LMFDB - Embedded newform 546.8.a.r.1.6

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:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 264981x^{4} + 17519669x^{3} + 15113237808x^{2} - 1787613752904x - 21984668630064 $ x^6 - x^5 - 264981x^4 + 17519669x^3 + 15113237808x^2 - 1787613752904x - 21984668630064
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-462.924$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +496.924 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +496.924 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +3975.39 q^{10} -3824.74 q^{11} -1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} -13417.0 q^{15} +4096.00 q^{16} -2147.73 q^{17} +5832.00 q^{18} -18544.8 q^{19} +31803.1 q^{20} +9261.00 q^{21} -30597.9 q^{22} -67563.5 q^{23} -13824.0 q^{24} +168809. q^{25} +17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} +58711.4 q^{29} -107336. q^{30} +157539. q^{31} +32768.0 q^{32} +103268. q^{33} -17181.9 q^{34} -170445. q^{35} +46656.0 q^{36} +381564. q^{37} -148359. q^{38} -59319.0 q^{39} +254425. q^{40} +227136. q^{41} +74088.0 q^{42} +532865. q^{43} -244783. q^{44} +362258. q^{45} -540508. q^{46} +714364. q^{47} -110592. q^{48} +117649. q^{49} +1.35047e6 q^{50} +57988.8 q^{51} +140608. q^{52} -352284. q^{53} -157464. q^{54} -1.90061e6 q^{55} -175616. q^{56} +500710. q^{57} +469691. q^{58} -534961. q^{59} -858685. q^{60} +947554. q^{61} +1.26032e6 q^{62} -250047. q^{63} +262144. q^{64} +1.09174e6 q^{65} +826144. q^{66} +2.20515e6 q^{67} -137455. q^{68} +1.82421e6 q^{69} -1.36356e6 q^{70} -5.03775e6 q^{71} +373248. q^{72} +1.46454e6 q^{73} +3.05251e6 q^{74} -4.55783e6 q^{75} -1.18687e6 q^{76} +1.31189e6 q^{77} -474552. q^{78} +8.61725e6 q^{79} +2.03540e6 q^{80} +531441. q^{81} +1.81709e6 q^{82} -8.80720e6 q^{83} +592704. q^{84} -1.06726e6 q^{85} +4.26292e6 q^{86} -1.58521e6 q^{87} -1.95827e6 q^{88} +3.11870e6 q^{89} +2.89806e6 q^{90} -753571. q^{91} -4.32406e6 q^{92} -4.25357e6 q^{93} +5.71491e6 q^{94} -9.21537e6 q^{95} -884736. q^{96} +2.00663e6 q^{97} +941192. q^{98} -2.78824e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 203 q^{5} - 1296 q^{6} - 2058 q^{7} + 3072 q^{8} + 4374 q^{9}+O(q^{10}) $ 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 203 * q^5 - 1296 * q^6 - 2058 * q^7 + 3072 * q^8 + 4374 * q^9	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 203 q^{5} - 1296 q^{6} - 2058 q^{7} + 3072 q^{8} + 4374 q^{9} + 1624 q^{10} - 2690 q^{11} - 10368 q^{12} + 13182 q^{13} - 16464 q^{14} - 5481 q^{15} + 24576 q^{16} + 2910 q^{17} + 34992 q^{18} - 13055 q^{19} + 12992 q^{20} + 55566 q^{21} - 21520 q^{22} + 11581 q^{23} - 82944 q^{24} + 68081 q^{25} + 105456 q^{26} - 118098 q^{27} - 131712 q^{28} - 92335 q^{29} - 43848 q^{30} - 83081 q^{31} + 196608 q^{32} + 72630 q^{33} + 23280 q^{34} - 69629 q^{35} + 279936 q^{36} - 265114 q^{37} - 104440 q^{38} - 355914 q^{39} + 103936 q^{40} - 367468 q^{41} + 444528 q^{42} + 454955 q^{43} - 172160 q^{44} + 147987 q^{45} + 92648 q^{46} + 733973 q^{47} - 663552 q^{48} + 705894 q^{49} + 544648 q^{50} - 78570 q^{51} + 843648 q^{52} - 1577379 q^{53} - 944784 q^{54} + 2231118 q^{55} - 1053696 q^{56} + 352485 q^{57} - 738680 q^{58} + 2062708 q^{59} - 350784 q^{60} - 271270 q^{61} - 664648 q^{62} - 1500282 q^{63} + 1572864 q^{64} + 445991 q^{65} + 581040 q^{66} - 758674 q^{67} + 186240 q^{68} - 312687 q^{69} - 557032 q^{70} - 6138216 q^{71} + 2239488 q^{72} + 6361979 q^{73} - 2120912 q^{74} - 1838187 q^{75} - 835520 q^{76} + 922670 q^{77} - 2847312 q^{78} - 899781 q^{79} + 831488 q^{80} + 3188646 q^{81} - 2939744 q^{82} + 3313561 q^{83} + 3556224 q^{84} + 5307940 q^{85} + 3639640 q^{86} + 2493045 q^{87} - 1377280 q^{88} + 11210703 q^{89} + 1183896 q^{90} - 4521426 q^{91} + 741184 q^{92} + 2243187 q^{93} + 5871784 q^{94} + 12912395 q^{95} - 5308416 q^{96} + 28682643 q^{97} + 5647152 q^{98} - 1961010 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 203 * q^5 - 1296 * q^6 - 2058 * q^7 + 3072 * q^8 + 4374 * q^9 + 1624 * q^10 - 2690 * q^11 - 10368 * q^12 + 13182 * q^13 - 16464 * q^14 - 5481 * q^15 + 24576 * q^16 + 2910 * q^17 + 34992 * q^18 - 13055 * q^19 + 12992 * q^20 + 55566 * q^21 - 21520 * q^22 + 11581 * q^23 - 82944 * q^24 + 68081 * q^25 + 105456 * q^26 - 118098 * q^27 - 131712 * q^28 - 92335 * q^29 - 43848 * q^30 - 83081 * q^31 + 196608 * q^32 + 72630 * q^33 + 23280 * q^34 - 69629 * q^35 + 279936 * q^36 - 265114 * q^37 - 104440 * q^38 - 355914 * q^39 + 103936 * q^40 - 367468 * q^41 + 444528 * q^42 + 454955 * q^43 - 172160 * q^44 + 147987 * q^45 + 92648 * q^46 + 733973 * q^47 - 663552 * q^48 + 705894 * q^49 + 544648 * q^50 - 78570 * q^51 + 843648 * q^52 - 1577379 * q^53 - 944784 * q^54 + 2231118 * q^55 - 1053696 * q^56 + 352485 * q^57 - 738680 * q^58 + 2062708 * q^59 - 350784 * q^60 - 271270 * q^61 - 664648 * q^62 - 1500282 * q^63 + 1572864 * q^64 + 445991 * q^65 + 581040 * q^66 - 758674 * q^67 + 186240 * q^68 - 312687 * q^69 - 557032 * q^70 - 6138216 * q^71 + 2239488 * q^72 + 6361979 * q^73 - 2120912 * q^74 - 1838187 * q^75 - 835520 * q^76 + 922670 * q^77 - 2847312 * q^78 - 899781 * q^79 + 831488 * q^80 + 3188646 * q^81 - 2939744 * q^82 + 3313561 * q^83 + 3556224 * q^84 + 5307940 * q^85 + 3639640 * q^86 + 2493045 * q^87 - 1377280 * q^88 + 11210703 * q^89 + 1183896 * q^90 - 4521426 * q^91 + 741184 * q^92 + 2243187 * q^93 + 5871784 * q^94 + 12912395 * q^95 - 5308416 * q^96 + 28682643 * q^97 + 5647152 * q^98 - 1961010 * 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
$5$	496.924	1.77785	0.888925	−	0.458053i	$-0.151453\pi$
$5$	496.924	1.77785	0.888925	+	0.458053i	$0.151453\pi$
$6$	−216.000	−0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	3975.39	1.25713
$11$	−3824.74	−0.866418	−0.433209	−	0.901293i	$-0.642619\pi$
$11$	−3824.74	−0.866418	−0.433209	+	0.901293i	$0.642619\pi$
$12$	−1728.00	−0.288675
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	−2744.00	−0.267261
$15$	−13417.0	−1.02644
$16$	4096.00	0.250000
$17$	−2147.73	−0.106025	−0.0530126	−	0.998594i	$-0.516882\pi$
$17$	−2147.73	−0.106025	−0.0530126	+	0.998594i	$0.516882\pi$
$18$	5832.00	0.235702
$19$	−18544.8	−0.620276	−0.310138	−	0.950691i	$-0.600375\pi$
$19$	−18544.8	−0.620276	−0.310138	+	0.950691i	$0.600375\pi$
$20$	31803.1	0.888925
$21$	9261.00	0.218218
$22$	−30597.9	−0.612650
$23$	−67563.5	−1.15788	−0.578941	−	0.815369i	$-0.696534\pi$
$23$	−67563.5	−1.15788	−0.578941	+	0.815369i	$0.696534\pi$
$24$	−13824.0	−0.204124
$25$	168809.	2.16075
$26$	17576.0	0.196116
$27$	−19683.0	−0.192450
$28$	−21952.0	−0.188982
$29$	58711.4	0.447022	0.223511	−	0.974701i	$-0.428248\pi$
