LMFDB - Embedded newform 74.8.e.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,8,Mod(11,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("74.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	74.e (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$23.1164918858$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	74.11
Dual form			74.8.e.a.27.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.92820 + 4.00000i) q^{2} +(-3.53023 + 6.11453i) q^{3} +(32.0000 - 55.4256i) q^{4} +(-112.662 - 65.0457i) q^{5} -56.4836i q^{6} +(-91.9227 + 159.215i) q^{7} +512.000i q^{8} +(1068.57 + 1850.83i) q^{9} +1040.73 q^{10} +2791.74 q^{11} +(225.935 + 391.330i) q^{12} +(-10311.4 - 5953.29i) q^{13} -1470.76i q^{14} +(795.448 - 459.252i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(-21213.5 + 12247.6i) q^{17} +(-14806.6 - 8548.60i) q^{18} +(35647.2 + 20580.9i) q^{19} +(-7210.39 + 4162.92i) q^{20} +(-649.016 - 1124.13i) q^{21} +(-19341.7 + 11167.0i) q^{22} -22712.8i q^{23} +(-3130.64 - 1807.48i) q^{24} +(-30600.6 - 53001.8i) q^{25} +95252.7 q^{26} -30530.5 q^{27} +(5883.05 + 10189.7i) q^{28} -78263.6i q^{29} +(-3674.02 + 6363.58i) q^{30} -180429. i q^{31} +(28377.9 + 16384.0i) q^{32} +(-9855.47 + 17070.2i) q^{33} +(97981.1 - 169708. i) q^{34} +(20712.5 - 11958.3i) q^{35} +136778. q^{36} +(182948. - 247915. i) q^{37} -329295. q^{38} +(72803.2 - 42033.0i) q^{39} +(33303.4 - 57683.2i) q^{40} +(304110. - 526734. i) q^{41} +(8993.03 + 5192.13i) q^{42} -746888. i q^{43} +(89335.6 - 154734. i) q^{44} -278025. i q^{45} +(90851.1 + 157359. i) q^{46} -605637. q^{47} +28919.6 q^{48} +(394872. + 683938. i) q^{49} +(424015. + 244805. i) q^{50} -172948. i q^{51} +(-659930. + 381011. i) q^{52} +(-459254. - 795452. i) q^{53} +(211521. - 122122. i) q^{54} +(-314524. - 181590. i) q^{55} +(-81518.0 - 47064.4i) q^{56} +(-251685. + 145311. i) q^{57} +(313054. + 542226. i) q^{58} +(2.09786e6 - 1.21120e6i) q^{59} -58784.3i q^{60} +(-1.48145e6 - 855313. i) q^{61} +(721717. + 1.25005e6i) q^{62} -392905. q^{63} -262144. q^{64} +(774472. + 1.34142e6i) q^{65} -157688. i q^{66} +(-2.39541e6 + 4.14897e6i) q^{67} +1.56770e6i q^{68} +(138878. + 80181.3i) q^{69} +(-95666.8 + 165700. i) q^{70} +(2.11372e6 - 3.66107e6i) q^{71} +(-947623. + 547110. i) q^{72} -2.75576e6 q^{73} +(-275843. + 2.44940e6i) q^{74} +432109. q^{75} +(2.28142e6 - 1.31718e6i) q^{76} +(-256624. + 444486. i) q^{77} +(-336264. + 582426. i) q^{78} +(-3.19167e6 - 1.84271e6i) q^{79} +532854. i q^{80} +(-2.22919e6 + 3.86108e6i) q^{81} +4.86576e6i q^{82} +(807564. + 1.39874e6i) q^{83} -83074.1 q^{84} +3.18662e6 q^{85} +(2.98755e6 + 5.17459e6i) q^{86} +(478545. + 276288. i) q^{87} +1.42937e6i q^{88} +(-8.77436e6 + 5.06588e6i) q^{89} +(1.11210e6 + 1.92621e6i) q^{90} +(1.89571e6 - 1.09449e6i) q^{91} +(-1.25887e6 - 726809. i) q^{92} +(1.10324e6 + 636956. i) q^{93} +(4.19597e6 - 2.42255e6i) q^{94} +(-2.67740e6 - 4.63739e6i) q^{95} +(-200361. + 115679. i) q^{96} -9.44667e6i q^{97} +(-5.47151e6 - 3.15898e6i) q^{98} +(2.98318e6 + 5.16702e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 28 q^{3} + 1536 q^{4} + 252 q^{5} + 52 q^{7} - 24028 q^{9} + 4864 q^{10} - 8352 q^{11} - 1792 q^{12} - 5136 q^{13} - 16632 q^{15} - 98304 q^{16} + 28980 q^{17} - 66096 q^{19} + 16128 q^{20} - 64344 q^{21}+ \cdots + 50165480 q^{99}+O(q^{100}) $ 48 * q + 28 * q^3 + 1536 * q^4 + 252 * q^5 + 52 * q^7 - 24028 * q^9 + 4864 * q^10 - 8352 * q^11 - 1792 * q^12 - 5136 * q^13 - 16632 * q^15 - 98304 * q^16 + 28980 * q^17 - 66096 * q^19 + 16128 * q^20 - 64344 * q^21 + 675072 * q^25 + 533952 * q^26 - 444416 * q^27 - 3328 * q^28 - 114528 * q^30 + 120916 * q^33 + 120992 * q^34 + 865908 * q^35 - 3075584 * q^36 - 500268 * q^37 + 879360 * q^38 - 669984 * q^39 + 155648 * q^40 + 1024524 * q^41 - 589728 * q^42 - 267264 * q^44 - 729888 * q^46 - 2144712 * q^47 - 229376 * q^48 - 3570900 * q^49 + 2919168 * q^50 - 328704 * q^52 - 2231700 * q^53 + 3784320 * q^54 + 3781260 * q^55 - 1487472 * q^57 + 468064 * q^58 - 10302480 * q^59 + 10141752 * q^61 + 4388256 * q^62 + 9348424 * q^63 - 12582912 * q^64 + 1169736 * q^65 - 1473864 * q^67 + 14887176 * q^69 - 310528 * q^70 + 3017772 * q^71 + 16773224 * q^73 - 2565696 * q^74 - 10623504 * q^75 - 4230144 * q^76 + 15133908 * q^77 - 763328 * q^78 - 2776836 * q^79 - 29469256 * q^81 - 1844556 * q^83 - 8236032 * q^84 - 9520960 * q^85 - 1972416 * q^86 - 51259224 * q^87 + 33361344 * q^89 - 28098496 * q^90 + 91933608 * q^91 + 4193280 * q^92 - 9874476 * q^93 - 28885728 * q^94 - 40830084 * q^95 + 11612160 * q^98 + 50165480 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−6.92820	+	4.00000i	−0.612372	+	0.353553i
$2$	−6.92820	+	4.00000i	−0.612372	+	0.353553i
$3$	−3.53023	+	6.11453i	−0.0754881	+	0.130749i	−0.901298	−	0.433199i	$-0.857385\pi$
$3$	−3.53023	+	6.11453i	−0.0754881	+	0.130749i	0.825810	+	0.563948i	$0.190718\pi$
$4$	32.0000	−	55.4256i	0.250000	−	0.433013i
$5$	−112.662	−	65.0457i	−0.403073	−	0.232714i	0.284736	−	0.958606i	$-0.408094\pi$
$5$	−112.662	−	65.0457i	−0.403073	−	0.232714i	−0.687809	+	0.725892i	$0.741427\pi$
$6$		−	56.4836i		−	0.106756i
$7$	−91.9227	+	159.215i	−0.101293	+	0.175445i	−0.912218	−	0.409706i	$-0.865631\pi$
$7$	−91.9227	+	159.215i	−0.101293	+	0.175445i	0.810925	+	0.585151i	$0.198965\pi$
$8$			512.000i			0.353553i
$9$	1068.57	+	1850.83i	0.488603	+	0.846285i
$10$	1040.73			0.329108
$11$	2791.74			0.632412			0.316206	−	0.948691i	$-0.397591\pi$
$11$	2791.74			0.632412			0.316206	+	0.948691i	$0.397591\pi$
$12$	225.935	+	391.330i	0.0377440	+	0.0653746i
$13$	−10311.4	−	5953.29i	−1.30172	−	0.751546i	−0.321018	−	0.947073i	$-0.604025\pi$
$13$	−10311.4	−	5953.29i	−1.30172	−	0.751546i	−0.980698	+	0.195527i	$0.937358\pi$
$14$		−	1470.76i		−	0.143250i
$15$	795.448	−	459.252i	0.0608545	−	0.0351343i
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	−21213.5	+	12247.6i	−1.04723	+	0.604618i	−0.921872	−	0.387494i	$-0.873341\pi$
$17$	−21213.5	+	12247.6i	−1.04723	+	0.604618i	−0.125357	+	0.992112i	$0.540008\pi$
$18$	−14806.6	−	8548.60i	−0.598414	−	0.345495i
$19$	35647.2	+	20580.9i	1.19231	+	0.688378i	0.958829	−	0.283984i	$-0.0916563\pi$
$19$	35647.2	+	20580.9i	1.19231	+	0.688378i	0.233477	+	0.972362i	$0.424990\pi$
$20$	−7210.39	+	4162.92i	−0.201537	+	0.116357i
$21$	−649.016	−	1124.13i	−0.0152928	−	0.0264880i
$22$	−19341.7	+	11167.0i	−0.387272	+	0.223592i
$23$		−	22712.8i		−	0.389245i	−0.980878	−	0.194622i	$-0.937652\pi$
$23$		−	22712.8i		−	0.389245i	0.980878	−	0.194622i	$-0.0623481\pi$
$24$	−3130.64	−	1807.48i	−0.0462268	−	0.0266891i
$25$	−30600.6	−	53001.8i	−0.391688	−	0.678423i
$26$	95252.7			1.06285
$27$	−30530.5			−0.298511
$28$	5883.05	+	10189.7i	0.0506465	+	0.0877224i
$29$		−	78263.6i		−	0.595891i	−0.954583	−	0.297946i	$-0.903699\pi$
$29$		−	78263.6i		−	0.595891i	0.954583	−	0.297946i	$-0.0963014\pi$
$30$	−3674.02	+	6363.58i	−0.0248437	+	0.0430306i
$31$		−	180429.i		−	1.08778i	−0.839157	−	0.543890i	$-0.816951\pi$
$31$		−	180429.i		−	1.08778i	0.839157	−	0.543890i	$-0.183049\pi$
$32$	28377.9	+	16384.0i	0.153093	+	0.0883883i
$33$	−9855.47	+	17070.2i	−0.0477396	+	0.0826874i
$34$	97981.1	−	169708.i	0.427530	−	0.740503i
$35$	20712.5	−	11958.3i	0.0816570	−	0.0471447i
$36$	136778.			0.488603
$37$	182948.	−	247915.i	0.593775	−	0.804631i
$37$	182948.	−	247915.i	0.593775	−	0.804631i
$38$	−329295.			−0.973514
$39$	72803.2	−	42033.0i	0.196528	−	0.113466i
$40$	33303.4	−	57683.2i	0.0822770	−	0.142508i
$41$	304110.	−	526734.i	0.689108	−	1.19357i	−0.283019	−	0.959114i	$-0.591336\pi$
$41$	304110.	−	526734.i	0.689108	−	1.19357i	0.972127	−	0.234456i	$-0.0753309\pi$
$42$	8993.03	+	5192.13i	0.0187298	+	0.0108137i
$43$		−	746888.i		−	1.43257i	−0.697808	−	0.716285i	$-0.745841\pi$
$43$		−	746888.i		−	1.43257i	0.697808	−	0.716285i	$-0.254159\pi$
$44$	89335.6	−	154734.i	0.158103	−	0.273843i
$45$		−	278025.i		−	0.454820i
$46$	90851.1	+	157359.i	0.137619	+	0.238363i
$47$	−605637.			−0.850883			−0.425441	−	0.904986i	$-0.639881\pi$
$47$	−605637.			−0.850883			−0.425441	+	0.904986i	$0.639881\pi$
$48$	28919.6			0.0377440
$49$	394872.	+	683938.i	0.479479	+	0.830483i
$50$	424015.	+	244805.i	0.479718	+	0.276965i
$51$		−	172948.i		−	0.182566i
$52$	−659930.	+	381011.i	−0.650858	+	0.375773i
$53$	−459254.	−	795452.i	−0.423728	−	0.733919i	0.572572	−	0.819854i	$-0.305946\pi$
$53$	−459254.	−	795452.i	−0.423728	−	0.733919i	−0.996301	+	0.0859350i	$0.972612\pi$
$54$	211521.	−	122122.i	0.182800	−	0.105540i
$55$	−314524.	−	181590.i	−0.254908	−	0.147171i
$56$	−81518.0	−	47064.4i	−0.0620291	−	0.0358125i
$57$	−251685.	+	145311.i	−0.180010	+	0.103929i
$58$	313054.	+	542226.i	0.210679	+	0.364907i
$59$	2.09786e6	−	1.21120e6i	1.32983	−	0.767776i	0.344555	−	0.938766i	$-0.388030\pi$
$59$	2.09786e6	−	1.21120e6i	1.32983	−	0.767776i	0.985273	+	0.170990i	$0.0546965\pi$
$60$		−	58784.3i		−	0.0351343i
$61$	−1.48145e6	−	855313.i	−0.835664	−	0.482471i	0.0201243	−	0.999797i	$-0.493594\pi$
$61$	−1.48145e6	−	855313.i	−0.835664	−	0.482471i	−0.855788	+	0.517327i	$0.826927\pi$
$62$	721717.	+	1.25005e6i	0.384588	+	0.666126i
$63$	−392905.			−0.197968
$64$	−262144.			−0.125000
$65$	774472.	+	1.34142e6i	0.349791	+	0.605856i
$66$		−	157688.i		−	0.0675140i
