LMFDB - Embedded newform 546.8.a.m.1.5

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			1.5
Root			$-301.195$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +361.195 q^{5} +216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +361.195 q^{5} +216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +2889.56 q^{10} +5881.46 q^{11} +1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} +9752.26 q^{15} +4096.00 q^{16} +34919.0 q^{17} +5832.00 q^{18} +9175.72 q^{19} +23116.5 q^{20} -9261.00 q^{21} +47051.7 q^{22} -32926.6 q^{23} +13824.0 q^{24} +52336.7 q^{25} -17576.0 q^{26} +19683.0 q^{27} -21952.0 q^{28} +100383. q^{29} +78018.1 q^{30} -109103. q^{31} +32768.0 q^{32} +158799. q^{33} +279352. q^{34} -123890. q^{35} +46656.0 q^{36} +62077.8 q^{37} +73405.7 q^{38} -59319.0 q^{39} +184932. q^{40} +159299. q^{41} -74088.0 q^{42} -352734. q^{43} +376413. q^{44} +263311. q^{45} -263413. q^{46} -1.27492e6 q^{47} +110592. q^{48} +117649. q^{49} +418694. q^{50} +942814. q^{51} -140608. q^{52} +1.33132e6 q^{53} +157464. q^{54} +2.12435e6 q^{55} -175616. q^{56} +247744. q^{57} +803061. q^{58} -779245. q^{59} +624145. q^{60} +3.00020e6 q^{61} -872826. q^{62} -250047. q^{63} +262144. q^{64} -793545. q^{65} +1.27040e6 q^{66} -4.18585e6 q^{67} +2.23482e6 q^{68} -889018. q^{69} -991119. q^{70} -713501. q^{71} +373248. q^{72} +1.17446e6 q^{73} +496623. q^{74} +1.41309e6 q^{75} +587246. q^{76} -2.01734e6 q^{77} -474552. q^{78} +5.48048e6 q^{79} +1.47945e6 q^{80} +531441. q^{81} +1.27439e6 q^{82} -3.36335e6 q^{83} -592704. q^{84} +1.26126e7 q^{85} -2.82187e6 q^{86} +2.71033e6 q^{87} +3.01131e6 q^{88} +6.94464e6 q^{89} +2.10649e6 q^{90} +753571. q^{91} -2.10730e6 q^{92} -2.94579e6 q^{93} -1.01994e7 q^{94} +3.31422e6 q^{95} +884736. q^{96} -5.86210e6 q^{97} +941192. q^{98} +4.28758e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	361.195	1.29225	0.646125	−	0.763232i	$-0.276388\pi$
$5$	361.195	1.29225	0.646125	+	0.763232i	$0.276388\pi$
$6$	216.000	0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	2889.56	0.913759
$11$	5881.46	1.33233	0.666163	−	0.745806i	$-0.267935\pi$
$11$	5881.46	1.33233	0.666163	+	0.745806i	$0.267935\pi$
$12$	1728.00	0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−2744.00	−0.267261
$15$	9752.26	0.746081
$16$	4096.00	0.250000
$17$	34919.0	1.72382	0.861908	−	0.507065i	$-0.169270\pi$
$17$	34919.0	1.72382	0.861908	+	0.507065i	$0.169270\pi$
$18$	5832.00	0.235702
$19$	9175.72	0.306904	0.153452	−	0.988156i	$-0.450961\pi$
$19$	9175.72	0.306904	0.153452	+	0.988156i	$0.450961\pi$
$20$	23116.5	0.646125
$21$	−9261.00	−0.218218
$22$	47051.7	0.942097
$23$	−32926.6	−0.564286	−0.282143	−	0.959372i	$-0.591045\pi$
$23$	−32926.6	−0.564286	−0.282143	+	0.959372i	$0.591045\pi$
$24$	13824.0	0.204124
$25$	52336.7	0.669910
$26$	−17576.0	−0.196116
$27$	19683.0	0.192450
$28$	−21952.0	−0.188982
$29$	100383.	0.764303	0.382151	−	0.924100i	$-0.375183\pi$
$29$	100383.	0.764303	0.382151	+	0.924100i	$0.375183\pi$
$30$	78018.1	0.527559
$31$	−109103.	−0.657767	−0.328883	−	0.944371i	$-0.606672\pi$
$31$	−109103.	−0.657767	−0.328883	+	0.944371i	$0.606672\pi$
$32$	32768.0	0.176777
$33$	158799.	0.769219
$34$	279352.	1.21892
$35$	−123890.	−0.488425
$36$	46656.0	0.166667
$37$	62077.8	0.201479	0.100740	−	0.994913i	$-0.467879\pi$
$37$	62077.8	0.201479	0.100740	+	0.994913i	$0.467879\pi$
$38$	73405.7	0.217014
$39$	−59319.0	−0.160128
$40$	184932.	0.456879
$41$	159299.	0.360968	0.180484	−	0.983578i	$-0.442234\pi$
$41$	159299.	0.360968	0.180484	+	0.983578i	$0.442234\pi$
$42$	−74088.0	−0.154303
$43$	−352734.	−0.676561	−0.338281	−	0.941045i	$-0.609845\pi$
$43$	−352734.	−0.676561	−0.338281	+	0.941045i	$0.609845\pi$
$44$	376413.	0.666163
$45$	263311.	0.430750
$46$	−263413.	−0.399010
$47$	−1.27492e6	−1.79118	−0.895592	−	0.444876i	$-0.853248\pi$
$47$	−1.27492e6	−1.79118	−0.895592	+	0.444876i	$0.853248\pi$
$48$	110592.	0.144338
$49$	117649.	0.142857
$50$	418694.	0.473698
$51$	942814.	0.995245
$52$	−140608.	−0.138675
$53$	1.33132e6	1.22834	0.614170	−	0.789174i	$-0.289491\pi$
$53$	1.33132e6	1.22834	0.614170	+	0.789174i	$0.289491\pi$
$54$	157464.	0.136083
$55$	2.12435e6	1.72170
$56$	−175616.	−0.133631
$57$	247744.	0.177191
$58$	803061.	0.540444
$59$	−779245.	−0.493961	−0.246980	−	0.969021i	$-0.579438\pi$
$59$	−779245.	−0.493961	−0.246980	+	0.969021i	$0.579438\pi$
$60$	624145.	0.373040
$61$	3.00020e6	1.69237	0.846187	−	0.532886i	$-0.178892\pi$
$61$	3.00020e6	1.69237	0.846187	+	0.532886i	$0.178892\pi$
$62$	−872826.	−0.465111
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	−793545.	−0.358406
$66$	1.27040e6	0.543920
$67$	−4.18585e6	−1.70028	−0.850142	−	0.526554i	$-0.823484\pi$
$67$	−4.18585e6	−1.70028	−0.850142	+	0.526554i	$0.823484\pi$
$68$	2.23482e6	0.861908
$69$	−889018.	−0.325791
$70$	−991119.	−0.345368
$71$	−713501.	−0.236587	−0.118293	−	0.992979i	$-0.537742\pi$
$71$	−713501.	−0.236587	−0.118293	+	0.992979i	$0.537742\pi$
$72$	373248.	0.117851
$73$	1.17446e6	0.353353	0.176677	−	0.984269i	$-0.443465\pi$
$73$	1.17446e6	0.353353	0.176677	+	0.984269i	$0.443465\pi$
$74$	496623.	0.142467
$75$	1.41309e6	0.386773
$76$	587246.	0.153452
$77$	−2.01734e6	−0.503572
$78$	−474552.	−0.113228
$79$	5.48048e6	1.25061	0.625307	−	0.780378i	$-0.284974\pi$
$79$	5.48048e6	1.25061	0.625307	+	0.780378i	$0.284974\pi$
$80$	1.47945e6	0.323063
$81$	531441.	0.111111
$82$	1.27439e6	0.255243
$83$	−3.36335e6	−0.645653	−0.322826	−	0.946458i	$-0.604633\pi$
$83$	−3.36335e6	−0.645653	−0.322826	+	0.946458i	$0.604633\pi$
$84$	−592704.	−0.109109
$85$	1.26126e7	2.22760
$86$	−2.82187e6	−0.478401
$87$	2.71033e6	0.441270
$88$	3.01131e6	0.471049
$89$	6.94464e6	1.04420	0.522101	−	0.852884i	$-0.325148\pi$
$89$	6.94464e6	1.04420	0.522101	+	0.852884i	$0.325148\pi$
