LMFDB - Embedded newform 546.8.a.m.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,8,Mod(1,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

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

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

chi := DirichletCharacter("546.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	546.a (trivial)

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:	yes
Analytic conductor:	$170.562223914$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 197669x^{3} - 12910499x^{2} + 9274302080x + 1050512243200 $ x^5 - x^4 - 197669x^3 - 12910499x^2 + 9274302080*x + 1050512243200
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-233.276$ of defining polynomial
Character	$\chi$	$=$	546.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +293.276 q^{5} +216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +293.276 q^{5} +216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +2346.21 q^{10} +2655.50 q^{11} +1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} +7918.45 q^{15} +4096.00 q^{16} -15243.7 q^{17} +5832.00 q^{18} -18173.1 q^{19} +18769.7 q^{20} -9261.00 q^{21} +21244.0 q^{22} +92567.9 q^{23} +13824.0 q^{24} +7885.72 q^{25} -17576.0 q^{26} +19683.0 q^{27} -21952.0 q^{28} -32764.1 q^{29} +63347.6 q^{30} +191710. q^{31} +32768.0 q^{32} +71698.6 q^{33} -121949. q^{34} -100594. q^{35} +46656.0 q^{36} +312465. q^{37} -145385. q^{38} -59319.0 q^{39} +150157. q^{40} +730641. q^{41} -74088.0 q^{42} +43693.1 q^{43} +169952. q^{44} +213798. q^{45} +740544. q^{46} +482639. q^{47} +110592. q^{48} +117649. q^{49} +63085.8 q^{50} -411579. q^{51} -140608. q^{52} -1.08833e6 q^{53} +157464. q^{54} +778795. q^{55} -175616. q^{56} -490674. q^{57} -262113. q^{58} -185709. q^{59} +506781. q^{60} -2.15574e6 q^{61} +1.53368e6 q^{62} -250047. q^{63} +262144. q^{64} -644327. q^{65} +573588. q^{66} +4.10752e6 q^{67} -975596. q^{68} +2.49933e6 q^{69} -804749. q^{70} +1.53252e6 q^{71} +373248. q^{72} +4.07434e6 q^{73} +2.49972e6 q^{74} +212914. q^{75} -1.16308e6 q^{76} -910837. q^{77} -474552. q^{78} -3.30442e6 q^{79} +1.20126e6 q^{80} +531441. q^{81} +5.84513e6 q^{82} +2.37662e6 q^{83} -592704. q^{84} -4.47060e6 q^{85} +349545. q^{86} -884630. q^{87} +1.35962e6 q^{88} +8.79472e6 q^{89} +1.71038e6 q^{90} +753571. q^{91} +5.92435e6 q^{92} +5.17617e6 q^{93} +3.86111e6 q^{94} -5.32973e6 q^{95} +884736. q^{96} +1.11605e7 q^{97} +941192. q^{98} +1.93586e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 40 q^{2} + 135 q^{3} + 320 q^{4} + 299 q^{5} + 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9}+O(q^{10}) $ 5 * q + 40 * q^2 + 135 * q^3 + 320 * q^4 + 299 * q^5 + 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9	\( 5 q + 40 q^{2} + 135 q^{3} + 320 q^{4} + 299 q^{5} + 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9} + 2392 q^{10} + 1838 q^{11} + 8640 q^{12} - 10985 q^{13} - 13720 q^{14} + 8073 q^{15} + 20480 q^{16} + 56444 q^{17} + 29160 q^{18} - 20639 q^{19} + 19136 q^{20} - 46305 q^{21} + 14704 q^{22} + 74395 q^{23} + 69120 q^{24} + 22594 q^{25} - 87880 q^{26} + 98415 q^{27} - 109760 q^{28} + 130059 q^{29} + 64584 q^{30} + 330083 q^{31} + 163840 q^{32} + 49626 q^{33} + 451552 q^{34} - 102557 q^{35} + 233280 q^{36} + 410632 q^{37} - 165112 q^{38} - 296595 q^{39} + 153088 q^{40} + 172558 q^{41} - 370440 q^{42} + 886497 q^{43} + 117632 q^{44} + 217971 q^{45} + 595160 q^{46} + 763969 q^{47} + 552960 q^{48} + 588245 q^{49} + 180752 q^{50} + 1523988 q^{51} - 703040 q^{52} + 1714575 q^{53} + 787320 q^{54} + 2699318 q^{55} - 878080 q^{56} - 557253 q^{57} + 1040472 q^{58} + 603580 q^{59} + 516672 q^{60} + 6172268 q^{61} + 2640664 q^{62} - 1250235 q^{63} + 1310720 q^{64} - 656903 q^{65} + 397008 q^{66} + 5490834 q^{67} + 3612416 q^{68} + 2008665 q^{69} - 820456 q^{70} - 1581200 q^{71} + 1866240 q^{72} + 2100143 q^{73} + 3285056 q^{74} + 610038 q^{75} - 1320896 q^{76} - 630434 q^{77} - 2372760 q^{78} + 6357137 q^{79} + 1224704 q^{80} + 2657205 q^{81} + 1380464 q^{82} + 5292133 q^{83} - 2963520 q^{84} - 836908 q^{85} + 7091976 q^{86} + 3511593 q^{87} + 941056 q^{88} + 13229719 q^{89} + 1743768 q^{90} + 3767855 q^{91} + 4761280 q^{92} + 8912241 q^{93} + 6111752 q^{94} + 25806433 q^{95} + 4423680 q^{96} + 22321383 q^{97} + 4705960 q^{98} + 1339902 q^{99}+O(q^{100}) \) 5 * q + 40 * q^2 + 135 * q^3 + 320 * q^4 + 299 * q^5 + 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9 + 2392 * q^10 + 1838 * q^11 + 8640 * q^12 - 10985 * q^13 - 13720 * q^14 + 8073 * q^15 + 20480 * q^16 + 56444 * q^17 + 29160 * q^18 - 20639 * q^19 + 19136 * q^20 - 46305 * q^21 + 14704 * q^22 + 74395 * q^23 + 69120 * q^24 + 22594 * q^25 - 87880 * q^26 + 98415 * q^27 - 109760 * q^28 + 130059 * q^29 + 64584 * q^30 + 330083 * q^31 + 163840 * q^32 + 49626 * q^33 + 451552 * q^34 - 102557 * q^35 + 233280 * q^36 + 410632 * q^37 - 165112 * q^38 - 296595 * q^39 + 153088 * q^40 + 172558 * q^41 - 370440 * q^42 + 886497 * q^43 + 117632 * q^44 + 217971 * q^45 + 595160 * q^46 + 763969 * q^47 + 552960 * q^48 + 588245 * q^49 + 180752 * q^50 + 1523988 * q^51 - 703040 * q^52 + 1714575 * q^53 + 787320 * q^54 + 2699318 * q^55 - 878080 * q^56 - 557253 * q^57 + 1040472 * q^58 + 603580 * q^59 + 516672 * q^60 + 6172268 * q^61 + 2640664 * q^62 - 1250235 * q^63 + 1310720 * q^64 - 656903 * q^65 + 397008 * q^66 + 5490834 * q^67 + 3612416 * q^68 + 2008665 * q^69 - 820456 * q^70 - 1581200 * q^71 + 1866240 * q^72 + 2100143 * q^73 + 3285056 * q^74 + 610038 * q^75 - 1320896 * q^76 - 630434 * q^77 - 2372760 * q^78 + 6357137 * q^79 + 1224704 * q^80 + 2657205 * q^81 + 1380464 * q^82 + 5292133 * q^83 - 2963520 * q^84 - 836908 * q^85 + 7091976 * q^86 + 3511593 * q^87 + 941056 * q^88 + 13229719 * q^89 + 1743768 * q^90 + 3767855 * q^91 + 4761280 * q^92 + 8912241 * q^93 + 6111752 * q^94 + 25806433 * q^95 + 4423680 * q^96 + 22321383 * q^97 + 4705960 * q^98 + 1339902 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	8.00000	0.707107
$2$	8.00000	0.707107
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	64.0000	0.500000
$5$	293.276	1.04926	0.524628	−	0.851332i	$-0.324205\pi$
$5$	293.276	1.04926	0.524628	+	0.851332i	$0.324205\pi$
$6$	216.000	0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	2346.21	0.741936
$11$	2655.50	0.601551	0.300775	−	0.953695i	$-0.402755\pi$
$11$	2655.50	0.601551	0.300775	+	0.953695i	$0.402755\pi$
$12$	1728.00	0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−2744.00	−0.267261
$15$	7918.45	0.605788
$16$	4096.00	0.250000
$17$	−15243.7	−0.752521	−0.376261	−	0.926514i	$-0.622790\pi$
$17$	−15243.7	−0.752521	−0.376261	+	0.926514i	$0.622790\pi$
$18$	5832.00	0.235702
$19$	−18173.1	−0.607843	−0.303922	−	0.952697i	$-0.598296\pi$