$67$	−2.39541e6	+	4.14897e6i	−0.973011	+	1.68531i	−0.286664	+	0.958031i	$0.592546\pi$
$67$	−2.39541e6	+	4.14897e6i	−0.973011	+	1.68531i	−0.686347	+	0.727274i	$0.740787\pi$
$68$			1.56770e6i			0.604618i
$69$	138878.	+	80181.3i	0.0508934	+	0.0293833i
$70$	−95666.8	+	165700.i	−0.0333363	+	0.0577402i
$71$	2.11372e6	−	3.66107e6i	0.700879	−	1.21396i	−0.267280	−	0.963619i	$-0.586125\pi$
$71$	2.11372e6	−	3.66107e6i	0.700879	−	1.21396i	0.968158	−	0.250338i	$-0.0805419\pi$
$72$	−947623.	+	547110.i	−0.299207	+	0.172747i
$73$	−2.75576e6			−0.829109			−0.414554	−	0.910025i	$-0.636063\pi$
$73$	−2.75576e6			−0.829109			−0.414554	+	0.910025i	$0.636063\pi$
$74$	−275843.	+	2.44940e6i	−0.0791318	+	0.702665i
$75$	432109.			0.118271
$76$	2.28142e6	−	1.31718e6i	0.596153	−	0.344189i
$77$	−256624.	+	444486.i	−0.0640590	+	0.110953i
$78$	−336264.	+	582426.i	−0.0802323	+	0.138966i
$79$	−3.19167e6	−	1.84271e6i	−0.728322	−	0.420497i	0.0894860	−	0.995988i	$-0.471478\pi$
$79$	−3.19167e6	−	1.84271e6i	−0.728322	−	0.420497i	−0.817808	+	0.575491i	$0.804811\pi$
$80$			532854.i			0.116357i
$81$	−2.22919e6	+	3.86108e6i	−0.466069	+	0.807255i
$82$			4.86576e6i			0.974546i
$83$	807564.	+	1.39874e6i	0.155026	+	0.268512i	0.933068	−	0.359699i	$-0.117121\pi$
$83$	807564.	+	1.39874e6i	0.155026	+	0.268512i	−0.778043	+	0.628211i	$0.783787\pi$
$84$	−83074.1			−0.0152928
$85$	3.18662e6			0.562814
$86$	2.98755e6	+	5.17459e6i	0.506490	+	0.877266i
$87$	478545.	+	276288.i	0.0779123	+	0.0449827i
$88$			1.42937e6i			0.223592i
$89$	−8.77436e6	+	5.06588e6i	−1.31932	+	0.761710i	−0.983619	−	0.180258i	$-0.942307\pi$
$89$	−8.77436e6	+	5.06588e6i	−1.31932	+	0.761710i	−0.335701	+	0.941969i	$0.608973\pi$
$90$	1.11210e6	+	1.92621e6i	0.160803	+	0.278519i
$91$	1.89571e6	−	1.09449e6i	0.263710	−	0.152253i
$92$	−1.25887e6	−	726809.i	−0.168548	−	0.0973112i
$93$	1.10324e6	+	636956.i	0.142226	+	0.0821144i
$94$	4.19597e6	−	2.42255e6i	0.521057	−	0.300832i
$95$	−2.67740e6	−	4.63739e6i	−0.320391	−	0.554934i
$96$	−200361.	+	115679.i	−0.0231134	+	0.0133445i
$97$		−	9.44667e6i		−	1.05094i	−0.850812	−	0.525469i	$-0.823890\pi$
$97$		−	9.44667e6i		−	1.05094i	0.850812	−	0.525469i	$-0.176110\pi$
$98$	−5.47151e6	−	3.15898e6i	−0.587240	−	0.339043i
$99$	2.98318e6	+	5.16702e6i	0.308999	+	0.535201i
$100$	−3.91688e6			−0.391688
$101$	1.04694e7			1.01111			0.505553	−	0.862796i	$-0.331289\pi$
$101$	1.04694e7			1.01111			0.505553	+	0.862796i	$0.331289\pi$
$102$	691791.	+	1.19822e6i	0.0645468	+	0.111798i
$103$		−	9.07463e6i		−	0.818274i	−0.912473	−	0.409137i	$-0.865830\pi$
$103$		−	9.07463e6i		−	0.818274i	0.912473	−	0.409137i	$-0.134170\pi$
$104$	3.04809e6	−	5.27944e6i	0.265712	−	0.460226i
$105$			168863.i			0.0142355i
$106$	6.36361e6	+	3.67403e6i	0.518959	+	0.299621i
$107$	−5.01596e6	+	8.68789e6i	−0.395832	+	0.685601i	−0.993207	−	0.116361i	$-0.962877\pi$
$107$	−5.01596e6	+	8.68789e6i	−0.395832	+	0.685601i	0.597375	+	0.801962i	$0.296210\pi$
$108$	−976975.	+	1.69217e6i	−0.0746277	+	0.129259i
$109$	−4.45289e6	+	2.57088e6i	−0.329344	+	0.190147i	−0.655550	−	0.755152i	$-0.727563\pi$
$109$	−4.45289e6	+	2.57088e6i	−0.329344	+	0.190147i	0.326206	+	0.945299i	$0.394230\pi$
$110$	2.90545e6			0.208132
$111$	870035.	+	1.99384e6i	0.0603818	+	0.138376i
$112$	753031.			0.0506465
$113$	2.08530e7	−	1.20395e7i	1.35954	−	0.784933i	0.369982	−	0.929039i	$-0.379364\pi$
$113$	2.08530e7	−	1.20395e7i	1.35954	−	0.784933i	0.989562	+	0.144105i	$0.0460304\pi$
$114$	1.16249e6	−	2.01348e6i	0.0734887	−	0.127286i
$115$	−1.47737e6	+	2.55888e6i	−0.0905829	+	0.156894i
$116$	−4.33781e6	−	2.50444e6i	−0.258028	−	0.148973i
$117$		−	2.54462e7i		−	1.46883i
$118$	−9.68962e6	+	1.67829e7i	−0.542900	+	0.940330i
$119$		−	4.50334e6i		−	0.244974i
$120$	235137.	+	407269.i	0.0124219	+	0.0215153i
$121$	−1.16934e7			−0.600055
$122$	1.36850e7			0.682316
$123$	2.14716e6	+	3.71898e6i	0.104039	+	0.180201i
$124$	−1.00004e7	−	5.77373e6i	−0.471022	−	0.271945i
$125$			1.81251e7i			0.830035i
$126$	2.72213e6	−	1.57162e6i	0.121230	−	0.0699924i
$127$	−1.27764e7	−	2.21294e7i	−0.553474	−	0.958644i	−0.998021	−	0.0628889i	$-0.979969\pi$
$127$	−1.27764e7	−	2.21294e7i	−0.553474	−	0.958644i	0.444547	−	0.895756i	$-0.353365\pi$
$128$	1.81619e6	−	1.04858e6i	0.0765466	−	0.0441942i
$129$	4.56687e6	+	2.63668e6i	0.187307	+	0.108142i
$130$	−1.07314e7	−	6.19578e6i	−0.428405	−	0.247340i
$131$	−2.74241e7	+	1.58333e7i	−1.06582	+	0.615351i	−0.927036	−	0.374972i	$-0.877652\pi$
$131$	−2.74241e7	+	1.58333e7i	−1.06582	+	0.615351i	−0.138783	+	0.990323i	$0.544319\pi$
$132$	630750.	+	1.09249e6i	0.0238698	+	0.0413437i
$133$	−6.55357e6	+	3.78371e6i	−0.241545	+	0.139456i
$134$		−	3.83266e7i		−	1.37605i
$135$	3.43964e6	+	1.98587e6i	0.120322	+	0.0694678i
$136$	−6.27079e6	−	1.08613e7i	−0.213765	−	0.370251i
$137$	4.49227e7			1.49260			0.746301	−	0.665609i	$-0.231828\pi$
$137$	4.49227e7			1.49260			0.746301	+	0.665609i	$0.231828\pi$
$138$	−1.28290e6			−0.0415543
$139$	1.71181e6	+	2.96494e6i	0.0540634	+	0.0936406i	0.891791	−	0.452448i	$-0.149449\pi$
$139$	1.71181e6	+	2.96494e6i	0.0540634	+	0.0936406i	−0.837727	+	0.546089i	$0.816116\pi$
$140$		−	1.53067e6i		−	0.0471447i
$141$	2.13804e6	−	3.70319e6i	0.0642315	−	0.111252i
$142$			3.38195e7i			0.991192i
$143$	−2.87868e7	−	1.66200e7i	−0.823221	−	0.475287i
$144$	4.37688e6	−	7.58098e6i	0.122151	−	0.211571i
$145$	−5.09071e6	+	8.81737e6i	−0.138672	+	0.240188i
$146$	1.90925e7	−	1.10230e7i	0.507723	−	0.293134i
$147$	−5.57595e6			−0.144780
$148$	−7.88650e6	−	1.80733e7i	−0.199971	−	0.458270i
$149$	5.41642e7			1.34141			0.670703	−	0.741726i	$-0.265993\pi$
$149$	5.41642e7			1.34141			0.670703	+	0.741726i	$0.265993\pi$
$150$	−2.99374e6	+	1.72843e6i	−0.0724260	+	0.0418151i
$151$	1.49917e7	−	2.59664e7i	0.354350	−	0.613752i	−0.632657	−	0.774433i	$-0.718036\pi$
$151$	1.49917e7	−	2.59664e7i	0.354350	−	0.613752i	0.987006	+	0.160680i	$0.0513688\pi$
$152$	−1.05374e7	+	1.82514e7i	−0.243378	+	0.421544i
$153$	−4.53365e7	−	2.61750e7i	−1.02336	−	0.590837i
$154$		−	4.10599e6i		−	0.0905931i
$155$	−1.17361e7	+	2.03276e7i	−0.253142	+	0.438455i
$156$		−	5.38022e6i		−	0.113466i
$157$	−1.33370e7	−	2.31003e7i	−0.275048	−	0.476397i	0.695099	−	0.718914i	$-0.255360\pi$
$157$	−1.33370e7	−	2.31003e7i	−0.275048	−	0.476397i	−0.970147	+	0.242517i	$0.922027\pi$
$158$	2.94834e7			0.594672
$159$	6.48509e6			0.127946
$160$	−2.13142e6	−	3.69172e6i	−0.0411385	−	0.0712540i
$161$	3.61621e6	+	2.08782e6i	0.0682909	+	0.0394278i
$162$		−	3.56671e7i		−	0.659121i
$163$	5.55162e7	−	3.20523e7i	1.00407	−	0.579699i	0.0946188	−	0.995514i	$-0.469837\pi$
$163$	5.55162e7	−	3.20523e7i	1.00407	−	0.579699i	0.909449	+	0.415814i	$0.136503\pi$
$164$	−1.94630e7	−	3.37110e7i	−0.344554	−	0.596785i
$165$	2.22068e6	−	1.28211e6i	0.0384851	−	0.0222194i
$166$	−1.11899e7	−	6.46051e6i	−0.189867	−	0.109620i
$167$	1.83641e7	+	1.06025e7i	0.305114	+	0.176158i	0.644738	−	0.764404i	$-0.276966\pi$
$167$	1.83641e7	+	1.06025e7i	0.305114	+	0.176158i	−0.339624	+	0.940561i	$0.610300\pi$
$168$	575554.	−	332296.i	0.00936491	−	0.00540683i
$169$	3.95092e7	+	6.84319e7i	0.629643	+	1.09057i
$170$	−2.20776e7	+	1.27465e7i	−0.344651	+	0.198985i
$171$			8.79690e7i			1.34538i
$172$	−4.13967e7	−	2.39004e7i	−0.620321	−	0.358142i
$173$	6.12592e7	+	1.06104e8i	0.899519	+	1.55801i	0.828111	+	0.560565i	$0.189416\pi$
$173$	6.12592e7	+	1.06104e8i	0.899519	+	1.55801i	0.0714081	+	0.997447i	$0.477251\pi$
$174$	−4.42061e6			−0.0636151
$175$	1.12516e7			0.158701
$176$	−5.71748e6	−	9.90297e6i	−0.0790515	−	0.136921i
$177$			1.71033e7i			0.231832i
$178$	4.05270e7	−	7.01949e7i	0.538610	−	0.932900i
$179$		−	7.39367e7i		−	0.963550i	−0.876295	−	0.481775i	$-0.839992\pi$
$179$		−	7.39367e7i		−	0.963550i	0.876295	−	0.481775i	$-0.160008\pi$
$180$	−1.54097e7	−	8.89679e6i	−0.196943	−	0.113705i
$181$	−4.98686e7	+	8.63749e7i	−0.625104	+	1.08271i	0.363417	+	0.931627i	$0.381610\pi$
$181$	−4.98686e7	+	8.63749e7i	−0.625104	+	1.08271i	−0.988521	+	0.151085i	$0.951723\pi$
$182$	−8.75589e6	+	1.51656e7i	−0.107659	+	0.186471i
$183$	1.04597e7	−	6.03890e6i	0.126165	−	0.0728416i
$184$	1.16289e7			0.137619
$185$	−3.67372e7	+	1.60307e7i	−0.426584	+	0.186145i
$186$	−1.01913e7			−0.116127
$187$	−5.92226e7	+	3.41922e7i	−0.662281	+	0.382368i
$188$	−1.93804e7	+	3.35678e7i	−0.212721	+	0.368443i
$189$	2.80644e6	−	4.86090e6i	0.0302371	−	0.0523722i
$190$	3.70991e7	+	2.14192e7i	0.392397	+	0.226551i
$191$		−	1.31569e7i		−	0.136627i	−0.997664	−	0.0683137i	$-0.978238\pi$
$191$		−	1.31569e7i		−	0.136627i	0.997664	−	0.0683137i	$-0.0217619\pi$
$192$	925428.	−	1.60289e6i	0.00943601	−	0.0163436i
$193$			8.64739e6i			0.0865834i	0.999062	+	0.0432917i	$0.0137845\pi$
$193$			8.64739e6i			0.0865834i	−0.999062	+	0.0432917i	$0.986216\pi$
$194$	3.77867e7	+	6.54484e7i	0.371563	+	0.643566i
$195$	−1.09363e7			−0.105620
$196$	5.05436e7			0.479479
$197$	−5.73765e7	−	9.93790e7i	−0.534690	−	0.926111i	−0.999178	−	0.0405312i	$-0.987095\pi$
$197$	−5.73765e7	−	9.93790e7i	−0.534690	−	0.926111i	0.464488	−	0.885579i	$-0.346238\pi$
$198$	−4.13362e7	−	2.38655e7i	−0.378444	−	0.218495i
$199$			2.21171e8i			1.98949i	0.102389	+	0.994744i	$0.467352\pi$
$199$			2.21171e8i			1.98949i	−0.102389	+	0.994744i	$0.532648\pi$
$200$	2.71369e7	−	1.56675e7i	0.239859	−	0.138483i
$201$	−1.69127e7	−	2.92936e7i	−0.146902	−	0.254441i
