	0.864572i
$416$	80124.3	+	454408.i	0.0227003	+	0.128740i
$417$	53811.2	+	539092.i	0.0151542	+	0.151818i
$418$	557746.	−	203003.i	0.156133	−	0.0568279i
$419$	−4.84840e6	+	1.76467e6i	−1.34916	+	0.491054i	−0.912686	−	0.408662i	$-0.865996\pi$
$419$	−4.84840e6	+	1.76467e6i	−1.34916	+	0.491054i	−0.436475	+	0.899716i	$0.643773\pi$
$420$	421395.	−	302806.i	0.116564	−	0.0837609i
$421$	659377.	+	3.73951e6i	0.181313	+	1.02828i	0.930602	+	0.366033i	$0.119284\pi$
$421$	659377.	+	3.73951e6i	0.181313	+	1.02828i	−0.749289	+	0.662243i	$0.769605\pi$
$422$	−407103.	+	705124.i	−0.111282	+	0.192745i
$423$	−281306.	−	319072.i	−0.0764412	−	0.0867038i
$424$	2.31529e6	+	4.01020e6i	0.625448	+	1.08331i
$425$	10898.6	−	9145.02i	0.00292684	−	0.00245591i
$426$	1.93061e6	+	145154.i	0.515432	+	0.0387529i
$427$	602399.	−	3.41637e6i	0.159887	−	0.906767i
$428$	−455313.	−	382053.i	−0.120144	−	0.100812i
$429$	116305.	−	456294.i	0.0305110	−	0.119702i
$430$	1.85010e6	+	673381.i	0.482530	+	0.175626i
$431$	3.99989e6			1.03718			0.518592	−	0.855022i	$-0.326457\pi$
$431$	3.99989e6			1.03718			0.518592	+	0.855022i	$0.326457\pi$
$432$	−2.30735e6	−	1.49264e6i	−0.594845	−	0.384810i
$433$	−6.69763e6			−1.71673			−0.858364	−	0.513041i	$-0.828519\pi$
$433$	−6.69763e6			−1.71673			−0.858364	+	0.513041i	$0.828519\pi$
$434$	−3.92900e6	−	1.43004e6i	−1.00128	−	0.364438i
$435$	−3.68679e6	+	1.03633e6i	−0.934168	+	0.262588i
$436$	−611807.	−	513367.i	−0.154134	−	0.129334i
$437$	544996.	−	3.09082e6i	0.136518	−	0.774231i
$438$	1.78195e6	−	2.61226e6i	0.443823	−	0.650627i
$439$	617375.	−	518039.i	0.152893	−	0.128292i	−0.563132	−	0.826367i	$-0.690404\pi$
$439$	617375.	−	518039.i	0.152893	−	0.128292i	0.716025	+	0.698074i	$0.245959\pi$
$440$	−951538.	−	1.64811e6i	−0.234312	−	0.405840i
$441$	−2.52997e6	−	382597.i	−0.619469	−	0.0936796i
$442$	225028.	−	389760.i	0.0547874	−	0.0948946i
$443$	−235339.	−	1.33467e6i	−0.0569750	−	0.323121i	0.942978	−	0.332856i	$-0.108012\pi$
$443$	−235339.	−	1.33467e6i	−0.0569750	−	0.323121i	−0.999953	+	0.00973492i	$0.996901\pi$
$444$	1.65477e6	+	747149.i	0.398365	+	0.179866i
$445$	3.73393e6	−	1.35904e6i	0.893853	−	0.325336i
$446$	−3.67048e6	+	1.33594e6i	−0.873746	+	0.318018i
$447$	−4.52106e6	−	2.04131e6i	−1.07022	−	0.483215i
$448$	501076.	+	2.84174e6i	0.117953	+	0.668944i
$449$	88201.9	−	152770.i	0.0206472	−	0.0357621i	−0.855517	−	0.517774i	$-0.826761\pi$
$449$	88201.9	−	152770.i	0.0206472	−	0.0357621i	0.876164	+	0.482012i	$0.160094\pi$
$450$	−20245.8	+	25362.0i	−0.00471306	+	0.00590407i
$451$	480583.	+	832394.i	0.111257	+	0.192703i
$452$	657059.	−	551338.i	0.151272	−	0.126932i
$453$	4.71651e6	−	6.91422e6i	1.07988	−	1.58306i
$454$	−1.00665e6	+	5.70899e6i	−0.229213	+	1.29993i
$455$	−583653.	−	489743.i	−0.132168	−	0.110902i
$456$	2.01483e6	−	566354.i	0.453760	−	0.127549i
$457$	−7.05454e6	−	2.56764e6i	−1.58008	−	0.575101i	−0.604857	−	0.796334i	$-0.706770\pi$
$457$	−7.05454e6	−	2.56764e6i	−1.58008	−	0.575101i	−0.975221	+	0.221233i	$0.928992\pi$
$458$	992351.			0.221056
$459$	−586778.	−	1.90725e6i	−0.130000	−	0.422548i
$460$	−1.92071e6			−0.423220
$461$	3.51594e6	+	1.27970e6i	0.770529	+	0.280450i	0.697218	−	0.716859i	$-0.254421\pi$
$461$	3.51594e6	+	1.27970e6i	0.770529	+	0.280450i	0.0733115	+	0.997309i	$0.476643\pi$
$462$	263729.	−	1.03467e6i	0.0574848	−	0.225527i
$463$	5.17568e6	+	4.34291e6i	1.12206	+	0.941518i	0.998707	−	0.0508448i	$-0.0161914\pi$
$463$	5.17568e6	+	4.34291e6i	1.12206	+	0.941518i	0.123351	+	0.992363i	$0.460636\pi$
$464$	556039.	−	3.15346e6i	0.119898	−	0.679973i
$465$	9.23379e6	+	694246.i	1.98038	+	0.148895i
$466$	−2.22146e6	+	1.86403e6i	−0.473886	+	0.397637i
$467$	3.42075e6	+	5.92492e6i	0.725821	+	1.25716i	0.958635	+	0.284638i	$0.0918733\pi$
$467$	3.42075e6	+	5.92492e6i	0.725821	+	1.25716i	−0.232814	+	0.972521i	$0.574793\pi$
$468$	101081.	−	300366.i	0.0213332	−	0.0633923i
$469$	−1.66519e6	+	2.88419e6i	−0.349567	+	0.605468i
$470$	83661.1	+	474466.i	0.0174694	+	0.0990741i
$471$	4.06942e6	−	2.92421e6i	0.845240	−	0.607373i
$472$	6.78672e6	−	2.47016e6i	1.40218	−	0.510353i
$473$	−1.17526e6	+	427761.i	−0.241536	+	0.0879121i
$474$	543301.	+	5.44290e6i	0.111069	+	1.11272i
$475$	−3219.71	−	18259.9i	−0.000654760	−	0.00371333i
$476$	−157527.	+	272844.i	−0.0318666	+	0.0551946i
$477$	−140636.	−	5.75214e6i	−0.0283010	−	1.15753i
$478$	−3.12972e6	−	5.42083e6i	−0.626520	−	1.08516i
$479$	−6.78077e6	+	5.68974e6i	−1.35033	+	1.13306i	−0.371490	+	0.928437i	$0.621153\pi$
$479$	−6.78077e6	+	5.68974e6i	−1.35033	+	1.13306i	−0.978841	+	0.204625i	$0.934403\pi$
$480$	−1.00488e6	−	2.08795e6i	−0.199072	−	0.413636i
$481$	462922.	−	2.62536e6i	0.0912316	−	0.517400i
$482$	−2.94522e6	−	2.47133e6i	−0.577431	−	0.484523i
$483$	−4.04085e6	−	3.94326e6i	−0.788142	−	0.769108i
$484$	−925558.	−	336876.i	−0.179593	−	0.0653666i
$485$	−1.94659e6			−0.375769
$486$	2.17195e6	+	4.00001e6i	0.417119	+	0.768192i
$487$	511949.			0.0978148			0.0489074	−	0.998803i	$-0.484426\pi$
$487$	511949.			0.0978148			0.0489074	+	0.998803i	$0.484426\pi$
$488$	−8.04636e6	−	2.92863e6i	−1.52950	−	0.556693i
$489$	1.20311e6	+	1.17406e6i	0.227528	+	0.222033i
$490$	2.22007e6	+	1.86286e6i	0.417711	+	0.350501i
$491$	1.22498e6	−	6.94722e6i	0.229312	−	1.30049i	−0.624957	−	0.780659i	$-0.714884\pi$
$491$	1.22498e6	−	6.94722e6i	0.229312	−	1.30049i	0.854269	−	0.519831i	$-0.174005\pi$
$492$	280534.	+	582899.i	0.0522483	+	0.108563i
$493$	1.78119e6	−	1.49459e6i	0.330059	−	0.276953i
$494$	−293268.	−	507956.i	−0.0540689	−	0.0936502i
$495$	57798.7	+	2.36401e6i	0.0106024	+	0.433647i
$496$	−3.87122e6	+	6.70515e6i	−0.706551	+	1.22378i
$497$	345555.	+	1.95974e6i	0.0627518	+	0.355883i
