LMFDB - Embedded newform 38.7.f.a.3.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,7,Mod(3,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("38.3");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	38.f (of order $18$, 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:	$8.74205517755$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.3
Character	$\chi$	$=$	38.3
Dual form			38.7.f.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.63616 + 4.33340i) q^{2} +(0.501194 + 1.37702i) q^{3} +(-5.55674 - 31.5138i) q^{4} +(6.94044 - 39.3612i) q^{5} +(-7.78959 - 2.83518i) q^{6} +(159.899 + 276.953i) q^{7} +(156.767 + 90.5097i) q^{8} +(556.801 - 467.212i) q^{9} +O(q^{10})$	\(q+(-3.63616 + 4.33340i) q^{2} +(0.501194 + 1.37702i) q^{3} +(-5.55674 - 31.5138i) q^{4} +(6.94044 - 39.3612i) q^{5} +(-7.78959 - 2.83518i) q^{6} +(159.899 + 276.953i) q^{7} +(156.767 + 90.5097i) q^{8} +(556.801 - 467.212i) q^{9} +(145.331 + 173.199i) q^{10} +(-397.184 + 687.943i) q^{11} +(40.6102 - 23.4463i) q^{12} +(-1239.64 + 3405.88i) q^{13} +(-1781.57 - 314.139i) q^{14} +(57.6796 - 10.1705i) q^{15} +(-962.245 + 350.229i) q^{16} +(7315.30 + 6138.26i) q^{17} +4111.70i q^{18} +(-6856.34 - 191.002i) q^{19} -1278.99 q^{20} +(-301.230 + 358.991i) q^{21} +(-1536.91 - 4222.62i) q^{22} +(1890.50 + 10721.6i) q^{23} +(-46.0627 + 261.234i) q^{24} +(13181.6 + 4797.70i) q^{25} +(-10251.5 - 17756.1i) q^{26} +(1847.57 + 1066.70i) q^{27} +(7839.35 - 6578.00i) q^{28} +(-14623.6 - 17427.8i) q^{29} +(-165.659 + 286.930i) q^{30} +(42007.4 - 24253.0i) q^{31} +(1981.19 - 5443.28i) q^{32} +(-1146.38 - 202.137i) q^{33} +(-53199.1 + 9380.44i) q^{34} +(12011.0 - 4371.64i) q^{35} +(-17817.6 - 14950.8i) q^{36} -48361.1i q^{37} +(25758.4 - 29016.8i) q^{38} -5311.25 q^{39} +(4650.60 - 5542.37i) q^{40} +(23686.7 + 65078.6i) q^{41} +(-460.336 - 2610.70i) q^{42} +(-2452.93 + 13911.2i) q^{43} +(23886.8 + 8694.07i) q^{44} +(-14525.6 - 25159.0i) q^{45} +(-53335.0 - 30793.0i) q^{46} +(-94771.7 + 79522.9i) q^{47} +(-964.543 - 1149.50i) q^{48} +(7689.04 - 13317.8i) q^{49} +(-68720.6 + 39675.8i) q^{50} +(-4786.12 + 13149.8i) q^{51} +(114221. + 20140.2i) q^{52} +(82869.6 - 14612.1i) q^{53} +(-11340.5 + 4127.60i) q^{54} +(24321.6 + 20408.2i) q^{55} +57889.7i q^{56} +(-3173.34 - 9537.04i) q^{57} +128695. q^{58} +(-132397. + 157784. i) q^{59} +(-641.021 - 1761.19i) q^{60} +(-17807.8 - 100993. i) q^{61} +(-47647.6 + 270223. i) q^{62} +(218428. + 79501.3i) q^{63} +(16384.0 + 28377.9i) q^{64} +(125456. + 72431.9i) q^{65} +(5044.34 - 4232.71i) q^{66} +(-178215. - 212389. i) q^{67} +(152791. - 264642. i) q^{68} +(-13816.3 + 7976.84i) q^{69} +(-24729.7 + 67944.4i) q^{70} +(-115332. - 20336.1i) q^{71} +(129575. - 22847.7i) q^{72} +(-506532. + 184362. i) q^{73} +(209568. + 175849. i) q^{74} +20555.8i q^{75} +(32079.7 + 217131. i) q^{76} -254037. q^{77} +(19312.5 - 23015.8i) q^{78} +(-235113. - 645968. i) q^{79} +(7107.01 + 40305.8i) q^{80} +(91469.1 - 518747. i) q^{81} +(-368140. - 133992. i) q^{82} +(364817. + 631882. i) q^{83} +(12987.1 + 7498.08i) q^{84} +(292381. - 245336. i) q^{85} +(-51363.8 - 61213.0i) q^{86} +(16669.1 - 28871.7i) q^{87} +(-124531. + 71898.0i) q^{88} +(367399. - 1.00942e6i) q^{89} +(161841. + 28537.0i) q^{90} +(-1.14149e6 + 201275. i) q^{91} +(327373. - 119154. i) q^{92} +(54450.7 + 45689.6i) q^{93} -699841. i q^{94} +(-55104.1 + 268548. i) q^{95} +8488.46 q^{96} +(916880. - 1.09270e6i) q^{97} +(29752.9 + 81745.3i) q^{98} +(100262. + 568617. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30 q^{3} - 240 q^{6} + 432 q^{7} + 690 q^{9}+O(q^{10}) $ 60 * q + 30 * q^3 - 240 * q^6 + 432 * q^7 + 690 * q^9	\( 60 q + 30 q^{3} - 240 q^{6} + 432 q^{7} + 690 q^{9} - 3360 q^{11} + 9660 q^{13} + 2496 q^{14} - 37464 q^{15} + 7704 q^{17} + 46704 q^{19} + 21504 q^{20} + 78732 q^{21} - 20304 q^{22} - 54120 q^{23} + 7680 q^{24} - 41328 q^{25} - 25536 q^{26} - 124830 q^{27} + 65280 q^{28} - 21840 q^{29} + 30780 q^{31} - 54582 q^{33} - 70560 q^{34} - 56796 q^{35} - 22080 q^{36} + 52080 q^{38} + 496344 q^{39} + 83394 q^{41} + 38880 q^{42} - 294384 q^{43} - 8448 q^{44} - 391824 q^{45} + 738720 q^{46} + 639264 q^{47} + 61440 q^{48} - 85530 q^{49} - 689472 q^{50} - 215478 q^{51} - 456960 q^{52} - 1189428 q^{53} - 907200 q^{54} - 316512 q^{55} + 517776 q^{57} + 440640 q^{58} + 957390 q^{59} + 586752 q^{60} + 1390404 q^{61} + 978384 q^{62} + 2002152 q^{63} + 983040 q^{64} - 878940 q^{65} - 976992 q^{66} - 2920854 q^{67} - 78144 q^{68} - 2667600 q^{69} - 643392 q^{70} + 1585980 q^{71} + 706560 q^{72} + 1734648 q^{73} - 1167552 q^{74} - 411264 q^{76} - 1481400 q^{77} - 2170608 q^{78} + 4991952 q^{79} + 40002 q^{81} + 2299392 q^{82} - 30672 q^{83} + 1313280 q^{84} + 815976 q^{85} - 1424976 q^{86} - 125892 q^{87} - 6804636 q^{89} - 2283456 q^{90} - 3838704 q^{91} - 244992 q^{92} - 3271128 q^{93} - 4631640 q^{95} + 2112390 q^{97} + 7177728 q^{98} + 21467982 q^{99}+O(q^{100}) \) 60 * q + 30 * q^3 - 240 * q^6 + 432 * q^7 + 690 * q^9 - 3360 * q^11 + 9660 * q^13 + 2496 * q^14 - 37464 * q^15 + 7704 * q^17 + 46704 * q^19 + 21504 * q^20 + 78732 * q^21 - 20304 * q^22 - 54120 * q^23 + 7680 * q^24 - 41328 * q^25 - 25536 * q^26 - 124830 * q^27 + 65280 * q^28 - 21840 * q^29 + 30780 * q^31 - 54582 * q^33 - 70560 * q^34 - 56796 * q^35 - 22080 * q^36 + 52080 * q^38 + 496344 * q^39 + 83394 * q^41 + 38880 * q^42 - 294384 * q^43 - 8448 * q^44 - 391824 * q^45 + 738720 * q^46 + 639264 * q^47 + 61440 * q^48 - 85530 * q^49 - 689472 * q^50 - 215478 * q^51 - 456960 * q^52 - 1189428 * q^53 - 907200 * q^54 - 316512 * q^55 + 517776 * q^57 + 440640 * q^58 + 957390 * q^59 + 586752 * q^60 + 1390404 * q^61 + 978384 * q^62 + 2002152 * q^63 + 983040 * q^64 - 878940 * q^65 - 976992 * q^66 - 2920854 * q^67 - 78144 * q^68 - 2667600 * q^69 - 643392 * q^70 + 1585980 * q^71 + 706560 * q^72 + 1734648 * q^73 - 1167552 * q^74 - 411264 * q^76 - 1481400 * q^77 - 2170608 * q^78 + 4991952 * q^79 + 40002 * q^81 + 2299392 * q^82 - 30672 * q^83 + 1313280 * q^84 + 815976 * q^85 - 1424976 * q^86 - 125892 * q^87 - 6804636 * q^89 - 2283456 * q^90 - 3838704 * q^91 - 244992 * q^92 - 3271128 * q^93 - 4631640 * q^95 + 2112390 * q^97 + 7177728 * q^98 + 21467982 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−3.63616	+	4.33340i	−0.454519	+	0.541675i
$2$	−3.63616	+	4.33340i	−0.454519	+	0.541675i
$3$	0.501194	+	1.37702i	0.0185627	+	0.0510007i	0.948628	−	0.316394i	$-0.102472\pi$
$3$	0.501194	+	1.37702i	0.0185627	+	0.0510007i	−0.930065	+	0.367395i	$0.880250\pi$
$4$	−5.55674	−	31.5138i	−0.0868241	−	0.492404i
$5$	6.94044	−	39.3612i	0.0555235	−	0.314889i	−0.944379	−	0.328859i	$-0.893336\pi$
$5$	6.94044	−	39.3612i	0.0555235	−	0.314889i	0.999902	+	0.0139700i	$0.00444692\pi$
$6$	−7.78959	−	2.83518i	−0.0360629	−	0.0131258i
$7$	159.899	+	276.953i	0.466178	+	0.807444i	0.999254	−	0.0386233i	$-0.0122972\pi$
$7$	159.899	+	276.953i	0.466178	+	0.807444i	−0.533076	+	0.846068i	$0.678964\pi$
$8$	156.767	+	90.5097i	0.306186	+	0.176777i
$9$	556.801	−	467.212i	0.763788	−	0.640894i
$10$	145.331	+	173.199i	0.145331	+	0.173199i
$11$	−397.184	+	687.943i	−0.298410	+	0.516862i	−0.975772	−	0.218788i	$-0.929790\pi$
$11$	−397.184	+	687.943i	−0.298410	+	0.516862i	0.677362	+	0.735650i	$0.263123\pi$
$12$	40.6102	−	23.4463i	0.0235012	−	0.0135685i
$13$	−1239.64	+	3405.88i	−0.564241	+	1.55024i	0.249115	+	0.968474i	$0.419860\pi$
$13$	−1239.64	+	3405.88i	−0.564241	+	1.55024i	−0.813356	+	0.581766i	$0.802362\pi$
$14$	−1781.57	−	314.139i	−0.649260	−	0.114482i
$15$	57.6796	−	10.1705i	0.0170902	−	0.00301347i
$16$	−962.245	+	350.229i	−0.234923	+	0.0855050i
$17$	7315.30	+	6138.26i	1.48897	+	1.24939i	0.895912	+	0.444231i	$0.146523\pi$
$17$	7315.30	+	6138.26i	1.48897	+	1.24939i	0.593055	+	0.805162i	$0.297922\pi$
$18$			4111.70i			0.705024i
$19$	−6856.34	−	191.002i	−0.999612	−	0.0278469i
$19$	−6856.34	−	191.002i	−0.999612	−	0.0278469i
$20$	−1278.99			−0.159874
$21$	−301.230	+	358.991i	−0.0325267	+	0.0387638i
$22$	−1536.91	−	4222.62i	−0.144338	−	0.396565i
$23$	1890.50	+	10721.6i	0.155380	+	0.881201i	0.958438	+	0.285301i	$0.0920935\pi$
$23$	1890.50	+	10721.6i	0.155380	+	0.881201i	−0.803059	+	0.595900i	$0.796795\pi$
$24$	−46.0627	+	261.234i	−0.00333208	+	0.0188972i
$25$	13181.6	+	4797.70i	0.843620	+	0.307053i
$26$	−10251.5	−	17756.1i	−0.583268	−	1.01025i
$27$	1847.57	+	1066.70i	0.0938665	+	0.0541939i
$28$	7839.35	−	6578.00i	0.357113	−	0.299654i
$29$	−14623.6	−	17427.8i	−0.599600	−	0.714575i	0.377821	−	0.925879i	$-0.376674\pi$
$29$	−14623.6	−	17427.8i	−0.599600	−	0.714575i	−0.977420	+	0.211304i	$0.932229\pi$
$30$	−165.659	+	286.930i	−0.00613553	+	0.0106270i
$31$	42007.4	−	24253.0i	1.41007	−	0.814105i	0.414677	−	0.909969i	$-0.363895\pi$
$31$	42007.4	−	24253.0i	1.41007	−	0.814105i	0.995395	+	0.0958633i	$0.0305612\pi$
$32$	1981.19	−	5443.28i	0.0604612	−	0.166116i
$33$	−1146.38	−	202.137i	−0.0318996	−	0.00562476i
$34$	−53199.1	+	9380.44i	−1.35353	+	0.238664i
$35$	12011.0	−	4371.64i	0.280139	−	0.101962i
$36$	−17817.6	−	14950.8i	−0.381894	−	0.320447i
$37$		−	48361.1i		−	0.954754i	−0.878699	−	0.477377i	$-0.841588\pi$
$37$		−	48361.1i		−	0.954754i	0.878699	−	0.477377i	$-0.158412\pi$
$38$	25758.4	−	29016.8i	0.469427	−	0.528808i
$39$	−5311.25			−0.0895371
$40$	4650.60	−	5542.37i	0.0726656	−	0.0865995i
$41$	23686.7	+	65078.6i	0.343679	+	0.944250i	0.984317	+	0.176407i	$0.0564475\pi$
$41$	23686.7	+	65078.6i	0.343679	+	0.944250i	−0.640639	+	0.767843i	$0.721330\pi$
$42$	−460.336	−	2610.70i	−0.00621337	−	0.0352378i
$43$	−2452.93	+	13911.2i	−0.0308517	+	0.174969i	−0.996340	−	0.0854773i	$-0.972758\pi$
$43$	−2452.93	+	13911.2i	−0.0308517	+	0.174969i	0.965488	+	0.260446i	$0.0838696\pi$
$44$	23886.8	+	8694.07i	0.280414	+	0.102062i
$45$	−14525.6	−	25159.0i	−0.159403	−	0.276093i
$46$	−53335.0	−	30793.0i	−0.547948	−	0.316358i
$47$	−94771.7	+	79522.9i	−0.912820	+	0.765947i	−0.972653	−	0.232262i	$-0.925387\pi$
$47$	−94771.7	+	79522.9i	−0.912820	+	0.765947i	0.0598336	+	0.998208i	$0.480943\pi$
$48$	−964.543	−	1149.50i	−0.00872163	−	0.0103940i
$49$	7689.04	−	13317.8i	0.0653558	−	0.113200i
$50$	−68720.6	+	39675.8i	−0.549765	+	0.317407i
$51$	−4786.12	+	13149.8i	−0.0360806	+	0.0991305i
$52$	114221.	+	20140.2i	0.812334	+	0.143236i