$202$	−7.25340e7	+	4.18775e7i	−0.619173	+	0.357480i
$203$	1.24607e7	+	7.19420e6i	0.104546	+	0.0603596i
$204$	−9.58574e6	−	5.53433e6i	−0.0790533	−	0.0456415i
$205$	−6.85236e7	+	3.95621e7i	−0.555522	+	0.320731i
$206$	3.62985e7	+	6.28709e7i	0.289303	+	0.501088i
$207$	4.20374e7	−	2.42703e7i	0.329412	−	0.190186i
$208$			4.87694e7i			0.375773i
$209$	9.95176e7	+	5.74565e7i	0.754029	+	0.435339i
$210$	−675451.	−	1.16992e6i	−0.00503299	−	0.00871740i
$211$	−2.22834e8			−1.63302			−0.816512	−	0.577328i	$-0.804095\pi$
$211$	−2.22834e8			−1.63302			−0.816512	+	0.577328i	$0.804095\pi$
$212$	−5.87845e7			−0.423728
$213$	1.49238e7	+	2.58488e7i	0.105816	+	0.183279i
$214$		−	8.02553e7i		−	0.559791i
$215$	−4.85818e7	+	8.41462e7i	−0.333380	+	0.577430i
$216$		−	1.56316e7i		−	0.105540i
$217$	2.87270e7	+	1.65855e7i	0.190845	+	0.110184i
$218$	2.05670e7	−	3.56231e7i	0.134454	−	0.232881i
$219$	9.72847e6	−	1.68502e7i	0.0625878	−	0.108405i
$220$	−2.01295e7	+	1.16218e7i	−0.127454	+	0.0735857i
$221$	2.91655e8			1.81759
$222$	−1.40031e7	−	1.03336e7i	−0.0858994	−	0.0633893i
$223$	−2.06034e8			−1.24415			−0.622075	−	0.782958i	$-0.713710\pi$
$223$	−2.06034e8			−1.24415			−0.622075	+	0.782958i	$0.713710\pi$
$224$	−5.21715e6	+	3.01212e6i	−0.0310145	+	0.0179063i
$225$	6.53981e7	−	1.13273e8i	0.382760	−	0.662960i
$226$	−9.63158e7	+	1.66824e8i	−0.555032	+	0.961343i
$227$	9.09545e7	+	5.25126e7i	0.516100	+	0.297970i	0.735337	−	0.677701i	$-0.237024\pi$
$227$	9.09545e7	+	5.25126e7i	0.516100	+	0.297970i	−0.219238	+	0.975671i	$0.570357\pi$
$228$			1.85998e7i			0.103929i
$229$	6.48805e7	−	1.12376e8i	0.357018	−	0.618373i	−0.630443	−	0.776235i	$-0.717127\pi$
$229$	6.48805e7	−	1.12376e8i	0.357018	−	0.618373i	0.987461	+	0.157862i	$0.0504601\pi$
$230$		−	2.36379e7i		−	0.128104i
$231$	−1.81188e6	−	3.13827e6i	−0.00967138	−	0.0167513i
$232$	4.00710e7			0.210679
$233$	−9.62279e7			−0.498374			−0.249187	−	0.968455i	$-0.580163\pi$
$233$	−9.62279e7			−0.498374			−0.249187	+	0.968455i	$0.580163\pi$
$234$	1.01785e8	+	1.76296e8i	0.519310	+	0.899472i
$235$	6.82325e7	+	3.93940e7i	0.342968	+	0.198013i
$236$		−	1.55034e8i		−	0.767776i
$237$	2.25347e7	−	1.30104e7i	0.109959	−	0.0634850i
$238$	1.80134e7	+	3.12001e7i	0.0866116	+	0.150016i
$239$	−1.02019e8	+	5.89006e7i	−0.483379	+	0.279079i	−0.721823	−	0.692077i	$-0.756696\pi$
$239$	−1.02019e8	+	5.89006e7i	−0.483379	+	0.279079i	0.238445	+	0.971156i	$0.423362\pi$
$240$	−3.25815e6	−	1.88110e6i	−0.0152136	−	0.00878358i
$241$	4.66869e7	+	2.69547e7i	0.214850	+	0.124044i	0.603563	−	0.797315i	$-0.293747\pi$
$241$	4.66869e7	+	2.69547e7i	0.214850	+	0.124044i	−0.388713	+	0.921359i	$0.627080\pi$
$242$	8.10140e7	−	4.67735e7i	0.367457	−	0.212151i
$243$	−4.91242e7	−	8.50856e7i	−0.219621	−	0.380394i
$244$	−9.48126e7	+	5.47401e7i	−0.417832	+	0.241235i
$245$		−	1.02739e8i		−	0.446327i
$246$	−2.97519e7	−	1.71773e7i	−0.127421	−	0.0735666i
$247$	−2.45049e8	−	4.24437e8i	−1.03470	−	1.79215i
$248$	9.23797e7			0.384588
$249$	−1.14035e7			−0.0468104
$250$	−7.25005e7	−	1.25575e8i	−0.293462	−	0.508290i
$251$		−	4.01520e8i		−	1.60269i	−0.598204	−	0.801344i	$-0.704119\pi$
$251$		−	4.01520e8i		−	1.60269i	0.598204	−	0.801344i	$-0.295881\pi$
$252$	−1.25730e7	+	2.17770e7i	−0.0494921	+	0.0857228i
$253$		−	6.34081e7i		−	0.246163i
$254$	1.77036e8	+	1.02212e8i	0.677864	+	0.391365i
$255$	−1.12495e7	+	1.94847e7i	−0.0424857	+	0.0735874i
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	2.28008e8	−	1.31640e8i	0.837884	−	0.483752i	−0.0186605	−	0.999826i	$-0.505940\pi$
$257$	2.28008e8	−	1.31640e8i	0.837884	−	0.483752i	0.856544	+	0.516073i	$0.172607\pi$
$258$	−4.21869e7			−0.152936
$259$	2.26546e7	+	5.19171e7i	0.0810229	+	0.185678i
$260$	9.91324e7			0.349791
$261$	1.44852e8	−	8.36305e7i	0.504294	−	0.291154i
$262$	1.26667e8	−	2.19393e8i	0.435119	−	0.753648i
$263$	6.39010e7	−	1.10680e8i	0.216602	−	0.375166i	−0.737165	−	0.675713i	$-0.763836\pi$
$263$	6.39010e7	−	1.10680e8i	0.216602	−	0.375166i	0.953767	+	0.300547i	$0.0971692\pi$
$264$	−8.73993e6	−	5.04600e6i	−0.0292344	−	0.0168785i
$265$			1.19490e8i			0.394431i
$266$	3.02697e7	−	5.24286e7i	0.0986102	−	0.170798i
$267$		−	7.15348e7i		−	0.230000i
$268$	1.53306e8	+	2.65534e8i	0.486506	+	0.842653i
$269$	−1.69266e8			−0.530197			−0.265098	−	0.964221i	$-0.585404\pi$
$269$	−1.69266e8			−0.530197			−0.265098	+	0.964221i	$0.585404\pi$
$270$	−3.17740e7			−0.0982423
$271$	−1.36745e8	−	2.36848e8i	−0.417366	−	0.722900i	0.578307	−	0.815819i	$-0.303713\pi$
$271$	−1.36745e8	−	2.36848e8i	−0.417366	−	0.722900i	−0.995674	+	0.0929193i	$0.970380\pi$
$272$	8.68906e7	+	5.01663e7i	0.261807	+	0.151155i
$273$			1.54551e7i			0.0459731i
$274$	−3.11234e8	+	1.79691e8i	−0.914028	+	0.527715i
$275$	−8.54289e7	−	1.47967e8i	−0.247708	−	0.429043i
$276$	8.88819e6	−	5.13160e6i	0.0254467	−	0.0146917i
$277$	−2.81899e8	−	1.62754e8i	−0.796918	−	0.460101i	0.0454743	−	0.998966i	$-0.485520\pi$
$277$	−2.81899e8	−	1.62754e8i	−0.796918	−	0.460101i	−0.842392	+	0.538865i	$0.818853\pi$
$278$	−2.37195e7	−	1.36945e7i	−0.0662139	−	0.0382286i
$279$	3.33943e8	−	1.92802e8i	0.920572	−	0.531492i
$280$	6.12267e6	+	1.06048e7i	0.0166682	+	0.0288701i
$281$	4.43246e8	−	2.55908e8i	1.19172	−	0.688037i	0.233020	−	0.972472i	$-0.425139\pi$
$281$	4.43246e8	−	2.55908e8i	1.19172	−	0.688037i	0.958695	+	0.284435i	$0.0918060\pi$
$282$			3.42086e7i			0.0908371i
$283$	4.25142e7	+	2.45456e7i	0.111502	+	0.0643755i	0.554714	−	0.832041i	$-0.312828\pi$
$283$	4.25142e7	+	2.45456e7i	0.111502	+	0.0643755i	−0.443212	+	0.896417i	$0.646161\pi$
$284$	−1.35278e8	−	2.34308e8i	−0.350439	−	0.606979i
$285$	3.78073e7			0.0967429
$286$	2.65921e8			0.672157
$287$	5.59093e7	+	9.68377e7i	0.139604	+	0.241801i
$288$			7.00301e7i			0.172747i
$289$	9.48400e7	−	1.64268e8i	0.231126	−	0.400322i
$290$		−	8.14513e7i		−	0.196112i
$291$	5.77620e7	+	3.33489e7i	0.137409	+	0.0793334i
$292$	−8.81844e7	+	1.52740e8i	−0.207277	+	0.359015i
$293$	−6.00579e7	+	1.04023e8i	−0.139487	+	0.241598i	−0.927302	−	0.374313i	$-0.877879\pi$
$293$	−6.00579e7	+	1.04023e8i	−0.139487	+	0.241598i	0.787816	+	0.615911i	$0.211212\pi$
$294$	3.86313e7	−	2.23038e7i	0.0886592	−	0.0511874i
$295$	−3.15134e8			−0.714691
$296$	1.26932e8	+	9.36695e7i	0.284480	+	0.209931i
$297$	−8.52331e7			−0.188782
$298$	−3.75260e8	+	2.16657e8i	−0.821440	+	0.474259i
$299$	−1.35216e8	+	2.34201e8i	−0.292535	+	0.506686i
$300$	1.38275e7	−	2.39499e7i	0.0295678	−	0.0512129i
$301$	1.18916e8	+	6.86559e7i	0.251337	+	0.145109i
$302$			2.39868e8i			0.501127i
$303$	−3.69593e7	+	6.40154e7i	−0.0763264	+	0.132201i
$304$		−	1.68599e8i		−	0.344189i
$305$	1.11269e8	+	1.92723e8i	0.224556	+	0.388942i
$306$	4.18801e8			0.835569
$307$	−5.39304e8			−1.06377			−0.531887	−	0.846815i	$-0.678517\pi$
$307$	−5.39304e8			−1.06377			−0.531887	+	0.846815i	$0.678517\pi$
$308$	1.64239e7	+	2.84471e7i	0.0320295	+	0.0554767i
$309$	5.54871e7	+	3.20355e7i	0.106989	+	0.0617699i
$310$		−	1.87778e8i		−	0.357997i
$311$	−5.97850e8	+	3.45169e8i	−1.12702	+	0.650684i	−0.943183	−	0.332274i	$-0.892184\pi$
$311$	−5.97850e8	+	3.45169e8i	−1.12702	+	0.650684i	−0.183834	+	0.982957i	$0.558851\pi$
$312$	2.15209e7	+	3.72753e7i	0.0401161	+	0.0694832i
$313$	2.12241e8	−	1.22537e8i	0.391222	−	0.225872i	−0.291467	−	0.956581i	$-0.594143\pi$
$313$	2.12241e8	−	1.22537e8i	0.391222	−	0.225872i	0.682690	+	0.730709i	$0.260810\pi$
$314$	1.84802e8	+	1.06696e8i	0.336863	+	0.194488i
$315$	4.42656e7	+	2.55568e7i	0.0797958	+	0.0460701i
$316$	−2.04267e8	+	1.17934e8i	−0.364161	+	0.210248i
$317$	2.98819e8	+	5.17569e8i	0.526866	+	0.912559i	0.999510	+	0.0313053i	$0.00996641\pi$
$317$	2.98819e8	+	5.17569e8i	0.526866	+	0.912559i	−0.472644	+	0.881254i	$0.656700\pi$
$318$	−4.49300e7	+	2.59404e7i	−0.0783505	+	0.0452357i
$319$		−	2.18491e8i		−	0.376849i
$320$	2.95338e7	+	1.70513e7i	0.0503842	+	0.0290893i
$321$	−3.54150e7	−	6.13405e7i	−0.0597612	−	0.103509i
$322$	−3.34051e7			−0.0557593
$323$	−1.00827e9			−1.66482
$324$	1.42668e8	+	2.47109e8i	0.233035	+	0.403628i
$325$			7.28698e8i			1.17749i
$326$	−2.56418e8	+	4.44130e8i	−0.409909	+	0.709983i
$327$		−	3.63032e7i		−	0.0574153i
$328$	2.69688e8	+	1.55704e8i	0.421991	+	0.243637i
$329$	5.56718e7	−	9.64263e7i	0.0861885	−	0.149283i
$330$	−1.02569e7	+	1.77655e7i	−0.0157115	+	0.0272131i
$331$	−6.11740e8	+	3.53188e8i	−0.927191	+	0.535314i	−0.885922	−	0.463834i	$-0.846473\pi$
$331$	−6.11740e8	+	3.53188e8i	−0.927191	+	0.535314i	−0.0412688	+	0.999148i	$0.513140\pi$
$332$	1.03368e8			0.155026
$333$	6.54341e8	+	7.36898e7i	0.971068	+	0.109358i
$334$	−1.69641e8			−0.249125
$335$	5.39745e8	−	3.11622e8i	0.784390	−	0.452868i
$336$	−2.65837e6	+	4.60443e6i	−0.00382321	+	0.00662199i
$337$	−2.18599e8	+	3.78624e8i	−0.311131	+	0.538894i	−0.978607	−	0.205737i	$-0.934041\pi$
$337$	−2.18599e8	+	3.78624e8i	−0.311131	+	0.538894i	0.667477	+	0.744631i	$0.267374\pi$
$338$	−5.47455e8	−	3.16073e8i	−0.771152	−	0.445225i
$339$			1.70008e8i			0.237012i
$340$	1.01972e8	−	1.76621e8i	0.140703	−	0.243705i
$341$		−	5.03711e8i		−	0.687925i
$342$	−3.51876e8	−	6.09467e8i	−0.475662	−	0.823871i
$343$	−2.96595e8			−0.396858
$344$	3.82406e8			0.506490
$345$	−1.04309e7	−	1.80668e7i	−0.0136759	−	0.0236873i
$346$	−8.48833e8	−	4.90074e8i	−1.10168	−	0.636056i
$347$			5.83905e8i			0.750220i	0.926980	+	0.375110i	$0.122395\pi$