$29$	58711.4	0.447022	0.223511	+	0.974701i	$0.428248\pi$
$30$	−107336.	−0.725804
$31$	157539.	0.949781	0.474890	−	0.880045i	$-0.342488\pi$
$31$	157539.	0.949781	0.474890	+	0.880045i	$0.342488\pi$
$32$	32768.0	0.176777
$33$	103268.	0.500227
$34$	−17181.9	−0.0749712
$35$	−170445.	−0.671964
$36$	46656.0	0.166667
$37$	381564.	1.23840	0.619200	−	0.785233i	$-0.287457\pi$
$37$	381564.	1.23840	0.619200	+	0.785233i	$0.287457\pi$
$38$	−148359.	−0.438602
$39$	−59319.0	−0.160128
$40$	254425.	0.628565
$41$	227136.	0.514686	0.257343	−	0.966320i	$-0.417153\pi$
$41$	227136.	0.514686	0.257343	+	0.966320i	$0.417153\pi$
$42$	74088.0	0.154303
$43$	532865.	1.02206	0.511031	−	0.859562i	$-0.329264\pi$
$43$	532865.	1.02206	0.511031	+	0.859562i	$0.329264\pi$
$44$	−244783.	−0.433209
$45$	362258.	0.592617
$46$	−540508.	−0.818747
$47$	714364.	1.00364	0.501819	−	0.864973i	$-0.332664\pi$
$47$	714364.	1.00364	0.501819	+	0.864973i	$0.332664\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	1.35047e6	1.52788
$51$	57988.8	0.0612137
$52$	140608.	0.138675
$53$	−352284.	−0.325033	−0.162516	−	0.986706i	$-0.551961\pi$
$53$	−352284.	−0.325033	−0.162516	+	0.986706i	$0.551961\pi$
$54$	−157464.	−0.136083
$55$	−1.90061e6	−1.54036
$56$	−175616.	−0.133631
$57$	500710.	0.358117
$58$	469691.	0.316093
$59$	−534961.	−0.339109	−0.169555	−	0.985521i	$-0.554233\pi$
$59$	−534961.	−0.339109	−0.169555	+	0.985521i	$0.554233\pi$
$60$	−858685.	−0.513221
$61$	947554.	0.534502	0.267251	−	0.963627i	$-0.413885\pi$
$61$	947554.	0.534502	0.267251	+	0.963627i	$0.413885\pi$
$62$	1.26032e6	0.671596
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	1.09174e6	0.493087
$66$	826144.	0.353714
$67$	2.20515e6	0.895728	0.447864	−	0.894102i	$-0.352185\pi$
$67$	2.20515e6	0.895728	0.447864	+	0.894102i	$0.352185\pi$
$68$	−137455.	−0.0530126
$69$	1.82421e6	0.668504
$70$	−1.36356e6	−0.475150
$71$	−5.03775e6	−1.67044	−0.835222	−	0.549912i	$-0.814661\pi$
$71$	−5.03775e6	−1.67044	−0.835222	+	0.549912i	$0.814661\pi$
$72$	373248.	0.117851
$73$	1.46454e6	0.440628	0.220314	−	0.975429i	$-0.429292\pi$
$73$	1.46454e6	0.440628	0.220314	+	0.975429i	$0.429292\pi$
$74$	3.05251e6	0.875681
$75$	−4.55783e6	−1.24751
$76$	−1.18687e6	−0.310138
$77$	1.31189e6	0.327475
$78$	−474552.	−0.113228
$79$	8.61725e6	1.96641	0.983204	−	0.182509i	$-0.0584217\pi$
$79$	8.61725e6	1.96641	0.983204	+	0.182509i	$0.0584217\pi$
$80$	2.03540e6	0.444462
$81$	531441.	0.111111
$82$	1.81709e6	0.363938
$83$	−8.80720e6	−1.69069	−0.845346	−	0.534219i	$-0.820606\pi$
$83$	−8.80720e6	−1.69069	−0.845346	+	0.534219i	$0.820606\pi$
$84$	592704.	0.109109
$85$	−1.06726e6	−0.188497
$86$	4.26292e6	0.722707
$87$	−1.58521e6	−0.258089
$88$	−1.95827e6	−0.306325
$89$	3.11870e6	0.468930	0.234465	−	0.972125i	$-0.424666\pi$
$89$	3.11870e6	0.468930	0.234465	+	0.972125i	$0.424666\pi$
$90$	2.89806e6	0.419043
$91$	−753571.	−0.104828
$92$	−4.32406e6	−0.578941
$93$	−4.25357e6	−0.548356
$94$	5.71491e6	0.709679
$95$	−9.21537e6	−1.10276
$96$	−884736.	−0.102062
$97$	2.00663e6	0.223238	0.111619	−	0.993751i	$-0.464396\pi$
$97$	2.00663e6	0.223238	0.111619	+	0.993751i	$0.464396\pi$
$98$	941192.	0.101015
$99$	−2.78824e6	−0.288806
$100$	1.08037e7	1.08037
$101$	1.91316e7	1.84767	0.923837	−	0.382785i	$-0.125035\pi$
$101$	1.91316e7	1.84767	0.923837	+	0.382785i	$0.125035\pi$
$102$	463910.	0.0432846
$103$	1.37161e6	0.123680	0.0618400	−	0.998086i	$-0.480303\pi$
$103$	1.37161e6	0.123680	0.0618400	+	0.998086i	$0.480303\pi$
$104$	1.12486e6	0.0980581
$105$	4.60201e6	0.387959
$106$	−2.81827e6	−0.229833
$107$	2.35974e7	1.86218	0.931088	−	0.364795i	$-0.118861\pi$
$107$	2.35974e7	1.86218	0.931088	+	0.364795i	$0.118861\pi$
$108$	−1.25971e6	−0.0962250
$109$	8.39526e6	0.620928	0.310464	−	0.950585i	$-0.399516\pi$
$109$	8.39526e6	0.620928	0.310464	+	0.950585i	$0.399516\pi$
$110$	−1.52048e7	−1.08920
$111$	−1.03022e7	−0.714991
$112$	−1.40493e6	−0.0944911
$113$	−7.06983e6	−0.460930	−0.230465	−	0.973081i	$-0.574025\pi$
$113$	−7.06983e6	−0.460930	−0.230465	+	0.973081i	$0.574025\pi$
$114$	4.00568e6	0.253227
$115$	−3.35739e7	−2.05854
$116$	3.75753e6	0.223511
$117$	1.60161e6	0.0924500
$118$	−4.27969e6	−0.239787
$119$	736673.	0.0400738
$120$	−6.86948e6	−0.362902
$121$	−4.85853e6	−0.249319
$122$	7.58043e6	0.377950
$123$	−6.13267e6	−0.297154
$124$	1.00825e7	0.474890
$125$	4.50629e7	2.06364
$126$	−2.00038e6	−0.0890871
$127$	−985521.	−0.0426926	−0.0213463	−	0.999772i	$-0.506795\pi$
$127$	−985521.	−0.0426926	−0.0213463	+	0.999772i	$0.506795\pi$
$128$	2.09715e6	0.0883883
$129$	−1.43873e7	−0.590088
$130$	8.73394e6	0.348665
$131$	−3.54561e7	−1.37798	−0.688988	−	0.724773i	$-0.741945\pi$
$131$	−3.54561e7	−1.37798	−0.688988	+	0.724773i	$0.741945\pi$
$132$	6.60915e6	0.250113
$133$	6.36088e6	0.234442
$134$	1.76412e7	0.633375
$135$	−9.78096e6	−0.342147
$136$	−1.09964e6	−0.0374856
$137$	2.66368e7	0.885034	0.442517	−	0.896760i	$-0.354086\pi$
$137$	2.66368e7	0.885034	0.442517	+	0.896760i	$0.354086\pi$
$138$	1.45937e7	0.472704
$139$	−5.67858e7	−1.79345	−0.896723	−	0.442592i	$-0.854059\pi$
$139$	−5.67858e7	−1.79345	−0.896723	+	0.442592i	$0.854059\pi$
$140$	−1.09085e7	−0.335982
$141$	−1.92878e7	−0.579451
$142$	−4.03020e7	−1.18118
$143$	−8.40296e6	−0.240301
$144$	2.98598e6	0.0833333
$145$	2.91751e7	0.794739
$146$	1.17163e7	0.311571
$147$	−3.17652e6	−0.0824786
$148$	2.44201e7	0.619200
$149$	−7.19892e7	−1.78285	−0.891427	−	0.453165i	$-0.850295\pi$
$149$	−7.19892e7	−1.78285	−0.891427	+	0.453165i	$0.850295\pi$
$150$	−3.64627e7	−0.882122
$151$	−3.22126e7	−0.761388	−0.380694	−	0.924701i	$-0.624315\pi$
$151$	−3.22126e7	−0.761388	−0.380694	+	0.924701i	$0.624315\pi$
$152$	−9.49495e6	−0.219301
$153$	−1.56570e6	−0.0353417
$154$	1.04951e7	0.231560
$155$	7.82852e7	1.68857
$156$	−3.79642e6	−0.0800641
$157$	−8.76407e7	−1.80741	−0.903706	−	0.428153i	$-0.859164\pi$
$157$	−8.76407e7	−1.80741	−0.903706	+	0.428153i	$0.859164\pi$
$158$	6.89380e7	1.39046
$159$	9.51167e6	0.187658
$160$	1.62832e7	0.314282
$161$	2.31743e7	0.437639
$162$	4.25153e6	0.0785674
$163$	7.24820e7	1.31091	0.655456	−	0.755233i	$-0.272476\pi$
$163$	7.24820e7	1.31091	0.655456	+	0.755233i	$0.272476\pi$
$164$	1.45367e7	0.257343
$165$	5.13164e7	0.889328
$166$	−7.04576e7	−1.19550
$167$	7.83523e7	1.30180	0.650900	−	0.759163i	$-0.274392\pi$
$167$	7.83523e7	1.30180	0.650900	+	0.759163i	$0.274392\pi$
$168$	4.74163e6	0.0771517
$169$	4.82681e6	0.0769231
$170$	−8.53808e6	−0.133287
$171$	−1.35192e7	−0.206759
$172$	3.41033e7	0.511031
$173$	2.63684e7	0.387189	0.193595	−	0.981082i	$-0.437985\pi$
$173$	2.63684e7	0.387189	0.193595	+	0.981082i	$0.437985\pi$
$174$	−1.26817e7	−0.182496
$175$	−5.79013e7	−0.816687
$176$	−1.56661e7	−0.216605