$53$	82869.6	−	14612.1i	0.556631	−	0.0981491i	0.111746	−	0.993737i	$-0.464356\pi$
$53$	82869.6	−	14612.1i	0.556631	−	0.0981491i	0.444885	+	0.895588i	$0.353245\pi$
$54$	−11340.5	+	4127.60i	−0.0720196	+	0.0262130i
$55$	24321.6	+	20408.2i	0.146185	+	0.122664i
$56$			57889.7i			0.329638i
$57$	−3173.34	−	9537.04i	−0.0171353	−	0.0514978i
$58$	128695.			0.659597
$59$	−132397.	+	157784.i	−0.644645	+	0.768258i	−0.985096	−	0.172004i	$-0.944976\pi$
$59$	−132397.	+	157784.i	−0.644645	+	0.768258i	0.340451	+	0.940262i	$0.389420\pi$
$60$	−641.021	−	1761.19i	−0.00296769	−	0.00815366i
$61$	−17807.8	−	100993.i	−0.0784552	−	0.444942i	−0.998578	−	0.0533114i	$-0.983022\pi$
$61$	−17807.8	−	100993.i	−0.0784552	−	0.444942i	0.920123	−	0.391630i	$-0.128089\pi$
$62$	−47647.6	+	270223.i	−0.199924	+	1.13383i
$63$	218428.	+	79501.3i	0.873548	+	0.317945i
$64$	16384.0	+	28377.9i	0.0625000	+	0.108253i
$65$	125456.	+	72431.9i	0.456825	+	0.263748i
$66$	5044.34	−	4232.71i	0.0175458	−	0.0147227i
$67$	−178215.	−	212389.i	−0.592544	−	0.706166i	0.383549	−	0.923520i	$-0.374702\pi$
$67$	−178215.	−	212389.i	−0.592544	−	0.706166i	−0.976093	+	0.217354i	$0.930257\pi$
$68$	152791.	−	264642.i	0.485927	−	0.841651i
$69$	−13816.3	+	7976.84i	−0.0420576	+	0.0242820i
$70$	−24729.7	+	67944.4i	−0.0720983	+	0.198089i
$71$	−115332.	−	20336.1i	−0.322236	−	0.0568190i	0.0101903	−	0.999948i	$-0.496756\pi$
$71$	−115332.	−	20336.1i	−0.322236	−	0.0568190i	−0.332427	+	0.943129i	$0.607867\pi$
$72$	129575.	−	22847.7i	0.347156	−	0.0612131i
$73$	−506532.	+	184362.i	−1.30208	+	0.473919i	−0.897674	−	0.440660i	$-0.854744\pi$
$73$	−506532.	+	184362.i	−1.30208	+	0.473919i	−0.404407	+	0.914579i	$0.632522\pi$
$74$	209568.	+	175849.i	0.517166	+	0.433954i
$75$			20555.8i			0.0487249i
$76$	32079.7	+	217131.i	0.0730785	+	0.494631i
$77$	−254037.			−0.556449
$78$	19312.5	−	23015.8i	0.0406964	−	0.0485001i
$79$	−235113.	−	645968.i	−0.476865	−	1.31018i	−0.912140	−	0.409878i	$-0.865571\pi$
$79$	−235113.	−	645968.i	−0.476865	−	1.31018i	0.435275	−	0.900297i	$-0.356651\pi$
$80$	7107.01	+	40305.8i	0.0138809	+	0.0787223i
$81$	91469.1	−	518747.i	0.172115	−	0.976114i
$82$	−368140.	−	133992.i	−0.667685	−	0.243018i
$83$	364817.	+	631882.i	0.638030	+	1.10510i	0.985864	+	0.167545i	$0.0535839\pi$
$83$	364817.	+	631882.i	0.638030	+	1.10510i	−0.347834	+	0.937556i	$0.613083\pi$
$84$	12987.1	+	7498.08i	0.0219115	+	0.0126506i
$85$	292381.	−	245336.i	0.476093	−	0.399489i
$86$	−51363.8	−	61213.0i	−0.0807535	−	0.0962383i
$87$	16669.1	−	28871.7i	0.0253136	−	0.0438445i
$88$	−124531.	+	71898.0i	−0.182738	+	0.105504i
$89$	367399.	−	1.00942e6i	0.521157	−	1.43187i	−0.348078	−	0.937466i	$-0.613166\pi$
$89$	367399.	−	1.00942e6i	0.521157	−	1.43187i	0.869234	−	0.494400i	$-0.164612\pi$
$90$	161841.	+	28537.0i	0.222005	+	0.0391454i
$91$	−1.14149e6	+	201275.i	−1.51477	+	0.267095i
$92$	327373.	−	119154.i	0.420416	−	0.153019i
$93$	54450.7	+	45689.6i	0.0676947	+	0.0568026i
$94$		−	699841.i		−	0.842590i
$95$	−55104.1	+	268548.i	−0.0642707	+	0.313221i
$96$	8488.46			0.00959434
$97$	916880.	−	1.09270e6i	1.00461	−	1.19725i	0.0243157	−	0.999704i	$-0.492259\pi$
$97$	916880.	−	1.09270e6i	1.00461	−	1.19725i	0.980294	−	0.197543i	$-0.0632962\pi$
$98$	29752.9	+	81745.3i	0.0316119	+	0.0868530i
$99$	100262.	+	568617.i	0.103331	+	0.586022i
$100$	77947.4	−	442061.i	0.0779474	−	0.442061i
$101$	476036.	+	173263.i	0.462036	+	0.168167i	0.562541	−	0.826769i	$-0.309824\pi$
$101$	476036.	+	173263.i	0.462036	+	0.168167i	−0.100505	+	0.994937i	$0.532046\pi$
$102$	−39580.1	−	68554.8i	−0.0372972	−	0.0646007i
$103$	576196.	+	332667.i	0.527301	+	0.304437i	0.739917	−	0.672699i	$-0.234865\pi$
$103$	576196.	+	332667.i	0.527301	+	0.304437i	−0.212616	+	0.977136i	$0.568198\pi$
$104$	−502599.	+	421731.i	−0.446809	+	0.374917i
$105$	12039.7	+	14348.3i	0.0104003	+	0.0123946i
$106$	−238006.	+	412239.i	−0.199835	+	0.346124i
$107$	−485802.	+	280478.i	−0.396559	+	0.228953i	−0.684998	−	0.728545i	$-0.740197\pi$
$107$	−485802.	+	280478.i	−0.396559	+	0.228953i	0.288439	+	0.957498i	$0.406864\pi$
$108$	23349.3	−	64151.6i	0.0185354	−	0.0509256i
$109$	−601940.	−	106138.i	−0.464808	−	0.0819582i	−0.0636603	−	0.997972i	$-0.520277\pi$
$109$	−601940.	−	106138.i	−0.464808	−	0.0819582i	−0.401148	+	0.916013i	$0.631389\pi$
$110$	−176874.	+	31187.7i	−0.132888	+	0.0234318i
$111$	66594.2	−	24238.3i	0.0486931	−	0.0177228i
$112$	−250859.	−	210496.i	−0.178557	−	0.149827i
$113$		−	292747.i		−	0.202888i	−0.994841	−	0.101444i	$-0.967654\pi$
$113$		−	292747.i		−	0.202888i	0.994841	−	0.101444i	$-0.0323463\pi$
$114$	52866.6	+	20926.8i	0.0356834	+	0.0141250i
$115$	435135.			0.286108
$116$	−467956.	+	557689.i	−0.299800	+	0.357287i
$117$	901034.	+	2.47557e6i	0.562579	+	1.54567i
$118$	−202327.	−	1.14745e6i	−0.123143	−	0.698376i
$119$	−530303.	+	3.00750e6i	−0.314690	+	1.78470i
$120$	9962.80	+	3626.16i	0.00576551	+	0.00209847i
$121$	570270.	+	987737.i	0.321903	+	0.557552i
$122$	502397.	+	290059.i	0.276673	+	0.159737i
$123$	−77742.9	+	65234.0i	−0.0417778	+	0.0350557i
$124$	−997730.	−	1.18905e6i	−0.523297	−	0.623641i
$125$	592582.	−	1.02638e6i	0.303402	−	0.525507i
$126$	−1.13875e6	+	657457.i	−0.569268	+	0.328667i
$127$	−535271.	+	1.47065e6i	−0.261314	+	0.717954i	0.737765	+	0.675057i	$0.235881\pi$
$127$	−535271.	+	1.47065e6i	−0.261314	+	0.717954i	−0.999079	+	0.0428972i	$0.986341\pi$
$128$	−182548.	−	32188.1i	−0.0870455	−	0.0153485i
$129$	−20385.4	+	3594.50i	−0.00949622	+	0.00167444i
$130$	−770053.	+	280276.i	−0.350502	+	0.127572i
$131$	2.69997e6	+	2.26555e6i	1.20101	+	1.00777i	0.999601	+	0.0282576i	$0.00899587\pi$
$131$	2.69997e6	+	2.26555e6i	1.20101	+	1.00777i	0.201407	+	0.979508i	$0.435449\pi$
$132$			37249.9i			0.0161959i
$133$	−1.04342e6	−	1.92943e6i	−0.443513	−	0.820113i
$134$	1.56838e6			0.651835
$135$	54809.4	−	65319.4i	0.0222769	−	0.0265485i
$136$	591228.	+	1.62438e6i	0.235038	+	0.645762i
$137$	−331125.	−	1.87791e6i	−0.128775	−	0.730318i	−0.978994	−	0.203889i	$-0.934642\pi$
$137$	−331125.	−	1.87791e6i	−0.128775	−	0.730318i	0.850219	−	0.526429i	$-0.176469\pi$
$138$	15671.3	−	88876.6i	0.00596306	−	0.0338182i
$139$	−1.98092e6	−	720997.i	−0.737604	−	0.268466i	−0.0542242	−	0.998529i	$-0.517269\pi$
$139$	−1.98092e6	−	720997.i	−0.737604	−	0.268466i	−0.683380	+	0.730063i	$0.739491\pi$
$140$	−204509.	−	354220.i	−0.0745295	−	0.129089i
$141$	−157003.	−	90646.0i	−0.0560082	−	0.0323364i
$142$	507489.	−	425834.i	0.177240	−	0.148722i
$143$	−1.85068e6	−	2.20556e6i	−0.632884	−	0.754242i
$144$	−372149.	+	644580.i	−0.124632	+	0.215869i
$145$	−787472.	+	454647.i	−0.258304	+	0.149132i
$146$	1.04291e6	−	2.86538e6i	0.335111	−	0.920710i
$147$	22192.6	+	3913.15i	0.00698644	+	0.00123190i
$148$	−1.52405e6	+	268730.i	−0.470124	+	0.0828956i
$149$	1.56771e6	−	570600.i	0.473922	−	0.172494i	−0.0940060	−	0.995572i	$-0.529967\pi$
$149$	1.56771e6	−	570600.i	0.473922	−	0.172494i	0.567928	+	0.823078i	$0.307745\pi$
$150$	−89076.7	−	74744.2i	−0.0263931	−	0.0221464i
$151$		−	366451.i		−	0.106435i	−0.998583	−	0.0532175i	$-0.983052\pi$
$151$		−	366451.i		−	0.106435i	0.998583	−	0.0532175i	$-0.0169477\pi$
$152$	−1.05756e6	−	650508.i	−0.301145	−	0.185234i
$153$	6.94104e6			1.93798
$154$	923720.	−	1.10085e6i	0.252917	−	0.301415i
$155$	−663077.	−	1.82179e6i	−0.178061	−	0.489219i
$156$	29513.3	+	167378.i	0.00777398	+	0.0440884i
$157$	1.00444e6	−	5.69648e6i	0.259553	−	1.47200i	−0.524556	−	0.851376i	$-0.675769\pi$
$157$	1.00444e6	−	5.69648e6i	0.259553	−	1.47200i	0.784109	−	0.620623i	$-0.213120\pi$
$158$	3.65415e6	+	1.33000e6i	0.926434	+	0.337194i
$159$	61654.9	+	106789.i	0.0153383	+	0.0265667i
$160$	−200504.	−	115761.i	−0.0489511	−	0.0282619i
$161$	−2.66709e6	+	2.23795e6i	−0.639086	+	0.536257i
$162$	1.91534e6	+	2.28262e6i	0.450507	+	0.536893i
$163$	3.08843e6	−	5.34932e6i	0.713140	−	1.23520i	−0.250532	−	0.968108i	$-0.580606\pi$
$163$	3.08843e6	−	5.34932e6i	0.713140	−	1.23520i	0.963672	−	0.267087i	$-0.0860611\pi$
$164$	1.91926e6	−	1.10808e6i	0.435113	−	0.251212i
$165$	−15912.7	+	43719.8i	−0.00354235	+	0.00973254i
$166$	−4.06473e6	−	716722.i	−0.888603	−	0.156685i
$167$	−7.47053e6	+	1.31726e6i	−1.60399	+	0.282827i	−0.902772	−	0.430119i	$-0.858472\pi$
$167$	−7.47053e6	+	1.31726e6i	−1.60399	+	0.282827i	−0.701219	+	0.712946i	$0.747361\pi$
$168$	−79715.1	+	29013.9i	−0.0168118	+	0.00611898i
$169$	−6.36574e6	−	5.34149e6i	−1.31883	−	1.10663i
$170$			2.15908e6i			0.439464i
$171$	−3.90686e6	+	3.09701e6i	−0.781339	+	0.619377i
$172$	452027.			0.0888340
$173$	623629.	−	743212.i	0.120445	−	0.143541i	−0.702453	−	0.711731i	$-0.747912\pi$
$173$	623629.	−	743212.i	0.120445	−	0.143541i	0.822897	+	0.568190i	$0.192356\pi$
$174$	64501.3	+	177216.i	0.0122439	+	0.0336399i
$175$	778982.	+	4.41783e6i	0.145349	+	0.824318i
$176$	141251.	−	801075.i	0.0259092	−	0.146938i
$177$	−283628.	−	103232.i	−0.0511480	−	0.0186164i
$178$	3.03831e6	+	5.26250e6i	0.538730	+	0.933108i
$179$	5.42066e6	+	3.12962e6i	0.945134	+	0.545673i	0.891566	−	0.452891i	$-0.149607\pi$
$179$	5.42066e6	+	3.12962e6i	0.945134	+	0.545673i	0.0535679	+	0.998564i	$0.482941\pi$
$180$	−712142.	+	597558.i	−0.122109	+	0.102462i
$181$	−3.25800e6	−	3.88273e6i	−0.549433	−	0.654789i	0.417842	−	0.908520i	$-0.362787\pi$
$181$	−3.25800e6	−	3.88273e6i	−0.549433	−	0.654789i	−0.967275	+	0.253731i	$0.918342\pi$
$182$	3.27842e6	−	5.67838e6i	0.543813	−	0.941913i
$183$	130144.	−	75138.9i	0.0212360	−	0.0122606i
$184$	−674037.	+	1.85190e6i	−0.108201	+	0.297279i
$185$	−1.90355e6	−	335647.i	−0.300642	−	0.0530113i
$186$	−395983.	+	69822.4i	−0.0615371	+	0.0108507i
$187$	−7.12829e6	+	2.59449e6i	−1.09009	+	0.396759i
$188$	3.03269e6	+	2.54473e6i	0.456410	+	0.382973i
$189$			682256.i			0.101056i
$190$	−963359.	−	1.21527e6i	−0.140452	−	0.177179i
$191$	4.42865e6			0.635581			0.317790	−	0.948161i	$-0.397059\pi$
$191$	4.42865e6			0.635581			0.317790	+	0.948161i	$0.397059\pi$
$192$	−30865.4	+	36783.9i	−0.00436082	+	0.00519702i
$193$	3.32940e6	+	9.14745e6i	0.463120	+	1.27241i	0.923126	+	0.384497i	$0.125625\pi$
$193$	3.32940e6	+	9.14745e6i	0.463120	+	1.27241i	−0.460006	+	0.887916i	$0.652153\pi$
$194$	1.40117e6	+	7.94642e6i	0.191905	+	1.08834i
$195$	−36862.4	+	209057.i	−0.00497141	+	0.0281943i
$196$	−462421.	−	168308.i	−0.0614143	−	0.0223530i
$197$	935332.	+	1.62004e6i	0.122340	+	0.211898i	0.920690	−	0.390295i	$-0.127627\pi$