$498$	−481796.	−	4.82673e6i	−0.0870542	−	0.872127i
$499$	−2.71524e6	+	988267.i	−0.488154	+	0.177674i	−0.574358	−	0.818604i	$-0.694748\pi$
$499$	−2.71524e6	+	988267.i	−0.488154	+	0.177674i	0.0862043	+	0.996277i	$0.472526\pi$
$500$	−1.24445e6	+	452942.i	−0.222614	+	0.0810248i
$501$	4.23637e6	−	3.04417e6i	0.754049	−	0.541845i
$502$	33764.8	+	191489.i	0.00598004	+	0.0339145i
$503$	1.76698e6	−	3.06050e6i	0.311395	−	0.539351i	−0.667270	−	0.744816i	$-0.732537\pi$
$503$	1.76698e6	−	3.06050e6i	0.311395	−	0.539351i	0.978665	+	0.205465i	$0.0658706\pi$
$504$	1.20087e6	−	3.56842e6i	0.210581	−	0.625748i
$505$	−2.79090e6	−	4.83399e6i	−0.486986	−	0.843484i
$506$	−3.02759e6	+	2.54045e6i	−0.525678	+	0.441097i
$507$	5.30758e6	+	399052.i	0.917015	+	0.0689461i
$508$	−238811.	+	1.35436e6i	−0.0410577	+	0.232850i
$509$	5.80859e6	+	4.87398e6i	0.993748	+	0.833853i	0.986106	−	0.166118i	$-0.0531231\pi$
$509$	5.80859e6	+	4.87398e6i	0.993748	+	0.833853i	0.00764170	+	0.999971i	$0.497568\pi$
$510$	−558238.	+	2.19010e6i	−0.0950372	+	0.372854i
$511$	3.05420e6	+	1.11164e6i	0.517423	+	0.188326i
$512$	6.47740e6			1.09201
$513$	−2.53498e6	−	580548.i	−0.425286	−	0.0973969i
$514$	−541601.			−0.0904214
$515$	793767.	+	288908.i	0.131879	+	0.0479999i
$516$	−810346.	+	227782.i	−0.133982	+	0.0376613i
$517$	−234449.	−	196726.i	−0.0385764	−	0.0323694i
$518$	1.04970e6	−	5.95316e6i	0.171886	−	0.974817i
$519$	−422143.	+	618845.i	−0.0687925	+	0.100847i
$520$	−1.44064e6	+	1.20884e6i	−0.233639	+	0.196047i
$521$	−2.45258e6	−	4.24800e6i	−0.395849	−	0.685630i	0.597360	−	0.801973i	$-0.296216\pi$
$521$	−2.45258e6	−	4.24800e6i	−0.395849	−	0.685630i	−0.993209	+	0.116343i	$0.962883\pi$
$522$	−3.30881e6	+	4.14496e6i	−0.531491	+	0.665801i
$523$	608423.	−	1.05382e6i	0.0972639	−	0.168466i	−0.813287	−	0.581862i	$-0.802324\pi$
$523$	608423.	−	1.05382e6i	0.0972639	−	0.168466i	0.910551	+	0.413396i	$0.135658\pi$
$524$	151113.	+	857002.i	0.0240421	+	0.136350i
$525$	−30400.3	−	13726.1i	−0.00481371	−	0.00217344i
$526$	−16114.1	+	5865.06i	−0.00253947	+	0.000924290i
$527$	−5.28303e6	+	1.92287e6i	−0.828623	+	0.301594i
$528$	−1.80204e6	−	813641.i	−0.281306	−	0.127013i
$529$	2.51132e6	+	1.42424e7i	0.390179	+	2.21281i
$530$	−3.25848e6	+	5.64386e6i	−0.503878	+	0.872743i
$531$	−8.87334e6	−	1.34188e6i	−1.36569	−	0.206527i
$532$	205297.	+	355585.i	0.0314488	+	0.0544708i
$533$	727607.	−	610535.i	0.110938	−	0.0930877i
$534$	3.10103e6	−	4.54599e6i	0.470601	−	0.689883i
$535$	761032.	−	4.31603e6i	0.114953	−	0.651928i
$536$	6.29718e6	+	5.28396e6i	0.946748	+	0.794416i
$537$	−5.22969e6	+	1.47003e6i	−0.782601	+	0.219983i
$538$	−891633.	−	324528.i	−0.132810	−	0.0483389i
$539$	−1.84100e6			−0.272949
$540$	−80496.2	+	1.58949e6i	−0.0118793	+	0.234570i
$541$	4.85060e6			0.712528			0.356264	−	0.934385i	$-0.384050\pi$
$541$	4.85060e6			0.712528			0.356264	+	0.934385i	$0.384050\pi$
$542$	9.77990e6	+	3.55959e6i	1.43000	+	0.520478i
$543$	−486297.	+	1.90786e6i	−0.0707786	+	0.277681i
$544$	1.07772e6	+	904318.i	0.156139	+	0.131016i
$545$	1.02260e6	−	5.79948e6i	0.147474	−	0.836368i
$546$	−1.05218e6	−	79108.9i	−0.151046	−	0.0113565i
$547$	3.40648e6	−	2.85838e6i	0.486786	−	0.408462i	−0.366087	−	0.930581i	$-0.619303\pi$
$547$	3.40648e6	−	2.85838e6i	0.486786	−	0.408462i	0.852873	+	0.522119i	$0.174858\pi$
$548$	427170.	+	739880.i	0.0607644	+	0.105247i
$549$	7.03636e6	+	7.98103e6i	0.996362	+	1.13013i
$550$	−11674.4	+	20220.7i	−0.00164562	+	0.00285029i
$551$	−526204.	−	2.98425e6i	−0.0738372	−	0.418752i
$552$	−1.13173e7	+	8.13238e6i	−1.58087	+	1.13598i
$553$	−5.28320e6	+	1.92293e6i	−0.734656	+	0.267393i
$554$	−5.53929e6	+	2.01614e6i	−0.766796	+	0.279091i
$555$	1.32972e6	+	1.33214e7i	0.183243	+	1.83577i
$556$	45556.1	+	258361.i	0.00624970	+	0.0354438i
$557$	1.28448e6	−	2.22479e6i	0.175424	−	0.303844i	−0.764884	−	0.644169i	$-0.777204\pi$
$557$	1.28448e6	−	2.22479e6i	0.175424	−	0.303844i	0.940308	+	0.340324i	$0.110537\pi$
$558$	1.09458e7	−	6.68147e6i	1.48820	−	0.908420i
$559$	617965.	+	1.07035e6i	0.0836440	+	0.144876i
$560$	−2.45072e6	+	2.05640e6i	−0.330236	+	0.277101i
$561$	−622624.	−	1.29370e6i	−0.0835254	−	0.173551i
$562$	1.75986e6	−	9.98065e6i	0.235037	−	1.33296i
$563$	−1.33722e6	−	1.12206e6i	−0.177800	−	0.149192i	0.549545	−	0.835464i	$-0.314801\pi$
$563$	−1.33722e6	−	1.12206e6i	−0.177800	−	0.149192i	−0.727344	+	0.686273i	$0.759246\pi$
$564$	−147420.	−	143860.i	−0.0195146	−	0.0190433i
$565$	5.94310e6	+	2.16311e6i	0.783234	+	0.285074i
$566$	−1.75830e6			−0.230703
$567$	−3.43261e6	+	3.17875e6i	−0.448401	+	0.415240i
$568$	4.91187e6			0.638816
$569$	−8.28379e6	−	3.01505e6i	−1.07263	−	0.390404i	−0.255468	−	0.966817i	$-0.582230\pi$
$569$	−8.28379e6	−	3.01505e6i	−1.07263	−	0.390404i	−0.817158	+	0.576413i	$0.804452\pi$
$570$	2.10809e6	+	2.05718e6i	0.271771	+	0.265207i
$571$	−7.69634e6	−	6.45800e6i	−0.987857	−	0.828910i	−0.00260075	−	0.999997i	$-0.500828\pi$
$571$	−7.69634e6	−	6.45800e6i	−0.987857	−	0.828910i	−0.985256	+	0.171086i	$0.945272\pi$
$572$	39595.3	−	224556.i	0.00506004	−	0.0286969i
$573$	4.39591e6	+	9.13392e6i	0.559323	+	1.16217i
$574$	1.64989e6	−	1.38442e6i	0.209014	−	0.175383i
$575$	61731.6	+	106922.i	0.00778642	+	0.0134865i
$576$	−7.77042e6	−	4.23647e6i	−0.975862	−	0.532045i
$577$	6.17493e6	−	1.06953e7i	0.772134	−	1.33738i	−0.164257	−	0.986418i	$-0.552523\pi$
$577$	6.17493e6	−	1.06953e7i	0.772134	−	1.33738i	0.936391	−	0.350958i	$-0.114144\pi$
$578$	980893.	+	5.56292e6i	0.122124	+	0.692602i
$579$	−227368.	−	2.27781e6i	−0.0281859	−	0.282372i
$580$	−1.74264e6	+	634270.i	−0.215099	+	0.0782896i
$581$	4.68511e6	−	1.70524e6i	0.575810	−	0.209578i