$177$	1.44439e7	0.195785
$178$	2.49496e7	0.331584
$179$	1.43940e8	1.87584	0.937920	−	0.346852i	$-0.112749\pi$
$179$	1.43940e8	1.87584	0.937920	+	0.346852i	$0.112749\pi$
$180$	2.31845e7	0.296308
$181$	7.83164e7	0.981698	0.490849	−	0.871245i	$-0.336687\pi$
$181$	7.83164e7	0.981698	0.490849	+	0.871245i	$0.336687\pi$
$182$	−6.02857e6	−0.0741249
$183$	−2.55840e7	−0.308595
$184$	−3.45925e7	−0.409373
$185$	1.89608e8	2.20169
$186$	−3.40285e7	−0.387746
$187$	8.21452e6	0.0918622
$188$	4.57193e7	0.501819
$189$	6.75127e6	0.0727393
$190$	−7.37230e7	−0.779768
$191$	6.34840e7	0.659246	0.329623	−	0.944113i	$-0.393078\pi$
$191$	6.34840e7	0.659246	0.329623	+	0.944113i	$0.393078\pi$
$192$	−7.07789e6	−0.0721688
$193$	9.55888e7	0.957098	0.478549	−	0.878061i	$-0.341163\pi$
$193$	9.55888e7	0.957098	0.478549	+	0.878061i	$0.341163\pi$
$194$	1.60531e7	0.157853
$195$	−2.94770e7	−0.284684
$196$	7.52954e6	0.0714286
$197$	8.28275e7	0.771867	0.385934	−	0.922527i	$-0.373879\pi$
$197$	8.28275e7	0.771867	0.385934	+	0.922527i	$0.373879\pi$
$198$	−2.23059e7	−0.204217
$199$	−8.13880e7	−0.732107	−0.366053	−	0.930594i	$-0.619291\pi$
$199$	−8.13880e7	−0.732107	−0.366053	+	0.930594i	$0.619291\pi$
$200$	8.64300e7	0.763940
$201$	−5.95390e7	−0.517149
$202$	1.53052e8	1.30650
$203$	−2.01380e7	−0.168959
$204$	3.71128e6	0.0306068
$205$	1.12869e8	0.915035
$206$	1.09729e7	0.0874550
$207$	−4.92538e7	−0.385961
$208$	8.99891e6	0.0693375
$209$	7.09292e7	0.537419
$210$	3.68161e7	0.274328
$211$	1.89709e8	1.39027	0.695134	−	0.718880i	$-0.255345\pi$
$211$	1.89709e8	1.39027	0.695134	+	0.718880i	$0.255345\pi$
$212$	−2.25462e7	−0.162516
$213$	1.36019e8	0.964432
$214$	1.88779e8	1.31676
$215$	2.64793e8	1.81707
$216$	−1.00777e7	−0.0680414
$217$	−5.40360e7	−0.358983
$218$	6.71621e7	0.439063
$219$	−3.95426e7	−0.254396
$220$	−1.21639e8	−0.770181
$221$	−4.71857e6	−0.0294061
$222$	−8.24178e7	−0.505575
$223$	4.32655e7	0.261261	0.130630	−	0.991431i	$-0.458300\pi$
$223$	4.32655e7	0.261261	0.130630	+	0.991431i	$0.458300\pi$
$224$	−1.12394e7	−0.0668153
$225$	1.23061e8	0.720250
$226$	−5.65587e7	−0.325926
$227$	1.76524e7	0.100164	0.0500821	−	0.998745i	$-0.484052\pi$
$227$	1.76524e7	0.100164	0.0500821	+	0.998745i	$0.484052\pi$
$228$	3.20455e7	0.179058
$229$	2.28130e8	1.25533	0.627664	−	0.778484i	$-0.284011\pi$
$229$	2.28130e8	1.25533	0.627664	+	0.778484i	$0.284011\pi$
$230$	−2.68591e8	−1.45561
$231$	−3.54209e7	−0.189068
$232$	3.00602e7	0.158046
$233$	−9.21660e7	−0.477337	−0.238668	−	0.971101i	$-0.576711\pi$
$233$	−9.21660e7	−0.477337	−0.238668	+	0.971101i	$0.576711\pi$
$234$	1.28129e7	0.0653720
$235$	3.54985e8	1.78432
$236$	−3.42375e7	−0.169555
$237$	−2.32666e8	−1.13531
$238$	5.89338e6	0.0283364
$239$	1.66857e8	0.790591	0.395296	−	0.918554i	$-0.370642\pi$
$239$	1.66857e8	0.790591	0.395296	+	0.918554i	$0.370642\pi$
$240$	−5.49558e7	−0.256611
$241$	2.35779e8	1.08504	0.542519	−	0.840043i	$-0.317471\pi$
$241$	2.35779e8	1.08504	0.542519	+	0.840043i	$0.317471\pi$
$242$	−3.88682e7	−0.176295
$243$	−1.43489e7	−0.0641500
$244$	6.06435e7	0.267251
$245$	5.84626e7	0.253979
$246$	−4.90614e7	−0.210120
$247$	−4.07430e7	−0.172034
$248$	8.06602e7	0.335798
$249$	2.37794e8	0.976121
$250$	3.60503e8	1.45921
$251$	−1.87788e8	−0.749564	−0.374782	−	0.927113i	$-0.622282\pi$
$251$	−1.87788e8	−0.749564	−0.374782	+	0.927113i	$0.622282\pi$
$252$	−1.60030e7	−0.0629941
$253$	2.58413e8	1.00321
$254$	−7.88417e6	−0.0301883
$255$	2.88160e7	0.108829
$256$	1.67772e7	0.0625000
$257$	2.09400e8	0.769502	0.384751	−	0.923020i	$-0.374287\pi$
$257$	2.09400e8	0.769502	0.384751	+	0.923020i	$0.374287\pi$
$258$	−1.15099e8	−0.417255
$259$	−1.30876e8	−0.468071
$260$	6.98715e7	0.246543
$261$	4.28006e7	0.149007
$262$	−2.83649e8	−0.974376
$263$	−3.30860e8	−1.12150	−0.560749	−	0.827986i	$-0.689487\pi$
$263$	−3.30860e8	−1.12150	−0.560749	+	0.827986i	$0.689487\pi$
$264$	5.28732e7	0.176857
$265$	−1.75058e8	−0.577860
$266$	5.08870e7	0.165776
$267$	−8.42048e7	−0.270737
$268$	1.41130e8	0.447864
$269$	3.78010e8	1.18405	0.592025	−	0.805920i	$-0.298329\pi$
$269$	3.78010e8	1.18405	0.592025	+	0.805920i	$0.298329\pi$
$270$	−7.82477e7	−0.241935
$271$	6.09647e6	0.0186074	0.00930371	−	0.999957i	$-0.497038\pi$
$271$	6.09647e6	0.0186074	0.00930371	+	0.999957i	$0.497038\pi$
$272$	−8.79712e6	−0.0265063
$273$	2.03464e7	0.0605228
$274$	2.13094e8	0.625813
$275$	−6.45649e8	−1.87211
$276$	1.16750e8	0.334252
$277$	−3.85685e8	−1.09032	−0.545159	−	0.838333i	$-0.683531\pi$
$277$	−3.85685e8	−1.09032	−0.545159	+	0.838333i	$0.683531\pi$
$278$	−4.54287e8	−1.26816
$279$	1.14846e8	0.316594
$280$	−8.72678e7	−0.237575
$281$	−6.82120e7	−0.183396	−0.0916978	−	0.995787i	$-0.529229\pi$
$281$	−6.82120e7	−0.183396	−0.0916978	+	0.995787i	$0.529229\pi$
$282$	−1.54303e8	−0.409733
$283$	−6.19700e7	−0.162528	−0.0812642	−	0.996693i	$-0.525896\pi$
$283$	−6.19700e7	−0.162528	−0.0812642	+	0.996693i	$0.525896\pi$
$284$	−3.22416e8	−0.835222
$285$	2.48815e8	0.636678
$286$	−6.72236e7	−0.169919
$287$	−7.79076e7	−0.194533
$288$	2.38879e7	0.0589256
$289$	−4.05726e8	−0.988759
$290$	2.33401e8	0.561965
$291$	−5.41791e7	−0.128886
$292$	9.37307e7	0.220314
$293$	−4.88598e6	−0.0113479	−0.00567395	−	0.999984i	$-0.501806\pi$
$293$	−4.88598e6	−0.0113479	−0.00567395	+	0.999984i	$0.501806\pi$
$294$	−2.54122e7	−0.0583212
$295$	−2.65835e8	−0.602886
$296$	1.95361e8	0.437841
$297$	7.52824e7	0.166742
$298$	−5.75914e8	−1.26067
$299$	−1.48437e8	−0.321139
$300$	−2.91701e8	−0.623755
$301$	−1.82773e8	−0.386303
$302$	−2.57701e8	−0.538383
$303$	−5.16552e8	−1.06676
$304$	−7.59596e7	−0.155069
$305$	4.70862e8	0.950265
$306$	−1.25256e7	−0.0249904
$307$	−2.64128e8	−0.520992	−0.260496	−	0.965475i	$-0.583886\pi$
$307$	−2.64128e8	−0.520992	−0.260496	+	0.965475i	$0.583886\pi$
$308$	8.39607e7	0.163738
$309$	−3.70334e7	−0.0714067
$310$	6.26281e8	1.19400
$311$	5.56532e8	1.04913	0.524564	−	0.851371i	$-0.324228\pi$
$311$	5.56532e8	1.04913	0.524564	+	0.851371i	$0.324228\pi$
$312$	−3.03713e7	−0.0566139
$313$	−4.42785e8	−0.816183	−0.408091	−	0.912941i	$-0.633806\pi$
$313$	−4.42785e8	−0.816183	−0.408091	+	0.912941i	$0.633806\pi$
$314$	−7.01126e8	−1.27803
$315$	−1.24254e8	−0.223988
$316$	5.51504e8	0.983204
$317$	2.33443e8	0.411599	0.205799	−	0.978594i	$-0.434021\pi$
$317$	2.33443e8	0.411599	0.205799	+	0.978594i	$0.434021\pi$
$318$	7.60933e7	0.132694
$319$	−2.24556e8	−0.387308
$320$	1.30266e8	0.222231
$321$	−6.37130e8	−1.07513
$322$	1.85394e8	0.309457
$323$	3.98294e7	0.0657649
$324$	3.40122e7	0.0555556
$325$	3.70872e8	0.599284
$326$	5.79856e8	0.926955
$327$	−2.26672e8	−0.358493
$328$	1.16294e8	0.181969
$329$	−2.45027e8	−0.379339
$330$	4.10531e8	0.628850