$347$			5.83905e8i			0.750220i	−0.926980	+	0.375110i	$0.877605\pi$
$348$	3.06269e7	−	1.76825e7i	0.0389561	−	0.0224913i
$349$	5.42845e8	+	9.40235e8i	0.683576	+	1.18399i	0.973882	+	0.227054i	$0.0729095\pi$
$349$	5.42845e8	+	9.40235e8i	0.683576	+	1.18399i	−0.290306	+	0.956934i	$0.593757\pi$
$350$	−7.79531e7	+	4.50063e7i	−0.0971842	+	0.0561093i
$351$	3.14812e8	+	1.81757e8i	0.388577	+	0.224345i
$352$	7.92237e7	+	4.57398e7i	0.0968180	+	0.0558979i
$353$	1.51139e8	−	8.72599e7i	0.182879	−	0.105585i	−0.405766	−	0.913977i	$-0.632995\pi$
$353$	1.51139e8	−	8.72599e7i	0.182879	−	0.105585i	0.588645	+	0.808392i	$0.299662\pi$
$354$	−6.84131e7	−	1.18495e8i	−0.0819649	−	0.141967i
$355$	−4.76273e8	+	2.74976e8i	−0.565011	+	0.326209i
$356$			6.48432e8i			0.761710i
$357$	2.75359e7	+	1.58978e7i	0.0320302	+	0.0184927i
$358$	2.95747e8	+	5.12248e8i	0.340667	+	0.590052i
$359$	1.09648e9			1.25075			0.625375	−	0.780325i	$-0.284946\pi$
$359$	1.09648e9			1.25075			0.625375	+	0.780325i	$0.284946\pi$
$360$	1.42349e8			0.160803
$361$	4.00213e8	+	6.93189e8i	0.447729	+	0.775490i
$362$		−	7.97898e8i		−	0.884030i
$363$	4.12803e7	−	7.14995e7i	0.0452970	−	0.0784567i
$364$		−	1.40094e8i		−	0.152253i
$365$	3.10471e8	+	1.79250e8i	0.334192	+	0.192946i
$366$	−4.83112e7	+	8.36775e7i	−0.0515068	+	0.0892123i
$367$	−4.59750e8	+	7.96310e8i	−0.485501	+	0.840913i	−0.999861	−	0.0166615i	$-0.994696\pi$
$367$	−4.59750e8	+	7.96310e8i	−0.485501	+	0.840913i	0.514360	+	0.857574i	$0.328030\pi$
$368$	−8.05677e7	+	4.65158e7i	−0.0842740	+	0.0486556i
$369$	1.29986e9			1.34680
$370$	1.90400e8	−	2.58013e8i	0.195416	−	0.264810i
$371$	1.68864e8			0.171683
$372$	7.06074e7	−	4.07652e7i	0.0711131	−	0.0410572i
$373$	3.20496e8	−	5.55115e8i	0.319773	−	0.553863i	−0.660668	−	0.750679i	$-0.729727\pi$
$373$	3.20496e8	−	5.55115e8i	0.319773	−	0.553863i	0.980441	+	0.196816i	$0.0630600\pi$
$374$	2.73538e8	−	4.73781e8i	0.270375	−	0.468303i
$375$	−1.10827e8	−	6.39859e7i	−0.108526	−	0.0626577i
$376$		−	3.10086e8i		−	0.300832i
$377$	−4.65926e8	+	8.07008e8i	−0.447840	+	0.775681i
$378$			4.49031e7i			0.0427617i
$379$	−7.29765e8	−	1.26399e9i	−0.688566	−	1.19263i	−0.972302	−	0.233729i	$-0.924907\pi$
$379$	−7.29765e8	−	1.26399e9i	−0.688566	−	1.19263i	0.283735	−	0.958903i	$-0.408426\pi$
$380$	−3.42707e8			−0.320391
$381$	1.80415e8			0.167123
$382$	5.26277e7	+	9.11539e7i	0.0483051	+	0.0836669i
$383$	−1.11911e9	−	6.46116e8i	−1.01783	−	0.587645i	−0.104356	−	0.994540i	$-0.533278\pi$
$383$	−1.11911e9	−	6.46116e8i	−1.01783	−	0.587645i	−0.913475	+	0.406895i	$0.866612\pi$
$384$			1.48068e7i			0.0133445i
$385$	5.78238e7	−	3.33846e7i	0.0516409	−	0.0298149i
$386$	−3.45896e7	−	5.99109e7i	−0.0306119	−	0.0530213i
$387$	1.38236e9	−	7.98105e8i	1.21236	−	0.699958i
$388$	−5.23587e8	−	3.02293e8i	−0.455070	−	0.262735i
$389$	−1.62684e9	−	9.39256e8i	−1.40127	−	0.809022i	−0.406744	−	0.913542i	$-0.633336\pi$
$389$	−1.62684e9	−	9.39256e8i	−1.40127	−	0.809022i	−0.994523	+	0.104520i	$0.966669\pi$
$390$	7.57686e7	−	4.37450e7i	0.0646790	−	0.0373424i
$391$	2.78178e8	+	4.81818e8i	0.235344	+	0.407629i
$392$	−3.50176e8	+	2.02174e8i	−0.293620	+	0.169522i
$393$		−	2.23581e8i		−	0.185807i
$394$	7.95032e8	+	4.59012e8i	0.654859	+	0.378083i
$395$	2.39721e8	+	4.15209e8i	0.195711	+	0.338982i
$396$	3.81847e8			0.308999
$397$	−5.14959e8			−0.413053			−0.206526	−	0.978441i	$-0.566216\pi$
$397$	−5.14959e8			−0.413053			−0.206526	+	0.978441i	$0.566216\pi$
$398$	−8.84682e8	−	1.53231e9i	−0.703391	−	1.21831i
$399$		−	5.34294e7i		−	0.0421090i
$400$	−1.25340e8	+	2.17096e8i	−0.0979220	+	0.169606i
$401$			7.16832e7i			0.0555152i	0.999615	+	0.0277576i	$0.00883666\pi$
$401$			7.16832e7i			0.0555152i	−0.999615	+	0.0277576i	$0.991163\pi$
$402$	2.34349e8	+	1.35301e8i	0.179917	+	0.103875i
$403$	−1.07415e9	+	1.86048e9i	−0.817516	+	1.41598i
$404$	3.35020e8	−	5.80272e8i	0.252776	−	0.437821i
$405$	5.02293e8	−	2.89999e8i	0.375720	−	0.216922i
$406$	−1.15107e8			−0.0853614
$407$	5.10744e8	−	6.92114e8i	0.375511	−	0.508858i
$408$	8.85493e7			0.0645468
$409$	6.61439e8	−	3.81882e8i	0.478034	−	0.275993i	−0.241563	−	0.970385i	$-0.577660\pi$
$409$	6.61439e8	−	3.81882e8i	0.478034	−	0.275993i	0.719597	+	0.694392i	$0.244327\pi$
$410$	3.16497e8	−	5.48188e8i	0.226791	−	0.392814i
$411$	−1.58587e8	+	2.74682e8i	−0.112674	+	0.195157i
$412$	−5.02967e8	−	2.90388e8i	−0.354323	−	0.204568i
$413$			4.45348e8i			0.311082i
$414$	−1.94162e8	+	3.36299e8i	−0.134482	+	0.232930i
$415$		−	2.10114e8i		−	0.144307i
$416$	−1.95078e8	−	3.37884e8i	−0.132856	−	0.230113i
$417$	−2.41723e7			−0.0163246
$418$	−9.19305e8			−0.615662
$419$	5.95145e8	+	1.03082e9i	0.395252	+	0.684596i	0.993133	−	0.116988i	$-0.0373240\pi$
$419$	5.95145e8	+	1.03082e9i	0.395252	+	0.684596i	−0.597882	+	0.801584i	$0.703991\pi$
$420$	9.35933e6	+	5.40361e6i	0.00616413	+	0.00355886i
$421$		−	1.18770e9i		−	0.775743i	−0.921714	−	0.387871i	$-0.873211\pi$
$421$		−	1.18770e9i		−	0.775743i	0.921714	−	0.387871i	$-0.126789\pi$
$422$	1.54384e9	−	8.91335e8i	1.00002	−	0.577361i
$423$	−6.47168e8	−	1.12093e9i	−0.415744	−	0.720090i
$424$	4.07271e8	−	2.35138e8i	0.259480	−	0.149811i
$425$	1.29829e9	+	7.49571e8i	0.820374	+	0.473643i
$426$	−2.06790e8	−	1.19391e8i	−0.129598	−	0.0748232i
$427$	2.72357e8	−	1.57245e8i	0.169294	−	0.0977418i
$428$	3.21021e8	+	5.56025e8i	0.197916	+	0.342800i
$429$	2.03248e8	−	1.17345e8i	0.124287	−	0.0717570i
$430$		−	7.77309e8i		−	0.471470i
$431$	−1.09428e9	−	6.31780e8i	−0.658349	−	0.380098i	0.133299	−	0.991076i	$-0.457443\pi$
$431$	−1.09428e9	−	6.31780e8i	−0.658349	−	0.380098i	−0.791648	+	0.610978i	$0.790776\pi$
$432$	6.25264e7	+	1.08299e8i	0.0373139	+	0.0646295i
$433$	−1.00375e9			−0.594180			−0.297090	−	0.954849i	$-0.596016\pi$
$433$	−1.00375e9			−0.594180			−0.297090	+	0.954849i	$0.596016\pi$
$434$	−2.65369e8			−0.155824
$435$	−3.59427e7	−	6.22546e7i	−0.0209362	−	0.0362626i
$436$			3.29073e8i			0.190147i
$437$	4.67450e8	−	8.09647e8i	0.267948	−	0.464099i
$438$			1.55655e8i			0.0885126i
$439$	−5.19557e8	−	2.99967e8i	−0.293095	−	0.169218i	0.346242	−	0.938145i	$-0.387458\pi$
$439$	−5.19557e8	−	2.99967e8i	−0.293095	−	0.169218i	−0.639337	+	0.768927i	$0.720791\pi$
$440$	9.29743e7	−	1.61036e8i	0.0520330	−	0.0901238i
$441$	−8.43901e8	+	1.46168e9i	−0.468550	+	0.811553i
$442$	−2.02065e9	+	1.16662e9i	−1.11304	+	0.642616i
$443$	−6.01786e8			−0.328874			−0.164437	−	0.986388i	$-0.552581\pi$
$443$	−6.01786e8			−0.328874			−0.164437	+	0.986388i	$0.552581\pi$
$444$	1.38351e8	+	1.55806e7i	0.0750139	+	0.00844782i
$445$	1.31805e9			0.709044
$446$	1.42745e9	−	8.24137e8i	0.761883	−	0.439873i
$447$	−1.91212e8	+	3.31189e8i	−0.101260	+	0.175388i
$448$	2.40970e7	−	4.17372e7i	0.0126616	−	0.0219306i
$449$	7.35845e8	+	4.24840e8i	0.383640	+	0.221495i	0.679401	−	0.733767i	$-0.262240\pi$
$449$	7.35845e8	+	4.24840e8i	0.383640	+	0.221495i	−0.295761	+	0.955262i	$0.595573\pi$
$450$			1.04637e9i			0.541304i
$451$	8.48996e8	−	1.47050e9i	0.435800	−	0.754829i
$452$		−	1.54105e9i		−	0.784933i
$453$	1.05848e8	+	1.83335e8i	0.0534984	+	0.0926619i
$454$	−8.40202e8			−0.421394
$455$	−2.84766e8			−0.141726
$456$	−7.43991e7	−	1.28863e8i	−0.0367443	−	0.0636431i
$457$	3.98109e6	+	2.29848e6i	0.00195117	+	0.00112651i	0.500975	−	0.865462i	$-0.332975\pi$
$457$	3.98109e6	+	2.29848e6i	0.00195117	+	0.00112651i	−0.499024	+	0.866588i	$0.666308\pi$
$458$			1.03809e9i			0.504900i
$459$	6.47659e8	−	3.73926e8i	0.312609	−	0.180485i
$460$	9.45515e7	+	1.63768e8i	0.0452914	+	0.0784471i
$461$	−6.63931e8	+	3.83321e8i	−0.315624	+	0.182226i	−0.649440	−	0.760413i	$-0.724997\pi$
$461$	−6.63931e8	+	3.83321e8i	−0.315624	+	0.182226i	0.333816	+	0.942638i	$0.391663\pi$
$462$	2.51062e7	+	1.44951e7i	0.0118450	+	0.00683870i
$463$	2.60647e9	+	1.50485e9i	1.22045	+	0.704626i	0.965013	−	0.262201i	$-0.0844483\pi$
$463$	2.60647e9	+	1.50485e9i	1.22045	+	0.704626i	0.255434	+	0.966826i	$0.417782\pi$
$464$	−2.77620e8	+	1.60284e8i	−0.129014	+	0.0744864i
$465$	−8.28625e7	−	1.43522e8i	−0.0382184	−	0.0661962i
$466$	6.66686e8	−	3.84911e8i	0.305190	−	0.176202i
$467$		−	6.15420e8i		−	0.279616i	−0.990179	−	0.139808i	$-0.955351\pi$
$467$		−	6.15420e8i		−	0.279616i	0.990179	−	0.139808i	$-0.0446486\pi$
$468$	−1.41037e9	−	8.14277e8i	−0.636022	−	0.367208i
$469$	−4.40385e8	−	7.62769e8i	−0.197119	−	0.341419i
$470$	−6.30305e8			−0.280032
$471$	1.88330e8			0.0830513
$472$	6.20136e8	+	1.07411e9i	0.271450	+	0.470165i
$473$		−	2.08511e9i		−	0.905974i
$474$	−1.04083e8	+	1.80277e8i	−0.0448907	+	0.0777529i
$475$		−	2.51916e9i		−	1.07852i
$476$	−2.49601e8	−	1.44107e8i	−0.106077	−	0.0612436i
$477$	9.81495e8	−	1.70000e9i	0.414070	−	0.717190i
$478$	4.71205e8	−	8.16150e8i	0.197339	−	0.341800i
$479$	−9.08083e8	+	5.24282e8i	−0.377530	+	0.217967i	−0.676743	−	0.736219i	$-0.736609\pi$
$479$	−9.08083e8	+	5.24282e8i	−0.377530	+	0.217967i	0.299213	+	0.954186i	$0.403276\pi$
$480$	3.00975e7			0.0124219
$481$	−3.36236e9	+	1.46721e9i	−1.37764	+	0.601151i
$482$	−4.31275e8			−0.175424
$483$	−2.55321e7	+	1.47410e7i	−0.0103103	+	0.00595266i
$484$	−3.74188e8	+	6.48112e8i	−0.150014	+	0.259831i
$485$	−6.14465e8	+	1.06428e9i	−0.244569	+	0.423605i
$486$	6.80685e8	+	3.92994e8i	0.268979	+	0.155295i
$487$		−	7.90388e8i		−	0.310091i	−0.987907	−	0.155045i	$-0.950448\pi$