$197$	935332.	+	1.62004e6i	0.122340	+	0.211898i	−0.798350	+	0.602193i	$0.794294\pi$
$198$	−2.82861e6	−	1.63310e6i	−0.364400	−	0.210386i
$199$	−422099.	+	354183.i	−0.0535618	+	0.0449437i	−0.669176	−	0.743104i	$-0.733353\pi$
$199$	−422099.	+	354183.i	−0.0535618	+	0.0449437i	0.615614	+	0.788048i	$0.288908\pi$
$200$	1.63220e6	+	1.94518e6i	0.204025	+	0.243148i
$201$	203143.	−	351854.i	0.0250157	−	0.0433285i
$202$	−2.48176e6	+	1.43285e6i	−0.301097	+	0.173838i
$203$	2.48837e6	−	6.83675e6i	0.297459	−	0.817262i
$204$	440995.	+	77759.3i	0.0519449	+	0.00915929i
$205$	2.72597e6	−	480661.i	0.316416	−	0.0557927i
$206$	−3.53672e6	+	1.28726e6i	−0.404575	+	0.147253i
$207$	6.06188e6	+	5.08652e6i	0.683434	+	0.573469i
$208$		−	3.71144e6i		−	0.412433i
$209$	2.85463e6	−	4.64091e6i	0.312687	−	0.508351i
$210$	−105955.			−0.0114410
$211$	−2.15802e6	+	2.57182e6i	−0.229724	+	0.273775i	−0.868577	−	0.495554i	$-0.834965\pi$
$211$	−2.15802e6	+	2.57182e6i	−0.229724	+	0.273775i	0.638853	+	0.769329i	$0.279409\pi$
$212$	−920970.	−	2.53034e6i	−0.0966580	−	0.265566i
$213$	−29800.4	−	169007.i	−0.00308378	−	0.0174890i
$214$	551028.	−	3.12503e6i	0.0562254	−	0.318870i
$215$	530538.	+	193100.i	0.0533828	+	0.0194298i
$216$	193093.	+	334447.i	0.0191604	+	0.0331868i
$217$	1.34339e7	+	7.75607e6i	1.31469	+	0.759036i
$218$	2.64869e6	−	2.22251e6i	0.255659	−	0.214523i
$219$	−507741.	−	605102.i	−0.0483404	−	0.0576098i
$220$	507994.	−	879871.i	0.0477079	−	0.0826325i
$221$	−2.99745e7	+	1.73058e7i	−2.77699	+	1.60330i
$222$	−137113.	+	376714.i	−0.0125319	+	0.0344312i
$223$	−6.32076e6	−	1.11452e6i	−0.569974	−	0.100502i	−0.118769	−	0.992922i	$-0.537895\pi$
$223$	−6.32076e6	−	1.11452e6i	−0.569974	−	0.100502i	−0.451205	+	0.892420i	$0.649006\pi$
$224$	1.82433e6	−	321678.i	0.162315	−	0.0286205i
$225$	9.58106e6	−	3.48722e6i	0.841135	−	0.306148i
$226$	1.26859e6	+	1.06447e6i	0.109900	+	0.0922168i
$227$		−	1.77368e7i		−	1.51634i	−0.652056	−	0.758171i	$-0.726093\pi$
$227$		−	1.77368e7i		−	1.51634i	0.652056	−	0.758171i	$-0.273907\pi$
$228$	−282915.	+	152999.i	−0.0238700	+	0.0129088i
$229$	9.58970e6			0.798543			0.399272	−	0.916833i	$-0.369263\pi$
$229$	9.58970e6			0.798543			0.399272	+	0.916833i	$0.369263\pi$
$230$	−1.58222e6	+	1.88561e6i	−0.130042	+	0.154978i
$231$	−127322.	−	349814.i	−0.0103292	−	0.0283793i
$232$	−715127.	−	4.05568e6i	−0.0572689	−	0.324788i
$233$	−483175.	+	2.74022e6i	−0.0381977	+	0.216630i	−0.997932	−	0.0642798i	$-0.979525\pi$
$233$	−483175.	+	2.74022e6i	−0.0381977	+	0.216630i	0.959734	+	0.280910i	$0.0906361\pi$
$234$	−1.40039e7	−	5.09702e6i	−1.09296	−	0.397803i
$235$	2.47236e6	+	4.28225e6i	0.190506	+	0.329965i
$236$	5.70807e6	+	3.29556e6i	0.434264	+	0.250722i
$237$	771672.	−	647510.i	0.0579679	−	0.0486409i
$238$	−1.11044e7	−	1.32338e7i	−0.823694	−	0.981640i
$239$	3.88330e6	−	6.72608e6i	0.284451	−	0.492684i	−0.688025	−	0.725687i	$-0.741522\pi$
$239$	3.88330e6	−	6.72608e6i	0.284451	−	0.492684i	0.972476	+	0.233004i	$0.0748554\pi$
$240$	−51939.9	+	29987.5i	−0.00375723	+	0.00216924i
$241$	−1.23672e6	+	3.39787e6i	−0.0883530	+	0.242748i	−0.975998	−	0.217781i	$-0.930118\pi$
$241$	−1.23672e6	+	3.39787e6i	−0.0883530	+	0.242748i	0.887645	+	0.460529i	$0.152340\pi$
$242$	−6.35385e6	−	1.12036e6i	−0.448323	−	0.0790515i
$243$	2.29179e6	−	404104.i	0.159718	−	0.0281627i
$244$	−3.08373e6	+	1.12239e6i	−0.212279	+	0.0772633i
$245$	−470839.	−	395081.i	−0.0320165	−	0.0268651i
$246$		−	574092.i		−	0.0385635i
$247$	9.14991e6	−	2.31151e7i	0.607192	−	1.53393i
$248$	8.78053e6			0.575659
$249$	−687269.	+	819056.i	−0.0445173	+	0.0530537i
$250$	2.29300e6	+	6.29998e6i	0.146752	+	0.403199i
$251$	4.06507e6	+	2.30542e7i	0.257067	+	1.45790i	0.790710	+	0.612191i	$0.209712\pi$
$251$	4.06507e6	+	2.30542e7i	0.257067	+	1.45790i	−0.533643	+	0.845710i	$0.679177\pi$
$252$	1.29164e6	−	7.32527e6i	0.0807125	−	0.457744i
$253$	−8.12671e6	−	2.95788e6i	−0.501826	−	0.182650i
$254$	−4.42657e6	−	7.66704e6i	−0.270126	−	0.467872i
$255$	484372.	+	279652.i	0.0292118	+	0.0168655i
$256$	803256.	−	674012.i	0.0478778	−	0.0401742i
$257$	1.52929e6	+	1.82254e6i	0.0900931	+	0.107369i	0.809208	−	0.587523i	$-0.199897\pi$
$257$	1.52929e6	+	1.82254e6i	0.0900931	+	0.107369i	−0.719114	+	0.694892i	$0.755452\pi$
$258$	58548.2	−	101408.i	0.00340921	−	0.00590493i
$259$	1.33938e7	−	7.73290e6i	0.770911	−	0.445085i
$260$	1.58548e6	−	4.35608e6i	0.0902072	−	0.247842i
$261$	−1.62849e7	−	2.87147e6i	−0.915934	−	0.161504i
$262$	−1.96351e7	+	3.46219e6i	−1.09176	+	0.192507i
$263$	3.21365e6	−	1.16967e6i	0.176657	−	0.0642980i	−0.252177	−	0.967681i	$-0.581147\pi$
$263$	3.21365e6	−	1.16967e6i	0.176657	−	0.0642980i	0.428834	+	0.903383i	$0.358924\pi$
$264$	−161419.	−	135447.i	−0.00877289	−	0.00736133i
$265$		−	3.36326e6i		−	0.180727i
$266$	1.21550e7	+	2.49412e6i	0.645820	+	0.132517i
$267$	1.57413e6			0.0827002
$268$	−5.70289e6	+	6.79644e6i	−0.296272	+	0.353083i
$269$	−1.04009e6	−	2.85761e6i	−0.0534334	−	0.146807i	0.910105	−	0.414379i	$-0.136001\pi$
$269$	−1.04009e6	−	2.85761e6i	−0.0534334	−	0.146807i	−0.963538	+	0.267572i	$0.913779\pi$
$270$	83759.3	+	475023.i	0.00425541	+	0.0241337i
$271$	826188.	−	4.68554e6i	0.0415117	−	0.235425i	−0.956992	−	0.290116i	$-0.906306\pi$
$271$	826188.	−	4.68554e6i	0.0415117	−	0.235425i	0.998503	+	0.0546909i	$0.0174173\pi$
$272$	−9.18891e6	−	3.34449e6i	−0.456622	−	0.166197i
$273$	−849265.	−	1.47097e6i	−0.0417403	−	0.0722963i
$274$	9.34174e6	+	5.39346e6i	0.454126	+	0.262190i
$275$	−8.53605e6	+	7.16259e6i	−0.410449	+	0.344407i
$276$	328155.	+	391079.i	0.0156081	+	0.0186011i
$277$	8.58373e6	−	1.48675e7i	0.403866	−	0.699516i	−0.590323	−	0.807167i	$-0.701000\pi$
$277$	8.58373e6	−	1.48675e7i	0.403866	−	0.699516i	0.994189	+	0.107651i	$0.0343330\pi$
$278$	1.03273e7	−	5.96248e6i	0.480677	−	0.277519i
$279$	1.20585e7	−	3.31305e7i	0.555240	−	1.52551i
$280$	2.27860e6	+	401780.i	0.103799	+	0.0183026i
$281$	−2.12200e7	+	3.74166e6i	−0.956371	+	0.168634i	−0.629989	−	0.776604i	$-0.716941\pi$
$281$	−2.12200e7	+	3.74166e6i	−0.956371	+	0.168634i	−0.326382	+	0.945238i	$0.605829\pi$
$282$	963695.	−	350756.i	0.0429727	−	0.0156408i
$283$	1.56994e7	+	1.31734e7i	0.692668	+	0.581217i	0.919677	−	0.392675i	$-0.128450\pi$
$283$	1.56994e7	+	1.31734e7i	0.692668	+	0.581217i	−0.227009	+	0.973893i	$0.572895\pi$
$284$			3.74756e6i			0.163604i
$285$	−397413.	+	58715.2i	−0.0171675	+	0.00253639i
$286$	1.62869e7			0.696212
$287$	−1.42363e7	+	1.69661e7i	−0.602213	+	0.717690i
$288$	−1.44003e6	−	3.95646e6i	−0.0602831	−	0.165626i
$289$	1.16439e7	+	6.60356e7i	0.482396	+	2.73580i
$290$	893202.	−	5.06560e6i	0.0366231	−	0.207700i
$291$	1.96420e6	+	714909.i	0.0797088	+	0.0290116i
$292$	8.62464e6	+	1.49383e7i	0.346411	+	0.600002i
$293$	1.46453e7	+	8.45547e6i	0.582231	+	0.336151i	0.762019	−	0.647554i	$-0.224208\pi$
$293$	1.46453e7	+	8.45547e6i	0.582231	+	0.336151i	−0.179789	+	0.983705i	$0.557541\pi$
$294$	−97652.9	+	81940.5i	−0.00384276	+	0.00322446i
$295$	5.29167e6	+	6.30637e6i	0.206123	+	0.245648i
$296$	4.37715e6	−	7.58145e6i	0.168778	−	0.292332i
$297$	−1.46765e6	+	847350.i	−0.0560215	+	0.0323440i
$298$	−3.22780e6	+	8.86831e6i	−0.121971	+	0.335114i
$299$	−3.88599e7	−	6.85205e6i	−1.45374	−	0.256334i
$300$	647794.	−	114223.i	0.0239924	−	0.00423050i
$301$	−4.24499e6	+	1.54505e6i	−0.155660	+	0.0566556i
$302$	1.58798e6	+	1.33247e6i	0.0576532	+	0.0483768i
$303$			742349.i			0.0266858i
$304$	6.66438e6	−	2.21750e6i	0.237213	−	0.0789300i
$305$	−4.09881e6			−0.144463
$306$	−2.52387e7	+	3.00783e7i	−0.880851	+	1.04976i
$307$	−8.91896e6	−	2.45046e7i	−0.308247	−	0.846902i	−0.992999	−	0.118125i	$-0.962312\pi$
$307$	−8.91896e6	−	2.45046e7i	−0.308247	−	0.846902i	0.684752	−	0.728776i	$-0.259911\pi$
$308$	1.41162e6	+	8.00570e6i	0.0483132	+	0.273998i
$309$	−169303.	+	960163.i	−0.00573837	+	0.0325439i
$310$	1.03056e7	+	3.75093e6i	0.345930	+	0.125908i
$311$	355915.	+	616462.i	0.0118322	+	0.0204939i	0.871881	−	0.489718i	$-0.162900\pi$
$311$	355915.	+	616462.i	0.0118322	+	0.0204939i	−0.860049	+	0.510212i	$0.829567\pi$
$312$	−832631.	−	480720.i	−0.0274150	−	0.0158281i
$313$	−2.00407e6	+	1.68161e6i	−0.0653552	+	0.0548395i	−0.674880	−	0.737927i	$-0.735805\pi$
$313$	−2.00407e6	+	1.68161e6i	−0.0653552	+	0.0548395i	0.609525	+	0.792767i	$0.291360\pi$
$314$	2.10328e7	+	2.50659e7i	0.679374	+	0.809646i
$315$	4.64525e6	−	8.04581e6i	0.148620	−	0.257417i
$316$	−1.90505e7	+	1.09988e7i	−0.603732	+	0.348565i
$317$	−478802.	+	1.31550e6i	−0.0150307	+	0.0412964i	−0.946981	−	0.321289i	$-0.895884\pi$
$317$	−478802.	+	1.31550e6i	−0.0150307	+	0.0412964i	0.931950	+	0.362586i	$0.118106\pi$
$318$	−686948.	−	121128.i	−0.0213620	−	0.00376670i
$319$	1.77976e7	−	3.13819e6i	0.548263	−	0.0966735i
$320$	1.23070e6	−	447938.i	0.0375580	−	0.0136700i
$321$	−629704.	−	528384.i	−0.0190380	−	0.0159748i
$322$		−	1.96951e7i		−	0.589916i
$323$	−4.89838e7	−	4.34833e7i	−1.45360	−	1.29037i
$324$	−1.68560e7			−0.495586
$325$	−3.26807e7	+	3.89474e7i	−0.952010	+	1.13456i
$326$	1.19507e7	+	3.28344e7i	0.344939	+	0.947711i
$327$	−155534.	−	882078.i	−0.00444818	−	0.0252269i
$328$	−2.17695e6	+	1.23461e7i	−0.0616916	+	0.349871i
$329$	−3.71780e7	−	1.35317e7i	−1.04400	−	0.379983i
$330$	−131594.	−	227928.i	−0.00366181	−	0.00634243i
$331$	5.82701e7	+	3.36423e7i	1.60680	+	0.927686i	0.990080	+	0.140503i	$0.0448720\pi$
$331$	5.82701e7	+	3.36423e7i	1.60680	+	0.927686i	0.616719	+	0.787183i	$0.288461\pi$
$332$	1.78858e7	−	1.50080e7i	0.488760	−	0.410118i
$333$	−2.25949e7	−	2.69276e7i	−0.611896	−	0.729229i
$334$	2.14558e7	−	3.71626e7i	0.575845	−	0.997393i
$335$	−9.59676e6	+	5.54069e6i	−0.255264	+	0.147377i
$336$	164128.	−	450937.i	0.00432677	−	0.0118877i
$337$	2.38379e7	+	4.20326e6i	0.622842	+	0.109824i	0.476158	−	0.879360i	$-0.342029\pi$
$337$	2.38379e7	+	4.20326e6i	0.622842	+	0.109824i	0.146684	+	0.989183i	$0.453140\pi$
$338$	4.62937e7	−	8.16282e6i	1.19887	−	0.211393i
$339$	403118.	−	146723.i	0.0103475	−	0.00376617i
$340$	−9.35618e6	−	7.85077e6i	−0.238047	−	0.199745i
$341$			3.85316e7i			0.971749i
$342$	785343.	−	2.81912e7i	0.0196327	−	0.704750i
$343$	4.25418e7			1.05423
$344$	−1.64364e6	+	1.95881e6i	−0.0403768	+	0.0481192i
$345$	218087.	+	599188.i	0.00531095	+	0.0145917i
$346$	953025.	+	5.40487e6i	0.0230078	+	0.130484i