$582$	−2.18922e6	+	1.57313e6i	−0.267906	+	0.192512i
$583$	−718879.	−	4.07697e6i	−0.0875960	−	0.496782i
$584$	4.01127e6	−	6.94772e6i	0.486687	−	0.842966i
$585$	2.29071e6	−	461911.i	0.276745	−	0.0558044i
$586$	−5.25548e6	−	9.10276e6i	−0.632220	−	1.09504i
$587$	4.22298e6	−	3.54350e6i	0.505853	−	0.424461i	−0.353814	−	0.935316i	$-0.615116\pi$
$587$	4.22298e6	−	3.54350e6i	0.505853	−	0.424461i	0.859667	+	0.510855i	$0.170671\pi$
$588$	−1.23556e6	−	92895.8i	−0.147373	−	0.0110803i
$589$	−1.27232e6	+	7.21569e6i	−0.151115	+	0.857017i
$590$	7.78641e6	+	6.53358e6i	0.920889	+	0.772718i
$591$	2.24108e6	−	8.79230e6i	0.263930	−	1.03546i
$592$	−1.05187e7	−	3.82850e6i	−1.23356	−	0.448978i
$593$	4.66785e6			0.545105			0.272553	−	0.962141i	$-0.412132\pi$
$593$	4.66785e6			0.545105			0.272553	+	0.962141i	$0.412132\pi$
$594$	1.97547e6	+	2.61196e6i	0.229723	+	0.303739i
$595$	−2.32306e6			−0.269010
$596$	−2.25723e6	−	821563.i	−0.260291	−	0.0947382i
$597$	−1.05013e7	+	2.95185e6i	−1.20589	+	0.338968i
$598$	2.99186e6	+	2.51047e6i	0.342128	+	0.287079i
$599$	−434546.	+	2.46443e6i	−0.0494845	+	0.280640i	−0.999502	−	0.0315562i	$-0.989954\pi$
$599$	−434546.	+	2.46443e6i	−0.0494845	+	0.280640i	0.950017	+	0.312197i	$0.101065\pi$
$600$	−46395.6	+	68014.2i	−0.00526137	+	0.00771297i
$601$	−3.12387e6	+	2.62124e6i	−0.352783	+	0.296020i	−0.801906	−	0.597450i	$-0.796181\pi$
$601$	−3.12387e6	+	2.62124e6i	−0.352783	+	0.296020i	0.449124	+	0.893470i	$0.351736\pi$
$602$	1.40127e6	+	2.42707e6i	0.157591	+	0.272955i
$603$	−3.72712e6	−	9.51020e6i	−0.417426	−	1.06511i
$604$	2.02647e6	−	3.50995e6i	0.226021	−	0.391480i
$605$	−1.26114e6	−	7.15230e6i	−0.140080	−	0.794433i
$606$	−7.04533e6	−	3.18105e6i	−0.779327	−	0.351875i
$607$	−2.59806e6	+	945616.i	−0.286205	+	0.104170i	−0.481133	−	0.876647i	$-0.659775\pi$
$607$	−2.59806e6	+	945616.i	−0.286205	+	0.104170i	0.194928	+	0.980817i	$0.437553\pi$
$608$	1.72293e6	−	627096.i	0.189021	−	0.0687979i
$609$	−4.96840e6	−	2.24329e6i	−0.542841	−	0.245099i
$610$	−2.09263e6	−	1.18679e7i	−0.227703	−	1.29137i
$611$	−151220.	+	261920.i	−0.0163872	+	0.0283835i
$612$	−352585.	−	899665.i	−0.0380527	−	0.0970962i
$613$	574430.	+	994941.i	0.0617427	+	0.106942i	0.895244	−	0.445575i	$-0.147001\pi$
$613$	574430.	+	994941.i	0.0617427	+	0.106942i	−0.833502	+	0.552517i	$0.813668\pi$
$614$	5.80271e6	−	4.86906e6i	0.621170	−	0.521223i
$615$	−2.68794e6	+	3.94041e6i	−0.286571	+	0.420101i
$616$	470402.	−	2.66778e6i	0.0499479	−	0.283269i
$617$	1.08923e7	+	9.13973e6i	1.15188	+	0.966541i	0.999762	−	0.0218210i	$-0.00694640\pi$
$617$	1.08923e7	+	9.13973e6i	1.15188	+	0.966541i	0.152117	+	0.988362i	$0.451391\pi$
$618$	1.12618e6	−	316562.i	0.118615	−	0.0333417i
$619$	4.86132e6	+	1.76938e6i	0.509950	+	0.185607i	0.584164	−	0.811636i	$-0.301422\pi$
$619$	4.86132e6	+	1.76938e6i	0.509950	+	0.185607i	−0.0742138	+	0.997242i	$0.523645\pi$
$620$	4.48399e6			0.468474
$621$	1.71839e7	−	2.14063e6i	1.78811	−	0.222748i
$622$	6.73216e6			0.697716
$623$	5.31507e6	+	1.93453e6i	0.548642	+	0.199689i
$624$	−482596.	+	1.89334e6i	−0.0496161	+	0.194656i
$625$	−7.41569e6	−	6.22250e6i	−0.759367	−	0.637184i
$626$	721968.	−	4.09449e6i	0.0736347	−	0.417603i
$627$	−1.86585e6	−	140285.i	−0.189543	−	0.0142509i
$628$	1.85887e6	−	1.55977e6i	0.188083	−	0.157820i
$629$	−4.06413e6	−	7.03927e6i	−0.409582	−	0.709416i
$630$	5.19430e6	−	1.04741e6i	0.521406	−	0.105139i
$631$	−4.91051e6	+	8.50526e6i	−0.490968	+	0.850382i	−0.999946	−	0.0103979i	$-0.996690\pi$
$631$	−4.91051e6	+	8.50526e6i	−0.490968	+	0.850382i	0.508978	+	0.860780i	$0.330024\pi$
$632$	2.40980e6	+	1.36667e7i	0.239987	+	1.36104i
$633$	2.08442e6	−	1.49782e6i	0.206764	−	0.148577i
$634$	−5.03388e6	+	1.83218e6i	−0.497370	+	0.181028i
$635$	−9.52897e6	+	3.46826e6i	−0.937803	+	0.341332i
$636$	−276743.	−	2.77247e6i	−0.0271290	−	0.271784i
$637$	315913.	+	1.79163e6i	0.0308474	+	0.174944i
$638$	−1.90798e6	+	3.30472e6i	−0.185576	+	0.321427i
$639$	−5.35869e6	−	2.92158e6i	−0.519166	−	0.283052i
$640$	2.63366e6	+	4.56163e6i	0.254161	+	0.440220i
$641$	2.91108e6	−	2.44269e6i	0.279840	−	0.234813i	−0.492055	−	0.870564i	$-0.663754\pi$
$641$	2.91108e6	−	2.44269e6i	0.279840	−	0.234813i	0.771894	+	0.635751i	$0.219310\pi$
$642$	−2.63209e6	−	5.46901e6i	−0.252036	−	0.523686i
$643$	−2.43630e6	+	1.38170e7i	−0.232383	+	1.31791i	0.615673	+	0.788001i	$0.288884\pi$
$643$	−2.43630e6	+	1.38170e7i	−0.232383	+	1.31791i	−0.848056	+	0.529906i	$0.822227\pi$
$644$	−2.09439e6	−	1.75740e6i	−0.198996	−	0.166977i
$645$	−4.44211e6	−	4.33483e6i	−0.420426	−	0.410272i
$646$	−1.68051e6	−	611655.i	−0.158438	−	0.0576667i
$647$	−1.53989e7			−1.44620			−0.723100	−	0.690743i	$-0.757284\pi$
$647$	−1.53989e7			−1.44620			−0.723100	+	0.690743i	$0.757284\pi$
$648$	6.25568e6	+	9.70649e6i	0.585244	+	0.908081i
$649$	−6.45690e6			−0.601744
$650$	21681.8	+	7891.54i	0.00201285	+	0.000732619i
$651$	9.43356e6	+	9.20574e6i	0.872415	+	0.851346i
$652$	623581.	+	523246.i	0.0574479	+	0.0482045i
$653$	−2.21899e6	+	1.25845e7i	−0.203644	+	1.15492i	0.695915	+	0.718124i	$0.254999\pi$
$653$	−2.21899e6	+	1.25845e7i	−0.203644	+	1.15492i	−0.899559	+	0.436799i	$0.856112\pi$
$654$	−3.53676e6	−	7.34875e6i	−0.323341	−	0.671845i
$655$	−4.91542e6	+	4.12453e6i	−0.447670	+	0.375639i
$656$	−1.99412e6	−	3.45393e6i	−0.180923	−	0.313367i
$657$	−8.50867e6	+	5.19383e6i	−0.769039	+	0.469434i
$658$	−342899.	+	593919.i	−0.0308746	+	0.0534764i
$659$	−1.15230e6	−	6.53504e6i	−0.103360	−	0.586185i	−0.991863	−	0.127313i	$-0.959365\pi$
$659$	−1.15230e6	−	6.53504e6i	−0.103360	−	0.586185i	0.888502	−	0.458872i	$-0.151746\pi$
$660$	113736.	+	1.13943e6i	0.0101634	+	0.101819i