$331$	1.18852e9	1.80139	0.900693	−	0.434455i	$-0.143059\pi$
$331$	1.18852e9	1.80139	0.900693	+	0.434455i	$0.143059\pi$
$332$	−5.63661e8	−0.845346
$333$	2.78160e8	0.412800
$334$	6.26819e8	0.920512
$335$	1.09579e9	1.59247
$336$	3.79331e7	0.0545545
$337$	3.54795e8	0.504978	0.252489	−	0.967600i	$-0.418751\pi$
$337$	3.54795e8	0.504978	0.252489	+	0.967600i	$0.418751\pi$
$338$	3.86145e7	0.0543928
$339$	1.90885e8	0.266118
$340$	−6.83047e7	−0.0942485
$341$	−6.02548e8	−0.822908
$342$	−1.08153e8	−0.146201
$343$	−4.03536e7	−0.0539949
$344$	2.72827e8	0.361354
$345$	9.06496e8	1.18850
$346$	2.10948e8	0.273784
$347$	−4.52712e8	−0.581659	−0.290830	−	0.956775i	$-0.593931\pi$
$347$	−4.52712e8	−0.581659	−0.290830	+	0.956775i	$0.593931\pi$
$348$	−1.01453e8	−0.129044
$349$	3.15340e8	0.397091	0.198545	−	0.980092i	$-0.436378\pi$
$349$	3.15340e8	0.397091	0.198545	+	0.980092i	$0.436378\pi$
$350$	−4.63211e8	−0.577485
$351$	−4.32436e7	−0.0533761
$352$	−1.25329e8	−0.153163
$353$	7.96217e8	0.963429	0.481715	−	0.876328i	$-0.340014\pi$
$353$	7.96217e8	0.963429	0.481715	+	0.876328i	$0.340014\pi$
$354$	1.15552e8	0.138441
$355$	−2.50338e9	−2.96980
$356$	1.99597e8	0.234465
$357$	−1.98902e7	−0.0231366
$358$	1.15152e9	1.32642
$359$	−1.65187e9	−1.88428	−0.942142	−	0.335214i	$-0.891191\pi$
$359$	−1.65187e9	−1.88428	−0.942142	+	0.335214i	$0.891191\pi$
$360$	1.85476e8	0.209522
$361$	−5.49961e8	−0.615257
$362$	6.26531e8	0.694165
$363$	1.31180e8	0.143945
$364$	−4.82285e7	−0.0524142
$365$	7.27766e8	0.783370
$366$	−2.04672e8	−0.218210
$367$	3.40603e8	0.359681	0.179840	−	0.983696i	$-0.442442\pi$
$367$	3.40603e8	0.359681	0.179840	+	0.983696i	$0.442442\pi$
$368$	−2.76740e8	−0.289471
$369$	1.65582e8	0.171562
$370$	1.51687e9	1.55683
$371$	1.20833e8	0.122851
$372$	−2.72228e8	−0.274178
$373$	−5.88708e8	−0.587380	−0.293690	−	0.955901i	$-0.594883\pi$
$373$	−5.88708e8	−0.587380	−0.293690	+	0.955901i	$0.594883\pi$
$374$	6.57162e7	0.0649564
$375$	−1.21670e9	−1.19144
$376$	3.65754e8	0.354840
$377$	1.28989e8	0.123982
$378$	5.40102e7	0.0514344
$379$	8.60219e6	0.00811655	0.00405828	−	0.999992i	$-0.498708\pi$
$379$	8.60219e6	0.00811655	0.00405828	+	0.999992i	$0.498708\pi$
$380$	−5.89784e8	−0.551379
$381$	2.66091e7	0.0246486
$382$	5.07872e8	0.466157
$383$	−1.84752e9	−1.68032	−0.840161	−	0.542338i	$-0.817539\pi$
$383$	−1.84752e9	−1.68032	−0.840161	+	0.542338i	$0.817539\pi$
$384$	−5.66231e7	−0.0510310
$385$	6.51908e8	0.582202
$386$	7.64710e8	0.676770
$387$	3.88458e8	0.340687
$388$	1.28425e8	0.111619
$389$	1.35859e8	0.117021	0.0585105	−	0.998287i	$-0.481365\pi$
$389$	1.35859e8	0.117021	0.0585105	+	0.998287i	$0.481365\pi$
$390$	−2.35816e8	−0.201302
$391$	1.45108e8	0.122765
$392$	6.02363e7	0.0505076
$393$	9.57315e8	0.795574
$394$	6.62620e8	0.545793
$395$	4.28212e9	3.49598
$396$	−1.78447e8	−0.144403
$397$	6.42588e8	0.515425	0.257713	−	0.966222i	$-0.417031\pi$
$397$	6.42588e8	0.515425	0.257713	+	0.966222i	$0.417031\pi$
$398$	−6.51104e8	−0.517678
$399$	−1.71744e8	−0.135355
$400$	6.91440e8	0.540187
$401$	−2.24032e9	−1.73502	−0.867511	−	0.497418i	$-0.834281\pi$
$401$	−2.24032e9	−1.73502	−0.867511	+	0.497418i	$0.834281\pi$
$402$	−4.76312e8	−0.365679
$403$	3.46114e8	0.263422
$404$	1.22442e9	0.923837
$405$	2.64086e8	0.197539
$406$	−1.61104e8	−0.119472
$407$	−1.45938e9	−1.07297
$408$	2.96903e7	0.0216423
$409$	7.64379e8	0.552430	0.276215	−	0.961096i	$-0.410920\pi$
$409$	7.64379e8	0.552430	0.276215	+	0.961096i	$0.410920\pi$
$410$	9.02955e8	0.647027
$411$	−7.19193e8	−0.510975
$412$	8.77829e7	0.0618400
$413$	1.83492e8	0.128171
$414$	−3.94030e8	−0.272916
$415$	−4.37651e9	−3.00580
$416$	7.19913e7	0.0490290
$417$	1.53322e9	1.03545
$418$	5.67433e8	0.380012
$419$	−5.63647e8	−0.374333	−0.187166	−	0.982328i	$-0.559930\pi$
$419$	−5.63647e8	−0.374333	−0.187166	+	0.982328i	$0.559930\pi$
$420$	2.94529e8	0.193979
$421$	−1.67916e8	−0.109674	−0.0548371	−	0.998495i	$-0.517464\pi$
$421$	−1.67916e8	−0.109674	−0.0548371	+	0.998495i	$0.517464\pi$
$422$	1.51767e9	0.983068
$423$	5.20771e8	0.334546
$424$	−1.80369e8	−0.114917
$425$	−3.62556e8	−0.229094
$426$	1.08815e9	0.681956
$427$	−3.25011e8	−0.202023
$428$	1.51023e9	0.931088
$429$	2.26880e8	0.138738
$430$	2.11835e9	1.28486
$431$	4.07362e8	0.245081	0.122541	−	0.992463i	$-0.460896\pi$
$431$	4.07362e8	0.245081	0.122541	+	0.992463i	$0.460896\pi$
$432$	−8.06216e7	−0.0481125
$433$	−1.43524e9	−0.849604	−0.424802	−	0.905286i	$-0.639656\pi$
$433$	−1.43524e9	−0.849604	−0.424802	+	0.905286i	$0.639656\pi$
$434$	−4.32288e8	−0.253840
$435$	−7.87728e8	−0.458843
$436$	5.37297e8	0.310464
$437$	1.25295e9	0.718207
$438$	−3.16341e8	−0.179885
$439$	8.80200e8	0.496541	0.248271	−	0.968691i	$-0.420138\pi$
$439$	8.80200e8	0.496541	0.248271	+	0.968691i	$0.420138\pi$
$440$	−9.73110e8	−0.544600
$441$	8.57661e7	0.0476190
$442$	−3.77486e7	−0.0207933
$443$	1.78113e9	0.973382	0.486691	−	0.873574i	$-0.338204\pi$
$443$	1.78113e9	0.973382	0.486691	+	0.873574i	$0.338204\pi$
$444$	−6.59342e8	−0.357495
$445$	1.54976e9	0.833687
$446$	3.46124e8	0.184739
$447$	1.94371e9	1.02933
$448$	−8.99154e7	−0.0472456
$449$	−1.92118e7	−0.0100162	−0.00500812	−	0.999987i	$-0.501594\pi$
$449$	−1.92118e7	−0.0100162	−0.00500812	+	0.999987i	$0.501594\pi$
$450$	9.84492e8	0.509294
$451$	−8.68736e8	−0.445934
$452$	−4.52469e8	−0.230465
$453$	8.69740e8	0.439588
$454$	1.41219e8	0.0708268
$455$	−3.74468e8	−0.186369
$456$	2.56364e8	0.126613
$457$	−1.53351e9	−0.751591	−0.375795	−	0.926703i	$-0.622630\pi$
$457$	−1.53351e9	−0.751591	−0.375795	+	0.926703i	$0.622630\pi$
$458$	1.82504e9	0.887651
$459$	4.22738e7	0.0204046
$460$	−2.14873e9	−1.02927
$461$	−1.15224e9	−0.547757	−0.273879	−	0.961764i	$-0.588307\pi$
$461$	−1.15224e9	−0.547757	−0.273879	+	0.961764i	$0.588307\pi$
$462$	−2.83367e8	−0.133691
$463$	−9.11439e8	−0.426770	−0.213385	−	0.976968i	$-0.568449\pi$
$463$	−9.11439e8	−0.426770	−0.213385	+	0.976968i	$0.568449\pi$
$464$	2.40482e8	0.111756
$465$	−2.11370e9	−0.974895
$466$	−7.37328e8	−0.337528
$467$	−2.27214e9	−1.03235	−0.516174	−	0.856484i	$-0.672644\pi$
$467$	−2.27214e9	−1.03235	−0.516174	+	0.856484i	$0.672644\pi$
$468$	1.02503e8	0.0462250
$469$	−7.56366e8	−0.338553
$470$	2.83988e9	1.26170
$471$	2.36630e9	1.04351
$472$	−2.73900e8	−0.119893
$473$	−2.03807e9	−0.885533
$474$	−1.86133e9	−0.802783
$475$	−3.13053e9	−1.34026
$476$	4.71470e7	0.0200369
$477$	−2.56815e8	−0.108344
$478$	1.33486e9	0.559032
$479$	6.50250e8	0.270337	0.135169	−	0.990823i	$-0.456842\pi$
$479$	6.50250e8	0.270337	0.135169	+	0.990823i	$0.456842\pi$
$480$	−4.39647e8	−0.181451
$481$	8.38296e8	0.343471
$482$	1.88623e9	0.767238
$483$	−6.25705e8	−0.252671
$484$	−3.10946e8	−0.124660
$485$	9.97145e8	0.396883