$19$	−18173.1	−0.607843	−0.303922	+	0.952697i	$0.598296\pi$
$20$	18769.7	0.524628
$21$	−9261.00	−0.218218
$22$	21244.0	0.425361
$23$	92567.9	1.58640	0.793201	−	0.608960i	$-0.208413\pi$
$23$	92567.9	1.58640	0.793201	+	0.608960i	$0.208413\pi$
$24$	13824.0	0.204124
$25$	7885.72	0.100937
$26$	−17576.0	−0.196116
$27$	19683.0	0.192450
$28$	−21952.0	−0.188982
$29$	−32764.1	−0.249462	−0.124731	−	0.992191i	$-0.539807\pi$
$29$	−32764.1	−0.249462	−0.124731	+	0.992191i	$0.539807\pi$
$30$	63347.6	0.428357
$31$	191710.	1.15579	0.577895	−	0.816111i	$-0.303874\pi$
$31$	191710.	1.15579	0.577895	+	0.816111i	$0.303874\pi$
$32$	32768.0	0.176777
$33$	71698.6	0.347305
$34$	−121949.	−0.532113
$35$	−100594.	−0.396581
$36$	46656.0	0.166667
$37$	312465.	1.01413	0.507066	−	0.861907i	$-0.330730\pi$
$37$	312465.	1.01413	0.507066	+	0.861907i	$0.330730\pi$
$38$	−145385.	−0.429810
$39$	−59319.0	−0.160128
$40$	150157.	0.370968
$41$	730641.	1.65562	0.827810	−	0.561009i	$-0.189587\pi$
$41$	730641.	1.65562	0.827810	+	0.561009i	$0.189587\pi$
$42$	−74088.0	−0.154303
$43$	43693.1	0.0838057	0.0419029	−	0.999122i	$-0.486658\pi$
$43$	43693.1	0.0838057	0.0419029	+	0.999122i	$0.486658\pi$
$44$	169952.	0.300775
$45$	213798.	0.349752
$46$	740544.	1.12176
$47$	482639.	0.678078	0.339039	−	0.940772i	$-0.389898\pi$
$47$	482639.	0.678078	0.339039	+	0.940772i	$0.389898\pi$
$48$	110592.	0.144338
$49$	117649.	0.142857
$50$	63085.8	0.0713734
$51$	−411579.	−0.434468
$52$	−140608.	−0.138675
$53$	−1.08833e6	−1.00414	−0.502070	−	0.864827i	$-0.667428\pi$
$53$	−1.08833e6	−1.00414	−0.502070	+	0.864827i	$0.667428\pi$
$54$	157464.	0.136083
$55$	778795.	0.631180
$56$	−175616.	−0.133631
$57$	−490674.	−0.350939
$58$	−262113.	−0.176397
$59$	−185709.	−0.117720	−0.0588602	−	0.998266i	$-0.518747\pi$
$59$	−185709.	−0.117720	−0.0588602	+	0.998266i	$0.518747\pi$
$60$	506781.	0.302894
$61$	−2.15574e6	−1.21602	−0.608011	−	0.793929i	$-0.708032\pi$
$61$	−2.15574e6	−1.21602	−0.608011	+	0.793929i	$0.708032\pi$
$62$	1.53368e6	0.817266
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	−644327.	−0.291011
$66$	573588.	0.245582
$67$	4.10752e6	1.66847	0.834235	−	0.551409i	$-0.185910\pi$
$67$	4.10752e6	1.66847	0.834235	+	0.551409i	$0.185910\pi$
$68$	−975596.	−0.376261
$69$	2.49933e6	0.915910
$70$	−804749.	−0.280425
$71$	1.53252e6	0.508162	0.254081	−	0.967183i	$-0.418227\pi$
$71$	1.53252e6	0.508162	0.254081	+	0.967183i	$0.418227\pi$
$72$	373248.	0.117851
$73$	4.07434e6	1.22582	0.612911	−	0.790152i	$-0.289998\pi$
$73$	4.07434e6	1.22582	0.612911	+	0.790152i	$0.289998\pi$
$74$	2.49972e6	0.717100
$75$	212914.	0.0582761
$76$	−1.16308e6	−0.303922
$77$	−910837.	−0.227365
$78$	−474552.	−0.113228
$79$	−3.30442e6	−0.754051	−0.377025	−	0.926203i	$-0.623053\pi$
$79$	−3.30442e6	−0.754051	−0.377025	+	0.926203i	$0.623053\pi$
$80$	1.20126e6	0.262314
$81$	531441.	0.111111
$82$	5.84513e6	1.17070
$83$	2.37662e6	0.456233	0.228117	−	0.973634i	$-0.426743\pi$
$83$	2.37662e6	0.456233	0.228117	+	0.973634i	$0.426743\pi$
$84$	−592704.	−0.109109
$85$	−4.47060e6	−0.789587
$86$	349545.	0.0592596
$87$	−884630.	−0.144027
$88$	1.35962e6	0.212680
$89$	8.79472e6	1.32238	0.661191	−	0.750218i	$-0.270051\pi$
$89$	8.79472e6	1.32238	0.661191	+	0.750218i	$0.270051\pi$
$90$	1.71038e6	0.247312
$91$	753571.	0.104828
$92$	5.92435e6	0.793201
$93$	5.17617e6	0.667295
$94$	3.86111e6	0.479474
$95$	−5.32973e6	−0.637783
$96$	884736.	0.102062
$97$	1.11605e7	1.24161	0.620804	−	0.783966i	$-0.286806\pi$
$97$	1.11605e7	1.24161	0.620804	+	0.783966i	$0.286806\pi$
$98$	941192.	0.101015
$99$	1.93586e6	0.200517
$100$	504686.	0.0504686
$101$	−7.04184e6	−0.680082	−0.340041	−	0.940411i	$-0.610441\pi$
$101$	−7.04184e6	−0.680082	−0.340041	+	0.940411i	$0.610441\pi$
$102$	−3.29264e6	−0.307215
$103$	3.18332e6	0.287045	0.143522	−	0.989647i	$-0.454157\pi$
$103$	3.18332e6	0.287045	0.143522	+	0.989647i	$0.454157\pi$
$104$	−1.12486e6	−0.0980581
$105$	−2.71603e6	−0.228966
$106$	−8.70662e6	−0.710034
$107$	1.26764e7	1.00035	0.500174	−	0.865925i	$-0.333269\pi$
$107$	1.26764e7	1.00035	0.500174	+	0.865925i	$0.333269\pi$
$108$	1.25971e6	0.0962250
$109$	−4.34498e6	−0.321362	−0.160681	−	0.987006i	$-0.551369\pi$
$109$	−4.34498e6	−0.321362	−0.160681	+	0.987006i	$0.551369\pi$
$110$	6.23036e6	0.446312
$111$	8.43654e6	0.585510
$112$	−1.40493e6	−0.0944911
$113$	−2.32704e7	−1.51715	−0.758575	−	0.651586i	$-0.774104\pi$
$113$	−2.32704e7	−1.51715	−0.758575	+	0.651586i	$0.774104\pi$
$114$	−3.92539e6	−0.248151
$115$	2.71479e7	1.66454
$116$	−2.09690e6	−0.124731
$117$	−1.60161e6	−0.0924500
$118$	−1.48567e6	−0.0832408
$119$	5.22858e6	0.284426
$120$	4.05425e6	0.214178
$121$	−1.24355e7	−0.638137
$122$	−1.72459e7	−0.859857
$123$	1.97273e7	0.955873
$124$	1.22694e7	0.577895
$125$	−2.05995e7	−0.943347
$126$	−2.00038e6	−0.0890871
$127$	−2.66536e6	−0.115463	−0.0577316	−	0.998332i	$-0.518387\pi$
$127$	−2.66536e6	−0.115463	−0.0577316	+	0.998332i	$0.518387\pi$
$128$	2.09715e6	0.0883883
$129$	1.17972e6	0.0483853
$130$	−5.15462e6	−0.205776
$131$	−2.41514e7	−0.938625	−0.469313	−	0.883032i	$-0.655498\pi$
$131$	−2.41514e7	−0.938625	−0.469313	+	0.883032i	$0.655498\pi$
$132$	4.58871e6	0.173653
$133$	6.23338e6	0.229743
$134$	3.28602e7	1.17979
$135$	5.77255e6	0.201929
$136$	−7.80477e6	−0.266056
$137$	−4.61182e7	−1.53232	−0.766161	−	0.642649i	$-0.777836\pi$
$137$	−4.61182e7	−1.53232	−0.766161	+	0.642649i	$0.777836\pi$
$138$	1.99947e7	0.647646
$139$	3.34972e7	1.05793	0.528965	−	0.848644i	$-0.322580\pi$
$139$	3.34972e7	1.05793	0.528965	+	0.848644i	$0.322580\pi$
$140$	−6.43799e6	−0.198291
$141$	1.30312e7	0.391489
$142$	1.22602e7	0.359325
$143$	−5.83414e6	−0.166840
$144$	2.98598e6	0.0833333
$145$	−9.60892e6	−0.261750
$146$	3.25947e7	0.866787
$147$	3.17652e6	0.0824786
$148$	1.99977e7	0.507066
$149$	−4.78478e6	−0.118498	−0.0592488	−	0.998243i	$-0.518871\pi$
$149$	−4.78478e6	−0.118498	−0.0592488	+	0.998243i	$0.518871\pi$
$150$	1.70332e6	0.0412074
$151$	9.45109e6	0.223389	0.111695	−	0.993743i	$-0.464372\pi$
$151$	9.45109e6	0.223389	0.111695	+	0.993743i	$0.464372\pi$
$152$	−9.30463e6	−0.214905
$153$	−1.11126e7	−0.250840
$154$	−7.28670e6	−0.160771
$155$	5.62239e7	1.21272
$156$	−3.79642e6	−0.0800641
$157$	1.38952e7	0.286561	0.143280	−	0.989682i	$-0.454235\pi$
$157$	1.38952e7	0.286561	0.143280	+	0.989682i	$0.454235\pi$
$158$	−2.64354e7	−0.533194
$159$	−2.93848e7	−0.579740
$160$	9.61006e6	0.185484
$161$	−3.17508e7	−0.599604
$162$	4.25153e6	0.0785674
$163$	−1.75438e7	−0.317297	−0.158649	−	0.987335i	$-0.550714\pi$
$163$	−1.75438e7	−0.317297	−0.158649	+	0.987335i	$0.550714\pi$
$164$	4.67610e7	0.827810
$165$	2.10275e7	0.364412
$166$	1.90130e7	0.322606
$167$	−9.28968e7	−1.54345	−0.771726	−	0.635956i	$-0.780606\pi$