$487$		−	7.90388e8i		−	0.310091i	0.987907	−	0.155045i	$-0.0495524\pi$
$488$	4.37920e8	−	7.58501e8i	0.170579	−	0.295452i
$489$			4.52608e8i			0.175041i
$490$	4.10955e8	+	7.11796e8i	0.157800	+	0.273318i
$491$	9.96799e8			0.380034			0.190017	−	0.981781i	$-0.439146\pi$
$491$	9.96799e8			0.380034			0.190017	+	0.981781i	$0.439146\pi$
$492$	2.74836e8			0.104039
$493$	9.58544e8	+	1.66025e9i	0.360287	+	0.624035i
$494$	3.39549e9	+	1.96039e9i	1.26724	+	0.731641i
$495$		−	7.76172e8i		−	0.287634i
$496$	−6.40025e8	+	3.69519e8i	−0.235511	+	0.135972i
$497$	3.88597e8	+	6.73070e8i	0.141988	+	0.245931i
$498$	7.90060e7	−	4.56142e7i	0.0286654	−	0.0165500i
$499$	1.24944e8	+	7.21364e7i	0.0450156	+	0.0259898i	0.522339	−	0.852738i	$-0.325060\pi$
$499$	1.24944e8	+	7.21364e7i	0.0450156	+	0.0259898i	−0.477323	+	0.878728i	$0.658393\pi$
$500$	1.00460e9	+	5.80004e8i	0.359416	+	0.207509i
$501$	−1.29659e8	+	7.48587e7i	−0.0460650	+	0.0265956i
$502$	1.60608e9	+	2.78181e9i	0.566636	+	0.981442i
$503$	−2.36708e9	+	1.36664e9i	−0.829327	+	0.478812i	−0.853622	−	0.520893i	$-0.825599\pi$
$503$	−2.36708e9	+	1.36664e9i	−0.829327	+	0.478812i	0.0242953	+	0.999705i	$0.492266\pi$
$504$		−	2.01167e8i		−	0.0699924i
$505$	−1.17951e9	−	6.80988e8i	−0.407549	−	0.235299i
$506$	2.53632e8	+	4.39304e8i	0.0870318	+	0.150744i
$507$	−5.57905e8			−0.190122
$508$	−1.63538e9			−0.553474
$509$	2.04896e8	+	3.54891e8i	0.0688687	+	0.119284i	0.898404	−	0.439171i	$-0.144728\pi$
$509$	2.04896e8	+	3.54891e8i	0.0688687	+	0.119284i	−0.829535	+	0.558455i	$0.811394\pi$
$510$		−	1.79992e8i		−	0.0600839i
$511$	2.53317e8	−	4.38758e8i	0.0839830	−	0.145463i
$512$		−	1.34218e8i		−	0.0441942i
$513$	−1.08833e9	−	6.28345e8i	−0.355917	−	0.205488i
$514$	−1.05312e9	+	1.82406e9i	−0.342065	+	0.592473i
$515$	−5.90265e8	+	1.02237e9i	−0.190424	+	0.329824i
$516$	2.92280e8	−	1.68748e8i	0.0936536	−	0.0540710i
$517$	−1.69078e9			−0.538109
$518$	−3.64624e8	−	2.69074e8i	−0.115263	−	0.0850583i
$519$	−8.65036e8			−0.271612
$520$	−6.86810e8	+	3.96530e8i	−0.214203	+	0.123670i
$521$	3.14859e9	−	5.45352e9i	0.975403	−	1.68945i	0.296806	−	0.954938i	$-0.404078\pi$
$521$	3.14859e9	−	5.45352e9i	0.975403	−	1.68945i	0.678597	−	0.734511i	$-0.262588\pi$
$522$	−6.69044e8	+	1.15882e9i	−0.205877	+	0.356590i
$523$	−2.97113e9	−	1.71538e9i	−0.908167	−	0.524331i	−0.0283262	−	0.999599i	$-0.509018\pi$
$523$	−2.97113e9	−	1.71538e9i	−0.908167	−	0.524331i	−0.879841	+	0.475268i	$0.842351\pi$
$524$			2.02667e9i			0.615351i
$525$	−3.97206e7	+	6.87981e7i	−0.0119800	+	0.0207500i
$526$			1.02242e9i			0.306322i
$527$	2.20983e9	+	3.82754e9i	0.657691	+	1.13915i
$528$	8.07360e7			0.0238698
$529$	2.88896e9			0.848489
$530$	−4.77960e8	−	8.27851e8i	−0.139452	−	0.241539i
$531$	4.48345e9	+	2.58852e9i	1.29952	+	0.750276i
$532$			4.84315e8i			0.139456i
$533$	−6.27161e9	+	3.62091e9i	−1.79405	+	1.03579i
$534$	2.86139e8	+	4.95608e8i	0.0813173	+	0.140846i
$535$	1.13022e9	−	6.52533e8i	0.319098	−	0.184232i
$536$	−2.12427e9	−	1.22645e9i	−0.595845	−	0.344011i
$537$	4.52088e8	+	2.61013e8i	0.125983	+	0.0727366i
$538$	1.17271e9	−	6.77064e8i	0.324678	−	0.187453i
$539$	1.10238e9	+	1.90938e9i	0.303229	+	0.525207i
$540$	2.20137e8	−	1.27096e8i	0.0601609	−	0.0347339i
$541$			2.81998e9i			0.765695i	0.923812	+	0.382848i	$0.125057\pi$
$541$			2.81998e9i			0.765695i	−0.923812	+	0.382848i	$0.874943\pi$
$542$	1.89479e9	+	1.09396e9i	0.511167	+	0.295123i
$543$	−3.52095e8	−	6.09846e8i	−0.0943758	−	0.163464i
$544$	−8.02661e8			−0.213765
$545$	6.68898e8			0.177000
$546$	−6.18206e7	−	1.07076e8i	−0.0162539	−	0.0281526i
$547$		−	3.92186e9i		−	1.02456i	−0.858820	−	0.512278i	$-0.828802\pi$
$547$		−	3.92186e9i		−	1.02456i	0.858820	−	0.512278i	$-0.171198\pi$
$548$	1.43753e9	−	2.48987e9i	0.373151	−	0.646316i
$549$		−	3.65587e9i		−	0.942947i
$550$	1.18374e9	+	6.83431e8i	0.303379	+	0.175156i
$551$	1.61074e9	−	2.78988e9i	0.410198	−	0.710485i
$552$	−4.10528e7	+	7.11056e7i	−0.0103886	+	0.0179935i
$553$	5.86774e8	−	3.38774e8i	0.147548	−	0.0851868i
$554$	2.60407e9			0.650681
$555$	3.16704e7	−	2.81223e8i	0.00786372	−	0.0698273i
$556$	2.19112e8			0.0540634
$557$	3.42540e8	−	1.97766e8i	0.0839882	−	0.0484906i	−0.457418	−	0.889252i	$-0.651226\pi$
$557$	3.42540e8	−	1.97766e8i	0.0839882	−	0.0484906i	0.541406	+	0.840761i	$0.317892\pi$
$558$	−1.54242e9	+	2.67154e9i	−0.375822	+	0.650942i
$559$	−4.44644e9	+	7.70146e9i	−1.07664	+	1.86480i
$560$	−8.48383e7	−	4.89814e7i	−0.0204143	−	0.0117862i
$561$		−	4.82825e8i		−	0.115457i
$562$	−2.04726e9	+	3.54597e9i	−0.486516	+	0.842670i
$563$			3.88922e9i			0.918507i	0.888305	+	0.459254i	$0.151883\pi$
$563$			3.88922e9i			0.918507i	−0.888305	+	0.459254i	$0.848117\pi$
$564$	−1.36834e8	−	2.37004e8i	−0.0321158	−	0.0556261i
$565$	−3.13246e9			−0.730661
$566$	−3.92729e8			−0.0910407
$567$	−4.09827e8	−	7.09841e8i	−0.0944191	−	0.163539i
$568$	1.87447e9	+	1.08222e9i	0.429199	+	0.247798i
$569$		−	1.64280e9i		−	0.373845i	−0.982375	−	0.186923i	$-0.940149\pi$
$569$		−	1.64280e9i		−	0.373845i	0.982375	−	0.186923i	$-0.0598513\pi$
$570$	−2.61937e8	+	1.51229e8i	−0.0592427	+	0.0342038i
$571$	8.15113e8	+	1.41182e9i	0.183228	+	0.317360i	0.942978	−	0.332855i	$-0.108012\pi$
$571$	8.15113e8	+	1.41182e9i	0.183228	+	0.317360i	−0.759750	+	0.650215i	$0.774679\pi$
$572$	−1.84235e9	+	1.06368e9i	−0.411611	+	0.237643i
$573$	8.04485e7	+	4.64470e7i	0.0178639	+	0.0103137i
$574$	−7.74701e8	−	4.47274e8i	−0.170979	−	0.0987148i
$575$	−1.20382e9	+	6.95025e8i	−0.264073	+	0.152462i
$576$	−2.80121e8	−	4.85183e8i	−0.0610754	−	0.105786i
$577$	1.42001e9	−	8.19844e8i	0.307735	−	0.177671i	−0.338178	−	0.941082i	$-0.609810\pi$
$577$	1.42001e9	−	8.19844e8i	0.307735	−	0.177671i	0.645912	+	0.763412i	$0.276477\pi$
$578$			1.51744e9i			0.326862i
$579$	−5.28748e7	−	3.05273e7i	−0.0113207	−	0.00653601i
$580$	3.25805e8	+	5.64311e8i	0.0693362	+	0.120094i
$581$	−2.96934e8			−0.0628121
$582$	−5.33582e8			−0.112194
$583$	−1.28212e9	−	2.22069e9i	−0.267971	−	0.464140i
$584$		−	1.41095e9i		−	0.293134i
$585$	−1.65516e9	+	2.86683e9i	−0.341818	+	0.592046i
$586$		−	9.60926e8i		−	0.197264i
$587$	−4.55125e8	−	2.62766e8i	−0.0928746	−	0.0536212i	0.452843	−	0.891590i	$-0.350410\pi$
$587$	−4.55125e8	−	2.62766e8i	−0.0928746	−	0.0536212i	−0.545718	+	0.837969i	$0.683743\pi$
$588$	−1.78430e8	+	3.09051e8i	−0.0361950	+	0.0626915i
$589$	3.71340e9	−	6.43179e9i	0.748804	−	1.29697i
$590$	2.18331e9	−	1.26054e9i	0.437657	−	0.252681i
$591$	8.10208e8			0.161451
$592$	−1.25409e9	−	1.41232e8i	−0.248430	−	0.0279773i
$593$	−9.78488e9			−1.92692			−0.963461	−	0.267848i	$-0.913687\pi$
$593$	−9.78488e9			−1.92692			−0.963461	+	0.267848i	$0.913687\pi$
$594$	5.90512e8	−	3.40932e8i	0.115605	−	0.0667445i
$595$	−2.92923e8	+	5.07358e8i	−0.0570091	+	0.0987427i
$596$	1.73325e9	−	3.00208e9i	0.335352	−	0.580846i
$597$	−1.35235e9	−	7.80783e8i	−0.260124	−	0.150183i
$598$		−	2.16345e9i		−	0.413707i
$599$	2.82732e9	−	4.89706e9i	0.537504	−	0.930983i	−0.461534	−	0.887122i	$-0.652701\pi$
$599$	2.82732e9	−	4.89706e9i	0.537504	−	0.930983i	0.999038	−	0.0438610i	$-0.0139659\pi$
$600$			2.21240e8i			0.0418151i
$601$	−3.07801e9	−	5.33127e9i	−0.578375	−	1.00177i	−0.995666	−	0.0930014i	$-0.970354\pi$
$601$	−3.07801e9	−	5.33127e9i	−0.578375	−	1.00177i	0.417291	−	0.908773i	$-0.362979\pi$
$602$	−1.09849e9			−0.205216
$603$	−1.02387e10			−1.90167
$604$	−9.59471e8	−	1.66185e9i	−0.177175	−	0.306876i
$605$	1.31740e9	+	7.60603e8i	0.241866	+	0.139641i
$606$		−	5.91349e8i		−	0.107942i
$607$	9.20197e9	−	5.31276e9i	1.67002	−	0.964184i	0.702391	−	0.711792i	$-0.252116\pi$
$607$	9.20197e9	−	5.31276e9i	1.67002	−	0.964184i	0.967625	−	0.252392i	$-0.0812173\pi$
$608$	6.74396e8	+	1.16809e9i	0.121689	+	0.210772i
$609$	−8.79784e7	+	5.07943e7i	−0.0157839	+	0.00911286i
$610$	−1.54179e9	−	8.90151e8i	−0.275024	−	0.158785i
$611$	6.24497e9	+	3.60553e9i	1.10761	+	0.639478i
$612$	−2.90154e9	+	1.67520e9i	−0.511680	+	0.295418i
$613$	3.74166e9	+	6.48074e9i	0.656073	+	1.13635i	0.981624	+	0.190827i	$0.0611170\pi$
$613$	3.74166e9	+	6.48074e9i	0.656073	+	1.13635i	−0.325551	+	0.945525i	$0.605550\pi$
$614$	3.73641e9	−	2.15722e9i	0.651426	−	0.376101i
$615$		−	5.58653e8i		−	0.0968454i
$616$	−2.27577e8	−	1.31392e8i	−0.0392279	−	0.0226483i
$617$	3.49211e9	+	6.04851e9i	0.598535	+	1.03669i	0.993038	+	0.117799i	$0.0375837\pi$
$617$	3.49211e9	+	6.04851e9i	0.598535	+	1.03669i	−0.394502	+	0.918895i	$0.629083\pi$
$618$	−5.12568e8			−0.0873558
$619$	1.18218e9			0.200339			0.100169	−	0.994970i	$-0.468062\pi$
$619$	1.18218e9			0.200339			0.100169	+	0.994970i	$0.468062\pi$
$620$	7.51113e8	+	1.30097e9i	0.126571	+	0.219227i
$621$			6.93432e8i			0.116194i
$622$	2.76135e9	−	4.78280e9i	0.460103	−	0.796921i
$623$		−	1.86268e9i		−	0.308624i
$624$	−2.98202e8	−	1.72167e8i	−0.0491320	−	0.0283664i
$625$	−1.21171e9	+	2.09875e9i	−0.198527	+	0.343859i
$626$	−9.80298e8	+	1.69793e9i	−0.159716	+	0.276636i
$627$	−7.02640e8	+	4.05669e8i	−0.113840	+	0.0657258i
$628$	−1.70713e9			−0.275048
$629$	−8.44607e8	+	7.49984e9i	−0.135325	+	1.20164i
$630$	−4.08909e8			−0.0651530
$631$	4.38910e9	−	2.53405e9i	0.695461	−	0.401524i	−0.110194	−	0.993910i	$-0.535147\pi$
$631$	4.38910e9	−	2.53405e9i	0.695461	−	0.401524i	0.805654	+	0.592386i	$0.201814\pi$
$632$	9.43469e8	−	1.63414e9i	0.148668	−	0.257501i