$486$	−1.14791e8	−0.0453609
$487$	−1.88694e9	−0.740299	−0.370150	−	0.928972i	$-0.620694\pi$
$487$	−1.88694e9	−0.740299	−0.370150	+	0.928972i	$0.620694\pi$
$488$	4.85148e8	0.188975
$489$	−1.95701e9	−0.756856
$490$	4.67701e8	0.179590
$491$	1.64654e9	0.627750	0.313875	−	0.949464i	$-0.398373\pi$
$491$	1.64654e9	0.627750	0.313875	+	0.949464i	$0.398373\pi$
$492$	−3.92491e8	−0.148577
$493$	−1.26096e8	−0.0473957
$494$	−3.25944e8	−0.121646
$495$	−1.38554e9	−0.513454
$496$	6.45282e8	0.237445
$497$	1.72795e9	0.631369
$498$	1.90235e9	0.690222
$499$	−4.13719e9	−1.49057	−0.745287	−	0.666744i	$-0.767687\pi$
$499$	−4.13719e9	−1.49057	−0.745287	+	0.666744i	$0.767687\pi$
$500$	2.88402e9	1.03182
$501$	−2.11551e9	−0.751595
$502$	−1.50230e9	−0.530022
$503$	−2.42528e9	−0.849717	−0.424858	−	0.905260i	$-0.639676\pi$
$503$	−2.42528e9	−0.849717	−0.424858	+	0.905260i	$0.639676\pi$
$504$	−1.28024e8	−0.0445435
$505$	9.50693e9	3.28489
$506$	2.06730e9	0.709377
$507$	−1.30324e8	−0.0444116
$508$	−6.30734e7	−0.0213463
$509$	−1.44039e9	−0.484135	−0.242068	−	0.970259i	$-0.577826\pi$
$509$	−1.44039e9	−0.484135	−0.242068	+	0.970259i	$0.577826\pi$
$510$	2.30528e8	0.0769535
$511$	−5.02338e8	−0.166542
$512$	1.34218e8	0.0441942
$513$	3.65018e8	0.119372
$514$	1.67520e9	0.544120
$515$	6.81585e8	0.219884
$516$	−9.20790e8	−0.295044
$517$	−2.73226e9	−0.869570
$518$	−1.04701e9	−0.330976
$519$	−7.11948e8	−0.223544
$520$	5.58972e8	0.174333
$521$	1.57419e9	0.487668	0.243834	−	0.969817i	$-0.421595\pi$
$521$	1.57419e9	0.487668	0.243834	+	0.969817i	$0.421595\pi$
$522$	3.42405e8	0.105364
$523$	3.48172e9	1.06424	0.532118	−	0.846670i	$-0.321396\pi$
$523$	3.48172e9	1.06424	0.532118	+	0.846670i	$0.321396\pi$
$524$	−2.26919e9	−0.688988
$525$	1.56334e9	0.471514
$526$	−2.64688e9	−0.793020
$527$	−3.38353e8	−0.100701
$528$	4.22986e8	0.125057
$529$	1.16000e9	0.340693
$530$	−1.40047e9	−0.408609
$531$	−3.89986e8	−0.113036
$532$	4.07096e8	0.117221
$533$	4.99018e8	0.142748
$534$	−6.73638e8	−0.191440
$535$	1.17261e10	3.31067
$536$	1.12904e9	0.316688
$537$	−3.88638e9	−1.08302
$538$	3.02408e9	0.837250
$539$	−4.49977e8	−0.123774
$540$	−6.25981e8	−0.171074
$541$	−5.58813e9	−1.51731	−0.758657	−	0.651490i	$-0.774144\pi$
$541$	−5.58813e9	−1.51731	−0.758657	+	0.651490i	$0.774144\pi$
$542$	4.87718e7	0.0131574
$543$	−2.11454e9	−0.566783
$544$	−7.03769e7	−0.0187428
$545$	4.17181e9	1.10392
$546$	1.62771e8	0.0427960
$547$	−8.36867e8	−0.218625	−0.109313	−	0.994007i	$-0.534865\pi$
$547$	−8.36867e8	−0.218625	−0.109313	+	0.994007i	$0.534865\pi$
$548$	1.70475e9	0.442517
$549$	6.90767e8	0.178167
$550$	−5.16519e9	−1.32378
$551$	−1.08879e9	−0.277277
$552$	9.33998e8	0.236352
$553$	−2.95572e9	−0.743233
$554$	−3.08548e9	−0.770971
$555$	−5.11942e9	−1.27115
$556$	−3.63429e9	−0.896723
$557$	−2.13091e9	−0.522483	−0.261242	−	0.965273i	$-0.584132\pi$
$557$	−2.13091e9	−0.522483	−0.261242	+	0.965273i	$0.584132\pi$
$558$	9.18770e8	0.223865
$559$	1.17070e9	0.283469
$560$	−6.98143e8	−0.167991
$561$	−2.21792e8	−0.0530367
$562$	−5.45696e8	−0.129680
$563$	−4.67407e9	−1.10386	−0.551932	−	0.833889i	$-0.686109\pi$
$563$	−4.67407e9	−1.10386	−0.551932	+	0.833889i	$0.686109\pi$
$564$	−1.23442e9	−0.289725
$565$	−3.51317e9	−0.819464
$566$	−4.95760e8	−0.114925
$567$	−1.82284e8	−0.0419961
$568$	−2.57933e9	−0.590591
$569$	−3.10951e9	−0.707618	−0.353809	−	0.935318i	$-0.615114\pi$
$569$	−3.10951e9	−0.707618	−0.353809	+	0.935318i	$0.615114\pi$
$570$	1.99052e9	0.450199
$571$	1.90010e9	0.427121	0.213560	−	0.976930i	$-0.431494\pi$
$571$	1.90010e9	0.427121	0.213560	+	0.976930i	$0.431494\pi$
$572$	−5.37789e8	−0.120151
$573$	−1.71407e9	−0.380616
$574$	−6.23261e8	−0.137556
$575$	−1.14053e10	−2.50190
$576$	1.91103e8	0.0416667
$577$	2.04455e8	0.0443081	0.0221541	−	0.999755i	$-0.492948\pi$
$577$	2.04455e8	0.0443081	0.0221541	+	0.999755i	$0.492948\pi$
$578$	−3.24581e9	−0.699158
$579$	−2.58090e9	−0.552581
$580$	1.86721e9	0.397369
$581$	3.02087e9	0.639021
$582$	−4.33433e8	−0.0911363
$583$	1.34740e9	0.281615
$584$	7.49845e8	0.155785
$585$	7.95880e8	0.164362
$586$	−3.90879e7	−0.00802417
$587$	−2.35979e9	−0.481548	−0.240774	−	0.970581i	$-0.577401\pi$
$587$	−2.35979e9	−0.481548	−0.240774	+	0.970581i	$0.577401\pi$
$588$	−2.03297e8	−0.0412393
$589$	−2.92154e9	−0.589127
$590$	−2.12668e9	−0.426304
$591$	−2.23634e9	−0.445638
$592$	1.56289e9	0.309600
$593$	1.48166e9	0.291780	0.145890	−	0.989301i	$-0.453395\pi$
$593$	1.48166e9	0.291780	0.145890	+	0.989301i	$0.453395\pi$
$594$	6.02259e8	0.117905
$595$	3.66070e8	0.0712451
$596$	−4.60731e9	−0.891427
$597$	2.19747e9	0.422682
$598$	−1.18750e9	−0.227080
$599$	−3.55355e9	−0.675568	−0.337784	−	0.941224i	$-0.609677\pi$
$599$	−3.55355e9	−0.675568	−0.337784	+	0.941224i	$0.609677\pi$
$600$	−2.33361e9	−0.441061
$601$	5.40134e9	1.01494	0.507470	−	0.861669i	$-0.330581\pi$
$601$	5.40134e9	1.01494	0.507470	+	0.861669i	$0.330581\pi$
$602$	−1.46218e9	−0.273158
$603$	1.60755e9	0.298576
$604$	−2.06160e9	−0.380694
$605$	−2.41432e9	−0.443252
$606$	−4.13242e9	−0.754310
$607$	4.42281e9	0.802672	0.401336	−	0.915931i	$-0.368546\pi$
$607$	4.42281e9	0.802672	0.401336	+	0.915931i	$0.368546\pi$
$608$	−6.07677e8	−0.109650
$609$	5.43726e8	0.0975483
$610$	3.76690e9	0.671939
$611$	1.56946e9	0.278359
$612$	−1.00205e8	−0.0176709
$613$	4.76865e9	0.836149	0.418075	−	0.908413i	$-0.362705\pi$
$613$	4.76865e9	0.836149	0.418075	+	0.908413i	$0.362705\pi$
$614$	−2.11303e9	−0.368397
$615$	−3.04747e9	−0.528295
$616$	6.71686e8	0.115780
$617$	1.10275e10	1.89008	0.945040	−	0.326955i	$-0.106023\pi$
$617$	1.10275e10	1.89008	0.945040	+	0.326955i	$0.106023\pi$
$618$	−2.96267e8	−0.0504922
$619$	−1.49822e9	−0.253897	−0.126949	−	0.991909i	$-0.540518\pi$
$619$	−1.49822e9	−0.253897	−0.126949	+	0.991909i	$0.540518\pi$
$620$	5.01025e9	0.844284
$621$	1.32985e9	0.222835
$622$	4.45225e9	0.741846
$623$	−1.06971e9	−0.177239
$624$	−2.42971e8	−0.0400320
$625$	9.20465e9	1.50809
$626$	−3.54228e9	−0.577129
$627$	−1.91509e9	−0.310279
$628$	−5.60901e9	−0.903706
$629$	−8.19497e8	−0.131302
$630$	−9.94035e8	−0.158383
$631$	6.65589e9	1.05464	0.527319	−	0.849668i	$-0.323197\pi$
$631$	6.65589e9	1.05464	0.527319	+	0.849668i	$0.323197\pi$
$632$	4.41203e9	0.695230
$633$	−5.12213e9	−0.802672
$634$	1.86755e9	0.291044
$635$	−4.89729e8	−0.0759011
$636$	6.08747e8	0.0938289
$637$	2.58475e8	0.0396214
$638$	−1.79645e9	−0.273868
$639$	−3.67252e9	−0.556815
$640$	1.04213e9	0.157141
$641$	6.55404e9	0.982892	0.491446	−	0.870908i	$-0.336469\pi$
$641$	6.55404e9	0.982892	0.491446	+	0.870908i	$0.336469\pi$
$642$	−5.09704e9	−0.760230
$643$	−3.63452e9	−0.539149	−0.269574	−	0.962980i	$-0.586883\pi$
$643$	−3.63452e9	−0.539149	−0.269574	+	0.962980i	$0.586883\pi$