$167$	−9.28968e7	−1.54345	−0.771726	+	0.635956i	$0.780606\pi$
$168$	−4.74163e6	−0.0771517
$169$	4.82681e6	0.0769231
$170$	−3.57648e7	−0.558322
$171$	−1.32482e7	−0.202614
$172$	2.79636e6	0.0419029
$173$	8.25270e7	1.21181	0.605905	−	0.795537i	$-0.292811\pi$
$173$	8.25270e7	1.21181	0.605905	+	0.795537i	$0.292811\pi$
$174$	−7.07704e6	−0.101843
$175$	−2.70480e6	−0.0381507
$176$	1.08769e7	0.150388
$177$	−5.01415e6	−0.0679659
$178$	7.03577e7	0.935065
$179$	2.04603e7	0.266640	0.133320	−	0.991073i	$-0.457436\pi$
$179$	2.04603e7	0.266640	0.133320	+	0.991073i	$0.457436\pi$
$180$	1.36831e7	0.174876
$181$	−4.33168e7	−0.542977	−0.271489	−	0.962442i	$-0.587516\pi$
$181$	−4.33168e7	−0.542977	−0.271489	+	0.962442i	$0.587516\pi$
$182$	6.02857e6	0.0741249
$183$	−5.82049e7	−0.702070
$184$	4.73948e7	0.560878
$185$	9.16383e7	1.06408
$186$	4.14093e7	0.471849
$187$	−4.04796e7	−0.452680
$188$	3.08889e7	0.339039
$189$	−6.75127e6	−0.0727393
$190$	−4.26379e7	−0.450981
$191$	7.06721e7	0.733890	0.366945	−	0.930243i	$-0.380404\pi$
$191$	7.06721e7	0.733890	0.366945	+	0.930243i	$0.380404\pi$
$192$	7.07789e6	0.0721688
$193$	9.37068e7	0.938254	0.469127	−	0.883131i	$-0.344569\pi$
$193$	9.37068e7	0.938254	0.469127	+	0.883131i	$0.344569\pi$
$194$	8.92843e7	0.877949
$195$	−1.73968e7	−0.168015
$196$	7.52954e6	0.0714286
$197$	1.64198e8	1.53016	0.765081	−	0.643934i	$-0.222699\pi$
$197$	1.64198e8	1.53016	0.765081	+	0.643934i	$0.222699\pi$
$198$	1.54869e7	0.141787
$199$	−6.66395e6	−0.0599440	−0.0299720	−	0.999551i	$-0.509542\pi$
$199$	−6.66395e6	−0.0599440	−0.0299720	+	0.999551i	$0.509542\pi$
$200$	4.03749e6	0.0356867
$201$	1.10903e8	0.963291
$202$	−5.63347e7	−0.480891
$203$	1.12381e7	0.0942879
$204$	−2.63411e7	−0.217234
$205$	2.14279e8	1.73717
$206$	2.54665e7	0.202971
$207$	6.74820e7	0.528801
$208$	−8.99891e6	−0.0693375
$209$	−4.82587e7	−0.365649
$210$	−2.17282e7	−0.161904
$211$	−1.12925e7	−0.0827560	−0.0413780	−	0.999144i	$-0.513175\pi$
$211$	−1.12925e7	−0.0827560	−0.0413780	+	0.999144i	$0.513175\pi$
$212$	−6.96529e7	−0.502070
$213$	4.13781e7	0.293388
$214$	1.01411e8	0.707353
$215$	1.28141e7	0.0879336
$216$	1.00777e7	0.0680414
$217$	−6.57565e7	−0.436847
$218$	−3.47598e7	−0.227237
$219$	1.10007e8	0.707728
$220$	4.98429e7	0.315590
$221$	3.34904e7	0.208712
$222$	6.74923e7	0.414018
$223$	2.54415e8	1.53630	0.768151	−	0.640269i	$-0.221177\pi$
$223$	2.54415e8	1.53630	0.768151	+	0.640269i	$0.221177\pi$
$224$	−1.12394e7	−0.0668153
$225$	5.74869e6	0.0336457
$226$	−1.86163e8	−1.07279
$227$	−1.83630e8	−1.04197	−0.520984	−	0.853567i	$-0.674435\pi$
$227$	−1.83630e8	−1.04197	−0.520984	+	0.853567i	$0.674435\pi$
$228$	−3.14031e7	−0.175469
$229$	−4.61214e7	−0.253792	−0.126896	−	0.991916i	$-0.540501\pi$
$229$	−4.61214e7	−0.253792	−0.126896	+	0.991916i	$0.540501\pi$
$230$	2.17184e8	1.17701
$231$	−2.45926e7	−0.131269
$232$	−1.67752e7	−0.0881983
$233$	−2.11544e8	−1.09561	−0.547804	−	0.836607i	$-0.684536\pi$
$233$	−2.11544e8	−1.09561	−0.547804	+	0.836607i	$0.684536\pi$
$234$	−1.28129e7	−0.0653720
$235$	1.41546e8	0.711477
$236$	−1.18854e7	−0.0588602
$237$	−8.92194e7	−0.435351
$238$	4.18287e7	0.201120
$239$	−4.14545e7	−0.196417	−0.0982086	−	0.995166i	$-0.531311\pi$
$239$	−4.14545e7	−0.196417	−0.0982086	+	0.995166i	$0.531311\pi$
$240$	3.24340e7	0.151447
$241$	−5.27404e7	−0.242708	−0.121354	−	0.992609i	$-0.538724\pi$
$241$	−5.27404e7	−0.242708	−0.121354	+	0.992609i	$0.538724\pi$
$242$	−9.94838e7	−0.451231
$243$	1.43489e7	0.0641500
$244$	−1.37967e8	−0.608011
$245$	3.45036e7	0.149894
$246$	1.57818e8	0.675904
$247$	3.99263e7	0.168585
$248$	9.81555e7	0.408633
$249$	6.41688e7	0.263407
$250$	−1.64796e8	−0.667047
$251$	−4.66578e8	−1.86237	−0.931186	−	0.364544i	$-0.881225\pi$
$251$	−4.66578e8	−1.86237	−0.931186	+	0.364544i	$0.881225\pi$
$252$	−1.60030e7	−0.0629941
$253$	2.45814e8	0.954301
$254$	−2.13229e7	−0.0816448
$255$	−1.20706e8	−0.455868
$256$	1.67772e7	0.0625000
$257$	−9.61288e7	−0.353254	−0.176627	−	0.984278i	$-0.556519\pi$
$257$	−9.61288e7	−0.353254	−0.176627	+	0.984278i	$0.556519\pi$
$258$	9.43772e6	0.0342135
$259$	−1.07175e8	−0.383306
$260$	−4.12369e7	−0.145506
$261$	−2.38850e7	−0.0831541
$262$	−1.93211e8	−0.663708
$263$	2.37548e8	0.805206	0.402603	−	0.915375i	$-0.368106\pi$
$263$	2.37548e8	0.805206	0.402603	+	0.915375i	$0.368106\pi$
$264$	3.67097e7	0.122791
$265$	−3.19180e8	−1.05360
$266$	4.98670e7	0.162453
$267$	2.37457e8	0.763478
$268$	2.62882e8	0.834235
$269$	4.00675e8	1.25505	0.627523	−	0.778598i	$-0.284069\pi$
$269$	4.00675e8	1.25505	0.627523	+	0.778598i	$0.284069\pi$
$270$	4.61804e7	0.142786
$271$	−8.09647e7	−0.247117	−0.123559	−	0.992337i	$-0.539431\pi$
$271$	−8.09647e7	−0.247117	−0.123559	+	0.992337i	$0.539431\pi$
$272$	−6.24381e7	−0.188130
$273$	2.03464e7	0.0605228
$274$	−3.68945e8	−1.08352
$275$	2.09405e7	0.0607188
$276$	1.59957e8	0.457955
$277$	4.14169e8	1.17084	0.585421	−	0.810729i	$-0.300929\pi$
$277$	4.14169e8	1.17084	0.585421	+	0.810729i	$0.300929\pi$
$278$	2.67978e8	0.748069
$279$	1.39757e8	0.385263
$280$	−5.15039e7	−0.140213
$281$	1.22566e8	0.329533	0.164766	−	0.986333i	$-0.447313\pi$
$281$	1.22566e8	0.329533	0.164766	+	0.986333i	$0.447313\pi$
$282$	1.04250e8	0.276824
$283$	3.09333e8	0.811287	0.405643	−	0.914031i	$-0.367048\pi$
$283$	3.09333e8	0.811287	0.405643	+	0.914031i	$0.367048\pi$
$284$	9.80814e7	0.254081
$285$	−1.43903e8	−0.368224
$286$	−4.66731e7	−0.117974
$287$	−2.50610e8	−0.625766
$288$	2.38879e7	0.0589256
$289$	−1.77969e8	−0.433712
$290$	−7.68713e7	−0.185085
$291$	3.01335e8	0.716842
$292$	2.60758e8	0.612911
$293$	1.98194e8	0.460313	0.230157	−	0.973154i	$-0.426076\pi$
$293$	1.98194e8	0.460313	0.230157	+	0.973154i	$0.426076\pi$
$294$	2.54122e7	0.0583212
$295$	−5.44640e7	−0.123519
$296$	1.59982e8	0.358550
$297$	5.22682e7	0.115768
$298$	−3.82782e7	−0.0837905
$299$	−2.03372e8	−0.439989
$300$	1.36265e7	0.0291381
$301$	−1.49867e7	−0.0316756
$302$	7.56087e7	0.157960
$303$	−1.90130e8	−0.392646
$304$	−7.44371e7	−0.151961
$305$	−6.32225e8	−1.27592
$306$	−8.89012e7	−0.177371
$307$	2.83733e8	0.559661	0.279831	−	0.960049i	$-0.409722\pi$
$307$	2.83733e8	0.559661	0.279831	+	0.960049i	$0.409722\pi$
$308$	−5.82936e7	−0.113682
$309$	8.59495e7	0.165725
$310$	4.49791e8	0.857521
$311$	−1.97298e8	−0.371931	−0.185965	−	0.982556i	$-0.559541\pi$
$311$	−1.97298e8	−0.371931	−0.185965	+	0.982556i	$0.559541\pi$
$312$	−3.03713e7	−0.0566139
$313$	−1.14294e8	−0.210678	−0.105339	−	0.994436i	$-0.533593\pi$
$313$	−1.14294e8	−0.210678	−0.105339	+	0.994436i	$0.533593\pi$
$314$	1.11162e8	0.202629
$315$	−7.33327e7	−0.132194
$316$	−2.11483e8	−0.377025
$317$	2.05790e8	0.362841	0.181420	−	0.983406i	$-0.441931\pi$
$317$	2.05790e8	0.362841	0.181420	+	0.983406i	$0.441931\pi$
$318$	−2.35079e8	−0.409938
$319$	−8.70051e7	−0.150064
$320$	7.68805e7	0.131157