$347$	1.14914e7	−	6.51707e7i	0.275032	−	1.55978i	−0.463829	−	0.885925i	$-0.653525\pi$
$347$	1.14914e7	−	6.51707e7i	0.275032	−	1.55978i	0.738861	−	0.673858i	$-0.235364\pi$
$348$	−1.00248e6	−	364874.i	−0.0237870	−	0.00865776i
$349$	−3.54786e7	−	6.14507e7i	−0.834622	−	1.44561i	−0.894337	−	0.447393i	$-0.852353\pi$
$349$	−3.54786e7	−	6.14507e7i	−0.834622	−	1.44561i	0.0597151	−	0.998215i	$-0.480981\pi$
$350$	−2.19767e7	−	1.26883e7i	−0.512577	−	0.295936i
$351$	−5.92336e6	+	4.97029e6i	−0.136977	+	0.114937i
$352$	2.95777e6	+	3.52493e6i	0.0678166	+	0.0808207i
$353$	3.86365e7	−	6.69204e7i	0.878362	−	1.52137i	0.0252252	−	0.999682i	$-0.491970\pi$
$353$	3.86365e7	−	6.69204e7i	0.878362	−	1.52137i	0.853137	−	0.521687i	$-0.174697\pi$
$354$	1.47866e6	−	853705.i	0.0333318	−	0.0192441i
$355$	−1.60091e6	+	4.39846e6i	−0.0357834	+	0.0983140i
$356$	−3.38523e7	−	5.96907e6i	−0.750305	−	0.132299i
$357$	−4.40717e6	+	777103.i	−0.0968623	+	0.0170794i
$358$	−3.32723e7	+	1.21101e7i	−0.725159	+	0.263936i
$359$	−4.65522e7	−	3.90620e7i	−1.00614	−	0.844249i	−0.0183143	−	0.999832i	$-0.505830\pi$
$359$	−4.65522e7	−	3.90620e7i	−1.00614	−	0.844249i	−0.987823	+	0.155583i	$0.950274\pi$
$360$		−	5.25881e6i		−	0.112715i
$361$	4.69729e7	+	2.61915e6i	0.998449	+	0.0556722i
$362$	2.86720e7			0.604411
$363$	−1.07432e6	+	1.28032e6i	−0.0224601	+	0.0267669i
$364$	1.26859e7	+	3.48542e7i	0.263037	+	0.722688i
$365$	3.74117e6	+	2.12172e7i	0.0769359	+	0.436325i
$366$	−147618.	+	837185.i	−0.00301090	+	0.0170757i
$367$	−1.73086e7	−	6.29982e6i	−0.350158	−	0.127447i	0.160952	−	0.986962i	$-0.448543\pi$
$367$	−1.73086e7	−	6.29982e6i	−0.350158	−	0.127447i	−0.511110	+	0.859515i	$0.670766\pi$
$368$	−5.57413e6	−	9.65467e6i	−0.111849	−	0.193729i
$369$	4.35943e7	+	2.51692e7i	0.867662	+	0.500945i
$370$	8.37610e6	−	7.02839e6i	0.165362	−	0.138756i
$371$	1.72977e7	+	2.06145e7i	0.338739	+	0.403694i
$372$	1.13729e6	−	1.96984e6i	0.0220923	−	0.0382650i
$373$	−4.49006e7	+	2.59234e7i	−0.865218	+	0.499534i	−0.865756	−	0.500466i	$-0.833162\pi$
$373$	−4.49006e7	+	2.59234e7i	−0.865218	+	0.499534i	0.000538474		1.00000i	$0.499829\pi$
$374$	1.46766e7	−	4.03237e7i	0.280551	−	0.770807i
$375$	1.71035e6	+	301580.i	0.0324332	+	0.00571885i
$376$	−2.20547e7	+	3.88884e6i	−0.414894	+	0.0731571i
$377$	7.74848e7	−	2.82022e7i	1.44608	−	0.526330i
$378$	−2.95649e6	−	2.48079e6i	−0.0547395	−	0.0459319i
$379$		−	4.40997e7i		−	0.810062i	−0.914303	−	0.405031i	$-0.867261\pi$
$379$		−	4.40997e7i		−	0.810062i	0.914303	−	0.405031i	$-0.132739\pi$
$380$	8.76918e6	+	244289.i	0.159812	+	0.00445199i
$381$	−2.29338e6			−0.0414669
$382$	−1.61032e7	+	1.91911e7i	−0.288884	+	0.344278i
$383$	631764.	+	1.73576e6i	0.0112450	+	0.0308953i	0.945188	−	0.326526i	$-0.105878\pi$
$383$	631764.	+	1.73576e6i	0.0112450	+	0.0308953i	−0.933943	+	0.357422i	$0.883656\pi$
$384$	−47168.2	−	267504.i	−0.000833020	−	0.00472429i
$385$	−1.76313e6	+	9.99921e6i	−0.0308960	+	0.175220i
$386$	−5.17458e7	−	1.88339e7i	−0.899732	−	0.327476i
$387$	5.13370e6	+	8.89184e6i	0.0885723	+	0.153412i
$388$	−3.95299e7	−	2.28226e7i	−0.676754	−	0.390724i
$389$	−1.77620e7	+	1.49041e7i	−0.301747	+	0.253195i	−0.781071	−	0.624442i	$-0.785326\pi$
$389$	−1.77620e7	+	1.49041e7i	−0.301747	+	0.253195i	0.479324	+	0.877638i	$0.340882\pi$
$390$	−771891.	−	919904.i	−0.0130125	−	0.0155077i
$391$	−5.19823e7	+	9.00359e7i	−0.869611	+	1.50621i
$392$	2.41078e6	−	1.39187e6i	0.0400221	−	0.0231068i
$393$	−1.76649e6	+	4.85339e6i	−0.0291027	+	0.0799591i
$394$	−1.04213e7	−	1.83756e6i	−0.170386	−	0.0300436i
$395$	−2.70578e7	+	4.77103e6i	−0.439038	+	0.0774142i
$396$	1.73622e7	−	6.31931e6i	0.279588	−	0.101762i
$397$	2.17777e7	+	1.82737e7i	0.348049	+	0.292048i	0.800006	−	0.599992i	$-0.204830\pi$
$397$	2.17777e7	+	1.82737e7i	0.348049	+	0.292048i	−0.451957	+	0.892040i	$0.649274\pi$
$398$		−	3.11699e6i		−	0.0494409i
$399$	2.13390e6	−	2.40383e6i	0.0335935	−	0.0378430i
$400$	−1.43642e7			−0.224440
$401$	1.08562e7	−	1.29379e7i	0.168363	−	0.200647i	−0.675265	−	0.737575i	$-0.735971\pi$
$401$	1.08562e7	−	1.29379e7i	0.168363	−	0.200647i	0.843628	+	0.536928i	$0.180415\pi$
$402$	786064.	+	2.15969e6i	0.0120998	+	0.0332441i
$403$	3.05287e7	+	1.73137e8i	0.466438	+	2.64530i
$404$	2.81498e6	−	1.59645e7i	0.0426904	−	0.242109i
$405$	−1.97836e7	−	7.20066e6i	−0.297811	−	0.108394i
$406$	2.05783e7	+	3.56426e7i	0.307490	+	0.532588i
$407$	3.32697e7	+	1.92083e7i	0.493476	+	0.284908i
$408$	−1.94049e6	+	1.62826e6i	−0.0285713	+	0.0239742i
$409$	−1.30142e7	−	1.55097e7i	−0.190216	−	0.226690i	0.662505	−	0.749058i	$-0.269493\pi$
$409$	−1.30142e7	−	1.55097e7i	−0.190216	−	0.226690i	−0.852720	+	0.522367i	$0.825049\pi$
$410$	−7.82914e6	+	1.35605e7i	−0.113596	+	0.196754i
$411$	2.41995e6	−	1.39716e6i	0.0348563	−	0.0201243i
$412$	7.28184e6	−	2.00067e7i	0.104124	−	0.286077i
$413$	−6.48689e7	−	1.14381e7i	−0.920845	−	0.162370i
$414$	−4.40839e7	+	7.77318e6i	−0.621268	+	0.109546i
$415$	2.74036e7	−	9.97410e6i	0.383410	−	0.139550i
$416$	1.60832e7	+	1.34954e7i	0.223405	+	0.187459i
$417$		−	3.08913e6i		−	0.0426018i
$418$	9.73105e6	+	2.92453e7i	0.133239	+	0.400431i
$419$	6.39678e7			0.869599			0.434800	−	0.900527i	$-0.356819\pi$
$419$	6.39678e7			0.869599			0.434800	+	0.900527i	$0.356819\pi$
$420$	385269.	−	459146.i	0.00520015	−	0.00619730i
$421$	−2.20659e7	−	6.06255e7i	−0.295716	−	0.812473i	−0.995203	−	0.0978279i	$-0.968811\pi$
$421$	−2.20659e7	−	6.06255e7i	−0.295716	−	0.812473i	0.699487	−	0.714645i	$-0.253412\pi$
$422$	−3.29786e6	−	1.87031e7i	−0.0438829	−	0.248872i
$423$	−1.56150e7	+	8.85569e7i	−0.206310	+	1.17004i
$424$	1.43138e7	+	5.20979e6i	0.187783	+	0.0683475i
$425$	6.69776e7	+	1.16009e8i	0.872494	+	1.51120i
$426$	840732.	+	485397.i	0.0108750	+	0.00627868i
$427$	2.51230e7	−	2.10807e7i	0.322691	−	0.270770i
$428$	1.15384e7	+	1.37509e7i	0.147168	+	0.175388i
$429$	2.10954e6	−	3.65384e6i	0.0267188	−	0.0462783i
$430$	−2.76590e6	+	1.59689e6i	−0.0347881	+	0.0200849i
$431$	−2.74647e7	+	7.54587e7i	−0.343039	+	0.942492i	0.641469	+	0.767149i	$0.278325\pi$
$431$	−2.74647e7	+	7.54587e7i	−0.343039	+	0.942492i	−0.984508	+	0.175342i	$0.943897\pi$
$432$	−2.15141e6	−	379351.i	−0.0266853	−	0.00470533i
$433$	7.25618e7	−	1.27946e7i	0.893808	−	0.157602i	0.292165	−	0.956368i	$-0.405624\pi$
$433$	7.25618e7	−	1.27946e7i	0.893808	−	0.157602i	0.601643	+	0.798765i	$0.294513\pi$
$434$	−8.24579e7	+	3.00122e7i	−1.00870	+	0.367138i
$435$	−1.02073e6	−	856497.i	−0.0124007	−	0.0104054i
$436$			1.95592e7i			0.235989i
$437$	−1.09141e7	−	7.38718e7i	−0.130781	−	0.885186i
$438$	4.46838e6			0.0531774
$439$	6.75667e7	−	8.05229e7i	0.798618	−	0.951756i	−0.200994	−	0.979592i	$-0.564417\pi$
$439$	6.75667e7	−	8.05229e7i	0.798618	−	0.951756i	0.999612	+	0.0278361i	$0.00886167\pi$
$440$	1.96569e6	+	5.40069e6i	0.0230758	+	0.0634002i
$441$	−1.94097e6	−	1.10078e7i	−0.0226310	−	0.128347i
$442$	3.39990e7	−	1.92818e8i	0.393731	−	2.23296i
$443$	−3.82431e7	−	1.39193e7i	−0.439888	−	0.160106i	0.112576	−	0.993643i	$-0.464090\pi$
$443$	−3.82431e7	−	1.39193e7i	−0.439888	−	0.160106i	−0.552463	+	0.833537i	$0.686312\pi$
$444$	−1.13389e6	−	1.96395e6i	−0.0129545	−	0.0224379i
$445$	−3.71821e7	−	2.14671e7i	−0.421943	−	0.243609i
$446$	2.78129e7	−	2.33378e7i	0.313504	−	0.263061i
$447$	1.57145e6	+	1.87279e6i	0.0175946	+	0.0209684i
$448$	−5.23957e6	+	9.07521e6i	−0.0582723	+	0.100931i
$449$	9.39540e6	−	5.42443e6i	0.103795	−	0.0599260i	−0.447204	−	0.894432i	$-0.647580\pi$
$449$	9.39540e6	−	5.42443e6i	0.103795	−	0.0599260i	0.550999	+	0.834506i	$0.314247\pi$
$450$	−1.97267e7	+	5.41986e7i	−0.216479	+	0.594772i
$451$	−5.41783e7	−	9.55310e6i	−0.590604	−	0.104139i
$452$	−9.22559e6	+	1.62672e6i	−0.0999031	+	0.0176156i
$453$	504610.	−	183663.i	0.00542826	−	0.00197573i
$454$	7.68606e7	+	6.44937e7i	0.821365	+	0.689207i
$455$			4.63272e7i			0.491815i
$456$	365718.	−	1.78231e6i	0.00385702	−	0.0187971i
$457$	−4.15165e7			−0.434983			−0.217492	−	0.976062i	$-0.569787\pi$
$457$	−4.15165e7			−0.434983			−0.217492	+	0.976062i	$0.569787\pi$
$458$	−3.48696e7	+	4.15560e7i	−0.362953	+	0.432551i
$459$	6.96789e6	+	1.91441e7i	0.0720548	+	0.197969i
$460$	−2.41793e6	−	1.37128e7i	−0.0248411	−	0.140881i
$461$	−1.86566e6	+	1.05807e7i	−0.0190428	+	0.107997i	−0.992848	−	0.119388i	$-0.961907\pi$
$461$	−1.86566e6	+	1.05807e7i	−0.0190428	+	0.107997i	0.973805	+	0.227385i	$0.0730177\pi$
$462$	1.97885e6	+	720242.i	0.0200672	+	0.00730386i
$463$	−5.54303e7	−	9.60081e7i	−0.558476	−	0.967308i	−0.997624	−	0.0688938i	$-0.978053\pi$
$463$	−5.54303e7	−	9.60081e7i	−0.558476	−	0.967308i	0.439148	−	0.898415i	$-0.355280\pi$
$464$	2.01752e7	+	1.16482e7i	0.201960	+	0.116601i
$465$	2.17631e6	−	1.82614e6i	0.0216452	−	0.0181625i
$466$	−1.01176e7	−	1.20577e7i	−0.0999814	−	0.119153i
$467$	916750.	−	1.58786e6i	0.00900120	−	0.0155905i	−0.861490	−	0.507775i	$-0.830468\pi$
$467$	916750.	−	1.58786e6i	0.00900120	−	0.0155905i	0.870491	+	0.492184i	$0.163801\pi$
$468$	7.30079e7	−	4.21511e7i	0.712250	−	0.411218i
$469$	3.03253e7	−	8.33181e7i	0.293959	−	0.807645i
$470$	−2.75466e7	−	4.85720e6i	−0.265322	−	0.0467835i
$471$	8.34758e6	−	1.47190e6i	0.0798910	−	0.0140869i
$472$	−3.50364e7	+	1.27522e7i	−0.333191	+	0.121272i
$473$	−8.59587e6	−	7.21280e6i	−0.0812282	−	0.0681585i
$474$			5.69841e6i			0.0535080i
$475$	−8.94609e7	−	3.54124e7i	−0.834743	−	0.330426i
$476$	9.77247e7			0.906115
$477$	3.93149e7	−	4.68537e7i	0.362245	−	0.431707i
$478$	1.50265e7	+	4.12850e7i	0.137586	+	0.378014i
$479$	−2.91060e7	−	1.65069e8i	−0.264836	−	1.50196i	−0.769503	−	0.638644i	$-0.779496\pi$
$479$	−2.91060e7	−	1.65069e8i	−0.264836	−	1.50196i	0.504667	−	0.863314i	$-0.331615\pi$
$480$	58913.6	−	334116.i	0.000532711	−	0.00302116i
$481$	1.64712e8	+	5.99503e7i	1.48010	+	0.538711i
$482$	−1.02274e7	−	1.77144e7i	−0.0913324	−	0.158192i
$483$	−4.41843e6	−	2.55098e6i	−0.0392127	−	0.0226394i
$484$	2.79586e7	−	2.34600e7i	0.246592	−	0.206915i
$485$	−3.66462e7	−	4.36733e7i	−0.321221	−	0.382816i
$486$	−6.58215e6	+	1.14006e7i	−0.0573401	+	0.0993160i
$487$	−1.66714e8	+	9.62525e7i	−1.44340	+	0.833345i	−0.998075	−	0.0620255i	$-0.980244\pi$
$487$	−1.66714e8	+	9.62525e7i	−1.44340	+	0.833345i	−0.445322	+	0.895371i	$0.646911\pi$
$488$	6.34918e6	−	1.74442e7i	0.0546334	−	0.150104i
$489$	8.91401e6	+	1.57178e6i	0.0762336	+	0.0134420i
$490$	3.42409e6	−	603759.i	0.0291043	−	0.00513187i