$644$	1.48315e9	0.218819
$645$	−7.14942e9	−1.04909
$646$	3.18635e8	0.0465028
$647$	8.91495e9	1.29406	0.647029	−	0.762465i	$-0.276011\pi$
$647$	8.91495e9	1.29406	0.647029	+	0.762465i	$0.276011\pi$
$648$	2.72098e8	0.0392837
$649$	2.04609e9	0.293811
$650$	2.96698e9	0.423758
$651$	1.45897e9	0.207259
$652$	4.63885e9	0.655456
$653$	3.92610e9	0.551779	0.275889	−	0.961189i	$-0.411028\pi$
$653$	3.92610e9	0.551779	0.275889	+	0.961189i	$0.411028\pi$
$654$	−1.81338e9	−0.253493
$655$	−1.76190e10	−2.44983
$656$	9.30349e8	0.128672
$657$	1.06765e9	0.146876
$658$	−1.96021e9	−0.268233
$659$	3.58393e8	0.0487822	0.0243911	−	0.999702i	$-0.492235\pi$
$659$	3.58393e8	0.0487822	0.0243911	+	0.999702i	$0.492235\pi$
$660$	3.28425e9	0.444664
$661$	−1.07820e10	−1.45210	−0.726049	−	0.687643i	$-0.758646\pi$
$661$	−1.07820e10	−1.45210	−0.726049	+	0.687643i	$0.758646\pi$
$662$	9.50813e9	1.27377
$663$	1.27401e8	0.0169776
$664$	−4.50929e9	−0.597750
$665$	3.16087e9	0.416803
$666$	2.22528e9	0.291894
$667$	−3.96675e9	−0.517600
$668$	5.01455e9	0.650900
$669$	−1.16817e9	−0.150839
$670$	8.76633e9	1.12605
$671$	−3.62415e9	−0.463103
$672$	3.03464e8	0.0385758
$673$	−4.39366e9	−0.555615	−0.277808	−	0.960637i	$-0.589608\pi$
$673$	−4.39366e9	−0.555615	−0.277808	+	0.960637i	$0.589608\pi$
$674$	2.83836e9	0.357073
$675$	−3.32266e9	−0.415836
$676$	3.08916e8	0.0384615
$677$	8.11370e9	1.00498	0.502491	−	0.864582i	$-0.332417\pi$
$677$	8.11370e9	1.00498	0.502491	+	0.864582i	$0.332417\pi$
$678$	1.52708e9	0.188174
$679$	−6.88276e8	−0.0843758
$680$	−5.46437e8	−0.0666437
$681$	−4.76614e8	−0.0578298
$682$	−4.82038e9	−0.581884
$683$	−1.09490e10	−1.31493	−0.657466	−	0.753484i	$-0.728372\pi$
$683$	−1.09490e10	−1.31493	−0.657466	+	0.753484i	$0.728372\pi$
$684$	−8.65228e8	−0.103379
$685$	1.32365e10	1.57346
$686$	−3.22829e8	−0.0381802
$687$	−6.15950e9	−0.724764
$688$	2.18261e9	0.255516
$689$	−7.73968e8	−0.0901479
$690$	7.25197e9	0.840396
$691$	−1.34406e9	−0.154969	−0.0774844	−	0.996994i	$-0.524689\pi$
$691$	−1.34406e9	−0.154969	−0.0774844	+	0.996994i	$0.524689\pi$
$692$	1.68758e9	0.193595
$693$	9.56365e8	0.109158
$694$	−3.62169e9	−0.411295
$695$	−2.82183e10	−3.18848
$696$	−8.11626e8	−0.0912481
$697$	−4.87828e8	−0.0545697
$698$	2.52272e9	0.280786
$699$	2.48848e9	0.275591
$700$	−3.70569e9	−0.408343
$701$	−1.54593e10	−1.69503	−0.847516	−	0.530769i	$-0.821903\pi$
$701$	−1.54593e10	−1.69503	−0.847516	+	0.530769i	$0.821903\pi$
$702$	−3.45948e8	−0.0377426
$703$	−7.07604e9	−0.768151
$704$	−1.00263e9	−0.108302
$705$	−9.58459e9	−1.03018
$706$	6.36973e9	0.681247
$707$	−6.56212e9	−0.698355
$708$	9.24412e8	0.0978924
$709$	−1.07079e10	−1.12835	−0.564176	−	0.825655i	$-0.690806\pi$
$709$	−1.07079e10	−1.12835	−0.564176	+	0.825655i	$0.690806\pi$
$710$	−2.00270e10	−2.09997
$711$	6.28197e9	0.655470
$712$	1.59677e9	0.165792
$713$	−1.06439e10	−1.09973
$714$	−1.59121e8	−0.0163600
$715$	−4.17563e9	−0.427219
$716$	9.21216e9	0.937920
$717$	−4.50514e9	−0.456448
$718$	−1.32150e10	−1.33239
$719$	−1.74028e10	−1.74610	−0.873050	−	0.487631i	$-0.837861\pi$
$719$	−1.74028e10	−1.74610	−0.873050	+	0.487631i	$0.837861\pi$
$720$	1.48381e9	0.148154
$721$	−4.70461e8	−0.0467466
$722$	−4.39969e9	−0.435053
$723$	−6.36603e9	−0.626447
$724$	5.01225e9	0.490849
$725$	9.91098e9	0.965904
$726$	1.04944e9	0.101784
$727$	1.21160e10	1.16947	0.584733	−	0.811226i	$-0.301199\pi$
$727$	1.21160e10	1.16947	0.584733	+	0.811226i	$0.301199\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	5.82213e9	0.553926
$731$	−1.14445e9	−0.108364
$732$	−1.63737e9	−0.154298
$733$	1.12175e10	1.05204	0.526021	−	0.850471i	$-0.323683\pi$
$733$	1.12175e10	1.05204	0.526021	+	0.850471i	$0.323683\pi$
$734$	2.72483e9	0.254333
$735$	−1.57849e9	−0.146635
$736$	−2.21392e9	−0.204687
$737$	−8.43412e9	−0.776075
$738$	1.32466e9	0.121313
$739$	−9.44143e9	−0.860562	−0.430281	−	0.902695i	$-0.641586\pi$
$739$	−9.44143e9	−0.860562	−0.430281	+	0.902695i	$0.641586\pi$
$740$	1.21349e10	1.10085
$741$	1.10006e9	0.0993237
$742$	9.66667e8	0.0868687
$743$	1.86509e10	1.66817	0.834083	−	0.551639i	$-0.185997\pi$
$743$	1.86509e10	1.66817	0.834083	+	0.551639i	$0.185997\pi$
$744$	−2.17783e9	−0.193873
$745$	−3.57732e10	−3.16965
$746$	−4.70967e9	−0.415340
$747$	−6.42045e9	−0.563564
$748$	5.25730e8	0.0459311
$749$	−8.09390e9	−0.703836
$750$	−9.73358e9	−0.842477
$751$	6.87622e8	0.0592394	0.0296197	−	0.999561i	$-0.490570\pi$
$751$	6.87622e8	0.0592394	0.0296197	+	0.999561i	$0.490570\pi$
$752$	2.92603e9	0.250909
$753$	5.07026e9	0.432761
$754$	1.03191e9	0.0876683
$755$	−1.60072e10	−1.35363
$756$	4.32081e8	0.0363696
$757$	6.41867e9	0.537786	0.268893	−	0.963170i	$-0.413342\pi$
$757$	6.41867e9	0.537786	0.268893	+	0.963170i	$0.413342\pi$
$758$	6.88175e7	0.00573927
$759$	−6.97715e9	−0.579204
$760$	−4.71827e9	−0.389884
$761$	−5.67316e9	−0.466636	−0.233318	−	0.972400i	$-0.574958\pi$
$761$	−5.67316e9	−0.466636	−0.233318	+	0.972400i	$0.574958\pi$
$762$	2.12873e8	0.0174292
$763$	−2.87957e9	−0.234689
$764$	4.06298e9	0.329623
$765$	−7.78033e8	−0.0628323
$766$	−1.47801e10	−1.18817
$767$	−1.17531e9	−0.0940520
$768$	−4.52985e8	−0.0360844
$769$	2.70852e9	0.214778	0.107389	−	0.994217i	$-0.465751\pi$
$769$	2.70852e9	0.214778	0.107389	+	0.994217i	$0.465751\pi$
$770$	5.21526e9	0.411679
$771$	−5.65379e9	−0.444272
$772$	6.11768e9	0.478549
$773$	9.88293e8	0.0769587	0.0384793	−	0.999259i	$-0.487749\pi$
$773$	9.88293e8	0.0769587	0.0384793	+	0.999259i	$0.487749\pi$
$774$	3.10767e9	0.240902
$775$	2.65940e10	2.05224
$776$	1.02740e9	0.0789264
$777$	3.53366e9	0.270241
$778$	1.08687e9	0.0827464
$779$	−4.21220e9	−0.319248
$780$	−1.88653e9	−0.142342
$781$	1.92681e10	1.44730
$782$	1.16087e9	0.0868078
$783$	−1.15562e9	−0.0860295
$784$	4.81890e8	0.0357143
$785$	−4.35508e10	−3.21331
$786$	7.65852e9	0.562556
$787$	1.24048e10	0.907146	0.453573	−	0.891219i	$-0.350149\pi$
$787$	1.24048e10	0.907146	0.453573	+	0.891219i	$0.350149\pi$
$788$	5.30096e9	0.385934
$789$	8.93321e9	0.647498
$790$	3.42569e10	2.47203
$791$	2.42495e9	0.174215
$792$	−1.42758e9	−0.102108
$793$	2.08178e9	0.148244
$794$	5.14070e9	0.364461
$795$	4.72658e9	0.333627
$796$	−5.20883e9	−0.366053
$797$	−9.25871e9	−0.647808	−0.323904	−	0.946090i	$-0.604995\pi$
$797$	−9.25871e9	−0.647808	−0.323904	+	0.946090i	$0.604995\pi$
$798$	−1.37395e9	−0.0957107
$799$	−1.53426e9	−0.106411
$800$	5.53152e9	0.381970
$801$	2.27353e9	0.156310
$802$	−1.79226e10	−1.22685
$803$	−5.60149e9	−0.381768
$804$	−3.81050e9	−0.258574
$805$	1.15159e10	0.778056
$806$	2.76891e9	0.186267
$807$	−1.02063e10	−0.683611
$808$	9.79536e9	0.653252
$809$	−2.49825e10	−1.65888	−0.829441	−	0.558595i	$-0.811341\pi$