$321$	3.42262e8	0.577551
$322$	−2.54006e8	−0.423984
$323$	2.77025e8	0.457415
$324$	3.40122e7	0.0555556
$325$	−1.73249e7	−0.0279949
$326$	−1.40350e8	−0.224363
$327$	−1.17314e8	−0.185539
$328$	3.74088e8	0.585350
$329$	−1.65545e8	−0.256289
$330$	1.68220e8	0.257678
$331$	3.94439e8	0.597835	0.298918	−	0.954279i	$-0.403374\pi$
$331$	3.94439e8	0.597835	0.298918	+	0.954279i	$0.403374\pi$
$332$	1.52104e8	0.228117
$333$	2.27787e8	0.338044
$334$	−7.43174e8	−1.09138
$335$	1.20464e9	1.75065
$336$	−3.79331e7	−0.0545545
$337$	4.14965e6	0.00590618	0.00295309	−	0.999996i	$-0.499060\pi$
$337$	4.14965e6	0.00590618	0.00295309	+	0.999996i	$0.499060\pi$
$338$	3.86145e7	0.0543928
$339$	−6.28300e8	−0.875927
$340$	−2.86119e8	−0.394793
$341$	5.09086e8	0.695266
$342$	−1.05986e8	−0.143270
$343$	−4.03536e7	−0.0539949
$344$	2.23709e7	0.0296298
$345$	7.32994e8	0.961023
$346$	6.60216e8	0.856879
$347$	−4.27951e8	−0.549846	−0.274923	−	0.961466i	$-0.588652\pi$
$347$	−4.27951e8	−0.549846	−0.274923	+	0.961466i	$0.588652\pi$
$348$	−5.66163e7	−0.0720136
$349$	−3.16986e8	−0.399164	−0.199582	−	0.979881i	$-0.563958\pi$
$349$	−3.16986e8	−0.399164	−0.199582	+	0.979881i	$0.563958\pi$
$350$	−2.16384e7	−0.0269766
$351$	−4.32436e7	−0.0533761
$352$	8.70155e7	0.106340
$353$	1.10682e9	1.33927	0.669634	−	0.742691i	$-0.266451\pi$
$353$	1.10682e9	1.33927	0.669634	+	0.742691i	$0.266451\pi$
$354$	−4.01132e7	−0.0480591
$355$	4.49451e8	0.533192
$356$	5.62862e8	0.661191
$357$	1.41172e8	0.164214
$358$	1.63682e8	0.188543
$359$	−7.11409e8	−0.811501	−0.405750	−	0.913984i	$-0.632990\pi$
$359$	−7.11409e8	−0.811501	−0.405750	+	0.913984i	$0.632990\pi$
$360$	1.09465e8	0.123656
$361$	−5.63610e8	−0.630526
$362$	−3.46534e8	−0.383943
$363$	−3.35758e8	−0.368428
$364$	4.82285e7	0.0524142
$365$	1.19491e9	1.28620
$366$	−4.65639e8	−0.496439
$367$	−2.23649e8	−0.236176	−0.118088	−	0.993003i	$-0.537676\pi$
$367$	−2.23649e8	−0.236176	−0.118088	+	0.993003i	$0.537676\pi$
$368$	3.79158e8	0.396600
$369$	5.32637e8	0.551873
$370$	7.33106e8	0.752421
$371$	3.73296e8	0.379529
$372$	3.31275e8	0.333648
$373$	−5.99837e8	−0.598484	−0.299242	−	0.954177i	$-0.596734\pi$
$373$	−5.99837e8	−0.598484	−0.299242	+	0.954177i	$0.596734\pi$
$374$	−3.23837e8	−0.320093
$375$	−5.56186e8	−0.544641
$376$	2.47111e8	0.239737
$377$	7.19827e7	0.0691884
$378$	−5.40102e7	−0.0514344
$379$	−4.14201e8	−0.390817	−0.195409	−	0.980722i	$-0.562603\pi$
$379$	−4.14201e8	−0.390817	−0.195409	+	0.980722i	$0.562603\pi$
$380$	−3.41103e8	−0.318891
$381$	−7.19648e7	−0.0666627
$382$	5.65377e8	0.518939
$383$	−1.18355e9	−1.07644	−0.538220	−	0.842804i	$-0.680903\pi$
$383$	−1.18355e9	−1.07644	−0.538220	+	0.842804i	$0.680903\pi$
$384$	5.66231e7	0.0510310
$385$	−2.67127e8	−0.238564
$386$	7.49655e8	0.663446
$387$	3.18523e7	0.0279352
$388$	7.14275e8	0.620804
$389$	3.94260e8	0.339593	0.169796	−	0.985479i	$-0.445689\pi$
$389$	3.94260e8	0.339593	0.169796	+	0.985479i	$0.445689\pi$
$390$	−1.39175e8	−0.118805
$391$	−1.41108e9	−1.19380
$392$	6.02363e7	0.0505076
$393$	−6.52087e8	−0.541915
$394$	1.31359e9	1.08199
$395$	−9.69107e8	−0.791192
$396$	1.23895e8	0.100258
$397$	3.79680e8	0.304544	0.152272	−	0.988339i	$-0.451341\pi$
$397$	3.79680e8	0.304544	0.152272	+	0.988339i	$0.451341\pi$
$398$	−5.33116e7	−0.0423868
$399$	1.68301e8	0.132642
$400$	3.22999e7	0.0252343
$401$	6.95783e8	0.538851	0.269425	−	0.963021i	$-0.413166\pi$
$401$	6.95783e8	0.538851	0.269425	+	0.963021i	$0.413166\pi$
$402$	8.87225e8	0.681150
$403$	−4.21187e8	−0.320558
$404$	−4.50678e8	−0.340041
$405$	1.55859e8	0.116584
$406$	8.99047e7	0.0666716
$407$	8.29750e8	0.610052
$408$	−2.10729e8	−0.153608
$409$	5.46148e8	0.394710	0.197355	−	0.980332i	$-0.436765\pi$
$409$	5.46148e8	0.394710	0.197355	+	0.980332i	$0.436765\pi$
$410$	1.71424e9	1.22836
$411$	−1.24519e9	−0.884687
$412$	2.03732e8	0.143522
$413$	6.36983e7	0.0444941
$414$	5.39856e8	0.373918
$415$	6.97006e8	0.478705
$416$	−7.19913e7	−0.0490290
$417$	9.04424e8	0.610796
$418$	−3.86070e8	−0.258553
$419$	−1.02912e9	−0.683469	−0.341735	−	0.939796i	$-0.611014\pi$
$419$	−1.02912e9	−0.683469	−0.341735	+	0.939796i	$0.611014\pi$
$420$	−1.73826e8	−0.114483
$421$	2.13611e9	1.39520	0.697599	−	0.716488i	$-0.254252\pi$
$421$	2.13611e9	1.39520	0.697599	+	0.716488i	$0.254252\pi$
$422$	−9.03396e7	−0.0585173
$423$	3.51844e8	0.226026
$424$	−5.57223e8	−0.355017
$425$	−1.20207e8	−0.0759574
$426$	3.31025e8	0.207456
$427$	7.39418e8	0.459613
$428$	8.11287e8	0.500174
$429$	−1.57522e8	−0.0963252
$430$	1.02513e8	0.0621785
$431$	−1.71835e9	−1.03381	−0.516906	−	0.856042i	$-0.672916\pi$
$431$	−1.71835e9	−1.03381	−0.516906	+	0.856042i	$0.672916\pi$
$432$	8.06216e7	0.0481125
$433$	−6.39328e8	−0.378457	−0.189228	−	0.981933i	$-0.560599\pi$
$433$	−6.39328e8	−0.378457	−0.189228	+	0.981933i	$0.560599\pi$
$434$	−5.26052e8	−0.308898
$435$	−2.59441e8	−0.151121
$436$	−2.78079e8	−0.160681
$437$	−1.68225e9	−0.964284
$438$	8.80058e8	0.500440
$439$	1.64099e8	0.0925718	0.0462859	−	0.998928i	$-0.485261\pi$
$439$	1.64099e8	0.0925718	0.0462859	+	0.998928i	$0.485261\pi$
$440$	3.98743e8	0.223156
$441$	8.57661e7	0.0476190
$442$	2.67923e8	0.147582
$443$	−2.15834e9	−1.17952	−0.589761	−	0.807578i	$-0.700778\pi$
$443$	−2.15834e9	−1.17952	−0.589761	+	0.807578i	$0.700778\pi$
$444$	5.39939e8	0.292755
$445$	2.57928e9	1.38752
$446$	2.03532e9	1.08633
$447$	−1.29189e8	−0.0684146
$448$	−8.99154e7	−0.0472456
$449$	−2.53498e9	−1.32164	−0.660819	−	0.750545i	$-0.729791\pi$
$449$	−2.53498e9	−1.32164	−0.660819	+	0.750545i	$0.729791\pi$
$450$	4.59895e7	0.0237911
$451$	1.94022e9	0.995939
$452$	−1.48930e9	−0.758575
$453$	2.55179e8	0.128974
$454$	−1.46904e9	−0.736782
$455$	2.21004e8	0.109992
$456$	−2.51225e8	−0.124076
$457$	−2.71505e9	−1.33067	−0.665337	−	0.746543i	$-0.731712\pi$
$457$	−2.71505e9	−1.33067	−0.665337	+	0.746543i	$0.731712\pi$
$458$	−3.68971e8	−0.179458
$459$	−3.00041e8	−0.144823
$460$	1.73747e9	0.832270
$461$	−2.82877e9	−1.34476	−0.672379	−	0.740207i	$-0.734727\pi$
$461$	−2.82877e9	−1.34476	−0.672379	+	0.740207i	$0.734727\pi$
$462$	−1.96741e8	−0.0928213
$463$	2.77949e9	1.30146	0.650732	−	0.759308i	$-0.274462\pi$
$463$	2.77949e9	1.30146	0.650732	+	0.759308i	$0.274462\pi$
$464$	−1.34202e8	−0.0623656
$465$	1.51804e9	0.700163
$466$	−1.69235e9	−0.774712
$467$	1.21049e9	0.549984	0.274992	−	0.961446i	$-0.411325\pi$
$467$	1.21049e9	0.549984	0.274992	+	0.961446i	$0.411325\pi$
$468$	−1.02503e8	−0.0462250
$469$	−1.40888e9	−0.630622
$470$	1.13237e9	0.503090
$471$	3.75171e8	0.165446
$472$	−9.50831e7	−0.0416204
$473$	1.16027e8	0.0504134
$474$	−7.13755e8	−0.307840
$475$	−1.43308e8	−0.0613540
$476$	3.34629e8	0.142213
$477$	−7.93390e8	−0.334713
$478$	−3.31636e8	−0.138888
$479$	1.33300e9	0.554185	0.277092	−	0.960843i	$-0.410629\pi$