$90$	2.10649e6	0.304586
$91$	753571.	0.104828
$92$	−2.10730e6	−0.282143
$93$	−2.94579e6	−0.379762
$94$	−1.01994e7	−1.26656
$95$	3.31422e6	0.396597
$96$	884736.	0.102062
$97$	−5.86210e6	−0.652157	−0.326078	−	0.945343i	$-0.605727\pi$
$97$	−5.86210e6	−0.652157	−0.326078	+	0.945343i	$0.605727\pi$
$98$	941192.	0.101015
$99$	4.28758e6	0.444109
$100$	3.34955e6	0.334955
$101$	1.10453e7	1.06672	0.533360	−	0.845888i	$-0.320929\pi$
$101$	1.10453e7	1.06672	0.533360	+	0.845888i	$0.320929\pi$
$102$	7.54251e6	0.703745
$103$	4.41515e6	0.398121	0.199061	−	0.979987i	$-0.436211\pi$
$103$	4.41515e6	0.398121	0.199061	+	0.979987i	$0.436211\pi$
$104$	−1.12486e6	−0.0980581
$105$	−3.34503e6	−0.281992
$106$	1.06506e7	0.868567
$107$	−1.71608e6	−0.135423	−0.0677116	−	0.997705i	$-0.521570\pi$
$107$	−1.71608e6	−0.135423	−0.0677116	+	0.997705i	$0.521570\pi$
$108$	1.25971e6	0.0962250
$109$	9.87936e6	0.730695	0.365348	−	0.930871i	$-0.380950\pi$
$109$	9.87936e6	0.730695	0.365348	+	0.930871i	$0.380950\pi$
$110$	1.69948e7	1.21743
$111$	1.67610e6	0.116324
$112$	−1.40493e6	−0.0944911
$113$	−2.00572e7	−1.30767	−0.653833	−	0.756639i	$-0.726840\pi$
$113$	−2.00572e7	−1.30767	−0.653833	+	0.756639i	$0.726840\pi$
$114$	1.98196e6	0.125293
$115$	−1.18929e7	−0.729198
$116$	6.42448e6	0.382151
$117$	−1.60161e6	−0.0924500
$118$	−6.23396e6	−0.349283
$119$	−1.19772e7	−0.651541
$120$	4.99316e6	0.263779
$121$	1.51044e7	0.775095
$122$	2.40016e7	1.19669
$123$	4.30107e6	0.208405
$124$	−6.98261e6	−0.328883
$125$	−9.31458e6	−0.426558
$126$	−2.00038e6	−0.0890871
$127$	7.01643e6	0.303951	0.151975	−	0.988384i	$-0.451437\pi$
$127$	7.01643e6	0.303951	0.151975	+	0.988384i	$0.451437\pi$
$128$	2.09715e6	0.0883883
$129$	−9.52381e6	−0.390613
$130$	−6.34836e6	−0.253431
$131$	2.38056e7	0.925186	0.462593	−	0.886571i	$-0.346919\pi$
$131$	2.38056e7	0.925186	0.462593	+	0.886571i	$0.346919\pi$
$132$	1.01632e7	0.384610
$133$	−3.14727e6	−0.115999
$134$	−3.34868e7	−1.20228
$135$	7.10940e6	0.248694
$136$	1.78785e7	0.609461
$137$	−5.93369e7	−1.97153	−0.985764	−	0.168136i	$-0.946225\pi$
$137$	−5.93369e7	−1.97153	−0.985764	+	0.168136i	$0.946225\pi$
$138$	−7.11214e6	−0.230369
$139$	−4.80539e7	−1.51767	−0.758834	−	0.651284i	$-0.774231\pi$
$139$	−4.80539e7	−1.51767	−0.758834	+	0.651284i	$0.774231\pi$
$140$	−7.92895e6	−0.244212
$141$	−3.44228e7	−1.03414
$142$	−5.70801e6	−0.167292
$143$	−1.29216e7	−0.369521
$144$	2.98598e6	0.0833333
$145$	3.62577e7	0.987670
$146$	9.39570e6	0.249859
$147$	3.17652e6	0.0824786
$148$	3.97298e6	0.100740
$149$	−1.91372e6	−0.0473944	−0.0236972	−	0.999719i	$-0.507544\pi$
$149$	−1.91372e6	−0.0473944	−0.0236972	+	0.999719i	$0.507544\pi$
$150$	1.13047e7	0.273490
$151$	6.15935e7	1.45585	0.727923	−	0.685658i	$-0.240486\pi$
$151$	6.15935e7	1.45585	0.727923	+	0.685658i	$0.240486\pi$
$152$	4.69797e6	0.108507
$153$	2.54560e7	0.574605
$154$	−1.61387e7	−0.356079
$155$	−3.94075e7	−0.849999
$156$	−3.79642e6	−0.0800641
$157$	−3.39122e7	−0.699371	−0.349686	−	0.936867i	$-0.613712\pi$
$157$	−3.39122e7	−0.699371	−0.349686	+	0.936867i	$0.613712\pi$
$158$	4.38438e7	0.884318
$159$	3.59458e7	0.709182
$160$	1.18356e7	0.228440
$161$	1.12938e7	0.213280
$162$	4.25153e6	0.0785674
$163$	−2.95442e7	−0.534337	−0.267169	−	0.963650i	$-0.586088\pi$
$163$	−2.95442e7	−0.534337	−0.267169	+	0.963650i	$0.586088\pi$
$164$	1.01951e7	0.180484
$165$	5.73575e7	0.994024
$166$	−2.69068e7	−0.456545
$167$	−3.89910e7	−0.647824	−0.323912	−	0.946087i	$-0.604998\pi$
$167$	−3.89910e7	−0.647824	−0.323912	+	0.946087i	$0.604998\pi$
$168$	−4.74163e6	−0.0771517
$169$	4.82681e6	0.0769231
$170$	1.00901e8	1.57515
$171$	6.68910e6	0.102301
$172$	−2.25750e7	−0.338281
$173$	−5.19687e7	−0.763099	−0.381549	−	0.924348i	$-0.624609\pi$
$173$	−5.19687e7	−0.763099	−0.381549	+	0.924348i	$0.624609\pi$
$174$	2.16826e7	0.312025
$175$	−1.79515e7	−0.253202
$176$	2.40905e7	0.333082
$177$	−2.10396e7	−0.285188
$178$	5.55571e7	0.738362
$179$	1.11039e8	1.44707	0.723537	−	0.690285i	$-0.242515\pi$
$179$	1.11039e8	1.44707	0.723537	+	0.690285i	$0.242515\pi$
$180$	1.68519e7	0.215375
$181$	8.78431e7	1.10112	0.550558	−	0.834797i	$-0.314415\pi$
$181$	8.78431e7	1.10112	0.550558	+	0.834797i	$0.314415\pi$
$182$	6.02857e6	0.0741249
$183$	8.10055e7	0.977093
$184$	−1.68584e7	−0.199505
$185$	2.24222e7	0.260362
$186$	−2.35663e7	−0.268532
$187$	2.05375e8	2.29669
$188$	−8.15949e7	−0.895592
$189$	−6.75127e6	−0.0727393
$190$	2.65138e7	0.280436
$191$	−3.38212e7	−0.351214	−0.175607	−	0.984460i	$-0.556189\pi$
$191$	−3.38212e7	−0.351214	−0.175607	+	0.984460i	$0.556189\pi$
$192$	7.07789e6	0.0721688
$193$	1.50150e8	1.50340	0.751700	−	0.659505i	$-0.229234\pi$
$193$	1.50150e8	1.50340	0.751700	+	0.659505i	$0.229234\pi$
$194$	−4.68968e7	−0.461144
$195$	−2.14257e7	−0.206926
$196$	7.52954e6	0.0714286
$197$	−1.96620e7	−0.183229	−0.0916147	−	0.995795i	$-0.529203\pi$
$197$	−1.96620e7	−0.183229	−0.0916147	+	0.995795i	$0.529203\pi$
$198$	3.43007e7	0.314032
$199$	1.71007e8	1.53826	0.769129	−	0.639093i	$-0.220690\pi$
$199$	1.71007e8	1.53826	0.769129	+	0.639093i	$0.220690\pi$
$200$	2.67964e7	0.236849
$201$	−1.13018e8	−0.981659
$202$	8.83620e7	0.754286
$203$	−3.44312e7	−0.288879
$204$	6.03401e7	0.497623
$205$	5.75379e7	0.466461
$206$	3.53212e7	0.281514
$207$	−2.40035e7	−0.188095
$208$	−8.99891e6	−0.0693375
$209$	5.39666e7	0.408896
$210$	−2.67602e7	−0.199399
$211$	9.23159e7	0.676532	0.338266	−	0.941051i	$-0.390160\pi$
$211$	9.23159e7	0.676532	0.338266	+	0.941051i	$0.390160\pi$
$212$	8.52048e7	0.614170
$213$	−1.92645e7	−0.136593
$214$	−1.37286e7	−0.0957587
$215$	−1.27406e8	−0.874287
$216$	1.00777e7	0.0680414
$217$	3.74224e7	0.248612
$218$	7.90349e7	0.516680
$219$	3.17105e7	0.204009
$220$	1.35959e8	0.860850
$221$	−7.67171e7	−0.478100
$222$	1.34088e7	0.0822536
$223$	−3.09666e8	−1.86994	−0.934968	−	0.354732i	$-0.884572\pi$