$661$	1.83192e6	−	666764.i	0.163081	−	0.0593565i	−0.259190	−	0.965826i	$-0.583455\pi$
$661$	1.83192e6	−	666764.i	0.163081	−	0.0593565i	0.422270	+	0.906470i	$0.361233\pi$
$662$	1.76831e6	−	643614.i	0.156825	−	0.0570795i
$663$	−1.15217e6	+	827927.i	−0.101796	+	0.0731489i
$664$	−2.13700e6	−	1.21195e7i	−0.188098	−	1.06675i
$665$	−1.51377e6	+	2.62192e6i	−0.132741	+	0.229914i
$666$	1.22611e7	+	1.39072e7i	1.07114	+	1.21494i
$667$	1.00889e7	+	1.74746e7i	0.878074	+	1.52087i
$668$	1.93513e6	−	1.62376e6i	0.167791	−	0.140793i
$669$	1.22790e7	+	923202.i	1.06071	+	0.0797502i
$670$	−2.00896e6	+	1.13934e7i	−0.172896	+	0.980542i
$671$	5.86432e6	+	4.92075e6i	0.502818	+	0.421915i
$672$	814685.	−	3.19620e6i	0.0695932	−	0.273031i
$673$	1.24854e7	+	4.54432e6i	1.06259	+	0.386750i	0.813400	−	0.581705i	$-0.197614\pi$
$673$	1.24854e7	+	4.54432e6i	1.06259	+	0.386750i	0.249188	+	0.968455i	$0.419836\pi$
$674$	−1.09044e7			−0.924600
$675$	91071.0	−	46605.1i	0.00769344	−	0.00393708i
$676$	2.57740e6			0.216927
$677$	7.00046e6	+	2.54796e6i	0.587023	+	0.213659i	0.618419	−	0.785848i	$-0.287773\pi$
$677$	7.00046e6	+	2.54796e6i	0.587023	+	0.213659i	−0.0313968	+	0.999507i	$0.509996\pi$
$678$	8.43197e6	−	2.37016e6i	0.704457	−	0.198018i
$679$	−2.12262e6	−	1.78109e6i	−0.176684	−	0.148256i
$680$	−995704.	+	5.64692e6i	−0.0825768	+	0.468316i
$681$	1.02984e7	−	1.50970e7i	0.850946	−	1.24745i
$682$	7.06805e6	−	5.93080e6i	0.581887	−	0.488261i
$683$	−1.58891e6	−	2.75208e6i	−0.130331	−	0.225740i	0.793473	−	0.608605i	$-0.208271\pi$
$683$	−1.58891e6	−	2.75208e6i	−0.130331	−	0.225740i	−0.923804	+	0.382865i	$0.874937\pi$
$684$	−1.24516e6	−	188300.i	−0.101762	−	0.0153890i
$685$	−3.14976e6	+	5.45554e6i	−0.256478	+	0.444233i
$686$	1.85974e6	+	1.05471e7i	0.150884	+	0.855705i
$687$	−2.85120e6	−	1.28735e6i	−0.230481	−	0.104065i
$688$	4.87663e6	−	1.77495e6i	0.392779	−	0.142960i
$689$	−3.84429e6	+	1.39921e6i	−0.308509	+	0.112288i
$690$	−1.78758e7	−	8.07111e6i	−1.42936	−	0.645372i
$691$	−2.13192e6	−	1.20907e7i	−0.169854	−	0.963288i	−0.943918	−	0.330181i	$-0.892890\pi$
$691$	−2.13192e6	−	1.20907e7i	−0.169854	−	0.963288i	0.774064	−	0.633107i	$-0.218221\pi$
$692$	−181376.	+	314152.i	−0.0143984	+	0.0249387i
$693$	−2.09999e6	+	2.63067e6i	−0.166106	+	0.208081i
$694$	9.21321e6	+	1.59577e7i	0.726127	+	1.25769i
$695$	−1.48186e6	+	1.24343e6i	−0.116371	+	0.0976468i
$696$	−7.58255e6	+	1.11157e7i	−0.593324	+	0.869790i
$697$	502889.	−	2.85203e6i	0.0392094	−	0.222368i
$698$	−1.09373e7	−	9.17750e6i	−0.849713	−	0.712994i
$699$	8.80080e6	−	2.47384e6i	0.681285	−	0.191504i
$700$	−15177.9	−	5524.32i	−0.00117076	−	0.000426122i
$701$	−1.76379e7			−1.35566			−0.677831	−	0.735218i	$-0.737080\pi$
$701$	−1.76379e7			−1.35566			−0.677831	+	0.735218i	$0.737080\pi$
$702$	2.20293e6	−	2.37071e6i	0.168717	−	0.181566i
$703$	−1.05932e7			−0.808421
$704$	−5.98368e6	−	2.17788e6i	−0.455027	−	0.165616i
$705$	375138.	−	1.47175e6i	0.0284262	−	0.111523i
$706$	−1.29518e6	−	1.08679e6i	−0.0977955	−	0.0820601i
$707$	1.37971e6	−	7.82473e6i	0.103810	−	0.588736i
$708$	−4.33345e6	−	325812.i	−0.324901	−	0.0244278i
$709$	−2.48074e6	+	2.08159e6i	−0.185339	+	0.155518i	−0.730736	−	0.682660i	$-0.760823\pi$
$709$	−2.48074e6	+	2.08159e6i	−0.185339	+	0.155518i	0.545398	+	0.838177i	$0.316379\pi$
$710$	3.45642e6	+	5.98669e6i	0.257324	+	0.445698i
$711$	5.49992e6	−	1.63432e7i	0.408021	−	1.21245i
$712$	6.98060e6	−	1.20908e7i	0.516051	−	0.893827i
$713$	−8.47204e6	−	4.80474e7i	−0.624115	−	3.53953i
$714$	−2.61261e6	+	1.87737e6i	−0.191791	+	0.137818i
$715$	1.57992e6	−	575045.i	0.115577	−	0.0420666i
$716$	−2.47193e6	+	899708.i	−0.180199	+	0.0655872i
$717$	1.95994e6	+	1.96351e7i	0.142379	+	1.42638i
$718$	72495.3	+	411141.i	0.00524806	+	0.0297632i
$719$	−302551.	+	524034.i	−0.0218261	+	0.0378040i	−0.876732	−	0.480979i	$-0.840281\pi$
$719$	−302551.	+	524034.i	−0.0218261	+	0.0378040i	0.854906	+	0.518783i	$0.173615\pi$
$720$	−239829.	−	9.80920e6i	−0.0172413	−	0.705184i
$721$	601202.	+	1.04131e6i	0.0430707	+	0.0746006i
$722$	7.59397e6	−	6.37210e6i	0.542158	−	0.454925i
$723$	5.25615e6	+	1.09213e7i	0.373957	+	0.777016i
$724$	−165556.	+	938916.i	−0.0117381	+	0.0665703i
$725$	91317.2	+	76624.2i	0.00645220	+	0.00541404i
$726$	−7.19844e6	−	7.02459e6i	−0.506870	−	0.494629i
$727$	5.52641e6	+	2.01145e6i	0.387799	+	0.141147i	0.528559	−	0.848896i	$-0.322732\pi$
$727$	5.52641e6	+	2.01145e6i	0.387799	+	0.141147i	−0.140760	+	0.990044i	$0.544955\pi$
$728$	−2.67697e6			−0.187204
$729$	−1.05131e6	−	1.43103e7i	−0.0732679	−	0.997312i
$730$	1.12907e7			0.784177
$731$	3.54111e6	+	1.28886e6i	0.245101	+	0.0892096i
$732$	3.68745e6	+	3.59840e6i	0.254360	+	0.248217i
$733$	1.54078e7	+	1.29287e7i	1.05921	+	0.888779i	0.994031	−	0.109095i	$-0.0347953\pi$
$733$	1.54078e7	+	1.29287e7i	1.05921	+	0.888779i	0.0651741	+	0.997874i	$0.479240\pi$
$734$	3.24274e6	−	1.83905e7i	0.222163	−	1.25995i
$735$	−3.96202e6	−	8.23236e6i	−0.270519	−	0.562090i
$736$	−9.35251e6	+	7.84769e6i	−0.636405	+	0.534007i
$737$	−3.67462e6	−	6.36463e6i	−0.249197	−	0.431623i
$738$	161459.	+	6.60380e6i	0.0109124	+	0.446327i
$739$	−7.44415e6	+	1.28936e7i	−0.501423	+	0.868489i	0.498576	+	0.866846i	$0.333856\pi$
$739$	−7.44415e6	+	1.28936e7i	−0.501423	+	0.868489i	−0.999999	+	0.00164344i	$0.999477\pi$
$740$	1.12573e6	+	6.38434e6i	0.0755710	+	0.428585i
$741$	183655.	+	1.83990e6i	0.0122873	+	0.123097i
$742$	−8.71714e6	+	3.17278e6i	−0.581252	+	0.211558i
$743$	−2.30298e7	+	8.38217e6i	−1.53045	+	0.557037i	−0.963731	−	0.266875i	$-0.914009\pi$
$743$	−2.30298e7	+	8.38217e6i	−1.53045	+	0.557037i	−0.566717	+	0.823913i	$0.691787\pi$
$744$	2.64208e7	−	1.89855e7i	1.74990	−	1.25744i