$633$	7.86654e8	−	1.36253e9i	0.123274	−	0.213517i
$634$	−4.14055e9	−	2.39055e9i	−0.645277	−	0.372551i
$635$			3.32421e9i			0.515205i
$636$	2.07523e8	−	3.59440e8i	0.0319864	−	0.0554022i
$637$		−	9.40315e9i		−	1.44140i
$638$	8.73966e8	+	1.51375e9i	0.133236	+	0.230772i
$639$	9.03466e9			1.36981
$640$	−2.72821e8			−0.0411385
$641$	−4.44442e9	−	7.69797e9i	−0.666519	−	1.15444i	−0.978871	−	0.204478i	$-0.934450\pi$
$641$	−4.44442e9	−	7.69797e9i	−0.666519	−	1.15444i	0.312352	−	0.949966i	$-0.398883\pi$
$642$	4.90724e8	+	2.83320e8i	0.0731922	+	0.0422575i
$643$		−	7.63767e9i		−	1.13298i	−0.824068	−	0.566490i	$-0.808301\pi$
$643$		−	7.63767e9i		−	1.13298i	0.824068	−	0.566490i	$-0.191699\pi$
$644$	2.31437e8	−	1.33620e8i	0.0341455	−	0.0197139i
$645$	−3.43010e8	−	5.94110e8i	−0.0503324	−	0.0871782i
$646$	6.98550e9	−	4.03308e9i	1.01949	−	0.588604i
$647$	6.87468e9	+	3.96910e9i	0.997901	+	0.576139i	0.907627	−	0.419778i	$-0.137892\pi$
$647$	6.87468e9	+	3.96910e9i	0.997901	+	0.576139i	0.0902747	+	0.995917i	$0.471225\pi$
$648$	−1.97687e9	−	1.14135e9i	−0.285408	−	0.164780i
$649$	5.85669e9	−	3.38136e9i	0.840999	−	0.485551i
$650$	−2.91479e9	−	5.04857e9i	−0.416304	−	0.721060i
$651$	−2.02826e8	+	1.17101e8i	−0.0288131	+	0.0166352i
$652$		−	4.10269e9i		−	0.579699i
$653$	−7.37316e9	−	4.25689e9i	−1.03623	−	0.598269i	−0.117469	−	0.993077i	$-0.537478\pi$
$653$	−7.37316e9	−	4.25689e9i	−1.03623	−	0.598269i	−0.918764	+	0.394807i	$0.870811\pi$
$654$	1.45213e8	+	2.51516e8i	0.0202994	+	0.0351595i
$655$	4.11956e9			0.572804
$656$	−2.49127e9			−0.344554
$657$	−2.94474e9	−	5.10043e9i	−0.405105	−	0.701663i
$658$			8.90748e8i			0.121889i
$659$	1.75346e9	−	3.03709e9i	0.238670	−	0.413389i	−0.721663	−	0.692245i	$-0.756622\pi$
$659$	1.75346e9	−	3.03709e9i	0.238670	−	0.413389i	0.960333	+	0.278856i	$0.0899552\pi$
$660$		−	1.64110e8i		−	0.0222194i
$661$	−5.21632e9	−	3.01164e9i	−0.702520	−	0.405600i	0.105765	−	0.994391i	$-0.466271\pi$
$661$	−5.21632e9	−	3.01164e9i	−0.702520	−	0.405600i	−0.808285	+	0.588791i	$0.799604\pi$
$662$	2.82551e9	−	4.89392e9i	0.378524	−	0.655623i
$663$	−1.02961e9	+	1.78334e9i	−0.137207	+	0.237649i
$664$	−7.16156e8	+	4.13473e8i	−0.0949334	+	0.0548099i
$665$	9.84455e8			0.129814
$666$	−4.82817e9	+	2.10683e9i	−0.633319	+	0.276356i
$667$	−1.77758e9			−0.231947
$668$	1.17530e9	−	6.78562e8i	0.152557	−	0.0880789i
$669$	7.27348e8	−	1.25980e9i	0.0939185	−	0.162672i
$670$	−2.49298e9	+	4.31796e9i	−0.320226	+	0.554647i
$671$	−4.13581e9	−	2.38781e9i	−0.528484	−	0.305120i
$672$		−	4.25339e7i		−	0.00540683i
$673$	−1.64797e9	+	2.85438e9i	−0.208400	+	0.360959i	−0.951211	−	0.308542i	$-0.900159\pi$
$673$	−1.64797e9	+	2.85438e9i	−0.208400	+	0.360959i	0.742811	+	0.669502i	$0.233492\pi$
$674$		−	3.49758e9i		−	0.440005i
$675$	9.34251e8	+	1.61817e9i	0.116923	+	0.202517i
$676$	5.05717e9			0.629643
$677$	7.88056e9			0.976105			0.488052	−	0.872814i	$-0.337707\pi$
$677$	7.88056e9			0.976105			0.488052	+	0.872814i	$0.337707\pi$
$678$	−6.80033e8	−	1.17785e9i	−0.0837966	−	0.145140i
$679$	1.50405e9	+	8.68363e8i	0.184382	+	0.106453i
$680$			1.63155e9i			0.198985i
$681$	−6.42180e8	+	3.70763e8i	−0.0779188	+	0.0449864i
$682$	2.01484e9	+	3.48981e9i	0.243218	+	0.421266i
$683$	−1.33708e9	+	7.71963e8i	−0.160577	+	0.0927095i	−0.578135	−	0.815941i	$-0.696219\pi$
$683$	−1.33708e9	+	7.71963e8i	−0.160577	+	0.0927095i	0.417558	+	0.908650i	$0.362886\pi$
$684$	4.87574e9	+	2.81501e9i	0.582565	+	0.336344i
$685$	−5.06110e9	−	2.92203e9i	−0.601628	−	0.347350i
$686$	2.05487e9	−	1.18638e9i	0.243025	−	0.140310i
$687$	4.58086e8	+	7.93428e8i	0.0539012	+	0.0933596i
$688$	−2.64939e9	+	1.52963e9i	−0.310160	+	0.179071i
$689$			1.09363e10i			1.27381i
$690$	1.44535e8	+	8.34471e7i	0.0167494	+	0.00967029i
$691$	7.09874e9	+	1.22954e10i	0.818480	+	1.41765i	0.906802	+	0.421556i	$0.138516\pi$
$691$	7.09874e9	+	1.22954e10i	0.818480	+	1.41765i	−0.0883226	+	0.996092i	$0.528151\pi$
$692$	7.84118e9			0.899519
$693$	−1.09689e9			−0.125198
$694$	−2.33562e9	−	4.04541e9i	−0.265243	−	0.459414i
$695$		−	4.45383e8i		−	0.0503253i
$696$	−1.41460e8	+	2.45015e8i	−0.0159038	+	0.0275461i
$697$			1.48985e10i			1.66659i
$698$	−7.52188e9	−	4.34276e9i	−0.837206	−	0.483361i
$699$	3.39706e8	−	5.88389e8i	0.0376213	−	0.0651620i
$700$	3.60050e8	−	6.23625e8i	0.0396753	−	0.0687196i
$701$	−1.41055e10	+	8.14384e9i	−1.54660	+	0.892927i	−0.548197	+	0.836349i	$0.684686\pi$
$701$	−1.41055e10	+	8.14384e9i	−1.54660	+	0.892927i	−0.998398	+	0.0565783i	$0.981981\pi$
$702$	−2.90811e9			−0.317271
$703$	1.16239e10	−	5.07223e9i	1.26185	−	0.550624i
$704$	−7.31837e8			−0.0790515
$705$	−4.81753e8	+	2.78140e8i	−0.0517800	+	0.0298952i
$706$	−6.98079e8	+	1.20911e9i	−0.0746601	+	0.129315i
$707$	−9.62374e8	+	1.66688e9i	−0.102418	+	0.177393i
$708$	9.47960e8	+	5.47305e8i	0.100386	+	0.0579580i
$709$			1.54843e10i			1.63166i	0.578289	+	0.815832i	$0.303721\pi$
$709$			1.54843e10i			1.63166i	−0.578289	+	0.815832i	$0.696279\pi$
$710$	2.19981e9	−	3.81018e9i	0.230665	−	0.399523i
$711$		−	7.87631e9i		−	0.821824i
$712$	−2.59373e9	−	4.49247e9i	−0.269305	−	0.466450i
$713$	−4.09805e9			−0.423412
$714$	−2.54365e8			−0.0261526
$715$	2.16212e9	+	3.74491e9i	0.221212	+	0.383151i
$716$	−4.09799e9	−	2.36597e9i	−0.417230	−	0.240888i
$717$		−	8.31730e8i		−	0.0842685i
$718$	−7.59664e9	+	4.38592e9i	−0.765924	+	0.442207i
$719$	−2.01328e9	−	3.48711e9i	−0.202001	−	0.349876i	0.747172	−	0.664631i	$-0.231411\pi$
$719$	−2.01328e9	−	3.48711e9i	−0.202001	−	0.349876i	−0.949173	+	0.314755i	$0.898078\pi$
$720$	−9.86220e8	+	5.69395e8i	−0.0984714	+	0.0568525i
$721$	1.44481e9	+	8.34164e8i	0.143562	+	0.0828854i
$722$	−5.54551e9	−	3.20170e9i	−0.548354	−	0.316592i
$723$	−3.29631e8	+	1.90312e8i	−0.0324372	+	0.0187276i
$724$	3.19159e9	+	5.52800e9i	0.312552	+	0.541356i
$725$	−4.14811e9	+	2.39491e9i	−0.404266	+	0.233403i
$726$			6.60484e8i			0.0640596i
$727$	1.19671e10	+	6.90923e9i	1.15510	+	0.666898i	0.950125	−	0.311869i	$-0.100955\pi$
$727$	1.19671e10	+	6.90923e9i	1.15510	+	0.666898i	0.204976	+	0.978767i	$0.434288\pi$
$728$	5.60377e8	+	9.70601e8i	0.0538295	+	0.0932354i
$729$	−9.05682e9			−0.865823
$730$	−2.86801e9			−0.272866
$731$	9.14761e9	+	1.58441e10i	0.866157	+	1.50023i
$732$		−	7.72980e8i		−	0.0728416i
$733$	3.40011e9	−	5.88917e9i	0.318882	−	0.552319i	−0.661373	−	0.750057i	$-0.730026\pi$
$733$	3.40011e9	−	5.88917e9i	0.318882	−	0.552319i	0.980255	+	0.197738i	$0.0633594\pi$
$734$		−	7.35600e9i		−	0.686603i
$735$	6.28200e8	+	3.62692e8i	0.0583569	+	0.0336924i
$736$	3.72126e8	−	6.44541e8i	0.0344047	−	0.0595907i
$737$	−6.68736e9	+	1.15828e10i	−0.615344	+	1.06581i
$738$	−9.00568e9	+	5.19943e9i	−0.824744	+	0.476166i
$739$	−1.98151e10			−1.80610			−0.903050	−	0.429536i	$-0.858677\pi$
$739$	−1.98151e10			−1.80610			−0.903050	+	0.429536i	$0.858677\pi$
$740$	−2.87078e8	+	2.54916e9i	−0.0260429	+	0.231253i
$741$	3.46031e9			0.312429
$742$	−1.16992e9	+	6.75454e8i	−0.105134	+	0.0606991i
$743$	−5.47820e9	+	9.48853e9i	−0.489979	+	0.848668i	−0.999933	−	0.0115330i	$-0.996329\pi$
$743$	−5.47820e9	+	9.48853e9i	−0.489979	+	0.848668i	0.509955	+	0.860201i	$0.329662\pi$
$744$	−3.26121e8	+	5.64859e8i	−0.0290318	+	0.0502846i
$745$	−6.10227e9	−	3.52315e9i	−0.540685	−	0.312165i
$746$			5.12794e9i			0.452227i
$747$	−1.72589e9	+	2.98932e9i	−0.151492	+	0.262392i
$748$			4.37660e9i			0.382368i
$749$	−9.22161e8	−	1.59723e9i	−0.0801900	−	0.138893i
$750$	1.02377e9			0.0886114
$751$	1.25251e10			1.07905			0.539527	−	0.841969i	$-0.318603\pi$
$751$	1.25251e10			1.07905			0.539527	+	0.841969i	$0.318603\pi$
$752$	1.24034e9	+	2.14834e9i	0.106360	+	0.184222i
$753$	2.45511e9	+	1.41746e9i	0.209550	+	0.120984i
$754$		−	7.45482e9i		−	0.633341i
$755$	−3.37801e9	+	1.95029e9i	−0.285658	+	0.164925i
$756$	−1.79612e8	−	3.11098e8i	−0.0151185	−	0.0261861i
$757$	1.44260e10	−	8.32883e9i	1.20867	−	0.697828i	0.246204	−	0.969218i	$-0.420817\pi$
$757$	1.44260e10	−	8.32883e9i	1.20867	−	0.697828i	0.962470	+	0.271390i	$0.0874832\pi$
$758$	1.01119e10	+	5.83812e9i	0.843318	+	0.486890i
$759$	3.87711e8	+	2.23845e8i	0.0321856	+	0.0185824i
$760$	2.37434e9	−	1.37083e9i	0.196199	−	0.113275i
$761$	8.68096e8	+	1.50359e9i	0.0714038	+	0.123675i	0.899517	−	0.436886i	$-0.143919\pi$
$761$	8.68096e8	+	1.50359e9i	0.0714038	+	0.123675i	−0.828113	+	0.560561i	$0.810585\pi$
$762$	−1.24995e9	+	7.21660e8i	−0.102341	+	0.0590868i
$763$		−	9.45289e8i		−	0.0770422i
$764$	−7.29231e8	−	4.21022e8i	−0.0591614	−	0.0341569i
$765$	3.40515e9	+	5.89789e9i	0.274992	+	0.476301i
$766$	1.03379e10			0.831056
$767$	−2.88426e10			−2.30808
$768$	−5.92274e7	−	1.02585e8i	−0.00471800	−	0.00817182i
$769$		−	1.14613e10i		−	0.908851i	−0.890785	−	0.454426i	$-0.849845\pi$
$769$		−	1.14613e10i		−	0.908851i	0.890785	−	0.454426i	$-0.150155\pi$
$770$	−2.67077e8	+	4.62590e8i	−0.0210823	+	0.0365156i
$771$			1.85888e9i			0.146070i
$772$	4.79287e8	+	2.76717e8i	0.0374917	+	0.0216458i
$773$	−4.71107e8	+	8.15982e8i	−0.0366853	+	0.0635407i	−0.883785	−	0.467893i	$-0.845013\pi$
$773$	−4.71107e8	+	8.15982e8i	−0.0366853	+	0.0635407i	0.847100	+	0.531434i	$0.178347\pi$
$774$	−6.38484e9	+	1.10589e10i	−0.494945	+	0.857270i
$775$	−9.56308e9	+	5.52124e9i	−0.737975	+	0.426070i
$776$	4.83669e9			0.371563
$777$	−3.97425e8	−	4.47567e7i	−0.0303935	−	0.00342282i
$778$	1.50281e10			1.14413