$223$	−3.09666e8	−1.86994	−0.934968	+	0.354732i	$0.884572\pi$
$224$	−1.12394e7	−0.0668153
$225$	3.81535e7	0.223303
$226$	−1.60458e8	−0.924659
$227$	2.50894e8	1.42364	0.711819	−	0.702363i	$-0.247872\pi$
$227$	2.50894e8	1.42364	0.711819	+	0.702363i	$0.247872\pi$
$228$	1.58556e7	0.0885955
$229$	4.31976e6	0.0237704	0.0118852	−	0.999929i	$-0.496217\pi$
$229$	4.31976e6	0.0237704	0.0118852	+	0.999929i	$0.496217\pi$
$230$	−9.51433e7	−0.515621
$231$	−5.44682e7	−0.290738
$232$	5.13959e7	0.270222
$233$	−2.03227e7	−0.105253	−0.0526267	−	0.998614i	$-0.516759\pi$
$233$	−2.03227e7	−0.105253	−0.0526267	+	0.998614i	$0.516759\pi$
$234$	−1.28129e7	−0.0653720
$235$	−4.60494e8	−2.31466
$236$	−4.98717e7	−0.246980
$237$	1.47973e8	0.722043
$238$	−9.58178e7	−0.460709
$239$	1.26815e8	0.600865	0.300433	−	0.953803i	$-0.402869\pi$
$239$	1.26815e8	0.600865	0.300433	+	0.953803i	$0.402869\pi$
$240$	3.99453e7	0.186520
$241$	−2.03321e8	−0.935672	−0.467836	−	0.883815i	$-0.654966\pi$
$241$	−2.03321e8	−0.935672	−0.467836	+	0.883815i	$0.654966\pi$
$242$	1.20835e8	0.548075
$243$	1.43489e7	0.0641500
$244$	1.92013e8	0.846187
$245$	4.24942e7	0.184607
$246$	3.44085e7	0.147365
$247$	−2.01591e7	−0.0851198
$248$	−5.58609e7	−0.232556
$249$	−9.08105e7	−0.372768
$250$	−7.45167e7	−0.301622
$251$	−1.86574e7	−0.0744719	−0.0372360	−	0.999307i	$-0.511855\pi$
$251$	−1.86574e7	−0.0744719	−0.0372360	+	0.999307i	$0.511855\pi$
$252$	−1.60030e7	−0.0629941
$253$	−1.93656e8	−0.751813
$254$	5.61315e7	0.214926
$255$	3.40539e8	1.28611
$256$	1.67772e7	0.0625000
$257$	2.84544e8	1.04564	0.522821	−	0.852442i	$-0.324880\pi$
$257$	2.84544e8	1.04564	0.522821	+	0.852442i	$0.324880\pi$
$258$	−7.61905e7	−0.276205
$259$	−2.12927e7	−0.0761520
$260$	−5.07869e7	−0.179203
$261$	7.31789e7	0.254768
$262$	1.90445e8	0.654205
$263$	−7.94639e7	−0.269355	−0.134677	−	0.990890i	$-0.543000\pi$
$263$	−7.94639e7	−0.269355	−0.134677	+	0.990890i	$0.543000\pi$
$264$	8.13053e7	0.271960
$265$	4.80868e8	1.58732
$266$	−2.51782e7	−0.0820235
$267$	1.87505e8	0.602870
$268$	−2.67894e8	−0.850142
$269$	−2.49289e8	−0.780854	−0.390427	−	0.920634i	$-0.627673\pi$
$269$	−2.49289e8	−0.780854	−0.390427	+	0.920634i	$0.627673\pi$
$270$	5.68752e7	0.175853
$271$	3.42233e8	1.04455	0.522276	−	0.852777i	$-0.325083\pi$
$271$	3.42233e8	1.04455	0.522276	+	0.852777i	$0.325083\pi$
$272$	1.43028e8	0.430954
$273$	2.03464e7	0.0605228
$274$	−4.74695e8	−1.39408
$275$	3.07817e8	0.892540
$276$	−5.68971e7	−0.162895
$277$	−2.00567e8	−0.566996	−0.283498	−	0.958973i	$-0.591495\pi$
$277$	−2.00567e8	−0.566996	−0.283498	+	0.958973i	$0.591495\pi$
$278$	−3.84431e8	−1.07315
$279$	−7.95363e7	−0.219256
$280$	−6.34316e7	−0.172684
$281$	−2.09661e8	−0.563695	−0.281848	−	0.959459i	$-0.590947\pi$
$281$	−2.09661e8	−0.563695	−0.281848	+	0.959459i	$0.590947\pi$
$282$	−2.75383e8	−0.731248
$283$	1.21217e8	0.317915	0.158957	−	0.987285i	$-0.449187\pi$
$283$	1.21217e8	0.317915	0.158957	+	0.987285i	$0.449187\pi$
$284$	−4.56640e7	−0.118293
$285$	8.94840e7	0.228975
$286$	−1.03373e8	−0.261291
$287$	−5.46395e7	−0.136433
$288$	2.38879e7	0.0589256
$289$	8.08999e8	1.97154
$290$	2.90061e8	0.698388
$291$	−1.58277e8	−0.376523
$292$	7.51656e7	0.176677
$293$	−1.14289e8	−0.265442	−0.132721	−	0.991153i	$-0.542371\pi$
$293$	−1.14289e8	−0.265442	−0.132721	+	0.991153i	$0.542371\pi$
$294$	2.54122e7	0.0583212
$295$	−2.81459e8	−0.638321
$296$	3.17838e7	0.0712337
$297$	1.15765e8	0.256406
$298$	−1.53098e7	−0.0335129
$299$	7.23397e7	0.156505
$300$	9.04379e7	0.193386
$301$	1.20988e8	0.255716
$302$	4.92748e8	1.02944
$303$	2.98222e8	0.615872
$304$	3.75837e7	0.0767260
$305$	1.08366e9	2.18697
$306$	2.03648e8	0.406307
$307$	9.88101e7	0.194902	0.0974512	−	0.995240i	$-0.468931\pi$
$307$	9.88101e7	0.194902	0.0974512	+	0.995240i	$0.468931\pi$
$308$	−1.29110e8	−0.251786
$309$	1.19209e8	0.229855
$310$	−3.15260e8	−0.601040
$311$	−6.82210e8	−1.28605	−0.643024	−	0.765846i	$-0.722320\pi$
$311$	−6.82210e8	−1.28605	−0.643024	+	0.765846i	$0.722320\pi$
$312$	−3.03713e7	−0.0566139
$313$	−7.88979e8	−1.45432	−0.727160	−	0.686468i	$-0.759160\pi$
$313$	−7.88979e8	−1.45432	−0.727160	+	0.686468i	$0.759160\pi$
$314$	−2.71298e8	−0.494530
$315$	−9.03157e7	−0.162808
$316$	3.50751e8	0.625307
$317$	−1.46477e8	−0.258262	−0.129131	−	0.991628i	$-0.541219\pi$
$317$	−1.46477e8	−0.258262	−0.129131	+	0.991628i	$0.541219\pi$
$318$	2.87566e8	0.501467
$319$	5.90396e8	1.01830
$320$	9.46851e7	0.161531
$321$	−4.63341e7	−0.0781867
$322$	9.03505e7	0.150812
$323$	3.20407e8	0.529046
$324$	3.40122e7	0.0555556
$325$	−1.14984e8	−0.185800
$326$	−2.36353e8	−0.377833
$327$	2.66743e8	0.421867
$328$	8.15610e7	0.127622
$329$	4.37297e8	0.677004
$330$	4.58860e8	0.702881
$331$	−3.02116e8	−0.457906	−0.228953	−	0.973437i	$-0.573530\pi$
$331$	−3.02116e8	−0.457906	−0.228953	+	0.973437i	$0.573530\pi$
$332$	−2.15255e8	−0.322826
$333$	4.52547e7	0.0671598
$334$	−3.11928e8	−0.458081
$335$	−1.51191e9	−2.19719
$336$	−3.79331e7	−0.0545545
$337$	8.80990e8	1.25391	0.626955	−	0.779055i	$-0.284301\pi$
$337$	8.80990e8	1.25391	0.626955	+	0.779055i	$0.284301\pi$
$338$	3.86145e7	0.0543928
$339$	−5.41545e8	−0.754981
$340$	8.07205e8	1.11380
$341$	−6.41687e8	−0.876360
$342$	5.35128e7	0.0723379
$343$	−4.03536e7	−0.0539949
$344$	−1.80600e8	−0.239201
$345$	−3.21109e8	−0.421003
$346$	−4.15750e8	−0.539592
$347$	7.33216e8	0.942060	0.471030	−	0.882117i	$-0.343882\pi$
$347$	7.33216e8	0.942060	0.471030	+	0.882117i	$0.343882\pi$
$348$	1.73461e8	0.220635
$349$	8.87276e7	0.111730	0.0558650	−	0.998438i	$-0.482208\pi$
$349$	8.87276e7	0.111730	0.0558650	+	0.998438i	$0.482208\pi$
$350$	−1.43612e8	−0.179041
$351$	−4.32436e7	−0.0533761
$352$	1.92724e8	0.235524
$353$	1.73712e8	0.210193	0.105096	−	0.994462i	$-0.466485\pi$
$353$	1.73712e8	0.210193	0.105096	+	0.994462i	$0.466485\pi$