$479$	1.33300e9	0.554185	0.277092	+	0.960843i	$0.410629\pi$
$480$	2.59472e8	0.107089
$481$	−6.86485e8	−0.281270
$482$	−4.21923e8	−0.171620
$483$	−8.57272e8	−0.346181
$484$	−7.95871e8	−0.319068
$485$	3.27312e9	1.30276
$486$	1.14791e8	0.0453609
$487$	−1.62030e9	−0.635686	−0.317843	−	0.948143i	$-0.602959\pi$
$487$	−1.62030e9	−0.635686	−0.317843	+	0.948143i	$0.602959\pi$
$488$	−1.10374e9	−0.429929
$489$	−4.73682e8	−0.183192
$490$	2.76029e8	0.105991
$491$	−3.58029e9	−1.36500	−0.682501	−	0.730885i	$-0.739108\pi$
$491$	−3.58029e9	−1.36500	−0.682501	+	0.730885i	$0.739108\pi$
$492$	1.26255e9	0.477936
$493$	4.99445e8	0.187726
$494$	3.19411e8	0.119208
$495$	5.67741e8	0.210393
$496$	7.85244e8	0.288947
$497$	−5.25655e8	−0.192067
$498$	5.13351e8	0.186257
$499$	8.83468e8	0.318302	0.159151	−	0.987254i	$-0.449124\pi$
$499$	8.83468e8	0.318302	0.159151	+	0.987254i	$0.449124\pi$
$500$	−1.31837e9	−0.471673
$501$	−2.50821e9	−0.891112
$502$	−3.73263e9	−1.31690
$503$	−3.16367e9	−1.10842	−0.554208	−	0.832378i	$-0.686979\pi$
$503$	−3.16367e9	−1.10842	−0.554208	+	0.832378i	$0.686979\pi$
$504$	−1.28024e8	−0.0445435
$505$	−2.06520e9	−0.713580
$506$	1.96651e9	0.674793
$507$	1.30324e8	0.0444116
$508$	−1.70583e8	−0.0577316
$509$	2.69133e9	0.904596	0.452298	−	0.891867i	$-0.350604\pi$
$509$	2.69133e9	0.904596	0.452298	+	0.891867i	$0.350604\pi$
$510$	−9.65650e8	−0.322348
$511$	−1.39750e9	−0.463317
$512$	1.34218e8	0.0441942
$513$	−3.57701e8	−0.116980
$514$	−7.69030e8	−0.249788
$515$	9.33590e8	0.301183
$516$	7.55018e7	0.0241926
$517$	1.28165e9	0.407898
$518$	−8.57403e8	−0.271038
$519$	2.22823e9	0.699639
$520$	−3.29895e8	−0.102888
$521$	−1.99511e6	−0.000618066 0	−0.000309033	−	1.00000i	$-0.500098\pi$
$521$	−1.99511e6	−0.000618066 0	−0.000309033		1.00000i	$0.500098\pi$
$522$	−1.91080e8	−0.0587989
$523$	−4.39613e9	−1.34374	−0.671869	−	0.740670i	$-0.734508\pi$
$523$	−4.39613e9	−1.34374	−0.671869	+	0.740670i	$0.734508\pi$
$524$	−1.54569e9	−0.469313
$525$	−7.30296e7	−0.0220263
$526$	1.90039e9	0.569366
$527$	−2.92236e9	−0.869756
$528$	2.93677e8	0.0868264
$529$	5.16400e9	1.51667
$530$	−2.55344e9	−0.745007
$531$	−1.35382e8	−0.0392401
$532$	3.98936e8	0.114872
$533$	−1.60522e9	−0.459186
$534$	1.89966e9	0.539860
$535$	3.71767e9	1.04962
$536$	2.10305e9	0.589893
$537$	5.52428e8	0.153945
$538$	3.20540e9	0.887452
$539$	3.12417e8	0.0859358
$540$	3.69443e8	0.100965
$541$	−2.95416e8	−0.0802127	−0.0401064	−	0.999195i	$-0.512770\pi$
$541$	−2.95416e8	−0.0802127	−0.0401064	+	0.999195i	$0.512770\pi$
$542$	−6.47718e8	−0.174738
$543$	−1.16955e9	−0.313488
$544$	−4.99505e8	−0.133028
$545$	−1.27428e9	−0.337191
$546$	1.62771e8	0.0427960
$547$	−3.88443e9	−1.01478	−0.507390	−	0.861717i	$-0.669390\pi$
$547$	−3.88443e9	−1.01478	−0.507390	+	0.861717i	$0.669390\pi$
$548$	−2.95156e9	−0.766161
$549$	−1.57153e9	−0.405340
$550$	1.67524e8	0.0429347
$551$	5.95425e8	0.151634
$552$	1.27966e9	0.323823
$553$	1.13342e9	0.285004
$554$	3.31335e9	0.827910
$555$	2.47423e9	0.614349
$556$	2.14382e9	0.528965
$557$	2.37248e9	0.581714	0.290857	−	0.956767i	$-0.406060\pi$
$557$	2.37248e9	0.581714	0.290857	+	0.956767i	$0.406060\pi$
$558$	1.11805e9	0.272422
$559$	−9.59938e7	−0.0232435
$560$	−4.12031e8	−0.0991453
$561$	−1.09295e9	−0.261355
$562$	9.80529e8	0.233015
$563$	3.03328e9	0.716364	0.358182	−	0.933652i	$-0.383397\pi$
$563$	3.03328e9	0.716364	0.358182	+	0.933652i	$0.383397\pi$
$564$	8.34000e8	0.195744
$565$	−6.82464e9	−1.59188
$566$	2.47467e9	0.573666
$567$	−1.82284e8	−0.0419961
$568$	7.84651e8	0.179662
$569$	−6.38227e9	−1.45239	−0.726194	−	0.687490i	$-0.758712\pi$
$569$	−6.38227e9	−1.45239	−0.726194	+	0.687490i	$0.758712\pi$
$570$	−1.15122e9	−0.260374
$571$	−1.09084e9	−0.245208	−0.122604	−	0.992456i	$-0.539124\pi$
$571$	−1.09084e9	−0.245208	−0.122604	+	0.992456i	$0.539124\pi$
$572$	−3.73385e8	−0.0834201
$573$	1.90815e9	0.423712
$574$	−2.00488e9	−0.442483
$575$	7.29965e8	0.160127
$576$	1.91103e8	0.0416667
$577$	−8.51184e9	−1.84462	−0.922312	−	0.386445i	$-0.873703\pi$
$577$	−8.51184e9	−1.84462	−0.922312	+	0.386445i	$0.873703\pi$
$578$	−1.42375e9	−0.306681
$579$	2.53008e9	0.541701
$580$	−6.14971e8	−0.130875
$581$	−8.15182e8	−0.172440
$582$	2.41068e9	0.506884
$583$	−2.89005e9	−0.604041
$584$	2.08606e9	0.433393
$585$	−4.69714e8	−0.0970037
$586$	1.58555e9	0.325491
$587$	−2.10447e9	−0.429448	−0.214724	−	0.976675i	$-0.568885\pi$
$587$	−2.10447e9	−0.429448	−0.214724	+	0.976675i	$0.568885\pi$
$588$	2.03297e8	0.0412393
$589$	−3.48396e9	−0.702539
$590$	−4.35712e8	−0.0873409
$591$	4.43336e9	0.883439
$592$	1.27985e9	0.253533
$593$	9.65769e9	1.90187	0.950937	−	0.309383i	$-0.100123\pi$
$593$	9.65769e9	1.90187	0.950937	+	0.309383i	$0.100123\pi$
$594$	4.18146e8	0.0818607
$595$	1.53342e9	0.298436
$596$	−3.06226e8	−0.0592488
$597$	−1.79927e8	−0.0346087
$598$	−1.62697e9	−0.311119
$599$	1.53620e9	0.292047	0.146024	−	0.989281i	$-0.453352\pi$
$599$	1.53620e9	0.292047	0.146024	+	0.989281i	$0.453352\pi$
$600$	1.09012e8	0.0206037
$601$	−3.91715e8	−0.0736053	−0.0368026	−	0.999323i	$-0.511717\pi$
$601$	−3.91715e8	−0.0736053	−0.0368026	+	0.999323i	$0.511717\pi$
$602$	−1.19894e8	−0.0223980
$603$	2.99439e9	0.556157
$604$	6.04870e8	0.111695
$605$	−3.64703e9	−0.669569
$606$	−1.52104e9	−0.277642
$607$	−9.08900e9	−1.64951	−0.824756	−	0.565488i	$-0.808688\pi$
$607$	−9.08900e9	−1.64951	−0.824756	+	0.565488i	$0.808688\pi$
$608$	−5.95496e8	−0.107453
$609$	3.03428e8	0.0544372
$610$	−5.05780e9	−0.902210
$611$	−1.06036e9	−0.188065
$612$	−7.11209e8	−0.125420
$613$	3.77174e9	0.661349	0.330674	−	0.943745i	$-0.392724\pi$
$613$	3.77174e9	0.661349	0.330674	+	0.943745i	$0.392724\pi$
$614$	2.26986e9	0.395740
$615$	5.78554e9	1.00295
$616$	−4.66349e8	−0.0803856
$617$	−9.27856e9	−1.59031	−0.795156	−	0.606405i	$-0.792611\pi$
$617$	−9.27856e9	−1.59031	−0.795156	+	0.606405i	$0.792611\pi$
$618$	6.87596e8	0.117186
$619$	4.43289e9	0.751225	0.375613	−	0.926777i	$-0.377432\pi$
$619$	4.43289e9	0.751225	0.375613	+	0.926777i	$0.377432\pi$
$620$	3.59833e9	0.606359
$621$	1.82201e9	0.305303
$622$	−1.57839e9	−0.262995
$623$	−3.01659e9	−0.499813
$624$	−2.42971e8	−0.0400320
$625$	−6.65740e9	−1.09075
$626$	−9.14353e8	−0.148972
$627$	−1.30299e9	−0.211107
$628$	8.89294e8	0.143280
$629$	−4.76311e9	−0.763156
$630$	−5.86662e8	−0.0934751
$631$	−3.39978e9	−0.538702	−0.269351	−	0.963042i	$-0.586809\pi$
$631$	−3.39978e9	−0.538702	−0.269351	+	0.963042i	$0.586809\pi$
$632$	−1.69186e9	−0.266597
$633$	−3.04896e8	−0.0477792
$634$	1.64632e9	0.256567
$635$	−7.81687e8	−0.121150
$636$	−1.88063e9	−0.289870
$637$	−2.58475e8	−0.0396214
$638$	−6.96041e8	−0.106111
$639$	1.11721e9	0.169387
$640$	6.15044e8	0.0927420
$641$	2.14174e9	0.321192	0.160596	−	0.987020i	$-0.448658\pi$
$641$	2.14174e9	0.321192	0.160596	+	0.987020i	$0.448658\pi$