$809$	−2.49825e10	−1.65888	−0.829441	+	0.558595i	$0.811341\pi$
$810$	2.11269e9	0.139681
$811$	2.50005e10	1.64579	0.822896	−	0.568192i	$-0.192357\pi$
$811$	2.50005e10	1.64579	0.822896	+	0.568192i	$0.192357\pi$
$812$	−1.28883e9	−0.0844793
$813$	−1.64605e8	−0.0107430
$814$	−1.16751e10	−0.758706
$815$	3.60181e10	2.33061
$816$	2.37522e8	0.0153034
$817$	−9.88188e9	−0.633961
$818$	6.11503e9	0.390627
$819$	−5.49353e8	−0.0349428
$820$	7.22364e9	0.457517
$821$	−1.73071e10	−1.09150	−0.545749	−	0.837949i	$-0.683755\pi$
$821$	−1.73071e10	−1.09150	−0.545749	+	0.837949i	$0.683755\pi$
$822$	−5.75355e9	−0.361314
$823$	2.31932e10	1.45031	0.725155	−	0.688586i	$-0.241768\pi$
$823$	2.31932e10	1.45031	0.725155	+	0.688586i	$0.241768\pi$
$824$	7.02263e8	0.0437275
$825$	1.74325e10	1.08087
$826$	1.46793e9	0.0906308
$827$	−2.05547e10	−1.26369	−0.631846	−	0.775094i	$-0.717702\pi$
$827$	−2.05547e10	−1.26369	−0.631846	+	0.775094i	$0.717702\pi$
$828$	−3.15224e9	−0.192980
$829$	2.49310e10	1.51984	0.759921	−	0.650015i	$-0.225237\pi$
$829$	2.49310e10	1.51984	0.759921	+	0.650015i	$0.225237\pi$
$830$	−3.50121e10	−2.12542
$831$	1.04135e10	0.629495
$832$	5.75930e8	0.0346688
$833$	−2.52679e8	−0.0151465
$834$	1.22657e10	0.732171
$835$	3.89352e10	2.31441
$836$	4.53947e9	0.268709
$837$	−3.10085e9	−0.182785
$838$	−4.50918e9	−0.264693
$839$	1.12662e10	0.658582	0.329291	−	0.944228i	$-0.393190\pi$
$839$	1.12662e10	0.658582	0.329291	+	0.944228i	$0.393190\pi$
$840$	2.35623e9	0.137164
$841$	−1.38028e10	−0.800171
$842$	−1.34333e9	−0.0775514
$843$	1.84173e9	0.105884
$844$	1.21414e10	0.695134
$845$	2.39856e9	0.136758
$846$	4.16617e9	0.236560
$847$	1.66647e9	0.0942338
$848$	−1.44296e9	−0.0812582
$849$	1.67319e9	0.0938358
$850$	−2.90045e9	−0.161994
$851$	−2.57798e10	−1.43392
$852$	8.70523e9	0.482216
$853$	−1.90222e10	−1.04940	−0.524699	−	0.851288i	$-0.675822\pi$
$853$	−1.90222e10	−1.04940	−0.524699	+	0.851288i	$0.675822\pi$
$854$	−2.60009e9	−0.142852
$855$	−6.71801e9	−0.367586
$856$	1.20819e10	0.658379
$857$	2.03465e10	1.10422	0.552110	−	0.833771i	$-0.313823\pi$
$857$	2.03465e10	1.10422	0.552110	+	0.833771i	$0.313823\pi$
$858$	1.81504e9	0.0981026
$859$	2.83480e10	1.52597	0.762987	−	0.646414i	$-0.223732\pi$
$859$	2.83480e10	1.52597	0.762987	+	0.646414i	$0.223732\pi$
$860$	1.69468e10	0.908537
$861$	2.10351e9	0.112314
$862$	3.25890e9	0.173299
$863$	−2.07145e10	−1.09708	−0.548539	−	0.836125i	$-0.684816\pi$
$863$	−2.07145e10	−1.09708	−0.548539	+	0.836125i	$0.684816\pi$
$864$	−6.44973e8	−0.0340207
$865$	1.31031e10	0.688364
$866$	−1.14819e10	−0.600761
$867$	1.09546e10	0.570860
$868$	−3.45831e9	−0.179492
$869$	−3.29587e10	−1.70373
$870$	−6.30182e9	−0.324451
$871$	4.84471e9	0.248430
$872$	4.29837e9	0.219531
$873$	1.46284e9	0.0744125
$874$	1.00236e10	0.507849
$875$	−1.54566e10	−0.779982
$876$	−2.53073e9	−0.127198
$877$	−1.44434e10	−0.723052	−0.361526	−	0.932362i	$-0.617744\pi$
$877$	−1.44434e10	−0.723052	−0.361526	+	0.932362i	$0.617744\pi$
$878$	7.04160e9	0.351108
$879$	1.31922e8	0.00655171
$880$	−7.78488e9	−0.385090
$881$	6.80586e9	0.335326	0.167663	−	0.985844i	$-0.446378\pi$
$881$	6.80586e9	0.335326	0.167663	+	0.985844i	$0.446378\pi$
$882$	6.86129e8	0.0336718
$883$	−2.73622e10	−1.33748	−0.668741	−	0.743495i	$-0.733167\pi$
$883$	−2.73622e10	−1.33748	−0.668741	+	0.743495i	$0.733167\pi$
$884$	−3.01989e8	−0.0147031
$885$	7.17754e9	0.348076
$886$	1.42491e10	0.688285
$887$	1.70834e10	0.821941	0.410970	−	0.911649i	$-0.365190\pi$
$887$	1.70834e10	0.821941	0.410970	+	0.911649i	$0.365190\pi$
$888$	−5.27474e9	−0.252787
$889$	3.38034e8	0.0161363
$890$	1.23980e10	0.589506
$891$	−2.03262e9	−0.0962687
$892$	2.76899e9	0.130630
$893$	−1.32478e10	−0.622533
$894$	1.55497e10	0.727847
$895$	7.15272e10	3.33496
$896$	−7.19323e8	−0.0334077
$897$	4.00780e9	0.185410
$898$	−1.53694e8	−0.00708255
$899$	9.24936e9	0.424573
$900$	7.87593e9	0.360125
$901$	7.56612e8	0.0344617
$902$	−6.94989e9	−0.315323
$903$	4.93486e9	0.223032
$904$	−3.61975e9	−0.162963
$905$	3.89173e10	1.74531
$906$	6.95792e9	0.310835
$907$	−1.38221e10	−0.615103	−0.307551	−	0.951531i	$-0.599510\pi$
$907$	−1.38221e10	−0.615103	−0.307551	+	0.951531i	$0.599510\pi$
$908$	1.12975e9	0.0500821
$909$	1.39469e10	0.615892
$910$	−2.99574e9	−0.131783
$911$	2.21664e10	0.971360	0.485680	−	0.874137i	$-0.338572\pi$
$911$	2.21664e10	0.971360	0.485680	+	0.874137i	$0.338572\pi$
$912$	2.05091e9	0.0895292
$913$	3.36853e10	1.46485
$914$	−1.22681e10	−0.531455
$915$	−1.27133e10	−0.548636
$916$	1.46003e10	0.627664
$917$	1.21614e10	0.520826
$918$	3.38191e8	0.0144282
$919$	1.73285e9	0.0736474	0.0368237	−	0.999322i	$-0.488276\pi$
$919$	1.73285e9	0.0736474	0.0368237	+	0.999322i	$0.488276\pi$
$920$	−1.71898e10	−0.727804
$921$	7.13147e9	0.300795
$922$	−9.21789e9	−0.387323
$923$	−1.10679e10	−0.463298
$924$	−2.26694e9	−0.0945340
$925$	6.44112e10	2.67587
$926$	−7.29151e9	−0.301772
$927$	9.99902e8	0.0412267
$928$	1.92385e9	0.0790231
$929$	4.89668e9	0.200377	0.100188	−	0.994968i	$-0.468055\pi$
$929$	4.89668e9	0.200377	0.100188	+	0.994968i	$0.468055\pi$
$930$	−1.69096e10	−0.689355
$931$	−2.18178e9	−0.0886109
$932$	−5.89862e9	−0.238668
$933$	−1.50264e10	−0.605714
$934$	−1.81771e10	−0.729981
$935$	4.08200e9	0.163317
$936$	8.20026e8	0.0326860
$937$	8.45195e9	0.335636	0.167818	−	0.985818i	$-0.446328\pi$
$937$	8.45195e9	0.335636	0.167818	+	0.985818i	$0.446328\pi$
$938$	−6.05093e9	−0.239393
$939$	1.19552e10	0.471223
$940$	2.27190e10	0.892159
$941$	3.53018e10	1.38113	0.690563	−	0.723273i	$-0.257363\pi$
$941$	3.53018e10	1.38113	0.690563	+	0.723273i	$0.257363\pi$
$942$	1.89304e10	0.737873
$943$	−1.53461e10	−0.595946
$944$	−2.19120e9	−0.0847773
$945$	3.35487e9	0.129320
$946$	−1.63046e10	−0.626167
$947$	−1.87980e10	−0.719263	−0.359631	−	0.933094i	$-0.617098\pi$
$947$	−1.87980e10	−0.719263	−0.359631	+	0.933094i	$0.617098\pi$
$948$	−1.48906e10	−0.567653
$949$	3.21760e9	0.122208
$950$	−2.50442e10	−0.947708
$951$	−6.30297e9	−0.237637
$952$	3.77176e8	0.0141682
$953$	−3.46583e10	−1.29712	−0.648562	−	0.761162i	$-0.724629\pi$
$953$	−3.46583e10	−1.29712	−0.648562	+	0.761162i	$0.724629\pi$
$954$	−2.05452e9	−0.0766110
$955$	3.15467e10	1.17204
$956$	1.06789e10	0.395296
$957$	6.06301e9	0.223613
$958$	5.20200e9	0.191157
$959$	−9.13642e9	−0.334511
$960$	−3.51717e9	−0.128305
$961$	−2.69393e9	−0.0979163
$962$	6.70637e9	0.242870
$963$	1.72025e10	0.620725
$964$	1.50898e10	0.542519
$965$	4.75004e10	1.70158
$966$	−5.00564e9	−0.178665
$967$	4.51149e10	1.60446	0.802228	−	0.597018i	$-0.203648\pi$
$967$	4.51149e10	1.60446	0.802228	+	0.597018i	$0.203648\pi$
$968$	−2.48757e9	−0.0881477
$969$	−1.07539e9	−0.0379694
$970$	7.97716e9	0.280638