$745$	−3.07564e6	−	1.74428e7i	−0.203023	−	1.15140i
$746$	1.07568e6	−	1.86313e6i	0.0707679	−	0.122574i
$747$	−4.87730e6	+	1.44931e7i	−0.319799	+	0.950296i
$748$	−347619.	−	602093.i	−0.0227169	−	0.0393468i
$749$	4.77892e6	−	4.00999e6i	0.311261	−	0.261179i
$750$	−1.34852e7	−	1.01389e6i	−0.875398	−	0.0658171i
$751$	1.66509e6	−	9.44320e6i	0.107730	−	0.610969i	−0.882364	−	0.470567i	$-0.844049\pi$
$751$	1.66509e6	−	9.44320e6i	0.107730	−	0.610969i	0.990095	−	0.140402i	$-0.0448395\pi$
$752$	972818.	+	816291.i	0.0627317	+	0.0526381i
$753$	151402.	−	593985.i	0.00973069	−	0.0381758i
$754$	3.54351e6	+	1.28973e6i	0.226989	+	0.0826174i
$755$	2.98846e7			1.90801
$756$	−1.54212e6	+	1.65957e6i	−0.0981327	+	0.105607i
$757$	−2.11227e6			−0.133971			−0.0669853	−	0.997754i	$-0.521338\pi$
$757$	−2.11227e6			−0.133971			−0.0669853	+	0.997754i	$0.521338\pi$
$758$	−3.35291e6	−	1.22036e6i	−0.211957	−	0.0771462i
$759$	1.19944e7	−	3.37155e6i	0.755745	−	0.212435i
$760$	5.72457e6	+	4.80348e6i	0.359508	+	0.301663i
$761$	−4.81787e6	+	2.73235e7i	−0.301574	+	1.71031i	0.337635	+	0.941277i	$0.390373\pi$
$761$	−4.81787e6	+	2.73235e7i	−0.301574	+	1.71031i	−0.639209	+	0.769033i	$0.720738\pi$
$762$	−7.91382e6	+	1.16014e7i	−0.493741	+	0.723804i
$763$	6.42147e6	−	5.38825e6i	0.399322	−	0.335071i
$764$	2.45429e6	+	4.25096e6i	0.152122	+	0.263484i
$765$	4.44507e6	−	5.56836e6i	0.274615	−	0.344012i
$766$	−1.64014e6	+	2.84081e6i	−0.100997	+	0.174933i
$767$	1.10800e6	+	6.28376e6i	0.0680065	+	0.385684i
$768$	−9.90987e6	−	4.47442e6i	−0.606268	−	0.273737i
$769$	232063.	−	84463.9i	0.0141511	−	0.00515057i	−0.334935	−	0.942241i	$-0.608714\pi$
$769$	232063.	−	84463.9i	0.0141511	−	0.00515057i	0.349086	+	0.937091i	$0.386492\pi$
$770$	3.58257e6	−	1.30395e6i	0.217755	−	0.0792562i
$771$	1.55611e6	+	702603.i	0.0942770	+	0.0425671i
$772$	−192487.	−	1.09165e6i	−0.0116241	−	0.0659235i
$773$	−1.02650e7	+	1.77795e7i	−0.617887	+	1.07021i	0.371983	+	0.928239i	$0.378678\pi$
$773$	−1.02650e7	+	1.77795e7i	−0.617887	+	1.07021i	−0.989871	+	0.141973i	$0.954655\pi$
$774$	−8.49895e6	−	1.28526e6i	−0.509933	−	0.0771149i
$775$	−144116.	−	249616.i	−0.00861900	−	0.0149285i
$776$	−5.23928e6	+	4.39628e6i	−0.312333	+	0.262078i
$777$	−1.07388e7	+	1.57427e7i	−0.638124	+	0.935465i
$778$	−109871.	+	623111.i	−0.00650781	+	0.0369076i
$779$	−2.89125e6	−	2.42604e6i	−0.170703	−	0.143237i
$780$	1.08936e6	−	306211.i	0.0641113	−	0.0180212i
$781$	−4.12650e6	−	1.50192e6i	−0.242078	−	0.0881091i
$782$	1.19082e7			0.696353
$783$	1.48840e7	−	7.61678e6i	0.867589	−	0.443984i
$784$	7.63900e6			0.443861
$785$	1.68134e7	+	6.11959e6i	0.973828	+	0.354444i
$786$	−2.19487e6	+	8.61100e6i	−0.126722	+	0.497161i
$787$	−2.11449e7	−	1.77427e7i	−1.21694	−	1.02113i	−0.998979	−	0.0451755i	$-0.985615\pi$
$787$	−2.11449e7	−	1.77427e7i	−1.21694	−	1.02113i	−0.217960	−	0.975958i	$-0.569940\pi$
$788$	762960.	−	4.32696e6i	0.0437710	−	0.248238i
$789$	53907.3	+	4053.04i	0.00308287	+	0.000231787i
$790$	−1.49615e7	+	1.25542e7i	−0.852917	+	0.715682i
$791$	4.50132e6	+	7.79652e6i	0.255799	+	0.443057i
$792$	5.49456e6	+	6.23223e6i	0.311258	+	0.353046i
$793$	3.78249e6	−	6.55147e6i	0.213597	−	0.369961i
$794$	611824.	+	3.46982e6i	0.0344409	+	0.195324i
$795$	1.66838e7	−	1.19887e7i	0.936219	−	0.672749i
$796$	−4.96369e6	+	1.80663e6i	−0.277665	+	0.101062i
$797$	1.97980e7	−	7.20589e6i	1.10402	−	0.401830i	0.275222	−	0.961381i	$-0.411249\pi$
$797$	1.97980e7	−	7.20589e6i	1.10402	−	0.401830i	0.828796	+	0.559551i	$0.189026\pi$
$798$	416449.	+	4.17207e6i	0.0231502	+	0.231923i
$799$	160128.	+	908132.i	0.00887362	+	0.0503248i
$800$	−36063.4	+	62463.7i	−0.00199224	+	0.00345067i
$801$	−1.48072e7	+	9.03856e6i	−0.815439	+	0.497758i
$802$	−6.22116e6	−	1.07754e7i	−0.341535	−	0.591556i
$803$	−5.49434e6	+	4.61030e6i	−0.300695	+	0.252313i
$804$	−2.14501e6	−	4.45694e6i	−0.117028	−	0.243163i
$805$	3.50067e6	−	1.98533e7i	0.190397	−	1.07980i
$806$	−6.98464e6	−	5.86081e6i	−0.378710	−	0.317775i
$807$	2.14082e6	+	2.08912e6i	0.115717	+	0.112922i
$808$	−1.84291e7	−	6.70763e6i	−0.993058	−	0.361444i
$809$	−1.73483e7			−0.931936			−0.465968	−	0.884802i	$-0.654294\pi$
$809$	−1.73483e7			−0.931936			−0.465968	+	0.884802i	$0.654294\pi$
$810$	−7.42844e6	+	1.44549e7i	−0.397818	+	0.774109i
$811$	3.09399e6			0.165183			0.0825917	−	0.996583i	$-0.473680\pi$
$811$	3.09399e6			0.165183			0.0825917	+	0.996583i	$0.473680\pi$
$812$	−2.48057e6	−	902853.i	−0.132026	−	0.0480537i
$813$	−2.34816e7	−	2.29145e7i	−1.24595	−	1.21586i
$814$	1.02188e7	+	8.57458e6i	0.540553	+	0.453578i
$815$	−1.04228e6	+	5.91108e6i	−0.0549657	+	0.311726i
$816$	2.58351e6	+	5.36806e6i	0.135826	+	0.282223i
$817$	3.76215e6	−	3.15682e6i	0.197188	−	0.165461i
$818$	832920.	+	1.44266e6i	0.0435231	+	0.0753843i
$819$	2.92049e6	+	1.59226e6i	0.152141	+	0.0829479i
$820$	−1.15489e6	+	2.00032e6i	−0.0599798	+	0.103888i
$821$	3.85270e6	+	2.18498e7i	0.199484	+	1.13133i	0.905887	+	0.423519i	$0.139205\pi$
$821$	3.85270e6	+	2.18498e7i	0.199484	+	1.13133i	−0.706403	+	0.707810i	$0.749683\pi$
$822$	866522.	+	8.68099e6i	0.0447301	+	0.448115i
$823$	−7.83264e6	+	2.85085e6i	−0.403096	+	0.146715i	−0.535609	−	0.844466i	$-0.679918\pi$
$823$	−7.83264e6	+	2.85085e6i	−0.403096	+	0.146715i	0.132512	+	0.991181i	$0.457696\pi$
$824$	2.78892e6	−	1.01508e6i	0.143093	−	0.0520815i
$825$	59774.4	−	42952.7i	0.00305760	−	0.00219713i
$826$	2.51245e6	+	1.42488e7i	0.128129	+	0.726654i
$827$	1.19335e7	−	2.06694e7i	0.606742	−	1.05091i	−0.385032	−	0.922903i	$-0.625809\pi$
$827$	1.19335e7	−	2.06694e7i	0.606742	−	1.05091i	0.991774	−	0.128004i	$-0.0408572\pi$
$828$	8.22002e6	−	1.65753e6i	0.416674	−	0.0840206i