$642$	2.73809e9	0.408391
$643$	−8.76427e9	−1.30010	−0.650051	−	0.759891i	$-0.725252\pi$
$643$	−8.76427e9	−1.30010	−0.650051	+	0.759891i	$0.725252\pi$
$644$	−2.03205e9	−0.299802
$645$	3.45982e8	0.0507685
$646$	2.21620e9	0.323441
$647$	−2.17316e9	−0.315447	−0.157724	−	0.987483i	$-0.550416\pi$
$647$	−2.17316e9	−0.315447	−0.157724	+	0.987483i	$0.550416\pi$
$648$	2.72098e8	0.0392837
$649$	−4.93151e8	−0.0708147
$650$	−1.38599e8	−0.0197954
$651$	−1.77543e9	−0.252214
$652$	−1.12280e9	−0.158649
$653$	−6.07939e9	−0.854405	−0.427203	−	0.904156i	$-0.640501\pi$
$653$	−6.07939e9	−0.854405	−0.427203	+	0.904156i	$0.640501\pi$
$654$	−9.38515e8	−0.131196
$655$	−7.08301e9	−0.984858
$656$	2.99271e9	0.413905
$657$	2.97019e9	0.408607
$658$	−1.32436e9	−0.181224
$659$	−2.72789e9	−0.371302	−0.185651	−	0.982616i	$-0.559439\pi$
$659$	−2.72789e9	−0.371302	−0.185651	+	0.982616i	$0.559439\pi$
$660$	1.34576e9	0.182206
$661$	4.80542e9	0.647182	0.323591	−	0.946197i	$-0.395110\pi$
$661$	4.80542e9	0.647182	0.323591	+	0.946197i	$0.395110\pi$
$662$	3.15551e9	0.422733
$663$	9.04240e8	0.120500
$664$	1.21683e9	0.161303
$665$	1.82810e9	0.241059
$666$	1.82229e9	0.239033
$667$	−3.03290e9	−0.395748
$668$	−5.94539e9	−0.771726
$669$	6.86922e9	0.886984
$670$	9.63710e9	1.23790
$671$	−5.72456e9	−0.731499
$672$	−3.03464e8	−0.0385758
$673$	−8.13635e9	−1.02891	−0.514455	−	0.857518i	$-0.672006\pi$
$673$	−8.13635e9	−1.02891	−0.514455	+	0.857518i	$0.672006\pi$
$674$	3.31972e7	0.00417630
$675$	1.55215e8	0.0194254
$676$	3.08916e8	0.0384615
$677$	−8.04527e9	−0.996506	−0.498253	−	0.867032i	$-0.666025\pi$
$677$	−8.04527e9	−0.996506	−0.498253	+	0.867032i	$0.666025\pi$
$678$	−5.02640e9	−0.619374
$679$	−3.82807e9	−0.469283
$680$	−2.28895e9	−0.279161
$681$	−4.95802e9	−0.601580
$682$	4.07269e9	0.491627
$683$	1.00751e10	1.20998	0.604991	−	0.796232i	$-0.293177\pi$
$683$	1.00751e10	1.20998	0.604991	+	0.796232i	$0.293177\pi$
$684$	−8.47885e8	−0.101307
$685$	−1.35253e10	−1.60780
$686$	−3.22829e8	−0.0381802
$687$	−1.24528e9	−0.146527
$688$	1.78967e8	0.0209514
$689$	2.39105e9	0.278498
$690$	5.86396e9	0.679546
$691$	−1.64264e10	−1.89395	−0.946977	−	0.321302i	$-0.895880\pi$
$691$	−1.64264e10	−1.89395	−0.946977	+	0.321302i	$0.895880\pi$
$692$	5.28173e9	0.605905
$693$	−6.64000e8	−0.0757883
$694$	−3.42361e9	−0.388800
$695$	9.82392e9	1.11004
$696$	−4.52931e8	−0.0509213
$697$	−1.11377e10	−1.24589
$698$	−2.53589e9	−0.282252
$699$	−5.71169e9	−0.632550
$700$	−1.73107e8	−0.0190753
$701$	−1.00620e10	−1.10324	−0.551622	−	0.834095i	$-0.685991\pi$
$701$	−1.00620e10	−1.10324	−0.551622	+	0.834095i	$0.685991\pi$
$702$	−3.45948e8	−0.0377426
$703$	−5.67845e9	−0.616434
$704$	6.96124e8	0.0751938
$705$	3.82175e9	0.410772
$706$	8.85460e9	0.947005
$707$	2.41535e9	0.257047
$708$	−3.20906e8	−0.0339829
$709$	2.30941e8	0.0243355	0.0121677	−	0.999926i	$-0.496127\pi$
$709$	2.30941e8	0.0243355	0.0121677	+	0.999926i	$0.496127\pi$
$710$	3.59561e9	0.377024
$711$	−2.40892e9	−0.251350
$712$	4.50290e9	0.467533
$713$	1.77462e10	1.83355
$714$	1.12937e9	0.116117
$715$	−1.71101e9	−0.175058
$716$	1.30946e9	0.133320
$717$	−1.11927e9	−0.113401
$718$	−5.69127e9	−0.573818
$719$	1.68991e10	1.69556	0.847779	−	0.530350i	$-0.177939\pi$
$719$	1.68991e10	1.69556	0.847779	+	0.530350i	$0.177939\pi$
$720$	8.75717e8	0.0874380
$721$	−1.09188e9	−0.108493
$722$	−4.50888e9	−0.445850
$723$	−1.42399e9	−0.140127
$724$	−2.77228e9	−0.271489
$725$	−2.58368e8	−0.0251800
$726$	−2.68606e9	−0.260518
$727$	−1.22957e10	−1.18681	−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−1.22957e10	−1.18681	−0.593407	+	0.804902i	$0.702218\pi$
$728$	3.85828e8	0.0370625
$729$	3.87420e8	0.0370370
$730$	9.55924e9	0.909481
$731$	−6.66045e8	−0.0630656
$732$	−3.72511e9	−0.351035
$733$	1.20913e10	1.13399	0.566994	−	0.823722i	$-0.308106\pi$
$733$	1.20913e10	1.13399	0.566994	+	0.823722i	$0.308106\pi$
$734$	−1.78919e9	−0.167002
$735$	9.31597e8	0.0865411
$736$	3.03327e9	0.280439
$737$	1.09075e10	1.00367
$738$	4.26110e9	0.390233
$739$	1.83975e10	1.67688	0.838441	−	0.544993i	$-0.183468\pi$
$739$	1.83975e10	1.67688	0.838441	+	0.544993i	$0.183468\pi$
$740$	5.86485e9	0.532042
$741$	1.07801e9	0.0973328
$742$	2.98637e9	0.268367
$743$	−1.27926e10	−1.14419	−0.572095	−	0.820187i	$-0.693869\pi$
$743$	−1.27926e10	−1.14419	−0.572095	+	0.820187i	$0.693869\pi$
$744$	2.65020e9	0.235924
$745$	−1.40326e9	−0.124334
$746$	−4.79870e9	−0.423192
$747$	1.73256e9	0.152078
$748$	−2.59070e9	−0.226340
$749$	−4.34799e9	−0.378096
$750$	−4.44949e9	−0.385120
$751$	−9.16776e9	−0.789812	−0.394906	−	0.918722i	$-0.629223\pi$
$751$	−9.16776e9	−0.789812	−0.394906	+	0.918722i	$0.629223\pi$
$752$	1.97689e9	0.169520
$753$	−1.25976e10	−1.07524
$754$	5.75862e8	0.0489236
$755$	2.77178e9	0.234392
$756$	−4.32081e8	−0.0363696
$757$	−2.13936e10	−1.79246	−0.896229	−	0.443592i	$-0.853704\pi$
$757$	−2.13936e10	−1.79246	−0.896229	+	0.443592i	$0.853704\pi$
$758$	−3.31361e9	−0.276349
$759$	6.63699e9	0.550966
$760$	−2.72882e9	−0.225490
$761$	−1.82263e10	−1.49917	−0.749587	−	0.661905i	$-0.769748\pi$
$761$	−1.82263e10	−1.49917	−0.749587	+	0.661905i	$0.769748\pi$
$762$	−5.75719e8	−0.0471376
$763$	1.49033e9	0.121463
$764$	4.52301e9	0.366945
$765$	−3.25907e9	−0.263196
$766$	−9.46838e9	−0.761158
$767$	4.08003e8	0.0326497
$768$	4.52985e8	0.0360844
$769$	−1.14269e10	−0.906124	−0.453062	−	0.891479i	$-0.649668\pi$
$769$	−1.14269e10	−0.906124	−0.453062	+	0.891479i	$0.649668\pi$
$770$	−2.13701e9	−0.168690
$771$	−2.59548e9	−0.203951
$772$	5.99724e9	0.469127
$773$	−2.18828e10	−1.70402	−0.852011	−	0.523524i	$-0.824617\pi$
$773$	−2.18828e10	−1.70402	−0.852011	+	0.523524i	$0.824617\pi$
$774$	2.54818e8	0.0197532
$775$	1.51177e9	0.116662
$776$	5.71420e9	0.438974
$777$	−2.89373e9	−0.221302
$778$	3.15408e9	0.240129
$779$	−1.32780e10	−1.00636
$780$	−1.11340e9	−0.0840077
$781$	4.06961e9	0.305685
$782$	−1.12886e10	−0.844145
$783$	−6.44896e8	−0.0480091
$784$	4.81890e8	0.0357143
$785$	4.07513e9	0.300675
$786$	−5.21670e9	−0.383192
$787$	−1.56896e10	−1.14736	−0.573681	−	0.819079i	$-0.694485\pi$
$787$	−1.56896e10	−1.14736	−0.573681	+	0.819079i	$0.694485\pi$
$788$	1.05087e10	0.765081
$789$	6.41380e9	0.464886
$790$	−7.75285e9	−0.559457
$791$	7.98173e9	0.573429
$792$	9.91161e8	0.0708934
$793$	4.73615e9	0.337264
$794$	3.03744e9	0.215345
$795$	−8.61786e9	−0.608295
$796$	−4.26493e8	−0.0299720
$797$	2.18427e10	1.52827	0.764137	−	0.645054i	$-0.223165\pi$
$797$	2.18427e10	1.52827	0.764137	+	0.645054i	$0.223165\pi$
$798$	1.34641e9	0.0937923
$799$	−7.35719e9	−0.510268
$800$	2.58399e8	0.0178433
$801$	6.41135e9	0.440794
$802$	5.56626e9	0.381025
$803$	1.08194e10	0.737394
$804$	7.09780e9	0.481646
$805$	−9.31174e9	−0.629137
$806$	−3.36949e9	−0.226669
$807$	1.08182e10	0.724601