$354$	−1.68317e8	−0.201659
$355$	−2.57713e8	−0.305729
$356$	4.44457e8	0.522101
$357$	−3.23385e8	−0.376167
$358$	8.88314e8	1.02324
$359$	−5.16192e8	−0.588817	−0.294409	−	0.955680i	$-0.595123\pi$
$359$	−5.16192e8	−0.588817	−0.294409	+	0.955680i	$0.595123\pi$
$360$	1.34815e8	0.152293
$361$	−8.09678e8	−0.905810
$362$	7.02745e8	0.778606
$363$	4.07819e8	0.447501
$364$	4.82285e7	0.0524142
$365$	4.24210e8	0.456621
$366$	6.48044e8	0.690909
$367$	−4.86122e8	−0.513350	−0.256675	−	0.966498i	$-0.582627\pi$
$367$	−4.86122e8	−0.513350	−0.256675	+	0.966498i	$0.582627\pi$
$368$	−1.34867e8	−0.141071
$369$	1.16129e8	0.120323
$370$	1.79378e8	0.184103
$371$	−4.56644e8	−0.464269
$372$	−1.88530e8	−0.189881
$373$	1.59978e9	1.59617	0.798087	−	0.602543i	$-0.205846\pi$
$373$	1.59978e9	1.59617	0.798087	+	0.602543i	$0.205846\pi$
$374$	1.64300e9	1.62400
$375$	−2.51494e8	−0.246274
$376$	−6.52759e8	−0.633279
$377$	−2.20541e8	−0.211979
$378$	−5.40102e7	−0.0514344
$379$	1.24470e9	1.17443	0.587215	−	0.809431i	$-0.300224\pi$
$379$	1.24470e9	1.17443	0.587215	+	0.809431i	$0.300224\pi$
$380$	2.12110e8	0.198298
$381$	1.89444e8	0.175486
$382$	−2.70569e8	−0.248346
$383$	−1.45836e9	−1.32639	−0.663193	−	0.748448i	$-0.730799\pi$
$383$	−1.45836e9	−1.32639	−0.663193	+	0.748448i	$0.730799\pi$
$384$	5.66231e7	0.0510310
$385$	−7.28653e8	−0.650741
$386$	1.20120e9	1.06307
$387$	−2.57143e8	−0.225520
$388$	−3.75174e8	−0.326078
$389$	8.61234e8	0.741819	0.370909	−	0.928669i	$-0.379046\pi$
$389$	8.61234e8	0.741819	0.370909	+	0.928669i	$0.379046\pi$
$390$	−1.71406e8	−0.146319
$391$	−1.14976e9	−0.972725
$392$	6.02363e7	0.0505076
$393$	6.42750e8	0.534156
$394$	−1.57296e8	−0.129563
$395$	1.97952e9	1.61611
$396$	2.74405e8	0.222054
$397$	4.93699e8	0.396000	0.198000	−	0.980202i	$-0.436555\pi$
$397$	4.93699e8	0.396000	0.198000	+	0.980202i	$0.436555\pi$
$398$	1.36806e9	1.08771
$399$	−8.49763e7	−0.0669719
$400$	2.14371e8	0.167478
$401$	7.50619e7	0.0581319	0.0290659	−	0.999577i	$-0.490747\pi$
$401$	7.50619e7	0.0581319	0.0290659	+	0.999577i	$0.490747\pi$
$402$	−9.04143e8	−0.694138
$403$	2.39700e8	0.182432
$404$	7.06896e8	0.533360
$405$	1.91954e8	0.143583
$406$	−2.75450e8	−0.204268
$407$	3.65108e8	0.268436
$408$	4.82721e8	0.351872
$409$	9.44912e8	0.682904	0.341452	−	0.939899i	$-0.389081\pi$
$409$	9.44912e8	0.682904	0.341452	+	0.939899i	$0.389081\pi$
$410$	4.60303e8	0.329838
$411$	−1.60210e9	−1.13826
$412$	2.82570e8	0.199061
$413$	2.67281e8	0.186700
$414$	−1.92028e8	−0.133003
$415$	−1.21483e9	−0.834345
$416$	−7.19913e7	−0.0490290
$417$	−1.29746e9	−0.876226
$418$	4.31733e8	0.289133
$419$	−1.20197e9	−0.798259	−0.399129	−	0.916895i	$-0.630688\pi$
$419$	−1.20197e9	−0.798259	−0.399129	+	0.916895i	$0.630688\pi$
$420$	−2.14082e8	−0.140996
$421$	−3.89922e8	−0.254677	−0.127339	−	0.991859i	$-0.540643\pi$
$421$	−3.89922e8	−0.254677	−0.127339	+	0.991859i	$0.540643\pi$
$422$	7.38528e8	0.478380
$423$	−9.29416e8	−0.597061
$424$	6.81638e8	0.434283
$425$	1.82755e9	1.15480
$426$	−1.54116e8	−0.0965861
$427$	−1.02907e9	−0.639657
$428$	−1.09829e8	−0.0677116
$429$	−3.48882e8	−0.213343
$430$	−1.01924e9	−0.618214
$431$	9.69554e8	0.583313	0.291657	−	0.956523i	$-0.405794\pi$
$431$	9.69554e8	0.583313	0.291657	+	0.956523i	$0.405794\pi$
$432$	8.06216e7	0.0481125
$433$	2.32516e9	1.37640	0.688202	−	0.725519i	$-0.258400\pi$
$433$	2.32516e9	1.37640	0.688202	+	0.725519i	$0.258400\pi$
$434$	2.99379e8	0.175796
$435$	9.78957e8	0.570232
$436$	6.32279e8	0.365348
$437$	−3.02125e8	−0.173182
$438$	2.53684e8	0.144256
$439$	−1.33956e9	−0.755680	−0.377840	−	0.925871i	$-0.623333\pi$
$439$	−1.33956e9	−0.755680	−0.377840	+	0.925871i	$0.623333\pi$
$440$	1.08767e9	0.608713
$441$	8.57661e7	0.0476190
$442$	−6.13737e8	−0.338068
$443$	−1.11733e9	−0.610615	−0.305307	−	0.952254i	$-0.598759\pi$
$443$	−1.11733e9	−0.610615	−0.305307	+	0.952254i	$0.598759\pi$
$444$	1.07270e8	0.0581621
$445$	2.50837e9	1.34937
$446$	−2.47733e9	−1.32224
$447$	−5.16705e7	−0.0273631
$448$	−8.99154e7	−0.0472456
$449$	−5.27115e8	−0.274817	−0.137408	−	0.990514i	$-0.543877\pi$
$449$	−5.27115e8	−0.274817	−0.137408	+	0.990514i	$0.543877\pi$
$450$	3.05228e8	0.157899
$451$	9.36910e8	0.480928
$452$	−1.28366e9	−0.653833
$453$	1.66303e9	0.840534
$454$	2.00715e9	1.00666
$455$	2.72186e8	0.135465
$456$	1.26845e8	0.0626465
$457$	−1.92090e9	−0.941451	−0.470725	−	0.882280i	$-0.656008\pi$
$457$	−1.92090e9	−0.941451	−0.470725	+	0.882280i	$0.656008\pi$
$458$	3.45581e7	0.0168082
$459$	6.87311e8	0.331748
$460$	−7.61146e8	−0.364599
$461$	−2.59122e9	−1.23183	−0.615916	−	0.787812i	$-0.711214\pi$
$461$	−2.59122e9	−1.23183	−0.615916	+	0.787812i	$0.711214\pi$
$462$	−4.35746e8	−0.205583
$463$	−2.62379e9	−1.22856	−0.614279	−	0.789089i	$-0.710553\pi$
$463$	−2.62379e9	−1.22856	−0.614279	+	0.789089i	$0.710553\pi$
$464$	4.11167e8	0.191076
$465$	−1.06400e9	−0.490747
$466$	−1.62582e8	−0.0744254
$467$	−1.80004e8	−0.0817851	−0.0408925	−	0.999164i	$-0.513020\pi$
$467$	−1.80004e8	−0.0817851	−0.0408925	+	0.999164i	$0.513020\pi$
$468$	−1.02503e8	−0.0462250
$469$	1.43574e9	0.642647
$470$	−3.68396e9	−1.63671
$471$	−9.15631e8	−0.403782
$472$	−3.98974e8	−0.174641
$473$	−2.07459e9	−0.901401
$474$	1.18378e9	0.510561
$475$	4.80227e8	0.205598
$476$	−7.66542e8	−0.325771
$477$	9.70535e8	0.409446
$478$	1.01452e9	0.424876
$479$	−7.57745e8	−0.315028	−0.157514	−	0.987517i	$-0.550348\pi$
$479$	−7.57745e8	−0.315028	−0.157514	+	0.987517i	$0.550348\pi$
$480$	3.19562e8	0.131890
$481$	−1.36385e8	−0.0558803
$482$	−1.62657e9	−0.661620
$483$	3.04933e8	0.123137
$484$	9.66682e8	0.387548
$485$	−2.11736e9	−0.842750
$486$	1.14791e8	0.0453609
$487$	1.01647e9	0.398790	0.199395	−	0.979919i	$-0.436102\pi$
$487$	1.01647e9	0.398790	0.199395	+	0.979919i	$0.436102\pi$
$488$	1.53610e9	0.598345