$829$	−1.16314e7	−	2.01463e7i	−0.587824	−	1.01814i	−0.994517	−	0.104576i	$-0.966651\pi$
$829$	−1.16314e7	−	2.01463e7i	−0.587824	−	1.01814i	0.406693	−	0.913565i	$-0.366682\pi$
$830$	1.32677e7	−	1.11330e7i	0.668500	−	0.560938i
$831$	1.85309e7	+	1.39325e6i	0.930878	+	0.0699884i
$832$	−1.09269e6	+	6.19696e6i	−0.0547254	+	0.310363i
$833$	4.24923e6	+	3.56553e6i	0.212177	+	0.178038i
$834$	−661690.	+	2.59597e6i	−0.0329412	+	0.129236i
$835$	1.75032e7	+	6.37065e6i	0.868764	+	0.316204i
$836$	−906071.			−0.0448380
$837$	−4.01168e7	+	4.99742e6i	−1.97930	+	0.246565i
$838$	−2.55132e7			−1.25503
$839$	1.08447e7	+	3.94716e6i	0.531881	+	0.193589i	0.593978	−	0.804481i	$-0.297557\pi$
$839$	1.08447e7	+	3.94716e6i	0.531881	+	0.193589i	−0.0620970	+	0.998070i	$0.519779\pi$
$840$	1.29418e7	−	3.63786e6i	0.632846	−	0.177888i
$841$	−788265.	−	661433.i	−0.0384310	−	0.0322475i
$842$	−3.26051e6	+	1.84913e7i	−0.158491	+	0.898849i
$843$	−1.80040e7	+	2.63932e7i	−0.872569	+	1.27915i
$844$	952138.	−	798939.i	0.0460091	−	0.0386062i
$845$	9.50227e6	+	1.64584e7i	0.457810	+	0.792951i
$846$	−767497.	−	1.95836e6i	−0.0368681	−	0.0940735i
$847$	5.16901e6	−	8.95299e6i	0.247571	−	0.428805i
$848$	2.98291e6	+	1.69169e7i	0.142446	+	0.807851i
$849$	5.05191e6	+	2.28100e6i	0.240540	+	0.108606i
$850$	66108.2	−	24061.4i	0.00313840	−	0.00114228i
$851$	6.62832e7	−	2.41251e7i	3.13747	−	1.14195i
$852$	−2.69366e6	−	1.21622e6i	−0.127129	−	0.0574000i
$853$	3.16606e6	+	1.79556e7i	0.148987	+	0.844945i	0.964079	+	0.265614i	$0.0855748\pi$
$853$	3.16606e6	+	1.79556e7i	0.148987	+	0.844945i	−0.815093	+	0.579330i	$0.803314\pi$
$854$	8.57701e6	−	1.48558e7i	0.402431	−	0.697031i
$855$	−3.38820e6	−	8.64542e6i	−0.158509	−	0.404456i
$856$	−7.69920e6	−	1.33354e7i	−0.359138	−	0.622045i
$857$	−2.98716e7	+	2.50653e7i	−1.38933	+	1.16579i	−0.423724	+	0.905791i	$0.639277\pi$
$857$	−2.98716e7	+	2.50653e7i	−1.38933	+	1.16579i	−0.965609	+	0.259998i	$0.916278\pi$
$858$	1.31213e6	−	1.92353e6i	0.0608497	−	0.0892032i
$859$	595591.	−	3.37777e6i	0.0275401	−	0.156188i	−0.967936	−	0.251195i	$-0.919176\pi$
$859$	595591.	−	3.37777e6i	0.0275401	−	0.156188i	0.995477	+	0.0950075i	$0.0302875\pi$
$860$	−2.30237e6	−	1.93192e6i	−0.106152	−	0.0890722i
$861$	−6.53640e6	+	1.83733e6i	−0.300490	+	0.0844656i
$862$	1.85860e7	+	6.76476e6i	0.851959	+	0.310088i
$863$	1.90060e7			0.868686			0.434343	−	0.900748i	$-0.356981\pi$
$863$	1.90060e7			0.868686			0.434343	+	0.900748i	$0.356981\pi$
$864$	6.10242e6	+	8.06859e6i	0.278111	+	0.367717i
$865$	−2.67476e6			−0.121547
$866$	−3.11214e7	−	1.13273e7i	−1.41015	−	0.513252i
$867$	4.39834e6	−	1.72557e7i	0.198720	−	0.779626i
$868$	4.88947e6	+	4.10275e6i	0.220273	+	0.184831i
$869$	2.15442e6	−	1.22183e7i	0.0967791	−	0.548862i
$870$	−1.88838e7	−	1.41979e6i	−0.845847	−	0.0635953i
$871$	−5.56341e6	+	4.66825e6i	−0.248482	+	0.208501i
$872$	−1.03455e7	−	1.79189e7i	−0.460743	−	0.798030i
$873$	8.33080e6	−	1.67987e6i	0.369957	−	0.0746002i
$874$	7.75971e6	−	1.34402e7i	0.343611	−	0.595151i
$875$	−2.41369e6	−	1.36887e7i	−0.106576	−	0.604424i
$876$	−3.92008e6	+	2.81689e6i	−0.172597	+	0.124025i
$877$	3.35765e7	−	1.22209e7i	1.47413	−	0.536541i	0.524914	−	0.851155i	$-0.324098\pi$
$877$	3.35765e7	−	1.22209e7i	1.47413	−	0.536541i	0.949219	+	0.314615i	$0.101875\pi$
$878$	3.74484e6	−	1.36301e6i	0.163944	−	0.0596709i
$879$	3.29117e6	+	3.29716e7i	0.143674	+	1.43936i
$880$	−1.22591e6	−	6.95251e6i	−0.0533646	−	0.302646i
$881$	−9.59250e6	+	1.66147e7i	−0.416382	+	0.721195i	−0.995572	−	0.0939973i	$-0.970035\pi$
$881$	−9.59250e6	+	1.66147e7i	−0.416382	+	0.721195i	0.579190	+	0.815192i	$0.303369\pi$
$882$	−1.11088e7	−	6.05657e6i	−0.480834	−	0.262153i
$883$	−1.03384e7	−	1.79066e7i	−0.446222	−	0.772879i	0.551914	−	0.833901i	$-0.313898\pi$
$883$	−1.03384e7	−	1.79066e7i	−0.446222	−	0.772879i	−0.998136	+	0.0610214i	$0.980564\pi$
$884$	−526298.	+	441617.i	−0.0226517	+	0.0190070i
$885$	−1.38959e7	−	2.88732e7i	−0.596388	−	1.23919i
$886$	1.16371e6	−	6.59974e6i	0.0498037	−	0.282451i
$887$	−2.37488e7	−	1.99276e7i	−1.01352	−	0.850445i	−0.0247210	−	0.999694i	$-0.507870\pi$
$887$	−2.37488e7	−	1.99276e7i	−1.01352	−	0.850445i	−0.988800	+	0.149250i	$0.952314\pi$
$888$	3.36647e7	+	3.28517e7i	1.43266	+	1.39806i
$889$	−1.35640e7	−	4.93691e6i	−0.575618	−	0.209508i
$890$	1.96486e7			0.831491
$891$	−2.28745e6	−	1.00673e7i	−0.0965290	−	0.424835i
$892$	5.96277e6			0.250920
$893$	1.12931e6	+	411034.i	0.0473897	+	0.0172484i
$894$	−1.75554e7	−	1.71314e7i	−0.734625	−	0.716884i
$895$	−1.48587e7	−	1.24679e7i	−0.620044	−	0.520279i
$896$	−1.30198e6	+	7.38387e6i	−0.0541792	+	0.307266i
$897$	−5.33938e6	−	1.10943e7i	−0.221569	−	0.460381i
$898$	668212.	−	560696.i	0.0276518	−	0.0232026i
$899$	−2.35532e7	−	4.07953e7i	−0.971963	−	1.68349i
$900$	42284.1	−	25810.9i	0.00174009	−	0.00106218i
$901$	−6.23677e6	+	1.08024e7i	−0.255946	+	0.443311i
$902$	825317.	+	4.68061e6i	0.0337757	+	0.191552i
$903$	−877527.	−	8.79124e6i	−0.0358130	−	0.358782i
$904$	2.08812e7	−	7.60014e6i	0.849835	−	0.309315i
$905$	−6.60599e6	+	2.40438e6i	−0.268112	+	0.0975848i
$906$	3.36095e7	−	2.41511e7i	1.36032	−	0.977499i
$907$	−1.44897e6	−	8.21753e6i	−0.0584846	−	0.331683i	0.941501	−	0.337010i	$-0.109416\pi$
$907$	−1.44897e6	−	8.21753e6i	−0.0584846	−	0.331683i	−0.999986	+	0.00532684i	$0.998304\pi$
$908$	4.42476e6	−	7.66390e6i	0.178104	−	0.308486i
$909$	1.61158e7	+	1.82794e7i	0.646908	+	0.733758i
$910$	−1.88375e6	−	3.26275e6i	−0.0754084	−	0.130611i
$911$	−1.72842e7	+	1.45032e7i	−0.690008	+	0.578986i	−0.918912	−	0.394464i	$-0.870930\pi$
$911$	−1.72842e7	+	1.45032e7i	−0.690008	+	0.578986i	0.228903	+	0.973449i	$0.426486\pi$