$808$	−3.60542e9	−0.240445
$809$	−1.32224e10	−0.877992	−0.438996	−	0.898489i	$-0.644666\pi$
$809$	−1.32224e10	−0.877992	−0.438996	+	0.898489i	$0.644666\pi$
$810$	1.24687e9	0.0824373
$811$	1.44955e10	0.954243	0.477121	−	0.878837i	$-0.341680\pi$
$811$	1.44955e10	0.954243	0.477121	+	0.878837i	$0.341680\pi$
$812$	7.19237e8	0.0471440
$813$	−2.18605e9	−0.142673
$814$	6.63800e9	0.431372
$815$	−5.14516e9	−0.332926
$816$	−1.68583e9	−0.108617
$817$	−7.94040e8	−0.0509408
$818$	4.36918e9	0.279102
$819$	5.49353e8	0.0349428
$820$	1.37139e10	0.868584
$821$	−8.02005e9	−0.505797	−0.252898	−	0.967493i	$-0.581384\pi$
$821$	−8.02005e9	−0.505797	−0.252898	+	0.967493i	$0.581384\pi$
$822$	−9.96152e9	−0.625568
$823$	−8.76172e9	−0.547886	−0.273943	−	0.961746i	$-0.588328\pi$
$823$	−8.76172e9	−0.547886	−0.273943	+	0.961746i	$0.588328\pi$
$824$	1.62986e9	0.101486
$825$	5.65395e8	0.0350560
$826$	5.09586e8	0.0314621
$827$	2.47118e10	1.51927	0.759635	−	0.650350i	$-0.225378\pi$
$827$	2.47118e10	1.51927	0.759635	+	0.650350i	$0.225378\pi$
$828$	4.31885e9	0.264400
$829$	−3.04675e10	−1.85736	−0.928681	−	0.370879i	$-0.879056\pi$
$829$	−3.04675e10	−1.85736	−0.928681	+	0.370879i	$0.879056\pi$
$830$	5.57605e9	0.338496
$831$	1.11826e10	0.675986
$832$	−5.75930e8	−0.0346688
$833$	−1.79340e9	−0.107503
$834$	7.23539e9	0.431898
$835$	−2.72444e10	−1.61947
$836$	−3.08856e9	−0.182824
$837$	3.77343e9	0.222432
$838$	−8.23300e9	−0.483286
$839$	2.84565e10	1.66347	0.831736	−	0.555172i	$-0.187348\pi$
$839$	2.84565e10	1.66347	0.831736	+	0.555172i	$0.187348\pi$
$840$	−1.39061e9	−0.0809518
$841$	−1.61764e10	−0.937769
$842$	1.70889e10	0.986554
$843$	3.30929e9	0.190256
$844$	−7.22717e8	−0.0413780
$845$	1.41559e9	0.0807120
$846$	2.81475e9	0.159825
$847$	4.26537e9	0.241193
$848$	−4.45779e9	−0.251035
$849$	8.35200e9	0.468397
$850$	−9.61659e8	−0.0537100
$851$	2.89242e10	1.60882
$852$	2.64820e9	0.146694
$853$	2.73801e10	1.51047	0.755236	−	0.655453i	$-0.227522\pi$
$853$	2.73801e10	1.51047	0.755236	+	0.655453i	$0.227522\pi$
$854$	5.91534e9	0.324995
$855$	−3.88538e9	−0.212594
$856$	6.49030e9	0.353677
$857$	3.58732e10	1.94687	0.973436	−	0.228961i	$-0.0735327\pi$
$857$	3.58732e10	1.94687	0.973436	+	0.228961i	$0.0735327\pi$
$858$	−1.26017e9	−0.0681122
$859$	3.58260e9	0.192851	0.0964256	−	0.995340i	$-0.469259\pi$
$859$	3.58260e9	0.192851	0.0964256	+	0.995340i	$0.469259\pi$
$860$	8.20105e8	0.0439668
$861$	−6.76647e9	−0.361286
$862$	−1.37468e10	−0.731015
$863$	−2.22290e10	−1.17729	−0.588643	−	0.808393i	$-0.700337\pi$
$863$	−2.22290e10	−1.17729	−0.588643	+	0.808393i	$0.700337\pi$
$864$	6.44973e8	0.0340207
$865$	2.42032e10	1.27150
$866$	−5.11462e9	−0.267609
$867$	−4.80516e9	−0.250404
$868$	−4.20842e9	−0.218424
$869$	−8.77490e9	−0.453600
$870$	−2.07553e9	−0.106859
$871$	−9.02423e9	−0.462750
$872$	−2.22463e9	−0.113619
$873$	8.13603e9	0.413869
$874$	−1.34580e10	−0.681852
$875$	7.06562e9	0.356552
$876$	7.04046e9	0.353864
$877$	−3.10644e10	−1.55512	−0.777562	−	0.628807i	$-0.783544\pi$
$877$	−3.10644e10	−1.55512	−0.777562	+	0.628807i	$0.783544\pi$
$878$	1.31279e9	0.0654582
$879$	5.35123e9	0.265762
$880$	3.18994e9	0.157795
$881$	3.99473e10	1.96821	0.984105	−	0.177589i	$-0.0568297\pi$
$881$	3.99473e10	1.96821	0.984105	+	0.177589i	$0.0568297\pi$
$882$	6.86129e8	0.0336718
$883$	−1.58446e10	−0.774495	−0.387247	−	0.921976i	$-0.626574\pi$
$883$	−1.58446e10	−0.774495	−0.387247	+	0.921976i	$0.626574\pi$
$884$	2.14338e9	0.104356
$885$	−1.47053e9	−0.0713135
$886$	−1.72667e10	−0.834048
$887$	1.78077e10	0.856790	0.428395	−	0.903592i	$-0.359079\pi$
$887$	1.78077e10	0.856790	0.428395	+	0.903592i	$0.359079\pi$
$888$	4.31951e9	0.207009
$889$	9.14220e8	0.0436410
$890$	2.06342e10	0.981122
$891$	1.41124e9	0.0668390
$892$	1.62826e10	0.768151
$893$	−8.77105e9	−0.412165
$894$	−1.03351e9	−0.0483764
$895$	6.00051e9	0.279774
$896$	−7.19323e8	−0.0334077
$897$	−5.49104e9	−0.254028
$898$	−2.02798e10	−0.934539
$899$	−6.28120e9	−0.288326
$900$	3.67916e8	0.0168229
$901$	1.65901e10	0.755636
$902$	1.55218e10	0.704235
$903$	−4.04642e8	−0.0182879
$904$	−1.19144e10	−0.536394
$905$	−1.27038e10	−0.569722
$906$	2.04143e9	0.0911983
$907$	−1.35570e10	−0.603308	−0.301654	−	0.953417i	$-0.597539\pi$
$907$	−1.35570e10	−0.603308	−0.301654	+	0.953417i	$0.597539\pi$
$908$	−1.17523e10	−0.520984
$909$	−5.13350e9	−0.226694
$910$	1.76803e9	0.0777760
$911$	3.91227e10	1.71441	0.857205	−	0.514976i	$-0.172199\pi$
$911$	3.91227e10	1.71441	0.857205	+	0.514976i	$0.172199\pi$
$912$	−2.00980e9	−0.0877346
$913$	6.31113e9	0.274448
$914$	−2.17204e10	−0.940929
$915$	−1.70701e10	−0.736651
$916$	−2.95177e9	−0.126896
$917$	8.28392e9	0.354767
$918$	−2.40033e9	−0.102405
$919$	−3.96217e10	−1.68395	−0.841974	−	0.539518i	$-0.818607\pi$
$919$	−3.96217e10	−1.68395	−0.841974	+	0.539518i	$0.818607\pi$
$920$	1.38997e10	0.588504
$921$	7.66079e9	0.323121
$922$	−2.26301e10	−0.950888
$923$	−3.36695e9	−0.140939
$924$	−1.57393e9	−0.0656346
$925$	2.46401e9	0.102364
$926$	2.22359e10	0.920273
$927$	2.32064e9	0.0956816
$928$	−1.07361e9	−0.0440991
$929$	2.73958e10	1.12106	0.560529	−	0.828135i	$-0.310598\pi$
$929$	2.73958e10	1.12106	0.560529	+	0.828135i	$0.310598\pi$
$930$	1.21444e10	0.495090
$931$	−2.13805e9	−0.0868348
$932$	−1.35388e10	−0.547804
$933$	−5.32706e9	−0.214734
$934$	9.68388e9	0.388898
$935$	−1.18717e10	−0.474977
$936$	−8.20026e8	−0.0326860
$937$	−1.15104e9	−0.0457089	−0.0228545	−	0.999739i	$-0.507275\pi$
$937$	−1.15104e9	−0.0457089	−0.0228545	+	0.999739i	$0.507275\pi$
$938$	−1.12710e10	−0.445917
$939$	−3.08594e9	−0.121635
$940$	9.05896e9	0.355739
$941$	4.46646e9	0.174743	0.0873715	−	0.996176i	$-0.472153\pi$
$941$	4.46646e9	0.174743	0.0873715	+	0.996176i	$0.472153\pi$
$942$	3.00137e9	0.116988
$943$	6.76340e10	2.62648
$944$	−7.60665e8	−0.0294301
$945$	−1.97998e9	−0.0763221
$946$	9.28218e8	0.0356477
$947$	9.53211e9	0.364724	0.182362	−	0.983231i	$-0.441626\pi$
$947$	9.53211e9	0.364724	0.182362	+	0.983231i	$0.441626\pi$
$948$	−5.71004e9	−0.217676
$949$	−8.95133e9	−0.339982
$950$	−1.14646e9	−0.0433838
$951$	5.55632e9	0.209486
$952$	2.67703e9	0.100560
$953$	3.24931e10	1.21609	0.608046	−	0.793902i	$-0.291953\pi$
$953$	3.24931e10	1.21609	0.608046	+	0.793902i	$0.291953\pi$
$954$	−6.34712e9	−0.236678
$955$	2.07264e10	0.770038
$956$	−2.65309e9	−0.0982086
$957$	−2.34914e9	−0.0866397
$958$	1.06640e10	0.391868
$959$	1.58185e10	0.579163
$960$	2.07577e9	0.0757235
$961$	9.24006e9	0.335848
$962$	−5.49188e9	−0.198888
$963$	9.24107e9	0.333450
$964$	−3.37538e9	−0.121354
$965$	2.74819e10	0.984469
$966$	−6.85817e9	−0.244787
$967$	8.85870e9	0.315048	0.157524	−	0.987515i	$-0.449649\pi$
$967$	8.85870e9	0.315048	0.157524	+	0.987515i	$0.449649\pi$
$968$	−6.36697e9	−0.225615
$969$	7.47968e9	0.264089