$489$	−7.97693e8	−0.308500
$490$	3.39954e8	0.130537
$491$	2.63760e9	1.00560	0.502798	−	0.864404i	$-0.332304\pi$
$491$	2.63760e9	1.00560	0.502798	+	0.864404i	$0.332304\pi$
$492$	2.75268e8	0.104203
$493$	3.50526e9	1.31752
$494$	−1.61272e8	−0.0601888
$495$	1.54865e9	0.573900
$496$	−4.46887e8	−0.164442
$497$	2.44731e8	0.0894213
$498$	−7.26484e8	−0.263587
$499$	−1.61011e9	−0.580103	−0.290051	−	0.957011i	$-0.593672\pi$
$499$	−1.61011e9	−0.580103	−0.290051	+	0.957011i	$0.593672\pi$
$500$	−5.96133e8	−0.213279
$501$	−1.05276e9	−0.374021
$502$	−1.49259e8	−0.0526596
$503$	−4.20236e9	−1.47233	−0.736164	−	0.676803i	$-0.763365\pi$
$503$	−4.20236e9	−1.47233	−0.736164	+	0.676803i	$0.763365\pi$
$504$	−1.28024e8	−0.0445435
$505$	3.98949e9	1.37847
$506$	−1.54925e9	−0.531612
$507$	1.30324e8	0.0444116
$508$	4.49052e8	0.151975
$509$	−4.78310e9	−1.60767	−0.803836	−	0.594851i	$-0.797211\pi$
$509$	−4.78310e9	−1.60767	−0.803836	+	0.594851i	$0.797211\pi$
$510$	2.72432e9	0.909414
$511$	−4.02841e8	−0.133555
$512$	1.34218e8	0.0441942
$513$	1.80606e8	0.0590637
$514$	2.27635e9	0.739381
$515$	1.59473e9	0.514472
$516$	−6.09524e8	−0.195306
$517$	−7.49839e9	−2.38644
$518$	−1.70342e8	−0.0538476
$519$	−1.40316e9	−0.440575
$520$	−4.06295e8	−0.126716
$521$	−4.87595e8	−0.151052	−0.0755261	−	0.997144i	$-0.524064\pi$
$521$	−4.87595e8	−0.151052	−0.0755261	+	0.997144i	$0.524064\pi$
$522$	5.85431e8	0.180148
$523$	−3.03786e9	−0.928564	−0.464282	−	0.885688i	$-0.653687\pi$
$523$	−3.03786e9	−0.928564	−0.464282	+	0.885688i	$0.653687\pi$
$524$	1.52356e9	0.462593
$525$	−4.84691e8	−0.146186
$526$	−6.35711e8	−0.190463
$527$	−3.80978e9	−1.13387
$528$	6.50443e8	0.192305
$529$	−2.32067e9	−0.681581
$530$	3.84694e9	1.12241
$531$	−5.68070e8	−0.164654
$532$	−2.01425e8	−0.0579994
$533$	−3.49980e8	−0.100115
$534$	1.50004e9	0.426294
$535$	−6.19838e8	−0.175001
$536$	−2.14315e9	−0.601141
$537$	2.99806e9	0.835469
$538$	−1.99431e9	−0.552147
$539$	6.91948e8	0.190332
$540$	4.55002e8	0.124347
$541$	4.45818e9	1.21051	0.605253	−	0.796033i	$-0.293072\pi$
$541$	4.45818e9	1.21051	0.605253	+	0.796033i	$0.293072\pi$
$542$	2.73787e9	0.738610
$543$	2.37176e9	0.635729
$544$	1.14423e9	0.304730
$545$	3.56838e9	0.944241
$546$	1.62771e8	0.0427960
$547$	−4.91430e9	−1.28383	−0.641913	−	0.766778i	$-0.721859\pi$
$547$	−4.91430e9	−1.28383	−0.641913	+	0.766778i	$0.721859\pi$
$548$	−3.79756e9	−0.985764
$549$	2.18715e9	0.564125
$550$	2.46253e9	0.631121
$551$	9.21082e8	0.234567
$552$	−4.55177e8	−0.115184
$553$	−1.87980e9	−0.472688
$554$	−1.60453e9	−0.400927
$555$	6.05399e8	0.150320
$556$	−3.07545e9	−0.758834
$557$	6.85076e8	0.167975	0.0839877	−	0.996467i	$-0.473234\pi$
$557$	6.85076e8	0.167975	0.0839877	+	0.996467i	$0.473234\pi$
$558$	−6.36290e8	−0.155037
$559$	7.74956e8	0.187644
$560$	−5.07453e8	−0.122106
$561$	5.54512e9	1.32599
$562$	−1.67728e9	−0.398593
$563$	8.61914e8	0.203556	0.101778	−	0.994807i	$-0.467547\pi$
$563$	8.61914e8	0.203556	0.101778	+	0.994807i	$0.467547\pi$
$564$	−2.20306e9	−0.517070
$565$	−7.24457e9	−1.68983
$566$	9.69735e8	0.224800
$567$	−1.82284e8	−0.0419961
$568$	−3.65312e8	−0.0836460
$569$	−2.82427e9	−0.642708	−0.321354	−	0.946959i	$-0.604138\pi$
$569$	−2.82427e9	−0.642708	−0.321354	+	0.946959i	$0.604138\pi$
$570$	7.15872e8	0.161910
$571$	−5.19087e9	−1.16685	−0.583423	−	0.812168i	$-0.698287\pi$
$571$	−5.19087e9	−1.16685	−0.583423	+	0.812168i	$0.698287\pi$
$572$	−8.26980e8	−0.184761
$573$	−9.13172e8	−0.202774
$574$	−4.37116e8	−0.0964728
$575$	−1.72327e9	−0.378021
$576$	1.91103e8	0.0416667
$577$	5.99615e9	1.29944	0.649721	−	0.760173i	$-0.274886\pi$
$577$	5.99615e9	1.29944	0.649721	+	0.760173i	$0.274886\pi$
$578$	6.47200e9	1.39409
$579$	4.05405e9	0.867989
$580$	2.32049e9	0.493835
$581$	1.15363e9	0.244034
$582$	−1.26621e9	−0.266242
$583$	7.83013e9	1.63655
$584$	6.01325e8	0.124929
$585$	−5.78494e8	−0.119469
$586$	−9.14315e8	−0.187696
$587$	−7.72104e9	−1.57559	−0.787794	−	0.615939i	$-0.788777\pi$
$587$	−7.72104e9	−1.57559	−0.787794	+	0.615939i	$0.788777\pi$
$588$	2.03297e8	0.0412393
$589$	−1.00110e9	−0.201871
$590$	−2.25168e9	−0.451361
$591$	−5.30873e8	−0.105788
$592$	2.54271e8	0.0503698
$593$	−2.16517e8	−0.0426384	−0.0213192	−	0.999773i	$-0.506787\pi$
$593$	−2.16517e8	−0.0426384	−0.0213192	+	0.999773i	$0.506787\pi$
$594$	9.26118e8	0.181307
$595$	−4.32611e9	−0.841954
$596$	−1.22478e8	−0.0236972
$597$	4.61720e9	0.888114
$598$	5.78718e8	0.110666
$599$	−6.55826e9	−1.24679	−0.623397	−	0.781906i	$-0.714248\pi$
$599$	−6.55826e9	−1.24679	−0.623397	+	0.781906i	$0.714248\pi$
$600$	7.23503e8	0.136745
$601$	−5.89888e9	−1.10843	−0.554216	−	0.832373i	$-0.686982\pi$
$601$	−5.89888e9	−1.10843	−0.554216	+	0.832373i	$0.686982\pi$
$602$	9.67901e8	0.180819
$603$	−3.05148e9	−0.566761
$604$	3.94199e9	0.727923
$605$	5.45564e9	1.00162
$606$	2.38577e9	0.435487
$607$	1.37617e9	0.249754	0.124877	−	0.992172i	$-0.460146\pi$
$607$	1.37617e9	0.249754	0.124877	+	0.992172i	$0.460146\pi$
$608$	3.00670e8	0.0542535
$609$	−9.29643e8	−0.166784
$610$	8.66927e9	1.54642
$611$	2.80100e9	0.496785
$612$	1.62918e9	0.287303
$613$	−7.26434e9	−1.27375	−0.636876	−	0.770967i	$-0.719774\pi$
$613$	−7.26434e9	−1.27375	−0.636876	+	0.770967i	$0.719774\pi$
$614$	7.90481e8	0.137817
$615$	1.55352e9	0.269312
$616$	−1.03288e9	−0.178040
$617$	−8.89980e9	−1.52539	−0.762697	−	0.646756i	$-0.776125\pi$
$617$	−8.89980e9	−1.52539	−0.762697	+	0.646756i	$0.776125\pi$
$618$	9.53673e8	0.162532
$619$	3.77964e9	0.640520	0.320260	−	0.947330i	$-0.396230\pi$
$619$	3.77964e9	0.640520	0.320260	+	0.947330i	$0.396230\pi$
$620$	−2.52208e9	−0.425000
$621$	−6.48094e8	−0.108597
$622$	−5.45768e9	−0.909373
$623$	−2.38201e9	−0.394671
$624$	−2.42971e8	−0.0400320
$625$	−7.45319e9	−1.22113
$626$	−6.31183e9	−1.02836
$627$	1.45710e9	0.236076
$628$	−2.17038e9	−0.349686