$912$	7.74215e6	+	582096.i	0.308230	+	0.0231744i
$913$	−1.91053e6	+	1.08351e7i	−0.0758537	+	0.430188i
$914$	−2.84374e7	−	2.38618e7i	−1.12596	−	0.944795i
$915$	−9.38341e6	+	3.68134e7i	−0.370517	+	1.45363i
$916$	−1.42352e6	−	518118.i	−0.0560562	−	0.0204028i
$917$	−9.13377e6			−0.358696
$918$	499069.	−	9.85467e6i	0.0195458	−	0.385954i
$919$	3.06929e7			1.19881			0.599403	−	0.800447i	$-0.295405\pi$
$919$	3.06929e7			1.19881			0.599403	+	0.800447i	$0.295405\pi$
$920$	−4.67591e7	−	1.70189e7i	−1.82136	−	0.662922i
$921$	−2.29887e7	+	6.46196e6i	−0.893029	+	0.251024i
$922$	1.41730e7	+	1.18926e7i	0.549079	+	0.460732i
$923$	−753549.	+	4.27359e6i	−0.0291143	+	0.165116i
$924$	−918531.	+	1.34653e6i	−0.0353927	+	0.0518843i
$925$	319223.	−	267860.i	0.0122671	−	0.0102933i
$926$	1.67046e7	+	2.89332e7i	0.640190	+	1.10884i
$927$	−3.64639e6	−	551428.i	−0.139368	−	0.0210760i
$928$	−5.89393e6	+	1.02086e7i	−0.224665	+	0.389131i
$929$	273993.	+	1.55389e6i	0.0104160	+	0.0590721i	0.989573	−	0.144034i	$-0.0460075\pi$
$929$	273993.	+	1.55389e6i	0.0104160	+	0.0590721i	−0.979157	+	0.203106i	$0.934896\pi$
$930$	4.17319e7	+	1.88424e7i	1.58220	+	0.714380i
$931$	6.79315e6	−	2.47251e6i	0.256860	−	0.0934895i
$932$	4.15989e6	−	1.51408e6i	0.156871	−	0.0570963i
$933$	−1.93427e7	−	8.73344e6i	−0.727466	−	0.328459i
$934$	5.87455e6	+	3.33162e7i	0.220347	+	1.24965i
$935$	2.56318e6	−	4.43957e6i	0.0958850	−	0.166078i
$936$	5.12226e6	−	6.41668e6i	0.191105	−	0.239398i
$937$	−2.96575e6	−	5.13683e6i	−0.110353	−	0.191138i	0.805559	−	0.592515i	$-0.201865\pi$
$937$	−2.96575e6	−	5.13683e6i	−0.110353	−	0.191138i	−0.915913	+	0.401377i	$0.868532\pi$
$938$	−1.26153e7	+	1.05855e7i	−0.468157	+	0.392831i
$939$	−7.38600e6	+	1.08276e7i	−0.273367	+	0.400745i
$940$	127713.	−	724296.i	0.00471428	−	0.0267360i
$941$	579022.	+	485857.i	0.0213167	+	0.0178869i	0.653384	−	0.757027i	$-0.273349\pi$
$941$	579022.	+	485857.i	0.0213167	+	0.0178869i	−0.632067	+	0.774914i	$0.717793\pi$
$942$	2.38546e7	−	6.70536e6i	0.875881	−	0.246204i
$943$	2.36161e7	+	8.59557e6i	0.864827	+	0.314771i
$944$	2.67922e7			0.978538
$945$	−1.62829e7	−	3.72903e6i	−0.593134	−	0.135837i
$946$	−6.18446e6			−0.224685
$947$	2.22341e7	+	8.09254e6i	0.805645	+	0.293231i	0.711824	−	0.702358i	$-0.247869\pi$
$947$	2.22341e7	+	8.09254e6i	0.805645	+	0.293231i	0.0938215	+	0.995589i	$0.470092\pi$
$948$	2.06244e6	−	8.09145e6i	0.0745351	−	0.292419i
$949$	5.42950e6	+	4.55589e6i	0.195702	+	0.164213i
$950$	15920.9	−	90292.1i	0.000572347	−	0.00324594i
$951$	1.68401e7	+	1.26613e6i	0.603799	+	0.0453968i
$952$	−6.25254e6	+	5.24651e6i	−0.223596	+	0.187619i
$953$	1.90904e7	+	3.30656e7i	0.680900	+	1.17935i	0.974707	+	0.223488i	$0.0717443\pi$
$953$	1.90904e7	+	3.30656e7i	0.680900	+	1.17935i	−0.293807	+	0.955865i	$0.594922\pi$
$954$	9.07473e6	−	2.69659e7i	0.322822	−	0.959277i
$955$	−1.80969e7	+	3.13447e7i	−0.642088	+	1.11213i
$956$	1.65927e6	+	9.41017e6i	0.0587181	+	0.333007i
$957$	9.76908e6	−	7.01987e6i	0.344805	−	0.247770i
$958$	−4.11304e7	+	1.49702e7i	−1.44794	+	0.527005i
$959$	−8.42628e6	+	3.06691e6i	−0.295862	+	0.107685i
$960$	−3.13870e6	−	3.14442e7i	−0.109919	−	1.10119i
$961$	1.48070e7	+	8.39748e7i	0.517201	+	2.93319i
$962$	6.59113e6	−	1.14162e7i	0.229627	−	0.397725i
$963$	467668.	+	1.91280e7i	0.0162507	+	0.664666i
$964$	2.93458e6	+	5.08284e6i	0.101707	+	0.176163i
$965$	6.26127e6	−	5.25383e6i	0.216443	−	0.181617i
$966$	−1.21073e7	−	2.51569e7i	−0.417452	−	0.867389i
$967$	−4.48070e6	+	2.54113e7i	−0.154092	+	0.873899i	0.805519	+	0.592570i	$0.201886\pi$
$967$	−4.48070e6	+	2.54113e7i	−0.154092	+	0.873899i	−0.959611	+	0.281329i	$0.909225\pi$
$968$	−1.95475e7	−	1.64023e7i	−0.670506	−	0.562621i
$969$	4.03491e6	+	3.93747e6i	0.138046	+	0.134712i
$970$	−9.04510e6	−	3.29215e6i	−0.308662	−	0.112344i
$971$	−1.88243e7			−0.640725			−0.320362	−	0.947295i	$-0.603805\pi$
$971$	−1.88243e7			−0.640725			−0.320362	+	0.947295i	$0.603805\pi$
$972$	−1.02720e6	−	6.87197e6i	−0.0348729	−	0.233300i
$973$	−2.75357e6			−0.0932424
$974$	2.37884e6	+	865827.i	0.0803467	+	0.0292438i
$975$	−52058.2	−	50801.0i	−0.00175379	−	0.00171144i
$976$	−2.43333e7	−	2.04181e7i	−0.817668	−	0.686105i
$977$	−3.79638e6	+	2.15303e7i	−0.127243	+	0.721629i	0.852708	+	0.522388i	$0.174959\pi$
$977$	−3.79638e6	+	2.15303e7i	−0.127243	+	0.721629i	−0.979950	+	0.199241i	$0.936152\pi$
$978$	3.60482e6	+	7.49017e6i	0.120514	+	0.250406i
$979$	−9.56152e6	+	8.02307e6i	−0.318838	+	0.267537i
$980$	−2.21204e6	−	3.83137e6i	−0.0735747	−	0.127435i
$981$	628409.	+	2.57024e7i	0.0208483	+	0.852709i
$982$	1.74414e7	−	3.02094e7i	0.577169	−	0.999686i
$983$	3.23530e6	+	1.83483e7i	0.106790	+	0.605637i	0.990490	+	0.137583i	$0.0439334\pi$
$983$	3.23530e6	+	1.83483e7i	0.106790	+	0.605637i	−0.883700	+	0.468054i	$0.844955\pi$
$984$	1.66460e6	+	1.66763e7i	0.0548051	+	0.549049i
$985$	3.04435e7	−	1.10805e7i	0.999777	−	0.363889i
$986$	1.08042e7	−	3.93241e6i	0.353917	−	0.128815i
$987$	1.75568e6	−	1.26160e6i	0.0573658	−	0.0412220i
$988$	155481.	+	881776.i	0.00506739	+	0.0287386i
$989$	−1.63510e7	+	2.83207e7i	−0.531561	+	0.920691i
$990$	−3.72953e6	+	1.10824e7i	−0.120939	+	0.359375i
$991$	7.10731e6	+	1.23102e7i	0.229891	+	0.398182i	0.957776	−	0.287517i	$-0.0928298\pi$
$991$	7.10731e6	+	1.23102e7i	0.229891	+	0.398182i	−0.727885	+	0.685699i	$0.759496\pi$
$992$	2.18339e7	−	1.83208e7i	0.704453	−	0.591107i
$993$	−5.91562e6	−	444768.i	−0.190383	−	0.0143140i
$994$	−1.70871e6	+	9.69060e6i	−0.0548534	+	0.311089i
$995$	−2.98366e7	−	2.50359e7i	−0.955414	−	0.801687i
$996$	−1.82896e6	+	7.17544e6i	−0.0584192	+	0.229192i
$997$	−5.50150e7	−	2.00238e7i	−1.75284	−	0.637983i	−0.753042	−	0.657972i	$-0.771415\pi$