$779$	2.16813e10	−	1.25177e10i	1.64326	−	0.948734i
$780$	−3.49960e8	+	6.06149e8i	−0.0264051	+	0.0457349i
$781$	5.90095e9	−	1.02207e10i	0.443244	−	0.767722i
$782$	−3.85455e9	−	2.22542e9i	−0.288237	−	0.166414i
$783$			2.38942e9i			0.177880i
$784$	1.61740e9	−	2.80141e9i	0.119870	−	0.207621i
$785$			3.47005e9i			0.256030i
$786$	8.94324e8	+	1.54901e9i	0.0656925	+	0.113783i
$787$	−5.19623e9			−0.379994			−0.189997	−	0.981785i	$-0.560848\pi$
$787$	−5.19623e9			−0.379994			−0.189997	+	0.981785i	$0.560848\pi$
$788$	−7.34419e9			−0.534690
$789$	4.51170e8	+	7.81450e8i	0.0327018	+	0.0566411i
$790$	−3.32167e9	−	1.91777e9i	−0.239697	−	0.138389i
$791$			4.42680e9i			0.318033i
$792$	−2.64552e9	+	1.52739e9i	−0.189222	+	0.109248i
$793$	1.01839e10	+	1.76390e10i	0.725198	+	1.25608i
$794$	3.56774e9	−	2.05983e9i	0.252942	−	0.146036i
$795$	−7.30626e8	−	4.21827e8i	−0.0515715	−	0.0297748i
$796$	1.22585e10	+	7.07746e9i	0.861474	+	0.497372i
$797$	9.05798e8	−	5.22963e8i	0.0633763	−	0.0365903i	−0.467977	−	0.883741i	$-0.655017\pi$
$797$	9.05798e8	−	5.22963e8i	0.0633763	−	0.0365903i	0.531353	+	0.847150i	$0.321684\pi$
$798$	2.13718e8	+	3.70170e8i	0.0148878	+	0.0257864i
$799$	1.28477e10	−	7.41762e9i	0.891069	−	0.514459i
$800$		−	2.00544e9i		−	0.138483i
$801$	−1.87521e10	−	1.08265e10i	−1.28925	−	0.744348i
$802$	−2.86733e8	−	4.96636e8i	−0.0196276	−	0.0339960i
$803$	−7.69336e9			−0.524339
$804$	−2.16482e9			−0.146902
$805$	−2.71607e8	−	4.70438e8i	−0.0183508	−	0.0317846i
$806$		−	1.71864e10i		−	1.15614i
$807$	5.97548e8	−	1.03498e9i	0.0400235	−	0.0693228i
$808$			5.36032e9i			0.357480i
$809$	−2.91175e9	−	1.68110e9i	−0.193346	−	0.111628i	0.400202	−	0.916427i	$-0.368940\pi$
$809$	−2.91175e9	−	1.68110e9i	−0.193346	−	0.111628i	−0.593548	+	0.804799i	$0.702273\pi$
$810$	−2.31999e9	+	4.01834e9i	−0.153387	+	0.265674i
$811$	7.13221e9	−	1.23533e10i	0.469517	−	0.813227i	−0.529876	−	0.848075i	$-0.677762\pi$
$811$	7.13221e9	−	1.23533e10i	0.469517	−	0.813227i	0.999393	+	0.0348485i	$0.0110949\pi$
$812$	7.97486e8	−	4.60429e8i	0.0522730	−	0.0301798i
$813$	1.93096e9			0.126025
$814$	−7.70082e8	+	6.83808e9i	−0.0500439	+	0.444374i
$815$	−8.33945e9			−0.539617
$816$	−6.13488e8	+	3.54197e8i	−0.0395267	+	0.0228207i
$817$	1.53716e10	−	2.66245e10i	0.986150	−	1.70806i
$818$	−3.05506e9	+	5.29152e9i	−0.195156	+	0.338021i
$819$	4.05141e9	+	2.33908e9i	0.257699	+	0.148782i
$820$			5.06395e9i			0.320731i
$821$	1.24857e10	−	2.16259e10i	0.787431	−	1.36387i	−0.140105	−	0.990137i	$-0.544744\pi$
$821$	1.24857e10	−	2.16259e10i	0.787431	−	1.36387i	0.927536	−	0.373733i	$-0.121923\pi$
$822$		−	2.53740e9i		−	0.159345i
$823$	1.57779e9	+	2.73281e9i	0.0986619	+	0.170887i	0.911131	−	0.412117i	$-0.135210\pi$
$823$	1.57779e9	+	2.73281e9i	0.0986619	+	0.170887i	−0.812469	+	0.583004i	$0.801877\pi$
$824$	4.64621e9			0.289303
$825$	1.20633e9			0.0747961
$826$	−1.78139e9	−	3.08546e9i	−0.109984	−	0.190498i
$827$	−7.39001e9	−	4.26663e9i	−0.454335	−	0.262310i	0.255324	−	0.966855i	$-0.417818\pi$
$827$	−7.39001e9	−	4.26663e9i	−0.454335	−	0.262310i	−0.709659	+	0.704545i	$0.751151\pi$
$828$		−	3.10660e9i		−	0.190186i
$829$	−9.44694e9	+	5.45419e9i	−0.575904	+	0.332498i	−0.759504	−	0.650503i	$-0.774558\pi$
$829$	−9.44694e9	+	5.45419e9i	−0.575904	+	0.332498i	0.183600	+	0.983001i	$0.441225\pi$
$830$	8.40457e8	+	1.45571e9i	0.0510202	+	0.0883695i
$831$	1.99033e9	−	1.14912e9i	0.120316	−	0.0694643i
$832$	2.70307e9	+	1.56062e9i	0.162714	+	0.0939433i
$833$	−1.67533e10	−	9.67250e9i	−1.00425	−	0.579804i
$834$	1.67471e8	−	9.66892e7i	0.00999672	−	0.00577161i
$835$	−1.37930e9	−	2.38901e9i	−0.0819890	−	0.142009i
$836$	6.36913e9	−	3.67722e9i	0.377015	−	0.217669i
$837$			5.50859e9i			0.324714i
$838$	−8.24657e9	−	4.76116e9i	−0.484083	−	0.279485i
$839$	2.74554e8	+	4.75541e8i	0.0160495	+	0.0277985i	0.873939	−	0.486036i	$-0.161558\pi$
$839$	2.74554e8	+	4.75541e8i	0.0160495	+	0.0277985i	−0.857889	+	0.513835i	$0.828224\pi$
$840$	−8.64577e7			−0.00503299
$841$	1.11247e10			0.644914
$842$	4.75078e9	+	8.22859e9i	0.274266	+	0.475043i
$843$			3.61366e9i			0.207754i
$844$	−7.13068e9	+	1.23507e10i	−0.408256	+	0.707120i
$845$		−	1.02796e10i		−	0.586108i
$846$	8.96743e9	+	5.17735e9i	0.509180	+	0.293975i
$847$	1.07489e9	−	1.86176e9i	0.0607814	−	0.105276i
$848$	−1.88111e9	+	3.25817e9i	−0.105932	+	0.183480i
$849$	−3.00169e8	+	1.73303e8i	−0.0168341	+	0.00971916i
$850$	−1.19931e10			−0.669833
$851$	−5.63084e9	−	4.15526e9i	−0.313198	−	0.231124i
$852$	1.91025e9			0.105816
$853$	−1.54312e10	+	8.90918e9i	−0.851289	+	0.491492i	−0.861086	−	0.508460i	$-0.830215\pi$
$853$	−1.54312e10	+	8.90918e9i	−0.851289	+	0.491492i	0.00979666	+	0.999952i	$0.496882\pi$
$854$	−1.25796e9	+	2.17886e9i	−0.0691139	+	0.119709i
$855$	5.72200e9	−	9.91080e9i	0.313088	−	0.542285i
$856$	−4.44820e9	−	2.56817e9i	−0.242396	−	0.139948i
$857$			3.96017e9i			0.214922i	0.994209	+	0.107461i	$0.0342721\pi$
$857$			3.96017e9i			0.214922i	−0.994209	+	0.107461i	$0.965728\pi$
$858$	−9.38760e8	+	1.62598e9i	−0.0507399	+	0.0878840i
$859$		−	1.30522e9i		−	0.0702599i	−0.999383	−	0.0351300i	$-0.988815\pi$
$859$		−	1.30522e9i		−	0.0702599i	0.999383	−	0.0351300i	$-0.0111845\pi$
$860$	3.10924e9	+	5.38535e9i	0.166690	+	0.288715i
$861$	−7.89490e8			−0.0421537
$862$	1.01085e10			0.537540
$863$	−4.90543e9	−	8.49646e9i	−0.259800	−	0.449987i	0.706388	−	0.707825i	$-0.250323\pi$
$863$	−4.90543e9	−	8.49646e9i	−0.259800	−	0.449987i	−0.966188	+	0.257838i	$0.916990\pi$
$864$	−8.66391e8	−	5.00211e8i	−0.0457000	−	0.0263849i
$865$		−	1.59386e10i		−	0.837324i
$866$	6.95419e9	−	4.01500e9i	0.363859	−	0.210074i
$867$	6.69614e8	+	1.15981e9i	0.0348945	+	0.0604391i
$868$	1.83853e9	−	1.06147e9i	0.0954226	−	0.0550922i
$869$	−8.91031e9	−	5.14437e9i	−0.460600	−	0.265927i
$870$	4.98037e8	+	2.87542e8i	0.0256415	+	0.0148042i
$871$	4.94001e10	−	2.85212e10i	2.53317	−	1.46253i
$872$	−1.31629e9	−	2.27988e9i	−0.0672270	−	0.116441i
$873$	1.74841e10	−	1.00945e10i	0.889394	−	0.513492i
$874$			7.47920e9i			0.378935i
$875$	−2.88579e9	−	1.66611e9i	−0.145625	−	0.0840768i
$876$	−6.22622e8	−	1.07841e9i	−0.0312939	−	0.0542027i
$877$	−1.31333e10			−0.657469			−0.328735	−	0.944422i	$-0.606622\pi$
$877$	−1.31333e10			−0.657469			−0.328735	+	0.944422i	$0.606622\pi$
$878$	4.79947e9			0.239311
$879$	−4.24036e8	−	7.34452e8i	−0.0210592	−	0.0364756i
$880$			1.48759e9i			0.0735857i
$881$	−3.42120e9	+	5.92569e9i	−0.168563	+	0.291960i	−0.937915	−	0.346866i	$-0.887246\pi$
$881$	−3.42120e9	+	5.92569e9i	−0.168563	+	0.291960i	0.769352	+	0.638825i	$0.220579\pi$
$882$		−	1.35024e10i		−	0.662630i
$883$	−1.35724e10	−	7.83604e9i	−0.663430	−	0.383031i	0.130153	−	0.991494i	$-0.458453\pi$
$883$	−1.35724e10	−	7.83604e9i	−0.663430	−	0.383031i	−0.793583	+	0.608463i	$0.791787\pi$
$884$	9.33297e9	−	1.61652e10i	0.454398	−	0.787041i
$885$	1.11249e9	−	1.92690e9i	0.0539506	−	0.0934452i
$886$	4.16930e9	−	2.40714e9i	0.201393	−	0.116274i
$887$	−8.99717e9			−0.432886			−0.216443	−	0.976295i	$-0.569445\pi$
$887$	−8.99717e9			−0.432886			−0.216443	+	0.976295i	$0.569445\pi$
$888$	−1.02085e9	+	4.45458e8i	−0.0489232	+	0.0213482i
$889$	4.69778e9			0.224252
$890$	−9.13174e9	+	5.27221e9i	−0.434199	+	0.250685i
$891$	−6.22333e9	+	1.07791e10i	−0.294748	+	0.510518i
$892$	−6.59310e9	+	1.14196e10i	−0.311037	+	0.538733i
$893$	−2.15893e10	−	1.24646e10i	−1.01451	−	0.585729i
$894$		−	3.05939e9i		−	0.143203i
$895$	−4.80926e9	+	8.32989e9i	−0.224232	+	0.388381i
$896$			3.85552e8i			0.0179063i
$897$	−9.54685e8	−	1.65356e9i	−0.0441659	−	0.0764975i
$898$	−6.79745e9			−0.313241
$899$	−1.41210e10			−0.648198
$900$	−4.18548e9	−	7.24946e9i	−0.191380	−	0.331480i
$901$	1.94848e10	+	1.12496e10i	0.887482	+	0.512388i
$902$			1.35839e10i			0.616315i
$903$	−8.39598e8	+	4.84742e8i	−0.0379459	+	0.0219080i
$904$	6.16421e9	+	1.06767e10i	0.277516	+	0.480672i
$905$	1.12366e10	−	6.48747e9i	0.503925	−	0.290941i
$906$	−1.46668e9	−	8.46788e8i	−0.0655219	−	0.0378291i
$907$	2.04510e10	+	1.18074e10i	0.910101	+	0.525447i	0.880464	−	0.474114i	$-0.157231\pi$
$907$	2.04510e10	+	1.18074e10i	0.910101	+	0.525447i	0.0296374	+	0.999561i	$0.490565\pi$
$908$	5.82109e9	−	3.36081e9i	0.258050	−	0.148985i
$909$	1.11873e10	+	1.93770e10i	0.494029	+	0.855683i
$910$	1.97292e9	−	1.13906e9i	0.0867889	−	0.0501076i
$911$		−	1.86170e10i		−	0.815821i	−0.913022	−	0.407910i	$-0.866258\pi$
$911$		−	1.86170e10i		−	0.815821i	0.913022	−	0.407910i	$-0.133742\pi$
$912$	1.03090e9	+	5.95193e8i	0.0450025	+	0.0259822i
$913$	2.25451e9	+	3.90492e9i	0.0980401	+	0.169810i
$914$	−3.67757e7			−0.00159312
$915$	−1.57122e9			−0.0678051
$916$	−4.15235e9	−	7.19209e9i	−0.178509	−	0.309187i
$917$		−	5.82177e9i		−	0.249323i
$918$	−2.99141e9	+	5.18127e9i	−0.127622	+	0.221048i
$919$		−	4.39636e10i		−	1.86848i	−0.356640	−	0.934242i	$-0.616078\pi$
$919$		−	4.39636e10i		−	1.86848i	0.356640	−	0.934242i	$-0.383922\pi$
$920$	−1.31014e9	−	7.56412e8i	−0.0554705	−	0.0320259i
$921$	1.90387e9	−	3.29759e9i	0.0803022	−	0.139088i
$922$	3.06657e9	−	5.31145e9i	0.128853	−	0.223180i
$923$	−4.35908e10	+	2.51672e10i	−1.82469	+	1.05349i
$924$	−2.31921e8			−0.00967138
$925$	−1.87383e10	−	2.11024e9i	−0.778455	−	0.0876670i
$926$	−2.40775e10			−0.996491
$927$	1.67956e10	−	9.69692e9i	0.692493	−	0.399811i
$928$	1.28227e9	−	2.22096e9i	0.0526698	−	0.0912268i