$970$	2.61849e10	0.921193
$971$	2.14391e10	0.751518	0.375759	−	0.926717i	$-0.377382\pi$
$971$	2.14391e10	0.751518	0.375759	+	0.926717i	$0.377382\pi$
$972$	9.18330e8	0.0320750
$973$	−1.14895e10	−0.399860
$974$	−1.29624e10	−0.449498
$975$	−4.67773e8	−0.0161629
$976$	−8.82990e9	−0.304005
$977$	4.01896e10	1.37874	0.689371	−	0.724408i	$-0.257887\pi$
$977$	4.01896e10	1.37874	0.689371	+	0.724408i	$0.257887\pi$
$978$	−3.78945e9	−0.129536
$979$	2.33544e10	0.795480
$980$	2.20823e9	0.0749468
$981$	−3.16749e9	−0.107121
$982$	−2.86423e10	−0.965202
$983$	−3.50632e10	−1.17737	−0.588686	−	0.808362i	$-0.700355\pi$
$983$	−3.50632e10	−1.17737	−0.588686	+	0.808362i	$0.700355\pi$
$984$	1.01004e10	0.337952
$985$	4.81555e10	1.60553
$986$	3.99556e9	0.132742
$987$	−4.46972e9	−0.147969
$988$	2.55528e9	0.0842927
$989$	4.04458e9	0.132950
$990$	4.54193e9	0.148771
$991$	3.00394e10	0.980467	0.490233	−	0.871591i	$-0.336912\pi$
$991$	3.00394e10	0.980467	0.490233	+	0.871591i	$0.336912\pi$
$992$	6.28195e9	0.204317
$993$	1.06498e10	0.345160
$994$	−4.20524e9	−0.135812
$995$	−1.95437e9	−0.0628966
$996$	4.10681e9	0.131703
$997$	−2.53048e10	−0.808667	−0.404333	−	0.914612i	$-0.632496\pi$
$997$	−2.53048e10	−0.808667	−0.404333	+	0.914612i	$0.632496\pi$
$998$	7.06774e9	0.225073
$999$	6.15024e9	0.195170

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.m.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.m.1.4	✓	5	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	546.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +293.276 q^{5} +216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +293.276 q^{5} +216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +2346.21 q^{10} +2655.50 q^{11} +1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} +7918.45 q^{15} +4096.00 q^{16} -15243.7 q^{17} +5832.00 q^{18} -18173.1 q^{19} +18769.7 q^{20} -9261.00 q^{21} +21244.0 q^{22} +92567.9 q^{23} +13824.0 q^{24} +7885.72 q^{25} -17576.0 q^{26} +19683.0 q^{27} -21952.0 q^{28} -32764.1 q^{29} +63347.6 q^{30} +191710. q^{31} +32768.0 q^{32} +71698.6 q^{33} -121949. q^{34} -100594. q^{35} +46656.0 q^{36} +312465. q^{37} -145385. q^{38} -59319.0 q^{39} +150157. q^{40} +730641. q^{41} -74088.0 q^{42} +43693.1 q^{43} +169952. q^{44} +213798. q^{45} +740544. q^{46} +482639. q^{47} +110592. q^{48} +117649. q^{49} +63085.8 q^{50} -411579. q^{51} -140608. q^{52} -1.08833e6 q^{53} +157464. q^{54} +778795. q^{55} -175616. q^{56} -490674. q^{57} -262113. q^{58} -185709. q^{59} +506781. q^{60} -2.15574e6 q^{61} +1.53368e6 q^{62} -250047. q^{63} +262144. q^{64} -644327. q^{65} +573588. q^{66} +4.10752e6 q^{67} -975596. q^{68} +2.49933e6 q^{69} -804749. q^{70} +1.53252e6 q^{71} +373248. q^{72} +4.07434e6 q^{73} +2.49972e6 q^{74} +212914. q^{75} -1.16308e6 q^{76} -910837. q^{77} -474552. q^{78} -3.30442e6 q^{79} +1.20126e6 q^{80} +531441. q^{81} +5.84513e6 q^{82} +2.37662e6 q^{83} -592704. q^{84} -4.47060e6 q^{85} +349545. q^{86} -884630. q^{87} +1.35962e6 q^{88} +8.79472e6 q^{89} +1.71038e6 q^{90} +753571. q^{91} +5.92435e6 q^{92} +5.17617e6 q^{93} +3.86111e6 q^{94} -5.32973e6 q^{95} +884736. q^{96} +1.11605e7 q^{97} +941192. q^{98} +1.93586e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 40 q^{2} + 135 q^{3} + 320 q^{4} + 299 q^{5} + 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9}+O(q^{10}) \) 5 * q + 40 * q^2 + 135 * q^3 + 320 * q^4 + 299 * q^5 + 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9	\( 5 q + 40 q^{2} + 135 q^{3} + 320 q^{4} + 299 q^{5} + 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9} + 2392 q^{10} + 1838 q^{11} + 8640 q^{12} - 10985 q^{13} - 13720 q^{14} + 8073 q^{15} + 20480 q^{16} + 56444 q^{17} + 29160 q^{18} - 20639 q^{19} + 19136 q^{20} - 46305 q^{21} + 14704 q^{22} + 74395 q^{23} + 69120 q^{24} + 22594 q^{25} - 87880 q^{26} + 98415 q^{27} - 109760 q^{28} + 130059 q^{29} + 64584 q^{30} + 330083 q^{31} + 163840 q^{32} + 49626 q^{33} + 451552 q^{34} - 102557 q^{35} + 233280 q^{36} + 410632 q^{37} - 165112 q^{38} - 296595 q^{39} + 153088 q^{40} + 172558 q^{41} - 370440 q^{42} + 886497 q^{43} + 117632 q^{44} + 217971 q^{45} + 595160 q^{46} + 763969 q^{47} + 552960 q^{48} + 588245 q^{49} + 180752 q^{50} + 1523988 q^{51} - 703040 q^{52} + 1714575 q^{53} + 787320 q^{54} + 2699318 q^{55} - 878080 q^{56} - 557253 q^{57} + 1040472 q^{58} + 603580 q^{59} + 516672 q^{60} + 6172268 q^{61} + 2640664 q^{62} - 1250235 q^{63} + 1310720 q^{64} - 656903 q^{65} + 397008 q^{66} + 5490834 q^{67} + 3612416 q^{68} + 2008665 q^{69} - 820456 q^{70} - 1581200 q^{71} + 1866240 q^{72} + 2100143 q^{73} + 3285056 q^{74} + 610038 q^{75} - 1320896 q^{76} - 630434 q^{77} - 2372760 q^{78} + 6357137 q^{79} + 1224704 q^{80} + 2657205 q^{81} + 1380464 q^{82} + 5292133 q^{83} - 2963520 q^{84} - 836908 q^{85} + 7091976 q^{86} + 3511593 q^{87} + 941056 q^{88} + 13229719 q^{89} + 1743768 q^{90} + 3767855 q^{91} + 4761280 q^{92} + 8912241 q^{93} + 6111752 q^{94} + 25806433 q^{95} + 4423680 q^{96} + 22321383 q^{97} + 4705960 q^{98} + 1339902 q^{99}+O(q^{100}) \) 5 * q + 40 * q^2 + 135 * q^3 + 320 * q^4 + 299 * q^5 + 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9 + 2392 * q^10 + 1838 * q^11 + 8640 * q^12 - 10985 * q^13 - 13720 * q^14 + 8073 * q^15 + 20480 * q^16 + 56444 * q^17 + 29160 * q^18 - 20639 * q^19 + 19136 * q^20 - 46305 * q^21 + 14704 * q^22 + 74395 * q^23 + 69120 * q^24 + 22594 * q^25 - 87880 * q^26 + 98415 * q^27 - 109760 * q^28 + 130059 * q^29 + 64584 * q^30 + 330083 * q^31 + 163840 * q^32 + 49626 * q^33 + 451552 * q^34 - 102557 * q^35 + 233280 * q^36 + 410632 * q^37 - 165112 * q^38 - 296595 * q^39 + 153088 * q^40 + 172558 * q^41 - 370440 * q^42 + 886497 * q^43 + 117632 * q^44 + 217971 * q^45 + 595160 * q^46 + 763969 * q^47 + 552960 * q^48 + 588245 * q^49 + 180752 * q^50 + 1523988 * q^51 - 703040 * q^52 + 1714575 * q^53 + 787320 * q^54 + 2699318 * q^55 - 878080 * q^56 - 557253 * q^57 + 1040472 * q^58 + 603580 * q^59 + 516672 * q^60 + 6172268 * q^61 + 2640664 * q^62 - 1250235 * q^63 + 1310720 * q^64 - 656903 * q^65 + 397008 * q^66 + 5490834 * q^67 + 3612416 * q^68 + 2008665 * q^69 - 820456 * q^70 - 1581200 * q^71 + 1866240 * q^72 + 2100143 * q^73 + 3285056 * q^74 + 610038 * q^75 - 1320896 * q^76 - 630434 * q^77 - 2372760 * q^78 + 6357137 * q^79 + 1224704 * q^80 + 2657205 * q^81 + 1380464 * q^82 + 5292133 * q^83 - 2963520 * q^84 - 836908 * q^85 + 7091976 * q^86 + 3511593 * q^87 + 941056 * q^88 + 13229719 * q^89 + 1743768 * q^90 + 3767855 * q^91 + 4761280 * q^92 + 8912241 * q^93 + 6111752 * q^94 + 25806433 * q^95 + 4423680 * q^96 + 22321383 * q^97 + 4705960 * q^98 + 1339902 * q^99

Introduction

L-functions

Modular forms

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