$629$	2.16770e9	0.347313
$630$	−7.22526e8	−0.115123
$631$	−1.05546e10	−1.67240	−0.836200	−	0.548424i	$-0.815228\pi$
$631$	−1.05546e10	−1.67240	−0.836200	+	0.548424i	$0.815228\pi$
$632$	2.80600e9	0.442159
$633$	2.49253e9	0.390596
$634$	−1.17181e9	−0.182619
$635$	2.53430e9	0.392781
$636$	2.30053e9	0.354591
$637$	−2.58475e8	−0.0396214
$638$	4.72317e9	0.720047
$639$	−5.20142e8	−0.0788622
$640$	7.57481e8	0.114220
$641$	2.84140e9	0.426117	0.213058	−	0.977039i	$-0.431658\pi$
$641$	2.84140e9	0.426117	0.213058	+	0.977039i	$0.431658\pi$
$642$	−3.70672e8	−0.0552863
$643$	4.61129e9	0.684043	0.342022	−	0.939692i	$-0.388888\pi$
$643$	4.61129e9	0.684043	0.342022	+	0.939692i	$0.388888\pi$
$644$	7.22804e8	0.106640
$645$	−3.43995e9	−0.504770
$646$	2.56326e9	0.374092
$647$	−4.94293e9	−0.717496	−0.358748	−	0.933434i	$-0.616796\pi$
$647$	−4.94293e9	−0.717496	−0.358748	+	0.933434i	$0.616796\pi$
$648$	2.72098e8	0.0392837
$649$	−4.58310e9	−0.658117
$650$	−9.19871e8	−0.131380
$651$	1.01041e9	0.143536
$652$	−1.89083e9	−0.267169
$653$	−8.74292e9	−1.22874	−0.614370	−	0.789018i	$-0.710590\pi$
$653$	−8.74292e9	−1.22874	−0.614370	+	0.789018i	$0.710590\pi$
$654$	2.13394e9	0.298305
$655$	8.59845e9	1.19557
$656$	6.52488e8	0.0902421
$657$	8.56184e8	0.117784
$658$	3.49838e9	0.478714
$659$	3.60118e9	0.490169	0.245084	−	0.969502i	$-0.421184\pi$
$659$	3.60118e9	0.490169	0.245084	+	0.969502i	$0.421184\pi$
$660$	3.67088e9	0.497012
$661$	−1.06972e10	−1.44067	−0.720337	−	0.693625i	$-0.756013\pi$
$661$	−1.06972e10	−1.44067	−0.720337	+	0.693625i	$0.756013\pi$
$662$	−2.41693e9	−0.323789
$663$	−2.07136e9	−0.276031
$664$	−1.72204e9	−0.228273
$665$	−1.13678e9	−0.149899
$666$	3.62038e8	0.0474891
$667$	−3.30525e9	−0.431285
$668$	−2.49543e9	−0.323912
$669$	−8.36099e9	−1.07961
$670$	−1.20952e10	−1.55365
$671$	1.76456e10	2.25480
$672$	−3.03464e8	−0.0385758
$673$	−1.47416e10	−1.86419	−0.932097	−	0.362208i	$-0.882023\pi$
$673$	−1.47416e10	−1.86419	−0.932097	+	0.362208i	$0.882023\pi$
$674$	7.04792e9	0.886648
$675$	1.03014e9	0.128924
$676$	3.08916e8	0.0384615
$677$	1.35423e10	1.67739	0.838694	−	0.544603i	$-0.183320\pi$
$677$	1.35423e10	1.67739	0.838694	+	0.544603i	$0.183320\pi$
$678$	−4.33236e9	−0.533852
$679$	2.01070e9	0.246492
$680$	6.45764e9	0.787576
$681$	6.77413e9	0.821937
$682$	−5.13349e9	−0.619680
$683$	7.31936e9	0.879024	0.439512	−	0.898237i	$-0.355151\pi$
$683$	7.31936e9	0.879024	0.439512	+	0.898237i	$0.355151\pi$
$684$	4.28102e8	0.0511507
$685$	−2.14322e10	−2.54771
$686$	−3.22829e8	−0.0381802
$687$	1.16634e8	0.0137238
$688$	−1.44480e9	−0.169140
$689$	−2.92492e9	−0.340680
$690$	−2.56887e9	−0.297694
$691$	1.09431e10	1.26173	0.630864	−	0.775894i	$-0.282701\pi$
$691$	1.09431e10	1.26173	0.630864	+	0.775894i	$0.282701\pi$
$692$	−3.32600e9	−0.381549
$693$	−1.47064e9	−0.167857
$694$	5.86572e9	0.666137
$695$	−1.73568e10	−1.96121
$696$	1.38769e9	0.156013
$697$	5.56256e9	0.622243
$698$	7.09820e8	0.0790050
$699$	−5.48713e8	−0.0607681
$700$	−1.14890e9	−0.126601
$701$	−1.12615e10	−1.23476	−0.617381	−	0.786665i	$-0.711806\pi$
$701$	−1.12615e10	−1.23476	−0.617381	+	0.786665i	$0.711806\pi$
$702$	−3.45948e8	−0.0377426
$703$	5.69609e8	0.0618348
$704$	1.54179e9	0.166541
$705$	−1.24334e10	−1.33637
$706$	1.38969e9	0.148629
$707$	−3.78852e9	−0.403183
$708$	−1.34654e9	−0.142594
$709$	−1.26095e10	−1.32873	−0.664366	−	0.747408i	$-0.731298\pi$
$709$	−1.26095e10	−1.32873	−0.664366	+	0.747408i	$0.731298\pi$
$710$	−2.06170e9	−0.216183
$711$	3.99527e9	0.416872
$712$	3.55565e9	0.369181
$713$	3.59240e9	0.371168
$714$	−2.58708e9	−0.265991
$715$	−4.66720e9	−0.477514
$716$	7.10651e9	0.723537
$717$	3.42400e9	0.346910
$718$	−4.12954e9	−0.416357
$719$	8.27190e9	0.829954	0.414977	−	0.909832i	$-0.363790\pi$
$719$	8.27190e9	0.829954	0.414977	+	0.909832i	$0.363790\pi$
$720$	1.07852e9	0.107688
$721$	−1.51440e9	−0.150476
$722$	−6.47742e9	−0.640504
$723$	−5.48968e9	−0.540210
$724$	5.62196e9	0.550558
$725$	5.25370e9	0.512014
$726$	3.26255e9	0.316431
$727$	−1.67032e10	−1.61224	−0.806119	−	0.591754i	$-0.798436\pi$
$727$	−1.67032e10	−1.61224	−0.806119	+	0.591754i	$0.798436\pi$
$728$	3.85828e8	0.0370625
$729$	3.87420e8	0.0370370
$730$	3.39368e9	0.322880
$731$	−1.23171e10	−1.16627
$732$	5.18435e9	0.488546
$733$	−6.12141e9	−0.574100	−0.287050	−	0.957916i	$-0.592675\pi$
$733$	−6.12141e9	−0.574100	−0.287050	+	0.957916i	$0.592675\pi$
$734$	−3.88897e9	−0.362993
$735$	1.14734e9	0.106583
$736$	−1.07894e9	−0.0997526
$737$	−2.46189e10	−2.26533
$738$	9.29031e8	0.0850810
$739$	−1.49914e9	−0.136643	−0.0683214	−	0.997663i	$-0.521764\pi$
$739$	−1.49914e9	−0.136643	−0.0683214	+	0.997663i	$0.521764\pi$
$740$	1.43502e9	0.130181
$741$	−5.44294e8	−0.0491440
$742$	−3.65315e9	−0.328287
$743$	−1.14979e10	−1.02839	−0.514194	−	0.857674i	$-0.671909\pi$
$743$	−1.14979e10	−1.02839	−0.514194	+	0.857674i	$0.671909\pi$
$744$	−1.50824e9	−0.134266
$745$	−6.91226e8	−0.0612454
$746$	1.27983e10	1.12866
$747$	−2.45188e9	−0.215218
$748$	1.31440e10	1.14834
$749$	5.88614e8	0.0511852
$750$	−2.01195e9	−0.174142
$751$	3.49696e9	0.301267	0.150633	−	0.988590i	$-0.451869\pi$
$751$	3.49696e9	0.301267	0.150633	+	0.988590i	$0.451869\pi$
$752$	−5.22207e9	−0.447796
$753$	−5.03749e8	−0.0429964
$754$	−1.76432e9	−0.149892
$755$	2.22473e10	1.88132
$756$	−4.32081e8	−0.0363696
$757$	−2.26305e10	−1.89609	−0.948044	−	0.318140i	$-0.896942\pi$
$757$	−2.26305e10	−1.89609	−0.948044	+	0.318140i	$0.896942\pi$
$758$	9.95759e9	0.830447
$759$	−5.22872e9	−0.434060
$760$	1.69688e9	0.140218
$761$	1.90681e10	1.56842	0.784210	−	0.620496i	$-0.213069\pi$
$761$	1.90681e10	1.56842	0.784210	+	0.620496i	$0.213069\pi$
$762$	1.51555e9	0.124087
$763$	−3.38862e9	−0.276177
$764$	−2.16456e9	−0.175607
$765$	9.19457e9	0.742534
$766$	−1.16669e10	−0.937897
$767$	1.71200e9	0.137000