$929$	−1.72058e10	+	2.98013e10i	−0.704075	+	1.21949i	0.262949	+	0.964810i	$0.415305\pi$
$929$	−1.72058e10	+	2.98013e10i	−0.704075	+	1.21949i	−0.967024	+	0.254685i	$0.918028\pi$
$930$	1.14818e9	+	6.62900e8i	0.0468078	+	0.0270245i
$931$			3.25073e10i			1.32025i
$932$	−3.07929e9	+	5.33349e9i	−0.124593	+	0.215802i
$933$		−	4.87410e9i		−	0.196475i
$934$	2.46168e9	+	4.26376e9i	0.0988593	+	0.171229i
$935$	8.89622e9			0.355930
$936$	1.30284e10			0.519310
$937$	−1.32473e10	−	2.29449e10i	−0.526063	−	0.911167i	−0.999539	−	0.0303606i	$-0.990334\pi$
$937$	−1.32473e10	−	2.29449e10i	−0.526063	−	0.911167i	0.473476	−	0.880806i	$-0.342999\pi$
$938$	6.10215e9	+	3.52308e9i	0.241420	+	0.139384i
$939$			1.73034e9i			0.0682027i
$940$	4.36688e9	−	2.52122e9i	0.171484	−	0.0990064i
$941$	1.13352e10	+	1.96331e10i	0.443471	+	0.768114i	0.997944	−	0.0640873i	$-0.0204136\pi$
$941$	1.13352e10	+	1.96331e10i	0.443471	+	0.768114i	−0.554473	+	0.832201i	$0.687080\pi$
$942$	−1.30479e9	+	7.53320e8i	−0.0508583	+	0.0293631i
$943$	−1.19636e10	−	6.90718e9i	−0.464591	−	0.268232i
$944$	−8.59285e9	−	4.96109e9i	−0.332457	−	0.191944i
$945$	−6.32361e8	+	3.65094e8i	−0.0243755	+	0.0140732i
$946$	8.34046e9	+	1.44461e10i	0.320310	+	0.554794i
$947$	1.51618e10	−	8.75367e9i	0.580131	−	0.334939i	−0.181055	−	0.983473i	$-0.557951\pi$
$947$	1.51618e10	−	8.75367e9i	0.580131	−	0.334939i	0.761185	+	0.648534i	$0.224618\pi$
$948$		−	1.66533e9i		−	0.0634850i
$949$	2.84158e10	+	1.64059e10i	1.07926	+	0.623114i
$950$	1.00766e10	+	1.74532e10i	0.381314	+	0.660455i
$951$	−4.21959e9			−0.159088
$952$	2.30571e9			0.0866116
$953$	1.56911e10	+	2.71778e10i	0.587257	+	1.01716i	0.994590	+	0.103879i	$0.0331255\pi$
$953$	1.56911e10	+	2.71778e10i	0.587257	+	1.01716i	−0.407333	+	0.913280i	$0.633541\pi$
$954$			1.57039e10i			0.585584i
$955$	−8.55801e8	+	1.48229e9i	−0.0317952	+	0.0550709i
$956$			7.53927e9i			0.279079i
$957$	1.33597e9	+	7.71325e8i	0.0492727	+	0.0284476i
$958$	4.19425e9	−	7.26466e9i	0.154126	−	0.266954i
$959$	−4.12942e9	+	7.15236e9i	−0.151190	+	0.261869i
$960$	−2.08522e8	+	1.20390e8i	−0.00760681	+	0.00439179i
$961$	−5.04206e9			−0.183264
$962$	1.74263e10	−	2.36146e10i	0.631092	−	0.855199i
$963$	−2.14397e10			−0.773619
$964$	2.98796e9	−	1.72510e9i	0.107425	−	0.0620219i
$965$	5.62475e8	−	9.74236e8i	0.0201492	−	0.0348995i
$966$	1.17928e8	−	2.04257e8i	0.00420916	−	0.00729048i
$967$	−3.98163e10	−	2.29880e10i	−1.41602	−	0.817538i	−0.420071	−	0.907491i	$-0.637995\pi$
$967$	−3.98163e10	−	2.29880e10i	−1.41602	−	0.817538i	−0.995946	+	0.0899535i	$0.971328\pi$
$968$		−	5.98700e9i		−	0.212151i
$969$	3.55943e9	−	6.16511e9i	0.125674	−	0.217674i
$970$		−	9.83144e9i		−	0.345872i
$971$	2.60977e10	+	4.52025e10i	0.914818	+	1.58451i	0.807167	+	0.590323i	$0.201000\pi$
$971$	2.60977e10	+	4.52025e10i	0.914818	+	1.58451i	0.107652	+	0.994189i	$0.465667\pi$
$972$	−6.28790e9			−0.219621
$973$	−6.29416e8			−0.0219050
$974$	3.16155e9	+	5.47597e9i	0.109634	+	0.189891i
$975$	−4.45565e9	−	2.57247e9i	−0.153955	−	0.0888862i
$976$			7.00673e9i			0.241235i
$977$	2.28712e10	−	1.32047e10i	0.784616	−	0.452999i	−0.0534474	−	0.998571i	$-0.517021\pi$
$977$	2.28712e10	−	1.32047e10i	0.784616	−	0.452999i	0.838064	+	0.545572i	$0.183688\pi$
$978$	−1.81043e9	−	3.13576e9i	−0.0618865	−	0.107191i
$979$	−2.44957e10	+	1.41426e10i	−0.834354	+	0.481715i
$980$	−5.69436e9	−	3.28764e9i	−0.193265	−	0.111582i
$981$	−9.51650e9	−	5.49435e9i	−0.321837	−	0.185813i
$982$	−6.90603e9	+	3.98720e9i	−0.232722	+	0.134362i
$983$	1.93040e10	+	3.34356e10i	0.648203	+	1.12272i	0.983552	+	0.180626i	$0.0578125\pi$
$983$	1.93040e10	+	3.34356e10i	0.648203	+	1.12272i	−0.335349	+	0.942094i	$0.608854\pi$
$984$	−1.90412e9	+	1.09934e9i	−0.0637106	+	0.0367833i
$985$			1.49284e10i			0.497721i
$986$	−1.32820e10	−	7.66835e9i	−0.441259	−	0.254761i
$987$	3.93068e8	+	6.80814e8i	0.0130124	+	0.0225382i
$988$	−3.13662e10			−1.03470
$989$	−1.69639e10			−0.557620
$990$	3.10469e9	+	5.37748e9i	0.101694	+	0.176139i
$991$		−	3.83319e10i		−	1.25113i	−0.780172	−	0.625565i	$-0.784868\pi$
$991$		−	3.83319e10i		−	1.25113i	0.780172	−	0.625565i	$-0.215132\pi$
$992$	2.95615e9	−	5.12020e9i	0.0961470	−	0.166532i
$993$		−	4.98734e9i		−	0.161639i
$994$	−5.38456e9	−	3.10878e9i	−0.173899	−	0.100401i
$995$	1.43862e10	−	2.49176e10i	0.462983	−	0.801910i
$996$	−3.64913e8	+	6.32048e8i	−0.0117026	+	0.0202695i
$997$	5.22388e10	−	3.01601e10i	1.66940	−	0.963828i	0.701436	−	0.712732i	$-0.252543\pi$
$997$	5.22388e10	−	3.01601e10i	1.66940	−	0.963828i	0.967962	−	0.251095i	$-0.0807908\pi$
$998$	−1.15418e9			−0.0367551
$999$	−5.58550e9	+	7.56896e9i	−0.177249	+	0.240191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.8.e.a.11.6	✓	48
37.27	even	6	inner	74.8.e.a.27.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.8.e.a.11.6	✓	48	1.1	even	1	trivial
74.8.e.a.27.6	yes	48	37.27	even	6	inner

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	74.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.92820 + 4.00000i) q^{2} +(-3.53023 + 6.11453i) q^{3} +(32.0000 - 55.4256i) q^{4} +(-112.662 - 65.0457i) q^{5} -56.4836i q^{6} +(-91.9227 + 159.215i) q^{7} +512.000i q^{8} +(1068.57 + 1850.83i) q^{9} +1040.73 q^{10} +2791.74 q^{11} +(225.935 + 391.330i) q^{12} +(-10311.4 - 5953.29i) q^{13} -1470.76i q^{14} +(795.448 - 459.252i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(-21213.5 + 12247.6i) q^{17} +(-14806.6 - 8548.60i) q^{18} +(35647.2 + 20580.9i) q^{19} +(-7210.39 + 4162.92i) q^{20} +(-649.016 - 1124.13i) q^{21} +(-19341.7 + 11167.0i) q^{22} -22712.8i q^{23} +(-3130.64 - 1807.48i) q^{24} +(-30600.6 - 53001.8i) q^{25} +95252.7 q^{26} -30530.5 q^{27} +(5883.05 + 10189.7i) q^{28} -78263.6i q^{29} +(-3674.02 + 6363.58i) q^{30} -180429. i q^{31} +(28377.9 + 16384.0i) q^{32} +(-9855.47 + 17070.2i) q^{33} +(97981.1 - 169708. i) q^{34} +(20712.5 - 11958.3i) q^{35} +136778. q^{36} +(182948. - 247915. i) q^{37} -329295. q^{38} +(72803.2 - 42033.0i) q^{39} +(33303.4 - 57683.2i) q^{40} +(304110. - 526734. i) q^{41} +(8993.03 + 5192.13i) q^{42} -746888. i q^{43} +(89335.6 - 154734. i) q^{44} -278025. i q^{45} +(90851.1 + 157359. i) q^{46} -605637. q^{47} +28919.6 q^{48} +(394872. + 683938. i) q^{49} +(424015. + 244805. i) q^{50} -172948. i q^{51} +(-659930. + 381011. i) q^{52} +(-459254. - 795452. i) q^{53} +(211521. - 122122. i) q^{54} +(-314524. - 181590. i) q^{55} +(-81518.0 - 47064.4i) q^{56} +(-251685. + 145311. i) q^{57} +(313054. + 542226. i) q^{58} +(2.09786e6 - 1.21120e6i) q^{59} -58784.3i q^{60} +(-1.48145e6 - 855313. i) q^{61} +(721717. + 1.25005e6i) q^{62} -392905. q^{63} -262144. q^{64} +(774472. + 1.34142e6i) q^{65} -157688. i q^{66} +(-2.39541e6 + 4.14897e6i) q^{67} +1.56770e6i q^{68} +(138878. + 80181.3i) q^{69} +(-95666.8 + 165700. i) q^{70} +(2.11372e6 - 3.66107e6i) q^{71} +(-947623. + 547110. i) q^{72} -2.75576e6 q^{73} +(-275843. + 2.44940e6i) q^{74} +432109. q^{75} +(2.28142e6 - 1.31718e6i) q^{76} +(-256624. + 444486. i) q^{77} +(-336264. + 582426. i) q^{78} +(-3.19167e6 - 1.84271e6i) q^{79} +532854. i q^{80} +(-2.22919e6 + 3.86108e6i) q^{81} +4.86576e6i q^{82} +(807564. + 1.39874e6i) q^{83} -83074.1 q^{84} +3.18662e6 q^{85} +(2.98755e6 + 5.17459e6i) q^{86} +(478545. + 276288. i) q^{87} +1.42937e6i q^{88} +(-8.77436e6 + 5.06588e6i) q^{89} +(1.11210e6 + 1.92621e6i) q^{90} +(1.89571e6 - 1.09449e6i) q^{91} +(-1.25887e6 - 726809. i) q^{92} +(1.10324e6 + 636956. i) q^{93} +(4.19597e6 - 2.42255e6i) q^{94} +(-2.67740e6 - 4.63739e6i) q^{95} +(-200361. + 115679. i) q^{96} -9.44667e6i q^{97} +(-5.47151e6 - 3.15898e6i) q^{98} +(2.98318e6 + 5.16702e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 28 q^{3} + 1536 q^{4} + 252 q^{5} + 52 q^{7} - 24028 q^{9} + 4864 q^{10} - 8352 q^{11} - 1792 q^{12} - 5136 q^{13} - 16632 q^{15} - 98304 q^{16} + 28980 q^{17} - 66096 q^{19} + 16128 q^{20} - 64344 q^{21}+ \cdots + 50165480 q^{99}+O(q^{100}) \) 48 * q + 28 * q^3 + 1536 * q^4 + 252 * q^5 + 52 * q^7 - 24028 * q^9 + 4864 * q^10 - 8352 * q^11 - 1792 * q^12 - 5136 * q^13 - 16632 * q^15 - 98304 * q^16 + 28980 * q^17 - 66096 * q^19 + 16128 * q^20 - 64344 * q^21 + 675072 * q^25 + 533952 * q^26 - 444416 * q^27 - 3328 * q^28 - 114528 * q^30 + 120916 * q^33 + 120992 * q^34 + 865908 * q^35 - 3075584 * q^36 - 500268 * q^37 + 879360 * q^38 - 669984 * q^39 + 155648 * q^40 + 1024524 * q^41 - 589728 * q^42 - 267264 * q^44 - 729888 * q^46 - 2144712 * q^47 - 229376 * q^48 - 3570900 * q^49 + 2919168 * q^50 - 328704 * q^52 - 2231700 * q^53 + 3784320 * q^54 + 3781260 * q^55 - 1487472 * q^57 + 468064 * q^58 - 10302480 * q^59 + 10141752 * q^61 + 4388256 * q^62 + 9348424 * q^63 - 12582912 * q^64 + 1169736 * q^65 - 1473864 * q^67 + 14887176 * q^69 - 310528 * q^70 + 3017772 * q^71 + 16773224 * q^73 - 2565696 * q^74 - 10623504 * q^75 - 4230144 * q^76 + 15133908 * q^77 - 763328 * q^78 - 2776836 * q^79 - 29469256 * q^81 - 1844556 * q^83 - 8236032 * q^84 - 9520960 * q^85 - 1972416 * q^86 - 51259224 * q^87 + 33361344 * q^89 - 28098496 * q^90 + 91933608 * q^91 + 4193280 * q^92 - 9874476 * q^93 - 28885728 * q^94 - 40830084 * q^95 + 11612160 * q^98 + 50165480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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