$491$	−5.83126e7	+	2.12241e7i	−0.492627	+	0.179302i	−0.576375	−	0.817185i	$-0.695533\pi$
$491$	−5.83126e7	+	2.12241e7i	−0.492627	+	0.179302i	0.0837479	+	0.996487i	$0.473311\pi$
$492$	2.48777e6	+	2.08749e6i	0.0208889	+	0.0175279i
$493$		−	2.17253e8i		−	1.81311i
$494$	6.68964e7	+	1.23700e8i	0.554909	+	1.02610i
$495$	2.30773e7			0.190269
$496$	−3.19274e7	+	3.80496e7i	−0.261648	+	0.311820i
$497$	−1.28093e7	−	3.51933e7i	−0.104341	−	0.286676i
$498$	−1.05028e6	−	5.95643e6i	−0.00850387	−	0.0482279i
$499$	−1.70623e7	+	9.67649e7i	−0.137320	+	0.778782i	0.835895	+	0.548889i	$0.184949\pi$
$499$	−1.70623e7	+	9.67649e7i	−0.137320	+	0.778782i	−0.973216	+	0.229894i	$0.926162\pi$
$500$	−3.56381e7	−	1.29712e7i	−0.285104	−	0.103770i
$501$	−5.55807e6	−	9.62686e6i	−0.0441988	−	0.0765546i
$502$	−1.14684e8	−	6.62129e7i	−0.906551	−	0.523398i
$503$	−1.24332e8	+	1.04327e8i	−0.976963	+	0.819769i	−0.983628	−	0.180209i	$-0.942323\pi$
$503$	−1.24332e8	+	1.04327e8i	−0.976963	+	0.819769i	0.00666557	+	0.999978i	$0.497878\pi$
$504$	2.70467e7	+	3.22330e7i	0.211263	+	0.251773i
$505$	1.01237e7	−	1.75348e7i	0.0786080	−	0.136153i
$506$	4.23676e7	−	2.44610e7i	0.327026	−	0.188809i
$507$	4.16486e6	−	1.14429e7i	0.0319578	−	0.0878033i
$508$	4.93201e7	+	8.69646e6i	0.376212	+	0.0663363i
$509$	1.55861e6	−	274824.i	0.0118191	−	0.00208402i	−0.167736	−	0.985832i	$-0.553645\pi$
$509$	1.55861e6	−	274824.i	0.0118191	−	0.00208402i	0.179555	+	0.983748i	$0.442534\pi$
$510$	−2.97310e6	+	1.08212e6i	−0.0224129	+	0.00815764i
$511$	−1.32054e8	−	1.10806e8i	−0.989665	−	0.830427i
$512$			5.93164e6i			0.0441942i
$513$	−1.24639e7	−	7.66653e6i	−0.0923210	−	0.0567867i
$514$	−1.34586e7			−0.0991081
$515$	1.70932e7	−	2.03709e7i	0.125142	−	0.149138i
$516$	226553.	+	622450.i	0.00164900	+	0.00453059i
$517$	−1.70654e7	−	9.67827e7i	−0.123494	−	0.700368i
$518$	−1.51921e7	+	8.61587e7i	−0.109302	+	0.619883i
$519$	1.33598e6	+	486256.i	0.00955645	+	0.00347826i
$520$	1.31116e7	+	2.27099e7i	0.0932491	+	0.161512i
$521$	1.76156e8	+	1.01704e8i	1.24561	+	0.719156i	0.970232	−	0.242179i	$-0.0778621\pi$
$521$	1.76156e8	+	1.01704e8i	1.24561	+	0.719156i	0.275383	+	0.961335i	$0.411195\pi$
$522$	7.16577e7	−	6.01280e7i	0.503792	−	0.422732i
$523$	−3.41767e7	−	4.07302e7i	−0.238905	−	0.284716i	0.633248	−	0.773949i	$-0.281721\pi$
$523$	−3.41767e7	−	4.07302e7i	−0.238905	−	0.284716i	−0.872153	+	0.489233i	$0.837277\pi$
$524$	5.63931e7	−	9.76757e7i	0.391951	−	0.678879i
$525$	−5.69301e6	+	3.28686e6i	−0.0393427	+	0.0227145i
$526$	−6.61667e6	+	1.81792e7i	−0.0454655	+	0.124916i
$527$	4.56168e8	+	8.04348e7i	3.11669	+	0.549556i
$528$	1.17389e6	−	206988.i	0.00797490	−	0.00140619i
$529$	2.77301e7	−	1.00929e7i	0.187320	−	0.0681790i
$530$	1.45744e7	+	1.22293e7i	0.0978952	+	0.0821439i
$531$			1.49712e8i			0.999935i
$532$	−5.50057e7	+	4.36036e7i	−0.365319	+	0.289593i
$533$	−2.51013e8			−1.65773
$534$	−5.72378e6	+	6.82134e6i	−0.0375889	+	0.0447967i
$535$	7.66826e6	+	2.10684e7i	0.0500766	+	0.137584i
$536$	−8.71510e6	−	4.94258e7i	−0.0565950	−	0.320966i
$537$	−1.59274e6	+	9.03290e6i	−0.0102854	+	0.0583317i
$538$	1.61651e7	+	5.88362e6i	0.103808	+	0.0377831i
$539$	6.10793e6	+	1.05792e7i	0.0390057	+	0.0675598i
$540$	−2.36303e6	−	1.36429e6i	−0.0150068	−	0.00866416i
$541$	−1.86792e8	+	1.56738e8i	−1.17969	+	0.989877i	−0.179708	+	0.983720i	$0.557515\pi$
$541$	−1.86792e8	+	1.56738e8i	−1.17969	+	0.989877i	−0.999981	+	0.00615686i	$0.998040\pi$
$542$	1.73002e7	+	2.06176e7i	0.108656	+	0.129491i
$543$	3.71370e6	−	6.43232e6i	0.0231957	−	0.0401761i
$544$	4.79053e7	−	2.76581e7i	0.297569	−	0.171801i
$545$	−8.35545e6	+	2.29564e7i	−0.0516155	+	0.141812i
$546$	9.46236e6	+	1.66847e6i	0.0581329	+	0.0102504i
$547$	−1.95747e8	+	3.45155e7i	−1.19601	+	0.210888i	−0.735972	−	0.677012i	$-0.763275\pi$
$547$	−1.95747e8	+	3.45155e7i	−1.19601	+	0.210888i	−0.460036	+	0.887900i	$0.652163\pi$
$548$	−5.73401e7	+	2.08701e7i	−0.348431	+	0.126818i
$549$	−5.71007e7	−	4.79132e7i	−0.345084	−	0.289560i
$550$		−	6.30344e7i		−	0.378870i
$551$	9.69359e7	+	1.22284e8i	0.579468	+	0.730995i
$552$	−2.88793e6			−0.0171699
$553$	1.41309e8	−	1.68405e8i	0.835590	−	0.995817i
$554$	3.32149e7	+	9.12571e7i	0.195346	+	0.536707i
$555$	−491855.	−	2.78945e6i	−0.00287712	−	0.0163170i
$556$	−1.17139e7	+	6.64329e7i	−0.0681519	+	0.386509i
$557$	2.06407e8	+	7.51261e7i	1.19443	+	0.434736i	0.861276	−	0.508138i	$-0.169666\pi$
$557$	2.06407e8	+	7.51261e7i	1.19443	+	0.434736i	0.333151	+	0.942874i	$0.391888\pi$
$558$	9.97211e7	+	1.72722e8i	0.573964	+	0.994134i
$559$	−4.43392e7	−	2.55993e7i	−0.253836	−	0.146552i
$560$	−1.00264e7	+	8.41318e6i	−0.0570929	+	0.0479067i
$561$	−7.14531e6	−	8.51545e6i	−0.0404700	−	0.0482302i
$562$	6.09451e7	−	1.05560e8i	0.343344	−	0.594690i
$563$	1.18947e8	−	6.86743e7i	0.666546	−	0.384830i	−0.128221	−	0.991746i	$-0.540927\pi$
$563$	1.18947e8	−	6.86743e7i	0.666546	−	0.384830i	0.794767	+	0.606915i	$0.207593\pi$
$564$	−1.98418e6	+	5.45148e6i	−0.0110597	+	0.0303863i
$565$	−1.15229e7	−	2.03179e6i	−0.0638874	−	0.0112651i
$566$	−1.14171e8	+	2.01315e7i	−0.629662	+	0.111026i
$567$	1.58295e8	−	5.76145e7i	0.868394	−	0.316069i
$568$	−1.62397e7	−	1.36267e7i	−0.0886200	−	0.0743611i
$569$			2.36806e8i			1.28545i	0.766096	+	0.642726i	$0.222197\pi$
$569$			2.36806e8i			1.28545i	−0.766096	+	0.642726i	$0.777803\pi$
$570$	1.19062e6	−	1.93565e6i	0.00642908	−	0.0104521i
$571$	4.71063e7			0.253029			0.126515	−	0.991965i	$-0.459621\pi$
$571$	4.71063e7			0.253029			0.126515	+	0.991965i	$0.459621\pi$
$572$	−5.92219e7	+	7.05779e7i	−0.316442	+	0.377121i
$573$	2.21961e6	+	6.09833e6i	0.0117981	+	0.0324151i
$574$	−2.17557e7	−	1.23383e8i	−0.115037	−	0.652408i
$575$	−2.65191e7	+	1.50397e8i	−0.139494	+	0.791109i
$576$	2.23811e7	+	8.14607e6i	0.117116	+	0.0426266i
$577$	−7.97978e7	−	1.38214e8i	−0.415397	−	0.719488i	0.580073	−	0.814564i	$-0.303024\pi$
$577$	−7.97978e7	−	1.38214e8i	−0.415397	−	0.719488i	−0.995470	+	0.0950759i	$0.969691\pi$
$578$	−3.28498e8	−	1.89658e8i	−1.70117	−	0.982174i
$579$	−1.09275e7	+	9.16929e6i	−0.0562972	+	0.0472389i
$580$	1.87035e7	+	2.22899e7i	0.0958601	+	0.114242i
$581$	−1.16668e8	+	2.02075e8i	−0.594872	+	1.03035i
$582$	−1.02401e7	+	5.91213e6i	−0.0519441	+	0.0299899i
$583$	−2.28621e7	+	6.28132e7i	−0.115375	+	0.316990i
$584$	−9.60942e7	−	1.69440e7i	−0.482457	−	0.0850702i
$585$	1.03695e8	−	1.82842e7i	0.517952	−	0.0913290i
$586$	−8.98935e7	+	3.27186e7i	−0.446720	+	0.162593i
$587$	2.45957e8	+	2.06382e8i	1.21603	+	1.02037i	0.999023	+	0.0441999i	$0.0140739\pi$
$587$	2.45957e8	+	2.06382e8i	1.21603	+	1.02037i	0.217007	+	0.976170i	$0.430371\pi$
$588$		−	721118.i		−	0.00354711i
$589$	−2.92650e8	+	1.58263e8i	−1.43220	+	0.774523i
$590$	−4.65694e7			−0.226749
$591$	−1.76205e6	+	2.09992e6i	−0.00853601	+	0.0101728i
$592$	1.69375e7	+	4.65353e7i	0.0816363	+	0.224294i
$593$	5.44218e6	+	3.08641e7i	0.0260981	+	0.148010i	0.995072	−	0.0991524i	$-0.0316131\pi$
$593$	5.44218e6	+	3.08641e7i	0.0260981	+	0.148010i	−0.968974	+	0.247162i	$0.920502\pi$
$594$	1.66471e6	−	9.44103e6i	0.00794290	−	0.0450464i
$595$	1.14698e8	+	4.17467e7i	0.544510	+	0.198185i
$596$	−2.66932e7	−	4.62339e7i	−0.126084	−	0.218385i
$597$	−699270.	−	403724.i	−0.00328641	−	0.00189741i
$598$	1.70993e8	−	1.43480e8i	0.799605	−	0.670948i
$599$	−1.91712e8	−	2.28473e8i	−0.892006	−	1.06305i	−0.997641	−	0.0686469i	$-0.978132\pi$
$599$	−1.91712e8	−	2.28473e8i	−0.892006	−	1.06305i	0.105635	−	0.994405i	$-0.466313\pi$
$600$	−1.86050e6	+	3.22248e6i	−0.00861344	+	0.0149189i
$601$	2.15252e8	−	1.24276e8i	0.991570	−	0.572483i	0.0858270	−	0.996310i	$-0.472647\pi$
$601$	2.15252e8	−	1.24276e8i	0.991570	−	0.572483i	0.905743	+	0.423827i	$0.139313\pi$
$602$	8.74012e6	−	2.40133e7i	0.0400615	−	0.110068i
$603$	−1.98461e8	−	3.49940e7i	−0.905155	−	0.159603i
$604$	−1.15483e7	+	2.03627e6i	−0.0524090	+	0.00924113i
$605$	4.28364e7	−	1.55912e7i	0.193440	−	0.0704065i
$606$	−3.21690e6	−	2.69930e6i	−0.0144550	−	0.0121292i
$607$			5.86785e7i			0.262369i	0.991358	+	0.131185i	$0.0418781\pi$
$607$			5.86785e7i			0.262369i	−0.991358	+	0.131185i	$0.958122\pi$
$608$	−1.46234e7	+	3.69426e7i	−0.0650636	+	0.164368i
$609$	1.06615e7			0.0472026
$610$	1.49039e7	−	1.77618e7i	0.0656615	−	0.0782523i
$611$	−1.53363e8	−	4.21360e8i	−0.672351	−	1.84727i
$612$	−3.85696e7	−	2.18739e8i	−0.168264	−	0.954271i
$613$	−1.34126e7	+	7.60669e7i	−0.0582282	+	0.330228i	−0.999982	−	0.00607597i	$-0.998066\pi$
$613$	−1.34126e7	+	7.60669e7i	−0.0582282	+	0.330228i	0.941753	+	0.336304i	$0.109177\pi$
$614$	1.38619e8	+	5.04532e7i	0.598850	+	0.217964i
$615$	2.02812e6	+	3.51280e6i	0.00871902	+	0.0151018i
$616$	−3.98248e7	−	2.29928e7i	−0.170377	−	0.0983673i
$617$	4.42907e7	−	3.71643e7i	0.188563	−	0.158223i	−0.543619	−	0.839332i	$-0.682946\pi$
$617$	4.42907e7	−	3.71643e7i	0.188563	−	0.158223i	0.732182	+	0.681109i	$0.238502\pi$
$618$	−3.54516e6	−	4.22496e6i	−0.0150200	−	0.0179002i
$619$	−8.74485e7	+	1.51465e8i	−0.368706	+	0.638618i	−0.989364	−	0.145464i	$-0.953533\pi$
$619$	−8.74485e7	+	1.51465e8i	−0.368706	+	0.638618i	0.620657	+	0.784082i	$0.286866\pi$
$620$	−5.37270e7	+	3.10193e7i	−0.225433	+	0.130154i
$621$	−7.94383e6	+	2.18255e7i	−0.0331708	+	0.0911359i
$622$	−3.96554e6	−	699232.i	−0.0164790	−	0.00290570i
$623$	3.38309e8	−	5.96531e7i	1.39910	−	0.246700i
$624$	5.11073e6	−	1.86015e6i	0.0210343	−	0.00765588i
$625$	1.31615e8	+	1.10438e8i	0.539095	+	0.452354i
$626$		−	1.47991e7i		−	0.0603269i
$627$	7.82134e6	+	1.60488e6i	0.0317306	+	0.00651089i
$628$	−1.85099e8			−0.747354
$629$	2.96854e8	−	3.53776e8i	1.19286	−	1.42160i
$630$	1.79749e7	+	4.93855e7i	0.0718859	+	0.197505i
$631$	−6.80566e7	−	3.85968e8i	−0.270883	−	1.53626i	−0.751742	−	0.659457i	$-0.770786\pi$
$631$	−6.80566e7	−	3.85968e8i	−0.270883	−	1.53626i	0.480859	−	0.876798i	$-0.340325\pi$
$632$	2.16083e7	−	1.22547e8i	0.0855990	−	0.485456i
$633$	−4.62303e6	−	1.68265e6i	−0.0182270	−	0.00663409i
$634$	−3.95958e6	−	6.85820e6i	−0.0155375	−	0.0269118i
$635$	5.41713e7	+	3.12758e7i	0.211567	+	0.122148i
$636$	3.02275e6	−	2.53639e6i	0.0117498	−	0.00985925i
$637$	3.58272e7	+	4.26972e7i	0.138610	+	0.165189i
$638$	−5.11157e7	+	8.85350e7i	−0.196831	+	0.340920i
$639$	−7.37183e7	+	4.25613e7i	−0.282535	+	0.163122i
$640$	−2.53392e6	+	6.96189e6i	−0.00966614	+	0.0265575i