$997$	−5.50150e7	−	2.00238e7i	−1.75284	−	0.637983i	−0.999800	+	0.0199894i	$0.993637\pi$
$998$	−1.42881e7			−0.454097
$999$	−1.71869e7	−	5.58640e7i	−0.544859	−	1.77100i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.6.e.a.4.10	✓	84
3.2	odd	2		81.6.e.a.64.5		84
27.7	even	9	inner	27.6.e.a.7.10	yes	84
27.13	even	9		729.6.a.c.1.14		42
27.14	odd	18		729.6.a.e.1.29		42
27.20	odd	18		81.6.e.a.19.5		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.6.e.a.4.10	✓	84	1.1	even	1	trivial
27.6.e.a.7.10	yes	84	27.7	even	9	inner
81.6.e.a.19.5		84	27.20	odd	18
81.6.e.a.64.5		84	3.2	odd	2
729.6.a.c.1.14		42	27.13	even	9
729.6.a.e.1.29		42	27.14	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(4.64663 + 1.69124i) q^{2} +(-11.1566 - 10.8872i) q^{3} +(-5.78253 - 4.85212i) q^{4} +(9.66519 - 54.8140i) q^{5} +(-33.4278 - 69.4570i) q^{6} +(60.6928 - 50.9273i) q^{7} +(-97.7806 - 169.361i) q^{8} +(5.93943 + 242.927i) q^{9} +O(q^{10})\)	\(q+(4.64663 + 1.69124i) q^{2} +(-11.1566 - 10.8872i) q^{3} +(-5.78253 - 4.85212i) q^{4} +(9.66519 - 54.8140i) q^{5} +(-33.4278 - 69.4570i) q^{6} +(60.6928 - 50.9273i) q^{7} +(-97.7806 - 169.361i) q^{8} +(5.93943 + 242.927i) q^{9} +(137.614 - 238.354i) q^{10} +(30.3601 + 172.181i) q^{11} +(11.6876 + 117.088i) q^{12} +(162.354 - 59.0920i) q^{13} +(368.147 - 133.995i) q^{14} +(-704.600 + 506.312i) q^{15} +(-125.976 - 714.444i) q^{16} +(263.395 - 456.213i) q^{17} +(-383.249 + 1138.84i) q^{18} +(-343.270 - 594.561i) q^{19} +(-321.853 + 270.067i) q^{20} +(-1231.58 - 92.5967i) q^{21} +(-150.126 + 851.406i) q^{22} +(3501.96 + 2938.49i) q^{23} +(-752.961 + 2954.05i) q^{24} +(25.3785 + 9.23702i) q^{25} +854.338 q^{26} +(2578.53 - 2774.91i) q^{27} -598.063 q^{28} +(4147.67 + 1509.63i) q^{29} +(-4130.31 + 1161.00i) q^{30} +(-8175.51 - 6860.06i) q^{31} +(-463.753 + 2630.08i) q^{32} +(1535.84 - 2251.49i) q^{33} +(1995.46 - 1674.39i) q^{34} +(-2204.92 - 3819.04i) q^{35} +(1144.37 - 1433.55i) q^{36} +(7714.90 - 13362.6i) q^{37} +(-589.506 - 3343.25i) q^{38} +(-2454.66 - 1108.31i) q^{39} +(-10228.4 + 3722.84i) q^{40} +(5165.96 - 1880.26i) q^{41} +(-5566.09 - 2513.15i) q^{42} +(1242.19 + 7044.79i) q^{43} +(659.882 - 1142.95i) q^{44} +(13373.2 + 2022.38i) q^{45} +(11302.6 + 19576.7i) q^{46} +(-1340.96 + 1125.20i) q^{47} +(-6372.81 + 9342.29i) q^{48} +(-1828.48 + 10369.8i) q^{49} +(102.303 + 85.8421i) q^{50} +(-7905.45 + 2222.16i) q^{51} +(-1225.54 - 446.059i) q^{52} -23678.4 q^{53} +(16674.5 - 8533.07i) q^{54} +9731.35 q^{55} +(-14559.7 - 5299.29i) q^{56} +(-2643.36 + 10370.5i) q^{57} +(16719.6 + 14029.4i) q^{58} +(-6413.00 + 36369.9i) q^{59} +(6531.05 + 491.039i) q^{60} +(33541.7 - 28144.8i) q^{61} +(-26386.6 - 45702.9i) q^{62} +(12732.1 + 14441.5i) q^{63} +(-18210.4 + 31541.4i) q^{64} +(-1669.89 - 9470.42i) q^{65} +(10944.3 - 7864.35i) q^{66} +(-39499.8 + 14376.8i) q^{67} +(-3736.68 + 1360.04i) q^{68} +(-7078.12 - 70910.0i) q^{69} +(-3786.57 - 21474.7i) q^{70} +(-12558.4 + 21751.8i) q^{71} +(40561.7 - 24759.5i) q^{72} +(20511.6 + 35527.1i) q^{73} +(58447.6 - 49043.4i) q^{74} +(-182.573 - 379.354i) q^{75} +(-899.911 + 5103.65i) q^{76} +(10611.3 + 8903.97i) q^{77} +(-9531.51 - 9301.31i) q^{78} +(-66682.8 - 24270.6i) q^{79} -40379.1 q^{80} +(-58978.4 + 2885.70i) q^{81} +27184.3 q^{82} +(59133.9 + 21523.0i) q^{83} +(6672.35 + 6511.21i) q^{84} +(-22461.1 - 18847.1i) q^{85} +(-6142.42 + 34835.4i) q^{86} +(-29838.3 - 61998.7i) q^{87} +(26192.1 - 21977.7i) q^{88} +(35695.2 + 61825.9i) q^{89} +(58720.2 + 32014.5i) q^{90} +(6844.32 - 11854.7i) q^{91} +(-5992.27 - 33983.8i) q^{92} +(16524.2 + 165543. i) q^{93} +(-8133.90 + 2960.50i) q^{94} +(-35908.0 + 13069.5i) q^{95} +(33808.0 - 24293.7i) q^{96} +(-6073.03 - 34441.8i) q^{97} +(-26034.1 + 45092.3i) q^{98} +(-41647.1 + 8397.95i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 93 q^{5} - 126 q^{6} - 6 q^{7} + 573 q^{8} + 324 q^{9}+O(q^{10}) \) 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	\( 84 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 93 q^{5} - 126 q^{6} - 6 q^{7} + 573 q^{8} + 324 q^{9} - 3 q^{10} + 111 q^{11} - 2769 q^{12} - 6 q^{13} - 1641 q^{14} + 1989 q^{15} + 90 q^{16} + 3465 q^{17} - 99 q^{18} - 3 q^{19} + 9987 q^{20} + 5424 q^{21} - 2850 q^{22} - 7716 q^{23} - 18486 q^{24} + 4953 q^{25} - 7806 q^{26} - 8109 q^{27} - 12 q^{28} - 20418 q^{29} - 6453 q^{30} - 6657 q^{31} + 51192 q^{32} + 50634 q^{33} - 11394 q^{34} + 35868 q^{35} - 3600 q^{36} - 3 q^{37} - 44076 q^{38} - 13971 q^{39} + 12441 q^{40} - 79077 q^{41} - 64422 q^{42} - 9465 q^{43} + 110757 q^{44} + 92493 q^{45} - 3 q^{46} + 103557 q^{47} + 134049 q^{48} + 5484 q^{49} - 105513 q^{50} - 124866 q^{51} + 68625 q^{52} - 206406 q^{53} - 350946 q^{54} - 12 q^{55} - 147237 q^{56} + 67767 q^{57} - 9753 q^{58} + 116484 q^{59} + 241290 q^{60} - 70116 q^{61} + 246066 q^{62} + 135981 q^{63} - 86019 q^{64} - 19815 q^{65} - 32931 q^{66} + 48117 q^{67} - 48105 q^{68} + 25263 q^{69} + 270111 q^{70} + 279531 q^{71} + 441684 q^{72} - 27012 q^{73} + 233691 q^{74} + 18399 q^{75} - 125670 q^{76} - 345135 q^{77} - 520974 q^{78} - 216186 q^{79} - 924114 q^{80} - 428616 q^{81} - 12 q^{82} - 370401 q^{83} - 522390 q^{84} - 43731 q^{85} + 116682 q^{86} + 304173 q^{87} + 371418 q^{88} + 154827 q^{89} + 327366 q^{90} - 91002 q^{91} + 1279059 q^{92} + 890079 q^{93} + 11667 q^{94} + 1087671 q^{95} + 1165698 q^{96} - 420621 q^{97} + 463410 q^{98} - 28323 q^{99}+O(q^{100}) \) 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

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Database

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