$768$	4.52985e8	0.0360844
$769$	1.22708e10	0.973037	0.486518	−	0.873670i	$-0.338267\pi$
$769$	1.22708e10	0.973037	0.486518	+	0.873670i	$0.338267\pi$
$770$	−5.82923e9	−0.460144
$771$	7.68268e9	0.603702
$772$	9.60960e9	0.751700
$773$	1.51039e10	1.17615	0.588073	−	0.808808i	$-0.299887\pi$
$773$	1.51039e10	1.17615	0.588073	+	0.808808i	$0.299887\pi$
$774$	−2.05714e9	−0.159467
$775$	−5.71011e9	−0.440645
$776$	−3.00139e9	−0.230572
$777$	−5.74903e8	−0.0439664
$778$	6.88987e9	0.524545
$779$	1.46168e9	0.110783
$780$	−1.37125e9	−0.103463
$781$	−4.19643e9	−0.315211
$782$	−9.19811e9	−0.687820
$783$	1.97583e9	0.147090
$784$	4.81890e8	0.0357143
$785$	−1.22489e10	−0.903763
$786$	5.14200e9	0.377706
$787$	4.21151e9	0.307983	0.153991	−	0.988072i	$-0.450787\pi$
$787$	4.21151e9	0.307983	0.153991	+	0.988072i	$0.450787\pi$
$788$	−1.25837e9	−0.0916147
$789$	−2.14552e9	−0.155512
$790$	1.58362e10	1.14276
$791$	6.87963e9	0.494251
$792$	2.19524e9	0.157016
$793$	−6.59145e9	−0.469380
$794$	3.94959e9	0.280014
$795$	1.29834e10	0.916440
$796$	1.09445e10	0.769129
$797$	1.16779e10	0.817075	0.408537	−	0.912742i	$-0.366039\pi$
$797$	1.16779e10	0.817075	0.408537	+	0.912742i	$0.366039\pi$
$798$	−6.79811e8	−0.0473563
$799$	−4.45189e10	−3.08767
$800$	1.71497e9	0.118425
$801$	5.06264e9	0.348067
$802$	6.00495e8	0.0411054
$803$	6.90756e9	0.470782
$804$	−7.23314e9	−0.490830
$805$	4.07927e9	0.275611
$806$	1.91760e9	0.128999
$807$	−6.73080e9	−0.450826
$808$	5.65517e9	0.377143
$809$	2.04218e10	1.35604	0.678022	−	0.735041i	$-0.262837\pi$
$809$	2.04218e10	1.35604	0.678022	+	0.735041i	$0.262837\pi$
$810$	1.53563e9	0.101529
$811$	−2.73757e10	−1.80216	−0.901078	−	0.433657i	$-0.857223\pi$
$811$	−2.73757e10	−1.80216	−0.901078	+	0.433657i	$0.857223\pi$
$812$	−2.20360e9	−0.144440
$813$	9.24030e9	0.603072
$814$	2.92087e9	0.189813
$815$	−1.06712e10	−0.690497
$816$	3.86176e9	0.248811
$817$	−3.23658e9	−0.207639
$818$	7.55930e9	0.482886
$819$	5.49353e8	0.0349428
$820$	3.68243e9	0.233231
$821$	−1.60589e10	−1.01278	−0.506390	−	0.862304i	$-0.669021\pi$
$821$	−1.60589e10	−1.01278	−0.506390	+	0.862304i	$0.669021\pi$
$822$	−1.28168e10	−0.804873
$823$	2.27859e10	1.42484	0.712420	−	0.701754i	$-0.247599\pi$
$823$	2.27859e10	1.42484	0.712420	+	0.701754i	$0.247599\pi$
$824$	2.26056e9	0.140757
$825$	8.31105e9	0.515308
$826$	2.13825e9	0.132017
$827$	−1.54025e9	−0.0946938	−0.0473469	−	0.998879i	$-0.515077\pi$
$827$	−1.54025e9	−0.0946938	−0.0473469	+	0.998879i	$0.515077\pi$
$828$	−1.53622e9	−0.0940476
$829$	−1.78456e10	−1.08790	−0.543952	−	0.839117i	$-0.683073\pi$
$829$	−1.78456e10	−1.08790	−0.543952	+	0.839117i	$0.683073\pi$
$830$	−9.71860e9	−0.589971
$831$	−5.41530e9	−0.327355
$832$	−5.75930e8	−0.0346688
$833$	4.10819e9	0.246259
$834$	−1.03796e10	−0.619585
$835$	−1.40834e10	−0.837151
$836$	3.45386e9	0.204448
$837$	−2.14748e9	−0.126587
$838$	−9.61574e9	−0.564454
$839$	2.17246e9	0.126995	0.0634973	−	0.997982i	$-0.479775\pi$
$839$	2.17246e9	0.126995	0.0634973	+	0.997982i	$0.479775\pi$
$840$	−1.71265e9	−0.0996993
$841$	−7.17322e9	−0.415842
$842$	−3.11937e9	−0.180084
$843$	−5.66083e9	−0.325450
$844$	5.90822e9	0.338266
$845$	1.74342e9	0.0994039
$846$	−7.43533e9	−0.422186
$847$	−5.18081e9	−0.292958
$848$	5.45310e9	0.307085
$849$	3.27286e9	0.183548
$850$	1.46204e10	0.816568
$851$	−2.04401e9	−0.113692
$852$	−1.23293e9	−0.0682967
$853$	−2.05079e10	−1.13135	−0.565677	−	0.824627i	$-0.691385\pi$
$853$	−2.05079e10	−1.13135	−0.565677	+	0.824627i	$0.691385\pi$
$854$	−8.23256e9	−0.452306
$855$	2.41607e9	0.132199
$856$	−8.78631e8	−0.0478794
$857$	−2.94164e10	−1.59645	−0.798227	−	0.602357i	$-0.794229\pi$
$857$	−2.94164e10	−1.59645	−0.798227	+	0.602357i	$0.794229\pi$
$858$	−2.79106e9	−0.150856
$859$	1.16301e10	0.626047	0.313023	−	0.949745i	$-0.398658\pi$
$859$	1.16301e10	0.626047	0.313023	+	0.949745i	$0.398658\pi$
$860$	−8.15396e9	−0.437143
$861$	−1.47527e9	−0.0787697
$862$	7.75644e9	0.412465
$863$	1.94901e10	1.03223	0.516116	−	0.856519i	$-0.327377\pi$
$863$	1.94901e10	1.03223	0.516116	+	0.856519i	$0.327377\pi$
$864$	6.44973e8	0.0340207
$865$	−1.87708e10	−0.986115
$866$	1.86013e10	0.973265
$867$	2.18430e10	1.13827
$868$	2.39504e9	0.124306
$869$	3.22332e10	1.66623
$870$	7.83166e9	0.403215
$871$	9.19630e9	0.471574
$872$	5.05823e9	0.258340
$873$	−4.27347e9	−0.217386
$874$	−2.41700e9	−0.122458
$875$	3.19490e9	0.161224
$876$	2.02947e9	0.102004
$877$	−1.15756e10	−0.579486	−0.289743	−	0.957104i	$-0.593570\pi$
$877$	−1.15756e10	−0.579486	−0.289743	+	0.957104i	$0.593570\pi$
$878$	−1.07165e10	−0.534346
$879$	−3.08581e9	−0.153253
$880$	8.70135e9	0.430425
$881$	3.90909e10	1.92601	0.963007	−	0.269475i	$-0.0868501\pi$
$881$	3.90909e10	1.92601	0.963007	+	0.269475i	$0.0868501\pi$
$882$	6.86129e8	0.0336718
$883$	−2.89335e10	−1.41429	−0.707145	−	0.707069i	$-0.750017\pi$
$883$	−2.89335e10	−1.41429	−0.707145	+	0.707069i	$0.750017\pi$
$884$	−4.90989e9	−0.239050
$885$	−7.59941e9	−0.368535
$886$	−8.93861e9	−0.431770
$887$	2.94626e10	1.41755	0.708774	−	0.705435i	$-0.249248\pi$
$887$	2.94626e10	1.41755	0.708774	+	0.705435i	$0.249248\pi$
$888$	8.58164e8	0.0411268
$889$	−2.40664e9	−0.114883
$890$	2.00669e10	0.954149
$891$	3.12565e9	0.148036
$892$	−1.98186e10	−0.934968
$893$	−1.16983e10	−0.549722
$894$	−4.13364e8	−0.0193487
$895$	4.01068e10	1.86998
$896$	−7.19323e8	−0.0334077
$897$	1.95317e9	0.0903581
$898$	−4.21692e9	−0.194325
$899$	−1.09521e10	−0.502733
$900$	2.44182e9	0.111652
$901$	4.64885e10	2.11743
$902$	7.49528e9	0.340067
$903$	3.26667e9	0.147638
$904$	−1.02693e10	−0.462329
$905$	3.17285e10	1.42292
$906$	1.33042e10	0.594347
$907$	2.92582e10	1.30203	0.651017	−	0.759063i	$-0.274343\pi$
$907$	2.92582e10	1.30203	0.651017	+	0.759063i	$0.274343\pi$
$908$	1.60572e10	0.711819
$909$	8.05199e9	0.355574
$910$	2.17749e9	0.0957880