$641$	1.06266e8	+	1.87376e7i	0.403480	+	0.0711444i	0.371706	−	0.928351i	$-0.378773\pi$
$641$	1.06266e8	+	1.87376e7i	0.403480	+	0.0711444i	0.0317743	+	0.999495i	$0.489884\pi$
$642$	4.57940e6	−	807472.i	0.0173063	−	0.00305156i
$643$	2.07784e8	−	7.56272e7i	0.781591	−	0.284476i	0.0797549	−	0.996815i	$-0.474586\pi$
$643$	2.07784e8	−	7.56272e7i	0.781591	−	0.284476i	0.701836	+	0.712339i	$0.252364\pi$
$644$	8.53468e7	+	7.16144e7i	0.319543	+	0.268128i
$645$			827342.i			0.00308323i
$646$	3.66543e8	−	5.41544e7i	1.35965	−	0.200880i
$647$	−5.41361e8			−1.99882			−0.999411	−	0.0343284i	$-0.989071\pi$
$647$	−5.41361e8			−1.99882			−0.999411	+	0.0343284i	$0.989071\pi$
$648$	6.12910e7	−	7.30437e7i	0.225253	−	0.268447i
$649$	−5.59606e7	−	1.53750e8i	−0.204714	−	0.562448i
$650$	−4.99424e7	−	2.83237e8i	−0.181857	−	1.03136i
$651$	−3.94726e6	+	2.23860e7i	−0.0143071	+	0.0811399i
$652$	−1.85739e8	−	6.76035e7i	−0.670133	−	0.243908i
$653$	6.84577e7	+	1.18572e8i	0.245857	+	0.425837i	0.962372	−	0.271734i	$-0.0875972\pi$
$653$	6.84577e7	+	1.18572e8i	0.245857	+	0.425837i	−0.716515	+	0.697572i	$0.754264\pi$
$654$	4.38794e6	+	2.53338e6i	0.0156866	+	0.00905664i
$655$	1.07914e8	−	9.05503e7i	0.384019	−	0.322230i
$656$	−4.55848e7	−	5.43258e7i	−0.161476	−	0.192440i
$657$	−1.95901e8	+	3.39311e8i	−0.690782	+	1.19647i
$658$	1.93823e8	−	1.11904e8i	0.680344	−	0.392797i
$659$	8.43093e7	−	2.31638e8i	0.294591	−	0.809382i	−0.700789	−	0.713369i	$-0.747169\pi$
$659$	8.43093e7	−	2.31638e8i	0.294591	−	0.809382i	0.995380	−	0.0960135i	$-0.0306092\pi$
$660$	1.46620e6	+	258531.i	0.00509990	+	0.000899250i
$661$	−2.73092e8	+	4.81535e7i	−0.945594	+	0.166734i	−0.625125	−	0.780525i	$-0.714952\pi$
$661$	−2.73092e8	+	4.81535e7i	−0.945594	+	0.166734i	−0.320470	+	0.947259i	$0.603841\pi$
$662$	−3.57665e8	+	1.30179e8i	−1.23283	+	0.448712i
$663$	−3.88534e7	−	3.26019e7i	−0.133318	−	0.111867i
$664$			1.32078e8i			0.451156i
$665$	−8.31864e7	+	2.76793e7i	−0.282870	+	0.0941219i
$666$	1.98846e8			0.673124
$667$	1.59207e8	−	1.89736e8i	0.536519	−	0.639398i
$668$	8.30236e7	+	2.28106e8i	0.278530	+	0.765255i
$669$	−1.63321e6	−	9.26240e6i	−0.00545461	−	0.0309346i
$670$	1.08853e7	−	6.17334e7i	0.0361922	−	0.205256i
$671$	7.65506e7	+	2.78621e7i	0.253385	+	0.0922246i
$672$	1.35730e6	+	2.35091e6i	0.00447267	+	0.00774690i
$673$	−1.56272e8	−	9.02236e7i	−0.512667	−	0.295989i	0.221262	−	0.975214i	$-0.428982\pi$
$673$	−1.56272e8	−	9.02236e7i	−0.512667	−	0.295989i	−0.733929	+	0.679226i	$0.762316\pi$
$674$	−1.04893e8	+	8.80154e7i	−0.342583	+	0.287461i
$675$	1.92362e7	+	2.29249e7i	0.0625473	+	0.0745410i
$676$	−1.32958e8	+	2.30290e8i	−0.430403	+	0.745479i
$677$	8.34006e6	−	4.81514e6i	0.0268784	−	0.0155182i	−0.486501	−	0.873680i	$-0.661727\pi$
$677$	8.34006e6	−	4.81514e6i	0.0268784	−	0.0155182i	0.513379	+	0.858162i	$0.328394\pi$
$678$	−829991.	+	2.28038e6i	−0.00266308	+	0.00731675i
$679$	4.49234e8	+	7.92121e7i	1.43504	+	0.253036i
$680$	6.80411e7	−	1.19975e7i	0.216394	−	0.0381560i
$681$	2.44239e7	−	8.88956e6i	0.0773345	−	0.0281474i
$682$	−1.66973e8	−	1.40107e8i	−0.526372	−	0.441679i
$683$		−	3.47469e8i		−	1.09057i	−0.838251	−	0.545285i	$-0.816421\pi$
$683$		−	3.47469e8i		−	1.09057i	0.838251	−	0.545285i	$-0.183579\pi$
$684$	1.19308e8	+	1.05911e8i	0.372822	+	0.330957i
$685$	−7.62147e7			−0.237119
$686$	−1.54689e8	+	1.84351e8i	−0.479166	+	0.571048i
$687$	4.80630e6	+	1.32052e7i	0.0148231	+	0.0407263i
$688$	−2.51180e6	−	1.42451e7i	−0.00771293	−	0.0437422i
$689$	−5.29611e7	+	3.00357e8i	−0.161920	+	0.918292i
$690$	−3.38952e6	−	1.23368e6i	−0.0103179	−	0.00375541i
$691$	3.59472e7	+	6.22623e7i	0.108951	+	0.188708i	0.915346	−	0.402669i	$-0.131918\pi$
$691$	3.59472e7	+	6.22623e7i	0.108951	+	0.188708i	−0.806395	+	0.591378i	$0.798584\pi$
$692$	−2.68868e7	−	1.55231e7i	−0.0811374	−	0.0468447i
$693$	−1.41448e8	+	1.18689e8i	−0.425009	+	0.356625i
$694$	2.40627e8	+	2.86768e8i	0.719889	+	0.857930i
$695$	−4.21278e7	+	7.29674e7i	−0.125491	+	0.217358i
$696$	5.22634e6	−	3.01743e6i	0.0155014	−	0.00894971i
$697$	−2.26195e8	+	6.21465e8i	−0.668012	+	1.83535i
$698$	3.95296e8	+	6.97014e7i	1.16240	+	0.204963i
$699$	−4.01550e6	+	708041.i	−0.0117573	+	0.00207313i
$700$	1.34894e8	−	4.90974e7i	0.393277	−	0.143141i
$701$	−3.88006e8	−	3.25575e8i	−1.12638	−	0.945143i	−0.127469	−	0.991843i	$-0.540685\pi$
$701$	−3.88006e8	−	3.25575e8i	−1.12638	−	0.945143i	−0.998909	+	0.0466994i	$0.985130\pi$
$702$		−	4.37411e7i		−	0.126438i
$703$	−9.23708e6	+	3.31580e8i	−0.0265870	+	0.954384i
$704$	−2.60298e7			−0.0746025
$705$	−4.65761e6	+	5.55072e6i	−0.0132922	+	0.0158410i
$706$	1.49505e8	+	4.10761e8i	0.424855	+	1.16728i
$707$	2.81320e7	+	1.59545e8i	0.0796054	+	0.451465i
$708$	−1.67719e6	+	9.51184e6i	−0.00472589	+	0.0268018i
$709$	−1.14676e8	−	4.17385e7i	−0.321761	−	0.117111i	0.176090	−	0.984374i	$-0.443655\pi$
$709$	−1.14676e8	−	4.17385e7i	−0.321761	−	0.117111i	−0.497851	+	0.867263i	$0.665877\pi$
$710$	−1.32391e7	−	2.29309e7i	−0.0369900	−	0.0640686i
$711$	−4.32715e8	−	2.49828e8i	−1.20391	−	0.695076i
$712$	1.48959e8	−	1.24991e8i	0.412691	−	0.346289i
$713$	3.39446e8	+	4.04535e8i	0.936487	+	1.11606i
$714$	1.26577e7	−	2.19237e7i	0.0347743	−	0.0602309i
$715$	−9.96579e7	+	5.75375e7i	−0.272643	+	0.157410i
$716$	6.85052e7	−	1.88216e8i	0.186631	−	0.512765i
$717$	1.12082e7	+	1.97631e6i	0.0304074	+	0.00536164i
$718$	3.38542e8	−	5.96941e7i	0.914618	−	0.161272i
$719$	2.03372e8	−	7.40213e7i	0.547147	−	0.199145i	−0.0536313	−	0.998561i	$-0.517080\pi$
$719$	2.03372e8	−	7.40213e7i	0.547147	−	0.199145i	0.600779	+	0.799415i	$0.294857\pi$
$720$	2.27886e7	+	1.91219e7i	0.0610547	+	0.0512310i
$721$			2.12773e8i			0.567688i
$722$	−1.82151e8	+	1.94029e8i	−0.483971	+	0.515531i
$723$	−5.29877e6			−0.0140204
$724$	−1.04256e8	+	1.24247e8i	−0.274717	+	0.327394i
$725$	−1.09149e8	−	2.99885e8i	−0.286422	−	0.786938i
$726$	−1.64176e6	−	9.31089e6i	−0.00429042	−	0.0243322i
$727$	−7.38101e7	+	4.18598e8i	−0.192093	+	1.08942i	0.724404	+	0.689376i	$0.242115\pi$
$727$	−7.38101e7	+	4.18598e8i	−0.192093	+	1.08942i	−0.916497	+	0.400041i	$0.868996\pi$
$728$	−1.97165e8	−	7.17622e7i	−0.511018	−	0.185995i
$729$	−1.90295e8	−	3.29601e8i	−0.491185	−	0.850757i
$730$	−1.05546e8	−	6.09372e7i	−0.271315	−	0.156644i
$731$	−1.03335e8	+	8.67082e7i	−0.264542	+	0.221977i
$732$	−3.09110e6	−	3.68382e6i	−0.00788096	−	0.00939217i
$733$	−7.89113e7	+	1.36678e8i	−0.200367	+	0.347047i	−0.948647	−	0.316337i	$-0.897547\pi$
$733$	−7.89113e7	+	1.36678e8i	−0.200367	+	0.347047i	0.748279	+	0.663384i	$0.230880\pi$
$734$	9.02365e7	−	5.20981e7i	0.228189	−	0.131745i
$735$	308052.	−	846367.i	0.000775823	−	0.00213155i
$736$	6.21060e7	+	1.09510e7i	0.155776	+	0.0274675i
$737$	2.16895e8	−	3.82445e7i	0.541811	−	0.0955359i
$738$	−2.67584e8	+	9.73925e7i	−0.665718	+	0.242302i
$739$	−3.30320e8	−	2.77171e8i	−0.818467	−	0.686775i	0.134146	−	0.990962i	$-0.457171\pi$
$739$	−3.30320e8	−	2.77171e8i	−0.818467	−	0.686775i	−0.952612	+	0.304187i	$0.901615\pi$
$740$			6.18533e7i			0.152640i
$741$	3.64158e7	+	1.01446e6i	0.0895024	+	0.00249333i
$742$	−1.52228e8			−0.372635
$743$	2.89111e8	−	3.44549e8i	0.704851	−	0.840009i	−0.288215	−	0.957566i	$-0.593062\pi$
$743$	2.89111e8	−	3.44549e8i	0.704851	−	0.840009i	0.993066	+	0.117557i	$0.0375062\pi$
$744$	4.40075e6	+	1.20909e7i	0.0106858	+	0.0293590i
$745$	−1.15789e7	−	6.56671e7i	−0.0280026	−	0.158811i
$746$	5.09291e7	−	2.88834e8i	0.122673	−	0.695715i
$747$	4.98354e8	+	1.81386e8i	1.19557	+	0.435153i
$748$	1.21372e8	+	2.10223e8i	0.290011	+	0.502314i
$749$	−1.55359e8	−	8.96963e7i	−0.369734	−	0.213466i
$750$	−7.52595e6	+	6.31502e6i	−0.0178393	+	0.0149689i
$751$	6.05874e7	+	7.22052e7i	0.143042	+	0.170470i	0.832809	−	0.553561i	$-0.186731\pi$
$751$	6.05874e7	+	7.22052e7i	0.143042	+	0.170470i	−0.689767	+	0.724031i	$0.742287\pi$
$752$	6.33424e7	−	1.09712e8i	0.148950	−	0.257989i
$753$	−2.97086e7	+	1.71523e7i	−0.0695821	+	0.0401732i
$754$	−1.59536e8	+	4.38320e8i	−0.372172	+	1.02253i
$755$	−1.44239e7	−	2.54333e6i	−0.0335153	−	0.00590965i
$756$	2.15005e7	−	3.79112e6i	0.0497604	−	0.00877409i
$757$	−1.70722e8	+	6.21377e7i	−0.393551	+	0.143241i	−0.531213	−	0.847238i	$-0.678264\pi$
$757$	−1.70722e8	+	6.21377e7i	−0.393551	+	0.143241i	0.137662	+	0.990479i	$0.456041\pi$
$758$	1.91102e8	+	1.60353e8i	0.438790	+	0.368189i
$759$		−	1.26731e7i		−	0.0289839i
$760$	−3.29447e7	+	3.71121e7i	−0.0750490	+	0.0845424i
$761$	3.88610e8			0.881779			0.440889	−	0.897562i	$-0.354663\pi$
$761$	3.88610e8			0.881779			0.440889	+	0.897562i	$0.354663\pi$
$762$	8.33909e6	−	9.93814e6i	0.0188475	−	0.0224616i
$763$	−6.68543e7	−	1.83681e8i	−0.150507	−	0.413514i
$764$	−2.46088e7	−	1.39564e8i	−0.0551837	−	0.312962i
$765$	4.81738e7	−	2.73207e8i	0.107604	−	0.610251i
$766$	−9.81892e6	−	3.57380e6i	−0.0218463	−	0.00795140i
$767$	−3.73269e8	−	6.46521e8i	−0.827249	−	1.43284i
$768$	1.33071e6	+	768288.i	0.00293766	+	0.00169606i
$769$	2.65115e8	−	2.22458e8i	0.582983	−	0.489181i	−0.302942	−	0.953009i	$-0.597969\pi$
$769$	2.65115e8	−	2.22458e8i	0.582983	−	0.489181i	0.885925	+	0.463828i	$0.153525\pi$
$770$	−3.69196e7	−	4.39990e7i	−0.0808695	−	0.0963765i
$771$	−1.74320e6	+	3.01931e6i	−0.00380351	+	0.00658787i
$772$	2.69771e8	−	1.55752e8i	0.586331	−	0.338518i
$773$	−9.69369e7	+	2.66332e8i	−0.209870	+	0.576613i	−0.999307	−	0.0372181i	$-0.988150\pi$
$773$	−9.69369e7	+	2.66332e8i	−0.209870	+	0.576613i	0.789437	+	0.613832i	$0.210373\pi$
$774$	−5.71988e7	−	1.00857e7i	−0.123357	−	0.0217512i
$775$	6.70082e8	−	1.18154e8i	1.43954	−	0.253829i
$776$	2.42636e8	−	8.83124e7i	0.519243	−	0.188989i
$777$	1.73612e7	+	1.45678e7i	0.0370099	+	0.0310550i
$778$		−	1.31163e8i		−	0.278531i
$779$	−1.49974e8	−	4.50725e8i	−0.317251	−	0.953454i
$780$	6.79303e6			0.0143146
$781$	5.97981e7	−	7.12646e7i	0.125526	−	0.149596i
$782$	−2.01146e8	−	5.52645e8i	−0.420622	−	1.15565i
$783$	−8.42810e6	−	4.77981e7i	−0.0175568	−	0.0995693i
$784$	−2.73447e6	+	1.55079e7i	−0.00567446	+	0.0321814i
$785$	−2.17249e8	−	7.90721e7i	−0.449106	−	0.163461i
$786$	−1.46085e7	−	2.53026e7i	−0.0300841	−	0.0521072i
$787$	7.06455e8	+	4.07872e8i	1.44931	+	0.836757i	0.998440	−	0.0558347i	$-0.0177820\pi$
$787$	7.06455e8	+	4.07872e8i	1.44931	+	0.836757i	0.450866	+	0.892592i	$0.351115\pi$
$788$	4.58564e7	−	3.84781e7i	0.0937176	−	0.0786384i
$789$	3.22132e6	+	3.83902e6i	0.00655848	+	0.00781609i