$971$	5.39377e10	1.89071	0.945355	−	0.326044i	$-0.105716\pi$
$971$	5.39377e10	1.89071	0.945355	+	0.326044i	$0.105716\pi$
$972$	−9.18330e8	−0.0320750
$973$	1.94775e10	0.677859
$974$	−1.50955e10	−0.523471
$975$	−1.00136e10	−0.345997
$976$	3.88118e9	0.133626
$977$	−5.29565e9	−0.181672	−0.0908360	−	0.995866i	$-0.528954\pi$
$977$	−5.29565e9	−0.181672	−0.0908360	+	0.995866i	$0.528954\pi$
$978$	−1.56561e10	−0.535178
$979$	−1.19282e10	−0.406290
$980$	3.74161e9	0.126989
$981$	6.12015e9	0.206976
$982$	1.31723e10	0.443886
$983$	−3.48690e10	−1.17085	−0.585426	−	0.810726i	$-0.699073\pi$
$983$	−3.48690e10	−1.17085	−0.585426	+	0.810726i	$0.699073\pi$
$984$	−3.13993e9	−0.105060
$985$	4.11590e10	1.37226
$986$	−1.00877e9	−0.0335138
$987$	6.61572e9	0.219012
$988$	−2.60755e9	−0.0860169
$989$	−3.60022e10	−1.18343
$990$	−1.10843e10	−0.363067
$991$	−1.20597e10	−0.393622	−0.196811	−	0.980441i	$-0.563058\pi$
$991$	−1.20597e10	−0.393622	−0.196811	+	0.980441i	$0.563058\pi$
$992$	5.16225e9	0.167899
$993$	−3.20899e10	−1.04003
$994$	1.38236e10	0.446445
$995$	−4.04436e10	−1.30158
$996$	1.52188e10	0.488061
$997$	−3.70942e10	−1.18542	−0.592710	−	0.805416i	$-0.701942\pi$
$997$	−3.70942e10	−1.18542	−0.592710	+	0.805416i	$0.701942\pi$
$998$	−3.30975e10	−1.05399
$999$	−7.51032e9	−0.238330

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.r.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.r.1.6	✓	6	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)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +496.924 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +496.924 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +3975.39 q^{10} -3824.74 q^{11} -1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} -13417.0 q^{15} +4096.00 q^{16} -2147.73 q^{17} +5832.00 q^{18} -18544.8 q^{19} +31803.1 q^{20} +9261.00 q^{21} -30597.9 q^{22} -67563.5 q^{23} -13824.0 q^{24} +168809. q^{25} +17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} +58711.4 q^{29} -107336. q^{30} +157539. q^{31} +32768.0 q^{32} +103268. q^{33} -17181.9 q^{34} -170445. q^{35} +46656.0 q^{36} +381564. q^{37} -148359. q^{38} -59319.0 q^{39} +254425. q^{40} +227136. q^{41} +74088.0 q^{42} +532865. q^{43} -244783. q^{44} +362258. q^{45} -540508. q^{46} +714364. q^{47} -110592. q^{48} +117649. q^{49} +1.35047e6 q^{50} +57988.8 q^{51} +140608. q^{52} -352284. q^{53} -157464. q^{54} -1.90061e6 q^{55} -175616. q^{56} +500710. q^{57} +469691. q^{58} -534961. q^{59} -858685. q^{60} +947554. q^{61} +1.26032e6 q^{62} -250047. q^{63} +262144. q^{64} +1.09174e6 q^{65} +826144. q^{66} +2.20515e6 q^{67} -137455. q^{68} +1.82421e6 q^{69} -1.36356e6 q^{70} -5.03775e6 q^{71} +373248. q^{72} +1.46454e6 q^{73} +3.05251e6 q^{74} -4.55783e6 q^{75} -1.18687e6 q^{76} +1.31189e6 q^{77} -474552. q^{78} +8.61725e6 q^{79} +2.03540e6 q^{80} +531441. q^{81} +1.81709e6 q^{82} -8.80720e6 q^{83} +592704. q^{84} -1.06726e6 q^{85} +4.26292e6 q^{86} -1.58521e6 q^{87} -1.95827e6 q^{88} +3.11870e6 q^{89} +2.89806e6 q^{90} -753571. q^{91} -4.32406e6 q^{92} -4.25357e6 q^{93} +5.71491e6 q^{94} -9.21537e6 q^{95} -884736. q^{96} +2.00663e6 q^{97} +941192. q^{98} -2.78824e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 203 q^{5} - 1296 q^{6} - 2058 q^{7} + 3072 q^{8} + 4374 q^{9}+O(q^{10}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 203 * q^5 - 1296 * q^6 - 2058 * q^7 + 3072 * q^8 + 4374 * q^9	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 203 q^{5} - 1296 q^{6} - 2058 q^{7} + 3072 q^{8} + 4374 q^{9} + 1624 q^{10} - 2690 q^{11} - 10368 q^{12} + 13182 q^{13} - 16464 q^{14} - 5481 q^{15} + 24576 q^{16} + 2910 q^{17} + 34992 q^{18} - 13055 q^{19} + 12992 q^{20} + 55566 q^{21} - 21520 q^{22} + 11581 q^{23} - 82944 q^{24} + 68081 q^{25} + 105456 q^{26} - 118098 q^{27} - 131712 q^{28} - 92335 q^{29} - 43848 q^{30} - 83081 q^{31} + 196608 q^{32} + 72630 q^{33} + 23280 q^{34} - 69629 q^{35} + 279936 q^{36} - 265114 q^{37} - 104440 q^{38} - 355914 q^{39} + 103936 q^{40} - 367468 q^{41} + 444528 q^{42} + 454955 q^{43} - 172160 q^{44} + 147987 q^{45} + 92648 q^{46} + 733973 q^{47} - 663552 q^{48} + 705894 q^{49} + 544648 q^{50} - 78570 q^{51} + 843648 q^{52} - 1577379 q^{53} - 944784 q^{54} + 2231118 q^{55} - 1053696 q^{56} + 352485 q^{57} - 738680 q^{58} + 2062708 q^{59} - 350784 q^{60} - 271270 q^{61} - 664648 q^{62} - 1500282 q^{63} + 1572864 q^{64} + 445991 q^{65} + 581040 q^{66} - 758674 q^{67} + 186240 q^{68} - 312687 q^{69} - 557032 q^{70} - 6138216 q^{71} + 2239488 q^{72} + 6361979 q^{73} - 2120912 q^{74} - 1838187 q^{75} - 835520 q^{76} + 922670 q^{77} - 2847312 q^{78} - 899781 q^{79} + 831488 q^{80} + 3188646 q^{81} - 2939744 q^{82} + 3313561 q^{83} + 3556224 q^{84} + 5307940 q^{85} + 3639640 q^{86} + 2493045 q^{87} - 1377280 q^{88} + 11210703 q^{89} + 1183896 q^{90} - 4521426 q^{91} + 741184 q^{92} + 2243187 q^{93} + 5871784 q^{94} + 12912395 q^{95} - 5308416 q^{96} + 28682643 q^{97} + 5647152 q^{98} - 1961010 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 203 * q^5 - 1296 * q^6 - 2058 * q^7 + 3072 * q^8 + 4374 * q^9 + 1624 * q^10 - 2690 * q^11 - 10368 * q^12 + 13182 * q^13 - 16464 * q^14 - 5481 * q^15 + 24576 * q^16 + 2910 * q^17 + 34992 * q^18 - 13055 * q^19 + 12992 * q^20 + 55566 * q^21 - 21520 * q^22 + 11581 * q^23 - 82944 * q^24 + 68081 * q^25 + 105456 * q^26 - 118098 * q^27 - 131712 * q^28 - 92335 * q^29 - 43848 * q^30 - 83081 * q^31 + 196608 * q^32 + 72630 * q^33 + 23280 * q^34 - 69629 * q^35 + 279936 * q^36 - 265114 * q^37 - 104440 * q^38 - 355914 * q^39 + 103936 * q^40 - 367468 * q^41 + 444528 * q^42 + 454955 * q^43 - 172160 * q^44 + 147987 * q^45 + 92648 * q^46 + 733973 * q^47 - 663552 * q^48 + 705894 * q^49 + 544648 * q^50 - 78570 * q^51 + 843648 * q^52 - 1577379 * q^53 - 944784 * q^54 + 2231118 * q^55 - 1053696 * q^56 + 352485 * q^57 - 738680 * q^58 + 2062708 * q^59 - 350784 * q^60 - 271270 * q^61 - 664648 * q^62 - 1500282 * q^63 + 1572864 * q^64 + 445991 * q^65 + 581040 * q^66 - 758674 * q^67 + 186240 * q^68 - 312687 * q^69 - 557032 * q^70 - 6138216 * q^71 + 2239488 * q^72 + 6361979 * q^73 - 2120912 * q^74 - 1838187 * q^75 - 835520 * q^76 + 922670 * q^77 - 2847312 * q^78 - 899781 * q^79 + 831488 * q^80 + 3188646 * q^81 - 2939744 * q^82 + 3313561 * q^83 + 3556224 * q^84 + 5307940 * q^85 + 3639640 * q^86 + 2493045 * q^87 - 1377280 * q^88 + 11210703 * q^89 + 1183896 * q^90 - 4521426 * q^91 + 741184 * q^92 + 2243187 * q^93 + 5871784 * q^94 + 12912395 * q^95 - 5308416 * q^96 + 28682643 * q^97 + 5647152 * q^98 - 1961010 * q^99

Introduction

L-functions

Modular forms

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