$911$	−1.13326e10	−0.496611	−0.248306	−	0.968682i	$-0.579874\pi$
$911$	−1.13326e10	−0.496611	−0.248306	+	0.968682i	$0.579874\pi$
$912$	1.01476e9	0.0442978
$913$	−1.97814e10	−0.860221
$914$	−1.53672e10	−0.665706
$915$	2.92588e10	1.26265
$916$	2.76465e8	0.0118852
$917$	−8.16531e9	−0.349687
$918$	5.49849e9	0.234582
$919$	−3.15178e10	−1.33953	−0.669763	−	0.742575i	$-0.733604\pi$
$919$	−3.15178e10	−1.33953	−0.669763	+	0.742575i	$0.733604\pi$
$920$	−6.08917e9	−0.257811
$921$	2.66787e9	0.112527
$922$	−2.07298e10	−0.871037
$923$	1.56756e9	0.0656173
$924$	−3.48597e9	−0.145369
$925$	3.24895e9	0.134973
$926$	−2.09903e10	−0.868721
$927$	3.21865e9	0.132707
$928$	3.28934e9	0.135111
$929$	4.17852e10	1.70989	0.854944	−	0.518721i	$-0.173591\pi$
$929$	4.17852e10	1.70989	0.854944	+	0.518721i	$0.173591\pi$
$930$	−8.51203e9	−0.347011
$931$	1.07951e9	0.0438434
$932$	−1.30065e9	−0.0526267
$933$	−1.84197e10	−0.742500
$934$	−1.44004e9	−0.0578308
$935$	7.41803e10	2.96789
$936$	−8.20026e8	−0.0326860
$937$	2.43741e10	0.967922	0.483961	−	0.875090i	$-0.339198\pi$
$937$	2.43741e10	0.967922	0.483961	+	0.875090i	$0.339198\pi$
$938$	1.14860e10	0.454420
$939$	−2.13024e10	−0.839652
$940$	−2.94716e10	−1.15733
$941$	−1.89645e10	−0.741954	−0.370977	−	0.928642i	$-0.620977\pi$
$941$	−1.89645e10	−0.741954	−0.370977	+	0.928642i	$0.620977\pi$
$942$	−7.32504e9	−0.285517
$943$	−5.24517e9	−0.203689
$944$	−3.19179e9	−0.123490
$945$	−2.43852e9	−0.0939974
$946$	−1.65967e10	−0.637387
$947$	1.82225e9	0.0697242	0.0348621	−	0.999392i	$-0.488901\pi$
$947$	1.82225e9	0.0697242	0.0348621	+	0.999392i	$0.488901\pi$
$948$	9.47027e9	0.361021
$949$	−2.58030e9	−0.0980026
$950$	3.84182e9	0.145380
$951$	−3.95487e9	−0.149108
$952$	−6.13234e9	−0.230355
$953$	1.58127e10	0.591808	0.295904	−	0.955218i	$-0.404379\pi$
$953$	1.58127e10	0.591808	0.295904	+	0.955218i	$0.404379\pi$
$954$	7.76428e9	0.289522
$955$	−1.22160e10	−0.453857
$956$	8.11614e9	0.300433
$957$	1.59407e10	0.587916
$958$	−6.06196e9	−0.222758
$959$	2.03526e10	0.745167
$960$	2.55650e9	0.0932601
$961$	−1.56091e10	−0.567343
$962$	−1.09108e9	−0.0395133
$963$	−1.25102e9	−0.0451411
$964$	−1.30126e10	−0.467836
$965$	5.42334e10	1.94277
$966$	2.43946e9	0.0870712
$967$	−8.59717e9	−0.305747	−0.152874	−	0.988246i	$-0.548853\pi$
$967$	−8.59717e9	−0.305747	−0.152874	+	0.988246i	$0.548853\pi$
$968$	7.73346e9	0.274037
$969$	8.65099e9	0.305445
$970$	−1.69389e10	−0.595914
$971$	2.61660e9	0.0917212	0.0458606	−	0.998948i	$-0.485397\pi$
$971$	2.61660e9	0.0917212	0.0458606	+	0.998948i	$0.485397\pi$
$972$	9.18330e8	0.0320750
$973$	1.64825e10	0.573625
$974$	8.13178e9	0.281987
$975$	−3.10456e9	−0.107272
$976$	1.22888e10	0.423094
$977$	−3.36127e10	−1.15312	−0.576558	−	0.817056i	$-0.695605\pi$
$977$	−3.36127e10	−1.15312	−0.576558	+	0.817056i	$0.695605\pi$
$978$	−6.38154e9	−0.218142
$979$	4.08446e10	1.39122
$980$	2.71963e9	0.0923036
$981$	7.20206e9	0.243565
$982$	2.11008e10	0.711063
$983$	3.95280e10	1.32730	0.663648	−	0.748045i	$-0.269007\pi$
$983$	3.95280e10	1.32730	0.663648	+	0.748045i	$0.269007\pi$
$984$	2.20215e9	0.0736823
$985$	−7.10180e9	−0.236778
$986$	2.80421e10	0.931625
$987$	1.18070e10	0.390868
$988$	−1.29018e9	−0.0425599
$989$	1.16143e10	0.381774
$990$	1.23892e10	0.405808
$991$	1.10863e10	0.361850	0.180925	−	0.983497i	$-0.442091\pi$
$991$	1.10863e10	0.361850	0.180925	+	0.983497i	$0.442091\pi$
$992$	−3.57510e9	−0.116278
$993$	−8.15715e9	−0.264372
$994$	1.95785e9	0.0632304
$995$	6.17670e10	1.98781
$996$	−5.81187e9	−0.186384
$997$	2.25295e10	0.719976	0.359988	−	0.932957i	$-0.382781\pi$
$997$	2.25295e10	0.719976	0.359988	+	0.932957i	$0.382781\pi$
$998$	−1.28809e10	−0.410195
$999$	1.22188e9	0.0387747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.m.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.m.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +361.195 q^{5} +216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +361.195 q^{5} +216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +2889.56 q^{10} +5881.46 q^{11} +1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} +9752.26 q^{15} +4096.00 q^{16} +34919.0 q^{17} +5832.00 q^{18} +9175.72 q^{19} +23116.5 q^{20} -9261.00 q^{21} +47051.7 q^{22} -32926.6 q^{23} +13824.0 q^{24} +52336.7 q^{25} -17576.0 q^{26} +19683.0 q^{27} -21952.0 q^{28} +100383. q^{29} +78018.1 q^{30} -109103. q^{31} +32768.0 q^{32} +158799. q^{33} +279352. q^{34} -123890. q^{35} +46656.0 q^{36} +62077.8 q^{37} +73405.7 q^{38} -59319.0 q^{39} +184932. q^{40} +159299. q^{41} -74088.0 q^{42} -352734. q^{43} +376413. q^{44} +263311. q^{45} -263413. q^{46} -1.27492e6 q^{47} +110592. q^{48} +117649. q^{49} +418694. q^{50} +942814. q^{51} -140608. q^{52} +1.33132e6 q^{53} +157464. q^{54} +2.12435e6 q^{55} -175616. q^{56} +247744. q^{57} +803061. q^{58} -779245. q^{59} +624145. q^{60} +3.00020e6 q^{61} -872826. q^{62} -250047. q^{63} +262144. q^{64} -793545. q^{65} +1.27040e6 q^{66} -4.18585e6 q^{67} +2.23482e6 q^{68} -889018. q^{69} -991119. q^{70} -713501. q^{71} +373248. q^{72} +1.17446e6 q^{73} +496623. q^{74} +1.41309e6 q^{75} +587246. q^{76} -2.01734e6 q^{77} -474552. q^{78} +5.48048e6 q^{79} +1.47945e6 q^{80} +531441. q^{81} +1.27439e6 q^{82} -3.36335e6 q^{83} -592704. q^{84} +1.26126e7 q^{85} -2.82187e6 q^{86} +2.71033e6 q^{87} +3.01131e6 q^{88} +6.94464e6 q^{89} +2.10649e6 q^{90} +753571. q^{91} -2.10730e6 q^{92} -2.94579e6 q^{93} -1.01994e7 q^{94} +3.31422e6 q^{95} +884736. q^{96} -5.86210e6 q^{97} +941192. q^{98} +4.28758e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 40 q^{2} + 135 q^{3} + 320 q^{4} + 299 q^{5} + 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9}+O(q^{10}) \) 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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