$790$	7.77117e7	−	1.34601e8i	0.157618	−	0.273002i
$791$	8.10773e7	−	4.68100e7i	0.163821	−	0.0945822i
$792$	−3.57474e7	+	9.82152e7i	−0.0719564	+	0.197698i
$793$	3.66046e8	+	6.45438e7i	0.734034	+	0.129430i
$794$	−1.58374e8	+	2.79256e7i	−0.316390	+	0.0557881i
$795$	4.63127e6	−	1.68564e6i	0.00921719	−	0.00335478i
$796$	1.35072e7	+	1.13339e7i	0.0267809	+	0.0224718i
$797$			9.52938e8i			1.88230i	0.337983	+	0.941152i	$0.390255\pi$
$797$			9.52938e8i			1.88230i	−0.337983	+	0.941152i	$0.609745\pi$
$798$	2.65757e6	+	1.79878e7i	0.00522970	+	0.0353971i
$799$	−1.18142e9			−2.31613
$800$	5.22304e7	−	6.22458e7i	0.102013	−	0.121574i
$801$	−2.67045e8	−	7.33700e8i	−0.519621	−	1.42765i
$802$	1.65904e7	+	9.40888e7i	0.0321613	+	0.182396i
$803$	7.43554e7	−	4.21691e8i	0.143604	−	0.814418i
$804$	−1.22171e7	−	4.44665e6i	−0.0235071	−	0.00855588i
$805$	6.95776e7	+	1.20512e8i	0.133377	+	0.231016i
$806$	−8.61280e8	−	4.97260e8i	−1.64490	−	0.949683i
$807$	3.41370e6	−	2.86444e6i	0.00649539	−	0.00545028i
$808$	5.89450e7	+	7.02479e7i	0.111741	+	0.133168i
$809$	−2.34341e8	+	4.05890e8i	−0.442590	+	0.766589i	−0.997881	−	0.0650676i	$-0.979274\pi$
$809$	−2.34341e8	+	4.05890e8i	−0.442590	+	0.766589i	0.555291	+	0.831656i	$0.312607\pi$
$810$	1.03140e8	−	5.95478e7i	0.194076	−	0.112050i
$811$	1.27989e8	−	3.51648e8i	0.239945	−	0.659243i	−0.760012	−	0.649909i	$-0.774807\pi$
$811$	1.27989e8	−	3.51648e8i	0.239945	−	0.659243i	0.999956	−	0.00933339i	$-0.00297095\pi$
$812$	−2.29280e8	−	4.04282e7i	−0.428250	−	0.0755120i
$813$	6.86616e6	−	1.21069e6i	0.0127774	−	0.00225300i
$814$	−2.04211e8	+	7.43267e7i	−0.378622	+	0.137807i
$815$	−1.89120e8	−	1.58691e8i	−0.349354	−	0.293143i
$816$		−	1.43295e7i		−	0.0263731i
$817$	1.94752e7	−	9.49117e7i	0.0357121	−	0.174042i
$818$	1.14531e8			0.209249
$819$	−5.41543e8	+	6.45386e8i	−0.985783	+	1.17481i
$820$	−3.02950e7	−	8.32348e7i	−0.0549451	−	0.150960i
$821$	−1.14926e7	−	6.51777e7i	−0.0207677	−	0.117780i	0.972662	−	0.232227i	$-0.0746013\pi$
$821$	−1.14926e7	−	6.51777e7i	−0.0207677	−	0.117780i	−0.993429	+	0.114448i	$0.963490\pi$
$822$	−2.74487e6	+	1.55669e7i	−0.00494204	+	0.0280277i
$823$	5.13770e8	+	1.86997e8i	0.921656	+	0.335455i	0.758897	−	0.651210i	$-0.225738\pi$
$823$	5.13770e8	+	1.86997e8i	0.921656	+	0.335455i	0.162759	+	0.986666i	$0.447961\pi$
$824$	6.02191e7	+	1.04303e8i	0.107635	+	0.186429i
$825$	−1.41412e7	−	8.16445e6i	−0.0251841	−	0.0145400i
$826$	2.85439e8	−	2.39512e8i	0.506494	−	0.424999i
$827$	−7.54508e7	−	8.99187e7i	−0.133397	−	0.158977i	0.695211	−	0.718806i	$-0.255311\pi$
$827$	−7.54508e7	−	8.99187e7i	−0.133397	−	0.158977i	−0.828608	+	0.559829i	$0.810867\pi$
$828$	1.26612e8	−	2.19298e8i	0.223040	−	0.386316i
$829$	6.41061e8	−	3.70117e8i	1.12522	−	0.649643i	0.182488	−	0.983208i	$-0.441585\pi$
$829$	6.41061e8	−	3.70117e8i	1.12522	−	0.649643i	0.942727	+	0.333565i	$0.108252\pi$
$830$	−5.64220e7	+	1.55018e8i	−0.0986767	+	0.271112i
$831$	2.47749e7	+	4.36848e6i	0.0431726	+	0.00761250i
$832$	−1.16962e8	+	2.06235e7i	−0.203083	+	0.0358091i
$833$	1.37996e8	−	5.02264e7i	0.238743	−	0.0868954i
$834$	1.33864e7	+	1.12326e7i	0.0230763	+	0.0193633i
$835$			3.03191e8i			0.520783i
$836$	−1.62115e8	−	6.41719e7i	−0.277463	−	0.109831i
$837$	1.03483e8			0.176478
$838$	−2.32597e8	+	2.77198e8i	−0.395250	+	0.471040i
$839$	2.60755e8	+	7.16418e8i	0.441516	+	1.21306i	0.938495	+	0.345293i	$0.112220\pi$
$839$	2.60755e8	+	7.16418e8i	0.441516	+	1.21306i	−0.496979	+	0.867763i	$0.665557\pi$
$840$	588765.	+	3.33905e6i	0.000993354	+	0.00563359i
$841$	1.34136e7	−	7.60721e7i	0.0225505	−	0.127890i
$842$	3.42949e8	+	1.24823e8i	0.574505	+	0.209103i
$843$	−1.57877e7	−	2.73450e7i	−0.0263533	−	0.0456453i
$844$	9.30395e7	+	5.37164e7i	0.154753	+	0.0893469i
$845$	−2.54428e8	+	2.13491e8i	−0.421692	+	0.353842i
$846$	−3.26974e8	−	3.89673e8i	−0.540011	−	0.643560i
$847$	−1.82371e8	+	3.15877e8i	−0.300128	+	0.519837i
$848$	−7.46233e7	+	4.30838e7i	−0.122373	+	0.0706523i
$849$	−1.02716e7	+	2.82209e7i	−0.0167847	+	0.0461155i
$850$	−7.46252e8	−	1.31584e8i	−1.21515	−	0.214263i
$851$	5.18508e8	−	9.14269e7i	0.841330	−	0.148349i
$852$	−5.16045e6	+	1.87825e6i	−0.00834390	+	0.00303693i
$853$	−6.03825e6	−	5.06669e6i	−0.00972891	−	0.00816352i	0.637910	−	0.770111i	$-0.279799\pi$
$853$	−6.03825e6	−	5.06669e6i	−0.00972891	−	0.00816352i	−0.647639	+	0.761947i	$0.724244\pi$
$854$			1.85521e8i			0.297864i
$855$	9.47868e7	+	1.75273e8i	0.151652	+	0.280425i
$856$	−1.01544e8			−0.161894
$857$	−1.79510e8	+	2.13932e8i	−0.285198	+	0.339885i	−0.889555	−	0.456828i	$-0.848985\pi$
$857$	−1.79510e8	+	2.13932e8i	−0.285198	+	0.339885i	0.604357	+	0.796713i	$0.293430\pi$
$858$	8.16292e6	+	2.24274e7i	0.0129236	+	0.0355073i
$859$	1.03722e8	+	5.88236e8i	0.163641	+	0.928051i	0.950455	+	0.310862i	$0.100618\pi$
$859$	1.03722e8	+	5.88236e8i	0.163641	+	0.928051i	−0.786815	+	0.617189i	$0.788271\pi$
$860$	3.13726e6	−	1.77923e7i	0.00493237	−	0.0279729i
$861$	−3.04978e7	−	1.11003e7i	−0.0477814	−	0.0173910i
$862$	−2.27127e8	−	3.93395e8i	−0.354606	−	0.614196i
$863$	−5.61215e8	−	3.24018e8i	−0.873167	−	0.504123i	−0.00476742	−	0.999989i	$-0.501518\pi$
$863$	−5.61215e8	−	3.24018e8i	−0.873167	−	0.504123i	−0.868399	+	0.495866i	$0.834851\pi$
$864$	9.46674e6	−	7.94354e6i	0.0146777	−	0.0123161i
$865$	−2.49255e7	−	2.97050e7i	−0.0385119	−	0.0458967i
$866$	−2.08402e8	+	3.60962e8i	−0.320884	+	0.555787i
$867$	−8.50964e7	+	4.91305e7i	−0.130573	+	0.0753865i
$868$	1.69775e8	−	4.66453e8i	0.259606	−	0.713261i
$869$	5.37772e8	+	9.48237e7i	0.819481	+	0.144497i
$870$	7.42309e6	−	1.30889e6i	0.0112727	−	0.00198768i
$871$	9.44292e8	−	3.43694e8i	1.42906	−	0.520137i
$872$	−8.47579e7	−	7.11204e7i	−0.127829	−	0.107262i
$873$		−	1.03679e9i		−	1.55829i
$874$	3.59802e8	+	2.21314e8i	0.538926	+	0.331494i
$875$	3.79013e8			0.565757
$876$	−1.62477e7	+	1.93633e7i	−0.0241702	+	0.0288049i
$877$	4.14270e8	+	1.13820e9i	0.614165	+	1.68740i	0.720833	+	0.693109i	$0.243760\pi$
$877$	4.14270e8	+	1.13820e9i	0.614165	+	1.68740i	−0.106668	+	0.994295i	$0.534018\pi$
$878$	1.03255e8	+	5.85588e8i	0.152555	+	0.865184i
$879$	−4.30320e6	+	2.44047e7i	−0.00633614	+	0.0359341i
$880$	−3.05509e7	−	1.11196e7i	−0.0448307	−	0.0163171i
$881$	−1.08995e8	−	1.88784e8i	−0.159396	−	0.276082i	0.775255	−	0.631648i	$-0.217621\pi$
$881$	−1.08995e8	−	1.88784e8i	−0.159396	−	0.276082i	−0.934651	+	0.355566i	$0.884288\pi$
$882$	5.47588e7	+	3.16150e7i	0.0798084	+	0.0460774i
$883$	−6.10025e8	+	5.11872e8i	−0.886065	+	0.743497i	−0.967417	−	0.253189i	$-0.918521\pi$
$883$	−6.10025e8	+	5.11872e8i	−0.886065	+	0.743497i	0.0813519	+	0.996685i	$0.474076\pi$
$884$	7.11932e8	+	8.48448e8i	1.03058	+	1.22820i
$885$	−6.03184e6	+	1.04474e7i	−0.00870201	+	0.0150723i
$886$	1.99376e8	−	1.15110e8i	0.286663	−	0.165505i
$887$	−1.86306e8	+	5.11873e8i	−0.266967	+	0.733485i	0.731688	+	0.681639i	$0.238733\pi$
$887$	−1.86306e8	+	5.11873e8i	−0.266967	+	0.733485i	−0.998655	+	0.0518457i	$0.983490\pi$
$888$	1.26336e7	+	2.22764e6i	0.0180421	+	0.00318132i
$889$	−4.92890e8	+	8.69097e7i	−0.701527	+	0.123698i
$890$	2.28225e8	−	8.30672e7i	0.323738	−	0.117831i
$891$	3.20538e8	+	2.68963e8i	0.453155	+	0.380242i
$892$			2.05385e8i			0.289383i
$893$	6.64976e8	−	5.27134e8i	0.933795	−	0.740230i
$894$	−1.38296e7			−0.0193552
$895$	1.60807e8	−	1.91643e8i	0.224304	−	0.267315i
$896$	−2.02746e7	−	5.57041e7i	−0.0281857	−	0.0774395i
$897$	−1.00409e7	−	5.69450e7i	−0.0139122	−	0.0789002i
$898$	−1.06569e7	+	6.04381e7i	−0.0147164	+	0.0834607i
$899$	−1.03698e9	−	3.77429e8i	−1.42722	−	0.519465i
$900$	−1.63135e8	−	2.82558e8i	−0.223779	−	0.387597i
$901$	6.95909e8	+	4.01783e8i	0.951433	+	0.549310i
$902$	2.38398e8	−	2.00040e8i	0.324851	−	0.272582i
$903$	−4.25512e6	−	5.07106e6i	−0.00577895	−	0.00688708i
$904$	2.64965e7	−	4.58932e7i	0.0358660	−	0.0621217i
$905$	−1.75441e8	+	1.01291e8i	−0.236692	+	0.136654i
$906$	−1.03895e6	+	2.85450e6i	−0.00139705	+	0.00383836i
$907$	−5.94741e8	−	1.04869e8i	−0.797088	−	0.140548i	−0.239751	−	0.970834i	$-0.577066\pi$
$907$	−5.94741e8	−	1.04869e8i	−0.797088	−	0.140548i	−0.557337	+	0.830286i	$0.688177\pi$
$908$	−5.58954e8	+	9.85587e7i	−0.746653	+	0.131655i
$909$	3.46008e8	−	1.25937e8i	0.460675	−	0.167672i
$910$	−2.00754e8	−	1.68453e8i	−0.266404	−	0.223539i
$911$			4.66269e8i			0.616710i	0.951271	+	0.308355i	$0.0997785\pi$
$911$			4.66269e8i			0.616710i	−0.951271	+	0.308355i	$0.900222\pi$
$912$	6.39368e6	+	8.06557e6i	0.00842881	+	0.0106329i
$913$	−5.79598e8			−0.761579
$914$	1.50961e8	−	1.79908e8i	0.197708	−	0.235620i
$915$	−2.05430e6	−	5.64413e6i	−0.00268164	−	0.00736774i
$916$	−5.32875e7	−	3.02208e8i	−0.0693328	−	0.393206i
$917$	−1.95728e8	+	1.11003e9i	−0.253831	+	1.43955i
$918$	−1.08295e8	−	3.94163e7i	−0.139985	−	0.0509505i
$919$	2.00142e8	+	3.46656e8i	0.257865	+	0.446635i	0.965670	−	0.259773i	$-0.0836478\pi$
$919$	2.00142e8	+	3.46656e8i	0.257865	+	0.446635i	−0.707805	+	0.706408i	$0.750314\pi$
$920$	6.82149e7	+	3.93839e7i	0.0876023	+	0.0505772i
$921$	2.92732e7	−	2.45631e7i	0.0374707	−	0.0314416i
$922$	−3.90666e7	−	4.65577e7i	−0.0498439	−	0.0594017i
$923$	2.12232e8	−	3.67597e8i	0.269902	−	0.467484i
$924$	−1.03165e7	+	5.95623e6i	−0.0130773	+	0.00755015i
$925$	2.32022e8	−	6.37476e8i	0.293160	−	0.805450i
$926$	6.17595e8	+	1.08899e8i	0.777805	+	0.137148i
$927$	4.76252e8	−	8.39762e7i	0.597858	−	0.105418i
$928$	−1.23836e8	+	4.50728e7i	−0.154955	+	0.0563989i
$929$	−2.61954e8	−	2.19805e8i	−0.326721	−	0.274152i	0.464641	−	0.885499i	$-0.346183\pi$
$929$	−2.61954e8	−	2.19805e8i	−0.326721	−	0.274152i	−0.791362	+	0.611347i	$0.790628\pi$
$930$			1.60709e7i			0.0199799i
$931$	−5.52624e7	+	8.98428e7i	−0.0684827	+	0.111336i
$932$	8.90398e7			0.109986
$933$	−670498.	+	799068.i	−0.000825567	+	0.000983873i
$934$	3.54738e6	+	9.74635e6i	0.00435379	+	0.0119619i
$935$	5.26486e7	+	2.98585e8i	0.0644098	+	0.365286i
$936$	−8.28104e7	+	4.69641e8i	−0.100985	+	0.572715i
$937$	−1.09340e9	−	3.97963e8i	−1.32910	−	0.483754i	−0.422738	−	0.906252i	$-0.638931\pi$
$937$	−1.09340e9	−	3.97963e8i	−1.32910	−	0.483754i	−0.906364	+	0.422498i	$0.861153\pi$
$938$	2.50783e8	+	4.34369e8i	0.303871	+	0.526321i
$939$	−3.32004e6	−	1.91683e6i	−0.00401002	−	0.00231519i
$940$	1.21212e8	−	1.01709e8i	0.145936	−	0.122455i
$941$	−3.71556e8	−	4.42803e8i	−0.445918	−	0.531425i	0.495526	−	0.868593i	$-0.334975\pi$
$941$	−3.71556e8	−	4.42803e8i	−0.445918	−	0.531425i	−0.941444	+	0.337168i	$0.890531\pi$
$942$	−2.39747e7	+	4.15255e7i	−0.0286815	+	0.0496778i
$943$	−6.52965e8	+	3.76990e8i	−0.778673	+	0.449567i
$944$	7.21374e7	−	1.98196e8i	0.0857521	−	0.235602i
$945$	2.68544e7	+	4.73516e6i	0.0318215	+	0.00561098i
$946$	6.25119e7	−	1.10225e7i	0.0738396	−	0.0130199i
$947$	−1.47553e9	+	5.37049e8i	−1.73739	+	0.632359i	−0.999112	−	0.0421342i	$-0.986584\pi$
$947$	−1.47553e9	+	5.37049e8i	−1.73739	+	0.632359i	−0.738281	+	0.674493i	$0.764362\pi$
$948$	−2.46935e7	−	2.07203e7i	−0.0289840	−	0.0243204i
$949$		−	1.95373e9i		−	2.28594i
$950$	4.78750e8	−	2.58905e8i	0.558390	−	0.301974i
$951$	−2.05144e6			−0.00238516
$952$	−3.55342e8	+	4.23480e8i	−0.411847	+	0.490820i
$953$	−1.42254e8	−	3.90840e8i	−0.164356	−	0.451565i	0.829987	−	0.557783i	$-0.188348\pi$
$953$	−1.42254e8	−	3.90840e8i	−0.164356	−	0.451565i	−0.994343	+	0.106218i	$0.966126\pi$
$954$	6.00807e7	+	3.40735e8i	0.0691975	+	0.392438i
$955$	3.07367e7	−	1.74317e8i	0.0352897	−	0.200138i
$956$	−2.33543e8	−	8.50027e7i	−0.267296	−	0.0972880i
$957$	1.32414e7	+	2.29348e7i	0.0151077	+	0.0261673i
$958$	8.21142e8	+	4.74087e8i	0.933946	+	0.539214i
$959$	4.67146e8	−	3.91982e8i	0.529659	−	0.444437i
$960$	1.23364e6	+	1.47019e6i	0.00139436	+	0.00166173i
$961$	7.32665e8	−	1.26901e9i	0.825535	−	1.42987i
$962$	−8.58708e8	+	4.95775e8i	−0.964540	+	0.556877i
$963$	−1.39453e8	+	3.83143e8i	−0.156152	+	0.429024i
$964$	1.13952e8	+	2.00928e7i	0.127201	+	0.0224290i
$965$	3.83162e8	−	6.75618e7i	0.426383	−	0.0751829i
$966$	2.71205e7	−	9.87106e6i	0.0300861	−	0.0109505i
$967$	7.13663e8	+	5.98835e8i	0.789249	+	0.662258i	0.945559	−	0.325449i	$-0.105516\pi$
$967$	7.13663e8	+	5.98835e8i	0.789249	+	0.662258i	−0.156311	+	0.987708i	$0.549960\pi$
$968$			2.06460e8i			0.227620i
$969$	3.53269e7	−	8.92451e7i	0.0388270	−	0.0980873i
$970$	3.22505e8			0.353363
$971$	8.81579e7	−	1.05062e8i	0.0962949	−	0.114760i	−0.715745	−	0.698362i	$-0.753913\pi$
$971$	8.81579e7	−	1.05062e8i	0.0962949	−	0.114760i	0.812040	+	0.583602i	$0.198357\pi$
$972$	−2.54697e7	−	6.99775e7i	−0.0277348	−	0.0762008i
$973$	−1.17065e8	−	6.63911e8i	−0.127084	−	0.720727i
$974$	1.89098e8	−	1.07243e9i	0.204649	−	1.16062i
$975$	−7.00106e7	−	2.54818e7i	−0.0755353	−	0.0274926i
$976$	5.25062e7	+	9.09435e7i	0.0564757	+	0.0978188i
$977$	5.06974e8	+	2.92702e8i	0.543628	+	0.313864i	0.746548	−	0.665331i	$-0.231710\pi$
$977$	5.06974e8	+	2.92702e8i	0.543628	+	0.313864i	−0.202920	+	0.979195i	$0.565043\pi$
$978$	−3.92239e7	+	3.29128e7i	−0.0419309	+	0.0351842i
$979$	5.48499e8	+	6.53675e8i	0.584558	+	0.696649i
$980$	−9.83419e6	+	1.70333e7i	−0.0104487	+	0.0180976i
$981$	−3.84750e8	+	2.22135e8i	−0.407541	+	0.235294i
$982$	1.20061e8	−	3.29866e8i	0.126785	−	0.348340i
$983$	−1.30408e9	−	2.29944e8i	−1.37291	−	0.242081i	−0.561945	−	0.827174i	$-0.689947\pi$
$983$	−1.30408e9	−	2.29944e8i	−1.37291	−	0.242081i	−0.810966	+	0.585093i	$0.801058\pi$
$984$	−1.80918e7	+	3.19008e6i	−0.0189888	+	0.00334824i
$985$	7.02584e7	−	2.55720e7i	0.0735173	−	0.0267581i
$986$	9.41445e8	+	7.89966e8i	0.982119	+	0.824096i
$987$		−	5.79769e7i		−	0.0602981i
$988$	−7.79289e8	−	1.59904e8i	−0.808030	−	0.165802i
$989$	−1.53788e8			−0.158976
$990$	−8.39126e7	+	1.00003e8i	−0.0864812	+	0.103064i
$991$	−6.56567e8	−	1.80390e9i	−0.674618	−	1.85350i	−0.492741	−	0.870176i	$-0.664005\pi$
$991$	−6.56567e8	−	1.80390e9i	−0.674618	−	1.85350i	−0.181877	−	0.983321i	$-0.558217\pi$
$992$	−4.87911e7	−	2.76708e8i	−0.0499811	−	0.283457i
$993$	−1.71214e7	+	9.71003e7i	−0.0174860	+	0.0991683i
$994$	1.99083e8	+	7.24604e7i	0.202710	+	0.0737805i
$995$	1.10115e7	+	1.90725e7i	0.0111784	+	0.0193615i
$996$	2.96306e7	+	1.71072e7i	0.0299890	+	0.0173142i
$997$	9.28189e8	−	7.78843e8i	0.936593	−	0.785895i	−0.0403964	−	0.999184i	$-0.512862\pi$
$997$	9.28189e8	−	7.78843e8i	0.936593	−	0.785895i	0.976989	+	0.213289i	$0.0684176\pi$
$998$	−3.57280e8	−	4.25790e8i	−0.359432	−	0.428355i
$999$	5.15867e7	−	8.93508e7i	0.0517418	−	0.0896194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.7.f.a.3.3	✓	60
19.13	odd	18	inner	38.7.f.a.13.3	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.7.f.a.3.3	✓	60	1.1	even	1	trivial
38.7.f.a.13.3	yes	60	19.13	odd	18	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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	38.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.63616 + 4.33340i) q^{2} +(0.501194 + 1.37702i) q^{3} +(-5.55674 - 31.5138i) q^{4} +(6.94044 - 39.3612i) q^{5} +(-7.78959 - 2.83518i) q^{6} +(159.899 + 276.953i) q^{7} +(156.767 + 90.5097i) q^{8} +(556.801 - 467.212i) q^{9} +O(q^{10})\)	\(q+(-3.63616 + 4.33340i) q^{2} +(0.501194 + 1.37702i) q^{3} +(-5.55674 - 31.5138i) q^{4} +(6.94044 - 39.3612i) q^{5} +(-7.78959 - 2.83518i) q^{6} +(159.899 + 276.953i) q^{7} +(156.767 + 90.5097i) q^{8} +(556.801 - 467.212i) q^{9} +(145.331 + 173.199i) q^{10} +(-397.184 + 687.943i) q^{11} +(40.6102 - 23.4463i) q^{12} +(-1239.64 + 3405.88i) q^{13} +(-1781.57 - 314.139i) q^{14} +(57.6796 - 10.1705i) q^{15} +(-962.245 + 350.229i) q^{16} +(7315.30 + 6138.26i) q^{17} +4111.70i q^{18} +(-6856.34 - 191.002i) q^{19} -1278.99 q^{20} +(-301.230 + 358.991i) q^{21} +(-1536.91 - 4222.62i) q^{22} +(1890.50 + 10721.6i) q^{23} +(-46.0627 + 261.234i) q^{24} +(13181.6 + 4797.70i) q^{25} +(-10251.5 - 17756.1i) q^{26} +(1847.57 + 1066.70i) q^{27} +(7839.35 - 6578.00i) q^{28} +(-14623.6 - 17427.8i) q^{29} +(-165.659 + 286.930i) q^{30} +(42007.4 - 24253.0i) q^{31} +(1981.19 - 5443.28i) q^{32} +(-1146.38 - 202.137i) q^{33} +(-53199.1 + 9380.44i) q^{34} +(12011.0 - 4371.64i) q^{35} +(-17817.6 - 14950.8i) q^{36} -48361.1i q^{37} +(25758.4 - 29016.8i) q^{38} -5311.25 q^{39} +(4650.60 - 5542.37i) q^{40} +(23686.7 + 65078.6i) q^{41} +(-460.336 - 2610.70i) q^{42} +(-2452.93 + 13911.2i) q^{43} +(23886.8 + 8694.07i) q^{44} +(-14525.6 - 25159.0i) q^{45} +(-53335.0 - 30793.0i) q^{46} +(-94771.7 + 79522.9i) q^{47} +(-964.543 - 1149.50i) q^{48} +(7689.04 - 13317.8i) q^{49} +(-68720.6 + 39675.8i) q^{50} +(-4786.12 + 13149.8i) q^{51} +(114221. + 20140.2i) q^{52} +(82869.6 - 14612.1i) q^{53} +(-11340.5 + 4127.60i) q^{54} +(24321.6 + 20408.2i) q^{55} +57889.7i q^{56} +(-3173.34 - 9537.04i) q^{57} +128695. q^{58} +(-132397. + 157784. i) q^{59} +(-641.021 - 1761.19i) q^{60} +(-17807.8 - 100993. i) q^{61} +(-47647.6 + 270223. i) q^{62} +(218428. + 79501.3i) q^{63} +(16384.0 + 28377.9i) q^{64} +(125456. + 72431.9i) q^{65} +(5044.34 - 4232.71i) q^{66} +(-178215. - 212389. i) q^{67} +(152791. - 264642. i) q^{68} +(-13816.3 + 7976.84i) q^{69} +(-24729.7 + 67944.4i) q^{70} +(-115332. - 20336.1i) q^{71} +(129575. - 22847.7i) q^{72} +(-506532. + 184362. i) q^{73} +(209568. + 175849. i) q^{74} +20555.8i q^{75} +(32079.7 + 217131. i) q^{76} -254037. q^{77} +(19312.5 - 23015.8i) q^{78} +(-235113. - 645968. i) q^{79} +(7107.01 + 40305.8i) q^{80} +(91469.1 - 518747. i) q^{81} +(-368140. - 133992. i) q^{82} +(364817. + 631882. i) q^{83} +(12987.1 + 7498.08i) q^{84} +(292381. - 245336. i) q^{85} +(-51363.8 - 61213.0i) q^{86} +(16669.1 - 28871.7i) q^{87} +(-124531. + 71898.0i) q^{88} +(367399. - 1.00942e6i) q^{89} +(161841. + 28537.0i) q^{90} +(-1.14149e6 + 201275. i) q^{91} +(327373. - 119154. i) q^{92} +(54450.7 + 45689.6i) q^{93} -699841. i q^{94} +(-55104.1 + 268548. i) q^{95} +8488.46 q^{96} +(916880. - 1.09270e6i) q^{97} +(29752.9 + 81745.3i) q^{98} +(100262. + 568617. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 240 q^{6} + 432 q^{7} + 690 q^{9}+O(q^{10}) \) 60 * q + 30 * q^3 - 240 * q^6 + 432 * q^7 + 690 * q^9	\( 60 q + 30 q^{3} - 240 q^{6} + 432 q^{7} + 690 q^{9} - 3360 q^{11} + 9660 q^{13} + 2496 q^{14} - 37464 q^{15} + 7704 q^{17} + 46704 q^{19} + 21504 q^{20} + 78732 q^{21} - 20304 q^{22} - 54120 q^{23} + 7680 q^{24} - 41328 q^{25} - 25536 q^{26} - 124830 q^{27} + 65280 q^{28} - 21840 q^{29} + 30780 q^{31} - 54582 q^{33} - 70560 q^{34} - 56796 q^{35} - 22080 q^{36} + 52080 q^{38} + 496344 q^{39} + 83394 q^{41} + 38880 q^{42} - 294384 q^{43} - 8448 q^{44} - 391824 q^{45} + 738720 q^{46} + 639264 q^{47} + 61440 q^{48} - 85530 q^{49} - 689472 q^{50} - 215478 q^{51} - 456960 q^{52} - 1189428 q^{53} - 907200 q^{54} - 316512 q^{55} + 517776 q^{57} + 440640 q^{58} + 957390 q^{59} + 586752 q^{60} + 1390404 q^{61} + 978384 q^{62} + 2002152 q^{63} + 983040 q^{64} - 878940 q^{65} - 976992 q^{66} - 2920854 q^{67} - 78144 q^{68} - 2667600 q^{69} - 643392 q^{70} + 1585980 q^{71} + 706560 q^{72} + 1734648 q^{73} - 1167552 q^{74} - 411264 q^{76} - 1481400 q^{77} - 2170608 q^{78} + 4991952 q^{79} + 40002 q^{81} + 2299392 q^{82} - 30672 q^{83} + 1313280 q^{84} + 815976 q^{85} - 1424976 q^{86} - 125892 q^{87} - 6804636 q^{89} - 2283456 q^{90} - 3838704 q^{91} - 244992 q^{92} - 3271128 q^{93} - 4631640 q^{95} + 2112390 q^{97} + 7177728 q^{98} + 21467982 q^{99}+O(q^{100}) \) 60 * q + 30 * q^3 - 240 * q^6 + 432 * q^7 + 690 * q^9 - 3360 * q^11 + 9660 * q^13 + 2496 * q^14 - 37464 * q^15 + 7704 * q^17 + 46704 * q^19 + 21504 * q^20 + 78732 * q^21 - 20304 * q^22 - 54120 * q^23 + 7680 * q^24 - 41328 * q^25 - 25536 * q^26 - 124830 * q^27 + 65280 * q^28 - 21840 * q^29 + 30780 * q^31 - 54582 * q^33 - 70560 * q^34 - 56796 * q^35 - 22080 * q^36 + 52080 * q^38 + 496344 * q^39 + 83394 * q^41 + 38880 * q^42 - 294384 * q^43 - 8448 * q^44 - 391824 * q^45 + 738720 * q^46 + 639264 * q^47 + 61440 * q^48 - 85530 * q^49 - 689472 * q^50 - 215478 * q^51 - 456960 * q^52 - 1189428 * q^53 - 907200 * q^54 - 316512 * q^55 + 517776 * q^57 + 440640 * q^58 + 957390 * q^59 + 586752 * q^60 + 1390404 * q^61 + 978384 * q^62 + 2002152 * q^63 + 983040 * q^64 - 878940 * q^65 - 976992 * q^66 - 2920854 * q^67 - 78144 * q^68 - 2667600 * q^69 - 643392 * q^70 + 1585980 * q^71 + 706560 * q^72 + 1734648 * q^73 - 1167552 * q^74 - 411264 * q^76 - 1481400 * q^77 - 2170608 * q^78 + 4991952 * q^79 + 40002 * q^81 + 2299392 * q^82 - 30672 * q^83 + 1313280 * q^84 + 815976 * q^85 - 1424976 * q^86 - 125892 * q^87 - 6804636 * q^89 - 2283456 * q^90 - 3838704 * q^91 - 244992 * q^92 - 3271128 * q^93 - 4631640 * q^95 + 2112390 * q^97 + 7177728 * q^98 + 21467982 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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